Properties

Label 171.3.p.c.46.1
Level $171$
Weight $3$
Character 171.46
Analytic conductor $4.659$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.65941252056\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.92607408.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 46.1
Root \(0.500000 + 2.69511i\) of defining polynomial
Character \(\chi\) \(=\) 171.46
Dual form 171.3.p.c.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.08403 - 1.78057i) q^{2} +(4.34085 + 7.51857i) q^{4} +(-2.32722 + 4.03087i) q^{5} -10.6817 q^{7} -16.6722i q^{8} +O(q^{10})\) \(q+(-3.08403 - 1.78057i) q^{2} +(4.34085 + 7.51857i) q^{4} +(-2.32722 + 4.03087i) q^{5} -10.6817 q^{7} -16.6722i q^{8} +(14.3545 - 8.28756i) q^{10} +6.37280 q^{11} +(15.3770 - 8.87792i) q^{13} +(32.9427 + 19.0195i) q^{14} +(-12.3225 + 21.3432i) q^{16} +(5.84976 - 10.1321i) q^{17} +(-3.88643 - 18.5983i) q^{19} -40.4085 q^{20} +(-19.6539 - 11.3472i) q^{22} +(-13.9817 - 24.2170i) q^{23} +(1.66807 + 2.88918i) q^{25} -63.2310 q^{26} +(-46.3676 - 80.3110i) q^{28} +(33.2498 - 19.1968i) q^{29} +42.9440i q^{31} +(18.2521 - 10.5379i) q^{32} +(-36.0817 + 20.8318i) q^{34} +(24.8587 - 43.0565i) q^{35} -33.9790i q^{37} +(-21.1296 + 64.2778i) q^{38} +(67.2032 + 38.7998i) q^{40} +(-16.3728 - 9.45284i) q^{41} +(26.5089 - 45.9148i) q^{43} +(27.6634 + 47.9143i) q^{44} +99.5813i q^{46} +(12.0272 + 20.8318i) q^{47} +65.0986 q^{49} -11.8804i q^{50} +(133.499 + 77.0754i) q^{52} +(13.3224 - 7.69168i) q^{53} +(-14.8309 + 25.6879i) q^{55} +178.087i q^{56} -136.725 q^{58} +(-25.6539 - 14.8113i) q^{59} +(-21.3403 - 36.9626i) q^{61} +(76.4648 - 132.441i) q^{62} +23.5266 q^{64} +82.6436i q^{65} +(-15.1585 + 8.75178i) q^{67} +101.572 q^{68} +(-153.330 + 88.5252i) q^{70} +(74.6028 + 43.0719i) q^{71} +(46.2352 - 80.0817i) q^{73} +(-60.5019 + 104.792i) q^{74} +(122.962 - 109.953i) q^{76} -68.0723 q^{77} +(-26.3908 - 15.2367i) q^{79} +(-57.3545 - 99.3409i) q^{80} +(33.6629 + 58.3058i) q^{82} -77.1154 q^{83} +(27.2274 + 47.1592i) q^{85} +(-163.509 + 94.4019i) q^{86} -106.248i q^{88} +(76.8129 - 44.3479i) q^{89} +(-164.253 + 94.8312i) q^{91} +(121.385 - 210.244i) q^{92} -85.6613i q^{94} +(84.0118 + 27.6166i) q^{95} +(-1.82351 - 1.05281i) q^{97} +(-200.766 - 115.912i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.08403 1.78057i −1.54202 0.890284i −0.998711 0.0507494i \(-0.983839\pi\)
−0.543306 0.839535i \(-0.682828\pi\)
\(3\) 0 0
\(4\) 4.34085 + 7.51857i 1.08521 + 1.87964i
\(5\) −2.32722 + 4.03087i −0.465445 + 0.806174i −0.999221 0.0394517i \(-0.987439\pi\)
0.533777 + 0.845625i \(0.320772\pi\)
\(6\) 0 0
\(7\) −10.6817 −1.52596 −0.762978 0.646424i \(-0.776264\pi\)
−0.762978 + 0.646424i \(0.776264\pi\)
\(8\) 16.6722i 2.08402i
\(9\) 0 0
\(10\) 14.3545 8.28756i 1.43545 0.828756i
\(11\) 6.37280 0.579346 0.289673 0.957126i \(-0.406453\pi\)
0.289673 + 0.957126i \(0.406453\pi\)
\(12\) 0 0
\(13\) 15.3770 8.87792i 1.18285 0.682917i 0.226176 0.974087i \(-0.427378\pi\)
0.956671 + 0.291170i \(0.0940444\pi\)
\(14\) 32.9427 + 19.0195i 2.35305 + 1.35853i
\(15\) 0 0
\(16\) −12.3225 + 21.3432i −0.770157 + 1.33395i
\(17\) 5.84976 10.1321i 0.344104 0.596005i −0.641087 0.767468i \(-0.721516\pi\)
0.985191 + 0.171463i \(0.0548495\pi\)
\(18\) 0 0
\(19\) −3.88643 18.5983i −0.204549 0.978856i
\(20\) −40.4085 −2.02042
\(21\) 0 0
\(22\) −19.6539 11.3472i −0.893361 0.515782i
\(23\) −13.9817 24.2170i −0.607899 1.05291i −0.991586 0.129448i \(-0.958679\pi\)
0.383688 0.923463i \(-0.374654\pi\)
\(24\) 0 0
\(25\) 1.66807 + 2.88918i 0.0667228 + 0.115567i
\(26\) −63.2310 −2.43196
\(27\) 0 0
\(28\) −46.3676 80.3110i −1.65599 2.86825i
\(29\) 33.2498 19.1968i 1.14655 0.661958i 0.198502 0.980100i \(-0.436392\pi\)
0.948043 + 0.318142i \(0.103059\pi\)
\(30\) 0 0
\(31\) 42.9440i 1.38529i 0.721278 + 0.692645i \(0.243555\pi\)
−0.721278 + 0.692645i \(0.756445\pi\)
\(32\) 18.2521 10.5379i 0.570378 0.329308i
\(33\) 0 0
\(34\) −36.0817 + 20.8318i −1.06123 + 0.612700i
\(35\) 24.8587 43.0565i 0.710248 1.23019i
\(36\) 0 0
\(37\) 33.9790i 0.918351i −0.888346 0.459176i \(-0.848145\pi\)
0.888346 0.459176i \(-0.151855\pi\)
\(38\) −21.1296 + 64.2778i −0.556043 + 1.69152i
\(39\) 0 0
\(40\) 67.2032 + 38.7998i 1.68008 + 0.969995i
\(41\) −16.3728 9.45284i −0.399337 0.230557i 0.286861 0.957972i \(-0.407388\pi\)
−0.686198 + 0.727415i \(0.740722\pi\)
\(42\) 0 0
\(43\) 26.5089 45.9148i 0.616486 1.06779i −0.373635 0.927576i \(-0.621889\pi\)
0.990122 0.140210i \(-0.0447778\pi\)
\(44\) 27.6634 + 47.9143i 0.628713 + 1.08896i
\(45\) 0 0
\(46\) 99.5813i 2.16481i
