Properties

Label 300.2.j.b.7.3
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 7.3
Root \(0.581861 + 1.28897i\) of defining polynomial
Character \(\chi\) \(=\) 300.7
Dual form 300.2.j.b.43.3

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.581861 + 1.28897i 0.411438 + 0.911438i
\(3\) −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 −0.921915 0.387392i \(-0.873376\pi\)
0.387392 + 0.921915i \(0.373376\pi\)
\(8\) −2.70318 0.832353i −0.955719 0.294281i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 5.29150i 1.59545i 0.603023 + 0.797724i \(0.293963\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 1.99607 0.125246i 0.576217 0.0361554i
\(13\) −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 \(0.750000\pi\)
\(18\) −1.28897 + 0.581861i −0.303813 + 0.137146i
\(19\) 5.29150 1.21395 0.606977 0.794719i \(-0.292382\pi\)
0.606977 + 0.794719i \(0.292382\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) −6.82058 + 3.07892i −1.45415 + 0.656428i
\(23\) −2.82843 2.82843i −0.589768 0.589768i 0.347801 0.937568i \(-0.386929\pi\)
−0.937568 + 0.347801i \(0.886929\pi\)
\(24\) 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
\(28\) −0.250492 3.99215i −0.0473385 0.754445i
\(29\) 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 \(0.157621\pi\)
−0.879883 + 0.475191i \(0.842379\pi\)
\(32\) 4.82450 2.95367i 0.852859 0.522141i
\(33\) 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 \(0.606763\pi\)
\(38\) 3.07892 + 6.82058i 0.499467 + 1.10644i
\(39\) 5.29150 0.847319
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 1.16372 + 2.57794i 0.179566 + 0.397784i
\(43\) 5.65685 + 5.65685i 0.862662 + 0.862662i 0.991647 0.128984i \(-0.0411717\pi\)
−0.128984 + 0.991647i \(0.541172\pi\)
\(44\) −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 \(0.250000\pi\)
\(48\) −2.45269 + 3.15980i −0.354015 + 0.456077i
\(49\) 3.00000i 0.428571i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.662739 10.5622i −0.0919053 1.46472i
\(53\) 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
\(58\) 10.3117 4.65489i 1.35400 0.611217i
\(59\) −5.29150 −0.688895 −0.344447 0.938806i \(-0.611934\pi\)
−0.344447 + 0.938806i \(0.611934\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) −6.82058 + 3.07892i −0.866214 + 0.391023i
\(63\) −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 \(-0.488112\pi\)
0.999303 0.0373395i \(-0.0118883\pi\)
\(68\) 0 0
\(69\) 4.00000i 0.481543i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0.832353 2.70318i 0.0980937 0.318573i
\(73\) −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
\(78\) 3.07892 + 6.82058i 0.348619 + 0.772278i
\(79\) −5.29150 −0.595341 −0.297670 0.954669i \(-0.596210\pi\)
−0.297670 + 0.954669i \(0.596210\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −1.16372 2.57794i −0.128512 0.284685i
\(83\) 8.48528 + 8.48528i 0.931381 + 0.931381i 0.997792 0.0664117i \(-0.0211551\pi\)
−0.0664117 + 0.997792i \(0.521155\pi\)
\(84\) −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
\(88\) 4.40440 14.3039i 0.469510 1.52480i
\(89\) 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
\(92\) 7.98430 0.500983i 0.832421 0.0522311i
\(93\) 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 \(0.569455\pi\)
\(98\) −3.86690 + 1.74558i −0.390616 + 0.176330i
\(99\) −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 0.466488 0.884528i \(-0.345519\pi\)
−0.884528 + 0.466488i \(0.845519\pi\)
\(104\) 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 −0.830481 0.557047i \(-0.811934\pi\)
0.557047 + 0.830481i \(0.311934\pi\)
\(108\) 0.125246 + 1.99607i 0.0120518 + 0.192072i
\(109\) 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
