Properties

Label 324.2.h.d.107.4
Level $324$
Weight $2$
Character 324.107
Analytic conductor $2.587$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.58715302549\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.12960000.1
Defining polynomial: \(x^{8} - 3 x^{6} + 8 x^{4} - 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.4
Root \(-1.40126 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 324.107
Dual form 324.2.h.d.215.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.40126 - 0.190983i) q^{2} +(1.92705 - 0.535233i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.35410 + 1.93649i) q^{7} +(2.59808 - 1.11803i) q^{8} +O(q^{10})\) \(q+(1.40126 - 0.190983i) q^{2} +(1.92705 - 0.535233i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.35410 + 1.93649i) q^{7} +(2.59808 - 1.11803i) q^{8} +(-2.50000 + 1.93649i) q^{10} +(0.866025 - 1.50000i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(5.06980 + 2.07295i) q^{14} +(3.42705 - 2.06284i) q^{16} +4.47214i q^{17} +(-3.13331 + 3.19098i) q^{20} +(0.927051 - 2.26728i) q^{22} +(-3.46410 - 6.00000i) q^{23} +(-1.73205 - 2.23607i) q^{26} +(7.50000 + 1.93649i) q^{28} +(-3.87298 - 2.23607i) q^{29} +(3.35410 - 1.93649i) q^{31} +(4.40822 - 3.54508i) q^{32} +(0.854102 + 6.26662i) q^{34} -8.66025 q^{35} -4.00000 q^{37} +(-3.78115 + 5.06980i) q^{40} +(-7.74597 + 4.47214i) q^{41} +(-6.70820 - 3.87298i) q^{43} +(0.866025 - 3.35410i) q^{44} +(-6.00000 - 7.74597i) q^{46} +(-1.73205 + 3.00000i) q^{47} +(4.00000 + 6.92820i) q^{49} +(-2.85410 - 2.80252i) q^{52} -2.23607i q^{53} +3.87298i q^{55} +(10.8793 + 1.28115i) q^{56} +(-5.85410 - 2.39364i) q^{58} +(1.73205 + 3.00000i) q^{59} +(2.00000 - 3.46410i) q^{61} +(4.33013 - 3.35410i) q^{62} +(5.50000 - 5.80948i) q^{64} +(3.87298 + 2.23607i) q^{65} +(-6.70820 + 3.87298i) q^{67} +(2.39364 + 8.61803i) q^{68} +(-12.1353 + 1.65396i) q^{70} +10.3923 q^{71} +5.00000 q^{73} +(-5.60503 + 0.763932i) q^{74} +(5.80948 - 3.35410i) q^{77} +(-6.70820 - 3.87298i) q^{79} +(-4.33013 + 7.82624i) q^{80} +(-10.0000 + 7.74597i) q^{82} +(6.06218 - 10.5000i) q^{83} +(-5.00000 - 8.66025i) q^{85} +(-10.1396 - 4.14590i) q^{86} +(0.572949 - 4.86536i) q^{88} +4.47214i q^{89} -7.74597i q^{91} +(-9.88690 - 9.70820i) q^{92} +(-1.85410 + 4.53457i) q^{94} +(-5.50000 + 9.52628i) q^{97} +(6.92820 + 8.94427i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} + O(q^{10}) \) \( 8q + 2q^{4} - 20q^{10} - 8q^{13} + 14q^{16} - 6q^{22} + 60q^{28} - 20q^{34} - 32q^{37} + 10q^{40} - 48q^{46} + 32q^{49} + 4q^{52} - 20q^{58} + 16q^{61} + 44q^{64} - 30q^{70} + 40q^{73} - 80q^{82} - 40q^{85} + 18q^{88} + 12q^{94} - 44q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40126 0.190983i 0.990839 0.135045i
\(3\) 0 0
\(4\) 1.92705 0.535233i 0.963525 0.267617i
\(5\) −1.93649 + 1.11803i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 3.35410 + 1.93649i 1.26773 + 0.731925i 0.974558 0.224134i \(-0.0719554\pi\)
0.293173 + 0.956059i \(0.405289\pi\)
\(8\) 2.59808 1.11803i 0.918559 0.395285i
\(9\) 0 0
\(10\) −2.50000 + 1.93649i −0.790569 + 0.612372i
\(11\) 0.866025 1.50000i 0.261116 0.452267i −0.705422 0.708787i \(-0.749243\pi\)
0.966539 + 0.256520i \(0.0825760\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 5.06980 + 2.07295i 1.35496 + 0.554019i
\(15\) 0 0
\(16\) 3.42705 2.06284i 0.856763 0.515711i
\(17\) 4.47214i 1.08465i 0.840168 + 0.542326i \(0.182456\pi\)
−0.840168 + 0.542326i \(0.817544\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −3.13331 + 3.19098i −0.700629 + 0.713525i
\(21\) 0 0
\(22\) 0.927051 2.26728i 0.197648 0.483387i
\(23\) −3.46410 6.00000i −0.722315 1.25109i −0.960070 0.279761i \(-0.909745\pi\)
0.237754 0.971325i \(-0.423589\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.73205 2.23607i −0.339683 0.438529i
\(27\) 0 0
\(28\) 7.50000 + 1.93649i 1.41737 + 0.365963i
\(29\) −3.87298 2.23607i −0.719195 0.415227i 0.0952614 0.995452i \(-0.469631\pi\)
−0.814456 + 0.580225i \(0.802965\pi\)
\(30\) 0 0
\(31\) 3.35410 1.93649i 0.602414 0.347804i −0.167576 0.985859i \(-0.553594\pi\)
0.769991 + 0.638055i \(0.220261\pi\)
\(32\) 4.40822 3.54508i 0.779270 0.626688i
\(33\) 0 0
\(34\) 0.854102 + 6.26662i 0.146477 + 1.07472i
\(35\) −8.66025 −1.46385
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −3.78115 + 5.06980i −0.597853 + 0.801606i
\(41\) −7.74597 + 4.47214i −1.20972 + 0.698430i −0.962697 0.270580i \(-0.912784\pi\)
−0.247019 + 0.969011i \(0.579451\pi\)
\(42\) 0 0
\(43\) −6.70820 3.87298i −1.02299 0.590624i −0.108022 0.994148i \(-0.534452\pi\)
−0.914969 + 0.403524i \(0.867785\pi\)
