Properties

Label 324.2.h.d.107.2
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 107.2
Root \(0.535233 + 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 324.107
Dual form 324.2.h.d.215.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.535233 - 1.30902i) q^{2} +(-1.42705 + 1.40126i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.35410 - 1.93649i) q^{7} +(2.59808 + 1.11803i) q^{8} +O(q^{10})\) \(q+(-0.535233 - 1.30902i) q^{2} +(-1.42705 + 1.40126i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.35410 - 1.93649i) q^{7} +(2.59808 + 1.11803i) q^{8} +(-2.50000 - 1.93649i) q^{10} +(0.866025 - 1.50000i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.739674 + 5.42705i) q^{14} +(0.0729490 - 3.99933i) q^{16} -4.47214i q^{17} +(-1.19682 + 4.30902i) q^{20} +(-2.42705 - 0.330792i) q^{22} +(-3.46410 - 6.00000i) q^{23} +(-1.73205 + 2.23607i) q^{26} +(7.50000 - 1.93649i) q^{28} +(3.87298 + 2.23607i) q^{29} +(-3.35410 + 1.93649i) q^{31} +(-5.27424 + 2.04508i) q^{32} +(-5.85410 + 2.39364i) q^{34} -8.66025 q^{35} -4.00000 q^{37} +(6.28115 - 0.739674i) q^{40} +(7.74597 - 4.47214i) q^{41} +(6.70820 + 3.87298i) q^{43} +(0.866025 + 3.35410i) q^{44} +(-6.00000 + 7.74597i) q^{46} +(-1.73205 + 3.00000i) q^{47} +(4.00000 + 6.92820i) q^{49} +(3.85410 + 1.07047i) q^{52} +2.23607i q^{53} -3.87298i q^{55} +(-6.54915 - 8.78115i) q^{56} +(0.854102 - 6.26662i) q^{58} +(1.73205 + 3.00000i) q^{59} +(2.00000 - 3.46410i) q^{61} +(4.33013 + 3.35410i) q^{62} +(5.50000 + 5.80948i) q^{64} +(-3.87298 - 2.23607i) q^{65} +(6.70820 - 3.87298i) q^{67} +(6.26662 + 6.38197i) q^{68} +(4.63525 + 11.3364i) q^{70} +10.3923 q^{71} +5.00000 q^{73} +(2.14093 + 5.23607i) q^{74} +(-5.80948 + 3.35410i) q^{77} +(6.70820 + 3.87298i) q^{79} +(-4.33013 - 7.82624i) q^{80} +(-10.0000 - 7.74597i) q^{82} +(6.06218 - 10.5000i) q^{83} +(-5.00000 - 8.66025i) q^{85} +(1.47935 - 10.8541i) q^{86} +(3.92705 - 2.92887i) q^{88} -4.47214i q^{89} +7.74597i q^{91} +(13.3510 + 3.70820i) q^{92} +(4.85410 + 0.661585i) q^{94} +(-5.50000 + 9.52628i) q^{97} +(6.92820 - 8.94427i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} + O(q^{10}) \) \( 8q + 2q^{4} - 20q^{10} - 8q^{13} + 14q^{16} - 6q^{22} + 60q^{28} - 20q^{34} - 32q^{37} + 10q^{40} - 48q^{46} + 32q^{49} + 4q^{52} - 20q^{58} + 16q^{61} + 44q^{64} - 30q^{70} + 40q^{73} - 80q^{82} - 40q^{85} + 18q^{88} + 12q^{94} - 44q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.535233 1.30902i −0.378467 0.925615i
\(3\) 0 0
\(4\) −1.42705 + 1.40126i −0.713525 + 0.700629i
\(5\) 1.93649 1.11803i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) −3.35410 1.93649i −1.26773 0.731925i −0.293173 0.956059i \(-0.594711\pi\)
−0.974558 + 0.224134i \(0.928045\pi\)
\(8\) 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 \(0.922790\pi\)
\(14\) −0.739674 + 5.42705i −0.197686 + 1.45044i
\(15\) 0 0
\(16\) 0.0729490 3.99933i 0.0182373 0.999834i
\(17\) 4.47214i 1.08465i −0.840168 0.542326i \(-0.817544\pi\)
