Properties

Label 819.2.et.c.271.1
Level $819$
Weight $2$
Character 819.271
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 271.1
Character \(\chi\) \(=\) 819.271
Dual form 819.2.et.c.136.1

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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 −0.962640 0.270784i \(-0.912717\pi\)
−0.270784 0.962640i \(-0.587283\pi\)
\(3\) 0 0
\(4\) 4.08534i 2.04267i
\(5\) −0.130892 0.488495i −0.0585366 0.218462i 0.930461 0.366390i \(-0.119406\pi\)
−0.988998 + 0.147928i \(0.952740\pi\)
\(6\) 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 0.658197 + 0.752846i \(0.271320\pi\)
−0.193592 + 0.981082i \(0.562014\pi\)
\(12\) 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 −0.771711 0.635973i \(-0.780599\pi\)
−0.986308 + 0.164913i \(0.947266\pi\)
\(20\) 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 \(-0.678398\pi\)
0.531571 0.847014i \(-0.321602\pi\)
\(24\) 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 0.623932 0.781479i \(-0.285534\pi\)
−0.988746 + 0.149602i \(0.952201\pi\)
\(30\) 0 0
\(31\) −2.37727 0.636987i −0.426970 0.114406i 0.0389336 0.999242i \(-0.487604\pi\)
−0.465903 + 0.884836i \(0.654271\pi\)
\(32\) 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 −0.632932 0.774208i \(-0.718149\pi\)
0.774208 + 0.632932i \(0.218149\pi\)
\(38\) 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 −0.412927 0.910764i \(-0.635494\pi\)
−0.812987 + 0.582281i \(0.802160\pi\)
\(42\) 0 0
\(43\) −0.152677 0.0881483i −0.0232831 0.0134425i 0.488313 0.872668i \(-0.337612\pi\)
−0.511596 + 0.859226i \(0.670946\pi\)
\(44\) −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 −0.377730 0.925916i \(-0.623295\pi\)
0.135834 + 0.990732i \(0.456629\pi\)
\(48\) 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 0.809845 0.586643i \(-0.199551\pi\)
−0.912971 + 0.408025i \(0.866218\pi\)
\(54\) 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 0.876286 0.481791i \(-0.160014\pi\)
−0.481791 + 0.876286i \(0.660014\pi\)
\(60\) 0 0
\(61\) −6.74749 + 3.89567i −0.863928 + 0.498789i −0.865326 0.501210i \(-0.832888\pi\)
0.00139788 + 0.999999i \(0.499555\pi\)
\(62\) 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 −0.679341 0.733822i \(-0.737734\pi\)
−0.221416 + 0.975179i \(0.571068\pi\)
\(68\) 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 −0.625461 0.780256i \(-0.715089\pi\)
−0.151537 + 0.988452i \(0.548422\pi\)
\(72\) 0 0
\(73\) −3.27893 + 12.2371i −0.383770 + 1.43225i 0.456327 + 0.889812i \(0.349165\pi\)
−0.840097 + 0.542437i \(0.817502\pi\)
\(74\) −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 −0.477551 0.878604i \(-0.658475\pi\)
0.999669 0.0257307i \(-0.00819123\pi\)
\(80\) 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 −0.792350 0.610067i \(-0.791143\pi\)
0.610067 + 0.792350i \(0.291143\pi\)
\(84\) 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 0.528652 0.848839i \(-0.322698\pi\)
−0.848839 + 0.528652i \(0.822698\pi\)
\(90\) 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 0.908676 0.417503i \(-0.137095\pi\)
−0.995688 + 0.0927700i \(0.970428\pi\)
\(98\) −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 −0.955591 0.294695i \(-0.904782\pi\)
0.733009 + 0.680219i \(0.238115\pi\)
\(102\) 0 0
\(103\) 2.07621 3.59610i 0.204575 0.354335i −0.745422 0.666593i \(-0.767752\pi\)
0.949997 + 0.312258i \(0.101085\pi\)
