Properties

Label 300.2.h.c.299.4
Level $300$
Weight $2$
Character 300.299
Analytic conductor $2.396$
Analytic rank $0$
Dimension $16$
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.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 2 x^{14} + 10 x^{13} - 42 x^{11} + 134 x^{10} + 110 x^{9} + 92 x^{8} + 142 x^{7} + 1514 x^{6} + 1102 x^{5} + 249 x^{4} - 1056 x^{3} + 392 x^{2} - 280 x + 100\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 299.4
Root \(1.10359 - 2.13477i\) of defining polynomial
Character \(\chi\) \(=\) 300.299
Dual form 300.2.h.c.299.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 - 0.758030i) q^{4} +(-1.47722 - 1.95392i) q^{6} -3.56393 q^{7} +(-2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} +O(q^{10})\) \(q+(-1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 - 0.758030i) q^{4} +(-1.47722 - 1.95392i) q^{6} -3.56393 q^{7} +(-2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} -4.20732 q^{11} +(2.58348 + 2.30774i) q^{12} +2.70156i q^{13} +(4.94525 - 0.973477i) q^{14} +(2.85078 - 2.80590i) q^{16} +0.828216 q^{17} +(1.92320 - 3.78171i) q^{18} +5.07999i q^{19} +(-2.70156 - 5.55034i) q^{21} +(5.83802 - 1.14922i) q^{22} +1.09259i q^{23} +(-4.21515 - 2.49651i) q^{24} +(-0.737925 - 3.74865i) q^{26} +(-5.07999 - 1.09259i) q^{27} +(-6.59605 + 2.70156i) q^{28} -5.55034i q^{29} +6.59605i q^{31} +(-3.18928 + 4.67210i) q^{32} +(-3.18928 - 6.55234i) q^{33} +(-1.14922 + 0.226225i) q^{34} +(-1.63564 + 5.77275i) q^{36} -5.40312i q^{37} +(-1.38758 - 7.04891i) q^{38} +(-4.20732 + 2.04787i) q^{39} +10.2725i q^{41} +(5.26471 + 6.96364i) q^{42} +0.531805 q^{43} +(-7.78683 + 3.18928i) q^{44} +(-0.298438 - 1.51606i) q^{46} -6.22947i q^{47} +(6.53078 + 2.31276i) q^{48} +5.70156 q^{49} +(0.627812 + 1.28984i) q^{51} +(2.04787 + 5.00000i) q^{52} +5.55034 q^{53} +(7.34735 + 0.128476i) q^{54} +(8.41464 - 5.55034i) q^{56} +(-7.91140 + 3.85078i) q^{57} +(1.51606 + 7.70156i) q^{58} +0.701562 q^{61} +(-1.80169 - 9.15257i) q^{62} +(6.59605 - 8.41464i) q^{63} +(3.14922 - 7.35408i) q^{64} +(6.21515 + 8.22079i) q^{66} +2.04787 q^{67} +(1.53285 - 0.627812i) q^{68} +(-1.70156 + 0.828216i) q^{69} +11.3663 q^{71} +(0.692770 - 8.45695i) q^{72} +7.70156i q^{73} +(1.47585 + 7.49729i) q^{74} +(3.85078 + 9.40194i) q^{76} +14.9946 q^{77} +(5.27865 - 3.99080i) q^{78} -7.12785i q^{79} +(-2.14922 - 8.73961i) q^{81} +(-2.80590 - 14.2539i) q^{82} +3.11473i q^{83} +(-9.20732 - 8.22459i) q^{84} +(-0.737925 + 0.145261i) q^{86} +(8.64391 - 4.20732i) q^{87} +(9.93375 - 6.55234i) q^{88} +4.72212i q^{89} -9.62817i q^{91} +(0.828216 + 2.02214i) q^{92} +(-10.2725 + 5.00000i) q^{93} +(1.70156 + 8.64391i) q^{94} +(-9.69374 - 1.42528i) q^{96} +8.10469i q^{97} +(-7.91140 + 1.55737i) q^{98} +(7.78683 - 9.93375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{4} + 6q^{6} - 4q^{9} + O(q^{10}) \) \( 16q + 4q^{4} + 6q^{6} - 4q^{9} + 20q^{16} + 8q^{21} - 26q^{24} - 44q^{34} - 42q^{36} - 56q^{46} + 40q^{49} + 56q^{54} - 40q^{61} + 76q^{64} + 58q^{66} + 24q^{69} + 36q^{76} - 60q^{81} - 80q^{84} - 24q^{94} - 78q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38758 + 0.273147i −0.981170 + 0.193144i
\(3\) 0.758030 + 1.55737i 0.437649 + 0.899146i
\(4\) 1.85078 0.758030i 0.925391 0.379015i
\(5\) 0 0
\(6\) −1.47722 1.95392i −0.603073 0.797686i
\(7\) −3.56393 −1.34704 −0.673519 0.739170i \(-0.735218\pi\)
−0.673519 + 0.739170i \(0.735218\pi\)
\(8\) −2.36106 + 1.55737i −0.834761 + 0.550612i
\(9\) −1.85078 + 2.36106i −0.616927 + 0.787020i
\(10\) 0 0
\(11\) −4.20732 −1.26856 −0.634278 0.773105i \(-0.718702\pi\)
−0.634278 + 0.773105i \(0.718702\pi\)
\(12\) 2.58348 + 2.30774i 0.745786 + 0.666186i
\(13\) 2.70156i 0.749279i 0.927171 + 0.374639i \(0.122233\pi\)
−0.927171 + 0.374639i \(0.877767\pi\)
\(14\) 4.94525 0.973477i 1.32167 0.260173i
\(15\) 0 0
\(16\) 2.85078 2.80590i 0.712695 0.701474i
\(17\) 0.828216 0.200872 0.100436 0.994944i \(-0.467976\pi\)
0.100436 + 0.994944i \(0.467976\pi\)
\(18\) 1.92320 3.78171i 0.453302 0.891357i
\(19\) 5.07999i 1.16543i 0.812677 + 0.582714i \(0.198009\pi\)
−0.812677 + 0.582714i \(0.801991\pi\)
\(20\) 0 0
\(21\) −2.70156 5.55034i −0.589529 1.21118i
\(22\) 5.83802 1.14922i 1.24467 0.245014i
\(23\) 1.09259i 0.227821i 0.993491 + 0.113910i \(0.0363377\pi\)
−0.993491 + 0.113910i \(0.963662\pi\)
\(24\) −4.21515 2.49651i −0.860413 0.509597i
\(25\) 0 0
\(26\) −0.737925 3.74865i −0.144719 0.735170i
\(27\) −5.07999 1.09259i −0.977644 0.210269i
\(28\) −6.59605 + 2.70156i −1.24654 + 0.510547i
\(29\) 5.55034i 1.03067i −0.856988 0.515336i \(-0.827667\pi\)
0.856988 0.515336i \(-0.172333\pi\)
\(30\) 0 0
\(31\) 6.59605i 1.18468i 0.805686 + 0.592342i \(0.201797\pi\)
−0.805686 + 0.592342i \(0.798203\pi\)
\(32\) −3.18928 + 4.67210i −0.563790 + 0.825918i
\(33\) −3.18928 6.55234i −0.555182 1.14062i
\(34\) −1.14922 + 0.226225i −0.197089 + 0.0387972i
\(35\) 0 0
\(36\) −1.63564 + 5.77275i −0.272606 + 0.962126i
\(37\) 5.40312i 0.888268i −0.895960 0.444134i \(-0.853511\pi\)
