Properties

Label 1638.2.r.a.1387.1
Level $1638$
Weight $2$
Character 1638.1387
Analytic conductor $13.079$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1387.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1638.1387
Dual form 1638.2.r.a.757.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -4.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -4.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.00000 - 3.46410i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 + 2.59808i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(-1.50000 - 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +11.0000 q^{25} +(-1.00000 - 3.46410i) q^{26} +(-0.500000 + 0.866025i) q^{28} +(-4.50000 + 7.79423i) q^{29} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +5.00000 q^{34} +(2.00000 + 3.46410i) q^{35} +(-2.00000 + 3.46410i) q^{37} +3.00000 q^{38} -4.00000 q^{40} +(2.50000 - 4.33013i) q^{41} +3.00000 q^{44} +(3.00000 + 5.19615i) q^{46} +3.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(-5.50000 + 9.52628i) q^{50} +(3.50000 + 0.866025i) q^{52} +11.0000 q^{53} +(6.00000 - 10.3923i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-4.50000 - 7.79423i) q^{58} +(1.00000 + 1.73205i) q^{59} +(0.500000 + 0.866025i) q^{61} +(2.00000 - 3.46410i) q^{62} +1.00000 q^{64} +(10.0000 - 10.3923i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-2.50000 + 4.33013i) q^{68} -4.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +12.0000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(-1.50000 + 2.59808i) q^{76} +3.00000 q^{77} +11.0000 q^{79} +(2.00000 - 3.46410i) q^{80} +(2.50000 + 4.33013i) q^{82} -6.00000 q^{83} +(10.0000 + 17.3205i) q^{85} +(-1.50000 + 2.59808i) q^{88} +(3.50000 - 6.06218i) q^{89} +(3.50000 + 0.866025i) q^{91} -6.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} +(6.00000 + 10.3923i) q^{95} +(6.00000 + 10.3923i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - 8q^{5} - q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - 8q^{5} - q^{7} + 2q^{8} + 4q^{10} - 3q^{11} - 5q^{13} + 2q^{14} - q^{16} - 5q^{17} - 3q^{19} + 4q^{20} - 3q^{22} + 6q^{23} + 22q^{25} - 2q^{26} - q^{28} - 9q^{29} - 8q^{31} - q^{32} + 10q^{34} + 4q^{35} - 4q^{37} + 6q^{38} - 8q^{40} + 5q^{41} + 6q^{44} + 6q^{46} + 6q^{47} - q^{49} - 11q^{50} + 7q^{52} + 22q^{53} + 12q^{55} - q^{56} - 9q^{58} + 2q^{59} + q^{61} + 4q^{62} + 2q^{64} + 20q^{65} - 2q^{67} - 5q^{68} - 8q^{70} + 6q^{71} + 24q^{73} - 4q^{74} - 3q^{76} + 6q^{77} + 22q^{79} + 4q^{80} + 5q^{82} - 12q^{83} + 20q^{85} - 3q^{88} + 7q^{89} + 7q^{91} - 12q^{92} - 3q^{94} + 12q^{95} + 12q^{97} - q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 2.00000 3.46410i 0.632456 1.09545i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.50000 4.33013i −0.606339 1.05021i −0.991838 0.127502i \(-0.959304\pi\)
0.385499 0.922708i \(-0.374029\pi\)
\(18\) 0 0
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) 2.00000 + 3.46410i 0.447214 + 0.774597i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) −1.00000 3.46410i −0.196116 0.679366i
\(27\) 0 0
\(28\) −0.500000 + 0.866025i −0.0944911 + 0.163663i
\(29\) −4.50000 + 7.79423i −0.835629 + 1.44735i 0.0578882 + 0.998323i \(0.481563\pi\)
−0.893517 + 0.449029i \(0.851770\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 5.00000 0.857493
\(35\) 2.00000 + 3.46410i 0.338062 + 0.585540i
\(36\) 0 0
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 3.00000 0.486664
\(39\) 0 0
\(40\) −4.00000 −0.632456
\(41\) 2.50000 4.33013i 0.390434 0.676252i −0.602072 0.798441i \(-0.705658\pi\)
0.992507 + 0.122189i \(0.0389915\pi\)
\(42\) 0 0
\(43\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −5.50000 + 9.52628i −0.777817 + 1.34722i
\(51\) 0 0
\(52\) 3.50000 + 0.866025i 0.485363 + 0.120096i
\(53\) 11.0000 1.51097 0.755483 0.655168i \(-0.227402\pi\)
0.755483 + 0.655168i \(0.227402\pi\)
\(54\) 0 0
\(55\) 6.00000 10.3923i 0.809040 1.40130i
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 0 0
