Properties

Label 483.2.h.c.160.6
Level $483$
Weight $2$
Character 483.160
Analytic conductor $3.857$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 17 x^{10} + 92 x^{8} + 180 x^{6} + 92 x^{4} + 17 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 160.6
Root \(0.466018i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.c.160.8

$q$-expansion

\(f(q)\) \(=\) \(q+1.17819 q^{2} -1.00000i q^{3} -0.611859 q^{4} +1.67982 q^{5} -1.17819i q^{6} +(2.04406 - 1.67982i) q^{7} -3.07728 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.17819 q^{2} -1.00000i q^{3} -0.611859 q^{4} +1.67982 q^{5} -1.17819i q^{6} +(2.04406 - 1.67982i) q^{7} -3.07728 q^{8} -1.00000 q^{9} +1.97916 q^{10} -3.72389i q^{11} +0.611859i q^{12} -0.821806i q^{13} +(2.40830 - 1.97916i) q^{14} -1.67982i q^{15} -2.40191 q^{16} +1.97916 q^{17} -1.17819 q^{18} +3.72389 q^{19} -1.02781 q^{20} +(-1.67982 - 2.04406i) q^{21} -4.38746i q^{22} +(4.61186 + 1.31558i) q^{23} +3.07728i q^{24} -2.17819 q^{25} -0.968247i q^{26} +1.00000i q^{27} +(-1.25068 + 1.02781i) q^{28} -5.79005 q^{29} -1.97916i q^{30} +0.566335i q^{31} +3.32464 q^{32} -3.72389 q^{33} +2.33183 q^{34} +(3.43366 - 2.82181i) q^{35} +0.611859 q^{36} -1.25068i q^{37} +4.38746 q^{38} -0.821806 q^{39} -5.16928 q^{40} -5.00000i q^{41} +(-1.97916 - 2.40830i) q^{42} +7.01863i q^{43} +2.27849i q^{44} -1.67982 q^{45} +(5.43366 + 1.55001i) q^{46} +5.14644i q^{47} +2.40191i q^{48} +(1.35639 - 6.86733i) q^{49} -2.56634 q^{50} -1.97916i q^{51} +0.502829i q^{52} +0.0649054i q^{53} +1.17819i q^{54} -6.25547i q^{55} +(-6.29015 + 5.16928i) q^{56} -3.72389i q^{57} -6.82181 q^{58} +11.0455i q^{59} +1.02781i q^{60} +9.36202 q^{61} +0.667253i q^{62} +(-2.04406 + 1.67982i) q^{63} +8.72089 q^{64} -1.38049i q^{65} -4.38746 q^{66} +5.03947i q^{67} -1.21096 q^{68} +(1.31558 - 4.61186i) q^{69} +(4.04552 - 3.32464i) q^{70} -6.40191 q^{71} +3.07728 q^{72} +15.8811i q^{73} -1.47354i q^{74} +2.17819i q^{75} -2.27849 q^{76} +(-6.25547 - 7.61186i) q^{77} -0.968247 q^{78} +17.6032i q^{79} -4.03479 q^{80} +1.00000 q^{81} -5.89097i q^{82} -9.29712 q^{83} +(1.02781 + 1.25068i) q^{84} +3.32464 q^{85} +8.26931i q^{86} +5.79005i q^{87} +11.4594i q^{88} -11.8352 q^{89} -1.97916 q^{90} +(-1.38049 - 1.67982i) q^{91} +(-2.82181 - 0.804951i) q^{92} +0.566335 q^{93} +6.06351i q^{94} +6.25547 q^{95} -3.32464i q^{96} +14.9720 q^{97} +(1.59809 - 8.09105i) q^{98} +3.72389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{2} + 36q^{4} - 24q^{8} - 12q^{9} + O(q^{10}) \) \( 12q + 4q^{2} + 36q^{4} - 24q^{8} - 12q^{9} + 68q^{16} - 4q^{18} + 12q^{23} - 16q^{25} - 16q^{29} - 44q^{32} + 8q^{35} - 36q^{36} - 20q^{39} + 32q^{46} - 4q^{49} - 64q^{50} - 92q^{58} + 112q^{64} - 28q^{70} + 20q^{71} + 24q^{72} - 52q^{77} + 52q^{78} + 12q^{81} - 44q^{85} - 44q^{92} + 40q^{93} + 52q^{95} + 116q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.17819 0.833109 0.416555 0.909111i \(-0.363238\pi\)
0.416555 + 0.909111i \(0.363238\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −0.611859 −0.305929
\(5\) 1.67982 0.751240 0.375620 0.926774i \(-0.377430\pi\)
0.375620 + 0.926774i \(0.377430\pi\)
\(6\) 1.17819i 0.480996i
\(7\) 2.04406 1.67982i 0.772583 0.634913i
\(8\) −3.07728 −1.08798
\(9\) −1.00000 −0.333333
\(10\) 1.97916 0.625865
\(11\) 3.72389i 1.12279i −0.827547 0.561397i \(-0.810264\pi\)
0.827547 0.561397i \(-0.189736\pi\)
\(12\) 0.611859i 0.176628i
\(13\) 0.821806i 0.227928i −0.993485 0.113964i \(-0.963645\pi\)
0.993485 0.113964i \(-0.0363548\pi\)
\(14\) 2.40830 1.97916i 0.643646 0.528952i
\(15\) 1.67982i 0.433728i
\(16\) −2.40191 −0.600478
\(17\) 1.97916 0.480016 0.240008 0.970771i \(-0.422850\pi\)
0.240008 + 0.970771i \(0.422850\pi\)
\(18\) −1.17819 −0.277703
\(19\) 3.72389 0.854318 0.427159 0.904176i \(-0.359514\pi\)
0.427159 + 0.904176i \(0.359514\pi\)
\(20\) −1.02781 −0.229826
\(21\) −1.67982 2.04406i −0.366567 0.446051i
\(22\) 4.38746i 0.935410i
\(23\) 4.61186 + 1.31558i 0.961639 + 0.274318i
\(24\) 3.07728i 0.628146i
\(25\) −2.17819 −0.435639
\(26\) 0.968247i 0.189889i
\(27\) 1.00000i 0.192450i
\(28\) −1.25068 + 1.02781i −0.236356 + 0.194239i
\(29\) −5.79005 −1.07519 −0.537593 0.843205i \(-0.680666\pi\)
−0.537593 + 0.843205i \(0.680666\pi\)
\(30\) 1.97916i 0.361343i
\(31\) 0.566335i 0.101717i 0.998706 + 0.0508584i \(0.0161957\pi\)
−0.998706 + 0.0508584i \(0.983804\pi\)
\(32\) 3.32464 0.587718
\(33\) −3.72389 −0.648245
\(34\) 2.33183 0.399906
\(35\) 3.43366 2.82181i 0.580395 0.476972i
\(36\) 0.611859 0.101976
\(37\) 1.25068i 0.205610i −0.994702 0.102805i \(-0.967218\pi\)
0.994702 0.102805i \(-0.0327818\pi\)
\(38\) 4.38746 0.711740
