Properties

Label 1950.2.z.m.1699.2
Level $1950$
Weight $2$
Character 1950.1699
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
Defining polynomial: \(x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1699.2
Root \(1.35234 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1699
Dual form 1950.2.z.m.1849.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(0.486319 - 0.280776i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(0.486319 - 0.280776i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.78078 + 3.08440i) q^{11} +1.00000i q^{12} +(-1.35234 + 3.34233i) q^{13} -0.561553 q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.43674 - 2.56155i) q^{17} -1.00000i q^{18} +(-3.28078 - 5.68247i) q^{19} +0.561553 q^{21} +(3.08440 - 1.78078i) q^{22} +(4.05703 + 2.34233i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.84233 - 2.21837i) q^{26} +1.00000i q^{27} +(0.486319 + 0.280776i) q^{28} +(-3.56155 + 6.16879i) q^{29} +4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.08440 + 1.78078i) q^{33} -5.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(3.08440 + 1.78078i) q^{37} +6.56155i q^{38} +(-2.84233 + 2.21837i) q^{39} +(-2.56155 + 4.43674i) q^{41} +(-0.486319 - 0.280776i) q^{42} +(-3.95042 + 2.28078i) q^{43} -3.56155 q^{44} +(-2.34233 - 4.05703i) q^{46} +4.00000i q^{47} +(-0.866025 + 0.500000i) q^{48} +(-3.34233 + 5.78908i) q^{49} +5.12311 q^{51} +(-3.57071 + 0.500000i) q^{52} +12.2462i q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.280776 - 0.486319i) q^{56} -6.56155i q^{57} +(6.16879 - 3.56155i) q^{58} +(3.12311 + 5.40938i) q^{59} +(-5.34233 - 9.25319i) q^{61} +(-3.46410 - 2.00000i) q^{62} +(0.486319 + 0.280776i) q^{63} -1.00000 q^{64} +3.56155 q^{66} +(7.62775 + 4.40388i) q^{67} +(4.43674 + 2.56155i) q^{68} +(2.34233 + 4.05703i) q^{69} +(-4.21922 - 7.30791i) q^{71} +(0.866025 - 0.500000i) q^{72} -9.00000i q^{73} +(-1.78078 - 3.08440i) q^{74} +(3.28078 - 5.68247i) q^{76} +2.00000i q^{77} +(3.57071 - 0.500000i) q^{78} -4.80776 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.43674 - 2.56155i) q^{82} -2.43845i q^{83} +(0.280776 + 0.486319i) q^{84} +4.56155 q^{86} +(-6.16879 + 3.56155i) q^{87} +(3.08440 + 1.78078i) q^{88} +(-3.12311 + 5.40938i) q^{89} +(0.280776 + 2.00514i) q^{91} +4.68466i q^{92} +(3.46410 + 2.00000i) q^{93} +(2.00000 - 3.46410i) q^{94} +1.00000 q^{96} +(15.4220 - 8.90388i) q^{97} +(5.78908 - 3.34233i) q^{98} -3.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} - 6q^{11} + 12q^{14} - 4q^{16} - 18q^{19} - 12q^{21} + 4q^{24} - 2q^{26} - 12q^{29} + 32q^{31} - 8q^{34} - 4q^{36} + 2q^{39} - 4q^{41} - 12q^{44} + 6q^{46} - 2q^{49} + 8q^{51} + 4q^{54} + 6q^{56} - 8q^{59} - 18q^{61} - 8q^{64} + 12q^{66} - 6q^{69} - 42q^{71} - 6q^{74} + 18q^{76} + 44q^{79} - 4q^{81} - 6q^{84} + 20q^{86} + 8q^{89} - 6q^{91} + 16q^{94} + 8q^{96} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 0.486319 0.280776i 0.183811 0.106124i −0.405271 0.914197i \(-0.632823\pi\)
0.589082 + 0.808073i \(0.299489\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.78078 + 3.08440i −0.536924 + 0.929980i 0.462143 + 0.886805i \(0.347081\pi\)
−0.999068 + 0.0431749i \(0.986253\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −1.35234 + 3.34233i −0.375073 + 0.926995i
\(14\) −0.561553 −0.150081
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 4.43674 2.56155i 1.07607 0.621268i 0.146235 0.989250i \(-0.453285\pi\)
0.929833 + 0.367982i \(0.119951\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.28078 5.68247i −0.752662 1.30365i −0.946528 0.322620i \(-0.895436\pi\)
0.193867 0.981028i \(-0.437897\pi\)
\(20\) 0 0
\(21\) 0.561553 0.122541
\(22\) 3.08440 1.78078i 0.657595 0.379663i
\(23\) 4.05703 + 2.34233i 0.845950 + 0.488409i 0.859282 0.511502i \(-0.170911\pi\)
−0.0133324 + 0.999911i \(0.504244\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) 2.84233 2.21837i 0.557427 0.435058i
\(27\) 1.00000i 0.192450i
\(28\) 0.486319 + 0.280776i 0.0919057 + 0.0530618i
\(29\) −3.56155 + 6.16879i −0.661364 + 1.14552i 0.318894 + 0.947790i \(0.396689\pi\)
−0.980257 + 0.197725i \(0.936645\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −3.08440 + 1.78078i −0.536924 + 0.309993i
\(34\) −5.12311 −0.878605
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 3.08440 + 1.78078i 0.507071 + 0.292758i 0.731629 0.681703i \(-0.238760\pi\)
−0.224558 + 0.974461i \(0.572094\pi\)
\(38\) 6.56155i 1.06442i
\(39\) −2.84233 + 2.21837i −0.455137 + 0.355223i
\(40\) 0 0
\(41\) −2.56155 + 4.43674i −0.400047 + 0.692902i −0.993731 0.111796i \(-0.964340\pi\)
0.593684 + 0.804698i \(0.297673\pi\)
\(42\) −0.486319 0.280776i −0.0750407 0.0433247i
\(43\) −3.95042 + 2.28078i −0.602433 + 0.347815i −0.769998 0.638046i \(-0.779743\pi\)
0.167565 + 0.985861i \(0.446410\pi\)
\(44\) −3.56155 −0.536924
\(45\) 0 0
\(46\) −2.34233 4.05703i −0.345358 0.598177i
\(47\) 4.00000i 0.583460i 0.956501 + 0.291730i \(0.0942309\pi\)
−0.956501 + 0.291730i \(0.905769\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) −3.34233 + 5.78908i −0.477476 + 0.827012i
