Properties

Label 225.2.f.b.143.1
Level $225$
Weight $2$
Character 225.143
Analytic conductor $1.797$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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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 143.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 225.143
Dual form 225.2.f.b.107.1

$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(3\) 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 \(-0.856148\pi\)
0.436698 + 0.899608i \(0.356148\pi\)
\(8\) 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 0.999815 + 0.0192343i \(0.00612285\pi\)
0.0192343 + 0.999815i \(0.493877\pi\)
\(14\) 4.24264 1.13389
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 1.73205 + 1.73205i 0.420084 + 0.420084i 0.885233 0.465149i \(-0.153999\pi\)
−0.465149 + 0.885233i \(0.653999\pi\)
\(18\) 0 0
\(19\) 5.00000i 1.14708i −0.819178 0.573539i \(-0.805570\pi\)
0.819178 0.573539i \(-0.194430\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 7.34847 7.34847i 1.56670 1.56670i
\(23\) −1.73205 + 1.73205i −0.361158 + 0.361158i −0.864239 0.503081i \(-0.832200\pi\)
0.503081 + 0.864239i \(0.332200\pi\)
\(24\) 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 \(-0.371119\pi\)
0.393919 + 0.919145i \(0.371119\pi\)
\(30\) 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 \(-0.841910\pi\)
0.476488 + 0.879181i \(0.341910\pi\)
\(38\) −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 \(-0.207838\pi\)
−0.607527 + 0.794299i \(0.707838\pi\)
\(44\) −16.9706 −2.55841
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 5.19615 + 5.19615i 0.757937 + 0.757937i 0.975947 0.218010i \(-0.0699565\pi\)
−0.218010 + 0.975947i \(0.569956\pi\)
\(48\) 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 −0.0472225 0.998884i \(-0.515037\pi\)
0.998884 + 0.0472225i \(0.0150370\pi\)
\(54\) 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 \(-0.810815\pi\)
−0.828517 + 0.559964i \(0.810815\pi\)
\(60\) 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 \(-0.852812\pi\)
0.446103 + 0.894982i \(0.352812\pi\)
\(68\) −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 \(-0.314979\pi\)
−0.835770 + 0.549079i \(0.814979\pi\)
\(74\) 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 \(0.0358886\pi\)
−0.993651 + 0.112509i \(0.964111\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 14.6969 14.6969i 1.62301 1.62301i
\(83\) −1.73205 + 1.73205i −0.190117 + 0.190117i −0.795747 0.605629i \(-0.792921\pi\)
0.605629 + 0.795747i \(0.292921\pi\)
\(84\) 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 \(-0.351524\pi\)
0.449719 + 0.893170i \(0.351524\pi\)
\(90\) 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 \(-0.538946\pi\)
0.992524 + 0.122046i \(0.0389457\pi\)
\(98\) 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 −0.972065 0.234712i \(-0.924585\pi\)
−0.234712 0.972065i \(-0.575415\pi\)
\(104\) 25.4558 2.49615
\(105\) 0 0
\(106\) −24.0000 −2.33109
\(107\) 10.3923 + 10.3923i 1.00466 + 1.00466i 0.999989 + 0.00467295i \(0.00148745\pi\)
0.00467295 + 0.999989i \(0.498513\pi\)
\(108\) 0 0
\(109\) 5.00000i 0.478913i 0.970907 + 0.239457i \(0.0769693\pi\)
−0.970907 + 0.239457i \(0.923031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 4.89898 4.89898i 0.462910 0.462910i
\(113\) 10.3923 10.3923i 0.977626 0.977626i −0.0221293 0.999755i \(-0.507045\pi\)
0.999755 + 0.0221293i \(0.00704455\pi\)
\(114\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) 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 0.232662 0.972558i \(-0.425256\pi\)
