Properties

Label 1638.2.bj.g.127.4
Level $1638$
Weight $2$
Character 1638.127
Analytic conductor $13.079$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + 3842 x^{4} - 3394 x^{3} + 2141 x^{2} - 832 x + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.4
Root \(0.500000 - 1.73154i\) of defining polynomial
Character \(\chi\) \(=\) 1638.127
Dual form 1638.2.bj.g.1135.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.71131i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.71131i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-1.85566 - 3.21409i) q^{10} +(5.00118 - 2.88743i) q^{11} +(2.87757 + 2.17246i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.106098 - 0.183768i) q^{17} +(1.85081 + 1.06857i) q^{19} +(-3.21409 - 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} +(-1.23970 - 2.14722i) q^{23} -8.77384 q^{25} +(3.57828 + 0.442616i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-0.0492830 - 0.0853606i) q^{29} -2.31076i q^{31} +(-0.866025 - 0.500000i) q^{32} -0.212197i q^{34} +(-1.85566 + 3.21409i) q^{35} +(6.81859 - 3.93672i) q^{37} +2.13714 q^{38} -3.71131 q^{40} +(-6.51354 + 3.76060i) q^{41} +(2.28987 - 3.96617i) q^{43} -5.77486i q^{44} +(-2.14722 - 1.23970i) q^{46} +9.15570i q^{47} +(0.500000 + 0.866025i) q^{49} +(-7.59837 + 4.38692i) q^{50} +(3.32019 - 1.40582i) q^{52} -12.0948 q^{53} +(-10.7162 - 18.5609i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.0853606 - 0.0492830i) q^{58} +(0.200843 + 0.115957i) q^{59} +(-4.01605 + 6.95601i) q^{61} +(-1.15538 - 2.00118i) q^{62} -1.00000 q^{64} +(8.06267 - 10.6796i) q^{65} +(-11.2323 + 6.48500i) q^{67} +(-0.106098 - 0.183768i) q^{68} +3.71131i q^{70} +(-6.37721 - 3.68188i) q^{71} -5.60414i q^{73} +(3.93672 - 6.81859i) q^{74} +(1.85081 - 1.06857i) q^{76} -5.77486 q^{77} -9.19749 q^{79} +(-3.21409 + 1.85566i) q^{80} +(-3.76060 + 6.51354i) q^{82} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} -4.57973i q^{86} +(-2.88743 - 5.00118i) q^{88} +(10.2335 - 5.90833i) q^{89} +(-1.40582 - 3.32019i) q^{91} -2.47940 q^{92} +(4.57785 + 7.92907i) q^{94} +(3.96579 - 6.86895i) q^{95} +(12.1952 + 7.04093i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 3.71131i 1.65975i −0.557950 0.829875i \(-0.688412\pi\)
0.557950 0.829875i \(-0.311588\pi\)
\(6\) 0 0
\(7\) −0.866025 0.500000i −0.327327 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.85566 3.21409i −0.586810 1.01638i
\(11\) 5.00118 2.88743i 1.50791 0.870594i 0.507955 0.861384i \(-0.330402\pi\)
0.999958 0.00920984i \(-0.00293162\pi\)
\(12\) 0 0
\(13\) 2.87757 + 2.17246i 0.798095 + 0.602531i
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.106098 0.183768i 0.0257327 0.0445703i −0.852872 0.522120i \(-0.825141\pi\)
0.878605 + 0.477549i \(0.158475\pi\)
\(18\) 0 0
\(19\) 1.85081 + 1.06857i 0.424606 + 0.245146i 0.697046 0.717026i \(-0.254497\pi\)
−0.272440 + 0.962173i \(0.587831\pi\)
\(20\) −3.21409 1.85566i −0.718693 0.414937i
\(21\) 0 0
\(22\) 2.88743 5.00118i 0.615603 1.06626i
\(23\) −1.23970 2.14722i −0.258495 0.447727i 0.707344 0.706870i \(-0.249893\pi\)
−0.965839 + 0.259143i \(0.916560\pi\)
\(24\) 0 0
\(25\) −8.77384 −1.75477
\(26\) 3.57828 + 0.442616i 0.701759 + 0.0868041i
\(27\) 0 0
\(28\) −0.866025 + 0.500000i −0.163663 + 0.0944911i
\(29\) −0.0492830 0.0853606i −0.00915162 0.0158511i 0.861413 0.507905i \(-0.169580\pi\)
−0.870565 + 0.492054i \(0.836246\pi\)
\(30\) 0 0
\(31\) 2.31076i 0.415025i −0.978232 0.207513i \(-0.933463\pi\)
0.978232 0.207513i \(-0.0665368\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 0.212197i 0.0363915i
\(35\) −1.85566 + 3.21409i −0.313663 + 0.543281i
\(36\) 0 0
\(37\) 6.81859 3.93672i 1.12097 0.647192i 0.179321 0.983791i \(-0.442610\pi\)
0.941648 + 0.336599i \(0.109277\pi\)
\(38\) 2.13714 0.346689
\(39\) 0 0
\(40\) −3.71131 −0.586810
\(41\) −6.51354 + 3.76060i −1.01724 + 0.587306i −0.913305 0.407277i \(-0.866478\pi\)
−0.103940 + 0.994584i \(0.533145\pi\)
\(42\) 0 0
\(43\) 2.28987 3.96617i 0.349201 0.604835i −0.636906 0.770941i \(-0.719786\pi\)
0.986108 + 0.166107i \(0.0531196\pi\)
\(44\) 5.77486i 0.870594i
\(45\) 0 0
\(46\) −2.14722 1.23970i −0.316591 0.182784i
\(47\) 9.15570i 1.33550i 0.744388 + 0.667748i \(0.232742\pi\)
−0.744388 + 0.667748i \(0.767258\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −7.59837 + 4.38692i −1.07457 + 0.620404i
\(51\) 0 0
\(52\) 3.32019 1.40582i 0.460427 0.194953i
\(53\) −12.0948 −1.66135 −0.830674 0.556759i \(-0.812045\pi\)
−0.830674 + 0.556759i \(0.812045\pi\)
\(54\) 0 0
\(55\) −10.7162 18.5609i −1.44497 2.50276i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) −0.0853606 0.0492830i −0.0112084 0.00647117i