\(39\) −0.821806 −0.131594
\(40\) −5.16928 −0.817335
\(41\) 5.00000i 0.780869i −0.920631 0.390434i \(-0.872325\pi\)
0.920631 0.390434i \(-0.127675\pi\)
\(42\) −1.97916 2.40830i −0.305391 0.371609i
\(43\) 7.01863i 1.07033i 0.844747 + 0.535165i \(0.179751\pi\)
−0.844747 + 0.535165i \(0.820249\pi\)
\(44\) 2.27849i 0.343496i
\(45\) −1.67982 −0.250413
\(46\) 5.43366 + 1.55001i 0.801150 + 0.228537i
\(47\) 5.14644i 0.750686i 0.926886 + 0.375343i \(0.122475\pi\)
−0.926886 + 0.375343i \(0.877525\pi\)
\(48\) 2.40191i 0.346686i
\(49\) 1.35639 6.86733i 0.193770 0.981047i
\(50\) −2.56634 −0.362935
\(51\) 1.97916i 0.277138i
\(52\) 0.502829i 0.0697299i
\(53\) 0.0649054i 0.00891544i 0.999990 + 0.00445772i \(0.00141894\pi\)
−0.999990 + 0.00445772i \(0.998581\pi\)
\(54\) 1.17819i 0.160332i
\(55\) 6.25547i 0.843487i
\(56\) −6.29015 + 5.16928i −0.840556 + 0.690774i
\(57\) 3.72389i 0.493241i
\(58\) −6.82181 −0.895747
\(59\) 11.0455i 1.43800i 0.695008 + 0.719002i \(0.255401\pi\)
−0.695008 + 0.719002i \(0.744599\pi\)
\(60\) 1.02781i 0.132690i
\(61\) 9.36202 1.19868 0.599342 0.800493i \(-0.295429\pi\)
0.599342 + 0.800493i \(0.295429\pi\)
\(62\) 0.667253i 0.0847412i
\(63\) −2.04406 + 1.67982i −0.257528 + 0.211638i
\(64\) 8.72089 1.09011
\(65\) 1.38049i 0.171229i
\(66\) −4.38746 −0.540059
\(67\) 5.03947i 0.615669i 0.951440 + 0.307835i \(0.0996043\pi\)
−0.951440 + 0.307835i \(0.900396\pi\)
\(68\) −1.21096 −0.146851
\(69\) 1.31558 4.61186i 0.158378 0.555203i
\(70\) 4.04552 3.32464i 0.483533 0.397370i
\(71\) −6.40191 −0.759767 −0.379884 0.925034i \(-0.624036\pi\)
−0.379884 + 0.925034i \(0.624036\pi\)
\(72\) 3.07728 0.362661
\(73\) 15.8811i 1.85874i 0.369147 + 0.929371i \(0.379650\pi\)
−0.369147 + 0.929371i \(0.620350\pi\)
\(74\) 1.47354i 0.171296i
\(75\) 2.17819i 0.251516i
\(76\) −2.27849 −0.261361
\(77\) −6.25547 7.61186i −0.712877 0.867452i
\(78\) −0.968247 −0.109632
\(79\) 17.6032i 1.98051i 0.139256 + 0.990256i \(0.455529\pi\)
−0.139256 + 0.990256i \(0.544471\pi\)
\(80\) −4.03479 −0.451103
\(81\) 1.00000 0.111111
\(82\) 5.89097i 0.650549i
\(83\) −9.29712 −1.02049 −0.510246 0.860029i \(-0.670446\pi\)
−0.510246 + 0.860029i \(0.670446\pi\)
\(84\) 1.02781 + 1.25068i 0.112144 + 0.136460i
\(85\) 3.32464 0.360607
\(86\) 8.26931i 0.891702i
\(87\) 5.79005i 0.620759i
\(88\) 11.4594i 1.22158i
\(89\) −11.8352 −1.25453 −0.627266 0.778805i \(-0.715826\pi\)
−0.627266 + 0.778805i \(0.715826\pi\)
\(90\) −1.97916 −0.208622
\(91\) −1.38049 1.67982i −0.144715 0.176093i
\(92\) −2.82181 0.804951i −0.294194 0.0839219i
\(93\) 0.566335 0.0587262
\(94\) 6.06351i 0.625403i
\(95\) 6.25547 0.641798
\(96\) 3.32464i 0.339319i
\(97\) 14.9720 1.52018 0.760089 0.649819i \(-0.225155\pi\)
0.760089 + 0.649819i \(0.225155\pi\)
\(98\) 1.59809 8.09105i 0.161431 0.817319i
\(99\) 3.72389i 0.374265i
\(100\) 1.33275 0.133275
\(101\) 12.2692i 1.22084i 0.792080 + 0.610418i \(0.208998\pi\)
−0.792080 + 0.610418i \(0.791002\pi\)
\(102\) 2.33183i 0.230886i
\(103\) 8.33421 0.821194 0.410597 0.911817i \(-0.365320\pi\)
0.410597 + 0.911817i \(0.365320\pi\)
\(104\) 2.52892i 0.247981i
\(105\) −2.82181 3.43366i −0.275380 0.335091i
\(106\) 0.0764712i 0.00742754i
\(107\) 15.1949i 1.46894i −0.678639 0.734472i \(-0.737430\pi\)
0.678639 0.734472i \(-0.262570\pi\)
\(108\) 0.611859i 0.0588761i
\(109\) 7.22491i 0.692021i −0.938231 0.346010i \(-0.887536\pi\)
0.938231 0.346010i \(-0.112464\pi\)
\(110\) 7.37016i 0.702717i
\(111\) −1.25068 −0.118709
\(112\) −4.90966 + 4.03479i −0.463919 + 0.381251i
\(113\) 3.00697i 0.282872i 0.989947 + 0.141436i \(0.0451720\pi\)
−0.989947 + 0.141436i \(0.954828\pi\)
\(114\) 4.38746i 0.410923i
\(115\) 7.74711 + 2.20995i 0.722421 + 0.206079i
\(116\) 3.54269 0.328931
\(117\) 0.821806i 0.0759760i
\(118\) 13.0138i 1.19801i
\(119\) 4.04552 3.32464i 0.370853 0.304769i
\(120\) 5.16928i 0.471889i
\(121\) −2.86733 −0.260666
\(122\) 11.0303 0.998635
\(123\) −5.00000 −0.450835
\(124\) 0.346517i 0.0311182i
\(125\) −12.0581 −1.07851
\(126\) −2.40830 + 1.97916i −0.214549 + 0.176317i
\(127\) −2.32464 −0.206278 −0.103139 0.994667i \(-0.532889\pi\)
−0.103139 + 0.994667i \(0.532889\pi\)
\(128\) 3.62563 0.320463
\(129\) 7.01863 0.617956
\(130\) 1.62648i 0.142652i
\(131\) 6.13267i 0.535814i −0.963445 0.267907i \(-0.913668\pi\)
0.963445 0.267907i \(-0.0863320\pi\)
\(132\) 2.27849 0.198317
\(133\) 7.61186 6.25547i 0.660032 0.542418i
\(134\) 5.93747i 0.512920i
\(135\) 1.67982i 0.144576i
\(136\) −6.09042 −0.522249
\(137\) 17.7611i 1.51744i −0.651419 0.758718i \(-0.725826\pi\)
0.651419 0.758718i \(-0.274174\pi\)
\(138\) 1.55001 5.43366i 0.131946 0.462544i
