Properties

Label 819.2.et.c.136.1
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 136.1
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.74432 + 1.74432i) q^{2} -4.08534i q^{4} +(-0.130892 + 0.488495i) q^{5} +(1.09376 + 2.40909i) q^{7} +(3.63751 + 3.63751i) q^{8} +O(q^{10})\) \(q+(-1.74432 + 1.74432i) q^{2} -4.08534i q^{4} +(-0.130892 + 0.488495i) q^{5} +(1.09376 + 2.40909i) q^{7} +(3.63751 + 3.63751i) q^{8} +(-0.623777 - 1.08041i) q^{10} +(1.54092 - 5.75079i) q^{11} +(-3.50782 - 0.833795i) q^{13} +(-6.11010 - 2.29436i) q^{14} -4.51932 q^{16} -0.933228 q^{17} +(-7.66303 + 2.05330i) q^{19} +(1.99567 + 0.534738i) q^{20} +(7.34338 + 12.7191i) q^{22} +8.12427i q^{23} +(4.10863 + 2.37212i) q^{25} +(7.57318 - 4.66436i) q^{26} +(9.84193 - 4.46838i) q^{28} +(-1.96458 + 3.40276i) q^{29} +(-2.37727 + 0.636987i) q^{31} +(0.608140 - 0.608140i) q^{32} +(1.62785 - 1.62785i) q^{34} +(-1.31999 + 0.218966i) q^{35} +(0.859350 + 0.859350i) q^{37} +(9.78519 - 16.9484i) q^{38} +(-2.25303 + 1.30079i) q^{40} +(-7.84968 + 2.10332i) q^{41} +(-0.152677 + 0.0881483i) q^{43} +(-23.4939 - 6.29518i) q^{44} +(-14.1714 - 14.1714i) q^{46} +(-1.65836 - 0.444356i) q^{47} +(-4.60738 + 5.26992i) q^{49} +(-11.3045 + 3.02904i) q^{50} +(-3.40634 + 14.3306i) q^{52} +(-0.750763 + 1.30036i) q^{53} +(2.60754 + 1.50546i) q^{55} +(-4.78451 + 12.7416i) q^{56} +(-2.50865 - 9.36239i) q^{58} +(3.03017 - 3.03017i) q^{59} +(-6.74749 - 3.89567i) q^{61} +(3.03561 - 5.25784i) q^{62} -6.91705i q^{64} +(0.866450 - 1.60442i) q^{65} +(-7.37302 - 1.97559i) q^{67} +3.81255i q^{68} +(1.92055 - 2.68444i) q^{70} +(-6.54710 - 1.75429i) q^{71} +(-3.27893 - 12.2371i) q^{73} -2.99797 q^{74} +(8.38844 + 31.3061i) q^{76} +(15.5395 - 2.57777i) q^{77} +(4.64069 + 8.03790i) q^{79} +(0.591542 - 2.20767i) q^{80} +(10.0235 - 17.3613i) q^{82} +(-1.66068 - 1.66068i) q^{83} +(0.122152 - 0.455878i) q^{85} +(0.112560 - 0.420078i) q^{86} +(26.5237 - 15.3134i) q^{88} +(-3.02064 + 3.02064i) q^{89} +(-1.82802 - 9.36260i) q^{91} +33.1904 q^{92} +(3.66782 - 2.11762i) q^{94} -4.01211i q^{95} +(-0.856967 + 3.19825i) q^{97} +(-1.15567 - 17.2292i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.74432 + 1.74432i −1.23342 + 1.23342i −0.270784 + 0.962640i \(0.587283\pi\)
−0.962640 + 0.270784i \(0.912717\pi\)
\(3\) 0 0
\(4\) 4.08534i 2.04267i
\(5\) −0.130892 + 0.488495i −0.0585366 + 0.218462i −0.988998 0.147928i \(-0.952740\pi\)
0.930461 + 0.366390i \(0.119406\pi\)
\(6\) 0 0
\(7\) 1.09376 + 2.40909i 0.413402 + 0.910549i
\(8\) 3.63751 + 3.63751i 1.28605 + 1.28605i
\(9\) 0 0
\(10\) −0.623777 1.08041i −0.197255 0.341656i
\(11\) 1.54092 5.75079i 0.464605 1.73393i −0.193592 0.981082i \(-0.562014\pi\)
0.658197 0.752846i \(-0.271320\pi\)
\(12\) 0 0
\(13\) −3.50782 0.833795i −0.972894 0.231253i
\(14\) −6.11010 2.29436i −1.63299 0.613193i
\(15\) 0 0
\(16\) −4.51932 −1.12983
\(17\) −0.933228 −0.226341 −0.113171 0.993576i \(-0.536101\pi\)
−0.113171 + 0.993576i \(0.536101\pi\)
\(18\) 0 0
\(19\) −7.66303 + 2.05330i −1.75802 + 0.471060i −0.986308 0.164913i \(-0.947266\pi\)
−0.771711 + 0.635973i \(0.780599\pi\)
\(20\) 1.99567 + 0.534738i 0.446245 + 0.119571i
\(21\) 0 0
\(22\) 7.34338 + 12.7191i 1.56561 + 2.71172i
\(23\) 8.12427i 1.69403i 0.531571 + 0.847014i \(0.321602\pi\)
−0.531571 + 0.847014i \(0.678398\pi\)
\(24\) 0 0
\(25\) 4.10863 + 2.37212i 0.821726 + 0.474424i
\(26\) 7.57318 4.66436i 1.48522 0.914757i
\(27\) 0 0
\(28\) 9.84193 4.46838i 1.85995 0.844444i
\(29\) −1.96458 + 3.40276i −0.364814 + 0.631877i −0.988746 0.149602i \(-0.952201\pi\)
0.623932 + 0.781479i \(0.285534\pi\)
\(30\) 0 0
\(31\) −2.37727 + 0.636987i −0.426970 + 0.114406i −0.465903 0.884836i \(-0.654271\pi\)
0.0389336 + 0.999242i \(0.487604\pi\)
\(32\) 0.608140 0.608140i 0.107505 0.107505i
\(33\) 0 0
\(34\) 1.62785 1.62785i 0.279174 0.279174i
\(35\) −1.31999 + 0.218966i −0.223119 + 0.0370120i
\(36\) 0 0
\(37\) 0.859350 + 0.859350i 0.141276 + 0.141276i 0.774208 0.632932i \(-0.218149\pi\)
−0.632932 + 0.774208i \(0.718149\pi\)
\(38\) 9.78519 16.9484i 1.58737 2.74940i
\(39\) 0 0
\(40\) −2.25303 + 1.30079i −0.356235 + 0.205672i
\(41\) −7.84968 + 2.10332i −1.22591 + 0.328483i −0.812987 0.582281i \(-0.802160\pi\)
−0.412927 + 0.910764i \(0.635494\pi\)
\(42\) 0 0
\(43\) −0.152677 + 0.0881483i −0.0232831 + 0.0134425i −0.511596 0.859226i \(-0.670946\pi\)
0.488313 + 0.872668i \(0.337612\pi\)
\(44\) −23.4939 6.29518i −3.54184 0.949034i
\(45\) 0 0
\(46\) −14.1714 14.1714i −2.08945 2.08945i
\(47\) −1.65836 0.444356i −0.241897 0.0648160i 0.135834 0.990732i \(-0.456629\pi\)
−0.377730 + 0.925916i \(0.623295\pi\)
\(48\) 0 0
\(49\) −4.60738 + 5.26992i −0.658198 + 0.752845i
\(50\) −11.3045 + 3.02904i −1.59870 + 0.428371i
\(51\) 0 0
\(52\) −3.40634 + 14.3306i −0.472374 + 1.98730i
\(53\) −0.750763 + 1.30036i −0.103125 + 0.178618i −0.912971 0.408025i \(-0.866218\pi\)
