Properties

Label 225.2.f.b.107.2
Level $225$
Weight $2$
Character 225.107
Analytic conductor $1.797$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 225.107
Dual form 225.2.f.b.143.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73205 + 1.73205i) q^{2} -4.00000i q^{4} +(1.22474 + 1.22474i) q^{7} +(3.46410 + 3.46410i) q^{8} +O(q^{10})\) \(q+(-1.73205 + 1.73205i) q^{2} -4.00000i q^{4} +(1.22474 + 1.22474i) q^{7} +(3.46410 + 3.46410i) q^{8} +4.24264i q^{11} +(-3.67423 + 3.67423i) q^{13} -4.24264 q^{14} -4.00000 q^{16} +(1.73205 - 1.73205i) q^{17} +5.00000i q^{19} +(-7.34847 - 7.34847i) q^{22} +(-1.73205 - 1.73205i) q^{23} -12.7279i q^{26} +(4.89898 - 4.89898i) q^{28} -4.24264 q^{29} +1.00000 q^{31} +6.00000i q^{34} +(2.44949 + 2.44949i) q^{37} +(-8.66025 - 8.66025i) q^{38} +8.48528i q^{41} +(-1.22474 + 1.22474i) q^{43} +16.9706 q^{44} +6.00000 q^{46} +(5.19615 - 5.19615i) q^{47} -4.00000i q^{49} +(14.6969 + 14.6969i) q^{52} +(6.92820 + 6.92820i) q^{53} +8.48528i q^{56} +(7.34847 - 7.34847i) q^{58} +12.7279 q^{59} -7.00000 q^{61} +(-1.73205 + 1.73205i) q^{62} -8.00000i q^{64} +(3.67423 + 3.67423i) q^{67} +(-6.92820 - 6.92820i) q^{68} -8.48528i q^{71} +(2.44949 - 2.44949i) q^{73} -8.48528 q^{74} +20.0000 q^{76} +(-5.19615 + 5.19615i) q^{77} -2.00000i q^{79} +(-14.6969 - 14.6969i) q^{82} +(-1.73205 - 1.73205i) q^{83} -4.24264i q^{86} +(-14.6969 + 14.6969i) q^{88} -8.48528 q^{89} -9.00000 q^{91} +(-6.92820 + 6.92820i) q^{92} +18.0000i q^{94} +(-8.57321 - 8.57321i) q^{97} +(6.92820 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 32 q^{16} + 8 q^{31} + 48 q^{46} - 56 q^{61} + 160 q^{76} - 72 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 + 1.73205i −1.22474 + 1.22474i −0.258819 + 0.965926i \(0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) 0 0
\(4\) 4.00000i 2.00000i
\(5\) 0 0
\(6\) 0 0
\(7\) 1.22474 + 1.22474i 0.462910 + 0.462910i 0.899608 0.436698i \(-0.143852\pi\)
−0.436698 + 0.899608i \(0.643852\pi\)
\(8\) 3.46410 + 3.46410i 1.22474 + 1.22474i
\(9\) 0 0
\(10\) 0 0
\(11\) 4.24264i 1.27920i 0.768706 + 0.639602i \(0.220901\pi\)
−0.768706 + 0.639602i \(0.779099\pi\)
\(12\) 0 0
\(13\) −3.67423 + 3.67423i −1.01905 + 1.01905i −0.0192343 + 0.999815i \(0.506123\pi\)
−0.999815 + 0.0192343i \(0.993877\pi\)
\(14\) −4.24264 −1.13389
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 1.73205 1.73205i 0.420084 0.420084i −0.465149 0.885233i \(-0.653999\pi\)
0.885233 + 0.465149i \(0.153999\pi\)
\(18\) 0 0
\(19\) 5.00000i 1.14708i 0.819178 + 0.573539i \(0.194430\pi\)
−0.819178 + 0.573539i \(0.805570\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −7.34847 7.34847i −1.56670 1.56670i
\(23\) −1.73205 1.73205i −0.361158 0.361158i 0.503081 0.864239i \(-0.332200\pi\)
−0.864239 + 0.503081i \(0.832200\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 12.7279i 2.49615i
\(27\) 0 0
\(28\) 4.89898 4.89898i 0.925820 0.925820i
\(29\) −4.24264 −0.787839 −0.393919 0.919145i \(-0.628881\pi\)
−0.393919 + 0.919145i \(0.628881\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 6.00000i 1.02899i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.44949 + 2.44949i 0.402694 + 0.402694i 0.879181 0.476488i \(-0.158090\pi\)
−0.476488 + 0.879181i \(0.658090\pi\)
\(38\) −8.66025 8.66025i −1.40488 1.40488i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.48528i 1.32518i 0.748983 + 0.662589i \(0.230542\pi\)
−0.748983 + 0.662589i \(0.769458\pi\)
\(42\) 0 0
\(43\) −1.22474 + 1.22474i −0.186772 + 0.186772i −0.794299 0.607527i \(-0.792162\pi\)
0.607527 + 0.794299i \(0.292162\pi\)
\(44\) 16.9706 2.55841
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 5.19615 5.19615i 0.757937 0.757937i −0.218010 0.975947i \(-0.569956\pi\)
0.975947 + 0.218010i \(0.0699565\pi\)
\(48\) 0 0
\(49\) 4.00000i 0.571429i
\(50\) 0 0
\(51\) 0 0
\(52\) 14.6969 + 14.6969i 2.03810 + 2.03810i
\(53\) 6.92820 + 6.92820i 0.951662 + 0.951662i 0.998884 0.0472225i \(-0.0150370\pi\)
