Properties

Label 847.2.f.i.372.1
Level $847$
Weight $2$
Character 847.372
Analytic conductor $6.763$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 372.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 847.372
Dual form 847.2.f.i.148.1

$q$-expansion

\(f(q)\) \(=\) \(q+(2.42705 - 1.76336i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{7} +(1.85410 - 5.70634i) q^{9} +O(q^{10})\) \(q+(2.42705 - 1.76336i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{7} +(1.85410 - 5.70634i) q^{9} +6.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(-2.42705 - 1.76336i) q^{15} +(1.23607 + 3.80423i) q^{16} +(0.618034 + 1.90211i) q^{17} +(4.85410 - 3.52671i) q^{19} +(0.618034 - 1.90211i) q^{20} +3.00000 q^{21} -5.00000 q^{23} +(3.23607 - 2.35114i) q^{25} +(-2.78115 - 8.55951i) q^{27} +(0.618034 + 1.90211i) q^{28} +(-8.09017 - 5.87785i) q^{29} +(0.309017 - 0.951057i) q^{31} +(0.309017 - 0.951057i) q^{35} +(9.70820 - 7.05342i) q^{36} +(4.04508 + 2.93893i) q^{37} +(3.70820 + 11.4127i) q^{39} +(1.61803 - 1.17557i) q^{41} -8.00000 q^{43} -6.00000 q^{45} +(-6.47214 + 4.70228i) q^{47} +(9.70820 + 7.05342i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.85410 + 3.52671i) q^{51} +(-6.47214 + 4.70228i) q^{52} +(-1.85410 + 5.70634i) q^{53} +(5.56231 - 17.1190i) q^{57} +(-2.42705 - 1.76336i) q^{59} +(-1.85410 - 5.70634i) q^{60} +(-0.618034 - 1.90211i) q^{61} +(4.85410 - 3.52671i) q^{63} +(-2.47214 + 7.60845i) q^{64} +4.00000 q^{65} -3.00000 q^{67} +(-1.23607 + 3.80423i) q^{68} +(-12.1353 + 8.81678i) q^{69} +(0.309017 + 0.951057i) q^{71} +(-8.09017 - 5.87785i) q^{73} +(3.70820 - 11.4127i) q^{75} +12.0000 q^{76} +(1.85410 - 5.70634i) q^{79} +(3.23607 - 2.35114i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(3.70820 + 11.4127i) q^{83} +(4.85410 + 3.52671i) q^{84} +(1.61803 - 1.17557i) q^{85} -30.0000 q^{87} -15.0000 q^{89} +(-3.23607 + 2.35114i) q^{91} +(-8.09017 - 5.87785i) q^{92} +(-0.927051 - 2.85317i) q^{93} +(-4.85410 - 3.52671i) q^{95} +(-1.54508 + 4.75528i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{3} + 2 q^{4} + q^{5} + q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{3} + 2 q^{4} + q^{5} + q^{7} - 6 q^{9} + 24 q^{12} + 4 q^{13} - 3 q^{15} - 4 q^{16} - 2 q^{17} + 6 q^{19} - 2 q^{20} + 12 q^{21} - 20 q^{23} + 4 q^{25} + 9 q^{27} - 2 q^{28} - 10 q^{29} - q^{31} - q^{35} + 12 q^{36} + 5 q^{37} - 12 q^{39} + 2 q^{41} - 32 q^{43} - 24 q^{45} - 8 q^{47} + 12 q^{48} - q^{49} + 6 q^{51} - 8 q^{52} + 6 q^{53} - 18 q^{57} - 3 q^{59} + 6 q^{60} + 2 q^{61} + 6 q^{63} + 8 q^{64} + 16 q^{65} - 12 q^{67} + 4 q^{68} - 15 q^{69} - q^{71} - 10 q^{73} - 12 q^{75} + 48 q^{76} - 6 q^{79} + 4 q^{80} - 9 q^{81} - 12 q^{83} + 6 q^{84} + 2 q^{85} - 120 q^{87} - 60 q^{89} - 4 q^{91} - 10 q^{92} + 3 q^{93} - 6 q^{95} + 5 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(3\) 2.42705 1.76336i 1.40126 1.01807i 0.406737 0.913545i \(-0.366667\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(4\) 1.61803 + 1.17557i 0.809017 + 0.587785i
\(5\) −0.309017 0.951057i −0.138197 0.425325i 0.857877 0.513855i \(-0.171783\pi\)
−0.996074 + 0.0885298i \(0.971783\pi\)
\(6\) 0 0
\(7\) 0.809017 + 0.587785i 0.305780 + 0.222162i
\(8\) 0 0
\(9\) 1.85410 5.70634i 0.618034 1.90211i
\(10\) 0 0
\(11\) 0 0
\(12\) 6.00000 1.73205
\(13\) −1.23607 + 3.80423i −0.342824 + 1.05510i 0.619915 + 0.784669i \(0.287167\pi\)
−0.962739 + 0.270434i \(0.912833\pi\)
\(14\) 0 0
\(15\) −2.42705 1.76336i −0.626662 0.455296i
\(16\) 1.23607 + 3.80423i 0.309017 + 0.951057i
\(17\) 0.618034 + 1.90211i 0.149895 + 0.461330i 0.997608 0.0691254i \(-0.0220209\pi\)
−0.847713 + 0.530456i \(0.822021\pi\)
\(18\) 0 0
\(19\) 4.85410 3.52671i 1.11361 0.809083i 0.130379 0.991464i \(-0.458380\pi\)
0.983228 + 0.182381i \(0.0583804\pi\)
\(20\) 0.618034 1.90211i 0.138197 0.425325i
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) −5.00000 −1.04257 −0.521286 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 0 0
\(25\) 3.23607 2.35114i 0.647214 0.470228i
\(26\) 0 0
\(27\) −2.78115 8.55951i −0.535233 1.64728i
\(28\) 0.618034 + 1.90211i 0.116797 + 0.359466i
\(29\) −8.09017 5.87785i −1.50231 1.09149i −0.969451 0.245284i \(-0.921119\pi\)
−0.532855 0.846206i \(-0.678881\pi\)
\(30\) 0 0
\(31\) 0.309017 0.951057i 0.0555011 0.170815i −0.919463 0.393176i \(-0.871376\pi\)
0.974964 + 0.222361i \(0.0713764\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.309017 0.951057i 0.0522334 0.160758i