\(59\) 0.200843 + 0.115957i 0.0261476 + 0.0150963i 0.513017 0.858379i \(-0.328528\pi\)
−0.486869 + 0.873475i \(0.661861\pi\)
\(60\) 0 0
\(61\) −4.01605 + 6.95601i −0.514203 + 0.890626i 0.485661 + 0.874147i \(0.338579\pi\)
−0.999864 + 0.0164787i \(0.994754\pi\)
\(62\) −1.15538 2.00118i −0.146734 0.254150i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 8.06267 10.6796i 1.00005 1.32464i
\(66\) 0 0
\(67\) −11.2323 + 6.48500i −1.37225 + 0.792269i −0.991211 0.132291i \(-0.957767\pi\)
−0.381039 + 0.924559i \(0.624433\pi\)
\(68\) −0.106098 0.183768i −0.0128663 0.0222851i
\(69\) 0 0
\(70\) 3.71131i 0.443587i
\(71\) −6.37721 3.68188i −0.756836 0.436959i 0.0713229 0.997453i \(-0.477278\pi\)
−0.828158 + 0.560494i \(0.810611\pi\)
\(72\) 0 0
\(73\) 5.60414i 0.655915i −0.944692 0.327958i \(-0.893640\pi\)
0.944692 0.327958i \(-0.106360\pi\)
\(74\) 3.93672 6.81859i 0.457634 0.792645i
\(75\) 0 0
\(76\) 1.85081 1.06857i 0.212303 0.122573i
\(77\) −5.77486 −0.658107
\(78\) 0 0
\(79\) −9.19749 −1.03480 −0.517399 0.855744i \(-0.673100\pi\)
−0.517399 + 0.855744i \(0.673100\pi\)
\(80\) −3.21409 + 1.85566i −0.359346 + 0.207469i
\(81\) 0 0
\(82\) −3.76060 + 6.51354i −0.415288 + 0.719301i
\(83\) 3.17186i 0.348157i 0.984732 + 0.174078i \(0.0556946\pi\)
−0.984732 + 0.174078i \(0.944305\pi\)
\(84\) 0 0
\(85\) −0.682021 0.393765i −0.0739755 0.0427098i
\(86\) 4.57973i 0.493845i
\(87\) 0 0
\(88\) −2.88743 5.00118i −0.307801 0.533128i
\(89\) 10.2335 5.90833i 1.08475 0.626282i 0.152577 0.988292i \(-0.451243\pi\)
0.932174 + 0.362010i \(0.117909\pi\)
\(90\) 0 0
\(91\) −1.40582 3.32019i −0.147370 0.348050i
\(92\) −2.47940 −0.258495
\(93\) 0 0
\(94\) 4.57785 + 7.92907i 0.472169 + 0.817821i
\(95\) 3.96579 6.86895i 0.406882 0.704740i
\(96\) 0 0
\(97\) 12.1952 + 7.04093i 1.23824 + 0.714898i 0.968734 0.248101i \(-0.0798064\pi\)
0.269506 + 0.962999i \(0.413140\pi\)
\(98\) 0.866025 + 0.500000i 0.0874818 + 0.0505076i
\(99\) 0 0
\(100\) −4.38692 + 7.59837i −0.438692 + 0.759837i
\(101\) 3.07622 + 5.32816i 0.306095 + 0.530172i 0.977505 0.210914i \(-0.0676441\pi\)
−0.671410 + 0.741087i \(0.734311\pi\)
\(102\) 0 0
\(103\) 19.3491 1.90652 0.953260 0.302152i \(-0.0977050\pi\)
0.953260 + 0.302152i \(0.0977050\pi\)
\(104\) 2.17246 2.87757i 0.213027 0.282169i
\(105\) 0 0
\(106\) −10.4744 + 6.04740i −1.01736 + 0.587375i
\(107\) 5.82506 + 10.0893i 0.563130 + 0.975369i 0.997221 + 0.0745005i \(0.0237362\pi\)
−0.434091 + 0.900869i \(0.642930\pi\)
\(108\) 0 0
\(109\) 5.73307i 0.549129i 0.961569 + 0.274564i \(0.0885336\pi\)
−0.961569 + 0.274564i \(0.911466\pi\)
\(110\) −18.5609 10.7162i −1.76972 1.02175i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 8.25971 14.3062i 0.777008 1.34582i −0.156650 0.987654i \(-0.550070\pi\)
0.933659 0.358164i \(-0.116597\pi\)
\(114\) 0 0
\(115\) −7.96901 + 4.60091i −0.743114 + 0.429037i
\(116\) −0.0985660 −0.00915162
\(117\) 0 0
\(118\) 0.231914 0.0213494
\(119\) −0.183768 + 0.106098i −0.0168460 + 0.00972603i
\(120\) 0 0
\(121\) 11.1745 19.3549i 1.01587 1.75953i
\(122\) 8.03211i 0.727193i
\(123\) 0 0
\(124\) −2.00118 1.15538i −0.179711 0.103756i
\(125\) 14.0059i 1.25273i
\(126\) 0 0
\(127\) −5.89420 10.2090i −0.523025 0.905907i −0.999641 0.0267947i \(-0.991470\pi\)
0.476616 0.879112i \(-0.341863\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 1.64269 13.2801i 0.144073 1.16474i
\(131\) 5.12859 0.448087 0.224043 0.974579i \(-0.428074\pi\)
0.224043 + 0.974579i \(0.428074\pi\)
\(132\) 0 0
\(133\) −1.06857 1.85081i −0.0926566 0.160486i
\(134\) −6.48500 + 11.2323i −0.560219 + 0.970327i
\(135\) 0 0
\(136\) −0.183768 0.106098i −0.0157580 0.00909787i
\(137\) 8.13482 + 4.69664i 0.695005 + 0.401261i 0.805484 0.592617i \(-0.201905\pi\)
−0.110479 + 0.993878i \(0.535239\pi\)
\(138\) 0 0
\(139\) −7.57063 + 13.1127i −0.642133 + 1.11221i 0.342823 + 0.939400i \(0.388617\pi\)
−0.984956 + 0.172806i \(0.944717\pi\)
\(140\) 1.85566 + 3.21409i 0.156832 + 0.271640i
\(141\) 0 0
\(142\) −7.36377 −0.617954
\(143\) 20.6641 + 2.55605i 1.72802 + 0.213747i
\(144\) 0 0
\(145\) −0.316800 + 0.182905i −0.0263088 + 0.0151894i
\(146\) −2.80207 4.85333i −0.231901 0.401664i
\(147\) 0 0
\(148\) 7.87343i 0.647192i
\(149\) 17.8425 + 10.3013i 1.46171 + 0.843919i 0.999091 0.0426374i \(-0.0135760\pi\)
0.462620 + 0.886557i \(0.346909\pi\)
\(150\) 0 0
\(151\) 11.9407i 0.971721i −0.874036 0.485861i \(-0.838506\pi\)
0.874036 0.485861i \(-0.161494\pi\)
\(152\) 1.06857 1.85081i 0.0866723 0.150121i
\(153\) 0 0
\(154\) −5.00118 + 2.88743i −0.403007 + 0.232676i
\(155\) −8.57596 −0.688838
