Properties

Label 668.2.e.a.297.13
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 297.13
Character \(\chi\) \(=\) 668.297
Dual form 668.2.e.a.9.13

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

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

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
\(3\) 0.353640 2.65381i 0.204174 1.53218i −0.526927 0.849910i \(-0.676656\pi\)
0.731101 0.682269i \(-0.239007\pi\)
\(4\) 0 0
\(5\) −1.27217 + 0.562563i −0.568930 + 0.251586i −0.668835 0.743411i \(-0.733207\pi\)
0.0999044 + 0.994997i \(0.468146\pi\)
\(6\) 0 0
\(7\) −1.92428 4.13797i −0.727308 1.56401i −0.822640 0.568562i \(-0.807500\pi\)
0.0953327 0.995445i \(-0.469608\pi\)
\(8\) 0 0
\(9\) −4.02235 1.09139i −1.34078 0.363798i
\(10\) 0 0
\(11\) −1.02081 1.30885i −0.307786 0.394632i 0.609549 0.792749i \(-0.291351\pi\)
−0.917335 + 0.398117i \(0.869664\pi\)
\(12\) 0 0
\(13\) 1.42096 + 2.77578i 0.394102 + 0.769864i 0.999664 0.0259349i \(-0.00825627\pi\)
−0.605562 + 0.795798i \(0.707051\pi\)
\(14\) 0 0
\(15\) 1.04305 + 3.57504i 0.269314 + 0.923070i
\(16\) 0 0
\(17\) −2.44034 + 0.185090i −0.591869 + 0.0448909i −0.368156 0.929764i \(-0.620011\pi\)
−0.223713 + 0.974655i \(0.571818\pi\)
\(18\) 0 0
\(19\) 2.03980 + 3.06846i 0.467961 + 0.703953i 0.988724 0.149748i \(-0.0478463\pi\)
−0.520763 + 0.853701i \(0.674352\pi\)
\(20\) 0 0
\(21\) −11.6619 + 3.64331i −2.54484 + 0.795036i
\(22\) 0 0
\(23\) 0.849459 0.337813i 0.177124 0.0704389i −0.279287 0.960208i \(-0.590098\pi\)
0.456412 + 0.889769i \(0.349134\pi\)
\(24\) 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 −0.0904136 0.995904i \(-0.528819\pi\)
−0.749660 + 0.661824i \(0.769783\pi\)
\(30\) 0 0
\(31\) −2.76400 0.638732i −0.496429 0.114720i −0.0304875 0.999535i \(-0.509706\pi\)
−0.465941 + 0.884816i \(0.654284\pi\)
\(32\) 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 0.526020 0.850472i \(-0.323684\pi\)
0.883752 + 0.467955i \(0.155009\pi\)
\(38\) 0 0
\(39\) 7.86891 2.78932i 1.26003 0.446649i
\(40\) 0 0
\(41\) −5.33729 2.60595i −0.833545 0.406981i −0.0280663 0.999606i \(-0.508935\pi\)
−0.805478 + 0.592625i \(0.798092\pi\)
\(42\) 0 0
\(43\) −0.373781 3.93828i −0.0570010 0.600582i −0.977657 0.210207i \(-0.932586\pi\)
0.920656 0.390375i \(-0.127655\pi\)
\(44\) 0 0
\(45\) 5.73107 0.874387i 0.854338 0.130346i
\(46\) 0 0
\(47\) 0.147189 7.77648i 0.0214698 1.13432i −0.812656 0.582743i \(-0.801979\pi\)
0.834126 0.551574i \(-0.185972\pi\)
\(48\) 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 −0.969699 0.244304i \(-0.921441\pi\)
0.995599 + 0.0937150i \(0.0298742\pi\)
\(54\) 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 −0.620676 0.784067i \(-0.713142\pi\)
−0.731832 + 0.681485i \(0.761335\pi\)
\(60\) 0 0
\(61\) 5.52223 + 5.62774i 0.707049 + 0.720558i 0.969691 0.244335i \(-0.0785697\pi\)
−0.262642 + 0.964893i \(0.584594\pi\)
\(62\) 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 −0.165996 0.986126i \(-0.553084\pi\)
