Properties

Label 637.2.x.b.80.6
Level $637$
Weight $2$
Character 637.80
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
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.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 80.6
Character \(\chi\) \(=\) 637.80
Dual form 637.2.x.b.215.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.239080 + 0.892257i) q^{2} +1.14107i q^{3} +(0.993087 - 0.573359i) q^{4} +(-1.02497 + 3.82526i) q^{5} +(-1.01813 + 0.272807i) q^{6} +(2.05537 + 2.05537i) q^{8} +1.69796 q^{9} +O(q^{10})\) \(q+(0.239080 + 0.892257i) q^{2} +1.14107i q^{3} +(0.993087 - 0.573359i) q^{4} +(-1.02497 + 3.82526i) q^{5} +(-1.01813 + 0.272807i) q^{6} +(2.05537 + 2.05537i) q^{8} +1.69796 q^{9} -3.65816 q^{10} +(1.48892 + 1.48892i) q^{11} +(0.654243 + 1.13318i) q^{12} +(3.41094 - 1.16855i) q^{13} +(-4.36489 - 1.16957i) q^{15} +(-0.195801 + 0.339138i) q^{16} +(-1.58621 - 2.74739i) q^{17} +(0.405947 + 1.51502i) q^{18} +(-0.825689 - 0.825689i) q^{19} +(1.17536 + 4.38649i) q^{20} +(-0.972529 + 1.68447i) q^{22} +(-3.26418 - 1.88457i) q^{23} +(-2.34532 + 2.34532i) q^{24} +(-9.25190 - 5.34158i) q^{25} +(1.85813 + 2.76406i) q^{26} +5.36070i q^{27} +(-0.584891 - 1.01306i) q^{29} -4.17422i q^{30} +(-4.88736 + 1.30956i) q^{31} +(5.26595 + 1.41101i) q^{32} +(-1.69896 + 1.69896i) q^{33} +(2.07215 - 2.07215i) q^{34} +(1.68622 - 0.973539i) q^{36} +(-4.26868 + 1.14379i) q^{37} +(0.539321 - 0.934132i) q^{38} +(1.33339 + 3.89212i) q^{39} +(-9.96900 + 5.75561i) q^{40} +(1.85922 - 6.93869i) q^{41} +(-1.91410 - 1.10511i) q^{43} +(2.33231 + 0.624941i) q^{44} +(-1.74036 + 6.49513i) q^{45} +(0.901126 - 3.36305i) q^{46} +(11.2261 + 3.00801i) q^{47} +(-0.386980 - 0.223423i) q^{48} +(2.55413 - 9.53214i) q^{50} +(3.13497 - 1.80998i) q^{51} +(2.71736 - 3.11616i) q^{52} +(-2.44630 + 4.23711i) q^{53} +(-4.78313 + 1.28163i) q^{54} +(-7.22161 + 4.16940i) q^{55} +(0.942169 - 0.942169i) q^{57} +(0.764076 - 0.764076i) q^{58} +(-0.236582 - 0.0633920i) q^{59} +(-5.00530 + 1.34116i) q^{60} -12.3685i q^{61} +(-2.33694 - 4.04770i) q^{62} +5.81913i q^{64} +(0.973870 + 14.2454i) q^{65} +(-1.92210 - 1.10972i) q^{66} +(7.28743 - 7.28743i) q^{67} +(-3.15048 - 1.81893i) q^{68} +(2.15043 - 3.72465i) q^{69} +(1.60477 + 5.98907i) q^{71} +(3.48993 + 3.48993i) q^{72} +(-1.27338 - 4.75231i) q^{73} +(-2.04111 - 3.53530i) q^{74} +(6.09513 - 10.5571i) q^{75} +(-1.29340 - 0.346564i) q^{76} +(-3.15399 + 2.12026i) q^{78} +(1.34840 + 2.33549i) q^{79} +(-1.09660 - 1.09660i) q^{80} -1.02306 q^{81} +6.63560 q^{82} +(3.31162 + 3.31162i) q^{83} +(12.1353 - 3.25165i) q^{85} +(0.528416 - 1.97208i) q^{86} +(1.15597 - 0.667402i) q^{87} +6.12055i q^{88} +(-1.80032 - 6.71890i) q^{89} -6.21141 q^{90} -4.32215 q^{92} +(-1.49431 - 5.57683i) q^{93} +10.7357i q^{94} +(4.00478 - 2.31216i) q^{95} +(-1.61006 + 6.00882i) q^{96} +(-15.8523 + 4.24762i) q^{97} +(2.52812 + 2.52812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.239080 + 0.892257i 0.169055 + 0.630921i 0.997488 + 0.0708335i \(0.0225659\pi\)
−0.828433 + 0.560088i \(0.810767\pi\)
\(3\) 1.14107i 0.658797i 0.944191 + 0.329399i \(0.106846\pi\)
−0.944191 + 0.329399i \(0.893154\pi\)
\(4\) 0.993087 0.573359i 0.496543 0.286679i
\(5\) −1.02497 + 3.82526i −0.458383 + 1.71071i 0.219566 + 0.975598i \(0.429536\pi\)
−0.677948 + 0.735110i \(0.737131\pi\)
\(6\) −1.01813 + 0.272807i −0.415649 + 0.111373i
\(7\) 0 0
\(8\) 2.05537 + 2.05537i 0.726682 + 0.726682i
\(9\) 1.69796 0.565986
\(10\) −3.65816 −1.15681
\(11\) 1.48892 + 1.48892i 0.448926 + 0.448926i 0.894997 0.446071i \(-0.147177\pi\)
−0.446071 + 0.894997i \(0.647177\pi\)
\(12\) 0.654243 + 1.13318i 0.188864 + 0.327121i
\(13\) 3.41094 1.16855i 0.946024 0.324097i
\(14\) 0 0
\(15\) −4.36489 1.16957i −1.12701 0.301981i
\(16\) −0.195801 + 0.339138i −0.0489503 + 0.0847845i
\(17\) −1.58621 2.74739i −0.384712 0.666341i 0.607017 0.794689i \(-0.292366\pi\)
−0.991729 + 0.128348i \(0.959033\pi\)
\(18\) 0.405947 + 1.51502i 0.0956827 + 0.357093i
\(19\) −0.825689 0.825689i −0.189426 0.189426i 0.606022 0.795448i \(-0.292764\pi\)
−0.795448 + 0.606022i \(0.792764\pi\)
\(20\) 1.17536 + 4.38649i 0.262818 + 0.980849i
\(21\) 0 0
\(22\) −0.972529 + 1.68447i −0.207344 + 0.359130i
\(23\) −3.26418 1.88457i −0.680628 0.392961i 0.119464 0.992839i \(-0.461882\pi\)
−0.800092 + 0.599878i \(0.795216\pi\)
\(24\) −2.34532 + 2.34532i −0.478736 + 0.478736i
\(25\) −9.25190 5.34158i −1.85038 1.06832i
\(26\) 1.85813 + 2.76406i 0.364409 + 0.542076i
\(27\) 5.36070i 1.03167i
\(28\) 0 0
\(29\) −0.584891 1.01306i −0.108612 0.188121i 0.806596 0.591102i \(-0.201307\pi\)
−0.915208 + 0.402982i \(0.867974\pi\)
\(30\) 4.17422i 0.762106i
\(31\) −4.88736 + 1.30956i −0.877796 + 0.235205i −0.669456 0.742852i \(-0.733473\pi\)
−0.208340 + 0.978056i \(0.566806\pi\)
\(32\) 5.26595 + 1.41101i 0.930898 + 0.249433i
\(33\) −1.69896 + 1.69896i −0.295751 + 0.295751i
\(34\) 2.07215 2.07215i 0.355371 0.355371i
\(35\) 0 0
\(36\) 1.68622 0.973539i 0.281037 0.162257i
\(37\) −4.26868 + 1.14379i −0.701766 + 0.188038i −0.592022 0.805922i \(-0.701670\pi\)
−0.109745 + 0.993960i \(0.535003\pi\)
\(38\) 0.539321 0.934132i 0.0874895 0.151536i
\(39\) 1.33339 + 3.89212i 0.213514 + 0.623238i
\(40\) −9.96900 + 5.75561i −1.57624 + 0.910041i
\(41\) 1.85922 6.93869i 0.290361 1.08364i −0.654472 0.756087i \(-0.727109\pi\)
0.944832 0.327555i \(-0.106225\pi\)
\(42\) 0 0
\(43\) −1.91410 1.10511i −0.291897 0.168527i 0.346900 0.937902i \(-0.387234\pi\)
−0.638797 + 0.769375i \(0.720568\pi\)