\(58\) −4.50000 7.79423i −0.590879 1.02343i
\(59\) 1.00000 + 1.73205i 0.130189 + 0.225494i 0.923749 0.382998i \(-0.125108\pi\)
−0.793560 + 0.608492i \(0.791775\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 2.00000 3.46410i 0.254000 0.439941i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 10.0000 10.3923i 1.24035 1.28901i
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) −2.50000 + 4.33013i −0.303170 + 0.525105i
\(69\) 0 0
\(70\) −4.00000 −0.478091
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) 0 0
\(73\) 12.0000 1.40449 0.702247 0.711934i \(-0.252180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(74\) −2.00000 3.46410i −0.232495 0.402694i
\(75\) 0 0
\(76\) −1.50000 + 2.59808i −0.172062 + 0.298020i
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) 11.0000 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) 2.00000 3.46410i 0.223607 0.387298i
\(81\) 0 0
\(82\) 2.50000 + 4.33013i 0.276079 + 0.478183i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 10.0000 + 17.3205i 1.08465 + 1.87867i
\(86\) 0 0
\(87\) 0 0
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) 3.50000 6.06218i 0.370999 0.642590i −0.618720 0.785611i \(-0.712349\pi\)
0.989720 + 0.143022i \(0.0456819\pi\)
\(90\) 0 0
\(91\) 3.50000 + 0.866025i 0.366900 + 0.0907841i
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) 6.00000 + 10.3923i 0.615587 + 1.06623i
\(96\) 0 0
\(97\) 6.00000 + 10.3923i 0.609208 + 1.05518i 0.991371 + 0.131084i \(0.0418458\pi\)
−0.382164 + 0.924095i \(0.624821\pi\)
\(98\) −0.500000 0.866025i −0.0505076 0.0874818i
\(99\) 0 0
\(100\) −5.50000 9.52628i −0.550000 0.952628i
\(101\) 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) 0 0
\(103\) 20.0000 1.97066 0.985329 0.170664i \(-0.0545913\pi\)
0.985329 + 0.170664i \(0.0545913\pi\)
\(104\) −2.50000 + 2.59808i −0.245145 + 0.254762i
\(105\) 0 0
\(106\) −5.50000 + 9.52628i −0.534207 + 0.925274i
\(107\) 8.50000 14.7224i 0.821726 1.42327i −0.0826699 0.996577i \(-0.526345\pi\)
0.904396 0.426694i \(-0.140322\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 6.00000 + 10.3923i 0.572078 + 0.990867i
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) 6.00000 + 10.3923i 0.564433 + 0.977626i 0.997102 + 0.0760733i \(0.0242383\pi\)
−0.432670 + 0.901553i \(0.642428\pi\)
\(114\) 0 0
\(115\) −12.0000 + 20.7846i −1.11901 + 1.93817i
\(116\) 9.00000 0.835629
\(117\) 0 0
\(118\) −2.00000 −0.184115
\(119\) −2.50000 + 4.33013i −0.229175 + 0.396942i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −1.00000 −0.0905357
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) −4.00000 + 6.92820i −0.354943 + 0.614779i −0.987108 0.160055i \(-0.948833\pi\)
0.632166 + 0.774833i \(0.282166\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 4.00000 + 13.8564i 0.350823 + 1.21529i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) −1.50000 + 2.59808i −0.130066 + 0.225282i
\(134\) −1.00000 1.73205i −0.0863868 0.149626i
\(135\) 0 0
\(136\) −2.50000 4.33013i −0.214373 0.371305i
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) 0 0
\(139\) −6.50000 11.2583i −0.551323 0.954919i −0.998179 0.0603135i \(-0.980790\pi\)
0.446857 0.894606i \(-0.352543\pi\)
\(140\) 2.00000 3.46410i 0.169031 0.292770i
\(141\) 0 0
\(142\) −6.00000 −0.503509
\(143\) −3.00000 10.3923i −0.250873 0.869048i
\(144\) 0 0
\(145\) 18.0000 31.1769i 1.49482 2.58910i
\(146\) −6.00000 + 10.3923i −0.496564 + 0.860073i
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) −11.0000 −0.895167 −0.447584 0.894242i \(-0.647715\pi\)
−0.447584 + 0.894242i \(0.647715\pi\)
\(152\) −1.50000 2.59808i −0.121666 0.210732i
\(153\) 0 0
\(154\) −1.50000 + 2.59808i −0.120873 + 0.209359i
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) −5.50000 + 9.52628i −0.437557 + 0.757870i
\(159\) 0 0
\(160\) 2.00000 + 3.46410i 0.158114 + 0.273861i
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) −8.00000 + 13.8564i −0.619059 + 1.07224i 0.370599 + 0.928793i \(0.379152\pi\)
