Properties

Label 1078.2.e.n.67.2
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(-0.309017 + 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.n.177.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.618034 - 1.07047i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.618034 - 1.07047i) q^{5} -1.23607 q^{6} +1.00000 q^{8} +(0.736068 + 1.27491i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.618034 - 1.07047i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.618034 - 1.07047i) q^{5} -1.23607 q^{6} +1.00000 q^{8} +(0.736068 + 1.27491i) q^{9} +(-0.618034 + 1.07047i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.618034 + 1.07047i) q^{12} +3.23607 q^{13} -1.52786 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.23607 - 2.14093i) q^{17} +(0.736068 - 1.27491i) q^{18} +(-3.61803 - 6.26662i) q^{19} +1.23607 q^{20} +1.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(0.618034 - 1.07047i) q^{24} +(1.73607 - 3.00696i) q^{25} +(-1.61803 - 2.80252i) q^{26} +5.52786 q^{27} +4.47214 q^{29} +(0.763932 + 1.32317i) q^{30} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.618034 + 1.07047i) q^{33} -2.47214 q^{34} -1.47214 q^{36} +(-3.47214 - 6.01392i) q^{37} +(-3.61803 + 6.26662i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-0.618034 - 1.07047i) q^{40} +2.47214 q^{41} -10.4721 q^{43} +(-0.500000 - 0.866025i) q^{44} +(0.909830 - 1.57587i) q^{45} +(-2.00000 + 3.46410i) q^{46} +(-1.00000 - 1.73205i) q^{47} -1.23607 q^{48} -3.47214 q^{50} +(-1.52786 - 2.64634i) q^{51} +(-1.61803 + 2.80252i) q^{52} +(-4.23607 + 7.33708i) q^{53} +(-2.76393 - 4.78727i) q^{54} +1.23607 q^{55} -8.94427 q^{57} +(-2.23607 - 3.87298i) q^{58} +(1.38197 - 2.39364i) q^{59} +(0.763932 - 1.32317i) q^{60} +(-0.381966 - 0.661585i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(0.618034 - 1.07047i) q^{66} +(-5.70820 + 9.88690i) q^{67} +(1.23607 + 2.14093i) q^{68} -4.94427 q^{69} +6.47214 q^{71} +(0.736068 + 1.27491i) q^{72} +(6.47214 - 11.2101i) q^{73} +(-3.47214 + 6.01392i) q^{74} +(-2.14590 - 3.71680i) q^{75} +7.23607 q^{76} -4.00000 q^{78} +(-0.618034 + 1.07047i) q^{80} +(1.20820 - 2.09267i) q^{81} +(-1.23607 - 2.14093i) q^{82} +12.1803 q^{83} -3.05573 q^{85} +(5.23607 + 9.06914i) q^{86} +(2.76393 - 4.78727i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(5.00000 + 8.66025i) q^{89} -1.81966 q^{90} +4.00000 q^{92} +(-1.23607 - 2.14093i) q^{93} +(-1.00000 + 1.73205i) q^{94} +(-4.47214 + 7.74597i) q^{95} +(0.618034 + 1.07047i) q^{96} -12.4721 q^{97} -1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{8} - 6 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 24 q^{15} - 2 q^{16} - 4 q^{17} - 6 q^{18} - 10 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 40 q^{27} + 12 q^{30} + 4 q^{31} - 2 q^{32} - 2 q^{33} + 8 q^{34} + 12 q^{36} + 4 q^{37} - 10 q^{38} + 8 q^{39} + 2 q^{40} - 8 q^{41} - 24 q^{43} - 2 q^{44} + 26 q^{45} - 8 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} - 24 q^{51} - 2 q^{52} - 8 q^{53} - 20 q^{54} - 4 q^{55} + 10 q^{59} + 12 q^{60} - 6 q^{61} - 8 q^{62} + 4 q^{64} - 8 q^{65} - 2 q^{66} + 4 q^{67} - 4 q^{68} + 16 q^{69} + 8 q^{71} - 6 q^{72} + 8 q^{73} + 4 q^{74} - 22 q^{75} + 20 q^{76} - 16 q^{78} + 2 q^{80} - 22 q^{81} + 4 q^{82} + 4 q^{83} - 48 q^{85} + 12 q^{86} + 20 q^{87} - 2 q^{88} + 20 q^{89} - 52 q^{90} + 16 q^{92} + 4 q^{93} - 4 q^{94} - 2 q^{96} - 32 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 0.618034 1.07047i 0.356822 0.618034i −0.630606 0.776103i \(-0.717194\pi\)
0.987428 + 0.158069i \(0.0505269\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.618034 1.07047i −0.276393 0.478727i 0.694092 0.719886i \(-0.255806\pi\)
−0.970486 + 0.241159i \(0.922473\pi\)
\(6\) −1.23607 −0.504623
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0.736068 + 1.27491i 0.245356 + 0.424969i
\(10\) −0.618034 + 1.07047i −0.195440 + 0.338511i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 0.618034 + 1.07047i 0.178411 + 0.309017i
\(13\) 3.23607 0.897524 0.448762 0.893651i \(-0.351865\pi\)
0.448762 + 0.893651i \(0.351865\pi\)
\(14\) 0 0
\(15\) −1.52786 −0.394493
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.23607 2.14093i 0.299791 0.519252i −0.676297 0.736629i \(-0.736417\pi\)
0.976088 + 0.217376i \(0.0697499\pi\)
\(18\) 0.736068 1.27491i 0.173493 0.300498i
\(19\) −3.61803 6.26662i −0.830034 1.43766i −0.898011 0.439974i \(-0.854988\pi\)
0.0679766 0.997687i \(-0.478346\pi\)
\(20\) 1.23607 0.276393
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0.618034 1.07047i 0.126156 0.218508i
\(25\) 1.73607 3.00696i 0.347214 0.601392i
\(26\) −1.61803 2.80252i −0.317323 0.549619i
\(27\) 5.52786 1.06384
\(28\) 0 0
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) 0.763932 + 1.32317i 0.139474 + 0.241577i
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0.618034 + 1.07047i 0.107586 + 0.186344i
\(34\) −2.47214 −0.423968
\(35\) 0 0
\(36\) −1.47214 −0.245356
\(37\) −3.47214 6.01392i −0.570816 0.988682i −0.996482 0.0838017i \(-0.973294\pi\)
0.425667 0.904880i \(-0.360040\pi\)
