Properties

Label 354.2.c.a.353.3
Level 354
Weight 2
Character 354.353
Analytic conductor 2.827
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 354.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(2.82670423155\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: 10.0.41542366334681088.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 353.3
Root \(1.43134 - 0.975334i\)
Character \(\chi\) = 354.353
Dual form 354.2.c.a.353.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.43134 - 0.975334i) q^{3} +1.00000 q^{4} +0.0999120i q^{5} +(1.43134 + 0.975334i) q^{6} +2.48626 q^{7} -1.00000 q^{8} +(1.09745 + 2.79206i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.43134 - 0.975334i) q^{3} +1.00000 q^{4} +0.0999120i q^{5} +(1.43134 + 0.975334i) q^{6} +2.48626 q^{7} -1.00000 q^{8} +(1.09745 + 2.79206i) q^{9} -0.0999120i q^{10} -1.50375 q^{11} +(-1.43134 - 0.975334i) q^{12} +3.74859i q^{13} -2.48626 q^{14} +(0.0974475 - 0.143008i) q^{15} +1.00000 q^{16} -6.68366i q^{17} +(-1.09745 - 2.79206i) q^{18} +3.99002 q^{19} +0.0999120i q^{20} +(-3.55868 - 2.42494i) q^{21} +1.50375 q^{22} +7.31226 q^{23} +(1.43134 + 0.975334i) q^{24} +4.99002 q^{25} -3.74859i q^{26} +(1.15238 - 5.06676i) q^{27} +2.48626 q^{28} +3.18348i q^{29} +(-0.0974475 + 0.143008i) q^{30} -9.23530i q^{31} -1.00000 q^{32} +(2.15238 + 1.46666i) q^{33} +6.68366i q^{34} +0.248408i q^{35} +(1.09745 + 2.79206i) q^{36} +0.665027i q^{37} -3.99002 q^{38} +(3.65613 - 5.36550i) q^{39} -0.0999120i q^{40} +3.99875i q^{41} +(3.55868 + 2.42494i) q^{42} -10.0506i q^{43} -1.50375 q^{44} +(-0.278960 + 0.109648i) q^{45} -7.31226 q^{46} +4.30475 q^{47} +(-1.43134 - 0.975334i) q^{48} -0.818487 q^{49} -4.99002 q^{50} +(-6.51880 + 9.56657i) q^{51} +3.74859i q^{52} +0.250155i q^{53} +(-1.15238 + 5.06676i) q^{54} -0.150243i q^{55} -2.48626 q^{56} +(-5.71106 - 3.89160i) q^{57} -3.18348i q^{58} +(7.65780 - 0.598474i) q^{59} +(0.0974475 - 0.143008i) q^{60} +13.2188i q^{61} +9.23530i q^{62} +(2.72855 + 6.94181i) q^{63} +1.00000 q^{64} -0.374529 q^{65} +(-2.15238 - 1.46666i) q^{66} +7.06709i q^{67} -6.68366i q^{68} +(-10.4663 - 7.13189i) q^{69} -0.248408i q^{70} +10.1991i q^{71} +(-1.09745 - 2.79206i) q^{72} -11.3305i q^{73} -0.665027i q^{74} +(-7.14239 - 4.86693i) q^{75} +3.99002 q^{76} -3.73873 q^{77} +(-3.65613 + 5.36550i) q^{78} -9.13074 q^{79} +0.0999120i q^{80} +(-6.59122 + 6.12828i) q^{81} -3.99875i q^{82} +5.43398 q^{83} +(-3.55868 - 2.42494i) q^{84} +0.667778 q^{85} +10.0506i q^{86} +(3.10495 - 4.55663i) q^{87} +1.50375 q^{88} -8.23497 q^{89} +(0.278960 - 0.109648i) q^{90} +9.31999i q^{91} +7.31226 q^{92} +(-9.00751 + 13.2188i) q^{93} -4.30475 q^{94} +0.398650i q^{95} +(1.43134 + 0.975334i) q^{96} -3.83328i q^{97} +0.818487 q^{98} +(-1.65029 - 4.19857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - q^{3} + 10q^{4} + q^{6} - 2q^{7} - 10q^{8} + 3q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - q^{3} + 10q^{4} + q^{6} - 2q^{7} - 10q^{8} + 3q^{9} + 4q^{11} - q^{12} + 2q^{14} - 7q^{15} + 10q^{16} - 3q^{18} - 6q^{19} - 3q^{21} - 4q^{22} - 8q^{23} + q^{24} + 4q^{25} - 10q^{27} - 2q^{28} + 7q^{30} - 10q^{32} + 3q^{36} + 6q^{38} - 4q^{39} + 3q^{42} + 4q^{44} - 11q^{45} + 8q^{46} - q^{48} + 8q^{49} - 4q^{50} + 2q^{51} + 10q^{54} + 2q^{56} - 3q^{57} + 20q^{59} - 7q^{60} - 19q^{63} + 10q^{64} + 16q^{65} + 14q^{69} - 3q^{72} - 4q^{75} - 6q^{76} + 48q^{77} + 4q^{78} + 6q^{79} + 7q^{81} + 12q^{83} - 3q^{84} - 4q^{85} - 15q^{87} - 4q^{88} - 16q^{89} + 11q^{90} - 8q^{92} - 52q^{93} + q^{96} - 8q^{98} + 2q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.43134 0.975334i −0.826382 0.563109i
\(4\) 1.00000 0.500000
\(5\) 0.0999120i 0.0446820i 0.999750 + 0.0223410i \(0.00711195\pi\)
−0.999750 + 0.0223410i \(0.992888\pi\)
\(6\) 1.43134 + 0.975334i 0.584341 + 0.398178i
\(7\) 2.48626 0.939720 0.469860 0.882741i \(-0.344304\pi\)
0.469860 + 0.882741i \(0.344304\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.09745 + 2.79206i 0.365816 + 0.930687i
\(10\) 0.0999120i 0.0315949i
\(11\) −1.50375 −0.453399 −0.226699 0.973965i \(-0.572793\pi\)
−0.226699 + 0.973965i \(0.572793\pi\)
\(12\) −1.43134 0.975334i −0.413191 0.281555i
\(13\) 3.74859i 1.03967i 0.854266 + 0.519836i \(0.174007\pi\)
−0.854266 + 0.519836i \(0.825993\pi\)
\(14\) −2.48626 −0.664482
\(15\) 0.0974475 0.143008i 0.0251608 0.0369244i
\(16\) 1.00000 0.250000
\(17\) 6.68366i 1.62103i −0.585721 0.810513i \(-0.699188\pi\)
0.585721 0.810513i \(-0.300812\pi\)
\(18\) −1.09745 2.79206i −0.258671 0.658095i
\(19\) 3.99002 0.915373 0.457686 0.889114i \(-0.348678\pi\)
0.457686 + 0.889114i \(0.348678\pi\)
\(20\) 0.0999120i 0.0223410i
\(21\) −3.55868 2.42494i −0.776568 0.529165i
\(22\) 1.50375 0.320601
\(23\) 7.31226 1.52471 0.762356 0.647158i \(-0.224043\pi\)
0.762356 + 0.647158i \(0.224043\pi\)
\(24\) 1.43134 + 0.975334i 0.292170 + 0.199089i
\(25\) 4.99002 0.998004
\(26\) 3.74859i 0.735159i
\(27\) 1.15238 5.06676i 0.221775 0.975098i
\(28\) 2.48626 0.469860
\(29\) 3.18348i 0.591157i 0.955318 + 0.295578i \(0.0955124\pi\)
