Properties

Label 276.2.i.a.121.2
Level $276$
Weight $2$
Character 276.121
Analytic conductor $2.204$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.20387109579\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + 15500 x^{12} - 28190 x^{11} + 41920 x^{10} - 33520 x^{9} - 13837 x^{8} + 78980 x^{7} - 92652 x^{6} - 52852 x^{5} + 177374 x^{4} + 151360 x^{3} + 115323 x^{2} + 12834 x + 529\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 121.2
Root \(-0.404188 + 2.81119i\) of defining polynomial
Character \(\chi\) \(=\) 276.121
Dual form 276.2.i.a.73.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.959493 - 0.281733i) q^{3} +(-0.332496 + 0.213682i) q^{5} +(-0.440112 + 3.06105i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\) \(q+(-0.959493 - 0.281733i) q^{3} +(-0.332496 + 0.213682i) q^{5} +(-0.440112 + 3.06105i) q^{7} +(0.841254 + 0.540641i) q^{9} +(1.09466 + 2.39697i) q^{11} +(0.315289 + 2.19288i) q^{13} +(0.379229 - 0.111352i) q^{15} +(2.42879 - 2.80297i) q^{17} +(4.61122 + 5.32163i) q^{19} +(1.28468 - 2.81306i) q^{21} +(-4.06629 + 2.54269i) q^{23} +(-2.01218 + 4.40606i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(4.37075 - 5.04411i) q^{29} +(-2.22075 + 0.652070i) q^{31} +(-0.375014 - 2.60828i) q^{33} +(-0.507756 - 1.11183i) q^{35} +(-4.80517 - 3.08810i) q^{37} +(0.315289 - 2.19288i) q^{39} +(-2.36514 + 1.51998i) q^{41} +(3.75382 + 1.10222i) q^{43} -0.395239 q^{45} -4.37944 q^{47} +(-2.45987 - 0.722282i) q^{49} +(-3.12009 + 2.00516i) q^{51} +(1.80647 - 12.5643i) q^{53} +(-0.876162 - 0.563075i) q^{55} +(-2.92516 - 6.40520i) q^{57} +(-1.40772 - 9.79088i) q^{59} +(6.36499 - 1.86893i) q^{61} +(-2.02517 + 2.33718i) q^{63} +(-0.573412 - 0.661753i) q^{65} +(0.559732 - 1.22564i) q^{67} +(4.61794 - 1.29408i) q^{69} +(-3.25308 + 7.12324i) q^{71} +(4.16279 + 4.80412i) q^{73} +(3.17201 - 3.66069i) q^{75} +(-7.81903 + 2.29587i) q^{77} +(-1.05877 - 7.36392i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-0.579976 - 0.372728i) q^{83} +(-0.208617 + 1.45097i) q^{85} +(-5.61479 + 3.60841i) q^{87} +(5.91112 + 1.73566i) q^{89} -6.85128 q^{91} +2.31450 q^{93} +(-2.67035 - 0.784086i) q^{95} +(-4.89824 + 3.14790i) q^{97} +(-0.375014 + 2.60828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10}) \) \( 20q - 2q^{3} - 4q^{5} - 2q^{9} - 22q^{13} + 7q^{15} + 7q^{17} + 19q^{19} + 20q^{23} + 20q^{25} - 2q^{27} + 32q^{29} - 3q^{31} + 11q^{33} - 26q^{35} - 10q^{37} - 22q^{39} - 40q^{41} + 8q^{43} - 4q^{45} - 18q^{47} - 34q^{49} - 26q^{51} - 34q^{53} - 17q^{55} - 3q^{57} - 32q^{59} + 32q^{61} + 49q^{65} + 35q^{67} - 2q^{69} + 33q^{71} - q^{73} - 2q^{75} - 50q^{77} + 22q^{79} - 2q^{81} - 14q^{83} - 9q^{85} - 12q^{87} + 10q^{89} - 72q^{91} + 30q^{93} - 51q^{95} - 4q^{97} + 11q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(139\) \(185\)
\(\chi(n)\) \(e\left(\frac{9}{11}\right)\) \(1\) \(1\)

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
\(3\) −0.959493 0.281733i −0.553964 0.162658i
\(4\) 0 0
\(5\) −0.332496 + 0.213682i −0.148697 + 0.0955616i −0.612874 0.790181i \(-0.709987\pi\)
0.464177 + 0.885743i \(0.346350\pi\)
\(6\) 0 0
\(7\) −0.440112 + 3.06105i −0.166347 + 1.15697i 0.720010 + 0.693964i \(0.244137\pi\)
−0.886356 + 0.463003i \(0.846772\pi\)
\(8\) 0 0
\(9\) 0.841254 + 0.540641i 0.280418 + 0.180214i
\(10\) 0 0
\(11\) 1.09466 + 2.39697i 0.330053 + 0.722715i 0.999803 0.0198719i \(-0.00632584\pi\)
−0.669750 + 0.742587i \(0.733599\pi\)
\(12\) 0 0
\(13\) 0.315289 + 2.19288i 0.0874454 + 0.608196i 0.985673 + 0.168666i \(0.0539459\pi\)
−0.898228 + 0.439530i \(0.855145\pi\)
\(14\) 0 0
\(15\) 0.379229 0.111352i 0.0979165 0.0287509i
\(16\) 0 0
\(17\) 2.42879 2.80297i 0.589068 0.679821i −0.380461 0.924797i \(-0.624235\pi\)
0.969529 + 0.244976i \(0.0787802\pi\)
\(18\) 0 0
\(19\) 4.61122 + 5.32163i 1.05789 + 1.22087i 0.974509 + 0.224348i \(0.0720253\pi\)
0.0833775 + 0.996518i \(0.473429\pi\)
\(20\) 0 0
\(21\) 1.28468 2.81306i 0.280341 0.613860i
\(22\) 0 0
\(23\) −4.06629 + 2.54269i −0.847881 + 0.530187i
\(24\) 0 0
\(25\) −2.01218 + 4.40606i −0.402436 + 0.881213i
\(26\) 0 0
\(27\) −0.654861 0.755750i −0.126028 0.145444i
\(28\) 0 0
\(29\) 4.37075 5.04411i 0.811627 0.936668i −0.187331 0.982297i \(-0.559984\pi\)
0.998958 + 0.0456288i \(0.0145291\pi\)
\(30\) 0 0
\(31\) −2.22075 + 0.652070i −0.398858 + 0.117115i −0.475009 0.879981i \(-0.657555\pi\)
0.0761510 + 0.997096i \(0.475737\pi\)
\(32\) 0 0
\(33\) −0.375014 2.60828i −0.0652816 0.454044i
\(34\) 0 0
\(35\) −0.507756 1.11183i −0.0858264 0.187934i
