Properties

Label 668.2.e.a.9.3
Level $668$
Weight $2$
Character 668.9
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 9.3
Character \(\chi\) \(=\) 668.9
Dual form 668.2.e.a.297.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.342745 - 2.57205i) q^{3} +(-0.628586 - 0.277966i) q^{5} +(-1.47454 + 3.17087i) q^{7} +(-3.60268 + 0.977525i) q^{9} +O(q^{10})\) \(q+(-0.342745 - 2.57205i) q^{3} +(-0.628586 - 0.277966i) q^{5} +(-1.47454 + 3.17087i) q^{7} +(-3.60268 + 0.977525i) q^{9} +(-0.684433 + 0.877554i) q^{11} +(-1.75582 + 3.42993i) q^{13} +(-0.499499 + 1.71203i) q^{15} +(0.451009 + 0.0342072i) q^{17} +(-4.29462 + 6.46039i) q^{19} +(8.66104 + 2.70581i) q^{21} +(1.87555 + 0.745869i) q^{23} +(-3.04651 - 3.34934i) q^{25} +(0.736103 + 1.75360i) q^{27} +(-0.785163 + 0.312244i) q^{29} +(-1.72875 + 0.399495i) q^{31} +(2.49170 + 1.45962i) q^{33} +(1.80827 - 1.58329i) q^{35} +(-3.03378 - 0.823165i) q^{37} +(9.42376 + 3.34047i) q^{39} +(8.80006 - 4.29666i) q^{41} +(0.281863 - 2.96980i) q^{43} +(2.53631 + 0.386964i) q^{45} +(0.207333 + 10.9540i) q^{47} +(-3.36935 - 3.99834i) q^{49} +(-0.0665982 - 1.17174i) q^{51} +(1.65631 + 9.63007i) q^{53} +(0.674155 - 0.361369i) q^{55} +(18.0884 + 8.83174i) q^{57} +(-11.8163 + 0.896218i) q^{59} +(10.0304 - 10.2220i) q^{61} +(2.21270 - 12.8650i) q^{63} +(2.05709 - 1.66795i) q^{65} +(-4.03799 + 1.78563i) q^{67} +(1.27558 - 5.07965i) q^{69} +(-8.69542 + 0.991644i) q^{71} +(-1.19028 + 0.892634i) q^{73} +(-7.57052 + 8.98376i) q^{75} +(-1.77338 - 3.46424i) q^{77} +(-2.45274 + 6.52457i) q^{79} +(-5.40490 + 3.16615i) q^{81} +(-1.50388 + 2.08647i) q^{83} +(-0.273989 - 0.146867i) q^{85} +(1.07222 + 1.91246i) q^{87} +(1.02809 + 3.52376i) q^{89} +(-8.28682 - 10.6251i) q^{91} +(1.62004 + 4.30950i) q^{93} +(4.49531 - 2.86715i) q^{95} +(-2.71211 - 0.626740i) q^{97} +(1.60796 - 3.83060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{11}{83}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.342745 2.57205i −0.197884 1.48498i −0.755648 0.654977i \(-0.772678\pi\)
0.557765 0.829999i \(-0.311659\pi\)
\(4\) 0 0
\(5\) −0.628586 0.277966i −0.281112 0.124310i 0.259069 0.965859i \(-0.416584\pi\)
−0.540181 + 0.841549i \(0.681644\pi\)
\(6\) 0 0
\(7\) −1.47454 + 3.17087i −0.557325 + 1.19848i 0.401861 + 0.915701i \(0.368364\pi\)
−0.959186 + 0.282775i \(0.908745\pi\)
\(8\) 0 0
\(9\) −3.60268 + 0.977525i −1.20089 + 0.325842i
\(10\) 0 0
\(11\) −0.684433 + 0.877554i −0.206364 + 0.264593i −0.880533 0.473985i \(-0.842815\pi\)
0.674169 + 0.738577i \(0.264502\pi\)
\(12\) 0 0
\(13\) −1.75582 + 3.42993i −0.486977 + 0.951291i 0.508922 + 0.860813i \(0.330044\pi\)
−0.995898 + 0.0904779i \(0.971161\pi\)
\(14\) 0 0
\(15\) −0.499499 + 1.71203i −0.128970 + 0.442044i
\(16\) 0 0
\(17\) 0.451009 + 0.0342072i 0.109386 + 0.00829646i 0.130208 0.991487i \(-0.458436\pi\)
−0.0208221 + 0.999783i \(0.506628\pi\)
\(18\) 0 0
\(19\) −4.29462 + 6.46039i −0.985254 + 1.48212i −0.112681 + 0.993631i \(0.535944\pi\)
−0.872573 + 0.488484i \(0.837550\pi\)
\(20\) 0 0
\(21\) 8.66104 + 2.70581i 1.88999 + 0.590456i
\(22\) 0 0
\(23\) 1.87555 + 0.745869i 0.391079 + 0.155524i 0.556797 0.830649i \(-0.312030\pi\)
−0.165718 + 0.986173i \(0.552994\pi\)
\(24\) 0 0
\(25\) −3.04651 3.34934i −0.609302 0.669868i
\(26\) 0 0
\(27\) 0.736103 + 1.75360i 0.141663 + 0.337480i
\(28\) 0 0
\(29\) −0.785163 + 0.312244i −0.145801 + 0.0579823i −0.441293 0.897363i \(-0.645480\pi\)
0.295492 + 0.955345i \(0.404516\pi\)
\(30\) 0 0
\(31\) −1.72875 + 0.399495i −0.310492 + 0.0717515i −0.377525 0.925999i \(-0.623225\pi\)
0.0670335 + 0.997751i \(0.478647\pi\)
\(32\) 0 0
\(33\) 2.49170 + 1.45962i 0.433750 + 0.254087i
\(34\) 0 0
\(35\) 1.80827 1.58329i 0.305654 0.267625i
\(36\) 0 0
\(37\) −3.03378 0.823165i −0.498751 0.135328i 0.00359603 0.999994i \(-0.498855\pi\)
−0.502347 + 0.864666i \(0.667530\pi\)
\(38\) 0 0
\(39\) 9.42376 + 3.34047i 1.50901 + 0.534904i
\(40\) 0 0
\(41\) 8.80006 4.29666i 1.37434 0.671025i 0.404447 0.914562i \(-0.367464\pi\)
0.969892 + 0.243536i \(0.0783075\pi\)
\(42\) 0 0
\(43\) 0.281863 2.96980i 0.0429837 0.452890i −0.947938 0.318454i \(-0.896837\pi\)
0.990922 0.134437i \(-0.0429225\pi\)
\(44\) 0 0
\(45\) 2.53631 + 0.386964i 0.378091 + 0.0576852i
\(46\) 0 0
\(47\) 0.207333 + 10.9540i 0.0302426 + 1.59781i 0.616279 + 0.787528i \(0.288639\pi\)
−0.586037 + 0.810284i \(0.699313\pi\)
\(48\) 0 0
\(49\) −3.36935 3.99834i −0.481336 0.571191i
\(50\) 0 0
\(51\) −0.0665982 1.17174i −0.00932561 0.164077i