−0.955318 + 0.295578i \(0.904488\pi\)
\(30\) −0.0974475 + 0.143008i −0.0177914 + 0.0261095i
\(31\) 9.23530i 1.65871i −0.558722 0.829355i \(-0.688708\pi\)
0.558722 0.829355i \(-0.311292\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.15238 + 1.46666i 0.374681 + 0.255313i
\(34\) 6.68366i 1.14624i
\(35\) 0.248408i 0.0419885i
\(36\) 1.09745 + 2.79206i 0.182908 + 0.465344i
\(37\) 0.665027i 0.109330i 0.998505 + 0.0546649i \(0.0174090\pi\)
−0.998505 + 0.0546649i \(0.982591\pi\)
\(38\) −3.99002 −0.647266
\(39\) 3.65613 5.36550i 0.585449 0.859167i
\(40\) 0.0999120i 0.0157975i
\(41\) 3.99875i 0.624499i 0.950000 + 0.312250i \(0.101083\pi\)
−0.950000 + 0.312250i \(0.898917\pi\)
\(42\) 3.55868 + 2.42494i 0.549116 + 0.374176i
\(43\) 10.0506i 1.53270i −0.642424 0.766349i \(-0.722071\pi\)
0.642424 0.766349i \(-0.277929\pi\)
\(44\) −1.50375 −0.226699
\(45\) −0.278960 + 0.109648i −0.0415850 + 0.0163454i
\(46\) −7.31226 −1.07813
\(47\) 4.30475 0.627913 0.313956 0.949437i \(-0.398345\pi\)
0.313956 + 0.949437i \(0.398345\pi\)
\(48\) −1.43134 0.975334i −0.206596 0.140777i
\(49\) −0.818487 −0.116927
\(50\) −4.99002 −0.705695
\(51\) −6.51880 + 9.56657i −0.912815 + 1.33959i
\(52\) 3.74859i 0.519836i
\(53\) 0.250155i 0.0343614i 0.999852 + 0.0171807i \(0.00546906\pi\)
−0.999852 + 0.0171807i \(0.994531\pi\)
\(54\) −1.15238 + 5.06676i −0.156819 + 0.689498i
\(55\) 0.150243i 0.0202587i
\(56\) −2.48626 −0.332241
\(57\) −5.71106 3.89160i −0.756448 0.515455i
\(58\) 3.18348i 0.418011i
\(59\) 7.65780 0.598474i 0.996960 0.0779147i
\(60\) 0.0974475 0.143008i 0.0125804 0.0184622i
\(61\) 13.2188i 1.69250i 0.532788 + 0.846249i \(0.321144\pi\)
−0.532788 + 0.846249i \(0.678856\pi\)
\(62\) 9.23530i 1.17288i
\(63\) 2.72855 + 6.94181i 0.343764 + 0.874585i
\(64\) 1.00000 0.125000
\(65\) −0.374529 −0.0464546
\(66\) −2.15238 1.46666i −0.264939 0.180533i
\(67\) 7.06709i 0.863382i 0.902022 + 0.431691i \(0.142083\pi\)
−0.902022 + 0.431691i \(0.857917\pi\)
\(68\) 6.68366i 0.810513i
\(69\) −10.4663 7.13189i −1.25999 0.858579i
\(70\) 0.248408i 0.0296904i
\(71\) 10.1991i 1.21041i 0.796071 + 0.605203i \(0.206908\pi\)
−0.796071 + 0.605203i \(0.793092\pi\)
\(72\) −1.09745 2.79206i −0.129335 0.329048i
\(73\) 11.3305i 1.32613i −0.748562 0.663065i \(-0.769255\pi\)
0.748562 0.663065i \(-0.230745\pi\)
\(74\) 0.665027i 0.0773078i
\(75\) −7.14239 4.86693i −0.824733 0.561985i
\(76\) 3.99002 0.457686
\(77\) −3.73873 −0.426068
\(78\) −3.65613 + 5.36550i −0.413975 + 0.607523i
\(79\) −9.13074 −1.02729 −0.513645 0.858003i \(-0.671705\pi\)
−0.513645 + 0.858003i \(0.671705\pi\)
\(80\) 0.0999120i 0.0111705i
\(81\) −6.59122 + 6.12828i −0.732358 + 0.680920i
\(82\) 3.99875i 0.441588i
\(83\) 5.43398 0.596456 0.298228 0.954495i \(-0.403604\pi\)
0.298228 + 0.954495i \(0.403604\pi\)
\(84\) −3.55868 2.42494i −0.388284 0.264582i
\(85\) 0.667778 0.0724307
\(86\) 10.0506i 1.08378i
\(87\) 3.10495 4.55663i 0.332886 0.488522i
\(88\) 1.50375 0.160301
\(89\) −8.23497 −0.872906 −0.436453 0.899727i \(-0.643765\pi\)
−0.436453 + 0.899727i \(0.643765\pi\)
\(90\) 0.278960 0.109648i 0.0294050 0.0115579i
\(91\) 9.31999i 0.977001i
\(92\) 7.31226 0.762356
\(93\) −9.00751 + 13.2188i −0.934035 + 1.37073i
\(94\) −4.30475 −0.444001
\(95\) 0.398650i 0.0409007i
\(96\) 1.43134 + 0.975334i 0.146085 + 0.0995446i
\(97\) 3.83328i 0.389211i −0.980882 0.194605i \(-0.937657\pi\)
0.980882 0.194605i \(-0.0623426\pi\)
\(98\) 0.818487 0.0826797
\(99\) −1.65029 4.19857i −0.165860 0.421972i
\(100\) 4.99002 0.499002
\(101\) −9.73873 −0.969040 −0.484520 0.874780i \(-0.661006\pi\)
−0.484520 + 0.874780i \(0.661006\pi\)
\(102\) 6.51880 9.56657i 0.645458 0.947231i
\(103\) 1.88836i 0.186066i −0.995663 0.0930330i \(-0.970344\pi\)
0.995663 0.0930330i \(-0.0296562\pi\)
\(104\) 3.74859i 0.367580i
\(105\) 0.242280 0.355555i 0.0236441 0.0346986i
\(106\) 0.250155i 0.0242972i
\(107\) 1.98828i 0.192214i 0.995371 + 0.0961069i \(0.0306391\pi\)
−0.995371 + 0.0961069i \(0.969361\pi\)
\(108\) 1.15238 5.06676i 0.110887 0.487549i
\(109\) 9.53579i 0.913363i 0.889630 + 0.456682i \(0.150962\pi\)
−0.889630 + 0.456682i \(0.849038\pi\)
\(110\) 0.150243i 0.0143251i
\(111\) 0.648623 0.951877i 0.0615646 0.0903482i
\(112\) 2.48626 0.234930
\(113\) 13.6203 1.28129 0.640647 0.767836i \(-0.278666\pi\)
0.640647 + 0.767836i \(0.278666\pi\)
\(114\) 5.71106 + 3.89160i 0.534890 + 0.364482i
\(115\) 0.730582i 0.0681271i
\(116\) 3.18348i 0.295578i
\(117\) −10.4663 + 4.11388i −0.967610 + 0.380329i
\(118\) −7.65780 + 0.598474i −0.704957 + 0.0550940i
\(119\) 16.6174i 1.52331i
\(120\) −0.0974475 + 0.143008i −0.00889570 + 0.0130547i
\(121\) −8.73873 −0.794430
\(122\) 13.2188i 1.19678i
\(123\) 3.90011 5.72355i 0.351661 0.516075i
\(124\) 9.23530i 0.829355i
\(125\) 0.998122i 0.0892748i
\(126\) −2.72855 6.94181i −0.243078 0.618425i
\(127\) −1.08727 −0.0964792 −0.0482396 0.998836i \(-0.515361\pi\)
−0.0482396 + 0.998836i \(0.515361\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.80267 + 14.3858i −0.863077 + 1.26659i
\(130\) 0.374529 0.0328484
\(131\) 2.06978 0.180837 0.0904186 0.995904i \(-0.471179\pi\)
