Properties

Label 668.2.e.a.9.5
Level $668$
Weight $2$
Character 668.9
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 9.5
Character \(\chi\) \(=\) 668.9
Dual form 668.2.e.a.297.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.178407 - 1.33882i) q^{3} +(-1.62557 - 0.718841i) q^{5} +(-0.315447 + 0.678340i) q^{7} +(1.13471 - 0.307883i) q^{9} +O(q^{10})\) \(q+(-0.178407 - 1.33882i) q^{3} +(-1.62557 - 0.718841i) q^{5} +(-0.315447 + 0.678340i) q^{7} +(1.13471 - 0.307883i) q^{9} +(1.52116 - 1.95037i) q^{11} +(1.00511 - 1.96345i) q^{13} +(-0.672384 + 2.30459i) q^{15} +(-5.09594 - 0.386506i) q^{17} +(1.04555 - 1.57282i) q^{19} +(0.964452 + 0.301306i) q^{21} +(-4.90068 - 1.94890i) q^{23} +(-1.23861 - 1.36174i) q^{25} +(-2.18295 - 5.20038i) q^{27} +(-2.38370 + 0.947953i) q^{29} +(-2.94022 + 0.679454i) q^{31} +(-2.88258 - 1.68859i) q^{33} +(1.00040 - 0.875933i) q^{35} +(-0.619516 - 0.168095i) q^{37} +(-2.80803 - 0.995372i) q^{39} +(-6.16684 + 3.01098i) q^{41} +(0.510488 - 5.37867i) q^{43} +(-2.06587 - 0.315188i) q^{45} +(-0.0873353 - 4.61420i) q^{47} +(4.15014 + 4.92488i) q^{49} +(0.391691 + 6.89149i) q^{51} +(0.991179 + 5.76288i) q^{53} +(-3.87475 + 2.07700i) q^{55} +(-2.29226 - 1.11920i) q^{57} +(5.11457 - 0.387920i) q^{59} +(-3.03294 + 3.09088i) q^{61} +(-0.149091 + 0.866838i) q^{63} +(-3.04530 + 2.46922i) q^{65} +(4.23717 - 1.87371i) q^{67} +(-1.73491 + 6.90882i) q^{69} +(4.23010 - 0.482409i) q^{71} +(10.1577 - 7.61759i) q^{73} +(-1.60214 + 1.90122i) q^{75} +(0.843169 + 1.64710i) q^{77} +(2.69600 - 7.17167i) q^{79} +(-3.52945 + 2.06753i) q^{81} +(4.97769 - 6.90601i) q^{83} +(8.00597 + 4.29146i) q^{85} +(1.69441 + 3.02223i) q^{87} +(-4.27601 - 14.6560i) q^{89} +(1.01483 + 1.30118i) q^{91} +(1.43422 + 3.81520i) q^{93} +(-2.83023 + 1.80515i) q^{95} +(-9.87660 - 2.28238i) q^{97} +(1.12558 - 2.68144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) −0.178407 1.33882i −0.103004 0.772967i −0.964290 0.264848i \(-0.914678\pi\)
0.861287 0.508119i \(-0.169659\pi\)
\(4\) 0 0
\(5\) −1.62557 0.718841i −0.726977 0.321476i 0.00762730 0.999971i \(-0.497572\pi\)
−0.734605 + 0.678495i \(0.762632\pi\)
\(6\) 0 0
\(7\) −0.315447 + 0.678340i −0.119228 + 0.256388i −0.957258 0.289236i \(-0.906599\pi\)
0.838030 + 0.545624i \(0.183707\pi\)
\(8\) 0 0
\(9\) 1.13471 0.307883i 0.378236 0.102628i
\(10\) 0 0
\(11\) 1.52116 1.95037i 0.458646 0.588059i −0.502335 0.864673i \(-0.667526\pi\)
0.960981 + 0.276614i \(0.0892124\pi\)
\(12\) 0 0
\(13\) 1.00511 1.96345i 0.278769 0.544564i −0.708095 0.706117i \(-0.750445\pi\)
0.986864 + 0.161553i \(0.0516502\pi\)
\(14\) 0 0
\(15\) −0.672384 + 2.30459i −0.173609 + 0.595043i
\(16\) 0 0
\(17\) −5.09594 0.386506i −1.23595 0.0937415i −0.558620 0.829424i \(-0.688669\pi\)
−0.677327 + 0.735682i \(0.736862\pi\)
\(18\) 0 0
\(19\) 1.04555 1.57282i 0.239866 0.360830i −0.693071 0.720869i \(-0.743743\pi\)
0.932937 + 0.360039i \(0.117237\pi\)
\(20\) 0 0
\(21\) 0.964452 + 0.301306i 0.210461 + 0.0657503i
\(22\) 0 0
\(23\) −4.90068 1.94890i −1.02186 0.406375i −0.202275 0.979329i \(-0.564833\pi\)
−0.819587 + 0.572954i \(0.805797\pi\)
\(24\) 0 0
\(25\) −1.23861 1.36174i −0.247723 0.272347i
\(26\) 0 0
\(27\) −2.18295 5.20038i −0.420109 1.00081i
\(28\) 0 0
\(29\) −2.38370 + 0.947953i −0.442643 + 0.176030i −0.580218 0.814461i \(-0.697033\pi\)
0.137576 + 0.990491i \(0.456069\pi\)
\(30\) 0 0
\(31\) −2.94022 + 0.679454i −0.528079 + 0.122034i −0.480770 0.876847i \(-0.659643\pi\)
−0.0473088 + 0.998880i \(0.515064\pi\)
\(32\) 0 0
\(33\) −2.88258 1.68859i −0.501792 0.293946i
\(34\) 0 0
\(35\) 1.00040 0.875933i 0.169099 0.148060i
\(36\) 0 0
\(37\) −0.619516 0.168095i −0.101848 0.0276346i 0.210576 0.977578i \(-0.432466\pi\)
−0.312424 + 0.949943i \(0.601141\pi\)
\(38\) 0 0
\(39\) −2.80803 0.995372i −0.449644 0.159387i
\(40\) 0 0
\(41\) −6.16684 + 3.01098i −0.963098 + 0.470236i −0.851982 0.523571i \(-0.824599\pi\)
−0.111117 + 0.993807i \(0.535443\pi\)
\(42\) 0 0
\(43\) 0.510488 5.37867i 0.0778487 0.820239i −0.868200 0.496215i \(-0.834723\pi\)
0.946049 0.324025i \(-0.105036\pi\)
\(44\) 0 0
\(45\) −2.06587 0.315188i −0.307961 0.0469855i
\(46\) 0 0
\(47\) −0.0873353 4.61420i −0.0127392 0.673050i −0.947854 0.318705i \(-0.896752\pi\)
0.935115 0.354345i \(-0.115296\pi\)
\(48\) 0 0
\(49\) 4.15014 + 4.92488i 0.592877 + 0.703554i
\(50\) 0 0
\(51\) 0.391691 + 6.89149i 0.0548477 + 0.965002i
\(52\) 0 0
\(53\) 0.991179 + 5.76288i 0.136149 + 0.791592i 0.970634 + 0.240561i \(0.0773316\pi\)
