Properties

Label 380.2.i.c.201.4
Level $380$
Weight $2$
Character 380.201
Analytic conductor $3.034$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(121,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.4
Root \(-1.26041 + 2.18309i\) of defining polynomial
Character \(\chi\) \(=\) 380.201
Dual form 380.2.i.c.121.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26041 - 2.18309i) q^{3} +(-0.500000 + 0.866025i) q^{5} +2.72743 q^{7} +(-1.67727 - 2.90511i) q^{9} +O(q^{10})\) \(q+(1.26041 - 2.18309i) q^{3} +(-0.500000 + 0.866025i) q^{5} +2.72743 q^{7} +(-1.67727 - 2.90511i) q^{9} +3.31421 q^{11} +(-1.62412 - 2.81306i) q^{13} +(1.26041 + 2.18309i) q^{15} +(1.17727 - 2.03909i) q^{17} +(-3.11494 + 3.04912i) q^{19} +(3.43768 - 5.95423i) q^{21} +(-1.07396 - 1.86016i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.893714 q^{27} +(1.96702 + 3.40697i) q^{29} -10.1896 q^{31} +(4.17727 - 7.23524i) q^{33} +(-1.36371 + 2.36202i) q^{35} -3.68579 q^{37} -8.18825 q^{39} +(0.363714 - 0.629971i) q^{41} +(1.18645 - 2.05499i) q^{43} +3.35453 q^{45} +(5.51164 + 9.54644i) q^{47} +0.438860 q^{49} +(-2.96768 - 5.14017i) q^{51} +(4.49148 + 7.77947i) q^{53} +(-1.65711 + 2.87019i) q^{55} +(2.73041 + 10.6434i) q^{57} +(5.48784 - 9.50521i) q^{59} +(4.22743 + 7.32212i) q^{61} +(-4.57462 - 7.92348i) q^{63} +3.24825 q^{65} +(4.87535 + 8.44436i) q^{67} -5.41453 q^{69} +(-3.45850 + 5.99029i) q^{71} +(1.24025 - 2.14818i) q^{73} -2.52082 q^{75} +9.03927 q^{77} +(-5.99948 + 10.3914i) q^{79} +(3.90535 - 6.76427i) q^{81} +4.68711 q^{83} +(1.17727 + 2.03909i) q^{85} +9.91699 q^{87} +(-4.27205 - 7.39941i) q^{89} +(-4.42968 - 7.67243i) q^{91} +(-12.8430 + 22.2448i) q^{93} +(-1.08314 - 4.22218i) q^{95} +(-3.61494 + 6.26127i) q^{97} +(-5.55882 - 9.62816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 4 q^{5} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} - 4 q^{5} - 5 q^{9} + 4 q^{11} + 9 q^{13} - q^{15} + q^{17} + 3 q^{19} + 8 q^{21} - 4 q^{25} + 20 q^{27} + 5 q^{29} - 20 q^{31} + 25 q^{33} - 52 q^{37} - 54 q^{39} - 8 q^{41} + 7 q^{43} + 10 q^{45} + 16 q^{47} + 20 q^{49} + 12 q^{51} + 5 q^{53} - 2 q^{55} + 27 q^{57} + 11 q^{59} + 12 q^{61} - 3 q^{63} - 18 q^{65} + 6 q^{69} + 14 q^{71} - 4 q^{73} + 2 q^{75} - 44 q^{77} + 13 q^{79} - 24 q^{81} + 10 q^{83} + q^{85} - 4 q^{87} + 5 q^{89} - 46 q^{91} - 28 q^{93} - 6 q^{95} - q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.26041 2.18309i 0.727698 1.26041i −0.230156 0.973154i \(-0.573924\pi\)
0.957854 0.287256i \(-0.0927431\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.72743 1.03087 0.515435 0.856928i \(-0.327630\pi\)
0.515435 + 0.856928i \(0.327630\pi\)
\(8\) 0 0
\(9\) −1.67727 2.90511i −0.559089 0.968370i
\(10\) 0 0
\(11\) 3.31421 0.999273 0.499636 0.866235i \(-0.333467\pi\)
0.499636 + 0.866235i \(0.333467\pi\)
\(12\) 0 0
\(13\) −1.62412 2.81306i −0.450451 0.780204i 0.547963 0.836502i \(-0.315403\pi\)
−0.998414 + 0.0562987i \(0.982070\pi\)
\(14\) 0 0
\(15\) 1.26041 + 2.18309i 0.325436 + 0.563672i
\(16\) 0 0
\(17\) 1.17727 2.03909i 0.285529 0.494551i −0.687208 0.726460i \(-0.741164\pi\)
0.972737 + 0.231910i \(0.0744974\pi\)
\(18\) 0 0
\(19\) −3.11494 + 3.04912i −0.714617 + 0.699516i
\(20\) 0 0
\(21\) 3.43768 5.95423i 0.750163 1.29932i
\(22\) 0 0
\(23\) −1.07396 1.86016i −0.223937 0.387870i 0.732063 0.681237i \(-0.238558\pi\)
−0.956000 + 0.293367i \(0.905224\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −0.893714 −0.171995
\(28\) 0 0
\(29\) 1.96702 + 3.40697i 0.365266 + 0.632659i 0.988819 0.149122i \(-0.0476447\pi\)
−0.623553 + 0.781781i \(0.714311\pi\)
\(30\) 0 0
\(31\) −10.1896 −1.83010 −0.915050 0.403340i \(-0.867849\pi\)
−0.915050 + 0.403340i \(0.867849\pi\)
\(32\) 0 0
\(33\) 4.17727 7.23524i 0.727169 1.25949i
\(34\) 0 0
\(35\) −1.36371 + 2.36202i −0.230510 + 0.399254i
\(36\) 0 0
\(37\) −3.68579 −0.605940 −0.302970 0.953000i \(-0.597978\pi\)
−0.302970 + 0.953000i \(0.597978\pi\)
\(38\) 0 0
\(39\) −8.18825 −1.31117
\(40\) 0 0
\(41\) 0.363714 0.629971i 0.0568025 0.0983849i −0.836226 0.548385i \(-0.815243\pi\)
0.893028 + 0.450000i \(0.148576\pi\)
\(42\) 0 0
