Properties

Label 210.3.o.a.31.2
Level 210
Weight 3
Character 210.31
Analytic conductor 5.722
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.3317760000.3
Defining polynomial: \(x^{8} - 4 x^{6} + 7 x^{4} - 36 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Root \(-1.72286 + 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 210.31
Dual form 210.3.o.a.61.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(6.51658 - 2.55620i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(6.51658 - 2.55620i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(-5.79240 + 10.0327i) q^{11} +(-3.00000 + 1.73205i) q^{12} -7.86371i q^{13} +(-7.73861 - 6.17364i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(23.9080 + 13.8033i) q^{17} +(2.12132 - 3.67423i) q^{18} +(27.2149 - 15.7125i) q^{19} +4.47214i q^{20} +(11.9886 + 1.80922i) q^{21} +16.3834 q^{22} +(-9.07959 - 15.7263i) q^{23} +(4.24264 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-9.63104 + 5.56049i) q^{26} +5.19615i q^{27} +(-2.08911 + 13.8433i) q^{28} -2.30331 q^{29} +(-2.73861 - 4.74342i) q^{30} +(-4.55860 - 2.63191i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-17.3772 + 10.0327i) q^{33} -39.0416i q^{34} +(9.76139 - 12.2358i) q^{35} -6.00000 q^{36} +(-0.993142 - 1.72017i) q^{37} +(-38.4876 - 22.2208i) q^{38} +(6.81018 - 11.7956i) q^{39} +(5.47723 - 3.16228i) q^{40} -22.1905i q^{41} +(-6.26139 - 15.9623i) q^{42} +49.8368 q^{43} +(-11.5848 - 20.0655i) q^{44} +(5.80948 + 3.35410i) q^{45} +(-12.8405 + 22.2404i) q^{46} +(-66.3956 + 38.3335i) q^{47} -6.92820i q^{48} +(35.9317 - 33.3154i) q^{49} -7.07107 q^{50} +(23.9080 + 41.4099i) q^{51} +(13.6204 + 7.86371i) q^{52} +(-28.5477 + 49.4461i) q^{53} +(6.36396 - 3.67423i) q^{54} +25.9044i q^{55} +(18.4317 - 7.23003i) q^{56} +54.4297 q^{57} +(1.62869 + 2.82097i) q^{58} +(-60.9245 - 35.1748i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(-58.5590 + 33.8091i) q^{61} +7.44416i q^{62} +(16.4161 + 13.0963i) q^{63} +8.00000 q^{64} +(-8.79190 - 15.2280i) q^{65} +(24.5751 + 14.1884i) q^{66} +(-49.0823 + 85.0131i) q^{67} +(-47.8160 + 27.6066i) q^{68} -31.4526i q^{69} +(-21.8881 - 3.30318i) q^{70} -34.2597 q^{71} +(4.24264 + 7.34847i) q^{72} +(16.8801 + 9.74573i) q^{73} +(-1.40452 + 2.43269i) q^{74} +(7.50000 - 4.33013i) q^{75} +62.8501i q^{76} +(-12.1010 + 80.1856i) q^{77} -19.2621 q^{78} +(-45.2142 - 78.3134i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-27.1777 + 15.6911i) q^{82} +133.803i q^{83} +(-15.1223 + 18.9557i) q^{84} +61.7302 q^{85} +(-35.2400 - 61.0374i) q^{86} +(-3.45496 - 1.99472i) q^{87} +(-16.3834 + 28.3768i) q^{88} +(-9.58232 + 5.53235i) q^{89} -9.48683i q^{90} +(-20.1012 - 51.2445i) q^{91} +36.3184 q^{92} +(-4.55860 - 7.89573i) q^{93} +(93.8975 + 54.2118i) q^{94} +(35.1342 - 60.8543i) q^{95} +(-8.48528 + 4.89898i) q^{96} -72.3112i q^{97} +(-66.2104 - 20.4496i) q^{98} -34.7544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 12q^{3} - 8q^{4} + 12q^{9} + O(q^{10}) \) \( 8q + 12q^{3} - 8q^{4} + 12q^{9} - 4q^{11} - 24q^{12} - 40q^{14} - 16q^{16} + 84q^{17} + 108q^{19} - 48q^{22} + 12q^{23} + 20q^{25} - 96q^{26} + 72q^{29} - 132q^{31} - 12q^{33} + 100q^{35} - 48q^{36} - 96q^{37} - 168q^{38} + 24q^{39} - 72q^{42} - 112q^{43} - 8q^{44} + 8q^{46} - 24q^{47} + 156q^{49} + 84q^{51} + 48q^{52} + 32q^{53} + 16q^{56} + 216q^{57} + 104q^{58} + 132q^{59} + 96q^{61} + 64q^{64} + 20q^{65} - 72q^{66} - 120q^{67} - 168q^{68} + 8q^{71} + 24q^{73} - 16q^{74} + 60q^{75} - 216q^{77} - 192q^{78} + 12q^{79} - 36q^{81} + 24q^{82} + 120q^{85} - 40q^{86} + 108q^{87} + 48q^{88} + 492q^{89} - 308q^{91} - 48q^{92} - 132q^{93} + 480q^{94} - 40q^{95} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) 1.50000 + 0.866025i 0.500000 + 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 1.93649 1.11803i 0.387298 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) 6.51658 2.55620i 0.930940 0.365172i
\(8\) 2.82843 0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) −2.73861 1.58114i −0.273861 0.158114i
\(11\) −5.79240 + 10.0327i −0.526582 + 0.912066i 0.472939 + 0.881095i \(0.343193\pi\)
−0.999520 + 0.0309707i \(0.990140\pi\)
\(12\) −3.00000 + 1.73205i −0.250000 + 0.144338i
\(13\) 7.86371i 0.604901i −0.953165 0.302451i \(-0.902195\pi\)
0.953165 0.302451i \(-0.0978047\pi\)
\(14\) −7.73861 6.17364i −0.552758 0.440975i
\(15\) 3.87298 0.258199
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 23.9080 + 13.8033i 1.40635 + 0.811959i 0.995034 0.0995321i \(-0.0317346\pi\)
0.411320 + 0.911491i \(0.365068\pi\)
\(18\) 2.12132 3.67423i 0.117851 0.204124i
\(19\) 27.2149 15.7125i 1.43236 0.826974i 0.435061 0.900401i \(-0.356727\pi\)
0.997301 + 0.0734266i \(0.0233935\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 11.9886 + 1.80922i 0.570886 + 0.0861535i
\(22\) 16.3834 0.744699
\(23\) −9.07959 15.7263i −0.394765 0.683753i 0.598306 0.801268i \(-0.295841\pi\)
−0.993071 + 0.117515i \(0.962507\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −9.63104 + 5.56049i −0.370425 + 0.213865i
\(27\) 5.19615i 0.192450i
\(28\) −2.08911 + 13.8433i −0.0746112 + 0.494402i
\(29\) −2.30331 −0.0794244 −0.0397122 0.999211i \(-0.512644\pi\)
−0.0397122 + 0.999211i \(0.512644\pi\)
\(30\) −2.73861 4.74342i −0.0912871 0.158114i
\(31\) −4.55860 2.63191i −0.147052 0.0849003i 0.424669 0.905349i \(-0.360391\pi\)
−0.571721 + 0.820448i \(0.693724\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) −17.3772 + 10.0327i −0.526582 + 0.304022i
\(34\) 39.0416i 1.14828i
\(35\) 9.76139 12.2358i 0.278897 0.349595i
\(36\) −6.00000 −0.166667
\(37\) −0.993142 1.72017i −0.0268417 0.0464912i 0.852293 0.523065i \(-0.175212\pi\)
−0.879134 + 0.476574i \(0.841878\pi\)
\(38\) −38.4876 22.2208i −1.01283 0.584759i
\(39\) 6.81018 11.7956i 0.174620 0.302451i
