Properties

Label 980.2.q.c.569.1
Level $980$
Weight $2$
Character 980.569
Analytic conductor $7.825$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 569.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 980.569
Dual form 980.2.q.c.949.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.59808 + 1.50000i) q^{3} +(-0.133975 + 2.23205i) q^{5} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(-2.59808 + 1.50000i) q^{3} +(-0.133975 + 2.23205i) q^{5} +(3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{11} -1.00000i q^{13} +(-3.00000 - 6.00000i) q^{15} +(-4.33013 + 2.50000i) q^{17} +(4.00000 - 6.92820i) q^{19} +(-1.73205 - 1.00000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +9.00000i q^{27} +1.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(7.79423 + 4.50000i) q^{33} +(8.66025 + 5.00000i) q^{37} +(1.50000 + 2.59808i) q^{39} +6.00000 q^{41} -4.00000i q^{43} +(11.1962 + 7.39230i) q^{45} +(-9.52628 - 5.50000i) q^{47} +(7.50000 - 12.9904i) q^{51} +(5.19615 - 3.00000i) q^{53} +(6.00000 - 3.00000i) q^{55} +24.0000i q^{57} +(5.00000 + 8.66025i) q^{59} +(2.23205 + 0.133975i) q^{65} +(8.66025 - 5.00000i) q^{67} +6.00000 q^{69} +(8.66025 - 5.00000i) q^{73} +(13.7942 - 5.89230i) q^{75} +(-3.50000 + 6.06218i) q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000i q^{83} +(-5.00000 - 10.0000i) q^{85} +(-2.59808 + 1.50000i) q^{87} +(-4.00000 + 6.92820i) q^{89} +(5.19615 + 3.00000i) q^{93} +(14.9282 + 9.85641i) q^{95} +3.00000i q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{5} + 12 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{5} + 12 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{31} + 6 q^{39} + 24 q^{41} + 24 q^{45} + 30 q^{51} + 24 q^{55} + 20 q^{59} + 2 q^{65} + 24 q^{69} + 24 q^{75} - 14 q^{79} - 18 q^{81} - 20 q^{85} - 16 q^{89} + 32 q^{95} - 72 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.59808 + 1.50000i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) −0.133975 + 2.23205i −0.0599153 + 0.998203i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 3.00000 5.19615i 1.00000 1.73205i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i −0.990338 0.138675i \(-0.955716\pi\)
0.990338 0.138675i \(-0.0442844\pi\)
\(14\) 0 0
\(15\) −3.00000 6.00000i −0.774597 1.54919i
\(16\) 0 0
\(17\) −4.33013 + 2.50000i −1.05021 + 0.606339i −0.922708 0.385499i \(-0.874029\pi\)
−0.127502 + 0.991838i \(0.540696\pi\)
\(18\) 0 0
\(19\) 4.00000 6.92820i 0.917663 1.58944i 0.114708 0.993399i \(-0.463407\pi\)
0.802955 0.596040i \(-0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.73205 1.00000i −0.361158 0.208514i 0.308431 0.951247i \(-0.400196\pi\)
−0.669588 + 0.742732i \(0.733529\pi\)
\(24\) 0 0
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) 0 0
\(27\) 9.00000i 1.73205i
\(28\) 0 0
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) 0 0
\(33\) 7.79423 + 4.50000i 1.35680 + 0.783349i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.66025 + 5.00000i 1.42374 + 0.821995i 0.996616 0.0821995i \(-0.0261945\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(38\) 0 0
\(39\) 1.50000 + 2.59808i 0.240192 + 0.416025i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 0 0
\(45\) 11.1962 + 7.39230i 1.66902 + 1.10198i
\(46\) 0 0
\(47\) −9.52628 5.50000i −1.38955 0.802257i −0.396286 0.918127i \(-0.629701\pi\)
−0.993264 + 0.115870i \(0.963035\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 7.50000 12.9904i 1.05021 1.81902i
\(52\) 0 0
\(53\) 5.19615 3.00000i 0.713746 0.412082i −0.0987002 0.995117i \(-0.531468\pi\)
0.812447 + 0.583036i \(0.198135\pi\)