−0.0472225 + 0.998884i \(0.515037\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 8.48528i 1.13389i
\(57\) 0 0
\(58\) 7.34847 7.34847i 0.964901 0.964901i
\(59\) 12.7279 1.65703 0.828517 0.559964i \(-0.189185\pi\)
0.828517 + 0.559964i \(0.189185\pi\)
\(60\) 0 0
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) −1.73205 + 1.73205i −0.219971 + 0.219971i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 3.67423 + 3.67423i 0.448879 + 0.448879i 0.894982 0.446103i \(-0.147188\pi\)
−0.446103 + 0.894982i \(0.647188\pi\)
\(68\) −6.92820 6.92820i −0.840168 0.840168i
\(69\) 0 0
\(70\) 0 0
\(71\) 8.48528i 1.00702i −0.863990 0.503509i \(-0.832042\pi\)
0.863990 0.503509i \(-0.167958\pi\)
\(72\) 0 0
\(73\) 2.44949 2.44949i 0.286691 0.286691i −0.549079 0.835770i \(-0.685021\pi\)
0.835770 + 0.549079i \(0.185021\pi\)
\(74\) −8.48528 −0.986394
\(75\) 0 0
\(76\) 20.0000 2.29416
\(77\) −5.19615 + 5.19615i −0.592157 + 0.592157i
\(78\) 0 0
\(79\) 2.00000i 0.225018i −0.993651 0.112509i \(-0.964111\pi\)
0.993651 0.112509i \(-0.0358886\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −14.6969 14.6969i −1.62301 1.62301i
\(83\) −1.73205 1.73205i −0.190117 0.190117i 0.605629 0.795747i \(-0.292921\pi\)
−0.795747 + 0.605629i \(0.792921\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.24264i 0.457496i
\(87\) 0 0
\(88\) −14.6969 + 14.6969i −1.56670 + 1.56670i
\(89\) −8.48528 −0.899438 −0.449719 0.893170i \(-0.648476\pi\)
−0.449719 + 0.893170i \(0.648476\pi\)
\(90\) 0 0
\(91\) −9.00000 −0.943456
\(92\) −6.92820 + 6.92820i −0.722315 + 0.722315i
\(93\) 0 0
\(94\) 18.0000i 1.85656i
\(95\) 0 0
\(96\) 0 0
\(97\) −8.57321 8.57321i −0.870478 0.870478i 0.122046 0.992524i \(-0.461054\pi\)
−0.992524 + 0.122046i \(0.961054\pi\)
\(98\) 6.92820 + 6.92820i 0.699854 + 0.699854i
\(99\) 0 0
\(100\) 0 0
\(101\) 8.48528i 0.844317i −0.906522 0.422159i \(-0.861273\pi\)
0.906522 0.422159i \(-0.138727\pi\)
\(102\) 0 0
\(103\) 12.2474 12.2474i 1.20678 1.20678i 0.234712 0.972065i \(-0.424585\pi\)
0.972065 0.234712i \(-0.0754147\pi\)
\(104\) −25.4558 −2.49615
\(105\) 0 0
\(106\) −24.0000 −2.33109
\(107\) 10.3923 10.3923i 1.00466 1.00466i 0.00467295 0.999989i \(-0.498513\pi\)
0.999989 0.00467295i \(-0.00148745\pi\)
\(108\) 0 0
\(109\) 5.00000i 0.478913i −0.970907 0.239457i \(-0.923031\pi\)
0.970907 0.239457i \(-0.0769693\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −4.89898 4.89898i −0.462910 0.462910i
\(113\) 10.3923 + 10.3923i 0.977626 + 0.977626i 0.999755 0.0221293i \(-0.00704455\pi\)
−0.0221293 + 0.999755i \(0.507045\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 16.9706i 1.57568i
\(117\) 0 0
\(118\) −22.0454 + 22.0454i −2.02944 + 2.02944i
\(119\) 4.24264 0.388922
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 12.1244 12.1244i 1.09769 1.09769i
\(123\) 0 0
\(124\) 4.00000i 0.359211i
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) 13.8564 + 13.8564i 1.22474 + 1.22474i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −6.12372 + 6.12372i −0.530994 + 0.530994i
\(134\) −12.7279 −1.09952
\(135\) 0 0
\(136\) 12.0000 1.02899
\(137\) −8.66025 + 8.66025i −0.739895 + 0.739895i −0.972558 0.232662i \(-0.925256\pi\)
0.232662 + 0.972558i \(0.425256\pi\)
\(138\) 0 0
\(139\) 2.00000i 0.169638i 0.996396 + 0.0848189i \(0.0270312\pi\)
−0.996396 + 0.0848189i \(0.972969\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 14.6969 + 14.6969i 1.23334 + 1.23334i
\(143\) −15.5885 15.5885i −1.30357 1.30357i
\(144\) 0 0
\(145\) 0 0
\(146\) 8.48528i 0.702247i
\(147\) 0 0
\(148\) 9.79796 9.79796i 0.805387 0.805387i
\(149\) 4.24264 0.347571 0.173785 0.984784i \(-0.444400\pi\)
0.173785 + 0.984784i \(0.444400\pi\)
\(150\) 0 0
\(151\) 13.0000 1.05792 0.528962 0.848645i \(-0.322581\pi\)
0.528962 + 0.848645i \(0.322581\pi\)
\(152\) −17.3205 + 17.3205i −1.40488 + 1.40488i
\(153\) 0 0
\(154\) 18.0000i 1.45048i
\(155\) 0 0
\(156\) 0 0
\(157\) −6.12372 6.12372i −0.488726 0.488726i 0.419178 0.907904i \(-0.362318\pi\)
