Properties

Label 1078.2.e.q.67.1
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 67.1
Root \(-0.309017 + 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.q.177.1

$q$-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 −0.987428 0.158069i \(-0.949473\pi\)
0.630606 + 0.776103i \(0.282806\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.618034 + 1.07047i 0.276393 + 0.478727i 0.970486 0.241159i \(-0.0775275\pi\)
−0.694092 + 0.719886i \(0.744194\pi\)
\(6\) 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 \(-0.648135\pi\)
−0.448762 + 0.893651i \(0.648135\pi\)
\(14\) 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 −0.976088 0.217376i \(-0.930250\pi\)
0.676297 + 0.736629i \(0.263583\pi\)
\(18\) 0.736068 1.27491i 0.173493 0.300498i
\(19\) 3.61803 + 6.26662i 0.830034 + 1.43766i 0.898011 + 0.439974i \(0.145012\pi\)
−0.0679766 + 0.997687i \(0.521654\pi\)
\(20\) −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 −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) −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 \(-0.561835\pi\)
−0.193041 + 0.981191i \(0.561835\pi\)
\(42\) 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 0.929695 0.368329i \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 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 −0.941852 0.336029i \(-0.890916\pi\)
0.761935 + 0.647653i \(0.224249\pi\)
\(60\) 0.763932 1.32317i 0.0986232 0.170820i
\(61\) 0.381966 + 0.661585i 0.0489057 + 0.0847072i 0.889442 0.457048i \(-0.151093\pi\)
−0.840536 + 0.541755i \(0.817760\pi\)
\(62\) 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 \(0.440249\pi\)
−0.944119 + 0.329606i \(0.893084\pi\)
\(74\) −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 \(-0.733056\pi\)
−0.668483 + 0.743727i \(0.733056\pi\)
\(84\) 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 \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 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 \(-0.281751\pi\)
0.633177 + 0.774007i \(0.281751\pi\)
\(98\) 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 −0.994551 0.104256i \(-0.966754\pi\)
0.587563 + 0.809178i \(0.300087\pi\)
\(102\) −1.52786 + 2.64634i −0.151281 + 0.262027i
\(103\) 7.47214 + 12.9421i 0.736251 + 1.27522i 0.954172 + 0.299258i \(0.0967393\pi\)
−0.217921 + 0.975966i \(0.569927\pi\)
\(104\) −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 0.743007 0.669284i \(-0.233399\pi\)
−0.951120 + 0.308821i \(0.900066\pi\)
\(132\) 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 \(-0.872327\pi\)
−0.920633 + 0.390429i \(0.872327\pi\)
\(140\) 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 \(-0.664867\pi\)
0.999984 0.00565427i \(-0.00179982\pi\)
\(158\) 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 \(-0.354371\pi\)
0.441714 + 0.897156i \(0.354371\pi\)
\(168\) 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 0.920956 0.389667i \(-0.127410\pi\)
−0.797939 + 0.602738i \(0.794076\pi\)
\(174\) 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 \(-0.388470\pi\)
0.343256 + 0.939242i \(0.388470\pi\)
\(182\) 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 \(0.401000\pi\)
−0.977490 + 0.210984i \(0.932333\pi\)
\(200\) 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 \(-0.505032\pi\)
−0.0158083 + 0.999875i \(0.505032\pi\)
\(224\) 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 \(-0.612942\pi\)
0.985790 0.167982i \(-0.0537249\pi\)
\(228\) 4.47214 7.74597i 0.296174 0.512989i
\(229\) −8.61803 14.9269i −0.569496 0.986396i −0.996616 0.0822006i \(-0.973805\pi\)
0.427120 0.904195i \(-0.359528\pi\)
\(230\) −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 −0.999992 0.00400327i \(-0.998726\pi\)
0.503463 + 0.864017i \(0.332059\pi\)
\(242\) −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 \(-0.125992\pi\)
0.922682 + 0.385562i \(0.125992\pi\)
\(252\) 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 0.737176 0.675701i \(-0.236159\pi\)
−0.953762 + 0.300563i \(0.902825\pi\)
\(258\) −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 \(-0.589193\pi\)
0.970526 0.240995i \(-0.0774736\pi\)
\(270\) −3.41641 + 5.91739i −0.207916 + 0.360121i
\(271\) −0.472136 0.817763i −0.0286802 0.0496756i 0.851329 0.524632i \(-0.175797\pi\)
−0.880009 + 0.474957i \(0.842464\pi\)
\(272\) 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 −0.997336 0.0729407i \(-0.976762\pi\)
0.561837 + 0.827248i \(0.310095\pi\)
\(284\) −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 \(-0.784033\pi\)
−0.778527 + 0.627611i \(0.784033\pi\)
\(294\) 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 \(-0.767033\pi\)
−0.743915 + 0.668274i \(0.767033\pi\)
