Properties

Label 483.2.h.c.160.4
Level $483$
Weight $2$
Character 483.160
Analytic conductor $3.857$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 17 x^{10} + 92 x^{8} + 180 x^{6} + 92 x^{4} + 17 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 160.4
Root \(2.92914i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.c.160.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.69639 q^{2} +1.00000i q^{3} +5.27053 q^{4} +2.58774 q^{5} -2.69639i q^{6} +(0.551006 + 2.58774i) q^{7} -8.81864 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.69639 q^{2} +1.00000i q^{3} +5.27053 q^{4} +2.58774 q^{5} -2.69639i q^{6} +(0.551006 + 2.58774i) q^{7} -8.81864 q^{8} -1.00000 q^{9} -6.97756 q^{10} +3.13874i q^{11} +5.27053i q^{12} +4.69639i q^{13} +(-1.48573 - 6.97756i) q^{14} +2.58774i q^{15} +13.2375 q^{16} -6.97756 q^{17} +2.69639 q^{18} +3.13874 q^{19} +13.6388 q^{20} +(-2.58774 + 0.551006i) q^{21} -8.46329i q^{22} +(-1.27053 - 4.62447i) q^{23} -8.81864i q^{24} +1.69639 q^{25} -12.6633i q^{26} -1.00000i q^{27} +(2.90409 + 13.6388i) q^{28} +3.96693 q^{29} -6.97756i q^{30} -2.57414i q^{31} -18.0561 q^{32} -3.13874 q^{33} +18.8142 q^{34} +(1.42586 + 6.69639i) q^{35} -5.27053 q^{36} -2.90409i q^{37} -8.46329 q^{38} -4.69639 q^{39} -22.8203 q^{40} +5.00000i q^{41} +(6.97756 - 1.48573i) q^{42} -0.785656i q^{43} +16.5429i q^{44} -2.58774 q^{45} +(3.42586 + 12.4694i) q^{46} +12.3597i q^{47} +13.2375i q^{48} +(-6.39279 + 2.85172i) q^{49} -4.57414 q^{50} -6.97756i q^{51} +24.7525i q^{52} -7.52857i q^{53} +2.69639i q^{54} +8.12225i q^{55} +(-4.85912 - 22.8203i) q^{56} +3.13874i q^{57} -10.6964 q^{58} -3.15532i q^{59} +13.6388i q^{60} -8.22864 q^{61} +6.94090i q^{62} +(-0.551006 - 2.58774i) q^{63} +22.2114 q^{64} +12.1530i q^{65} +8.46329 q^{66} -7.76322i q^{67} -36.7755 q^{68} +(4.62447 - 1.27053i) q^{69} +(-3.84468 - 18.0561i) q^{70} +9.23746 q^{71} +8.81864 q^{72} +9.65628i q^{73} +7.83058i q^{74} +1.69639i q^{75} +16.5429 q^{76} +(-8.12225 + 1.72947i) q^{77} +12.6633 q^{78} -1.50395i q^{79} +34.2551 q^{80} +1.00000 q^{81} -13.4820i q^{82} +15.7572 q^{83} +(-13.6388 + 2.90409i) q^{84} -18.0561 q^{85} +2.11844i q^{86} +3.96693i q^{87} -27.6795i q^{88} +2.18580 q^{89} +6.97756 q^{90} +(-12.1530 + 2.58774i) q^{91} +(-6.69639 - 24.3734i) q^{92} +2.57414 q^{93} -33.3266i q^{94} +8.12225 q^{95} -18.0561i q^{96} -7.74499 q^{97} +(17.2375 - 7.68935i) q^{98} -3.13874i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + 68 q^{16} - 4 q^{18} + 12 q^{23} - 16 q^{25} - 16 q^{29} - 44 q^{32} + 8 q^{35} - 36 q^{36} - 20 q^{39} + 32 q^{46} - 4 q^{49} - 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} + 20 q^{71} + 24 q^{72} - 52 q^{77} + 52 q^{78} + 12 q^{81} - 44 q^{85} - 44 q^{92} + 40 q^{93} + 52 q^{95} + 116 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69639 −1.90664 −0.953319 0.301966i \(-0.902357\pi\)
−0.953319 + 0.301966i \(0.902357\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 5.27053 2.63527
\(5\) 2.58774 1.15727 0.578636 0.815586i \(-0.303585\pi\)
0.578636 + 0.815586i \(0.303585\pi\)
\(6\) 2.69639i 1.10080i
\(7\) 0.551006 + 2.58774i 0.208261 + 0.978073i
\(8\) −8.81864 −3.11786
\(9\) −1.00000 −0.333333
\(10\) −6.97756 −2.20650
\(11\) 3.13874i 0.946367i 0.880964 + 0.473184i \(0.156895\pi\)
−0.880964 + 0.473184i \(0.843105\pi\)
\(12\) 5.27053i 1.52147i
\(13\) 4.69639i 1.30254i 0.758844 + 0.651272i \(0.225765\pi\)
−0.758844 + 0.651272i \(0.774235\pi\)
\(14\) −1.48573 6.97756i −0.397077 1.86483i
\(15\) 2.58774i 0.668151i
\(16\) 13.2375 3.30937
\(17\) −6.97756 −1.69231 −0.846154 0.532939i \(-0.821087\pi\)
−0.846154 + 0.532939i \(0.821087\pi\)
\(18\) 2.69639 0.635546
\(19\) 3.13874 0.720077 0.360039 0.932937i \(-0.382763\pi\)
0.360039 + 0.932937i \(0.382763\pi\)
\(20\) 13.6388 3.04972
\(21\) −2.58774 + 0.551006i −0.564691 + 0.120239i
\(22\) 8.46329i 1.80438i
\(23\) −1.27053 4.62447i −0.264925 0.964269i
\(24\) 8.81864i 1.80010i
\(25\) 1.69639 0.339279
\(26\) 12.6633i 2.48348i
\(27\) 1.00000i 0.192450i
\(28\) 2.90409 + 13.6388i 0.548822 + 2.57748i
\(29\) 3.96693 0.736640 0.368320 0.929699i \(-0.379933\pi\)
0.368320 + 0.929699i \(0.379933\pi\)
\(30\) 6.97756i 1.27392i
\(31\) 2.57414i 0.462329i −0.972915 0.231165i \(-0.925746\pi\)
0.972915 0.231165i \(-0.0742536\pi\)
\(32\) −18.0561 −3.19190
\(33\) −3.13874 −0.546385
\(34\) 18.8142 3.22662
\(35\) 1.42586 + 6.69639i 0.241014 + 1.13190i
\(36\) −5.27053 −0.878422
\(37\) 2.90409i 0.477430i −0.971090 0.238715i \(-0.923274\pi\)
0.971090 0.238715i \(-0.0767262\pi\)
\(38\) −8.46329 −1.37293
