Properties

Label 300.2.j.b.7.4
Level $300$
Weight $2$
Character 300.7
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.157351936.1
Defining polynomial: \(x^{8} + x^{4} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.4
Root \(1.28897 + 0.581861i\) of defining polynomial
Character \(\chi\) \(=\) 300.7
Dual form 300.2.j.b.43.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.28897 + 0.581861i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.32288 + 1.50000i) q^{4} +(0.500000 + 1.32288i) q^{6} +(1.41421 - 1.41421i) q^{7} +(0.832353 + 2.70318i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(1.28897 + 0.581861i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.32288 + 1.50000i) q^{4} +(0.500000 + 1.32288i) q^{6} +(1.41421 - 1.41421i) q^{7} +(0.832353 + 2.70318i) q^{8} +1.00000i q^{9} -5.29150i q^{11} +(-0.125246 + 1.99607i) q^{12} +(-3.74166 + 3.74166i) q^{13} +(2.64575 - 1.00000i) q^{14} +(-0.500000 + 3.96863i) q^{16} +(-0.581861 + 1.28897i) q^{18} -5.29150 q^{19} +2.00000 q^{21} +(3.07892 - 6.82058i) q^{22} +(2.82843 + 2.82843i) q^{23} +(-1.32288 + 2.50000i) q^{24} +(-7.00000 + 2.64575i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.99215 + 0.250492i) q^{28} -8.00000i q^{29} -5.29150i q^{31} +(-2.95367 + 4.82450i) q^{32} +(3.74166 - 3.74166i) q^{33} +(-1.50000 + 1.32288i) q^{36} +(3.74166 + 3.74166i) q^{37} +(-6.82058 - 3.07892i) q^{38} -5.29150 q^{39} -2.00000 q^{41} +(2.57794 + 1.16372i) q^{42} +(-5.65685 - 5.65685i) q^{43} +(7.93725 - 7.00000i) q^{44} +(2.00000 + 5.29150i) q^{46} +(-3.15980 + 2.45269i) q^{48} +3.00000i q^{49} +(-10.5622 - 0.662739i) q^{52} +(7.48331 - 7.48331i) q^{53} +(-1.32288 + 0.500000i) q^{54} +(5.00000 + 2.64575i) q^{56} +(-3.74166 - 3.74166i) q^{57} +(4.65489 - 10.3117i) q^{58} +5.29150 q^{59} +6.00000 q^{61} +(3.07892 - 6.82058i) q^{62} +(1.41421 + 1.41421i) q^{63} +(-6.61438 + 4.50000i) q^{64} +(7.00000 - 2.64575i) q^{66} +(-8.48528 + 8.48528i) q^{67} +4.00000i q^{69} +(-2.70318 + 0.832353i) q^{72} +(-7.48331 + 7.48331i) q^{73} +(2.64575 + 7.00000i) q^{74} +(-7.00000 - 7.93725i) q^{76} +(-7.48331 - 7.48331i) q^{77} +(-6.82058 - 3.07892i) q^{78} +5.29150 q^{79} -1.00000 q^{81} +(-2.57794 - 1.16372i) q^{82} +(-8.48528 - 8.48528i) q^{83} +(2.64575 + 3.00000i) q^{84} +(-4.00000 - 10.5830i) q^{86} +(5.65685 - 5.65685i) q^{87} +(14.3039 - 4.40440i) q^{88} +6.00000i q^{89} +10.5830i q^{91} +(-0.500983 + 7.98430i) q^{92} +(3.74166 - 3.74166i) q^{93} +(-5.50000 + 1.32288i) q^{96} +(7.48331 + 7.48331i) q^{97} +(-1.74558 + 3.86690i) q^{98} +5.29150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{6} + O(q^{10}) \) \( 8q + 4q^{6} - 4q^{16} + 16q^{21} - 56q^{26} - 12q^{36} - 16q^{41} + 16q^{46} + 40q^{56} + 48q^{61} + 56q^{66} - 56q^{76} - 8q^{81} - 32q^{86} - 44q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28897 + 0.581861i 0.911438 + 0.411438i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.32288 + 1.50000i 0.661438 + 0.750000i
\(5\) 0 0
\(6\) 0.500000 + 1.32288i 0.204124 + 0.540062i
\(7\) 1.41421 1.41421i 0.534522 0.534522i −0.387392 0.921915i \(-0.626624\pi\)
0.921915 + 0.387392i \(0.126624\pi\)
\(8\) 0.832353 + 2.70318i 0.294281 + 0.955719i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 5.29150i 1.59545i −0.603023 0.797724i \(-0.706037\pi\)
0.603023 0.797724i \(-0.293963\pi\)
\(12\) −0.125246 + 1.99607i −0.0361554 + 0.576217i
\(13\) −3.74166 + 3.74166i −1.03775 + 1.03775i −0.0384901 + 0.999259i \(0.512255\pi\)
−0.999259 + 0.0384901i \(0.987745\pi\)
\(14\) 2.64575 1.00000i 0.707107 0.267261i
\(15\) 0 0
\(16\) −0.500000 + 3.96863i −0.125000 + 0.992157i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.581861 + 1.28897i −0.137146 + 0.303813i
\(19\) −5.29150 −1.21395 −0.606977 0.794719i \(-0.707618\pi\)
−0.606977 + 0.794719i \(0.707618\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 3.07892 6.82058i 0.656428 1.45415i
\(23\) 2.82843 + 2.82843i 0.589768 + 0.589768i 0.937568 0.347801i \(-0.113071\pi\)
−0.347801 + 0.937568i \(0.613071\pi\)
\(24\) −1.32288 + 2.50000i −0.270031 + 0.510310i
\(25\) 0 0
\(26\) −7.00000 + 2.64575i −1.37281 + 0.518875i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 3.99215 + 0.250492i 0.754445 + 0.0473385i
\(29\) 8.00000i 1.48556i −0.669534 0.742781i \(-0.733506\pi\)
0.669534 0.742781i \(-0.266494\pi\)
\(30\) 0 0
\(31\) 5.29150i 0.950382i −0.879883 0.475191i \(-0.842379\pi\)
0.879883 0.475191i \(-0.157621\pi\)
\(32\) −2.95367 + 4.82450i −0.522141 + 0.852859i
\(33\) 3.74166 3.74166i 0.651339 0.651339i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.50000 + 1.32288i −0.250000 + 0.220479i
\(37\) 3.74166 + 3.74166i 0.615125 + 0.615125i 0.944277 0.329152i \(-0.106763\pi\)
−0.329152 + 0.944277i \(0.606763\pi\)
