Properties

Label 684.3.b.a.683.1
Level $684$
Weight $3$
Character 684.683
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 683.1
Character \(\chi\) \(=\) 684.683
Dual form 684.3.b.a.683.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.98202 - 0.267543i) q^{2} +(3.85684 + 1.06055i) q^{4} +4.56953i q^{5} +9.67098i q^{7} +(-7.36061 - 3.13391i) q^{8} +O(q^{10})\) \(q+(-1.98202 - 0.267543i) q^{2} +(3.85684 + 1.06055i) q^{4} +4.56953i q^{5} +9.67098i q^{7} +(-7.36061 - 3.13391i) q^{8} +(1.22255 - 9.05693i) q^{10} +2.25916 q^{11} +14.4261i q^{13} +(2.58740 - 19.1681i) q^{14} +(13.7505 + 8.18077i) q^{16} +2.47152i q^{17} +(8.92923 + 16.7711i) q^{19} +(-4.84623 + 17.6240i) q^{20} +(-4.47770 - 0.604422i) q^{22} -29.0241 q^{23} +4.11936 q^{25} +(3.85960 - 28.5928i) q^{26} +(-10.2566 + 37.2994i) q^{28} +10.3633 q^{29} -4.02586 q^{31} +(-25.0650 - 19.8933i) q^{32} +(0.661237 - 4.89861i) q^{34} -44.1919 q^{35} -33.0030i q^{37} +(-13.2110 - 35.6296i) q^{38} +(14.3205 - 33.6346i) q^{40} +1.46331 q^{41} -26.0088i q^{43} +(8.71321 + 2.39596i) q^{44} +(57.5265 + 7.76519i) q^{46} +6.14434 q^{47} -44.5278 q^{49} +(-8.16467 - 1.10211i) q^{50} +(-15.2996 + 55.6391i) q^{52} -16.4054 q^{53} +10.3233i q^{55} +(30.3080 - 71.1843i) q^{56} +(-20.5404 - 2.77264i) q^{58} -57.3091i q^{59} +94.3814 q^{61} +(7.97935 + 1.07709i) q^{62} +(44.3572 + 46.1350i) q^{64} -65.9205 q^{65} -120.267 q^{67} +(-2.62118 + 9.53225i) q^{68} +(87.5893 + 11.8232i) q^{70} +102.072i q^{71} +10.8998 q^{73} +(-8.82973 + 65.4128i) q^{74} +(16.6520 + 74.1533i) q^{76} +21.8483i q^{77} -54.0890 q^{79} +(-37.3823 + 62.8332i) q^{80} +(-2.90031 - 0.391498i) q^{82} -68.5339 q^{83} -11.2937 q^{85} +(-6.95846 + 51.5500i) q^{86} +(-16.6288 - 7.08000i) q^{88} +7.00476 q^{89} -139.514 q^{91} +(-111.941 - 30.7816i) q^{92} +(-12.1782 - 1.64387i) q^{94} +(-76.6360 + 40.8024i) q^{95} -29.0407i q^{97} +(88.2551 + 11.9131i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 8 q^{4} + O(q^{10}) \) \( 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98202 0.267543i −0.991012 0.133771i
\(3\) 0 0
\(4\) 3.85684 + 1.06055i 0.964210 + 0.265138i
\(5\) 4.56953i 0.913907i 0.889491 + 0.456953i \(0.151059\pi\)
−0.889491 + 0.456953i \(0.848941\pi\)
\(6\) 0 0
\(7\) 9.67098i 1.38157i 0.723061 + 0.690784i \(0.242734\pi\)
−0.723061 + 0.690784i \(0.757266\pi\)
\(8\) −7.36061 3.13391i −0.920076 0.391739i
\(9\) 0 0
\(10\) 1.22255 9.05693i 0.122255 0.905693i
\(11\) 2.25916 0.205378 0.102689 0.994714i \(-0.467255\pi\)
0.102689 + 0.994714i \(0.467255\pi\)
\(12\) 0 0
\(13\) 14.4261i 1.10970i 0.831951 + 0.554849i \(0.187224\pi\)
−0.831951 + 0.554849i \(0.812776\pi\)
\(14\) 2.58740 19.1681i 0.184814 1.36915i
\(15\) 0 0
\(16\) 13.7505 + 8.18077i 0.859403 + 0.511298i
\(17\) 2.47152i 0.145383i 0.997354 + 0.0726917i \(0.0231589\pi\)
−0.997354 + 0.0726917i \(0.976841\pi\)
\(18\) 0 0
\(19\) 8.92923 + 16.7711i 0.469959 + 0.882688i
\(20\) −4.84623 + 17.6240i −0.242312 + 0.881198i
\(21\) 0 0
\(22\) −4.47770 0.604422i −0.203532 0.0274737i
\(23\) −29.0241 −1.26192 −0.630958 0.775817i \(-0.717338\pi\)
−0.630958 + 0.775817i \(0.717338\pi\)
\(24\) 0 0
\(25\) 4.11936 0.164774
\(26\) 3.85960 28.5928i 0.148446 1.09972i
\(27\) 0 0
\(28\) −10.2566 + 37.2994i −0.366307 + 1.33212i
\(29\) 10.3633 0.357356 0.178678 0.983908i \(-0.442818\pi\)
0.178678 + 0.983908i \(0.442818\pi\)
\(30\) 0 0
\(31\) −4.02586 −0.129866 −0.0649332 0.997890i \(-0.520683\pi\)
−0.0649332 + 0.997890i \(0.520683\pi\)
\(32\) −25.0650 19.8933i −0.783282 0.621666i
\(33\) 0 0
\(34\) 0.661237 4.89861i 0.0194482 0.144077i
\(35\) −44.1919 −1.26262
\(36\) 0 0
\(37\) 33.0030i 0.891974i −0.895040 0.445987i \(-0.852853\pi\)
0.895040 0.445987i \(-0.147147\pi\)
\(38\) −13.2110 35.6296i −0.347657 0.937622i
\(39\) 0 0
\(40\) 14.3205 33.6346i 0.358013 0.840864i
\(41\) 1.46331 0.0356905 0.0178452 0.999841i \(-0.494319\pi\)
0.0178452 + 0.999841i \(0.494319\pi\)
\(42\) 0 0
\(43\) 26.0088i 0.604855i −0.953172 0.302428i \(-0.902203\pi\)
0.953172 0.302428i \(-0.0977971\pi\)
\(44\) 8.71321 + 2.39596i 0.198028 + 0.0544536i
\(45\) 0 0
\(46\) 57.5265 + 7.76519i 1.25058 + 0.168808i
\(47\) 6.14434 0.130731 0.0653653 0.997861i \(-0.479179\pi\)
0.0653653 + 0.997861i \(0.479179\pi\)
\(48\) 0 0
\(49\) −44.5278 −0.908730
\(50\) −8.16467 1.10211i −0.163293 0.0220421i
\(51\) 0 0
\(52\) −15.2996 + 55.6391i −0.294224 + 1.06998i