\(36\) 0 0
\(37\) −4.80517 3.08810i −0.789966 0.507680i 0.0823615 0.996603i \(-0.473754\pi\)
−0.872327 + 0.488922i \(0.837390\pi\)
\(38\) 0 0
\(39\) 0.315289 2.19288i 0.0504866 0.351142i
\(40\) 0 0
\(41\) −2.36514 + 1.51998i −0.369372 + 0.237381i −0.712138 0.702040i \(-0.752273\pi\)
0.342765 + 0.939421i \(0.388636\pi\)
\(42\) 0 0
\(43\) 3.75382 + 1.10222i 0.572451 + 0.168087i 0.555131 0.831763i \(-0.312668\pi\)
0.0173207 + 0.999850i \(0.494486\pi\)
\(44\) 0 0
\(45\) −0.395239 −0.0589187
\(46\) 0 0
\(47\) −4.37944 −0.638808 −0.319404 0.947619i \(-0.603483\pi\)
−0.319404 + 0.947619i \(0.603483\pi\)
\(48\) 0 0
\(49\) −2.45987 0.722282i −0.351410 0.103183i
\(50\) 0 0
\(51\) −3.12009 + 2.00516i −0.436901 + 0.280779i
\(52\) 0 0
\(53\) 1.80647 12.5643i 0.248138 1.72584i −0.360821 0.932635i \(-0.617504\pi\)
0.608959 0.793202i \(-0.291587\pi\)
\(54\) 0 0
\(55\) −0.876162 0.563075i −0.118142 0.0759250i
\(56\) 0 0
\(57\) −2.92516 6.40520i −0.387446 0.848389i
\(58\) 0 0
\(59\) −1.40772 9.79088i −0.183269 1.27466i −0.848968 0.528444i \(-0.822776\pi\)
0.665699 0.746220i \(-0.268133\pi\)
\(60\) 0 0
\(61\) 6.36499 1.86893i 0.814954 0.239292i 0.152412 0.988317i \(-0.451296\pi\)
0.662542 + 0.749025i \(0.269478\pi\)
\(62\) 0 0
\(63\) −2.02517 + 2.33718i −0.255148 + 0.294456i
\(64\) 0 0
\(65\) −0.573412 0.661753i −0.0711231 0.0820804i
\(66\) 0 0
\(67\) 0.559732 1.22564i 0.0683822 0.149736i −0.872355 0.488874i \(-0.837408\pi\)
0.940737 + 0.339138i \(0.110135\pi\)
\(68\) 0 0
\(69\) 4.61794 1.29408i 0.555934 0.155790i
\(70\) 0 0
\(71\) −3.25308 + 7.12324i −0.386069 + 0.845374i 0.612426 + 0.790528i \(0.290194\pi\)
−0.998495 + 0.0548454i \(0.982533\pi\)
\(72\) 0 0
\(73\) 4.16279 + 4.80412i 0.487218 + 0.562280i 0.945120 0.326723i \(-0.105944\pi\)
−0.457902 + 0.889003i \(0.651399\pi\)
\(74\) 0 0
\(75\) 3.17201 3.66069i 0.366272 0.422700i
\(76\) 0 0
\(77\) −7.81903 + 2.29587i −0.891061 + 0.261639i
\(78\) 0 0
\(79\) −1.05877 7.36392i −0.119121 0.828505i −0.958527 0.285001i \(-0.908006\pi\)
0.839406 0.543505i \(-0.182903\pi\)
\(80\) 0 0
\(81\) 0.415415 + 0.909632i 0.0461572 + 0.101070i
\(82\) 0 0
\(83\) −0.579976 0.372728i −0.0636606 0.0409122i 0.508423 0.861107i \(-0.330229\pi\)
−0.572084 + 0.820195i \(0.693865\pi\)
\(84\) 0 0
\(85\) −0.208617 + 1.45097i −0.0226277 + 0.157379i
\(86\) 0 0
\(87\) −5.61479 + 3.60841i −0.601969 + 0.386862i
\(88\) 0 0
\(89\) 5.91112 + 1.73566i 0.626578 + 0.183980i 0.579580 0.814915i \(-0.303217\pi\)
0.0469975 + 0.998895i \(0.485035\pi\)
\(90\) 0 0
\(91\) −6.85128 −0.718210
\(92\) 0 0
\(93\) 2.31450 0.240002
\(94\) 0 0
\(95\) −2.67035 0.784086i −0.273972 0.0804455i
\(96\) 0 0
\(97\) −4.89824 + 3.14790i −0.497340 + 0.319621i −0.765152 0.643850i \(-0.777336\pi\)
0.267811 + 0.963471i \(0.413700\pi\)
\(98\) 0 0
\(99\) −0.375014 + 2.60828i −0.0376904 + 0.262142i
\(100\) 0 0
\(101\) 7.86524 + 5.05468i 0.782620 + 0.502959i 0.869902 0.493224i \(-0.164182\pi\)
−0.0872820 + 0.996184i \(0.527818\pi\)
\(102\) 0 0
\(103\) 0.945200 + 2.06970i 0.0931334 + 0.203934i 0.950466 0.310830i \(-0.100607\pi\)
−0.857332 + 0.514764i \(0.827880\pi\)
\(104\) 0 0
\(105\) 0.173949 + 1.20985i 0.0169757 + 0.118069i
\(106\) 0 0
\(107\) 12.1337 3.56279i 1.17301 0.344428i 0.363536 0.931580i \(-0.381569\pi\)
0.809476 + 0.587153i \(0.199751\pi\)
\(108\) 0 0
\(109\) 0.145524 0.167943i 0.0139387 0.0160861i −0.748737 0.662867i \(-0.769340\pi\)
0.762676 + 0.646781i \(0.223885\pi\)
\(110\) 0 0
\(111\) 3.74051 + 4.31678i 0.355034 + 0.409731i
\(112\) 0 0
\(113\) 1.84385 4.03747i 0.173455 0.379813i −0.802860 0.596167i \(-0.796689\pi\)
0.976315 + 0.216355i \(0.0694167\pi\)
\(114\) 0 0
\(115\) 0.808699 1.71433i 0.0754116 0.159862i
\(116\) 0 0
\(117\) −0.920324 + 2.01523i −0.0850840 + 0.186308i
\(118\) 0 0
\(119\) 7.51109 + 8.66826i 0.688541 + 0.794618i
\(120\) 0 0
\(121\) 2.65626 3.06549i 0.241479 0.278681i
\(122\) 0 0
\(123\) 2.69756 0.792075i 0.243231 0.0714190i
\(124\) 0 0
\(125\) −0.553697 3.85105i −0.0495241 0.344448i
\(126\) 0 0
\(127\) −3.38374 7.40936i −0.300258 0.657474i 0.698023 0.716075i \(-0.254063\pi\)
−0.998281 + 0.0586010i \(0.981336\pi\)
\(128\) 0 0
\(129\) −3.29123 2.11514i −0.289776 0.186228i
\(130\) 0 0
\(131\) −2.51207 + 17.4719i −0.219481 + 1.52652i 0.520480 + 0.853874i \(0.325753\pi\)
−0.739961 + 0.672650i \(0.765156\pi\)
\(132\) 0 0
\(133\) −18.3192 + 11.7731i −1.58848 + 1.02085i
\(134\) 0 0
\(135\) 0.379229 + 0.111352i 0.0326388 + 0.00958362i
\(136\) 0 0
\(137\) −13.3712 −1.14238 −0.571191 0.820817i \(-0.693518\pi\)
