Properties

Label 300.2.e.e.251.4
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 251.4
Root \(0.273147 + 1.38758i\) of defining polynomial
Character \(\chi\) \(=\) 300.251
Dual form 300.2.e.e.251.3

$q$-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 \(0.235218\pi\)
−0.739170 + 0.673519i \(0.764782\pi\)
\(8\) 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 \(-0.377767\pi\)
0.374639 + 0.927171i \(0.377767\pi\)
\(14\) −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 \(-0.967976\pi\)
0.994944 0.100436i \(-0.0320237\pi\)
\(18\) −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 \(-0.463662\pi\)
0.113910 + 0.993491i \(0.463662\pi\)
\(24\) 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 \(-0.353511\pi\)
0.444134 + 0.895960i \(0.353511\pi\)
\(38\) −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 \(0.0129109\pi\)
−0.999178 + 0.0405498i \(0.987089\pi\)
\(44\) 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 \(-0.349879\pi\)
0.454331 + 0.890833i \(0.349879\pi\)
\(48\) 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 \(0.124489\pi\)
−0.924493 + 0.381199i \(0.875511\pi\)
\(54\) −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 \(-0.960077\pi\)
0.992145 0.125093i \(-0.0399230\pi\)
\(68\) −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 \(-0.351174\pi\)
0.450700 + 0.892676i \(0.351174\pi\)
\(74\) −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 \(-0.445319\pi\)
0.170943 + 0.985281i \(0.445319\pi\)
\(84\) 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 \(-0.634979\pi\)
−0.411453 + 0.911431i \(0.634979\pi\)
\(98\) 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 \(-0.935327\pi\)
0.979430 0.201782i \(-0.0646733\pi\)
\(104\) 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 \(-0.864857\pi\)
−0.911218 + 0.411924i \(0.864857\pi\)
\(108\) 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 \(0.267189\pi\)
−0.667910 + 0.744242i \(0.732811\pi\)
\(114\) −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 \(-0.744218\pi\)
0.694147 0.719833i \(-0.255782\pi\)
\(128\) 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 \(0.0878433\pi\)
−0.962162 + 0.272478i \(0.912157\pi\)
\(138\) −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 \(-0.604830\pi\)
−0.323412 + 0.946258i \(0.604830\pi\)
\(158\) 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 \(-0.936248\pi\)
0.980010 0.198948i \(-0.0637523\pi\)
\(164\) −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 \(-0.540477\pi\)
−0.126821 + 0.991926i \(0.540477\pi\)
\(168\) 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 \(-0.806940\pi\)
0.821639 0.570008i \(-0.193060\pi\)
\(174\) 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 \(-0.567012\pi\)
−0.208971 + 0.977922i \(0.567012\pi\)
\(194\) 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 \(0.109222\pi\)
−0.941706 + 0.336437i \(0.890778\pi\)
\(198\) 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 \(0.176092\pi\)
−0.850843 + 0.525421i \(0.823908\pi\)
\(224\) −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 \(-0.373157\pi\)
0.388026 + 0.921648i \(0.373157\pi\)
\(228\) 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 \(-0.836572\pi\)
0.871067 0.491164i \(-0.163428\pi\)
\(234\) −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 \(-0.887465\pi\)
0.938153 0.346221i \(-0.112535\pi\)
\(258\) −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 \(-0.686347\pi\)
−0.552555 + 0.833476i \(0.686347\pi\)
\(264\) −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 \(-0.819997\pi\)
−0.844323 + 0.535834i \(0.819997\pi\)
\(278\) 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 \(0.0584511\pi\)
−0.983187 + 0.182599i \(0.941549\pi\)
\(284\) −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 \(0.186035\pi\)
−0.834017 + 0.551739i \(0.813965\pi\)
\(294\) 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 \(0.197778\pi\)
−0.813100 + 0.582125i \(0.802222\pi\)
\(308\) −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 \(-0.278278\pi\)
0.641584 + 0.767053i \(0.278278\pi\)
\(314\) 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 \(0.318728\pi\)
−0.539197 + 0.842180i \(0.681272\pi\)