\(43\) 1.18645 2.05499i 0.180931 0.313383i −0.761267 0.648439i \(-0.775422\pi\)
0.942198 + 0.335057i \(0.108755\pi\)
\(44\) 0 0
\(45\) 3.35453 0.500064
\(46\) 0 0
\(47\) 5.51164 + 9.54644i 0.803955 + 1.39249i 0.916994 + 0.398901i \(0.130608\pi\)
−0.113039 + 0.993591i \(0.536058\pi\)
\(48\) 0 0
\(49\) 0.438860 0.0626942
\(50\) 0 0
\(51\) −2.96768 5.14017i −0.415558 0.719767i
\(52\) 0 0
\(53\) 4.49148 + 7.77947i 0.616952 + 1.06859i 0.990039 + 0.140796i \(0.0449661\pi\)
−0.373087 + 0.927797i \(0.621701\pi\)
\(54\) 0 0
\(55\) −1.65711 + 2.87019i −0.223444 + 0.387017i
\(56\) 0 0
\(57\) 2.73041 + 10.6434i 0.361652 + 1.40975i
\(58\) 0 0
\(59\) 5.48784 9.50521i 0.714456 1.23747i −0.248714 0.968577i \(-0.580008\pi\)
0.963169 0.268896i \(-0.0866589\pi\)
\(60\) 0 0
\(61\) 4.22743 + 7.32212i 0.541267 + 0.937501i 0.998832 + 0.0483251i \(0.0153884\pi\)
−0.457565 + 0.889176i \(0.651278\pi\)
\(62\) 0 0
\(63\) −4.57462 7.92348i −0.576348 0.998264i
\(64\) 0 0
\(65\) 3.24825 0.402895
\(66\) 0 0
\(67\) 4.87535 + 8.44436i 0.595619 + 1.03164i 0.993459 + 0.114188i \(0.0364266\pi\)
−0.397840 + 0.917455i \(0.630240\pi\)
\(68\) 0 0
\(69\) −5.41453 −0.651833
\(70\) 0 0
\(71\) −3.45850 + 5.99029i −0.410448 + 0.710917i −0.994939 0.100484i \(-0.967961\pi\)
0.584491 + 0.811400i \(0.301294\pi\)
\(72\) 0 0
\(73\) 1.24025 2.14818i 0.145160 0.251425i −0.784272 0.620417i \(-0.786964\pi\)
0.929433 + 0.368992i \(0.120297\pi\)
\(74\) 0 0
\(75\) −2.52082 −0.291079
\(76\) 0 0
\(77\) 9.03927 1.03012
\(78\) 0 0
\(79\) −5.99948 + 10.3914i −0.674994 + 1.16912i 0.301477 + 0.953474i \(0.402520\pi\)
−0.976471 + 0.215650i \(0.930813\pi\)
\(80\) 0 0
\(81\) 3.90535 6.76427i 0.433928 0.751586i
\(82\) 0 0
\(83\) 4.68711 0.514477 0.257238 0.966348i \(-0.417187\pi\)
0.257238 + 0.966348i \(0.417187\pi\)
\(84\) 0 0
\(85\) 1.17727 + 2.03909i 0.127692 + 0.221170i
\(86\) 0 0
\(87\) 9.91699 1.06321
\(88\) 0 0
\(89\) −4.27205 7.39941i −0.452836 0.784336i 0.545725 0.837965i \(-0.316254\pi\)
−0.998561 + 0.0536291i \(0.982921\pi\)
\(90\) 0 0
\(91\) −4.42968 7.67243i −0.464357 0.804289i
\(92\) 0 0
\(93\) −12.8430 + 22.2448i −1.33176 + 2.30668i
\(94\) 0 0
\(95\) −1.08314 4.22218i −0.111128 0.433186i
\(96\) 0 0
\(97\) −3.61494 + 6.26127i −0.367042 + 0.635735i −0.989102 0.147235i \(-0.952963\pi\)
0.622060 + 0.782970i \(0.286296\pi\)
\(98\) 0 0
\(99\) −5.55882 9.62816i −0.558682 0.967666i
\(100\) 0 0
\(101\) 2.88818 + 5.00247i 0.287384 + 0.497764i 0.973185 0.230026i \(-0.0738810\pi\)
−0.685800 + 0.727790i \(0.740548\pi\)
\(102\) 0 0
\(103\) −15.0576 −1.48367 −0.741836 0.670581i \(-0.766045\pi\)
−0.741836 + 0.670581i \(0.766045\pi\)
\(104\) 0 0
\(105\) 3.43768 + 5.95423i 0.335483 + 0.581073i
\(106\) 0 0
\(107\) −15.1896 −1.46843 −0.734215 0.678917i \(-0.762450\pi\)
−0.734215 + 0.678917i \(0.762450\pi\)
\(108\) 0 0
\(109\) 6.31057 10.9302i 0.604443 1.04693i −0.387696 0.921787i \(-0.626729\pi\)
0.992139 0.125139i \(-0.0399376\pi\)
\(110\) 0 0
\(111\) −4.64560 + 8.04642i −0.440941 + 0.763732i
\(112\) 0 0
\(113\) −6.10761 −0.574555 −0.287278 0.957847i \(-0.592750\pi\)
−0.287278 + 0.957847i \(0.592750\pi\)
\(114\) 0 0
\(115\) 2.14793 0.200295
\(116\) 0 0
\(117\) −5.44818 + 9.43652i −0.503684 + 0.872406i
\(118\) 0 0
\(119\) 3.21091 5.56146i 0.294344 0.509818i
\(120\) 0 0
\(121\) −0.0159950 −0.00145409
\(122\) 0 0
\(123\) −0.916857 1.58804i −0.0826702 0.143189i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 4.56114 + 7.90013i 0.404736 + 0.701023i 0.994291 0.106705i \(-0.0340302\pi\)
−0.589555 + 0.807728i \(0.700697\pi\)
\(128\) 0 0
\(129\) −2.99082 5.18025i −0.263327 0.456096i
\(130\) 0 0
\(131\) −11.1328 + 19.2825i −0.972676 + 1.68472i −0.285274 + 0.958446i \(0.592085\pi\)
−0.687402 + 0.726277i \(0.741249\pi\)
\(132\) 0 0
\(133\) −8.49578 + 8.31625i −0.736678 + 0.721110i
\(134\) 0 0
\(135\) 0.446857 0.773979i 0.0384593 0.0666135i
\(136\) 0 0
\(137\) 3.81355 + 6.60527i 0.325814 + 0.564326i 0.981677 0.190554i \(-0.0610284\pi\)
−0.655863 + 0.754880i \(0.727695\pi\)
\(138\) 0 0
\(139\) −8.45916 14.6517i −0.717496 1.24274i −0.961989 0.273089i \(-0.911955\pi\)
0.244493 0.969651i \(-0.421379\pi\)
\(140\) 0 0