\(44\) 2.33231 + 0.624941i 0.351609 + 0.0942134i
\(45\) −1.74036 + 6.49513i −0.259438 + 0.968236i
\(46\) 0.901126 3.36305i 0.132864 0.495854i
\(47\) 11.2261 + 3.00801i 1.63749 + 0.438764i 0.956072 0.293132i \(-0.0946977\pi\)
0.681416 + 0.731896i \(0.261364\pi\)
\(48\) −0.386980 0.223423i −0.0558558 0.0322484i
\(49\) 0 0
\(50\) 2.55413 9.53214i 0.361208 1.34805i
\(51\) 3.13497 1.80998i 0.438984 0.253447i
\(52\) 2.71736 3.11616i 0.376830 0.432134i
\(53\) −2.44630 + 4.23711i −0.336025 + 0.582012i −0.983681 0.179921i \(-0.942416\pi\)
0.647656 + 0.761933i \(0.275749\pi\)
\(54\) −4.78313 + 1.28163i −0.650901 + 0.174408i
\(55\) −7.22161 + 4.16940i −0.973762 + 0.562202i
\(56\) 0 0
\(57\) 0.942169 0.942169i 0.124793 0.124793i
\(58\) 0.764076 0.764076i 0.100328 0.100328i
\(59\) −0.236582 0.0633920i −0.0308004 0.00825293i 0.243386 0.969930i \(-0.421742\pi\)
−0.274186 + 0.961677i \(0.588409\pi\)
\(60\) −5.00530 + 1.34116i −0.646181 + 0.173144i
\(61\) 12.3685i 1.58362i −0.610767 0.791811i \(-0.709139\pi\)
0.610767 0.791811i \(-0.290861\pi\)
\(62\) −2.33694 4.04770i −0.296791 0.514058i
\(63\) 0 0
\(64\) 5.81913i 0.727392i
\(65\) 0.973870 + 14.2454i 0.120794 + 1.76693i
\(66\) −1.92210 1.10972i −0.236594 0.136598i
\(67\) 7.28743 7.28743i 0.890301 0.890301i −0.104250 0.994551i \(-0.533244\pi\)
0.994551 + 0.104250i \(0.0332442\pi\)
\(68\) −3.15048 1.81893i −0.382052 0.220578i
\(69\) 2.15043 3.72465i 0.258881 0.448396i
\(70\) 0 0
\(71\) 1.60477 + 5.98907i 0.190451 + 0.710772i 0.993398 + 0.114722i \(0.0365976\pi\)
−0.802947 + 0.596051i \(0.796736\pi\)
\(72\) 3.48993 + 3.48993i 0.411292 + 0.411292i
\(73\) −1.27338 4.75231i −0.149037 0.556216i −0.999542 0.0302484i \(-0.990370\pi\)
0.850505 0.525967i \(-0.176297\pi\)
\(74\) −2.04111 3.53530i −0.237274 0.410971i
\(75\) 6.09513 10.5571i 0.703804 1.21903i
\(76\) −1.29340 0.346564i −0.148363 0.0397537i
\(77\) 0 0
\(78\) −3.15399 + 2.12026i −0.357119 + 0.240072i
\(79\) 1.34840 + 2.33549i 0.151707 + 0.262764i 0.931855 0.362831i \(-0.118190\pi\)
−0.780148 + 0.625595i \(0.784856\pi\)
\(80\) −1.09660 1.09660i −0.122603 0.122603i
\(81\) −1.02306 −0.113674
\(82\) 6.63560 0.732779
\(83\) 3.31162 + 3.31162i 0.363497 + 0.363497i 0.865099 0.501602i \(-0.167256\pi\)
−0.501602 + 0.865099i \(0.667256\pi\)
\(84\) 0 0
\(85\) 12.1353 3.25165i 1.31626 0.352691i
\(86\) 0.528416 1.97208i 0.0569806 0.212654i
\(87\) 1.15597 0.667402i 0.123933 0.0715530i
\(88\) 6.12055i 0.652453i
\(89\) −1.80032 6.71890i −0.190834 0.712202i −0.993306 0.115512i \(-0.963149\pi\)
0.802472 0.596690i \(-0.203518\pi\)
\(90\) −6.21141 −0.654740
\(91\) 0 0
\(92\) −4.32215 −0.450615
\(93\) −1.49431 5.57683i −0.154952 0.578290i
\(94\) 10.7357i 1.10730i
\(95\) 4.00478 2.31216i 0.410882 0.237223i
\(96\) −1.61006 + 6.00882i −0.164326 + 0.613273i
\(97\) −15.8523 + 4.24762i −1.60956 + 0.431280i −0.947912 0.318533i \(-0.896810\pi\)
−0.661649 + 0.749814i \(0.730143\pi\)
\(98\) 0 0
\(99\) 2.52812 + 2.52812i 0.254086 + 0.254086i
\(100\) −12.2506 −1.22506
\(101\) 3.62029 0.360233 0.180116 0.983645i \(-0.442353\pi\)
0.180116 + 0.983645i \(0.442353\pi\)
\(102\) 2.36447 + 2.36447i 0.234118 + 0.234118i
\(103\) 0.795369 + 1.37762i 0.0783700 + 0.135741i 0.902547 0.430592i \(-0.141695\pi\)
−0.824177 + 0.566333i \(0.808362\pi\)
\(104\) 9.41252 + 4.60893i 0.922973 + 0.451943i
\(105\) 0 0
\(106\) −4.36545 1.16972i −0.424010 0.113613i
\(107\) 7.44322 12.8920i 0.719563 1.24632i −0.241610 0.970373i \(-0.577676\pi\)
0.961173 0.275946i \(-0.0889911\pi\)
\(108\) 3.07361 + 5.32364i 0.295758 + 0.512268i
\(109\) −0.868870 3.24267i −0.0832226 0.310591i 0.911749 0.410748i \(-0.134732\pi\)
−0.994972 + 0.100157i \(0.968066\pi\)
\(110\) −5.44672 5.44672i −0.519324 0.519324i
\(111\) −1.30514 4.87086i −0.123879 0.462322i
\(112\) 0 0
\(113\) −4.88202 + 8.45591i −0.459262 + 0.795465i −0.998922 0.0464177i \(-0.985219\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(114\) 1.06591 + 0.615404i 0.0998317 + 0.0576378i
\(115\) 10.5547 10.5547i 0.984228 0.984228i
\(116\) −1.16170 0.670705i −0.107861 0.0622734i
\(117\) 5.79163 1.98414i 0.535436 0.183434i
\(118\) 0.226248i 0.0208278i
\(119\) 0 0
\(120\) −6.56755 11.3753i −0.599533 1.03842i
\(121\) 6.56623i 0.596930i
\(122\) 11.0359 2.95705i 0.999140 0.267719i
\(123\) 7.91753 + 2.12150i 0.713900 + 0.191289i
\(124\) −4.10272 + 4.10272i −0.368436 + 0.368436i
\(125\) 15.9145 15.9145i 1.42343 1.42343i
\(126\) 0 0
\(127\) −6.81869 + 3.93677i −0.605061 + 0.349332i −0.771030 0.636799i \(-0.780258\pi\)
0.165969 + 0.986131i \(0.446925\pi\)
\(128\) 5.33974 1.43078i 0.471971 0.126464i
\(129\) 1.26100 2.18412i 0.111025 0.192301i
\(130\) −12.4778 + 4.27474i −1.09437 + 0.374919i
\(131\) 1.83447 1.05913i 0.160279 0.0925369i −0.417715 0.908578i \(-0.637169\pi\)
0.577994 + 0.816041i \(0.303836\pi\)
\(132\) −0.713102 + 2.66133i −0.0620676 + 0.231639i
\(133\) 0 0
\(134\) 8.24454 + 4.75999i 0.712220 + 0.411200i
\(135\) −20.5061 5.49458i −1.76488 0.472898i
\(136\) 2.38666 8.90714i 0.204654 0.763781i
\(137\) −3.02455 + 11.2878i −0.258405 + 0.964380i 0.707760 + 0.706453i \(0.249706\pi\)
−0.966164 + 0.257927i \(0.916961\pi\)
\(138\) 3.83747 + 1.02825i 0.326668 + 0.0875303i
\(139\) −3.88166 2.24108i −0.329238 0.190086i 0.326265 0.945278i \(-0.394210\pi\)
−0.655503 + 0.755193i \(0.727543\pi\)
\(140\) 0 0
\(141\) −3.43235 + 12.8097i −0.289056 + 1.07877i
\(142\) −4.96013 + 2.86373i −0.416245 + 0.240319i
\(143\) 6.81849 + 3.33874i 0.570191 + 0.279200i
\(144\) −0.332462 + 0.575842i −0.0277052 + 0.0479868i