\(139\) 16.3465i 1.38649i −0.720700 0.693247i \(-0.756180\pi\)
0.720700 0.693247i \(-0.243820\pi\)
\(140\) −2.10092 + 1.72655i −0.177560 + 0.145920i
\(141\) 5.14644 0.433409
\(142\) −7.54269 −0.632969
\(143\) −3.06031 −0.255916
\(144\) 2.40191 0.200159
\(145\) −9.72626 −0.807722
\(146\) 18.7110i 1.54853i
\(147\) −6.86733 1.35639i −0.566408 0.111873i
\(148\) 0.765238i 0.0629022i
\(149\) 18.5661i 1.52099i −0.649342 0.760497i \(-0.724955\pi\)
0.649342 0.760497i \(-0.275045\pi\)
\(150\) 2.56634i 0.209540i
\(151\) −1.30099 −0.105873 −0.0529367 0.998598i \(-0.516858\pi\)
−0.0529367 + 0.998598i \(0.516858\pi\)
\(152\) −11.4594 −0.929482
\(153\) −1.97916 −0.160005
\(154\) −7.37016 8.96825i −0.593904 0.722682i
\(155\) 0.951343i 0.0764137i
\(156\) 0.502829 0.0402585
\(157\) 7.60573 0.607003 0.303502 0.952831i \(-0.401844\pi\)
0.303502 + 0.952831i \(0.401844\pi\)
\(158\) 20.7400i 1.64998i
\(159\) 0.0649054 0.00514733
\(160\) 5.58480 0.441517
\(161\) 11.6369 5.05797i 0.917114 0.398624i
\(162\) 1.17819 0.0925677
\(163\) −6.68914 −0.523934 −0.261967 0.965077i \(-0.584371\pi\)
−0.261967 + 0.965077i \(0.584371\pi\)
\(164\) 3.05929i 0.238891i
\(165\) −6.25547 −0.486988
\(166\) −10.9538 −0.850181
\(167\) 2.79816i 0.216528i 0.994122 + 0.108264i \(0.0345293\pi\)
−0.994122 + 0.108264i \(0.965471\pi\)
\(168\) 5.16928 + 6.29015i 0.398819 + 0.485295i
\(169\) 12.3246 0.948049
\(170\) 3.91707 0.300425
\(171\) −3.72389 −0.284773
\(172\) 4.29441i 0.327446i
\(173\) 5.88110i 0.447132i 0.974689 + 0.223566i \(0.0717698\pi\)
−0.974689 + 0.223566i \(0.928230\pi\)
\(174\) 6.82181i 0.517160i
\(175\) −4.45237 + 3.65898i −0.336567 + 0.276593i
\(176\) 8.94445i 0.674213i
\(177\) 11.0455 0.830232
\(178\) −13.9442 −1.04516
\(179\) −0.100918 −0.00754294 −0.00377147 0.999993i \(-0.501200\pi\)
−0.00377147 + 0.999993i \(0.501200\pi\)
\(180\) 1.02781 0.0766088
\(181\) −12.6568 −0.940770 −0.470385 0.882461i \(-0.655885\pi\)
−0.470385 + 0.882461i \(0.655885\pi\)
\(182\) −1.62648 1.97916i −0.120563 0.146705i
\(183\) 9.36202i 0.692061i
\(184\) −14.1920 4.04841i −1.04625 0.298453i
\(185\) 2.10092i 0.154463i
\(186\) 0.667253 0.0489254
\(187\) 7.37016i 0.538959i
\(188\) 3.14889i 0.229657i
\(189\) 1.67982 + 2.04406i 0.122189 + 0.148684i
\(190\) 7.37016 0.534687
\(191\) 7.16000i 0.518080i 0.965867 + 0.259040i \(0.0834061\pi\)
−0.965867 + 0.259040i \(0.916594\pi\)
\(192\) 8.72089i 0.629376i
\(193\) −6.79005 −0.488759 −0.244379 0.969680i \(-0.578584\pi\)
−0.244379 + 0.969680i \(0.578584\pi\)
\(194\) 17.6399 1.26647
\(195\) −1.38049 −0.0988588
\(196\) −0.829918 + 4.20184i −0.0592799 + 0.300131i
\(197\) −14.4930 −1.03258 −0.516290 0.856414i \(-0.672687\pi\)
−0.516290 + 0.856414i \(0.672687\pi\)
\(198\) 4.38746i 0.311803i
\(199\) 11.3412 0.803955 0.401978 0.915650i \(-0.368323\pi\)
0.401978 + 0.915650i \(0.368323\pi\)
\(200\) 6.70291 0.473967
\(201\) 5.03947 0.355457
\(202\) 14.4555i 1.01709i
\(203\) −11.8352 + 9.72626i −0.830671 + 0.682650i
\(204\) 1.21096i 0.0847845i
\(205\) 8.39912i 0.586620i
\(206\) 9.81932 0.684144
\(207\) −4.61186 1.31558i −0.320546 0.0914394i
\(208\) 1.97391i 0.136866i
\(209\) 13.8673i 0.959223i
\(210\) −3.32464 4.04552i −0.229422 0.279168i
\(211\) 10.6436 0.732736 0.366368 0.930470i \(-0.380601\pi\)
0.366368 + 0.930470i \(0.380601\pi\)
\(212\) 0.0397129i 0.00272750i
\(213\) 6.40191i 0.438652i
\(214\) 17.9025i 1.22379i
\(215\) 11.7901i 0.804075i
\(216\) 3.07728i 0.209382i
\(217\) 0.951343 + 1.15763i 0.0645814 + 0.0785847i
\(218\) 8.51235i 0.576529i
\(219\) 15.8811 1.07315
\(220\) 3.82746i 0.258048i
\(221\) 1.62648i 0.109409i
\(222\) −1.47354 −0.0988976
\(223\) 0.877200i 0.0587417i 0.999569 + 0.0293708i \(0.00935037\pi\)
−0.999569 + 0.0293708i \(0.990650\pi\)
\(224\) 6.79576 5.58480i 0.454061 0.373150i
\(225\) 2.17819 0.145213
\(226\) 3.54280i 0.235663i
\(227\) −7.95339 −0.527885 −0.263942 0.964538i \(-0.585023\pi\)
−0.263942 + 0.964538i \(0.585023\pi\)
\(228\) 2.27849i 0.150897i
\(229\) 12.3293 0.814742 0.407371 0.913263i \(-0.366446\pi\)
0.407371 + 0.913263i \(0.366446\pi\)
\(230\) 9.12760 + 2.60375i 0.601856 + 0.171686i
\(231\) −7.61186 + 6.25547i −0.500824 + 0.411580i
\(232\) 17.8176 1.16978
\(233\) −3.38814 −0.221965 −0.110982 0.993822i \(-0.535400\pi\)
−0.110982 + 0.993822i \(0.535400\pi\)
\(234\) 0.968247i 0.0632963i
\(235\) 8.64511i 0.563945i
\(236\) 6.75830i 0.439928i
\(237\) 17.6032 1.14345
\(238\) 4.76641 3.91707i 0.308961 0.253906i
\(239\) −13.7445 −0.889060 −0.444530 0.895764i \(-0.646629\pi\)
−0.444530 + 0.895764i \(0.646629\pi\)
\(240\) 4.03479i 0.260444i
\(241\) 19.0883 1.22958 0.614792 0.788689i \(-0.289240\pi\)
0.614792 + 0.788689i \(0.289240\pi\)