\(47\) 12.0272 + 20.8318i 0.255899 + 0.443230i 0.965139 0.261737i \(-0.0842952\pi\)
−0.709240 + 0.704967i \(0.750962\pi\)
\(48\) 0 0
\(49\) 65.0986 1.32854
\(50\) 11.8804i 0.237609i
\(51\) 0 0
\(52\) 133.499 + 77.0754i 2.56728 + 1.48222i
\(53\) 13.3224 7.69168i 0.251366 0.145126i −0.369024 0.929420i \(-0.620308\pi\)
0.620389 + 0.784294i \(0.286975\pi\)
\(54\) 0 0
\(55\) −14.8309 + 25.6879i −0.269653 + 0.467053i
\(56\) 178.087i 3.18012i
\(57\) 0 0
\(58\) −136.725 −2.35732
\(59\) −25.6539 14.8113i −0.434813 0.251039i 0.266582 0.963812i \(-0.414106\pi\)
−0.701395 + 0.712773i \(0.747439\pi\)
\(60\) 0 0
\(61\) −21.3403 36.9626i −0.349842 0.605944i 0.636379 0.771376i \(-0.280431\pi\)
−0.986221 + 0.165433i \(0.947098\pi\)
\(62\) 76.4648 132.441i 1.23330 2.13614i
\(63\) 0 0
\(64\) 23.5266 0.367603
\(65\) 82.6436i 1.27144i
\(66\) 0 0
\(67\) −15.1585 + 8.75178i −0.226247 + 0.130624i −0.608839 0.793294i \(-0.708365\pi\)
0.382593 + 0.923917i \(0.375031\pi\)
\(68\) 101.572 1.49370
\(69\) 0 0
\(70\) −153.330 + 88.5252i −2.19043 + 1.26465i
\(71\) 74.6028 + 43.0719i 1.05074 + 0.606647i 0.922857 0.385142i \(-0.125847\pi\)
0.127886 + 0.991789i \(0.459181\pi\)
\(72\) 0 0
\(73\) 46.2352 80.0817i 0.633359 1.09701i −0.353502 0.935434i \(-0.615009\pi\)
0.986860 0.161576i \(-0.0516576\pi\)
\(74\) −60.5019 + 104.792i −0.817593 + 1.41611i
\(75\) 0 0
\(76\) 122.962 109.953i 1.61792 1.44674i
\(77\) −68.0723 −0.884056
\(78\) 0 0
\(79\) −26.3908 15.2367i −0.334060 0.192870i 0.323582 0.946200i \(-0.395113\pi\)
−0.657642 + 0.753330i \(0.728446\pi\)
\(80\) −57.3545 99.3409i −0.716931 1.24176i
\(81\) 0 0
\(82\) 33.6629 + 58.3058i 0.410523 + 0.711046i
\(83\) −77.1154 −0.929101 −0.464551 0.885547i \(-0.653784\pi\)
−0.464551 + 0.885547i \(0.653784\pi\)
\(84\) 0 0
\(85\) 27.2274 + 47.1592i 0.320322 + 0.554815i
\(86\) −163.509 + 94.4019i −1.90127 + 1.09770i
\(87\) 0 0
\(88\) 106.248i 1.20737i
\(89\) 76.8129 44.3479i 0.863066 0.498291i −0.00197195 0.999998i \(-0.500628\pi\)
0.865038 + 0.501707i \(0.167294\pi\)
\(90\) 0 0
\(91\) −164.253 + 94.8312i −1.80497 + 1.04210i
\(92\) 121.385 210.244i 1.31940 2.28526i
\(93\) 0 0
\(94\) 85.6613i 0.911291i
\(95\) 84.0118 + 27.6166i 0.884334 + 0.290702i
\(96\) 0 0
\(97\) −1.82351 1.05281i −0.0187991 0.0108537i 0.490571 0.871401i \(-0.336788\pi\)
−0.509370 + 0.860548i \(0.670122\pi\)
\(98\) −200.766 115.912i −2.04864 1.18278i
\(99\) 0 0
\(100\) −14.4817 + 25.0830i −0.144817 + 0.250830i
\(101\) 13.7690 + 23.8486i 0.136327 + 0.236125i 0.926104 0.377269i \(-0.123137\pi\)
−0.789777 + 0.613395i \(0.789804\pi\)
\(102\) 0 0
\(103\) 102.351i 0.993696i −0.867837 0.496848i \(-0.834491\pi\)
0.867837 0.496848i \(-0.165509\pi\)
\(104\) −148.014 256.368i −1.42321 2.46508i
\(105\) 0 0
\(106\) −54.7823 −0.516814
\(107\) 0.549592i 0.00513638i 0.999997 + 0.00256819i \(0.000817481\pi\)
−0.999997 + 0.00256819i \(0.999183\pi\)
\(108\) 0 0
\(109\) 80.7219 + 46.6048i 0.740568 + 0.427567i 0.822276 0.569089i \(-0.192704\pi\)
−0.0817076 + 0.996656i \(0.526037\pi\)
\(110\) 91.4782 52.8150i 0.831620 0.480136i
\(111\) 0 0
\(112\) 131.625 227.982i 1.17523 2.03555i
\(113\) 55.4186i 0.490430i −0.969469 0.245215i \(-0.921141\pi\)
0.969469 0.245215i \(-0.0788586\pi\)
\(114\) 0 0
\(115\) 130.154 1.13177
\(116\) 288.665 + 166.661i 2.48849 + 1.43673i
\(117\) 0 0
\(118\) 52.7451 + 91.3572i 0.446992 + 0.774214i
\(119\) −62.4854 + 108.228i −0.525087 + 0.909478i
\(120\) 0 0
\(121\) −80.3874 −0.664359
\(122\) 151.992i 1.24583i
\(123\) 0 0
\(124\) −322.877 + 186.413i −2.60385 + 1.50333i
\(125\) −131.889 −1.05511
\(126\) 0 0
\(127\) −82.7181 + 47.7573i −0.651324 + 0.376042i −0.788963 0.614441i \(-0.789382\pi\)
0.137640 + 0.990482i \(0.456048\pi\)
\(128\) −145.565 84.0422i −1.13723 0.656580i
\(129\) 0 0
\(130\) 147.153 254.876i 1.13194 1.96058i
\(131\) 84.0762 145.624i 0.641803 1.11164i −0.343227 0.939252i \(-0.611520\pi\)
0.985030 0.172383i \(-0.0551466\pi\)
\(132\) 0 0
\(133\) 41.5136 + 198.661i 0.312133 + 1.49369i
\(134\) 62.3326 0.465168
\(135\) 0 0
\(136\) −168.924 97.5281i −1.24209 0.717119i
\(137\) −59.3774 102.845i −0.433412 0.750691i 0.563753 0.825943i \(-0.309357\pi\)
−0.997165 + 0.0752526i \(0.976024\pi\)
\(138\) 0 0
\(139\) −55.1822 95.5784i −0.396994 0.687614i 0.596359 0.802718i \(-0.296613\pi\)
−0.993354 + 0.115104i \(0.963280\pi\)
\(140\) 431.631 3.08308
\(141\) 0 0
\(142\) −153.385 265.671i −1.08018 1.87092i
\(143\) 97.9947 56.5772i 0.685277 0.395645i
\(144\) 0 0
\(145\) 178.701i 1.23242i
\(146\) −285.182 + 164.650i −1.95330 + 1.12774i
\(147\) 0 0
\(148\) 255.473 147.498i 1.72617 0.996605i
