Properties

Label 570.2.c.c.569.1
Level $570$
Weight $2$
Character 570.569
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1499238400.2
Defining polynomial: \(x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 59 x^{4} - 66 x^{3} + 54 x^{2} - 26 x + 5\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 569.1
Root \(0.500000 - 1.08454i\) of defining polynomial
Character \(\chi\) \(=\) 570.569
Dual form 570.2.c.c.569.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-0.500000 - 1.65831i) q^{3} -1.00000 q^{4} +(-0.584541 - 2.15831i) q^{5} +(-1.65831 + 0.500000i) q^{6} +4.86140i q^{7} +1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-0.500000 - 1.65831i) q^{3} -1.00000 q^{4} +(-0.584541 - 2.15831i) q^{5} +(-1.65831 + 0.500000i) q^{6} +4.86140i q^{7} +1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +(-2.15831 + 0.584541i) q^{10} +2.31662i q^{11} +(0.500000 + 1.65831i) q^{12} -3.31662 q^{13} +4.86140 q^{14} +(-3.28689 + 2.04851i) q^{15} +1.00000 q^{16} -4.86140 q^{17} +(1.65831 + 2.50000i) q^{18} +(2.31662 + 3.69232i) q^{19} +(0.584541 + 2.15831i) q^{20} +(8.06173 - 2.43070i) q^{21} +2.31662 q^{22} -6.03049 q^{23} +(1.65831 - 0.500000i) q^{24} +(-4.31662 + 2.52324i) q^{25} +3.31662i q^{26} +(4.00000 + 3.31662i) q^{27} -4.86140i q^{28} +1.35416 q^{29} +(2.04851 + 3.28689i) q^{30} -8.55373i q^{31} -1.00000i q^{32} +(3.84169 - 1.15831i) q^{33} +4.86140i q^{34} +(10.4924 - 2.84169i) q^{35} +(2.50000 - 1.65831i) q^{36} -2.00000 q^{37} +(3.69232 - 2.31662i) q^{38} +(1.65831 + 5.50000i) q^{39} +(2.15831 - 0.584541i) q^{40} +3.50724 q^{41} +(-2.43070 - 8.06173i) q^{42} +1.16908i q^{43} -2.31662i q^{44} +(5.04051 + 4.42643i) q^{45} +6.03049i q^{46} +5.04648 q^{47} +(-0.500000 - 1.65831i) q^{48} -16.6332 q^{49} +(2.52324 + 4.31662i) q^{50} +(2.43070 + 8.06173i) q^{51} +3.31662 q^{52} -1.00000i q^{53} +(3.31662 - 4.00000i) q^{54} +(5.00000 - 1.35416i) q^{55} -4.86140 q^{56} +(4.96471 - 5.68785i) q^{57} -1.35416i q^{58} -9.90789 q^{59} +(3.28689 - 2.04851i) q^{60} +4.31662 q^{61} -8.55373 q^{62} +(-8.06173 - 12.1535i) q^{63} -1.00000 q^{64} +(1.93870 + 7.15831i) q^{65} +(-1.15831 - 3.84169i) q^{66} -7.00000 q^{67} +4.86140 q^{68} +(3.01524 + 10.0004i) q^{69} +(-2.84169 - 10.4924i) q^{70} -10.8919 q^{71} +(-1.65831 - 2.50000i) q^{72} +11.0770i q^{73} +2.00000i q^{74} +(6.34264 + 5.89669i) q^{75} +(-2.31662 - 3.69232i) q^{76} -11.2620 q^{77} +(5.50000 - 1.65831i) q^{78} +4.67632i q^{79} +(-0.584541 - 2.15831i) q^{80} +(3.50000 - 8.29156i) q^{81} -3.50724i q^{82} +9.72281 q^{83} +(-8.06173 + 2.43070i) q^{84} +(2.84169 + 10.4924i) q^{85} +1.16908 q^{86} +(-0.677081 - 2.24562i) q^{87} -2.31662 q^{88} -8.55373 q^{89} +(4.42643 - 5.04051i) q^{90} -16.1235i q^{91} +6.03049 q^{92} +(-14.1848 + 4.27686i) q^{93} -5.04648i q^{94} +(6.61503 - 7.15831i) q^{95} +(-1.65831 + 0.500000i) q^{96} -16.6332 q^{97} +16.6332i q^{98} +(-3.84169 - 5.79156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} - 8q^{4} - 20q^{9} + O(q^{10}) \) \( 8q - 4q^{3} - 8q^{4} - 20q^{9} - 4q^{10} + 4q^{12} - 22q^{15} + 8q^{16} - 8q^{19} - 8q^{22} - 8q^{25} + 32q^{27} + 2q^{30} + 44q^{33} + 20q^{36} - 16q^{37} + 4q^{40} + 22q^{45} - 4q^{48} - 80q^{49} + 40q^{55} + 4q^{57} + 22q^{60} + 8q^{61} - 8q^{64} + 4q^{66} - 56q^{67} - 36q^{70} + 4q^{75} + 8q^{76} + 44q^{78} + 28q^{81} + 36q^{85} + 8q^{88} + 10q^{90} - 80q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.500000 1.65831i −0.288675 0.957427i
\(4\) −1.00000 −0.500000
\(5\) −0.584541 2.15831i −0.261414 0.965227i
\(6\) −1.65831 + 0.500000i −0.677003 + 0.204124i
\(7\) 4.86140i 1.83744i 0.394912 + 0.918719i \(0.370775\pi\)
−0.394912 + 0.918719i \(0.629225\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.50000 + 1.65831i −0.833333 + 0.552771i
\(10\) −2.15831 + 0.584541i −0.682518 + 0.184848i
\(11\) 2.31662i 0.698489i 0.937032 + 0.349244i \(0.113562\pi\)
−0.937032 + 0.349244i \(0.886438\pi\)
\(12\) 0.500000 + 1.65831i 0.144338 + 0.478714i
\(13\) −3.31662 −0.919866 −0.459933 0.887954i \(-0.652127\pi\)
−0.459933 + 0.887954i \(0.652127\pi\)
\(14\) 4.86140 1.29926
\(15\) −3.28689 + 2.04851i −0.848670 + 0.528922i
\(16\) 1.00000 0.250000
\(17\) −4.86140 −1.17906 −0.589532 0.807745i \(-0.700688\pi\)
−0.589532 + 0.807745i \(0.700688\pi\)
\(18\) 1.65831 + 2.50000i 0.390868 + 0.589256i
\(19\) 2.31662 + 3.69232i 0.531470 + 0.847077i
\(20\) 0.584541 + 2.15831i 0.130707 + 0.482613i
\(21\) 8.06173 2.43070i 1.75921 0.530423i
\(22\) 2.31662 0.493906
\(23\) −6.03049 −1.25744 −0.628722 0.777631i \(-0.716421\pi\)
−0.628722 + 0.777631i \(0.716421\pi\)
\(24\) 1.65831 0.500000i 0.338502 0.102062i
\(25\) −4.31662 + 2.52324i −0.863325 + 0.504648i
\(26\) 3.31662i 0.650444i
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 4.86140i 0.918719i
\(29\) 1.35416 0.251461 0.125731 0.992064i \(-0.459872\pi\)
0.125731 + 0.992064i \(0.459872\pi\)
\(30\) 2.04851 + 3.28689i 0.374004 + 0.600101i
\(31\) 8.55373i 1.53629i −0.640273 0.768147i \(-0.721179\pi\)
0.640273 0.768147i \(-0.278821\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.84169 1.15831i 0.668752 0.201636i
\(34\) 4.86140i 0.833724i
\(35\) 10.4924 2.84169i 1.77354 0.480333i
\(36\) 2.50000 1.65831i 0.416667 0.276385i
