Properties

Label 668.2.e.a.297.3
Level $668$
Weight $2$
Character 668.297
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

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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 297.3
Character \(\chi\) \(=\) 668.297
Dual form 668.2.e.a.9.3

$q$-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 \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{72}{83}\right)\) \(1\)

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 0.557765 + 0.829999i \(0.311659\pi\)
−0.755648 + 0.654977i \(0.772678\pi\)
\(4\) 0 0
\(5\) −0.628586 + 0.277966i −0.281112 + 0.124310i −0.540181 0.841549i \(-0.681644\pi\)
0.259069 + 0.965859i \(0.416584\pi\)
\(6\) 0 0
\(7\) −1.47454 3.17087i −0.557325 1.19848i −0.959186 0.282775i \(-0.908745\pi\)
0.401861 0.915701i \(-0.368364\pi\)
\(8\) 0 0
\(9\) −3.60268 0.977525i −1.20089 0.325842i
\(10\) 0 0
\(11\) −0.684433 0.877554i −0.206364 0.264593i 0.674169 0.738577i \(-0.264502\pi\)
−0.880533 + 0.473985i \(0.842815\pi\)
\(12\) 0 0
\(13\) −1.75582 3.42993i −0.486977 0.951291i −0.995898 0.0904779i \(-0.971161\pi\)
0.508922 0.860813i \(-0.330044\pi\)
\(14\) 0 0
\(15\) −0.499499 1.71203i −0.128970 0.442044i
\(16\) 0 0
\(17\) 0.451009 0.0342072i 0.109386 0.00829646i −0.0208221 0.999783i \(-0.506628\pi\)
0.130208 + 0.991487i \(0.458436\pi\)
\(18\) 0 0
\(19\) −4.29462 6.46039i −0.985254 1.48212i −0.872573 0.488484i \(-0.837550\pi\)
−0.112681 0.993631i \(-0.535944\pi\)
\(20\) 0 0
\(21\) 8.66104 2.70581i 1.88999 0.590456i
\(22\) 0 0
\(23\) 1.87555 0.745869i 0.391079 0.155524i −0.165718 0.986173i \(-0.552994\pi\)
0.556797 + 0.830649i \(0.312030\pi\)
\(24\) 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 0.295492 0.955345i \(-0.404516\pi\)
−0.441293 + 0.897363i \(0.645480\pi\)
\(30\) 0 0
\(31\) −1.72875 0.399495i −0.310492 0.0717515i 0.0670335 0.997751i \(-0.478647\pi\)
−0.377525 + 0.925999i \(0.623225\pi\)
\(32\) 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 −0.502347 0.864666i \(-0.667530\pi\)
0.00359603 + 0.999994i \(0.498855\pi\)
\(38\) 0 0
\(39\) 9.42376 3.34047i 1.50901 0.534904i
\(40\) 0 0
\(41\) 8.80006 + 4.29666i 1.37434 + 0.671025i 0.969892 0.243536i \(-0.0783075\pi\)
0.404447 + 0.914562i \(0.367464\pi\)
\(42\) 0 0
\(43\) 0.281863 + 2.96980i 0.0429837 + 0.452890i 0.990922 + 0.134437i \(0.0429225\pi\)
−0.947938 + 0.318454i \(0.896837\pi\)
\(44\) 0 0
\(45\) 2.53631 0.386964i 0.378091 0.0576852i
\(46\) 0 0
\(47\) 0.207333 10.9540i 0.0302426 1.59781i −0.586037 0.810284i \(-0.699313\pi\)
0.616279 0.787528i \(-0.288639\pi\)
\(48\) 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 −0.616877 0.787060i \(-0.711602\pi\)
0.844388 0.535731i \(-0.179964\pi\)
\(54\) 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 −0.721047 0.692886i \(-0.756339\pi\)
−0.817303 + 0.576209i \(0.804532\pi\)
\(60\) 0 0
\(61\) 10.0304 + 10.2220i 1.28426 + 1.30880i 0.927128 + 0.374744i \(0.122269\pi\)
0.357132 + 0.934054i \(0.383755\pi\)
