Properties

Label 115.2.b.b.24.3
Level $115$
Weight $2$
Character 115.24
Analytic conductor $0.918$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 115.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.918279623245\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.527896576.2
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} + 7 x^{4} - 10 x^{3} + 8 x^{2} + 4 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 24.3
Root \(0.790245 - 0.790245i\) of defining polynomial
Character \(\chi\) \(=\) 115.24
Dual form 115.2.b.b.24.6

$q$-expansion

\(f(q)\) \(=\) \(q-0.751024i q^{2} +0.580491i q^{3} +1.43596 q^{4} +(-0.209755 + 2.22621i) q^{5} +0.435963 q^{6} +0.315061i q^{7} -2.58049i q^{8} +2.66303 q^{9} +O(q^{10})\) \(q-0.751024i q^{2} +0.580491i q^{3} +1.43596 q^{4} +(-0.209755 + 2.22621i) q^{5} +0.435963 q^{6} +0.315061i q^{7} -2.58049i q^{8} +2.66303 q^{9} +(1.67194 + 0.157531i) q^{10} -4.34797 q^{11} +0.833563i q^{12} -4.58049i q^{13} +0.236619 q^{14} +(-1.29229 - 0.121761i) q^{15} +0.933914 q^{16} +0.917461i q^{17} -2.00000i q^{18} -2.76748 q^{19} +(-0.301200 + 3.19675i) q^{20} -0.182890 q^{21} +3.26543i q^{22} +1.00000i q^{23} +1.49795 q^{24} +(-4.91201 - 0.933914i) q^{25} -3.44006 q^{26} +3.28734i q^{27} +0.452416i q^{28} -7.03291 q^{29} +(-0.0914452 + 0.970544i) q^{30} -0.867829 q^{31} -5.86237i q^{32} -2.52396i q^{33} +0.689035 q^{34} +(-0.701392 - 0.0660856i) q^{35} +3.82401 q^{36} +4.68904i q^{37} +2.07844i q^{38} +2.65893 q^{39} +(5.74471 + 0.541270i) q^{40} +4.69184 q^{41} +0.137355i q^{42} -9.08944i q^{43} -6.24352 q^{44} +(-0.558583 + 5.92846i) q^{45} +0.751024 q^{46} +8.24762i q^{47} +0.542129i q^{48} +6.90074 q^{49} +(-0.701392 + 3.68904i) q^{50} -0.532578 q^{51} -6.57741i q^{52} -10.9048i q^{53} +2.46887 q^{54} +(0.912006 - 9.67948i) q^{55} +0.813013 q^{56} -1.60650i q^{57} +5.28188i q^{58} -1.50205 q^{59} +(-1.85569 - 0.174844i) q^{60} +11.4634 q^{61} +0.651760i q^{62} +0.839018i q^{63} -2.53496 q^{64} +(10.1971 + 0.960779i) q^{65} -1.89555 q^{66} -1.68494i q^{67} +1.31744i q^{68} -0.580491 q^{69} +(-0.0496318 + 0.526763i) q^{70} -5.36578 q^{71} -6.87193i q^{72} +10.1484i q^{73} +3.52158 q^{74} +(0.542129 - 2.85138i) q^{75} -3.97400 q^{76} -1.36988i q^{77} -1.99692i q^{78} -7.39760 q^{79} +(-0.195893 + 2.07909i) q^{80} +6.08082 q^{81} -3.52369i q^{82} +15.3052i q^{83} -0.262624 q^{84} +(-2.04246 - 0.192442i) q^{85} -6.82639 q^{86} -4.08254i q^{87} +11.2199i q^{88} +10.9326 q^{89} +(4.45242 + 0.419509i) q^{90} +1.44314 q^{91} +1.43596i q^{92} -0.503767i q^{93} +6.19416 q^{94} +(0.580491 - 6.16098i) q^{95} +3.40306 q^{96} +14.2158i q^{97} -5.18262i q^{98} -11.5788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9} + 6 q^{10} + 4 q^{11} + 8 q^{14} + 6 q^{15} + 4 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{21} + 24 q^{24} - 16 q^{25} + 12 q^{26} - 8 q^{29} - 2 q^{30} - 28 q^{34} + 28 q^{35} - 16 q^{36} + 16 q^{39} - 10 q^{40} - 16 q^{41} - 12 q^{44} + 24 q^{45} + 28 q^{50} + 20 q^{51} - 44 q^{54} - 16 q^{55} + 28 q^{56} - 16 q^{60} - 16 q^{61} + 40 q^{64} - 14 q^{65} - 16 q^{66} + 4 q^{69} - 28 q^{70} - 48 q^{71} + 72 q^{74} - 36 q^{76} - 48 q^{79} - 2 q^{80} + 16 q^{81} - 4 q^{84} + 12 q^{85} + 28 q^{86} + 16 q^{89} - 4 q^{90} + 52 q^{91} + 84 q^{94} - 4 q^{95} + 60 q^{96} - 72 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.751024i 0.531054i −0.964103 0.265527i \(-0.914454\pi\)
0.964103 0.265527i \(-0.0855460\pi\)
\(3\) 0.580491i 0.335147i 0.985860 + 0.167573i \(0.0535931\pi\)
−0.985860 + 0.167573i \(0.946407\pi\)
\(4\) 1.43596 0.717981
\(5\) −0.209755 + 2.22621i −0.0938051 + 0.995591i
\(6\) 0.435963 0.177981
\(7\) 0.315061i 0.119082i 0.998226 + 0.0595410i \(0.0189637\pi\)
−0.998226 + 0.0595410i \(0.981036\pi\)
\(8\) 2.58049i 0.912341i
\(9\) 2.66303 0.887677
\(10\) 1.67194 + 0.157531i 0.528713 + 0.0498156i
\(11\) −4.34797 −1.31096 −0.655481 0.755212i \(-0.727534\pi\)
−0.655481 + 0.755212i \(0.727534\pi\)
\(12\) 0.833563i 0.240629i
\(13\) 4.58049i 1.27040i −0.772348 0.635200i \(-0.780918\pi\)
0.772348 0.635200i \(-0.219082\pi\)
\(14\) 0.236619 0.0632390
\(15\) −1.29229 0.121761i −0.333669 0.0314385i
\(16\) 0.933914 0.233479
\(17\) 0.917461i 0.222517i 0.993792 + 0.111258i \(0.0354881\pi\)
−0.993792 + 0.111258i \(0.964512\pi\)
\(18\) 2.00000i 0.471405i
\(19\) −2.76748 −0.634903 −0.317451 0.948275i \(-0.602827\pi\)
−0.317451 + 0.948275i \(0.602827\pi\)
\(20\) −0.301200 + 3.19675i −0.0673503 + 0.714815i
\(21\) −0.182890 −0.0399099
\(22\) 3.26543i 0.696192i
\(23\) 1.00000i 0.208514i
\(24\) 1.49795 0.305768
\(25\) −4.91201 0.933914i −0.982401 0.186783i
\(26\) −3.44006 −0.674651
\(27\) 3.28734i 0.632648i
\(28\) 0.452416i 0.0854987i
\(29\) −7.03291 −1.30598 −0.652989 0.757367i \(-0.726485\pi\)