\(156\) 0 0
\(157\) 9.34022 0.745431 0.372715 0.927946i \(-0.378427\pi\)
0.372715 + 0.927946i \(0.378427\pi\)
\(158\) −7.96526 + 4.59875i −0.633682 + 0.365857i
\(159\) 0 0
\(160\) −1.85566 + 3.21409i −0.146703 + 0.254096i
\(161\) 2.47940i 0.195404i
\(162\) 0 0
\(163\) 3.87746 + 2.23865i 0.303706 + 0.175345i 0.644106 0.764936i \(-0.277229\pi\)
−0.340401 + 0.940280i \(0.610563\pi\)
\(164\) 7.52119i 0.587306i
\(165\) 0 0
\(166\) 1.58593 + 2.74691i 0.123092 + 0.213202i
\(167\) −12.7365 + 7.35342i −0.985579 + 0.569025i −0.903950 0.427638i \(-0.859346\pi\)
−0.0816295 + 0.996663i \(0.526012\pi\)
\(168\) 0 0
\(169\) 3.56086 + 12.5028i 0.273912 + 0.961755i
\(170\) −0.787529 −0.0604008
\(171\) 0 0
\(172\) −2.28987 3.96617i −0.174601 0.302417i
\(173\) −6.88286 + 11.9215i −0.523294 + 0.906372i 0.476339 + 0.879262i \(0.341964\pi\)
−0.999632 + 0.0271097i \(0.991370\pi\)
\(174\) 0 0
\(175\) 7.59837 + 4.38692i 0.574383 + 0.331620i
\(176\) −5.00118 2.88743i −0.376978 0.217648i
\(177\) 0 0
\(178\) 5.90833 10.2335i 0.442848 0.767035i
\(179\) −7.63936 13.2318i −0.570992 0.988988i −0.996464 0.0840164i \(-0.973225\pi\)
0.425472 0.904972i \(-0.360108\pi\)
\(180\) 0 0
\(181\) −1.66748 −0.123943 −0.0619713 0.998078i \(-0.519739\pi\)
−0.0619713 + 0.998078i \(0.519739\pi\)
\(182\) −2.87757 2.17246i −0.213300 0.161033i
\(183\) 0 0
\(184\) −2.14722 + 1.23970i −0.158295 + 0.0913919i
\(185\) −14.6104 25.3059i −1.07418 1.86053i
\(186\) 0 0
\(187\) 1.22541i 0.0896108i
\(188\) 7.92907 + 4.57785i 0.578287 + 0.333874i
\(189\) 0 0
\(190\) 7.93158i 0.575418i
\(191\) 0.0604880 0.104768i 0.00437676 0.00758076i −0.863829 0.503786i \(-0.831940\pi\)
0.868205 + 0.496205i \(0.165273\pi\)
\(192\) 0 0
\(193\) −2.38633 + 1.37775i −0.171772 + 0.0991725i −0.583421 0.812170i \(-0.698286\pi\)
0.411649 + 0.911342i \(0.364953\pi\)
\(194\) 14.0819 1.01102
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 13.0989 7.56267i 0.933260 0.538818i 0.0454187 0.998968i \(-0.485538\pi\)
0.887841 + 0.460150i \(0.152204\pi\)
\(198\) 0 0
\(199\) 2.65320 4.59548i 0.188080 0.325765i −0.756530 0.653959i \(-0.773107\pi\)
0.944610 + 0.328194i \(0.106440\pi\)
\(200\) 8.77384i 0.620404i
\(201\) 0 0
\(202\) 5.32816 + 3.07622i 0.374888 + 0.216442i
\(203\) 0.0985660i 0.00691798i
\(204\) 0 0
\(205\) 13.9567 + 24.1738i 0.974782 + 1.68837i
\(206\) 16.7568 9.67453i 1.16750 0.674056i
\(207\) 0 0
\(208\) 0.442616 3.57828i 0.0306899 0.248109i
\(209\) 12.3417 0.853691
\(210\) 0 0
\(211\) −8.94910 15.5003i −0.616081 1.06708i −0.990194 0.139701i \(-0.955386\pi\)
0.374112 0.927383i \(-0.377947\pi\)
\(212\) −6.04740 + 10.4744i −0.415337 + 0.719385i
\(213\) 0 0
\(214\) 10.0893 + 5.82506i 0.689690 + 0.398193i
\(215\) −14.7197 8.49841i −1.00387 0.579587i
\(216\) 0 0
\(217\) −1.15538 + 2.00118i −0.0784324 + 0.135849i
\(218\) 2.86654 + 4.96499i 0.194146 + 0.336271i
\(219\) 0 0
\(220\) −21.4323 −1.44497
\(221\) 0.704534 0.298312i 0.0473921 0.0200666i
\(222\) 0 0
\(223\) −14.2362 + 8.21925i −0.953324 + 0.550402i −0.894112 0.447844i \(-0.852192\pi\)
−0.0592118 + 0.998245i \(0.518859\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 16.5194i 1.09886i
\(227\) 4.87655 + 2.81547i 0.323668 + 0.186870i 0.653026 0.757335i \(-0.273499\pi\)
−0.329359 + 0.944205i \(0.606832\pi\)
\(228\) 0 0
\(229\) 27.7225i 1.83196i −0.401228 0.915978i \(-0.631416\pi\)
0.401228 0.915978i \(-0.368584\pi\)
\(230\) −4.60091 + 7.96901i −0.303375 + 0.525461i
\(231\) 0 0
\(232\) −0.0853606 + 0.0492830i −0.00560420 + 0.00323559i
\(233\) 20.1104 1.31747 0.658737 0.752374i \(-0.271091\pi\)
0.658737 + 0.752374i \(0.271091\pi\)
\(234\) 0 0
\(235\) 33.9797 2.21659
\(236\) 0.200843 0.115957i 0.0130738 0.00754816i
\(237\) 0 0
\(238\) −0.106098 + 0.183768i −0.00687734 + 0.0119119i
\(239\) 6.62968i 0.428838i 0.976742 + 0.214419i \(0.0687858\pi\)
−0.976742 + 0.214419i \(0.931214\pi\)
\(240\) 0 0
\(241\) 1.40025 + 0.808433i 0.0901978 + 0.0520757i 0.544420 0.838812i \(-0.316750\pi\)
−0.454223 + 0.890888i \(0.650083\pi\)
\(242\) 22.3491i 1.43665i
\(243\) 0 0
\(244\) 4.01605 + 6.95601i 0.257102 + 0.445313i
\(245\) 3.21409 1.85566i 0.205341 0.118554i
\(246\) 0 0
\(247\) 3.00444 + 7.09570i 0.191168 + 0.451489i
\(248\) −2.31076 −0.146734
\(249\) 0 0
\(250\) 7.00296 + 12.1295i 0.442906 + 0.767136i
\(251\) −0.253506 + 0.439085i −0.0160011 + 0.0277148i −0.873915 0.486079i \(-0.838427\pi\)
0.857914 + 0.513793i \(0.171760\pi\)
\(252\) 0 0
\(253\) −12.3999 7.15910i −0.779576 0.450089i
\(254\) −10.2090 5.89420i −0.640573 0.369835i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.82032 + 8.34903i 0.300683 + 0.520798i 0.976291 0.216463i \(-0.0694520\pi\)