−0.907904 + 0.419178i \(0.862318\pi\)
\(158\) 3.46410 + 3.46410i 0.275589 + 0.275589i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.24264i 0.334367i
\(162\) 0 0
\(163\) 11.0227 11.0227i 0.863365 0.863365i −0.128363 0.991727i \(-0.540972\pi\)
0.991727 + 0.128363i \(0.0409721\pi\)
\(164\) 33.9411 2.65036
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) −17.3205 + 17.3205i −1.34030 + 1.34030i −0.444544 + 0.895757i \(0.646634\pi\)
−0.895757 + 0.444544i \(0.853366\pi\)
\(168\) 0 0
\(169\) 14.0000i 1.07692i
\(170\) 0 0
\(171\) 0 0
\(172\) 4.89898 + 4.89898i 0.373544 + 0.373544i
\(173\) 1.73205 + 1.73205i 0.131685 + 0.131685i 0.769877 0.638192i \(-0.220317\pi\)
−0.638192 + 0.769877i \(0.720317\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 16.9706i 1.27920i
\(177\) 0 0
\(178\) 14.6969 14.6969i 1.10158 1.10158i
\(179\) −4.24264 −0.317110 −0.158555 0.987350i \(-0.550683\pi\)
−0.158555 + 0.987350i \(0.550683\pi\)
\(180\) 0 0
\(181\) 19.0000 1.41226 0.706129 0.708083i \(-0.250440\pi\)
0.706129 + 0.708083i \(0.250440\pi\)
\(182\) 15.5885 15.5885i 1.15549 1.15549i
\(183\) 0 0
\(184\) 12.0000i 0.884652i
\(185\) 0 0
\(186\) 0 0
\(187\) 7.34847 + 7.34847i 0.537373 + 0.537373i
\(188\) −20.7846 20.7846i −1.51587 1.51587i
\(189\) 0 0
\(190\) 0 0
\(191\) 12.7279i 0.920960i −0.887670 0.460480i \(-0.847677\pi\)
0.887670 0.460480i \(-0.152323\pi\)
\(192\) 0 0
\(193\) −15.9217 + 15.9217i −1.14607 + 1.14607i −0.158749 + 0.987319i \(0.550746\pi\)
−0.987319 + 0.158749i \(0.949254\pi\)
\(194\) 29.6985 2.13223
\(195\) 0 0
\(196\) −16.0000 −1.14286
\(197\) −1.73205 + 1.73205i −0.123404 + 0.123404i −0.766111 0.642708i \(-0.777811\pi\)
0.642708 + 0.766111i \(0.277811\pi\)
\(198\) 0 0
\(199\) 25.0000i 1.77220i 0.463491 + 0.886102i \(0.346597\pi\)
−0.463491 + 0.886102i \(0.653403\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 14.6969 + 14.6969i 1.03407 + 1.03407i
\(203\) −5.19615 5.19615i −0.364698 0.364698i
\(204\) 0 0
\(205\) 0 0
\(206\) 42.4264i 2.95599i
\(207\) 0 0
\(208\) 14.6969 14.6969i 1.01905 1.01905i
\(209\) −21.2132 −1.46735
\(210\) 0 0
\(211\) 11.0000 0.757271 0.378636 0.925546i \(-0.376393\pi\)
0.378636 + 0.925546i \(0.376393\pi\)
\(212\) 27.7128 27.7128i 1.90332 1.90332i
\(213\) 0 0
\(214\) 36.0000i 2.46091i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.22474 + 1.22474i 0.0831411 + 0.0831411i
\(218\) 8.66025 + 8.66025i 0.586546 + 0.586546i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.7279i 0.856173i
\(222\) 0 0
\(223\) −6.12372 + 6.12372i −0.410075 + 0.410075i −0.881765 0.471690i \(-0.843644\pi\)
0.471690 + 0.881765i \(0.343644\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −36.0000 −2.39468
\(227\) 13.8564 13.8564i 0.919682 0.919682i −0.0773240 0.997006i \(-0.524638\pi\)
0.997006 + 0.0773240i \(0.0246376\pi\)
\(228\) 0 0
\(229\) 1.00000i 0.0660819i −0.999454 0.0330409i \(-0.989481\pi\)
0.999454 0.0330409i \(-0.0105192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −14.6969 14.6969i −0.964901 0.964901i
\(233\) −10.3923 10.3923i −0.680823 0.680823i 0.279363 0.960186i \(-0.409877\pi\)
−0.960186 + 0.279363i \(0.909877\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 50.9117i 3.31407i
\(237\) 0 0
\(238\) −7.34847 + 7.34847i −0.476331 + 0.476331i
\(239\) 16.9706 1.09773 0.548867 0.835910i \(-0.315059\pi\)
0.548867 + 0.835910i \(0.315059\pi\)
\(240\) 0 0
\(241\) 5.00000 0.322078 0.161039 0.986948i \(-0.448515\pi\)
0.161039 + 0.986948i \(0.448515\pi\)
\(242\) 12.1244 12.1244i 0.779383 0.779383i
\(243\) 0 0
\(244\) 28.0000i 1.79252i
\(245\) 0 0
\(246\) 0 0
\(247\) −18.3712 18.3712i −1.16893 1.16893i
\(248\) 3.46410 + 3.46410i 0.219971 + 0.219971i
\(249\) 0 0
\(250\) 0 0
\(251\) 8.48528i 0.535586i 0.963476 + 0.267793i \(0.0862944\pi\)
−0.963476 + 0.267793i \(0.913706\pi\)
\(252\) 0 0
\(253\) 7.34847 7.34847i 0.461994 0.461994i
\(254\) 0 0
\(255\) 0 0
\(256\) −32.0000 −2.00000
\(257\) −13.8564 + 13.8564i −0.864339 + 0.864339i −0.991839 0.127500i \(-0.959305\pi\)
