Properties

Label 2394.2.o.a.505.1
Level $2394$
Weight $2$
Character 2394.505
Analytic conductor $19.116$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.o (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1161862439\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 798)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 505.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2394.505
Dual form 2394.2.o.a.1261.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} -4.00000 q^{11} +(-1.50000 - 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 + 4.33013i) q^{19} +3.00000 q^{20} +(2.00000 - 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-2.00000 - 3.46410i) q^{25} +3.00000 q^{26} +(0.500000 + 0.866025i) q^{28} -6.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{34} +(1.50000 - 2.59808i) q^{35} +4.00000 q^{37} +(-3.50000 - 2.59808i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(2.00000 - 3.46410i) q^{41} +(3.00000 - 5.19615i) q^{43} +(2.00000 + 3.46410i) q^{44} -1.00000 q^{46} +(-1.00000 - 1.73205i) q^{47} +1.00000 q^{49} +4.00000 q^{50} +(-1.50000 + 2.59808i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(6.00000 - 10.3923i) q^{55} -1.00000 q^{56} +(6.50000 - 11.2583i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(3.00000 - 5.19615i) q^{62} +1.00000 q^{64} +9.00000 q^{65} +(6.00000 + 10.3923i) q^{67} +2.00000 q^{68} +(1.50000 + 2.59808i) q^{70} +(-3.50000 + 6.06218i) q^{71} +(1.00000 - 1.73205i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(4.00000 - 1.73205i) q^{76} +4.00000 q^{77} +(4.00000 - 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(2.00000 + 3.46410i) q^{82} -17.0000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(3.00000 + 5.19615i) q^{86} -4.00000 q^{88} +(2.00000 + 3.46410i) q^{89} +(1.50000 + 2.59808i) q^{91} +(0.500000 - 0.866025i) q^{92} +2.00000 q^{94} +(-10.5000 - 7.79423i) q^{95} +(5.00000 - 8.66025i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 3 q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 3 q^{5} - 2 q^{7} + 2 q^{8} - 3 q^{10} - 8 q^{11} - 3 q^{13} + q^{14} - q^{16} - 2 q^{17} - q^{19} + 6 q^{20} + 4 q^{22} + q^{23} - 4 q^{25} + 6 q^{26} + q^{28} - 12 q^{31} - q^{32} - 2 q^{34} + 3 q^{35} + 8 q^{37} - 7 q^{38} - 3 q^{40} + 4 q^{41} + 6 q^{43} + 4 q^{44} - 2 q^{46} - 2 q^{47} + 2 q^{49} + 8 q^{50} - 3 q^{52} - 4 q^{53} + 12 q^{55} - 2 q^{56} + 13 q^{59} - 5 q^{61} + 6 q^{62} + 2 q^{64} + 18 q^{65} + 12 q^{67} + 4 q^{68} + 3 q^{70} - 7 q^{71} + 2 q^{73} - 4 q^{74} + 8 q^{76} + 8 q^{77} + 8 q^{79} - 3 q^{80} + 4 q^{82} - 34 q^{83} - 6 q^{85} + 6 q^{86} - 8 q^{88} + 4 q^{89} + 3 q^{91} + q^{92} + 4 q^{94} - 21 q^{95} + 10 q^{97} - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(1009\) \(1711\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943882i \(0.969911\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0 0
\(19\) −0.500000 + 4.33013i −0.114708 + 0.993399i
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 3.00000 0.588348
\(27\) 0 0
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0 0
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.00000 1.73205i −0.171499 0.297044i
\(35\) 1.50000 2.59808i 0.253546 0.439155i
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) −3.50000 2.59808i −0.567775 0.421464i
\(39\) 0 0
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) 2.00000 3.46410i 0.312348 0.541002i −0.666523 0.745485i \(-0.732218\pi\)
0.978870 + 0.204483i \(0.0655513\pi\)
\(42\) 0 0
\(43\) 3.00000 5.19615i 0.457496 0.792406i −0.541332 0.840809i \(-0.682080\pi\)
0.998828 + 0.0484030i \(0.0154132\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) −1.50000 + 2.59808i −0.208013 + 0.360288i
\(53\) −2.00000 3.46410i −0.274721 0.475831i 0.695344 0.718677i \(-0.255252\pi\)
−0.970065 + 0.242846i \(0.921919\pi\)
\(54\) 0 0
\(55\) 6.00000 10.3923i 0.809040 1.40130i
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) 0 0
\(59\) 6.50000 11.2583i 0.846228 1.46571i −0.0383226 0.999265i \(-0.512201\pi\)
0.884551 0.466444i \(-0.154465\pi\)