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 3.69232 2.31662i 0.598974 0.375806i
\(39\) 1.65831 + 5.50000i 0.265543 + 0.880705i
\(40\) 2.15831 0.584541i 0.341259 0.0924240i
\(41\) 3.50724 0.547739 0.273870 0.961767i \(-0.411696\pi\)
0.273870 + 0.961767i \(0.411696\pi\)
\(42\) −2.43070 8.06173i −0.375065 1.24395i
\(43\) 1.16908i 0.178283i 0.996019 + 0.0891416i \(0.0284124\pi\)
−0.996019 + 0.0891416i \(0.971588\pi\)
\(44\) 2.31662i 0.349244i
\(45\) 5.04051 + 4.42643i 0.751394 + 0.659853i
\(46\) 6.03049i 0.889147i
\(47\) 5.04648 0.736105 0.368053 0.929805i \(-0.380025\pi\)
0.368053 + 0.929805i \(0.380025\pi\)
\(48\) −0.500000 1.65831i −0.0721688 0.239357i
\(49\) −16.6332 −2.37618
\(50\) 2.52324 + 4.31662i 0.356840 + 0.610463i
\(51\) 2.43070 + 8.06173i 0.340366 + 1.12887i
\(52\) 3.31662 0.459933
\(53\) 1.00000i 0.137361i −0.997639 0.0686803i \(-0.978121\pi\)
0.997639 0.0686803i \(-0.0218788\pi\)
\(54\) 3.31662 4.00000i 0.451335 0.544331i
\(55\) 5.00000 1.35416i 0.674200 0.182595i
\(56\) −4.86140 −0.649632
\(57\) 4.96471 5.68785i 0.657592 0.753374i
\(58\) 1.35416i 0.177810i
\(59\) −9.90789 −1.28990 −0.644949 0.764226i \(-0.723121\pi\)
−0.644949 + 0.764226i \(0.723121\pi\)
\(60\) 3.28689 2.04851i 0.424335 0.264461i
\(61\) 4.31662 0.552687 0.276344 0.961059i \(-0.410877\pi\)
0.276344 + 0.961059i \(0.410877\pi\)
\(62\) −8.55373 −1.08632
\(63\) −8.06173 12.1535i −1.01568 1.53120i
\(64\) −1.00000 −0.125000
\(65\) 1.93870 + 7.15831i 0.240466 + 0.887879i
\(66\) −1.15831 3.84169i −0.142578 0.472879i
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) 4.86140 0.589532
\(69\) 3.01524 + 10.0004i 0.362993 + 1.20391i
\(70\) −2.84169 10.4924i −0.339647 1.25409i
\(71\) −10.8919 −1.29263 −0.646315 0.763071i \(-0.723691\pi\)
−0.646315 + 0.763071i \(0.723691\pi\)
\(72\) −1.65831 2.50000i −0.195434 0.294628i
\(73\) 11.0770i 1.29646i 0.761444 + 0.648231i \(0.224491\pi\)
−0.761444 + 0.648231i \(0.775509\pi\)
\(74\) 2.00000i 0.232495i
\(75\) 6.34264 + 5.89669i 0.732385 + 0.680891i
\(76\) −2.31662 3.69232i −0.265735 0.423539i
\(77\) −11.2620 −1.28343
\(78\) 5.50000 1.65831i 0.622752 0.187767i
\(79\) 4.67632i 0.526128i 0.964778 + 0.263064i \(0.0847330\pi\)
−0.964778 + 0.263064i \(0.915267\pi\)
\(80\) −0.584541 2.15831i −0.0653536 0.241307i
\(81\) 3.50000 8.29156i 0.388889 0.921285i
\(82\) 3.50724i 0.387310i
\(83\) 9.72281 1.06722 0.533608 0.845732i \(-0.320836\pi\)
0.533608 + 0.845732i \(0.320836\pi\)
\(84\) −8.06173 + 2.43070i −0.879606 + 0.265211i
\(85\) 2.84169 + 10.4924i 0.308224 + 1.13806i
\(86\) 1.16908 0.126065
\(87\) −0.677081 2.24562i −0.0725907 0.240756i
\(88\) −2.31662 −0.246953
\(89\) −8.55373 −0.906693 −0.453347 0.891334i \(-0.649770\pi\)
−0.453347 + 0.891334i \(0.649770\pi\)
\(90\) 4.42643 5.04051i 0.466587 0.531316i
\(91\) 16.1235i 1.69020i
\(92\) 6.03049 0.628722
\(93\) −14.1848 + 4.27686i −1.47089 + 0.443490i
\(94\) 5.04648i 0.520505i
\(95\) 6.61503 7.15831i 0.678687 0.734427i
\(96\) −1.65831 + 0.500000i −0.169251 + 0.0510310i
\(97\) −16.6332 −1.68885 −0.844425 0.535673i \(-0.820058\pi\)
−0.844425 + 0.535673i \(0.820058\pi\)
\(98\) 16.6332i 1.68021i
\(99\) −3.84169 5.79156i −0.386104 0.582074i
\(100\) 4.31662 2.52324i 0.431662 0.252324i
\(101\) 7.68338i 0.764524i 0.924054 + 0.382262i \(0.124855\pi\)
−0.924054 + 0.382262i \(0.875145\pi\)
\(102\) 8.06173 2.43070i 0.798230 0.240675i
\(103\) 15.5831 1.53545 0.767725 0.640779i \(-0.221388\pi\)
0.767725 + 0.640779i \(0.221388\pi\)
\(104\) 3.31662i 0.325222i
\(105\) −9.95862 15.9789i −0.971862 1.55938i
\(106\) −1.00000 −0.0971286
\(107\) 19.9499i 1.92863i −0.264763 0.964314i \(-0.585294\pi\)
0.264763 0.964314i \(-0.414706\pi\)
\(108\) −4.00000 3.31662i −0.384900 0.319142i
\(109\) 17.2925i 1.65632i 0.560489 + 0.828162i \(0.310613\pi\)
−0.560489 + 0.828162i \(0.689387\pi\)
\(110\) −1.35416 5.00000i −0.129114 0.476731i
\(111\) 1.00000 + 3.31662i 0.0949158 + 0.314800i
\(112\) 4.86140i 0.459360i
\(113\) 8.31662i 0.782362i −0.920314 0.391181i \(-0.872067\pi\)
0.920314 0.391181i \(-0.127933\pi\)
\(114\) −5.68785 4.96471i −0.532716 0.464988i
\(115\) 3.52506 + 13.0157i 0.328714 + 1.21372i
\(116\) −1.35416 −0.125731
\(117\) 8.29156 5.50000i 0.766555 0.508475i
\(118\) 9.90789i 0.912095i
\(119\) 23.6332i 2.16646i
\(120\) −2.04851 3.28689i −0.187002 0.300050i
\(121\) 5.63325 0.512114
\(122\) 4.31662i 0.390809i
\(123\) −1.75362 5.81610i −0.158119 0.524420i
\(124\) 8.55373i 0.768147i
\(125\) 7.96919 + 7.84169i 0.712786 + 0.701382i
\(126\) −12.1535 + 8.06173i −1.08272 + 0.718196i
\(127\) 3.36675 0.298751 0.149375 0.988781i \(-0.452274\pi\)
0.149375 + 0.988781i \(0.452274\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.93870 0.584541i 0.170693 0.0514659i
\(130\) 7.15831 1.93870i 0.627826 0.170035i
\(131\) 10.0000i 0.873704i 0.899533 + 0.436852i \(0.143907\pi\)
−0.899533 + 0.436852i \(0.856093\pi\)
\(132\) −3.84169 + 1.15831i −0.334376 + 0.100818i
\(133\) −17.9499 + 11.2620i −1.55645 + 0.976544i
\(134\) 7.00000i 0.604708i
\(135\) 4.82015 10.5720i 0.414852 0.909889i
\(136\) 4.86140i 0.416862i
\(137\) −4.86140 −0.415338 −0.207669 0.978199i \(-0.566588\pi\)
−0.207669 + 0.978199i \(0.566588\pi\)
\(138\) 10.0004 3.01524i 0.851293 0.256674i
