Properties

Label 1950.2.i.z.451.1
Level $1950$
Weight $2$
Character 1950.451
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.1
Root \(-0.780776 - 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 1950.451
Dual form 1950.2.i.z.601.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.280776 - 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.280776 - 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.78078 + 3.08440i) q^{11} +1.00000 q^{12} +(-3.34233 - 1.35234i) q^{13} +0.561553 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.56155 - 4.43674i) q^{17} +1.00000 q^{18} +(3.28078 + 5.68247i) q^{19} +0.561553 q^{21} +(-1.78078 - 3.08440i) q^{22} +(-2.34233 + 4.05703i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.84233 - 2.21837i) q^{26} +1.00000 q^{27} +(-0.280776 + 0.486319i) q^{28} +(3.56155 - 6.16879i) q^{29} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.78078 - 3.08440i) q^{33} +5.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(1.78078 - 3.08440i) q^{37} -6.56155 q^{38} +(2.84233 - 2.21837i) q^{39} +(-2.56155 + 4.43674i) q^{41} +(-0.280776 + 0.486319i) q^{42} +(-2.28078 - 3.95042i) q^{43} +3.56155 q^{44} +(-2.34233 - 4.05703i) q^{46} +4.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.34233 - 5.78908i) q^{49} +5.12311 q^{51} +(0.500000 + 3.57071i) q^{52} -12.2462 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.280776 - 0.486319i) q^{56} -6.56155 q^{57} +(3.56155 + 6.16879i) q^{58} +(-3.12311 - 5.40938i) q^{59} +(-5.34233 - 9.25319i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-0.280776 + 0.486319i) q^{63} +1.00000 q^{64} +3.56155 q^{66} +(4.40388 - 7.62775i) q^{67} +(-2.56155 + 4.43674i) q^{68} +(-2.34233 - 4.05703i) q^{69} +(-4.21922 - 7.30791i) q^{71} +(-0.500000 - 0.866025i) q^{72} +9.00000 q^{73} +(1.78078 + 3.08440i) q^{74} +(3.28078 - 5.68247i) q^{76} +2.00000 q^{77} +(0.500000 + 3.57071i) q^{78} +4.80776 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.56155 - 4.43674i) q^{82} +2.43845 q^{83} +(-0.280776 - 0.486319i) q^{84} +4.56155 q^{86} +(3.56155 + 6.16879i) q^{87} +(-1.78078 + 3.08440i) q^{88} +(3.12311 - 5.40938i) q^{89} +(0.280776 + 2.00514i) q^{91} +4.68466 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-2.00000 + 3.46410i) q^{94} +1.00000 q^{96} +(-8.90388 - 15.4220i) q^{97} +(3.34233 + 5.78908i) q^{98} +3.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9} - 3 q^{11} + 4 q^{12} - q^{13} - 6 q^{14} - 2 q^{16} - 2 q^{17} + 4 q^{18} + 9 q^{19} - 6 q^{21} - 3 q^{22} + 3 q^{23} - 2 q^{24} - q^{26} + 4 q^{27} + 3 q^{28} + 6 q^{29} + 16 q^{31} - 2 q^{32} - 3 q^{33} + 4 q^{34} - 2 q^{36} + 3 q^{37} - 18 q^{38} - q^{39} - 2 q^{41} + 3 q^{42} - 5 q^{43} + 6 q^{44} + 3 q^{46} + 16 q^{47} - 2 q^{48} + q^{49} + 4 q^{51} + 2 q^{52} - 16 q^{53} - 2 q^{54} + 3 q^{56} - 18 q^{57} + 6 q^{58} + 4 q^{59} - 9 q^{61} - 8 q^{62} + 3 q^{63} + 4 q^{64} + 6 q^{66} - 3 q^{67} - 2 q^{68} + 3 q^{69} - 21 q^{71} - 2 q^{72} + 36 q^{73} + 3 q^{74} + 9 q^{76} + 8 q^{77} + 2 q^{78} - 22 q^{79} - 2 q^{81} - 2 q^{82} + 18 q^{83} + 3 q^{84} + 10 q^{86} + 6 q^{87} - 3 q^{88} - 4 q^{89} - 3 q^{91} - 6 q^{92} - 8 q^{93} - 8 q^{94} + 4 q^{96} - 15 q^{97} + q^{98} + 6 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −0.280776 0.486319i −0.106124 0.183811i 0.808073 0.589082i \(-0.200511\pi\)
−0.914197 + 0.405271i \(0.867177\pi\)
\(8\) 1.00000 0.353553
\(9\) −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 \(0.986253\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.34233 1.35234i −0.926995 0.375073i
\(14\) 0.561553 0.150081
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.56155 4.43674i −0.621268 1.07607i −0.989250 0.146235i \(-0.953285\pi\)
0.367982 0.929833i \(-0.380049\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.28078 + 5.68247i 0.752662 + 1.30365i 0.946528 + 0.322620i \(0.104564\pi\)
−0.193867 + 0.981028i \(0.562103\pi\)
\(20\) 0 0
\(21\) 0.561553 0.122541
\(22\) −1.78078 3.08440i −0.379663 0.657595i
\(23\) −2.34233 + 4.05703i −0.488409 + 0.845950i −0.999911 0.0133324i \(-0.995756\pi\)
0.511502 + 0.859282i \(0.329089\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 2.84233 2.21837i 0.557427 0.435058i
\(27\) 1.00000 0.192450
\(28\) −0.280776 + 0.486319i −0.0530618 + 0.0919057i
\(29\) 3.56155 6.16879i 0.661364 1.14552i −0.318894 0.947790i \(-0.603311\pi\)
0.980257 0.197725i \(-0.0633554\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.78078 3.08440i −0.309993 0.536924i
\(34\) 5.12311 0.878605
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 1.78078 3.08440i 0.292758 0.507071i −0.681703 0.731629i \(-0.738760\pi\)
0.974461 + 0.224558i \(0.0720937\pi\)
\(38\) −6.56155 −1.06442
\(39\) 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 \(0.297673\pi\)
\(42\) −0.280776 + 0.486319i −0.0433247 + 0.0750407i