−0.989658 + 0.143448i \(0.954181\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) −20.0000 −1.53393
\(171\) 0 0
\(172\) 0 0
\(173\) −1.00000 1.73205i −0.0760286 0.131685i 0.825505 0.564396i \(-0.190891\pi\)
−0.901533 + 0.432710i \(0.857557\pi\)
\(174\) 0 0
\(175\) −5.50000 9.52628i −0.415761 0.720119i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) 3.50000 + 6.06218i 0.262336 + 0.454379i
\(179\) 12.0000 20.7846i 0.896922 1.55351i 0.0655145 0.997852i \(-0.479131\pi\)
0.831408 0.555663i \(-0.187536\pi\)
\(180\) 0 0
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) −2.50000 + 2.59808i −0.185312 + 0.192582i
\(183\) 0 0
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) 8.00000 13.8564i 0.588172 1.01874i
\(186\) 0 0
\(187\) 15.0000 1.09691
\(188\) −1.50000 2.59808i −0.109399 0.189484i
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i \(-0.236317\pi\)
−0.953912 + 0.300088i \(0.902984\pi\)
\(192\) 0 0
\(193\) −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i \(-0.988315\pi\)
0.531446 + 0.847092i \(0.321649\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −9.50000 + 16.4545i −0.676847 + 1.17233i 0.299078 + 0.954229i \(0.403321\pi\)
−0.975925 + 0.218105i \(0.930013\pi\)
\(198\) 0 0
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 11.0000 0.777817
\(201\) 0 0
\(202\) 5.00000 + 8.66025i 0.351799 + 0.609333i
\(203\) 9.00000 0.631676
\(204\) 0 0
\(205\) −10.0000 + 17.3205i −0.698430 + 1.20972i
\(206\) −10.0000 + 17.3205i −0.696733 + 1.20678i
\(207\) 0 0
\(208\) −1.00000 3.46410i −0.0693375 0.240192i
\(209\) 9.00000 0.622543
\(210\) 0 0
\(211\) −7.00000 + 12.1244i −0.481900 + 0.834675i −0.999784 0.0207756i \(-0.993386\pi\)
0.517884 + 0.855451i \(0.326720\pi\)
\(212\) −5.50000 9.52628i −0.377742 0.654268i
\(213\) 0 0
\(214\) 8.50000 + 14.7224i 0.581048 + 1.00640i
\(215\) 0 0
\(216\) 0 0
\(217\) 2.00000 + 3.46410i 0.135769 + 0.235159i
\(218\) 1.00000 1.73205i 0.0677285 0.117309i
\(219\) 0 0
\(220\) −12.0000 −0.809040
\(221\) 17.5000 + 4.33013i 1.17718 + 0.291276i
\(222\) 0 0
\(223\) 8.00000 13.8564i 0.535720 0.927894i −0.463409 0.886145i \(-0.653374\pi\)
0.999128 0.0417488i \(-0.0132929\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) −12.0000 −0.798228
\(227\) 7.00000 + 12.1244i 0.464606 + 0.804722i 0.999184 0.0403978i \(-0.0128625\pi\)
−0.534577 + 0.845120i \(0.679529\pi\)
\(228\) 0 0
\(229\) −5.00000 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) −12.0000 20.7846i −0.791257 1.37050i
\(231\) 0 0
\(232\) −4.50000 + 7.79423i −0.295439 + 0.511716i
\(233\) −4.00000 −0.262049 −0.131024 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) 1.00000 1.73205i 0.0650945 0.112747i
\(237\) 0 0
\(238\) −2.50000 4.33013i −0.162051 0.280680i
\(239\) 26.0000 1.68180 0.840900 0.541190i \(-0.182026\pi\)
0.840900 + 0.541190i \(0.182026\pi\)
\(240\) 0 0
\(241\) −6.00000 10.3923i −0.386494 0.669427i 0.605481 0.795860i \(-0.292981\pi\)
−0.991975 + 0.126432i \(0.959647\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0 0
\(244\) 0.500000 0.866025i 0.0320092 0.0554416i
\(245\) 2.00000 3.46410i 0.127775 0.221313i
\(246\) 0 0
\(247\) 10.5000 + 2.59808i 0.668099 + 0.165312i
\(248\) −4.00000 −0.254000
\(249\) 0 0
\(250\) 12.0000 20.7846i 0.758947 1.31453i
\(251\) 7.00000 + 12.1244i 0.441836 + 0.765283i 0.997826 0.0659066i \(-0.0209939\pi\)
−0.555990 + 0.831189i \(0.687661\pi\)
\(252\) 0 0
\(253\) 9.00000 + 15.5885i 0.565825 + 0.980038i
\(254\) −4.00000 6.92820i −0.250982 0.434714i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.50000 6.06218i 0.218324 0.378148i −0.735972 0.677012i \(-0.763274\pi\)
0.954296 + 0.298864i \(0.0966077\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) −14.0000 3.46410i −0.868243 0.214834i
\(261\) 0 0
\(262\) 6.00000 10.3923i 0.370681 0.642039i
\(263\) −13.0000 + 22.5167i −0.801614 + 1.38844i 0.116939 + 0.993139i \(0.462692\pi\)
−0.918553 + 0.395298i \(0.870641\pi\)
\(264\) 0 0
\(265\) −44.0000 −2.70290
\(266\) −1.50000 2.59808i −0.0919709 0.159298i
\(267\) 0 0