−0.841189 + 0.540741i \(0.818144\pi\)
\(68\) 0 0
\(69\) −0.596091 2.37377i −0.0717609 0.285768i
\(70\) 0 0
\(71\) 11.0551 + 1.26074i 1.31200 + 0.149623i 0.741097 0.671397i \(-0.234306\pi\)
0.570899 + 0.821020i \(0.306595\pi\)
\(72\) 0 0
\(73\) −3.43668 2.57728i −0.402233 0.301648i 0.379583 0.925158i \(-0.376068\pi\)
−0.781816 + 0.623510i \(0.785706\pi\)
\(74\) 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 0.911436 0.411443i \(-0.134975\pi\)
−0.956766 + 0.290858i \(0.906059\pi\)
\(80\) 0 0
\(81\) −3.56612 2.08901i −0.396236 0.232112i
\(82\) 0 0
\(83\) −4.94246 6.85715i −0.542506 0.752670i 0.447410 0.894329i \(-0.352347\pi\)
−0.989915 + 0.141659i \(0.954756\pi\)
\(84\) 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 −0.927942 0.372726i \(-0.878423\pi\)
0.982786 + 0.184746i \(0.0591462\pi\)
\(90\) 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 0.0542136 0.998529i \(-0.482735\pi\)
0.486821 + 0.873502i \(0.338157\pi\)
\(98\) 0 0
\(99\) 2.67759 + 6.37874i 0.269108 + 0.641088i
\(100\) 0 0
\(101\) 1.81295 19.1019i 0.180396 1.90071i −0.206282 0.978493i \(-0.566136\pi\)
0.386678 0.922215i \(-0.373623\pi\)
\(102\) 0 0
\(103\) 15.3371 + 10.6195i 1.51121 + 1.04637i 0.979969 + 0.199149i \(0.0638177\pi\)
0.531245 + 0.847218i \(0.321724\pi\)
\(104\) 0 0
\(105\) 12.7863 11.1955i 1.24781 1.09256i
\(106\) 0 0
\(107\) 3.90543 2.70413i 0.377552 0.261418i −0.365277 0.930899i \(-0.619026\pi\)
0.742829 + 0.669481i \(0.233483\pi\)
\(108\) 0 0
\(109\) −1.47392 + 0.940081i −0.141176 + 0.0900434i −0.606443 0.795127i \(-0.707404\pi\)
0.465267 + 0.885170i \(0.345958\pi\)
\(110\) 0 0
\(111\) −3.14222 23.5801i −0.298246 2.23812i
\(112\) 0 0
\(113\) −5.49114 8.97979i −0.516563 0.844748i 0.482959 0.875643i \(-0.339562\pi\)
−0.999523 + 0.0308949i \(0.990164\pi\)
\(114\) 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 −0.650924 0.759143i \(-0.725618\pi\)
−0.463284 + 0.886210i \(0.653329\pi\)
\(128\) 0 0
\(129\) −10.5836 0.400787i −0.931837 0.0352874i
\(130\) 0 0
\(131\) −0.0538156 0.946843i −0.00470189 0.0827261i 0.995181 0.0980596i \(-0.0312636\pi\)
−0.999882 + 0.0153335i \(0.995119\pi\)
\(132\) 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 0.722592 0.691275i \(-0.242951\pi\)
0.125900 + 0.992043i \(0.459818\pi\)
\(138\) 0 0
\(139\) 0.544827 0.514740i 0.0462116 0.0436597i −0.663298 0.748355i \(-0.730844\pi\)
0.709510 + 0.704695i \(0.248916\pi\)
\(140\) 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 −0.319631 + 0.947542i \(0.603559\pi\)
−0.993144 + 0.116894i \(0.962706\pi\)
\(150\) 0 0
\(151\) 12.4663 9.34887i 1.01449 0.760800i 0.0432888 0.999063i \(-0.486216\pi\)
0.971201 + 0.238263i \(0.0765779\pi\)
\(152\) 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 −0.499420 0.866360i \(-0.666453\pi\)
0.807136 0.590366i \(-0.201017\pi\)
\(158\) 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 −0.805955 0.591976i \(-0.798348\pi\)
0.289619 0.957142i \(-0.406471\pi\)
