Properties

Label 980.2.c.e.979.9
Level $980$
Weight $2$
Character 980.979
Analytic conductor $7.825$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 979.9
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.e.979.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23364 - 0.691471i) q^{2} -2.08008i q^{3} +(1.04374 + 1.70605i) q^{4} +(1.52262 + 1.63757i) q^{5} +(-1.43832 + 2.56607i) q^{6} +(-0.107908 - 2.82637i) q^{8} -1.32674 q^{9} +O(q^{10})\) \(q+(-1.23364 - 0.691471i) q^{2} -2.08008i q^{3} +(1.04374 + 1.70605i) q^{4} +(1.52262 + 1.63757i) q^{5} +(-1.43832 + 2.56607i) q^{6} +(-0.107908 - 2.82637i) q^{8} -1.32674 q^{9} +(-0.746026 - 3.07302i) q^{10} -0.775046i q^{11} +(3.54873 - 2.17106i) q^{12} +4.18932 q^{13} +(3.40628 - 3.16717i) q^{15} +(-1.82123 + 3.56134i) q^{16} -4.18028 q^{17} +(1.63672 + 0.917404i) q^{18} -4.88478 q^{19} +(-1.20458 + 4.30685i) q^{20} +(-0.535922 + 0.956127i) q^{22} +1.89723 q^{23} +(-5.87908 + 0.224457i) q^{24} +(-0.363284 + 4.98679i) q^{25} +(-5.16812 - 2.89680i) q^{26} -3.48051i q^{27} +9.98465 q^{29} +(-6.39213 + 1.55180i) q^{30} +10.3484 q^{31} +(4.70931 - 3.13408i) q^{32} -1.61216 q^{33} +(5.15697 + 2.89055i) q^{34} +(-1.38477 - 2.26349i) q^{36} -3.41776i q^{37} +(6.02606 + 3.37768i) q^{38} -8.71414i q^{39} +(4.46408 - 4.48018i) q^{40} -3.02483i q^{41} +9.19046 q^{43} +(1.32227 - 0.808943i) q^{44} +(-2.02012 - 2.17264i) q^{45} +(-2.34050 - 1.31188i) q^{46} -8.27241i q^{47} +(7.40787 + 3.78831i) q^{48} +(3.89638 - 5.90070i) q^{50} +8.69534i q^{51} +(4.37255 + 7.14721i) q^{52} +2.59095i q^{53} +(-2.40667 + 4.29370i) q^{54} +(1.26919 - 1.18010i) q^{55} +10.1607i q^{57} +(-12.3175 - 6.90410i) q^{58} -4.60753 q^{59} +(8.95861 + 2.50562i) q^{60} -3.26207i q^{61} +(-12.7662 - 7.15559i) q^{62} +(-7.97671 + 0.609973i) q^{64} +(6.37873 + 6.86032i) q^{65} +(1.98882 + 1.11476i) q^{66} -2.27069 q^{67} +(-4.36311 - 7.13179i) q^{68} -3.94640i q^{69} +4.41264i q^{71} +(0.143166 + 3.74986i) q^{72} +2.74922 q^{73} +(-2.36328 + 4.21629i) q^{74} +(10.3729 + 0.755660i) q^{75} +(-5.09842 - 8.33369i) q^{76} +(-6.02557 + 10.7501i) q^{78} +14.2136i q^{79} +(-8.60498 + 2.44015i) q^{80} -11.2200 q^{81} +(-2.09158 + 3.73155i) q^{82} -2.36160i q^{83} +(-6.36497 - 6.84552i) q^{85} +(-11.3377 - 6.35493i) q^{86} -20.7689i q^{87} +(-2.19056 + 0.0836333i) q^{88} -14.3543i q^{89} +(0.989784 + 4.07711i) q^{90} +(1.98021 + 3.23678i) q^{92} -21.5254i q^{93} +(-5.72013 + 10.2052i) q^{94} +(-7.43764 - 7.99917i) q^{95} +(-6.51914 - 9.79574i) q^{96} -14.4115 q^{97} +1.02829i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{4} - 64q^{9} + O(q^{10}) \) \( 48q + 16q^{4} - 64q^{9} + 16q^{16} - 16q^{25} - 48q^{29} - 8q^{30} + 176q^{36} - 48q^{44} - 32q^{46} + 32q^{50} + 24q^{60} - 80q^{64} - 16q^{65} - 112q^{74} - 48q^{81} - 64q^{85} - 112q^{86} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23364 0.691471i −0.872315 0.488944i
\(3\) 2.08008i 1.20094i −0.799649 0.600468i \(-0.794981\pi\)
0.799649 0.600468i \(-0.205019\pi\)
\(4\) 1.04374 + 1.70605i 0.521868 + 0.853026i
\(5\) 1.52262 + 1.63757i 0.680934 + 0.732344i
\(6\) −1.43832 + 2.56607i −0.587190 + 1.04759i
\(7\) 0 0
\(8\) −0.107908 2.82637i −0.0381511 0.999272i
\(9\) −1.32674 −0.442248
\(10\) −0.746026 3.07302i −0.235914 0.971774i
\(11\) 0.775046i 0.233685i −0.993150 0.116843i \(-0.962723\pi\)
0.993150 0.116843i \(-0.0372773\pi\)
\(12\) 3.54873 2.17106i 1.02443 0.626730i
\(13\) 4.18932 1.16191 0.580955 0.813936i \(-0.302679\pi\)
0.580955 + 0.813936i \(0.302679\pi\)
\(14\) 0 0
\(15\) 3.40628 3.16717i 0.879499 0.817759i
\(16\) −1.82123 + 3.56134i −0.455308 + 0.890334i
\(17\) −4.18028 −1.01387 −0.506934 0.861985i \(-0.669221\pi\)
−0.506934 + 0.861985i \(0.669221\pi\)
\(18\) 1.63672 + 0.917404i 0.385779 + 0.216234i
\(19\) −4.88478 −1.12064 −0.560322 0.828275i \(-0.689323\pi\)
−0.560322 + 0.828275i \(0.689323\pi\)
\(20\) −1.20458 + 4.30685i −0.269351 + 0.963042i
\(21\) 0 0
\(22\) −0.535922 + 0.956127i −0.114259 + 0.203847i
\(23\) 1.89723 0.395601 0.197800 0.980242i \(-0.436620\pi\)
0.197800 + 0.980242i \(0.436620\pi\)
\(24\) −5.87908 + 0.224457i −1.20006 + 0.0458170i
\(25\) −0.363284 + 4.98679i −0.0726567 + 0.997357i
\(26\) −5.16812 2.89680i −1.01355 0.568108i
\(27\) 3.48051i 0.669825i
\(28\) 0 0
\(29\) 9.98465 1.85410 0.927052 0.374933i \(-0.122334\pi\)
0.927052 + 0.374933i \(0.122334\pi\)
\(30\) −6.39213 + 1.55180i −1.16704 + 0.283318i
\(31\) 10.3484 1.85862 0.929310 0.369300i \(-0.120403\pi\)
0.929310 + 0.369300i \(0.120403\pi\)
\(32\) 4.70931 3.13408i 0.832496 0.554032i
\(33\) −1.61216 −0.280641
\(34\) 5.15697 + 2.89055i 0.884413 + 0.495725i
\(35\) 0 0
\(36\) −1.38477 2.26349i −0.230795 0.377249i
\(37\) 3.41776i 0.561877i −0.959726 0.280938i \(-0.909354\pi\)
0.959726 0.280938i \(-0.0906456\pi\)
\(38\) 6.02606 + 3.37768i 0.977555 + 0.547932i
\(39\) 8.71414i 1.39538i
\(40\) 4.46408 4.48018i 0.705833 0.708378i
\(41\) 3.02483i 0.472399i −0.971705 0.236199i \(-0.924098\pi\)
0.971705 0.236199i \(-0.0759019\pi\)
\(42\) 0 0
\(43\) 9.19046 1.40153 0.700766 0.713392i \(-0.252842\pi\)