\(36\) 9.70820 7.05342i 1.61803 1.17557i
\(37\) 4.04508 + 2.93893i 0.665008 + 0.483157i 0.868350 0.495951i \(-0.165181\pi\)
−0.203343 + 0.979108i \(0.565181\pi\)
\(38\) 0 0
\(39\) 3.70820 + 11.4127i 0.593788 + 1.82749i
\(40\) 0 0
\(41\) 1.61803 1.17557i 0.252694 0.183593i −0.454226 0.890887i \(-0.650084\pi\)
0.706920 + 0.707293i \(0.250084\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) 0 0
\(47\) −6.47214 + 4.70228i −0.944058 + 0.685898i −0.949394 0.314087i \(-0.898301\pi\)
0.00533600 + 0.999986i \(0.498301\pi\)
\(48\) 9.70820 + 7.05342i 1.40126 + 1.01807i
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 4.85410 + 3.52671i 0.679710 + 0.493838i
\(52\) −6.47214 + 4.70228i −0.897524 + 0.652089i
\(53\) −1.85410 + 5.70634i −0.254680 + 0.783826i 0.739212 + 0.673473i \(0.235198\pi\)
−0.993892 + 0.110353i \(0.964802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.56231 17.1190i 0.736745 2.26747i
\(58\) 0 0
\(59\) −2.42705 1.76336i −0.315975 0.229569i 0.418481 0.908226i \(-0.362563\pi\)
−0.734456 + 0.678656i \(0.762563\pi\)
\(60\) −1.85410 5.70634i −0.239364 0.736685i
\(61\) −0.618034 1.90211i −0.0791311 0.243541i 0.903663 0.428244i \(-0.140868\pi\)
−0.982794 + 0.184703i \(0.940868\pi\)
\(62\) 0 0
\(63\) 4.85410 3.52671i 0.611559 0.444324i
\(64\) −2.47214 + 7.60845i −0.309017 + 0.951057i
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) −3.00000 −0.366508 −0.183254 0.983066i \(-0.558663\pi\)
−0.183254 + 0.983066i \(0.558663\pi\)
\(68\) −1.23607 + 3.80423i −0.149895 + 0.461330i
\(69\) −12.1353 + 8.81678i −1.46091 + 1.06142i
\(70\) 0 0
\(71\) 0.309017 + 0.951057i 0.0366736 + 0.112870i 0.967717 0.252038i \(-0.0811007\pi\)
−0.931044 + 0.364907i \(0.881101\pi\)
\(72\) 0 0
\(73\) −8.09017 5.87785i −0.946883 0.687951i 0.00318477 0.999995i \(-0.498986\pi\)
−0.950068 + 0.312044i \(0.898986\pi\)
\(74\) 0 0
\(75\) 3.70820 11.4127i 0.428187 1.31782i
\(76\) 12.0000 1.37649
\(77\) 0 0
\(78\) 0 0
\(79\) 1.85410 5.70634i 0.208603 0.642013i −0.790943 0.611889i \(-0.790410\pi\)
0.999546 0.0301240i \(-0.00959021\pi\)
\(80\) 3.23607 2.35114i 0.361803 0.262866i
\(81\) −7.28115 5.29007i −0.809017 0.587785i
\(82\) 0 0
\(83\) 3.70820 + 11.4127i 0.407028 + 1.25270i 0.919190 + 0.393815i \(0.128845\pi\)
−0.512161 + 0.858889i \(0.671155\pi\)
\(84\) 4.85410 + 3.52671i 0.529626 + 0.384796i
\(85\) 1.61803 1.17557i 0.175500 0.127509i
\(86\) 0 0
\(87\) −30.0000 −3.21634
\(88\) 0 0
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 0 0
\(91\) −3.23607 + 2.35114i −0.339232 + 0.246467i
\(92\) −8.09017 5.87785i −0.843459 0.612808i
\(93\) −0.927051 2.85317i −0.0961307 0.295860i
\(94\) 0 0
\(95\) −4.85410 3.52671i −0.498020 0.361833i
\(96\) 0 0
\(97\) −1.54508 + 4.75528i −0.156880 + 0.482826i −0.998346 0.0574829i \(-0.981693\pi\)
0.841467 + 0.540309i \(0.181693\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.00000 0.800000
\(101\) −3.70820 + 11.4127i −0.368980 + 1.13560i 0.578471 + 0.815703i \(0.303650\pi\)
−0.947451 + 0.319901i \(0.896350\pi\)
\(102\) 0 0
\(103\) 9.70820 + 7.05342i 0.956578 + 0.694994i 0.952353 0.304997i \(-0.0986553\pi\)
0.00422434 + 0.999991i \(0.498655\pi\)
\(104\) 0 0
\(105\) −0.927051 2.85317i −0.0904709 0.278441i
\(106\) 0 0
\(107\) 8.09017 5.87785i 0.782106 0.568233i −0.123504 0.992344i \(-0.539413\pi\)
0.905610 + 0.424111i \(0.139413\pi\)
\(108\) 5.56231 17.1190i 0.535233 1.64728i
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 15.0000 1.42374
\(112\) −1.23607 + 3.80423i −0.116797 + 0.359466i
\(113\) 15.3713 11.1679i 1.44601 1.05059i 0.459270 0.888297i \(-0.348111\pi\)
0.986743 0.162293i \(-0.0518889\pi\)
\(114\) 0 0
\(115\) 1.54508 + 4.75528i 0.144080 + 0.443432i
\(116\) −6.18034 19.0211i −0.573830 1.76607i
\(117\) 19.4164 + 14.1068i 1.79505 + 1.30418i
\(118\) 0 0
\(119\) −0.618034 + 1.90211i −0.0566551 + 0.174366i
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 1.85410 5.70634i 0.167179 0.514523i
\(124\) 1.61803 1.17557i 0.145304 0.105569i
\(125\) −7.28115 5.29007i −0.651246 0.473158i
\(126\) 0 0
\(127\) 0.618034 + 1.90211i 0.0548416 + 0.168785i 0.974726 0.223405i \(-0.0717174\pi\)
−0.919884 + 0.392191i \(0.871717\pi\)
\(128\) 0 0
\(129\) −19.4164 + 14.1068i −1.70952 + 1.24204i
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) 6.00000 0.520266
\(134\) 0 0
\(135\) −7.28115 + 5.29007i −0.626662 + 0.455296i
\(136\) 0 0
\(137\) −0.927051 2.85317i −0.0792033 0.243763i 0.903613 0.428350i \(-0.140905\pi\)
