Properties

Label 300.2.e.d.251.5
Level $300$
Weight $2$
Character 300.251
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.4521217600.1
Defining polynomial: \(x^{8} + x^{6} - 2 x^{4} + 4 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.5
Root \(-0.273147 - 1.38758i\) of defining polynomial
Character \(\chi\) \(=\) 300.251
Dual form 300.2.e.d.251.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.273147 - 1.38758i) q^{2} +(-1.55737 - 0.758030i) q^{3} +(-1.85078 - 0.758030i) q^{4} +(-1.47722 + 1.95392i) q^{6} -3.56393i q^{7} +(-1.55737 + 2.36106i) q^{8} +(1.85078 + 2.36106i) q^{9} +O(q^{10})\) \(q+(0.273147 - 1.38758i) q^{2} +(-1.55737 - 0.758030i) q^{3} +(-1.85078 - 0.758030i) q^{4} +(-1.47722 + 1.95392i) q^{6} -3.56393i q^{7} +(-1.55737 + 2.36106i) q^{8} +(1.85078 + 2.36106i) q^{9} -4.20732 q^{11} +(2.30774 + 2.58348i) q^{12} -2.70156 q^{13} +(-4.94525 - 0.973477i) q^{14} +(2.85078 + 2.80590i) q^{16} +0.828216i q^{17} +(3.78171 - 1.92320i) q^{18} +5.07999i q^{19} +(-2.70156 + 5.55034i) q^{21} +(-1.14922 + 5.83802i) q^{22} -1.09259 q^{23} +(4.21515 - 2.49651i) q^{24} +(-0.737925 + 3.74865i) q^{26} +(-1.09259 - 5.07999i) q^{27} +(-2.70156 + 6.59605i) q^{28} -5.55034i q^{29} -6.59605i q^{31} +(4.67210 - 3.18928i) q^{32} +(6.55234 + 3.18928i) q^{33} +(1.14922 + 0.226225i) q^{34} +(-1.63564 - 5.77275i) q^{36} -5.40312 q^{37} +(7.04891 + 1.38758i) q^{38} +(4.20732 + 2.04787i) q^{39} -10.2725i q^{41} +(6.96364 + 5.26471i) q^{42} -0.531805i q^{43} +(7.78683 + 3.18928i) q^{44} +(-0.298438 + 1.51606i) q^{46} -6.22947 q^{47} +(-2.31276 - 6.53078i) q^{48} -5.70156 q^{49} +(0.627812 - 1.28984i) q^{51} +(5.00000 + 2.04787i) q^{52} -5.55034i q^{53} +(-7.34735 + 0.128476i) q^{54} +(8.41464 + 5.55034i) q^{56} +(3.85078 - 7.91140i) q^{57} +(-7.70156 - 1.51606i) q^{58} +0.701562 q^{61} +(-9.15257 - 1.80169i) q^{62} +(8.41464 - 6.59605i) q^{63} +(-3.14922 - 7.35408i) q^{64} +(6.21515 - 8.22079i) q^{66} +2.04787i q^{67} +(0.627812 - 1.53285i) q^{68} +(1.70156 + 0.828216i) q^{69} +11.3663 q^{71} +(-8.45695 + 0.692770i) q^{72} -7.70156 q^{73} +(-1.47585 + 7.49729i) q^{74} +(3.85078 - 9.40194i) q^{76} +14.9946i q^{77} +(3.99080 - 5.27865i) q^{78} -7.12785i q^{79} +(-2.14922 + 8.73961i) q^{81} +(-14.2539 - 2.80590i) q^{82} -3.11473 q^{83} +(9.20732 - 8.22459i) q^{84} +(-0.737925 - 0.145261i) q^{86} +(-4.20732 + 8.64391i) q^{87} +(6.55234 - 9.93375i) q^{88} +4.72212i q^{89} +9.62817i q^{91} +(2.02214 + 0.828216i) q^{92} +(-5.00000 + 10.2725i) q^{93} +(-1.70156 + 8.64391i) q^{94} +(-9.69374 + 1.42528i) q^{96} +8.10469 q^{97} +(-1.55737 + 7.91140i) q^{98} +(-7.78683 - 9.93375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{4} + 3q^{6} + 2q^{9} + O(q^{10}) \) \( 8q - 2q^{4} + 3q^{6} + 2q^{9} - 11q^{12} + 4q^{13} + 10q^{16} + 7q^{18} + 4q^{21} - 22q^{22} + 13q^{24} + 4q^{28} + 14q^{33} + 22q^{34} - 21q^{36} + 8q^{37} + 36q^{42} - 28q^{46} - 15q^{48} - 20q^{49} + 40q^{52} - 28q^{54} + 18q^{57} - 36q^{58} - 20q^{61} - 38q^{64} + 29q^{66} - 12q^{69} - 51q^{72} - 36q^{73} + 18q^{76} + 22q^{78} - 30q^{81} - 50q^{82} + 40q^{84} + 14q^{88} - 40q^{93} + 12q^{94} - 39q^{96} - 12q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.273147 1.38758i 0.193144 0.981170i
\(3\) −1.55737 0.758030i −0.899146 0.437649i
\(4\) −1.85078 0.758030i −0.925391 0.379015i
\(5\) 0 0
\(6\) −1.47722 + 1.95392i −0.603073 + 0.797686i
\(7\) 3.56393i 1.34704i −0.739170 0.673519i \(-0.764782\pi\)
0.739170 0.673519i \(-0.235218\pi\)
\(8\) −1.55737 + 2.36106i −0.550612 + 0.834761i
\(9\) 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 \(0.718702\pi\)
\(12\) 2.30774 + 2.58348i 0.666186 + 0.745786i
\(13\) −2.70156 −0.749279 −0.374639 0.927171i \(-0.622233\pi\)
−0.374639 + 0.927171i \(0.622233\pi\)
\(14\) −4.94525 0.973477i −1.32167 0.260173i
\(15\) 0 0
\(16\) 2.85078 + 2.80590i 0.712695 + 0.701474i
\(17\) 0.828216i 0.200872i 0.994944 + 0.100436i \(0.0320237\pi\)
−0.994944 + 0.100436i \(0.967976\pi\)
\(18\) 3.78171 1.92320i 0.891357 0.453302i
\(19\) 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
\(22\) −1.14922 + 5.83802i −0.245014 + 1.24467i
\(23\) −1.09259 −0.227821 −0.113910 0.993491i \(-0.536338\pi\)
−0.113910 + 0.993491i \(0.536338\pi\)
\(24\) 4.21515 2.49651i 0.860413 0.509597i
\(25\) 0 0
\(26\) −0.737925 + 3.74865i −0.144719 + 0.735170i
\(27\) −1.09259 5.07999i −0.210269 0.977644i
\(28\) −2.70156 + 6.59605i −0.510547 + 1.24654i
\(29\) 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 \(-0.798203\pi\)
0.805686 0.592342i \(-0.201797\pi\)
\(32\) 4.67210 3.18928i 0.825918 0.563790i
\(33\) 6.55234 + 3.18928i 1.14062 + 0.555182i
\(34\) 1.14922 + 0.226225i 0.197089 + 0.0387972i
\(35\) 0 0