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) −10.4924 + 2.84169i −0.886772 + 0.240166i
\(141\) −2.52324 8.36865i −0.212495 0.704767i
\(142\) 10.8919i 0.914027i
\(143\) 7.68338i 0.642516i
\(144\) −2.50000 + 1.65831i −0.208333 + 0.138193i
\(145\) −0.791562 2.92270i −0.0657356 0.242717i
\(146\) 11.0770 0.916736
\(147\) 8.31662 + 27.5831i 0.685944 + 2.27502i
\(148\) 2.00000 0.164399
\(149\) 4.00000i 0.327693i −0.986486 0.163846i \(-0.947610\pi\)
0.986486 0.163846i \(-0.0523901\pi\)
\(150\) 5.89669 6.34264i 0.481463 0.517874i
\(151\) 2.70832i 0.220400i −0.993909 0.110200i \(-0.964851\pi\)
0.993909 0.110200i \(-0.0351492\pi\)
\(152\) −3.69232 + 2.31662i −0.299487 + 0.187903i
\(153\) 12.1535 8.06173i 0.982553 0.651752i
\(154\) 11.2620i 0.907522i
\(155\) −18.4616 + 5.00000i −1.48287 + 0.401610i
\(156\) −1.65831 5.50000i −0.132771 0.440352i
\(157\) 2.33816i 0.186606i −0.995638 0.0933028i \(-0.970258\pi\)
0.995638 0.0933028i \(-0.0297425\pi\)
\(158\) 4.67632 0.372028
\(159\) −1.65831 + 0.500000i −0.131513 + 0.0396526i
\(160\) −2.15831 + 0.584541i −0.170630 + 0.0462120i
\(161\) 29.3166i 2.31047i
\(162\) −8.29156 3.50000i −0.651447 0.274986i
\(163\) 15.9384i 1.24839i −0.781269 0.624195i \(-0.785427\pi\)
0.781269 0.624195i \(-0.214573\pi\)
\(164\) −3.50724 −0.273870
\(165\) −4.74562 7.61448i −0.369446 0.592787i
\(166\) 9.72281i 0.754636i
\(167\) 5.05013i 0.390790i 0.980725 + 0.195395i \(0.0625990\pi\)
−0.980725 + 0.195395i \(0.937401\pi\)
\(168\) 2.43070 + 8.06173i 0.187533 + 0.621976i
\(169\) −2.00000 −0.153846
\(170\) 10.4924 2.84169i 0.804733 0.217947i
\(171\) −11.9146 5.38912i −0.911131 0.412116i
\(172\) 1.16908i 0.0891416i
\(173\) 13.2665i 1.00863i 0.863519 + 0.504317i \(0.168256\pi\)
−0.863519 + 0.504317i \(0.831744\pi\)
\(174\) −2.24562 + 0.677081i −0.170240 + 0.0513293i
\(175\) −12.2665 20.9849i −0.927260 1.58631i
\(176\) 2.31662i 0.174622i
\(177\) 4.95394 + 16.4304i 0.372361 + 1.23498i
\(178\) 8.55373i 0.641129i
\(179\) −2.70832 −0.202429 −0.101215 0.994865i \(-0.532273\pi\)
−0.101215 + 0.994865i \(0.532273\pi\)
\(180\) −5.04051 4.42643i −0.375697 0.329927i
\(181\) 2.70832i 0.201308i 0.994921 + 0.100654i \(0.0320935\pi\)
−0.994921 + 0.100654i \(0.967906\pi\)
\(182\) −16.1235 −1.19515
\(183\) −2.15831 7.15831i −0.159547 0.529158i
\(184\) 6.03049i 0.444573i
\(185\) 1.16908 + 4.31662i 0.0859525 + 0.317365i
\(186\) 4.27686 + 14.1848i 0.313595 + 1.04008i
\(187\) 11.2620i 0.823563i
\(188\) −5.04648 −0.368053
\(189\) −16.1235 + 19.4456i −1.17281 + 1.41446i
\(190\) −7.15831 6.61503i −0.519319 0.479904i
\(191\) 5.00000i 0.361787i 0.983503 + 0.180894i \(0.0578990\pi\)
−0.983503 + 0.180894i \(0.942101\pi\)
\(192\) 0.500000 + 1.65831i 0.0360844 + 0.119678i
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 16.6332i 1.19420i
\(195\) 10.9014 6.79413i 0.780663 0.486538i
\(196\) 16.6332 1.18809
\(197\) −6.21557 −0.442841 −0.221420 0.975178i \(-0.571069\pi\)
−0.221420 + 0.975178i \(0.571069\pi\)
\(198\) −5.79156 + 3.84169i −0.411588 + 0.273017i
\(199\) 21.2164 1.50399 0.751994 0.659169i \(-0.229092\pi\)
0.751994 + 0.659169i \(0.229092\pi\)
\(200\) −2.52324 4.31662i −0.178420 0.305231i
\(201\) 3.50000 + 11.6082i 0.246871 + 0.818778i
\(202\) 7.68338 0.540600
\(203\) 6.58312i 0.462045i
\(204\) −2.43070 8.06173i −0.170183 0.564434i
\(205\) −2.05013 7.56973i −0.143187 0.528693i
\(206\) 15.5831i 1.08573i
\(207\) 15.0762 10.0004i 1.04787 0.695078i
\(208\) −3.31662 −0.229967
\(209\) −8.55373 + 5.36675i −0.591674 + 0.371226i
\(210\) −15.9789 + 9.95862i −1.10265 + 0.687210i
\(211\) 18.4616i 1.27095i 0.772121 + 0.635475i \(0.219196\pi\)
−0.772121 + 0.635475i \(0.780804\pi\)
\(212\) 1.00000i 0.0686803i
\(213\) 5.44594 + 18.0622i 0.373150 + 1.23760i
\(214\) −19.9499 −1.36375
\(215\) 2.52324 0.683375i 0.172084 0.0466058i
\(216\) −3.31662 + 4.00000i −0.225668 + 0.272166i
\(217\) 41.5831 2.82285
\(218\) 17.2925 1.17120
\(219\) 18.3691 5.53848i 1.24127 0.374256i
\(220\) −5.00000 + 1.35416i −0.337100 + 0.0912975i
\(221\) 16.1235 1.08458
\(222\) 3.31662 1.00000i 0.222597 0.0671156i
\(223\) 23.2665 1.55804 0.779020 0.626999i \(-0.215717\pi\)
0.779020 + 0.626999i \(0.215717\pi\)
\(224\) 4.86140 0.324816
\(225\) 6.60724 13.4664i 0.440483 0.897761i
\(226\) −8.31662 −0.553214
\(227\) 0.0501256i 0.00332695i 0.999999 + 0.00166348i \(0.000529502\pi\)
−0.999999 + 0.00166348i \(0.999470\pi\)
\(228\) −4.96471 + 5.68785i −0.328796 + 0.376687i
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 13.0157 3.52506i 0.858228 0.232436i
\(231\) 5.63102 + 18.6760i 0.370494 + 1.22879i
\(232\) 1.35416i 0.0889050i
\(233\) 15.1395 0.991818 0.495909 0.868374i \(-0.334835\pi\)
0.495909 + 0.868374i \(0.334835\pi\)
\(234\) −5.50000 8.29156i −0.359546 0.542036i
\(235\) −2.94987 10.8919i −0.192429 0.710509i
\(236\) 9.90789 0.644949
\(237\) 7.75481 2.33816i 0.503729 0.151880i
\(238\) −23.6332 −1.53192
\(239\) 6.36675i 0.411831i 0.978570 + 0.205915i \(0.0660172\pi\)
−0.978570 + 0.205915i \(0.933983\pi\)
\(240\) −3.28689 + 2.04851i −0.212168 + 0.132231i
\(241\) 17.1075i 1.10199i −0.834509 0.550994i \(-0.814249\pi\)
0.834509 0.550994i \(-0.185751\pi\)
\(242\) 5.63325i 0.362119i
\(243\) −15.5000 1.65831i −0.994325 0.106381i
