Properties

Label 668.2.e.a.9.13
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 9.13
Character \(\chi\) \(=\) 668.9
Dual form 668.2.e.a.297.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.353640 + 2.65381i) q^{3} +(-1.27217 - 0.562563i) q^{5} +(-1.92428 + 4.13797i) q^{7} +(-4.02235 + 1.09139i) q^{9} +O(q^{10})\) \(q+(0.353640 + 2.65381i) q^{3} +(-1.27217 - 0.562563i) q^{5} +(-1.92428 + 4.13797i) q^{7} +(-4.02235 + 1.09139i) q^{9} +(-1.02081 + 1.30885i) q^{11} +(1.42096 - 2.77578i) q^{13} +(1.04305 - 3.57504i) q^{15} +(-2.44034 - 0.185090i) q^{17} +(2.03980 - 3.06846i) q^{19} +(-11.6619 - 3.64331i) q^{21} +(0.849459 + 0.337813i) q^{23} +(-2.06243 - 2.26745i) q^{25} +(-1.21010 - 2.88279i) q^{27} +(-4.52393 + 1.79908i) q^{29} +(-2.76400 + 0.638732i) q^{31} +(-3.83443 - 2.24618i) q^{33} +(4.77587 - 4.18167i) q^{35} +(8.57531 + 2.32676i) q^{37} +(7.86891 + 2.78932i) q^{39} +(-5.33729 + 2.60595i) q^{41} +(-0.373781 + 3.93828i) q^{43} +(5.73107 + 0.874387i) q^{45} +(0.147189 + 7.77648i) q^{47} +(-8.90922 - 10.5724i) q^{49} +(-0.371807 - 6.54166i) q^{51} +(0.188558 + 1.09630i) q^{53} +(2.03495 - 1.09080i) q^{55} +(8.86447 + 4.32811i) q^{57} +(-10.3888 + 0.787950i) q^{59} +(5.52223 - 5.62774i) q^{61} +(3.22394 - 18.7445i) q^{63} +(-3.36924 + 2.73188i) q^{65} +(-8.24417 + 3.64564i) q^{67} +(-0.596091 + 2.37377i) q^{69} +(11.0551 - 1.26074i) q^{71} +(-3.43668 + 2.57728i) q^{73} +(5.28802 - 6.27517i) q^{75} +(-3.45165 - 6.74267i) q^{77} +(-0.402907 + 1.07178i) q^{79} +(-3.56612 + 2.08901i) q^{81} +(-4.94246 + 6.85715i) q^{83} +(3.00039 + 1.60831i) q^{85} +(-6.37426 - 11.3694i) q^{87} +(0.517404 + 1.77340i) q^{89} +(8.75181 + 11.2212i) q^{91} +(-2.67253 - 7.10926i) q^{93} +(-4.32116 + 2.75608i) q^{95} +(5.32857 + 1.23138i) q^{97} +(2.67759 - 6.37874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) 0.353640 + 2.65381i 0.204174 + 1.53218i 0.731101 + 0.682269i \(0.239007\pi\)
−0.526927 + 0.849910i \(0.676656\pi\)
\(4\) 0 0
\(5\) −1.27217 0.562563i −0.568930 0.251586i 0.0999044 0.994997i \(-0.468146\pi\)
−0.668835 + 0.743411i \(0.733207\pi\)
\(6\) 0 0
\(7\) −1.92428 + 4.13797i −0.727308 + 1.56401i 0.0953327 + 0.995445i \(0.469608\pi\)
−0.822640 + 0.568562i \(0.807500\pi\)
\(8\) 0 0
\(9\) −4.02235 + 1.09139i −1.34078 + 0.363798i
\(10\) 0 0
\(11\) −1.02081 + 1.30885i −0.307786 + 0.394632i −0.917335 0.398117i \(-0.869664\pi\)
0.609549 + 0.792749i \(0.291351\pi\)
\(12\) 0 0
\(13\) 1.42096 2.77578i 0.394102 0.769864i −0.605562 0.795798i \(-0.707051\pi\)
0.999664 + 0.0259349i \(0.00825627\pi\)
\(14\) 0 0
\(15\) 1.04305 3.57504i 0.269314 0.923070i
\(16\) 0 0
\(17\) −2.44034 0.185090i −0.591869 0.0448909i −0.223713 0.974655i \(-0.571818\pi\)
−0.368156 + 0.929764i \(0.620011\pi\)
\(18\) 0 0
\(19\) 2.03980 3.06846i 0.467961 0.703953i −0.520763 0.853701i \(-0.674352\pi\)
0.988724 + 0.149748i \(0.0478463\pi\)
\(20\) 0 0
\(21\) −11.6619 3.64331i −2.54484 0.795036i
\(22\) 0 0
\(23\) 0.849459 + 0.337813i 0.177124 + 0.0704389i 0.456412 0.889769i \(-0.349134\pi\)
−0.279287 + 0.960208i \(0.590098\pi\)
\(24\) 0 0
\(25\) −2.06243 2.26745i −0.412486 0.453489i
\(26\) 0 0
\(27\) −1.21010 2.88279i −0.232884 0.554793i
\(28\) 0 0
\(29\) −4.52393 + 1.79908i −0.840073 + 0.334081i −0.749660 0.661824i \(-0.769783\pi\)
−0.0904136 + 0.995904i \(0.528819\pi\)
\(30\) 0 0
\(31\) −2.76400 + 0.638732i −0.496429 + 0.114720i −0.465941 0.884816i \(-0.654284\pi\)
−0.0304875 + 0.999535i \(0.509706\pi\)
\(32\) 0 0
\(33\) −3.83443 2.24618i −0.667489 0.391010i
\(34\) 0 0
\(35\) 4.77587 4.18167i 0.807269 0.706831i
\(36\) 0 0
\(37\) 8.57531 + 2.32676i 1.40977 + 0.382517i 0.883752 0.467955i \(-0.155009\pi\)
0.526020 + 0.850472i \(0.323684\pi\)
\(38\) 0 0
\(39\) 7.86891 + 2.78932i 1.26003 + 0.446649i
\(40\) 0 0
\(41\) −5.33729 + 2.60595i −0.833545 + 0.406981i −0.805478 0.592625i \(-0.798092\pi\)
−0.0280663 + 0.999606i \(0.508935\pi\)
\(42\) 0 0
\(43\) −0.373781 + 3.93828i −0.0570010 + 0.600582i 0.920656 + 0.390375i \(0.127655\pi\)
−0.977657 + 0.210207i \(0.932586\pi\)
\(44\) 0 0
\(45\) 5.73107 + 0.874387i 0.854338 + 0.130346i
\(46\) 0 0
\(47\) 0.147189 + 7.77648i 0.0214698 + 1.13432i 0.834126 + 0.551574i \(0.185972\pi\)
−0.812656 + 0.582743i \(0.801979\pi\)
\(48\) 0 0
\(49\) −8.90922 10.5724i −1.27275 1.51034i
\(50\) 0 0
\(51\) −0.371807 6.54166i −0.0520634 0.916015i
\(52\) 0 0
\(53\) 0.188558 + 1.09630i 0.0259004 + 0.150589i 0.995599 0.0937150i \(-0.0298742\pi\)