\(60\) 0 0
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) 3.00000 5.19615i 0.381000 0.659912i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 9.00000 1.11631
\(66\) 0 0
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) 1.50000 + 2.59808i 0.179284 + 0.310530i
\(71\) −3.50000 + 6.06218i −0.415374 + 0.719448i −0.995468 0.0951014i \(-0.969682\pi\)
0.580094 + 0.814550i \(0.303016\pi\)
\(72\) 0 0
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) 4.00000 1.73205i 0.458831 0.198680i
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) 0 0
\(82\) 2.00000 + 3.46410i 0.220863 + 0.382546i
\(83\) −17.0000 −1.86599 −0.932996 0.359886i \(-0.882816\pi\)
−0.932996 + 0.359886i \(0.882816\pi\)
\(84\) 0 0
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) 3.00000 + 5.19615i 0.323498 + 0.560316i
\(87\) 0 0
\(88\) −4.00000 −0.426401
\(89\) 2.00000 + 3.46410i 0.212000 + 0.367194i 0.952340 0.305038i \(-0.0986691\pi\)
−0.740341 + 0.672232i \(0.765336\pi\)
\(90\) 0 0
\(91\) 1.50000 + 2.59808i 0.157243 + 0.272352i
\(92\) 0.500000 0.866025i 0.0521286 0.0902894i
\(93\) 0 0
\(94\) 2.00000 0.206284
\(95\) −10.5000 7.79423i −1.07728 0.799671i
\(96\) 0 0
\(97\) 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i \(-0.663839\pi\)
0.999961 0.00888289i \(-0.00282755\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −1.50000 2.59808i −0.147087 0.254762i
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) 10.0000 0.966736 0.483368 0.875417i \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 0 0
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) 6.00000 + 10.3923i 0.572078 + 0.990867i
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 5.00000 0.470360 0.235180 0.971952i \(-0.424432\pi\)
0.235180 + 0.971952i \(0.424432\pi\)
\(114\) 0 0
\(115\) −3.00000 −0.279751
\(116\) 0 0
\(117\) 0 0
\(118\) 6.50000 + 11.2583i 0.598374 + 1.03641i
\(119\) 1.00000 1.73205i 0.0916698 0.158777i
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 5.00000 0.452679
\(123\) 0 0
\(124\) 3.00000 + 5.19615i 0.269408 + 0.466628i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 5.50000 + 9.52628i 0.488046 + 0.845321i 0.999905 0.0137486i \(-0.00437646\pi\)
−0.511859 + 0.859069i \(0.671043\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −4.50000 + 7.79423i −0.394676 + 0.683599i
\(131\) −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i \(-0.961954\pi\)
0.599699 + 0.800226i \(0.295287\pi\)
\(132\) 0 0
\(133\) 0.500000 4.33013i 0.0433555 0.375470i
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −10.5000 18.1865i −0.897076 1.55378i −0.831215 0.555952i \(-0.812354\pi\)
−0.0658609 0.997829i \(-0.520979\pi\)
\(138\) 0 0
\(139\) 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) −3.00000 −0.253546
\(141\) 0 0
\(142\) −3.50000 6.06218i −0.293713 0.508727i
\(143\) 6.00000 + 10.3923i 0.501745 + 0.869048i
\(144\) 0 0
\(145\) 0 0
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) 0 0
\(148\) −2.00000 3.46410i −0.164399 0.284747i
\(149\) 10.0000 17.3205i 0.819232 1.41895i −0.0870170 0.996207i \(-0.527733\pi\)
0.906249 0.422744i \(-0.138933\pi\)
\(150\) 0 0
\(151\) 19.0000 1.54620 0.773099 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) −0.500000 + 4.33013i −0.0405554 + 0.351220i
\(153\) 0 0
\(154\) −2.00000 + 3.46410i −0.161165 + 0.279145i
\(155\) 9.00000 15.5885i 0.722897 1.25210i
\(156\) 0 0
\(157\) 4.50000 7.79423i 0.359139 0.622047i −0.628678 0.777666i \(-0.716404\pi\)
0.987817 + 0.155618i \(0.0497370\pi\)
\(158\) 4.00000 + 6.92820i 0.318223 + 0.551178i
\(159\) 0 0
\(160\) 3.00000 0.237171
\(161\) −0.500000 0.866025i −0.0394055 0.0682524i
\(162\) 0 0
\(163\) 14.0000 1.09656 0.548282 0.836293i \(-0.315282\pi\)
0.548282 + 0.836293i \(0.315282\pi\)
\(164\) −4.00000 −0.312348
\(165\) 0 0
\(166\) 8.50000 14.7224i 0.659728 1.14268i
\(167\) −9.00000 15.5885i −0.696441 1.20627i −0.969693 0.244328i \(-0.921432\pi\)
0.273252 0.961943i \(-0.411901\pi\)
\(168\) 0 0
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 6.00000 0.460179