−0.652989 + 0.757367i \(0.726485\pi\)
\(30\) −0.0914452 + 0.970544i −0.0166955 + 0.177196i
\(31\) −0.867829 −0.155867 −0.0779333 0.996959i \(-0.524832\pi\)
−0.0779333 + 0.996959i \(0.524832\pi\)
\(32\) 5.86237i 1.03633i
\(33\) 2.52396i 0.439364i
\(34\) 0.689035 0.118169
\(35\) −0.701392 0.0660856i −0.118557 0.0111705i
\(36\) 3.82401 0.637335
\(37\) 4.68904i 0.770873i 0.922734 + 0.385436i \(0.125949\pi\)
−0.922734 + 0.385436i \(0.874051\pi\)
\(38\) 2.07844i 0.337168i
\(39\) 2.65893 0.425770
\(40\) 5.74471 + 0.541270i 0.908318 + 0.0855822i
\(41\) 4.69184 0.732742 0.366371 0.930469i \(-0.380600\pi\)
0.366371 + 0.930469i \(0.380600\pi\)
\(42\) 0.137355i 0.0211943i
\(43\) 9.08944i 1.38613i −0.720877 0.693063i \(-0.756261\pi\)
0.720877 0.693063i \(-0.243739\pi\)
\(44\) −6.24352 −0.941246
\(45\) −0.558583 + 5.92846i −0.0832686 + 0.883763i
\(46\) 0.751024 0.110732
\(47\) 8.24762i 1.20304i 0.798858 + 0.601519i \(0.205438\pi\)
−0.798858 + 0.601519i \(0.794562\pi\)
\(48\) 0.542129i 0.0782496i
\(49\) 6.90074 0.985819
\(50\) −0.701392 + 3.68904i −0.0991919 + 0.521708i
\(51\) −0.532578 −0.0745758
\(52\) 6.57741i 0.912123i
\(53\) 10.9048i 1.49789i −0.662630 0.748947i \(-0.730560\pi\)
0.662630 0.748947i \(-0.269440\pi\)
\(54\) 2.46887 0.335971
\(55\) 0.912006 9.67948i 0.122975 1.30518i
\(56\) 0.813013 0.108643
\(57\) 1.60650i 0.212786i
\(58\) 5.28188i 0.693545i
\(59\) −1.50205 −0.195550 −0.0977750 0.995209i \(-0.531173\pi\)
−0.0977750 + 0.995209i \(0.531173\pi\)
\(60\) −1.85569 0.174844i −0.239568 0.0225722i
\(61\) 11.4634 1.46774 0.733870 0.679290i \(-0.237712\pi\)
0.733870 + 0.679290i \(0.237712\pi\)
\(62\) 0.651760i 0.0827737i
\(63\) 0.839018i 0.105706i
\(64\) −2.53496 −0.316869
\(65\) 10.1971 + 0.960779i 1.26480 + 0.119170i
\(66\) −1.89555 −0.233326
\(67\) 1.68494i 0.205848i −0.994689 0.102924i \(-0.967180\pi\)
0.994689 0.102924i \(-0.0328198\pi\)
\(68\) 1.31744i 0.159763i
\(69\) −0.580491 −0.0698829
\(70\) −0.0496318 + 0.526763i −0.00593214 + 0.0629602i
\(71\) −5.36578 −0.636801 −0.318401 0.947956i \(-0.603146\pi\)
−0.318401 + 0.947956i \(0.603146\pi\)
\(72\) 6.87193i 0.809864i
\(73\) 10.1484i 1.18778i 0.804548 + 0.593888i \(0.202408\pi\)
−0.804548 + 0.593888i \(0.797592\pi\)
\(74\) 3.52158 0.409375
\(75\) 0.542129 2.85138i 0.0625997 0.329248i
\(76\) −3.97400 −0.455848
\(77\) 1.36988i 0.156112i
\(78\) 1.99692i 0.226107i
\(79\) −7.39760 −0.832295 −0.416148 0.909297i \(-0.636620\pi\)
−0.416148 + 0.909297i \(0.636620\pi\)
\(80\) −0.195893 + 2.07909i −0.0219015 + 0.232449i
\(81\) 6.08082 0.675647
\(82\) 3.52369i 0.389126i
\(83\) 15.3052i 1.67997i 0.542611 + 0.839984i \(0.317436\pi\)
−0.542611 + 0.839984i \(0.682564\pi\)
\(84\) −0.262624 −0.0286546
\(85\) −2.04246 0.192442i −0.221536 0.0208732i
\(86\) −6.82639 −0.736109
\(87\) 4.08254i 0.437694i
\(88\) 11.2199i 1.19604i
\(89\) 10.9326 1.15885 0.579424 0.815026i \(-0.303277\pi\)
0.579424 + 0.815026i \(0.303277\pi\)
\(90\) 4.45242 + 0.419509i 0.469326 + 0.0442201i
\(91\) 1.44314 0.151282
\(92\) 1.43596i 0.149709i
\(93\) 0.503767i 0.0522382i
\(94\) 6.19416 0.638879
\(95\) 0.580491 6.16098i 0.0595571 0.632103i
\(96\) 3.40306 0.347323
\(97\) 14.2158i 1.44340i 0.692208 + 0.721698i \(0.256638\pi\)
−0.692208 + 0.721698i \(0.743362\pi\)
\(98\) 5.18262i 0.523524i
\(99\) −11.5788 −1.16371
\(100\) −7.05346 1.34107i −0.705346 0.134107i
\(101\) −8.16508 −0.812456 −0.406228 0.913772i \(-0.633156\pi\)
−0.406228 + 0.913772i \(0.633156\pi\)
\(102\) 0.399979i 0.0396038i
\(103\) 0.287338i 0.0283122i −0.999900 0.0141561i \(-0.995494\pi\)
0.999900 0.0141561i \(-0.00450618\pi\)
\(104\) −11.8199 −1.15904
\(105\) 0.0383621 0.407152i 0.00374375 0.0397340i
\(106\) −8.18979 −0.795463
\(107\) 14.0935i 1.36247i −0.732063 0.681237i \(-0.761442\pi\)
0.732063 0.681237i \(-0.238558\pi\)
\(108\) 4.72049i 0.454230i
\(109\) −1.76338 −0.168901 −0.0844506 0.996428i \(-0.526914\pi\)
−0.0844506 + 0.996428i \(0.526914\pi\)
\(110\) −7.26953 0.684939i −0.693122 0.0653063i
\(111\) −2.72194 −0.258355
\(112\) 0.294240i 0.0278031i
\(113\) 0.315061i 0.0296385i 0.999890 + 0.0148192i \(0.00471728\pi\)
−0.999890 + 0.0148192i \(0.995283\pi\)
\(114\) −1.20652 −0.113001
\(115\) −2.22621 0.209755i −0.207595 0.0195597i
\(116\) −10.0990 −0.937668
\(117\) 12.1980i 1.12770i
\(118\) 1.12807i 0.103848i
\(119\) −0.289056 −0.0264978
\(120\) −0.314202 + 3.33475i −0.0286826 + 0.304420i
\(121\) 7.90483 0.718621
\(122\) 8.60930i 0.779450i
\(123\) 2.72357i 0.245576i
\(124\) −1.24617 −0.111909
\(125\) 3.10940 10.7393i 0.278114 0.960548i
\(126\) 0.630123 0.0561358
\(127\) 21.3284i 1.89259i 0.323300 + 0.946296i \(0.395208\pi\)
−0.323300 + 0.946296i \(0.604792\pi\)
\(128\) 9.82094i 0.868056i
\(129\) 5.27634 0.464556
\(130\) 0.721568 7.65829i 0.0632857 0.671676i
