Properties

Label 819.2.et.c.136.9
Level $819$
Weight $2$
Character 819.136
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 136.9
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.79515 - 1.79515i) q^{2} -4.44512i q^{4} +(0.590961 - 2.20549i) q^{5} +(-2.51335 - 0.826467i) q^{7} +(-4.38935 - 4.38935i) q^{8} +O(q^{10})\) \(q+(1.79515 - 1.79515i) q^{2} -4.44512i q^{4} +(0.590961 - 2.20549i) q^{5} +(-2.51335 - 0.826467i) q^{7} +(-4.38935 - 4.38935i) q^{8} +(-2.89833 - 5.02005i) q^{10} +(0.449206 - 1.67646i) q^{11} +(-1.05331 + 3.44826i) q^{13} +(-5.99548 + 3.02821i) q^{14} -6.86883 q^{16} +7.51920 q^{17} +(-5.80433 + 1.55527i) q^{19} +(-9.80368 - 2.62689i) q^{20} +(-2.20310 - 3.81588i) q^{22} -0.0216755i q^{23} +(-0.184846 - 0.106721i) q^{25} +(4.29929 + 8.08100i) q^{26} +(-3.67374 + 11.1722i) q^{28} +(-0.432921 + 0.749842i) q^{29} +(5.81230 - 1.55740i) q^{31} +(-3.55188 + 3.55188i) q^{32} +(13.4981 - 13.4981i) q^{34} +(-3.30806 + 5.05478i) q^{35} +(-6.64042 - 6.64042i) q^{37} +(-7.62770 + 13.2116i) q^{38} +(-12.2746 + 7.08675i) q^{40} +(2.45125 - 0.656811i) q^{41} +(1.71095 - 0.987815i) q^{43} +(-7.45205 - 1.99677i) q^{44} +(-0.0389108 - 0.0389108i) q^{46} +(-5.62025 - 1.50594i) q^{47} +(5.63390 + 4.15441i) q^{49} +(-0.523405 + 0.140246i) q^{50} +(15.3279 + 4.68210i) q^{52} +(6.87167 - 11.9021i) q^{53} +(-3.43196 - 1.98144i) q^{55} +(7.40434 + 14.6596i) q^{56} +(0.568919 + 2.12324i) q^{58} +(4.10621 - 4.10621i) q^{59} +(3.12149 + 1.80219i) q^{61} +(7.63818 - 13.2297i) q^{62} -0.985368i q^{64} +(6.98266 + 4.36087i) q^{65} +(1.08555 + 0.290873i) q^{67} -33.4237i q^{68} +(3.13562 + 15.0125i) q^{70} +(-12.5434 - 3.36098i) q^{71} +(2.56726 + 9.58115i) q^{73} -23.8411 q^{74} +(6.91334 + 25.8009i) q^{76} +(-2.51455 + 3.84228i) q^{77} +(2.16727 + 3.75382i) q^{79} +(-4.05921 + 15.1492i) q^{80} +(3.22129 - 5.57944i) q^{82} +(8.64819 + 8.64819i) q^{83} +(4.44355 - 16.5836i) q^{85} +(1.29813 - 4.84468i) q^{86} +(-9.33028 + 5.38684i) q^{88} +(-1.71535 + 1.71535i) q^{89} +(5.49723 - 7.79618i) q^{91} -0.0963502 q^{92} +(-12.7926 + 7.38580i) q^{94} +13.7205i q^{95} +(-1.99188 + 7.43379i) q^{97} +(17.5715 - 2.65591i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.79515 1.79515i 1.26936 1.26936i 0.322944 0.946418i \(-0.395328\pi\)
0.946418 0.322944i \(-0.104672\pi\)
\(3\) 0 0
\(4\) 4.44512i 2.22256i
\(5\) 0.590961 2.20549i 0.264286 0.986327i −0.698401 0.715707i \(-0.746105\pi\)
0.962686 0.270620i \(-0.0872287\pi\)
\(6\) 0 0
\(7\) −2.51335 0.826467i −0.949959 0.312375i
\(8\) −4.38935 4.38935i −1.55187 1.55187i
\(9\) 0 0
\(10\) −2.89833 5.02005i −0.916532 1.58748i
\(11\) 0.449206 1.67646i 0.135441 0.505471i −0.864555 0.502538i \(-0.832400\pi\)
0.999996 0.00293308i \(-0.000933629\pi\)
\(12\) 0 0
\(13\) −1.05331 + 3.44826i −0.292137 + 0.956377i
\(14\) −5.99548 + 3.02821i −1.60236 + 0.809324i
\(15\) 0 0
\(16\) −6.86883 −1.71721
\(17\) 7.51920 1.82367 0.911837 0.410552i \(-0.134664\pi\)
0.911837 + 0.410552i \(0.134664\pi\)
\(18\) 0 0
\(19\) −5.80433 + 1.55527i −1.33161 + 0.356803i −0.853313 0.521399i \(-0.825411\pi\)
−0.478292 + 0.878201i \(0.658744\pi\)
\(20\) −9.80368 2.62689i −2.19217 0.587390i
\(21\) 0 0
\(22\) −2.20310 3.81588i −0.469703 0.813549i
\(23\) 0.0216755i 0.00451966i −0.999997 0.00225983i \(-0.999281\pi\)
0.999997 0.00225983i \(-0.000719326\pi\)
\(24\) 0 0
\(25\) −0.184846 0.106721i −0.0369691 0.0213441i
\(26\) 4.29929 + 8.08100i 0.843161 + 1.58481i
\(27\) 0 0
\(28\) −3.67374 + 11.1722i −0.694272 + 2.11134i
\(29\) −0.432921 + 0.749842i −0.0803915 + 0.139242i −0.903418 0.428761i \(-0.858950\pi\)
0.823027 + 0.568003i \(0.192284\pi\)
\(30\) 0 0
\(31\) 5.81230 1.55740i 1.04392 0.279718i 0.304183 0.952614i \(-0.401616\pi\)
0.739737 + 0.672896i \(0.234950\pi\)
\(32\) −3.55188 + 3.55188i −0.627889 + 0.627889i
\(33\) 0 0
\(34\) 13.4981 13.4981i 2.31490 2.31490i
\(35\) −3.30806 + 5.05478i −0.559165 + 0.854414i
\(36\) 0 0
\(37\) −6.64042 6.64042i −1.09168 1.09168i −0.995349 0.0963296i \(-0.969290\pi\)
−0.0963296 0.995349i \(-0.530710\pi\)
\(38\) −7.62770 + 13.2116i −1.23738 + 2.14320i
\(39\) 0 0
\(40\) −12.2746 + 7.08675i −1.94079 + 1.12051i
\(41\) 2.45125 0.656811i 0.382822 0.102577i −0.0622757 0.998059i \(-0.519836\pi\)
0.445097 + 0.895482i \(0.353169\pi\)
\(42\) 0 0
\(43\) 1.71095 0.987815i 0.260917 0.150640i −0.363836 0.931463i \(-0.618533\pi\)
0.624753 + 0.780823i \(0.285200\pi\)
\(44\) −7.45205 1.99677i −1.12344 0.301025i
\(45\) 0 0
\(46\) −0.0389108 0.0389108i −0.00573708 0.00573708i
\(47\) −5.62025 1.50594i −0.819798 0.219664i −0.175540 0.984472i \(-0.556167\pi\)
−0.644258 + 0.764808i \(0.722834\pi\)
\(48\) 0 0
\(49\) 5.63390 + 4.15441i 0.804843 + 0.593487i
\(50\) −0.523405 + 0.140246i −0.0740206 + 0.0198338i
\(51\) 0 0
\(52\) 15.3279 + 4.68210i 2.12560 + 0.649291i
\(53\) 6.87167 11.9021i 0.943897 1.63488i 0.185952 0.982559i \(-0.440463\pi\)
