Properties

Label 276.2.i.a.193.2
Level $276$
Weight $2$
Character 276.193
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 193.2
Root \(1.02355 - 2.24127i\) of defining polynomial
Character \(\chi\) \(=\) 276.193
Dual form 276.2.i.a.133.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.654861 - 0.755750i) q^{3} +(0.217172 + 1.51046i) q^{5} +(-1.55685 + 3.40903i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(-0.654861 - 0.755750i) q^{3} +(0.217172 + 1.51046i) q^{5} +(-1.55685 + 3.40903i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(1.04445 + 0.306679i) q^{11} +(1.25796 + 2.75455i) q^{13} +(0.999315 - 1.15327i) q^{15} +(2.61063 + 1.67775i) q^{17} +(-3.49220 + 2.24430i) q^{19} +(3.59589 - 1.05585i) q^{21} +(2.35317 - 4.17883i) q^{23} +(2.56313 - 0.752602i) q^{25} +(0.841254 - 0.540641i) q^{27} +(2.24106 + 1.44024i) q^{29} +(-4.45761 + 5.14435i) q^{31} +(-0.452198 - 0.990176i) q^{33} +(-5.48731 - 1.61122i) q^{35} +(-0.973540 + 6.77112i) q^{37} +(1.25796 - 2.75455i) q^{39} +(-1.41678 - 9.85394i) q^{41} +(-2.62449 - 3.02882i) q^{43} -1.52600 q^{45} -1.56940 q^{47} +(-4.61365 - 5.32444i) q^{49} +(-0.441641 - 3.07168i) q^{51} +(-1.19196 + 2.61003i) q^{53} +(-0.236402 + 1.64421i) q^{55} +(3.98303 + 1.16952i) q^{57} +(-6.11707 - 13.3945i) q^{59} +(3.42833 - 3.95650i) q^{61} +(-3.15276 - 2.02616i) q^{63} +(-3.88745 + 2.49831i) q^{65} +(4.44565 - 1.30536i) q^{67} +(-4.69914 + 0.958148i) q^{69} +(14.6278 - 4.29512i) q^{71} +(2.70682 - 1.73957i) q^{73} +(-2.24727 - 1.44423i) q^{75} +(-2.67153 + 3.08311i) q^{77} +(-1.28701 - 2.81816i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-0.773779 + 5.38175i) q^{83} +(-1.96723 + 4.30763i) q^{85} +(-0.379120 - 2.63684i) q^{87} +(9.86433 + 11.3840i) q^{89} -11.3488 q^{91} +6.80696 q^{93} +(-4.14834 - 4.78744i) q^{95} +(0.546130 + 3.79842i) q^{97} +(-0.452198 + 0.990176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10}) \) \( 20q - 2q^{3} - 4q^{5} - 2q^{9} - 22q^{13} + 7q^{15} + 7q^{17} + 19q^{19} + 20q^{23} + 20q^{25} - 2q^{27} + 32q^{29} - 3q^{31} + 11q^{33} - 26q^{35} - 10q^{37} - 22q^{39} - 40q^{41} + 8q^{43} - 4q^{45} - 18q^{47} - 34q^{49} - 26q^{51} - 34q^{53} - 17q^{55} - 3q^{57} - 32q^{59} + 32q^{61} + 49q^{65} + 35q^{67} - 2q^{69} + 33q^{71} - q^{73} - 2q^{75} - 50q^{77} + 22q^{79} - 2q^{81} - 14q^{83} - 9q^{85} - 12q^{87} + 10q^{89} - 72q^{91} + 30q^{93} - 51q^{95} - 4q^{97} + 11q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(97\) \(139\) \(185\)
\(\chi(n)\) \(e\left(\frac{5}{11}\right)\) \(1\) \(1\)

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
\(3\) −0.654861 0.755750i −0.378084 0.436332i
\(4\) 0 0
\(5\) 0.217172 + 1.51046i 0.0971222 + 0.675500i 0.978976 + 0.203977i \(0.0653866\pi\)
−0.881854 + 0.471523i \(0.843704\pi\)
\(6\) 0 0
\(7\) −1.55685 + 3.40903i −0.588434 + 1.28849i 0.347950 + 0.937513i \(0.386878\pi\)
−0.936384 + 0.350977i \(0.885849\pi\)
\(8\) 0 0
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) 0 0
\(11\) 1.04445 + 0.306679i 0.314914 + 0.0924671i 0.435370 0.900252i \(-0.356617\pi\)
−0.120456 + 0.992719i \(0.538436\pi\)
\(12\) 0 0
\(13\) 1.25796 + 2.75455i 0.348895 + 0.763974i 0.999988 + 0.00497557i \(0.00158378\pi\)
−0.651092 + 0.758999i \(0.725689\pi\)
\(14\) 0 0
\(15\) 0.999315 1.15327i 0.258022 0.297773i
\(16\) 0 0
\(17\) 2.61063 + 1.67775i 0.633171 + 0.406915i 0.817483 0.575953i \(-0.195369\pi\)
−0.184311 + 0.982868i \(0.559005\pi\)
\(18\) 0 0
\(19\) −3.49220 + 2.24430i −0.801166 + 0.514878i −0.875996 0.482318i \(-0.839795\pi\)
0.0748303 + 0.997196i \(0.476158\pi\)
\(20\) 0 0
\(21\) 3.59589 1.05585i 0.784687 0.230405i
\(22\) 0 0
\(23\) 2.35317 4.17883i 0.490669 0.871346i
\(24\) 0 0
\(25\) 2.56313 0.752602i 0.512626 0.150520i
\(26\) 0 0
\(27\) 0.841254 0.540641i 0.161899 0.104046i
\(28\) 0 0
\(29\) 2.24106 + 1.44024i 0.416154 + 0.267446i 0.731919 0.681391i \(-0.238625\pi\)
−0.315765 + 0.948837i \(0.602261\pi\)
\(30\) 0 0
\(31\) −4.45761 + 5.14435i −0.800610 + 0.923953i −0.998415 0.0562882i \(-0.982073\pi\)
0.197804 + 0.980241i \(0.436619\pi\)
\(32\) 0 0
\(33\) −0.452198 0.990176i −0.0787176 0.172368i
\(34\) 0 0
\(35\) −5.48731 1.61122i −0.927525 0.272346i
\(36\) 0 0
\(37\) −0.973540 + 6.77112i −0.160049 + 1.11317i 0.738488 + 0.674267i \(0.235540\pi\)
−0.898537 + 0.438898i \(0.855369\pi\)
\(38\) 0 0
\(39\) 1.25796 2.75455i 0.201435 0.441081i
\(40\) 0 0
\(41\) −1.41678 9.85394i −0.221264 1.53893i −0.733265 0.679943i \(-0.762005\pi\)