\(52\) 0 0
\(53\) 1.65631 + 9.63007i 0.227512 + 1.32279i 0.844388 + 0.535731i \(0.179964\pi\)
−0.616877 + 0.787060i \(0.711602\pi\)
\(54\) 0 0
\(55\) 0.674155 0.361369i 0.0909030 0.0487270i
\(56\) 0 0
\(57\) 18.0884 + 8.83174i 2.39587 + 1.16979i
\(58\) 0 0
\(59\) −11.8163 + 0.896218i −1.53835 + 0.116678i −0.817303 0.576209i \(-0.804532\pi\)
−0.721047 + 0.692886i \(0.756339\pi\)
\(60\) 0 0
\(61\) 10.0304 10.2220i 1.28426 1.30880i 0.357132 0.934054i \(-0.383755\pi\)
0.927128 0.374744i \(-0.122269\pi\)
\(62\) 0 0
\(63\) 2.21270 12.8650i 0.278775 1.62084i
\(64\) 0 0
\(65\) 2.05709 1.66795i 0.255150 0.206883i
\(66\) 0 0
\(67\) −4.03799 + 1.78563i −0.493319 + 0.218150i −0.636103 0.771604i \(-0.719455\pi\)
0.142784 + 0.989754i \(0.454395\pi\)
\(68\) 0 0
\(69\) 1.27558 5.07965i 0.153562 0.611519i
\(70\) 0 0
\(71\) −8.69542 + 0.991644i −1.03196 + 0.117686i −0.612808 0.790231i \(-0.709960\pi\)
−0.419148 + 0.907918i \(0.637671\pi\)
\(72\) 0 0
\(73\) −1.19028 + 0.892634i −0.139312 + 0.104475i −0.667344 0.744750i \(-0.732569\pi\)
0.528032 + 0.849225i \(0.322930\pi\)
\(74\) 0 0
\(75\) −7.57052 + 8.98376i −0.874168 + 1.03735i
\(76\) 0 0
\(77\) −1.77338 3.46424i −0.202096 0.394787i
\(78\) 0 0
\(79\) −2.45274 + 6.52457i −0.275955 + 0.734072i 0.723106 + 0.690737i \(0.242714\pi\)
−0.999061 + 0.0433345i \(0.986202\pi\)
\(80\) 0 0
\(81\) −5.40490 + 3.16615i −0.600544 + 0.351794i
\(82\) 0 0
\(83\) −1.50388 + 2.08647i −0.165072 + 0.229020i −0.885649 0.464355i \(-0.846286\pi\)
0.720578 + 0.693374i \(0.243877\pi\)
\(84\) 0 0
\(85\) −0.273989 0.146867i −0.0297183 0.0159300i
\(86\) 0 0
\(87\) 1.07222 + 1.91246i 0.114954 + 0.205038i
\(88\) 0 0
\(89\) 1.02809 + 3.52376i 0.108977 + 0.373517i 0.996123 0.0879713i \(-0.0280384\pi\)
−0.887146 + 0.461489i \(0.847315\pi\)
\(90\) 0 0
\(91\) −8.28682 10.6251i −0.868695 1.11381i
\(92\) 0 0
\(93\) 1.62004 + 4.30950i 0.167991 + 0.446875i
\(94\) 0 0
\(95\) 4.49531 2.86715i 0.461209 0.294163i
\(96\) 0 0
\(97\) −2.71211 0.626740i −0.275373 0.0636358i 0.0852100 0.996363i \(-0.472844\pi\)
−0.360583 + 0.932727i \(0.617422\pi\)
\(98\) 0 0
\(99\) 1.60796 3.83060i 0.161606 0.384989i
\(100\) 0 0
\(101\) −0.783642 8.25670i −0.0779753 0.821573i −0.945810 0.324720i \(-0.894730\pi\)
0.867835 0.496853i \(-0.165511\pi\)
\(102\) 0 0
\(103\) 1.29322 0.895429i 0.127425 0.0882292i −0.503838 0.863798i \(-0.668079\pi\)
0.631263 + 0.775569i \(0.282537\pi\)
\(104\) 0 0
\(105\) −4.69208 4.10831i −0.457901 0.400930i
\(106\) 0 0
\(107\) −10.2876 7.12314i −0.994539 0.688620i −0.0439371 0.999034i \(-0.513990\pi\)
−0.950601 + 0.310414i \(0.899532\pi\)
\(108\) 0 0
\(109\) −13.9444 8.89388i −1.33563 0.851880i −0.339575 0.940579i \(-0.610283\pi\)
−0.996058 + 0.0886995i \(0.971729\pi\)
\(110\) 0 0
\(111\) −1.07741 + 8.08520i −0.102263 + 0.767413i
\(112\) 0 0
\(113\) −0.974842 + 1.59418i −0.0917055 + 0.149968i −0.895685 0.444689i \(-0.853314\pi\)
0.803980 + 0.594657i \(0.202712\pi\)
\(114\) 0 0
\(115\) −0.971616 0.990181i −0.0906037 0.0923348i
\(116\) 0 0
\(117\) 2.97282 14.0733i 0.274837 1.30108i
\(118\) 0 0
\(119\) −0.773499 + 1.37965i −0.0709065 + 0.126472i
\(120\) 0 0
\(121\) 2.37744 + 9.46751i 0.216131 + 0.860682i
\(122\) 0 0
\(123\) −14.0674 21.1616i −1.26842 1.90808i
\(124\) 0 0
\(125\) 2.07064 + 6.21236i 0.185204 + 0.555650i
\(126\) 0 0
\(127\) 18.8365 + 2.14816i 1.67147 + 0.190618i 0.897012 0.442005i \(-0.145733\pi\)
0.774459 + 0.632624i \(0.218022\pi\)
\(128\) 0 0
\(129\) −7.73510 + 0.292917i −0.681037 + 0.0257899i
\(130\) 0 0
\(131\) −0.696551 + 12.2553i −0.0608580 + 1.07075i 0.812278 + 0.583271i \(0.198227\pi\)
−0.873136 + 0.487477i \(0.837917\pi\)
\(132\) 0 0
\(133\) −14.1524 23.1438i −1.22717 2.00682i
\(134\) 0 0
\(135\) 0.0247363 1.30690i 0.00212896 0.112480i
\(136\) 0 0
\(137\) −2.87001 + 1.01734i −0.245201 + 0.0869173i −0.453866 0.891070i \(-0.649956\pi\)
0.208665 + 0.977987i \(0.433088\pi\)
\(138\) 0 0
\(139\) −13.9728 13.2012i −1.18516 1.11971i −0.990309 0.138879i \(-0.955650\pi\)
−0.194851 0.980833i \(-0.562422\pi\)
\(140\) 0 0
\(141\) 28.1033 4.28772i 2.36673 0.361091i
\(142\) 0 0
\(143\) −1.80821 3.88838i −0.151210 0.325163i
\(144\) 0 0
\(145\) 0.580335 + 0.0219765i 0.0481942 + 0.00182505i
\(146\) 0 0
\(147\) −9.12911 + 10.0366i −0.752956 + 0.827803i
\(148\) 0 0
\(149\) 5.90270 + 4.78608i 0.483568 + 0.392091i 0.840305 0.542114i \(-0.182376\pi\)
−0.356737 + 0.934205i \(0.616111\pi\)
\(150\) 0 0
\(151\) 1.26088 + 0.945573i 0.102609 + 0.0769497i 0.650035 0.759904i \(-0.274754\pi\)