−0.834485 + 0.551031i \(0.814235\pi\)
\(54\) 0 0
\(55\) −3.87475 + 2.07700i −0.522472 + 0.280062i
\(56\) 0 0
\(57\) −2.29226 1.11920i −0.303617 0.148242i
\(58\) 0 0
\(59\) 5.11457 0.387920i 0.665861 0.0505028i 0.261642 0.965165i \(-0.415736\pi\)
0.404219 + 0.914662i \(0.367543\pi\)
\(60\) 0 0
\(61\) −3.03294 + 3.09088i −0.388328 + 0.395747i −0.879954 0.475059i \(-0.842427\pi\)
0.491626 + 0.870806i \(0.336403\pi\)
\(62\) 0 0
\(63\) −0.149091 + 0.866838i −0.0187837 + 0.109211i
\(64\) 0 0
\(65\) −3.04530 + 2.46922i −0.377723 + 0.306268i
\(66\) 0 0
\(67\) 4.23717 1.87371i 0.517653 0.228911i −0.129070 0.991636i \(-0.541199\pi\)
0.646723 + 0.762725i \(0.276139\pi\)
\(68\) 0 0
\(69\) −1.73491 + 6.90882i −0.208859 + 0.831724i
\(70\) 0 0
\(71\) 4.23010 0.482409i 0.502020 0.0572515i 0.141378 0.989956i \(-0.454847\pi\)
0.360642 + 0.932704i \(0.382558\pi\)
\(72\) 0 0
\(73\) 10.1577 7.61759i 1.18887 0.891571i 0.192893 0.981220i \(-0.438213\pi\)
0.995973 + 0.0896486i \(0.0285744\pi\)
\(74\) 0 0
\(75\) −1.60214 + 1.90122i −0.184999 + 0.219534i
\(76\) 0 0
\(77\) 0.843169 + 1.64710i 0.0960881 + 0.187704i
\(78\) 0 0
\(79\) 2.69600 7.17167i 0.303323 0.806876i −0.692979 0.720958i \(-0.743702\pi\)
0.996302 0.0859178i \(-0.0273823\pi\)
\(80\) 0 0
\(81\) −3.52945 + 2.06753i −0.392162 + 0.229725i
\(82\) 0 0
\(83\) 4.97769 6.90601i 0.546372 0.758034i −0.444066 0.895994i \(-0.646464\pi\)
0.990438 + 0.137961i \(0.0440547\pi\)
\(84\) 0 0
\(85\) 8.00597 + 4.29146i 0.868370 + 0.465475i
\(86\) 0 0
\(87\) 1.69441 + 3.02223i 0.181660 + 0.324017i
\(88\) 0 0
\(89\) −4.27601 14.6560i −0.453256 1.55353i −0.790711 0.612190i \(-0.790289\pi\)
0.337455 0.941342i \(-0.390434\pi\)
\(90\) 0 0
\(91\) 1.01483 + 1.30118i 0.106383 + 0.136400i
\(92\) 0 0
\(93\) 1.43422 + 3.81520i 0.148722 + 0.395618i
\(94\) 0 0
\(95\) −2.83023 + 1.80515i −0.290375 + 0.185204i
\(96\) 0 0
\(97\) −9.87660 2.28238i −1.00282 0.231741i −0.308356 0.951271i \(-0.599779\pi\)
−0.694461 + 0.719530i \(0.744357\pi\)
\(98\) 0 0
\(99\) 1.12558 2.68144i 0.113125 0.269495i
\(100\) 0 0
\(101\) 0.521352 + 5.49313i 0.0518764 + 0.546587i 0.983217 + 0.182438i \(0.0583990\pi\)
−0.931341 + 0.364149i \(0.881360\pi\)
\(102\) 0 0
\(103\) 8.67399 6.00589i 0.854674 0.591778i −0.0589852 0.998259i \(-0.518786\pi\)
0.913659 + 0.406481i \(0.133244\pi\)
\(104\) 0 0
\(105\) −1.35119 1.18308i −0.131863 0.115457i
\(106\) 0 0
\(107\) −0.506253 0.350531i −0.0489413 0.0338871i 0.544539 0.838735i \(-0.316704\pi\)
−0.593481 + 0.804848i \(0.702247\pi\)
\(108\) 0 0
\(109\) 7.16033 + 4.56693i 0.685835 + 0.437432i 0.834172 0.551505i \(-0.185946\pi\)
−0.148337 + 0.988937i \(0.547392\pi\)
\(110\) 0 0
\(111\) −0.114523 + 0.859409i −0.0108700 + 0.0815715i
\(112\) 0 0
\(113\) 2.49697 4.08335i 0.234895 0.384129i −0.713786 0.700364i \(-0.753021\pi\)
0.948681 + 0.316235i \(0.102419\pi\)
\(114\) 0 0
\(115\) 6.56545 + 6.69089i 0.612231 + 0.623929i
\(116\) 0 0
\(117\) 0.535997 2.53740i 0.0495529 0.234583i
\(118\) 0 0
\(119\) 1.86968 3.33485i 0.171393 0.305706i
\(120\) 0 0
\(121\) 1.18906 + 4.73513i 0.108097 + 0.430466i
\(122\) 0 0
\(123\) 5.13137 + 7.71910i 0.462680 + 0.696008i
\(124\) 0 0
\(125\) 3.84475 + 11.5351i 0.343885 + 1.03173i
\(126\) 0 0
\(127\) 8.26235 + 0.942255i 0.733165 + 0.0836116i 0.471896 0.881654i \(-0.343570\pi\)
0.261269 + 0.965266i \(0.415859\pi\)
\(128\) 0 0
\(129\) −7.29214 + 0.276143i −0.642037 + 0.0243130i
\(130\) 0 0
\(131\) 0.488687 8.59807i 0.0426968 0.751217i −0.903691 0.428185i \(-0.859153\pi\)
0.946388 0.323032i \(-0.104702\pi\)
\(132\) 0 0
\(133\) 0.737091 + 1.20538i 0.0639139 + 0.104520i
\(134\) 0 0
\(135\) −0.189707 + 10.0228i −0.0163273 + 0.862624i
\(136\) 0 0
\(137\) −8.84862 + 3.13660i −0.755989 + 0.267978i −0.684054 0.729431i \(-0.739785\pi\)
−0.0719346 + 0.997409i \(0.522917\pi\)
\(138\) 0 0
\(139\) 5.75643 + 5.43854i 0.488254 + 0.461291i 0.890989 0.454026i \(-0.150013\pi\)
−0.402735 + 0.915317i \(0.631940\pi\)
\(140\) 0 0
\(141\) −6.16199 + 0.940133i −0.518934 + 0.0791735i
\(142\) 0 0
\(143\) −2.30053 4.94707i −0.192380 0.413694i
\(144\) 0 0
\(145\) 4.55631 + 0.172541i 0.378381 + 0.0143288i
\(146\) 0 0
\(147\) 5.85310 6.43492i 0.482756 0.530743i
\(148\) 0 0
\(149\) 0.328823 + 0.266619i 0.0269382 + 0.0218423i 0.643185 0.765711i \(-0.277613\pi\)
−0.616247 + 0.787553i \(0.711348\pi\)
\(150\) 0 0
\(151\) 3.92316 + 2.94211i 0.319262 + 0.239426i 0.747533 0.664225i \(-0.231238\pi\)
−0.428270 + 0.903651i \(0.640877\pi\)
\(152\) 0 0