−0.972558 + 0.232662i \(0.925256\pi\)
\(138\) 0 0
\(139\) 2.00000i 0.169638i −0.996396 0.0848189i \(-0.972969\pi\)
0.996396 0.0848189i \(-0.0270312\pi\)
\(140\) 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 \(-0.555600\pi\)
−0.173785 + 0.984784i \(0.555600\pi\)
\(150\) 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 \(-0.637682\pi\)
0.907904 + 0.419178i \(0.137682\pi\)
\(158\) 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 \(-0.459028\pi\)
−0.991727 + 0.128363i \(0.959028\pi\)
\(164\) −33.9411 −2.65036
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) −17.3205 17.3205i −1.34030 1.34030i −0.895757 0.444544i \(-0.853366\pi\)
−0.444544 0.895757i \(-0.646634\pi\)
\(168\) 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 −0.638192 0.769877i \(-0.720317\pi\)
0.769877 + 0.638192i \(0.220317\pi\)
\(174\) 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 \(-0.449317\pi\)
0.158555 + 0.987350i \(0.449317\pi\)
\(180\) 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 0.987319 + 0.158749i \(0.0507460\pi\)
0.158749 + 0.987319i \(0.449254\pi\)
\(194\) −29.6985 −2.13223
\(195\) 0 0
\(196\) −16.0000 −1.14286
\(197\) −1.73205 1.73205i −0.123404 0.123404i 0.642708 0.766111i \(-0.277811\pi\)
−0.766111 + 0.642708i \(0.777811\pi\)
\(198\) 0 0
\(199\) 25.0000i 1.77220i −0.463491 0.886102i \(-0.653403\pi\)
0.463491 0.886102i \(-0.346597\pi\)
\(200\) 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 \(-0.156356\pi\)
−0.471690 + 0.881765i \(0.656356\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −36.0000 −2.39468
\(227\) 13.8564 + 13.8564i 0.919682 + 0.919682i 0.997006 0.0773240i \(-0.0246376\pi\)
−0.0773240 + 0.997006i \(0.524638\pi\)
\(228\) 0 0
\(229\) 1.00000i 0.0660819i 0.999454 + 0.0330409i \(0.0105192\pi\)
−0.999454 + 0.0330409i \(0.989481\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 14.6969 14.6969i 0.964901 0.964901i
\(233\) −10.3923 + 10.3923i −0.680823 + 0.680823i −0.960186 0.279363i \(-0.909877\pi\)
0.279363 + 0.960186i \(0.409877\pi\)
\(234\) 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 \(-0.684941\pi\)
−0.548867 + 0.835910i \(0.684941\pi\)
\(240\) 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 0.127500 0.991839i \(-0.459305\pi\)
−0.991839 + 0.127500i \(0.959305\pi\)
\(258\) 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 −0.950756 0.309939i \(-0.899691\pi\)
0.309939 + 0.950756i \(0.399691\pi\)
\(264\) 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 \(-0.139590\pi\)
0.905374 + 0.424614i \(0.139590\pi\)
\(270\) 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 \(-0.631328\pi\)
0.916089 + 0.400975i \(0.131328\pi\)
\(278\) −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 \(-0.0583827\pi\)
−0.182388 + 0.983227i \(0.558383\pi\)
\(284\) 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 −0.654701 0.755888i \(-0.727205\pi\)
0.755888 + 0.654701i \(0.227205\pi\)
\(294\) 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 −0.421069 + 0.907028i \(0.638345\pi\)
−0.907028 + 0.421069i \(0.861655\pi\)
\(308\) 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 \(-0.296914\pi\)
−0.803281 + 0.595601i \(0.796914\pi\)
\(314\) −21.2132 −1.19713
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 3.46410 + 3.46410i 0.194563 + 0.194563i 0.797665 0.603101i \(-0.206069\pi\)
−0.603101 + 0.797665i \(0.706069\pi\)
\(318\) 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 −0.000741840 1.00000i \(0.500236\pi\)
−1.00000 0.000741840i \(0.999764\pi\)
\(338\) 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 0.988441 0.151608i \(-0.0484453\pi\)