\(244\) −4.31662 −0.276344
\(245\) 9.72281 + 35.8997i 0.621167 + 2.29355i
\(246\) −5.81610 + 1.75362i −0.370821 + 0.111807i
\(247\) −7.68338 12.2461i −0.488881 0.779198i
\(248\) 8.55373 0.543162
\(249\) −4.86140 16.1235i −0.308079 1.02178i
\(250\) 7.84169 7.96919i 0.495952 0.504016i
\(251\) 1.58312i 0.0999259i 0.998751 + 0.0499629i \(0.0159103\pi\)
−0.998751 + 0.0499629i \(0.984090\pi\)
\(252\) 8.06173 + 12.1535i 0.507841 + 0.765599i
\(253\) 13.9704i 0.878310i
\(254\) 3.36675i 0.211249i
\(255\) 15.9789 9.95862i 1.00064 0.623633i
\(256\) 1.00000 0.0625000
\(257\) 14.9499i 0.932548i −0.884640 0.466274i \(-0.845596\pi\)
0.884640 0.466274i \(-0.154404\pi\)
\(258\) −0.584541 1.93870i −0.0363919 0.120698i
\(259\) 9.72281i 0.604146i
\(260\) −1.93870 7.15831i −0.120233 0.443940i
\(261\) −3.38540 + 2.24562i −0.209551 + 0.139001i
\(262\) 10.0000 0.617802
\(263\) −21.7838 −1.34325 −0.671623 0.740893i \(-0.734402\pi\)
−0.671623 + 0.740893i \(0.734402\pi\)
\(264\) 1.15831 + 3.84169i 0.0712892 + 0.236440i
\(265\) −2.15831 + 0.584541i −0.132584 + 0.0359080i
\(266\) 11.2620 + 17.9499i 0.690521 + 1.10058i
\(267\) 4.27686 + 14.1848i 0.261740 + 0.868093i
\(268\) 7.00000 0.427593
\(269\) 14.3991 0.877931 0.438965 0.898504i \(-0.355345\pi\)
0.438965 + 0.898504i \(0.355345\pi\)
\(270\) −10.5720 4.82015i −0.643388 0.293345i
\(271\) 9.31662 0.565945 0.282972 0.959128i \(-0.408680\pi\)
0.282972 + 0.959128i \(0.408680\pi\)
\(272\) −4.86140 −0.294766
\(273\) −26.7377 + 8.06173i −1.61824 + 0.487918i
\(274\) 4.86140i 0.293688i
\(275\) −5.84541 10.0000i −0.352491 0.603023i
\(276\) −3.01524 10.0004i −0.181496 0.601955i
\(277\) 12.0610i 0.724673i 0.932047 + 0.362337i \(0.118021\pi\)
−0.932047 + 0.362337i \(0.881979\pi\)
\(278\) 10.0000i 0.599760i
\(279\) 14.1848 + 21.3843i 0.849219 + 1.28025i
\(280\) 2.84169 + 10.4924i 0.169823 + 0.627043i
\(281\) −13.6002 −0.811321 −0.405660 0.914024i \(-0.632958\pi\)
−0.405660 + 0.914024i \(0.632958\pi\)
\(282\) −8.36865 + 2.52324i −0.498346 + 0.150257i
\(283\) 15.1395i 0.899947i 0.893042 + 0.449974i \(0.148567\pi\)
−0.893042 + 0.449974i \(0.851433\pi\)
\(284\) 10.8919 0.646315
\(285\) −15.1782 7.39062i −0.899081 0.437783i
\(286\) −7.68338 −0.454328
\(287\) 17.0501i 1.00644i
\(288\) 1.65831 + 2.50000i 0.0977170 + 0.147314i
\(289\) 6.63325 0.390191
\(290\) −2.92270 + 0.791562i −0.171627 + 0.0464821i
\(291\) 8.31662 + 27.5831i 0.487529 + 1.61695i
\(292\) 11.0770i 0.648231i
\(293\) 8.26650i 0.482934i 0.970409 + 0.241467i \(0.0776286\pi\)
−0.970409 + 0.241467i \(0.922371\pi\)
\(294\) 27.5831 8.31662i 1.60868 0.485035i
\(295\) 5.79156 + 21.3843i 0.337198 + 1.24504i
\(296\) 2.00000i 0.116248i
\(297\) −7.68338 + 9.26650i −0.445835 + 0.537697i
\(298\) −4.00000 −0.231714
\(299\) 20.0009 1.15668
\(300\) −6.34264 5.89669i −0.366192 0.340446i
\(301\) −5.68338 −0.327584
\(302\) −2.70832 −0.155846
\(303\) 12.7414 3.84169i 0.731976 0.220699i
\(304\) 2.31662 + 3.69232i 0.132868 + 0.211769i
\(305\) −2.52324 9.31662i −0.144480 0.533468i
\(306\) −8.06173 12.1535i −0.460858 0.694770i
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 11.2620 0.641715
\(309\) −7.79156 25.8417i −0.443246 1.47008i
\(310\) 5.00000 + 18.4616i 0.283981 + 1.04855i
\(311\) 18.8997i 1.07171i −0.844311 0.535853i \(-0.819990\pi\)
0.844311 0.535853i \(-0.180010\pi\)
\(312\) −5.50000 + 1.65831i −0.311376 + 0.0938835i
\(313\) 28.5546i 1.61400i −0.590551 0.807000i \(-0.701090\pi\)
0.590551 0.807000i \(-0.298910\pi\)
\(314\) −2.33816 −0.131950
\(315\) −21.5187 + 24.5039i −1.21244 + 1.38064i
\(316\) 4.67632i 0.263064i
\(317\) 17.0000i 0.954815i 0.878682 + 0.477408i \(0.158423\pi\)
−0.878682 + 0.477408i \(0.841577\pi\)
\(318\) 0.500000 + 1.65831i 0.0280386 + 0.0929935i
\(319\) 3.13708i 0.175643i
\(320\) 0.584541 + 2.15831i 0.0326768 + 0.120653i
\(321\) −33.0831 + 9.97494i −1.84652 + 0.556747i
\(322\) −29.3166 −1.63375
\(323\) −11.2620 17.9499i −0.626637 0.998758i
\(324\) −3.50000 + 8.29156i −0.194444 + 0.460642i
\(325\) 14.3166 8.36865i 0.794143 0.464209i
\(326\) −15.9384 −0.882745
\(327\) 28.6764 8.64627i 1.58581 0.478140i
\(328\) 3.50724i 0.193655i
\(329\) 24.5330i 1.35255i
\(330\) −7.61448 + 4.74562i −0.419163 + 0.261238i
\(331\) 15.7533i 0.865879i 0.901423 + 0.432940i \(0.142524\pi\)
−0.901423 + 0.432940i \(0.857476\pi\)
\(332\) −9.72281 −0.533608
\(333\) 5.00000 3.31662i 0.273998 0.181750i
\(334\) 5.05013 0.276331
\(335\) 4.09178 + 15.1082i 0.223558 + 0.825448i
\(336\) 8.06173 2.43070i 0.439803 0.132606i
\(337\) −18.2164 −0.992309 −0.496155 0.868234i \(-0.665255\pi\)
−0.496155 + 0.868234i \(0.665255\pi\)
\(338\) 2.00000i 0.108786i
\(339\) −13.7916 + 4.15831i −0.749055 + 0.225849i
\(340\) −2.84169 10.4924i −0.154112 0.569032i
\(341\) 19.8158 1.07308
\(342\) −5.38912 + 11.9146i −0.291410 + 0.644267i
\(343\) 46.8311i 2.52864i
\(344\) −1.16908 −0.0630326
\(345\) 19.8215 12.3535i 1.06715 0.665090i
\(346\) 13.2665 0.713211
\(347\) 24.8623 1.33468 0.667338 0.744755i \(-0.267434\pi\)
0.667338 + 0.744755i \(0.267434\pi\)
\(348\) 0.677081 + 2.24562i 0.0362953 + 0.120378i
\(349\) −4.63325 −0.248012 −0.124006 0.992281i \(-0.539574\pi\)
−0.124006 + 0.992281i \(0.539574\pi\)