0.757945 0.652319i \(-0.226204\pi\)
\(54\) 0 0
\(55\) −3.43196 1.98144i −0.462765 0.267177i
\(56\) 7.40434 + 14.6596i 0.989446 + 1.95898i
\(57\) 0 0
\(58\) 0.568919 + 2.12324i 0.0747028 + 0.278795i
\(59\) 4.10621 4.10621i 0.534583 0.534583i −0.387350 0.921933i \(-0.626609\pi\)
0.921933 + 0.387350i \(0.126609\pi\)
\(60\) 0 0
\(61\) 3.12149 + 1.80219i 0.399666 + 0.230747i 0.686340 0.727281i \(-0.259216\pi\)
−0.286674 + 0.958028i \(0.592550\pi\)
\(62\) 7.63818 13.2297i 0.970050 1.68018i
\(63\) 0 0
\(64\) 0.985368i 0.123171i
\(65\) 6.98266 + 4.36087i 0.866093 + 0.540899i
\(66\) 0 0
\(67\) 1.08555 + 0.290873i 0.132621 + 0.0355357i 0.324519 0.945879i \(-0.394798\pi\)
−0.191898 + 0.981415i \(0.561464\pi\)
\(68\) 33.4237i 4.05322i
\(69\) 0 0
\(70\) 3.13562 + 15.0125i 0.374778 + 1.79434i
\(71\) −12.5434 3.36098i −1.48862 0.398875i −0.579350 0.815079i \(-0.696694\pi\)
−0.909272 + 0.416203i \(0.863360\pi\)
\(72\) 0 0
\(73\) 2.56726 + 9.58115i 0.300475 + 1.12139i 0.936771 + 0.349943i \(0.113799\pi\)
−0.636296 + 0.771445i \(0.719534\pi\)
\(74\) −23.8411 −2.77147
\(75\) 0 0
\(76\) 6.91334 + 25.8009i 0.793014 + 2.95957i
\(77\) −2.51455 + 3.84228i −0.286560 + 0.437868i
\(78\) 0 0
\(79\) 2.16727 + 3.75382i 0.243837 + 0.422338i 0.961804 0.273739i \(-0.0882606\pi\)
−0.717967 + 0.696077i \(0.754927\pi\)
\(80\) −4.05921 + 15.1492i −0.453833 + 1.69373i
\(81\) 0 0
\(82\) 3.22129 5.57944i 0.355732 0.616146i
\(83\) 8.64819 + 8.64819i 0.949263 + 0.949263i 0.998774 0.0495109i \(-0.0157663\pi\)
−0.0495109 + 0.998774i \(0.515766\pi\)
\(84\) 0 0
\(85\) 4.44355 16.5836i 0.481971 1.79874i
\(86\) 1.29813 4.84468i 0.139981 0.522415i
\(87\) 0 0
\(88\) −9.33028 + 5.38684i −0.994611 + 0.574239i
\(89\) −1.71535 + 1.71535i −0.181826 + 0.181826i −0.792151 0.610325i \(-0.791039\pi\)
0.610325 + 0.792151i \(0.291039\pi\)
\(90\) 0 0
\(91\) 5.49723 7.79618i 0.576266 0.817262i
\(92\) −0.0963502 −0.0100452
\(93\) 0 0
\(94\) −12.7926 + 7.38580i −1.31945 + 0.761787i
\(95\) 13.7205i 1.40770i
\(96\) 0 0
\(97\) −1.99188 + 7.43379i −0.202245 + 0.754787i 0.788027 + 0.615641i \(0.211103\pi\)
−0.990272 + 0.139147i \(0.955564\pi\)
\(98\) 17.5715 2.65591i 1.77499 0.268288i
\(99\) 0 0
\(100\) −0.474386 + 0.821660i −0.0474386 + 0.0821660i
\(101\) 2.23088 + 3.86399i 0.221981 + 0.384482i 0.955409 0.295285i \(-0.0954145\pi\)
−0.733429 + 0.679766i \(0.762081\pi\)
\(102\) 0 0
\(103\) 4.23657 + 7.33795i 0.417441 + 0.723030i 0.995681 0.0928371i \(-0.0295936\pi\)
−0.578240 + 0.815867i \(0.696260\pi\)
\(104\) 19.7590 10.5123i 1.93753 1.03081i
\(105\) 0 0
\(106\) −9.03034 33.7017i −0.877104 3.27340i
\(107\) −10.1376 −0.980042 −0.490021 0.871711i \(-0.663011\pi\)
−0.490021 + 0.871711i \(0.663011\pi\)
\(108\) 0 0
\(109\) −1.05231 3.92728i −0.100793 0.376165i 0.897041 0.441948i \(-0.145712\pi\)
−0.997834 + 0.0657825i \(0.979046\pi\)
\(110\) −9.71785 + 2.60389i −0.926561 + 0.248271i
\(111\) 0 0
\(112\) 17.2638 + 5.67686i 1.63128 + 0.536413i
\(113\) 2.30418 + 3.99096i 0.216759 + 0.375438i 0.953815 0.300394i \(-0.0971180\pi\)
−0.737056 + 0.675831i \(0.763785\pi\)
\(114\) 0 0
\(115\) −0.0478052 0.0128094i −0.00445786 0.00119448i
\(116\) 3.33314 + 1.92439i 0.309474 + 0.178675i
\(117\) 0 0
\(118\) 14.7425i 1.35716i
\(119\) −18.8984 6.21437i −1.73242 0.569671i
\(120\) 0 0
\(121\) 6.91755 + 3.99385i 0.628869 + 0.363077i
\(122\) 8.83874 2.36833i 0.800222 0.214419i
\(123\) 0 0
\(124\) −6.92283 25.8364i −0.621689 2.32017i
\(125\) 7.72806 7.72806i 0.691219 0.691219i
\(126\) 0 0
\(127\) 2.76191 + 1.59459i 0.245080 + 0.141497i 0.617509 0.786564i \(-0.288142\pi\)
−0.372430 + 0.928060i \(0.621475\pi\)
\(128\) −8.87264 8.87264i −0.784238 0.784238i
\(129\) 0 0
\(130\) 20.3633 4.70652i 1.78598 0.412789i
\(131\) 7.19475 4.15389i 0.628608 0.362927i −0.151605 0.988441i \(-0.548444\pi\)
0.780213 + 0.625514i \(0.215111\pi\)
\(132\) 0 0
\(133\) 15.8737 + 0.888154i 1.37643 + 0.0770127i
\(134\) 2.47088 1.42657i 0.213452 0.123237i
\(135\) 0 0
\(136\) −33.0044 33.0044i −2.83010 2.83010i
\(137\) −3.54760 3.54760i −0.303092 0.303092i 0.539131 0.842222i \(-0.318753\pi\)
−0.842222 + 0.539131i \(0.818753\pi\)
\(138\) 0 0
\(139\) 2.35400 1.35908i 0.199663 0.115276i −0.396835 0.917890i \(-0.629892\pi\)
0.596498 + 0.802614i \(0.296558\pi\)
\(140\) 22.4691 + 14.7047i 1.89899 + 1.24278i
\(141\) 0 0
\(142\) −28.5506 + 16.4837i −2.39592 + 1.38328i
\(143\) 5.30772 + 3.31481i 0.443854 + 0.277199i
\(144\) 0 0
\(145\) 1.39793 + 1.39793i 0.116092 + 0.116092i
\(146\) 21.8082 + 12.5910i 1.80486 + 1.04204i
\(147\) 0 0
\(148\) −29.5175 + 29.5175i −2.42632 + 2.42632i
\(149\) 5.83717 + 21.7846i 0.478200 + 1.78467i 0.608904 + 0.793244i \(0.291610\pi\)
−0.130704 + 0.991421i \(0.541724\pi\)
\(150\) 0 0
\(151\) 20.2079 5.41469i 1.64450 0.440641i 0.686431 0.727195i \(-0.259176\pi\)
0.958064 + 0.286553i \(0.0925096\pi\)
\(152\) 32.3038 + 18.6506i 2.62019 + 1.51277i