\(54\) 0 0
\(55\) 6.00000 3.00000i 0.809040 0.404520i
\(56\) 0 0
\(57\) 24.0000i 3.17888i
\(58\) 0 0
\(59\) 5.00000 + 8.66025i 0.650945 + 1.12747i 0.982894 + 0.184172i \(0.0589603\pi\)
−0.331949 + 0.943297i \(0.607706\pi\)
\(60\) 0 0
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.23205 + 0.133975i 0.276852 + 0.0166175i
\(66\) 0 0
\(67\) 8.66025 5.00000i 1.05802 0.610847i 0.133135 0.991098i \(-0.457496\pi\)
0.924883 + 0.380251i \(0.124162\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 8.66025 5.00000i 1.01361 0.585206i 0.101361 0.994850i \(-0.467680\pi\)
0.912245 + 0.409644i \(0.134347\pi\)
\(74\) 0 0
\(75\) 13.7942 5.89230i 1.59282 0.680385i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −3.50000 + 6.06218i −0.393781 + 0.682048i −0.992945 0.118578i \(-0.962166\pi\)
0.599164 + 0.800626i \(0.295500\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) −5.00000 10.0000i −0.542326 1.08465i
\(86\) 0 0
\(87\) −2.59808 + 1.50000i −0.278543 + 0.160817i
\(88\) 0 0
\(89\) −4.00000 + 6.92820i −0.423999 + 0.734388i −0.996326 0.0856373i \(-0.972707\pi\)
0.572327 + 0.820025i \(0.306041\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 5.19615 + 3.00000i 0.538816 + 0.311086i
\(94\) 0 0
\(95\) 14.9282 + 9.85641i 1.53160 + 1.01125i
\(96\) 0 0
\(97\) 3.00000i 0.304604i 0.988334 + 0.152302i \(0.0486686\pi\)
−0.988334 + 0.152302i \(0.951331\pi\)
\(98\) 0 0
\(99\) −18.0000 −1.80907
\(100\) 0 0
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 0 0
\(103\) −4.33013 2.50000i −0.426660 0.246332i 0.271263 0.962505i \(-0.412559\pi\)
−0.697923 + 0.716173i \(0.745892\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.92820 + 4.00000i 0.669775 + 0.386695i 0.795991 0.605308i \(-0.206950\pi\)
−0.126217 + 0.992003i \(0.540283\pi\)
\(108\) 0 0
\(109\) −3.50000 6.06218i −0.335239 0.580651i 0.648292 0.761392i \(-0.275484\pi\)
−0.983531 + 0.180741i \(0.942150\pi\)
\(110\) 0 0
\(111\) −30.0000 −2.84747
\(112\) 0 0
\(113\) 10.0000i 0.940721i −0.882474 0.470360i \(-0.844124\pi\)
0.882474 0.470360i \(-0.155876\pi\)
\(114\) 0 0
\(115\) 2.46410 3.73205i 0.229779 0.348016i
\(116\) 0 0
\(117\) −5.19615 3.00000i −0.480384 0.277350i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) −15.5885 + 9.00000i −1.40556 + 0.811503i
\(124\) 0 0
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 0 0
\(129\) 6.00000 + 10.3923i 0.528271 + 0.914991i
\(130\) 0 0
\(131\) 1.00000 1.73205i 0.0873704 0.151330i −0.819028 0.573753i \(-0.805487\pi\)
0.906399 + 0.422423i \(0.138820\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −20.0885 1.20577i −1.72894 0.103776i
\(136\) 0 0
\(137\) −3.46410 + 2.00000i −0.295958 + 0.170872i −0.640626 0.767853i \(-0.721325\pi\)
0.344668 + 0.938725i \(0.387992\pi\)
\(138\) 0 0
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 0 0
\(141\) 33.0000 2.77910
\(142\) 0 0
\(143\) −2.59808 + 1.50000i −0.217262 + 0.125436i
\(144\) 0 0
\(145\) −0.133975 + 2.23205i −0.0111260 + 0.185362i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) −4.50000 7.79423i −0.366205 0.634285i 0.622764 0.782410i \(-0.286010\pi\)
−0.988969 + 0.148124i \(0.952676\pi\)
\(152\) 0 0
\(153\) 30.0000i 2.42536i
\(154\) 0 0
\(155\) 4.00000 2.00000i 0.321288 0.160644i
\(156\) 0 0
\(157\) −15.5885 + 9.00000i −1.24409 + 0.718278i −0.969925 0.243403i \(-0.921736\pi\)
−0.274169 + 0.961681i \(0.588403\pi\)
\(158\) 0 0
\(159\) −9.00000 + 15.5885i −0.713746 + 1.23625i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −5.19615 3.00000i −0.406994 0.234978i 0.282503 0.959266i \(-0.408835\pi\)