\(53\) −16.4054 −0.309536 −0.154768 0.987951i \(-0.549463\pi\)
−0.154768 + 0.987951i \(0.549463\pi\)
\(54\) 0 0
\(55\) 10.3233i 0.187696i
\(56\) 30.3080 71.1843i 0.541214 1.27115i
\(57\) 0 0
\(58\) −20.5404 2.77264i −0.354145 0.0478041i
\(59\) 57.3091i 0.971341i −0.874142 0.485670i \(-0.838576\pi\)
0.874142 0.485670i \(-0.161424\pi\)
\(60\) 0 0
\(61\) 94.3814 1.54724 0.773618 0.633652i \(-0.218445\pi\)
0.773618 + 0.633652i \(0.218445\pi\)
\(62\) 7.97935 + 1.07709i 0.128699 + 0.0173724i
\(63\) 0 0
\(64\) 44.3572 + 46.1350i 0.693081 + 0.720860i
\(65\) −65.9205 −1.01416
\(66\) 0 0
\(67\) −120.267 −1.79503 −0.897515 0.440985i \(-0.854629\pi\)
−0.897515 + 0.440985i \(0.854629\pi\)
\(68\) −2.62118 + 9.53225i −0.0385467 + 0.140180i
\(69\) 0 0
\(70\) 87.5893 + 11.8232i 1.25128 + 0.168903i
\(71\) 102.072i 1.43763i 0.695202 + 0.718814i \(0.255315\pi\)
−0.695202 + 0.718814i \(0.744685\pi\)
\(72\) 0 0
\(73\) 10.8998 0.149313 0.0746563 0.997209i \(-0.476214\pi\)
0.0746563 + 0.997209i \(0.476214\pi\)
\(74\) −8.82973 + 65.4128i −0.119321 + 0.883957i
\(75\) 0 0
\(76\) 16.6520 + 74.1533i 0.219105 + 0.975701i
\(77\) 21.8483i 0.283744i
\(78\) 0 0
\(79\) −54.0890 −0.684671 −0.342336 0.939578i \(-0.611218\pi\)
−0.342336 + 0.939578i \(0.611218\pi\)
\(80\) −37.3823 + 62.8332i −0.467279 + 0.785415i
\(81\) 0 0
\(82\) −2.90031 0.391498i −0.0353697 0.00477436i
\(83\) −68.5339 −0.825710 −0.412855 0.910797i \(-0.635468\pi\)
−0.412855 + 0.910797i \(0.635468\pi\)
\(84\) 0 0
\(85\) −11.2937 −0.132867
\(86\) −6.95846 + 51.5500i −0.0809124 + 0.599419i
\(87\) 0 0
\(88\) −16.6288 7.08000i −0.188963 0.0804546i
\(89\) 7.00476 0.0787051 0.0393526 0.999225i \(-0.487470\pi\)
0.0393526 + 0.999225i \(0.487470\pi\)
\(90\) 0 0
\(91\) −139.514 −1.53312
\(92\) −111.941 30.7816i −1.21675 0.334583i
\(93\) 0 0
\(94\) −12.1782 1.64387i −0.129556 0.0174880i
\(95\) −76.6360 + 40.8024i −0.806695 + 0.429499i
\(96\) 0 0
\(97\) 29.0407i 0.299389i −0.988732 0.149694i \(-0.952171\pi\)
0.988732 0.149694i \(-0.0478290\pi\)
\(98\) 88.2551 + 11.9131i 0.900563 + 0.121562i
\(99\) 0 0
\(100\) 15.8877 + 4.36880i 0.158877 + 0.0436880i
\(101\) 33.9604i 0.336241i −0.985766 0.168121i \(-0.946230\pi\)
0.985766 0.168121i \(-0.0537698\pi\)
\(102\) 0 0
\(103\) −145.195 −1.40966 −0.704832 0.709374i \(-0.748978\pi\)
−0.704832 + 0.709374i \(0.748978\pi\)
\(104\) 45.2101 106.185i 0.434712 1.02101i
\(105\) 0 0
\(106\) 32.5160 + 4.38916i 0.306754 + 0.0414072i
\(107\) 21.3857i 0.199866i 0.994994 + 0.0999332i \(0.0318629\pi\)
−0.994994 + 0.0999332i \(0.968137\pi\)
\(108\) 0 0
\(109\) 182.880i 1.67780i 0.544285 + 0.838900i \(0.316801\pi\)
−0.544285 + 0.838900i \(0.683199\pi\)
\(110\) 2.76192 20.4610i 0.0251084 0.186009i
\(111\) 0 0
\(112\) −79.1160 + 132.980i −0.706393 + 1.18732i
\(113\) 186.968 1.65458 0.827292 0.561773i \(-0.189880\pi\)
0.827292 + 0.561773i \(0.189880\pi\)
\(114\) 0 0
\(115\) 132.627i 1.15327i
\(116\) 39.9698 + 10.9909i 0.344567 + 0.0947489i
\(117\) 0 0
\(118\) −15.3326 + 113.588i −0.129938 + 0.962610i
\(119\) −23.9020 −0.200857
\(120\) 0 0
\(121\) −115.896 −0.957820
\(122\) −187.066 25.2511i −1.53333 0.206976i
\(123\) 0 0
\(124\) −15.5271 4.26964i −0.125219 0.0344326i
\(125\) 133.062i 1.06450i
\(126\) 0 0
\(127\) −183.161 −1.44221 −0.721106 0.692825i \(-0.756366\pi\)
−0.721106 + 0.692825i \(0.756366\pi\)
\(128\) −75.5739 103.308i −0.590421 0.807095i
\(129\) 0 0
\(130\) 130.656 + 17.6366i 1.00505 + 0.135666i
\(131\) −117.754 −0.898885 −0.449443 0.893309i \(-0.648377\pi\)
−0.449443 + 0.893309i \(0.648377\pi\)
\(132\) 0 0
\(133\) −162.193 + 86.3544i −1.21949 + 0.649281i
\(134\) 238.372 + 32.1766i 1.77890 + 0.240124i
\(135\) 0 0
\(136\) 7.74552 18.1919i 0.0569524 0.133764i
\(137\) 20.2096i 0.147516i −0.997276 0.0737578i \(-0.976501\pi\)
0.997276 0.0737578i \(-0.0234992\pi\)
\(138\) 0 0
\(139\) 121.016i 0.870615i −0.900282 0.435308i \(-0.856640\pi\)
0.900282 0.435308i \(-0.143360\pi\)
\(140\) −170.441 46.8678i −1.21744 0.334770i
\(141\) 0 0
\(142\) 27.3085 202.308i 0.192314 1.42471i
\(143\) 32.5908i 0.227908i
\(144\) 0 0
\(145\) 47.3556i 0.326591i
\(146\) −21.6037 2.91617i −0.147971 0.0199738i
\(147\) 0 0
\(148\) 35.0015 127.287i 0.236496 0.860050i
\(149\) 197.800i 1.32752i 0.747946 + 0.663760i \(0.231040\pi\)
−0.747946 + 0.663760i \(0.768960\pi\)
\(150\) 0 0
\(151\) 174.253 1.15399 0.576997 0.816746i \(-0.304225\pi\)
0.576997 + 0.816746i \(0.304225\pi\)