\(43\) −2.28078 3.95042i −0.347815 0.602433i 0.638046 0.769998i \(-0.279743\pi\)
−0.985861 + 0.167565i \(0.946410\pi\)
\(44\) 3.56155 0.536924
\(45\) 0 0
\(46\) −2.34233 4.05703i −0.345358 0.598177i
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 3.34233 5.78908i 0.477476 0.827012i
\(50\) 0 0
\(51\) 5.12311 0.717378
\(52\) 0.500000 + 3.57071i 0.0693375 + 0.495169i
\(53\) −12.2462 −1.68215 −0.841073 0.540921i \(-0.818076\pi\)
−0.841073 + 0.540921i \(0.818076\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −0.280776 0.486319i −0.0375203 0.0649871i
\(57\) −6.56155 −0.869099
\(58\) 3.56155 + 6.16879i 0.467655 + 0.810002i
\(59\) −3.12311 5.40938i −0.406594 0.704241i 0.587912 0.808925i \(-0.299950\pi\)
−0.994506 + 0.104684i \(0.966617\pi\)
\(60\) 0 0
\(61\) −5.34233 9.25319i −0.684015 1.18475i −0.973745 0.227641i \(-0.926899\pi\)
0.289730 0.957108i \(-0.406434\pi\)
\(62\) −2.00000 + 3.46410i −0.254000 + 0.439941i
\(63\) −0.280776 + 0.486319i −0.0353745 + 0.0612704i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.56155 0.438397
\(67\) 4.40388 7.62775i 0.538020 0.931878i −0.460991 0.887405i \(-0.652506\pi\)
0.999011 0.0444727i \(-0.0141608\pi\)
\(68\) −2.56155 + 4.43674i −0.310634 + 0.538034i
\(69\) −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 \(-0.333602\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 9.00000 1.05337 0.526685 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) 1.78078 + 3.08440i 0.207011 + 0.358554i
\(75\) 0 0
\(76\) 3.28078 5.68247i 0.376331 0.651824i
\(77\) 2.00000 0.227921
\(78\) 0.500000 + 3.57071i 0.0566139 + 0.404304i
\(79\) 4.80776 0.540916 0.270458 0.962732i \(-0.412825\pi\)
0.270458 + 0.962732i \(0.412825\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.56155 4.43674i −0.282876 0.489956i
\(83\) 2.43845 0.267654 0.133827 0.991005i \(-0.457273\pi\)
0.133827 + 0.991005i \(0.457273\pi\)
\(84\) −0.280776 0.486319i −0.0306352 0.0530618i
\(85\) 0 0
\(86\) 4.56155 0.491885
\(87\) 3.56155 + 6.16879i 0.381839 + 0.661364i
\(88\) −1.78078 + 3.08440i −0.189831 + 0.328798i
\(89\) 3.12311 5.40938i 0.331049 0.573393i −0.651669 0.758503i \(-0.725931\pi\)
0.982718 + 0.185110i \(0.0592643\pi\)
\(90\) 0 0
\(91\) 0.280776 + 2.00514i 0.0294334 + 0.210196i
\(92\) 4.68466 0.488409
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) −2.00000 + 3.46410i −0.206284 + 0.357295i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −8.90388 15.4220i −0.904052 1.56586i −0.822184 0.569221i \(-0.807245\pi\)
−0.0818678 0.996643i \(-0.526089\pi\)
\(98\) 3.34233 + 5.78908i 0.337626 + 0.584786i
\(99\) 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 \(0.996398\pi\)
\(102\) −2.56155 + 4.43674i −0.253632 + 0.439303i
\(103\) −8.56155 −0.843595 −0.421797 0.906690i \(-0.638601\pi\)
−0.421797 + 0.906690i \(0.638601\pi\)
\(104\) −3.34233 1.35234i −0.327742 0.132608i
\(105\) 0 0
\(106\) 6.12311 10.6055i 0.594729 1.03010i
\(107\) 9.68466 16.7743i 0.936251 1.62163i 0.163864 0.986483i \(-0.447604\pi\)
0.772387 0.635152i \(-0.219062\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 17.8078 1.70567 0.852837 0.522177i \(-0.174880\pi\)
0.852837 + 0.522177i \(0.174880\pi\)
\(110\) 0 0
\(111\) 1.78078 + 3.08440i 0.169024 + 0.292758i
\(112\) 0.561553 0.0530618
\(113\) −2.00000 3.46410i −0.188144 0.325875i 0.756487 0.654008i \(-0.226914\pi\)
−0.944632 + 0.328133i \(0.893581\pi\)
\(114\) 3.28078 5.68247i 0.307273 0.532212i
\(115\) 0 0
\(116\) −7.12311 −0.661364
\(117\) 0.500000 + 3.57071i 0.0462250 + 0.330113i
\(118\) 6.24621 0.575010
\(119\) −1.43845 + 2.49146i −0.131862 + 0.228392i
\(120\) 0 0
\(121\) −0.842329 1.45896i −0.0765754 0.132632i
\(122\) 10.6847 0.967344
\(123\) −2.56155 4.43674i −0.230967 0.400047i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 0 0
\(126\) −0.280776 0.486319i −0.0250136 0.0433247i
\(127\) −0.596118 + 1.03251i −0.0528969 + 0.0916201i −0.891261 0.453490i \(-0.850179\pi\)
0.838364 + 0.545110i \(0.183512\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 4.56155 0.401622
\(130\) 0 0
\(131\) 9.12311 0.797089 0.398545 0.917149i \(-0.369515\pi\)
0.398545 + 0.917149i \(0.369515\pi\)
\(132\) −1.78078 + 3.08440i −0.154997 + 0.268462i
\(133\) 1.84233 3.19101i 0.159750 0.276695i
\(134\) 4.40388 + 7.62775i 0.380437 + 0.658937i
\(135\) 0 0
\(136\) −2.56155 4.43674i −0.219651 0.380447i
\(137\) 8.24621 + 14.2829i 0.704521 + 1.22027i 0.966864 + 0.255292i \(0.0821716\pi\)
−0.262343 + 0.964975i \(0.584495\pi\)
\(138\) 4.68466 0.398785
\(139\) −8.71922 15.1021i −0.739555 1.28095i −0.952696 0.303925i \(-0.901703\pi\)
0.213141 0.977021i \(-0.431631\pi\)
\(140\) 0 0
\(141\) −2.00000 + 3.46410i −0.168430 + 0.291730i
\(142\) 8.43845 0.708139
\(143\) 10.1231 7.90084i 0.846537 0.660702i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −4.50000 + 7.79423i −0.372423 + 0.645055i