−0.689497 + 0.724288i \(0.742169\pi\)
\(164\) 0 0
\(165\) −11.0885 + 16.7942i −0.863235 + 1.30743i
\(166\) 0 0
\(167\) 3.00000i 0.232147i 0.993241 + 0.116073i \(0.0370308\pi\)
−0.993241 + 0.116073i \(0.962969\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −24.0000 41.5692i −1.83533 3.17888i
\(172\) 0 0
\(173\) −7.79423 4.50000i −0.592584 0.342129i 0.173534 0.984828i \(-0.444481\pi\)
−0.766119 + 0.642699i \(0.777815\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −25.9808 15.0000i −1.95283 1.12747i
\(178\) 0 0
\(179\) 2.00000 + 3.46410i 0.149487 + 0.258919i 0.931038 0.364922i \(-0.118904\pi\)
−0.781551 + 0.623841i \(0.785571\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −12.3205 + 18.6603i −0.905822 + 1.37193i
\(186\) 0 0
\(187\) 12.9904 + 7.50000i 0.949951 + 0.548454i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.50000 + 6.06218i −0.253251 + 0.438644i −0.964419 0.264378i \(-0.914833\pi\)
0.711168 + 0.703022i \(0.248167\pi\)
\(192\) 0 0
\(193\) 6.92820 4.00000i 0.498703 0.287926i −0.229475 0.973315i \(-0.573701\pi\)
0.728178 + 0.685388i \(0.240368\pi\)
\(194\) 0 0
\(195\) −6.00000 + 3.00000i −0.429669 + 0.214834i
\(196\) 0 0
\(197\) 10.0000i 0.712470i −0.934396 0.356235i \(-0.884060\pi\)
0.934396 0.356235i \(-0.115940\pi\)
\(198\) 0 0
\(199\) −9.00000 15.5885i −0.637993 1.10504i −0.985873 0.167497i \(-0.946431\pi\)
0.347879 0.937539i \(-0.386902\pi\)
\(200\) 0 0
\(201\) −15.0000 + 25.9808i −1.05802 + 1.83254i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.803848 + 13.3923i −0.0561432 + 0.935359i
\(206\) 0 0
\(207\) −10.3923 + 6.00000i −0.722315 + 0.417029i
\(208\) 0 0
\(209\) −24.0000 −1.66011
\(210\) 0 0
\(211\) −3.00000 −0.206529 −0.103264 0.994654i \(-0.532929\pi\)
−0.103264 + 0.994654i \(0.532929\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.92820 + 0.535898i 0.608898 + 0.0365480i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −15.0000 + 25.9808i −1.01361 + 1.75562i
\(220\) 0 0
\(221\) 2.50000 + 4.33013i 0.168168 + 0.291276i
\(222\) 0 0
\(223\) 19.0000i 1.27233i −0.771551 0.636167i \(-0.780519\pi\)
0.771551 0.636167i \(-0.219481\pi\)
\(224\) 0 0
\(225\) −18.0000 + 24.0000i −1.20000 + 1.60000i
\(226\) 0 0
\(227\) 23.3827 13.5000i 1.55196 0.896026i 0.553981 0.832529i \(-0.313108\pi\)
0.997982 0.0634974i \(-0.0202255\pi\)
\(228\) 0 0
\(229\) 13.0000 22.5167i 0.859064 1.48794i −0.0137585 0.999905i \(-0.504380\pi\)
0.872823 0.488037i \(-0.162287\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.8564 8.00000i −0.907763 0.524097i −0.0280525 0.999606i \(-0.508931\pi\)
−0.879711 + 0.475509i \(0.842264\pi\)
\(234\) 0 0
\(235\) 13.5526 20.5263i 0.884071 1.33899i
\(236\) 0 0
\(237\) 21.0000i 1.36410i
\(238\) 0 0
\(239\) −5.00000 −0.323423 −0.161712 0.986838i \(-0.551701\pi\)
−0.161712 + 0.986838i \(0.551701\pi\)
\(240\) 0 0
\(241\) −9.00000 15.5885i −0.579741 1.00414i −0.995509 0.0946700i \(-0.969820\pi\)
0.415768 0.909471i \(-0.363513\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.92820 4.00000i −0.440831 0.254514i
\(248\) 0 0
\(249\) 18.0000 + 31.1769i 1.14070 + 1.97576i
\(250\) 0 0
\(251\) −2.00000 −0.126239 −0.0631194 0.998006i \(-0.520105\pi\)
−0.0631194 + 0.998006i \(0.520105\pi\)
\(252\) 0 0
\(253\) 6.00000i 0.377217i
\(254\) 0 0
\(255\) 27.9904 + 18.4808i 1.75283 + 1.15731i
\(256\) 0 0
\(257\) −5.19615 3.00000i −0.324127 0.187135i 0.329104 0.944294i \(-0.393253\pi\)
−0.653231 + 0.757159i \(0.726587\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) 0 0
\(263\) −20.7846 + 12.0000i −1.28163 + 0.739952i −0.977147 0.212565i \(-0.931818\pi\)
