Properties

Label 370.2.n.b.359.1
Level $370$
Weight $2$
Character 370.359
Analytic conductor $2.954$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 359.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 370.359
Dual form 370.2.n.b.269.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.86603 - 1.23205i) q^{5} +(-3.46410 - 2.00000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.86603 - 1.23205i) q^{5} +(-3.46410 - 2.00000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.00000 + 2.00000i) q^{10} -3.00000 q^{11} +(-0.866025 - 0.500000i) q^{13} +4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(-1.50000 + 2.59808i) q^{19} +(-0.133975 - 2.23205i) q^{20} +(2.59808 - 1.50000i) q^{22} -1.00000i q^{23} +(1.96410 - 4.59808i) q^{25} +1.00000 q^{26} +(-3.46410 + 2.00000i) q^{28} +6.00000 q^{29} -4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(3.00000 - 5.19615i) q^{34} +(-8.92820 + 0.535898i) q^{35} -3.00000 q^{36} +(2.59808 - 5.50000i) q^{37} -3.00000i q^{38} +(1.23205 + 1.86603i) q^{40} +(5.00000 - 8.66025i) q^{41} -2.00000i q^{43} +(-1.50000 + 2.59808i) q^{44} +(-6.00000 - 3.00000i) q^{45} +(0.500000 + 0.866025i) q^{46} -11.0000i q^{47} +(4.50000 + 7.79423i) q^{49} +(0.598076 + 4.96410i) q^{50} +(-0.866025 + 0.500000i) q^{52} +(8.66025 - 5.00000i) q^{53} +(-5.59808 + 3.69615i) q^{55} +(2.00000 - 3.46410i) q^{56} +(-5.19615 + 3.00000i) q^{58} +(7.50000 + 12.9904i) q^{59} +(-6.00000 + 10.3923i) q^{61} +(3.46410 - 2.00000i) q^{62} +12.0000i q^{63} -1.00000 q^{64} +(-2.23205 + 0.133975i) q^{65} +(-1.73205 - 1.00000i) q^{67} +6.00000i q^{68} +(7.46410 - 4.92820i) q^{70} +(3.00000 - 5.19615i) q^{71} +(2.59808 - 1.50000i) q^{72} -2.00000i q^{73} +(0.500000 + 6.06218i) q^{74} +(1.50000 + 2.59808i) q^{76} +(10.3923 + 6.00000i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-2.00000 - 1.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +10.0000i q^{82} +(5.19615 - 3.00000i) q^{83} +(-6.00000 + 12.0000i) q^{85} +(1.00000 + 1.73205i) q^{86} -3.00000i q^{88} +(-7.50000 - 12.9904i) q^{89} +(6.69615 - 0.401924i) q^{90} +(2.00000 + 3.46410i) q^{91} +(-0.866025 - 0.500000i) q^{92} +(5.50000 + 9.52628i) q^{94} +(0.401924 + 6.69615i) q^{95} +2.00000i q^{97} +(-7.79423 - 4.50000i) q^{98} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{5} - 6q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{5} - 6q^{9} - 4q^{10} - 12q^{11} + 16q^{14} - 2q^{16} - 6q^{19} - 4q^{20} - 6q^{25} + 4q^{26} + 24q^{29} - 16q^{31} + 12q^{34} - 8q^{35} - 12q^{36} - 2q^{40} + 20q^{41} - 6q^{44} - 24q^{45} + 2q^{46} + 18q^{49} - 8q^{50} - 12q^{55} + 8q^{56} + 30q^{59} - 24q^{61} - 4q^{64} - 2q^{65} + 16q^{70} + 12q^{71} + 2q^{74} + 6q^{76} + 8q^{79} - 8q^{80} - 18q^{81} - 24q^{85} + 4q^{86} - 30q^{89} + 6q^{90} + 8q^{91} + 22q^{94} + 12q^{95} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.86603 1.23205i 0.834512 0.550990i
\(6\) 0 0
\(7\) −3.46410 2.00000i −1.30931 0.755929i −0.327327 0.944911i \(-0.606148\pi\)
−0.981981 + 0.188982i \(0.939481\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) −1.00000 + 2.00000i −0.316228 + 0.632456i
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) −0.866025 0.500000i −0.240192 0.138675i 0.375073 0.926995i \(-0.377618\pi\)
−0.615265 + 0.788320i \(0.710951\pi\)
\(14\) 4.00000 1.06904
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −5.19615 + 3.00000i −1.26025 + 0.727607i −0.973123 0.230285i \(-0.926034\pi\)
−0.287129 + 0.957892i \(0.592701\pi\)
\(18\) 2.59808 + 1.50000i 0.612372 + 0.353553i
\(19\) −1.50000 + 2.59808i −0.344124 + 0.596040i −0.985194 0.171442i \(-0.945157\pi\)
0.641071 + 0.767482i \(0.278491\pi\)
\(20\) −0.133975 2.23205i −0.0299576 0.499102i
\(21\) 0 0
\(22\) 2.59808 1.50000i 0.553912 0.319801i
\(23\) 1.00000i 0.208514i −0.994550 0.104257i \(-0.966753\pi\)
0.994550 0.104257i \(-0.0332465\pi\)
\(24\) 0 0
\(25\) 1.96410 4.59808i 0.392820 0.919615i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) −3.46410 + 2.00000i −0.654654 + 0.377964i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 3.00000 5.19615i 0.514496 0.891133i
\(35\) −8.92820 + 0.535898i −1.50914 + 0.0905834i
\(36\) −3.00000 −0.500000
\(37\) 2.59808 5.50000i 0.427121 0.904194i
\(38\) 3.00000i 0.486664i
\(39\) 0 0
\(40\) 1.23205 + 1.86603i 0.194804 + 0.295045i
\(41\) 5.00000 8.66025i 0.780869 1.35250i −0.150567 0.988600i \(-0.548110\pi\)
0.931436 0.363905i \(-0.118557\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) −6.00000 3.00000i −0.894427 0.447214i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) 11.0000i 1.60451i −0.596978 0.802257i \(-0.703632\pi\)
0.596978 0.802257i \(-0.296368\pi\)
\(48\) 0 0
\(49\) 4.50000 + 7.79423i 0.642857 + 1.11346i