−0.547427 + 0.836854i \(0.684393\pi\)
\(152\) 0 0
\(153\) −1.65828 + 0.317635i −0.134064 + 0.0256792i
\(154\) 0 0
\(155\) 1.19771 + 0.229415i 0.0962024 + 0.0184271i
\(156\) 0 0
\(157\) 1.33505 + 6.32011i 0.106548 + 0.504399i 0.998621 + 0.0525064i \(0.0167210\pi\)
−0.892072 + 0.451893i \(0.850749\pi\)
\(158\) 0 0
\(159\) 24.2014 7.56078i 1.91929 0.599609i
\(160\) 0 0
\(161\) −5.13063 + 4.84730i −0.404350 + 0.382021i
\(162\) 0 0
\(163\) 2.63149 7.89501i 0.206114 0.618385i −0.793834 0.608135i \(-0.791918\pi\)
0.999947 0.0102502i \(-0.00326278\pi\)
\(164\) 0 0
\(165\) −1.16052 1.61011i −0.0903467 0.125347i
\(166\) 0 0
\(167\) 9.42530 + 8.84102i 0.729352 + 0.684139i
\(168\) 0 0
\(169\) −1.08015 1.49860i −0.0830888 0.115277i
\(170\) 0 0
\(171\) 9.15696 27.4728i 0.700250 2.10090i
\(172\) 0 0
\(173\) −5.14672 + 4.86250i −0.391298 + 0.369689i −0.857056 0.515223i \(-0.827709\pi\)
0.465759 + 0.884912i \(0.345781\pi\)
\(174\) 0 0
\(175\) 15.1125 4.72133i 1.14240 0.356899i
\(176\) 0 0
\(177\) 6.35509 + 30.0850i 0.477678 + 2.26132i
\(178\) 0 0
\(179\) −5.78349 1.10780i −0.432279 0.0828008i −0.0326264 0.999468i \(-0.510387\pi\)
−0.399652 + 0.916667i \(0.630869\pi\)
\(180\) 0 0
\(181\) 4.02778 0.771500i 0.299382 0.0573452i −0.0362358 0.999343i \(-0.511537\pi\)
0.335618 + 0.941998i \(0.391055\pi\)
\(182\) 0 0
\(183\) −29.7295 22.2952i −2.19767 1.64811i
\(184\) 0 0
\(185\) 1.67818 + 1.36072i 0.123382 + 0.100042i
\(186\) 0 0
\(187\) −0.338704 + 0.372372i −0.0247685 + 0.0272305i
\(188\) 0 0
\(189\) −6.64585 0.251669i −0.483414 0.0183062i
\(190\) 0 0
\(191\) −7.00703 15.0680i −0.507011 1.09028i −0.978089 0.208188i \(-0.933243\pi\)
0.471078 0.882092i \(-0.343865\pi\)
\(192\) 0 0
\(193\) 4.06364 0.619988i 0.292507 0.0446277i −0.00291102 0.999996i \(-0.500927\pi\)
0.295418 + 0.955368i \(0.404541\pi\)
\(194\) 0 0
\(195\) −4.99510 4.71926i −0.357707 0.337953i
\(196\) 0 0
\(197\) 13.1975 4.67815i 0.940280 0.333304i 0.180567 0.983563i \(-0.442207\pi\)
0.759713 + 0.650258i \(0.225339\pi\)
\(198\) 0 0
\(199\) 0.108310 5.72234i 0.00767787 0.405646i −0.975194 0.221354i \(-0.928952\pi\)
0.982871 0.184292i \(-0.0589993\pi\)
\(200\) 0 0
\(201\) 5.97675 + 9.77392i 0.421568 + 0.689399i
\(202\) 0 0
\(203\) 0.167673 2.95007i 0.0117683 0.207054i
\(204\) 0 0
\(205\) −6.72592 + 0.254701i −0.469758 + 0.0177891i
\(206\) 0 0
\(207\) −7.48610 0.853731i −0.520320 0.0593384i
\(208\) 0 0
\(209\) −2.72996 8.19047i −0.188836 0.566547i
\(210\) 0 0
\(211\) 0.530613 + 0.798200i 0.0365289 + 0.0549503i 0.850593 0.525825i \(-0.176243\pi\)
−0.814064 + 0.580776i \(0.802749\pi\)
\(212\) 0 0
\(213\) 5.53087 + 22.0252i 0.378969 + 1.50914i
\(214\) 0 0
\(215\) −1.00268 + 1.78843i −0.0683821 + 0.121970i
\(216\) 0 0
\(217\) 1.28236 6.07070i 0.0870525 0.412106i
\(218\) 0 0
\(219\) 2.70387 + 2.75553i 0.182710 + 0.186201i
\(220\) 0 0
\(221\) −0.909218 + 1.48687i −0.0611606 + 0.100017i
\(222\) 0 0
\(223\) −1.78496 + 13.3949i −0.119530 + 0.896986i 0.824207 + 0.566289i \(0.191621\pi\)
−0.943737 + 0.330697i \(0.892716\pi\)
\(224\) 0 0
\(225\) 14.2497 + 9.08857i 0.949977 + 0.605904i
\(226\) 0 0
\(227\) 9.19734 + 6.36826i 0.610449 + 0.422676i 0.833804 0.552061i \(-0.186159\pi\)
−0.223354 + 0.974737i \(0.571701\pi\)
\(228\) 0 0
\(229\) −1.13129 0.990539i −0.0747578 0.0654566i 0.620560 0.784159i \(-0.286905\pi\)
−0.695318 + 0.718702i \(0.744737\pi\)
\(230\) 0 0
\(231\) −8.30240 + 5.74859i −0.546258 + 0.378230i
\(232\) 0 0
\(233\) −1.32294 13.9389i −0.0866686 0.913168i −0.927983 0.372622i \(-0.878459\pi\)
0.841315 0.540546i \(-0.181782\pi\)
\(234\) 0 0
\(235\) 2.91452 6.94319i 0.190123 0.452924i
\(236\) 0 0
\(237\) 17.6222 + 4.07231i 1.14469 + 0.264525i
\(238\) 0 0
\(239\) −3.76269 + 2.39988i −0.243388 + 0.155235i −0.653806 0.756662i \(-0.726829\pi\)
0.410418 + 0.911898i \(0.365383\pi\)
\(240\) 0 0
\(241\) −1.80058 4.78976i −0.115986 0.308536i 0.865252 0.501337i \(-0.167158\pi\)
−0.981238 + 0.192801i \(0.938243\pi\)
\(242\) 0 0
\(243\) 13.5049 + 17.3154i 0.866338 + 1.11079i
\(244\) 0 0
\(245\) 1.00653 + 3.44986i 0.0643046 + 0.220404i
\(246\) 0 0
\(247\) −14.6181 26.0735i −0.930126 1.65902i
\(248\) 0 0
\(249\) 5.88196 + 3.15292i 0.372754 + 0.199808i
\(250\) 0 0
\(251\) 10.1718 14.1123i 0.642039 0.890762i −0.357021 0.934096i \(-0.616208\pi\)
0.999061 + 0.0433343i \(0.0137980\pi\)
\(252\) 0 0
\(253\) −1.93823 + 1.13540i −0.121855 + 0.0713819i
\(254\) 0 0
\(255\) −0.283842 + 0.755053i −0.0177749 + 0.0472833i