0.0904186 + 0.995904i \(0.471179\pi\)
\(132\) 2.15238 + 1.46666i 0.187340 + 0.127656i
\(133\) 9.92024 0.860194
\(134\) 7.06709i 0.610503i
\(135\) 0.506230 + 0.115136i 0.0435693 + 0.00990934i
\(136\) 6.68366i 0.573119i
\(137\) 3.26816i 0.279218i 0.990207 + 0.139609i \(0.0445846\pi\)
−0.990207 + 0.139609i \(0.955415\pi\)
\(138\) 10.4663 + 7.13189i 0.890951 + 0.607107i
\(139\) 16.2500 1.37831 0.689153 0.724616i \(-0.257983\pi\)
0.689153 + 0.724616i \(0.257983\pi\)
\(140\) 0.248408i 0.0209943i
\(141\) −6.16155 4.19857i −0.518896 0.353583i
\(142\) 10.1991i 0.855887i
\(143\) 5.63696i 0.471386i
\(144\) 1.09745 + 2.79206i 0.0914540 + 0.232672i
\(145\) −0.318067 −0.0264141
\(146\) 11.3305i 0.937716i
\(147\) 1.17153 + 0.798298i 0.0966262 + 0.0658425i
\(148\) 0.665027i 0.0546649i
\(149\) 4.42980 0.362904 0.181452 0.983400i \(-0.441920\pi\)
0.181452 + 0.983400i \(0.441920\pi\)
\(150\) 7.14239 + 4.86693i 0.583174 + 0.397383i
\(151\) 12.6194i 1.02695i −0.858105 0.513474i \(-0.828358\pi\)
0.858105 0.513474i \(-0.171642\pi\)
\(152\) −3.99002 −0.323633
\(153\) 18.6612 7.33497i 1.50867 0.592997i
\(154\) 3.73873 0.301275
\(155\) 0.922717 0.0741144
\(156\) 3.65613 5.36550i 0.292725 0.429583i
\(157\) 15.4024i 1.22925i 0.788820 + 0.614624i \(0.210692\pi\)
−0.788820 + 0.614624i \(0.789308\pi\)
\(158\) 9.13074 0.726403
\(159\) 0.243984 0.358056i 0.0193492 0.0283957i
\(160\) 0.0999120i 0.00789873i
\(161\) 18.1802 1.43280
\(162\) 6.59122 6.12828i 0.517855 0.481483i
\(163\) −11.2458 −0.880840 −0.440420 0.897792i \(-0.645170\pi\)
−0.440420 + 0.897792i \(0.645170\pi\)
\(164\) 3.99875i 0.312250i
\(165\) −0.146537 + 0.215048i −0.0114079 + 0.0167415i
\(166\) −5.43398 −0.421758
\(167\) 7.44685i 0.576255i 0.957592 + 0.288127i \(0.0930327\pi\)
−0.957592 + 0.288127i \(0.906967\pi\)
\(168\) 3.55868 + 2.42494i 0.274558 + 0.187088i
\(169\) −1.05194 −0.0809185
\(170\) −0.667778 −0.0512162
\(171\) 4.37883 + 11.1404i 0.334858 + 0.851926i
\(172\) 10.0506i 0.766349i
\(173\) 1.87828 0.142803 0.0714016 0.997448i \(-0.477253\pi\)
0.0714016 + 0.997448i \(0.477253\pi\)
\(174\) −3.10495 + 4.55663i −0.235386 + 0.345437i
\(175\) 12.4065 0.937844
\(176\) −1.50375 −0.113350
\(177\) −11.5446 6.61229i −0.867745 0.497010i
\(178\) 8.23497 0.617237
\(179\) −14.4415 −1.07941 −0.539703 0.841855i \(-0.681464\pi\)
−0.539703 + 0.841855i \(0.681464\pi\)
\(180\) −0.278960 + 0.109648i −0.0207925 + 0.00817269i
\(181\) −19.5756 −1.45504 −0.727520 0.686087i \(-0.759327\pi\)
−0.727520 + 0.686087i \(0.759327\pi\)
\(182\) 9.31999i 0.690844i
\(183\) 12.8928 18.9206i 0.953061 1.39865i
\(184\) −7.31226 −0.539067
\(185\) −0.0664441 −0.00488507
\(186\) 9.00751 13.2188i 0.660462 0.969251i
\(187\) 10.0506i 0.734971i
\(188\) 4.30475 0.313956
\(189\) 2.86511 12.5973i 0.208406 0.916319i
\(190\) 0.398650i 0.0289211i
\(191\) −2.00333 −0.144956 −0.0724780 0.997370i \(-0.523091\pi\)
−0.0724780 + 0.997370i \(0.523091\pi\)
\(192\) −1.43134 0.975334i −0.103298 0.0703887i
\(193\) 6.79102 0.488828 0.244414 0.969671i \(-0.421404\pi\)
0.244414 + 0.969671i \(0.421404\pi\)
\(194\) 3.83328i 0.275213i
\(195\) 0.536077 + 0.365291i 0.0383893 + 0.0261590i
\(196\) −0.818487 −0.0584634
\(197\) 3.36517i 0.239758i −0.992789 0.119879i \(-0.961749\pi\)
0.992789 0.119879i \(-0.0382507\pi\)
\(198\) 1.65029 + 4.19857i 0.117281 + 0.298379i
\(199\) −12.2483 −0.868258 −0.434129 0.900851i \(-0.642944\pi\)
−0.434129 + 0.900851i \(0.642944\pi\)
\(200\) −4.99002 −0.352848
\(201\) 6.89277 10.1154i 0.486179 0.713484i
\(202\) 9.73873 0.685214
\(203\) 7.91497i 0.555522i
\(204\) −6.51880 + 9.56657i −0.456407 + 0.669794i
\(205\) −0.399523 −0.0279039
\(206\) 1.88836i 0.131569i
\(207\) 8.02482 + 20.4163i 0.557763 + 1.41903i
\(208\) 3.74859i 0.259918i
\(209\) −6.00000 −0.415029
\(210\) −0.242280 + 0.355555i −0.0167189 + 0.0245356i
\(211\) 2.12329i 0.146174i 0.997326 + 0.0730868i \(0.0232850\pi\)
−0.997326 + 0.0730868i \(0.976715\pi\)
\(212\) 0.250155i 0.0171807i
\(213\) 9.94750 14.5983i 0.681591 1.00026i
\(214\) 1.98828i 0.135916i
\(215\) 1.00417 0.0684840
\(216\) −1.15238 + 5.06676i −0.0784093 + 0.344749i
\(217\) 22.9614i 1.55872i
\(218\) 9.53579i 0.645845i
\(219\) −11.0510 + 16.2177i −0.746756 + 1.09589i
\(220\) 0.150243i 0.0101294i
\(221\) 25.0543 1.68534
\(222\) −0.648623 + 0.951877i −0.0435327 + 0.0638858i
\(223\) 5.17553 0.346579 0.173290 0.984871i \(-0.444560\pi\)
0.173290 + 0.984871i \(0.444560\pi\)
\(224\) −2.48626 −0.166121
\(225\) 5.47628 + 13.9324i 0.365085 + 0.928829i
\(226\) −13.6203 −0.906012
\(227\) −29.3591 −1.94863 −0.974315 0.225190i \(-0.927700\pi\)
−0.974315 + 0.225190i \(0.927700\pi\)
\(228\) −5.71106 3.89160i −0.378224 0.257727i
\(229\) 7.00153i 0.462674i −0.972874 0.231337i \(-0.925690\pi\)
0.972874 0.231337i \(-0.0743100\pi\)
\(230\) 0.730582i 0.0481731i
\(231\) 5.35138 + 3.64651i 0.352095 + 0.239923i
\(232\) 3.18348i 0.209006i
\(233\) −24.8628 −1.62882 −0.814409 0.580292i \(-0.802939\pi\)
−0.814409 + 0.580292i \(0.802939\pi\)
\(234\) 10.4663 4.11388i 0.684203 0.268933i
\(235\) 0.430096i 0.0280564i
