Properties

Label 370.2.n.b.269.2
Level $370$
Weight $2$
Character 370.269
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 269.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 370.269
Dual form 370.2.n.b.359.2

$q$-expansion

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

Character values

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

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.133975 + 2.23205i 0.0599153 + 0.998203i
\(6\) 0 0
\(7\) 3.46410 2.00000i 1.30931 0.755929i 0.327327 0.944911i \(-0.393852\pi\)
0.981981 + 0.188982i \(0.0605189\pi\)
\(8\) 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 \(-0.622382\pi\)
0.615265 + 0.788320i \(0.289049\pi\)
\(14\) 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 \(-0.0739659\pi\)
0.287129 + 0.957892i \(0.407299\pi\)
\(18\) −2.59808 + 1.50000i −0.612372 + 0.353553i
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) −1.86603 + 1.23205i −0.417256 + 0.275495i
\(21\) 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
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) 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
\(35\) 4.92820 + 7.46410i 0.833018 + 1.26166i
\(36\) −3.00000 −0.500000
\(37\) −2.59808 5.50000i −0.427121 0.904194i
\(38\) 3.00000i 0.486664i
\(39\) 0 0
\(40\) −2.23205 + 0.133975i −0.352918 + 0.0211832i
\(41\) 5.00000 + 8.66025i 0.780869 + 1.35250i 0.931436 + 0.363905i \(0.118557\pi\)
−0.150567 + 0.988600i \(0.548110\pi\)
\(42\) 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
\(50\) −4.59808 1.96410i −0.650266 0.277766i
\(51\) 0 0
\(52\) 0.866025 + 0.500000i 0.120096 + 0.0693375i
\(53\) −8.66025 5.00000i −1.18958 0.686803i −0.231367 0.972867i \(-0.574320\pi\)
−0.958211 + 0.286064i \(0.907653\pi\)
\(54\) 0 0
\(55\) −0.401924 6.69615i −0.0541954 0.902909i
\(56\) 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 0.301239 0.953549i \(-0.402600\pi\)
0.675178 0.737655i \(-0.264067\pi\)
\(60\) 0 0
\(61\) −6.00000 10.3923i −0.768221 1.33060i −0.938527 0.345207i \(-0.887809\pi\)
0.170305 0.985391i \(-0.445525\pi\)
\(62\) −3.46410 2.00000i −0.439941 0.254000i
\(63\) 12.0000i 1.51186i
\(64\) −1.00000 −0.125000
\(65\) 1.23205 + 1.86603i 0.152817 + 0.231452i
\(66\) 0 0
\(67\) 1.73205 1.00000i 0.211604 0.122169i −0.390453 0.920623i \(-0.627682\pi\)
0.602056 + 0.798454i \(0.294348\pi\)
\(68\) 6.00000i 0.727607i
\(69\) 0 0
\(70\) 0.535898 + 8.92820i 0.0640521 + 1.06712i
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) −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 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) −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 \(-0.440144\pi\)
−0.757290 + 0.653079i \(0.773477\pi\)
\(84\) 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 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) −3.69615 5.59808i −0.389609 0.590089i
\(91\) 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
\(95\) 5.59808 3.69615i 0.574351 0.379217i
\(96\) 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 \(-0.540283\pi\)
0.795991 + 0.605308i \(0.206950\pi\)
\(108\) 0 0
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) 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 \(-0.489209\pi\)
−0.848581 + 0.529065i \(0.822543\pi\)
\(114\) 0 0
\(115\) 2.23205 0.133975i 0.208140 0.0124932i
\(116\) 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 \(-0.0613325\pi\)
0.324910 + 0.945745i \(0.394666\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0.133975 + 2.23205i 0.0117503 + 0.195764i