\(36\) −1.63564 5.77275i −0.272606 0.962126i
\(37\) −5.40312 −0.888268 −0.444134 0.895960i \(-0.646489\pi\)
−0.444134 + 0.895960i \(0.646489\pi\)
\(38\) 7.04891 + 1.38758i 1.14348 + 0.225096i
\(39\) 4.20732 + 2.04787i 0.673711 + 0.327921i
\(40\) 0 0
\(41\) 10.2725i 1.60429i −0.597130 0.802144i \(-0.703692\pi\)
0.597130 0.802144i \(-0.296308\pi\)
\(42\) 6.96364 + 5.26471i 1.07451 + 0.812362i
\(43\) 0.531805i 0.0810995i −0.999178 0.0405498i \(-0.987089\pi\)
0.999178 0.0405498i \(-0.0129109\pi\)
\(44\) 7.78683 + 3.18928i 1.17391 + 0.480802i
\(45\) 0 0
\(46\) −0.298438 + 1.51606i −0.0440023 + 0.223531i
\(47\) −6.22947 −0.908661 −0.454331 0.890833i \(-0.650121\pi\)
−0.454331 + 0.890833i \(0.650121\pi\)
\(48\) −2.31276 6.53078i −0.333818 0.942638i
\(49\) −5.70156 −0.814509
\(50\) 0 0
\(51\) 0.627812 1.28984i 0.0879113 0.180613i
\(52\) 5.00000 + 2.04787i 0.693375 + 0.283988i
\(53\) 5.55034i 0.762398i −0.924493 0.381199i \(-0.875511\pi\)
0.924493 0.381199i \(-0.124489\pi\)
\(54\) −7.34735 + 0.128476i −0.999847 + 0.0174833i
\(55\) 0 0
\(56\) 8.41464 + 5.55034i 1.12445 + 0.741695i
\(57\) 3.85078 7.91140i 0.510048 1.04789i
\(58\) −7.70156 1.51606i −1.01126 0.199068i
\(59\) 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 \(0.485699\pi\)
\(62\) −9.15257 1.80169i −1.16238 0.228815i
\(63\) 8.41464 6.59605i 1.06015 0.831024i
\(64\) −3.14922 7.35408i −0.393652 0.919259i
\(65\) 0 0
\(66\) 6.21515 8.22079i 0.765032 1.01191i
\(67\) 2.04787i 0.250187i 0.992145 + 0.125093i \(0.0399230\pi\)
−0.992145 + 0.125093i \(0.960077\pi\)
\(68\) 0.627812 1.53285i 0.0761334 0.185885i
\(69\) 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 \(0.264373\pi\)
\(72\) −8.45695 + 0.692770i −0.996662 + 0.0816437i
\(73\) −7.70156 −0.901400 −0.450700 0.892676i \(-0.648826\pi\)
−0.450700 + 0.892676i \(0.648826\pi\)
\(74\) −1.47585 + 7.49729i −0.171564 + 0.871542i
\(75\) 0 0
\(76\) 3.85078 9.40194i 0.441715 1.07848i
\(77\) 14.9946i 1.70879i
\(78\) 3.99080 5.27865i 0.451870 0.597689i
\(79\) 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
\(82\) −14.2539 2.80590i −1.57408 0.309859i
\(83\) −3.11473 −0.341886 −0.170943 0.985281i \(-0.554681\pi\)
−0.170943 + 0.985281i \(0.554681\pi\)
\(84\) 9.20732 8.22459i 1.00460 0.897377i
\(85\) 0 0
\(86\) −0.737925 0.145261i −0.0795724 0.0156639i
\(87\) −4.20732 + 8.64391i −0.451072 + 0.926724i
\(88\) 6.55234 9.93375i 0.698482 1.05894i
\(89\) 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
\(92\) 2.02214 + 0.828216i 0.210823 + 0.0863474i
\(93\) −5.00000 + 10.2725i −0.518476 + 1.06520i
\(94\) −1.70156 + 8.64391i −0.175503 + 0.891551i
\(95\) 0 0
\(96\) −9.69374 + 1.42528i −0.989363 + 0.145467i
\(97\) 8.10469 0.822906 0.411453 0.911431i \(-0.365021\pi\)
0.411453 + 0.911431i \(0.365021\pi\)
\(98\) −1.55737 + 7.91140i −0.157318 + 0.799172i
\(99\) −7.78683 9.93375i −0.782606 0.998379i
\(100\) 0 0
\(101\) 7.20677i 0.717100i −0.933510 0.358550i \(-0.883271\pi\)
0.933510 0.358550i \(-0.116729\pi\)
\(102\) −1.61827 1.22346i −0.160233 0.121140i
\(103\) 4.09573i 0.403564i 0.979430 + 0.201782i \(0.0646733\pi\)
−0.979430 + 0.201782i \(0.935327\pi\)
\(104\) 4.20732 6.37855i 0.412562 0.625469i
\(105\) 0 0
\(106\) −7.70156 1.51606i −0.748042 0.147253i
\(107\) 18.8514 1.82244 0.911218 0.411924i \(-0.135143\pi\)
0.911218 + 0.411924i \(0.135143\pi\)
\(108\) −1.82864 + 10.2302i −0.175961 + 0.984397i
\(109\) 8.70156 0.833458 0.416729 0.909031i \(-0.363176\pi\)
0.416729 + 0.909031i \(0.363176\pi\)
\(110\) 0 0
\(111\) 8.41464 + 4.09573i 0.798683 + 0.388750i
\(112\) 10.0000 10.1600i 0.944911 0.960027i
\(113\) 15.8228i 1.48848i −0.667910 0.744242i \(-0.732811\pi\)
0.667910 0.744242i \(-0.267189\pi\)
\(114\) −9.92590 7.50426i −0.929646 0.702838i
\(115\) 0 0
\(116\) −4.20732 + 10.2725i −0.390640 + 0.953774i
\(117\) −5.00000 6.37855i −0.462250 0.589697i
\(118\) 0 0
\(119\) 2.95170 0.270582
\(120\) 0 0
\(121\) 6.70156 0.609233
\(122\) 0.191630 0.973477i 0.0173493 0.0881344i
\(123\) −7.78683 + 15.9980i −0.702115 + 1.44249i
\(124\) −5.00000 + 12.2078i −0.449013 + 1.09630i
\(125\) 0 0
\(126\) −6.85413 13.4777i −0.610615 1.20069i
\(127\) 16.2242i 1.43967i 0.694147 + 0.719833i \(0.255782\pi\)
−0.694147 + 0.719833i \(0.744218\pi\)
\(128\) −11.0646 + 2.36106i −0.977982 + 0.208690i
\(129\) −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 \(0.832135\pi\)
\(132\) −9.70939 10.8695i −0.845094 0.946071i
\(133\) 18.1047 1.56988
\(134\) 2.84159 + 0.559369i 0.245476 + 0.0483221i
\(135\) 0 0
\(136\) −1.95547 1.28984i −0.167680 0.110602i
\(137\) 6.37855i 0.544957i −0.962162 0.272478i \(-0.912157\pi\)
0.962162 0.272478i \(-0.0878433\pi\)
\(138\) 1.61400 2.13484i 0.137392 0.181729i
\(139\) 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