\(131\) 8.11373 0.708900 0.354450 0.935075i \(-0.384668\pi\)
0.354450 + 0.935075i \(0.384668\pi\)
\(132\) 3.62431i 0.315455i
\(133\) 0.871925i 0.0756055i
\(134\) −1.26543 −0.109316
\(135\) −7.31830 0.689534i −0.629859 0.0593456i
\(136\) 2.36750 0.203011
\(137\) 7.22680i 0.617427i 0.951155 + 0.308713i \(0.0998984\pi\)
−0.951155 + 0.308713i \(0.900102\pi\)
\(138\) 0.435963i 0.0371116i
\(139\) 10.8431 0.919701 0.459850 0.887996i \(-0.347903\pi\)
0.459850 + 0.887996i \(0.347903\pi\)
\(140\) −1.00717 0.0948964i −0.0851217 0.00802021i
\(141\) −4.78767 −0.403194
\(142\) 4.02983i 0.338176i
\(143\) 19.9158i 1.66545i
\(144\) 2.48704 0.207254
\(145\) 1.47518 15.6567i 0.122507 1.30022i
\(146\) 7.62166 0.630773
\(147\) 4.00582i 0.330394i
\(148\) 6.73328i 0.553472i
\(149\) 7.90074 0.647254 0.323627 0.946185i \(-0.395098\pi\)
0.323627 + 0.946185i \(0.395098\pi\)
\(150\) −2.14145 0.407152i −0.174849 0.0332438i
\(151\) −8.03700 −0.654042 −0.327021 0.945017i \(-0.606045\pi\)
−0.327021 + 0.945017i \(0.606045\pi\)
\(152\) 7.14145i 0.579248i
\(153\) 2.44323i 0.197523i
\(154\) −1.02881 −0.0829039
\(155\) 0.182031 1.93197i 0.0146211 0.155179i
\(156\) 3.81813 0.305695
\(157\) 4.75928i 0.379832i 0.981800 + 0.189916i \(0.0608216\pi\)
−0.981800 + 0.189916i \(0.939178\pi\)
\(158\) 5.55578i 0.441994i
\(159\) 6.33016 0.502014
\(160\) 13.0509 + 1.22966i 1.03176 + 0.0972131i
\(161\) −0.315061 −0.0248303
\(162\) 4.56684i 0.358805i
\(163\) 2.11545i 0.165695i −0.996562 0.0828473i \(-0.973599\pi\)
0.996562 0.0828473i \(-0.0264014\pi\)
\(164\) 6.73731 0.526095
\(165\) 5.61885 + 0.529411i 0.437427 + 0.0412146i
\(166\) 11.4946 0.892154
\(167\) 15.8760i 1.22852i −0.789102 0.614262i \(-0.789454\pi\)
0.789102 0.614262i \(-0.210546\pi\)
\(168\) 0.471947i 0.0364115i
\(169\) −7.98090 −0.613915
\(170\) −0.144528 + 1.53394i −0.0110848 + 0.117648i
\(171\) −7.36988 −0.563589
\(172\) 13.0521i 0.995213i
\(173\) 0.0767241i 0.00583323i 0.999996 + 0.00291661i \(0.000928388\pi\)
−0.999996 + 0.00291661i \(0.999072\pi\)
\(174\) −3.06609 −0.232439
\(175\) 0.294240 1.54758i 0.0222425 0.116986i
\(176\) −4.06063 −0.306082
\(177\) 0.871925i 0.0655379i
\(178\) 8.21061i 0.615412i
\(179\) 20.7247 1.54904 0.774520 0.632549i \(-0.217991\pi\)
0.774520 + 0.632549i \(0.217991\pi\)
\(180\) −0.802104 + 8.51305i −0.0597853 + 0.634525i
\(181\) −11.5610 −0.859319 −0.429660 0.902991i \(-0.641366\pi\)
−0.429660 + 0.902991i \(0.641366\pi\)
\(182\) 1.08383i 0.0803388i
\(183\) 6.65441i 0.491908i
\(184\) 2.58049 0.190236
\(185\) −10.4388 0.983546i −0.767474 0.0723118i
\(186\) −0.378341 −0.0277413
\(187\) 3.98909i 0.291711i
\(188\) 11.8433i 0.863759i
\(189\) −1.03571 −0.0753371
\(190\) −4.62705 0.435963i −0.335681 0.0316281i
\(191\) 21.9683 1.58957 0.794784 0.606892i \(-0.207584\pi\)
0.794784 + 0.606892i \(0.207584\pi\)
\(192\) 1.47152i 0.106198i
\(193\) 20.2914i 1.46061i −0.683122 0.730305i \(-0.739378\pi\)
0.683122 0.730305i \(-0.260622\pi\)
\(194\) 10.6764 0.766521
\(195\) −0.557723 + 5.91934i −0.0399394 + 0.423893i
\(196\) 9.90920 0.707800
\(197\) 8.62159i 0.614263i 0.951667 + 0.307131i \(0.0993691\pi\)
−0.951667 + 0.307131i \(0.900631\pi\)
\(198\) 8.69594i 0.617993i
\(199\) −20.7796 −1.47302 −0.736512 0.676424i \(-0.763529\pi\)
−0.736512 + 0.676424i \(0.763529\pi\)
\(200\) −2.40996 + 12.6754i −0.170410 + 0.896285i
\(201\) 0.978092 0.0689893
\(202\) 6.13217i 0.431458i
\(203\) 2.21580i 0.155519i
\(204\) −0.764762 −0.0535440
\(205\) −0.984135 + 10.4450i −0.0687350 + 0.729512i
\(206\) −0.215798 −0.0150353
\(207\) 2.66303i 0.185093i
\(208\) 4.27779i 0.296611i
\(209\) 12.0329 0.832334
\(210\) −0.305781 0.0288108i −0.0211009 0.00198814i
\(211\) −4.16508 −0.286736 −0.143368 0.989669i \(-0.545793\pi\)
−0.143368 + 0.989669i \(0.545793\pi\)
\(212\) 15.6589i 1.07546i
\(213\) 3.11479i 0.213422i
\(214\) −10.5846 −0.723548
\(215\) 20.2350 + 1.90655i 1.38001 + 0.130026i
\(216\) 8.48295 0.577191
\(217\) 0.273419i 0.0185609i
\(218\) 1.32434i 0.0896958i
\(219\) −5.89103 −0.398079
\(220\) 1.30961 13.8994i 0.0882937 0.937096i
\(221\) 4.20242 0.282685
\(222\) 2.04424i 0.137201i
\(223\) 18.7618i 1.25638i −0.778060 0.628190i \(-0.783796\pi\)
0.778060 0.628190i \(-0.216204\pi\)
\(224\) 1.84701 0.123408
\(225\) −13.0808 2.48704i −0.872055 0.165803i
\(226\) 0.236619 0.0157396
\(227\) 10.9637i 0.727689i −0.931460 0.363845i \(-0.881464\pi\)
0.931460 0.363845i \(-0.118536\pi\)
\(228\) 2.30687i 0.152776i
\(229\) −25.9367 −1.71394 −0.856971 0.515364i \(-0.827657\pi\)
−0.856971 + 0.515364i \(0.827657\pi\)
\(230\) −0.157531 + 1.67194i −0.0103873 + 0.110244i
\(231\) 0.795201 0.0523204
\(232\) 18.1484i 1.19150i
\(233\) 8.23942i 0.539783i −0.962891 0.269891i \(-0.913012\pi\)
0.962891 0.269891i \(-0.0869878\pi\)
\(234\) −9.16098 −0.598872