0.127500 + 0.991839i \(0.459305\pi\)
\(258\) 0 0
\(259\) 6.00000i 0.372822i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −10.3923 10.3923i −0.640817 0.640817i 0.309939 0.950756i \(-0.399691\pi\)
−0.950756 + 0.309939i \(0.899691\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 21.2132i 1.30066i
\(267\) 0 0
\(268\) 14.6969 14.6969i 0.897758 0.897758i
\(269\) −29.6985 −1.81075 −0.905374 0.424614i \(-0.860410\pi\)
−0.905374 + 0.424614i \(0.860410\pi\)
\(270\) 0 0
\(271\) 14.0000 0.850439 0.425220 0.905090i \(-0.360197\pi\)
0.425220 + 0.905090i \(0.360197\pi\)
\(272\) −6.92820 + 6.92820i −0.420084 + 0.420084i
\(273\) 0 0
\(274\) 30.0000i 1.81237i
\(275\) 0 0
\(276\) 0 0
\(277\) −8.57321 8.57321i −0.515115 0.515115i 0.400975 0.916089i \(-0.368672\pi\)
−0.916089 + 0.400975i \(0.868672\pi\)
\(278\) −3.46410 3.46410i −0.207763 0.207763i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.24264i 0.253095i −0.991961 0.126547i \(-0.959610\pi\)
0.991961 0.126547i \(-0.0403896\pi\)
\(282\) 0 0
\(283\) −13.4722 + 13.4722i −0.800839 + 0.800839i −0.983227 0.182388i \(-0.941617\pi\)
0.182388 + 0.983227i \(0.441617\pi\)
\(284\) −33.9411 −2.01404
\(285\) 0 0
\(286\) 54.0000 3.19309
\(287\) −10.3923 + 10.3923i −0.613438 + 0.613438i
\(288\) 0 0
\(289\) 11.0000i 0.647059i
\(290\) 0 0
\(291\) 0 0
\(292\) −9.79796 9.79796i −0.573382 0.573382i
\(293\) 1.73205 + 1.73205i 0.101187 + 0.101187i 0.755888 0.654701i \(-0.227205\pi\)
−0.654701 + 0.755888i \(0.727205\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 16.9706i 0.986394i
\(297\) 0 0
\(298\) −7.34847 + 7.34847i −0.425685 + 0.425685i
\(299\) 12.7279 0.736075
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) −22.5167 + 22.5167i −1.29569 + 1.29569i
\(303\) 0 0
\(304\) 20.0000i 1.14708i
\(305\) 0 0
\(306\) 0 0
\(307\) 23.2702 + 23.2702i 1.32810 + 1.32810i 0.907028 + 0.421069i \(0.138345\pi\)
0.421069 + 0.907028i \(0.361655\pi\)
\(308\) 20.7846 + 20.7846i 1.18431 + 1.18431i
\(309\) 0 0
\(310\) 0 0
\(311\) 4.24264i 0.240578i −0.992739 0.120289i \(-0.961618\pi\)
0.992739 0.120289i \(-0.0383821\pi\)
\(312\) 0 0
\(313\) 3.67423 3.67423i 0.207680 0.207680i −0.595601 0.803281i \(-0.703086\pi\)
0.803281 + 0.595601i \(0.203086\pi\)
\(314\) 21.2132 1.19713
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 3.46410 3.46410i 0.194563 0.194563i −0.603101 0.797665i \(-0.706069\pi\)
0.797665 + 0.603101i \(0.206069\pi\)
\(318\) 0 0
\(319\) 18.0000i 1.00781i
\(320\) 0 0
\(321\) 0 0
\(322\) 7.34847 + 7.34847i 0.409514 + 0.409514i
\(323\) 8.66025 + 8.66025i 0.481869 + 0.481869i
\(324\) 0 0
\(325\) 0 0
\(326\) 38.1838i 2.11480i
\(327\) 0 0
\(328\) −29.3939 + 29.3939i −1.62301 + 1.62301i
\(329\) 12.7279 0.701713
\(330\) 0 0
\(331\) −22.0000 −1.20923 −0.604615 0.796518i \(-0.706673\pi\)
−0.604615 + 0.796518i \(0.706673\pi\)
\(332\) −6.92820 + 6.92820i −0.380235 + 0.380235i
\(333\) 0 0
\(334\) 60.0000i 3.28305i
\(335\) 0 0
\(336\) 0 0
\(337\) 18.3712 + 18.3712i 1.00074 + 1.00074i 1.00000 0.000741840i \(0.000236135\pi\)
0.000741840 1.00000i \(0.499764\pi\)
\(338\) 24.2487 + 24.2487i 1.31896 + 1.31896i
\(339\) 0 0
\(340\) 0 0
\(341\) 4.24264i 0.229752i
\(342\) 0 0
\(343\) 13.4722 13.4722i 0.727430 0.727430i
\(344\) −8.48528 −0.457496
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 15.5885 15.5885i 0.836832 0.836832i −0.151608 0.988441i \(-0.548445\pi\)
0.988441 + 0.151608i \(0.0484453\pi\)
\(348\) 0 0
\(349\) 16.0000i 0.856460i −0.903670 0.428230i \(-0.859137\pi\)
0.903670 0.428230i \(-0.140863\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 15.5885 + 15.5885i 0.829690 + 0.829690i 0.987474 0.157784i \(-0.0504349\pi\)
−0.157784 + 0.987474i \(0.550435\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 33.9411i 1.79888i
\(357\) 0 0
\(358\) 7.34847 7.34847i 0.388379 0.388379i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −6.00000 −0.315789
\(362\) −32.9090 + 32.9090i −1.72966 + 1.72966i
\(363\) 0 0