\(50\) 0.598076 + 4.96410i 0.0845807 + 0.702030i
\(51\) 0 0
\(52\) −0.866025 + 0.500000i −0.120096 + 0.0693375i
\(53\) 8.66025 5.00000i 1.18958 0.686803i 0.231367 0.972867i \(-0.425680\pi\)
0.958211 + 0.286064i \(0.0923469\pi\)
\(54\) 0 0
\(55\) −5.59808 + 3.69615i −0.754844 + 0.498389i
\(56\) 2.00000 3.46410i 0.267261 0.462910i
\(57\) 0 0
\(58\) −5.19615 + 3.00000i −0.682288 + 0.393919i
\(59\) 7.50000 + 12.9904i 0.976417 + 1.69120i 0.675178 + 0.737655i \(0.264067\pi\)
0.301239 + 0.953549i \(0.402600\pi\)
\(60\) 0 0
\(61\) −6.00000 + 10.3923i −0.768221 + 1.33060i 0.170305 + 0.985391i \(0.445525\pi\)
−0.938527 + 0.345207i \(0.887809\pi\)
\(62\) 3.46410 2.00000i 0.439941 0.254000i
\(63\) 12.0000i 1.51186i
\(64\) −1.00000 −0.125000
\(65\) −2.23205 + 0.133975i −0.276852 + 0.0166175i
\(66\) 0 0
\(67\) −1.73205 1.00000i −0.211604 0.122169i 0.390453 0.920623i \(-0.372318\pi\)
−0.602056 + 0.798454i \(0.705652\pi\)
\(68\) 6.00000i 0.727607i
\(69\) 0 0
\(70\) 7.46410 4.92820i 0.892131 0.589033i
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) 2.59808 1.50000i 0.306186 0.176777i
\(73\) 2.00000i 0.234082i −0.993127 0.117041i \(-0.962659\pi\)
0.993127 0.117041i \(-0.0373409\pi\)
\(74\) 0.500000 + 6.06218i 0.0581238 + 0.704714i
\(75\) 0 0
\(76\) 1.50000 + 2.59808i 0.172062 + 0.298020i
\(77\) 10.3923 + 6.00000i 1.18431 + 0.683763i
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) −2.00000 1.00000i −0.223607 0.111803i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 10.0000i 1.10432i
\(83\) 5.19615 3.00000i 0.570352 0.329293i −0.186938 0.982372i \(-0.559856\pi\)
0.757290 + 0.653079i \(0.226523\pi\)
\(84\) 0 0
\(85\) −6.00000 + 12.0000i −0.650791 + 1.30158i
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 0 0
\(88\) 3.00000i 0.319801i
\(89\) −7.50000 12.9904i −0.794998 1.37698i −0.922840 0.385183i \(-0.874138\pi\)
0.127842 0.991795i \(-0.459195\pi\)
\(90\) 6.69615 0.401924i 0.705836 0.0423665i
\(91\) 2.00000 + 3.46410i 0.209657 + 0.363137i
\(92\) −0.866025 0.500000i −0.0902894 0.0521286i
\(93\) 0 0
\(94\) 5.50000 + 9.52628i 0.567282 + 0.982561i
\(95\) 0.401924 + 6.69615i 0.0412365 + 0.687011i
\(96\) 0 0
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) −7.79423 4.50000i −0.787336 0.454569i
\(99\) 4.50000 + 7.79423i 0.452267 + 0.783349i
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 0 0
\(103\) 9.00000i 0.886796i 0.896325 + 0.443398i \(0.146227\pi\)
−0.896325 + 0.443398i \(0.853773\pi\)
\(104\) 0.500000 0.866025i 0.0490290 0.0849208i
\(105\) 0 0
\(106\) −5.00000 + 8.66025i −0.485643 + 0.841158i
\(107\) −6.92820 4.00000i −0.669775 0.386695i 0.126217 0.992003i \(-0.459717\pi\)
−0.795991 + 0.605308i \(0.793050\pi\)
\(108\) 0 0
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 3.00000 6.00000i 0.286039 0.572078i
\(111\) 0 0
\(112\) 4.00000i 0.377964i
\(113\) 8.66025 5.00000i 0.814688 0.470360i −0.0338931 0.999425i \(-0.510791\pi\)
0.848581 + 0.529065i \(0.177457\pi\)
\(114\) 0 0
\(115\) −1.23205 1.86603i −0.114889 0.174008i
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 3.00000i 0.277350i
\(118\) −12.9904 7.50000i −1.19586 0.690431i
\(119\) 24.0000 2.20008
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 12.0000i 1.08643i
\(123\) 0 0
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) −6.00000 10.3923i −0.534522 0.925820i
\(127\) −14.7224 + 8.50000i −1.30640 + 0.754253i −0.981494 0.191492i \(-0.938667\pi\)
−0.324910 + 0.945745i \(0.605334\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 1.86603 1.23205i 0.163661 0.108058i
\(131\) −10.0000 17.3205i −0.873704 1.51330i −0.858137 0.513421i \(-0.828378\pi\)
−0.0155672 0.999879i \(-0.504955\pi\)
\(132\) 0 0
\(133\) 10.3923 6.00000i 0.901127 0.520266i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) 6.00000i 0.512615i 0.966595 + 0.256307i \(0.0825059\pi\)
−0.966595 + 0.256307i \(0.917494\pi\)
\(138\) 0 0
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) −4.00000 + 8.00000i −0.338062 + 0.676123i
\(141\) 0 0
\(142\) 6.00000i 0.503509i
\(143\) 2.59808 + 1.50000i 0.217262 + 0.125436i
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) 11.1962 7.39230i 0.929790 0.613898i
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) 0 0
\(148\) −3.46410 5.00000i −0.284747 0.410997i
\(149\) 16.0000 1.31077 0.655386 0.755295i \(-0.272506\pi\)
0.655386 + 0.755295i \(0.272506\pi\)
\(150\) 0 0
\(151\) 1.00000 1.73205i 0.0813788 0.140952i −0.822464 0.568818i \(-0.807401\pi\)
0.903842 + 0.427865i \(0.140734\pi\)
\(152\) −2.59808 1.50000i −0.210732 0.121666i
\(153\) 15.5885 + 9.00000i 1.26025 + 0.727607i
\(154\) −12.0000 −0.966988
\(155\) −7.46410 + 4.92820i −0.599531 + 0.395843i
\(156\) 0 0