\(141\) 27.7877 2.34015
\(142\) 0 0
\(143\) −5.38269 9.32309i −0.450123 0.779636i
\(144\) 0 0
\(145\) −3.93403 −0.326704
\(146\) 0 0
\(147\) 0.553143 0.958072i 0.0456225 0.0790204i
\(148\) 0 0
\(149\) 6.19809 10.7354i 0.507767 0.879478i −0.492193 0.870486i \(-0.663804\pi\)
0.999960 0.00899193i \(-0.00286226\pi\)
\(150\) 0 0
\(151\) −14.4549 −1.17632 −0.588160 0.808745i \(-0.700147\pi\)
−0.588160 + 0.808745i \(0.700147\pi\)
\(152\) 0 0
\(153\) −7.89836 −0.638544
\(154\) 0 0
\(155\) 5.09478 8.82442i 0.409223 0.708795i
\(156\) 0 0
\(157\) 9.10642 15.7728i 0.726772 1.25881i −0.231469 0.972842i \(-0.574353\pi\)
0.958241 0.285963i \(-0.0923135\pi\)
\(158\) 0 0
\(159\) 22.6444 1.79582
\(160\) 0 0
\(161\) −2.92916 5.07345i −0.230850 0.399844i
\(162\) 0 0
\(163\) 19.2642 1.50889 0.754446 0.656362i \(-0.227906\pi\)
0.754446 + 0.656362i \(0.227906\pi\)
\(164\) 0 0
\(165\) 4.17727 + 7.23524i 0.325200 + 0.563263i
\(166\) 0 0
\(167\) −2.84289 4.92404i −0.219990 0.381033i 0.734815 0.678268i \(-0.237269\pi\)
−0.954805 + 0.297234i \(0.903936\pi\)
\(168\) 0 0
\(169\) 1.22445 2.12080i 0.0941881 0.163139i
\(170\) 0 0
\(171\) 14.0826 + 3.93507i 1.07692 + 0.300922i
\(172\) 0 0
\(173\) 4.57760 7.92864i 0.348029 0.602804i −0.637870 0.770144i \(-0.720184\pi\)
0.985899 + 0.167340i \(0.0535178\pi\)
\(174\) 0 0
\(175\) −1.36371 2.36202i −0.103087 0.178552i
\(176\) 0 0
\(177\) −13.8338 23.9609i −1.03982 1.80101i
\(178\) 0 0
\(179\) 12.1810 0.910448 0.455224 0.890377i \(-0.349559\pi\)
0.455224 + 0.890377i \(0.349559\pi\)
\(180\) 0 0
\(181\) −7.70608 13.3473i −0.572789 0.992099i −0.996278 0.0861980i \(-0.972528\pi\)
0.423489 0.905901i \(-0.360805\pi\)
\(182\) 0 0
\(183\) 21.3132 1.57551
\(184\) 0 0
\(185\) 1.84289 3.19199i 0.135492 0.234679i
\(186\) 0 0
\(187\) 3.90171 6.75796i 0.285321 0.494191i
\(188\) 0 0
\(189\) −2.43754 −0.177305
\(190\) 0 0
\(191\) −16.2482 −1.17568 −0.587841 0.808977i \(-0.700022\pi\)
−0.587841 + 0.808977i \(0.700022\pi\)
\(192\) 0 0
\(193\) −0.425514 + 0.737011i −0.0306292 + 0.0530512i −0.880934 0.473240i \(-0.843084\pi\)
0.850305 + 0.526291i \(0.176418\pi\)
\(194\) 0 0
\(195\) 4.09412 7.09123i 0.293186 0.507813i
\(196\) 0 0
\(197\) 19.9843 1.42382 0.711910 0.702270i \(-0.247830\pi\)
0.711910 + 0.702270i \(0.247830\pi\)
\(198\) 0 0
\(199\) 3.22861 + 5.59212i 0.228870 + 0.396415i 0.957474 0.288521i \(-0.0931636\pi\)
−0.728603 + 0.684936i \(0.759830\pi\)
\(200\) 0 0
\(201\) 24.5798 1.73372
\(202\) 0 0
\(203\) 5.36490 + 9.29227i 0.376542 + 0.652190i
\(204\) 0 0
\(205\) 0.363714 + 0.629971i 0.0254029 + 0.0439990i
\(206\) 0 0
\(207\) −3.60264 + 6.23996i −0.250401 + 0.433707i
\(208\) 0 0
\(209\) −10.3236 + 10.1054i −0.714097 + 0.699007i
\(210\) 0 0
\(211\) −5.27205 + 9.13146i −0.362943 + 0.628635i −0.988444 0.151588i \(-0.951561\pi\)
0.625501 + 0.780223i \(0.284895\pi\)
\(212\) 0 0
\(213\) 8.71825 + 15.1004i 0.597364 + 1.03467i
\(214\) 0 0
\(215\) 1.18645 + 2.05499i 0.0809150 + 0.140149i
\(216\) 0 0
\(217\) −27.7913 −1.88660
\(218\) 0 0
\(219\) −3.12645 5.41516i −0.211266 0.365923i
\(220\) 0 0
\(221\) −7.64811 −0.514467
\(222\) 0 0
\(223\) −4.86319 + 8.42329i −0.325663 + 0.564065i −0.981646 0.190710i \(-0.938921\pi\)
0.655983 + 0.754776i \(0.272254\pi\)
\(224\) 0 0
\(225\) −1.67727 + 2.90511i −0.111818 + 0.193674i
\(226\) 0 0
\(227\) 22.5798 1.49867 0.749336 0.662190i \(-0.230373\pi\)
0.749336 + 0.662190i \(0.230373\pi\)
\(228\) 0 0
\(229\) −16.2239 −1.07211 −0.536053 0.844184i \(-0.680085\pi\)
−0.536053 + 0.844184i \(0.680085\pi\)
\(230\) 0 0
\(231\) 11.3932 19.7336i 0.749617 1.29837i
\(232\) 0 0
\(233\) 9.33139 16.1624i 0.611320 1.05884i −0.379699 0.925110i \(-0.623972\pi\)
0.991018 0.133727i \(-0.0426944\pi\)
\(234\) 0 0
\(235\) −11.0233 −0.719079
\(236\) 0 0
\(237\) 15.1236 + 26.1948i 0.982383 + 1.70154i
\(238\) 0 0
\(239\) 0.602780 0.0389906 0.0194953 0.999810i \(-0.493794\pi\)
0.0194953 + 0.999810i \(0.493794\pi\)
\(240\) 0 0
\(241\) −10.9408 18.9500i −0.704759 1.22068i −0.966779 0.255615i \(-0.917722\pi\)
0.262020 0.965062i \(-0.415611\pi\)
\(242\) 0 0
\(243\) −11.1853 19.3734i −0.717535 1.24281i
\(244\) 0 0