\(147\) 3.34233 + 5.78908i 0.275671 + 0.477476i
\(148\) −3.56155 −0.292758
\(149\) −3.12311 5.40938i −0.255855 0.443153i 0.709273 0.704934i \(-0.249024\pi\)
−0.965127 + 0.261781i \(0.915690\pi\)
\(150\) 0 0
\(151\) −4.31534 −0.351178 −0.175589 0.984464i \(-0.556183\pi\)
−0.175589 + 0.984464i \(0.556183\pi\)
\(152\) 3.28078 + 5.68247i 0.266106 + 0.460909i
\(153\) −2.56155 + 4.43674i −0.207089 + 0.358689i
\(154\) −1.00000 + 1.73205i −0.0805823 + 0.139573i
\(155\) 0 0
\(156\) −3.34233 1.35234i −0.267601 0.108274i
\(157\) 0.753789 0.0601589 0.0300794 0.999548i \(-0.490424\pi\)
0.0300794 + 0.999548i \(0.490424\pi\)
\(158\) −2.40388 + 4.16365i −0.191243 + 0.331242i
\(159\) 6.12311 10.6055i 0.485594 0.841073i
\(160\) 0 0
\(161\) 2.63068 0.207327
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −8.24621 14.2829i −0.645893 1.11872i −0.984094 0.177646i \(-0.943152\pi\)
0.338201 0.941074i \(-0.390182\pi\)
\(164\) 5.12311 0.400047
\(165\) 0 0
\(166\) −1.21922 + 2.11176i −0.0946301 + 0.163904i
\(167\) −5.65767 + 9.79937i −0.437804 + 0.758298i −0.997520 0.0703862i \(-0.977577\pi\)
0.559716 + 0.828684i \(0.310910\pi\)
\(168\) 0.561553 0.0433247
\(169\) 9.34233 + 9.03996i 0.718641 + 0.695382i
\(170\) 0 0
\(171\) 3.28078 5.68247i 0.250887 0.434549i
\(172\) −2.28078 + 3.95042i −0.173908 + 0.301217i
\(173\) 8.56155 + 14.8290i 0.650923 + 1.12743i 0.982899 + 0.184144i \(0.0589512\pi\)
−0.331977 + 0.943288i \(0.607715\pi\)
\(174\) −7.12311 −0.540001
\(175\) 0 0
\(176\) −1.78078 3.08440i −0.134231 0.232495i
\(177\) 6.24621 0.469494
\(178\) 3.12311 + 5.40938i 0.234087 + 0.405450i
\(179\) 1.65767 2.87117i 0.123900 0.214601i −0.797402 0.603448i \(-0.793793\pi\)
0.921302 + 0.388847i \(0.127126\pi\)
\(180\) 0 0
\(181\) 17.4924 1.30020 0.650101 0.759848i \(-0.274727\pi\)
0.650101 + 0.759848i \(0.274727\pi\)
\(182\) −1.87689 0.759413i −0.139125 0.0562914i
\(183\) 10.6847 0.789833
\(184\) −2.34233 + 4.05703i −0.172679 + 0.299088i
\(185\) 0 0
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 18.2462 1.33430
\(188\) −2.00000 3.46410i −0.145865 0.252646i
\(189\) −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 \(0.678372\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.50000 + 2.59808i −0.107972 + 0.187014i −0.914949 0.403570i \(-0.867769\pi\)
0.806976 + 0.590584i \(0.201102\pi\)
\(194\) 17.8078 1.27852
\(195\) 0 0
\(196\) −6.68466 −0.477476
\(197\) 1.56155 2.70469i 0.111256 0.192701i −0.805021 0.593246i \(-0.797846\pi\)
0.916277 + 0.400545i \(0.131179\pi\)
\(198\) −1.78078 + 3.08440i −0.126554 + 0.219198i
\(199\) 4.28078 + 7.41452i 0.303456 + 0.525602i 0.976916 0.213622i \(-0.0685261\pi\)
−0.673460 + 0.739223i \(0.735193\pi\)
\(200\) 0 0
\(201\) 4.40388 + 7.62775i 0.310626 + 0.538020i
\(202\) −5.12311 8.87348i −0.360460 0.624336i
\(203\) −4.00000 −0.280745
\(204\) −2.56155 4.43674i −0.179345 0.310634i
\(205\) 0 0
\(206\) 4.28078 7.41452i 0.298256 0.516594i
\(207\) 4.68466 0.325606
\(208\) 2.84233 2.21837i 0.197080 0.153816i
\(209\) −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 \(0.0878172\pi\)
\(212\) 6.12311 + 10.6055i 0.420537 + 0.728391i
\(213\) 8.43845 0.578193
\(214\) 9.68466 + 16.7743i 0.662030 + 1.14667i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −1.12311 1.94528i −0.0762414 0.132054i
\(218\) −8.90388 + 15.4220i −0.603047 + 1.04451i
\(219\) −4.50000 + 7.79423i −0.304082 + 0.526685i
\(220\) 0 0
\(221\) 2.56155 + 18.2931i 0.172309 + 1.23053i
\(222\) −3.56155 −0.239036
\(223\) 2.28078 3.95042i 0.152732 0.264540i −0.779499 0.626404i \(-0.784526\pi\)
0.932231 + 0.361864i \(0.117860\pi\)
\(224\) −0.280776 + 0.486319i −0.0187602 + 0.0324936i
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) −8.65767 14.9955i −0.574630 0.995288i −0.996082 0.0884373i \(-0.971813\pi\)
0.421452 0.906851i \(-0.361521\pi\)
\(228\) 3.28078 + 5.68247i 0.217275 + 0.376331i
\(229\) −23.4924 −1.55242 −0.776211 0.630473i \(-0.782861\pi\)
−0.776211 + 0.630473i \(0.782861\pi\)
\(230\) 0 0
\(231\) −1.00000 + 1.73205i −0.0657952 + 0.113961i
\(232\) 3.56155 6.16879i 0.233827 0.405001i
\(233\) −0.630683 −0.0413174 −0.0206587 0.999787i \(-0.506576\pi\)
−0.0206587 + 0.999787i \(0.506576\pi\)
\(234\) −3.34233 1.35234i −0.218495 0.0884055i
\(235\) 0 0
\(236\) −3.12311 + 5.40938i −0.203297 + 0.352120i
\(237\) −2.40388 + 4.16365i −0.156149 + 0.270458i
\(238\) −1.43845 2.49146i −0.0932407 0.161498i
\(239\) −10.0540 −0.650338 −0.325169 0.945656i \(-0.605421\pi\)
−0.325169 + 0.945656i \(0.605421\pi\)
\(240\) 0 0
\(241\) −5.71922 9.90599i −0.368408 0.638101i 0.620909 0.783883i \(-0.286764\pi\)
−0.989317 + 0.145782i \(0.953430\pi\)
\(242\) 1.68466 0.108294
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −5.34233 + 9.25319i −0.342008 + 0.592375i
\(245\) 0 0