\(44\) 0.866025 3.35410i 0.130558 0.505650i
\(45\) 0 0
\(46\) −6.00000 7.74597i −0.884652 1.14208i
\(47\) −1.73205 + 3.00000i −0.252646 + 0.437595i −0.964253 0.264982i \(-0.914634\pi\)
0.711608 + 0.702577i \(0.247967\pi\)
\(48\) 0 0
\(49\) 4.00000 + 6.92820i 0.571429 + 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.85410 2.80252i −0.395793 0.388639i
\(53\) 2.23607i 0.307148i −0.988137 0.153574i \(-0.950922\pi\)
0.988137 0.153574i \(-0.0490783\pi\)
\(54\) 0 0
\(55\) 3.87298i 0.522233i
\(56\) 10.8793 + 1.28115i 1.45380 + 0.171201i
\(57\) 0 0
\(58\) −5.85410 2.39364i −0.768681 0.314300i
\(59\) 1.73205 + 3.00000i 0.225494 + 0.390567i 0.956467 0.291839i \(-0.0942671\pi\)
−0.730974 + 0.682406i \(0.760934\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 4.33013 3.35410i 0.549927 0.425971i
\(63\) 0 0
\(64\) 5.50000 5.80948i 0.687500 0.726184i
\(65\) 3.87298 + 2.23607i 0.480384 + 0.277350i
\(66\) 0 0
\(67\) −6.70820 + 3.87298i −0.819538 + 0.473160i −0.850257 0.526368i \(-0.823553\pi\)
0.0307194 + 0.999528i \(0.490220\pi\)
\(68\) 2.39364 + 8.61803i 0.290271 + 1.04509i
\(69\) 0 0
\(70\) −12.1353 + 1.65396i −1.45044 + 0.197686i
\(71\) 10.3923 1.23334 0.616670 0.787222i \(-0.288481\pi\)
0.616670 + 0.787222i \(0.288481\pi\)
\(72\) 0 0
\(73\) 5.00000 0.585206 0.292603 0.956234i \(-0.405479\pi\)
0.292603 + 0.956234i \(0.405479\pi\)
\(74\) −5.60503 + 0.763932i −0.651572 + 0.0888053i
\(75\) 0 0
\(76\) 0 0
\(77\) 5.80948 3.35410i 0.662051 0.382235i
\(78\) 0 0
\(79\) −6.70820 3.87298i −0.754732 0.435745i 0.0726692 0.997356i \(-0.476848\pi\)
−0.827401 + 0.561611i \(0.810182\pi\)
\(80\) −4.33013 + 7.82624i −0.484123 + 0.875000i
\(81\) 0 0
\(82\) −10.0000 + 7.74597i −1.10432 + 0.855399i
\(83\) 6.06218 10.5000i 0.665410 1.15252i −0.313763 0.949501i \(-0.601590\pi\)
0.979174 0.203024i \(-0.0650768\pi\)
\(84\) 0 0
\(85\) −5.00000 8.66025i −0.542326 0.939336i
\(86\) −10.1396 4.14590i −1.09338 0.447064i
\(87\) 0 0
\(88\) 0.572949 4.86536i 0.0610766 0.518649i
\(89\) 4.47214i 0.474045i 0.971504 + 0.237023i \(0.0761716\pi\)
−0.971504 + 0.237023i \(0.923828\pi\)
\(90\) 0 0
\(91\) 7.74597i 0.811998i
\(92\) −9.88690 9.70820i −1.03078 1.01215i
\(93\) 0 0
\(94\) −1.85410 + 4.53457i −0.191236 + 0.467705i
\(95\) 0 0
\(96\) 0 0
\(97\) −5.50000 + 9.52628i −0.558440 + 0.967247i 0.439187 + 0.898396i \(0.355267\pi\)
−0.997627 + 0.0688512i \(0.978067\pi\)
\(98\) 6.92820 + 8.94427i 0.699854 + 0.903508i
\(99\) 0 0
\(100\) 0 0
\(101\) 1.93649 + 1.11803i 0.192688 + 0.111249i 0.593240 0.805025i \(-0.297848\pi\)
−0.400552 + 0.916274i \(0.631182\pi\)
\(102\) 0 0
\(103\) −6.70820 + 3.87298i −0.660979 + 0.381616i −0.792650 0.609677i \(-0.791299\pi\)
0.131671 + 0.991293i \(0.457966\pi\)
\(104\) −4.53457 3.38197i −0.444651 0.331629i
\(105\) 0 0
\(106\) −0.427051 3.13331i −0.0414789 0.304334i
\(107\) 5.19615 0.502331 0.251166 0.967944i \(-0.419186\pi\)
0.251166 + 0.967944i \(0.419186\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0.739674 + 5.42705i 0.0705251 + 0.517449i
\(111\) 0 0
\(112\) 15.4894 0.282530i 1.46361 0.0266966i
\(113\) 15.4919 8.94427i 1.45736 0.841406i 0.458478 0.888706i \(-0.348395\pi\)
0.998881 + 0.0472996i \(0.0150615\pi\)
\(114\) 0 0
\(115\) 13.4164 + 7.74597i 1.25109 + 0.722315i
\(116\) −8.66025 2.23607i −0.804084 0.207614i
\(117\) 0 0
\(118\) 3.00000 + 3.87298i 0.276172 + 0.356537i
\(119\) −8.66025 + 15.0000i −0.793884 + 1.37505i
\(120\) 0 0
\(121\) 4.00000 + 6.92820i 0.363636 + 0.629837i
\(122\) 2.14093 5.23607i 0.193831 0.474051i
\(123\) 0 0
\(124\) 5.42705 5.52694i 0.487364 0.496334i
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) 11.6190i 1.03102i −0.856885 0.515508i \(-0.827603\pi\)
0.856885 0.515508i \(-0.172397\pi\)
\(128\) 6.59741 9.19098i 0.583134 0.812376i
\(129\) 0 0
\(130\) 5.85410 + 2.39364i 0.513439 + 0.209936i
\(131\) 9.52628 + 16.5000i 0.832315 + 1.44161i 0.896198 + 0.443654i \(0.146318\pi\)
−0.0638831 + 0.997957i \(0.520348\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.66025 + 6.70820i −0.748132 + 0.579501i
\(135\) 0 0
\(136\) 5.00000 + 11.6190i 0.428746 + 0.996317i
\(137\) −3.87298 2.23607i −0.330891 0.191040i 0.325345 0.945595i \(-0.394519\pi\)
−0.656237 + 0.754555i \(0.727853\pi\)
\(138\) 0 0
\(139\) 13.4164 7.74597i 1.13796 0.657004i 0.192039 0.981387i \(-0.438490\pi\)
0.945926 + 0.324383i \(0.105157\pi\)
\(140\) −16.6888 + 4.63525i −1.41046 + 0.391751i
\(141\) 0 0
\(142\) 14.5623 1.98475i 1.22204 0.166557i
\(143\) −3.46410 −0.289683
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) 7.00629 0.954915i 0.579845 0.0790293i
\(147\) 0 0