\(164\) 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 0.995777 0.0918047i \(-0.0292635\pi\)
−0.0351511 + 0.999382i \(0.511191\pi\)
\(174\) 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 −0.950285 0.311380i \(-0.899209\pi\)
−0.767957 + 0.640501i \(0.778727\pi\)
\(180\) 0 0
\(181\) 13.1961 + 2.52765i 0.980859 + 0.187879i 0.653422 0.756994i \(-0.273333\pi\)
0.327438 + 0.944873i \(0.393815\pi\)
\(182\) 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 −0.985678 0.168639i \(-0.946063\pi\)
0.764125 + 0.645069i \(0.223171\pi\)
\(192\) 0 0
\(193\) 6.74809 + 1.02955i 0.485738 + 0.0741089i 0.389071 0.921208i \(-0.372796\pi\)
0.0966675 + 0.995317i \(0.469182\pi\)
\(194\) 0 0
\(195\) −8.44140 + 7.97524i −0.604501 + 0.571119i
\(196\) 0 0
\(197\) 6.52278 + 2.31215i 0.464729 + 0.164734i 0.556157 0.831078i \(-0.312275\pi\)
−0.0914274 + 0.995812i \(0.529143\pi\)
\(198\) 0 0
\(199\) 0.0916647 + 4.84293i 0.00649794 + 0.343306i 0.988225 + 0.153010i \(0.0488967\pi\)
−0.981727 + 0.190296i \(0.939055\pi\)
\(200\) 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 −0.270833 0.962626i \(-0.587299\pi\)
0.992424 0.122861i \(-0.0392068\pi\)
\(212\) 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 0.764792 + 0.644277i \(0.222842\pi\)
−0.569391 + 0.822067i \(0.692821\pi\)
\(224\) 0 0
\(225\) 10.7705 6.86952i 0.718033 0.457968i
\(226\) 0 0
\(227\) 13.6337 9.44002i 0.904903 0.626556i −0.0228551 0.999739i \(-0.507276\pi\)
0.927758 + 0.373182i \(0.121733\pi\)
\(228\) 0 0
\(229\) 18.9957 16.6323i 1.25527 1.09909i 0.264383 0.964418i \(-0.414832\pi\)
0.990890 0.134676i \(-0.0429995\pi\)
\(230\) 0 0
\(231\) 16.6731 + 11.5445i 1.09701 + 0.759573i
\(232\) 0 0
\(233\) −1.34582 + 14.1800i −0.0881677 + 0.928964i 0.836444 + 0.548053i \(0.184631\pi\)
−0.924612 + 0.380911i \(0.875610\pi\)
\(234\) 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 0.662303 0.749236i \(-0.269579\pi\)
−0.400101 + 0.916471i \(0.631025\pi\)
\(240\) 0 0
\(241\) −6.17134 + 16.4165i −0.397531 + 1.05748i 0.573643 + 0.819106i \(0.305530\pi\)
−0.971174 + 0.238373i \(0.923386\pi\)
\(242\) 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 0.724164 0.689628i \(-0.242226\pi\)
−0.883229 + 0.468941i \(0.844636\pi\)
\(252\) 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 0.398732 + 0.917067i \(0.369450\pi\)
−0.977104 + 0.212760i \(0.931755\pi\)
\(258\) 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 −0.486929 0.873441i \(-0.661883\pi\)
−0.671087 + 0.741379i \(0.734172\pi\)
\(264\) 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 −0.992743 0.120256i \(-0.961629\pi\)
−0.322837 0.946455i \(-0.604636\pi\)
\(270\) 0 0
\(271\) −0.543356 3.15916i −0.0330065 0.191905i 0.964344 0.264652i \(-0.0852572\pi\)
−0.997350 + 0.0727469i \(0.976823\pi\)
\(272\) 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 −0.0318116 0.999494i \(-0.510128\pi\)
0.768565 + 0.639772i \(0.220971\pi\)
\(278\) 0 0
