Properties

Label 1638.2.r.a.757.1
Level $1638$
Weight $2$
Character 1638.757
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 757.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1638.757
Dual form 1638.2.r.a.1387.1

$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

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

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 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 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 0.385499 + 0.922708i \(0.374029\pi\)
−0.991838 + 0.127502i \(0.959304\pi\)
\(18\) 0 0
\(19\) −1.50000 + 2.59808i −0.344124 + 0.596040i −0.985194 0.171442i \(-0.945157\pi\)
0.641071 + 0.767482i \(0.278491\pi\)
\(20\) 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 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 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 −0.893517 0.449029i \(-0.851770\pi\)
0.0578882 0.998323i \(-0.481563\pi\)
\(30\) 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 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 3.00000 0.486664
\(39\) 0 0
\(40\) −4.00000 −0.632456
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) 0 0
\(43\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(44\) 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 −0.793560 0.608492i \(-0.791775\pi\)
0.923749 + 0.382998i \(0.125108\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 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 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) −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 −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) 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 0.989720 0.143022i \(-0.0456819\pi\)
−0.618720 + 0.785611i \(0.712349\pi\)
\(90\) 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 −0.382164 0.924095i \(-0.624821\pi\)
0.991371 0.131084i \(-0.0418458\pi\)
\(98\) −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 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) 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 0.904396 + 0.426694i \(0.140322\pi\)
−0.0826699 + 0.996577i \(0.526345\pi\)
\(108\) 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 −0.432670 0.901553i \(-0.642428\pi\)
0.997102 0.0760733i \(-0.0242383\pi\)
\(114\) 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 0.632166 0.774833i \(-0.282166\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(128\) −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 0.169226 + 0.985577i \(0.445873\pi\)
−0.938148 + 0.346235i \(0.887460\pi\)
\(138\) 0 0
\(139\) −6.50000 + 11.2583i −0.551323 + 0.954919i 0.446857 + 0.894606i \(0.352543\pi\)
−0.998179 + 0.0603135i \(0.980790\pi\)
\(140\) 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 −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 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 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) −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 −0.989658 0.143448i \(-0.954181\pi\)
0.370599 0.928793i \(-0.379152\pi\)
\(168\) 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 −0.901533 0.432710i \(-0.857557\pi\)
0.825505 + 0.564396i \(0.190891\pi\)
\(174\) 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 0.831408 + 0.555663i \(0.187536\pi\)
0.0655145 + 0.997852i \(0.479131\pi\)
\(180\) 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 −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 0 0
\(193\) −6.50000 11.2583i −0.467880 0.810392i 0.531446 0.847092i \(-0.321649\pi\)
−0.999326 + 0.0366998i \(0.988315\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −9.50000 16.4545i −0.676847 1.17233i −0.975925 0.218105i \(-0.930013\pi\)
0.299078 0.954229i \(-0.403321\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 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 0.517884 0.855451i \(-0.326720\pi\)
−0.999784 + 0.0207756i \(0.993386\pi\)
\(212\) −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 0.999128 + 0.0417488i \(0.0132929\pi\)
−0.463409 + 0.886145i \(0.653374\pi\)
\(224\) −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 −0.534577 0.845120i \(-0.679529\pi\)
0.999184 + 0.0403978i \(0.0128625\pi\)
\(228\) 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 −0.991975 0.126432i \(-0.959647\pi\)
0.605481 + 0.795860i \(0.292981\pi\)
\(242\) −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 −0.555990 0.831189i \(-0.687661\pi\)
0.997826 + 0.0659066i \(0.0209939\pi\)
\(252\) 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 0.954296 0.298864i \(-0.0966077\pi\)
−0.735972 + 0.677012i \(0.763274\pi\)
\(258\) 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 −0.918553 0.395298i \(-0.870641\pi\)
0.116939 0.993139i \(-0.462692\pi\)
\(264\) 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 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) 6.00000 + 10.3923i 0.364474 + 0.631288i 0.988692 0.149963i \(-0.0479155\pi\)
−0.624218 + 0.781251i \(0.714582\pi\)
\(272\) 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 −0.995997 0.0893846i \(-0.971510\pi\)
0.575408 + 0.817867i \(0.304843\pi\)
\(278\) 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 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 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 −0.267052 0.963682i \(-0.586049\pi\)
0.968099 0.250568i \(-0.0806172\pi\)
\(294\) 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 −0.892199 0.451643i \(-0.850838\pi\)
0.837234 + 0.546845i \(0.184171\pi\)
\(332\) 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 −0.679789 0.733408i \(-0.737929\pi\)
0.975044 + 0.222010i \(0.0712619\pi\)
\(348\) 0 0
\(349\) 17.0000 + 29.4449i 0.909989 + 1.57615i 0.814076 + 0.580758i \(0.197244\pi\)
0.0959126 + 0.995390i \(0.469423\pi\)
\(350\) 11.0000 0.587975
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) 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 0.529607 0.848243i \(-0.322339\pi\)
−0.999404 + 0.0345320i \(0.989006\pi\)
\(368\) 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 −0.0291379 + 0.999575i \(0.509276\pi\)
−0.851089 + 0.525022i \(0.824057\pi\)