0.700766 + 0.713392i \(0.252842\pi\)
\(44\) 1.32227 0.808943i 0.199340 0.121953i
\(45\) −2.02012 2.17264i −0.301142 0.323878i
\(46\) −2.34050 1.31188i −0.345089 0.193427i
\(47\) 8.27241i 1.20665i −0.797494 0.603327i \(-0.793841\pi\)
0.797494 0.603327i \(-0.206159\pi\)
\(48\) 7.40787 + 3.78831i 1.06923 + 0.546796i
\(49\) 0 0
\(50\) 3.89638 5.90070i 0.551031 0.834485i
\(51\) 8.69534i 1.21759i
\(52\) 4.37255 + 7.14721i 0.606363 + 0.991139i
\(53\) 2.59095i 0.355895i 0.984040 + 0.177947i \(0.0569457\pi\)
−0.984040 + 0.177947i \(0.943054\pi\)
\(54\) −2.40667 + 4.29370i −0.327507 + 0.584299i
\(55\) 1.26919 1.18010i 0.171138 0.159124i
\(56\) 0 0
\(57\) 10.1607i 1.34582i
\(58\) −12.3175 6.90410i −1.61736 0.906553i
\(59\) −4.60753 −0.599849 −0.299925 0.953963i \(-0.596962\pi\)
−0.299925 + 0.953963i \(0.596962\pi\)
\(60\) 8.95861 + 2.50562i 1.15655 + 0.323474i
\(61\) 3.26207i 0.417666i −0.977951 0.208833i \(-0.933034\pi\)
0.977951 0.208833i \(-0.0669664\pi\)
\(62\) −12.7662 7.15559i −1.62130 0.908761i
\(63\) 0 0
\(64\) −7.97671 + 0.609973i −0.997089 + 0.0762466i
\(65\) 6.37873 + 6.86032i 0.791184 + 0.850918i
\(66\) 1.98882 + 1.11476i 0.244807 + 0.137218i
\(67\) −2.27069 −0.277409 −0.138705 0.990334i \(-0.544294\pi\)
−0.138705 + 0.990334i \(0.544294\pi\)
\(68\) −4.36311 7.13179i −0.529105 0.864856i
\(69\) 3.94640i 0.475091i
\(70\) 0 0
\(71\) 4.41264i 0.523684i 0.965111 + 0.261842i \(0.0843300\pi\)
−0.965111 + 0.261842i \(0.915670\pi\)
\(72\) 0.143166 + 3.74986i 0.0168722 + 0.441926i
\(73\) 2.74922 0.321772 0.160886 0.986973i \(-0.448565\pi\)
0.160886 + 0.986973i \(0.448565\pi\)
\(74\) −2.36328 + 4.21629i −0.274726 + 0.490134i
\(75\) 10.3729 + 0.755660i 1.19776 + 0.0872561i
\(76\) −5.09842 8.33369i −0.584828 0.955940i
\(77\) 0 0
\(78\) −6.02557 + 10.7501i −0.682262 + 1.21721i
\(79\) 14.2136i 1.59915i 0.600565 + 0.799576i \(0.294943\pi\)
−0.600565 + 0.799576i \(0.705057\pi\)
\(80\) −8.60498 + 2.44015i −0.962066 + 0.272817i
\(81\) −11.2200 −1.24666
\(82\) −2.09158 + 3.73155i −0.230977 + 0.412081i
\(83\) 2.36160i 0.259220i −0.991565 0.129610i \(-0.958628\pi\)
0.991565 0.129610i \(-0.0413725\pi\)
\(84\) 0 0
\(85\) −6.36497 6.84552i −0.690378 0.742501i
\(86\) −11.3377 6.35493i −1.22258 0.685270i
\(87\) 20.7689i 2.22666i
\(88\) −2.19056 + 0.0836333i −0.233515 + 0.00891534i
\(89\) 14.3543i 1.52155i −0.649016 0.760775i \(-0.724819\pi\)
0.649016 0.760775i \(-0.275181\pi\)
\(90\) 0.989784 + 4.07711i 0.104332 + 0.429765i
\(91\) 0 0
\(92\) 1.98021 + 3.23678i 0.206451 + 0.337458i
\(93\) 21.5254i 2.23208i
\(94\) −5.72013 + 10.2052i −0.589986 + 1.05258i
\(95\) −7.43764 7.99917i −0.763086 0.820698i
\(96\) −6.51914 9.79574i −0.665357 0.999774i
\(97\) −14.4115 −1.46327 −0.731633 0.681699i \(-0.761241\pi\)
−0.731633 + 0.681699i \(0.761241\pi\)
\(98\) 0 0
\(99\) 1.02829i 0.103347i
\(100\) −8.88689 + 4.58510i −0.888689 + 0.458510i
\(101\) 1.69179i 0.168339i 0.996451 + 0.0841696i \(0.0268237\pi\)
−0.996451 + 0.0841696i \(0.973176\pi\)
\(102\) 6.01257 10.7269i 0.595334 1.06212i
\(103\) 0.553547i 0.0545426i −0.999628 0.0272713i \(-0.991318\pi\)
0.999628 0.0272713i \(-0.00868180\pi\)
\(104\) −0.452060 11.8406i −0.0443281 1.16106i
\(105\) 0 0
\(106\) 1.79157 3.19630i 0.174013 0.310452i
\(107\) 8.09142 0.782227 0.391114 0.920342i \(-0.372090\pi\)
0.391114 + 0.920342i \(0.372090\pi\)
\(108\) 5.93794 3.63273i 0.571378 0.349560i
\(109\) 13.8026 1.32205 0.661026 0.750363i \(-0.270121\pi\)
0.661026 + 0.750363i \(0.270121\pi\)
\(110\) −2.38173 + 0.578204i −0.227089 + 0.0551296i
\(111\) −7.10923 −0.674778
\(112\) 0 0
\(113\) 13.0010i 1.22303i −0.791232 0.611516i \(-0.790560\pi\)
0.791232 0.611516i \(-0.209440\pi\)
\(114\) 7.02586 12.5347i 0.658032 1.17398i
\(115\) 2.88876 + 3.10686i 0.269378 + 0.289716i
\(116\) 10.4213 + 17.0343i 0.967597 + 1.58160i
\(117\) −5.55815 −0.513852
\(118\) 5.68403 + 3.18597i 0.523258 + 0.293293i
\(119\) 0 0
\(120\) −9.31914 9.28565i −0.850717 0.847660i
\(121\) 10.3993 0.945391
\(122\) −2.25563 + 4.02422i −0.204215 + 0.364336i
\(123\) −6.29189 −0.567321
\(124\) 10.8009 + 17.6548i 0.969954 + 1.58545i
\(125\) −8.71936 + 6.99805i −0.779883 + 0.625925i
\(126\) 0 0
\(127\) −15.3261 −1.35997 −0.679987 0.733224i \(-0.738015\pi\)
−0.679987 + 0.733224i \(0.738015\pi\)
\(128\) 10.2622 + 4.76318i 0.907056 + 0.421010i
\(129\) 19.1169i 1.68315i
\(130\) −3.12534 12.8739i −0.274111 1.12911i
\(131\) −13.9878 −1.22212 −0.611058 0.791586i \(-0.709256\pi\)
−0.611058 + 0.791586i \(0.709256\pi\)
\(132\) −1.68267 2.75043i −0.146457 0.239394i
\(133\) 0 0
\(134\) 2.80122 + 1.57012i 0.241988 + 0.135637i
\(135\) 5.69959 5.29948i 0.490543 0.456107i
\(136\) 0.451084 + 11.8150i 0.0386802 + 1.01313i
\(137\) 3.49309i 0.298435i −0.988804 0.149217i \(-0.952325\pi\)
0.988804 0.149217i \(-0.0476754\pi\)
\(138\) −2.72882 + 4.86844i −0.232293 + 0.414429i
\(139\) 13.1731 1.11733 0.558664 0.829394i \(-0.311314\pi\)
0.558664 + 0.829394i \(0.311314\pi\)
\(140\) 0 0
\(141\) −17.2073 −1.44911
\(142\) 3.05121 5.44361i 0.256052 0.456818i
\(143\) 3.24692i 0.271521i
\(144\) 2.41631 4.72498i 0.201359 0.393748i