\(38\) −3.61803 + 6.26662i −0.586923 + 1.01658i
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) −0.618034 1.07047i −0.0977198 0.169256i
\(41\) 2.47214 0.386083 0.193041 0.981191i \(-0.438165\pi\)
0.193041 + 0.981191i \(0.438165\pi\)
\(42\) 0 0
\(43\) −10.4721 −1.59699 −0.798493 0.602004i \(-0.794369\pi\)
−0.798493 + 0.602004i \(0.794369\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 0.909830 1.57587i 0.135629 0.234917i
\(46\) −2.00000 + 3.46410i −0.294884 + 0.510754i
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) −1.23607 −0.178411
\(49\) 0 0
\(50\) −3.47214 −0.491034
\(51\) −1.52786 2.64634i −0.213944 0.370561i
\(52\) −1.61803 + 2.80252i −0.224381 + 0.388639i
\(53\) −4.23607 + 7.33708i −0.581869 + 1.00783i 0.413389 + 0.910554i \(0.364345\pi\)
−0.995258 + 0.0972717i \(0.968988\pi\)
\(54\) −2.76393 4.78727i −0.376124 0.651465i
\(55\) 1.23607 0.166671
\(56\) 0 0
\(57\) −8.94427 −1.18470
\(58\) −2.23607 3.87298i −0.293610 0.508548i
\(59\) 1.38197 2.39364i 0.179917 0.311625i −0.761935 0.647653i \(-0.775751\pi\)
0.941852 + 0.336029i \(0.109084\pi\)
\(60\) 0.763932 1.32317i 0.0986232 0.170820i
\(61\) −0.381966 0.661585i −0.0489057 0.0847072i 0.840536 0.541755i \(-0.182240\pi\)
−0.889442 + 0.457048i \(0.848907\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0.618034 1.07047i 0.0760747 0.131765i
\(67\) −5.70820 + 9.88690i −0.697368 + 1.20788i 0.272008 + 0.962295i \(0.412312\pi\)
−0.969376 + 0.245582i \(0.921021\pi\)
\(68\) 1.23607 + 2.14093i 0.149895 + 0.259626i
\(69\) −4.94427 −0.595220
\(70\) 0 0
\(71\) 6.47214 0.768101 0.384051 0.923312i \(-0.374529\pi\)
0.384051 + 0.923312i \(0.374529\pi\)
\(72\) 0.736068 + 1.27491i 0.0867464 + 0.150249i
\(73\) 6.47214 11.2101i 0.757506 1.31204i −0.186612 0.982434i \(-0.559751\pi\)
0.944119 0.329606i \(-0.106916\pi\)
\(74\) −3.47214 + 6.01392i −0.403628 + 0.699104i
\(75\) −2.14590 3.71680i −0.247787 0.429180i
\(76\) 7.23607 0.830034
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −0.618034 + 1.07047i −0.0690983 + 0.119682i
\(81\) 1.20820 2.09267i 0.134245 0.232519i
\(82\) −1.23607 2.14093i −0.136501 0.236426i
\(83\) 12.1803 1.33697 0.668483 0.743727i \(-0.266944\pi\)
0.668483 + 0.743727i \(0.266944\pi\)
\(84\) 0 0
\(85\) −3.05573 −0.331440
\(86\) 5.23607 + 9.06914i 0.564620 + 0.977950i
\(87\) 2.76393 4.78727i 0.296325 0.513249i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) −1.81966 −0.191809
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) −1.23607 2.14093i −0.128174 0.222004i
\(94\) −1.00000 + 1.73205i −0.103142 + 0.178647i
\(95\) −4.47214 + 7.74597i −0.458831 + 0.794719i
\(96\) 0.618034 + 1.07047i 0.0630778 + 0.109254i
\(97\) −12.4721 −1.26635 −0.633177 0.774007i \(-0.718249\pi\)
−0.633177 + 0.774007i \(0.718249\pi\)
\(98\) 0 0
\(99\) −1.47214 −0.147955
\(100\) 1.73607 + 3.00696i 0.173607 + 0.300696i
\(101\) 4.09017 7.08438i 0.406987 0.704922i −0.587563 0.809178i \(-0.699913\pi\)
0.994551 + 0.104256i \(0.0332461\pi\)
\(102\) −1.52786 + 2.64634i −0.151281 + 0.262027i
\(103\) −7.47214 12.9421i −0.736251 1.27522i −0.954172 0.299258i \(-0.903261\pi\)
0.217921 0.975966i \(-0.430073\pi\)
\(104\) 3.23607 0.317323
\(105\) 0 0
\(106\) 8.47214 0.822887
\(107\) −1.23607 2.14093i −0.119495 0.206972i 0.800073 0.599903i \(-0.204794\pi\)
−0.919568 + 0.392932i \(0.871461\pi\)
\(108\) −2.76393 + 4.78727i −0.265959 + 0.460655i
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) −0.618034 1.07047i −0.0589272 0.102065i
\(111\) −8.58359 −0.814719
\(112\) 0 0
\(113\) −0.472136 −0.0444148 −0.0222074 0.999753i \(-0.507069\pi\)
−0.0222074 + 0.999753i \(0.507069\pi\)
\(114\) 4.47214 + 7.74597i 0.418854 + 0.725476i
\(115\) −2.47214 + 4.28187i −0.230528 + 0.399286i
\(116\) −2.23607 + 3.87298i −0.207614 + 0.359597i
\(117\) 2.38197 + 4.12569i 0.220213 + 0.381420i
\(118\) −2.76393 −0.254441
\(119\) 0 0
\(120\) −1.52786 −0.139474
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −0.381966 + 0.661585i −0.0345816 + 0.0598970i
\(123\) 1.52786 2.64634i 0.137763 0.238612i
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) −10.4721 −0.936656
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −6.47214 + 11.2101i −0.569840 + 0.986991i
\(130\) −2.00000 + 3.46410i −0.175412 + 0.303822i
\(131\) 2.38197 + 4.12569i 0.208113 + 0.360463i 0.951120 0.308821i \(-0.0999344\pi\)
−0.743007 + 0.669284i \(0.766601\pi\)
\(132\) −1.23607 −0.107586
\(133\) 0 0
\(134\) 11.4164 0.986227
\(135\) −3.41641 5.91739i −0.294038 0.509288i
\(136\) 1.23607 2.14093i 0.105992 0.183583i
\(137\) 9.94427 17.2240i 0.849596 1.47154i −0.0319723 0.999489i \(-0.510179\pi\)
0.881569 0.472056i \(-0.156488\pi\)
\(138\) 2.47214 + 4.28187i 0.210442 + 0.364497i
\(139\) 21.7082 1.84127 0.920633 0.390429i \(-0.127673\pi\)
0.920633 + 0.390429i \(0.127673\pi\)
\(140\) 0 0
\(141\) −2.47214 −0.208191
\(142\) −3.23607 5.60503i −0.271565 0.470364i
\(143\) −1.61803 + 2.80252i −0.135307 + 0.234358i
\(144\) 0.736068 1.27491i 0.0613390 0.106242i
\(145\) −2.76393 4.78727i −0.229532 0.397561i
\(146\) −12.9443 −1.07128
\(147\) 0 0
\(148\) 6.94427 0.570816