\(242\) −3.37827 −0.217163
\(243\) 1.00000i 0.0641500i
\(244\) −5.72824 −0.366713
\(245\) 2.27849 11.5359i 0.145568 0.737002i
\(246\) −5.89097 −0.375595
\(247\) 3.06031i 0.194723i
\(248\) 1.74277i 0.110666i
\(249\) 9.29712i 0.589181i
\(250\) −14.2068 −0.898516
\(251\) 7.57758 0.478293 0.239146 0.970984i \(-0.423132\pi\)
0.239146 + 0.970984i \(0.423132\pi\)
\(252\) 1.25068 1.02781i 0.0787853 0.0647462i
\(253\) 4.89908 17.1740i 0.308003 1.07972i
\(254\) −2.73887 −0.171852
\(255\) 3.32464i 0.208197i
\(256\) −13.1701 −0.823130
\(257\) 22.1048i 1.37886i −0.724352 0.689430i \(-0.757861\pi\)
0.724352 0.689430i \(-0.242139\pi\)
\(258\) 8.26931 0.514824
\(259\) −2.10092 2.55646i −0.130545 0.158851i
\(260\) 0.844664i 0.0523838i
\(261\) 5.79005 0.358395
\(262\) 7.22548i 0.446391i
\(263\) 8.67030i 0.534634i 0.963609 + 0.267317i \(0.0861371\pi\)
−0.963609 + 0.267317i \(0.913863\pi\)
\(264\) 11.4594 0.705279
\(265\) 0.109030i 0.00669764i
\(266\) 8.96825 7.37016i 0.549878 0.451893i
\(267\) 11.8352i 0.724305i
\(268\) 3.08344i 0.188351i
\(269\) 19.6891i 1.20047i 0.799825 + 0.600234i \(0.204926\pi\)
−0.799825 + 0.600234i \(0.795074\pi\)
\(270\) 1.97916i 0.120448i
\(271\) 4.65738i 0.282916i −0.989944 0.141458i \(-0.954821\pi\)
0.989944 0.141458i \(-0.0451790\pi\)
\(272\) −4.75376 −0.288239
\(273\) −1.67982 + 1.38049i −0.101668 + 0.0835510i
\(274\) 20.9261i 1.26419i
\(275\) 8.11135i 0.489133i
\(276\) −0.804951 + 2.82181i −0.0484524 + 0.169853i
\(277\) −23.5011 −1.41204 −0.706021 0.708191i \(-0.749512\pi\)
−0.706021 + 0.708191i \(0.749512\pi\)
\(278\) 19.2594i 1.15510i
\(279\) 0.566335i 0.0339056i
\(280\) −10.5663 + 8.68348i −0.631459 + 0.518937i
\(281\) 1.90269i 0.113505i 0.998388 + 0.0567524i \(0.0180746\pi\)
−0.998388 + 0.0567524i \(0.981925\pi\)
\(282\) 6.06351 0.361077
\(283\) −12.3574 −0.734573 −0.367287 0.930108i \(-0.619713\pi\)
−0.367287 + 0.930108i \(0.619713\pi\)
\(284\) 3.91707 0.232435
\(285\) 6.25547i 0.370542i
\(286\) −3.60564 −0.213206
\(287\) −8.39912 10.2203i −0.495784 0.603286i
\(288\) −3.32464 −0.195906
\(289\) −13.0829 −0.769584
\(290\) −11.4594 −0.672921
\(291\) 14.9720i 0.877675i
\(292\) 9.71699i 0.568644i
\(293\) 28.4871 1.66423 0.832116 0.554601i \(-0.187129\pi\)
0.832116 + 0.554601i \(0.187129\pi\)
\(294\) −8.09105 1.59809i −0.471879 0.0932024i
\(295\) 18.5545i 1.08029i
\(296\) 3.84868i 0.223700i
\(297\) 3.72389 0.216082
\(298\) 21.8745i 1.26715i
\(299\) 1.08115 3.79005i 0.0625248 0.219184i
\(300\) 1.33275i 0.0769462i
\(301\) 11.7901 + 14.3465i 0.679567 + 0.826920i
\(302\) −1.53282 −0.0882041
\(303\) 12.2692 0.704849
\(304\) −8.94445 −0.512999
\(305\) 15.7265 0.900499
\(306\) −2.33183 −0.133302
\(307\) 24.0357i 1.37179i 0.727702 + 0.685894i \(0.240588\pi\)
−0.727702 + 0.685894i \(0.759412\pi\)
\(308\) 3.82746 + 4.65738i 0.218090 + 0.265379i
\(309\) 8.33421i 0.474117i
\(310\) 1.12087i 0.0636610i
\(311\) 11.7029i 0.663611i −0.943348 0.331805i \(-0.892342\pi\)
0.943348 0.331805i \(-0.107658\pi\)
\(312\) 2.52892 0.143172
\(313\) −18.5661 −1.04942 −0.524709 0.851282i \(-0.675826\pi\)
−0.524709 + 0.851282i \(0.675826\pi\)
\(314\) 8.96103 0.505700
\(315\) −3.43366 + 2.82181i −0.193465 + 0.158991i
\(316\) 10.7707i 0.605897i
\(317\) −19.1503 −1.07559 −0.537795 0.843076i \(-0.680743\pi\)
−0.537795 + 0.843076i \(0.680743\pi\)
\(318\) 0.0764712 0.00428829
\(319\) 21.5615i 1.20721i
\(320\) 14.6496 0.818935
\(321\) −15.1949 −0.848095
\(322\) 13.7105 5.95927i 0.764056 0.332097i
\(323\) 7.37016 0.410087
\(324\) −0.611859 −0.0339922
\(325\) 1.79005i 0.0992943i
\(326\) −7.88110 −0.436494
\(327\) −7.22491 −0.399538
\(328\) 15.3864i 0.849571i
\(329\) 8.64511 + 10.5197i 0.476620 + 0.579967i
\(330\) −7.37016 −0.405714
\(331\) 16.8811 0.927869 0.463935 0.885869i \(-0.346437\pi\)
0.463935 + 0.885869i \(0.346437\pi\)
\(332\) 5.68852 0.312198
\(333\) 1.25068i 0.0685367i
\(334\) 3.29678i 0.180392i
\(335\) 8.46542i 0.462515i
\(336\) 4.03479 + 4.90966i 0.220116 + 0.267844i
\(337\) 32.7447i 1.78372i −0.452313 0.891859i \(-0.649401\pi\)
0.452313 0.891859i \(-0.350599\pi\)
\(338\) 14.5208 0.789828
\(339\) 3.00697 0.163316
\(340\) −2.03421 −0.110320
\(341\) 2.10897 0.114207
\(342\) −4.38746 −0.237247
\(343\) −8.76336 16.3157i −0.473177 0.880968i
\(344\) 21.5983i 1.16450i
\(345\) 2.20995 7.74711i 0.118980 0.417090i
\(346\) 6.92908i 0.372509i
\(347\) 9.01377 0.483885 0.241942 0.970291i \(-0.422216\pi\)
0.241942 + 0.970291i \(0.422216\pi\)
\(348\) 3.54269i 0.189908i
\(349\) 23.6337i 1.26509i −0.774526 0.632543i \(-0.782011\pi\)
0.774526 0.632543i \(-0.217989\pi\)
\(350\) −5.24575 + 4.31099i −0.280397 + 0.230432i