\(236\) 7.65780 0.598474i 0.498480 0.0389574i
\(237\) 13.0692 + 8.90552i 0.848934 + 0.578476i
\(238\) 16.6174i 1.07714i
\(239\) 3.43288i 0.222055i −0.993817 0.111027i \(-0.964586\pi\)
0.993817 0.111027i \(-0.0354141\pi\)
\(240\) 0.0974475 0.143008i 0.00629021 0.00923110i
\(241\) 8.12675 0.523490 0.261745 0.965137i \(-0.415702\pi\)
0.261745 + 0.965137i \(0.415702\pi\)
\(242\) 8.73873 0.561747
\(243\) 15.4114 2.34300i 0.988640 0.150303i
\(244\) 13.2188i 0.846249i
\(245\) 0.0817767i 0.00522452i
\(246\) −3.90011 + 5.72355i −0.248662 + 0.364920i
\(247\) 14.9569i 0.951688i
\(248\) 9.23530i 0.586442i
\(249\) −7.77785 5.29994i −0.492901 0.335870i
\(250\) 0.998122i 0.0631268i
\(251\) 19.2860i 1.21732i −0.793429 0.608662i \(-0.791706\pi\)
0.793429 0.608662i \(-0.208294\pi\)
\(252\) 2.72855 + 6.94181i 0.171882 + 0.437293i
\(253\) −10.9958 −0.691302
\(254\) 1.08727 0.0682211
\(255\) −0.955814 0.651306i −0.0598554 0.0407864i
\(256\) 1.00000 0.0625000
\(257\) 31.2661i 1.95033i −0.221483 0.975164i \(-0.571090\pi\)
0.221483 0.975164i \(-0.428910\pi\)
\(258\) 9.80267 14.3858i 0.610287 0.895618i
\(259\) 1.65343i 0.102739i
\(260\) −0.374529 −0.0232273
\(261\) −8.88846 + 3.49370i −0.550182 + 0.216255i
\(262\) −2.06978 −0.127871
\(263\) 21.5816i 1.33078i −0.746496 0.665390i \(-0.768265\pi\)
0.746496 0.665390i \(-0.231735\pi\)
\(264\) −2.15238 1.46666i −0.132470 0.0902667i
\(265\) −0.0249935 −0.00153534
\(266\) −9.92024 −0.608249
\(267\) 11.7870 + 8.03185i 0.721354 + 0.491541i
\(268\) 7.06709i 0.431691i
\(269\) 1.12922 0.0688500 0.0344250 0.999407i \(-0.489040\pi\)
0.0344250 + 0.999407i \(0.489040\pi\)
\(270\) −0.506230 0.115136i −0.0308082 0.00700696i
\(271\) −1.65329 −0.100430 −0.0502151 0.998738i \(-0.515991\pi\)
−0.0502151 + 0.998738i \(0.515991\pi\)
\(272\) 6.68366i 0.405256i
\(273\) 9.09010 13.3400i 0.550158 0.807376i
\(274\) 3.26816i 0.197437i
\(275\) −7.50375 −0.452493
\(276\) −10.4663 7.13189i −0.629997 0.429289i
\(277\) 2.31824 0.139290 0.0696448 0.997572i \(-0.477813\pi\)
0.0696448 + 0.997572i \(0.477813\pi\)
\(278\) −16.2500 −0.974609
\(279\) 25.7855 10.1353i 1.54374 0.606782i
\(280\) 0.248408i 0.0148452i
\(281\) 23.6300i 1.40965i 0.709381 + 0.704825i \(0.248974\pi\)
−0.709381 + 0.704825i \(0.751026\pi\)
\(282\) 6.16155 + 4.19857i 0.366915 + 0.250021i
\(283\) 23.8843i 1.41977i −0.704317 0.709886i \(-0.748746\pi\)
0.704317 0.709886i \(-0.251254\pi\)
\(284\) 10.1991i 0.605203i
\(285\) 0.388817 0.570603i 0.0230316 0.0337996i
\(286\) 5.63696i 0.333320i
\(287\) 9.94194i 0.586854i
\(288\) −1.09745 2.79206i −0.0646677 0.164524i
\(289\) −27.6713 −1.62773
\(290\) 0.318067 0.0186776
\(291\) −3.73873 + 5.48671i −0.219168 + 0.321637i
\(292\) 11.3305i 0.663065i
\(293\) 6.61014i 0.386168i −0.981182 0.193084i \(-0.938151\pi\)
0.981182 0.193084i \(-0.0618490\pi\)
\(294\) −1.17153 0.798298i −0.0683250 0.0465577i
\(295\) 0.0597947 + 0.765105i 0.00348138 + 0.0445462i
\(296\) 0.665027i 0.0386539i
\(297\) −1.73289 + 7.61915i −0.100552 + 0.442108i
\(298\) −4.42980 −0.256612
\(299\) 27.4107i 1.58520i
\(300\) −7.14239 4.86693i −0.412366 0.280993i
\(301\) 24.9884i 1.44031i
\(302\) 12.6194i 0.726162i
\(303\) 13.9394 + 9.49851i 0.800797 + 0.545675i
\(304\) 3.99002 0.228843
\(305\) −1.32072 −0.0756241
\(306\) −18.6612 + 7.33497i −1.06679 + 0.419312i
\(307\) −27.6453 −1.57780 −0.788901 0.614520i \(-0.789350\pi\)
−0.788901 + 0.614520i \(0.789350\pi\)
\(308\) −3.73873 −0.213034
\(309\) −1.84178 + 2.70288i −0.104775 + 0.153762i
\(310\) −0.922717 −0.0524068
\(311\) 23.5349i 1.33454i 0.744814 + 0.667272i \(0.232538\pi\)
−0.744814 + 0.667272i \(0.767462\pi\)
\(312\) −3.65613 + 5.36550i −0.206988 + 0.303761i
\(313\) 26.8677i 1.51866i 0.650709 + 0.759328i \(0.274472\pi\)
−0.650709 + 0.759328i \(0.725528\pi\)
\(314\) 15.4024i 0.869210i
\(315\) −0.693569 + 0.272614i −0.0390782 + 0.0153601i
\(316\) −9.13074 −0.513645
\(317\) 32.1230i 1.80421i 0.431518 + 0.902104i \(0.357978\pi\)
−0.431518 + 0.902104i \(0.642022\pi\)
\(318\) −0.243984 + 0.358056i −0.0136820 + 0.0200788i
\(319\) 4.78716i 0.268030i
\(320\) 0.0999120i 0.00558525i
\(321\) 1.93923 2.84589i 0.108237 0.158842i
\(322\) −18.1802 −1.01314
\(323\) 26.6679i 1.48384i
\(324\) −6.59122 + 6.12828i −0.366179 + 0.340460i
\(325\) 18.7055i 1.03760i
\(326\) 11.2458 0.622848
\(327\) 9.30058 13.6489i 0.514323 0.754787i
\(328\) 3.99875i 0.220794i
\(329\) 10.7028 0.590062
\(330\) 0.146537 0.215048i 0.00806660 0.0118380i
\(331\) −19.7922 −1.08788 −0.543939 0.839125i \(-0.683068\pi\)
−0.543939 + 0.839125i \(0.683068\pi\)
\(332\) 5.43398 0.298228
\(333\) −1.85680 + 0.729832i −0.101752 + 0.0399946i
\(334\) 7.44685i 0.407474i
\(335\) −0.706087 −0.0385776
\(336\) −3.55868 2.42494i −0.194142 0.132291i
\(337\) 13.2034i 0.719237i 0.933099 + 0.359618i \(0.117093\pi\)
−0.933099 + 0.359618i \(0.882907\pi\)
\(338\) 1.05194 0.0572180
\(339\) −19.4953 13.2844i −1.05884 0.721509i
\(340\) 0.667778 0.0362153
\(341\) 13.8876i 0.752056i
\(342\) −4.37883 11.1404i −0.236780 0.602403i
\(343\) −19.4388 −1.04960
\(344\) 10.0506i 0.541891i
\(345\) 0.712561 1.04571i 0.0383630 0.0562991i