\(268\) 2.00000 0.122169
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) 0 0
\(271\) 6.00000 10.3923i 0.364474 0.631288i −0.624218 0.781251i \(-0.714582\pi\)
0.988692 + 0.149963i \(0.0479155\pi\)
\(272\) 5.00000 0.303170
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) −16.5000 + 28.5788i −0.994987 + 1.72337i
\(276\) 0 0
\(277\) −7.00000 12.1244i −0.420589 0.728482i 0.575408 0.817867i \(-0.304843\pi\)
−0.995997 + 0.0893846i \(0.971510\pi\)
\(278\) 13.0000 0.779688
\(279\) 0 0
\(280\) 2.00000 + 3.46410i 0.119523 + 0.207020i
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) 0 0
\(286\) 10.5000 + 2.59808i 0.620878 + 0.153627i
\(287\) −5.00000 −0.295141
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 18.0000 + 31.1769i 1.05700 + 1.83077i
\(291\) 0 0
\(292\) −6.00000 10.3923i −0.351123 0.608164i
\(293\) 12.0000 + 20.7846i 0.701047 + 1.21425i 0.968099 + 0.250568i \(0.0806172\pi\)
−0.267052 + 0.963682i \(0.586049\pi\)
\(294\) 0 0
\(295\) −4.00000 6.92820i −0.232889 0.403376i
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) 0 0
\(298\) −18.0000 −1.04271
\(299\) 6.00000 + 20.7846i 0.346989 + 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) 5.50000 9.52628i 0.316489 0.548176i
\(303\) 0 0
\(304\) 3.00000 0.172062
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) 0 0
\(307\) 21.0000 1.19853 0.599267 0.800549i \(-0.295459\pi\)
0.599267 + 0.800549i \(0.295459\pi\)
\(308\) −1.50000 2.59808i −0.0854704 0.148039i
\(309\) 0 0
\(310\) −8.00000 + 13.8564i −0.454369 + 0.786991i
\(311\) 19.0000 1.07739 0.538696 0.842500i \(-0.318917\pi\)
0.538696 + 0.842500i \(0.318917\pi\)
\(312\) 0 0
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 1.00000 1.73205i 0.0564333 0.0977453i
\(315\) 0 0
\(316\) −5.50000 9.52628i −0.309399 0.535895i
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) −13.5000 23.3827i −0.755855 1.30918i
\(320\) −4.00000 −0.223607
\(321\) 0 0
\(322\) 3.00000 5.19615i 0.167183 0.289570i
\(323\) −7.50000 + 12.9904i −0.417311 + 0.722804i
\(324\) 0 0
\(325\) −27.5000 + 28.5788i −1.52543 + 1.58527i
\(326\) 20.0000 1.10770
\(327\) 0 0
\(328\) 2.50000 4.33013i 0.138039 0.239091i
\(329\) −1.50000 2.59808i −0.0826977 0.143237i
\(330\) 0 0
\(331\) −1.00000 1.73205i −0.0549650 0.0952021i 0.837234 0.546845i \(-0.184171\pi\)
−0.892199 + 0.451643i \(0.850838\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) 0 0
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) 4.00000 6.92820i 0.218543 0.378528i
\(336\) 0 0
\(337\) 31.0000 1.68868 0.844339 0.535810i \(-0.179994\pi\)
0.844339 + 0.535810i \(0.179994\pi\)
\(338\) 11.5000 + 6.06218i 0.625518 + 0.329739i
\(339\) 0 0
\(340\) 10.0000 17.3205i 0.542326 0.939336i
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) 5.50000 + 9.52628i 0.295255 + 0.511397i 0.975044 0.222010i \(-0.0712619\pi\)
−0.679789 + 0.733408i \(0.737929\pi\)
\(348\) 0 0
\(349\) 17.0000 29.4449i 0.909989 1.57615i 0.0959126 0.995390i \(-0.469423\pi\)
0.814076 0.580758i \(-0.197244\pi\)
\(350\) 11.0000 0.587975
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 0 0
\(355\) −12.0000 20.7846i −0.636894 1.10313i
\(356\) −7.00000 −0.370999
\(357\) 0 0
\(358\) 12.0000 + 20.7846i 0.634220 + 1.09850i
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) 0 0
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) 2.50000 4.33013i 0.131397 0.227586i
\(363\) 0 0
\(364\) −1.00000 3.46410i −0.0524142 0.181568i
\(365\) −48.0000 −2.51243
\(366\) 0 0
\(367\) −9.00000 + 15.5885i −0.469796 + 0.813711i −0.999404 0.0345320i \(-0.989006\pi\)
0.529607 + 0.848243i \(0.322339\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 0 0
\(370\) 8.00000 + 13.8564i 0.415900 + 0.720360i
\(371\) −5.50000 9.52628i −0.285546 0.494580i
\(372\) 0 0
\(373\) −17.0000 29.4449i −0.880227 1.52460i −0.851089 0.525022i \(-0.824057\pi\)
−0.0291379 0.999575i \(-0.509276\pi\)
\(374\) −7.50000 + 12.9904i −0.387816 + 0.671717i
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) −9.00000 31.1769i −0.463524 1.60569i