−0.982816 + 0.184588i \(0.940905\pi\)
\(138\) 0 0
\(139\) 8.09017 + 5.87785i 0.686199 + 0.498553i 0.875409 0.483384i \(-0.160592\pi\)
−0.189209 + 0.981937i \(0.560592\pi\)
\(140\) 1.61803 1.17557i 0.136749 0.0993538i
\(141\) −7.41641 + 22.8254i −0.624574 + 1.92224i
\(142\) 0 0
\(143\) 0 0
\(144\) 24.0000 2.00000
\(145\) −3.09017 + 9.51057i −0.256625 + 0.789809i
\(146\) 0 0
\(147\) 2.42705 + 1.76336i 0.200180 + 0.145439i
\(148\) 3.09017 + 9.51057i 0.254010 + 0.781764i
\(149\) −6.79837 20.9232i −0.556944 1.71410i −0.690752 0.723092i \(-0.742720\pi\)
0.133808 0.991007i \(-0.457280\pi\)
\(150\) 0 0
\(151\) −4.85410 + 3.52671i −0.395021 + 0.287000i −0.767510 0.641037i \(-0.778505\pi\)
0.372489 + 0.928037i \(0.378505\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) −7.41641 + 22.8254i −0.593788 + 1.82749i
\(157\) −5.66312 + 4.11450i −0.451966 + 0.328373i −0.790372 0.612628i \(-0.790112\pi\)
0.338405 + 0.941000i \(0.390112\pi\)
\(158\) 0 0
\(159\) 5.56231 + 17.1190i 0.441120 + 1.35763i
\(160\) 0 0
\(161\) −4.04508 2.93893i −0.318797 0.231620i
\(162\) 0 0
\(163\) 1.23607 3.80423i 0.0968163 0.297970i −0.890906 0.454187i \(-0.849930\pi\)
0.987723 + 0.156217i \(0.0499299\pi\)
\(164\) 4.00000 0.312348
\(165\) 0 0
\(166\) 0 0
\(167\) −0.618034 + 1.90211i −0.0478249 + 0.147190i −0.972117 0.234495i \(-0.924656\pi\)
0.924292 + 0.381685i \(0.124656\pi\)
\(168\) 0 0
\(169\) −2.42705 1.76336i −0.186696 0.135643i
\(170\) 0 0
\(171\) −11.1246 34.2380i −0.850720 2.61825i
\(172\) −12.9443 9.40456i −0.986991 0.717091i
\(173\) −12.9443 + 9.40456i −0.984135 + 0.715016i −0.958629 0.284659i \(-0.908120\pi\)
−0.0255059 + 0.999675i \(0.508120\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) −9.00000 −0.676481
\(178\) 0 0
\(179\) −0.809017 + 0.587785i −0.0604688 + 0.0439331i −0.617609 0.786485i \(-0.711899\pi\)
0.557140 + 0.830418i \(0.311899\pi\)
\(180\) −9.70820 7.05342i −0.723607 0.525731i
\(181\) 1.54508 + 4.75528i 0.114845 + 0.353457i 0.991915 0.126906i \(-0.0405047\pi\)
−0.877069 + 0.480364i \(0.840505\pi\)
\(182\) 0 0
\(183\) −4.85410 3.52671i −0.358826 0.260702i
\(184\) 0 0
\(185\) 1.54508 4.75528i 0.113597 0.349615i
\(186\) 0 0
\(187\) 0 0
\(188\) −16.0000 −1.16692
\(189\) 2.78115 8.55951i 0.202299 0.622613i
\(190\) 0 0
\(191\) −4.04508 2.93893i −0.292692 0.212653i 0.431742 0.901997i \(-0.357899\pi\)
−0.724434 + 0.689344i \(0.757899\pi\)
\(192\) 7.41641 + 22.8254i 0.535233 + 1.64728i
\(193\) 4.32624 + 13.3148i 0.311409 + 0.958420i 0.977207 + 0.212287i \(0.0680913\pi\)
−0.665798 + 0.746132i \(0.731909\pi\)
\(194\) 0 0
\(195\) 9.70820 7.05342i 0.695219 0.505106i
\(196\) −0.618034 + 1.90211i −0.0441453 + 0.135865i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 0 0
\(201\) −7.28115 + 5.29007i −0.513573 + 0.373133i
\(202\) 0 0
\(203\) −3.09017 9.51057i −0.216887 0.667511i
\(204\) 3.70820 + 11.4127i 0.259626 + 0.799047i
\(205\) −1.61803 1.17557i −0.113008 0.0821054i
\(206\) 0 0
\(207\) −9.27051 + 28.5317i −0.644345 + 1.98309i
\(208\) −16.0000 −1.10940
\(209\) 0 0
\(210\) 0 0
\(211\) −0.618034 + 1.90211i −0.0425472 + 0.130947i −0.970074 0.242810i \(-0.921931\pi\)
0.927527 + 0.373757i \(0.121931\pi\)
\(212\) −9.70820 + 7.05342i −0.666762 + 0.484431i
\(213\) 2.42705 + 1.76336i 0.166299 + 0.120823i
\(214\) 0 0
\(215\) 2.47214 + 7.60845i 0.168598 + 0.518892i
\(216\) 0 0
\(217\) 0.809017 0.587785i 0.0549197 0.0399015i
\(218\) 0 0
\(219\) −30.0000 −2.02721
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) −0.809017 + 0.587785i −0.0541758 + 0.0393610i −0.614544 0.788883i \(-0.710660\pi\)
0.560368 + 0.828244i \(0.310660\pi\)
\(224\) 0 0
\(225\) −7.41641 22.8254i −0.494427 1.52169i
\(226\) 0 0
\(227\) −3.23607 2.35114i −0.214785 0.156051i 0.475191 0.879883i \(-0.342379\pi\)
−0.689976 + 0.723832i \(0.742379\pi\)
\(228\) 29.1246 21.1603i 1.92882 1.40137i
\(229\) −2.16312 + 6.65740i −0.142943 + 0.439933i −0.996741 0.0806717i \(-0.974293\pi\)
0.853798 + 0.520605i \(0.174293\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.85410 5.70634i 0.121466 0.373835i −0.871774 0.489907i \(-0.837031\pi\)
0.993241 + 0.116073i \(0.0370306\pi\)
\(234\) 0 0
\(235\) 6.47214 + 4.70228i 0.422196 + 0.306743i
\(236\) −1.85410 5.70634i −0.120692 0.371451i
\(237\) −5.56231 17.1190i −0.361311 1.11200i
\(238\) 0 0
\(239\) −3.23607 + 2.35114i −0.209324 + 0.152083i −0.687508 0.726177i \(-0.741295\pi\)
0.478184 + 0.878260i \(0.341295\pi\)
\(240\) 3.70820 11.4127i 0.239364 0.736685i
