Properties

Label 804.2.e.b.535.18
Level 804
Weight 2
Character 804.535
Analytic conductor 6.420
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(34\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 535.18
Character \(\chi\) = 804.535
Dual form 804.2.e.b.535.17

$q$-expansion

\(f(q)\) \(=\) \(q+(0.219472 + 1.39708i) q^{2} +1.00000 q^{3} +(-1.90366 + 0.613241i) q^{4} +3.15947i q^{5} +(0.219472 + 1.39708i) q^{6} -0.761043 q^{7} +(-1.27455 - 2.52498i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.219472 + 1.39708i) q^{2} +1.00000 q^{3} +(-1.90366 + 0.613241i) q^{4} +3.15947i q^{5} +(0.219472 + 1.39708i) q^{6} -0.761043 q^{7} +(-1.27455 - 2.52498i) q^{8} +1.00000 q^{9} +(-4.41403 + 0.693416i) q^{10} -5.14871 q^{11} +(-1.90366 + 0.613241i) q^{12} +4.67319i q^{13} +(-0.167028 - 1.06324i) q^{14} +3.15947i q^{15} +(3.24787 - 2.33481i) q^{16} +1.78889 q^{17} +(0.219472 + 1.39708i) q^{18} -5.49920i q^{19} +(-1.93751 - 6.01456i) q^{20} -0.761043 q^{21} +(-1.13000 - 7.19316i) q^{22} +2.96158i q^{23} +(-1.27455 - 2.52498i) q^{24} -4.98223 q^{25} +(-6.52882 + 1.02564i) q^{26} +1.00000 q^{27} +(1.44877 - 0.466703i) q^{28} -9.79158 q^{29} +(-4.41403 + 0.693416i) q^{30} -3.67432 q^{31} +(3.97473 + 4.02511i) q^{32} -5.14871 q^{33} +(0.392611 + 2.49922i) q^{34} -2.40449i q^{35} +(-1.90366 + 0.613241i) q^{36} +8.38084 q^{37} +(7.68282 - 1.20692i) q^{38} +4.67319i q^{39} +(7.97759 - 4.02689i) q^{40} -1.00221i q^{41} +(-0.167028 - 1.06324i) q^{42} +7.22273 q^{43} +(9.80142 - 3.15740i) q^{44} +3.15947i q^{45} +(-4.13756 + 0.649985i) q^{46} +11.6884i q^{47} +(3.24787 - 2.33481i) q^{48} -6.42081 q^{49} +(-1.09346 - 6.96057i) q^{50} +1.78889 q^{51} +(-2.86579 - 8.89618i) q^{52} +9.25172i q^{53} +(0.219472 + 1.39708i) q^{54} -16.2672i q^{55} +(0.969986 + 1.92162i) q^{56} -5.49920i q^{57} +(-2.14898 - 13.6796i) q^{58} +0.539474i q^{59} +(-1.93751 - 6.01456i) q^{60} +2.35281i q^{61} +(-0.806411 - 5.13332i) q^{62} -0.761043 q^{63} +(-4.75105 + 6.43642i) q^{64} -14.7648 q^{65} +(-1.13000 - 7.19316i) q^{66} +(8.09955 - 1.18208i) q^{67} +(-3.40544 + 1.09702i) q^{68} +2.96158i q^{69} +(3.35927 - 0.527719i) q^{70} -11.8375i q^{71} +(-1.27455 - 2.52498i) q^{72} -7.50732 q^{73} +(1.83936 + 11.7087i) q^{74} -4.98223 q^{75} +(3.37233 + 10.4686i) q^{76} +3.91839 q^{77} +(-6.52882 + 1.02564i) q^{78} -4.41239 q^{79} +(7.37675 + 10.2615i) q^{80} +1.00000 q^{81} +(1.40016 - 0.219956i) q^{82} +8.49721i q^{83} +(1.44877 - 0.466703i) q^{84} +5.65193i q^{85} +(1.58519 + 10.0907i) q^{86} -9.79158 q^{87} +(6.56228 + 13.0004i) q^{88} +13.5366 q^{89} +(-4.41403 + 0.693416i) q^{90} -3.55650i q^{91} +(-1.81616 - 5.63785i) q^{92} -3.67432 q^{93} +(-16.3297 + 2.56529i) q^{94} +17.3745 q^{95} +(3.97473 + 4.02511i) q^{96} +8.80067i q^{97} +(-1.40919 - 8.97039i) q^{98} -5.14871 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 34q^{3} + 2q^{4} + 4q^{7} - 6q^{8} + 34q^{9} + O(q^{10}) \) \( 34q + 34q^{3} + 2q^{4} + 4q^{7} - 6q^{8} + 34q^{9} - 6q^{10} + 2q^{12} - 4q^{14} + 2q^{16} - 12q^{20} + 4q^{21} - 8q^{22} - 6q^{24} - 34q^{25} + 10q^{26} + 34q^{27} - 8q^{28} - 16q^{29} - 6q^{30} - 4q^{31} + 2q^{36} + 12q^{37} + 26q^{38} - 18q^{40} - 4q^{42} - 4q^{43} + 26q^{44} - 4q^{46} + 2q^{48} + 46q^{49} - 18q^{50} + 32q^{52} + 14q^{56} + 4q^{58} - 12q^{60} - 2q^{62} + 4q^{63} + 26q^{64} - 8q^{66} - 18q^{67} - 34q^{68} + 56q^{70} - 6q^{72} + 12q^{73} + 22q^{74} - 34q^{75} - 32q^{76} - 8q^{77} + 10q^{78} - 12q^{79} - 2q^{80} + 34q^{81} + 26q^{82} - 8q^{84} + 6q^{86} - 16q^{87} - 28q^{88} - 6q^{90} - 46q^{92} - 4q^{93} + 32q^{94} - 40q^{95} - 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.219472 + 1.39708i 0.155190 + 0.987885i
\(3\) 1.00000 0.577350
\(4\) −1.90366 + 0.613241i −0.951832 + 0.306620i
\(5\) 3.15947i 1.41296i 0.707735 + 0.706478i \(0.249717\pi\)
−0.707735 + 0.706478i \(0.750283\pi\)
\(6\) 0.219472 + 1.39708i 0.0895992 + 0.570355i
\(7\) −0.761043 −0.287647 −0.143824 0.989603i \(-0.545940\pi\)
−0.143824 + 0.989603i \(0.545940\pi\)
\(8\) −1.27455 2.52498i −0.450621 0.892715i
\(9\) 1.00000 0.333333
\(10\) −4.41403 + 0.693416i −1.39584 + 0.219277i
\(11\) −5.14871 −1.55239 −0.776197 0.630490i \(-0.782854\pi\)
−0.776197 + 0.630490i \(0.782854\pi\)
\(12\) −1.90366 + 0.613241i −0.549540 + 0.177027i
\(13\) 4.67319i 1.29611i 0.761594 + 0.648055i \(0.224417\pi\)
−0.761594 + 0.648055i \(0.775583\pi\)
\(14\) −0.167028 1.06324i −0.0446401 0.284162i
\(15\) 3.15947i 0.815771i
\(16\) 3.24787 2.33481i 0.811968 0.583702i
\(17\) 1.78889 0.433869 0.216934 0.976186i \(-0.430394\pi\)
0.216934 + 0.976186i \(0.430394\pi\)
\(18\) 0.219472 + 1.39708i 0.0517301 + 0.329295i
\(19\) 5.49920i 1.26160i −0.775945 0.630801i \(-0.782726\pi\)
0.775945 0.630801i \(-0.217274\pi\)
\(20\) −1.93751 6.01456i −0.433241 1.34490i
\(21\) −0.761043 −0.166073
\(22\) −1.13000 7.19316i −0.240917 1.53359i
\(23\) 2.96158i 0.617532i 0.951138 + 0.308766i \(0.0999160\pi\)
−0.951138 + 0.308766i \(0.900084\pi\)
\(24\) −1.27455 2.52498i −0.260166 0.515410i
\(25\) −4.98223 −0.996445
\(26\) −6.52882 + 1.02564i −1.28041 + 0.201144i
\(27\) 1.00000 0.192450
\(28\) 1.44877 0.466703i 0.273792 0.0881985i
\(29\) −9.79158 −1.81825 −0.909125 0.416523i \(-0.863249\pi\)
−0.909125 + 0.416523i \(0.863249\pi\)
\(30\) −4.41403 + 0.693416i −0.805887 + 0.126600i