\(157\) −4.33013 + 2.50000i −0.345582 + 0.199522i −0.662738 0.748852i \(-0.730606\pi\)
0.317156 + 0.948373i \(0.397272\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 0 0
\(160\) 2.23205 0.133975i 0.176459 0.0105916i
\(161\) −2.00000 + 3.46410i −0.157622 + 0.273009i
\(162\) 9.00000i 0.707107i
\(163\) −5.19615 + 3.00000i −0.406994 + 0.234978i −0.689497 0.724288i \(-0.742169\pi\)
0.282503 + 0.959266i \(0.408835\pi\)
\(164\) −5.00000 8.66025i −0.390434 0.676252i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 6.92820 + 4.00000i 0.536120 + 0.309529i 0.743505 0.668730i \(-0.233162\pi\)
−0.207385 + 0.978259i \(0.566495\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) −0.803848 13.3923i −0.0616523 1.02714i
\(171\) 9.00000 0.688247
\(172\) −1.73205 1.00000i −0.132068 0.0762493i
\(173\) −4.33013 + 2.50000i −0.329213 + 0.190071i −0.655492 0.755202i \(-0.727539\pi\)
0.326278 + 0.945274i \(0.394205\pi\)
\(174\) 0 0
\(175\) −16.0000 + 12.0000i −1.20949 + 0.907115i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 0 0
\(178\) 12.9904 + 7.50000i 0.973670 + 0.562149i
\(179\) −1.00000 −0.0747435 −0.0373718 0.999301i \(-0.511899\pi\)
−0.0373718 + 0.999301i \(0.511899\pi\)
\(180\) −5.59808 + 3.69615i −0.417256 + 0.275495i
\(181\) 8.00000 13.8564i 0.594635 1.02994i −0.398963 0.916967i \(-0.630630\pi\)
0.993598 0.112972i \(-0.0360369\pi\)
\(182\) −3.46410 2.00000i −0.256776 0.148250i
\(183\) 0 0
\(184\) 1.00000 0.0737210
\(185\) −1.92820 13.4641i −0.141764 0.989900i
\(186\) 0 0
\(187\) 15.5885 9.00000i 1.13994 0.658145i
\(188\) −9.52628 5.50000i −0.694775 0.401129i
\(189\) 0 0
\(190\) −3.69615 5.59808i −0.268147 0.406127i
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) 16.0000i 1.15171i −0.817554 0.575853i \(-0.804670\pi\)
0.817554 0.575853i \(-0.195330\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) −19.0526 + 11.0000i −1.35744 + 0.783718i −0.989278 0.146045i \(-0.953346\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(198\) −7.79423 4.50000i −0.553912 0.319801i
\(199\) −22.0000 −1.55954 −0.779769 0.626067i \(-0.784664\pi\)
−0.779769 + 0.626067i \(0.784664\pi\)
\(200\) 4.59808 + 1.96410i 0.325133 + 0.138883i
\(201\) 0 0
\(202\) 3.46410 2.00000i 0.243733 0.140720i
\(203\) −20.7846 12.0000i −1.45879 0.842235i
\(204\) 0 0
\(205\) −1.33975 22.3205i −0.0935719 1.55893i
\(206\) −4.50000 7.79423i −0.313530 0.543050i
\(207\) −2.59808 + 1.50000i −0.180579 + 0.104257i
\(208\) 1.00000i 0.0693375i
\(209\) 4.50000 7.79423i 0.311272 0.539138i
\(210\) 0 0
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) 10.0000i 0.686803i
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) −2.46410 3.73205i −0.168050 0.254524i
\(216\) 0 0
\(217\) 13.8564 + 8.00000i 0.940634 + 0.543075i
\(218\) −8.66025 5.00000i −0.586546 0.338643i
\(219\) 0 0
\(220\) 0.401924 + 6.69615i 0.0270977 + 0.451455i
\(221\) 6.00000 0.403604
\(222\) 0 0
\(223\) 5.00000i 0.334825i −0.985887 0.167412i \(-0.946459\pi\)
0.985887 0.167412i \(-0.0535411\pi\)
\(224\) −2.00000 3.46410i −0.133631 0.231455i
\(225\) −14.8923 + 1.79423i −0.992820 + 0.119615i
\(226\) −5.00000 + 8.66025i −0.332595 + 0.576072i
\(227\) 24.2487 + 14.0000i 1.60944 + 0.929213i 0.989494 + 0.144571i \(0.0461801\pi\)
0.619949 + 0.784642i \(0.287153\pi\)
\(228\) 0 0
\(229\) 1.00000 1.73205i 0.0660819 0.114457i −0.831092 0.556136i \(-0.812283\pi\)
0.897173 + 0.441679i \(0.145617\pi\)
\(230\) 2.00000 + 1.00000i 0.131876 + 0.0659380i
\(231\) 0 0
\(232\) 6.00000i 0.393919i
\(233\) 18.0000i 1.17922i 0.807688 + 0.589610i \(0.200718\pi\)
−0.807688 + 0.589610i \(0.799282\pi\)
\(234\) −1.50000 2.59808i −0.0980581 0.169842i
\(235\) −13.5526 20.5263i −0.884071 1.33899i
\(236\) 15.0000 0.976417
\(237\) 0 0
\(238\) −20.7846 + 12.0000i −1.34727 + 0.777844i
\(239\) −10.0000 17.3205i −0.646846 1.12037i −0.983872 0.178875i \(-0.942754\pi\)
0.337026 0.941495i \(-0.390579\pi\)
\(240\) 0 0
\(241\) −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i \(-0.905720\pi\)
0.731001 + 0.682376i \(0.239053\pi\)
\(242\) 1.73205 1.00000i 0.111340 0.0642824i
\(243\) 0 0
\(244\) 6.00000 + 10.3923i 0.384111 + 0.665299i
\(245\) 18.0000 + 9.00000i 1.14998 + 0.574989i
\(246\) 0 0
\(247\) 2.59808 1.50000i 0.165312 0.0954427i
\(248\) 4.00000i 0.254000i
\(249\) 0 0
\(250\) 7.23205 + 8.52628i 0.457395 + 0.539249i
\(251\) −1.00000 −0.0631194 −0.0315597 0.999502i \(-0.510047\pi\)
−0.0315597 + 0.999502i \(0.510047\pi\)
\(252\) 10.3923 + 6.00000i 0.654654 + 0.377964i
\(253\) 3.00000i 0.188608i
\(254\) 8.50000 14.7224i 0.533337 0.923768i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 0 0
\(259\) −20.0000 + 13.8564i −1.24274 + 0.860995i
\(260\) −1.00000 + 2.00000i −0.0620174 + 0.124035i
\(261\) −9.00000 15.5885i −0.557086 0.964901i