\(246\) 5.12311 0.326637
\(247\) −3.28078 23.4294i −0.208751 1.49078i
\(248\) 4.00000 0.254000
\(249\) −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 \(0.783597\pi\)
\(252\) 0.561553 0.0353745
\(253\) −8.34233 14.4493i −0.524478 0.908422i
\(254\) −0.596118 1.03251i −0.0374038 0.0647852i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −13.8078 + 23.9157i −0.861305 + 1.49182i 0.00936553 + 0.999956i \(0.497019\pi\)
−0.870670 + 0.491867i \(0.836315\pi\)
\(258\) −2.28078 + 3.95042i −0.141995 + 0.245942i
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) −7.12311 −0.440909
\(262\) −4.56155 + 7.90084i −0.281814 + 0.488116i
\(263\) −9.34233 + 16.1814i −0.576073 + 0.997787i 0.419851 + 0.907593i \(0.362082\pi\)
−0.995924 + 0.0901944i \(0.971251\pi\)
\(264\) −1.78078 3.08440i −0.109599 0.189831i
\(265\) 0 0
\(266\) 1.84233 + 3.19101i 0.112960 + 0.195653i
\(267\) 3.12311 + 5.40938i 0.191131 + 0.331049i
\(268\) −8.80776 −0.538020
\(269\) −10.6847 18.5064i −0.651455 1.12835i −0.982770 0.184833i \(-0.940826\pi\)
0.331315 0.943520i \(-0.392508\pi\)
\(270\) 0 0
\(271\) 9.96543 17.2606i 0.605357 1.04851i −0.386638 0.922232i \(-0.626364\pi\)
0.991995 0.126278i \(-0.0403030\pi\)
\(272\) 5.12311 0.310634
\(273\) −1.87689 0.759413i −0.113595 0.0459618i
\(274\) −16.4924 −0.996344
\(275\) 0 0
\(276\) −2.34233 + 4.05703i −0.140992 + 0.244205i
\(277\) −2.50000 4.33013i −0.150210 0.260172i 0.781094 0.624413i \(-0.214662\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 17.4384 1.04589
\(279\) −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 \(0.683181\pi\)
\(282\) −2.00000 3.46410i −0.119098 0.206284i
\(283\) 5.80776 10.0593i 0.345236 0.597966i −0.640161 0.768241i \(-0.721132\pi\)
0.985397 + 0.170275i \(0.0544656\pi\)
\(284\) −4.21922 + 7.30791i −0.250365 + 0.433645i
\(285\) 0 0
\(286\) 1.78078 + 12.7173i 0.105300 + 0.751989i
\(287\) 2.87689 0.169818
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −4.62311 + 8.00745i −0.271947 + 0.471027i
\(290\) 0 0
\(291\) 17.8078 1.04391
\(292\) −4.50000 7.79423i −0.263343 0.456123i
\(293\) −1.87689 3.25088i −0.109649 0.189918i 0.805979 0.591944i \(-0.201639\pi\)
−0.915628 + 0.402026i \(0.868306\pi\)
\(294\) −6.68466 −0.389857
\(295\) 0 0
\(296\) 1.78078 3.08440i 0.103506 0.179277i
\(297\) −1.78078 + 3.08440i −0.103331 + 0.178975i
\(298\) 6.24621 0.361833
\(299\) 13.3153 10.3923i 0.770046 0.601003i
\(300\) 0 0
\(301\) −1.28078 + 2.21837i −0.0738227 + 0.127865i
\(302\) 2.15767 3.73720i 0.124160 0.215051i
\(303\) −5.12311 8.87348i −0.294315 0.509768i
\(304\) −6.56155 −0.376331
\(305\) 0 0
\(306\) −2.56155 4.43674i −0.146434 0.253632i
\(307\) 5.75379 0.328386 0.164193 0.986428i \(-0.447498\pi\)
0.164193 + 0.986428i \(0.447498\pi\)
\(308\) −1.00000 1.73205i −0.0569803 0.0986928i
\(309\) 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 \(0.722379\pi\)
\(312\) 2.84233 2.21837i 0.160915 0.125590i
\(313\) 31.0000 1.75222 0.876112 0.482108i \(-0.160129\pi\)
0.876112 + 0.482108i \(0.160129\pi\)
\(314\) −0.376894 + 0.652800i −0.0212694 + 0.0368396i
\(315\) 0 0
\(316\) −2.40388 4.16365i −0.135229 0.234223i
\(317\) −0.246211 −0.0138286 −0.00691430 0.999976i \(-0.502201\pi\)
−0.00691430 + 0.999976i \(0.502201\pi\)
\(318\) 6.12311 + 10.6055i 0.343367 + 0.594729i
\(319\) 12.6847 + 21.9705i 0.710205 + 1.23011i
\(320\) 0 0
\(321\) 9.68466 + 16.7743i 0.540545 + 0.936251i
\(322\) −1.31534 + 2.27824i −0.0733011 + 0.126961i
\(323\) 16.8078 29.1119i 0.935209 1.61983i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 16.4924 0.913431
\(327\) −8.90388 + 15.4220i −0.492386 + 0.852837i
\(328\) −2.56155 + 4.43674i −0.141438 + 0.244978i
\(329\) −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 \(0.795494\pi\)
\(332\) −1.21922 2.11176i −0.0669136 0.115898i
\(333\) −3.56155 −0.195172
\(334\) −5.65767 9.79937i −0.309574 0.536198i
\(335\) 0 0
\(336\) −0.280776 + 0.486319i −0.0153176 + 0.0265309i
\(337\) −29.0540 −1.58267 −0.791335 0.611382i \(-0.790614\pi\)
−0.791335 + 0.611382i \(0.790614\pi\)
\(338\) −12.5000 + 3.57071i −0.679910 + 0.194221i
\(339\) 4.00000 0.217250
\(340\) 0 0
\(341\) −7.12311 + 12.3376i −0.385738 + 0.668117i
\(342\) 3.28078 + 5.68247i 0.177404 + 0.307273i
\(343\) −7.68466 −0.414933
\(344\) −2.28078 3.95042i −0.122971 0.212992i
\(345\) 0 0
\(346\) −17.1231 −0.920544
\(347\) 2.09612 + 3.63058i 0.112526 + 0.194900i 0.916788 0.399374i \(-0.130773\pi\)
−0.804262 + 0.594274i \(0.797439\pi\)
\(348\) 3.56155 6.16879i 0.190919 0.330682i
\(349\) 1.37689 2.38485i 0.0737035 0.127658i −0.826818 0.562469i \(-0.809851\pi\)
0.900522 + 0.434811i \(0.143185\pi\)
\(350\) 0 0
\(351\) −3.34233 1.35234i −0.178400 0.0721828i
\(352\) 3.56155 0.189831
\(353\) 7.12311 12.3376i 0.379125 0.656663i −0.611810 0.791004i \(-0.709558\pi\)
0.990935 + 0.134341i \(0.0428918\pi\)