\(39\) −4.69639 −0.752025
\(40\) −22.8203 −3.60821
\(41\) 5.00000i 0.780869i 0.920631 + 0.390434i \(0.127675\pi\)
−0.920631 + 0.390434i \(0.872325\pi\)
\(42\) 6.97756 1.48573i 1.07666 0.229253i
\(43\) 0.785656i 0.119811i −0.998204 0.0599057i \(-0.980920\pi\)
0.998204 0.0599057i \(-0.0190800\pi\)
\(44\) 16.5429i 2.49393i
\(45\) −2.58774 −0.385757
\(46\) 3.42586 + 12.4694i 0.505115 + 1.83851i
\(47\) 12.3597i 1.80285i 0.432936 + 0.901425i \(0.357478\pi\)
−0.432936 + 0.901425i \(0.642522\pi\)
\(48\) 13.2375i 1.91066i
\(49\) −6.39279 + 2.85172i −0.913255 + 0.407388i
\(50\) −4.57414 −0.646881
\(51\) 6.97756i 0.977054i
\(52\) 24.7525i 3.43255i
\(53\) 7.52857i 1.03413i −0.855947 0.517064i \(-0.827025\pi\)
0.855947 0.517064i \(-0.172975\pi\)
\(54\) 2.69639i 0.366933i
\(55\) 8.12225i 1.09520i
\(56\) −4.85912 22.8203i −0.649328 3.04950i
\(57\) 3.13874i 0.415737i
\(58\) −10.6964 −1.40451
\(59\) 3.15532i 0.410788i −0.978679 0.205394i \(-0.934152\pi\)
0.978679 0.205394i \(-0.0658476\pi\)
\(60\) 13.6388i 1.76076i
\(61\) −8.22864 −1.05357 −0.526785 0.849999i \(-0.676603\pi\)
−0.526785 + 0.849999i \(0.676603\pi\)
\(62\) 6.94090i 0.881495i
\(63\) −0.551006 2.58774i −0.0694202 0.326024i
\(64\) 22.2114 2.77643
\(65\) 12.1530i 1.50740i
\(66\) 8.46329 1.04176
\(67\) 7.76322i 0.948428i −0.880410 0.474214i \(-0.842732\pi\)
0.880410 0.474214i \(-0.157268\pi\)
\(68\) −36.7755 −4.45968
\(69\) 4.62447 1.27053i 0.556721 0.152954i
\(70\) −3.84468 18.0561i −0.459527 2.15812i
\(71\) 9.23746 1.09628 0.548142 0.836385i \(-0.315335\pi\)
0.548142 + 0.836385i \(0.315335\pi\)
\(72\) 8.81864 1.03929
\(73\) 9.65628i 1.13018i 0.825029 + 0.565091i \(0.191159\pi\)
−0.825029 + 0.565091i \(0.808841\pi\)
\(74\) 7.83058i 0.910286i
\(75\) 1.69639i 0.195883i
\(76\) 16.5429 1.89760
\(77\) −8.12225 + 1.72947i −0.925616 + 0.197091i
\(78\) 12.6633 1.43384
\(79\) 1.50395i 0.169208i −0.996415 0.0846039i \(-0.973038\pi\)
0.996415 0.0846039i \(-0.0269625\pi\)
\(80\) 34.2551 3.82984
\(81\) 1.00000 0.111111
\(82\) 13.4820i 1.48883i
\(83\) 15.7572 1.72958 0.864789 0.502136i \(-0.167452\pi\)
0.864789 + 0.502136i \(0.167452\pi\)
\(84\) −13.6388 + 2.90409i −1.48811 + 0.316863i
\(85\) −18.0561 −1.95846
\(86\) 2.11844i 0.228437i
\(87\) 3.96693i 0.425299i
\(88\) 27.6795i 2.95064i
\(89\) 2.18580 0.231694 0.115847 0.993267i \(-0.463042\pi\)
0.115847 + 0.993267i \(0.463042\pi\)
\(90\) 6.97756 0.735499
\(91\) −12.1530 + 2.58774i −1.27398 + 0.271269i
\(92\) −6.69639 24.3734i −0.698147 2.54111i
\(93\) 2.57414 0.266926
\(94\) 33.3266i 3.43738i
\(95\) 8.12225 0.833325
\(96\) 18.0561i 1.84284i
\(97\) −7.74499 −0.786385 −0.393192 0.919456i \(-0.628629\pi\)
−0.393192 + 0.919456i \(0.628629\pi\)
\(98\) 17.2375 7.68935i 1.74125 0.776742i
\(99\) 3.13874i 0.315456i
\(100\) 8.94090 0.894090
\(101\) 7.38574i 0.734909i 0.930042 + 0.367454i \(0.119771\pi\)
−0.930042 + 0.367454i \(0.880229\pi\)
\(102\) 18.8142i 1.86289i
\(103\) 5.41013 0.533076 0.266538 0.963824i \(-0.414120\pi\)
0.266538 + 0.963824i \(0.414120\pi\)
\(104\) 41.4158i 4.06116i
\(105\) −6.69639 + 1.42586i −0.653501 + 0.139150i
\(106\) 20.3000i 1.97171i
\(107\) 2.98968i 0.289023i 0.989503 + 0.144512i \(0.0461611\pi\)
−0.989503 + 0.144512i \(0.953839\pi\)
\(108\) 5.27053i 0.507157i
\(109\) 4.45718i 0.426921i −0.976952 0.213460i \(-0.931527\pi\)
0.976952 0.213460i \(-0.0684734\pi\)
\(110\) 21.9008i 2.08816i
\(111\) 2.90409 0.275644
\(112\) 7.29392 + 34.2551i 0.689210 + 3.23680i
\(113\) 20.6163i 1.93942i 0.244257 + 0.969710i \(0.421456\pi\)
−0.244257 + 0.969710i \(0.578544\pi\)
\(114\) 8.46329i 0.792660i
\(115\) −3.28781 11.9669i −0.306590 1.11592i
\(116\) 20.9078 1.94124
\(117\) 4.69639i 0.434182i
\(118\) 8.50799i 0.783224i
\(119\) −3.84468 18.0561i −0.352441 1.65520i
\(120\) 22.8203i 2.08320i
\(121\) 1.14828 0.104389
\(122\) 22.1876 2.00877
\(123\) −5.00000 −0.450835
\(124\) 13.5671i 1.21836i
\(125\) −8.54887 −0.764634
\(126\) 1.48573 + 6.97756i 0.132359 + 0.621611i
\(127\) 19.0561 1.69096 0.845478 0.534010i \(-0.179316\pi\)
0.845478 + 0.534010i \(0.179316\pi\)
\(128\) −23.7785 −2.10174
\(129\) 0.785656 0.0691732
\(130\) 32.7694i 2.87406i
\(131\) 10.1483i 0.886660i 0.896359 + 0.443330i \(0.146203\pi\)
−0.896359 + 0.443330i \(0.853797\pi\)
\(132\) −16.5429 −1.43987
\(133\) 1.72947 + 8.12225i 0.149964 + 0.704289i
\(134\) 20.9327i 1.80831i
\(135\) 2.58774i 0.222717i
\(136\) 61.5326 5.27638
\(137\) 4.71006i 0.402407i 0.979549 + 0.201204i \(0.0644853\pi\)
−0.979549 + 0.201204i \(0.935515\pi\)
\(138\) −12.4694 + 3.42586i −1.06147 + 0.291628i
