Properties

Label 91.2.c.a.64.6
Level $91$
Weight $2$
Character 91.64
Analytic conductor $0.727$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.6
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 91.64
Dual form 91.2.c.a.64.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.48119i q^{2} +1.67513 q^{3} -4.15633 q^{4} -0.675131i q^{5} +4.15633i q^{6} +1.00000i q^{7} -5.35026i q^{8} -0.193937 q^{9} +O(q^{10})\) \(q+2.48119i q^{2} +1.67513 q^{3} -4.15633 q^{4} -0.675131i q^{5} +4.15633i q^{6} +1.00000i q^{7} -5.35026i q^{8} -0.193937 q^{9} +1.67513 q^{10} -4.48119i q^{11} -6.96239 q^{12} +(3.28726 - 1.48119i) q^{13} -2.48119 q^{14} -1.13093i q^{15} +4.96239 q^{16} -3.28726 q^{17} -0.481194i q^{18} +5.21933i q^{19} +2.80606i q^{20} +1.67513i q^{21} +11.1187 q^{22} +4.76845 q^{23} -8.96239i q^{24} +4.54420 q^{25} +(3.67513 + 8.15633i) q^{26} -5.35026 q^{27} -4.15633i q^{28} -9.31265 q^{29} +2.80606 q^{30} -1.63752i q^{31} +1.61213i q^{32} -7.50659i q^{33} -8.15633i q^{34} +0.675131 q^{35} +0.806063 q^{36} +1.44358i q^{37} -12.9502 q^{38} +(5.50659 - 2.48119i) q^{39} -3.61213 q^{40} +7.92478i q^{41} -4.15633 q^{42} -4.61213 q^{43} +18.6253i q^{44} +0.130933i q^{45} +11.8315i q^{46} -7.86907i q^{47} +8.31265 q^{48} -1.00000 q^{49} +11.2750i q^{50} -5.50659 q^{51} +(-13.6629 + 6.15633i) q^{52} -3.15633 q^{53} -13.2750i q^{54} -3.02539 q^{55} +5.35026 q^{56} +8.74306i q^{57} -23.1065i q^{58} +2.54420i q^{59} +4.70052i q^{60} -2.31265 q^{61} +4.06300 q^{62} -0.193937i q^{63} +5.92478 q^{64} +(-1.00000 - 2.21933i) q^{65} +18.6253 q^{66} -7.35026i q^{67} +13.6629 q^{68} +7.98778 q^{69} +1.67513i q^{70} -7.75623i q^{71} +1.03761i q^{72} +15.1441i q^{73} -3.58181 q^{74} +7.61213 q^{75} -21.6932i q^{76} +4.48119 q^{77} +(6.15633 + 13.6629i) q^{78} +14.6629 q^{79} -3.35026i q^{80} -8.38058 q^{81} -19.6629 q^{82} +1.45088i q^{83} -6.96239i q^{84} +2.21933i q^{85} -11.4436i q^{86} -15.5999 q^{87} -23.9756 q^{88} +7.79384i q^{89} -0.324869 q^{90} +(1.48119 + 3.28726i) q^{91} -19.8192 q^{92} -2.74306i q^{93} +19.5247 q^{94} +3.52373 q^{95} +2.70052i q^{96} +17.9805i q^{97} -2.48119i q^{98} +0.869067i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 4q^{4} - 2q^{9} + O(q^{10}) \) \( 6q - 4q^{4} - 2q^{9} - 20q^{12} + 8q^{13} - 4q^{14} + 8q^{16} - 8q^{17} + 24q^{22} + 6q^{23} + 8q^{25} + 12q^{26} - 12q^{27} - 14q^{29} + 16q^{30} - 6q^{35} + 4q^{36} - 4q^{38} - 8q^{39} - 20q^{40} - 4q^{42} - 26q^{43} + 8q^{48} - 6q^{49} + 8q^{51} - 20q^{52} + 2q^{53} + 12q^{55} + 12q^{56} + 28q^{61} + 16q^{62} - 8q^{64} - 6q^{65} + 28q^{66} + 20q^{68} - 4q^{69} - 24q^{74} + 44q^{75} + 16q^{77} + 16q^{78} + 26q^{79} - 26q^{81} - 56q^{82} - 40q^{87} - 40q^{88} - 12q^{90} - 2q^{91} - 36q^{92} + 20q^{94} + 58q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.48119i 1.75447i 0.480062 + 0.877235i \(0.340614\pi\)
−0.480062 + 0.877235i \(0.659386\pi\)
\(3\) 1.67513 0.967137 0.483569 0.875306i \(-0.339340\pi\)
0.483569 + 0.875306i \(0.339340\pi\)
\(4\) −4.15633 −2.07816
\(5\) 0.675131i 0.301928i −0.988539 0.150964i \(-0.951762\pi\)
0.988539 0.150964i \(-0.0482377\pi\)
\(6\) 4.15633i 1.69681i
\(7\) 1.00000i 0.377964i
\(8\) 5.35026i 1.89160i
\(9\) −0.193937 −0.0646455
\(10\) 1.67513 0.529723
\(11\) 4.48119i 1.35113i −0.737300 0.675565i \(-0.763900\pi\)
0.737300 0.675565i \(-0.236100\pi\)
\(12\) −6.96239 −2.00987
\(13\) 3.28726 1.48119i 0.911721 0.410809i
\(14\) −2.48119 −0.663127
\(15\) 1.13093i 0.292006i
\(16\) 4.96239 1.24060
\(17\) −3.28726 −0.797277 −0.398639 0.917108i \(-0.630517\pi\)
−0.398639 + 0.917108i \(0.630517\pi\)
\(18\) 0.481194i 0.113419i
\(19\) 5.21933i 1.19740i 0.800975 + 0.598698i \(0.204315\pi\)
−0.800975 + 0.598698i \(0.795685\pi\)
\(20\) 2.80606i 0.627455i
\(21\) 1.67513i 0.365544i
\(22\) 11.1187 2.37052
\(23\) 4.76845 0.994291 0.497145 0.867667i \(-0.334382\pi\)
0.497145 + 0.867667i \(0.334382\pi\)
\(24\) 8.96239i 1.82944i
\(25\) 4.54420 0.908840
\(26\) 3.67513 + 8.15633i 0.720752 + 1.59959i
\(27\) −5.35026 −1.02966
\(28\) 4.15633i 0.785472i
\(29\) −9.31265 −1.72932 −0.864658 0.502361i \(-0.832465\pi\)
−0.864658 + 0.502361i \(0.832465\pi\)
\(30\) 2.80606 0.512315
\(31\) 1.63752i 0.294107i −0.989129 0.147054i \(-0.953021\pi\)
0.989129 0.147054i \(-0.0469790\pi\)
\(32\) 1.61213i 0.284986i
\(33\) 7.50659i 1.30673i
\(34\) 8.15633i 1.39880i
\(35\) 0.675131 0.114118
\(36\) 0.806063 0.134344