\(351\) 0.821806 0.0438648
\(352\) 12.3806i 0.659886i
\(353\) 20.0357i 1.06639i −0.845992 0.533195i \(-0.820991\pi\)
0.845992 0.533195i \(-0.179009\pi\)
\(354\) 13.0138 0.691674
\(355\) −10.7541 −0.570767
\(356\) 7.24149 0.383798
\(357\) −3.32464 4.04552i −0.175958 0.214112i
\(358\) −0.118901 −0.00628409
\(359\) 1.67982i 0.0886577i −0.999017 0.0443288i \(-0.985885\pi\)
0.999017 0.0443288i \(-0.0141149\pi\)
\(360\) 5.16928 0.272445
\(361\) −5.13267 −0.270141
\(362\) −14.9121 −0.783764
\(363\) 2.86733i 0.150496i
\(364\) 0.844664 + 1.02781i 0.0442724 + 0.0538721i
\(365\) 26.6774i 1.39636i
\(366\) 11.0303i 0.576562i
\(367\) 5.53352 0.288847 0.144424 0.989516i \(-0.453867\pi\)
0.144424 + 0.989516i \(0.453867\pi\)
\(368\) −11.0773 3.15991i −0.577443 0.164722i
\(369\) 5.00000i 0.260290i
\(370\) 2.47529i 0.128684i
\(371\) 0.109030 + 0.132671i 0.00566053 + 0.00688792i
\(372\) −0.346517 −0.0179661
\(373\) 11.1998i 0.579904i 0.957041 + 0.289952i \(0.0936393\pi\)
−0.957041 + 0.289952i \(0.906361\pi\)
\(374\) 8.68348i 0.449012i
\(375\) 12.0581i 0.622677i
\(376\) 15.8370i 0.816732i
\(377\) 4.75830i 0.245065i
\(378\) 1.97916 + 2.40830i 0.101797 + 0.123870i
\(379\) 6.71929i 0.345147i 0.984997 + 0.172573i \(0.0552082\pi\)
−0.984997 + 0.172573i \(0.944792\pi\)
\(380\) −3.82746 −0.196345
\(381\) 2.32464i 0.119095i
\(382\) 8.43587i 0.431617i
\(383\) 25.9655 1.32678 0.663389 0.748275i \(-0.269118\pi\)
0.663389 + 0.748275i \(0.269118\pi\)
\(384\) 3.62563i 0.185020i
\(385\) −10.5081 12.7866i −0.535542 0.651664i
\(386\) −8.00000 −0.407189
\(387\) 7.01863i 0.356777i
\(388\) −9.16076 −0.465067
\(389\) 9.29712i 0.471383i −0.971828 0.235691i \(-0.924265\pi\)
0.971828 0.235691i \(-0.0757354\pi\)
\(390\) −1.62648 −0.0823602
\(391\) 9.12760 + 2.60375i 0.461602 + 0.131677i
\(392\) −4.17398 + 21.1327i −0.210818 + 1.06736i
\(393\) −6.13267 −0.309352
\(394\) −17.0755 −0.860252
\(395\) 29.5702i 1.48784i
\(396\) 2.27849i 0.114499i
\(397\) 3.02188i 0.151664i 0.997121 + 0.0758320i \(0.0241613\pi\)
−0.997121 + 0.0758320i \(0.975839\pi\)
\(398\) 13.3621 0.669782
\(399\) −6.25547 7.61186i −0.313165 0.381070i
\(400\) 5.23183 0.261591
\(401\) 33.8540i 1.69059i 0.534300 + 0.845295i \(0.320575\pi\)
−0.534300 + 0.845295i \(0.679425\pi\)
\(402\) 5.93747 0.296134
\(403\) 0.465418 0.0231841
\(404\) 7.50704i 0.373489i
\(405\) 1.67982 0.0834711
\(406\) −13.9442 + 11.4594i −0.692039 + 0.568722i
\(407\) −4.65738 −0.230858
\(408\) 6.09042i 0.301520i
\(409\) 18.8592i 0.932528i 0.884646 + 0.466264i \(0.154400\pi\)
−0.884646 + 0.466264i \(0.845600\pi\)
\(410\) 9.89579i 0.488718i
\(411\) −17.7611 −0.876092
\(412\) −5.09936 −0.251227
\(413\) 18.5545 + 22.5777i 0.913009 + 1.11098i
\(414\) −5.43366 1.55001i −0.267050 0.0761790i
\(415\) −15.6175 −0.766634
\(416\) 2.73220i 0.133957i
\(417\) −16.3465 −0.800492
\(418\) 16.3384i 0.799138i
\(419\) −25.9490 −1.26769 −0.633845 0.773460i \(-0.718524\pi\)
−0.633845 + 0.773460i \(0.718524\pi\)
\(420\) 1.72655 + 2.10092i 0.0842468 + 0.102514i
\(421\) 1.15763i 0.0564192i 0.999602 + 0.0282096i \(0.00898059\pi\)
−0.999602 + 0.0282096i \(0.991019\pi\)
\(422\) 12.5402 0.610449
\(423\) 5.14644i 0.250229i
\(424\) 0.199732i 0.00969984i
\(425\) −4.31099 −0.209114
\(426\) 7.54269i 0.365445i
\(427\) 19.1366 15.7265i 0.926084 0.761061i
\(428\) 9.29712i 0.449393i
\(429\) 3.06031i 0.147753i
\(430\) 13.8910i 0.669882i
\(431\) 37.6962i 1.81576i 0.419230 + 0.907880i \(0.362300\pi\)
−0.419230 + 0.907880i \(0.637700\pi\)
\(432\) 2.40191i 0.115562i
\(433\) −39.9213 −1.91850 −0.959248 0.282566i \(-0.908814\pi\)
−0.959248 + 0.282566i \(0.908814\pi\)
\(434\) 1.12087 + 1.36391i 0.0538033 + 0.0654696i
\(435\) 9.72626i 0.466339i
\(436\) 4.42062i 0.211709i
\(437\) 17.1740 + 4.89908i 0.821546 + 0.234355i
\(438\) 18.7110 0.894047
\(439\) 16.3483i 0.780261i 0.920760 + 0.390130i \(0.127570\pi\)
−0.920760 + 0.390130i \(0.872430\pi\)
\(440\) 19.2498i 0.917699i
\(441\) −1.35639 + 6.86733i −0.0645899 + 0.327016i
\(442\) 1.91631i 0.0911497i
\(443\) 12.1821 0.578789 0.289394 0.957210i \(-0.406546\pi\)
0.289394 + 0.957210i \(0.406546\pi\)
\(444\) 0.765238 0.0363166
\(445\) −19.8811 −0.942455
\(446\) 1.03351i 0.0489382i
\(447\) −18.5661 −0.878146
\(448\) 17.8260 14.6496i 0.842202 0.692126i
\(449\) 6.70291 0.316330 0.158165 0.987413i \(-0.449442\pi\)
0.158165 + 0.987413i \(0.449442\pi\)
\(450\) 2.56634 0.120978
\(451\) −18.6194 −0.876755
\(452\) 1.83984i 0.0865389i
\(453\) 1.30099i 0.0611260i
\(454\) −9.37064 −0.439786
\(455\) −2.31898 2.82181i −0.108715 0.132288i
\(456\) 11.4594i 0.536637i
\(457\) 27.3828i 1.28091i 0.767995 + 0.640456i \(0.221255\pi\)