\(171\) 0 0
\(172\) −6.00000 −0.457496
\(173\) 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i \(-0.640193\pi\)
0.996544 0.0830722i \(-0.0264732\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) 2.00000 3.46410i 0.150756 0.261116i
\(177\) 0 0
\(178\) −4.00000 −0.299813
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0 0
\(181\) −1.50000 2.59808i −0.111494 0.193113i 0.804879 0.593439i \(-0.202230\pi\)
−0.916373 + 0.400326i \(0.868897\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) −6.00000 + 10.3923i −0.441129 + 0.764057i
\(186\) 0 0
\(187\) 4.00000 6.92820i 0.292509 0.506640i
\(188\) −1.00000 + 1.73205i −0.0729325 + 0.126323i
\(189\) 0 0
\(190\) 12.0000 5.19615i 0.870572 0.376969i
\(191\) 11.0000 0.795932 0.397966 0.917400i \(-0.369716\pi\)
0.397966 + 0.917400i \(0.369716\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) 5.00000 + 8.66025i 0.358979 + 0.621770i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) −4.00000 −0.284988 −0.142494 0.989796i \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(198\) 0 0
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) −2.00000 3.46410i −0.141421 0.244949i
\(201\) 0 0
\(202\) −14.0000 −0.985037
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) 0 0
\(207\) 0 0
\(208\) 3.00000 0.208013
\(209\) 2.00000 17.3205i 0.138343 1.19808i
\(210\) 0 0
\(211\) 4.00000 6.92820i 0.275371 0.476957i −0.694857 0.719148i \(-0.744533\pi\)
0.970229 + 0.242190i \(0.0778659\pi\)
\(212\) −2.00000 + 3.46410i −0.137361 + 0.237915i
\(213\) 0 0
\(214\) −5.00000 + 8.66025i −0.341793 + 0.592003i
\(215\) 9.00000 + 15.5885i 0.613795 + 1.06312i
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) 2.00000 + 3.46410i 0.135457 + 0.234619i
\(219\) 0 0
\(220\) −12.0000 −0.809040
\(221\) 6.00000 0.403604
\(222\) 0 0
\(223\) 9.00000 15.5885i 0.602685 1.04388i −0.389728 0.920930i \(-0.627431\pi\)
0.992413 0.122950i \(-0.0392356\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) −2.50000 + 4.33013i −0.166298 + 0.288036i
\(227\) −5.00000 −0.331862 −0.165931 0.986137i \(-0.553063\pi\)
−0.165931 + 0.986137i \(0.553063\pi\)
\(228\) 0 0
\(229\) −17.0000 −1.12339 −0.561696 0.827344i \(-0.689851\pi\)
−0.561696 + 0.827344i \(0.689851\pi\)
\(230\) 1.50000 2.59808i 0.0989071 0.171312i
\(231\) 0 0
\(232\) 0 0
\(233\) 4.50000 7.79423i 0.294805 0.510617i −0.680135 0.733087i \(-0.738079\pi\)
0.974939 + 0.222470i \(0.0714120\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) −13.0000 −0.846228
\(237\) 0 0
\(238\) 1.00000 + 1.73205i 0.0648204 + 0.112272i
\(239\) −27.0000 −1.74648 −0.873242 0.487286i \(-0.837987\pi\)
−0.873242 + 0.487286i \(0.837987\pi\)
\(240\) 0 0
\(241\) −11.0000 19.0526i −0.708572 1.22728i −0.965387 0.260822i \(-0.916006\pi\)
0.256814 0.966461i \(-0.417327\pi\)
\(242\) −2.50000 + 4.33013i −0.160706 + 0.278351i
\(243\) 0 0
\(244\) −2.50000 + 4.33013i −0.160046 + 0.277208i
\(245\) −1.50000 + 2.59808i −0.0958315 + 0.165985i
\(246\) 0 0
\(247\) 12.0000 5.19615i 0.763542 0.330623i
\(248\) −6.00000 −0.381000
\(249\) 0 0
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) 10.5000 + 18.1865i 0.662754 + 1.14792i 0.979889 + 0.199543i \(0.0639459\pi\)
−0.317135 + 0.948380i \(0.602721\pi\)
\(252\) 0 0
\(253\) −2.00000 3.46410i −0.125739 0.217786i
\(254\) −11.0000 −0.690201
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) −4.50000 7.79423i −0.279078 0.483378i
\(261\) 0 0
\(262\) −4.50000 7.79423i −0.278011 0.481529i
\(263\) −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i \(-0.862817\pi\)
0.816066 + 0.577959i \(0.196151\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) 3.50000 + 2.59808i 0.214599 + 0.159298i
\(267\) 0 0
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) 0 0
\(271\) −13.0000 + 22.5167i −0.789694 + 1.36779i 0.136461 + 0.990645i \(0.456427\pi\)
−0.926155 + 0.377144i \(0.876906\pi\)
\(272\) −1.00000 1.73205i −0.0606339 0.105021i
\(273\) 0 0
\(274\) 21.0000 1.26866
\(275\) 8.00000 + 13.8564i 0.482418 + 0.835573i
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −16.0000 −0.959616