−0.571191 + 0.820817i \(0.693518\pi\)
\(138\) 0 0
\(139\) 23.4118 1.98576 0.992881 0.119108i \(-0.0380034\pi\)
0.992881 + 0.119108i \(0.0380034\pi\)
\(140\) 0 0
\(141\) 4.20205 + 1.23383i 0.353876 + 0.103907i
\(142\) 0 0
\(143\) −4.91115 + 3.15620i −0.410691 + 0.263935i
\(144\) 0 0
\(145\) −0.375419 + 2.61110i −0.0311769 + 0.216840i
\(146\) 0 0
\(147\) 2.15673 + 1.38605i 0.177884 + 0.114319i
\(148\) 0 0
\(149\) 9.60048 + 21.0221i 0.786502 + 1.72220i 0.686404 + 0.727221i \(0.259188\pi\)
0.100098 + 0.994978i \(0.468084\pi\)
\(150\) 0 0
\(151\) −2.80811 19.5308i −0.228520 1.58939i −0.704348 0.709855i \(-0.748760\pi\)
0.475827 0.879539i \(-0.342149\pi\)
\(152\) 0 0
\(153\) 3.55863 1.04491i 0.287698 0.0844758i
\(154\) 0 0
\(155\) 0.599053 0.691345i 0.0481171 0.0555301i
\(156\) 0 0
\(157\) 3.08803 + 3.56377i 0.246451 + 0.284420i 0.865475 0.500953i \(-0.167017\pi\)
−0.619023 + 0.785372i \(0.712471\pi\)
\(158\) 0 0
\(159\) −5.27306 + 11.5464i −0.418181 + 0.915689i
\(160\) 0 0
\(161\) −5.99367 13.5662i −0.472367 1.06917i
\(162\) 0 0
\(163\) 3.18435 6.97275i 0.249417 0.546148i −0.742967 0.669328i \(-0.766582\pi\)
0.992384 + 0.123180i \(0.0393093\pi\)
\(164\) 0 0
\(165\) 0.682034 + 0.787110i 0.0530963 + 0.0612764i
\(166\) 0 0
\(167\) −13.4153 + 15.4821i −1.03811 + 1.19804i −0.0582568 + 0.998302i \(0.518554\pi\)
−0.979850 + 0.199737i \(0.935991\pi\)
\(168\) 0 0
\(169\) 7.76408 2.27974i 0.597237 0.175365i
\(170\) 0 0
\(171\) 1.00211 + 6.96986i 0.0766336 + 0.532998i
\(172\) 0 0
\(173\) 6.46235 + 14.1506i 0.491323 + 1.07585i 0.979193 + 0.202931i \(0.0650468\pi\)
−0.487870 + 0.872916i \(0.662226\pi\)
\(174\) 0 0
\(175\) −12.6016 8.09855i −0.952590 0.612193i
\(176\) 0 0
\(177\) −1.40772 + 9.79088i −0.105810 + 0.735927i
\(178\) 0 0
\(179\) 12.2018 7.84161i 0.912004 0.586110i 0.00167699 0.999999i \(-0.499466\pi\)
0.910327 + 0.413889i \(0.135830\pi\)
\(180\) 0 0
\(181\) −4.91748 1.44390i −0.365513 0.107324i 0.0938180 0.995589i \(-0.470093\pi\)
−0.459331 + 0.888265i \(0.651911\pi\)
\(182\) 0 0
\(183\) −6.63370 −0.490378
\(184\) 0 0
\(185\) 2.25757 0.165980
\(186\) 0 0
\(187\) 9.37736 + 2.75344i 0.685740 + 0.201352i
\(188\) 0 0
\(189\) 2.60160 1.67195i 0.189238 0.121616i
\(190\) 0 0
\(191\) 1.24708 8.67363i 0.0902355 0.627602i −0.893645 0.448775i \(-0.851861\pi\)
0.983881 0.178827i \(-0.0572303\pi\)
\(192\) 0 0
\(193\) 6.40555 + 4.11659i 0.461081 + 0.296319i 0.750484 0.660888i \(-0.229820\pi\)
−0.289403 + 0.957207i \(0.593457\pi\)
\(194\) 0 0
\(195\) 0.363748 + 0.796496i 0.0260485 + 0.0570383i
\(196\) 0 0
\(197\) −3.03344 21.0981i −0.216124 1.50318i −0.752160 0.658980i \(-0.770988\pi\)
0.536036 0.844195i \(-0.319921\pi\)
\(198\) 0 0
\(199\) 24.3686 7.15526i 1.72744 0.507223i 0.741025 0.671478i \(-0.234340\pi\)
0.986418 + 0.164255i \(0.0525220\pi\)
\(200\) 0 0
\(201\) −0.882362 + 1.01830i −0.0622370 + 0.0718254i
\(202\) 0 0
\(203\) 13.5167 + 15.5990i 0.948683 + 1.09484i
\(204\) 0 0
\(205\) 0.461605 1.01077i 0.0322399 0.0705956i
\(206\) 0 0
\(207\) −4.79546 0.0593580i −0.333308 0.00412567i
\(208\) 0 0
\(209\) −7.70809 + 16.8784i −0.533180 + 1.16750i
\(210\) 0 0
\(211\) −12.8102 14.7838i −0.881891 1.01776i −0.999694 0.0247197i \(-0.992131\pi\)
0.117803 0.993037i \(-0.462415\pi\)
\(212\) 0 0
\(213\) 5.12815 5.91821i 0.351375 0.405509i
\(214\) 0 0
\(215\) −1.48365 + 0.435640i −0.101184 + 0.0297104i
\(216\) 0 0
\(217\) −1.01864 7.08479i −0.0691498 0.480947i
\(218\) 0 0
\(219\) −2.64069 5.78231i −0.178442 0.390733i
\(220\) 0 0
\(221\) 6.91236 + 4.44230i 0.464976 + 0.298822i
\(222\) 0 0
\(223\) −1.00285 + 6.97494i −0.0671555 + 0.467077i 0.928299 + 0.371835i \(0.121271\pi\)
−0.995454 + 0.0952414i \(0.969638\pi\)
\(224\) 0 0
\(225\) −4.07485 + 2.61875i −0.271657 + 0.174583i
\(226\) 0 0
\(227\) −22.6593 6.65336i −1.50395 0.441599i −0.576986 0.816754i \(-0.695771\pi\)
−0.926962 + 0.375156i \(0.877589\pi\)
\(228\) 0 0
\(229\) −24.5083 −1.61956 −0.809778 0.586736i \(-0.800412\pi\)
−0.809778 + 0.586736i \(0.800412\pi\)
\(230\) 0 0
\(231\) 8.14913 0.536173
\(232\) 0 0
\(233\) 0.683723 + 0.200759i 0.0447922 + 0.0131522i 0.304052 0.952655i \(-0.401660\pi\)
−0.259260 + 0.965808i \(0.583479\pi\)
\(234\) 0 0
\(235\) 1.45615 0.935810i 0.0949886 0.0610455i
\(236\) 0 0
\(237\) −1.05877 + 7.36392i −0.0687746 + 0.478338i
\(238\) 0 0
\(239\) −1.28510 0.825882i −0.0831261 0.0534219i 0.498418 0.866937i \(-0.333915\pi\)
−0.581544 + 0.813515i \(0.697551\pi\)
\(240\) 0 0
\(241\) −11.3499 24.8528i −0.731111 1.60091i −0.797647 0.603125i \(-0.793922\pi\)