0.840168 0.542326i \(-0.182456\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −1.19682 + 4.30902i −0.267617 + 0.963525i
\(21\) 0 0
\(22\) −2.42705 0.330792i −0.517449 0.0705251i
\(23\) −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 0.814456 0.580225i \(-0.197035\pi\)
−0.0952614 + 0.995452i \(0.530369\pi\)
\(30\) 0 0
\(31\) −3.35410 + 1.93649i −0.602414 + 0.347804i −0.769991 0.638055i \(-0.779739\pi\)
0.167576 + 0.985859i \(0.446406\pi\)
\(32\) −5.27424 + 2.04508i −0.932363 + 0.361523i
\(33\) 0 0
\(34\) −5.85410 + 2.39364i −1.00397 + 0.410505i
\(35\) −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
\(40\) 6.28115 0.739674i 0.993137 0.116953i
\(41\) 7.74597 4.47214i 1.20972 0.698430i 0.247019 0.969011i \(-0.420549\pi\)
0.962697 + 0.270580i \(0.0872155\pi\)
\(42\) 0 0
\(43\) 6.70820 + 3.87298i 1.02299 + 0.590624i 0.914969 0.403524i \(-0.132215\pi\)
0.108022 + 0.994148i \(0.465548\pi\)
\(44\) 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
\(52\) 3.85410 + 1.07047i 0.534468 + 0.148447i
\(53\) 2.23607i 0.307148i 0.988137 + 0.153574i \(0.0490783\pi\)
−0.988137 + 0.153574i \(0.950922\pi\)
\(54\) 0 0
\(55\) 3.87298i 0.522233i
\(56\) −6.54915 8.78115i −0.875167 1.17343i
\(57\) 0 0
\(58\) 0.854102 6.26662i 0.112149 0.822847i
\(59\) 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 −0.0307194 0.999528i \(-0.509780\pi\)
0.850257 + 0.526368i \(0.176447\pi\)
\(68\) 6.26662 + 6.38197i 0.759939 + 0.773927i
\(69\) 0 0
\(70\) 4.63525 + 11.3364i 0.554019 + 1.35496i
\(71\) 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 \(0.405479\pi\)
\(74\) 2.14093 + 5.23607i 0.248878 + 0.608681i
\(75\) 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 0.827401 0.561611i \(-0.189818\pi\)
−0.0726692 + 0.997356i \(0.523152\pi\)
\(80\) −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
\(86\) 1.47935 10.8541i 0.159522 1.17043i
\(87\) 0 0
\(88\) 3.92705 2.92887i 0.418625 0.312218i
\(89\) 4.47214i 0.474045i −0.971504 0.237023i \(-0.923828\pi\)
0.971504 0.237023i \(-0.0761716\pi\)
\(90\) 0 0
\(91\) 7.74597i 0.811998i
\(92\) 13.3510 + 3.70820i 1.39194 + 0.386607i
\(93\) 0 0
\(94\) 4.85410 + 0.661585i 0.500662 + 0.0682372i
\(95\) 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 0.400552 0.916274i \(-0.368818\pi\)
−0.593240 + 0.805025i \(0.702152\pi\)
\(102\) 0 0
\(103\) 6.70820 3.87298i 0.660979 0.381616i −0.131671 0.991293i \(-0.542034\pi\)
0.792650 + 0.609677i \(0.208701\pi\)
\(104\) −0.661585 5.61803i −0.0648737 0.550894i
\(105\) 0 0
\(106\) 2.92705 1.19682i 0.284300 0.116245i
\(107\) 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 \(0.561356\pi\)
\(110\) −5.06980 + 2.07295i −0.483387 + 0.197648i
\(111\) 0 0
\(112\) −7.98936 + 13.2729i −0.754923 + 1.25417i
\(113\) −15.4919 + 8.94427i −1.45736 + 0.841406i −0.998881 0.0472996i \(-0.984938\pi\)
−0.458478 + 0.888706i \(0.651605\pi\)
\(114\) 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
\(122\) −5.60503 0.763932i −0.507456 0.0691632i
\(123\) 0 0
\(124\) 2.07295 7.46344i 0.186156 0.670236i
