Properties

Label 1800.2.k.j.901.1
Level $1800$
Weight $2$
Character 1800.901
Analytic conductor $14.373$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.k (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3730723638\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 901.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1800.901
Dual form 1800.2.k.j.901.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} -0.732051 q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} -0.732051 q^{7} +(-2.00000 - 2.00000i) q^{8} +2.00000i q^{11} +3.46410i q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 + 3.46410i) q^{16} +3.46410 q^{17} +0.535898i q^{19} +(0.732051 - 2.73205i) q^{22} -6.19615 q^{23} +(1.26795 - 4.73205i) q^{26} +(-1.26795 - 0.732051i) q^{28} -6.92820i q^{29} -5.46410 q^{31} +(-1.46410 - 5.46410i) q^{32} +(-4.73205 - 1.26795i) q^{34} +2.00000i q^{37} +(0.196152 - 0.732051i) q^{38} -1.46410 q^{41} +5.26795i q^{43} +(-2.00000 + 3.46410i) q^{44} +(8.46410 + 2.26795i) q^{46} +3.26795 q^{47} -6.46410 q^{49} +(-3.46410 + 6.00000i) q^{52} +11.4641i q^{53} +(1.46410 + 1.46410i) q^{56} +(-2.53590 + 9.46410i) q^{58} +7.46410i q^{59} -8.92820i q^{61} +(7.46410 + 2.00000i) q^{62} +8.00000i q^{64} -10.7321i q^{67} +(6.00000 + 3.46410i) q^{68} -5.46410 q^{71} -7.46410 q^{73} +(0.732051 - 2.73205i) q^{74} +(-0.535898 + 0.928203i) q^{76} -1.46410i q^{77} -1.07180 q^{79} +(2.00000 + 0.535898i) q^{82} +1.26795i q^{83} +(1.92820 - 7.19615i) q^{86} +(4.00000 - 4.00000i) q^{88} -8.92820 q^{89} -2.53590i q^{91} +(-10.7321 - 6.19615i) q^{92} +(-4.46410 - 1.19615i) q^{94} +14.3923 q^{97} +(8.83013 + 2.36603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 4q^{7} - 8q^{8} + O(q^{10}) \) \( 4q - 2q^{2} + 4q^{7} - 8q^{8} + 4q^{14} + 8q^{16} - 4q^{22} - 4q^{23} + 12q^{26} - 12q^{28} - 8q^{31} + 8q^{32} - 12q^{34} - 20q^{38} + 8q^{41} - 8q^{44} + 20q^{46} + 20q^{47} - 12q^{49} - 8q^{56} - 24q^{58} + 16q^{62} + 24q^{68} - 8q^{71} - 16q^{73} - 4q^{74} - 16q^{76} - 32q^{79} + 8q^{82} - 20q^{86} + 16q^{88} - 8q^{89} - 36q^{92} - 4q^{94} + 16q^{97} + 18q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1001\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 0.366025i −0.965926 0.258819i
\(3\) 0 0
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.732051 −0.276689 −0.138345 0.990384i \(-0.544178\pi\)
−0.138345 + 0.990384i \(0.544178\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000i 0.603023i 0.953463 + 0.301511i \(0.0974911\pi\)
−0.953463 + 0.301511i \(0.902509\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) 1.00000 + 0.267949i 0.267261 + 0.0716124i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 3.46410 0.840168 0.420084 0.907485i \(-0.362001\pi\)
0.420084 + 0.907485i \(0.362001\pi\)
\(18\) 0 0
\(19\) 0.535898i 0.122944i 0.998109 + 0.0614718i \(0.0195794\pi\)
−0.998109 + 0.0614718i \(0.980421\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.732051 2.73205i 0.156074 0.582475i
\(23\) −6.19615 −1.29199 −0.645994 0.763343i \(-0.723557\pi\)
−0.645994 + 0.763343i \(0.723557\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.26795 4.73205i 0.248665 0.928032i
\(27\) 0 0
\(28\) −1.26795 0.732051i −0.239620 0.138345i
\(29\) 6.92820i 1.28654i −0.765641 0.643268i \(-0.777578\pi\)
0.765641 0.643268i \(-0.222422\pi\)
\(30\) 0 0
\(31\) −5.46410 −0.981382 −0.490691 0.871334i \(-0.663256\pi\)
−0.490691 + 0.871334i \(0.663256\pi\)
\(32\) −1.46410 5.46410i −0.258819 0.965926i
\(33\) 0 0
\(34\) −4.73205 1.26795i −0.811540 0.217451i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 0.196152 0.732051i 0.0318201 0.118754i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.46410 −0.228654 −0.114327 0.993443i \(-0.536471\pi\)
−0.114327 + 0.993443i \(0.536471\pi\)
\(42\) 0 0
\(43\) 5.26795i 0.803355i 0.915781 + 0.401677i \(0.131573\pi\)
−0.915781 + 0.401677i \(0.868427\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 0 0
\(46\) 8.46410 + 2.26795i 1.24796 + 0.334391i
\(47\) 3.26795 0.476679 0.238340 0.971182i \(-0.423397\pi\)
0.238340 + 0.971182i \(0.423397\pi\)