\(354\) −3.12311 + 5.40938i −0.165991 + 0.287505i
\(355\) 0 0
\(356\) −6.24621 −0.331049
\(357\) −1.43845 2.49146i −0.0761307 0.131862i
\(358\) 1.65767 + 2.87117i 0.0876106 + 0.151746i
\(359\) −13.1231 −0.692611 −0.346306 0.938122i \(-0.612564\pi\)
−0.346306 + 0.938122i \(0.612564\pi\)
\(360\) 0 0
\(361\) −12.0270 + 20.8314i −0.632999 + 1.09639i
\(362\) −8.74621 + 15.1489i −0.459691 + 0.796208i
\(363\) 1.68466 0.0884216
\(364\) 1.59612 1.24573i 0.0836593 0.0652941i
\(365\) 0 0
\(366\) −5.34233 + 9.25319i −0.279248 + 0.483672i
\(367\) 15.4039 26.6803i 0.804076 1.39270i −0.112837 0.993614i \(-0.535994\pi\)
0.916913 0.399087i \(-0.130673\pi\)
\(368\) −2.34233 4.05703i −0.122102 0.211487i
\(369\) 5.12311 0.266698
\(370\) 0 0
\(371\) 3.43845 + 5.95557i 0.178515 + 0.309198i
\(372\) 4.00000 0.207390
\(373\) −11.7462 20.3450i −0.608196 1.05343i −0.991538 0.129819i \(-0.958560\pi\)
0.383342 0.923607i \(-0.374773\pi\)
\(374\) −9.12311 + 15.8017i −0.471745 + 0.817086i
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) −20.2462 + 15.8017i −1.04273 + 0.813828i
\(378\) 0.561553 0.0288832
\(379\) −6.52699 + 11.3051i −0.335269 + 0.580703i −0.983536 0.180710i \(-0.942160\pi\)
0.648268 + 0.761413i \(0.275494\pi\)
\(380\) 0 0
\(381\) −0.596118 1.03251i −0.0305400 0.0528969i
\(382\) −12.9309 −0.661601
\(383\) 4.78078 + 8.28055i 0.244286 + 0.423116i 0.961931 0.273293i \(-0.0881130\pi\)
−0.717644 + 0.696410i \(0.754780\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) −1.50000 2.59808i −0.0763480 0.132239i
\(387\) −2.28078 + 3.95042i −0.115938 + 0.200811i
\(388\) −8.90388 + 15.4220i −0.452026 + 0.782932i
\(389\) −13.3693 −0.677851 −0.338926 0.940813i \(-0.610064\pi\)
−0.338926 + 0.940813i \(0.610064\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 3.34233 5.78908i 0.168813 0.292393i
\(393\) −4.56155 + 7.90084i −0.230100 + 0.398545i
\(394\) 1.56155 + 2.70469i 0.0786699 + 0.136260i
\(395\) 0 0
\(396\) −1.78078 3.08440i −0.0894874 0.154997i
\(397\) −5.40388 9.35980i −0.271213 0.469755i 0.697960 0.716137i \(-0.254091\pi\)
−0.969173 + 0.246382i \(0.920758\pi\)
\(398\) −8.56155 −0.429152
\(399\) 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 \(-0.216212\pi\)
\(402\) −8.80776 −0.439291
\(403\) −13.3693 5.40938i −0.665973 0.269460i
\(404\) 10.2462 0.509768
\(405\) 0 0
\(406\) 2.00000 3.46410i 0.0992583 0.171920i
\(407\) 6.34233 + 10.9852i 0.314378 + 0.544518i
\(408\) 5.12311 0.253632
\(409\) 0.123106 + 0.213225i 0.00608718 + 0.0105433i 0.869053 0.494719i \(-0.164729\pi\)
−0.862966 + 0.505262i \(0.831396\pi\)
\(410\) 0 0
\(411\) −16.4924 −0.813511
\(412\) 4.28078 + 7.41452i 0.210899 + 0.365287i
\(413\) −1.75379 + 3.03765i −0.0862983 + 0.149473i
\(414\) −2.34233 + 4.05703i −0.115119 + 0.199392i
\(415\) 0 0
\(416\) 0.500000 + 3.57071i 0.0245145 + 0.175069i
\(417\) 17.4384 0.853964
\(418\) 11.6847 20.2384i 0.571515 0.989894i
\(419\) −8.46543 + 14.6626i −0.413564 + 0.716313i −0.995276 0.0970811i \(-0.969049\pi\)
0.581713 + 0.813394i \(0.302383\pi\)
\(420\) 0 0
\(421\) 14.7538 0.719056 0.359528 0.933134i \(-0.382938\pi\)
0.359528 + 0.933134i \(0.382938\pi\)
\(422\) 3.56155 + 6.16879i 0.173374 + 0.300292i
\(423\) −2.00000 3.46410i −0.0972433 0.168430i
\(424\) −12.2462 −0.594729
\(425\) 0 0
\(426\) −4.21922 + 7.30791i −0.204422 + 0.354069i
\(427\) −3.00000 + 5.19615i −0.145180 + 0.251459i
\(428\) −19.3693 −0.936251
\(429\) 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 \(0.901958\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 0.657671 + 1.13912i 0.0316056 + 0.0547426i 0.881396 0.472379i \(-0.156605\pi\)
−0.849790 + 0.527121i \(0.823271\pi\)
\(434\) 2.24621 0.107822
\(435\) 0 0
\(436\) −8.90388 15.4220i −0.426419 0.738579i
\(437\) −30.7386 −1.47043
\(438\) −4.50000 7.79423i −0.215018 0.372423i
\(439\) −10.9654 + 18.9927i −0.523352 + 0.906472i 0.476279 + 0.879294i \(0.341985\pi\)
−0.999631 + 0.0271774i \(0.991348\pi\)
\(440\) 0 0
\(441\) −6.68466 −0.318317
\(442\) −17.1231 6.92820i −0.814463 0.329541i
\(443\) 17.8078 0.846072 0.423036 0.906113i \(-0.360964\pi\)
0.423036 + 0.906113i \(0.360964\pi\)
\(444\) 1.78078 3.08440i 0.0845119 0.146379i
\(445\) 0 0
\(446\) 2.28078 + 3.95042i 0.107998 + 0.187058i
\(447\) 6.24621 0.295436
\(448\) −0.280776 0.486319i −0.0132654 0.0229764i
\(449\) −2.56155 4.43674i −0.120887 0.209383i 0.799231 0.601024i \(-0.205241\pi\)
−0.920118 + 0.391642i \(0.871907\pi\)
\(450\) 0 0
\(451\) −9.12311 15.8017i −0.429590 0.744072i
\(452\) −2.00000 + 3.46410i −0.0940721 + 0.162938i
\(453\) 2.15767 3.73720i 0.101376 0.175589i
\(454\) 17.3153 0.812649
\(455\) 0 0
\(456\) −6.56155 −0.307273
\(457\) −18.7462 + 32.4694i −0.876911 + 1.51885i −0.0221975 + 0.999754i \(0.507066\pi\)
−0.854713 + 0.519100i \(0.826267\pi\)
\(458\) 11.7462 20.3450i 0.548864 0.950661i
