Properties

Label 980.2.x.k.667.14
Level $980$
Weight $2$
Character 980.667
Analytic conductor $7.825$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 667.14
Character \(\chi\) \(=\) 980.667
Dual form 980.2.x.k.263.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.996542 - 1.00345i) q^{2} +(-0.463343 + 1.72922i) q^{3} +(-0.0138066 - 1.99995i) q^{4} +(-1.91033 + 1.16218i) q^{5} +(1.27344 + 2.18818i) q^{6} +(-2.02060 - 1.97918i) q^{8} +(-0.177443 - 0.102447i) q^{9} +O(q^{10})\) \(q+(0.996542 - 1.00345i) q^{2} +(-0.463343 + 1.72922i) q^{3} +(-0.0138066 - 1.99995i) q^{4} +(-1.91033 + 1.16218i) q^{5} +(1.27344 + 2.18818i) q^{6} +(-2.02060 - 1.97918i) q^{8} +(-0.177443 - 0.102447i) q^{9} +(-0.737542 + 3.07507i) q^{10} +(-1.83014 + 1.05663i) q^{11} +(3.46476 + 0.902790i) q^{12} +(2.86476 - 2.86476i) q^{13} +(-1.12452 - 3.84186i) q^{15} +(-3.99962 + 0.0552250i) q^{16} +(-1.63626 + 6.10660i) q^{17} +(-0.279629 + 0.0759618i) q^{18} +(-1.47623 + 2.55691i) q^{19} +(2.35067 + 3.80452i) q^{20} +(-0.763541 + 2.88943i) q^{22} +(-5.38640 + 1.44328i) q^{23} +(4.35868 - 2.57703i) q^{24} +(2.29870 - 4.44027i) q^{25} +(-0.0197764 - 5.72949i) q^{26} +(-3.53826 + 3.53826i) q^{27} +2.86818i q^{29} +(-4.97573 - 2.70019i) q^{30} +(-5.20796 + 3.00682i) q^{31} +(-3.93037 + 4.06843i) q^{32} +(-0.979169 - 3.65431i) q^{33} +(4.49704 + 7.72739i) q^{34} +(-0.202439 + 0.356292i) q^{36} +(-5.34722 + 1.43278i) q^{37} +(1.09459 + 4.02938i) q^{38} +(3.62644 + 6.28117i) q^{39} +(6.16017 + 1.43259i) q^{40} -7.98984 q^{41} +(5.64967 + 5.64967i) q^{43} +(2.13849 + 3.64561i) q^{44} +(0.458035 - 0.0105130i) q^{45} +(-3.91952 + 6.84325i) q^{46} +(-1.57515 - 5.87853i) q^{47} +(1.75770 - 6.94181i) q^{48} +(-2.16482 - 6.73153i) q^{50} +(-9.80152 - 5.65891i) q^{51} +(-5.76894 - 5.68983i) q^{52} +(0.766587 + 0.205406i) q^{53} +(0.0244258 + 7.07649i) q^{54} +(2.26818 - 4.14546i) q^{55} +(-3.73746 - 3.73746i) q^{57} +(2.87806 + 2.85826i) q^{58} +(-2.48910 - 4.31124i) q^{59} +(-7.66802 + 2.30203i) q^{60} +(-0.843662 + 1.46127i) q^{61} +(-2.17278 + 8.22233i) q^{62} +(0.165668 + 7.99828i) q^{64} +(-2.14328 + 8.80198i) q^{65} +(-4.64268 - 2.65913i) q^{66} +(11.0122 + 2.95071i) q^{67} +(12.2355 + 3.18813i) q^{68} -9.98301i q^{69} +0.610925i q^{71} +(0.155781 + 0.558196i) q^{72} +(4.41548 + 1.18312i) q^{73} +(-3.89101 + 6.79348i) q^{74} +(6.61312 + 6.03233i) q^{75} +(5.13407 + 2.91709i) q^{76} +(9.91671 + 2.62052i) q^{78} +(7.12694 - 12.3442i) q^{79} +(7.57640 - 4.75376i) q^{80} +(-4.78635 - 8.29020i) q^{81} +(-7.96221 + 8.01737i) q^{82} +(5.51624 + 5.51624i) q^{83} +(-3.97115 - 13.5672i) q^{85} +(11.2993 - 0.0390015i) q^{86} +(-4.95971 - 1.32895i) q^{87} +(5.78927 + 1.48715i) q^{88} +(-1.80030 - 1.03940i) q^{89} +(0.445902 - 0.470090i) q^{90} +(2.96086 + 10.7526i) q^{92} +(-2.78638 - 10.3989i) q^{93} +(-7.46849 - 4.27763i) q^{94} +(-0.151490 - 6.60017i) q^{95} +(-5.21411 - 8.68157i) q^{96} +(-1.95542 - 1.95542i) q^{97} +0.432994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 16q^{6} + O(q^{10}) \) \( 72q - 16q^{6} + 16q^{10} + 16q^{12} - 8q^{13} + 8q^{16} + 20q^{17} - 28q^{18} + 40q^{20} + 8q^{22} + 20q^{25} + 32q^{26} + 4q^{30} - 20q^{37} + 36q^{40} - 20q^{45} - 16q^{46} - 48q^{48} + 80q^{50} - 16q^{52} + 44q^{53} - 32q^{57} + 4q^{58} - 40q^{60} + 64q^{61} + 80q^{62} - 4q^{65} - 32q^{66} - 80q^{68} - 80q^{72} - 52q^{73} + 16q^{76} - 152q^{78} + 20q^{80} + 36q^{81} - 56q^{82} - 40q^{85} - 56q^{86} + 40q^{88} - 32q^{90} - 112q^{92} - 32q^{93} - 120q^{96} + 40q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.996542 1.00345i 0.704662 0.709543i
\(3\) −0.463343 + 1.72922i −0.267511 + 0.998366i 0.693184 + 0.720761i \(0.256207\pi\)
−0.960695 + 0.277605i \(0.910459\pi\)
\(4\) −0.0138066 1.99995i −0.00690329 0.999976i
\(5\) −1.91033 + 1.16218i −0.854324 + 0.519741i
\(6\) 1.27344 + 2.18818i 0.519879 + 0.893322i
\(7\) 0 0
\(8\) −2.02060 1.97918i −0.714391 0.699747i
\(9\) −0.177443 0.102447i −0.0591476 0.0341489i
\(10\) −0.737542 + 3.07507i −0.233231 + 0.972421i
\(11\) −1.83014 + 1.05663i −0.551809 + 0.318587i −0.749851 0.661606i \(-0.769875\pi\)
0.198042 + 0.980193i \(0.436542\pi\)
\(12\) 3.46476 + 0.902790i 1.00019 + 0.260613i
\(13\) 2.86476 2.86476i 0.794542 0.794542i −0.187687 0.982229i \(-0.560099\pi\)
0.982229 + 0.187687i \(0.0600992\pi\)
\(14\) 0 0
\(15\) −1.12452 3.84186i −0.290350 0.991965i
\(16\) −3.99962 + 0.0552250i −0.999905 + 0.0138062i
\(17\) −1.63626 + 6.10660i −0.396851 + 1.48107i 0.421753 + 0.906711i \(0.361415\pi\)
−0.818604 + 0.574358i \(0.805252\pi\)
\(18\) −0.279629 + 0.0759618i −0.0659092 + 0.0179044i
\(19\) −1.47623 + 2.55691i −0.338671 + 0.586595i −0.984183 0.177155i \(-0.943311\pi\)
0.645512 + 0.763750i \(0.276644\pi\)
\(20\) 2.35067 + 3.80452i 0.525626 + 0.850716i
\(21\) 0 0
\(22\) −0.763541 + 2.88943i −0.162788 + 0.616029i
\(23\) −5.38640 + 1.44328i −1.12314 + 0.300945i −0.772154 0.635435i \(-0.780821\pi\)
−0.350988 + 0.936380i \(0.614154\pi\)
\(24\) 4.35868 2.57703i 0.889711 0.526033i
\(25\) 2.29870 4.44027i 0.459740 0.888054i
\(26\) −0.0197764 5.72949i −0.00387847 1.12364i
\(27\) −3.53826 + 3.53826i −0.680939 + 0.680939i
\(28\) 0 0
\(29\) 2.86818i 0.532607i 0.963889 + 0.266303i \(0.0858023\pi\)
−0.963889 + 0.266303i \(0.914198\pi\)
\(30\) −4.97573 2.70019i −0.908441 0.492984i
\(31\) −5.20796 + 3.00682i −0.935378 + 0.540041i −0.888508 0.458860i \(-0.848258\pi\)
−0.0468695 + 0.998901i \(0.514924\pi\)
\(32\) −3.93037 + 4.06843i −0.694799 + 0.719204i
\(33\) −0.979169 3.65431i −0.170451 0.636133i
\(34\) 4.49704 + 7.72739i 0.771237 + 1.32524i
\(35\) 0 0
\(36\) −0.202439 + 0.356292i −0.0337398 + 0.0593819i
\(37\) −5.34722 + 1.43278i −0.879078 + 0.235548i −0.670009 0.742353i \(-0.733710\pi\)