\(40\) 5.47723 3.16228i 0.136931 0.0790569i
\(41\) 22.1905i 0.541233i −0.962687 0.270616i \(-0.912773\pi\)
0.962687 0.270616i \(-0.0872275\pi\)
\(42\) −6.26139 15.9623i −0.149081 0.380055i
\(43\) 49.8368 1.15900 0.579498 0.814974i \(-0.303249\pi\)
0.579498 + 0.814974i \(0.303249\pi\)
\(44\) −11.5848 20.0655i −0.263291 0.456033i
\(45\) 5.80948 + 3.35410i 0.129099 + 0.0745356i
\(46\) −12.8405 + 22.2404i −0.279141 + 0.483486i
\(47\) −66.3956 + 38.3335i −1.41267 + 0.815606i −0.995639 0.0932854i \(-0.970263\pi\)
−0.417032 + 0.908892i \(0.636930\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 35.9317 33.3154i 0.733300 0.679906i
\(50\) −7.07107 −0.141421
\(51\) 23.9080 + 41.4099i 0.468785 + 0.811959i
\(52\) 13.6204 + 7.86371i 0.261930 + 0.151225i
\(53\) −28.5477 + 49.4461i −0.538636 + 0.932945i 0.460342 + 0.887742i \(0.347727\pi\)
−0.998978 + 0.0452033i \(0.985606\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 25.9044i 0.470989i
\(56\) 18.4317 7.23003i 0.329137 0.129108i
\(57\) 54.4297 0.954908
\(58\) 1.62869 + 2.82097i 0.0280808 + 0.0486373i
\(59\) −60.9245 35.1748i −1.03262 0.596182i −0.114885 0.993379i \(-0.536650\pi\)
−0.917734 + 0.397196i \(0.869983\pi\)
\(60\) −3.87298 + 6.70820i −0.0645497 + 0.111803i
\(61\) −58.5590 + 33.8091i −0.959984 + 0.554247i −0.896168 0.443715i \(-0.853660\pi\)
−0.0638160 + 0.997962i \(0.520327\pi\)
\(62\) 7.44416i 0.120067i
\(63\) 16.4161 + 13.0963i 0.260573 + 0.207877i
\(64\) 8.00000 0.125000
\(65\) −8.79190 15.2280i −0.135260 0.234277i
\(66\) 24.5751 + 14.1884i 0.372349 + 0.214976i
\(67\) −49.0823 + 85.0131i −0.732572 + 1.26885i 0.223208 + 0.974771i \(0.428347\pi\)
−0.955780 + 0.294081i \(0.904986\pi\)
\(68\) −47.8160 + 27.6066i −0.703177 + 0.405979i
\(69\) 31.4526i 0.455835i
\(70\) −21.8881 3.30318i −0.312687 0.0471882i
\(71\) −34.2597 −0.482531 −0.241266 0.970459i \(-0.577563\pi\)
−0.241266 + 0.970459i \(0.577563\pi\)
\(72\) 4.24264 + 7.34847i 0.0589256 + 0.102062i
\(73\) 16.8801 + 9.74573i 0.231234 + 0.133503i 0.611141 0.791521i \(-0.290711\pi\)
−0.379907 + 0.925025i \(0.624044\pi\)
\(74\) −1.40452 + 2.43269i −0.0189799 + 0.0328742i
\(75\) 7.50000 4.33013i 0.100000 0.0577350i
\(76\) 62.8501i 0.826974i
\(77\) −12.1010 + 80.1856i −0.157155 + 1.04137i
\(78\) −19.2621 −0.246950
\(79\) −45.2142 78.3134i −0.572332 0.991308i −0.996326 0.0856432i \(-0.972705\pi\)
0.423994 0.905665i \(-0.360628\pi\)
\(80\) −7.74597 4.47214i −0.0968246 0.0559017i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −27.1777 + 15.6911i −0.331436 + 0.191355i
\(83\) 133.803i 1.61209i 0.591854 + 0.806045i \(0.298396\pi\)
−0.591854 + 0.806045i \(0.701604\pi\)
\(84\) −15.1223 + 18.9557i −0.180027 + 0.225663i
\(85\) 61.7302 0.726238
\(86\) −35.2400 61.0374i −0.409767 0.709737i
\(87\) −3.45496 1.99472i −0.0397122 0.0229279i
\(88\) −16.3834 + 28.3768i −0.186175 + 0.322464i
\(89\) −9.58232 + 5.53235i −0.107666 + 0.0621613i −0.552866 0.833270i \(-0.686466\pi\)
0.445200 + 0.895431i \(0.353133\pi\)
\(90\) 9.48683i 0.105409i
\(91\) −20.1012 51.2445i −0.220893 0.563127i
\(92\) 36.3184 0.394765
\(93\) −4.55860 7.89573i −0.0490172 0.0849003i
\(94\) 93.8975 + 54.2118i 0.998910 + 0.576721i
\(95\) 35.1342 60.8543i 0.369834 0.640572i
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) 72.3112i 0.745476i −0.927937 0.372738i \(-0.878419\pi\)
0.927937 0.372738i \(-0.121581\pi\)
\(98\) −66.2104 20.4496i −0.675616 0.208669i
\(99\) −34.7544 −0.351054
\(100\) 5.00000 + 8.66025i 0.0500000 + 0.0866025i
\(101\) 43.8670 + 25.3266i 0.434327 + 0.250759i 0.701188 0.712976i \(-0.252653\pi\)
−0.266861 + 0.963735i \(0.585987\pi\)
\(102\) 33.8110 58.5625i 0.331481 0.574142i
\(103\) −171.442 + 98.9823i −1.66449 + 0.960993i −0.693958 + 0.720015i \(0.744135\pi\)
−0.970531 + 0.240978i \(0.922532\pi\)
\(104\) 22.2419i 0.213865i
\(105\) 25.2386 9.90012i 0.240368 0.0942869i
\(106\) 80.7451 0.761746
\(107\) −73.9679 128.116i −0.691289 1.19735i −0.971416 0.237384i \(-0.923710\pi\)
0.280127 0.959963i \(-0.409623\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) 27.1610 47.0442i 0.249183 0.431598i −0.714116 0.700027i \(-0.753171\pi\)
0.963299 + 0.268429i \(0.0865046\pi\)
\(110\) 31.7263 18.3172i 0.288421 0.166520i
\(111\) 3.44035i 0.0309941i
\(112\) −21.8881 17.4617i −0.195429 0.155908i
\(113\) 47.7883 0.422906 0.211453 0.977388i \(-0.432181\pi\)
0.211453 + 0.977388i \(0.432181\pi\)
\(114\) −38.4876 66.6625i −0.337611 0.584759i
\(115\) −35.1651 20.3026i −0.305784 0.176544i
\(116\) 2.30331 3.98945i 0.0198561 0.0343918i
\(117\) 20.4305 11.7956i 0.174620 0.100817i
\(118\) 99.4892i 0.843129i
\(119\) 191.083 + 28.8367i 1.60574 + 0.242325i
\(120\) 10.9545 0.0912871
\(121\) −6.60372 11.4380i −0.0545762 0.0945288i
\(122\) 82.8150 + 47.8132i 0.678811 + 0.391912i
\(123\) 19.2176 33.2858i 0.156240 0.270616i
\(124\) 9.11720 5.26382i 0.0735258 0.0424501i
\(125\) 11.1803i 0.0894427i
\(126\) 4.43168 29.3660i 0.0351720 0.233063i
\(127\) −101.973 −0.802940 −0.401470 0.915872i \(-0.631501\pi\)
−0.401470 + 0.915872i \(0.631501\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) 74.7552 + 43.1600i 0.579498 + 0.334573i
\(130\) −12.4336 + 21.5357i −0.0956433 + 0.165659i
\(131\) −64.6037 + 37.2990i −0.493158 + 0.284725i −0.725884 0.687817i \(-0.758569\pi\)
0.232726 + 0.972542i \(0.425236\pi\)
\(132\) 40.1309i 0.304022i
\(133\) 137.184 171.959i 1.03146 1.29292i
\(134\) 138.826 1.03601
\(135\) 5.80948 + 10.0623i 0.0430331 + 0.0745356i
\(136\) 67.6221 + 39.0416i 0.497221 + 0.287071i
\(137\) 123.449 213.821i 0.901091 1.56074i 0.0750109 0.997183i \(-0.476101\pi\)
0.826080 0.563553i \(-0.190566\pi\)
\(138\) −38.5215 + 22.2404i −0.279141 + 0.161162i
\(139\) 155.917i 1.12170i −0.827916 0.560852i \(-0.810474\pi\)
0.827916 0.560852i \(-0.189526\pi\)