0.809845 + 0.586643i \(0.199551\pi\)
\(54\) 0 0
\(55\) 2.60754 + 1.50546i 0.351601 + 0.202997i
\(56\) −4.78451 + 12.7416i −0.639357 + 1.70267i
\(57\) 0 0
\(58\) −2.50865 9.36239i −0.329401 1.22934i
\(59\) 3.03017 3.03017i 0.394495 0.394495i −0.481791 0.876286i \(-0.660014\pi\)
0.876286 + 0.481791i \(0.160014\pi\)
\(60\) 0 0
\(61\) −6.74749 3.89567i −0.863928 0.498789i 0.00139788 0.999999i \(-0.499555\pi\)
−0.865326 + 0.501210i \(0.832888\pi\)
\(62\) 3.03561 5.25784i 0.385523 0.667746i
\(63\) 0 0
\(64\) 6.91705i 0.864631i
\(65\) 0.866450 1.60442i 0.107470 0.199003i
\(66\) 0 0
\(67\) −7.37302 1.97559i −0.900757 0.241357i −0.221416 0.975179i \(-0.571068\pi\)
−0.679341 + 0.733822i \(0.737734\pi\)
\(68\) 3.81255i 0.462340i
\(69\) 0 0
\(70\) 1.92055 2.68444i 0.229549 0.320852i
\(71\) −6.54710 1.75429i −0.776998 0.208196i −0.151537 0.988452i \(-0.548422\pi\)
−0.625461 + 0.780256i \(0.715089\pi\)
\(72\) 0 0
\(73\) −3.27893 12.2371i −0.383770 1.43225i −0.840097 0.542437i \(-0.817502\pi\)
0.456327 0.889812i \(-0.349165\pi\)
\(74\) −2.99797 −0.348507
\(75\) 0 0
\(76\) 8.38844 + 31.3061i 0.962220 + 3.59105i
\(77\) 15.5395 2.57777i 1.77089 0.293764i
\(78\) 0 0
\(79\) 4.64069 + 8.03790i 0.522118 + 0.904335i 0.999669 + 0.0257307i \(0.00819123\pi\)
−0.477551 + 0.878604i \(0.658475\pi\)
\(80\) 0.591542 2.20767i 0.0661364 0.246824i
\(81\) 0 0
\(82\) 10.0235 17.3613i 1.10691 1.91723i
\(83\) −1.66068 1.66068i −0.182284 0.182284i 0.610067 0.792350i \(-0.291143\pi\)
−0.792350 + 0.610067i \(0.791143\pi\)
\(84\) 0 0
\(85\) 0.122152 0.455878i 0.0132492 0.0494469i
\(86\) 0.112560 0.420078i 0.0121376 0.0452982i
\(87\) 0 0
\(88\) 26.5237 15.3134i 2.82743 1.63242i
\(89\) −3.02064 + 3.02064i −0.320187 + 0.320187i −0.848839 0.528652i \(-0.822698\pi\)
0.528652 + 0.848839i \(0.322698\pi\)
\(90\) 0 0
\(91\) −1.82802 9.36260i −0.191629 0.981467i
\(92\) 33.1904 3.46034
\(93\) 0 0
\(94\) 3.66782 2.11762i 0.378307 0.218416i
\(95\) 4.01211i 0.411634i
\(96\) 0 0
\(97\) −0.856967 + 3.19825i −0.0870119 + 0.324733i −0.995688 0.0927700i \(-0.970428\pi\)
0.908676 + 0.417503i \(0.137095\pi\)
\(98\) −1.15567 17.2292i −0.116741 1.74041i
\(99\) 0 0
\(100\) 9.69091 16.7852i 0.969091 1.67852i
\(101\) −2.23693 3.87447i −0.222583 0.385524i 0.733009 0.680219i \(-0.238115\pi\)
−0.955591 + 0.294695i \(0.904782\pi\)
\(102\) 0 0
\(103\) 2.07621 + 3.59610i 0.204575 + 0.354335i 0.949997 0.312258i \(-0.101085\pi\)
−0.745422 + 0.666593i \(0.767752\pi\)
\(104\) −9.72678 15.7927i −0.953789 1.54860i
\(105\) 0 0
\(106\) −0.958675 3.57782i −0.0931148 0.347509i
\(107\) −9.43055 −0.911686 −0.455843 0.890060i \(-0.650662\pi\)
−0.455843 + 0.890060i \(0.650662\pi\)
\(108\) 0 0
\(109\) 1.78152 + 6.64872i 0.170638 + 0.636832i 0.997254 + 0.0740637i \(0.0235968\pi\)
−0.826615 + 0.562768i \(0.809737\pi\)
\(110\) −7.17442 + 1.92238i −0.684054 + 0.183292i
\(111\) 0 0
\(112\) −4.94304 10.8874i −0.467074 1.02876i
\(113\) 2.13688 + 3.70118i 0.201020 + 0.348178i 0.948857 0.315705i \(-0.102241\pi\)
−0.747837 + 0.663882i \(0.768908\pi\)
\(114\) 0 0
\(115\) −3.96867 1.06340i −0.370080 0.0991627i
\(116\) 13.9014 + 8.02599i 1.29072 + 0.745195i
\(117\) 0 0
\(118\) 10.5712i 0.973160i
\(119\) −1.02073 2.24823i −0.0935698 0.206095i
\(120\) 0 0
\(121\) −21.1709 12.2230i −1.92462 1.11118i
\(122\) 18.5651 4.97451i 1.68081 0.450371i
\(123\) 0 0
\(124\) 2.60231 + 9.71194i 0.233694 + 0.872158i
\(125\) −3.48457 + 3.48457i −0.311670 + 0.311670i
\(126\) 0 0
\(127\) 9.06211 + 5.23201i 0.804132 + 0.464266i 0.844914 0.534902i \(-0.179652\pi\)
−0.0407820 + 0.999168i \(0.512985\pi\)
\(128\) 13.2819 + 13.2819i 1.17396 + 1.17396i
\(129\) 0 0
\(130\) 1.28725 + 4.30999i 0.112899 + 0.378011i
\(131\) 13.7862 7.95947i 1.20451 0.695422i 0.242952 0.970038i \(-0.421884\pi\)
0.961554 + 0.274617i \(0.0885509\pi\)
\(132\) 0 0
\(133\) −13.3281 16.2151i −1.15569 1.40603i
\(134\) 16.3070 9.41486i 1.40871 0.813320i
\(135\) 0 0
\(136\) −3.39463 3.39463i −0.291087 0.291087i
\(137\) 13.6514 + 13.6514i 1.16631 + 1.16631i 0.983067 + 0.183247i \(0.0586608\pi\)
0.183247 + 0.983067i \(0.441339\pi\)
\(138\) 0 0
\(139\) −6.10481 + 3.52462i −0.517804 + 0.298954i −0.736036 0.676943i \(-0.763304\pi\)
0.218232 + 0.975897i \(0.429971\pi\)
\(140\) 0.894551 + 5.39261i 0.0756034 + 0.455759i
\(141\) 0 0
\(142\) 14.4803 8.36022i 1.21516 0.701574i
\(143\) −10.2002 + 18.8879i −0.852987 + 1.57949i
\(144\) 0 0
\(145\) −1.40508 1.40508i −0.116686 0.116686i
\(146\) 27.0651 + 15.6260i 2.23992 + 1.29322i
\(147\) 0 0
\(148\) 3.51074 3.51074i 0.288581 0.288581i
\(149\) −3.76840 14.0639i −0.308720 1.15216i −0.929696 0.368328i \(-0.879930\pi\)
0.620976 0.783829i \(-0.286736\pi\)
\(150\) 0 0
\(151\) −4.94839 + 1.32592i −0.402694 + 0.107902i −0.454481 0.890757i \(-0.650175\pi\)
0.0517866 + 0.998658i \(0.483508\pi\)
\(152\) −35.3432 20.4054i −2.86672 1.65510i
\(153\) 0 0