−0.767995 + 0.640456i \(0.778745\pi\)
\(458\) 14.5263 0.678769
\(459\) 1.97916i 0.0923792i
\(460\) −4.74013 1.35218i −0.221010 0.0630455i
\(461\) 34.2357i 1.59452i −0.603638 0.797258i \(-0.706283\pi\)
0.603638 0.797258i \(-0.293717\pi\)
\(462\) −8.96825 + 7.37016i −0.417241 + 0.342891i
\(463\) 22.8892 1.06375 0.531876 0.846822i \(-0.321487\pi\)
0.531876 + 0.846822i \(0.321487\pi\)
\(464\) 13.9072 0.645625
\(465\) 0.951343 0.0441175
\(466\) −3.99189 −0.184921
\(467\) 6.19709 0.286767 0.143384 0.989667i \(-0.454202\pi\)
0.143384 + 0.989667i \(0.454202\pi\)
\(468\) 0.502829i 0.0232433i
\(469\) 8.46542 + 10.3010i 0.390897 + 0.475656i
\(470\) 10.1856i 0.469828i
\(471\) 7.60573i 0.350454i
\(472\) 33.9901i 1.56452i
\(473\) 26.1366 1.20176
\(474\) 20.7400 0.952618
\(475\) −8.11135 −0.372174
\(476\) −2.47529 + 2.03421i −0.113455 + 0.0932377i
\(477\) 0.0649054i 0.00297181i
\(478\) −16.1937 −0.740684
\(479\) −34.1418 −1.55998 −0.779989 0.625793i \(-0.784775\pi\)
−0.779989 + 0.625793i \(0.784775\pi\)
\(480\) 5.58480i 0.254910i
\(481\) −1.02781 −0.0468643
\(482\) 22.4897 1.02438
\(483\) −5.05797 11.6369i −0.230146 0.529496i
\(484\) 1.75440 0.0797455
\(485\) 25.1503 1.14202
\(486\) 1.17819i 0.0534440i
\(487\) 27.6793 1.25427 0.627134 0.778912i \(-0.284228\pi\)
0.627134 + 0.778912i \(0.284228\pi\)
\(488\) −28.8095 −1.30415
\(489\) 6.68914i 0.302493i
\(490\) 2.68451 13.5915i 0.121274 0.614003i
\(491\) 5.62563 0.253881 0.126941 0.991910i \(-0.459484\pi\)
0.126941 + 0.991910i \(0.459484\pi\)
\(492\) 3.05929 0.137924
\(493\) −11.4594 −0.516107
\(494\) 3.60564i 0.162225i
\(495\) 6.25547i 0.281162i
\(496\) 1.36029i 0.0610787i
\(497\) −13.0859 + 10.7541i −0.586983 + 0.482386i
\(498\) 10.9538i 0.490852i
\(499\) −16.2555 −0.727695 −0.363847 0.931459i \(-0.618537\pi\)
−0.363847 + 0.931459i \(0.618537\pi\)
\(500\) 7.37785 0.329948
\(501\) 2.79816 0.125013
\(502\) 8.92786 0.398470
\(503\) −16.5754 −0.739059 −0.369530 0.929219i \(-0.620481\pi\)
−0.369530 + 0.929219i \(0.620481\pi\)
\(504\) 6.29015 5.16928i 0.280185 0.230258i
\(505\) 20.6102i 0.917140i
\(506\) 5.77207 20.2343i 0.256600 0.899527i
\(507\) 12.3246i 0.547356i
\(508\) 1.42235 0.0631065
\(509\) 24.3067i 1.07737i 0.842506 + 0.538687i \(0.181079\pi\)
−0.842506 + 0.538687i \(0.818921\pi\)
\(510\) 3.91707i 0.173451i
\(511\) 26.6774 + 32.4620i 1.18014 + 1.43603i
\(512\) −22.7682 −1.00622
\(513\) 3.72389i 0.164414i
\(514\) 26.0438i 1.14874i
\(515\) 14.0000 0.616914
\(516\) −4.29441 −0.189051
\(517\) 19.1648 0.842865
\(518\) −2.47529 3.01201i −0.108758 0.132340i
\(519\) 5.88110 0.258152
\(520\) 4.24815i 0.186293i
\(521\) −15.1783 −0.664973 −0.332487 0.943108i \(-0.607888\pi\)
−0.332487 + 0.943108i \(0.607888\pi\)
\(522\) 6.82181 0.298582
\(523\) −21.4569 −0.938244 −0.469122 0.883133i \(-0.655430\pi\)
−0.469122 + 0.883133i \(0.655430\pi\)
\(524\) 3.75233i 0.163921i
\(525\) 3.65898 + 4.45237i 0.159691 + 0.194317i
\(526\) 10.2153i 0.445408i
\(527\) 1.12087i 0.0488257i
\(528\) 8.94445 0.389257
\(529\) 19.5385 + 12.1346i 0.849499 + 0.527590i
\(530\) 0.128458i 0.00557986i
\(531\) 11.0455i 0.479335i
\(532\) −4.65738 + 3.82746i −0.201923 + 0.165942i
\(533\) −4.10903 −0.177982
\(534\) 13.9442i 0.603425i
\(535\) 25.5247i 1.10353i
\(536\) 15.5078i 0.669837i
\(537\) 0.100918i 0.00435492i
\(538\) 23.1976i 1.00012i
\(539\) −25.5732 5.05104i −1.10151 0.217563i
\(540\) 1.02781i 0.0442301i
\(541\) −35.3920 −1.52162 −0.760811 0.648973i \(-0.775199\pi\)
−0.760811 + 0.648973i \(0.775199\pi\)
\(542\) 5.48730i 0.235700i
\(543\) 12.6568i 0.543154i
\(544\) 6.57998 0.282114
\(545\) 12.1366i 0.519874i
\(546\) −1.97916 + 1.62648i −0.0847001 + 0.0696071i
\(547\) −13.4792 −0.576328 −0.288164 0.957581i \(-0.593045\pi\)
−0.288164 + 0.957581i \(0.593045\pi\)
\(548\) 10.8673i 0.464228i
\(549\) −9.36202 −0.399561
\(550\) 9.55674i 0.407501i
\(551\) −21.5615 −0.918551
\(552\) −4.04841 + 14.1920i −0.172312 + 0.604050i
\(553\) 29.5702 + 35.9820i 1.25745 + 1.53011i
\(554\) −27.6888 −1.17639
\(555\) −2.10092 −0.0891790
\(556\) 10.0018i 0.424169i
\(557\) 46.4826i 1.96953i −0.173883 0.984766i \(-0.555631\pi\)
0.173883 0.984766i \(-0.444369\pi\)
\(558\) 0.667253i 0.0282471i
\(559\) 5.76795 0.243958
\(560\) −8.24736 + 6.77773i −0.348515 + 0.286411i
\(561\) −7.37016 −0.311168
\(562\) 2.24173i 0.0945618i
\(563\) 4.98613 0.210140 0.105070 0.994465i \(-0.466493\pi\)
0.105070 + 0.994465i \(0.466493\pi\)
\(564\) −3.14889 −0.132592
\(565\) 5.05118i 0.212505i
\(566\) −14.5595 −0.611979
\(567\) 2.04406 1.67982i 0.0858426 0.0705459i
\(568\) 19.7005 0.826613
\(569\) 7.34611i 0.307965i 0.988074 + 0.153982i \(0.0492099\pi\)