0.895960 0.444134i \(-0.146489\pi\)
\(38\) −1.38758 7.04891i −0.225096 1.14348i
\(39\) −4.20732 + 2.04787i −0.673711 + 0.327921i
\(40\) 0 0
\(41\) 10.2725i 1.60429i 0.597130 + 0.802144i \(0.296308\pi\)
−0.597130 + 0.802144i \(0.703692\pi\)
\(42\) 5.26471 + 6.96364i 0.812362 + 1.07451i
\(43\) 0.531805 0.0810995 0.0405498 0.999178i \(-0.487089\pi\)
0.0405498 + 0.999178i \(0.487089\pi\)
\(44\) −7.78683 + 3.18928i −1.17391 + 0.480802i
\(45\) 0 0
\(46\) −0.298438 1.51606i −0.0440023 0.223531i
\(47\) 6.22947i 0.908661i −0.890833 0.454331i \(-0.849879\pi\)
0.890833 0.454331i \(-0.150121\pi\)
\(48\) 6.53078 + 2.31276i 0.942638 + 0.333818i
\(49\) 5.70156 0.814509
\(50\) 0 0
\(51\) 0.627812 + 1.28984i 0.0879113 + 0.180613i
\(52\) 2.04787 + 5.00000i 0.283988 + 0.693375i
\(53\) 5.55034 0.762398 0.381199 0.924493i \(-0.375511\pi\)
0.381199 + 0.924493i \(0.375511\pi\)
\(54\) 7.34735 + 0.128476i 0.999847 + 0.0174833i
\(55\) 0 0
\(56\) 8.41464 5.55034i 1.12445 0.741695i
\(57\) −7.91140 + 3.85078i −1.04789 + 0.510048i
\(58\) 1.51606 + 7.70156i 0.199068 + 1.01126i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0.701562 0.0898258 0.0449129 0.998991i \(-0.485699\pi\)
0.0449129 + 0.998991i \(0.485699\pi\)
\(62\) −1.80169 9.15257i −0.228815 1.16238i
\(63\) 6.59605 8.41464i 0.831024 1.06015i
\(64\) 3.14922 7.35408i 0.393652 0.919259i
\(65\) 0 0
\(66\) 6.21515 + 8.22079i 0.765032 + 1.01191i
\(67\) 2.04787 0.250187 0.125093 0.992145i \(-0.460077\pi\)
0.125093 + 0.992145i \(0.460077\pi\)
\(68\) 1.53285 0.627812i 0.185885 0.0761334i
\(69\) −1.70156 + 0.828216i −0.204844 + 0.0997054i
\(70\) 0 0
\(71\) 11.3663 1.34894 0.674468 0.738304i \(-0.264373\pi\)
0.674468 + 0.738304i \(0.264373\pi\)
\(72\) 0.692770 8.45695i 0.0816437 0.996662i
\(73\) 7.70156i 0.901400i 0.892676 + 0.450700i \(0.148826\pi\)
−0.892676 + 0.450700i \(0.851174\pi\)
\(74\) 1.47585 + 7.49729i 0.171564 + 0.871542i
\(75\) 0 0
\(76\) 3.85078 + 9.40194i 0.441715 + 1.07848i
\(77\) 14.9946 1.70879
\(78\) 5.27865 3.99080i 0.597689 0.451870i
\(79\) 7.12785i 0.801946i −0.916090 0.400973i \(-0.868672\pi\)
0.916090 0.400973i \(-0.131328\pi\)
\(80\) 0 0
\(81\) −2.14922 8.73961i −0.238802 0.971068i
\(82\) −2.80590 14.2539i −0.309859 1.57408i
\(83\) 3.11473i 0.341886i 0.985281 + 0.170943i \(0.0546815\pi\)
−0.985281 + 0.170943i \(0.945319\pi\)
\(84\) −9.20732 8.22459i −1.00460 0.897377i
\(85\) 0 0
\(86\) −0.737925 + 0.145261i −0.0795724 + 0.0156639i
\(87\) 8.64391 4.20732i 0.926724 0.451072i
\(88\) 9.93375 6.55234i 1.05894 0.698482i
\(89\) 4.72212i 0.500544i 0.968176 + 0.250272i \(0.0805200\pi\)
−0.968176 + 0.250272i \(0.919480\pi\)
\(90\) 0 0
\(91\) 9.62817i 1.00931i
\(92\) 0.828216 + 2.02214i 0.0863474 + 0.210823i
\(93\) −10.2725 + 5.00000i −1.06520 + 0.518476i
\(94\) 1.70156 + 8.64391i 0.175503 + 0.891551i
\(95\) 0 0
\(96\) −9.69374 1.42528i −0.989363 0.145467i
\(97\) 8.10469i 0.822906i 0.911431 + 0.411453i \(0.134979\pi\)
−0.911431 + 0.411453i \(0.865021\pi\)
\(98\) −7.91140 + 1.55737i −0.799172 + 0.157318i
\(99\) 7.78683 9.93375i 0.782606 0.998379i
\(100\) 0 0
\(101\) 7.20677i 0.717100i 0.933510 + 0.358550i \(0.116729\pi\)
−0.933510 + 0.358550i \(0.883271\pi\)
\(102\) −1.22346 1.61827i −0.121140 0.160233i
\(103\) −4.09573 −0.403564 −0.201782 0.979430i \(-0.564673\pi\)
−0.201782 + 0.979430i \(0.564673\pi\)
\(104\) −4.20732 6.37855i −0.412562 0.625469i
\(105\) 0 0
\(106\) −7.70156 + 1.51606i −0.748042 + 0.147253i
\(107\) 18.8514i 1.82244i 0.411924 + 0.911218i \(0.364857\pi\)
−0.411924 + 0.911218i \(0.635143\pi\)
\(108\) −10.2302 + 1.82864i −0.984397 + 0.175961i
\(109\) −8.70156 −0.833458 −0.416729 0.909031i \(-0.636824\pi\)
−0.416729 + 0.909031i \(0.636824\pi\)
\(110\) 0 0
\(111\) 8.41464 4.09573i 0.798683 0.388750i
\(112\) −10.1600 + 10.0000i −0.960027 + 0.944911i
\(113\) 15.8228 1.48848 0.744242 0.667910i \(-0.232811\pi\)
0.744242 + 0.667910i \(0.232811\pi\)
\(114\) 9.92590 7.50426i 0.929646 0.702838i
\(115\) 0 0
\(116\) −4.20732 10.2725i −0.390640 0.953774i
\(117\) −6.37855 5.00000i −0.589697 0.462250i
\(118\) 0 0
\(119\) −2.95170 −0.270582
\(120\) 0 0
\(121\) 6.70156 0.609233
\(122\) −0.973477 + 0.191630i −0.0881344 + 0.0173493i
\(123\) −15.9980 + 7.78683i −1.44249 + 0.702115i
\(124\) 5.00000 + 12.2078i 0.449013 + 1.09630i
\(125\) 0 0
\(126\) −6.85413 + 13.4777i −0.610615 + 1.20069i
\(127\) 16.2242 1.43967 0.719833 0.694147i \(-0.244218\pi\)
0.719833 + 0.694147i \(0.244218\pi\)
\(128\) −2.36106 + 11.0646i −0.208690 + 0.977982i
\(129\) 0.403124 + 0.828216i 0.0354931 + 0.0729203i
\(130\) 0 0
\(131\) −19.7810 −1.72827 −0.864136 0.503258i \(-0.832135\pi\)
−0.864136 + 0.503258i \(0.832135\pi\)
\(132\) −10.8695 9.70939i −0.946071 0.845094i
\(133\) 18.1047i 1.56988i
\(134\) −2.84159 + 0.559369i −0.245476 + 0.0483221i
\(135\) 0 0
\(136\) −1.95547 + 1.28984i −0.167680 + 0.110602i
\(137\) −6.37855 −0.544957 −0.272478 0.962162i \(-0.587843\pi\)
−0.272478 + 0.962162i \(0.587843\pi\)
\(138\) 2.13484 1.61400i 0.181729 0.137392i