\(153\) −5.90140 + 1.13038i −0.477100 + 0.0913860i
\(154\) 0 0
\(155\) 5.26795 + 1.00905i 0.423132 + 0.0810488i
\(156\) 0 0
\(157\) 1.25035 + 5.91916i 0.0997891 + 0.472401i 0.999365 + 0.0356359i \(0.0113457\pi\)
−0.899576 + 0.436765i \(0.856124\pi\)
\(158\) 0 0
\(159\) 7.53862 2.35515i 0.597851 0.186775i
\(160\) 0 0
\(161\) 2.86792 2.70955i 0.226024 0.213542i
\(162\) 0 0
\(163\) 0.802028 2.40625i 0.0628196 0.188472i −0.912588 0.408880i \(-0.865919\pi\)
0.975408 + 0.220408i \(0.0707388\pi\)
\(164\) 0 0
\(165\) 3.47201 + 4.81704i 0.270295 + 0.375006i
\(166\) 0 0
\(167\) −0.554686 12.9109i −0.0429229 0.999078i
\(168\) 0 0
\(169\) 4.75645 + 6.59907i 0.365881 + 0.507621i
\(170\) 0 0
\(171\) 0.702150 2.10660i 0.0536948 0.161096i
\(172\) 0 0
\(173\) −18.3727 + 17.3581i −1.39685 + 1.31971i −0.508120 + 0.861286i \(0.669659\pi\)
−0.888732 + 0.458427i \(0.848413\pi\)
\(174\) 0 0
\(175\) 1.31444 0.410645i 0.0993622 0.0310419i
\(176\) 0 0
\(177\) −1.43183 6.77828i −0.107623 0.509487i
\(178\) 0 0
\(179\) 12.0773 + 2.31334i 0.902699 + 0.172907i 0.618433 0.785838i \(-0.287768\pi\)
0.284267 + 0.958745i \(0.408250\pi\)
\(180\) 0 0
\(181\) 2.29641 0.439865i 0.170691 0.0326949i −0.102068 0.994777i \(-0.532546\pi\)
0.272759 + 0.962083i \(0.412064\pi\)
\(182\) 0 0
\(183\) 4.67923 + 3.50911i 0.345899 + 0.259401i
\(184\) 0 0
\(185\) 0.886234 + 0.718584i 0.0651572 + 0.0528313i
\(186\) 0 0
\(187\) −8.50555 + 9.35103i −0.621987 + 0.683815i
\(188\) 0 0
\(189\) 4.21623 + 0.159663i 0.306686 + 0.0116138i
\(190\) 0 0
\(191\) −1.27526 2.74233i −0.0922747 0.198428i 0.855170 0.518348i \(-0.173453\pi\)
−0.947445 + 0.319919i \(0.896344\pi\)
\(192\) 0 0
\(193\) 15.5268 2.36891i 1.11764 0.170518i 0.434407 0.900717i \(-0.356958\pi\)
0.683235 + 0.730199i \(0.260573\pi\)
\(194\) 0 0
\(195\) 3.84914 + 3.63657i 0.275642 + 0.260421i
\(196\) 0 0
\(197\) −3.87834 + 1.37477i −0.276320 + 0.0979482i −0.468655 0.883381i \(-0.655261\pi\)
0.192335 + 0.981329i \(0.438394\pi\)
\(198\) 0 0
\(199\) −0.00538423 + 0.284466i −0.000381678 + 0.0201653i −0.999961 0.00884054i \(-0.997186\pi\)
0.999579 + 0.0290058i \(0.00923413\pi\)
\(200\) 0 0
\(201\) −3.26451 5.33852i −0.230261 0.376551i
\(202\) 0 0
\(203\) 0.108899 1.91599i 0.00764320 0.134476i
\(204\) 0 0
\(205\) 12.1891 0.461582i 0.851320 0.0322383i
\(206\) 0 0
\(207\) −6.16087 0.702599i −0.428210 0.0488340i
\(208\) 0 0
\(209\) −1.47714 4.43172i −0.102176 0.306549i
\(210\) 0 0
\(211\) 12.8567 + 19.3404i 0.885095 + 1.33145i 0.942886 + 0.333117i \(0.108100\pi\)
−0.0577908 + 0.998329i \(0.518406\pi\)
\(212\) 0 0
\(213\) −1.40054 5.57727i −0.0959634 0.382148i
\(214\) 0 0
\(215\) −4.69624 + 8.37645i −0.320281 + 0.571269i
\(216\) 0 0
\(217\) 0.466583 2.20880i 0.0316737 0.149943i
\(218\) 0 0
\(219\) −12.0108 12.2403i −0.811613 0.827120i
\(220\) 0 0
\(221\) −5.88089 + 9.61716i −0.395591 + 0.646920i
\(222\) 0 0
\(223\) −3.89849 + 29.2554i −0.261062 + 1.95909i 0.0212846 + 0.999773i \(0.493224\pi\)
−0.282347 + 0.959312i \(0.591113\pi\)
\(224\) 0 0
\(225\) −1.82472 1.16382i −0.121648 0.0775883i
\(226\) 0 0
\(227\) 10.9288 + 7.56710i 0.725368 + 0.502246i 0.873562 0.486712i \(-0.161804\pi\)
−0.148194 + 0.988958i \(0.547346\pi\)
\(228\) 0 0
\(229\) 1.26483 + 1.10747i 0.0835826 + 0.0731835i 0.699527 0.714606i \(-0.253394\pi\)
−0.615944 + 0.787790i \(0.711225\pi\)
\(230\) 0 0
\(231\) 2.05474 1.42271i 0.135192 0.0936072i
\(232\) 0 0
\(233\) 0.0609304 + 0.641982i 0.00399168 + 0.0420577i 0.997300 0.0734352i \(-0.0233962\pi\)
−0.993308 + 0.115493i \(0.963155\pi\)
\(234\) 0 0
\(235\) −3.17491 + 7.56349i −0.207108 + 0.493387i
\(236\) 0 0
\(237\) −10.0826 2.32997i −0.654932 0.151348i
\(238\) 0 0
\(239\) −14.2242 + 9.07232i −0.920086 + 0.586840i −0.910678 0.413116i \(-0.864440\pi\)
−0.00940770 + 0.999956i \(0.502995\pi\)
\(240\) 0 0
\(241\) −4.90485 13.0475i −0.315949 0.840462i −0.994387 0.105804i \(-0.966258\pi\)
0.678438 0.734658i \(-0.262657\pi\)
\(242\) 0 0
\(243\) −7.00800 8.98539i −0.449563 0.576413i
\(244\) 0 0
\(245\) −3.20614 10.9890i −0.204833 0.702063i
\(246\) 0 0
\(247\) −2.03726 3.63376i −0.129628 0.231211i
\(248\) 0 0
\(249\) −10.1340 5.43213i −0.642214 0.344248i
\(250\) 0 0
\(251\) 6.89835 9.57074i 0.435420 0.604099i −0.535198 0.844727i \(-0.679763\pi\)
0.970618 + 0.240627i \(0.0773532\pi\)
\(252\) 0 0
\(253\) −11.2558 + 6.59355i −0.707645 + 0.414533i
\(254\) 0 0
\(255\) 4.31717 11.4842i 0.270352 0.719167i
\(256\) 0 0
\(257\) −7.71616 15.0732i −0.481321 0.940242i −0.996535 0.0831802i \(-0.973492\pi\)