\(350\) −20.9849 + 12.2665i −1.12169 + 0.655672i
\(351\) −13.2665 11.0000i −0.708113 0.587137i
\(352\) 2.31662 0.123477
\(353\) −20.0009 −1.06454 −0.532269 0.846575i \(-0.678661\pi\)
−0.532269 + 0.846575i \(0.678661\pi\)
\(354\) 16.4304 4.95394i 0.873265 0.263299i
\(355\) 6.36675 + 23.5081i 0.337912 + 1.24768i
\(356\) 8.55373 0.453347
\(357\) −39.1913 + 11.8166i −2.07422 + 0.625402i
\(358\) 2.70832i 0.143139i
\(359\) 34.8997i 1.84194i 0.389636 + 0.920969i \(0.372601\pi\)
−0.389636 + 0.920969i \(0.627399\pi\)
\(360\) −4.42643 + 5.04051i −0.233293 + 0.265658i
\(361\) −8.26650 + 17.1075i −0.435079 + 0.900392i
\(362\) 2.70832 0.142346
\(363\) −2.81662 9.34169i −0.147834 0.490311i
\(364\) 16.1235i 0.845099i
\(365\) 23.9076 6.47494i 1.25138 0.338914i
\(366\) −7.15831 + 2.15831i −0.374171 + 0.112817i
\(367\) 2.33816i 0.122051i −0.998136 0.0610255i \(-0.980563\pi\)
0.998136 0.0610255i \(-0.0194371\pi\)
\(368\) −6.03049 −0.314361
\(369\) −8.76811 + 5.81610i −0.456449 + 0.302774i
\(370\) 4.31662 1.16908i 0.224411 0.0607776i
\(371\) 4.86140 0.252392
\(372\) 14.1848 4.27686i 0.735445 0.221745i
\(373\) 16.6834 0.863832 0.431916 0.901914i \(-0.357838\pi\)
0.431916 + 0.901914i \(0.357838\pi\)
\(374\) −11.2620 −0.582347
\(375\) 9.01937 17.1362i 0.465758 0.884912i
\(376\) 5.04648i 0.260253i
\(377\) −4.49124 −0.231311
\(378\) 19.4456 + 16.1235i 1.00017 + 0.829301i
\(379\) 22.7678i 1.16950i −0.811213 0.584751i \(-0.801192\pi\)
0.811213 0.584751i \(-0.198808\pi\)
\(380\) −6.61503 + 7.15831i −0.339344 + 0.367214i
\(381\) −1.68338 5.58312i −0.0862419 0.286032i
\(382\) 5.00000 0.255822
\(383\) 25.5831i 1.30724i 0.756824 + 0.653618i \(0.226750\pi\)
−0.756824 + 0.653618i \(0.773250\pi\)
\(384\) 1.65831 0.500000i 0.0846254 0.0255155i
\(385\) 6.58312 + 24.3070i 0.335507 + 1.23880i
\(386\) 6.00000i 0.305392i
\(387\) −1.93870 2.92270i −0.0985497 0.148569i
\(388\) 16.6332 0.844425
\(389\) 30.2164i 1.53203i −0.642822 0.766015i \(-0.722237\pi\)
0.642822 0.766015i \(-0.277763\pi\)
\(390\) −6.79413 10.9014i −0.344034 0.552012i
\(391\) 29.3166 1.48261
\(392\) 16.6332i 0.840106i
\(393\) 16.5831 5.00000i 0.836508 0.252217i
\(394\) 6.21557i 0.313136i
\(395\) 10.0930 2.73350i 0.507832 0.137537i
\(396\) 3.84169 + 5.79156i 0.193052 + 0.291037i
\(397\) 16.7373i 0.840021i −0.907519 0.420010i \(-0.862026\pi\)
0.907519 0.420010i \(-0.137974\pi\)
\(398\) 21.2164i 1.06348i
\(399\) 27.6509 + 24.1355i 1.38428 + 1.20829i
\(400\) −4.31662 + 2.52324i −0.215831 + 0.126162i
\(401\) 8.92389 0.445638 0.222819 0.974860i \(-0.428474\pi\)
0.222819 + 0.974860i \(0.428474\pi\)
\(402\) 11.6082 3.50000i 0.578964 0.174564i
\(403\) 28.3695i 1.41319i
\(404\) 7.68338i 0.382262i
\(405\) −19.9417 2.70734i −0.990910 0.134529i
\(406\) 6.58312 0.326715
\(407\) 4.63325i 0.229662i
\(408\) −8.06173 + 2.43070i −0.399115 + 0.120338i
\(409\) 1.16908i 0.0578073i −0.999582 0.0289037i \(-0.990798\pi\)
0.999582 0.0289037i \(-0.00920160\pi\)
\(410\) −7.56973 + 2.05013i −0.373842 + 0.101248i
\(411\) 2.43070 + 8.06173i 0.119898 + 0.397656i
\(412\) −15.5831 −0.767725
\(413\) 48.1662i 2.37011i
\(414\) −10.0004 15.0762i −0.491494 0.740955i
\(415\) −5.68338 20.9849i −0.278986 1.03011i
\(416\) 3.31662i 0.162611i
\(417\) 5.00000 + 16.5831i 0.244851 + 0.812079i
\(418\) 5.36675 + 8.55373i 0.262496 + 0.418376i
\(419\) 22.9499i 1.12117i 0.828095 + 0.560587i \(0.189425\pi\)
−0.828095 + 0.560587i \(0.810575\pi\)
\(420\) 9.95862 + 15.9789i 0.485931 + 0.779690i
\(421\) 24.3070i 1.18465i −0.805699 0.592326i \(-0.798210\pi\)
0.805699 0.592326i \(-0.201790\pi\)
\(422\) 18.4616 0.898697
\(423\) −12.6162 + 8.36865i −0.613421 + 0.406898i
\(424\) 1.00000 0.0485643
\(425\) 20.9849 12.2665i 1.01792 0.595013i
\(426\) 18.0622 5.44594i 0.875114 0.263857i
\(427\) 20.9849i 1.01553i
\(428\) 19.9499i 0.964314i
\(429\) −12.7414 + 3.84169i −0.615162 + 0.185478i
\(430\) −0.683375 2.52324i −0.0329553 0.121682i
\(431\) −33.4160 −1.60959 −0.804796 0.593552i \(-0.797725\pi\)
−0.804796 + 0.593552i \(0.797725\pi\)
\(432\) 4.00000 + 3.31662i 0.192450 + 0.159571i
\(433\) −8.31662 −0.399671 −0.199836 0.979829i \(-0.564041\pi\)
−0.199836 + 0.979829i \(0.564041\pi\)
\(434\) 41.5831i 1.99605i
\(435\) −4.45097 + 2.77401i −0.213408 + 0.133004i
\(436\) 17.2925i 0.828162i
\(437\) −13.9704 22.2665i −0.668293 1.06515i
\(438\) −5.53848 18.3691i −0.264639 0.877708i
\(439\) 1.16908i 0.0557972i −0.999611 0.0278986i \(-0.991118\pi\)
0.999611 0.0278986i \(-0.00888155\pi\)
\(440\) 1.35416 + 5.00000i 0.0645571 + 0.238366i
\(441\) 41.5831 27.5831i 1.98015 1.31348i
\(442\) 16.1235i 0.766914i
\(443\) 3.87740 0.184221 0.0921105 0.995749i \(-0.470639\pi\)
0.0921105 + 0.995749i \(0.470639\pi\)
\(444\) −1.00000 3.31662i −0.0474579 0.157400i
\(445\) 5.00000 + 18.4616i 0.237023 + 0.875164i
\(446\) 23.2665i 1.10170i
\(447\) −6.63325 + 2.00000i −0.313742 + 0.0945968i
\(448\) 4.86140i 0.229680i
\(449\) −31.5066 −1.48689 −0.743444 0.668798i \(-0.766809\pi\)
−0.743444 + 0.668798i \(0.766809\pi\)
\(450\) −13.4664 6.60724i −0.634813 0.311468i
\(451\) 8.12497i 0.382590i
\(452\) 8.31662i 0.391181i
\(453\) −4.49124 + 1.35416i −0.211017 + 0.0636240i
\(454\) 0.0501256 0.00235251
\(455\) −34.7994 + 9.42481i −1.63142 + 0.441842i