−0.675608 + 0.737261i \(0.736119\pi\)
\(258\) 0 0
\(259\) −7.87343 −0.489231
\(260\) −5.21745 12.3223i −0.323573 0.764194i
\(261\) 0 0
\(262\) 4.44149 2.56429i 0.274396 0.158423i
\(263\) −3.67309 6.36197i −0.226492 0.392296i 0.730274 0.683155i \(-0.239392\pi\)
−0.956766 + 0.290858i \(0.906059\pi\)
\(264\) 0 0
\(265\) 44.8876i 2.75742i
\(266\) −1.85081 1.06857i −0.113481 0.0655181i
\(267\) 0 0
\(268\) 12.9700i 0.792269i
\(269\) 11.1770 19.3592i 0.681476 1.18035i −0.293055 0.956096i \(-0.594672\pi\)
0.974530 0.224255i \(-0.0719949\pi\)
\(270\) 0 0
\(271\) −8.32891 + 4.80870i −0.505945 + 0.292108i −0.731165 0.682200i \(-0.761023\pi\)
0.225220 + 0.974308i \(0.427690\pi\)
\(272\) −0.212197 −0.0128663
\(273\) 0 0
\(274\) 9.39328 0.567469
\(275\) −43.8796 + 25.3339i −2.64604 + 1.52769i
\(276\) 0 0
\(277\) 5.08945 8.81518i 0.305795 0.529653i −0.671643 0.740875i \(-0.734411\pi\)
0.977438 + 0.211222i \(0.0677444\pi\)
\(278\) 15.1413i 0.908113i
\(279\) 0 0
\(280\) 3.21409 + 1.85566i 0.192079 + 0.110897i
\(281\) 14.1692i 0.845265i 0.906301 + 0.422633i \(0.138894\pi\)
−0.906301 + 0.422633i \(0.861106\pi\)
\(282\) 0 0
\(283\) 9.46631 + 16.3961i 0.562714 + 0.974649i 0.997258 + 0.0739986i \(0.0235760\pi\)
−0.434545 + 0.900650i \(0.643091\pi\)
\(284\) −6.37721 + 3.68188i −0.378418 + 0.218480i
\(285\) 0 0
\(286\) 19.1736 8.11844i 1.13376 0.480053i
\(287\) 7.52119 0.443962
\(288\) 0 0
\(289\) 8.47749 + 14.6834i 0.498676 + 0.863732i
\(290\) −0.182905 + 0.316800i −0.0107405 + 0.0186031i
\(291\) 0 0
\(292\) −4.85333 2.80207i −0.284020 0.163979i
\(293\) −3.16950 1.82991i −0.185164 0.106905i 0.404553 0.914515i \(-0.367427\pi\)
−0.589717 + 0.807610i \(0.700761\pi\)
\(294\) 0 0
\(295\) 0.430353 0.745393i 0.0250561 0.0433985i
\(296\) −3.93672 6.81859i −0.228817 0.396323i
\(297\) 0 0
\(298\) 20.6027 1.19348
\(299\) 1.09742 8.87198i 0.0634655 0.513080i
\(300\) 0 0
\(301\) −3.96617 + 2.28987i −0.228606 + 0.131986i
\(302\) −5.97036 10.3410i −0.343555 0.595055i
\(303\) 0 0
\(304\) 2.13714i 0.122573i
\(305\) 25.8159 + 14.9048i 1.47822 + 0.853448i
\(306\) 0 0
\(307\) 19.6987i 1.12426i 0.827048 + 0.562132i \(0.190019\pi\)
−0.827048 + 0.562132i \(0.809981\pi\)
\(308\) −2.88743 + 5.00118i −0.164527 + 0.284969i
\(309\) 0 0
\(310\) −7.42700 + 4.28798i −0.421825 + 0.243541i
\(311\) −16.9685 −0.962195 −0.481098 0.876667i \(-0.659762\pi\)
−0.481098 + 0.876667i \(0.659762\pi\)
\(312\) 0 0
\(313\) −4.53794 −0.256500 −0.128250 0.991742i \(-0.540936\pi\)
−0.128250 + 0.991742i \(0.540936\pi\)
\(314\) 8.08887 4.67011i 0.456481 0.263550i
\(315\) 0 0
\(316\) −4.59875 + 7.96526i −0.258700 + 0.448081i
\(317\) 29.1866i 1.63928i 0.572877 + 0.819641i \(0.305827\pi\)
−0.572877 + 0.819641i \(0.694173\pi\)
\(318\) 0 0
\(319\) −0.492946 0.284603i −0.0275997 0.0159347i
\(320\) 3.71131i 0.207469i
\(321\) 0 0
\(322\) 1.23970 + 2.14722i 0.0690857 + 0.119660i
\(323\) 0.392737 0.226747i 0.0218525 0.0126165i
\(324\) 0 0
\(325\) −25.2474 19.0608i −1.40047 1.05730i
\(326\) 4.47730 0.247975
\(327\) 0 0
\(328\) 3.76060 + 6.51354i 0.207644 + 0.359650i
\(329\) 4.57785 7.92907i 0.252385 0.437144i
\(330\) 0 0
\(331\) 4.16161 + 2.40271i 0.228743 + 0.132065i 0.609992 0.792408i \(-0.291173\pi\)
−0.381249 + 0.924472i \(0.624506\pi\)
\(332\) 2.74691 + 1.58593i 0.150756 + 0.0870392i
\(333\) 0 0
\(334\) −7.35342 + 12.7365i −0.402361 + 0.696910i
\(335\) 24.0679 + 41.6868i 1.31497 + 2.27759i
\(336\) 0 0
\(337\) 17.7312 0.965883 0.482941 0.875653i \(-0.339568\pi\)
0.482941 + 0.875653i \(0.339568\pi\)
\(338\) 9.33520 + 9.04732i 0.507768 + 0.492109i
\(339\) 0 0
\(340\) −0.682021 + 0.393765i −0.0369878 + 0.0213549i
\(341\) −6.67217 11.5565i −0.361318 0.625822i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −3.96617 2.28987i −0.213841 0.123461i
\(345\) 0 0
\(346\) 13.7657i 0.740049i
\(347\) −8.35240 + 14.4668i −0.448380 + 0.776617i −0.998281 0.0586128i \(-0.981332\pi\)
0.549901 + 0.835230i \(0.314666\pi\)
\(348\) 0 0
\(349\) 0.0173616 0.0100237i 0.000929347 0.000536559i −0.499535 0.866294i \(-0.666496\pi\)
0.500465 + 0.865757i \(0.333163\pi\)
\(350\) 8.77384 0.468982
\(351\) 0 0
\(352\) −5.77486 −0.307801
\(353\) −25.8299 + 14.9129i −1.37479 + 0.793734i −0.991526 0.129905i \(-0.958533\pi\)
−0.383262 + 0.923640i \(0.625199\pi\)
\(354\) 0 0
\(355\) −13.6646 + 23.6678i −0.725243 + 1.25616i
\(356\) 11.8167i 0.626282i
\(357\) 0 0
\(358\) −13.2318 7.63936i −0.699320 0.403753i
\(359\) 18.3351i 0.967687i −0.875154 0.483844i \(-0.839240\pi\)
0.875154 0.483844i \(-0.160760\pi\)
\(360\) 0 0
\(361\) −7.21632 12.4990i −0.379806 0.657844i