\(364\) 36.0000i 1.88691i
\(365\) 0 0
\(366\) 0 0
\(367\) −11.0227 11.0227i −0.575380 0.575380i 0.358247 0.933627i \(-0.383375\pi\)
−0.933627 + 0.358247i \(0.883375\pi\)
\(368\) 6.92820 + 6.92820i 0.361158 + 0.361158i
\(369\) 0 0
\(370\) 0 0
\(371\) 16.9706i 0.881068i
\(372\) 0 0
\(373\) 1.22474 1.22474i 0.0634149 0.0634149i −0.674688 0.738103i \(-0.735722\pi\)
0.738103 + 0.674688i \(0.235722\pi\)
\(374\) −25.4558 −1.31629
\(375\) 0 0
\(376\) 36.0000 1.85656
\(377\) 15.5885 15.5885i 0.802846 0.802846i
\(378\) 0 0
\(379\) 1.00000i 0.0513665i −0.999670 0.0256833i \(-0.991824\pi\)
0.999670 0.0256833i \(-0.00817614\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 22.0454 + 22.0454i 1.12794 + 1.12794i
\(383\) −3.46410 3.46410i −0.177007 0.177007i 0.613043 0.790050i \(-0.289945\pi\)
−0.790050 + 0.613043i \(0.789945\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 55.1543i 2.80728i
\(387\) 0 0
\(388\) −34.2929 + 34.2929i −1.74096 + 1.74096i
\(389\) 16.9706 0.860442 0.430221 0.902724i \(-0.358436\pi\)
0.430221 + 0.902724i \(0.358436\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) 13.8564 13.8564i 0.699854 0.699854i
\(393\) 0 0
\(394\) 6.00000i 0.302276i
\(395\) 0 0
\(396\) 0 0
\(397\) −8.57321 8.57321i −0.430277 0.430277i 0.458445 0.888723i \(-0.348406\pi\)
−0.888723 + 0.458445i \(0.848406\pi\)
\(398\) −43.3013 43.3013i −2.17050 2.17050i
\(399\) 0 0
\(400\) 0 0
\(401\) 16.9706i 0.847469i −0.905786 0.423735i \(-0.860719\pi\)
0.905786 0.423735i \(-0.139281\pi\)
\(402\) 0 0
\(403\) −3.67423 + 3.67423i −0.183027 + 0.183027i
\(404\) −33.9411 −1.68863
\(405\) 0 0
\(406\) 18.0000 0.893325
\(407\) −10.3923 + 10.3923i −0.515127 + 0.515127i
\(408\) 0 0
\(409\) 11.0000i 0.543915i 0.962309 + 0.271957i \(0.0876710\pi\)
−0.962309 + 0.271957i \(0.912329\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −48.9898 48.9898i −2.41355 2.41355i
\(413\) 15.5885 + 15.5885i 0.767058 + 0.767058i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 36.7423 36.7423i 1.79713 1.79713i
\(419\) −8.48528 −0.414533 −0.207267 0.978285i \(-0.566457\pi\)
−0.207267 + 0.978285i \(0.566457\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −19.0526 + 19.0526i −0.927464 + 0.927464i
\(423\) 0 0
\(424\) 48.0000i 2.33109i
\(425\) 0 0
\(426\) 0 0
\(427\) −8.57321 8.57321i −0.414887 0.414887i
\(428\) −41.5692 41.5692i −2.00932 2.00932i
\(429\) 0 0
\(430\) 0 0
\(431\) 29.6985i 1.43053i −0.698856 0.715263i \(-0.746307\pi\)
0.698856 0.715263i \(-0.253693\pi\)
\(432\) 0 0
\(433\) 1.22474 1.22474i 0.0588575 0.0588575i −0.677065 0.735923i \(-0.736749\pi\)
0.735923 + 0.677065i \(0.236749\pi\)
\(434\) −4.24264 −0.203653
\(435\) 0 0
\(436\) −20.0000 −0.957826
\(437\) 8.66025 8.66025i 0.414276 0.414276i
\(438\) 0 0
\(439\) 11.0000i 0.525001i −0.964932 0.262501i \(-0.915453\pi\)
0.964932 0.262501i \(-0.0845472\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −22.0454 22.0454i −1.04859 1.04859i
\(443\) 17.3205 + 17.3205i 0.822922 + 0.822922i 0.986526 0.163604i \(-0.0523119\pi\)
−0.163604 + 0.986526i \(0.552312\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 21.2132i 1.00447i
\(447\) 0 0
\(448\) 9.79796 9.79796i 0.462910 0.462910i
\(449\) 33.9411 1.60178 0.800890 0.598811i \(-0.204360\pi\)
0.800890 + 0.598811i \(0.204360\pi\)
\(450\) 0 0
\(451\) −36.0000 −1.69517
\(452\) 41.5692 41.5692i 1.95525 1.95525i
\(453\) 0 0
\(454\) 48.0000i 2.25275i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(458\) 1.73205 + 1.73205i 0.0809334 + 0.0809334i
\(459\) 0 0
\(460\) 0 0
\(461\) 16.9706i 0.790398i 0.918596 + 0.395199i \(0.129324\pi\)
−0.918596 + 0.395199i \(0.870676\pi\)
\(462\) 0 0
\(463\) 24.4949 24.4949i 1.13837 1.13837i 0.149633 0.988742i \(-0.452191\pi\)
0.988742 0.149633i \(-0.0478091\pi\)
\(464\) 16.9706 0.787839
\(465\) 0 0
\(466\) 36.0000 1.66767
\(467\) 19.0526 19.0526i 0.881647 0.881647i −0.112055 0.993702i \(-0.535743\pi\)
0.993702 + 0.112055i \(0.0357432\pi\)
\(468\) 0 0
\(469\) 9.00000i 0.415581i