\(149\) 11.1803 + 19.3649i 0.915929 + 1.58644i 0.805535 + 0.592548i \(0.201878\pi\)
0.110394 + 0.993888i \(0.464789\pi\)
\(150\) −2.14590 + 3.71680i −0.175212 + 0.303476i
\(151\) −6.00000 + 10.3923i −0.488273 + 0.845714i −0.999909 0.0134886i \(-0.995706\pi\)
0.511636 + 0.859202i \(0.329040\pi\)
\(152\) −3.61803 6.26662i −0.293461 0.508290i
\(153\) 3.63932 0.294222
\(154\) 0 0
\(155\) −2.47214 −0.198567
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) −6.32624 + 10.9574i −0.504889 + 0.874493i 0.495095 + 0.868839i \(0.335133\pi\)
−0.999984 + 0.00565427i \(0.998200\pi\)
\(158\) 0 0
\(159\) 5.23607 + 9.06914i 0.415247 + 0.719229i
\(160\) 1.23607 0.0977198
\(161\) 0 0
\(162\) −2.41641 −0.189851
\(163\) 9.70820 + 16.8151i 0.760405 + 1.31706i 0.942642 + 0.333806i \(0.108333\pi\)
−0.182237 + 0.983255i \(0.558334\pi\)
\(164\) −1.23607 + 2.14093i −0.0965207 + 0.167179i
\(165\) 0.763932 1.32317i 0.0594720 0.103009i
\(166\) −6.09017 10.5485i −0.472689 0.818721i
\(167\) −11.4164 −0.883428 −0.441714 0.897156i \(-0.645629\pi\)
−0.441714 + 0.897156i \(0.645629\pi\)
\(168\) 0 0
\(169\) −2.52786 −0.194451
\(170\) 1.52786 + 2.64634i 0.117182 + 0.202965i
\(171\) 5.32624 9.22531i 0.407308 0.705477i
\(172\) 5.23607 9.06914i 0.399246 0.691515i
\(173\) −1.61803 2.80252i −0.123017 0.213071i 0.797939 0.602738i \(-0.205924\pi\)
−0.920956 + 0.389667i \(0.872590\pi\)
\(174\) −5.52786 −0.419066
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) −1.70820 2.95870i −0.128396 0.222389i
\(178\) 5.00000 8.66025i 0.374766 0.649113i
\(179\) 4.47214 7.74597i 0.334263 0.578961i −0.649080 0.760720i \(-0.724846\pi\)
0.983343 + 0.181760i \(0.0581792\pi\)
\(180\) 0.909830 + 1.57587i 0.0678147 + 0.117459i
\(181\) −9.23607 −0.686512 −0.343256 0.939242i \(-0.611530\pi\)
−0.343256 + 0.939242i \(0.611530\pi\)
\(182\) 0 0
\(183\) −0.944272 −0.0698026
\(184\) −2.00000 3.46410i −0.147442 0.255377i
\(185\) −4.29180 + 7.43361i −0.315539 + 0.546530i
\(186\) −1.23607 + 2.14093i −0.0906329 + 0.156981i
\(187\) 1.23607 + 2.14093i 0.0903902 + 0.156560i
\(188\) 2.00000 0.145865
\(189\) 0 0
\(190\) 8.94427 0.648886
\(191\) 1.23607 + 2.14093i 0.0894387 + 0.154912i 0.907274 0.420540i \(-0.138159\pi\)
−0.817835 + 0.575452i \(0.804826\pi\)
\(192\) 0.618034 1.07047i 0.0446028 0.0772542i
\(193\) 7.47214 12.9421i 0.537856 0.931594i −0.461163 0.887315i \(-0.652568\pi\)
0.999019 0.0442787i \(-0.0140990\pi\)
\(194\) 6.23607 + 10.8012i 0.447724 + 0.775480i
\(195\) −4.94427 −0.354067
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0.736068 + 1.27491i 0.0523101 + 0.0906037i
\(199\) 9.47214 16.4062i 0.671462 1.16301i −0.306028 0.952023i \(-0.599000\pi\)
0.977490 0.210984i \(-0.0676666\pi\)
\(200\) 1.73607 3.00696i 0.122759 0.212624i
\(201\) 7.05573 + 12.2209i 0.497673 + 0.861994i
\(202\) −8.18034 −0.575567
\(203\) 0 0
\(204\) 3.05573 0.213944
\(205\) −1.52786 2.64634i −0.106711 0.184828i
\(206\) −7.47214 + 12.9421i −0.520608 + 0.901720i
\(207\) 2.94427 5.09963i 0.204641 0.354449i
\(208\) −1.61803 2.80252i −0.112190 0.194320i
\(209\) 7.23607 0.500529
\(210\) 0 0
\(211\) −13.5279 −0.931297 −0.465648 0.884970i \(-0.654179\pi\)
−0.465648 + 0.884970i \(0.654179\pi\)
\(212\) −4.23607 7.33708i −0.290934 0.503913i
\(213\) 4.00000 6.92820i 0.274075 0.474713i
\(214\) −1.23607 + 2.14093i −0.0844959 + 0.146351i
\(215\) 6.47214 + 11.2101i 0.441396 + 0.764520i
\(216\) 5.52786 0.376124
\(217\) 0 0
\(218\) −10.0000 −0.677285
\(219\) −8.00000 13.8564i −0.540590 0.936329i
\(220\) −0.618034 + 1.07047i −0.0416678 + 0.0721708i
\(221\) 4.00000 6.92820i 0.269069 0.466041i
\(222\) 4.29180 + 7.43361i 0.288046 + 0.498911i
\(223\) 0.472136 0.0316166 0.0158083 0.999875i \(-0.494968\pi\)
0.0158083 + 0.999875i \(0.494968\pi\)
\(224\) 0 0
\(225\) 5.11146 0.340764
\(226\) 0.236068 + 0.408882i 0.0157030 + 0.0271984i
\(227\) −9.61803 + 16.6589i −0.638371 + 1.10569i 0.347419 + 0.937710i \(0.387058\pi\)
−0.985790 + 0.167982i \(0.946275\pi\)
\(228\) 4.47214 7.74597i 0.296174 0.512989i
\(229\) 8.61803 + 14.9269i 0.569496 + 0.986396i 0.996616 + 0.0822006i \(0.0261948\pi\)
−0.427120 + 0.904195i \(0.640472\pi\)
\(230\) 4.94427 0.326016
\(231\) 0 0
\(232\) 4.47214 0.293610
\(233\) 7.47214 + 12.9421i 0.489516 + 0.847866i 0.999927 0.0120640i \(-0.00384018\pi\)
−0.510411 + 0.859930i \(0.670507\pi\)
\(234\) 2.38197 4.12569i 0.155714 0.269705i
\(235\) −1.23607 + 2.14093i −0.0806322 + 0.139659i
\(236\) 1.38197 + 2.39364i 0.0899583 + 0.155812i
\(237\) 0 0
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0.763932 + 1.32317i 0.0493116 + 0.0854102i
\(241\) 7.70820 13.3510i 0.496529 0.860014i −0.503463 0.864017i \(-0.667941\pi\)
0.999992 + 0.00400327i \(0.00127428\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 6.79837 + 11.7751i 0.436116 + 0.755375i
\(244\) 0.763932 0.0489057
\(245\) 0 0
\(246\) −3.05573 −0.194826
\(247\) −11.7082 20.2792i −0.744975 1.29033i
\(248\) 1.00000 1.73205i 0.0635001 0.109985i
\(249\) 7.52786 13.0386i 0.477059 0.826290i
\(250\) 5.23607 + 9.06914i 0.331158 + 0.573583i
\(251\) −29.2361 −1.84536 −0.922682 0.385562i \(-0.874008\pi\)