\(262\) 17.3205 + 10.0000i 1.07006 + 0.617802i
\(263\) 16.4545 + 9.50000i 1.01463 + 0.585795i 0.912543 0.408981i \(-0.134116\pi\)
0.102084 + 0.994776i \(0.467449\pi\)
\(264\) 0 0
\(265\) 10.0000 20.0000i 0.614295 1.22859i
\(266\) −6.00000 + 10.3923i −0.367884 + 0.637193i
\(267\) 0 0
\(268\) −1.73205 + 1.00000i −0.105802 + 0.0610847i
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 10.0000 + 17.3205i 0.607457 + 1.05215i 0.991658 + 0.128897i \(0.0411435\pi\)
−0.384201 + 0.923249i \(0.625523\pi\)
\(272\) 5.19615 + 3.00000i 0.315063 + 0.181902i
\(273\) 0 0
\(274\) −3.00000 5.19615i −0.181237 0.313911i
\(275\) −5.89230 + 13.7942i −0.355319 + 0.831823i
\(276\) 0 0
\(277\) 5.19615 + 3.00000i 0.312207 + 0.180253i 0.647913 0.761714i \(-0.275642\pi\)
−0.335707 + 0.941966i \(0.608975\pi\)
\(278\) 4.33013 + 2.50000i 0.259704 + 0.149940i
\(279\) 6.00000 + 10.3923i 0.359211 + 0.622171i
\(280\) −0.535898 8.92820i −0.0320261 0.533562i
\(281\) 1.50000 + 2.59808i 0.0894825 + 0.154988i 0.907293 0.420500i \(-0.138145\pi\)
−0.817810 + 0.575488i \(0.804812\pi\)
\(282\) 0 0
\(283\) 3.46410 + 2.00000i 0.205919 + 0.118888i 0.599414 0.800439i \(-0.295400\pi\)
−0.393494 + 0.919327i \(0.628734\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) −34.6410 + 20.0000i −2.04479 + 1.18056i
\(288\) 3.00000i 0.176777i
\(289\) 9.50000 16.4545i 0.558824 0.967911i
\(290\) −6.00000 + 12.0000i −0.352332 + 0.704664i
\(291\) 0 0
\(292\) −1.73205 1.00000i −0.101361 0.0585206i
\(293\) 2.59808 + 1.50000i 0.151781 + 0.0876309i 0.573967 0.818878i \(-0.305404\pi\)
−0.422186 + 0.906509i \(0.638737\pi\)
\(294\) 0 0
\(295\) 30.0000 + 15.0000i 1.74667 + 0.873334i
\(296\) 5.50000 + 2.59808i 0.319681 + 0.151010i
\(297\) 0 0
\(298\) −13.8564 + 8.00000i −0.802680 + 0.463428i
\(299\) −0.500000 + 0.866025i −0.0289157 + 0.0500835i
\(300\) 0 0
\(301\) −4.00000 + 6.92820i −0.230556 + 0.399335i
\(302\) 2.00000i 0.115087i
\(303\) 0 0
\(304\) 3.00000 0.172062
\(305\) 1.60770 + 26.7846i 0.0920564 + 1.53368i
\(306\) −18.0000 −1.02899
\(307\) 32.0000i 1.82634i −0.407583 0.913168i \(-0.633628\pi\)
0.407583 0.913168i \(-0.366372\pi\)
\(308\) 10.3923 6.00000i 0.592157 0.341882i
\(309\) 0 0
\(310\) 4.00000 8.00000i 0.227185 0.454369i
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 0 0
\(313\) 27.7128 16.0000i 1.56642 0.904373i 0.569839 0.821756i \(-0.307005\pi\)
0.996581 0.0826174i \(-0.0263280\pi\)
\(314\) 2.50000 4.33013i 0.141083 0.244363i
\(315\) 14.7846 + 22.3923i 0.833018 + 1.26166i
\(316\) −2.00000 3.46410i −0.112509 0.194871i
\(317\) 7.79423 4.50000i 0.437767 0.252745i −0.264883 0.964281i \(-0.585333\pi\)
0.702650 + 0.711535i \(0.252000\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) −1.86603 + 1.23205i −0.104314 + 0.0688737i
\(321\) 0 0
\(322\) 4.00000i 0.222911i
\(323\) 18.0000i 1.00155i
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) −4.00000 + 3.00000i −0.221880 + 0.166410i
\(326\) 3.00000 5.19615i 0.166155 0.287788i
\(327\) 0 0
\(328\) 8.66025 + 5.00000i 0.478183 + 0.276079i
\(329\) −22.0000 + 38.1051i −1.21290 + 2.10080i
\(330\) 0 0
\(331\) 6.50000 + 11.2583i 0.357272 + 0.618814i 0.987504 0.157593i \(-0.0503735\pi\)
−0.630232 + 0.776407i \(0.717040\pi\)
\(332\) 6.00000i 0.329293i
\(333\) −18.1865 + 1.50000i −0.996616 + 0.0821995i
\(334\) −8.00000 −0.437741
\(335\) −4.46410 + 0.267949i −0.243900 + 0.0146396i
\(336\) 0 0
\(337\) −6.92820 4.00000i −0.377403 0.217894i 0.299285 0.954164i \(-0.403252\pi\)
−0.676688 + 0.736270i \(0.736585\pi\)
\(338\) 10.3923 + 6.00000i 0.565267 + 0.326357i
\(339\) 0 0
\(340\) 7.39230 + 11.1962i 0.400904 + 0.607197i
\(341\) 12.0000 0.649836
\(342\) −7.79423 + 4.50000i −0.421464 + 0.243332i
\(343\) 8.00000i 0.431959i
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) 2.50000 4.33013i 0.134401 0.232789i
\(347\) 30.0000i 1.61048i −0.592946 0.805242i \(-0.702035\pi\)
0.592946 0.805242i \(-0.297965\pi\)
\(348\) 0 0
\(349\) 3.00000 + 5.19615i 0.160586 + 0.278144i 0.935079 0.354439i \(-0.115328\pi\)
−0.774493 + 0.632583i \(0.781995\pi\)
\(350\) 7.85641 18.3923i 0.419943 0.983110i
\(351\) 0 0
\(352\) −2.59808 1.50000i −0.138478 0.0799503i
\(353\) −15.5885 + 9.00000i −0.829690 + 0.479022i −0.853746 0.520689i \(-0.825675\pi\)
0.0240566 + 0.999711i \(0.492342\pi\)
\(354\) 0 0
\(355\) −0.803848 13.3923i −0.0426638 0.710790i
\(356\) −15.0000 −0.794998
\(357\) 0 0
\(358\) 0.866025 0.500000i 0.0457709 0.0264258i
\(359\) 26.0000 1.37223 0.686114 0.727494i \(-0.259315\pi\)
0.686114 + 0.727494i \(0.259315\pi\)
\(360\) 3.00000 6.00000i 0.158114 0.316228i
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) 16.0000i 0.840941i
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) −2.46410 3.73205i −0.128977 0.195344i