\(149\) −28.8719 + 50.0077i −0.193771 + 0.335622i −0.946497 0.322712i \(-0.895405\pi\)
0.752726 + 0.658334i \(0.228739\pi\)
\(150\) 0 0
\(151\) 205.459i 1.36066i 0.732908 + 0.680328i \(0.238163\pi\)
−0.732908 + 0.680328i \(0.761837\pi\)
\(152\) −310.073 + 64.7951i −2.03996 + 0.426284i
\(153\) 0 0
\(154\) 209.937 + 121.207i 1.36323 + 0.787061i
\(155\) −173.102 99.9403i −1.11678 0.644776i
\(156\) 0 0
\(157\) −55.6080 + 96.3159i −0.354191 + 0.613477i −0.986979 0.160848i \(-0.948577\pi\)
0.632788 + 0.774325i \(0.281910\pi\)
\(158\) 54.2600 + 93.9811i 0.343418 + 0.594817i
\(159\) 0 0
\(160\) 98.0958i 0.613099i
\(161\) 149.348 + 258.678i 0.927627 + 1.60670i
\(162\) 0 0
\(163\) 69.1905 0.424481 0.212241 0.977217i \(-0.431924\pi\)
0.212241 + 0.977217i \(0.431924\pi\)
\(164\) 164.133i 1.00081i
\(165\) 0 0
\(166\) 237.827 + 137.309i 1.43269 + 0.827164i
\(167\) −181.817 + 104.972i −1.08873 + 0.628577i −0.933237 0.359261i \(-0.883029\pi\)
−0.155490 + 0.987837i \(0.549696\pi\)
\(168\) 0 0
\(169\) 73.1350 126.674i 0.432751 0.749547i
\(170\) 193.921i 1.14071i
\(171\) 0 0
\(172\) 460.285 2.67607
\(173\) 264.781 + 152.871i 1.53053 + 0.883649i 0.999337 + 0.0363949i \(0.0115874\pi\)
0.531188 + 0.847254i \(0.321746\pi\)
\(174\) 0 0
\(175\) −17.8178 30.8613i −0.101816 0.176351i
\(176\) −78.5290 + 136.016i −0.446187 + 0.772819i
\(177\) 0 0
\(178\) −315.858 −1.77448
\(179\) 303.001i 1.69274i −0.532593 0.846371i \(-0.678782\pi\)
0.532593 0.846371i \(-0.321218\pi\)
\(180\) 0 0
\(181\) −62.8763 + 36.3016i −0.347383 + 0.200561i −0.663532 0.748148i \(-0.730943\pi\)
0.316149 + 0.948709i \(0.397610\pi\)
\(182\) 675.414 3.71107
\(183\) 0 0
\(184\) −403.749 + 233.104i −2.19429 + 1.26687i
\(185\) 136.965 + 79.0767i 0.740350 + 0.427442i
\(186\) 0 0
\(187\) 37.2794 64.5698i 0.199355 0.345293i
\(188\) −104.417 + 180.855i −0.555409 + 0.961997i
\(189\) 0 0
\(190\) −209.922 234.759i −1.10485 1.23558i
\(191\) 48.5734 0.254311 0.127156 0.991883i \(-0.459415\pi\)
0.127156 + 0.991883i \(0.459415\pi\)
\(192\) 0 0
\(193\) 9.48401 + 5.47559i 0.0491399 + 0.0283710i 0.524369 0.851491i \(-0.324301\pi\)
−0.475229 + 0.879862i \(0.657635\pi\)
\(194\) 3.74919 + 6.49378i 0.0193257 + 0.0334731i
\(195\) 0 0
\(196\) 282.583 + 489.448i 1.44175 + 2.49718i
\(197\) −104.442 −0.530163 −0.265082 0.964226i \(-0.585399\pi\)
−0.265082 + 0.964226i \(0.585399\pi\)
\(198\) 0 0
\(199\) −140.643 243.602i −0.706751 1.22413i −0.966056 0.258333i \(-0.916827\pi\)
0.259305 0.965795i \(-0.416506\pi\)
\(200\) 48.1689 27.8103i 0.240844 0.139052i
\(201\) 0 0
\(202\) 98.0667i 0.485479i
\(203\) −355.164 + 205.054i −1.74958 + 1.01012i
\(204\) 0 0
\(205\) 76.2063 43.9977i 0.371738 0.214623i
\(206\) −182.242 + 315.653i −0.884672 + 1.53230i
\(207\) 0 0
\(208\) 437.593i 2.10381i
\(209\) −24.7674 118.523i −0.118504 0.567096i
\(210\) 0 0
\(211\) 89.2808 + 51.5463i 0.423132 + 0.244295i 0.696416 0.717638i \(-0.254777\pi\)
−0.273285 + 0.961933i \(0.588110\pi\)
\(212\) 115.661 + 66.7768i 0.545570 + 0.314985i
\(213\) 0 0
\(214\) 0.978587 1.69496i 0.00457284 0.00792038i
\(215\) 123.384 + 213.708i 0.573880 + 0.993990i
\(216\) 0 0
\(217\) 458.715i 2.11389i
\(218\) −165.966 287.462i −0.761313 1.31863i
\(219\) 0 0
\(220\) −257.515 −1.17052
\(221\) 207.735i 0.939977i
\(222\) 0 0
\(223\) −68.9560 39.8118i −0.309220 0.178528i 0.337357 0.941377i \(-0.390467\pi\)
−0.646577 + 0.762848i \(0.723800\pi\)
\(224\) −194.963 + 112.562i −0.870372 + 0.502510i
\(225\) 0 0
\(226\) −98.6766 + 170.913i −0.436622 + 0.756252i
\(227\) 131.031i 0.577228i −0.957446 0.288614i \(-0.906806\pi\)
0.957446 0.288614i \(-0.0931944\pi\)
\(228\) 0 0
\(229\) 30.3537 0.132549 0.0662745 0.997801i \(-0.478889\pi\)
0.0662745 + 0.997801i \(0.478889\pi\)
\(230\) −401.399 231.748i −1.74521 1.00760i
\(231\) 0 0
\(232\) −320.052 554.346i −1.37953 2.38942i
\(233\) 47.0484 81.4902i 0.201924 0.349743i −0.747224 0.664572i \(-0.768614\pi\)
0.949148 + 0.314829i \(0.101947\pi\)
\(234\) 0 0
\(235\) −111.960 −0.476427
\(236\) 257.175i 1.08972i
\(237\) 0 0
\(238\) 385.414 222.519i 1.61939 0.934954i
\(239\) −375.297 −1.57028 −0.785141 0.619317i \(-0.787409\pi\)
−0.785141 + 0.619317i \(0.787409\pi\)
\(240\) 0 0
\(241\) 0.482424 0.278528i 0.00200176 0.00115572i −0.498999 0.866603i \(-0.666299\pi\)
0.501001 + 0.865447i \(0.332965\pi\)
\(242\) 247.917 + 143.135i 1.02445 + 0.591468i
\(243\) 0 0
\(244\) 185.270 320.898i 0.759305 1.31515i
\(245\) −151.499 + 262.404i −0.618363 + 1.07104i
\(246\) 0 0
\(247\) −224.876 251.482i −0.910428 1.01815i
\(248\) 715.969 2.88697
\(249\) 0 0
\(250\) 406.750 + 234.837i 1.62700 + 0.939350i