\(256\) 0 0
\(257\) 13.5416 + 26.4529i 0.844699 + 1.65009i 0.756508 + 0.653984i \(0.226904\pi\)
0.0881912 + 0.996104i \(0.471891\pi\)
\(258\) 0 0
\(259\) 7.08360 8.40594i 0.440153 0.522320i
\(260\) 0 0
\(261\) 2.52346 1.89243i 0.156199 0.117139i
\(262\) 0 0
\(263\) 8.07758 0.921184i 0.498085 0.0568027i 0.139352 0.990243i \(-0.455498\pi\)
0.358733 + 0.933440i \(0.383209\pi\)
\(264\) 0 0
\(265\) 1.63570 6.51372i 0.100480 0.400135i
\(266\) 0 0
\(267\) 8.71092 3.85204i 0.533100 0.235741i
\(268\) 0 0
\(269\) 14.6225 11.8563i 0.891548 0.722893i −0.0699951 0.997547i \(-0.522298\pi\)
0.961543 + 0.274654i \(0.0885634\pi\)
\(270\) 0 0
\(271\) −0.249854 + 1.45269i −0.0151775 + 0.0882446i −0.992130 0.125213i \(-0.960039\pi\)
0.976952 + 0.213457i \(0.0684724\pi\)
\(272\) 0 0
\(273\) −24.4880 + 24.9558i −1.48208 + 1.51040i
\(274\) 0 0
\(275\) 5.02436 0.381077i 0.302980 0.0229798i
\(276\) 0 0
\(277\) −16.5315 8.07157i −0.993282 0.484973i −0.130990 0.991384i \(-0.541815\pi\)
−0.862293 + 0.506410i \(0.830972\pi\)
\(278\) 0 0
\(279\) 5.83760 3.12914i 0.349488 0.187337i
\(280\) 0 0
\(281\) −0.355865 2.06905i −0.0212291 0.123429i 0.972981 0.230887i \(-0.0741628\pi\)
−0.994210 + 0.107458i \(0.965729\pi\)
\(282\) 0 0
\(283\) 0.480369 + 8.45171i 0.0285550 + 0.502402i 0.980548 + 0.196281i \(0.0628866\pi\)
−0.951993 + 0.306121i \(0.900969\pi\)
\(284\) 0 0
\(285\) −8.91521 10.5795i −0.528091 0.626674i
\(286\) 0 0
\(287\) 0.648068 + 34.2395i 0.0382542 + 2.02109i
\(288\) 0 0
\(289\) −16.6033 2.53316i −0.976664 0.149009i
\(290\) 0 0
\(291\) −0.682449 + 7.19050i −0.0400058 + 0.421515i
\(292\) 0 0
\(293\) −28.6730 + 13.9997i −1.67510 + 0.817871i −0.678576 + 0.734531i \(0.737402\pi\)
−0.996521 + 0.0833408i \(0.973441\pi\)
\(294\) 0 0
\(295\) 7.67667 + 2.72118i 0.446953 + 0.158433i
\(296\) 0 0
\(297\) −2.04269 0.554249i −0.118529 0.0321608i
\(298\) 0 0
\(299\) −5.85140 + 5.12338i −0.338395 + 0.296293i
\(300\) 0 0
\(301\) 9.00123 + 5.27285i 0.518822 + 0.303922i
\(302\) 0 0
\(303\) −20.9681 + 4.84551i −1.20459 + 0.278367i
\(304\) 0 0
\(305\) −9.14634 + 3.63732i −0.523718 + 0.208272i
\(306\) 0 0
\(307\) 0.0140733 + 0.0335264i 0.000803204 + 0.00191345i 0.922460 0.386093i \(-0.126176\pi\)
−0.921657 + 0.388007i \(0.873164\pi\)
\(308\) 0 0
\(309\) −2.74634 3.01933i −0.156234 0.171764i
\(310\) 0 0
\(311\) 17.2635 + 6.86536i 0.978924 + 0.389299i 0.803572 0.595207i \(-0.202930\pi\)
0.175352 + 0.984506i \(0.443894\pi\)
\(312\) 0 0
\(313\) 19.7941 + 6.18389i 1.11883 + 0.349534i 0.801030 0.598624i \(-0.204286\pi\)
0.317797 + 0.948159i \(0.397057\pi\)
\(314\) 0 0
\(315\) −4.96691 + 7.47171i −0.279854 + 0.420983i
\(316\) 0 0
\(317\) 23.3162 + 1.76844i 1.30957 + 0.0993254i 0.711822 0.702360i \(-0.247870\pi\)
0.597746 + 0.801686i \(0.296063\pi\)
\(318\) 0 0
\(319\) 0.263380 0.902733i 0.0147465 0.0505434i
\(320\) 0 0
\(321\) −14.7951 + 28.9017i −0.825782 + 1.61313i
\(322\) 0 0
\(323\) −2.15790 + 2.76678i −0.120069 + 0.153948i
\(324\) 0 0
\(325\) 16.8371 4.56846i 0.933955 0.253413i
\(326\) 0 0
\(327\) −18.0962 + 38.9141i −1.00072 + 2.15196i
\(328\) 0 0
\(329\) −35.0396 15.4948i −1.93179 0.854256i
\(330\) 0 0
\(331\) −0.837922 6.28800i −0.0460564 0.345620i −0.999086 0.0427432i \(-0.986390\pi\)
0.953030 0.302877i \(-0.0979471\pi\)
\(332\) 0 0
\(333\) 11.7344 0.643042
\(334\) 0 0
\(335\) 3.03457 0.165796
\(336\) 0 0
\(337\) −4.11955 30.9142i −0.224406 1.68401i −0.635255 0.772302i \(-0.719105\pi\)
0.410849 0.911703i \(-0.365232\pi\)
\(338\) 0 0
\(339\) 4.43445 + 1.96095i 0.240846 + 0.106504i
\(340\) 0 0
\(341\) 0.832631 1.79050i 0.0450895 0.0969608i
\(342\) 0 0
\(343\) −5.97803 + 1.62204i −0.322783 + 0.0875817i
\(344\) 0 0
\(345\) −2.21378 + 2.83843i −0.119186 + 0.152816i
\(346\) 0 0
\(347\) −15.4454 + 30.1721i −0.829154 + 1.61972i −0.0451374 + 0.998981i \(0.514373\pi\)
−0.784016 + 0.620740i \(0.786832\pi\)
\(348\) 0 0
\(349\) −5.73871 + 19.6694i −0.307186 + 1.05288i 0.649163 + 0.760649i \(0.275119\pi\)
−0.956349 + 0.292227i \(0.905604\pi\)
\(350\) 0 0
\(351\) −7.30718 0.554220i −0.390028 0.0295821i
\(352\) 0 0
\(353\) −7.38945 + 11.1159i −0.393301 + 0.591641i −0.975120 0.221677i \(-0.928847\pi\)
0.581820 + 0.813318i \(0.302341\pi\)
\(354\) 0 0
\(355\) 5.74146 + 1.79370i 0.304725 + 0.0951995i
\(356\) 0 0
\(357\) 3.81365 + 1.51661i 0.201840 + 0.0802677i
\(358\) 0 0
\(359\) −10.2274 11.2440i −0.539780 0.593436i 0.407754 0.913092i \(-0.366312\pi\)
−0.947534 + 0.319656i \(0.896433\pi\)
\(360\) 0 0