\(346\) −1.87828 −0.100977
\(347\) −22.1634 −1.18979 −0.594897 0.803802i \(-0.702807\pi\)
−0.594897 + 0.803802i \(0.702807\pi\)
\(348\) 3.10495 4.55663i 0.166443 0.244261i
\(349\) 4.57136i 0.244700i −0.992487 0.122350i \(-0.960957\pi\)
0.992487 0.122350i \(-0.0390430\pi\)
\(350\) −12.4065 −0.663156
\(351\) 18.9932 + 4.31979i 1.01378 + 0.230573i
\(352\) 1.50375 0.0801503
\(353\) 15.9218 0.847430 0.423715 0.905796i \(-0.360726\pi\)
0.423715 + 0.905796i \(0.360726\pi\)
\(354\) 11.5446 + 6.61229i 0.613588 + 0.351439i
\(355\) −1.01901 −0.0540834
\(356\) −8.23497 −0.436453
\(357\) −16.2075 + 23.7850i −0.857790 + 1.25884i
\(358\) 14.4415 0.763256
\(359\) 37.7987i 1.99494i 0.0710832 + 0.997470i \(0.477354\pi\)
−0.0710832 + 0.997470i \(0.522646\pi\)
\(360\) 0.278960 0.109648i 0.0147025 0.00577896i
\(361\) −3.07976 −0.162093
\(362\) 19.5756 1.02887
\(363\) 12.5081 + 8.52318i 0.656503 + 0.447351i
\(364\) 9.31999i 0.488500i
\(365\) 1.13205 0.0592541
\(366\) −12.8928 + 18.9206i −0.673916 + 0.988995i
\(367\) 14.5489i 0.759445i 0.925100 + 0.379723i \(0.123981\pi\)
−0.925100 + 0.379723i \(0.876019\pi\)
\(368\) 7.31226 0.381178
\(369\) −11.1647 + 4.38841i −0.581214 + 0.228452i
\(370\) 0.0664441 0.00345427
\(371\) 0.621951i 0.0322901i
\(372\) −9.00751 + 13.2188i −0.467017 + 0.685364i
\(373\) 20.4733 1.06007 0.530033 0.847977i \(-0.322179\pi\)
0.530033 + 0.847977i \(0.322179\pi\)
\(374\) 10.0506i 0.519703i
\(375\) 0.973502 1.42865i 0.0502714 0.0737751i
\(376\) −4.30475 −0.222001
\(377\) −11.9336 −0.614609
\(378\) −2.86511 + 12.5973i −0.147365 + 0.647935i
\(379\) −11.5722 −0.594425 −0.297213 0.954811i \(-0.596057\pi\)
−0.297213 + 0.954811i \(0.596057\pi\)
\(380\) 0.398650i 0.0204503i
\(381\) 1.55624 + 1.06045i 0.0797287 + 0.0543283i
\(382\) 2.00333 0.102499
\(383\) 10.0251i 0.512256i −0.966643 0.256128i \(-0.917553\pi\)
0.966643 0.256128i \(-0.0824469\pi\)
\(384\) 1.43134 + 0.975334i 0.0730426 + 0.0497723i
\(385\) 0.373544i 0.0190375i
\(386\) −6.79102 −0.345654
\(387\) 28.0618 11.0300i 1.42646 0.560685i
\(388\) 3.83328i 0.194605i
\(389\) 29.0531i 1.47305i −0.676410 0.736525i \(-0.736465\pi\)
0.676410 0.736525i \(-0.263535\pi\)
\(390\) −0.536077 0.365291i −0.0271453 0.0184972i
\(391\) 48.8727i 2.47160i
\(392\) 0.818487 0.0413398
\(393\) −2.96255 2.01872i −0.149441 0.101831i
\(394\) 3.36517i 0.169535i
\(395\) 0.912271i 0.0459013i
\(396\) −1.65029 4.19857i −0.0829302 0.210986i
\(397\) 37.9877i 1.90655i −0.302109 0.953273i \(-0.597691\pi\)
0.302109 0.953273i \(-0.402309\pi\)
\(398\) 12.2483 0.613951
\(399\) −14.1992 9.67555i −0.710849 0.484383i
\(400\) 4.99002 0.249501
\(401\) 5.22747 0.261047 0.130524 0.991445i \(-0.458334\pi\)
0.130524 + 0.991445i \(0.458334\pi\)
\(402\) −6.89277 + 10.1154i −0.343780 + 0.504509i
\(403\) 34.6194 1.72451
\(404\) −9.73873 −0.484520
\(405\) −0.612289 0.658541i −0.0304249 0.0327232i
\(406\) 7.91497i 0.392813i
\(407\) 1.00004i 0.0495699i
\(408\) 6.51880 9.56657i 0.322729 0.473616i
\(409\) 19.5017i 0.964296i 0.876090 + 0.482148i \(0.160143\pi\)
−0.876090 + 0.482148i \(0.839857\pi\)
\(410\) 0.399523 0.0197310
\(411\) 3.18755 4.67784i 0.157230 0.230741i
\(412\) 1.88836i 0.0930330i
\(413\) 19.0393 1.48797i 0.936863 0.0732180i
\(414\) −8.02482 20.4163i −0.394398 1.00341i
\(415\) 0.542919i 0.0266509i
\(416\) 3.74859i 0.183790i
\(417\) −23.2592 15.8492i −1.13901 0.776137i
\(418\) 6.00000 0.293470
\(419\) 28.2270 1.37898 0.689490 0.724295i \(-0.257835\pi\)
0.689490 + 0.724295i \(0.257835\pi\)
\(420\) 0.242280 0.355555i 0.0118221 0.0173493i
\(421\) 12.3690i 0.602830i −0.953493 0.301415i \(-0.902541\pi\)
0.953493 0.301415i \(-0.0974589\pi\)
\(422\) 2.12329i 0.103360i
\(423\) 4.72424 + 12.0191i 0.229700 + 0.584390i
\(424\) 0.250155i 0.0121486i
\(425\) 33.3516i 1.61779i
\(426\) −9.94750 + 14.5983i −0.481958 + 0.707290i
\(427\) 32.8655i 1.59047i
\(428\) 1.98828i 0.0961069i
\(429\) −5.49791 + 8.06838i −0.265442 + 0.389545i
\(430\) −1.00417 −0.0484255
\(431\) −15.4958 −0.746406 −0.373203 0.927750i \(-0.621741\pi\)
−0.373203 + 0.927750i \(0.621741\pi\)
\(432\) 1.15238 5.06676i 0.0554437 0.243774i
\(433\) 24.9628 1.19963 0.599817 0.800137i \(-0.295240\pi\)
0.599817 + 0.800137i \(0.295240\pi\)
\(434\) 22.9614i 1.10218i
\(435\) 0.455261 + 0.310222i 0.0218281 + 0.0148740i
\(436\) 9.53579i 0.456682i
\(437\) 29.1760 1.39568
\(438\) 11.0510 16.2177i 0.528036 0.774912i
\(439\) 40.6897 1.94201 0.971006 0.239055i \(-0.0768376\pi\)
0.971006 + 0.239055i \(0.0768376\pi\)
\(440\) 0.150243i 0.00716255i
\(441\) −0.898247 2.28527i −0.0427737 0.108822i
\(442\) −25.0543 −1.19171
\(443\) −32.3516 −1.53707 −0.768535 0.639808i \(-0.779014\pi\)
−0.768535 + 0.639808i \(0.779014\pi\)
\(444\) 0.648623 0.951877i 0.0307823 0.0451741i
\(445\) 0.822772i 0.0390032i
\(446\) −5.17553 −0.245068
\(447\) −6.34054 4.32054i −0.299897 0.204354i
\(448\) 2.48626 0.117465
\(449\) 29.6661i 1.40003i 0.714129 + 0.700014i \(0.246823\pi\)
−0.714129 + 0.700014i \(0.753177\pi\)
\(450\) −5.47628 13.9324i −0.258154 0.656781i
\(451\) 6.01313i 0.283147i