\(142\) 3.10469 15.7718i 0.260539 1.32354i
\(143\) 11.3663 0.950501
\(144\) −1.34872 + 11.9240i −0.112393 + 0.993664i
\(145\) 0 0
\(146\) −2.10366 + 10.6866i −0.174100 + 0.884427i
\(147\) 8.87942 + 4.32196i 0.732362 + 0.356469i
\(148\) 10.0000 + 4.09573i 0.821995 + 0.336667i
\(149\) 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 \(0.0602951\pi\)
−0.982113 + 0.188292i \(0.939705\pi\)
\(152\) −11.9942 7.91140i −0.972854 0.641699i
\(153\) −1.95547 + 1.53285i −0.158090 + 0.123923i
\(154\) 20.8062 + 4.09573i 1.67662 + 0.330043i
\(155\) 0 0
\(156\) −6.23449 6.97943i −0.499159 0.558801i
\(157\) 8.10469 0.646824 0.323412 0.946258i \(-0.395170\pi\)
0.323412 + 0.946258i \(0.395170\pi\)
\(158\) −9.89049 1.94695i −0.786845 0.154891i
\(159\) −4.20732 + 8.64391i −0.333662 + 0.685507i
\(160\) 0 0
\(161\) 3.89391i 0.306883i
\(162\) 11.5399 + 5.36943i 0.906660 + 0.421862i
\(163\) 5.07999i 0.397895i 0.980010 + 0.198948i \(0.0637523\pi\)
−0.980010 + 0.198948i \(0.936248\pi\)
\(164\) −7.78683 + 19.0121i −0.608049 + 1.48459i
\(165\) 0 0
\(166\) −0.850781 + 4.32196i −0.0660334 + 0.335449i
\(167\) 3.27777 0.253641 0.126821 0.991926i \(-0.459523\pi\)
0.126821 + 0.991926i \(0.459523\pi\)
\(168\) −8.89736 15.0225i −0.686447 1.15901i
\(169\) −5.70156 −0.438582
\(170\) 0 0
\(171\) −11.9942 + 9.40194i −0.917216 + 0.718984i
\(172\) −0.403124 + 0.984255i −0.0307379 + 0.0750487i
\(173\) 14.9946i 1.14002i 0.821639 + 0.570008i \(0.193060\pi\)
−0.821639 + 0.570008i \(0.806940\pi\)
\(174\) 10.8449 + 8.19908i 0.822152 + 0.621570i
\(175\) 0 0
\(176\) −11.9942 11.8053i −0.904093 0.889858i
\(177\) 0 0
\(178\) 6.55234 + 1.28984i 0.491119 + 0.0966772i
\(179\) −15.5737 −1.16403 −0.582015 0.813178i \(-0.697736\pi\)
−0.582015 + 0.813178i \(0.697736\pi\)
\(180\) 0 0
\(181\) −21.5078 −1.59866 −0.799331 0.600890i \(-0.794813\pi\)
−0.799331 + 0.600890i \(0.794813\pi\)
\(182\) 13.3599 + 2.62991i 0.990301 + 0.194942i
\(183\) −1.09259 0.531805i −0.0807665 0.0393122i
\(184\) 1.70156 2.57967i 0.125441 0.190176i
\(185\) 0 0
\(186\) 12.8882 + 9.74382i 0.945006 + 0.714451i
\(187\) 3.48457i 0.254817i
\(188\) 11.5294 + 4.72212i 0.840866 + 0.344396i
\(189\) −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 \(0.365103\pi\)
\(192\) −0.670121 + 13.8402i −0.0483618 + 0.998830i
\(193\) 5.80625 0.417943 0.208971 0.977922i \(-0.432988\pi\)
0.208971 + 0.977922i \(0.432988\pi\)
\(194\) 2.21377 11.2459i 0.158940 0.807411i
\(195\) 0 0
\(196\) 10.5523 + 4.32196i 0.753739 + 0.308711i
\(197\) 9.44424i 0.672875i −0.941706 0.336437i \(-0.890778\pi\)
0.941706 0.336437i \(-0.109222\pi\)
\(198\) −15.9109 + 8.09151i −1.13074 + 0.575039i
\(199\) 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
\(202\) −10.0000 1.96851i −0.703598 0.138504i
\(203\) −19.7810 −1.38835
\(204\) −2.13968 + 1.91130i −0.149807 + 0.133818i
\(205\) 0 0
\(206\) 5.68317 + 1.11874i 0.395965 + 0.0779462i
\(207\) −2.02214 2.57967i −0.140549 0.179299i
\(208\) −7.70156 7.58030i −0.534007 0.525599i
\(209\) 21.3731i 1.47841i
\(210\) 0 0
\(211\) 14.1763i 0.975940i 0.872860 + 0.487970i \(0.162262\pi\)
−0.872860 + 0.487970i \(0.837738\pi\)
\(212\) −4.20732 + 10.2725i −0.288960 + 0.705515i
\(213\) −17.7016 8.61603i −1.21289 0.590361i
\(214\) 5.14922 26.1580i 0.351993 1.78812i
\(215\) 0 0
\(216\) 13.6957 + 5.33173i 0.931876 + 0.362778i
\(217\) −23.5078 −1.59581
\(218\) 2.37681 12.0742i 0.160978 0.817765i
\(219\) 11.9942 + 5.83802i 0.810490 + 0.394497i
\(220\) 0 0
\(221\) 2.23748i 0.150509i
\(222\) 7.98161 10.5573i 0.535691 0.708559i
\(223\) 15.6924i 1.05084i −0.850843 0.525421i \(-0.823908\pi\)
0.850843 0.525421i \(-0.176092\pi\)
\(224\) −11.3663 16.6510i −0.759446 1.11254i
\(225\) 0 0
\(226\) −21.9555 4.32196i −1.46046 0.287492i
\(227\) −11.6924 −0.776053 −0.388026 0.921648i \(-0.626843\pi\)
−0.388026 + 0.921648i \(0.626843\pi\)
\(228\) −13.1240 + 11.7233i −0.869160 + 0.776392i
\(229\) 8.70156 0.575015 0.287508 0.957778i \(-0.407173\pi\)
0.287508 + 0.957778i \(0.407173\pi\)
\(230\) 0 0
\(231\) 11.3663 23.3521i 0.747850 1.53645i
\(232\) 13.1047 + 8.64391i 0.860365 + 0.567501i
\(233\) 14.9946i 0.982328i 0.871067 + 0.491164i \(0.163428\pi\)
−0.871067 + 0.491164i \(0.836572\pi\)
\(234\) −10.2165 + 5.19564i −0.667875 + 0.339649i
\(235\) 0 0
\(236\) 0 0
\(237\) −5.40312 + 11.1007i −0.350971 + 0.721066i
\(238\) 0.806248 4.09573i 0.0522613 0.265487i
\(239\) 5.46295 0.353369 0.176684 0.984268i \(-0.443463\pi\)
0.176684 + 0.984268i \(0.443463\pi\)
\(240\) 0 0
\(241\) 7.00000 0.450910 0.225455 0.974254i \(-0.427613\pi\)
0.225455 + 0.974254i \(0.427613\pi\)
\(242\) 1.83051 9.29898i 0.117670 0.597761i
\(243\) 9.97201 11.9816i 0.639705 0.768621i