−0.209069 + 0.977901i \(0.567043\pi\)
\(38\) 1.09459 + 4.02938i 0.177566 + 0.653652i
\(39\) 3.62644 + 6.28117i 0.580695 + 1.00579i
\(40\) 6.16017 + 1.43259i 0.974008 + 0.226513i
\(41\) −7.98984 −1.24780 −0.623902 0.781503i \(-0.714453\pi\)
−0.623902 + 0.781503i \(0.714453\pi\)
\(42\) 0 0
\(43\) 5.64967 + 5.64967i 0.861567 + 0.861567i 0.991520 0.129954i \(-0.0414828\pi\)
−0.129954 + 0.991520i \(0.541483\pi\)
\(44\) 2.13849 + 3.64561i 0.322389 + 0.549597i
\(45\) 0.458035 0.0105130i 0.0682798 0.00156719i
\(46\) −3.91952 + 6.84325i −0.577902 + 1.00898i
\(47\) −1.57515 5.87853i −0.229759 0.857472i −0.980442 0.196810i \(-0.936942\pi\)
0.750683 0.660663i \(-0.229725\pi\)
\(48\) 1.75770 6.94181i 0.253702 1.00196i
\(49\) 0 0
\(50\) −2.16482 6.73153i −0.306152 0.951983i
\(51\) −9.80152 5.65891i −1.37249 0.792406i
\(52\) −5.76894 5.68983i −0.800008 0.789038i
\(53\) 0.766587 + 0.205406i 0.105299 + 0.0282147i 0.311084 0.950383i \(-0.399308\pi\)
−0.205785 + 0.978597i \(0.565975\pi\)
\(54\) 0.0244258 + 7.07649i 0.00332393 + 0.962988i
\(55\) 2.26818 4.14546i 0.305841 0.558974i
\(56\) 0 0
\(57\) −3.73746 3.73746i −0.495038 0.495038i
\(58\) 2.87806 + 2.85826i 0.377908 + 0.375308i
\(59\) −2.48910 4.31124i −0.324053 0.561276i 0.657268 0.753657i \(-0.271712\pi\)
−0.981320 + 0.192382i \(0.938379\pi\)
\(60\) −7.66802 + 2.30203i −0.989937 + 0.297191i
\(61\) −0.843662 + 1.46127i −0.108020 + 0.187096i −0.914968 0.403526i \(-0.867784\pi\)
0.806948 + 0.590622i \(0.201118\pi\)
\(62\) −2.17278 + 8.22233i −0.275943 + 1.04424i
\(63\) 0 0
\(64\) 0.165668 + 7.99828i 0.0207085 + 0.999786i
\(65\) −2.14328 + 8.80198i −0.265841 + 1.09175i
\(66\) −4.64268 2.65913i −0.571475 0.327316i
\(67\) 11.0122 + 2.95071i 1.34535 + 0.360486i 0.858417 0.512952i \(-0.171448\pi\)
0.486935 + 0.873438i \(0.338115\pi\)
\(68\) 12.2355 + 3.18813i 1.48377 + 0.386618i
\(69\) 9.98301i 1.20181i
\(70\) 0 0
\(71\) 0.610925i 0.0725035i 0.999343 + 0.0362518i \(0.0115418\pi\)
−0.999343 + 0.0362518i \(0.988458\pi\)
\(72\) 0.155781 + 0.558196i 0.0183589 + 0.0657840i
\(73\) 4.41548 + 1.18312i 0.516793 + 0.138474i 0.507783 0.861485i \(-0.330465\pi\)
0.00901016 + 0.999959i \(0.497132\pi\)
\(74\) −3.89101 + 6.79348i −0.452321 + 0.789726i
\(75\) 6.61312 + 6.03233i 0.763617 + 0.696553i
\(76\) 5.13407 + 2.91709i 0.588919 + 0.334613i
\(77\) 0 0
\(78\) 9.91671 + 2.62052i 1.12285 + 0.296716i
\(79\) 7.12694 12.3442i 0.801843 1.38883i −0.116558 0.993184i \(-0.537186\pi\)
0.918401 0.395650i \(-0.129481\pi\)
\(80\) 7.57640 4.75376i 0.847067 0.531486i
\(81\) −4.78635 8.29020i −0.531817 0.921133i
\(82\) −7.96221 + 8.01737i −0.879279 + 0.885370i
\(83\) 5.51624 + 5.51624i 0.605486 + 0.605486i 0.941763 0.336277i \(-0.109168\pi\)
−0.336277 + 0.941763i \(0.609168\pi\)
\(84\) 0 0
\(85\) −3.97115 13.5672i −0.430732 1.47157i
\(86\) 11.2993 0.0390015i 1.21843 0.00420564i
\(87\) −4.95971 1.32895i −0.531737 0.142478i
\(88\) 5.78927 + 1.48715i 0.617138 + 0.158531i
\(89\) −1.80030 1.03940i −0.190831 0.110176i 0.401540 0.915841i \(-0.368475\pi\)
−0.592372 + 0.805665i \(0.701808\pi\)
\(90\) 0.445902 0.470090i 0.0470022 0.0495518i
\(91\) 0 0
\(92\) 2.96086 + 10.7526i 0.308691 + 1.12104i
\(93\) −2.78638 10.3989i −0.288934 1.07832i
\(94\) −7.46849 4.27763i −0.770316 0.441204i
\(95\) −0.151490 6.60017i −0.0155426 0.677163i
\(96\) −5.21411 8.68157i −0.532163 0.886059i
\(97\) −1.95542 1.95542i −0.198543 0.198543i 0.600832 0.799375i \(-0.294836\pi\)
−0.799375 + 0.600832i \(0.794836\pi\)
\(98\) 0 0
\(99\) 0.432994 0.0435176
\(100\) −8.91206 4.53598i −0.891206 0.453598i
\(101\) −0.631568 1.09391i −0.0628434 0.108848i 0.832892 0.553436i \(-0.186684\pi\)
−0.895735 + 0.444588i \(0.853350\pi\)
\(102\) −15.4460 + 4.19595i −1.52939 + 0.415461i
\(103\) 12.5525 3.36344i 1.23684 0.331409i 0.419599 0.907710i \(-0.362171\pi\)
0.817238 + 0.576300i \(0.195504\pi\)
\(104\) −11.4584 + 0.118656i −1.12359 + 0.0116352i
\(105\) 0 0
\(106\) 0.970051 0.564533i 0.0942197 0.0548322i
\(107\) 5.00010 + 18.6606i 0.483378 + 1.80399i 0.587255 + 0.809402i \(0.300209\pi\)
−0.103877 + 0.994590i \(0.533125\pi\)
\(108\) 7.12521 + 7.02751i 0.685624 + 0.676222i
\(109\) 11.7830 6.80291i 1.12860 0.651600i 0.185021 0.982735i \(-0.440765\pi\)
0.943584 + 0.331134i \(0.107431\pi\)
\(110\) −1.89941 6.40713i −0.181102 0.610895i
\(111\) 9.91040i 0.940654i
\(112\) 0 0
\(113\) −7.72607 + 7.72607i −0.726807 + 0.726807i −0.969982 0.243175i \(-0.921811\pi\)
0.243175 + 0.969982i \(0.421811\pi\)
\(114\) −7.47487 + 0.0258009i −0.700086 + 0.00241647i
\(115\) 8.61244 9.01708i 0.803114 0.840847i
\(116\) 5.73621 0.0395997i 0.532594 0.00367674i
\(117\) −0.801816 + 0.214846i −0.0741279 + 0.0198625i
\(118\) −6.80658 1.79866i −0.626597 0.165580i
\(119\) 0 0
\(120\) −5.33154 + 9.98851i −0.486701 + 0.911822i
\(121\) −3.26705 + 5.65869i −0.297004 + 0.514427i
\(122\) 0.625556 + 2.30278i 0.0566352 + 0.208484i
\(123\) 3.70204 13.8162i 0.333802 1.24576i
\(124\) 6.08540 + 10.3742i 0.546485 + 0.931628i
\(125\) 0.769107 + 11.1539i 0.0687910 + 0.997631i
\(126\) 0 0
\(127\) −3.84193 + 3.84193i −0.340917 + 0.340917i −0.856712 0.515795i \(-0.827496\pi\)
0.515795 + 0.856712i \(0.327496\pi\)
\(128\) 8.19094 + 7.80439i 0.723984 + 0.689817i
\(129\) −12.3873 + 7.15179i −1.09064 + 0.629680i
\(130\) 6.69645 + 10.9222i 0.587317 + 0.957941i
\(131\) −10.0683 5.81295i −0.879674 0.507880i −0.00912320 0.999958i \(-0.502904\pi\)
−0.870551 + 0.492078i \(0.836237\pi\)
\(132\) −7.29492 + 2.00874i −0.634942 + 0.174839i
\(133\) 0 0
\(134\) 13.9350 8.10963i 1.20380 0.700565i
\(135\) 2.64716 10.8713i 0.227831 0.935654i
\(136\) 15.3923 9.10056i 1.31988 0.780367i
\(137\) 5.52298 20.6120i 0.471860 1.76101i −0.161219 0.986919i \(-0.551543\pi\)
0.633079 0.774087i \(-0.281791\pi\)