\(154\) −22.6095 + 31.6025i −1.82193 + 2.54660i
\(155\) 1.24466i 0.0999735i
\(156\) 0 0
\(157\) 0.998876 + 0.576701i 0.0797190 + 0.0460258i 0.539330 0.842095i \(-0.318678\pi\)
−0.459611 + 0.888121i \(0.652011\pi\)
\(158\) −22.1156 5.92585i −1.75942 0.471435i
\(159\) 0 0
\(160\) 0.217473 + 0.376674i 0.0171927 + 0.0297787i
\(161\) −19.5721 + 8.88599i −1.54249 + 0.700314i
\(162\) 0 0
\(163\) −13.2155 + 3.54108i −1.03512 + 0.277359i −0.736089 0.676885i \(-0.763329\pi\)
−0.299029 + 0.954244i \(0.596663\pi\)
\(164\) 8.59276 + 32.0686i 0.670982 + 2.50414i
\(165\) 0 0
\(166\) 5.79354 0.449666
\(167\) 0.561041 + 2.09383i 0.0434146 + 0.162026i 0.984230 0.176894i \(-0.0566051\pi\)
−0.940815 + 0.338920i \(0.889938\pi\)
\(168\) 0 0
\(169\) 11.6096 + 5.84960i 0.893044 + 0.449970i
\(170\) 0.582126 + 1.00827i 0.0446470 + 0.0773309i
\(171\) 0 0
\(172\) 0.360116 + 0.623739i 0.0274586 + 0.0475596i
\(173\) −1.38571 + 2.40012i −0.105354 + 0.182478i −0.913883 0.405978i \(-0.866931\pi\)
0.808529 + 0.588456i \(0.200264\pi\)
\(174\) 0 0
\(175\) −1.22079 + 12.4926i −0.0922828 + 0.944350i
\(176\) −6.96390 + 25.9896i −0.524924 + 1.95904i
\(177\) 0 0
\(178\) 10.5380i 0.789854i
\(179\) −7.91226 + 4.56814i −0.591390 + 0.341439i −0.765647 0.643261i \(-0.777581\pi\)
0.174257 + 0.984700i \(0.444248\pi\)
\(180\) 0 0
\(181\) 12.3155 0.915405 0.457703 0.889105i \(-0.348672\pi\)
0.457703 + 0.889105i \(0.348672\pi\)
\(182\) 19.5201 + 13.1428i 1.44693 + 0.974206i
\(183\) 0 0
\(184\) −29.5521 + 29.5521i −2.17861 + 2.17861i
\(185\) −0.532271 + 0.307307i −0.0391333 + 0.0225936i
\(186\) 0 0
\(187\) −1.43803 + 5.36680i −0.105159 + 0.392459i
\(188\) −1.81535 + 6.77497i −0.132398 + 0.494115i
\(189\) 0 0
\(190\) 6.99843 + 6.99843i 0.507720 + 0.507720i
\(191\) −0.267357 + 0.463075i −0.0193452 + 0.0335069i −0.875536 0.483153i \(-0.839491\pi\)
0.856191 + 0.516660i \(0.172825\pi\)
\(192\) 0 0
\(193\) −1.74626 + 6.51711i −0.125698 + 0.469112i −0.999864 0.0165163i \(-0.994742\pi\)
0.874165 + 0.485628i \(0.161409\pi\)
\(194\) −4.08395 7.07361i −0.293211 0.507856i
\(195\) 0 0
\(196\) 21.5294 + 18.8227i 1.53781 + 1.34448i
\(197\) 0.252665 + 0.942958i 0.0180016 + 0.0671830i 0.974342 0.225071i \(-0.0722614\pi\)
−0.956341 + 0.292254i \(0.905595\pi\)
\(198\) 0 0
\(199\) −15.1705 −1.07541 −0.537703 0.843134i \(-0.680708\pi\)
−0.537703 + 0.843134i \(0.680708\pi\)
\(200\) 6.31658 + 23.5738i 0.446650 + 1.66692i
\(201\) 0 0
\(202\) 10.6603 + 2.85641i 0.750053 + 0.200976i
\(203\) −10.3463 1.01105i −0.726169 0.0709620i
\(204\) 0 0
\(205\) 4.10984i 0.287044i
\(206\) −9.89436 2.65119i −0.689373 0.184717i
\(207\) 0 0
\(208\) 15.8529 + 3.76819i 1.09920 + 0.261277i
\(209\) 47.2324i 3.26714i
\(210\) 0 0
\(211\) 10.0981 17.4904i 0.695180 1.20409i −0.274940 0.961461i \(-0.588658\pi\)
0.970120 0.242626i \(-0.0780088\pi\)
\(212\) 5.31241 + 3.06712i 0.364858 + 0.210651i
\(213\) 0 0
\(214\) 16.4500 16.4500i 1.12450 1.12450i
\(215\) −0.0230758 0.0861201i −0.00157376 0.00587334i
\(216\) 0 0
\(217\) −4.13471 5.03033i −0.280683 0.341481i
\(218\) −14.7051 8.48998i −0.995953 0.575014i
\(219\) 0 0
\(220\) 6.15033 10.6527i 0.414655 0.718204i
\(221\) 3.27359 + 0.778121i 0.220206 + 0.0523421i
\(222\) 0 0
\(223\) 18.5472 4.96970i 1.24201 0.332796i 0.422765 0.906239i \(-0.361059\pi\)
0.819245 + 0.573444i \(0.194393\pi\)
\(224\) 2.13022 + 0.799903i 0.142331 + 0.0534457i
\(225\) 0 0
\(226\) −10.1835 2.72865i −0.677394 0.181507i
\(227\) −15.5280 15.5280i −1.03063 1.03063i −0.999516 0.0311110i \(-0.990095\pi\)
−0.0311110 0.999516i \(-0.509905\pi\)
\(228\) 0 0
\(229\) 25.3854 + 6.80200i 1.67751 + 0.449489i 0.967121 0.254316i \(-0.0818503\pi\)
0.710394 + 0.703805i \(0.248517\pi\)
\(230\) 8.77757 5.06773i 0.578776 0.334156i
\(231\) 0 0
\(232\) −19.5238 + 5.23138i −1.28180 + 0.343457i
\(233\) 8.80891 5.08583i 0.577091 0.333184i −0.182886 0.983134i \(-0.558544\pi\)
0.759976 + 0.649951i \(0.225210\pi\)
\(234\) 0 0
\(235\) 0.434132 0.751939i 0.0283197 0.0490511i
\(236\) −12.3793 12.3793i −0.805823 0.805823i
\(237\) 0 0
\(238\) 5.70212 + 2.14116i 0.369613 + 0.138791i
\(239\) 0.836974 0.836974i 0.0541394 0.0541394i −0.679519 0.733658i \(-0.737811\pi\)
0.733658 + 0.679519i \(0.237811\pi\)
\(240\) 0 0
\(241\) −9.04828 + 9.04828i −0.582851 + 0.582851i −0.935686 0.352835i \(-0.885218\pi\)
0.352835 + 0.935686i \(0.385218\pi\)
\(242\) 58.2498 15.6080i 3.74444 1.00332i
\(243\) 0 0
\(244\) −15.9151 + 27.5658i −1.01886 + 1.76472i
\(245\) −1.97126 2.94047i −0.125939 0.187860i
\(246\) 0 0
\(247\) 28.5925 0.813213i 1.81930 0.0517435i
\(248\) −10.9644 6.33028i −0.696239 0.401973i
\(249\) 0 0
\(250\) 12.1565i 0.768842i
\(251\) −7.87428 13.6386i −0.497020 0.860864i 0.502974 0.864301i \(-0.332239\pi\)
−0.999994 + 0.00343776i \(0.998906\pi\)
\(252\) 0 0
\(253\) 46.7210 + 12.5188i 2.93732 + 0.787053i
\(254\) −24.9336 + 6.68093i −1.56447 + 0.419199i
\(255\) 0 0