\(145\) 15.2028 + 16.3506i 1.26252 + 1.35784i
\(146\) −3.39155 1.90101i −0.280687 0.157329i
\(147\) 0 0
\(148\) 5.83088 3.56724i 0.479296 0.293225i
\(149\) −10.0480 −0.823162 −0.411581 0.911373i \(-0.635023\pi\)
−0.411581 + 0.911373i \(0.635023\pi\)
\(150\) −12.2739 8.10479i −1.00216 0.661753i
\(151\) 19.8927i 1.61885i 0.587226 + 0.809423i \(0.300220\pi\)
−0.587226 + 0.809423i \(0.699780\pi\)
\(152\) 0.527104 + 13.8062i 0.0427538 + 1.11983i
\(153\) 5.54616 0.448381
\(154\) 0 0
\(155\) 15.7566 + 16.9462i 1.26560 + 1.36115i
\(156\) 14.8668 9.09525i 1.19029 0.728203i
\(157\) −13.8342 −1.10409 −0.552046 0.833814i \(-0.686153\pi\)
−0.552046 + 0.833814i \(0.686153\pi\)
\(158\) 9.82828 17.5344i 0.781896 1.39497i
\(159\) 5.38939 0.427407
\(160\) 12.3027 + 2.93983i 0.972617 + 0.232414i
\(161\) 0 0
\(162\) 13.8414 + 7.75829i 1.08748 + 0.609549i
\(163\) 8.06959 0.632059 0.316030 0.948749i \(-0.397650\pi\)
0.316030 + 0.948749i \(0.397650\pi\)
\(164\) 5.16052 3.15712i 0.402969 0.246530i
\(165\) −2.45470 2.64003i −0.191098 0.205526i
\(166\) −1.63298 + 2.91337i −0.126744 + 0.226121i
\(167\) 18.9334i 1.46511i 0.680707 + 0.732555i \(0.261673\pi\)
−0.680707 + 0.732555i \(0.738327\pi\)
\(168\) 0 0
\(169\) 4.55043 0.350033
\(170\) 3.11860 + 12.8461i 0.239186 + 0.985250i
\(171\) 6.48084 0.495602
\(172\) 9.59240 + 15.6794i 0.731414 + 1.19554i
\(173\) −8.81376 −0.670098 −0.335049 0.942201i \(-0.608753\pi\)
−0.335049 + 0.942201i \(0.608753\pi\)
\(174\) −14.3611 + 25.6213i −1.08871 + 1.94235i
\(175\) 0 0
\(176\) 2.76020 + 1.41154i 0.208058 + 0.106399i
\(177\) 9.58404i 0.720381i
\(178\) −9.92557 + 17.7080i −0.743953 + 1.32727i
\(179\) 5.78641i 0.432496i −0.976338 0.216248i \(-0.930618\pi\)
0.976338 0.216248i \(-0.0693820\pi\)
\(180\) 1.59816 5.71409i 0.119120 0.425903i
\(181\) 1.23162i 0.0915458i 0.998952 + 0.0457729i \(0.0145751\pi\)
−0.998952 + 0.0457729i \(0.985425\pi\)
\(182\) 0 0
\(183\) −6.78538 −0.501590
\(184\) −0.204726 5.36228i −0.0150926 0.395313i
\(185\) 5.59683 5.20394i 0.411487 0.382601i
\(186\) −14.8842 + 26.5546i −1.09136 + 1.94708i
\(187\) 3.23991i 0.236926i
\(188\) 14.1132 8.63420i 1.02931 0.629714i
\(189\) 0 0
\(190\) 3.64417 + 15.0110i 0.264376 + 1.08901i
\(191\) 17.4435i 1.26217i −0.775713 0.631085i \(-0.782610\pi\)
0.775713 0.631085i \(-0.217390\pi\)
\(192\) 1.26879 + 16.5922i 0.0915673 + 1.19744i
\(193\) 9.52923i 0.685929i −0.939348 0.342964i \(-0.888569\pi\)
0.939348 0.342964i \(-0.111431\pi\)
\(194\) 17.7786 + 9.96513i 1.27643 + 0.715455i
\(195\) 14.2700 13.2683i 1.02190 0.950161i
\(196\) 0 0
\(197\) 5.88709i 0.419438i −0.977762 0.209719i \(-0.932745\pi\)
0.977762 0.209719i \(-0.0672548\pi\)
\(198\) 0.711030 1.26853i 0.0505307 0.0901508i
\(199\) 13.9826 0.991201 0.495600 0.868551i \(-0.334948\pi\)
0.495600 + 0.868551i \(0.334948\pi\)
\(200\) 14.1337 + 0.488662i 0.999403 + 0.0345536i
\(201\) 4.72322i 0.333151i
\(202\) 1.16982 2.08706i 0.0823084 0.146845i
\(203\) 0 0
\(204\) −14.8347 + 9.07563i −1.03864 + 0.635421i
\(205\) 4.95338 4.60565i 0.345959 0.321673i
\(206\) −0.382762 + 0.682878i −0.0266683 + 0.0475784i
\(207\) −2.51714 −0.174953
\(208\) −7.62973 + 14.9196i −0.529027 + 1.03449i
\(209\) 3.78592i 0.261878i
\(210\) 0 0
\(211\) 20.4896i 1.41056i 0.708927 + 0.705282i \(0.249180\pi\)
−0.708927 + 0.705282i \(0.750820\pi\)
\(212\) −4.42030 + 2.70427i −0.303588 + 0.185730i
\(213\) 9.17866 0.628911
\(214\) −9.98190 5.59499i −0.682349 0.382465i
\(215\) 13.9935 + 15.0500i 0.954351 + 1.02640i
\(216\) −9.83721 + 0.375574i −0.669337 + 0.0255546i
\(217\) 0 0
\(218\) −17.0275 9.54412i −1.15325 0.646410i
\(219\) 5.71861i 0.386428i
\(220\) 3.33801 + 0.933602i 0.225048 + 0.0629434i
\(221\) −17.5126 −1.17802
\(222\) 8.77023 + 4.91582i 0.588619 + 0.329929i
\(223\) 4.98483i 0.333809i −0.985973 0.166904i \(-0.946623\pi\)
0.985973 0.166904i \(-0.0533771\pi\)
\(224\) 0 0
\(225\) 0.481984 6.61618i 0.0321323 0.441079i
\(226\) −8.98983 + 16.0386i −0.597994 + 1.06687i
\(227\) 4.16916i 0.276717i −0.990382 0.138358i \(-0.955817\pi\)
0.990382 0.138358i \(-0.0441826\pi\)
\(228\) −17.3348 + 10.6051i −1.14802 + 0.702341i
\(229\) 1.01300i 0.0669407i −0.999440 0.0334703i \(-0.989344\pi\)
0.999440 0.0334703i \(-0.0106559\pi\)
\(230\) −1.41539 5.83024i −0.0933278 0.384435i
\(231\) 0 0
\(232\) −1.07742 28.2203i −0.0707361 1.85275i
\(233\) 19.7247i 1.29221i 0.763250 + 0.646104i \(0.223603\pi\)
−0.763250 + 0.646104i \(0.776397\pi\)
\(234\) 6.85676 + 3.84330i 0.448241 + 0.251245i
\(235\) 13.5467 12.5957i 0.883687 0.821652i
\(236\) −4.80904 7.86069i −0.313042 0.511687i
\(237\) 29.5654 1.92048
\(238\) 0 0
\(239\) 21.5726i 1.39541i −0.716383 0.697707i \(-0.754204\pi\)
0.716383 0.697707i \(-0.245796\pi\)
\(240\) 5.07570 + 17.8991i 0.327635 + 1.15538i
\(241\) 10.4033i 0.670133i 0.942194 + 0.335067i \(0.108759\pi\)
−0.942194 + 0.335067i \(0.891241\pi\)
\(242\) −12.8290 7.19082i −0.824679 0.462243i
\(243\) 12.8969i 0.827340i
\(244\) 5.56527 3.40474i 0.356280 0.217966i
\(245\) 0 0
\(246\) 7.76193 + 4.35066i 0.494883 + 0.277388i
\(247\) −20.4639 −1.30209