\(279\) 0 0
\(280\) 1.50000 2.59808i 0.0896421 0.155265i
\(281\) −13.0000 22.5167i −0.775515 1.34323i −0.934505 0.355951i \(-0.884157\pi\)
0.158990 0.987280i \(-0.449176\pi\)
\(282\) 0 0
\(283\) −12.5000 + 21.6506i −0.743048 + 1.28700i 0.208053 + 0.978117i \(0.433287\pi\)
−0.951101 + 0.308879i \(0.900046\pi\)
\(284\) 7.00000 0.415374
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) −2.00000 + 3.46410i −0.118056 + 0.204479i
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) 0 0
\(292\) −2.00000 −0.117041
\(293\) 19.0000 1.10999 0.554996 0.831853i \(-0.312720\pi\)
0.554996 + 0.831853i \(0.312720\pi\)
\(294\) 0 0
\(295\) 19.5000 + 33.7750i 1.13533 + 1.96646i
\(296\) 4.00000 0.232495
\(297\) 0 0
\(298\) 10.0000 + 17.3205i 0.579284 + 1.00335i
\(299\) 1.50000 2.59808i 0.0867472 0.150251i
\(300\) 0 0
\(301\) −3.00000 + 5.19615i −0.172917 + 0.299501i
\(302\) −9.50000 + 16.4545i −0.546664 + 0.946849i
\(303\) 0 0
\(304\) −3.50000 2.59808i −0.200739 0.149010i
\(305\) 15.0000 0.858898
\(306\) 0 0
\(307\) −7.50000 + 12.9904i −0.428048 + 0.741400i −0.996700 0.0811780i \(-0.974132\pi\)
0.568652 + 0.822578i \(0.307465\pi\)
\(308\) −2.00000 3.46410i −0.113961 0.197386i
\(309\) 0 0
\(310\) 9.00000 + 15.5885i 0.511166 + 0.885365i
\(311\) 2.00000 0.113410 0.0567048 0.998391i \(-0.481941\pi\)
0.0567048 + 0.998391i \(0.481941\pi\)
\(312\) 0 0
\(313\) −12.0000 20.7846i −0.678280 1.17482i −0.975499 0.220006i \(-0.929392\pi\)
0.297218 0.954810i \(-0.403941\pi\)
\(314\) 4.50000 + 7.79423i 0.253950 + 0.439854i
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.50000 + 2.59808i −0.0838525 + 0.145237i
\(321\) 0 0
\(322\) 1.00000 0.0557278
\(323\) −7.00000 5.19615i −0.389490 0.289122i
\(324\) 0 0
\(325\) −6.00000 + 10.3923i −0.332820 + 0.576461i
\(326\) −7.00000 + 12.1244i −0.387694 + 0.671506i
\(327\) 0 0
\(328\) 2.00000 3.46410i 0.110432 0.191273i
\(329\) 1.00000 + 1.73205i 0.0551318 + 0.0954911i
\(330\) 0 0
\(331\) −24.0000 −1.31916 −0.659580 0.751635i \(-0.729266\pi\)
−0.659580 + 0.751635i \(0.729266\pi\)
\(332\) 8.50000 + 14.7224i 0.466498 + 0.807998i
\(333\) 0 0
\(334\) 18.0000 0.984916
\(335\) −36.0000 −1.96689
\(336\) 0 0
\(337\) −8.50000 + 14.7224i −0.463025 + 0.801982i −0.999110 0.0421818i \(-0.986569\pi\)
0.536085 + 0.844164i \(0.319902\pi\)
\(338\) 2.00000 + 3.46410i 0.108786 + 0.188422i
\(339\) 0 0
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 3.00000 5.19615i 0.161749 0.280158i
\(345\) 0 0
\(346\) 7.50000 + 12.9904i 0.403202 + 0.698367i
\(347\) 11.0000 19.0526i 0.590511 1.02279i −0.403653 0.914912i \(-0.632260\pi\)
0.994164 0.107883i \(-0.0344071\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) 2.00000 + 3.46410i 0.106600 + 0.184637i
\(353\) −12.0000 −0.638696 −0.319348 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) 0 0
\(355\) −10.5000 18.1865i −0.557282 0.965241i
\(356\) 2.00000 3.46410i 0.106000 0.183597i
\(357\) 0 0
\(358\) 5.00000 8.66025i 0.264258 0.457709i
\(359\) 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i \(-0.615019\pi\)
0.986865 0.161546i \(-0.0516481\pi\)
\(360\) 0 0
\(361\) −18.5000 4.33013i −0.973684 0.227901i
\(362\) 3.00000 0.157676
\(363\) 0 0
\(364\) 1.50000 2.59808i 0.0786214 0.136176i
\(365\) 3.00000 + 5.19615i 0.157027 + 0.271979i
\(366\) 0 0
\(367\) −16.0000 27.7128i −0.835193 1.44660i −0.893873 0.448320i \(-0.852022\pi\)
0.0586798 0.998277i \(-0.481311\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 0 0
\(370\) −6.00000 10.3923i −0.311925 0.540270i
\(371\) 2.00000 + 3.46410i 0.103835 + 0.179847i
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 4.00000 + 6.92820i 0.206835 + 0.358249i
\(375\) 0 0
\(376\) −1.00000 1.73205i −0.0515711 0.0893237i
\(377\) 0 0
\(378\) 0 0
\(379\) −34.0000 −1.74646 −0.873231 0.487306i \(-0.837980\pi\)
−0.873231 + 0.487306i \(0.837980\pi\)
\(380\) −1.50000 + 12.9904i −0.0769484 + 0.666392i
\(381\) 0 0
\(382\) −5.50000 + 9.52628i −0.281404 + 0.487407i
\(383\) −2.00000 + 3.46410i −0.102195 + 0.177007i −0.912589 0.408879i \(-0.865920\pi\)