\(31\) −3.67432 −0.659927 −0.329963 0.943994i \(-0.607036\pi\)
−0.329963 + 0.943994i \(0.607036\pi\)
\(32\) 3.97473 + 4.02511i 0.702640 + 0.711546i
\(33\) −5.14871 −0.896276
\(34\) 0.392611 + 2.49922i 0.0673323 + 0.428612i
\(35\) 2.40449i 0.406433i
\(36\) −1.90366 + 0.613241i −0.317277 + 0.102207i
\(37\) 8.38084 1.37780 0.688901 0.724856i \(-0.258094\pi\)
0.688901 + 0.724856i \(0.258094\pi\)
\(38\) 7.68282 1.20692i 1.24632 0.195789i
\(39\) 4.67319i 0.748309i
\(40\) 7.97759 4.02689i 1.26137 0.636707i
\(41\) 1.00221i 0.156518i −0.996933 0.0782591i \(-0.975064\pi\)
0.996933 0.0782591i \(-0.0249361\pi\)
\(42\) −0.167028 1.06324i −0.0257730 0.164061i
\(43\) 7.22273 1.10146 0.550728 0.834685i \(-0.314350\pi\)
0.550728 + 0.834685i \(0.314350\pi\)
\(44\) 9.80142 3.15740i 1.47762 0.475996i
\(45\) 3.15947i 0.470985i
\(46\) −4.13756 + 0.649985i −0.610050 + 0.0958350i
\(47\) 11.6884i 1.70493i 0.522781 + 0.852467i \(0.324894\pi\)
−0.522781 + 0.852467i \(0.675106\pi\)
\(48\) 3.24787 2.33481i 0.468790 0.337001i
\(49\) −6.42081 −0.917259
\(50\) −1.09346 6.96057i −0.154639 0.984373i
\(51\) 1.78889 0.250494
\(52\) −2.86579 8.89618i −0.397414 1.23368i
\(53\) 9.25172i 1.27082i 0.772174 + 0.635411i \(0.219169\pi\)
−0.772174 + 0.635411i \(0.780831\pi\)
\(54\) 0.219472 + 1.39708i 0.0298664 + 0.190118i
\(55\) 16.2672i 2.19347i
\(56\) 0.969986 + 1.92162i 0.129620 + 0.256787i
\(57\) 5.49920i 0.728386i
\(58\) −2.14898 13.6796i −0.282175 1.79622i
\(59\) 0.539474i 0.0702335i 0.999383 + 0.0351168i \(0.0111803\pi\)
−0.999383 + 0.0351168i \(0.988820\pi\)
\(60\) −1.93751 6.01456i −0.250132 0.776477i
\(61\) 2.35281i 0.301247i 0.988591 + 0.150624i \(0.0481281\pi\)
−0.988591 + 0.150624i \(0.951872\pi\)
\(62\) −0.806411 5.13332i −0.102414 0.651932i
\(63\) −0.761043 −0.0958824
\(64\) −4.75105 + 6.43642i −0.593882 + 0.804552i
\(65\) −14.7648 −1.83135
\(66\) −1.13000 7.19316i −0.139093 0.885417i
\(67\) 8.09955 1.18208i 0.989517 0.144415i
\(68\) −3.40544 + 1.09702i −0.412970 + 0.133033i
\(69\) 2.96158i 0.356532i
\(70\) 3.35927 0.527719i 0.401509 0.0630745i
\(71\) 11.8375i 1.40486i −0.711754 0.702429i \(-0.752099\pi\)
0.711754 0.702429i \(-0.247901\pi\)
\(72\) −1.27455 2.52498i −0.150207 0.297572i
\(73\) −7.50732 −0.878665 −0.439333 0.898324i \(-0.644785\pi\)
−0.439333 + 0.898324i \(0.644785\pi\)
\(74\) 1.83936 + 11.7087i 0.213822 + 1.36111i
\(75\) −4.98223 −0.575298
\(76\) 3.37233 + 10.4686i 0.386833 + 1.20083i
\(77\) 3.91839 0.446542
\(78\) −6.52882 + 1.02564i −0.739243 + 0.116130i
\(79\) −4.41239 −0.496432 −0.248216 0.968705i \(-0.579844\pi\)
−0.248216 + 0.968705i \(0.579844\pi\)
\(80\) 7.37675 + 10.2615i 0.824746 + 1.14728i
\(81\) 1.00000 0.111111
\(82\) 1.40016 0.219956i 0.154622 0.0242901i
\(83\) 8.49721i 0.932689i 0.884603 + 0.466345i \(0.154429\pi\)
−0.884603 + 0.466345i \(0.845571\pi\)
\(84\) 1.44877 0.466703i 0.158074 0.0509215i
\(85\) 5.65193i 0.613038i
\(86\) 1.58519 + 10.0907i 0.170935 + 1.08811i
\(87\) −9.79158 −1.04977
\(88\) 6.56228 + 13.0004i 0.699541 + 1.38585i
\(89\) 13.5366 1.43488 0.717439 0.696622i \(-0.245314\pi\)
0.717439 + 0.696622i \(0.245314\pi\)
\(90\) −4.41403 + 0.693416i −0.465279 + 0.0730924i
\(91\) 3.55650i 0.372823i
\(92\) −1.81616 5.63785i −0.189348 0.587786i
\(93\) −3.67432 −0.381009
\(94\) −16.3297 + 2.56529i −1.68428 + 0.264589i
\(95\) 17.3745 1.78259
\(96\) 3.97473 + 4.02511i 0.405669 + 0.410811i
\(97\) 8.80067i 0.893572i 0.894641 + 0.446786i \(0.147431\pi\)
−0.894641 + 0.446786i \(0.852569\pi\)
\(98\) −1.40919 8.97039i −0.142350 0.906146i
\(99\) −5.14871 −0.517465
\(100\) 9.48449 3.05531i 0.948449 0.305531i
\(101\) 2.11655i 0.210604i 0.994440 + 0.105302i \(0.0335810\pi\)
−0.994440 + 0.105302i \(0.966419\pi\)
\(102\) 0.392611 + 2.49922i 0.0388743 + 0.247459i
\(103\) 3.03894i 0.299436i −0.988729 0.149718i \(-0.952163\pi\)
0.988729 0.149718i \(-0.0478366\pi\)
\(104\) 11.7997 5.95621i 1.15706 0.584054i
\(105\) 2.40449i 0.234654i
\(106\) −12.9254 + 2.03050i −1.25542 + 0.197219i
\(107\) 0.802128i 0.0775447i 0.999248 + 0.0387723i \(0.0123447\pi\)
−0.999248 + 0.0387723i \(0.987655\pi\)
\(108\) −1.90366 + 0.613241i −0.183180 + 0.0590091i
\(109\) 3.94940i 0.378284i 0.981950 + 0.189142i \(0.0605707\pi\)
−0.981950 + 0.189142i \(0.939429\pi\)
\(110\) 22.7265 3.57020i 2.16689 0.340405i
\(111\) 8.38084 0.795474
\(112\) −2.47177 + 1.77689i −0.233560 + 0.167900i
\(113\) 5.98304i 0.562837i −0.959585 0.281419i \(-0.909195\pi\)
0.959585 0.281419i \(-0.0908050\pi\)
\(114\) 7.68282 1.20692i 0.719562 0.113039i
\(115\) −9.35701 −0.872545
\(116\) 18.6399 6.00460i 1.73067 0.557513i
\(117\) 4.67319i 0.432037i
\(118\) −0.753688 + 0.118400i −0.0693826 + 0.0108996i
\(119\) −1.36142 −0.124801
\(120\) 7.97759 4.02689i 0.728251 0.367603i
\(121\) 15.5092 1.40993
\(122\) −3.28707 + 0.516378i −0.297597 + 0.0467507i
\(123\) 1.00221i 0.0903658i
\(124\) 6.99467 2.25324i 0.628140 0.202347i
\(125\) 0.0561519i 0.00502238i
\(126\) −0.167028 1.06324i −0.0148800 0.0947208i
\(127\) 3.50210i 0.310761i 0.987855 + 0.155381i \(0.0496604\pi\)
−0.987855 + 0.155381i \(0.950340\pi\)
\(128\) −10.0349 5.22499i −0.886970 0.461828i
\(129\) 7.22273 0.635926
\(130\) −3.24046 20.6276i −0.284207 1.80916i
\(131\) 16.7878i 1.46676i 0.679820 + 0.733379i \(0.262058\pi\)
−0.679820 + 0.733379i \(0.737942\pi\)