\(48\) 0 0
\(49\) −6.46410 −0.923443
\(50\) 0 0
\(51\) 0 0
\(52\) −3.46410 + 6.00000i −0.480384 + 0.832050i
\(53\) 11.4641i 1.57472i 0.616496 + 0.787358i \(0.288551\pi\)
−0.616496 + 0.787358i \(0.711449\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.46410 + 1.46410i 0.195649 + 0.195649i
\(57\) 0 0
\(58\) −2.53590 + 9.46410i −0.332980 + 1.24270i
\(59\) 7.46410i 0.971743i 0.874030 + 0.485872i \(0.161498\pi\)
−0.874030 + 0.485872i \(0.838502\pi\)
\(60\) 0 0
\(61\) 8.92820i 1.14314i −0.820554 0.571570i \(-0.806335\pi\)
0.820554 0.571570i \(-0.193665\pi\)
\(62\) 7.46410 + 2.00000i 0.947942 + 0.254000i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 10.7321i 1.31113i −0.755139 0.655564i \(-0.772431\pi\)
0.755139 0.655564i \(-0.227569\pi\)
\(68\) 6.00000 + 3.46410i 0.727607 + 0.420084i
\(69\) 0 0
\(70\) 0 0
\(71\) −5.46410 −0.648470 −0.324235 0.945977i \(-0.605107\pi\)
−0.324235 + 0.945977i \(0.605107\pi\)
\(72\) 0 0
\(73\) −7.46410 −0.873607 −0.436804 0.899557i \(-0.643889\pi\)
−0.436804 + 0.899557i \(0.643889\pi\)
\(74\) 0.732051 2.73205i 0.0850992 0.317594i
\(75\) 0 0
\(76\) −0.535898 + 0.928203i −0.0614718 + 0.106472i
\(77\) 1.46410i 0.166850i
\(78\) 0 0
\(79\) −1.07180 −0.120587 −0.0602933 0.998181i \(-0.519204\pi\)
−0.0602933 + 0.998181i \(0.519204\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 2.00000 + 0.535898i 0.220863 + 0.0591801i
\(83\) 1.26795i 0.139176i 0.997576 + 0.0695878i \(0.0221684\pi\)
−0.997576 + 0.0695878i \(0.977832\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.92820 7.19615i 0.207924 0.775981i
\(87\) 0 0
\(88\) 4.00000 4.00000i 0.426401 0.426401i
\(89\) −8.92820 −0.946388 −0.473194 0.880958i \(-0.656899\pi\)
−0.473194 + 0.880958i \(0.656899\pi\)
\(90\) 0 0
\(91\) 2.53590i 0.265834i
\(92\) −10.7321 6.19615i −1.11889 0.645994i
\(93\) 0 0
\(94\) −4.46410 1.19615i −0.460437 0.123374i
\(95\) 0 0
\(96\) 0 0
\(97\) 14.3923 1.46132 0.730659 0.682743i \(-0.239213\pi\)
0.730659 + 0.682743i \(0.239213\pi\)
\(98\) 8.83013 + 2.36603i 0.891978 + 0.239005i
\(99\) 0 0
\(100\) 0 0
\(101\) 2.92820i 0.291367i −0.989331 0.145684i \(-0.953462\pi\)
0.989331 0.145684i \(-0.0465381\pi\)
\(102\) 0 0
\(103\) −15.6603 −1.54305 −0.771525 0.636199i \(-0.780506\pi\)
−0.771525 + 0.636199i \(0.780506\pi\)
\(104\) 6.92820 6.92820i 0.679366 0.679366i
\(105\) 0 0
\(106\) 4.19615 15.6603i 0.407566 1.52106i
\(107\) 2.73205i 0.264117i 0.991242 + 0.132059i \(0.0421587\pi\)
−0.991242 + 0.132059i \(0.957841\pi\)
\(108\) 0 0
\(109\) 16.9282i 1.62143i 0.585443 + 0.810714i \(0.300921\pi\)
−0.585443 + 0.810714i \(0.699079\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.46410 2.53590i −0.138345 0.239620i
\(113\) −12.9282 −1.21618 −0.608092 0.793867i \(-0.708065\pi\)
−0.608092 + 0.793867i \(0.708065\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.92820 12.0000i 0.643268 1.11417i
\(117\) 0 0
\(118\) 2.73205 10.1962i 0.251506 0.938632i
\(119\) −2.53590 −0.232465
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) −3.26795 + 12.1962i −0.295866 + 1.10419i
\(123\) 0 0
\(124\) −9.46410 5.46410i −0.849901 0.490691i
\(125\) 0 0
\(126\) 0 0
\(127\) −16.7321 −1.48473 −0.742365 0.669996i \(-0.766296\pi\)
−0.742365 + 0.669996i \(0.766296\pi\)
\(128\) 2.92820 10.9282i 0.258819 0.965926i
\(129\) 0 0
\(130\) 0 0
\(131\) 19.8564i 1.73486i 0.497557 + 0.867431i \(0.334230\pi\)
−0.497557 + 0.867431i \(0.665770\pi\)
\(132\) 0 0
\(133\) 0.392305i 0.0340171i
\(134\) −3.92820 + 14.6603i −0.339345 + 1.26645i
\(135\) 0 0
\(136\) −6.92820 6.92820i −0.594089 0.594089i
\(137\) 4.92820 0.421045 0.210522 0.977589i \(-0.432484\pi\)
0.210522 + 0.977589i \(0.432484\pi\)
\(138\) 0 0
\(139\) 0.535898i 0.0454543i −0.999742 0.0227272i \(-0.992765\pi\)
0.999742 0.0227272i \(-0.00723490\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.46410 + 2.00000i 0.626373 + 0.167836i
\(143\) −6.92820 −0.579365
\(144\) 0 0
\(145\) 0 0
\(146\) 10.1962 + 2.73205i 0.843840 + 0.226106i
\(147\) 0 0
\(148\) −2.00000 + 3.46410i −0.164399 + 0.284747i
\(149\) 7.85641i 0.643622i 0.946804 + 0.321811i \(0.104292\pi\)