\(131\) −10.0000 + 17.3205i −0.873704 + 1.51330i −0.0155672 + 0.999879i \(0.504955\pi\)
−0.858137 + 0.513421i \(0.828378\pi\)
\(132\) 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 −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) −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
\(145\) 0.803848 + 13.3923i 0.0667559 + 1.11217i
\(146\) 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 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) 2.59808 1.50000i 0.210732 0.121666i
\(153\) −15.5885 + 9.00000i −1.26025 + 0.727607i
\(154\) −12.0000 −0.966988
\(155\) −0.535898 8.92820i −0.0430444 0.717131i
\(156\) 0 0
\(157\) 4.33013 + 2.50000i 0.345582 + 0.199522i 0.662738 0.748852i \(-0.269394\pi\)
−0.317156 + 0.948373i \(0.602728\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 0 0
\(160\) −1.23205 1.86603i −0.0974022 0.147522i
\(161\) −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 \(-0.257831\pi\)
−0.282503 + 0.959266i \(0.591165\pi\)
\(164\) −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 \(-0.766838\pi\)
0.207385 + 0.978259i \(0.433505\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) −11.1962 + 7.39230i −0.858706 + 0.566964i
\(171\) 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 \(-0.272461\pi\)
−0.326278 + 0.945274i \(0.605795\pi\)
\(174\) 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 \(0.511899\pi\)
\(180\) −0.401924 6.69615i −0.0299576 0.499102i
\(181\) 8.00000 + 13.8564i 0.594635 + 1.02994i 0.993598 + 0.112972i \(0.0360369\pi\)
−0.398963 + 0.916967i \(0.630630\pi\)
\(182\) 3.46410 2.00000i 0.256776 0.148250i
\(183\) 0 0
\(184\) 1.00000 0.0737210
\(185\) 11.9282 6.53590i 0.876979 0.480529i
\(186\) 0 0
\(187\) −15.5885 9.00000i −1.13994 0.658145i
\(188\) 9.52628 5.50000i 0.694775 0.401129i
\(189\) 0 0
\(190\) 6.69615 0.401924i 0.485790 0.0291586i
\(191\) 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 \(-0.0466543\pi\)
0.368161 + 0.929762i \(0.379988\pi\)
\(198\) 7.79423 4.50000i 0.553912 0.319801i
\(199\) −22.0000 −1.55954 −0.779769 0.626067i \(-0.784664\pi\)
−0.779769 + 0.626067i \(0.784664\pi\)
\(200\) −0.598076 4.96410i −0.0422904 0.351015i
\(201\) 0 0
\(202\) −3.46410 2.00000i −0.243733 0.140720i
\(203\) 20.7846 12.0000i 1.45879 0.842235i
\(204\) 0 0
\(205\) −18.6603 + 12.3205i −1.30329 + 0.860502i
\(206\) −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
\(215\) 4.46410 0.267949i 0.304449 0.0182740i
\(216\) 0 0
\(217\) −13.8564 + 8.00000i −0.940634 + 0.543075i
\(218\) 8.66025 5.00000i 0.586546 0.338643i
\(219\) 0 0
\(220\) 5.59808 3.69615i 0.377422 0.249195i
\(221\) 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
\(225\) 5.89230 13.7942i 0.392820 0.919615i
\(226\) −5.00000 8.66025i −0.332595 0.576072i
\(227\) −24.2487 + 14.0000i −1.60944 + 0.929213i −0.619949 + 0.784642i \(0.712847\pi\)
−0.989494 + 0.144571i \(0.953820\pi\)
\(228\) 0 0
\(229\) 1.00000 + 1.73205i 0.0660819 + 0.114457i 0.897173 0.441679i \(-0.145617\pi\)
−0.831092 + 0.556136i \(0.812283\pi\)
\(230\) 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
\(235\) 24.5526 1.47372i 1.60163 0.0961349i
\(236\) 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 0.337026 + 0.941495i \(0.390579\pi\)
−0.983872 + 0.178875i \(0.942754\pi\)
\(240\) 0 0
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) −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
\(250\) 3.76795 10.5263i 0.238306 0.665740i