\(244\) −1.29844 0.531805i −0.0831240 0.0340453i
\(245\) 0 0
\(246\) 20.0716 + 15.1747i 1.27972 + 0.967503i
\(247\) 13.7239i 0.873231i
\(248\) 15.5737 + 10.2725i 0.988929 + 0.652302i
\(249\) 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 \(0.487383\pi\)
\(252\) −20.5737 + 5.82928i −1.29602 + 0.367210i
\(253\) 4.59688 0.289003
\(254\) 22.5125 + 4.43160i 1.41256 + 0.278063i
\(255\) 0 0
\(256\) 0.253905 + 15.9980i 0.0158691 + 0.999874i
\(257\) 11.1007i 0.692441i 0.938153 + 0.346221i \(0.112535\pi\)
−0.938153 + 0.346221i \(0.887465\pi\)
\(258\) 1.03911 + 0.785594i 0.0646920 + 0.0489089i
\(259\) 19.2563i 1.19653i
\(260\) 0 0
\(261\) 13.1047 10.2725i 0.811160 0.635849i
\(262\) −5.40312 + 27.4478i −0.333806 + 1.69573i
\(263\) 17.9219 1.10511 0.552555 0.833476i \(-0.313653\pi\)
0.552555 + 0.833476i \(0.313653\pi\)
\(264\) −17.7345 + 10.5036i −1.09148 + 0.646452i
\(265\) 0 0
\(266\) 4.94525 25.1218i 0.303213 1.54032i
\(267\) 3.57951 7.35408i 0.219062 0.450062i
\(268\) 1.55234 3.79015i 0.0948245 0.231520i
\(269\) 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 \(-0.734080\pi\)
0.670872 0.741573i \(-0.265920\pi\)
\(272\) −2.32389 + 2.36106i −0.140906 + 0.143160i
\(273\) 7.29844 14.9946i 0.441722 0.907513i
\(274\) −8.85078 1.74228i −0.534695 0.105255i
\(275\) 0 0
\(276\) −2.52141 2.82268i −0.151771 0.169905i
\(277\) 28.1047 1.68865 0.844323 0.535834i \(-0.180003\pi\)
0.844323 + 0.535834i \(0.180003\pi\)
\(278\) −2.10366 0.414108i −0.126169 0.0248365i
\(279\) 15.5737 12.2078i 0.932371 0.730864i
\(280\) 0 0
\(281\) 7.20677i 0.429920i 0.976623 + 0.214960i \(0.0689621\pi\)
−0.976623 + 0.214960i \(0.931038\pi\)
\(282\) 9.20230 12.1719i 0.547989 0.724826i
\(283\) 6.14360i 0.365199i −0.983187 0.182599i \(-0.941549\pi\)
0.983187 0.182599i \(-0.0584511\pi\)
\(284\) −21.0366 8.61603i −1.24829 0.511267i
\(285\) 0 0
\(286\) 3.10469 15.7718i 0.183584 0.932604i
\(287\) −36.6103 −2.16104
\(288\) 16.1771 + 5.12846i 0.953245 + 0.302197i
\(289\) 16.3141 0.959651
\(290\) 0 0
\(291\) −12.6220 6.14360i −0.739913 0.360144i
\(292\) 14.2539 + 5.83802i 0.834147 + 0.341644i
\(293\) 18.8885i 1.10348i −0.834017 0.551739i \(-0.813965\pi\)
0.834017 0.551739i \(-0.186035\pi\)
\(294\) 8.42247 11.1404i 0.491208 0.649722i
\(295\) 0 0
\(296\) 8.41464 12.7571i 0.489091 0.741492i
\(297\) 4.59688 + 21.3731i 0.266738 + 1.24020i
\(298\) 2.29844 + 0.452450i 0.133145 + 0.0262097i
\(299\) 2.95170 0.170701
\(300\) 0 0
\(301\) −1.89531 −0.109244
\(302\) 6.42110 + 1.26400i 0.369493 + 0.0727350i
\(303\) −5.46295 + 11.2236i −0.313838 + 0.644778i
\(304\) −14.2539 + 14.4819i −0.817518 + 0.830595i
\(305\) 0 0
\(306\) 1.59282 + 3.13207i 0.0910556 + 0.179048i
\(307\) 20.3993i 1.16425i −0.813100 0.582125i \(-0.802222\pi\)
0.813100 0.582125i \(-0.197778\pi\)
\(308\) 11.3663 27.7517i 0.647657 1.58130i
\(309\) 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 \(0.341670\pi\)
\(312\) −11.3875 + 6.74447i −0.644689 + 0.381830i
\(313\) −22.7016 −1.28317 −0.641584 0.767053i \(-0.721722\pi\)
−0.641584 + 0.767053i \(0.721722\pi\)
\(314\) 2.21377 11.2459i 0.124930 0.634645i
\(315\) 0 0
\(316\) −5.40312 + 13.1921i −0.303949 + 0.742113i
\(317\) 29.9892i 1.68436i −0.539197 0.842180i \(-0.681272\pi\)
0.539197 0.842180i \(-0.318728\pi\)
\(318\) 10.8449 + 8.19908i 0.608154 + 0.459781i
\(319\) 23.3521i 1.30746i
\(320\) 0 0
\(321\) −29.3586 14.2900i −1.63864 0.797587i
\(322\) 5.40312 + 1.06361i 0.301104 + 0.0592727i
\(323\) −4.20732 −0.234102
\(324\) 10.6026 14.5459i 0.589035 0.808108i
\(325\) 0 0
\(326\) 7.04891 + 1.38758i 0.390403 + 0.0768512i
\(327\) −13.5515 6.59605i −0.749401 0.364762i
\(328\) 24.2539 + 15.9980i 1.33920 + 0.883341i
\(329\) 22.2014i 1.22400i
\(330\) 0 0
\(331\) 30.0275i 1.65046i −0.564798 0.825229i \(-0.691046\pi\)
0.564798 0.825229i \(-0.308954\pi\)
\(332\) 5.76469 + 2.36106i 0.316378 + 0.129580i
\(333\) −10.0000 12.7571i −0.547997 0.699085i
\(334\) 0.895314 4.54818i 0.0489894 0.248865i
\(335\) 0 0
\(336\) −23.2752 + 8.24250i −1.26977 + 0.449665i
\(337\) −0.403124 −0.0219596 −0.0109798 0.999940i \(-0.503495\pi\)
−0.0109798 + 0.999940i \(0.503495\pi\)
\(338\) −1.55737 + 7.91140i −0.0847096 + 0.430323i
\(339\) −11.9942 + 24.6419i −0.651433 + 1.33836i
\(340\) 0 0
\(341\) 27.7517i 1.50284i
\(342\) 9.76981 + 19.2110i 0.528291 + 1.03881i
\(343\) 4.62754i 0.249863i
\(344\) 1.25562 + 0.828216i 0.0676987 + 0.0446544i
\(345\) 0 0
\(346\) 20.8062 + 4.09573i 1.11855 + 0.220188i
\(347\) 13.3885 0.718732 0.359366 0.933197i \(-0.382993\pi\)
0.359366 + 0.933197i \(0.382993\pi\)
\(348\) 14.3392 12.8087i 0.768661 0.686619i
\(349\) −12.2094 −0.653553 −0.326776 0.945102i \(-0.605962\pi\)
−0.326776 + 0.945102i \(0.605962\pi\)
\(350\) 0 0