\(104\) −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 −0.826615 0.562768i \(-0.809737\pi\)
0.997254 0.0740637i \(-0.0235968\pi\)
\(110\) −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 −0.747837 0.663882i \(-0.768908\pi\)
0.948857 + 0.315705i \(0.102241\pi\)
\(114\) 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 −0.0407820 0.999168i \(-0.512985\pi\)
0.844914 + 0.534902i \(0.179652\pi\)
\(128\) 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 0.961554 0.274617i \(-0.0885509\pi\)
0.242952 + 0.970038i \(0.421884\pi\)
\(132\) 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 0.183247 0.983067i \(-0.441339\pi\)
0.983067 0.183247i \(-0.0586608\pi\)
\(138\) 0 0
\(139\) −6.10481 3.52462i −0.517804 0.298954i 0.218232 0.975897i \(-0.429971\pi\)
−0.736036 + 0.676943i \(0.763304\pi\)
\(140\) 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 0.620976 + 0.783829i \(0.286736\pi\)
−0.929696 + 0.368328i \(0.879930\pi\)
\(150\) 0 0
\(151\) −4.94839 1.32592i −0.402694 0.107902i 0.0517866 0.998658i \(-0.483508\pi\)
−0.454481 + 0.890757i \(0.650175\pi\)
\(152\) −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 −0.459611 0.888121i \(-0.652011\pi\)
0.539330 + 0.842095i \(0.318678\pi\)
\(158\) −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 −0.299029 0.954244i \(-0.596663\pi\)
−0.736089 + 0.676885i \(0.763329\pi\)
\(164\) 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 −0.940815 0.338920i \(-0.889938\pi\)
0.984230 + 0.176894i \(0.0566051\pi\)
\(168\) 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 0.808529 0.588456i \(-0.200264\pi\)
−0.913883 + 0.405978i \(0.866931\pi\)
\(174\) 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 0.174257 0.984700i \(-0.444248\pi\)
−0.765647 + 0.643261i \(0.777581\pi\)
\(180\) 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 0.856191 0.516660i \(-0.172825\pi\)
−0.875536 + 0.483153i \(0.839491\pi\)
\(192\) 0 0
\(193\) −1.74626 6.51711i −0.125698 0.469112i 0.874165 0.485628i \(-0.161409\pi\)
−0.999864 + 0.0165163i \(0.994742\pi\)
\(194\) −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 −0.956341 0.292254i \(-0.905595\pi\)
0.974342 + 0.225071i \(0.0722614\pi\)
\(198\) 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 0.970120 + 0.242626i \(0.0780088\pi\)
−0.274940 + 0.961461i \(0.588658\pi\)
\(212\) 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 0.819245 0.573444i \(-0.194393\pi\)
0.422765 + 0.906239i \(0.361059\pi\)
\(224\) 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 −0.0311110 + 0.999516i \(0.509905\pi\)
−0.999516 + 0.0311110i \(0.990095\pi\)
\(228\) 0 0
\(229\) 25.3854 6.80200i 1.67751 0.449489i 0.710394 0.703805i \(-0.248517\pi\)
0.967121 + 0.254316i \(0.0818503\pi\)
\(230\) 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 0.759976 0.649951i \(-0.225210\pi\)
−0.182886 + 0.983134i \(0.558544\pi\)
\(234\) 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 0.733658 0.679519i \(-0.237811\pi\)
−0.679519 + 0.733658i \(0.737811\pi\)
\(240\) 0 0
\(241\) −9.04828 9.04828i −0.582851 0.582851i 0.352835 0.935686i \(-0.385218\pi\)
−0.935686 + 0.352835i \(0.885218\pi\)
\(242\) 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 −0.999994 0.00343776i \(-0.998906\pi\)
0.502974 + 0.864301i \(0.332239\pi\)
\(252\) 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 −0.978371 0.206857i \(-0.933676\pi\)
0.668329 + 0.743866i \(0.267010\pi\)
\(264\) 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 \(-0.646776\pi\)