\(251\) −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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 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 \(-0.865884\pi\)
−0.102084 + 0.994776i \(0.532551\pi\)
\(264\) 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 −0.384201 0.923249i \(-0.625523\pi\)
0.991658 0.128897i \(-0.0411435\pi\)
\(272\) −5.19615 + 3.00000i −0.315063 + 0.181902i
\(273\) 0 0
\(274\) −3.00000 + 5.19615i −0.181237 + 0.313911i
\(275\) 14.8923 1.79423i 0.898040 0.108196i
\(276\) 0 0
\(277\) −5.19615 + 3.00000i −0.312207 + 0.180253i −0.647913 0.761714i \(-0.724358\pi\)
0.335707 + 0.941966i \(0.391025\pi\)
\(278\) −4.33013 + 2.50000i −0.259704 + 0.149940i
\(279\) 6.00000 10.3923i 0.359211 0.622171i
\(280\) −7.46410 + 4.92820i −0.446065 + 0.294516i
\(281\) 1.50000 2.59808i 0.0894825 0.154988i −0.817810 0.575488i \(-0.804812\pi\)
0.907293 + 0.420500i \(0.138145\pi\)
\(282\) 0 0
\(283\) −3.46410 + 2.00000i −0.205919 + 0.118888i −0.599414 0.800439i \(-0.704600\pi\)
0.393494 + 0.919327i \(0.371266\pi\)
\(284\) −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 \(-0.694596\pi\)
0.422186 + 0.906509i \(0.361263\pi\)
\(294\) 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
\(305\) 22.3923 14.7846i 1.28218 0.846564i
\(306\) −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 −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) −27.7128 16.0000i −1.56642 0.904373i −0.996581 0.0826174i \(-0.973672\pi\)
−0.569839 0.821756i \(-0.692995\pi\)
\(314\) 2.50000 + 4.33013i 0.141083 + 0.244363i
\(315\) −26.7846 + 1.60770i −1.50914 + 0.0905834i
\(316\) −2.00000 + 3.46410i −0.112509 + 0.194871i
\(317\) −7.79423 4.50000i −0.437767 0.252745i 0.264883 0.964281i \(-0.414667\pi\)
−0.702650 + 0.711535i \(0.748000\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) −0.133975 2.23205i −0.00748941 0.124775i
\(321\) 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 −0.630232 0.776407i \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503735\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 18.1865 + 1.50000i 0.996616 + 0.0821995i
\(334\) −8.00000 −0.437741
\(335\) 2.46410 + 3.73205i 0.134628 + 0.203904i
\(336\) 0 0
\(337\) 6.92820 4.00000i 0.377403 0.217894i −0.299285 0.954164i \(-0.596748\pi\)
0.676688 + 0.736270i \(0.263415\pi\)
\(338\) −10.3923 + 6.00000i −0.565267 + 0.326357i
\(339\) 0 0
\(340\) −13.3923 + 0.803848i −0.726300 + 0.0435948i
\(341\) 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 −0.774493 0.632583i \(-0.781995\pi\)
0.935079 + 0.354439i \(0.115328\pi\)
\(350\) −19.8564 + 2.39230i −1.06137 + 0.127874i
\(351\) 0 0
\(352\) 2.59808 1.50000i 0.138478 0.0799503i
\(353\) 15.5885 + 9.00000i 0.829690 + 0.479022i 0.853746 0.520689i \(-0.174325\pi\)
−0.0240566 + 0.999711i \(0.507658\pi\)
\(354\) 0 0
\(355\) −11.1962 + 7.39230i −0.594230 + 0.392343i
\(356\) −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
\(365\) 4.46410 0.267949i 0.233662 0.0140251i
\(366\) 0 0
\(367\) 11.2583 6.50000i 0.587680 0.339297i −0.176500 0.984301i \(-0.556477\pi\)
0.764180 + 0.645003i \(0.223144\pi\)
\(368\) 0.866025 + 0.500000i 0.0451447 + 0.0260643i
\(369\) −30.0000 −1.56174
\(370\) 13.5981 + 0.303848i 0.706930 + 0.0157963i
\(371\) −40.0000 −2.07670
\(372\) 0 0
\(373\) −19.9186 + 11.5000i −1.03135 + 0.595447i −0.917370 0.398036i \(-0.869692\pi\)
−0.113975 + 0.993484i \(0.536359\pi\)
\(374\) −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 0.373739 + 0.927534i \(0.378076\pi\)