\(351\) 2.95170 + 13.7239i 0.157550 + 0.732527i
\(352\) −19.6570 + 13.4183i −1.04772 + 0.715199i
\(353\) 29.4081i 1.56524i 0.622502 + 0.782618i \(0.286116\pi\)
−0.622502 + 0.782618i \(0.713884\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.57951 8.73961i 0.189714 0.463199i
\(357\) −4.59688 2.23748i −0.243292 0.118420i
\(358\) −4.25391 + 21.6098i −0.224826 + 1.14211i
\(359\) 36.6103 1.93222 0.966108 0.258137i \(-0.0831087\pi\)
0.966108 + 0.258137i \(0.0831087\pi\)
\(360\) 0 0
\(361\) −6.80625 −0.358224
\(362\) −5.87480 + 29.8439i −0.308773 + 1.56856i
\(363\) −10.4368 5.07999i −0.547789 0.266630i
\(364\) 7.29844 17.8196i 0.382542 0.934002i
\(365\) 0 0
\(366\) −1.03636 + 1.37080i −0.0541715 + 0.0716528i
\(367\) 3.56393i 0.186035i −0.995664 0.0930177i \(-0.970349\pi\)
0.995664 0.0930177i \(-0.0296513\pi\)
\(368\) −3.11473 3.06569i −0.162367 0.159810i
\(369\) 24.2539 19.0121i 1.26261 0.989729i
\(370\) 0 0
\(371\) −19.7810 −1.02698
\(372\) 17.0407 15.2219i 0.883521 0.789220i
\(373\) 17.2984 0.895679 0.447840 0.894114i \(-0.352194\pi\)
0.447840 + 0.894114i \(0.352194\pi\)
\(374\) −4.83513 0.951801i −0.250019 0.0492165i
\(375\) 0 0
\(376\) 9.70156 14.7082i 0.500320 0.758515i
\(377\) 14.9946i 0.772260i
\(378\) 0.457877 + 26.1854i 0.0235507 + 1.34683i
\(379\) 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
\(382\) 3.10469 15.7718i 0.158850 0.806953i
\(383\) 12.4589 0.636622 0.318311 0.947986i \(-0.396884\pi\)
0.318311 + 0.947986i \(0.396884\pi\)
\(384\) 19.0214 + 4.71026i 0.970681 + 0.240370i
\(385\) 0 0
\(386\) 1.58596 8.05666i 0.0807233 0.410073i
\(387\) 1.25562 0.984255i 0.0638270 0.0500325i
\(388\) −15.0000 6.14360i −0.761510 0.311894i
\(389\) 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
\(392\) 8.87942 13.4617i 0.448479 0.679920i
\(393\) 30.8062 + 14.9946i 1.55397 + 0.756377i
\(394\) −13.1047 2.57967i −0.660205 0.129962i
\(395\) 0 0
\(396\) 6.88165 + 24.2878i 0.345816 + 1.22051i
\(397\) −28.9109 −1.45100 −0.725499 0.688223i \(-0.758391\pi\)
−0.725499 + 0.688223i \(0.758391\pi\)
\(398\) −21.7745 4.28634i −1.09146 0.214855i
\(399\) −28.1956 13.7239i −1.41155 0.687054i
\(400\) 0 0
\(401\) 30.8174i 1.53895i 0.638679 + 0.769473i \(0.279481\pi\)
−0.638679 + 0.769473i \(0.720519\pi\)
\(402\) −4.00137 3.02515i −0.199570 0.150881i
\(403\) 17.8196i 0.887659i
\(404\) −5.46295 + 13.3382i −0.271792 + 0.663598i
\(405\) 0 0
\(406\) −5.40312 + 27.4478i −0.268153 + 1.36221i
\(407\) 22.7327 1.12682
\(408\) 2.06765 + 3.49105i 0.102364 + 0.172833i
\(409\) −27.2094 −1.34542 −0.672708 0.739908i \(-0.734869\pi\)
−0.672708 + 0.739908i \(0.734869\pi\)
\(410\) 0 0
\(411\) −4.83513 + 9.93375i −0.238500 + 0.489996i
\(412\) 3.10469 7.58030i 0.152957 0.373455i
\(413\) 0 0
\(414\) −4.13185 + 2.10127i −0.203070 + 0.103272i
\(415\) 0 0
\(416\) −12.6220 + 8.61603i −0.618843 + 0.422436i
\(417\) −1.14922 + 2.36106i −0.0562775 + 0.115622i
\(418\) −29.6570 5.83802i −1.45057 0.285547i
\(419\) −10.1107 −0.493941 −0.246970 0.969023i \(-0.579435\pi\)
−0.246970 + 0.969023i \(0.579435\pi\)
\(420\) 0 0
\(421\) 24.2094 1.17989 0.589946 0.807442i \(-0.299149\pi\)
0.589946 + 0.807442i \(0.299149\pi\)
\(422\) 19.6709 + 3.87223i 0.957563 + 0.188497i
\(423\) −11.5294 14.7082i −0.560578 0.715135i
\(424\) 13.1047 + 8.64391i 0.636420 + 0.419785i
\(425\) 0 0
\(426\) −16.7906 + 22.2090i −0.813507 + 1.07603i
\(427\) 2.50031i 0.120999i
\(428\) −34.8899 14.2900i −1.68647 0.690731i
\(429\) −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 \(0.658062\pi\)
\(432\) 11.1392 17.5476i 0.535934 0.844260i
\(433\) −31.2094 −1.49983 −0.749913 0.661536i \(-0.769905\pi\)
−0.749913 + 0.661536i \(0.769905\pi\)
\(434\) −6.42110 + 32.6191i −0.308222 + 1.56577i
\(435\) 0 0
\(436\) −16.1047 6.59605i −0.771275 0.315893i
\(437\) 5.55034i 0.265509i
\(438\) 11.3769 15.0483i 0.543610 0.719034i
\(439\) 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
\(442\) −3.10469 0.611161i −0.147675 0.0290699i
\(443\) −11.2033 −0.532285 −0.266143 0.963934i \(-0.585749\pi\)
−0.266143 + 0.963934i \(0.585749\pi\)
\(444\) −12.4690 13.9589i −0.591752 0.662458i
\(445\) 0 0
\(446\) −21.7745 4.28634i −1.03105 0.202964i
\(447\) 1.25562 2.57967i 0.0593890 0.122014i
\(448\) −26.2094 + 11.2236i −1.23828 + 0.530264i
\(449\) 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
\(452\) −11.9942 + 29.2845i −0.564158 + 1.37743i
\(453\) 3.50781 7.20677i 0.164811 0.338604i
\(454\) −3.19375 + 16.2242i −0.149890 + 0.761440i
\(455\) 0 0
\(456\) 12.6822 + 21.4129i 0.593899 + 1.00275i
\(457\) −16.8953 −0.790329 −0.395165 0.918610i \(-0.629312\pi\)
−0.395165 + 0.918610i \(0.629312\pi\)
\(458\) 2.37681 12.0742i 0.111061 0.564188i
\(459\) 4.20732 0.904899i 0.196381 0.0422371i
\(460\) 0 0