\(50\) 0 0
\(51\) 5.12311 0.717378
\(52\) −3.57071 + 0.500000i −0.495169 + 0.0693375i
\(53\) 12.2462i 1.68215i 0.540921 + 0.841073i \(0.318076\pi\)
−0.540921 + 0.841073i \(0.681924\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) −0.280776 0.486319i −0.0375203 0.0649871i
\(57\) 6.56155i 0.869099i
\(58\) 6.16879 3.56155i 0.810002 0.467655i
\(59\) 3.12311 + 5.40938i 0.406594 + 0.704241i 0.994506 0.104684i \(-0.0333831\pi\)
−0.587912 + 0.808925i \(0.700050\pi\)
\(60\) 0 0
\(61\) −5.34233 9.25319i −0.684015 1.18475i −0.973745 0.227641i \(-0.926899\pi\)
0.289730 0.957108i \(-0.406434\pi\)
\(62\) −3.46410 2.00000i −0.439941 0.254000i
\(63\) 0.486319 + 0.280776i 0.0612704 + 0.0353745i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 3.56155 0.438397
\(67\) 7.62775 + 4.40388i 0.931878 + 0.538020i 0.887405 0.460991i \(-0.152506\pi\)
0.0444727 + 0.999011i \(0.485839\pi\)
\(68\) 4.43674 + 2.56155i 0.538034 + 0.310634i
\(69\) 2.34233 + 4.05703i 0.281983 + 0.488409i
\(70\) 0 0
\(71\) −4.21922 7.30791i −0.500730 0.867289i −1.00000 0.000842810i \(-0.999732\pi\)
0.499270 0.866447i \(-0.333602\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 9.00000i 1.05337i −0.850060 0.526685i \(-0.823435\pi\)
0.850060 0.526685i \(-0.176565\pi\)
\(74\) −1.78078 3.08440i −0.207011 0.358554i
\(75\) 0 0
\(76\) 3.28078 5.68247i 0.376331 0.651824i
\(77\) 2.00000i 0.227921i
\(78\) 3.57071 0.500000i 0.404304 0.0566139i
\(79\) −4.80776 −0.540916 −0.270458 0.962732i \(-0.587175\pi\)
−0.270458 + 0.962732i \(0.587175\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.43674 2.56155i 0.489956 0.282876i
\(83\) 2.43845i 0.267654i −0.991005 0.133827i \(-0.957273\pi\)
0.991005 0.133827i \(-0.0427267\pi\)
\(84\) 0.280776 + 0.486319i 0.0306352 + 0.0530618i
\(85\) 0 0
\(86\) 4.56155 0.491885
\(87\) −6.16879 + 3.56155i −0.661364 + 0.381839i
\(88\) 3.08440 + 1.78078i 0.328798 + 0.189831i
\(89\) −3.12311 + 5.40938i −0.331049 + 0.573393i −0.982718 0.185110i \(-0.940736\pi\)
0.651669 + 0.758503i \(0.274069\pi\)
\(90\) 0 0
\(91\) 0.280776 + 2.00514i 0.0294334 + 0.210196i
\(92\) 4.68466i 0.488409i
\(93\) 3.46410 + 2.00000i 0.359211 + 0.207390i
\(94\) 2.00000 3.46410i 0.206284 0.357295i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 15.4220 8.90388i 1.56586 0.904052i 0.569221 0.822184i \(-0.307245\pi\)
0.996643 0.0818678i \(-0.0260885\pi\)
\(98\) 5.78908 3.34233i 0.584786 0.337626i
\(99\) −3.56155 −0.357950
\(100\) 0 0
\(101\) −5.12311 + 8.87348i −0.509768 + 0.882944i 0.490168 + 0.871628i \(0.336935\pi\)
−0.999936 + 0.0113162i \(0.996398\pi\)
\(102\) −4.43674 2.56155i −0.439303 0.253632i
\(103\) 8.56155i 0.843595i 0.906690 + 0.421797i \(0.138601\pi\)
−0.906690 + 0.421797i \(0.861399\pi\)
\(104\) 3.34233 + 1.35234i 0.327742 + 0.132608i
\(105\) 0 0
\(106\) 6.12311 10.6055i 0.594729 1.03010i
\(107\) 16.7743 + 9.68466i 1.62163 + 0.936251i 0.986483 + 0.163864i \(0.0523958\pi\)
0.635152 + 0.772387i \(0.280938\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) −17.8078 −1.70567 −0.852837 0.522177i \(-0.825120\pi\)
−0.852837 + 0.522177i \(0.825120\pi\)
\(110\) 0 0
\(111\) 1.78078 + 3.08440i 0.169024 + 0.292758i
\(112\) 0.561553i 0.0530618i
\(113\) −3.46410 + 2.00000i −0.325875 + 0.188144i −0.654008 0.756487i \(-0.726914\pi\)
0.328133 + 0.944632i \(0.393581\pi\)
\(114\) −3.28078 + 5.68247i −0.307273 + 0.532212i
\(115\) 0 0
\(116\) −7.12311 −0.661364
\(117\) −3.57071 + 0.500000i −0.330113 + 0.0462250i
\(118\) 6.24621i 0.575010i
\(119\) 1.43845 2.49146i 0.131862 0.228392i
\(120\) 0 0
\(121\) −0.842329 1.45896i −0.0765754 0.132632i
\(122\) 10.6847i 0.967344i
\(123\) −4.43674 + 2.56155i −0.400047 + 0.230967i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 0 0
\(126\) −0.280776 0.486319i −0.0250136 0.0433247i
\(127\) −1.03251 0.596118i −0.0916201 0.0528969i 0.453490 0.891261i \(-0.350179\pi\)
−0.545110 + 0.838364i \(0.683512\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −4.56155 −0.401622
\(130\) 0 0
\(131\) 9.12311 0.797089 0.398545 0.917149i \(-0.369515\pi\)
0.398545 + 0.917149i \(0.369515\pi\)
\(132\) −3.08440 1.78078i −0.268462 0.154997i
\(133\) −3.19101 1.84233i −0.276695 0.159750i
\(134\) −4.40388 7.62775i −0.380437 0.658937i
\(135\) 0 0
\(136\) −2.56155 4.43674i −0.219651 0.380447i
\(137\) −14.2829 + 8.24621i −1.22027 + 0.704521i −0.964975 0.262343i \(-0.915505\pi\)
−0.255292 + 0.966864i \(0.582172\pi\)
\(138\) 4.68466i 0.398785i
\(139\) 8.71922 + 15.1021i 0.739555 + 1.28095i 0.952696 + 0.303925i \(0.0982973\pi\)
−0.213141 + 0.977021i \(0.568369\pi\)
\(140\) 0 0
\(141\) −2.00000 + 3.46410i −0.168430 + 0.291730i
\(142\) 8.43845i 0.708139i
\(143\) −7.90084 10.1231i −0.660702 0.846537i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −4.50000 + 7.79423i −0.372423 + 0.645055i
\(147\) −5.78908 + 3.34233i −0.477476 + 0.275671i
\(148\) 3.56155i 0.292758i
\(149\) 3.12311 + 5.40938i 0.255855 + 0.443153i 0.965127 0.261781i \(-0.0843098\pi\)
−0.709273 + 0.704934i \(0.750976\pi\)