\(248\) −1.11667 29.2483i −0.0709084 1.85727i
\(249\) −4.91233 −0.311306
\(250\) 15.5955 2.60389i 0.986346 0.164685i
\(251\) −6.03246 −0.380766 −0.190383 0.981710i \(-0.560973\pi\)
−0.190383 + 0.981710i \(0.560973\pi\)
\(252\) 0 0
\(253\) 1.47044i 0.0924460i
\(254\) 18.9069 + 10.5976i 1.18633 + 0.664951i
\(255\) −14.2392 + 13.2397i −0.891696 + 0.829099i
\(256\) −9.36622 12.9720i −0.585389 0.810753i
\(257\) 1.61961 0.101029 0.0505144 0.998723i \(-0.483914\pi\)
0.0505144 + 0.998723i \(0.483914\pi\)
\(258\) −13.2188 + 23.5834i −0.822966 + 1.46824i
\(259\) 0 0
\(260\) −5.04636 + 18.0428i −0.312962 + 1.11897i
\(261\) −13.2471 −0.819973
\(262\) 17.2559 + 9.67213i 1.06607 + 0.597546i
\(263\) −5.03108 −0.310229 −0.155115 0.987896i \(-0.549575\pi\)
−0.155115 + 0.987896i \(0.549575\pi\)
\(264\) 0.173964 + 4.55655i 0.0107067 + 0.280436i
\(265\) −4.24287 + 3.94502i −0.260637 + 0.242341i
\(266\) 0 0
\(267\) −29.8581 −1.82728
\(268\) −2.37000 3.87392i −0.144771 0.236637i
\(269\) 12.5171i 0.763184i 0.924331 + 0.381592i \(0.124624\pi\)
−0.924331 + 0.381592i \(0.875376\pi\)
\(270\) −10.6957 + 2.59655i −0.650919 + 0.158021i
\(271\) 3.66170 0.222432 0.111216 0.993796i \(-0.464525\pi\)
0.111216 + 0.993796i \(0.464525\pi\)
\(272\) 7.61327 14.8874i 0.461622 0.902681i
\(273\) 0 0
\(274\) −2.41537 + 4.30921i −0.145918 + 0.260329i
\(275\) 3.86499 + 0.281561i 0.233067 + 0.0169788i
\(276\) 6.73277 4.11900i 0.405265 0.247935i
\(277\) 25.8916i 1.55568i 0.628464 + 0.777839i \(0.283684\pi\)
−0.628464 + 0.777839i \(0.716316\pi\)
\(278\) −16.2509 9.10882i −0.974662 0.546311i
\(279\) −13.7296 −0.821970
\(280\) 0 0
\(281\) 14.7079 0.877397 0.438698 0.898634i \(-0.355440\pi\)
0.438698 + 0.898634i \(0.355440\pi\)
\(282\) 21.2276 + 11.8983i 1.26408 + 0.708536i
\(283\) 30.2185i 1.79631i 0.439683 + 0.898153i \(0.355091\pi\)
−0.439683 + 0.898153i \(0.644909\pi\)
\(284\) −7.52820 + 4.60563i −0.446716 + 0.273294i
\(285\) −16.6389 + 15.4709i −0.985606 + 0.916417i
\(286\) −2.24515 + 4.00553i −0.132758 + 0.236852i
\(287\) 0 0
\(288\) −6.24804 + 4.15811i −0.368169 + 0.245019i
\(289\) 0.474782 0.0279283
\(290\) −7.44881 30.6830i −0.437409 1.80177i
\(291\) 29.9771i 1.75729i
\(292\) 2.86946 + 4.69032i 0.167923 + 0.274480i
\(293\) −13.9578 −0.815421 −0.407710 0.913111i \(-0.633673\pi\)
−0.407710 + 0.913111i \(0.633673\pi\)
\(294\) 0 0
\(295\) −7.01550 7.54516i −0.408458 0.439296i
\(296\) −9.65985 + 0.368802i −0.561468 + 0.0214362i
\(297\) −2.69756 −0.156528
\(298\) 12.3956 + 6.94788i 0.718056 + 0.402480i
\(299\) 7.94813 0.459652
\(300\) 9.53739 + 18.4855i 0.550642 + 1.06726i
\(301\) 0 0
\(302\) 13.7552 24.5405i 0.791525 1.41214i
\(303\) 3.51906 0.202165
\(304\) 8.89632 17.3963i 0.510239 0.997748i
\(305\) 5.34188 4.96688i 0.305875 0.284403i
\(306\) −6.84197 3.83501i −0.391129 0.219233i
\(307\) 23.2065i 1.32446i 0.749300 + 0.662231i \(0.230390\pi\)
−0.749300 + 0.662231i \(0.769610\pi\)
\(308\) 0 0
\(309\) −1.15142 −0.0655022
\(310\) −7.72014 31.8007i −0.438475 1.80616i
\(311\) 4.76466 0.270179 0.135090 0.990833i \(-0.456868\pi\)
0.135090 + 0.990833i \(0.456868\pi\)
\(312\) −24.6294 + 0.940321i −1.39436 + 0.0532352i
\(313\) 0.0995344 0.00562602 0.00281301 0.999996i \(-0.499105\pi\)
0.00281301 + 0.999996i \(0.499105\pi\)
\(314\) 17.0665 + 9.56597i 0.963116 + 0.539839i
\(315\) 0 0
\(316\) −24.2491 + 14.8352i −1.36412 + 0.834546i
\(317\) 17.6855i 0.993316i 0.867946 + 0.496658i \(0.165440\pi\)
−0.867946 + 0.496658i \(0.834560\pi\)
\(318\) −6.64857 3.72661i −0.372833 0.208978i
\(319\) 7.73856i 0.433276i
\(320\) −13.1443 12.1337i −0.734791 0.678294i
\(321\) 16.8308i 0.939405i
\(322\) 0 0
\(323\) 20.4198 1.13619
\(324\) −11.7107 19.1419i −0.650594 1.06344i
\(325\) −1.52191 + 20.8913i −0.0844205 + 1.15884i
\(326\) −9.95497 5.57989i −0.551355 0.309041i
\(327\) 28.7106i 1.58770i
\(328\) −8.54928 + 0.326402i −0.472055 + 0.0180225i
\(329\) 0 0
\(330\) 1.20271 + 4.95419i 0.0662071 + 0.272719i
\(331\) 4.14193i 0.227661i 0.993500 + 0.113831i \(0.0363121\pi\)
−0.993500 + 0.113831i \(0.963688\pi\)
\(332\) 4.02902 2.46489i 0.221121 0.135278i
\(333\) 4.53449i 0.248489i
\(334\) 13.0919 23.3570i 0.716357 1.27804i
\(335\) −3.45739 3.71842i −0.188897 0.203159i
\(336\) 0 0
\(337\) 28.4342i 1.54891i 0.632630 + 0.774454i \(0.281975\pi\)
−0.632630 + 0.774454i \(0.718025\pi\)
\(338\) −5.61359 3.14649i −0.305339 0.171147i
\(339\) −27.0432 −1.46878
\(340\) 5.03547 18.0039i 0.273087 0.976397i
\(341\) 8.02045i 0.434332i
\(342\) −7.99503 4.48132i −0.432322 0.242322i
\(343\) 0 0
\(344\) −0.991720 25.9756i −0.0534699 1.40051i
\(345\) 6.46252 6.00886i 0.347930 0.323506i
\(346\) 10.8730 + 6.09446i 0.584536 + 0.327640i
\(347\) −21.4721 −1.15268 −0.576342 0.817209i \(-0.695520\pi\)
−0.576342 + 0.817209i \(0.695520\pi\)
\(348\) 35.4328 21.6772i 1.89940 1.16202i
\(349\) 13.8800i 0.742981i 0.928437 + 0.371490i \(0.121153\pi\)
−0.928437 + 0.371490i \(0.878847\pi\)
\(350\) 0 0
\(351\) 14.5810i 0.778276i
\(352\) −2.42905 3.64993i −0.129469 0.194542i
\(353\) 10.9664 0.583682 0.291841 0.956467i \(-0.405732\pi\)