0.444942 0.895559i \(-0.353224\pi\)
\(270\) 0 0
\(271\) 1.15041 + 1.15041i 0.0698825 + 0.0698825i 0.741184 0.671302i \(-0.234265\pi\)
−0.671302 + 0.741184i \(0.734265\pi\)
\(272\) 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 \(-0.625536\pi\)
0.384239 0.923233i \(-0.374464\pi\)
\(278\) 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 −0.581197 0.813763i \(-0.697415\pi\)
0.813763 + 0.581197i \(0.197415\pi\)
\(282\) 0 0
\(283\) −3.66949 + 6.35574i −0.218128 + 0.377809i −0.954236 0.299055i \(-0.903328\pi\)
0.736107 + 0.676865i \(0.236662\pi\)
\(284\) −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 −0.816076 0.577944i \(-0.803855\pi\)
−0.417771 + 0.908552i \(0.637188\pi\)
\(294\) 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 0.771747 0.635929i \(-0.219383\pi\)
−0.635929 + 0.771747i \(0.719383\pi\)
\(308\) −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 0.632250 0.774764i \(-0.282132\pi\)
−0.987091 + 0.160162i \(0.948798\pi\)
\(312\) 0 0
\(313\) 8.39852 + 4.84889i 0.474713 + 0.274075i 0.718210 0.695826i \(-0.244962\pi\)
−0.243498 + 0.969901i \(0.578295\pi\)
\(314\) −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 0.436913 0.899504i \(-0.356072\pi\)
0.828130 + 0.560536i \(0.189405\pi\)
\(318\) 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 −0.554310 0.832310i \(-0.687018\pi\)
0.896202 0.443647i \(-0.146315\pi\)
\(332\) −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 \(-0.939624\pi\)
0.982065 0.188542i \(-0.0603762\pi\)
\(338\) −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 −0.997933 0.0642689i \(-0.979528\pi\)
0.896369 + 0.443308i \(0.146195\pi\)
\(350\) −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 −0.882081 0.471098i \(-0.843858\pi\)
0.528355 0.849023i \(-0.322809\pi\)
\(354\) 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 0.948521 0.316716i \(-0.102580\pi\)
−0.979801 + 0.199977i \(0.935913\pi\)
\(360\) 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 0.964919 0.262547i \(-0.0845624\pi\)
0.255088 + 0.966918i \(0.417896\pi\)
\(368\) 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 0.997228 0.0744019i \(-0.0237048\pi\)
−0.563048 + 0.826424i \(0.690371\pi\)
\(374\) −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 0.609131 + 0.793070i \(0.291518\pi\)
−0.924058 + 0.382253i \(0.875148\pi\)
\(380\) −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 −0.273454 0.961885i \(-0.588166\pi\)
−0.717761 + 0.696290i \(0.754833\pi\)
\(384\) 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 0.440078 0.897959i \(-0.354951\pi\)
0.997695 + 0.0678608i \(0.0216174\pi\)
\(390\) 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 −0.985603 0.169076i \(-0.945922\pi\)
0.938095 + 0.346377i \(0.112588\pi\)
\(398\) 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 −0.600752 0.799436i \(-0.705132\pi\)
0.799436 + 0.600752i \(0.205132\pi\)
\(402\) 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 −0.862834 0.505487i \(-0.831313\pi\)
0.505487 + 0.862834i \(0.331313\pi\)
\(410\) 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 −0.154265 0.988029i \(-0.549301\pi\)
0.778526 + 0.627612i \(0.215968\pi\)
\(420\) 0 0
\(421\) −15.6726 15.6726i −0.763838 0.763838i 0.213176 0.977014i \(-0.431619\pi\)
−0.977014 + 0.213176i \(0.931619\pi\)
\(422\) 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 0.381918 0.924196i \(-0.375264\pi\)