\(150\) 0 0
\(151\) −4.31534 −0.351178 −0.175589 0.984464i \(-0.556183\pi\)
−0.175589 + 0.984464i \(0.556183\pi\)
\(152\) −5.68247 + 3.28078i −0.460909 + 0.266106i
\(153\) 4.43674 + 2.56155i 0.358689 + 0.207089i
\(154\) 1.00000 1.73205i 0.0805823 0.139573i
\(155\) 0 0
\(156\) −3.34233 1.35234i −0.267601 0.108274i
\(157\) 0.753789i 0.0601589i 0.999548 + 0.0300794i \(0.00957603\pi\)
−0.999548 + 0.0300794i \(0.990424\pi\)
\(158\) 4.16365 + 2.40388i 0.331242 + 0.191243i
\(159\) −6.12311 + 10.6055i −0.485594 + 0.841073i
\(160\) 0 0
\(161\) 2.63068 0.207327
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −14.2829 + 8.24621i −1.11872 + 0.645893i −0.941074 0.338201i \(-0.890182\pi\)
−0.177646 + 0.984094i \(0.556848\pi\)
\(164\) −5.12311 −0.400047
\(165\) 0 0
\(166\) −1.21922 + 2.11176i −0.0946301 + 0.163904i
\(167\) −9.79937 5.65767i −0.758298 0.437804i 0.0703862 0.997520i \(-0.477577\pi\)
−0.828684 + 0.559716i \(0.810910\pi\)
\(168\) 0.561553i 0.0433247i
\(169\) −9.34233 9.03996i −0.718641 0.695382i
\(170\) 0 0
\(171\) 3.28078 5.68247i 0.250887 0.434549i
\(172\) −3.95042 2.28078i −0.301217 0.173908i
\(173\) 14.8290 8.56155i 1.12743 0.650923i 0.184144 0.982899i \(-0.441049\pi\)
0.943288 + 0.331977i \(0.107715\pi\)
\(174\) 7.12311 0.540001
\(175\) 0 0
\(176\) −1.78078 3.08440i −0.134231 0.232495i
\(177\) 6.24621i 0.469494i
\(178\) 5.40938 3.12311i 0.405450 0.234087i
\(179\) −1.65767 + 2.87117i −0.123900 + 0.214601i −0.921302 0.388847i \(-0.872874\pi\)
0.797402 + 0.603448i \(0.206207\pi\)
\(180\) 0 0
\(181\) 17.4924 1.30020 0.650101 0.759848i \(-0.274727\pi\)
0.650101 + 0.759848i \(0.274727\pi\)
\(182\) 0.759413 1.87689i 0.0562914 0.139125i
\(183\) 10.6847i 0.789833i
\(184\) 2.34233 4.05703i 0.172679 0.299088i
\(185\) 0 0
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 18.2462i 1.33430i
\(188\) −3.46410 + 2.00000i −0.252646 + 0.145865i
\(189\) 0.280776 + 0.486319i 0.0204235 + 0.0353745i
\(190\) 0 0
\(191\) 6.46543 + 11.1985i 0.467822 + 0.810292i 0.999324 0.0367651i \(-0.0117053\pi\)
−0.531501 + 0.847057i \(0.678372\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 2.59808 + 1.50000i 0.187014 + 0.107972i 0.590584 0.806976i \(-0.298898\pi\)
−0.403570 + 0.914949i \(0.632231\pi\)
\(194\) −17.8078 −1.27852
\(195\) 0 0
\(196\) −6.68466 −0.477476
\(197\) 2.70469 + 1.56155i 0.192701 + 0.111256i 0.593246 0.805021i \(-0.297846\pi\)
−0.400545 + 0.916277i \(0.631179\pi\)
\(198\) 3.08440 + 1.78078i 0.219198 + 0.126554i
\(199\) −4.28078 7.41452i −0.303456 0.525602i 0.673460 0.739223i \(-0.264807\pi\)
−0.976916 + 0.213622i \(0.931474\pi\)
\(200\) 0 0
\(201\) 4.40388 + 7.62775i 0.310626 + 0.538020i
\(202\) 8.87348 5.12311i 0.624336 0.360460i
\(203\) 4.00000i 0.280745i
\(204\) 2.56155 + 4.43674i 0.179345 + 0.310634i
\(205\) 0 0
\(206\) 4.28078 7.41452i 0.298256 0.516594i
\(207\) 4.68466i 0.325606i
\(208\) −2.21837 2.84233i −0.153816 0.197080i
\(209\) 23.3693 1.61649
\(210\) 0 0
\(211\) 3.56155 6.16879i 0.245187 0.424677i −0.716997 0.697076i \(-0.754484\pi\)
0.962184 + 0.272399i \(0.0878172\pi\)
\(212\) −10.6055 + 6.12311i −0.728391 + 0.420537i
\(213\) 8.43845i 0.578193i
\(214\) −9.68466 16.7743i −0.662030 1.14667i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 1.94528 1.12311i 0.132054 0.0762414i
\(218\) 15.4220 + 8.90388i 1.04451 + 0.603047i
\(219\) 4.50000 7.79423i 0.304082 0.526685i
\(220\) 0 0
\(221\) 2.56155 + 18.2931i 0.172309 + 1.23053i
\(222\) 3.56155i 0.239036i
\(223\) −3.95042 2.28078i −0.264540 0.152732i 0.361864 0.932231i \(-0.382140\pi\)
−0.626404 + 0.779499i \(0.715474\pi\)
\(224\) 0.280776 0.486319i 0.0187602 0.0324936i
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) 14.9955 8.65767i 0.995288 0.574630i 0.0884373 0.996082i \(-0.471813\pi\)
0.906851 + 0.421452i \(0.138479\pi\)
\(228\) 5.68247 3.28078i 0.376331 0.217275i
\(229\) 23.4924 1.55242 0.776211 0.630473i \(-0.217139\pi\)
0.776211 + 0.630473i \(0.217139\pi\)
\(230\) 0 0
\(231\) −1.00000 + 1.73205i −0.0657952 + 0.113961i
\(232\) 6.16879 + 3.56155i 0.405001 + 0.233827i
\(233\) 0.630683i 0.0413174i 0.999787 + 0.0206587i \(0.00657634\pi\)
−0.999787 + 0.0206587i \(0.993424\pi\)
\(234\) 3.34233 + 1.35234i 0.218495 + 0.0884055i
\(235\) 0 0
\(236\) −3.12311 + 5.40938i −0.203297 + 0.352120i
\(237\) −4.16365 2.40388i −0.270458 0.156149i
\(238\) −2.49146 + 1.43845i −0.161498 + 0.0932407i
\(239\) 10.0540 0.650338 0.325169 0.945656i \(-0.394579\pi\)
0.325169 + 0.945656i \(0.394579\pi\)
\(240\) 0 0
\(241\) −5.71922 9.90599i −0.368408 0.638101i 0.620909 0.783883i \(-0.286764\pi\)
−0.989317 + 0.145782i \(0.953430\pi\)
\(242\) 1.68466i 0.108294i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 5.34233 9.25319i 0.342008 0.592375i
\(245\) 0 0
\(246\) 5.12311 0.326637
\(247\) 23.4294 3.28078i 1.49078 0.208751i
\(248\) 4.00000i 0.254000i
\(249\) 1.21922 2.11176i 0.0772652 0.133827i
\(250\) 0 0
\(251\) 2.46543 + 4.27026i 0.155617 + 0.269536i 0.933283 0.359141i \(-0.116930\pi\)
−0.777667 + 0.628677i \(0.783597\pi\)
\(252\) 0.561553i 0.0353745i