−0.946804 + 0.321811i \(0.895708\pi\)
\(150\) 0 0
\(151\) −12.3923 −1.00847 −0.504236 0.863566i \(-0.668226\pi\)
−0.504236 + 0.863566i \(0.668226\pi\)
\(152\) 1.07180 1.07180i 0.0869342 0.0869342i
\(153\) 0 0
\(154\) −0.535898 + 2.00000i −0.0431839 + 0.161165i
\(155\) 0 0
\(156\) 0 0
\(157\) 3.07180i 0.245156i 0.992459 + 0.122578i \(0.0391162\pi\)
−0.992459 + 0.122578i \(0.960884\pi\)
\(158\) 1.46410 + 0.392305i 0.116478 + 0.0312101i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.53590 0.357479
\(162\) 0 0
\(163\) 0.196152i 0.0153638i 0.999970 + 0.00768192i \(0.00244526\pi\)
−0.999970 + 0.00768192i \(0.997555\pi\)
\(164\) −2.53590 1.46410i −0.198020 0.114327i
\(165\) 0 0
\(166\) 0.464102 1.73205i 0.0360213 0.134433i
\(167\) −9.80385 −0.758645 −0.379322 0.925265i \(-0.623843\pi\)
−0.379322 + 0.925265i \(0.623843\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) −5.26795 + 9.12436i −0.401677 + 0.695726i
\(173\) 2.00000i 0.152057i 0.997106 + 0.0760286i \(0.0242240\pi\)
−0.997106 + 0.0760286i \(0.975776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.92820 + 4.00000i −0.522233 + 0.301511i
\(177\) 0 0
\(178\) 12.1962 + 3.26795i 0.914140 + 0.244943i
\(179\) 8.53590i 0.638003i 0.947754 + 0.319002i \(0.103348\pi\)
−0.947754 + 0.319002i \(0.896652\pi\)
\(180\) 0 0
\(181\) 16.0000i 1.18927i 0.803996 + 0.594635i \(0.202704\pi\)
−0.803996 + 0.594635i \(0.797296\pi\)
\(182\) −0.928203 + 3.46410i −0.0688030 + 0.256776i
\(183\) 0 0
\(184\) 12.3923 + 12.3923i 0.913573 + 0.913573i
\(185\) 0 0
\(186\) 0 0
\(187\) 6.92820i 0.506640i
\(188\) 5.66025 + 3.26795i 0.412816 + 0.238340i
\(189\) 0 0
\(190\) 0 0
\(191\) −15.3205 −1.10855 −0.554277 0.832333i \(-0.687005\pi\)
−0.554277 + 0.832333i \(0.687005\pi\)
\(192\) 0 0
\(193\) −0.535898 −0.0385748 −0.0192874 0.999814i \(-0.506140\pi\)
−0.0192874 + 0.999814i \(0.506140\pi\)
\(194\) −19.6603 5.26795i −1.41152 0.378217i
\(195\) 0 0
\(196\) −11.1962 6.46410i −0.799725 0.461722i
\(197\) 19.4641i 1.38676i −0.720572 0.693380i \(-0.756121\pi\)
0.720572 0.693380i \(-0.243879\pi\)
\(198\) 0 0
\(199\) −1.85641 −0.131597 −0.0657986 0.997833i \(-0.520959\pi\)
−0.0657986 + 0.997833i \(0.520959\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −1.07180 + 4.00000i −0.0754114 + 0.281439i
\(203\) 5.07180i 0.355970i
\(204\) 0 0
\(205\) 0 0
\(206\) 21.3923 + 5.73205i 1.49047 + 0.399371i
\(207\) 0 0
\(208\) −12.0000 + 6.92820i −0.832050 + 0.480384i
\(209\) −1.07180 −0.0741377
\(210\) 0 0
\(211\) 26.7846i 1.84393i 0.387275 + 0.921964i \(0.373416\pi\)
−0.387275 + 0.921964i \(0.626584\pi\)
\(212\) −11.4641 + 19.8564i −0.787358 + 1.36374i
\(213\) 0 0
\(214\) 1.00000 3.73205i 0.0683586 0.255118i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 6.19615 23.1244i 0.419656 1.56618i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000i 0.807207i
\(222\) 0 0
\(223\) 5.80385 0.388654 0.194327 0.980937i \(-0.437748\pi\)
0.194327 + 0.980937i \(0.437748\pi\)
\(224\) 1.07180 + 4.00000i 0.0716124 + 0.267261i
\(225\) 0 0
\(226\) 17.6603 + 4.73205i 1.17474 + 0.314771i
\(227\) 10.0526i 0.667212i 0.942713 + 0.333606i \(0.108265\pi\)
−0.942713 + 0.333606i \(0.891735\pi\)
\(228\) 0 0
\(229\) 4.00000i 0.264327i −0.991228 0.132164i \(-0.957808\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −13.8564 + 13.8564i −0.909718 + 0.909718i
\(233\) −5.32051 −0.348558 −0.174279 0.984696i \(-0.555759\pi\)
−0.174279 + 0.984696i \(0.555759\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −7.46410 + 12.9282i −0.485872 + 0.841554i
\(237\) 0 0
\(238\) 3.46410 + 0.928203i 0.224544 + 0.0601665i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 16.3923 1.05592 0.527961 0.849269i \(-0.322957\pi\)
0.527961 + 0.849269i \(0.322957\pi\)
\(242\) −9.56218 2.56218i −0.614680 0.164703i
\(243\) 0 0
\(244\) 8.92820 15.4641i 0.571570 0.989988i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.85641 −0.118120
\(248\) 10.9282 + 10.9282i 0.693942 + 0.693942i
\(249\) 0 0
\(250\) 0 0
\(251\) 24.9282i 1.57345i −0.617301 0.786727i \(-0.711774\pi\)
0.617301 0.786727i \(-0.288226\pi\)