\(145\) 4.47472 1.19900i 0.371605 0.0995713i
\(146\) 3.93584 2.27236i 0.325733 0.188062i
\(147\) 0 0
\(148\) −3.58337 + 3.58337i −0.294551 + 0.294551i
\(149\) 3.22134 3.22134i 0.263903 0.263903i −0.562735 0.826638i \(-0.690251\pi\)
0.826638 + 0.562735i \(0.190251\pi\)
\(150\) 10.8768 + 2.91444i 0.888090 + 0.237963i
\(151\) 14.6306 3.92025i 1.19062 0.319026i 0.391489 0.920183i \(-0.371960\pi\)
0.799131 + 0.601157i \(0.205293\pi\)
\(152\) 3.39418i 0.275305i
\(153\) −2.69331 4.66496i −0.217742 0.377140i
\(154\) 0 0
\(155\) 20.0377i 1.60947i
\(156\) 3.55576 + 3.10070i 0.284689 + 0.248255i
\(157\) 12.1069 + 6.98994i 0.966239 + 0.557858i 0.898088 0.439817i \(-0.144957\pi\)
0.0681513 + 0.997675i \(0.478290\pi\)
\(158\) −1.76149 + 1.76149i −0.140136 + 0.140136i
\(159\) −4.83484 2.79140i −0.383428 0.221372i
\(160\) −10.7949 + 18.6974i −0.853415 + 1.47816i
\(161\) 0 0
\(162\) −0.244594 0.912837i −0.0192171 0.0717192i
\(163\) 16.5003 + 16.5003i 1.29240 + 1.29240i 0.933297 + 0.359107i \(0.116919\pi\)
0.359107 + 0.933297i \(0.383081\pi\)
\(164\) −2.13200 7.95672i −0.166481 0.621315i
\(165\) −4.75758 8.24037i −0.370377 0.641512i
\(166\) −2.16307 + 3.74655i −0.167887 + 0.290789i
\(167\) 10.8156 + 2.89803i 0.836935 + 0.224256i 0.651737 0.758445i \(-0.274041\pi\)
0.185198 + 0.982701i \(0.440707\pi\)
\(168\) 0 0
\(169\) 10.2690 7.97168i 0.789923 0.613207i
\(170\) 5.80261 + 10.0504i 0.445040 + 0.770832i
\(171\) −1.40198 1.40198i −0.107212 0.107212i
\(172\) −2.53449 −0.193253
\(173\) 3.32856 0.253066 0.126533 0.991962i \(-0.459615\pi\)
0.126533 + 0.991962i \(0.459615\pi\)
\(174\) 0.871864 + 0.871864i 0.0660959 + 0.0660959i
\(175\) 0 0
\(176\) −0.796482 + 0.213417i −0.0600371 + 0.0160869i
\(177\) 0.0723347 0.269957i 0.00543701 0.0202912i
\(178\) 5.56457 3.21270i 0.417082 0.240802i
\(179\) 0.255535i 0.0190996i −0.999954 0.00954980i \(-0.996960\pi\)
0.999954 0.00954980i \(-0.00303984\pi\)
\(180\) 1.99571 + 7.44808i 0.148751 + 0.555147i
\(181\) 7.65115 0.568705 0.284353 0.958720i \(-0.408221\pi\)
0.284353 + 0.958720i \(0.408221\pi\)
\(182\) 0 0
\(183\) 14.1133 1.04329
\(184\) −2.83559 10.5826i −0.209042 0.780157i
\(185\) 17.5011i 1.28671i
\(186\) 4.61871 2.66661i 0.338660 0.195525i
\(187\) 1.72891 6.45239i 0.126431 0.471845i
\(188\) 12.8731 3.44934i 0.938868 0.251569i
\(189\) 0 0
\(190\) 3.02050 + 3.02050i 0.219130 + 0.219130i
\(191\) −14.5107 −1.04996 −0.524978 0.851116i \(-0.675927\pi\)
−0.524978 + 0.851116i \(0.675927\pi\)
\(192\) −6.64004 −0.479204
\(193\) 5.69196 + 5.69196i 0.409716 + 0.409716i 0.881639 0.471924i \(-0.156440\pi\)
−0.471924 + 0.881639i \(0.656440\pi\)
\(194\) −7.57994 13.1288i −0.544208 0.942596i
\(195\) −16.2551 + 1.11125i −1.16405 + 0.0795785i
\(196\) 0 0
\(197\) 6.28115 + 1.68303i 0.447514 + 0.119911i 0.475536 0.879696i \(-0.342254\pi\)
−0.0280221 + 0.999607i \(0.508921\pi\)
\(198\) −1.65131 + 2.86016i −0.117354 + 0.203263i
\(199\) 3.53990 + 6.13129i 0.250937 + 0.434636i 0.963784 0.266684i \(-0.0859280\pi\)
−0.712847 + 0.701320i \(0.752595\pi\)
\(200\) −8.03712 29.9949i −0.568310 2.12096i
\(201\) 8.31547 + 8.31547i 0.586528 + 0.586528i
\(202\) 0.865539 + 3.23023i 0.0608991 + 0.227279i
\(203\) 0 0
\(204\) 2.07553 3.59493i 0.145316 0.251695i
\(205\) 24.6366 + 14.2240i 1.72070 + 0.993445i
\(206\) −1.03903 + 1.03903i −0.0723929 + 0.0723929i
\(207\) −5.54243 3.19993i −0.385226 0.222410i
\(208\) −0.271568 + 1.38558i −0.0188298 + 0.0960728i
\(209\) 2.45877i 0.170077i
\(210\) 0 0
\(211\) −3.81923 6.61509i −0.262926 0.455402i 0.704092 0.710109i \(-0.251354\pi\)
−0.967018 + 0.254707i \(0.918021\pi\)
\(212\) 5.61043i 0.385326i
\(213\) −6.83395 + 1.83115i −0.468255 + 0.125469i
\(214\) 13.2825 + 3.55904i 0.907975 + 0.243291i
\(215\) 6.18921 6.18921i 0.422101 0.422101i
\(216\) −11.0182 + 11.0182i −0.749694 + 0.749694i
\(217\) 0 0
\(218\) 2.68556 1.55051i 0.181889 0.105014i
\(219\) 5.42272 1.45301i 0.366433 0.0981855i
\(220\) −4.78112 + 8.28115i −0.322343 + 0.558315i
\(221\) −8.62092 7.51763i −0.579906 0.505690i
\(222\) 4.03403 2.32905i 0.270746 0.156315i
\(223\) 1.74359 6.50716i 0.116759 0.435752i −0.882653 0.470025i \(-0.844245\pi\)
0.999413 + 0.0342732i \(0.0109116\pi\)
\(224\) 0 0
\(225\) −15.7093 9.06979i −1.04729 0.604652i
\(226\) −8.71204 2.33438i −0.579516 0.155281i
\(227\) −4.18872 + 15.6325i −0.278015 + 1.03757i 0.675778 + 0.737105i \(0.263808\pi\)
−0.953794 + 0.300462i \(0.902859\pi\)
\(228\) 0.395455 1.47586i 0.0261896 0.0977410i
\(229\) −18.9495 5.07751i −1.25222 0.335531i −0.429027 0.903292i \(-0.641143\pi\)
−0.823194 + 0.567760i \(0.807810\pi\)
\(230\) 11.9409 + 6.89408i 0.787359 + 0.454582i
\(231\) 0 0
\(232\) 0.880046 3.28438i 0.0577778 0.215630i
\(233\) −9.61575 + 5.55165i −0.629949 + 0.363701i −0.780732 0.624866i \(-0.785154\pi\)
0.150784 + 0.988567i \(0.451820\pi\)
\(234\) 3.15503 + 4.69326i 0.206251 + 0.306808i
\(235\) −23.0128 + 39.8594i −1.50119 + 2.60014i
\(236\) −0.271293 + 0.0726927i −0.0176597 + 0.00473189i
\(237\) −2.66496 + 1.53862i −0.173108 + 0.0999439i
\(238\) 0 0
\(239\) −18.0241 + 18.0241i −1.16588 + 1.16588i −0.182716 + 0.983166i \(0.558489\pi\)
−0.983166 + 0.182716i \(0.941511\pi\)
\(240\) 1.25130 1.25130i 0.0807708 0.0807708i
\(241\) −24.5725 6.58419i −1.58286 0.424125i −0.643048 0.765826i \(-0.722330\pi\)
−0.939809 + 0.341701i \(0.888997\pi\)
\(242\) 5.85877 1.56985i 0.376616 0.100914i
\(243\) 14.9147i 0.956779i
\(244\) −7.09158 12.2830i −0.453992 0.786337i
\(245\) 0 0
\(246\) 7.57168i 0.482753i
\(247\) −3.78123 1.85152i −0.240594 0.117809i