\(152\) −13.1655 151.429i −0.0866152 0.996242i
\(153\) 0 0
\(154\) 5.84535 43.3038i 0.0379568 0.281193i
\(155\) 18.3963i 0.118686i
\(156\) 0 0
\(157\) 240.144 1.52958 0.764790 0.644280i \(-0.222843\pi\)
0.764790 + 0.644280i \(0.222843\pi\)
\(158\) 107.206 + 14.4711i 0.678517 + 0.0915895i
\(159\) 0 0
\(160\) 90.9032 114.535i 0.568145 0.715847i
\(161\) 280.691i 1.74342i
\(162\) 0 0
\(163\) 75.1019i 0.460748i −0.973102 0.230374i \(-0.926005\pi\)
0.973102 0.230374i \(-0.0739949\pi\)
\(164\) 5.64375 + 1.55192i 0.0344131 + 0.00946291i
\(165\) 0 0
\(166\) 135.836 + 18.3358i 0.818288 + 0.110456i
\(167\) 237.513i 1.42223i 0.703075 + 0.711116i \(0.251810\pi\)
−0.703075 + 0.711116i \(0.748190\pi\)
\(168\) 0 0
\(169\) −39.1119 −0.231431
\(170\) 22.3844 + 3.02155i 0.131673 + 0.0177738i
\(171\) 0 0
\(172\) 27.5837 100.312i 0.160370 0.583208i
\(173\) −155.335 −0.897890 −0.448945 0.893559i \(-0.648200\pi\)
−0.448945 + 0.893559i \(0.648200\pi\)
\(174\) 0 0
\(175\) 39.8382i 0.227647i
\(176\) 31.0644 + 18.4816i 0.176502 + 0.105009i
\(177\) 0 0
\(178\) −13.8836 1.87407i −0.0779978 0.0105285i
\(179\) 344.237i 1.92311i 0.274611 + 0.961555i \(0.411451\pi\)
−0.274611 + 0.961555i \(0.588549\pi\)
\(180\) 0 0
\(181\) 258.376i 1.42749i −0.700405 0.713746i \(-0.746997\pi\)
0.700405 0.713746i \(-0.253003\pi\)
\(182\) 276.521 + 37.3261i 1.51934 + 0.205088i
\(183\) 0 0
\(184\) 213.635 + 90.9590i 1.16106 + 0.494342i
\(185\) 150.808 0.815181
\(186\) 0 0
\(187\) 5.58355i 0.0298585i
\(188\) 23.6977 + 6.51640i 0.126052 + 0.0346617i
\(189\) 0 0
\(190\) 162.811 60.3680i 0.856899 0.317726i
\(191\) 337.360 1.76628 0.883142 0.469106i \(-0.155424\pi\)
0.883142 + 0.469106i \(0.155424\pi\)
\(192\) 0 0
\(193\) 1.65785i 0.00858991i 0.999991 + 0.00429495i \(0.00136713\pi\)
−0.999991 + 0.00429495i \(0.998633\pi\)
\(194\) −7.76964 + 57.5594i −0.0400497 + 0.296698i
\(195\) 0 0
\(196\) −171.737 47.2241i −0.876207 0.240939i
\(197\) 55.4402i 0.281422i 0.990051 + 0.140711i \(0.0449389\pi\)
−0.990051 + 0.140711i \(0.955061\pi\)
\(198\) 0 0
\(199\) 218.233i 1.09665i −0.836267 0.548323i \(-0.815266\pi\)
0.836267 0.548323i \(-0.184734\pi\)
\(200\) −30.3210 12.9097i −0.151605 0.0645486i
\(201\) 0 0
\(202\) −9.08586 + 67.3103i −0.0449795 + 0.333219i
\(203\) 100.224i 0.493712i
\(204\) 0 0
\(205\) 6.68664i 0.0326178i
\(206\) 287.781 + 38.8460i 1.39699 + 0.188573i
\(207\) 0 0
\(208\) −118.016 + 198.365i −0.567387 + 0.953679i
\(209\) 20.1725 + 37.8885i 0.0965193 + 0.181285i
\(210\) 0 0
\(211\) 166.163 0.787503 0.393751 0.919217i \(-0.371177\pi\)
0.393751 + 0.919217i \(0.371177\pi\)
\(212\) −63.2732 17.3988i −0.298458 0.0820700i
\(213\) 0 0
\(214\) 5.72160 42.3870i 0.0267364 0.198070i
\(215\) 118.848 0.552781
\(216\) 0 0
\(217\) 38.9340i 0.179419i
\(218\) 48.9283 362.473i 0.224442 1.66272i
\(219\) 0 0
\(220\) −10.9484 + 39.8153i −0.0497655 + 0.180979i
\(221\) −35.6543 −0.161332
\(222\) 0 0
\(223\) 65.0594 0.291746 0.145873 0.989303i \(-0.453401\pi\)
0.145873 + 0.989303i \(0.453401\pi\)
\(224\) 192.388 242.403i 0.858874 1.08216i
\(225\) 0 0
\(226\) −370.575 50.0219i −1.63971 0.221336i
\(227\) 224.720i 0.989954i −0.868906 0.494977i \(-0.835176\pi\)
0.868906 0.494977i \(-0.164824\pi\)
\(228\) 0 0
\(229\) −54.6061 −0.238454 −0.119227 0.992867i \(-0.538042\pi\)
−0.119227 + 0.992867i \(0.538042\pi\)
\(230\) −35.4833 + 262.869i −0.154275 + 1.14291i
\(231\) 0 0
\(232\) −76.2805 32.4778i −0.328795 0.139991i
\(233\) 353.980i 1.51923i −0.650376 0.759613i \(-0.725388\pi\)
0.650376 0.759613i \(-0.274612\pi\)
\(234\) 0 0
\(235\) 28.0768i 0.119476i
\(236\) 60.7793 221.032i 0.257540 0.936577i
\(237\) 0 0
\(238\) 47.3743 + 6.39481i 0.199052 + 0.0268689i
\(239\) 352.007 1.47283 0.736416 0.676529i \(-0.236517\pi\)
0.736416 + 0.676529i \(0.236517\pi\)
\(240\) 0 0
\(241\) 207.188i 0.859702i −0.902900 0.429851i \(-0.858566\pi\)
0.902900 0.429851i \(-0.141434\pi\)
\(242\) 229.709 + 31.0072i 0.949211 + 0.128129i
\(243\) 0 0
\(244\) 364.014 + 100.096i 1.49186 + 0.410231i
\(245\) 203.471i 0.830495i
\(246\) 0 0
\(247\) −241.941 + 128.814i −0.979518 + 0.521513i
\(248\) 29.6328 + 12.6167i 0.119487 + 0.0508738i
\(249\) 0 0
\(250\) 35.5998 263.732i 0.142399 1.05493i
\(251\) −250.965 −0.999861 −0.499931 0.866065i \(-0.666641\pi\)
−0.499931 + 0.866065i \(0.666641\pi\)
\(252\) 0 0
\(253\) −65.5700 −0.259170
\(254\) 363.029 + 49.0034i 1.42925 + 0.192927i
\(255\) 0 0