\(245\) −0.219430 + 0.380064i −0.0140189 + 0.0242814i
\(246\) 0 0
\(247\) 13.6364 + 3.81039i 0.867665 + 0.242449i
\(248\) 0 0
\(249\) 5.90768 10.2324i 0.374384 0.648452i
\(250\) 0 0
\(251\) −4.13629 7.16426i −0.261080 0.452204i 0.705449 0.708761i \(-0.250745\pi\)
−0.966529 + 0.256557i \(0.917412\pi\)
\(252\) 0 0
\(253\) −3.55934 6.16496i −0.223774 0.387588i
\(254\) 0 0
\(255\) 5.93535 0.371686
\(256\) 0 0
\(257\) −7.09544 12.2897i −0.442602 0.766608i 0.555280 0.831663i \(-0.312611\pi\)
−0.997882 + 0.0650550i \(0.979278\pi\)
\(258\) 0 0
\(259\) −10.0527 −0.624645
\(260\) 0 0
\(261\) 6.59842 11.4288i 0.408432 0.707425i
\(262\) 0 0
\(263\) 9.27153 16.0588i 0.571707 0.990225i −0.424684 0.905342i \(-0.639615\pi\)
0.996391 0.0848836i \(-0.0270518\pi\)
\(264\) 0 0
\(265\) −8.98296 −0.551819
\(266\) 0 0
\(267\) −21.5381 −1.31811
\(268\) 0 0
\(269\) −3.33371 + 5.77416i −0.203260 + 0.352057i −0.949577 0.313534i \(-0.898487\pi\)
0.746317 + 0.665591i \(0.231820\pi\)
\(270\) 0 0
\(271\) −11.0331 + 19.1099i −0.670214 + 1.16085i 0.307629 + 0.951506i \(0.400464\pi\)
−0.977843 + 0.209339i \(0.932869\pi\)
\(272\) 0 0
\(273\) −22.3328 −1.35165
\(274\) 0 0
\(275\) −1.65711 2.87019i −0.0999273 0.173079i
\(276\) 0 0
\(277\) −24.4624 −1.46980 −0.734902 0.678173i \(-0.762772\pi\)
−0.734902 + 0.678173i \(0.762772\pi\)
\(278\) 0 0
\(279\) 17.0906 + 29.6018i 1.02319 + 1.77221i
\(280\) 0 0
\(281\) −9.33139 16.1624i −0.556664 0.964170i −0.997772 0.0667164i \(-0.978748\pi\)
0.441108 0.897454i \(-0.354586\pi\)
\(282\) 0 0
\(283\) −2.24811 + 3.89384i −0.133636 + 0.231465i −0.925076 0.379783i \(-0.875999\pi\)
0.791439 + 0.611248i \(0.209332\pi\)
\(284\) 0 0
\(285\) −10.5826 2.95707i −0.626860 0.175162i
\(286\) 0 0
\(287\) 0.992002 1.71820i 0.0585561 0.101422i
\(288\) 0 0
\(289\) 5.72809 + 9.92134i 0.336946 + 0.583608i
\(290\) 0 0
\(291\) 9.11262 + 15.7835i 0.534191 + 0.925246i
\(292\) 0 0
\(293\) 1.27021 0.0742063 0.0371031 0.999311i \(-0.488187\pi\)
0.0371031 + 0.999311i \(0.488187\pi\)
\(294\) 0 0
\(295\) 5.48784 + 9.50521i 0.319514 + 0.553415i
\(296\) 0 0
\(297\) −2.96196 −0.171870
\(298\) 0 0
\(299\) −3.48850 + 6.04225i −0.201745 + 0.349433i
\(300\) 0 0
\(301\) 3.23595 5.60483i 0.186517 0.323057i
\(302\) 0 0
\(303\) 14.5611 0.836516
\(304\) 0 0
\(305\) −8.45485 −0.484124
\(306\) 0 0
\(307\) 4.32638 7.49350i 0.246919 0.427677i −0.715750 0.698356i \(-0.753915\pi\)
0.962669 + 0.270680i \(0.0872484\pi\)
\(308\) 0 0
\(309\) −18.9788 + 32.8722i −1.07967 + 1.87004i
\(310\) 0 0
\(311\) 23.8497 1.35239 0.676196 0.736721i \(-0.263627\pi\)
0.676196 + 0.736721i \(0.263627\pi\)
\(312\) 0 0
\(313\) 0.388175 + 0.672340i 0.0219410 + 0.0380029i 0.876787 0.480878i \(-0.159682\pi\)
−0.854846 + 0.518881i \(0.826349\pi\)
\(314\) 0 0
\(315\) 9.14925 0.515502
\(316\) 0 0
\(317\) 6.92116 + 11.9878i 0.388731 + 0.673302i 0.992279 0.124025i \(-0.0395802\pi\)
−0.603548 + 0.797327i \(0.706247\pi\)
\(318\) 0 0
\(319\) 6.51911 + 11.2914i 0.365000 + 0.632199i
\(320\) 0 0
\(321\) −19.1451 + 33.1603i −1.06857 + 1.85082i
\(322\) 0 0
\(323\) 2.55030 + 9.94126i 0.141902 + 0.553147i
\(324\) 0 0
\(325\) −1.62412 + 2.81306i −0.0900902 + 0.156041i
\(326\) 0 0
\(327\) −15.9078 27.5531i −0.879704 1.52369i
\(328\) 0 0
\(329\) 15.0326 + 26.0372i 0.828774 + 1.43548i
\(330\) 0 0
\(331\) 28.6993 1.57746 0.788728 0.614742i \(-0.210740\pi\)
0.788728 + 0.614742i \(0.210740\pi\)
\(332\) 0 0
\(333\) 6.18205 + 10.7076i 0.338774 + 0.586774i
\(334\) 0 0
\(335\) −9.75071 −0.532738
\(336\) 0 0
\(337\) 17.6628 30.5928i 0.962153 1.66650i 0.245076 0.969504i \(-0.421187\pi\)
0.717077 0.696994i \(-0.245480\pi\)
\(338\) 0 0
\(339\) −7.69809 + 13.3335i −0.418103 + 0.724175i
\(340\) 0 0
\(341\) −33.7704 −1.82877
\(342\) 0 0
\(343\) −17.8950 −0.966241
\(344\) 0 0
\(345\) 2.70727 4.68912i 0.145754 0.252454i
\(346\) 0 0
\(347\) −13.0031 + 22.5221i −0.698044 + 1.20905i 0.271100 + 0.962551i \(0.412613\pi\)
−0.969144 + 0.246496i \(0.920721\pi\)
\(348\) 0 0
\(349\) 2.44757 0.131015 0.0655077 0.997852i \(-0.479133\pi\)
0.0655077 + 0.997852i \(0.479133\pi\)
\(350\) 0 0
\(351\) 1.45150 + 2.51408i 0.0774755 + 0.134191i
\(352\) 0 0