\(38\) −6.82058 3.07892i −1.10644 0.499467i
\(39\) −5.29150 −0.847319
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 2.57794 + 1.16372i 0.397784 + 0.179566i
\(43\) −5.65685 5.65685i −0.862662 0.862662i 0.128984 0.991647i \(-0.458828\pi\)
−0.991647 + 0.128984i \(0.958828\pi\)
\(44\) 7.93725 7.00000i 1.19659 1.05529i
\(45\) 0 0
\(46\) 2.00000 + 5.29150i 0.294884 + 0.780189i
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) −3.15980 + 2.45269i −0.456077 + 0.354015i
\(49\) 3.00000i 0.428571i
\(50\) 0 0
\(51\) 0 0
\(52\) −10.5622 0.662739i −1.46472 0.0919053i
\(53\) 7.48331 7.48331i 1.02791 1.02791i 0.0283132 0.999599i \(-0.490986\pi\)
0.999599 0.0283132i \(-0.00901359\pi\)
\(54\) −1.32288 + 0.500000i −0.180021 + 0.0680414i
\(55\) 0 0
\(56\) 5.00000 + 2.64575i 0.668153 + 0.353553i
\(57\) −3.74166 3.74166i −0.495595 0.495595i
\(58\) 4.65489 10.3117i 0.611217 1.35400i
\(59\) 5.29150 0.688895 0.344447 0.938806i \(-0.388066\pi\)
0.344447 + 0.938806i \(0.388066\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 3.07892 6.82058i 0.391023 0.866214i
\(63\) 1.41421 + 1.41421i 0.178174 + 0.178174i
\(64\) −6.61438 + 4.50000i −0.826797 + 0.562500i
\(65\) 0 0
\(66\) 7.00000 2.64575i 0.861640 0.325669i
\(67\) −8.48528 + 8.48528i −1.03664 + 1.03664i −0.0373395 + 0.999303i \(0.511888\pi\)
−0.999303 + 0.0373395i \(0.988112\pi\)
\(68\) 0 0
\(69\) 4.00000i 0.481543i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −2.70318 + 0.832353i −0.318573 + 0.0980937i
\(73\) −7.48331 + 7.48331i −0.875856 + 0.875856i −0.993103 0.117247i \(-0.962593\pi\)
0.117247 + 0.993103i \(0.462593\pi\)
\(74\) 2.64575 + 7.00000i 0.307562 + 0.813733i
\(75\) 0 0
\(76\) −7.00000 7.93725i −0.802955 0.910465i
\(77\) −7.48331 7.48331i −0.852803 0.852803i
\(78\) −6.82058 3.07892i −0.772278 0.348619i
\(79\) 5.29150 0.595341 0.297670 0.954669i \(-0.403790\pi\)
0.297670 + 0.954669i \(0.403790\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −2.57794 1.16372i −0.284685 0.128512i
\(83\) −8.48528 8.48528i −0.931381 0.931381i 0.0664117 0.997792i \(-0.478845\pi\)
−0.997792 + 0.0664117i \(0.978845\pi\)
\(84\) 2.64575 + 3.00000i 0.288675 + 0.327327i
\(85\) 0 0
\(86\) −4.00000 10.5830i −0.431331 1.14119i
\(87\) 5.65685 5.65685i 0.606478 0.606478i
\(88\) 14.3039 4.40440i 1.52480 0.469510i
\(89\) 6.00000i 0.635999i 0.948091 + 0.317999i \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) 0 0
\(91\) 10.5830i 1.10940i
\(92\) −0.500983 + 7.98430i −0.0522311 + 0.832421i
\(93\) 3.74166 3.74166i 0.387992 0.387992i
\(94\) 0 0
\(95\) 0 0
\(96\) −5.50000 + 1.32288i −0.561341 + 0.135015i
\(97\) 7.48331 + 7.48331i 0.759815 + 0.759815i 0.976289 0.216473i \(-0.0694554\pi\)
−0.216473 + 0.976289i \(0.569455\pi\)
\(98\) −1.74558 + 3.86690i −0.176330 + 0.390616i
\(99\) 5.29150 0.531816
\(100\) 0 0
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 0 0
\(103\) 4.24264 + 4.24264i 0.418040 + 0.418040i 0.884528 0.466488i \(-0.154481\pi\)
−0.466488 + 0.884528i \(0.654481\pi\)
\(104\) −13.2288 7.00000i −1.29719 0.686406i
\(105\) 0 0
\(106\) 14.0000 5.29150i 1.35980 0.513956i
\(107\) 2.82843 2.82843i 0.273434 0.273434i −0.557047 0.830481i \(-0.688066\pi\)
0.830481 + 0.557047i \(0.188066\pi\)
\(108\) −1.99607 0.125246i −0.192072 0.0120518i
\(109\) 2.00000i 0.191565i 0.995402 + 0.0957826i \(0.0305354\pi\)
−0.995402 + 0.0957826i \(0.969465\pi\)
\(110\) 0 0
\(111\) 5.29150i 0.502247i
\(112\) 4.90538 + 6.31959i 0.463515 + 0.597145i
\(113\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(114\) −2.64575 7.00000i −0.247797 0.655610i
\(115\) 0 0
\(116\) 12.0000 10.5830i 1.11417 0.982607i
\(117\) −3.74166 3.74166i −0.345916 0.345916i
\(118\) 6.82058 + 3.07892i 0.627885 + 0.283437i
\(119\) 0 0
\(120\) 0 0
\(121\) −17.0000 −1.54545
\(122\) 7.73381 + 3.49117i 0.700186 + 0.316075i
\(123\) −1.41421 1.41421i −0.127515 0.127515i
\(124\) 7.93725 7.00000i 0.712786 0.628619i
\(125\) 0 0
\(126\) 1.00000 + 2.64575i 0.0890871 + 0.235702i
\(127\) 1.41421 1.41421i 0.125491 0.125491i −0.641572 0.767063i \(-0.721717\pi\)
0.767063 + 0.641572i \(0.221717\pi\)
\(128\) −11.1441 + 1.95171i −0.985008 + 0.172508i
\(129\) 8.00000i 0.704361i
\(130\) 0 0
\(131\) 15.8745i 1.38696i 0.720475 + 0.693481i \(0.243924\pi\)
−0.720475 + 0.693481i \(0.756076\pi\)
\(132\) 10.5622 + 0.662739i 0.919324 + 0.0576840i
\(133\) −7.48331 + 7.48331i −0.648886 + 0.648886i
\(134\) −15.8745 + 6.00000i −1.37135 + 0.518321i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(138\) −2.32744 + 5.15587i −0.198125 + 0.438897i
\(139\) 5.29150 0.448819 0.224410 0.974495i \(-0.427955\pi\)
0.224410 + 0.974495i \(0.427955\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 19.7990 + 19.7990i 1.65567 + 1.65567i
\(144\) −3.96863 0.500000i −0.330719 0.0416667i
\(145\) 0 0