\(253\) −14.4493 + 8.34233i −0.908422 + 0.524478i
\(254\) 0.596118 + 1.03251i 0.0374038 + 0.0647852i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −23.9157 13.8078i −1.49182 0.861305i −0.491867 0.870670i \(-0.663685\pi\)
−0.999956 + 0.00936553i \(0.997019\pi\)
\(258\) 3.95042 + 2.28078i 0.245942 + 0.141995i
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) −7.12311 −0.440909
\(262\) −7.90084 4.56155i −0.488116 0.281814i
\(263\) 16.1814 + 9.34233i 0.997787 + 0.576073i 0.907593 0.419851i \(-0.137918\pi\)
0.0901944 + 0.995924i \(0.471251\pi\)
\(264\) 1.78078 + 3.08440i 0.109599 + 0.189831i
\(265\) 0 0
\(266\) 1.84233 + 3.19101i 0.112960 + 0.195653i
\(267\) −5.40938 + 3.12311i −0.331049 + 0.191131i
\(268\) 8.80776i 0.538020i
\(269\) 10.6847 + 18.5064i 0.651455 + 1.12835i 0.982770 + 0.184833i \(0.0591745\pi\)
−0.331315 + 0.943520i \(0.607492\pi\)
\(270\) 0 0
\(271\) 9.96543 17.2606i 0.605357 1.04851i −0.386638 0.922232i \(-0.626364\pi\)
0.991995 0.126278i \(-0.0403030\pi\)
\(272\) 5.12311i 0.310634i
\(273\) −0.759413 + 1.87689i −0.0459618 + 0.113595i
\(274\) 16.4924 0.996344
\(275\) 0 0
\(276\) −2.34233 + 4.05703i −0.140992 + 0.244205i
\(277\) 4.33013 2.50000i 0.260172 0.150210i −0.364241 0.931305i \(-0.618672\pi\)
0.624413 + 0.781094i \(0.285338\pi\)
\(278\) 17.4384i 1.04589i
\(279\) 2.00000 + 3.46410i 0.119737 + 0.207390i
\(280\) 0 0
\(281\) −18.2462 −1.08848 −0.544239 0.838930i \(-0.683181\pi\)
−0.544239 + 0.838930i \(0.683181\pi\)
\(282\) 3.46410 2.00000i 0.206284 0.119098i
\(283\) −10.0593 5.80776i −0.597966 0.345236i 0.170275 0.985397i \(-0.445534\pi\)
−0.768241 + 0.640161i \(0.778868\pi\)
\(284\) 4.21922 7.30791i 0.250365 0.433645i
\(285\) 0 0
\(286\) 1.78078 + 12.7173i 0.105300 + 0.751989i
\(287\) 2.87689i 0.169818i
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) 4.62311 8.00745i 0.271947 0.471027i
\(290\) 0 0
\(291\) 17.8078 1.04391
\(292\) 7.79423 4.50000i 0.456123 0.263343i
\(293\) −3.25088 + 1.87689i −0.189918 + 0.109649i −0.591944 0.805979i \(-0.701639\pi\)
0.402026 + 0.915628i \(0.368306\pi\)
\(294\) 6.68466 0.389857
\(295\) 0 0
\(296\) 1.78078 3.08440i 0.103506 0.179277i
\(297\) −3.08440 1.78078i −0.178975 0.103331i
\(298\) 6.24621i 0.361833i
\(299\) −13.3153 + 10.3923i −0.770046 + 0.601003i
\(300\) 0 0
\(301\) −1.28078 + 2.21837i −0.0738227 + 0.127865i
\(302\) 3.73720 + 2.15767i 0.215051 + 0.124160i
\(303\) −8.87348 + 5.12311i −0.509768 + 0.294315i
\(304\) 6.56155 0.376331
\(305\) 0 0
\(306\) −2.56155 4.43674i −0.146434 0.253632i
\(307\) 5.75379i 0.328386i 0.986428 + 0.164193i \(0.0525020\pi\)
−0.986428 + 0.164193i \(0.947498\pi\)
\(308\) −1.73205 + 1.00000i −0.0986928 + 0.0569803i
\(309\) −4.28078 + 7.41452i −0.243525 + 0.421797i
\(310\) 0 0
\(311\) −22.6847 −1.28633 −0.643164 0.765728i \(-0.722379\pi\)
−0.643164 + 0.765728i \(0.722379\pi\)
\(312\) 2.21837 + 2.84233i 0.125590 + 0.160915i
\(313\) 31.0000i 1.75222i −0.482108 0.876112i \(-0.660129\pi\)
0.482108 0.876112i \(-0.339871\pi\)
\(314\) 0.376894 0.652800i 0.0212694 0.0368396i
\(315\) 0 0
\(316\) −2.40388 4.16365i −0.135229 0.234223i
\(317\) 0.246211i 0.0138286i −0.999976 0.00691430i \(-0.997799\pi\)
0.999976 0.00691430i \(-0.00220091\pi\)
\(318\) 10.6055 6.12311i 0.594729 0.343367i
\(319\) −12.6847 21.9705i −0.710205 1.23011i
\(320\) 0 0
\(321\) 9.68466 + 16.7743i 0.540545 + 0.936251i
\(322\) −2.27824 1.31534i −0.126961 0.0733011i
\(323\) −29.1119 16.8078i −1.61983 0.935209i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 16.4924 0.913431
\(327\) −15.4220 8.90388i −0.852837 0.492386i
\(328\) 4.43674 + 2.56155i 0.244978 + 0.141438i
\(329\) 1.12311 + 1.94528i 0.0619188 + 0.107247i
\(330\) 0 0
\(331\) 2.15767 + 3.73720i 0.118596 + 0.205415i 0.919212 0.393764i \(-0.128827\pi\)
−0.800615 + 0.599179i \(0.795494\pi\)
\(332\) 2.11176 1.21922i 0.115898 0.0669136i
\(333\) 3.56155i 0.195172i
\(334\) 5.65767 + 9.79937i 0.309574 + 0.536198i
\(335\) 0 0
\(336\) −0.280776 + 0.486319i −0.0153176 + 0.0265309i
\(337\) 29.0540i 1.58267i −0.611382 0.791335i \(-0.709386\pi\)
0.611382 0.791335i \(-0.290614\pi\)
\(338\) 3.57071 + 12.5000i 0.194221 + 0.679910i
\(339\) −4.00000 −0.217250
\(340\) 0 0
\(341\) −7.12311 + 12.3376i −0.385738 + 0.668117i
\(342\) −5.68247 + 3.28078i −0.307273 + 0.177404i
\(343\) 7.68466i 0.414933i
\(344\) 2.28078 + 3.95042i 0.122971 + 0.212992i
\(345\) 0 0
\(346\) −17.1231 −0.920544
\(347\) −3.63058 + 2.09612i −0.194900 + 0.112526i −0.594274 0.804262i \(-0.702561\pi\)
0.399374 + 0.916788i \(0.369227\pi\)
\(348\) −6.16879 3.56155i −0.330682 0.190919i
\(349\) −1.37689 + 2.38485i −0.0737035 + 0.127658i −0.900522 0.434811i \(-0.856815\pi\)
0.826818 + 0.562469i \(0.190149\pi\)
\(350\) 0 0
\(351\) −3.34233 1.35234i −0.178400 0.0721828i
\(352\) 3.56155i 0.189831i
\(353\) −12.3376 7.12311i −0.656663 0.379125i 0.134341 0.990935i \(-0.457108\pi\)
−0.791004 + 0.611810i \(0.790442\pi\)
\(354\) 3.12311 5.40938i 0.165991 0.287505i
\(355\) 0 0
\(356\) −6.24621 −0.331049
\(357\) 2.49146 1.43845i 0.131862 0.0761307i