\(251\) −117.309 203.185i −0.467367 0.809504i 0.531938 0.846783i \(-0.321464\pi\)
−0.999305 + 0.0372799i \(0.988131\pi\)
\(252\) 0 0
\(253\) −89.1024 154.330i −0.352183 0.610000i
\(254\) 340.141 1.33914
\(255\) 0 0
\(256\) 252.232 + 436.879i 0.985283 + 1.70656i
\(257\) 11.0702 6.39141i 0.0430749 0.0248693i −0.478308 0.878192i \(-0.658750\pi\)
0.521383 + 0.853323i \(0.325416\pi\)
\(258\) 0 0
\(259\) 362.953i 1.40136i
\(260\) −621.361 + 358.743i −2.38985 + 1.37978i
\(261\) 0 0
\(262\) −518.588 + 299.407i −1.97934 + 1.14277i
\(263\) −106.457 + 184.389i −0.404780 + 0.701099i −0.994296 0.106657i \(-0.965985\pi\)
0.589516 + 0.807757i \(0.299319\pi\)
\(264\) 0 0
\(265\) 71.6010i 0.270193i
\(266\) 225.700 686.595i 0.848497 2.58119i
\(267\) 0 0
\(268\) −131.602 75.9803i −0.491051 0.283508i
\(269\) 438.717 + 253.293i 1.63092 + 0.941610i 0.983811 + 0.179211i \(0.0573544\pi\)
0.647106 + 0.762400i \(0.275979\pi\)
\(270\) 0 0
\(271\) 110.063 190.635i 0.406136 0.703449i −0.588317 0.808631i \(-0.700209\pi\)
0.994453 + 0.105182i \(0.0335425\pi\)
\(272\) 144.168 + 249.706i 0.530028 + 0.918035i
\(273\) 0 0
\(274\) 422.902i 1.54344i
\(275\) 10.6303 + 18.4122i 0.0386556 + 0.0669534i
\(276\) 0 0
\(277\) 262.083 0.946148 0.473074 0.881023i \(-0.343144\pi\)
0.473074 + 0.881023i \(0.343144\pi\)
\(278\) 393.023i 1.41375i
\(279\) 0 0
\(280\) −717.844 414.448i −2.56373 1.48017i
\(281\) 346.203 199.880i 1.23204 0.711317i 0.264583 0.964363i \(-0.414766\pi\)
0.967454 + 0.253046i \(0.0814322\pi\)
\(282\) 0 0
\(283\) 41.2358 71.4225i 0.145710 0.252376i −0.783928 0.620852i \(-0.786787\pi\)
0.929637 + 0.368475i \(0.120120\pi\)
\(284\) 747.875i 2.63336i
\(285\) 0 0
\(286\) −402.959 −1.40895
\(287\) 174.889 + 100.972i 0.609370 + 0.351820i
\(288\) 0 0
\(289\) 76.0605 + 131.741i 0.263185 + 0.455850i
\(290\) 318.189 551.120i 1.09720 1.90041i
\(291\) 0 0
\(292\) 802.800 2.74931
\(293\) 223.552i 0.762977i 0.924374 + 0.381489i \(0.124588\pi\)
−0.924374 + 0.381489i \(0.875412\pi\)
\(294\) 0 0
\(295\) 119.405 68.9384i 0.404762 0.233690i
\(296\) −566.503 −1.91386
\(297\) 0 0
\(298\) 178.084 102.817i 0.597598 0.345023i
\(299\) −429.993 248.256i −1.43810 0.830289i
\(300\) 0 0
\(301\) −283.160 + 490.448i −0.940731 + 1.62939i
\(302\) 365.834 633.643i 1.21137 2.09816i
\(303\) 0 0
\(304\) 444.838 + 146.229i 1.46328 + 0.481015i
\(305\) 198.655 0.651328
\(306\) 0 0
\(307\) 339.034 + 195.741i 1.10434 + 0.637594i 0.937359 0.348366i \(-0.113263\pi\)
0.166986 + 0.985959i \(0.446597\pi\)
\(308\) −295.492 511.806i −0.959388 1.66171i
\(309\) 0 0
\(310\) 355.901 + 616.439i 1.14807 + 1.98851i
\(311\) −375.828 −1.20845 −0.604224 0.796814i \(-0.706517\pi\)
−0.604224 + 0.796814i \(0.706517\pi\)
\(312\) 0 0
\(313\) 75.3935 + 130.585i 0.240874 + 0.417206i 0.960963 0.276675i \(-0.0892327\pi\)
−0.720090 + 0.693881i \(0.755899\pi\)
\(314\) 342.994 198.028i 1.09234 0.630661i
\(315\) 0 0
\(316\) 264.561i 0.837218i
\(317\) 438.163 252.973i 1.38222 0.798024i 0.389796 0.920901i \(-0.372546\pi\)
0.992422 + 0.122878i \(0.0392123\pi\)
\(318\) 0 0
\(319\) 211.895 122.337i 0.664246 0.383503i
\(320\) −54.7517 + 94.8327i −0.171099 + 0.296352i
\(321\) 0 0
\(322\) 1063.70i 3.30341i
\(323\) −211.174 69.4179i −0.653789 0.214916i
\(324\) 0 0
\(325\) 51.2998 + 29.6180i 0.157846 + 0.0911322i
\(326\) −213.386 123.198i −0.654558 0.377909i
\(327\) 0 0
\(328\) −157.599 + 272.970i −0.480485 + 0.832225i
\(329\) −128.471 222.519i −0.390491 0.676349i
\(330\) 0 0
\(331\) 443.028i 1.33845i −0.743058 0.669227i \(-0.766626\pi\)
0.743058 0.669227i \(-0.233374\pi\)
\(332\) −334.746 579.797i −1.00827 1.74638i
\(333\) 0 0
\(334\) 747.642 2.23845
\(335\) 81.4694i 0.243192i
\(336\) 0 0
\(337\) 168.764 + 97.4357i 0.500782 + 0.289127i 0.729037 0.684475i \(-0.239968\pi\)
−0.228254 + 0.973602i \(0.573302\pi\)
\(338\) −451.102 + 260.444i −1.33462 + 0.770543i
\(339\) 0 0
\(340\) −236.380 + 409.422i −0.695235 + 1.20418i
\(341\) 273.674i 0.802562i
\(342\) 0 0
\(343\) −171.960 −0.501341
\(344\) −765.498 441.961i −2.22529 1.28477i
\(345\) 0 0
\(346\) −544.396 942.921i −1.57340 2.72520i
\(347\) −262.446 + 454.570i −0.756329 + 1.31000i 0.188382 + 0.982096i \(0.439676\pi\)
−0.944711 + 0.327905i \(0.893658\pi\)
\(348\) 0 0
\(349\) −369.064 −1.05749 −0.528745 0.848781i \(-0.677337\pi\)
−0.528745 + 0.848781i \(0.677337\pi\)
\(350\) 126.903i 0.362581i
\(351\) 0 0
\(352\) 116.317 67.1557i 0.330446 0.190783i
\(353\) −323.725 −0.917067 −0.458533 0.888677i \(-0.651625\pi\)
−0.458533 + 0.888677i \(0.651625\pi\)
\(354\) 0 0
\(355\) −347.235 + 200.476i −0.978126 + 0.564721i
\(356\) 666.866 + 385.015i 1.87322 + 1.08150i