−0.969699 + 0.244304i \(0.921441\pi\)
\(54\) 0 0
\(55\) 2.03495 1.09080i 0.274393 0.147083i
\(56\) 0 0
\(57\) 8.86447 + 4.32811i 1.17413 + 0.573272i
\(58\) 0 0
\(59\) −10.3888 + 0.787950i −1.35251 + 0.102582i −0.731832 0.681485i \(-0.761335\pi\)
−0.620676 + 0.784067i \(0.713142\pi\)
\(60\) 0 0
\(61\) 5.52223 5.62774i 0.707049 0.720558i −0.262642 0.964893i \(-0.584594\pi\)
0.969691 + 0.244335i \(0.0785697\pi\)
\(62\) 0 0
\(63\) 3.22394 18.7445i 0.406178 2.36159i
\(64\) 0 0
\(65\) −3.36924 + 2.73188i −0.417903 + 0.338848i
\(66\) 0 0
\(67\) −8.24417 + 3.64564i −1.00719 + 0.445386i −0.841189 0.540741i \(-0.818144\pi\)
−0.165996 + 0.986126i \(0.553084\pi\)
\(68\) 0 0
\(69\) −0.596091 + 2.37377i −0.0717609 + 0.285768i
\(70\) 0 0
\(71\) 11.0551 1.26074i 1.31200 0.149623i 0.570899 0.821020i \(-0.306595\pi\)
0.741097 + 0.671397i \(0.234306\pi\)
\(72\) 0 0
\(73\) −3.43668 + 2.57728i −0.402233 + 0.301648i −0.781816 0.623510i \(-0.785706\pi\)
0.379583 + 0.925158i \(0.376068\pi\)
\(74\) 0 0
\(75\) 5.28802 6.27517i 0.610608 0.724594i
\(76\) 0 0
\(77\) −3.45165 6.74267i −0.393352 0.768399i
\(78\) 0 0
\(79\) −0.402907 + 1.07178i −0.0453305 + 0.120585i −0.956766 0.290858i \(-0.906059\pi\)
0.911436 + 0.411443i \(0.134975\pi\)
\(80\) 0 0
\(81\) −3.56612 + 2.08901i −0.396236 + 0.232112i
\(82\) 0 0
\(83\) −4.94246 + 6.85715i −0.542506 + 0.752670i −0.989915 0.141659i \(-0.954756\pi\)
0.447410 + 0.894329i \(0.352347\pi\)
\(84\) 0 0
\(85\) 3.00039 + 1.60831i 0.325438 + 0.174446i
\(86\) 0 0
\(87\) −6.37426 11.3694i −0.683393 1.21893i
\(88\) 0 0
\(89\) 0.517404 + 1.77340i 0.0548448 + 0.187980i 0.982786 0.184746i \(-0.0591462\pi\)
−0.927942 + 0.372726i \(0.878423\pi\)
\(90\) 0 0
\(91\) 8.75181 + 11.2212i 0.917439 + 1.17631i
\(92\) 0 0
\(93\) −2.67253 7.10926i −0.277129 0.737195i
\(94\) 0 0
\(95\) −4.32116 + 2.75608i −0.443342 + 0.282768i
\(96\) 0 0
\(97\) 5.32857 + 1.23138i 0.541034 + 0.125027i 0.486821 0.873502i \(-0.338157\pi\)
0.0542136 + 0.998529i \(0.482735\pi\)
\(98\) 0 0
\(99\) 2.67759 6.37874i 0.269108 0.641088i
\(100\) 0 0
\(101\) 1.81295 + 19.1019i 0.180396 + 1.90071i 0.386678 + 0.922215i \(0.373623\pi\)
−0.206282 + 0.978493i \(0.566136\pi\)
\(102\) 0 0
\(103\) 15.3371 10.6195i 1.51121 1.04637i 0.531245 0.847218i \(-0.321724\pi\)
0.979969 0.199149i \(-0.0638177\pi\)
\(104\) 0 0
\(105\) 12.7863 + 11.1955i 1.24781 + 1.09256i
\(106\) 0 0
\(107\) 3.90543 + 2.70413i 0.377552 + 0.261418i 0.742829 0.669481i \(-0.233483\pi\)
−0.365277 + 0.930899i \(0.619026\pi\)
\(108\) 0 0
\(109\) −1.47392 0.940081i −0.141176 0.0900434i 0.465267 0.885170i \(-0.345958\pi\)
−0.606443 + 0.795127i \(0.707404\pi\)
\(110\) 0 0
\(111\) −3.14222 + 23.5801i −0.298246 + 2.23812i
\(112\) 0 0
\(113\) −5.49114 + 8.97979i −0.516563 + 0.844748i −0.999523 0.0308949i \(-0.990164\pi\)
0.482959 + 0.875643i \(0.339562\pi\)
\(114\) 0 0
\(115\) −0.890612 0.907629i −0.0830500 0.0846368i
\(116\) 0 0
\(117\) −2.68610 + 12.7160i −0.248330 + 1.17559i
\(118\) 0 0
\(119\) 5.46178 9.74189i 0.500680 0.893038i
\(120\) 0 0
\(121\) 2.00807 + 7.99659i 0.182552 + 0.726963i
\(122\) 0 0
\(123\) −8.80318 13.2426i −0.793756 1.19405i
\(124\) 0 0
\(125\) 3.54740 + 10.6430i 0.317289 + 0.951935i
\(126\) 0 0
\(127\) −12.5565 1.43197i −1.11421 0.127067i −0.463284 0.886210i \(-0.653329\pi\)
−0.650924 + 0.759143i \(0.725618\pi\)
\(128\) 0 0
\(129\) −10.5836 + 0.400787i −0.931837 + 0.0352874i
\(130\) 0 0
\(131\) −0.0538156 + 0.946843i −0.00470189 + 0.0827261i −0.999882 0.0153335i \(-0.995119\pi\)
0.995181 + 0.0980596i \(0.0312636\pi\)
\(132\) 0 0
\(133\) 8.77208 + 14.3452i 0.760636 + 1.24389i
\(134\) 0 0
\(135\) −0.0822996 + 4.34815i −0.00708322 + 0.374229i
\(136\) 0 0
\(137\) 9.93134 3.52040i 0.848491 0.300768i 0.125900 0.992043i \(-0.459818\pi\)
0.722592 + 0.691275i \(0.242951\pi\)
\(138\) 0 0
\(139\) 0.544827 + 0.514740i 0.0462116 + 0.0436597i 0.709510 0.704695i \(-0.248916\pi\)
−0.663298 + 0.748355i \(0.730844\pi\)
\(140\) 0 0
\(141\) −20.5853 + 3.14069i −1.73359 + 0.264494i
\(142\) 0 0
\(143\) 2.18255 + 4.69336i 0.182514 + 0.392479i
\(144\) 0 0
\(145\) 6.76729 + 0.256268i 0.561993 + 0.0212819i
\(146\) 0 0
\(147\) 24.9064 27.3822i 2.05425 2.25845i
\(148\) 0 0
\(149\) −16.0245 12.9931i −1.31278 1.06444i −0.993144 0.116894i \(-0.962706\pi\)
−0.319631 0.947542i \(-0.603559\pi\)
\(150\) 0 0
\(151\) 12.4663 + 9.34887i 1.01449 + 0.760800i 0.971201 0.238263i \(-0.0765779\pi\)
0.0432888 + 0.999063i \(0.486216\pi\)
\(152\) 0 0