\(256\) 122.150 + 224.979i 0.477148 + 0.878823i
\(257\) 56.2756 0.218971 0.109486 0.993988i \(-0.465080\pi\)
0.109486 + 0.993988i \(0.465080\pi\)
\(258\) 0 0
\(259\) 319.171 1.23232
\(260\) −254.245 69.9122i −0.977865 0.268893i
\(261\) 0 0
\(262\) 233.391 + 31.5042i 0.890806 + 0.120245i
\(263\) 116.802 0.444112 0.222056 0.975034i \(-0.428723\pi\)
0.222056 + 0.975034i \(0.428723\pi\)
\(264\) 0 0
\(265\) 74.9652i 0.282888i
\(266\) 344.573 127.763i 1.29539 0.480312i
\(267\) 0 0
\(268\) −463.851 127.549i −1.73079 0.475931i
\(269\) −436.834 −1.62392 −0.811959 0.583714i \(-0.801599\pi\)
−0.811959 + 0.583714i \(0.801599\pi\)
\(270\) 0 0
\(271\) 198.846i 0.733747i −0.930271 0.366874i \(-0.880428\pi\)
0.930271 0.366874i \(-0.119572\pi\)
\(272\) −20.2189 + 33.9845i −0.0743343 + 0.124943i
\(273\) 0 0
\(274\) −5.40695 + 40.0560i −0.0197334 + 0.146190i
\(275\) 9.30628 0.0338410
\(276\) 0 0
\(277\) −91.4350 −0.330090 −0.165045 0.986286i \(-0.552777\pi\)
−0.165045 + 0.986286i \(0.552777\pi\)
\(278\) −32.3769 + 239.856i −0.116464 + 0.862791i
\(279\) 0 0
\(280\) 325.279 + 138.493i 1.16171 + 0.494619i
\(281\) −293.552 −1.04467 −0.522334 0.852741i \(-0.674939\pi\)
−0.522334 + 0.852741i \(0.674939\pi\)
\(282\) 0 0
\(283\) 172.782i 0.610538i 0.952266 + 0.305269i \(0.0987465\pi\)
−0.952266 + 0.305269i \(0.901254\pi\)
\(284\) −108.252 + 393.674i −0.381170 + 1.38618i
\(285\) 0 0
\(286\) 8.71944 64.5957i 0.0304875 0.225859i
\(287\) 14.1516i 0.0493088i
\(288\) 0 0
\(289\) 282.892 0.978864
\(290\) 12.6697 93.8600i 0.0436885 0.323655i
\(291\) 0 0
\(292\) 42.0389 + 11.5598i 0.143969 + 0.0395885i
\(293\) 455.722 1.55537 0.777683 0.628657i \(-0.216395\pi\)
0.777683 + 0.628657i \(0.216395\pi\)
\(294\) 0 0
\(295\) 261.876 0.887715
\(296\) −103.429 + 242.922i −0.349421 + 0.820684i
\(297\) 0 0
\(298\) 52.9201 392.045i 0.177584 1.31559i
\(299\) 418.704i 1.40035i
\(300\) 0 0
\(301\) 251.530 0.835649
\(302\) −345.374 46.6202i −1.14362 0.154371i
\(303\) 0 0
\(304\) −14.4193 + 303.658i −0.0474321 + 0.998874i
\(305\) 431.279i 1.41403i
\(306\) 0 0
\(307\) 433.832 1.41313 0.706567 0.707646i \(-0.250243\pi\)
0.706567 + 0.707646i \(0.250243\pi\)
\(308\) −23.1712 + 84.2653i −0.0752313 + 0.273588i
\(309\) 0 0
\(310\) −4.92180 + 36.4619i −0.0158768 + 0.117619i
\(311\) 62.7106 0.201642 0.100821 0.994905i \(-0.467853\pi\)
0.100821 + 0.994905i \(0.467853\pi\)
\(312\) 0 0
\(313\) −222.649 −0.711339 −0.355669 0.934612i \(-0.615747\pi\)
−0.355669 + 0.934612i \(0.615747\pi\)
\(314\) −475.971 64.2488i −1.51583 0.204614i
\(315\) 0 0
\(316\) −208.613 57.3643i −0.660167 0.181533i
\(317\) 277.405 0.875093 0.437547 0.899196i \(-0.355847\pi\)
0.437547 + 0.899196i \(0.355847\pi\)
\(318\) 0 0
\(319\) 23.4124 0.0733931
\(320\) −210.816 + 202.692i −0.658799 + 0.633411i
\(321\) 0 0
\(322\) −75.0970 + 556.337i −0.233220 + 1.72775i
\(323\) −41.4500 + 22.0688i −0.128328 + 0.0683243i
\(324\) 0 0
\(325\) 59.4262i 0.182850i
\(326\) −20.0930 + 148.854i −0.0616349 + 0.456607i
\(327\) 0 0
\(328\) −10.7708 4.58588i −0.0328379 0.0139813i
\(329\) 59.4217i 0.180613i
\(330\) 0 0
\(331\) −481.784 −1.45554 −0.727771 0.685820i \(-0.759444\pi\)
−0.727771 + 0.685820i \(0.759444\pi\)
\(332\) −264.324 72.6839i −0.796158 0.218927i
\(333\) 0 0
\(334\) 63.5448 470.756i 0.190254 1.40945i
\(335\) 549.564i 1.64049i
\(336\) 0 0
\(337\) 197.246i 0.585300i 0.956220 + 0.292650i \(0.0945371\pi\)
−0.956220 + 0.292650i \(0.905463\pi\)
\(338\) 77.5207 + 10.4641i 0.229351 + 0.0309589i
\(339\) 0 0
\(340\) −43.5580 11.9776i −0.128112 0.0352281i
\(341\) −9.09505 −0.0266717
\(342\) 0 0
\(343\) 43.2508i 0.126096i
\(344\) −81.5092 + 191.440i −0.236945 + 0.556513i
\(345\) 0 0
\(346\) 307.878 + 41.5588i 0.889820 + 0.120112i
\(347\) 63.7435 0.183699 0.0918494 0.995773i \(-0.470722\pi\)
0.0918494 + 0.995773i \(0.470722\pi\)
\(348\) 0 0
\(349\) 124.985 0.358122 0.179061 0.983838i \(-0.442694\pi\)
0.179061 + 0.983838i \(0.442694\pi\)
\(350\) 10.6584 78.9603i 0.0304527 0.225601i
\(351\) 0 0
\(352\) −56.6258 44.9421i −0.160869 0.127677i
\(353\) 367.068i 1.03985i 0.854211 + 0.519926i \(0.174041\pi\)
−0.854211 + 0.519926i \(0.825959\pi\)
\(354\) 0 0
\(355\) −466.420 −1.31386
\(356\) 27.0162 + 7.42892i 0.0758883 + 0.0208678i
\(357\) 0 0
\(358\) 92.0981 682.286i 0.257257 1.90583i
\(359\) 55.1266 0.153556 0.0767781 0.997048i \(-0.475537\pi\)
0.0767781 + 0.997048i \(0.475537\pi\)
\(360\) 0 0