\(248\) −12.7370 7.35368i −0.808797 0.466959i
\(249\) −3.77879 + 3.77879i −0.239471 + 0.239471i
\(250\) 18.0046 + 10.3950i 1.13871 + 0.657437i
\(251\) 3.01219 5.21727i 0.190128 0.329311i −0.755165 0.655535i \(-0.772443\pi\)
0.945292 + 0.326224i \(0.105776\pi\)
\(252\) 0 0
\(253\) −2.05412 7.66608i −0.129141 0.481962i
\(254\) −5.14282 5.14282i −0.322689 0.322689i
\(255\) 3.71036 + 13.8472i 0.232352 + 0.867148i
\(256\) 8.37238 + 14.5014i 0.523274 + 0.906337i
\(257\) −12.2067 + 21.1426i −0.761434 + 1.31884i 0.180678 + 0.983542i \(0.442171\pi\)
−0.942112 + 0.335300i \(0.891162\pi\)
\(258\) 2.25028 + 0.602960i 0.140096 + 0.0375387i
\(259\) 0 0
\(260\) 9.13489 + 13.5886i 0.566522 + 0.842728i
\(261\) −0.993120 1.72014i −0.0614726 0.106474i
\(262\) 1.38360 + 1.38360i 0.0854794 + 0.0854794i
\(263\) −15.1408 −0.933624 −0.466812 0.884357i \(-0.654597\pi\)
−0.466812 + 0.884357i \(0.654597\pi\)
\(264\) −6.98398 −0.429834
\(265\) −13.7007 13.7007i −0.841624 0.841624i
\(266\) 0 0
\(267\) 7.66674 2.05430i 0.469197 0.125721i
\(268\) 3.05874 11.4154i 0.186842 0.697304i
\(269\) 3.06678 1.77061i 0.186985 0.107956i −0.403585 0.914942i \(-0.632236\pi\)
0.590570 + 0.806986i \(0.298903\pi\)
\(270\) 19.6103i 1.19345i
\(271\) −0.195709 0.730396i −0.0118885 0.0443684i 0.959727 0.280935i \(-0.0906445\pi\)
−0.971615 + 0.236567i \(0.923978\pi\)
\(272\) 1.24233 0.0753271
\(273\) 0 0
\(274\) −10.7947 −0.652133
\(275\) −5.82214 21.7285i −0.351088 1.31028i
\(276\) 4.93187i 0.296864i
\(277\) 9.03071 5.21388i 0.542603 0.313272i −0.203530 0.979069i \(-0.565242\pi\)
0.746133 + 0.665797i \(0.231908\pi\)
\(278\) 1.07159 3.99923i 0.0642698 0.239858i
\(279\) −8.29854 + 2.22359i −0.496820 + 0.133123i
\(280\) 0 0
\(281\) −18.1394 18.1394i −1.08211 1.08211i −0.996313 0.0857959i \(-0.972657\pi\)
−0.0857959 0.996313i \(-0.527343\pi\)
\(282\) −12.2502 −0.729487
\(283\) 0.0492199 0.00292582 0.00146291 0.999999i \(-0.499534\pi\)
0.00146291 + 0.999999i \(0.499534\pi\)
\(284\) 5.02756 + 5.02756i 0.298331 + 0.298331i
\(285\) 2.63834 + 4.56974i 0.156282 + 0.270688i
\(286\) −1.34885 + 6.88207i −0.0797594 + 0.406945i
\(287\) 0 0
\(288\) 8.94137 + 2.39583i 0.526875 + 0.141176i
\(289\) 3.46789 6.00656i 0.203993 0.353327i
\(290\) 2.13963 + 3.70594i 0.125643 + 0.217621i
\(291\) −4.84683 18.0886i −0.284126 1.06037i
\(292\) −3.98935 3.98935i −0.233459 0.233459i
\(293\) −4.26864 15.9308i −0.249377 0.930686i −0.971133 0.238539i \(-0.923332\pi\)
0.721756 0.692147i \(-0.243335\pi\)
\(294\) 0 0
\(295\) 0.484981 0.840012i 0.0282367 0.0489074i
\(296\) −11.1246 6.42279i −0.646604 0.373317i
\(297\) −7.98166 + 7.98166i −0.463143 + 0.463143i
\(298\) 3.64443 + 2.10411i 0.211116 + 0.121888i
\(299\) −13.3361 2.61382i −0.771247 0.151161i
\(300\) 13.9788i 0.807065i
\(301\) 0 0
\(302\) 6.99575 + 12.1170i 0.402560 + 0.697255i
\(303\) 4.13101i 0.237320i
\(304\) 0.441693 0.118351i 0.0253328 0.00678791i
\(305\) 47.3126 + 12.6774i 2.70911 + 0.725905i
\(306\) 3.51843 3.51843i 0.201135 0.201135i
\(307\) −13.8117 + 13.8117i −0.788274 + 0.788274i −0.981211 0.192937i \(-0.938199\pi\)
0.192937 + 0.981211i \(0.438199\pi\)
\(308\) 0 0
\(309\) −1.57196 + 0.907572i −0.0894257 + 0.0516300i
\(310\) 17.8788 4.79060i 1.01545 0.272088i
\(311\) 2.25556 3.90675i 0.127901 0.221531i −0.794962 0.606659i \(-0.792509\pi\)
0.922863 + 0.385128i \(0.125843\pi\)
\(312\) −5.25912 + 10.7403i −0.297739 + 0.608052i
\(313\) 26.8350 15.4932i 1.51681 0.875728i 0.517000 0.855985i \(-0.327049\pi\)
0.999805 0.0197427i \(-0.00628470\pi\)
\(314\) −3.34231 + 12.4737i −0.188617 + 0.703929i
\(315\) 0 0
\(316\) 2.67815 + 1.54623i 0.150658 + 0.0869823i
\(317\) −5.92099 1.58652i −0.332556 0.0891081i 0.0886774 0.996060i \(-0.471736\pi\)
−0.421233 + 0.906952i \(0.638403\pi\)
\(318\) 1.33473 4.98129i 0.0748481 0.279337i
\(319\) 0.637511 2.37922i 0.0356938 0.133211i
\(320\) −22.2597 5.96447i −1.24435 0.333424i
\(321\) 14.7107 + 8.49323i 0.821072 + 0.474046i
\(322\) 0 0
\(323\) −0.958777 + 3.57820i −0.0533478 + 0.199097i
\(324\) −1.01599 + 0.586583i −0.0564440 + 0.0325879i
\(325\) −37.7995 7.40854i −2.09674 0.410952i
\(326\) −10.7776 + 18.6674i −0.596918 + 1.03389i
\(327\) 3.70011 0.991442i 0.204617 0.0548268i
\(328\) 18.0829 10.4402i 0.998462 0.576462i
\(329\) 0 0
\(330\) 6.21509 6.21509i 0.342129 0.342129i
\(331\) 11.8222 11.8222i 0.649807 0.649807i −0.303139 0.952946i \(-0.598035\pi\)
0.952946 + 0.303139i \(0.0980348\pi\)
\(332\) 5.18747 + 1.38998i 0.284699 + 0.0762849i
\(333\) −7.24804 + 1.94211i −0.397190 + 0.106427i
\(334\) 10.3431i 0.565952i
\(335\) 20.4069 + 35.3457i 1.11495 + 1.93114i
\(336\) 0 0
\(337\) 12.4651i 0.679017i 0.940603 + 0.339508i \(0.110261\pi\)
−0.940603 + 0.339508i \(0.889739\pi\)
\(338\) 9.56790 + 7.25672i 0.520425 + 0.394713i
\(339\) −9.64879 5.57073i −0.524050 0.302561i
\(340\) 10.1871 10.1871i 0.552471 0.552471i
\(341\) −9.22673 5.32706i −0.499656 0.288476i
\(342\) 0.915745 1.58612i 0.0495178 0.0857674i
\(343\) 0 0
\(344\) −1.66278 6.20557i −0.0896509 0.334582i
\(345\) 12.0436 + 12.0436i 0.648407 + 0.648407i
\(346\) 0.795792 + 2.96994i 0.0427820 + 0.159665i
\(347\) −13.1263 22.7355i −0.704659 1.22050i −0.966815 0.255479i \(-0.917767\pi\)
0.262156 0.965026i \(-0.415566\pi\)
\(348\) 0.765322 1.32558i 0.0410256 0.0710583i
\(349\) −7.06951 1.89427i −0.378422 0.101398i 0.0645937 0.997912i \(-0.479425\pi\)
−0.443016 + 0.896514i \(0.646092\pi\)
\(350\) 0 0
\(351\) 6.26423 + 18.2850i 0.334360 + 0.975982i
\(352\) 5.73971 + 9.94146i 0.305927 + 0.529882i