−0.304487 + 0.952517i \(0.598485\pi\)
\(264\) 0 0
\(265\) 6.00000 + 12.0000i 0.368577 + 0.737154i
\(266\) 0 0
\(267\) 24.0000i 1.46878i
\(268\) 0 0
\(269\) −1.00000 1.73205i −0.0609711 0.105605i 0.833929 0.551872i \(-0.186086\pi\)
−0.894900 + 0.446267i \(0.852753\pi\)
\(270\) 0 0
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.89230 + 13.7942i 0.355319 + 0.831823i
\(276\) 0 0
\(277\) 12.1244 7.00000i 0.728482 0.420589i −0.0893846 0.995997i \(-0.528490\pi\)
0.817867 + 0.575408i \(0.195157\pi\)
\(278\) 0 0
\(279\) −12.0000 −0.718421
\(280\) 0 0
\(281\) 15.0000 0.894825 0.447412 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(282\) 0 0
\(283\) 6.06218 3.50000i 0.360359 0.208053i −0.308879 0.951101i \(-0.599954\pi\)
0.669238 + 0.743048i \(0.266621\pi\)
\(284\) 0 0
\(285\) −53.5692 3.21539i −3.17317 0.190463i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) −4.50000 7.79423i −0.263795 0.456906i
\(292\) 0 0
\(293\) 15.0000i 0.876309i −0.898900 0.438155i \(-0.855632\pi\)
0.898900 0.438155i \(-0.144368\pi\)
\(294\) 0 0
\(295\) −20.0000 + 10.0000i −1.16445 + 0.582223i
\(296\) 0 0
\(297\) 23.3827 13.5000i 1.35680 0.783349i
\(298\) 0 0
\(299\) −1.00000 + 1.73205i −0.0578315 + 0.100167i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 31.1769 + 18.0000i 1.79107 + 1.03407i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 19.0000i 1.08439i −0.840254 0.542194i \(-0.817594\pi\)
0.840254 0.542194i \(-0.182406\pi\)
\(308\) 0 0
\(309\) 15.0000 0.853320
\(310\) 0 0
\(311\) 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i \(-0.0561621\pi\)
−0.644246 + 0.764818i \(0.722829\pi\)
\(312\) 0 0
\(313\) −6.06218 3.50000i −0.342655 0.197832i 0.318791 0.947825i \(-0.396723\pi\)
−0.661445 + 0.749993i \(0.730057\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 24.2487 + 14.0000i 1.36194 + 0.786318i 0.989882 0.141890i \(-0.0453179\pi\)
0.372061 + 0.928208i \(0.378651\pi\)
\(318\) 0 0
\(319\) −1.50000 2.59808i −0.0839839 0.145464i
\(320\) 0 0
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) 40.0000i 2.22566i
\(324\) 0 0
\(325\) −0.598076 + 4.96410i −0.0331753 + 0.275359i
\(326\) 0 0
\(327\) 18.1865 + 10.5000i 1.00572 + 0.580651i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) 0 0
\(333\) 51.9615 30.0000i 2.84747 1.64399i
\(334\) 0 0
\(335\) 10.0000 + 20.0000i 0.546358 + 1.09272i
\(336\) 0 0
\(337\) 22.0000i 1.19842i −0.800593 0.599208i \(-0.795482\pi\)
0.800593 0.599208i \(-0.204518\pi\)
\(338\) 0 0
\(339\) 15.0000 + 25.9808i 0.814688 + 1.41108i
\(340\) 0 0
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.803848 + 13.3923i −0.0432777 + 0.721017i
\(346\) 0 0
\(347\) −15.5885 + 9.00000i −0.836832 + 0.483145i −0.856186 0.516667i \(-0.827172\pi\)
0.0193540 + 0.999813i \(0.493839\pi\)
\(348\) 0 0
\(349\) 36.0000 1.92704 0.963518 0.267644i \(-0.0862451\pi\)
0.963518 + 0.267644i \(0.0862451\pi\)
\(350\) 0 0
\(351\) 9.00000 0.480384
\(352\) 0 0
\(353\) 7.79423 4.50000i 0.414845 0.239511i −0.278024 0.960574i \(-0.589680\pi\)
0.692869 + 0.721063i \(0.256346\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 14.0000 24.2487i 0.738892 1.27980i −0.214103 0.976811i \(-0.568683\pi\)
0.952995 0.302987i \(-0.0979839\pi\)
\(360\) 0 0
\(361\) −22.5000 38.9711i −1.18421 2.05111i
\(362\) 0 0
\(363\) 6.00000i 0.314918i
\(364\) 0 0
\(365\) 10.0000 + 20.0000i 0.523424 + 1.04685i
\(366\) 0 0
\(367\) 16.4545 9.50000i 0.858917 0.495896i −0.00473247 0.999989i \(-0.501506\pi\)
0.863649 + 0.504093i \(0.168173\pi\)
\(368\) 0 0