\(62\) 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 0.142784 0.989754i \(-0.454395\pi\)
−0.636103 + 0.771604i \(0.719455\pi\)
\(68\) 0 0
\(69\) 1.27558 + 5.07965i 0.153562 + 0.611519i
\(70\) 0 0
\(71\) −8.69542 0.991644i −1.03196 0.117686i −0.419148 0.907918i \(-0.637671\pi\)
−0.612808 + 0.790231i \(0.709960\pi\)
\(72\) 0 0
\(73\) −1.19028 0.892634i −0.139312 0.104475i 0.528032 0.849225i \(-0.322930\pi\)
−0.667344 + 0.744750i \(0.732569\pi\)
\(74\) 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 −0.999061 0.0433345i \(-0.986202\pi\)
0.723106 0.690737i \(-0.242714\pi\)
\(80\) 0 0
\(81\) −5.40490 3.16615i −0.600544 0.351794i
\(82\) 0 0
\(83\) −1.50388 2.08647i −0.165072 0.229020i 0.720578 0.693374i \(-0.243877\pi\)
−0.885649 + 0.464355i \(0.846286\pi\)
\(84\) 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 −0.887146 0.461489i \(-0.847315\pi\)
0.996123 + 0.0879713i \(0.0280384\pi\)
\(90\) 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 −0.360583 0.932727i \(-0.617422\pi\)
0.0852100 + 0.996363i \(0.472844\pi\)
\(98\) 0 0
\(99\) 1.60796 + 3.83060i 0.161606 + 0.384989i
\(100\) 0 0
\(101\) −0.783642 + 8.25670i −0.0779753 + 0.821573i 0.867835 + 0.496853i \(0.165511\pi\)
−0.945810 + 0.324720i \(0.894730\pi\)
\(102\) 0 0
\(103\) 1.29322 + 0.895429i 0.127425 + 0.0882292i 0.631263 0.775569i \(-0.282537\pi\)
−0.503838 + 0.863798i \(0.668079\pi\)
\(104\) 0 0
\(105\) −4.69208 + 4.10831i −0.457901 + 0.400930i
\(106\) 0 0
\(107\) −10.2876 + 7.12314i −0.994539 + 0.688620i −0.950601 0.310414i \(-0.899532\pi\)
−0.0439371 + 0.999034i \(0.513990\pi\)
\(108\) 0 0
\(109\) −13.9444 + 8.89388i −1.33563 + 0.851880i −0.996058 0.0886995i \(-0.971729\pi\)
−0.339575 + 0.940579i \(0.610283\pi\)
\(110\) 0 0
\(111\) −1.07741 8.08520i −0.102263 0.767413i
\(112\) 0 0
\(113\) −0.974842 1.59418i −0.0917055 0.149968i 0.803980 0.594657i \(-0.202712\pi\)
−0.895685 + 0.444689i \(0.853314\pi\)
\(114\) 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 0.774459 0.632624i \(-0.218022\pi\)
0.897012 + 0.442005i \(0.145733\pi\)
\(128\) 0 0
\(129\) −7.73510 0.292917i −0.681037 0.0257899i
\(130\) 0 0
\(131\) −0.696551 12.2553i −0.0608580 1.07075i −0.873136 0.487477i \(-0.837917\pi\)
0.812278 0.583271i \(-0.198227\pi\)
\(132\) 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 0.208665 0.977987i \(-0.433088\pi\)
−0.453866 + 0.891070i \(0.649956\pi\)
\(138\) 0 0
\(139\) −13.9728 + 13.2012i −1.18516 + 1.11971i −0.194851 + 0.980833i \(0.562422\pi\)
−0.990309 + 0.138879i \(0.955650\pi\)
\(140\) 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 −0.356737 0.934205i \(-0.616111\pi\)
0.840305 + 0.542114i \(0.182376\pi\)
\(150\) 0 0
\(151\) 1.26088 0.945573i 0.102609 0.0769497i −0.547427 0.836854i \(-0.684393\pi\)
0.650035 + 0.759904i \(0.274754\pi\)
\(152\) 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 −0.892072 0.451893i \(-0.850749\pi\)
0.998621 0.0525064i \(-0.0167210\pi\)