\(112\) 6.31959 + 4.90538i 0.597145 + 0.463515i
\(113\) 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
\(118\) −3.07892 6.82058i −0.283437 0.627885i
\(119\) 0 0
\(120\) 0 0
\(121\) −17.0000 −1.54545
\(122\) 3.49117 + 7.73381i 0.316075 + 0.700186i
\(123\) 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 −0.767063 0.641572i \(-0.778283\pi\)
0.641572 + 0.767063i \(0.278283\pi\)
\(128\) −1.95171 + 11.1441i −0.172508 + 0.985008i
\(129\) 8.00000i 0.704361i
\(130\) 0 0
\(131\) 15.8745i 1.38696i −0.720475 0.693481i \(-0.756076\pi\)
0.720475 0.693481i \(-0.243924\pi\)
\(132\) 0.662739 + 10.5622i 0.0576840 + 0.919324i
\(133\) −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 \(0.750000\pi\)
\(138\) −5.15587 + 2.32744i −0.438897 + 0.198125i
\(139\) −5.29150 −0.448819 −0.224410 0.974495i \(-0.572045\pi\)
−0.224410 + 0.974495i \(0.572045\pi\)
\(140\) 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
\(148\) −10.5622 + 0.662739i −0.868210 + 0.0544768i
\(149\) 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 \(-0.776472\pi\)
0.763401 0.645925i \(-0.223528\pi\)
\(152\) −14.3039 4.40440i −1.16020 0.357244i
\(153\) 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 \(0.682278\pi\)
\(158\) −3.07892 6.82058i −0.244946 0.542616i
\(159\) −10.5830 −0.839287
\(160\) 0 0
\(161\) 8.00000 0.630488
\(162\) −0.581861 1.28897i −0.0457153 0.101271i
\(163\) 5.65685 + 5.65685i 0.443079 + 0.443079i 0.893045 0.449966i \(-0.148564\pi\)
−0.449966 + 0.893045i \(0.648564\pi\)
\(164\) 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 −0.954577 0.297966i \(-0.903692\pi\)
0.297966 + 0.954577i \(0.403692\pi\)
\(168\) −5.40636 1.66471i −0.417110 0.128435i
\(169\) 15.0000i 1.15385i
\(170\) 0 0
\(171\) 5.29150i 0.404651i
\(172\) −15.9686 + 1.00197i −1.21759 + 0.0763992i
\(173\) −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
\(178\) −7.73381 + 3.49117i −0.579673 + 0.261674i
\(179\) 5.29150 0.395505 0.197753 0.980252i \(-0.436636\pi\)
0.197753 + 0.980252i \(0.436636\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 13.6412 6.15784i 1.01115 0.456449i
\(183\) −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 \(-0.874932\pi\)
0.923798 0.382880i \(-0.125068\pi\)
\(192\) −1.49509 7.85905i −0.107899 0.567178i
\(193\) 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 \(0.478118\pi\)
\(198\) −3.07892 6.82058i −0.218809 0.484717i
\(199\) −5.29150 −0.375105 −0.187552 0.982255i \(-0.560055\pi\)
−0.187552 + 0.982255i \(0.560055\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.846415
\(202\) −2.32744 5.15587i −0.163758 0.362766i
\(203\) 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
\(208\) 16.7201 + 12.9784i 1.15933 + 0.899891i
\(209\) 28.0000i 1.93680i
\(210\) 0 0
\(211\) 26.4575i 1.82141i 0.413057 + 0.910705i \(0.364461\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 1.32548 + 21.1245i 0.0910341 + 1.45083i
\(213\) 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
\(218\) −2.57794 + 1.16372i −0.174600 + 0.0788172i
\(219\) 10.5830 0.715133
\(220\) 0 0
\(221\) 0 0
\(222\) 6.82058 3.07892i 0.457767 0.206643i
\(223\) −9.89949 9.89949i −0.662919 0.662919i 0.293148 0.956067i \(-0.405297\pi\)
−0.956067 + 0.293148i \(0.905297\pi\)
\(224\) −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 \(-0.370487\pi\)
0.918361 0.395744i \(-0.129513\pi\)
\(228\) 10.5622 0.662739i 0.699501 0.0438909i
\(229\) 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
\(232\) −6.65882 + 21.6255i −0.437173 + 1.41978i
\(233\) 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 \(-0.388801\pi\)
0.342279 + 0.939598i \(0.388801\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) −9.89164 21.9125i −0.635858 1.40859i