\(132\) 9.80142 3.15740i 0.853104 0.274816i
\(133\) 4.18513i 0.362896i
\(134\) 3.42909 + 11.0563i 0.296229 + 0.955117i
\(135\) 3.15947i 0.271924i
\(136\) −2.28002 4.51690i −0.195510 0.387321i
\(137\) 3.76333i 0.321523i 0.986993 + 0.160762i \(0.0513950\pi\)
−0.986993 + 0.160762i \(0.948605\pi\)
\(138\) −4.13756 + 0.649985i −0.352213 + 0.0553304i
\(139\) −11.5820 −0.982371 −0.491186 0.871055i \(-0.663436\pi\)
−0.491186 + 0.871055i \(0.663436\pi\)
\(140\) 1.47453 + 4.57734i 0.124621 + 0.386856i
\(141\) 11.6884i 0.984344i
\(142\) 16.5380 2.59801i 1.38784 0.218020i
\(143\) 24.0609i 2.01207i
\(144\) 3.24787 2.33481i 0.270656 0.194567i
\(145\) 30.9362i 2.56911i
\(146\) −1.64765 10.4883i −0.136360 0.868020i
\(147\) −6.42081 −0.529580
\(148\) −15.9543 + 5.13947i −1.31144 + 0.422462i
\(149\) −1.02591 −0.0840456 −0.0420228 0.999117i \(-0.513380\pi\)
−0.0420228 + 0.999117i \(0.513380\pi\)
\(150\) −1.09346 6.96057i −0.0892807 0.568328i
\(151\) 5.39710i 0.439210i −0.975589 0.219605i \(-0.929523\pi\)
0.975589 0.219605i \(-0.0704768\pi\)
\(152\) −13.8854 + 7.00899i −1.12625 + 0.568504i
\(153\) 1.78889 0.144623
\(154\) 0.859979 + 5.47431i 0.0692991 + 0.441132i
\(155\) 11.6089i 0.932448i
\(156\) −2.86579 8.89618i −0.229447 0.712265i
\(157\) 21.7154 1.73308 0.866540 0.499107i \(-0.166339\pi\)
0.866540 + 0.499107i \(0.166339\pi\)
\(158\) −0.968397 6.16446i −0.0770415 0.490418i
\(159\) 9.25172i 0.733709i
\(160\) −12.7172 + 12.5580i −1.00538 + 0.992800i
\(161\) 2.25389i 0.177631i
\(162\) 0.219472 + 1.39708i 0.0172434 + 0.109765i
\(163\) 12.4095i 0.971985i 0.873963 + 0.485992i \(0.161542\pi\)
−0.873963 + 0.485992i \(0.838458\pi\)
\(164\) 0.614593 + 1.90786i 0.0479917 + 0.148979i
\(165\) 16.2672i 1.26640i
\(166\) −11.8713 + 1.86490i −0.921390 + 0.144744i
\(167\) 23.7645i 1.83895i 0.393147 + 0.919476i \(0.371386\pi\)
−0.393147 + 0.919476i \(0.628614\pi\)
\(168\) 0.969986 + 1.92162i 0.0748361 + 0.148256i
\(169\) −8.83872 −0.679901
\(170\) −7.89619 + 1.24044i −0.605610 + 0.0951375i
\(171\) 5.49920i 0.420534i
\(172\) −13.7497 + 4.42927i −1.04840 + 0.337729i
\(173\) 21.5848 1.64106 0.820529 0.571604i \(-0.193679\pi\)
0.820529 + 0.571604i \(0.193679\pi\)
\(174\) −2.14898 13.6796i −0.162914 1.03705i
\(175\) 3.79169 0.286625
\(176\) −16.7224 + 12.0213i −1.26049 + 0.906136i
\(177\) 0.539474i 0.0405494i
\(178\) 2.97091 + 18.9117i 0.222679 + 1.41749i
\(179\) 25.0137 1.86961 0.934806 0.355159i \(-0.115573\pi\)
0.934806 + 0.355159i \(0.115573\pi\)
\(180\) −1.93751 6.01456i −0.144414 0.448299i
\(181\) 7.26648 0.540113 0.270057 0.962844i \(-0.412958\pi\)
0.270057 + 0.962844i \(0.412958\pi\)
\(182\) 4.96872 0.780554i 0.368306 0.0578585i
\(183\) 2.35281i 0.173925i
\(184\) 7.47793 3.77467i 0.551280 0.278273i
\(185\) 26.4790i 1.94677i
\(186\) −0.806411 5.13332i −0.0591289 0.376393i
\(187\) −9.21046 −0.673536
\(188\) −7.16783 22.2509i −0.522767 1.62281i
\(189\) −0.761043 −0.0553578
\(190\) 3.81323 + 24.2736i 0.276641 + 1.76099i
\(191\) 15.0240 1.08710 0.543548 0.839378i \(-0.317081\pi\)
0.543548 + 0.839378i \(0.317081\pi\)
\(192\) −4.75105 + 6.43642i −0.342878 + 0.464508i
\(193\) −7.14965 −0.514643 −0.257322 0.966326i \(-0.582840\pi\)
−0.257322 + 0.966326i \(0.582840\pi\)
\(194\) −12.2952 + 1.93150i −0.882746 + 0.138674i
\(195\) −14.7648 −1.05733
\(196\) 12.2231 3.93750i 0.873076 0.281250i
\(197\) 0.740496i 0.0527582i 0.999652 + 0.0263791i \(0.00839770\pi\)
−0.999652 + 0.0263791i \(0.991602\pi\)
\(198\) −1.13000 7.19316i −0.0803056 0.511196i
\(199\) 13.5738i 0.962219i −0.876660 0.481110i \(-0.840234\pi\)
0.876660 0.481110i \(-0.159766\pi\)
\(200\) 6.35009 + 12.5800i 0.449019 + 0.889542i
\(201\) 8.09955 1.18208i 0.571298 0.0833778i
\(202\) −2.95699 + 0.464524i −0.208053 + 0.0326838i
\(203\) 7.45181 0.523015
\(204\) −3.40544 + 1.09702i −0.238428 + 0.0768066i
\(205\) 3.16643 0.221153
\(206\) 4.24565 0.666964i 0.295808 0.0464696i
\(207\) 2.96158i 0.205844i
\(208\) 10.9110 + 15.1779i 0.756542 + 1.05240i
\(209\) 28.3138i 1.95850i
\(210\) 3.35927 0.527719i 0.231811 0.0364161i
\(211\) 26.1007i 1.79685i −0.439131 0.898423i \(-0.644714\pi\)
0.439131 0.898423i \(-0.355286\pi\)
\(212\) −5.67353 17.6122i −0.389660 1.20961i
\(213\) 11.8375i 0.811095i
\(214\) −1.12064 + 0.176045i −0.0766052 + 0.0120342i
\(215\) 22.8200i 1.55631i
\(216\) −1.27455 2.52498i −0.0867220 0.171803i
\(217\) 2.79632 0.189826
\(218\) −5.51763 + 0.866785i −0.373701 + 0.0587061i
\(219\) −7.50732 −0.507298
\(220\) 9.97570 + 30.9672i 0.672562 + 2.08781i
\(221\) 8.35981i 0.562342i
\(222\) 1.83936 + 11.7087i 0.123450 + 0.785836i
\(223\) 12.4915i 0.836490i −0.908334 0.418245i \(-0.862645\pi\)
0.908334 0.418245i \(-0.137355\pi\)
\(224\) −3.02494 3.06328i −0.202113 0.204674i
\(225\) −4.98223 −0.332148
\(226\) 8.35879 1.31311i 0.556018 0.0873469i
\(227\) 19.5880i 1.30010i 0.759892 + 0.650050i \(0.225252\pi\)
−0.759892 + 0.650050i \(0.774748\pi\)
\(228\) 3.37233 + 10.4686i 0.223338 + 0.693301i
\(229\) 20.1069i 1.32870i 0.747421 + 0.664351i \(0.231292\pi\)
−0.747421 + 0.664351i \(0.768708\pi\)
\(230\) −2.05360 13.0725i −0.135411 0.861974i
\(231\) 3.91839 0.257811
\(232\) 12.4798 + 24.7235i 0.819341 + 1.62318i
\(233\) 10.1151i 0.662662i −0.943515 0.331331i \(-0.892502\pi\)
0.943515 0.331331i \(-0.107498\pi\)
\(234\) −6.52882 + 1.02564i −0.426802 + 0.0670479i