\(358\) 2.87117 1.65767i 0.151746 0.0876106i
\(359\) 13.1231 0.692611 0.346306 0.938122i \(-0.387436\pi\)
0.346306 + 0.938122i \(0.387436\pi\)
\(360\) 0 0
\(361\) −12.0270 + 20.8314i −0.632999 + 1.09639i
\(362\) −15.1489 8.74621i −0.796208 0.459691i
\(363\) 1.68466i 0.0884216i
\(364\) −1.59612 + 1.24573i −0.0836593 + 0.0652941i
\(365\) 0 0
\(366\) −5.34233 + 9.25319i −0.279248 + 0.483672i
\(367\) 26.6803 + 15.4039i 1.39270 + 0.804076i 0.993614 0.112837i \(-0.0359938\pi\)
0.399087 + 0.916913i \(0.369327\pi\)
\(368\) −4.05703 + 2.34233i −0.211487 + 0.122102i
\(369\) −5.12311 −0.266698
\(370\) 0 0
\(371\) 3.43845 + 5.95557i 0.178515 + 0.309198i
\(372\) 4.00000i 0.207390i
\(373\) −20.3450 + 11.7462i −1.05343 + 0.608196i −0.923607 0.383342i \(-0.874773\pi\)
−0.129819 + 0.991538i \(0.541440\pi\)
\(374\) 9.12311 15.8017i 0.471745 0.817086i
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) −15.8017 20.2462i −0.813828 1.04273i
\(378\) 0.561553i 0.0288832i
\(379\) 6.52699 11.3051i 0.335269 0.580703i −0.648268 0.761413i \(-0.724506\pi\)
0.983536 + 0.180710i \(0.0578395\pi\)
\(380\) 0 0
\(381\) −0.596118 1.03251i −0.0305400 0.0528969i
\(382\) 12.9309i 0.661601i
\(383\) 8.28055 4.78078i 0.423116 0.244286i −0.273293 0.961931i \(-0.588113\pi\)
0.696410 + 0.717644i \(0.254780\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −1.50000 2.59808i −0.0763480 0.132239i
\(387\) −3.95042 2.28078i −0.200811 0.115938i
\(388\) 15.4220 + 8.90388i 0.782932 + 0.452026i
\(389\) 13.3693 0.677851 0.338926 0.940813i \(-0.389936\pi\)
0.338926 + 0.940813i \(0.389936\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 5.78908 + 3.34233i 0.292393 + 0.168813i
\(393\) 7.90084 + 4.56155i 0.398545 + 0.230100i
\(394\) −1.56155 2.70469i −0.0786699 0.136260i
\(395\) 0 0
\(396\) −1.78078 3.08440i −0.0894874 0.154997i
\(397\) 9.35980 5.40388i 0.469755 0.271213i −0.246382 0.969173i \(-0.579242\pi\)
0.716137 + 0.697960i \(0.245909\pi\)
\(398\) 8.56155i 0.429152i
\(399\) −1.84233 3.19101i −0.0922318 0.159750i
\(400\) 0 0
\(401\) 18.6847 32.3628i 0.933067 1.61612i 0.155023 0.987911i \(-0.450455\pi\)
0.778045 0.628209i \(-0.216212\pi\)
\(402\) 8.80776i 0.439291i
\(403\) −5.40938 + 13.3693i −0.269460 + 0.665973i
\(404\) −10.2462 −0.509768
\(405\) 0 0
\(406\) 2.00000 3.46410i 0.0992583 0.171920i
\(407\) −10.9852 + 6.34233i −0.544518 + 0.314378i
\(408\) 5.12311i 0.253632i
\(409\) −0.123106 0.213225i −0.00608718 0.0105433i 0.862966 0.505262i \(-0.168604\pi\)
−0.869053 + 0.494719i \(0.835271\pi\)
\(410\) 0 0
\(411\) −16.4924 −0.813511
\(412\) −7.41452 + 4.28078i −0.365287 + 0.210899i
\(413\) 3.03765 + 1.75379i 0.149473 + 0.0862983i
\(414\) 2.34233 4.05703i 0.115119 0.199392i
\(415\) 0 0
\(416\) 0.500000 + 3.57071i 0.0245145 + 0.175069i
\(417\) 17.4384i 0.853964i
\(418\) −20.2384 11.6847i −0.989894 0.571515i
\(419\) 8.46543 14.6626i 0.413564 0.716313i −0.581713 0.813394i \(-0.697617\pi\)
0.995276 + 0.0970811i \(0.0309506\pi\)
\(420\) 0 0
\(421\) 14.7538 0.719056 0.359528 0.933134i \(-0.382938\pi\)
0.359528 + 0.933134i \(0.382938\pi\)
\(422\) −6.16879 + 3.56155i −0.300292 + 0.173374i
\(423\) −3.46410 + 2.00000i −0.168430 + 0.0972433i
\(424\) 12.2462 0.594729
\(425\) 0 0
\(426\) −4.21922 + 7.30791i −0.204422 + 0.354069i
\(427\) −5.19615 3.00000i −0.251459 0.145180i
\(428\) 19.3693i 0.936251i
\(429\) −1.78078 12.7173i −0.0859767 0.613996i
\(430\) 0 0
\(431\) −15.3423 + 26.5737i −0.739014 + 1.28001i 0.213926 + 0.976850i \(0.431375\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 1.13912 0.657671i 0.0547426 0.0316056i −0.472379 0.881396i \(-0.656605\pi\)
0.527121 + 0.849790i \(0.323271\pi\)
\(434\) −2.24621 −0.107822
\(435\) 0 0
\(436\) −8.90388 15.4220i −0.426419 0.738579i
\(437\) 30.7386i 1.47043i
\(438\) −7.79423 + 4.50000i −0.372423 + 0.215018i
\(439\) 10.9654 18.9927i 0.523352 0.906472i −0.476279 0.879294i \(-0.658015\pi\)
0.999631 0.0271774i \(-0.00865191\pi\)
\(440\) 0 0
\(441\) −6.68466 −0.318317
\(442\) 6.92820 17.1231i 0.329541 0.814463i
\(443\) 17.8078i 0.846072i −0.906113 0.423036i \(-0.860964\pi\)
0.906113 0.423036i \(-0.139036\pi\)
\(444\) −1.78078 + 3.08440i −0.0845119 + 0.146379i
\(445\) 0 0
\(446\) 2.28078 + 3.95042i 0.107998 + 0.187058i
\(447\) 6.24621i 0.295436i
\(448\) −0.486319 + 0.280776i −0.0229764 + 0.0132654i
\(449\) 2.56155 + 4.43674i 0.120887 + 0.209383i 0.920118 0.391642i \(-0.128093\pi\)
−0.799231 + 0.601024i \(0.794759\pi\)
\(450\) 0 0
\(451\) −9.12311 15.8017i −0.429590 0.744072i
\(452\) −3.46410 2.00000i −0.162938 0.0940721i
\(453\) −3.73720 2.15767i −0.175589 0.101376i
\(454\) −17.3153 −0.812649
\(455\) 0 0
\(456\) −6.56155 −0.307273
\(457\) −32.4694 18.7462i −1.51885 0.876911i −0.999754 0.0221975i \(-0.992934\pi\)
−0.519100 0.854713i \(-0.673733\pi\)
\(458\) −20.3450 11.7462i −0.950661 0.548864i
\(459\) 2.56155 + 4.43674i 0.119563 + 0.207089i
\(460\) 0 0
\(461\) −17.6847 30.6307i −0.823657 1.42662i −0.902942 0.429763i \(-0.858597\pi\)
0.0792850 0.996852i \(-0.474736\pi\)
\(462\) 1.73205 1.00000i 0.0805823 0.0465242i