\(158\) 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 0.999947 + 0.0102502i \(0.00326278\pi\)
−0.793834 + 0.608135i \(0.791918\pi\)
\(164\) 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 0.465759 0.884912i \(-0.345781\pi\)
−0.857056 + 0.515223i \(0.827709\pi\)
\(174\) 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 −0.399652 0.916667i \(-0.630869\pi\)
−0.0326264 + 0.999468i \(0.510387\pi\)
\(180\) 0 0
\(181\) 4.02778 + 0.771500i 0.299382 + 0.0573452i 0.335618 0.941998i \(-0.391055\pi\)
−0.0362358 + 0.999343i \(0.511537\pi\)
\(182\) 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 0.471078 + 0.882092i \(0.343865\pi\)
−0.978089 + 0.208188i \(0.933243\pi\)
\(192\) 0 0
\(193\) 4.06364 + 0.619988i 0.292507 + 0.0446277i 0.295418 0.955368i \(-0.404541\pi\)
−0.00291102 + 0.999996i \(0.500927\pi\)
\(194\) 0 0
\(195\) −4.99510 + 4.71926i −0.357707 + 0.337953i
\(196\) 0 0
\(197\) 13.1975 + 4.67815i 0.940280 + 0.333304i 0.759713 0.650258i \(-0.225339\pi\)
0.180567 + 0.983563i \(0.442207\pi\)
\(198\) 0 0
\(199\) 0.108310 + 5.72234i 0.00767787 + 0.405646i 0.982871 + 0.184292i \(0.0589993\pi\)
−0.975194 + 0.221354i \(0.928952\pi\)
\(200\) 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 −0.814064 0.580776i \(-0.802749\pi\)
0.850593 + 0.525825i \(0.176243\pi\)
\(212\) 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 −0.943737 0.330697i \(-0.892716\pi\)
0.824207 0.566289i \(-0.191621\pi\)
\(224\) 0 0
\(225\) 14.2497 9.08857i 0.949977 0.605904i
\(226\) 0 0
\(227\) 9.19734 6.36826i 0.610449 0.422676i −0.223354 0.974737i \(-0.571701\pi\)
0.833804 + 0.552061i \(0.186159\pi\)
\(228\) 0 0
\(229\) −1.13129 + 0.990539i −0.0747578 + 0.0654566i −0.695318 0.718702i \(-0.744737\pi\)
0.620560 + 0.784159i \(0.286905\pi\)
\(230\) 0 0
\(231\) −8.30240 5.74859i −0.546258 0.378230i
\(232\) 0 0
\(233\) −1.32294 + 13.9389i −0.0866686 + 0.913168i 0.841315 + 0.540546i \(0.181782\pi\)
−0.927983 + 0.372622i \(0.878459\pi\)
\(234\) 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 0.410418 0.911898i \(-0.365383\pi\)
−0.653806 + 0.756662i \(0.726829\pi\)
\(240\) 0 0
\(241\) −1.80058 + 4.78976i −0.115986 + 0.308536i −0.981238 0.192801i \(-0.938243\pi\)
0.865252 + 0.501337i \(0.167158\pi\)
\(242\) 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 0.999061 0.0433343i \(-0.0137980\pi\)
−0.357021 + 0.934096i \(0.616208\pi\)
\(252\) 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 0.0881912 0.996104i \(-0.471891\pi\)
0.756508 0.653984i \(-0.226904\pi\)
\(258\) 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 0.358733 0.933440i \(-0.383209\pi\)
0.139352 + 0.990243i \(0.455498\pi\)
\(264\) 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 0.961543 0.274654i \(-0.0885634\pi\)
−0.0699951 + 0.997547i \(0.522298\pi\)
\(270\) 0 0
\(271\) −0.249854 1.45269i −0.0151775 0.0882446i 0.976952 0.213457i \(-0.0684724\pi\)
−0.992130 + 0.125213i \(0.960039\pi\)
\(272\) 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 −0.862293 0.506410i \(-0.830972\pi\)