\(459\) −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 \(-0.474736\pi\)
\(462\) −1.00000 1.73205i −0.0465242 0.0805823i
\(463\) 7.19224 0.334252 0.167126 0.985936i \(-0.446551\pi\)
0.167126 + 0.985936i \(0.446551\pi\)
\(464\) 3.56155 + 6.16879i 0.165341 + 0.286379i
\(465\) 0 0
\(466\) 0.315342 0.546188i 0.0146079 0.0253017i
\(467\) −7.56155 −0.349907 −0.174953 0.984577i \(-0.555978\pi\)
−0.174953 + 0.984577i \(0.555978\pi\)
\(468\) 2.84233 2.21837i 0.131387 0.102544i
\(469\) −4.94602 −0.228386
\(470\) 0 0
\(471\) −0.376894 + 0.652800i −0.0173664 + 0.0300794i
\(472\) −3.12311 5.40938i −0.143753 0.248987i
\(473\) 16.2462 0.747002
\(474\) −2.40388 4.16365i −0.110414 0.191243i
\(475\) 0 0
\(476\) 2.87689 0.131862
\(477\) 6.12311 + 10.6055i 0.280358 + 0.485594i
\(478\) 5.02699 8.70700i 0.229929 0.398249i
\(479\) −14.8078 + 25.6478i −0.676584 + 1.17188i 0.299419 + 0.954122i \(0.403207\pi\)
−0.976003 + 0.217756i \(0.930126\pi\)
\(480\) 0 0
\(481\) −10.1231 + 7.90084i −0.461574 + 0.360247i
\(482\) 11.4384 0.521007
\(483\) −1.31534 + 2.27824i −0.0598501 + 0.103663i
\(484\) −0.842329 + 1.45896i −0.0382877 + 0.0663162i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −15.1577 26.2539i −0.686860 1.18968i −0.972849 0.231443i \(-0.925655\pi\)
0.285989 0.958233i \(-0.407678\pi\)
\(488\) −5.34233 9.25319i −0.241836 0.418872i
\(489\) 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 \(-0.00117620\pi\)
\(492\) −2.56155 + 4.43674i −0.115484 + 0.200024i
\(493\) −36.4924 −1.64354
\(494\) 21.9309 + 8.87348i 0.986716 + 0.399237i
\(495\) 0 0
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) −2.36932 + 4.10378i −0.106278 + 0.184080i
\(498\) −1.21922 2.11176i −0.0546347 0.0946301i
\(499\) −31.0540 −1.39017 −0.695083 0.718929i \(-0.744633\pi\)
−0.695083 + 0.718929i \(0.744633\pi\)
\(500\) 0 0
\(501\) −5.65767 9.79937i −0.252766 0.437804i
\(502\) −4.93087 −0.220075
\(503\) 18.3423 + 31.7698i 0.817844 + 1.41655i 0.907268 + 0.420554i \(0.138164\pi\)
−0.0894236 + 0.995994i \(0.528502\pi\)
\(504\) −0.280776 + 0.486319i −0.0125068 + 0.0216624i
\(505\) 0 0
\(506\) 16.6847 0.741724
\(507\) −12.5000 + 3.57071i −0.555144 + 0.158581i
\(508\) 1.19224 0.0528969
\(509\) −0.123106 + 0.213225i −0.00545656 + 0.00945104i −0.868741 0.495267i \(-0.835070\pi\)
0.863284 + 0.504718i \(0.168404\pi\)
\(510\) 0 0
\(511\) −2.52699 4.37687i −0.111787 0.193621i
\(512\) 1.00000 0.0441942
\(513\) 3.28078 + 5.68247i 0.144850 + 0.250887i
\(514\) −13.8078 23.9157i −0.609034 1.05488i
\(515\) 0 0
\(516\) −2.28078 3.95042i −0.100406 0.173908i
\(517\) −7.12311 + 12.3376i −0.313274 + 0.542606i
\(518\) 1.00000 1.73205i 0.0439375 0.0761019i
\(519\) −17.1231 −0.751621
\(520\) 0 0
\(521\) −14.7386 −0.645711 −0.322856 0.946448i \(-0.604643\pi\)
−0.322856 + 0.946448i \(0.604643\pi\)
\(522\) 3.56155 6.16879i 0.155885 0.270001i
\(523\) 1.96543 3.40423i 0.0859425 0.148857i −0.819850 0.572578i \(-0.805943\pi\)
0.905792 + 0.423722i \(0.139277\pi\)
\(524\) −4.56155 7.90084i −0.199272 0.345150i
\(525\) 0 0
\(526\) −9.34233 16.1814i −0.407345 0.705542i
\(527\) −10.2462 17.7470i −0.446332 0.773070i
\(528\) 3.56155 0.154997
\(529\) 0.526988 + 0.912769i 0.0229125 + 0.0396856i
\(530\) 0 0
\(531\) −3.12311 + 5.40938i −0.135531 + 0.234747i
\(532\) −3.68466 −0.159750
\(533\) 14.5616 11.3649i 0.630731 0.492270i
\(534\) −6.24621 −0.270300
\(535\) 0 0
\(536\) 4.40388 7.62775i 0.190219 0.329469i
\(537\) 1.65767 + 2.87117i 0.0715338 + 0.123900i
\(538\) 21.3693 0.921297
\(539\) 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 \(0.767839\pi\)
\(542\) 9.96543 + 17.2606i 0.428052 + 0.741408i
\(543\) −8.74621 + 15.1489i −0.375336 + 0.650101i
\(544\) −2.56155 + 4.43674i −0.109826 + 0.190224i
\(545\) 0 0
\(546\) 1.59612 1.24573i 0.0683075 0.0533124i
\(547\) −2.06913 −0.0884696 −0.0442348 0.999021i \(-0.514085\pi\)
−0.0442348 + 0.999021i \(0.514085\pi\)
\(548\) 8.24621 14.2829i 0.352261 0.610133i
\(549\) −5.34233 + 9.25319i −0.228005 + 0.394916i
\(550\) 0 0
\(551\) 46.7386 1.99113
\(552\) −2.34233 4.05703i −0.0996962 0.172679i
\(553\) −1.34991 2.33811i −0.0574039 0.0994264i
\(554\) 5.00000 0.212430
\(555\) 0 0
\(556\) −8.71922 + 15.1021i −0.369777 + 0.640473i
\(557\) −4.80776 + 8.32729i −0.203712 + 0.352839i −0.949721 0.313096i \(-0.898634\pi\)
0.746010 + 0.665935i \(0.231967\pi\)
\(558\) 4.00000 0.169334
\(559\) 2.28078 + 16.2880i 0.0964666 + 0.688909i
\(560\) 0 0
\(561\) −9.12311 + 15.8017i −0.385178 + 0.667148i
\(562\) 9.12311 15.8017i 0.384835 0.666554i
\(563\) −0.0961180 0.166481i −0.00405089 0.00701635i 0.863993 0.503504i \(-0.167956\pi\)
−0.868044 + 0.496488i \(0.834623\pi\)
\(564\) 4.00000 0.168430
\(565\) 0 0
\(566\) 5.80776 + 10.0593i 0.244119 + 0.422826i
\(567\) 0.561553 0.0235830
\(568\) −4.21922 7.30791i −0.177035 0.306633i