\(139\) 1.51606i 0.128591i −0.997931 0.0642953i \(-0.979520\pi\)
0.997931 0.0642953i \(-0.0204799\pi\)
\(140\) 0 0
\(141\) 9.70156 4.72212i 0.817019 0.397674i
\(142\) −15.7718 + 3.10469i −1.32354 + 0.260539i
\(143\) 11.3663i 0.950501i
\(144\) 1.34872 + 11.9240i 0.112393 + 0.993664i
\(145\) 0 0
\(146\) −2.10366 10.6866i −0.174100 0.884427i
\(147\) 4.32196 + 8.87942i 0.356469 + 0.732362i
\(148\) −4.09573 10.0000i −0.336667 0.821995i
\(149\) 1.65643i 0.135700i 0.997696 + 0.0678501i \(0.0216139\pi\)
−0.997696 + 0.0678501i \(0.978386\pi\)
\(150\) 0 0
\(151\) 4.62754i 0.376583i −0.982113 0.188292i \(-0.939705\pi\)
0.982113 0.188292i \(-0.0602951\pi\)
\(152\) −7.91140 11.9942i −0.641699 0.972854i
\(153\) −1.53285 + 1.95547i −0.123923 + 0.158090i
\(154\) −20.8062 + 4.09573i −1.67662 + 0.330043i
\(155\) 0 0
\(156\) −6.23449 + 6.97943i −0.499159 + 0.558801i
\(157\) 8.10469i 0.646824i 0.946258 + 0.323412i \(0.104830\pi\)
−0.946258 + 0.323412i \(0.895170\pi\)
\(158\) 1.94695 + 9.89049i 0.154891 + 0.786845i
\(159\) 4.20732 + 8.64391i 0.333662 + 0.685507i
\(160\) 0 0
\(161\) 3.89391i 0.306883i
\(162\) 5.36943 + 11.5399i 0.421862 + 0.906660i
\(163\) −5.07999 −0.397895 −0.198948 0.980010i \(-0.563752\pi\)
−0.198948 + 0.980010i \(0.563752\pi\)
\(164\) 7.78683 + 19.0121i 0.608049 + 1.48459i
\(165\) 0 0
\(166\) −0.850781 4.32196i −0.0660334 0.335449i
\(167\) 3.27777i 0.253641i 0.991926 + 0.126821i \(0.0404773\pi\)
−0.991926 + 0.126821i \(0.959523\pi\)
\(168\) 15.0225 + 8.89736i 1.15901 + 0.686447i
\(169\) 5.70156 0.438582
\(170\) 0 0
\(171\) −11.9942 9.40194i −0.917216 0.718984i
\(172\) 0.984255 0.403124i 0.0750487 0.0307379i
\(173\) −14.9946 −1.14002 −0.570008 0.821639i \(-0.693060\pi\)
−0.570008 + 0.821639i \(0.693060\pi\)
\(174\) −10.8449 + 8.19908i −0.822152 + 0.621570i
\(175\) 0 0
\(176\) −11.9942 + 11.8053i −0.904093 + 0.889858i
\(177\) 0 0
\(178\) −1.28984 6.55234i −0.0966772 0.491119i
\(179\) 15.5737 1.16403 0.582015 0.813178i \(-0.302264\pi\)
0.582015 + 0.813178i \(0.302264\pi\)
\(180\) 0 0
\(181\) −21.5078 −1.59866 −0.799331 0.600890i \(-0.794813\pi\)
−0.799331 + 0.600890i \(0.794813\pi\)
\(182\) 2.62991 + 13.3599i 0.194942 + 0.990301i
\(183\) 0.531805 + 1.09259i 0.0393122 + 0.0807665i
\(184\) −1.70156 2.57967i −0.125441 0.190176i
\(185\) 0 0
\(186\) 12.8882 9.74382i 0.945006 0.714451i
\(187\) −3.48457 −0.254817
\(188\) −4.72212 11.5294i −0.344396 0.840866i
\(189\) 18.1047 + 3.89391i 1.31692 + 0.283240i
\(190\) 0 0
\(191\) 11.3663 0.822440 0.411220 0.911536i \(-0.365103\pi\)
0.411220 + 0.911536i \(0.365103\pi\)
\(192\) 13.8402 0.670121i 0.998830 0.0483618i
\(193\) 5.80625i 0.417943i −0.977922 0.208971i \(-0.932988\pi\)
0.977922 0.208971i \(-0.0670116\pi\)
\(194\) −2.21377 11.2459i −0.158940 0.807411i
\(195\) 0 0
\(196\) 10.5523 4.32196i 0.753739 0.308711i
\(197\) −9.44424 −0.672875 −0.336437 0.941706i \(-0.609222\pi\)
−0.336437 + 0.941706i \(0.609222\pi\)
\(198\) −8.09151 + 15.9109i −0.575039 + 1.13074i
\(199\) 15.6924i 1.11241i −0.831047 0.556203i \(-0.812258\pi\)
0.831047 0.556203i \(-0.187742\pi\)
\(200\) 0 0
\(201\) 1.55234 + 3.18928i 0.109494 + 0.224954i
\(202\) −1.96851 10.0000i −0.138504 0.703598i
\(203\) 19.7810i 1.38835i
\(204\) 2.13968 + 1.91130i 0.149807 + 0.133818i
\(205\) 0 0
\(206\) 5.68317 1.11874i 0.395965 0.0779462i
\(207\) −2.57967 2.02214i −0.179299 0.140549i
\(208\) 7.58030 + 7.70156i 0.525599 + 0.534007i
\(209\) 21.3731i 1.47841i
\(210\) 0 0
\(211\) 14.1763i 0.975940i −0.872860 0.487970i \(-0.837738\pi\)
0.872860 0.487970i \(-0.162262\pi\)
\(212\) 10.2725 4.20732i 0.705515 0.288960i
\(213\) 8.61603 + 17.7016i 0.590361 + 1.21289i
\(214\) −5.14922 26.1580i −0.351993 1.78812i
\(215\) 0 0
\(216\) 13.6957 5.33173i 0.931876 0.362778i
\(217\) 23.5078i 1.59581i
\(218\) 12.0742 2.37681i 0.817765 0.160978i
\(219\) −11.9942 + 5.83802i −0.810490 + 0.394497i
\(220\) 0 0
\(221\) 2.23748i 0.150509i
\(222\) −10.5573 + 7.98161i −0.708559 + 0.535691i
\(223\) 15.6924 1.05084 0.525421 0.850843i \(-0.323908\pi\)
0.525421 + 0.850843i \(0.323908\pi\)
\(224\) 11.3663 16.6510i 0.759446 1.11254i
\(225\) 0 0
\(226\) −21.9555 + 4.32196i −1.46046 + 0.287492i
\(227\) 11.6924i 0.776053i −0.921648 0.388026i \(-0.873157\pi\)
0.921648 0.388026i \(-0.126843\pi\)
\(228\) −11.7233 + 13.1240i −0.776392 + 0.869160i
\(229\) −8.70156 −0.575015 −0.287508 0.957778i \(-0.592827\pi\)
−0.287508 + 0.957778i \(0.592827\pi\)
\(230\) 0 0
\(231\) 11.3663 + 23.3521i 0.747850 + 1.53645i
\(232\) 8.64391 + 13.1047i 0.567501 + 0.860365i
\(233\) −14.9946 −0.982328 −0.491164 0.871067i \(-0.663428\pi\)
−0.491164 + 0.871067i \(0.663428\pi\)
\(234\) 10.2165 + 5.19564i 0.667875 + 0.339649i
\(235\) 0 0
\(236\) 0 0
\(237\) 11.1007 5.40312i 0.721066 0.350971i
\(238\) 4.09573 0.806248i 0.265487 0.0522613i
\(239\) −5.46295 −0.353369 −0.176684 0.984268i \(-0.556537\pi\)
−0.176684 + 0.984268i \(0.556537\pi\)
\(240\) 0 0
\(241\) 7.00000 0.450910 0.225455 0.974254i \(-0.427613\pi\)
0.225455 + 0.974254i \(0.427613\pi\)