\(463\) 7.19224i 0.334252i −0.985936 0.167126i \(-0.946551\pi\)
0.985936 0.167126i \(-0.0534486\pi\)
\(464\) −3.56155 6.16879i −0.165341 0.286379i
\(465\) 0 0
\(466\) 0.315342 0.546188i 0.0146079 0.0253017i
\(467\) 7.56155i 0.349907i −0.984577 0.174953i \(-0.944022\pi\)
0.984577 0.174953i \(-0.0559775\pi\)
\(468\) −2.21837 2.84233i −0.102544 0.131387i
\(469\) 4.94602 0.228386
\(470\) 0 0
\(471\) −0.376894 + 0.652800i −0.0173664 + 0.0300794i
\(472\) 5.40938 3.12311i 0.248987 0.143753i
\(473\) 16.2462i 0.747002i
\(474\) 2.40388 + 4.16365i 0.110414 + 0.191243i
\(475\) 0 0
\(476\) 2.87689 0.131862
\(477\) −10.6055 + 6.12311i −0.485594 + 0.280358i
\(478\) −8.70700 5.02699i −0.398249 0.229929i
\(479\) 14.8078 25.6478i 0.676584 1.17188i −0.299419 0.954122i \(-0.596793\pi\)
0.976003 0.217756i \(-0.0698738\pi\)
\(480\) 0 0
\(481\) −10.1231 + 7.90084i −0.461574 + 0.360247i
\(482\) 11.4384i 0.521007i
\(483\) 2.27824 + 1.31534i 0.103663 + 0.0598501i
\(484\) 0.842329 1.45896i 0.0382877 0.0663162i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 26.2539 15.1577i 1.18968 0.686860i 0.231443 0.972849i \(-0.425655\pi\)
0.958233 + 0.285989i \(0.0923220\pi\)
\(488\) −9.25319 + 5.34233i −0.418872 + 0.241836i
\(489\) −16.4924 −0.745813
\(490\) 0 0
\(491\) 11.1501 19.3125i 0.503197 0.871562i −0.496797 0.867867i \(-0.665490\pi\)
0.999993 0.00369513i \(-0.00117620\pi\)
\(492\) −4.43674 2.56155i −0.200024 0.115484i
\(493\) 36.4924i 1.64354i
\(494\) −21.9309 8.87348i −0.986716 0.399237i
\(495\) 0 0
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) −4.10378 2.36932i −0.184080 0.106278i
\(498\) −2.11176 + 1.21922i −0.0946301 + 0.0546347i
\(499\) 31.0540 1.39017 0.695083 0.718929i \(-0.255367\pi\)
0.695083 + 0.718929i \(0.255367\pi\)
\(500\) 0 0
\(501\) −5.65767 9.79937i −0.252766 0.437804i
\(502\) 4.93087i 0.220075i
\(503\) 31.7698 18.3423i 1.41655 0.817844i 0.420554 0.907268i \(-0.361836\pi\)
0.995994 + 0.0894236i \(0.0285025\pi\)
\(504\) 0.280776 0.486319i 0.0125068 0.0216624i
\(505\) 0 0
\(506\) 16.6847 0.741724
\(507\) −3.57071 12.5000i −0.158581 0.555144i
\(508\) 1.19224i 0.0528969i
\(509\) 0.123106 0.213225i 0.00545656 0.00945104i −0.863284 0.504718i \(-0.831596\pi\)
0.868741 + 0.495267i \(0.164930\pi\)
\(510\) 0 0
\(511\) −2.52699 4.37687i −0.111787 0.193621i
\(512\) 1.00000i 0.0441942i
\(513\) 5.68247 3.28078i 0.250887 0.144850i
\(514\) 13.8078 + 23.9157i 0.609034 + 1.05488i
\(515\) 0 0
\(516\) −2.28078 3.95042i −0.100406 0.173908i
\(517\) −12.3376 7.12311i −0.542606 0.313274i
\(518\) −1.73205 1.00000i −0.0761019 0.0439375i
\(519\) 17.1231 0.751621
\(520\) 0 0
\(521\) −14.7386 −0.645711 −0.322856 0.946448i \(-0.604643\pi\)
−0.322856 + 0.946448i \(0.604643\pi\)
\(522\) 6.16879 + 3.56155i 0.270001 + 0.155885i
\(523\) −3.40423 1.96543i −0.148857 0.0859425i 0.423722 0.905792i \(-0.360723\pi\)
−0.572578 + 0.819850i \(0.694057\pi\)
\(524\) 4.56155 + 7.90084i 0.199272 + 0.345150i
\(525\) 0 0
\(526\) −9.34233 16.1814i −0.407345 0.705542i
\(527\) 17.7470 10.2462i 0.773070 0.446332i
\(528\) 3.56155i 0.154997i
\(529\) −0.526988 0.912769i −0.0229125 0.0396856i
\(530\) 0 0
\(531\) −3.12311 + 5.40938i −0.135531 + 0.234747i
\(532\) 3.68466i 0.159750i
\(533\) −11.3649 14.5616i −0.492270 0.630731i
\(534\) 6.24621 0.270300
\(535\) 0 0
\(536\) 4.40388 7.62775i 0.190219 0.329469i
\(537\) −2.87117 + 1.65767i −0.123900 + 0.0715338i
\(538\) 21.3693i 0.921297i
\(539\) −11.9039 20.6181i −0.512736 0.888086i
\(540\) 0 0
\(541\) −34.6847 −1.49121 −0.745605 0.666388i \(-0.767839\pi\)
−0.745605 + 0.666388i \(0.767839\pi\)
\(542\) −17.2606 + 9.96543i −0.741408 + 0.428052i
\(543\) 15.1489 + 8.74621i 0.650101 + 0.375336i
\(544\) 2.56155 4.43674i 0.109826 0.190224i
\(545\) 0 0
\(546\) 1.59612 1.24573i 0.0683075 0.0533124i
\(547\) 2.06913i 0.0884696i −0.999021 0.0442348i \(-0.985915\pi\)
0.999021 0.0442348i \(-0.0140850\pi\)
\(548\) −14.2829 8.24621i −0.610133 0.352261i
\(549\) 5.34233 9.25319i 0.228005 0.394916i
\(550\) 0 0
\(551\) 46.7386 1.99113
\(552\) 4.05703 2.34233i 0.172679 0.0996962i
\(553\) −2.33811 + 1.34991i −0.0994264 + 0.0574039i
\(554\) −5.00000 −0.212430
\(555\) 0 0
\(556\) −8.71922 + 15.1021i −0.369777 + 0.640473i
\(557\) −8.32729 4.80776i −0.352839 0.203712i 0.313096 0.949721i \(-0.398634\pi\)
−0.665935 + 0.746010i \(0.731967\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −2.28078 16.2880i −0.0964666 0.688909i
\(560\) 0 0
\(561\) −9.12311 + 15.8017i −0.385178 + 0.667148i
\(562\) 15.8017 + 9.12311i 0.666554 + 0.384835i
\(563\) −0.166481 + 0.0961180i −0.00701635 + 0.00405089i −0.503504 0.863993i \(-0.667956\pi\)
0.496488 + 0.868044i \(0.334623\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) 5.80776 + 10.0593i 0.244119 + 0.422826i
\(567\) 0.561553i 0.0235830i
\(568\) −7.30791 + 4.21922i −0.306633 + 0.177035i
\(569\) −22.2462 + 38.5316i −0.932610 + 1.61533i −0.153768 + 0.988107i \(0.549141\pi\)
−0.778842 + 0.627220i \(0.784193\pi\)
\(570\) 0 0
\(571\) −40.4233 −1.69166 −0.845831 0.533451i \(-0.820895\pi\)