\(357\) 0 0
\(358\) −539.514 + 934.465i −1.50702 + 2.61024i
\(359\) 6.25614 10.8359i 0.0174266 0.0301837i −0.857181 0.515016i \(-0.827786\pi\)
0.874607 + 0.484832i \(0.161119\pi\)
\(360\) 0 0
\(361\) −330.791 + 144.562i −0.916320 + 0.400448i
\(362\) 258.550 0.714227
\(363\) 0 0
\(364\) −1425.99 823.296i −3.91756 2.26180i
\(365\) 215.199 + 372.736i 0.589587 + 1.02119i
\(366\) 0 0
\(367\) −44.3159 76.7574i −0.120752 0.209148i 0.799313 0.600916i \(-0.205197\pi\)
−0.920064 + 0.391767i \(0.871864\pi\)
\(368\) 689.157 1.87271
\(369\) 0 0
\(370\) −281.603 487.750i −0.761089 1.31824i
\(371\) −142.306 + 82.1602i −0.383573 + 0.221456i
\(372\) 0 0
\(373\) 406.489i 1.08978i −0.838507 0.544892i \(-0.816571\pi\)
0.838507 0.544892i \(-0.183429\pi\)
\(374\) −229.942 + 132.757i −0.614818 + 0.354965i
\(375\) 0 0
\(376\) 347.311 200.520i 0.923699 0.533298i
\(377\) 340.855 590.378i 0.904125 1.56599i
\(378\) 0 0
\(379\) 433.800i 1.14459i 0.820047 + 0.572296i \(0.193947\pi\)
−0.820047 + 0.572296i \(0.806053\pi\)
\(380\) 157.045 + 751.528i 0.413275 + 1.97770i
\(381\) 0 0
\(382\) −149.802 86.4883i −0.392152 0.226409i
\(383\) 355.819 + 205.432i 0.929031 + 0.536377i 0.886505 0.462719i \(-0.153126\pi\)
0.0425263 + 0.999095i \(0.486459\pi\)
\(384\) 0 0
\(385\) 158.419 274.391i 0.411479 0.712703i
\(386\) −19.4993 33.7738i −0.0505164 0.0874970i
\(387\) 0 0
\(388\) 18.2803i 0.0471141i
\(389\) 94.6013 + 163.854i 0.243191 + 0.421219i 0.961621 0.274380i \(-0.0884725\pi\)
−0.718430 + 0.695599i \(0.755139\pi\)
\(390\) 0 0
\(391\) −327.158 −0.836721
\(392\) 1085.33i 2.76871i
\(393\) 0 0
\(394\) 322.103 + 185.966i 0.817521 + 0.471996i
\(395\) 122.834 70.9185i 0.310973 0.179540i
\(396\) 0 0
\(397\) −220.839 + 382.504i −0.556269 + 0.963487i 0.441534 + 0.897244i \(0.354434\pi\)
−0.997804 + 0.0662425i \(0.978899\pi\)
\(398\) 1001.70i 2.51684i
\(399\) 0 0
\(400\) −82.2192 −0.205548
\(401\) −320.526 185.056i −0.799316 0.461485i 0.0439159 0.999035i \(-0.486017\pi\)
−0.843232 + 0.537550i \(0.819350\pi\)
\(402\) 0 0
\(403\) 381.254 + 660.351i 0.946039 + 1.63859i
\(404\) −119.538 + 207.047i −0.295887 + 0.512491i
\(405\) 0 0
\(406\) 1460.45 3.59717
\(407\) 216.541i 0.532043i
\(408\) 0 0
\(409\) 418.387 241.556i 1.02295 0.590602i 0.107995 0.994151i \(-0.465557\pi\)
0.914958 + 0.403550i \(0.132224\pi\)
\(410\) −313.364 −0.764302
\(411\) 0 0
\(412\) 769.531 444.289i 1.86779 1.07837i
\(413\) 274.028 + 158.210i 0.663505 + 0.383075i
\(414\) 0 0
\(415\) 179.465 310.842i 0.432445 0.749017i
\(416\) 187.109 324.082i 0.449780 0.779042i
\(417\) 0 0
\(418\) −134.655 + 409.630i −0.322141 + 0.979975i
\(419\) 295.264 0.704687 0.352344 0.935871i \(-0.385385\pi\)
0.352344 + 0.935871i \(0.385385\pi\)
\(420\) 0 0
\(421\) −449.581 259.566i −1.06789 0.616545i −0.140284 0.990111i \(-0.544802\pi\)
−0.927604 + 0.373566i \(0.878135\pi\)
\(422\) −183.563 317.941i −0.434984 0.753415i
\(423\) 0 0
\(424\) −128.237 222.113i −0.302446 0.523851i
\(425\) 39.0312 0.0918382
\(426\) 0 0
\(427\) 227.951 + 394.823i 0.533843 + 0.924644i
\(428\) −4.13215 + 2.38570i −0.00965455 + 0.00557406i
\(429\) 0 0
\(430\) 878.777i 2.04367i
\(431\) 195.895 113.100i 0.454514 0.262414i −0.255221 0.966883i \(-0.582148\pi\)
0.709735 + 0.704469i \(0.248815\pi\)
\(432\) 0 0
\(433\) −251.769 + 145.359i −0.581452 + 0.335702i −0.761710 0.647918i \(-0.775640\pi\)
0.180258 + 0.983619i \(0.442307\pi\)
\(434\) −816.773 + 1414.69i −1.88197 + 3.25966i
\(435\) 0 0
\(436\) 809.218i 1.85600i
\(437\) −396.055 + 354.152i −0.906304 + 0.810417i
\(438\) 0 0
\(439\) 251.921 + 145.447i 0.573852 + 0.331314i 0.758686 0.651456i \(-0.225842\pi\)
−0.184834 + 0.982770i \(0.559175\pi\)
\(440\) 428.273 + 247.264i 0.973348 + 0.561963i
\(441\) 0 0
\(442\) −369.886 + 640.662i −0.836847 + 1.44946i
\(443\) 217.722 + 377.106i 0.491473 + 0.851256i 0.999952 0.00981853i \(-0.00312539\pi\)
−0.508479 + 0.861074i \(0.669792\pi\)
\(444\) 0 0
\(445\) 412.830i 0.927708i
\(446\) 141.775 + 245.562i 0.317882 + 0.550587i
\(447\) 0 0
\(448\) −251.304 −0.560947
\(449\) 263.736i 0.587385i −0.955900 0.293692i \(-0.905116\pi\)
0.955900 0.293692i \(-0.0948842\pi\)
\(450\) 0 0
\(451\) −104.341 60.2411i −0.231354 0.133572i
\(452\) 416.669 240.564i 0.921833 0.532221i
\(453\) 0 0
\(454\) −233.309 + 404.103i −0.513897 + 0.890096i
\(455\) 882.774i 1.94016i
\(456\) 0 0
\(457\) 641.042 1.40272 0.701359 0.712809i \(-0.252577\pi\)
0.701359 + 0.712809i \(0.252577\pi\)
\(458\) −93.6119 54.0469i −0.204393 0.118006i
\(459\) 0 0
\(460\) 564.978 + 978.570i 1.22821 + 2.12733i