0.515214 0.857062i \(-0.327713\pi\)
\(258\) 0 0
\(259\) 0.309450 0.367217i 0.0192283 0.0228178i
\(260\) 0 0
\(261\) −2.41295 + 1.80955i −0.149358 + 0.112008i
\(262\) 0 0
\(263\) 13.6299 1.55439i 0.840458 0.0958476i 0.317555 0.948240i \(-0.397138\pi\)
0.522903 + 0.852392i \(0.324849\pi\)
\(264\) 0 0
\(265\) 2.53136 10.0805i 0.155500 0.619238i
\(266\) 0 0
\(267\) −18.8588 + 8.33954i −1.15414 + 0.510372i
\(268\) 0 0
\(269\) 19.6986 15.9722i 1.20104 0.973840i 0.201059 0.979579i \(-0.435562\pi\)
0.999984 + 0.00573887i \(0.00182675\pi\)
\(270\) 0 0
\(271\) 0.424924 2.47058i 0.0258123 0.150077i −0.969762 0.244051i \(-0.921523\pi\)
0.995575 + 0.0939745i \(0.0299572\pi\)
\(272\) 0 0
\(273\) 1.56098 1.59081i 0.0944751 0.0962802i
\(274\) 0 0
\(275\) −4.54002 + 0.344342i −0.273773 + 0.0207646i
\(276\) 0 0
\(277\) −5.97460 2.91712i −0.358979 0.175273i 0.250418 0.968138i \(-0.419432\pi\)
−0.609397 + 0.792865i \(0.708588\pi\)
\(278\) 0 0
\(279\) −3.12709 + 1.67623i −0.187214 + 0.100353i
\(280\) 0 0
\(281\) 3.32801 + 19.3496i 0.198532 + 1.15430i 0.898119 + 0.439752i \(0.144934\pi\)
−0.699587 + 0.714547i \(0.746633\pi\)
\(282\) 0 0
\(283\) −0.576932 10.1507i −0.0342950 0.603394i −0.968861 0.247605i \(-0.920357\pi\)
0.934566 0.355790i \(-0.115788\pi\)
\(284\) 0 0
\(285\) 2.92170 + 3.46711i 0.173066 + 0.205374i
\(286\) 0 0
\(287\) −0.0971552 5.13302i −0.00573489 0.302992i
\(288\) 0 0
\(289\) 9.01366 + 1.37521i 0.530215 + 0.0808948i
\(290\) 0 0
\(291\) −1.29364 + 13.6302i −0.0758343 + 0.799015i
\(292\) 0 0
\(293\) 1.54535 0.754521i 0.0902802 0.0440796i −0.393055 0.919515i \(-0.628582\pi\)
0.483335 + 0.875435i \(0.339425\pi\)
\(294\) 0 0
\(295\) −8.59295 3.04598i −0.500301 0.177344i
\(296\) 0 0
\(297\) −13.4633 3.65303i −0.781219 0.211970i
\(298\) 0 0
\(299\) −8.75233 + 7.66339i −0.506160 + 0.443185i
\(300\) 0 0
\(301\) 3.48753 + 2.04297i 0.201018 + 0.117755i
\(302\) 0 0
\(303\) 7.26130 1.67801i 0.417150 0.0963992i
\(304\) 0 0
\(305\) 7.15211 2.84425i 0.409529 0.162861i
\(306\) 0 0
\(307\) −5.33342 12.7056i −0.304394 0.725149i −0.999978 0.00670386i \(-0.997866\pi\)
0.695583 0.718445i \(-0.255146\pi\)
\(308\) 0 0
\(309\) −9.58830 10.5414i −0.545459 0.599680i
\(310\) 0 0
\(311\) −4.96995 1.97645i −0.281820 0.112074i 0.224348 0.974509i \(-0.427975\pi\)
−0.506168 + 0.862435i \(0.668938\pi\)
\(312\) 0 0
\(313\) −8.06704 2.52023i −0.455976 0.142452i 0.0615787 0.998102i \(-0.480386\pi\)
−0.517555 + 0.855650i \(0.673158\pi\)
\(314\) 0 0
\(315\) 0.865476 1.30193i 0.0487641 0.0733557i
\(316\) 0 0
\(317\) 3.64542 + 0.276490i 0.204747 + 0.0155292i 0.177603 0.984102i \(-0.443166\pi\)
0.0271444 + 0.999632i \(0.491359\pi\)
\(318\) 0 0
\(319\) −1.77713 + 6.09109i −0.0995001 + 0.341036i
\(320\) 0 0
\(321\) −0.378978 + 0.740319i −0.0211525 + 0.0413205i
\(322\) 0 0
\(323\) −5.93597 + 7.61089i −0.330286 + 0.423481i
\(324\) 0 0
\(325\) −3.91866 + 1.06326i −0.217368 + 0.0589791i
\(326\) 0 0
\(327\) 4.83683 10.4012i 0.267477 0.575185i
\(328\) 0 0
\(329\) 3.15754 + 1.39629i 0.174081 + 0.0769801i
\(330\) 0 0
\(331\) −2.26456 16.9939i −0.124472 0.934071i −0.936553 0.350526i \(-0.886003\pi\)
0.812081 0.583544i \(-0.198335\pi\)
\(332\) 0 0
\(333\) −0.754723 −0.0413586
\(334\) 0 0
\(335\) −8.23473 −0.449911
\(336\) 0 0
\(337\) −1.85690 13.9347i −0.101152 0.759070i −0.966275 0.257511i \(-0.917098\pi\)
0.865124 0.501559i \(-0.167240\pi\)
\(338\) 0 0
\(339\) −5.91234 2.61449i −0.321114 0.142000i
\(340\) 0 0
\(341\) −3.14734 + 6.76807i −0.170438 + 0.366512i
\(342\) 0 0
\(343\) −9.70384 + 2.63297i −0.523958 + 0.142167i
\(344\) 0 0
\(345\) 7.78657 9.98365i 0.419215 0.537502i
\(346\) 0 0
\(347\) 11.0232 21.5333i 0.591754 1.15597i −0.381096 0.924535i \(-0.624453\pi\)
0.972850 0.231435i \(-0.0743419\pi\)
\(348\) 0 0
\(349\) 7.33606 25.1443i 0.392690 1.34594i −0.488245 0.872707i \(-0.662363\pi\)
0.880936 0.473236i \(-0.156914\pi\)
\(350\) 0 0
\(351\) −12.4048 0.940856i −0.662121 0.0502192i
\(352\) 0 0
\(353\) −5.94264 + 8.93950i −0.316295 + 0.475801i −0.956225 0.292631i \(-0.905469\pi\)
0.639931 + 0.768433i \(0.278963\pi\)
\(354\) 0 0
\(355\) −7.22310 2.25658i −0.383362 0.119767i
\(356\) 0 0
\(357\) −4.79833 1.90820i −0.253955 0.100993i
\(358\) 0 0
\(359\) −8.46472 9.30614i −0.446751 0.491159i 0.474431 0.880293i \(-0.342654\pi\)
−0.921181 + 0.389133i \(0.872774\pi\)
\(360\) 0 0
\(361\) 5.97337 + 14.2302i 0.314388 + 0.748957i
\(362\) 0 0
\(363\) 6.12734 2.43672i 0.321602 0.127895i
\(364\) 0 0
\(365\) −21.9879 + 5.08117i −1.15090 + 0.265961i