\(318\) −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 \(-0.496505\pi\)
0.0109798 + 0.999940i \(0.496505\pi\)
\(338\) 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 \(-0.617007\pi\)
−0.359366 + 0.933197i \(0.617007\pi\)
\(348\) −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 \(-0.713884\pi\)
0.622502 0.782618i \(-0.286116\pi\)
\(354\) 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 \(0.0296513\pi\)
−0.995664 + 0.0930177i \(0.970349\pi\)
\(368\) 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 \(-0.647806\pi\)
−0.447840 + 0.894114i \(0.647806\pi\)
\(374\) −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 \(-0.603116\pi\)
−0.318311 + 0.947986i \(0.603116\pi\)
\(384\) 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 \(-0.241609\pi\)
0.725499 + 0.688223i \(0.241609\pi\)
\(398\) 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 \(-0.230095\pi\)
0.749913 + 0.661536i \(0.230095\pi\)
\(434\) −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 \(-0.414251\pi\)
0.266143 + 0.963934i \(0.414251\pi\)
\(444\) −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 \(-0.370688\pi\)
0.395165 + 0.918610i \(0.370688\pi\)
\(458\) −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 \(0.0529656\pi\)
−0.986188 + 0.165630i \(0.947034\pi\)
\(464\) 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 \(-0.494354\pi\)
0.0177351 + 0.999843i \(0.494354\pi\)
\(468\) −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 \(-0.719588\pi\)
0.636427 0.771337i \(-0.280412\pi\)
\(488\) 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 \(-0.244713\pi\)
0.718753 + 0.695265i \(0.244713\pi\)
\(504\) 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 \(-0.758526\pi\)
0.725790 0.687916i \(-0.241474\pi\)
\(524\) 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 \(-0.845400\pi\)
0.884352 0.466820i \(-0.154600\pi\)
\(548\) 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 \(-0.881044\pi\)
0.930979 0.365073i \(-0.118956\pi\)
\(558\) 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 \(-0.718312\pi\)
−0.633328 + 0.773883i \(0.718312\pi\)
\(564\) −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 \(-0.497329\pi\)
0.00839114 + 0.999965i \(0.497329\pi\)
\(578\) −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 \(-0.525523\pi\)
−0.0800982 + 0.996787i \(0.525523\pi\)
\(588\) 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 \(0.352607\pi\)
−0.446678 + 0.894695i \(0.647393\pi\)
\(594\) 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 \(-0.811939\pi\)
0.830489 0.557036i \(-0.188061\pi\)
\(608\) −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 \(-0.638032\pi\)
−0.420178 + 0.907442i \(0.638032\pi\)
\(614\) −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 \(-0.879866\pi\)
0.929622 0.368515i \(-0.120134\pi\)
\(618\) 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 \(0.144839\pi\)
−0.898250 + 0.439485i \(0.855161\pi\)
\(644\) 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 \(-0.486323\pi\)
0.0429541 + 0.999077i \(0.486323\pi\)
\(648\) 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 \(-0.951306\pi\)
0.988322 0.152380i \(-0.0486939\pi\)
\(654\) −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 \(-0.504947\pi\)
−0.0155393 + 0.999879i \(0.504947\pi\)
\(674\) −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 \(-0.976159\pi\)
0.997196 0.0748275i \(-0.0238406\pi\)
\(678\) −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 \(-0.624616\pi\)
−0.381568 + 0.924341i \(0.624616\pi\)
\(684\) 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 \(0.315399\pi\)
−0.547975 + 0.836495i \(0.684601\pi\)
\(728\) 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 \(-0.625539\pi\)
−0.384248 + 0.923230i \(0.625539\pi\)
\(734\) −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 \(-0.317204\pi\)
0.543222 + 0.839589i \(0.317204\pi\)
\(744\) −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 \(-0.448226\pi\)
0.161937 + 0.986801i \(0.448226\pi\)
\(758\) 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 \(0.0318254\pi\)
−0.995006 + 0.0998159i \(0.968175\pi\)
\(774\) −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