Properties

Label 1512.2.c.g.757.24
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.24
Character \(\chi\) \(=\) 1512.757
Dual form 1512.2.c.g.757.23

$q$-expansion

\(f(q)\) \(=\) \(q+(1.40920 + 0.118957i) q^{2} +(1.97170 + 0.335269i) q^{4} +3.46300i q^{5} +1.00000 q^{7} +(2.73864 + 0.707009i) q^{8} +O(q^{10})\) \(q+(1.40920 + 0.118957i) q^{2} +(1.97170 + 0.335269i) q^{4} +3.46300i q^{5} +1.00000 q^{7} +(2.73864 + 0.707009i) q^{8} +(-0.411948 + 4.88007i) q^{10} -3.31902i q^{11} +3.10840i q^{13} +(1.40920 + 0.118957i) q^{14} +(3.77519 + 1.32210i) q^{16} -1.40277 q^{17} +4.80674i q^{19} +(-1.16104 + 6.82800i) q^{20} +(0.394821 - 4.67717i) q^{22} +8.79960 q^{23} -6.99238 q^{25} +(-0.369766 + 4.38037i) q^{26} +(1.97170 + 0.335269i) q^{28} -9.87397i q^{29} -7.83557 q^{31} +(5.16273 + 2.31219i) q^{32} +(-1.97678 - 0.166869i) q^{34} +3.46300i q^{35} +5.42317i q^{37} +(-0.571795 + 6.77366i) q^{38} +(-2.44837 + 9.48391i) q^{40} -11.5710 q^{41} +7.03957i q^{43} +(1.11276 - 6.54411i) q^{44} +(12.4004 + 1.04677i) q^{46} +11.2916 q^{47} +1.00000 q^{49} +(-9.85368 - 0.831793i) q^{50} +(-1.04215 + 6.12884i) q^{52} +6.51655i q^{53} +11.4938 q^{55} +(2.73864 + 0.707009i) q^{56} +(1.17458 - 13.9144i) q^{58} -3.89654i q^{59} -9.42334i q^{61} +(-11.0419 - 0.932096i) q^{62} +(7.00028 + 3.87248i) q^{64} -10.7644 q^{65} -0.909712i q^{67} +(-2.76583 - 0.470304i) q^{68} +(-0.411948 + 4.88007i) q^{70} -6.42314 q^{71} +1.56257 q^{73} +(-0.645124 + 7.64234i) q^{74} +(-1.61155 + 9.47744i) q^{76} -3.31902i q^{77} -11.1619 q^{79} +(-4.57843 + 13.0735i) q^{80} +(-16.3059 - 1.37645i) q^{82} -0.370241i q^{83} -4.85778i q^{85} +(-0.837406 + 9.92018i) q^{86} +(2.34658 - 9.08960i) q^{88} +4.85047 q^{89} +3.10840i q^{91} +(17.3502 + 2.95023i) q^{92} +(15.9121 + 1.34321i) q^{94} -16.6457 q^{95} +1.63283 q^{97} +(1.40920 + 0.118957i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 6q^{4} + 24q^{7} + O(q^{10}) \) \( 24q + 6q^{4} + 24q^{7} - 16q^{10} + 2q^{16} + 16q^{22} - 24q^{25} + 6q^{28} + 8q^{31} + 22q^{34} + 26q^{46} + 24q^{49} - 6q^{52} + 16q^{55} - 58q^{58} + 6q^{64} - 16q^{70} + 60q^{76} + 8q^{79} - 28q^{82} + 12q^{88} + 36q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40920 + 0.118957i 0.996456 + 0.0841153i
\(3\) 0 0
\(4\) 1.97170 + 0.335269i 0.985849 + 0.167634i
\(5\) 3.46300i 1.54870i 0.632757 + 0.774351i \(0.281923\pi\)
−0.632757 + 0.774351i \(0.718077\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.73864 + 0.707009i 0.968255 + 0.249965i
\(9\) 0 0
\(10\) −0.411948 + 4.88007i −0.130269 + 1.54321i
\(11\) 3.31902i 1.00072i −0.865817 0.500361i \(-0.833201\pi\)
0.865817 0.500361i \(-0.166799\pi\)
\(12\) 0 0
\(13\) 3.10840i 0.862116i 0.902324 + 0.431058i \(0.141860\pi\)
−0.902324 + 0.431058i \(0.858140\pi\)
\(14\) 1.40920 + 0.118957i 0.376625 + 0.0317926i
\(15\) 0 0
\(16\) 3.77519 + 1.32210i 0.943797 + 0.330524i
\(17\) −1.40277 −0.340221 −0.170110 0.985425i \(-0.554412\pi\)
−0.170110 + 0.985425i \(0.554412\pi\)
\(18\) 0 0
\(19\) 4.80674i 1.10274i 0.834260 + 0.551371i \(0.185895\pi\)
−0.834260 + 0.551371i \(0.814105\pi\)
\(20\) −1.16104 + 6.82800i −0.259616 + 1.52679i
\(21\) 0 0
\(22\) 0.394821 4.67717i 0.0841761 0.997176i
\(23\) 8.79960 1.83484 0.917421 0.397917i \(-0.130267\pi\)
0.917421 + 0.397917i \(0.130267\pi\)
\(24\) 0 0
\(25\) −6.99238 −1.39848
\(26\) −0.369766 + 4.38037i −0.0725172 + 0.859061i
\(27\) 0 0
\(28\) 1.97170 + 0.335269i 0.372616 + 0.0633598i
\(29\) 9.87397i 1.83355i −0.399404 0.916775i \(-0.630783\pi\)
0.399404 0.916775i \(-0.369217\pi\)
\(30\) 0 0
\(31\) −7.83557 −1.40731 −0.703655 0.710541i \(-0.748450\pi\)
−0.703655 + 0.710541i \(0.748450\pi\)
\(32\) 5.16273 + 2.31219i 0.912650 + 0.408741i
\(33\) 0 0
\(34\) −1.97678 0.166869i −0.339015 0.0286178i
\(35\) 3.46300i 0.585354i
\(36\) 0 0
\(37\) 5.42317i 0.891564i 0.895142 + 0.445782i \(0.147074\pi\)
−0.895142 + 0.445782i \(0.852926\pi\)
\(38\) −0.571795 + 6.77366i −0.0927574 + 1.09883i
\(39\) 0 0
\(40\) −2.44837 + 9.48391i −0.387122 + 1.49954i
\(41\) −11.5710 −1.80708 −0.903542 0.428499i \(-0.859043\pi\)
−0.903542 + 0.428499i \(0.859043\pi\)
\(42\) 0 0
\(43\) 7.03957i 1.07352i 0.843733 + 0.536762i \(0.180353\pi\)
−0.843733 + 0.536762i \(0.819647\pi\)
\(44\) 1.11276 6.54411i 0.167756 0.986562i
\(45\) 0 0
\(46\) 12.4004 + 1.04677i 1.82834 + 0.154338i
\(47\) 11.2916 1.64704 0.823522 0.567284i \(-0.192006\pi\)