\(353\) −4.85103 −0.258194 −0.129097 0.991632i \(-0.541208\pi\)
−0.129097 + 0.991632i \(0.541208\pi\)
\(354\) 0 0
\(355\) −3.45850 5.99029i −0.183558 0.317932i
\(356\) 0 0
\(357\) −8.09412 14.0194i −0.428386 0.741987i
\(358\) 0 0
\(359\) 3.67376 6.36314i 0.193894 0.335834i −0.752644 0.658428i \(-0.771222\pi\)
0.946537 + 0.322594i \(0.104555\pi\)
\(360\) 0 0
\(361\) 0.405741 18.9957i 0.0213548 0.999772i
\(362\) 0 0
\(363\) −0.0201603 + 0.0349186i −0.00105814 + 0.00183275i
\(364\) 0 0
\(365\) 1.24025 + 2.14818i 0.0649176 + 0.112441i
\(366\) 0 0
\(367\) −6.51784 11.2892i −0.340228 0.589293i 0.644247 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(368\) 0 0
\(369\) −2.44018 −0.127031
\(370\) 0 0
\(371\) 12.2502 + 21.2179i 0.635998 + 1.10158i
\(372\) 0 0
\(373\) −28.5514 −1.47833 −0.739167 0.673522i \(-0.764781\pi\)
−0.739167 + 0.673522i \(0.764781\pi\)
\(374\) 0 0
\(375\) 1.26041 2.18309i 0.0650873 0.112734i
\(376\) 0 0
\(377\) 6.38936 11.0667i 0.329069 0.569964i
\(378\) 0 0
\(379\) 13.2128 0.678698 0.339349 0.940661i \(-0.389793\pi\)
0.339349 + 0.940661i \(0.389793\pi\)
\(380\) 0 0
\(381\) 22.9956 1.17810
\(382\) 0 0
\(383\) 18.8309 32.6160i 0.962212 1.66660i 0.245287 0.969450i \(-0.421118\pi\)
0.716925 0.697150i \(-0.245549\pi\)
\(384\) 0 0
\(385\) −4.51964 + 7.82824i −0.230342 + 0.398964i
\(386\) 0 0
\(387\) −7.95995 −0.404627
\(388\) 0 0
\(389\) 12.8223 + 22.2090i 0.650119 + 1.12604i 0.983094 + 0.183103i \(0.0586142\pi\)
−0.332975 + 0.942936i \(0.608052\pi\)
\(390\) 0 0
\(391\) −5.05736 −0.255762
\(392\) 0 0
\(393\) 28.0637 + 48.6078i 1.41563 + 2.45194i
\(394\) 0 0
\(395\) −5.99948 10.3914i −0.301866 0.522848i
\(396\) 0 0
\(397\) 16.6366 28.8154i 0.834965 1.44620i −0.0590940 0.998252i \(-0.518821\pi\)
0.894059 0.447949i \(-0.147845\pi\)
\(398\) 0 0
\(399\) 7.44699 + 29.0290i 0.372816 + 1.45327i
\(400\) 0 0
\(401\) −4.70674 + 8.15232i −0.235044 + 0.407107i −0.959285 0.282439i \(-0.908857\pi\)
0.724242 + 0.689546i \(0.242190\pi\)
\(402\) 0 0
\(403\) 16.5491 + 28.6639i 0.824370 + 1.42785i
\(404\) 0 0
\(405\) 3.90535 + 6.76427i 0.194059 + 0.336119i
\(406\) 0 0
\(407\) −12.2155 −0.605499
\(408\) 0 0
\(409\) 1.25545 + 2.17450i 0.0620779 + 0.107522i 0.895394 0.445275i \(-0.146894\pi\)
−0.833316 + 0.552797i \(0.813561\pi\)
\(410\) 0 0
\(411\) 19.2266 0.948376
\(412\) 0 0
\(413\) 14.9677 25.9248i 0.736511 1.27567i
\(414\) 0 0
\(415\) −2.34355 + 4.05915i −0.115041 + 0.199256i
\(416\) 0 0
\(417\) −42.6480 −2.08848
\(418\) 0 0
\(419\) −39.5638 −1.93282 −0.966409 0.257011i \(-0.917262\pi\)
−0.966409 + 0.257011i \(0.917262\pi\)
\(420\) 0 0
\(421\) 7.07892 12.2611i 0.345006 0.597567i −0.640349 0.768084i \(-0.721210\pi\)
0.985355 + 0.170517i \(0.0545437\pi\)
\(422\) 0 0
\(423\) 18.4890 32.0238i 0.898965 1.55705i
\(424\) 0 0
\(425\) −2.35453 −0.114212
\(426\) 0 0
\(427\) 11.5300 + 19.9705i 0.557976 + 0.966442i
\(428\) 0 0
\(429\) −27.1376 −1.31022
\(430\) 0 0
\(431\) 3.26287 + 5.65145i 0.157167 + 0.272221i 0.933846 0.357676i \(-0.116431\pi\)
−0.776679 + 0.629897i \(0.783097\pi\)
\(432\) 0 0
\(433\) 4.30073 + 7.44908i 0.206680 + 0.357980i 0.950667 0.310214i \(-0.100401\pi\)
−0.743987 + 0.668194i \(0.767067\pi\)
\(434\) 0 0
\(435\) −4.95850 + 8.58837i −0.237742 + 0.411781i
\(436\) 0 0
\(437\) 9.01718 + 2.51965i 0.431350 + 0.120531i
\(438\) 0 0
\(439\) 5.77939 10.0102i 0.275835 0.477760i −0.694510 0.719483i \(-0.744379\pi\)
0.970345 + 0.241722i \(0.0777123\pi\)
\(440\) 0 0
\(441\) −0.736084 1.27494i −0.0350516 0.0607112i
\(442\) 0 0
\(443\) 5.69629 + 9.86626i 0.270639 + 0.468760i 0.969026 0.246960i \(-0.0794318\pi\)
−0.698387 + 0.715721i \(0.746098\pi\)
\(444\) 0 0
\(445\) 8.54410 0.405029
\(446\) 0 0
\(447\) −15.6243 27.0620i −0.739002 1.27999i
\(448\) 0 0
\(449\) 17.2252 0.812909 0.406455 0.913671i \(-0.366765\pi\)
0.406455 + 0.913671i \(0.366765\pi\)
\(450\) 0 0
\(451\) 1.20542 2.08786i 0.0567612 0.0983133i
\(452\) 0 0
\(453\) −18.2190 + 31.5563i −0.856005 + 1.48264i
\(454\) 0 0
\(455\) 8.85936 0.415333
\(456\) 0 0
\(457\) −26.1885 −1.22505 −0.612524 0.790452i \(-0.709846\pi\)
−0.612524 + 0.790452i \(0.709846\pi\)
\(458\) 0 0
\(459\) −1.05214 + 1.82236i −0.0491097 + 0.0850605i