\(256\) −32.5017 −2.03135
\(257\) 13.0956 0.816883 0.408442 0.912784i \(-0.366072\pi\)
0.408442 + 0.912784i \(0.366072\pi\)
\(258\) 0 0
\(259\) −1.13033 + 3.01017i −0.0702350 + 0.187043i
\(260\) −6.55458 3.53974i −0.406498 0.219526i
\(261\) 0 0
\(262\) −10.1637 + 37.9315i −0.627917 + 2.34342i
\(263\) −5.02804 8.70882i −0.310042 0.537009i 0.668329 0.743866i \(-0.267010\pi\)
−0.978371 + 0.206857i \(0.933676\pi\)
\(264\) 0 0
\(265\) −0.536951 0.536951i −0.0329846 0.0329846i
\(266\) 51.5329 + 5.03584i 3.15968 + 0.308767i
\(267\) 0 0
\(268\) −8.07097 + 30.1213i −0.493013 + 1.83995i
\(269\) 29.3765i 1.79112i 0.444942 + 0.895559i \(0.353224\pi\)
−0.444942 + 0.895559i \(0.646776\pi\)
\(270\) 0 0
\(271\) 1.15041 1.15041i 0.0698825 0.0698825i −0.671302 0.741184i \(-0.734265\pi\)
0.741184 + 0.671302i \(0.234265\pi\)
\(272\) 4.21755 0.255727
\(273\) 0 0
\(274\) −47.6248 −2.87712
\(275\) 19.9726 19.9726i 1.20440 1.20440i
\(276\) 0 0
\(277\) 30.7313i 1.84647i 0.384239 + 0.923233i \(0.374464\pi\)
−0.384239 + 0.923233i \(0.625536\pi\)
\(278\) 4.50070 16.7969i 0.269934 1.00741i
\(279\) 0 0
\(280\) −5.59797 4.00499i −0.334543 0.239344i
\(281\) 3.89852 + 3.89852i 0.232566 + 0.232566i 0.813763 0.581197i \(-0.197415\pi\)
−0.581197 + 0.813763i \(0.697415\pi\)
\(282\) 0 0
\(283\) −3.66949 6.35574i −0.218128 0.377809i 0.736107 0.676865i \(-0.236662\pi\)
−0.954236 + 0.299055i \(0.903328\pi\)
\(284\) −7.16687 + 26.7471i −0.425276 + 1.58715i
\(285\) 0 0
\(286\) −15.1541 50.7392i −0.896081 3.00027i
\(287\) −13.6527 16.6100i −0.805895 0.980459i
\(288\) 0 0
\(289\) −16.1291 −0.948770
\(290\) 4.90185 0.287846
\(291\) 0 0
\(292\) −49.9929 + 13.3955i −2.92561 + 0.783915i
\(293\) −21.1201 5.65910i −1.23385 0.330608i −0.417771 0.908552i \(-0.637188\pi\)
−0.816076 + 0.577944i \(0.803855\pi\)
\(294\) 0 0
\(295\) 1.08360 + 1.87685i 0.0630897 + 0.109275i
\(296\) 6.25179i 0.363378i
\(297\) 0 0
\(298\) 31.1053 + 17.9586i 1.80188 + 1.04032i
\(299\) 6.77398 28.4985i 0.391749 1.64811i
\(300\) 0 0
\(301\) −0.379349 0.271400i −0.0218653 0.0156432i
\(302\) 6.31877 10.9444i 0.363604 0.629781i
\(303\) 0 0
\(304\) 34.6317 9.27953i 1.98626 0.532217i
\(305\) 2.78621 2.78621i 0.159538 0.159538i
\(306\) 0 0
\(307\) 2.37972 2.37972i 0.135818 0.135818i −0.635929 0.771747i \(-0.719383\pi\)
0.771747 + 0.635929i \(0.219383\pi\)
\(308\) −10.5311 63.4843i −0.600063 3.61735i
\(309\) 0 0
\(310\) 2.17109 + 2.17109i 0.123310 + 0.123310i
\(311\) −6.25768 + 10.8386i −0.354841 + 0.614602i −0.987091 0.160162i \(-0.948798\pi\)
0.632250 + 0.774764i \(0.282132\pi\)
\(312\) 0 0
\(313\) 8.39852 4.84889i 0.474713 0.274075i −0.243498 0.969901i \(-0.578295\pi\)
0.718210 + 0.695826i \(0.244962\pi\)
\(314\) −2.74832 + 0.736410i −0.155097 + 0.0415580i
\(315\) 0 0
\(316\) 32.8376 18.9588i 1.84726 1.06651i
\(317\) 22.5235 + 6.03514i 1.26504 + 0.338967i 0.828130 0.560536i \(-0.189405\pi\)
0.436913 + 0.899504i \(0.356072\pi\)
\(318\) 0 0
\(319\) 16.5413 + 16.5413i 0.926135 + 0.926135i
\(320\) 3.37895 + 0.905386i 0.188889 + 0.0506126i
\(321\) 0 0
\(322\) 18.6400 49.6401i 1.03877 2.76633i
\(323\) 7.15135 1.91620i 0.397912 0.106620i
\(324\) 0 0
\(325\) −12.4345 11.7467i −0.689740 0.651591i
\(326\) 16.8753 29.2289i 0.934638 1.61884i
\(327\) 0 0
\(328\) −36.2041 20.9025i −1.99904 1.15414i
\(329\) −0.743354 4.48115i −0.0409824 0.247054i
\(330\) 0 0
\(331\) 6.22017 + 23.2140i 0.341892 + 1.27596i 0.896202 + 0.443647i \(0.146315\pi\)
−0.554310 + 0.832310i \(0.687018\pi\)
\(332\) −6.78445 + 6.78445i −0.372345 + 0.372345i
\(333\) 0 0
\(334\) −4.63096 2.67369i −0.253395 0.146298i
\(335\) 1.93014 3.34309i 0.105455 0.182653i
\(336\) 0 0
\(337\) 6.92235i 0.377085i 0.982065 + 0.188542i \(0.0603762\pi\)
−0.982065 + 0.188542i \(0.939624\pi\)
\(338\) −30.4545 + 10.0473i −1.65651 + 0.546499i
\(339\) 0 0
\(340\) −1.86241 0.499032i −0.101004 0.0270638i
\(341\) 14.6527i 0.793489i
\(342\) 0 0
\(343\) −17.7350 5.33556i −0.957602 0.288093i
\(344\) −0.876006 0.234725i −0.0472311 0.0126555i
\(345\) 0 0
\(346\) −1.76946 6.60373i −0.0951270 0.355019i
\(347\) −27.6471 −1.48418 −0.742088 0.670302i \(-0.766165\pi\)
−0.742088 + 0.670302i \(0.766165\pi\)
\(348\) 0 0
\(349\) −1.89736 7.08103i −0.101563 0.379039i 0.896369 0.443308i \(-0.146195\pi\)
−0.997933 + 0.0642689i \(0.979528\pi\)
\(350\) −19.6617 23.9206i −1.05096 1.27861i
\(351\) 0 0
\(352\) −2.56019 4.43438i −0.136459 0.236353i
\(353\) −6.64590 + 24.8028i −0.353725 + 1.32012i 0.528355 + 0.849023i \(0.322809\pi\)
−0.882081 + 0.471098i \(0.843858\pi\)
\(354\) 0 0
\(355\) 1.71393 2.96861i 0.0909657 0.157557i
\(356\) 12.3403 + 12.3403i 0.654037 + 0.654037i
\(357\) 0 0
\(358\) 5.83322 21.7699i 0.308295 1.15057i
\(359\) −0.592674 + 2.21189i −0.0312801 + 0.116739i −0.979801 0.199977i \(-0.935913\pi\)
0.948521 + 0.316716i \(0.102580\pi\)
\(360\) 0 0
\(361\) 38.0515 21.9690i 2.00271 1.15626i