\(37\) 1.44358i 0.237324i 0.992935 + 0.118662i \(0.0378604\pi\)
−0.992935 + 0.118662i \(0.962140\pi\)
\(38\) −12.9502 −2.10079
\(39\) 5.50659 2.48119i 0.881760 0.397309i
\(40\) −3.61213 −0.571127
\(41\) 7.92478i 1.23764i 0.785532 + 0.618821i \(0.212389\pi\)
−0.785532 + 0.618821i \(0.787611\pi\)
\(42\) −4.15633 −0.641335
\(43\) −4.61213 −0.703343 −0.351671 0.936124i \(-0.614387\pi\)
−0.351671 + 0.936124i \(0.614387\pi\)
\(44\) 18.6253i 2.80787i
\(45\) 0.130933i 0.0195183i
\(46\) 11.8315i 1.74445i
\(47\) 7.86907i 1.14782i −0.818918 0.573911i \(-0.805426\pi\)
0.818918 0.573911i \(-0.194574\pi\)
\(48\) 8.31265 1.19983
\(49\) −1.00000 −0.142857
\(50\) 11.2750i 1.59453i
\(51\) −5.50659 −0.771076
\(52\) −13.6629 + 6.15633i −1.89471 + 0.853729i
\(53\) −3.15633 −0.433555 −0.216777 0.976221i \(-0.569555\pi\)
−0.216777 + 0.976221i \(0.569555\pi\)
\(54\) 13.2750i 1.80650i
\(55\) −3.02539 −0.407944
\(56\) 5.35026 0.714959
\(57\) 8.74306i 1.15805i
\(58\) 23.1065i 3.03403i
\(59\) 2.54420i 0.331226i 0.986191 + 0.165613i \(0.0529603\pi\)
−0.986191 + 0.165613i \(0.947040\pi\)
\(60\) 4.70052i 0.606835i
\(61\) −2.31265 −0.296105 −0.148052 0.988980i \(-0.547300\pi\)
−0.148052 + 0.988980i \(0.547300\pi\)
\(62\) 4.06300 0.516002
\(63\) 0.193937i 0.0244337i
\(64\) 5.92478 0.740597
\(65\) −1.00000 2.21933i −0.124035 0.275274i
\(66\) 18.6253 2.29262
\(67\) 7.35026i 0.897977i −0.893537 0.448989i \(-0.851784\pi\)
0.893537 0.448989i \(-0.148216\pi\)
\(68\) 13.6629 1.65687
\(69\) 7.98778 0.961616
\(70\) 1.67513i 0.200216i
\(71\) 7.75623i 0.920496i −0.887791 0.460248i \(-0.847761\pi\)
0.887791 0.460248i \(-0.152239\pi\)
\(72\) 1.03761i 0.122284i
\(73\) 15.1441i 1.77248i 0.463223 + 0.886242i \(0.346693\pi\)
−0.463223 + 0.886242i \(0.653307\pi\)
\(74\) −3.58181 −0.416377
\(75\) 7.61213 0.878973
\(76\) 21.6932i 2.48838i
\(77\) 4.48119 0.510679
\(78\) 6.15633 + 13.6629i 0.697067 + 1.54702i
\(79\) 14.6629 1.64971 0.824853 0.565347i \(-0.191258\pi\)
0.824853 + 0.565347i \(0.191258\pi\)
\(80\) 3.35026i 0.374571i
\(81\) −8.38058 −0.931175
\(82\) −19.6629 −2.17141
\(83\) 1.45088i 0.159254i 0.996825 + 0.0796272i \(0.0253730\pi\)
−0.996825 + 0.0796272i \(0.974627\pi\)
\(84\) 6.96239i 0.759659i
\(85\) 2.21933i 0.240720i
\(86\) 11.4436i 1.23399i
\(87\) −15.5999 −1.67249
\(88\) −23.9756 −2.55580
\(89\) 7.79384i 0.826146i 0.910698 + 0.413073i \(0.135545\pi\)
−0.910698 + 0.413073i \(0.864455\pi\)
\(90\) −0.324869 −0.0342442
\(91\) 1.48119 + 3.28726i 0.155271 + 0.344598i
\(92\) −19.8192 −2.06630
\(93\) 2.74306i 0.284442i
\(94\) 19.5247 2.01382
\(95\) 3.52373 0.361527
\(96\) 2.70052i 0.275621i
\(97\) 17.9805i 1.82564i 0.408360 + 0.912821i \(0.366101\pi\)
−0.408360 + 0.912821i \(0.633899\pi\)
\(98\) 2.48119i 0.250638i
\(99\) 0.869067i 0.0873446i
\(100\) −18.8872 −1.88872
\(101\) 9.33804 0.929170 0.464585 0.885529i \(-0.346204\pi\)
0.464585 + 0.885529i \(0.346204\pi\)
\(102\) 13.6629i 1.35283i
\(103\) 6.23743 0.614592 0.307296 0.951614i \(-0.400576\pi\)
0.307296 + 0.951614i \(0.400576\pi\)
\(104\) −7.92478 17.5877i −0.777088 1.72461i
\(105\) 1.13093 0.110368
\(106\) 7.83146i 0.760658i
\(107\) 7.24472 0.700374 0.350187 0.936680i \(-0.386118\pi\)
0.350187 + 0.936680i \(0.386118\pi\)
\(108\) 22.2374 2.13980
\(109\) 4.79384i 0.459167i −0.973289 0.229584i \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(110\) 7.50659i 0.715725i
\(111\) 2.41819i 0.229524i
\(112\) 4.96239i 0.468902i
\(113\) −9.34297 −0.878912 −0.439456 0.898264i \(-0.644829\pi\)
−0.439456 + 0.898264i \(0.644829\pi\)
\(114\) −21.6932 −2.03176
\(115\) 3.21933i 0.300204i
\(116\) 38.7064 3.59380
\(117\) −0.637519 + 0.287258i −0.0589387 + 0.0265570i
\(118\) −6.31265 −0.581127
\(119\) 3.28726i 0.301342i
\(120\) −6.05079 −0.552359
\(121\) −9.08110 −0.825555
\(122\) 5.73813i 0.519506i
\(123\) 13.2750i 1.19697i
\(124\) 6.80606i 0.611203i
\(125\) 6.44358i 0.576332i
\(126\) 0.481194 0.0428682
\(127\) −1.38058 −0.122507 −0.0612533 0.998122i \(-0.519510\pi\)
−0.0612533 + 0.998122i \(0.519510\pi\)
\(128\) 17.9248i 1.58434i
\(129\) −7.72592 −0.680229
\(130\) 5.50659 2.48119i 0.482960 0.217615i
\(131\) 12.4993 1.09207 0.546034 0.837763i \(-0.316137\pi\)
0.546034 + 0.837763i \(0.316137\pi\)
\(132\) 31.1998i 2.71560i
\(133\) −5.21933 −0.452573
\(134\) 18.2374 1.57547
\(135\) 3.61213i 0.310882i
\(136\) 17.5877i 1.50813i
\(137\) 3.20616i 0.273920i −0.990577 0.136960i \(-0.956267\pi\)