0.291841 + 0.956467i \(0.405732\pi\)
\(354\) 6.62709 11.8233i 0.352226 0.628399i
\(355\) −7.22602 + 6.71876i −0.383517 + 0.356595i
\(356\) 24.4892 14.9821i 1.29792 0.794048i
\(357\) 0 0
\(358\) −4.00113 + 7.13834i −0.211466 + 0.377273i
\(359\) 26.1577i 1.38055i −0.723547 0.690275i \(-0.757490\pi\)
0.723547 0.690275i \(-0.242510\pi\)
\(360\) −5.92268 + 5.94404i −0.312153 + 0.313279i
\(361\) 4.86105 0.255845
\(362\) 0.851631 1.51938i 0.0447607 0.0798568i
\(363\) 21.6314i 1.13535i
\(364\) 0 0
\(365\) 4.18601 + 4.50205i 0.219106 + 0.235648i
\(366\) 8.37072 + 4.69189i 0.437544 + 0.245249i
\(367\) 6.54021i 0.341396i −0.985323 0.170698i \(-0.945398\pi\)
0.985323 0.170698i \(-0.0546023\pi\)
\(368\) −3.45531 + 6.75669i −0.180120 + 0.352217i
\(369\) 4.01317i 0.208917i
\(370\) −10.5028 + 2.54974i −0.546017 + 0.132555i
\(371\) 0 0
\(372\) 36.7235 22.4669i 1.90403 1.16485i
\(373\) 2.77938i 0.143911i −0.997408 0.0719555i \(-0.977076\pi\)
0.997408 0.0719555i \(-0.0229240\pi\)
\(374\) 2.24030 3.99688i 0.115843 0.206674i
\(375\) 14.5565 + 18.1370i 0.751696 + 0.936590i
\(376\) −23.3809 + 0.892655i −1.20578 + 0.0460352i
\(377\) 41.8289 2.15430
\(378\) 0 0
\(379\) 7.04001i 0.361621i −0.983518 0.180811i \(-0.942128\pi\)
0.983518 0.180811i \(-0.0578721\pi\)
\(380\) 5.88409 21.0380i 0.301847 1.07923i
\(381\) 31.8796i 1.63324i
\(382\) −12.0617 + 21.5191i −0.617131 + 1.10101i
\(383\) 5.64777i 0.288588i 0.989535 + 0.144294i \(0.0460910\pi\)
−0.989535 + 0.144294i \(0.953909\pi\)
\(384\) 9.90780 21.3462i 0.505606 1.08932i
\(385\) 0 0
\(386\) −6.58918 + 11.7556i −0.335381 + 0.598346i
\(387\) −12.1934 −0.619824
\(388\) −15.0418 24.5868i −0.763631 1.24820i
\(389\) 19.1856 0.972750 0.486375 0.873750i \(-0.338319\pi\)
0.486375 + 0.873750i \(0.338319\pi\)
\(390\) −26.7787 + 6.50097i −1.35599 + 0.329189i
\(391\) −7.93098 −0.401087
\(392\) 0 0
\(393\) 29.0957i 1.46768i
\(394\) −4.07075 + 7.26255i −0.205081 + 0.365882i
\(395\) −23.2758 + 21.6418i −1.17113 + 1.08892i
\(396\) −1.75431 + 1.07326i −0.0881574 + 0.0539333i
\(397\) −15.3584 −0.770816 −0.385408 0.922746i \(-0.625939\pi\)
−0.385408 + 0.922746i \(0.625939\pi\)
\(398\) −17.2495 9.66857i −0.864639 0.484642i
\(399\) 0 0
\(400\) −17.0980 10.3759i −0.854900 0.518794i
\(401\) 8.95131 0.447007 0.223504 0.974703i \(-0.428251\pi\)
0.223504 + 0.974703i \(0.428251\pi\)
\(402\) 3.26597 5.82676i 0.162892 0.290612i
\(403\) 43.3526 2.15955
\(404\) −2.88628 + 1.76578i −0.143598 + 0.0878507i
\(405\) −17.0837 18.3735i −0.848897 0.912988i
\(406\) 0 0
\(407\) −2.64892 −0.131302
\(408\) 24.5762 0.938293i 1.21670 0.0464524i
\(409\) 4.50853i 0.222933i 0.993768 + 0.111466i \(0.0355547\pi\)
−0.993768 + 0.111466i \(0.964445\pi\)
\(410\) −9.29536 + 2.25660i −0.459065 + 0.111446i
\(411\) −7.26591 −0.358401
\(412\) 0.944381 0.577757i 0.0465263 0.0284640i
\(413\) 0 0
\(414\) 3.10525 + 1.74053i 0.152615 + 0.0855424i
\(415\) 3.86730 3.59581i 0.189838 0.176512i
\(416\) 19.7288 13.1297i 0.967284 0.643735i
\(417\) 27.4011i 1.34184i
\(418\) 2.61786 4.67047i 0.128044 0.228440i
\(419\) −29.0565 −1.41950 −0.709751 0.704453i \(-0.751192\pi\)
−0.709751 + 0.704453i \(0.751192\pi\)
\(420\) 0 0
\(421\) −11.9368 −0.581763 −0.290882 0.956759i \(-0.593949\pi\)
−0.290882 + 0.956759i \(0.593949\pi\)
\(422\) 14.1680 25.2768i 0.689687 1.23046i
\(423\) 10.9754i 0.533640i
\(424\) 7.32298 0.279583i 0.355636 0.0135778i
\(425\) 1.51863 20.8462i 0.0736643 1.01119i
\(426\) −11.3232 6.34678i −0.548609 0.307502i
\(427\) 0 0
\(428\) 8.44530 + 13.8044i 0.408219 + 0.667261i
\(429\) −6.75385 −0.326079
\(430\) −6.85632 28.2424i −0.330641 1.36197i
\(431\) 12.9912i 0.625764i −0.949792 0.312882i \(-0.898706\pi\)
0.949792 0.312882i \(-0.101294\pi\)
\(432\) 12.3953 + 6.33882i 0.596368 + 0.304977i
\(433\) −15.4967 −0.744724 −0.372362 0.928088i \(-0.621452\pi\)
−0.372362 + 0.928088i \(0.621452\pi\)
\(434\) 0 0
\(435\) 34.0106 31.6231i 1.63068 1.51621i
\(436\) 14.4063 + 23.5480i 0.689937 + 1.12775i
\(437\) −9.26757 −0.443328
\(438\) −3.95425 + 7.05471i −0.188942 + 0.337087i
\(439\) −2.54235 −0.121340 −0.0606698 0.998158i \(-0.519324\pi\)
−0.0606698 + 0.998158i \(0.519324\pi\)
\(440\) −3.47234 3.45986i −0.165537 0.164943i
\(441\) 0 0
\(442\) 21.6042 + 12.1094i 1.02761 + 0.575987i
\(443\) −30.0971 −1.42995 −0.714977 0.699148i \(-0.753563\pi\)
−0.714977 + 0.699148i \(0.753563\pi\)
\(444\) −7.42015 12.1287i −0.352145 0.575603i
\(445\) 23.5062 21.8560i 1.11430 1.03608i
\(446\) −3.44686 + 6.14948i −0.163214 + 0.291186i
\(447\) 20.9006i 0.988565i
\(448\) 0 0
\(449\) 6.40778 0.302402 0.151201 0.988503i \(-0.451686\pi\)
0.151201 + 0.988503i \(0.451686\pi\)
\(450\) −5.16949 + 7.82871i −0.243692 + 0.369049i
\(451\) −2.34438 −0.110393
\(452\) 22.1804 13.5696i 1.04328 0.638261i
\(453\) 41.3785 1.94413
\(454\) −2.88285 + 5.14324i −0.135299 + 0.241384i
\(455\) 0 0
\(456\) 28.7180 1.09642i 1.34484 0.0513446i
\(457\) 3.15627i 0.147644i 0.997271 + 0.0738220i \(0.0235197\pi\)
−0.997271 + 0.0738220i \(0.976480\pi\)
\(458\) −0.700458 + 1.24967i −0.0327302 + 0.0583934i
\(459\) 14.5495i 0.679114i