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) 11.6190i 1.03102i 0.856885 + 0.515508i \(0.172397\pi\)
−0.856885 + 0.515508i \(0.827603\pi\)
\(128\) 4.66092 10.3090i 0.411971 0.911197i
\(129\) 0 0
\(130\) −0.854102 + 6.26662i −0.0749097 + 0.549619i
\(131\) 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 0.656237 0.754555i \(-0.272147\pi\)
−0.325345 + 0.945595i \(0.605481\pi\)
\(138\) 0 0
\(139\) −13.4164 + 7.74597i −1.13796 + 0.657004i −0.945926 0.324383i \(-0.894843\pi\)
−0.192039 + 0.981387i \(0.561510\pi\)
\(140\) 12.3586 12.1353i 1.04449 1.02562i
\(141\) 0 0
\(142\) −5.56231 13.6037i −0.466778 1.14160i
\(143\) −3.46410 −0.289683
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) −2.67617 6.54508i −0.221481 0.541675i
\(147\) 0 0
\(148\) 5.70820 5.60503i 0.469211 0.460731i
\(149\) 1.93649 1.11803i 0.158644 0.0915929i −0.418576 0.908182i \(-0.637471\pi\)
0.577220 + 0.816589i \(0.304137\pi\)
\(150\) 0 0
\(151\) −3.35410 1.93649i −0.272953 0.157589i 0.357276 0.933999i \(-0.383706\pi\)
−0.630229 + 0.776409i \(0.717039\pi\)
\(152\) 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 \(-0.460821\pi\)
\(158\) 1.47935 10.8541i 0.117691 0.863506i
\(159\) 0 0
\(160\) −7.92705 + 9.85707i −0.626688 + 0.779270i
\(161\) 26.8328i 2.11472i
\(162\) 0 0
\(163\) 23.2379i 1.82013i −0.414462 0.910066i \(-0.636030\pi\)
0.414462 0.910066i \(-0.363970\pi\)
\(164\) −4.78727 + 17.2361i −0.373823 + 1.34591i
\(165\) 0 0
\(166\) −16.9894 2.31555i −1.31863 0.179721i
\(167\) 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 −0.113444 0.993544i \(-0.536188\pi\)
−0.917157 + 0.398527i \(0.869522\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5.93583 3.57295i −0.447430 0.269321i
\(177\) 0 0
\(178\) −5.85410 + 2.39364i −0.438783 + 0.179411i
\(179\) −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 \(0.702704\pi\)
\(182\) 10.1396 4.14590i 0.751597 0.307314i
\(183\) 0 0
\(184\) −2.29180 19.4614i −0.168953 1.43472i
\(185\) −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 \(0.477068\pi\)
\(194\) 15.4138 + 2.10081i 1.10665 + 0.150830i
\(195\) 0 0
\(196\) −15.4164 4.28187i −1.10117 0.305848i
\(197\) 24.5967i 1.75245i −0.481906 0.876223i \(-0.660055\pi\)
0.481906 0.876223i \(-0.339945\pi\)
\(198\) 0 0
\(199\) 11.6190i 0.823646i −0.911264 0.411823i \(-0.864892\pi\)
0.911264 0.411823i \(-0.135108\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −0.427051 + 3.13331i −0.0300472 + 0.220459i
\(203\) −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 −0.884789 0.465991i \(-0.845698\pi\)
−0.0388343 + 0.999246i \(0.512364\pi\)
\(212\) −3.13331 3.19098i −0.215197 0.219158i
\(213\) 0 0
\(214\) −2.78115 6.80185i −0.190116 0.464965i
\(215\) 17.3205 1.18125
\(216\) 0 0
\(217\) 15.0000 1.01827
\(218\) 2.14093 + 5.23607i 0.145002 + 0.354631i
\(219\) 0 0
\(220\) 5.42705 + 5.52694i 0.365892 + 0.372627i
\(221\) −7.74597 + 4.47214i −0.521050 + 0.300828i
\(222\) 0 0
\(223\) 6.70820 + 3.87298i 0.449215 + 0.259354i 0.707498 0.706715i \(-0.249824\pi\)