\(460\) 0 0
\(461\) −20.2166 + 35.0162i −0.941580 + 1.63086i −0.179122 + 0.983827i \(0.557326\pi\)
−0.762458 + 0.647038i \(0.776008\pi\)
\(462\) 0 0
\(463\) 9.48542 0.440825 0.220412 0.975407i \(-0.429260\pi\)
0.220412 + 0.975407i \(0.429260\pi\)
\(464\) 0 0
\(465\) −12.8430 22.2448i −0.595581 1.03158i
\(466\) 0 0
\(467\) −39.2462 −1.81610 −0.908048 0.418867i \(-0.862427\pi\)
−0.908048 + 0.418867i \(0.862427\pi\)
\(468\) 0 0
\(469\) 13.2972 + 23.0314i 0.614006 + 1.06349i
\(470\) 0 0
\(471\) −22.9557 39.7604i −1.05774 1.83206i
\(472\) 0 0
\(473\) 3.93214 6.81066i 0.180800 0.313155i
\(474\) 0 0
\(475\) 4.19809 + 1.17306i 0.192621 + 0.0538237i
\(476\) 0 0
\(477\) 15.0668 26.0965i 0.689862 1.19488i
\(478\) 0 0
\(479\) −2.72677 4.72290i −0.124589 0.215795i 0.796983 0.604002i \(-0.206428\pi\)
−0.921572 + 0.388207i \(0.873095\pi\)
\(480\) 0 0
\(481\) 5.98617 + 10.3684i 0.272946 + 0.472756i
\(482\) 0 0
\(483\) −14.7677 −0.671956
\(484\) 0 0
\(485\) −3.61494 6.26127i −0.164146 0.284309i
\(486\) 0 0
\(487\) 25.0662 1.13586 0.567930 0.823077i \(-0.307744\pi\)
0.567930 + 0.823077i \(0.307744\pi\)
\(488\) 0 0
\(489\) 24.2808 42.0557i 1.09802 1.90182i
\(490\) 0 0
\(491\) −14.8412 + 25.7057i −0.669773 + 1.16008i 0.308194 + 0.951324i \(0.400275\pi\)
−0.977967 + 0.208758i \(0.933058\pi\)
\(492\) 0 0
\(493\) 9.26281 0.417176
\(494\) 0 0
\(495\) 11.1176 0.499701
\(496\) 0 0
\(497\) −9.43280 + 16.3381i −0.423119 + 0.732863i
\(498\) 0 0
\(499\) 6.85519 11.8735i 0.306881 0.531533i −0.670798 0.741640i \(-0.734048\pi\)
0.977678 + 0.210108i \(0.0673814\pi\)
\(500\) 0 0
\(501\) −14.3328 −0.640344
\(502\) 0 0
\(503\) −18.3253 31.7404i −0.817086 1.41523i −0.907820 0.419359i \(-0.862255\pi\)
0.0907343 0.995875i \(-0.471079\pi\)
\(504\) 0 0
\(505\) −5.77635 −0.257044
\(506\) 0 0
\(507\) −3.08661 5.34616i −0.137081 0.237431i
\(508\) 0 0
\(509\) 6.32519 + 10.9556i 0.280359 + 0.485596i 0.971473 0.237149i \(-0.0762131\pi\)
−0.691114 + 0.722746i \(0.742880\pi\)
\(510\) 0 0
\(511\) 3.38269 5.85899i 0.149641 0.259187i
\(512\) 0 0
\(513\) 2.78387 2.72504i 0.122911 0.120314i
\(514\) 0 0
\(515\) 7.52882 13.0403i 0.331759 0.574624i
\(516\) 0 0
\(517\) 18.2667 + 31.6389i 0.803371 + 1.39148i
\(518\) 0 0
\(519\) −11.5393 19.9867i −0.506520 0.877318i
\(520\) 0 0
\(521\) 16.3339 0.715601 0.357800 0.933798i \(-0.383527\pi\)
0.357800 + 0.933798i \(0.383527\pi\)
\(522\) 0 0
\(523\) 4.56734 + 7.91086i 0.199716 + 0.345918i 0.948436 0.316968i \(-0.102665\pi\)
−0.748720 + 0.662886i \(0.769331\pi\)
\(524\) 0 0
\(525\) −6.87535 −0.300065
\(526\) 0 0
\(527\) −11.9958 + 20.7774i −0.522547 + 0.905078i
\(528\) 0 0
\(529\) 9.19321 15.9231i 0.399705 0.692309i
\(530\) 0 0
\(531\) −36.8183 −1.59778
\(532\) 0 0
\(533\) −2.36286 −0.102347
\(534\) 0 0
\(535\) 7.59478 13.1545i 0.328351 0.568721i
\(536\) 0 0
\(537\) 15.3530 26.5922i 0.662531 1.14754i
\(538\) 0 0
\(539\) 1.45447 0.0626486
\(540\) 0 0
\(541\) 1.45954 + 2.52800i 0.0627507 + 0.108687i 0.895694 0.444671i \(-0.146679\pi\)
−0.832943 + 0.553358i \(0.813346\pi\)
\(542\) 0 0
\(543\) −38.8513 −1.66727
\(544\) 0 0
\(545\) 6.31057 + 10.9302i 0.270315 + 0.468200i
\(546\) 0 0
\(547\) 1.73973 + 3.01329i 0.0743853 + 0.128839i 0.900819 0.434195i \(-0.142967\pi\)
−0.826433 + 0.563034i \(0.809634\pi\)
\(548\) 0 0
\(549\) 14.1810 24.5623i 0.605232 1.04829i
\(550\) 0 0
\(551\) −16.5154 4.61486i −0.703580 0.196600i
\(552\) 0 0
\(553\) −16.3631 + 28.3418i −0.695831 + 1.20522i
\(554\) 0 0
\(555\) −4.64560 8.04642i −0.197195 0.341552i
\(556\) 0 0
\(557\) −7.96280 13.7920i −0.337395 0.584385i 0.646547 0.762874i \(-0.276212\pi\)
−0.983942 + 0.178489i \(0.942879\pi\)
\(558\) 0 0
\(559\) −7.70775 −0.326003
\(560\) 0 0
\(561\) −9.83551 17.0356i −0.415256 0.719244i
\(562\) 0 0
\(563\) 19.6274 0.827195 0.413598 0.910460i \(-0.364272\pi\)
0.413598 + 0.910460i \(0.364272\pi\)
\(564\) 0 0
\(565\) 3.05380 5.28934i 0.128474 0.222524i
\(566\) 0 0
\(567\) 10.6516 18.4491i 0.447324 0.774788i
\(568\) 0 0
\(569\) −11.7544 −0.492770 −0.246385 0.969172i \(-0.579243\pi\)
−0.246385 + 0.969172i \(0.579243\pi\)
\(570\) 0 0