\(241\) −12.0000 −0.772988 −0.386494 0.922292i \(-0.626314\pi\)
−0.386494 + 0.922292i \(0.626314\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 1.23607 3.80423i 0.0791311 0.243541i
\(245\) 0.809017 0.587785i 0.0516862 0.0375522i
\(246\) 0 0
\(247\) 7.41641 + 22.8254i 0.471895 + 1.45234i
\(248\) 0 0
\(249\) 29.1246 + 21.1603i 1.84570 + 1.34098i
\(250\) 0 0
\(251\) −6.48936 + 19.9722i −0.409605 + 1.26063i 0.507384 + 0.861720i \(0.330613\pi\)
−0.916989 + 0.398913i \(0.869387\pi\)
\(252\) 12.0000 0.755929
\(253\) 0 0
\(254\) 0 0
\(255\) 1.85410 5.70634i 0.116108 0.357345i
\(256\) −12.9443 + 9.40456i −0.809017 + 0.587785i
\(257\) 4.85410 + 3.52671i 0.302791 + 0.219990i 0.728797 0.684730i \(-0.240080\pi\)
−0.426006 + 0.904720i \(0.640080\pi\)
\(258\) 0 0
\(259\) 1.54508 + 4.75528i 0.0960069 + 0.295479i
\(260\) 6.47214 + 4.70228i 0.401385 + 0.291623i
\(261\) −48.5410 + 35.2671i −3.00461 + 2.18298i
\(262\) 0 0
\(263\) 18.0000 1.10993 0.554964 0.831875i \(-0.312732\pi\)
0.554964 + 0.831875i \(0.312732\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) −36.4058 + 26.4503i −2.22800 + 1.61873i
\(268\) −4.85410 3.52671i −0.296511 0.215428i
\(269\) −5.56231 17.1190i −0.339140 1.04376i −0.964647 0.263546i \(-0.915108\pi\)
0.625507 0.780219i \(-0.284892\pi\)
\(270\) 0 0
\(271\) −12.9443 9.40456i −0.786309 0.571287i 0.120557 0.992706i \(-0.461532\pi\)
−0.906866 + 0.421420i \(0.861532\pi\)
\(272\) −6.47214 + 4.70228i −0.392431 + 0.285118i
\(273\) −3.70820 + 11.4127i −0.224431 + 0.690727i
\(274\) 0 0
\(275\) 0 0
\(276\) −30.0000 −1.80579
\(277\) 7.41641 22.8254i 0.445609 1.37144i −0.436206 0.899847i \(-0.643678\pi\)
0.881815 0.471596i \(-0.156322\pi\)
\(278\) 0 0
\(279\) −4.85410 3.52671i −0.290607 0.211139i
\(280\) 0 0
\(281\) −1.23607 3.80423i −0.0737376 0.226941i 0.907394 0.420280i \(-0.138068\pi\)
−0.981132 + 0.193339i \(0.938068\pi\)
\(282\) 0 0
\(283\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(284\) −0.618034 + 1.90211i −0.0366736 + 0.112870i
\(285\) −18.0000 −1.06623
\(286\) 0 0
\(287\) 2.00000 0.118056
\(288\) 0 0
\(289\) 10.5172 7.64121i 0.618660 0.449483i
\(290\) 0 0
\(291\) 4.63525 + 14.2658i 0.271723 + 0.836279i
\(292\) −6.18034 19.0211i −0.361677 1.11313i
\(293\) 4.85410 + 3.52671i 0.283580 + 0.206033i 0.720477 0.693479i \(-0.243923\pi\)
−0.436898 + 0.899511i \(0.643923\pi\)
\(294\) 0 0
\(295\) −0.927051 + 2.85317i −0.0539750 + 0.166118i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.18034 19.0211i 0.357418 1.10002i
\(300\) 19.4164 14.1068i 1.12101 0.814459i
\(301\) −6.47214 4.70228i −0.373048 0.271035i
\(302\) 0 0
\(303\) 11.1246 + 34.2380i 0.639092 + 1.96692i
\(304\) 19.4164 + 14.1068i 1.11361 + 0.809083i
\(305\) −1.61803 + 1.17557i −0.0926484 + 0.0673130i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 36.0000 2.04797
\(310\) 0 0
\(311\) −6.47214 + 4.70228i −0.367001 + 0.266642i −0.755966 0.654611i \(-0.772833\pi\)
0.388965 + 0.921252i \(0.372833\pi\)
\(312\) 0 0
\(313\) −7.10739 21.8743i −0.401733 1.23641i −0.923592 0.383377i \(-0.874761\pi\)
0.521859 0.853032i \(-0.325239\pi\)
\(314\) 0 0
\(315\) −4.85410 3.52671i −0.273498 0.198708i
\(316\) 9.70820 7.05342i 0.546129 0.396786i
\(317\) 2.78115 8.55951i 0.156205 0.480750i −0.842076 0.539359i \(-0.818667\pi\)
0.998281 + 0.0586092i \(0.0186666\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 8.00000 0.447214
\(321\) 9.27051 28.5317i 0.517429 1.59248i
\(322\) 0 0
\(323\) 9.70820 + 7.05342i 0.540179 + 0.392463i
\(324\) −5.56231 17.1190i −0.309017 0.951057i
\(325\) 4.94427 + 15.2169i 0.274259 + 0.844082i
\(326\) 0 0
\(327\) 9.70820 7.05342i 0.536865 0.390055i
\(328\) 0 0
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) −7.41641 + 22.8254i −0.407028 + 1.25270i
\(333\) 24.2705 17.6336i 1.33002 0.966313i
\(334\) 0 0
\(335\) 0.927051 + 2.85317i 0.0506502 + 0.155885i
\(336\) 3.70820 + 11.4127i 0.202299 + 0.622613i
\(337\) 14.5623 + 10.5801i 0.793259 + 0.576337i 0.908929 0.416951i \(-0.136901\pi\)
−0.115670 + 0.993288i \(0.536901\pi\)
\(338\) 0 0
\(339\) 17.6140 54.2102i 0.956659 2.94430i
\(340\) 4.00000 0.216930
\(341\) 0 0
\(342\) 0 0
\(343\) −0.309017 + 0.951057i −0.0166853 + 0.0513522i
\(344\) 0 0
\(345\) 12.1353 + 8.81678i 0.653340 + 0.474679i
\(346\) 0 0
\(347\) 4.32624 + 13.3148i 0.232245 + 0.714775i 0.997475 + 0.0710189i \(0.0226251\pi\)
−0.765230 + 0.643757i \(0.777375\pi\)
\(348\) −48.5410 35.2671i −2.60207 1.89052i