\(140\) 11.4317 + 29.1430i 0.0816548 + 0.208165i
\(141\) −132.791 −0.941781
\(142\) 24.2253 + 41.9594i 0.170601 + 0.295489i
\(143\) 78.8945 + 45.5498i 0.551710 + 0.318530i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) −4.46034 + 2.57518i −0.0307609 + 0.0177598i
\(146\) 27.5651i 0.188802i
\(147\) 82.7495 18.8553i 0.562922 0.128268i
\(148\) 3.97257 0.0268417
\(149\) −81.5452 141.240i −0.547283 0.947922i −0.998459 0.0554872i \(-0.982329\pi\)
0.451176 0.892435i \(-0.351005\pi\)
\(150\) −10.6066 6.12372i −0.0707107 0.0408248i
\(151\) 37.5149 64.9778i 0.248443 0.430316i −0.714651 0.699481i \(-0.753414\pi\)
0.963094 + 0.269165i \(0.0867477\pi\)
\(152\) 76.9753 44.4417i 0.506416 0.292380i
\(153\) 82.8198i 0.541306i
\(154\) 106.764 41.8792i 0.693270 0.271943i
\(155\) −11.7703 −0.0759371
\(156\) 13.6204 + 23.5911i 0.0873100 + 0.151225i
\(157\) −194.622 112.365i −1.23963 0.715702i −0.270614 0.962688i \(-0.587227\pi\)
−0.969019 + 0.246986i \(0.920560\pi\)
\(158\) −63.9426 + 110.752i −0.404700 + 0.700961i
\(159\) −85.6431 + 49.4461i −0.538636 + 0.310982i
\(160\) 12.6491i 0.0790569i
\(161\) −99.3675 79.2726i −0.617190 0.492376i
\(162\) 12.7279 0.0785674
\(163\) 115.059 + 199.288i 0.705882 + 1.22262i 0.966372 + 0.257147i \(0.0827823\pi\)
−0.260491 + 0.965476i \(0.583884\pi\)
\(164\) 38.4351 + 22.1905i 0.234361 + 0.135308i
\(165\) −22.4339 + 38.8566i −0.135963 + 0.235494i
\(166\) 163.875 94.6133i 0.987199 0.569960i
\(167\) 277.788i 1.66340i 0.555223 + 0.831702i \(0.312633\pi\)
−0.555223 + 0.831702i \(0.687367\pi\)
\(168\) 33.9089 + 5.11726i 0.201839 + 0.0304599i
\(169\) 107.162 0.634095
\(170\) −43.6499 75.6038i −0.256764 0.444728i
\(171\) 81.6446 + 47.1375i 0.477454 + 0.275658i
\(172\) −49.8368 + 86.3199i −0.289749 + 0.501860i
\(173\) 109.176 63.0327i 0.631074 0.364351i −0.150094 0.988672i \(-0.547958\pi\)
0.781168 + 0.624321i \(0.214624\pi\)
\(174\) 5.64193i 0.0324249i
\(175\) 5.22278 34.6081i 0.0298445 0.197761i
\(176\) 46.3392 0.263291
\(177\) −60.9245 105.524i −0.344206 0.596182i
\(178\) 13.5514 + 7.82393i 0.0761317 + 0.0439547i
\(179\) −38.5535 + 66.7766i −0.215382 + 0.373053i −0.953391 0.301738i \(-0.902433\pi\)
0.738008 + 0.674792i \(0.235766\pi\)
\(180\) −11.6190 + 6.70820i −0.0645497 + 0.0372678i
\(181\) 212.012i 1.17134i 0.810551 + 0.585668i \(0.199168\pi\)
−0.810551 + 0.585668i \(0.800832\pi\)
\(182\) −48.5478 + 60.8542i −0.266746 + 0.334364i
\(183\) −117.118 −0.639989
\(184\) −25.6810 44.4807i −0.139570 0.241743i
\(185\) −3.84642 2.22073i −0.0207915 0.0120040i
\(186\) −6.44683 + 11.1662i −0.0346604 + 0.0600336i
\(187\) −276.969 + 159.908i −1.48112 + 0.855125i
\(188\) 153.334i 0.815606i
\(189\) 13.2824 + 33.8612i 0.0702773 + 0.179160i
\(190\) −99.3747 −0.523025
\(191\) −82.8480 143.497i −0.433759 0.751293i 0.563434 0.826161i \(-0.309480\pi\)
−0.997193 + 0.0748682i \(0.976146\pi\)
\(192\) 12.0000 + 6.92820i 0.0625000 + 0.0360844i
\(193\) 52.6497 91.1920i 0.272796 0.472497i −0.696780 0.717285i \(-0.745385\pi\)
0.969577 + 0.244787i \(0.0787181\pi\)
\(194\) −88.5627 + 51.1317i −0.456509 + 0.263566i
\(195\) 30.4560i 0.156185i
\(196\) 21.7723 + 95.5509i 0.111083 + 0.487504i
\(197\) 244.736 1.24231 0.621156 0.783687i \(-0.286663\pi\)
0.621156 + 0.783687i \(0.286663\pi\)
\(198\) 24.5751 + 42.5653i 0.124116 + 0.214976i
\(199\) 84.8416 + 48.9833i 0.426340 + 0.246147i 0.697786 0.716306i \(-0.254169\pi\)
−0.271446 + 0.962454i \(0.587502\pi\)
\(200\) 7.07107 12.2474i 0.0353553 0.0612372i
\(201\) −147.247 + 85.0131i −0.732572 + 0.422951i
\(202\) 71.6346i 0.354627i
\(203\) −15.0097 + 5.88772i −0.0739394 + 0.0290035i
\(204\) −95.6321 −0.468785
\(205\) −24.8098 42.9718i −0.121023 0.209619i
\(206\) 242.456 + 139.982i 1.17697 + 0.679525i
\(207\) 27.2388 47.1790i 0.131588 0.227918i
\(208\) −27.2407 + 15.7274i −0.130965 + 0.0756126i
\(209\) 364.052i 1.74188i
\(210\) −29.9715 23.9104i −0.142722 0.113859i
\(211\) −388.914 −1.84319 −0.921597 0.388149i \(-0.873114\pi\)
−0.921597 + 0.388149i \(0.873114\pi\)
\(212\) −57.0954 98.8922i −0.269318 0.466473i
\(213\) −51.3896 29.6698i −0.241266 0.139295i
\(214\) −104.606 + 181.184i −0.488815 + 0.846652i
\(215\) 96.5086 55.7193i 0.448877 0.259159i
\(216\) 14.6969i 0.0680414i
\(217\) −36.4342 5.49835i −0.167899 0.0253380i
\(218\) −76.8228 −0.352398
\(219\) 16.8801 + 29.2372i 0.0770781 + 0.133503i
\(220\) −44.8677 25.9044i −0.203944 0.117747i
\(221\) 108.545 188.006i 0.491155 0.850705i
\(222\) −4.21355 + 2.43269i −0.0189799 + 0.0109581i
\(223\) 251.913i 1.12965i −0.825210 0.564827i \(-0.808943\pi\)
0.825210 0.564827i \(-0.191057\pi\)
\(224\) −5.90890 + 39.1546i −0.0263790 + 0.174797i
\(225\) 15.0000 0.0666667
\(226\) −33.7915 58.5285i −0.149520 0.258976i
\(227\) 231.941 + 133.911i 1.02176 + 0.589916i 0.914615 0.404327i \(-0.132494\pi\)
0.107150 + 0.994243i \(0.465827\pi\)
\(228\) −54.4297 + 94.2751i −0.238727 + 0.413487i
\(229\) 299.237 172.765i 1.30671 0.754431i 0.325167 0.945657i \(-0.394580\pi\)
0.981546 + 0.191226i \(0.0612463\pi\)
\(230\) 57.4244i 0.249671i
\(231\) −87.5942 + 109.799i −0.379196 + 0.475319i
\(232\) −6.51474 −0.0280808
\(233\) 144.032 + 249.471i 0.618164 + 1.07069i 0.989821 + 0.142321i \(0.0454566\pi\)
−0.371656 + 0.928370i \(0.621210\pi\)
\(234\) −28.8931 16.6815i −0.123475 0.0712883i
\(235\) −85.7163 + 148.465i −0.364750 + 0.631766i
\(236\) 121.849 70.3495i 0.516309 0.298091i
\(237\) 156.627i 0.660872i
\(238\) −99.7983 254.418i −0.419320 1.06898i
\(239\) −188.810 −0.789999 −0.395000 0.918681i \(-0.629255\pi\)
−0.395000 + 0.918681i \(0.629255\pi\)
\(240\) −7.74597 13.4164i −0.0322749 0.0559017i
\(241\) 84.7389 + 48.9240i 0.351614 + 0.203004i 0.665396 0.746491i \(-0.268263\pi\)
−0.313782 + 0.949495i \(0.601596\pi\)
\(242\) −9.33908 + 16.1758i −0.0385912 + 0.0668420i