0.823522 + 0.567284i \(0.192006\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −9.85368 0.831793i −1.39352 0.117633i
\(51\) 0 0
\(52\) −1.04215 + 6.12884i −0.144520 + 0.849917i
\(53\) 6.51655i 0.895117i 0.894255 + 0.447559i \(0.147706\pi\)
−0.894255 + 0.447559i \(0.852294\pi\)
\(54\) 0 0
\(55\) 11.4938 1.54982
\(56\) 2.73864 + 0.707009i 0.365966 + 0.0944780i
\(57\) 0 0
\(58\) 1.17458 13.9144i 0.154230 1.82705i
\(59\) 3.89654i 0.507287i −0.967298 0.253643i \(-0.918371\pi\)
0.967298 0.253643i \(-0.0816290\pi\)
\(60\) 0 0
\(61\) 9.42334i 1.20653i −0.797539 0.603267i \(-0.793865\pi\)
0.797539 0.603267i \(-0.206135\pi\)
\(62\) −11.0419 0.932096i −1.40232 0.118376i
\(63\) 0 0
\(64\) 7.00028 + 3.87248i 0.875035 + 0.484060i
\(65\) −10.7644 −1.33516
\(66\) 0 0
\(67\) 0.909712i 0.111139i −0.998455 0.0555695i \(-0.982303\pi\)
0.998455 0.0555695i \(-0.0176974\pi\)
\(68\) −2.76583 0.470304i −0.335406 0.0570327i
\(69\) 0 0
\(70\) −0.411948 + 4.88007i −0.0492372 + 0.583280i
\(71\) −6.42314 −0.762286 −0.381143 0.924516i \(-0.624469\pi\)
−0.381143 + 0.924516i \(0.624469\pi\)
\(72\) 0 0
\(73\) 1.56257 0.182884 0.0914422 0.995810i \(-0.470852\pi\)
0.0914422 + 0.995810i \(0.470852\pi\)
\(74\) −0.645124 + 7.64234i −0.0749942 + 0.888404i
\(75\) 0 0
\(76\) −1.61155 + 9.47744i −0.184857 + 1.08714i
\(77\) 3.31902i 0.378238i
\(78\) 0 0
\(79\) −11.1619 −1.25582 −0.627908 0.778288i \(-0.716088\pi\)
−0.627908 + 0.778288i \(0.716088\pi\)
\(80\) −4.57843 + 13.0735i −0.511884 + 1.46166i
\(81\) 0 0
\(82\) −16.3059 1.37645i −1.80068 0.152003i
\(83\) 0.370241i 0.0406392i −0.999794 0.0203196i \(-0.993532\pi\)
0.999794 0.0203196i \(-0.00646837\pi\)
\(84\) 0 0
\(85\) 4.85778i 0.526900i
\(86\) −0.837406 + 9.92018i −0.0902999 + 1.06972i
\(87\) 0 0
\(88\) 2.34658 9.08960i 0.250146 0.968954i
\(89\) 4.85047 0.514149 0.257075 0.966392i \(-0.417241\pi\)
0.257075 + 0.966392i \(0.417241\pi\)
\(90\) 0 0
\(91\) 3.10840i 0.325849i
\(92\) 17.3502 + 2.95023i 1.80888 + 0.307583i
\(93\) 0 0
\(94\) 15.9121 + 1.34321i 1.64121 + 0.138542i
\(95\) −16.6457 −1.70782
\(96\) 0 0
\(97\) 1.63283 0.165789 0.0828946 0.996558i \(-0.473584\pi\)
0.0828946 + 0.996558i \(0.473584\pi\)
\(98\) 1.40920 + 0.118957i 0.142351 + 0.0120165i
\(99\) 0 0
\(100\) −13.7869 2.34433i −1.37869 0.234433i
\(101\) 13.1650i 1.30997i −0.755643 0.654983i \(-0.772676\pi\)
0.755643 0.654983i \(-0.227324\pi\)
\(102\) 0 0
\(103\) 15.6983 1.54680 0.773399 0.633920i \(-0.218555\pi\)
0.773399 + 0.633920i \(0.218555\pi\)
\(104\) −2.19767 + 8.51280i −0.215499 + 0.834748i
\(105\) 0 0
\(106\) −0.775190 + 9.18314i −0.0752931 + 0.891945i
\(107\) 9.37257i 0.906081i −0.891490 0.453040i \(-0.850339\pi\)
0.891490 0.453040i \(-0.149661\pi\)
\(108\) 0 0
\(109\) 7.31490i 0.700640i −0.936630 0.350320i \(-0.886073\pi\)
0.936630 0.350320i \(-0.113927\pi\)
\(110\) 16.1970 + 1.36727i 1.54433 + 0.130364i
\(111\) 0 0
\(112\) 3.77519 + 1.32210i 0.356722 + 0.124927i
\(113\) 10.9153 1.02683 0.513414 0.858141i \(-0.328380\pi\)
0.513414 + 0.858141i \(0.328380\pi\)
\(114\) 0 0
\(115\) 30.4730i 2.84162i
\(116\) 3.31043 19.4685i 0.307366 1.80760i
\(117\) 0 0
\(118\) 0.463521 5.49102i 0.0426706 0.505489i
\(119\) −1.40277 −0.128591
\(120\) 0 0
\(121\) −0.0159016 −0.00144560
\(122\) 1.12097 13.2794i 0.101488 1.20226i
\(123\) 0 0
\(124\) −15.4494 2.62702i −1.38740 0.235914i
\(125\) 6.89962i 0.617121i
\(126\) 0 0
\(127\) 3.37545 0.299523 0.149761 0.988722i \(-0.452149\pi\)
0.149761 + 0.988722i \(0.452149\pi\)
\(128\) 9.40414 + 6.28984i 0.831217 + 0.555949i
\(129\) 0 0
\(130\) −15.1692 1.28050i −1.33043 0.112307i
\(131\) 7.15460i 0.625100i −0.949901 0.312550i \(-0.898817\pi\)
0.949901 0.312550i \(-0.101183\pi\)
\(132\) 0 0
\(133\) 4.80674i 0.416797i
\(134\) 0.108217 1.28197i 0.00934850 0.110745i
\(135\) 0 0
\(136\) −3.84167 0.991767i −0.329420 0.0850434i
\(137\) 4.22854 0.361269 0.180634 0.983550i \(-0.442185\pi\)
0.180634 + 0.983550i \(0.442185\pi\)
\(138\) 0 0
\(139\) 3.31473i 0.281152i 0.990070 + 0.140576i \(0.0448954\pi\)
−0.990070 + 0.140576i \(0.955105\pi\)
\(140\) −1.16104 + 6.82800i −0.0981255 + 0.577071i
\(141\) 0 0
\(142\) −9.05150 0.764077i −0.759585 0.0641199i
\(143\) 10.3169 0.862739
\(144\) 0 0
\(145\) 34.1936 2.83962
\(146\) 2.20197 + 0.185878i 0.182236 + 0.0153834i
\(147\) 0 0
\(148\) −1.81822 + 10.6929i −0.149457 + 0.878948i