\(153\) 10.0179 1.91888i 0.809899 0.155132i
\(154\) 0 0
\(155\) 3.87559 + 0.742350i 0.311295 + 0.0596270i
\(156\) 0 0
\(157\) 3.85567 + 18.2527i 0.307716 + 1.45673i 0.807136 + 0.590366i \(0.201017\pi\)
−0.499420 + 0.866360i \(0.666453\pi\)
\(158\) 0 0
\(159\) −2.84271 + 0.888094i −0.225441 + 0.0704304i
\(160\) 0 0
\(161\) −3.03246 + 2.86499i −0.238991 + 0.225793i
\(162\) 0 0
\(163\) −6.59214 + 19.7778i −0.516336 + 1.54912i 0.289619 + 0.957142i \(0.406471\pi\)
−0.805955 + 0.591976i \(0.798348\pi\)
\(164\) 0 0
\(165\) 3.61442 + 5.01463i 0.281382 + 0.390388i
\(166\) 0 0
\(167\) 3.39197 12.4697i 0.262479 0.964938i
\(168\) 0 0
\(169\) 1.91549 + 2.65754i 0.147345 + 0.204426i
\(170\) 0 0
\(171\) −4.85587 + 14.5686i −0.371338 + 1.11409i
\(172\) 0 0
\(173\) 12.6351 11.9373i 0.960626 0.907577i −0.0351511 0.999382i \(-0.511191\pi\)
0.995777 + 0.0918047i \(0.0292635\pi\)
\(174\) 0 0
\(175\) 13.3513 4.17110i 1.00926 0.315306i
\(176\) 0 0
\(177\) −5.76497 27.2913i −0.433322 2.05134i
\(178\) 0 0
\(179\) −22.9885 4.40333i −1.71824 0.329121i −0.767957 0.640501i \(-0.778727\pi\)
−0.950285 + 0.311380i \(0.899209\pi\)
\(180\) 0 0
\(181\) 13.1961 2.52765i 0.980859 0.187879i 0.327438 0.944873i \(-0.393815\pi\)
0.653422 + 0.756994i \(0.273333\pi\)
\(182\) 0 0
\(183\) 16.8878 + 12.6648i 1.24839 + 0.936206i
\(184\) 0 0
\(185\) −9.60027 7.78418i −0.705826 0.572304i
\(186\) 0 0
\(187\) 2.73338 3.00509i 0.199884 0.219754i
\(188\) 0 0
\(189\) 14.2575 + 0.539911i 1.03708 + 0.0392727i
\(190\) 0 0
\(191\) −3.06193 6.58439i −0.221553 0.476429i 0.764125 0.645069i \(-0.223171\pi\)
−0.985678 + 0.168639i \(0.946063\pi\)
\(192\) 0 0
\(193\) 6.74809 1.02955i 0.485738 0.0741089i 0.0966675 0.995317i \(-0.469182\pi\)
0.389071 + 0.921208i \(0.372796\pi\)
\(194\) 0 0
\(195\) −8.44140 7.97524i −0.604501 0.571119i
\(196\) 0 0
\(197\) 6.52278 2.31215i 0.464729 0.164734i −0.0914274 0.995812i \(-0.529143\pi\)
0.556157 + 0.831078i \(0.312275\pi\)
\(198\) 0 0
\(199\) 0.0916647 4.84293i 0.00649794 0.343306i −0.981727 0.190296i \(-0.939055\pi\)
0.988225 0.153010i \(-0.0488967\pi\)
\(200\) 0 0
\(201\) −12.5903 20.5892i −0.888052 1.45225i
\(202\) 0 0
\(203\) 1.26075 22.1818i 0.0884870 1.55686i
\(204\) 0 0
\(205\) 8.25593 0.312641i 0.576619 0.0218358i
\(206\) 0 0
\(207\) −3.78551 0.431707i −0.263111 0.0300057i
\(208\) 0 0
\(209\) 1.93390 + 5.80210i 0.133770 + 0.401340i
\(210\) 0 0
\(211\) 10.4817 + 15.7676i 0.721591 + 1.08549i 0.992424 + 0.122861i \(0.0392068\pi\)
−0.270833 + 0.962626i \(0.587299\pi\)
\(212\) 0 0
\(213\) 7.25530 + 28.8923i 0.497125 + 1.97966i
\(214\) 0 0
\(215\) 2.69104 4.79987i 0.183527 0.327348i
\(216\) 0 0
\(217\) 2.67564 12.6665i 0.181634 0.859855i
\(218\) 0 0
\(219\) −8.05497 8.20887i −0.544304 0.554704i
\(220\) 0 0
\(221\) −3.98138 + 6.51084i −0.267817 + 0.437967i
\(222\) 0 0
\(223\) 2.91796 21.8972i 0.195401 1.46634i −0.569391 0.822067i \(-0.692821\pi\)
0.764792 0.644277i \(-0.222842\pi\)
\(224\) 0 0
\(225\) 10.7705 + 6.86952i 0.718033 + 0.457968i
\(226\) 0 0
\(227\) 13.6337 + 9.44002i 0.904903 + 0.626556i 0.927758 0.373182i \(-0.121733\pi\)
−0.0228551 + 0.999739i \(0.507276\pi\)
\(228\) 0 0
\(229\) 18.9957 + 16.6323i 1.25527 + 1.09909i 0.990890 + 0.134676i \(0.0429995\pi\)
0.264383 + 0.964418i \(0.414832\pi\)
\(230\) 0 0
\(231\) 16.6731 11.5445i 1.09701 0.759573i
\(232\) 0 0
\(233\) −1.34582 14.1800i −0.0881677 0.928964i −0.924612 0.380911i \(-0.875610\pi\)
0.836444 0.548053i \(-0.184631\pi\)
\(234\) 0 0
\(235\) 4.18751 9.97578i 0.273163 0.650748i
\(236\) 0 0
\(237\) −2.98678 0.690215i −0.194012 0.0448343i
\(238\) 0 0
\(239\) 4.05354 2.58539i 0.262202 0.167235i −0.400101 0.916471i \(-0.631025\pi\)
0.662303 + 0.749236i \(0.269579\pi\)
\(240\) 0 0
\(241\) −6.17134 16.4165i −0.397531 1.05748i −0.971174 0.238373i \(-0.923386\pi\)
0.573643 0.819106i \(-0.305530\pi\)
\(242\) 0 0
\(243\) −12.5733 16.1210i −0.806576 1.03416i
\(244\) 0 0
\(245\) 5.38639 + 18.4618i 0.344124 + 1.17948i
\(246\) 0 0
\(247\) −5.61892 10.0222i −0.357523 0.637696i
\(248\) 0 0
\(249\) −19.9454 10.6914i −1.26399 0.677541i
\(250\) 0 0
\(251\) −2.52008 + 3.49634i −0.159066 + 0.220687i −0.883229 0.468941i \(-0.844636\pi\)
0.724164 + 0.689628i \(0.242226\pi\)
\(252\) 0 0
\(253\) −1.30928 + 0.766968i −0.0823139 + 0.0482189i
\(254\) 0 0
\(255\) −3.20709 + 8.53124i −0.200836 + 0.534247i
\(256\) 0 0
\(257\) −9.27201 18.1125i −0.578372 1.12983i −0.977104 0.212760i \(-0.931755\pi\)
0.398732 0.917067i \(-0.369450\pi\)
