Properties

Label 300.2.j.b.7.1
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 7.1
Root \(-1.28897 - 0.581861i\) of defining polynomial
Character \(\chi\) \(=\) 300.7
Dual form 300.2.j.b.43.1

$q$-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 −0.921915 0.387392i \(-0.873376\pi\)
0.387392 + 0.921915i \(0.373376\pi\)
\(8\) −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 \(-0.487745\pi\)
0.999259 0.0384901i \(-0.0122548\pi\)
\(14\) 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 0.347801 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
\(28\) −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 0.329152 0.944277i \(-0.393237\pi\)
−0.944277 + 0.329152i \(0.893237\pi\)
\(38\) 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 0.991647 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 \(0.250000\pi\)
\(48\) 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 \(0.509014\pi\)
−0.999599 + 0.0283132i \(0.990986\pi\)
\(54\) −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 \(-0.488112\pi\)
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 \(\pi\)
\(72\) 2.70318 0.832353i 0.318573 0.0980937i
\(73\) 7.48331 7.48331i 0.875856 0.875856i −0.117247 0.993103i \(-0.537407\pi\)
0.993103 + 0.117247i \(0.0374069\pi\)
\(74\) 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 0.997792 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
\(88\) −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 0.216473 0.976289i \(-0.430545\pi\)
−0.976289 + 0.216473i \(0.930545\pi\)
\(98\) 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 0.466488 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 \(0.311934\pi\)
\(108\) 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 −0.767063 0.641572i \(-0.778283\pi\)
0.641572 + 0.767063i \(0.278283\pi\)
\(128\) 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 0.541855 0.840472i \(-0.317722\pi\)
−0.840472 + 0.541855i \(0.817722\pi\)
\(158\) −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 0.893045 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 \(0.403692\pi\)
\(168\) −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 −0.362887 0.931833i \(-0.618209\pi\)
0.931833 + 0.362887i \(0.118209\pi\)
\(174\) 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 \(-0.978118\pi\)
−0.0686902 0.997638i \(-0.521882\pi\)
\(198\) −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 0.293148 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 \(-0.129513\pi\)
\(228\) −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 −0.999813 0.0193169i \(-0.993851\pi\)
0.0193169 + 0.999813i \(0.493851\pi\)
\(234\) −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 0.997928 0.0643356i \(-0.0204928\pi\)
−0.0643356 + 0.997928i \(0.520493\pi\)
\(258\) −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 0.918544 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
\(268\) 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 \(0.0424447\pi\)
0.132949 + 0.991123i \(0.457555\pi\)
\(278\) −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 \(0.0629267\pi\)
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
\(288\) 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 −0.118584 0.992944i \(-0.537836\pi\)
0.992944 + 0.118584i \(0.0378355\pi\)
\(294\) −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 −0.422215 0.906496i \(-0.638747\pi\)
0.906496 + 0.422215i \(0.138747\pi\)
\(308\) −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 −0.989627 0.143663i \(-0.954112\pi\)
0.143663 + 0.989627i \(0.454112\pi\)
\(314\) 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 0.880916 0.473273i \(-0.156928\pi\)
−0.473273 + 0.880916i \(0.656928\pi\)
\(338\) −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 −0.897180 0.441666i \(-0.854388\pi\)
0.441666 + 0.897180i \(0.354388\pi\)
\(348\) −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 −0.185963 0.982557i \(-0.559541\pi\)
0.982557 + 0.185963i \(0.0595406\pi\)
\(354\) 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 −0.292020 0.956412i \(-0.594327\pi\)
0.956412 + 0.292020i \(0.0943274\pi\)
\(368\) 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 −0.999524 0.0308458i \(-0.990180\pi\)
0.0308458 + 0.999524i \(0.490180\pi\)
\(374\) 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 0.547653 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
\(388\) 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 0.606951 0.794739i \(-0.292392\pi\)
−0.794739 + 0.606951i \(0.792392\pi\)
\(398\) −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 −0.863675 0.504050i \(-0.831843\pi\)
0.504050 + 0.863675i \(0.331843\pi\)
\(434\) −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 0.771099 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
\(448\) 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 0.510075 0.860130i \(-0.329618\pi\)
−0.860130 + 0.510075i \(0.829618\pi\)
\(458\) 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 \(-0.960051\pi\)
−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 \(-0.0633445\pi\)
\(468\) −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 −0.848928 0.528508i \(-0.822752\pi\)
0.528508 + 0.848928i \(0.322752\pi\)
\(488\) −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 0.912819 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
\(508\) −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 −0.817623 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
\(552\) 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 0.0476304 0.998865i \(-0.484833\pi\)
−0.998865 + 0.0476304i \(0.984833\pi\)
\(558\) −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 0.644988 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 \(0.0353161\pi\)
−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 0.997989 0.0633857i \(-0.0201898\pi\)
−0.0633857 + 0.997989i \(0.520190\pi\)
\(578\) −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 −0.985700 0.168508i \(-0.946105\pi\)
0.168508 + 0.985700i \(0.446105\pi\)
\(588\) 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 −0.944143 0.329537i \(-0.893107\pi\)
0.329537 + 0.944143i \(0.393107\pi\)
\(594\) 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 −0.0238948 0.999714i \(-0.507607\pi\)
0.999714 + 0.0238948i \(0.00760667\pi\)
\(608\) −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 −0.443100 0.896472i \(-0.646121\pi\)
0.896472 + 0.443100i \(0.146121\pi\)
\(614\) −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 \(0.0746782\pi\)
0.232462 + 0.972605i \(0.425322\pi\)
\(618\) 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 −0.289881 0.957063i \(-0.593616\pi\)
0.957063 + 0.289881i \(0.0936157\pi\)
\(648\) 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 −0.836471 0.548011i \(-0.815385\pi\)
0.548011 + 0.836471i \(0.315385\pi\)
\(674\) −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 0.933581 0.358367i \(-0.116666\pi\)
−0.358367 + 0.933581i \(0.616666\pi\)
\(678\) 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 0.525879 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
\(688\) −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 −0.980961 0.194207i \(-0.937787\pi\)
0.194207 + 0.980961i \(0.437787\pi\)
\(728\) 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 −0.0320765 0.999485i \(-0.510212\pi\)
0.999485 + 0.0320765i \(0.0102120\pi\)
\(734\) −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 \(0.0927759\pi\)
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 \(-0.839647\pi\)
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 \(-0.917031\pi\)
−0.257715 0.966221i \(-0.582969\pi\)
\(758\) −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 −0.923033 0.384721i \(-0.874298\pi\)
0.384721 + 0.923033i \(0.374298\pi\)
\(774\) 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 −0.177534 0.984115i \(-0.556812\pi\)
0.984115 + 0.177534i \(0.0568121\pi\)
\(788\) 2.65095 42.2489i 0.0944363