\(138\) −10.0174 9.94849i −0.852738 0.846872i
\(139\) 5.05787 0.429003 0.214501 0.976724i \(-0.431187\pi\)
0.214501 + 0.976724i \(0.431187\pi\)
\(140\) 0 0
\(141\) 10.8951 0.917535
\(142\) 0.613030 + 0.608813i 0.0514444 + 0.0510905i
\(143\) −2.21592 + 8.26993i −0.185305 + 0.691566i
\(144\) 0.715361 + 0.399948i 0.0596134 + 0.0333290i
\(145\) −3.33332 5.47915i −0.276817 0.455019i
\(146\) 5.58741 3.25166i 0.462418 0.269109i
\(147\) 0 0
\(148\) 2.93933 + 10.6744i 0.241611 + 0.877431i
\(149\) 6.53199 + 3.77124i 0.535121 + 0.308952i 0.743099 0.669181i \(-0.233355\pi\)
−0.207978 + 0.978133i \(0.566688\pi\)
\(150\) 12.6434 0.624439i 1.03233 0.0509852i
\(151\) −12.0674 + 6.96711i −0.982030 + 0.566975i −0.902883 0.429887i \(-0.858553\pi\)
−0.0791478 + 0.996863i \(0.525220\pi\)
\(152\) 8.04346 2.24476i 0.652411 0.182074i
\(153\) 0.915944 0.915944i 0.0740496 0.0740496i
\(154\) 0 0
\(155\) 6.45446 11.7966i 0.518435 0.947524i
\(156\) 12.5120 7.33942i 1.00176 0.587624i
\(157\) −2.06532 + 7.70790i −0.164831 + 0.615157i 0.833231 + 0.552925i \(0.186488\pi\)
−0.998062 + 0.0622318i \(0.980178\pi\)
\(158\) −5.28446 19.4530i −0.420409 1.54760i
\(159\) −0.710386 + 1.23043i −0.0563373 + 0.0975791i
\(160\) 2.78007 12.3398i 0.219784 0.975549i
\(161\) 0 0
\(162\) −13.0886 3.45869i −1.02833 0.271741i
\(163\) 13.4557 3.60545i 1.05393 0.282400i 0.310057 0.950718i \(-0.399652\pi\)
0.743876 + 0.668318i \(0.232985\pi\)
\(164\) 0.110312 + 15.9793i 0.00861395 + 1.24777i
\(165\) 6.11748 + 5.84296i 0.476245 + 0.454874i
\(166\) 11.0324 0.0380804i 0.856282 0.00295561i
\(167\) 14.0288 14.0288i 1.08558 1.08558i 0.0896054 0.995977i \(-0.471439\pi\)
0.995977 0.0896054i \(-0.0285606\pi\)
\(168\) 0 0
\(169\) 3.41370i 0.262592i
\(170\) −17.5714 9.53548i −1.34767 0.731338i
\(171\) 0.523893 0.302470i 0.0400631 0.0231304i
\(172\) 11.2211 11.3771i 0.855598 0.867494i
\(173\) 3.24936 + 12.1268i 0.247044 + 0.921982i 0.972345 + 0.233550i \(0.0750342\pi\)
−0.725300 + 0.688432i \(0.758299\pi\)
\(174\) −6.27609 + 3.65244i −0.475789 + 0.276891i
\(175\) 0 0
\(176\) 7.26153 4.32720i 0.547358 0.326175i
\(177\) 8.60839 2.30661i 0.647046 0.173376i
\(178\) −2.83706 + 0.770693i −0.212647 + 0.0577659i
\(179\) 1.72867 + 2.99414i 0.129207 + 0.223792i 0.923369 0.383913i \(-0.125424\pi\)
−0.794163 + 0.607705i \(0.792090\pi\)
\(180\) −0.0273495 0.915902i −0.00203851 0.0682673i
\(181\) −16.0960 −1.19640 −0.598202 0.801345i \(-0.704118\pi\)
−0.598202 + 0.801345i \(0.704118\pi\)
\(182\) 0 0
\(183\) −2.13595 2.13595i −0.157894 0.157894i
\(184\) 13.7403 + 7.74437i 1.01295 + 0.570923i
\(185\) 8.54980 8.95149i 0.628594 0.658127i
\(186\) −13.2115 7.56697i −0.968713 0.554838i
\(187\) −3.45786 12.9049i −0.252863 0.943699i
\(188\) −11.7350 + 3.23138i −0.855866 + 0.235673i
\(189\) 0 0
\(190\) −6.77388 6.42533i −0.491429 0.466143i
\(191\) 4.59262 + 2.65155i 0.332310 + 0.191860i 0.656866 0.754007i \(-0.271882\pi\)
−0.324556 + 0.945866i \(0.605215\pi\)
\(192\) −13.9076 3.41948i −1.00369 0.246779i
\(193\) −21.6160 5.79200i −1.55596 0.416917i −0.624576 0.780964i \(-0.714728\pi\)
−0.931381 + 0.364047i \(0.881395\pi\)
\(194\) −3.91081 + 0.0134989i −0.280780 + 0.000969164i
\(195\) −14.2275 7.78454i −1.01885 0.557462i
\(196\) 0 0
\(197\) 5.33556 + 5.33556i 0.380143 + 0.380143i 0.871154 0.491011i \(-0.163372\pi\)
−0.491011 + 0.871154i \(0.663372\pi\)
\(198\) 0.431497 0.434486i 0.0306652 0.0308776i
\(199\) −5.94289 10.2934i −0.421280 0.729679i 0.574785 0.818305i \(-0.305086\pi\)
−0.996065 + 0.0886258i \(0.971752\pi\)
\(200\) −13.4329 + 4.42247i −0.949847 + 0.312716i
\(201\) −10.2048 + 17.6753i −0.719795 + 1.24672i
\(202\) −1.72706 0.456381i −0.121516 0.0321109i
\(203\) 0 0
\(204\) −11.1822 + 19.6807i −0.782912 + 1.37792i
\(205\) 15.2632 9.28559i 1.06603 0.648534i
\(206\) 9.13409 15.9476i 0.636402 1.11112i
\(207\) 1.10364 + 0.295719i 0.0767081 + 0.0205539i
\(208\) −11.2997 + 11.6162i −0.783496 + 0.805435i
\(209\) 6.23934i 0.431584i
\(210\) 0 0
\(211\) 2.04430i 0.140735i −0.997521 0.0703677i \(-0.977583\pi\)
0.997521 0.0703677i \(-0.0224173\pi\)
\(212\) 0.400219 1.53597i 0.0274872 0.105491i
\(213\) −1.05643 0.283068i −0.0723851 0.0193955i
\(214\) 23.7078 + 13.5788i 1.62063 + 0.928227i
\(215\) −17.3586 4.22681i −1.18385 0.288266i
\(216\) 14.1523 0.146552i 0.962942 0.00997163i
\(217\) 0 0
\(218\) 4.91589 18.6030i 0.332946 1.25995i
\(219\) −4.09177 + 7.08715i −0.276496 + 0.478905i
\(220\) −8.32205 4.47902i −0.561072 0.301975i
\(221\) 12.8065 + 22.1815i 0.861456 + 1.49209i
\(222\) −9.94455 9.87613i −0.667434 0.662843i
\(223\) 13.1600 + 13.1600i 0.881261 + 0.881261i 0.993663 0.112402i \(-0.0358544\pi\)
−0.112402 + 0.993663i \(0.535854\pi\)
\(224\) 0 0
\(225\) −0.862778 + 0.552400i −0.0575185 + 0.0368267i
\(226\) 0.0533356 + 15.4520i 0.00354783 + 1.02785i
\(227\) 5.37597 + 1.44049i 0.356816 + 0.0956085i 0.432774 0.901502i \(-0.357535\pi\)
−0.0759580 + 0.997111i \(0.524202\pi\)
\(228\) −7.42313 + 7.52634i −0.491609 + 0.498444i
\(229\) −7.11068 4.10535i −0.469887 0.271289i 0.246305 0.969192i \(-0.420783\pi\)
−0.716192 + 0.697903i \(0.754117\pi\)
\(230\) −0.465490 17.6280i −0.0306935 1.16236i
\(231\) 0 0
\(232\) 5.67664 5.79544i 0.372690 0.380489i
\(233\) −3.10326 11.5815i −0.203302 0.758732i −0.989961 0.141344i \(-0.954858\pi\)
0.786659 0.617388i \(-0.211809\pi\)
\(234\) −0.583457 + 1.01868i −0.0381418 + 0.0665933i
\(235\) 9.84094 + 9.39932i 0.641952 + 0.613144i
\(236\) −8.58791 + 5.03760i −0.559025 + 0.327920i
\(237\) 18.0437 + 18.0437i 1.17206 + 1.17206i
\(238\) 0 0
\(239\) −18.5038 −1.19691 −0.598456 0.801155i \(-0.704219\pi\)
−0.598456 + 0.801155i \(0.704219\pi\)
\(240\) 4.70982 + 15.3039i 0.304018 + 0.987862i
\(241\) −0.0411841 0.0713330i −0.00265290 0.00459496i 0.864696 0.502296i \(-0.167511\pi\)