0.0665361 0.997784i \(-0.478805\pi\)
\(242\) 0 0
\(243\) −0.142315 0.989821i −0.00912950 0.0634971i
\(244\) 0 0
\(245\) 0.972235 0.285474i 0.0621138 0.0182383i
\(246\) 0 0
\(247\) −10.2158 + 11.7897i −0.650019 + 0.750162i
\(248\) 0 0
\(249\) 0.451473 + 0.521028i 0.0286109 + 0.0330188i
\(250\) 0 0
\(251\) 9.87995 21.6341i 0.623617 1.36553i −0.289243 0.957256i \(-0.593403\pi\)
0.912859 0.408274i \(-0.133869\pi\)
\(252\) 0 0
\(253\) −10.5460 6.96342i −0.663020 0.437786i
\(254\) 0 0
\(255\) 0.608951 1.33342i 0.0381340 0.0835019i
\(256\) 0 0
\(257\) 10.4861 + 12.1017i 0.654108 + 0.754880i 0.981803 0.189903i \(-0.0608174\pi\)
−0.327695 + 0.944783i \(0.606272\pi\)
\(258\) 0 0
\(259\) 11.5676 13.3498i 0.718778 0.829514i
\(260\) 0 0
\(261\) 6.40396 1.88037i 0.396395 0.116392i
\(262\) 0 0
\(263\) −3.96549 27.5806i −0.244522 1.70069i −0.628877 0.777505i \(-0.716485\pi\)
0.384354 0.923186i \(-0.374424\pi\)
\(264\) 0 0
\(265\) 2.08412 + 4.56358i 0.128026 + 0.280339i
\(266\) 0 0
\(267\) −5.18269 3.33071i −0.317175 0.203836i
\(268\) 0 0
\(269\) 0.678639 4.72004i 0.0413774 0.287786i −0.958618 0.284696i \(-0.908107\pi\)
0.999995 0.00308994i \(-0.000983561\pi\)
\(270\) 0 0
\(271\) −10.5864 + 6.80348i −0.643080 + 0.413282i −0.821132 0.570739i \(-0.806657\pi\)
0.178052 + 0.984021i \(0.443020\pi\)
\(272\) 0 0
\(273\) 6.57376 + 1.93023i 0.397862 + 0.116823i
\(274\) 0 0
\(275\) −12.7639 −0.769691
\(276\) 0 0
\(277\) −19.2855 −1.15875 −0.579376 0.815060i \(-0.696704\pi\)
−0.579376 + 0.815060i \(0.696704\pi\)
\(278\) 0 0
\(279\) −2.22075 0.652070i −0.132953 0.0390384i
\(280\) 0 0
\(281\) 2.56835 1.65058i 0.153215 0.0984653i −0.461787 0.886991i \(-0.652792\pi\)
0.615002 + 0.788526i \(0.289155\pi\)
\(282\) 0 0
\(283\) 4.33156 30.1266i 0.257484 1.79084i −0.293119 0.956076i \(-0.594693\pi\)
0.550603 0.834767i \(-0.314398\pi\)
\(284\) 0 0
\(285\) 2.34128 + 1.50465i 0.138685 + 0.0891277i
\(286\) 0 0
\(287\) −3.61181 7.90876i −0.213198 0.466839i
\(288\) 0 0
\(289\) 0.461716 + 3.21131i 0.0271598 + 0.188900i
\(290\) 0 0
\(291\) 5.58669 1.64040i 0.327498 0.0961620i
\(292\) 0 0
\(293\) 5.30169 6.11848i 0.309728 0.357445i −0.579449 0.815009i \(-0.696732\pi\)
0.889177 + 0.457563i \(0.151278\pi\)
\(294\) 0 0
\(295\) 2.56020 + 2.95462i 0.149060 + 0.172025i
\(296\) 0 0
\(297\) 1.09466 2.39697i 0.0635187 0.139087i
\(298\) 0 0
\(299\) −6.85787 8.11522i −0.396601 0.469315i
\(300\) 0 0
\(301\) −5.02605 + 11.0055i −0.289697 + 0.634347i
\(302\) 0 0
\(303\) −6.12257 7.06582i −0.351732 0.405921i
\(304\) 0 0
\(305\) −1.71698 + 1.98150i −0.0983139 + 0.113460i
\(306\) 0 0
\(307\) 7.75969 2.27845i 0.442869 0.130038i −0.0526927 0.998611i \(-0.516780\pi\)
0.495562 + 0.868573i \(0.334962\pi\)
\(308\) 0 0
\(309\) −0.323811 2.25216i −0.0184210 0.128121i
\(310\) 0 0
\(311\) −0.338709 0.741670i −0.0192064 0.0420562i 0.899786 0.436332i \(-0.143723\pi\)
−0.918992 + 0.394276i \(0.870995\pi\)
\(312\) 0 0
\(313\) 24.3434 + 15.6445i 1.37597 + 0.884281i 0.999118 0.0419935i \(-0.0133709\pi\)
0.376850 + 0.926274i \(0.377007\pi\)
\(314\) 0 0
\(315\) 0.173949 1.20985i 0.00980094 0.0681671i
\(316\) 0 0
\(317\) −29.1679 + 18.7451i −1.63823 + 1.05283i −0.695903 + 0.718135i \(0.744996\pi\)
−0.942328 + 0.334692i \(0.891368\pi\)
\(318\) 0 0
\(319\) 16.8751 + 4.95498i 0.944824 + 0.277425i
\(320\) 0 0
\(321\) −12.6460 −0.705830
\(322\) 0 0
\(323\) 26.1161 1.45314
\(324\) 0 0
\(325\) −10.2964 3.02330i −0.571141 0.167702i
\(326\) 0 0
\(327\) −0.186944 + 0.120142i −0.0103380 + 0.00664386i
\(328\) 0 0
\(329\) 1.92745 13.4057i 0.106264 0.739080i
\(330\) 0 0
\(331\) 11.7815 + 7.57152i 0.647570 + 0.416168i 0.822778 0.568363i \(-0.192423\pi\)
−0.175207 + 0.984532i \(0.556060\pi\)
\(332\) 0 0
\(333\) −2.37282 5.19575i −0.130030 0.284725i
\(334\) 0 0
\(335\) 0.0757893 + 0.527126i 0.00414081 + 0.0288000i
\(336\) 0 0
\(337\) 11.2111 3.29189i 0.610710 0.179321i 0.0382703 0.999267i \(-0.487815\pi\)
0.572440 + 0.819947i \(0.305997\pi\)
\(338\) 0 0
\(339\) −2.90665 + 3.35445i −0.157867 + 0.182189i
\(340\) 0 0
\(341\) −3.99396 4.60928i −0.216285 0.249606i
\(342\) 0 0
\(343\) −5.69921 + 12.4795i −0.307729 + 0.673832i
\(344\) 0 0
\(345\) −1.25892 + 1.41705i −0.0677781 + 0.0762914i
\(346\) 0 0
\(347\) −12.7515 + 27.9220i −0.684538 + 1.49893i 0.173223 + 0.984883i \(0.444582\pi\)
−0.857762 + 0.514048i \(0.828145\pi\)
\(348\) 0 0
\(349\) 18.4824 + 21.3299i 0.989342 + 1.14176i 0.989901 + 0.141762i \(0.0452768\pi\)
−0.000558286 1.00000i \(0.500178\pi\)
\(350\) 0 0