\(148\) −7.70820 + 2.14093i −0.633610 + 0.175984i
\(149\) −1.93649 + 1.11803i −0.158644 + 0.0915929i −0.577220 0.816589i \(-0.695863\pi\)
0.418576 + 0.908182i \(0.362529\pi\)
\(150\) 0 0
\(151\) 3.35410 + 1.93649i 0.272953 + 0.157589i 0.630229 0.776409i \(-0.282961\pi\)
−0.357276 + 0.933999i \(0.616294\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 7.50000 5.80948i 0.604367 0.468141i
\(155\) −4.33013 + 7.50000i −0.347804 + 0.602414i
\(156\) 0 0
\(157\) −10.0000 17.3205i −0.798087 1.38233i −0.920860 0.389892i \(-0.872512\pi\)
0.122774 0.992435i \(-0.460821\pi\)
\(158\) −10.1396 4.14590i −0.806663 0.329830i
\(159\) 0 0
\(160\) −4.57295 + 11.7936i −0.361523 + 0.932363i
\(161\) 26.8328i 2.11472i
\(162\) 0 0
\(163\) 23.2379i 1.82013i 0.414462 + 0.910066i \(0.363970\pi\)
−0.414462 + 0.910066i \(0.636030\pi\)
\(164\) −12.5332 + 12.7639i −0.978681 + 0.996696i
\(165\) 0 0
\(166\) 6.48936 15.8710i 0.503672 1.23183i
\(167\) 1.73205 + 3.00000i 0.134030 + 0.232147i 0.925227 0.379415i \(-0.123875\pi\)
−0.791196 + 0.611562i \(0.790541\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) −8.66025 11.1803i −0.664211 0.857493i
\(171\) 0 0
\(172\) −15.0000 3.87298i −1.14374 0.295312i
\(173\) 13.5554 + 7.82624i 1.03060 + 0.595018i 0.917157 0.398527i \(-0.130478\pi\)
0.113444 + 0.993544i \(0.463812\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.126351 6.92705i −0.00952410 0.522146i
\(177\) 0 0
\(178\) 0.854102 + 6.26662i 0.0640176 + 0.469703i
\(179\) −5.19615 −0.388379 −0.194189 0.980964i \(-0.562208\pi\)
−0.194189 + 0.980964i \(0.562208\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −1.47935 10.8541i −0.109657 0.804560i
\(183\) 0 0
\(184\) −15.7082 11.7155i −1.15802 0.863676i
\(185\) 7.74597 4.47214i 0.569495 0.328798i
\(186\) 0 0
\(187\) 6.70820 + 3.87298i 0.490552 + 0.283221i
\(188\) −1.73205 + 6.70820i −0.126323 + 0.489246i
\(189\) 0 0
\(190\) 0 0
\(191\) 8.66025 15.0000i 0.626634 1.08536i −0.361588 0.932338i \(-0.617765\pi\)
0.988222 0.153024i \(-0.0489012\pi\)
\(192\) 0 0
\(193\) 12.5000 + 21.6506i 0.899770 + 1.55845i 0.827788 + 0.561041i \(0.189599\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) −5.88756 + 14.3992i −0.422702 + 1.03380i
\(195\) 0 0
\(196\) 11.4164 + 11.2101i 0.815458 + 0.800719i
\(197\) 24.5967i 1.75245i 0.481906 + 0.876223i \(0.339945\pi\)
−0.481906 + 0.876223i \(0.660055\pi\)
\(198\) 0 0
\(199\) 11.6190i 0.823646i 0.911264 + 0.411823i \(0.135108\pi\)
−0.911264 + 0.411823i \(0.864892\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2.92705 + 1.19682i 0.205947 + 0.0842078i
\(203\) −8.66025 15.0000i −0.607831 1.05279i
\(204\) 0 0
\(205\) 10.0000 17.3205i 0.698430 1.20972i
\(206\) −8.66025 + 6.70820i −0.603388 + 0.467383i
\(207\) 0 0
\(208\) −7.00000 3.87298i −0.485363 0.268543i
\(209\) 0 0
\(210\) 0 0
\(211\) 13.4164 7.74597i 0.923624 0.533254i 0.0388343 0.999246i \(-0.487636\pi\)
0.884789 + 0.465991i \(0.154302\pi\)
\(212\) −1.19682 4.30902i −0.0821978 0.295945i
\(213\) 0 0
\(214\) 7.28115 0.992377i 0.497729 0.0678375i
\(215\) 17.3205 1.18125
\(216\) 0 0
\(217\) 15.0000 1.01827
\(218\) −5.60503 + 0.763932i −0.379621 + 0.0517400i
\(219\) 0 0
\(220\) 2.07295 + 7.46344i 0.139758 + 0.503185i
\(221\) 7.74597 4.47214i 0.521050 0.300828i
\(222\) 0 0
\(223\) −6.70820 3.87298i −0.449215 0.259354i 0.258284 0.966069i \(-0.416843\pi\)
−0.707498 + 0.706715i \(0.750176\pi\)
\(224\) 21.6506 3.35410i 1.44659 0.224105i
\(225\) 0 0
\(226\) 20.0000 15.4919i 1.33038 1.03051i
\(227\) −1.73205 + 3.00000i −0.114960 + 0.199117i −0.917764 0.397127i \(-0.870007\pi\)
0.802804 + 0.596244i \(0.203341\pi\)
\(228\) 0 0
\(229\) −1.00000 1.73205i −0.0660819 0.114457i 0.831092 0.556136i \(-0.187717\pi\)
−0.897173 + 0.441679i \(0.854383\pi\)
\(230\) 20.2792 + 8.29180i 1.33717 + 0.546745i
\(231\) 0 0
\(232\) −12.5623 1.47935i −0.824756 0.0971240i
\(233\) 4.47214i 0.292979i 0.989212 + 0.146490i \(0.0467975\pi\)
−0.989212 + 0.146490i \(0.953202\pi\)
\(234\) 0 0
\(235\) 7.74597i 0.505291i
\(236\) 4.94345 + 4.85410i 0.321791 + 0.315975i
\(237\) 0 0
\(238\) −9.27051 + 22.6728i −0.600918 + 1.46966i
\(239\) 6.92820 + 12.0000i 0.448148 + 0.776215i 0.998266 0.0588719i \(-0.0187503\pi\)
−0.550117 + 0.835087i \(0.685417\pi\)
\(240\) 0 0
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 6.92820 + 8.94427i 0.445362 + 0.574960i
\(243\) 0 0
\(244\) 2.00000 7.74597i 0.128037 0.495885i
\(245\) −15.4919 8.94427i −0.989743 0.571429i
\(246\) 0 0
\(247\) 0 0
\(248\) 6.54915 8.78115i 0.415871 0.557604i
\(249\) 0 0
\(250\) −2.13525 15.6665i −0.135045 0.990839i
\(251\) 10.3923 0.655956 0.327978 0.944685i \(-0.393633\pi\)