−0.922682 + 0.385562i \(0.874008\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 6.00000 + 10.3923i 0.376473 + 0.652071i
\(255\) −1.88854 + 3.27105i −0.118265 + 0.204841i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.47214 + 6.01392i 0.216586 + 0.375138i 0.953762 0.300563i \(-0.0971745\pi\)
−0.737176 + 0.675701i \(0.763841\pi\)
\(258\) 12.9443 0.805875
\(259\) 0 0
\(260\) 4.00000 0.248069
\(261\) 3.29180 + 5.70156i 0.203757 + 0.352918i
\(262\) 2.38197 4.12569i 0.147158 0.254886i
\(263\) 2.47214 4.28187i 0.152438 0.264031i −0.779685 0.626172i \(-0.784621\pi\)
0.932123 + 0.362141i \(0.117954\pi\)
\(264\) 0.618034 + 1.07047i 0.0380374 + 0.0658826i
\(265\) 10.4721 0.643298
\(266\) 0 0
\(267\) 12.3607 0.756461
\(268\) −5.70820 9.88690i −0.348684 0.603938i
\(269\) −11.3820 + 19.7141i −0.693971 + 1.20199i 0.276556 + 0.960998i \(0.410807\pi\)
−0.970526 + 0.240995i \(0.922526\pi\)
\(270\) −3.41641 + 5.91739i −0.207916 + 0.360121i
\(271\) 0.472136 + 0.817763i 0.0286802 + 0.0496756i 0.880009 0.474957i \(-0.157536\pi\)
−0.851329 + 0.524632i \(0.824203\pi\)
\(272\) −2.47214 −0.149895
\(273\) 0 0
\(274\) −19.8885 −1.20151
\(275\) 1.73607 + 3.00696i 0.104689 + 0.181326i
\(276\) 2.47214 4.28187i 0.148805 0.257738i
\(277\) −1.76393 + 3.05522i −0.105984 + 0.183570i −0.914140 0.405399i \(-0.867133\pi\)
0.808156 + 0.588969i \(0.200466\pi\)
\(278\) −10.8541 18.7999i −0.650986 1.12754i
\(279\) 2.94427 0.176269
\(280\) 0 0
\(281\) 28.8328 1.72002 0.860011 0.510276i \(-0.170457\pi\)
0.860011 + 0.510276i \(0.170457\pi\)
\(282\) 1.23607 + 2.14093i 0.0736068 + 0.127491i
\(283\) 7.32624 12.6894i 0.435500 0.754308i −0.561837 0.827248i \(-0.689905\pi\)
0.997336 + 0.0729407i \(0.0232384\pi\)
\(284\) −3.23607 + 5.60503i −0.192025 + 0.332598i
\(285\) 5.52786 + 9.57454i 0.327442 + 0.567147i
\(286\) 3.23607 0.191353
\(287\) 0 0
\(288\) −1.47214 −0.0867464
\(289\) 5.44427 + 9.42976i 0.320251 + 0.554692i
\(290\) −2.76393 + 4.78727i −0.162304 + 0.281118i
\(291\) −7.70820 + 13.3510i −0.451863 + 0.782650i
\(292\) 6.47214 + 11.2101i 0.378753 + 0.656020i
\(293\) 26.6525 1.55705 0.778527 0.627611i \(-0.215967\pi\)
0.778527 + 0.627611i \(0.215967\pi\)
\(294\) 0 0
\(295\) −3.41641 −0.198911
\(296\) −3.47214 6.01392i −0.201814 0.349552i
\(297\) −2.76393 + 4.78727i −0.160380 + 0.277786i
\(298\) 11.1803 19.3649i 0.647660 1.12178i
\(299\) −6.47214 11.2101i −0.374293 0.648295i
\(300\) 4.29180 0.247787
\(301\) 0 0
\(302\) 12.0000 0.690522
\(303\) −5.05573 8.75678i −0.290444 0.503064i
\(304\) −3.61803 + 6.26662i −0.207508 + 0.359415i
\(305\) −0.472136 + 0.817763i −0.0270344 + 0.0468250i
\(306\) −1.81966 3.15174i −0.104023 0.180173i
\(307\) 26.0689 1.48783 0.743915 0.668274i \(-0.232967\pi\)
0.743915 + 0.668274i \(0.232967\pi\)
\(308\) 0 0
\(309\) −18.4721 −1.05084
\(310\) 1.23607 + 2.14093i 0.0702039 + 0.121597i
\(311\) −10.7082 + 18.5472i −0.607207 + 1.05171i 0.384492 + 0.923128i \(0.374377\pi\)
−0.991699 + 0.128584i \(0.958957\pi\)
\(312\) 2.00000 3.46410i 0.113228 0.196116i
\(313\) 9.76393 + 16.9116i 0.551890 + 0.955902i 0.998138 + 0.0609924i \(0.0194265\pi\)
−0.446248 + 0.894909i \(0.647240\pi\)
\(314\) 12.6525 0.714021
\(315\) 0 0
\(316\) 0 0
\(317\) 15.4721 + 26.7985i 0.869002 + 1.50516i 0.863018 + 0.505173i \(0.168571\pi\)
0.00598366 + 0.999982i \(0.498095\pi\)
\(318\) 5.23607 9.06914i 0.293624 0.508572i
\(319\) −2.23607 + 3.87298i −0.125196 + 0.216845i
\(320\) −0.618034 1.07047i −0.0345492 0.0598409i
\(321\) −3.05573 −0.170554
\(322\) 0 0
\(323\) −17.8885 −0.995345
\(324\) 1.20820 + 2.09267i 0.0671224 + 0.116259i
\(325\) 5.61803 9.73072i 0.311632 0.539763i
\(326\) 9.70820 16.8151i 0.537688 0.931302i
\(327\) −6.18034 10.7047i −0.341774 0.591969i
\(328\) 2.47214 0.136501
\(329\) 0 0
\(330\) −1.52786 −0.0841061
\(331\) 8.47214 + 14.6742i 0.465671 + 0.806565i 0.999232 0.0391964i \(-0.0124798\pi\)
−0.533561 + 0.845762i \(0.679146\pi\)
\(332\) −6.09017 + 10.5485i −0.334241 + 0.578923i
\(333\) 5.11146 8.85330i 0.280106 0.485158i
\(334\) 5.70820 + 9.88690i 0.312339 + 0.540987i
\(335\) 14.1115 0.770991
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 1.26393 + 2.18919i 0.0687488 + 0.119076i
\(339\) −0.291796 + 0.505406i −0.0158482 + 0.0274499i
\(340\) 1.52786 2.64634i 0.0828601 0.143518i
\(341\) 1.00000 + 1.73205i 0.0541530 + 0.0937958i
\(342\) −10.6525 −0.576020
\(343\) 0 0
\(344\) −10.4721 −0.564620
\(345\) 3.05573 + 5.29268i 0.164515 + 0.284948i
\(346\) −1.61803 + 2.80252i −0.0869860 + 0.150664i
\(347\) −1.23607 + 2.14093i −0.0663556 + 0.114931i −0.897295 0.441432i \(-0.854471\pi\)
0.830939 + 0.556364i \(0.187804\pi\)
\(348\) 2.76393 + 4.78727i 0.148162 + 0.256625i
\(349\) −21.7082 −1.16201 −0.581007 0.813899i \(-0.697341\pi\)
−0.581007 + 0.813899i \(0.697341\pi\)
\(350\) 0 0
\(351\) 17.8885 0.954820
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −8.52786 + 14.7707i −0.453892 + 0.786165i −0.998624 0.0524459i \(-0.983298\pi\)
0.544731 + 0.838611i \(0.316632\pi\)
\(354\) −1.70820 + 2.95870i −0.0907900 + 0.157253i