\(362\) −21.4823 + 21.4823i −1.12908 + 1.12908i
\(363\) 0 0
\(364\) −38.2494 + 7.46809i −2.00481 + 0.391434i
\(365\) 6.40697 0.335356
\(366\) 0 0
\(367\) 23.3720 13.4938i 1.22001 0.704371i 0.255088 0.966918i \(-0.417896\pi\)
0.964919 + 0.262547i \(0.0845624\pi\)
\(368\) 36.7162i 1.91396i
\(369\) 0 0
\(370\) 0.392410 1.46450i 0.0204004 0.0761355i
\(371\) −3.95383 0.386372i −0.205273 0.0200595i
\(372\) 0 0
\(373\) 8.38541 14.5240i 0.434180 0.752022i −0.563048 0.826424i \(-0.690371\pi\)
0.997228 + 0.0744019i \(0.0237048\pi\)
\(374\) −6.85305 11.8698i −0.354363 0.613774i
\(375\) 0 0
\(376\) −4.41595 7.64865i −0.227735 0.394449i
\(377\) 9.72861 10.2982i 0.501049 0.530384i
\(378\) 0 0
\(379\) −6.13097 22.8811i −0.314927 1.17532i −0.924058 0.382253i \(-0.875148\pi\)
0.609131 0.793070i \(-0.291518\pi\)
\(380\) −16.3908 −0.840833
\(381\) 0 0
\(382\) −0.341397 1.27411i −0.0174674 0.0651892i
\(383\) −19.3985 + 5.19780i −0.991215 + 0.265595i −0.717761 0.696290i \(-0.754833\pi\)
−0.273454 + 0.961885i \(0.588166\pi\)
\(384\) 0 0
\(385\) −0.774771 + 7.92840i −0.0394860 + 0.404069i
\(386\) −8.32193 14.4140i −0.423575 0.733653i
\(387\) 0 0
\(388\) 13.0659 + 3.50100i 0.663321 + 0.177736i
\(389\) 28.3573 + 16.3721i 1.43777 + 0.830099i 0.997695 0.0678608i \(-0.0216174\pi\)
0.440078 + 0.897959i \(0.354951\pi\)
\(390\) 0 0
\(391\) 7.58180i 0.383428i
\(392\) −35.9288 + 2.40997i −1.81468 + 0.121722i
\(393\) 0 0
\(394\) −2.08555 1.20410i −0.105069 0.0606614i
\(395\) −4.53391 + 1.21486i −0.228126 + 0.0611261i
\(396\) 0 0
\(397\) −0.946584 3.53270i −0.0475077 0.177301i 0.938095 0.346377i \(-0.112588\pi\)
−0.985603 + 0.169076i \(0.945922\pi\)
\(398\) 26.4622 26.4622i 1.32643 1.32643i
\(399\) 0 0
\(400\) −18.5682 10.7204i −0.928411 0.536018i
\(401\) 3.97864 + 3.97864i 0.198684 + 0.198684i 0.799436 0.600752i \(-0.205132\pi\)
−0.600752 + 0.799436i \(0.705132\pi\)
\(402\) 0 0
\(403\) 8.87014 0.252279i 0.441853 0.0125669i
\(404\) −15.8285 + 9.13860i −0.787499 + 0.454663i
\(405\) 0 0
\(406\) 19.8110 16.2837i 0.983201 0.808149i
\(407\) 6.26613 3.61775i 0.310601 0.179325i
\(408\) 0 0
\(409\) −7.22691 7.22691i −0.357348 0.357348i 0.505487 0.862834i \(-0.331313\pi\)
−0.862834 + 0.505487i \(0.831313\pi\)
\(410\) 7.16890 + 7.16890i 0.354047 + 0.354047i
\(411\) 0 0
\(412\) 14.6913 8.48202i 0.723788 0.417879i
\(413\) 10.6142 + 3.98567i 0.522292 + 0.196122i
\(414\) 0 0
\(415\) 1.02861 0.593866i 0.0504923 0.0291517i
\(416\) −2.64031 + 1.62618i −0.129452 + 0.0797300i
\(417\) 0 0
\(418\) −82.3887 82.3887i −4.02976 4.02976i
\(419\) 12.7783 + 7.37756i 0.624261 + 0.360417i 0.778526 0.627612i \(-0.215968\pi\)
−0.154265 + 0.988029i \(0.549301\pi\)
\(420\) 0 0
\(421\) −15.6726 + 15.6726i −0.763838 + 0.763838i −0.977014 0.213176i \(-0.931619\pi\)
0.213176 + 0.977014i \(0.431619\pi\)
\(422\) 12.8946 + 48.1232i 0.627698 + 2.34260i
\(423\) 0 0
\(424\) −7.46098 + 1.99916i −0.362337 + 0.0970879i
\(425\) −3.83429 2.21373i −0.185990 0.107382i
\(426\) 0 0
\(427\) 2.00486 20.5162i 0.0970222 0.992849i
\(428\) 38.5270i 1.86227i
\(429\) 0 0
\(430\) 0.190473 + 0.109970i 0.00918543 + 0.00530321i
\(431\) 24.3888 + 6.53496i 1.17477 + 0.314778i 0.792849 0.609418i \(-0.208597\pi\)
0.381918 + 0.924196i \(0.375264\pi\)
\(432\) 0 0
\(433\) 12.7247 + 22.0399i 0.611512 + 1.05917i 0.990986 + 0.133967i \(0.0427717\pi\)
−0.379474 + 0.925203i \(0.623895\pi\)
\(434\) 15.9868 + 1.56225i 0.767391 + 0.0749903i
\(435\) 0 0
\(436\) 27.1623 7.27811i 1.30084 0.348558i
\(437\) −16.6816 62.2565i −0.797989 2.97813i
\(438\) 0 0
\(439\) −12.5999 −0.601362 −0.300681 0.953725i \(-0.597214\pi\)
−0.300681 + 0.953725i \(0.597214\pi\)
\(440\) 4.00881 + 14.9611i 0.191113 + 0.713242i
\(441\) 0 0
\(442\) −7.06751 + 4.35292i −0.336167 + 0.207047i
\(443\) 5.24317 + 9.08144i 0.249111 + 0.431472i 0.963279 0.268501i \(-0.0865284\pi\)
−0.714169 + 0.699974i \(0.753195\pi\)
\(444\) 0 0
\(445\) −1.08019 1.87095i −0.0512060 0.0886914i
\(446\) −23.6835 + 41.0211i −1.12145 + 1.94240i
\(447\) 0 0
\(448\) 16.6638 7.56558i 0.787288 0.357440i
\(449\) 1.45535 5.43146i 0.0686824 0.256326i −0.923044 0.384694i \(-0.874307\pi\)
0.991727 + 0.128368i \(0.0409737\pi\)
\(450\) 0 0
\(451\) 48.3829i 2.27826i
\(452\) 15.1206 8.72987i 0.711212 0.410618i
\(453\) 0 0
\(454\) 54.1716 2.54240
\(455\) 4.81286 + 0.332509i 0.225630 + 0.0155883i
\(456\) 0 0
\(457\) 8.37852 8.37852i 0.391930 0.391930i −0.483445 0.875375i \(-0.660615\pi\)
0.875375 + 0.483445i \(0.160615\pi\)
\(458\) −56.1453 + 32.4155i −2.62350 + 1.51468i
\(459\) 0 0
\(460\) −4.34436 + 16.2134i −0.202557 + 0.755952i
\(461\) 2.12757 7.94019i 0.0990907 0.369812i −0.898517 0.438938i \(-0.855355\pi\)
0.997608 + 0.0691268i \(0.0220213\pi\)
\(462\) 0 0
\(463\) −21.3807 21.3807i −0.993646 0.993646i 0.00633382 0.999980i \(-0.497984\pi\)
−0.999980 + 0.00633382i \(0.997984\pi\)
\(464\) 8.87858 15.3782i 0.412178 0.713913i