0.990577 0.136960i \(-0.0437332\pi\)
\(138\) 19.8192i 1.68713i
\(139\) −0.249646 −0.0211747 −0.0105874 0.999944i \(-0.503370\pi\)
−0.0105874 + 0.999944i \(0.503370\pi\)
\(140\) −2.80606 −0.237156
\(141\) 13.1817i 1.11010i
\(142\) 19.2447 1.61498
\(143\) −6.63752 14.7308i −0.555057 1.23185i
\(144\) −0.962389 −0.0801991
\(145\) 6.28726i 0.522128i
\(146\) −37.5755 −3.10977
\(147\) −1.67513 −0.138162
\(148\) 6.00000i 0.493197i
\(149\) 4.03269i 0.330371i 0.986263 + 0.165185i \(0.0528222\pi\)
−0.986263 + 0.165185i \(0.947178\pi\)
\(150\) 18.8872i 1.54213i
\(151\) 1.56959i 0.127731i −0.997958 0.0638657i \(-0.979657\pi\)
0.997958 0.0638657i \(-0.0203429\pi\)
\(152\) 27.9248 2.26500
\(153\) 0.637519 0.0515404
\(154\) 11.1187i 0.895971i
\(155\) −1.10554 −0.0887991
\(156\) −22.8872 + 10.3127i −1.83244 + 0.825673i
\(157\) 2.89938 0.231396 0.115698 0.993284i \(-0.463090\pi\)
0.115698 + 0.993284i \(0.463090\pi\)
\(158\) 36.3815i 2.89436i
\(159\) −5.28726 −0.419307
\(160\) 1.08840 0.0860453
\(161\) 4.76845i 0.375807i
\(162\) 20.7938i 1.63372i
\(163\) 17.2750i 1.35309i −0.736403 0.676543i \(-0.763477\pi\)
0.736403 0.676543i \(-0.236523\pi\)
\(164\) 32.9380i 2.57202i
\(165\) −5.06793 −0.394538
\(166\) −3.59991 −0.279407
\(167\) 16.2931i 1.26080i −0.776270 0.630400i \(-0.782891\pi\)
0.776270 0.630400i \(-0.217109\pi\)
\(168\) 8.96239 0.691463
\(169\) 8.61213 9.73813i 0.662471 0.749087i
\(170\) −5.50659 −0.422336
\(171\) 1.01222i 0.0774063i
\(172\) 19.1695 1.46166
\(173\) 2.17442 0.165318 0.0826592 0.996578i \(-0.473659\pi\)
0.0826592 + 0.996578i \(0.473659\pi\)
\(174\) 38.7064i 2.93432i
\(175\) 4.54420i 0.343509i
\(176\) 22.2374i 1.67621i
\(177\) 4.26187i 0.320341i
\(178\) −19.3380 −1.44945
\(179\) −0.551493 −0.0412205 −0.0206102 0.999788i \(-0.506561\pi\)
−0.0206102 + 0.999788i \(0.506561\pi\)
\(180\) 0.544198i 0.0405621i
\(181\) 0.511511 0.0380203 0.0190102 0.999819i \(-0.493949\pi\)
0.0190102 + 0.999819i \(0.493949\pi\)
\(182\) −8.15633 + 3.67513i −0.604587 + 0.272419i
\(183\) −3.87399 −0.286374
\(184\) 25.5125i 1.88080i
\(185\) 0.974607 0.0716546
\(186\) 6.80606 0.499045
\(187\) 14.7308i 1.07723i
\(188\) 32.7064i 2.38536i
\(189\) 5.35026i 0.389174i
\(190\) 8.74306i 0.634288i
\(191\) −16.5442 −1.19710 −0.598548 0.801087i \(-0.704255\pi\)
−0.598548 + 0.801087i \(0.704255\pi\)
\(192\) 9.92478 0.716259
\(193\) 7.41090i 0.533448i −0.963773 0.266724i \(-0.914059\pi\)
0.963773 0.266724i \(-0.0859412\pi\)
\(194\) −44.6131 −3.20303
\(195\) −1.67513 3.71767i −0.119959 0.266228i
\(196\) 4.15633 0.296880
\(197\) 7.14903i 0.509347i −0.967027 0.254674i \(-0.918032\pi\)
0.967027 0.254674i \(-0.0819681\pi\)
\(198\) −2.15633 −0.153243
\(199\) 5.10062 0.361573 0.180787 0.983522i \(-0.442136\pi\)
0.180787 + 0.983522i \(0.442136\pi\)
\(200\) 24.3127i 1.71916i
\(201\) 12.3127i 0.868467i
\(202\) 23.1695i 1.63020i
\(203\) 9.31265i 0.653620i
\(204\) 22.8872 1.60242
\(205\) 5.35026 0.373678
\(206\) 15.4763i 1.07828i
\(207\) −0.924777 −0.0642765
\(208\) 16.3127 7.35026i 1.13108 0.509649i
\(209\) 23.3888 1.61784
\(210\) 2.80606i 0.193637i
\(211\) 0.193937 0.0133511 0.00667557 0.999978i \(-0.497875\pi\)
0.00667557 + 0.999978i \(0.497875\pi\)
\(212\) 13.1187 0.900997
\(213\) 12.9927i 0.890246i
\(214\) 17.9756i 1.22878i
\(215\) 3.11379i 0.212359i
\(216\) 28.6253i 1.94771i
\(217\) 1.63752 0.111162
\(218\) 11.8945 0.805594
\(219\) 25.3684i 1.71423i
\(220\) 12.5745 0.847774
\(221\) −10.8061 + 4.86907i −0.726894 + 0.327529i
\(222\) −6.00000 −0.402694
\(223\) 5.83875i 0.390992i −0.980705 0.195496i \(-0.937368\pi\)
0.980705 0.195496i \(-0.0626316\pi\)
\(224\) −1.61213 −0.107715
\(225\) −0.881286 −0.0587524
\(226\) 23.1817i 1.54202i
\(227\) 3.68735i 0.244738i 0.992485 + 0.122369i \(0.0390491\pi\)
−0.992485 + 0.122369i \(0.960951\pi\)
\(228\) 36.3390i 2.40661i
\(229\) 5.65703i 0.373827i 0.982376 + 0.186914i \(0.0598484\pi\)
−0.982376 + 0.186914i \(0.940152\pi\)
\(230\) 7.98778 0.526699
\(231\) 7.50659 0.493897
\(232\) 49.8251i 3.27118i
\(233\) −10.3258 −0.676467 −0.338234 0.941062i \(-0.609829\pi\)
−0.338234 + 0.941062i \(0.609829\pi\)
\(234\) −0.712742 1.58181i −0.0465934 0.103406i
\(235\) −5.31265 −0.346559
\(236\) 10.5745i 0.688342i
\(237\) 24.5623 1.59549
\(238\) 8.15633 0.528696
\(239\) 22.2882i 1.44170i 0.693089 + 0.720852i \(0.256249\pi\)
−0.693089 + 0.720852i \(0.743751\pi\)
\(240\) 5.61213i 0.362261i