\(139\) 2.43290i 0.206356i 0.994663 + 0.103178i \(0.0329011\pi\)
−0.994663 + 0.103178i \(0.967099\pi\)
\(140\) 7.51504 + 35.2936i 0.635137 + 2.98285i
\(141\) −12.3597 −1.04088
\(142\) −24.9078 −2.09022
\(143\) −14.7408 −1.23269
\(144\) −13.2375 −1.10312
\(145\) 10.2654 0.852493
\(146\) 26.0371i 2.15485i
\(147\) −2.85172 6.39279i −0.235206 0.527268i
\(148\) 15.3061i 1.25816i
\(149\) 19.6634i 1.61089i −0.592673 0.805443i \(-0.701927\pi\)
0.592673 0.805443i \(-0.298073\pi\)
\(150\) 4.57414i 0.373477i
\(151\) 4.72242 0.384305 0.192153 0.981365i \(-0.438453\pi\)
0.192153 + 0.981365i \(0.438453\pi\)
\(152\) −27.6795 −2.24510
\(153\) 6.97756 0.564102
\(154\) 21.9008 4.66332i 1.76482 0.375781i
\(155\) 6.66121i 0.535041i
\(156\) −24.7525 −1.98179
\(157\) 9.48360 0.756873 0.378437 0.925627i \(-0.376462\pi\)
0.378437 + 0.925627i \(0.376462\pi\)
\(158\) 4.05524i 0.322618i
\(159\) 7.52857 0.597054
\(160\) −46.7245 −3.69389
\(161\) 11.2669 5.83592i 0.887953 0.459935i
\(162\) −2.69639 −0.211849
\(163\) −6.54811 −0.512888 −0.256444 0.966559i \(-0.582551\pi\)
−0.256444 + 0.966559i \(0.582551\pi\)
\(164\) 26.3527i 2.05780i
\(165\) −8.12225 −0.632316
\(166\) −42.4876 −3.29768
\(167\) 22.0301i 1.70474i −0.522941 0.852369i \(-0.675165\pi\)
0.522941 0.852369i \(-0.324835\pi\)
\(168\) 22.8203 4.85912i 1.76063 0.374889i
\(169\) −9.05611 −0.696623
\(170\) 48.6864 3.73407
\(171\) −3.13874 −0.240026
\(172\) 4.14083i 0.315735i
\(173\) 19.6563i 1.49444i 0.664577 + 0.747220i \(0.268612\pi\)
−0.664577 + 0.747220i \(0.731388\pi\)
\(174\) 10.6964i 0.810891i
\(175\) 0.934722 + 4.38982i 0.0706583 + 0.331839i
\(176\) 41.5490i 3.13187i
\(177\) 3.15532 0.237169
\(178\) −5.89377 −0.441757
\(179\) 9.51504 0.711187 0.355594 0.934641i \(-0.384279\pi\)
0.355594 + 0.934641i \(0.384279\pi\)
\(180\) −13.6388 −1.01657
\(181\) 10.5817 0.786533 0.393267 0.919424i \(-0.371345\pi\)
0.393267 + 0.919424i \(0.371345\pi\)
\(182\) 32.7694 6.97756i 2.42903 0.517211i
\(183\) 8.22864i 0.608278i
\(184\) 11.2044 + 40.7816i 0.825998 + 3.00646i
\(185\) 7.51504i 0.552517i
\(186\) −6.94090 −0.508931
\(187\) 21.9008i 1.60154i
\(188\) 65.1423i 4.75099i
\(189\) 2.58774 0.551006i 0.188230 0.0400798i
\(190\) −21.9008 −1.58885
\(191\) 11.9857i 0.867258i 0.901091 + 0.433629i \(0.142767\pi\)
−0.901091 + 0.433629i \(0.857233\pi\)
\(192\) 22.2114i 1.60297i
\(193\) 2.96693 0.213564 0.106782 0.994282i \(-0.465945\pi\)
0.106782 + 0.994282i \(0.465945\pi\)
\(194\) 20.8835 1.49935
\(195\) −12.1530 −0.870297
\(196\) −33.6934 + 15.0301i −2.40667 + 1.07358i
\(197\) 16.9268 1.20599 0.602993 0.797747i \(-0.293975\pi\)
0.602993 + 0.797747i \(0.293975\pi\)
\(198\) 8.46329i 0.601460i
\(199\) −15.2062 −1.07794 −0.538969 0.842325i \(-0.681186\pi\)
−0.538969 + 0.842325i \(0.681186\pi\)
\(200\) −14.9599 −1.05782
\(201\) 7.76322 0.547575
\(202\) 19.9149i 1.40121i
\(203\) 2.18580 + 10.2654i 0.153413 + 0.720488i
\(204\) 36.7755i 2.57480i
\(205\) 12.9387i 0.903678i
\(206\) −14.5878 −1.01638
\(207\) 1.27053 + 4.62447i 0.0883082 + 0.321423i
\(208\) 62.1683i 4.31060i
\(209\) 9.85172i 0.681458i
\(210\) 18.0561 3.84468i 1.24599 0.265308i
\(211\) 18.3928 1.26621 0.633106 0.774065i \(-0.281780\pi\)
0.633106 + 0.774065i \(0.281780\pi\)
\(212\) 39.6796i 2.72520i
\(213\) 9.23746i 0.632940i
\(214\) 8.06135i 0.551062i
\(215\) 2.03307i 0.138654i
\(216\) 8.81864i 0.600033i
\(217\) 6.66121 1.41837i 0.452192 0.0962850i
\(218\) 12.0183i 0.813983i
\(219\) −9.65628 −0.652511
\(220\) 42.8086i 2.88616i
\(221\) 32.7694i 2.20431i
\(222\) −7.83058 −0.525554
\(223\) 3.02603i 0.202638i −0.994854 0.101319i \(-0.967694\pi\)
0.994854 0.101319i \(-0.0323063\pi\)
\(224\) −9.94902 46.7245i −0.664747 3.12191i
\(225\) −1.69639 −0.113093
\(226\) 55.5897i 3.69777i
\(227\) 8.53065 0.566199 0.283100 0.959091i \(-0.408637\pi\)
0.283100 + 0.959091i \(0.408637\pi\)
\(228\) 16.5429i 1.09558i
\(229\) 10.8346 0.715971 0.357985 0.933727i \(-0.383464\pi\)
0.357985 + 0.933727i \(0.383464\pi\)
\(230\) 8.86523 + 32.2675i 0.584556 + 2.12766i
\(231\) −1.72947 8.12225i −0.113791 0.534405i
\(232\) −34.9829 −2.29674
\(233\) −9.27053 −0.607333 −0.303666 0.952778i \(-0.598211\pi\)
−0.303666 + 0.952778i \(0.598211\pi\)
\(234\) 12.6633i 0.827827i
\(235\) 31.9837i 2.08639i
\(236\) 16.6302i 1.08254i
\(237\) 1.50395 0.0976921
\(238\) 10.3668 + 48.6864i 0.671977 + 3.15587i
\(239\) −11.8777 −0.768308 −0.384154 0.923269i \(-0.625507\pi\)
−0.384154 + 0.923269i \(0.625507\pi\)
\(240\) 34.2551i 2.21116i
\(241\) −18.4940 −1.19130 −0.595652 0.803243i \(-0.703106\pi\)
−0.595652 + 0.803243i \(0.703106\pi\)