0.512001 0.858985i \(-0.328904\pi\)
\(42\) 0 0
\(43\) −2.62449 3.02882i −0.400231 0.461891i 0.519483 0.854481i \(-0.326125\pi\)
−0.919714 + 0.392590i \(0.871579\pi\)
\(44\) 0 0
\(45\) −1.52600 −0.227482
\(46\) 0 0
\(47\) −1.56940 −0.228921 −0.114461 0.993428i \(-0.536514\pi\)
−0.114461 + 0.993428i \(0.536514\pi\)
\(48\) 0 0
\(49\) −4.61365 5.32444i −0.659093 0.760634i
\(50\) 0 0
\(51\) −0.441641 3.07168i −0.0618421 0.430121i
\(52\) 0 0
\(53\) −1.19196 + 2.61003i −0.163728 + 0.358515i −0.973658 0.228011i \(-0.926778\pi\)
0.809930 + 0.586526i \(0.199505\pi\)
\(54\) 0 0
\(55\) −0.236402 + 1.64421i −0.0318764 + 0.221705i
\(56\) 0 0
\(57\) 3.98303 + 1.16952i 0.527566 + 0.154907i
\(58\) 0 0
\(59\) −6.11707 13.3945i −0.796374 1.74382i −0.657429 0.753517i \(-0.728356\pi\)
−0.138946 0.990300i \(-0.544371\pi\)
\(60\) 0 0
\(61\) 3.42833 3.95650i 0.438952 0.506578i −0.492565 0.870276i \(-0.663940\pi\)
0.931517 + 0.363698i \(0.118486\pi\)
\(62\) 0 0
\(63\) −3.15276 2.02616i −0.397211 0.255272i
\(64\) 0 0
\(65\) −3.88745 + 2.49831i −0.482179 + 0.309878i
\(66\) 0 0
\(67\) 4.44565 1.30536i 0.543123 0.159475i 0.00134834 0.999999i \(-0.499571\pi\)
0.541775 + 0.840524i \(0.317753\pi\)
\(68\) 0 0
\(69\) −4.69914 + 0.958148i −0.565710 + 0.115347i
\(70\) 0 0
\(71\) 14.6278 4.29512i 1.73600 0.509736i 0.747937 0.663770i \(-0.231044\pi\)
0.988066 + 0.154033i \(0.0492263\pi\)
\(72\) 0 0
\(73\) 2.70682 1.73957i 0.316809 0.203601i −0.372566 0.928006i \(-0.621522\pi\)
0.689375 + 0.724405i \(0.257885\pi\)
\(74\) 0 0
\(75\) −2.24727 1.44423i −0.259492 0.166766i
\(76\) 0 0
\(77\) −2.67153 + 3.08311i −0.304449 + 0.351353i
\(78\) 0 0
\(79\) −1.28701 2.81816i −0.144800 0.317068i 0.823311 0.567591i \(-0.192125\pi\)
−0.968111 + 0.250523i \(0.919397\pi\)
\(80\) 0 0
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) 0 0
\(83\) −0.773779 + 5.38175i −0.0849333 + 0.590724i 0.902260 + 0.431193i \(0.141907\pi\)
−0.987193 + 0.159531i \(0.949002\pi\)
\(84\) 0 0
\(85\) −1.96723 + 4.30763i −0.213376 + 0.467228i
\(86\) 0 0
\(87\) −0.379120 2.63684i −0.0406459 0.282699i
\(88\) 0 0
\(89\) 9.86433 + 11.3840i 1.04562 + 1.20671i 0.977915 + 0.209001i \(0.0670212\pi\)
0.0677018 + 0.997706i \(0.478433\pi\)
\(90\) 0 0
\(91\) −11.3488 −1.18968
\(92\) 0 0
\(93\) 6.80696 0.705848
\(94\) 0 0
\(95\) −4.14834 4.78744i −0.425611 0.491181i
\(96\) 0 0
\(97\) 0.546130 + 3.79842i 0.0554511 + 0.385671i 0.998581 + 0.0532474i \(0.0169572\pi\)
−0.943130 + 0.332423i \(0.892134\pi\)
\(98\) 0 0
\(99\) −0.452198 + 0.990176i −0.0454476 + 0.0995164i
\(100\) 0 0
\(101\) 1.05517 7.33887i 0.104993 0.730245i −0.867521 0.497401i \(-0.834288\pi\)
0.972514 0.232844i \(-0.0748031\pi\)
\(102\) 0 0
\(103\) 12.7260 + 3.73670i 1.25393 + 0.368188i 0.840233 0.542225i \(-0.182418\pi\)
0.413700 + 0.910413i \(0.364236\pi\)
\(104\) 0 0
\(105\) 2.37575 + 5.20216i 0.231849 + 0.507679i
\(106\) 0 0
\(107\) 0.152798 0.176338i 0.0147716 0.0170473i −0.748316 0.663343i \(-0.769137\pi\)
0.763087 + 0.646295i \(0.223683\pi\)
\(108\) 0 0
\(109\) −9.97148 6.40828i −0.955095 0.613802i −0.0324583 0.999473i \(-0.510334\pi\)
−0.922636 + 0.385671i \(0.873970\pi\)
\(110\) 0 0
\(111\) 5.75481 3.69839i 0.546222 0.351036i
\(112\) 0 0
\(113\) 7.65402 2.24742i 0.720030 0.211420i 0.0988662 0.995101i \(-0.468478\pi\)
0.621164 + 0.783681i \(0.286660\pi\)
\(114\) 0 0
\(115\) 6.82301 + 2.64685i 0.636249 + 0.246820i
\(116\) 0 0
\(117\) −2.90554 + 0.853143i −0.268617 + 0.0788731i
\(118\) 0 0
\(119\) −9.78386 + 6.28771i −0.896885 + 0.576393i
\(120\) 0 0
\(121\) −8.25696 5.30643i −0.750633 0.482402i
\(122\) 0 0
\(123\) −6.51932 + 7.52369i −0.587827 + 0.678389i
\(124\) 0 0
\(125\) 4.86303 + 10.6485i 0.434962 + 0.952435i
\(126\) 0 0
\(127\) 9.85281 + 2.89305i 0.874296 + 0.256716i 0.687941 0.725766i \(-0.258515\pi\)
0.186354 + 0.982483i \(0.440333\pi\)
\(128\) 0 0
\(129\) −0.570356 + 3.96691i −0.0502170 + 0.349267i
\(130\) 0 0
\(131\) −8.47190 + 18.5509i −0.740193 + 1.62080i 0.0430434 + 0.999073i \(0.486295\pi\)
−0.783237 + 0.621724i \(0.786433\pi\)
\(132\) 0 0
\(133\) −2.21405 15.3990i −0.191982 1.33527i
\(134\) 0 0
\(135\) 0.999315 + 1.15327i 0.0860073 + 0.0992578i
\(136\) 0 0
\(137\) 9.77788 0.835380 0.417690 0.908590i \(-0.362840\pi\)
0.417690 + 0.908590i \(0.362840\pi\)
\(138\) 0 0
\(139\) −3.43414 −0.291280 −0.145640 0.989338i \(-0.546524\pi\)
−0.145640 + 0.989338i \(0.546524\pi\)
\(140\) 0 0
\(141\) 1.02774 + 1.18608i 0.0865515 + 0.0998857i