\(569\) 22.2462 38.5316i 0.932610 1.61533i 0.153768 0.988107i \(-0.450859\pi\)
0.778842 0.627220i \(-0.215807\pi\)
\(570\) 0 0
\(571\) −40.4233 −1.69166 −0.845831 0.533451i \(-0.820895\pi\)
−0.845831 + 0.533451i \(0.820895\pi\)
\(572\) −11.9039 4.81645i −0.497726 0.201386i
\(573\) −12.9309 −0.540195
\(574\) −1.43845 + 2.49146i −0.0600396 + 0.103992i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 23.0000 0.957503 0.478751 0.877951i \(-0.341090\pi\)
0.478751 + 0.877951i \(0.341090\pi\)
\(578\) −4.62311 8.00745i −0.192296 0.333066i
\(579\) −1.50000 2.59808i −0.0623379 0.107972i
\(580\) 0 0
\(581\) −0.684658 1.18586i −0.0284044 0.0491979i
\(582\) −8.90388 + 15.4220i −0.369078 + 0.639261i
\(583\) 21.8078 37.7722i 0.903185 1.56436i
\(584\) 9.00000 0.372423
\(585\) 0 0
\(586\) 3.75379 0.155068
\(587\) −5.46543 + 9.46641i −0.225583 + 0.390721i −0.956494 0.291752i \(-0.905762\pi\)
0.730911 + 0.682472i \(0.239095\pi\)
\(588\) 3.34233 5.78908i 0.137835 0.238738i
\(589\) 13.1231 + 22.7299i 0.540728 + 0.936569i
\(590\) 0 0
\(591\) 1.56155 + 2.70469i 0.0642337 + 0.111256i
\(592\) 1.78078 + 3.08440i 0.0731895 + 0.126768i
\(593\) 26.9848 1.10813 0.554067 0.832472i \(-0.313075\pi\)
0.554067 + 0.832472i \(0.313075\pi\)
\(594\) −1.78078 3.08440i −0.0730661 0.126554i
\(595\) 0 0
\(596\) −3.12311 + 5.40938i −0.127927 + 0.221577i
\(597\) −8.56155 −0.350401
\(598\) 2.34233 + 16.7276i 0.0957850 + 0.684041i
\(599\) −30.6847 −1.25374 −0.626871 0.779123i \(-0.715665\pi\)
−0.626871 + 0.779123i \(0.715665\pi\)
\(600\) 0 0
\(601\) −7.40388 + 12.8239i −0.302011 + 0.523098i −0.976591 0.215103i \(-0.930991\pi\)
0.674581 + 0.738201i \(0.264324\pi\)
\(602\) −1.28078 2.21837i −0.0522005 0.0904140i
\(603\) −8.80776 −0.358680
\(604\) 2.15767 + 3.73720i 0.0877944 + 0.152064i
\(605\) 0 0
\(606\) 10.2462 0.416224
\(607\) 7.31534 + 12.6705i 0.296921 + 0.514281i 0.975430 0.220310i \(-0.0707070\pi\)
−0.678509 + 0.734592i \(0.737374\pi\)
\(608\) 3.28078 5.68247i 0.133053 0.230455i
\(609\) 2.00000 3.46410i 0.0810441 0.140372i
\(610\) 0 0
\(611\) −13.3693 5.40938i −0.540865 0.218840i
\(612\) 5.12311 0.207089
\(613\) −16.7732 + 29.0520i −0.677463 + 1.17340i 0.298279 + 0.954479i \(0.403587\pi\)
−0.975742 + 0.218922i \(0.929746\pi\)
\(614\) −2.87689 + 4.98293i −0.116102 + 0.201095i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −11.3153 19.5987i −0.455538 0.789016i 0.543180 0.839616i \(-0.317220\pi\)
−0.998719 + 0.0506001i \(0.983887\pi\)
\(618\) 4.28078 + 7.41452i 0.172198 + 0.298256i
\(619\) 41.3002 1.65999 0.829997 0.557767i \(-0.188342\pi\)
0.829997 + 0.557767i \(0.188342\pi\)
\(620\) 0 0
\(621\) −2.34233 + 4.05703i −0.0939944 + 0.162803i
\(622\) 11.3423 19.6455i 0.454786 0.787712i
\(623\) −3.50758 −0.140528
\(624\) 0.500000 + 3.57071i 0.0200160 + 0.142943i
\(625\) 0 0
\(626\) −15.5000 + 26.8468i −0.619505 + 1.07301i
\(627\) 11.6847 20.2384i 0.466640 0.808245i
\(628\) −0.376894 0.652800i −0.0150397 0.0260496i
\(629\) −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 \(0.859143\pi\)
\(632\) 4.80776 0.191243
\(633\) 3.56155 + 6.16879i 0.141559 + 0.245187i
\(634\) 0.123106 0.213225i 0.00488915 0.00846825i
\(635\) 0 0
\(636\) −12.2462 −0.485594
\(637\) −19.0000 + 14.8290i −0.752807 + 0.587548i
\(638\) −25.3693 −1.00438
\(639\) −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 \(0.974683\pi\)
\(642\) −19.3693 −0.764446
\(643\) 22.7732 + 39.4443i 0.898087 + 1.55553i 0.829937 + 0.557858i \(0.188377\pi\)
0.0681507 + 0.997675i \(0.478290\pi\)
\(644\) −1.31534 2.27824i −0.0518317 0.0897752i
\(645\) 0 0
\(646\) 16.8078 + 29.1119i 0.661293 + 1.14539i
\(647\) 14.7116 25.4813i 0.578374 1.00177i −0.417291 0.908773i \(-0.637021\pi\)
0.995666 0.0930013i \(-0.0296461\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 22.2462 0.873240
\(650\) 0 0
\(651\) 2.24621 0.0880360
\(652\) −8.24621 + 14.2829i −0.322947 + 0.559360i
\(653\) −1.80776 + 3.13114i −0.0707433 + 0.122531i −0.899227 0.437482i \(-0.855870\pi\)
0.828484 + 0.560013i \(0.189204\pi\)
\(654\) −8.90388 15.4220i −0.348169 0.603047i
\(655\) 0 0
\(656\) −2.56155 4.43674i −0.100012 0.173226i
\(657\) −4.50000 7.79423i −0.175562 0.304082i
\(658\) 2.24621 0.0875664
\(659\) −15.3423 26.5737i −0.597652 1.03516i −0.993167 0.116704i \(-0.962767\pi\)
0.395514 0.918460i \(-0.370566\pi\)
\(660\) 0 0
\(661\) −10.7732 + 18.6597i −0.419029 + 0.725779i −0.995842 0.0910968i \(-0.970963\pi\)
0.576813 + 0.816876i \(0.304296\pi\)
\(662\) −4.31534 −0.167721
\(663\) −17.1231 6.92820i −0.665006 0.269069i
\(664\) 2.43845 0.0946301
\(665\) 0 0
\(666\) 1.78078 3.08440i 0.0690037 0.119518i
\(667\) 16.6847 + 28.8987i 0.646033 + 1.11896i
\(668\) 11.3153 0.437804
\(669\) 2.28078 + 3.95042i 0.0881799 + 0.152732i
\(670\) 0 0
\(671\) 38.0540 1.46906
\(672\) −0.280776 0.486319i −0.0108312 0.0187602i