\(252\) 0 0
\(253\) 12.3923i 0.779098i
\(254\) 22.8564 + 6.12436i 1.43414 + 0.384276i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) 1.46410i 0.0909748i
\(260\) 0 0
\(261\) 0 0
\(262\) 7.26795 27.1244i 0.449015 1.67575i
\(263\) −11.6603 −0.719002 −0.359501 0.933145i \(-0.617053\pi\)
−0.359501 + 0.933145i \(0.617053\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.143594 + 0.535898i −0.00880428 + 0.0328580i
\(267\) 0 0
\(268\) 10.7321 18.5885i 0.655564 1.13547i
\(269\) 8.92820i 0.544362i 0.962246 + 0.272181i \(0.0877450\pi\)
−0.962246 + 0.272181i \(0.912255\pi\)
\(270\) 0 0
\(271\) −19.3205 −1.17364 −0.586819 0.809718i \(-0.699620\pi\)
−0.586819 + 0.809718i \(0.699620\pi\)
\(272\) 6.92820 + 12.0000i 0.420084 + 0.727607i
\(273\) 0 0
\(274\) −6.73205 1.80385i −0.406698 0.108974i
\(275\) 0 0
\(276\) 0 0
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) −0.196152 + 0.732051i −0.0117644 + 0.0439055i
\(279\) 0 0
\(280\) 0 0
\(281\) −10.5359 −0.628519 −0.314260 0.949337i \(-0.601756\pi\)
−0.314260 + 0.949337i \(0.601756\pi\)
\(282\) 0 0
\(283\) 9.66025i 0.574242i 0.957894 + 0.287121i \(0.0926983\pi\)
−0.957894 + 0.287121i \(0.907302\pi\)
\(284\) −9.46410 5.46410i −0.561591 0.324235i
\(285\) 0 0
\(286\) 9.46410 + 2.53590i 0.559624 + 0.149951i
\(287\) 1.07180 0.0632662
\(288\) 0 0
\(289\) −5.00000 −0.294118
\(290\) 0 0
\(291\) 0 0
\(292\) −12.9282 7.46410i −0.756566 0.436804i
\(293\) 15.8564i 0.926341i −0.886269 0.463171i \(-0.846712\pi\)
0.886269 0.463171i \(-0.153288\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.00000 4.00000i 0.232495 0.232495i
\(297\) 0 0
\(298\) 2.87564 10.7321i 0.166582 0.621691i
\(299\) 21.4641i 1.24130i
\(300\) 0 0
\(301\) 3.85641i 0.222280i
\(302\) 16.9282 + 4.53590i 0.974109 + 0.261012i
\(303\) 0 0
\(304\) −1.85641 + 1.07180i −0.106472 + 0.0614718i
\(305\) 0 0
\(306\) 0 0
\(307\) 24.9808i 1.42573i 0.701303 + 0.712864i \(0.252602\pi\)
−0.701303 + 0.712864i \(0.747398\pi\)
\(308\) 1.46410 2.53590i 0.0834249 0.144496i
\(309\) 0 0
\(310\) 0 0
\(311\) −31.3205 −1.77602 −0.888012 0.459821i \(-0.847914\pi\)
−0.888012 + 0.459821i \(0.847914\pi\)
\(312\) 0 0
\(313\) 4.14359 0.234210 0.117105 0.993120i \(-0.462639\pi\)
0.117105 + 0.993120i \(0.462639\pi\)
\(314\) 1.12436 4.19615i 0.0634511 0.236803i
\(315\) 0 0
\(316\) −1.85641 1.07180i −0.104431 0.0602933i
\(317\) 8.53590i 0.479424i 0.970844 + 0.239712i \(0.0770530\pi\)
−0.970844 + 0.239712i \(0.922947\pi\)
\(318\) 0 0
\(319\) 13.8564 0.775810
\(320\) 0 0
\(321\) 0 0
\(322\) −6.19615 1.66025i −0.345298 0.0925223i
\(323\) 1.85641i 0.103293i
\(324\) 0 0
\(325\) 0 0
\(326\) 0.0717968 0.267949i 0.00397646 0.0148403i
\(327\) 0 0
\(328\) 2.92820 + 2.92820i 0.161683 + 0.161683i
\(329\) −2.39230 −0.131892
\(330\) 0 0
\(331\) 14.0000i 0.769510i −0.923019 0.384755i \(-0.874286\pi\)
0.923019 0.384755i \(-0.125714\pi\)
\(332\) −1.26795 + 2.19615i −0.0695878 + 0.120530i
\(333\) 0 0
\(334\) 13.3923 + 3.58846i 0.732794 + 0.196352i
\(335\) 0 0
\(336\) 0 0
\(337\) 19.8564 1.08165 0.540824 0.841136i \(-0.318113\pi\)
0.540824 + 0.841136i \(0.318113\pi\)
\(338\) −1.36603 0.366025i −0.0743020 0.0199092i
\(339\) 0 0
\(340\) 0 0
\(341\) 10.9282i 0.591795i
\(342\) 0 0
\(343\) 9.85641 0.532196
\(344\) 10.5359 10.5359i 0.568058 0.568058i
\(345\) 0 0
\(346\) 0.732051 2.73205i 0.0393553 0.146876i
\(347\) 1.66025i 0.0891271i −0.999007 0.0445636i \(-0.985810\pi\)
0.999007 0.0445636i \(-0.0141897\pi\)
\(348\) 0 0
\(349\) 28.0000i 1.49881i −0.662114 0.749403i \(-0.730341\pi\)
0.662114 0.749403i \(-0.269659\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.9282 2.92820i 0.582475 0.156074i
\(353\) 12.9282 0.688099 0.344049 0.938952i \(-0.388201\pi\)
0.344049 + 0.938952i \(0.388201\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −15.4641 8.92820i −0.819596 0.473194i
\(357\) 0 0
\(358\) 3.12436 11.6603i 0.165127 0.616264i
\(359\) −18.9282 −0.998992 −0.499496 0.866316i \(-0.666482\pi\)
−0.499496 + 0.866316i \(0.666482\pi\)
\(360\) 0 0
\(361\) 18.7128 0.984885
\(362\) 5.85641 21.8564i 0.307806 1.14875i