−0.845831 + 0.533451i \(0.820895\pi\)
\(572\) 4.81645 11.9039i 0.201386 0.497726i
\(573\) 12.9309i 0.540195i
\(574\) 1.43845 2.49146i 0.0600396 0.103992i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 23.0000i 0.957503i 0.877951 + 0.478751i \(0.158910\pi\)
−0.877951 + 0.478751i \(0.841090\pi\)
\(578\) −8.00745 + 4.62311i −0.333066 + 0.192296i
\(579\) 1.50000 + 2.59808i 0.0623379 + 0.107972i
\(580\) 0 0
\(581\) −0.684658 1.18586i −0.0284044 0.0491979i
\(582\) −15.4220 8.90388i −0.639261 0.369078i
\(583\) −37.7722 21.8078i −1.56436 0.903185i
\(584\) −9.00000 −0.372423
\(585\) 0 0
\(586\) 3.75379 0.155068
\(587\) −9.46641 5.46543i −0.390721 0.225583i 0.291752 0.956494i \(-0.405762\pi\)
−0.682472 + 0.730911i \(0.739095\pi\)
\(588\) −5.78908 3.34233i −0.238738 0.137835i
\(589\) −13.1231 22.7299i −0.540728 0.936569i
\(590\) 0 0
\(591\) 1.56155 + 2.70469i 0.0642337 + 0.111256i
\(592\) −3.08440 + 1.78078i −0.126768 + 0.0731895i
\(593\) 26.9848i 1.10813i −0.832472 0.554067i \(-0.813075\pi\)
0.832472 0.554067i \(-0.186925\pi\)
\(594\) 1.78078 + 3.08440i 0.0730661 + 0.126554i
\(595\) 0 0
\(596\) −3.12311 + 5.40938i −0.127927 + 0.221577i
\(597\) 8.56155i 0.350401i
\(598\) 16.7276 2.34233i 0.684041 0.0957850i
\(599\) 30.6847 1.25374 0.626871 0.779123i \(-0.284335\pi\)
0.626871 + 0.779123i \(0.284335\pi\)
\(600\) 0 0
\(601\) −7.40388 + 12.8239i −0.302011 + 0.523098i −0.976591 0.215103i \(-0.930991\pi\)
0.674581 + 0.738201i \(0.264324\pi\)
\(602\) 2.21837 1.28078i 0.0904140 0.0522005i
\(603\) 8.80776i 0.358680i
\(604\) −2.15767 3.73720i −0.0877944 0.152064i
\(605\) 0 0
\(606\) 10.2462 0.416224
\(607\) −12.6705 + 7.31534i −0.514281 + 0.296921i −0.734592 0.678509i \(-0.762626\pi\)
0.220310 + 0.975430i \(0.429293\pi\)
\(608\) −5.68247 3.28078i −0.230455 0.133053i
\(609\) −2.00000 + 3.46410i −0.0810441 + 0.140372i
\(610\) 0 0
\(611\) −13.3693 5.40938i −0.540865 0.218840i
\(612\) 5.12311i 0.207089i
\(613\) 29.0520 + 16.7732i 1.17340 + 0.677463i 0.954479 0.298279i \(-0.0964127\pi\)
0.218922 + 0.975742i \(0.429746\pi\)
\(614\) 2.87689 4.98293i 0.116102 0.201095i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) 19.5987 11.3153i 0.789016 0.455538i −0.0506001 0.998719i \(-0.516113\pi\)
0.839616 + 0.543180i \(0.182780\pi\)
\(618\) 7.41452 4.28078i 0.298256 0.172198i
\(619\) −41.3002 −1.65999 −0.829997 0.557767i \(-0.811658\pi\)
−0.829997 + 0.557767i \(0.811658\pi\)
\(620\) 0 0
\(621\) −2.34233 + 4.05703i −0.0939944 + 0.162803i
\(622\) 19.6455 + 11.3423i 0.787712 + 0.454786i
\(623\) 3.50758i 0.140528i
\(624\) −0.500000 3.57071i −0.0200160 0.142943i
\(625\) 0 0
\(626\) −15.5000 + 26.8468i −0.619505 + 1.07301i
\(627\) 20.2384 + 11.6847i 0.808245 + 0.466640i
\(628\) −0.652800 + 0.376894i −0.0260496 + 0.0150397i
\(629\) 18.2462 0.727524
\(630\) 0 0
\(631\) −2.03457 3.52397i −0.0809948 0.140287i 0.822683 0.568501i \(-0.192476\pi\)
−0.903677 + 0.428214i \(0.859143\pi\)
\(632\) 4.80776i 0.191243i
\(633\) 6.16879 3.56155i 0.245187 0.141559i
\(634\) −0.123106 + 0.213225i −0.00488915 + 0.00846825i
\(635\) 0 0
\(636\) −12.2462 −0.485594
\(637\) −14.8290 19.0000i −0.587548 0.752807i
\(638\) 25.3693i 1.00438i
\(639\) 4.21922 7.30791i 0.166910 0.289096i
\(640\) 0 0
\(641\) −10.8769 18.8393i −0.429611 0.744109i 0.567227 0.823561i \(-0.308016\pi\)
−0.996839 + 0.0794524i \(0.974683\pi\)
\(642\) 19.3693i 0.764446i
\(643\) 39.4443 22.7732i 1.55553 0.898087i 0.557858 0.829937i \(-0.311623\pi\)
0.997675 0.0681507i \(-0.0217099\pi\)
\(644\) 1.31534 + 2.27824i 0.0518317 + 0.0897752i
\(645\) 0 0
\(646\) 16.8078 + 29.1119i 0.661293 + 1.14539i
\(647\) 25.4813 + 14.7116i 1.00177 + 0.578374i 0.908773 0.417291i \(-0.137021\pi\)
0.0930013 + 0.995666i \(0.470354\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −22.2462 −0.873240
\(650\) 0 0
\(651\) 2.24621 0.0880360
\(652\) −14.2829 8.24621i −0.559360 0.322947i
\(653\) 3.13114 + 1.80776i 0.122531 + 0.0707433i 0.560013 0.828484i \(-0.310796\pi\)
−0.437482 + 0.899227i \(0.644130\pi\)
\(654\) 8.90388 + 15.4220i 0.348169 + 0.603047i
\(655\) 0 0
\(656\) −2.56155 4.43674i −0.100012 0.173226i
\(657\) 7.79423 4.50000i 0.304082 0.175562i
\(658\) 2.24621i 0.0875664i
\(659\) 15.3423 + 26.5737i 0.597652 + 1.03516i 0.993167 + 0.116704i \(0.0372330\pi\)
−0.395514 + 0.918460i \(0.629434\pi\)
\(660\) 0 0
\(661\) −10.7732 + 18.6597i −0.419029 + 0.725779i −0.995842 0.0910968i \(-0.970963\pi\)
0.576813 + 0.816876i \(0.304296\pi\)
\(662\) 4.31534i 0.167721i
\(663\) −6.92820 + 17.1231i −0.269069 + 0.665006i
\(664\) −2.43845 −0.0946301
\(665\) 0 0
\(666\) 1.78078 3.08440i 0.0690037 0.119518i
\(667\) −28.8987 + 16.6847i −1.11896 + 0.646033i
\(668\) 11.3153i 0.437804i
\(669\) −2.28078 3.95042i −0.0881799 0.152732i
\(670\) 0 0
\(671\) 38.0540 1.46906
\(672\) 0.486319 0.280776i 0.0187602 0.0108312i
\(673\) 39.1844 + 22.6231i 1.51045 + 0.872057i 0.999926 + 0.0121912i \(0.00388067\pi\)
0.510521 + 0.859865i \(0.329453\pi\)
\(674\) −14.5270 + 25.1615i −0.559559 + 0.969184i
\(675\) 0 0