\(369\) 18.0000 31.1769i 0.937043 1.62301i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −27.7128 16.0000i −1.43492 0.828449i −0.437425 0.899255i \(-0.644109\pi\)
−0.997490 + 0.0708063i \(0.977443\pi\)
\(374\) 0 0
\(375\) 11.3038 + 31.5788i 0.583728 + 1.63072i
\(376\) 0 0
\(377\) 1.00000i 0.0515026i
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) −3.00000 5.19615i −0.153695 0.266207i
\(382\) 0 0
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −20.7846 12.0000i −1.05654 0.609994i
\(388\) 0 0
\(389\) 4.50000 + 7.79423i 0.228159 + 0.395183i 0.957263 0.289220i \(-0.0933960\pi\)
−0.729103 + 0.684403i \(0.760063\pi\)
\(390\) 0 0
\(391\) 10.0000 0.505722
\(392\) 0 0
\(393\) 6.00000i 0.302660i
\(394\) 0 0
\(395\) −13.0622 8.62436i −0.657229 0.433938i
\(396\) 0 0
\(397\) 14.7224 + 8.50000i 0.738898 + 0.426603i 0.821668 0.569966i \(-0.193044\pi\)
−0.0827707 + 0.996569i \(0.526377\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i \(-0.597840\pi\)
0.976714 0.214544i \(-0.0688266\pi\)
\(402\) 0 0
\(403\) −1.73205 + 1.00000i −0.0862796 + 0.0498135i
\(404\) 0 0
\(405\) 18.0000 9.00000i 0.894427 0.447214i
\(406\) 0 0
\(407\) 30.0000i 1.48704i
\(408\) 0 0
\(409\) −2.00000 3.46410i −0.0988936 0.171289i 0.812333 0.583193i \(-0.198197\pi\)
−0.911227 + 0.411905i \(0.864864\pi\)
\(410\) 0 0
\(411\) 6.00000 10.3923i 0.295958 0.512615i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 26.7846 + 1.60770i 1.31480 + 0.0789187i
\(416\) 0 0
\(417\) −25.9808 + 15.0000i −1.27228 + 0.734553i
\(418\) 0 0
\(419\) 2.00000 0.0977064 0.0488532 0.998806i \(-0.484443\pi\)
0.0488532 + 0.998806i \(0.484443\pi\)
\(420\) 0 0
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) 0 0
\(423\) −57.1577 + 33.0000i −2.77910 + 1.60451i
\(424\) 0 0
\(425\) 22.9904 9.82051i 1.11520 0.476365i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 4.50000 7.79423i 0.217262 0.376309i
\(430\) 0 0
\(431\) 18.5000 + 32.0429i 0.891114 + 1.54345i 0.838542 + 0.544837i \(0.183408\pi\)
0.0525716 + 0.998617i \(0.483258\pi\)
\(432\) 0 0
\(433\) 38.0000i 1.82616i 0.407777 + 0.913082i \(0.366304\pi\)
−0.407777 + 0.913082i \(0.633696\pi\)
\(434\) 0 0
\(435\) −3.00000 6.00000i −0.143839 0.287678i
\(436\) 0 0
\(437\) −13.8564 + 8.00000i −0.662842 + 0.382692i
\(438\) 0 0
\(439\) −13.0000 + 22.5167i −0.620456 + 1.07466i 0.368945 + 0.929451i \(0.379719\pi\)
−0.989401 + 0.145210i \(0.953614\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.3923 6.00000i −0.493753 0.285069i 0.232377 0.972626i \(-0.425350\pi\)
−0.726130 + 0.687557i \(0.758683\pi\)
\(444\) 0 0
\(445\) −14.9282 9.85641i −0.707665 0.467238i
\(446\) 0 0
\(447\) 18.0000i 0.851371i
\(448\) 0 0
\(449\) −11.0000 −0.519122 −0.259561 0.965727i \(-0.583578\pi\)
−0.259561 + 0.965727i \(0.583578\pi\)
\(450\) 0 0
\(451\) −9.00000 15.5885i −0.423793 0.734032i
\(452\) 0 0
\(453\) 23.3827 + 13.5000i 1.09861 + 0.634285i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −19.0526 11.0000i −0.891241 0.514558i −0.0168929 0.999857i \(-0.505377\pi\)
−0.874348 + 0.485299i \(0.838711\pi\)
\(458\) 0 0
\(459\) −22.5000 38.9711i −1.05021 1.81902i
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i 0.995671 + 0.0929479i \(0.0296290\pi\)
−0.995671 + 0.0929479i \(0.970371\pi\)
\(464\) 0 0
\(465\) −7.39230 + 11.1962i −0.342810 + 0.519209i
\(466\) 0 0
\(467\) 19.9186 + 11.5000i 0.921722 + 0.532157i 0.884184 0.467139i \(-0.154715\pi\)
0.0375381 + 0.999295i \(0.488048\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 27.0000 46.7654i 1.24409 2.15483i
\(472\) 0 0
\(473\) −10.3923 + 6.00000i −0.477839 + 0.275880i
\(474\) 0 0