−0.258284 + 0.966069i \(0.583157\pi\)
\(224\) 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 \(0.854383\pi\)
\(230\) −2.95870 + 21.7082i −0.195091 + 1.43140i
\(231\) 0 0
\(232\) 7.56231 + 10.1396i 0.496490 + 0.665697i
\(233\) 4.47214i 0.292979i −0.989212 0.146490i \(-0.953202\pi\)
0.989212 0.146490i \(-0.0467975\pi\)
\(234\) 0 0
\(235\) 7.74597i 0.505291i
\(236\) −6.67550 1.85410i −0.434538 0.120692i
\(237\) 0 0
\(238\) 24.2705 + 3.30792i 1.57322 + 0.214421i
\(239\) 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
\(248\) −10.8793 + 1.28115i −0.690835 + 0.0813533i
\(249\) 0 0
\(250\) 14.6353 5.98409i 0.925615 0.378467i
\(251\) 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
\(254\) 15.2094 6.21885i 0.954323 0.390205i
\(255\) 0 0
\(256\) −15.9894 0.583495i −0.999335 0.0364684i
\(257\) 19.3649 11.1803i 1.20795 0.697410i 0.245639 0.969361i \(-0.421002\pi\)
0.962311 + 0.271951i \(0.0876688\pi\)
\(258\) 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
\(268\) −4.14590 + 14.9269i −0.253251 + 0.911804i
\(269\) 4.47214i 0.272671i −0.990663 0.136335i \(-0.956467\pi\)
0.990663 0.136335i \(-0.0435325\pi\)
\(270\) 0 0
\(271\) 11.6190i 0.705801i 0.935661 + 0.352900i \(0.114805\pi\)
−0.935661 + 0.352900i \(0.885195\pi\)
\(272\) −17.8856 0.326238i −1.08447 0.0197811i
\(273\) 0 0
\(274\) 0.854102 6.26662i 0.0515982 0.378580i
\(275\) 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 0.611053 0.791590i \(-0.290746\pi\)
−0.380010 + 0.924982i \(0.624080\pi\)
\(282\) 0 0
\(283\) 26.8328 15.4919i 1.59505 0.920900i 0.602623 0.798026i \(-0.294122\pi\)
0.992422 0.122874i \(-0.0392111\pi\)
\(284\) −14.8303 + 14.5623i −0.880019 + 0.864114i
\(285\) 0 0
\(286\) 1.85410 + 4.53457i 0.109635 + 0.268135i
\(287\) −34.6410 −2.04479
\(288\) 0 0
\(289\) −3.00000 −0.176471
\(290\) −5.35233 13.0902i −0.314300 0.768681i
\(291\) 0 0
\(292\) −7.13525 + 7.00629i −0.417559 + 0.410012i
\(293\) 19.3649 11.1803i 1.13131 0.653162i 0.187046 0.982351i \(-0.440109\pi\)
0.944264 + 0.329189i \(0.106775\pi\)
\(294\) 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
\(302\) −0.739674 + 5.42705i −0.0425635 + 0.312292i
\(303\) 0 0
\(304\) 0 0
\(305\) 8.94427i 0.512148i
\(306\) 0 0
\(307\) 23.2379i 1.32626i 0.748506 + 0.663129i \(0.230772\pi\)
−0.748506 + 0.663129i \(0.769228\pi\)
\(308\) 3.59045 12.9271i 0.204585 0.736587i
\(309\) 0 0
\(310\) 12.1353 + 1.65396i 0.689236 + 0.0939387i
\(311\) −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 0.0684306 0.997656i \(-0.478201\pi\)
−0.829780 + 0.558091i \(0.811534\pi\)
\(318\) 0 0
\(319\) 6.70820 3.87298i 0.375587 0.216845i
\(320\) 17.1459 + 5.10081i 0.958485 + 0.285144i
\(321\) 0 0
\(322\) 35.1246 14.3618i 1.95742 0.800352i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) −30.4188 + 12.4377i −1.68474 + 0.688860i
\(327\) 0 0
\(328\) 25.1246 2.95870i 1.38727 0.163367i
\(329\) 11.6190 6.70820i 0.640573 0.369835i
\(330\) 0 0
\(331\) 6.70820 + 3.87298i 0.368716 + 0.212878i 0.672897 0.739736i \(-0.265050\pi\)