\(378\) 0 0
\(379\) 9.00000 15.5885i 0.462299 0.800725i −0.536776 0.843725i \(-0.680358\pi\)
0.999075 + 0.0429994i \(0.0136914\pi\)
\(380\) 6.00000 10.3923i 0.307794 0.533114i
\(381\) 0 0
\(382\) 6.00000 0.306987
\(383\) −5.50000 9.52628i −0.281037 0.486770i 0.690604 0.723234i \(-0.257345\pi\)
−0.971640 + 0.236463i \(0.924012\pi\)
\(384\) 0 0
\(385\) −12.0000 −0.611577
\(386\) −6.50000 11.2583i −0.330841 0.573034i
\(387\) 0 0
\(388\) 6.00000 10.3923i 0.304604 0.527589i
\(389\) 26.0000 1.31825 0.659126 0.752032i \(-0.270926\pi\)
0.659126 + 0.752032i \(0.270926\pi\)
\(390\) 0 0
\(391\) −30.0000 −1.51717
\(392\) −0.500000 + 0.866025i −0.0252538 + 0.0437409i
\(393\) 0 0
\(394\) −9.50000 16.4545i −0.478603 0.828965i
\(395\) −44.0000 −2.21388
\(396\) 0 0
\(397\) 11.5000 + 19.9186i 0.577168 + 0.999685i 0.995802 + 0.0915300i \(0.0291757\pi\)
−0.418634 + 0.908155i \(0.637491\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −5.50000 + 9.52628i −0.275000 + 0.476314i
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) 10.0000 10.3923i 0.498135 0.517678i
\(404\) −10.0000 −0.497519
\(405\) 0 0
\(406\) −4.50000 + 7.79423i −0.223331 + 0.386821i
\(407\) −6.00000 10.3923i −0.297409 0.515127i
\(408\) 0 0
\(409\) 1.00000 + 1.73205i 0.0494468 + 0.0856444i 0.889689 0.456566i \(-0.150921\pi\)
−0.840243 + 0.542211i \(0.817588\pi\)
\(410\) −10.0000 17.3205i −0.493865 0.855399i
\(411\) 0 0
\(412\) −10.0000 17.3205i −0.492665 0.853320i
\(413\) 1.00000 1.73205i 0.0492068 0.0852286i
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) 3.50000 + 0.866025i 0.171602 + 0.0424604i
\(417\) 0 0
\(418\) −4.50000 + 7.79423i −0.220102 + 0.381228i
\(419\) 9.00000 15.5885i 0.439679 0.761546i −0.557986 0.829851i \(-0.688426\pi\)
0.997665 + 0.0683046i \(0.0217590\pi\)
\(420\) 0 0
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) −7.00000 12.1244i −0.340755 0.590204i
\(423\) 0 0
\(424\) 11.0000 0.534207
\(425\) −27.5000 47.6314i −1.33395 2.31046i
\(426\) 0 0
\(427\) 0.500000 0.866025i 0.0241967 0.0419099i
\(428\) −17.0000 −0.821726
\(429\) 0 0
\(430\) 0 0
\(431\) 19.0000 32.9090i 0.915198 1.58517i 0.108586 0.994087i \(-0.465368\pi\)
0.806611 0.591082i \(-0.201299\pi\)
\(432\) 0 0
\(433\) −17.0000 29.4449i −0.816968 1.41503i −0.907906 0.419173i \(-0.862320\pi\)
0.0909384 0.995857i \(-0.471013\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) −18.0000 −0.861057
\(438\) 0 0
\(439\) −20.0000 + 34.6410i −0.954548 + 1.65333i −0.219149 + 0.975691i \(0.570328\pi\)
−0.735399 + 0.677634i \(0.763005\pi\)
\(440\) 6.00000 10.3923i 0.286039 0.495434i
\(441\) 0 0
\(442\) −12.5000 + 12.9904i −0.594564 + 0.617889i
\(443\) 15.0000 0.712672 0.356336 0.934358i \(-0.384026\pi\)
0.356336 + 0.934358i \(0.384026\pi\)
\(444\) 0 0
\(445\) −14.0000 + 24.2487i −0.663664 + 1.14950i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) 0 0
\(448\) −0.500000 0.866025i −0.0236228 0.0409159i
\(449\) 10.0000 + 17.3205i 0.471929 + 0.817405i 0.999484 0.0321156i \(-0.0102245\pi\)
−0.527555 + 0.849521i \(0.676891\pi\)
\(450\) 0 0
\(451\) 7.50000 + 12.9904i 0.353161 + 0.611693i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) 0 0
\(454\) −14.0000 −0.657053
\(455\) −14.0000 3.46410i −0.656330 0.162400i
\(456\) 0 0
\(457\) 1.00000 1.73205i 0.0467780 0.0810219i −0.841688 0.539964i \(-0.818438\pi\)
0.888466 + 0.458942i \(0.151771\pi\)
\(458\) 2.50000 4.33013i 0.116817 0.202334i
\(459\) 0 0
\(460\) 24.0000 1.11901
\(461\) −16.0000 27.7128i −0.745194 1.29071i −0.950104 0.311933i \(-0.899023\pi\)
0.204910 0.978781i \(-0.434310\pi\)
\(462\) 0 0
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) −4.50000 7.79423i −0.208907 0.361838i
\(465\) 0 0
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 2.00000 0.0923514
\(470\) 6.00000 10.3923i 0.276759 0.479361i
\(471\) 0 0
\(472\) 1.00000 + 1.73205i 0.0460287 + 0.0797241i
\(473\) 0 0
\(474\) 0 0
\(475\) −16.5000 28.5788i −0.757072 1.31129i
\(476\) 5.00000 0.229175
\(477\) 0 0