\(242\) −3.09622 −0.199033
\(243\) 1.00000i 0.0641500i
\(244\) −43.3693 −2.77644
\(245\) −16.5429 + 7.37950i −1.05688 + 0.471459i
\(246\) 13.4820 0.859579
\(247\) 14.7408i 0.937933i
\(248\) 22.7004i 1.44148i
\(249\) 15.7572i 0.998572i
\(250\) 23.0511 1.45788
\(251\) 21.3346 1.34663 0.673315 0.739356i \(-0.264870\pi\)
0.673315 + 0.739356i \(0.264870\pi\)
\(252\) −2.90409 13.6388i −0.182941 0.859162i
\(253\) 14.5150 3.98788i 0.912553 0.250716i
\(254\) −51.3827 −3.22404
\(255\) 18.0561i 1.13072i
\(256\) 19.6934 1.23084
\(257\) 15.1973i 0.947984i −0.880529 0.473992i \(-0.842812\pi\)
0.880529 0.473992i \(-0.157188\pi\)
\(258\) −2.11844 −0.131888
\(259\) 7.51504 1.60017i 0.466962 0.0994299i
\(260\) 64.0530i 3.97240i
\(261\) −3.96693 −0.245547
\(262\) 27.3638i 1.69054i
\(263\) 15.2244i 0.938778i −0.882991 0.469389i \(-0.844474\pi\)
0.882991 0.469389i \(-0.155526\pi\)
\(264\) 27.6795 1.70355
\(265\) 19.4820i 1.19677i
\(266\) −4.66332 21.9008i −0.285926 1.34282i
\(267\) 2.18580i 0.133769i
\(268\) 40.9163i 2.49936i
\(269\) 19.5481i 1.19187i −0.803033 0.595935i \(-0.796782\pi\)
0.803033 0.595935i \(-0.203218\pi\)
\(270\) 6.97756i 0.424641i
\(271\) 9.11521i 0.553710i −0.960912 0.276855i \(-0.910708\pi\)
0.960912 0.276855i \(-0.0892921\pi\)
\(272\) −92.3652 −5.60046
\(273\) −2.58774 12.1530i −0.156617 0.735535i
\(274\) 12.7002i 0.767245i
\(275\) 5.32454i 0.321082i
\(276\) 24.3734 6.69639i 1.46711 0.403075i
\(277\) −21.0702 −1.26599 −0.632993 0.774158i \(-0.718174\pi\)
−0.632993 + 0.774158i \(0.718174\pi\)
\(278\) 6.56006i 0.393446i
\(279\) 2.57414i 0.154110i
\(280\) −12.5741 59.0531i −0.751449 3.52910i
\(281\) 13.3224i 0.794748i −0.917657 0.397374i \(-0.869922\pi\)
0.917657 0.397374i \(-0.130078\pi\)
\(282\) 33.3266 1.98457
\(283\) 1.01643 0.0604203 0.0302101 0.999544i \(-0.490382\pi\)
0.0302101 + 0.999544i \(0.490382\pi\)
\(284\) 48.6864 2.88900
\(285\) 8.12225i 0.481121i
\(286\) 39.7469 2.35028
\(287\) −12.9387 + 2.75503i −0.763747 + 0.162624i
\(288\) 18.0561 1.06397
\(289\) 31.6864 1.86390
\(290\) −27.6795 −1.62539
\(291\) 7.74499i 0.454020i
\(292\) 50.8937i 2.97833i
\(293\) −7.34305 −0.428986 −0.214493 0.976726i \(-0.568810\pi\)
−0.214493 + 0.976726i \(0.568810\pi\)
\(294\) 7.68935 + 17.2375i 0.448452 + 1.00531i
\(295\) 8.16516i 0.475394i
\(296\) 25.6102i 1.48856i
\(297\) 3.13874 0.182128
\(298\) 53.0202i 3.07138i
\(299\) 21.7183 5.96693i 1.25600 0.345076i
\(300\) 8.94090i 0.516203i
\(301\) 2.03307 0.432901i 0.117184 0.0249520i
\(302\) −12.7335 −0.732731
\(303\) −7.38574 −0.424300
\(304\) 41.5490 2.38300
\(305\) −21.2936 −1.21927
\(306\) −18.8142 −1.07554
\(307\) 9.98101i 0.569646i −0.958580 0.284823i \(-0.908065\pi\)
0.958580 0.284823i \(-0.0919349\pi\)
\(308\) −42.8086 + 9.11521i −2.43925 + 0.519387i
\(309\) 5.41013i 0.307771i
\(310\) 17.9612i 1.02013i
\(311\) 9.95988i 0.564773i −0.959301 0.282387i \(-0.908874\pi\)
0.959301 0.282387i \(-0.0911261\pi\)
\(312\) 41.4158 2.34471
\(313\) 19.6634 1.11144 0.555720 0.831370i \(-0.312443\pi\)
0.555720 + 0.831370i \(0.312443\pi\)
\(314\) −25.5715 −1.44308
\(315\) −1.42586 6.69639i −0.0803380 0.377299i
\(316\) 7.92663i 0.445908i
\(317\) 26.0420 1.46267 0.731333 0.682021i \(-0.238899\pi\)
0.731333 + 0.682021i \(0.238899\pi\)
\(318\) −20.3000 −1.13837
\(319\) 12.4512i 0.697132i
\(320\) 57.4774 3.21308
\(321\) −2.98968 −0.166868
\(322\) −30.3799 + 15.7359i −1.69300 + 0.876929i
\(323\) −21.9008 −1.21859
\(324\) 5.27053 0.292807
\(325\) 7.96693i 0.441926i
\(326\) 17.6563 0.977891
\(327\) 4.45718 0.246483
\(328\) 44.0932i 2.43464i
\(329\) −31.9837 + 6.81027i −1.76332 + 0.375462i
\(330\) 21.9008 1.20560
\(331\) −8.65628 −0.475792 −0.237896 0.971291i \(-0.576458\pi\)
−0.237896 + 0.971291i \(0.576458\pi\)
\(332\) 83.0489 4.55790
\(333\) 2.90409i 0.159143i
\(334\) 59.4017i 3.25032i
\(335\) 20.0892i 1.09759i
\(336\) −34.2551 + 7.29392i −1.86877 + 0.397916i
\(337\) 30.8635i 1.68124i −0.541625 0.840620i \(-0.682191\pi\)
0.541625 0.840620i \(-0.317809\pi\)
\(338\) 24.4188 1.32821
\(339\) −20.6163 −1.11973
\(340\) −95.1653 −5.16106
\(341\) 8.07957 0.437533
\(342\) 8.46329 0.457642
\(343\) −10.9020 14.9715i −0.588651 0.808388i
\(344\) 6.92842i 0.373556i
\(345\) 11.9669 3.28781i 0.644278 0.177010i
\(346\) 53.0010i 2.84935i
\(347\) −12.5080 −0.671464 −0.335732 0.941957i \(-0.608984\pi\)
−0.335732 + 0.941957i \(0.608984\pi\)
\(348\) 20.9078i 1.12078i
\(349\) 25.2185i 1.34991i 0.737857 + 0.674957i \(0.235838\pi\)
−0.737857 + 0.674957i \(0.764162\pi\)
\(350\) −2.52038 11.8367i −0.134720 0.632697i
\(351\) 4.69639 0.250675