\(361\) −15.9389 37.9708i −0.838889 1.99846i
\(362\) 0 0
\(363\) 23.5361 9.35984i 1.23532 0.491264i
\(364\) 0 0
\(365\) 0.996317 0.230239i 0.0521496 0.0120512i
\(366\) 0 0
\(367\) 20.3131 + 11.8992i 1.06033 + 0.621135i 0.928953 0.370197i \(-0.120710\pi\)
0.131380 + 0.991332i \(0.458059\pi\)
\(368\) 0 0
\(369\) −27.5037 + 24.0818i −1.43179 + 1.25365i
\(370\) 0 0
\(371\) −32.9780 8.94801i −1.71213 0.464557i
\(372\) 0 0
\(373\) −25.6709 9.09967i −1.32919 0.471163i −0.427684 0.903928i \(-0.640671\pi\)
−0.901507 + 0.432765i \(0.857538\pi\)
\(374\) 0 0
\(375\) 15.2688 7.45505i 0.788479 0.384977i
\(376\) 0 0
\(377\) 0.307631 3.24130i 0.0158438 0.166935i
\(378\) 0 0
\(379\) 0.504284 + 0.0769384i 0.0259033 + 0.00395206i 0.163763 0.986500i \(-0.447637\pi\)
−0.137860 + 0.990452i \(0.544022\pi\)
\(380\) 0 0
\(381\) −0.930947 49.1849i −0.0476939 2.51982i
\(382\) 0 0
\(383\) 16.4205 + 19.4858i 0.839047 + 0.995677i 0.999962 + 0.00870907i \(0.00277222\pi\)
−0.160915 + 0.986968i \(0.551445\pi\)
\(384\) 0 0
\(385\) 0.151783 + 2.67051i 0.00773560 + 0.136102i
\(386\) 0 0
\(387\) 1.88759 + 10.9748i 0.0959517 + 0.557879i
\(388\) 0 0
\(389\) 31.2826 16.7685i 1.58609 0.850198i 0.586915 0.809649i \(-0.300342\pi\)
0.999178 0.0405490i \(-0.0129107\pi\)
\(390\) 0 0
\(391\) 0.820374 + 0.400550i 0.0414881 + 0.0202567i
\(392\) 0 0
\(393\) 31.7600 2.40887i 1.60208 0.121511i
\(394\) 0 0
\(395\) 3.35536 3.41947i 0.168827 0.172052i
\(396\) 0 0
\(397\) −5.29930 + 30.8110i −0.265964 + 1.54636i 0.478132 + 0.878288i \(0.341314\pi\)
−0.744096 + 0.668072i \(0.767120\pi\)
\(398\) 0 0
\(399\) −54.6765 + 44.3333i −2.73725 + 2.21944i
\(400\) 0 0
\(401\) 9.75140 4.31215i 0.486962 0.215339i −0.146354 0.989232i \(-0.546754\pi\)
0.633315 + 0.773894i \(0.281694\pi\)
\(402\) 0 0
\(403\) 1.66513 6.63091i 0.0829458 0.330309i
\(404\) 0 0
\(405\) 4.27752 0.487817i 0.212552 0.0242398i
\(406\) 0 0
\(407\) 2.79879 2.09891i 0.138731 0.104039i
\(408\) 0 0
\(409\) −1.41572 + 1.68000i −0.0700028 + 0.0830707i −0.798564 0.601910i \(-0.794406\pi\)
0.728561 + 0.684981i \(0.240190\pi\)
\(410\) 0 0
\(411\) 3.60034 + 7.03312i 0.177592 + 0.346918i
\(412\) 0 0
\(413\) 14.5818 38.7894i 0.717526 1.90870i
\(414\) 0 0
\(415\) 1.52528 0.893498i 0.0748731 0.0438601i
\(416\) 0 0
\(417\) −29.1651 + 40.4635i −1.42822 + 1.98151i
\(418\) 0 0
\(419\) −5.62711 3.01632i −0.274903 0.147357i 0.329208 0.944258i \(-0.393218\pi\)
−0.604110 + 0.796901i \(0.706471\pi\)
\(420\) 0 0
\(421\) −4.64951 8.29309i −0.226603 0.404180i 0.735230 0.677818i \(-0.237074\pi\)
−0.961833 + 0.273638i \(0.911773\pi\)
\(422\) 0 0
\(423\) −11.4548 39.2612i −0.556952 1.90895i
\(424\) 0 0
\(425\) −1.25943 1.61479i −0.0610913 0.0783290i
\(426\) 0 0
\(427\) 17.6225 + 46.8779i 0.852812 + 2.26858i
\(428\) 0 0
\(429\) −9.38138 + 5.98353i −0.452937 + 0.288888i
\(430\) 0 0
\(431\) 17.3643 + 4.01272i 0.836411 + 0.193286i 0.621565 0.783362i \(-0.286497\pi\)
0.214845 + 0.976648i \(0.431075\pi\)
\(432\) 0 0
\(433\) −5.38277 + 12.8232i −0.258679 + 0.616244i −0.998393 0.0566781i \(-0.981949\pi\)
0.739713 + 0.672922i \(0.234961\pi\)
\(434\) 0 0
\(435\) −0.142382 1.50019i −0.00682671 0.0719285i
\(436\) 0 0
\(437\) −12.8734 + 8.91355i −0.615817 + 0.426393i
\(438\) 0 0
\(439\) −0.866088 0.758332i −0.0413361 0.0361932i 0.637836 0.770172i \(-0.279830\pi\)
−0.679172 + 0.733979i \(0.737661\pi\)
\(440\) 0 0
\(441\) 16.0472 + 11.1111i 0.764151 + 0.529100i
\(442\) 0 0
\(443\) 27.8462 + 17.7606i 1.32301 + 0.843829i 0.994906 0.100812i \(-0.0321440\pi\)
0.328106 + 0.944641i \(0.393590\pi\)
\(444\) 0 0
\(445\) 0.333244 2.50075i 0.0157973 0.118547i
\(446\) 0 0
\(447\) 10.2869 16.8225i 0.486555 0.795675i
\(448\) 0 0
\(449\) 24.3688 + 24.8344i 1.15004 + 1.17201i 0.982524 + 0.186138i \(0.0595972\pi\)
0.167511 + 0.985870i \(0.446427\pi\)
\(450\) 0 0
\(451\) −2.25250 + 10.6633i −0.106066 + 0.502116i
\(452\) 0 0
\(453\) 1.99991 3.56713i 0.0939639 0.167598i
\(454\) 0 0
\(455\) 2.25557 + 8.98221i 0.105743 + 0.421092i
\(456\) 0 0
\(457\) 5.91364 + 8.89587i 0.276628 + 0.416131i 0.944685 0.327979i \(-0.106368\pi\)
−0.668057 + 0.744110i \(0.732874\pi\)
\(458\) 0 0
\(459\) 0.272003 + 0.816068i 0.0126960 + 0.0380908i
\(460\) 0 0
\(461\) 27.1600 + 3.09738i 1.26497 + 0.144259i 0.719867 0.694112i \(-0.244203\pi\)
0.545099 + 0.838372i \(0.316492\pi\)
\(462\) 0 0
\(463\) 20.4800 0.775550i 0.951788 0.0360429i 0.442619 0.896710i \(-0.354049\pi\)
0.509169 + 0.860667i \(0.329953\pi\)
\(464\) 0 0
\(465\) 0.179559 3.15921i 0.00832687 0.146505i