0.327978 + 0.944685i \(0.393633\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) −2.21902 16.2812i −0.139234 1.02157i
\(255\) 0 0
\(256\) 7.48936 14.1389i 0.468085 0.883684i
\(257\) −19.3649 + 11.1803i −1.20795 + 0.697410i −0.962311 0.271951i \(-0.912331\pi\)
−0.245639 + 0.969361i \(0.578998\pi\)
\(258\) 0 0
\(259\) −13.4164 7.74597i −0.833655 0.481311i
\(260\) 8.66025 + 2.23607i 0.537086 + 0.138675i
\(261\) 0 0
\(262\) 16.5000 + 21.3014i 1.01937 + 1.31601i
\(263\) 3.46410 6.00000i 0.213606 0.369976i −0.739235 0.673448i \(-0.764813\pi\)
0.952840 + 0.303472i \(0.0981459\pi\)
\(264\) 0 0
\(265\) 2.50000 + 4.33013i 0.153574 + 0.265998i
\(266\) 0 0
\(267\) 0 0
\(268\) −10.8541 + 11.0539i −0.663020 + 0.675224i
\(269\) 4.47214i 0.272671i 0.990663 + 0.136335i \(0.0435325\pi\)
−0.990663 + 0.136335i \(0.956467\pi\)
\(270\) 0 0
\(271\) 11.6190i 0.705801i −0.935661 0.352900i \(-0.885195\pi\)
0.935661 0.352900i \(-0.114805\pi\)
\(272\) 9.22531 + 15.3262i 0.559367 + 0.929290i
\(273\) 0 0
\(274\) −5.85410 2.39364i −0.353659 0.144605i
\(275\) 0 0
\(276\) 0 0
\(277\) −10.0000 + 17.3205i −0.600842 + 1.04069i 0.391852 + 0.920028i \(0.371834\pi\)
−0.992694 + 0.120660i \(0.961499\pi\)
\(278\) 17.3205 13.4164i 1.03882 0.804663i
\(279\) 0 0
\(280\) −22.5000 + 9.68246i −1.34463 + 0.578638i
\(281\) −3.87298 2.23607i −0.231043 0.133393i 0.380010 0.924982i \(-0.375920\pi\)
−0.611053 + 0.791590i \(0.709254\pi\)
\(282\) 0 0
\(283\) −26.8328 + 15.4919i −1.59505 + 0.920900i −0.602623 + 0.798026i \(0.705878\pi\)
−0.992422 + 0.122874i \(0.960789\pi\)
\(284\) 20.0265 5.56231i 1.18835 0.330062i
\(285\) 0 0
\(286\) −4.85410 + 0.661585i −0.287029 + 0.0391203i
\(287\) −34.6410 −2.04479
\(288\) 0 0
\(289\) −3.00000 −0.176471
\(290\) 14.0126 1.90983i 0.822847 0.112149i
\(291\) 0 0
\(292\) 9.63525 2.67617i 0.563861 0.156611i
\(293\) −19.3649 + 11.1803i −1.13131 + 0.653162i −0.944264 0.329189i \(-0.893225\pi\)
−0.187046 + 0.982351i \(0.559891\pi\)
\(294\) 0 0
\(295\) −6.70820 3.87298i −0.390567 0.225494i
\(296\) −10.3923 + 4.47214i −0.604040 + 0.259938i
\(297\) 0 0
\(298\) −2.50000 + 1.93649i −0.144821 + 0.112178i
\(299\) −6.92820 + 12.0000i −0.400668 + 0.693978i
\(300\) 0 0
\(301\) −15.0000 25.9808i −0.864586 1.49751i
\(302\) 5.06980 + 2.07295i 0.291734 + 0.119285i
\(303\) 0 0
\(304\) 0 0
\(305\) 8.94427i 0.512148i
\(306\) 0 0
\(307\) 23.2379i 1.32626i −0.748506 0.663129i \(-0.769228\pi\)
0.748506 0.663129i \(-0.230772\pi\)
\(308\) 9.39993 9.57295i 0.535611 0.545469i
\(309\) 0 0
\(310\) −4.63525 + 11.3364i −0.263265 + 0.643865i
\(311\) −13.8564 24.0000i −0.785725 1.36092i −0.928565 0.371169i \(-0.878957\pi\)
0.142840 0.989746i \(-0.454376\pi\)
\(312\) 0 0
\(313\) −2.50000 + 4.33013i −0.141308 + 0.244753i −0.927990 0.372606i \(-0.878464\pi\)
0.786681 + 0.617359i \(0.211798\pi\)
\(314\) −17.3205 22.3607i −0.977453 1.26189i
\(315\) 0 0
\(316\) −15.0000 3.87298i −0.843816 0.217872i
\(317\) 13.5554 + 7.82624i 0.761349 + 0.439565i 0.829780 0.558091i \(-0.188466\pi\)
−0.0684306 + 0.997656i \(0.521799\pi\)
\(318\) 0 0
\(319\) −6.70820 + 3.87298i −0.375587 + 0.216845i
\(320\) −4.15551 + 17.3992i −0.232300 + 0.972644i
\(321\) 0 0
\(322\) −5.12461 37.5997i −0.285583 2.09535i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 4.43804 + 32.5623i 0.245801 + 1.80346i
\(327\) 0 0
\(328\) −15.1246 + 20.2792i −0.835117 + 1.11973i
\(329\) −11.6190 + 6.70820i −0.640573 + 0.369835i
\(330\) 0 0
\(331\) −6.70820 3.87298i −0.368716 0.212878i 0.304181 0.952614i \(-0.401617\pi\)
−0.672897 + 0.739736i \(0.734950\pi\)
\(332\) 6.06218 23.4787i 0.332705 1.28856i
\(333\) 0 0
\(334\) 3.00000 + 3.87298i 0.164153 + 0.211920i
\(335\) 8.66025 15.0000i 0.473160 0.819538i
\(336\) 0 0
\(337\) 5.00000 + 8.66025i 0.272367 + 0.471754i 0.969468 0.245220i \(-0.0788601\pi\)
−0.697100 + 0.716974i \(0.745527\pi\)
\(338\) 4.81710 11.7812i 0.262016 0.640810i
\(339\) 0 0
\(340\) −14.2705 14.0126i −0.773927 0.759939i
\(341\) 6.70820i 0.363270i
\(342\) 0 0
\(343\) 3.87298i 0.209121i
\(344\) −21.7586 2.56231i −1.17314 0.138150i
\(345\) 0 0
\(346\) 20.4894 + 8.37772i 1.10151 + 0.450389i
\(347\) −16.4545 28.5000i −0.883323 1.52996i −0.847624 0.530598i \(-0.821968\pi\)
−0.0356990 0.999363i \(-0.511366\pi\)
\(348\) 0 0
\(349\) 8.00000 13.8564i 0.428230 0.741716i −0.568486 0.822693i \(-0.692471\pi\)
0.996716 + 0.0809766i \(0.0258039\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.50000 9.68246i −0.0799503 0.516077i
\(353\) −15.4919 8.94427i −0.824552 0.476056i 0.0274314 0.999624i \(-0.491267\pi\)
−0.851984 + 0.523568i \(0.824601\pi\)