\(352\) 56.6735i 3.02071i
\(353\) 5.98101i 0.318337i 0.987251 + 0.159169i \(0.0508813\pi\)
−0.987251 + 0.159169i \(0.949119\pi\)
\(354\) −8.50799 −0.452195
\(355\) 23.9041 1.26870
\(356\) 11.5203 0.610576
\(357\) 18.0561 3.84468i 0.955630 0.203482i
\(358\) −25.6563 −1.35598
\(359\) 2.58774i 0.136576i 0.997666 + 0.0682878i \(0.0217536\pi\)
−0.997666 + 0.0682878i \(0.978246\pi\)
\(360\) 22.8203 1.20274
\(361\) −9.14828 −0.481489
\(362\) −28.5325 −1.49963
\(363\) 1.14828i 0.0602692i
\(364\) −64.0530 + 13.6388i −3.35729 + 0.714866i
\(365\) 24.9879i 1.30793i
\(366\) 22.1876i 1.15977i
\(367\) 20.7836 1.08490 0.542448 0.840089i \(-0.317498\pi\)
0.542448 + 0.840089i \(0.317498\pi\)
\(368\) −16.8186 61.2163i −0.876732 3.19112i
\(369\) 5.00000i 0.260290i
\(370\) 20.2635i 1.05345i
\(371\) 19.4820 4.14828i 1.01145 0.215368i
\(372\) 13.5671 0.703421
\(373\) 2.43479i 0.126069i 0.998011 + 0.0630344i \(0.0200778\pi\)
−0.998011 + 0.0630344i \(0.979922\pi\)
\(374\) 59.0531i 3.05356i
\(375\) 8.54887i 0.441462i
\(376\) 108.996i 5.62103i
\(377\) 18.6302i 0.959507i
\(378\) −6.97756 + 1.48573i −0.358887 + 0.0764176i
\(379\) 10.3510i 0.531693i −0.964015 0.265846i \(-0.914349\pi\)
0.964015 0.265846i \(-0.0856514\pi\)
\(380\) 42.8086 2.19604
\(381\) 19.0561i 0.976274i
\(382\) 32.3183i 1.65355i
\(383\) −4.93695 −0.252266 −0.126133 0.992013i \(-0.540257\pi\)
−0.126133 + 0.992013i \(0.540257\pi\)
\(384\) 23.7785i 1.21344i
\(385\) −21.0183 + 4.47541i −1.07119 + 0.228088i
\(386\) −8.00000 −0.407189
\(387\) 0.785656i 0.0399372i
\(388\) −40.8203 −2.07233
\(389\) 15.7572i 0.798922i −0.916750 0.399461i \(-0.869197\pi\)
0.916750 0.399461i \(-0.130803\pi\)
\(390\) 32.7694 1.65934
\(391\) 8.86523 + 32.2675i 0.448334 + 1.63184i
\(392\) 56.3757 25.1483i 2.84740 1.27018i
\(393\) −10.1483 −0.511913
\(394\) −45.6413 −2.29938
\(395\) 3.89183i 0.195819i
\(396\) 16.5429i 0.831310i
\(397\) 10.4890i 0.526428i −0.964737 0.263214i \(-0.915217\pi\)
0.964737 0.263214i \(-0.0847826\pi\)
\(398\) 41.0019 2.05524
\(399\) −8.12225 + 1.72947i −0.406621 + 0.0865816i
\(400\) 22.4559 1.12280
\(401\) 20.9962i 1.04850i 0.851565 + 0.524249i \(0.175654\pi\)
−0.851565 + 0.524249i \(0.824346\pi\)
\(402\) −20.9327 −1.04403
\(403\) 12.0892 0.602205
\(404\) 38.9268i 1.93668i
\(405\) 2.58774 0.128586
\(406\) −5.89377 27.6795i −0.292503 1.37371i
\(407\) 9.11521 0.451824
\(408\) 61.5326i 3.04632i
\(409\) 14.1453i 0.699439i 0.936854 + 0.349720i \(0.113723\pi\)
−0.936854 + 0.349720i \(0.886277\pi\)
\(410\) 34.8878i 1.72299i
\(411\) −4.71006 −0.232330
\(412\) 28.5143 1.40480
\(413\) 8.16516 1.73860i 0.401781 0.0855510i
\(414\) −3.42586 12.4694i −0.168372 0.612837i
\(415\) 40.7755 2.00159
\(416\) 84.7986i 4.15759i
\(417\) −2.43290 −0.119140
\(418\) 26.5641i 1.29929i
\(419\) 20.9145 1.02174 0.510869 0.859659i \(-0.329324\pi\)
0.510869 + 0.859659i \(0.329324\pi\)
\(420\) −35.2936 + 7.51504i −1.72215 + 0.366696i
\(421\) 1.41837i 0.0691269i −0.999403 0.0345635i \(-0.988996\pi\)
0.999403 0.0345635i \(-0.0110041\pi\)
\(422\) −49.5942 −2.41421
\(423\) 12.3597i 0.600950i
\(424\) 66.3917i 3.22427i
\(425\) −11.8367 −0.574163
\(426\) 24.9078i 1.20679i
\(427\) −4.53403 21.2936i −0.219417 1.03047i
\(428\) 15.7572i 0.761653i
\(429\) 14.7408i 0.711691i
\(430\) 5.48196i 0.264364i
\(431\) 25.0283i 1.20557i −0.797904 0.602784i \(-0.794058\pi\)
0.797904 0.602784i \(-0.205942\pi\)
\(432\) 13.2375i 0.636888i
\(433\) 26.8717 1.29137 0.645686 0.763603i \(-0.276571\pi\)
0.645686 + 0.763603i \(0.276571\pi\)
\(434\) −17.9612 + 3.82447i −0.862166 + 0.183581i
\(435\) 10.2654i 0.492187i
\(436\) 23.4917i 1.12505i
\(437\) −3.98788 14.5150i −0.190766 0.694348i
\(438\) 26.0371 1.24410
\(439\) 20.3898i 0.973151i 0.873638 + 0.486576i \(0.161754\pi\)
−0.873638 + 0.486576i \(0.838246\pi\)
\(440\) 71.6272i 3.41470i
\(441\) 6.39279 2.85172i 0.304418 0.135796i
\(442\) 88.3591i 4.20281i
\(443\) −19.3787 −0.920710 −0.460355 0.887735i \(-0.652278\pi\)
−0.460355 + 0.887735i \(0.652278\pi\)
\(444\) 15.3061 0.726397
\(445\) 5.65628 0.268133
\(446\) 8.15937i 0.386357i
\(447\) 19.6634 0.930046
\(448\) 12.2386 + 57.4774i 0.578221 + 2.71555i
\(449\) −14.9599 −0.706001 −0.353000 0.935623i \(-0.614839\pi\)
−0.353000 + 0.935623i \(0.614839\pi\)
\(450\) 4.57414 0.215627
\(451\) −15.6937 −0.738989
\(452\) 108.659i 5.11089i
\(453\) 4.72242i 0.221879i
\(454\) −23.0020 −1.07954
\(455\) −31.4489 + 6.69639i −1.47435 + 0.313932i
\(456\) 27.6795i 1.29621i
\(457\) 26.5957i 1.24409i −0.782980 0.622047i \(-0.786301\pi\)
0.782980 0.622047i \(-0.213699\pi\)