\(461\) 323.490 560.302i 0.701714 1.21540i −0.266150 0.963932i \(-0.585752\pi\)
0.967864 0.251473i \(-0.0809150\pi\)
\(462\) 0 0
\(463\) −407.362 −0.879831 −0.439916 0.898039i \(-0.644992\pi\)
−0.439916 + 0.898039i \(0.644992\pi\)
\(464\) 946.211i 2.03925i
\(465\) 0 0
\(466\) −290.198 + 167.546i −0.622742 + 0.359540i
\(467\) −146.962 −0.314694 −0.157347 0.987543i \(-0.550294\pi\)
−0.157347 + 0.987543i \(0.550294\pi\)
\(468\) 0 0
\(469\) 161.919 93.4838i 0.345242 0.199326i
\(470\) 345.290 + 199.353i 0.734659 + 0.424155i
\(471\) 0 0
\(472\) −246.936 + 427.706i −0.523170 + 0.906158i
\(473\) 168.936 292.606i 0.357159 0.618617i
\(474\) 0 0
\(475\) 47.2509 42.2518i 0.0994757 0.0889512i
\(476\) −1084.96 −2.27932
\(477\) 0 0
\(478\) 1157.43 + 668.242i 2.42140 + 1.39800i
\(479\) 309.698 + 536.413i 0.646552 + 1.11986i 0.983941 + 0.178495i \(0.0571230\pi\)
−0.337389 + 0.941365i \(0.609544\pi\)
\(480\) 0 0
\(481\) −301.663 522.495i −0.627158 1.08627i
\(482\) −1.98375 −0.00411566
\(483\) 0 0
\(484\) −348.949 604.398i −0.720970 1.24876i
\(485\) 8.48745 4.90023i 0.0174999 0.0101036i
\(486\) 0 0
\(487\) 343.861i 0.706080i 0.935608 + 0.353040i \(0.114852\pi\)
−0.935608 + 0.353040i \(0.885148\pi\)
\(488\) −616.245 + 355.789i −1.26280 + 0.729077i
\(489\) 0 0
\(490\) 934.456 539.508i 1.90705 1.10104i
\(491\) 250.993 434.733i 0.511187 0.885402i −0.488729 0.872436i \(-0.662539\pi\)
0.999916 0.0129665i \(-0.00412747\pi\)
\(492\) 0 0
\(493\) 449.187i 0.911129i
\(494\) 245.743 + 1175.99i 0.497455 + 2.38054i
\(495\) 0 0
\(496\) −916.564 529.178i −1.84791 1.06689i
\(497\) −796.884 460.081i −1.60339 0.925717i
\(498\) 0 0
\(499\) 453.717 785.861i 0.909253 1.57487i 0.0941479 0.995558i \(-0.469987\pi\)
0.815105 0.579314i \(-0.196679\pi\)
\(500\) −572.510 991.616i −1.14502 1.98323i
\(501\) 0 0
\(502\) 835.508i 1.66436i
\(503\) −183.800 318.352i −0.365408 0.632906i 0.623433 0.781877i \(-0.285737\pi\)
−0.988842 + 0.148971i \(0.952404\pi\)
\(504\) 0 0
\(505\) −128.174 −0.253810
\(506\) 634.612i 1.25417i
\(507\) 0 0
\(508\) −718.133 414.614i −1.41365 0.816170i
\(509\) −406.585 + 234.742i −0.798791 + 0.461182i −0.843048 0.537838i \(-0.819241\pi\)
0.0442573 + 0.999020i \(0.485908\pi\)
\(510\) 0 0
\(511\) −493.870 + 855.408i −0.966478 + 1.67399i
\(512\) 1124.13i 2.19557i
\(513\) 0 0
\(514\) −45.5214 −0.0885630
\(515\) 412.562 + 238.193i 0.801092 + 0.462511i
\(516\) 0 0
\(517\) 76.6473 + 132.757i 0.148254 + 0.256783i
\(518\) 646.263 1119.36i 1.24761 2.16093i
\(519\) 0 0
\(520\) 1377.85 2.64970
\(521\) 691.695i 1.32763i 0.747897 + 0.663815i \(0.231064\pi\)
−0.747897 + 0.663815i \(0.768936\pi\)
\(522\) 0 0
\(523\) −70.7545 + 40.8501i −0.135286 + 0.0781073i −0.566115 0.824326i \(-0.691554\pi\)
0.430830 + 0.902433i \(0.358221\pi\)
\(524\) 1459.85 2.78597
\(525\) 0 0
\(526\) 656.635 379.108i 1.24836 0.720738i
\(527\) 435.113 + 251.212i 0.825640 + 0.476684i
\(528\) 0 0
\(529\) −126.474 + 219.060i −0.239081 + 0.414101i
\(530\) 127.491 220.820i 0.240548 0.416642i
\(531\) 0 0
\(532\) −1313.44 + 1174.48i −2.46888 + 2.20767i
\(533\) −335.686 −0.629806
\(534\) 0 0
\(535\) −2.21533 1.27902i −0.00414081 0.00239070i
\(536\) 145.911 + 252.725i 0.272222 + 0.471502i
\(537\) 0 0
\(538\) −902.012 1562.33i −1.67660 2.90396i
\(539\) 414.860 0.769685
\(540\) 0 0
\(541\) 373.182 + 646.370i 0.689800 + 1.19477i 0.971902 + 0.235384i \(0.0756349\pi\)
−0.282102 + 0.959384i \(0.591032\pi\)
\(542\) −678.876 + 391.949i −1.25254 + 0.723153i
\(543\) 0 0
\(544\) 246.576i 0.453264i
\(545\) −375.716 + 216.920i −0.689387 + 0.398018i
\(546\) 0 0
\(547\) 404.687 233.646i 0.739830 0.427141i −0.0821772 0.996618i \(-0.526187\pi\)
0.822008 + 0.569476i \(0.192854\pi\)
\(548\) 515.496 892.866i 0.940687 1.62932i
\(549\) 0 0
\(550\) 75.7117i 0.137658i
\(551\) −486.250 543.782i −0.882487 0.986900i
\(552\) 0 0
\(553\) 281.898 + 162.754i 0.509761 + 0.294311i
\(554\) −808.273 466.657i −1.45898 0.842341i
\(555\) 0 0
\(556\) 479.075 829.782i 0.861645 1.49241i
\(557\) −386.099 668.743i −0.693175 1.20061i −0.970792 0.239923i \(-0.922878\pi\)
0.277617 0.960692i \(-0.410456\pi\)
\(558\) 0 0
\(559\) 941.376i 1.68404i
\(560\) 612.643 + 1061.13i 1.09401 + 1.89487i
\(561\) 0 0
\(562\) −1423.60 −2.53310
\(563\) 195.273i 0.346844i 0.984848 + 0.173422i \(0.0554825\pi\)
−0.984848 + 0.173422i \(0.944518\pi\)
\(564\) 0 0
\(565\) 223.385 + 128.971i 0.395372 + 0.228268i
\(566\) −254.345 + 146.846i −0.449373 + 0.259446i
\(567\) 0 0
\(568\) 718.102 1243.79i 1.26426 2.18977i
\(569\) 579.517i 1.01848i 0.860624 + 0.509242i \(0.170074\pi\)
−0.860624 + 0.509242i \(0.829926\pi\)
\(570\) 0 0