\(362\) −1.44408 + 0.833739i −0.0758991 + 0.0438204i
\(363\) 0 0
\(364\) −3.57828 0.442616i −0.187553 0.0231994i
\(365\) −20.7987 −1.08866
\(366\) 0 0
\(367\) −0.672426 1.16468i −0.0351004 0.0607956i 0.847942 0.530090i \(-0.177842\pi\)
−0.883042 + 0.469294i \(0.844508\pi\)
\(368\) −1.23970 + 2.14722i −0.0646238 + 0.111932i
\(369\) 0 0
\(370\) −25.3059 14.6104i −1.31559 0.759558i
\(371\) 10.4744 + 6.04740i 0.543804 + 0.313965i
\(372\) 0 0
\(373\) 5.53575 9.58821i 0.286630 0.496458i −0.686373 0.727250i \(-0.740798\pi\)
0.973003 + 0.230791i \(0.0741315\pi\)
\(374\) −0.612704 1.06124i −0.0316822 0.0548752i
\(375\) 0 0
\(376\) 9.15570 0.472169
\(377\) 0.0436269 0.352697i 0.00224690 0.0181648i
\(378\) 0 0
\(379\) 14.5583 8.40523i 0.747808 0.431747i −0.0770930 0.997024i \(-0.524564\pi\)
0.824902 + 0.565276i \(0.191231\pi\)
\(380\) −3.96579 6.86895i −0.203441 0.352370i
\(381\) 0 0
\(382\) 0.120976i 0.00618967i
\(383\) −14.3562 8.28855i −0.733567 0.423525i 0.0861585 0.996281i \(-0.472541\pi\)
−0.819726 + 0.572756i \(0.805874\pi\)
\(384\) 0 0
\(385\) 21.4323i 1.09229i
\(386\) −1.37775 + 2.38633i −0.0701256 + 0.121461i
\(387\) 0 0
\(388\) 12.1952 7.04093i 0.619120 0.357449i
\(389\) 1.17013 0.0593280 0.0296640 0.999560i \(-0.490556\pi\)
0.0296640 + 0.999560i \(0.490556\pi\)
\(390\) 0 0
\(391\) −0.526121 −0.0266071
\(392\) 0.866025 0.500000i 0.0437409 0.0252538i
\(393\) 0 0
\(394\) 7.56267 13.0989i 0.381002 0.659914i
\(395\) 34.1348i 1.71751i
\(396\) 0 0
\(397\) 22.6877 + 13.0987i 1.13866 + 0.657406i 0.946099 0.323878i \(-0.104987\pi\)
0.192562 + 0.981285i \(0.438320\pi\)
\(398\) 5.30640i 0.265986i
\(399\) 0 0
\(400\) 4.38692 + 7.59837i 0.219346 + 0.379919i
\(401\) 9.84559 5.68436i 0.491665 0.283863i −0.233600 0.972333i \(-0.575051\pi\)
0.725265 + 0.688470i \(0.241717\pi\)
\(402\) 0 0
\(403\) 5.02003 6.64939i 0.250066 0.331230i
\(404\) 6.15243 0.306095
\(405\) 0 0
\(406\) 0.0492830 + 0.0853606i 0.00244587 + 0.00423638i
\(407\) 22.7340 39.3764i 1.12688 1.95182i
\(408\) 0 0
\(409\) −20.2056 11.6657i −0.999102 0.576832i −0.0911196 0.995840i \(-0.529045\pi\)
−0.907982 + 0.419008i \(0.862378\pi\)
\(410\) 24.1738 + 13.9567i 1.19386 + 0.689275i
\(411\) 0 0
\(412\) 9.67453 16.7568i 0.476630 0.825547i
\(413\) −0.115957 0.200843i −0.00570587 0.00988286i
\(414\) 0 0
\(415\) 11.7718 0.577853
\(416\) −1.40582 3.32019i −0.0689262 0.162786i
\(417\) 0 0
\(418\) 10.6882 6.17084i 0.522777 0.301826i
\(419\) −6.33402 10.9709i −0.309437 0.535961i 0.668802 0.743441i \(-0.266807\pi\)
−0.978239 + 0.207479i \(0.933474\pi\)
\(420\) 0 0
\(421\) 27.6625i 1.34819i −0.738646 0.674094i \(-0.764534\pi\)
0.738646 0.674094i \(-0.235466\pi\)
\(422\) −15.5003 8.94910i −0.754543 0.435635i
\(423\) 0 0
\(424\) 12.0948i 0.587375i
\(425\) −0.930892 + 1.61235i −0.0451549 + 0.0782105i
\(426\) 0 0
\(427\) 6.95601 4.01605i 0.336625 0.194351i
\(428\) 11.6501 0.563130
\(429\) 0 0
\(430\) −16.9968 −0.819660
\(431\) −5.55462 + 3.20696i −0.267557 + 0.154474i −0.627777 0.778393i \(-0.716035\pi\)
0.360220 + 0.932867i \(0.382702\pi\)
\(432\) 0 0
\(433\) −0.0325135 + 0.0563150i −0.00156250 + 0.00270633i −0.866806 0.498646i \(-0.833831\pi\)
0.865243 + 0.501353i \(0.167164\pi\)
\(434\) 2.31076i 0.110920i
\(435\) 0 0
\(436\) 4.96499 + 2.86654i 0.237780 + 0.137282i
\(437\) 5.29881i 0.253477i
\(438\) 0 0
\(439\) 18.3889 + 31.8505i 0.877655 + 1.52014i 0.853908 + 0.520424i \(0.174226\pi\)
0.0237469 + 0.999718i \(0.492440\pi\)
\(440\) −18.5609 + 10.7162i −0.884858 + 0.510873i
\(441\) 0 0
\(442\) 0.460989 0.610613i 0.0219270 0.0290439i
\(443\) 8.46383 0.402129 0.201064 0.979578i \(-0.435560\pi\)
0.201064 + 0.979578i \(0.435560\pi\)
\(444\) 0 0
\(445\) −21.9277 37.9798i −1.03947 1.80042i
\(446\) −8.21925 + 14.2362i −0.389193 + 0.674102i
\(447\) 0 0
\(448\) 0.866025 + 0.500000i 0.0409159 + 0.0236228i
\(449\) 19.5984 + 11.3152i 0.924907 + 0.533995i 0.885197 0.465216i \(-0.154023\pi\)
0.0397096 + 0.999211i \(0.487357\pi\)
\(450\) 0 0
\(451\) −21.7169 + 37.6148i −1.02261 + 1.77121i
\(452\) −8.25971 14.3062i −0.388504 0.672909i
\(453\) 0 0
\(454\) 5.63095 0.264274
\(455\) −12.3223 + 5.21745i −0.577677 + 0.244598i
\(456\) 0 0
\(457\) −14.1310 + 8.15851i −0.661018 + 0.381639i −0.792665 0.609658i \(-0.791307\pi\)
0.131647 + 0.991297i \(0.457974\pi\)
\(458\) −13.8613 24.0084i −0.647694 1.12184i
\(459\) 0 0
\(460\) 9.20183i 0.429037i
\(461\) −16.6951 9.63892i −0.777568 0.448929i 0.0579996 0.998317i \(-0.481528\pi\)
−0.835568 + 0.549387i \(0.814861\pi\)
\(462\) 0 0
\(463\) 2.70218i 0.125581i 0.998027 + 0.0627904i \(0.0200000\pi\)
−0.998027 + 0.0627904i \(0.980000\pi\)