\(571\) 32.4868 1.35953 0.679766 0.733429i \(-0.262081\pi\)
0.679766 + 0.733429i \(0.262081\pi\)
\(572\) 0 0
\(573\) −20.4795 + 35.4715i −0.855541 + 1.48184i
\(574\) 0 0
\(575\) −1.07396 + 1.86016i −0.0447873 + 0.0775740i
\(576\) 0 0
\(577\) 25.7287 1.07110 0.535551 0.844503i \(-0.320104\pi\)
0.535551 + 0.844503i \(0.320104\pi\)
\(578\) 0 0
\(579\) 1.07264 + 1.85787i 0.0445775 + 0.0772106i
\(580\) 0 0
\(581\) 12.7837 0.530359
\(582\) 0 0
\(583\) 14.8857 + 25.7828i 0.616503 + 1.06782i
\(584\) 0 0
\(585\) −5.44818 9.43652i −0.225254 0.390152i
\(586\) 0 0
\(587\) 20.8279 36.0750i 0.859659 1.48897i −0.0125958 0.999921i \(-0.504009\pi\)
0.872255 0.489052i \(-0.162657\pi\)
\(588\) 0 0
\(589\) 31.7399 31.0692i 1.30782 1.28018i
\(590\) 0 0
\(591\) 25.1884 43.6276i 1.03611 1.79460i
\(592\) 0 0
\(593\) −8.83267 15.2986i −0.362714 0.628239i 0.625692 0.780070i \(-0.284817\pi\)
−0.988407 + 0.151831i \(0.951483\pi\)
\(594\) 0 0
\(595\) 3.21091 + 5.56146i 0.131634 + 0.227998i
\(596\) 0 0
\(597\) 16.2775 0.666193
\(598\) 0 0
\(599\) 13.1925 + 22.8502i 0.539033 + 0.933632i 0.998956 + 0.0456738i \(0.0145435\pi\)
−0.459924 + 0.887959i \(0.652123\pi\)
\(600\) 0 0
\(601\) 9.46838 0.386223 0.193112 0.981177i \(-0.438142\pi\)
0.193112 + 0.981177i \(0.438142\pi\)
\(602\) 0 0
\(603\) 16.3545 28.3269i 0.666008 1.15356i
\(604\) 0 0
\(605\) 0.00799750 0.0138521i 0.000325145 0.000563167i
\(606\) 0 0
\(607\) −8.26529 −0.335478 −0.167739 0.985831i \(-0.553647\pi\)
−0.167739 + 0.985831i \(0.553647\pi\)
\(608\) 0 0
\(609\) 27.0479 1.09604
\(610\) 0 0
\(611\) 17.9032 31.0092i 0.724285 1.25450i
\(612\) 0 0
\(613\) −3.40417 + 5.89620i −0.137493 + 0.238145i −0.926547 0.376179i \(-0.877238\pi\)
0.789054 + 0.614324i \(0.210571\pi\)
\(614\) 0 0
\(615\) 1.83371 0.0739425
\(616\) 0 0
\(617\) −3.00668 5.20772i −0.121044 0.209655i 0.799135 0.601151i \(-0.205291\pi\)
−0.920180 + 0.391496i \(0.871958\pi\)
\(618\) 0 0
\(619\) 13.2299 0.531754 0.265877 0.964007i \(-0.414338\pi\)
0.265877 + 0.964007i \(0.414338\pi\)
\(620\) 0 0
\(621\) 0.959816 + 1.66245i 0.0385161 + 0.0667118i
\(622\) 0 0
\(623\) −11.6517 20.1813i −0.466816 0.808548i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 9.04916 + 35.2743i 0.361389 + 1.40872i
\(628\) 0 0
\(629\) −4.33915 + 7.51564i −0.173013 + 0.299668i
\(630\) 0 0
\(631\) 11.8932 + 20.5996i 0.473460 + 0.820058i 0.999538 0.0303788i \(-0.00967135\pi\)
−0.526078 + 0.850436i \(0.676338\pi\)
\(632\) 0 0
\(633\) 13.2899 + 23.0188i 0.528226 + 0.914914i
\(634\) 0 0
\(635\) −9.12228 −0.362007
\(636\) 0 0
\(637\) −0.712762 1.23454i −0.0282407 0.0489143i
\(638\) 0 0
\(639\) 23.2033 0.917908
\(640\) 0 0
\(641\) −6.14239 + 10.6389i −0.242610 + 0.420212i −0.961457 0.274956i \(-0.911337\pi\)
0.718847 + 0.695168i \(0.244670\pi\)
\(642\) 0 0
\(643\) −14.5776 + 25.2492i −0.574885 + 0.995729i 0.421170 + 0.906982i \(0.361620\pi\)
−0.996054 + 0.0887474i \(0.971714\pi\)
\(644\) 0 0
\(645\) 5.98164 0.235527
\(646\) 0 0
\(647\) −36.7499 −1.44479 −0.722394 0.691481i \(-0.756958\pi\)
−0.722394 + 0.691481i \(0.756958\pi\)
\(648\) 0 0
\(649\) 18.1879 31.5023i 0.713936 1.23657i
\(650\) 0 0
\(651\) −35.0284 + 60.6710i −1.37287 + 2.37788i
\(652\) 0 0
\(653\) 24.7707 0.969351 0.484675 0.874694i \(-0.338938\pi\)
0.484675 + 0.874694i \(0.338938\pi\)
\(654\) 0 0
\(655\) −11.1328 19.2825i −0.434994 0.753431i
\(656\) 0 0
\(657\) −8.32092 −0.324630
\(658\) 0 0
\(659\) −11.1156 19.2528i −0.433002 0.749982i 0.564128 0.825687i \(-0.309213\pi\)
−0.997130 + 0.0757053i \(0.975879\pi\)
\(660\) 0 0
\(661\) −20.4684 35.4524i −0.796130 1.37894i −0.922119 0.386905i \(-0.873544\pi\)
0.125990 0.992032i \(-0.459789\pi\)
\(662\) 0 0
\(663\) −9.63975 + 16.6965i −0.374377 + 0.648440i
\(664\) 0 0
\(665\) −2.95419 11.5157i −0.114559 0.446559i
\(666\) 0 0
\(667\) 4.22501 7.31793i 0.163593 0.283351i
\(668\) 0 0
\(669\) 12.2592 + 21.2336i 0.473969 + 0.820939i
\(670\) 0 0
\(671\) 14.0106 + 24.2671i 0.540873 + 0.936819i
\(672\) 0 0
\(673\) −33.5992 −1.29515 −0.647577 0.762000i \(-0.724217\pi\)
−0.647577 + 0.762000i \(0.724217\pi\)
\(674\) 0 0
\(675\) 0.446857 + 0.773979i 0.0171995 + 0.0297905i
\(676\) 0 0