\(258\) 0 0
\(259\) −26.1293 + 31.0071i −1.62360 + 1.92669i
\(260\) 0 0
\(261\) 16.2333 12.1739i 1.00482 0.753546i
\(262\) 0 0
\(263\) −18.7799 + 2.14170i −1.15802 + 0.132063i −0.671087 0.741379i \(-0.734172\pi\)
−0.486929 + 0.873441i \(0.661883\pi\)
\(264\) 0 0
\(265\) 0.376864 1.50076i 0.0231505 0.0921908i
\(266\) 0 0
\(267\) −4.52329 + 2.00024i −0.276821 + 0.122413i
\(268\) 0 0
\(269\) −21.5771 + 17.4953i −1.31558 + 1.06671i −0.322837 + 0.946455i \(0.604636\pi\)
−0.992743 + 0.120256i \(0.961629\pi\)
\(270\) 0 0
\(271\) −0.543356 + 3.15916i −0.0330065 + 0.191905i −0.997350 0.0727469i \(-0.976823\pi\)
0.964344 + 0.264652i \(0.0852572\pi\)
\(272\) 0 0
\(273\) −26.6841 + 27.1939i −1.61500 + 1.64585i
\(274\) 0 0
\(275\) 5.07309 0.384773i 0.305919 0.0232027i
\(276\) 0 0
\(277\) 12.2620 + 5.98697i 0.736754 + 0.359722i 0.768565 0.639772i \(-0.220971\pi\)
−0.0318116 + 0.999494i \(0.510128\pi\)
\(278\) 0 0
\(279\) 10.4207 5.58581i 0.623868 0.334414i
\(280\) 0 0
\(281\) 1.30313 + 7.57659i 0.0777380 + 0.451982i 0.998138 + 0.0610025i \(0.0194298\pi\)
−0.920400 + 0.390979i \(0.872137\pi\)
\(282\) 0 0
\(283\) 0.0611089 + 1.07516i 0.00363255 + 0.0639119i 0.999693 0.0247603i \(-0.00788224\pi\)
−0.996061 + 0.0886721i \(0.971738\pi\)
\(284\) 0 0
\(285\) −8.84225 10.4929i −0.523770 0.621546i
\(286\) 0 0
\(287\) −0.512938 27.1001i −0.0302778 1.59967i
\(288\) 0 0
\(289\) −10.8845 1.66065i −0.640267 0.0976853i
\(290\) 0 0
\(291\) −1.38345 + 14.5765i −0.0810993 + 0.854489i
\(292\) 0 0
\(293\) −24.7562 + 12.0873i −1.44627 + 0.706148i −0.983597 0.180380i \(-0.942267\pi\)
−0.462676 + 0.886527i \(0.653111\pi\)
\(294\) 0 0
\(295\) 13.6596 + 4.84196i 0.795291 + 0.281910i
\(296\) 0 0
\(297\) 5.00841 + 1.35895i 0.290618 + 0.0788541i
\(298\) 0 0
\(299\) 2.14474 1.87790i 0.124033 0.108602i
\(300\) 0 0
\(301\) −15.5772 9.12502i −0.897857 0.525958i
\(302\) 0 0
\(303\) −50.0517 + 11.5664i −2.87539 + 0.664474i
\(304\) 0 0
\(305\) −10.1911 + 4.05282i −0.583543 + 0.232064i
\(306\) 0 0
\(307\) 3.94119 + 9.38899i 0.224936 + 0.535858i 0.994741 0.102421i \(-0.0326588\pi\)
−0.769805 + 0.638279i \(0.779647\pi\)
\(308\) 0 0
\(309\) 33.6059 + 36.9464i 1.91177 + 2.10181i
\(310\) 0 0
\(311\) 6.12273 + 2.43489i 0.347188 + 0.138070i 0.536620 0.843824i \(-0.319701\pi\)
−0.189432 + 0.981894i \(0.560665\pi\)
\(312\) 0 0
\(313\) 5.76287 + 1.80038i 0.325736 + 0.101764i 0.456693 0.889624i \(-0.349034\pi\)
−0.130957 + 0.991388i \(0.541805\pi\)
\(314\) 0 0
\(315\) −14.6464 + 22.0325i −0.825228 + 1.24139i
\(316\) 0 0
\(317\) 9.95103 + 0.754746i 0.558906 + 0.0423907i 0.352051 0.935981i \(-0.385484\pi\)
0.206855 + 0.978372i \(0.433677\pi\)
\(318\) 0 0
\(319\) 2.26336 7.75765i 0.126724 0.434345i
\(320\) 0 0
\(321\) −5.79513 + 11.3206i −0.323453 + 0.631853i
\(322\) 0 0
\(323\) −5.54573 + 7.11054i −0.308573 + 0.395641i
\(324\) 0 0
\(325\) −9.22456 + 2.50292i −0.511686 + 0.138837i
\(326\) 0 0
\(327\) 1.97356 4.24396i 0.109138 0.234692i
\(328\) 0 0
\(329\) −32.4621 14.3550i −1.78969 0.791418i
\(330\) 0 0
\(331\) 2.65889 + 19.9531i 0.146146 + 1.09672i 0.898817 + 0.438324i \(0.144428\pi\)
−0.752671 + 0.658397i \(0.771235\pi\)
\(332\) 0 0
\(333\) −37.0323 −2.02936
\(334\) 0 0
\(335\) 12.5389 0.685071
\(336\) 0 0
\(337\) −2.47199 18.5505i −0.134658 1.01051i −0.920130 0.391612i \(-0.871917\pi\)
0.785473 0.618896i \(-0.212420\pi\)
\(338\) 0 0
\(339\) −25.7726 11.3969i −1.39977 0.618992i
\(340\) 0 0
\(341\) 1.98552 4.26967i 0.107522 0.231216i
\(342\) 0 0
\(343\) 30.0621 8.15683i 1.62320 0.440427i
\(344\) 0 0
\(345\) 2.09372 2.68449i 0.112722 0.144528i
\(346\) 0 0
\(347\) 12.7087 24.8259i 0.682237 1.33272i −0.249069 0.968486i \(-0.580125\pi\)
0.931306 0.364238i \(-0.118670\pi\)
\(348\) 0 0
\(349\) 4.14212 14.1971i 0.221722 0.759952i −0.770713 0.637183i \(-0.780100\pi\)
0.992435 0.122769i \(-0.0391775\pi\)
\(350\) 0 0
\(351\) −9.72150 0.737336i −0.518895 0.0393561i
\(352\) 0 0
\(353\) 20.0247 30.1232i 1.06581 1.60329i 0.307324 0.951605i \(-0.400567\pi\)
0.758486 0.651689i \(-0.225939\pi\)
\(354\) 0 0
\(355\) −14.7731 4.61530i −0.784077 0.244955i
\(356\) 0 0
\(357\) 27.7847 + 11.0494i 1.47052 + 0.584797i
\(358\) 0 0
\(359\) 18.4046 + 20.2341i 0.971360 + 1.06792i 0.997667 + 0.0682629i \(0.0217457\pi\)
−0.0263072 + 0.999654i \(0.508375\pi\)
\(360\) 0 0
\(361\) 2.09928 + 5.00104i 0.110488 + 0.263213i
\(362\) 0 0
\(363\) −20.5113 + 8.15695i −1.07657 + 0.428129i
\(364\) 0 0