\(279\) 10.4207 + 5.58581i 0.623868 + 0.334414i
\(280\) 0 0
\(281\) 1.30313 7.57659i 0.0777380 0.451982i −0.920400 0.390979i \(-0.872137\pi\)
0.998138 0.0610025i \(-0.0194298\pi\)
\(282\) 0 0
\(283\) 0.0611089 1.07516i 0.00363255 0.0639119i −0.996061 0.0886721i \(-0.971738\pi\)
0.999693 + 0.0247603i \(0.00788224\pi\)
\(284\) 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 −0.462676 0.886527i \(-0.653111\pi\)
−0.983597 + 0.180380i \(0.942267\pi\)
\(294\) 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 −0.769805 0.638279i \(-0.779647\pi\)
0.994741 + 0.102421i \(0.0326588\pi\)
\(308\) 0 0
\(309\) 33.6059 36.9464i 1.91177 2.10181i
\(310\) 0 0
\(311\) 6.12273 2.43489i 0.347188 0.138070i −0.189432 0.981894i \(-0.560665\pi\)
0.536620 + 0.843824i \(0.319701\pi\)
\(312\) 0 0
\(313\) 5.76287 1.80038i 0.325736 0.101764i −0.130957 0.991388i \(-0.541805\pi\)
0.456693 + 0.889624i \(0.349034\pi\)
\(314\) 0 0
\(315\) −14.6464 22.0325i −0.825228 1.24139i
\(316\) 0 0
\(317\) 9.95103 0.754746i 0.558906 0.0423907i 0.206855 0.978372i \(-0.433677\pi\)
0.352051 + 0.935981i \(0.385484\pi\)
\(318\) 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 −0.752671 0.658397i \(-0.771235\pi\)
0.898817 0.438324i \(-0.144428\pi\)
\(332\) 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 0.785473 + 0.618896i \(0.212420\pi\)
−0.920130 + 0.391612i \(0.871917\pi\)
\(338\) 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 0.931306 + 0.364238i \(0.118670\pi\)
−0.249069 + 0.968486i \(0.580125\pi\)
\(348\) 0 0
\(349\) 4.14212 + 14.1971i 0.221722 + 0.759952i 0.992435 + 0.122769i \(0.0391775\pi\)
−0.770713 + 0.637183i \(0.780100\pi\)
\(350\) 0 0
\(351\) −9.72150 + 0.737336i −0.518895 + 0.0393561i
\(352\) 0 0
\(353\) 20.0247 + 30.1232i 1.06581 + 1.60329i 0.758486 + 0.651689i \(0.225939\pi\)
0.307324 + 0.951605i \(0.400567\pi\)
\(354\) 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 −0.0263072 0.999654i \(-0.508375\pi\)
0.997667 0.0682629i \(-0.0217457\pi\)
\(360\) 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 −0.823913 0.566716i \(-0.808214\pi\)
0.0914050 + 0.995814i \(0.470864\pi\)
\(368\) 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 −0.888257 0.459346i \(-0.848084\pi\)
−0.400652 + 0.916230i \(0.631216\pi\)
\(374\) 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 −0.456467 0.889740i \(-0.650885\pi\)
−0.170381 + 0.985378i \(0.554500\pi\)
\(380\) 0 0
\(381\) −0.640298 + 33.8290i −0.0328035 + 1.73311i
\(382\) 0 0
\(383\) 18.7732 22.2777i 0.959266 1.13834i −0.0310519 0.999518i \(-0.509886\pi\)
0.990318 0.138821i \(-0.0443312\pi\)
\(384\) 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 0.450281 0.892887i \(-0.351324\pi\)
−0.494304 + 0.869289i \(0.664577\pi\)
\(390\) 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 0.978305 + 0.207169i \(0.0664248\pi\)
−0.852872 + 0.522120i \(0.825141\pi\)
\(398\) 0 0
\(399\) −34.9673 28.3525i −1.75055 1.41940i
\(400\) 0 0