\(235\) −36.9292 −2.40900
\(236\) −0.330828 1.02698i −0.0215350 0.0668505i
\(237\) −4.41239 −0.286615
\(238\) −0.298794 1.90201i −0.0193679 0.123289i
\(239\) −10.4706 −0.677286 −0.338643 0.940915i \(-0.609968\pi\)
−0.338643 + 0.940915i \(0.609968\pi\)
\(240\) 7.37675 + 10.2615i 0.476167 + 0.662380i
\(241\) 12.9470 0.833989 0.416994 0.908909i \(-0.363083\pi\)
0.416994 + 0.908909i \(0.363083\pi\)
\(242\) 3.40385 + 21.6676i 0.218808 + 1.39285i
\(243\) 1.00000 0.0641500
\(244\) −1.44284 4.47897i −0.0923685 0.286737i
\(245\) 20.2863i 1.29605i
\(246\) 1.40016 0.219956i 0.0892710 0.0140239i
\(247\) 25.6988 1.63518
\(248\) 4.68309 + 9.27758i 0.297377 + 0.589127i
\(249\) 8.49721i 0.538489i
\(250\) −0.0784487 + 0.0123238i −0.00496153 + 0.000779425i
\(251\) −16.0783 −1.01485 −0.507425 0.861696i \(-0.669403\pi\)
−0.507425 + 0.861696i \(0.669403\pi\)
\(252\) 1.44877 0.466703i 0.0912640 0.0293995i
\(253\) 15.2483i 0.958653i
\(254\) −4.89272 + 0.768615i −0.306996 + 0.0482272i
\(255\) 5.65193i 0.353937i
\(256\) 5.09734 15.1663i 0.318584 0.947895i
\(257\) −8.88242 −0.554070 −0.277035 0.960860i \(-0.589352\pi\)
−0.277035 + 0.960860i \(0.589352\pi\)
\(258\) 1.58519 + 10.0907i 0.0986896 + 0.628222i
\(259\) −6.37818 −0.396321
\(260\) 28.1072 9.05437i 1.74313 0.561528i
\(261\) −9.79158 −0.606083
\(262\) −23.4539 + 3.68446i −1.44899 + 0.227627i
\(263\) 13.4038i 0.826517i −0.910614 0.413258i \(-0.864391\pi\)
0.910614 0.413258i \(-0.135609\pi\)
\(264\) 6.56228 + 13.0004i 0.403880 + 0.800119i
\(265\) −29.2305 −1.79561
\(266\) −5.84696 + 0.918520i −0.358500 + 0.0563181i
\(267\) 13.5366 0.828427
\(268\) −14.6939 + 7.21727i −0.897574 + 0.440865i
\(269\) 2.97179 0.181193 0.0905967 0.995888i \(-0.471123\pi\)
0.0905967 + 0.995888i \(0.471123\pi\)
\(270\) −4.41403 + 0.693416i −0.268629 + 0.0421999i
\(271\) −3.46516 −0.210494 −0.105247 0.994446i \(-0.533563\pi\)
−0.105247 + 0.994446i \(0.533563\pi\)
\(272\) 5.81007 4.17671i 0.352287 0.253250i
\(273\) 3.55650i 0.215249i
\(274\) −5.25768 + 0.825948i −0.317628 + 0.0498973i
\(275\) 25.6521 1.54688
\(276\) −1.81616 5.63785i −0.109320 0.339359i
\(277\) 16.7532 1.00660 0.503302 0.864111i \(-0.332118\pi\)
0.503302 + 0.864111i \(0.332118\pi\)
\(278\) −2.54193 16.1810i −0.152455 0.970469i
\(279\) −3.67432 −0.219976
\(280\) −6.07129 + 3.06464i −0.362829 + 0.183147i
\(281\) 30.6334i 1.82743i −0.406351 0.913717i \(-0.633199\pi\)
0.406351 0.913717i \(-0.366801\pi\)
\(282\) −16.3297 + 2.56529i −0.972418 + 0.152761i
\(283\) 19.2949i 1.14696i 0.819218 + 0.573482i \(0.194408\pi\)
−0.819218 + 0.573482i \(0.805592\pi\)
\(284\) 7.25926 + 22.5347i 0.430758 + 1.33719i
\(285\) 17.3745 1.02918
\(286\) 33.6150 5.28071i 1.98770 0.312255i
\(287\) 0.762722i 0.0450220i
\(288\) 3.97473 + 4.02511i 0.234213 + 0.237182i
\(289\) −13.7999 −0.811758
\(290\) 43.2203 6.78963i 2.53798 0.398701i
\(291\) 8.80067i 0.515904i
\(292\) 14.2914 4.60380i 0.836342 0.269417i
\(293\) −32.3179 −1.88803 −0.944017 0.329898i \(-0.892986\pi\)
−0.944017 + 0.329898i \(0.892986\pi\)
\(294\) −1.40919 8.97039i −0.0821857 0.523164i
\(295\) −1.70445 −0.0992369
\(296\) −10.6818 21.1615i −0.620866 1.22998i
\(297\) −5.14871 −0.298759
\(298\) −0.225158 1.43327i −0.0130431 0.0830274i
\(299\) −13.8400 −0.800389
\(300\) 9.48449 3.05531i 0.547587 0.176398i
\(301\) −5.49681 −0.316831
\(302\) 7.54018 1.18451i 0.433889 0.0681611i
\(303\) 2.11655i 0.121593i
\(304\) −12.8396 17.8607i −0.736400 1.02438i
\(305\) −7.43364 −0.425649
\(306\) 0.392611 + 2.49922i 0.0224441 + 0.142871i
\(307\) 4.06916i 0.232239i 0.993235 + 0.116120i \(0.0370456\pi\)
−0.993235 + 0.116120i \(0.962954\pi\)
\(308\) −7.45930 + 2.40292i −0.425033 + 0.136919i
\(309\) 3.03894i 0.172880i
\(310\) 16.2185 2.54783i 0.921151 0.144707i
\(311\) −22.5473 −1.27854 −0.639270 0.768982i \(-0.720763\pi\)
−0.639270 + 0.768982i \(0.720763\pi\)
\(312\) 11.7997 5.95621i 0.668027 0.337204i
\(313\) 20.6491i 1.16716i −0.812057 0.583578i \(-0.801652\pi\)
0.812057 0.583578i \(-0.198348\pi\)
\(314\) 4.76594 + 30.3382i 0.268957 + 1.71208i
\(315\) 2.40449i 0.135478i
\(316\) 8.39970 2.70586i 0.472520 0.152216i
\(317\) 13.8868 0.779962 0.389981 0.920823i \(-0.372482\pi\)
0.389981 + 0.920823i \(0.372482\pi\)
\(318\) −12.9254 + 2.03050i −0.724820 + 0.113865i
\(319\) 50.4140 2.82264
\(320\) −20.3356 15.0108i −1.13680 0.839129i
\(321\) 0.802128i 0.0447704i
\(322\) 3.14886 0.494666i 0.175479 0.0275667i
\(323\) 9.83744i 0.547370i
\(324\) −1.90366 + 0.613241i −0.105759 + 0.0340689i
\(325\) 23.2829i 1.29150i
\(326\) −17.3370 + 2.72354i −0.960209 + 0.150843i
\(327\) 3.94940i 0.218402i
\(328\) −2.53055 + 1.27736i −0.139726 + 0.0705303i
\(329\) 8.89541i 0.490420i
\(330\) 22.7265 3.57020i 1.25106 0.196533i
\(331\) 6.20476 0.341044 0.170522 0.985354i \(-0.445455\pi\)
0.170522 + 0.985354i \(0.445455\pi\)
\(332\) −5.21083 16.1758i −0.285982 0.887764i
\(333\) 8.38084 0.459267
\(334\) −33.2009 + 5.21565i −1.81667 + 0.285388i
\(335\) 3.73476 + 25.5902i 0.204052 + 1.39814i
\(336\) −2.47177 + 1.77689i −0.134846 + 0.0969373i
\(337\) 17.2073i 0.937343i 0.883373 + 0.468672i \(0.155267\pi\)
−0.883373 + 0.468672i \(0.844733\pi\)
\(338\) −1.93985 12.3484i −0.105514 0.671664i
\(339\) 5.98304i 0.324954i
\(340\) −3.46599 10.7594i −0.187970 0.583509i
\(341\) 18.9180 1.02447
\(342\) 7.68282 1.20692i 0.415439 0.0652628i