\(235\) −18.3609 1.72998i −1.19773 0.112851i
\(236\) −2.15689 −0.140401
\(237\) 4.29424i 0.278941i
\(238\) 0.217088i 0.0140718i
\(239\) −16.0508 −1.03824 −0.519120 0.854701i \(-0.673740\pi\)
−0.519120 + 0.854701i \(0.673740\pi\)
\(240\) −1.20689 0.113714i −0.0779045 0.00734021i
\(241\) −2.09755 −0.135115 −0.0675574 0.997715i \(-0.521521\pi\)
−0.0675574 + 0.997715i \(0.521521\pi\)
\(242\) 5.93672i 0.381627i
\(243\) 13.3919i 0.859089i
\(244\) 16.4610 1.05381
\(245\) −1.44746 + 15.3625i −0.0924749 + 0.981473i
\(246\) 2.04547 0.130414
\(247\) 12.6764i 0.806580i
\(248\) 2.23942i 0.142204i
\(249\) −8.88455 −0.563036
\(250\) −8.06544 2.33524i −0.510103 0.147693i
\(251\) −13.7018 −0.864847 −0.432423 0.901671i \(-0.642341\pi\)
−0.432423 + 0.901671i \(0.642341\pi\)
\(252\) 1.20480i 0.0758952i
\(253\) 4.34797i 0.273354i
\(254\) 16.0182 1.00507
\(255\) 0.111711 1.18563i 0.00699559 0.0742470i
\(256\) −12.4457 −0.777854
\(257\) 0.998281i 0.0622711i −0.999515 0.0311355i \(-0.990088\pi\)
0.999515 0.0311355i \(-0.00991235\pi\)
\(258\) 3.96266i 0.246704i
\(259\) −1.47733 −0.0917971
\(260\) 14.6427 + 1.37964i 0.908101 + 0.0855618i
\(261\) −18.7288 −1.15929
\(262\) 6.09361i 0.376464i
\(263\) 9.18527i 0.566388i −0.959063 0.283194i \(-0.908606\pi\)
0.959063 0.283194i \(-0.0913940\pi\)
\(264\) −6.51305 −0.400850
\(265\) 24.2764 + 2.28734i 1.49129 + 0.140510i
\(266\) −0.654837 −0.0401506
\(267\) 6.34625i 0.388384i
\(268\) 2.41951i 0.147795i
\(269\) −21.4398 −1.30721 −0.653603 0.756837i \(-0.726744\pi\)
−0.653603 + 0.756837i \(0.726744\pi\)
\(270\) −0.517857 + 5.49622i −0.0315158 + 0.334489i
\(271\) −25.2488 −1.53376 −0.766878 0.641793i \(-0.778191\pi\)
−0.766878 + 0.641793i \(0.778191\pi\)
\(272\) 0.856830i 0.0519529i
\(273\) 0.837727i 0.0507016i
\(274\) 5.42750 0.327887
\(275\) 21.3572 + 4.06063i 1.28789 + 0.244865i
\(276\) −0.833563 −0.0501746
\(277\) 30.8114i 1.85128i 0.378409 + 0.925638i \(0.376471\pi\)
−0.378409 + 0.925638i \(0.623529\pi\)
\(278\) 8.14344i 0.488411i
\(279\) −2.31105 −0.138359
\(280\) −0.170533 + 1.80994i −0.0101913 + 0.108164i
\(281\) 3.60821 0.215248 0.107624 0.994192i \(-0.465676\pi\)
0.107624 + 0.994192i \(0.465676\pi\)
\(282\) 3.59565i 0.214118i
\(283\) 5.23942i 0.311451i 0.987800 + 0.155726i \(0.0497716\pi\)
−0.987800 + 0.155726i \(0.950228\pi\)
\(284\) −7.70506 −0.457211
\(285\) 3.57639 + 0.336970i 0.211847 + 0.0199604i
\(286\) 14.9573 0.884442
\(287\) 1.47822i 0.0872565i
\(288\) 15.6117i 0.919927i
\(289\) 16.1583 0.950486
\(290\) −11.7586 1.10790i −0.690487 0.0650581i
\(291\) −8.25214 −0.483749
\(292\) 14.5727i 0.852800i
\(293\) 1.90074i 0.111042i −0.998458 0.0555211i \(-0.982318\pi\)
0.998458 0.0555211i \(-0.0176820\pi\)
\(294\) 3.00846 0.175457
\(295\) 0.315061 3.34387i 0.0183436 0.194688i
\(296\) 12.1000 0.703299
\(297\) 14.2932i 0.829378i
\(298\) 5.93364i 0.343727i
\(299\) 4.58049 0.264897
\(300\) 0.778477 4.09447i 0.0449454 0.236394i
\(301\) 2.86373 0.165063
\(302\) 6.03598i 0.347332i
\(303\) 4.73975i 0.272292i
\(304\) −2.58459 −0.148236
\(305\) −2.40450 + 25.5199i −0.137681 + 1.46127i
\(306\) 1.83492 0.104895
\(307\) 2.82467i 0.161213i 0.996746 + 0.0806063i \(0.0256856\pi\)
−0.996746 + 0.0806063i \(0.974314\pi\)
\(308\) 1.96709i 0.112086i
\(309\) 0.166797 0.00948875
\(310\) −1.45095 0.136710i −0.0824087 0.00776459i
\(311\) 16.1028 0.913107 0.456554 0.889696i \(-0.349084\pi\)
0.456554 + 0.889696i \(0.349084\pi\)
\(312\) 6.86135i 0.388448i
\(313\) 26.3740i 1.49075i −0.666648 0.745373i \(-0.732272\pi\)
0.666648 0.745373i \(-0.267728\pi\)
\(314\) 3.57434 0.201712
\(315\) −1.86783 0.175988i −0.105240 0.00991579i
\(316\) −10.6227 −0.597572
\(317\) 15.5020i 0.870682i −0.900266 0.435341i \(-0.856628\pi\)
0.900266 0.435341i \(-0.143372\pi\)
\(318\) 4.75410i 0.266597i
\(319\) 30.5789 1.71209
\(320\) 0.531718 5.64334i 0.0297240 0.315472i
\(321\) 8.18117 0.456628
\(322\) 0.236619i 0.0131862i
\(323\) 2.53905i 0.141277i
\(324\) 8.73183 0.485102
\(325\) −4.27779 + 22.4994i −0.237289 + 1.24804i
\(326\) −1.58875 −0.0879928
\(327\) 1.02363i 0.0566067i
\(328\) 12.1073i 0.668511i
\(329\) −2.59851 −0.143260
\(330\) 0.397601 4.21989i 0.0218872 0.232298i
\(331\) 19.0302 1.04599 0.522997 0.852335i \(-0.324814\pi\)
0.522997 + 0.852335i \(0.324814\pi\)
\(332\) 21.9778i 1.20619i
\(333\) 12.4870i 0.684286i
\(334\) −11.9233 −0.652413
\(335\) 3.75102 + 0.353423i 0.204940 + 0.0193096i
\(336\) −0.170804 −0.00931812
\(337\) 4.09354i 0.222989i −0.993765 0.111495i \(-0.964436\pi\)
0.993765 0.111495i \(-0.0355638\pi\)
\(338\) 5.99385i 0.326022i
\(339\) −0.182890 −0.00993324
\(340\) −2.93289 0.276339i −0.159059 0.0149866i
\(341\) 3.77329 0.204335
\(342\) 5.53496i 0.299296i
\(343\) 4.37959i 0.236475i
\(344\) −23.4552 −1.26462
\(345\) 0.121761 1.29229i 0.00655537 0.0695748i