\(461\) 7.20677i 0.335653i −0.985817 0.167826i \(-0.946325\pi\)
0.985817 0.167826i \(-0.0536748\pi\)
\(462\) −29.2983 22.1503i −1.36308 1.03053i
\(463\) 7.12785i 0.331259i −0.986188 0.165630i \(-0.947034\pi\)
0.986188 0.165630i \(-0.0529656\pi\)
\(464\) 15.5737 15.8228i 0.722989 0.734555i
\(465\) 0 0
\(466\) 20.8062 + 4.09573i 0.963831 + 0.189731i
\(467\) −0.766519 −0.0354703 −0.0177351 0.999843i \(-0.505646\pi\)
−0.0177351 + 0.999843i \(0.505646\pi\)
\(468\) 4.41877 + 15.5955i 0.204258 + 0.720900i
\(469\) 7.29844 0.337011
\(470\) 0 0
\(471\) −12.6220 6.14360i −0.581590 0.283082i
\(472\) 0 0
\(473\) 2.23748i 0.102879i
\(474\) 13.9273 + 10.5294i 0.639701 + 0.483632i
\(475\) 0 0
\(476\) −5.46295 2.23748i −0.250394 0.102555i
\(477\) 13.1047 10.2725i 0.600022 0.470344i
\(478\) 1.49219 7.58030i 0.0682512 0.346715i
\(479\) −42.0732 −1.92237 −0.961187 0.275897i \(-0.911025\pi\)
−0.961187 + 0.275897i \(0.911025\pi\)
\(480\) 0 0
\(481\) 14.5969 0.665560
\(482\) 1.91203 9.71309i 0.0870906 0.442419i
\(483\) 2.95170 6.06424i 0.134307 0.275932i
\(484\) −12.4031 5.07999i −0.563778 0.230908i
\(485\) 0 0
\(486\) −13.9017 17.1098i −0.630592 0.776114i
\(487\) 34.0438i 1.54267i 0.636427 + 0.771337i \(0.280412\pi\)
−0.636427 + 0.771337i \(0.719588\pi\)
\(488\) −1.09259 + 1.65643i −0.0494592 + 0.0749831i
\(489\) 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 \(0.376011\pi\)
\(492\) 26.5387 23.7061i 1.19646 1.06875i
\(493\) 4.59688 0.207033
\(494\) −19.0431 3.74865i −0.856788 0.168660i
\(495\) 0 0
\(496\) 18.5078 18.8039i 0.831025 0.844319i
\(497\) 40.5088i 1.81707i
\(498\) 4.60115 6.08595i 0.206182 0.272718i
\(499\) 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
\(502\) 0.342970 1.74228i 0.0153075 0.0777620i
\(503\) −32.2399 −1.43751 −0.718753 0.695265i \(-0.755287\pi\)
−0.718753 + 0.695265i \(0.755287\pi\)
\(504\) 2.46898 + 30.1400i 0.109977 + 1.34254i
\(505\) 0 0
\(506\) 1.25562 6.37855i 0.0558193 0.283561i
\(507\) 8.87942 + 4.32196i 0.394349 + 0.191945i
\(508\) 12.2984 30.0275i 0.545655 1.33225i
\(509\) 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
\(512\) 22.2679 + 4.01749i 0.984112 + 0.177550i
\(513\) 25.8062 5.55034i 1.13937 0.245053i
\(514\) 15.4031 + 3.03212i 0.679403 + 0.133741i
\(515\) 0 0
\(516\) 1.37391 1.22727i 0.0604829 0.0540273i
\(517\) 26.2094 1.15269
\(518\) 26.7198 + 5.25982i 1.17400 + 0.231103i
\(519\) 11.3663 23.3521i 0.498927 1.02504i
\(520\) 0 0
\(521\) 10.2725i 0.450045i 0.974354 + 0.225022i \(0.0722455\pi\)
−0.974354 + 0.225022i \(0.927754\pi\)
\(522\) −10.6744 20.9898i −0.467206 0.918697i
\(523\) 31.4642i 1.37583i 0.725790 + 0.687916i \(0.241474\pi\)
−0.725790 + 0.687916i \(0.758526\pi\)
\(524\) 36.6103 + 14.9946i 1.59933 + 0.655041i
\(525\) 0 0
\(526\) 4.89531 24.8681i 0.213446 1.08430i
\(527\) 5.46295 0.237970
\(528\) 9.73052 + 27.4771i 0.423467 + 1.19579i
\(529\) −21.8062 −0.948098
\(530\) 0 0
\(531\) 0 0
\(532\) −33.5078 13.7239i −1.45275 0.595006i
\(533\) 27.7517i 1.20206i
\(534\) −9.22667 6.97562i −0.399277 0.301865i
\(535\) 0 0
\(536\) −4.83513 3.18928i −0.208846 0.137756i
\(537\) 24.2539 + 11.8053i 1.04663 + 0.509437i
\(538\) 20.8062 + 4.09573i 0.897021 + 0.176579i
\(539\) 23.9883 1.03325
\(540\) 0 0
\(541\) −19.2984 −0.829705 −0.414852 0.909889i \(-0.636167\pi\)
−0.414852 + 0.909889i \(0.636167\pi\)
\(542\) −33.8788 6.66908i −1.45522 0.286461i
\(543\) 33.4955 + 16.3036i 1.43743 + 0.699653i
\(544\) 2.64141 + 3.86951i 0.113249 + 0.165904i
\(545\) 0 0
\(546\) −18.8127 14.2229i −0.805109 0.608685i
\(547\) 21.8360i 0.933640i 0.884352 + 0.466820i \(0.154600\pi\)
−0.884352 + 0.466820i \(0.845400\pi\)
\(548\) −4.83513 + 11.8053i −0.206547 + 0.504298i
\(549\) 1.29844 + 1.65643i 0.0554160 + 0.0706948i
\(550\) 0 0
\(551\) 28.1956 1.20117
\(552\) −4.60542 + 2.72766i −0.196020 + 0.116097i
\(553\) −25.4031 −1.08025
\(554\) 7.67672 38.9976i 0.326153 1.65685i
\(555\) 0 0
\(556\) −1.14922 + 2.80590i −0.0487377 + 0.118996i
\(557\) 17.2321i 0.730146i 0.930979 + 0.365073i \(0.118956\pi\)
−0.930979 + 0.365073i \(0.881044\pi\)
\(558\) −12.6855 24.9443i −0.537020 1.05598i
\(559\) 1.43670i 0.0607661i
\(560\) 0 0
\(561\) −2.64141 + 5.42675i −0.111520 + 0.229118i
\(562\) 10.0000 + 1.96851i 0.421825 + 0.0830366i
\(563\) 30.0547 1.26666 0.633328 0.773883i \(-0.281688\pi\)
0.633328 + 0.773883i \(0.281688\pi\)
\(564\) −14.3760 16.0937i −0.605337 0.677667i
\(565\) 0 0
\(566\) −8.52476 1.67811i −0.358322 0.0705361i
\(567\) 31.1473 + 7.65966i 1.30806 + 0.321675i
\(568\) −17.7016 + 26.8366i −0.742741 + 1.12604i
\(569\) 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 \(-0.757571\pi\)
0.723724 0.690090i \(-0.242429\pi\)
\(572\) −21.0366 8.61603i −0.879585 0.360254i