0.810394 + 0.585886i \(0.199253\pi\)
\(384\) 0 0
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) −2.50000 4.33013i −0.127247 0.220398i
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) 4.00000 + 6.92820i 0.202808 + 0.351274i 0.949432 0.313972i \(-0.101660\pi\)
−0.746624 + 0.665246i \(0.768327\pi\)
\(390\) 0 0
\(391\) −2.00000 −0.101144
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) 2.00000 3.46410i 0.100759 0.174519i
\(395\) 12.0000 + 20.7846i 0.603786 + 1.04579i
\(396\) 0 0
\(397\) −9.00000 + 15.5885i −0.451697 + 0.782362i −0.998492 0.0549046i \(-0.982515\pi\)
0.546795 + 0.837267i \(0.315848\pi\)
\(398\) 14.0000 0.701757
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) 0 0
\(403\) 9.00000 + 15.5885i 0.448322 + 0.776516i
\(404\) 7.00000 12.1244i 0.348263 0.603209i
\(405\) 0 0
\(406\) 0 0
\(407\) −16.0000 −0.793091
\(408\) 0 0
\(409\) −12.0000 20.7846i −0.593362 1.02773i −0.993776 0.111398i \(-0.964467\pi\)
0.400414 0.916334i \(-0.368866\pi\)
\(410\) −12.0000 −0.592638
\(411\) 0 0
\(412\) 0 0
\(413\) −6.50000 + 11.2583i −0.319844 + 0.553986i
\(414\) 0 0
\(415\) 25.5000 44.1673i 1.25175 2.16809i
\(416\) −1.50000 + 2.59808i −0.0735436 + 0.127381i
\(417\) 0 0
\(418\) 14.0000 + 10.3923i 0.684762 + 0.508304i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 4.00000 6.92820i 0.194948 0.337660i −0.751935 0.659237i \(-0.770879\pi\)
0.946883 + 0.321577i \(0.104213\pi\)
\(422\) 4.00000 + 6.92820i 0.194717 + 0.337260i
\(423\) 0 0
\(424\) −2.00000 3.46410i −0.0971286 0.168232i
\(425\) 8.00000 0.388057
\(426\) 0 0
\(427\) 2.50000 + 4.33013i 0.120983 + 0.209550i
\(428\) −5.00000 8.66025i −0.241684 0.418609i
\(429\) 0 0
\(430\) −18.0000 −0.868037
\(431\) −8.00000 13.8564i −0.385346 0.667440i 0.606471 0.795106i \(-0.292585\pi\)
−0.991817 + 0.127666i \(0.959251\pi\)
\(432\) 0 0
\(433\) 12.0000 + 20.7846i 0.576683 + 0.998845i 0.995857 + 0.0909384i \(0.0289866\pi\)
−0.419173 + 0.907906i \(0.637680\pi\)
\(434\) −3.00000 + 5.19615i −0.144005 + 0.249423i
\(435\) 0 0
\(436\) −4.00000 −0.191565
\(437\) −4.00000 + 1.73205i −0.191346 + 0.0828552i
\(438\) 0 0
\(439\) −5.00000 + 8.66025i −0.238637 + 0.413331i −0.960323 0.278889i \(-0.910034\pi\)
0.721686 + 0.692220i \(0.243367\pi\)
\(440\) 6.00000 10.3923i 0.286039 0.495434i
\(441\) 0 0
\(442\) −3.00000 + 5.19615i −0.142695 + 0.247156i
\(443\) 9.00000 + 15.5885i 0.427603 + 0.740630i 0.996660 0.0816684i \(-0.0260248\pi\)
−0.569057 + 0.822298i \(0.692691\pi\)
\(444\) 0 0
\(445\) −12.0000 −0.568855
\(446\) 9.00000 + 15.5885i 0.426162 + 0.738135i
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) 39.0000 1.84052 0.920262 0.391303i \(-0.127976\pi\)
0.920262 + 0.391303i \(0.127976\pi\)
\(450\) 0 0
\(451\) −8.00000 + 13.8564i −0.376705 + 0.652473i
\(452\) −2.50000 4.33013i −0.117590 0.203672i
\(453\) 0 0
\(454\) 2.50000 4.33013i 0.117331 0.203223i
\(455\) −9.00000 −0.421927
\(456\) 0 0
\(457\) −7.00000 −0.327446 −0.163723 0.986506i \(-0.552350\pi\)
−0.163723 + 0.986506i \(0.552350\pi\)
\(458\) 8.50000 14.7224i 0.397179 0.687934i
\(459\) 0 0
\(460\) 1.50000 + 2.59808i 0.0699379 + 0.121136i
\(461\) −16.5000 + 28.5788i −0.768482 + 1.33105i 0.169904 + 0.985461i \(0.445654\pi\)
−0.938386 + 0.345589i \(0.887679\pi\)
\(462\) 0 0
\(463\) −9.00000 −0.418265 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 4.50000 + 7.79423i 0.208458 + 0.361061i
\(467\) 4.00000 0.185098 0.0925490 0.995708i \(-0.470499\pi\)
0.0925490 + 0.995708i \(0.470499\pi\)
\(468\) 0 0
\(469\) −6.00000 10.3923i −0.277054 0.479872i
\(470\) −3.00000 + 5.19615i −0.138380 + 0.239681i
\(471\) 0 0
\(472\) 6.50000 11.2583i 0.299187 0.518207i
\(473\) −12.0000 + 20.7846i −0.551761 + 0.955677i
\(474\) 0 0
\(475\) 16.0000 6.92820i 0.734130 0.317888i
\(476\) −2.00000 −0.0916698
\(477\) 0 0
\(478\) 13.5000 23.3827i 0.617476 1.06950i
\(479\) −21.0000 36.3731i −0.959514 1.66193i −0.723681 0.690134i \(-0.757551\pi\)
−0.235833 0.971794i \(-0.575782\pi\)
\(480\) 0 0
\(481\) −6.00000 10.3923i −0.273576 0.473848i
\(482\) 22.0000 1.00207
\(483\) 0 0