\(149\) 7.08433i 0.580371i −0.956970 0.290185i \(-0.906283\pi\)
0.956970 0.290185i \(-0.0937169\pi\)
\(150\) 0 0
\(151\) 0.252443 0.0205436 0.0102718 0.999947i \(-0.496730\pi\)
0.0102718 + 0.999947i \(0.496730\pi\)
\(152\) −3.39841 + 13.1639i −0.275647 + 1.06773i
\(153\) 0 0
\(154\) 0.394821 4.67717i 0.0318156 0.376897i
\(155\) 27.1346i 2.17950i
\(156\) 0 0
\(157\) 3.11021i 0.248222i 0.992268 + 0.124111i \(0.0396078\pi\)
−0.992268 + 0.124111i \(0.960392\pi\)
\(158\) −15.7294 1.32779i −1.25136 0.105633i
\(159\) 0 0
\(160\) −8.00711 + 17.8785i −0.633018 + 1.41342i
\(161\) 8.79960 0.693505
\(162\) 0 0
\(163\) 18.5595i 1.45369i −0.686800 0.726847i \(-0.740985\pi\)
0.686800 0.726847i \(-0.259015\pi\)
\(164\) −22.8145 3.87939i −1.78151 0.302930i
\(165\) 0 0
\(166\) 0.0440427 0.521744i 0.00341838 0.0404952i
\(167\) −14.3221 −1.10828 −0.554140 0.832424i \(-0.686953\pi\)
−0.554140 + 0.832424i \(0.686953\pi\)
\(168\) 0 0
\(169\) 3.33782 0.256755
\(170\) 0.577867 6.84559i 0.0443204 0.525033i
\(171\) 0 0
\(172\) −2.36015 + 13.8799i −0.179960 + 1.05833i
\(173\) 1.40183i 0.106579i 0.998579 + 0.0532896i \(0.0169707\pi\)
−0.998579 + 0.0532896i \(0.983029\pi\)
\(174\) 0 0
\(175\) −6.99238 −0.528574
\(176\) 4.38807 12.5299i 0.330763 0.944479i
\(177\) 0 0
\(178\) 6.83530 + 0.576998i 0.512327 + 0.0432478i
\(179\) 3.46849i 0.259247i 0.991563 + 0.129624i \(0.0413769\pi\)
−0.991563 + 0.129624i \(0.958623\pi\)
\(180\) 0 0
\(181\) 19.3992i 1.44193i −0.692972 0.720965i \(-0.743699\pi\)
0.692972 0.720965i \(-0.256301\pi\)
\(182\) −0.369766 + 4.38037i −0.0274089 + 0.324695i
\(183\) 0 0
\(184\) 24.0989 + 6.22139i 1.77660 + 0.458647i
\(185\) −18.7805 −1.38077
\(186\) 0 0
\(187\) 4.65581i 0.340466i
\(188\) 22.2636 + 3.78571i 1.62374 + 0.276101i
\(189\) 0 0
\(190\) −23.4572 1.98013i −1.70176 0.143654i
\(191\) 23.4610 1.69758 0.848790 0.528729i \(-0.177331\pi\)
0.848790 + 0.528729i \(0.177331\pi\)
\(192\) 0 0
\(193\) −15.5374 −1.11840 −0.559202 0.829031i \(-0.688893\pi\)
−0.559202 + 0.829031i \(0.688893\pi\)
\(194\) 2.30099 + 0.194237i 0.165202 + 0.0139454i
\(195\) 0 0
\(196\) 1.97170 + 0.335269i 0.140836 + 0.0239478i
\(197\) 14.8278i 1.05643i −0.849109 0.528217i \(-0.822861\pi\)
0.849109 0.528217i \(-0.177139\pi\)
\(198\) 0 0
\(199\) 13.2095 0.936397 0.468199 0.883623i \(-0.344903\pi\)
0.468199 + 0.883623i \(0.344903\pi\)
\(200\) −19.1496 4.94367i −1.35408 0.349571i
\(201\) 0 0
\(202\) 1.56607 18.5521i 0.110188 1.30532i
\(203\) 9.87397i 0.693017i
\(204\) 0 0
\(205\) 40.0703i 2.79863i
\(206\) 22.1220 + 1.86742i 1.54132 + 0.130109i
\(207\) 0 0
\(208\) −4.10962 + 11.7348i −0.284951 + 0.813663i
\(209\) 15.9537 1.10354
\(210\) 0 0
\(211\) 12.3790i 0.852206i 0.904675 + 0.426103i \(0.140114\pi\)
−0.904675 + 0.426103i \(0.859886\pi\)
\(212\) −2.18480 + 12.8487i −0.150052 + 0.882451i
\(213\) 0 0
\(214\) 1.11493 13.2078i 0.0762153 0.902870i
\(215\) −24.3781 −1.66257
\(216\) 0 0
\(217\) −7.83557 −0.531913
\(218\) 0.870158 10.3082i 0.0589345 0.698157i
\(219\) 0 0
\(220\) 22.6623 + 3.85350i 1.52789 + 0.259803i
\(221\) 4.36036i 0.293310i
\(222\) 0 0
\(223\) 2.91170 0.194982 0.0974910 0.995236i \(-0.468918\pi\)
0.0974910 + 0.995236i \(0.468918\pi\)
\(224\) 5.16273 + 2.31219i 0.344949 + 0.154490i
\(225\) 0 0
\(226\) 15.3819 + 1.29846i 1.02319 + 0.0863720i
\(227\) 11.3550i 0.753658i −0.926283 0.376829i \(-0.877014\pi\)
0.926283 0.376829i \(-0.122986\pi\)
\(228\) 0 0
\(229\) 17.4776i 1.15495i 0.816407 + 0.577477i \(0.195963\pi\)
−0.816407 + 0.577477i \(0.804037\pi\)
\(230\) −3.62498 + 42.9426i −0.239024 + 2.83155i
\(231\) 0 0
\(232\) 6.98098 27.0412i 0.458324 1.77534i
\(233\) 1.98827 0.130256 0.0651279 0.997877i \(-0.479254\pi\)
0.0651279 + 0.997877i \(0.479254\pi\)
\(234\) 0 0
\(235\) 39.1027i 2.55078i
\(236\) 1.30639 7.68281i 0.0850387 0.500108i
\(237\) 0 0
\(238\) −1.97678 0.166869i −0.128136 0.0108165i
\(239\) −21.3430 −1.38056 −0.690282 0.723540i \(-0.742514\pi\)
−0.690282 + 0.723540i \(0.742514\pi\)
\(240\) 0 0
\(241\) −13.3714 −0.861330 −0.430665 0.902512i \(-0.641721\pi\)
−0.430665 + 0.902512i \(0.641721\pi\)
\(242\) −0.0224085 0.00189160i −0.00144047 0.000121597i
\(243\) 0 0
\(244\) 3.15935 18.5800i 0.202257 1.18946i
\(245\) 3.46300i 0.221243i
\(246\) 0 0
\(247\) −14.9413 −0.950691
\(248\) −21.4588 5.53982i −1.36264 0.351779i
\(249\) 0 0
\(250\) 0.820758 9.72296i 0.0519093 0.614934i