\(475\) −24.0000 + 32.0000i −1.10120 + 1.46826i
\(476\) 0 0
\(477\) 36.0000i 1.64833i
\(478\) 0 0
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 0 0
\(481\) 5.00000 8.66025i 0.227980 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.69615 0.401924i −0.304057 0.0182504i
\(486\) 0 0
\(487\) 22.5167 13.0000i 1.02033 0.589086i 0.106129 0.994352i \(-0.466154\pi\)
0.914199 + 0.405266i \(0.132821\pi\)
\(488\) 0 0
\(489\) 18.0000 0.813988
\(490\) 0 0
\(491\) 33.0000 1.48927 0.744635 0.667472i \(-0.232624\pi\)
0.744635 + 0.667472i \(0.232624\pi\)
\(492\) 0 0
\(493\) −4.33013 + 2.50000i −0.195019 + 0.112594i
\(494\) 0 0
\(495\) 2.41154 40.1769i 0.108391 1.80582i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −14.5000 + 25.1147i −0.649109 + 1.12429i 0.334227 + 0.942493i \(0.391525\pi\)
−0.983336 + 0.181797i \(0.941809\pi\)
\(500\) 0 0
\(501\) −4.50000 7.79423i −0.201045 0.348220i
\(502\) 0 0
\(503\) 1.00000i 0.0445878i −0.999751 0.0222939i \(-0.992903\pi\)
0.999751 0.0222939i \(-0.00709696\pi\)
\(504\) 0 0
\(505\) 24.0000 12.0000i 1.06799 0.533993i
\(506\) 0 0
\(507\) −31.1769 + 18.0000i −1.38462 + 0.799408i
\(508\) 0 0
\(509\) −13.0000 + 22.5167i −0.576215 + 0.998033i 0.419694 + 0.907666i \(0.362138\pi\)
−0.995908 + 0.0903676i \(0.971196\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 62.3538 + 36.0000i 2.75299 + 1.58944i
\(514\) 0 0
\(515\) 6.16025 9.33013i 0.271453 0.411135i
\(516\) 0 0
\(517\) 33.0000i 1.45134i
\(518\) 0 0
\(519\) 27.0000 1.18517
\(520\) 0 0
\(521\) 6.00000 + 10.3923i 0.262865 + 0.455295i 0.967002 0.254769i \(-0.0819994\pi\)
−0.704137 + 0.710064i \(0.748666\pi\)
\(522\) 0 0
\(523\) −17.3205 10.0000i −0.757373 0.437269i 0.0709788 0.997478i \(-0.477388\pi\)
−0.828352 + 0.560208i \(0.810721\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.66025 + 5.00000i 0.377247 + 0.217803i
\(528\) 0 0
\(529\) −9.50000 16.4545i −0.413043 0.715412i
\(530\) 0 0
\(531\) 60.0000 2.60378
\(532\) 0 0
\(533\) 6.00000i 0.259889i
\(534\) 0 0
\(535\) −9.85641 + 14.9282i −0.426130 + 0.645403i
\(536\) 0 0
\(537\) −10.3923 6.00000i −0.448461 0.258919i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0 0
\(543\) −25.9808 + 15.0000i −1.11494 + 0.643712i
\(544\) 0 0
\(545\) 14.0000 7.00000i 0.599694 0.299847i
\(546\) 0 0
\(547\) 8.00000i 0.342055i 0.985266 + 0.171028i \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 4.01924 66.9615i 0.170607 2.84236i
\(556\) 0 0
\(557\) −17.3205 + 10.0000i −0.733893 + 0.423714i −0.819845 0.572586i \(-0.805940\pi\)
0.0859514 + 0.996299i \(0.472607\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) −45.0000 −1.89990
\(562\) 0 0
\(563\) 13.8564 8.00000i 0.583978 0.337160i −0.178735 0.983897i \(-0.557200\pi\)
0.762713 + 0.646737i \(0.223867\pi\)
\(564\) 0 0
\(565\) 22.3205 + 1.33975i 0.939031 + 0.0563635i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 0 0
\(573\) 21.0000i 0.877288i
\(574\) 0 0
\(575\) 8.00000 + 6.00000i 0.333623 + 0.250217i
\(576\) 0 0
\(577\) 14.7224 8.50000i 0.612903 0.353860i −0.161198 0.986922i \(-0.551536\pi\)
0.774101 + 0.633062i \(0.218202\pi\)
\(578\) 0 0
\(579\) −12.0000 + 20.7846i −0.498703 + 0.863779i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −15.5885 9.00000i −0.645608 0.372742i
\(584\) 0 0
\(585\) 7.39230 11.1962i 0.305634 0.462904i
\(586\) 0 0
\(587\) 28.0000i 1.15568i 0.816149 + 0.577842i \(0.196105\pi\)
−0.816149 + 0.577842i \(0.803895\pi\)
\(588\) 0 0
\(589\) −16.0000 −0.659269
\(590\) 0 0
\(591\) 15.0000 + 25.9808i 0.617018 + 1.06871i
\(592\) 0 0