−0.988074 + 0.153982i \(0.950790\pi\)
\(570\) 7.37016i 0.308702i
\(571\) 25.2039i 1.05475i 0.849633 + 0.527375i \(0.176824\pi\)
−0.849633 + 0.527375i \(0.823176\pi\)
\(572\) 1.87248 0.0782923
\(573\) 7.16000 0.299113
\(574\) −9.89579 12.0415i −0.413042 0.502603i
\(575\) −10.0455 2.86560i −0.418927 0.119504i
\(576\) −8.72089 −0.363370
\(577\) 5.84545i 0.243349i −0.992570 0.121675i \(-0.961174\pi\)
0.992570 0.121675i \(-0.0388264\pi\)
\(578\) −15.4142 −0.641148
\(579\) 6.79005i 0.282185i
\(580\) 5.95110 0.247106
\(581\) −19.0039 + 15.6175i −0.788415 + 0.647924i
\(582\) 17.6399i 0.731199i
\(583\) 0.241700 0.0100102
\(584\) 48.8705i 2.02228i
\(585\) 1.38049i 0.0570762i
\(586\) 33.5633 1.38649
\(587\) 14.0318i 0.579152i 0.957155 + 0.289576i \(0.0935144\pi\)
−0.957155 + 0.289576i \(0.906486\pi\)
\(588\) 4.20184 + 0.829918i 0.173281 + 0.0342252i
\(589\) 2.10897i 0.0868985i
\(590\) 21.8608i 0.899996i
\(591\) 14.4930i 0.596161i
\(592\) 3.00402i 0.123464i
\(593\) 1.70712i 0.0701029i 0.999386 + 0.0350515i \(0.0111595\pi\)
−0.999386 + 0.0350515i \(0.988840\pi\)
\(594\) 4.38746 0.180020
\(595\) 6.79576 5.58480i 0.278599 0.228954i
\(596\) 11.3598i 0.465317i
\(597\) 11.3412i 0.464164i
\(598\) 1.27381 4.46542i 0.0520899 0.182605i
\(599\) 2.97636 0.121611 0.0608054 0.998150i \(-0.480633\pi\)
0.0608054 + 0.998150i \(0.480633\pi\)
\(600\) 6.70291i 0.273645i
\(601\) 10.7502i 0.438509i −0.975668 0.219255i \(-0.929637\pi\)
0.975668 0.219255i \(-0.0703625\pi\)
\(602\) 13.8910 + 16.9030i 0.566154 + 0.688914i
\(603\) 5.03947i 0.205223i
\(604\) 0.796024 0.0323898
\(605\) −4.81661 −0.195823
\(606\) 14.4555 0.587216
\(607\) 26.4019i 1.07162i 0.844338 + 0.535810i \(0.179994\pi\)
−0.844338 + 0.535810i \(0.820006\pi\)
\(608\) 12.3806 0.502098
\(609\) 9.72626 + 11.8352i 0.394128 + 0.479588i
\(610\) 18.5289 0.750214
\(611\) 4.22938 0.171102
\(612\) 1.21096 0.0489504
\(613\) 36.7167i 1.48297i −0.670968 0.741486i \(-0.734121\pi\)
0.670968 0.741486i \(-0.265879\pi\)
\(614\) 28.3187i 1.14285i
\(615\) −8.39912 −0.338685
\(616\) 19.2498 + 23.4238i 0.775597 + 0.943772i
\(617\) 0.688767i 0.0277287i 0.999904 + 0.0138644i \(0.00441330\pi\)
−0.999904 + 0.0138644i \(0.995587\pi\)
\(618\) 9.81932i 0.394991i
\(619\) 9.51998 0.382640 0.191320 0.981528i \(-0.438723\pi\)
0.191320 + 0.981528i \(0.438723\pi\)
\(620\) 0.582088i 0.0233772i
\(621\) −1.31558 + 4.61186i −0.0527925 + 0.185068i
\(622\) 13.7883i 0.552860i
\(623\) −24.1920 + 19.8811i −0.969231 + 0.796519i
\(624\) 1.97391 0.0790194
\(625\) −9.36450 −0.374580
\(626\) −21.8745 −0.874279
\(627\) −13.8673 −0.553808
\(628\) −4.65363 −0.185700
\(629\) 2.47529i 0.0986962i
\(630\) −4.04552 + 3.32464i −0.161178 + 0.132457i
\(631\) 23.8032i 0.947592i 0.880635 + 0.473796i \(0.157117\pi\)
−0.880635 + 0.473796i \(0.842883\pi\)
\(632\) 54.1699i 2.15476i
\(633\) 10.6436i 0.423046i
\(634\) −22.5628 −0.896084
\(635\) −3.90498 −0.154964
\(636\) −0.0397129 −0.00157472
\(637\) −5.64361 1.11469i −0.223608 0.0441655i
\(638\) 25.4036i 1.00574i
\(639\) 6.40191 0.253256
\(640\) 6.09042 0.240745
\(641\) 14.4383i 0.570277i 0.958486 + 0.285138i \(0.0920395\pi\)
−0.958486 + 0.285138i \(0.907960\pi\)
\(642\) −17.9025 −0.706556
\(643\) −3.08846 −0.121797 −0.0608985 0.998144i \(-0.519397\pi\)
−0.0608985 + 0.998144i \(0.519397\pi\)
\(644\) −7.12012 + 3.09476i −0.280572 + 0.121951i
\(645\) 11.7901 0.464233
\(646\) 8.68348 0.341647
\(647\) 49.1503i 1.93230i −0.257982 0.966150i \(-0.583058\pi\)
0.257982 0.966150i \(-0.416942\pi\)
\(648\) −3.07728 −0.120887
\(649\) 41.1323 1.61458
\(650\) 2.10903i 0.0827229i
\(651\) 1.15763 0.951343i 0.0453709 0.0372861i
\(652\) 4.09281 0.160287
\(653\) −21.3684 −0.836210 −0.418105 0.908399i \(-0.637306\pi\)
−0.418105 + 0.908399i \(0.637306\pi\)
\(654\) −8.51235 −0.332859
\(655\) 10.3018i 0.402525i
\(656\) 12.0096i 0.468894i
\(657\) 15.8811i 0.619581i
\(658\) 10.1856 + 12.3942i 0.397077 + 0.483176i
\(659\) 19.0601i 0.742478i −0.928537 0.371239i \(-0.878933\pi\)
0.928537 0.371239i \(-0.121067\pi\)
\(660\) 3.82746 0.148984
\(661\) −26.3500 −1.02489 −0.512447 0.858719i \(-0.671261\pi\)
−0.512447 + 0.858719i \(0.671261\pi\)
\(662\) 19.8892 0.773016
\(663\) −1.62648 −0.0631674
\(664\) 28.6098 1.11028
\(665\) 12.7866 10.5081i 0.495842 0.407486i
\(666\) 1.47354i 0.0570986i
\(667\) −26.7029 7.61730i −1.03394 0.294943i
\(668\) 1.71208i 0.0662424i
\(669\) 0.877200 0.0339145
\(670\) 9.97391i 0.385326i
\(671\) 34.8631i 1.34588i
\(672\) −5.58480 6.79576i −0.215438 0.262152i
\(673\) −31.4474 −1.21221 −0.606105 0.795385i \(-0.707269\pi\)
−0.606105 + 0.795385i \(0.707269\pi\)
\(674\) 38.5796i 1.48603i