\(346\) 0.0576217 0.00309776
\(347\) 17.4357i 0.935997i −0.883729 0.467998i \(-0.844975\pi\)
0.883729 0.467998i \(-0.155025\pi\)
\(348\) 5.86237i 0.314256i
\(349\) −8.48770 −0.454336 −0.227168 0.973856i \(-0.572947\pi\)
−0.227168 + 0.973856i \(0.572947\pi\)
\(350\) −1.16227 0.220982i −0.0621261 0.0118120i
\(351\) 15.0576 0.803716
\(352\) 25.4894i 1.35859i
\(353\) 20.5696i 1.09481i −0.836868 0.547404i \(-0.815616\pi\)
0.836868 0.547404i \(-0.184384\pi\)
\(354\) −0.654837 −0.0348042
\(355\) 1.12550 11.9453i 0.0597352 0.633993i
\(356\) 15.6987 0.832032
\(357\) 0.167795i 0.00888064i
\(358\) 15.5648i 0.822625i
\(359\) 22.4121 1.18286 0.591432 0.806355i \(-0.298563\pi\)
0.591432 + 0.806355i \(0.298563\pi\)
\(360\) 15.2983 + 1.44142i 0.806293 + 0.0759694i
\(361\) −11.3411 −0.596898
\(362\) 8.68256i 0.456345i
\(363\) 4.58868i 0.240843i
\(364\) 2.07229 0.108617
\(365\) −22.5923 2.12866i −1.18254 0.111419i
\(366\) 4.99762 0.261230
\(367\) 21.9401i 1.14526i −0.819812 0.572632i \(-0.805922\pi\)
0.819812 0.572632i \(-0.194078\pi\)
\(368\) 0.933914i 0.0486837i
\(369\) 12.4945 0.650438
\(370\) −0.738667 + 7.83977i −0.0384015 + 0.407570i
\(371\) 3.43569 0.178372
\(372\) 0.723390i 0.0375060i
\(373\) 0.853821i 0.0442092i −0.999756 0.0221046i \(-0.992963\pi\)
0.999756 0.0221046i \(-0.00703668\pi\)
\(374\) −2.99590 −0.154914
\(375\) 6.23404 + 1.80498i 0.321924 + 0.0932088i
\(376\) 21.2829 1.09758
\(377\) 32.2142i 1.65911i
\(378\) 0.777846i 0.0400081i
\(379\) 2.52049 0.129469 0.0647345 0.997903i \(-0.479380\pi\)
0.0647345 + 0.997903i \(0.479380\pi\)
\(380\) 0.833563 8.84694i 0.0427609 0.453838i
\(381\) −12.3810 −0.634296
\(382\) 16.4987i 0.844147i
\(383\) 13.5983i 0.694841i 0.937709 + 0.347420i \(0.112942\pi\)
−0.937709 + 0.347420i \(0.887058\pi\)
\(384\) 5.70096 0.290926
\(385\) 3.04963 + 0.287338i 0.155424 + 0.0146441i
\(386\) −15.2394 −0.775663
\(387\) 24.2055i 1.23043i
\(388\) 20.4134i 1.03633i
\(389\) −10.7398 −0.544527 −0.272264 0.962223i \(-0.587772\pi\)
−0.272264 + 0.962223i \(0.587772\pi\)
\(390\) 4.44557 + 0.418864i 0.225110 + 0.0212100i
\(391\) −0.917461 −0.0463980
\(392\) 17.8073i 0.899404i
\(393\) 4.70995i 0.237585i
\(394\) 6.47502 0.326207
\(395\) 1.55168 16.4686i 0.0780735 0.828625i
\(396\) −16.6267 −0.835522
\(397\) 19.5868i 0.983031i 0.870869 + 0.491516i \(0.163557\pi\)
−0.870869 + 0.491516i \(0.836443\pi\)
\(398\) 15.6060i 0.782256i
\(399\) 0.506145 0.0253389
\(400\) −4.58739 0.872196i −0.229370 0.0436098i
\(401\) −8.01209 −0.400105 −0.200052 0.979785i \(-0.564111\pi\)
−0.200052 + 0.979785i \(0.564111\pi\)
\(402\) 0.734570i 0.0366370i
\(403\) 3.97508i 0.198013i
\(404\) −11.7247 −0.583328
\(405\) −1.27548 + 13.5372i −0.0633791 + 0.672668i
\(406\) −1.66412 −0.0825888
\(407\) 20.3878i 1.01058i
\(408\) 1.37431i 0.0680386i
\(409\) 28.2350 1.39613 0.698065 0.716034i \(-0.254045\pi\)
0.698065 + 0.716034i \(0.254045\pi\)
\(410\) 7.84446 + 0.739109i 0.387410 + 0.0365020i
\(411\) −4.19509 −0.206929
\(412\) 0.412607i 0.0203277i
\(413\) 0.473237i 0.0232865i
\(414\) 2.00000 0.0982946
\(415\) −34.0726 3.21034i −1.67256 0.157590i
\(416\) −26.8526 −1.31655
\(417\) 6.29433i 0.308235i
\(418\) 9.03700i 0.442014i
\(419\) 21.9470 1.07218 0.536091 0.844160i \(-0.319900\pi\)
0.536091 + 0.844160i \(0.319900\pi\)
\(420\) 0.0550865 0.584655i 0.00268795 0.0285282i
\(421\) 0.747198 0.0364162 0.0182081 0.999834i \(-0.494204\pi\)
0.0182081 + 0.999834i \(0.494204\pi\)
\(422\) 3.12807i 0.152272i
\(423\) 21.9637i 1.06791i
\(424\) −28.1398 −1.36659
\(425\) 0.856830 4.50657i 0.0415624 0.218601i
\(426\) −2.33928 −0.113339
\(427\) 3.61168i 0.174781i
\(428\) 20.2378i 0.978231i
\(429\) −11.5610 −0.558168
\(430\) 1.43187 15.1970i 0.0690507 0.732863i
\(431\) 27.3642 1.31808 0.659042 0.752106i \(-0.270962\pi\)
0.659042 + 0.752106i \(0.270962\pi\)
\(432\) 3.07009i 0.147710i
\(433\) 25.4265i 1.22192i −0.791662 0.610960i \(-0.790784\pi\)
0.791662 0.610960i \(-0.209216\pi\)
\(434\) −0.205345 −0.00985685
\(435\) 9.08858 + 0.856331i 0.435764 + 0.0410579i
\(436\) −2.53215 −0.121268
\(437\) 2.76748i 0.132386i
\(438\) 4.42430i 0.211401i
\(439\) 30.8097 1.47047 0.735233 0.677815i \(-0.237073\pi\)
0.735233 + 0.677815i \(0.237073\pi\)
\(440\) −24.9778 2.35342i −1.19077 0.112195i
\(441\) 18.3769 0.875089
\(442\) 3.15612i 0.150121i
\(443\) 24.5778i 1.16773i 0.811852 + 0.583863i \(0.198459\pi\)
−0.811852 + 0.583863i \(0.801541\pi\)
\(444\) −3.90861 −0.185494
\(445\) −2.29315 + 24.3381i −0.108706 + 1.15374i
\(446\) −14.0905 −0.667206
\(447\) 4.58631i 0.216925i
\(448\) 0.798667i 0.0377335i
\(449\) −38.6816 −1.82550 −0.912749 0.408522i \(-0.866044\pi\)
−0.912749 + 0.408522i \(0.866044\pi\)
\(450\) −1.86783 + 9.82401i −0.0880503 + 0.463108i
\(451\) −20.4000 −0.960597
\(452\) 0.452416i 0.0212799i