\(353\) −19.2744 19.2744i −1.02587 1.02587i −0.999656 0.0262143i \(-0.991655\pi\)
−0.0262143 0.999656i \(-0.508345\pi\)
\(354\) 0.258165 0.0137213
\(355\) −24.5546 −1.30322
\(356\) −5.64022 5.64022i −0.298931 0.298931i
\(357\) 0 0
\(358\) 0.228003 0.0610933i 0.0120503 0.00322888i
\(359\) −8.04040 + 30.0072i −0.424356 + 1.58372i 0.340969 + 0.940074i \(0.389245\pi\)
−0.765325 + 0.643644i \(0.777422\pi\)
\(360\) −16.9269 + 9.77278i −0.892128 + 0.515071i
\(361\) 17.6365i 0.928236i
\(362\) 1.82923 + 6.82679i 0.0961424 + 0.358808i
\(363\) 7.49254 0.393256
\(364\) 0 0
\(365\) 19.4840 1.01984
\(366\) 3.37420 + 12.5927i 0.176372 + 0.658231i
\(367\) 25.1296i 1.31175i 0.754867 + 0.655877i \(0.227701\pi\)
−0.754867 + 0.655877i \(0.772299\pi\)
\(368\) 1.27826 0.738004i 0.0666339 0.0384711i
\(369\) 3.15687 11.7816i 0.164340 0.613326i
\(370\) 15.6155 4.18417i 0.811813 0.217525i
\(371\) 0 0
\(372\) −4.68150 4.68150i −0.242724 0.242724i
\(373\) −3.10820 −0.160937 −0.0804683 0.996757i \(-0.525642\pi\)
−0.0804683 + 0.996757i \(0.525642\pi\)
\(374\) 6.17054 0.319071
\(375\) 18.1595 + 18.1595i 0.937755 + 0.937755i
\(376\) 16.8911 + 29.2562i 0.871091 + 1.50877i
\(377\) −3.17884 2.77202i −0.163718 0.142766i
\(378\) 0 0
\(379\) −4.35536 1.16702i −0.223720 0.0599456i 0.145218 0.989400i \(-0.453612\pi\)
−0.368938 + 0.929454i \(0.620278\pi\)
\(380\) 2.65140 4.59235i 0.136014 0.235583i
\(381\) −4.49213 7.78060i −0.230139 0.398612i
\(382\) −3.46921 12.9473i −0.177500 0.662440i
\(383\) 23.7683 + 23.7683i 1.21450 + 1.21450i 0.969530 + 0.244974i \(0.0787795\pi\)
0.244974 + 0.969530i \(0.421221\pi\)
\(384\) 1.63262 + 6.09302i 0.0833143 + 0.310933i
\(385\) 0 0
\(386\) −3.71786 + 6.43952i −0.189234 + 0.327763i
\(387\) −3.25006 1.87642i −0.165210 0.0953839i
\(388\) −13.3073 + 13.3073i −0.675577 + 0.675577i
\(389\) −17.8940 10.3311i −0.907263 0.523809i −0.0277136 0.999616i \(-0.508823\pi\)
−0.879550 + 0.475807i \(0.842156\pi\)
\(390\) −4.87778 14.2380i −0.246996 0.720970i
\(391\) 11.9573i 0.604707i
\(392\) 0 0
\(393\) 1.20855 + 2.09326i 0.0609631 + 0.105591i
\(394\) 6.00678i 0.302617i
\(395\) −10.3159 + 2.76415i −0.519051 + 0.139079i
\(396\) 3.96017 + 1.06112i 0.199006 + 0.0533235i
\(397\) −5.19736 + 5.19736i −0.260848 + 0.260848i −0.825399 0.564550i \(-0.809050\pi\)
0.564550 + 0.825399i \(0.309050\pi\)
\(398\) −4.62437 + 4.62437i −0.231799 + 0.231799i
\(399\) 0 0
\(400\) 3.62307 2.09178i 0.181153 0.104589i
\(401\) −1.38785 + 0.371875i −0.0693062 + 0.0185705i −0.293306 0.956019i \(-0.594755\pi\)
0.223999 + 0.974589i \(0.428089\pi\)
\(402\) −5.43148 + 9.40760i −0.270898 + 0.469208i
\(403\) −15.1402 + 10.1780i −0.754187 + 0.507000i
\(404\) 3.59527 2.07573i 0.178871 0.103271i
\(405\) 1.04862 3.91348i 0.0521061 0.194463i
\(406\) 0 0
\(407\) −8.05873 4.65271i −0.399457 0.230626i
\(408\) 10.1637 + 2.72335i 0.503177 + 0.134826i
\(409\) 1.78773 6.67192i 0.0883978 0.329905i −0.907538 0.419970i \(-0.862041\pi\)
0.995936 + 0.0900646i \(0.0287074\pi\)
\(410\) −6.80132 + 25.3829i −0.335893 + 1.25357i
\(411\) −12.8802 3.45123i −0.635331 0.170236i
\(412\) 1.57974 + 0.912063i 0.0778282 + 0.0449341i
\(413\) 0 0
\(414\) 1.53007 5.71031i 0.0751990 0.280647i
\(415\) −16.0621 + 9.27346i −0.788458 + 0.455216i
\(416\) 19.6107 1.34066i 0.961492 0.0657310i
\(417\) 2.55723 4.42925i 0.125228 0.216901i
\(418\) 2.19385 0.587842i 0.107305 0.0287523i
\(419\) −7.98102 + 4.60785i −0.389899 + 0.225108i −0.682116 0.731244i \(-0.738940\pi\)
0.292218 + 0.956352i \(0.405607\pi\)
\(420\) 0 0
\(421\) 9.26432 9.26432i 0.451515 0.451515i −0.444342 0.895857i \(-0.646562\pi\)
0.895857 + 0.444342i \(0.146562\pi\)
\(422\) 4.98927 4.98927i 0.242874 0.242874i
\(423\) 19.0614 + 5.10748i 0.926795 + 0.248334i
\(424\) −13.7369 + 3.68078i −0.667120 + 0.178754i
\(425\) 33.8915i 1.64398i
\(426\) −3.26772 5.65985i −0.158321 0.274221i
\(427\) 0 0
\(428\) 17.0705i 0.825136i
\(429\) −3.80974 + 7.78038i −0.183936 + 0.375640i
\(430\) 7.00209 + 4.04266i 0.337671 + 0.194954i
\(431\) 4.60076 4.60076i 0.221611 0.221611i −0.587566 0.809176i \(-0.699914\pi\)
0.809176 + 0.587566i \(0.199914\pi\)
\(432\) −1.81802 1.04963i −0.0874694 0.0505005i
\(433\) 12.5684 21.7691i 0.604000 1.04616i −0.388209 0.921571i \(-0.626906\pi\)
0.992209 0.124587i \(-0.0397606\pi\)
\(434\) 0 0
\(435\) 1.36814 + 5.10597i 0.0655973 + 0.244812i
\(436\) −2.72207 2.72207i −0.130364 0.130364i
\(437\) 1.13912 + 4.25126i 0.0544916 + 0.203365i
\(438\) 2.59292 + 4.49107i 0.123895 + 0.214592i
\(439\) −8.84493 + 15.3199i −0.422145 + 0.731177i −0.996149 0.0876754i \(-0.972056\pi\)
0.574004 + 0.818853i \(0.305390\pi\)
\(440\) −23.4127 6.27341i −1.11616 0.299073i
\(441\) 0 0
\(442\) 4.64657 9.48939i 0.221015 0.451364i
\(443\) 7.16955 + 12.4180i 0.340635 + 0.589998i 0.984551 0.175099i \(-0.0560245\pi\)
−0.643915 + 0.765097i \(0.722691\pi\)
\(444\) −4.08887 4.08887i −0.194049 0.194049i
\(445\) 27.5468 1.30584
\(446\) 6.22292 0.294664
\(447\) 3.67578 + 3.67578i 0.173858 + 0.173858i
\(448\) 0 0
\(449\) −2.82768 + 0.757676i −0.133447 + 0.0357569i −0.324924 0.945740i \(-0.605339\pi\)
0.191477 + 0.981497i \(0.438672\pi\)
\(450\) 4.33680 16.1852i 0.204439 0.762976i
\(451\) 13.0994 7.56293i 0.616826 0.356124i
\(452\) 11.1966i 0.526644i
\(453\) 4.47329 + 16.6945i 0.210173 + 0.784378i
\(454\) −14.9497 −0.701623
\(455\) 0 0
\(456\) 3.87300 0.181370
\(457\) −6.30680 23.5373i −0.295020 1.10103i −0.941202 0.337845i \(-0.890302\pi\)
0.646182 0.763183i \(-0.276365\pi\)
\(458\) 18.1218i 0.846776i