\(374\) −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 0.999075 0.0429994i \(-0.0136914\pi\)
−0.536776 + 0.843725i \(0.680358\pi\)
\(380\) 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 −0.971640 0.236463i \(-0.924012\pi\)
0.690604 + 0.723234i \(0.257345\pi\)
\(384\) 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 −0.418634 0.908155i \(-0.637491\pi\)
0.995802 0.0915300i \(-0.0291757\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −5.50000 9.52628i −0.275000 0.476314i
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 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 −0.840243 0.542211i \(-0.817588\pi\)
0.889689 + 0.456566i \(0.150921\pi\)
\(410\) −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 0.997665 0.0683046i \(-0.0217590\pi\)
−0.557986 + 0.829851i \(0.688426\pi\)
\(420\) 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 0.806611 + 0.591082i \(0.201299\pi\)
0.108586 + 0.994087i \(0.465368\pi\)
\(432\) 0 0
\(433\) −17.0000 + 29.4449i −0.816968 + 1.41503i 0.0909384 + 0.995857i \(0.471013\pi\)
−0.907906 + 0.419173i \(0.862320\pi\)
\(434\) −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 −0.735399 0.677634i \(-0.763005\pi\)
−0.219149 0.975691i \(-0.570328\pi\)
\(440\) 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 −0.527555 0.849521i \(-0.676891\pi\)
0.999484 + 0.0321156i \(0.0102245\pi\)
\(450\) 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 0.888466 0.458942i \(-0.151771\pi\)
−0.841688 + 0.539964i \(0.818438\pi\)
\(458\) 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 0.204910 + 0.978781i \(0.434310\pi\)
−0.950104 + 0.311933i \(0.899023\pi\)
\(462\) 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 −0.945917 0.324408i \(-0.894835\pi\)
0.192013 0.981392i \(-0.438498\pi\)
\(480\) 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 −0.523815 0.851832i \(-0.675492\pi\)
0.999616 + 0.0277214i \(0.00882512\pi\)
\(488\) 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 0.547173 0.837020i \(-0.315704\pi\)
−0.998467 + 0.0553560i \(0.982371\pi\)
\(492\) 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 −0.630705 0.776022i \(-0.717234\pi\)
0.987408 + 0.158196i \(0.0505677\pi\)
\(504\) 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 −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 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 −0.994190 0.107640i \(-0.965671\pi\)
0.403876 0.914814i \(-0.367663\pi\)
\(524\) 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 0.958702 0.284413i \(-0.0917985\pi\)
−0.725660 + 0.688054i \(0.758465\pi\)
\(558\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 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 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 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 0.715226 0.698893i \(-0.246324\pi\)
−0.962872 + 0.269957i \(0.912990\pi\)
\(588\) 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 0.830808 + 0.556560i \(0.187879\pi\)
0.0665912 + 0.997780i \(0.478788\pi\)
\(602\) 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 −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) −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 0.773869 0.633345i \(-0.218319\pi\)
−0.935428 + 0.353518i \(0.884985\pi\)
\(614\) −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 −0.747653 0.664090i \(-0.768819\pi\)
0.948945 + 0.315441i \(0.102153\pi\)
\(618\) 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 −0.707149 0.707064i \(-0.750019\pi\)
0.965910 + 0.258877i \(0.0833525\pi\)
\(632\) 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 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) 0 0
\(643\) 8.50000 14.7224i 0.335207 0.580596i −0.648317 0.761370i \(-0.724527\pi\)
0.983525 + 0.180774i \(0.0578603\pi\)
\(644\) 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 0.974951 0.222419i \(-0.0713952\pi\)
−0.680096 + 0.733123i \(0.738062\pi\)
\(648\) 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 −0.999456 0.0329874i \(-0.989498\pi\)
0.471160 0.882048i \(-0.343835\pi\)
\(654\) 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 −0.183436 0.983032i \(-0.558722\pi\)
0.943049 0.332655i \(-0.107945\pi\)
\(660\) 0 0
\(661\) 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) 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 0.554639 0.832091i \(-0.312856\pi\)
−0.997932 + 0.0642860i \(0.979523\pi\)
\(674\) −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 −0.991439 0.130573i \(-0.958318\pi\)
0.608799 + 0.793324i \(0.291651\pi\)
\(684\) 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 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) −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 −0.944509 0.328484i \(-0.893462\pi\)
0.756730 + 0.653727i \(0.226796\pi\)
\(710\) 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 −0.875198 0.483764i \(-0.839269\pi\)
0.856551 + 0.516062i \(0.172602\pi\)
\(720\) 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 0.597347 + 0.801983i \(0.296222\pi\)
0.395864 + 0.918309i \(0.370445\pi\)
\(740\) −16.0000 −0.588172
\(741\) 0 0
\(742\) 11.0000 0.403823
\(743\) 14.0000 + 24.2487i 0.513610 + 0.889599i 0.999875 + 0.0157876i \(0.00502557\pi\)
−0.486265 + 0.873811i \(0.661641\pi\)
\(744\) 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 −0.996993 0.0774878i \(-0.975310\pi\)
0.431390 0.902165i \(-0.358023\pi\)
\(752\) −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 0.593899 0.804539i \(-0.297588\pi\)
−0.993701 + 0.112062i \(0.964254\pi\)
\(758\) 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 −0.999459 0.0328858i \(-0.989530\pi\)
0.528209 + 0.849114i \(0.322864\pi\)
\(762\) 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 0.899831 0.436239i \(-0.143690\pi\)
−0.827709 + 0.561157i \(0.810356\pi\)
\(770\) 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 −0.657542 0.753418i \(-0.728404\pi\)
0.981250 + 0.192740i \(0.0617373\pi\)
\(774\) 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 −0.751192 0.660084i \(-0.770521\pi\)
0.947245 + 0.320509i \(0.103854\pi\)
\(788\) 19.0000 0.676847
\(789\) 0 0