−0.867349 + 0.497701i \(0.834178\pi\)
\(242\) 2.42244 + 8.91743i 0.155720 + 0.573234i
\(243\) 2.05324 0.550164i 0.131715 0.0352930i
\(244\) 2.93411 + 1.66711i 0.187837 + 0.106726i
\(245\) 0 0
\(246\) −10.1746 17.4832i −0.648707 1.11469i
\(247\) 3.09588 + 11.5540i 0.196986 + 0.735162i
\(248\) 16.4743 + 4.23193i 1.04612 + 0.268728i
\(249\) −12.0947 + 6.98289i −0.766471 + 0.442522i
\(250\) 11.9587 + 10.3435i 0.756337 + 0.654182i
\(251\) 9.07743i 0.572963i 0.958086 + 0.286481i \(0.0924856\pi\)
−0.958086 + 0.286481i \(0.907514\pi\)
\(252\) 0 0
\(253\) 8.33287 8.33287i 0.523883 0.523883i
\(254\) 0.0265221 + 7.68382i 0.00166415 + 0.482126i
\(255\) 25.3008 0.580715i 1.58439 0.0363658i
\(256\) 15.9939 0.441758i 0.999619 0.0276099i
\(257\) 7.03925 1.88616i 0.439097 0.117656i −0.0324965 0.999472i \(-0.510346\pi\)
0.471593 + 0.881816i \(0.343679\pi\)
\(258\) −5.16800 + 19.5570i −0.321746 + 1.21757i
\(259\) 0 0
\(260\) 17.6331 + 4.16492i 1.09356 + 0.258298i
\(261\) 0.293835 0.508937i 0.0181879 0.0315024i
\(262\) −15.8665 + 4.31017i −0.980236 + 0.266283i
\(263\) 1.38891 5.18349i 0.0856441 0.319628i −0.909791 0.415066i \(-0.863759\pi\)
0.995435 + 0.0954380i \(0.0304252\pi\)
\(264\) −5.25403 + 9.32186i −0.323363 + 0.573721i
\(265\) −1.70315 + 0.498515i −0.104624 + 0.0306236i
\(266\) 0 0
\(267\) 2.63151 2.63151i 0.161046 0.161046i
\(268\) 5.74923 22.0646i 0.351190 1.34781i
\(269\) 4.69186 2.70885i 0.286068 0.165161i −0.350099 0.936713i \(-0.613852\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(270\) −8.27078 13.4900i −0.503343 0.820976i
\(271\) −7.10365 4.10129i −0.431516 0.249136i 0.268476 0.963286i \(-0.413480\pi\)
−0.699992 + 0.714151i \(0.746813\pi\)
\(272\) 6.20718 24.5145i 0.376365 1.48641i
\(273\) 0 0
\(274\) −15.1792 26.0828i −0.917008 1.57572i
\(275\) 0.484792 + 10.5552i 0.0292341 + 0.636503i
\(276\) −19.9655 + 0.137831i −1.20178 + 0.00829646i
\(277\) −3.92432 + 14.6458i −0.235790 + 0.879979i 0.742002 + 0.670398i \(0.233877\pi\)
−0.977791 + 0.209581i \(0.932790\pi\)
\(278\) 5.04038 5.07530i 0.302302 0.304396i
\(279\) 1.23215 0.0737671
\(280\) 0 0
\(281\) −23.7586 −1.41732 −0.708659 0.705551i \(-0.750700\pi\)
−0.708659 + 0.705551i \(0.750700\pi\)
\(282\) 10.8575 10.9327i 0.646552 0.651031i
\(283\) −6.13117 + 22.8818i −0.364460 + 1.36018i 0.503691 + 0.863884i \(0.331975\pi\)
−0.868151 + 0.496300i \(0.834692\pi\)
\(284\) 1.22182 0.00843479i 0.0725018 0.000500513i
\(285\) 11.4833 + 2.79618i 0.680214 + 0.165632i
\(286\) 6.09016 + 10.4649i 0.360119 + 0.618802i
\(287\) 0 0
\(288\) 1.11421 0.319261i 0.0656557 0.0188126i
\(289\) −19.8908 11.4840i −1.17005 0.675528i
\(290\) −8.81983 2.11540i −0.517918 0.124221i
\(291\) 4.28738 2.47532i 0.251331 0.145106i
\(292\) 2.30523 8.84709i 0.134903 0.517736i
\(293\) 18.6078 18.6078i 1.08708 1.08708i 0.0912527 0.995828i \(-0.470913\pi\)
0.995828 0.0912527i \(-0.0290871\pi\)
\(294\) 0 0
\(295\) 9.76540 + 5.34311i 0.568564 + 0.311088i
\(296\) 13.6404 + 7.68804i 0.792829 + 0.446859i
\(297\) 2.73688 10.2142i 0.158810 0.592687i
\(298\) 10.2936 2.79629i 0.596295 0.161985i
\(299\) −11.2961 + 19.5654i −0.653270 + 1.13150i
\(300\) 11.9731 13.3092i 0.691265 0.768408i
\(301\) 0 0
\(302\) −5.03455 + 19.0520i −0.289706 + 1.09632i
\(303\) 2.18424 0.585266i 0.125481 0.0336226i
\(304\) 5.76316 10.3082i 0.330540 0.591215i
\(305\) −0.0865763 3.77198i −0.00495734 0.215983i
\(306\) −0.00632306 1.83188i −0.000361465 0.104721i
\(307\) −19.1930 + 19.1930i −1.09540 + 1.09540i −0.100459 + 0.994941i \(0.532031\pi\)
−0.994941 + 0.100459i \(0.967969\pi\)
\(308\) 0 0
\(309\) 23.2645i 1.32347i
\(310\) −5.40508 18.2325i −0.306988 1.03554i
\(311\) 11.9923 6.92373i 0.680018 0.392609i −0.119844 0.992793i \(-0.538239\pi\)
0.799862 + 0.600184i \(0.204906\pi\)
\(312\) 5.10400 19.8691i 0.288957 1.12487i
\(313\) −6.08759 22.7192i −0.344091 1.28417i −0.893670 0.448724i \(-0.851879\pi\)
0.549579 0.835441i \(-0.314788\pi\)
\(314\) 5.67627 + 9.75368i 0.320331 + 0.550432i
\(315\) 0 0
\(316\) −24.7863 14.0831i −1.39434 0.792237i
\(317\) 0.796585 0.213444i 0.0447407 0.0119882i −0.236379 0.971661i \(-0.575961\pi\)
0.281120 + 0.959673i \(0.409294\pi\)
\(318\) 0.526735 + 1.93901i 0.0295378 + 0.108734i
\(319\) −3.03061 5.24917i −0.169682 0.293897i
\(320\) −9.61189 15.0868i −0.537321 0.843378i
\(321\) −34.5851 −1.93035
\(322\) 0 0
\(323\) −13.1985 13.1985i −0.734386 0.734386i
\(324\) −16.5139 + 9.68693i −0.917440 + 0.538163i
\(325\) −6.13509 19.3055i −0.340313 1.07088i
\(326\) 9.79131 17.0951i 0.542291 0.946807i
\(327\) 6.30416 + 23.5275i 0.348621 + 1.30107i
\(328\) 16.1443 + 15.8134i 0.891419 + 0.873146i
\(329\) 0 0
\(330\) 11.9594 0.315804i 0.658344 0.0173844i
\(331\) −12.4271 7.17480i −0.683056 0.394363i 0.117949 0.993020i \(-0.462368\pi\)
−0.801006 + 0.598657i \(0.795701\pi\)
\(332\) 10.9561 11.1084i 0.601292 0.609652i
\(333\) 1.09561 + 0.293568i 0.0600390 + 0.0160874i
\(334\) −0.0968456 28.0575i −0.00529915 1.53524i
\(335\) −24.4661 + 7.16128i −1.33673 + 0.391262i
\(336\) 0 0
\(337\) 0.0624771 + 0.0624771i 0.00340335 + 0.00340335i 0.708806 0.705403i \(-0.249234\pi\)
−0.705403 + 0.708806i \(0.749234\pi\)
\(338\) −3.42546 3.40190i −0.186321 0.185039i
\(339\) −9.78026 16.9399i −0.531191 0.920049i
\(340\) −27.0790 + 8.12943i −1.46856 + 0.440880i
\(341\) 6.35422 11.0058i 0.344100 0.595999i
\(342\) 0.218570 0.827122i 0.0118189 0.0447256i
\(343\) 0 0
\(344\) −0.234005 22.5975i −0.0126167 1.21837i
\(345\) 11.6020 + 19.0708i 0.624631 + 1.02674i
\(346\) 15.4067 + 8.82430i 0.828269 + 0.474397i
\(347\) −8.52161 2.28336i −0.457464 0.122577i 0.0227259 0.999742i \(-0.492766\pi\)
−0.480190 + 0.877165i \(0.659432\pi\)
\(348\) −2.58936 + 9.93753i −0.138804 + 0.532708i
\(349\) 3.77799i 0.202231i −0.994875 0.101116i \(-0.967759\pi\)