\(363\) 0 0
\(364\) 2.53590 4.39230i 0.132917 0.230219i
\(365\) 0 0
\(366\) 0 0
\(367\) −2.87564 −0.150107 −0.0750537 0.997179i \(-0.523913\pi\)
−0.0750537 + 0.997179i \(0.523913\pi\)
\(368\) −12.3923 21.4641i −0.645994 1.11889i
\(369\) 0 0
\(370\) 0 0
\(371\) 8.39230i 0.435707i
\(372\) 0 0
\(373\) 25.7128i 1.33136i 0.746238 + 0.665679i \(0.231858\pi\)
−0.746238 + 0.665679i \(0.768142\pi\)
\(374\) 2.53590 9.46410i 0.131128 0.489377i
\(375\) 0 0
\(376\) −6.53590 6.53590i −0.337063 0.337063i
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 36.2487i 1.86197i −0.365056 0.930986i \(-0.618950\pi\)
0.365056 0.930986i \(-0.381050\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 20.9282 + 5.60770i 1.07078 + 0.286915i
\(383\) 21.1244 1.07940 0.539702 0.841856i \(-0.318537\pi\)
0.539702 + 0.841856i \(0.318537\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.732051 + 0.196152i 0.0372604 + 0.00998390i
\(387\) 0 0
\(388\) 24.9282 + 14.3923i 1.26554 + 0.730659i
\(389\) 6.78461i 0.343993i −0.985098 0.171997i \(-0.944978\pi\)
0.985098 0.171997i \(-0.0550218\pi\)
\(390\) 0 0
\(391\) −21.4641 −1.08549
\(392\) 12.9282 + 12.9282i 0.652973 + 0.652973i
\(393\) 0 0
\(394\) −7.12436 + 26.5885i −0.358920 + 1.33951i
\(395\) 0 0
\(396\) 0 0
\(397\) 32.2487i 1.61852i −0.587453 0.809258i \(-0.699869\pi\)
0.587453 0.809258i \(-0.300131\pi\)
\(398\) 2.53590 + 0.679492i 0.127113 + 0.0340599i
\(399\) 0 0
\(400\) 0 0
\(401\) 7.85641 0.392330 0.196165 0.980571i \(-0.437151\pi\)
0.196165 + 0.980571i \(0.437151\pi\)
\(402\) 0 0
\(403\) 18.9282i 0.942881i
\(404\) 2.92820 5.07180i 0.145684 0.252331i
\(405\) 0 0
\(406\) 1.85641 6.92820i 0.0921319 0.343841i
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −11.3205 −0.559763 −0.279882 0.960035i \(-0.590295\pi\)
−0.279882 + 0.960035i \(0.590295\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −27.1244 15.6603i −1.33632 0.771525i
\(413\) 5.46410i 0.268871i
\(414\) 0 0
\(415\) 0 0
\(416\) 18.9282 5.07180i 0.928032 0.248665i
\(417\) 0 0
\(418\) 1.46410 + 0.392305i 0.0716116 + 0.0191883i
\(419\) 18.3923i 0.898523i −0.893400 0.449261i \(-0.851687\pi\)
0.893400 0.449261i \(-0.148313\pi\)
\(420\) 0 0
\(421\) 0.143594i 0.00699832i 0.999994 + 0.00349916i \(0.00111382\pi\)
−0.999994 + 0.00349916i \(0.998886\pi\)
\(422\) 9.80385 36.5885i 0.477244 1.78110i
\(423\) 0 0
\(424\) 22.9282 22.9282i 1.11349 1.11349i
\(425\) 0 0
\(426\) 0 0
\(427\) 6.53590i 0.316294i
\(428\) −2.73205 + 4.73205i −0.132059 + 0.228732i
\(429\) 0 0
\(430\) 0 0
\(431\) 21.4641 1.03389 0.516945 0.856019i \(-0.327069\pi\)
0.516945 + 0.856019i \(0.327069\pi\)
\(432\) 0 0
\(433\) 19.4641 0.935385 0.467693 0.883891i \(-0.345085\pi\)
0.467693 + 0.883891i \(0.345085\pi\)
\(434\) −5.46410 1.46410i −0.262285 0.0702791i
\(435\) 0 0
\(436\) −16.9282 + 29.3205i −0.810714 + 1.40420i
\(437\) 3.32051i 0.158841i
\(438\) 0 0
\(439\) 40.7846 1.94654 0.973272 0.229657i \(-0.0737605\pi\)
0.973272 + 0.229657i \(0.0737605\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.39230 16.3923i 0.208921 0.779702i
\(443\) 20.9808i 0.996826i 0.866940 + 0.498413i \(0.166084\pi\)
−0.866940 + 0.498413i \(0.833916\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −7.92820 2.12436i −0.375411 0.100591i
\(447\) 0 0
\(448\) 5.85641i 0.276689i
\(449\) 23.3205 1.10056 0.550281 0.834979i \(-0.314520\pi\)
0.550281 + 0.834979i \(0.314520\pi\)
\(450\) 0 0
\(451\) 2.92820i 0.137884i
\(452\) −22.3923 12.9282i −1.05325 0.608092i
\(453\) 0 0
\(454\) 3.67949 13.7321i 0.172687 0.644477i
\(455\) 0 0
\(456\) 0 0
\(457\) 26.7846 1.25293 0.626466 0.779449i \(-0.284501\pi\)
0.626466 + 0.779449i \(0.284501\pi\)
\(458\) −1.46410 + 5.46410i −0.0684130 + 0.255321i
\(459\) 0 0
\(460\) 0 0
\(461\) 10.9282i 0.508977i 0.967076 + 0.254489i \(0.0819071\pi\)
−0.967076 + 0.254489i \(0.918093\pi\)
\(462\) 0 0
\(463\) 11.2679 0.523666 0.261833 0.965113i \(-0.415673\pi\)
0.261833 + 0.965113i \(0.415673\pi\)
\(464\) 24.0000 13.8564i 1.11417 0.643268i
\(465\) 0 0
\(466\) 7.26795 + 1.94744i 0.336681 + 0.0902135i