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) −8.94427 −0.472719
\(359\) −13.4164 23.2379i −0.708091 1.22645i −0.965564 0.260164i \(-0.916223\pi\)
0.257473 0.966285i \(-0.417110\pi\)
\(360\) 0.909830 1.57587i 0.0479523 0.0830557i
\(361\) −16.6803 + 28.8912i −0.877913 + 1.52059i
\(362\) 4.61803 + 7.99867i 0.242718 + 0.420401i
\(363\) −1.23607 −0.0648767
\(364\) 0 0
\(365\) −16.0000 −0.837478
\(366\) 0.472136 + 0.817763i 0.0246789 + 0.0427452i
\(367\) −2.70820 + 4.69075i −0.141367 + 0.244855i −0.928012 0.372551i \(-0.878483\pi\)
0.786645 + 0.617406i \(0.211816\pi\)
\(368\) −2.00000 + 3.46410i −0.104257 + 0.180579i
\(369\) 1.81966 + 3.15174i 0.0947277 + 0.164073i
\(370\) 8.58359 0.446240
\(371\) 0 0
\(372\) 2.47214 0.128174
\(373\) 3.00000 + 5.19615i 0.155334 + 0.269047i 0.933181 0.359408i \(-0.117021\pi\)
−0.777847 + 0.628454i \(0.783688\pi\)
\(374\) 1.23607 2.14093i 0.0639156 0.110705i
\(375\) −6.47214 + 11.2101i −0.334220 + 0.578885i
\(376\) −1.00000 1.73205i −0.0515711 0.0893237i
\(377\) 14.4721 0.745353
\(378\) 0 0
\(379\) 14.4721 0.743384 0.371692 0.928356i \(-0.378778\pi\)
0.371692 + 0.928356i \(0.378778\pi\)
\(380\) −4.47214 7.74597i −0.229416 0.397360i
\(381\) −7.41641 + 12.8456i −0.379954 + 0.658100i
\(382\) 1.23607 2.14093i 0.0632427 0.109540i
\(383\) −11.9443 20.6881i −0.610324 1.05711i −0.991186 0.132480i \(-0.957706\pi\)
0.380862 0.924632i \(-0.375627\pi\)
\(384\) −1.23607 −0.0630778
\(385\) 0 0
\(386\) −14.9443 −0.760643
\(387\) −7.70820 13.3510i −0.391830 0.678670i
\(388\) 6.23607 10.8012i 0.316588 0.548347i
\(389\) −16.7082 + 28.9395i −0.847140 + 1.46729i 0.0366105 + 0.999330i \(0.488344\pi\)
−0.883750 + 0.467959i \(0.844989\pi\)
\(390\) 2.47214 + 4.28187i 0.125181 + 0.216821i
\(391\) −9.88854 −0.500085
\(392\) 0 0
\(393\) 5.88854 0.297038
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) 0 0
\(396\) 0.736068 1.27491i 0.0369888 0.0640665i
\(397\) −11.8541 20.5319i −0.594940 1.03047i −0.993555 0.113348i \(-0.963842\pi\)
0.398615 0.917118i \(-0.369491\pi\)
\(398\) −18.9443 −0.949591
\(399\) 0 0
\(400\) −3.47214 −0.173607
\(401\) −7.18034 12.4367i −0.358569 0.621060i 0.629153 0.777282i \(-0.283402\pi\)
−0.987722 + 0.156222i \(0.950069\pi\)
\(402\) 7.05573 12.2209i 0.351908 0.609522i
\(403\) 3.23607 5.60503i 0.161200 0.279207i
\(404\) 4.09017 + 7.08438i 0.203494 + 0.352461i
\(405\) −2.98684 −0.148417
\(406\) 0 0
\(407\) 6.94427 0.344215
\(408\) −1.52786 2.64634i −0.0756405 0.131013i
\(409\) 1.70820 2.95870i 0.0844652 0.146298i −0.820698 0.571362i \(-0.806415\pi\)
0.905163 + 0.425064i \(0.139748\pi\)
\(410\) −1.52786 + 2.64634i −0.0754558 + 0.130693i
\(411\) −12.2918 21.2900i −0.606310 1.05016i
\(412\) 14.9443 0.736251
\(413\) 0 0
\(414\) −5.88854 −0.289406
\(415\) −7.52786 13.0386i −0.369528 0.640042i
\(416\) −1.61803 + 2.80252i −0.0793306 + 0.137405i
\(417\) 13.4164 23.2379i 0.657004 1.13796i
\(418\) −3.61803 6.26662i −0.176964 0.306510i
\(419\) −17.2361 −0.842037 −0.421019 0.907052i \(-0.638327\pi\)
−0.421019 + 0.907052i \(0.638327\pi\)
\(420\) 0 0
\(421\) 16.4721 0.802803 0.401401 0.915902i \(-0.368523\pi\)
0.401401 + 0.915902i \(0.368523\pi\)
\(422\) 6.76393 + 11.7155i 0.329263 + 0.570300i
\(423\) 1.47214 2.54981i 0.0715777 0.123976i
\(424\) −4.23607 + 7.33708i −0.205722 + 0.356320i
\(425\) −4.29180 7.43361i −0.208183 0.360583i
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) 2.47214 0.119495
\(429\) 2.00000 + 3.46410i 0.0965609 + 0.167248i
\(430\) 6.47214 11.2101i 0.312114 0.540597i
\(431\) −11.5279 + 19.9668i −0.555278 + 0.961769i 0.442604 + 0.896717i \(0.354055\pi\)
−0.997882 + 0.0650521i \(0.979279\pi\)
\(432\) −2.76393 4.78727i −0.132980 0.230328i
\(433\) −28.4721 −1.36828 −0.684142 0.729349i \(-0.739823\pi\)
−0.684142 + 0.729349i \(0.739823\pi\)
\(434\) 0 0
\(435\) −6.83282 −0.327608
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) −14.4721 + 25.0665i −0.692296 + 1.19909i
\(438\) −8.00000 + 13.8564i −0.382255 + 0.662085i
\(439\) 4.47214 + 7.74597i 0.213443 + 0.369695i 0.952790 0.303630i \(-0.0981988\pi\)
−0.739347 + 0.673325i \(0.764865\pi\)
\(440\) 1.23607 0.0589272
\(441\) 0 0
\(442\) −8.00000 −0.380521
\(443\) 12.4721 + 21.6024i 0.592569 + 1.02636i 0.993885 + 0.110420i \(0.0352196\pi\)
−0.401316 + 0.915940i \(0.631447\pi\)
\(444\) 4.29180 7.43361i 0.203680 0.352783i
\(445\) 6.18034 10.7047i 0.292976 0.507450i
\(446\) −0.236068 0.408882i −0.0111781 0.0193611i
\(447\) 27.6393 1.30729
\(448\) 0 0
\(449\) 18.9443 0.894035 0.447018 0.894525i \(-0.352486\pi\)
0.447018 + 0.894525i \(0.352486\pi\)
\(450\) −2.55573 4.42665i −0.120478 0.208674i
\(451\) −1.23607 + 2.14093i −0.0582042 + 0.100813i
\(452\) 0.236068 0.408882i 0.0111037 0.0192322i
\(453\) 7.41641 + 12.8456i 0.348453 + 0.603539i
\(454\) 19.2361 0.902793
\(455\) 0 0
\(456\) −8.94427 −0.418854
\(457\) −13.4721 23.3344i −0.630200 1.09154i −0.987511 0.157553i \(-0.949640\pi\)
0.357311 0.933986i \(-0.383694\pi\)
\(458\) 8.61803 14.9269i 0.402694 0.697487i
\(459\) 6.83282 11.8348i 0.318929 0.552400i
\(460\) −2.47214 4.28187i −0.115264 0.199643i