\(251\) 1.92814i 0.121703i 0.998147 + 0.0608514i \(0.0193816\pi\)
−0.998147 + 0.0608514i \(0.980618\pi\)
\(252\) 0 0
\(253\) 29.2060i 1.83617i
\(254\) 4.75669 + 0.401533i 0.298461 + 0.0251944i
\(255\) 0 0
\(256\) 12.5041 + 9.98234i 0.781507 + 0.623896i
\(257\) −5.22415 −0.325873 −0.162937 0.986637i \(-0.552097\pi\)
−0.162937 + 0.986637i \(0.552097\pi\)
\(258\) 0 0
\(259\) 5.42317i 0.336980i
\(260\) −21.2242 3.60897i −1.31627 0.223819i
\(261\) 0 0
\(262\) 0.851089 10.0823i 0.0525805 0.622885i
\(263\) −4.69624 −0.289583 −0.144791 0.989462i \(-0.546251\pi\)
−0.144791 + 0.989462i \(0.546251\pi\)
\(264\) 0 0
\(265\) −22.5668 −1.38627
\(266\) −0.571795 + 6.77366i −0.0350590 + 0.415320i
\(267\) 0 0
\(268\) 0.304998 1.79368i 0.0186307 0.109566i
\(269\) 26.9906i 1.64565i −0.568297 0.822824i \(-0.692397\pi\)
0.568297 0.822824i \(-0.307603\pi\)
\(270\) 0 0
\(271\) 2.75175 0.167157 0.0835784 0.996501i \(-0.473365\pi\)
0.0835784 + 0.996501i \(0.473365\pi\)
\(272\) −5.29571 1.85459i −0.321099 0.112451i
\(273\) 0 0
\(274\) 5.95887 + 0.503015i 0.359988 + 0.0303882i
\(275\) 23.2079i 1.39949i
\(276\) 0 0
\(277\) 12.0526i 0.724173i −0.932145 0.362086i \(-0.882065\pi\)
0.932145 0.362086i \(-0.117935\pi\)
\(278\) −0.394311 + 4.67113i −0.0236492 + 0.280156i
\(279\) 0 0
\(280\) −2.44837 + 9.48391i −0.146318 + 0.566772i
\(281\) −6.74449 −0.402342 −0.201171 0.979556i \(-0.564475\pi\)
−0.201171 + 0.979556i \(0.564475\pi\)
\(282\) 0 0
\(283\) 8.53083i 0.507105i −0.967322 0.253552i \(-0.918401\pi\)
0.967322 0.253552i \(-0.0815991\pi\)
\(284\) −12.6645 2.15348i −0.751499 0.127785i
\(285\) 0 0
\(286\) 14.5385 + 1.22726i 0.859682 + 0.0725696i
\(287\) −11.5710 −0.683014
\(288\) 0 0
\(289\) −15.0322 −0.884250
\(290\) 48.1856 + 4.06756i 2.82956 + 0.238856i
\(291\) 0 0
\(292\) 3.08091 + 0.523879i 0.180296 + 0.0306577i
\(293\) 11.2926i 0.659718i −0.944030 0.329859i \(-0.892999\pi\)
0.944030 0.329859i \(-0.107001\pi\)
\(294\) 0 0
\(295\) 13.4937 0.785636
\(296\) −3.83423 + 14.8521i −0.222860 + 0.863261i
\(297\) 0 0
\(298\) 0.842730 9.98324i 0.0488180 0.578314i
\(299\) 27.3527i 1.58185i
\(300\) 0 0
\(301\) 7.03957i 0.405754i
\(302\) 0.355744 + 0.0300299i 0.0204708 + 0.00172803i
\(303\) 0 0
\(304\) −6.35498 + 18.1463i −0.364483 + 1.04076i
\(305\) 32.6330 1.86856
\(306\) 0 0
\(307\) 9.15810i 0.522680i −0.965247 0.261340i \(-0.915836\pi\)
0.965247 0.261340i \(-0.0841644\pi\)
\(308\) 1.11276 6.54411i 0.0634056 0.372885i
\(309\) 0 0
\(310\) 3.22785 38.2381i 0.183330 2.17178i
\(311\) 10.0122 0.567741 0.283870 0.958863i \(-0.408381\pi\)
0.283870 + 0.958863i \(0.408381\pi\)
\(312\) 0 0
\(313\) −10.3334 −0.584076 −0.292038 0.956407i \(-0.594333\pi\)
−0.292038 + 0.956407i \(0.594333\pi\)
\(314\) −0.369981 + 4.38291i −0.0208792 + 0.247342i
\(315\) 0 0
\(316\) −22.0080 3.74225i −1.23804 0.210518i
\(317\) 34.9339i 1.96208i 0.193794 + 0.981042i \(0.437921\pi\)
−0.193794 + 0.981042i \(0.562079\pi\)
\(318\) 0 0
\(319\) −32.7719 −1.83487
\(320\) −13.4104 + 24.2420i −0.749665 + 1.35517i
\(321\) 0 0
\(322\) 12.4004 + 1.04677i 0.691048 + 0.0583344i
\(323\) 6.74273i 0.375175i
\(324\) 0 0
\(325\) 21.7352i 1.20565i
\(326\) 2.20778 26.1541i 0.122278 1.44854i
\(327\) 0 0
\(328\) −31.6887 8.18079i −1.74972 0.451708i
\(329\) 11.2916 0.622524
\(330\) 0 0
\(331\) 8.71488i 0.479013i 0.970895 + 0.239507i \(0.0769857\pi\)
−0.970895 + 0.239507i \(0.923014\pi\)
\(332\) 0.124130 0.730003i 0.00681252 0.0400641i
\(333\) 0 0
\(334\) −20.1828 1.70372i −1.10435 0.0932233i
\(335\) 3.15034 0.172121
\(336\) 0 0
\(337\) −8.63703 −0.470489 −0.235244 0.971936i \(-0.575589\pi\)
−0.235244 + 0.971936i \(0.575589\pi\)
\(338\) 4.70366 + 0.397057i 0.255846 + 0.0215971i
\(339\) 0 0
\(340\) 1.62866 9.57808i 0.0883266 0.519444i
\(341\) 26.0064i 1.40833i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −4.97704 + 19.2788i −0.268344 + 1.03945i
\(345\) 0 0
\(346\) −0.166758 + 1.97546i −0.00896495 + 0.106202i
\(347\) 28.2190i 1.51488i 0.652907 + 0.757438i \(0.273549\pi\)
−0.652907 + 0.757438i \(0.726451\pi\)
\(348\) 0 0
\(349\) 13.6266i 0.729416i 0.931122 + 0.364708i \(0.118831\pi\)
−0.931122 + 0.364708i \(0.881169\pi\)
\(350\) −9.85368 0.831793i −0.526701 0.0444612i
\(351\) 0 0
\(352\) 7.67420 17.1352i 0.409036 0.913310i
\(353\) −32.4282 −1.72598 −0.862990 0.505220i \(-0.831411\pi\)
−0.862990 + 0.505220i \(0.831411\pi\)
\(354\) 0 0