\(241\) 29.4264i 1.89552i −0.318979 0.947762i \(-0.603340\pi\)
0.318979 0.947762i \(-0.396660\pi\)
\(242\) 22.5320i 1.44841i
\(243\) 2.01222 0.129084
\(244\) 9.61213 0.615353
\(245\) 0.675131i 0.0431325i
\(246\) −32.9380 −2.10005
\(247\) 7.73084 + 17.1573i 0.491902 + 1.09169i
\(248\) −8.76116 −0.556334
\(249\) 2.43041i 0.154021i
\(250\) 15.9878 1.01116
\(251\) −21.5247 −1.35863 −0.679313 0.733849i \(-0.737722\pi\)
−0.679313 + 0.733849i \(0.737722\pi\)
\(252\) 0.806063i 0.0507772i
\(253\) 21.3684i 1.34342i
\(254\) 3.42548i 0.214934i
\(255\) 3.71767i 0.232809i
\(256\) −32.6253 −2.03908
\(257\) 0.661957 0.0412917 0.0206459 0.999787i \(-0.493428\pi\)
0.0206459 + 0.999787i \(0.493428\pi\)
\(258\) 19.1695i 1.19344i
\(259\) −1.44358 −0.0896999
\(260\) 4.15633 + 9.22425i 0.257764 + 0.572064i
\(261\) 1.80606 0.111793
\(262\) 31.0132i 1.91600i
\(263\) 5.18664 0.319822 0.159911 0.987131i \(-0.448879\pi\)
0.159911 + 0.987131i \(0.448879\pi\)
\(264\) −40.1622 −2.47181
\(265\) 2.13093i 0.130902i
\(266\) 12.9502i 0.794026i
\(267\) 13.0557i 0.798996i
\(268\) 30.5501i 1.86614i
\(269\) 27.2506 1.66150 0.830749 0.556647i \(-0.187912\pi\)
0.830749 + 0.556647i \(0.187912\pi\)
\(270\) −8.96239 −0.545434
\(271\) 18.7612i 1.13966i 0.821763 + 0.569830i \(0.192991\pi\)
−0.821763 + 0.569830i \(0.807009\pi\)
\(272\) −16.3127 −0.989100
\(273\) 2.48119 + 5.50659i 0.150169 + 0.333274i
\(274\) 7.95509 0.480585
\(275\) 20.3634i 1.22796i
\(276\) −33.1998 −1.99839
\(277\) −15.4241 −0.926743 −0.463371 0.886164i \(-0.653360\pi\)
−0.463371 + 0.886164i \(0.653360\pi\)
\(278\) 0.619421i 0.0371504i
\(279\) 0.317575i 0.0190127i
\(280\) 3.61213i 0.215866i
\(281\) 24.8446i 1.48211i 0.671446 + 0.741053i \(0.265673\pi\)
−0.671446 + 0.741053i \(0.734327\pi\)
\(282\) 32.7064 1.94764
\(283\) −22.8872 −1.36050 −0.680250 0.732980i \(-0.738129\pi\)
−0.680250 + 0.732980i \(0.738129\pi\)
\(284\) 32.2374i 1.91294i
\(285\) 5.90271 0.349646
\(286\) 36.5501 16.4690i 2.16125 0.973831i
\(287\) −7.92478 −0.467785
\(288\) 0.312650i 0.0184231i
\(289\) −6.19394 −0.364349
\(290\) −15.5999 −0.916058
\(291\) 30.1197i 1.76565i
\(292\) 62.9438i 3.68351i
\(293\) 25.2193i 1.47333i −0.676258 0.736664i \(-0.736400\pi\)
0.676258 0.736664i \(-0.263600\pi\)
\(294\) 4.15633i 0.242402i
\(295\) 1.71767 0.100006
\(296\) 7.72355 0.448922
\(297\) 23.9756i 1.39120i
\(298\) −10.0059 −0.579625
\(299\) 15.6751 7.06300i 0.906516 0.408464i
\(300\) −31.6385 −1.82665
\(301\) 4.61213i 0.265839i
\(302\) 3.89446 0.224101
\(303\) 15.6424 0.898635
\(304\) 25.9003i 1.48549i
\(305\) 1.56134i 0.0894022i
\(306\) 1.58181i 0.0904260i
\(307\) 7.24965i 0.413759i −0.978366 0.206880i \(-0.933669\pi\)
0.978366 0.206880i \(-0.0663308\pi\)
\(308\) −18.6253 −1.06128
\(309\) 10.4485 0.594395
\(310\) 2.74306i 0.155795i
\(311\) 20.2398 1.14769 0.573847 0.818963i \(-0.305450\pi\)
0.573847 + 0.818963i \(0.305450\pi\)
\(312\) −13.2750 29.4617i −0.751551 1.66794i
\(313\) −33.1368 −1.87300 −0.936502 0.350663i \(-0.885956\pi\)
−0.936502 + 0.350663i \(0.885956\pi\)
\(314\) 7.19394i 0.405977i
\(315\) −0.130933 −0.00737721
\(316\) −60.9438 −3.42836
\(317\) 17.0132i 0.955555i −0.878481 0.477778i \(-0.841443\pi\)
0.878481 0.477778i \(-0.158557\pi\)
\(318\) 13.1187i 0.735661i
\(319\) 41.7318i 2.33653i
\(320\) 4.00000i 0.223607i
\(321\) 12.1359 0.677357
\(322\) −11.8315 −0.659341
\(323\) 17.1573i 0.954657i
\(324\) 34.8324 1.93513
\(325\) 14.9380 6.73084i 0.828608 0.373360i
\(326\) 42.8627 2.37395
\(327\) 8.03032i 0.444078i
\(328\) 42.3996 2.34113
\(329\) 7.86907 0.433836
\(330\) 12.5745i 0.692204i
\(331\) 10.8364i 0.595621i 0.954625 + 0.297811i \(0.0962564\pi\)
−0.954625 + 0.297811i \(0.903744\pi\)
\(332\) 6.03032i 0.330957i
\(333\) 0.279964i 0.0153419i
\(334\) 40.4264 2.21204
\(335\) −4.96239 −0.271124
\(336\) 8.31265i 0.453492i
\(337\) −2.96968 −0.161769 −0.0808845 0.996723i \(-0.525774\pi\)
−0.0808845 + 0.996723i \(0.525774\pi\)
\(338\) 24.1622 + 21.3684i 1.31425 + 1.16229i
\(339\) −15.6507 −0.850029
\(340\) 9.22425i 0.500255i
\(341\) −7.33804 −0.397377
\(342\) 2.51151 0.135807
\(343\) 1.00000i 0.0539949i
\(344\) 24.6761i 1.33045i
\(345\) 5.39280i 0.290338i
\(346\) 5.39517i 0.290046i
\(347\) 30.7367 1.65003 0.825017 0.565108i \(-0.191166\pi\)
0.825017 + 0.565108i \(0.191166\pi\)
\(348\) 64.8383 3.47570
\(349\) 2.00492i 0.107321i −0.998559 0.0536606i \(-0.982911\pi\)
0.998559 0.0536606i \(-0.0170889\pi\)