\(366\) 0 0
\(367\) −9.68957 5.67608i −0.505792 0.296289i 0.230360 0.973105i \(-0.426010\pi\)
−0.736152 + 0.676817i \(0.763359\pi\)
\(368\) 0 0
\(369\) −6.07053 + 5.31525i −0.316019 + 0.276701i
\(370\) 0 0
\(371\) −4.22185 1.14553i −0.219188 0.0594728i
\(372\) 0 0
\(373\) 19.5807 + 6.94083i 1.01385 + 0.359383i 0.788592 0.614917i \(-0.210810\pi\)
0.225257 + 0.974299i \(0.427678\pi\)
\(374\) 0 0
\(375\) 14.7574 7.20536i 0.762070 0.372083i
\(376\) 0 0
\(377\) −0.534636 + 5.63310i −0.0275351 + 0.290119i
\(378\) 0 0
\(379\) 15.2625 + 2.32859i 0.783981 + 0.119612i 0.530451 0.847716i \(-0.322023\pi\)
0.253530 + 0.967327i \(0.418408\pi\)
\(380\) 0 0
\(381\) −0.212554 11.2299i −0.0108895 0.575325i
\(382\) 0 0
\(383\) −8.66296 10.2801i −0.442656 0.525290i 0.496843 0.867840i \(-0.334492\pi\)
−0.939499 + 0.342550i \(0.888709\pi\)
\(384\) 0 0
\(385\) −0.186628 3.28358i −0.00951147 0.167347i
\(386\) 0 0
\(387\) −1.07675 6.26039i −0.0547342 0.318233i
\(388\) 0 0
\(389\) 28.6810 15.3740i 1.45418 0.779491i 0.460076 0.887879i \(-0.347822\pi\)
0.994109 + 0.108389i \(0.0345691\pi\)
\(390\) 0 0
\(391\) 24.2203 + 11.8256i 1.22487 + 0.598048i
\(392\) 0 0
\(393\) −11.5984 + 0.879695i −0.585064 + 0.0443747i
\(394\) 0 0
\(395\) −9.53783 + 9.72006i −0.479900 + 0.489069i
\(396\) 0 0
\(397\) 1.15923 6.73993i 0.0581799 0.338267i −0.941818 0.336124i \(-0.890884\pi\)
0.999998 0.00214363i \(-0.000682340\pi\)
\(398\) 0 0
\(399\) 1.48229 1.20188i 0.0742071 0.0601693i
\(400\) 0 0
\(401\) 1.45558 0.643669i 0.0726881 0.0321433i −0.367767 0.929918i \(-0.619877\pi\)
0.440455 + 0.897775i \(0.354817\pi\)
\(402\) 0 0
\(403\) −1.62118 + 6.45591i −0.0807567 + 0.321592i
\(404\) 0 0
\(405\) 7.22360 0.823795i 0.358944 0.0409347i
\(406\) 0 0
\(407\) −1.27023 + 0.952587i −0.0629629 + 0.0472180i
\(408\) 0 0
\(409\) −7.07516 + 8.39593i −0.349844 + 0.415152i −0.910901 0.412625i \(-0.864612\pi\)
0.561057 + 0.827777i \(0.310395\pi\)
\(410\) 0 0
\(411\) 5.77800 + 11.2871i 0.285008 + 0.556752i
\(412\) 0 0
\(413\) −1.35024 + 3.59179i −0.0664408 + 0.176740i
\(414\) 0 0
\(415\) −13.0559 + 7.64805i −0.640889 + 0.375428i
\(416\) 0 0
\(417\) 6.25423 8.67709i 0.306271 0.424919i
\(418\) 0 0
\(419\) −14.9602 8.01916i −0.730854 0.391762i 0.0644917 0.997918i \(-0.479457\pi\)
−0.795345 + 0.606157i \(0.792710\pi\)
\(420\) 0 0
\(421\) 15.3593 + 27.3956i 0.748566 + 1.33518i 0.935683 + 0.352841i \(0.114785\pi\)
−0.187117 + 0.982338i \(0.559914\pi\)
\(422\) 0 0
\(423\) −1.51973 5.20888i −0.0738920 0.253264i
\(424\) 0 0
\(425\) 5.78558 + 7.41806i 0.280642 + 0.359829i
\(426\) 0 0
\(427\) −1.13994 3.03237i −0.0551655 0.146747i
\(428\) 0 0
\(429\) −6.21279 + 3.96258i −0.299957 + 0.191315i
\(430\) 0 0
\(431\) −21.2836 4.91841i −1.02519 0.236912i −0.321120 0.947039i \(-0.604059\pi\)
−0.704074 + 0.710127i \(0.748638\pi\)
\(432\) 0 0
\(433\) 15.6620 37.3111i 0.752667 1.79306i 0.160860 0.986977i \(-0.448573\pi\)
0.591807 0.806080i \(-0.298415\pi\)
\(434\) 0 0
\(435\) −0.581878 6.13085i −0.0278989 0.293952i
\(436\) 0 0
\(437\) −8.18920 + 5.67021i −0.391742 + 0.271243i
\(438\) 0 0
\(439\) 4.19431 + 3.67246i 0.200183 + 0.175277i 0.752989 0.658033i \(-0.228611\pi\)
−0.552806 + 0.833310i \(0.686443\pi\)
\(440\) 0 0
\(441\) 6.22548 + 4.31054i 0.296452 + 0.205264i
\(442\) 0 0
\(443\) −22.9919 14.6645i −1.09238 0.696731i −0.136545 0.990634i \(-0.543600\pi\)
−0.955835 + 0.293903i \(0.905046\pi\)
\(444\) 0 0
\(445\) −3.58437 + 26.8981i −0.169915 + 1.27509i
\(446\) 0 0
\(447\) 0.298290 0.487801i 0.0141086 0.0230722i
\(448\) 0 0
\(449\) 4.67534 + 4.76467i 0.220643 + 0.224859i 0.815177 0.579212i \(-0.196639\pi\)
−0.594534 + 0.804070i \(0.702664\pi\)
\(450\) 0 0
\(451\) −3.50820 + 16.6078i −0.165195 + 0.782030i
\(452\) 0 0
\(453\) 3.23903 5.77730i 0.152183 0.271441i
\(454\) 0 0
\(455\) −0.714337 2.84465i −0.0334886 0.133359i
\(456\) 0 0
\(457\) 6.50895 + 9.79140i 0.304476 + 0.458022i 0.952912 0.303247i \(-0.0980706\pi\)
−0.648436 + 0.761269i \(0.724577\pi\)
\(458\) 0 0
\(459\) 9.11421 + 27.3446i 0.425415 + 1.27633i
\(460\) 0 0
\(461\) 6.63987 + 0.757225i 0.309250 + 0.0352675i 0.266552 0.963821i \(-0.414116\pi\)
0.0426977 + 0.999088i \(0.486405\pi\)
\(462\) 0 0
\(463\) −33.0015 + 1.24972i −1.53371 + 0.0580795i −0.791118 0.611664i \(-0.790501\pi\)
−0.742593 + 0.669743i \(0.766404\pi\)
\(464\) 0 0
\(465\) 0.411093 7.23286i 0.0190640 0.335416i
\(466\) 0 0
\(467\) −11.7946 19.2879i −0.545787 0.892539i −0.999999 0.00164469i \(-0.999476\pi\)