\(365\) 5.82191 1.34538i 0.304733 0.0704206i
\(366\) 0 0
\(367\) −14.0328 8.22033i −0.732508 0.429098i 0.0914050 0.995814i \(-0.470864\pi\)
−0.823913 + 0.566716i \(0.808214\pi\)
\(368\) 0 0
\(369\) 18.6243 16.3071i 0.969543 0.848915i
\(370\) 0 0
\(371\) −4.89932 1.32935i −0.254360 0.0690162i
\(372\) 0 0
\(373\) −24.8930 8.82390i −1.28891 0.456884i −0.400652 0.916230i \(-0.631216\pi\)
−0.888257 + 0.459346i \(0.848084\pi\)
\(374\) 0 0
\(375\) −26.9899 + 13.1779i −1.39375 + 0.680505i
\(376\) 0 0
\(377\) −1.43445 + 15.1139i −0.0738781 + 0.778404i
\(378\) 0 0
\(379\) −12.2034 1.86187i −0.626848 0.0956380i −0.170381 0.985378i \(-0.554500\pi\)
−0.456467 + 0.889740i \(0.650885\pi\)
\(380\) 0 0
\(381\) −0.640298 33.8290i −0.0328035 1.73311i
\(382\) 0 0
\(383\) 18.7732 + 22.2777i 0.959266 + 1.13834i 0.990318 + 0.138821i \(0.0443312\pi\)
−0.0310519 + 0.999518i \(0.509886\pi\)
\(384\) 0 0
\(385\) 0.597899 + 10.5196i 0.0304718 + 0.536127i
\(386\) 0 0
\(387\) −2.79474 16.2491i −0.142064 0.825986i
\(388\) 0 0
\(389\) −0.868271 + 0.465422i −0.0440231 + 0.0235978i −0.494304 0.869289i \(-0.664577\pi\)
0.450281 + 0.892887i \(0.351324\pi\)
\(390\) 0 0
\(391\) −2.01044 0.981605i −0.101672 0.0496419i
\(392\) 0 0
\(393\) −2.53178 + 0.192025i −0.127711 + 0.00968638i
\(394\) 0 0
\(395\) 1.11551 1.13682i 0.0561273 0.0571997i
\(396\) 0 0
\(397\) 2.49924 14.5310i 0.125433 0.729288i −0.852872 0.522120i \(-0.825141\pi\)
0.978305 0.207169i \(-0.0664248\pi\)
\(398\) 0 0
\(399\) −34.9673 + 28.3525i −1.75055 + 1.41940i
\(400\) 0 0
\(401\) −30.0457 + 13.2865i −1.50041 + 0.663495i −0.981522 0.191347i \(-0.938714\pi\)
−0.518889 + 0.854842i \(0.673654\pi\)
\(402\) 0 0
\(403\) −2.15454 + 8.57987i −0.107325 + 0.427394i
\(404\) 0 0
\(405\) 5.71190 0.651397i 0.283826 0.0323682i
\(406\) 0 0
\(407\) −11.7991 + 8.84858i −0.584862 + 0.438608i
\(408\) 0 0
\(409\) 22.2793 26.4384i 1.10164 1.30729i 0.153961 0.988077i \(-0.450797\pi\)
0.947682 0.319217i \(-0.103420\pi\)
\(410\) 0 0
\(411\) 12.8546 + 25.1110i 0.634070 + 1.23863i
\(412\) 0 0
\(413\) 16.7304 44.5049i 0.823250 2.18994i
\(414\) 0 0
\(415\) 10.1452 5.94299i 0.498009 0.291730i
\(416\) 0 0
\(417\) −1.17335 + 1.62790i −0.0574592 + 0.0797186i
\(418\) 0 0
\(419\) 5.22057 + 2.79840i 0.255042 + 0.136711i 0.594989 0.803734i \(-0.297156\pi\)
−0.339948 + 0.940444i \(0.610409\pi\)
\(420\) 0 0
\(421\) −17.7062 31.5817i −0.862949 1.53920i −0.842040 0.539416i \(-0.818645\pi\)
−0.0209090 0.999781i \(-0.506656\pi\)
\(422\) 0 0
\(423\) −9.07925 31.1191i −0.441448 1.51306i
\(424\) 0 0
\(425\) 4.61335 + 5.91507i 0.223780 + 0.286923i
\(426\) 0 0
\(427\) 12.6612 + 33.6802i 0.612716 + 1.62990i
\(428\) 0 0
\(429\) −11.6835 + 7.45183i −0.564083 + 0.359778i
\(430\) 0 0
\(431\) 9.62732 + 2.22477i 0.463732 + 0.107164i 0.450553 0.892750i \(-0.351227\pi\)
0.0131784 + 0.999913i \(0.495805\pi\)
\(432\) 0 0
\(433\) 7.08343 16.8747i 0.340408 0.810944i −0.657917 0.753091i \(-0.728562\pi\)
0.998325 0.0578538i \(-0.0184257\pi\)
\(434\) 0 0
\(435\) 1.71310 + 18.0497i 0.0821367 + 0.865419i
\(436\) 0 0
\(437\) 2.76929 1.91746i 0.132473 0.0917246i
\(438\) 0 0
\(439\) 2.32757 + 2.03798i 0.111089 + 0.0972674i 0.712499 0.701673i \(-0.247563\pi\)
−0.601411 + 0.798940i \(0.705394\pi\)
\(440\) 0 0
\(441\) 47.3746 + 32.8022i 2.25593 + 1.56201i
\(442\) 0 0
\(443\) 6.60000 + 4.20954i 0.313575 + 0.200001i 0.685150 0.728402i \(-0.259736\pi\)
−0.371575 + 0.928403i \(0.621182\pi\)
\(444\) 0 0
\(445\) 0.339424 2.54713i 0.0160902 0.120746i
\(446\) 0 0
\(447\) 28.8144 47.1208i 1.36287 2.22874i
\(448\) 0 0
\(449\) 9.90408 + 10.0933i 0.467403 + 0.476333i 0.906560 0.422077i \(-0.138699\pi\)
−0.439157 + 0.898410i \(0.644723\pi\)
\(450\) 0 0
\(451\) 2.03758 9.64588i 0.0959458 0.454207i
\(452\) 0 0
\(453\) −20.4016 + 36.3892i −0.958550 + 1.70972i
\(454\) 0 0
\(455\) −4.82110 19.1987i −0.226017 0.900051i
\(456\) 0 0
\(457\) 3.99718 + 6.01295i 0.186980 + 0.281274i 0.914311 0.405014i \(-0.132733\pi\)
−0.727330 + 0.686287i \(0.759239\pi\)
\(458\) 0 0
\(459\) 2.41948 + 7.25896i 0.112932 + 0.338819i
\(460\) 0 0
\(461\) 0.207477 + 0.0236611i 0.00966318 + 0.00110201i 0.118138 0.992997i \(-0.462308\pi\)
−0.108475 + 0.994099i \(0.534597\pi\)
\(462\) 0 0
\(463\) 37.4153 1.41686i 1.73884 0.0658473i 0.850763 0.525550i \(-0.176140\pi\)
0.888073 + 0.459703i \(0.152044\pi\)
\(464\) 0 0
\(465\) −0.599494 + 10.5476i −0.0278009 + 0.489134i
\(466\) 0 0
\(467\) −4.37084 7.14773i −0.202258 0.330757i 0.735822 0.677175i \(-0.236796\pi\)