\(242\) −9.29898 + 1.83051i −0.597761 + 0.117670i
\(243\) 11.9816 9.97201i 0.768621 0.639705i
\(244\) 1.29844 0.531805i 0.0831240 0.0340453i
\(245\) 0 0
\(246\) 20.0716 15.1747i 1.27972 0.967503i
\(247\) −13.7239 −0.873231
\(248\) −10.2725 15.5737i −0.652302 0.988929i
\(249\) −4.85078 + 2.36106i −0.307406 + 0.149626i
\(250\) 0 0
\(251\) 1.25562 0.0792543 0.0396272 0.999215i \(-0.487383\pi\)
0.0396272 + 0.999215i \(0.487383\pi\)
\(252\) 5.82928 20.5737i 0.367210 1.29602i
\(253\) 4.59688i 0.289003i
\(254\) −22.5125 + 4.43160i −1.41256 + 0.278063i
\(255\) 0 0
\(256\) 0.253905 15.9980i 0.0158691 0.999874i
\(257\) 11.1007 0.692441 0.346221 0.938153i \(-0.387465\pi\)
0.346221 + 0.938153i \(0.387465\pi\)
\(258\) −0.785594 1.03911i −0.0489089 0.0646920i
\(259\) 19.2563i 1.19653i
\(260\) 0 0
\(261\) 13.1047 + 10.2725i 0.811160 + 0.635849i
\(262\) 27.4478 5.40312i 1.69573 0.333806i
\(263\) 17.9219i 1.10511i −0.833476 0.552555i \(-0.813653\pi\)
0.833476 0.552555i \(-0.186347\pi\)
\(264\) 17.7345 + 10.5036i 1.09148 + 0.646452i
\(265\) 0 0
\(266\) 4.94525 + 25.1218i 0.303213 + 1.54032i
\(267\) −7.35408 + 3.57951i −0.450062 + 0.219062i
\(268\) 3.79015 1.55234i 0.231520 0.0948245i
\(269\) 14.9946i 0.914236i 0.889406 + 0.457118i \(0.151118\pi\)
−0.889406 + 0.457118i \(0.848882\pi\)
\(270\) 0 0
\(271\) 24.4157i 1.48315i 0.670872 + 0.741573i \(0.265920\pi\)
−0.670872 + 0.741573i \(0.734080\pi\)
\(272\) 2.36106 2.32389i 0.143160 0.140906i
\(273\) 14.9946 7.29844i 0.907513 0.441722i
\(274\) 8.85078 1.74228i 0.534695 0.105255i
\(275\) 0 0
\(276\) −2.52141 + 2.82268i −0.151771 + 0.169905i
\(277\) 28.1047i 1.68865i 0.535834 + 0.844323i \(0.319997\pi\)
−0.535834 + 0.844323i \(0.680003\pi\)
\(278\) 0.414108 + 2.10366i 0.0248365 + 0.126169i
\(279\) −15.5737 12.2078i −0.932371 0.730864i
\(280\) 0 0
\(281\) 7.20677i 0.429920i −0.976623 0.214960i \(-0.931038\pi\)
0.976623 0.214960i \(-0.0689621\pi\)
\(282\) −12.1719 + 9.20230i −0.724826 + 0.547989i
\(283\) 6.14360 0.365199 0.182599 0.983187i \(-0.441549\pi\)
0.182599 + 0.983187i \(0.441549\pi\)
\(284\) 21.0366 8.61603i 1.24829 0.511267i
\(285\) 0 0
\(286\) 3.10469 + 15.7718i 0.183584 + 0.932604i
\(287\) 36.6103i 2.16104i
\(288\) −5.12846 16.1771i −0.302197 0.953245i
\(289\) −16.3141 −0.959651
\(290\) 0 0
\(291\) −12.6220 + 6.14360i −0.739913 + 0.360144i
\(292\) 5.83802 + 14.2539i 0.341644 + 0.834147i
\(293\) 18.8885 1.10348 0.551739 0.834017i \(-0.313965\pi\)
0.551739 + 0.834017i \(0.313965\pi\)
\(294\) −8.42247 11.1404i −0.491208 0.649722i
\(295\) 0 0
\(296\) 8.41464 + 12.7571i 0.489091 + 0.741492i
\(297\) 21.3731 + 4.59688i 1.24020 + 0.266738i
\(298\) −0.452450 2.29844i −0.0262097 0.133145i
\(299\) −2.95170 −0.170701
\(300\) 0 0
\(301\) −1.89531 −0.109244
\(302\) 1.26400 + 6.42110i 0.0727350 + 0.369493i
\(303\) −11.2236 + 5.46295i −0.644778 + 0.313838i
\(304\) 14.2539 + 14.4819i 0.817518 + 0.830595i
\(305\) 0 0
\(306\) 1.59282 3.13207i 0.0910556 0.179048i
\(307\) −20.3993 −1.16425 −0.582125 0.813100i \(-0.697778\pi\)
−0.582125 + 0.813100i \(0.697778\pi\)
\(308\) 27.7517 11.3663i 1.58130 0.647657i
\(309\) −3.10469 6.37855i −0.176619 0.362863i
\(310\) 0 0
\(311\) 16.8293 0.954301 0.477151 0.878821i \(-0.341670\pi\)
0.477151 + 0.878821i \(0.341670\pi\)
\(312\) 6.74447 11.3875i 0.381830 0.644689i
\(313\) 22.7016i 1.28317i 0.767053 + 0.641584i \(0.221722\pi\)
−0.767053 + 0.641584i \(0.778278\pi\)
\(314\) −2.21377 11.2459i −0.124930 0.634645i
\(315\) 0 0
\(316\) −5.40312 13.1921i −0.303949 0.742113i
\(317\) −29.9892 −1.68436 −0.842180 0.539197i \(-0.818728\pi\)
−0.842180 + 0.539197i \(0.818728\pi\)
\(318\) −8.19908 10.8449i −0.459781 0.608154i
\(319\) 23.3521i 1.30746i
\(320\) 0 0
\(321\) −29.3586 + 14.2900i −1.63864 + 0.797587i
\(322\) 1.06361 + 5.40312i 0.0592727 + 0.301104i
\(323\) 4.20732i 0.234102i
\(324\) −10.6026 14.5459i −0.589035 0.808108i
\(325\) 0 0
\(326\) 7.04891 1.38758i 0.390403 0.0768512i
\(327\) −6.59605 13.5515i −0.364762 0.749401i
\(328\) −15.9980 24.2539i −0.883341 1.33920i
\(329\) 22.2014i 1.22400i
\(330\) 0 0
\(331\) 30.0275i 1.65046i 0.564798 + 0.825229i \(0.308954\pi\)
−0.564798 + 0.825229i \(0.691046\pi\)
\(332\) 2.36106 + 5.76469i 0.129580 + 0.316378i
\(333\) 12.7571 + 10.0000i 0.699085 + 0.547997i
\(334\) −0.895314 4.54818i −0.0489894 0.248865i
\(335\) 0 0
\(336\) −23.2752 8.24250i −1.26977 0.449665i
\(337\) 0.403124i 0.0219596i −0.999940 0.0109798i \(-0.996505\pi\)
0.999940 0.0109798i \(-0.00349505\pi\)
\(338\) −7.91140 + 1.55737i −0.430323 + 0.0847096i
\(339\) 11.9942 + 24.6419i 0.651433 + 1.33836i
\(340\) 0 0
\(341\) 27.7517i 1.50284i
\(342\) 19.2110 + 9.76981i 1.03881 + 0.528291i
\(343\) 4.62754 0.249863
\(344\) −1.25562 + 0.828216i −0.0676987 + 0.0446544i
\(345\) 0 0
\(346\) 20.8062 4.09573i 1.11855 0.220188i
\(347\) 13.3885i 0.718732i 0.933197 + 0.359366i \(0.117007\pi\)
−0.933197 + 0.359366i \(0.882993\pi\)
\(348\) 12.8087 14.3392i 0.686619 0.768661i
\(349\) 12.2094 0.653553 0.326776 0.945102i \(-0.394038\pi\)