\(458\) −29.2143 −1.36510
\(459\) 6.97756i 0.325685i
\(460\) −17.3285 63.0721i −0.807946 2.94075i
\(461\) 23.7736i 1.10725i 0.832767 + 0.553624i \(0.186756\pi\)
−0.832767 + 0.553624i \(0.813244\pi\)
\(462\) 4.66332 + 21.9008i 0.216957 + 1.01892i
\(463\) 26.3407 1.22416 0.612079 0.790797i \(-0.290334\pi\)
0.612079 + 0.790797i \(0.290334\pi\)
\(464\) 52.5120 2.43781
\(465\) 6.66121 0.308906
\(466\) 24.9970 1.15796
\(467\) 9.18158 0.424873 0.212436 0.977175i \(-0.431860\pi\)
0.212436 + 0.977175i \(0.431860\pi\)
\(468\) 24.7525i 1.14418i
\(469\) 20.0892 4.27758i 0.927632 0.197520i
\(470\) 86.2406i 3.97798i
\(471\) 9.48360i 0.436981i
\(472\) 27.8257i 1.28078i
\(473\) 2.46597 0.113386
\(474\) −4.05524 −0.186263
\(475\) 5.32454 0.244307
\(476\) −20.2635 95.1653i −0.928776 4.36190i
\(477\) 7.52857i 0.344709i
\(478\) 32.0271 1.46488
\(479\) 2.73292 0.124871 0.0624353 0.998049i \(-0.480113\pi\)
0.0624353 + 0.998049i \(0.480113\pi\)
\(480\) 46.7245i 2.13267i
\(481\) 13.6388 0.621874
\(482\) 49.8671 2.27138
\(483\) 5.83592 + 11.2669i 0.265544 + 0.512660i
\(484\) 6.05206 0.275094
\(485\) −20.0420 −0.910061
\(486\) 2.69639i 0.122311i
\(487\) 21.3738 0.968539 0.484270 0.874919i \(-0.339085\pi\)
0.484270 + 0.874919i \(0.339085\pi\)
\(488\) 72.5654 3.28488
\(489\) 6.54811i 0.296116i
\(490\) 44.6060 19.8980i 2.01510 0.898901i
\(491\) −21.7785 −0.982851 −0.491426 0.870920i \(-0.663524\pi\)
−0.491426 + 0.870920i \(0.663524\pi\)
\(492\) −26.3527 −1.18807
\(493\) −27.6795 −1.24662
\(494\) 39.7469i 1.78830i
\(495\) 8.12225i 0.365068i
\(496\) 34.0751i 1.53002i
\(497\) 5.08989 + 23.9041i 0.228313 + 1.07225i
\(498\) 42.4876i 1.90392i
\(499\) −18.1223 −0.811263 −0.405632 0.914037i \(-0.632948\pi\)
−0.405632 + 0.914037i \(0.632948\pi\)
\(500\) −45.0571 −2.01502
\(501\) 22.0301 0.984231
\(502\) −57.5265 −2.56753
\(503\) −15.1427 −0.675180 −0.337590 0.941293i \(-0.609612\pi\)
−0.337590 + 0.941293i \(0.609612\pi\)
\(504\) 4.85912 + 22.8203i 0.216443 + 1.01650i
\(505\) 19.1124i 0.850490i
\(506\) −39.1382 + 10.7529i −1.73991 + 0.478025i
\(507\) 9.05611i 0.402196i
\(508\) 100.436 4.45612
\(509\) 32.2274i 1.42846i 0.699913 + 0.714228i \(0.253222\pi\)
−0.699913 + 0.714228i \(0.746778\pi\)
\(510\) 48.6864i 2.15587i
\(511\) −24.9879 + 5.32066i −1.10540 + 0.235372i
\(512\) −5.54407 −0.245015
\(513\) 3.13874i 0.138579i
\(514\) 40.9780i 1.80746i
\(515\) 14.0000 0.616914
\(516\) 4.14083 0.182290
\(517\) −38.7940 −1.70616
\(518\) −20.2635 + 4.31469i −0.890327 + 0.189577i
\(519\) −19.6563 −0.862815
\(520\) 107.173i 4.69986i
\(521\) 12.9878 0.569007 0.284504 0.958675i \(-0.408171\pi\)
0.284504 + 0.958675i \(0.408171\pi\)
\(522\) 10.6964 0.468168
\(523\) −19.6998 −0.861413 −0.430707 0.902492i \(-0.641736\pi\)
−0.430707 + 0.902492i \(0.641736\pi\)
\(524\) 53.4869i 2.33658i
\(525\) −4.38982 + 0.934722i −0.191588 + 0.0407946i
\(526\) 41.0510i 1.78991i
\(527\) 17.9612i 0.782403i
\(528\) −41.5490 −1.80819
\(529\) −19.7715 + 11.7511i −0.859630 + 0.510917i
\(530\) 52.5310i 2.28180i
\(531\) 3.15532i 0.136929i
\(532\) 9.11521 + 42.8086i 0.395194 + 1.85599i
\(533\) −23.4820 −1.01712
\(534\) 5.89377i 0.255048i
\(535\) 7.73651i 0.334478i
\(536\) 68.4610i 2.95707i
\(537\) 9.51504i 0.410604i
\(538\) 52.7094i 2.27246i
\(539\) −8.95081 20.0653i −0.385539 0.864275i
\(540\) 13.6388i 0.586919i
\(541\) −13.5882 −0.584203 −0.292102 0.956387i \(-0.594355\pi\)
−0.292102 + 0.956387i \(0.594355\pi\)
\(542\) 24.5782i 1.05572i
\(543\) 10.5817i 0.454105i
\(544\) 125.988 5.40167
\(545\) 11.5340i 0.494063i
\(546\) 6.97756 + 32.7694i 0.298612 + 1.40240i
\(547\) −3.58118 −0.153120 −0.0765602 0.997065i \(-0.524394\pi\)
−0.0765602 + 0.997065i \(0.524394\pi\)
\(548\) 24.8245i 1.06045i
\(549\) 8.22864 0.351190
\(550\) 14.3571i 0.612187i
\(551\) 12.4512 0.530438
\(552\) −40.7816 + 11.2044i −1.73578 + 0.476890i
\(553\) 3.89183 0.828686i 0.165498 0.0352393i
\(554\) 56.8135 2.41377
\(555\) 7.51504 0.318996
\(556\) 12.8227i 0.543803i
\(557\) 19.7269i 0.835854i −0.908481 0.417927i \(-0.862757\pi\)
0.908481 0.417927i \(-0.137243\pi\)
\(558\) 6.94090i 0.293832i
\(559\) 3.68975 0.156060
\(560\) 18.8747 + 88.6432i 0.797604 + 3.74586i
\(561\) 21.9008 0.924652
\(562\) 35.9225i 1.51530i
\(563\) −27.5939 −1.16294 −0.581472 0.813567i \(-0.697523\pi\)
−0.581472 + 0.813567i \(0.697523\pi\)
\(564\) −65.1423 −2.74299
\(565\) 53.3497i 2.24444i
\(566\) −2.74069 −0.115200
\(567\) 0.551006 + 2.58774i 0.0231401 + 0.108675i
\(568\) −81.4619 −3.41806
\(569\) 20.6307i 0.864883i 0.901662 + 0.432441i \(0.142348\pi\)
−0.901662 + 0.432441i \(0.857652\pi\)