\(146\) −14.0000 + 5.29150i −1.15865 + 0.437928i
\(147\) −2.12132 + 2.12132i −0.174964 + 0.174964i
\(148\) −0.662739 + 10.5622i −0.0544768 + 0.868210i
\(149\) 4.00000i 0.327693i 0.986486 + 0.163846i \(0.0523901\pi\)
−0.986486 + 0.163846i \(0.947610\pi\)
\(150\) 0 0
\(151\) 15.8745i 1.29185i 0.763401 + 0.645925i \(0.223528\pi\)
−0.763401 + 0.645925i \(0.776472\pi\)
\(152\) −4.40440 14.3039i −0.357244 1.16020i
\(153\) 0 0
\(154\) −5.29150 14.0000i −0.426401 1.12815i
\(155\) 0 0
\(156\) −7.00000 7.93725i −0.560449 0.635489i
\(157\) 3.74166 + 3.74166i 0.298617 + 0.298617i 0.840472 0.541855i \(-0.182278\pi\)
−0.541855 + 0.840472i \(0.682278\pi\)
\(158\) 6.82058 + 3.07892i 0.542616 + 0.244946i
\(159\) 10.5830 0.839287
\(160\) 0 0
\(161\) 8.00000 0.630488
\(162\) −1.28897 0.581861i −0.101271 0.0457153i
\(163\) −5.65685 5.65685i −0.443079 0.443079i 0.449966 0.893045i \(-0.351436\pi\)
−0.893045 + 0.449966i \(0.851436\pi\)
\(164\) −2.64575 3.00000i −0.206598 0.234261i
\(165\) 0 0
\(166\) −6.00000 15.8745i −0.465690 1.23210i
\(167\) 8.48528 8.48528i 0.656611 0.656611i −0.297966 0.954577i \(-0.596308\pi\)
0.954577 + 0.297966i \(0.0963081\pi\)
\(168\) 1.66471 + 5.40636i 0.128435 + 0.417110i
\(169\) 15.0000i 1.15385i
\(170\) 0 0
\(171\) 5.29150i 0.404651i
\(172\) 1.00197 15.9686i 0.0763992 1.21759i
\(173\) −7.48331 + 7.48331i −0.568946 + 0.568946i −0.931833 0.362887i \(-0.881791\pi\)
0.362887 + 0.931833i \(0.381791\pi\)
\(174\) 10.5830 4.00000i 0.802296 0.303239i
\(175\) 0 0
\(176\) 21.0000 + 2.64575i 1.58293 + 0.199431i
\(177\) 3.74166 + 3.74166i 0.281240 + 0.281240i
\(178\) −3.49117 + 7.73381i −0.261674 + 0.579673i
\(179\) −5.29150 −0.395505 −0.197753 0.980252i \(-0.563364\pi\)
−0.197753 + 0.980252i \(0.563364\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −6.15784 + 13.6412i −0.456449 + 1.01115i
\(183\) 4.24264 + 4.24264i 0.313625 + 0.313625i
\(184\) −5.29150 + 10.0000i −0.390095 + 0.737210i
\(185\) 0 0
\(186\) 7.00000 2.64575i 0.513265 0.193996i
\(187\) 0 0
\(188\) 0 0
\(189\) 2.00000i 0.145479i
\(190\) 0 0
\(191\) 10.5830i 0.765759i 0.923798 + 0.382880i \(0.125068\pi\)
−0.923798 + 0.382880i \(0.874932\pi\)
\(192\) −7.85905 1.49509i −0.567178 0.107899i
\(193\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(194\) 5.29150 + 14.0000i 0.379908 + 1.00514i
\(195\) 0 0
\(196\) −4.50000 + 3.96863i −0.321429 + 0.283473i
\(197\) 14.9666 + 14.9666i 1.06633 + 1.06633i 0.997638 + 0.0686902i \(0.0218820\pi\)
0.0686902 + 0.997638i \(0.478118\pi\)
\(198\) 6.82058 + 3.07892i 0.484717 + 0.218809i
\(199\) 5.29150 0.375105 0.187552 0.982255i \(-0.439945\pi\)
0.187552 + 0.982255i \(0.439945\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.846415
\(202\) −5.15587 2.32744i −0.362766 0.163758i
\(203\) −11.3137 11.3137i −0.794067 0.794067i
\(204\) 0 0
\(205\) 0 0
\(206\) 3.00000 + 7.93725i 0.209020 + 0.553015i
\(207\) −2.82843 + 2.82843i −0.196589 + 0.196589i
\(208\) −12.9784 16.7201i −0.899891 1.15933i
\(209\) 28.0000i 1.93680i
\(210\) 0 0
\(211\) 26.4575i 1.82141i −0.413057 0.910705i \(-0.635539\pi\)
0.413057 0.910705i \(-0.364461\pi\)
\(212\) 21.1245 + 1.32548i 1.45083 + 0.0910341i
\(213\) 0 0
\(214\) 5.29150 2.00000i 0.361720 0.136717i
\(215\) 0 0
\(216\) −2.50000 1.32288i −0.170103 0.0900103i
\(217\) −7.48331 7.48331i −0.508001 0.508001i
\(218\) −1.16372 + 2.57794i −0.0788172 + 0.174600i
\(219\) −10.5830 −0.715133
\(220\) 0 0
\(221\) 0 0
\(222\) −3.07892 + 6.82058i −0.206643 + 0.457767i
\(223\) 9.89949 + 9.89949i 0.662919 + 0.662919i 0.956067 0.293148i \(-0.0947028\pi\)
−0.293148 + 0.956067i \(0.594703\pi\)
\(224\) 2.64575 + 11.0000i 0.176777 + 0.734968i
\(225\) 0 0
\(226\) 0 0
\(227\) −19.7990 + 19.7990i −1.31411 + 1.31411i −0.395744 + 0.918361i \(0.629513\pi\)
−0.918361 + 0.395744i \(0.870487\pi\)
\(228\) 0.662739 10.5622i 0.0438909 0.699501i
\(229\) 14.0000i 0.925146i 0.886581 + 0.462573i \(0.153074\pi\)
−0.886581 + 0.462573i \(0.846926\pi\)
\(230\) 0 0
\(231\) 10.5830i 0.696311i
\(232\) 21.6255 6.65882i 1.41978 0.437173i
\(233\) 14.9666 14.9666i 0.980497 0.980497i −0.0193169 0.999813i \(-0.506149\pi\)
0.999813 + 0.0193169i \(0.00614915\pi\)
\(234\) −2.64575 7.00000i −0.172958 0.457604i
\(235\) 0 0
\(236\) 7.00000 + 7.93725i 0.455661 + 0.516671i
\(237\) 3.74166 + 3.74166i 0.243047 + 0.243047i
\(238\) 0 0
\(239\) −10.5830 −0.684558 −0.342279 0.939598i \(-0.611199\pi\)
−0.342279 + 0.939598i \(0.611199\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) −21.9125 9.89164i −1.40859 0.635858i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 7.93725 + 9.00000i 0.508131 + 0.576166i
\(245\) 0 0
\(246\) −1.00000 2.64575i −0.0637577 0.168687i
\(247\) 19.7990 19.7990i 1.25978 1.25978i
\(248\) 14.3039 4.40440i 0.908298 0.279679i
\(249\) 12.0000i 0.760469i