\(466\) 0 0
\(467\) −18.6146 30.4409i −0.861380 1.40863i −0.912120 0.409923i \(-0.865556\pi\)
0.0507400 0.998712i \(-0.483842\pi\)
\(468\) 0 0
\(469\) 0.292183 15.4369i 0.0134918 0.712812i
\(470\) 0 0
\(471\) 15.7981 5.60000i 0.727937 0.258034i
\(472\) 0 0
\(473\) 2.41325 + 2.27998i 0.110961 + 0.104834i
\(474\) 0 0
\(475\) 34.7217 5.29747i 1.59314 0.243065i
\(476\) 0 0
\(477\) −15.3808 33.0749i −0.704238 1.51440i
\(478\) 0 0
\(479\) 31.9110 + 1.20842i 1.45805 + 0.0552143i 0.754905 0.655834i \(-0.227683\pi\)
0.703143 + 0.711048i \(0.251779\pi\)
\(480\) 0 0
\(481\) 8.15018 8.96033i 0.371616 0.408556i
\(482\) 0 0
\(483\) 14.2260 + 11.5349i 0.647306 + 0.524855i
\(484\) 0 0
\(485\) 1.53058 + 1.14783i 0.0695000 + 0.0521204i
\(486\) 0 0
\(487\) −25.0487 + 4.79796i −1.13507 + 0.217416i −0.721070 0.692862i \(-0.756349\pi\)
−0.413997 + 0.910278i \(0.635868\pi\)
\(488\) 0 0
\(489\) −21.2083 4.06235i −0.959074 0.183706i
\(490\) 0 0
\(491\) 1.93532 + 9.16181i 0.0873400 + 0.413467i 0.999989 + 0.00472219i \(0.00150313\pi\)
−0.912649 + 0.408744i \(0.865967\pi\)
\(492\) 0 0
\(493\) −0.364796 + 0.113967i −0.0164296 + 0.00513279i
\(494\) 0 0
\(495\) −2.07552 + 1.96090i −0.0932875 + 0.0881359i
\(496\) 0 0
\(497\) 9.67740 29.0343i 0.434091 1.30236i
\(498\) 0 0
\(499\) −16.1029 22.3411i −0.720865 1.00012i −0.999214 0.0396442i \(-0.987378\pi\)
0.278349 0.960480i \(-0.410213\pi\)
\(500\) 0 0
\(501\) 19.5091 27.2726i 0.871603 1.21845i
\(502\) 0 0
\(503\) −17.8658 24.7869i −0.796597 1.10519i −0.992218 0.124515i \(-0.960263\pi\)
0.195621 0.980680i \(-0.437328\pi\)
\(504\) 0 0
\(505\) −1.80250 + 5.40787i −0.0802100 + 0.240647i
\(506\) 0 0
\(507\) −3.48427 + 3.29186i −0.154742 + 0.146196i
\(508\) 0 0
\(509\) 34.5730 10.8010i 1.53242 0.478746i 0.588384 0.808582i \(-0.299765\pi\)
0.944038 + 0.329836i \(0.106993\pi\)
\(510\) 0 0
\(511\) −1.07530 5.09046i −0.0475685 0.225189i
\(512\) 0 0
\(513\) −14.4902 2.77553i −0.639758 0.122542i
\(514\) 0 0
\(515\) −1.06180 + 0.203382i −0.0467885 + 0.00896209i
\(516\) 0 0
\(517\) −9.75468 7.31536i −0.429010 0.321729i
\(518\) 0 0
\(519\) 14.2706 + 11.5710i 0.626411 + 0.507912i
\(520\) 0 0
\(521\) −12.0305 + 13.2264i −0.527067 + 0.579460i −0.944194 0.329388i \(-0.893157\pi\)
0.417127 + 0.908848i \(0.363037\pi\)
\(522\) 0 0
\(523\) 29.3291 + 1.11065i 1.28247 + 0.0485654i 0.670258 0.742128i \(-0.266183\pi\)
0.612212 + 0.790693i \(0.290280\pi\)
\(524\) 0 0
\(525\) −17.3233 37.2521i −0.756049 1.62581i
\(526\) 0 0
\(527\) −0.793345 + 0.121040i −0.0345586 + 0.00527260i
\(528\) 0 0
\(529\) −13.7572 12.9975i −0.598138 0.565107i
\(530\) 0 0
\(531\) 41.6942 14.7795i 1.80937 0.641375i
\(532\) 0 0
\(533\) −0.714092 + 37.7277i −0.0309308 + 1.63417i
\(534\) 0 0
\(535\) 4.48664 + 7.33710i 0.193974 + 0.317211i
\(536\) 0 0
\(537\) −0.867055 + 15.2552i −0.0374162 + 0.658309i
\(538\) 0 0
\(539\) 5.81485 0.220200i 0.250463 0.00948470i
\(540\) 0 0
\(541\) −19.2562 2.19602i −0.827888 0.0944141i −0.310938 0.950430i \(-0.600643\pi\)
−0.516949 + 0.856016i \(0.672932\pi\)
\(542\) 0 0
\(543\) −3.36484 10.0952i −0.144399 0.433228i
\(544\) 0 0
\(545\) 6.29306 + 9.46664i 0.269565 + 0.405506i
\(546\) 0 0
\(547\) 10.9889 + 43.7602i 0.469850 + 1.87105i 0.490802 + 0.871271i \(0.336704\pi\)
−0.0209517 + 0.999780i \(0.506670\pi\)
\(548\) 0 0
\(549\) −26.1440 + 46.6317i −1.11580 + 1.99019i
\(550\) 0 0
\(551\) 1.35476 6.41343i 0.0577148 0.273221i
\(552\) 0 0
\(553\) −17.0719 17.3981i −0.725971 0.739842i
\(554\) 0 0
\(555\) 2.92465 4.78275i 0.124145 0.203017i
\(556\) 0 0
\(557\) 3.91055 29.3459i 0.165695 1.24342i −0.689180 0.724590i \(-0.742029\pi\)
0.854875 0.518834i \(-0.173634\pi\)
\(558\) 0 0
\(559\) 9.69130 + 6.18120i 0.409898 + 0.261437i
\(560\) 0 0
\(561\) 1.07385 + 0.743536i 0.0453380 + 0.0313921i
\(562\) 0 0
\(563\) 30.9466 + 27.0963i 1.30424 + 1.14197i 0.980648 + 0.195779i \(0.0627234\pi\)
0.323597 + 0.946195i \(0.395108\pi\)
\(564\) 0 0
\(565\) 1.05590 0.731107i 0.0444221 0.0307579i
\(566\) 0 0
\(567\) −2.06968 21.8068i −0.0869184 0.915801i
\(568\) 0 0
\(569\) 12.5823 29.9745i 0.527478 1.25659i −0.411120 0.911581i \(-0.634862\pi\)
0.938598 0.345013i \(-0.112126\pi\)
\(570\) 0 0
\(571\) −16.2231 3.74899i −0.678915 0.156890i −0.128409 0.991721i \(-0.540987\pi\)
−0.550506 + 0.834831i \(0.685565\pi\)
\(572\) 0 0
\(573\) −36.3540 + 23.1869i −1.51871 + 0.968648i
\(574\) 0 0
\(575\) −3.21570 8.55414i −0.134104 0.356733i
\(576\) 0 0