\(243\) 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
\(248\) 4.40440 14.3039i 0.279679 0.908298i
\(249\) 12.0000i 0.760469i
\(250\) 0 0
\(251\) 5.29150i 0.333997i 0.985957 + 0.166998i \(0.0534075\pi\)
−0.985957 + 0.166998i \(0.946593\pi\)
\(252\) 3.99215 0.250492i 0.251482 0.0157795i
\(253\) 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 \(0.979507\pi\)
\(258\) 10.3117 4.65489i 0.641981 0.289801i
\(259\) −10.5830 −0.657596
\(260\) 0 0
\(261\) 8.00000 0.495188
\(262\) 20.4617 9.23676i 1.26413 0.570649i
\(263\) 8.48528 + 8.48528i 0.523225 + 0.523225i 0.918544 0.395319i \(-0.129366\pi\)
−0.395319 + 0.918544i \(0.629366\pi\)
\(264\) −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
\(268\) 1.50295 + 23.9529i 0.0918073 + 1.46316i
\(269\) 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 \(0.160145\pi\)
−0.876087 + 0.482154i \(0.839855\pi\)
\(272\) 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 \(-0.542445\pi\)
\(278\) −3.07892 6.82058i −0.184661 0.409071i
\(279\) −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 \(0.0629267\pi\)
0.196405 + 0.980523i \(0.437073\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 14.0000 37.0405i 0.827837 2.19025i
\(287\) 2.82843 2.82843i 0.166957 0.166957i
\(288\) 2.95367 + 4.82450i 0.174047 + 0.284286i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) 10.5830i 0.620387i
\(292\) −1.32548 21.1245i −0.0775677 1.23622i
\(293\) −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
\(298\) −5.15587 + 2.32744i −0.298672 + 0.134825i
\(299\) 21.1660 1.22406
\(300\) 0 0
\(301\) −16.0000 −0.922225
\(302\) 20.4617 9.23676i 1.17744 0.531516i
\(303\) 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 −0.422215 0.906496i \(-0.638747\pi\)
0.906496 + 0.422215i \(0.138747\pi\)
\(308\) 21.1245 1.32548i 1.20368 0.0755261i
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 31.7490i 1.80032i 0.435558 + 0.900161i \(0.356551\pi\)
−0.435558 + 0.900161i \(0.643449\pi\)
\(312\) −14.3039 4.40440i −0.809798 0.249350i
\(313\) 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 \(0.750000\pi\)
\(318\) −6.15784 13.6412i −0.345314 0.764958i
\(319\) 42.3320 2.37014
\(320\) 0 0
\(321\) 4.00000 0.223258
\(322\) 4.65489 + 10.3117i 0.259407 + 0.574651i
\(323\) 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
\(328\) 5.40636 + 1.66471i 0.298516 + 0.0919180i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.29150i 0.290847i −0.989369 0.145424i \(-0.953545\pi\)
0.989369 0.145424i \(-0.0464545\pi\)
\(332\) −23.9529 + 1.50295i −1.31459 + 0.0824851i
\(333\) −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 \(0.843072\pi\)
\(338\) 19.3345 8.72791i 1.05166 0.474736i
\(339\) 0 0
\(340\) 0 0
\(341\) −28.0000 −1.51629
\(342\) −6.82058 + 3.07892i −0.368815 + 0.166489i
\(343\) −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 −0.897180 0.441666i \(-0.854388\pi\)
0.441666 + 0.897180i \(0.354388\pi\)
\(348\) −1.00197 15.9686i −0.0537110 0.856007i
\(349\) 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
\(352\) 15.6294 + 25.5289i 0.833048 + 1.36069i
\(353\) −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
\(358\) 3.07892 + 6.82058i 0.162726 + 0.360479i
\(359\) −10.5830 −0.558550 −0.279275 0.960211i \(-0.590094\pi\)
−0.279275 + 0.960211i \(0.590094\pi\)
\(360\) 0 0
\(361\) 9.00000 0.473684
\(362\) 1.16372 + 2.57794i 0.0611639 + 0.135493i
\(363\) 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 −0.292020 0.956412i \(-0.594327\pi\)
0.956412 + 0.292020i \(0.0943274\pi\)
\(368\) −9.81076 + 12.6392i −0.511421 + 0.658863i
\(369\) 2.00000i 0.104116i
\(370\) 0 0
\(371\) 21.1660i 1.09888i
\(372\) 0.662739 + 10.5622i 0.0343614 + 0.547626i