\(153\) 0 0
\(154\) 2.38347 + 11.4115i 0.192066 + 0.919561i
\(155\) 13.7394i 1.10357i
\(156\) 0 0
\(157\) 5.68992 + 3.28508i 0.454105 + 0.262178i 0.709563 0.704643i \(-0.248893\pi\)
−0.255457 + 0.966820i \(0.582226\pi\)
\(158\) 10.6292 + 2.84809i 0.845616 + 0.226582i
\(159\) 0 0
\(160\) 5.73463 + 9.93267i 0.453362 + 0.785246i
\(161\) −0.0179141 + 0.0544782i −0.00141183 + 0.00429349i
\(162\) 0 0
\(163\) −23.4341 + 6.27914i −1.83550 + 0.491820i −0.998468 0.0553377i \(-0.982376\pi\)
−0.837030 + 0.547158i \(0.815710\pi\)
\(164\) −2.91960 10.8961i −0.227983 0.850843i
\(165\) 0 0
\(166\) 31.0496 2.40992
\(167\) 1.98472 + 7.40707i 0.153582 + 0.573176i 0.999223 + 0.0394232i \(0.0125520\pi\)
−0.845641 + 0.533753i \(0.820781\pi\)
\(168\) 0 0
\(169\) −10.7811 7.26421i −0.829312 0.558785i
\(170\) −21.7931 37.7468i −1.67146 2.89505i
\(171\) 0 0
\(172\) −4.39095 7.60536i −0.334807 0.579903i
\(173\) −0.111832 + 0.193699i −0.00850246 + 0.0147267i −0.870245 0.492619i \(-0.836040\pi\)
0.861743 + 0.507345i \(0.169373\pi\)
\(174\) 0 0
\(175\) 0.376381 + 0.420996i 0.0284518 + 0.0318243i
\(176\) −3.08552 + 11.5153i −0.232580 + 0.867999i
\(177\) 0 0
\(178\) 6.15860i 0.461607i
\(179\) 9.40968 5.43268i 0.703312 0.406058i −0.105268 0.994444i \(-0.533570\pi\)
0.808580 + 0.588386i \(0.200237\pi\)
\(180\) 0 0
\(181\) 0.436016 0.0324088 0.0162044 0.999869i \(-0.494842\pi\)
0.0162044 + 0.999869i \(0.494842\pi\)
\(182\) −4.12697 23.8637i −0.305911 1.76889i
\(183\) 0 0
\(184\) −0.0951414 + 0.0951414i −0.00701391 + 0.00701391i
\(185\) −18.5697 + 10.7212i −1.36527 + 0.788238i
\(186\) 0 0
\(187\) 3.37767 12.6056i 0.246999 0.921815i
\(188\) −6.69409 + 24.9827i −0.488216 + 1.82205i
\(189\) 0 0
\(190\) 24.6304 + 24.6304i 1.78688 + 1.78688i
\(191\) −4.42223 + 7.65952i −0.319981 + 0.554223i −0.980484 0.196600i \(-0.937010\pi\)
0.660503 + 0.750824i \(0.270343\pi\)
\(192\) 0 0
\(193\) −2.33215 + 8.70371i −0.167872 + 0.626507i 0.829784 + 0.558084i \(0.188463\pi\)
−0.997656 + 0.0684229i \(0.978203\pi\)
\(194\) 9.76905 + 16.9205i 0.701377 + 1.21482i
\(195\) 0 0
\(196\) 18.4668 25.0434i 1.31906 1.78881i
\(197\) 3.23591 + 12.0766i 0.230549 + 0.860421i 0.980105 + 0.198480i \(0.0636005\pi\)
−0.749556 + 0.661941i \(0.769733\pi\)
\(198\) 0 0
\(199\) −8.34509 −0.591568 −0.295784 0.955255i \(-0.595581\pi\)
−0.295784 + 0.955255i \(0.595581\pi\)
\(200\) 0.342918 + 1.27979i 0.0242479 + 0.0904945i
\(201\) 0 0
\(202\) 10.9412 + 2.93169i 0.769820 + 0.206273i
\(203\) 1.70781 1.52682i 0.119864 0.107162i
\(204\) 0 0
\(205\) 5.79438i 0.404697i
\(206\) 20.7780 + 5.56744i 1.44767 + 0.387902i
\(207\) 0 0
\(208\) 7.23503 23.6856i 0.501659 1.64230i
\(209\) 10.4294i 0.721413i
\(210\) 0 0
\(211\) −0.0517275 + 0.0895946i −0.00356106 + 0.00616794i −0.867800 0.496913i \(-0.834467\pi\)
0.864239 + 0.503081i \(0.167800\pi\)
\(212\) −52.9062 30.5454i −3.63361 2.09787i
\(213\) 0 0
\(214\) −18.1986 + 18.1986i −1.24403 + 1.24403i
\(215\) −1.16752 4.35724i −0.0796242 0.297162i
\(216\) 0 0
\(217\) −15.8955 0.889374i −1.07906 0.0603746i
\(218\) −8.93911 5.16100i −0.605433 0.349547i
\(219\) 0 0
\(220\) −8.80774 + 15.2554i −0.593817 + 1.02852i
\(221\) −7.92008 + 25.9282i −0.532762 + 1.74412i
\(222\) 0 0
\(223\) 25.3112 6.78211i 1.69496 0.454163i 0.723298 0.690536i \(-0.242625\pi\)
0.971663 + 0.236372i \(0.0759585\pi\)
\(224\) 11.8626 5.99162i 0.792606 0.400332i
\(225\) 0 0
\(226\) 11.3007 + 3.02802i 0.751712 + 0.201421i
\(227\) −9.62565 9.62565i −0.638877 0.638877i 0.311401 0.950278i \(-0.399202\pi\)
−0.950278 + 0.311401i \(0.899202\pi\)
\(228\) 0 0
\(229\) −23.4824 6.29210i −1.55176 0.415794i −0.621719 0.783241i \(-0.713565\pi\)
−0.930044 + 0.367447i \(0.880232\pi\)
\(230\) −0.108812 + 0.0628227i −0.00717486 + 0.00414241i
\(231\) 0 0
\(232\) 5.19156 1.39107i 0.340843 0.0913285i
\(233\) 8.29904 4.79145i 0.543688 0.313899i −0.202884 0.979203i \(-0.565031\pi\)
0.746572 + 0.665304i \(0.231698\pi\)
\(234\) 0 0
\(235\) −6.64269 + 11.5055i −0.433321 + 0.750535i
\(236\) −18.2526 18.2526i −1.18814 1.18814i
\(237\) 0 0
\(238\) −45.0812 + 22.7698i −2.92218 + 1.47594i
\(239\) −5.64222 + 5.64222i −0.364965 + 0.364965i −0.865637 0.500672i \(-0.833086\pi\)
0.500672 + 0.865637i \(0.333086\pi\)
\(240\) 0 0
\(241\) −17.9441 + 17.9441i −1.15588 + 1.15588i −0.170526 + 0.985353i \(0.554547\pi\)
−0.985353 + 0.170526i \(0.945453\pi\)
\(242\) 19.5876 5.24848i 1.25914 0.337385i
\(243\) 0 0
\(244\) 8.01095 13.8754i 0.512849 0.888280i
\(245\) 12.4919 9.97045i 0.798081 0.636989i
\(246\) 0 0
\(247\) 0.750811 21.6531i 0.0477729 1.37775i
\(248\) −32.3482 18.6762i −2.05411 1.18594i
\(249\) 0 0
\(250\) 27.7460i 1.75481i
\(251\) −5.75368 9.96567i −0.363169 0.629027i 0.625311 0.780375i \(-0.284972\pi\)
−0.988481 + 0.151348i \(0.951639\pi\)
\(252\) 0 0
\(253\) −0.0363381 0.00973676i −0.00228456 0.000612145i
\(254\) 7.82055 2.09551i 0.490705 0.131484i