\(459\) 14.7280 8.50319i 0.687442 0.396895i
\(460\) 4.43009 16.5333i 0.206554 0.770870i
\(461\) 20.1416 5.39694i 0.938090 0.251360i 0.242789 0.970079i \(-0.421938\pi\)
0.695301 + 0.718719i \(0.255271\pi\)
\(462\) 0 0
\(463\) 8.98662 + 8.98662i 0.417644 + 0.417644i 0.884391 0.466747i \(-0.154574\pi\)
−0.466747 + 0.884391i \(0.654574\pi\)
\(464\) 0.458090 0.0212663
\(465\) 22.8644 1.06031
\(466\) −7.25243 7.25243i −0.335963 0.335963i
\(467\) −11.5521 20.0088i −0.534566 0.925895i −0.999184 0.0403838i \(-0.987142\pi\)
0.464619 0.885511i \(-0.346191\pi\)
\(468\) 4.61396 5.29111i 0.213281 0.244582i
\(469\) 0 0
\(470\) −41.0668 11.0038i −1.89427 0.507568i
\(471\) −7.97602 + 13.8149i −0.367516 + 0.636556i
\(472\) −0.355969 0.616557i −0.0163848 0.0283793i
\(473\) −1.20453 4.49535i −0.0553842 0.206697i
\(474\) −2.00998 2.00998i −0.0923215 0.0923215i
\(475\) 3.22870 + 12.0497i 0.148143 + 0.552877i
\(476\) 0 0
\(477\) −4.15371 + 7.19444i −0.190185 + 0.329411i
\(478\) −20.3913 11.7729i −0.932678 0.538482i
\(479\) 7.82481 7.82481i 0.357525 0.357525i −0.505375 0.862900i \(-0.668646\pi\)
0.862900 + 0.505375i \(0.168646\pi\)
\(480\) −21.3350 12.3178i −0.973807 0.562227i
\(481\) −13.2236 + 8.88955i −0.602945 + 0.405328i
\(482\) 23.4992i 1.07036i
\(483\) 0 0
\(484\) −3.76481 6.52084i −0.171128 0.296402i
\(485\) 64.9930i 2.95118i
\(486\) −13.3078 + 3.56580i −0.603652 + 0.161748i
\(487\) −30.1548 8.07996i −1.36644 0.366138i −0.500266 0.865872i \(-0.666764\pi\)
−0.866179 + 0.499734i \(0.833431\pi\)
\(488\) 25.4217 25.4217i 1.15079 1.15079i
\(489\) −18.8280 + 18.8280i −0.851432 + 0.851432i
\(490\) 0 0
\(491\) 19.5025 11.2598i 0.880137 0.508147i 0.00943333 0.999956i \(-0.496997\pi\)
0.870704 + 0.491808i \(0.163664\pi\)
\(492\) 9.07918 2.43276i 0.409321 0.109677i
\(493\) −1.85552 + 3.21385i −0.0835683 + 0.144745i
\(494\) 0.748014 3.81649i 0.0336547 0.171712i
\(495\) −12.2620 + 7.07946i −0.551135 + 0.318198i
\(496\) 0.512829 1.91390i 0.0230267 0.0859368i
\(497\) 0 0
\(498\) −4.27508 2.46822i −0.191571 0.110604i
\(499\) −22.0367 5.90470i −0.986496 0.264331i −0.270718 0.962659i \(-0.587261\pi\)
−0.715778 + 0.698328i \(0.753928\pi\)
\(500\) 6.67975 24.9292i 0.298728 1.11487i
\(501\) −3.30686 + 12.3414i −0.147739 + 0.551371i
\(502\) 5.37530 + 1.44031i 0.239911 + 0.0642841i
\(503\) −3.72935 2.15314i −0.166283 0.0960037i 0.414549 0.910027i \(-0.363939\pi\)
−0.580832 + 0.814023i \(0.697273\pi\)
\(504\) 0 0
\(505\) −3.71071 + 13.8486i −0.165124 + 0.616253i
\(506\) 6.34901 3.66561i 0.282248 0.162956i
\(507\) 9.09625 + 11.7176i 0.403979 + 0.520399i
\(508\) −4.51437 + 7.81911i −0.200293 + 0.346917i
\(509\) −26.1818 + 7.01539i −1.16049 + 0.310952i −0.787161 0.616748i \(-0.788450\pi\)
−0.373327 + 0.927700i \(0.621783\pi\)
\(510\) −11.4682 + 6.62119i −0.507822 + 0.293191i
\(511\) 0 0
\(512\) −3.11938 + 3.11938i −0.137858 + 0.137858i
\(513\) 4.42627 4.42627i 0.195425 0.195425i
\(514\) −21.7831 5.83675i −0.960809 0.257448i
\(515\) −6.08498 + 1.63047i −0.268136 + 0.0718469i
\(516\) 2.89203i 0.127314i
\(517\) 12.2360 + 21.1934i 0.538139 + 0.932084i
\(518\) 0 0
\(519\) 3.79813i 0.166719i
\(520\) −27.2779 + 31.2813i −1.19622 + 1.37177i
\(521\) 12.0981 + 6.98482i 0.530026 + 0.306011i 0.741027 0.671475i \(-0.234339\pi\)
−0.211001 + 0.977486i \(0.567672\pi\)
\(522\) 1.29737 1.29737i 0.0567843 0.0567843i
\(523\) 35.9424 + 20.7514i 1.57165 + 0.907394i 0.995967 + 0.0897221i \(0.0285979\pi\)
0.575685 + 0.817672i \(0.304735\pi\)
\(524\) 1.21453 2.10362i 0.0530569 0.0918972i
\(525\) 0 0
\(526\) −3.61986 13.5095i −0.157834 0.589043i
\(527\) 11.3503 + 11.3503i 0.494425 + 0.494425i
\(528\) −0.243523 0.908842i −0.0105980 0.0395523i
\(529\) −4.39677 7.61543i −0.191164 0.331106i
\(530\) 8.94896 15.5001i 0.388718 0.673279i
\(531\) −0.401707 0.107637i −0.0174326 0.00467105i
\(532\) 0 0
\(533\) −1.76652 25.8400i −0.0765163 1.11926i
\(534\) 3.66592 + 6.34956i 0.158640 + 0.274773i
\(535\) 41.6862 + 41.6862i 1.80225 + 1.80225i
\(536\) 29.9567 1.29393
\(537\) 0.291584 0.0125828
\(538\) 2.31304 + 2.31304i 0.0997223 + 0.0997223i
\(539\) 0 0
\(540\) −23.5147 + 6.30074i −1.01191 + 0.271141i
\(541\) −1.61721 + 6.03551i −0.0695292 + 0.259487i −0.991937 0.126730i \(-0.959552\pi\)
0.922408 + 0.386217i \(0.126218\pi\)
\(542\) 0.604911 0.349246i 0.0259832 0.0150014i
\(543\) 8.73050i 0.374661i
\(544\) −4.47630 16.7058i −0.191920 0.716255i
\(545\) 13.2946 0.569478
\(546\) 0 0
\(547\) −25.9633 −1.11011 −0.555055 0.831814i \(-0.687303\pi\)
−0.555055 + 0.831814i \(0.687303\pi\)
\(548\) 3.46831 + 12.9439i 0.148159 + 0.552936i
\(549\) 21.0012i 0.896308i
\(550\) 17.9955 10.3897i 0.767330 0.443018i
\(551\) −0.353535 + 1.31941i −0.0150611 + 0.0562088i
\(552\) 12.0755 3.23561i 0.513965 0.137717i
\(553\) 0 0
\(554\) 6.81118 + 6.81118i 0.289379 + 0.289379i
\(555\) 19.9700 0.847681
\(556\) −5.13976 −0.217975
\(557\) 21.7708 + 21.7708i 0.922458 + 0.922458i 0.997203 0.0747448i \(-0.0238142\pi\)
−0.0747448 + 0.997203i \(0.523814\pi\)
\(558\) −3.96802 6.87282i −0.167980 0.290950i
\(559\) −7.82024 1.53273i −0.330761 0.0648276i
\(560\) 0 0
\(561\) 7.36263 + 1.97281i 0.310850 + 0.0832921i
\(562\) 11.8483 20.5218i 0.499790 0.865661i
\(563\) −16.1301 27.9382i −0.679804 1.17745i −0.975040 0.222030i \(-0.928732\pi\)
0.295236 0.955424i \(-0.404602\pi\)
\(564\) 3.93594 + 14.6891i 0.165733 + 0.618524i
\(565\) −27.3421 27.3421i −1.15029 1.15029i
\(566\) 0.0117675 + 0.0439168i 0.000494624 + 0.00184596i
\(567\) 0 0
\(568\) −9.01135 + 15.6081i −0.378108 + 0.654902i