\(373\) 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
\(378\) −2.57794 + 1.16372i −0.132595 + 0.0598554i
\(379\) −5.29150 −0.271806 −0.135903 0.990722i \(-0.543394\pi\)
−0.135903 + 0.990722i \(0.543394\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 13.6412 6.15784i 0.697942 0.315062i
\(383\) −5.65685 5.65685i −0.289052 0.289052i 0.547653 0.836705i \(-0.315521\pi\)
−0.836705 + 0.547653i \(0.815521\pi\)
\(384\) 9.26013 6.50000i 0.472554 0.331702i
\(385\) 0 0
\(386\) 0 0
\(387\) −5.65685 + 5.65685i −0.287554 + 0.287554i
\(388\) −21.1245 + 1.32548i −1.07243 + 0.0672909i
\(389\) 24.0000i 1.21685i −0.793612 0.608424i \(-0.791802\pi\)
0.793612 0.608424i \(-0.208198\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 2.49706 8.10954i 0.126120 0.409594i
\(393\) −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 \(0.707608\pi\)
\(398\) −3.07892 6.82058i −0.154332 0.341885i
\(399\) 10.5830 0.529813
\(400\) 0 0
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) −6.98233 15.4676i −0.348247 0.771454i
\(403\) −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
\(412\) 11.9764 0.751475i 0.590037 0.0370225i
\(413\) 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
\(418\) −36.0911 + 16.2921i −1.76527 + 0.796873i
\(419\) −15.8745 −0.775520 −0.387760 0.921760i \(-0.626751\pi\)
−0.387760 + 0.921760i \(0.626751\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) −34.1029 + 15.3946i −1.66010 + 0.749397i
\(423\) 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
\(428\) −0.500983 7.98430i −0.0242159 0.385936i
\(429\) 28.0000i 1.35185i
\(430\) 0 0
\(431\) 10.5830i 0.509765i −0.966972 0.254883i \(-0.917963\pi\)
0.966972 0.254883i \(-0.0820369\pi\)
\(432\) −3.15980 2.45269i −0.152026 0.118005i
\(433\) 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
\(438\) 6.15784 + 13.6412i 0.294233 + 0.651799i
\(439\) −5.29150 −0.252550 −0.126275 0.991995i \(-0.540302\pi\)
−0.126275 + 0.991995i \(0.540302\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) 2.82843 + 2.82843i 0.134383 + 0.134383i 0.771099 0.636716i \(-0.219708\pi\)
−0.636716 + 0.771099i \(0.719708\pi\)
\(444\) 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
\(448\) −15.7181 + 2.99018i −0.742611 + 0.141273i
\(449\) 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 \(0.670382\pi\)
\(458\) −18.0455 + 8.14605i −0.843213 + 0.380640i
\(459\) 0 0
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) −13.6412 + 6.15784i −0.634644 + 0.286489i
\(463\) −24.0416 24.0416i −1.11731 1.11731i −0.992135 0.125175i \(-0.960051\pi\)
−0.125175 0.992135i \(-0.539949\pi\)
\(464\) −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 \(-0.436655\pi\)
0.980264 0.197692i \(-0.0633445\pi\)
\(468\) 10.5622 0.662739i 0.488239 0.0306351i
\(469\) 24.0000i 1.10822i
\(470\) 0 0
\(471\) 5.29150i 0.243820i
\(472\) 14.3039 + 4.40440i 0.658390 + 0.202729i
\(473\) −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
\(478\) 6.15784 + 13.6412i 0.281653 + 0.623932i
\(479\) −42.3320 −1.93420 −0.967100 0.254398i \(-0.918123\pi\)
−0.967100 + 0.254398i \(0.918123\pi\)
\(480\) 0 0
\(481\) −28.0000 −1.27669
\(482\) 8.14605 + 18.0455i 0.371043 + 0.821952i
\(483\) −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 −0.848928 0.528508i \(-0.822752\pi\)
0.528508 + 0.848928i \(0.322752\pi\)
\(488\) −16.2191 4.99412i −0.734204 0.226073i
\(489\) 8.00000i 0.361773i
\(490\) 0 0
\(491\) 15.8745i 0.716407i −0.933644 0.358203i \(-0.883389\pi\)
0.933644 0.358203i \(-0.116611\pi\)
\(492\) −3.99215 + 0.250492i −0.179980 + 0.0112930i
\(493\) 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
\(498\) 15.4676 6.98233i 0.693120 0.312886i
\(499\) 15.8745 0.710641 0.355320 0.934745i \(-0.384372\pi\)