\(593\) −2.59808 1.50000i −0.106690 0.0615976i 0.445705 0.895180i \(-0.352953\pi\)
−0.552396 + 0.833582i \(0.686286\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 46.7654 + 27.0000i 1.91398 + 1.10504i
\(598\) 0 0
\(599\) −10.5000 18.1865i −0.429018 0.743082i 0.567768 0.823189i \(-0.307807\pi\)
−0.996786 + 0.0801071i \(0.974474\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 0 0
\(603\) 60.0000i 2.44339i
\(604\) 0 0
\(605\) 3.73205 + 2.46410i 0.151729 + 0.100180i
\(606\) 0 0
\(607\) −4.33013 2.50000i −0.175754 0.101472i 0.409542 0.912291i \(-0.365689\pi\)
−0.585296 + 0.810819i \(0.699022\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.50000 + 9.52628i −0.222506 + 0.385392i
\(612\) 0 0
\(613\) −10.3923 + 6.00000i −0.419741 + 0.242338i −0.694967 0.719042i \(-0.744581\pi\)
0.275225 + 0.961380i \(0.411248\pi\)
\(614\) 0 0
\(615\) −18.0000 36.0000i −0.725830 1.45166i
\(616\) 0 0
\(617\) 34.0000i 1.36879i 0.729112 + 0.684394i \(0.239933\pi\)
−0.729112 + 0.684394i \(0.760067\pi\)
\(618\) 0 0
\(619\) 1.00000 + 1.73205i 0.0401934 + 0.0696170i 0.885422 0.464787i \(-0.153869\pi\)
−0.845229 + 0.534404i \(0.820536\pi\)
\(620\) 0 0
\(621\) 9.00000 15.5885i 0.361158 0.625543i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 0 0
\(627\) 62.3538 36.0000i 2.49017 1.43770i
\(628\) 0 0
\(629\) −50.0000 −1.99363
\(630\) 0 0
\(631\) 15.0000 0.597141 0.298570 0.954388i \(-0.403490\pi\)
0.298570 + 0.954388i \(0.403490\pi\)
\(632\) 0 0
\(633\) 7.79423 4.50000i 0.309793 0.178859i
\(634\) 0 0
\(635\) −4.46410 0.267949i −0.177152 0.0106332i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 13.0000 + 22.5167i 0.513469 + 0.889355i 0.999878 + 0.0156233i \(0.00497325\pi\)
−0.486409 + 0.873731i \(0.661693\pi\)
\(642\) 0 0
\(643\) 5.00000i 0.197181i 0.995128 + 0.0985904i \(0.0314334\pi\)
−0.995128 + 0.0985904i \(0.968567\pi\)
\(644\) 0 0
\(645\) −24.0000 + 12.0000i −0.944999 + 0.472500i
\(646\) 0 0
\(647\) −20.7846 + 12.0000i −0.817127 + 0.471769i −0.849425 0.527710i \(-0.823051\pi\)
0.0322975 + 0.999478i \(0.489718\pi\)
\(648\) 0 0
\(649\) 15.0000 25.9808i 0.588802 1.01983i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −31.1769 18.0000i −1.22005 0.704394i −0.255119 0.966910i \(-0.582115\pi\)
−0.964928 + 0.262515i \(0.915448\pi\)
\(654\) 0 0
\(655\) 3.73205 + 2.46410i 0.145823 + 0.0962804i
\(656\) 0 0
\(657\) 60.0000i 2.34082i
\(658\) 0 0
\(659\) −39.0000 −1.51922 −0.759612 0.650376i \(-0.774611\pi\)
−0.759612 + 0.650376i \(0.774611\pi\)
\(660\) 0 0
\(661\) 14.0000 + 24.2487i 0.544537 + 0.943166i 0.998636 + 0.0522143i \(0.0166279\pi\)
−0.454099 + 0.890951i \(0.650039\pi\)
\(662\) 0 0
\(663\) −12.9904 7.50000i −0.504505 0.291276i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.73205 1.00000i −0.0670653 0.0387202i
\(668\) 0 0
\(669\) 28.5000 + 49.3634i 1.10187 + 1.90850i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 16.0000i 0.616755i −0.951264 0.308377i \(-0.900214\pi\)
0.951264 0.308377i \(-0.0997859\pi\)
\(674\) 0 0
\(675\) 5.38269 44.6769i 0.207180 1.71962i
\(676\) 0 0
\(677\) 9.52628 + 5.50000i 0.366125 + 0.211382i 0.671764 0.740765i \(-0.265537\pi\)
−0.305639 + 0.952147i \(0.598870\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −40.5000 + 70.1481i −1.55196 + 2.68808i
\(682\) 0 0
\(683\) 34.6410 20.0000i 1.32550 0.765279i 0.340901 0.940099i \(-0.389268\pi\)
0.984600 + 0.174820i \(0.0559345\pi\)
\(684\) 0 0
\(685\) −4.00000 8.00000i −0.152832 0.305664i
\(686\) 0 0
\(687\) 78.0000i 2.97589i
\(688\) 0 0
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 0 0