\(349\) 27.5066 19.9847i 1.47239 1.06976i 0.492482 0.870323i \(-0.336090\pi\)
0.979911 0.199434i \(-0.0639103\pi\)
\(350\) 0 0
\(351\) 36.0000 1.92154
\(352\) 0 0
\(353\) 9.00000 0.479022 0.239511 0.970894i \(-0.423013\pi\)
0.239511 + 0.970894i \(0.423013\pi\)
\(354\) 0 0
\(355\) 0.809017 0.587785i 0.0429382 0.0311964i
\(356\) −24.2705 17.6336i −1.28633 0.934577i
\(357\) 1.85410 + 5.70634i 0.0981295 + 0.302011i
\(358\) 0 0
\(359\) −6.47214 4.70228i −0.341586 0.248177i 0.403745 0.914872i \(-0.367708\pi\)
−0.745331 + 0.666695i \(0.767708\pi\)
\(360\) 0 0
\(361\) 5.25329 16.1680i 0.276489 0.850945i
\(362\) 0 0
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) −3.09017 + 9.51057i −0.161747 + 0.497806i
\(366\) 0 0
\(367\) 8.89919 + 6.46564i 0.464534 + 0.337504i 0.795307 0.606207i \(-0.207310\pi\)
−0.330773 + 0.943710i \(0.607310\pi\)
\(368\) −6.18034 19.0211i −0.322172 0.991545i
\(369\) −3.70820 11.4127i −0.193041 0.594120i
\(370\) 0 0
\(371\) −4.85410 + 3.52671i −0.252012 + 0.183098i
\(372\) 1.85410 5.70634i 0.0961307 0.295860i
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) −27.0000 −1.39427
\(376\) 0 0
\(377\) 32.3607 23.5114i 1.66666 1.21090i
\(378\) 0 0
\(379\) −8.96149 27.5806i −0.460321 1.41672i −0.864773 0.502163i \(-0.832538\pi\)
0.404452 0.914559i \(-0.367462\pi\)
\(380\) −3.70820 11.4127i −0.190227 0.585458i
\(381\) 4.85410 + 3.52671i 0.248683 + 0.180679i
\(382\) 0 0
\(383\) 5.25329 16.1680i 0.268431 0.826144i −0.722453 0.691420i \(-0.756985\pi\)
0.990883 0.134724i \(-0.0430147\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −14.8328 + 45.6507i −0.753994 + 2.32056i
\(388\) −8.09017 + 5.87785i −0.410716 + 0.298403i
\(389\) −7.28115 5.29007i −0.369169 0.268217i 0.387697 0.921787i \(-0.373271\pi\)
−0.756866 + 0.653570i \(0.773271\pi\)
\(390\) 0 0
\(391\) −3.09017 9.51057i −0.156277 0.480970i
\(392\) 0 0
\(393\) 43.6869 31.7404i 2.20371 1.60109i
\(394\) 0 0
\(395\) −6.00000 −0.301893
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 0 0
\(399\) 14.5623 10.5801i 0.729027 0.529669i
\(400\) 12.9443 + 9.40456i 0.647214 + 0.470228i
\(401\) −1.85410 5.70634i −0.0925894 0.284961i 0.894029 0.448010i \(-0.147867\pi\)
−0.986618 + 0.163049i \(0.947867\pi\)
\(402\) 0 0
\(403\) 3.23607 + 2.35114i 0.161200 + 0.117119i
\(404\) −19.4164 + 14.1068i −0.966002 + 0.701842i
\(405\) −2.78115 + 8.55951i −0.138197 + 0.425325i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −8.03444 + 24.7275i −0.397278 + 1.22269i 0.529896 + 0.848063i \(0.322231\pi\)
−0.927174 + 0.374632i \(0.877769\pi\)
\(410\) 0 0
\(411\) −7.28115 5.29007i −0.359153 0.260940i
\(412\) 7.41641 + 22.8254i 0.365380 + 1.12452i
\(413\) −0.927051 2.85317i −0.0456172 0.140395i
\(414\) 0 0
\(415\) 9.70820 7.05342i 0.476557 0.346239i
\(416\) 0 0
\(417\) 30.0000 1.46911
\(418\) 0 0
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) 1.85410 5.70634i 0.0904709 0.278441i
\(421\) −17.7984 + 12.9313i −0.867440 + 0.630232i −0.929899 0.367816i \(-0.880106\pi\)
0.0624590 + 0.998048i \(0.480106\pi\)
\(422\) 0 0
\(423\) 14.8328 + 45.6507i 0.721196 + 2.21961i
\(424\) 0 0
\(425\) 6.47214 + 4.70228i 0.313945 + 0.228094i
\(426\) 0 0
\(427\) 0.618034 1.90211i 0.0299088 0.0920497i
\(428\) 20.0000 0.966736
\(429\) 0 0
\(430\) 0 0
\(431\) −6.18034 + 19.0211i −0.297696 + 0.916216i 0.684606 + 0.728913i \(0.259974\pi\)
−0.982302 + 0.187302i \(0.940026\pi\)
\(432\) 29.1246 21.1603i 1.40126 1.01807i
\(433\) 20.2254 + 14.6946i 0.971972 + 0.706179i 0.955900 0.293692i \(-0.0948840\pi\)
0.0160718 + 0.999871i \(0.494884\pi\)
\(434\) 0 0
\(435\) 9.27051 + 28.5317i 0.444487 + 1.36799i
\(436\) 6.47214 + 4.70228i 0.309959 + 0.225198i
\(437\) −24.2705 + 17.6336i −1.16102 + 0.843527i
\(438\) 0 0
\(439\) −14.0000 −0.668184 −0.334092 0.942541i \(-0.608430\pi\)
−0.334092 + 0.942541i \(0.608430\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) 0 0
\(443\) 31.5517 22.9236i 1.49906 1.08913i 0.528313 0.849050i \(-0.322825\pi\)
0.970752 0.240084i \(-0.0771751\pi\)
\(444\) 24.2705 + 17.6336i 1.15183 + 0.836852i
\(445\) 4.63525 + 14.2658i 0.219732 + 0.676266i
\(446\) 0 0
\(447\) −53.3951 38.7938i −2.52550 1.83489i
\(448\) −6.47214 + 4.70228i −0.305780 + 0.222162i
\(449\) 4.63525 14.2658i 0.218751 0.673247i −0.780115 0.625636i \(-0.784839\pi\)
0.998866 0.0476105i \(-0.0151606\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 38.0000 1.78737
\(453\) −5.56231 + 17.1190i −0.261340 + 0.804322i
\(454\) 0 0
\(455\) 3.23607 + 2.35114i 0.151709 + 0.110223i