\(571\) −145.886 −0.255492 −0.127746 0.991807i \(-0.540774\pi\)
−0.127746 + 0.991807i \(0.540774\pi\)
\(572\) 850.760 + 491.186i 1.48734 + 0.858717i
\(573\) 0 0
\(574\) −359.576 622.805i −0.626440 1.08503i
\(575\) 46.6448 80.7911i 0.0811214 0.140506i
\(576\) 0 0
\(577\) −1037.54 −1.79817 −0.899084 0.437777i \(-0.855766\pi\)
−0.899084 + 0.437777i \(0.855766\pi\)
\(578\) 541.724i 0.937239i
\(579\) 0 0
\(580\) −1343.57 + 775.713i −2.31651 + 1.33744i
\(581\) 823.723 1.41777
\(582\) 0 0
\(583\) 84.9009 49.0176i 0.145628 0.0840782i
\(584\) −1335.13 770.840i −2.28619 1.31993i
\(585\) 0 0
\(586\) 398.050 689.443i 0.679266 1.17652i
\(587\) −441.521 + 764.737i −0.752165 + 1.30279i 0.194606 + 0.980882i \(0.437657\pi\)
−0.946771 + 0.321907i \(0.895676\pi\)
\(588\) 0 0
\(589\) 798.684 166.899i 1.35600 0.283360i
\(590\) −490.998 −0.832201
\(591\) 0 0
\(592\) 725.221 + 418.707i 1.22504 + 0.707275i
\(593\) −119.583 207.125i −0.201658 0.349283i 0.747404 0.664369i \(-0.231300\pi\)
−0.949063 + 0.315087i \(0.897966\pi\)
\(594\) 0 0
\(595\) −290.835 503.741i −0.488798 0.846623i
\(596\) −501.315 −0.841132
\(597\) 0 0
\(598\) 884.075 + 1531.26i 1.47839 + 2.56064i
\(599\) 793.604 458.187i 1.32488 0.764920i 0.340378 0.940289i \(-0.389445\pi\)
0.984503 + 0.175368i \(0.0561116\pi\)
\(600\) 0 0
\(601\) 789.891i 1.31429i −0.753762 0.657147i \(-0.771763\pi\)
0.753762 0.657147i \(-0.228237\pi\)
\(602\) 1746.55 1008.37i 2.90125 1.67504i
\(603\) 0 0
\(604\) −1544.76 + 891.867i −2.55755 + 1.47660i
\(605\) 187.079 324.031i 0.309222 0.535588i
\(606\) 0 0
\(607\) 653.712i 1.07696i −0.842640 0.538478i \(-0.819000\pi\)
0.842640 0.538478i \(-0.181000\pi\)
\(608\) −266.921 298.503i −0.439015 0.490959i
\(609\) 0 0
\(610\) −612.659 353.719i −1.00436 0.579867i
\(611\) 369.886 + 213.554i 0.605379 + 0.349515i
\(612\) 0 0
\(613\) 528.343 915.118i 0.861898 1.49285i −0.00819687 0.999966i \(-0.502609\pi\)
0.870095 0.492885i \(-0.164057\pi\)
\(614\) −697.061 1207.35i −1.13528 1.96636i
\(615\) 0 0
\(616\) 1134.91i 1.84239i
\(617\) 501.032 + 867.813i 0.812045 + 1.40650i 0.911430 + 0.411455i \(0.134979\pi\)
−0.0993850 + 0.995049i \(0.531688\pi\)
\(618\) 0 0
\(619\) 252.948 0.408640 0.204320 0.978904i \(-0.434502\pi\)
0.204320 + 0.978904i \(0.434502\pi\)
\(620\) 1735.30i 2.79887i
\(621\) 0 0
\(622\) 1159.07 + 669.187i 1.86345 + 1.07586i
\(623\) −820.491 + 473.711i −1.31700 + 0.760371i
\(624\) 0 0
\(625\) 265.233 459.398i 0.424373 0.735036i
\(626\) 536.973i 0.857784i
\(627\) 0 0
\(628\) −965.543 −1.53749
\(629\) −344.278 198.769i −0.547342 0.316008i
\(630\) 0 0
\(631\) −605.640 1049.00i −0.959809 1.66244i −0.722957 0.690893i \(-0.757217\pi\)
−0.236853 0.971546i \(-0.576116\pi\)
\(632\) −254.029 + 439.991i −0.401944 + 0.696188i
\(633\) 0 0
\(634\) −1801.75 −2.84187
\(635\) 444.568i 0.700107i
\(636\) 0 0
\(637\) 1001.02 577.940i 1.57146 0.907284i
\(638\) −871.320 −1.36571
\(639\) 0 0
\(640\) 677.526 391.170i 1.05863 0.611203i
\(641\) −89.1040 51.4442i −0.139008 0.0802562i 0.428883 0.903360i \(-0.358907\pi\)
−0.567891 + 0.823104i \(0.692241\pi\)
\(642\) 0 0
\(643\) −384.990 + 666.822i −0.598740 + 1.03705i 0.394267 + 0.918996i \(0.370998\pi\)
−0.993007 + 0.118052i \(0.962335\pi\)
\(644\) −1296.59 + 2245.76i −2.01334 + 3.48721i
\(645\) 0 0
\(646\) 527.665 + 590.097i 0.816818 + 0.913463i
\(647\) 790.984 1.22254 0.611270 0.791422i \(-0.290659\pi\)
0.611270 + 0.791422i \(0.290659\pi\)
\(648\) 0 0
\(649\) −163.488 94.3896i −0.251907 0.145438i
\(650\) −105.474 182.686i −0.162267 0.281055i
\(651\) 0 0
\(652\) 300.345 + 520.213i 0.460652 + 0.797873i
\(653\) −320.503 −0.490816 −0.245408 0.969420i \(-0.578922\pi\)
−0.245408 + 0.969420i \(0.578922\pi\)
\(654\) 0 0
\(655\) 391.328 + 677.800i 0.597447 + 1.03481i
\(656\) 403.508 232.966i 0.615104 0.355130i
\(657\) 0 0
\(658\) 915.008i 1.39059i
\(659\) 616.112 355.713i 0.934920 0.539776i 0.0465558 0.998916i \(-0.485175\pi\)
0.888364 + 0.459139i \(0.151842\pi\)
\(660\) 0 0
\(661\) −410.779 + 237.163i −0.621451 + 0.358795i −0.777434 0.628965i \(-0.783479\pi\)
0.155983 + 0.987760i \(0.450146\pi\)
\(662\) −788.842 + 1366.31i −1.19160 + 2.06392i
\(663\) 0 0
\(664\) 1285.68i 1.93626i
\(665\) −897.388 294.993i −1.34946 0.443598i
\(666\) 0 0
\(667\) −929.776 536.806i −1.39397 0.804807i
\(668\) −1578.48 911.338i −2.36300 1.36428i
\(669\) 0 0
\(670\) −145.062 + 251.254i −0.216510 + 0.375006i
\(671\) −135.998 235.555i −0.202679 0.351051i
\(672\) 0 0
\(673\) 648.662i 0.963836i 0.876216 + 0.481918i \(0.160060\pi\)
−0.876216 + 0.481918i \(0.839940\pi\)
\(674\) −346.982 600.990i −0.514810 0.891677i