\(452\) 13.6203 0.640647
\(453\) −12.3081 + 18.0625i −0.578284 + 0.848652i
\(454\) 29.3591 1.37789
\(455\) −0.931179 −0.0436543
\(456\) 5.71106 + 3.89160i 0.267445 + 0.182241i
\(457\) 15.2368i 0.712747i −0.934343 0.356374i \(-0.884013\pi\)
0.934343 0.356374i \(-0.115987\pi\)
\(458\) 7.00153i 0.327160i
\(459\) −33.8645 7.70209i −1.58066 0.359503i
\(460\) 0.730582i 0.0340636i
\(461\) 19.8024i 0.922290i −0.887325 0.461145i \(-0.847439\pi\)
0.887325 0.461145i \(-0.152561\pi\)
\(462\) −5.35138 3.64651i −0.248969 0.169651i
\(463\) 22.7494i 1.05725i 0.848854 + 0.528627i \(0.177293\pi\)
−0.848854 + 0.528627i \(0.822707\pi\)
\(464\) 3.18348i 0.147789i
\(465\) −1.32072 0.899957i −0.0612469 0.0417345i
\(466\) 24.8628 1.15175
\(467\) −10.9522 −0.506809 −0.253404 0.967360i \(-0.581550\pi\)
−0.253404 + 0.967360i \(0.581550\pi\)
\(468\) −10.4663 + 4.11388i −0.483805 + 0.190164i
\(469\) 17.5707i 0.811337i
\(470\) 0.430096i 0.0198389i
\(471\) 15.0225 22.0461i 0.692201 1.01583i
\(472\) −7.65780 + 0.598474i −0.352479 + 0.0275470i
\(473\) 15.1136i 0.694923i
\(474\) −13.0692 8.90552i −0.600287 0.409044i
\(475\) 19.9103 0.913545
\(476\) 16.6174i 0.761655i
\(477\) −0.698448 + 0.274532i −0.0319797 + 0.0125699i
\(478\) 3.43288i 0.157016i
\(479\) 29.5038i 1.34806i −0.738702 0.674032i \(-0.764561\pi\)
0.738702 0.674032i \(-0.235439\pi\)
\(480\) −0.0974475 + 0.143008i −0.00444785 + 0.00652737i
\(481\) −2.49291 −0.113667
\(482\) −8.12675 −0.370163
\(483\) −26.0220 17.7318i −1.18404 0.806824i
\(484\) −8.73873 −0.397215
\(485\) 0.382990 0.0173907
\(486\) −15.4114 + 2.34300i −0.699074 + 0.106280i
\(487\) 14.4863 0.656435 0.328218 0.944602i \(-0.393552\pi\)
0.328218 + 0.944602i \(0.393552\pi\)
\(488\) 13.2188i 0.598388i
\(489\) 16.0965 + 10.9684i 0.727911 + 0.496009i
\(490\) 0.0817767i 0.00369429i
\(491\) 18.1129i 0.817423i −0.912664 0.408711i \(-0.865978\pi\)
0.912664 0.408711i \(-0.134022\pi\)
\(492\) 3.90011 5.72355i 0.175831 0.258038i
\(493\) 21.2773 0.958281
\(494\) 14.9569i 0.672945i
\(495\) 0.419487 0.164884i 0.0188546 0.00741097i
\(496\) 9.23530i 0.414677i
\(497\) 25.3576i 1.13744i
\(498\) 7.77785 + 5.29994i 0.348534 + 0.237496i
\(499\) 21.6305 0.968314 0.484157 0.874981i \(-0.339126\pi\)
0.484157 + 0.874981i \(0.339126\pi\)
\(500\) 0.998122i 0.0446374i
\(501\) 7.26317 10.6590i 0.324494 0.476207i
\(502\) 19.2860i 0.860778i
\(503\) 34.7181 1.54801 0.774003 0.633182i \(-0.218252\pi\)
0.774003 + 0.633182i \(0.218252\pi\)
\(504\) −2.72855 6.94181i −0.121539 0.309213i
\(505\) 0.973015i 0.0432986i
\(506\) 10.9958 0.488824
\(507\) 1.50568 + 1.02599i 0.0668697 + 0.0455660i
\(508\) −1.08727 −0.0482396
\(509\) 40.8081 1.80879 0.904393 0.426701i \(-0.140324\pi\)
0.904393 + 0.426701i \(0.140324\pi\)
\(510\) 0.955814 + 0.651306i 0.0423242 + 0.0288403i
\(511\) 28.1705i 1.24619i
\(512\) −1.00000 −0.0441942
\(513\) 4.59800 20.2165i 0.203007 0.892578i
\(514\) 31.2661i 1.37909i
\(515\) 0.188670 0.00831380
\(516\) −9.80267 + 14.3858i −0.431538 + 0.633297i
\(517\) −6.47328 −0.284695
\(518\) 1.65343i 0.0726477i
\(519\) −2.68845 1.83195i −0.118010 0.0804138i
\(520\) 0.374529 0.0164242
\(521\) 19.7972i 0.867330i −0.901074 0.433665i \(-0.857220\pi\)
0.901074 0.433665i \(-0.142780\pi\)
\(522\) 8.88846 3.49370i 0.389038 0.152915i
\(523\) −28.8761 −1.26267 −0.631333 0.775512i \(-0.717492\pi\)
−0.631333 + 0.775512i \(0.717492\pi\)
\(524\) 2.06978 0.0904186
\(525\) −17.7579 12.1005i −0.775018 0.528108i
\(526\) 21.5816i 0.941003i
\(527\) −61.7256 −2.68881
\(528\) 2.15238 + 1.46666i 0.0936701 + 0.0638282i
\(529\) 30.4691 1.32474
\(530\) 0.0249935 0.00108565
\(531\) 10.0750 + 20.7242i 0.437218 + 0.899356i
\(532\) 9.92024 0.430097
\(533\) −14.9897 −0.649275
\(534\) −11.7870 8.03185i −0.510074 0.347572i
\(535\) −0.198652 −0.00858850
\(536\) 7.06709i 0.305252i
\(537\) 20.6706 + 14.0853i 0.892003 + 0.607824i
\(538\) −1.12922 −0.0486843
\(539\) 1.23080 0.0530144
\(540\) 0.506230 + 0.115136i 0.0217847 + 0.00495467i
\(541\) 8.25440i 0.354884i 0.984131 + 0.177442i \(0.0567823\pi\)
−0.984131 + 0.177442i \(0.943218\pi\)
\(542\) 1.65329 0.0710149
\(543\) 28.0192 + 19.0927i 1.20242 + 0.819346i
\(544\) 6.68366i 0.286560i
\(545\) −0.952739 −0.0408109
\(546\) −9.09010 + 13.3400i −0.389021 + 0.570901i
\(547\) −11.9184 −0.509595 −0.254798 0.966994i \(-0.582009\pi\)
−0.254798 + 0.966994i \(0.582009\pi\)
\(548\) 3.26816i 0.139609i
\(549\) −36.9078 + 14.5070i −1.57519 + 0.619142i
\(550\) 7.50375 0.319961
\(551\) 12.7021i 0.541129i
\(552\) 10.4663 + 7.13189i 0.445475 + 0.303554i
\(553\) −22.7014 −0.965364
\(554\) −2.31824 −0.0984927
\(555\) 0.0951039 + 0.0648052i 0.00403694 + 0.00275083i
\(556\) 16.2500 0.689153
\(557\) 39.6450i 1.67981i −0.542731 0.839907i \(-0.682610\pi\)
0.542731 0.839907i \(-0.317390\pi\)
\(558\) −25.7855 + 10.1353i −1.09159 + 0.429060i
\(559\) 37.6755 1.59350
\(560\) 0.248408i 0.0104971i
\(561\) 9.80267 14.3858i 0.413869 0.607367i
\(562\) 23.6300i 0.996773i
\(563\) −13.2738 −0.559423 −0.279711 0.960084i \(-0.590239\pi\)
−0.279711 + 0.960084i \(0.590239\pi\)
\(564\) −6.16155 4.19857i −0.259448 0.176792i
