Properties

Label 912.2.bn.m.65.1
Level $912$
Weight $2$
Character 912.65
Analytic conductor $7.282$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bn (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.1
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 912.65
Dual form 912.2.bn.m.449.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.57313 + 0.724745i) q^{3} +(1.22474 + 0.707107i) q^{5} +3.73205 q^{7} +(1.94949 - 2.28024i) q^{9} +O(q^{10})\) \(q+(-1.57313 + 0.724745i) q^{3} +(1.22474 + 0.707107i) q^{5} +3.73205 q^{7} +(1.94949 - 2.28024i) q^{9} +0.378937i q^{11} +(3.23205 - 1.86603i) q^{13} +(-2.43916 - 0.224745i) q^{15} +(-4.24264 - 2.44949i) q^{17} +(1.73205 - 4.00000i) q^{19} +(-5.87101 + 2.70478i) q^{21} +(0.328169 - 0.189469i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(-1.41421 + 5.00000i) q^{27} +(3.86370 + 6.69213i) q^{29} -4.46410i q^{31} +(-0.274633 - 0.596119i) q^{33} +(4.57081 + 2.63896i) q^{35} +4.26795i q^{37} +(-3.73205 + 5.27792i) q^{39} +(2.82843 - 4.89898i) q^{41} +(1.13397 - 1.96410i) q^{43} +(4.00000 - 1.41421i) q^{45} +(9.14162 - 5.27792i) q^{47} +6.92820 q^{49} +(8.44949 + 0.778539i) q^{51} +(3.01790 + 5.22715i) q^{53} +(-0.267949 + 0.464102i) q^{55} +(0.174235 + 7.54782i) q^{57} +(-4.19187 + 7.26054i) q^{59} +(1.76795 + 3.06218i) q^{61} +(7.27559 - 8.50997i) q^{63} +5.27792 q^{65} +(-0.866025 + 0.500000i) q^{67} +(-0.378937 + 0.535898i) q^{69} +(-1.79315 + 3.10583i) q^{71} +(1.50000 - 2.59808i) q^{73} +(4.24264 + 3.00000i) q^{75} +1.41421i q^{77} +(3.06218 + 1.76795i) q^{79} +(-1.39898 - 8.89060i) q^{81} +7.72741i q^{83} +(-3.46410 - 6.00000i) q^{85} +(-10.9282 - 7.72741i) q^{87} +(3.67423 + 6.36396i) q^{89} +(12.0622 - 6.96410i) q^{91} +(3.23533 + 7.02262i) q^{93} +(4.94975 - 3.67423i) q^{95} +(6.46410 + 3.73205i) q^{97} +(0.864068 + 0.738735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 16 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 16 q^{7} - 4 q^{9} + 12 q^{13} - 12 q^{21} - 12 q^{25} + 24 q^{33} - 16 q^{39} + 16 q^{43} + 32 q^{45} + 48 q^{51} - 16 q^{55} - 28 q^{57} + 28 q^{61} - 8 q^{63} + 12 q^{73} - 24 q^{79} + 28 q^{81} - 32 q^{87} + 48 q^{91} - 4 q^{93} + 24 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(1\)

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 0
\(3\) −1.57313 + 0.724745i −0.908248 + 0.418432i
\(4\) 0 0
\(5\) 1.22474 + 0.707107i 0.547723 + 0.316228i 0.748203 0.663470i \(-0.230917\pi\)
−0.200480 + 0.979698i \(0.564250\pi\)
\(6\) 0 0
\(7\) 3.73205 1.41058 0.705291 0.708918i \(-0.250816\pi\)
0.705291 + 0.708918i \(0.250816\pi\)
\(8\) 0 0
\(9\) 1.94949 2.28024i 0.649830 0.760080i
\(10\) 0 0
\(11\) 0.378937i 0.114254i 0.998367 + 0.0571270i \(0.0181940\pi\)
−0.998367 + 0.0571270i \(0.981806\pi\)
\(12\) 0 0
\(13\) 3.23205 1.86603i 0.896410 0.517542i 0.0203760 0.999792i \(-0.493514\pi\)
0.876034 + 0.482250i \(0.160180\pi\)
\(14\) 0 0
\(15\) −2.43916 0.224745i −0.629788 0.0580289i
\(16\) 0 0
\(17\) −4.24264 2.44949i −1.02899 0.594089i −0.112296 0.993675i \(-0.535820\pi\)
−0.916696 + 0.399586i \(0.869154\pi\)
\(18\) 0 0
\(19\) 1.73205 4.00000i 0.397360 0.917663i
\(20\) 0 0
\(21\) −5.87101 + 2.70478i −1.28116 + 0.590232i
\(22\) 0 0
\(23\) 0.328169 0.189469i 0.0684280 0.0395070i −0.465396 0.885103i \(-0.654088\pi\)
0.533824 + 0.845596i \(0.320755\pi\)
\(24\) 0 0
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) 0 0
\(27\) −1.41421 + 5.00000i −0.272166 + 0.962250i
\(28\) 0 0
\(29\) 3.86370 + 6.69213i 0.717472 + 1.24270i 0.961998 + 0.273055i \(0.0880341\pi\)
−0.244527 + 0.969643i \(0.578633\pi\)
\(30\) 0 0
\(31\) 4.46410i 0.801776i −0.916127 0.400888i \(-0.868702\pi\)
0.916127 0.400888i \(-0.131298\pi\)
\(32\) 0 0
\(33\) −0.274633 0.596119i −0.0478075 0.103771i
\(34\) 0 0
\(35\) 4.57081 + 2.63896i 0.772608 + 0.446065i
\(36\) 0 0
\(37\) 4.26795i 0.701647i 0.936442 + 0.350823i \(0.114098\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 0 0
\(39\) −3.73205 + 5.27792i −0.597606 + 0.845143i
\(40\) 0 0
\(41\) 2.82843 4.89898i 0.441726 0.765092i −0.556092 0.831121i \(-0.687700\pi\)
0.997818 + 0.0660290i \(0.0210330\pi\)
\(42\) 0 0
\(43\) 1.13397 1.96410i 0.172930 0.299523i −0.766513 0.642228i \(-0.778010\pi\)
0.939443 + 0.342706i \(0.111343\pi\)
\(44\) 0 0
\(45\) 4.00000 1.41421i 0.596285 0.210819i