\(255\) 0 0
\(256\) −29.8847 −1.86779
\(257\) 27.3825 1.70807 0.854036 0.520213i \(-0.174148\pi\)
0.854036 + 0.520213i \(0.174148\pi\)
\(258\) 0 0
\(259\) 11.2017 + 22.1778i 0.696037 + 1.37806i
\(260\) 19.3846 31.0388i 1.20218 1.92494i
\(261\) 0 0
\(262\) 5.45879 20.3725i 0.337245 1.25862i
\(263\) −10.1358 17.5557i −0.624998 1.08253i −0.988541 0.150951i \(-0.951767\pi\)
0.363544 0.931577i \(-0.381567\pi\)
\(264\) 0 0
\(265\) −22.1891 22.1891i −1.36307 1.36307i
\(266\) 30.0901 26.9013i 1.84494 1.64943i
\(267\) 0 0
\(268\) 1.29296 4.82540i 0.0789803 0.294758i
\(269\) 1.81548i 0.110692i −0.998467 0.0553458i \(-0.982374\pi\)
0.998467 0.0553458i \(-0.0176261\pi\)
\(270\) 0 0
\(271\) −15.5693 + 15.5693i −0.945768 + 0.945768i −0.998603 0.0528356i \(-0.983174\pi\)
0.0528356 + 0.998603i \(0.483174\pi\)
\(272\) −51.6481 −3.13163
\(273\) 0 0
\(274\) −12.7369 −0.769466
\(275\) −0.261946 + 0.261946i −0.0157960 + 0.0157960i
\(276\) 0 0
\(277\) 20.3006i 1.21975i −0.792499 0.609873i \(-0.791221\pi\)
0.792499 0.609873i \(-0.208779\pi\)
\(278\) 1.78602 6.66553i 0.107119 0.399772i
\(279\) 0 0
\(280\) 36.7074 7.66696i 2.19369 0.458188i
\(281\) 14.1904 + 14.1904i 0.846529 + 0.846529i 0.989698 0.143169i \(-0.0457293\pi\)
−0.143169 + 0.989698i \(0.545729\pi\)
\(282\) 0 0
\(283\) 3.40103 + 5.89076i 0.202171 + 0.350170i 0.949228 0.314590i \(-0.101867\pi\)
−0.747057 + 0.664760i \(0.768534\pi\)
\(284\) −14.9400 + 55.7567i −0.886523 + 3.30855i
\(285\) 0 0
\(286\) 15.4787 3.57755i 0.915276 0.211545i
\(287\) −6.70370 0.375080i −0.395707 0.0221403i
\(288\) 0 0
\(289\) 39.5384 2.32579
\(290\) 5.01900 0.294726
\(291\) 0 0
\(292\) 42.5893 11.4118i 2.49235 0.667823i
\(293\) −20.5482 5.50587i −1.20044 0.321656i −0.397435 0.917630i \(-0.630099\pi\)
−0.803004 + 0.595974i \(0.796766\pi\)
\(294\) 0 0
\(295\) −6.62962 11.4828i −0.385991 0.668557i
\(296\) 58.2943i 3.38829i
\(297\) 0 0
\(298\) 49.5852 + 28.6280i 2.87239 + 1.65838i
\(299\) 0.0747429 + 0.0228311i 0.00432249 + 0.00132036i
\(300\) 0 0
\(301\) −5.11661 + 1.06869i −0.294917 + 0.0615982i
\(302\) 26.5560 45.9964i 1.52813 2.64679i
\(303\) 0 0
\(304\) 39.8690 10.6829i 2.28664 0.612704i
\(305\) 5.81940 5.81940i 0.333218 0.333218i
\(306\) 0 0
\(307\) −17.4862 + 17.4862i −0.997992 + 0.997992i −0.999998 0.00200593i \(-0.999361\pi\)
0.00200593 + 0.999998i \(0.499361\pi\)
\(308\) 17.0794 + 11.1775i 0.973188 + 0.636895i
\(309\) 0 0
\(310\) −24.6642 24.6642i −1.40083 1.40083i
\(311\) −1.90903 + 3.30654i −0.108251 + 0.187497i −0.915062 0.403314i \(-0.867858\pi\)
0.806811 + 0.590810i \(0.201192\pi\)
\(312\) 0 0
\(313\) −11.1229 + 6.42180i −0.628702 + 0.362981i −0.780249 0.625469i \(-0.784908\pi\)
0.151547 + 0.988450i \(0.451575\pi\)
\(314\) 16.1115 4.31705i 0.909223 0.243625i
\(315\) 0 0
\(316\) 16.6862 9.63376i 0.938670 0.541941i
\(317\) 9.13383 + 2.44740i 0.513007 + 0.137460i 0.506030 0.862516i \(-0.331112\pi\)
0.00697710 + 0.999976i \(0.497779\pi\)
\(318\) 0 0
\(319\) 1.06261 + 1.06261i 0.0594946 + 0.0594946i
\(320\) −2.17322 0.582314i −0.121487 0.0325523i
\(321\) 0 0
\(322\) 0.0656381 + 0.129955i 0.00365787 + 0.00724211i
\(323\) −43.6439 + 11.6944i −2.42841 + 0.650692i
\(324\) 0 0
\(325\) 0.562701 0.524986i 0.0312131 0.0291210i
\(326\) −30.7956 + 53.3396i −1.70561 + 2.95421i
\(327\) 0 0
\(328\) −13.6424 7.87643i −0.753275 0.434903i
\(329\) 12.8811 + 8.42992i 0.710157 + 0.464756i
\(330\) 0 0
\(331\) 4.06709 + 15.1786i 0.223547 + 0.834290i 0.982981 + 0.183706i \(0.0588094\pi\)
−0.759434 + 0.650585i \(0.774524\pi\)
\(332\) 38.4422 38.4422i 2.10979 2.10979i
\(333\) 0 0
\(334\) 16.8596 + 9.73392i 0.922519 + 0.532617i
\(335\) 1.28304 2.22228i 0.0700997 0.121416i
\(336\) 0 0
\(337\) 1.41323i 0.0769835i −0.999259 0.0384917i \(-0.987745\pi\)
0.999259 0.0384917i \(-0.0122553\pi\)
\(338\) −32.3939 + 6.31328i −1.76200 + 0.343397i
\(339\) 0 0
\(340\) −73.7159 19.7521i −3.99780 1.07121i
\(341\) 10.4437i 0.565557i
\(342\) 0 0
\(343\) −10.7265 15.0977i −0.579177 0.815201i
\(344\) −11.8458 3.17407i −0.638683 0.171135i
\(345\) 0 0
\(346\) 0.146963 + 0.548475i 0.00790081 + 0.0294862i
\(347\) −5.50183 −0.295353 −0.147677 0.989036i \(-0.547180\pi\)
−0.147677 + 0.989036i \(0.547180\pi\)
\(348\) 0 0
\(349\) 3.51381 + 13.1137i 0.188090 + 0.701960i 0.993948 + 0.109852i \(0.0350377\pi\)
−0.805858 + 0.592109i \(0.798296\pi\)
\(350\) 1.43141 + 0.0800892i 0.0765121 + 0.00428095i
\(351\) 0 0
\(352\) 4.35905 + 7.55010i 0.232338 + 0.402421i
\(353\) −2.00920 + 7.49845i −0.106939 + 0.399102i −0.998558 0.0536846i \(-0.982903\pi\)
0.891619 + 0.452787i \(0.149570\pi\)
\(354\) 0 0
\(355\) −14.8253 + 25.6781i −0.786843 + 1.36285i
\(356\) 7.62491 + 7.62491i 0.404120 + 0.404120i
\(357\) 0 0
\(358\) 7.13930 26.6442i 0.377324 1.40819i
\(359\) 5.89881 22.0147i 0.311327 1.16189i −0.616033 0.787720i \(-0.711261\pi\)
0.927360 0.374169i \(-0.122072\pi\)
\(360\) 0 0