\(460\) −2.28536 + 8.17111i −0.106556 + 0.380980i
\(461\) 9.88170i 0.460237i 0.973163 + 0.230118i \(0.0739114\pi\)
−0.973163 + 0.230118i \(0.926089\pi\)
\(462\) 0 0
\(463\) −9.55216 −0.443926 −0.221963 0.975055i \(-0.571246\pi\)
−0.221963 + 0.975055i \(0.571246\pi\)
\(464\) −18.1844 + 35.5587i −0.844189 + 1.65077i
\(465\) 35.2495 32.7750i 1.63465 1.51990i
\(466\) 13.6391 24.3332i 0.631817 1.12721i
\(467\) 13.4654i 0.623104i 0.950229 + 0.311552i \(0.100849\pi\)
−0.950229 + 0.311552i \(0.899151\pi\)
\(468\) −5.80124 9.48250i −0.268163 0.438329i
\(469\) 0 0
\(470\) −25.4213 + 6.17143i −1.17260 + 0.284667i
\(471\) 28.7764i 1.32594i
\(472\) 0.497187 + 13.0226i 0.0228849 + 0.599413i
\(473\) 7.12302i 0.327517i
\(474\) −36.4731 20.4436i −1.67526 0.939007i
\(475\) 1.77456 24.3593i 0.0814224 1.11768i
\(476\) 0 0
\(477\) 3.43753i 0.157394i
\(478\) −14.9168 + 26.6128i −0.682280 + 1.21724i
\(479\) −14.0240 −0.640773 −0.320387 0.947287i \(-0.603813\pi\)
−0.320387 + 0.947287i \(0.603813\pi\)
\(480\) 6.11510 25.5907i 0.279115 1.16805i
\(481\) 14.3181i 0.652850i
\(482\) 7.19356 12.8339i 0.327658 0.584568i
\(483\) 0 0
\(484\) 10.8541 + 17.7418i 0.493369 + 0.806444i
\(485\) −21.9432 23.5999i −0.996388 1.07161i
\(486\) 8.91787 15.9102i 0.404523 0.721701i
\(487\) 30.3378 1.37474 0.687368 0.726309i \(-0.258766\pi\)
0.687368 + 0.726309i \(0.258766\pi\)
\(488\) −9.21982 + 0.352002i −0.417362 + 0.0159344i
\(489\) 16.7854i 0.759063i
\(490\) 0 0
\(491\) 8.93052i 0.403029i −0.979486 0.201514i \(-0.935414\pi\)
0.979486 0.201514i \(-0.0645862\pi\)
\(492\) −6.56707 10.7343i −0.296066 0.483940i
\(493\) −41.7387 −1.87982
\(494\) 25.2451 + 14.1502i 1.13583 + 0.636648i
\(495\) −1.68389 + 1.56568i −0.0756853 + 0.0703723i
\(496\) −18.8468 + 36.8540i −0.846245 + 1.65479i
\(497\) 0 0
\(498\) 6.06005 + 3.39673i 0.271557 + 0.152211i
\(499\) 5.52736i 0.247439i 0.992317 + 0.123719i \(0.0394822\pi\)
−0.992317 + 0.123719i \(0.960518\pi\)
\(500\) −21.0398 7.57157i −0.940926 0.338611i
\(501\) 39.3830 1.75950
\(502\) 7.44189 + 4.17127i 0.332148 + 0.186173i
\(503\) 20.6496i 0.920720i 0.887732 + 0.460360i \(0.152280\pi\)
−0.887732 + 0.460360i \(0.847720\pi\)
\(504\) 0 0
\(505\) −2.77042 + 2.57594i −0.123282 + 0.114628i
\(506\) −1.01677 + 1.81400i −0.0452009 + 0.0806420i
\(507\) 9.46527i 0.420367i
\(508\) −15.9964 26.1472i −0.709727 1.16009i
\(509\) 29.8021i 1.32095i 0.750846 + 0.660477i \(0.229646\pi\)
−0.750846 + 0.660477i \(0.770354\pi\)
\(510\) 26.7209 6.48695i 1.18322 0.287247i
\(511\) 0 0
\(512\) 2.58476 + 22.4793i 0.114231 + 0.993454i
\(513\) 17.0015i 0.750636i
\(514\) −1.99802 1.11992i −0.0881289 0.0493974i
\(515\) 0.906473 0.842839i 0.0399440 0.0371399i
\(516\) 32.6144 19.9530i 1.43577 0.878381i
\(517\) −6.41149 −0.281977
\(518\) 0 0
\(519\) 18.3333i 0.804745i
\(520\) 18.7015 18.7689i 0.820114 0.823071i
\(521\) 35.0853i 1.53711i −0.639781 0.768557i \(-0.720975\pi\)
0.639781 0.768557i \(-0.279025\pi\)
\(522\) 16.3421 + 9.15996i 0.715275 + 0.400921i
\(523\) 21.8889i 0.957135i −0.878051 0.478567i \(-0.841156\pi\)
0.878051 0.478567i \(-0.158844\pi\)
\(524\) −14.5995 23.8639i −0.637783 1.04250i
\(525\) 0 0
\(526\) 6.20654 + 3.47884i 0.270618 + 0.151685i
\(527\) −43.2591 −1.88440
\(528\) 2.93612 5.74144i 0.127778 0.249864i
\(529\) −19.4005 −0.843500
\(530\) 7.96205 1.93292i 0.345849 0.0839606i
\(531\) 6.11301 0.265282
\(532\) 0 0
\(533\) 12.6720i 0.548885i
\(534\) 36.8341 + 20.6460i 1.59397 + 0.893440i
\(535\) 12.3201 + 13.2503i 0.532646 + 0.572860i
\(536\) 0.245025 + 6.41781i 0.0105835 + 0.277207i
\(537\) −12.0362 −0.519400
\(538\) 8.65524 15.4416i 0.373154 0.665737i
\(539\) 0 0
\(540\) 14.9901 + 4.19254i 0.645070 + 0.180418i
\(541\) −25.4381 −1.09367 −0.546834 0.837241i \(-0.684167\pi\)
−0.546834 + 0.837241i \(0.684167\pi\)
\(542\) −4.51722 2.53196i −0.194031 0.108757i
\(543\) 2.56188 0.109941
\(544\) −19.6862 + 13.1013i −0.844041 + 0.561715i
\(545\) 21.0161 + 22.6028i 0.900231 + 0.968198i
\(546\) 0 0
\(547\) −43.6348 −1.86569 −0.932845 0.360278i \(-0.882682\pi\)
−0.932845 + 0.360278i \(0.882682\pi\)
\(548\) 5.95939 3.64586i 0.254573 0.155743i
\(549\) 4.32793i 0.184712i
\(550\) −4.57331 3.01987i −0.195007 0.128768i
\(551\) −48.7728 −2.07779
\(552\) −11.1540 + 0.425847i −0.474745 + 0.0181252i
\(553\) 0 0
\(554\) 17.9033 31.9410i 0.760639 1.35704i
\(555\) −10.8246 11.6419i −0.459479 0.494170i
\(556\) 13.7492 + 22.4740i 0.583098 + 0.953111i
\(557\) 18.0557i 0.765044i 0.923946 + 0.382522i \(0.124944\pi\)
−0.923946 + 0.382522i \(0.875056\pi\)
\(558\) 16.9374 + 9.49363i 0.717017 + 0.401897i
\(559\) 38.5018 1.62845
\(560\) 0 0
\(561\) 6.73928 0.284533
\(562\) −18.1442 10.1701i −0.765367 0.428998i
\(563\) 5.17801i 0.218227i −0.994029 0.109113i \(-0.965199\pi\)
0.994029 0.109113i \(-0.0348012\pi\)
\(564\) −17.9599 29.3565i −0.756246 1.23613i
\(565\) 21.2901 19.7955i 0.895681 0.832805i
\(566\) 20.8953 37.2788i 0.878293 1.56695i
\(567\) 0 0
\(568\) 12.4717 0.476157i 0.523303 0.0199791i
\(569\) 21.7914 0.913544 0.456772 0.889584i \(-0.349005\pi\)
0.456772 + 0.889584i \(0.349005\pi\)