\(350\) −11.2750 −0.602676
\(351\) −17.5877 + 7.92478i −0.938761 + 0.422993i
\(352\) 7.22425 0.385054
\(353\) 17.2546i 0.918368i 0.888341 + 0.459184i \(0.151858\pi\)
−0.888341 + 0.459184i \(0.848142\pi\)
\(354\) −10.5745 −0.562029
\(355\) −5.23647 −0.277923
\(356\) 32.3938i 1.71687i
\(357\) 5.50659i 0.291439i
\(358\) 1.36836i 0.0723201i
\(359\) 7.10650i 0.375066i 0.982258 + 0.187533i \(0.0600492\pi\)
−0.982258 + 0.187533i \(0.939951\pi\)
\(360\) 0.700523 0.0369208
\(361\) −8.24140 −0.433758
\(362\) 1.26916i 0.0667055i
\(363\) −15.2120 −0.798425
\(364\) −6.15633 13.6629i −0.322679 0.716131i
\(365\) 10.2243 0.535162
\(366\) 9.61213i 0.502434i
\(367\) −27.2628 −1.42311 −0.711554 0.702632i \(-0.752008\pi\)
−0.711554 + 0.702632i \(0.752008\pi\)
\(368\) 23.6629 1.23351
\(369\) 1.53690i 0.0800080i
\(370\) 2.41819i 0.125716i
\(371\) 3.15633i 0.163868i
\(372\) 11.4010i 0.591117i
\(373\) −5.91890 −0.306469 −0.153234 0.988190i \(-0.548969\pi\)
−0.153234 + 0.988190i \(0.548969\pi\)
\(374\) −36.5501 −1.88996
\(375\) 10.7938i 0.557392i
\(376\) −42.1016 −2.17122
\(377\) −30.6131 + 13.7938i −1.57665 + 0.710419i
\(378\) 13.2750 0.682794
\(379\) 28.9706i 1.48812i −0.668112 0.744061i \(-0.732897\pi\)
0.668112 0.744061i \(-0.267103\pi\)
\(380\) −14.6458 −0.751312
\(381\) −2.31265 −0.118481
\(382\) 41.0494i 2.10027i
\(383\) 23.2243i 1.18670i 0.804943 + 0.593352i \(0.202196\pi\)
−0.804943 + 0.593352i \(0.797804\pi\)
\(384\) 30.0263i 1.53228i
\(385\) 3.02539i 0.154188i
\(386\) 18.3879 0.935918
\(387\) 0.894460 0.0454680
\(388\) 74.7328i 3.79398i
\(389\) −16.1319 −0.817919 −0.408960 0.912552i \(-0.634108\pi\)
−0.408960 + 0.912552i \(0.634108\pi\)
\(390\) 9.22425 4.15633i 0.467088 0.210464i
\(391\) −15.6751 −0.792725
\(392\) 5.35026i 0.270229i
\(393\) 20.9380 1.05618
\(394\) 17.7381 0.893634
\(395\) 9.89938i 0.498092i
\(396\) 3.61213i 0.181516i
\(397\) 24.0557i 1.20732i −0.797241 0.603661i \(-0.793708\pi\)
0.797241 0.603661i \(-0.206292\pi\)
\(398\) 12.6556i 0.634369i
\(399\) −8.74306 −0.437700
\(400\) 22.5501 1.12750
\(401\) 2.77575i 0.138614i −0.997595 0.0693071i \(-0.977921\pi\)
0.997595 0.0693071i \(-0.0220788\pi\)
\(402\) 30.5501 1.52370
\(403\) −2.42548 5.38295i −0.120822 0.268144i
\(404\) −38.8119 −1.93097
\(405\) 5.65799i 0.281148i
\(406\) 23.1065 1.14676
\(407\) 6.46898 0.320655
\(408\) 29.4617i 1.45857i
\(409\) 20.1309i 0.995411i −0.867346 0.497705i \(-0.834176\pi\)
0.867346 0.497705i \(-0.165824\pi\)
\(410\) 13.2750i 0.655607i
\(411\) 5.37073i 0.264919i
\(412\) −25.9248 −1.27722
\(413\) −2.54420 −0.125192
\(414\) 2.29455i 0.112771i
\(415\) 0.979532 0.0480833
\(416\) 2.38787 + 5.29948i 0.117075 + 0.259828i
\(417\) −0.418190 −0.0204789
\(418\) 58.0322i 2.83845i
\(419\) −0.385503 −0.0188331 −0.00941654 0.999956i \(-0.502997\pi\)
−0.00941654 + 0.999956i \(0.502997\pi\)
\(420\) −4.70052 −0.229362
\(421\) 15.6810i 0.764246i 0.924112 + 0.382123i \(0.124807\pi\)
−0.924112 + 0.382123i \(0.875193\pi\)
\(422\) 0.481194i 0.0234242i
\(423\) 1.52610i 0.0742015i
\(424\) 16.8872i 0.820113i
\(425\) −14.9380 −0.724597
\(426\) 32.2374 1.56191
\(427\) 2.31265i 0.111917i
\(428\) −30.1114 −1.45549
\(429\) −11.1187 24.6761i −0.536817 1.19137i
\(430\) −7.72592 −0.372577
\(431\) 1.53690i 0.0740301i 0.999315 + 0.0370150i \(0.0117849\pi\)
−0.999315 + 0.0370150i \(0.988215\pi\)
\(432\) −26.5501 −1.27739
\(433\) 26.0362 1.25122 0.625610 0.780136i \(-0.284850\pi\)
0.625610 + 0.780136i \(0.284850\pi\)
\(434\) 4.06300i 0.195030i
\(435\) 10.5320i 0.504970i
\(436\) 19.9248i 0.954224i
\(437\) 24.8881i 1.19056i
\(438\) −62.9438 −3.00757
\(439\) −19.1246 −0.912767 −0.456384 0.889783i \(-0.650855\pi\)
−0.456384 + 0.889783i \(0.650855\pi\)
\(440\) 16.1866i 0.771668i
\(441\) 0.193937 0.00923507
\(442\) −12.0811 26.8119i −0.574639 1.27531i
\(443\) −12.6180 −0.599500 −0.299750 0.954018i \(-0.596903\pi\)
−0.299750 + 0.954018i \(0.596903\pi\)
\(444\) 10.0508i 0.476989i
\(445\) 5.26187 0.249436
\(446\) 14.4871 0.685983
\(447\) 6.75528i 0.319514i
\(448\) 5.92478i 0.279919i
\(449\) 1.02302i 0.0482794i 0.999709 + 0.0241397i \(0.00768466\pi\)
−0.999709 + 0.0241397i \(0.992315\pi\)
\(450\) 2.18664i 0.103079i
\(451\) 35.5125 1.67222
\(452\) 38.8324 1.82652
\(453\) 2.62927i 0.123534i
\(454\) −9.14903 −0.429385
\(455\) 2.21933 1.00000i 0.104044 0.0468807i
\(456\) 46.7777 2.19056
\(457\) 28.5320i 1.33467i 0.744758 + 0.667335i \(0.232565\pi\)