−0.990137 + 0.140100i \(0.955258\pi\)
\(380\) 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 \(-0.809681\pi\)
0.0742364 + 0.997241i \(0.476348\pi\)
\(384\) 0 0
\(385\) −14.7846 22.3923i −0.753493 1.14122i
\(386\) 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 0.810859 0.585241i \(-0.199000\pi\)
−0.912263 + 0.409604i \(0.865667\pi\)
\(390\) 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
\(395\) −7.46410 + 4.92820i −0.375560 + 0.247965i
\(396\) 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
\(400\) 1.96410 4.59808i 0.0982051 0.229904i
\(401\) 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
\(405\) 16.7942 11.0885i 0.834512 0.550990i
\(406\) 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 0.454759 + 0.890614i \(0.349725\pi\)
−0.998674 + 0.0514740i \(0.983608\pi\)
\(410\) −22.3205 + 1.33975i −1.10233 + 0.0661653i
\(411\) 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 0.380464 + 0.924796i \(0.375764\pi\)
−0.991129 + 0.132907i \(0.957569\pi\)
\(420\) 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
\(425\) −27.5885 11.7846i −1.33824 0.571638i
\(426\) 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 0.991817 0.127666i \(-0.0407486\pi\)
−0.606471 + 0.795106i \(0.707415\pi\)
\(432\) 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 0.841175 0.540763i \(-0.181865\pi\)
−0.888902 + 0.458097i \(0.848531\pi\)
\(440\) 6.69615 0.401924i 0.319227 0.0191610i
\(441\) 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 −0.965637 0.259895i \(-0.916312\pi\)
0.257743 0.966213i \(-0.417021\pi\)
\(450\) 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 \(-0.458593\pi\)
0.923567 + 0.383437i \(0.125260\pi\)
\(458\) 2.00000i 0.0934539i
\(459\) 0 0
\(460\) 1.23205 + 1.86603i 0.0574447 + 0.0870039i
\(461\) −18.0000 + 31.1769i −0.838344 + 1.45205i 0.0529352 + 0.998598i \(0.483142\pi\)
−0.891279 + 0.453456i \(0.850191\pi\)
\(462\) 0 0
\(463\) −6.92820 + 4.00000i −0.321981 + 0.185896i −0.652275 0.757982i \(-0.726185\pi\)
0.330294 + 0.943878i \(0.392852\pi\)
\(464\) −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 −0.789314 0.613990i \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 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
\(485\) −4.46410 + 0.267949i −0.202704 + 0.0121669i
\(486\) 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
\(490\) 11.0885 + 16.7942i 0.500925 + 0.758686i
\(491\) 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 0.915756 + 0.401735i \(0.131593\pi\)
−0.109965 + 0.993935i \(0.535074\pi\)
\(500\) 8.52628 7.23205i 0.381307 0.323427i
\(501\) 0 0
\(502\) −0.866025 0.500000i −0.0386526 0.0223161i
\(503\) 13.8564 + 8.00000i 0.617827 + 0.356702i 0.776022 0.630705i \(-0.217234\pi\)
−0.158196 + 0.987408i \(0.550568\pi\)
\(504\) −12.0000 −0.534522
\(505\) −0.535898 8.92820i −0.0238472 0.397300i
\(506\) −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 0.123187 + 0.992384i \(0.460689\pi\)
−0.921023 + 0.389509i \(0.872645\pi\)
\(510\) 0 0
\(511\) −4.00000 6.92820i −0.176950 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 0 0
\(515\) −20.0885 + 1.20577i −0.885203 + 0.0531326i
\(516\) 0 0
\(517\) 33.0000i 1.45134i
\(518\) −10.3923 22.0000i −0.456612 0.966625i
\(519\) 0 0
\(520\) −1.86603 + 1.23205i −0.0818306 + 0.0540290i
\(521\) −2.50000 4.33013i −0.109527 0.189706i 0.806052 0.591845i \(-0.201600\pi\)
−0.915579 + 0.402139i \(0.868267\pi\)
\(522\) −15.5885 + 9.00000i −0.682288 + 0.393919i
\(523\) −13.8564 + 8.00000i −0.605898 + 0.349816i −0.771358 0.636401i \(-0.780422\pi\)