0.326776 + 0.945102i \(0.394038\pi\)
\(350\) 0 0
\(351\) 2.95170 13.7239i 0.157550 0.732527i
\(352\) 13.4183 19.6570i 0.715199 1.04772i
\(353\) −29.4081 −1.56524 −0.782618 0.622502i \(-0.786116\pi\)
−0.782618 + 0.622502i \(0.786116\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.57951 + 8.73961i 0.189714 + 0.463199i
\(357\) −2.23748 4.59688i −0.118420 0.243292i
\(358\) −21.6098 + 4.25391i −1.14211 + 0.224826i
\(359\) −36.6103 −1.93222 −0.966108 0.258137i \(-0.916891\pi\)
−0.966108 + 0.258137i \(0.916891\pi\)
\(360\) 0 0
\(361\) −6.80625 −0.358224
\(362\) 29.8439 5.87480i 1.56856 0.308773i
\(363\) 5.07999 + 10.4368i 0.266630 + 0.547789i
\(364\) −7.29844 17.8196i −0.382542 0.934002i
\(365\) 0 0
\(366\) −1.03636 1.37080i −0.0541715 0.0716528i
\(367\) −3.56393 −0.186035 −0.0930177 0.995664i \(-0.529651\pi\)
−0.0930177 + 0.995664i \(0.529651\pi\)
\(368\) 3.06569 + 3.11473i 0.159810 + 0.162367i
\(369\) −24.2539 19.0121i −1.26261 0.989729i
\(370\) 0 0
\(371\) −19.7810 −1.02698
\(372\) −15.2219 + 17.0407i −0.789220 + 0.883521i
\(373\) 17.2984i 0.895679i −0.894114 0.447840i \(-0.852194\pi\)
0.894114 0.447840i \(-0.147806\pi\)
\(374\) 4.83513 0.951801i 0.250019 0.0492165i
\(375\) 0 0
\(376\) 9.70156 + 14.7082i 0.500320 + 0.758515i
\(377\) 14.9946 0.772260
\(378\) −26.1854 0.457877i −1.34683 0.0235507i
\(379\) 21.3042i 1.09432i −0.837027 0.547162i \(-0.815708\pi\)
0.837027 0.547162i \(-0.184292\pi\)
\(380\) 0 0
\(381\) 12.2984 + 25.2670i 0.630068 + 1.29447i
\(382\) −15.7718 + 3.10469i −0.806953 + 0.158850i
\(383\) 12.4589i 0.636622i −0.947986 0.318311i \(-0.896884\pi\)
0.947986 0.318311i \(-0.103116\pi\)
\(384\) −19.0214 + 4.71026i −0.970681 + 0.240370i
\(385\) 0 0
\(386\) 1.58596 + 8.05666i 0.0807233 + 0.410073i
\(387\) −0.984255 + 1.25562i −0.0500325 + 0.0638270i
\(388\) 6.14360 + 15.0000i 0.311894 + 0.761510i
\(389\) 19.9639i 1.01221i −0.862472 0.506104i \(-0.831085\pi\)
0.862472 0.506104i \(-0.168915\pi\)
\(390\) 0 0
\(391\) 0.904899i 0.0457627i
\(392\) −13.4617 + 8.87942i −0.679920 + 0.448479i
\(393\) −14.9946 30.8062i −0.756377 1.55397i
\(394\) 13.1047 2.57967i 0.660205 0.129962i
\(395\) 0 0
\(396\) 6.88165 24.2878i 0.345816 1.22051i
\(397\) 28.9109i 1.45100i −0.688223 0.725499i \(-0.741609\pi\)
0.688223 0.725499i \(-0.258391\pi\)
\(398\) 4.28634 + 21.7745i 0.214855 + 1.09146i
\(399\) 28.1956 13.7239i 1.41155 0.687054i
\(400\) 0 0
\(401\) 30.8174i 1.53895i −0.638679 0.769473i \(-0.720519\pi\)
0.638679 0.769473i \(-0.279481\pi\)
\(402\) −3.02515 4.00137i −0.150881 0.199570i
\(403\) −17.8196 −0.887659
\(404\) 5.46295 + 13.3382i 0.271792 + 0.663598i
\(405\) 0 0
\(406\) −5.40312 27.4478i −0.268153 1.36221i
\(407\) 22.7327i 1.12682i
\(408\) −3.49105 2.06765i −0.172833 0.102364i
\(409\) 27.2094 1.34542 0.672708 0.739908i \(-0.265131\pi\)
0.672708 + 0.739908i \(0.265131\pi\)
\(410\) 0 0
\(411\) −4.83513 9.93375i −0.238500 0.489996i
\(412\) −7.58030 + 3.10469i −0.373455 + 0.152957i
\(413\) 0 0
\(414\) 4.13185 + 2.10127i 0.203070 + 0.103272i
\(415\) 0 0
\(416\) −12.6220 8.61603i −0.618843 0.422436i
\(417\) 2.36106 1.14922i 0.115622 0.0562775i
\(418\) 5.83802 + 29.6570i 0.285547 + 1.45057i
\(419\) 10.1107 0.493941 0.246970 0.969023i \(-0.420565\pi\)
0.246970 + 0.969023i \(0.420565\pi\)
\(420\) 0 0
\(421\) 24.2094 1.17989 0.589946 0.807442i \(-0.299149\pi\)
0.589946 + 0.807442i \(0.299149\pi\)
\(422\) 3.87223 + 19.6709i 0.188497 + 0.957563i
\(423\) 14.7082 + 11.5294i 0.715135 + 0.560578i
\(424\) −13.1047 + 8.64391i −0.636420 + 0.419785i
\(425\) 0 0
\(426\) −16.7906 22.2090i −0.813507 1.07603i
\(427\) −2.50031 −0.120999
\(428\) 14.2900 + 34.8899i 0.690731 + 1.68647i
\(429\) 17.7016 8.61603i 0.854639 0.415986i
\(430\) 0 0
\(431\) −19.7810 −0.952817 −0.476408 0.879224i \(-0.658062\pi\)
−0.476408 + 0.879224i \(0.658062\pi\)
\(432\) −17.5476 + 11.1392i −0.844260 + 0.535934i
\(433\) 31.2094i 1.49983i 0.661536 + 0.749913i \(0.269905\pi\)
−0.661536 + 0.749913i \(0.730095\pi\)
\(434\) 6.42110 + 32.6191i 0.308222 + 1.56577i
\(435\) 0 0
\(436\) −16.1047 + 6.59605i −0.771275 + 0.315893i
\(437\) −5.55034 −0.265509
\(438\) 15.0483 11.3769i 0.719034 0.543610i
\(439\) 21.9154i 1.04596i 0.852344 + 0.522981i \(0.175180\pi\)
−0.852344 + 0.522981i \(0.824820\pi\)
\(440\) 0 0
\(441\) −10.5523 + 13.4617i −0.502493 + 0.641035i
\(442\) −0.611161 3.10469i −0.0290699 0.147675i
\(443\) 11.2033i 0.532285i 0.963934 + 0.266143i \(0.0857492\pi\)
−0.963934 + 0.266143i \(0.914251\pi\)
\(444\) 12.4690 13.9589i 0.591752 0.662458i
\(445\) 0 0
\(446\) −21.7745 + 4.28634i −1.03105 + 0.202964i
\(447\) −2.57967 + 1.25562i −0.122014 + 0.0593890i
\(448\) −11.2236 + 26.2094i −0.530264 + 1.23828i
\(449\) 19.1357i 0.903068i 0.892254 + 0.451534i \(0.149123\pi\)
−0.892254 + 0.451534i \(0.850877\pi\)
\(450\) 0 0
\(451\) 43.2196i 2.03513i
\(452\) 29.2845 11.9942i 1.37743 0.564158i
\(453\) 7.20677 3.50781i 0.338604 0.164811i
\(454\) 3.19375 + 16.2242i 0.149890 + 0.761440i
\(455\) 0 0