0.355320 + 0.934745i \(0.384372\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) −6.82058 + 3.07892i −0.304417 + 0.137419i
\(503\) 11.3137 + 11.3137i 0.504453 + 0.504453i 0.912819 0.408365i \(-0.133901\pi\)
−0.408365 + 0.912819i \(0.633901\pi\)
\(504\) 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
\(508\) −0.250492 3.99215i −0.0111138 0.177123i
\(509\) 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
\(512\) −14.1343 17.6698i −0.624653 0.780903i
\(513\) 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
\(518\) −6.15784 13.6412i −0.270560 0.599358i
\(519\) 10.5830 0.464542
\(520\) 0 0
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) 4.65489 + 10.3117i 0.203739 + 0.451333i
\(523\) 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
\(528\) −16.7201 12.9784i −0.727648 0.564813i
\(529\) 7.00000i 0.304348i
\(530\) 0 0
\(531\) 5.29150i 0.229632i
\(532\) −1.32548 21.1245i −0.0574667 0.915862i
\(533\) 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
\(538\) 30.9352 13.9647i 1.33371 0.602059i
\(539\) −15.8745 −0.683763
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) −20.4617 + 9.23676i −0.878906 + 0.396753i
\(543\) −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 −0.817623 0.575754i \(-0.804709\pi\)
0.575754 + 0.817623i \(0.304709\pi\)
\(548\) 0 0
\(549\) 6.00000i 0.256074i
\(550\) 0 0
\(551\) 42.3320i 1.80340i
\(552\) 3.32941 10.8127i 0.141709 0.460220i
\(553\) 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 \(0.515167\pi\)
\(558\) −3.07892 6.82058i −0.130341 0.288738i
\(559\) −42.3320 −1.79045
\(560\) 0 0
\(561\) 0 0
\(562\) 15.1284 + 33.5132i 0.638152 + 1.41367i
\(563\) −2.82843 2.82843i −0.119204 0.119204i 0.644988 0.764192i \(-0.276862\pi\)
−0.764192 + 0.644988i \(0.776862\pi\)
\(564\) 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 \(-0.964684\pi\)
0.993852 0.110721i \(-0.0353161\pi\)
\(572\) 55.8901 3.50688i 2.33688 0.146630i
\(573\) −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 \(0.979810\pi\)
\(578\) 21.9125 9.89164i 0.911438 0.411438i
\(579\) 0 0
\(580\) 0 0
\(581\) −24.0000 −0.995688
\(582\) 13.6412 6.15784i 0.565444 0.255251i
\(583\) 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 −0.985700 0.168508i \(-0.946105\pi\)
0.168508 + 0.985700i \(0.446105\pi\)
\(588\) 0.375737 + 5.98822i 0.0154952 + 0.246950i
\(589\) 28.0000i 1.15372i
\(590\) 0 0
\(591\) 21.1660i 0.870653i
\(592\) 12.9784 16.7201i 0.533410 0.687191i
\(593\) 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
\(598\) 12.3157 + 27.2823i 0.503625 + 1.11566i
\(599\) 31.7490 1.29723 0.648615 0.761117i \(-0.275349\pi\)
0.648615 + 0.761117i \(0.275349\pi\)
\(600\) 0 0
\(601\) −14.0000 −0.571072 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) −9.30978 20.6235i −0.379438 0.840550i
\(603\) 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 −0.0238948 0.999714i \(-0.507607\pi\)
0.999714 + 0.0238948i \(0.00760667\pi\)
\(608\) 25.5289 15.6294i 1.03533 0.633855i
\(609\) 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 \(-0.574678\pi\)
\(618\) −7.73381 + 3.49117i −0.311099 + 0.140435i
\(619\) 5.29150 0.212683 0.106342 0.994330i \(-0.466086\pi\)
0.106342 + 0.994330i \(0.466086\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) −40.9235 + 18.4735i −1.64088 + 0.740720i
\(623\) −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
\(628\) −10.5622 + 0.662739i −0.421479 + 0.0264461i
\(629\) 0 0
\(630\) 0 0
\(631\) 5.29150i 0.210651i −0.994438 0.105326i \(-0.966411\pi\)
0.994438 0.105326i \(-0.0335885\pi\)
\(632\) 14.3039 + 4.40440i 0.568978 + 0.175197i
\(633\) 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
\(638\) 24.6314 + 54.5646i 0.975164 + 2.16023i