\(250\) 0 0
\(251\) 5.29150i 0.333997i −0.985957 0.166998i \(-0.946593\pi\)
0.985957 0.166998i \(-0.0534075\pi\)
\(252\) −0.250492 + 3.99215i −0.0157795 + 0.251482i
\(253\) 14.9666 14.9666i 0.940944 0.940944i
\(254\) 2.64575 1.00000i 0.166009 0.0627456i
\(255\) 0 0
\(256\) −15.5000 3.96863i −0.968750 0.248039i
\(257\) −14.9666 14.9666i −0.933593 0.933593i 0.0643356 0.997928i \(-0.479507\pi\)
−0.997928 + 0.0643356i \(0.979507\pi\)
\(258\) 4.65489 10.3117i 0.289801 0.641981i
\(259\) 10.5830 0.657596
\(260\) 0 0
\(261\) 8.00000 0.495188
\(262\) −9.23676 + 20.4617i −0.570649 + 1.26413i
\(263\) −8.48528 8.48528i −0.523225 0.523225i 0.395319 0.918544i \(-0.370634\pi\)
−0.918544 + 0.395319i \(0.870634\pi\)
\(264\) 13.2288 + 7.00000i 0.814174 + 0.430820i
\(265\) 0 0
\(266\) −14.0000 + 5.29150i −0.858395 + 0.324443i
\(267\) −4.24264 + 4.24264i −0.259645 + 0.259645i
\(268\) −23.9529 1.50295i −1.46316 0.0918073i
\(269\) 24.0000i 1.46331i −0.681677 0.731653i \(-0.738749\pi\)
0.681677 0.731653i \(-0.261251\pi\)
\(270\) 0 0
\(271\) 15.8745i 0.964308i −0.876087 0.482154i \(-0.839855\pi\)
0.876087 0.482154i \(-0.160145\pi\)
\(272\) 0 0
\(273\) −7.48331 + 7.48331i −0.452911 + 0.452911i
\(274\) 0 0
\(275\) 0 0
\(276\) −6.00000 + 5.29150i −0.361158 + 0.318511i
\(277\) −18.7083 18.7083i −1.12407 1.12407i −0.991123 0.132949i \(-0.957555\pi\)
−0.132949 0.991123i \(-0.542445\pi\)
\(278\) 6.82058 + 3.07892i 0.409071 + 0.184661i
\(279\) 5.29150 0.316794
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 0 0
\(283\) −19.7990 19.7990i −1.17693 1.17693i −0.980523 0.196405i \(-0.937073\pi\)
−0.196405 0.980523i \(-0.562927\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 14.0000 + 37.0405i 0.827837 + 2.19025i
\(287\) −2.82843 + 2.82843i −0.166957 + 0.166957i
\(288\) −4.82450 2.95367i −0.284286 0.174047i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) 10.5830i 0.620387i
\(292\) −21.1245 1.32548i −1.23622 0.0775677i
\(293\) −14.9666 + 14.9666i −0.874360 + 0.874360i −0.992944 0.118584i \(-0.962164\pi\)
0.118584 + 0.992944i \(0.462164\pi\)
\(294\) −3.96863 + 1.50000i −0.231455 + 0.0874818i
\(295\) 0 0
\(296\) −7.00000 + 13.2288i −0.406867 + 0.768906i
\(297\) 3.74166 + 3.74166i 0.217113 + 0.217113i
\(298\) −2.32744 + 5.15587i −0.134825 + 0.298672i
\(299\) −21.1660 −1.22406
\(300\) 0 0
\(301\) −16.0000 −0.922225
\(302\) −9.23676 + 20.4617i −0.531516 + 1.17744i
\(303\) −2.82843 2.82843i −0.162489 0.162489i
\(304\) 2.64575 21.0000i 0.151744 1.20443i
\(305\) 0 0
\(306\) 0 0
\(307\) −8.48528 + 8.48528i −0.484281 + 0.484281i −0.906496 0.422215i \(-0.861253\pi\)
0.422215 + 0.906496i \(0.361253\pi\)
\(308\) 1.32548 21.1245i 0.0755261 1.20368i
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 31.7490i 1.80032i −0.435558 0.900161i \(-0.643449\pi\)
0.435558 0.900161i \(-0.356551\pi\)
\(312\) −4.40440 14.3039i −0.249350 0.809798i
\(313\) 14.9666 14.9666i 0.845964 0.845964i −0.143663 0.989627i \(-0.545888\pi\)
0.989627 + 0.143663i \(0.0458881\pi\)
\(314\) 2.64575 + 7.00000i 0.149308 + 0.395033i
\(315\) 0 0
\(316\) 7.00000 + 7.93725i 0.393781 + 0.446505i
\(317\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(318\) 13.6412 + 6.15784i 0.764958 + 0.345314i
\(319\) −42.3320 −2.37014
\(320\) 0 0
\(321\) 4.00000 0.223258
\(322\) 10.3117 + 4.65489i 0.574651 + 0.259407i
\(323\) 0 0
\(324\) −1.32288 1.50000i −0.0734931 0.0833333i
\(325\) 0 0
\(326\) −4.00000 10.5830i −0.221540 0.586138i
\(327\) −1.41421 + 1.41421i −0.0782062 + 0.0782062i
\(328\) −1.66471 5.40636i −0.0919180 0.298516i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.29150i 0.290847i 0.989369 + 0.145424i \(0.0464545\pi\)
−0.989369 + 0.145424i \(0.953545\pi\)
\(332\) 1.50295 23.9529i 0.0824851 1.31459i
\(333\) −3.74166 + 3.74166i −0.205042 + 0.205042i
\(334\) 15.8745 6.00000i 0.868614 0.328305i
\(335\) 0 0
\(336\) −1.00000 + 7.93725i −0.0545545 + 0.433013i
\(337\) −7.48331 7.48331i −0.407642 0.407642i 0.473273 0.880916i \(-0.343072\pi\)
−0.880916 + 0.473273i \(0.843072\pi\)
\(338\) 8.72791 19.3345i 0.474736 1.05166i
\(339\) 0 0
\(340\) 0 0
\(341\) −28.0000 −1.51629
\(342\) 3.07892 6.82058i 0.166489 0.368815i
\(343\) 14.1421 + 14.1421i 0.763604 + 0.763604i
\(344\) 10.5830 20.0000i 0.570597 1.07833i
\(345\) 0 0
\(346\) −14.0000 + 5.29150i −0.752645 + 0.284473i
\(347\) 8.48528 8.48528i 0.455514 0.455514i −0.441666 0.897180i \(-0.645612\pi\)
0.897180 + 0.441666i \(0.145612\pi\)
\(348\) 15.9686 + 1.00197i 0.856007 + 0.0537110i
\(349\) 2.00000i 0.107058i −0.998566 0.0535288i \(-0.982953\pi\)
0.998566 0.0535288i \(-0.0170469\pi\)
\(350\) 0 0
\(351\) 5.29150i 0.282440i
\(352\) 25.5289 + 15.6294i 1.36069 + 0.833048i
\(353\) −14.9666 + 14.9666i −0.796593 + 0.796593i −0.982557 0.185963i \(-0.940459\pi\)