\(570\) 21.9008i 0.917323i
\(571\) 32.8185i 1.37341i 0.726935 + 0.686706i \(0.240944\pi\)
−0.726935 + 0.686706i \(0.759056\pi\)
\(572\) −77.6918 −3.24846
\(573\) −11.9857 −0.500712
\(574\) 34.8878 7.42864i 1.45619 0.310065i
\(575\) −2.15532 7.84492i −0.0898833 0.327156i
\(576\) −22.2114 −0.925476
\(577\) 5.63729i 0.234683i −0.993092 0.117342i \(-0.962563\pi\)
0.993092 0.117342i \(-0.0374373\pi\)
\(578\) −85.4388 −3.55379
\(579\) 2.96693i 0.123301i
\(580\) 54.1040 2.24655
\(581\) 8.68231 + 40.7755i 0.360203 + 1.69165i
\(582\) 20.8835i 0.865651i
\(583\) 23.6302 0.978665
\(584\) 85.1553i 3.52375i
\(585\) 12.1530i 0.502466i
\(586\) 19.7998 0.817920
\(587\) 27.6633i 1.14179i −0.821024 0.570894i \(-0.806597\pi\)
0.821024 0.570894i \(-0.193403\pi\)
\(588\) −15.0301 33.6934i −0.619830 1.38949i
\(589\) 8.07957i 0.332913i
\(590\) 22.0165i 0.906404i
\(591\) 16.9268i 0.696276i
\(592\) 38.4428i 1.57999i
\(593\) 36.7194i 1.50789i −0.656940 0.753943i \(-0.728149\pi\)
0.656940 0.753943i \(-0.271851\pi\)
\(594\) −8.46329 −0.347253
\(595\) −9.94902 46.7245i −0.407870 1.91552i
\(596\) 103.637i 4.24512i
\(597\) 15.2062i 0.622348i
\(598\) −58.5612 + 16.0892i −2.39474 + 0.657935i
\(599\) 18.3337 0.749094 0.374547 0.927208i \(-0.377798\pi\)
0.374547 + 0.927208i \(0.377798\pi\)
\(600\) 14.9599i 0.610735i
\(601\) 41.6272i 1.69801i −0.528384 0.849005i \(-0.677202\pi\)
0.528384 0.849005i \(-0.322798\pi\)
\(602\) −5.48196 + 1.16727i −0.223428 + 0.0475744i
\(603\) 7.76322i 0.316143i
\(604\) 24.8897 1.01275
\(605\) 2.97146 0.120807
\(606\) 19.9149 0.808986
\(607\) 10.7625i 0.436838i −0.975855 0.218419i \(-0.929910\pi\)
0.975855 0.218419i \(-0.0700899\pi\)
\(608\) −56.6735 −2.29841
\(609\) −10.2654 + 2.18580i −0.415974 + 0.0885730i
\(610\) 57.4158 2.32470
\(611\) −58.0461 −2.34829
\(612\) 36.7755 1.48656
\(613\) 30.2181i 1.22050i 0.792210 + 0.610248i \(0.208930\pi\)
−0.792210 + 0.610248i \(0.791070\pi\)
\(614\) 26.9127i 1.08611i
\(615\) −12.9387 −0.521739
\(616\) 71.6272 15.2515i 2.88594 0.614502i
\(617\) 35.6061i 1.43345i −0.697357 0.716724i \(-0.745641\pi\)
0.697357 0.716724i \(-0.254359\pi\)
\(618\) 14.5878i 0.586809i
\(619\) −5.02253 −0.201873 −0.100936 0.994893i \(-0.532184\pi\)
−0.100936 + 0.994893i \(0.532184\pi\)
\(620\) 35.1081i 1.40998i
\(621\) −4.62447 + 1.27053i −0.185574 + 0.0509848i
\(622\) 26.8558i 1.07682i
\(623\) 1.20439 + 5.65628i 0.0482528 + 0.226614i
\(624\) −62.1683 −2.48872
\(625\) −30.6042 −1.22417
\(626\) −53.0202 −2.11911
\(627\) −9.85172 −0.393440
\(628\) 49.9836 1.99456
\(629\) 20.2635i 0.807958i
\(630\) 3.84468 + 18.0561i 0.153176 + 0.719372i
\(631\) 48.3736i 1.92572i 0.269995 + 0.962862i \(0.412978\pi\)
−0.269995 + 0.962862i \(0.587022\pi\)
\(632\) 13.2628i 0.527566i
\(633\) 18.3928i 0.731048i
\(634\) −70.2195 −2.78877
\(635\) 49.3122 1.95690
\(636\) 39.6796 1.57340
\(637\) −13.3928 30.0230i −0.530641 1.18956i
\(638\) 33.5732i 1.32918i
\(639\) −9.23746 −0.365428
\(640\) −61.5326 −2.43229
\(641\) 18.9142i 0.747065i −0.927617 0.373532i \(-0.878146\pi\)
0.927617 0.373532i \(-0.121854\pi\)
\(642\) 8.06135 0.318156
\(643\) −2.88975 −0.113961 −0.0569803 0.998375i \(-0.518147\pi\)
−0.0569803 + 0.998375i \(0.518147\pi\)
\(644\) 59.3823 30.7584i 2.33999 1.21205i
\(645\) 2.03307 0.0800522
\(646\) 59.0531 2.32341
\(647\) 3.95798i 0.155604i 0.996969 + 0.0778021i \(0.0247902\pi\)
−0.996969 + 0.0778021i \(0.975210\pi\)
\(648\) −8.81864 −0.346429
\(649\) 9.90376 0.388757
\(650\) 21.4820i 0.842592i
\(651\) 1.41837 + 6.66121i 0.0555902 + 0.261073i
\(652\) −34.5120 −1.35160
\(653\) −14.9219 −0.583939 −0.291970 0.956428i \(-0.594311\pi\)
−0.291970 + 0.956428i \(0.594311\pi\)
\(654\) −12.0183 −0.469953
\(655\) 26.2611i 1.02611i
\(656\) 66.1873i 2.58418i
\(657\) 9.65628i 0.376727i
\(658\) 86.2406 18.3632i 3.36201 0.715871i
\(659\) 6.64298i 0.258774i −0.991594 0.129387i \(-0.958699\pi\)
0.991594 0.129387i \(-0.0413009\pi\)
\(660\) −42.8086 −1.66632
\(661\) 3.57160 0.138919 0.0694595 0.997585i \(-0.477873\pi\)
0.0694595 + 0.997585i \(0.477873\pi\)
\(662\) 23.3407 0.907163
\(663\) 32.7694 1.27266
\(664\) −138.957 −5.39258
\(665\) 4.47541 + 21.0183i 0.173549 + 0.815053i
\(666\) 7.83058i 0.303429i
\(667\) −5.04012 18.3449i −0.195154 0.710319i
\(668\) 116.110i 4.49244i
\(669\) 3.02603 0.116993
\(670\) 54.1683i 2.09270i
\(671\) 25.8276i 0.997063i
\(672\) 46.7245 9.94902i 1.80244 0.383792i
\(673\) −7.91786 −0.305211 −0.152606 0.988287i \(-0.548766\pi\)
−0.152606 + 0.988287i \(0.548766\pi\)
\(674\) 83.2200i 3.20552i
\(675\) 1.69639i 0.0652942i