\(343\) 10.2138 0.551494
\(344\) −9.20572 18.2373i −0.496339 0.983287i
\(345\) −9.35701 −0.503764
\(346\) 4.73726 + 30.1556i 0.254677 + 1.62118i
\(347\) −1.25418 −0.0673279 −0.0336639 0.999433i \(-0.510718\pi\)
−0.0336639 + 0.999433i \(0.510718\pi\)
\(348\) 18.6399 6.00460i 0.999202 0.321880i
\(349\) −20.6929 −1.10767 −0.553833 0.832628i \(-0.686835\pi\)
−0.553833 + 0.832628i \(0.686835\pi\)
\(350\) 0.832171 + 5.29729i 0.0444814 + 0.283152i
\(351\) 4.67319i 0.249436i
\(352\) −20.4647 20.7241i −1.09077 1.10460i
\(353\) 12.0262i 0.640089i −0.947403 0.320044i \(-0.896302\pi\)
0.947403 0.320044i \(-0.103698\pi\)
\(354\) −0.753688 + 0.118400i −0.0400581 + 0.00629287i
\(355\) 37.4003 1.98500
\(356\) −25.7691 + 8.30120i −1.36576 + 0.439963i
\(357\) −1.36142 −0.0720540
\(358\) 5.48982 + 34.9461i 0.290146 + 1.84696i
\(359\) 11.0056i 0.580854i −0.956897 0.290427i \(-0.906203\pi\)
0.956897 0.290427i \(-0.0937973\pi\)
\(360\) 7.97759 4.02689i 0.420456 0.212236i
\(361\) −11.2412 −0.591640
\(362\) 1.59479 + 10.1519i 0.0838204 + 0.533570i
\(363\) 15.5092 0.814024
\(364\) 2.18099 + 6.77038i 0.114315 + 0.354864i
\(365\) 23.7191i 1.24152i
\(366\) −3.28707 + 0.516378i −0.171818 + 0.0269915i
\(367\) 13.4477 0.701965 0.350982 0.936382i \(-0.385848\pi\)
0.350982 + 0.936382i \(0.385848\pi\)
\(368\) 6.91472 + 9.61883i 0.360455 + 0.501416i
\(369\) 1.00221i 0.0521727i
\(370\) −36.9932 + 5.81140i −1.92319 + 0.302120i
\(371\) 7.04096i 0.365548i
\(372\) 6.99467 2.25324i 0.362657 0.116825i
\(373\) 35.9353i 1.86066i −0.366725 0.930329i \(-0.619521\pi\)
0.366725 0.930329i \(-0.380479\pi\)
\(374\) −2.02144 12.8677i −0.104526 0.665375i
\(375\) 0.0561519i 0.00289967i
\(376\) 29.5131 14.8975i 1.52202 0.768278i
\(377\) 45.7579i 2.35665i
\(378\) −0.167028 1.06324i −0.00859099 0.0546871i
\(379\) −29.3622 −1.50824 −0.754118 0.656739i \(-0.771935\pi\)
−0.754118 + 0.656739i \(0.771935\pi\)
\(380\) −33.0753 + 10.6548i −1.69672 + 0.546578i
\(381\) 3.50210i 0.179418i
\(382\) 3.29734 + 20.9897i 0.168707 + 1.07393i
\(383\) −22.1970 −1.13421 −0.567107 0.823644i \(-0.691937\pi\)
−0.567107 + 0.823644i \(0.691937\pi\)
\(384\) −10.0349 5.22499i −0.512092 0.266636i
\(385\) 12.3800i 0.630945i
\(386\) −1.56915 9.98863i −0.0798677 0.508408i
\(387\) 7.22273 0.367152
\(388\) −5.39693 16.7535i −0.273987 0.850530i
\(389\) −6.29515 −0.319177 −0.159588 0.987184i \(-0.551017\pi\)
−0.159588 + 0.987184i \(0.551017\pi\)
\(390\) −3.24046 20.6276i −0.164087 1.04452i
\(391\) 5.29793i 0.267928i
\(392\) 8.18363 + 16.2124i 0.413336 + 0.818851i
\(393\) 16.7878i 0.846833i
\(394\) −1.03453 + 0.162518i −0.0521190 + 0.00818756i
\(395\) 13.9408i 0.701437i
\(396\) 9.80142 3.15740i 0.492540 0.158665i
\(397\) 24.8494 1.24716 0.623579 0.781761i \(-0.285678\pi\)
0.623579 + 0.781761i \(0.285678\pi\)
\(398\) 18.9636 2.97907i 0.950562 0.149327i
\(399\) 4.18513i 0.209518i
\(400\) −16.1816 + 11.6325i −0.809082 + 0.581627i
\(401\) 22.5349i 1.12534i −0.826683 0.562668i \(-0.809775\pi\)
0.826683 0.562668i \(-0.190225\pi\)
\(402\) 3.42909 + 11.0563i 0.171028 + 0.551437i
\(403\) 17.1708i 0.855338i
\(404\) −1.29795 4.02920i −0.0645756 0.200460i
\(405\) 3.15947i 0.156995i
\(406\) 1.63547 + 10.4108i 0.0811669 + 0.516678i
\(407\) −43.1505 −2.13889
\(408\) −2.28002 4.51690i −0.112878 0.223620i
\(409\) 16.8732i 0.834328i −0.908831 0.417164i \(-0.863024\pi\)
0.908831 0.417164i \(-0.136976\pi\)
\(410\) 0.694945 + 4.42376i 0.0343209 + 0.218474i
\(411\) 3.76333i 0.185631i
\(412\) 1.86360 + 5.78513i 0.0918132 + 0.285013i
\(413\) 0.410563i 0.0202025i
\(414\) −4.13756 + 0.649985i −0.203350 + 0.0319450i
\(415\) −26.8466 −1.31785
\(416\) −18.8101 + 18.5747i −0.922241 + 0.910699i
\(417\) −11.5820 −0.567172
\(418\) −39.5566 + 6.21409i −1.93478 + 0.303941i
\(419\) 17.8232i 0.870720i −0.900256 0.435360i \(-0.856621\pi\)
0.900256 0.435360i \(-0.143379\pi\)
\(420\) 1.47453 + 4.57734i 0.0719498 + 0.223351i
\(421\) 11.6776 0.569133 0.284567 0.958656i \(-0.408150\pi\)
0.284567 + 0.958656i \(0.408150\pi\)
\(422\) 36.4647 5.72838i 1.77508 0.278853i
\(423\) 11.6884i 0.568311i
\(424\) 23.3604 11.7918i 1.13448 0.572658i
\(425\) −8.91264 −0.432327
\(426\) 16.5380 2.59801i 0.801268 0.125874i
\(427\) 1.79059i 0.0866529i
\(428\) −0.491898 1.52698i −0.0237768 0.0738095i
\(429\) 24.0609i 1.16167i
\(430\) −31.8813 + 5.00836i −1.53745 + 0.241524i
\(431\) 12.4402i 0.599222i 0.954061 + 0.299611i \(0.0968570\pi\)
−0.954061 + 0.299611i \(0.903143\pi\)
\(432\) 3.24787 2.33481i 0.156263 0.112334i
\(433\) 1.55511i 0.0747338i −0.999302 0.0373669i \(-0.988103\pi\)
0.999302 0.0373669i \(-0.0118970\pi\)
\(434\) 0.613714 + 3.90668i 0.0294592 + 0.187526i
\(435\) 30.9362i 1.48328i
\(436\) −2.42193 7.51833i −0.115990 0.360063i
\(437\) 16.2863 0.779079
\(438\) −1.64765 10.4883i −0.0787277 0.501152i
\(439\) 34.3737i 1.64057i −0.571958 0.820283i \(-0.693816\pi\)
0.571958 0.820283i \(-0.306184\pi\)
\(440\) −41.0743 + 20.7333i −1.95814 + 0.988421i
\(441\) −6.42081 −0.305753
\(442\) −11.6793 + 1.83475i −0.555529 + 0.0872700i
\(443\) −12.2786 −0.583373 −0.291687 0.956514i \(-0.594216\pi\)
−0.291687 + 0.956514i \(0.594216\pi\)
\(444\) −15.9543 + 5.13947i −0.757157 + 0.243909i
\(445\) 42.7685i 2.02742i
\(446\) 17.4516 2.74153i 0.826356 0.129815i
\(447\) −1.02591 −0.0485238