\(461\) −24.7639 −1.15337 −0.576686 0.816966i \(-0.695654\pi\)
−0.576686 + 0.816966i \(0.695654\pi\)
\(462\) 0 0
\(463\) −30.4721 −1.41616 −0.708080 0.706132i \(-0.750438\pi\)
−0.708080 + 0.706132i \(0.750438\pi\)
\(464\) −2.23607 3.87298i −0.103807 0.179799i
\(465\) −1.52786 + 2.64634i −0.0708530 + 0.122721i
\(466\) 7.47214 12.9421i 0.346140 0.599532i
\(467\) −13.5623 23.4906i −0.627589 1.08702i −0.988034 0.154235i \(-0.950709\pi\)
0.360445 0.932780i \(-0.382625\pi\)
\(468\) −4.76393 −0.220213
\(469\) 0 0
\(470\) 2.47214 0.114031
\(471\) 7.81966 + 13.5440i 0.360311 + 0.624077i
\(472\) 1.38197 2.39364i 0.0636101 0.110176i
\(473\) 5.23607 9.06914i 0.240755 0.416999i
\(474\) 0 0
\(475\) −25.1246 −1.15280
\(476\) 0 0
\(477\) −12.4721 −0.571060
\(478\) −10.0000 17.3205i −0.457389 0.792222i
\(479\) 6.18034 10.7047i 0.282387 0.489109i −0.689585 0.724205i \(-0.742207\pi\)
0.971972 + 0.235096i \(0.0755405\pi\)
\(480\) 0.763932 1.32317i 0.0348686 0.0603941i
\(481\) −11.2361 19.4614i −0.512321 0.887365i
\(482\) −15.4164 −0.702198
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 7.70820 + 13.3510i 0.350012 + 0.606238i
\(486\) 6.79837 11.7751i 0.308381 0.534131i
\(487\) −8.47214 + 14.6742i −0.383909 + 0.664950i −0.991617 0.129210i \(-0.958756\pi\)
0.607708 + 0.794160i \(0.292089\pi\)
\(488\) −0.381966 0.661585i −0.0172908 0.0299485i
\(489\) 24.0000 1.08532
\(490\) 0 0
\(491\) −16.9443 −0.764684 −0.382342 0.924021i \(-0.624882\pi\)
−0.382342 + 0.924021i \(0.624882\pi\)
\(492\) 1.52786 + 2.64634i 0.0688814 + 0.119306i
\(493\) 5.52786 9.57454i 0.248962 0.431216i
\(494\) −11.7082 + 20.2792i −0.526777 + 0.912405i
\(495\) 0.909830 + 1.57587i 0.0408938 + 0.0708302i
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) −15.0557 −0.674663
\(499\) 16.1803 + 28.0252i 0.724331 + 1.25458i 0.959249 + 0.282564i \(0.0911848\pi\)
−0.234917 + 0.972015i \(0.575482\pi\)
\(500\) 5.23607 9.06914i 0.234164 0.405584i
\(501\) −7.05573 + 12.2209i −0.315227 + 0.545989i
\(502\) 14.6180 + 25.3192i 0.652435 + 1.13005i
\(503\) −4.00000 −0.178351 −0.0891756 0.996016i \(-0.528423\pi\)
−0.0891756 + 0.996016i \(0.528423\pi\)
\(504\) 0 0
\(505\) −10.1115 −0.449954
\(506\) −2.00000 3.46410i −0.0889108 0.153998i
\(507\) −1.56231 + 2.70599i −0.0693844 + 0.120177i
\(508\) 6.00000 10.3923i 0.266207 0.461084i
\(509\) 12.0344 + 20.8443i 0.533417 + 0.923906i 0.999238 + 0.0390268i \(0.0124258\pi\)
−0.465821 + 0.884879i \(0.654241\pi\)
\(510\) 3.77709 0.167252
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −20.0000 34.6410i −0.883022 1.52944i
\(514\) 3.47214 6.01392i 0.153149 0.265262i
\(515\) −9.23607 + 15.9973i −0.406990 + 0.704927i
\(516\) −6.47214 11.2101i −0.284920 0.493496i
\(517\) 2.00000 0.0879599
\(518\) 0 0
\(519\) −4.00000 −0.175581
\(520\) −2.00000 3.46410i −0.0877058 0.151911i
\(521\) −5.18034 + 8.97261i −0.226955 + 0.393097i −0.956904 0.290404i \(-0.906210\pi\)
0.729949 + 0.683501i \(0.239544\pi\)
\(522\) 3.29180 5.70156i 0.144078 0.249550i
\(523\) −7.14590 12.3771i −0.312468 0.541211i 0.666428 0.745570i \(-0.267822\pi\)
−0.978896 + 0.204359i \(0.934489\pi\)
\(524\) −4.76393 −0.208113
\(525\) 0 0
\(526\) −4.94427 −0.215580
\(527\) −2.47214 4.28187i −0.107688 0.186521i
\(528\) 0.618034 1.07047i 0.0268965 0.0465861i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −5.23607 9.06914i −0.227440 0.393938i
\(531\) 4.06888 0.176575
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) −6.18034 10.7047i −0.267449 0.463236i
\(535\) −1.52786 + 2.64634i −0.0660553 + 0.114411i
\(536\) −5.70820 + 9.88690i −0.246557 + 0.427049i
\(537\) −5.52786 9.57454i −0.238545 0.413172i
\(538\) 22.7639 0.981423
\(539\) 0 0
\(540\) 6.83282 0.294038
\(541\) 13.4721 + 23.3344i 0.579212 + 1.00323i 0.995570 + 0.0940243i \(0.0299731\pi\)
−0.416358 + 0.909201i \(0.636694\pi\)
\(542\) 0.472136 0.817763i 0.0202800 0.0351259i
\(543\) −5.70820 + 9.88690i −0.244962 + 0.424287i
\(544\) 1.23607 + 2.14093i 0.0529960 + 0.0917917i
\(545\) −12.3607 −0.529473
\(546\) 0 0
\(547\) −0.944272 −0.0403742 −0.0201871 0.999796i \(-0.506426\pi\)
−0.0201871 + 0.999796i \(0.506426\pi\)
\(548\) 9.94427 + 17.2240i 0.424798 + 0.735772i
\(549\) 0.562306 0.973942i 0.0239986 0.0415668i
\(550\) 1.73607 3.00696i 0.0740262 0.128217i
\(551\) −16.1803 28.0252i −0.689306 1.19391i
\(552\) −4.94427 −0.210442
\(553\) 0 0
\(554\) 3.52786 0.149885
\(555\) 5.30495 + 9.18845i 0.225183 + 0.390028i
\(556\) −10.8541 + 18.7999i −0.460316 + 0.797291i
\(557\) −12.4164 + 21.5058i −0.526100 + 0.911232i 0.473438 + 0.880827i \(0.343013\pi\)
−0.999538 + 0.0304047i \(0.990320\pi\)
\(558\) −1.47214 2.54981i −0.0623205 0.107942i
\(559\) −33.8885 −1.43333
\(560\) 0 0
\(561\) 3.05573 0.129013
\(562\) −14.4164 24.9700i −0.608119 1.05329i
\(563\) 15.6180 27.0512i 0.658222 1.14007i −0.322854 0.946449i \(-0.604642\pi\)
0.981076 0.193625i \(-0.0620244\pi\)
\(564\) 1.23607 2.14093i 0.0520479 0.0901495i
\(565\) 0.291796 + 0.505406i 0.0122760 + 0.0212626i
\(566\) −14.6525 −0.615889
\(567\) 0 0
\(568\) 6.47214 0.271565
\(569\) 18.4164 + 31.8982i 0.772056 + 1.33724i 0.936434 + 0.350843i \(0.114105\pi\)