\(456\) 12.6822 21.4129i 0.593899 1.00275i
\(457\) 16.8953i 0.790329i −0.918610 0.395165i \(-0.870688\pi\)
0.918610 0.395165i \(-0.129312\pi\)
\(458\) 12.0742 2.37681i 0.564188 0.111061i
\(459\) −4.20732 0.904899i −0.196381 0.0422371i
\(460\) 0 0
\(461\) 7.20677i 0.335653i 0.985817 + 0.167826i \(0.0536748\pi\)
−0.985817 + 0.167826i \(0.946325\pi\)
\(462\) −22.1503 29.2983i −1.03053 1.36308i
\(463\) 7.12785 0.331259 0.165630 0.986188i \(-0.447034\pi\)
0.165630 + 0.986188i \(0.447034\pi\)
\(464\) −15.5737 15.8228i −0.722989 0.734555i
\(465\) 0 0
\(466\) 20.8062 4.09573i 0.963831 0.189731i
\(467\) 0.766519i 0.0354703i −0.999843 0.0177351i \(-0.994354\pi\)
0.999843 0.0177351i \(-0.00564557\pi\)
\(468\) −15.5955 4.41877i −0.720900 0.204258i
\(469\) −7.29844 −0.337011
\(470\) 0 0
\(471\) −12.6220 + 6.14360i −0.581590 + 0.283082i
\(472\) 0 0
\(473\) −2.23748 −0.102879
\(474\) −13.9273 + 10.5294i −0.639701 + 0.483632i
\(475\) 0 0
\(476\) −5.46295 + 2.23748i −0.250394 + 0.102555i
\(477\) −10.2725 + 13.1047i −0.470344 + 0.600022i
\(478\) 7.58030 1.49219i 0.346715 0.0682512i
\(479\) 42.0732 1.92237 0.961187 0.275897i \(-0.0889747\pi\)
0.961187 + 0.275897i \(0.0889747\pi\)
\(480\) 0 0
\(481\) 14.5969 0.665560
\(482\) −9.71309 + 1.91203i −0.442419 + 0.0870906i
\(483\) 6.06424 2.95170i 0.275932 0.134307i
\(484\) 12.4031 5.07999i 0.563778 0.230908i
\(485\) 0 0
\(486\) −13.9017 + 17.1098i −0.630592 + 0.776114i
\(487\) 34.0438 1.54267 0.771337 0.636427i \(-0.219588\pi\)
0.771337 + 0.636427i \(0.219588\pi\)
\(488\) −1.65643 + 1.09259i −0.0749831 + 0.0494592i
\(489\) −3.85078 7.91140i −0.174138 0.357766i
\(490\) 0 0
\(491\) 16.8293 0.759495 0.379748 0.925090i \(-0.376011\pi\)
0.379748 + 0.925090i \(0.376011\pi\)
\(492\) −23.7061 + 26.5387i −1.06875 + 1.19646i
\(493\) 4.59688i 0.207033i
\(494\) 19.0431 3.74865i 0.856788 0.168660i
\(495\) 0 0
\(496\) 18.5078 + 18.8039i 0.831025 + 0.844319i
\(497\) −40.5088 −1.81707
\(498\) 6.08595 4.60115i 0.272718 0.206182i
\(499\) 22.9790i 1.02868i −0.857586 0.514340i \(-0.828037\pi\)
0.857586 0.514340i \(-0.171963\pi\)
\(500\) 0 0
\(501\) −5.10469 + 2.48465i −0.228061 + 0.111006i
\(502\) −1.74228 + 0.342970i −0.0777620 + 0.0153075i
\(503\) 32.2399i 1.43751i 0.695265 + 0.718753i \(0.255287\pi\)
−0.695265 + 0.718753i \(0.744713\pi\)
\(504\) −2.46898 + 30.1400i −0.109977 + 1.34254i
\(505\) 0 0
\(506\) 1.25562 + 6.37855i 0.0558193 + 0.283561i
\(507\) 4.32196 + 8.87942i 0.191945 + 0.394349i
\(508\) 30.0275 12.2984i 1.33225 0.545655i
\(509\) 42.7463i 1.89470i 0.320207 + 0.947348i \(0.396247\pi\)
−0.320207 + 0.947348i \(0.603753\pi\)
\(510\) 0 0
\(511\) 27.4478i 1.21422i
\(512\) 4.01749 + 22.2679i 0.177550 + 0.984112i
\(513\) 5.55034 25.8062i 0.245053 1.13937i
\(514\) −15.4031 + 3.03212i −0.679403 + 0.133741i
\(515\) 0 0
\(516\) 1.37391 + 1.22727i 0.0604829 + 0.0540273i
\(517\) 26.2094i 1.15269i
\(518\) −5.25982 26.7198i −0.231103 1.17400i
\(519\) −11.3663 23.3521i −0.498927 1.02504i
\(520\) 0 0
\(521\) 10.2725i 0.450045i −0.974354 0.225022i \(-0.927754\pi\)
0.974354 0.225022i \(-0.0722455\pi\)
\(522\) −20.9898 10.6744i −0.918697 0.467206i
\(523\) −31.4642 −1.37583 −0.687916 0.725790i \(-0.741474\pi\)
−0.687916 + 0.725790i \(0.741474\pi\)
\(524\) −36.6103 + 14.9946i −1.59933 + 0.655041i
\(525\) 0 0
\(526\) 4.89531 + 24.8681i 0.213446 + 1.08430i
\(527\) 5.46295i 0.237970i
\(528\) −27.4771 9.73052i −1.19579 0.423467i
\(529\) 21.8062 0.948098
\(530\) 0 0
\(531\) 0 0
\(532\) −13.7239 33.5078i −0.595006 1.45275i
\(533\) −27.7517 −1.20206
\(534\) 9.22667 6.97562i 0.399277 0.301865i
\(535\) 0 0
\(536\) −4.83513 + 3.18928i −0.208846 + 0.137756i
\(537\) 11.8053 + 24.2539i 0.509437 + 1.04663i
\(538\) −4.09573 20.8062i −0.176579 0.897021i
\(539\) −23.9883 −1.03325
\(540\) 0 0
\(541\) −19.2984 −0.829705 −0.414852 0.909889i \(-0.636167\pi\)
−0.414852 + 0.909889i \(0.636167\pi\)
\(542\) −6.66908 33.8788i −0.286461 1.45522i
\(543\) −16.3036 33.4955i −0.699653 1.43743i
\(544\) −2.64141 + 3.86951i −0.113249 + 0.165904i
\(545\) 0 0
\(546\) −18.8127 + 14.2229i −0.805109 + 0.608685i
\(547\) 21.8360 0.933640 0.466820 0.884352i \(-0.345400\pi\)
0.466820 + 0.884352i \(0.345400\pi\)
\(548\) −11.8053 + 4.83513i −0.504298 + 0.206547i
\(549\) −1.29844 + 1.65643i −0.0554160 + 0.0706948i
\(550\) 0 0
\(551\) 28.1956 1.20117
\(552\) 2.72766 4.60542i 0.116097 0.196020i
\(553\) 25.4031i 1.08025i
\(554\) −7.67672 38.9976i −0.326153 1.65685i
\(555\) 0 0
\(556\) −1.14922 2.80590i −0.0487377 0.118996i
\(557\) 17.2321 0.730146 0.365073 0.930979i \(-0.381044\pi\)
0.365073 + 0.930979i \(0.381044\pi\)
\(558\) 24.9443 + 12.6855i 1.05598 + 0.537020i
\(559\) 1.43670i 0.0607661i
\(560\) 0 0
\(561\) −2.64141 5.42675i −0.111520 0.229118i
\(562\) 1.96851 + 10.0000i 0.0830366 + 0.421825i
\(563\) 30.0547i 1.26666i −0.773883 0.633328i \(-0.781688\pi\)
0.773883 0.633328i \(-0.218312\pi\)
\(564\) 14.3760 16.0937i 0.605337 0.677667i
\(565\) 0 0
\(566\) −8.52476 + 1.67811i −0.358322 + 0.0705361i