−0.304181 + 0.952614i \(0.598383\pi\)
\(332\) 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 \(0.745527\pi\)
\(338\) −12.6113 1.71885i −0.685966 0.0934930i
\(339\) 0 0
\(340\) 19.2705 + 5.35233i 1.04509 + 0.290271i
\(341\) 6.70820i 0.363270i
\(342\) 0 0
\(343\) 3.87298i 0.209121i
\(344\) 13.0983 + 17.5623i 0.706213 + 0.946896i
\(345\) 0 0
\(346\) −2.98936 + 21.9332i −0.160709 + 1.17913i
\(347\) −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 0.851984 0.523568i \(-0.175399\pi\)
−0.0274314 + 0.999624i \(0.508733\pi\)
\(354\) 0 0
\(355\) 20.1246 11.6190i 1.06810 0.616670i
\(356\) 6.26662 + 6.38197i 0.332130 + 0.338244i
\(357\) 0 0
\(358\) 2.78115 + 6.80185i 0.146989 + 0.359489i
\(359\) −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
\(362\) 8.56373 + 20.9443i 0.450100 + 1.10081i
\(363\) 0 0
\(364\) −10.8541 11.0539i −0.568910 0.579381i
\(365\) 9.68246 5.59017i 0.506803 0.292603i
\(366\) 0 0
\(367\) −23.4787 13.5554i −1.22558 0.707588i −0.259477 0.965749i \(-0.583550\pi\)
−0.966102 + 0.258161i \(0.916883\pi\)
\(368\) −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 \(0.749977\pi\)
\(374\) −1.47935 + 10.8541i −0.0764953 + 0.561252i
\(375\) 0 0
\(376\) −7.85410 + 5.85774i −0.405044 + 0.302090i
\(377\) 8.94427i 0.460653i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −24.2705 3.30792i −1.24179 0.169248i
\(383\) 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 0.450104 0.892976i \(-0.351387\pi\)
−0.548288 + 0.836290i \(0.684720\pi\)
\(390\) 0 0
\(391\) −26.8328 + 15.4919i −1.35699 + 0.783461i
\(392\) 2.64634 + 22.4721i 0.133660 + 1.13501i
\(393\) 0 0
\(394\) −32.1976 + 13.1650i −1.62209 + 0.663243i
\(395\) 17.3205 0.871489
\(396\) 0 0
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) −15.2094 + 6.21885i −0.762378 + 0.311723i
\(399\) 0 0
\(400\) 0 0
\(401\) −15.4919 + 8.94427i −0.773630 + 0.446656i −0.834168 0.551510i \(-0.814052\pi\)
0.0605379 + 0.998166i \(0.480718\pi\)
\(402\) 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 \(0.777967\pi\)
\(410\) −28.0252 3.81966i −1.38406 0.188640i
\(411\) 0 0
\(412\) −4.14590 + 14.9269i −0.204254 + 0.735394i
\(413\) 13.4164i 0.660178i
\(414\) 0 0
\(415\) 27.1109i 1.33082i
\(416\) 8.81643 + 7.09017i 0.432261 + 0.347624i
\(417\) 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
\(428\) −7.41517 + 7.28115i −0.358426 + 0.351948i
\(429\) 0 0
\(430\) −9.27051 22.6728i −0.447064 1.09338i
\(431\) 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 \(0.601123\pi\)
\(434\) −8.02850 19.6353i −0.385380 0.942522i
\(435\) 0 0
\(436\) 5.70820 5.60503i 0.273373 0.268432i
\(437\) 0 0
\(438\) 0 0
\(439\) −3.35410 1.93649i −0.160083 0.0924237i 0.417819 0.908530i \(-0.362795\pi\)
−0.577901 + 0.816107i \(0.696128\pi\)
\(440\) 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
\(446\) 1.47935 10.8541i 0.0700492 0.513957i
\(447\) 0 0
\(448\) −7.19756 30.1363i −0.340053 1.42381i
\(449\) 17.8885i 0.844213i −0.906546 0.422106i \(-0.861291\pi\)