−0.151608 + 0.988441i \(0.548445\pi\)
\(348\) 0 0
\(349\) 16.0000i 0.856460i 0.903670 + 0.428230i \(0.140863\pi\)
−0.903670 + 0.428230i \(0.859137\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 15.5885 15.5885i 0.829690 0.829690i −0.157784 0.987474i \(-0.550435\pi\)
0.987474 + 0.157784i \(0.0504349\pi\)
\(354\) 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 \(-0.616625\pi\)
0.933627 + 0.358247i \(0.116625\pi\)
\(368\) 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 \(-0.264278\pi\)
−0.738103 + 0.674688i \(0.764278\pi\)
\(374\) 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 \(0.00817614\pi\)
−0.999670 + 0.0256833i \(0.991824\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −22.0454 + 22.0454i −1.12794 + 1.12794i
\(383\) −3.46410 + 3.46410i −0.177007 + 0.177007i −0.790050 0.613043i \(-0.789945\pi\)
0.613043 + 0.790050i \(0.289945\pi\)
\(384\) 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 \(-0.641564\pi\)
−0.430221 + 0.902724i \(0.641564\pi\)
\(390\) 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 \(-0.651594\pi\)
0.888723 + 0.458445i \(0.151594\pi\)
\(398\) −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 \(-0.912329\pi\)
0.962309 0.271957i \(-0.0876710\pi\)
\(410\) 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 \(-0.433543\pi\)
0.207267 + 0.978285i \(0.433543\pi\)
\(420\) 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 \(-0.263251\pi\)
−0.735923 + 0.677065i \(0.763251\pi\)
\(434\) 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 \(0.0845472\pi\)
−0.964932 + 0.262501i \(0.915453\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 22.0454 22.0454i 1.04859 1.04859i
\(443\) 17.3205 17.3205i 0.822922 0.822922i −0.163604 0.986526i \(-0.552312\pi\)
0.986526 + 0.163604i \(0.0523119\pi\)
\(444\) 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 \(-0.795640\pi\)
−0.800890 + 0.598811i \(0.795640\pi\)
\(450\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(458\) 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 −0.988742 0.149633i \(-0.952191\pi\)
−0.149633 0.988742i \(-0.547809\pi\)
\(464\) −16.9706 −0.787839
\(465\) 0 0
\(466\) 36.0000 1.66767
\(467\) 19.0526 + 19.0526i 0.881647 + 0.881647i 0.993702 0.112055i \(-0.0357432\pi\)
−0.112055 + 0.993702i \(0.535743\pi\)
\(468\) 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 \(-0.162608\pi\)
0.872330 + 0.488917i \(0.162608\pi\)
\(480\) 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 \(-0.950341\pi\)
0.155378 + 0.987855i \(0.450341\pi\)
\(488\) −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 \(-0.992875\pi\)
0.999749 0.0223831i \(-0.00712535\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 14.6969 14.6969i 0.655956 0.655956i
\(503\) 13.8564 13.8564i 0.617827 0.617827i −0.327147 0.944974i \(-0.606087\pi\)
0.944974 + 0.327147i \(0.106087\pi\)
\(504\) 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 \(-0.529974\pi\)
−0.0940259 + 0.995570i \(0.529974\pi\)
\(510\) 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 \(-0.113237\pi\)
−0.348289 + 0.937387i \(0.613237\pi\)
\(524\) 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 \(-0.870740\pi\)
0.395013 + 0.918676i \(0.370740\pi\)
\(548\) 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 0.294995 0.955499i \(-0.404682\pi\)
−0.955499 + 0.294995i \(0.904682\pi\)
\(558\) 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 0.0999679 0.994991i \(-0.468126\pi\)
0.994991 0.0999679i \(-0.0318740\pi\)
\(564\) 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 \(-0.585963\pi\)