\(567\) 7.65966 + 31.1473i 0.321675 + 1.30806i
\(568\) −26.8366 + 17.7016i −1.12604 + 0.742741i
\(569\) 43.5745i 1.82674i −0.407133 0.913369i \(-0.633472\pi\)
0.407133 0.913369i \(-0.366528\pi\)
\(570\) 0 0
\(571\) 32.9802i 1.38018i 0.723724 + 0.690090i \(0.242429\pi\)
−0.723724 + 0.690090i \(0.757571\pi\)
\(572\) −8.61603 21.0366i −0.360254 0.879585i
\(573\) 8.61603 + 17.7016i 0.359940 + 0.739493i
\(574\) 10.0000 + 50.7999i 0.417392 + 2.12034i
\(575\) 0 0
\(576\) 11.5349 + 21.0463i 0.480621 + 0.876928i
\(577\) 0.403124i 0.0167823i −0.999965 0.00839114i \(-0.997329\pi\)
0.999965 0.00839114i \(-0.00267101\pi\)
\(578\) 22.6371 4.45614i 0.941581 0.185351i
\(579\) 9.04246 4.40131i 0.375792 0.182912i
\(580\) 0 0
\(581\) 11.1007i 0.460534i
\(582\) 15.8359 11.9724i 0.656421 0.496273i
\(583\) −23.3521 −0.967144
\(584\) −11.9942 18.1839i −0.496322 0.752453i
\(585\) 0 0
\(586\) −26.2094 + 5.15934i −1.08270 + 0.213130i
\(587\) 3.88125i 0.160196i 0.996787 + 0.0800982i \(0.0255234\pi\)
−0.996787 + 0.0800982i \(0.974477\pi\)
\(588\) 14.7299 + 13.1577i 0.607449 + 0.542614i
\(589\) −33.5078 −1.38067
\(590\) 0 0
\(591\) −7.15902 14.7082i −0.294483 0.605012i
\(592\) −15.1606 15.4031i −0.623097 0.633065i
\(593\) 43.5745 1.78939 0.894695 0.446678i \(-0.147393\pi\)
0.894695 + 0.446678i \(0.147393\pi\)
\(594\) −30.9127 0.540538i −1.26836 0.0221785i
\(595\) 0 0
\(596\) 1.25562 + 3.06569i 0.0514324 + 0.125576i
\(597\) 24.4388 11.8953i 1.00021 0.486843i
\(598\) 4.09573 0.806248i 0.167487 0.0329700i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 24.0156 0.979618 0.489809 0.871830i \(-0.337067\pi\)
0.489809 + 0.871830i \(0.337067\pi\)
\(602\) 2.62991 0.517700i 0.107187 0.0210999i
\(603\) −3.79015 + 4.83513i −0.154347 + 0.196902i
\(604\) −3.50781 8.56455i −0.142731 0.348487i
\(605\) 0 0
\(606\) 14.0815 10.6460i 0.572021 0.432464i
\(607\) 27.4478 1.11407 0.557036 0.830489i \(-0.311939\pi\)
0.557036 + 0.830489i \(0.311939\pi\)
\(608\) −23.7342 16.2015i −0.962549 0.657057i
\(609\) −30.8062 + 14.9946i −1.24833 + 0.607611i
\(610\) 0 0
\(611\) 16.8293 0.680840
\(612\) −1.35466 + 4.78108i −0.0547588 + 0.193264i
\(613\) 20.8062i 0.840356i −0.907442 0.420178i \(-0.861968\pi\)
0.907442 0.420178i \(-0.138032\pi\)
\(614\) 28.3057 5.57201i 1.14233 0.224868i
\(615\) 0 0
\(616\) −35.4031 + 23.3521i −1.42643 + 0.940881i
\(617\) 18.3074 0.737030 0.368515 0.929622i \(-0.379866\pi\)
0.368515 + 0.929622i \(0.379866\pi\)
\(618\) 6.05030 + 8.00274i 0.243379 + 0.321918i
\(619\) 26.9160i 1.08184i −0.841073 0.540922i \(-0.818075\pi\)
0.841073 0.540922i \(-0.181925\pi\)
\(620\) 0 0
\(621\) 1.19375 5.55034i 0.0479036 0.222727i
\(622\) −23.3521 + 4.59688i −0.936332 + 0.184318i
\(623\) 16.8293i 0.674251i
\(624\) −6.24806 + 17.6433i −0.250123 + 0.706298i
\(625\) 0 0
\(626\) −6.20087 31.5003i −0.247837 1.25901i
\(627\) 33.2858 16.2015i 1.32931 0.647025i
\(628\) 6.14360 + 15.0000i 0.245156 + 0.598565i
\(629\) 4.47495i 0.178428i
\(630\) 0 0
\(631\) 2.65903i 0.105854i 0.998598 + 0.0529271i \(0.0168551\pi\)
−0.998598 + 0.0529271i \(0.983145\pi\)
\(632\) 11.1007 + 16.8293i 0.441561 + 0.669433i
\(633\) 22.0778 10.7461i 0.877512 0.427119i
\(634\) 41.6125 8.19146i 1.65264 0.325324i
\(635\) 0 0
\(636\) 14.3392 + 12.8087i 0.568585 + 0.507898i
\(637\) 15.4031i 0.610294i
\(638\) −6.37855 32.4030i −0.252529 1.28285i
\(639\) −21.0366 + 26.8366i −0.832196 + 1.06164i
\(640\) 0 0
\(641\) 41.0898i 1.62295i 0.584386 + 0.811476i \(0.301335\pi\)
−0.584386 + 0.811476i \(0.698665\pi\)
\(642\) 36.8343 27.8477i 1.45373 1.09906i
\(643\) 22.2885 0.878971 0.439485 0.898250i \(-0.355161\pi\)
0.439485 + 0.898250i \(0.355161\pi\)
\(644\) −2.95170 7.20677i −0.116313 0.283986i
\(645\) 0 0
\(646\) −1.14922 5.83802i −0.0452154 0.229694i
\(647\) 2.18518i 0.0859082i −0.999077 0.0429541i \(-0.986323\pi\)
0.999077 0.0429541i \(-0.0136769\pi\)
\(648\) 18.6852 + 17.2876i 0.734025 + 0.679123i
\(649\) 0 0
\(650\) 0 0
\(651\) 36.6103 17.8196i 1.43487 0.698406i
\(652\) −9.40194 + 3.85078i −0.368208 + 0.150808i
\(653\) −7.78781 −0.304761 −0.152380 0.988322i \(-0.548694\pi\)
−0.152380 + 0.988322i \(0.548694\pi\)
\(654\) 12.8541 + 17.0022i 0.502636 + 0.664838i
\(655\) 0 0
\(656\) 28.8234 + 29.2845i 1.12537 + 1.14337i
\(657\) −18.1839 14.2539i −0.709420 0.556098i
\(658\) −6.06424 30.8062i −0.236409 1.20095i
\(659\) 21.0366 0.819470 0.409735 0.912205i \(-0.365621\pi\)
0.409735 + 0.912205i \(0.365621\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) −8.20192 41.6656i −0.318777 1.61938i
\(663\) −3.48457 + 1.69607i −0.135329 + 0.0658700i
\(664\) −4.85078 7.35408i −0.188247 0.285393i
\(665\) 0 0
\(666\) −20.4330 10.3913i −0.791764 0.402654i
\(667\) 6.06424 0.234808
\(668\) 2.48465 + 6.06643i 0.0961339 + 0.234717i
\(669\) 11.8953 + 24.4388i 0.459899 + 0.944860i
\(670\) 0 0
\(671\) −2.95170 −0.113949
\(672\) 34.5478 + 5.07959i 1.33271 + 0.195950i
\(673\) 0.806248i 0.0310786i −0.999879 0.0155393i \(-0.995053\pi\)
0.999879 0.0155393i \(-0.00494651\pi\)