\(243\) −13.5000 + 7.79423i −0.0555556 + 0.0320750i
\(244\) 135.236i 0.554247i
\(245\) 32.3337 104.688i 0.131974 0.427297i
\(246\) −54.3555 −0.220957
\(247\) −123.559 214.010i −0.500238 0.866437i
\(248\) −12.8937 7.44416i −0.0519906 0.0300168i
\(249\) −115.877 + 200.705i −0.465370 + 0.806045i
\(250\) −13.6931 + 7.90569i −0.0547723 + 0.0316228i
\(251\) 241.345i 0.961533i 0.876849 + 0.480767i \(0.159642\pi\)
−0.876849 + 0.480767i \(0.840358\pi\)
\(252\) −39.0995 + 15.3372i −0.155157 + 0.0608619i
\(253\) 210.370 0.831504
\(254\) 72.1061 + 124.891i 0.283882 + 0.491698i
\(255\) 92.5954 + 53.4600i 0.363119 + 0.209647i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −10.8807 + 6.28197i −0.0423373 + 0.0244435i −0.521019 0.853545i \(-0.674448\pi\)
0.478682 + 0.877988i \(0.341115\pi\)
\(258\) 122.075i 0.473158i
\(259\) −10.8690 8.67098i −0.0419653 0.0334787i
\(260\) 35.1676 0.135260
\(261\) −3.45496 5.98417i −0.0132374 0.0229279i
\(262\) 91.3635 + 52.7487i 0.348716 + 0.201331i
\(263\) 106.240 184.014i 0.403956 0.699672i −0.590244 0.807225i \(-0.700968\pi\)
0.994199 + 0.107554i \(0.0343017\pi\)
\(264\) −49.1501 + 28.3768i −0.186175 + 0.107488i
\(265\) 127.669i 0.481771i
\(266\) −307.609 46.4219i −1.15642 0.174518i
\(267\) −19.1646 −0.0717777
\(268\) −98.1647 170.026i −0.366286 0.634426i
\(269\) −289.769 167.298i −1.07721 0.621927i −0.147067 0.989127i \(-0.546983\pi\)
−0.930142 + 0.367200i \(0.880317\pi\)
\(270\) 8.21584 14.2302i 0.0304290 0.0527046i
\(271\) −157.920 + 91.1752i −0.582731 + 0.336440i −0.762218 0.647321i \(-0.775889\pi\)
0.179487 + 0.983760i \(0.442556\pi\)
\(272\) 110.426i 0.405979i
\(273\) 14.2272 94.2750i 0.0521144 0.345330i
\(274\) −349.168 −1.27434
\(275\) 28.9620 + 50.1636i 0.105316 + 0.182413i
\(276\) 54.4776 + 31.4526i 0.197382 + 0.113959i
\(277\) −83.3807 + 144.420i −0.301013 + 0.521370i −0.976366 0.216125i \(-0.930658\pi\)
0.675353 + 0.737495i \(0.263991\pi\)
\(278\) −190.958 + 110.250i −0.686900 + 0.396582i
\(279\) 15.7915i 0.0566002i
\(280\) 27.6094 34.6081i 0.0986049 0.123600i
\(281\) 38.3085 0.136329 0.0681647 0.997674i \(-0.478286\pi\)
0.0681647 + 0.997674i \(0.478286\pi\)
\(282\) 93.8975 + 162.635i 0.332970 + 0.576721i
\(283\) −333.849 192.748i −1.17968 0.681088i −0.223739 0.974649i \(-0.571826\pi\)
−0.955940 + 0.293561i \(0.905160\pi\)
\(284\) 34.2597 59.3396i 0.120633 0.208942i
\(285\) 105.403 60.8543i 0.369834 0.213524i
\(286\) 128.834i 0.450469i
\(287\) −56.7235 144.606i −0.197643 0.503855i
\(288\) −16.9706 −0.0589256
\(289\) 236.562 + 409.738i 0.818555 + 1.41778i
\(290\) 6.30787 + 3.64185i 0.0217513 + 0.0125581i
\(291\) 62.6233 108.467i 0.215200 0.372738i
\(292\) −33.7602 + 19.4915i −0.115617 + 0.0667516i
\(293\) 90.9844i 0.310527i −0.987873 0.155264i \(-0.950377\pi\)
0.987873 0.155264i \(-0.0496227\pi\)
\(294\) −81.6057 88.0143i −0.277570 0.299368i
\(295\) −157.306 −0.533242
\(296\) −2.80903 4.86538i −0.00948997 0.0164371i
\(297\) −52.1316 30.0982i −0.175527 0.101341i
\(298\) −115.322 + 199.744i −0.386988 + 0.670282i
\(299\) −123.667 + 71.3993i −0.413603 + 0.238794i
\(300\) 17.3205i 0.0577350i
\(301\) 324.766 127.393i 1.07896 0.423232i
\(302\) −106.108 −0.351352
\(303\) 43.8670 + 75.9799i 0.144776 + 0.250759i
\(304\) −108.859 62.8501i −0.358090 0.206744i
\(305\) −75.5994 + 130.942i −0.247867 + 0.429318i
\(306\) 101.433 58.5625i 0.331481 0.191381i
\(307\) 508.077i 1.65497i 0.561485 + 0.827487i \(0.310230\pi\)
−0.561485 + 0.827487i \(0.689770\pi\)
\(308\) −126.785 101.145i −0.411638 0.328393i
\(309\) −342.885 −1.10966
\(310\) 8.32283 + 14.4156i 0.0268478 + 0.0465018i
\(311\) 90.3447 + 52.1605i 0.290497 + 0.167719i 0.638166 0.769899i \(-0.279693\pi\)
−0.347669 + 0.937617i \(0.613027\pi\)
\(312\) 19.2621 33.3629i 0.0617375 0.106932i
\(313\) 230.249 132.934i 0.735619 0.424710i −0.0848550 0.996393i \(-0.527043\pi\)
0.820474 + 0.571683i \(0.193709\pi\)
\(314\) 317.817i 1.01216i
\(315\) 46.4317 + 7.00710i 0.147402 + 0.0222447i
\(316\) 180.857 0.572332
\(317\) 5.36113 + 9.28575i 0.0169121 + 0.0292926i 0.874358 0.485282i \(-0.161283\pi\)
−0.857446 + 0.514575i \(0.827950\pi\)
\(318\) 121.118 + 69.9273i 0.380873 + 0.219897i
\(319\) 13.3417 23.1085i 0.0418234 0.0724403i
\(320\) 15.4919 8.94427i 0.0484123 0.0279508i
\(321\) 256.232i 0.798231i
\(322\) −26.8252 + 177.754i −0.0833081 + 0.552031i
\(323\) 867.538 2.68588
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) −34.0509 19.6593i −0.104772 0.0604901i
\(326\) 162.718 281.835i 0.499134 0.864525i
\(327\) 81.4829 47.0442i 0.249183 0.143866i
\(328\) 62.7643i 0.191355i
\(329\) −334.684 + 419.524i −1.01728 + 1.27515i
\(330\) 63.4525 0.192280
\(331\) 176.460 + 305.638i 0.533113 + 0.923379i 0.999252 + 0.0386675i \(0.0123113\pi\)
−0.466139 + 0.884711i \(0.654355\pi\)
\(332\) −231.754 133.803i −0.698055 0.403022i
\(333\) 2.97943 5.16052i 0.00894723 0.0154971i
\(334\) 340.220 196.426i 1.01862 0.588102i
\(335\) 219.503i 0.655233i
\(336\) −17.7099 45.1482i −0.0527080 0.134370i
\(337\) 220.634 0.654699 0.327349 0.944903i \(-0.393845\pi\)
0.327349 + 0.944903i \(0.393845\pi\)
\(338\) −75.7750 131.246i −0.224186 0.388302i
\(339\) 71.6825 + 41.3859i 0.211453 + 0.122082i
\(340\) −61.7302 + 106.920i −0.181560 + 0.314470i
\(341\) 52.8104 30.4901i 0.154869 0.0894138i
\(342\) 133.325i 0.389839i
\(343\) 148.991 308.951i 0.434376 0.900732i
\(344\) 140.960 0.409767
\(345\) −35.1651 60.9078i −0.101928 0.176544i
\(346\) −154.398 89.1417i −0.446237 0.257635i
\(347\) 128.004 221.710i 0.368888 0.638933i −0.620504 0.784204i \(-0.713072\pi\)
0.989392 + 0.145270i \(0.0464051\pi\)
\(348\) 6.90993 3.98945i 0.0198561 0.0114639i
\(349\) 407.250i 1.16691i 0.812147 + 0.583453i \(0.198299\pi\)
−0.812147 + 0.583453i \(0.801701\pi\)