\(456\) 0 0
\(457\) 2.47214 + 7.60845i 0.115642 + 0.355908i 0.992080 0.125605i \(-0.0400872\pi\)
−0.876439 + 0.481514i \(0.840087\pi\)
\(458\) 0 0
\(459\) 14.5623 10.5801i 0.679710 0.493838i
\(460\) −3.09017 + 9.51057i −0.144080 + 0.443432i
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) 12.3607 38.0423i 0.573830 1.76607i
\(465\) −2.42705 + 1.76336i −0.112552 + 0.0817737i
\(466\) 0 0
\(467\) 0.927051 + 2.85317i 0.0428988 + 0.132029i 0.970212 0.242257i \(-0.0778878\pi\)
−0.927313 + 0.374286i \(0.877888\pi\)
\(468\) 14.8328 + 45.6507i 0.685647 + 2.11020i
\(469\) −2.42705 1.76336i −0.112071 0.0814242i
\(470\) 0 0
\(471\) −6.48936 + 19.9722i −0.299014 + 0.920270i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 7.41641 22.8254i 0.340288 1.04730i
\(476\) −3.23607 + 2.35114i −0.148325 + 0.107764i
\(477\) 29.1246 + 21.1603i 1.33352 + 0.968862i
\(478\) 0 0
\(479\) −8.65248 26.6296i −0.395342 1.21674i −0.928695 0.370844i \(-0.879068\pi\)
0.533353 0.845893i \(-0.320932\pi\)
\(480\) 0 0
\(481\) −16.1803 + 11.7557i −0.737760 + 0.536014i
\(482\) 0 0
\(483\) −15.0000 −0.682524
\(484\) 0 0
\(485\) 5.00000 0.227038
\(486\) 0 0
\(487\) 10.5172 7.64121i 0.476581 0.346256i −0.323420 0.946256i \(-0.604833\pi\)
0.800000 + 0.599999i \(0.204833\pi\)
\(488\) 0 0
\(489\) −3.70820 11.4127i −0.167691 0.516099i
\(490\) 0 0
\(491\) 24.2705 + 17.6336i 1.09531 + 0.795791i 0.980289 0.197571i \(-0.0633054\pi\)
0.115024 + 0.993363i \(0.463305\pi\)
\(492\) 9.70820 7.05342i 0.437680 0.317993i
\(493\) 6.18034 19.0211i 0.278349 0.856669i
\(494\) 0 0
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) −0.309017 + 0.951057i −0.0138613 + 0.0426607i
\(498\) 0 0
\(499\) −35.5967 25.8626i −1.59353 1.15777i −0.898674 0.438617i \(-0.855468\pi\)
−0.694855 0.719150i \(-0.744532\pi\)
\(500\) −5.56231 17.1190i −0.248754 0.765586i
\(501\) 1.85410 + 5.70634i 0.0828352 + 0.254940i
\(502\) 0 0
\(503\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) −1.23607 + 3.80423i −0.0548416 + 0.168785i
\(509\) 25.0795 18.2213i 1.11163 0.807647i 0.128711 0.991682i \(-0.458916\pi\)
0.982920 + 0.184035i \(0.0589161\pi\)
\(510\) 0 0
\(511\) −3.09017 9.51057i −0.136701 0.420723i
\(512\) 0 0
\(513\) −43.6869 31.7404i −1.92882 1.40137i
\(514\) 0 0
\(515\) 3.70820 11.4127i 0.163403 0.502903i
\(516\) −48.0000 −2.11308
\(517\) 0 0
\(518\) 0 0
\(519\) −14.8328 + 45.6507i −0.651088 + 2.00384i
\(520\) 0 0
\(521\) −5.66312 4.11450i −0.248106 0.180259i 0.456781 0.889579i \(-0.349002\pi\)
−0.704887 + 0.709320i \(0.749002\pi\)
\(522\) 0 0
\(523\) 9.88854 + 30.4338i 0.432396 + 1.33078i 0.895732 + 0.444595i \(0.146652\pi\)
−0.463336 + 0.886183i \(0.653348\pi\)
\(524\) 29.1246 + 21.1603i 1.27231 + 0.924391i
\(525\) 9.70820 7.05342i 0.423701 0.307837i
\(526\) 0 0
\(527\) 2.00000 0.0871214
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) −14.5623 + 10.5801i −0.631950 + 0.459139i
\(532\) 9.70820 + 7.05342i 0.420904 + 0.305805i
\(533\) 2.47214 + 7.60845i 0.107080 + 0.329559i
\(534\) 0 0
\(535\) −8.09017 5.87785i −0.349769 0.254122i
\(536\) 0 0
\(537\) −0.927051 + 2.85317i −0.0400052 + 0.123123i
\(538\) 0 0
\(539\) 0 0
\(540\) −18.0000 −0.774597
\(541\) 9.88854 30.4338i 0.425142 1.30845i −0.477717 0.878514i \(-0.658536\pi\)
0.902859 0.429938i \(-0.141464\pi\)
\(542\) 0 0
\(543\) 12.1353 + 8.81678i 0.520774 + 0.378364i
\(544\) 0 0
\(545\) −1.23607 3.80423i −0.0529473 0.162955i
\(546\) 0 0
\(547\) 19.4164 14.1068i 0.830186 0.603165i −0.0894262 0.995993i \(-0.528503\pi\)
0.919612 + 0.392828i \(0.128503\pi\)
\(548\) 1.85410 5.70634i 0.0792033 0.243763i
\(549\) −12.0000 −0.512148
\(550\) 0 0
\(551\) −60.0000 −2.55609
\(552\) 0 0
\(553\) 4.85410 3.52671i 0.206417 0.149971i
\(554\) 0 0
\(555\) −4.63525 14.2658i −0.196756 0.605552i
\(556\) 6.18034 + 19.0211i 0.262105 + 0.806676i
\(557\) −11.3262 8.22899i −0.479908 0.348674i 0.321382 0.946950i \(-0.395853\pi\)
−0.801290 + 0.598276i \(0.795853\pi\)
\(558\) 0 0
\(559\) 9.88854 30.4338i 0.418241 1.28721i
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) 0 0
\(563\) 6.18034 19.0211i 0.260470 0.801645i −0.732232 0.681055i \(-0.761521\pi\)
0.992702 0.120590i \(-0.0384786\pi\)
\(564\) −38.8328 + 28.2137i −1.63516 + 1.18801i
\(565\) −15.3713 11.1679i −0.646676 0.469838i
\(566\) 0 0
\(567\) −2.78115 8.55951i −0.116797 0.359466i
\(568\) 0 0
\(569\) 14.5623 10.5801i 0.610484 0.443542i −0.239101 0.970995i \(-0.576853\pi\)