\(354\) 0 0
\(355\) −20.1246 + 11.6190i −1.06810 + 0.616670i
\(356\) 2.39364 + 8.61803i 0.126862 + 0.456755i
\(357\) 0 0
\(358\) −7.28115 + 0.992377i −0.384821 + 0.0524487i
\(359\) −31.1769 −1.64545 −0.822727 0.568436i \(-0.807549\pi\)
−0.822727 + 0.568436i \(0.807549\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) −22.4201 + 3.05573i −1.17838 + 0.160606i
\(363\) 0 0
\(364\) −4.14590 14.9269i −0.217304 0.782381i
\(365\) −9.68246 + 5.59017i −0.506803 + 0.292603i
\(366\) 0 0
\(367\) 23.4787 + 13.5554i 1.22558 + 0.707588i 0.966102 0.258161i \(-0.0831165\pi\)
0.259477 + 0.965749i \(0.416450\pi\)
\(368\) −24.2487 13.4164i −1.26405 0.699379i
\(369\) 0 0
\(370\) 10.0000 7.74597i 0.519875 0.402694i
\(371\) 4.33013 7.50000i 0.224809 0.389381i
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 10.1396 + 4.14590i 0.524306 + 0.214379i
\(375\) 0 0
\(376\) −1.14590 + 9.73072i −0.0590952 + 0.501824i
\(377\) 8.94427i 0.460653i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 9.27051 22.6728i 0.474321 1.16004i
\(383\) 12.1244 + 21.0000i 0.619526 + 1.07305i 0.989572 + 0.144037i \(0.0460083\pi\)
−0.370047 + 0.929013i \(0.620658\pi\)
\(384\) 0 0
\(385\) −7.50000 + 12.9904i −0.382235 + 0.662051i
\(386\) 21.6506 + 27.9508i 1.10199 + 1.42266i
\(387\) 0 0
\(388\) −5.50000 + 21.3014i −0.279220 + 1.08142i
\(389\) 1.93649 + 1.11803i 0.0981840 + 0.0566866i 0.548288 0.836290i \(-0.315280\pi\)
−0.450104 + 0.892976i \(0.648613\pi\)
\(390\) 0 0
\(391\) 26.8328 15.4919i 1.35699 0.783461i
\(392\) 18.1383 + 13.5279i 0.916121 + 0.683260i
\(393\) 0 0
\(394\) 4.69756 + 34.4664i 0.236660 + 1.73639i
\(395\) 17.3205 0.871489
\(396\) 0 0
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 2.21902 + 16.2812i 0.111230 + 0.816100i
\(399\) 0 0
\(400\) 0 0
\(401\) 15.4919 8.94427i 0.773630 0.446656i −0.0605379 0.998166i \(-0.519282\pi\)
0.834168 + 0.551510i \(0.185948\pi\)
\(402\) 0 0
\(403\) −6.70820 3.87298i −0.334159 0.192927i
\(404\) 4.33013 + 1.11803i 0.215432 + 0.0556243i
\(405\) 0 0
\(406\) −15.0000 19.3649i −0.744438 0.961065i
\(407\) −3.46410 + 6.00000i −0.171709 + 0.297409i
\(408\) 0 0
\(409\) 3.50000 + 6.06218i 0.173064 + 0.299755i 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 10.7047 26.1803i 0.528666 1.29295i
\(411\) 0 0
\(412\) −10.8541 + 11.0539i −0.534743 + 0.544586i
\(413\) 13.4164i 0.660178i
\(414\) 0 0
\(415\) 27.1109i 1.33082i
\(416\) −10.5485 4.09017i −0.517182 0.200537i
\(417\) 0 0
\(418\) 0 0
\(419\) −8.66025 15.0000i −0.423081 0.732798i 0.573158 0.819445i \(-0.305718\pi\)
−0.996239 + 0.0866469i \(0.972385\pi\)
\(420\) 0 0
\(421\) 2.00000 3.46410i 0.0974740 0.168830i −0.813164 0.582034i \(-0.802257\pi\)
0.910638 + 0.413204i \(0.135590\pi\)
\(422\) 17.3205 13.4164i 0.843149 0.653101i
\(423\) 0 0
\(424\) −2.50000 5.80948i −0.121411 0.282133i
\(425\) 0 0
\(426\) 0 0
\(427\) 13.4164 7.74597i 0.649265 0.374854i
\(428\) 10.0133 2.78115i 0.484009 0.134432i
\(429\) 0 0
\(430\) 24.2705 3.30792i 1.17043 0.159522i
\(431\) 10.3923 0.500580 0.250290 0.968171i \(-0.419474\pi\)
0.250290 + 0.968171i \(0.419474\pi\)
\(432\) 0 0
\(433\) −13.0000 −0.624740 −0.312370 0.949960i \(-0.601123\pi\)
−0.312370 + 0.949960i \(0.601123\pi\)
\(434\) 21.0189 2.86475i 1.00894 0.137512i
\(435\) 0 0
\(436\) −7.70820 + 2.14093i −0.369156 + 0.102532i
\(437\) 0 0
\(438\) 0 0
\(439\) 3.35410 + 1.93649i 0.160083 + 0.0924237i 0.577901 0.816107i \(-0.303872\pi\)
−0.417819 + 0.908530i \(0.637205\pi\)
\(440\) 4.33013 + 10.0623i 0.206431 + 0.479702i
\(441\) 0 0
\(442\) 10.0000 7.74597i 0.475651 0.368438i
\(443\) −12.1244 + 21.0000i −0.576046 + 0.997740i 0.419882 + 0.907579i \(0.362072\pi\)
−0.995927 + 0.0901612i \(0.971262\pi\)
\(444\) 0 0
\(445\) −5.00000 8.66025i −0.237023 0.410535i
\(446\) −10.1396 4.14590i −0.480124 0.196314i
\(447\) 0 0
\(448\) 29.6976 8.83487i 1.40308 0.417408i
\(449\) 17.8885i 0.844213i 0.906546 + 0.422106i \(0.138709\pi\)
−0.906546 + 0.422106i \(0.861291\pi\)
\(450\) 0 0
\(451\) 15.4919i 0.729487i
\(452\) 25.0665 25.5279i 1.17903 1.20073i
\(453\) 0 0
\(454\) −1.85410 + 4.53457i −0.0870173 + 0.212818i
\(455\) 8.66025 + 15.0000i 0.405999 + 0.703211i
\(456\) 0 0
\(457\) 15.5000 26.8468i 0.725059 1.25584i −0.233890 0.972263i \(-0.575146\pi\)
0.958950 0.283577i \(-0.0915211\pi\)
\(458\) −1.73205 2.23607i −0.0809334 0.104485i
\(459\) 0 0
\(460\) 30.0000 + 7.74597i 1.39876 + 0.361158i
\(461\) −32.9204 19.0066i −1.53325 0.885225i −0.999209 0.0397685i \(-0.987338\pi\)
−0.534045 0.845456i \(-0.679329\pi\)
\(462\) 0 0
\(463\) 3.35410 1.93649i 0.155878 0.0899964i −0.420032 0.907509i \(-0.637981\pi\)