\(456\) 5.68785 + 4.96471i 0.266358 + 0.232494i
\(457\) 18.8318i 0.880913i 0.897774 + 0.440457i \(0.145183\pi\)
−0.897774 + 0.440457i \(0.854817\pi\)
\(458\) 0 0
\(459\) −19.4456 16.1235i −0.907644 0.752578i
\(460\) −3.52506 13.0157i −0.164357 0.606859i
\(461\) 11.5831i 0.539480i 0.962933 + 0.269740i \(0.0869377\pi\)
−0.962933 + 0.269740i \(0.913062\pi\)
\(462\) 18.6760 5.63102i 0.868886 0.261979i
\(463\) 4.67632i 0.217327i −0.994079 0.108664i \(-0.965343\pi\)
0.994079 0.108664i \(-0.0346571\pi\)
\(464\) 1.35416 0.0628653
\(465\) 17.5224 + 28.1151i 0.812580 + 1.30381i
\(466\) 15.1395i 0.701322i
\(467\) 8.18357 0.378690 0.189345 0.981911i \(-0.439363\pi\)
0.189345 + 0.981911i \(0.439363\pi\)
\(468\) −8.29156 + 5.50000i −0.383278 + 0.254238i
\(469\) 34.0298i 1.57135i
\(470\) −10.8919 + 2.94987i −0.502405 + 0.136068i
\(471\) −3.87740 + 1.16908i −0.178661 + 0.0538684i
\(472\) 9.90789i 0.456048i
\(473\) −2.70832 −0.124529
\(474\) −2.33816 7.75481i −0.107395 0.356190i
\(475\) −19.3166 10.0930i −0.886308 0.463097i
\(476\) 23.6332i 1.08323i
\(477\) 1.65831 + 2.50000i 0.0759289 + 0.114467i
\(478\) 6.36675 0.291208
\(479\) 14.0000i 0.639676i −0.947472 0.319838i \(-0.896371\pi\)
0.947472 0.319838i \(-0.103629\pi\)
\(480\) 2.04851 + 3.28689i 0.0935011 + 0.150025i
\(481\) 6.63325 0.302450
\(482\) −17.1075 −0.779223
\(483\) −48.6161 + 14.6583i −2.21211 + 0.666976i
\(484\) −5.63325 −0.256057
\(485\) 9.72281 + 35.8997i 0.441490 + 1.63012i
\(486\) −1.65831 + 15.5000i −0.0752226 + 0.703094i
\(487\) 16.5330 0.749182 0.374591 0.927190i \(-0.377783\pi\)
0.374591 + 0.927190i \(0.377783\pi\)
\(488\) 4.31662i 0.195404i
\(489\) −26.4308 + 7.96919i −1.19524 + 0.360379i
\(490\) 35.8997 9.72281i 1.62179 0.439232i
\(491\) 41.5831i 1.87662i −0.345795 0.938310i \(-0.612391\pi\)
0.345795 0.938310i \(-0.387609\pi\)
\(492\) 1.75362 + 5.81610i 0.0790594 + 0.262210i
\(493\) −6.58312 −0.296489
\(494\) −12.2461 + 7.68338i −0.550976 + 0.345691i
\(495\) −10.2544 + 11.6770i −0.460900 + 0.524841i
\(496\) 8.55373i 0.384074i
\(497\) 52.9499i 2.37513i
\(498\) −16.1235 + 4.86140i −0.722509 + 0.217845i
\(499\) 41.5831 1.86152 0.930758 0.365635i \(-0.119148\pi\)
0.930758 + 0.365635i \(0.119148\pi\)
\(500\) −7.96919 7.84169i −0.356393 0.350691i
\(501\) 8.37469 2.52506i 0.374153 0.112811i
\(502\) 1.58312 0.0706583
\(503\) 13.7853 0.614656 0.307328 0.951604i \(-0.400565\pi\)
0.307328 + 0.951604i \(0.400565\pi\)
\(504\) 12.1535 8.06173i 0.541360 0.359098i
\(505\) 16.5831 4.49124i 0.737939 0.199858i
\(506\) −13.9704 −0.621059
\(507\) 1.00000 + 3.31662i 0.0444116 + 0.147296i
\(508\) −3.36675 −0.149375
\(509\) 17.1075 0.758275 0.379137 0.925340i \(-0.376221\pi\)
0.379137 + 0.925340i \(0.376221\pi\)
\(510\) −9.95862 15.9789i −0.440975 0.707557i
\(511\) −53.8496 −2.38217
\(512\) 1.00000i 0.0441942i
\(513\) −2.97955 + 22.4527i −0.131550 + 0.991309i
\(514\) −14.9499 −0.659411
\(515\) −9.10897 33.6332i −0.401389 1.48206i
\(516\) −1.93870 + 0.584541i −0.0853466 + 0.0257330i
\(517\) 11.6908i 0.514161i
\(518\) −9.72281 −0.427196
\(519\) 22.0000 6.63325i 0.965693 0.291167i
\(520\) −7.15831 + 1.93870i −0.313913 + 0.0850177i
\(521\) −41.9697 −1.83873 −0.919363 0.393410i \(-0.871295\pi\)
−0.919363 + 0.393410i \(0.871295\pi\)
\(522\) 2.24562 + 3.38540i 0.0982882 + 0.148175i
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 10.0000i 0.436852i
\(525\) −28.6662 + 30.8341i −1.25110 + 1.34571i
\(526\) 21.7838i 0.949818i
\(527\) 41.5831i 1.81139i
\(528\) 3.84169 1.15831i 0.167188 0.0504091i
\(529\) 13.3668 0.581163
\(530\) 0.584541 + 2.15831i 0.0253908 + 0.0937511i
\(531\) 24.7697 16.4304i 1.07491 0.713017i
\(532\) 17.9499 11.2620i 0.778226 0.488272i
\(533\) −11.6322 −0.503847
\(534\) 14.1848 4.27686i 0.613834 0.185078i
\(535\) −43.0581 + 11.6615i −1.86156 + 0.504171i
\(536\) 7.00000i 0.302354i
\(537\) 1.35416 + 4.49124i 0.0584364 + 0.193811i
\(538\) 14.3991i 0.620791i
\(539\) 38.5330i 1.65973i
\(540\) −4.82015 + 10.5720i −0.207426 + 0.454944i
\(541\) −28.8496 −1.24034 −0.620171 0.784467i \(-0.712937\pi\)
−0.620171 + 0.784467i \(0.712937\pi\)
\(542\) 9.31662i 0.400183i
\(543\) 4.49124 1.35416i 0.192738 0.0581126i
\(544\) 4.86140i 0.208431i
\(545\) 37.3227 10.1082i 1.59873 0.432987i
\(546\) 8.06173 + 26.7377i 0.345010 + 1.14427i
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 4.86140 0.207669
\(549\) −10.7916 + 7.15831i −0.460573 + 0.305509i
\(550\) −10.0000 + 5.84541i −0.426401 + 0.249249i
\(551\) 3.13708 + 5.00000i 0.133644 + 0.213007i
\(552\) −10.0004 + 3.01524i −0.425646 + 0.128337i
\(553\) −22.7335 −0.966727
\(554\) 12.0610 0.512422
\(555\) 6.57377 4.09701i 0.279041 0.173909i
\(556\) 10.0000 0.424094
\(557\) −34.5851 −1.46542 −0.732708 0.680543i \(-0.761744\pi\)
−0.732708 + 0.680543i \(0.761744\pi\)
\(558\) 21.3843 14.1848i 0.905270 0.600488i
\(559\) 3.87740i 0.163997i
\(560\) 10.4924 2.84169i 0.443386 0.120083i
\(561\) −18.6760 + 5.63102i −0.788501 + 0.237742i
\(562\) 13.6002i 0.573690i
\(563\) 9.89975i 0.417225i −0.977998 0.208612i \(-0.933105\pi\)
0.977998 0.208612i \(-0.0668947\pi\)
\(564\) 2.52324 + 8.36865i 0.106248 + 0.352384i
\(565\) −17.9499 + 4.86140i −0.755157 + 0.204521i
\(566\) 15.1395 0.636359
\(567\) 40.3086 + 17.0149i 1.69280 + 0.714559i