0.454211 0.890894i \(-0.349921\pi\)
\(468\) 0 0
\(469\) −0.0655896 + 3.46530i −0.00302864 + 0.160013i
\(470\) 0 0
\(471\) 7.70161 2.73002i 0.354872 0.125793i
\(472\) 0 0
\(473\) −9.71386 9.17744i −0.446644 0.421979i
\(474\) 0 0
\(475\) −3.43681 + 0.524352i −0.157691 + 0.0240589i
\(476\) 0 0
\(477\) 2.89899 + 6.23401i 0.132736 + 0.285436i
\(478\) 0 0
\(479\) −16.4200 0.621804i −0.750251 0.0284110i −0.340052 0.940407i \(-0.610445\pi\)
−0.410200 + 0.911996i \(0.634541\pi\)
\(480\) 0 0
\(481\) −0.952732 + 1.04744i −0.0434408 + 0.0477590i
\(482\) 0 0
\(483\) −4.13925 3.35623i −0.188343 0.152714i
\(484\) 0 0
\(485\) 14.4145 + 10.8099i 0.654527 + 0.490852i
\(486\) 0 0
\(487\) −3.82656 + 0.732958i −0.173398 + 0.0332135i −0.274089 0.961704i \(-0.588376\pi\)
0.100691 + 0.994918i \(0.467895\pi\)
\(488\) 0 0
\(489\) −3.36462 0.644476i −0.152154 0.0291442i
\(490\) 0 0
\(491\) 6.82817 + 32.3245i 0.308151 + 1.45878i 0.806204 + 0.591638i \(0.201518\pi\)
−0.498053 + 0.867147i \(0.665952\pi\)
\(492\) 0 0
\(493\) 12.5136 3.90939i 0.563584 0.176070i
\(494\) 0 0
\(495\) −3.75724 + 3.54975i −0.168875 + 0.159550i
\(496\) 0 0
\(497\) −1.00714 + 3.02162i −0.0451762 + 0.135538i
\(498\) 0 0
\(499\) −14.2960 19.8341i −0.639975 0.887898i 0.358992 0.933341i \(-0.383121\pi\)
−0.998967 + 0.0454426i \(0.985530\pi\)
\(500\) 0 0
\(501\) −17.1864 + 3.04603i −0.767834 + 0.136087i
\(502\) 0 0
\(503\) 7.81845 + 10.8473i 0.348608 + 0.483657i 0.948657 0.316306i \(-0.102443\pi\)
−0.600049 + 0.799963i \(0.704852\pi\)
\(504\) 0 0
\(505\) 3.10120 9.30424i 0.138001 0.414033i
\(506\) 0 0
\(507\) 7.98638 7.54535i 0.354688 0.335101i
\(508\) 0 0
\(509\) −20.8205 + 6.50457i −0.922854 + 0.288310i −0.722466 0.691407i \(-0.756991\pi\)
−0.200388 + 0.979717i \(0.564220\pi\)
\(510\) 0 0
\(511\) 1.96310 + 9.29330i 0.0868425 + 0.411112i
\(512\) 0 0
\(513\) −10.4617 2.00388i −0.461894 0.0884734i
\(514\) 0 0
\(515\) −18.4175 + 3.52777i −0.811571 + 0.155452i
\(516\) 0 0
\(517\) −9.13225 6.84858i −0.401636 0.301200i
\(518\) 0 0
\(519\) 26.5172 + 21.5009i 1.16398 + 0.943786i
\(520\) 0 0
\(521\) −6.29575 + 6.92157i −0.275822 + 0.303240i −0.861965 0.506968i \(-0.830766\pi\)
0.586143 + 0.810208i \(0.300646\pi\)
\(522\) 0 0
\(523\) 26.7865 + 1.01437i 1.17129 + 0.0443552i 0.616308 0.787505i \(-0.288628\pi\)
0.554985 + 0.831860i \(0.312724\pi\)
\(524\) 0 0
\(525\) −0.784285 1.68653i −0.0342290 0.0736063i
\(526\) 0 0
\(527\) 15.2458 2.32604i 0.664117 0.101324i
\(528\) 0 0
\(529\) 3.49991 + 3.30663i 0.152170 + 0.143767i
\(530\) 0 0
\(531\) 5.68411 2.01487i 0.246669 0.0874378i
\(532\) 0 0
\(533\) −0.286462 + 15.1347i −0.0124080 + 0.655556i
\(534\) 0 0
\(535\) 0.570975 + 0.933728i 0.0246854 + 0.0403686i
\(536\) 0 0
\(537\) 0.942470 16.5820i 0.0406706 0.715567i
\(538\) 0 0
\(539\) 15.9183 0.602806i 0.685652 0.0259647i
\(540\) 0 0
\(541\) 23.2197 + 2.64802i 0.998293 + 0.113847i 0.597117 0.802154i \(-0.296313\pi\)
0.401175 + 0.916001i \(0.368602\pi\)
\(542\) 0 0
\(543\) −0.998596 2.99600i −0.0428539 0.128571i
\(544\) 0 0
\(545\) −8.35673 12.5710i −0.357963 0.538483i
\(546\) 0 0
\(547\) −0.723280 2.88027i −0.0309252 0.123151i 0.952468 0.304638i \(-0.0985355\pi\)
−0.983393 + 0.181487i \(0.941909\pi\)
\(548\) 0 0
\(549\) −2.48986 + 4.44104i −0.106265 + 0.189539i
\(550\) 0 0
\(551\) −1.00133 + 4.74028i −0.0426580 + 0.201943i
\(552\) 0 0
\(553\) 4.01438 + 4.09108i 0.170709 + 0.173971i
\(554\) 0 0
\(555\) 0.803943 1.31471i 0.0341255 0.0558062i
\(556\) 0 0
\(557\) −0.855637 + 6.42094i −0.0362545 + 0.272064i 0.963732 + 0.266872i \(0.0859901\pi\)
−0.999987 + 0.00519209i \(0.998347\pi\)
\(558\) 0 0
\(559\) −10.0477 6.40850i −0.424971 0.271051i
\(560\) 0 0
\(561\) 14.0368 + 9.71909i 0.592634 + 0.410341i
\(562\) 0 0
\(563\) 15.2328 + 13.3376i 0.641986 + 0.562112i 0.916781 0.399391i \(-0.130778\pi\)
−0.274794 + 0.961503i \(0.588610\pi\)
\(564\) 0 0
\(565\) −6.99428 + 4.84285i −0.294252 + 0.203740i
\(566\) 0 0
\(567\) −0.289130 3.04636i −0.0121423 0.127935i
\(568\) 0 0
\(569\) 11.3650 27.0744i 0.476444 1.13502i −0.488500 0.872564i \(-0.662456\pi\)
0.964944 0.262455i \(-0.0845321\pi\)
\(570\) 0 0
\(571\) 10.3478 + 2.39127i 0.433042 + 0.100071i 0.436047 0.899924i \(-0.356378\pi\)
−0.00300504 + 0.999995i \(0.500957\pi\)
\(572\) 0 0
\(573\) −3.44397 + 2.19660i −0.143874 + 0.0917642i
\(574\) 0 0
\(575\) 3.41616 + 9.08738i 0.142464 + 0.378970i
\(576\) 0 0
\(577\) 12.5334 + 16.0698i 0.521771 + 0.668996i 0.974950 0.222424i \(-0.0713968\pi\)