\(308\) 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 \(-0.625623\pi\)
0.991699 0.128584i \(-0.0410433\pi\)
\(312\) 2.00000 3.46410i 0.113228 0.196116i
\(313\) −9.76393 16.9116i −0.551890 0.955902i −0.998138 0.0609924i \(-0.980573\pi\)
0.446248 0.894909i \(-0.352760\pi\)
\(314\) −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 \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(350\) 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 −0.544731 0.838611i \(-0.683368\pi\)
0.998624 + 0.0524459i \(0.0167017\pi\)
\(354\) −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 −0.786645 0.617406i \(-0.788184\pi\)
0.928012 + 0.372551i \(0.121517\pi\)
\(368\) −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 \(0.0422940\pi\)
−0.380862 + 0.924632i \(0.624373\pi\)
\(384\) 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 \(0.0361577\pi\)
−0.398615 + 0.917118i \(0.630509\pi\)
\(398\) 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 −0.905163 0.425064i \(-0.860252\pi\)
0.820698 + 0.571362i \(0.193585\pi\)
\(410\) −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 \(-0.361673\pi\)
0.421019 + 0.907052i \(0.361673\pi\)
\(420\) 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 \(-0.260177\pi\)
0.684142 + 0.729349i \(0.260177\pi\)
\(434\) 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 0.739347 0.673325i \(-0.235135\pi\)
−0.952790 + 0.303630i \(0.901801\pi\)
\(440\) −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 \(-0.304346\pi\)
0.576686 + 0.816966i \(0.304346\pi\)
\(462\) 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 \(0.0492913\pi\)
−0.360445 + 0.932780i \(0.617375\pi\)
\(468\) 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 −0.971972 0.235096i \(-0.924460\pi\)
0.689585 + 0.724205i \(0.257793\pi\)
\(480\) 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 \(-0.471577\pi\)
0.0891756 + 0.996016i \(0.471577\pi\)
\(504\) 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 \(-0.987574\pi\)
0.465821 0.884879i \(-0.345759\pi\)
\(510\) −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 −0.729949 0.683501i \(-0.760456\pi\)
0.956904 + 0.290404i \(0.0937897\pi\)
\(522\) 3.29180 5.70156i 0.144078 0.249550i
\(523\) 7.14590 + 12.3771i 0.312468 + 0.541211i 0.978896 0.204359i \(-0.0655109\pi\)
−0.666428 + 0.745570i \(0.732178\pi\)
\(524\) 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 \(0.395358\pi\)
−0.981076 + 0.193625i \(0.937976\pi\)
\(564\) 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 \(0.356193\pi\)
−0.997422 + 0.0717545i \(0.977140\pi\)
\(578\) 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 \(-0.538322\pi\)
−0.120102 + 0.992762i \(0.538322\pi\)
\(588\) 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 0.507184 0.861838i \(-0.330686\pi\)
−0.999965 + 0.00831589i \(0.997353\pi\)
\(594\) −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 \(-0.751500\pi\)
−0.710430 + 0.703768i \(0.751500\pi\)
\(602\) 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 \(0.0583216\pi\)
−0.333842 + 0.942629i \(0.608345\pi\)
\(608\) −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 −0.989967 0.141301i \(-0.954872\pi\)
0.617353 + 0.786686i \(0.288205\pi\)
\(620\) 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 \(-0.620638\pi\)
−0.369989 + 0.929036i \(0.620638\pi\)
\(644\) 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 \(-0.641527\pi\)
0.996883 0.0788961i \(-0.0251395\pi\)
\(648\) 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 −0.834042 0.551701i \(-0.813979\pi\)
0.894808 + 0.446451i \(0.147312\pi\)
\(662\) 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 \(0.000350865\pi\)
−0.499045 + 0.866576i \(0.666316\pi\)
\(678\) −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 0.720241 0.693723i \(-0.244031\pi\)
−0.960903 + 0.276886i \(0.910698\pi\)
\(692\) −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 0.665320 0.746559i \(-0.268295\pi\)
−0.979199 + 0.202904i \(0.934962\pi\)
\(720\) 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 \(-0.391672\pi\)
0.333792 + 0.942647i \(0.391672\pi\)
\(728\) 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 \(-0.804860\pi\)
−0.0893332 0.996002i \(-0.528474\pi\)
\(734\) −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 0.950743 0.309979i \(-0.100322\pi\)
−0.743821 + 0.668379i \(0.766989\pi\)
\(762\) −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 \(-0.786218\pi\)
−0.782818 + 0.622251i \(0.786218\pi\)
\(770\) 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 −0.971998 0.234989i \(-0.924495\pi\)
0.689506 + 0.724280i \(0.257828\pi\)
\(774\) −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 −0.115796 + 0.200564i </