\(350\) −46.0792 + 18.0751i −0.131655 + 0.0516431i
\(351\) 40.8611 0.116413
\(352\) −32.7667 56.7537i −0.0930873 0.161232i
\(353\) −505.099 291.619i −1.43087 0.826116i −0.433687 0.901064i \(-0.642788\pi\)
−0.997187 + 0.0749482i \(0.976121\pi\)
\(354\) −86.1602 + 149.234i −0.243390 + 0.421565i
\(355\) −66.3437 + 38.3035i −0.186884 + 0.107897i
\(356\) 22.1294i 0.0621613i
\(357\) 261.651 + 208.737i 0.732915 + 0.584698i
\(358\) 109.046 0.304597
\(359\) −345.764 598.881i −0.963131 1.66819i −0.714554 0.699580i \(-0.753370\pi\)
−0.248577 0.968612i \(-0.579963\pi\)
\(360\) 16.4317 + 9.48683i 0.0456435 + 0.0263523i
\(361\) 313.266 542.593i 0.867773 1.50303i
\(362\) 259.660 149.915i 0.717294 0.414130i
\(363\) 22.8760i 0.0630192i
\(364\) 108.859 + 16.4282i 0.299064 + 0.0451324i
\(365\) 43.5842 0.119409
\(366\) 82.8150 + 143.440i 0.226270 + 0.391912i
\(367\) 198.949 + 114.863i 0.542096 + 0.312980i 0.745928 0.666026i \(-0.232006\pi\)
−0.203832 + 0.979006i \(0.565340\pi\)
\(368\) −36.3184 + 62.9053i −0.0986912 + 0.170938i
\(369\) 57.6527 33.2858i 0.156240 0.0902054i
\(370\) 6.28118i 0.0169762i
\(371\) −59.6394 + 395.193i −0.160753 + 1.06521i
\(372\) 18.2344 0.0490172
\(373\) 202.304 + 350.401i 0.542371 + 0.939414i 0.998767 + 0.0496372i \(0.0158065\pi\)
−0.456397 + 0.889776i \(0.650860\pi\)
\(374\) 391.694 + 226.145i 1.04731 + 0.604665i
\(375\) 9.68246 16.7705i 0.0258199 0.0447214i
\(376\) −187.795 + 108.424i −0.499455 + 0.288360i
\(377\) 18.1126i 0.0480439i
\(378\) 32.0792 40.2110i 0.0848656 0.106378i
\(379\) 265.866 0.701493 0.350746 0.936471i \(-0.385928\pi\)
0.350746 + 0.936471i \(0.385928\pi\)
\(380\) 70.2685 + 121.709i 0.184917 + 0.320286i
\(381\) −152.960 88.3115i −0.401470 0.231789i
\(382\) −117.165 + 202.935i −0.306714 + 0.531244i
\(383\) 265.353 153.202i 0.692829 0.400005i −0.111842 0.993726i \(-0.535675\pi\)
0.804671 + 0.593721i \(0.202342\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 66.2168 + 168.808i 0.171992 + 0.438462i
\(386\) −148.916 −0.385792
\(387\) 74.7552 + 129.480i 0.193166 + 0.334573i
\(388\) 125.247 + 72.3112i 0.322801 + 0.186369i
\(389\) −53.1772 + 92.1056i −0.136702 + 0.236775i −0.926246 0.376918i \(-0.876984\pi\)
0.789544 + 0.613694i \(0.210317\pi\)
\(390\) −37.3009 + 21.5357i −0.0956433 + 0.0552197i
\(391\) 501.314i 1.28213i
\(392\) 101.630 94.2301i 0.259261 0.240383i
\(393\) −129.207 −0.328772
\(394\) −173.054 299.739i −0.439224 0.760758i
\(395\) −175.114 101.102i −0.443327 0.255955i
\(396\) 34.7544 60.1964i 0.0877636 0.152011i
\(397\) −188.643 + 108.913i −0.475172 + 0.274341i −0.718402 0.695628i \(-0.755126\pi\)
0.243230 + 0.969969i \(0.421793\pi\)
\(398\) 138.546i 0.348105i
\(399\) 354.696 139.133i 0.888962 0.348705i
\(400\) −20.0000 −0.0500000
\(401\) −30.9907 53.6775i −0.0772836 0.133859i 0.824793 0.565434i \(-0.191291\pi\)
−0.902077 + 0.431575i \(0.857958\pi\)
\(402\) 208.239 + 120.227i 0.518007 + 0.299071i
\(403\) −20.6966 + 35.8475i −0.0513563 + 0.0889517i
\(404\) −87.7341 + 50.6533i −0.217164 + 0.125379i
\(405\) 20.1246i 0.0496904i
\(406\) 17.8244 + 14.2198i 0.0439025 + 0.0350242i
\(407\) 23.0107 0.0565373
\(408\) 67.6221 + 117.125i 0.165740 + 0.287071i
\(409\) −376.167 217.180i −0.919724 0.531003i −0.0361772 0.999345i \(-0.511518\pi\)
−0.883547 + 0.468342i \(0.844851\pi\)
\(410\) −35.0863 + 60.7713i −0.0855764 + 0.148223i
\(411\) 370.348 213.821i 0.901091 0.520245i
\(412\) 395.929i 0.960993i
\(413\) −486.933 73.4840i −1.17901 0.177927i
\(414\) −77.0429 −0.186094
\(415\) 149.597 + 259.109i 0.360474 + 0.624360i
\(416\) 38.5242 + 22.2419i 0.0926062 + 0.0534662i
\(417\) 135.028 233.875i 0.323808 0.560852i
\(418\) 445.871 257.424i 1.06668 0.615847i
\(419\) 457.221i 1.09122i −0.838040 0.545609i \(-0.816298\pi\)
0.838040 0.545609i \(-0.183702\pi\)
\(420\) −8.09110 + 53.6147i −0.0192645 + 0.127654i
\(421\) −653.149 −1.55142 −0.775712 0.631088i \(-0.782609\pi\)
−0.775712 + 0.631088i \(0.782609\pi\)
\(422\) 275.004 + 476.320i 0.651667 + 1.12872i
\(423\) −199.187 115.000i −0.470891 0.271869i
\(424\) −80.7451 + 139.855i −0.190437 + 0.329846i
\(425\) 119.540 69.0165i 0.281271 0.162392i
\(426\) 83.9188i 0.196993i
\(427\) −295.182 + 370.008i −0.691293 + 0.866530i
\(428\) 295.872 0.691289
\(429\) 78.8945 + 136.649i 0.183903 + 0.318530i
\(430\) −136.484 78.7989i −0.317404 0.183253i
\(431\) 235.128 407.253i 0.545540 0.944904i −0.453032 0.891494i \(-0.649658\pi\)
0.998573 0.0534095i \(-0.0170089\pi\)
\(432\) 18.0000 10.3923i 0.0416667 0.0240563i
\(433\) 32.0299i 0.0739719i −0.999316 0.0369860i \(-0.988224\pi\)
0.999316 0.0369860i \(-0.0117757\pi\)
\(434\) 19.0288 + 48.5105i 0.0438451 + 0.111775i
\(435\) −8.92068 −0.0205073
\(436\) 54.3219 + 94.0883i 0.124592 + 0.215799i
\(437\) −494.200 285.326i −1.13089 0.652921i
\(438\) 23.8721 41.3476i 0.0545024 0.0944010i
\(439\) 331.028 191.119i 0.754051 0.435352i −0.0731046 0.997324i \(-0.523291\pi\)
0.827156 + 0.561973i \(0.189957\pi\)
\(440\) 73.2687i 0.166520i
\(441\) 140.453 + 43.3802i 0.318488 + 0.0983677i
\(442\) −307.012 −0.694598
\(443\) −61.8708 107.163i −0.139663 0.241904i 0.787706 0.616051i \(-0.211269\pi\)
−0.927369 + 0.374148i \(0.877935\pi\)
\(444\) 5.95885 + 3.44035i 0.0134208 + 0.00774853i
\(445\) −12.3707 + 21.4267i −0.0277994 + 0.0481499i
\(446\) −308.529 + 178.129i −0.691769 + 0.399393i
\(447\) 282.481i 0.631948i
\(448\) 52.1327 20.4496i 0.116368 0.0456464i
\(449\) −266.985 −0.594622 −0.297311 0.954781i \(-0.596090\pi\)
−0.297311 + 0.954781i \(0.596090\pi\)
\(450\) −10.6066 18.3712i −0.0235702 0.0408248i
\(451\) 222.632 + 128.536i 0.493640 + 0.285003i
\(452\) −47.7883 + 82.7718i −0.105726 + 0.183124i
\(453\) 112.545 64.9778i 0.248443 0.143439i
\(454\) 378.757i 0.834267i
\(455\) −96.2190 76.7608i −0.211470 0.168705i
\(456\) 153.951 0.337611