\(570\) 31.2241 7.58017i 1.30784 0.317499i
\(571\) 16.2217i 0.678857i −0.940632 0.339429i \(-0.889766\pi\)
0.940632 0.339429i \(-0.110234\pi\)
\(572\) 5.53941 3.38892i 0.231614 0.141698i
\(573\) −36.2840 −1.51579
\(574\) 0 0
\(575\) −0.689234 + 9.46110i −0.0287431 + 0.394555i
\(576\) 10.5830 0.809277i 0.440960 0.0337199i
\(577\) 43.3118 1.80309 0.901547 0.432680i \(-0.142432\pi\)
0.901547 + 0.432680i \(0.142432\pi\)
\(578\) −0.585710 0.328298i −0.0243623 0.0136554i
\(579\) −19.8216 −0.823757
\(580\) −12.0273 + 43.0024i −0.499406 + 1.78558i
\(581\) 0 0
\(582\) 20.7283 36.9809i 0.859215 1.53291i
\(583\) 2.00811 0.0831673
\(584\) −0.296662 7.77032i −0.0122760 0.321538i
\(585\) −8.46293 9.10188i −0.349899 0.376316i
\(586\) 17.2188 + 9.65139i 0.711304 + 0.398695i
\(587\) 30.4825i 1.25815i 0.777345 + 0.629074i \(0.216566\pi\)
−0.777345 + 0.629074i \(0.783434\pi\)
\(588\) 0 0
\(589\) −50.5494 −2.08285
\(590\) 3.43734 + 14.1590i 0.141513 + 0.582918i
\(591\) −12.2456 −0.503718
\(592\) 12.1718 + 6.22454i 0.500258 + 0.255827i
\(593\) 16.2338 0.666644 0.333322 0.942813i \(-0.391830\pi\)
0.333322 + 0.942813i \(0.391830\pi\)
\(594\) 3.32781 + 1.86528i 0.136542 + 0.0765335i
\(595\) 0 0
\(596\) −10.4874 17.1424i −0.429582 0.702179i
\(597\) 29.0850i 1.19037i
\(598\) −9.80513 5.49590i −0.400962 0.224744i
\(599\) 21.3963i 0.874228i 0.899406 + 0.437114i \(0.143999\pi\)
−0.899406 + 0.437114i \(0.856001\pi\)
\(600\) 1.01646 29.3992i 0.0414967 1.20022i
\(601\) 6.40965i 0.261455i −0.991418 0.130728i \(-0.958269\pi\)
0.991418 0.130728i \(-0.0417313\pi\)
\(602\) 0 0
\(603\) 3.01262 0.122683
\(604\) −33.9380 + 20.7627i −1.38092 + 0.844824i
\(605\) 15.8341 + 17.0296i 0.643749 + 0.692352i
\(606\) −4.34125 2.43333i −0.176351 0.0988471i
\(607\) 45.6549i 1.85307i −0.376205 0.926537i \(-0.622771\pi\)
0.376205 0.926537i \(-0.377229\pi\)
\(608\) −23.0039 + 15.3093i −0.932932 + 0.620873i
\(609\) 0 0
\(610\) −10.0244 + 2.43359i −0.405877 + 0.0985332i
\(611\) 34.6558i 1.40202i
\(612\) 5.78873 + 9.46205i 0.233995 + 0.382481i
\(613\) 1.69974i 0.0686517i −0.999411 0.0343259i \(-0.989072\pi\)
0.999411 0.0343259i \(-0.0109284\pi\)
\(614\) 16.0466 28.6284i 0.647588 1.15535i
\(615\) −9.58014 10.3034i −0.386308 0.415474i
\(616\) 0 0
\(617\) 21.5543i 0.867744i 0.900975 + 0.433872i \(0.142853\pi\)
−0.900975 + 0.433872i \(0.857147\pi\)
\(618\) 1.42044 + 0.796176i 0.0571386 + 0.0320269i
\(619\) 0.210519 0.00846148 0.00423074 0.999991i \(-0.498653\pi\)
0.00423074 + 0.999991i \(0.498653\pi\)
\(620\) −12.4654 + 44.5689i −0.500622 + 1.78993i
\(621\) 6.60335i 0.264983i
\(622\) −5.87788 3.29463i −0.235681 0.132102i
\(623\) 0 0
\(624\) 31.0340 + 15.8705i 1.24235 + 0.635327i
\(625\) −24.7360 3.62324i −0.989442 0.144929i
\(626\) −0.122790 0.0688252i −0.00490766 0.00275081i
\(627\) 7.87504 0.314499
\(628\) −14.4393 23.6019i −0.576190 0.941820i
\(629\) 14.2872i 0.569669i
\(630\) 0 0
\(631\) 30.0918i 1.19793i −0.800774 0.598967i \(-0.795578\pi\)
0.800774 0.598967i \(-0.204422\pi\)
\(632\) 40.1728 1.53375i 1.59799 0.0610094i
\(633\) 42.6201 1.69400
\(634\) 12.2290 21.8175i 0.485676 0.866485i
\(635\) −23.3358 25.0976i −0.926053 0.995970i
\(636\) 5.62510 + 9.19459i 0.223050 + 0.364589i
\(637\) 0 0
\(638\) −5.35099 + 9.54660i −0.211848 + 0.377953i
\(639\) 5.85444i 0.231598i
\(640\) 7.82529 + 24.0575i 0.309322 + 0.950957i
\(641\) −28.1931 −1.11356 −0.556780 0.830660i \(-0.687963\pi\)
−0.556780 + 0.830660i \(0.687963\pi\)
\(642\) −11.6380 + 20.7632i −0.459316 + 0.819457i
\(643\) 0.884403i 0.0348774i −0.999848 0.0174387i \(-0.994449\pi\)
0.999848 0.0174387i \(-0.00555120\pi\)
\(644\) 0 0
\(645\) 31.3053 29.1077i 1.23265 1.14611i
\(646\) −25.1906 14.1197i −0.991112 0.555531i
\(647\) 31.8257i 1.25120i −0.780145 0.625599i \(-0.784855\pi\)
0.780145 0.625599i \(-0.215145\pi\)
\(648\) 1.21072 + 31.7118i 0.0475616 + 1.24576i
\(649\) 3.57105i 0.140176i
\(650\) 16.3232 24.7199i 0.640248 0.969595i
\(651\) 0 0
\(652\) 8.42252 + 13.7671i 0.329851 + 0.539163i
\(653\) 31.6920i 1.24020i 0.784522 + 0.620101i \(0.212909\pi\)
−0.784522 + 0.620101i \(0.787091\pi\)
\(654\) −19.8526 + 35.4186i −0.776297 + 1.38498i
\(655\) −21.2980 22.9060i −0.832181 0.895010i
\(656\) 10.7724 + 5.50892i 0.420593 + 0.215087i
\(657\) −3.64751 −0.142303
\(658\) 0 0
\(659\) 21.5313i 0.838739i 0.907816 + 0.419370i \(0.137749\pi\)
−0.907816 + 0.419370i \(0.862251\pi\)
\(660\) 1.94197 6.94333i 0.0755910 0.270269i
\(661\) 21.1758i 0.823642i −0.911265 0.411821i \(-0.864893\pi\)
0.911265 0.411821i \(-0.135107\pi\)
\(662\) 2.86403 5.10965i 0.111314 0.198592i
\(663\) 36.4276i 1.41473i
\(664\) −6.67476 + 0.254835i −0.259031 + 0.00988951i
\(665\) 0 0
\(666\) 3.13547 5.59393i 0.121497 0.216760i
\(667\) 18.9432 0.733485
\(668\) −32.3014 + 19.7615i −1.24978 + 0.764594i
\(669\) −10.3689 −0.400883
\(670\) 1.69399 + 6.97788i 0.0654447 + 0.269579i
\(671\) −2.52825 −0.0976022
\(672\) 0 0
\(673\) 33.5756i 1.29424i −0.762387 0.647121i \(-0.775973\pi\)
0.762387 0.647121i \(-0.224027\pi\)
\(674\) 19.6614 35.0775i 0.757329 1.35114i
\(675\) 17.3566 + 1.26441i 0.668055 + 0.0486673i