\(453\) 4.66541i 0.219200i
\(454\) −8.23404 −0.386443
\(455\) −0.302704 + 3.21272i −0.0141910 + 0.150615i
\(456\) −4.14555 −0.194133
\(457\) 6.40041i 0.299398i −0.988732 0.149699i \(-0.952169\pi\)
0.988732 0.149699i \(-0.0478305\pi\)
\(458\) 19.4791i 0.910196i
\(459\) −3.01600 −0.140775
\(460\) −3.19675 0.301200i −0.149049 0.0140435i
\(461\) −23.8337 −1.11005 −0.555024 0.831835i \(-0.687291\pi\)
−0.555024 + 0.831835i \(0.687291\pi\)
\(462\) 0.597215i 0.0277850i
\(463\) 26.5529i 1.23402i 0.786957 + 0.617008i \(0.211655\pi\)
−0.786957 + 0.617008i \(0.788345\pi\)
\(464\) −6.56813 −0.304918
\(465\) 1.12149 + 0.105667i 0.0520078 + 0.00490021i
\(466\) −6.18801 −0.286654
\(467\) 18.6049i 0.860931i 0.902607 + 0.430465i \(0.141651\pi\)
−0.902607 + 0.430465i \(0.858349\pi\)
\(468\) 17.5159i 0.809671i
\(469\) 0.530859 0.0245128
\(470\) −1.29925 + 13.7895i −0.0599301 + 0.636062i
\(471\) −2.76272 −0.127300
\(472\) 3.87602i 0.178408i
\(473\) 39.5206i 1.81716i
\(474\) −3.22508 −0.148133
\(475\) 13.5939 + 2.58459i 0.623729 + 0.118589i
\(476\) −0.415074 −0.0190249
\(477\) 29.0399i 1.32965i
\(478\) 12.0545i 0.551362i
\(479\) −29.9627 −1.36903 −0.684514 0.728999i \(-0.739986\pi\)
−0.684514 + 0.728999i \(0.739986\pi\)
\(480\) −0.713806 + 7.57591i −0.0325806 + 0.345791i
\(481\) 21.4781 0.979316
\(482\) 1.57531i 0.0717533i
\(483\) 0.182890i 0.00832180i
\(484\) 11.3510 0.515957
\(485\) −31.6473 2.98183i −1.43703 0.135398i
\(486\) 10.0576 0.456223
\(487\) 37.2265i 1.68689i −0.537214 0.843446i \(-0.680523\pi\)
0.537214 0.843446i \(-0.319477\pi\)
\(488\) 29.5812i 1.33908i
\(489\) 1.22800 0.0555320
\(490\) 11.5376 + 1.08708i 0.521215 + 0.0491092i
\(491\) −0.691841 −0.0312224 −0.0156112 0.999878i \(-0.504969\pi\)
−0.0156112 + 0.999878i \(0.504969\pi\)
\(492\) 3.91095i 0.176319i
\(493\) 6.45242i 0.290602i
\(494\) 9.52029 0.428338
\(495\) 2.42870 25.7768i 0.109162 1.15858i
\(496\) −0.810478 −0.0363915
\(497\) 1.69055i 0.0758315i
\(498\) 6.67251i 0.299003i
\(499\) 24.7988 1.11014 0.555072 0.831802i \(-0.312691\pi\)
0.555072 + 0.831802i \(0.312691\pi\)
\(500\) 4.46499 15.4212i 0.199680 0.689656i
\(501\) 9.21589 0.411735
\(502\) 10.2903i 0.459281i
\(503\) 22.6049i 1.00790i −0.863732 0.503951i \(-0.831879\pi\)
0.863732 0.503951i \(-0.168121\pi\)
\(504\) 2.16508 0.0964403
\(505\) 1.71266 18.1772i 0.0762125 0.808873i
\(506\) −3.26543 −0.145166
\(507\) 4.63284i 0.205752i
\(508\) 30.6268i 1.35885i
\(509\) 19.1240 0.847655 0.423828 0.905743i \(-0.360686\pi\)
0.423828 + 0.905743i \(0.360686\pi\)
\(510\) −0.890436 0.0838973i −0.0394292 0.00371504i
\(511\) −3.19735 −0.141443
\(512\) 10.2949i 0.454973i
\(513\) 9.09763i 0.401670i
\(514\) −0.749733 −0.0330693
\(515\) 0.639674 + 0.0602704i 0.0281874 + 0.00265583i
\(516\) 7.57663 0.333542
\(517\) 35.8604i 1.57714i
\(518\) 1.10951i 0.0487492i
\(519\) −0.0445377 −0.00195499
\(520\) 2.47928 26.3136i 0.108724 1.15393i
\(521\) 12.8425 0.562638 0.281319 0.959614i \(-0.409228\pi\)
0.281319 + 0.959614i \(0.409228\pi\)
\(522\) 14.0658i 0.615644i
\(523\) 32.8289i 1.43551i 0.696298 + 0.717753i \(0.254829\pi\)
−0.696298 + 0.717753i \(0.745171\pi\)
\(524\) 11.6510 0.508977
\(525\) 0.898358 + 0.170804i 0.0392076 + 0.00745449i
\(526\) −6.89836 −0.300783
\(527\) 0.796199i 0.0346830i
\(528\) 2.35716i 0.102582i
\(529\) −1.00000 −0.0434783
\(530\) 1.71785 18.2322i 0.0746185 0.791955i
\(531\) −4.00000 −0.173585
\(532\) 1.25205i 0.0542834i
\(533\) 21.4909i 0.930876i
\(534\) 4.76619 0.206253
\(535\) 31.3752 + 2.95618i 1.35647 + 0.127807i
\(536\) −4.34797 −0.187804
\(537\) 12.0305i 0.519156i
\(538\) 16.1018i 0.694198i
\(539\) −30.0042 −1.29237
\(540\) −10.5088 0.990145i −0.452227 0.0426091i
\(541\) −25.7261 −1.10605 −0.553026 0.833164i \(-0.686527\pi\)
−0.553026 + 0.833164i \(0.686527\pi\)
\(542\) 18.9625i 0.814507i
\(543\) 6.71103i 0.287998i
\(544\) 5.37850 0.230601
\(545\) 0.369877 3.92565i 0.0158438 0.168157i
\(546\) 0.629153 0.0269253
\(547\) 36.0191i 1.54006i 0.638005 + 0.770032i \(0.279760\pi\)
−0.638005 + 0.770032i \(0.720240\pi\)
\(548\) 10.3774i 0.443301i
\(549\) 30.5274 1.30288
\(550\) 3.04963 16.0398i 0.130037 0.683940i
\(551\) 19.4634 0.829169
\(552\) 1.49795i 0.0637571i
\(553\) 2.33070i 0.0991114i
\(554\) 23.1401 0.983128
\(555\) 0.570940 6.05961i 0.0242350 0.257216i
\(556\) 15.5703 0.660328
\(557\) 36.2148i 1.53447i −0.641366 0.767235i \(-0.721632\pi\)
0.641366 0.767235i \(-0.278368\pi\)
\(558\) 1.73566i 0.0734763i
\(559\) −41.6341 −1.76094
\(560\) −0.655040 0.0617183i −0.0276805 0.00260807i
\(561\) 2.31563 0.0977660
\(562\) 2.70986i 0.114308i
\(563\) 23.3308i 0.983277i 0.870799 + 0.491638i \(0.163602\pi\)
−0.870799 + 0.491638i \(0.836398\pi\)
\(564\) −6.87491 −0.289486
\(565\) −0.701392 0.0660856i −0.0295078 0.00278024i