0.575910 + 0.817513i \(0.304648\pi\)
\(464\) −17.8856 + 0.326238i −0.830317 + 0.0151452i
\(465\) 0 0
\(466\) 0.854102 + 6.26662i 0.0395655 + 0.290296i
\(467\) −5.19615 −0.240449 −0.120225 0.992747i \(-0.538361\pi\)
−0.120225 + 0.992747i \(0.538361\pi\)
\(468\) 0 0
\(469\) −30.0000 −1.38527
\(470\) −1.47935 10.8541i −0.0682372 0.500662i
\(471\) 0 0
\(472\) 7.85410 + 5.85774i 0.361514 + 0.269624i
\(473\) −11.6190 + 6.70820i −0.534240 + 0.308444i
\(474\) 0 0
\(475\) 0 0
\(476\) −8.66025 + 33.5410i −0.396942 + 1.53735i
\(477\) 0 0
\(478\) 12.0000 + 15.4919i 0.548867 + 0.708585i
\(479\) 8.66025 15.0000i 0.395697 0.685367i −0.597493 0.801874i \(-0.703836\pi\)
0.993190 + 0.116507i \(0.0371697\pi\)
\(480\) 0 0
\(481\) 4.00000 + 6.92820i 0.182384 + 0.315899i
\(482\) −7.49326 + 18.3262i −0.341309 + 0.834737i
\(483\) 0 0
\(484\) 11.4164 + 11.2101i 0.518928 + 0.509549i
\(485\) 24.5967i 1.11688i
\(486\) 0 0
\(487\) 23.2379i 1.05301i −0.850172 0.526505i \(-0.823502\pi\)
0.850172 0.526505i \(-0.176498\pi\)
\(488\) 1.32317 11.2361i 0.0598970 0.508633i
\(489\) 0 0
\(490\) −23.4164 9.57454i −1.05785 0.432534i
\(491\) 4.33013 + 7.50000i 0.195416 + 0.338470i 0.947037 0.321125i \(-0.104061\pi\)
−0.751621 + 0.659595i \(0.770728\pi\)
\(492\) 0 0
\(493\) 10.0000 17.3205i 0.450377 0.780076i
\(494\) 0 0
\(495\) 0 0
\(496\) 7.50000 13.5554i 0.336760 0.608657i
\(497\) 34.8569 + 20.1246i 1.56354 + 0.902712i
\(498\) 0 0
\(499\) 33.5410 19.3649i 1.50150 0.866893i 0.501504 0.865155i \(-0.332780\pi\)
0.999998 0.00173727i \(-0.000552990\pi\)
\(500\) −5.98409 21.5451i −0.267617 0.963525i
\(501\) 0 0
\(502\) 14.5623 1.98475i 0.649948 0.0885839i
\(503\) 20.7846 0.926740 0.463370 0.886165i \(-0.346640\pi\)
0.463370 + 0.886165i \(0.346640\pi\)
\(504\) 0 0
\(505\) −5.00000 −0.222497
\(506\) −16.8151 + 2.29180i −0.747522 + 0.101883i
\(507\) 0 0
\(508\) −6.21885 22.3903i −0.275917 0.993409i
\(509\) 9.68246 5.59017i 0.429167 0.247780i −0.269824 0.962910i \(-0.586966\pi\)
0.698992 + 0.715130i \(0.253632\pi\)
\(510\) 0 0
\(511\) 16.7705 + 9.68246i 0.741884 + 0.428327i
\(512\) 7.79423 21.2426i 0.344459 0.938801i
\(513\) 0 0
\(514\) −25.0000 + 19.3649i −1.10270 + 0.854150i
\(515\) 8.66025 15.0000i 0.381616 0.660979i
\(516\) 0 0
\(517\) 3.00000 + 5.19615i 0.131940 + 0.228527i
\(518\) −20.2792 8.29180i −0.891017 0.364321i
\(519\) 0 0
\(520\) 12.5623 + 1.47935i 0.550894 + 0.0648737i
\(521\) 22.3607i 0.979639i −0.871824 0.489820i \(-0.837063\pi\)
0.871824 0.489820i \(-0.162937\pi\)
\(522\) 0 0
\(523\) 23.2379i 1.01612i 0.861321 + 0.508061i \(0.169638\pi\)
−0.861321 + 0.508061i \(0.830362\pi\)
\(524\) 27.1890 + 26.6976i 1.18776 + 1.16629i
\(525\) 0 0
\(526\) 3.70820 9.06914i 0.161685 0.395433i
\(527\) 8.66025 + 15.0000i 0.377247 + 0.653410i
\(528\) 0 0
\(529\) −12.5000 + 21.6506i −0.543478 + 0.941332i
\(530\) 4.33013 + 5.59017i 0.188089 + 0.242821i
\(531\) 0 0
\(532\) 0 0
\(533\) 15.4919 + 8.94427i 0.671030 + 0.387419i
\(534\) 0 0
\(535\) −10.0623 + 5.80948i −0.435031 + 0.251166i
\(536\) −13.0983 + 17.5623i −0.565760 + 0.758576i
\(537\) 0 0
\(538\) 0.854102 + 6.26662i 0.0368230 + 0.270173i
\(539\) 13.8564 0.596838
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) −2.21902 16.2812i −0.0953152 0.699335i
\(543\) 0 0
\(544\) 15.8541 + 19.7141i 0.679739 + 0.845237i
\(545\) 7.74597 4.47214i 0.331801 0.191565i
\(546\) 0 0
\(547\) −6.70820 3.87298i −0.286822 0.165597i 0.349686 0.936867i \(-0.386288\pi\)
−0.636508 + 0.771270i \(0.719622\pi\)
\(548\) −8.66025 2.23607i −0.369948 0.0955201i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −15.0000 25.9808i −0.637865 1.10481i
\(554\) −10.7047 + 26.1803i −0.454798 + 1.11230i
\(555\) 0 0
\(556\) 21.7082 22.1078i 0.920633 0.937579i
\(557\) 15.6525i 0.663217i −0.943417 0.331608i \(-0.892409\pi\)
0.943417 0.331608i \(-0.107591\pi\)
\(558\) 0 0
\(559\) 15.4919i 0.655239i
\(560\) −29.6791 + 17.8647i −1.25417 + 0.754923i
\(561\) 0 0
\(562\) −5.85410 2.39364i −0.246940 0.100969i
\(563\) 9.52628 + 16.5000i 0.401485 + 0.695392i 0.993905 0.110237i \(-0.0351609\pi\)
−0.592421 + 0.805629i \(0.701828\pi\)
\(564\) 0 0
\(565\) −20.0000 + 34.6410i −0.841406 + 1.45736i
\(566\) −34.6410 + 26.8328i −1.45607 + 1.12787i
\(567\) 0 0
\(568\) 27.0000 11.6190i 1.13289 0.487520i
\(569\) 30.9839 + 17.8885i 1.29891 + 0.749927i 0.980216 0.197930i \(-0.0634220\pi\)
0.318695 + 0.947857i \(0.396755\pi\)
\(570\) 0 0
\(571\) −6.70820 + 3.87298i −0.280730 + 0.162079i −0.633754 0.773535i \(-0.718487\pi\)
0.353024 + 0.935614i \(0.385153\pi\)
\(572\) −6.67550 + 1.85410i −0.279117 + 0.0775239i