\(46\) 0 0
\(47\) 9.14162 5.27792i 1.33344 0.769863i 0.347617 0.937637i \(-0.386991\pi\)
0.985826 + 0.167773i \(0.0536577\pi\)
\(48\) 0 0
\(49\) 6.92820 0.989743
\(50\) 0 0
\(51\) 8.44949 + 0.778539i 1.18317 + 0.109017i
\(52\) 0 0
\(53\) 3.01790 + 5.22715i 0.414540 + 0.718004i 0.995380 0.0960135i \(-0.0306092\pi\)
−0.580840 + 0.814018i \(0.697276\pi\)
\(54\) 0 0
\(55\) −0.267949 + 0.464102i −0.0361303 + 0.0625794i
\(56\) 0 0
\(57\) 0.174235 + 7.54782i 0.0230779 + 0.999734i
\(58\) 0 0
\(59\) −4.19187 + 7.26054i −0.545735 + 0.945241i 0.452825 + 0.891599i \(0.350416\pi\)
−0.998560 + 0.0536419i \(0.982917\pi\)
\(60\) 0 0
\(61\) 1.76795 + 3.06218i 0.226363 + 0.392072i 0.956727 0.290986i \(-0.0939832\pi\)
−0.730365 + 0.683057i \(0.760650\pi\)
\(62\) 0 0
\(63\) 7.27559 8.50997i 0.916639 1.07216i
\(64\) 0 0
\(65\) 5.27792 0.654645
\(66\) 0 0
\(67\) −0.866025 + 0.500000i −0.105802 + 0.0610847i −0.551967 0.833866i \(-0.686123\pi\)
0.446165 + 0.894951i \(0.352789\pi\)
\(68\) 0 0
\(69\) −0.378937 + 0.535898i −0.0456187 + 0.0645146i
\(70\) 0 0
\(71\) −1.79315 + 3.10583i −0.212808 + 0.368594i −0.952592 0.304250i \(-0.901594\pi\)
0.739784 + 0.672844i \(0.234928\pi\)
\(72\) 0 0
\(73\) 1.50000 2.59808i 0.175562 0.304082i −0.764794 0.644275i \(-0.777159\pi\)
0.940356 + 0.340193i \(0.110493\pi\)
\(74\) 0 0
\(75\) 4.24264 + 3.00000i 0.489898 + 0.346410i
\(76\) 0 0
\(77\) 1.41421i 0.161165i
\(78\) 0 0
\(79\) 3.06218 + 1.76795i 0.344522 + 0.198910i 0.662270 0.749265i \(-0.269593\pi\)
−0.317748 + 0.948175i \(0.602927\pi\)
\(80\) 0 0
\(81\) −1.39898 8.89060i −0.155442 0.987845i
\(82\) 0 0
\(83\) 7.72741i 0.848193i 0.905617 + 0.424097i \(0.139408\pi\)
−0.905617 + 0.424097i \(0.860592\pi\)
\(84\) 0 0
\(85\) −3.46410 6.00000i −0.375735 0.650791i
\(86\) 0 0
\(87\) −10.9282 7.72741i −1.17163 0.828465i
\(88\) 0 0
\(89\) 3.67423 + 6.36396i 0.389468 + 0.674579i 0.992378 0.123231i \(-0.0393255\pi\)
−0.602910 + 0.797809i \(0.705992\pi\)
\(90\) 0 0
\(91\) 12.0622 6.96410i 1.26446 0.730036i
\(92\) 0 0
\(93\) 3.23533 + 7.02262i 0.335489 + 0.728212i
\(94\) 0 0
\(95\) 4.94975 3.67423i 0.507833 0.376969i
\(96\) 0 0
\(97\) 6.46410 + 3.73205i 0.656330 + 0.378932i 0.790877 0.611975i \(-0.209625\pi\)
−0.134547 + 0.990907i \(0.542958\pi\)
\(98\) 0 0
\(99\) 0.864068 + 0.738735i 0.0868421 + 0.0742456i
\(100\) 0 0
\(101\) 6.69213 3.86370i 0.665892 0.384453i −0.128626 0.991693i \(-0.541057\pi\)
0.794518 + 0.607240i \(0.207723\pi\)
\(102\) 0 0
\(103\) 10.4641i 1.03106i 0.856872 + 0.515529i \(0.172405\pi\)
−0.856872 + 0.515529i \(0.827595\pi\)
\(104\) 0 0
\(105\) −9.10306 0.838759i −0.888368 0.0818545i
\(106\) 0 0
\(107\) −4.89898 −0.473602 −0.236801 0.971558i \(-0.576099\pi\)
−0.236801 + 0.971558i \(0.576099\pi\)
\(108\) 0 0
\(109\) −12.4641 7.19615i −1.19384 0.689266i −0.234668 0.972076i \(-0.575400\pi\)
−0.959176 + 0.282809i \(0.908734\pi\)
\(110\) 0 0
\(111\) −3.09317 6.71405i −0.293591 0.637269i
\(112\) 0 0
\(113\) −18.6622 −1.75559 −0.877795 0.479036i \(-0.840986\pi\)
−0.877795 + 0.479036i \(0.840986\pi\)
\(114\) 0 0
\(115\) 0.535898 0.0499728
\(116\) 0 0
\(117\) 2.04587 11.0076i 0.189140 1.01766i
\(118\) 0 0
\(119\) −15.8338 9.14162i −1.45148 0.838011i
\(120\) 0 0
\(121\) 10.8564 0.986946
\(122\) 0 0
\(123\) −0.898979 + 9.75663i −0.0810583 + 0.879726i
\(124\) 0 0
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) −6.80385 + 3.92820i −0.603744 + 0.348572i −0.770513 0.637424i \(-0.780000\pi\)
0.166769 + 0.985996i \(0.446667\pi\)
\(128\) 0 0
\(129\) −0.360419 + 3.91163i −0.0317332 + 0.344400i
\(130\) 0 0
\(131\) −6.03579 3.48477i −0.527350 0.304465i 0.212587 0.977142i \(-0.431811\pi\)
−0.739936 + 0.672677i \(0.765144\pi\)
\(132\) 0 0
\(133\) 6.46410 14.9282i 0.560509 1.29444i
\(134\) 0 0
\(135\) −5.26758 + 5.12372i −0.453362 + 0.440980i
\(136\) 0 0
\(137\) 0.656339 0.378937i 0.0560748 0.0323748i −0.471700 0.881759i \(-0.656360\pi\)
0.527775 + 0.849384i \(0.323026\pi\)
\(138\) 0 0
\(139\) 6.59808 + 11.4282i 0.559642 + 0.969328i 0.997526 + 0.0702964i \(0.0223945\pi\)
−0.437885 + 0.899031i \(0.644272\pi\)
\(140\) 0 0
\(141\) −10.5558 + 14.9282i −0.888962 + 1.25718i
\(142\) 0 0
\(143\) 0.707107 + 1.22474i 0.0591312 + 0.102418i
\(144\) 0 0
\(145\) 10.9282i 0.907538i
\(146\) 0 0
\(147\) −10.8990 + 5.02118i −0.898933 + 0.414140i