0.994875 0.101116i \(-0.0322412\pi\)
\(350\) 0 0
\(351\) 20.2726i 1.08207i
\(352\) 2.89430 11.5988i 0.154267 0.618217i
\(353\) 1.20055 + 0.321686i 0.0638987 + 0.0171216i 0.290627 0.956836i \(-0.406136\pi\)
−0.226728 + 0.973958i \(0.572803\pi\)
\(354\) 6.26407 10.9367i 0.332932 0.581279i
\(355\) −0.710002 1.16707i −0.0376830 0.0619415i
\(356\) −2.05390 + 3.61486i −0.108856 + 0.191587i
\(357\) 0 0
\(358\) 4.72714 + 1.24916i 0.249837 + 0.0660203i
\(359\) −8.75216 + 15.1592i −0.461922 + 0.800072i −0.999057 0.0434246i \(-0.986173\pi\)
0.537135 + 0.843496i \(0.319507\pi\)
\(360\) −0.946313 0.885292i −0.0498751 0.0466590i
\(361\) 5.14148 + 8.90531i 0.270604 + 0.468701i
\(362\) −16.0403 + 16.1514i −0.843061 + 0.848901i
\(363\) −8.27137 8.27137i −0.434134 0.434134i
\(364\) 0 0
\(365\) −9.81001 + 2.87141i −0.513479 + 0.150296i
\(366\) −4.27187 + 0.0147451i −0.223294 + 0.000770741i
\(367\) −15.0382 4.02948i −0.784988 0.210337i −0.156006 0.987756i \(-0.549862\pi\)
−0.628983 + 0.777419i \(0.716528\pi\)
\(368\) 21.4638 6.07004i 1.11888 0.316423i
\(369\) 1.41774 + 0.818532i 0.0738046 + 0.0426111i
\(370\) −0.462104 17.4998i −0.0240237 0.909771i
\(371\) 0 0
\(372\) −20.7589 + 5.71620i −1.07630 + 0.296371i
\(373\) 0.203640 + 0.759994i 0.0105441 + 0.0393510i 0.970997 0.239090i \(-0.0768490\pi\)
−0.960453 + 0.278441i \(0.910182\pi\)
\(374\) −16.3953 9.39050i −0.847779 0.485571i
\(375\) −19.6438 3.83811i −1.01440 0.198199i
\(376\) −8.45195 + 14.9957i −0.435876 + 0.773344i
\(377\) 8.21663 + 8.21663i 0.423178 + 0.423178i
\(378\) 0 0
\(379\) 9.14995 0.470001 0.235001 0.971995i \(-0.424491\pi\)
0.235001 + 0.971995i \(0.424491\pi\)
\(380\) −13.1979 + 0.394099i −0.677039 + 0.0202168i
\(381\) −4.86342 8.42369i −0.249161 0.431559i
\(382\) 7.23743 1.96606i 0.370299 0.100593i
\(383\) 8.15515 2.18517i 0.416709 0.111657i −0.0443718 0.999015i \(-0.514129\pi\)
0.461080 + 0.887358i \(0.347462\pi\)
\(384\) −17.2907 + 10.5478i −0.882364 + 0.538267i
\(385\) 0 0
\(386\) −27.3533 + 15.9185i −1.39224 + 0.810233i
\(387\) −0.423703 1.58128i −0.0215381 0.0803811i
\(388\) −3.88375 + 3.93774i −0.197167 + 0.199908i
\(389\) −24.8832 + 14.3663i −1.26163 + 0.728400i −0.973389 0.229159i \(-0.926402\pi\)
−0.288237 + 0.957559i \(0.593069\pi\)
\(390\) −21.9897 + 6.51890i −1.11349 + 0.330098i
\(391\) 35.2542i 1.78288i
\(392\) 0 0
\(393\) 14.7170 14.7170i 0.742373 0.742373i
\(394\) 10.6711 0.0368331i 0.537600 0.00185563i
\(395\) 0.731364 + 31.8643i 0.0367989 + 1.60326i
\(396\) −0.00597817 0.865968i −0.000300414 0.0435165i
\(397\) 24.6559 6.60652i 1.23744 0.331572i 0.419969 0.907538i \(-0.362041\pi\)
0.817473 + 0.575967i \(0.195374\pi\)
\(398\) −16.2512 4.29443i −0.814599 0.215260i
\(399\) 0 0
\(400\) −8.94870 + 17.8863i −0.447435 + 0.894316i
\(401\) −13.0839 + 22.6620i −0.653380 + 1.13169i 0.328917 + 0.944359i \(0.393316\pi\)
−0.982297 + 0.187329i \(0.940017\pi\)
\(402\) 7.56666 + 27.8542i 0.377391 + 1.38924i
\(403\) −6.30575 + 23.5334i −0.314112 + 1.17228i
\(404\) −2.17904 + 1.27821i −0.108411 + 0.0635933i
\(405\) 18.7782 + 10.2744i 0.933094 + 0.510540i
\(406\) 0 0
\(407\) 8.27226 8.27226i 0.410041 0.410041i
\(408\) 8.60496 + 30.8334i 0.426009 + 1.52648i
\(409\) 0.853122 0.492550i 0.0421842 0.0243550i −0.478760 0.877946i \(-0.658913\pi\)
0.520944 + 0.853591i \(0.325580\pi\)
\(410\) 5.89284 24.5693i 0.291027 1.21339i
\(411\) 33.0837 + 19.1009i 1.63190 + 0.942178i
\(412\) −6.90002 25.0580i −0.339940 1.23452i
\(413\) 0 0
\(414\) 1.39656 0.812743i 0.0686371 0.0399442i
\(415\) −16.9487 4.12699i −0.831977 0.202586i
\(416\) 0.395509 + 22.9147i 0.0193914 + 1.12348i
\(417\) −2.34353 + 8.74617i −0.114763 + 0.428302i
\(418\) −6.26084 6.21777i −0.306228 0.304121i
\(419\) −16.7317 −0.817399 −0.408699 0.912669i \(-0.634018\pi\)
−0.408699 + 0.912669i \(0.634018\pi\)
\(420\) 0 0
\(421\) 35.5024 1.73028 0.865140 0.501530i \(-0.167229\pi\)
0.865140 + 0.501530i \(0.167229\pi\)
\(422\) −2.05134 2.03723i −0.0998578 0.0991708i
\(423\) −0.322737 + 1.20447i −0.0156920 + 0.0585634i
\(424\) −1.14243 1.93226i −0.0554814 0.0938389i
\(425\) 23.3537 + 21.3027i 1.13282 + 1.03333i
\(426\) −1.33682 + 0.777976i −0.0647689 + 0.0376930i
\(427\) 0 0
\(428\) 37.2514 10.2576i 1.80061 0.495820i
\(429\) −13.2738 7.66363i −0.640865 0.370004i
\(430\) −21.5400 + 13.2062i −1.03875 + 0.636861i
\(431\) −0.906153 + 0.523167i −0.0436478 + 0.0252001i −0.521665 0.853150i \(-0.674689\pi\)
0.478017 + 0.878350i \(0.341356\pi\)
\(432\) 13.9563 14.3471i 0.671473 0.690275i
\(433\) 9.24591 9.24591i 0.444330 0.444330i −0.449134 0.893464i \(-0.648267\pi\)
0.893464 + 0.449134i \(0.148267\pi\)
\(434\) 0 0
\(435\) 11.0191 3.22532i 0.528327 0.154642i
\(436\) −13.7682 23.4715i −0.659376 1.12408i
\(437\) 4.26123 15.9031i 0.203842 0.760750i
\(438\) 3.03395 + 11.1685i 0.144968 + 0.533652i
\(439\) 11.3657 19.6860i 0.542455 0.939559i −0.456307 0.889822i \(-0.650828\pi\)
0.998762 0.0497373i \(-0.0158384\pi\)
\(440\) −12.7877 + 3.88719i −0.609631 + 0.185315i
\(441\) 0 0
\(442\) 35.0201 + 9.25416i 1.66573 + 0.440176i
\(443\) 22.5471 6.04148i 1.07125 0.287040i 0.320241 0.947336i \(-0.396236\pi\)
0.751005 + 0.660296i \(0.229569\pi\)
\(444\) −19.8203 + 0.136829i −0.940631 + 0.00649360i
\(445\) 4.64713 0.106663i 0.220295 0.00505632i
\(446\) 26.3199 0.0908480i 1.24628 0.00430178i
\(447\) −9.54787 + 9.54787i −0.451599 + 0.451599i
\(448\) 0 0
\(449\) 18.0937i 0.853895i 0.904276 + 0.426947i \(0.140411\pi\)
−0.904276 + 0.426947i \(0.859589\pi\)
\(450\) −0.305492 + 1.41624i −0.0144010 + 0.0667622i
\(451\) 14.6226 8.44234i 0.688549 0.397534i
\(452\) 15.5584 + 15.3451i 0.731807 + 0.721773i
\(453\) −6.45633 24.0954i −0.303345 1.13210i
\(454\) 6.80284 3.95899i 0.319273 0.185805i
\(455\) 0 0