\(467\) 25.6603i 1.18741i −0.804681 0.593707i \(-0.797664\pi\)
0.804681 0.593707i \(-0.202336\pi\)
\(468\) 0 0
\(469\) 7.85641i 0.362775i
\(470\) 0 0
\(471\) 0 0
\(472\) 14.9282 14.9282i 0.687126 0.687126i
\(473\) −10.5359 −0.484441
\(474\) 0 0
\(475\) 0 0
\(476\) −4.39230 2.53590i −0.201321 0.116233i
\(477\) 0 0
\(478\) −27.3205 7.32051i −1.24961 0.334832i
\(479\) −5.85641 −0.267586 −0.133793 0.991009i \(-0.542716\pi\)
−0.133793 + 0.991009i \(0.542716\pi\)
\(480\) 0 0
\(481\) −6.92820 −0.315899
\(482\) −22.3923 6.00000i −1.01994 0.273293i
\(483\) 0 0
\(484\) 12.1244 + 7.00000i 0.551107 + 0.318182i
\(485\) 0 0
\(486\) 0 0
\(487\) −6.58846 −0.298551 −0.149276 0.988796i \(-0.547694\pi\)
−0.149276 + 0.988796i \(0.547694\pi\)
\(488\) −17.8564 + 17.8564i −0.808322 + 0.808322i
\(489\) 0 0
\(490\) 0 0
\(491\) 16.9282i 0.763959i 0.924171 + 0.381980i \(0.124758\pi\)
−0.924171 + 0.381980i \(0.875242\pi\)
\(492\) 0 0
\(493\) 24.0000i 1.08091i
\(494\) 2.53590 + 0.679492i 0.114095 + 0.0305718i
\(495\) 0 0
\(496\) −10.9282 18.9282i −0.490691 0.849901i
\(497\) 4.00000 0.179425
\(498\) 0 0
\(499\) 31.4641i 1.40853i 0.709939 + 0.704263i \(0.248723\pi\)
−0.709939 + 0.704263i \(0.751277\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −9.12436 + 34.0526i −0.407240 + 1.51984i
\(503\) −0.339746 −0.0151485 −0.00757426 0.999971i \(-0.502411\pi\)
−0.00757426 + 0.999971i \(0.502411\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.53590 + 16.9282i −0.201645 + 0.752550i
\(507\) 0 0
\(508\) −28.9808 16.7321i −1.28581 0.742365i
\(509\) 1.85641i 0.0822838i 0.999153 + 0.0411419i \(0.0130996\pi\)
−0.999153 + 0.0411419i \(0.986900\pi\)
\(510\) 0 0
\(511\) 5.46410 0.241718
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 0 0
\(514\) 2.73205 + 0.732051i 0.120506 + 0.0322894i
\(515\) 0 0
\(516\) 0 0
\(517\) 6.53590i 0.287448i
\(518\) −0.535898 + 2.00000i −0.0235460 + 0.0878750i
\(519\) 0 0
\(520\) 0 0
\(521\) 43.8564 1.92138 0.960692 0.277616i \(-0.0895444\pi\)
0.960692 + 0.277616i \(0.0895444\pi\)
\(522\) 0 0
\(523\) 11.8038i 0.516146i 0.966125 + 0.258073i \(0.0830875\pi\)
−0.966125 + 0.258073i \(0.916912\pi\)
\(524\) −19.8564 + 34.3923i −0.867431 + 1.50243i
\(525\) 0 0
\(526\) 15.9282 + 4.26795i 0.694503 + 0.186091i
\(527\) −18.9282 −0.824525
\(528\) 0 0
\(529\) 15.3923 0.669231
\(530\) 0 0
\(531\) 0 0
\(532\) 0.392305 0.679492i 0.0170086 0.0294597i
\(533\) 5.07180i 0.219684i
\(534\) 0 0
\(535\) 0 0
\(536\) −21.4641 + 21.4641i −0.927108 + 0.927108i
\(537\) 0 0
\(538\) 3.26795 12.1962i 0.140891 0.525813i
\(539\) 12.9282i 0.556857i
\(540\) 0 0
\(541\) 26.9282i 1.15773i −0.815422 0.578867i \(-0.803495\pi\)
0.815422 0.578867i \(-0.196505\pi\)
\(542\) 26.3923 + 7.07180i 1.13365 + 0.303760i
\(543\) 0 0
\(544\) −5.07180 18.9282i −0.217451 0.811540i
\(545\) 0 0
\(546\) 0 0
\(547\) 33.2679i 1.42243i −0.702972 0.711217i \(-0.748144\pi\)
0.702972 0.711217i \(-0.251856\pi\)
\(548\) 8.53590 + 4.92820i 0.364636 + 0.210522i
\(549\) 0 0
\(550\) 0 0
\(551\) 3.71281 0.158171
\(552\) 0 0
\(553\) 0.784610 0.0333650
\(554\) −0.732051 + 2.73205i −0.0311019 + 0.116074i
\(555\) 0 0
\(556\) 0.535898 0.928203i 0.0227272 0.0393646i
\(557\) 14.7846i 0.626444i 0.949680 + 0.313222i \(0.101408\pi\)
−0.949680 + 0.313222i \(0.898592\pi\)
\(558\) 0 0
\(559\) −18.2487 −0.771838
\(560\) 0 0
\(561\) 0 0
\(562\) 14.3923 + 3.85641i 0.607103 + 0.162673i
\(563\) 22.0526i 0.929405i −0.885467 0.464702i \(-0.846161\pi\)
0.885467 0.464702i \(-0.153839\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 3.53590 13.1962i 0.148625 0.554676i
\(567\) 0 0
\(568\) 10.9282 + 10.9282i 0.458537 + 0.458537i
\(569\) 13.4641 0.564445 0.282222 0.959349i \(-0.408928\pi\)
0.282222 + 0.959349i \(0.408928\pi\)
\(570\) 0 0
\(571\) 6.78461i 0.283927i 0.989872 + 0.141964i \(0.0453416\pi\)
−0.989872 + 0.141964i \(0.954658\pi\)
\(572\) −12.0000 6.92820i −0.501745 0.289683i
\(573\) 0 0
\(574\) −1.46410 0.392305i −0.0611104 0.0163745i
\(575\) 0 0
\(576\) 0 0
\(577\) −39.5692 −1.64729 −0.823644 0.567107i \(-0.808063\pi\)
−0.823644 + 0.567107i \(0.808063\pi\)