\(355\) 22.2433i 1.18055i
\(356\) 9.56367 + 1.62621i 0.506874 + 0.0861891i
\(357\) 0 0
\(358\) −0.412602 + 4.88781i −0.0218067 + 0.258329i
\(359\) −12.9995 −0.686087 −0.343044 0.939319i \(-0.611458\pi\)
−0.343044 + 0.939319i \(0.611458\pi\)
\(360\) 0 0
\(361\) −4.10474 −0.216039
\(362\) 2.30767 27.3374i 0.121288 1.43682i
\(363\) 0 0
\(364\) −1.04215 + 6.12884i −0.0546236 + 0.321238i
\(365\) 5.41117i 0.283233i
\(366\) 0 0
\(367\) −7.55576 −0.394408 −0.197204 0.980363i \(-0.563186\pi\)
−0.197204 + 0.980363i \(0.563186\pi\)
\(368\) 33.2201 + 11.6339i 1.73172 + 0.606460i
\(369\) 0 0
\(370\) −26.4654 2.23407i −1.37587 0.116144i
\(371\) 6.51655i 0.338323i
\(372\) 0 0
\(373\) 34.6651i 1.79489i −0.441124 0.897446i \(-0.645420\pi\)
0.441124 0.897446i \(-0.354580\pi\)
\(374\) −0.553841 + 6.56097i −0.0286384 + 0.339260i
\(375\) 0 0
\(376\) 30.9235 + 7.98324i 1.59476 + 0.411704i
\(377\) 30.6923 1.58073
\(378\) 0 0
\(379\) 0.308373i 0.0158401i 0.999969 + 0.00792004i \(0.00252105\pi\)
−0.999969 + 0.00792004i \(0.997479\pi\)
\(380\) −32.8204 5.58080i −1.68365 0.286289i
\(381\) 0 0
\(382\) 33.0613 + 2.79085i 1.69156 + 0.142793i
\(383\) 4.36024 0.222798 0.111399 0.993776i \(-0.464467\pi\)
0.111399 + 0.993776i \(0.464467\pi\)
\(384\) 0 0
\(385\) 11.4938 0.585777
\(386\) −21.8953 1.84828i −1.11444 0.0940750i
\(387\) 0 0
\(388\) 3.21946 + 0.547439i 0.163443 + 0.0277920i
\(389\) 1.33391i 0.0676317i 0.999428 + 0.0338159i \(0.0107660\pi\)
−0.999428 + 0.0338159i \(0.989234\pi\)
\(390\) 0 0
\(391\) −12.3438 −0.624251
\(392\) 2.73864 + 0.707009i 0.138322 + 0.0357093i
\(393\) 0 0
\(394\) 1.76387 20.8953i 0.0888623 1.05269i
\(395\) 38.6538i 1.94488i
\(396\) 0 0
\(397\) 6.92952i 0.347783i 0.984765 + 0.173891i \(0.0556342\pi\)
−0.984765 + 0.173891i \(0.944366\pi\)
\(398\) 18.6149 + 1.57136i 0.933079 + 0.0787653i
\(399\) 0 0
\(400\) −26.3976 9.24461i −1.31988 0.462231i
\(401\) −23.9669 −1.19685 −0.598426 0.801178i \(-0.704207\pi\)
−0.598426 + 0.801178i \(0.704207\pi\)
\(402\) 0 0
\(403\) 24.3561i 1.21327i
\(404\) 4.41382 25.9574i 0.219596 1.29143i
\(405\) 0 0
\(406\) 1.17458 13.9144i 0.0582933 0.690561i
\(407\) 17.9996 0.892208
\(408\) 0 0
\(409\) 21.6936 1.07268 0.536340 0.844002i \(-0.319807\pi\)
0.536340 + 0.844002i \(0.319807\pi\)
\(410\) 4.76665 56.4672i 0.235408 2.78872i
\(411\) 0 0
\(412\) 30.9523 + 5.26314i 1.52491 + 0.259296i
\(413\) 3.89654i 0.191736i
\(414\) 0 0
\(415\) 1.28214 0.0629380
\(416\) −7.18722 + 16.0479i −0.352382 + 0.786811i
\(417\) 0 0
\(418\) 22.4819 + 1.89780i 1.09963 + 0.0928245i
\(419\) 27.5910i 1.34791i −0.738772 0.673955i \(-0.764594\pi\)
0.738772 0.673955i \(-0.235406\pi\)
\(420\) 0 0
\(421\) 38.3335i 1.86826i −0.356929 0.934131i \(-0.616176\pi\)
0.356929 0.934131i \(-0.383824\pi\)
\(422\) −1.47257 + 17.4445i −0.0716836 + 0.849186i
\(423\) 0 0
\(424\) −4.60726 + 17.8465i −0.223748 + 0.866702i
\(425\) 9.80867 0.475790
\(426\) 0 0
\(427\) 9.42334i 0.456027i
\(428\) 3.14233 18.4799i 0.151890 0.893259i
\(429\) 0 0
\(430\) −34.3536 2.89994i −1.65668 0.139848i
\(431\) 2.22510 0.107179 0.0535896 0.998563i \(-0.482934\pi\)
0.0535896 + 0.998563i \(0.482934\pi\)
\(432\) 0 0
\(433\) 28.2235 1.35633 0.678167 0.734908i \(-0.262775\pi\)
0.678167 + 0.734908i \(0.262775\pi\)
\(434\) −11.0419 0.932096i −0.530028 0.0447421i
\(435\) 0 0
\(436\) 2.45246 14.4228i 0.117451 0.690725i
\(437\) 42.2974i 2.02336i
\(438\) 0 0
\(439\) −5.63936 −0.269152 −0.134576 0.990903i \(-0.542967\pi\)
−0.134576 + 0.990903i \(0.542967\pi\)
\(440\) 31.4773 + 8.12620i 1.50062 + 0.387401i
\(441\) 0 0
\(442\) 0.518696 6.14463i 0.0246718 0.292270i
\(443\) 5.81672i 0.276361i 0.990407 + 0.138180i \(0.0441254\pi\)
−0.990407 + 0.138180i \(0.955875\pi\)
\(444\) 0 0
\(445\) 16.7972i 0.796264i
\(446\) 4.10318 + 0.346367i 0.194291 + 0.0164010i
\(447\) 0 0
\(448\) 7.00028 + 3.87248i 0.330732 + 0.182958i
\(449\) −1.66921 −0.0787748 −0.0393874 0.999224i \(-0.512541\pi\)
−0.0393874 + 0.999224i \(0.512541\pi\)
\(450\) 0 0
\(451\) 38.4043i 1.80839i
\(452\) 21.5218 + 3.65957i 1.01230 + 0.172132i
\(453\) 0 0
\(454\) 1.35076 16.0015i 0.0633942 0.750987i
\(455\) −10.7644 −0.504643
\(456\) 0 0
\(457\) −16.4606 −0.769994 −0.384997 0.922918i \(-0.625797\pi\)
−0.384997 + 0.922918i \(0.625797\pi\)
\(458\) −2.07908 + 24.6295i −0.0971493 + 1.15086i
\(459\) 0 0
\(460\) −10.2167 + 60.0836i −0.476354 + 2.80141i