0.185963 + 0.982557i \(0.440459\pi\)
\(354\) 2.64575 + 7.00000i 0.140620 + 0.372046i
\(355\) 0 0
\(356\) −9.00000 + 7.93725i −0.476999 + 0.420674i
\(357\) 0 0
\(358\) −6.82058 3.07892i −0.360479 0.162726i
\(359\) 10.5830 0.558550 0.279275 0.960211i \(-0.409906\pi\)
0.279275 + 0.960211i \(0.409906\pi\)
\(360\) 0 0
\(361\) 9.00000 0.473684
\(362\) 2.57794 + 1.16372i 0.135493 + 0.0611639i
\(363\) −12.0208 12.0208i −0.630929 0.630929i
\(364\) −15.8745 + 14.0000i −0.832050 + 0.733799i
\(365\) 0 0
\(366\) 3.00000 + 7.93725i 0.156813 + 0.414887i
\(367\) −12.7279 + 12.7279i −0.664392 + 0.664392i −0.956412 0.292020i \(-0.905673\pi\)
0.292020 + 0.956412i \(0.405673\pi\)
\(368\) −12.6392 + 9.81076i −0.658863 + 0.511421i
\(369\) 2.00000i 0.104116i
\(370\) 0 0
\(371\) 21.1660i 1.09888i
\(372\) 10.5622 + 0.662739i 0.547626 + 0.0343614i
\(373\) 18.7083 18.7083i 0.968678 0.968678i −0.0308458 0.999524i \(-0.509820\pi\)
0.999524 + 0.0308458i \(0.00982007\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 29.9333 + 29.9333i 1.54164 + 1.54164i
\(378\) −1.16372 + 2.57794i −0.0598554 + 0.132595i
\(379\) 5.29150 0.271806 0.135903 0.990722i \(-0.456606\pi\)
0.135903 + 0.990722i \(0.456606\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) −6.15784 + 13.6412i −0.315062 + 0.697942i
\(383\) 5.65685 + 5.65685i 0.289052 + 0.289052i 0.836705 0.547653i \(-0.184479\pi\)
−0.547653 + 0.836705i \(0.684479\pi\)
\(384\) −9.26013 6.50000i −0.472554 0.331702i
\(385\) 0 0
\(386\) 0 0
\(387\) 5.65685 5.65685i 0.287554 0.287554i
\(388\) −1.32548 + 21.1245i −0.0672909 + 1.07243i
\(389\) 24.0000i 1.21685i −0.793612 0.608424i \(-0.791802\pi\)
0.793612 0.608424i \(-0.208198\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −8.10954 + 2.49706i −0.409594 + 0.126120i
\(393\) −11.2250 + 11.2250i −0.566225 + 0.566225i
\(394\) 10.5830 + 28.0000i 0.533164 + 1.41062i
\(395\) 0 0
\(396\) 7.00000 + 7.93725i 0.351763 + 0.398862i
\(397\) 3.74166 + 3.74166i 0.187788 + 0.187788i 0.794739 0.606951i \(-0.207608\pi\)
−0.606951 + 0.794739i \(0.707608\pi\)
\(398\) 6.82058 + 3.07892i 0.341885 + 0.154332i
\(399\) −10.5830 −0.529813
\(400\) 0 0
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) −15.4676 6.98233i −0.771454 0.348247i
\(403\) 19.7990 + 19.7990i 0.986258 + 0.986258i
\(404\) −5.29150 6.00000i −0.263262 0.298511i
\(405\) 0 0
\(406\) −8.00000 21.1660i −0.397033 1.05045i
\(407\) 19.7990 19.7990i 0.981399 0.981399i
\(408\) 0 0
\(409\) 10.0000i 0.494468i 0.968956 + 0.247234i \(0.0795217\pi\)
−0.968956 + 0.247234i \(0.920478\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.751475 + 11.9764i −0.0370225 + 0.590037i
\(413\) 7.48331 7.48331i 0.368230 0.368230i
\(414\) −5.29150 + 2.00000i −0.260063 + 0.0982946i
\(415\) 0 0
\(416\) −7.00000 29.1033i −0.343203 1.42690i
\(417\) 3.74166 + 3.74166i 0.183230 + 0.183230i
\(418\) −16.2921 + 36.0911i −0.796873 + 1.76527i
\(419\) 15.8745 0.775520 0.387760 0.921760i \(-0.373249\pi\)
0.387760 + 0.921760i \(0.373249\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 15.3946 34.1029i 0.749397 1.66010i
\(423\) 0 0
\(424\) 26.4575 + 14.0000i 1.28489 + 0.679900i
\(425\) 0 0
\(426\) 0 0
\(427\) 8.48528 8.48528i 0.410632 0.410632i
\(428\) 7.98430 + 0.500983i 0.385936 + 0.0242159i
\(429\) 28.0000i 1.35185i
\(430\) 0 0
\(431\) 10.5830i 0.509765i 0.966972 + 0.254883i \(0.0820369\pi\)
−0.966972 + 0.254883i \(0.917963\pi\)
\(432\) −2.45269 3.15980i −0.118005 0.152026i
\(433\) 7.48331 7.48331i 0.359625 0.359625i −0.504050 0.863675i \(-0.668157\pi\)
0.863675 + 0.504050i \(0.168157\pi\)
\(434\) −5.29150 14.0000i −0.254000 0.672022i
\(435\) 0 0
\(436\) −3.00000 + 2.64575i −0.143674 + 0.126709i
\(437\) −14.9666 14.9666i −0.715951 0.715951i
\(438\) −13.6412 6.15784i −0.651799 0.294233i
\(439\) 5.29150 0.252550 0.126275 0.991995i \(-0.459698\pi\)
0.126275 + 0.991995i \(0.459698\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −2.82843 2.82843i −0.134383 0.134383i 0.636716 0.771099i \(-0.280292\pi\)
−0.771099 + 0.636716i \(0.780292\pi\)
\(444\) −7.93725 + 7.00000i −0.376685 + 0.332205i
\(445\) 0 0
\(446\) 7.00000 + 18.5203i 0.331460 + 0.876960i
\(447\) −2.82843 + 2.82843i −0.133780 + 0.133780i
\(448\) −2.99018 + 15.7181i −0.141273 + 0.742611i
\(449\) 22.0000i 1.03824i 0.854700 + 0.519122i \(0.173741\pi\)
−0.854700 + 0.519122i \(0.826259\pi\)
\(450\) 0 0
\(451\) 10.5830i 0.498334i
\(452\) 0 0
\(453\) −11.2250 + 11.2250i −0.527395 + 0.527395i
\(454\) −37.0405 + 14.0000i −1.73840 + 0.657053i
\(455\) 0 0
\(456\) 7.00000 13.2288i 0.327805 0.619493i
\(457\) 7.48331 + 7.48331i 0.350055 + 0.350055i 0.860130 0.510075i \(-0.170382\pi\)
−0.510075 + 0.860130i \(0.670382\pi\)
\(458\) −8.14605 + 18.0455i −0.380640 + 0.843213i
\(459\) 0 0