\(148\) 0 0
\(149\) −14.6090 8.43451i −1.19682 0.690982i −0.236972 0.971516i \(-0.576155\pi\)
−0.959844 + 0.280534i \(0.909488\pi\)
\(150\) 0 0
\(151\) 2.00000i 0.162758i −0.996683 0.0813788i \(-0.974068\pi\)
0.996683 0.0813788i \(-0.0259324\pi\)
\(152\) 0 0
\(153\) −13.8564 + 4.89898i −1.12022 + 0.396059i
\(154\) 0 0
\(155\) 3.15660 5.46739i 0.253544 0.439151i
\(156\) 0 0
\(157\) −1.76795 + 3.06218i −0.141098 + 0.244388i −0.927910 0.372804i \(-0.878397\pi\)
0.786813 + 0.617192i \(0.211730\pi\)
\(158\) 0 0
\(159\) −8.53590 6.03579i −0.676941 0.478669i
\(160\) 0 0
\(161\) 1.22474 0.707107i 0.0965234 0.0557278i
\(162\) 0 0
\(163\) −5.19615 −0.406994 −0.203497 0.979076i \(-0.565231\pi\)
−0.203497 + 0.979076i \(0.565231\pi\)
\(164\) 0 0
\(165\) 0.0851642 0.924288i 0.00663003 0.0719557i
\(166\) 0 0
\(167\) −3.81294 6.60420i −0.295054 0.511048i 0.679944 0.733264i \(-0.262004\pi\)
−0.974997 + 0.222216i \(0.928671\pi\)
\(168\) 0 0
\(169\) 0.464102 0.803848i 0.0357001 0.0618344i
\(170\) 0 0
\(171\) −5.74434 11.7474i −0.439281 0.898350i
\(172\) 0 0
\(173\) −5.93426 + 10.2784i −0.451173 + 0.781455i −0.998459 0.0554909i \(-0.982328\pi\)
0.547286 + 0.836946i \(0.315661\pi\)
\(174\) 0 0
\(175\) −5.59808 9.69615i −0.423175 0.732960i
\(176\) 0 0
\(177\) 1.33233 14.4598i 0.100144 1.08687i
\(178\) 0 0
\(179\) 1.41421 0.105703 0.0528516 0.998602i \(-0.483169\pi\)
0.0528516 + 0.998602i \(0.483169\pi\)
\(180\) 0 0
\(181\) −3.00000 + 1.73205i −0.222988 + 0.128742i −0.607333 0.794447i \(-0.707761\pi\)
0.384345 + 0.923190i \(0.374427\pi\)
\(182\) 0 0
\(183\) −5.00052 3.53590i −0.369649 0.261381i
\(184\) 0 0
\(185\) −3.01790 + 5.22715i −0.221880 + 0.384308i
\(186\) 0 0
\(187\) 0.928203 1.60770i 0.0678769 0.117566i
\(188\) 0 0
\(189\) −5.27792 + 18.6603i −0.383912 + 1.35733i
\(190\) 0 0
\(191\) 1.69161i 0.122401i −0.998125 0.0612005i \(-0.980507\pi\)
0.998125 0.0612005i \(-0.0194929\pi\)
\(192\) 0 0
\(193\) 11.4282 + 6.59808i 0.822620 + 0.474940i 0.851319 0.524648i \(-0.175803\pi\)
−0.0286991 + 0.999588i \(0.509136\pi\)
\(194\) 0 0
\(195\) −8.30286 + 3.82514i −0.594580 + 0.273924i
\(196\) 0 0
\(197\) 9.14162i 0.651313i −0.945488 0.325657i \(-0.894415\pi\)
0.945488 0.325657i \(-0.105585\pi\)
\(198\) 0 0
\(199\) −6.40192 11.0885i −0.453820 0.786040i 0.544799 0.838567i \(-0.316606\pi\)
−0.998620 + 0.0525267i \(0.983273\pi\)
\(200\) 0 0
\(201\) 1.00000 1.41421i 0.0705346 0.0997509i
\(202\) 0 0
\(203\) 14.4195 + 24.9754i 1.01205 + 1.75293i
\(204\) 0 0
\(205\) 6.92820 4.00000i 0.483887 0.279372i
\(206\) 0 0
\(207\) 0.207729 1.11767i 0.0144382 0.0776836i
\(208\) 0 0
\(209\) 1.51575 + 0.656339i 0.104847 + 0.0453999i
\(210\) 0 0
\(211\) 9.52628 + 5.50000i 0.655816 + 0.378636i 0.790681 0.612228i \(-0.209727\pi\)
−0.134865 + 0.990864i \(0.543060\pi\)
\(212\) 0 0
\(213\) 0.569930 6.18546i 0.0390510 0.423820i
\(214\) 0 0
\(215\) 2.77766 1.60368i 0.189435 0.109370i
\(216\) 0 0
\(217\) 16.6603i 1.13097i
\(218\) 0 0
\(219\) −0.476756 + 5.17423i −0.0322162 + 0.349642i
\(220\) 0 0
\(221\) −18.2832 −1.22986
\(222\) 0 0
\(223\) 8.13397 + 4.69615i 0.544691 + 0.314478i 0.746978 0.664849i \(-0.231504\pi\)
−0.202287 + 0.979326i \(0.564837\pi\)
\(224\) 0 0
\(225\) −8.84847 1.64456i −0.589898 0.109638i
\(226\) 0 0
\(227\) −24.5964 −1.63252 −0.816261 0.577683i \(-0.803957\pi\)
−0.816261 + 0.577683i \(0.803957\pi\)
\(228\) 0 0
\(229\) 9.39230 0.620661 0.310330 0.950629i \(-0.399560\pi\)
0.310330 + 0.950629i \(0.399560\pi\)
\(230\) 0 0
\(231\) −1.02494 2.22474i −0.0674364 0.146377i
\(232\) 0 0
\(233\) −3.10583 1.79315i −0.203470 0.117473i 0.394803 0.918766i \(-0.370813\pi\)
−0.598273 + 0.801292i \(0.704146\pi\)
\(234\) 0 0
\(235\) 14.9282 0.973809
\(236\) 0 0
\(237\) −6.09852 0.561920i −0.396142 0.0365006i
\(238\) 0 0
\(239\) 29.9759i 1.93898i −0.245133 0.969489i \(-0.578832\pi\)
0.245133 0.969489i \(-0.421168\pi\)
\(240\) 0 0
\(241\) −24.8205 + 14.3301i −1.59883 + 0.923085i −0.607116 + 0.794613i \(0.707674\pi\)
−0.991713 + 0.128472i \(0.958993\pi\)
\(242\) 0 0
\(243\) 8.64420 + 12.9722i 0.554526 + 0.832167i
\(244\) 0 0
\(245\) 8.48528 + 4.89898i 0.542105 + 0.312984i
\(246\) 0 0
\(247\) −1.86603 16.1603i −0.118732 1.02825i
\(248\) 0 0
\(249\) −5.60040 12.1562i −0.354911 0.770370i
\(250\) 0 0