\(361\) 14.8169 8.55456i 0.779839 0.450240i
\(362\) 0.782713 0.782713i 0.0411385 0.0411385i
\(363\) 0 0
\(364\) −34.6550 24.4358i −1.81641 1.28079i
\(365\) 22.6483 1.18547
\(366\) 0 0
\(367\) −18.4248 + 10.6376i −0.961767 + 0.555276i −0.896716 0.442606i \(-0.854054\pi\)
−0.0650505 + 0.997882i \(0.520721\pi\)
\(368\) 0.148885i 0.00776119i
\(369\) 0 0
\(370\) −14.0891 + 52.5814i −0.732460 + 2.73358i
\(371\) −27.1076 + 24.2350i −1.40736 + 1.25822i
\(372\) 0 0
\(373\) −8.32600 + 14.4210i −0.431104 + 0.746694i −0.996969 0.0778044i \(-0.975209\pi\)
0.565865 + 0.824498i \(0.308542\pi\)
\(374\) −16.5656 28.6924i −0.856584 1.48365i
\(375\) 0 0
\(376\) 18.0591 + 31.2793i 0.931329 + 1.61311i
\(377\) −2.12965 2.28265i −0.109683 0.117562i
\(378\) 0 0
\(379\) −4.72716 17.6420i −0.242818 0.906209i −0.974468 0.224528i \(-0.927916\pi\)
0.731649 0.681681i \(-0.238751\pi\)
\(380\) 60.9893 3.12869
\(381\) 0 0
\(382\) 5.81142 + 21.6885i 0.297338 + 1.10968i
\(383\) −25.7773 + 6.90700i −1.31716 + 0.352931i −0.847912 0.530137i \(-0.822140\pi\)
−0.469245 + 0.883068i \(0.655474\pi\)
\(384\) 0 0
\(385\) 6.98813 + 7.81646i 0.356148 + 0.398364i
\(386\) 11.4379 + 19.8110i 0.582174 + 1.00835i
\(387\) 0 0
\(388\) 33.0441 + 8.85414i 1.67756 + 0.449501i
\(389\) 0.958138 + 0.553181i 0.0485795 + 0.0280474i 0.524093 0.851661i \(-0.324404\pi\)
−0.475514 + 0.879708i \(0.657738\pi\)
\(390\) 0 0
\(391\) 0.162983i 0.00824238i
\(392\) −6.49402 42.9643i −0.327997 2.17003i
\(393\) 0 0
\(394\) 27.4882 + 15.8703i 1.38484 + 0.799535i
\(395\) 9.55980 2.56154i 0.481006 0.128885i
\(396\) 0 0
\(397\) 3.67238 + 13.7055i 0.184311 + 0.687860i 0.994777 + 0.102073i \(0.0325476\pi\)
−0.810465 + 0.585787i \(0.800786\pi\)
\(398\) −14.9807 + 14.9807i −0.750913 + 0.750913i
\(399\) 0 0
\(400\) 1.26967 + 0.733046i 0.0634837 + 0.0366523i
\(401\) 1.61276 + 1.61276i 0.0805374 + 0.0805374i 0.746228 0.665691i \(-0.231863\pi\)
−0.665691 + 0.746228i \(0.731863\pi\)
\(402\) 0 0
\(403\) −0.751842 + 21.6828i −0.0374519 + 1.08010i
\(404\) 17.1759 9.91652i 0.854533 0.493365i
\(405\) 0 0
\(406\) 0.324889 5.80664i 0.0161239 0.288179i
\(407\) −14.1153 + 8.14948i −0.699670 + 0.403955i
\(408\) 0 0
\(409\) 13.9463 + 13.9463i 0.689598 + 0.689598i 0.962143 0.272545i \(-0.0878654\pi\)
−0.272545 + 0.962143i \(0.587865\pi\)
\(410\) −10.4018 10.4018i −0.513707 0.513707i
\(411\) 0 0
\(412\) 32.6180 18.8320i 1.60698 0.927788i
\(413\) −13.7140 + 6.92672i −0.674823 + 0.340841i
\(414\) 0 0
\(415\) 24.1843 13.9628i 1.18716 0.685407i
\(416\) −8.50658 15.9891i −0.417069 0.783928i
\(417\) 0 0
\(418\) 18.7222 + 18.7222i 0.915735 + 0.915735i
\(419\) 11.9093 + 6.87586i 0.581809 + 0.335908i 0.761852 0.647751i \(-0.224290\pi\)
−0.180043 + 0.983659i \(0.557624\pi\)
\(420\) 0 0
\(421\) −18.9223 + 18.9223i −0.922215 + 0.922215i −0.997186 0.0749709i \(-0.976114\pi\)
0.0749709 + 0.997186i \(0.476114\pi\)
\(422\) 0.0679771 + 0.253694i 0.00330907 + 0.0123496i
\(423\) 0 0
\(424\) −82.4046 + 22.0802i −4.00192 + 1.07231i
\(425\) −1.38989 0.802454i −0.0674196 0.0389247i
\(426\) 0 0
\(427\) −6.35595 7.10935i −0.307586 0.344046i
\(428\) 45.0630i 2.17820i
\(429\) 0 0
\(430\) −9.91777 5.72603i −0.478277 0.276134i
\(431\) 27.4744 + 7.36174i 1.32340 + 0.354603i 0.850249 0.526381i \(-0.176451\pi\)
0.473147 + 0.880984i \(0.343118\pi\)
\(432\) 0 0
\(433\) −12.8931 22.3315i −0.619602 1.07318i −0.989558 0.144132i \(-0.953961\pi\)
0.369957 0.929049i \(-0.379372\pi\)
\(434\) −30.1314 + 26.9383i −1.44635 + 1.29308i
\(435\) 0 0
\(436\) −17.4572 + 4.67765i −0.836049 + 0.224019i
\(437\) 0.0337112 + 0.125812i 0.00161262 + 0.00601840i
\(438\) 0 0
\(439\) −2.47750 −0.118244 −0.0591222 0.998251i \(-0.518830\pi\)
−0.0591222 + 0.998251i \(0.518830\pi\)
\(440\) 6.36682 + 23.7613i 0.303526 + 1.13277i
\(441\) 0 0
\(442\) 32.3273 + 60.7627i 1.53765 + 2.89019i
\(443\) 11.6371 + 20.1560i 0.552894 + 0.957641i 0.998064 + 0.0621947i \(0.0198100\pi\)
−0.445170 + 0.895446i \(0.646857\pi\)
\(444\) 0 0
\(445\) 2.76948 + 4.79689i 0.131286 + 0.227394i
\(446\) 33.2624 57.6122i 1.57502 2.72802i
\(447\) 0 0
\(448\) −0.814374 + 2.47658i −0.0384756 + 0.117007i
\(449\) 2.13306 7.96070i 0.100665 0.375688i −0.897152 0.441722i \(-0.854368\pi\)
0.997817 + 0.0660335i \(0.0210344\pi\)
\(450\) 0 0
\(451\) 4.40447i 0.207398i
\(452\) 17.7403 10.2424i 0.834433 0.481760i
\(453\) 0 0
\(454\) −34.5590 −1.62193
\(455\) −13.9458 16.7313i −0.653789 0.784377i
\(456\) 0 0
\(457\) −3.90295 + 3.90295i −0.182572 + 0.182572i −0.792476 0.609903i \(-0.791208\pi\)
0.609903 + 0.792476i \(0.291208\pi\)
\(458\) −53.4497 + 30.8592i −2.49754 + 1.44196i
\(459\) 0 0
\(460\) −0.0569391 + 0.212500i −0.00265480 + 0.00990785i
\(461\) 8.89222 33.1862i 0.414152 1.54564i −0.372377 0.928082i \(-0.621457\pi\)
0.786529 0.617554i \(-0.211876\pi\)
\(462\) 0 0
\(463\) 10.3935 + 10.3935i 0.483025 + 0.483025i 0.906096 0.423072i \(-0.139048\pi\)