0.906546 0.422106i \(-0.138709\pi\)
\(450\) 0 0
\(451\) 15.4919i 0.729487i
\(452\) 9.57454 34.4721i 0.450349 1.62143i
\(453\) 0 0
\(454\) 4.85410 + 0.661585i 0.227814 + 0.0310497i
\(455\) 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 \(0.0126621\pi\)
0.534045 + 0.845456i \(0.320671\pi\)
\(462\) 0 0
\(463\) −3.35410 + 1.93649i −0.155878 + 0.0899964i −0.575910 0.817513i \(-0.695352\pi\)
0.420032 + 0.907509i \(0.362019\pi\)
\(464\) 9.22531 15.3262i 0.428274 0.711503i
\(465\) 0 0
\(466\) −5.85410 + 2.39364i −0.271186 + 0.110883i
\(467\) −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
\(470\) 10.1396 4.14590i 0.467705 0.191236i
\(471\) 0 0
\(472\) 1.14590 + 9.73072i 0.0527442 + 0.447893i
\(473\) 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
\(482\) 19.6176 + 2.67376i 0.893558 + 0.121787i
\(483\) 0 0
\(484\) −15.4164 4.28187i −0.700746 0.194630i
\(485\) 24.5967i 1.11688i
\(486\) 0 0
\(487\) 23.2379i 1.05301i 0.850172 + 0.526505i \(0.176498\pi\)
−0.850172 + 0.526505i \(0.823502\pi\)
\(488\) 9.06914 6.76393i 0.410540 0.306189i
\(489\) 0 0
\(490\) 3.41641 25.0665i 0.154338 1.13239i
\(491\) 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 \(0.667220\pi\)
−0.999998 + 0.00173727i \(0.999447\pi\)
\(500\) −15.6665 15.9549i −0.700629 0.713525i
\(501\) 0 0
\(502\) −5.56231 13.6037i −0.248258 0.607163i
\(503\) 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
\(506\) 6.42280 + 15.7082i 0.285528 + 0.698315i
\(507\) 0 0
\(508\) −16.2812 16.5808i −0.722359 0.735656i
\(509\) −9.68246 + 5.59017i −0.429167 + 0.247780i −0.698992 0.715130i \(-0.746368\pi\)
0.269824 + 0.962910i \(0.413034\pi\)
\(510\) 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
\(518\) 2.95870 21.7082i 0.129998 0.953804i
\(519\) 0 0
\(520\) −7.56231 10.1396i −0.331629 0.444651i
\(521\) 22.3607i 0.979639i 0.871824 + 0.489820i \(0.162937\pi\)
−0.871824 + 0.489820i \(0.837063\pi\)
\(522\) 0 0
\(523\) 23.2379i 1.01612i −0.861321 0.508061i \(-0.830362\pi\)
0.861321 0.508061i \(-0.169638\pi\)
\(524\) −36.7153 10.1976i −1.60391 0.445483i
\(525\) 0 0
\(526\) −9.70820 1.32317i −0.423298 0.0576929i
\(527\) 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
\(536\) 21.7586 2.56231i 0.939826 0.110675i
\(537\) 0 0
\(538\) −5.85410 + 2.39364i −0.252388 + 0.103197i
\(539\) 13.8564 0.596838
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) 15.2094 6.21885i 0.653300 0.267122i
\(543\) 0 0
\(544\) 9.14590 + 23.5871i 0.392127 + 1.01129i
\(545\) −7.74597 + 4.47214i −0.331801 + 0.191565i
\(546\) 0 0
\(547\) 6.70820 + 3.87298i 0.286822 + 0.165597i 0.636508 0.771270i \(-0.280378\pi\)
−0.349686 + 0.936867i \(0.613712\pi\)
\(548\) −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
\(554\) 28.0252 + 3.81966i 1.19068 + 0.162282i
\(555\) 0 0
\(556\) 8.29180 29.8537i 0.351650 1.26608i
\(557\) 15.6525i 0.663217i 0.943417 + 0.331608i \(0.107591\pi\)
−0.943417 + 0.331608i \(0.892409\pi\)
\(558\) 0 0
\(559\) 15.4919i 0.655239i