\(569\) −3.82034 2.20567i −0.160157 0.0924666i 0.417779 0.908548i \(-0.362808\pi\)
−0.577936 + 0.816082i \(0.696142\pi\)
\(570\) −3.44661 + 3.44661i −0.144363 + 0.144363i
\(571\) −30.0822 17.3680i −1.25890 0.726826i −0.286039 0.958218i \(-0.592339\pi\)
−0.972861 + 0.231392i \(0.925672\pi\)
\(572\) 8.68565 0.593782i 0.363165 0.0248273i
\(573\) 16.5577i 0.691709i
\(574\) 0 0
\(575\) 20.1332 + 34.8717i 0.839613 + 1.45425i
\(576\) 9.88065i 0.411694i
\(577\) 32.6785 8.75618i 1.36042 0.364524i 0.496452 0.868064i \(-0.334636\pi\)
0.863972 + 0.503540i \(0.167969\pi\)
\(578\) 6.18850 + 1.65820i 0.257408 + 0.0689721i
\(579\) −6.49492 + 6.49492i −0.269920 + 0.269920i
\(580\) 3.75633 3.75633i 0.155973 0.155973i
\(581\) 0 0
\(582\) 14.9809 8.64925i 0.620980 0.358523i
\(583\) −9.95106 + 2.66638i −0.412131 + 0.110430i
\(584\) 7.15047 12.3850i 0.295889 0.512494i
\(585\) 1.65359 + 24.1882i 0.0683675 + 1.00006i
\(586\) 13.1938 7.61745i 0.545031 0.314674i
\(587\) −4.46785 + 16.6742i −0.184408 + 0.688219i 0.810349 + 0.585948i \(0.199278\pi\)
−0.994757 + 0.102271i \(0.967389\pi\)
\(588\) 0 0
\(589\) 5.11673 + 2.95415i 0.210831 + 0.121723i
\(590\) 0.865456 + 0.231898i 0.0356303 + 0.00954710i
\(591\) −1.92046 + 7.16724i −0.0789970 + 0.294821i
\(592\) 0.447911 1.67163i 0.0184090 0.0687034i
\(593\) 24.2880 + 6.50794i 0.997387 + 0.267249i 0.720351 0.693610i \(-0.243981\pi\)
0.277037 + 0.960859i \(0.410648\pi\)
\(594\) −9.02994 5.21344i −0.370503 0.213910i
\(595\) 0 0
\(596\) 1.35209 5.04606i 0.0553837 0.206695i
\(597\) −6.99624 + 4.03928i −0.286337 + 0.165317i
\(598\) −0.856196 12.5242i −0.0350125 0.512151i
\(599\) 0.438119 0.758845i 0.0179011 0.0310056i −0.856936 0.515423i \(-0.827635\pi\)
0.874837 + 0.484417i \(0.160968\pi\)
\(600\) 34.2263 9.17092i 1.39728 0.374401i
\(601\) 19.6980 11.3726i 0.803496 0.463899i −0.0411960 0.999151i \(-0.513117\pi\)
0.844692 + 0.535252i \(0.179783\pi\)
\(602\) 0 0
\(603\) 12.3737 12.3737i 0.503898 0.503898i
\(604\) 12.2817 12.2817i 0.499737 0.499737i
\(605\) 25.1175 + 6.73022i 1.02117 + 0.273622i
\(606\) −3.68593 + 0.987641i −0.149730 + 0.0401202i
\(607\) 30.8708i 1.25301i −0.779418 0.626504i \(-0.784485\pi\)
0.779418 0.626504i \(-0.215515\pi\)
\(608\) −3.18298 5.51309i −0.129087 0.223585i
\(609\) 0 0
\(610\) 45.2459i 1.83195i
\(611\) 41.8064 2.85803i 1.69130 0.115624i
\(612\) −5.34939 3.08847i −0.216236 0.124844i
\(613\) 33.2772 33.2772i 1.34405 1.34405i 0.452071 0.891982i \(-0.350685\pi\)
0.891982 0.452071i \(-0.149315\pi\)
\(614\) −15.6257 9.02148i −0.630601 0.364077i
\(615\) −16.2305 + 28.1121i −0.654479 + 1.13359i
\(616\) 0 0
\(617\) −1.88092 7.01970i −0.0757231 0.282602i 0.917673 0.397336i \(-0.130065\pi\)
−0.993396 + 0.114734i \(0.963399\pi\)
\(618\) −1.18561 1.18561i −0.0476923 0.0476923i
\(619\) 5.34817 + 19.9596i 0.214961 + 0.802246i 0.986180 + 0.165676i \(0.0529806\pi\)
−0.771219 + 0.636570i \(0.780353\pi\)
\(620\) −11.4888 19.8992i −0.461401 0.799170i
\(621\) 10.1026 17.4983i 0.405405 0.702182i
\(622\) 4.02508 + 1.07852i 0.161391 + 0.0432446i
\(623\) 0 0
\(624\) −1.58105 0.309878i −0.0632925 0.0124050i
\(625\) 17.8571 + 30.9295i 0.714285 + 1.23718i
\(626\) 20.2396 + 20.2396i 0.808939 + 0.808939i
\(627\) 2.80563 0.112046
\(628\) 16.0310 0.639706
\(629\) 9.91345 + 9.91345i 0.395275 + 0.395275i
\(630\) 0 0
\(631\) 5.77115 1.54637i 0.229746 0.0615602i −0.142109 0.989851i \(-0.545388\pi\)
0.371855 + 0.928291i \(0.378722\pi\)
\(632\) −2.02884 + 7.57174i −0.0807030 + 0.301188i
\(633\) 7.54829 4.35801i 0.300018 0.173215i
\(634\) 5.66235i 0.224881i
\(635\) −8.07018 30.1183i −0.320255 1.19521i
\(636\) −6.40189 −0.253852
\(637\) 0 0
\(638\) 2.27530 0.0900798
\(639\) 2.72483 + 10.1692i 0.107793 + 0.402287i
\(640\) 21.8924i 0.865373i
\(641\) −19.3092 + 11.1482i −0.762667 + 0.440326i −0.830253 0.557387i \(-0.811804\pi\)
0.0675854 + 0.997713i \(0.478470\pi\)
\(642\) −4.06112 + 15.1563i −0.160280 + 0.598171i
\(643\) −19.2524 + 5.15868i −0.759242 + 0.203438i −0.617614 0.786481i \(-0.711901\pi\)
−0.141629 + 0.989920i \(0.545234\pi\)
\(644\) 0 0
\(645\) 7.06233 + 7.06233i 0.278079 + 0.278079i
\(646\) −3.42190 −0.134633
\(647\) −14.8646 −0.584389 −0.292195 0.956359i \(-0.594385\pi\)
−0.292195 + 0.956359i \(0.594385\pi\)
\(648\) −2.10277 2.10277i −0.0826047 0.0826047i
\(649\) −0.257866 0.446638i −0.0101221 0.0175321i
\(650\) −2.42678 35.4981i −0.0951861 1.39235i
\(651\) 0 0
\(652\) 25.8468 + 6.92564i 1.01224 + 0.271229i
\(653\) −16.5493 + 28.6642i −0.647623 + 1.12172i 0.336067 + 0.941838i \(0.390903\pi\)
−0.983689 + 0.179877i \(0.942430\pi\)
\(654\) 1.76924 + 3.06442i 0.0691828 + 0.119828i
\(655\) 2.17117 + 8.10292i 0.0848346 + 0.316607i
\(656\) 1.98914 + 1.98914i 0.0776627 + 0.0776627i
\(657\) −2.16214 8.06922i −0.0843531 0.314810i
\(658\) 0 0
\(659\) 23.6093 40.8925i 0.919687 1.59295i 0.119797 0.992798i \(-0.461776\pi\)
0.799890 0.600147i \(-0.204891\pi\)
\(660\) −9.44937 5.45560i −0.367816 0.212359i
\(661\) 11.7411 11.7411i 0.456675 0.456675i −0.440888 0.897562i \(-0.645336\pi\)
0.897562 + 0.440888i \(0.145336\pi\)
\(662\) 13.3749 + 7.72200i 0.519830 + 0.300124i
\(663\) 8.57814 9.83707i 0.333147 0.382040i
\(664\) 13.6132i 0.528293i
\(665\) 0 0
\(666\) −3.46572 6.00280i −0.134294 0.232604i
\(667\) 4.40908i 0.170720i
\(668\) 12.4024 3.32322i 0.479864 0.128579i
\(669\) 7.42513 + 1.98956i 0.287072 + 0.0769207i
\(670\) −26.6586 + 26.6586i −1.02991 + 1.02991i
\(671\) 18.4157 18.4157i 0.710929 0.710929i
\(672\) 0 0
\(673\) −22.5906 + 13.0427i −0.870802 + 0.502758i −0.867615 0.497237i \(-0.834348\pi\)