\(361\) −201.538 + 299.506i −0.558276 + 0.829655i
\(362\) −69.1266 + 512.107i −0.190958 + 1.41466i
\(363\) 0 0
\(364\) −538.085 147.962i −1.47825 0.406490i
\(365\) 49.8071i 0.136458i
\(366\) 0 0
\(367\) 330.645i 0.900939i 0.892792 + 0.450470i \(0.148743\pi\)
−0.892792 + 0.450470i \(0.851257\pi\)
\(368\) −399.094 237.439i −1.08450 0.645216i
\(369\) 0 0
\(370\) −298.906 40.3477i −0.807854 0.109048i
\(371\) 158.657i 0.427646i
\(372\) 0 0
\(373\) 575.367i 1.54254i 0.636510 + 0.771269i \(0.280378\pi\)
−0.636510 + 0.771269i \(0.719622\pi\)
\(374\) 1.49384 11.0667i 0.00399422 0.0295902i
\(375\) 0 0
\(376\) −45.2261 19.2558i −0.120282 0.0512123i
\(377\) 149.502i 0.396558i
\(378\) 0 0
\(379\) 439.139 1.15868 0.579339 0.815087i \(-0.303311\pi\)
0.579339 + 0.815087i \(0.303311\pi\)
\(380\) −338.846 + 76.0919i −0.891700 + 0.200242i
\(381\) 0 0
\(382\) −668.656 90.2583i −1.75041 0.236278i
\(383\) 145.105i 0.378865i 0.981894 + 0.189433i \(0.0606649\pi\)
−0.981894 + 0.189433i \(0.939335\pi\)
\(384\) 0 0
\(385\) −99.8363 −0.259315
\(386\) 0.443547 3.28590i 0.00114908 0.00851270i
\(387\) 0 0
\(388\) 30.7992 112.005i 0.0793794 0.288674i
\(389\) 573.996i 1.47557i −0.675037 0.737783i \(-0.735873\pi\)
0.675037 0.737783i \(-0.264127\pi\)
\(390\) 0 0
\(391\) 71.7336i 0.183462i
\(392\) 327.752 + 139.546i 0.836101 + 0.355985i
\(393\) 0 0
\(394\) 14.8326 109.884i 0.0376463 0.278893i
\(395\) 247.162i 0.625726i
\(396\) 0 0
\(397\) −472.658 −1.19057 −0.595287 0.803513i \(-0.702962\pi\)
−0.595287 + 0.803513i \(0.702962\pi\)
\(398\) −58.3866 + 432.542i −0.146700 + 1.08679i
\(399\) 0 0
\(400\) 56.6430 + 33.6995i 0.141608 + 0.0842488i
\(401\) −479.989 −1.19698 −0.598490 0.801131i \(-0.704232\pi\)
−0.598490 + 0.801131i \(0.704232\pi\)
\(402\) 0 0
\(403\) 58.0774i 0.144113i
\(404\) 36.0168 130.980i 0.0891505 0.324207i
\(405\) 0 0
\(406\) 26.8141 198.646i 0.0660446 0.489275i
\(407\) 74.5590i 0.183192i
\(408\) 0 0
\(409\) 361.938i 0.884933i −0.896785 0.442466i \(-0.854104\pi\)
0.896785 0.442466i \(-0.145896\pi\)
\(410\) 1.78896 13.2531i 0.00436332 0.0323246i
\(411\) 0 0
\(412\) −559.996 153.987i −1.35921 0.373756i
\(413\) 554.235 1.34197
\(414\) 0 0
\(415\) 313.168i 0.754622i
\(416\) 286.983 361.590i 0.689862 0.869207i
\(417\) 0 0
\(418\) −29.8457 80.4929i −0.0714011 0.192567i
\(419\) −382.181 −0.912127 −0.456064 0.889947i \(-0.650741\pi\)
−0.456064 + 0.889947i \(0.650741\pi\)
\(420\) 0 0
\(421\) 499.229i 1.18582i −0.805270 0.592908i \(-0.797980\pi\)
0.805270 0.592908i \(-0.202020\pi\)
\(422\) −329.339 44.4558i −0.780425 0.105345i
\(423\) 0 0
\(424\) 120.754 + 51.4132i 0.284797 + 0.121258i
\(425\) 10.1811i 0.0239555i
\(426\) 0 0
\(427\) 912.760i 2.13761i
\(428\) −22.6807 + 82.4813i −0.0529923 + 0.192713i
\(429\) 0 0
\(430\) −235.560 31.7969i −0.547813 0.0739464i
\(431\) 697.824i 1.61908i 0.587064 + 0.809541i \(0.300284\pi\)
−0.587064 + 0.809541i \(0.699716\pi\)
\(432\) 0 0
\(433\) 487.071i 1.12488i 0.826839 + 0.562438i \(0.190137\pi\)
−0.826839 + 0.562438i \(0.809863\pi\)
\(434\) −10.4165 + 77.1681i −0.0240012 + 0.177807i
\(435\) 0 0
\(436\) −193.954 + 705.340i −0.444849 + 1.61775i
\(437\) −259.163 486.765i −0.593050 1.11388i
\(438\) 0 0
\(439\) 710.575 1.61862 0.809311 0.587381i \(-0.199841\pi\)
0.809311 + 0.587381i \(0.199841\pi\)
\(440\) 32.3523 75.9858i 0.0735280 0.172695i
\(441\) 0 0
\(442\) 70.6677 + 9.53906i 0.159882 + 0.0215816i
\(443\) −229.818 −0.518776 −0.259388 0.965773i \(-0.583521\pi\)
−0.259388 + 0.965773i \(0.583521\pi\)
\(444\) 0 0
\(445\) 32.0085i 0.0719292i
\(446\) −128.949 17.4062i −0.289124 0.0390273i
\(447\) 0 0
\(448\) −446.171 + 428.977i −0.995917 + 0.957538i
\(449\) 516.327 1.14995 0.574974 0.818172i \(-0.305012\pi\)
0.574974 + 0.818172i \(0.305012\pi\)
\(450\) 0 0
\(451\) 3.30584 0.00733003
\(452\) 721.106 + 198.289i 1.59537 + 0.438693i
\(453\) 0 0
\(454\) −60.1221 + 445.400i −0.132428 + 0.981057i
\(455\) 637.515i 1.40113i
\(456\) 0 0
\(457\) 524.409 1.14750 0.573752 0.819029i \(-0.305487\pi\)
0.573752 + 0.819029i \(0.305487\pi\)
\(458\) 108.231 + 14.6095i 0.236311 + 0.0318984i
\(459\) 0 0
\(460\) 140.658 511.520i 0.305777 1.11200i
\(461\) 367.478i 0.797133i 0.917139 + 0.398567i \(0.130492\pi\)
−0.917139 + 0.398567i \(0.869508\pi\)
\(462\) 0 0
\(463\) 209.731i 0.452983i 0.974013 + 0.226492i \(0.0727256\pi\)
−0.974013 + 0.226492i \(0.927274\pi\)
\(464\) 142.501 + 84.7801i 0.307113 + 0.182716i