\(568\) 10.8919i 0.457014i
\(569\) 17.1075 0.717182 0.358591 0.933495i \(-0.383257\pi\)
0.358591 + 0.933495i \(0.383257\pi\)
\(570\) −7.39062 + 15.1782i −0.309559 + 0.635746i
\(571\) −25.6834 −1.07482 −0.537408 0.843322i \(-0.680596\pi\)
−0.537408 + 0.843322i \(0.680596\pi\)
\(572\) 7.68338i 0.321258i
\(573\) 8.29156 2.50000i 0.346385 0.104439i
\(574\) 17.0501 0.711658
\(575\) 26.0313 15.2164i 1.08558 0.634567i
\(576\) 2.50000 1.65831i 0.104167 0.0690963i
\(577\) 6.40065i 0.266462i −0.991085 0.133231i \(-0.957465\pi\)
0.991085 0.133231i \(-0.0425353\pi\)
\(578\) 6.63325i 0.275907i
\(579\) 3.00000 + 9.94987i 0.124676 + 0.413503i
\(580\) 0.791562 + 2.92270i 0.0328678 + 0.121359i
\(581\) 47.2665i 1.96094i
\(582\) 27.5831 8.31662i 1.14336 0.344735i
\(583\) 2.31662 0.0959448
\(584\) −11.0770 −0.458368
\(585\) −16.7175 14.6808i −0.691182 0.606977i
\(586\) 8.26650 0.341486
\(587\) −26.0313 −1.07443 −0.537214 0.843446i \(-0.680523\pi\)
−0.537214 + 0.843446i \(0.680523\pi\)
\(588\) −8.31662 27.5831i −0.342972 1.13751i
\(589\) 31.5831 19.8158i 1.30136 0.816495i
\(590\) 21.3843 5.79156i 0.880378 0.238435i
\(591\) 3.10778 + 10.3073i 0.127837 + 0.423988i
\(592\) −2.00000 −0.0821995
\(593\) −21.7838 −0.894553 −0.447276 0.894396i \(-0.647606\pi\)
−0.447276 + 0.894396i \(0.647606\pi\)
\(594\) 9.26650 + 7.68338i 0.380209 + 0.315253i
\(595\) −51.0079 + 13.8146i −2.09112 + 0.566343i
\(596\) 4.00000i 0.163846i
\(597\) −10.6082 35.1834i −0.434164 1.43996i
\(598\) 20.0009i 0.817896i
\(599\) −48.1853 −1.96880 −0.984399 0.175953i \(-0.943699\pi\)
−0.984399 + 0.175953i \(0.943699\pi\)
\(600\) −5.89669 + 6.34264i −0.240731 + 0.258937i
\(601\) 22.9529i 0.936267i 0.883658 + 0.468133i \(0.155073\pi\)
−0.883658 + 0.468133i \(0.844927\pi\)
\(602\) 5.68338i 0.231637i
\(603\) 17.5000 11.6082i 0.712655 0.472722i
\(604\) 2.70832i 0.110200i
\(605\) −3.29286 12.1583i −0.133874 0.494306i
\(606\) −3.84169 12.7414i −0.156058 0.517585i
\(607\) 23.3668 0.948427 0.474214 0.880410i \(-0.342732\pi\)
0.474214 + 0.880410i \(0.342732\pi\)
\(608\) 3.69232 2.31662i 0.149743 0.0939515i
\(609\) 10.9169 3.29156i 0.442374 0.133381i
\(610\) −9.31662 + 2.52324i −0.377219 + 0.102163i
\(611\) −16.7373 −0.677118
\(612\) −12.1535 + 8.06173i −0.491277 + 0.325876i
\(613\) 13.2301i 0.534357i −0.963647 0.267178i \(-0.913909\pi\)
0.963647 0.267178i \(-0.0860913\pi\)
\(614\) 2.00000i 0.0807134i
\(615\) −11.5279 + 7.18461i −0.464850 + 0.289712i
\(616\) 11.2620i 0.453761i
\(617\) −17.4776 −0.703622 −0.351811 0.936071i \(-0.614434\pi\)
−0.351811 + 0.936071i \(0.614434\pi\)
\(618\) −25.8417 + 7.79156i −1.03951 + 0.313423i
\(619\) −31.5831 −1.26943 −0.634716 0.772745i \(-0.718883\pi\)
−0.634716 + 0.772745i \(0.718883\pi\)
\(620\) 18.4616 5.00000i 0.741436 0.200805i
\(621\) −24.1219 20.0009i −0.967980 0.802607i
\(622\) −18.8997 −0.757811
\(623\) 41.5831i 1.66599i
\(624\) 1.65831 + 5.50000i 0.0663856 + 0.220176i
\(625\) 12.2665 21.7838i 0.490660 0.871351i
\(626\) −28.5546 −1.14127
\(627\) 13.1766 + 11.5014i 0.526223 + 0.459321i
\(628\) 2.33816i 0.0933028i
\(629\) 9.72281 0.387674
\(630\) 24.5039 + 21.5187i 0.976260 + 0.857324i
\(631\) 15.8997 0.632959 0.316480 0.948599i \(-0.397499\pi\)
0.316480 + 0.948599i \(0.397499\pi\)
\(632\) −4.67632 −0.186014
\(633\) 30.6151 9.23081i 1.21684 0.366892i
\(634\) 17.0000 0.675156
\(635\) −1.96800 7.26650i −0.0780978 0.288362i
\(636\) 1.65831 0.500000i 0.0657564 0.0198263i
\(637\) 55.1662 2.18577
\(638\) 3.13708 0.124198
\(639\) 27.2297 18.0622i 1.07719 0.714528i
\(640\) 2.15831 0.584541i 0.0853148 0.0231060i
\(641\) 23.3230 0.921204 0.460602 0.887607i \(-0.347634\pi\)
0.460602 + 0.887607i \(0.347634\pi\)
\(642\) 9.97494 + 33.0831i 0.393679 + 1.30569i
\(643\) 46.6460i 1.83954i 0.392458 + 0.919770i \(0.371625\pi\)
−0.392458 + 0.919770i \(0.628375\pi\)
\(644\) 29.3166i 1.15524i
\(645\) −2.39487 3.84264i −0.0942979 0.151304i
\(646\) −17.9499 + 11.2620i −0.706228 + 0.443099i
\(647\) 3.69232 0.145160 0.0725801 0.997363i \(-0.476877\pi\)
0.0725801 + 0.997363i \(0.476877\pi\)
\(648\) 8.29156 + 3.50000i 0.325723 + 0.137493i
\(649\) 22.9529i 0.900979i
\(650\) −8.36865 14.3166i −0.328245 0.561544i
\(651\) −20.7916 68.9578i −0.814886 2.70267i
\(652\) 15.9384i 0.624195i
\(653\) 26.8303 1.04995 0.524975 0.851118i \(-0.324075\pi\)
0.524975 + 0.851118i \(0.324075\pi\)
\(654\) −8.64627 28.6764i −0.338096 1.12134i
\(655\) 21.5831 5.84541i 0.843322 0.228399i
\(656\) 3.50724 0.136935
\(657\) −18.3691 27.6924i −0.716646 1.08038i
\(658\) 24.5330 0.956396
\(659\) 12.6162 0.491458 0.245729 0.969339i \(-0.420973\pi\)
0.245729 + 0.969339i \(0.420973\pi\)
\(660\) 4.74562 + 7.61448i 0.184723 + 0.296393i
\(661\) 21.5987i 0.840092i 0.907503 + 0.420046i \(0.137986\pi\)
−0.907503 + 0.420046i \(0.862014\pi\)
\(662\) 15.7533 0.612269
\(663\) −8.06173 26.7377i −0.313092 1.03841i
\(664\) 9.72281i 0.377318i
\(665\) 34.7994 + 32.1583i 1.34946 + 1.24705i
\(666\) −3.31662 5.00000i −0.128517 0.193746i
\(667\) −8.16625 −0.316198
\(668\) 5.05013i 0.195395i
\(669\) −11.6332 38.5831i −0.449767 1.49171i
\(670\) 15.1082 4.09178i 0.583680 0.158079i
\(671\) 10.0000i 0.386046i
\(672\) −2.43070 8.06173i −0.0937664 0.310988i