\(573\) 0 0
\(574\) −48.5410 + 6.61585i −2.02606 + 0.276140i
\(575\) 0 0
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) −4.20378 + 0.572949i −0.174854 + 0.0238315i
\(579\) 0 0
\(580\) 19.2705 5.35233i 0.800164 0.222243i
\(581\) 40.6663 23.4787i 1.68712 0.974061i
\(582\) 0 0
\(583\) −3.35410 1.93649i −0.138913 0.0802013i
\(584\) 12.9904 5.59017i 0.537546 0.231323i
\(585\) 0 0
\(586\) −25.0000 + 19.3649i −1.03274 + 0.799957i
\(587\) −9.52628 + 16.5000i −0.393192 + 0.681028i −0.992869 0.119214i \(-0.961962\pi\)
0.599677 + 0.800242i \(0.295296\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −10.1396 4.14590i −0.417441 0.170684i
\(591\) 0 0
\(592\) −13.7082 + 8.25137i −0.563404 + 0.339129i
\(593\) 4.47214i 0.183649i 0.995775 + 0.0918243i \(0.0292698\pi\)
−0.995775 + 0.0918243i \(0.970730\pi\)
\(594\) 0 0
\(595\) 38.7298i 1.58777i
\(596\) −3.13331 + 3.19098i −0.128345 + 0.130708i
\(597\) 0 0
\(598\) −7.41641 + 18.1383i −0.303279 + 0.741729i
\(599\) −8.66025 15.0000i −0.353848 0.612883i 0.633072 0.774093i \(-0.281794\pi\)
−0.986920 + 0.161210i \(0.948460\pi\)
\(600\) 0 0
\(601\) 15.5000 26.8468i 0.632258 1.09510i −0.354831 0.934931i \(-0.615462\pi\)
0.987089 0.160173i \(-0.0512051\pi\)
\(602\) −25.9808 33.5410i −1.05890 1.36703i
\(603\) 0 0
\(604\) 7.50000 + 1.93649i 0.305171 + 0.0787947i
\(605\) −15.4919 8.94427i −0.629837 0.363636i
\(606\) 0 0
\(607\) −6.70820 + 3.87298i −0.272278 + 0.157200i −0.629922 0.776658i \(-0.716913\pi\)
0.357645 + 0.933858i \(0.383580\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.70820 + 12.5332i 0.0691632 + 0.507456i
\(611\) 6.92820 0.280285
\(612\) 0 0
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) −4.43804 32.5623i −0.179105 1.31411i
\(615\) 0 0
\(616\) 11.3435 15.2094i 0.457041 0.612804i
\(617\) 15.4919 8.94427i 0.623682 0.360083i −0.154619 0.987974i \(-0.549415\pi\)
0.778301 + 0.627891i \(0.216082\pi\)
\(618\) 0 0
\(619\) 33.5410 + 19.3649i 1.34813 + 0.778342i 0.987984 0.154555i \(-0.0493945\pi\)
0.360143 + 0.932897i \(0.382728\pi\)
\(620\) −4.33013 + 16.7705i −0.173902 + 0.673520i
\(621\) 0 0
\(622\) −24.0000 30.9839i −0.962312 1.24234i
\(623\) −8.66025 + 15.0000i −0.346966 + 0.600962i
\(624\) 0 0
\(625\) 12.5000 + 21.6506i 0.500000 + 0.866025i
\(626\) −2.67617 + 6.54508i −0.106961 + 0.261594i
\(627\) 0 0
\(628\) −28.5410 28.0252i −1.13891 1.11833i
\(629\) 17.8885i 0.713263i
\(630\) 0 0
\(631\) 34.8569i 1.38763i −0.720154 0.693815i \(-0.755929\pi\)
0.720154 0.693815i \(-0.244071\pi\)
\(632\) −21.7586 2.56231i −0.865509 0.101923i
\(633\) 0 0
\(634\) 20.4894 + 8.37772i 0.813736 + 0.332722i
\(635\) 12.9904 + 22.5000i 0.515508 + 0.892885i
\(636\) 0 0
\(637\) 8.00000 13.8564i 0.316972 0.549011i
\(638\) −8.66025 + 6.70820i −0.342863 + 0.265580i
\(639\) 0 0
\(640\) −2.50000 + 25.1744i −0.0988212 + 0.995105i
\(641\) −38.7298 22.3607i −1.52974 0.883194i −0.999372 0.0354238i \(-0.988722\pi\)
−0.530364 0.847770i \(-0.677945\pi\)
\(642\) 0 0
\(643\) −26.8328 + 15.4919i −1.05818 + 0.610942i −0.924929 0.380140i \(-0.875876\pi\)
−0.133254 + 0.991082i \(0.542543\pi\)
\(644\) −14.3618 51.7082i −0.565935 2.03759i
\(645\) 0 0
\(646\) 0 0
\(647\) −20.7846 −0.817127 −0.408564 0.912730i \(-0.633970\pi\)
−0.408564 + 0.912730i \(0.633970\pi\)
\(648\) 0 0
\(649\) 6.00000 0.235521
\(650\) 0 0
\(651\) 0 0
\(652\) 12.4377 + 44.7806i 0.487098 + 1.75374i
\(653\) 9.68246 5.59017i 0.378904 0.218760i −0.298437 0.954429i \(-0.596465\pi\)
0.677341 + 0.735669i \(0.263132\pi\)
\(654\) 0 0
\(655\) −36.8951 21.3014i −1.44161 0.832315i
\(656\) −17.3205 + 31.3050i −0.676252 + 1.22225i
\(657\) 0 0
\(658\) −15.0000 + 11.6190i −0.584761 + 0.452954i
\(659\) −4.33013 + 7.50000i −0.168678 + 0.292159i −0.937955 0.346756i \(-0.887283\pi\)
0.769277 + 0.638915i \(0.220616\pi\)
\(660\) 0 0
\(661\) 8.00000 + 13.8564i 0.311164 + 0.538952i 0.978615 0.205702i \(-0.0659478\pi\)
−0.667451 + 0.744654i \(0.732615\pi\)
\(662\) −10.1396 4.14590i −0.394087 0.161135i
\(663\) 0 0
\(664\) 4.01064 34.0575i 0.155643 1.32169i
\(665\) 0 0
\(666\) 0 0
\(667\) 30.9839i 1.19970i
\(668\) 4.94345 + 4.85410i 0.191268 + 0.187811i
\(669\) 0 0
\(670\) 9.27051 22.6728i 0.358151 0.875928i
\(671\) −3.46410 6.00000i −0.133730 0.231627i
\(672\) 0 0
\(673\) −11.5000 + 19.9186i −0.443292 + 0.767805i −0.997932 0.0642860i \(-0.979523\pi\)
0.554639 + 0.832091i \(0.312856\pi\)
\(674\) 8.66025 + 11.1803i 0.333581 + 0.430651i
\(675\) 0 0
\(676\) 4.50000 17.4284i 0.173077 0.670324i
\(677\) 19.3649 + 11.1803i 0.744254 + 0.429695i 0.823614 0.567151i \(-0.191954\pi\)
−0.0793599 + 0.996846i \(0.525288\pi\)