0.792849 + 0.609418i \(0.208597\pi\)
\(432\) 0 0
\(433\) 12.7247 22.0399i 0.611512 1.05917i −0.379474 0.925203i \(-0.623895\pi\)
0.990986 0.133967i \(-0.0427717\pi\)
\(434\) 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 −0.714169 0.699974i \(-0.753195\pi\)
0.963279 + 0.268501i \(0.0865284\pi\)
\(444\) 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 0.991727 0.128368i \(-0.0409737\pi\)
−0.923044 + 0.384694i \(0.874307\pi\)
\(450\) 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 0.875375 0.483445i \(-0.160615\pi\)
−0.483445 + 0.875375i \(0.660615\pi\)
\(458\) −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 0.997608 0.0691268i \(-0.0220213\pi\)
−0.898517 + 0.438938i \(0.855355\pi\)
\(462\) 0 0
\(463\) −21.3807 + 21.3807i −0.993646 + 0.993646i −0.999980 0.00633382i \(-0.997984\pi\)
0.00633382 + 0.999980i \(0.497984\pi\)
\(464\) 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 0.314846 + 0.949143i \(0.398047\pi\)
−0.979405 + 0.201907i \(0.935286\pi\)
\(468\) 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 −0.615464 0.788165i \(-0.711032\pi\)
−0.138925 + 0.990303i \(0.544365\pi\)
\(480\) 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 0.421526 0.906816i \(-0.361494\pi\)
−0.906816 + 0.421526i \(0.861494\pi\)
\(488\) −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 −0.590822 0.806802i \(-0.701196\pi\)
0.403300 + 0.915068i \(0.367863\pi\)
\(492\) 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 −0.570336 0.821411i \(-0.693187\pi\)
−0.0832201 + 0.996531i \(0.526520\pi\)
\(500\) 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 0.777887 0.628405i \(-0.216292\pi\)
−0.155271 + 0.987872i \(0.549625\pi\)
\(504\) 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 0.0397455 0.999210i \(-0.487345\pi\)
0.999210 0.0397455i \(-0.0126547\pi\)
\(510\) 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 −0.304113 0.952636i \(-0.598360\pi\)
0.672950 + 0.739688i \(0.265027\pi\)
\(522\) 0 0
\(523\) 19.4487i 0.850434i −0.905091 0.425217i \(-0.860198\pi\)
0.905091 0.425217i \(-0.139802\pi\)
\(524\) −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 0.999498 0.0316700i \(-0.0100826\pi\)
−0.881426 + 0.472322i \(0.843416\pi\)
\(542\) 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 −0.984420 0.175831i \(-0.943739\pi\)
0.764618 0.644484i \(-0.222928\pi\)
\(558\) 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 \(0.168727\pi\)
−0.862771 + 0.505595i \(0.831273\pi\)
\(570\) 0 0
\(571\) −15.0931 + 8.71402i −0.631628 + 0.364671i −0.781382 0.624053i \(-0.785485\pi\)
0.149754 + 0.988723i \(0.452152\pi\)
\(572\) 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 0.669339 0.742957i \(-0.266577\pi\)
0.208186 + 0.978089i \(0.433244\pi\)
\(578\) 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 −0.0291829 0.999574i \(-0.509291\pi\)
−0.525060 + 0.851065i \(0.675957\pi\)
\(588\) 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 0.481873 0.876241i \(-0.339957\pi\)
0.855435 + 0.517911i \(0.173290\pi\)
\(594\) 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 0.966590 0.256326i \(-0.0825120\pi\)
−0.705280 + 0.708929i \(0.749179\pi\)
\(600\) 0 0
\(601\) 26.5897 15.3516i 1.08462 0.626205i 0.152480 0.988307i \(-0.451274\pi\)
0.932138 + 0.362102i \(0.117941\pi\)
\(602\) 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 0.0527827 0.998606i \(-0.483191\pi\)
0.891210 + 0.453592i \(0.149858\pi\)