\(142\) 0 0
\(143\) 0.469117 + 3.26278i 0.0392296 + 0.272848i
\(144\) 0 0
\(145\) −1.68874 + 3.69782i −0.140242 + 0.307087i
\(146\) 0 0
\(147\) −1.00264 + 6.97353i −0.0826965 + 0.575167i
\(148\) 0 0
\(149\) −19.5536 5.74146i −1.60189 0.470359i −0.645822 0.763488i \(-0.723485\pi\)
−0.956073 + 0.293130i \(0.905303\pi\)
\(150\) 0 0
\(151\) 5.81632 + 12.7360i 0.473325 + 1.03644i 0.984245 + 0.176810i \(0.0565777\pi\)
−0.510920 + 0.859629i \(0.670695\pi\)
\(152\) 0 0
\(153\) −2.03221 + 2.34529i −0.164294 + 0.189606i
\(154\) 0 0
\(155\) −8.73843 5.61585i −0.701887 0.451076i
\(156\) 0 0
\(157\) 15.1481 9.73511i 1.20895 0.776946i 0.228469 0.973551i \(-0.426628\pi\)
0.980483 + 0.196605i \(0.0629916\pi\)
\(158\) 0 0
\(159\) 2.75310 0.808382i 0.218335 0.0641089i
\(160\) 0 0
\(161\) 10.5822 + 14.5278i 0.833995 + 1.14495i
\(162\) 0 0
\(163\) 10.8066 3.17311i 0.846439 0.248537i 0.170375 0.985379i \(-0.445502\pi\)
0.676065 + 0.736842i \(0.263684\pi\)
\(164\) 0 0
\(165\) 1.39742 0.898068i 0.108789 0.0699145i
\(166\) 0 0
\(167\) 15.6618 + 10.0652i 1.21194 + 0.778870i 0.980983 0.194093i \(-0.0621764\pi\)
0.230962 + 0.972963i \(0.425813\pi\)
\(168\) 0 0
\(169\) 2.50812 2.89452i 0.192932 0.222656i
\(170\) 0 0
\(171\) −1.72447 3.77605i −0.131873 0.288762i
\(172\) 0 0
\(173\) −11.1330 3.26895i −0.846427 0.248533i −0.170368 0.985381i \(-0.554496\pi\)
−0.676059 + 0.736847i \(0.736314\pi\)
\(174\) 0 0
\(175\) −1.42476 + 9.90946i −0.107702 + 0.749085i
\(176\) 0 0
\(177\) −6.11707 + 13.3945i −0.459787 + 1.00679i
\(178\) 0 0
\(179\) −1.66482 11.5791i −0.124434 0.865461i −0.952437 0.304736i \(-0.901432\pi\)
0.828002 0.560725i \(-0.189477\pi\)
\(180\) 0 0
\(181\) 9.76420 + 11.2685i 0.725767 + 0.837580i 0.991988 0.126332i \(-0.0403205\pi\)
−0.266221 + 0.963912i \(0.585775\pi\)
\(182\) 0 0
\(183\) −5.23520 −0.386997
\(184\) 0 0
\(185\) −10.4390 −0.767487
\(186\) 0 0
\(187\) 2.21215 + 2.55296i 0.161768 + 0.186691i
\(188\) 0 0
\(189\) 0.533353 + 3.70955i 0.0387957 + 0.269830i
\(190\) 0 0
\(191\) 3.72672 8.16038i 0.269656 0.590465i −0.725560 0.688159i \(-0.758419\pi\)
0.995217 + 0.0976939i \(0.0311466\pi\)
\(192\) 0 0
\(193\) 3.17993 22.1169i 0.228897 1.59201i −0.473873 0.880593i \(-0.657144\pi\)
0.702769 0.711418i \(-0.251947\pi\)
\(194\) 0 0
\(195\) 4.43384 + 1.30189i 0.317514 + 0.0932304i
\(196\) 0 0
\(197\) 2.12840 + 4.66054i 0.151642 + 0.332050i 0.970173 0.242412i \(-0.0779386\pi\)
−0.818531 + 0.574462i \(0.805211\pi\)
\(198\) 0 0
\(199\) 17.4100 20.0922i 1.23416 1.42430i 0.364097 0.931361i \(-0.381378\pi\)
0.870065 0.492937i \(-0.164077\pi\)
\(200\) 0 0
\(201\) −3.89781 2.50497i −0.274930 0.176687i
\(202\) 0 0
\(203\) −8.39881 + 5.39759i −0.589481 + 0.378836i
\(204\) 0 0
\(205\) 14.5763 4.28000i 1.01806 0.298928i
\(206\) 0 0
\(207\) 3.80140 + 2.92392i 0.264216 + 0.203227i
\(208\) 0 0
\(209\) −4.33572 + 1.27308i −0.299908 + 0.0880609i
\(210\) 0 0
\(211\) −10.3560 + 6.65540i −0.712937 + 0.458177i −0.846173 0.532908i \(-0.821099\pi\)
0.133237 + 0.991084i \(0.457463\pi\)
\(212\) 0 0
\(213\) −12.8252 8.24227i −0.878769 0.564751i
\(214\) 0 0
\(215\) 4.00496 4.62197i 0.273136 0.315216i
\(216\) 0 0
\(217\) −10.5974 23.2051i −0.719399 1.57526i
\(218\) 0 0
\(219\) −3.08726 0.906503i −0.208618 0.0612558i
\(220\) 0 0
\(221\) −1.33738 + 9.30166i −0.0899617 + 0.625697i
\(222\) 0 0
\(223\) −4.00684 + 8.77376i −0.268318 + 0.587535i −0.995049 0.0993879i \(-0.968312\pi\)
0.726731 + 0.686922i \(0.241039\pi\)
\(224\) 0 0
\(225\) 0.380171 + 2.64415i 0.0253447 + 0.176276i
\(226\) 0 0
\(227\) 12.1922 + 14.0705i 0.809223 + 0.933893i 0.998849 0.0479634i \(-0.0152731\pi\)
−0.189626 + 0.981856i \(0.560728\pi\)
\(228\) 0 0
\(229\) −6.22102 −0.411097 −0.205548 0.978647i \(-0.565898\pi\)
−0.205548 + 0.978647i \(0.565898\pi\)
\(230\) 0 0
\(231\) 4.07954 0.268414
\(232\) 0 0
\(233\) 2.42419 + 2.79767i 0.158814 + 0.183281i 0.829580 0.558388i \(-0.188580\pi\)
−0.670766 + 0.741669i \(0.734034\pi\)
\(234\) 0 0
\(235\) −0.340831 2.37053i −0.0222333 0.154636i
\(236\) 0 0
\(237\) −1.28701 + 2.81816i −0.0836003 + 0.183059i
\(238\) 0 0
\(239\) 2.28878 15.9188i 0.148049 1.02970i −0.771359 0.636400i \(-0.780423\pi\)
0.919408 0.393304i \(-0.128668\pi\)
\(240\) 0 0
\(241\) −27.6789 8.12724i −1.78295 0.523522i −0.787291 0.616581i \(-0.788517\pi\)
−0.995661 + 0.0930597i \(0.970335\pi\)
\(242\) 0 0
\(243\) 0.415415 + 0.909632i 0.0266489 + 0.0583529i
\(244\) 0 0
\(245\) 7.04041 8.12507i 0.449795 0.519092i