\(577\) −18.3055 23.4707i −0.762070 0.977098i −0.999983 0.00581146i \(-0.998150\pi\)
0.237913 0.971286i \(-0.423537\pi\)
\(578\) 0 0
\(579\) −2.98743 10.2394i −0.124154 0.425535i
\(580\) 0 0
\(581\) −4.39839 7.84518i −0.182476 0.325473i
\(582\) 0 0
\(583\) −9.58454 5.13763i −0.396951 0.212779i
\(584\) 0 0
\(585\) −5.78056 + 8.01992i −0.238997 + 0.331583i
\(586\) 0 0
\(587\) −39.7603 + 23.2913i −1.64108 + 0.961334i −0.664200 + 0.747555i \(0.731228\pi\)
−0.976882 + 0.213779i \(0.931423\pi\)
\(588\) 0 0
\(589\) 4.84342 12.8841i 0.199569 0.530878i
\(590\) 0 0
\(591\) −16.5558 32.3412i −0.681016 1.33034i
\(592\) 0 0
\(593\) −6.16470 + 7.31551i −0.253154 + 0.300412i −0.876371 0.481637i \(-0.840042\pi\)
0.623217 + 0.782049i \(0.285825\pi\)
\(594\) 0 0
\(595\) 0.869706 0.652222i 0.0356545 0.0267385i
\(596\) 0 0
\(597\) −14.7553 + 1.68273i −0.603894 + 0.0688694i
\(598\) 0 0
\(599\) 2.97573 11.8500i 0.121585 0.484179i −0.878396 0.477934i \(-0.841386\pi\)
0.999980 0.00624497i \(-0.00198785\pi\)
\(600\) 0 0
\(601\) 33.2171 14.6889i 1.35495 0.599172i 0.405793 0.913965i \(-0.366995\pi\)
0.949160 + 0.314793i \(0.101935\pi\)
\(602\) 0 0
\(603\) 12.8021 10.3803i 0.521341 0.422719i
\(604\) 0 0
\(605\) 1.13722 6.61199i 0.0462346 0.268815i
\(606\) 0 0
\(607\) −18.1556 + 18.5025i −0.736915 + 0.750995i −0.975470 0.220134i \(-0.929350\pi\)
0.238555 + 0.971129i \(0.423326\pi\)
\(608\) 0 0
\(609\) −7.64520 + 0.579858i −0.309799 + 0.0234970i
\(610\) 0 0
\(611\) −37.9356 18.5222i −1.53471 0.749328i
\(612\) 0 0
\(613\) 13.2654 7.11069i 0.535784 0.287198i −0.182195 0.983262i \(-0.558320\pi\)
0.717979 + 0.696064i \(0.245067\pi\)
\(614\) 0 0
\(615\) 2.96038 + 17.2121i 0.119374 + 0.694060i
\(616\) 0 0
\(617\) −0.902893 15.8857i −0.0363491 0.639534i −0.963970 0.266011i \(-0.914294\pi\)
0.927621 0.373523i \(-0.121850\pi\)
\(618\) 0 0
\(619\) −31.6936 37.6101i −1.27387 1.51168i −0.752959 0.658068i \(-0.771374\pi\)
−0.520915 0.853609i \(-0.674409\pi\)
\(620\) 0 0
\(621\) 0.0726437 + 3.83799i 0.00291509 + 0.154013i
\(622\) 0 0
\(623\) −12.6893 1.93601i −0.508387 0.0775644i
\(624\) 0 0
\(625\) −1.71371 + 18.0562i −0.0685485 + 0.722249i
\(626\) 0 0
\(627\) −20.1307 + 9.82886i −0.803941 + 0.392527i
\(628\) 0 0
\(629\) −1.34010 0.475032i −0.0534335 0.0189408i
\(630\) 0 0
\(631\) −33.4699 9.08148i −1.33242 0.361528i −0.476742 0.879043i \(-0.658182\pi\)
−0.855674 + 0.517515i \(0.826857\pi\)
\(632\) 0 0
\(633\) 1.87115 1.63834i 0.0743715 0.0651184i
\(634\) 0 0
\(635\) −11.2433 6.58621i −0.446175 0.261366i
\(636\) 0 0
\(637\) 19.6300 4.53629i 0.777768 0.179734i
\(638\) 0 0
\(639\) 30.3574 12.0726i 1.20092 0.477583i
\(640\) 0 0
\(641\) −0.939261 2.23757i −0.0370986 0.0883789i 0.902450 0.430795i \(-0.141767\pi\)
−0.939548 + 0.342416i \(0.888755\pi\)
\(642\) 0 0
\(643\) 11.8122 + 12.9863i 0.465827 + 0.512131i 0.926940 0.375210i \(-0.122429\pi\)
−0.461113 + 0.887341i \(0.652550\pi\)
\(644\) 0 0
\(645\) 4.94359 + 1.96597i 0.194654 + 0.0774100i
\(646\) 0 0
\(647\) −20.7221 6.47381i −0.814669 0.254512i −0.137653 0.990480i \(-0.543956\pi\)
−0.677016 + 0.735969i \(0.736727\pi\)
\(648\) 0 0
\(649\) 7.30097 10.9828i 0.286588 0.431114i
\(650\) 0 0
\(651\) −16.0537 1.21761i −0.629194 0.0477218i
\(652\) 0 0
\(653\) −8.84150 + 30.3041i −0.345994 + 1.18589i 0.581966 + 0.813213i \(0.302284\pi\)
−0.927960 + 0.372680i \(0.878439\pi\)
\(654\) 0 0
\(655\) 3.84439 7.50987i 0.150213 0.293435i
\(656\) 0 0
\(657\) 3.41564 4.37940i 0.133257 0.170857i
\(658\) 0 0
\(659\) −4.13341 + 1.12153i −0.161015 + 0.0436886i −0.341459 0.939897i \(-0.610921\pi\)
0.180444 + 0.983585i \(0.442246\pi\)
\(660\) 0 0
\(661\) 0.0648022 0.139351i 0.00252051 0.00542013i −0.905487 0.424373i \(-0.860494\pi\)
0.908008 + 0.418953i \(0.137603\pi\)
\(662\) 0 0
\(663\) 4.13593 + 1.82894i 0.160626 + 0.0710303i
\(664\) 0 0
\(665\) 2.46283 + 18.4818i 0.0955044 + 0.716692i
\(666\) 0 0
\(667\) −1.70550 −0.0660374
\(668\) 0 0
\(669\) 35.0641 1.35566
\(670\) 0 0
\(671\) 2.10527 + 15.7985i 0.0812729 + 0.609895i
\(672\) 0 0
\(673\) −12.4433 5.50251i −0.479652 0.212106i 0.150451 0.988617i \(-0.451927\pi\)
−0.630104 + 0.776511i \(0.716988\pi\)
\(674\) 0 0
\(675\) 3.63085 7.80781i 0.139752 0.300523i
\(676\) 0 0
\(677\) −12.9525 + 3.51444i −0.497806 + 0.135071i −0.501909 0.864920i \(-0.667369\pi\)
0.00410280 + 0.999992i \(0.498694\pi\)
\(678\) 0 0
\(679\) 5.98643 7.67558i 0.229738 0.294562i
\(680\) 0 0
\(681\) 13.2272 25.8388i 0.506866 0.990144i
\(682\) 0 0
\(683\) 9.67319 33.1548i 0.370134 1.26863i −0.535486 0.844544i \(-0.679872\pi\)