\(578\) 6.83013 + 1.83013i 0.284096 + 0.0761232i
\(579\) 0 0
\(580\) 0 0
\(581\) 0.928203i 0.0385084i
\(582\) 0 0
\(583\) −22.9282 −0.949589
\(584\) 14.9282 + 14.9282i 0.617733 + 0.617733i
\(585\) 0 0
\(586\) −5.80385 + 21.6603i −0.239755 + 0.894777i
\(587\) 3.80385i 0.157002i −0.996914 0.0785008i \(-0.974987\pi\)
0.996914 0.0785008i \(-0.0250133\pi\)
\(588\) 0 0
\(589\) 2.92820i 0.120655i
\(590\) 0 0
\(591\) 0 0
\(592\) −6.92820 + 4.00000i −0.284747 + 0.164399i
\(593\) 32.6410 1.34041 0.670203 0.742178i \(-0.266207\pi\)
0.670203 + 0.742178i \(0.266207\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −7.85641 + 13.6077i −0.321811 + 0.557393i
\(597\) 0 0
\(598\) −7.85641 + 29.3205i −0.321272 + 1.19900i
\(599\) 34.6410 1.41539 0.707697 0.706516i \(-0.249734\pi\)
0.707697 + 0.706516i \(0.249734\pi\)
\(600\) 0 0
\(601\) 18.5359 0.756095 0.378048 0.925786i \(-0.376596\pi\)
0.378048 + 0.925786i \(0.376596\pi\)
\(602\) −1.41154 + 5.26795i −0.0575302 + 0.214706i
\(603\) 0 0
\(604\) −21.4641 12.3923i −0.873362 0.504236i
\(605\) 0 0
\(606\) 0 0
\(607\) −30.9808 −1.25747 −0.628735 0.777619i \(-0.716427\pi\)
−0.628735 + 0.777619i \(0.716427\pi\)
\(608\) 2.92820 0.784610i 0.118754 0.0318201i
\(609\) 0 0
\(610\) 0 0
\(611\) 11.3205i 0.457979i
\(612\) 0 0
\(613\) 26.3923i 1.06598i −0.846123 0.532988i \(-0.821069\pi\)
0.846123 0.532988i \(-0.178931\pi\)
\(614\) 9.14359 34.1244i 0.369005 1.37715i
\(615\) 0 0
\(616\) −2.92820 + 2.92820i −0.117981 + 0.117981i
\(617\) −20.5359 −0.826744 −0.413372 0.910562i \(-0.635649\pi\)
−0.413372 + 0.910562i \(0.635649\pi\)
\(618\) 0 0
\(619\) 1.32051i 0.0530757i 0.999648 + 0.0265379i \(0.00844825\pi\)
−0.999648 + 0.0265379i \(0.991552\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 42.7846 + 11.4641i 1.71551 + 0.459669i
\(623\) 6.53590 0.261855
\(624\) 0 0
\(625\) 0 0
\(626\) −5.66025 1.51666i −0.226229 0.0606179i
\(627\) 0 0
\(628\) −3.07180 + 5.32051i −0.122578 + 0.212311i
\(629\) 6.92820i 0.276246i
\(630\) 0 0
\(631\) −23.3205 −0.928375 −0.464187 0.885737i \(-0.653654\pi\)
−0.464187 + 0.885737i \(0.653654\pi\)
\(632\) 2.14359 + 2.14359i 0.0852676 + 0.0852676i
\(633\) 0 0
\(634\) 3.12436 11.6603i 0.124084 0.463088i
\(635\) 0 0
\(636\) 0 0
\(637\) 22.3923i 0.887215i
\(638\) −18.9282 5.07180i −0.749375 0.200794i
\(639\) 0 0
\(640\) 0 0
\(641\) −0.392305 −0.0154951 −0.00774755 0.999970i \(-0.502466\pi\)
−0.00774755 + 0.999970i \(0.502466\pi\)
\(642\) 0 0
\(643\) 39.1244i 1.54291i −0.636281 0.771457i \(-0.719528\pi\)
0.636281 0.771457i \(-0.280472\pi\)
\(644\) 7.85641 + 4.53590i 0.309586 + 0.178739i
\(645\) 0 0
\(646\) 0.679492 2.53590i 0.0267343 0.0997736i
\(647\) 16.7321 0.657805 0.328902 0.944364i \(-0.393321\pi\)
0.328902 + 0.944364i \(0.393321\pi\)
\(648\) 0 0
\(649\) −14.9282 −0.585983
\(650\) 0 0
\(651\) 0 0
\(652\) −0.196152 + 0.339746i −0.00768192 + 0.0133055i
\(653\) 12.2487i 0.479329i 0.970856 + 0.239665i \(0.0770375\pi\)
−0.970856 + 0.239665i \(0.922963\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2.92820 5.07180i −0.114327 0.198020i
\(657\) 0 0
\(658\) 3.26795 + 0.875644i 0.127398 + 0.0341362i
\(659\) 17.3205i 0.674711i 0.941377 + 0.337356i \(0.109532\pi\)
−0.941377 + 0.337356i \(0.890468\pi\)
\(660\) 0 0
\(661\) 8.14359i 0.316749i −0.987379 0.158375i \(-0.949375\pi\)
0.987379 0.158375i \(-0.0506253\pi\)
\(662\) −5.12436 + 19.1244i −0.199164 + 0.743289i
\(663\) 0 0
\(664\) 2.53590 2.53590i 0.0984119 0.0984119i
\(665\) 0 0
\(666\) 0 0
\(667\) 42.9282i 1.66219i
\(668\) −16.9808 9.80385i −0.657005 0.379322i
\(669\) 0 0
\(670\) 0 0
\(671\) 17.8564 0.689339
\(672\) 0 0
\(673\) −12.5359 −0.483223 −0.241612 0.970373i \(-0.577676\pi\)
−0.241612 + 0.970373i \(0.577676\pi\)
\(674\) −27.1244 7.26795i −1.04479 0.279951i
\(675\) 0 0
\(676\) 1.73205 + 1.00000i 0.0666173 + 0.0384615i
\(677\) 17.6077i 0.676719i 0.941017 + 0.338359i \(0.109872\pi\)
−0.941017 + 0.338359i \(0.890128\pi\)
\(678\) 0 0
\(679\) −10.5359 −0.404331
\(680\) 0 0
\(681\) 0 0
\(682\) −4.00000 + 14.9282i −0.153168 + 0.571630i
\(683\) 16.9808i 0.649751i −0.945757 0.324875i \(-0.894678\pi\)