\(366\) 0 0
\(367\) −11.2583 6.50000i −0.587680 0.339297i 0.176500 0.984301i \(-0.443523\pi\)
−0.764180 + 0.645003i \(0.776856\pi\)
\(368\) −0.866025 + 0.500000i −0.0451447 + 0.0260643i
\(369\) −30.0000 −1.56174
\(370\) 8.40192 + 10.6962i 0.436795 + 0.556066i
\(371\) −40.0000 −2.07670
\(372\) 0 0
\(373\) 19.9186 + 11.5000i 1.03135 + 0.595447i 0.917370 0.398036i \(-0.130308\pi\)
0.113975 + 0.993484i \(0.463641\pi\)
\(374\) −9.00000 + 15.5885i −0.465379 + 0.806060i
\(375\) 0 0
\(376\) 11.0000 0.567282
\(377\) −5.19615 3.00000i −0.267615 0.154508i
\(378\) 0 0
\(379\) −12.0000 20.7846i −0.616399 1.06763i −0.990137 0.140100i \(-0.955258\pi\)
0.373739 0.927534i \(-0.378076\pi\)
\(380\) 6.00000 + 3.00000i 0.307794 + 0.153897i
\(381\) 0 0
\(382\) −3.46410 + 2.00000i −0.177239 + 0.102329i
\(383\) 14.7224 + 8.50000i 0.752281 + 0.434330i 0.826518 0.562911i \(-0.190319\pi\)
−0.0742364 + 0.997241i \(0.523652\pi\)
\(384\) 0 0
\(385\) 26.7846 1.60770i 1.36507 0.0819357i
\(386\) 8.00000 + 13.8564i 0.407189 + 0.705273i
\(387\) −5.19615 + 3.00000i −0.264135 + 0.152499i
\(388\) 1.73205 + 1.00000i 0.0879316 + 0.0507673i
\(389\) −2.00000 + 3.46410i −0.101404 + 0.175637i −0.912263 0.409604i \(-0.865667\pi\)
0.810859 + 0.585241i \(0.199000\pi\)
\(390\) 0 0
\(391\) 3.00000 + 5.19615i 0.151717 + 0.262781i
\(392\) −7.79423 + 4.50000i −0.393668 + 0.227284i
\(393\) 0 0
\(394\) 11.0000 19.0526i 0.554172 0.959854i
\(395\) −0.535898 8.92820i −0.0269640 0.449227i
\(396\) 9.00000 0.452267
\(397\) 5.00000i 0.250943i 0.992097 + 0.125471i \(0.0400443\pi\)
−0.992097 + 0.125471i \(0.959956\pi\)
\(398\) 19.0526 11.0000i 0.955018 0.551380i
\(399\) 0 0
\(400\) −4.96410 + 0.598076i −0.248205 + 0.0299038i
\(401\) 25.0000 1.24844 0.624220 0.781248i \(-0.285417\pi\)
0.624220 + 0.781248i \(0.285417\pi\)
\(402\) 0 0
\(403\) 3.46410 + 2.00000i 0.172559 + 0.0996271i
\(404\) −2.00000 + 3.46410i −0.0995037 + 0.172345i
\(405\) 1.20577 + 20.0885i 0.0599153 + 0.998203i
\(406\) 24.0000 1.19110
\(407\) −7.79423 + 16.5000i −0.386346 + 0.817875i
\(408\) 0 0
\(409\) −11.0000 19.0526i −0.543915 0.942088i −0.998674 0.0514740i \(-0.983608\pi\)
0.454759 0.890614i \(-0.349725\pi\)
\(410\) 12.3205 + 18.6603i 0.608467 + 0.921564i
\(411\) 0 0
\(412\) 7.79423 + 4.50000i 0.383994 + 0.221699i
\(413\) 60.0000i 2.95241i
\(414\) 1.50000 2.59808i 0.0737210 0.127688i
\(415\) 6.00000 12.0000i 0.294528 0.589057i
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 0 0
\(418\) 9.00000i 0.440204i
\(419\) −12.5000 21.6506i −0.610665 1.05770i −0.991129 0.132907i \(-0.957569\pi\)
0.380464 0.924796i \(-0.375764\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 0.866025 0.500000i 0.0421575 0.0243396i
\(423\) −28.5788 + 16.5000i −1.38955 + 0.802257i
\(424\) 5.00000 + 8.66025i 0.242821 + 0.420579i
\(425\) 3.58846 + 29.7846i 0.174066 + 1.44477i
\(426\) 0 0
\(427\) 41.5692 24.0000i 2.01168 1.16144i
\(428\) −6.92820 + 4.00000i −0.334887 + 0.193347i
\(429\) 0 0
\(430\) 4.00000 + 2.00000i 0.192897 + 0.0964486i
\(431\) 8.00000 13.8564i 0.385346 0.667440i −0.606471 0.795106i \(-0.707415\pi\)
0.991817 + 0.127666i \(0.0407486\pi\)
\(432\) 0 0
\(433\) 34.0000i 1.63394i 0.576683 + 0.816968i \(0.304347\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) 2.59808 + 1.50000i 0.124283 + 0.0717547i
\(438\) 0 0
\(439\) −1.00000 + 1.73205i −0.0477274 + 0.0826663i −0.888902 0.458097i \(-0.848531\pi\)
0.841175 + 0.540763i \(0.181865\pi\)
\(440\) −3.69615 5.59808i −0.176207 0.266878i
\(441\) 13.5000 23.3827i 0.642857 1.11346i
\(442\) −5.19615 + 3.00000i −0.247156 + 0.142695i
\(443\) 34.0000i 1.61539i −0.589601 0.807694i \(-0.700715\pi\)
0.589601 0.807694i \(-0.299285\pi\)
\(444\) 0 0
\(445\) −30.0000 15.0000i −1.42214 0.711068i
\(446\) 2.50000 + 4.33013i 0.118378 + 0.205037i
\(447\) 0 0
\(448\) 3.46410 + 2.00000i 0.163663 + 0.0944911i
\(449\) −15.0000 + 25.9808i −0.707894 + 1.22611i 0.257743 + 0.966213i \(0.417021\pi\)
−0.965637 + 0.259895i \(0.916312\pi\)
\(450\) 12.0000 9.00000i 0.565685 0.424264i
\(451\) −15.0000 + 25.9808i −0.706322 + 1.22339i
\(452\) 10.0000i 0.470360i
\(453\) 0 0
\(454\) −28.0000 −1.31411
\(455\) 8.00000 + 4.00000i 0.375046 + 0.187523i
\(456\) 0 0
\(457\) −22.5167 13.0000i −1.05328 0.608114i −0.129718 0.991551i \(-0.541407\pi\)
−0.923567 + 0.383437i \(0.874740\pi\)
\(458\) 2.00000i 0.0934539i
\(459\) 0 0
\(460\) −2.23205 + 0.133975i −0.104070 + 0.00624660i
\(461\) −18.0000 31.1769i −0.838344 1.45205i −0.891279 0.453456i \(-0.850191\pi\)
0.0529352 0.998598i \(-0.483142\pi\)
\(462\) 0 0
\(463\) 6.92820 + 4.00000i 0.321981 + 0.185896i 0.652275 0.757982i \(-0.273815\pi\)
−0.330294 + 0.943878i \(0.607148\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 0 0