−0.130990 + 0.991384i \(0.541815\pi\)
\(278\) 0 0
\(279\) 5.83760 + 3.12914i 0.349488 + 0.187337i
\(280\) 0 0
\(281\) −0.355865 + 2.06905i −0.0212291 + 0.123429i −0.994210 0.107458i \(-0.965729\pi\)
0.972981 + 0.230887i \(0.0741628\pi\)
\(282\) 0 0
\(283\) 0.480369 8.45171i 0.0285550 0.502402i −0.951993 0.306121i \(-0.900969\pi\)
0.980548 0.196281i \(-0.0628866\pi\)
\(284\) 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 −0.996521 0.0833408i \(-0.973441\pi\)
−0.678576 0.734531i \(-0.737402\pi\)
\(294\) 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 −0.921657 0.388007i \(-0.873164\pi\)
0.922460 + 0.386093i \(0.126176\pi\)
\(308\) 0 0
\(309\) −2.74634 + 3.01933i −0.156234 + 0.171764i
\(310\) 0 0
\(311\) 17.2635 6.86536i 0.978924 0.389299i 0.175352 0.984506i \(-0.443894\pi\)
0.803572 + 0.595207i \(0.202930\pi\)
\(312\) 0 0
\(313\) 19.7941 6.18389i 1.11883 0.349534i 0.317797 0.948159i \(-0.397057\pi\)
0.801030 + 0.598624i \(0.204286\pi\)
\(314\) 0 0
\(315\) −4.96691 7.47171i −0.279854 0.420983i
\(316\) 0 0
\(317\) 23.3162 1.76844i 1.30957 0.0993254i 0.597746 0.801686i \(-0.296063\pi\)
0.711822 + 0.702360i \(0.247870\pi\)
\(318\) 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 0.953030 + 0.302877i \(0.0979471\pi\)
−0.999086 + 0.0427432i \(0.986390\pi\)
\(332\) 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 0.410849 + 0.911703i \(0.365232\pi\)
−0.635255 + 0.772302i \(0.719105\pi\)
\(338\) 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 −0.784016 0.620740i \(-0.786832\pi\)
−0.0451374 0.998981i \(-0.514373\pi\)
\(348\) 0 0
\(349\) −5.73871 19.6694i −0.307186 1.05288i −0.956349 0.292227i \(-0.905604\pi\)
0.649163 0.760649i \(-0.275119\pi\)
\(350\) 0 0
\(351\) −7.30718 + 0.554220i −0.390028 + 0.0295821i
\(352\) 0 0
\(353\) −7.38945 11.1159i −0.393301 0.591641i 0.581820 0.813318i \(-0.302341\pi\)
−0.975120 + 0.221677i \(0.928847\pi\)
\(354\) 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 −0.947534 0.319656i \(-0.896433\pi\)
0.407754 + 0.913092i \(0.366312\pi\)
\(360\) 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 0.131380 0.991332i \(-0.458059\pi\)
0.928953 + 0.370197i \(0.120710\pi\)
\(368\) 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 −0.901507 0.432765i \(-0.857538\pi\)
−0.427684 + 0.903928i \(0.640671\pi\)
\(374\) 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 −0.137860 0.990452i \(-0.544022\pi\)
0.163763 + 0.986500i \(0.447637\pi\)
\(380\) 0 0
\(381\) −0.930947 + 49.1849i −0.0476939 + 2.51982i
\(382\) 0 0
\(383\) 16.4205 19.4858i 0.839047 0.995677i −0.160915 0.986968i \(-0.551445\pi\)
0.999962 0.00870907i \(-0.00277222\pi\)
\(384\) 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 0.999178 + 0.0405490i \(0.0129107\pi\)
0.586915 + 0.809649i \(0.300342\pi\)
\(390\) 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 −0.744096 0.668072i \(-0.767120\pi\)
0.478132 0.878288i \(-0.341314\pi\)
\(398\) 0 0
\(399\) −54.6765 44.3333i −2.73725 2.21944i