−0.938081 + 0.346417i \(0.887398\pi\)
\(468\) 0 0
\(469\) 0.778477 41.1294i 0.0359467 1.89918i
\(470\) 0 0
\(471\) −47.0758 + 16.6871i −2.16914 + 0.768902i
\(472\) 0 0
\(473\) −4.77304 4.50946i −0.219465 0.207345i
\(474\) 0 0
\(475\) −11.1645 + 1.70336i −0.512263 + 0.0781557i
\(476\) 0 0
\(477\) −1.95494 4.20393i −0.0895108 0.192485i
\(478\) 0 0
\(479\) −35.0242 1.32632i −1.60030 0.0606011i −0.777481 0.628907i \(-0.783503\pi\)
−0.822818 + 0.568306i \(0.807599\pi\)
\(480\) 0 0
\(481\) 18.6437 20.4970i 0.850080 0.934581i
\(482\) 0 0
\(483\) −8.67556 7.03439i −0.394751 0.320076i
\(484\) 0 0
\(485\) −6.08610 4.56417i −0.276356 0.207248i
\(486\) 0 0
\(487\) 12.7672 2.44549i 0.578537 0.110816i 0.109488 0.993988i \(-0.465079\pi\)
0.469049 + 0.883172i \(0.344597\pi\)
\(488\) 0 0
\(489\) −54.8179 10.5001i −2.47895 0.474830i
\(490\) 0 0
\(491\) 0.549948 + 2.60345i 0.0248188 + 0.117492i 0.989053 0.147559i \(-0.0471415\pi\)
−0.964235 + 0.265051i \(0.914611\pi\)
\(492\) 0 0
\(493\) 11.3729 3.55303i 0.512210 0.160020i
\(494\) 0 0
\(495\) −6.99478 + 6.60851i −0.314392 + 0.297030i
\(496\) 0 0
\(497\) −16.0561 + 48.1717i −0.720214 + 2.16079i
\(498\) 0 0
\(499\) 1.26358 + 1.75308i 0.0565655 + 0.0784787i 0.838569 0.544795i \(-0.183393\pi\)
−0.782004 + 0.623274i \(0.785802\pi\)
\(500\) 0 0
\(501\) 34.2919 + 4.59186i 1.53205 + 0.205149i
\(502\) 0 0
\(503\) 0.968050 + 1.34307i 0.0431632 + 0.0598844i 0.832265 0.554378i \(-0.187044\pi\)
−0.789102 + 0.614263i \(0.789454\pi\)
\(504\) 0 0
\(505\) 8.43962 25.3207i 0.375558 1.12675i
\(506\) 0 0
\(507\) −6.37522 + 6.02317i −0.283134 + 0.267498i
\(508\) 0 0
\(509\) 21.3547 6.67146i 0.946532 0.295707i 0.214304 0.976767i \(-0.431252\pi\)
0.732228 + 0.681060i \(0.238481\pi\)
\(510\) 0 0
\(511\) −4.05161 19.1803i −0.179233 0.848486i
\(512\) 0 0
\(513\) −11.3141 2.16716i −0.499529 0.0956822i
\(514\) 0 0
\(515\) −25.4855 + 4.88162i −1.12303 + 0.215110i
\(516\) 0 0
\(517\) −10.3285 7.74567i −0.454246 0.340654i
\(518\) 0 0
\(519\) 36.1477 + 29.3096i 1.58671 + 1.28655i
\(520\) 0 0
\(521\) 20.4042 22.4324i 0.893922 0.982781i −0.106011 0.994365i \(-0.533808\pi\)
0.999933 + 0.0115838i \(0.00368731\pi\)
\(522\) 0 0
\(523\) 20.0969 + 0.761043i 0.878778 + 0.0332781i 0.473376 0.880860i \(-0.343035\pi\)
0.405402 + 0.914139i \(0.367132\pi\)
\(524\) 0 0
\(525\) 15.7909 + 33.9568i 0.689171 + 1.48200i
\(526\) 0 0
\(527\) 6.86332 1.04713i 0.298971 0.0456138i
\(528\) 0 0
\(529\) −16.1111 15.2214i −0.700481 0.661798i
\(530\) 0 0
\(531\) 40.9274 14.5077i 1.77610 0.629581i
\(532\) 0 0
\(533\) −0.350502 + 18.5181i −0.0151819 + 0.802108i
\(534\) 0 0
\(535\) −3.44712 5.63715i −0.149032 0.243715i
\(536\) 0 0
\(537\) 3.55596 62.5644i 0.153451 2.69985i
\(538\) 0 0
\(539\) 22.9322 0.868412i 0.987761 0.0374051i
\(540\) 0 0
\(541\) −2.26077 0.257822i −0.0971979 0.0110847i 0.0645731 0.997913i \(-0.479431\pi\)
−0.161771 + 0.986828i \(0.551721\pi\)
\(542\) 0 0
\(543\) 11.3746 + 34.1261i 0.488130 + 1.46449i
\(544\) 0 0
\(545\) 1.34622 + 2.02511i 0.0576657 + 0.0867463i
\(546\) 0 0
\(547\) 6.32334 + 25.1810i 0.270367 + 1.07666i 0.941955 + 0.335738i \(0.108986\pi\)
−0.671589 + 0.740924i \(0.734388\pi\)
\(548\) 0 0
\(549\) −16.0702 + 28.6636i −0.685861 + 1.22333i
\(550\) 0 0
\(551\) −3.70750 + 17.5513i −0.157945 + 0.747709i
\(552\) 0 0
\(553\) −3.65969 3.72962i −0.155626 0.158599i
\(554\) 0 0
\(555\) 17.2627 28.2301i 0.732761 1.19830i
\(556\) 0 0
\(557\) −0.203067 + 1.52387i −0.00860423 + 0.0645685i −0.995014 0.0997353i \(-0.968200\pi\)
0.986410 + 0.164304i \(0.0525377\pi\)
\(558\) 0 0
\(559\) 10.4007 + 6.63365i 0.439902 + 0.280574i
\(560\) 0 0
\(561\) 8.94157 + 6.19116i 0.377513 + 0.261391i
\(562\) 0 0
\(563\) −23.3989 20.4877i −0.986147 0.863453i 0.00448838 0.999990i \(-0.498571\pi\)
−0.990635 + 0.136537i \(0.956403\pi\)
\(564\) 0 0
\(565\) 12.0373 8.33468i 0.506415 0.350643i
\(566\) 0 0
\(567\) −1.78206 18.7763i −0.0748394 0.788532i
\(568\) 0 0
\(569\) −3.89729 + 9.28441i −0.163383 + 0.389223i −0.982979 0.183720i \(-0.941186\pi\)
0.819596 + 0.572942i \(0.194198\pi\)
\(570\) 0 0
\(571\) 12.6184 + 2.91599i 0.528066 + 0.122031i 0.480764 0.876850i \(-0.340359\pi\)
0.0473018 + 0.998881i \(0.484938\pi\)
\(572\) 0 0
\(573\) 16.3909 10.4543i 0.684740 0.436734i
\(574\) 0 0
\(575\) −0.985979 2.62282i −0.0411182 0.109379i
\(576\) 0 0
\(577\) 17.8157 + 22.8427i 0.741679 + 0.950953i 0.999885 0.0151365i \(-0.00481828\pi\)