\(246\) 0 0
\(247\) −10.5751 6.79619i −0.672876 0.432431i
\(248\) 0 0
\(249\) 4.57398 2.93952i 0.289864 0.186284i
\(250\) 0 0
\(251\) −0.175438 + 0.0515133i −0.0110736 + 0.00325149i −0.287265 0.957851i \(-0.592746\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(252\) 0 0
\(253\) 3.73933 3.64292i 0.235089 0.229028i
\(254\) 0 0
\(255\) 4.54375 1.33416i 0.284540 0.0835486i
\(256\) 0 0
\(257\) −20.6833 + 13.2923i −1.29019 + 0.829152i −0.992108 0.125389i \(-0.959982\pi\)
−0.298078 + 0.954541i \(0.596346\pi\)
\(258\) 0 0
\(259\) −21.5673 13.8604i −1.34012 0.861246i
\(260\) 0 0
\(261\) −1.74452 + 2.01328i −0.107983 + 0.124619i
\(262\) 0 0
\(263\) −4.88909 10.7056i −0.301474 0.660136i 0.696898 0.717170i \(-0.254563\pi\)
−0.998372 + 0.0570340i \(0.981836\pi\)
\(264\) 0 0
\(265\) −4.20122 1.23359i −0.258079 0.0757787i
\(266\) 0 0
\(267\) 2.14372 14.9099i 0.131194 0.912473i
\(268\) 0 0
\(269\) 1.90568 4.17285i 0.116191 0.254423i −0.842597 0.538544i \(-0.818975\pi\)
0.958788 + 0.284121i \(0.0917018\pi\)
\(270\) 0 0
\(271\) 1.13617 + 7.90226i 0.0690176 + 0.480028i 0.994790 + 0.101946i \(0.0325070\pi\)
−0.925772 + 0.378082i \(0.876584\pi\)
\(272\) 0 0
\(273\) 7.43187 + 8.57683i 0.449797 + 0.519094i
\(274\) 0 0
\(275\) 2.90787 0.175351
\(276\) 0 0
\(277\) 5.12957 0.308206 0.154103 0.988055i \(-0.450751\pi\)
0.154103 + 0.988055i \(0.450751\pi\)
\(278\) 0 0
\(279\) −4.45761 5.14435i −0.266870 0.307984i
\(280\) 0 0
\(281\) −3.79046 26.3632i −0.226120 1.57270i −0.714228 0.699913i \(-0.753222\pi\)
0.488108 0.872783i \(-0.337687\pi\)
\(282\) 0 0
\(283\) 1.47222 3.22371i 0.0875143 0.191630i −0.860815 0.508919i \(-0.830045\pi\)
0.948329 + 0.317289i \(0.102773\pi\)
\(284\) 0 0
\(285\) −0.901521 + 6.27022i −0.0534015 + 0.371416i
\(286\) 0 0
\(287\) 35.7981 + 10.5113i 2.11309 + 0.620460i
\(288\) 0 0
\(289\) −3.06150 6.70376i −0.180088 0.394339i
\(290\) 0 0
\(291\) 2.51301 2.90017i 0.147315 0.170011i
\(292\) 0 0
\(293\) −24.1167 15.4989i −1.40891 0.905454i −0.408940 0.912561i \(-0.634101\pi\)
−0.999975 + 0.00710728i \(0.997738\pi\)
\(294\) 0 0
\(295\) 18.9035 12.1485i 1.10060 0.707314i
\(296\) 0 0
\(297\) 1.04445 0.306679i 0.0606053 0.0177953i
\(298\) 0 0
\(299\) 14.4710 + 1.22511i 0.836878 + 0.0708497i
\(300\) 0 0
\(301\) 14.4113 4.23153i 0.830651 0.243901i
\(302\) 0 0
\(303\) −6.23734 + 4.00849i −0.358326 + 0.230282i
\(304\) 0 0
\(305\) 6.72069 + 4.31912i 0.384826 + 0.247312i
\(306\) 0 0
\(307\) −14.2345 + 16.4275i −0.812406 + 0.937566i −0.998993 0.0448722i \(-0.985712\pi\)
0.186587 + 0.982438i \(0.440257\pi\)
\(308\) 0 0
\(309\) −5.50977 12.0647i −0.313440 0.686338i
\(310\) 0 0
\(311\) −22.2553 6.53475i −1.26198 0.370552i −0.418751 0.908101i \(-0.637532\pi\)
−0.843232 + 0.537550i \(0.819350\pi\)
\(312\) 0 0
\(313\) −1.45243 + 10.1019i −0.0820964 + 0.570993i 0.906706 + 0.421763i \(0.138589\pi\)
−0.988802 + 0.149230i \(0.952320\pi\)
\(314\) 0 0
\(315\) 2.37575 5.20216i 0.133858 0.293109i
\(316\) 0 0
\(317\) −2.15164 14.9650i −0.120848 0.840518i −0.956599 0.291408i \(-0.905876\pi\)
0.835750 0.549109i \(-0.185033\pi\)
\(318\) 0 0
\(319\) 1.89899 + 2.19155i 0.106323 + 0.122703i
\(320\) 0 0
\(321\) −0.233329 −0.0130232
\(322\) 0 0
\(323\) −12.8822 −0.716787
\(324\) 0 0
\(325\) 5.29739 + 6.11351i 0.293846 + 0.339117i
\(326\) 0 0
\(327\) 1.68688 + 11.7325i 0.0932844 + 0.648807i
\(328\) 0 0
\(329\) 2.44333 5.35014i 0.134705 0.294963i
\(330\) 0 0
\(331\) −4.22495 + 29.3852i −0.232224 + 1.61515i 0.456222 + 0.889866i \(0.349202\pi\)
−0.688446 + 0.725288i \(0.741707\pi\)
\(332\) 0 0
\(333\) −6.56365 1.92726i −0.359686 0.105613i
\(334\) 0 0
\(335\) 2.93717 + 6.43151i 0.160475 + 0.351391i
\(336\) 0 0
\(337\) 5.04882 5.82664i 0.275027 0.317398i −0.601386 0.798959i \(-0.705385\pi\)
0.876413 + 0.481561i \(0.159930\pi\)
\(338\) 0 0
\(339\) −6.71081 4.31277i −0.364481 0.234238i
\(340\) 0 0
\(341\) −6.23342 + 4.00598i −0.337559 + 0.216936i
\(342\) 0 0
\(343\) 0.162669 0.0477638i 0.00878329 0.00257901i
\(344\) 0 0
\(345\) −2.46777 6.88980i −0.132860 0.370935i
\(346\) 0 0
\(347\) 7.73729 2.27187i 0.415359 0.121961i −0.0673742 0.997728i \(-0.521462\pi\)
0.482734 + 0.875767i \(0.339644\pi\)
\(348\) 0 0
\(349\) −13.0709 + 8.40018i −0.699671 + 0.449651i −0.841512 0.540238i \(-0.818334\pi\)
0.141841 + 0.989889i \(0.454698\pi\)
\(350\) 0 0
\(351\) 2.54748 + 1.63717i 0.135975 + 0.0873856i
\(352\) 0 0
\(353\) −5.62082 + 6.48678i −0.299166 + 0.345256i −0.885353 0.464920i \(-0.846083\pi\)