\(251\) 12.7279 7.34847i 0.803379 0.463831i −0.0412721 0.999148i \(-0.513141\pi\)
0.844651 + 0.535317i \(0.179808\pi\)
\(252\) 0 0
\(253\) 0.0717968 + 0.124356i 0.00451382 + 0.00781817i
\(254\) 0 0
\(255\) 9.79796 + 6.92820i 0.613572 + 0.433861i
\(256\) 0 0
\(257\) 1.60368 + 2.77766i 0.100035 + 0.173266i 0.911699 0.410859i \(-0.134771\pi\)
−0.811664 + 0.584125i \(0.801438\pi\)
\(258\) 0 0
\(259\) 15.9282i 0.989730i
\(260\) 0 0
\(261\) 22.7919 + 4.23607i 1.41078 + 0.262206i
\(262\) 0 0
\(263\) 0.480473 + 0.277401i 0.0296273 + 0.0171053i 0.514740 0.857346i \(-0.327888\pi\)
−0.485113 + 0.874451i \(0.661222\pi\)
\(264\) 0 0
\(265\) 8.53590i 0.524356i
\(266\) 0 0
\(267\) −10.3923 7.34847i −0.635999 0.449719i
\(268\) 0 0
\(269\) 3.01790 5.22715i 0.184004 0.318705i −0.759236 0.650815i \(-0.774427\pi\)
0.943241 + 0.332110i \(0.107761\pi\)
\(270\) 0 0
\(271\) −3.46410 + 6.00000i −0.210429 + 0.364474i −0.951849 0.306568i \(-0.900819\pi\)
0.741420 + 0.671042i \(0.234153\pi\)
\(272\) 0 0
\(273\) −13.9282 + 19.6975i −0.842973 + 1.19214i
\(274\) 0 0
\(275\) 0.984508 0.568406i 0.0593681 0.0342762i
\(276\) 0 0
\(277\) −9.85641 −0.592214 −0.296107 0.955155i \(-0.595689\pi\)
−0.296107 + 0.955155i \(0.595689\pi\)
\(278\) 0 0
\(279\) −10.1792 8.70272i −0.609414 0.521018i
\(280\) 0 0
\(281\) −7.53794 13.0561i −0.449676 0.778861i 0.548689 0.836027i \(-0.315127\pi\)
−0.998365 + 0.0571654i \(0.981794\pi\)
\(282\) 0 0
\(283\) −10.9282 + 18.9282i −0.649614 + 1.12516i 0.333601 + 0.942714i \(0.391736\pi\)
−0.983215 + 0.182450i \(0.941597\pi\)
\(284\) 0 0
\(285\) −5.12372 + 9.36736i −0.303503 + 0.554875i
\(286\) 0 0
\(287\) 10.5558 18.2832i 0.623091 1.07923i
\(288\) 0 0
\(289\) 3.50000 + 6.06218i 0.205882 + 0.356599i
\(290\) 0 0
\(291\) −12.8737 1.18618i −0.754668 0.0695354i
\(292\) 0 0
\(293\) 25.2528 1.47528 0.737641 0.675193i \(-0.235940\pi\)
0.737641 + 0.675193i \(0.235940\pi\)
\(294\) 0 0
\(295\) −10.2679 + 5.92820i −0.597823 + 0.345153i
\(296\) 0 0
\(297\) −1.89469 0.535898i −0.109941 0.0310960i
\(298\) 0 0
\(299\) 0.707107 1.22474i 0.0408930 0.0708288i
\(300\) 0 0
\(301\) 4.23205 7.33013i 0.243931 0.422501i
\(302\) 0 0
\(303\) −7.72741 + 10.9282i −0.443928 + 0.627809i
\(304\) 0 0
\(305\) 5.00052i 0.286329i
\(306\) 0 0
\(307\) 12.0000 + 6.92820i 0.684876 + 0.395413i 0.801690 0.597740i \(-0.203935\pi\)
−0.116814 + 0.993154i \(0.537268\pi\)
\(308\) 0 0
\(309\) −7.58380 16.4614i −0.431428 0.936457i
\(310\) 0 0
\(311\) 27.1475i 1.53939i 0.638411 + 0.769696i \(0.279592\pi\)
−0.638411 + 0.769696i \(0.720408\pi\)
\(312\) 0 0
\(313\) 12.3923 + 21.4641i 0.700454 + 1.21322i 0.968307 + 0.249763i \(0.0803527\pi\)
−0.267853 + 0.963460i \(0.586314\pi\)
\(314\) 0 0
\(315\) 14.9282 5.27792i 0.841109 0.297377i
\(316\) 0 0
\(317\) −6.88160 11.9193i −0.386509 0.669453i 0.605468 0.795870i \(-0.292986\pi\)
−0.991977 + 0.126416i \(0.959653\pi\)
\(318\) 0 0
\(319\) −2.53590 + 1.46410i −0.141983 + 0.0819740i
\(320\) 0 0
\(321\) 7.70674 3.55051i 0.430148 0.198170i
\(322\) 0 0
\(323\) −17.1464 + 12.7279i −0.954053 + 0.708201i
\(324\) 0 0
\(325\) −9.69615 5.59808i −0.537846 0.310525i
\(326\) 0 0
\(327\) 24.8231 + 2.28721i 1.37272 + 0.126483i
\(328\) 0 0
\(329\) 34.1170 19.6975i 1.88093 1.08596i
\(330\) 0 0
\(331\) 31.9282i 1.75493i −0.479638 0.877466i \(-0.659232\pi\)
0.479638 0.877466i \(-0.340768\pi\)
\(332\) 0 0
\(333\) 9.73194 + 8.32032i 0.533307 + 0.455951i
\(334\) 0 0
\(335\) −1.41421 −0.0772667
\(336\) 0 0
\(337\) 6.35641 + 3.66987i 0.346256 + 0.199911i 0.663035 0.748589i \(-0.269268\pi\)
−0.316779 + 0.948499i \(0.602601\pi\)
\(338\) 0 0
\(339\) 29.3581 13.5253i 1.59451 0.734594i
\(340\) 0 0
\(341\) 1.69161 0.0916061
\(342\) 0 0
\(343\) −0.267949 −0.0144679
\(344\) 0 0
\(345\) −0.843039 + 0.388390i −0.0453877 + 0.0209102i
\(346\) 0 0
\(347\) −21.5414 12.4369i −1.15640 0.667649i −0.205963 0.978560i \(-0.566032\pi\)
−0.950439 + 0.310911i \(0.899366\pi\)
\(348\) 0 0
\(349\) −11.3923 −0.609816 −0.304908 0.952382i \(-0.598626\pi\)
−0.304908 + 0.952382i \(0.598626\pi\)
\(350\) 0 0
\(351\) 4.75932 + 18.7992i 0.254034 + 1.00343i
\(352\) 0 0
\(353\) 11.9700i 0.637101i 0.947906 + 0.318551i \(0.103196\pi\)
−0.947906 + 0.318551i \(0.896804\pi\)
\(354\) 0 0
\(355\) −4.39230 + 2.53590i −0.233119 + 0.134592i
\(356\) 0 0
\(357\) 31.5339 + 2.90555i 1.66895 + 0.153778i