\(465\) 0 0
\(466\) −94.7047 + 701.596i −0.203229 + 1.50557i
\(467\) −631.041 −1.35127 −0.675633 0.737238i \(-0.736129\pi\)
−0.675633 + 0.737238i \(0.736129\pi\)
\(468\) 0 0
\(469\) 1163.10i 2.47995i
\(470\) 7.51174 55.6488i 0.0159824 0.118402i
\(471\) 0 0
\(472\) −179.602 + 421.830i −0.380512 + 0.893707i
\(473\) 58.7579i 0.124224i
\(474\) 0 0
\(475\) 36.7827 + 69.0861i 0.0774373 + 0.145444i
\(476\) −92.1862 25.3493i −0.193668 0.0532549i
\(477\) 0 0
\(478\) −697.686 94.1769i −1.45959 0.197023i
\(479\) 875.568 1.82791 0.913954 0.405818i \(-0.133013\pi\)
0.913954 + 0.405818i \(0.133013\pi\)
\(480\) 0 0
\(481\) 476.104 0.989822
\(482\) −55.4317 + 410.652i −0.115004 + 0.851975i
\(483\) 0 0
\(484\) −446.993 122.914i −0.923540 0.253955i
\(485\) 132.703 0.273613
\(486\) 0 0
\(487\) 614.907 1.26264 0.631321 0.775521i \(-0.282513\pi\)
0.631321 + 0.775521i \(0.282513\pi\)
\(488\) −694.705 295.783i −1.42357 0.606113i
\(489\) 0 0
\(490\) −54.4373 + 403.285i −0.111096 + 0.823030i
\(491\) 192.629 0.392320 0.196160 0.980572i \(-0.437153\pi\)
0.196160 + 0.980572i \(0.437153\pi\)
\(492\) 0 0
\(493\) 25.6132i 0.0519537i
\(494\) 513.996 190.583i 1.04048 0.385795i
\(495\) 0 0
\(496\) −55.3574 32.9346i −0.111608 0.0664005i
\(497\) −987.132 −1.98618
\(498\) 0 0
\(499\) 866.789i 1.73705i 0.495643 + 0.868526i \(0.334932\pi\)
−0.495643 + 0.868526i \(0.665068\pi\)
\(500\) −141.119 + 513.199i −0.282238 + 1.02640i
\(501\) 0 0
\(502\) 497.419 + 67.1440i 0.990875 + 0.133753i
\(503\) −801.068 −1.59258 −0.796291 0.604914i \(-0.793207\pi\)
−0.796291 + 0.604914i \(0.793207\pi\)
\(504\) 0 0
\(505\) 155.183 0.307293
\(506\) 129.961 + 17.5428i 0.256841 + 0.0346695i
\(507\) 0 0
\(508\) −706.422 194.252i −1.39060 0.382385i
\(509\) −577.610 −1.13479 −0.567397 0.823444i \(-0.692050\pi\)
−0.567397 + 0.823444i \(0.692050\pi\)
\(510\) 0 0
\(511\) 105.412i 0.206285i
\(512\) −181.913 478.594i −0.355298 0.934753i
\(513\) 0 0
\(514\) −111.540 15.0561i −0.217003 0.0292921i
\(515\) 663.475i 1.28830i
\(516\) 0 0
\(517\) 13.8810 0.0268492
\(518\) −632.606 85.3921i −1.22125 0.164850i
\(519\) 0 0
\(520\) 485.215 + 206.589i 0.933106 + 0.397287i
\(521\) 408.835 0.784713 0.392356 0.919813i \(-0.371660\pi\)
0.392356 + 0.919813i \(0.371660\pi\)
\(522\) 0 0
\(523\) −102.291 −0.195586 −0.0977928 0.995207i \(-0.531178\pi\)
−0.0977928 + 0.995207i \(0.531178\pi\)
\(524\) −454.158 124.884i −0.866715 0.238329i
\(525\) 0 0
\(526\) −231.504 31.2494i −0.440121 0.0594096i
\(527\) 9.94999i 0.0188804i
\(528\) 0 0
\(529\) 313.398 0.592434
\(530\) −20.0564 + 148.583i −0.0378423 + 0.280345i
\(531\) 0 0
\(532\) −717.135 + 161.041i −1.34800 + 0.302709i
\(533\) 21.1098i 0.0396057i
\(534\) 0 0
\(535\) −97.7227 −0.182659
\(536\) 885.238 + 376.906i 1.65156 + 0.703183i
\(537\) 0 0
\(538\) 865.816 + 116.872i 1.60932 + 0.217234i
\(539\) −100.595 −0.186633
\(540\) 0 0
\(541\) −198.431 −0.366785 −0.183393 0.983040i \(-0.558708\pi\)
−0.183393 + 0.983040i \(0.558708\pi\)
\(542\) −53.1997 + 394.117i −0.0981544 + 0.727152i
\(543\) 0 0
\(544\) 49.1667 61.9487i 0.0903800 0.113876i
\(545\) −835.678 −1.53335
\(546\) 0 0
\(547\) 82.8915 0.151538 0.0757692 0.997125i \(-0.475859\pi\)
0.0757692 + 0.997125i \(0.475859\pi\)
\(548\) 21.4334 77.9454i 0.0391121 0.142236i
\(549\) 0 0
\(550\) −18.4453 2.48983i −0.0335369 0.00452696i
\(551\) 92.5366 + 173.804i 0.167943 + 0.315434i
\(552\) 0 0
\(553\) 523.094i 0.945920i
\(554\) 181.226 + 24.4628i 0.327123 + 0.0441567i
\(555\) 0 0
\(556\) 128.343 466.738i 0.230834 0.839456i
\(557\) 770.595i 1.38347i 0.722149 + 0.691737i \(0.243154\pi\)
−0.722149 + 0.691737i \(0.756846\pi\)
\(558\) 0 0
\(559\) 375.205 0.671207
\(560\) −607.658 361.523i −1.08510 0.645578i
\(561\) 0 0
\(562\) 581.827 + 78.5377i 1.03528 + 0.139747i
\(563\) 608.743i 1.08125i −0.841264 0.540624i \(-0.818188\pi\)
0.841264 0.540624i \(-0.181812\pi\)
\(564\) 0 0
\(565\) 854.356i 1.51214i
\(566\) 46.2267 342.459i 0.0816726 0.605051i
\(567\) 0 0
\(568\) 319.884 751.309i 0.563175 1.32273i
\(569\) 668.134 1.17422 0.587112 0.809506i \(-0.300265\pi\)
0.587112 + 0.809506i \(0.300265\pi\)
\(570\) 0 0
\(571\) 365.096i 0.639398i 0.947519 + 0.319699i \(0.103582\pi\)
−0.947519 + 0.319699i \(0.896418\pi\)
\(572\) −34.5643 + 125.698i −0.0604270 + 0.219751i
\(573\) 0 0
\(574\) 3.78617 28.0489i 0.00659611 0.0488656i
\(575\) −119.561 −0.207932
\(576\) 0 0
\(577\) 562.686 0.975192 0.487596 0.873069i \(-0.337874\pi\)