0.165460 + 0.986216i \(0.447089\pi\)
\(524\) −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
\(530\) 18.6603 12.3205i 0.810550 0.535169i
\(531\) 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
\(535\) 9.85641 + 14.9282i 0.426130 + 0.645403i
\(536\) 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
\(550\) 13.7942 + 5.89230i 0.588188 + 0.251249i
\(551\) −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 \(-0.0869053\pi\)
0.247964 + 0.968769i \(0.420239\pi\)
\(558\) 10.3923 6.00000i 0.439941 0.254000i
\(559\) −1.00000 1.73205i −0.0422955 0.0732579i
\(560\) −8.92820 + 0.535898i −0.377285 + 0.0226458i
\(561\) 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 −0.969378 0.245573i \(-0.921024\pi\)
0.697362 + 0.716720i \(0.254357\pi\)
\(572\) −2.59808 1.50000i −0.108631 0.0627182i
\(573\) 0 0
\(574\) 20.0000 + 34.6410i 0.834784 + 1.44589i
\(575\) 0.598076 + 4.96410i 0.0249415 + 0.207017i
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) 17.3205 + 10.0000i 0.721062 + 0.416305i 0.815144 0.579259i \(-0.196658\pi\)
−0.0940813 + 0.995565i \(0.529991\pi\)
\(578\) 19.0000i 0.790296i
\(579\) 0 0
\(580\) −11.1962 + 7.39230i −0.464895 + 0.306949i
\(581\) −24.0000 −0.995688
\(582\) 0 0
\(583\) 25.9808 + 15.0000i 1.07601 + 0.621237i
\(584\) 2.00000 0.0827606
\(585\) −6.69615 + 0.401924i −0.276852 + 0.0166175i
\(586\) −3.00000 −0.123929
\(587\) −31.1769 + 18.0000i −1.28681 + 0.742940i −0.978084 0.208212i \(-0.933236\pi\)
−0.308725 + 0.951151i \(0.599902\pi\)
\(588\) 0 0
\(589\) 6.00000 + 10.3923i 0.247226 + 0.428207i
\(590\) 18.4808 + 27.9904i 0.760841 + 1.15235i
\(591\) 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
\(595\) 3.21539 + 53.5692i 0.131818 + 2.19612i
\(596\) 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 0.686842 0.726807i \(-0.258996\pi\)
−0.972854 + 0.231419i \(0.925663\pi\)
\(600\) 0 0
\(601\) 17.5000 30.3109i 0.713840 1.23641i −0.249565 0.968358i \(-0.580288\pi\)
0.963405 0.268049i \(-0.0863789\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 6.00000i 0.244339i
\(604\) −1.00000 + 1.73205i −0.0406894 + 0.0704761i
\(605\) −0.267949 4.46410i −0.0108937 0.181492i
\(606\) 0 0
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 2.59808 + 1.50000i 0.105366 + 0.0608330i
\(609\) 0 0
\(610\) 26.7846 1.60770i 1.08448 0.0650937i
\(611\) −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 \(-0.275156\pi\)
−0.334269 + 0.942478i \(0.608489\pi\)
\(614\) 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 \(-0.451351\pi\)
−0.779809 + 0.626017i \(0.784684\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 7.46410 4.92820i 0.299766 0.197921i
\(621\) 0 0
\(622\) 20.7846 12.0000i 0.833387 0.481156i
\(623\) 60.0000i 2.40385i
\(624\) 0 0
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −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 −0.845434 0.534080i \(-0.820658\pi\)
0.885244 + 0.465128i \(0.153992\pi\)
\(632\) −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 0.280234 + 0.959932i \(0.409588\pi\)
−0.971442 + 0.237276i \(0.923745\pi\)
\(642\) 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 −0.699748 + 0.714390i \(0.746704\pi\)
−0.968554 + 0.248805i \(0.919962\pi\)
\(648\) 7.79423 4.50000i 0.306186 0.176777i
\(649\) −22.5000 + 38.9711i −0.883202 + 1.52975i
\(650\) −4.96410 + 0.598076i −0.194708 + 0.0234585i
\(651\) 0 0
\(652\) 6.00000i 0.234978i
\(653\) 21.6506 12.5000i 0.847255 0.489163i −0.0124688 0.999922i \(-0.503969\pi\)