\(358\) 0 0
\(359\) 23.1822 + 13.3843i 1.22351 + 0.706394i 0.965665 0.259792i \(-0.0836539\pi\)
0.257846 + 0.966186i \(0.416987\pi\)
\(360\) 0 0
\(361\) −13.0000 13.8564i −0.684211 0.729285i
\(362\) 0 0
\(363\) −17.0786 + 7.86812i −0.896392 + 0.412969i
\(364\) 0 0
\(365\) 3.67423 2.12132i 0.192318 0.111035i
\(366\) 0 0
\(367\) −8.52628 14.7679i −0.445068 0.770881i 0.552989 0.833189i \(-0.313487\pi\)
−0.998057 + 0.0623080i \(0.980154\pi\)
\(368\) 0 0
\(369\) −5.65685 16.0000i −0.294484 0.832927i
\(370\) 0 0
\(371\) 11.2629 + 19.5080i 0.584743 + 1.01280i
\(372\) 0 0
\(373\) 12.5359i 0.649084i 0.945871 + 0.324542i \(0.105210\pi\)
−0.945871 + 0.324542i \(0.894790\pi\)
\(374\) 0 0
\(375\) 8.19955 + 17.7980i 0.423423 + 0.919083i
\(376\) 0 0
\(377\) 24.9754 + 14.4195i 1.28630 + 0.742644i
\(378\) 0 0
\(379\) 17.7846i 0.913534i −0.889586 0.456767i \(-0.849007\pi\)
0.889586 0.456767i \(-0.150993\pi\)
\(380\) 0 0
\(381\) 7.85641 11.1106i 0.402496 0.569215i
\(382\) 0 0
\(383\) −13.3335 + 23.0943i −0.681310 + 1.18006i 0.293272 + 0.956029i \(0.405256\pi\)
−0.974581 + 0.224034i \(0.928077\pi\)
\(384\) 0 0
\(385\) −1.00000 + 1.73205i −0.0509647 + 0.0882735i
\(386\) 0 0
\(387\) −2.26795 6.41473i −0.115286 0.326079i
\(388\) 0 0
\(389\) 4.33057 2.50026i 0.219569 0.126768i −0.386182 0.922423i \(-0.626206\pi\)
0.605751 + 0.795655i \(0.292873\pi\)
\(390\) 0 0
\(391\) −1.85641 −0.0938825
\(392\) 0 0
\(393\) 12.0207 + 1.10759i 0.606362 + 0.0558704i
\(394\) 0 0
\(395\) 2.50026 + 4.33057i 0.125802 + 0.217895i
\(396\) 0 0
\(397\) −4.16025 + 7.20577i −0.208797 + 0.361647i −0.951336 0.308156i \(-0.900288\pi\)
0.742539 + 0.669803i \(0.233622\pi\)
\(398\) 0 0
\(399\) 0.650252 + 28.1689i 0.0325533 + 1.41021i
\(400\) 0 0
\(401\) −5.74479 + 9.95026i −0.286881 + 0.496892i −0.973064 0.230537i \(-0.925952\pi\)
0.686183 + 0.727429i \(0.259285\pi\)
\(402\) 0 0
\(403\) −8.33013 14.4282i −0.414953 0.718720i
\(404\) 0 0
\(405\) 4.57321 11.8780i 0.227245 0.590220i
\(406\) 0 0
\(407\) −1.61729 −0.0801659
\(408\) 0 0
\(409\) 24.4641 14.1244i 1.20967 0.698404i 0.246984 0.969019i \(-0.420560\pi\)
0.962688 + 0.270615i \(0.0872270\pi\)
\(410\) 0 0
\(411\) −0.757875 + 1.07180i −0.0373832 + 0.0528678i
\(412\) 0 0
\(413\) −15.6443 + 27.0967i −0.769805 + 1.33334i
\(414\) 0 0
\(415\) −5.46410 + 9.46410i −0.268222 + 0.464574i
\(416\) 0 0
\(417\) −18.6622 13.1962i −0.913891 0.646218i
\(418\) 0 0
\(419\) 32.0464i 1.56557i −0.622292 0.782785i \(-0.713798\pi\)
0.622292 0.782785i \(-0.286202\pi\)
\(420\) 0 0
\(421\) −30.7128 17.7321i −1.49685 0.864207i −0.496857 0.867832i \(-0.665513\pi\)
−0.999993 + 0.00362487i \(0.998846\pi\)
\(422\) 0 0
\(423\) 5.78658 31.1343i 0.281353 1.51380i
\(424\) 0 0
\(425\) 14.6969i 0.712906i
\(426\) 0 0
\(427\) 6.59808 + 11.4282i 0.319303 + 0.553050i
\(428\) 0 0
\(429\) −2.00000 1.41421i −0.0965609 0.0682789i
\(430\) 0 0
\(431\) −12.7279 22.0454i −0.613082 1.06189i −0.990718 0.135935i \(-0.956596\pi\)
0.377635 0.925954i \(-0.376737\pi\)
\(432\) 0 0
\(433\) 2.89230 1.66987i 0.138995 0.0802490i −0.428890 0.903357i \(-0.641095\pi\)
0.567885 + 0.823108i \(0.307762\pi\)
\(434\) 0 0
\(435\) −7.92016 17.1915i −0.379743 0.824270i
\(436\) 0 0
\(437\) −0.189469 1.64085i −0.00906352 0.0784924i
\(438\) 0 0
\(439\) −19.4545 11.2321i −0.928512 0.536077i −0.0421712 0.999110i \(-0.513427\pi\)
−0.886341 + 0.463034i \(0.846761\pi\)
\(440\) 0 0
\(441\) 13.5065 15.7980i 0.643165 0.752284i
\(442\) 0 0
\(443\) 33.4607 19.3185i 1.58976 0.917850i 0.596419 0.802674i \(-0.296590\pi\)
0.993345 0.115177i \(-0.0367435\pi\)
\(444\) 0 0
\(445\) 10.3923i 0.492642i
\(446\) 0 0
\(447\) 29.0948 + 2.68080i 1.37614 + 0.126798i
\(448\) 0 0
\(449\) −34.4959 −1.62796 −0.813982 0.580890i \(-0.802704\pi\)
−0.813982 + 0.580890i \(0.802704\pi\)
\(450\) 0 0
\(451\) 1.85641 + 1.07180i 0.0874148 + 0.0504689i
\(452\) 0 0
\(453\) 1.44949 + 3.14626i 0.0681030 + 0.147824i
\(454\) 0 0
\(455\) 19.6975 0.923431
\(456\) 0 0
\(457\) −20.7128 −0.968905 −0.484452 0.874818i \(-0.660981\pi\)
−0.484452 + 0.874818i \(0.660981\pi\)
\(458\) 0 0
\(459\) 18.2474 17.7491i 0.851718 0.828457i
\(460\) 0 0
\(461\) −28.4737 16.4393i −1.32615 0.765656i −0.341452 0.939899i \(-0.610919\pi\)
−0.984703 + 0.174244i \(0.944252\pi\)
\(462\) 0 0
\(463\) 29.5885 1.37509 0.687546 0.726141i \(-0.258688\pi\)