0.487596 + 0.873069i \(0.337874\pi\)
\(578\) −560.698 75.6856i −0.970066 0.130944i
\(579\) 0 0
\(580\) −50.2232 + 182.643i −0.0865917 + 0.314902i
\(581\) 662.790i 1.14077i
\(582\) 0 0
\(583\) −37.0625 −0.0635720
\(584\) −80.2293 34.1591i −0.137379 0.0584916i
\(585\) 0 0
\(586\) −903.252 121.925i −1.54139 0.208063i
\(587\) 55.1680 0.0939830 0.0469915 0.998895i \(-0.485037\pi\)
0.0469915 + 0.998895i \(0.485037\pi\)
\(588\) 0 0
\(589\) −35.9478 67.5180i −0.0610320 0.114632i
\(590\) −519.044 70.0630i −0.879736 0.118751i
\(591\) 0 0
\(592\) 269.990 453.807i 0.456065 0.766565i
\(593\) 1053.15i 1.77598i 0.459865 + 0.887989i \(0.347898\pi\)
−0.459865 + 0.887989i \(0.652102\pi\)
\(594\) 0 0
\(595\) 109.221i 0.183565i
\(596\) −209.778 + 762.885i −0.351976 + 1.28001i
\(597\) 0 0
\(598\) −112.021 + 829.881i −0.187327 + 1.38776i
\(599\) 121.364i 0.202611i −0.994855 0.101306i \(-0.967698\pi\)
0.994855 0.101306i \(-0.0323020\pi\)
\(600\) 0 0
\(601\) 457.914i 0.761921i 0.924591 + 0.380960i \(0.124407\pi\)
−0.924591 + 0.380960i \(0.875593\pi\)
\(602\) −498.539 67.2951i −0.828138 0.111786i
\(603\) 0 0
\(604\) 672.066 + 184.805i 1.11269 + 0.305968i
\(605\) 529.592i 0.875358i
\(606\) 0 0
\(607\) 600.614 0.989479 0.494739 0.869041i \(-0.335264\pi\)
0.494739 + 0.869041i \(0.335264\pi\)
\(608\) 109.821 597.999i 0.180627 0.983552i
\(609\) 0 0
\(610\) 115.386 854.805i 0.189157 1.40132i
\(611\) 88.6387i 0.145072i
\(612\) 0 0
\(613\) −858.385 −1.40030 −0.700151 0.713995i \(-0.746884\pi\)
−0.700151 + 0.713995i \(0.746884\pi\)
\(614\) −859.866 116.069i −1.40043 0.189037i
\(615\) 0 0
\(616\) 68.4705 160.816i 0.111153 0.261066i
\(617\) 176.653i 0.286310i −0.989700 0.143155i \(-0.954275\pi\)
0.989700 0.143155i \(-0.0457247\pi\)
\(618\) 0 0
\(619\) 837.153i 1.35243i 0.736705 + 0.676214i \(0.236381\pi\)
−0.736705 + 0.676214i \(0.763619\pi\)
\(620\) 19.5103 70.9516i 0.0314682 0.114438i
\(621\) 0 0
\(622\) −124.294 16.7778i −0.199830 0.0269739i
\(623\) 67.7428i 0.108737i
\(624\) 0 0
\(625\) −505.047 −0.808075
\(626\) 441.296 + 59.5682i 0.704946 + 0.0951569i
\(627\) 0 0
\(628\) 926.197 + 254.685i 1.47484 + 0.405550i
\(629\) 81.5676 0.129678
\(630\) 0 0
\(631\) 594.388i 0.941978i −0.882139 0.470989i \(-0.843897\pi\)
0.882139 0.470989i \(-0.156103\pi\)
\(632\) 398.128 + 169.510i 0.629950 + 0.268212i
\(633\) 0 0
\(634\) −549.823 74.2176i −0.867228 0.117063i
\(635\) 836.960i 1.31805i
\(636\) 0 0
\(637\) 642.361i 1.00842i
\(638\) −46.4040 6.26382i −0.0727335 0.00981791i
\(639\) 0 0
\(640\) 472.070 345.338i 0.737610 0.539590i
\(641\) 854.404 1.33292 0.666462 0.745539i \(-0.267808\pi\)
0.666462 + 0.745539i \(0.267808\pi\)
\(642\) 0 0
\(643\) 619.587i 0.963587i 0.876285 + 0.481794i \(0.160014\pi\)
−0.876285 + 0.481794i \(0.839986\pi\)
\(644\) 297.688 1082.58i 0.462249 1.68103i
\(645\) 0 0
\(646\) 88.0593 32.6512i 0.136315 0.0505436i
\(647\) 154.357 0.238573 0.119287 0.992860i \(-0.461939\pi\)
0.119287 + 0.992860i \(0.461939\pi\)
\(648\) 0 0
\(649\) 129.470i 0.199492i
\(650\) 15.8991 117.784i 0.0244601 0.181206i
\(651\) 0 0
\(652\) 79.6495 289.656i 0.122162 0.444258i
\(653\) 707.136i 1.08290i 0.840732 + 0.541452i \(0.182125\pi\)
−0.840732 + 0.541452i \(0.817875\pi\)
\(654\) 0 0
\(655\) 538.081i 0.821497i
\(656\) 20.1212 + 11.9710i 0.0306725 + 0.0182485i
\(657\) 0 0
\(658\) 15.8979 117.775i 0.0241609 0.178990i
\(659\) 260.219i 0.394870i −0.980316 0.197435i \(-0.936739\pi\)
0.980316 0.197435i \(-0.0632611\pi\)
\(660\) 0 0
\(661\) 386.207i 0.584277i 0.956376 + 0.292139i \(0.0943669\pi\)
−0.956376 + 0.292139i \(0.905633\pi\)
\(662\) 954.908 + 128.898i 1.44246 + 0.194710i
\(663\) 0 0
\(664\) 504.451 + 214.779i 0.759716 + 0.323463i
\(665\) −394.599 741.145i −0.593382 1.11450i
\(666\) 0 0
\(667\) −300.786 −0.450954
\(668\) −251.895 + 916.049i −0.377088 + 1.37133i
\(669\) 0 0
\(670\) −147.032 + 1089.25i −0.219451 + 1.62574i
\(671\) 213.222 0.317768
\(672\) 0 0
\(673\) 923.068i 1.37157i 0.727804 + 0.685786i \(0.240541\pi\)
−0.727804 + 0.685786i \(0.759459\pi\)
\(674\) 52.7718 390.947i 0.0782965 0.580040i
\(675\) 0 0
\(676\) −150.848 41.4802i −0.223148 0.0613613i
\(677\) 223.855 0.330658 0.165329 0.986238i \(-0.447131\pi\)
0.165329 + 0.986238i \(0.447131\pi\)
\(678\) 0 0
\(679\) 280.852 0.413626
\(680\) 83.1284 + 35.3934i 0.122248 + 0.0520492i
\(681\) 0 0
\(682\) 18.0266 + 2.43332i 0.0264320 + 0.00356791i