\(478\) −13.0000 + 22.5167i −0.594606 + 1.02989i
\(479\) −16.5000 + 28.5788i −0.753904 + 1.30580i 0.192013 + 0.981392i \(0.438498\pi\)
−0.945917 + 0.324408i \(0.894835\pi\)
\(480\) 0 0
\(481\) −4.00000 13.8564i −0.182384 0.631798i
\(482\) 12.0000 0.546585
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −24.0000 41.5692i −1.08978 1.88756i
\(486\) 0 0
\(487\) 10.5000 + 18.1865i 0.475800 + 0.824110i 0.999616 0.0277214i \(-0.00882512\pi\)
−0.523815 + 0.851832i \(0.675492\pi\)
\(488\) 0.500000 + 0.866025i 0.0226339 + 0.0392031i
\(489\) 0 0
\(490\) 2.00000 + 3.46410i 0.0903508 + 0.156492i
\(491\) −10.0000 + 17.3205i −0.451294 + 0.781664i −0.998467 0.0553560i \(-0.982371\pi\)
0.547173 + 0.837020i \(0.315704\pi\)
\(492\) 0 0
\(493\) 45.0000 2.02670
\(494\) −7.50000 + 7.79423i −0.337441 + 0.350679i
\(495\) 0 0
\(496\) 2.00000 3.46410i 0.0898027 0.155543i
\(497\) 3.00000 5.19615i 0.134568 0.233079i
\(498\) 0 0
\(499\) 40.0000 1.79065 0.895323 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) 12.0000 + 20.7846i 0.536656 + 0.929516i
\(501\) 0 0
\(502\) −14.0000 −0.624851
\(503\) 8.00000 + 13.8564i 0.356702 + 0.617827i 0.987408 0.158196i \(-0.0505677\pi\)
−0.630705 + 0.776022i \(0.717234\pi\)
\(504\) 0 0
\(505\) −20.0000 + 34.6410i −0.889988 + 1.54150i
\(506\) −18.0000 −0.800198
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) 0 0
\(511\) −6.00000 10.3923i −0.265424 0.459728i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 3.50000 + 6.06218i 0.154378 + 0.267391i
\(515\) −80.0000 −3.52522
\(516\) 0 0
\(517\) −4.50000 + 7.79423i −0.197910 + 0.342790i
\(518\) −2.00000 + 3.46410i −0.0878750 + 0.152204i
\(519\) 0 0
\(520\) 10.0000 10.3923i 0.438529 0.455733i
\(521\) 5.00000 0.219054 0.109527 0.993984i \(-0.465066\pi\)
0.109527 + 0.993984i \(0.465066\pi\)
\(522\) 0 0
\(523\) −13.5000 + 23.3827i −0.590314 + 1.02245i 0.403876 + 0.914814i \(0.367663\pi\)
−0.994190 + 0.107640i \(0.965671\pi\)
\(524\) 6.00000 + 10.3923i 0.262111 + 0.453990i
\(525\) 0 0
\(526\) −13.0000 22.5167i −0.566827 0.981773i
\(527\) 10.0000 + 17.3205i 0.435607 + 0.754493i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 22.0000 38.1051i 0.955619 1.65518i
\(531\) 0 0
\(532\) 3.00000 0.130066
\(533\) 5.00000 + 17.3205i 0.216574 + 0.750234i
\(534\) 0 0
\(535\) −34.0000 + 58.8897i −1.46995 + 2.54602i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) 24.0000 1.03471
\(539\) −1.50000 2.59808i −0.0646096 0.111907i
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 6.00000 + 10.3923i 0.257722 + 0.446388i
\(543\) 0 0
\(544\) −2.50000 + 4.33013i −0.107187 + 0.185653i
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −9.00000 + 15.5885i −0.384461 + 0.665906i
\(549\) 0 0
\(550\) −16.5000 28.5788i −0.703562 1.21861i
\(551\) 27.0000 1.15024
\(552\) 0 0
\(553\) −5.50000 9.52628i −0.233884 0.405099i
\(554\) 14.0000 0.594803
\(555\) 0 0
\(556\) −6.50000 + 11.2583i −0.275661 + 0.477460i
\(557\) 5.50000 9.52628i 0.233042 0.403641i −0.725660 0.688054i \(-0.758465\pi\)
0.958702 + 0.284413i \(0.0917985\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −4.00000 −0.169031
\(561\) 0 0
\(562\) 15.0000 25.9808i 0.632737 1.09593i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 0 0
\(565\) −24.0000 41.5692i −1.00969 1.74883i
\(566\) 2.00000 + 3.46410i 0.0840663 + 0.145607i
\(567\) 0 0
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 38.0000 1.59025 0.795125 0.606445i \(-0.207405\pi\)
0.795125 + 0.606445i \(0.207405\pi\)
\(572\) −7.50000 + 7.79423i −0.313591 + 0.325893i
\(573\) 0 0
\(574\) 2.50000 4.33013i 0.104348 0.180736i
\(575\) 33.0000 57.1577i 1.37620 2.38364i
\(576\) 0 0
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) 0 0
\(580\) −36.0000 −1.49482
\(581\) 3.00000 + 5.19615i 0.124461 + 0.215573i
\(582\) 0 0
\(583\) −16.5000 + 28.5788i −0.683360 + 1.18361i
\(584\) 12.0000 0.496564
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) −6.00000 + 10.3923i −0.247647 + 0.428936i −0.962872 0.269957i \(-0.912990\pi\)