\(565\) 1.36084i 0.0572508i
\(566\) 23.8843i 1.00393i
\(567\) −16.3875 + 15.2365i −0.688211 + 0.639874i
\(568\) 10.1991i 0.427943i
\(569\) −36.7964 −1.54258 −0.771292 0.636481i \(-0.780389\pi\)
−0.771292 + 0.636481i \(0.780389\pi\)
\(570\) −0.388817 + 0.570603i −0.0162858 + 0.0238999i
\(571\) 35.3960i 1.48128i 0.671904 + 0.740638i \(0.265477\pi\)
−0.671904 + 0.740638i \(0.734523\pi\)
\(572\) 5.63696i 0.235693i
\(573\) 2.86744 + 1.95392i 0.119789 + 0.0816261i
\(574\) 9.94194i 0.414969i
\(575\) 36.4883 1.52167
\(576\) 1.09745 + 2.79206i 0.0457270 + 0.116336i
\(577\) −6.36488 −0.264973 −0.132487 0.991185i \(-0.542296\pi\)
−0.132487 + 0.991185i \(0.542296\pi\)
\(578\) 27.6713 1.15098
\(579\) −9.72023 6.62351i −0.403959 0.275264i
\(580\) −0.318067 −0.0132070
\(581\) 13.5103 0.560502
\(582\) 3.73873 5.48671i 0.154975 0.227432i
\(583\) 0.376171i 0.0155794i
\(584\) 11.3305i 0.468858i
\(585\) −0.411026 1.04571i −0.0169938 0.0432347i
\(586\) 6.61014i 0.273062i
\(587\) −33.9804 −1.40252 −0.701260 0.712906i \(-0.747379\pi\)
−0.701260 + 0.712906i \(0.747379\pi\)
\(588\) 1.17153 + 0.798298i 0.0483131 + 0.0329213i
\(589\) 36.8490i 1.51834i
\(590\) −0.0597947 0.765105i −0.00246171 0.0314989i
\(591\) −3.28216 + 4.81668i −0.135010 + 0.198132i
\(592\) 0.665027i 0.0273324i
\(593\) 18.0122i 0.739673i 0.929097 + 0.369836i \(0.120586\pi\)
−0.929097 + 0.369836i \(0.879414\pi\)
\(594\) 1.73289 7.61915i 0.0711013 0.312618i
\(595\) 1.66027 0.0680645
\(596\) 4.42980 0.181452
\(597\) 17.5314 + 11.9462i 0.717513 + 0.488924i
\(598\) 27.4107i 1.12091i
\(599\) 8.90046i 0.363663i −0.983330 0.181832i \(-0.941797\pi\)
0.983330 0.181832i \(-0.0582025\pi\)
\(600\) 7.14239 + 4.86693i 0.291587 + 0.198692i
\(601\) 23.4646i 0.957140i 0.878050 + 0.478570i \(0.158845\pi\)
−0.878050 + 0.478570i \(0.841155\pi\)
\(602\) 24.9884i 1.01845i
\(603\) −19.7317 + 7.75576i −0.803539 + 0.315839i
\(604\) 12.6194i 0.513474i
\(605\) 0.873103i 0.0354967i
\(606\) −13.9394 9.49851i −0.566249 0.385851i
\(607\) −32.2918 −1.31068 −0.655341 0.755333i \(-0.727475\pi\)
−0.655341 + 0.755333i \(0.727475\pi\)
\(608\) −3.99002 −0.161817
\(609\) 7.71974 11.3290i 0.312819 0.459073i
\(610\) 1.32072 0.0534743
\(611\) 16.1368i 0.652823i
\(612\) 18.6612 7.33497i 0.754334 0.296498i
\(613\) 13.0996i 0.529088i 0.964374 + 0.264544i \(0.0852215\pi\)
−0.964374 + 0.264544i \(0.914778\pi\)
\(614\) 27.6453 1.11567
\(615\) 0.571851 + 0.389668i 0.0230593 + 0.0157129i
\(616\) 3.73873 0.150638
\(617\) 24.6994i 0.994359i 0.867648 + 0.497180i \(0.165631\pi\)
−0.867648 + 0.497180i \(0.834369\pi\)
\(618\) 1.84178 2.70288i 0.0740875 0.108726i
\(619\) 14.6113 0.587278 0.293639 0.955916i \(-0.405134\pi\)
0.293639 + 0.955916i \(0.405134\pi\)
\(620\) 0.922717 0.0370572
\(621\) 8.42647 37.0494i 0.338143 1.48674i
\(622\) 23.5349i 0.943665i
\(623\) −20.4743 −0.820287
\(624\) 3.65613 5.36550i 0.146362 0.214792i
\(625\) 24.8504 0.994015
\(626\) 26.8677i 1.07385i
\(627\) 8.58802 + 5.85200i 0.342972 + 0.233707i
\(628\) 15.4024i 0.614624i
\(629\) 4.44481 0.177226
\(630\) 0.693569 0.272614i 0.0276325 0.0108612i
\(631\) −22.1980 −0.883690 −0.441845 0.897091i \(-0.645676\pi\)
−0.441845 + 0.897091i \(0.645676\pi\)
\(632\) 9.13074 0.363202
\(633\) 2.07092 3.03915i 0.0823117 0.120795i
\(634\) 32.1230i 1.27577i
\(635\) 0.108631i 0.00431088i
\(636\) 0.243984 0.358056i 0.00967461 0.0141978i
\(637\) 3.06817i 0.121565i
\(638\) 4.78716i 0.189526i
\(639\) −28.4764 + 11.1929i −1.12651 + 0.442786i
\(640\) 0.0999120i 0.00394937i
\(641\) 7.03082i 0.277701i 0.990313 + 0.138850i \(0.0443407\pi\)
−0.990313 + 0.138850i \(0.955659\pi\)
\(642\) −1.93923 + 2.84589i −0.0765354 + 0.112318i
\(643\) 16.0565 0.633205 0.316603 0.948558i \(-0.397458\pi\)
0.316603 + 0.948558i \(0.397458\pi\)
\(644\) 18.1802 0.716401
\(645\) −1.43731 0.979404i −0.0565940 0.0385640i
\(646\) 26.6679i 1.04924i
\(647\) 22.9346i 0.901651i −0.892612 0.450825i \(-0.851130\pi\)
0.892612 0.450825i \(-0.148870\pi\)
\(648\) 6.59122 6.12828i 0.258927 0.240742i
\(649\) −11.5154 + 0.899957i −0.452020 + 0.0353264i
\(650\) 18.7055i 0.733692i
\(651\) −22.3950 + 32.8655i −0.877731 + 1.28810i
\(652\) −11.2458 −0.440420
\(653\) 32.5353i 1.27321i 0.771192 + 0.636603i \(0.219661\pi\)
−0.771192 + 0.636603i \(0.780339\pi\)
\(654\) −9.30058 + 13.6489i −0.363681 + 0.533715i
\(655\) 0.206795i 0.00808017i
\(656\) 3.99875i 0.156125i
\(657\) 31.6354 12.4346i 1.23421 0.485120i
\(658\) −10.7028 −0.417237
\(659\) −20.1685 −0.785654 −0.392827 0.919612i \(-0.628503\pi\)
−0.392827 + 0.919612i \(0.628503\pi\)
\(660\) −0.146537 + 0.215048i −0.00570394 + 0.00837074i
\(661\) 1.93525 0.0752726 0.0376363 0.999292i \(-0.488017\pi\)
0.0376363 + 0.999292i \(0.488017\pi\)
\(662\) 19.7922 0.769245
\(663\) −35.8612 24.4363i −1.39273 0.949028i
\(664\) −5.43398 −0.210879
\(665\) 0.991151i 0.0384352i
\(666\) 1.85680 0.729832i 0.0719494 0.0282804i
\(667\) 23.2784i 0.901343i
\(668\) 7.44685i 0.288127i
\(669\) −7.40792 5.04787i −0.286407 0.195162i
\(670\) 0.706087 0.0272785
\(671\) 19.8778i 0.767376i