\(683\) 47.7204i 0.0698688i 0.999390 + 0.0349344i \(0.0111222\pi\)
−0.999390 + 0.0349344i \(0.988878\pi\)
\(684\) 0 0
\(685\) 92.3487 0.134816
\(686\) 11.5714 85.7241i 0.0168680 0.124962i
\(687\) 0 0
\(688\) 212.772 357.632i 0.309261 0.519815i
\(689\) 236.666i 0.343492i
\(690\) 0 0
\(691\) 725.953i 1.05058i −0.850922 0.525292i \(-0.823956\pi\)
0.850922 0.525292i \(-0.176044\pi\)
\(692\) −599.102 164.741i −0.865755 0.238065i
\(693\) 0 0
\(694\) −126.341 17.0541i −0.182048 0.0245737i
\(695\) 552.985 0.795661
\(696\) 0 0
\(697\) 3.61659i 0.00518880i
\(698\) −247.722 33.4387i −0.354903 0.0479065i
\(699\) 0 0
\(700\) −42.2505 + 153.650i −0.0603579 + 0.219500i
\(701\) 834.855i 1.19095i −0.803374 0.595474i \(-0.796964\pi\)
0.803374 0.595474i \(-0.203036\pi\)
\(702\) 0 0
\(703\) 553.496 294.692i 0.787335 0.419192i
\(704\) 100.210 + 104.226i 0.142344 + 0.148049i
\(705\) 0 0
\(706\) 98.2064 727.538i 0.139103 1.03051i
\(707\) 328.430 0.464540
\(708\) 0 0
\(709\) 301.789 0.425654 0.212827 0.977090i \(-0.431733\pi\)
0.212827 + 0.977090i \(0.431733\pi\)
\(710\) 924.455 + 124.787i 1.30205 + 0.175757i
\(711\) 0 0
\(712\) −51.5593 21.9523i −0.0724147 0.0308319i
\(713\) 116.847 0.163881
\(714\) 0 0
\(715\) −148.925 −0.208286
\(716\) −365.081 + 1327.67i −0.509890 + 1.85428i
\(717\) 0 0
\(718\) −109.262 14.7487i −0.152176 0.0205414i
\(719\) 607.670 0.845159 0.422580 0.906326i \(-0.361125\pi\)
0.422580 + 0.906326i \(0.361125\pi\)
\(720\) 0 0
\(721\) 1404.18i 1.94755i
\(722\) 479.583 539.707i 0.664243 0.747517i
\(723\) 0 0
\(724\) 274.021 996.515i 0.378483 1.37640i
\(725\) 42.6903 0.0588832
\(726\) 0 0
\(727\) 1210.47i 1.66502i −0.554011 0.832510i \(-0.686903\pi\)
0.554011 0.832510i \(-0.313097\pi\)
\(728\) 1026.91 + 437.226i 1.41059 + 0.600585i
\(729\) 0 0
\(730\) 13.3255 98.7189i 0.0182542 0.135231i
\(731\) 64.2812 0.0879359
\(732\) 0 0
\(733\) 611.968 0.834881 0.417441 0.908704i \(-0.362927\pi\)
0.417441 + 0.908704i \(0.362927\pi\)
\(734\) 88.4617 655.346i 0.120520 0.892842i
\(735\) 0 0
\(736\) 727.490 + 577.386i 0.988437 + 0.784491i
\(737\) −271.702 −0.368659
\(738\) 0 0
\(739\) 563.737i 0.762837i −0.924402 0.381419i \(-0.875436\pi\)
0.924402 0.381419i \(-0.124564\pi\)
\(740\) 581.644 + 159.940i 0.786006 + 0.216136i
\(741\) 0 0
\(742\) −42.4474 + 314.461i −0.0572068 + 0.423802i
\(743\) 475.145i 0.639496i 0.947503 + 0.319748i \(0.103598\pi\)
−0.947503 + 0.319748i \(0.896402\pi\)
\(744\) 0 0
\(745\) −903.856 −1.21323
\(746\) 153.935 1140.39i 0.206348 1.52867i
\(747\) 0 0
\(748\) −5.92165 + 21.5349i −0.00791664 + 0.0287899i
\(749\) −206.821 −0.276129
\(750\) 0 0
\(751\) −690.118 −0.918932 −0.459466 0.888195i \(-0.651959\pi\)
−0.459466 + 0.888195i \(0.651959\pi\)
\(752\) 84.4874 + 50.2654i 0.112350 + 0.0668423i
\(753\) 0 0
\(754\) 39.9983 296.317i 0.0530481 0.392994i
\(755\) 796.255i 1.05464i
\(756\) 0 0
\(757\) −565.079 −0.746471 −0.373236 0.927737i \(-0.621752\pi\)
−0.373236 + 0.927737i \(0.621752\pi\)
\(758\) −870.384 117.489i −1.14826 0.154998i
\(759\) 0 0
\(760\) 691.959 60.1602i 0.910472 0.0791582i
\(761\) 96.6715i 0.127032i 0.997981 + 0.0635161i \(0.0202314\pi\)
−0.997981 + 0.0635161i \(0.979769\pi\)
\(762\) 0 0
\(763\) −1768.63 −2.31800
\(764\) 1301.14 + 357.788i 1.70307 + 0.468309i
\(765\) 0 0
\(766\) 38.8219 287.603i 0.0506814 0.375460i
\(767\) 826.746 1.07790
\(768\) 0 0
\(769\) −711.471 −0.925189 −0.462595 0.886570i \(-0.653081\pi\)
−0.462595 + 0.886570i \(0.653081\pi\)
\(770\) 197.878 + 26.7105i 0.256984 + 0.0346890i
\(771\) 0 0
\(772\) −1.75824 + 6.39407i −0.00227751 + 0.00828248i
\(773\) 325.033 0.420482 0.210241 0.977650i \(-0.432575\pi\)
0.210241 + 0.977650i \(0.432575\pi\)
\(774\) 0 0
\(775\) −16.5840 −0.0213987
\(776\) −91.0111 + 213.757i −0.117282 + 0.275461i
\(777\) 0 0
\(778\) −153.568 + 1137.67i −0.197389 + 1.46230i
\(779\) 13.0662 + 24.5413i 0.0167731 + 0.0315035i
\(780\) 0 0
\(781\) 230.596i 0.295257i
\(782\) −19.1918 + 142.178i −0.0245420 + 0.181813i
\(783\) 0 0
\(784\) −612.277 364.272i −0.780966 0.464632i
\(785\) 1097.35i 1.39789i
\(786\) 0 0
\(787\) 556.671 0.707333 0.353666 0.935372i \(-0.384935\pi\)
0.353666 + 0.935372i \(0.384935\pi\)
\(788\) −58.7973 + 213.824i −0.0746158 + 0.271350i
\(789\) 0 0
\(790\) −66.1263 + 489.880i −0.0837042 + 0.620102i
\(791\) 1808.16i 2.28592i
\(792\) 0 0
\(793\) 1361.55i 1.71697i
\(794\) 936.819 + 126.456i 1.17987 + 0.159265i
\(795\)