−0.423072 + 0.906096i \(0.639048\pi\)
\(464\) 2.97367 5.15054i 0.138049 0.239108i
\(465\) 0 0
\(466\) 6.29664 23.4994i 0.291686 1.08859i
\(467\) 10.6589 + 18.4618i 0.493237 + 0.854311i 0.999970 0.00779214i \(-0.00248034\pi\)
−0.506733 + 0.862103i \(0.669147\pi\)
\(468\) 0 0
\(469\) −2.48798 1.62824i −0.114884 0.0751850i
\(470\) 8.72943 + 32.5787i 0.402658 + 1.50274i
\(471\) 0 0
\(472\) −36.0472 −1.65921
\(473\) −0.887464 3.31206i −0.0408056 0.152289i
\(474\) 0 0
\(475\) 1.23888 + 0.331958i 0.0568439 + 0.0152313i
\(476\) −27.6236 + 84.0057i −1.26613 + 3.85039i
\(477\) 0 0
\(478\) 20.2572i 0.926544i
\(479\) −14.3726 3.85114i −0.656703 0.175963i −0.0849452 0.996386i \(-0.527072\pi\)
−0.571758 + 0.820423i \(0.693738\pi\)
\(480\) 0 0
\(481\) 29.8924 15.9035i 1.36298 0.725137i
\(482\) 64.4246i 2.93446i
\(483\) 0 0
\(484\) 17.7531 30.7493i 0.806961 1.39770i
\(485\) 15.2181 + 8.78616i 0.691017 + 0.398959i
\(486\) 0 0
\(487\) 10.2062 10.2062i 0.462486 0.462486i −0.436984 0.899469i \(-0.643953\pi\)
0.899469 + 0.436984i \(0.143953\pi\)
\(488\) −5.79085 21.6117i −0.262139 0.978318i
\(489\) 0 0
\(490\) 4.52645 40.3233i 0.204484 1.82162i
\(491\) −0.458913 0.264954i −0.0207105 0.0119572i 0.489609 0.871942i \(-0.337140\pi\)
−0.510319 + 0.859985i \(0.670473\pi\)
\(492\) 0 0
\(493\) −3.25522 + 5.63821i −0.146608 + 0.253932i
\(494\) −37.5226 40.2183i −1.68822 1.80951i
\(495\) 0 0
\(496\) −39.9237 + 10.6975i −1.79263 + 0.480333i
\(497\) 28.7482 + 18.8140i 1.28953 + 0.843923i
\(498\) 0 0
\(499\) −24.5354 6.57425i −1.09836 0.294304i −0.336261 0.941769i \(-0.609163\pi\)
−0.762095 + 0.647465i \(0.775829\pi\)
\(500\) −34.3521 34.3521i −1.53627 1.53627i
\(501\) 0 0
\(502\) −28.2186 7.56114i −1.25946 0.337470i
\(503\) −18.0905 + 10.4445i −0.806615 + 0.465699i −0.845779 0.533533i \(-0.820864\pi\)
0.0391641 + 0.999233i \(0.487530\pi\)
\(504\) 0 0
\(505\) 9.84038 2.63672i 0.437891 0.117333i
\(506\) −0.0827112 + 0.0477533i −0.00367696 + 0.00212289i
\(507\) 0 0
\(508\) 7.08813 12.2770i 0.314485 0.544704i
\(509\) −8.17767 8.17767i −0.362469 0.362469i 0.502252 0.864721i \(-0.332505\pi\)
−0.864721 + 0.502252i \(0.832505\pi\)
\(510\) 0 0
\(511\) 1.46607 26.2026i 0.0648549 1.15913i
\(512\) −35.9022 + 35.9022i −1.58667 + 1.58667i
\(513\) 0 0
\(514\) 49.1556 49.1556i 2.16816 2.16816i
\(515\) 18.6875 5.00729i 0.823468 0.220647i
\(516\) 0 0
\(517\) −5.04930 + 8.74564i −0.222068 + 0.384633i
\(518\) 59.9211 + 19.7039i 2.63278 + 0.865739i
\(519\) 0 0
\(520\) −11.5080 49.7907i −0.504659 2.18347i
\(521\) −24.8573 14.3514i −1.08902 0.628746i −0.155705 0.987804i \(-0.549765\pi\)
−0.933315 + 0.359058i \(0.883098\pi\)
\(522\) 0 0
\(523\) 1.53739i 0.0672252i 0.999435 + 0.0336126i \(0.0107012\pi\)
−0.999435 + 0.0336126i \(0.989299\pi\)
\(524\) −18.4645 31.9815i −0.806627 1.39712i
\(525\) 0 0
\(526\) −49.7102 13.3198i −2.16747 0.580771i
\(527\) 43.7039 11.7104i 1.90377 0.510114i
\(528\) 0 0
\(529\) 22.9995 0.999980
\(530\) −79.6655 −3.46045
\(531\) 0 0
\(532\) 3.94795 70.5606i 0.171165 3.05919i
\(533\) −0.317078 + 9.14440i −0.0137342 + 0.396088i
\(534\) 0 0
\(535\) −5.99094 + 22.3585i −0.259011 + 0.966642i
\(536\) −3.48812 6.04160i −0.150664 0.260958i
\(537\) 0 0
\(538\) −3.25905 3.25905i −0.140508 0.140508i
\(539\) 9.49547 7.57882i 0.408999 0.326443i
\(540\) 0 0
\(541\) 10.2400 38.2161i 0.440251 1.64304i −0.287927 0.957652i \(-0.592966\pi\)
0.728178 0.685388i \(-0.240367\pi\)
\(542\) 55.8984i 2.40104i
\(543\) 0 0
\(544\) −26.7073 + 26.7073i −1.14507 + 1.14507i
\(545\) −9.28347 −0.397660
\(546\) 0 0
\(547\) 23.5304 1.00609 0.503043 0.864261i \(-0.332214\pi\)
0.503043 + 0.864261i \(0.332214\pi\)
\(548\) −15.7695 + 15.7695i −0.673639 + 0.673639i
\(549\) 0 0
\(550\) 0.940465i 0.0401016i
\(551\) 1.34662 5.02564i 0.0573678 0.214099i
\(552\) 0 0
\(553\) −2.34471 11.2259i −0.0997071 0.477372i
\(554\) −36.4426 36.4426i −1.54830 1.54830i
\(555\) 0 0
\(556\) −6.04127 10.4638i −0.256207 0.443764i
\(557\) 4.83024 18.0267i 0.204664 0.763816i −0.784888 0.619638i \(-0.787280\pi\)
0.989552 0.144178i \(-0.0460538\pi\)
\(558\) 0 0
\(559\) 1.60409 + 6.94028i 0.0678456 + 0.293542i
\(560\) 22.7225 34.7204i 0.960202 1.46721i
\(561\) 0 0
\(562\) 50.9478 2.14910
\(563\) −10.0368 −0.423000 −0.211500 0.977378i \(-0.567835\pi\)
−0.211500 + 0.977378i \(0.567835\pi\)
\(564\) 0 0
\(565\) 10.1637 2.72336i 0.427591 0.114573i
\(566\) 16.6802 + 4.46944i 0.701119 + 0.187864i
\(567\) 0 0
\(568\) 40.3046 + 69.8097i 1.69114 + 2.92915i
\(569\) 11.4381i 0.479510i −0.970833 0.239755i \(-0.922933\pi\)
0.970833 0.239755i \(-0.0770672\pi\)
\(570\) 0 0
\(571\) 37.6951 + 21.7633i 1.57749 + 0.910765i 0.995208 + 0.0977796i \(0.0311740\pi\)
0.582284 + 0.812986i \(0.302159\pi\)
\(572\) 14.7347 23.5934i 0.616090 0.986491i
\(573\) 0 0
\(574\) −12.7075 + 11.3608i −0.530400 + 0.474191i
\(575\) −0.00231322 + 0.00400662i −9.64681e−5 + 0.000167088i
\(576\) 0 0