−0.744758 + 0.667335i \(0.767435\pi\)
\(458\) −14.0362 −0.655868
\(459\) 17.5877 0.820923
\(460\) 13.3806i 0.623873i
\(461\) 25.3503i 1.18068i 0.807155 + 0.590340i \(0.201006\pi\)
−0.807155 + 0.590340i \(0.798994\pi\)
\(462\) 18.6253i 0.866527i
\(463\) 39.6810i 1.84413i −0.387032 0.922066i \(-0.626500\pi\)
0.387032 0.922066i \(-0.373500\pi\)
\(464\) −46.2130 −2.14538
\(465\) −1.85192 −0.0858809
\(466\) 25.6204i 1.18684i
\(467\) −1.95158 −0.0903086 −0.0451543 0.998980i \(-0.514378\pi\)
−0.0451543 + 0.998980i \(0.514378\pi\)
\(468\) 2.64974 1.19394i 0.122484 0.0551897i
\(469\) 7.35026 0.339404
\(470\) 13.1817i 0.608027i
\(471\) 4.85685 0.223792
\(472\) 13.6121 0.626549
\(473\) 20.6678i 0.950308i
\(474\) 60.9438i 2.79924i
\(475\) 23.7177i 1.08824i
\(476\) 13.6629i 0.626239i
\(477\) 0.612127 0.0280274
\(478\) −55.3014 −2.52943
\(479\) 26.1368i 1.19422i 0.802159 + 0.597111i \(0.203685\pi\)
−0.802159 + 0.597111i \(0.796315\pi\)
\(480\) 1.82321 0.0832176
\(481\) 2.13823 + 4.74543i 0.0974947 + 0.216373i
\(482\) 73.0127 3.32564
\(483\) 7.98778i 0.363457i
\(484\) 37.7440 1.71564
\(485\) 12.1392 0.551212
\(486\) 4.99271i 0.226474i
\(487\) 20.9624i 0.949896i −0.880014 0.474948i \(-0.842467\pi\)
0.880014 0.474948i \(-0.157533\pi\)
\(488\) 12.3733i 0.560112i
\(489\) 28.9380i 1.30862i
\(490\) −1.67513 −0.0756747
\(491\) 2.95651 0.133425 0.0667127 0.997772i \(-0.478749\pi\)
0.0667127 + 0.997772i \(0.478749\pi\)
\(492\) 55.1754i 2.48750i
\(493\) 30.6131 1.37874
\(494\) −42.5705 + 19.1817i −1.91534 + 0.863026i
\(495\) 0.586734 0.0263717
\(496\) 8.12601i 0.364869i
\(497\) 7.75623 0.347915
\(498\) −6.03032 −0.270225
\(499\) 2.85448i 0.127784i −0.997957 0.0638920i \(-0.979649\pi\)
0.997957 0.0638920i \(-0.0203513\pi\)
\(500\) 26.7816i 1.19771i
\(501\) 27.2931i 1.21937i
\(502\) 53.4069i 2.38367i
\(503\) 23.8641 1.06405 0.532025 0.846729i \(-0.321431\pi\)
0.532025 + 0.846729i \(0.321431\pi\)
\(504\) −1.03761 −0.0462189
\(505\) 6.30440i 0.280542i
\(506\) 53.0191 2.35698
\(507\) 14.4264 16.3127i 0.640701 0.724470i
\(508\) 5.73813 0.254589
\(509\) 11.1949i 0.496205i −0.968734 0.248102i \(-0.920193\pi\)
0.968734 0.248102i \(-0.0798070\pi\)
\(510\) −9.22425 −0.408457
\(511\) −15.1441 −0.669936
\(512\) 45.1002i 1.99316i
\(513\) 27.9248i 1.23291i
\(514\) 1.64244i 0.0724451i
\(515\) 4.21108i 0.185562i
\(516\) 32.1114 1.41363
\(517\) −35.2628 −1.55086
\(518\) 3.58181i 0.157376i
\(519\) 3.64244 0.159886
\(520\) −11.8740 + 5.35026i −0.520709 + 0.234624i
\(521\) −26.4894 −1.16052 −0.580262 0.814430i \(-0.697050\pi\)
−0.580262 + 0.814430i \(0.697050\pi\)
\(522\) 4.48119i 0.196137i
\(523\) −12.9525 −0.566375 −0.283188 0.959065i \(-0.591392\pi\)
−0.283188 + 0.959065i \(0.591392\pi\)
\(524\) −51.9511 −2.26950
\(525\) 7.61213i 0.332220i
\(526\) 12.8691i 0.561118i
\(527\) 5.38295i 0.234485i
\(528\) 37.2506i 1.62112i
\(529\) −0.261865 −0.0113854
\(530\) −5.28726 −0.229664
\(531\) 0.493413i 0.0214123i
\(532\) 21.6932 0.940521
\(533\) 11.7381 + 26.0508i 0.508435 + 1.12838i
\(534\) −32.3938 −1.40181
\(535\) 4.89114i 0.211462i
\(536\) −39.3258 −1.69862
\(537\) −0.923822 −0.0398659
\(538\) 67.6140i 2.91505i
\(539\) 4.48119i 0.193019i
\(540\) 15.0132i 0.646064i
\(541\) 28.0933i 1.20783i 0.797050 + 0.603913i \(0.206393\pi\)
−0.797050 + 0.603913i \(0.793607\pi\)
\(542\) −46.5501 −1.99950
\(543\) 0.856849 0.0367709
\(544\) 5.29948i 0.227213i
\(545\) −3.23647 −0.138635
\(546\) −13.6629 + 6.15633i −0.584719 + 0.263466i
\(547\) 14.8192 0.633625 0.316812 0.948488i \(-0.397387\pi\)
0.316812 + 0.948488i \(0.397387\pi\)
\(548\) 13.3258i 0.569251i
\(549\) 0.448507 0.0191418
\(550\) 50.5256 2.15442
\(551\) 48.6058i 2.07068i
\(552\) 42.7367i 1.81900i
\(553\) 14.6629i 0.623530i
\(554\) 38.2701i 1.62594i
\(555\) 1.63259 0.0692998
\(556\) 1.03761 0.0440045
\(557\) 18.3879i 0.779119i −0.921001 0.389560i \(-0.872627\pi\)
0.921001 0.389560i \(-0.127373\pi\)
\(558\) −0.787965 −0.0333572
\(559\) −15.1612 + 6.83146i −0.641253 + 0.288940i
\(560\) 3.35026 0.141574
\(561\) 24.6761i 1.04183i
\(562\) −61.6444 −2.60031
\(563\) 15.3357 0.646322 0.323161 0.946344i \(-0.395255\pi\)
0.323161 + 0.946344i \(0.395255\pi\)
\(564\) 54.7875i 2.30697i
\(565\) 6.30773i 0.265368i
\(566\) 56.7875i 2.38696i
\(567\) 8.38058i 0.351951i
\(568\) −41.4979 −1.74121
\(569\) −1.32250 −0.0554421 −0.0277210 0.999616i \(-0.508825\pi\)
−0.0277210 + 0.999616i \(0.508825\pi\)