0.586187 + 0.810176i \(0.300629\pi\)
\(354\) 0 0
\(355\) 9.66437 + 21.1620i 0.512931 + 1.12316i
\(356\) 0 0
\(357\) 11.1590 + 3.27658i 0.590597 + 0.173415i
\(358\) 0 0
\(359\) −4.80972 + 33.4524i −0.253847 + 1.76555i 0.320800 + 0.947147i \(0.396048\pi\)
−0.574648 + 0.818401i \(0.694861\pi\)
\(360\) 0 0
\(361\) −0.734308 + 1.60791i −0.0386478 + 0.0846268i
\(362\) 0 0
\(363\) 1.39683 + 9.71516i 0.0733146 + 0.509914i
\(364\) 0 0
\(365\) 3.21540 + 3.71076i 0.168302 + 0.194230i
\(366\) 0 0
\(367\) 13.4110 0.700047 0.350023 0.936741i \(-0.386174\pi\)
0.350023 + 0.936741i \(0.386174\pi\)
\(368\) 0 0
\(369\) 9.95527 0.518251
\(370\) 0 0
\(371\) −7.04195 8.12685i −0.365600 0.421925i
\(372\) 0 0
\(373\) 4.27644 + 29.7433i 0.221426 + 1.54005i 0.732652 + 0.680603i \(0.238282\pi\)
−0.511227 + 0.859446i \(0.670809\pi\)
\(374\) 0 0
\(375\) 4.86303 10.6485i 0.251126 0.549888i
\(376\) 0 0
\(377\) −1.14805 + 7.98487i −0.0591276 + 0.411242i
\(378\) 0 0
\(379\) 18.1461 + 5.32818i 0.932103 + 0.273690i 0.712317 0.701858i \(-0.247646\pi\)
0.219786 + 0.975548i \(0.429464\pi\)
\(380\) 0 0
\(381\) −4.26580 9.34080i −0.218544 0.478544i
\(382\) 0 0
\(383\) 5.12902 5.91920i 0.262081 0.302457i −0.609424 0.792845i \(-0.708599\pi\)
0.871505 + 0.490387i \(0.163145\pi\)
\(384\) 0 0
\(385\) −5.23711 3.36569i −0.266908 0.171531i
\(386\) 0 0
\(387\) 3.37149 2.16673i 0.171383 0.110141i
\(388\) 0 0
\(389\) 7.10650 2.08666i 0.360314 0.105798i −0.0965649 0.995327i \(-0.530786\pi\)
0.456879 + 0.889529i \(0.348967\pi\)
\(390\) 0 0
\(391\) 13.1543 6.96136i 0.665241 0.352051i
\(392\) 0 0
\(393\) 19.5677 5.74560i 0.987061 0.289827i
\(394\) 0 0
\(395\) 3.97723 2.55601i 0.200116 0.128607i
\(396\) 0 0
\(397\) −1.57016 1.00908i −0.0788042 0.0506444i 0.500645 0.865652i \(-0.333096\pi\)
−0.579450 + 0.815008i \(0.696732\pi\)
\(398\) 0 0
\(399\) −10.1879 + 11.7575i −0.510034 + 0.588611i
\(400\) 0 0
\(401\) −4.49667 9.84632i −0.224553 0.491702i 0.763502 0.645806i \(-0.223478\pi\)
−0.988055 + 0.154104i \(0.950751\pi\)
\(402\) 0 0
\(403\) −19.7779 5.80730i −0.985205 0.289282i
\(404\) 0 0
\(405\) 0.217172 1.51046i 0.0107914 0.0750555i
\(406\) 0 0
\(407\) −3.09338 + 6.77355i −0.153333 + 0.335752i
\(408\) 0 0
\(409\) 0.974102 + 6.77503i 0.0481663 + 0.335004i 0.999629 + 0.0272395i \(0.00867169\pi\)
−0.951463 + 0.307764i \(0.900419\pi\)
\(410\) 0 0
\(411\) −6.40315 7.38963i −0.315844 0.364503i
\(412\) 0 0
\(413\) 55.1856 2.71551
\(414\) 0 0
\(415\) −8.29699 −0.407283
\(416\) 0 0
\(417\) 2.24888 + 2.59535i 0.110128 + 0.127095i
\(418\) 0 0
\(419\) −4.08920 28.4410i −0.199771 1.38944i −0.804948 0.593345i \(-0.797807\pi\)
0.605177 0.796091i \(-0.293102\pi\)
\(420\) 0 0
\(421\) −11.4884 + 25.1561i −0.559911 + 1.22603i 0.392086 + 0.919928i \(0.371753\pi\)
−0.951997 + 0.306106i \(0.900974\pi\)
\(422\) 0 0
\(423\) 0.223350 1.55343i 0.0108596 0.0755304i
\(424\) 0 0
\(425\) 7.95406 + 2.33552i 0.385829 + 0.113290i
\(426\) 0 0
\(427\) 8.15042 + 17.8469i 0.394427 + 0.863674i
\(428\) 0 0
\(429\) 2.15864 2.49120i 0.104220 0.120276i
\(430\) 0 0
\(431\) 24.0681 + 15.4677i 1.15932 + 0.745050i 0.971474 0.237148i \(-0.0762125\pi\)
0.187848 + 0.982198i \(0.439849\pi\)
\(432\) 0 0
\(433\) −22.9578 + 14.7541i −1.10328 + 0.709035i −0.959819 0.280621i \(-0.909460\pi\)
−0.143461 + 0.989656i \(0.545823\pi\)
\(434\) 0 0
\(435\) 3.90051 1.14529i 0.187015 0.0549126i
\(436\) 0 0
\(437\) 1.16083 + 19.8745i 0.0555298 + 0.950727i
\(438\) 0 0
\(439\) 0.908894 0.266875i 0.0433791 0.0127373i −0.259971 0.965616i \(-0.583713\pi\)
0.303350 + 0.952879i \(0.401895\pi\)
\(440\) 0 0
\(441\) 5.92683 3.80894i 0.282230 0.181378i
\(442\) 0 0
\(443\) −18.3853 11.8155i −0.873510 0.561371i 0.0253144 0.999680i \(-0.491941\pi\)
−0.898825 + 0.438309i \(0.855578\pi\)
\(444\) 0 0
\(445\) −15.0529 + 17.3720i −0.713578 + 0.823512i
\(446\) 0 0
\(447\) 8.46579 + 18.5375i 0.400418 + 0.876793i
\(448\) 0 0
\(449\) −5.12412 1.50458i −0.241822 0.0710054i 0.158576 0.987347i \(-0.449310\pi\)
−0.400398 + 0.916341i \(0.631128\pi\)
\(450\) 0 0
\(451\) 1.54223 10.7265i 0.0726209 0.505090i
\(452\) 0 0
\(453\) 5.81632 12.7360i 0.273275 0.598388i
\(454\) 0 0
\(455\) −2.46464 17.1419i −0.115544 0.803626i
\(456\) 0 0
\(457\) 19.5938 + 22.6125i 0.916561 + 1.05777i 0.998132 + 0.0611006i \(0.0194611\pi\)
−0.0815702 + 0.996668i \(0.525993\pi\)
\(458\) 0 0
\(459\) 3.10326 0.144848
\(460\) 0 0
\(461\) −2.50571 −0.116702 −0.0583512 0.998296i \(-0.518584\pi\)