0.687546 + 0.726141i \(0.258688\pi\)
\(464\) 0 0
\(465\) −1.00328 + 10.8886i −0.0465262 + 0.504949i
\(466\) 0 0
\(467\) 22.6274i 1.04707i 0.852004 + 0.523536i \(0.175387\pi\)
−0.852004 + 0.523536i \(0.824613\pi\)
\(468\) 0 0
\(469\) −3.23205 + 1.86603i −0.149242 + 0.0861650i
\(470\) 0 0
\(471\) 0.561920 6.09852i 0.0258919 0.281005i
\(472\) 0 0
\(473\) 0.744272 + 0.429705i 0.0342216 + 0.0197579i
\(474\) 0 0
\(475\) −12.9904 + 1.50000i −0.596040 + 0.0688247i
\(476\) 0 0
\(477\) 17.8025 + 3.30875i 0.815121 + 0.151497i
\(478\) 0 0
\(479\) −10.2784 + 5.93426i −0.469634 + 0.271143i −0.716086 0.698012i \(-0.754068\pi\)
0.246453 + 0.969155i \(0.420735\pi\)
\(480\) 0 0
\(481\) 7.96410 + 13.7942i 0.363132 + 0.628963i
\(482\) 0 0
\(483\) −1.41421 + 2.00000i −0.0643489 + 0.0910032i
\(484\) 0 0
\(485\) 5.27792 + 9.14162i 0.239658 + 0.415100i
\(486\) 0 0
\(487\) 24.9282i 1.12960i 0.825226 + 0.564802i \(0.191048\pi\)
−0.825226 + 0.564802i \(0.808952\pi\)
\(488\) 0 0
\(489\) 8.17423 3.76588i 0.369652 0.170299i
\(490\) 0 0
\(491\) 8.66115 + 5.00052i 0.390872 + 0.225670i 0.682538 0.730850i \(-0.260876\pi\)
−0.291666 + 0.956520i \(0.594210\pi\)
\(492\) 0 0
\(493\) 37.8564i 1.70497i
\(494\) 0 0
\(495\) 0.535898 + 1.51575i 0.0240868 + 0.0681279i
\(496\) 0 0
\(497\) −6.69213 + 11.5911i −0.300183 + 0.519932i
\(498\) 0 0
\(499\) −8.06218 + 13.9641i −0.360913 + 0.625119i −0.988111 0.153740i \(-0.950868\pi\)
0.627199 + 0.778859i \(0.284201\pi\)
\(500\) 0 0
\(501\) 10.7846 + 7.62587i 0.481821 + 0.340699i
\(502\) 0 0
\(503\) −15.8338 + 9.14162i −0.705992 + 0.407605i −0.809575 0.587016i \(-0.800303\pi\)
0.103583 + 0.994621i \(0.466969\pi\)
\(504\) 0 0
\(505\) 10.9282 0.486299
\(506\) 0 0
\(507\) −0.147509 + 1.60091i −0.00655109 + 0.0710991i
\(508\) 0 0
\(509\) 6.79367 + 11.7670i 0.301124 + 0.521562i 0.976391 0.216011i \(-0.0693049\pi\)
−0.675267 + 0.737574i \(0.735972\pi\)
\(510\) 0 0
\(511\) 5.59808 9.69615i 0.247644 0.428933i
\(512\) 0 0
\(513\) 17.5505 + 14.3171i 0.774874 + 0.632116i
\(514\) 0 0
\(515\) −7.39924 + 12.8159i −0.326049 + 0.564734i
\(516\) 0 0
\(517\) 2.00000 + 3.46410i 0.0879599 + 0.152351i
\(518\) 0 0
\(519\) 1.88613 20.4702i 0.0827918 0.898540i
\(520\) 0 0
\(521\) 4.52004 0.198027 0.0990133 0.995086i \(-0.468431\pi\)
0.0990133 + 0.995086i \(0.468431\pi\)
\(522\) 0 0
\(523\) 14.5981 8.42820i 0.638329 0.368540i −0.145641 0.989337i \(-0.546525\pi\)
0.783971 + 0.620798i \(0.213191\pi\)
\(524\) 0 0
\(525\) 15.8338 + 11.1962i 0.691042 + 0.488640i
\(526\) 0 0
\(527\) −10.9348 + 18.9396i −0.476326 + 0.825021i
\(528\) 0 0
\(529\) −11.4282 + 19.7942i −0.496878 + 0.860619i
\(530\) 0 0
\(531\) 8.38375 + 23.7128i 0.363824 + 1.02905i
\(532\) 0 0
\(533\) 21.1117i 0.914448i
\(534\) 0 0
\(535\) −6.00000 3.46410i −0.259403 0.149766i
\(536\) 0 0
\(537\) −2.22474 + 1.02494i −0.0960048 + 0.0442296i
\(538\) 0 0
\(539\) 2.62536i 0.113082i
\(540\) 0 0
\(541\) 8.76795 + 15.1865i 0.376964 + 0.652920i 0.990619 0.136654i \(-0.0436349\pi\)
−0.613655 + 0.789574i \(0.710302\pi\)
\(542\) 0 0
\(543\) 3.46410 4.89898i 0.148659 0.210235i
\(544\) 0 0
\(545\) −10.1769 17.6269i −0.435930 0.755054i
\(546\) 0 0
\(547\) 11.1340 6.42820i 0.476054 0.274850i −0.242716 0.970097i \(-0.578038\pi\)
0.718771 + 0.695247i \(0.244705\pi\)
\(548\) 0 0
\(549\) 10.4291 + 1.93834i 0.445103 + 0.0827262i
\(550\) 0 0
\(551\) 33.4607 3.86370i 1.42547 0.164599i
\(552\) 0 0
\(553\) 11.4282 + 6.59808i 0.485977 + 0.280579i
\(554\) 0 0
\(555\) 0.959200 10.4102i 0.0407158 0.441888i
\(556\) 0 0
\(557\) 2.92996 1.69161i 0.124147 0.0716760i −0.436641 0.899636i \(-0.643832\pi\)
0.560787 + 0.827960i \(0.310499\pi\)
\(558\) 0 0
\(559\) 8.46410i 0.357993i
\(560\) 0 0
\(561\) −0.295018 + 3.20183i −0.0124557 + 0.135181i
\(562\) 0 0
\(563\) 3.38323 0.142586 0.0712931 0.997455i \(-0.477287\pi\)
0.0712931 + 0.997455i \(0.477287\pi\)
\(564\) 0 0
\(565\) −22.8564 13.1962i −0.961576 0.555166i
\(566\) 0 0
\(567\) −5.22106 33.1802i −0.219264 1.39344i
\(568\) 0 0
\(569\) 13.9391 0.584356 0.292178 0.956364i \(-0.405620\pi\)
0.292178 + 0.956364i \(0.405620\pi\)
\(570\) 0 0
\(571\) −25.1962 −1.05443 −0.527213 0.849733i \(-0.676763\pi\)
−0.527213 + 0.849733i \(0.676763\pi\)
\(572\) 0 0
\(573\) 1.22599 + 2.66113i 0.0512164 + 0.111170i
\(574\) 0 0