\(456\) 0.154803 + 14.9490i 0.00724931 + 0.700052i
\(457\) 17.5625 4.70586i 0.821540 0.220131i 0.176520 0.984297i \(-0.443516\pi\)
0.645020 + 0.764166i \(0.276849\pi\)
\(458\) −11.2056 + 3.04402i −0.523603 + 0.142238i
\(459\) −15.8173 27.3963i −0.738286 1.27875i
\(460\) −18.1526 17.1000i −0.846371 0.797290i
\(461\) 30.3805 1.41496 0.707481 0.706733i \(-0.249832\pi\)
0.707481 + 0.706733i \(0.249832\pi\)
\(462\) 0 0
\(463\) 20.1652 + 20.1652i 0.937156 + 0.937156i 0.998139 0.0609833i \(-0.0194236\pi\)
−0.0609833 + 0.998139i \(0.519424\pi\)
\(464\) −0.158395 11.4716i −0.00735330 0.532556i
\(465\) 17.4083 + 16.6271i 0.807288 + 0.771061i
\(466\) −14.7140 8.42754i −0.681612 0.390398i
\(467\) 5.42798 + 20.2575i 0.251177 + 0.937405i 0.970177 + 0.242396i \(0.0779332\pi\)
−0.719001 + 0.695009i \(0.755400\pi\)
\(468\) 0.440752 + 1.60063i 0.0203738 + 0.0739890i
\(469\) 0 0
\(470\) 19.2386 0.508020i 0.887411 0.0234332i
\(471\) −12.3717 7.14281i −0.570058 0.329123i
\(472\) −3.50326 + 13.6377i −0.161251 + 0.627725i
\(473\) −16.3093 4.37008i −0.749904 0.200936i
\(474\) 36.0871 0.124561i 1.65754 0.00572129i
\(475\) 7.95995 + 12.4324i 0.365227 + 0.570439i
\(476\) 0 0
\(477\) −0.114982 0.114982i −0.00526467 0.00526467i
\(478\) −18.4398 + 18.5676i −0.843419 + 0.849261i
\(479\) 13.9452 + 24.1538i 0.637172 + 1.10361i 0.986051 + 0.166446i \(0.0532292\pi\)
−0.348879 + 0.937168i \(0.613438\pi\)
\(480\) 20.0502 + 10.5249i 0.915160 + 0.480395i
\(481\) −11.2139 + 19.4231i −0.511311 + 0.885617i
\(482\) −0.112621 0.0297603i −0.00512972 0.00135555i
\(483\) 0 0
\(484\) 11.3622 + 6.45581i 0.516465 + 0.293446i
\(485\) 6.00803 + 1.46295i 0.272810 + 0.0664291i
\(486\) 1.49408 2.60858i 0.0677729 0.118327i
\(487\) −3.75898 1.00721i −0.170335 0.0456412i 0.172643 0.984984i \(-0.444769\pi\)
−0.342979 + 0.939343i \(0.611436\pi\)
\(488\) 4.59682 1.28288i 0.208088 0.0580730i
\(489\) 24.9385i 1.12776i
\(490\) 0 0
\(491\) 14.4151i 0.650544i 0.945620 + 0.325272i \(0.105456\pi\)
−0.945620 + 0.325272i \(0.894544\pi\)
\(492\) −27.6829 7.21315i −1.24804 0.325194i
\(493\) −17.5148 4.69308i −0.788827 0.211366i
\(494\) 14.6790 + 8.40748i 0.660438 + 0.378270i
\(495\) −0.827161 + 0.503215i −0.0371781 + 0.0226178i
\(496\) 20.6638 12.3137i 0.927833 0.552903i
\(497\) 0 0
\(498\) −5.04595 + 19.0951i −0.226114 + 0.855673i
\(499\) 1.47517 2.55507i 0.0660377 0.114381i −0.831116 0.556099i \(-0.812298\pi\)
0.897154 + 0.441718i \(0.145631\pi\)
\(500\) 22.2966 1.69217i 0.997132 0.0756763i
\(501\) 17.7588 + 30.7591i 0.793403 + 1.37422i
\(502\) 9.10871 + 9.04605i 0.406542 + 0.403745i
\(503\) 17.2036 + 17.2036i 0.767071 + 0.767071i 0.977590 0.210518i \(-0.0675152\pi\)
−0.210518 + 0.977590i \(0.567515\pi\)
\(504\) 0 0
\(505\) 2.47781 + 1.35573i 0.110261 + 0.0603291i
\(506\) −0.0575245 16.6656i −0.00255728 0.740878i
\(507\) 5.90305 + 1.58172i 0.262163 + 0.0702465i
\(508\) 7.73673 + 7.63064i 0.343262 + 0.338555i
\(509\) −2.32094 1.34000i −0.102874 0.0593944i 0.447680 0.894194i \(-0.352250\pi\)
−0.550554 + 0.834799i \(0.685584\pi\)
\(510\) 24.6306 25.9666i 1.09066 1.14982i
\(511\) 0 0
\(512\) 15.4953 16.4892i 0.684803 0.728728i
\(513\) −3.82372 14.2703i −0.168821 0.630049i
\(514\) 5.12225 8.94315i 0.225933 0.394465i
\(515\) −20.0705 + 21.0135i −0.884412 + 0.925965i
\(516\) 14.4743 + 24.6752i 0.637194 + 1.08627i
\(517\) 9.09421 + 9.09421i 0.399963 + 0.399963i
\(518\) 0 0
\(519\) −22.4755 −0.986563
\(520\) 21.7514 13.5434i 0.953864 0.593916i
\(521\) 22.5104 + 38.9891i 0.986196 + 1.70814i 0.636495 + 0.771281i \(0.280384\pi\)
0.349702 + 0.936861i \(0.386283\pi\)
\(522\) −0.217872 0.802025i −0.00953598 0.0351037i
\(523\) −6.11620 + 1.63883i −0.267443 + 0.0716610i −0.390048 0.920794i \(-0.627542\pi\)
0.122606 + 0.992455i \(0.460875\pi\)
\(524\) −11.4866 + 20.2164i −0.501795 + 0.883159i
\(525\) 0 0
\(526\) −3.81724 6.55927i −0.166440 0.285998i
\(527\) −9.83987 36.7229i −0.428632 1.59968i
\(528\) 4.11811 + 14.5618i 0.179218 + 0.633720i
\(529\) 7.01165 4.04818i 0.304854 0.176008i
\(530\) −1.19703 + 2.20581i −0.0519956 + 0.0958143i
\(531\) 1.02000i 0.0442641i
\(532\) 0 0
\(533\) −22.8890 + 22.8890i −0.991432 + 0.991432i
\(534\) −0.0181662 5.26300i −0.000786129 0.227752i
\(535\) −31.2388 29.8369i −1.35057 1.28996i
\(536\) −16.4113 27.7573i −0.708859 1.19893i
\(537\) −5.97849 + 1.60193i −0.257991 + 0.0691285i
\(538\) 1.95746 7.40751i 0.0843919 0.319360i
\(539\) 0 0
\(540\) −21.7787 5.14409i −0.937205 0.221367i
\(541\) −8.37685 + 14.5091i −0.360149 + 0.623796i −0.987985 0.154549i \(-0.950607\pi\)
0.627836 + 0.778345i \(0.283941\pi\)
\(542\) −11.1945 + 3.04101i −0.480845 + 0.130623i
\(543\) 7.45797 27.8335i 0.320052 1.19445i
\(544\) −18.4132 30.6583i −0.789460 1.31446i
\(545\) −14.6032 + 26.6897i −0.625531 + 1.14326i
\(546\) 0 0
\(547\) −12.5910 + 12.5910i −0.538352 + 0.538352i −0.923045 0.384693i \(-0.874307\pi\)
0.384693 + 0.923045i \(0.374307\pi\)
\(548\) −41.2994 10.7611i −1.76422 0.459692i
\(549\) 0.299404 0.172861i 0.0127782 0.00737752i
\(550\) 11.0747 + 10.0323i 0.472227 + 0.427777i
\(551\) −7.33366 4.23409i −0.312424 0.180378i
\(552\) −19.7582 + 20.1717i −0.840965 + 0.858564i
\(553\) 0 0
\(554\) 10.7855 + 18.5330i 0.458231 + 0.787391i
\(555\) 11.5176 + 18.9321i 0.488896 + 0.803623i
\(556\) −0.0698318 10.1155i −0.00296153 0.428993i
\(557\) −8.56509 + 31.9653i −0.362914 + 1.35441i 0.507312 + 0.861763i \(0.330639\pi\)
−0.870226 + 0.492652i \(0.836027\pi\)
\(558\) 1.22789 1.23640i 0.0519809 0.0523410i
\(559\) 32.3699 1.36910
\(560\) 0 0
\(561\) 23.9176 1.00980
\(562\) −23.6764 + 23.8404i −0.998730 + 1.00565i
\(563\) 5.05720 18.8737i 0.213136 0.795433i −0.773679 0.633578i \(-0.781586\pi\)
0.986815 0.161855i \(-0.0517478\pi\)
\(564\) −0.150424 21.7897i −0.00633401 0.917513i