\(351\) 1.45080 1.67431i 0.0774380 0.0893682i
\(352\) 0 0
\(353\) −15.1718 + 4.45484i −0.807514 + 0.237107i −0.659331 0.751853i \(-0.729161\pi\)
−0.148183 + 0.988960i \(0.547342\pi\)
\(354\) 0 0
\(355\) −0.440476 3.06358i −0.0233780 0.162598i
\(356\) 0 0
\(357\) −4.76471 10.4333i −0.252175 0.552187i
\(358\) 0 0
\(359\) 0.567977 + 0.365017i 0.0299767 + 0.0192648i 0.555543 0.831488i \(-0.312510\pi\)
−0.525567 + 0.850752i \(0.676147\pi\)
\(360\) 0 0
\(361\) −4.35243 + 30.2718i −0.229075 + 1.59325i
\(362\) 0 0
\(363\) −3.41232 + 2.19296i −0.179100 + 0.115101i
\(364\) 0 0
\(365\) −2.41067 0.707836i −0.126180 0.0370498i
\(366\) 0 0
\(367\) −14.9235 −0.778998 −0.389499 0.921027i \(-0.627352\pi\)
−0.389499 + 0.921027i \(0.627352\pi\)
\(368\) 0 0
\(369\) −2.81144 −0.146358
\(370\) 0 0
\(371\) 37.6648 + 11.0594i 1.95546 + 0.574175i
\(372\) 0 0
\(373\) 5.57634 3.58369i 0.288732 0.185557i −0.388255 0.921552i \(-0.626922\pi\)
0.676986 + 0.735995i \(0.263286\pi\)
\(374\) 0 0
\(375\) −0.553697 + 3.85105i −0.0285928 + 0.198867i
\(376\) 0 0
\(377\) 12.4392 + 7.99418i 0.640651 + 0.411721i
\(378\) 0 0
\(379\) 1.67512 + 3.66799i 0.0860449 + 0.188412i 0.947763 0.318975i \(-0.103339\pi\)
−0.861718 + 0.507387i \(0.830611\pi\)
\(380\) 0 0
\(381\) 1.15922 + 8.06254i 0.0593885 + 0.413056i
\(382\) 0 0
\(383\) −8.86688 + 2.60355i −0.453076 + 0.133035i −0.500306 0.865849i \(-0.666779\pi\)
0.0472294 + 0.998884i \(0.484961\pi\)
\(384\) 0 0
\(385\) 2.10921 2.43416i 0.107495 0.124056i
\(386\) 0 0
\(387\) 2.56201 + 2.95671i 0.130234 + 0.150298i
\(388\) 0 0
\(389\) 6.71406 14.7017i 0.340416 0.745407i −0.659564 0.751648i \(-0.729259\pi\)
0.999981 + 0.00624068i \(0.00198648\pi\)
\(390\) 0 0
\(391\) −2.74908 + 17.5734i −0.139027 + 0.888723i
\(392\) 0 0
\(393\) 7.33271 16.0564i 0.369886 0.809938i
\(394\) 0 0
\(395\) 1.92558 + 2.22223i 0.0968862 + 0.111813i
\(396\) 0 0
\(397\) 0.206863 0.238733i 0.0103822 0.0119817i −0.750535 0.660831i \(-0.770204\pi\)
0.760917 + 0.648849i \(0.224749\pi\)
\(398\) 0 0
\(399\) 20.8940 6.13504i 1.04601 0.307136i
\(400\) 0 0
\(401\) 0.204711 + 1.42380i 0.0102228 + 0.0711011i 0.994294 0.106672i \(-0.0340196\pi\)
−0.984071 + 0.177774i \(0.943111\pi\)
\(402\) 0 0
\(403\) −2.13009 4.66424i −0.106107 0.232343i
\(404\) 0 0
\(405\) −0.332496 0.213682i −0.0165219 0.0106180i
\(406\) 0 0
\(407\) 2.14205 14.8983i 0.106178 0.738482i
\(408\) 0 0
\(409\) −1.86910 + 1.20120i −0.0924211 + 0.0593954i −0.586035 0.810286i \(-0.699312\pi\)
0.493614 + 0.869681i \(0.335676\pi\)
\(410\) 0 0
\(411\) 12.8296 + 3.76711i 0.632838 + 0.185818i
\(412\) 0 0
\(413\) 30.5899 1.50523
\(414\) 0 0
\(415\) 0.272485 0.0133758
\(416\) 0 0
\(417\) −22.4635 6.59587i −1.10004 0.323001i
\(418\) 0 0
\(419\) −8.96288 + 5.76010i −0.437866 + 0.281399i −0.740944 0.671566i \(-0.765622\pi\)
0.303079 + 0.952965i \(0.401985\pi\)
\(420\) 0 0
\(421\) −2.54761 + 17.7190i −0.124163 + 0.863572i 0.828596 + 0.559846i \(0.189140\pi\)
−0.952759 + 0.303726i \(0.901769\pi\)
\(422\) 0 0
\(423\) −3.68422 2.36771i −0.179133 0.115122i
\(424\) 0 0
\(425\) 7.46291 + 16.3415i 0.362004 + 0.792679i
\(426\) 0 0
\(427\) 2.91957 + 20.3061i 0.141288 + 0.982681i
\(428\) 0 0
\(429\) 5.60142 1.64473i 0.270439 0.0794081i
\(430\) 0 0
\(431\) −1.11016 + 1.28119i −0.0534744 + 0.0617128i −0.781857 0.623458i \(-0.785727\pi\)
0.728382 + 0.685171i \(0.240273\pi\)
\(432\) 0 0
\(433\) 20.1428 + 23.2460i 0.968001 + 1.11713i 0.993079 + 0.117447i \(0.0374709\pi\)
−0.0250786 + 0.999685i \(0.507984\pi\)
\(434\) 0 0
\(435\) 1.09584 2.39956i 0.0525417 0.115050i
\(436\) 0 0
\(437\) −32.2818 9.91442i −1.54425 0.474271i
\(438\) 0 0
\(439\) −11.6426 + 25.4938i −0.555672 + 1.21675i 0.398411 + 0.917207i \(0.369562\pi\)
−0.954082 + 0.299544i \(0.903165\pi\)
\(440\) 0 0
\(441\) −1.67888 1.93753i −0.0799465 0.0922632i
\(442\) 0 0
\(443\) −5.96931 + 6.88895i −0.283611 + 0.327304i −0.879623 0.475671i \(-0.842205\pi\)
0.596013 + 0.802975i \(0.296751\pi\)
\(444\) 0 0
\(445\) −2.33630 + 0.686001i −0.110751 + 0.0325196i
\(446\) 0 0
\(447\) −3.28898 22.8753i −0.155563 1.08197i
\(448\) 0 0
\(449\) −16.2833 35.6554i −0.768456 1.68268i −0.730024 0.683422i \(-0.760491\pi\)
−0.0384319 0.999261i \(-0.512236\pi\)
\(450\) 0 0
\(451\) −6.23238 4.00531i −0.293471 0.188602i
\(452\) 0 0
\(453\) −2.80811 + 19.5308i −0.131936 + 0.917637i
\(454\) 0 0
\(455\) 2.27802 1.46400i 0.106795 0.0686333i
\(456\) 0 0
\(457\) 29.8827 + 8.77435i 1.39785 + 0.410447i 0.891946 0.452141i \(-0.149340\pi\)
0.505907 + 0.862588i \(0.331158\pi\)