0.859724 + 0.510759i \(0.170636\pi\)
\(654\) 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 0.999545 + 0.0301523i \(0.00959924\pi\)
−0.473660 + 0.880708i \(0.657067\pi\)
\(660\) 0 0
\(661\) −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i \(-0.952854\pi\)
0.366723 0.930330i \(-0.380480\pi\)
\(662\) 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
\(670\) 0.267949 + 4.46410i 0.0103518 + 0.172463i
\(671\) 18.0000 + 31.1769i 0.694882 + 1.20357i
\(672\) 0 0
\(673\) 20.7846 12.0000i 0.801188 0.462566i −0.0426985 0.999088i \(-0.513595\pi\)
0.843886 + 0.536522i \(0.180262\pi\)
\(674\) 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 \(-0.499057\pi\)
−0.864540 + 0.502564i \(0.832390\pi\)
\(684\) 4.50000 + 7.79423i 0.172062 + 0.298020i
\(685\) −13.3923 + 0.803848i −0.511694 + 0.0307134i
\(686\) 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 −0.382791 0.923835i \(-0.625037\pi\)
0.991460 0.130410i \(-0.0416295\pi\)
\(692\) 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
\(700\) −18.3923 7.85641i −0.695164 0.296944i
\(701\) 8.00000 13.8564i 0.302156 0.523349i −0.674468 0.738304i \(-0.735627\pi\)
0.976624 + 0.214955i \(0.0689604\pi\)
\(702\) 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 \(0.402864\pi\)
\(710\) −13.3923 + 0.803848i −0.502604 + 0.0301679i
\(711\) −12.0000 −0.450035
\(712\) −12.9904 7.50000i −0.486835 0.281074i
\(713\) 4.00000i 0.149801i
\(714\) 0 0
\(715\) −3.69615 5.59808i −0.138228 0.209356i
\(716\) −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 −0.256803 0.966464i \(-0.582669\pi\)
0.965384 0.260834i \(-0.0839974\pi\)
\(720\) 5.59808 3.69615i 0.208628 0.137747i
\(721\) 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
\(725\) −29.7846 + 3.58846i −1.10617 + 0.133272i
\(726\) 0 0
\(727\) 37.2391 21.5000i 1.38112 0.797391i 0.388829 0.921310i \(-0.372880\pi\)
0.992292 + 0.123919i \(0.0395463\pi\)
\(728\) 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 \(-0.906128\pi\)
−0.226704 + 0.973964i \(0.572795\pi\)
\(734\) 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 \(0.588973\pi\)
\(740\) 11.6244 + 7.06218i 0.427320 + 0.259611i
\(741\) 0 0
\(742\) −34.6410 20.0000i −1.27171 0.734223i
\(743\) −35.5070 + 20.5000i −1.30263 + 0.752072i −0.980854 0.194745i \(-0.937612\pi\)
−0.321773 + 0.946817i \(0.604279\pi\)
\(744\) 0 0
\(745\) 2.14359 + 35.7128i 0.0785352 + 1.30842i
\(746\) −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
\(755\) −3.73205 + 2.46410i −0.135823 + 0.0896778i
\(756\) 0 0
\(757\) −25.1147 14.5000i −0.912811 0.527011i −0.0314762 0.999505i \(-0.510021\pi\)
−0.881334 + 0.472493i \(0.843354\pi\)
\(758\) −20.7846 + 12.0000i −0.754931 + 0.435860i
\(759\) 0 0
\(760\) 3.69615 + 5.59808i 0.134074 + 0.203064i
\(761\) −0.500000 + 0.866025i −0.0181250 + 0.0313934i −0.874946 0.484221i \(-0.839103\pi\)
0.856821 + 0.515615i \(0.172436\pi\)
\(762\) 0 0
\(763\) 40.0000i 1.44810i
\(764\) 2.00000 + 3.46410i 0.0723575 + 0.125327i
\(765\) −22.1769 33.5885i −0.801808 1.21439i
\(766\) −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 \(0.629834\pi\)
\(770\) −1.60770 26.7846i −0.0579373 0.965250i
\(771\) 0 0
\(772\) 13.8564 8.00000i 0.498703 0.287926i
\(773\) −7.79423 + 4.50000i −0.280339 + 0.161854i −0.633577 0.773680i \(-0.718414\pi\)
0.353238 + 0.935534i \(0.385081\pi\)
\(774\) 3.00000 + 5.19615i 0.107833 + 0.186772i
\(775\) 19.8564 2.39230i 0.713263 0.0859341i
\(776\) −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