\(448\) 3.61576 4.89839i 0.170829 0.231427i
\(449\) 6.05108 0.285568 0.142784 0.989754i \(-0.454395\pi\)
0.142784 + 0.989754i \(0.454395\pi\)
\(450\) −1.09346 6.96057i −0.0515463 0.328124i
\(451\) 5.16007i 0.242978i
\(452\) 3.66905 + 11.3897i 0.172577 + 0.535726i
\(453\) 5.39710i 0.253578i
\(454\) −27.3660 + 4.29902i −1.28435 + 0.201763i
\(455\) 11.2366 0.526782
\(456\) −13.8854 + 7.00899i −0.650242 + 0.328226i
\(457\) −10.5677 −0.494337 −0.247169 0.968972i \(-0.579500\pi\)
−0.247169 + 0.968972i \(0.579500\pi\)
\(458\) −28.0910 + 4.41291i −1.31260 + 0.206202i
\(459\) 1.78889 0.0834981
\(460\) 17.8126 5.73810i 0.830516 0.267540i
\(461\) 9.54057 0.444349 0.222174 0.975007i \(-0.428685\pi\)
0.222174 + 0.975007i \(0.428685\pi\)
\(462\) 0.859979 + 5.47431i 0.0400098 + 0.254688i
\(463\) 19.5832 0.910110 0.455055 0.890463i \(-0.349620\pi\)
0.455055 + 0.890463i \(0.349620\pi\)
\(464\) −31.8018 + 22.8615i −1.47636 + 1.06132i
\(465\) 11.6089i 0.538349i
\(466\) 14.1316 2.21998i 0.654633 0.102839i
\(467\) 3.05326i 0.141288i −0.997502 0.0706439i \(-0.977495\pi\)
0.997502 0.0706439i \(-0.0225054\pi\)
\(468\) −2.86579 8.89618i −0.132471 0.411226i
\(469\) −6.16411 + 0.899618i −0.284632 + 0.0415405i
\(470\) −8.10494 51.5931i −0.373853 2.37981i
\(471\) 21.7154 1.00059
\(472\) 1.36216 0.687586i 0.0626986 0.0316487i
\(473\) −37.1878 −1.70990
\(474\) −0.968397 6.16446i −0.0444800 0.283143i
\(475\) 27.3982i 1.25712i
\(476\) 2.59169 0.834878i 0.118790 0.0382666i
\(477\) 9.25172i 0.423607i
\(478\) −2.29801 14.6283i −0.105108 0.669081i
\(479\) 19.4898i 0.890512i −0.895403 0.445256i \(-0.853113\pi\)
0.895403 0.445256i \(-0.146887\pi\)
\(480\) −12.7172 + 12.5580i −0.580458 + 0.573193i
\(481\) 39.1653i 1.78578i
\(482\) 2.84151 + 18.0880i 0.129427 + 0.823885i
\(483\) 2.25389i 0.102556i
\(484\) −29.5244 + 9.51089i −1.34202 + 0.432313i
\(485\) −27.8054 −1.26258
\(486\) 0.219472 + 1.39708i 0.00995547 + 0.0633728i
\(487\) −18.0005 −0.815682 −0.407841 0.913053i \(-0.633718\pi\)
−0.407841 + 0.913053i \(0.633718\pi\)
\(488\) 5.94081 2.99878i 0.268928 0.135748i
\(489\) 12.4095i 0.561176i
\(490\) 28.3416 4.45229i 1.28034 0.201134i
\(491\) 24.6443i 1.11218i −0.831121 0.556091i \(-0.812300\pi\)
0.831121 0.556091i \(-0.187700\pi\)
\(492\) 0.614593 + 1.90786i 0.0277080 + 0.0860130i
\(493\) −17.5160 −0.788882
\(494\) 5.64018 + 35.9033i 0.253763 + 1.61536i
\(495\) 16.2672i 0.731155i
\(496\) −11.9337 + 8.57883i −0.535839 + 0.385201i
\(497\) 9.00888i 0.404104i
\(498\) −11.8713 + 1.86490i −0.531965 + 0.0835683i
\(499\) 18.2260 0.815907 0.407953 0.913003i \(-0.366243\pi\)
0.407953 + 0.913003i \(0.366243\pi\)
\(500\) −0.0344347 0.106894i −0.00153996 0.00478046i
\(501\) 23.7645i 1.06172i
\(502\) −3.52873 22.4626i −0.157495 1.00256i
\(503\) −18.5070 −0.825187 −0.412594 0.910915i \(-0.635377\pi\)
−0.412594 + 0.910915i \(0.635377\pi\)
\(504\) 0.969986 + 1.92162i 0.0432066 + 0.0855957i
\(505\) −6.68716 −0.297575
\(506\) 21.3031 3.34658i 0.947039 0.148774i
\(507\) −8.83872 −0.392541
\(508\) −2.14763 6.66682i −0.0952858 0.295792i
\(509\) 38.4081 1.70241 0.851205 0.524833i \(-0.175872\pi\)
0.851205 + 0.524833i \(0.175872\pi\)
\(510\) −7.89619 + 1.24044i −0.349649 + 0.0549277i
\(511\) 5.71340 0.252746
\(512\) 22.3073 + 3.79280i 0.985852 + 0.167620i
\(513\) 5.49920i 0.242795i
\(514\) −1.94945 12.4094i −0.0859864 0.547357i
\(515\) 9.60144 0.423090
\(516\) −13.7497 + 4.42927i −0.605295 + 0.194988i
\(517\) 60.1804i 2.64673i
\(518\) −1.39983 8.91083i −0.0615052 0.391519i
\(519\) 21.5848 0.947466
\(520\) 18.8184 + 37.2808i 0.825243 + 1.63487i
\(521\) 23.3284i 1.02203i 0.859571 + 0.511017i \(0.170731\pi\)
−0.859571 + 0.511017i \(0.829269\pi\)
\(522\) −2.14898 13.6796i −0.0940583 0.598741i
\(523\) 1.12071i 0.0490051i 0.999700 + 0.0245025i \(0.00780018\pi\)
−0.999700 + 0.0245025i \(0.992200\pi\)
\(524\) −10.2950 31.9583i −0.449738 1.39611i
\(525\) 3.79169 0.165483
\(526\) 18.7262 2.94177i 0.816503 0.128267i
\(527\) −6.57294 −0.286322
\(528\) −16.7224 + 12.0213i −0.727747 + 0.523158i
\(529\) 14.2291 0.618655
\(530\) −6.41528 40.8373i −0.278662 1.77386i
\(531\) 0.539474i 0.0234112i
\(532\) −2.56649 7.96707i −0.111271 0.345416i
\(533\) 4.68350 0.202865
\(534\) 2.97091 + 18.9117i 0.128564 + 0.818390i
\(535\) −2.53430 −0.109567
\(536\) −13.3080 18.9446i −0.574818 0.818281i
\(537\) 25.0137 1.07942
\(538\) 0.652227 + 4.15183i 0.0281195 + 0.178998i
\(539\) 33.0589 1.42395
\(540\) −1.93751 6.01456i −0.0833773 0.258826i
\(541\) 2.12087i 0.0911831i 0.998960 + 0.0455916i \(0.0145173\pi\)
−0.998960 + 0.0455916i \(0.985483\pi\)
\(542\) −0.760507 4.84111i −0.0326666 0.207943i
\(543\) 7.26648 0.311835
\(544\) 7.11034 + 7.20046i 0.304854 + 0.308717i
\(545\) −12.4780 −0.534499
\(546\) 4.96872 0.780554i 0.212641 0.0334046i
\(547\) 18.3469 0.784458 0.392229 0.919868i \(-0.371704\pi\)
0.392229 + 0.919868i \(0.371704\pi\)
\(548\) −2.30783 7.16412i −0.0985856 0.306036i
\(549\) 2.35281i 0.100416i
\(550\) 5.62992 + 35.8380i 0.240060 + 1.52814i
\(551\) 53.8458i 2.29391i
\(552\) 7.47793 3.77467i 0.318282 0.160661i
\(553\) 3.35802 0.142797
\(554\) 3.67687 + 23.4056i 0.156215 + 0.994408i
\(555\) 26.4790i 1.12397i
\(556\) 22.0482 7.10255i 0.935052 0.301215i
\(557\) −17.1789 −0.727891 −0.363946 0.931420i \(-0.618571\pi\)
−0.363946 + 0.931420i \(0.618571\pi\)