\(458\) 0 0
\(459\) −3.70886 −0.173115
\(460\) 0 0
\(461\) 19.9022 0.926939 0.463469 0.886113i \(-0.346604\pi\)
0.463469 + 0.886113i \(0.346604\pi\)
\(462\) 0 0
\(463\) 2.03576 + 0.597752i 0.0946097 + 0.0277799i 0.328695 0.944436i \(-0.393391\pi\)
−0.234085 + 0.972216i \(0.575209\pi\)
\(464\) 0 0
\(465\) −0.769562 + 0.494567i −0.0356876 + 0.0229350i
\(466\) 0 0
\(467\) 4.25711 29.6089i 0.196996 1.37013i −0.615946 0.787789i \(-0.711226\pi\)
0.812941 0.582346i \(-0.197865\pi\)
\(468\) 0 0
\(469\) 3.50541 + 2.25279i 0.161865 + 0.104024i
\(470\) 0 0
\(471\) −1.95891 4.28941i −0.0902617 0.197646i
\(472\) 0 0
\(473\) 1.46717 + 10.2044i 0.0674603 + 0.469197i
\(474\) 0 0
\(475\) −32.7261 + 9.60924i −1.50157 + 0.440902i
\(476\) 0 0
\(477\) 8.31246 9.59309i 0.380601 0.439238i
\(478\) 0 0
\(479\) 20.4583 + 23.6101i 0.934764 + 1.07877i 0.996739 + 0.0806972i \(0.0257147\pi\)
−0.0619749 + 0.998078i \(0.519740\pi\)
\(480\) 0 0
\(481\) 5.25682 11.5108i 0.239690 0.524848i
\(482\) 0 0
\(483\) 1.92885 + 14.7053i 0.0877655 + 0.669113i
\(484\) 0 0
\(485\) 0.955993 2.09333i 0.0434094 0.0950533i
\(486\) 0 0
\(487\) 1.50158 + 1.73291i 0.0680429 + 0.0785257i 0.788750 0.614714i \(-0.210728\pi\)
−0.720708 + 0.693239i \(0.756183\pi\)
\(488\) 0 0
\(489\) −5.01981 + 5.79317i −0.227004 + 0.261976i
\(490\) 0 0
\(491\) −30.7180 + 9.01961i −1.38628 + 0.407049i −0.887951 0.459938i \(-0.847872\pi\)
−0.498331 + 0.866987i \(0.666053\pi\)
\(492\) 0 0
\(493\) −3.52288 24.5022i −0.158663 1.10352i
\(494\) 0 0
\(495\) −0.432653 0.947378i −0.0194463 0.0425815i
\(496\) 0 0
\(497\) −20.3729 13.0929i −0.913848 0.587295i
\(498\) 0 0
\(499\) −4.53308 + 31.5283i −0.202929 + 1.41140i 0.592607 + 0.805492i \(0.298099\pi\)
−0.795535 + 0.605907i \(0.792810\pi\)
\(500\) 0 0
\(501\) 17.2337 11.0754i 0.769944 0.494813i
\(502\) 0 0
\(503\) −21.5336 6.32282i −0.960134 0.281921i −0.236134 0.971721i \(-0.575880\pi\)
−0.724000 + 0.689800i \(0.757699\pi\)
\(504\) 0 0
\(505\) −3.69526 −0.164437
\(506\) 0 0
\(507\) −8.09186 −0.359372
\(508\) 0 0
\(509\) 16.2921 + 4.78378i 0.722133 + 0.212037i 0.622090 0.782946i \(-0.286284\pi\)
0.100043 + 0.994983i \(0.468102\pi\)
\(510\) 0 0
\(511\) −16.5377 + 10.6282i −0.731586 + 0.470162i
\(512\) 0 0
\(513\) 1.00211 6.96986i 0.0442444 0.307727i
\(514\) 0 0
\(515\) −0.756534 0.486195i −0.0333369 0.0214243i
\(516\) 0 0
\(517\) −4.79401 10.4974i −0.210840 0.461676i
\(518\) 0 0
\(519\) −2.21390 15.3980i −0.0971795 0.675898i
\(520\) 0 0
\(521\) 12.8096 3.76125i 0.561200 0.164783i 0.0111844 0.999937i \(-0.496440\pi\)
0.550016 + 0.835154i \(0.314622\pi\)
\(522\) 0 0
\(523\) −4.27548 + 4.93417i −0.186954 + 0.215756i −0.841487 0.540277i \(-0.818320\pi\)
0.654534 + 0.756033i \(0.272865\pi\)
\(524\) 0 0
\(525\) 9.80951 + 11.3208i 0.428122 + 0.494079i
\(526\) 0 0
\(527\) −3.56599 + 7.80843i −0.155337 + 0.340140i
\(528\) 0 0
\(529\) 10.0695 20.6786i 0.437803 0.899071i
\(530\) 0 0
\(531\) 4.10910 8.99768i 0.178320 0.390466i
\(532\) 0 0
\(533\) −4.07884 4.70723i −0.176674 0.203893i
\(534\) 0 0
\(535\) −3.27311 + 3.77738i −0.141509 + 0.163310i
\(536\) 0 0
\(537\) −13.9168 + 4.08633i −0.600553 + 0.176338i
\(538\) 0 0
\(539\) −0.961430 6.68689i −0.0414117 0.288025i
\(540\) 0 0
\(541\) −9.25561 20.2670i −0.397930 0.871345i −0.997476 0.0710046i \(-0.977379\pi\)
0.599546 0.800340i \(-0.295348\pi\)
\(542\) 0 0
\(543\) 4.31149 + 2.77083i 0.185024 + 0.118908i
\(544\) 0 0
\(545\) −0.0124996 + 0.0869364i −0.000535423 + 0.00372395i
\(546\) 0 0
\(547\) 3.96660 2.54918i 0.169600 0.108995i −0.453087 0.891466i \(-0.649677\pi\)
0.622687 + 0.782471i \(0.286041\pi\)
\(548\) 0 0
\(549\) 6.36499 + 1.86893i 0.271651 + 0.0797640i
\(550\) 0 0
\(551\) 46.9974 2.00216
\(552\) 0 0
\(553\) 23.0073 0.978369
\(554\) 0 0
\(555\) −2.16613 0.636032i −0.0919469 0.0269980i
\(556\) 0 0
\(557\) 13.4469 8.64180i 0.569764 0.366165i −0.223816 0.974631i \(-0.571851\pi\)
0.793580 + 0.608467i \(0.208215\pi\)
\(558\) 0 0
\(559\) −1.23350 + 8.57919i −0.0521716 + 0.362861i
\(560\) 0 0
\(561\) −8.22177 5.28381i −0.347124 0.223083i
\(562\) 0 0
\(563\) −2.59556 5.68349i −0.109390 0.239531i 0.847018 0.531564i \(-0.178395\pi\)
−0.956408 + 0.292033i \(0.905668\pi\)
\(564\) 0 0
\(565\) 0.249662 + 1.73644i 0.0105034 + 0.0730526i
\(566\) 0 0
\(567\) −2.96726 + 0.871265i −0.124613 + 0.0365897i
\(568\) 0 0
\(569\) 8.55803 9.87649i 0.358771 0.414044i −0.547456 0.836834i \(-0.684404\pi\)
0.906228 + 0.422790i \(0.138949\pi\)
\(570\) 0 0
\(571\) 4.06617 + 4.69261i 0.170164 + 0.196380i 0.834426 0.551120i \(-0.185799\pi\)