−0.0583512 + 0.998296i \(0.518584\pi\)
\(462\) 0 0
\(463\) −27.7850 32.0656i −1.29128 1.49021i −0.772021 0.635597i \(-0.780754\pi\)
−0.519257 0.854618i \(-0.673791\pi\)
\(464\) 0 0
\(465\) 1.47828 + 10.2817i 0.0685536 + 0.476801i
\(466\) 0 0
\(467\) −5.75868 + 12.6097i −0.266480 + 0.583509i −0.994814 0.101713i \(-0.967568\pi\)
0.728334 + 0.685222i \(0.240295\pi\)
\(468\) 0 0
\(469\) −2.47120 + 17.1876i −0.114110 + 0.793649i
\(470\) 0 0
\(471\) −17.2772 5.07305i −0.796092 0.233754i
\(472\) 0 0
\(473\) −1.81228 3.96833i −0.0833286 0.182464i
\(474\) 0 0
\(475\) −7.26189 + 8.38067i −0.333198 + 0.384531i
\(476\) 0 0
\(477\) −2.41383 1.55127i −0.110522 0.0710280i
\(478\) 0 0
\(479\) −10.6280 + 6.83019i −0.485605 + 0.312079i −0.760436 0.649413i \(-0.775015\pi\)
0.274831 + 0.961493i \(0.411378\pi\)
\(480\) 0 0
\(481\) −19.8761 + 5.83614i −0.906270 + 0.266105i
\(482\) 0 0
\(483\) 4.04951 17.5112i 0.184259 0.796787i
\(484\) 0 0
\(485\) −5.61877 + 1.64982i −0.255135 + 0.0749144i
\(486\) 0 0
\(487\) −13.1238 + 8.43416i −0.594697 + 0.382188i −0.803091 0.595857i \(-0.796813\pi\)
0.208394 + 0.978045i \(0.433176\pi\)
\(488\) 0 0
\(489\) −9.47490 6.08915i −0.428470 0.275361i
\(490\) 0 0
\(491\) 28.5515 32.9501i 1.28851 1.48702i 0.508790 0.860891i \(-0.330093\pi\)
0.779720 0.626129i \(-0.215361\pi\)
\(492\) 0 0
\(493\) 3.43421 + 7.51988i 0.154669 + 0.338678i
\(494\) 0 0
\(495\) −1.59383 0.467991i −0.0716373 0.0210346i
\(496\) 0 0
\(497\) −8.13116 + 56.5535i −0.364732 + 2.53677i
\(498\) 0 0
\(499\) 4.18252 9.15843i 0.187235 0.409988i −0.792615 0.609723i \(-0.791281\pi\)
0.979850 + 0.199735i \(0.0640081\pi\)
\(500\) 0 0
\(501\) −2.64950 18.4277i −0.118371 0.823289i
\(502\) 0 0
\(503\) 4.51425 + 5.20973i 0.201281 + 0.232290i 0.847412 0.530936i \(-0.178160\pi\)
−0.646131 + 0.763226i \(0.723614\pi\)
\(504\) 0 0
\(505\) 11.3143 0.503478
\(506\) 0 0
\(507\) −3.83000 −0.170096
\(508\) 0 0
\(509\) −12.7523 14.7170i −0.565236 0.652318i 0.399128 0.916895i \(-0.369313\pi\)
−0.964364 + 0.264578i \(0.914767\pi\)
\(510\) 0 0
\(511\) 1.71612 + 11.9359i 0.0759165 + 0.528011i
\(512\) 0 0
\(513\) −1.72447 + 3.77605i −0.0761370 + 0.166717i
\(514\) 0 0
\(515\) −2.88041 + 20.0337i −0.126926 + 0.882791i
\(516\) 0 0
\(517\) −1.63917 0.481303i −0.0720905 0.0211677i
\(518\) 0 0
\(519\) 4.82007 + 10.5545i 0.211577 + 0.463290i
\(520\) 0 0
\(521\) 21.9203 25.2973i 0.960344 1.10830i −0.0337122 0.999432i \(-0.510733\pi\)
0.994057 0.108865i \(-0.0347216\pi\)
\(522\) 0 0
\(523\) −26.8575 17.2602i −1.17439 0.754738i −0.200047 0.979786i \(-0.564110\pi\)
−0.974348 + 0.225049i \(0.927746\pi\)
\(524\) 0 0
\(525\) 8.42209 5.41255i 0.367570 0.236223i
\(526\) 0 0
\(527\) −20.2681 + 5.95126i −0.882893 + 0.259241i
\(528\) 0 0
\(529\) −11.9252 19.6670i −0.518488 0.855085i
\(530\) 0 0
\(531\) 14.1287 4.14857i 0.613134 0.180032i
\(532\) 0 0
\(533\) 25.3609 16.2985i 1.09850 0.705965i
\(534\) 0 0
\(535\) 0.299536 + 0.192500i 0.0129501 + 0.00832251i
\(536\) 0 0
\(537\) −7.66065 + 8.84087i −0.330582 + 0.381512i
\(538\) 0 0
\(539\) −3.18584 6.97603i −0.137224 0.300479i
\(540\) 0 0
\(541\) 30.5324 + 8.96512i 1.31269 + 0.385441i 0.861850 0.507163i \(-0.169306\pi\)
0.450841 + 0.892604i \(0.351124\pi\)
\(542\) 0 0
\(543\) 2.12196 14.7586i 0.0910622 0.633351i
\(544\) 0 0
\(545\) 7.51395 16.4533i 0.321862 0.704780i
\(546\) 0 0
\(547\) −5.24592 36.4862i −0.224299 1.56004i −0.721508 0.692406i \(-0.756551\pi\)
0.497209 0.867631i \(-0.334358\pi\)
\(548\) 0 0
\(549\) 3.42833 + 3.95650i 0.146317 + 0.168859i
\(550\) 0 0
\(551\) −11.0586 −0.471111
\(552\) 0 0
\(553\) 11.6109 0.493744
\(554\) 0 0
\(555\) 6.83606 + 7.88924i 0.290175 + 0.334880i
\(556\) 0 0
\(557\) −4.83552 33.6318i −0.204888 1.42503i −0.789519 0.613726i \(-0.789670\pi\)
0.584631 0.811299i \(-0.301239\pi\)
\(558\) 0 0
\(559\) 5.04153 11.0394i 0.213234 0.466917i
\(560\) 0 0
\(561\) 0.480746 3.34366i 0.0202971 0.141170i
\(562\) 0 0
\(563\) 17.9632 + 5.27448i 0.757059 + 0.222293i 0.637411 0.770524i \(-0.280005\pi\)
0.119648 + 0.992816i \(0.461823\pi\)
\(564\) 0 0
\(565\) 5.05689 + 11.0730i 0.212745 + 0.465846i
\(566\) 0 0
\(567\) 2.45422 2.83232i 0.103068 0.118946i
\(568\) 0 0
\(569\) 26.3796 + 16.9531i 1.10589 + 0.710712i 0.960394 0.278647i \(-0.0898860\pi\)
0.145495 + 0.989359i \(0.453522\pi\)
\(570\) 0 0
\(571\) 6.29897 4.04810i 0.263604 0.169408i −0.402162 0.915568i \(-0.631741\pi\)
0.665766 + 0.746161i \(0.268105\pi\)
\(572\) 0 0