\(678\) 0 0
\(679\) −36.8951 + 21.3014i −1.41590 + 0.817473i
\(680\) −22.6728 16.9098i −0.869464 0.648462i
\(681\) 0 0
\(682\) −1.28115 9.39993i −0.0490579 0.359942i
\(683\) −10.3923 −0.397650 −0.198825 0.980035i \(-0.563713\pi\)
−0.198825 + 0.980035i \(0.563713\pi\)
\(684\) 0 0
\(685\) 10.0000 0.382080
\(686\) 0.739674 + 5.42705i 0.0282409 + 0.207206i
\(687\) 0 0
\(688\) −30.9787 + 0.565061i −1.18105 + 0.0215427i
\(689\) −3.87298 + 2.23607i −0.147549 + 0.0851874i
\(690\) 0 0
\(691\) 13.4164 + 7.74597i 0.510384 + 0.294670i 0.732992 0.680238i \(-0.238123\pi\)
−0.222607 + 0.974908i \(0.571457\pi\)
\(692\) 30.3109 + 7.82624i 1.15225 + 0.297509i
\(693\) 0 0
\(694\) −28.5000 36.7933i −1.08185 1.39666i
\(695\) −17.3205 + 30.0000i −0.657004 + 1.13796i
\(696\) 0 0
\(697\) −20.0000 34.6410i −0.757554 1.31212i
\(698\) 8.56373 20.9443i 0.324142 0.792752i
\(699\) 0 0
\(700\) 0 0
\(701\) 15.6525i 0.591186i −0.955314 0.295593i \(-0.904483\pi\)
0.955314 0.295593i \(-0.0955172\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −3.95107 13.2812i −0.148912 0.500552i
\(705\) 0 0
\(706\) −23.4164 9.57454i −0.881288 0.360343i
\(707\) 4.33013 + 7.50000i 0.162851 + 0.282067i
\(708\) 0 0
\(709\) −16.0000 + 27.7128i −0.600893 + 1.04078i 0.391794 + 0.920053i \(0.371855\pi\)
−0.992686 + 0.120723i \(0.961479\pi\)
\(710\) −25.9808 + 20.1246i −0.975041 + 0.755263i
\(711\) 0 0
\(712\) 5.00000 + 11.6190i 0.187383 + 0.435439i
\(713\) −23.2379 13.4164i −0.870266 0.502448i
\(714\) 0 0
\(715\) 6.70820 3.87298i 0.250873 0.144841i
\(716\) −10.0133 + 2.78115i −0.374213 + 0.103937i
\(717\) 0 0
\(718\) −43.6869 + 5.95426i −1.63038 + 0.222211i
\(719\) 20.7846 0.775135 0.387568 0.921841i \(-0.373315\pi\)
0.387568 + 0.921841i \(0.373315\pi\)
\(720\) 0 0
\(721\) −30.0000 −1.11726
\(722\) 26.6239 3.62868i 0.990839 0.135045i
\(723\) 0 0
\(724\) −30.8328 + 8.56373i −1.14589 + 0.318269i
\(725\) 0 0
\(726\) 0 0
\(727\) −36.8951 21.3014i −1.36836 0.790026i −0.377645 0.925950i \(-0.623266\pi\)
−0.990719 + 0.135925i \(0.956599\pi\)
\(728\) −8.66025 20.1246i −0.320970 0.745868i
\(729\) 0 0
\(730\) −12.5000 + 9.68246i −0.462646 + 0.358364i
\(731\) 17.3205 30.0000i 0.640622 1.10959i
\(732\) 0 0
\(733\) −4.00000 6.92820i −0.147743 0.255899i 0.782650 0.622462i \(-0.213868\pi\)
−0.930393 + 0.366563i \(0.880534\pi\)
\(734\) 35.4886 + 14.5106i 1.30991 + 0.535598i
\(735\) 0 0
\(736\) −36.5410 14.1688i −1.34692 0.522268i
\(737\) 13.4164i 0.494200i
\(738\) 0 0
\(739\) 23.2379i 0.854820i −0.904058 0.427410i \(-0.859426\pi\)
0.904058 0.427410i \(-0.140574\pi\)
\(740\) 12.5332 12.7639i 0.460731 0.469211i
\(741\) 0 0
\(742\) 4.63525 11.3364i 0.170166 0.416173i
\(743\) 12.1244 + 21.0000i 0.444799 + 0.770415i 0.998038 0.0626075i \(-0.0199416\pi\)
−0.553239 + 0.833023i \(0.686608\pi\)
\(744\) 0 0
\(745\) 2.50000 4.33013i 0.0915929 0.158644i
\(746\) 8.66025 + 11.1803i 0.317074 + 0.409341i
\(747\) 0 0
\(748\) 15.0000 + 3.87298i 0.548454 + 0.141610i
\(749\) 17.4284 + 10.0623i 0.636821 + 0.367669i
\(750\) 0 0
\(751\) 3.35410 1.93649i 0.122393 0.0706636i −0.437554 0.899192i \(-0.644155\pi\)
0.559947 + 0.828529i \(0.310822\pi\)
\(752\) 0.252703 + 13.8541i 0.00921512 + 0.505207i
\(753\) 0 0
\(754\) 1.70820 + 12.5332i 0.0622091 + 0.456434i
\(755\) −8.66025 −0.315179
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.4919 8.94427i 0.561582 0.324230i −0.192198 0.981356i \(-0.561562\pi\)
0.753780 + 0.657127i \(0.228228\pi\)
\(762\) 0 0
\(763\) −13.4164 7.74597i −0.485707 0.280423i
\(764\) 8.66025 33.5410i 0.313317 1.21347i
\(765\) 0 0
\(766\) 21.0000 + 27.1109i 0.758761 + 0.979556i
\(767\) 3.46410 6.00000i 0.125081 0.216647i
\(768\) 0 0
\(769\) −5.50000 9.52628i −0.198335 0.343526i 0.749654 0.661830i \(-0.230220\pi\)
−0.947989 + 0.318304i \(0.896887\pi\)
\(770\) −8.02850 + 19.6353i −0.289327 + 0.707605i
\(771\) 0 0
\(772\) 35.6763 + 35.0315i 1.28402 + 1.26081i
\(773\) 4.47214i 0.160852i 0.996761 + 0.0804258i \(0.0256280\pi\)
−0.996761 + 0.0804258i \(0.974372\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −3.63871 + 30.8992i −0.130622 + 1.10922i
\(777\) 0 0
\(778\) 2.92705 + 1.19682i 0.104940 + 0.0429080i
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 15.5885i 0.322045 0.557799i
\(782\) 34.6410 26.8328i 1.23876 0.959540i
\(783\) 0 0
\(784\) 28.0000 + 15.4919i 1.00000 + 0.553283i
\(785\) 38.7298 + 22.3607i 1.38233 + 0.798087i
\(786\) 0 0
\(787\) 13.4164 7.74597i 0.478243 0.276114i −0.241441 0.970416i \(-0.577620\pi\)
0.719684 + 0.694302i \(0.244287\pi\)
\(788\) 13.1650 + 47.3992i 0.468984 + 1.68853i
\(789\) 0 0