0.849585 + 0.527452i \(0.176853\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) −15.0000 −0.626634
\(574\) 0 0
\(575\) −16.1803 + 11.7557i −0.674767 + 0.490247i
\(576\) 38.8328 + 28.2137i 1.61803 + 1.17557i
\(577\) −7.72542 23.7764i −0.321614 0.989825i −0.972946 0.231032i \(-0.925790\pi\)
0.651332 0.758793i \(-0.274210\pi\)
\(578\) 0 0
\(579\) 33.9787 + 24.6870i 1.41211 + 1.02596i
\(580\) −16.1803 + 11.7557i −0.671852 + 0.488129i
\(581\) −3.70820 + 11.4127i −0.153842 + 0.473478i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 7.41641 22.8254i 0.306631 0.943712i
\(586\) 0 0
\(587\) −29.1246 21.1603i −1.20210 0.873378i −0.207612 0.978211i \(-0.566569\pi\)
−0.994490 + 0.104834i \(0.966569\pi\)
\(588\) 1.85410 + 5.70634i 0.0764619 + 0.235325i
\(589\) −1.85410 5.70634i −0.0763969 0.235126i
\(590\) 0 0
\(591\) 43.6869 31.7404i 1.79704 1.30563i
\(592\) −6.18034 + 19.0211i −0.254010 + 0.781764i
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 2.00000 0.0819920
\(596\) 13.5967 41.8465i 0.556944 1.71410i
\(597\) −19.4164 + 14.1068i −0.794661 + 0.577355i
\(598\) 0 0
\(599\) −14.8328 45.6507i −0.606052 1.86524i −0.489388 0.872066i \(-0.662780\pi\)
−0.116664 0.993171i \(-0.537220\pi\)
\(600\) 0 0
\(601\) −6.47214 4.70228i −0.264004 0.191810i 0.447906 0.894080i \(-0.352170\pi\)
−0.711910 + 0.702270i \(0.752170\pi\)
\(602\) 0 0
\(603\) −5.56231 + 17.1190i −0.226515 + 0.697140i
\(604\) −12.0000 −0.488273
\(605\) 0 0
\(606\) 0 0
\(607\) −3.09017 + 9.51057i −0.125426 + 0.386022i −0.993978 0.109576i \(-0.965051\pi\)
0.868552 + 0.495597i \(0.165051\pi\)
\(608\) 0 0
\(609\) −24.2705 17.6336i −0.983491 0.714548i
\(610\) 0 0
\(611\) −9.88854 30.4338i −0.400048 1.23122i
\(612\) 19.4164 + 14.1068i 0.784862 + 0.570235i
\(613\) −12.9443 + 9.40456i −0.522814 + 0.379847i −0.817663 0.575697i \(-0.804731\pi\)
0.294849 + 0.955544i \(0.404731\pi\)
\(614\) 0 0
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −13.7533 + 9.99235i −0.552791 + 0.401626i −0.828814 0.559525i \(-0.810984\pi\)
0.276022 + 0.961151i \(0.410984\pi\)
\(620\) −1.61803 1.17557i −0.0649818 0.0472120i
\(621\) 13.9058 + 42.7975i 0.558019 + 1.71741i
\(622\) 0 0
\(623\) −12.1353 8.81678i −0.486189 0.353237i
\(624\) −38.8328 + 28.2137i −1.55456 + 1.12945i
\(625\) 3.39919 10.4616i 0.135967 0.418465i
\(626\) 0 0
\(627\) 0 0
\(628\) −14.0000 −0.558661
\(629\) −3.09017 + 9.51057i −0.123213 + 0.379211i
\(630\) 0 0
\(631\) −21.8435 15.8702i −0.869574 0.631783i 0.0608983 0.998144i \(-0.480603\pi\)
−0.930473 + 0.366361i \(0.880603\pi\)
\(632\) 0 0
\(633\) 1.85410 + 5.70634i 0.0736939 + 0.226807i
\(634\) 0 0
\(635\) 1.61803 1.17557i 0.0642097 0.0466511i
\(636\) −11.1246 + 34.2380i −0.441120 + 1.35763i
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) −12.1353 + 8.81678i −0.479314 + 0.348242i −0.801060 0.598584i \(-0.795730\pi\)
0.321746 + 0.946826i \(0.395730\pi\)
\(642\) 0 0
\(643\) −8.96149 27.5806i −0.353407 1.08767i −0.956928 0.290327i \(-0.906236\pi\)
0.603521 0.797347i \(-0.293764\pi\)
\(644\) −3.09017 9.51057i −0.121770 0.374769i
\(645\) 19.4164 + 14.1068i 0.764520 + 0.555457i
\(646\) 0 0
\(647\) −6.48936 + 19.9722i −0.255123 + 0.785188i 0.738682 + 0.674054i \(0.235448\pi\)
−0.993805 + 0.111134i \(0.964552\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0.927051 2.85317i 0.0363340 0.111825i
\(652\) 6.47214 4.70228i 0.253468 0.184156i
\(653\) 13.7533 + 9.99235i 0.538208 + 0.391031i 0.823419 0.567434i \(-0.192064\pi\)
−0.285211 + 0.958465i \(0.592064\pi\)
\(654\) 0 0
\(655\) −5.56231 17.1190i −0.217337 0.668895i
\(656\) 6.47214 + 4.70228i 0.252694 + 0.183593i
\(657\) −48.5410 + 35.2671i −1.89377 + 1.37590i
\(658\) 0 0
\(659\) −2.00000 −0.0779089 −0.0389545 0.999241i \(-0.512403\pi\)
−0.0389545 + 0.999241i \(0.512403\pi\)
\(660\) 0 0
\(661\) 35.0000 1.36134 0.680671 0.732589i \(-0.261688\pi\)
0.680671 + 0.732589i \(0.261688\pi\)
\(662\) 0 0
\(663\) −19.4164 + 14.1068i −0.754071 + 0.547865i
\(664\) 0 0
\(665\) −1.85410 5.70634i −0.0718990 0.221282i
\(666\) 0 0
\(667\) 40.4508 + 29.3893i 1.56626 + 1.13796i
\(668\) −3.23607 + 2.35114i −0.125207 + 0.0909684i
\(669\) −0.927051 + 2.85317i −0.0358419 + 0.110310i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.23607 3.80423i 0.0476469 0.146642i −0.924403 0.381418i \(-0.875436\pi\)
0.972049 + 0.234776i \(0.0754357\pi\)
\(674\) 0 0
\(675\) −29.1246 21.1603i −1.12101 0.814459i
\(676\) −1.85410 5.70634i −0.0713116 0.219475i