\(464\) −0.0492830 + 0.0853606i −0.00228791 + 0.00396277i
\(465\) 0 0
\(466\) 17.4161 10.0552i 0.806784 0.465797i
\(467\) 18.3906 0.851014 0.425507 0.904955i \(-0.360096\pi\)
0.425507 + 0.904955i \(0.360096\pi\)
\(468\) 0 0
\(469\) 12.9700 0.598899
\(470\) 29.4272 16.9898i 1.35738 0.783682i
\(471\) 0 0
\(472\) 0.115957 0.200843i 0.00533735 0.00924457i
\(473\) 26.4473i 1.21605i
\(474\) 0 0
\(475\) −16.2388 9.37545i −0.745085 0.430175i
\(476\) 0.212197i 0.00972603i
\(477\) 0 0
\(478\) 3.31484 + 5.74147i 0.151617 + 0.262609i
\(479\) −35.3951 + 20.4354i −1.61725 + 0.933717i −0.629617 + 0.776906i \(0.716788\pi\)
−0.987629 + 0.156811i \(0.949879\pi\)
\(480\) 0 0
\(481\) 28.1733 + 3.48491i 1.28459 + 0.158898i
\(482\) 1.61687 0.0736462
\(483\) 0 0
\(484\) −11.1745 19.3549i −0.507933 0.879766i
\(485\) 26.1311 45.2604i 1.18655 2.05517i
\(486\) 0 0
\(487\) 15.2674 + 8.81466i 0.691834 + 0.399430i 0.804299 0.594225i \(-0.202541\pi\)
−0.112465 + 0.993656i \(0.535875\pi\)
\(488\) 6.95601 + 4.01605i 0.314884 + 0.181798i
\(489\) 0 0
\(490\) 1.85566 3.21409i 0.0838300 0.145198i
\(491\) 9.42997 + 16.3332i 0.425569 + 0.737106i 0.996473 0.0839098i \(-0.0267408\pi\)
−0.570905 + 0.821016i \(0.693407\pi\)
\(492\) 0 0
\(493\) −0.0209154 −0.000941982
\(494\) 6.14977 + 4.64284i 0.276691 + 0.208891i
\(495\) 0 0
\(496\) −2.00118 + 1.15538i −0.0898556 + 0.0518782i
\(497\) 3.68188 + 6.37721i 0.165155 + 0.286057i
\(498\) 0 0
\(499\) 2.10742i 0.0943410i −0.998887 0.0471705i \(-0.984980\pi\)
0.998887 0.0471705i \(-0.0150204\pi\)
\(500\) 12.1295 + 7.00296i 0.542447 + 0.313182i
\(501\) 0 0
\(502\) 0.507011i 0.0226290i
\(503\) 10.8942 18.8693i 0.485749 0.841342i −0.514117 0.857720i \(-0.671880\pi\)
0.999866 + 0.0163784i \(0.00521363\pi\)
\(504\) 0 0
\(505\) 19.7745 11.4168i 0.879953 0.508041i
\(506\) −14.3182 −0.636521
\(507\) 0 0
\(508\) −11.7884 −0.523025
\(509\) 10.5636 6.09887i 0.468221 0.270328i −0.247273 0.968946i \(-0.579535\pi\)
0.715495 + 0.698618i \(0.246201\pi\)
\(510\) 0 0
\(511\) −2.80207 + 4.85333i −0.123956 + 0.214699i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 8.34903 + 4.82032i 0.368260 + 0.212615i
\(515\) 71.8104i 3.16435i
\(516\) 0 0
\(517\) 26.4365 + 45.7893i 1.16267 + 2.01381i
\(518\) −6.81859 + 3.93672i −0.299592 + 0.172969i
\(519\) 0 0
\(520\) −10.6796 8.06267i −0.468330 0.353571i
\(521\) 26.9765 1.18186 0.590932 0.806722i \(-0.298760\pi\)
0.590932 + 0.806722i \(0.298760\pi\)
\(522\) 0 0
\(523\) 1.87683 + 3.25076i 0.0820679 + 0.142146i 0.904138 0.427241i \(-0.140514\pi\)
−0.822070 + 0.569386i \(0.807181\pi\)
\(524\) 2.56429 4.44149i 0.112022 0.194027i
\(525\) 0 0
\(526\) −6.36197 3.67309i −0.277395 0.160154i
\(527\) −0.424644 0.245168i −0.0184978 0.0106797i
\(528\) 0 0
\(529\) 8.42629 14.5948i 0.366360 0.634555i
\(530\) 22.4438 + 38.8738i 0.974896 + 1.68857i
\(531\) 0 0
\(532\) −2.13714 −0.0926566
\(533\) −26.9129 3.32900i −1.16573 0.144195i
\(534\) 0 0
\(535\) 37.4445 21.6186i 1.61887 0.934654i
\(536\) 6.48500 + 11.2323i 0.280109 + 0.485163i
\(537\) 0 0
\(538\) 22.3541i 0.963752i
\(539\) 5.00118 + 2.88743i 0.215416 + 0.124371i
\(540\) 0 0
\(541\) 0.0135705i 0.000583440i 1.00000 0.000291720i \(9.28574e-5\pi\)
−1.00000 0.000291720i \(0.999907\pi\)
\(542\) −4.80870 + 8.32891i −0.206551 + 0.357757i
\(543\) 0 0
\(544\) −0.183768 + 0.106098i −0.00787899 + 0.00454894i
\(545\) 21.2772 0.911416
\(546\) 0 0
\(547\) −9.66115 −0.413081 −0.206540 0.978438i \(-0.566220\pi\)
−0.206540 + 0.978438i \(0.566220\pi\)
\(548\) 8.13482 4.69664i 0.347502 0.200631i
\(549\) 0 0
\(550\) −25.3339 + 43.8796i −1.08024 + 1.87103i
\(551\) 0.210649i 0.00897395i
\(552\) 0 0
\(553\) 7.96526 + 4.59875i 0.338717 + 0.195559i
\(554\) 10.1789i 0.432460i
\(555\) 0 0
\(556\) 7.57063 + 13.1127i 0.321066 + 0.556103i
\(557\) 21.6145 12.4791i 0.915834 0.528757i 0.0335307 0.999438i \(-0.489325\pi\)
0.882304 + 0.470680i \(0.155992\pi\)
\(558\) 0 0
\(559\) 15.2056 6.43830i 0.643128 0.272311i
\(560\) 3.71131 0.156832
\(561\) 0 0
\(562\) 7.08461 + 12.2709i 0.298846 + 0.517617i
\(563\) −7.94970 + 13.7693i −0.335040 + 0.580306i −0.983492 0.180949i \(-0.942083\pi\)
0.648453 + 0.761255i \(0.275416\pi\)
\(564\) 0 0
\(565\) −53.0949 30.6544i −2.23372 1.28964i
\(566\) 16.3961 + 9.46631i 0.689181 + 0.397899i
\(567\) 0 0
\(568\) −3.68188 + 6.37721i −0.154488 + 0.267582i
\(569\) 8.95465 + 15.5099i 0.375398 + 0.650209i 0.990387 0.138327i \(-0.0441725\pi\)
−0.614988 + 0.788536i \(0.710839\pi\)
\(570\) 0 0
\(571\) −12.5123 −0.523623 −0.261812 0.965119i \(-0.584320\pi\)
−0.261812 + 0.965119i \(0.584320\pi\)