\(470\) 0 0
\(471\) 0 0
\(472\) 44.0908 + 44.0908i 2.02944 + 2.02944i
\(473\) −5.19615 5.19615i −0.238919 0.238919i
\(474\) 0 0
\(475\) 0 0
\(476\) 16.9706i 0.777844i
\(477\) 0 0
\(478\) −29.3939 + 29.3939i −1.34444 + 1.34444i
\(479\) −38.1838 −1.74466 −0.872330 0.488917i \(-0.837392\pi\)
−0.872330 + 0.488917i \(0.837392\pi\)
\(480\) 0 0
\(481\) −18.0000 −0.820729
\(482\) −8.66025 + 8.66025i −0.394464 + 0.394464i
\(483\) 0 0
\(484\) 28.0000i 1.27273i
\(485\) 0 0
\(486\) 0 0
\(487\) 18.3712 + 18.3712i 0.832477 + 0.832477i 0.987855 0.155378i \(-0.0496595\pi\)
−0.155378 + 0.987855i \(0.549659\pi\)
\(488\) −24.2487 24.2487i −1.09769 1.09769i
\(489\) 0 0
\(490\) 0 0
\(491\) 42.4264i 1.91468i 0.288969 + 0.957338i \(0.406688\pi\)
−0.288969 + 0.957338i \(0.593312\pi\)
\(492\) 0 0
\(493\) −7.34847 + 7.34847i −0.330958 + 0.330958i
\(494\) 63.6396 2.86328
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 10.3923 10.3923i 0.466159 0.466159i
\(498\) 0 0
\(499\) 1.00000i 0.0447661i 0.999749 + 0.0223831i \(0.00712535\pi\)
−0.999749 + 0.0223831i \(0.992875\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −14.6969 14.6969i −0.655956 0.655956i
\(503\) 13.8564 + 13.8564i 0.617827 + 0.617827i 0.944974 0.327147i \(-0.106087\pi\)
−0.327147 + 0.944974i \(0.606087\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 25.4558i 1.13165i
\(507\) 0 0
\(508\) 0 0
\(509\) 4.24264 0.188052 0.0940259 0.995570i \(-0.470026\pi\)
0.0940259 + 0.995570i \(0.470026\pi\)
\(510\) 0 0
\(511\) 6.00000 0.265424
\(512\) 27.7128 27.7128i 1.22474 1.22474i
\(513\) 0 0
\(514\) 48.0000i 2.11719i
\(515\) 0 0
\(516\) 0 0
\(517\) 22.0454 + 22.0454i 0.969556 + 0.969556i
\(518\) −10.3923 10.3923i −0.456612 0.456612i
\(519\) 0 0
\(520\) 0 0
\(521\) 4.24264i 0.185873i 0.995672 + 0.0929367i \(0.0296254\pi\)
−0.995672 + 0.0929367i \(0.970375\pi\)
\(522\) 0 0
\(523\) −13.4722 + 13.4722i −0.589098 + 0.589098i −0.937387 0.348289i \(-0.886763\pi\)
0.348289 + 0.937387i \(0.386763\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 36.0000 1.56967
\(527\) 1.73205 1.73205i 0.0754493 0.0754493i
\(528\) 0 0
\(529\) 17.0000i 0.739130i
\(530\) 0 0
\(531\) 0 0
\(532\) 24.4949 + 24.4949i 1.06199 + 1.06199i
\(533\) −31.1769 31.1769i −1.35042 1.35042i
\(534\) 0 0
\(535\) 0 0
\(536\) 25.4558i 1.09952i
\(537\) 0 0
\(538\) 51.4393 51.4393i 2.21771 2.21771i
\(539\) 16.9706 0.730974
\(540\) 0 0
\(541\) −1.00000 −0.0429934 −0.0214967 0.999769i \(-0.506843\pi\)
−0.0214967 + 0.999769i \(0.506843\pi\)
\(542\) −24.2487 + 24.2487i −1.04157 + 1.04157i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 12.2474 + 12.2474i 0.523663 + 0.523663i 0.918676 0.395013i \(-0.129260\pi\)
−0.395013 + 0.918676i \(0.629260\pi\)
\(548\) 34.6410 + 34.6410i 1.47979 + 1.47979i
\(549\) 0 0
\(550\) 0 0
\(551\) 21.2132i 0.903713i
\(552\) 0 0
\(553\) 2.44949 2.44949i 0.104163 0.104163i
\(554\) 29.6985 1.26177
\(555\) 0 0
\(556\) 8.00000 0.339276
\(557\) −15.5885 + 15.5885i −0.660504 + 0.660504i −0.955499 0.294995i \(-0.904682\pi\)
0.294995 + 0.955499i \(0.404682\pi\)
\(558\) 0 0
\(559\) 9.00000i 0.380659i
\(560\) 0 0
\(561\) 0 0
\(562\) 7.34847 + 7.34847i 0.309976 + 0.309976i
\(563\) 25.9808 + 25.9808i 1.09496 + 1.09496i 0.994991 + 0.0999679i \(0.0318740\pi\)
0.0999679 + 0.994991i \(0.468126\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 46.6690i 1.96165i
\(567\) 0 0
\(568\) 29.3939 29.3939i 1.23334 1.23334i
\(569\) 12.7279 0.533582 0.266791 0.963754i \(-0.414037\pi\)
0.266791 + 0.963754i \(0.414037\pi\)
\(570\) 0 0
\(571\) 17.0000 0.711428 0.355714 0.934595i \(-0.384238\pi\)
0.355714 + 0.934595i \(0.384238\pi\)
\(572\) −62.3538 + 62.3538i −2.60714 + 2.60714i
\(573\) 0 0
\(574\) 36.0000i 1.50261i
\(575\) 0 0
\(576\) 0 0
\(577\) −23.2702 23.2702i −0.968749 0.968749i 0.0307771 0.999526i \(-0.490202\pi\)
−0.999526 + 0.0307771i \(0.990202\pi\)
\(578\) −19.0526 19.0526i −0.792482 0.792482i
\(579\) 0 0
\(580\) 0 0
\(581\) 4.24264i 0.176014i
\(582\) 0 0