\(401\) −30.0457 13.2865i −1.50041 0.663495i −0.518889 0.854842i \(-0.673654\pi\)
−0.981522 + 0.191347i \(0.938714\pi\)
\(402\) 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 0.947682 + 0.319217i \(0.103420\pi\)
0.153961 + 0.988077i \(0.450797\pi\)
\(410\) 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 −0.339948 0.940444i \(-0.610409\pi\)
0.594989 + 0.803734i \(0.297156\pi\)
\(420\) 0 0
\(421\) −17.7062 + 31.5817i −0.862949 + 1.53920i −0.0209090 + 0.999781i \(0.506656\pi\)
−0.842040 + 0.539416i \(0.818645\pi\)
\(422\) 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 0.0131784 0.999913i \(-0.495805\pi\)
0.450553 + 0.892750i \(0.351227\pi\)
\(432\) 0 0
\(433\) 7.08343 + 16.8747i 0.340408 + 0.810944i 0.998325 + 0.0578538i \(0.0184257\pi\)
−0.657917 + 0.753091i \(0.728562\pi\)
\(434\) 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 −0.601411 0.798940i \(-0.705394\pi\)
0.712499 + 0.701673i \(0.247563\pi\)
\(440\) 0 0
\(441\) 47.3746 32.8022i 2.25593 1.56201i
\(442\) 0 0
\(443\) 6.60000 4.20954i 0.313575 0.200001i −0.371575 0.928403i \(-0.621182\pi\)
0.685150 + 0.728402i \(0.259736\pi\)
\(444\) 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 −0.439157 0.898410i \(-0.644723\pi\)
0.906560 + 0.422077i \(0.138699\pi\)
\(450\) 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 −0.727330 0.686287i \(-0.759239\pi\)
0.914311 + 0.405014i \(0.132733\pi\)
\(458\) 0 0
\(459\) 2.41948 7.25896i 0.112932 0.338819i
\(460\) 0 0
\(461\) 0.207477 0.0236611i 0.00966318 0.00110201i −0.108475 0.994099i \(-0.534597\pi\)
0.118138 + 0.992997i \(0.462308\pi\)
\(462\) 0 0
\(463\) 37.4153 + 1.41686i 1.73884 + 0.0658473i 0.888073 0.459703i \(-0.152044\pi\)
0.850763 + 0.525550i \(0.176140\pi\)
\(464\) 0 0
\(465\) −0.599494 10.5476i −0.0278009 0.489134i
\(466\) 0 0
\(467\) −4.37084 + 7.14773i −0.202258 + 0.330757i −0.938081 0.346417i \(-0.887398\pi\)
0.735822 + 0.677175i \(0.236796\pi\)
\(468\) 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 −0.822818 0.568306i \(-0.807599\pi\)
−0.777481 + 0.628907i \(0.783503\pi\)
\(480\) 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 0.469049 0.883172i \(-0.344597\pi\)
0.109488 + 0.993988i \(0.465079\pi\)
\(488\) 0 0
\(489\) −54.8179 + 10.5001i −2.47895 + 0.474830i
\(490\) 0 0
\(491\) 0.549948 2.60345i 0.0248188 0.117492i −0.964235 0.265051i \(-0.914611\pi\)
0.989053 + 0.147559i \(0.0471415\pi\)
\(492\) 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 −0.782004 0.623274i \(-0.785802\pi\)
0.838569 + 0.544795i \(0.183393\pi\)
\(500\) 0 0
\(501\) 34.2919 4.59186i 1.53205 0.205149i
\(502\) 0 0
\(503\) 0.968050 1.34307i 0.0431632 0.0598844i −0.789102 0.614263i \(-0.789454\pi\)
0.832265 + 0.554378i \(0.187044\pi\)
\(504\) 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 0.732228 0.681060i \(-0.238481\pi\)
0.214304 + 0.976767i \(0.431252\pi\)
\(510\) 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 0.999933 0.0115838i \(-0.00368731\pi\)