\(400\) 0 0
\(401\) 9.75140 + 4.31215i 0.486962 + 0.215339i 0.633315 0.773894i \(-0.281694\pi\)
−0.146354 + 0.989232i \(0.546754\pi\)
\(402\) 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 0.728561 0.684981i \(-0.240190\pi\)
−0.798564 + 0.601910i \(0.794406\pi\)
\(410\) 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 −0.604110 0.796901i \(-0.706471\pi\)
0.329208 + 0.944258i \(0.393218\pi\)
\(420\) 0 0
\(421\) −4.64951 + 8.29309i −0.226603 + 0.404180i −0.961833 0.273638i \(-0.911773\pi\)
0.735230 + 0.677818i \(0.237074\pi\)
\(422\) 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 0.214845 0.976648i \(-0.431075\pi\)
0.621565 + 0.783362i \(0.286497\pi\)
\(432\) 0 0
\(433\) −5.38277 12.8232i −0.258679 0.616244i 0.739713 0.672922i \(-0.234961\pi\)
−0.998393 + 0.0566781i \(0.981949\pi\)
\(434\) 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 −0.679172 0.733979i \(-0.737661\pi\)
0.637836 + 0.770172i \(0.279830\pi\)
\(440\) 0 0
\(441\) 16.0472 11.1111i 0.764151 0.529100i
\(442\) 0 0
\(443\) 27.8462 17.7606i 1.32301 0.843829i 0.328106 0.944641i \(-0.393590\pi\)
0.994906 + 0.100812i \(0.0321440\pi\)
\(444\) 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 0.167511 0.985870i \(-0.446427\pi\)
0.982524 0.186138i \(-0.0595972\pi\)
\(450\) 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 −0.668057 0.744110i \(-0.732874\pi\)
0.944685 + 0.327979i \(0.106368\pi\)
\(458\) 0 0
\(459\) 0.272003 0.816068i 0.0126960 0.0380908i
\(460\) 0 0
\(461\) 27.1600 3.09738i 1.26497 0.144259i 0.545099 0.838372i \(-0.316492\pi\)
0.719867 + 0.694112i \(0.244203\pi\)
\(462\) 0 0
\(463\) 20.4800 + 0.775550i 0.951788 + 0.0360429i 0.509169 0.860667i \(-0.329953\pi\)
0.442619 + 0.896710i \(0.354049\pi\)
\(464\) 0 0
\(465\) 0.179559 + 3.15921i 0.00832687 + 0.146505i
\(466\) 0 0
\(467\) −18.6146 + 30.4409i −0.861380 + 1.40863i 0.0507400 + 0.998712i \(0.483842\pi\)
−0.912120 + 0.409923i \(0.865556\pi\)
\(468\) 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 0.703143 0.711048i \(-0.251779\pi\)
0.754905 + 0.655834i \(0.227683\pi\)
\(480\) 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 −0.413997 0.910278i \(-0.635868\pi\)
−0.721070 + 0.692862i \(0.756349\pi\)
\(488\) 0 0
\(489\) −21.2083 + 4.06235i −0.959074 + 0.183706i
\(490\) 0 0
\(491\) 1.93532 9.16181i 0.0873400 0.413467i −0.912649 0.408744i \(-0.865967\pi\)
0.999989 0.00472219i \(-0.00150313\pi\)
\(492\) 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 0.278349 + 0.960480i \(0.410213\pi\)
−0.999214 + 0.0396442i \(0.987378\pi\)
\(500\) 0 0
\(501\) 19.5091 + 27.2726i 0.871603 + 1.21845i
\(502\) 0 0
\(503\) −17.8658 + 24.7869i −0.796597 + 1.10519i 0.195621 + 0.980680i \(0.437328\pi\)
−0.992218 + 0.124515i \(0.960263\pi\)
\(504\) 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 0.944038 0.329836i \(-0.106993\pi\)
0.588384 + 0.808582i \(0.299765\pi\)
\(510\) 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 0.417127 0.908848i \(-0.363037\pi\)