\(461\) 22.7915i 1.06151i 0.847527 + 0.530753i \(0.178091\pi\)
−0.847527 + 0.530753i \(0.821909\pi\)
\(462\) 0 0
\(463\) −16.3165 −0.758293 −0.379146 0.925337i \(-0.623782\pi\)
−0.379146 + 0.925337i \(0.623782\pi\)
\(464\) 13.0544 37.2761i 0.606033 1.73050i
\(465\) 0 0
\(466\) 2.80187 + 0.236518i 0.129794 + 0.0109565i
\(467\) 33.3073i 1.54128i 0.637271 + 0.770639i \(0.280063\pi\)
−0.637271 + 0.770639i \(0.719937\pi\)
\(468\) 0 0
\(469\) 0.909712i 0.0420066i
\(470\) −4.65154 + 55.1036i −0.214560 + 2.54174i
\(471\) 0 0
\(472\) 2.75489 10.6712i 0.126804 0.491183i
\(473\) 23.3645 1.07430
\(474\) 0 0
\(475\) 33.6105i 1.54216i
\(476\) −2.76583 0.470304i −0.126772 0.0215563i
\(477\) 0 0
\(478\) −30.0766 2.53890i −1.37567 0.116127i
\(479\) 28.5717 1.30547 0.652737 0.757584i \(-0.273621\pi\)
0.652737 + 0.757584i \(0.273621\pi\)
\(480\) 0 0
\(481\) −16.8574 −0.768632
\(482\) −18.8430 1.59063i −0.858277 0.0724510i
\(483\) 0 0
\(484\) −0.0313531 0.00533130i −0.00142514 0.000242332i
\(485\) 5.65451i 0.256758i
\(486\) 0 0
\(487\) 39.0149 1.76793 0.883967 0.467550i \(-0.154863\pi\)
0.883967 + 0.467550i \(0.154863\pi\)
\(488\) 6.66238 25.8071i 0.301592 1.16823i
\(489\) 0 0
\(490\) −0.411948 + 4.88007i −0.0186099 + 0.220459i
\(491\) 12.5799i 0.567722i 0.958866 + 0.283861i \(0.0916153\pi\)
−0.958866 + 0.283861i \(0.908385\pi\)
\(492\) 0 0
\(493\) 13.8509i 0.623811i
\(494\) −21.0553 1.77737i −0.947322 0.0799677i
\(495\) 0 0
\(496\) −29.5808 10.3594i −1.32822 0.465151i
\(497\) −6.42314 −0.288117
\(498\) 0 0
\(499\) 17.3054i 0.774697i 0.921933 + 0.387349i \(0.126609\pi\)
−0.921933 + 0.387349i \(0.873391\pi\)
\(500\) 2.31323 13.6040i 0.103451 0.608388i
\(501\) 0 0
\(502\) −0.229365 + 2.71713i −0.0102371 + 0.121272i
\(503\) 18.1289 0.808326 0.404163 0.914687i \(-0.367563\pi\)
0.404163 + 0.914687i \(0.367563\pi\)
\(504\) 0 0
\(505\) 45.5904 2.02875
\(506\) 3.47426 41.1572i 0.154450 1.82966i
\(507\) 0 0
\(508\) 6.65537 + 1.13168i 0.295284 + 0.0502103i
\(509\) 17.3445i 0.768780i −0.923171 0.384390i \(-0.874412\pi\)
0.923171 0.384390i \(-0.125588\pi\)
\(510\) 0 0
\(511\) 1.56257 0.0691238
\(512\) 16.4333 + 15.5546i 0.726258 + 0.687422i
\(513\) 0 0
\(514\) −7.36188 0.621449i −0.324719 0.0274109i
\(515\) 54.3632i 2.39553i
\(516\) 0 0
\(517\) 37.4770i 1.64823i
\(518\) −0.645124 + 7.64234i −0.0283451 + 0.335785i
\(519\) 0 0
\(520\) −29.4798 7.61053i −1.29278 0.333744i
\(521\) −16.7507 −0.733861 −0.366930 0.930248i \(-0.619591\pi\)
−0.366930 + 0.930248i \(0.619591\pi\)
\(522\) 0 0
\(523\) 20.8692i 0.912545i 0.889840 + 0.456273i \(0.150816\pi\)
−0.889840 + 0.456273i \(0.849184\pi\)
\(524\) 2.39871 14.1067i 0.104788 0.616254i
\(525\) 0 0
\(526\) −6.61795 0.558651i −0.288556 0.0243583i
\(527\) 10.9915 0.478796
\(528\) 0 0
\(529\) 54.4329 2.36665
\(530\) −31.8012 2.68448i −1.38136 0.116606i
\(531\) 0 0
\(532\) −1.61155 + 9.47744i −0.0698695 + 0.410899i
\(533\) 35.9673i 1.55792i
\(534\) 0 0
\(535\) 32.4572 1.40325
\(536\) 0.643175 2.49137i 0.0277809 0.107611i
\(537\) 0 0
\(538\) 3.21072 38.0352i 0.138424 1.63982i
\(539\) 3.31902i 0.142960i
\(540\) 0 0
\(541\) 37.7498i 1.62299i 0.584359 + 0.811495i \(0.301346\pi\)
−0.584359 + 0.811495i \(0.698654\pi\)
\(542\) 3.87777 + 0.327340i 0.166564 + 0.0140604i
\(543\) 0 0
\(544\) −7.24210 3.24346i −0.310503 0.139062i
\(545\) 25.3315 1.08508
\(546\) 0 0
\(547\) 34.4520i 1.47306i 0.676404 + 0.736531i \(0.263537\pi\)
−0.676404 + 0.736531i \(0.736463\pi\)
\(548\) 8.33741 + 1.41770i 0.356156 + 0.0605611i
\(549\) 0 0
\(550\) −2.76074 + 32.7046i −0.117718 + 1.39453i
\(551\) 47.4616 2.02193
\(552\) 0 0
\(553\) −11.1619 −0.474653
\(554\) 1.43375 16.9846i 0.0609140 0.721606i
\(555\) 0 0
\(556\) −1.11133 + 6.53566i −0.0471308 + 0.277174i
\(557\) 27.7136i 1.17426i 0.809491 + 0.587132i \(0.199743\pi\)
−0.809491 + 0.587132i \(0.800257\pi\)
\(558\) 0 0
\(559\) −21.8818 −0.925503
\(560\) −4.57843 + 13.0735i −0.193474 + 0.552456i
\(561\) 0 0
\(562\) −9.50434 0.802304i −0.400917 0.0338432i
\(563\) 0.570384i 0.0240388i 0.999928 + 0.0120194i \(0.00382599\pi\)
−0.999928 + 0.0120194i \(0.996174\pi\)
\(564\) 0 0
\(565\) 37.7998i 1.59025i
\(566\) 1.01480 12.0217i 0.0426553 0.505308i
\(567\) 0 0
\(568\) −17.5907 4.54121i −0.738087 0.190545i
\(569\) −18.4090 −0.771745 −0.385872 0.922552i \(-0.626099\pi\)
−0.385872 + 0.922552i \(0.626099\pi\)
\(570\) 0 0