\(565\) 5.78027 23.7384i 0.243178 0.998680i
\(566\) 16.8507 + 28.9550i 0.708288 + 1.21707i
\(567\) 0 0
\(568\) 1.20913 1.23444i 0.0507341 0.0517958i
\(569\) 33.7127 + 19.4640i 1.41331 + 0.815974i 0.995699 0.0926518i \(-0.0295344\pi\)
0.417610 + 0.908626i \(0.362868\pi\)
\(570\) 14.2495 8.73639i 0.596844 0.365927i
\(571\) −17.7481 + 10.2468i −0.742733 + 0.428817i −0.823062 0.567951i \(-0.807736\pi\)
0.0803293 + 0.996768i \(0.474403\pi\)
\(572\) 16.5701 + 4.31756i 0.692829 + 0.180526i
\(573\) −6.71308 + 6.71308i −0.280443 + 0.280443i
\(574\) 0 0
\(575\) −5.97315 + 27.2347i −0.249097 + 1.13577i
\(576\) 0.790001 1.43621i 0.0329167 0.0598421i
\(577\) −1.81990 + 6.79196i −0.0757634 + 0.282753i −0.993405 0.114655i \(-0.963424\pi\)
0.917642 + 0.397408i \(0.130090\pi\)
\(578\) −31.3456 + 8.51511i −1.30381 + 0.354182i
\(579\) 20.0313 34.6952i 0.832472 1.44188i
\(580\) −10.9120 + 6.74213i −0.453097 + 0.279952i
\(581\) 0 0
\(582\) 1.78871 6.76892i 0.0741443 0.280581i
\(583\) −1.62000 + 0.434079i −0.0670937 + 0.0179777i
\(584\) −6.58031 11.1297i −0.272295 0.460549i
\(585\) 1.28204 1.34228i 0.0530059 0.0554963i
\(586\) −0.128456 37.2154i −0.00530646 1.53735i
\(587\) −4.00401 + 4.00401i −0.165263 + 0.165263i −0.784894 0.619631i \(-0.787282\pi\)
0.619631 + 0.784894i \(0.287282\pi\)
\(588\) 0 0
\(589\) 17.7550i 0.731584i
\(590\) 15.0932 4.47441i 0.621376 0.184209i
\(591\) −11.6986 + 6.75417i −0.481215 + 0.277829i
\(592\) 21.3077 6.02589i 0.875742 0.247663i
\(593\) 9.08806 + 33.9171i 0.373202 + 1.39281i 0.855954 + 0.517051i \(0.172970\pi\)
−0.482753 + 0.875757i \(0.660363\pi\)
\(594\) −7.52196 12.9252i −0.308630 0.530326i
\(595\) 0 0
\(596\) 7.45212 13.1157i 0.305251 0.537241i
\(597\) 20.5531 5.50720i 0.841184 0.225395i
\(598\) 8.37578 + 30.8328i 0.342511 + 1.26085i
\(599\) −0.687491 1.19077i −0.0280901 0.0486535i 0.851639 0.524129i \(-0.175609\pi\)
−0.879729 + 0.475476i \(0.842276\pi\)
\(600\) −1.42341 25.2775i −0.0581105 1.03195i
\(601\) −8.86739 −0.361708 −0.180854 0.983510i \(-0.557886\pi\)
−0.180854 + 0.983510i \(0.557886\pi\)
\(602\) 0 0
\(603\) −1.65174 1.65174i −0.0672642 0.0672642i
\(604\) 14.1005 + 24.0380i 0.573741 + 0.978093i
\(605\) −0.335263 14.6068i −0.0136304 0.593852i
\(606\) 1.58941 2.77501i 0.0645652 0.112727i
\(607\) 4.40882 + 16.4539i 0.178948 + 0.667845i 0.995845 + 0.0910609i \(0.0290258\pi\)
−0.816897 + 0.576784i \(0.804308\pi\)
\(608\) −4.60047 16.0556i −0.186574 0.651139i
\(609\) 0 0
\(610\) −3.87125 3.67206i −0.156742 0.148677i
\(611\) −21.3530 12.3282i −0.863851 0.498744i
\(612\) −1.84449 1.81920i −0.0745591 0.0735367i
\(613\) 27.5042 + 7.36973i 1.11088 + 0.297661i 0.767189 0.641421i \(-0.221655\pi\)
0.343695 + 0.939081i \(0.388321\pi\)
\(614\) 0.132495 + 38.3857i 0.00534708 + 1.54912i
\(615\) 8.98474 + 30.6959i 0.362300 + 1.23778i
\(616\) 0 0
\(617\) 0.247352 + 0.247352i 0.00995801 + 0.00995801i 0.712068 0.702110i \(-0.247759\pi\)
−0.702110 + 0.712068i \(0.747759\pi\)
\(618\) 23.3447 + 23.1841i 0.939060 + 0.932600i
\(619\) −4.44950 7.70677i −0.178841 0.309761i 0.762643 0.646820i \(-0.223901\pi\)
−0.941484 + 0.337059i \(0.890568\pi\)
\(620\) −23.6817 12.7457i −0.951080 0.511881i
\(621\) 13.9518 24.1652i 0.559866 0.969716i
\(622\) 5.00320 18.9334i 0.200610 0.759159i
\(623\) 0 0
\(624\) −14.8512 24.9220i −0.594525 0.997679i
\(625\) −14.4320 20.4137i −0.577279 0.816547i
\(626\) −28.8640 16.5321i −1.15364 0.660755i
\(627\) 10.7892 + 2.89096i 0.430879 + 0.115454i
\(628\) 15.4439 + 4.02413i 0.616280 + 0.160580i
\(629\) 34.9978i 1.39545i
\(630\) 0 0
\(631\) 30.9594i 1.23248i −0.787560 0.616238i \(-0.788656\pi\)
0.787560 0.616238i \(-0.211344\pi\)
\(632\) −38.8322 + 10.8372i −1.54466 + 0.431083i
\(633\) 3.53505 + 0.947212i 0.140505 + 0.0376483i
\(634\) 0.579651 1.01204i 0.0230209 0.0401931i
\(635\) 2.87435 11.8044i 0.114065 0.468441i
\(636\) 2.47060 + 1.40375i 0.0979657 + 0.0556624i
\(637\) 0 0
\(638\) −8.28739 2.18997i −0.328101 0.0867017i
\(639\) 0.0625872 0.108404i 0.00247591 0.00428841i
\(640\) −24.7174 5.38963i −0.977043 0.213044i
\(641\) −6.18079 10.7055i −0.244127 0.422840i 0.717759 0.696292i \(-0.245168\pi\)
−0.961886 + 0.273452i \(0.911835\pi\)
\(642\) −34.4656 + 34.7043i −1.36025 + 1.36967i
\(643\) 2.95024 + 2.95024i 0.116346 + 0.116346i 0.762883 0.646537i \(-0.223783\pi\)
−0.646537 + 0.762883i \(0.723783\pi\)
\(644\) 0 0
\(645\) 15.3521 28.0584i 0.604488 1.10480i
\(646\) −26.3969 + 0.0911138i −1.03857 + 0.00358482i
\(647\) 4.60847 + 1.23483i 0.181178 + 0.0485464i 0.348267 0.937395i \(-0.386770\pi\)
−0.167090 + 0.985942i \(0.553437\pi\)
\(648\) −6.73652 + 26.2243i −0.264635 + 1.03019i
\(649\) 9.11081 + 5.26013i 0.357630 + 0.206478i
\(650\) −25.4859 13.0825i −0.999640 0.513140i
\(651\) 0 0
\(652\) −7.39650 26.8610i −0.289669 1.05196i
\(653\) 2.16858 + 8.09326i 0.0848632 + 0.316714i 0.995288 0.0969603i \(-0.0309120\pi\)
−0.910425 + 0.413674i \(0.864245\pi\)
\(654\) 29.8909 + 17.1202i 1.16883 + 0.669454i
\(655\) 25.9895 0.596523i 1.01549 0.0233081i
\(656\) 31.9563 0.441239i 1.24768 0.0172275i
\(657\) −0.662288 0.662288i −0.0258383 0.0258383i
\(658\) 0 0
\(659\) −35.0426 −1.36507 −0.682534 0.730854i \(-0.739122\pi\)
−0.682534 + 0.730854i \(0.739122\pi\)
\(660\) 11.6012 12.3153i 0.451575 0.479374i
\(661\) −9.52109 16.4910i −0.370328 0.641426i 0.619288 0.785164i \(-0.287421\pi\)
−0.989616 + 0.143737i \(0.954088\pi\)
\(662\) −19.5837 + 5.31995i −0.761141 + 0.206766i
\(663\) −44.2904 + 11.8676i −1.72010 + 0.460899i
\(664\) −0.228479 22.0638i −0.00886670 0.856241i
\(665\) 0 0
\(666\) 1.38640 0.806832i 0.0537219 0.0312641i
\(667\) −4.13958 15.4491i −0.160285 0.598193i
\(668\) −28.2507 27.8633i −1.09305 1.07806i
\(669\) −28.8542 + 16.6590i −1.11557 + 0.644074i