\(583\) −29.3939 + 29.3939i −1.21737 + 1.21737i
\(584\) 16.9706 0.702247
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −13.8564 + 13.8564i −0.571915 + 0.571915i −0.932663 0.360748i \(-0.882521\pi\)
0.360748 + 0.932663i \(0.382521\pi\)
\(588\) 0 0
\(589\) 5.00000i 0.206021i
\(590\) 0 0
\(591\) 0 0
\(592\) −9.79796 9.79796i −0.402694 0.402694i
\(593\) −6.92820 6.92820i −0.284507 0.284507i 0.550396 0.834904i \(-0.314477\pi\)
−0.834904 + 0.550396i \(0.814477\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.9706i 0.695141i
\(597\) 0 0
\(598\) −22.0454 + 22.0454i −0.901504 + 0.901504i
\(599\) −25.4558 −1.04010 −0.520049 0.854137i \(-0.674086\pi\)
−0.520049 + 0.854137i \(0.674086\pi\)
\(600\) 0 0
\(601\) 43.0000 1.75401 0.877003 0.480484i \(-0.159539\pi\)
0.877003 + 0.480484i \(0.159539\pi\)
\(602\) 5.19615 5.19615i 0.211779 0.211779i
\(603\) 0 0
\(604\) 52.0000i 2.11585i
\(605\) 0 0
\(606\) 0 0
\(607\) −19.5959 19.5959i −0.795374 0.795374i 0.186988 0.982362i \(-0.440127\pi\)
−0.982362 + 0.186988i \(0.940127\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 38.1838i 1.54475i
\(612\) 0 0
\(613\) 26.9444 26.9444i 1.08827 1.08827i 0.0925671 0.995706i \(-0.470493\pi\)
0.995706 0.0925671i \(-0.0295073\pi\)
\(614\) −80.6102 −3.25316
\(615\) 0 0
\(616\) −36.0000 −1.45048
\(617\) 17.3205 17.3205i 0.697297 0.697297i −0.266529 0.963827i \(-0.585877\pi\)
0.963827 + 0.266529i \(0.0858769\pi\)
\(618\) 0 0
\(619\) 13.0000i 0.522514i 0.965269 + 0.261257i \(0.0841370\pi\)
−0.965269 + 0.261257i \(0.915863\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 7.34847 + 7.34847i 0.294647 + 0.294647i
\(623\) −10.3923 10.3923i −0.416359 0.416359i
\(624\) 0 0
\(625\) 0 0
\(626\) 12.7279i 0.508710i
\(627\) 0 0
\(628\) −24.4949 + 24.4949i −0.977453 + 0.977453i
\(629\) 8.48528 0.338330
\(630\) 0 0
\(631\) 35.0000 1.39333 0.696664 0.717398i \(-0.254667\pi\)
0.696664 + 0.717398i \(0.254667\pi\)
\(632\) 6.92820 6.92820i 0.275589 0.275589i
\(633\) 0 0
\(634\) 12.0000i 0.476581i
\(635\) 0 0
\(636\) 0 0
\(637\) 14.6969 + 14.6969i 0.582314 + 0.582314i
\(638\) 31.1769 + 31.1769i 1.23431 + 1.23431i
\(639\) 0 0
\(640\) 0 0
\(641\) 33.9411i 1.34059i 0.742093 + 0.670297i \(0.233833\pi\)
−0.742093 + 0.670297i \(0.766167\pi\)
\(642\) 0 0
\(643\) −29.3939 + 29.3939i −1.15918 + 1.15918i −0.174529 + 0.984652i \(0.555840\pi\)
−0.984652 + 0.174529i \(0.944160\pi\)
\(644\) −16.9706 −0.668734
\(645\) 0 0
\(646\) −30.0000 −1.18033
\(647\) −17.3205 + 17.3205i −0.680939 + 0.680939i −0.960212 0.279272i \(-0.909907\pi\)
0.279272 + 0.960212i \(0.409907\pi\)
\(648\) 0 0
\(649\) 54.0000i 2.11969i
\(650\) 0 0
\(651\) 0 0
\(652\) −44.0908 44.0908i −1.72673 1.72673i
\(653\) −19.0526 19.0526i −0.745584 0.745584i 0.228062 0.973647i \(-0.426761\pi\)
−0.973647 + 0.228062i \(0.926761\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 33.9411i 1.32518i
\(657\) 0 0
\(658\) −22.0454 + 22.0454i −0.859419 + 0.859419i
\(659\) 8.48528 0.330540 0.165270 0.986248i \(-0.447151\pi\)
0.165270 + 0.986248i \(0.447151\pi\)
\(660\) 0 0
\(661\) −20.0000 −0.777910 −0.388955 0.921257i \(-0.627164\pi\)
−0.388955 + 0.921257i \(0.627164\pi\)
\(662\) 38.1051 38.1051i 1.48100 1.48100i
\(663\) 0 0
\(664\) 12.0000i 0.465690i
\(665\) 0 0
\(666\) 0 0
\(667\) 7.34847 + 7.34847i 0.284534 + 0.284534i
\(668\) 69.2820 + 69.2820i 2.68060 + 2.68060i
\(669\) 0 0
\(670\) 0 0
\(671\) 29.6985i 1.14650i
\(672\) 0 0
\(673\) 2.44949 2.44949i 0.0944209 0.0944209i −0.658319 0.752739i \(-0.728732\pi\)
0.752739 + 0.658319i \(0.228732\pi\)
\(674\) −63.6396 −2.45131
\(675\) 0 0
\(676\) −56.0000 −2.15385
\(677\) 15.5885 15.5885i 0.599113 0.599113i −0.340963 0.940077i \(-0.610753\pi\)
0.940077 + 0.340963i \(0.110753\pi\)
\(678\) 0 0
\(679\) 21.0000i 0.805906i
\(680\) 0 0
\(681\) 0 0
\(682\) −7.34847 7.34847i −0.281387 0.281387i
\(683\) 6.92820 + 6.92820i 0.265100 + 0.265100i 0.827122 0.562022i \(-0.189976\pi\)