\(677\) 11.7426 + 36.1401i 0.451307 + 1.38898i 0.875417 + 0.483368i \(0.160587\pi\)
−0.424111 + 0.905610i \(0.639413\pi\)
\(678\) 0 0
\(679\) −4.04508 + 2.93893i −0.155236 + 0.112786i
\(680\) 0 0
\(681\) −12.0000 −0.459841
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 22.2492 68.4761i 0.850720 2.61825i
\(685\) −2.42705 + 1.76336i −0.0927329 + 0.0673744i
\(686\) 0 0
\(687\) 6.48936 + 19.9722i 0.247584 + 0.761986i
\(688\) −9.88854 30.4338i −0.376997 1.16028i
\(689\) −19.4164 14.1068i −0.739706 0.537428i
\(690\) 0 0
\(691\) 4.63525 14.2658i 0.176333 0.542698i −0.823358 0.567522i \(-0.807902\pi\)
0.999692 + 0.0248233i \(0.00790230\pi\)
\(692\) −32.0000 −1.21646
\(693\) 0 0
\(694\) 0 0
\(695\) 3.09017 9.51057i 0.117217 0.360756i
\(696\) 0 0
\(697\) 3.23607 + 2.35114i 0.122575 + 0.0890558i
\(698\) 0 0
\(699\) −5.56231 17.1190i −0.210386 0.647501i
\(700\) 6.47214 + 4.70228i 0.244624 + 0.177730i
\(701\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(702\) 0 0
\(703\) 30.0000 1.13147
\(704\) 0 0
\(705\) 24.0000 0.903892
\(706\) 0 0
\(707\) −9.70820 + 7.05342i −0.365115 + 0.265271i
\(708\) −14.5623 10.5801i −0.547285 0.397626i
\(709\) 12.0517 + 37.0912i 0.452610 + 1.39299i 0.873919 + 0.486072i \(0.161571\pi\)
−0.421309 + 0.906917i \(0.638429\pi\)
\(710\) 0 0
\(711\) −29.1246 21.1603i −1.09226 0.793572i
\(712\) 0 0
\(713\) −1.54508 + 4.75528i −0.0578639 + 0.178087i
\(714\) 0 0
\(715\) 0 0
\(716\) −2.00000 −0.0747435
\(717\) −3.70820 + 11.4127i −0.138485 + 0.426214i
\(718\) 0 0
\(719\) 8.89919 + 6.46564i 0.331884 + 0.241128i 0.741229 0.671252i \(-0.234243\pi\)
−0.409346 + 0.912379i \(0.634243\pi\)
\(720\) −7.41641 22.8254i −0.276393 0.850651i
\(721\) 3.70820 + 11.4127i 0.138101 + 0.425030i
\(722\) 0 0
\(723\) −29.1246 + 21.1603i −1.08316 + 0.786959i
\(724\) −3.09017 + 9.51057i −0.114845 + 0.353457i
\(725\) −40.0000 −1.48556
\(726\) 0 0
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) 0 0
\(729\) 21.8435 15.8702i 0.809017 0.587785i
\(730\) 0 0
\(731\) −4.94427 15.2169i −0.182871 0.562818i
\(732\) −3.70820 11.4127i −0.137059 0.421825i
\(733\) 3.23607 + 2.35114i 0.119527 + 0.0868414i 0.645943 0.763386i \(-0.276464\pi\)
−0.526416 + 0.850227i \(0.676464\pi\)
\(734\) 0 0
\(735\) 0.927051 2.85317i 0.0341948 0.105241i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −5.56231 + 17.1190i −0.204613 + 0.629733i 0.795116 + 0.606457i \(0.207410\pi\)
−0.999729 + 0.0232763i \(0.992590\pi\)
\(740\) 8.09017 5.87785i 0.297401 0.216074i
\(741\) 58.2492 + 42.3205i 2.13984 + 1.55468i
\(742\) 0 0
\(743\) −7.41641 22.8254i −0.272082 0.837381i −0.989977 0.141230i \(-0.954894\pi\)
0.717895 0.696151i \(-0.245106\pi\)
\(744\) 0 0
\(745\) −17.7984 + 12.9313i −0.652082 + 0.473765i
\(746\) 0 0
\(747\) 72.0000 2.63434
\(748\) 0 0
\(749\) 10.0000 0.365392
\(750\) 0 0
\(751\) 18.6074 13.5191i 0.678993 0.493318i −0.194030 0.980996i \(-0.562156\pi\)
0.873024 + 0.487678i \(0.162156\pi\)
\(752\) −25.8885 18.8091i −0.944058 0.685898i
\(753\) 19.4681 + 59.9166i 0.709456 + 2.18348i
\(754\) 0 0
\(755\) 4.85410 + 3.52671i 0.176659 + 0.128350i
\(756\) 14.5623 10.5801i 0.529626 0.384796i
\(757\) 11.7426 36.1401i 0.426794 1.31354i −0.474473 0.880270i \(-0.657361\pi\)
0.901266 0.433266i \(-0.142639\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −14.8328 + 45.6507i −0.537689 + 1.65484i 0.200077 + 0.979780i \(0.435881\pi\)
−0.737766 + 0.675057i \(0.764119\pi\)
\(762\) 0 0
\(763\) 3.23607 + 2.35114i 0.117154 + 0.0851170i
\(764\) −3.09017 9.51057i −0.111798 0.344080i
\(765\) −3.70820 11.4127i −0.134070 0.412626i
\(766\) 0 0
\(767\) 9.70820 7.05342i 0.350543 0.254684i
\(768\) −14.8328 + 45.6507i −0.535233 + 1.64728i
\(769\) 40.0000 1.44244 0.721218 0.692708i \(-0.243582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) −8.65248 + 26.6296i −0.311409 + 0.958420i
\(773\) 4.85410 3.52671i 0.174590 0.126847i −0.497059 0.867717i \(-0.665587\pi\)
0.671648 + 0.740870i \(0.265587\pi\)
\(774\) 0 0
\(775\) −1.23607 3.80423i −0.0444009 0.136652i
\(776\) 0 0
\(777\) 12.1353 + 8.81678i 0.435350 + 0.316300i
\(778\) 0 0
\(779\) 3.70820 11.4127i 0.132860 0.408902i
\(780\) 24.0000 0.859338
\(781\) 0 0
\(782\) 0 0
\(783\) −27.8115 + 85.5951i −0.993903 + 3.05892i
\(784\) −3.23607 + 2.35114i −0.115574 + 0.0839693i
\(785\) 5.66312 + 4.11450i 0.202125 + 0.146853i
\(786\) 0 0
\(787\) −6.79837 20.9232i −0.242336 0.745833i −0.996063 0.0886458i \(-0.971746\pi\)
0.753727 0.657187i \(-0.228254\pi\)
\(788\) 29.1246 + 21.1603i 1.03752 +