−0.453179 + 0.891420i \(0.649710\pi\)
\(578\) 0 0
\(579\) −5.94164 20.3649i −0.246926 0.846336i
\(580\) 0 0
\(581\) 3.11443 + 5.55504i 0.129208 + 0.230462i
\(582\) 0 0
\(583\) 12.7475 + 6.83307i 0.527947 + 0.282997i
\(584\) 0 0
\(585\) −2.69529 + 3.73943i −0.111437 + 0.154607i
\(586\) 0 0
\(587\) −23.6082 + 13.8295i −0.974417 + 0.570806i −0.904375 0.426738i \(-0.859663\pi\)
−0.0700414 + 0.997544i \(0.522313\pi\)
\(588\) 0 0
\(589\) −2.00549 + 5.33484i −0.0826349 + 0.219818i
\(590\) 0 0
\(591\) 2.53249 + 4.94712i 0.104173 + 0.203497i
\(592\) 0 0
\(593\) 15.6462 18.5670i 0.642513 0.762456i −0.341629 0.939835i \(-0.610979\pi\)
0.984143 + 0.177379i \(0.0567619\pi\)
\(594\) 0 0
\(595\) −5.43653 + 4.07704i −0.222876 + 0.167142i
\(596\) 0 0
\(597\) 0.381809 0.0435423i 0.0156264 0.00178207i
\(598\) 0 0
\(599\) 4.50942 17.9576i 0.184250 0.733726i −0.805702 0.592321i \(-0.798212\pi\)
0.989952 0.141405i \(-0.0451619\pi\)
\(600\) 0 0
\(601\) −10.6765 + 4.72122i −0.435502 + 0.192583i −0.610551 0.791977i \(-0.709052\pi\)
0.175049 + 0.984560i \(0.443992\pi\)
\(602\) 0 0
\(603\) 4.23107 3.43067i 0.172302 0.139708i
\(604\) 0 0
\(605\) 1.47090 8.55203i 0.0598004 0.347689i
\(606\) 0 0
\(607\) −15.0692 + 15.3571i −0.611639 + 0.623325i −0.947948 0.318426i \(-0.896846\pi\)
0.336308 + 0.941752i \(0.390822\pi\)
\(608\) 0 0
\(609\) −2.58459 + 0.196031i −0.104733 + 0.00794357i
\(610\) 0 0
\(611\) −9.14755 4.46632i −0.370070 0.180688i
\(612\) 0 0
\(613\) 18.0928 9.69835i 0.730762 0.391713i −0.0645484 0.997915i \(-0.520561\pi\)
0.795311 + 0.606202i \(0.207308\pi\)
\(614\) 0 0
\(615\) −2.79259 16.2366i −0.112608 0.654722i
\(616\) 0 0
\(617\) 0.687261 + 12.0918i 0.0276681 + 0.486799i 0.982099 + 0.188366i \(0.0603192\pi\)
−0.954431 + 0.298432i \(0.903536\pi\)
\(618\) 0 0
\(619\) 7.66809 + 9.09954i 0.308206 + 0.365741i 0.896606 0.442829i \(-0.146025\pi\)
−0.588400 + 0.808570i \(0.700242\pi\)
\(620\) 0 0
\(621\) 0.562900 + 29.7398i 0.0225884 + 1.19342i
\(622\) 0 0
\(623\) 11.2906 + 1.72260i 0.452348 + 0.0690146i
\(624\) 0 0
\(625\) 1.17233 12.3521i 0.0468933 0.494083i
\(626\) 0 0
\(627\) −5.66974 + 2.76827i −0.226428 + 0.110554i
\(628\) 0 0
\(629\) 3.09205 + 1.09605i 0.123288 + 0.0437023i
\(630\) 0 0
\(631\) 31.6735 + 8.59406i 1.26090 + 0.342124i 0.828721 0.559662i \(-0.189069\pi\)
0.432182 + 0.901786i \(0.357744\pi\)
\(632\) 0 0
\(633\) 23.5995 20.6633i 0.937996 0.821293i
\(634\) 0 0
\(635\) −12.7537 7.47102i −0.506115 0.296478i
\(636\) 0 0
\(637\) 13.8411 3.19854i 0.548406 0.126731i
\(638\) 0 0
\(639\) 4.65140 1.84977i 0.184006 0.0731758i
\(640\) 0 0
\(641\) −2.07015 4.93166i −0.0817661 0.194789i 0.876017 0.482280i \(-0.160191\pi\)
−0.957783 + 0.287491i \(0.907179\pi\)
\(642\) 0 0
\(643\) 26.2135 + 28.8192i 1.03376 + 1.13652i 0.990508 + 0.137455i \(0.0438922\pi\)
0.0432517 + 0.999064i \(0.486228\pi\)
\(644\) 0 0
\(645\) 12.0524 + 4.79300i 0.474562 + 0.188724i
\(646\) 0 0
\(647\) 30.5786 + 9.55310i 1.20217 + 0.375571i 0.832727 0.553683i \(-0.186778\pi\)
0.369441 + 0.929254i \(0.379549\pi\)
\(648\) 0 0
\(649\) 7.02348 10.5654i 0.275696 0.414728i
\(650\) 0 0
\(651\) −3.04042 0.230604i −0.119164 0.00903808i
\(652\) 0 0
\(653\) −0.493457 + 1.69132i −0.0193105 + 0.0661864i −0.969061 0.246822i \(-0.920614\pi\)
0.949750 + 0.313008i \(0.101337\pi\)
\(654\) 0 0
\(655\) −6.97504 + 13.6255i −0.272538 + 0.532392i
\(656\) 0 0
\(657\) 9.18067 11.7711i 0.358172 0.459235i
\(658\) 0 0
\(659\) 10.1231 2.74673i 0.394340 0.106997i −0.0591712 0.998248i \(-0.518846\pi\)
0.453512 + 0.891250i \(0.350171\pi\)
\(660\) 0 0
\(661\) −8.46552 + 18.2043i −0.329271 + 0.708066i −0.999416 0.0341638i \(-0.989123\pi\)
0.670146 + 0.742230i \(0.266232\pi\)
\(662\) 0 0
\(663\) 13.9248 + 6.15767i 0.540795 + 0.239144i
\(664\) 0 0
\(665\) −0.331715 2.48928i −0.0128634 0.0965303i
\(666\) 0 0
\(667\) 13.5292 0.523854
\(668\) 0 0
\(669\) 39.8632 1.54120
\(670\) 0 0
\(671\) 1.41480 + 10.6171i 0.0546178 + 0.409867i
\(672\) 0 0
\(673\) −25.7639 11.3930i −0.993123 0.439168i −0.156934 0.987609i \(-0.550161\pi\)
−0.836189 + 0.548441i \(0.815221\pi\)
\(674\) 0 0
\(675\) −4.37772 + 9.41388i −0.168499 + 0.362340i
\(676\) 0 0
\(677\) −7.80879 + 2.11878i −0.300116 + 0.0814314i −0.408738 0.912652i \(-0.634031\pi\)
0.108622 + 0.994083i \(0.465356\pi\)
\(678\) 0 0
\(679\) 4.66378 5.97972i 0.178979 0.229481i
\(680\) 0 0
\(681\) 8.18121 15.9817i 0.313504 0.612419i
\(682\) 0 0
\(683\) −4.86600 + 16.6782i −0.186192 + 0.638173i 0.812298 + 0.583243i \(0.198216\pi\)