\(466\) −9.00000 15.5885i −0.416917 0.722121i
\(467\) 6.00000i 0.277647i −0.990317 0.138823i \(-0.955668\pi\)
0.990317 0.138823i \(-0.0443321\pi\)
\(468\) 2.59808 + 1.50000i 0.120096 + 0.0693375i
\(469\) 4.00000 + 6.92820i 0.184703 + 0.319915i
\(470\) 22.0000 + 11.0000i 1.01478 + 0.507392i
\(471\) 0 0
\(472\) −12.9904 + 7.50000i −0.597931 + 0.345215i
\(473\) 6.00000i 0.275880i
\(474\) 0 0
\(475\) 9.00000 + 12.0000i 0.412948 + 0.550598i
\(476\) 12.0000 20.7846i 0.550019 0.952661i
\(477\) −25.9808 15.0000i −1.18958 0.686803i
\(478\) 17.3205 + 10.0000i 0.792222 + 0.457389i
\(479\) 3.00000 + 5.19615i 0.137073 + 0.237418i 0.926388 0.376571i \(-0.122897\pi\)
−0.789314 + 0.613990i \(0.789564\pi\)
\(480\) 0 0
\(481\) −5.00000 + 3.46410i −0.227980 + 0.157949i
\(482\) 7.00000i 0.318841i
\(483\) 0 0
\(484\) −1.00000 + 1.73205i −0.0454545 + 0.0787296i
\(485\) 2.46410 + 3.73205i 0.111889 + 0.169464i
\(486\) 0 0
\(487\) 24.0000i 1.08754i −0.839233 0.543772i \(-0.816996\pi\)
0.839233 0.543772i \(-0.183004\pi\)
\(488\) −10.3923 6.00000i −0.470438 0.271607i
\(489\) 0 0
\(490\) −20.0885 + 1.20577i −0.907504 + 0.0544712i
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) 0 0
\(493\) −31.1769 + 18.0000i −1.40414 + 0.810679i
\(494\) −1.50000 + 2.59808i −0.0674882 + 0.116893i
\(495\) 18.0000 + 9.00000i 0.809040 + 0.404520i
\(496\) 2.00000 + 3.46410i 0.0898027 + 0.155543i
\(497\) −20.7846 + 12.0000i −0.932317 + 0.538274i
\(498\) 0 0
\(499\) 18.0000 31.1769i 0.805791 1.39567i −0.109965 0.993935i \(-0.535074\pi\)
0.915756 0.401735i \(-0.131593\pi\)
\(500\) −10.5263 3.76795i −0.470750 0.168508i
\(501\) 0 0
\(502\) 0.866025 0.500000i 0.0386526 0.0223161i
\(503\) −13.8564 + 8.00000i −0.617827 + 0.356702i −0.776022 0.630705i \(-0.782766\pi\)
0.158196 + 0.987408i \(0.449432\pi\)
\(504\) −12.0000 −0.534522
\(505\) −7.46410 + 4.92820i −0.332148 + 0.219302i
\(506\) −1.50000 2.59808i −0.0666831 0.115499i
\(507\) 0 0
\(508\) 17.0000i 0.754253i
\(509\) −18.0000 31.1769i −0.797836 1.38189i −0.921023 0.389509i \(-0.872645\pi\)
0.123187 0.992384i \(-0.460689\pi\)
\(510\) 0 0
\(511\) −4.00000 + 6.92820i −0.176950 + 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 0 0
\(515\) 11.0885 + 16.7942i 0.488616 + 0.740042i
\(516\) 0 0
\(517\) 33.0000i 1.45134i
\(518\) 10.3923 22.0000i 0.456612 0.966625i
\(519\) 0 0
\(520\) −0.133975 2.23205i −0.00587517 0.0978819i
\(521\) −2.50000 + 4.33013i −0.109527 + 0.189706i −0.915579 0.402139i \(-0.868267\pi\)
0.806052 + 0.591845i \(0.201600\pi\)
\(522\) 15.5885 + 9.00000i 0.682288 + 0.393919i
\(523\) 13.8564 + 8.00000i 0.605898 + 0.349816i 0.771358 0.636401i \(-0.219578\pi\)
−0.165460 + 0.986216i \(0.552911\pi\)
\(524\) −20.0000 −0.873704
\(525\) 0 0
\(526\) −19.0000 −0.828439
\(527\) 20.7846 12.0000i 0.905392 0.522728i
\(528\) 0 0
\(529\) 22.0000 0.956522
\(530\) 1.33975 + 22.3205i 0.0581948 + 0.969541i
\(531\) 22.5000 38.9711i 0.976417 1.69120i
\(532\) 12.0000i 0.520266i
\(533\) −8.66025 + 5.00000i −0.375117 + 0.216574i
\(534\) 0 0
\(535\) −17.8564 + 1.07180i −0.772000 + 0.0463378i
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) 0 0
\(538\) 12.1244 7.00000i 0.522718 0.301791i
\(539\) −13.5000 23.3827i −0.581486 1.00716i
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) −17.3205 10.0000i −0.743980 0.429537i
\(543\) 0 0
\(544\) −6.00000 −0.257248
\(545\) 20.0000 + 10.0000i 0.856706 + 0.428353i
\(546\) 0 0
\(547\) 10.0000i 0.427569i −0.976881 0.213785i \(-0.931421\pi\)
0.976881 0.213785i \(-0.0685791\pi\)
\(548\) 5.19615 + 3.00000i 0.221969 + 0.128154i
\(549\) 36.0000 1.53644
\(550\) −1.79423 14.8923i −0.0765062 0.635010i
\(551\) −9.00000 + 15.5885i −0.383413 + 0.664091i
\(552\) 0 0
\(553\) −13.8564 + 8.00000i −0.589234 + 0.340195i
\(554\) −6.00000 −0.254916
\(555\) 0 0
\(556\) −5.00000 −0.212047
\(557\) −28.5788 + 16.5000i −1.21092 + 0.699127i −0.962961 0.269642i \(-0.913095\pi\)
−0.247964 + 0.968769i \(0.579761\pi\)
\(558\) −10.3923 6.00000i −0.439941 0.254000i
\(559\) −1.00000 + 1.73205i −0.0422955 + 0.0732579i
\(560\) 4.92820 + 7.46410i 0.208255 + 0.315416i
\(561\) 0 0
\(562\) −2.59808 1.50000i −0.109593 0.0632737i
\(563\) 4.00000i 0.168580i 0.996441 + 0.0842900i \(0.0268622\pi\)
−0.996441 + 0.0842900i \(0.973138\pi\)
\(564\) 0 0
\(565\) 10.0000 20.0000i 0.420703 0.841406i
\(566\) −4.00000 −0.168133
\(567\) 31.1769 18.0000i 1.30931 0.755929i
\(568\) 5.19615 + 3.00000i 0.218026 + 0.125877i
\(569\) −5.00000 −0.209611 −0.104805 0.994493i \(-0.533422\pi\)
−0.104805 + 0.994493i \(0.533422\pi\)
\(570\) 0 0
\(571\) −6.50000 11.2583i −0.272017 0.471146i 0.697362 0.716720i \(-0.254357\pi\)
−0.969378 + 0.245573i \(0.921024\pi\)
\(572\) 2.59808 1.50000i 0.108631 0.0627182i