−0.266791 + 0.963754i \(0.585963\pi\)
\(570\) 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 \(-0.509798\pi\)
0.999526 + 0.0307771i \(0.00979822\pi\)
\(578\) −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 0.360748 0.932663i \(-0.382521\pi\)
−0.932663 + 0.360748i \(0.882521\pi\)
\(588\) 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 −0.834904 0.550396i \(-0.814477\pi\)
0.550396 + 0.834904i \(0.314477\pi\)
\(594\) 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 \(-0.325914\pi\)
0.520049 + 0.854137i \(0.325914\pi\)
\(600\) 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 \(-0.559873\pi\)
0.982362 + 0.186988i \(0.0598727\pi\)
\(608\) 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 −0.995706 0.0925671i \(-0.970493\pi\)
−0.0925671 0.995706i \(-0.529507\pi\)
\(614\) 80.6102 3.25316
\(615\) 0 0
\(616\) −36.0000 −1.45048
\(617\) 17.3205 + 17.3205i 0.697297 + 0.697297i 0.963827 0.266529i \(-0.0858769\pi\)
−0.266529 + 0.963827i \(0.585877\pi\)
\(618\) 0 0
\(619\) 13.0000i 0.522514i −0.965269 0.261257i \(-0.915863\pi\)
0.965269 0.261257i \(-0.0841370\pi\)
\(620\) 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 0.984652 + 0.174529i \(0.0558404\pi\)
0.174529 + 0.984652i \(0.444160\pi\)
\(644\) 16.9706 0.668734
\(645\) 0 0
\(646\) −30.0000 −1.18033
\(647\) −17.3205 17.3205i −0.680939 0.680939i 0.279272 0.960212i \(-0.409907\pi\)
−0.960212 + 0.279272i \(0.909907\pi\)
\(648\) 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 −0.973647 0.228062i \(-0.926761\pi\)
0.228062 + 0.973647i \(0.426761\pi\)
\(654\) 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 \(-0.552849\pi\)
−0.165270 + 0.986248i \(0.552849\pi\)
\(660\) 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 \(-0.271268\pi\)
−0.752739 + 0.658319i \(0.771268\pi\)
\(674\) 63.6396 2.45131
\(675\) 0 0
\(676\) −56.0000 −2.15385
\(677\) 15.5885 + 15.5885i 0.599113 + 0.599113i 0.940077 0.340963i \(-0.110753\pi\)
−0.340963 + 0.940077i \(0.610753\pi\)
\(678\) 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 −0.562022 0.827122i \(-0.689976\pi\)
0.827122 + 0.562022i \(0.189976\pi\)
\(684\) 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 \(-0.720309\pi\)
0.638172 0.769894i \(-0.279691\pi\)
\(710\) 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 \(-0.370551\pi\)
0.395559 + 0.918440i \(0.370551\pi\)
\(720\) 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 0.401350 0.915925i \(-0.368541\pi\)
0.915925 0.401350i \(-0.131459\pi\)
\(728\) −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 \(-0.0547013\pi\)
−0.171005 + 0.985270i \(0.554701\pi\)
\(734\) −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 \(0.0588813\pi\)
−0.982940 + 0.183928i \(0.941119\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 29.3939 29.3939i 1.07908 1.07908i
\(743\) −20.7846 + 20.7846i −0.762513 + 0.762513i −0.976776 0.214263i \(-0.931265\pi\)
0.214263 + 0.976776i \(0.431265\pi\)
\(744\) 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 \(-0.884189\pi\)
0.355857 + 0.934540i \(0.384189\pi\)
\(758\) 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 \(0.175144\pi\)
−0.852404 + 0.522883i \(0.824856\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −63.6867 + 63.6867i −2.29214 + 2.29214i
\(773\) −27.7128 + 27.7128i −0.996761 + 0.996761i −0.999995 0.00323417i \(-0.998971\pi\)
0.00323417 + 0.999995i \(0.498971\pi\)
\(774\) 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 \(-0.574141\pi\)
0.972996 + 0.230820i \(0.0741409\pi\)
\(788\) 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 0.765793 0.643088i