0.715226 + 0.698893i \(0.246324\pi\)
\(588\) 0 0
\(589\) 6.00000 + 10.3923i 0.247226 + 0.428207i
\(590\) 8.00000 0.329355
\(591\) 0 0
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) −41.0000 −1.68367 −0.841834 0.539736i \(-0.818524\pi\)
−0.841834 + 0.539736i \(0.818524\pi\)
\(594\) 0 0
\(595\) 10.0000 17.3205i 0.409960 0.710072i
\(596\) 9.00000 15.5885i 0.368654 0.638528i
\(597\) 0 0
\(598\) −21.0000 5.19615i −0.858754 0.212486i
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) 22.0000 38.1051i 0.897399 1.55434i 0.0665912 0.997780i \(-0.478788\pi\)
0.830808 0.556560i \(-0.187879\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.50000 + 9.52628i 0.223792 + 0.387619i
\(605\) −4.00000 6.92820i −0.162623 0.281672i
\(606\) 0 0
\(607\) 4.00000 + 6.92820i 0.162355 + 0.281207i 0.935713 0.352763i \(-0.114758\pi\)
−0.773358 + 0.633970i \(0.781424\pi\)
\(608\) −1.50000 + 2.59808i −0.0608330 + 0.105366i
\(609\) 0 0
\(610\) 4.00000 0.161955
\(611\) −7.50000 + 7.79423i −0.303418 + 0.315321i
\(612\) 0 0
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) −10.5000 + 18.1865i −0.423746 + 0.733949i
\(615\) 0 0
\(616\) 3.00000 0.120873
\(617\) 5.00000 + 8.66025i 0.201292 + 0.348649i 0.948945 0.315441i \(-0.102153\pi\)
−0.747653 + 0.664090i \(0.768819\pi\)
\(618\) 0 0
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) −8.00000 13.8564i −0.321288 0.556487i
\(621\) 0 0
\(622\) −9.50000 + 16.4545i −0.380915 + 0.659765i
\(623\) −7.00000 −0.280449
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 7.00000 12.1244i 0.279776 0.484587i
\(627\) 0 0
\(628\) 1.00000 + 1.73205i 0.0399043 + 0.0691164i
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) 6.50000 + 11.2583i 0.258761 + 0.448187i 0.965910 0.258877i \(-0.0833525\pi\)
−0.707149 + 0.707064i \(0.750019\pi\)
\(632\) 11.0000 0.437557
\(633\) 0 0
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 16.0000 27.7128i 0.634941 1.09975i
\(636\) 0 0
\(637\) −1.00000 3.46410i −0.0396214 0.137253i
\(638\) 27.0000 1.06894
\(639\) 0 0
\(640\) 2.00000 3.46410i 0.0790569 0.136931i
\(641\) −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 0 0
\(643\) 8.50000 + 14.7224i 0.335207 + 0.580596i 0.983525 0.180774i \(-0.0578603\pi\)
−0.648317 + 0.761370i \(0.724527\pi\)
\(644\) 3.00000 + 5.19615i 0.118217 + 0.204757i
\(645\) 0 0
\(646\) −7.50000 12.9904i −0.295084 0.511100i
\(647\) 7.50000 12.9904i 0.294855 0.510705i −0.680096 0.733123i \(-0.738062\pi\)
0.974951 + 0.222419i \(0.0713952\pi\)
\(648\) 0 0
\(649\) −6.00000 −0.235521
\(650\) −11.0000 38.1051i −0.431455 1.49461i
\(651\) 0 0
\(652\) −10.0000 + 17.3205i −0.391630 + 0.678323i
\(653\) −13.5000 + 23.3827i −0.528296 + 0.915035i 0.471160 + 0.882048i \(0.343835\pi\)
−0.999456 + 0.0329874i \(0.989498\pi\)
\(654\) 0 0
\(655\) 48.0000 1.87552
\(656\) 2.50000 + 4.33013i 0.0976086 + 0.169063i
\(657\) 0 0
\(658\) 3.00000 0.116952
\(659\) 19.5000 + 33.7750i 0.759612 + 1.31569i 0.943049 + 0.332655i \(0.107945\pi\)
−0.183436 + 0.983032i \(0.558722\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) 2.00000 0.0777322
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 6.00000 10.3923i 0.232670 0.402996i
\(666\) 0 0
\(667\) 27.0000 + 46.7654i 1.04544 + 1.81076i
\(668\) 16.0000 0.619059
\(669\) 0 0
\(670\) 4.00000 + 6.92820i 0.154533 + 0.267660i
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) −11.5000 + 19.9186i −0.443292 + 0.767805i −0.997932 0.0642860i \(-0.979523\pi\)
0.554639 + 0.832091i \(0.312856\pi\)
\(674\) −15.5000 + 26.8468i −0.597038 + 1.03410i
\(675\) 0 0
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 26.0000 0.999261 0.499631 0.866239i \(-0.333469\pi\)
0.499631 + 0.866239i \(0.333469\pi\)
\(678\) 0 0
\(679\) 6.00000 10.3923i 0.230259 0.398820i
\(680\) 10.0000 + 17.3205i 0.383482 + 0.664211i
\(681\) 0 0
\(682\) 6.00000 + 10.3923i 0.229752 + 0.397942i
\(683\) −10.0000 17.3205i −0.382639 0.662751i 0.608799 0.793324i \(-0.291651\pi\)
−0.991439 + 0.130573i \(0.958318\pi\)
\(684\) 0 0