\(457\) 224.670 + 389.140i 0.491619 + 0.851509i 0.999953 0.00965069i \(-0.00307196\pi\)
−0.508334 + 0.861160i \(0.669739\pi\)
\(458\) −423.185 244.326i −0.923985 0.533463i
\(459\) −71.7241 + 124.230i −0.156262 + 0.270653i
\(460\) 70.3302 40.6052i 0.152892 0.0882721i
\(461\) 105.528i 0.228912i 0.993428 + 0.114456i \(0.0365125\pi\)
−0.993428 + 0.114456i \(0.963487\pi\)
\(462\) 196.414 + 29.6412i 0.425138 + 0.0641584i
\(463\) 588.555 1.27118 0.635588 0.772028i \(-0.280758\pi\)
0.635588 + 0.772028i \(0.280758\pi\)
\(464\) 4.60662 + 7.97889i 0.00992805 + 0.0171959i
\(465\) −17.6554 10.1933i −0.0379686 0.0219212i
\(466\) 203.692 352.805i 0.437108 0.757093i
\(467\) 316.668 182.829i 0.678091 0.391496i −0.121044 0.992647i \(-0.538624\pi\)
0.799135 + 0.601151i \(0.205291\pi\)
\(468\) 47.1823i 0.100817i
\(469\) −102.539 + 679.459i −0.218632 + 1.44874i
\(470\) 242.442 0.515835
\(471\) −194.622 337.096i −0.413211 0.715702i
\(472\) −172.320 99.4892i −0.365086 0.210782i
\(473\) −288.675 + 499.999i −0.610306 + 1.05708i
\(474\) −191.828 + 110.752i −0.404700 + 0.233654i
\(475\) 157.125i 0.330790i
\(476\) −241.029 + 302.128i −0.506364 + 0.634723i
\(477\) −171.286 −0.359091
\(478\) 133.509 + 231.244i 0.279307 + 0.483774i
\(479\) −421.907 243.588i −0.880808 0.508535i −0.00988318 0.999951i \(-0.503146\pi\)
−0.870925 + 0.491416i \(0.836479\pi\)
\(480\) −10.9545 + 18.9737i −0.0228218 + 0.0395285i
\(481\) −13.5270 + 7.80979i −0.0281226 + 0.0162366i
\(482\) 138.378i 0.287091i
\(483\) −80.3992 204.964i −0.166458 0.424355i
\(484\) 26.4149 0.0545762
\(485\) −80.8463 140.030i −0.166693 0.288722i
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) 97.8870 169.545i 0.201000 0.348142i −0.747851 0.663867i \(-0.768914\pi\)
0.948851 + 0.315725i \(0.102248\pi\)
\(488\) −165.630 + 95.6265i −0.339406 + 0.195956i
\(489\) 398.575i 0.815082i
\(490\) −151.079 + 34.4250i −0.308325 + 0.0702550i
\(491\) −349.221 −0.711244 −0.355622 0.934630i \(-0.615731\pi\)
−0.355622 + 0.934630i \(0.615731\pi\)
\(492\) 38.4351 + 66.5716i 0.0781202 + 0.135308i
\(493\) −55.0675 31.7933i −0.111699 0.0644894i
\(494\) −174.738 + 302.656i −0.353722 + 0.612664i
\(495\) −67.3016 + 38.8566i −0.135963 + 0.0784981i
\(496\) 21.0553i 0.0424501i
\(497\) −223.256 + 87.5747i −0.449208 + 0.176207i
\(498\) 327.750 0.658133
\(499\) 167.719 + 290.498i 0.336111 + 0.582161i 0.983698 0.179831i \(-0.0575550\pi\)
−0.647587 + 0.761992i \(0.724222\pi\)
\(500\) 19.3649 + 11.1803i 0.0387298 + 0.0223607i
\(501\) −240.572 + 416.683i −0.480183 + 0.831702i
\(502\) 295.586 170.657i 0.588817 0.339953i
\(503\) 523.663i 1.04108i 0.853837 + 0.520540i \(0.174269\pi\)
−0.853837 + 0.520540i \(0.825731\pi\)
\(504\) 46.4317 + 37.0419i 0.0921263 + 0.0734958i
\(505\) 113.264 0.224286
\(506\) −148.754 257.650i −0.293981 0.509190i
\(507\) 160.743 + 92.8050i 0.317047 + 0.183047i
\(508\) 101.973 176.623i 0.200735 0.347683i
\(509\) −417.731 + 241.177i −0.820690 + 0.473825i −0.850654 0.525726i \(-0.823794\pi\)
0.0299645 + 0.999551i \(0.490461\pi\)
\(510\) 151.208i 0.296485i
\(511\) 134.913 + 20.3599i 0.264017 + 0.0398433i
\(512\) 22.6274 0.0441942
\(513\) 81.6446 + 141.413i 0.159151 + 0.275658i
\(514\) 15.3876 + 8.88405i 0.0299370 + 0.0172841i
\(515\) −221.331 + 383.357i −0.429769 + 0.744382i
\(516\) −149.510 + 86.3199i −0.289749 + 0.167287i
\(517\) 888.171i 1.71793i
\(518\) −2.93419 + 19.4431i −0.00566446 + 0.0375349i
\(519\) 218.352 0.420716
\(520\) −24.8673 43.0713i −0.0478216 0.0828295i
\(521\) −61.7509 35.6519i −0.118524 0.0684298i 0.439566 0.898210i \(-0.355132\pi\)
−0.558090 + 0.829780i \(0.688466\pi\)
\(522\) −4.88606 + 8.46290i −0.00936026 + 0.0162124i
\(523\) −521.458 + 301.064i −0.997052 + 0.575648i −0.907375 0.420323i \(-0.861917\pi\)
−0.0896773 + 0.995971i \(0.528584\pi\)
\(524\) 149.196i 0.284725i
\(525\) 37.8057 47.3891i 0.0720108 0.0902650i
\(526\) −300.493 −0.571279
\(527\) −72.6581 125.847i −0.137871 0.238800i
\(528\) 69.5088 + 40.1309i 0.131645 + 0.0760055i
\(529\) 99.6220 172.550i 0.188321 0.326182i
\(530\) 156.362 90.2758i 0.295023 0.170332i
\(531\) 211.049i 0.397455i
\(532\) 160.657 + 409.568i 0.301987 + 0.769864i
\(533\) −174.500 −0.327392
\(534\) 13.5514 + 23.4718i 0.0253772 + 0.0439547i
\(535\) −286.476 165.397i −0.535470 0.309154i
\(536\) −138.826 + 240.453i −0.259003 + 0.448607i
\(537\) −115.660 + 66.7766i −0.215382 + 0.124351i
\(538\) 473.191i 0.879537i
\(539\) 126.114 + 553.469i 0.233977 + 1.02684i
\(540\) −23.2379 −0.0430331
\(541\) 301.657 + 522.485i 0.557591 + 0.965776i 0.997697 + 0.0678303i \(0.0216077\pi\)
−0.440106 + 0.897946i \(0.645059\pi\)
\(542\) 223.333 + 128.941i 0.412053 + 0.237899i
\(543\) −183.608 + 318.018i −0.338136 + 0.585668i
\(544\) −135.244 + 78.0833i −0.248611 + 0.143535i
\(545\) 121.468i 0.222876i
\(546\) −125.523 + 49.2378i −0.229896 + 0.0901791i
\(547\) −879.935 −1.60866 −0.804328 0.594185i \(-0.797475\pi\)
−0.804328 + 0.594185i \(0.797475\pi\)
\(548\) 246.899 + 427.642i 0.450546 + 0.780368i
\(549\) −175.677 101.427i −0.319995 0.184749i
\(550\) 40.9584 70.9421i 0.0744699 0.128986i
\(551\) −62.6842 + 36.1908i −0.113765 + 0.0656820i
\(552\) 88.9615i 0.161162i
\(553\) −494.827 394.759i −0.894805 0.713849i
\(554\) 235.836 0.425697
\(555\) −3.84642 6.66220i −0.00693049 0.0120040i
\(556\) 270.056 + 155.917i 0.485712 + 0.280426i
\(557\) 441.404 764.533i 0.792466 1.37259i −0.131970 0.991254i \(-0.542130\pi\)
0.924436 0.381338i \(-0.124536\pi\)
\(558\) −19.3405 + 11.1662i −0.0346604 + 0.0200112i
\(559\) 391.903i 0.701078i
\(560\) −61.9089 9.34279i −0.110552 0.0166836i
\(561\) −553.939 −0.987414
\(562\) −27.0882 46.9182i −0.0481997 0.0834843i
\(563\) −451.334 260.578i −0.801659 0.462838i 0.0423920 0.999101i \(-0.486502\pi\)
−0.844051 + 0.536263i \(0.819835\pi\)