\(573\) −17.7016 8.61603i −0.739493 0.359940i
\(574\) −10.0000 + 50.7999i −0.417392 + 2.12034i
\(575\) 0 0
\(576\) 11.5349 21.0463i 0.480621 0.876928i
\(577\) −0.403124 −0.0167823 −0.00839114 0.999965i \(-0.502671\pi\)
−0.00839114 + 0.999965i \(0.502671\pi\)
\(578\) 4.45614 22.6371i 0.185351 0.941581i
\(579\) −9.04246 4.40131i −0.375792 0.182912i
\(580\) 0 0
\(581\) 11.1007i 0.460534i
\(582\) −11.9724 + 15.8359i −0.496273 + 0.656421i
\(583\) 23.3521i 0.967144i
\(584\) 11.9942 18.1839i 0.496322 0.752453i
\(585\) 0 0
\(586\) −26.2094 5.15934i −1.08270 0.213130i
\(587\) 3.88125 0.160196 0.0800982 0.996787i \(-0.474477\pi\)
0.0800982 + 0.996787i \(0.474477\pi\)
\(588\) −13.1577 14.7299i −0.542614 0.607449i
\(589\) 33.5078 1.38067
\(590\) 0 0
\(591\) −7.15902 + 14.7082i −0.294483 + 0.605012i
\(592\) −15.4031 15.1606i −0.633065 0.623097i
\(593\) 43.5745i 1.78939i −0.446678 0.894695i \(-0.647393\pi\)
0.446678 0.894695i \(-0.352607\pi\)
\(594\) 30.9127 0.540538i 1.26836 0.0221785i
\(595\) 0 0
\(596\) 1.25562 3.06569i 0.0514324 0.125576i
\(597\) −11.8953 + 24.4388i −0.486843 + 1.00021i
\(598\) 0.806248 4.09573i 0.0329700 0.167487i
\(599\) 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 \(0.337067\pi\)
\(602\) −0.517700 + 2.62991i −0.0210999 + 0.107187i
\(603\) −4.83513 + 3.79015i −0.196902 + 0.154347i
\(604\) 3.50781 8.56455i 0.142731 0.348487i
\(605\) 0 0
\(606\) 14.0815 + 10.6460i 0.572021 + 0.432464i
\(607\) 27.4478i 1.11407i 0.830489 + 0.557036i \(0.188061\pi\)
−0.830489 + 0.557036i \(0.811939\pi\)
\(608\) 16.2015 + 23.7342i 0.657057 + 0.962549i
\(609\) 30.8062 + 14.9946i 1.24833 + 0.607611i
\(610\) 0 0
\(611\) 16.8293 0.680840
\(612\) 4.78108 1.35466i 0.193264 0.0547588i
\(613\) 20.8062 0.840356 0.420178 0.907442i \(-0.361968\pi\)
0.420178 + 0.907442i \(0.361968\pi\)
\(614\) −28.3057 5.57201i −1.14233 0.224868i
\(615\) 0 0
\(616\) −35.4031 23.3521i −1.42643 0.940881i
\(617\) 18.3074i 0.737030i 0.929622 + 0.368515i \(0.120134\pi\)
−0.929622 + 0.368515i \(0.879866\pi\)
\(618\) −8.00274 6.05030i −0.321918 0.243379i
\(619\) 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
\(622\) 4.59688 23.3521i 0.184318 0.936332i
\(623\) 16.8293 0.674251
\(624\) 6.24806 + 17.6433i 0.250123 + 0.706298i
\(625\) 0 0
\(626\) −6.20087 + 31.5003i −0.247837 + 1.25901i
\(627\) −16.2015 + 33.2858i −0.647025 + 1.32931i
\(628\) −15.0000 6.14360i −0.598565 0.245156i
\(629\) 4.47495i 0.178428i
\(630\) 0 0
\(631\) 2.65903i 0.105854i −0.998598 0.0529271i \(-0.983145\pi\)
0.998598 0.0529271i \(-0.0168551\pi\)
\(632\) 16.8293 + 11.1007i 0.669433 + 0.441561i
\(633\) 10.7461 22.0778i 0.427119 0.877512i
\(634\) −41.6125 8.19146i −1.65264 0.325324i
\(635\) 0 0
\(636\) 14.3392 12.8087i 0.568585 0.507898i
\(637\) 15.4031 0.610294
\(638\) 32.4030 + 6.37855i 1.28285 + 0.252529i
\(639\) 21.0366 + 26.8366i 0.832196 + 1.06164i
\(640\) 0 0
\(641\) 41.0898i 1.62295i −0.584386 0.811476i \(-0.698665\pi\)
0.584386 0.811476i \(-0.301335\pi\)
\(642\) −27.8477 + 36.8343i −1.09906 + 1.45373i
\(643\) 22.2885i 0.878971i −0.898250 0.439485i \(-0.855161\pi\)
0.898250 0.439485i \(-0.144839\pi\)
\(644\) 2.95170 7.20677i 0.116313 0.283986i
\(645\) 0 0
\(646\) −1.14922 + 5.83802i −0.0452154 + 0.229694i
\(647\) −2.18518 −0.0859082 −0.0429541 0.999077i \(-0.513677\pi\)
−0.0429541 + 0.999077i \(0.513677\pi\)
\(648\) −17.2876 18.6852i −0.679123 0.734025i
\(649\) 0 0
\(650\) 0 0
\(651\) 36.6103 + 17.8196i 1.43487 + 0.698406i
\(652\) 3.85078 9.40194i 0.150808 0.368208i
\(653\) 7.78781i 0.304761i 0.988322 + 0.152380i \(0.0486939\pi\)
−0.988322 + 0.152380i \(0.951306\pi\)
\(654\) −12.8541 + 17.0022i −0.502636 + 0.664838i
\(655\) 0 0
\(656\) 28.8234 29.2845i 1.12537 1.14337i
\(657\) −14.2539 18.1839i −0.556098 0.709420i
\(658\) 30.8062 + 6.06424i 1.20095 + 0.236409i
\(659\) −21.0366 −0.819470 −0.409735 0.912205i \(-0.634379\pi\)
−0.409735 + 0.912205i \(0.634379\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) −41.6656 8.20192i −1.61938 0.318777i
\(663\) −1.69607 + 3.48457i −0.0658700 + 0.135329i
\(664\) 4.85078 7.35408i 0.188247 0.285393i
\(665\) 0 0
\(666\) −20.4330 + 10.3913i −0.791764 + 0.402654i
\(667\) 6.06424i 0.234808i
\(668\) −6.06643 2.48465i −0.234717 0.0961339i
\(669\) −11.8953 + 24.4388i −0.459899 + 0.944860i
\(670\) 0 0
\(671\) −2.95170 −0.113949
\(672\) 5.07959 + 34.5478i 0.195950 + 1.33271i
\(673\) 0.806248 0.0310786 0.0155393 0.999879i \(-0.495053\pi\)
0.0155393 + 0.999879i \(0.495053\pi\)
\(674\) −0.110112 + 0.559369i −0.00424137 + 0.0215461i
\(675\) 0 0
\(676\) 10.5523 + 4.32196i 0.405859 + 0.166229i
\(677\) 3.89391i 0.149655i 0.997196 + 0.0748275i \(0.0238406\pi\)
−0.997196 + 0.0748275i \(0.976159\pi\)