\(570\) 14.6458i 0.613444i
\(571\) 37.9175 1.58680 0.793399 0.608702i \(-0.208310\pi\)
0.793399 + 0.608702i \(0.208310\pi\)
\(572\) 27.5877 + 61.2262i 1.15350 + 2.55999i
\(573\) −27.7137 −1.15776
\(574\) 19.6629i 0.820714i
\(575\) 21.6688 0.903651
\(576\) −1.14903 −0.0478763
\(577\) 12.8627i 0.535482i −0.963491 0.267741i \(-0.913723\pi\)
0.963491 0.267741i \(-0.0862772\pi\)
\(578\) 15.3684i 0.639240i
\(579\) 12.4142i 0.515917i
\(580\) 26.1319i 1.08507i
\(581\) −1.45088 −0.0601925
\(582\) −74.7328 −3.09777
\(583\) 14.1441i 0.585789i
\(584\) 81.0249 3.35284
\(585\) 0.193937 + 0.430409i 0.00801829 + 0.0177952i
\(586\) 62.5741 2.58491
\(587\) 31.0240i 1.28050i −0.768168 0.640248i \(-0.778831\pi\)
0.768168 0.640248i \(-0.221169\pi\)
\(588\) 6.96239 0.287124
\(589\) 8.54675 0.352163
\(590\) 4.26187i 0.175458i
\(591\) 11.9756i 0.492609i
\(592\) 7.16362i 0.294423i
\(593\) 11.4119i 0.468629i 0.972161 + 0.234314i \(0.0752845\pi\)
−0.972161 + 0.234314i \(0.924716\pi\)
\(594\) −59.4880 −2.44082
\(595\) −2.21933 −0.0909836
\(596\) 16.7612i 0.686564i
\(597\) 8.54420 0.349691
\(598\) 17.5247 + 38.8930i 0.716638 + 1.59045i
\(599\) 7.37328 0.301264 0.150632 0.988590i \(-0.451869\pi\)
0.150632 + 0.988590i \(0.451869\pi\)
\(600\) 40.7269i 1.66267i
\(601\) 17.2144 0.702190 0.351095 0.936340i \(-0.385809\pi\)
0.351095 + 0.936340i \(0.385809\pi\)
\(602\) 11.4436 0.466406
\(603\) 1.42548i 0.0580502i
\(604\) 6.52373i 0.265447i
\(605\) 6.13093i 0.249258i
\(606\) 38.8119i 1.57663i
\(607\) 32.4264 1.31615 0.658074 0.752953i \(-0.271371\pi\)
0.658074 + 0.752953i \(0.271371\pi\)
\(608\) −8.41422 −0.341242
\(609\) 15.5999i 0.632140i
\(610\) −3.87399 −0.156853
\(611\) −11.6556 25.8677i −0.471536 1.04649i
\(612\) −2.64974 −0.107109
\(613\) 35.6991i 1.44187i −0.693001 0.720937i \(-0.743712\pi\)
0.693001 0.720937i \(-0.256288\pi\)
\(614\) 17.9878 0.725928
\(615\) 8.96239 0.361398
\(616\) 23.9756i 0.966003i
\(617\) 20.3733i 0.820198i 0.912041 + 0.410099i \(0.134506\pi\)
−0.912041 + 0.410099i \(0.865494\pi\)
\(618\) 25.9248i 1.04285i
\(619\) 40.0118i 1.60821i 0.594488 + 0.804104i \(0.297355\pi\)
−0.594488 + 0.804104i \(0.702645\pi\)
\(620\) 4.59498 0.184539
\(621\) −25.5125 −1.02378
\(622\) 50.2189i 2.01359i
\(623\) −7.79384 −0.312254
\(624\) 27.3258 12.3127i 1.09391 0.492900i
\(625\) 18.3707 0.734829
\(626\) 82.2189i 3.28613i
\(627\) 39.1793 1.56467
\(628\) −12.0508 −0.480879
\(629\) 4.74543i 0.189213i
\(630\) 0.324869i 0.0129431i
\(631\) 16.3879i 0.652391i 0.945302 + 0.326195i \(0.105767\pi\)
−0.945302 + 0.326195i \(0.894233\pi\)
\(632\) 78.4504i 3.12059i
\(633\) 0.324869 0.0129124
\(634\) 42.2130 1.67649
\(635\) 0.932071i 0.0369881i
\(636\) 21.9756 0.871388
\(637\) −3.28726 + 1.48119i −0.130246 + 0.0586871i
\(638\) −103.545 −4.09937
\(639\) 1.50422i 0.0595059i
\(640\) 12.1016 0.478357
\(641\) 8.23884 0.325415 0.162707 0.986674i \(-0.447977\pi\)
0.162707 + 0.986674i \(0.447977\pi\)
\(642\) 30.1114i 1.18840i
\(643\) 30.4847i 1.20220i −0.799174 0.601100i \(-0.794729\pi\)
0.799174 0.601100i \(-0.205271\pi\)
\(644\) 19.8192i 0.780987i
\(645\) 5.21600i 0.205380i
\(646\) 42.5705 1.67492
\(647\) −28.8388 −1.13377 −0.566884 0.823798i \(-0.691851\pi\)
−0.566884 + 0.823798i \(0.691851\pi\)
\(648\) 44.8383i 1.76141i
\(649\) 11.4010 0.447530
\(650\) 16.7005 + 37.0640i 0.655048 + 1.45377i
\(651\) 2.74306 0.107509
\(652\) 71.8007i 2.81193i
\(653\) 21.4518 0.839475 0.419738 0.907646i \(-0.362122\pi\)
0.419738 + 0.907646i \(0.362122\pi\)
\(654\) 19.9248 0.779120
\(655\) 8.43866i 0.329726i
\(656\) 39.3258i 1.53542i
\(657\) 2.93700i 0.114583i
\(658\) 19.5247i 0.761151i
\(659\) −50.6589 −1.97339 −0.986696 0.162575i \(-0.948020\pi\)
−0.986696 + 0.162575i \(0.948020\pi\)
\(660\) 21.0640 0.819913
\(661\) 15.5477i 0.604736i 0.953191 + 0.302368i \(0.0977771\pi\)
−0.953191 + 0.302368i \(0.902223\pi\)
\(662\) −26.8872 −1.04500
\(663\) −18.1016 + 8.15633i −0.703007 + 0.316765i
\(664\) 7.76257 0.301246
\(665\) 3.52373i 0.136644i
\(666\) 0.694644 0.0269169
\(667\) −44.4069 −1.71944
\(668\) 67.7196i 2.62015i
\(669\) 9.78067i 0.378143i
\(670\) 12.3127i 0.475679i
\(671\) 10.3634i 0.400076i
\(672\) −2.70052 −0.104175
\(673\) 26.8700 1.03576 0.517882 0.855452i \(-0.326721\pi\)
0.517882 + 0.855452i \(0.326721\pi\)
\(674\) 7.36836i 0.283819i
\(675\) −24.3127 −0.935794
\(676\) −35.7948 + 40.4749i −1.37672 + 1.55673i
\(677\) 16.3757 0.629368 0.314684 0.949197i \(-0.398102\pi\)