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) 6.15784 13.6412i 0.286489 0.634644i
\(463\) 24.0416 + 24.0416i 1.11731 + 1.11731i 0.992135 + 0.125175i \(0.0399491\pi\)
0.125175 + 0.992135i \(0.460051\pi\)
\(464\) 31.7490 + 4.00000i 1.47391 + 0.185695i
\(465\) 0 0
\(466\) 28.0000 10.5830i 1.29707 0.490248i
\(467\) −25.4558 + 25.4558i −1.17796 + 1.17796i −0.197692 + 0.980264i \(0.563345\pi\)
−0.980264 + 0.197692i \(0.936655\pi\)
\(468\) 0.662739 10.5622i 0.0306351 0.488239i
\(469\) 24.0000i 1.10822i
\(470\) 0 0
\(471\) 5.29150i 0.243820i
\(472\) 4.40440 + 14.3039i 0.202729 + 0.658390i
\(473\) −29.9333 + 29.9333i −1.37633 + 1.37633i
\(474\) 2.64575 + 7.00000i 0.121523 + 0.321521i
\(475\) 0 0
\(476\) 0 0
\(477\) 7.48331 + 7.48331i 0.342637 + 0.342637i
\(478\) −13.6412 6.15784i −0.623932 0.281653i
\(479\) 42.3320 1.93420 0.967100 0.254398i \(-0.0818772\pi\)
0.967100 + 0.254398i \(0.0818772\pi\)
\(480\) 0 0
\(481\) −28.0000 −1.27669
\(482\) 18.0455 + 8.14605i 0.821952 + 0.371043i
\(483\) 5.65685 + 5.65685i 0.257396 + 0.257396i
\(484\) −22.4889 25.5000i −1.02222 1.15909i
\(485\) 0 0
\(486\) −0.500000 1.32288i −0.0226805 0.0600069i
\(487\) 7.07107 7.07107i 0.320421 0.320421i −0.528508 0.848928i \(-0.677248\pi\)
0.848928 + 0.528508i \(0.177248\pi\)
\(488\) 4.99412 + 16.2191i 0.226073 + 0.734204i
\(489\) 8.00000i 0.361773i
\(490\) 0 0
\(491\) 15.8745i 0.716407i 0.933644 + 0.358203i \(0.116611\pi\)
−0.933644 + 0.358203i \(0.883389\pi\)
\(492\) 0.250492 3.99215i 0.0112930 0.179980i
\(493\) 0 0
\(494\) 37.0405 14.0000i 1.66653 0.629890i
\(495\) 0 0
\(496\) 21.0000 + 2.64575i 0.942928 + 0.118798i
\(497\) 0 0
\(498\) 6.98233 15.4676i 0.312886 0.693120i
\(499\) −15.8745 −0.710641 −0.355320 0.934745i \(-0.615628\pi\)
−0.355320 + 0.934745i \(0.615628\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) 3.07892 6.82058i 0.137419 0.304417i
\(503\) −11.3137 11.3137i −0.504453 0.504453i 0.408365 0.912819i \(-0.366099\pi\)
−0.912819 + 0.408365i \(0.866099\pi\)
\(504\) −2.64575 + 5.00000i −0.117851 + 0.222718i
\(505\) 0 0
\(506\) 28.0000 10.5830i 1.24475 0.470472i
\(507\) 10.6066 10.6066i 0.471056 0.471056i
\(508\) 3.99215 + 0.250492i 0.177123 + 0.0111138i
\(509\) 36.0000i 1.59567i −0.602875 0.797836i \(-0.705978\pi\)
0.602875 0.797836i \(-0.294022\pi\)
\(510\) 0 0
\(511\) 21.1660i 0.936329i
\(512\) −17.6698 14.1343i −0.780903 0.624653i
\(513\) 3.74166 3.74166i 0.165198 0.165198i
\(514\) −10.5830 28.0000i −0.466796 1.23503i
\(515\) 0 0
\(516\) 12.0000 10.5830i 0.528271 0.465891i
\(517\) 0 0
\(518\) 13.6412 + 6.15784i 0.599358 + 0.270560i
\(519\) −10.5830 −0.464542
\(520\) 0 0
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) 10.3117 + 4.65489i 0.451333 + 0.203739i
\(523\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(524\) −23.8118 + 21.0000i −1.04022 + 0.917389i
\(525\) 0 0
\(526\) −6.00000 15.8745i −0.261612 0.692161i
\(527\) 0 0
\(528\) 12.9784 + 16.7201i 0.564813 + 0.727648i
\(529\) 7.00000i 0.304348i
\(530\) 0 0
\(531\) 5.29150i 0.229632i
\(532\) −21.1245 1.32548i −0.915862 0.0574667i
\(533\) 7.48331 7.48331i 0.324138 0.324138i
\(534\) −7.93725 + 3.00000i −0.343479 + 0.129823i
\(535\) 0 0
\(536\) −30.0000 15.8745i −1.29580 0.685674i
\(537\) −3.74166 3.74166i −0.161464 0.161464i
\(538\) 13.9647 30.9352i 0.602059 1.33371i
\(539\) 15.8745 0.683763
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 9.23676 20.4617i 0.396753 0.878906i
\(543\) 1.41421 + 1.41421i 0.0606897 + 0.0606897i
\(544\) 0 0
\(545\) 0 0
\(546\) −14.0000 + 5.29150i −0.599145 + 0.226455i
\(547\) 5.65685 5.65685i 0.241870 0.241870i −0.575754 0.817623i \(-0.695291\pi\)
0.817623 + 0.575754i \(0.195291\pi\)
\(548\) 0 0
\(549\) 6.00000i 0.256074i
\(550\) 0 0
\(551\) 42.3320i 1.80340i
\(552\) −10.8127 + 3.32941i −0.460220 + 0.141709i
\(553\) 7.48331 7.48331i 0.318223 0.318223i
\(554\) −13.2288 35.0000i −0.562036 1.48701i
\(555\) 0 0
\(556\) 7.00000 + 7.93725i 0.296866 + 0.336615i
\(557\) 22.4499 + 22.4499i 0.951235 + 0.951235i 0.998865 0.0476304i \(-0.0151670\pi\)
−0.0476304 + 0.998865i \(0.515167\pi\)
\(558\) 6.82058 + 3.07892i 0.288738 + 0.130341i
\(559\) 42.3320 1.79045
\(560\) 0 0
\(561\) 0 0
\(562\) 33.5132 + 15.1284i 1.41367 + 0.638152i
\(563\) 2.82843 + 2.82843i 0.119204 + 0.119204i 0.764192 0.644988i \(-0.223138\pi\)
−0.644988 + 0.764192i \(0.723138\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −14.0000 37.0405i −0.588464 1.55693i
\(567\) −1.41421 + 1.41421i −0.0593914 + 0.0593914i
\(568\) 0 0
\(569\) 6.00000i 0.251533i −0.992060 0.125767i \(-0.959861\pi\)
0.992060 0.125767i \(-0.0401390\pi\)
\(570\) 0 0
\(571\) 5.29150i 0.221442i 0.993852 + 0.110721i \(0.0353161\pi\)
−0.993852 + 0.110721i \(0.964684\pi\)
\(572\) −3.50688 + 55.8901i −0.146630 + 2.33688i