−0.562022 + 0.827122i \(0.689976\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 46.6690i 1.78183i
\(687\) 0 0
\(688\) 4.89898 4.89898i 0.186772 0.186772i
\(689\) −50.9117 −1.93958
\(690\) 0 0
\(691\) −32.0000 −1.21734 −0.608669 0.793424i \(-0.708296\pi\)
−0.608669 + 0.793424i \(0.708296\pi\)
\(692\) 6.92820 6.92820i 0.263371 0.263371i
\(693\) 0 0
\(694\) 54.0000i 2.04981i
\(695\) 0 0
\(696\) 0 0
\(697\) 14.6969 + 14.6969i 0.556686 + 0.556686i
\(698\) 27.7128 + 27.7128i 1.04895 + 1.04895i
\(699\) 0 0
\(700\) 0 0
\(701\) 21.2132i 0.801212i −0.916250 0.400606i \(-0.868800\pi\)
0.916250 0.400606i \(-0.131200\pi\)
\(702\) 0 0
\(703\) −12.2474 + 12.2474i −0.461921 + 0.461921i
\(704\) 33.9411 1.27920
\(705\) 0 0
\(706\) −54.0000 −2.03232
\(707\) 10.3923 10.3923i 0.390843 0.390843i
\(708\) 0 0
\(709\) 41.0000i 1.53979i 0.638172 + 0.769894i \(0.279691\pi\)
−0.638172 + 0.769894i \(0.720309\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −29.3939 29.3939i −1.10158 1.10158i
\(713\) −1.73205 1.73205i −0.0648658 0.0648658i
\(714\) 0 0
\(715\) 0 0
\(716\) 16.9706i 0.634220i
\(717\) 0 0
\(718\) 0 0
\(719\) −21.2132 −0.791119 −0.395559 0.918440i \(-0.629449\pi\)
−0.395559 + 0.918440i \(0.629449\pi\)
\(720\) 0 0
\(721\) 30.0000 1.11726
\(722\) 10.3923 10.3923i 0.386762 0.386762i
\(723\) 0 0
\(724\) 76.0000i 2.82452i
\(725\) 0 0
\(726\) 0 0
\(727\) −35.5176 35.5176i −1.31727 1.31727i −0.915925 0.401350i \(-0.868541\pi\)
−0.401350 0.915925i \(-0.631459\pi\)
\(728\) −31.1769 31.1769i −1.15549 1.15549i
\(729\) 0 0
\(730\) 0 0
\(731\) 4.24264i 0.156920i
\(732\) 0 0
\(733\) −22.0454 + 22.0454i −0.814266 + 0.814266i −0.985270 0.171005i \(-0.945299\pi\)
0.171005 + 0.985270i \(0.445299\pi\)
\(734\) 38.1838 1.40939
\(735\) 0 0
\(736\) 0 0
\(737\) −15.5885 + 15.5885i −0.574208 + 0.574208i
\(738\) 0 0
\(739\) 10.0000i 0.367856i −0.982940 0.183928i \(-0.941119\pi\)
0.982940 0.183928i \(-0.0588813\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −29.3939 29.3939i −1.07908 1.07908i
\(743\) −20.7846 20.7846i −0.762513 0.762513i 0.214263 0.976776i \(-0.431265\pi\)
−0.976776 + 0.214263i \(0.931265\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 4.24264i 0.155334i
\(747\) 0 0
\(748\) 29.3939 29.3939i 1.07475 1.07475i
\(749\) 25.4558 0.930136
\(750\) 0 0
\(751\) 46.0000 1.67856 0.839282 0.543696i \(-0.182976\pi\)
0.839282 + 0.543696i \(0.182976\pi\)
\(752\) −20.7846 + 20.7846i −0.757937 + 0.757937i
\(753\) 0 0
\(754\) 54.0000i 1.96656i
\(755\) 0 0
\(756\) 0 0
\(757\) 15.9217 + 15.9217i 0.578683 + 0.578683i 0.934540 0.355857i \(-0.115811\pi\)
−0.355857 + 0.934540i \(0.615811\pi\)
\(758\) 1.73205 + 1.73205i 0.0629109 + 0.0629109i
\(759\) 0 0
\(760\) 0 0
\(761\) 25.4558i 0.922774i −0.887199 0.461387i \(-0.847352\pi\)
0.887199 0.461387i \(-0.152648\pi\)
\(762\) 0 0
\(763\) 6.12372 6.12372i 0.221694 0.221694i
\(764\) −50.9117 −1.84192
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) −46.7654 + 46.7654i −1.68860 + 1.68860i
\(768\) 0 0
\(769\) 29.0000i 1.04577i −0.852404 0.522883i \(-0.824856\pi\)
0.852404 0.522883i \(-0.175144\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 63.6867 + 63.6867i 2.29214 + 2.29214i
\(773\) −27.7128 27.7128i −0.996761 0.996761i 0.00323417 0.999995i \(-0.498971\pi\)
−0.999995 + 0.00323417i \(0.998971\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 59.3970i 2.13223i
\(777\) 0 0
\(778\) −29.3939 + 29.3939i −1.05382 + 1.05382i
\(779\) −42.4264 −1.52008
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) 10.3923 10.3923i 0.371628 0.371628i
\(783\) 0 0
\(784\) 16.0000i 0.571429i
\(785\) 0 0
\(786\) 0 0
\(787\) −20.8207 20.8207i −0.742176 0.742176i 0.230820 0.972996i \(-0.425859\pi\)
−0.972996 + 0.230820i \(0.925859\pi\)
\(788\) 6.92820 + 6.92820i 0.246807 + 0.246807i
\(789\) 0 0
\(790\) 0 0
\(791\) 25.4558i 0.905106i
\(792\) 0 0
\(793\) 25.7196 25.7196i 0.913331 0.913331i
\(794\) 29.6985 1.05396
\(795\) 0 0
\(796\) 100.000 3.54441
\(797\) 3.46410 3.46410i 0.122705 0.122705i −0.643088 0.765793i