−0.258207 + 0.966090i \(0.583132\pi\)
\(578\) 0 0
\(579\) 5.11864 + 17.5441i 0.212723 + 0.729107i
\(580\) 0 0
\(581\) −18.8640 33.6468i −0.782613 1.39591i
\(582\) 0 0
\(583\) −1.62738 0.872327i −0.0673990 0.0361281i
\(584\) 0 0
\(585\) 10.5707 14.6657i 0.437045 0.606354i
\(586\) 0 0
\(587\) 33.1109 19.3961i 1.36663 0.800564i 0.374679 0.927155i \(-0.377753\pi\)
0.991955 + 0.126591i \(0.0404035\pi\)
\(588\) 0 0
\(589\) −3.67807 + 9.78411i −0.151552 + 0.403147i
\(590\) 0 0
\(591\) 8.44274 + 16.4926i 0.347288 + 0.678414i
\(592\) 0 0
\(593\) −14.3869 + 17.0726i −0.590799 + 0.701088i −0.975011 0.222157i \(-0.928690\pi\)
0.384212 + 0.923245i \(0.374473\pi\)
\(594\) 0 0
\(595\) −12.4287 + 9.32072i −0.509528 + 0.382112i
\(596\) 0 0
\(597\) 12.8847 1.46939i 0.527334 0.0601383i
\(598\) 0 0
\(599\) −7.93582 + 31.6023i −0.324249 + 1.29123i 0.561658 + 0.827370i \(0.310164\pi\)
−0.885907 + 0.463864i \(0.846463\pi\)
\(600\) 0 0
\(601\) −33.5540 + 14.8379i −1.36870 + 0.605249i −0.952643 0.304091i \(-0.901647\pi\)
−0.416054 + 0.909340i \(0.636587\pi\)
\(602\) 0 0
\(603\) 29.1821 23.6617i 1.18839 0.963577i
\(604\) 0 0
\(605\) 1.94399 11.3027i 0.0790343 0.459518i
\(606\) 0 0
\(607\) −5.62927 + 5.73682i −0.228485 + 0.232851i −0.818449 0.574579i \(-0.805166\pi\)
0.589964 + 0.807429i \(0.299142\pi\)
\(608\) 0 0
\(609\) 59.3123 4.49860i 2.40346 0.182292i
\(610\) 0 0
\(611\) 21.7950 + 10.6415i 0.881730 + 0.430508i
\(612\) 0 0
\(613\) −26.9527 + 14.4475i −1.08861 + 0.583530i −0.915885 0.401441i \(-0.868510\pi\)
−0.172723 + 0.984970i \(0.555257\pi\)
\(614\) 0 0
\(615\) 3.74932 + 21.7991i 0.151187 + 0.879026i
\(616\) 0 0
\(617\) −2.70668 47.6218i −0.108967 1.91718i −0.333557 0.942730i \(-0.608249\pi\)
0.224590 0.974453i \(-0.427896\pi\)
\(618\) 0 0
\(619\) −10.2087 12.1144i −0.410323 0.486921i 0.519738 0.854326i \(-0.326029\pi\)
−0.930061 + 0.367405i \(0.880246\pi\)
\(620\) 0 0
\(621\) −0.0540873 2.85760i −0.00217045 0.114672i
\(622\) 0 0
\(623\) −8.33391 1.27150i −0.333891 0.0509416i
\(624\) 0 0
\(625\) 0.0264074 0.278238i 0.00105630 0.0111295i
\(626\) 0 0
\(627\) −14.7138 + 7.18405i −0.587612 + 0.286903i
\(628\) 0 0
\(629\) −20.4960 7.26529i −0.817229 0.289686i
\(630\) 0 0
\(631\) 10.9037 + 2.95854i 0.434070 + 0.117777i 0.472192 0.881496i \(-0.343463\pi\)
−0.0381219 + 0.999273i \(0.512138\pi\)
\(632\) 0 0
\(633\) −38.1375 + 33.3925i −1.51583 + 1.32723i
\(634\) 0 0
\(635\) 15.1684 + 8.88552i 0.601938 + 0.352611i
\(636\) 0 0
\(637\) −42.0062 + 9.70720i −1.66435 + 0.384613i
\(638\) 0 0
\(639\) −43.0914 + 17.1366i −1.70467 + 0.677913i
\(640\) 0 0
\(641\) 1.50318 + 3.58098i 0.0593720 + 0.141440i 0.949029 0.315190i \(-0.102068\pi\)
−0.889657 + 0.456630i \(0.849056\pi\)
\(642\) 0 0
\(643\) −2.89854 3.18667i −0.114307 0.125670i 0.679931 0.733276i \(-0.262010\pi\)
−0.794239 + 0.607606i \(0.792130\pi\)
\(644\) 0 0
\(645\) 13.6896 + 5.44409i 0.539028 + 0.214361i
\(646\) 0 0
\(647\) 25.5138 + 7.97079i 1.00305 + 0.313364i 0.755243 0.655445i \(-0.227519\pi\)
0.247807 + 0.968809i \(0.420290\pi\)
\(648\) 0 0
\(649\) 9.57371 14.4017i 0.375801 0.565317i
\(650\) 0 0
\(651\) 34.5606 + 2.62128i 1.35454 + 0.102736i
\(652\) 0 0
\(653\) −4.87425 + 16.7065i −0.190744 + 0.653774i 0.807235 + 0.590230i \(0.200963\pi\)
−0.997979 + 0.0635436i \(0.979760\pi\)
\(654\) 0 0
\(655\) 0.601121 1.17427i 0.0234877 0.0458824i
\(656\) 0 0
\(657\) 11.0107 14.1175i 0.429568 0.550776i
\(658\) 0 0
\(659\) 3.13661 0.851065i 0.122185 0.0331528i −0.200247 0.979745i \(-0.564174\pi\)
0.322432 + 0.946593i \(0.395500\pi\)
\(660\) 0 0
\(661\) −10.7185 + 23.0491i −0.416901 + 0.896508i 0.579754 + 0.814791i \(0.303149\pi\)
−0.996656 + 0.0817162i \(0.973960\pi\)
\(662\) 0 0
\(663\) −18.6865 8.26334i −0.725725 0.320922i
\(664\) 0 0
\(665\) −3.08948 23.1843i −0.119805 0.899049i
\(666\) 0 0
\(667\) −4.45065 −0.172330
\(668\) 0 0
\(669\) 59.1429 2.28660
\(670\) 0 0
\(671\) 1.72869 + 12.9726i 0.0667355 + 0.500802i
\(672\) 0 0
\(673\) −13.5532 5.99332i −0.522436 0.231026i 0.126365 0.991984i \(-0.459669\pi\)
−0.648801 + 0.760958i \(0.724729\pi\)
\(674\) 0 0
\(675\) −4.04081 + 8.68940i −0.155531 + 0.334455i
\(676\) 0 0
\(677\) −2.23620 + 0.606754i −0.0859441 + 0.0233194i −0.304577 0.952488i \(-0.598515\pi\)
0.218633 + 0.975807i \(0.429840\pi\)
\(678\) 0 0
\(679\) −15.3490 + 19.6800i −0.589042 + 0.755248i
\(680\) 0 0
\(681\) −20.2306 + 39.5198i −0.775239 + 1.51440i
\(682\) 0 0
\(683\) −6.46713 + 22.1660i −0.247458 + 0.848159i 0.737497 + 0.675350i \(0.236007\pi\)