\(558\) −0.806411 5.13332i −0.0341381 0.217311i
\(559\) 33.7532i 1.42761i
\(560\) −5.61403 7.80948i −0.237236 0.330011i
\(561\) −9.21046 −0.388866
\(562\) 42.7973 6.72318i 1.80529 0.283600i
\(563\) −5.23605 −0.220673 −0.110337 0.993894i \(-0.535193\pi\)
−0.110337 + 0.993894i \(0.535193\pi\)
\(564\) −7.16783 22.2509i −0.301820 0.936930i
\(565\) 18.9032 0.795264
\(566\) −26.9565 + 4.23470i −1.13307 + 0.177998i
\(567\) −0.761043 −0.0319608
\(568\) −29.8896 + 15.0875i −1.25414 + 0.633058i
\(569\) 38.0114 1.59352 0.796761 0.604295i \(-0.206545\pi\)
0.796761 + 0.604295i \(0.206545\pi\)
\(570\) 3.81323 + 24.2736i 0.159719 + 1.01671i
\(571\) 17.6369i 0.738081i 0.929413 + 0.369041i \(0.120314\pi\)
−0.929413 + 0.369041i \(0.879686\pi\)
\(572\) 14.7551 + 45.8039i 0.616943 + 1.91516i
\(573\) 15.0240 0.627635
\(574\) −1.06558 + 0.167396i −0.0444766 + 0.00698699i
\(575\) 14.7553i 0.615337i
\(576\) −4.75105 + 6.43642i −0.197961 + 0.268184i
\(577\) 5.54549i 0.230862i 0.993316 + 0.115431i \(0.0368249\pi\)
−0.993316 + 0.115431i \(0.963175\pi\)
\(578\) −3.02869 19.2795i −0.125977 0.801923i
\(579\) −7.14965 −0.297129
\(580\) 18.9713 + 58.8920i 0.787741 + 2.44536i
\(581\) 6.46674i 0.268286i
\(582\) −12.2952 + 1.93150i −0.509654 + 0.0800634i
\(583\) 47.6344i 1.97282i
\(584\) 9.56844 + 18.9558i 0.395945 + 0.784398i
\(585\) −14.7648 −0.610449
\(586\) −7.09289 45.1507i −0.293005 1.86516i
\(587\) 39.7801 1.64190 0.820950 0.571000i \(-0.193445\pi\)
0.820950 + 0.571000i \(0.193445\pi\)
\(588\) 12.2231 3.93750i 0.504071 0.162380i
\(589\) 20.2058i 0.832565i
\(590\) −0.374080 2.38125i −0.0154006 0.0980346i
\(591\) 0.740496i 0.0304599i
\(592\) 27.2199 19.5677i 1.11873 0.804226i
\(593\) 36.6042i 1.50315i 0.659646 + 0.751576i \(0.270706\pi\)
−0.659646 + 0.751576i \(0.729294\pi\)
\(594\) −1.13000 7.19316i −0.0463645 0.295139i
\(595\) 4.30136i 0.176339i
\(596\) 1.95298 0.629128i 0.0799973 0.0257701i
\(597\) 13.5738i 0.555538i
\(598\) −3.03750 19.3356i −0.124213 0.790692i
\(599\) −41.8300 −1.70913 −0.854563 0.519348i \(-0.826175\pi\)
−0.854563 + 0.519348i \(0.826175\pi\)
\(600\) 6.35009 + 12.5800i 0.259241 + 0.513577i
\(601\) 9.98958 0.407484 0.203742 0.979025i \(-0.434690\pi\)
0.203742 + 0.979025i \(0.434690\pi\)
\(602\) −1.20640 7.67948i −0.0491691 0.312992i
\(603\) 8.09955 1.18208i 0.329839 0.0481382i
\(604\) 3.30972 + 10.2743i 0.134671 + 0.418054i
\(605\) 49.0009i 1.99217i
\(606\) −2.95699 + 0.464524i −0.120119 + 0.0188700i
\(607\) 13.8115i 0.560593i −0.959914 0.280296i \(-0.909567\pi\)
0.959914 0.280296i \(-0.0904327\pi\)
\(608\) 22.1349 21.8578i 0.897687 0.886452i
\(609\) 7.45181 0.301963
\(610\) −1.63148 10.3854i −0.0660566 0.420492i
\(611\) −54.6223 −2.20978
\(612\) −3.40544 + 1.09702i −0.137657 + 0.0443443i
\(613\) 30.6329 1.23725 0.618625 0.785686i \(-0.287690\pi\)
0.618625 + 0.785686i \(0.287690\pi\)
\(614\) −5.68495 + 0.893069i −0.229426 + 0.0360413i
\(615\) 3.16643 0.127683
\(616\) −4.99418 9.89387i −0.201221 0.398635i
\(617\) 2.14651 0.0864153 0.0432076 0.999066i \(-0.486242\pi\)
0.0432076 + 0.999066i \(0.486242\pi\)
\(618\) 4.24565 0.666964i 0.170785 0.0268292i
\(619\) 37.2149i 1.49579i 0.663815 + 0.747897i \(0.268936\pi\)
−0.663815 + 0.747897i \(0.731064\pi\)
\(620\) 7.11904 + 22.0994i 0.285908 + 0.887534i
\(621\) 2.96158i 0.118844i
\(622\) −4.94851 31.5004i −0.198417 1.26305i
\(623\) −10.3019 −0.412739
\(624\) 10.9110 + 15.1779i 0.436790 + 0.607603i
\(625\) −25.0885 −1.00354
\(626\) 28.8484 4.53191i 1.15302 0.181131i
\(627\) 28.3138i 1.13074i
\(628\) −41.3389 + 13.3168i −1.64960 + 0.531398i
\(629\) 14.9924 0.597785
\(630\) 3.35927 0.527719i 0.133836 0.0210248i
\(631\) −33.0047 −1.31390 −0.656948 0.753936i \(-0.728153\pi\)
−0.656948 + 0.753936i \(0.728153\pi\)
\(632\) 5.62380 + 11.1412i 0.223703 + 0.443173i
\(633\) 26.1007i 1.03741i
\(634\) 3.04778 + 19.4010i 0.121043 + 0.770513i
\(635\) −11.0648 −0.439092
\(636\) −5.67353 17.6122i −0.224970 0.698368i
\(637\) 30.0057i 1.18887i
\(638\) 11.0645 + 70.4324i 0.438047 + 2.78845i
\(639\) 11.8375i 0.468286i
\(640\) 16.5082 31.7050i 0.652543 1.25325i
\(641\) 5.64568i 0.222991i 0.993765 + 0.111495i \(0.0355640\pi\)
−0.993765 + 0.111495i \(0.964436\pi\)
\(642\) −1.12064 + 0.176045i −0.0442280 + 0.00694794i
\(643\) 18.7677i 0.740125i −0.929007 0.370063i \(-0.879336\pi\)
0.929007 0.370063i \(-0.120664\pi\)
\(644\) 1.38218 + 4.29065i 0.0544654 + 0.169075i
\(645\) 22.8200i 0.898536i
\(646\) 13.7437 2.15905i 0.540738 0.0849465i
\(647\) 19.8431 0.780112 0.390056 0.920791i \(-0.372456\pi\)
0.390056 + 0.920791i \(0.372456\pi\)
\(648\) −1.27455 2.52498i −0.0500690 0.0991906i
\(649\) 2.77760i 0.109030i
\(650\) 32.5281 5.10995i 1.27586 0.200429i
\(651\) 2.79632 0.109596
\(652\) −7.61000 23.6235i −0.298030 0.925166i
\(653\) 20.8367i 0.815402i 0.913116 + 0.407701i \(0.133669\pi\)
−0.913116 + 0.407701i \(0.866331\pi\)
\(654\) −5.51763 + 0.866785i −0.215756 + 0.0338940i
\(655\) −53.0405 −2.07246
\(656\) −2.33996 3.25503i −0.0913600 0.127088i
\(657\) −7.50732 −0.292888
\(658\) 12.4276 1.95230i 0.484478 0.0761084i
\(659\) 36.4813i 1.42111i 0.703641 + 0.710555i \(0.251556\pi\)
−0.703641 + 0.710555i \(0.748444\pi\)
\(660\) 9.97570 + 30.9672i 0.388304 + 1.20540i
\(661\) 26.5119i 1.03119i 0.856832 + 0.515596i \(0.172429\pi\)
−0.856832 + 0.515596i \(0.827571\pi\)