−0.944194 + 0.329388i \(0.893157\pi\)
\(522\) 0 0
\(523\) 29.3291 1.11065i 1.28247 0.0485654i 0.612212 0.790693i \(-0.290280\pi\)
0.670258 + 0.742128i \(0.266183\pi\)
\(524\) 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 −0.516949 0.856016i \(-0.672932\pi\)
−0.310938 + 0.950430i \(0.600643\pi\)
\(542\) 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 −0.0209517 0.999780i \(-0.506670\pi\)
0.490802 0.871271i \(-0.336704\pi\)
\(548\) 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 0.854875 + 0.518834i \(0.173634\pi\)
−0.689180 + 0.724590i \(0.742029\pi\)
\(558\) 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 0.323597 0.946195i \(-0.395108\pi\)
0.980648 0.195779i \(-0.0627234\pi\)
\(564\) 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 0.938598 + 0.345013i \(0.112126\pi\)
−0.411120 + 0.911581i \(0.634862\pi\)
\(570\) 0 0
\(571\) −16.2231 + 3.74899i −0.678915 + 0.156890i −0.550506 0.834831i \(-0.685565\pi\)
−0.128409 + 0.991721i \(0.540987\pi\)
\(572\) 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 0.237913 + 0.971286i \(0.423537\pi\)
−0.999983 + 0.00581146i \(0.998150\pi\)
\(578\) 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 −0.976882 0.213779i \(-0.931423\pi\)
−0.664200 0.747555i \(-0.731228\pi\)
\(588\) 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 0.623217 0.782049i \(-0.285825\pi\)
−0.876371 + 0.481637i \(0.840042\pi\)
\(594\) 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 0.999980 + 0.00624497i \(0.00198785\pi\)
−0.878396 + 0.477934i \(0.841386\pi\)
\(600\) 0 0
\(601\) 33.2171 + 14.6889i 1.35495 + 0.599172i 0.949160 0.314793i \(-0.101935\pi\)
0.405793 + 0.913965i \(0.366995\pi\)
\(602\) 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 0.238555 0.971129i \(-0.423326\pi\)
−0.975470 + 0.220134i \(0.929350\pi\)
\(608\) 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 0.717979 0.696064i \(-0.245067\pi\)
−0.182195 + 0.983262i \(0.558320\pi\)
\(614\) 0 0
\(615\) 2.96038 17.2121i 0.119374 0.694060i
\(616\) 0 0
\(617\) −0.902893 + 15.8857i −0.0363491 + 0.639534i 0.927621 + 0.373523i \(0.121850\pi\)
−0.963970 + 0.266011i \(0.914294\pi\)
\(618\) 0 0
\(619\) −31.6936 + 37.6101i −1.27387 + 1.51168i −0.520915 + 0.853609i \(0.674409\pi\)
−0.752959 + 0.658068i \(0.771374\pi\)
\(620\) 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 −0.855674 0.517515i \(-0.826857\pi\)
−0.476742 + 0.879043i \(0.658182\pi\)
\(632\) 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 −0.939548 0.342416i \(-0.888755\pi\)
0.902450 + 0.430795i \(0.141767\pi\)
\(642\) 0 0
\(643\) 11.8122 12.9863i 0.465827 0.512131i −0.461113 0.887341i \(-0.652550\pi\)
0.926940 + 0.375210i \(0.122429\pi\)
\(644\) 0 0
\(645\) 4.94359 1.96597i 0.194654 0.0774100i
\(646\) 0 0
\(647\) −20.7221 + 6.47381i −0.814669 + 0.254512i −0.677016 0.735969i \(-0.736727\pi\)
−0.137653 + 0.990480i \(0.543956\pi\)
\(648\) 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 −0.927960 0.372680i \(-0.878439\pi\)