\(465\) 0 0
\(466\) −6.49427 + 24.2369i −0.300841 + 1.12275i
\(467\) −14.3612 24.8744i −0.664559 1.15105i −0.979405 0.201907i \(-0.935286\pi\)
0.314846 0.949143i \(-0.398047\pi\)
\(468\) 0 0
\(469\) −3.30493 19.9230i −0.152607 0.919961i
\(470\) 0.554358 + 2.06889i 0.0255706 + 0.0954309i
\(471\) 0 0
\(472\) 22.0446 1.01468
\(473\) 0.271659 + 1.01384i 0.0124909 + 0.0466166i
\(474\) 0 0
\(475\) −36.3552 9.74136i −1.66809 0.446964i
\(476\) −9.18477 + 4.17001i −0.420983 + 0.191132i
\(477\) 0 0
\(478\) 2.91991i 0.133554i
\(479\) −16.5106 4.42401i −0.754390 0.202138i −0.138925 0.990303i \(-0.544365\pi\)
−0.615464 + 0.788165i \(0.711032\pi\)
\(480\) 0 0
\(481\) −2.29792 3.73097i −0.104776 0.170117i
\(482\) 31.5663i 1.43780i
\(483\) 0 0
\(484\) −49.9351 + 86.4902i −2.26978 + 3.93137i
\(485\) −1.45016 0.837249i −0.0658483 0.0380175i
\(486\) 0 0
\(487\) −10.7094 + 10.7094i −0.485290 + 0.485290i −0.906816 0.421526i \(-0.861494\pi\)
0.421526 + 0.906816i \(0.361494\pi\)
\(488\) −10.3735 38.7146i −0.469588 1.75253i
\(489\) 0 0
\(490\) 8.56766 + 1.69063i 0.387048 + 0.0763747i
\(491\) −4.15520 2.39900i −0.187521 0.108266i 0.403300 0.915068i \(-0.367863\pi\)
−0.590822 + 0.806802i \(0.701196\pi\)
\(492\) 0 0
\(493\) 1.83341 3.17555i 0.0825724 0.143020i
\(494\) −48.4562 + 51.2932i −2.18015 + 2.30779i
\(495\) 0 0
\(496\) 10.7436 2.87875i 0.482403 0.129259i
\(497\) −2.93471 17.6913i −0.131640 0.793563i
\(498\) 0 0
\(499\) −14.5993 3.91188i −0.653556 0.175120i −0.0832201 0.996531i \(-0.526520\pi\)
−0.570336 + 0.821411i \(0.693187\pi\)
\(500\) 14.2357 + 14.2357i 0.636638 + 0.636638i
\(501\) 0 0
\(502\) 37.5255 + 10.0549i 1.67485 + 0.448774i
\(503\) 13.9638 8.06201i 0.622615 0.359467i −0.155271 0.987872i \(-0.549625\pi\)
0.777887 + 0.628405i \(0.216292\pi\)
\(504\) 0 0
\(505\) 2.18546 0.585591i 0.0972515 0.0260585i
\(506\) −103.334 + 59.6596i −4.59373 + 2.65219i
\(507\) 0 0
\(508\) 21.3745 37.0218i 0.948342 1.64258i
\(509\) 23.4399 + 23.4399i 1.03896 + 1.03896i 0.999210 + 0.0397455i \(0.0126547\pi\)
0.0397455 + 0.999210i \(0.487345\pi\)
\(510\) 0 0
\(511\) 25.8940 21.2837i 1.14548 0.941536i
\(512\) 30.1297 30.1297i 1.33156 1.33156i
\(513\) 0 0
\(514\) −22.8430 + 22.8430i −1.00756 + 1.00756i
\(515\) −2.02844 + 0.543518i −0.0893837 + 0.0239503i
\(516\) 0 0
\(517\) −5.11080 + 8.85217i −0.224773 + 0.389318i
\(518\) −3.27906 7.22237i −0.144074 0.317333i
\(519\) 0 0
\(520\) 8.98780 2.68436i 0.394141 0.117717i
\(521\) 8.41886 + 4.86063i 0.368837 + 0.212948i 0.672950 0.739688i \(-0.265027\pi\)
−0.304113 + 0.952636i \(0.598360\pi\)
\(522\) 0 0
\(523\) 19.4487i 0.850434i 0.905091 + 0.425217i \(0.139802\pi\)
−0.905091 + 0.425217i \(0.860198\pi\)
\(524\) −32.5171 56.3213i −1.42052 2.46041i
\(525\) 0 0
\(526\) 23.9615 + 6.42047i 1.04477 + 0.279946i
\(527\) 2.21853 0.594454i 0.0966408 0.0258948i
\(528\) 0 0
\(529\) −43.0038 −1.86973
\(530\) 1.87323 0.0813681
\(531\) 0 0
\(532\) −66.2441 + 54.4498i −2.87204 + 2.36070i
\(533\) 29.2890 0.833021i 1.26865 0.0360821i
\(534\) 0 0
\(535\) 1.23438 4.60678i 0.0533671 0.199169i
\(536\) −19.6332 34.0057i −0.848024 1.46882i
\(537\) 0 0
\(538\) −51.2422 51.2422i −2.20921 2.20921i
\(539\) 23.2066 + 34.6166i 0.999578 + 1.49104i
\(540\) 0 0
\(541\) 2.74629 10.2493i 0.118072 0.440652i −0.881426 0.472322i \(-0.843416\pi\)
0.999498 + 0.0316700i \(0.0100826\pi\)
\(542\) 4.01338i 0.172389i
\(543\) 0 0
\(544\) −0.567533 + 0.567533i −0.0243328 + 0.0243328i
\(545\) −3.48105 −0.149112
\(546\) 0 0
\(547\) −23.4548 −1.00285 −0.501427 0.865200i \(-0.667192\pi\)
−0.501427 + 0.865200i \(0.667192\pi\)
\(548\) 55.7704 55.7704i 2.38239 2.38239i
\(549\) 0 0
\(550\) 69.6775i 2.97106i
\(551\) 8.06777 30.1093i 0.343699 1.28270i
\(552\) 0 0
\(553\) −14.2882 + 19.9713i −0.607596 + 0.849267i
\(554\) −53.6054 53.6054i −2.27748 2.27748i
\(555\) 0 0
\(556\) 14.3993 + 24.9402i 0.610664 + 1.05770i
\(557\) −5.18753 + 19.3601i −0.219803 + 0.820315i 0.764618 + 0.644484i \(0.222928\pi\)
−0.984420 + 0.175831i \(0.943739\pi\)
\(558\) 0 0
\(559\) 0.609062 0.181907i 0.0257606 0.00769383i
\(560\) 5.96546 0.989578i 0.252087 0.0418173i
\(561\) 0 0
\(562\) −13.6006 −0.573706
\(563\) 45.7544 1.92832 0.964159 0.265327i \(-0.0854799\pi\)
0.964159 + 0.265327i \(0.0854799\pi\)
\(564\) 0 0
\(565\) −2.08771 + 0.559400i −0.0878306 + 0.0235341i
\(566\) 17.4872 + 4.68569i 0.735044 + 0.196954i
\(567\) 0 0
\(568\) −17.4339 30.1964i −0.731510 1.26701i
\(569\) 24.1207i 1.01119i −0.862771 0.505595i \(-0.831273\pi\)
0.862771 0.505595i \(-0.168727\pi\)
\(570\) 0 0
\(571\) −15.0931 8.71402i −0.631628 0.364671i 0.149754 0.988723i \(-0.452152\pi\)
−0.781382 + 0.624053i \(0.785485\pi\)
\(572\) 77.1635 + 41.6715i 3.22637 + 1.74237i
\(573\) 0 0
\(574\) 52.7881 + 5.15850i 2.20333 + 0.215312i
\(575\) −19.2717 + 33.3796i −0.803687 + 1.39203i
\(576\) 0 0
\(577\) 21.0789 5.64807i 0.877525 0.235132i 0.208186 0.978089i \(-0.433244\pi\)