0.905621 0.424088i \(-0.139405\pi\)
\(684\) 0 0
\(685\) 2.08683 + 0.158278i 0.0797337 + 0.00604748i
\(686\) 0 0
\(687\) −2.15998 + 3.24925i −0.0824082 + 0.123966i
\(688\) 0 0
\(689\) −35.9386 11.2276i −1.36915 0.427739i
\(690\) 0 0
\(691\) 2.96200 + 1.17793i 0.112680 + 0.0448105i 0.425192 0.905103i \(-0.360207\pi\)
−0.312512 + 0.949914i \(0.601171\pi\)
\(692\) 0 0
\(693\) 9.77531 + 10.7470i 0.371333 + 0.408245i
\(694\) 0 0
\(695\) 5.11363 + 12.1821i 0.193971 + 0.462092i
\(696\) 0 0
\(697\) 4.11588 1.63680i 0.155900 0.0619984i
\(698\) 0 0
\(699\) −35.3982 + 8.18016i −1.33888 + 0.309402i
\(700\) 0 0
\(701\) −27.9464 16.3708i −1.05552 0.618316i −0.127880 0.991790i \(-0.540817\pi\)
−0.927641 + 0.373473i \(0.878167\pi\)
\(702\) 0 0
\(703\) 18.3469 16.0642i 0.691967 0.605875i
\(704\) 0 0
\(705\) −18.8572 5.11658i −0.710203 0.192701i
\(706\) 0 0
\(707\) 27.3364 + 9.69005i 1.02809 + 0.364432i
\(708\) 0 0
\(709\) −39.5453 + 19.3081i −1.48516 + 0.725132i −0.989654 0.143475i \(-0.954172\pi\)
−0.495502 + 0.868607i \(0.665016\pi\)
\(710\) 0 0
\(711\) 2.45850 25.9035i 0.0922009 0.971459i
\(712\) 0 0
\(713\) −3.54032 0.540145i −0.132586 0.0202286i
\(714\) 0 0
\(715\) 0.0557756 + 2.94680i 0.00208589 + 0.110204i
\(716\) 0 0
\(717\) 7.46227 + 8.85530i 0.278684 + 0.330707i
\(718\) 0 0
\(719\) −0.318918 5.61111i −0.0118936 0.209259i −0.998838 0.0481968i \(-0.984653\pi\)
0.986944 0.161062i \(-0.0514920\pi\)
\(720\) 0 0
\(721\) 0.932376 + 5.42099i 0.0347235 + 0.201888i
\(722\) 0 0
\(723\) −11.7024 + 6.27286i −0.435216 + 0.233290i
\(724\) 0 0
\(725\) 3.43782 + 1.67853i 0.127677 + 0.0623389i
\(726\) 0 0
\(727\) −14.4373 + 1.09501i −0.535451 + 0.0406118i −0.340577 0.940217i \(-0.610622\pi\)
−0.194874 + 0.980828i \(0.562430\pi\)
\(728\) 0 0
\(729\) 26.7460 27.2570i 0.990592 1.00952i
\(730\) 0 0
\(731\) 0.228711 1.32976i 0.00845919 0.0491831i
\(732\) 0 0
\(733\) −20.8780 + 16.9285i −0.771145 + 0.625267i −0.932310 0.361660i \(-0.882210\pi\)
0.161164 + 0.986928i \(0.448475\pi\)
\(734\) 0 0
\(735\) 8.52825 3.77127i 0.314569 0.139105i
\(736\) 0 0
\(737\) 1.19674 4.76571i 0.0440826 0.175547i
\(738\) 0 0
\(739\) 43.7111 4.98491i 1.60794 0.183373i 0.737394 0.675463i \(-0.236056\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(740\) 0 0
\(741\) −62.0523 + 46.5351i −2.27955 + 1.70951i
\(742\) 0 0
\(743\) −1.20878 + 1.43443i −0.0443458 + 0.0526242i −0.786411 0.617703i \(-0.788063\pi\)
0.742065 + 0.670328i \(0.233846\pi\)
\(744\) 0 0
\(745\) −2.37998 4.64921i −0.0871958 0.170334i
\(746\) 0 0
\(747\) 3.37840 8.98695i 0.123609 0.328815i
\(748\) 0 0
\(749\) 37.7561 22.1172i 1.37958 0.808145i
\(750\) 0 0
\(751\) 21.0067 29.1446i 0.766546 1.06350i −0.229381 0.973337i \(-0.573670\pi\)
0.995927 0.0901655i \(-0.0287396\pi\)
\(752\) 0 0
\(753\) −39.7840 21.3255i −1.44981 0.777146i
\(754\) 0 0
\(755\) −0.529731 0.944854i −0.0192789 0.0343868i
\(756\) 0 0
\(757\) −6.37968 21.8663i −0.231873 0.794744i −0.989807 0.142413i \(-0.954514\pi\)
0.757934 0.652331i \(-0.226209\pi\)
\(758\) 0 0
\(759\) 3.58462 + 4.59607i 0.130114 + 0.166827i
\(760\) 0 0
\(761\) 10.5749 + 28.1304i 0.383339 + 1.01973i 0.976666 + 0.214765i \(0.0688984\pi\)
−0.593327 + 0.804961i \(0.702186\pi\)
\(762\) 0 0
\(763\) 48.7630 31.1015i 1.76534 1.12595i
\(764\) 0 0
\(765\) 1.13066 + 0.261284i 0.0408791 + 0.00944675i
\(766\) 0 0
\(767\) 17.6733 42.1026i 0.638146 1.52024i
\(768\) 0 0
\(769\) 3.81369 + 40.1823i 0.137525 + 1.44901i 0.751524 + 0.659705i \(0.229319\pi\)
−0.613999 + 0.789307i \(0.710440\pi\)
\(770\) 0 0
\(771\) 63.3971 43.8962i 2.28319 1.58088i
\(772\) 0 0
\(773\) 14.5023 + 12.6980i 0.521613 + 0.456715i 0.878712 0.477351i \(-0.158403\pi\)
−0.357100 + 0.934066i \(0.616234\pi\)
\(774\) 0 0
\(775\) 6.60468 + 4.57309i 0.237247 + 0.164270i
\(776\) 0 0
\(777\) −24.0484 15.3383i −0.862732 0.550259i
\(778\) 0 0
\(779\) −10.0349 + 75.3043i −0.359536 + 2.69806i
\(780\) 0 0
\(781\) 5.08121 8.30942i 0.181820 0.297334i
\(782\) 0 0
\(783\) −1.12551 1.14702i −0.0402225 0.0409910i
\(784\) 0 0
\(785\) 0.917582 4.34383i 0.0327499 0.155038i
\(786\) 0 0
\(787\) 17.1049 30.5092i 0.609725 1.08754i −0.377165 0.926146i \(-0.623101\pi\)
0.986891 0.161390i \(-0.0515976\pi\)
\(788\) 0 0
\(789\) −5.13789 20.4603i −0.182914 0.728404i
\(790\) 0 0
\(791\) −3.61750 5.44179i −0.128623 0.193488i
\(792\) 0 0
\(793\) 17.4493 + 52.3516i 0.619643 + 1.85906i
\(794\) 0 0
\(795\) −17.3143 1.97456i −0.614074 0.0700303i
\(796\) 0 0