−0.984955 + 0.172809i \(0.944716\pi\)
\(684\) 0 0
\(685\) −14.6148 1.10847i −0.558401 0.0423525i
\(686\) 0 0
\(687\) −37.4214 + 56.2929i −1.42772 + 2.14771i
\(688\) 0 0
\(689\) 3.31104 + 1.03441i 0.126140 + 0.0394077i
\(690\) 0 0
\(691\) 47.0475 + 18.7099i 1.78977 + 0.711757i 0.994406 + 0.105627i \(0.0336851\pi\)
0.795366 + 0.606130i \(0.207279\pi\)
\(692\) 0 0
\(693\) 21.2426 + 23.3542i 0.806942 + 0.887154i
\(694\) 0 0
\(695\) −0.403537 0.961334i −0.0153070 0.0364655i
\(696\) 0 0
\(697\) 13.5071 5.37152i 0.511619 0.203461i
\(698\) 0 0
\(699\) 37.1552 8.58618i 1.40534 0.324759i
\(700\) 0 0
\(701\) 27.7970 + 16.2833i 1.04988 + 0.615011i 0.926092 0.377297i \(-0.123147\pi\)
0.123787 + 0.992309i \(0.460496\pi\)
\(702\) 0 0
\(703\) 24.6315 21.5669i 0.928993 0.813410i
\(704\) 0 0
\(705\) 27.9547 + 7.58503i 1.05284 + 0.285669i
\(706\) 0 0
\(707\) −82.5317 29.2553i −3.10392 1.10026i
\(708\) 0 0
\(709\) 24.1344 11.7837i 0.906386 0.442546i 0.0743274 0.997234i \(-0.476319\pi\)
0.832058 + 0.554688i \(0.187162\pi\)
\(710\) 0 0
\(711\) 0.450897 4.75080i 0.0169100 0.178169i
\(712\) 0 0
\(713\) −2.56368 0.391139i −0.0960104 0.0146483i
\(714\) 0 0
\(715\) −0.136251 7.19856i −0.00509549 0.269211i
\(716\) 0 0
\(717\) 8.29462 + 9.84304i 0.309768 + 0.367595i
\(718\) 0 0
\(719\) −0.870650 15.3184i −0.0324698 0.571280i −0.972890 0.231267i \(-0.925713\pi\)
0.940421 0.340013i \(-0.110432\pi\)
\(720\) 0 0
\(721\) 14.4302 + 83.8995i 0.537409 + 3.12458i
\(722\) 0 0
\(723\) 41.3838 22.1831i 1.53908 0.824998i
\(724\) 0 0
\(725\) 13.4096 + 6.54729i 0.498021 + 0.243160i
\(726\) 0 0
\(727\) −35.8496 + 2.71904i −1.32959 + 0.100844i −0.721161 0.692767i \(-0.756391\pi\)
−0.608425 + 0.793611i \(0.708199\pi\)
\(728\) 0 0
\(729\) 29.6518 30.2183i 1.09821 1.11920i
\(730\) 0 0
\(731\) 1.64109 9.54155i 0.0606978 0.352907i
\(732\) 0 0
\(733\) 18.2241 14.7766i 0.673123 0.545788i −0.231056 0.972940i \(-0.574218\pi\)
0.904180 + 0.427152i \(0.140483\pi\)
\(734\) 0 0
\(735\) −47.0893 + 20.8233i −1.73692 + 0.768079i
\(736\) 0 0
\(737\) 3.64415 14.5119i 0.134234 0.534551i
\(738\) 0 0
\(739\) 27.0443 3.08419i 0.994841 0.113454i 0.399335 0.916805i \(-0.369241\pi\)
0.595506 + 0.803351i \(0.296952\pi\)
\(740\) 0 0
\(741\) 24.6099 18.4558i 0.904068 0.677991i
\(742\) 0 0
\(743\) −34.0462 + 40.4018i −1.24903 + 1.48220i −0.436039 + 0.899928i \(0.643619\pi\)
−0.812994 + 0.582272i \(0.802164\pi\)
\(744\) 0 0
\(745\) 13.0763 + 25.5442i 0.479080 + 0.935865i
\(746\) 0 0
\(747\) 12.3964 32.9760i 0.453562 1.20653i
\(748\) 0 0
\(749\) −18.7047 + 10.9571i −0.683456 + 0.400364i
\(750\) 0 0
\(751\) −17.5201 + 24.3074i −0.639319 + 0.886988i −0.998936 0.0461119i \(-0.985317\pi\)
0.359617 + 0.933100i \(0.382907\pi\)
\(752\) 0 0
\(753\) −10.1698 5.45136i −0.370609 0.198659i
\(754\) 0 0
\(755\) −10.5998 18.9064i −0.385767 0.688073i
\(756\) 0 0
\(757\) 13.6888 + 46.9184i 0.497529 + 1.70528i 0.689856 + 0.723947i \(0.257674\pi\)
−0.192326 + 0.981331i \(0.561603\pi\)
\(758\) 0 0
\(759\) −2.49840 3.20336i −0.0906863 0.116275i
\(760\) 0 0
\(761\) 2.30305 + 6.12639i 0.0834857 + 0.222082i 0.971178 0.238355i \(-0.0766083\pi\)
−0.887692 + 0.460437i \(0.847693\pi\)
\(762\) 0 0
\(763\) 6.72626 4.29007i 0.243507 0.155311i
\(764\) 0 0
\(765\) −13.8239 3.19456i −0.499805 0.115500i
\(766\) 0 0
\(767\) −12.5749 + 29.9567i −0.454052 + 1.08167i
\(768\) 0 0
\(769\) −1.11672 11.7661i −0.0402698 0.424296i −0.992794 0.119833i \(-0.961764\pi\)
0.952524 0.304463i \(-0.0984769\pi\)
\(770\) 0 0
\(771\) 44.7883 31.0115i 1.61301 1.11685i
\(772\) 0 0
\(773\) 37.0460 + 32.4368i 1.33245 + 1.16667i 0.972289 + 0.233783i \(0.0751104\pi\)
0.360164 + 0.932889i \(0.382721\pi\)
\(774\) 0 0
\(775\) 7.14885 + 4.94988i 0.256794 + 0.177805i
\(776\) 0 0
\(777\) −91.5273 58.3770i −3.28353 2.09426i
\(778\) 0 0
\(779\) −2.89073 + 21.6929i −0.103571 + 0.777228i
\(780\) 0 0
\(781\) −9.63503 + 15.7564i −0.344768 + 0.563808i
\(782\) 0 0
\(783\) 10.6608 + 10.8645i 0.380985 + 0.388265i
\(784\) 0 0
\(785\) 5.36325 25.3896i 0.191422 0.906192i
\(786\) 0 0
\(787\) −16.3659 + 29.1911i −0.583382 + 1.04055i 0.408423 + 0.912793i \(0.366079\pi\)
−0.991806 + 0.127756i \(0.959222\pi\)
\(788\) 0 0
\(789\) −12.3250 49.0809i −0.438780 1.74732i
\(790\) 0 0
\(791\) −26.5917 40.0018i −0.945491 1.42230i
\(792\) 0 0
\(793\) −7.77454 23.3253i −0.276082 0.828304i
\(794\) 0 0
\(795\) 4.11600 + 0.469398i 0.145980 + 0.0166478i
\(796\) 0 0
\(797\)