\(573\) −8.60769 + 2.52745i −0.359591 + 0.105586i
\(574\) 0 0
\(575\) 2.88647 12.4819i 0.120374 0.520530i
\(576\) 0 0
\(577\) 39.5545 11.6142i 1.64668 0.483508i 0.678671 0.734442i \(-0.262556\pi\)
0.968004 + 0.250935i \(0.0807379\pi\)
\(578\) 0 0
\(579\) −18.7973 + 12.0803i −0.781188 + 0.502039i
\(580\) 0 0
\(581\) −17.1419 11.0164i −0.711165 0.457038i
\(582\) 0 0
\(583\) −2.04539 + 2.36050i −0.0847113 + 0.0977620i
\(584\) 0 0
\(585\) −1.91964 4.20343i −0.0793674 0.173790i
\(586\) 0 0
\(587\) −13.3002 3.90530i −0.548959 0.161189i −0.00452086 0.999990i \(-0.501439\pi\)
−0.544438 + 0.838801i \(0.683257\pi\)
\(588\) 0 0
\(589\) 4.02138 27.9693i 0.165698 1.15246i
\(590\) 0 0
\(591\) 2.12840 4.66054i 0.0875505 0.191709i
\(592\) 0 0
\(593\) 2.08436 + 14.4970i 0.0855943 + 0.595321i 0.986802 + 0.161933i \(0.0517729\pi\)
−0.901207 + 0.433388i \(0.857318\pi\)
\(594\) 0 0
\(595\) −11.6221 13.4127i −0.476461 0.549865i
\(596\) 0 0
\(597\) −26.5858 −1.08808
\(598\) 0 0
\(599\) −25.6306 −1.04724 −0.523618 0.851953i \(-0.675418\pi\)
−0.523618 + 0.851953i \(0.675418\pi\)
\(600\) 0 0
\(601\) 10.9786 + 12.6700i 0.447826 + 0.516819i 0.934112 0.356981i \(-0.116194\pi\)
−0.486286 + 0.873800i \(0.661649\pi\)
\(602\) 0 0
\(603\) 0.659392 + 4.58617i 0.0268525 + 0.186763i
\(604\) 0 0
\(605\) 6.22198 13.6242i 0.252960 0.553904i
\(606\) 0 0
\(607\) −1.47889 + 10.2859i −0.0600263 + 0.417492i 0.937546 + 0.347860i \(0.113092\pi\)
−0.997573 + 0.0696320i \(0.977818\pi\)
\(608\) 0 0
\(609\) 9.57928 + 2.81273i 0.388172 + 0.113978i
\(610\) 0 0
\(611\) −1.97425 4.32300i −0.0798695 0.174890i
\(612\) 0 0
\(613\) −14.6036 + 16.8534i −0.589833 + 0.680704i −0.969689 0.244342i \(-0.921428\pi\)
0.379856 + 0.925046i \(0.375974\pi\)
\(614\) 0 0
\(615\) −12.7801 8.21326i −0.515343 0.331191i
\(616\) 0 0
\(617\) −9.96316 + 6.40294i −0.401102 + 0.257773i −0.725604 0.688112i \(-0.758440\pi\)
0.324502 + 0.945885i \(0.394803\pi\)
\(618\) 0 0
\(619\) 36.4170 10.6930i 1.46372 0.429788i 0.549671 0.835381i \(-0.314753\pi\)
0.914054 + 0.405593i \(0.132935\pi\)
\(620\) 0 0
\(621\) −0.279637 4.78767i −0.0112215 0.192123i
\(622\) 0 0
\(623\) −54.1658 + 15.9045i −2.17011 + 0.637201i
\(624\) 0 0
\(625\) −3.79177 + 2.43682i −0.151671 + 0.0974729i
\(626\) 0 0
\(627\) 3.80142 + 2.44302i 0.151814 + 0.0975650i
\(628\) 0 0
\(629\) −13.9018 + 16.0435i −0.554302 + 0.639698i
\(630\) 0 0
\(631\) −3.01905 6.61079i −0.120186 0.263171i 0.839971 0.542631i \(-0.182572\pi\)
−0.960157 + 0.279460i \(0.909845\pi\)
\(632\) 0 0
\(633\) 11.8116 + 3.46819i 0.469467 + 0.137848i
\(634\) 0 0
\(635\) −2.23009 + 15.5106i −0.0884984 + 0.615520i
\(636\) 0 0
\(637\) 8.86263 19.4064i 0.351150 0.768911i
\(638\) 0 0
\(639\) 2.16964 + 15.0902i 0.0858297 + 0.596959i
\(640\) 0 0
\(641\) −17.1302 19.7693i −0.676601 0.780840i 0.308793 0.951129i \(-0.400075\pi\)
−0.985394 + 0.170290i \(0.945530\pi\)
\(642\) 0 0
\(643\) −33.0605 −1.30378 −0.651889 0.758314i \(-0.726023\pi\)
−0.651889 + 0.758314i \(0.726023\pi\)
\(644\) 0 0
\(645\) −6.11574 −0.240807
\(646\) 0 0
\(647\) −15.6327 18.0411i −0.614586 0.709271i 0.360083 0.932920i \(-0.382748\pi\)
−0.974670 + 0.223650i \(0.928203\pi\)
\(648\) 0 0
\(649\) −2.28117 15.8659i −0.0895438 0.622791i
\(650\) 0 0
\(651\) −10.5974 + 23.2051i −0.415345 + 0.909479i
\(652\) 0 0
\(653\) 5.83034 40.5509i 0.228159 1.58688i −0.477698 0.878524i \(-0.658529\pi\)
0.705857 0.708354i \(-0.250562\pi\)
\(654\) 0 0
\(655\) −29.8603 8.76777i −1.16674 0.342585i
\(656\) 0 0
\(657\) 1.33664 + 2.92683i 0.0521473 + 0.114187i
\(658\) 0 0
\(659\) 3.59931 4.15383i 0.140209 0.161810i −0.681302 0.732003i \(-0.738586\pi\)
0.821511 + 0.570192i \(0.193131\pi\)
\(660\) 0 0
\(661\) 17.4827 + 11.2354i 0.679997 + 0.437007i 0.834517 0.550982i \(-0.185747\pi\)
−0.154520 + 0.987990i \(0.549383\pi\)
\(662\) 0 0
\(663\) 7.90552 5.08057i 0.307025 0.197313i
\(664\) 0 0
\(665\) 22.7789 6.68848i 0.883326 0.259368i
\(666\) 0 0
\(667\) 11.2921 5.97588i 0.437232 0.231387i
\(668\) 0 0
\(669\) 9.25469 2.71742i 0.357807 0.105062i
\(670\) 0 0
\(671\) 4.79410 3.08098i 0.185074 0.118940i
\(672\) 0 0
\(673\) −9.76169 6.27346i −0.376285 0.241824i 0.338804 0.940857i \(-0.389978\pi\)
−0.715089 + 0.699033i \(0.753614\pi\)
\(674\) 0 0
\(675\) 1.74935 2.01886i 0.0673326 0.0777060i
\(676\) 0 0
\(677\) 3.65441 + 8.00205i 0.140450 + 0.307544i 0.966766 0.255664i \(-0.0822942\pi\)
−0.826315 + 0.563208i \(0.809567\pi\)
\(678\) 0 0