−0.164378 + 0.986397i \(0.552562\pi\)
\(570\) 5.52786 9.57454i 0.231537 0.401033i
\(571\) 5.05573 8.75678i 0.211576 0.366460i −0.740632 0.671911i \(-0.765474\pi\)
0.952208 + 0.305451i \(0.0988072\pi\)
\(572\) −1.61803 2.80252i −0.0676534 0.117179i
\(573\) 3.05573 0.127655
\(574\) 0 0
\(575\) −13.8885 −0.579192
\(576\) 0.736068 + 1.27491i 0.0306695 + 0.0531211i
\(577\) 13.4721 23.3344i 0.560852 0.971425i −0.436570 0.899670i \(-0.643807\pi\)
0.997422 0.0717545i \(-0.0228598\pi\)
\(578\) 5.44427 9.42976i 0.226452 0.392226i
\(579\) −9.23607 15.9973i −0.383838 0.664827i
\(580\) 5.52786 0.229532
\(581\) 0 0
\(582\) 15.4164 0.639031
\(583\) −4.23607 7.33708i −0.175440 0.303871i
\(584\) 6.47214 11.2101i 0.267819 0.463876i
\(585\) 2.94427 5.09963i 0.121731 0.210844i
\(586\) −13.3262 23.0817i −0.550502 0.953497i
\(587\) 5.81966 0.240203 0.120102 0.992762i \(-0.461678\pi\)
0.120102 + 0.992762i \(0.461678\pi\)
\(588\) 0 0
\(589\) −14.4721 −0.596314
\(590\) 1.70820 + 2.95870i 0.0703256 + 0.121808i
\(591\) 11.1246 19.2684i 0.457605 0.792596i
\(592\) −3.47214 + 6.01392i −0.142704 + 0.247170i
\(593\) 12.0000 + 20.7846i 0.492781 + 0.853522i 0.999965 0.00831589i \(-0.00264706\pi\)
−0.507184 + 0.861838i \(0.669314\pi\)
\(594\) 5.52786 0.226811
\(595\) 0 0
\(596\) −22.3607 −0.915929
\(597\) −11.7082 20.2792i −0.479185 0.829973i
\(598\) −6.47214 + 11.2101i −0.264665 + 0.458414i
\(599\) 16.1803 28.0252i 0.661111 1.14508i −0.319213 0.947683i \(-0.603419\pi\)
0.980324 0.197395i \(-0.0632480\pi\)
\(600\) −2.14590 3.71680i −0.0876059 0.151738i
\(601\) 34.8328 1.42086 0.710430 0.703768i \(-0.248500\pi\)
0.710430 + 0.703768i \(0.248500\pi\)
\(602\) 0 0
\(603\) −16.8065 −0.684414
\(604\) −6.00000 10.3923i −0.244137 0.422857i
\(605\) −0.618034 + 1.07047i −0.0251267 + 0.0435206i
\(606\) −5.05573 + 8.75678i −0.205375 + 0.355720i
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 7.23607 0.293461
\(609\) 0 0
\(610\) 0.944272 0.0382325
\(611\) −3.23607 5.60503i −0.130917 0.226755i
\(612\) −1.81966 + 3.15174i −0.0735554 + 0.127402i
\(613\) −14.2361 + 24.6576i −0.574989 + 0.995911i 0.421053 + 0.907036i \(0.361660\pi\)
−0.996043 + 0.0888750i \(0.971673\pi\)
\(614\) −13.0344 22.5763i −0.526027 0.911106i
\(615\) −3.77709 −0.152307
\(616\) 0 0
\(617\) 21.4164 0.862192 0.431096 0.902306i \(-0.358127\pi\)
0.431096 + 0.902306i \(0.358127\pi\)
\(618\) 9.23607 + 15.9973i 0.371529 + 0.643507i
\(619\) 9.27051 16.0570i 0.372613 0.645385i −0.617353 0.786686i \(-0.711795\pi\)
0.989967 + 0.141301i \(0.0451285\pi\)
\(620\) 1.23607 2.14093i 0.0496417 0.0859819i
\(621\) −11.0557 19.1491i −0.443651 0.768426i
\(622\) 21.4164 0.858720
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) −2.20820 3.82472i −0.0883282 0.152989i
\(626\) 9.76393 16.9116i 0.390245 0.675925i
\(627\) 4.47214 7.74597i 0.178600 0.309344i
\(628\) −6.32624 10.9574i −0.252444 0.437246i
\(629\) −17.1672 −0.684500
\(630\) 0 0
\(631\) −31.4164 −1.25067 −0.625334 0.780357i \(-0.715037\pi\)
−0.625334 + 0.780357i \(0.715037\pi\)
\(632\) 0 0
\(633\) −8.36068 + 14.4811i −0.332307 + 0.575573i
\(634\) 15.4721 26.7985i 0.614477 1.06431i
\(635\) 7.41641 + 12.8456i 0.294311 + 0.509762i
\(636\) −10.4721 −0.415247
\(637\) 0 0
\(638\) 4.47214 0.177054
\(639\) 4.76393 + 8.25137i 0.188458 + 0.326419i
\(640\) −0.618034 + 1.07047i −0.0244299 + 0.0423139i
\(641\) −13.7639 + 23.8398i −0.543643 + 0.941617i 0.455048 + 0.890467i \(0.349622\pi\)
−0.998691 + 0.0511499i \(0.983711\pi\)
\(642\) 1.52786 + 2.64634i 0.0603000 + 0.104443i
\(643\) 18.7639 0.739977 0.369989 0.929036i \(-0.379362\pi\)
0.369989 + 0.929036i \(0.379362\pi\)
\(644\) 0 0
\(645\) 16.0000 0.629999
\(646\) 8.94427 + 15.4919i 0.351908 + 0.609522i
\(647\) −14.4164 + 24.9700i −0.566767 + 0.981670i 0.430115 + 0.902774i \(0.358473\pi\)
−0.996883 + 0.0788961i \(0.974860\pi\)
\(648\) 1.20820 2.09267i 0.0474627 0.0822079i
\(649\) 1.38197 + 2.39364i 0.0542469 + 0.0939584i
\(650\) −11.2361 −0.440715
\(651\) 0 0
\(652\) −19.4164 −0.760405
\(653\) −23.1803 40.1495i −0.907117 1.57117i −0.818050 0.575147i \(-0.804945\pi\)
−0.0890665 0.996026i \(-0.528388\pi\)
\(654\) −6.18034 + 10.7047i −0.241670 + 0.418585i
\(655\) 2.94427 5.09963i 0.115042 0.199259i
\(656\) −1.23607 2.14093i −0.0482603 0.0835894i
\(657\) 19.0557 0.743435
\(658\) 0 0
\(659\) 16.5836 0.646005 0.323003 0.946398i \(-0.395308\pi\)
0.323003 + 0.946398i \(0.395308\pi\)
\(660\) 0.763932 + 1.32317i 0.0297360 + 0.0515043i
\(661\) −1.56231 + 2.70599i −0.0607667 + 0.105251i −0.894808 0.446451i \(-0.852688\pi\)
0.834042 + 0.551701i \(0.186021\pi\)
\(662\) 8.47214 14.6742i 0.329279 0.570328i
\(663\) −4.94427 8.56373i −0.192020 0.332588i
\(664\) 12.1803 0.472689
\(665\) 0 0
\(666\) −10.2229 −0.396130
\(667\) −8.94427 15.4919i −0.346324 0.599850i
\(668\) 5.70820 9.88690i 0.220857 0.382536i
\(669\) 0.291796 0.505406i 0.0112815 0.0195401i
\(670\) −7.05573 12.2209i −0.272587 0.472134i
\(671\) 0.763932 0.0294913
\(672\) 0 0
\(673\) −3.88854 −0.149892 −0.0749462 0.997188i \(-0.523878\pi\)
−0.0749462 + 0.997188i \(0.523878\pi\)