\(560\) −0.631757 + 34.6353i −0.0266966 + 1.46361i
\(561\) 0 0
\(562\) 0.854102 6.26662i 0.0360281 0.264341i
\(563\) 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 −0.318695 0.947857i \(-0.603245\pi\)
−0.980216 + 0.197930i \(0.936578\pi\)
\(570\) 0 0
\(571\) 6.70820 3.87298i 0.280730 0.162079i −0.353024 0.935614i \(-0.614847\pi\)
0.633754 + 0.773535i \(0.281513\pi\)
\(572\) 4.94345 4.85410i 0.206696 0.202960i
\(573\) 0 0
\(574\) 18.5410 + 45.3457i 0.773887 + 1.89269i
\(575\) 0 0
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 1.60570 + 3.92705i 0.0667883 + 0.163344i
\(579\) 0 0
\(580\) −14.2705 + 14.0126i −0.592551 + 0.581841i
\(581\) −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
\(590\) 1.47935 10.8541i 0.0609038 0.446856i
\(591\) 0 0
\(592\) −0.291796 + 15.9973i −0.0119927 + 0.657487i
\(593\) 4.47214i 0.183649i −0.995775 0.0918243i \(-0.970730\pi\)
0.995775 0.0918243i \(-0.0292698\pi\)
\(594\) 0 0
\(595\) 38.7298i 1.58777i
\(596\) −1.19682 + 4.30902i −0.0490236 + 0.176504i
\(597\) 0 0
\(598\) 19.4164 + 2.64634i 0.793996 + 0.108217i
\(599\) −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 −0.357645 0.933858i \(-0.616420\pi\)
0.629922 + 0.776658i \(0.283087\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −11.7082 + 4.78727i −0.474051 + 0.193831i
\(611\) 6.92820 0.280285
\(612\) 0 0
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) 30.4188 12.4377i 1.22760 0.501944i
\(615\) 0 0
\(616\) −18.8435 + 2.21902i −0.759225 + 0.0894069i
\(617\) −15.4919 + 8.94427i −0.623682 + 0.360083i −0.778301 0.627891i \(-0.783918\pi\)
0.154619 + 0.987974i \(0.450585\pi\)
\(618\) 0 0
\(619\) −33.5410 19.3649i −1.34813 0.778342i −0.360143 0.932897i \(-0.617272\pi\)
−0.987984 + 0.154555i \(0.950606\pi\)
\(620\) −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
\(626\) 7.00629 + 0.954915i 0.280028 + 0.0381661i
\(627\) 0 0
\(628\) 38.5410 + 10.7047i 1.53795 + 0.427163i
\(629\) 17.8885i 0.713263i
\(630\) 0 0
\(631\) 34.8569i 1.38763i 0.720154 + 0.693815i \(0.244071\pi\)
−0.720154 + 0.693815i \(0.755929\pi\)
\(632\) 13.0983 + 17.5623i 0.521022 + 0.698591i
\(633\) 0 0
\(634\) −2.98936 + 21.9332i −0.118723 + 0.871077i
\(635\) 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 \(0.0112781\pi\)
0.530364 + 0.847770i \(0.322055\pi\)
\(642\) 0 0
\(643\) 26.8328 15.4919i 1.05818 0.610942i 0.133254 0.991082i \(-0.457457\pi\)
0.924929 + 0.380140i \(0.124124\pi\)
\(644\) −37.5997 38.2918i −1.48164 1.50891i
\(645\) 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
\(652\) 32.5623 + 33.1617i 1.27524 + 1.29871i
\(653\) −9.68246 + 5.59017i −0.378904 + 0.218760i −0.677341 0.735669i \(-0.736868\pi\)
0.298437 + 0.954429i \(0.403535\pi\)
\(654\) 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 \(0.732615\pi\)
\(662\) 1.47935 10.8541i 0.0574965 0.421857i
\(663\) 0 0
\(664\) 27.4894 20.5021i 1.06679 0.795635i
\(665\) 0 0
\(666\) 0 0
\(667\) 30.9839i 1.19970i
\(668\) −6.67550 1.85410i −0.258283 0.0717374i
\(669\) 0 0