0.669339 + 0.742957i \(0.266577\pi\)
\(578\) 28.1344 28.1344i 1.17024 1.17024i
\(579\) 0 0
\(580\) −5.74025 + 5.74025i −0.238351 + 0.238351i
\(581\) 2.18434 5.81711i 0.0906217 0.241334i
\(582\) 0 0
\(583\) 6.32123 + 6.32123i 0.261799 + 0.261799i
\(584\) 32.5856 56.4399i 1.34840 2.33550i
\(585\) 0 0
\(586\) 46.7116 26.9689i 1.92964 1.11408i
\(587\) −13.4282 + 3.59809i −0.554243 + 0.148509i −0.525060 0.851065i \(-0.675957\pi\)
−0.0291829 + 0.999574i \(0.509291\pi\)
\(588\) 0 0
\(589\) 16.9091 9.76250i 0.696729 0.402257i
\(590\) −5.16399 1.38369i −0.212598 0.0569655i
\(591\) 0 0
\(592\) −3.88368 3.88368i −0.159618 0.159618i
\(593\) 32.5656 + 8.72592i 1.33731 + 0.358331i 0.855435 0.517911i \(-0.173290\pi\)
0.481873 + 0.876241i \(0.339957\pi\)
\(594\) 0 0
\(595\) 1.23185 0.204345i 0.0505010 0.00837735i
\(596\) −57.4557 + 15.3952i −2.35348 + 0.630612i
\(597\) 0 0
\(598\) 37.8946 + 61.5266i 1.54962 + 2.51601i
\(599\) 6.39544 11.0772i 0.261311 0.452603i −0.705280 0.708929i \(-0.749179\pi\)
0.966590 + 0.256326i \(0.0825120\pi\)
\(600\) 0 0
\(601\) 26.5897 + 15.3516i 1.08462 + 0.626205i 0.932138 0.362102i \(-0.117941\pi\)
0.152480 + 0.988307i \(0.451274\pi\)
\(602\) 1.13512 0.188299i 0.0462639 0.00767448i
\(603\) 0 0
\(604\) 5.41682 + 20.2158i 0.220407 + 0.822571i
\(605\) 8.74198 8.74198i 0.355412 0.355412i
\(606\) 0 0
\(607\) 23.2575 + 13.4277i 0.943992 + 0.545014i 0.891210 0.453592i \(-0.149858\pi\)
0.0527827 + 0.998606i \(0.483191\pi\)
\(608\) −3.41150 + 5.90889i −0.138355 + 0.239637i
\(609\) 0 0
\(610\) 9.72010i 0.393555i
\(611\) 5.44672 + 2.94145i 0.220351 + 0.118999i
\(612\) 0 0
\(613\) 10.3125 + 2.76321i 0.416516 + 0.111605i 0.460990 0.887405i \(-0.347494\pi\)
−0.0444737 + 0.999011i \(0.514161\pi\)
\(614\) 8.30201i 0.335042i
\(615\) 0 0
\(616\) 65.9019 + 47.1485i 2.65526 + 1.89967i
\(617\) 8.37021 + 2.24279i 0.336972 + 0.0902913i 0.423337 0.905972i \(-0.360859\pi\)
−0.0863653 + 0.996264i \(0.527525\pi\)
\(618\) 0 0
\(619\) −1.40877 5.25761i −0.0566233 0.211321i 0.931818 0.362926i \(-0.118222\pi\)
−0.988441 + 0.151605i \(0.951556\pi\)
\(620\) −5.08486 −0.204213
\(621\) 0 0
\(622\) −7.99065 29.8215i −0.320396 1.19573i
\(623\) −10.5808 3.97313i −0.423912 0.159180i
\(624\) 0 0
\(625\) 10.6145 + 18.3849i 0.424580 + 0.735394i
\(626\) −6.19171 + 23.1078i −0.247471 + 0.923573i
\(627\) 0 0
\(628\) 2.35602 4.08075i 0.0940154 0.162839i
\(629\) −0.801970 0.801970i −0.0319766 0.0319766i
\(630\) 0 0
\(631\) 1.72756 6.44735i 0.0687731 0.256665i −0.922976 0.384857i \(-0.874251\pi\)
0.991749 + 0.128192i \(0.0409174\pi\)
\(632\) −12.3574 + 46.1185i −0.491551 + 1.83449i
\(633\) 0 0
\(634\) −49.8155 + 28.7610i −1.97842 + 1.14224i
\(635\) −3.74197 + 3.74197i −0.148495 + 0.148495i
\(636\) 0 0
\(637\) 20.5559 14.6443i 0.814454 0.580228i
\(638\) −57.7068 −2.28463
\(639\) 0 0
\(640\) −8.22661 + 4.74964i −0.325185 + 0.187746i
\(641\) 3.66669i 0.144826i −0.997375 0.0724129i \(-0.976930\pi\)
0.997375 0.0724129i \(-0.0230699\pi\)
\(642\) 0 0
\(643\) −4.98038 + 18.5870i −0.196407 + 0.733001i 0.795491 + 0.605965i \(0.207213\pi\)
−0.991898 + 0.127036i \(0.959454\pi\)
\(644\) 36.3023 + 79.9585i 1.43051 + 3.15081i
\(645\) 0 0
\(646\) −9.13181 + 15.8168i −0.359286 + 0.622302i
\(647\) −1.07235 1.85736i −0.0421583 0.0730204i 0.844176 0.536066i \(-0.180090\pi\)
−0.886335 + 0.463045i \(0.846757\pi\)
\(648\) 0 0
\(649\) −12.7566 22.0952i −0.500742 0.867311i
\(650\) 42.1799 1.19966i 1.65443 0.0470544i
\(651\) 0 0
\(652\) 14.4665 + 53.9898i 0.566553 + 2.11440i
\(653\) 22.7955 0.892057 0.446029 0.895019i \(-0.352838\pi\)
0.446029 + 0.895019i \(0.352838\pi\)
\(654\) 0 0
\(655\) 2.08366 + 7.77632i 0.0814153 + 0.303846i
\(656\) 35.4752 9.50555i 1.38507 0.371129i
\(657\) 0 0
\(658\) 9.11323 + 6.51993i 0.355271 + 0.254173i
\(659\) 16.2426 + 28.1330i 0.632721 + 1.09591i 0.986993 + 0.160763i \(0.0513954\pi\)
−0.354272 + 0.935142i \(0.615271\pi\)
\(660\) 0 0
\(661\) −33.3853 8.94556i −1.29854 0.347942i −0.457641 0.889137i \(-0.651305\pi\)
−0.840897 + 0.541195i \(0.817972\pi\)
\(662\) −51.3428 29.6428i −1.99549 1.15210i
\(663\) 0 0
\(664\) 12.0815i 0.468853i
\(665\) 9.66553 4.38829i 0.374813 0.170170i
\(666\) 0 0
\(667\) −27.6450 15.9608i −1.07042 0.618005i
\(668\) 8.55402 2.29204i 0.330965 0.0886818i
\(669\) 0 0
\(670\) 2.46466 + 9.19823i 0.0952180 + 0.355359i
\(671\) −32.8005 + 32.8005i −1.26625 + 1.26625i
\(672\) 0 0
\(673\) −14.0303 8.10040i −0.540828 0.312247i 0.204586 0.978849i \(-0.434415\pi\)
−0.745415 + 0.666601i \(0.767748\pi\)
\(674\) −12.0748 12.0748i −0.465105 0.465105i
\(675\) 0 0
\(676\) 23.8976 47.4290i 0.919139 1.82419i
\(677\) −16.1987 + 9.35233i −0.622567 + 0.359439i −0.777868 0.628428i \(-0.783699\pi\)
0.155301 + 0.987867i \(0.450365\pi\)
\(678\) 0 0
\(679\) −8.64216 + 1.43360i −0.331656 + 0.0550166i
\(680\) 2.10259 1.21393i 0.0806306 0.0465521i