−0.664262 + 0.747500i \(0.731254\pi\)
\(572\) 0 0
\(573\) −3.64021 + 7.97094i −0.152072 + 0.332991i
\(574\) 0 0
\(575\) −3.02113 23.0327i −0.125990 0.960530i
\(576\) 0 0
\(577\) 18.8091 41.1861i 0.783031 1.71460i 0.0874304 0.996171i \(-0.472134\pi\)
0.695601 0.718429i \(-0.255138\pi\)
\(578\) 0 0
\(579\) −4.98630 5.75449i −0.207223 0.239149i
\(580\) 0 0
\(581\) 1.39619 1.61129i 0.0579238 0.0668477i
\(582\) 0 0
\(583\) 32.0937 9.42357i 1.32919 0.390284i
\(584\) 0 0
\(585\) −0.124614 0.866712i −0.00515217 0.0358341i
\(586\) 0 0
\(587\) 6.87091 + 15.0452i 0.283593 + 0.620982i 0.996797 0.0799747i \(-0.0254840\pi\)
−0.713204 + 0.700957i \(0.752757\pi\)
\(588\) 0 0
\(589\) −13.7104 8.81115i −0.564928 0.363057i
\(590\) 0 0
\(591\) −3.03344 + 21.0981i −0.124779 + 0.867859i
\(592\) 0 0
\(593\) −28.4481 + 18.2825i −1.16822 + 0.750772i −0.973185 0.230023i \(-0.926120\pi\)
−0.195039 + 0.980795i \(0.562483\pi\)
\(594\) 0 0
\(595\) −4.34966 1.27718i −0.178319 0.0523591i
\(596\) 0 0
\(597\) −25.3973 −1.03944
\(598\) 0 0
\(599\) −28.1009 −1.14817 −0.574085 0.818796i \(-0.694642\pi\)
−0.574085 + 0.818796i \(0.694642\pi\)
\(600\) 0 0
\(601\) −24.6957 7.25132i −1.00736 0.295788i −0.263887 0.964554i \(-0.585005\pi\)
−0.743473 + 0.668766i \(0.766823\pi\)
\(602\) 0 0
\(603\) 1.13351 0.728462i 0.0461600 0.0296653i
\(604\) 0 0
\(605\) −0.228156 + 1.58686i −0.00927586 + 0.0645151i
\(606\) 0 0
\(607\) 7.02454 + 4.51439i 0.285117 + 0.183234i 0.675380 0.737470i \(-0.263980\pi\)
−0.390263 + 0.920703i \(0.627616\pi\)
\(608\) 0 0
\(609\) −8.57437 18.7753i −0.347451 0.760812i
\(610\) 0 0
\(611\) −1.38079 9.60361i −0.0558608 0.388520i
\(612\) 0 0
\(613\) −2.17393 + 0.638325i −0.0878044 + 0.0257817i −0.325340 0.945597i \(-0.605479\pi\)
0.237535 + 0.971379i \(0.423660\pi\)
\(614\) 0 0
\(615\) −0.727675 + 0.839782i −0.0293427 + 0.0338633i
\(616\) 0 0
\(617\) −27.7560 32.0322i −1.11742 1.28957i −0.952931 0.303186i \(-0.901950\pi\)
−0.164484 0.986380i \(-0.552596\pi\)
\(618\) 0 0
\(619\) −1.39428 + 3.05306i −0.0560410 + 0.122713i −0.935581 0.353113i \(-0.885123\pi\)
0.879540 + 0.475825i \(0.157851\pi\)
\(620\) 0 0
\(621\) 4.58449 + 1.40799i 0.183969 + 0.0565008i
\(622\) 0 0
\(623\) −7.91450 + 17.3303i −0.317088 + 0.694326i
\(624\) 0 0
\(625\) −14.8530 17.1413i −0.594121 0.685652i
\(626\) 0 0
\(627\) 12.1510 14.0231i 0.485266 0.560027i
\(628\) 0 0
\(629\) −20.3266 + 5.96843i −0.810475 + 0.237977i
\(630\) 0 0
\(631\) −0.265066 1.84358i −0.0105521 0.0733916i 0.983865 0.178913i \(-0.0572580\pi\)
−0.994417 + 0.105521i \(0.966349\pi\)
\(632\) 0 0
\(633\) 8.12624 + 17.7940i 0.322989 + 0.707247i
\(634\) 0 0
\(635\) 2.70833 + 1.74054i 0.107477 + 0.0690711i
\(636\) 0 0
\(637\) 0.808311 5.62193i 0.0320265 0.222749i
\(638\) 0 0
\(639\) −6.58778 + 4.23371i −0.260608 + 0.167483i
\(640\) 0 0
\(641\) −42.9732 12.6181i −1.69734 0.498384i −0.717229 0.696837i \(-0.754590\pi\)
−0.980110 + 0.198454i \(0.936408\pi\)
\(642\) 0 0
\(643\) −31.1652 −1.22904 −0.614518 0.788903i \(-0.710650\pi\)
−0.614518 + 0.788903i \(0.710650\pi\)
\(644\) 0 0
\(645\) 1.54629 0.0608851
\(646\) 0 0
\(647\) 22.7754 + 6.68747i 0.895394 + 0.262911i 0.696881 0.717187i \(-0.254571\pi\)
0.198513 + 0.980098i \(0.436389\pi\)
\(648\) 0 0
\(649\) 21.9275 14.0920i 0.860730 0.553158i
\(650\) 0 0
\(651\) −1.01864 + 7.08479i −0.0399236 + 0.277675i
\(652\) 0 0
\(653\) 26.4780 + 17.0164i 1.03616 + 0.665902i 0.944035 0.329846i \(-0.106997\pi\)
0.0921282 + 0.995747i \(0.470633\pi\)
\(654\) 0 0
\(655\) −2.89817 6.34611i −0.113241 0.247963i
\(656\) 0 0
\(657\) 0.904661 + 6.29206i 0.0352942 + 0.245477i
\(658\) 0 0
\(659\) −7.87364 + 2.31191i −0.306714 + 0.0900592i −0.431468 0.902128i \(-0.642004\pi\)
0.124754 + 0.992188i \(0.460186\pi\)
\(660\) 0 0
\(661\) 12.5124 14.4401i 0.486677 0.561656i −0.458297 0.888799i \(-0.651541\pi\)
0.944975 + 0.327143i \(0.106086\pi\)
\(662\) 0 0
\(663\) −5.38082 6.20980i −0.208974 0.241168i
\(664\) 0 0
\(665\) 3.57538 7.82899i 0.138647 0.303595i
\(666\) 0 0
\(667\) −4.94713 + 31.6243i −0.191554 + 1.22450i
\(668\) 0 0
\(669\) 2.92729 6.40987i 0.113176 0.247820i
\(670\) 0 0
\(671\) 11.4473 + 13.2109i 0.441918 + 0.510000i
\(672\) 0 0
\(673\) 22.6217 26.1068i 0.872003 1.00634i −0.127891 0.991788i \(-0.540821\pi\)
0.999894 0.0145567i \(-0.00463371\pi\)
\(674\) 0 0
\(675\) 4.64758 1.36465i 0.178885 0.0525255i
\(676\) 0 0
\(677\) −0.808364 5.62230i −0.0310680 0.216082i 0.968373 0.249506i \(-0.0802681\pi\)
−0.999441 + 0.0334233i \(0.989359\pi\)