\(672\) 3.55868 + 2.42494i 0.137279 + 0.0935440i
\(673\) 16.8416i 0.649195i −0.945852 0.324597i \(-0.894771\pi\)
0.945852 0.324597i \(-0.105229\pi\)
\(674\) 13.2034i 0.508577i
\(675\) 5.75038 25.2832i 0.221332 0.973151i
\(676\) −1.05194 −0.0404593
\(677\) 30.0998i 1.15683i 0.815743 + 0.578415i \(0.196328\pi\)
−0.815743 + 0.578415i \(0.803672\pi\)
\(678\) 19.4953 + 13.2844i 0.748712 + 0.510184i
\(679\) 9.53055i 0.365749i
\(680\) −0.667778 −0.0256081
\(681\) 42.0227 + 28.6349i 1.61031 + 1.09729i
\(682\) 13.8876i 0.531784i
\(683\) 20.1948 0.772734 0.386367 0.922345i \(-0.373730\pi\)
0.386367 + 0.922345i \(0.373730\pi\)
\(684\) 4.37883 + 11.1404i 0.167429 + 0.425963i
\(685\) −0.326529 −0.0124760
\(686\) 19.4388 0.742178
\(687\) −6.82883 + 10.0215i −0.260536 + 0.382346i
\(688\) 10.0506i 0.383175i
\(689\) −0.937728 −0.0357246
\(690\) −0.712561 + 1.04571i −0.0271267 + 0.0398094i
\(691\) 33.9577i 1.29181i 0.763417 + 0.645906i \(0.223520\pi\)
−0.763417 + 0.645906i \(0.776480\pi\)
\(692\) 1.87828 0.0714016
\(693\) −4.10306 10.4388i −0.155862 0.396536i
\(694\) 22.1634 0.841311
\(695\) 1.62357i 0.0615854i
\(696\) −3.10495 + 4.55663i −0.117693 + 0.172718i
\(697\) 26.7263 1.01233
\(698\) 4.57136i 0.173029i
\(699\) 35.5871 + 24.2496i 1.34603 + 0.917202i
\(700\) 12.4065 0.468922
\(701\) −3.59083 −0.135624 −0.0678119 0.997698i \(-0.521602\pi\)
−0.0678119 + 0.997698i \(0.521602\pi\)
\(702\) −18.9932 4.31979i −0.716852 0.163040i
\(703\) 2.65347i 0.100077i
\(704\) −1.50375 −0.0566748
\(705\) 0.419487 0.615612i 0.0157988 0.0231853i
\(706\) −15.9218 −0.599223
\(707\) −24.2131 −0.910626
\(708\) −11.5446 6.61229i −0.433872 0.248505i
\(709\) 11.3787 0.427337 0.213668 0.976906i \(-0.431459\pi\)
0.213668 + 0.976906i \(0.431459\pi\)
\(710\) 1.01901 0.0382427
\(711\) −10.0205 25.4936i −0.375799 0.956085i
\(712\) 8.23497 0.308619
\(713\) 67.5309i 2.52905i
\(714\) 16.2075 23.7850i 0.606549 0.890132i
\(715\) 0.563199 0.0210625
\(716\) −14.4415 −0.539703
\(717\) −3.34821 + 4.91361i −0.125041 + 0.183502i
\(718\) 37.7987i 1.41064i
\(719\) 6.27578 0.234047 0.117023 0.993129i \(-0.462665\pi\)
0.117023 + 0.993129i \(0.462665\pi\)
\(720\) −0.278960 + 0.109648i −0.0103962 + 0.00408634i
\(721\) 4.69497i 0.174850i
\(722\) 3.07976 0.114617
\(723\) −11.6321 7.92629i −0.432603 0.294782i
\(724\) −19.5756 −0.727520
\(725\) 15.8856i 0.589977i
\(726\) −12.5081 8.52318i −0.464218 0.316325i
\(727\) 10.8245 0.401457 0.200729 0.979647i \(-0.435669\pi\)
0.200729 + 0.979647i \(0.435669\pi\)
\(728\) 9.31999i 0.345422i
\(729\) −24.3441 11.6776i −0.901632 0.432504i
\(730\) −1.13205 −0.0418990
\(731\) −67.1746 −2.48454
\(732\) 12.8928 18.9206i 0.476530 0.699325i
\(733\) −17.4775 −0.645545 −0.322772 0.946477i \(-0.604615\pi\)
−0.322772 + 0.946477i \(0.604615\pi\)
\(734\) 14.5489i 0.537009i
\(735\) −0.0797595 + 0.117050i −0.00294198 + 0.00431745i
\(736\) −7.31226 −0.269533
\(737\) 10.6272i 0.391456i
\(738\) 11.1647 4.38841i 0.410980 0.161540i
\(739\) 16.8480i 0.619762i 0.950775 + 0.309881i \(0.100289\pi\)
−0.950775 + 0.309881i \(0.899711\pi\)
\(740\) −0.0664441 −0.00244253
\(741\) 14.5880 21.4084i 0.535904 0.786458i
\(742\) 0.621951i 0.0228325i
\(743\) 19.6522i 0.720968i −0.932765 0.360484i \(-0.882612\pi\)
0.932765 0.360484i \(-0.117388\pi\)
\(744\) 9.00751 13.2188i 0.330231 0.484626i
\(745\) 0.442590i 0.0162153i
\(746\) −20.4733 −0.749580
\(747\) 5.96350 + 15.1720i 0.218193 + 0.555114i
\(748\) 10.0506i 0.367485i
\(749\) 4.94338i 0.180627i
\(750\) −0.973502 + 1.42865i −0.0355473 + 0.0521669i
\(751\) 24.7561i 0.903362i 0.892179 + 0.451681i \(0.149176\pi\)
−0.892179 + 0.451681i \(0.850824\pi\)
\(752\) 4.30475 0.156978
\(753\) −18.8103 + 27.6048i −0.685487 + 1.00598i
\(754\) 11.9336 0.434594
\(755\) 1.26082 0.0458861
\(756\) 2.86511 12.5973i 0.104203 0.458159i
\(757\) −37.6335 −1.36781 −0.683907 0.729569i \(-0.739721\pi\)
−0.683907 + 0.729569i \(0.739721\pi\)
\(758\) 11.5722 0.420322
\(759\) 15.7387 + 10.7246i 0.571280 + 0.389278i
\(760\) 0.398650i 0.0144606i
\(761\) 0.789332i 0.0286133i 0.999898 + 0.0143066i \(0.00455410\pi\)
−0.999898 + 0.0143066i \(0.995446\pi\)
\(762\) −1.55624 1.06045i −0.0563767 0.0384159i
\(763\) 23.7085i 0.858305i
\(764\) −2.00333 −0.0724780
\(765\) 0.732851 + 1.86448i 0.0264963 + 0.0674103i
\(766\) 10.0251i 0.362220i
\(767\) 2.24344 + 28.7059i 0.0810058 + 1.03651i
\(768\) −1.43134 0.975334i −0.0516489 0.0351943i
\(769\) 16.3975i 0.591308i 0.955295 + 0.295654i \(0.0955376\pi\)
−0.955295 + 0.295654i \(0.904462\pi\)
\(770\) 0.373544i 0.0134616i
\(771\) −30.4949 + 44.7524i −1.09825 + 1.61172i
\(772\) 6.79102 0.244414
\(773\) 23.4991 0.845205 0.422603 0.906315i \(-0.361117\pi\)
0.422603 + 0.906315i \(0.361117\pi\)
\(774\) −28.0618 + 11.0300i −1.00866 + 0.396464i
\(775\) 46.0843i 1.65540i
\(776\) 3.83328i 0.137607i
\(777\) 1.61265 2.36662i 0.0578535 0.0849020i
\(778\) 29.0531i 1.04160i
\(779\) 15.9551i 0.571650i
\(780\) 0.536077 + 0.365291i 0.0191946 + 0.0130795i
\(781\) 15.3369i 0.548797i
\(782\) 48.8727i 1.74768i
\(783\) 16.1299 + 3.66856i 0.576436 + 0.131104i
\(784\)