\(662\) 1.36177 + 8.66854i 0.0529268 + 0.336912i
\(663\) 8.35981i 0.324668i
\(664\) 21.4553 10.8301i 0.832626 0.420289i
\(665\) −13.2228 −0.512757
\(666\) 1.83936 + 11.7087i 0.0712738 + 0.453703i
\(667\) 28.9985i 1.12283i
\(668\) −14.5734 45.2396i −0.563860 1.75037i
\(669\) 12.4915i 0.482948i
\(670\) −34.9319 + 10.8341i −1.34954 + 0.418558i
\(671\) 12.1140i 0.467654i
\(672\) −3.02494 3.06328i −0.116690 0.118169i
\(673\) 22.4998i 0.867303i 0.901081 + 0.433651i \(0.142775\pi\)
−0.901081 + 0.433651i \(0.857225\pi\)
\(674\) −24.0400 + 3.77653i −0.925987 + 0.145467i
\(675\) −4.98223 −0.191766
\(676\) 16.8259 5.42026i 0.647152 0.208472i
\(677\) 20.4581i 0.786269i −0.919481 0.393135i \(-0.871391\pi\)
0.919481 0.393135i \(-0.128609\pi\)
\(678\) 8.35879 1.31311i 0.321017 0.0504298i
\(679\) 6.69769i 0.257034i
\(680\) 14.2710 7.20365i 0.547268 0.276247i
\(681\) 19.5880i 0.750613i
\(682\) 4.15198 + 26.4300i 0.158988 + 1.01206i
\(683\) −35.4929 −1.35810 −0.679049 0.734093i \(-0.737608\pi\)
−0.679049 + 0.734093i \(0.737608\pi\)
\(684\) 3.37233 + 10.4686i 0.128944 + 0.400278i
\(685\) −11.8901 −0.454298
\(686\) 2.24165 + 14.2695i 0.0855866 + 0.544813i
\(687\) 20.1069i 0.767127i
\(688\) 23.4585 16.8637i 0.894347 0.642922i
\(689\) −43.2350 −1.64712
\(690\) −2.05360 13.0725i −0.0781794 0.497661i
\(691\) 30.7924i 1.17140i 0.810529 + 0.585698i \(0.199180\pi\)
−0.810529 + 0.585698i \(0.800820\pi\)
\(692\) −41.0901 + 13.2367i −1.56201 + 0.503182i
\(693\) 3.91839 0.148847
\(694\) −0.275258 1.75219i −0.0104486 0.0665122i
\(695\) 36.5929i 1.38805i
\(696\) 12.4798 + 24.7235i 0.473047 + 0.937144i
\(697\) 1.79283i 0.0679083i
\(698\) −4.54152 28.9096i −0.171899 1.09425i
\(699\) 10.1151i 0.382588i
\(700\) −7.21810 + 2.32522i −0.272819 + 0.0878850i
\(701\) 21.7224i 0.820442i −0.911986 0.410221i \(-0.865452\pi\)
0.911986 0.410221i \(-0.134548\pi\)
\(702\) −6.52882 + 1.02564i −0.246414 + 0.0387102i
\(703\) 46.0879i 1.73824i
\(704\) 24.4618 33.1393i 0.921939 1.24898i
\(705\) −36.9292 −1.39083
\(706\) 16.8015 2.63941i 0.632334 0.0993357i
\(707\) 1.61079i 0.0605798i
\(708\) −0.330828 1.02698i −0.0124333 0.0385962i
\(709\) 10.8581 0.407786 0.203893 0.978993i \(-0.434641\pi\)
0.203893 + 0.978993i \(0.434641\pi\)
\(710\) 8.20834 + 52.2512i 0.308053 + 1.96095i
\(711\) −4.41239 −0.165477
\(712\) −17.2531 34.1797i −0.646586 1.28094i
\(713\) 10.8818i 0.407526i
\(714\) −0.298794 1.90201i −0.0111821 0.0711810i
\(715\) 76.0196 2.84297
\(716\) −47.6177 + 15.3394i −1.77956 + 0.573261i
\(717\) −10.4706 −0.391031
\(718\) 15.3757 2.41543i 0.573817 0.0901430i
\(719\) 10.3815i 0.387163i −0.981084 0.193581i \(-0.937990\pi\)
0.981084 0.193581i \(-0.0620104\pi\)
\(720\) 7.37675 + 10.2615i 0.274915 + 0.382425i
\(721\) 2.31277i 0.0861320i
\(722\) −2.46712 15.7048i −0.0918168 0.584472i
\(723\) 12.9470 0.481504
\(724\) −13.8329 + 4.45610i −0.514097 + 0.165610i
\(725\) 48.7839 1.81179
\(726\) 3.40385 + 21.6676i 0.126329 + 0.804161i
\(727\) 52.6865 1.95403 0.977017 0.213160i \(-0.0683756\pi\)
0.977017 + 0.213160i \(0.0683756\pi\)
\(728\) −8.98010 + 4.53293i −0.332824 + 0.168002i
\(729\) 1.00000 0.0370370
\(730\) 33.1375 5.20569i 1.22647 0.192671i
\(731\) 12.9206 0.477887
\(732\) −1.44284 4.47897i −0.0533290 0.165547i
\(733\) 3.17334i 0.117210i −0.998281 0.0586050i \(-0.981335\pi\)
0.998281 0.0586050i \(-0.0186652\pi\)
\(734\) 2.95140 + 18.7875i 0.108938 + 0.693460i
\(735\) 20.2863i 0.748273i
\(736\) −11.9207 + 11.7715i −0.439402 + 0.433903i
\(737\) −41.7022 + 6.08621i −1.53612 + 0.224189i
\(738\) 1.40016 0.219956i 0.0515406 0.00809671i
\(739\) 24.0808 0.885826 0.442913 0.896565i \(-0.353945\pi\)
0.442913 + 0.896565i \(0.353945\pi\)
\(740\) −16.2380 50.4071i −0.596920 1.85300i
\(741\) 25.6988 0.944069
\(742\) 9.83678 1.54530i 0.361120 0.0567296i
\(743\) 49.0043i 1.79779i 0.438160 + 0.898897i \(0.355630\pi\)
−0.438160 + 0.898897i \(0.644370\pi\)
\(744\) 4.68309 + 9.27758i 0.171691 + 0.340133i
\(745\) 3.24132i 0.118753i
\(746\) 50.2045 7.88680i 1.83812 0.288756i
\(747\) 8.49721i 0.310896i
\(748\) 17.5336 5.64823i 0.641093 0.206520i
\(749\) 0.610454i 0.0223055i
\(750\) −0.0784487 + 0.0123238i −0.00286454 + 0.000450001i
\(751\) 7.55434i 0.275662i −0.990456 0.137831i \(-0.955987\pi\)
0.990456 0.137831i \(-0.0440130\pi\)
\(752\) 27.2903 + 37.9625i 0.995173 + 1.38435i
\(753\) −16.0783 −0.585924
\(754\) 63.9275 10.0426i 2.32810 0.365730i
\(755\) 17.0520 0.620584
\(756\) 1.44877 0.466703i 0.0526913 0.0169738i
\(757\) 15.3960i 0.559576i 0.960062 + 0.279788i \(0.0902642\pi\)
−0.960062 + 0.279788i \(0.909736\pi\)
\(758\) −6.44420 41.0214i −0.234064 1.48996i
\(759\) 15.2483i 0.553479i
\(760\) −22.1447 43.8703i −0.803271 1.59134i
\(761\) −4.51530 −0.163680 −0.0818398 0.996646i \(-0.526080\pi\)
−0.0818398 + 0.996646i \(0.526080\pi\)
\(762\) −4.89272 + 0.768615i −0.177244 + 0.0278440i
\(763\) 3.00567i 0.108812i
\(764\) −28.6006 + 9.21331i −1.03473 + 0.333326i
\(765\) 5.65193i 0.204346i
\(766\) −4.87163 31.0110i −0.176019 1.12047i
\(767\) −2.52107 −0.0910304
\(768\) 5.09734 15.1663i 0.183934 0.547267i
\(769\) 7.38615i 0.266351i −0.991092 0.133176i \(-0.957483\pi\)
0.991092 0.133176i \(-0.0425174\pi\)
\(770\) −17.2959 + 2.71707i −0.623301 + 0.0979166i
\(771\) −8.88242 −0.319893
\(772\) 13.6105 4.38446i 0.489854 0.157800i