\(670\) −17.1956 + 31.6869i −0.664323 + 1.22417i
\(671\) 3.56577i 0.137655i
\(672\) 0 0
\(673\) −25.9196 + 25.9196i −0.999127 + 0.999127i −1.00000 0.000872915i \(-0.999722\pi\)
0.000872915 1.00000i \(0.499722\pi\)
\(674\) 0.124954 0.000431300i 0.00481303 1.66131e-5i
\(675\) 7.57744 + 23.8442i 0.291656 + 0.917765i
\(676\) −6.82724 + 0.0471315i −0.262586 + 0.00181275i
\(677\) −13.2916 + 3.56148i −0.510838 + 0.136879i −0.505026 0.863104i \(-0.668517\pi\)
−0.00581271 + 0.999983i \(0.501850\pi\)
\(678\) −26.7447 7.06737i −1.02712 0.271421i
\(679\) 0 0
\(680\) −18.8279 + 35.2736i −0.722018 + 1.35268i
\(681\) −4.98184 + 8.62881i −0.190905 + 0.330657i
\(682\) −4.71150 17.3439i −0.180413 0.664132i
\(683\) 2.14974 8.02293i 0.0822574 0.306989i −0.912523 0.409025i \(-0.865869\pi\)
0.994781 + 0.102036i \(0.0325357\pi\)
\(684\) −0.612158 1.04359i −0.0234065 0.0399025i
\(685\) 13.4041 + 45.7944i 0.512145 + 1.74971i
\(686\) 0 0
\(687\) 10.3937 10.3937i 0.396546 0.396546i
\(688\) −22.9085 22.2845i −0.873379 0.849589i
\(689\) 2.78453 1.60765i 0.106082 0.0612465i
\(690\) 30.6984 + 7.36289i 1.16867 + 0.280300i
\(691\) −7.15943 4.13350i −0.272357 0.157246i 0.357601 0.933874i \(-0.383595\pi\)
−0.629958 + 0.776629i \(0.716928\pi\)
\(692\) 24.2081 6.66600i 0.920255 0.253403i
\(693\) 0 0
\(694\) −10.7834 + 6.27551i −0.409331 + 0.238215i
\(695\) −9.66218 + 5.87813i −0.366507 + 0.222970i
\(696\) 7.39136 + 12.5015i 0.280169 + 0.473866i
\(697\) 13.0735 48.7908i 0.495192 1.84808i
\(698\) −3.79101 3.76493i −0.143492 0.142505i
\(699\) 21.4649 0.811878
\(700\) 0 0
\(701\) −14.1462 −0.534296 −0.267148 0.963656i \(-0.586081\pi\)
−0.267148 + 0.963656i \(0.586081\pi\)
\(702\) 20.3424 + 20.2025i 0.767775 + 0.762493i
\(703\) 4.23024 15.7875i 0.159547 0.595436i
\(704\) −8.75446 14.4630i −0.329946 0.545093i
\(705\) −20.8132 + 12.6620i −0.783872 + 0.476880i
\(706\) 1.51919 0.884111i 0.0571755 0.0332740i
\(707\) 0 0
\(708\) −4.73197 17.1845i −0.177838 0.645834i
\(709\) −10.2057 5.89228i −0.383284 0.221289i 0.295962 0.955200i \(-0.404360\pi\)
−0.679246 + 0.733910i \(0.737693\pi\)
\(710\) −1.87864 0.450583i −0.0705040 0.0169101i
\(711\) −2.52925 + 1.46026i −0.0948542 + 0.0547641i
\(712\) 1.58052 + 5.66334i 0.0592325 + 0.212243i
\(713\) 23.7125 23.7125i 0.888039 0.888039i
\(714\) 0 0
\(715\) −5.37797 18.3736i −0.201125 0.687132i
\(716\) 5.96426 3.49859i 0.222895 0.130748i
\(717\) 8.57362 31.9972i 0.320188 1.19496i
\(718\) 6.48952 + 23.8891i 0.242187 + 0.891533i
\(719\) 9.74435 16.8777i 0.363403 0.629433i −0.625115 0.780532i \(-0.714948\pi\)
0.988519 + 0.151100i \(0.0482815\pi\)
\(720\) −1.83138 + 0.0673431i −0.0682516 + 0.00250973i
\(721\) 0 0
\(722\) 14.0597 + 3.71532i 0.523248 + 0.138270i
\(723\) 0.142433 0.0381648i 0.00529714 0.00141936i
\(724\) 0.222230 + 32.1912i 0.00825913 + 1.19638i
\(725\) 12.7355 + 6.59307i 0.472983 + 0.244860i
\(726\) −16.5426 + 0.0571000i −0.613955 + 0.00211918i
\(727\) −21.7062 + 21.7062i −0.805039 + 0.805039i −0.983878 0.178839i \(-0.942766\pi\)
0.178839 + 0.983878i \(0.442766\pi\)
\(728\) 0 0
\(729\) 24.9127i 0.922692i
\(730\) −6.89479 + 12.7053i −0.255188 + 0.470244i
\(731\) −43.7446 + 25.2560i −1.61795 + 0.934126i
\(732\) −4.24230 + 4.30128i −0.156800 + 0.158980i
\(733\) −6.04984 22.5783i −0.223456 0.833949i −0.983017 0.183513i \(-0.941253\pi\)
0.759561 0.650436i \(-0.225414\pi\)
\(734\) −19.0296 + 11.0745i −0.702395 + 0.408767i
\(735\) 0 0
\(736\) 15.2987 27.5868i 0.563916 1.01686i
\(737\) −23.2717 + 6.23563i −0.857224 + 0.229693i
\(738\) 2.23419 0.606922i 0.0822417 0.0223411i
\(739\) −4.82260 8.35299i −0.177402 0.307270i 0.763588 0.645704i \(-0.223436\pi\)
−0.940990 + 0.338434i \(0.890103\pi\)
\(740\) −18.0206 16.9756i −0.662451 0.624035i
\(741\) −21.4138 −0.786657
\(742\) 0 0
\(743\) −24.5711 24.5711i −0.901426 0.901426i 0.0941337 0.995560i \(-0.469992\pi\)
−0.995560 + 0.0941337i \(0.969992\pi\)
\(744\) −14.9512 + 26.5268i −0.548137 + 0.972520i
\(745\) −16.8611 + 0.387004i −0.617742 + 0.0141787i
\(746\) 0.965548 + 0.553025i 0.0353512 + 0.0202477i
\(747\) −0.413697 1.54394i −0.0151364 0.0564897i
\(748\) −25.7614 + 7.09372i −0.941931 + 0.259372i
\(749\) 0 0
\(750\) −23.4273 + 15.8867i −0.855442 + 0.580100i
\(751\) 45.6939 + 26.3814i 1.66739 + 0.962671i 0.969035 + 0.246923i \(0.0794195\pi\)
0.698359 + 0.715747i \(0.253914\pi\)
\(752\) 6.62464 + 23.4249i 0.241576 + 0.854219i
\(753\) −15.6969 4.20597i −0.572027 0.153274i
\(754\) 16.4332 0.0567221i 0.598461 0.00206570i
\(755\) 14.9557 27.3339i 0.544292 0.994782i
\(756\) 0 0
\(757\) −4.54052 4.54052i −0.165028 0.165028i 0.619762 0.784790i \(-0.287229\pi\)
−0.784790 + 0.619762i \(0.787229\pi\)
\(758\) 9.11832 9.18148i 0.331192 0.333486i
\(759\) 10.5484 + 18.2703i 0.382882 + 0.663172i
\(760\) −12.7568 + 13.6361i −0.462739 + 0.494635i
\(761\) −5.96614 + 10.3337i −0.216272 + 0.374595i −0.953665 0.300869i \(-0.902723\pi\)
0.737393 + 0.675464i \(0.236057\pi\)
\(762\) −13.2993 3.51439i −0.481783 0.127313i
\(763\) 0 0
\(764\) 5.23957 9.22163i 0.189561 0.333627i
\(765\) −0.685265 + 2.81424i −0.0247758 + 0.101749i
\(766\) 5.93426 10.3609i 0.214413 0.374353i
\(767\) −19.4813 5.22001i −0.703430 0.188484i
\(768\) −6.64677 + 27.8617i −0.239845 + 1.00537i
\(769\) 29.2063i 1.05321i −0.850111 0.526603i \(-0.823465\pi\)
0.850111 0.526603i \(-0.176535\pi\)
\(770\) 0 0
\(771\) 13.0464i 0.469854i
\(772\) −11.2853 + 43.3110i −0.406166 + 1.55880i
\(773\) 34.7584 + 9.31348i 1.25017 + 0.334982i 0.822403 0.568906i \(-0.192633\pi\)
0.427769 + 0.903888i \(0.359300\pi\)
\(774\) −2.00897 1.15065i −0.0722109 0.0413593i
\(775\) 1.37955 + 30.0365i 0.0495550 + 1.07894i
\(776\) 0.0809921 + 7.82125i 0.00290745 + 0.280767i
\(777\) 0 0
\(778\) −10.3813 + 39.2855i −0.372188 + 1.40845i
\(779\) 11.7948