\(566\) 3.93493 0.165398
\(567\) 1.91583i 0.0804574i
\(568\) 13.8463i 0.580980i
\(569\) −15.6845 −0.657529 −0.328764 0.944412i \(-0.606632\pi\)
−0.328764 + 0.944412i \(0.606632\pi\)
\(570\) 0.253072 2.68596i 0.0106000 0.112502i
\(571\) 38.7600 1.62206 0.811028 0.585007i \(-0.198908\pi\)
0.811028 + 0.585007i \(0.198908\pi\)
\(572\) 28.5984i 1.19576i
\(573\) 12.7524i 0.532738i
\(574\) 1.11018 0.0463379
\(575\) 0.933914 4.91201i 0.0389469 0.204845i
\(576\) −6.75066 −0.281278
\(577\) 21.5902i 0.898812i 0.893328 + 0.449406i \(0.148364\pi\)
−0.893328 + 0.449406i \(0.851636\pi\)
\(578\) 12.1352i 0.504760i
\(579\) 11.7790 0.489518
\(580\) 2.11831 22.4825i 0.0879580 0.933533i
\(581\) −4.82209 −0.200054
\(582\) 6.19756i 0.256897i
\(583\) 47.4139i 1.96368i
\(584\) 26.1877 1.08366
\(585\) 27.1553 + 2.55858i 1.12273 + 0.105784i
\(586\) −1.42750 −0.0589694
\(587\) 24.3902i 1.00669i −0.864086 0.503345i \(-0.832103\pi\)
0.864086 0.503345i \(-0.167897\pi\)
\(588\) 5.75220i 0.237217i
\(589\) 2.40170 0.0989602
\(590\) −2.51133 0.236619i −0.103390 0.00974144i
\(591\) −5.00476 −0.205868
\(592\) 4.37916i 0.179982i
\(593\) 13.9747i 0.573874i −0.957949 0.286937i \(-0.907363\pi\)
0.957949 0.286937i \(-0.0926370\pi\)
\(594\) −10.7346 −0.440445
\(595\) 0.0606309 0.643500i 0.00248562 0.0263809i
\(596\) 11.3452 0.464716
\(597\) 12.0623i 0.493679i
\(598\) 3.44006i 0.140674i
\(599\) 20.9932 0.857758 0.428879 0.903362i \(-0.358909\pi\)
0.428879 + 0.903362i \(0.358909\pi\)
\(600\) −7.35795 1.39896i −0.300387 0.0571123i
\(601\) −13.3007 −0.542546 −0.271273 0.962502i \(-0.587445\pi\)
−0.271273 + 0.962502i \(0.587445\pi\)
\(602\) 2.15073i 0.0876573i
\(603\) 4.48704i 0.182726i
\(604\) −11.5408 −0.469590
\(605\) −1.65807 + 17.5978i −0.0674103 + 0.715452i
\(606\) −3.55967 −0.144602
\(607\) 12.3549i 0.501469i 0.968056 + 0.250734i \(0.0806721\pi\)
−0.968056 + 0.250734i \(0.919328\pi\)
\(608\) 16.2240i 0.657970i
\(609\) 1.28625 0.0521215
\(610\) 19.1661 + 1.80584i 0.776013 + 0.0731163i
\(611\) 37.7781 1.52834
\(612\) 3.50838i 0.141818i
\(613\) 14.6291i 0.590865i −0.955364 0.295432i \(-0.904536\pi\)
0.955364 0.295432i \(-0.0954637\pi\)
\(614\) 2.12140 0.0856126
\(615\) −6.06324 0.571281i −0.244493 0.0230363i
\(616\) −3.53496 −0.142427
\(617\) 17.3723i 0.699384i −0.936865 0.349692i \(-0.886286\pi\)
0.936865 0.349692i \(-0.113714\pi\)
\(618\) 0.125269i 0.00503904i
\(619\) −40.0049 −1.60793 −0.803967 0.594674i \(-0.797281\pi\)
−0.803967 + 0.594674i \(0.797281\pi\)
\(620\) 0.261390 2.77423i 0.0104977 0.111416i
\(621\) −3.28734 −0.131916
\(622\) 12.0936i 0.484909i
\(623\) 3.44443i 0.137998i
\(624\) 2.48322 0.0994082
\(625\) 23.2556 + 9.17479i 0.930224 + 0.366991i
\(626\) −19.8075 −0.791667
\(627\) 6.98499i 0.278954i
\(628\) 6.83416i 0.272712i
\(629\) −4.30201 −0.171532
\(630\) −0.132171 + 1.40278i −0.00526582 + 0.0558883i
\(631\) 15.7992 0.628956 0.314478 0.949265i \(-0.398171\pi\)
0.314478 + 0.949265i \(0.398171\pi\)
\(632\) 19.0894i 0.759337i
\(633\) 2.41779i 0.0960985i
\(634\) −11.6424 −0.462379
\(635\) −47.4815 4.47374i −1.88425 0.177535i
\(636\) 9.08987 0.360437
\(637\) 31.6088i 1.25238i
\(638\) 22.9655i 0.909211i
\(639\) −14.2892 −0.565273
\(640\) 21.8634 + 2.05999i 0.864229 + 0.0814281i
\(641\) −37.3861 −1.47666 −0.738332 0.674437i \(-0.764386\pi\)
−0.738332 + 0.674437i \(0.764386\pi\)
\(642\) 6.14426i 0.242495i
\(643\) 44.1766i 1.74216i −0.491145 0.871078i \(-0.663421\pi\)
0.491145 0.871078i \(-0.336579\pi\)
\(644\) −0.452416 −0.0178277
\(645\) −1.10674 + 11.7462i −0.0435777 + 0.462507i
\(646\) −1.90689 −0.0750256
\(647\) 4.88521i 0.192058i 0.995379 + 0.0960288i \(0.0306141\pi\)
−0.995379 + 0.0960288i \(0.969386\pi\)
\(648\) 15.6915i 0.616420i
\(649\) 6.53086 0.256359
\(650\) 16.8976 + 3.21272i 0.662778 + 0.126013i
\(651\) 0.158717 0.00622063
\(652\) 3.03770i 0.118966i
\(653\) 36.6211i 1.43309i 0.697540 + 0.716546i \(0.254278\pi\)
−0.697540 + 0.716546i \(0.745722\pi\)
\(654\) −0.768769 −0.0300612
\(655\) −1.70189 + 18.0628i −0.0664984 + 0.705774i
\(656\) 4.38178 0.171080
\(657\) 27.0254i 1.05436i
\(658\) 1.95154i 0.0760790i
\(659\) 10.3388 0.402743 0.201371 0.979515i \(-0.435460\pi\)
0.201371 + 0.979515i \(0.435460\pi\)
\(660\) 8.06846 + 0.760215i 0.314065 + 0.0295913i
\(661\) 6.46980 0.251646 0.125823 0.992053i \(-0.459843\pi\)
0.125823 + 0.992053i \(0.459843\pi\)
\(662\) 14.2921i 0.555480i
\(663\) 2.43947i 0.0947411i
\(664\) 39.4950 1.53270
\(665\) 1.94109 + 0.182890i 0.0752722 + 0.00709218i
\(666\) 9.37807 0.363393
\(667\) 7.03291i 0.272315i
\(668\) 22.7974i 0.882057i
\(669\) 10.8910 0.421071
\(670\) 0.265430 2.81711i 0.0102544 0.108834i
\(671\) −49.8426 −1.92415
\(672\) 1.07217i 0.0413599i
\(673\) 30.1889i 1.16370i 0.813297 + 0.581849i \(0.197670\pi\)
−0.813297 + 0.581849i \(0.802330\pi\)