\(685\) 36.0000 + 62.3538i 1.37549 + 2.38242i
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) 0 0
\(689\) −27.5000 + 28.5788i −1.04767 + 1.08877i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −1.00000 + 1.73205i −0.0380143 + 0.0658427i
\(693\) 0 0
\(694\) −11.0000 −0.417554
\(695\) 26.0000 + 45.0333i 0.986236 + 1.70821i
\(696\) 0 0
\(697\) −25.0000 −0.946943
\(698\) 17.0000 + 29.4449i 0.643459 + 1.11450i
\(699\) 0 0
\(700\) −5.50000 + 9.52628i −0.207880 + 0.360060i
\(701\) 21.0000 0.793159 0.396580 0.918000i \(-0.370197\pi\)
0.396580 + 0.918000i \(0.370197\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −9.00000 15.5885i −0.338719 0.586679i
\(707\) −10.0000 −0.376089
\(708\) 0 0
\(709\) −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) 24.0000 0.900704
\(711\) 0 0
\(712\) 3.50000 6.06218i 0.131168 0.227190i
\(713\) −12.0000 + 20.7846i −0.449404 + 0.778390i
\(714\) 0 0
\(715\) 12.0000 + 41.5692i 0.448775 + 1.55460i
\(716\) −24.0000 −0.896922
\(717\) 0 0
\(718\) −10.0000 + 17.3205i −0.373197 + 0.646396i
\(719\) −0.500000 0.866025i −0.0186469 0.0322973i 0.856551 0.516062i \(-0.172602\pi\)
−0.875198 + 0.483764i \(0.839269\pi\)
\(720\) 0 0
\(721\) −10.0000 17.3205i −0.372419 0.645049i
\(722\) 5.00000 + 8.66025i 0.186081 + 0.322301i
\(723\) 0 0
\(724\) 2.50000 + 4.33013i 0.0929118 + 0.160928i
\(725\) −49.5000 + 85.7365i −1.83838 + 3.18417i
\(726\) 0 0
\(727\) 12.0000 0.445055 0.222528 0.974926i \(-0.428569\pi\)
0.222528 + 0.974926i \(0.428569\pi\)
\(728\) 3.50000 + 0.866025i 0.129719 + 0.0320970i
\(729\) 0 0
\(730\) 24.0000 41.5692i 0.888280 1.53855i
\(731\) 0 0
\(732\) 0 0
\(733\) 13.0000 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) −9.00000 15.5885i −0.332196 0.575380i
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) −3.00000 5.19615i −0.110506 0.191403i
\(738\) 0 0
\(739\) 27.0000 46.7654i 0.993211 1.72029i 0.395864 0.918309i \(-0.370445\pi\)
0.597347 0.801983i \(-0.296222\pi\)
\(740\) −16.0000 −0.588172
\(741\) 0 0
\(742\) 11.0000 0.403823
\(743\) 14.0000 24.2487i 0.513610 0.889599i −0.486265 0.873811i \(-0.661641\pi\)
0.999875 0.0157876i \(-0.00502557\pi\)
\(744\) 0 0
\(745\) −36.0000 62.3538i −1.31894 2.28447i
\(746\) 34.0000 1.24483
\(747\) 0 0
\(748\) −7.50000 12.9904i −0.274227 0.474975i
\(749\) −17.0000 −0.621166
\(750\) 0 0
\(751\) −15.5000 + 26.8468i −0.565603 + 0.979653i 0.431390 + 0.902165i \(0.358023\pi\)
−0.996993 + 0.0774878i \(0.975310\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) 31.5000 + 7.79423i 1.14716 + 0.283849i
\(755\) 44.0000 1.60132
\(756\) 0 0
\(757\) −11.0000 + 19.0526i −0.399802 + 0.692477i −0.993701 0.112062i \(-0.964254\pi\)
0.593899 + 0.804539i \(0.297588\pi\)
\(758\) 9.00000 + 15.5885i 0.326895 + 0.566198i
\(759\) 0 0
\(760\) 6.00000 + 10.3923i 0.217643 + 0.376969i
\(761\) −13.0000 22.5167i −0.471250 0.816228i 0.528209 0.849114i \(-0.322864\pi\)
−0.999459 + 0.0328858i \(0.989530\pi\)
\(762\) 0 0
\(763\) 1.00000 + 1.73205i 0.0362024 + 0.0627044i
\(764\) −3.00000 + 5.19615i −0.108536 + 0.187990i
\(765\) 0 0
\(766\) 11.0000 0.397446
\(767\) −7.00000 1.73205i −0.252755 0.0625407i
\(768\) 0 0
\(769\) 2.00000 3.46410i 0.0721218 0.124919i −0.827709 0.561157i \(-0.810356\pi\)
0.899831 + 0.436239i \(0.143690\pi\)
\(770\) 6.00000 10.3923i 0.216225 0.374513i
\(771\) 0 0
\(772\) 13.0000 0.467880
\(773\) 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i \(-0.0617373\pi\)
−0.657542 + 0.753418i \(0.728404\pi\)
\(774\) 0 0
\(775\) −44.0000 −1.58053
\(776\) 6.00000 + 10.3923i 0.215387 + 0.373062i
\(777\) 0 0
\(778\) −13.0000 + 22.5167i −0.466073 + 0.807261i
\(779\) −15.0000 −0.537431
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 15.0000 25.9808i 0.536399 0.929070i
\(783\) 0 0
\(784\) −0.500000 0.866025i −0.0178571 0.0309295i
\(785\) 8.00000 0.285532
\(786\) 0 0
\(787\) 5.50000 + 9.52628i 0.196054 + 0.339575i 0.947245 0.320509i \(-0.103854\pi\)
−0.751192 + 0.660084i \(0.770521\pi\)
\(788\) 19.0000 0.676847
\(789\) 0 0