0.314684 + 0.949197i \(0.398102\pi\)
\(678\) 38.8324i 1.49135i
\(679\) −17.9805 −0.690028
\(680\) 11.8740 0.455347
\(681\) 6.17679i 0.236695i
\(682\) 18.2071i 0.697186i
\(683\) 15.7988i 0.604523i 0.953225 + 0.302262i \(0.0977416\pi\)
−0.953225 + 0.302262i \(0.902258\pi\)
\(684\) 4.20711i 0.160863i
\(685\) −2.16457 −0.0827041
\(686\) 2.48119 0.0947324
\(687\) 9.47627i 0.361542i
\(688\) −22.8872 −0.872565
\(689\) −10.3757 + 4.67513i −0.395281 + 0.178108i
\(690\) 13.3806 0.509390
\(691\) 7.56818i 0.287907i 0.989584 + 0.143953i \(0.0459816\pi\)
−0.989584 + 0.143953i \(0.954018\pi\)
\(692\) −9.03761 −0.343558
\(693\) −0.869067 −0.0330131
\(694\) 76.2638i 2.89493i
\(695\) 0.168544i 0.00639324i
\(696\) 83.4636i 3.16368i
\(697\) 26.0508i 0.986744i
\(698\) 4.97461 0.188292
\(699\) −17.2971 −0.654237
\(700\) 18.8872i 0.713868i
\(701\) −32.6629 −1.23366 −0.616831 0.787096i \(-0.711584\pi\)
−0.616831 + 0.787096i \(0.711584\pi\)
\(702\) −19.6629 43.6385i −0.742129 1.64703i
\(703\) −7.53453 −0.284170
\(704\) 26.5501i 1.00064i
\(705\) −8.89938 −0.335170
\(706\) −42.8119 −1.61125
\(707\) 9.33804i 0.351193i
\(708\) 17.7137i 0.665722i
\(709\) 25.0214i 0.939699i −0.882746 0.469850i \(-0.844308\pi\)
0.882746 0.469850i \(-0.155692\pi\)
\(710\) 12.9927i 0.487608i
\(711\) −2.84367 −0.106646
\(712\) 41.6991 1.56274
\(713\) 7.80843i 0.292428i
\(714\) 13.6629 0.511322
\(715\) −9.94525 + 4.48119i −0.371931 + 0.167587i
\(716\) 2.29218 0.0856629
\(717\) 37.3357i 1.39433i
\(718\) −17.6326 −0.658043
\(719\) 1.85192 0.0690651 0.0345326 0.999404i \(-0.489006\pi\)
0.0345326 + 0.999404i \(0.489006\pi\)
\(720\) 0.649738i 0.0242143i
\(721\) 6.23743i 0.232294i
\(722\) 20.4485i 0.761015i
\(723\) 49.2931i 1.83323i
\(724\) −2.12601 −0.0790125
\(725\) −42.3185 −1.57167
\(726\) 37.7440i 1.40081i
\(727\) −10.8265 −0.401534 −0.200767 0.979639i \(-0.564343\pi\)
−0.200767 + 0.979639i \(0.564343\pi\)
\(728\) 17.5877 7.92478i 0.651843 0.293712i
\(729\) 28.5125 1.05602
\(730\) 25.3684i 0.938925i
\(731\) 15.1612 0.560759
\(732\) 16.1016 0.595131
\(733\) 23.4264i 0.865275i −0.901568 0.432638i \(-0.857583\pi\)
0.901568 0.432638i \(-0.142417\pi\)
\(734\) 67.6444i 2.49680i
\(735\) 1.13093i 0.0417151i
\(736\) 7.68735i 0.283359i
\(737\) −32.9380 −1.21329
\(738\) 3.81336 0.140372
\(739\) 0.481194i 0.0177010i −0.999961 0.00885051i \(-0.997183\pi\)
0.999961 0.00885051i \(-0.00281724\pi\)
\(740\) −4.05079 −0.148910
\(741\) 12.9502 + 28.7407i 0.475736 + 1.05582i
\(742\) 7.83146 0.287502
\(743\) 13.7889i 0.505866i 0.967484 + 0.252933i \(0.0813953\pi\)
−0.967484 + 0.252933i \(0.918605\pi\)
\(744\) −14.6761 −0.538051
\(745\) 2.72259 0.0997480
\(746\) 14.6859i 0.537690i
\(747\) 0.281378i 0.0102951i
\(748\) 61.2262i 2.23865i
\(749\) 7.24472i 0.264716i
\(750\) 26.7816 0.977927
\(751\) 26.4617 0.965600 0.482800 0.875731i \(-0.339620\pi\)
0.482800 + 0.875731i \(0.339620\pi\)
\(752\) 39.0494i 1.42398i
\(753\) −36.0567 −1.31398
\(754\) −34.2252 75.9570i −1.24641 2.76619i
\(755\) −1.05968 −0.0385657
\(756\) 22.2374i 0.808767i
\(757\) −21.1114 −0.767308 −0.383654 0.923477i \(-0.625334\pi\)
−0.383654 + 0.923477i \(0.625334\pi\)
\(758\) 71.8818 2.61086
\(759\) 35.7948i 1.29927i
\(760\) 18.8529i 0.683866i
\(761\) 28.5247i 1.03402i 0.855980 + 0.517010i \(0.172955\pi\)
−0.855980 + 0.517010i \(0.827045\pi\)
\(762\) 5.73813i 0.207871i
\(763\) 4.79384 0.173549
\(764\) 68.7631 2.48776
\(765\) 0.430409i 0.0155615i
\(766\) −57.6239 −2.08204
\(767\) 3.76845 + 8.36344i 0.136071 + 0.301986i
\(768\) −54.6516 −1.97207
\(769\) 25.8388i 0.931769i 0.884845 + 0.465885i \(0.154264\pi\)
−0.884845 + 0.465885i \(0.845736\pi\)
\(770\) 7.50659 0.270519
\(771\) 1.10886 0.0399348
\(772\) 30.8021i 1.10859i
\(773\) 27.4010i 0.985547i 0.870158 + 0.492774i \(0.164017\pi\)
−0.870158 + 0.492774i \(0.835983\pi\)
\(774\) 2.21933i 0.0797721i
\(775\) 7.44121i 0.267296i
\(776\) 96.2003 3.45339
\(777\) −2.41819 −0.0867521
\(778\) 40.0263i 1.43501i
\(779\) −41.3620 −1.48195
\(780\) 6.96239 + 15.4518i 0.249294 + 0.553264i
\(781\) −34.7572 −1.24371
\(782\) 38.8930i 1.39081i
\(783\) 49.8251 1.78060
\(784\) −4.96239 −0.177228
\(785\) 1.95746i 0.0698649i
\(786\) 51.9511i 1.85304i
\(787\) 31.0240i 1.10589i −0.833219 0.552943i \(-0.813505\pi\)
0.833219 0.552943i \(-0.186495\pi\)
\(788\) 29.7137i 1.05851i
\(789\) 8.68830 0.309312
\(790\) 24.5623 0.873887
\(791\) 9.34297i 0.332198i