\(678\) 30.9165 + 23.3738i 1.18734 + 0.897664i
\(679\) 28.8845i 1.10849i
\(680\) 0 0
\(681\) 18.2094 + 8.86320i 0.697785 + 0.339639i
\(682\) 38.5078 + 7.58030i 1.47454 + 0.290265i
\(683\) 19.9440 0.763137 0.381568 0.924341i \(-0.375384\pi\)
0.381568 + 0.924341i \(0.375384\pi\)
\(684\) 29.3255 8.30900i 1.12129 0.317703i
\(685\) 0 0
\(686\) −6.42110 1.26400i −0.245159 0.0482597i
\(687\) −13.5515 6.59605i −0.517023 0.251655i
\(688\) 1.49219 1.51606i 0.0568892 0.0577992i
\(689\) 14.9946i 0.571248i
\(690\) 0 0
\(691\) 18.8039i 0.715333i −0.933849 0.357667i \(-0.883572\pi\)
0.933849 0.357667i \(-0.116428\pi\)
\(692\) 11.3663 27.7517i 0.432084 1.05496i
\(693\) −35.4031 + 27.7517i −1.34485 + 1.05420i
\(694\) 3.65703 18.5777i 0.138819 0.705198i
\(695\) 0 0
\(696\) −13.8565 23.3955i −0.525228 0.886803i
\(697\) 8.50781 0.322256
\(698\) −3.33496 + 16.9415i −0.126230 + 0.641247i
\(699\) 11.3663 23.3521i 0.429915 0.883256i
\(700\) 0 0
\(701\) 27.7517i 1.04817i −0.851667 0.524083i \(-0.824408\pi\)
0.851667 0.524083i \(-0.175592\pi\)
\(702\) 19.8493 0.347085i 0.749164 0.0130999i
\(703\) 27.4478i 1.03521i
\(704\) 13.2498 + 30.9410i 0.499370 + 1.16613i
\(705\) 0 0
\(706\) 40.8062 + 8.03275i 1.53576 + 0.302317i
\(707\) −25.6844 −0.965961
\(708\) 0 0
\(709\) −11.2984 −0.424322 −0.212161 0.977235i \(-0.568050\pi\)
−0.212161 + 0.977235i \(0.568050\pi\)
\(710\) 0 0
\(711\) 16.8293 13.1921i 0.631148 0.494742i
\(712\) −11.1492 7.35408i −0.417835 0.275606i
\(713\) 7.20677i 0.269896i
\(714\) −4.36031 + 5.76739i −0.163181 + 0.215839i
\(715\) 0 0
\(716\) 28.8234 + 11.8053i 1.07718 + 0.441185i
\(717\) −8.50781 4.14108i −0.317730 0.154651i
\(718\) 10.0000 50.7999i 0.373197 1.89583i
\(719\) −25.6844 −0.957866 −0.478933 0.877851i \(-0.658976\pi\)
−0.478933 + 0.877851i \(0.658976\pi\)
\(720\) 0 0
\(721\) 14.5969 0.543616
\(722\) −1.85911 + 9.44424i −0.0691889 + 0.351478i
\(723\) −10.9016 5.30621i −0.405434 0.197340i
\(724\) 39.8062 + 16.3036i 1.47939 + 0.605917i
\(725\) 0 0
\(726\) −9.89969 + 13.0943i −0.367412 + 0.485977i
\(727\) 45.1087i 1.67299i −0.547975 0.836495i \(-0.684601\pi\)
0.547975 0.836495i \(-0.315399\pi\)
\(728\) −22.7327 14.9946i −0.842529 0.555736i
\(729\) −24.6125 + 11.1007i −0.911574 + 0.411136i
\(730\) 0 0
\(731\) 0.440449 0.0162906
\(732\) 1.61902 + 1.81247i 0.0598407 + 0.0669908i
\(733\) 20.8062 0.768496 0.384248 0.923230i \(-0.374461\pi\)
0.384248 + 0.923230i \(0.374461\pi\)
\(734\) −4.94525 0.973477i −0.182532 0.0359317i
\(735\) 0 0
\(736\) −5.10469 + 3.48457i −0.188161 + 0.128443i
\(737\) 8.61603i 0.317376i
\(738\) −19.7560 38.8474i −0.727227 1.42999i
\(739\) 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
\(742\) −5.40312 + 27.4478i −0.198355 + 1.00764i
\(743\) −29.6143 −1.08644 −0.543222 0.839589i \(-0.682796\pi\)
−0.543222 + 0.839589i \(0.682796\pi\)
\(744\) −16.4671 27.8033i −0.603712 1.01932i
\(745\) 0 0
\(746\) 4.72502 24.0030i 0.172995 0.878814i
\(747\) −5.76469 7.35408i −0.210919 0.269072i
\(748\) −2.64141 + 6.44918i −0.0965795 + 0.235805i
\(749\) 67.1851i 2.45489i
\(750\) 0 0
\(751\) 28.3527i 1.03460i 0.855803 + 0.517302i \(0.173064\pi\)
−0.855803 + 0.517302i \(0.826936\pi\)
\(752\) −17.7588 17.4792i −0.647598 0.637402i
\(753\) −1.95547 0.951801i −0.0712612 0.0346856i
\(754\) 20.8062 + 4.09573i 0.757719 + 0.149158i
\(755\) 0 0
\(756\) 36.4595 + 6.51713i 1.32602 + 0.237026i
\(757\) −8.91093 −0.323873 −0.161937 0.986801i \(-0.551774\pi\)
−0.161937 + 0.986801i \(0.551774\pi\)
\(758\) −29.5614 5.81918i −1.07372 0.211362i
\(759\) −7.15902 3.48457i −0.259856 0.126482i
\(760\) 0 0
\(761\) 3.06569i 0.111131i 0.998455 + 0.0555656i \(0.0176962\pi\)
−0.998455 + 0.0555656i \(0.982304\pi\)
\(762\) −31.7009 23.9667i −1.14840 0.868224i
\(763\) 31.0117i 1.12270i
\(764\) −21.0366 8.61603i −0.761078 0.311717i
\(765\) 0 0
\(766\) 3.40312 17.2878i 0.122960 0.624634i
\(767\) 0 0
\(768\) 11.7315 25.1072i 0.423325 0.905978i
\(769\) −39.8062 −1.43545 −0.717725 0.696327i \(-0.754817\pi\)
−0.717725 + 0.696327i \(0.754817\pi\)
\(770\) 0 0
\(771\) 8.41464 17.2878i 0.303046 0.622606i
\(772\) −10.7461 4.40131i −0.386760 0.158407i
\(773\) 5.55034i 0.199632i −0.995006 0.0998159i \(-0.968175\pi\)
0.995006 0.0998159i \(-0.0318254\pi\)
\(774\) −1.02277 2.01113i −0.0367626 0.0722886i
\(775\) 0 0
\(776\) −12.6220 + 19.1357i −0.453102 + 0.686930i
\(777\) 14.5969 29.9892i 0.523660 1.07586i
\(778\) −27.7016 5.45308i −0.993149 0.195502i
\(779\) 52.1839 1.86968
\(780\) 0 0
\(781\) −47.8219 −1.71120
\(782\) −1.25562 0.247171i −0.0449010 0.00883881i
\(783\) −28.1956 + 6.06424i −1.00763 + 0.216718i
\(784\) −16.2539 15.9980i −0.580497 0.571357i
\(785\) 0 0
\(786\) 29.2209 38.6505i 1.04227 1.37862i
\(787\) 14.7875i &