\(564\) 132.791 230.001i 0.235445 0.407803i
\(565\) 92.5417 53.4290i 0.163791 0.0945646i
\(566\) 545.174i 0.963204i
\(567\) −9.40101 + 62.2946i −0.0165803 + 0.109867i
\(568\) −96.9011 −0.170601
\(569\) −122.400 212.004i −0.215115 0.372590i 0.738193 0.674589i \(-0.235679\pi\)
−0.953308 + 0.301999i \(0.902346\pi\)
\(570\) −149.062 86.0610i −0.261512 0.150984i
\(571\) 208.126 360.486i 0.364495 0.631323i −0.624200 0.781264i \(-0.714575\pi\)
0.988695 + 0.149941i \(0.0479084\pi\)
\(572\) −157.789 + 91.0995i −0.275855 + 0.159265i
\(573\) 286.994i 0.500862i
\(574\) −136.996 + 171.724i −0.238670 + 0.299171i
\(575\) −90.7959 −0.157906
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 669.929 + 386.784i 1.16106 + 0.670336i 0.951557 0.307473i \(-0.0994833\pi\)
0.209499 + 0.977809i \(0.432817\pi\)
\(578\) 334.550 579.457i 0.578806 1.00252i
\(579\) 157.949 91.1920i 0.272796 0.157499i
\(580\) 10.3007i 0.0177598i
\(581\) 342.028 + 871.941i 0.588689 + 1.50076i
\(582\) −177.125 −0.304339
\(583\) −330.719 572.823i −0.567272 0.982543i
\(584\) 47.7441 + 27.5651i 0.0817537 + 0.0472005i
\(585\) 26.3757 45.6841i 0.0450867 0.0780924i
\(586\) −111.433 + 64.3357i −0.190158 + 0.109788i
\(587\) 633.860i 1.07983i 0.841720 + 0.539915i \(0.181544\pi\)
−0.841720 + 0.539915i \(0.818456\pi\)
\(588\) −50.0911 + 162.182i −0.0851889 + 0.275819i
\(589\) −165.416 −0.280841
\(590\) 111.232 + 192.660i 0.188529 + 0.326543i
\(591\) 367.103 + 211.947i 0.621156 + 0.358625i
\(592\) −3.97257 + 6.88069i −0.00671042 + 0.0116228i
\(593\) 80.4028 46.4206i 0.135587 0.0782809i −0.430672 0.902508i \(-0.641724\pi\)
0.566259 + 0.824227i \(0.308390\pi\)
\(594\) 85.1305i 0.143317i
\(595\) 402.270 157.795i 0.676084 0.265201i
\(596\) 326.181 0.547283
\(597\) 84.8416 + 146.950i 0.142113 + 0.246147i
\(598\) 174.892 + 100.974i 0.292461 + 0.168853i
\(599\) 307.680 532.918i 0.513657 0.889679i −0.486218 0.873838i \(-0.661624\pi\)
0.999875 0.0158418i \(-0.00504280\pi\)
\(600\) 21.2132 12.2474i 0.0353553 0.0204124i
\(601\) 821.399i 1.36672i −0.730081 0.683360i \(-0.760518\pi\)
0.730081 0.683360i \(-0.239482\pi\)
\(602\) −385.668 307.675i −0.640644 0.511088i
\(603\) −294.494 −0.488381
\(604\) 75.0299 + 129.956i 0.124222 + 0.215158i
\(605\) −25.5761 14.7664i −0.0422746 0.0244072i
\(606\) 62.0374 107.452i 0.102372 0.177313i
\(607\) −869.979 + 502.282i −1.43324 + 0.827483i −0.997367 0.0725231i \(-0.976895\pi\)
−0.435876 + 0.900006i \(0.643562\pi\)
\(608\) 177.767i 0.292380i
\(609\) −27.6135 4.16720i −0.0453423 0.00684270i
\(610\) 213.827 0.350537
\(611\) 301.444 + 522.116i 0.493361 + 0.854527i
\(612\) −143.448 82.8198i −0.234392 0.135326i
\(613\) −556.873 + 964.532i −0.908438 + 1.57346i −0.0922038 + 0.995740i \(0.529391\pi\)
−0.816234 + 0.577721i \(0.803942\pi\)
\(614\) 622.264 359.265i 1.01346 0.585121i
\(615\) 85.9436i 0.139746i
\(616\) −34.2267 + 226.799i −0.0555628 + 0.368180i
\(617\) −463.256 −0.750820 −0.375410 0.926859i \(-0.622498\pi\)
−0.375410 + 0.926859i \(0.622498\pi\)
\(618\) 242.456 + 419.946i 0.392324 + 0.679525i
\(619\) 486.109 + 280.655i 0.785314 + 0.453401i 0.838310 0.545193i \(-0.183544\pi\)
−0.0529963 + 0.998595i \(0.516877\pi\)
\(620\) 11.7703 20.3867i 0.0189843 0.0328817i
\(621\) 81.7163 47.1790i 0.131588 0.0759725i
\(622\) 147.532i 0.237190i
\(623\) −48.3021 + 60.5464i −0.0775315 + 0.0971852i
\(624\) −54.4814 −0.0873100
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −325.621 187.997i −0.520161 0.300315i
\(627\) −315.279 + 546.079i −0.502837 + 0.870939i
\(628\) 389.245 224.731i 0.619816 0.357851i
\(629\) 54.8346i 0.0871774i
\(630\) −24.2502 61.8217i −0.0384925 0.0981297i
\(631\) 244.533 0.387533 0.193767 0.981048i \(-0.437930\pi\)
0.193767 + 0.981048i \(0.437930\pi\)
\(632\) −127.885 221.504i −0.202350 0.350480i
\(633\) −583.371 336.809i −0.921597 0.532084i
\(634\) 7.58178 13.1320i 0.0119587 0.0207130i
\(635\) −197.471 + 114.010i −0.310977 + 0.179543i
\(636\) 197.784i 0.310982i
\(637\) −261.983 282.556i −0.411276 0.443574i
\(638\) −37.7360 −0.0591473
\(639\) −51.3896 89.0094i −0.0804219 0.139295i
\(640\) −21.9089 12.6491i −0.0342327 0.0197642i
\(641\) −325.885 + 564.449i −0.508400 + 0.880575i 0.491553 + 0.870848i \(0.336430\pi\)
−0.999953 + 0.00972698i \(0.996904\pi\)
\(642\) −313.819 + 181.184i −0.488815 + 0.282217i
\(643\) 76.4894i 0.118957i 0.998230 + 0.0594786i \(0.0189438\pi\)
−0.998230 + 0.0594786i \(0.981056\pi\)
\(644\) 236.672 92.8371i 0.367503 0.144157i
\(645\) 193.017 0.299251
\(646\) −613.442 1062.51i −0.949601 1.64476i
\(647\) 141.933 + 81.9453i 0.219372 + 0.126654i 0.605659 0.795724i \(-0.292909\pi\)
−0.386288 + 0.922378i \(0.626243\pi\)
\(648\) −12.7279 + 22.0454i −0.0196419 + 0.0340207i
\(649\) 705.797 407.492i 1.08752 0.627877i
\(650\) 55.6049i 0.0855459i
\(651\) −49.8895 39.8004i −0.0766352 0.0611374i
\(652\) −460.235 −0.705882
\(653\) 557.431 + 965.499i 0.853647 + 1.47856i 0.877895 + 0.478854i \(0.158948\pi\)
−0.0242480 + 0.999706i \(0.507719\pi\)
\(654\) −115.234 66.5305i −0.176199 0.101729i
\(655\) −83.4031 + 144.458i −0.127333 + 0.220547i
\(656\) −76.8703 + 44.3811i −0.117180 + 0.0676541i
\(657\) 58.4744i 0.0890021i
\(658\) 750.467 + 113.254i 1.14053 + 0.172119i
\(659\) 1164.66 1.76732 0.883660 0.468130i \(-0.155072\pi\)
0.883660 + 0.468130i \(0.155072\pi\)
\(660\) −44.8677 77.7132i −0.0679814 0.117747i
\(661\) 542.087 + 312.974i 0.820101 + 0.473485i 0.850451 0.526054i \(-0.176329\pi\)
−0.0303505 + 0.999539i \(0.509662\pi\)
\(662\) 249.553 432.238i 0.376968 0.652928i
\(663\) 325.636 188.006i 0.491155 0.283568i
\(664\) 378.453i 0.569960i
\(665\) 73.3994 486.372i 0.110375 0.731387i
\(666\) −8.42709 −0.0126533
\(667\) 20.9131 + 36.2226i 0.0313540 + 0.0543067i
\(668\) −481.144 277.788i −0.720275 0.415851i