\(675\) 0 0
\(676\) 1269.87 1.87851
\(677\) 860.699i 1.27134i 0.771960 + 0.635671i \(0.219277\pi\)
−0.771960 + 0.635671i \(0.780723\pi\)
\(678\) 0 0
\(679\) 19.4782 + 11.2458i 0.0286866 + 0.0165622i
\(680\) 786.246 453.939i 1.15624 0.667558i
\(681\) 0 0
\(682\) 487.295 844.019i 0.714509 1.23757i
\(683\) 194.789i 0.285196i 0.989781 + 0.142598i \(0.0455456\pi\)
−0.989781 + 0.142598i \(0.954454\pi\)
\(684\) 0 0
\(685\) 552.738 0.806916
\(686\) 530.331 + 306.187i 0.773077 + 0.446336i
\(687\) 0 0
\(688\) 653.313 + 1131.57i 0.949583 + 1.64473i
\(689\) 136.572 236.550i 0.198218 0.343324i
\(690\) 0 0
\(691\) 719.067 1.04062 0.520309 0.853978i \(-0.325817\pi\)
0.520309 + 0.853978i \(0.325817\pi\)
\(692\) 2654.36i 3.83579i
\(693\) 0 0
\(694\) 1618.79 934.607i 2.33255 1.34670i
\(695\) 513.685 0.739115
\(696\) 0 0
\(697\) −191.554 + 110.594i −0.274826 + 0.158671i
\(698\) 1138.21 + 657.144i 1.63067 + 0.941467i
\(699\) 0 0
\(700\) 154.689 267.929i 0.220984 0.382755i
\(701\) −242.353 + 419.767i −0.345724 + 0.598812i −0.985485 0.169762i \(-0.945700\pi\)
0.639761 + 0.768574i \(0.279033\pi\)
\(702\) 0 0
\(703\) −631.951 + 132.057i −0.898934 + 0.187848i
\(704\) 149.931 0.212969
\(705\) 0 0
\(706\) 998.378 + 576.414i 1.41413 + 0.816450i
\(707\) −147.076 254.744i −0.208029 0.360317i
\(708\) 0 0
\(709\) 620.485 + 1074.71i 0.875156 + 1.51581i 0.856597 + 0.515987i \(0.172575\pi\)
0.0185591 + 0.999828i \(0.494092\pi\)
\(710\) 1427.84 2.01105
\(711\) 0 0
\(712\) −739.375 1280.64i −1.03845 1.79865i
\(713\) 1039.97 600.429i 1.45859 0.842116i
\(714\) 0 0
\(715\) 526.671i 0.736603i
\(716\) 2278.13 1315.28i 3.18175 1.83698i
\(717\) 0 0
\(718\) −38.5883 + 22.2790i −0.0537441 + 0.0310292i
\(719\) −65.3191 + 113.136i −0.0908471 + 0.157352i −0.907868 0.419256i \(-0.862291\pi\)
0.817021 + 0.576608i \(0.195624\pi\)
\(720\) 0 0
\(721\) 1093.28i 1.51634i
\(722\) 1277.57 + 143.163i 1.76949 + 0.198287i
\(723\) 0 0
\(724\) −545.873 315.160i −0.753968 0.435303i
\(725\) 110.926 + 64.0432i 0.153001 + 0.0883354i
\(726\) 0 0
\(727\) −566.505 + 981.216i −0.779237 + 1.34968i 0.153145 + 0.988204i \(0.451060\pi\)
−0.932382 + 0.361475i \(0.882273\pi\)
\(728\) 1581.04 + 2738.44i 2.17176 + 3.76160i
\(729\) 0 0
\(730\) 1532.71i 2.09960i
\(731\) −310.142 537.181i −0.424271 0.734858i
\(732\) 0 0
\(733\) −837.144 −1.14208 −0.571040 0.820922i \(-0.693460\pi\)
−0.571040 + 0.820922i \(0.693460\pi\)
\(734\) 315.630i 0.430014i
\(735\) 0 0
\(736\) −510.390 294.674i −0.693464 0.400372i
\(737\) −96.6023 + 55.7734i −0.131075 + 0.0756762i
\(738\) 0 0
\(739\) 144.463 250.216i 0.195484 0.338588i −0.751575 0.659647i \(-0.770706\pi\)
0.947059 + 0.321060i \(0.104039\pi\)
\(740\) 1373.04i 1.85546i
\(741\) 0 0
\(742\) 585.167 0.788635
\(743\) 66.4928 + 38.3896i 0.0894923 + 0.0516684i 0.544078 0.839034i \(-0.316879\pi\)
−0.454586 + 0.890703i \(0.650213\pi\)
\(744\) 0 0
\(745\) −134.383 232.758i −0.180380 0.312427i
\(746\) −723.782 + 1253.63i −0.970217 + 1.68046i
\(747\) 0 0
\(748\) 647.296 0.865370
\(749\) 5.87058i 0.00783789i
\(750\) 0 0
\(751\) 923.318 533.078i 1.22945 0.709824i 0.262536 0.964922i \(-0.415441\pi\)
0.966915 + 0.255098i \(0.0821078\pi\)
\(752\) −592.824 −0.788329
\(753\) 0 0
\(754\) −2102.42 + 1213.83i −2.78835 + 1.60986i
\(755\) −828.179 478.149i −1.09693 0.633310i
\(756\) 0 0
\(757\) 4.94030 8.55684i 0.00652615 0.0113036i −0.862744 0.505641i \(-0.831256\pi\)
0.869270 + 0.494338i \(0.164589\pi\)
\(758\) 772.411 1337.85i 1.01901 1.76498i
\(759\) 0 0
\(760\) 460.429 1400.66i 0.605827 1.84297i
\(761\) −1147.50 −1.50788 −0.753940 0.656944i \(-0.771849\pi\)
−0.753940 + 0.656944i \(0.771849\pi\)
\(762\) 0 0
\(763\) −862.247 497.819i −1.13007 0.652449i
\(764\) 210.850 + 365.203i 0.275982 + 0.478014i
\(765\) 0 0
\(766\) −731.572 1267.12i −0.955055 1.65420i
\(767\) −525.975 −0.685756
\(768\) 0 0
\(769\) 299.227 + 518.276i 0.389112 + 0.673961i 0.992330 0.123615i \(-0.0394486\pi\)
−0.603218 + 0.797576i \(0.706115\pi\)
\(770\) −977.142 + 564.153i −1.26902 + 0.732667i
\(771\) 0 0
\(772\) 95.0749i 0.123154i
\(773\) −858.414 + 495.605i −1.11050 + 0.641145i −0.938958 0.344032i \(-0.888207\pi\)
−0.171538 + 0.985177i \(0.554874\pi\)
\(774\) 0 0
\(775\) −124.073 + 71.6336i −0.160094 + 0.0924305i
\(776\) −17.5525 + 30.4019i −0.0226193 + 0.0391777i
\(777\) 0 0
\(778\) 673.776i 0.866036i
\(779\) −112.175 + 341.244i −0.143998 + 0.438053i
\(780\) 0 0
\(781\) 475.429 + 274.489i 0.608744 + 0.351458i
\(782\) 1008.97 + 582.527i 1.29024 + 0.744919i
\(783\) 0 0
\(784\) −802.178 + 1389.41i −1.02319 + 1.77221i
\(785\) −258.824 448.297i −0.329