\(679\) −13.7991 4.05179i −0.529562 0.155494i
\(680\) 0 0
\(681\) 2.64961 18.4285i 0.101533 0.706180i
\(682\) 0 0
\(683\) −11.9782 + 26.2287i −0.458334 + 1.00361i 0.529530 + 0.848291i \(0.322368\pi\)
−0.987864 + 0.155320i \(0.950359\pi\)
\(684\) 0 0
\(685\) 2.12348 + 14.7691i 0.0811340 + 0.564299i
\(686\) 0 0
\(687\) 4.07390 + 4.70153i 0.155429 + 0.179375i
\(688\) 0 0
\(689\) −8.68889 −0.331020
\(690\) 0 0
\(691\) 9.54501 0.363109 0.181555 0.983381i \(-0.441887\pi\)
0.181555 + 0.983381i \(0.441887\pi\)
\(692\) 0 0
\(693\) −2.67153 3.08311i −0.101483 0.117118i
\(694\) 0 0
\(695\) −0.745798 5.18714i −0.0282897 0.196759i
\(696\) 0 0
\(697\) 12.8338 28.1020i 0.486114 1.06444i
\(698\) 0 0
\(699\) 0.526828 3.66417i 0.0199265 0.138592i
\(700\) 0 0
\(701\) −10.3490 3.03875i −0.390878 0.114772i 0.0803874 0.996764i \(-0.474384\pi\)
−0.471265 + 0.881992i \(0.656202\pi\)
\(702\) 0 0
\(703\) −11.7966 25.8310i −0.444919 0.974236i
\(704\) 0 0
\(705\) −1.56833 + 1.80995i −0.0590667 + 0.0681666i
\(706\) 0 0
\(707\) 23.3757 + 15.0226i 0.879132 + 0.564984i
\(708\) 0 0
\(709\) 5.71727 3.67427i 0.214717 0.137990i −0.428862 0.903370i \(-0.641085\pi\)
0.643579 + 0.765380i \(0.277449\pi\)
\(710\) 0 0
\(711\) 2.97264 0.872845i 0.111483 0.0327342i
\(712\) 0 0
\(713\) 11.0079 + 30.7331i 0.412249 + 1.15096i
\(714\) 0 0
\(715\) −4.82644 + 1.41717i −0.180498 + 0.0529991i
\(716\) 0 0
\(717\) −13.5295 + 8.69488i −0.505268 + 0.324716i
\(718\) 0 0
\(719\) 31.3385 + 20.1400i 1.16873 + 0.751097i 0.973281 0.229617i \(-0.0737474\pi\)
0.195448 + 0.980714i \(0.437384\pi\)
\(720\) 0 0
\(721\) −32.5510 + 37.5659i −1.21226 + 1.39903i
\(722\) 0 0
\(723\) 11.9836 + 26.2405i 0.445676 + 0.975894i
\(724\) 0 0
\(725\) 6.82805 + 2.00490i 0.253587 + 0.0744600i
\(726\) 0 0
\(727\) 6.56541 45.6634i 0.243498 1.69356i −0.390801 0.920475i \(-0.627802\pi\)
0.634299 0.773088i \(-0.281289\pi\)
\(728\) 0 0
\(729\) 0.415415 0.909632i 0.0153857 0.0336901i
\(730\) 0 0
\(731\) −1.76996 12.3104i −0.0654645 0.455316i
\(732\) 0 0
\(733\) 22.8021 + 26.3150i 0.842214 + 0.971967i 0.999879 0.0155256i \(-0.00494217\pi\)
−0.157665 + 0.987493i \(0.550397\pi\)
\(734\) 0 0
\(735\) −10.7510 −0.396557
\(736\) 0 0
\(737\) 5.04360 0.185783
\(738\) 0 0
\(739\) 13.8178 + 15.9466i 0.508295 + 0.586604i 0.950661 0.310231i \(-0.100406\pi\)
−0.442366 + 0.896834i \(0.645861\pi\)
\(740\) 0 0
\(741\) 1.78899 + 12.4427i 0.0657201 + 0.457093i
\(742\) 0 0
\(743\) 11.7483 25.7253i 0.431005 0.943769i −0.562158 0.827030i \(-0.690029\pi\)
0.993163 0.116739i \(-0.0372441\pi\)
\(744\) 0 0
\(745\) 4.42577 30.7819i 0.162148 1.12776i
\(746\) 0 0
\(747\) −5.21685 1.53181i −0.190875 0.0560459i
\(748\) 0 0
\(749\) 0.363258 + 0.795425i 0.0132732 + 0.0290642i
\(750\) 0 0
\(751\) 2.79296 3.22325i 0.101917 0.117618i −0.702500 0.711684i \(-0.747933\pi\)
0.804416 + 0.594066i \(0.202478\pi\)
\(752\) 0 0
\(753\) 0.153819 + 0.0988533i 0.00560547 + 0.00360241i
\(754\) 0 0
\(755\) −17.9741 + 11.5512i −0.654143 + 0.420392i
\(756\) 0 0
\(757\) −35.9380 + 10.5523i −1.30619 + 0.383531i −0.859489 0.511154i \(-0.829218\pi\)
−0.446698 + 0.894685i \(0.647400\pi\)
\(758\) 0 0
\(759\) −5.20187 0.440389i −0.188816 0.0159851i
\(760\) 0 0
\(761\) −40.8916 + 12.0068i −1.48232 + 0.435248i −0.920081 0.391728i \(-0.871877\pi\)
−0.562237 + 0.826976i \(0.690059\pi\)
\(762\) 0 0
\(763\) 37.3701 24.0163i 1.35289 0.869449i
\(764\) 0 0
\(765\) −3.98382 2.56024i −0.144035 0.0925658i
\(766\) 0 0
\(767\) 29.2008 33.6995i 1.05438 1.21682i
\(768\) 0 0
\(769\) −7.88108 17.2572i −0.284199 0.622309i 0.712660 0.701510i \(-0.247490\pi\)
−0.996859 + 0.0792007i \(0.974763\pi\)
\(770\) 0 0
\(771\) 23.5903 + 6.92674i 0.849584 + 0.249461i
\(772\) 0 0
\(773\) −7.52233 + 52.3190i −0.270559 + 1.88178i 0.172081 + 0.985083i \(0.444951\pi\)
−0.442640 + 0.896699i \(0.645958\pi\)
\(774\) 0 0
\(775\) −7.55377 + 16.5404i −0.271339 + 0.594150i
\(776\) 0 0
\(777\) 3.64853 + 25.3761i 0.130890 + 0.910363i
\(778\) 0 0
\(779\) 27.0629 + 31.2323i 0.969629 + 1.11901i
\(780\) 0 0
\(781\) 16.5953 0.593826
\(782\) 0 0
\(783\) 2.66395 0.0952019
\(784\) 0 0
\(785\) 17.9943 + 20.7665i 0.642243 + 0.741188i
\(786\) 0 0
\(787\) −3.90826 27.1825i −0.139314 0.968952i −0.932808 0.360374i \(-0.882649\pi\)
0.793494 0.608578i \(-0.208260\pi\)
\(788\) 0 0
\(789\) −4.88909 + 10.7056i −0.174056 + 0.381130i
\(790\) 0 0
\(791\) −4.25464 + 29.5917i −0.151278 + 1.05216i
\(792\) 0 0
\(793\) 15.2111 + 4.46637i 0.540161 + 0.158606i
\(794\) 0