\(673\) −22.6231 + 39.1844i −0.872057 + 1.51045i −0.0121912 + 0.999926i \(0.503881\pi\)
−0.859865 + 0.510521i \(0.829453\pi\)
\(674\) 14.5270 25.1615i 0.559559 0.969184i
\(675\) 0 0
\(676\) 3.15767 12.6107i 0.121449 0.485026i
\(677\) −29.6155 −1.13822 −0.569109 0.822262i \(-0.692712\pi\)
−0.569109 + 0.822262i \(0.692712\pi\)
\(678\) −2.00000 + 3.46410i −0.0768095 + 0.133038i
\(679\) −5.00000 + 8.66025i −0.191882 + 0.332350i
\(680\) 0 0
\(681\) 17.3153 0.663525
\(682\) −7.12311 12.3376i −0.272758 0.472430i
\(683\) −9.78078 16.9408i −0.374251 0.648222i 0.615964 0.787775i \(-0.288767\pi\)
−0.990215 + 0.139553i \(0.955433\pi\)
\(684\) −6.56155 −0.250887
\(685\) 0 0
\(686\) 3.84233 6.65511i 0.146701 0.254093i
\(687\) 11.7462 20.3450i 0.448146 0.776211i
\(688\) 4.56155 0.173908
\(689\) 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 \(-0.236851\pi\)
\(692\) 8.56155 14.8290i 0.325461 0.563716i
\(693\) −1.00000 1.73205i −0.0379869 0.0657952i
\(694\) −4.19224 −0.159135
\(695\) 0 0
\(696\) 3.56155 + 6.16879i 0.135000 + 0.233827i
\(697\) 26.2462 0.994146
\(698\) 1.37689 + 2.38485i 0.0521162 + 0.0902679i
\(699\) 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 \(0.555116\pi\)
\(702\) 2.84233 2.21837i 0.107277 0.0837270i
\(703\) 23.3693 0.881390
\(704\) −1.78078 + 3.08440i −0.0671155 + 0.116248i
\(705\) 0 0
\(706\) 7.12311 + 12.3376i 0.268082 + 0.464331i
\(707\) 5.75379 0.216393
\(708\) −3.12311 5.40938i −0.117373 0.203297i
\(709\) 22.6231 + 39.1844i 0.849629 + 1.47160i 0.881540 + 0.472109i \(0.156507\pi\)
−0.0319115 + 0.999491i \(0.510159\pi\)
\(710\) 0 0
\(711\) −2.40388 4.16365i −0.0901526 0.156149i
\(712\) 3.12311 5.40938i 0.117043 0.202725i
\(713\) −9.36932 + 16.2281i −0.350884 + 0.607748i
\(714\) 2.87689 0.107665
\(715\) 0 0
\(716\) −3.31534 −0.123900
\(717\) 5.02699 8.70700i 0.187736 0.325169i
\(718\) 6.56155 11.3649i 0.244875 0.424136i
\(719\) 10.7808 + 18.6729i 0.402055 + 0.696380i 0.993974 0.109618i \(-0.0349627\pi\)
−0.591919 + 0.805998i \(0.701629\pi\)
\(720\) 0 0
\(721\) 2.40388 + 4.16365i 0.0895252 + 0.155062i
\(722\) −12.0270 20.8314i −0.447598 0.775263i
\(723\) 11.4384 0.425400
\(724\) −8.74621 15.1489i −0.325050 0.563004i
\(725\) 0 0
\(726\) −0.842329 + 1.45896i −0.0312618 + 0.0541470i
\(727\) 35.7926 1.32747 0.663737 0.747966i \(-0.268969\pi\)
0.663737 + 0.747966i \(0.268969\pi\)
\(728\) 0.280776 + 2.00514i 0.0104063 + 0.0743156i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −11.6847 + 20.2384i −0.432173 + 0.748545i
\(732\) −5.34233 9.25319i −0.197458 0.342008i
\(733\) 17.9848 0.664285 0.332143 0.943229i \(-0.392228\pi\)
0.332143 + 0.943229i \(0.392228\pi\)
\(734\) 15.4039 + 26.6803i 0.568568 + 0.984788i
\(735\) 0 0
\(736\) 4.68466 0.172679
\(737\) 15.6847 + 27.1666i 0.577752 + 1.00070i
\(738\) −2.56155 + 4.43674i −0.0942921 + 0.163319i
\(739\) 2.43845 4.22351i 0.0896997 0.155364i −0.817684 0.575667i \(-0.804743\pi\)
0.907384 + 0.420302i \(0.138076\pi\)
\(740\) 0 0
\(741\) 21.9309 + 8.87348i 0.805651 + 0.325975i
\(742\) −6.87689 −0.252459
\(743\) −1.43845 + 2.49146i −0.0527715 + 0.0914029i −0.891204 0.453602i \(-0.850139\pi\)
0.838433 + 0.545005i \(0.183472\pi\)
\(744\) −2.00000 + 3.46410i −0.0733236 + 0.127000i
\(745\) 0 0
\(746\) 23.4924 0.860119
\(747\) −1.21922 2.11176i −0.0446091 0.0772652i
\(748\) −9.12311 15.8017i −0.333574 0.577767i
\(749\) −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 \(0.955481\pi\)
\(752\) −2.00000 + 3.46410i −0.0729325 + 0.126323i
\(753\) −4.93087 −0.179691
\(754\) −3.56155 25.4346i −0.129704 0.926273i
\(755\) 0 0
\(756\) −0.280776 + 0.486319i −0.0102117 + 0.0176873i
\(757\) 9.15767 15.8616i 0.332841 0.576498i −0.650227 0.759740i \(-0.725326\pi\)
0.983068 + 0.183243i \(0.0586594\pi\)
\(758\) −6.52699 11.3051i −0.237071 0.410619i
\(759\) 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 \(-0.450990\pi\)
\(762\) 1.19224 0.0431902
\(763\) −5.00000 8.66025i −0.181012 0.313522i
\(764\) 6.46543 11.1985i 0.233911 0.405146i
\(765\) 0 0
\(766\) −9.56155 −0.345473
\(767\) 3.12311 + 22.3034i 0.112769 + 0.805330i
\(768\) 1.00000 0.0360844
\(769\) 10.8423 18.7795i 0.390984 0.677205i −0.601595 0.798801i \(-0.705468\pi\)
0.992580 + 0.121596i \(0.0388013\pi\)
\(770\) 0 0
\(771\) −13.8078 23.9157i −0.497274 0.861305i
\(772\) 3.00000 0.107972
\(773\) −5.80776 10.0593i −0.208891 0.361809i 0.742475 0.669874i \(-0.233652\pi\)
−0.951365 + 0.308065i \(0.900319\pi\)
\(774\) −2.28078 3.95042i −0.0819808 0.141995i
\(775\) 0 0
\(776\) −8.90388 15.4220i −0.319631 0.553617i
\(777\) 1.00000 1.73205i 0.0358748 0.0621370i
\(778\) 6.68466 11.5782i 0.239657 0.415097i
\(779\) −33.6155 −1.20440
\(780\) 0 0
\(781\) 30.0540 1.07542
\(782\) −12.0000 + 20.7846i −0.429119 + 0.743256i
\(783\) 3.56155 6.16879i 0.127280 0.220455i
\(784\) 3.34233 + 5.78908i 0.119369 + 0.206753i