\(575\) −0.984508 0.568406i −0.0410568 0.0237042i
\(576\) 0 0
\(577\) 42.9282 1.78712 0.893562 0.448939i \(-0.148198\pi\)
0.893562 + 0.448939i \(0.148198\pi\)
\(578\) 0 0
\(579\) −22.7600 2.09711i −0.945873 0.0871531i
\(580\) 0 0
\(581\) 28.8391i 1.19645i
\(582\) 0 0
\(583\) −1.98076 + 1.14359i −0.0820348 + 0.0473628i
\(584\) 0 0
\(585\) 10.2892 12.0349i 0.425408 0.497582i
\(586\) 0 0
\(587\) 9.29392 + 5.36585i 0.383601 + 0.221472i 0.679384 0.733783i \(-0.262247\pi\)
−0.295783 + 0.955255i \(0.595580\pi\)
\(588\) 0 0
\(589\) −17.8564 7.73205i −0.735760 0.318594i
\(590\) 0 0
\(591\) 6.62534 + 14.3810i 0.272530 + 0.591554i
\(592\) 0 0
\(593\) 21.7816 12.5756i 0.894463 0.516419i 0.0190636 0.999818i \(-0.493931\pi\)
0.875400 + 0.483400i \(0.160598\pi\)
\(594\) 0 0
\(595\) −12.9282 22.3923i −0.530005 0.917995i
\(596\) 0 0
\(597\) 18.1074 + 12.8038i 0.741086 + 0.524027i
\(598\) 0 0
\(599\) −8.43451 14.6090i −0.344625 0.596908i 0.640661 0.767824i \(-0.278661\pi\)
−0.985286 + 0.170916i \(0.945327\pi\)
\(600\) 0 0
\(601\) 44.3731i 1.81002i −0.425395 0.905008i \(-0.639865\pi\)
0.425395 0.905008i \(-0.360135\pi\)
\(602\) 0 0
\(603\) −0.548188 + 2.94949i −0.0223239 + 0.120113i
\(604\) 0 0
\(605\) 13.2963 + 7.67664i 0.540573 + 0.312100i
\(606\) 0 0
\(607\) 13.2487i 0.537749i −0.963175 0.268874i \(-0.913348\pi\)
0.963175 0.268874i \(-0.0866516\pi\)
\(608\) 0 0
\(609\) −40.7846 28.8391i −1.65268 1.16862i
\(610\) 0 0
\(611\) 19.6975 34.1170i 0.796874 1.38023i
\(612\) 0 0
\(613\) −11.3205 + 19.6077i −0.457231 + 0.791947i −0.998813 0.0487003i \(-0.984492\pi\)
0.541582 + 0.840648i \(0.317825\pi\)
\(614\) 0 0
\(615\) −8.00000 + 11.3137i −0.322591 + 0.456213i
\(616\) 0 0
\(617\) −22.4379 + 12.9546i −0.903318 + 0.521531i −0.878275 0.478156i \(-0.841305\pi\)
−0.0250427 + 0.999686i \(0.507972\pi\)
\(618\) 0 0
\(619\) −2.80385 −0.112696 −0.0563481 0.998411i \(-0.517946\pi\)
−0.0563481 + 0.998411i \(0.517946\pi\)
\(620\) 0 0
\(621\) 0.483242 + 1.90880i 0.0193918 + 0.0765974i
\(622\) 0 0
\(623\) 13.7124 + 23.7506i 0.549377 + 0.951549i
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.0200000 0.0346410i
\(626\) 0 0
\(627\) −2.86015 + 0.0660240i −0.114223 + 0.00263674i
\(628\) 0 0
\(629\) 10.4543 18.1074i 0.416840 0.721988i
\(630\) 0 0
\(631\) 24.5263 + 42.4808i 0.976376 + 1.69113i 0.675318 + 0.737526i \(0.264006\pi\)
0.301058 + 0.953606i \(0.402660\pi\)
\(632\) 0 0
\(633\) −18.9722 1.74810i −0.754077 0.0694809i
\(634\) 0 0
\(635\) −11.1106 −0.440912
\(636\) 0 0
\(637\) 22.3923 12.9282i 0.887215 0.512234i
\(638\) 0 0
\(639\) 3.58630 + 10.1436i 0.141872 + 0.401274i
\(640\) 0 0
\(641\) 6.41473 11.1106i 0.253367 0.438844i −0.711084 0.703107i \(-0.751795\pi\)
0.964451 + 0.264263i \(0.0851288\pi\)
\(642\) 0 0
\(643\) −21.7942 + 37.7487i −0.859480 + 1.48866i 0.0129447 + 0.999916i \(0.495879\pi\)
−0.872425 + 0.488748i \(0.837454\pi\)
\(644\) 0 0
\(645\) −3.20736 + 4.53590i −0.126290 + 0.178601i
\(646\) 0 0
\(647\) 20.5569i 0.808174i 0.914721 + 0.404087i \(0.132411\pi\)
−0.914721 + 0.404087i \(0.867589\pi\)
\(648\) 0 0
\(649\) −2.75129 1.58846i −0.107998 0.0623524i
\(650\) 0 0
\(651\) 12.0744 + 26.2088i 0.473234 + 1.02720i
\(652\) 0 0
\(653\) 47.1223i 1.84404i 0.387144 + 0.922019i \(0.373462\pi\)
−0.387144 + 0.922019i \(0.626538\pi\)
\(654\) 0 0
\(655\) −4.92820 8.53590i −0.192561 0.333525i
\(656\) 0 0
\(657\) −3.00000 8.48528i −0.117041 0.331042i
\(658\) 0 0
\(659\) −16.5409 28.6496i −0.644340 1.11603i −0.984453 0.175646i \(-0.943799\pi\)
0.340113 0.940385i \(-0.389535\pi\)
\(660\) 0 0
\(661\) 5.32051 3.07180i 0.206944 0.119479i −0.392946 0.919561i \(-0.628544\pi\)
0.599890 + 0.800082i \(0.295211\pi\)
\(662\) 0 0
\(663\) 28.7620 13.2507i 1.11702 0.514614i
\(664\) 0 0
\(665\) 18.4727 13.7124i 0.716341 0.531745i
\(666\) 0 0
\(667\) 2.53590 + 1.46410i 0.0981904 + 0.0566902i
\(668\) 0 0
\(669\) −16.1993 1.49261i −0.626302 0.0577077i
\(670\) 0 0
\(671\) −1.16037 + 0.669942i −0.0447957 + 0.0258628i
\(672\) 0 0
\(673\) 21.9808i 0.847296i 0.905827 + 0.423648i \(0.139251\pi\)
−0.905827 + 0.423648i \(0.860749\pi\)
\(674\) 0 0
\(675\) 15.1117 3.82577i 0.581650 0.147254i
\(676\) 0 0
\(677\) 18.8380 0.724005 0.362002 0.932177i \(-0.382093\pi\)
0.362002 + 0.932177i \(0.382093\pi\)
\(678\) 0 0
\(679\) 24.1244 + 13.9282i 0.925808 + 0.534515i