−0.998490 + 0.0549300i \(0.982506\pi\)
\(684\) 0 0
\(685\) 16.6388 + 1.26198i 0.635735 + 0.0482179i
\(686\) 0 0
\(687\) 1.25704 1.89096i 0.0479591 0.0721448i
\(688\) 0 0
\(689\) 12.3114 + 3.84622i 0.469027 + 0.146529i
\(690\) 0 0
\(691\) −45.3526 18.0359i −1.72530 0.686116i −0.725298 0.688435i \(-0.758298\pi\)
−0.999997 + 0.00231921i \(0.999262\pi\)
\(692\) 0 0
\(693\) 1.46386 + 1.60938i 0.0556076 + 0.0611352i
\(694\) 0 0
\(695\) −5.44803 12.9787i −0.206656 0.492310i
\(696\) 0 0
\(697\) 32.5896 12.9602i 1.23442 0.490904i
\(698\) 0 0
\(699\) 0.848627 0.196109i 0.0320980 0.00741753i
\(700\) 0 0
\(701\) 20.4845 + 11.9996i 0.773688 + 0.453220i 0.838652 0.544667i \(-0.183344\pi\)
−0.0649645 + 0.997888i \(0.520693\pi\)
\(702\) 0 0
\(703\) −0.912120 + 0.798636i −0.0344013 + 0.0301211i
\(704\) 0 0
\(705\) 10.6926 + 2.90124i 0.402705 + 0.109267i
\(706\) 0 0
\(707\) −3.89067 1.37914i −0.146324 0.0518679i
\(708\) 0 0
\(709\) 27.6459 13.4982i 1.03826 0.506936i 0.161005 0.986954i \(-0.448526\pi\)
0.877259 + 0.480018i \(0.159370\pi\)
\(710\) 0 0
\(711\) 0.851131 8.96780i 0.0319199 0.336319i
\(712\) 0 0
\(713\) 15.7333 + 2.40042i 0.589215 + 0.0898963i
\(714\) 0 0
\(715\) 0.183512 + 9.69552i 0.00686296 + 0.362592i
\(716\) 0 0
\(717\) 14.6839 + 17.4250i 0.548380 + 0.650750i
\(718\) 0 0
\(719\) −1.34456 23.6565i −0.0501436 0.882237i −0.920725 0.390213i \(-0.872402\pi\)
0.870581 0.492025i \(-0.163743\pi\)
\(720\) 0 0
\(721\) 1.33785 + 7.77845i 0.0498240 + 0.289685i
\(722\) 0 0
\(723\) −16.5931 + 8.89447i −0.617106 + 0.330789i
\(724\) 0 0
\(725\) 4.24335 + 2.07183i 0.157594 + 0.0769459i
\(726\) 0 0
\(727\) 4.25995 0.323100i 0.157993 0.0119831i 0.00360532 0.999994i \(-0.498852\pi\)
0.154387 + 0.988010i \(0.450660\pi\)
\(728\) 0 0
\(729\) −19.3742 + 19.7444i −0.717562 + 0.731272i
\(730\) 0 0
\(731\) −4.68030 + 27.2121i −0.173107 + 1.00647i
\(732\) 0 0
\(733\) −15.1193 + 12.2592i −0.558444 + 0.452803i −0.866933 0.498425i \(-0.833912\pi\)
0.308488 + 0.951228i \(0.400177\pi\)
\(734\) 0 0
\(735\) −14.1403 + 6.25297i −0.521574 + 0.230644i
\(736\) 0 0
\(737\) 2.79097 11.1143i 0.102807 0.409400i
\(738\) 0 0
\(739\) −21.0605 + 2.40179i −0.774724 + 0.0883512i −0.491704 0.870763i \(-0.663626\pi\)
−0.283021 + 0.959114i \(0.591337\pi\)
\(740\) 0 0
\(741\) −4.50148 + 3.37581i −0.165366 + 0.124014i
\(742\) 0 0
\(743\) −17.1243 + 20.3211i −0.628231 + 0.745507i −0.981803 0.189900i \(-0.939184\pi\)
0.353572 + 0.935407i \(0.384967\pi\)
\(744\) 0 0
\(745\) −0.342868 0.669780i −0.0125617 0.0245388i
\(746\) 0 0
\(747\) 3.52197 9.36885i 0.128862 0.342788i
\(748\) 0 0
\(749\) 0.397475 0.232838i 0.0145234 0.00850771i
\(750\) 0 0
\(751\) −2.48067 + 3.44167i −0.0905209 + 0.125588i −0.854062 0.520170i \(-0.825868\pi\)
0.763542 + 0.645759i \(0.223459\pi\)
\(752\) 0 0
\(753\) −14.0442 7.52815i −0.511799 0.274341i
\(754\) 0 0
\(755\) −4.26247 7.60274i −0.155127 0.276692i
\(756\) 0 0
\(757\) −10.7517 36.8513i −0.390776 1.33938i −0.883188 0.469020i \(-0.844607\pi\)
0.492411 0.870363i \(-0.336116\pi\)
\(758\) 0 0
\(759\) 10.8357 + 13.8931i 0.393311 + 0.504288i
\(760\) 0 0
\(761\) 6.43939 + 17.1295i 0.233428 + 0.620945i 0.999769 0.0214886i \(-0.00684055\pi\)
−0.766341 + 0.642434i \(0.777925\pi\)
\(762\) 0 0
\(763\) −5.35663 + 3.41651i −0.193923 + 0.123686i
\(764\) 0 0
\(765\) 10.4057 + 2.40465i 0.376219 + 0.0869403i
\(766\) 0 0
\(767\) 4.37907 10.4321i 0.158119 0.376682i
\(768\) 0 0
\(769\) −4.09025 43.0962i −0.147498 1.55409i −0.696063 0.717981i \(-0.745067\pi\)
0.548565 0.836108i \(-0.315174\pi\)
\(770\) 0 0
\(771\) −18.8037 + 13.0197i −0.677199 + 0.468893i
\(772\) 0 0
\(773\) 2.01479 + 1.76411i 0.0724668 + 0.0634507i 0.694222 0.719761i \(-0.255749\pi\)
−0.621755 + 0.783212i \(0.713580\pi\)
\(774\) 0 0
\(775\) 4.56704 + 3.16222i 0.164053 + 0.113590i
\(776\) 0 0
\(777\) −0.546846 0.348783i −0.0196180 0.0125125i
\(778\) 0 0
\(779\) −1.71202 + 12.8475i −0.0613395 + 0.460308i
\(780\) 0 0
\(781\) 5.49376 8.98408i 0.196582 0.321476i
\(782\) 0 0
\(783\) 10.1332 + 10.3268i 0.362132 + 0.369051i
\(784\) 0 0
\(785\) 2.22240 10.5208i 0.0793209 0.375504i
\(786\) 0 0
\(787\) −7.47450 + 13.3319i −0.266437 + 0.475230i −0.972495 0.232924i \(-0.925171\pi\)
0.706058 + 0.708154i \(0.250472\pi\)
\(788\) 0 0
\(789\) −4.51272 17.9707i −0.160657 0.639774i
\(790\) 0 0
\(791\) 1.98224 + 2.98187i 0.0704802 + 0.106023i
\(792\) 0 0
\(793\) 3.02036 + 9.06172i 0.107256 + 0.321791i
\(794\) 0 0
\(795\) −13.9475 1.59061i −0.494668 0.0564130i
\(796\) 0 0