0.945757 0.324875i \(-0.105322\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −13.4641 3.60770i −0.514062 0.137742i
\(687\) 0 0
\(688\) −18.2487 + 10.5359i −0.695726 + 0.401677i
\(689\) −39.7128 −1.51294
\(690\) 0 0
\(691\) 18.0000i 0.684752i 0.939563 + 0.342376i \(0.111232\pi\)
−0.939563 + 0.342376i \(0.888768\pi\)
\(692\) −2.00000 + 3.46410i −0.0760286 + 0.131685i
\(693\) 0 0
\(694\) −0.607695 + 2.26795i −0.0230678 + 0.0860902i
\(695\) 0 0
\(696\) 0 0
\(697\) −5.07180 −0.192108
\(698\) −10.2487 + 38.2487i −0.387919 + 1.44774i
\(699\) 0 0
\(700\) 0 0
\(701\) 19.0718i 0.720332i −0.932888 0.360166i \(-0.882720\pi\)
0.932888 0.360166i \(-0.117280\pi\)
\(702\) 0 0
\(703\) −1.07180 −0.0404236
\(704\) −16.0000 −0.603023
\(705\) 0 0
\(706\) −17.6603 4.73205i −0.664652 0.178093i
\(707\) 2.14359i 0.0806181i
\(708\) 0 0
\(709\) 12.7846i 0.480136i −0.970756 0.240068i \(-0.922830\pi\)
0.970756 0.240068i \(-0.0771698\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 17.8564 + 17.8564i 0.669197 + 0.669197i
\(713\) 33.8564 1.26793
\(714\) 0 0
\(715\) 0 0
\(716\) −8.53590 + 14.7846i −0.319002 + 0.552527i
\(717\) 0 0
\(718\) 25.8564 + 6.92820i 0.964953 + 0.258558i
\(719\) 1.85641 0.0692323 0.0346161 0.999401i \(-0.488979\pi\)
0.0346161 + 0.999401i \(0.488979\pi\)
\(720\) 0 0
\(721\) 11.4641 0.426945
\(722\) −25.5622 6.84936i −0.951326 0.254907i
\(723\) 0 0
\(724\) −16.0000 + 27.7128i −0.594635 + 1.02994i
\(725\) 0 0
\(726\) 0 0
\(727\) 24.0526 0.892060 0.446030 0.895018i \(-0.352837\pi\)
0.446030 + 0.895018i \(0.352837\pi\)
\(728\) −5.07180 + 5.07180i −0.187973 + 0.187973i
\(729\) 0 0
\(730\) 0 0
\(731\) 18.2487i 0.674953i
\(732\) 0 0
\(733\) 35.0718i 1.29541i 0.761893 + 0.647703i \(0.224270\pi\)
−0.761893 + 0.647703i \(0.775730\pi\)
\(734\) 3.92820 + 1.05256i 0.144993 + 0.0388507i
\(735\) 0 0
\(736\) 9.07180 + 33.8564i 0.334391 + 1.24796i
\(737\) 21.4641 0.790640
\(738\) 0 0
\(739\) 29.3205i 1.07857i 0.842123 + 0.539286i \(0.181306\pi\)
−0.842123 + 0.539286i \(0.818694\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.07180 + 11.4641i −0.112769 + 0.420860i
\(743\) 10.9808 0.402845 0.201423 0.979504i \(-0.435444\pi\)
0.201423 + 0.979504i \(0.435444\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 9.41154 35.1244i 0.344581 1.28599i
\(747\) 0 0
\(748\) −6.92820 + 12.0000i −0.253320 + 0.438763i
\(749\) 2.00000i 0.0730784i
\(750\) 0 0
\(751\) 26.2487 0.957829 0.478915 0.877862i \(-0.341030\pi\)
0.478915 + 0.877862i \(0.341030\pi\)
\(752\) 6.53590 + 11.3205i 0.238340 + 0.412816i
\(753\) 0 0
\(754\) −32.7846 8.78461i −1.19395 0.319917i
\(755\) 0 0
\(756\) 0 0
\(757\) 19.0718i 0.693176i 0.938017 + 0.346588i \(0.112660\pi\)
−0.938017 + 0.346588i \(0.887340\pi\)
\(758\) −13.2679 + 49.5167i −0.481914 + 1.79853i
\(759\) 0 0
\(760\) 0 0
\(761\) 5.71281 0.207089 0.103545 0.994625i \(-0.466982\pi\)
0.103545 + 0.994625i \(0.466982\pi\)
\(762\) 0 0
\(763\) 12.3923i 0.448632i
\(764\) −26.5359 15.3205i −0.960035 0.554277i
\(765\) 0 0
\(766\) −28.8564 7.73205i −1.04262 0.279370i
\(767\) −25.8564 −0.933621
\(768\) 0 0
\(769\) 12.9282 0.466203 0.233101 0.972452i \(-0.425113\pi\)
0.233101 + 0.972452i \(0.425113\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.928203 0.535898i −0.0334068 0.0192874i
\(773\) 22.3923i 0.805395i −0.915333 0.402698i \(-0.868073\pi\)
0.915333 0.402698i \(-0.131927\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −28.7846 28.7846i −1.03331 1.03331i
\(777\) 0 0
\(778\) −2.48334 + 9.26795i −0.0890320 + 0.332272i
\(779\) 0.784610i 0.0281116i
\(780\) 0 0
\(781\) 10.9282i 0.391042i
\(782\) 29.3205 + 7.85641i 1.04850 + 0.280945i
\(783\) 0 0
\(784\) −12.9282 22.3923i −0.461722 0.799725i
\(785\) 0 0
\(786\) 0 0
\(787\) 16.5885i 0.591315i −0.955294 0.295657i \(-0.904461\pi\)
0.955294 0.295657i \(-0.0955387\pi\)
\(788\) 19.4641 33.7128i 0.693380 1.20097i
\(789\) 0 0
\(790\) 0 0
\(791\) 9.46410 0.336505
\(792\) 0 0
\(793\) 30.9282 1.09829
\(794\) −11.8038 + 44.0526i −0.418903 + 1.56337i
\(795\) 0 0
\(796\) −3.21539 1.85641i −0.113966 0.0657986i
\(797\) 50.1051i