\(676\) 3.15767 12.6107i 0.121449 0.485026i
\(677\) 29.6155i 1.13822i −0.822262 0.569109i \(-0.807288\pi\)
0.822262 0.569109i \(-0.192712\pi\)
\(678\) 3.46410 + 2.00000i 0.133038 + 0.0768095i
\(679\) 5.00000 8.66025i 0.191882 0.332350i
\(680\) 0 0
\(681\) 17.3153 0.663525
\(682\) 12.3376 7.12311i 0.472430 0.272758i
\(683\) −16.9408 + 9.78078i −0.648222 + 0.374251i −0.787775 0.615964i \(-0.788767\pi\)
0.139553 + 0.990215i \(0.455433\pi\)
\(684\) 6.56155 0.250887
\(685\) 0 0
\(686\) 3.84233 6.65511i 0.146701 0.254093i
\(687\) 20.3450 + 11.7462i 0.776211 + 0.448146i
\(688\) 4.56155i 0.173908i
\(689\) −40.9309 16.5611i −1.55934 0.630927i
\(690\) 0 0
\(691\) 25.0885 43.4546i 0.954413 1.65309i 0.218707 0.975790i \(-0.429816\pi\)
0.735706 0.677301i \(-0.236851\pi\)
\(692\) 14.8290 + 8.56155i 0.563716 + 0.325461i
\(693\) −1.73205 + 1.00000i −0.0657952 + 0.0379869i
\(694\) 4.19224 0.159135
\(695\) 0 0
\(696\) 3.56155 + 6.16879i 0.135000 + 0.233827i
\(697\) 26.2462i 0.994146i
\(698\) 2.38485 1.37689i 0.0902679 0.0521162i
\(699\) −0.315342 + 0.546188i −0.0119273 + 0.0206587i
\(700\) 0 0
\(701\) −9.12311 −0.344575 −0.172287 0.985047i \(-0.555116\pi\)
−0.172287 + 0.985047i \(0.555116\pi\)
\(702\) 2.21837 + 2.84233i 0.0837270 + 0.107277i
\(703\) 23.3693i 0.881390i
\(704\) 1.78078 3.08440i 0.0671155 0.116248i
\(705\) 0 0
\(706\) 7.12311 + 12.3376i 0.268082 + 0.464331i
\(707\) 5.75379i 0.216393i
\(708\) −5.40938 + 3.12311i −0.203297 + 0.117373i
\(709\) −22.6231 39.1844i −0.849629 1.47160i −0.881540 0.472109i \(-0.843493\pi\)
0.0319115 0.999491i \(-0.489841\pi\)
\(710\) 0 0
\(711\) −2.40388 4.16365i −0.0901526 0.156149i
\(712\) 5.40938 + 3.12311i 0.202725 + 0.117043i
\(713\) 16.2281 + 9.36932i 0.607748 + 0.350884i
\(714\) −2.87689 −0.107665
\(715\) 0 0
\(716\) −3.31534 −0.123900
\(717\) 8.70700 + 5.02699i 0.325169 + 0.187736i
\(718\) −11.3649 6.56155i −0.424136 0.244875i
\(719\) −10.7808 18.6729i −0.402055 0.696380i 0.591919 0.805998i \(-0.298371\pi\)
−0.993974 + 0.109618i \(0.965037\pi\)
\(720\) 0 0
\(721\) 2.40388 + 4.16365i 0.0895252 + 0.155062i
\(722\) 20.8314 12.0270i 0.775263 0.447598i
\(723\) 11.4384i 0.425400i
\(724\) 8.74621 + 15.1489i 0.325050 + 0.563004i
\(725\) 0 0
\(726\) −0.842329 + 1.45896i −0.0312618 + 0.0541470i
\(727\) 35.7926i 1.32747i 0.747966 + 0.663737i \(0.231031\pi\)
−0.747966 + 0.663737i \(0.768969\pi\)
\(728\) 2.00514 0.280776i 0.0743156 0.0104063i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −11.6847 + 20.2384i −0.432173 + 0.748545i
\(732\) 9.25319 5.34233i 0.342008 0.197458i
\(733\) 17.9848i 0.664285i −0.943229 0.332143i \(-0.892228\pi\)
0.943229 0.332143i \(-0.107772\pi\)
\(734\) −15.4039 26.6803i −0.568568 0.984788i
\(735\) 0 0
\(736\) 4.68466 0.172679
\(737\) −27.1666 + 15.6847i −1.00070 + 0.577752i
\(738\) 4.43674 + 2.56155i 0.163319 + 0.0942921i
\(739\) −2.43845 + 4.22351i −0.0896997 + 0.155364i −0.907384 0.420302i \(-0.861924\pi\)
0.817684 + 0.575667i \(0.195257\pi\)
\(740\) 0 0
\(741\) 21.9309 + 8.87348i 0.805651 + 0.325975i
\(742\) 6.87689i 0.252459i
\(743\) 2.49146 + 1.43845i 0.0914029 + 0.0527715i 0.545005 0.838433i \(-0.316528\pi\)
−0.453602 + 0.891204i \(0.649861\pi\)
\(744\) 2.00000 3.46410i 0.0733236 0.127000i
\(745\) 0 0
\(746\) 23.4924 0.860119
\(747\) 2.11176 1.21922i 0.0772652 0.0446091i
\(748\) −15.8017 + 9.12311i −0.577767 + 0.333574i
\(749\) 10.8769 0.397433
\(750\) 0 0
\(751\) −16.8769 + 29.2316i −0.615847 + 1.06668i 0.374389 + 0.927272i \(0.377853\pi\)
−0.990235 + 0.139406i \(0.955481\pi\)
\(752\) −3.46410 2.00000i −0.126323 0.0729325i
\(753\) 4.93087i 0.179691i
\(754\) 3.56155 + 25.4346i 0.129704 + 0.926273i
\(755\) 0 0
\(756\) −0.280776 + 0.486319i −0.0102117 + 0.0176873i
\(757\) 15.8616 + 9.15767i 0.576498 + 0.332841i 0.759740 0.650227i \(-0.225326\pi\)
−0.183243 + 0.983068i \(0.558659\pi\)
\(758\) −11.3051 + 6.52699i −0.410619 + 0.237071i
\(759\) −16.6847 −0.605615
\(760\) 0 0
\(761\) −21.4924 37.2260i −0.779100 1.34944i −0.932461 0.361270i \(-0.882343\pi\)
0.153361 0.988170i \(-0.450990\pi\)
\(762\) 1.19224i 0.0431902i
\(763\) −8.66025 + 5.00000i −0.313522 + 0.181012i
\(764\) −6.46543 + 11.1985i −0.233911 + 0.405146i
\(765\) 0 0
\(766\) −9.56155 −0.345473
\(767\) −22.3034 + 3.12311i −0.805330 + 0.112769i
\(768\) 1.00000i 0.0360844i
\(769\) −10.8423 + 18.7795i −0.390984 + 0.677205i −0.992580 0.121596i \(-0.961199\pi\)
0.601595 + 0.798801i \(0.294532\pi\)
\(770\) 0 0
\(771\) −13.8078 23.9157i −0.497274 0.861305i
\(772\) 3.00000i 0.107972i
\(773\) −10.0593 + 5.80776i −0.361809 + 0.208891i −0.669874 0.742475i \(-0.733652\pi\)
0.308065 + 0.951365i \(0.400319\pi\)
\(774\) 2.28078 + 3.95042i 0.0819808 + 0.141995i
\(775\) 0 0
\(776\) −8.90388 15.4220i −0.319631 0.553617i
\(777\) 1.73205 + 1.00000i 0.0621370 + 0.0358748i
\(778\) −11.5782 6.68466i −0.415097 0.239657i
\(779\) 33.6155 1.20440
\(780\) 0 0
\(781\) 30.0540 1.07542
\(782\) −20.7846 12.0000i −0.743256 0.429119i
\(783\) −6.16879 3.56155i −0.220455 0.127280i
\(784\) −3.34233 5.78908i −0.119369 0.206753i