\(674\) −3.07435 −0.118419
\(675\) 3.07009 16.1474i 0.118168 0.621515i
\(676\) −11.4603 −0.440780
\(677\) 0.443226i 0.0170345i −0.999964 0.00851727i \(-0.997289\pi\)
0.999964 0.00851727i \(-0.00271117\pi\)
\(678\) 0.137355i 0.00527509i
\(679\) −4.47885 −0.171882
\(680\) −0.496594 + 5.27055i −0.0190435 + 0.202116i
\(681\) 6.36436 0.243883
\(682\) 2.83383i 0.108513i
\(683\) 25.7553i 0.985498i 0.870171 + 0.492749i \(0.164008\pi\)
−0.870171 + 0.492749i \(0.835992\pi\)
\(684\) −10.5829 −0.404646
\(685\) −16.0884 1.51585i −0.614704 0.0579178i
\(686\) 3.28917 0.125581
\(687\) 15.0560i 0.574422i
\(688\) 8.48876i 0.323631i
\(689\) −49.9495 −1.90292
\(690\) −0.970544 0.0914452i −0.0369480 0.00348126i
\(691\) 16.1707 0.615162 0.307581 0.951522i \(-0.400480\pi\)
0.307581 + 0.951522i \(0.400480\pi\)
\(692\) 0.110173i 0.00418815i
\(693\) 3.64802i 0.138577i
\(694\) −13.0946 −0.497065
\(695\) −2.27439 + 24.1390i −0.0862726 + 0.915646i
\(696\) −10.5350 −0.399326
\(697\) 4.30458i 0.163048i
\(698\) 6.37447i 0.241277i
\(699\) 4.78291 0.180906
\(700\) 0.422518 2.22227i 0.0159697 0.0839940i
\(701\) −26.5049 −1.00107 −0.500537 0.865715i \(-0.666864\pi\)
−0.500537 + 0.865715i \(0.666864\pi\)
\(702\) 11.3086i 0.426817i
\(703\) 12.9768i 0.489429i
\(704\) 11.0219 0.415404
\(705\) 1.00423 10.6583i 0.0378217 0.401416i
\(706\) −15.4483 −0.581403
\(707\) 2.57250i 0.0967489i
\(708\) 1.25205i 0.0470550i
\(709\) −38.6885 −1.45298 −0.726488 0.687179i \(-0.758849\pi\)
−0.726488 + 0.687179i \(0.758849\pi\)
\(710\) −8.97124 0.845275i −0.336685 0.0317226i
\(711\) −19.7000 −0.738809
\(712\) 28.2114i 1.05727i
\(713\) 0.867829i 0.0325004i
\(714\) −0.126018 −0.00471610
\(715\) −44.3368 4.17744i −1.65810 0.156227i
\(716\) 29.7600 1.11218
\(717\) 9.31735i 0.347963i
\(718\) 16.8320i 0.628165i
\(719\) −43.7242 −1.63064 −0.815319 0.579012i \(-0.803438\pi\)
−0.815319 + 0.579012i \(0.803438\pi\)
\(720\) −0.521668 + 5.53667i −0.0194414 + 0.206340i
\(721\) 0.0905291 0.00337148
\(722\) 8.51741i 0.316985i
\(723\) 1.21761i 0.0452833i
\(724\) −16.6011 −0.616975
\(725\) 34.5457 + 6.56813i 1.28299 + 0.243934i
\(726\) 3.44621 0.127901
\(727\) 37.2280i 1.38071i −0.723471 0.690355i \(-0.757455\pi\)
0.723471 0.690355i \(-0.242545\pi\)
\(728\) 3.72400i 0.138021i
\(729\) 10.4686 0.387726
\(730\) −1.59868 + 16.9674i −0.0591697 + 0.627992i
\(731\) 8.33921 0.308437
\(732\) 9.55548i 0.353181i
\(733\) 27.9656i 1.03293i 0.856308 + 0.516466i \(0.172753\pi\)
−0.856308 + 0.516466i \(0.827247\pi\)
\(734\) −16.4776 −0.608198
\(735\) −8.91778 0.840238i −0.328937 0.0309926i
\(736\) 5.86237 0.216090
\(737\) 7.32606i 0.269859i
\(738\) 9.38368i 0.345418i
\(739\) 30.4555 1.12032 0.560162 0.828383i \(-0.310739\pi\)
0.560162 + 0.828383i \(0.310739\pi\)
\(740\) −14.9897 1.41234i −0.551032 0.0519185i
\(741\) −7.35854 −0.270323
\(742\) 2.58029i 0.0947253i
\(743\) 1.97918i 0.0726090i 0.999341 + 0.0363045i \(0.0115586\pi\)
−0.999341 + 0.0363045i \(0.988441\pi\)
\(744\) −1.29997 −0.0476591
\(745\) −1.65722 + 17.5887i −0.0607157 + 0.644400i
\(746\) −0.641240 −0.0234775
\(747\) 40.7583i 1.49127i
\(748\) 5.72819i 0.209443i
\(749\) 4.44033 0.162246
\(750\) 1.35558 4.68192i 0.0494989 0.170959i
\(751\) 5.77719 0.210813 0.105406 0.994429i \(-0.466386\pi\)
0.105406 + 0.994429i \(0.466386\pi\)
\(752\) 7.70257i 0.280884i
\(753\) 7.95374i 0.289851i
\(754\) 24.1936 0.881080
\(755\) 1.68580 17.8920i 0.0613525 0.651158i
\(756\) −1.48725 −0.0540906
\(757\) 26.9857i 0.980814i 0.871494 + 0.490407i \(0.163152\pi\)
−0.871494 + 0.490407i \(0.836848\pi\)
\(758\) 1.89295i 0.0687550i
\(759\) 2.52396 0.0916138
\(760\) −15.8984 1.49795i −0.576694 0.0543364i
\(761\) 5.95209 0.215763 0.107881 0.994164i \(-0.465593\pi\)
0.107881 + 0.994164i \(0.465593\pi\)
\(762\) 9.29840i 0.336846i
\(763\) 0.555573i 0.0201131i
\(764\) 31.5456 1.14128
\(765\) −5.43913 0.512478i −0.196652 0.0185287i
\(766\) 10.2127 0.368998
\(767\) 6.88012i 0.248427i
\(768\) 7.22460i 0.260695i
\(769\) 29.5669 1.06621 0.533104 0.846050i \(-0.321025\pi\)
0.533104 + 0.846050i \(0.321025\pi\)
\(770\) 0.215798 2.29035i 0.00777681 0.0825384i
\(771\) 0.579493 0.0208699
\(772\) 29.1377i 1.04869i
\(773\) 2.24223i 0.0806474i 0.999187 + 0.0403237i \(0.0128389\pi\)
−0.999187 + 0.0403237i \(0.987161\pi\)
\(774\) −18.1789 −0.653426
\(775\) 4.26278 + 0.810478i 0.153124 + 0.0291132i
\(776\) 36.6837 1.31687
\(777\) 0.857579i 0.0307655i
\(778\) 8.06581i 0.289173i
\(779\) −12.9846 −0.465220
\(780\) −0.800870 + 8.49995i −0.0286757 + 0.304347i
\(781\) 23.3302 0.834822
\(782\) 0.689035i 0.0246398i
\(783\) 23.1195i 0.826225i
\(784\) 6.44470 0.230168
\(785\) −10.5952 0.998281i −0.378157 0.0356302i
\(786\) 3.53728 0.126171
\(787\) 6.28634i 0.224084i 0.993703 + 0.112042i \(0.0357391\pi\)