\(678\) 0 0
\(679\) −7.48011 16.3792i −0.287060 0.628575i
\(680\) 0 0
\(681\) 19.8669 + 12.7677i 0.761302 + 0.489259i
\(682\) 0 0
\(683\) 6.17313 42.9350i 0.236208 1.64286i −0.434161 0.900835i \(-0.642955\pi\)
0.670369 0.742028i \(-0.266136\pi\)
\(684\) 0 0
\(685\) 4.44588 2.85720i 0.169869 0.109168i
\(686\) 0 0
\(687\) 23.5156 + 6.90479i 0.897175 + 0.263434i
\(688\) 0 0
\(689\) 28.1215 1.07135
\(690\) 0 0
\(691\) −29.6785 −1.12902 −0.564511 0.825425i \(-0.690935\pi\)
−0.564511 + 0.825425i \(0.690935\pi\)
\(692\) 0 0
\(693\) −7.81903 2.29587i −0.297020 0.0872131i
\(694\) 0 0
\(695\) −7.78433 + 5.00269i −0.295276 + 0.189763i
\(696\) 0 0
\(697\) −1.48395 + 10.3211i −0.0562087 + 0.390940i
\(698\) 0 0
\(699\) −0.599467 0.385254i −0.0226739 0.0145716i
\(700\) 0 0
\(701\) 9.63854 + 21.1055i 0.364043 + 0.797142i 0.999684 + 0.0251573i \(0.00800866\pi\)
−0.635641 + 0.771985i \(0.719264\pi\)
\(702\) 0 0
\(703\) −5.72400 39.8113i −0.215885 1.50151i
\(704\) 0 0
\(705\) −1.66081 + 0.487658i −0.0625498 + 0.0183663i
\(706\) 0 0
\(707\) −18.9342 + 21.8512i −0.712094 + 0.821800i
\(708\) 0 0
\(709\) −27.3462 31.5591i −1.02701 1.18523i −0.982508 0.186219i \(-0.940377\pi\)
−0.0444980 0.999009i \(-0.514169\pi\)
\(710\) 0 0
\(711\) 3.09054 6.76734i 0.115904 0.253795i
\(712\) 0 0
\(713\) 7.37219 8.29817i 0.276091 0.310769i
\(714\) 0 0
\(715\) 0.958513 2.09885i 0.0358464 0.0784926i
\(716\) 0 0
\(717\) 1.00036 + 1.15448i 0.0373593 + 0.0431149i
\(718\) 0 0
\(719\) −17.9557 + 20.7220i −0.669635 + 0.772800i −0.984319 0.176396i \(-0.943556\pi\)
0.314684 + 0.949196i \(0.398101\pi\)
\(720\) 0 0
\(721\) −6.75145 + 1.98240i −0.251437 + 0.0738286i
\(722\) 0 0
\(723\) 3.88830 + 27.0437i 0.144607 + 1.00577i
\(724\) 0 0
\(725\) 13.4299 + 29.4075i 0.498775 + 1.09217i
\(726\) 0 0
\(727\) 19.3465 + 12.4333i 0.717523 + 0.461124i 0.847774 0.530357i \(-0.177942\pi\)
−0.130252 + 0.991481i \(0.541578\pi\)
\(728\) 0 0
\(729\) −0.142315 + 0.989821i −0.00527092 + 0.0366601i
\(730\) 0 0
\(731\) 12.2067 7.84478i 0.451482 0.290150i
\(732\) 0 0
\(733\) 8.58286 + 2.52016i 0.317015 + 0.0930841i 0.436369 0.899768i \(-0.356264\pi\)
−0.119354 + 0.992852i \(0.538082\pi\)
\(734\) 0 0
\(735\) −1.01328 −0.0373754
\(736\) 0 0
\(737\) 3.55055 0.130786
\(738\) 0 0
\(739\) −6.20386 1.82162i −0.228213 0.0670093i 0.165627 0.986188i \(-0.447035\pi\)
−0.393840 + 0.919179i \(0.628853\pi\)
\(740\) 0 0
\(741\) 13.1236 8.43401i 0.482107 0.309831i
\(742\) 0 0
\(743\) 5.68094 39.5118i 0.208414 1.44955i −0.569921 0.821699i \(-0.693026\pi\)
0.778335 0.627849i \(-0.216065\pi\)
\(744\) 0 0
\(745\) −7.68417 4.93832i −0.281526 0.180926i
\(746\) 0 0
\(747\) −0.286395 0.627117i −0.0104786 0.0229450i
\(748\) 0 0
\(749\) 5.56565 + 38.7100i 0.203365 + 1.41443i
\(750\) 0 0
\(751\) −1.95344 + 0.573581i −0.0712819 + 0.0209303i −0.317179 0.948366i \(-0.602736\pi\)
0.245897 + 0.969296i \(0.420917\pi\)
\(752\) 0 0
\(753\) −15.5748 + 17.9742i −0.567576 + 0.655017i
\(754\) 0 0
\(755\) 5.10707 + 5.89387i 0.185865 + 0.214500i
\(756\) 0 0
\(757\) −2.37358 + 5.19741i −0.0862692 + 0.188903i −0.947850 0.318718i \(-0.896748\pi\)
0.861580 + 0.507621i \(0.169475\pi\)
\(758\) 0 0
\(759\) 8.15697 + 9.65249i 0.296079 + 0.350363i
\(760\) 0 0
\(761\) −13.9068 + 30.4517i −0.504122 + 1.10387i 0.470986 + 0.882141i \(0.343898\pi\)
−0.975108 + 0.221732i \(0.928829\pi\)
\(762\) 0 0
\(763\) 0.450036 + 0.519370i 0.0162924 + 0.0188024i
\(764\) 0 0
\(765\) −0.959952 + 1.10784i −0.0347071 + 0.0400542i
\(766\) 0 0
\(767\) 21.0264 6.17391i 0.759219 0.222927i
\(768\) 0 0
\(769\) 3.10383 + 21.5876i 0.111927 + 0.778470i 0.966042 + 0.258386i \(0.0831905\pi\)
−0.854115 + 0.520085i \(0.825900\pi\)
\(770\) 0 0
\(771\) −6.65195 14.5657i −0.239564 0.524572i
\(772\) 0 0
\(773\) 16.3238 + 10.4907i 0.587127 + 0.377324i 0.800219 0.599709i \(-0.204717\pi\)
−0.213091 + 0.977032i \(0.568353\pi\)
\(774\) 0 0
\(775\) 1.59548 11.0968i 0.0573114 0.398610i
\(776\) 0 0
\(777\) −14.8601 + 9.55002i −0.533104 + 0.342605i
\(778\) 0 0
\(779\) −18.9949 5.57742i −0.680564 0.199832i
\(780\) 0 0
\(781\) −20.6353 −0.738388
\(782\) 0 0
\(783\) −6.67432 −0.238521
\(784\) 0 0
\(785\) −1.78827 0.525084i −0.0638261 0.0187410i
\(786\) 0 0
\(787\) 2.19114 1.40816i 0.0781055 0.0501954i −0.501005 0.865444i \(-0.667036\pi\)
0.579111 + 0.815249i \(0.303400\pi\)
\(788\) 0 0
\(789\) −3.96549 + 27.5806i −0.141175 + 0.981894i
\(790\) 0 0
\(791\) 11.5474 + 7.42105i 0.410578 + 0.263862i
\(792\) 0 0
\(793\) 6.10516 + 13.3684i 0.216800 + 0.474727i
\(794\) <