\(691\) 20.0000 34.6410i 0.760836 1.31781i −0.181584 0.983375i \(-0.558123\pi\)
0.942420 0.334431i \(-0.108544\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.33975 + 22.3205i −0.0508195 + 0.846665i
\(696\) 0 0
\(697\) −25.9808 + 15.0000i −0.984092 + 0.568166i
\(698\) 0 0
\(699\) 48.0000 1.81553
\(700\) 0 0
\(701\) −25.0000 −0.944237 −0.472118 0.881535i \(-0.656511\pi\)
−0.472118 + 0.881535i \(0.656511\pi\)
\(702\) 0 0
\(703\) 69.2820 40.0000i 2.61302 1.50863i
\(704\) 0 0
\(705\) −4.42116 + 73.6577i −0.166511 + 2.77411i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 7.50000 12.9904i 0.281668 0.487864i −0.690127 0.723688i \(-0.742446\pi\)
0.971796 + 0.235824i \(0.0757789\pi\)
\(710\) 0 0
\(711\) 21.0000 + 36.3731i 0.787562 + 1.36410i
\(712\) 0 0
\(713\) 4.00000i 0.149801i
\(714\) 0 0
\(715\) −3.00000 6.00000i −0.112194 0.224387i
\(716\) 0 0
\(717\) 12.9904 7.50000i 0.485135 0.280093i
\(718\) 0 0
\(719\) −1.00000 + 1.73205i −0.0372937 + 0.0645946i −0.884070 0.467355i \(-0.845207\pi\)
0.846776 + 0.531949i \(0.178540\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 46.7654 + 27.0000i 1.73922 + 1.00414i
\(724\) 0 0
\(725\) −4.96410 0.598076i −0.184362 0.0222120i
\(726\) 0 0
\(727\) 28.0000i 1.03846i 0.854634 + 0.519231i \(0.173782\pi\)
−0.854634 + 0.519231i \(0.826218\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 10.0000 + 17.3205i 0.369863 + 0.640622i
\(732\) 0 0
\(733\) 35.5070 + 20.5000i 1.31148 + 0.757185i 0.982342 0.187096i \(-0.0599076\pi\)
0.329141 + 0.944281i \(0.393241\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −25.9808 15.0000i −0.957014 0.552532i
\(738\) 0 0
\(739\) −2.50000 4.33013i −0.0919640 0.159286i 0.816373 0.577524i \(-0.195981\pi\)
−0.908337 + 0.418238i \(0.862648\pi\)
\(740\) 0 0
\(741\) 24.0000 0.881662
\(742\) 0 0
\(743\) 30.0000i 1.10059i 0.834969 + 0.550297i \(0.185485\pi\)
−0.834969 + 0.550297i \(0.814515\pi\)
\(744\) 0 0
\(745\) −11.1962 7.39230i −0.410195 0.270833i
\(746\) 0 0
\(747\) −62.3538 36.0000i −2.28141 1.31717i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) 0 0
\(753\) 5.19615 3.00000i 0.189358 0.109326i
\(754\) 0 0
\(755\) 18.0000 9.00000i 0.655087 0.327544i
\(756\) 0 0
\(757\) 48.0000i 1.74459i 0.488980 + 0.872295i \(0.337369\pi\)
−0.488980 + 0.872295i \(0.662631\pi\)
\(758\) 0 0
\(759\) −9.00000 15.5885i −0.326679 0.565825i
\(760\) 0 0
\(761\) −19.0000 + 32.9090i −0.688749 + 1.19295i 0.283493 + 0.958974i \(0.408507\pi\)
−0.972243 + 0.233975i \(0.924827\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −66.9615 4.01924i −2.42100 0.145316i
\(766\) 0 0
\(767\) 8.66025 5.00000i 0.312704 0.180540i
\(768\) 0 0
\(769\) 16.0000 0.576975 0.288487 0.957484i \(-0.406848\pi\)
0.288487 + 0.957484i \(0.406848\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 0 0
\(773\) 23.3827 13.5000i 0.841017 0.485561i −0.0165929 0.999862i \(-0.505282\pi\)
0.857610 + 0.514301i \(0.171949\pi\)
\(774\) 0 0
\(775\) 3.92820 + 9.19615i 0.141105 + 0.330336i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 24.0000 41.5692i 0.859889 1.48937i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 9.00000i 0.321634i
\(784\) 0 0
\(785\) −18.0000 36.0000i −0.642448 1.28490i
\(786\) 0 0
\(787\) 2.59808 1.50000i 0.0926114 0.0534692i −0.452979 0.891521i \(-0.649639\pi\)
0.545590 + 0.838052i \(0.316305\pi\)
\(788\) 0 0
\(789\) 36.0000 62.3538i 1.28163 2.21986i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −33.5885 22.1769i −1.19126 0.786534i
\(796\) 0 0
\(797\) 43.0000i 1.52314i 0.648084 + 0.761569i \(0.275571\pi\)
−0.648084 + 0.761569i \(0.724429\pi\)
\(798\)