\(674\) 0.110112 + 0.559369i 0.00424137 + 0.0215461i
\(675\) 0 0
\(676\) 10.5523 4.32196i 0.405859 0.166229i
\(677\) 3.89391 0.149655 0.0748275 0.997196i \(-0.476159\pi\)
0.0748275 + 0.997196i \(0.476159\pi\)
\(678\) −23.3738 30.9165i −0.897664 1.18734i
\(679\) 28.8845i 1.10849i
\(680\) 0 0
\(681\) 18.2094 8.86320i 0.697785 0.339639i
\(682\) 7.58030 + 38.5078i 0.290265 + 1.47454i
\(683\) 19.9440i 0.763137i −0.924341 0.381568i \(-0.875384\pi\)
0.924341 0.381568i \(-0.124616\pi\)
\(684\) −29.3255 8.30900i −1.12129 0.317703i
\(685\) 0 0
\(686\) −6.42110 + 1.26400i −0.245159 + 0.0482597i
\(687\) −6.59605 13.5515i −0.251655 0.517023i
\(688\) 1.51606 1.49219i 0.0577992 0.0568892i
\(689\) 14.9946i 0.571248i
\(690\) 0 0
\(691\) 18.8039i 0.715333i 0.933849 + 0.357667i \(0.116428\pi\)
−0.933849 + 0.357667i \(0.883572\pi\)
\(692\) −27.7517 + 11.3663i −1.05496 + 0.432084i
\(693\) −27.7517 + 35.4031i −1.05420 + 1.34485i
\(694\) −3.65703 18.5777i −0.138819 0.705198i
\(695\) 0 0
\(696\) −13.8565 + 23.3955i −0.525228 + 0.886803i
\(697\) 8.50781i 0.322256i
\(698\) −16.9415 + 3.33496i −0.641247 + 0.126230i
\(699\) −11.3663 23.3521i −0.429915 0.883256i
\(700\) 0 0
\(701\) 27.7517i 1.04817i 0.851667 + 0.524083i \(0.175592\pi\)
−0.851667 + 0.524083i \(0.824408\pi\)
\(702\) −0.347085 + 19.8493i −0.0130999 + 0.749164i
\(703\) 27.4478 1.03521
\(704\) −13.2498 + 30.9410i −0.499370 + 1.16613i
\(705\) 0 0
\(706\) 40.8062 8.03275i 1.53576 0.302317i
\(707\) 25.6844i 0.965961i
\(708\) 0 0
\(709\) 11.2984 0.424322 0.212161 0.977235i \(-0.431950\pi\)
0.212161 + 0.977235i \(0.431950\pi\)
\(710\) 0 0
\(711\) 16.8293 + 13.1921i 0.631148 + 0.494742i
\(712\) −7.35408 11.1492i −0.275606 0.417835i
\(713\) −7.20677 −0.269896
\(714\) 4.36031 + 5.76739i 0.163181 + 0.215839i
\(715\) 0 0
\(716\) 28.8234 11.8053i 1.07718 0.441185i
\(717\) −4.14108 8.50781i −0.154651 0.317730i
\(718\) 50.7999 10.0000i 1.89583 0.373197i
\(719\) 25.6844 0.957866 0.478933 0.877851i \(-0.341024\pi\)
0.478933 + 0.877851i \(0.341024\pi\)
\(720\) 0 0
\(721\) 14.5969 0.543616
\(722\) 9.44424 1.85911i 0.351478 0.0691889i
\(723\) 5.30621 + 10.9016i 0.197340 + 0.405434i
\(724\) −39.8062 + 16.3036i −1.47939 + 0.605917i
\(725\) 0 0
\(726\) −9.89969 13.0943i −0.367412 0.485977i
\(727\) −45.1087 −1.67299 −0.836495 0.547975i \(-0.815399\pi\)
−0.836495 + 0.547975i \(0.815399\pi\)
\(728\) 14.9946 + 22.7327i 0.555736 + 0.842529i
\(729\) 24.6125 + 11.1007i 0.911574 + 0.411136i
\(730\) 0 0
\(731\) 0.440449 0.0162906
\(732\) 1.81247 + 1.61902i 0.0669908 + 0.0598407i
\(733\) 20.8062i 0.768496i −0.923230 0.384248i \(-0.874461\pi\)
0.923230 0.384248i \(-0.125539\pi\)
\(734\) 4.94525 0.973477i 0.182532 0.0359317i
\(735\) 0 0
\(736\) −5.10469 3.48457i −0.188161 0.128443i
\(737\) −8.61603 −0.317376
\(738\) 38.8474 + 19.7560i 1.42999 + 0.727227i
\(739\) 52.9271i 1.94695i 0.228785 + 0.973477i \(0.426525\pi\)
−0.228785 + 0.973477i \(0.573475\pi\)
\(740\) 0 0
\(741\) −10.4031 21.3731i −0.382168 0.785162i
\(742\) 27.4478 5.40312i 1.00764 0.198355i
\(743\) 29.6143i 1.08644i 0.839589 + 0.543222i \(0.182796\pi\)
−0.839589 + 0.543222i \(0.817204\pi\)
\(744\) 16.4671 27.8033i 0.603712 1.01932i
\(745\) 0 0
\(746\) 4.72502 + 24.0030i 0.172995 + 0.878814i
\(747\) −7.35408 5.76469i −0.269072 0.210919i
\(748\) −6.44918 + 2.64141i −0.235805 + 0.0965795i
\(749\) 67.1851i 2.45489i
\(750\) 0 0
\(751\) 28.3527i 1.03460i −0.855803 0.517302i \(-0.826936\pi\)
0.855803 0.517302i \(-0.173064\pi\)
\(752\) −17.4792 17.7588i −0.637402 0.647598i
\(753\) 0.951801 + 1.95547i 0.0346856 + 0.0712612i
\(754\) −20.8062 + 4.09573i −0.757719 + 0.149158i
\(755\) 0 0
\(756\) 36.4595 6.51713i 1.32602 0.237026i
\(757\) 8.91093i 0.323873i −0.986801 0.161937i \(-0.948226\pi\)
0.986801 0.161937i \(-0.0517740\pi\)
\(758\) 5.81918 + 29.5614i 0.211362 + 1.07372i
\(759\) 7.15902 3.48457i 0.259856 0.126482i
\(760\) 0 0
\(761\) 3.06569i 0.111131i −0.998455 0.0555656i \(-0.982304\pi\)
0.998455 0.0555656i \(-0.0176962\pi\)
\(762\) −23.9667 31.7009i −0.868224 1.14840i
\(763\) 31.0117 1.12270
\(764\) 21.0366 8.61603i 0.761078 0.311717i
\(765\) 0 0
\(766\) 3.40312 + 17.2878i 0.122960 + 0.624634i
\(767\) 0 0
\(768\) 25.1072 11.7315i 0.905978 0.423325i
\(769\) 39.8062 1.43545 0.717725 0.696327i \(-0.245183\pi\)
0.717725 + 0.696327i \(0.245183\pi\)
\(770\) 0 0
\(771\) 8.41464 + 17.2878i 0.303046 + 0.622606i
\(772\) −4.40131 10.7461i −0.158407 0.386760i
\(773\) 5.55034 0.199632 0.0998159 0.995006i \(-0.468175\pi\)
0.0998159 + 0.995006i \(0.468175\pi\)
\(774\) 1.02277 2.01113i 0.0367626 0.0722886i
\(775\) 0 0
\(776\) −12.6220 19.1357i −0.453102 0.686930i
\(777\) −29.9892 + 14.5969i −1.07586 + 0.523660i
\(778\) 5.45308 + 27.7016i 0.195502 + 0.993149i
\(779\) −52.1839 −1.86968
\(780\) 0 0
\(781\) −47.8219 −1.71120
\(782\) −0.247171 1.25562i −0.00883881 0.0449010i
\(783\) −6.06424 + 28.1956i −0.216718 + 1.00763i
\(784\) 16.2539 15.9980i 0.580497 0.571357i
\(785\) 0 0
\(786\) 29.2209 + 38.6505i 1.04227 + 1.37862i
\(787\) −14.7875