\(676\) −47.7305 −1.83579
\(677\) 15.6794 0.602608 0.301304 0.953528i \(-0.402578\pi\)
0.301304 + 0.953528i \(0.402578\pi\)
\(678\) 55.5897 2.13491
\(679\) −4.26754 20.0420i −0.163773 0.769142i
\(680\) 159.230 6.10621
\(681\) 8.53065i 0.326895i
\(682\) −21.7857 −0.834218
\(683\) 18.6864 0.715013 0.357507 0.933911i \(-0.383627\pi\)
0.357507 + 0.933911i \(0.383627\pi\)
\(684\) −16.5429 −0.632532
\(685\) 12.1884i 0.465695i
\(686\) 29.3960 + 40.3692i 1.12234 + 1.54130i
\(687\) 10.8346i 0.413366i
\(688\) 10.4001i 0.396500i
\(689\) 35.3571 1.34700
\(690\) −32.2675 + 8.86523i −1.22840 + 0.337493i
\(691\) 32.0089i 1.21768i 0.793294 + 0.608839i \(0.208364\pi\)
−0.793294 + 0.608839i \(0.791636\pi\)
\(692\) 103.599i 3.93825i
\(693\) 8.12225 1.72947i 0.308539 0.0656970i
\(694\) 33.7265 1.28024
\(695\) 6.29571i 0.238810i
\(696\) 34.9829i 1.32602i
\(697\) 34.8878i 1.32147i
\(698\) 67.9989i 2.57380i
\(699\) 9.27053i 0.350644i
\(700\) 4.92648 + 23.1367i 0.186204 + 0.874485i
\(701\) 2.81463i 0.106307i −0.998586 0.0531535i \(-0.983073\pi\)
0.998586 0.0531535i \(-0.0169273\pi\)
\(702\) −12.6633 −0.477946
\(703\) 9.11521i 0.343787i
\(704\) 69.7160i 2.62752i
\(705\) −31.9837 −1.20458
\(706\) 16.1272i 0.606954i
\(707\) −19.1124 + 4.06959i −0.718795 + 0.153053i
\(708\) 16.6302 0.625003
\(709\) 3.45898i 0.129905i 0.997888 + 0.0649524i \(0.0206895\pi\)
−0.997888 + 0.0649524i \(0.979310\pi\)
\(710\) −64.4549 −2.41895
\(711\) 1.50395i 0.0564026i
\(712\) −19.2758 −0.722391
\(713\) −11.9040 + 3.27053i −0.445810 + 0.122482i
\(714\) −48.6864 + 10.3668i −1.82204 + 0.387966i
\(715\) −38.1453 −1.42655
\(716\) 50.1493 1.87417
\(717\) 11.8777i 0.443583i
\(718\) 6.97756i 0.260400i
\(719\) 2.89888i 0.108110i −0.998538 0.0540549i \(-0.982785\pi\)
0.998538 0.0540549i \(-0.0172146\pi\)
\(720\) −34.2551 −1.27661
\(721\) 2.98101 + 14.0000i 0.111019 + 0.521387i
\(722\) 24.6674 0.918024
\(723\) 18.4940i 0.687800i
\(724\) 55.7713 2.07273
\(725\) 6.72947 0.249926
\(726\) 3.09622i 0.114912i
\(727\) 48.9506 1.81548 0.907739 0.419536i \(-0.137807\pi\)
0.907739 + 0.419536i \(0.137807\pi\)
\(728\) 107.173 22.8203i 3.97211 0.845778i
\(729\) −1.00000 −0.0370370
\(730\) 67.3773i 2.49374i
\(731\) 5.48196i 0.202758i
\(732\) 43.3693i 1.60298i
\(733\) −43.2655 −1.59805 −0.799024 0.601299i \(-0.794650\pi\)
−0.799024 + 0.601299i \(0.794650\pi\)
\(734\) −56.0408 −2.06850
\(735\) −7.37950 16.5429i −0.272197 0.610193i
\(736\) 22.9409 + 83.5000i 0.845613 + 3.07785i
\(737\) 24.3668 0.897561
\(738\) 13.4820i 0.496278i
\(739\) 51.0111 1.87647 0.938237 0.345994i \(-0.112458\pi\)
0.938237 + 0.345994i \(0.112458\pi\)
\(740\) 39.6083i 1.45603i
\(741\) −14.7408 −0.541516
\(742\) −52.5310 + 11.1854i −1.92847 + 0.410629i
\(743\) 11.9002i 0.436575i −0.975885 0.218287i \(-0.929953\pi\)
0.975885 0.218287i \(-0.0700470\pi\)
\(744\) −22.7004 −0.832238
\(745\) 50.8837i 1.86423i
\(746\) 6.56516i 0.240368i
\(747\) −15.7572 −0.576526
\(748\) 115.429i 4.22050i
\(749\) −7.73651 + 1.64733i −0.282686 + 0.0601921i
\(750\) 23.0511i 0.841708i
\(751\) 3.82447i 0.139557i −0.997563 0.0697785i \(-0.977771\pi\)
0.997563 0.0697785i \(-0.0222292\pi\)
\(752\) 163.611i 5.96629i
\(753\) 21.3346i 0.777477i
\(754\) 50.2345i 1.82943i
\(755\) 12.2204 0.444746
\(756\) 13.6388 2.90409i 0.496037 0.105621i
\(757\) 14.3935i 0.523141i 0.965184 + 0.261570i \(0.0842404\pi\)
−0.965184 + 0.261570i \(0.915760\pi\)
\(758\) 27.9102i 1.01375i
\(759\) 3.98788 + 14.5150i 0.144751 + 0.526862i
\(760\) −71.6272 −2.59819
\(761\) 26.1814i 0.949073i −0.880236 0.474537i \(-0.842616\pi\)
0.880236 0.474537i \(-0.157384\pi\)
\(762\) 51.3827i 1.86140i
\(763\) 11.5340 2.45593i 0.417560 0.0889107i
\(764\) 63.1713i 2.28546i
\(765\) 18.0561 0.652820
\(766\) 13.3119 0.480980
\(767\) 14.8186 0.535070
\(768\) 19.6934i 0.710624i
\(769\) −39.1998 −1.41358 −0.706790 0.707423i \(-0.749858\pi\)
−0.706790 + 0.707423i \(0.749858\pi\)
\(770\) 56.6735 12.0675i 2.04237 0.434881i
\(771\) 15.1973 0.547319
\(772\) 15.6373 0.562798
\(773\) 55.1204 1.98254 0.991272 0.131835i \(-0.0420868\pi\)
0.991272 + 0.131835i \(0.0420868\pi\)
\(774\) 2.11844i 0.0761457i
\(775\) 4.36675i 0.156858i
\(776\) 68.3003 2.45184
\(777\) 1.60017 + 7.51504i 0.0574059 + 0.269600i
\(778\) 42.4876i 1.52325i
\(779\) 15.6937i 0.562286i
\(780\) −64.0530 −2.29347
\(781\) 28.9940i 1.03749i
\(782\) −23.9041 87.0059i −0.854810 3.11133i
\(783\) 3.96693i 0.141766i
\(784\) −84.6242 + 37.7495i −3.02229 + 1.34820i
\(785\) 24.5411 0.875908
\(786\) 27.3638 0.976033
\(787\) 37.0466 1.32057 0.660284 0.751016i \(-0.270436\pi\)