\(572\) 12.5456 16.6176i 0.524560 0.694817i
\(573\) 0 0
\(574\) 6.51354 3.76060i 0.271870 0.156964i
\(575\) 10.8769 + 18.8394i 0.453599 + 0.785657i
\(576\) 0 0
\(577\) 22.0910i 0.919662i −0.888007 0.459831i \(-0.847910\pi\)
0.888007 0.459831i \(-0.152090\pi\)
\(578\) 14.6834 + 8.47749i 0.610750 + 0.352617i
\(579\) 0 0
\(580\) 0.365809i 0.0151894i
\(581\) 1.58593 2.74691i 0.0657954 0.113961i
\(582\) 0 0
\(583\) −60.4883 + 34.9229i −2.50517 + 1.44636i
\(584\) −5.60414 −0.231901
\(585\) 0 0
\(586\) −3.65982 −0.151186
\(587\) 18.3007 10.5659i 0.755352 0.436102i −0.0722727 0.997385i \(-0.523025\pi\)
0.827624 + 0.561282i \(0.189692\pi\)
\(588\) 0 0
\(589\) 2.46921 4.27679i 0.101742 0.176222i
\(590\) 0.860706i 0.0354347i
\(591\) 0 0
\(592\) −6.81859 3.93672i −0.280242 0.161798i
\(593\) 8.95493i 0.367735i −0.982951 0.183867i \(-0.941138\pi\)
0.982951 0.183867i \(-0.0588617\pi\)
\(594\) 0 0
\(595\) 0.393765 + 0.682021i 0.0161428 + 0.0279601i
\(596\) 17.8425 10.3013i 0.730855 0.421960i
\(597\) 0 0
\(598\) −3.48560 8.23207i −0.142537 0.336635i
\(599\) −41.7996 −1.70788 −0.853942 0.520368i \(-0.825795\pi\)
−0.853942 + 0.520368i \(0.825795\pi\)
\(600\) 0 0
\(601\) −7.64481 13.2412i −0.311838 0.540120i 0.666922 0.745127i \(-0.267611\pi\)
−0.978760 + 0.205008i \(0.934278\pi\)
\(602\) −2.28987 + 3.96617i −0.0933280 + 0.161649i
\(603\) 0 0
\(604\) −10.3410 5.97036i −0.420768 0.242930i
\(605\) −71.8319 41.4722i −2.92038 1.68608i
\(606\) 0 0
\(607\) −7.30434 + 12.6515i −0.296474 + 0.513508i −0.975327 0.220766i \(-0.929144\pi\)
0.678853 + 0.734275i \(0.262478\pi\)
\(608\) −1.06857 1.85081i −0.0433362 0.0750604i
\(609\) 0 0
\(610\) 29.8097 1.20696
\(611\) −19.8904 + 26.3462i −0.804678 + 1.06585i
\(612\) 0 0
\(613\) −33.9623 + 19.6081i −1.37172 + 0.791965i −0.991145 0.132783i \(-0.957609\pi\)
−0.380579 + 0.924748i \(0.624275\pi\)
\(614\) 9.84935 + 17.0596i 0.397487 + 0.688468i
\(615\) 0 0
\(616\) 5.77486i 0.232676i
\(617\) −8.10486 4.67934i −0.326289 0.188383i 0.327903 0.944711i \(-0.393658\pi\)
−0.654192 + 0.756328i \(0.726991\pi\)
\(618\) 0 0
\(619\) 43.7075i 1.75675i −0.477970 0.878376i \(-0.658627\pi\)
0.477970 0.878376i \(-0.341373\pi\)
\(620\) −4.28798 + 7.42700i −0.172210 + 0.298276i
\(621\) 0 0
\(622\) −14.6952 + 8.48425i −0.589222 + 0.340187i
\(623\) −11.8167 −0.473424
\(624\) 0 0
\(625\) 8.11112 0.324445
\(626\) −3.92997 + 2.26897i −0.157073 + 0.0906863i
\(627\) 0 0
\(628\) 4.67011 8.08887i 0.186358 0.322781i
\(629\) 1.67072i 0.0666159i
\(630\) 0 0
\(631\) −18.0096 10.3978i −0.716951 0.413932i 0.0966785 0.995316i \(-0.469178\pi\)
−0.813629 + 0.581384i \(0.802511\pi\)
\(632\) 9.19749i 0.365857i
\(633\) 0 0
\(634\) 14.5933 + 25.2763i 0.579574 + 1.00385i
\(635\) −37.8890 + 21.8752i −1.50358 + 0.868091i
\(636\) 0 0
\(637\) −0.442616 + 3.57828i −0.0175371 + 0.141777i
\(638\) −0.569205 −0.0225350
\(639\) 0 0
\(640\) 1.85566 + 3.21409i 0.0733513 + 0.127048i
\(641\) 3.61897 6.26824i 0.142941 0.247581i −0.785662 0.618656i \(-0.787677\pi\)
0.928603 + 0.371075i \(0.121011\pi\)
\(642\) 0 0
\(643\) 34.7898 + 20.0859i 1.37198 + 0.792111i 0.991177 0.132547i \(-0.0423154\pi\)
0.380800 + 0.924658i \(0.375649\pi\)
\(644\) 2.14722 + 1.23970i 0.0846124 + 0.0488510i
\(645\) 0 0
\(646\) 0.226747 0.392737i 0.00892124 0.0154520i
\(647\) −7.27561 12.6017i −0.286034 0.495425i 0.686826 0.726822i \(-0.259004\pi\)
−0.972859 + 0.231397i \(0.925670\pi\)
\(648\) 0 0
\(649\) 1.33927 0.0525710
\(650\) −31.3953 3.88344i −1.23142 0.152321i
\(651\) 0 0
\(652\) 3.87746 2.23865i 0.151853 0.0876723i
\(653\) −24.8634 43.0646i −0.972978 1.68525i −0.686451 0.727176i \(-0.740832\pi\)
−0.286527 0.958072i \(-0.592501\pi\)
\(654\) 0 0
\(655\) 19.0338i 0.743712i
\(656\) 6.51354 + 3.76060i 0.254311 + 0.146827i
\(657\) 0 0
\(658\) 9.15570i 0.356926i
\(659\) −15.7988 + 27.3644i −0.615436 + 1.06597i 0.374872 + 0.927076i \(0.377687\pi\)
−0.990308 + 0.138889i \(0.955647\pi\)
\(660\) 0 0
\(661\) −21.5391 + 12.4356i −0.837775 + 0.483689i −0.856507 0.516135i \(-0.827370\pi\)
0.0187325 + 0.999825i \(0.494037\pi\)
\(662\) 4.80542 0.186768
\(663\) 0 0
\(664\) 3.17186 0.123092
\(665\) −6.86895 + 3.96579i −0.266367 + 0.153787i
\(666\) 0 0
\(667\) −0.122192 + 0.211643i −0.00473130 + 0.00819485i
\(668\) 14.7068i 0.569025i
\(669\) 0 0
\(670\) 41.6868 + 24.0679i 1.61050 + 0.929822i
\(671\) 46.3843i 1.79065i
\(672\) 0 0
\(673\) −10.8245 18.7486i −0.417254 0.722705i 0.578408 0.815748i \(-0.303674\pi\)
−0.995662 + 0.0930423i \(0.970341\pi\)
\(674\) 15.3557 8.86562i 0.591480 0.341491i
\(675\) 0 0
\(676\) 12.6082 + 3.16761i 0.484930 + 0.121831i