\(573\) 0 0
\(574\) 20.0000 34.6410i 0.834784 1.44589i
\(575\) −4.59808 1.96410i −0.191753 0.0819087i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −17.3205 + 10.0000i −0.721062 + 0.416305i −0.815144 0.579259i \(-0.803342\pi\)
0.0940813 + 0.995565i \(0.470009\pi\)
\(578\) 19.0000i 0.790296i
\(579\) 0 0
\(580\) −0.803848 13.3923i −0.0333780 0.556085i
\(581\) −24.0000 −0.995688
\(582\) 0 0
\(583\) −25.9808 + 15.0000i −1.07601 + 0.621237i
\(584\) 2.00000 0.0827606
\(585\) 3.69615 + 5.59808i 0.152817 + 0.231452i
\(586\) −3.00000 −0.123929
\(587\) 31.1769 + 18.0000i 1.28681 + 0.742940i 0.978084 0.208212i \(-0.0667643\pi\)
0.308725 + 0.951151i \(0.400098\pi\)
\(588\) 0 0
\(589\) 6.00000 10.3923i 0.247226 0.428207i
\(590\) −33.4808 + 2.00962i −1.37838 + 0.0827347i
\(591\) 0 0
\(592\) −6.06218 + 0.500000i −0.249154 + 0.0205499i
\(593\) 42.0000i 1.72473i −0.506284 0.862367i \(-0.668981\pi\)
0.506284 0.862367i \(-0.331019\pi\)
\(594\) 0 0
\(595\) 44.7846 29.5692i 1.83599 1.21222i
\(596\) 8.00000 13.8564i 0.327693 0.567581i
\(597\) 0 0
\(598\) 1.00000i 0.0408930i
\(599\) −7.00000 + 12.1244i −0.286012 + 0.495388i −0.972854 0.231419i \(-0.925663\pi\)
0.686842 + 0.726807i \(0.258996\pi\)
\(600\) 0 0
\(601\) 17.5000 + 30.3109i 0.713840 + 1.23641i 0.963405 + 0.268049i \(0.0863789\pi\)
−0.249565 + 0.968358i \(0.580288\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 6.00000i 0.244339i
\(604\) −1.00000 1.73205i −0.0406894 0.0704761i
\(605\) −3.73205 + 2.46410i −0.151729 + 0.100180i
\(606\) 0 0
\(607\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) −2.59808 + 1.50000i −0.105366 + 0.0608330i
\(609\) 0 0
\(610\) −14.7846 22.3923i −0.598611 0.906638i
\(611\) −5.50000 + 9.52628i −0.222506 + 0.385392i
\(612\) 15.5885 9.00000i 0.630126 0.363803i
\(613\) −7.79423 + 4.50000i −0.314806 + 0.181753i −0.649075 0.760724i \(-0.724844\pi\)
0.334269 + 0.942478i \(0.391511\pi\)
\(614\) 16.0000 + 27.7128i 0.645707 + 1.11840i
\(615\) 0 0
\(616\) −6.00000 + 10.3923i −0.241747 + 0.418718i
\(617\) 15.5885 9.00000i 0.627568 0.362326i −0.152242 0.988343i \(-0.548649\pi\)
0.779809 + 0.626017i \(0.215316\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0.535898 + 8.92820i 0.0215222 + 0.358565i
\(621\) 0 0
\(622\) −20.7846 12.0000i −0.833387 0.481156i
\(623\) 60.0000i 2.40385i
\(624\) 0 0
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) −16.0000 + 27.7128i −0.639489 + 1.10763i
\(627\) 0 0
\(628\) 5.00000i 0.199522i
\(629\) 3.00000 + 36.3731i 0.119618 + 1.45029i
\(630\) −24.0000 12.0000i −0.956183 0.478091i
\(631\) 1.00000 + 1.73205i 0.0398094 + 0.0689519i 0.885244 0.465128i \(-0.153992\pi\)
−0.845434 + 0.534080i \(0.820658\pi\)
\(632\) 3.46410 + 2.00000i 0.137795 + 0.0795557i
\(633\) 0 0
\(634\) −4.50000 + 7.79423i −0.178718 + 0.309548i
\(635\) −17.0000 + 34.0000i −0.674624 + 1.34925i
\(636\) 0 0
\(637\) 9.00000i 0.356593i
\(638\) 15.5885 9.00000i 0.617153 0.356313i
\(639\) −18.0000 −0.712069
\(640\) 1.00000 2.00000i 0.0395285 0.0790569i
\(641\) −17.5000 30.3109i −0.691208 1.19721i −0.971442 0.237276i \(-0.923745\pi\)
0.280234 0.959932i \(-0.409588\pi\)
\(642\) 0 0
\(643\) 16.0000i 0.630978i −0.948929 0.315489i \(-0.897831\pi\)
0.948929 0.315489i \(-0.102169\pi\)
\(644\) 2.00000 + 3.46410i 0.0788110 + 0.136505i
\(645\) 0 0
\(646\) 9.00000 + 15.5885i 0.354100 + 0.613320i
\(647\) 42.4352 + 24.5000i 1.66830 + 0.963194i 0.968554 + 0.248805i \(0.0800377\pi\)
0.699748 + 0.714390i \(0.253296\pi\)
\(648\) −7.79423 4.50000i −0.306186 0.176777i
\(649\) −22.5000 38.9711i −0.883202 1.52975i
\(650\) 1.96410 4.59808i 0.0770384 0.180351i
\(651\) 0 0
\(652\) 6.00000i 0.234978i
\(653\) −21.6506 12.5000i −0.847255 0.489163i 0.0124688 0.999922i \(-0.496031\pi\)
−0.859724 + 0.510759i \(0.829364\pi\)
\(654\) 0 0
\(655\) −40.0000 20.0000i −1.56293 0.781465i
\(656\) −10.0000 −0.390434
\(657\) −5.19615 + 3.00000i −0.202721 + 0.117041i
\(658\) 44.0000i 1.71530i
\(659\) 13.5000 23.3827i 0.525885 0.910860i −0.473660 0.880708i \(-0.657067\pi\)
0.999545 0.0301523i \(-0.00959924\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) −11.2583 6.50000i −0.437567 0.252630i
\(663\) 0 0
\(664\) 3.00000 + 5.19615i 0.116423 + 0.201650i
\(665\) 12.0000 24.0000i 0.465340 0.930680i
\(666\) 15.0000 10.3923i 0.581238 0.402694i
\(667\) 6.00000i 0.232321i
\(668\) 6.92820 4.00000i 0.268060 0.154765i
\(669\) 0 0
\(670\) 3.73205 2.46410i 0.144182 0.0951966i
\(671\) 18.0000 31.1769i 0.694882 1.20357i
\(672\) 0 0
\(673\) −20.7846 12.0000i −0.801188 0.462566i 0.0426985 0.999088i \(-0.486405\pi\)
−0.843886 + 0.536522i \(0.819738\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 27.0000i 1.03769i 0.854867 + 0.518847i \(0.173639\pi\)
−0.854867 + 0.518847i \(0.826361\pi\)