\(577\) 1.32152 0.354101i 0.0550158 0.0147414i −0.231206 0.972905i \(-0.574267\pi\)
0.286222 + 0.958163i \(0.407601\pi\)
\(578\) 70.9773 70.9773i 2.95227 2.95227i
\(579\) 0 0
\(580\) 6.21398 6.21398i 0.258021 0.258021i
\(581\) −14.5885 28.8834i −0.605234 1.19829i
\(582\) 0 0
\(583\) −16.8666 16.8666i −0.698541 0.698541i
\(584\) 30.7864 53.3236i 1.27395 2.20655i
\(585\) 0 0
\(586\) −46.7709 + 27.0032i −1.93209 + 1.11549i
\(587\) −20.9489 + 5.61323i −0.864652 + 0.231683i −0.663774 0.747933i \(-0.731046\pi\)
−0.200878 + 0.979616i \(0.564380\pi\)
\(588\) 0 0
\(589\) −31.3144 + 18.0794i −1.29029 + 0.744947i
\(590\) −32.5145 8.71225i −1.33860 0.358678i
\(591\) 0 0
\(592\) 45.6120 + 45.6120i 1.87464 + 1.87464i
\(593\) 4.07949 + 1.09310i 0.167525 + 0.0448881i 0.341606 0.939843i \(-0.389029\pi\)
−0.174082 + 0.984731i \(0.555696\pi\)
\(594\) 0 0
\(595\) −24.8740 + 38.0079i −1.01973 + 1.55817i
\(596\) 96.8352 25.9469i 3.96652 1.06283i
\(597\) 0 0
\(598\) 0.175160 0.0931894i 0.00716282 0.00381080i
\(599\) −9.66178 + 16.7347i −0.394770 + 0.683761i −0.993072 0.117510i \(-0.962509\pi\)
0.598302 + 0.801271i \(0.295842\pi\)
\(600\) 0 0
\(601\) 6.96892 + 4.02351i 0.284268 + 0.164122i 0.635354 0.772221i \(-0.280854\pi\)
−0.351086 + 0.936343i \(0.614187\pi\)
\(602\) −7.26662 + 11.1035i −0.296165 + 0.452546i
\(603\) 0 0
\(604\) −24.0689 89.8265i −0.979351 3.65499i
\(605\) 12.8964 12.8964i 0.524314 0.524314i
\(606\) 0 0
\(607\) −38.9494 22.4875i −1.58091 0.912737i −0.994727 0.102557i \(-0.967298\pi\)
−0.586180 0.810180i \(-0.699369\pi\)
\(608\) 15.0922 26.1404i 0.612068 1.06013i
\(609\) 0 0
\(610\) 20.8934i 0.845948i
\(611\) 11.1128 17.7939i 0.449575 0.719864i
\(612\) 0 0
\(613\) 5.22539 + 1.40014i 0.211051 + 0.0565510i 0.362796 0.931869i \(-0.381822\pi\)
−0.151744 + 0.988420i \(0.548489\pi\)
\(614\) 62.7808i 2.53363i
\(615\) 0 0
\(616\) 27.9023 5.82787i 1.12422 0.234811i
\(617\) −21.1557 5.66866i −0.851697 0.228212i −0.193540 0.981092i \(-0.561997\pi\)
−0.658157 + 0.752881i \(0.728664\pi\)
\(618\) 0 0
\(619\) −1.72873 6.45170i −0.0694834 0.259316i 0.922442 0.386135i \(-0.126190\pi\)
−0.991926 + 0.126819i \(0.959523\pi\)
\(620\) −61.0731 −2.45275
\(621\) 0 0
\(622\) 2.50873 + 9.36272i 0.100591 + 0.375411i
\(623\) 5.72895 2.89360i 0.229526 0.115929i
\(624\) 0 0
\(625\) −13.0108 22.5354i −0.520433 0.901416i
\(626\) −8.43914 + 31.4953i −0.337296 + 1.25881i
\(627\) 0 0
\(628\) 14.6026 25.2924i 0.582706 1.00928i
\(629\) −49.9307 49.9307i −1.99087 1.99087i
\(630\) 0 0
\(631\) −5.79046 + 21.6103i −0.230515 + 0.860293i 0.749605 + 0.661886i \(0.230244\pi\)
−0.980120 + 0.198407i \(0.936423\pi\)
\(632\) 6.96392 25.9897i 0.277010 1.03382i
\(633\) 0 0
\(634\) 20.7900 12.0031i 0.825678 0.476705i
\(635\) 5.14903 5.14903i 0.204333 0.204333i
\(636\) 0 0
\(637\) −20.2598 + 15.0513i −0.802721 + 0.596354i
\(638\) 3.81508 0.151040
\(639\) 0 0
\(640\) −24.8119 + 14.3252i −0.980778 + 0.566252i
\(641\) 2.21138i 0.0873444i 0.999046 + 0.0436722i \(0.0139057\pi\)
−0.999046 + 0.0436722i \(0.986094\pi\)
\(642\) 0 0
\(643\) 1.55263 5.79449i 0.0612297 0.228512i −0.928530 0.371258i \(-0.878926\pi\)
0.989759 + 0.142746i \(0.0455932\pi\)
\(644\) 0.242162 + 0.0796302i 0.00954253 + 0.00313787i
\(645\) 0 0
\(646\) −57.3543 + 99.3405i −2.25657 + 3.90850i
\(647\) −0.776754 1.34538i −0.0305373 0.0528922i 0.850353 0.526213i \(-0.176389\pi\)
−0.880890 + 0.473321i \(0.843055\pi\)
\(648\) 0 0
\(649\) −5.03936 8.72842i −0.197812 0.342621i
\(650\) 0.0677042 1.95256i 0.00265558 0.0765857i
\(651\) 0 0
\(652\) 27.9115 + 104.167i 1.09310 + 4.07950i
\(653\) −21.9754 −0.859962 −0.429981 0.902838i \(-0.641480\pi\)
−0.429981 + 0.902838i \(0.641480\pi\)
\(654\) 0 0
\(655\) −4.90957 18.3228i −0.191833 0.715930i
\(656\) −16.8373 + 4.51153i −0.657384 + 0.176146i
\(657\) 0 0
\(658\) 38.2564 7.99048i 1.49139 0.311501i
\(659\) −13.5876 23.5344i −0.529298 0.916771i −0.999416 0.0341676i \(-0.989122\pi\)
0.470118 0.882604i \(-0.344211\pi\)
\(660\) 0 0
\(661\) 10.4653 + 2.80418i 0.407055 + 0.109070i 0.456536 0.889705i \(-0.349090\pi\)
−0.0494809 + 0.998775i \(0.515757\pi\)
\(662\) 34.5488 + 19.9468i 1.34278 + 0.775254i
\(663\) 0 0
\(664\) 75.9199i 2.94626i
\(665\) 11.3396 34.4845i 0.439729 1.33725i
\(666\) 0 0
\(667\) 0.0162532 + 0.00938379i 0.000629327 + 0.000363342i
\(668\) 32.9253 8.82230i 1.27392 0.341345i
\(669\) 0 0
\(670\) −1.68609 6.29257i −0.0651393 0.243103i
\(671\) 4.42349 4.42349i 0.170767 0.170767i
\(672\) 0 0
\(673\) −33.8958 19.5698i −1.30659 0.754359i −0.325063 0.945692i \(-0.605386\pi\)
−0.981525 + 0.191333i \(0.938719\pi\)
\(674\) −2.53696 2.53696i −0.0977199 0.0977199i
\(675\) 0 0
\(676\) −32.2902 + 47.9231i −1.24193 + 1.84320i
\(677\) −13.3692 + 7.71873i −0.513822 + 0.296655i −0.734403 0.678714i \(-0.762538\pi\)
0.220582 + 0.975369i \(0.429204\pi\)
\(678\) 0 0
\(679\) 11.1501 17.0375i 0.427901 0.653841i