\(639\) 0 0
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 2.32744 + 5.15587i 0.0918569 + 0.203486i
\(643\) 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 −0.289881 0.957063i \(-0.593616\pi\)
0.957063 + 0.289881i \(0.0936157\pi\)
\(648\) 2.70318 + 0.832353i 0.106191 + 0.0326979i
\(649\) 28.0000i 1.09910i
\(650\) 0 0
\(651\) 10.5830i 0.414781i
\(652\) −15.9686 + 1.00197i −0.625378 + 0.0392400i
\(653\) 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 \(-0.600058\pi\)
−0.309192 + 0.951000i \(0.600058\pi\)
\(660\) 0 0
\(661\) 18.0000 0.700119 0.350059 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) 6.82058 3.07892i 0.265089 0.119666i
\(663\) 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
\(668\) −1.50295 23.9529i −0.0581509 0.926765i
\(669\) 14.0000i 0.541271i
\(670\) 0 0
\(671\) 31.7490i 1.22566i
\(672\) 9.64900 5.90735i 0.372218 0.227881i
\(673\) 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
\(682\) −16.2921 36.0911i −0.623857 1.38200i
\(683\) −8.48528 8.48528i −0.324680 0.324680i 0.525879 0.850559i \(-0.323736\pi\)
−0.850559 + 0.525879i \(0.823736\pi\)
\(684\) −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
\(688\) 19.6215 25.2784i 0.748063 0.963729i
\(689\) 56.0000i 2.13343i
\(690\) 0 0
\(691\) 37.0405i 1.40909i −0.709660 0.704544i \(-0.751152\pi\)
0.709660 0.704544i \(-0.248848\pi\)
\(692\) −1.32548 21.1245i −0.0503871 0.803032i
\(693\) 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
\(698\) 2.57794 1.16372i 0.0975763 0.0440475i
\(699\) −21.1660 −0.800572
\(700\) 0 0
\(701\) 36.0000 1.35970 0.679851 0.733351i \(-0.262045\pi\)
0.679851 + 0.733351i \(0.262045\pi\)
\(702\) −6.82058 + 3.07892i −0.257426 + 0.116206i
\(703\) 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
\(708\) −10.5622 + 0.662739i −0.396953 + 0.0249072i
\(709\) 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
\(712\) 4.99412 16.2191i 0.187162 0.607836i
\(713\) 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
\(718\) −6.15784 13.6412i −0.229808 0.509083i
\(719\) 31.7490 1.18404 0.592019 0.805924i \(-0.298331\pi\)
0.592019 + 0.805924i \(0.298331\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 5.23675 + 11.6007i 0.194892 + 0.431734i
\(723\) −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 −0.980961 0.194207i \(-0.937787\pi\)
0.194207 + 0.980961i \(0.437787\pi\)
\(728\) −8.80879 + 28.6078i −0.326476 + 1.06027i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 0 0
\(732\) 11.9764 0.751475i 0.442662 0.0277753i
\(733\) −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
\(738\) 2.57794 1.16372i 0.0948951 0.0428372i
\(739\) 26.4575 0.973255 0.486628 0.873609i \(-0.338227\pi\)
0.486628 + 0.873609i \(0.338227\pi\)
\(740\) 0 0
\(741\) 28.0000 1.02861
\(742\) −27.2823 + 12.3157i −1.00156 + 0.452123i
\(743\) 33.9411 + 33.9411i 1.24518 + 1.24518i 0.957824 + 0.287355i \(0.0927759\pi\)
0.287355 + 0.957824i \(0.407224\pi\)
\(744\) −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 \(0.160353\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) 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 \(0.417031\pi\)
\(758\) −3.07892 6.82058i −0.111831 0.247734i
\(759\) −21.1660 −0.768278
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 1.16372 + 2.57794i 0.0421572 + 0.0933887i
\(763\) −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
\(768\) 13.7664 + 8.15391i 0.496752 + 0.294229i
\(769\) 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
\(778\) 30.9352 13.9647i 1.10908 0.500657i
\(779\) −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 −0.177534 0.984115i \(-0.556812\pi\)
0.984115 + 0.177534i \(0.0568121\pi\)
\(788\) −42.2489