\(677\) −14.3935 −0.553187 −0.276594 0.960987i \(-0.589206\pi\)
−0.276594 + 0.960987i \(0.589206\pi\)
\(678\) 0 0
\(679\) −7.04093 12.1952i −0.270206 0.468011i
\(680\) −0.393765 + 0.682021i −0.0151002 + 0.0261543i
\(681\) 0 0
\(682\) −11.5565 6.67217i −0.442523 0.255491i
\(683\) 36.6968 + 21.1869i 1.40416 + 0.810694i 0.994817 0.101686i \(-0.0324235\pi\)
0.409346 + 0.912379i \(0.365757\pi\)
\(684\) 0 0
\(685\) 17.4307 30.1909i 0.665993 1.15353i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) −4.57973 −0.174601
\(689\) −34.8037 26.2754i −1.32591 1.00101i
\(690\) 0 0
\(691\) −19.8651 + 11.4691i −0.755703 + 0.436305i −0.827751 0.561096i \(-0.810380\pi\)
0.0720480 + 0.997401i \(0.477047\pi\)
\(692\) 6.88286 + 11.9215i 0.261647 + 0.453186i
\(693\) 0 0
\(694\) 16.7048i 0.634105i
\(695\) 48.6654 + 28.0970i 1.84598 + 1.06578i
\(696\) 0 0
\(697\) 1.59597i 0.0604518i
\(698\) 0.0100237 0.0173616i 0.000379404 0.000657147i
\(699\) 0 0
\(700\) 7.59837 4.38692i 0.287191 0.165810i
\(701\) −1.70699 −0.0644723 −0.0322361 0.999480i \(-0.510263\pi\)
−0.0322361 + 0.999480i \(0.510263\pi\)
\(702\) 0 0
\(703\) 16.8266 0.634627
\(704\) −5.00118 + 2.88743i −0.188489 + 0.108824i
\(705\) 0 0
\(706\) −14.9129 + 25.8299i −0.561255 + 0.972122i
\(707\) 6.15243i 0.231386i
\(708\) 0 0
\(709\) −15.7730 9.10657i −0.592369 0.342005i 0.173665 0.984805i \(-0.444439\pi\)
−0.766034 + 0.642800i \(0.777772\pi\)
\(710\) 27.3292i 1.02565i
\(711\) 0 0
\(712\) −5.90833 10.2335i −0.221424 0.383518i
\(713\) −4.96172 + 2.86465i −0.185818 + 0.107282i
\(714\) 0 0
\(715\) 9.48629 76.6909i 0.354767 2.86808i
\(716\) −15.2787 −0.570992
\(717\) 0 0
\(718\) −9.16753 15.8786i −0.342129 0.592585i
\(719\) −1.79107 + 3.10222i −0.0667956 + 0.115693i −0.897489 0.441037i \(-0.854611\pi\)
0.830694 + 0.556730i \(0.187944\pi\)
\(720\) 0 0
\(721\) −16.7568 9.67453i −0.624055 0.360298i
\(722\) −12.4990 7.21632i −0.465166 0.268564i
\(723\) 0 0
\(724\) −0.833739 + 1.44408i −0.0309857 + 0.0536688i
\(725\) 0.432401 + 0.748941i 0.0160590 + 0.0278150i
\(726\) 0 0
\(727\) 3.21747 0.119329 0.0596647 0.998218i \(-0.480997\pi\)
0.0596647 + 0.998218i \(0.480997\pi\)
\(728\) −3.32019 + 1.40582i −0.123054 + 0.0521033i
\(729\) 0 0
\(730\) −18.0122 + 10.3994i −0.666662 + 0.384898i
\(731\) −0.485903 0.841608i −0.0179718 0.0311280i
\(732\) 0 0
\(733\) 4.79233i 0.177009i 0.996076 + 0.0885043i \(0.0282087\pi\)
−0.996076 + 0.0885043i \(0.971791\pi\)
\(734\) −1.16468 0.672426i −0.0429890 0.0248197i
\(735\) 0 0
\(736\) 2.47940i 0.0913919i
\(737\) −37.4500 + 64.8653i −1.37949 + 2.38934i
\(738\) 0 0
\(739\) 9.69853 5.59945i 0.356766 0.205979i −0.310895 0.950444i \(-0.600629\pi\)
0.667661 + 0.744465i \(0.267295\pi\)
\(740\) −29.2208 −1.07418
\(741\) 0 0
\(742\) 12.0948 0.444014
\(743\) 33.1315 19.1285i 1.21548 0.701757i 0.251531 0.967849i \(-0.419066\pi\)
0.963947 + 0.266093i \(0.0857328\pi\)
\(744\) 0 0
\(745\) 38.2315 66.2189i 1.40069 2.42607i
\(746\) 11.0715i 0.405357i
\(747\) 0 0
\(748\) −1.06124 0.612704i −0.0388026 0.0224027i
\(749\) 11.6501i 0.425686i
\(750\) 0 0
\(751\) −0.920125 1.59370i −0.0335758 0.0581551i 0.848749 0.528796i \(-0.177356\pi\)
−0.882325 + 0.470641i \(0.844023\pi\)
\(752\) 7.92907 4.57785i 0.289143 0.166937i
\(753\) 0 0
\(754\) −0.138566 0.327258i −0.00504629 0.0119180i
\(755\) −44.3157 −1.61281
\(756\) 0 0
\(757\) 10.5961 + 18.3529i 0.385120 + 0.667048i 0.991786 0.127909i \(-0.0408266\pi\)
−0.606666 + 0.794957i \(0.707493\pi\)
\(758\) 8.40523 14.5583i 0.305292 0.528780i
\(759\) 0 0
\(760\) −6.86895 3.96579i −0.249163 0.143854i
\(761\) 12.2381 + 7.06566i 0.443630 + 0.256130i 0.705136 0.709072i \(-0.250886\pi\)
−0.261506 + 0.965202i \(0.584219\pi\)
\(762\) 0 0
\(763\) 2.86654 4.96499i 0.103776 0.179745i
\(764\) −0.0604880 0.104768i −0.00218838 0.00379038i
\(765\) 0 0
\(766\) −16.5771 −0.598955
\(767\) 0.326030 + 0.769999i 0.0117723 + 0.0278030i
\(768\) 0 0
\(769\) −26.5219 + 15.3124i −0.956405 + 0.552181i −0.895065 0.445936i \(-0.852871\pi\)
−0.0613401 + 0.998117i \(0.519537\pi\)
\(770\) 10.7162 + 18.5609i 0.386184 + 0.668890i
\(771\) 0 0
\(772\) 2.75550i 0.0991725i
\(773\) 8.48254 + 4.89740i 0.305096 + 0.176147i 0.644730 0.764411i \(-0.276970\pi\)
−0.339634 + 0.940558i \(0.610303\pi\)
\(774\) 0 0
\(775\) 20.2743i 0.728273i
\(776\) 7.04093 12.1952i 0.252755 0.437784i
\(777\) 0 0
\(778\) 1.01336 0.585065i 0.0363308 0.0209756i
\(779\) −16.0738 −0.575904
\(780\) 0 0
\(781\) −42.5248 −1.52166
\(782\) −0.455634 + 0.263061i −0.0162934 + 0.00940702i
\(783\) 0 0
\(784\) 0.500000 0.866025i 0.0178571 0.0309295i
\(785\) 34.6645i 1.23723i
\(786\) 0 0
\(787\) 17.8665 +