\(681\) 0 0
\(682\) −25.5591 25.5591i −0.978708 0.978708i
\(683\) −5.04992 5.04992i −0.193230 0.193230i 0.603860 0.797090i \(-0.293628\pi\)
−0.797090 + 0.603860i \(0.793628\pi\)
\(684\) 0 0
\(685\) −8.45547 + 4.88177i −0.323067 + 0.186523i
\(686\) 40.2426 21.6287i 1.53647 0.825788i
\(687\) 0 0
\(688\) 0.689998 0.398370i 0.0263059 0.0151877i
\(689\) 3.71777 3.93544i 0.141636 0.149928i
\(690\) 0 0
\(691\) 33.0564 + 33.0564i 1.25752 + 1.25752i 0.952271 + 0.305253i \(0.0987412\pi\)
0.305253 + 0.952271i \(0.401259\pi\)
\(692\) 9.80532 + 5.66110i 0.372742 + 0.215203i
\(693\) 0 0
\(694\) 48.2256 48.2256i 1.83062 1.83062i
\(695\) −0.922688 3.44352i −0.0349995 0.130620i
\(696\) 0 0
\(697\) 7.32554 1.96287i 0.277475 0.0743491i
\(698\) 15.6612 + 9.04201i 0.592786 + 0.342245i
\(699\) 0 0
\(700\) 51.0364 + 4.98733i 1.92899 + 0.188503i
\(701\) 12.2740i 0.463581i 0.972766 + 0.231790i \(0.0744584\pi\)
−0.972766 + 0.231790i \(0.925542\pi\)
\(702\) 0 0
\(703\) −8.34973 4.82072i −0.314916 0.181817i
\(704\) −39.7785 10.6586i −1.49921 0.401712i
\(705\) 0 0
\(706\) −31.6716 54.8568i −1.19198 2.06456i
\(707\) 6.88727 9.62668i 0.259023 0.362049i
\(708\) 0 0
\(709\) 42.5380 11.3980i 1.59755 0.428062i 0.653247 0.757145i \(-0.273406\pi\)
0.944301 + 0.329084i \(0.106740\pi\)
\(710\) 2.18857 + 8.16786i 0.0821356 + 0.306534i
\(711\) 0 0
\(712\) −21.9752 −0.823556
\(713\) −5.17505 19.3136i −0.193807 0.723299i
\(714\) 0 0
\(715\) −7.89153 7.45505i −0.295126 0.278803i
\(716\) 18.6624 + 32.3242i 0.697447 + 1.20801i
\(717\) 0 0
\(718\) −2.82444 4.89207i −0.105407 0.182570i
\(719\) −0.267002 + 0.462460i −0.00995748 + 0.0172469i −0.870961 0.491352i \(-0.836503\pi\)
0.861004 + 0.508599i \(0.169836\pi\)
\(720\) 0 0
\(721\) −6.39244 + 8.93504i −0.238067 + 0.332758i
\(722\) −28.0530 + 104.695i −1.04403 + 3.89635i
\(723\) 0 0
\(724\) 50.3131i 1.86987i
\(725\) −16.1435 + 9.32046i −0.599555 + 0.346153i
\(726\) 0 0
\(727\) −17.0326 −0.631703 −0.315851 0.948809i \(-0.602290\pi\)
−0.315851 + 0.948809i \(0.602290\pi\)
\(728\) 27.4071 40.7060i 1.01577 1.50866i
\(729\) 0 0
\(730\) −11.1758 + 11.1758i −0.413636 + 0.413636i
\(731\) 0.142483 0.0822625i 0.00526992 0.00304259i
\(732\) 0 0
\(733\) −7.48252 + 27.9251i −0.276373 + 1.03144i 0.678542 + 0.734561i \(0.262612\pi\)
−0.954916 + 0.296877i \(0.904055\pi\)
\(734\) −17.2307 + 64.3059i −0.635997 + 2.37357i
\(735\) 0 0
\(736\) 4.94070 + 4.94070i 0.182116 + 0.182116i
\(737\) −22.7224 + 39.3564i −0.836992 + 1.44971i
\(738\) 0 0
\(739\) −3.67777 + 13.7256i −0.135289 + 0.504906i 0.864707 + 0.502276i \(0.167504\pi\)
−0.999997 + 0.00262992i \(0.999163\pi\)
\(740\) 1.25545 + 2.17451i 0.0461513 + 0.0799364i
\(741\) 0 0
\(742\) 7.57072 6.22281i 0.277930 0.228446i
\(743\) −12.9109 48.1840i −0.473654 1.76770i −0.626470 0.779446i \(-0.715501\pi\)
0.152816 0.988255i \(-0.451166\pi\)
\(744\) 0 0
\(745\) 7.36339 0.269774
\(746\) 10.7076 + 39.9614i 0.392034 + 1.46309i
\(747\) 0 0
\(748\) 21.9252 + 5.87484i 0.801664 + 0.214805i
\(749\) −10.3148 22.7190i −0.376893 0.830135i
\(750\) 0 0
\(751\) 5.71485i 0.208538i −0.994549 0.104269i \(-0.966750\pi\)
0.994549 0.104269i \(-0.0332503\pi\)
\(752\) 7.49466 + 2.00819i 0.273302 + 0.0732311i
\(753\) 0 0
\(754\) 0.993553 + 34.9333i 0.0361831 + 1.27219i
\(755\) 2.59082i 0.0942894i
\(756\) 0 0
\(757\) −8.98844 + 15.5684i −0.326690 + 0.565844i −0.981853 0.189643i \(-0.939267\pi\)
0.655163 + 0.755488i \(0.272600\pi\)
\(758\) 50.6065 + 29.2177i 1.83811 + 1.06123i
\(759\) 0 0
\(760\) 14.5941 14.5941i 0.529384 0.529384i
\(761\) −9.13126 34.0783i −0.331008 1.23534i −0.908133 0.418682i \(-0.862492\pi\)
0.577125 0.816656i \(-0.304175\pi\)
\(762\) 0 0
\(763\) −14.0688 + 11.5639i −0.509324 + 0.418642i
\(764\) 1.89182 + 1.09224i 0.0684436 + 0.0395159i
\(765\) 0 0
\(766\) 24.7706 42.9039i 0.894997 1.55018i
\(767\) −13.1558 + 8.10275i −0.475030 + 0.292574i
\(768\) 0 0
\(769\) −31.5109 + 8.44333i −1.13631 + 0.304474i −0.777468 0.628923i \(-0.783496\pi\)
−0.358845 + 0.933397i \(0.616829\pi\)
\(770\) −12.4783 15.1812i −0.449685 0.547091i
\(771\) 0 0
\(772\) 26.6246 + 7.13404i 0.958241 + 0.256760i
\(773\) −21.4303 21.4303i −0.770796 0.770796i 0.207450 0.978246i \(-0.433484\pi\)
−0.978246 + 0.207450i \(0.933484\pi\)
\(774\) 0 0
\(775\) −11.2783 3.02202i −0.405129 0.108554i
\(776\) −14.7509 + 8.51642i −0.529526 + 0.305722i
\(777\) 0 0
\(778\) −78.0226 + 20.9061i −2.79725 + 0.749520i
\(779\) 55.8336 32.2355i 2.00045 1.15496i
\(780\) 0 0
\(781\) −20.1771 + 34.9478i −0.721994 + 1.25053i
\(782\) 13.2251 + 13.2251i 0.472929 + 0.472929i
\(783\) 0 0
\(784\) 20.8222 23.8164i 0.743651 0.850587i
\(785\) −0.412461 + 0.412461i −0.0147213 + 0.0147213i
\(786\) 0 0
\(787\) 8.37433 8.37433i 0.298513 0.298513i −0.541918 0.840431i \(-0.682302\pi\)
0.840431 + 0.541918i \(0.182302\pi\)
\(788\) 3.85230 1.03222i 0.137233 0.0367714i