\(680\) 0 0
\(681\) 38.6934 17.8261i 1.48274 0.683099i
\(682\) 0 0
\(683\) −16.3142 −0.624246 −0.312123 0.950042i \(-0.601040\pi\)
−0.312123 + 0.950042i \(0.601040\pi\)
\(684\) 0 0
\(685\) 1.07180 0.0409512
\(686\) 0 0
\(687\) −14.7753 + 6.80702i −0.563714 + 0.259704i
\(688\) 0 0
\(689\) 19.5080 + 11.2629i 0.743195 + 0.429084i
\(690\) 0 0
\(691\) −9.85641 −0.374955 −0.187478 0.982269i \(-0.560031\pi\)
−0.187478 + 0.982269i \(0.560031\pi\)
\(692\) 0 0
\(693\) 3.22474 + 2.75699i 0.122498 + 0.104730i
\(694\) 0 0
\(695\) 18.6622i 0.707897i
\(696\) 0 0
\(697\) −24.0000 + 13.8564i −0.909065 + 0.524849i
\(698\) 0 0
\(699\) 6.18546 + 0.569930i 0.233955 + 0.0215567i
\(700\) 0 0
\(701\) −17.2344 9.95026i −0.650933 0.375816i 0.137881 0.990449i \(-0.455971\pi\)
−0.788814 + 0.614633i \(0.789304\pi\)
\(702\) 0 0
\(703\) 17.0718 + 7.39230i 0.643875 + 0.278806i
\(704\) 0 0
\(705\) −23.4840 + 10.8191i −0.884460 + 0.407472i
\(706\) 0 0
\(707\) 24.9754 14.4195i 0.939295 0.542303i
\(708\) 0 0
\(709\) −21.1603 36.6506i −0.794690 1.37644i −0.923036 0.384714i \(-0.874300\pi\)
0.128346 0.991729i \(-0.459033\pi\)
\(710\) 0 0
\(711\) 10.0010 3.53590i 0.375068 0.132607i
\(712\) 0 0
\(713\) −0.845807 1.46498i −0.0316757 0.0548640i
\(714\) 0 0
\(715\) 2.00000i 0.0747958i
\(716\) 0 0
\(717\) 21.7249 + 47.1560i 0.811330 + 1.76107i
\(718\) 0 0
\(719\) −5.22715 3.01790i −0.194940 0.112549i 0.399353 0.916797i \(-0.369235\pi\)
−0.594293 + 0.804249i \(0.702568\pi\)
\(720\) 0 0
\(721\) 39.0526i 1.45439i
\(722\) 0 0
\(723\) 28.6603 40.5317i 1.06589 1.50739i
\(724\) 0 0
\(725\) 11.5911 20.0764i 0.430483 0.745618i
\(726\) 0 0
\(727\) −6.79423 + 11.7679i −0.251984 + 0.436449i −0.964072 0.265641i \(-0.914416\pi\)
0.712088 + 0.702090i \(0.247750\pi\)
\(728\) 0 0
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 0 0
\(731\) −9.62209 + 5.55532i −0.355886 + 0.205471i
\(732\) 0 0
\(733\) −35.7128 −1.31908 −0.659541 0.751668i \(-0.729249\pi\)
−0.659541 + 0.751668i \(0.729249\pi\)
\(734\) 0 0
\(735\) −16.8990 1.55708i −0.623328 0.0574337i
\(736\) 0 0
\(737\) −0.189469 0.328169i −0.00697917 0.0120883i
\(738\) 0 0
\(739\) −17.4019 + 30.1410i −0.640140 + 1.10876i 0.345261 + 0.938507i \(0.387790\pi\)
−0.985401 + 0.170249i \(0.945543\pi\)
\(740\) 0 0
\(741\) 14.6476 + 24.0698i 0.538092 + 0.884227i
\(742\) 0 0
\(743\) 3.53553 6.12372i 0.129706 0.224658i −0.793857 0.608105i \(-0.791930\pi\)
0.923563 + 0.383447i \(0.125263\pi\)
\(744\) 0 0
\(745\) −11.9282 20.6603i −0.437016 0.756933i
\(746\) 0 0
\(747\) 17.6203 + 15.0645i 0.644694 + 0.551181i
\(748\) 0 0
\(749\) −18.2832 −0.668055
\(750\) 0 0
\(751\) 7.45448 4.30385i 0.272018 0.157050i −0.357786 0.933803i \(-0.616468\pi\)
0.629804 + 0.776754i \(0.283135\pi\)
\(752\) 0 0
\(753\) −14.6969 + 20.7846i −0.535586 + 0.757433i
\(754\) 0 0
\(755\) 1.41421 2.44949i 0.0514685 0.0891461i
\(756\) 0 0
\(757\) −2.30385 + 3.99038i −0.0837348 + 0.145033i −0.904851 0.425728i \(-0.860018\pi\)
0.821117 + 0.570760i \(0.193352\pi\)
\(758\) 0 0
\(759\) −0.203072 0.143594i −0.00737104 0.00521212i
\(760\) 0 0
\(761\) 46.2629i 1.67703i −0.544879 0.838514i \(-0.683425\pi\)
0.544879 0.838514i \(-0.316575\pi\)
\(762\) 0 0
\(763\) −46.5167 26.8564i −1.68402 0.972267i
\(764\) 0 0
\(765\) −20.4347 3.79796i −0.738817 0.137315i
\(766\) 0 0
\(767\) 31.2886i 1.12976i
\(768\) 0 0
\(769\) 0.428203 + 0.741670i 0.0154414 + 0.0267453i 0.873643 0.486568i \(-0.161751\pi\)
−0.858201 + 0.513313i \(0.828418\pi\)
\(770\) 0 0
\(771\) −4.53590 3.20736i −0.163356 0.115510i
\(772\) 0 0
\(773\) 9.04008 + 15.6579i 0.325149 + 0.563175i 0.981543 0.191244i \(-0.0612521\pi\)
−0.656393 + 0.754419i \(0.727919\pi\)
\(774\) 0 0
\(775\) −11.5981 + 6.69615i −0.416615 + 0.240533i
\(776\) 0 0
\(777\) −11.5439 25.0572i −0.414135 0.898921i
\(778\) 0 0
\(779\) −14.6969 19.7990i −0.526572 0.709372i
\(780\) 0 0
\(781\) −1.17691 0.679492i −0.0421133 0.0243141i
\(782\) 0 0
\(783\) −38.9248 + 9.85441i −1.39106 + 0.352168i
\(784\) 0 0
\(785\) −4.33057 + 2.50026i −0.154565 + 0.0892380i
\(786\) 0 0
\(787\) 24.0718i 0.858067i 0.903289 + 0.429033i \(0.141146\pi\)
−0.903289 + 0.429033i \(0.858854\pi\)
\(788\) 0 0
\(789\) −0.956893 0.0881685i −0.0340663 0.00313888i
\(790\) 0 0
\(791\) −69.6482 −2.47640
\(792\) 0 0
\(793\) 11.4282 + 6.59808i 0.405827 + 0.234305i