\(674\) −9.00000 15.5885i −0.346667 0.600445i
\(675\) 9.59675 16.6221i 0.369379 0.639783i
\(676\) 1.26393 2.18919i 0.0486128 0.0841998i
\(677\) −13.0344 22.5763i −0.500954 0.867678i −0.999999 0.00110228i \(-0.999649\pi\)
0.499045 0.866576i \(-0.333684\pi\)
\(678\) 0.583592 0.0224127
\(679\) 0 0
\(680\) −3.05573 −0.117182
\(681\) 11.8885 + 20.5916i 0.455570 + 0.789070i
\(682\) 1.00000 1.73205i 0.0382920 0.0663237i
\(683\) −16.4721 + 28.5306i −0.630289 + 1.09169i 0.357204 + 0.934026i \(0.383730\pi\)
−0.987493 + 0.157666i \(0.949603\pi\)
\(684\) 5.32624 + 9.22531i 0.203654 + 0.352739i
\(685\) −24.5836 −0.939291
\(686\) 0 0
\(687\) 21.3050 0.812835
\(688\) 5.23607 + 9.06914i 0.199623 + 0.345758i
\(689\) −13.7082 + 23.7433i −0.522241 + 0.904548i
\(690\) 3.05573 5.29268i 0.116330 0.201489i
\(691\) 6.32624 + 10.9574i 0.240661 + 0.416838i 0.960903 0.276886i \(-0.0893023\pi\)
−0.720241 + 0.693723i \(0.755969\pi\)
\(692\) 3.23607 0.123017
\(693\) 0 0
\(694\) 2.47214 0.0938410
\(695\) −13.4164 23.2379i −0.508913 0.881464i
\(696\) 2.76393 4.78727i 0.104767 0.181461i
\(697\) 3.05573 5.29268i 0.115744 0.200474i
\(698\) 10.8541 + 18.7999i 0.410834 + 0.711585i
\(699\) 18.4721 0.698680
\(700\) 0 0
\(701\) −42.7214 −1.61356 −0.806782 0.590850i \(-0.798793\pi\)
−0.806782 + 0.590850i \(0.798793\pi\)
\(702\) −8.94427 15.4919i −0.337580 0.584705i
\(703\) −25.1246 + 43.5171i −0.947593 + 1.64128i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 1.52786 + 2.64634i 0.0575427 + 0.0996669i
\(706\) 17.0557 0.641901
\(707\) 0 0
\(708\) 3.41641 0.128396
\(709\) −2.23607 3.87298i −0.0839773 0.145453i 0.820978 0.570960i \(-0.193429\pi\)
−0.904955 + 0.425507i \(0.860096\pi\)
\(710\) −4.00000 + 6.92820i −0.150117 + 0.260011i
\(711\) 0 0
\(712\) 5.00000 + 8.66025i 0.187383 + 0.324557i
\(713\) −8.00000 −0.299602
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) 4.47214 + 7.74597i 0.167132 + 0.289480i
\(717\) 12.3607 21.4093i 0.461618 0.799546i
\(718\) −13.4164 + 23.2379i −0.500696 + 0.867231i
\(719\) 8.41641 + 14.5776i 0.313879 + 0.543654i 0.979199 0.202904i \(-0.0650380\pi\)
−0.665320 + 0.746559i \(0.731705\pi\)
\(720\) −1.81966 −0.0678147
\(721\) 0 0
\(722\) 33.3607 1.24156
\(723\) −9.52786 16.5027i −0.354345 0.613744i
\(724\) 4.61803 7.99867i 0.171628 0.297268i
\(725\) 7.76393 13.4475i 0.288345 0.499429i
\(726\) 0.618034 + 1.07047i 0.0229374 + 0.0397287i
\(727\) −18.0000 −0.667583 −0.333792 0.942647i \(-0.608328\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(728\) 0 0
\(729\) 24.0557 0.890953
\(730\) 8.00000 + 13.8564i 0.296093 + 0.512849i
\(731\) −12.9443 + 22.4201i −0.478761 + 0.829239i
\(732\) 0.472136 0.817763i 0.0174506 0.0302254i
\(733\) 24.5623 + 42.5432i 0.907229 + 1.57137i 0.817896 + 0.575366i \(0.195140\pi\)
0.0893332 + 0.996002i \(0.471526\pi\)
\(734\) 5.41641 0.199923
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) −5.70820 9.88690i −0.210264 0.364189i
\(738\) 1.81966 3.15174i 0.0669826 0.116017i
\(739\) −10.0000 + 17.3205i −0.367856 + 0.637145i −0.989230 0.146369i \(-0.953241\pi\)
0.621374 + 0.783514i \(0.286575\pi\)
\(740\) −4.29180 7.43361i −0.157770 0.273265i
\(741\) −28.9443 −1.06329
\(742\) 0 0
\(743\) 21.8885 0.803013 0.401506 0.915856i \(-0.368487\pi\)
0.401506 + 0.915856i \(0.368487\pi\)
\(744\) −1.23607 2.14093i −0.0453165 0.0784904i
\(745\) 13.8197 23.9364i 0.506313 0.876960i
\(746\) 3.00000 5.19615i 0.109838 0.190245i
\(747\) 8.96556 + 15.5288i 0.328033 + 0.568169i
\(748\) −2.47214 −0.0903902
\(749\) 0 0
\(750\) 12.9443 0.472658
\(751\) 8.47214 + 14.6742i 0.309153 + 0.535468i 0.978177 0.207772i \(-0.0666213\pi\)
−0.669025 + 0.743240i \(0.733288\pi\)
\(752\) −1.00000 + 1.73205i −0.0364662 + 0.0631614i
\(753\) −18.0689 + 31.2962i −0.658467 + 1.14050i
\(754\) −7.23607 12.5332i −0.263522 0.456434i
\(755\) 14.8328 0.539821
\(756\) 0 0
\(757\) −23.3050 −0.847033 −0.423516 0.905888i \(-0.639204\pi\)
−0.423516 + 0.905888i \(0.639204\pi\)
\(758\) −7.23607 12.5332i −0.262826 0.455228i
\(759\) 2.47214 4.28187i 0.0897329 0.155422i
\(760\) −4.47214 + 7.74597i −0.162221 + 0.280976i
\(761\) −5.70820 9.88690i −0.206922 0.358400i 0.743821 0.668379i \(-0.233011\pi\)
−0.950743 + 0.309979i \(0.899678\pi\)
\(762\) 14.8328 0.537336
\(763\) 0 0
\(764\) −2.47214 −0.0894387
\(765\) −2.24922 3.89577i −0.0813209 0.140852i
\(766\) −11.9443 + 20.6881i −0.431564 + 0.747491i
\(767\) 4.47214 7.74597i 0.161479 0.279691i
\(768\) 0.618034 + 1.07047i 0.0223014 + 0.0386271i
\(769\) 43.4164 1.56564 0.782818 0.622251i \(-0.213782\pi\)
0.782818 + 0.622251i \(0.213782\pi\)
\(770\) 0 0
\(771\) 8.58359 0.309131
\(772\) 7.47214 + 12.9421i 0.268928 + 0.465797i
\(773\) 7.85410 13.6037i 0.282492 0.489291i −0.689506 0.724280i \(-0.742172\pi\)
0.971998 + 0.234989i \(0.0755055\pi\)
\(774\) −7.70820 + 13.3510i −0.277066 + 0.479892i
\(775\) −3.47214 6.01392i −0.124723 0.216026i
\(776\) −12.4721 −0.447724
\(777\) 0 0
\(778\) 33.4164 1.19804
\(779\) −8.94427 15.4919i −0.320462 0.555056i
\(780\) 2.47214 4.28187i 0.0885167 0.153315i
\(781\) −3.23607 + 5.60503i