\(608\) −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 −0.0444737 0.999011i \(-0.514161\pi\)
0.460990 + 0.887405i \(0.347494\pi\)
\(614\) 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 −0.0863653 0.996264i \(-0.527525\pi\)
0.423337 + 0.905972i \(0.360859\pi\)
\(618\) 0 0
\(619\) −1.40877 + 5.25761i −0.0566233 + 0.211321i −0.988441 0.151605i \(-0.951556\pi\)
0.931818 + 0.362926i \(0.118222\pi\)
\(620\) −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 0.991749 0.128192i \(-0.0409174\pi\)
−0.922976 + 0.384857i \(0.874251\pi\)
\(632\) −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 \(0.0230699\pi\)
−0.997375 + 0.0724129i \(0.976930\pi\)
\(642\) 0 0
\(643\) −4.98038 18.5870i −0.196407 0.733001i −0.991898 0.127036i \(-0.959454\pi\)
0.795491 0.605965i \(-0.207213\pi\)
\(644\) 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 −0.886335 0.463045i \(-0.846757\pi\)
0.844176 + 0.536066i \(0.180090\pi\)
\(648\) 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 −0.354272 0.935142i \(-0.615271\pi\)
0.986993 0.160763i \(-0.0513954\pi\)
\(660\) 0 0
\(661\) −33.3853 + 8.94556i −1.29854 + 0.347942i −0.840897 0.541195i \(-0.817972\pi\)
−0.457641 + 0.889137i \(0.651305\pi\)
\(662\) −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 −0.745415 0.666601i \(-0.767748\pi\)
0.204586 + 0.978849i \(0.434415\pi\)
\(674\) −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 0.155301 0.987867i \(-0.450365\pi\)
−0.777868 + 0.628428i \(0.783699\pi\)
\(678\) 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 −0.797090 0.603860i \(-0.793628\pi\)
0.603860 + 0.797090i \(0.293628\pi\)
\(684\) 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 0.305253 0.952271i \(-0.401259\pi\)
0.952271 0.305253i \(-0.0987412\pi\)
\(692\) 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 \(-0.925542\pi\)
0.972766 0.231790i \(-0.0744584\pi\)
\(702\) 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 0.944301 0.329084i \(-0.106740\pi\)
0.653247 + 0.757145i \(0.273406\pi\)
\(710\) 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 0.861004 0.508599i \(-0.169836\pi\)
−0.870961 + 0.491352i \(0.836503\pi\)
\(720\) 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 −0.954916 0.296877i \(-0.904055\pi\)
0.678542 0.734561i \(-0.262612\pi\)
\(734\) −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 −0.999997 0.00262992i \(-0.999163\pi\)
0.864707 0.502276i \(-0.167504\pi\)
\(740\) 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 0.152816 + 0.988255i \(0.451166\pi\)
−0.626470 + 0.779446i \(0.715501\pi\)
\(744\) 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 \(0.0332503\pi\)
−0.994549 + 0.104269i \(0.966750\pi\)
\(752\) 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 0.655163 0.755488i \(-0.272600\pi\)
−0.981853 + 0.189643i \(0.939267\pi\)
\(758\) 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 0.577125 + 0.816656i \(0.304175\pi\)
−0.908133 + 0.418682i \(0.862492\pi\)
\(762\) 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 −0.358845 0.933397i \(-0.616829\pi\)
−0.777468 + 0.628923i \(0.783496\pi\)
\(770\) −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 −0.978246 0.207450i \(-0.933484\pi\)
0.207450 + 0.978246i \(0.433484\pi\)
\(774\) 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 0.840431 0.541918i \(-0.182302\pi\)
−0.541918 + 0.840431i \(0.682302\pi\)
\(788\) 3.85230 + 1.03222i 0.137233 + 0.0367714i