\(676\) 4.74944 + 7.76327i 0.182671 + 0.298587i
\(677\) 20.6996 0.795549 0.397775 0.917483i \(-0.369783\pi\)
0.397775 + 0.917483i \(0.369783\pi\)
\(678\) 33.3615 + 18.6996i 1.28124 + 0.718153i
\(679\) 0 0
\(680\) −18.6611 + 18.7284i −0.715621 + 0.718202i
\(681\) −8.67219 −0.332319
\(682\) −5.54591 + 9.89435i −0.212364 + 0.378874i
\(683\) −28.1216 −1.07604 −0.538021 0.842931i \(-0.680828\pi\)
−0.538021 + 0.842931i \(0.680828\pi\)
\(684\) 6.76429 + 11.0567i 0.258639 + 0.422762i
\(685\) 5.72018 5.31863i 0.218557 0.203214i
\(686\) 0 0
\(687\) −2.10712 −0.0803915
\(688\) −16.7380 + 32.7303i −0.638129 + 1.24783i
\(689\) 10.8543i 0.413517i
\(690\) −12.1274 + 2.94412i −0.461681 + 0.112081i
\(691\) 39.3458 1.49679 0.748393 0.663255i \(-0.230826\pi\)
0.748393 + 0.663255i \(0.230826\pi\)
\(692\) −9.19923 15.0367i −0.349702 0.571611i
\(693\) 0 0
\(694\) 26.4889 + 14.8474i 1.00550 + 0.563598i
\(695\) 20.0576 + 21.5719i 0.760827 + 0.818269i
\(696\) −58.7006 + 2.24112i −2.22504 + 0.0849495i
\(697\) 12.6446i 0.478950i
\(698\) 9.59764 17.1230i 0.363276 0.648114i
\(699\) 41.0290 1.55186
\(700\) 0 0
\(701\) −14.6649 −0.553887 −0.276944 0.960886i \(-0.589322\pi\)
−0.276944 + 0.960886i \(0.589322\pi\)
\(702\) −10.0823 + 17.9877i −0.380533 + 0.678902i
\(703\) 16.6950i 0.629664i
\(704\) 0.472757 + 6.18232i 0.0178177 + 0.233005i
\(705\) −26.2001 28.1782i −0.986752 1.06125i
\(706\) −13.5286 7.58295i −0.509155 0.285388i
\(707\) 0 0
\(708\) −16.3509 + 10.0032i −0.614504 + 0.375943i
\(709\) −1.65867 −0.0622927 −0.0311464 0.999515i \(-0.509916\pi\)
−0.0311464 + 0.999515i \(0.509916\pi\)
\(710\) 13.5601 3.29194i 0.508903 0.123544i
\(711\) 18.8578i 0.707221i
\(712\) −40.5705 + 1.54893i −1.52044 + 0.0580488i
\(713\) 19.6333 0.735272
\(714\) 0 0
\(715\) 5.31706 4.94381i 0.198847 0.184888i
\(716\) 9.87191 6.03948i 0.368931 0.225706i
\(717\) −44.8728 −1.67580
\(718\) −18.0873 + 32.2692i −0.675011 + 1.20427i
\(719\) 22.1781 0.827105 0.413552 0.910480i \(-0.364288\pi\)
0.413552 + 0.910480i \(0.364288\pi\)
\(720\) 11.4166 3.23745i 0.425471 0.120652i
\(721\) 0 0
\(722\) −5.99679 3.36128i −0.223177 0.125094i
\(723\) 21.6397 0.804787
\(724\) −2.10121 + 1.28549i −0.0780910 + 0.0477748i
\(725\) −3.62726 + 49.7913i −0.134713 + 1.84920i
\(726\) −14.9575 + 26.6854i −0.555125 + 0.990387i
\(727\) 31.0654i 1.15215i −0.817396 0.576076i \(-0.804583\pi\)
0.817396 0.576076i \(-0.195417\pi\)
\(728\) 0 0
\(729\) −6.83323 −0.253083
\(730\) −2.05099 8.44842i −0.0759106 0.312690i
\(731\) −38.4187 −1.42097
\(732\) −7.08214 11.5762i −0.261763 0.427869i
\(733\) −15.8014 −0.583638 −0.291819 0.956474i \(-0.594260\pi\)
−0.291819 + 0.956474i \(0.594260\pi\)
\(734\) −4.52237 + 8.06826i −0.166924 + 0.297805i
\(735\) 0 0
\(736\) 8.93466 5.94608i 0.329336 0.219175i
\(737\) 1.75989i 0.0648263i
\(738\) 2.77499 4.95081i 0.102149 0.182242i
\(739\) 7.82795i 0.287956i 0.989581 + 0.143978i \(0.0459894\pi\)
−0.989581 + 0.143978i \(0.954011\pi\)
\(740\) 14.7198 + 4.11696i 0.541111 + 0.151342i
\(741\) 42.5666i 1.56372i
\(742\) 0 0
\(743\) 37.7406 1.38457 0.692284 0.721625i \(-0.256605\pi\)
0.692284 + 0.721625i \(0.256605\pi\)
\(744\) −60.8388 + 2.32276i −2.23046 + 0.0851564i
\(745\) −15.2992 16.4543i −0.560519 0.602838i
\(746\) −1.92186 + 3.42876i −0.0703644 + 0.125536i
\(747\) 3.13324i 0.114639i
\(748\) −5.52746 + 3.38161i −0.202104 + 0.123644i
\(749\) 0 0
\(750\) −5.41631 32.4399i −0.197776 1.18454i
\(751\) 2.75141i 0.100400i −0.998739 0.0502001i \(-0.984014\pi\)
0.998739 0.0502001i \(-0.0159859\pi\)
\(752\) 29.4608 + 15.0660i 1.07433 + 0.549400i
\(753\) 12.5480i 0.457275i
\(754\) −51.6019 28.9235i −1.87923 1.05333i
\(755\) −32.5758 + 30.2890i −1.18555 + 1.10233i
\(756\) 0 0
\(757\) 19.3492i 0.703257i 0.936140 + 0.351628i \(0.114372\pi\)
−0.936140 + 0.351628i \(0.885628\pi\)
\(758\) −4.86796 + 8.68484i −0.176812 + 0.315448i
\(759\) −3.05864 −0.111022
\(760\) −21.8060 + 21.8847i −0.790988 + 0.793841i
\(761\) 15.2848i 0.554074i 0.960859 + 0.277037i \(0.0893524\pi\)
−0.960859 + 0.277037i \(0.910648\pi\)
\(762\) 22.0438 39.3280i 0.798564 1.42470i
\(763\) 0 0
\(764\) 29.7596 18.2064i 1.07666 0.658686i
\(765\) 8.44467 + 9.08224i 0.305318 + 0.328369i
\(766\) 3.90527 6.96732i 0.141103 0.251739i
\(767\) −19.3024 −0.696971
\(768\) −26.9829 + 19.4825i −0.973662 + 0.703015i
\(769\) 8.96913i 0.323435i −0.986837 0.161718i \(-0.948297\pi\)
0.986837 0.161718i \(-0.0517033\pi\)
\(770\) 0 0
\(771\) 3.36893i 0.121329i
\(772\) 16.2574 9.94599i 0.585115 0.357964i
\(773\) −6.68452 −0.240426 −0.120213 0.992748i \(-0.538358\pi\)
−0.120213 + 0.992748i \(0.538358\pi\)
\(774\) 15.0422 + 8.43136i 0.540682 + 0.303059i
\(775\) −3.75939 + 51.6050i −0.135041 + 1.85371i
\(776\) 1.55511 + 40.7322i 0.0558251 + 1.46220i
\(777\) 0 0
\(778\) −23.6682 13.2663i −0.848544 0.475620i
\(779\) 14.7756i 0.529391i
\(780\) 37.5305 + 10.4968i 1.34381 + 0.375847i
\(781\) 3.42000 0.122377
\(782\) 9.78398 + 5.48404i 0.349874 + 0.196109i
\(783\) 34.7517i 1.24193i
\(784\) 0 0
\(785\) −21.0642 22.6546i −0.751814 0.808576i
\(786\) 20.1188 35.8936i 0.717615