\(573\) −7.48331 + 7.48331i −0.312620 + 0.312620i
\(574\) −5.29150 + 2.00000i −0.220863 + 0.0834784i
\(575\) 0 0
\(576\) −4.50000 6.61438i −0.187500 0.275599i
\(577\) −22.4499 22.4499i −0.934603 0.934603i 0.0633857 0.997989i \(-0.479810\pi\)
−0.997989 + 0.0633857i \(0.979810\pi\)
\(578\) 9.89164 21.9125i 0.411438 0.911438i
\(579\) 0 0
\(580\) 0 0
\(581\) −24.0000 −0.995688
\(582\) −6.15784 + 13.6412i −0.255251 + 0.565444i
\(583\) −39.5980 39.5980i −1.63998 1.63998i
\(584\) −26.4575 14.0000i −1.09482 0.579324i
\(585\) 0 0
\(586\) −28.0000 + 10.5830i −1.15667 + 0.437180i
\(587\) 19.7990 19.7990i 0.817192 0.817192i −0.168508 0.985700i \(-0.553895\pi\)
0.985700 + 0.168508i \(0.0538950\pi\)
\(588\) −5.98822 0.375737i −0.246950 0.0154952i
\(589\) 28.0000i 1.15372i
\(590\) 0 0
\(591\) 21.1660i 0.870653i
\(592\) −16.7201 + 12.9784i −0.687191 + 0.533410i
\(593\) 14.9666 14.9666i 0.614606 0.614606i −0.329537 0.944143i \(-0.606893\pi\)
0.944143 + 0.329537i \(0.106893\pi\)
\(594\) 2.64575 + 7.00000i 0.108556 + 0.287213i
\(595\) 0 0
\(596\) −6.00000 + 5.29150i −0.245770 + 0.216748i
\(597\) 3.74166 + 3.74166i 0.153136 + 0.153136i
\(598\) −27.2823 12.3157i −1.11566 0.503625i
\(599\) −31.7490 −1.29723 −0.648615 0.761117i \(-0.724651\pi\)
−0.648615 + 0.761117i \(0.724651\pi\)
\(600\) 0 0
\(601\) −14.0000 −0.571072 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) −20.6235 9.30978i −0.840550 0.379438i
\(603\) −8.48528 8.48528i −0.345547 0.345547i
\(604\) −23.8118 + 21.0000i −0.968887 + 0.854478i
\(605\) 0 0
\(606\) −2.00000 5.29150i −0.0812444 0.214953i
\(607\) −24.0416 + 24.0416i −0.975820 + 0.975820i −0.999714 0.0238948i \(-0.992393\pi\)
0.0238948 + 0.999714i \(0.492393\pi\)
\(608\) 15.6294 25.5289i 0.633855 1.03533i
\(609\) 16.0000i 0.648353i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −11.2250 + 11.2250i −0.453372 + 0.453372i −0.896472 0.443100i \(-0.853879\pi\)
0.443100 + 0.896472i \(0.353879\pi\)
\(614\) −15.8745 + 6.00000i −0.640643 + 0.242140i
\(615\) 0 0
\(616\) 14.0000 26.4575i 0.564076 1.06600i
\(617\) −29.9333 29.9333i −1.20507 1.20507i −0.972605 0.232462i \(-0.925322\pi\)
−0.232462 0.972605i \(-0.574678\pi\)
\(618\) −3.49117 + 7.73381i −0.140435 + 0.311099i
\(619\) −5.29150 −0.212683 −0.106342 0.994330i \(-0.533914\pi\)
−0.106342 + 0.994330i \(0.533914\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) 18.4735 40.9235i 0.740720 1.64088i
\(623\) 8.48528 + 8.48528i 0.339956 + 0.339956i
\(624\) 2.64575 21.0000i 0.105915 0.840673i
\(625\) 0 0
\(626\) 28.0000 10.5830i 1.11911 0.422982i
\(627\) −19.7990 + 19.7990i −0.790695 + 0.790695i
\(628\) −0.662739 + 10.5622i −0.0264461 + 0.421479i
\(629\) 0 0
\(630\) 0 0
\(631\) 5.29150i 0.210651i 0.994438 + 0.105326i \(0.0335885\pi\)
−0.994438 + 0.105326i \(0.966411\pi\)
\(632\) 4.40440 + 14.3039i 0.175197 + 0.568978i
\(633\) 18.7083 18.7083i 0.743588 0.743588i
\(634\) 0 0
\(635\) 0 0
\(636\) 14.0000 + 15.8745i 0.555136 + 0.629465i
\(637\) −11.2250 11.2250i −0.444750 0.444750i
\(638\) −54.5646 24.6314i −2.16023 0.975164i
\(639\) 0 0
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 5.15587 + 2.32744i 0.203486 + 0.0918569i
\(643\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 10.5830 + 12.0000i 0.417029 + 0.472866i
\(645\) 0 0
\(646\) 0 0
\(647\) −16.9706 + 16.9706i −0.667182 + 0.667182i −0.957063 0.289881i \(-0.906384\pi\)
0.289881 + 0.957063i \(0.406384\pi\)
\(648\) −0.832353 2.70318i −0.0326979 0.106191i
\(649\) 28.0000i 1.09910i
\(650\) 0 0
\(651\) 10.5830i 0.414781i
\(652\) 1.00197 15.9686i 0.0392400 0.625378i
\(653\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(654\) −2.64575 + 1.00000i −0.103457 + 0.0391031i
\(655\) 0 0
\(656\) 1.00000 7.93725i 0.0390434 0.309898i
\(657\) −7.48331 7.48331i −0.291952 0.291952i
\(658\) 0 0
\(659\) 15.8745 0.618383 0.309192 0.951000i \(-0.399942\pi\)
0.309192 + 0.951000i \(0.399942\pi\)
\(660\) 0 0
\(661\) 18.0000 0.700119 0.350059 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) −3.07892 + 6.82058i −0.119666 + 0.265089i
\(663\) 0 0
\(664\) 15.8745 30.0000i 0.616050 1.16423i
\(665\) 0 0
\(666\) −7.00000 + 2.64575i −0.271244 + 0.102521i
\(667\) 22.6274 22.6274i 0.876137 0.876137i
\(668\) 23.9529 + 1.50295i 0.926765 + 0.0581509i
\(669\) 14.0000i 0.541271i
\(670\) 0 0
\(671\) 31.7490i 1.22566i
\(672\) −5.90735 + 9.64900i −0.227881 + 0.372218i
\(673\) 7.48331 7.48331i 0.288461 0.288461i −0.548011 0.836471i \(-0.684615\pi\)
0.836471 + 0.548011i \(0.184615\pi\)
\(674\) −5.29150 14.0000i −0.203821 0.539260i
\(675\) 0 0
\(676\) 22.5000 19.8431i 0.865385 0.763197i
\(677\) −14.9666 14.9666i −0.575214 0.575214i 0.358367 0.933581i \(-0.383334\pi\)
−0.933581 + 0.358367i \(0.883334\pi\)
\(678\) 0 0
\(679\) 21.1660 0.812277
\(680\) 0 0