−0.106011 + 0.994365i \(0.533808\pi\)
\(522\) 0 0
\(523\) 20.0969 0.761043i 0.878778 0.0332781i 0.405402 0.914139i \(-0.367132\pi\)
0.473376 + 0.880860i \(0.343035\pi\)
\(524\) 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 −0.161771 0.986828i \(-0.551721\pi\)
0.0645731 + 0.997913i \(0.479431\pi\)
\(542\) 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 −0.671589 0.740924i \(-0.734388\pi\)
0.941955 0.335738i \(-0.108986\pi\)
\(548\) 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 0.986410 0.164304i \(-0.0525377\pi\)
−0.995014 + 0.0997353i \(0.968200\pi\)
\(558\) 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 −0.990635 0.136537i \(-0.956403\pi\)
0.00448838 + 0.999990i \(0.498571\pi\)
\(564\) 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 0.819596 0.572942i \(-0.194198\pi\)
−0.982979 + 0.183720i \(0.941186\pi\)
\(570\) 0 0
\(571\) 12.6184 2.91599i 0.528066 0.122031i 0.0473018 0.998881i \(-0.484938\pi\)
0.480764 + 0.876850i \(0.340359\pi\)
\(572\) 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 −0.258207 0.966090i \(-0.583132\pi\)
0.999885 + 0.0151365i \(0.00481828\pi\)
\(578\) 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 0.991955 0.126591i \(-0.0404035\pi\)
0.374679 + 0.927155i \(0.377753\pi\)
\(588\) 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 0.384212 0.923245i \(-0.374473\pi\)
−0.975011 + 0.222157i \(0.928690\pi\)
\(594\) 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 −0.885907 0.463864i \(-0.846463\pi\)
0.561658 0.827370i \(-0.310164\pi\)
\(600\) 0 0
\(601\) −33.5540 14.8379i −1.36870 0.605249i −0.416054 0.909340i \(-0.636587\pi\)
−0.952643 + 0.304091i \(0.901647\pi\)
\(602\) 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 0.589964 0.807429i \(-0.299142\pi\)
−0.818449 + 0.574579i \(0.805166\pi\)
\(608\) 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 −0.172723 0.984970i \(-0.555257\pi\)
−0.915885 + 0.401441i \(0.868510\pi\)
\(614\) 0 0
\(615\) 3.74932 21.7991i 0.151187 0.879026i
\(616\) 0 0
\(617\) −2.70668 + 47.6218i −0.108967 + 1.91718i 0.224590 + 0.974453i \(0.427896\pi\)
−0.333557 + 0.942730i \(0.608249\pi\)
\(618\) 0 0
\(619\) −10.2087 + 12.1144i −0.410323 + 0.486921i −0.930061 0.367405i \(-0.880246\pi\)
0.519738 + 0.854326i \(0.326029\pi\)
\(620\) 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 −0.0381219 0.999273i \(-0.512138\pi\)
0.472192 + 0.881496i \(0.343463\pi\)
\(632\) 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 −0.889657 0.456630i \(-0.849056\pi\)
0.949029 + 0.315190i \(0.102068\pi\)
\(642\) 0 0
\(643\) −2.89854 + 3.18667i −0.114307 + 0.125670i −0.794239 0.607606i \(-0.792130\pi\)
0.679931 + 0.733276i \(0.262010\pi\)
\(644\) 0 0
\(645\) 13.6896 5.44409i 0.539028 0.214361i
\(646\) 0 0
\(647\) 25.5138 7.97079i 1.00305 0.313364i 0.247807 0.968809i \(-0.420290\pi\)
0.755243 + 0.655445i \(0.227519\pi\)
\(648\) 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 −0.997979 0.0635436i \(-0.979760\pi\)