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) 15.0000 + 25.9808i 0.681115 + 1.17973i
\(486\) 0 0
\(487\) −28.0000 −1.26880 −0.634401 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) −2.50000 4.33013i −0.113170 0.196016i
\(489\) 0 0
\(490\) −1.50000 2.59808i −0.0677631 0.117369i
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.50000 + 12.9904i −0.0674882 + 0.584465i
\(495\) 0 0
\(496\) 3.00000 5.19615i 0.134704 0.233314i
\(497\) 3.50000 6.06218i 0.156996 0.271926i
\(498\) 0 0
\(499\) 5.00000 8.66025i 0.223831 0.387686i −0.732137 0.681157i \(-0.761477\pi\)
0.955968 + 0.293471i \(0.0948104\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) 0 0
\(502\) −21.0000 −0.937276
\(503\) 11.0000 + 19.0526i 0.490466 + 0.849512i 0.999940 0.0109744i \(-0.00349334\pi\)
−0.509474 + 0.860486i \(0.670160\pi\)
\(504\) 0 0
\(505\) −42.0000 −1.86898
\(506\) 4.00000 0.177822
\(507\) 0 0
\(508\) 5.50000 9.52628i 0.244023 0.422660i
\(509\) −6.50000 11.2583i −0.288107 0.499017i 0.685251 0.728307i \(-0.259693\pi\)
−0.973358 + 0.229291i \(0.926359\pi\)
\(510\) 0 0
\(511\) −1.00000 + 1.73205i −0.0442374 + 0.0766214i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) 0 0
\(517\) 4.00000 + 6.92820i 0.175920 + 0.304702i
\(518\) 2.00000 3.46410i 0.0878750 0.152204i
\(519\) 0 0
\(520\) 9.00000 0.394676
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) 0 0
\(523\) 16.0000 + 27.7128i 0.699631 + 1.21180i 0.968594 + 0.248646i \(0.0799857\pi\)
−0.268963 + 0.963150i \(0.586681\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) −1.50000 2.59808i −0.0654031 0.113282i
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) −6.00000 + 10.3923i −0.260623 + 0.451413i
\(531\) 0 0
\(532\) −4.00000 + 1.73205i −0.173422 + 0.0750939i
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) −15.0000 + 25.9808i −0.648507 + 1.12325i
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 0 0
\(538\) 7.00000 + 12.1244i 0.301791 + 0.522718i
\(539\) −4.00000 −0.172292
\(540\) 0 0
\(541\) −16.0000 27.7128i −0.687894 1.19147i −0.972518 0.232828i \(-0.925202\pi\)
0.284624 0.958639i \(-0.408131\pi\)
\(542\) −13.0000 22.5167i −0.558398 0.967173i
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) 6.00000 + 10.3923i 0.257012 + 0.445157i
\(546\) 0 0
\(547\) 23.0000 + 39.8372i 0.983409 + 1.70331i 0.648803 + 0.760956i \(0.275270\pi\)
0.334606 + 0.942358i \(0.391397\pi\)
\(548\) −10.5000 + 18.1865i −0.448538 + 0.776890i
\(549\) 0 0
\(550\) −16.0000 −0.682242
\(551\) 0 0
\(552\) 0 0
\(553\) −4.00000 + 6.92820i −0.170097 + 0.294617i
\(554\) 1.00000 1.73205i 0.0424859 0.0735878i
\(555\) 0 0
\(556\) 8.00000 13.8564i 0.339276 0.587643i
\(557\) 11.0000 + 19.0526i 0.466085 + 0.807283i 0.999250 0.0387286i \(-0.0123308\pi\)
−0.533165 + 0.846011i \(0.678997\pi\)
\(558\) 0 0
\(559\) −18.0000 −0.761319
\(560\) 1.50000 + 2.59808i 0.0633866 + 0.109789i
\(561\) 0 0
\(562\) 26.0000 1.09674
\(563\) −33.0000 −1.39078 −0.695392 0.718631i \(-0.744769\pi\)
−0.695392 + 0.718631i \(0.744769\pi\)
\(564\) 0 0
\(565\) −7.50000 + 12.9904i −0.315527 + 0.546509i
\(566\) −12.5000 21.6506i −0.525414 0.910044i
\(567\) 0 0
\(568\) −3.50000 + 6.06218i −0.146857 + 0.254363i
\(569\) 9.00000 0.377300 0.188650 0.982044i \(-0.439589\pi\)
0.188650 + 0.982044i \(0.439589\pi\)
\(570\) 0 0
\(571\) 2.00000 0.0836974 0.0418487 0.999124i \(-0.486675\pi\)
0.0418487 + 0.999124i \(0.486675\pi\)
\(572\) 6.00000 10.3923i 0.250873 0.434524i
\(573\) 0 0
\(574\) −2.00000 3.46410i −0.0834784 0.144589i
\(575\) 2.00000 3.46410i 0.0834058 0.144463i
\(576\) 0 0
\(577\) −8.00000 −0.333044 −0.166522 0.986038i \(-0.553254\pi\)
−0.166522 + 0.986038i \(0.553254\pi\)
\(578\) −13.0000 −0.540729
\(579\) 0 0
\(580\) 0 0
\(581\) 17.0000 0.705279
\(582\) 0 0
\(583\) 8.00000 + 13.8564i 0.331326 + 0.573874i
\(584\) 1.00000 1.73205i 0.0413803 0.0716728i
\(585\) 0 0
\(586\) −9.50000 + 16.4545i −0.392441 + 0.679728i
\(587\) −10.0000 + 17.3205i −0.412744 + 0.714894i −0.995189 0.0979766i \(-0.968763\pi\)
0.582445 + 0.812870i \(0.302096\pi\)
\(588\) 0 0