\(681\) −28.0000 −1.07296
\(682\) −36.0911 16.2921i −1.38200 0.623857i
\(683\) 8.48528 + 8.48528i 0.324680 + 0.324680i 0.850559 0.525879i \(-0.176264\pi\)
−0.525879 + 0.850559i \(0.676264\pi\)
\(684\) 7.93725 7.00000i 0.303488 0.267652i
\(685\) 0 0
\(686\) 10.0000 + 26.4575i 0.381802 + 1.01015i
\(687\) −9.89949 + 9.89949i −0.377689 + 0.377689i
\(688\) 25.2784 19.6215i 0.963729 0.748063i
\(689\) 56.0000i 2.13343i
\(690\) 0 0
\(691\) 37.0405i 1.40909i 0.709660 + 0.704544i \(0.248848\pi\)
−0.709660 + 0.704544i \(0.751152\pi\)
\(692\) −21.1245 1.32548i −0.803032 0.0503871i
\(693\) 7.48331 7.48331i 0.284268 0.284268i
\(694\) 15.8745 6.00000i 0.602588 0.227757i
\(695\) 0 0
\(696\) 20.0000 + 10.5830i 0.758098 + 0.401148i
\(697\) 0 0
\(698\) 1.16372 2.57794i 0.0440475 0.0975763i
\(699\) 21.1660 0.800572
\(700\) 0 0
\(701\) 36.0000 1.35970 0.679851 0.733351i \(-0.262045\pi\)
0.679851 + 0.733351i \(0.262045\pi\)
\(702\) 3.07892 6.82058i 0.116206 0.257426i
\(703\) −19.7990 19.7990i −0.746733 0.746733i
\(704\) 23.8118 + 35.0000i 0.897440 + 1.31911i
\(705\) 0 0
\(706\) −28.0000 + 10.5830i −1.05379 + 0.398297i
\(707\) −5.65685 + 5.65685i −0.212748 + 0.212748i
\(708\) −0.662739 + 10.5622i −0.0249072 + 0.396953i
\(709\) 10.0000i 0.375558i −0.982211 0.187779i \(-0.939871\pi\)
0.982211 0.187779i \(-0.0601289\pi\)
\(710\) 0 0
\(711\) 5.29150i 0.198447i
\(712\) −16.2191 + 4.99412i −0.607836 + 0.187162i
\(713\) 14.9666 14.9666i 0.560505 0.560505i
\(714\) 0 0
\(715\) 0 0
\(716\) −7.00000 7.93725i −0.261602 0.296629i
\(717\) −7.48331 7.48331i −0.279470 0.279470i
\(718\) 13.6412 + 6.15784i 0.509083 + 0.229808i
\(719\) −31.7490 −1.18404 −0.592019 0.805924i \(-0.701669\pi\)
−0.592019 + 0.805924i \(0.701669\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 11.6007 + 5.23675i 0.431734 + 0.194892i
\(723\) 9.89949 + 9.89949i 0.368166 + 0.368166i
\(724\) 2.64575 + 3.00000i 0.0983286 + 0.111494i
\(725\) 0 0
\(726\) −8.50000 22.4889i −0.315465 0.834641i
\(727\) 21.2132 21.2132i 0.786754 0.786754i −0.194207 0.980961i \(-0.562213\pi\)
0.980961 + 0.194207i \(0.0622132\pi\)
\(728\) −28.6078 + 8.80879i −1.06027 + 0.326476i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.751475 + 11.9764i −0.0277753 + 0.442662i
\(733\) −26.1916 + 26.1916i −0.967409 + 0.967409i −0.999485 0.0320765i \(-0.989788\pi\)
0.0320765 + 0.999485i \(0.489788\pi\)
\(734\) −23.8118 + 9.00000i −0.878908 + 0.332196i
\(735\) 0 0
\(736\) −22.0000 + 5.29150i −0.810931 + 0.195047i
\(737\) 44.8999 + 44.8999i 1.65391 + 1.65391i
\(738\) 1.16372 2.57794i 0.0428372 0.0948951i
\(739\) −26.4575 −0.973255 −0.486628 0.873609i \(-0.661773\pi\)
−0.486628 + 0.873609i \(0.661773\pi\)
\(740\) 0 0
\(741\) 28.0000 1.02861
\(742\) 12.3157 27.2823i 0.452123 1.00156i
\(743\) −33.9411 33.9411i −1.24518 1.24518i −0.957824 0.287355i \(-0.907224\pi\)
−0.287355 0.957824i \(-0.592776\pi\)
\(744\) 13.2288 + 7.00000i 0.484990 + 0.256632i
\(745\) 0 0
\(746\) 35.0000 13.2288i 1.28144 0.484339i
\(747\) 8.48528 8.48528i 0.310460 0.310460i
\(748\) 0 0
\(749\) 8.00000i 0.292314i
\(750\) 0 0
\(751\) 26.4575i 0.965448i −0.875772 0.482724i \(-0.839647\pi\)
0.875772 0.482724i \(-0.160353\pi\)
\(752\) 0 0
\(753\) 3.74166 3.74166i 0.136354 0.136354i
\(754\) 21.1660 + 56.0000i 0.770821 + 2.03940i
\(755\) 0 0
\(756\) −3.00000 + 2.64575i −0.109109 + 0.0962250i
\(757\) 33.6749 + 33.6749i 1.22394 + 1.22394i 0.966221 + 0.257715i \(0.0829694\pi\)
0.257715 + 0.966221i \(0.417031\pi\)
\(758\) 6.82058 + 3.07892i 0.247734 + 0.111831i
\(759\) 21.1660 0.768278
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 2.57794 + 1.16372i 0.0933887 + 0.0421572i
\(763\) 2.82843 + 2.82843i 0.102396 + 0.102396i
\(764\) −15.8745 + 14.0000i −0.574320 + 0.506502i
\(765\) 0 0
\(766\) 4.00000 + 10.5830i 0.144526 + 0.382380i
\(767\) −19.7990 + 19.7990i −0.714900 + 0.714900i
\(768\) −8.15391 13.7664i −0.294229 0.496752i
\(769\) 14.0000i 0.504853i −0.967616 0.252426i \(-0.918771\pi\)
0.967616 0.252426i \(-0.0812286\pi\)
\(770\) 0 0
\(771\) 21.1660i 0.762275i
\(772\) 0 0
\(773\) 14.9666 14.9666i 0.538312 0.538312i −0.384721 0.923033i \(-0.625702\pi\)
0.923033 + 0.384721i \(0.125702\pi\)
\(774\) 10.5830 4.00000i 0.380398 0.143777i
\(775\) 0 0
\(776\) −14.0000 + 26.4575i −0.502571 + 0.949769i
\(777\) 7.48331 + 7.48331i 0.268462 + 0.268462i
\(778\) 13.9647 30.9352i 0.500657 1.10908i
\(779\) 10.5830 0.379176
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 5.65685 + 5.65685i 0.202159 + 0.202159i
\(784\) −11.9059 1.50000i −0.425210 0.0535714i
\(785\) 0 0
\(786\) −21.0000 + 7.93725i −0.749045 + 0.283112i
\(787\) −22.6274 + 22.6274i −0.806580 + 0.806580i −0.984115 0.177534i \(-0.943188\pi\)
0.177534 + 0.984115i \(0.443188\pi\)
\(788\) −2.65095 + 42.2489i −0.0944363 + 1.50506i