\(675\) 2.17819i 0.0838387i
\(676\) −7.54094 −0.290036
\(677\) 22.9586 0.882369 0.441185 0.897416i \(-0.354558\pi\)
0.441185 + 0.897416i \(0.354558\pi\)
\(678\) 3.54280 0.136060
\(679\) 30.6037 25.1503i 1.17446 0.965181i
\(680\) −10.2308 −0.392334
\(681\) 7.95339i 0.304775i
\(682\) 2.48477 0.0951469
\(683\) −26.0829 −0.998036 −0.499018 0.866592i \(-0.666306\pi\)
−0.499018 + 0.866592i \(0.666306\pi\)
\(684\) 2.27849 0.0871203
\(685\) 29.8356i 1.13996i
\(686\) −10.3249 19.2231i −0.394208 0.733942i
\(687\) 12.3293i 0.470392i
\(688\) 16.8581i 0.642710i
\(689\) 0.0533396 0.00203208
\(690\) 2.60375 9.12760i 0.0991229 0.347482i
\(691\) 22.9404i 0.872694i 0.899779 + 0.436347i \(0.143728\pi\)
−0.899779 + 0.436347i \(0.856272\pi\)
\(692\) 3.59840i 0.136791i
\(693\) 6.25547 + 7.61186i 0.237626 + 0.289151i
\(694\) 10.6200 0.403129
\(695\) 27.4593i 1.04159i
\(696\) 17.8176i 0.675374i
\(697\) 9.89579i 0.374830i
\(698\) 27.8451i 1.05395i
\(699\) 3.38814i 0.128151i
\(700\) 2.72422 2.23878i 0.102966 0.0846179i
\(701\) 42.0469i 1.58809i −0.607860 0.794044i \(-0.707972\pi\)
0.607860 0.794044i \(-0.292028\pi\)
\(702\) 0.968247 0.0365441
\(703\) 4.65738i 0.175656i
\(704\) 32.4756i 1.22397i
\(705\) 8.64511 0.325594
\(706\) 23.6059i 0.888419i
\(707\) 20.6102 + 25.0791i 0.775125 + 0.943197i
\(708\) −6.75830 −0.253992
\(709\) 25.1440i 0.944303i −0.881517 0.472152i \(-0.843478\pi\)
0.881517 0.472152i \(-0.156522\pi\)
\(710\) −12.6704 −0.475511
\(711\) 17.6032i 0.660171i
\(712\) 36.4203 1.36491
\(713\) −0.745061 + 2.61186i −0.0279028 + 0.0978149i
\(714\) −3.91707 4.76641i −0.146592 0.178378i
\(715\) −5.14078 −0.192254
\(716\) 0.0617473 0.00230761
\(717\) 13.7445i 0.513299i
\(718\) 1.97916i 0.0738615i
\(719\) 40.4831i 1.50976i 0.655860 + 0.754882i \(0.272306\pi\)
−0.655860 + 0.754882i \(0.727694\pi\)
\(720\) 4.03479 0.150368
\(721\) 17.0357 14.0000i 0.634441 0.521387i
\(722\) −6.04728 −0.225057
\(723\) 19.0883i 0.709901i
\(724\) 7.74415 0.287809
\(725\) 12.6119 0.468393
\(726\) 3.37827i 0.125379i
\(727\) 46.9536 1.74141 0.870706 0.491805i \(-0.163663\pi\)
0.870706 + 0.491805i \(0.163663\pi\)
\(728\) 4.24815 + 5.16928i 0.157447 + 0.191586i
\(729\) −1.00000 −0.0370370
\(730\) 31.4312i 1.16332i
\(731\) 13.8910i 0.513776i
\(732\) 5.72824i 0.211722i
\(733\) 30.7288 1.13499 0.567497 0.823375i \(-0.307912\pi\)
0.567497 + 0.823375i \(0.307912\pi\)
\(734\) 6.51956 0.240641
\(735\) −11.5359 2.27849i −0.425508 0.0840435i
\(736\) 15.3327 + 4.37383i 0.565173 + 0.161222i
\(737\) 18.7664 0.691270
\(738\) 5.89097i 0.216850i
\(739\) 45.8338 1.68602 0.843012 0.537895i \(-0.180780\pi\)
0.843012 + 0.537895i \(0.180780\pi\)
\(740\) 1.28546i 0.0472546i
\(741\) −3.06031 −0.112423
\(742\) 0.128458 + 0.156312i 0.00471584 + 0.00573839i
\(743\) 23.6056i 0.866004i −0.901393 0.433002i \(-0.857454\pi\)
0.901393 0.433002i \(-0.142546\pi\)
\(744\) −1.74277 −0.0638931
\(745\) 31.1878i 1.14263i
\(746\) 13.1955i 0.483123i
\(747\) 9.29712 0.340164
\(748\) 4.50950i 0.164883i
\(749\) −25.5247 31.0593i −0.932653 1.13488i
\(750\) 14.2068i 0.518758i
\(751\) 1.36391i 0.0497697i −0.999690 0.0248848i \(-0.992078\pi\)
0.999690 0.0248848i \(-0.00792191\pi\)
\(752\) 12.3613i 0.450770i
\(753\) 7.57758i 0.276142i
\(754\) 5.60620i 0.204166i
\(755\) −2.18544 −0.0795363
\(756\) −1.02781 1.25068i −0.0373812 0.0454867i
\(757\) 49.5797i 1.80201i −0.433814 0.901003i \(-0.642832\pi\)
0.433814 0.901003i \(-0.357168\pi\)
\(758\) 7.91663i 0.287545i
\(759\) −17.1740 4.89908i −0.623378 0.177825i
\(760\) −19.2498 −0.698264
\(761\) 31.9227i 1.15720i 0.815612 + 0.578599i \(0.196400\pi\)
−0.815612 + 0.578599i \(0.803600\pi\)
\(762\) 2.73887i 0.0992188i
\(763\) −12.1366 14.7682i −0.439373 0.534644i
\(764\) 4.38091i 0.158496i
\(765\) −3.32464 −0.120202
\(766\) 30.5924 1.10535
\(767\) 9.07728 0.327761
\(768\) 13.1701i 0.475234i
\(769\) −18.7009 −0.674372 −0.337186 0.941438i \(-0.609475\pi\)
−0.337186 + 0.941438i \(0.609475\pi\)
\(770\) −12.3806 15.0651i −0.446165 0.542907i
\(771\) −22.1048 −0.796086
\(772\) 4.15455 0.149526
\(773\) −6.40633 −0.230420 −0.115210 0.993341i \(-0.536754\pi\)
−0.115210 + 0.993341i \(0.536754\pi\)
\(774\) 8.26931i 0.297234i
\(775\) 1.23359i 0.0443118i
\(776\) −46.0730 −1.65393
\(777\) −2.55646 + 2.10092i −0.0917127 + 0.0753700i
\(778\) 10.9538i 0.392713i
\(779\) 18.6194i 0.667110i
\(780\) 0.844664 0.0302438
\(781\) 23.8400i 0.853062i
\(782\) 10.7541 + 3.06772i 0.384565 + 0.109701i
\(783\) 5.79005i 0.206920i
\(784\) −3.25792 + 16.4947i −0.116354 + 0.589097i
\(785\) 12.7763 0.456005
\(786\) −7.22548 −0.257724
\(787\) 46.2085 1.64716 0.823578 0.567204i \(-0.191975\pi\)