\(589\) 3.00000 25.9808i 0.123613 1.07052i
\(590\) −39.0000 −1.60560
\(591\) 0 0
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) −16.0000 27.7128i −0.657041 1.13803i −0.981378 0.192087i \(-0.938474\pi\)
0.324337 0.945942i \(-0.394859\pi\)
\(594\) 0 0
\(595\) 3.00000 + 5.19615i 0.122988 + 0.213021i
\(596\) −20.0000 −0.819232
\(597\) 0 0
\(598\) 1.50000 + 2.59808i 0.0613396 + 0.106243i
\(599\) −21.5000 37.2391i −0.878466 1.52155i −0.853024 0.521872i \(-0.825234\pi\)
−0.0254422 0.999676i \(-0.508099\pi\)
\(600\) 0 0
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) −3.00000 5.19615i −0.122271 0.211779i
\(603\) 0 0
\(604\) −9.50000 16.4545i −0.386550 0.669523i
\(605\) −7.50000 + 12.9904i −0.304918 + 0.528134i
\(606\) 0 0
\(607\) −16.0000 −0.649420 −0.324710 0.945814i \(-0.605267\pi\)
−0.324710 + 0.945814i \(0.605267\pi\)
\(608\) 4.00000 1.73205i 0.162221 0.0702439i
\(609\) 0 0
\(610\) −7.50000 + 12.9904i −0.303666 + 0.525965i
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) 0 0
\(613\) 5.00000 8.66025i 0.201948 0.349784i −0.747208 0.664590i \(-0.768606\pi\)
0.949156 + 0.314806i \(0.101939\pi\)
\(614\) −7.50000 12.9904i −0.302675 0.524249i
\(615\) 0 0
\(616\) 4.00000 0.161165
\(617\) −13.5000 23.3827i −0.543490 0.941351i −0.998700 0.0509678i \(-0.983769\pi\)
0.455211 0.890384i \(-0.349564\pi\)
\(618\) 0 0
\(619\) −5.00000 −0.200967 −0.100483 0.994939i \(-0.532039\pi\)
−0.100483 + 0.994939i \(0.532039\pi\)
\(620\) −18.0000 −0.722897
\(621\) 0 0
\(622\) −1.00000 + 1.73205i −0.0400963 + 0.0694489i
\(623\) −2.00000 3.46410i −0.0801283 0.138786i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 24.0000 0.959233
\(627\) 0 0
\(628\) −9.00000 −0.359139
\(629\) −4.00000 + 6.92820i −0.159490 + 0.276246i
\(630\) 0 0
\(631\) −4.00000 6.92820i −0.159237 0.275807i 0.775356 0.631524i \(-0.217570\pi\)
−0.934594 + 0.355716i \(0.884237\pi\)
\(632\) 4.00000 6.92820i 0.159111 0.275589i
\(633\) 0 0
\(634\) −6.00000 −0.238290
\(635\) −33.0000 −1.30957
\(636\) 0 0
\(637\) −1.50000 2.59808i −0.0594322 0.102940i
\(638\) 0 0
\(639\) 0 0
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) −8.50000 + 14.7224i −0.335730 + 0.581501i −0.983625 0.180229i \(-0.942316\pi\)
0.647895 + 0.761730i \(0.275650\pi\)
\(642\) 0 0
\(643\) 20.5000 35.5070i 0.808441 1.40026i −0.105502 0.994419i \(-0.533645\pi\)
0.913943 0.405842i \(-0.133022\pi\)
\(644\) −0.500000 + 0.866025i −0.0197028 + 0.0341262i
\(645\) 0 0
\(646\) 8.00000 3.46410i 0.314756 0.136293i
\(647\) −30.0000 −1.17942 −0.589711 0.807614i \(-0.700758\pi\)
−0.589711 + 0.807614i \(0.700758\pi\)
\(648\) 0 0
\(649\) −26.0000 + 45.0333i −1.02059 + 1.76771i
\(650\) −6.00000 10.3923i −0.235339 0.407620i
\(651\) 0 0
\(652\) −7.00000 12.1244i −0.274141 0.474826i
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 0 0
\(655\) −13.5000 23.3827i −0.527489 0.913637i
\(656\) 2.00000 + 3.46410i 0.0780869 + 0.135250i
\(657\) 0 0
\(658\) −2.00000 −0.0779681
\(659\) −13.0000 22.5167i −0.506408 0.877125i −0.999973 0.00741531i \(-0.997640\pi\)
0.493564 0.869709i \(-0.335694\pi\)
\(660\) 0 0
\(661\) 5.50000 + 9.52628i 0.213925 + 0.370529i 0.952940 0.303160i \(-0.0980418\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) 12.0000 20.7846i 0.466393 0.807817i
\(663\) 0 0
\(664\) −17.0000 −0.659728
\(665\) 10.5000 + 7.79423i 0.407173 + 0.302247i
\(666\) 0 0
\(667\) 0 0
\(668\) −9.00000 + 15.5885i −0.348220 + 0.603136i
\(669\) 0 0
\(670\) 18.0000 31.1769i 0.695401 1.20447i
\(671\) 10.0000 + 17.3205i 0.386046 + 0.668651i
\(672\) 0 0
\(673\) 11.0000 0.424019 0.212009 0.977268i \(-0.431999\pi\)
0.212009 + 0.977268i \(0.431999\pi\)
\(674\) −8.50000 14.7224i −0.327408 0.567087i
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 0 0
\(679\) −5.00000 + 8.66025i −0.191882 + 0.332350i
\(680\) −3.00000 5.19615i −0.115045 0.199263i
\(681\) 0 0
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) 63.0000 2.40711
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 0 0