\(670\) −24.2705 3.30792i −0.937652 0.127796i
\(671\) −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 0.0793599 0.996846i \(-0.474712\pi\)
−0.823614 + 0.567151i \(0.808046\pi\)
\(678\) 0 0
\(679\) 36.8951 21.3014i 1.41590 0.817473i
\(680\) −3.30792 28.0902i −0.126853 1.07721i
\(681\) 0 0
\(682\) 8.78115 3.59045i 0.336248 0.137486i
\(683\) −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
\(686\) −5.06980 + 2.07295i −0.193566 + 0.0791456i
\(687\) 0 0
\(688\) 15.9787 26.5458i 0.609183 1.01205i
\(689\) 3.87298 2.23607i 0.147549 0.0851874i
\(690\) 0 0
\(691\) −13.4164 7.74597i −0.510384 0.294670i 0.222607 0.974908i \(-0.428543\pi\)
−0.732992 + 0.680238i \(0.761877\pi\)
\(692\) 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
\(698\) −22.4201 3.05573i −0.848615 0.115661i
\(699\) 0 0
\(700\) 0 0
\(701\) 15.6525i 0.591186i 0.955314 + 0.295593i \(0.0955172\pi\)
−0.955314 + 0.295593i \(0.904483\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 13.4774 3.21885i 0.507947 0.121315i
\(705\) 0 0
\(706\) 3.41641 25.0665i 0.128578 0.943389i
\(707\) 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
\(716\) 7.41517 7.28115i 0.277118 0.272109i
\(717\) 0 0
\(718\) 16.6869 + 40.8111i 0.622750 + 1.52306i
\(719\) 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
\(722\) −10.1694 24.8713i −0.378467 0.925615i
\(723\) 0 0
\(724\) 22.8328 22.4201i 0.848575 0.833238i
\(725\) 0 0
\(726\) 0 0
\(727\) 36.8951 + 21.3014i 1.36836 + 0.790026i 0.990719 0.135925i \(-0.0434006\pi\)
0.377645 + 0.925950i \(0.376734\pi\)
\(728\) −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 \(0.880534\pi\)
\(734\) −5.17772 + 37.9894i −0.191113 + 1.40221i
\(735\) 0 0
\(736\) 30.5410 + 24.5611i 1.12576 + 0.905333i
\(737\) 13.4164i 0.494200i
\(738\) 0 0
\(739\) 23.2379i 0.854820i 0.904058 + 0.427410i \(0.140574\pi\)
−0.904058 + 0.427410i \(0.859426\pi\)
\(740\) 4.78727 17.2361i 0.175984 0.633610i
\(741\) 0 0
\(742\) −12.1353 1.65396i −0.445499 0.0607188i
\(743\) 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 −0.559947 0.828529i \(-0.689178\pi\)
0.437554 + 0.899192i \(0.355845\pi\)
\(752\) 11.8717 + 7.14590i 0.432915 + 0.260584i
\(753\) 0 0
\(754\) −11.7082 + 4.78727i −0.426388 + 0.174342i
\(755\) −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 −0.753780 0.657127i \(-0.771772\pi\)
0.192198 + 0.981356i \(0.438438\pi\)
\(762\) 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 \(0.896887\pi\)
\(770\) 21.0189 + 2.86475i 0.757468 + 0.103238i
\(771\) 0 0
\(772\) −48.1763 13.3808i −1.73390 0.481587i
\(773\) 4.47214i 0.160852i −0.996761 0.0804258i \(-0.974372\pi\)
0.996761 0.0804258i \(-0.0256280\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −24.9401 + 18.6008i −0.895298 + 0.667730i
\(777\) 0 0
\(778\) −0.427051 + 3.13331i −0.0153105 + 0.112335i
\(779\) 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 −0.719684 0.694302i \(-0.755713\pi\)
0.241441 + 0.970416i \(0.422380\pi\)
\(788\) 34.4664 + 35.1008i 1.22781 + 1.25041i
\(789\) 0 0