\(571\) 43.3534i 1.81428i 0.420824 + 0.907142i \(0.361741\pi\)
−0.420824 + 0.907142i \(0.638259\pi\)
\(572\) 20.3417 + 3.45892i 0.850531 + 0.144625i
\(573\) 0 0
\(574\) −16.3059 1.37645i −0.680593 0.0574519i
\(575\) −61.5301 −2.56598
\(576\) 0 0
\(577\) −39.6209 −1.64944 −0.824720 0.565541i \(-0.808667\pi\)
−0.824720 + 0.565541i \(0.808667\pi\)
\(578\) −21.1835 1.78819i −0.881116 0.0743790i
\(579\) 0 0
\(580\) 67.4194 + 11.4640i 2.79944 + 0.476018i
\(581\) 0.370241i 0.0153602i
\(582\) 0 0
\(583\) 21.6286 0.895764
\(584\) 4.27930 + 1.10475i 0.177079 + 0.0457148i
\(585\) 0 0
\(586\) 1.34333 15.9135i 0.0554924 0.657380i
\(587\) 13.4388i 0.554677i −0.960772 0.277338i \(-0.910548\pi\)
0.960772 0.277338i \(-0.0894523\pi\)
\(588\) 0 0
\(589\) 37.6636i 1.55190i
\(590\) 19.0154 + 1.60518i 0.782852 + 0.0660840i
\(591\) 0 0
\(592\) −7.16997 + 20.4735i −0.294684 + 0.841456i
\(593\) −22.3157 −0.916395 −0.458198 0.888850i \(-0.651505\pi\)
−0.458198 + 0.888850i \(0.651505\pi\)
\(594\) 0 0
\(595\) 4.85778i 0.199150i
\(596\) 2.37515 13.9682i 0.0972901 0.572158i
\(597\) 0 0
\(598\) −3.25380 + 38.5455i −0.133058 + 1.57624i
\(599\) 14.2622 0.582740 0.291370 0.956610i \(-0.405889\pi\)
0.291370 + 0.956610i \(0.405889\pi\)
\(600\) 0 0
\(601\) −2.40215 −0.0979858 −0.0489929 0.998799i \(-0.515601\pi\)
−0.0489929 + 0.998799i \(0.515601\pi\)
\(602\) −0.837406 + 9.92018i −0.0341301 + 0.404316i
\(603\) 0 0
\(604\) 0.497742 + 0.0846364i 0.0202529 + 0.00344381i
\(605\) 0.0550671i 0.00223880i
\(606\) 0 0
\(607\) −10.0506 −0.407940 −0.203970 0.978977i \(-0.565385\pi\)
−0.203970 + 0.978977i \(0.565385\pi\)
\(608\) −11.1141 + 24.8159i −0.450736 + 1.00642i
\(609\) 0 0
\(610\) 45.9865 + 3.88193i 1.86194 + 0.157175i
\(611\) 35.0988i 1.41994i
\(612\) 0 0
\(613\) 2.57394i 0.103961i −0.998648 0.0519803i \(-0.983447\pi\)
0.998648 0.0519803i \(-0.0165533\pi\)
\(614\) 1.08942 12.9056i 0.0439654 0.520828i
\(615\) 0 0
\(616\) 2.34658 9.08960i 0.0945463 0.366230i
\(617\) 36.3495 1.46337 0.731687 0.681640i \(-0.238733\pi\)
0.731687 + 0.681640i \(0.238733\pi\)
\(618\) 0 0
\(619\) 16.6498i 0.669211i −0.942358 0.334606i \(-0.891397\pi\)
0.942358 0.334606i \(-0.108603\pi\)
\(620\) 9.09739 53.5013i 0.365360 2.14866i
\(621\) 0 0
\(622\) 14.1092 + 1.19102i 0.565729 + 0.0477557i
\(623\) 4.85047 0.194330
\(624\) 0 0
\(625\) −11.0685 −0.442740
\(626\) −14.5618 1.22923i −0.582006 0.0491297i
\(627\) 0 0
\(628\) −1.04276 + 6.13240i −0.0416105 + 0.244709i
\(629\) 7.60744i 0.303328i
\(630\) 0 0
\(631\) 14.7898 0.588773 0.294387 0.955686i \(-0.404885\pi\)
0.294387 + 0.955686i \(0.404885\pi\)
\(632\) −30.5685 7.89158i −1.21595 0.313910i
\(633\) 0 0
\(634\) −4.15563 + 49.2289i −0.165041 + 1.95513i
\(635\) 11.6892i 0.463871i
\(636\) 0 0
\(637\) 3.10840i 0.123159i
\(638\) −46.1822 3.89845i −1.82837 0.154341i
\(639\) 0 0
\(640\) −21.7817 + 32.5666i −0.860998 + 1.28731i
\(641\) −32.8085 −1.29586 −0.647928 0.761701i \(-0.724364\pi\)
−0.647928 + 0.761701i \(0.724364\pi\)
\(642\) 0 0
\(643\) 15.3479i 0.605263i 0.953108 + 0.302631i \(0.0978651\pi\)
−0.953108 + 0.302631i \(0.902135\pi\)
\(644\) 17.3502 + 2.95023i 0.683692 + 0.116255i
\(645\) 0 0
\(646\) 0.802095 9.50186i 0.0315580 0.373846i
\(647\) 6.19107 0.243396 0.121698 0.992567i \(-0.461166\pi\)
0.121698 + 0.992567i \(0.461166\pi\)
\(648\) 0 0
\(649\) −12.9327 −0.507653
\(650\) 2.58555 30.6292i 0.101414 1.20138i
\(651\) 0 0
\(652\) 6.22243 36.5938i 0.243689 1.43312i
\(653\) 17.4848i 0.684234i −0.939657 0.342117i \(-0.888856\pi\)
0.939657 0.342117i \(-0.111144\pi\)
\(654\) 0 0
\(655\) 24.7764 0.968093
\(656\) −43.6827 15.2980i −1.70552 0.597286i
\(657\) 0 0
\(658\) 15.9121 + 1.34321i 0.620318 + 0.0523638i
\(659\) 13.8987i 0.541416i −0.962661 0.270708i \(-0.912742\pi\)
0.962661 0.270708i \(-0.0872578\pi\)
\(660\) 0 0
\(661\) 1.69978i 0.0661137i −0.999453 0.0330568i \(-0.989476\pi\)
0.999453 0.0330568i \(-0.0105242\pi\)
\(662\) −1.03670 + 12.2810i −0.0402923 + 0.477316i
\(663\) 0 0
\(664\) 0.261763 1.01395i 0.0101584 0.0393491i
\(665\) −16.6457 −0.645494
\(666\) 0 0
\(667\) 86.8869i 3.36428i
\(668\) −28.2389 4.80176i −1.09260 0.185786i
\(669\) 0 0
\(670\) 4.43946 + 0.374755i 0.171511 + 0.0144780i
\(671\) −31.2762 −1.20741
\(672\) 0 0
\(673\) −22.7847 −0.878284 −0.439142 0.898418i \(-0.644718\pi\)
−0.439142 + 0.898418i \(0.644718\pi\)
\(674\) −12.1713 1.02743i −0.468821 0.0395753i
\(675\) 0 0