0.581966 0.813213i \(-0.302284\pi\)
\(654\) 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 0.180444 0.983585i \(-0.442246\pi\)
−0.341459 + 0.939897i \(0.610921\pi\)
\(660\) 0 0
\(661\) 0.0648022 + 0.139351i 0.00252051 + 0.00542013i 0.908008 0.418953i \(-0.137603\pi\)
−0.905487 + 0.424373i \(0.860494\pi\)
\(662\) 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 −0.630104 0.776511i \(-0.716988\pi\)
0.150451 + 0.988617i \(0.451927\pi\)
\(674\) 0 0
\(675\) 3.63085 + 7.80781i 0.139752 + 0.300523i
\(676\) 0 0
\(677\) −12.9525 3.51444i −0.497806 0.135071i 0.00410280 0.999992i \(-0.498694\pi\)
−0.501909 + 0.864920i \(0.667369\pi\)
\(678\) 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 0.905621 + 0.424088i \(0.139405\pi\)
−0.535486 + 0.844544i \(0.679872\pi\)
\(684\) 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 −0.312512 0.949914i \(-0.601171\pi\)
0.425192 + 0.905103i \(0.360207\pi\)
\(692\) 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 −0.927641 0.373473i \(-0.878167\pi\)
−0.127880 + 0.991790i \(0.540817\pi\)
\(702\) 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 −0.495502 0.868607i \(-0.665016\pi\)
−0.989654 + 0.143475i \(0.954172\pi\)
\(710\) 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 0.986944 + 0.161062i \(0.0514920\pi\)
−0.998838 + 0.0481968i \(0.984653\pi\)
\(720\) 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 −0.194874 0.980828i \(-0.562430\pi\)
−0.340577 + 0.940217i \(0.610622\pi\)
\(728\) 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 0.161164 0.986928i \(-0.448475\pi\)
−0.932310 + 0.361660i \(0.882210\pi\)
\(734\) 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 0.870544 0.492090i \(-0.163767\pi\)
0.737394 + 0.675463i \(0.236056\pi\)
\(740\) 0 0
\(741\) −62.0523 46.5351i −2.27955 1.70951i
\(742\) 0 0
\(743\) −1.20878 1.43443i −0.0443458 0.0526242i 0.742065 0.670328i \(-0.233846\pi\)
−0.786411 + 0.617703i \(0.788063\pi\)
\(744\) 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 0.995927 + 0.0901655i \(0.0287396\pi\)
−0.229381 + 0.973337i \(0.573670\pi\)
\(752\) 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 0.757934 + 0.652331i \(0.226209\pi\)
−0.989807 + 0.142413i \(0.954514\pi\)
\(758\) 0 0
\(759\) 3.58462 4.59607i 0.130114 0.166827i
\(760\) 0 0
\(761\) 10.5749 28.1304i 0.383339 1.01973i −0.593327 0.804961i \(-0.702186\pi\)
0.976666 0.214765i \(-0.0688984\pi\)
\(762\) 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 −0.613999 0.789307i \(-0.710440\pi\)
0.751524 0.659705i \(-0.229319\pi\)
\(770\) 0 0
\(771\) 63.3971 + 43.8962i 2.28319 + 1.58088i
\(772\) 0 0
\(773\) 14.5023 12.6980i 0.521613 0.456715i −0.357100 0.934066i \(-0.616234\pi\)
0.878712 + 0.477351i \(0.158403\pi\)
\(774\) 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 0.986891 + 0.161390i \(0.0515976\pi\)
−0.377165 + 0.926146i \(0.623101\pi\)
\(788\) 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