0.807235 0.590230i \(-0.200963\pi\)
\(654\) 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 0.322432 0.946593i \(-0.395500\pi\)
−0.200247 + 0.979745i \(0.564174\pi\)
\(660\) 0 0
\(661\) −10.7185 23.0491i −0.416901 0.896508i −0.996656 0.0817162i \(-0.973960\pi\)
0.579754 0.814791i \(-0.303149\pi\)
\(662\) 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 −0.648801 0.760958i \(-0.724729\pi\)
0.126365 + 0.991984i \(0.459669\pi\)
\(674\) 0 0
\(675\) −4.04081 8.68940i −0.155531 0.334455i
\(676\) 0 0
\(677\) −2.23620 0.606754i −0.0859441 0.0233194i 0.218633 0.975807i \(-0.429840\pi\)
−0.304577 + 0.952488i \(0.598515\pi\)
\(678\) 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 −0.984955 0.172809i \(-0.944716\pi\)
0.737497 0.675350i \(-0.236007\pi\)
\(684\) 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 0.795366 0.606130i \(-0.207279\pi\)
0.994406 0.105627i \(-0.0336851\pi\)
\(692\) 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 0.123787 0.992309i \(-0.460496\pi\)
0.926092 + 0.377297i \(0.123147\pi\)
\(702\) 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 0.832058 0.554688i \(-0.187162\pi\)
0.0743274 + 0.997234i \(0.476319\pi\)
\(710\) 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 0.940421 + 0.340013i \(0.110432\pi\)
−0.972890 + 0.231267i \(0.925713\pi\)
\(720\) 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 −0.608425 0.793611i \(-0.708199\pi\)
−0.721161 + 0.692767i \(0.756391\pi\)
\(728\) 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 0.904180 0.427152i \(-0.140483\pi\)
−0.231056 + 0.972940i \(0.574218\pi\)
\(734\) 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 0.595506 0.803351i \(-0.296952\pi\)
0.399335 + 0.916805i \(0.369241\pi\)
\(740\) 0 0
\(741\) 24.6099 + 18.4558i 0.904068 + 0.677991i
\(742\) 0 0
\(743\) −34.0462 40.4018i −1.24903 1.48220i −0.812994 0.582272i \(-0.802164\pi\)
−0.436039 0.899928i \(-0.643619\pi\)
\(744\) 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 0.359617 0.933100i \(-0.382907\pi\)
−0.998936 + 0.0461119i \(0.985317\pi\)
\(752\) 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 −0.192326 0.981331i \(-0.561603\pi\)
0.689856 0.723947i \(-0.257674\pi\)
\(758\) 0 0
\(759\) −2.49840 + 3.20336i −0.0906863 + 0.116275i
\(760\) 0 0
\(761\) 2.30305 6.12639i 0.0834857 0.222082i −0.887692 0.460437i \(-0.847693\pi\)
0.971178 + 0.238355i \(0.0766083\pi\)
\(762\) 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 0.952524 + 0.304463i \(0.0984769\pi\)
−0.992794 + 0.119833i \(0.961764\pi\)
\(770\) 0 0
\(771\) 44.7883 + 31.0115i 1.61301 + 1.11685i
\(772\) 0 0
\(773\) 37.0460 32.4368i 1.33245 1.16667i 0.360164 0.932889i \(-0.382721\pi\)
0.972289 0.233783i \(-0.0751104\pi\)
\(774\) 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 −0.991806 0.127756i \(-0.959222\pi\)
0.408423 0.912793i \(-0.366079\pi\)
\(788\) 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