\(669\) 218.163 377.869i 0.326103 0.564827i
\(670\) 268.835 155.212i 0.401246 0.231660i
\(671\) 783.342i 1.16743i
\(672\) −42.7723 + 53.6147i −0.0636492 + 0.0797838i
\(673\) −38.0207 −0.0564943 −0.0282471 0.999601i \(-0.508993\pi\)
−0.0282471 + 0.999601i \(0.508993\pi\)
\(674\) −156.011 270.220i −0.231471 0.400920i
\(675\) 22.5000 + 12.9904i 0.0333333 + 0.0192450i
\(676\) −107.162 + 185.610i −0.158524 + 0.274571i
\(677\) 676.984 390.857i 0.999976 0.577336i 0.0917347 0.995783i \(-0.470759\pi\)
0.908241 + 0.418447i \(0.137426\pi\)
\(678\) 117.057i 0.172651i
\(679\) −184.842 471.222i −0.272227 0.693994i
\(680\) 174.599 0.256764
\(681\) 231.941 + 401.733i 0.340588 + 0.589916i
\(682\) −74.6852 43.1195i −0.109509 0.0632251i
\(683\) 67.2190 116.427i 0.0984172 0.170464i −0.812612 0.582804i \(-0.801955\pi\)
0.911030 + 0.412341i \(0.135289\pi\)
\(684\) −163.289 + 94.2751i −0.238727 + 0.137829i
\(685\) 552.083i 0.805960i
\(686\) −483.739 + 35.9855i −0.705158 + 0.0524570i
\(687\) 598.474 0.871142
\(688\) −99.6736 172.640i −0.144874 0.250930i
\(689\) 388.830 + 224.491i 0.564340 + 0.325822i
\(690\) −49.7310 + 86.1366i −0.0720739 + 0.124836i
\(691\) −393.253 + 227.045i −0.569107 + 0.328574i −0.756792 0.653655i \(-0.773235\pi\)
0.187686 + 0.982229i \(0.439901\pi\)
\(692\) 252.131i 0.364351i
\(693\) −226.480 + 88.8392i −0.326811 + 0.128195i
\(694\) −362.051 −0.521687
\(695\) −174.320 301.932i −0.250821 0.434434i
\(696\) −9.77211 5.64193i −0.0140404 0.00810622i
\(697\) 306.303 530.532i 0.439459 0.761165i
\(698\) 498.778 287.969i 0.714581 0.412564i
\(699\) 498.942i 0.713794i
\(700\) 54.7203 + 43.6543i 0.0781718 + 0.0623632i
\(701\) 982.015 1.40088 0.700439 0.713713i \(-0.252988\pi\)
0.700439 + 0.713713i \(0.252988\pi\)
\(702\) −28.8931 50.0444i −0.0411583 0.0712883i
\(703\) −54.0565 31.2095i −0.0768940 0.0443948i
\(704\) −46.3392 + 80.2618i −0.0658227 + 0.114008i
\(705\) −257.149 + 148.465i −0.364750 + 0.210589i
\(706\) 824.822i 1.16830i
\(707\) 350.603 + 52.9102i 0.495903 + 0.0748376i
\(708\) 243.698 0.344206
\(709\) 166.536 + 288.449i 0.234889 + 0.406839i 0.959240 0.282591i \(-0.0911940\pi\)
−0.724352 + 0.689431i \(0.757861\pi\)
\(710\) 93.8241 + 54.1694i 0.132147 + 0.0762949i
\(711\) 135.643 234.940i 0.190777 0.330436i
\(712\) −27.1029 + 15.6479i −0.0380658 + 0.0219773i
\(713\) 95.5866i 0.134063i
\(714\) 70.6351 468.055i 0.0989287 0.655539i
\(715\) 203.705 0.284902
\(716\) −77.1069 133.553i −0.107691 0.186527i
\(717\) −283.215 163.514i −0.395000 0.228053i
\(718\) −488.984 + 846.946i −0.681037 + 1.17959i
\(719\) 1055.73 609.523i 1.46832 0.847737i 0.468954 0.883223i \(-0.344631\pi\)
0.999370 + 0.0354852i \(0.0112977\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −864.200 + 1083.27i −1.19861 + 1.50245i
\(722\) −886.051 −1.22722
\(723\) 84.7389 + 146.772i 0.117205 + 0.203004i
\(724\) −367.215 212.012i −0.507203 0.292834i
\(725\) −5.75827 + 9.97362i −0.00794244 + 0.0137567i
\(726\) −28.0172 + 16.1758i −0.0385912 + 0.0222807i
\(727\) 215.108i 0.295885i −0.988996 0.147942i \(-0.952735\pi\)
0.988996 0.147942i \(-0.0472650\pi\)
\(728\) −56.8549 144.941i −0.0780974 0.199095i
\(729\) −27.0000 −0.0370370
\(730\) −30.8187 53.3796i −0.0422174 0.0731227i
\(731\) 1191.50 + 687.913i 1.62996 + 0.941057i
\(732\) 117.118 202.854i 0.159997 0.277124i
\(733\) −649.047 + 374.728i −0.885467 + 0.511225i −0.872457 0.488691i \(-0.837475\pi\)
−0.0130099 + 0.999915i \(0.504141\pi\)
\(734\) 324.883i 0.442620i
\(735\) 139.163 129.030i 0.189337 0.175551i
\(736\) 102.724 0.139570
\(737\) −568.609 984.859i −0.771518 1.33631i
\(738\) −81.5332 47.0732i −0.110479 0.0637849i
\(739\) 467.102 809.045i 0.632073 1.09478i −0.355054 0.934846i \(-0.615538\pi\)
0.987127 0.159937i \(-0.0511291\pi\)
\(740\) 7.69285 4.44147i 0.0103957 0.00600198i
\(741\) 428.020i 0.577625i
\(742\) 526.182 206.401i 0.709140 0.278168i
\(743\) 1232.47 1.65878 0.829389 0.558671i \(-0.188689\pi\)
0.829389 + 0.558671i \(0.188689\pi\)
\(744\) −12.8937 22.3325i −0.0173302 0.0300168i
\(745\) −315.823 182.341i −0.423924 0.244752i
\(746\) 286.101 495.542i 0.383514 0.664266i
\(747\) −347.632 + 200.705i −0.465370 + 0.268682i
\(748\) 639.634i 0.855125i
\(749\) −809.508 645.803i −1.08079 0.862220i
\(750\) −27.3861 −0.0365148
\(751\) −393.353 681.307i −0.523772 0.907200i −0.999617 0.0276709i \(-0.991191\pi\)
0.475845 0.879529i \(-0.342142\pi\)
\(752\) 265.582 + 153.334i 0.353168 + 0.203902i
\(753\) −209.011 + 362.017i −0.277571 + 0.480767i
\(754\) 22.1833 12.8075i 0.0294208 0.0169861i
\(755\) 167.772i 0.222214i
\(756\) −71.9316 10.8553i −0.0951477 0.0143589i
\(757\) 1303.18 1.72151 0.860753 0.509023i \(-0.169993\pi\)
0.860753 + 0.509023i \(0.169993\pi\)
\(758\) −187.995 325.618i −0.248015 0.429575i
\(759\) 315.556 + 182.186i 0.415752 + 0.240034i
\(760\) 99.3747 172.122i 0.130756 0.226476i
\(761\) 601.784 347.440i 0.790780 0.456557i −0.0494571 0.998776i \(-0.515749\pi\)
0.840237 + 0.542219i \(0.182416\pi\)
\(762\) 249.783i 0.327799i
\(763\) 56.7423 375.996i 0.0743674 0.492786i
\(764\) 331.392 0.433759
\(765\) 92.5954 + 160.380i 0.121040 + 0.209647i
\(766\) −375.266 216.660i −0.489904 0.282846i
\(767\) −276.604 + 479.093i −0.360631 + 0.624632i
\(768\) −24.0000 + 13.8564i −0.0312500 + 0.0180422i
\(769\) 263.988i 0.343287i −0.985159 0.171644i \(-0.945092\pi\)
0.985159 0.171644i \(-0.0549077\pi\)
\(770\) 159.924 200.464i 0.207694 0.260343i
\(771\) −21.7614 −0.0282249
\(772\) 105.299 + 182.384i 0.136398 + 0.236249i
\(773\) −136.278 78.6802i −0.176298 0.101786i 0.409254 0.912420i \(-0.365789\pi\)
−0.585552 + 0.810635i \(0.699122\pi\)
\(774\) 105.720 183.112i 0.136589 0.236579i
\(775\) −22.7930 + 13.1595i −0.0294103 + 0.0169801i
\(776\) 204.527i 0.263566i
\(777\) −8.79422 22.4193i −0.0113182 0.0288537i
\(778\) 150.408