\(678\) 0 0
\(679\) 4.00000 6.92820i 0.153506 0.265880i
\(680\) −12.0000 6.00000i −0.460179 0.230089i
\(681\) 0 0
\(682\) −10.3923 + 6.00000i −0.397942 + 0.229752i
\(683\) 22.5167 13.0000i 0.861576 0.497431i −0.00296369 0.999996i \(-0.500943\pi\)
0.864540 + 0.502564i \(0.167610\pi\)
\(684\) 4.50000 7.79423i 0.172062 0.298020i
\(685\) 7.39230 + 11.1962i 0.282445 + 0.427783i
\(686\) 4.00000 + 6.92820i 0.152721 + 0.264520i
\(687\) 0 0
\(688\) −1.73205 + 1.00000i −0.0660338 + 0.0381246i
\(689\) −10.0000 −0.380970
\(690\) 0 0
\(691\) 16.0000 + 27.7128i 0.608669 + 1.05425i 0.991460 + 0.130410i \(0.0416295\pi\)
−0.382791 + 0.923835i \(0.625037\pi\)
\(692\) 5.00000i 0.190071i
\(693\) 36.0000i 1.36753i
\(694\) 15.0000 + 25.9808i 0.569392 + 0.986216i
\(695\) −10.0000 5.00000i −0.379322 0.189661i
\(696\) 0 0
\(697\) 60.0000i 2.27266i
\(698\) −5.19615 3.00000i −0.196677 0.113552i
\(699\) 0 0
\(700\) 2.39230 + 19.8564i 0.0904206 + 0.750502i
\(701\) 8.00000 + 13.8564i 0.302156 + 0.523349i 0.976624 0.214955i \(-0.0689604\pi\)
−0.674468 + 0.738304i \(0.735627\pi\)
\(702\) 0 0
\(703\) 10.3923 + 15.0000i 0.391953 + 0.565736i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) 9.00000 15.5885i 0.338719 0.586679i
\(707\) 13.8564 + 8.00000i 0.521124 + 0.300871i
\(708\) 0 0
\(709\) 16.0000 0.600893 0.300446 0.953799i \(-0.402864\pi\)
0.300446 + 0.953799i \(0.402864\pi\)
\(710\) 7.39230 + 11.1962i 0.277428 + 0.420184i
\(711\) −12.0000 −0.450035
\(712\) 12.9904 7.50000i 0.486835 0.281074i
\(713\) 4.00000i 0.149801i
\(714\) 0 0
\(715\) 6.69615 0.401924i 0.250422 0.0150311i
\(716\) −0.500000 + 0.866025i −0.0186859 + 0.0323649i
\(717\) 0 0
\(718\) −22.5167 + 13.0000i −0.840314 + 0.485156i
\(719\) 19.0000 + 32.9090i 0.708580 + 1.22730i 0.965384 + 0.260834i \(0.0839974\pi\)
−0.256803 + 0.966464i \(0.582669\pi\)
\(720\) 0.401924 + 6.69615i 0.0149788 + 0.249551i
\(721\) 18.0000 31.1769i 0.670355 1.16109i
\(722\) −8.66025 5.00000i −0.322301 0.186081i
\(723\) 0 0
\(724\) −8.00000 13.8564i −0.297318 0.514969i
\(725\) 11.7846 27.5885i 0.437669 1.02461i
\(726\) 0 0
\(727\) −37.2391 21.5000i −1.38112 0.797391i −0.388829 0.921310i \(-0.627120\pi\)
−0.992292 + 0.123919i \(0.960454\pi\)
\(728\) −3.46410 + 2.00000i −0.128388 + 0.0741249i
\(729\) 27.0000 1.00000
\(730\) 4.00000 + 2.00000i 0.148047 + 0.0740233i
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) 32.0429 + 18.5000i 1.18353 + 0.683313i 0.956829 0.290651i \(-0.0938717\pi\)
0.226704 + 0.973964i \(0.427205\pi\)
\(734\) 13.0000 0.479839
\(735\) 0 0
\(736\) 0.500000 0.866025i 0.0184302 0.0319221i
\(737\) 5.19615 + 3.00000i 0.191403 + 0.110506i
\(738\) 25.9808 15.0000i 0.956365 0.552158i
\(739\) −15.0000 −0.551784 −0.275892 0.961189i \(-0.588973\pi\)
−0.275892 + 0.961189i \(0.588973\pi\)
\(740\) −12.6244 5.06218i −0.464081 0.186089i
\(741\) 0 0
\(742\) 34.6410 20.0000i 1.27171 0.734223i
\(743\) 35.5070 + 20.5000i 1.30263 + 0.752072i 0.980854 0.194745i \(-0.0623879\pi\)
0.321773 + 0.946817i \(0.395721\pi\)
\(744\) 0 0
\(745\) 29.8564 19.7128i 1.09385 0.722222i
\(746\) −23.0000 −0.842090
\(747\) −15.5885 9.00000i −0.570352 0.329293i
\(748\) 18.0000i 0.658145i
\(749\) 16.0000 + 27.7128i 0.584627 + 1.01260i
\(750\) 0 0
\(751\) 10.0000 0.364905 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(752\) −9.52628 + 5.50000i −0.347388 + 0.200564i
\(753\) 0 0
\(754\) 6.00000 0.218507
\(755\) −0.267949 4.46410i −0.00975167 0.162465i
\(756\) 0 0
\(757\) 25.1147 14.5000i 0.912811 0.527011i 0.0314762 0.999505i \(-0.489979\pi\)
0.881334 + 0.472493i \(0.156646\pi\)
\(758\) 20.7846 + 12.0000i 0.754931 + 0.435860i
\(759\) 0 0
\(760\) −6.69615 + 0.401924i −0.242895 + 0.0145793i
\(761\) −0.500000 0.866025i −0.0181250 0.0313934i 0.856821 0.515615i \(-0.172436\pi\)
−0.874946 + 0.484221i \(0.839103\pi\)
\(762\) 0 0
\(763\) 40.0000i 1.44810i
\(764\) 2.00000 3.46410i 0.0723575 0.125327i
\(765\) 40.1769 2.41154i 1.45260 0.0871895i
\(766\) −17.0000 −0.614235
\(767\) 15.0000i 0.541619i
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) −22.3923 + 14.7846i −0.806963 + 0.532800i
\(771\) 0 0
\(772\) −13.8564 8.00000i −0.498703 0.287926i
\(773\) 7.79423 + 4.50000i 0.280339 + 0.161854i 0.633577 0.773680i \(-0.281586\pi\)
−0.353238 + 0.935534i \(0.614919\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) −7.85641 + 18.3923i −0.282210 + 0.660671i
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) 4.00000i 0.143407i
\(779\) 15.0000 + 25.9808i 0.537431 + 0.930857i
\(780\) 0 0
\(781\) −9.00000 + 15.5885i −0.322045 + 0.557799i
\(782\) −5.19615 3.00000i −0.185814 0.107280i
\(783\) 0 0
\(784\) 4.50000 7.79423i 0.160714 0.278365i
\(785\) −5.00000 + 10.0000i −0.178458 + 0.356915i