\(680\) −92.2953 + 53.2867i −3.53936 + 2.04345i
\(681\) 0 0
\(682\) −18.7479 18.7479i −0.717896 0.717896i
\(683\) 33.0031 + 33.0031i 1.26283 + 1.26283i 0.949716 + 0.313112i \(0.101372\pi\)
0.313112 + 0.949716i \(0.398628\pi\)
\(684\) 0 0
\(685\) −9.92069 + 5.72771i −0.379050 + 0.218845i
\(686\) −46.3584 7.84700i −1.76997 0.299600i
\(687\) 0 0
\(688\) −11.7522 + 6.78514i −0.448049 + 0.258681i
\(689\) 33.8035 + 36.2320i 1.28781 + 1.38033i
\(690\) 0 0
\(691\) 3.43404 + 3.43404i 0.130637 + 0.130637i 0.769402 0.638765i \(-0.220554\pi\)
−0.638765 + 0.769402i \(0.720554\pi\)
\(692\) 0.861017 + 0.497108i 0.0327310 + 0.0188972i
\(693\) 0 0
\(694\) −9.87660 + 9.87660i −0.374910 + 0.374910i
\(695\) −1.60633 5.99489i −0.0609314 0.227399i
\(696\) 0 0
\(697\) 18.4315 4.93870i 0.698142 0.187067i
\(698\) 29.8489 + 17.2332i 1.12980 + 0.652288i
\(699\) 0 0
\(700\) 1.87137 1.67306i 0.0707313 0.0632357i
\(701\) 34.8788i 1.31735i −0.752426 0.658677i \(-0.771116\pi\)
0.752426 0.658677i \(-0.228884\pi\)
\(702\) 0 0
\(703\) 48.8709 + 28.2156i 1.84320 + 1.06417i
\(704\) −1.65193 0.442633i −0.0622594 0.0166824i
\(705\) 0 0
\(706\) 9.85401 + 17.0676i 0.370861 + 0.642349i
\(707\) −2.41352 11.5553i −0.0907699 0.434583i
\(708\) 0 0
\(709\) 42.8331 11.4771i 1.60863 0.431032i 0.660997 0.750388i \(-0.270134\pi\)
0.947635 + 0.319357i \(0.103467\pi\)
\(710\) 19.4825 + 72.7095i 0.731164 + 2.72874i
\(711\) 0 0
\(712\) 15.0585 0.564341
\(713\) −0.0337575 0.125985i −0.00126423 0.00471816i
\(714\) 0 0
\(715\) 10.4475 9.74722i 0.390713 0.364525i
\(716\) −24.1489 41.8271i −0.902487 1.56315i
\(717\) 0 0
\(718\) −28.9304 50.1088i −1.07967 1.87005i
\(719\) 11.7231 20.3050i 0.437197 0.757247i −0.560275 0.828306i \(-0.689305\pi\)
0.997472 + 0.0710594i \(0.0226380\pi\)
\(720\) 0 0
\(721\) −4.58342 21.9443i −0.170696 0.817247i
\(722\) 11.2419 41.9553i 0.418380 1.56141i
\(723\) 0 0
\(724\) 1.93814i 0.0720305i
\(725\) 0.160047 0.0924033i 0.00594400 0.00343177i
\(726\) 0 0
\(727\) −4.34538 −0.161161 −0.0805806 0.996748i \(-0.525677\pi\)
−0.0805806 + 0.996748i \(0.525677\pi\)
\(728\) −58.3494 + 10.0909i −2.16257 + 0.373994i
\(729\) 0 0
\(730\) 40.6571 40.6571i 1.50479 1.50479i
\(731\) 12.8650 7.42758i 0.475827 0.274719i
\(732\) 0 0
\(733\) 11.5162 42.9792i 0.425362 1.58747i −0.337768 0.941229i \(-0.609672\pi\)
0.763130 0.646245i \(-0.223661\pi\)
\(734\) −13.9792 + 52.1713i −0.515984 + 1.92568i
\(735\) 0 0
\(736\) 0.0769888 + 0.0769888i 0.00283784 + 0.00283784i
\(737\) 0.975271 1.68922i 0.0359246 0.0622232i
\(738\) 0 0
\(739\) 7.57142 28.2569i 0.278519 1.03945i −0.674927 0.737885i \(-0.735825\pi\)
0.953446 0.301564i \(-0.0975085\pi\)
\(740\) 47.6570 + 82.5443i 1.75190 + 3.03439i
\(741\) 0 0
\(742\) −5.15689 + 92.1676i −0.189315 + 3.38358i
\(743\) 2.66460 + 9.94444i 0.0977548 + 0.364826i 0.997423 0.0717489i \(-0.0228580\pi\)
−0.899668 + 0.436575i \(0.856191\pi\)
\(744\) 0 0
\(745\) 51.4954 1.88665
\(746\) 10.9415 + 40.8343i 0.400598 + 1.49505i
\(747\) 0 0
\(748\) −56.0335 15.0141i −2.04879 0.548971i
\(749\) 25.4795 + 8.37842i 0.931000 + 0.306141i
\(750\) 0 0
\(751\) 21.4555i 0.782923i −0.920194 0.391462i \(-0.871970\pi\)
0.920194 0.391462i \(-0.128030\pi\)
\(752\) 38.6046 + 10.3441i 1.40776 + 0.377209i
\(753\) 0 0
\(754\) −7.92073 0.274648i −0.288456 0.0100021i
\(755\) 47.7683i 1.73847i
\(756\) 0 0
\(757\) −18.9933 + 32.8973i −0.690322 + 1.19567i 0.281410 + 0.959588i \(0.409198\pi\)
−0.971732 + 0.236085i \(0.924136\pi\)
\(758\) −40.1560 23.1841i −1.45853 0.842084i
\(759\) 0 0
\(760\) 60.2242 60.2242i 2.18456 2.18456i
\(761\) 4.37608 + 16.3317i 0.158633 + 0.592025i 0.998767 + 0.0496467i \(0.0158095\pi\)
−0.840134 + 0.542379i \(0.817524\pi\)
\(762\) 0 0
\(763\) −0.600936 + 10.7403i −0.0217553 + 0.388827i
\(764\) 34.0475 + 19.6573i 1.23179 + 0.711177i
\(765\) 0 0
\(766\) −33.8749 + 58.6731i −1.22395 + 2.11995i
\(767\) 9.83418 + 18.4844i 0.355092 + 0.667434i
\(768\) 0 0
\(769\) 35.8744 9.61252i 1.29366 0.346636i 0.454614 0.890689i \(-0.349777\pi\)
0.839051 + 0.544052i \(0.183111\pi\)
\(770\) 26.5764 + 1.48698i 0.957748 + 0.0535872i
\(771\) 0 0
\(772\) 38.6890 + 10.3667i 1.39245 + 0.373106i
\(773\) −8.34392 8.34392i −0.300110 0.300110i 0.540947 0.841057i \(-0.318066\pi\)
−0.841057 + 0.540947i \(0.818066\pi\)
\(774\) 0 0
\(775\) −1.24059 0.332414i −0.0445631 0.0119407i
\(776\) 41.3726 23.8865i 1.48519 0.857474i
\(777\) 0 0
\(778\) 2.71304 0.726958i 0.0972673 0.0260627i
\(779\) −13.2064 + 7.62470i −0.473167 + 0.273183i
\(780\) 0 0
\(781\) −11.2691 + 19.5186i −0.403240 + 0.698431i
\(782\) −0.292578 0.292578i −0.0104626 0.0104626i
\(783\) 0 0
\(784\) −38.6983 28.5359i −1.38208 1.01914i
\(785\) 10.6077 10.6077i 0.378607 0.378607i
\(786\) 0 0
\(787\) 2.89556 2.89556i 0.103216 0.103216i −0.653613 0.756829i \(-0.726748\pi\)
0.756829 + 0.653613i \(0.226748\pi\)
\(788\) 53.6818 14.3840i 1.91234 0.512409i