−0.00318750 + 0.999995i \(0.501015\pi\)
\(674\) −11.1221 + 2.98015i −0.428406 + 0.114791i
\(675\) 28.6346 49.5967i 1.10215 1.90898i
\(676\) 5.62737 13.8044i 0.216437 0.530938i
\(677\) −16.8583 + 9.73314i −0.647917 + 0.374075i −0.787658 0.616113i \(-0.788706\pi\)
0.139741 + 0.990188i \(0.455373\pi\)
\(678\) 2.66370 9.94105i 0.102299 0.381784i
\(679\) 0 0
\(680\) 31.6258 + 18.2592i 1.21280 + 0.700208i
\(681\) −17.8378 4.77963i −0.683546 0.183156i
\(682\) 2.54718 9.50621i 0.0975366 0.364012i
\(683\) 5.35648 19.9907i 0.204960 0.764921i −0.784502 0.620127i \(-0.787081\pi\)
0.989462 0.144794i \(-0.0462521\pi\)
\(684\) −2.19613 0.588452i −0.0839712 0.0225000i
\(685\) −40.0786 23.1394i −1.53132 0.884110i
\(686\) 0 0
\(687\) 5.79380 21.6228i 0.221047 0.824960i
\(688\) 0.749566 0.432762i 0.0285769 0.0164989i
\(689\) −3.39290 + 17.3111i −0.129259 + 0.659502i
\(690\) −7.86663 + 13.6254i −0.299477 + 0.518710i
\(691\) 13.6373 3.65409i 0.518786 0.139008i 0.0100808 0.999949i \(-0.496791\pi\)
0.508705 + 0.860941i \(0.330124\pi\)
\(692\) 3.30555 1.90846i 0.125658 0.0725488i
\(693\) 0 0
\(694\) 17.1477 17.1477i 0.650916 0.650916i
\(695\) 12.5513 12.5513i 0.476098 0.476098i
\(696\) 3.74770 + 1.00419i 0.142056 + 0.0380639i
\(697\) −22.0124 + 5.89821i −0.833779 + 0.223411i
\(698\) 6.76071i 0.255896i
\(699\) −6.33483 10.9722i −0.239605 0.415008i
\(700\) 0 0
\(701\) 26.8075i 1.01251i 0.862385 + 0.506253i \(0.168970\pi\)
−0.862385 + 0.506253i \(0.831030\pi\)
\(702\) −14.8173 + 9.96088i −0.559243 + 0.375949i
\(703\) 4.46901 + 2.58019i 0.168552 + 0.0973135i
\(704\) −8.66423 + 8.66423i −0.326545 + 0.326545i
\(705\) −45.4824 26.2593i −1.71297 0.988981i
\(706\) 12.5896 21.8058i 0.473815 0.820672i
\(707\) 0 0
\(708\) −0.0829475 0.309564i −0.00311736 0.0116341i
\(709\) −20.3216 20.3216i −0.763192 0.763192i 0.213706 0.976898i \(-0.431447\pi\)
−0.976898 + 0.213706i \(0.931447\pi\)
\(710\) −5.87050 21.9090i −0.220316 0.822231i
\(711\) 2.28952 + 3.96557i 0.0858638 + 0.148720i
\(712\) 10.1095 17.5101i 0.378869 0.656220i
\(713\) 18.4212 + 4.93594i 0.689879 + 0.184852i
\(714\) 0 0
\(715\) −19.7603 + 22.6603i −0.738994 + 0.847449i
\(716\) −0.146513 0.253769i −0.00547547 0.00948378i
\(717\) −20.5668 20.5668i −0.768080 0.768080i
\(718\) −28.6964 −1.07094
\(719\) 2.91511 0.108715 0.0543577 0.998522i \(-0.482689\pi\)
0.0543577 + 0.998522i \(0.482689\pi\)
\(720\) −1.86198 1.86198i −0.0693918 0.0693918i
\(721\) 0 0
\(722\) 15.7363 4.21652i 0.585644 0.156923i
\(723\) 7.51303 28.0390i 0.279413 1.04278i
\(724\) 7.59825 4.38685i 0.282387 0.163036i
\(725\) 12.4970i 0.464126i
\(726\) 1.79131 + 6.68527i 0.0664818 + 0.248114i
\(727\) −26.1967 −0.971584 −0.485792 0.874075i \(-0.661469\pi\)
−0.485792 + 0.874075i \(0.661469\pi\)
\(728\) 0 0
\(729\) −20.0879 −0.743998
\(730\) 4.65822 + 17.3847i 0.172409 + 0.643437i
\(731\) 7.01171i 0.259337i
\(732\) 14.0157 8.09199i 0.518037 0.299089i
\(733\) −1.65037 + 6.15927i −0.0609579 + 0.227498i −0.989684 0.143269i \(-0.954239\pi\)
0.928726 + 0.370767i \(0.120905\pi\)
\(734\) −22.4221 + 6.00798i −0.827614 + 0.221758i
\(735\) 0 0
\(736\) −14.5299 14.5299i −0.535577 0.535577i
\(737\) 21.7008 0.799359
\(738\) 11.2670 0.414743
\(739\) 17.7953 + 17.7953i 0.654609 + 0.654609i 0.954099 0.299490i \(-0.0968165\pi\)
−0.299490 + 0.954099i \(0.596817\pi\)
\(740\) −10.0344 17.3802i −0.368873 0.638907i
\(741\) 2.11271 4.31465i 0.0776124 0.158503i
\(742\) 0 0
\(743\) −23.8890 6.40103i −0.876401 0.234831i −0.207547 0.978225i \(-0.566548\pi\)
−0.668854 + 0.743394i \(0.733215\pi\)
\(744\) 8.39107 14.5338i 0.307632 0.532834i
\(745\) 9.02067 + 15.6243i 0.330492 + 0.572429i
\(746\) −0.743108 2.77332i −0.0272071 0.101538i
\(747\) 5.62298 + 5.62298i 0.205734 + 0.205734i
\(748\) −1.98257 7.39907i −0.0724901 0.270537i
\(749\) 0 0
\(750\) −11.8614 + 20.5446i −0.433118 + 0.750182i
\(751\) −12.2932 7.09751i −0.448587 0.258992i 0.258646 0.965972i \(-0.416724\pi\)
−0.707233 + 0.706980i \(0.750057\pi\)
\(752\) −3.21821 + 3.21821i −0.117356 + 0.117356i
\(753\) 5.95327 + 3.43712i 0.216949 + 0.125256i
\(754\) 1.71336 3.49907i 0.0623967 0.127429i
\(755\) 59.9839i 2.18304i
\(756\) 0 0
\(757\) −12.3674 21.4210i −0.449502 0.778559i 0.548852 0.835920i \(-0.315065\pi\)
−0.998354 + 0.0573601i \(0.981732\pi\)
\(758\) 4.16511i 0.151284i
\(759\) 8.74753 2.34389i 0.317515 0.0850780i
\(760\) 12.9836 + 3.47895i 0.470966 + 0.126195i
\(761\) 8.21162 8.21162i 0.297671 0.297671i −0.542430 0.840101i \(-0.682496\pi\)
0.840101 + 0.542430i \(0.182496\pi\)
\(762\) 5.86832 5.86832i 0.212587 0.212587i
\(763\) 0 0
\(764\) −14.4104 + 8.31983i −0.521349 + 0.301001i
\(765\) 20.6052 5.52116i 0.744984 0.199618i
\(766\) −15.5249 + 26.8900i −0.560938 + 0.971574i
\(767\) −0.881044 + 0.0602313i −0.0318126 + 0.00217483i
\(768\) −16.5471 + 9.55348i −0.597092 + 0.344731i
\(769\) −9.18218 + 34.2684i −0.331118 + 1.23575i 0.576899 + 0.816815i \(0.304263\pi\)
−0.908017 + 0.418933i \(0.862404\pi\)
\(770\) 0 0
\(771\) −24.1252 13.9287i −0.868850 0.501631i
\(772\) 8.91614 + 2.38907i 0.320899 + 0.0859846i
\(773\) −5.21138 + 19.4491i −0.187440 + 0.699536i 0.806655 + 0.591023i \(0.201276\pi\)
−0.994095 + 0.108513i \(0.965391\pi\)
\(774\) 0.897229 3.34850i 0.0322502 0.120359i
\(775\) 52.2125 + 13.9903i 1.87553 + 0.502547i
\(776\) −41.3128 23.8519i −1.48304 0.856234i
\(777\) 0 0
\(778\) 4.93992 18.4360i 0.177105 0.660964i
\(779\) −7.26433 + 4.19406i −0.260272 + 0.150268i
\(780\) −15.5055 + 10.4236i −0.555187 + 0.373223i