\(688\) 3.00000 + 5.19615i 0.114374 + 0.198101i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) −41.0000 −1.55971 −0.779857 0.625958i \(-0.784708\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) −15.0000 −0.570214
\(693\) 0 0
\(694\) 11.0000 + 19.0526i 0.417554 + 0.723225i
\(695\) −48.0000 −1.82074
\(696\) 0 0
\(697\) 4.00000 + 6.92820i 0.151511 + 0.262424i
\(698\) −5.00000 + 8.66025i −0.189253 + 0.327795i
\(699\) 0 0
\(700\) 2.00000 3.46410i 0.0755929 0.130931i
\(701\) −1.00000 + 1.73205i −0.0377695 + 0.0654187i −0.884292 0.466934i \(-0.845359\pi\)
0.846523 + 0.532353i \(0.178692\pi\)
\(702\) 0 0
\(703\) −2.00000 + 17.3205i −0.0754314 + 0.653255i
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) 6.00000 10.3923i 0.225813 0.391120i
\(707\) −7.00000 12.1244i −0.263262 0.455983i
\(708\) 0 0
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) 21.0000 0.788116
\(711\) 0 0
\(712\) 2.00000 + 3.46410i 0.0749532 + 0.129823i
\(713\) −3.00000 5.19615i −0.112351 0.194597i
\(714\) 0 0
\(715\) −36.0000 −1.34632
\(716\) 5.00000 + 8.66025i 0.186859 + 0.323649i
\(717\) 0 0
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) 11.0000 19.0526i 0.410231 0.710541i −0.584684 0.811261i \(-0.698781\pi\)
0.994915 + 0.100721i \(0.0321148\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13.0000 13.8564i 0.483810 0.515682i
\(723\) 0 0
\(724\) −1.50000 + 2.59808i −0.0557471 + 0.0965567i
\(725\) 0 0
\(726\) 0 0
\(727\) −22.0000 + 38.1051i −0.815935 + 1.41324i 0.0927199 + 0.995692i \(0.470444\pi\)
−0.908655 + 0.417548i \(0.862889\pi\)
\(728\) 1.50000 + 2.59808i 0.0555937 + 0.0962911i
\(729\) 0 0
\(730\) −6.00000 −0.222070
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) −11.0000 −0.406294 −0.203147 0.979148i \(-0.565117\pi\)
−0.203147 + 0.979148i \(0.565117\pi\)
\(734\) 32.0000 1.18114
\(735\) 0 0
\(736\) 0.500000 0.866025i 0.0184302 0.0319221i
\(737\) −24.0000 41.5692i −0.884051 1.53122i
\(738\) 0 0
\(739\) 22.0000 38.1051i 0.809283 1.40172i −0.104078 0.994569i \(-0.533189\pi\)
0.913361 0.407150i \(-0.133477\pi\)
\(740\) 12.0000 0.441129
\(741\) 0 0
\(742\) −4.00000 −0.146845
\(743\) −1.50000 + 2.59808i −0.0550297 + 0.0953142i −0.892228 0.451585i \(-0.850859\pi\)
0.837198 + 0.546899i \(0.184192\pi\)
\(744\) 0 0
\(745\) 30.0000 + 51.9615i 1.09911 + 1.90372i
\(746\) 5.00000 8.66025i 0.183063 0.317074i
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) −10.0000 −0.365392
\(750\) 0 0
\(751\) −20.0000 34.6410i −0.729810 1.26407i −0.956963 0.290209i \(-0.906275\pi\)
0.227153 0.973859i \(-0.427058\pi\)
\(752\) 2.00000 0.0729325
\(753\) 0 0
\(754\) 0 0
\(755\) −28.5000 + 49.3634i −1.03722 + 1.79652i
\(756\) 0 0
\(757\) 23.0000 39.8372i 0.835949 1.44791i −0.0573060 0.998357i \(-0.518251\pi\)
0.893255 0.449550i \(-0.148416\pi\)
\(758\) 17.0000 29.4449i 0.617468 1.06949i
\(759\) 0 0
\(760\) −10.5000 7.79423i −0.380875 0.282726i
\(761\) −8.00000 −0.290000 −0.145000 0.989432i \(-0.546318\pi\)
−0.145000 + 0.989432i \(0.546318\pi\)
\(762\) 0 0
\(763\) −2.00000 + 3.46410i −0.0724049 + 0.125409i
\(764\) −5.50000 9.52628i −0.198983 0.344649i
\(765\) 0 0
\(766\) −2.00000 3.46410i −0.0722629 0.125163i
\(767\) −39.0000 −1.40821
\(768\) 0 0
\(769\) 15.0000 + 25.9808i 0.540914 + 0.936890i 0.998852 + 0.0479061i \(0.0152548\pi\)
−0.457938 + 0.888984i \(0.651412\pi\)
\(770\) −6.00000 10.3923i −0.216225 0.374513i
\(771\) 0 0
\(772\) 5.00000 0.179954
\(773\) 4.50000 + 7.79423i 0.161854 + 0.280339i 0.935534 0.353238i \(-0.114919\pi\)
−0.773680 + 0.633577i \(0.781586\pi\)
\(774\) 0 0
\(775\) 12.0000 + 20.7846i 0.431053 + 0.746605i
\(776\) 5.00000 8.66025i 0.179490 0.310885i
\(777\) 0 0
\(778\) −8.00000 −0.286814
\(779\) 14.0000 + 10.3923i 0.501602 + 0.372343i
\(780\) 0 0
\(781\) 14.0000 24.2487i 0.500959 0.867687i
\(782\) 1.00000 1.73205i 0.0357599 0.0619380i
\(783\) 0 0
\(784\) −0.500000 + 0.866025i −0.0178571 + 0.0309295i
\(785\) 13.5000 + 23.3827i 0.481836 + 0.834564i
\(786\) 0 0
\(787\) −47.0000 −1.67537 −0.837685 0.546154i \(-0.816091\pi\)
−0.837685 + 0.546154i \(0.816091\pi\)
\(788\) 2.00000 + 3.46410i 0.0712470 + 0.123404i