\(676\) 6.58118 + 1.11907i 0.253122 + 0.0430410i
\(677\) 34.2963i 1.31811i 0.752093 + 0.659057i \(0.229044\pi\)
−0.752093 + 0.659057i \(0.770956\pi\)
\(678\) 0 0
\(679\) 1.63283 0.0626624
\(680\) 3.43449 13.3037i 0.131707 0.510174i
\(681\) 0 0
\(682\) −3.09365 + 36.6483i −0.118462 + 1.40334i
\(683\) 10.5590i 0.404029i −0.979383 0.202014i \(-0.935251\pi\)
0.979383 0.202014i \(-0.0647487\pi\)
\(684\) 0 0
\(685\) 14.6434i 0.559497i
\(686\) 1.40920 + 0.118957i 0.0538036 + 0.00454180i
\(687\) 0 0
\(688\) −9.30700 + 26.5757i −0.354826 + 1.01319i
\(689\) −20.2561 −0.771695
\(690\) 0 0
\(691\) 14.3879i 0.547342i 0.961823 + 0.273671i \(0.0882380\pi\)
−0.961823 + 0.273671i \(0.911762\pi\)
\(692\) −0.469990 + 2.76399i −0.0178664 + 0.105071i
\(693\) 0 0
\(694\) −3.35685 + 39.7663i −0.127424 + 1.50951i
\(695\) −11.4789 −0.435421
\(696\) 0 0
\(697\) 16.2314 0.614807
\(698\) −1.62098 + 19.2027i −0.0613551 + 0.726831i
\(699\) 0 0
\(700\) −13.7869 2.34433i −0.521095 0.0886072i
\(701\) 17.8913i 0.675746i 0.941192 + 0.337873i \(0.109708\pi\)
−0.941192 + 0.337873i \(0.890292\pi\)
\(702\) 0 0
\(703\) −26.0678 −0.983165
\(704\) 12.8528 23.2341i 0.484410 0.875667i
\(705\) 0 0
\(706\) −45.6979 3.85757i −1.71986 0.145181i
\(707\) 13.1650i 0.495121i
\(708\) 0 0
\(709\) 22.0614i 0.828535i 0.910155 + 0.414267i \(0.135962\pi\)
−0.910155 + 0.414267i \(0.864038\pi\)
\(710\) 2.64600 31.3453i 0.0993026 1.17637i
\(711\) 0 0
\(712\) 13.2837 + 3.42933i 0.497828 + 0.128519i
\(713\) −68.9499 −2.58219
\(714\) 0 0
\(715\) 35.7273i 1.33613i
\(716\) −1.16288 + 6.83883i −0.0434588 + 0.255579i
\(717\) 0 0
\(718\) −18.3189 1.54638i −0.683656 0.0577104i
\(719\) 15.8888 0.592552 0.296276 0.955102i \(-0.404255\pi\)
0.296276 + 0.955102i \(0.404255\pi\)
\(720\) 0 0
\(721\) 15.6983 0.584634
\(722\) −5.78440 0.488287i −0.215273 0.0181722i
\(723\) 0 0
\(724\) 6.50394 38.2493i 0.241717 1.42153i
\(725\) 69.0425i 2.56418i
\(726\) 0 0
\(727\) −26.2510 −0.973595 −0.486798 0.873515i \(-0.661835\pi\)
−0.486798 + 0.873515i \(0.661835\pi\)
\(728\) −2.19767 + 8.51280i −0.0814510 + 0.315505i
\(729\) 0 0
\(730\) −0.643696 + 7.62542i −0.0238243 + 0.282230i
\(731\) 9.87487i 0.365235i
\(732\) 0 0
\(733\) 23.1441i 0.854848i 0.904051 + 0.427424i \(0.140579\pi\)
−0.904051 + 0.427424i \(0.859421\pi\)
\(734\) −10.6476 0.898811i −0.393010 0.0331757i
\(735\) 0 0
\(736\) 45.4299 + 20.3463i 1.67457 + 0.749975i
\(737\) −3.01935 −0.111219
\(738\) 0 0
\(739\) 11.2767i 0.414819i 0.978254 + 0.207409i \(0.0665032\pi\)
−0.978254 + 0.207409i \(0.933497\pi\)
\(740\) −37.0294 6.29650i −1.36123 0.231464i
\(741\) 0 0
\(742\) −0.775190 + 9.18314i −0.0284581 + 0.337124i
\(743\) 5.16580 0.189515 0.0947575 0.995500i \(-0.469792\pi\)
0.0947575 + 0.995500i \(0.469792\pi\)
\(744\) 0 0
\(745\) 24.5330 0.898821
\(746\) 4.12366 48.8502i 0.150978 1.78853i
\(747\) 0 0
\(748\) −1.56095 + 9.17985i −0.0570739 + 0.335649i
\(749\) 9.37257i 0.342466i
\(750\) 0 0
\(751\) 35.7670 1.30516 0.652578 0.757722i \(-0.273687\pi\)
0.652578 + 0.757722i \(0.273687\pi\)
\(752\) 42.6278 + 14.9286i 1.55448 + 0.544389i
\(753\) 0 0
\(754\) 43.2516 + 3.65106i 1.57513 + 0.132964i
\(755\) 0.874212i 0.0318158i
\(756\) 0 0
\(757\) 31.6174i 1.14916i 0.818450 + 0.574578i \(0.194834\pi\)
−0.818450 + 0.574578i \(0.805166\pi\)
\(758\) −0.0366832 + 0.434560i −0.00133239 + 0.0157839i
\(759\) 0 0
\(760\) −45.5867 11.7687i −1.65360 0.426895i
\(761\) −12.7856 −0.463477 −0.231738 0.972778i \(-0.574441\pi\)
−0.231738 + 0.972778i \(0.574441\pi\)
\(762\) 0 0
\(763\) 7.31490i 0.264817i
\(764\) 46.2581 + 7.86575i 1.67356 + 0.284573i
\(765\) 0 0
\(766\) 6.14446 + 0.518681i 0.222008 + 0.0187407i
\(767\) 12.1120 0.437340
\(768\) 0 0
\(769\) 6.55622 0.236423 0.118212 0.992988i \(-0.462284\pi\)
0.118212 + 0.992988i \(0.462284\pi\)
\(770\) 16.1970 + 1.36727i 0.583701 + 0.0492728i
\(771\) 0 0
\(772\) −30.6350 5.20920i −1.10258 0.187483i
\(773\) 27.7250i 0.997197i −0.866833 0.498599i \(-0.833848\pi\)
0.866833 0.498599i \(-0.166152\pi\)
\(774\) 0 0
\(775\) 54.7893 1.96809
\(776\) 4.47174 + 1.15443i 0.160526 + 0.0414416i
\(777\) 0 0
\(778\) −0.158677 + 1.87974i −0.00568886 + 0.0673920i
\(779\) 55.6187i 1.99275i
\(780\) 0 0
\(781\) 21.3185i 0.762837i
\(782\) −17.3949 1.46838i −0.622039 0.0525091i
\(783\) 0 0
\(784\) 3.77519 + 1.32210i 0.134828 + 0.0472178i
\(785\) −10.7707 −0.384421
\(786\) 0 0