\(673\) 13.2665 0.511386 0.255693 0.966758i \(-0.417696\pi\)
0.255693 + 0.966758i \(0.417696\pi\)
\(674\) 18.2164i 0.701668i
\(675\) −25.6351 4.22366i −0.986697 0.162569i
\(676\) 2.00000 0.0769231
\(677\) 20.1662i 0.775052i 0.921859 + 0.387526i \(0.126670\pi\)
−0.921859 + 0.387526i \(0.873330\pi\)
\(678\) 4.15831 + 13.7916i 0.159699 + 0.529662i
\(679\) 80.8609i 3.10316i
\(680\) −10.4924 + 2.84169i −0.402366 + 0.108974i
\(681\) 0.0831240 0.0250628i 0.00318532 0.000960409i
\(682\) 19.8158i 0.758785i
\(683\) 24.0000i 0.918334i 0.888350 + 0.459167i \(0.151852\pi\)
−0.888350 + 0.459167i \(0.848148\pi\)
\(684\) 11.9146 + 5.38912i 0.455566 + 0.206058i
\(685\) 2.84169 + 10.4924i 0.108575 + 0.400895i
\(686\) −46.8311 −1.78802
\(687\) 0 0
\(688\) 1.16908i 0.0445708i
\(689\) 3.31662i 0.126353i
\(690\) −12.3535 19.8215i −0.470289 0.754592i
\(691\) 25.8997 0.985273 0.492636 0.870235i \(-0.336033\pi\)
0.492636 + 0.870235i \(0.336033\pi\)
\(692\) 13.2665i 0.504317i
\(693\) 28.1551 18.6760i 1.06952 0.709442i
\(694\) 24.8623i 0.943758i
\(695\) 5.84541 + 21.5831i 0.221729 + 0.818695i
\(696\) 2.24562 0.677081i 0.0851201 0.0256647i
\(697\) −17.0501 −0.645820
\(698\) 4.63325i 0.175371i
\(699\) −7.56973 25.1059i −0.286313 0.949594i
\(700\) 12.2665 + 20.9849i 0.463630 + 0.793153i
\(701\) 10.7335i 0.405399i 0.979241 + 0.202699i \(0.0649714\pi\)
−0.979241 + 0.202699i \(0.935029\pi\)
\(702\) −11.0000 + 13.2665i −0.415168 + 0.500712i
\(703\) −4.63325 7.38465i −0.174746 0.278517i
\(704\) 2.31662i 0.0873111i
\(705\) −16.5872 + 10.3378i −0.624711 + 0.389342i
\(706\) 20.0009i 0.752742i
\(707\) −37.3520 −1.40477
\(708\) −4.95394 16.4304i −0.186181 0.617491i
\(709\) 15.3668 0.577110 0.288555 0.957463i \(-0.406825\pi\)
0.288555 + 0.957463i \(0.406825\pi\)
\(710\) 23.5081 6.36675i 0.882243 0.238940i
\(711\) −7.75481 11.6908i −0.290828 0.438440i
\(712\) 8.55373i 0.320564i
\(713\) 51.5831i 1.93180i
\(714\) 11.8166 + 39.1913i 0.442226 + 1.46670i
\(715\) −16.5831 + 4.49124i −0.620174 + 0.167963i
\(716\) 2.70832 0.101215
\(717\) 10.5581 3.18338i 0.394298 0.118885i
\(718\) 34.8997 1.30245
\(719\) 4.89975i 0.182730i 0.995817 + 0.0913649i \(0.0291230\pi\)
−0.995817 + 0.0913649i \(0.970877\pi\)
\(720\) 5.04051 + 4.42643i 0.187849 + 0.164963i
\(721\) 75.7559i 2.82130i
\(722\) 17.1075 + 8.26650i 0.636674 + 0.307647i
\(723\) −28.3695 + 8.55373i −1.05507 + 0.318117i
\(724\) 2.70832i 0.100654i
\(725\) −5.84541 + 3.41688i −0.217093 + 0.126900i
\(726\) −9.34169 + 2.81662i −0.346703 + 0.104535i
\(727\) 7.56973i 0.280746i 0.990099 + 0.140373i \(0.0448301\pi\)
−0.990099 + 0.140373i \(0.955170\pi\)
\(728\) 16.1235 0.597575
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) −6.47494 23.9076i −0.239648 0.884858i
\(731\) 5.68338i 0.210207i
\(732\) 2.15831 + 7.15831i 0.0797735 + 0.264579i
\(733\) 9.72281i 0.359120i 0.983747 + 0.179560i \(0.0574674\pi\)
−0.983747 + 0.179560i \(0.942533\pi\)
\(734\) −2.33816 −0.0863031
\(735\) 54.6716 34.0733i 2.01659 1.25681i
\(736\) 6.03049i 0.222287i
\(737\) 16.2164i 0.597338i
\(738\) 5.81610 + 8.76811i 0.214094 + 0.322759i
\(739\) 36.2164 1.33224 0.666120 0.745844i \(-0.267954\pi\)
0.666120 + 0.745844i \(0.267954\pi\)
\(740\) −1.16908 4.31662i −0.0429763 0.158682i
\(741\) −16.4661 + 18.8645i −0.604897 + 0.693003i
\(742\) 4.86140i 0.178468i
\(743\) 14.8496i 0.544780i 0.962187 + 0.272390i \(0.0878141\pi\)
−0.962187 + 0.272390i \(0.912186\pi\)
\(744\) −4.27686 14.1848i −0.156797 0.520038i
\(745\) −8.63325 + 2.33816i −0.316298 + 0.0856636i
\(746\) 16.6834i 0.610822i
\(747\) −24.3070 + 16.1235i −0.889347 + 0.589926i
\(748\) 11.2620i 0.411781i
\(749\) 96.9844 3.54373
\(750\) −17.1362 9.01937i −0.625727 0.329341i
\(751\) 22.9529i 0.837562i 0.908087 + 0.418781i \(0.137542\pi\)
−0.908087 + 0.418781i \(0.862458\pi\)
\(752\) 5.04648 0.184026
\(753\) 2.62531 0.791562i 0.0956718 0.0288461i
\(754\) 4.49124i 0.163561i
\(755\) −5.84541 + 1.58312i −0.212736 + 0.0576158i
\(756\) 16.1235 19.4456i 0.586404 0.707230i
\(757\) 19.4456i 0.706763i −0.935479 0.353381i \(-0.885032\pi\)
0.935479 0.353381i \(-0.114968\pi\)
\(758\) −22.7678 −0.826963
\(759\) −23.1672 + 6.98519i −0.840918 + 0.253546i
\(760\) 7.15831 + 6.61503i 0.259659 + 0.239952i
\(761\) 17.3166i 0.627727i 0.949468 + 0.313864i \(0.101623\pi\)
−0.949468 + 0.313864i \(0.898377\pi\)
\(762\) −5.58312 + 1.68338i −0.202255 + 0.0609822i
\(763\) −84.0660 −3.04339
\(764\) 5.00000i 0.180894i
\(765\) −24.5039 21.5187i −0.885942 0.778009i
\(766\) 25.5831 0.924356
\(767\) 32.8607 1.18653
\(768\) −0.500000 1.65831i −0.0180422 0.0598392i
\(769\) 18.1662 0.655092 0.327546 0.944835i \(-0.393778\pi\)
0.327546 + 0.944835i \(0.393778\pi\)
\(770\) 24.3070 6.58312i 0.875964 0.237239i
\(771\) −24.7916 + 7.47494i −0.892846 + 0.269203i
\(772\) 6.00000 0.215945
\(773\) 42.1662i 1.51661i 0.651897 + 0.758307i \(0.273973\pi\)
−0.651897 + 0.758307i \(0.726027\pi\)
\(774\) −2.92270 + 1.93870i −0.105054 + 0.0696852i
\(775\) 21.5831 + 36.9232i 0.775289 + 1.32632i
\(776\) 16.6332i 0.597099i
\(777\) −16.1235 + 4.86140i −0.578426 + 0.174402i
\(778\) −30.2164 −1.08331
\(779\) 8.12497 + 12.9499i 0.291107 + 0.463977i
\(780\) −10.9014 + 6.79413i −0.390332 + 0.243269i
\(781\) 25.2324i 0.902887i