\(677\) 29.5883 1.13717 0.568585 0.822624i \(-0.307491\pi\)
0.568585 + 0.822624i \(0.307491\pi\)
\(678\) 0 0
\(679\) −9.85949 + 17.0771i −0.378373 + 0.655361i
\(680\) 0 0
\(681\) 28.4598 49.2938i 1.09058 1.88894i
\(682\) 0 0
\(683\) 41.0567 1.57099 0.785495 0.618868i \(-0.212408\pi\)
0.785495 + 0.618868i \(0.212408\pi\)
\(684\) 0 0
\(685\) −7.62711 −0.291417
\(686\) 0 0
\(687\) −20.4488 + 35.4183i −0.780170 + 1.35129i
\(688\) 0 0
\(689\) 14.5894 25.2696i 0.555813 0.962697i
\(690\) 0 0
\(691\) 1.22497 0.0466000 0.0233000 0.999729i \(-0.492583\pi\)
0.0233000 + 0.999729i \(0.492583\pi\)
\(692\) 0 0
\(693\) −15.1613 26.2601i −0.575929 0.997538i
\(694\) 0 0
\(695\) 16.9183 0.641748
\(696\) 0 0
\(697\) −0.856376 1.48329i −0.0324375 0.0561835i
\(698\) 0 0
\(699\) −23.5228 40.7426i −0.889712 1.54103i
\(700\) 0 0
\(701\) −22.0101 + 38.1226i −0.831309 + 1.43987i 0.0656918 + 0.997840i \(0.479075\pi\)
−0.897001 + 0.442029i \(0.854259\pi\)
\(702\) 0 0
\(703\) 11.4810 11.2384i 0.433015 0.423865i
\(704\) 0 0
\(705\) −13.8939 + 24.0649i −0.523273 + 0.906335i
\(706\) 0 0
\(707\) 7.87729 + 13.6439i 0.296256 + 0.513130i
\(708\) 0 0
\(709\) −8.16255 14.1379i −0.306551 0.530962i 0.671055 0.741408i \(-0.265842\pi\)
−0.977605 + 0.210446i \(0.932508\pi\)
\(710\) 0 0
\(711\) 40.2509 1.50953
\(712\) 0 0
\(713\) 10.9432 + 18.9542i 0.409827 + 0.709841i
\(714\) 0 0
\(715\) 10.7654 0.402602
\(716\) 0 0
\(717\) 0.759750 1.31593i 0.0283734 0.0491442i
\(718\) 0 0
\(719\) −5.08574 + 8.80876i −0.189666 + 0.328511i −0.945139 0.326669i \(-0.894074\pi\)
0.755473 + 0.655180i \(0.227407\pi\)
\(720\) 0 0
\(721\) −41.0686 −1.52947
\(722\) 0 0
\(723\) −55.1595 −2.05141
\(724\) 0 0
\(725\) 1.96702 3.40697i 0.0730532 0.126532i
\(726\) 0 0
\(727\) −4.02148 + 6.96541i −0.149148 + 0.258333i −0.930913 0.365241i \(-0.880987\pi\)
0.781765 + 0.623574i \(0.214320\pi\)
\(728\) 0 0
\(729\) −32.9600 −1.22074
\(730\) 0 0
\(731\) −2.79353 4.83853i −0.103322 0.178960i
\(732\) 0 0
\(733\) 41.2325 1.52296 0.761479 0.648190i \(-0.224474\pi\)
0.761479 + 0.648190i \(0.224474\pi\)
\(734\) 0 0
\(735\) 0.553143 + 0.958072i 0.0204030 + 0.0353390i
\(736\) 0 0
\(737\) 16.1580 + 27.9864i 0.595186 + 1.03089i
\(738\) 0 0
\(739\) −16.5253 + 28.6227i −0.607893 + 1.05290i 0.383694 + 0.923460i \(0.374652\pi\)
−0.991587 + 0.129442i \(0.958681\pi\)
\(740\) 0 0
\(741\) 25.5059 24.9669i 0.936983 0.917184i
\(742\) 0 0
\(743\) −17.3933 + 30.1261i −0.638099 + 1.10522i 0.347750 + 0.937587i \(0.386946\pi\)
−0.985849 + 0.167633i \(0.946388\pi\)
\(744\) 0 0
\(745\) 6.19809 + 10.7354i 0.227080 + 0.393315i
\(746\) 0 0
\(747\) −7.86153 13.6166i −0.287638 0.498204i
\(748\) 0 0
\(749\) −41.4284 −1.51376
\(750\) 0 0
\(751\) 21.7350 + 37.6462i 0.793123 + 1.37373i 0.924024 + 0.382334i \(0.124879\pi\)
−0.130902 + 0.991395i \(0.541787\pi\)
\(752\) 0 0
\(753\) −20.8537 −0.759950
\(754\) 0 0
\(755\) 7.22743 12.5183i 0.263033 0.455587i
\(756\) 0 0
\(757\) 3.08494 5.34328i 0.112124 0.194205i −0.804502 0.593949i \(-0.797568\pi\)
0.916626 + 0.399745i \(0.130901\pi\)
\(758\) 0 0
\(759\) −17.9449 −0.651359
\(760\) 0 0
\(761\) −9.81318 −0.355728 −0.177864 0.984055i \(-0.556919\pi\)
−0.177864 + 0.984055i \(0.556919\pi\)
\(762\) 0 0
\(763\) 17.2116 29.8114i 0.623103 1.07925i
\(764\) 0 0
\(765\) 3.94918 6.84018i 0.142783 0.247307i
\(766\) 0 0
\(767\) −35.6517 −1.28731
\(768\) 0 0
\(769\) 20.7452 + 35.9317i 0.748090 + 1.29573i 0.948737 + 0.316066i \(0.102362\pi\)
−0.200647 + 0.979664i \(0.564305\pi\)
\(770\) 0 0
\(771\) −35.7727 −1.28832
\(772\) 0 0
\(773\) −20.8584 36.1279i −0.750226 1.29943i −0.947713 0.319124i \(-0.896611\pi\)
0.197487 0.980306i \(-0.436722\pi\)
\(774\) 0 0
\(775\) 5.09478 + 8.82442i 0.183010 + 0.316983i
\(776\) 0 0
\(777\) −12.6705 + 21.9460i −0.454553 + 0.787309i
\(778\) 0 0
\(779\) 0.787908 + 3.07133i 0.0282297 + 0.110042i
\(780\) 0 0
\(781\) −11.4622 + 19.8531i −0.410149 + 0.710400i
\(782\) 0 0
\(783\) −1.75795 3.04486i −0.0628240 0.108814i
\(784\) 0 0
\(785\) 9.10642 + 15.7728i 0.325022 + 0.562955i
\(786\) 0 0
\(787\) −13.0342 −0.464621 −0.232310 0.972642i \(-0.574629\pi\)
−0.232310 + 0.972642i \(0.574629\pi\)
\(788\) 0 0
\(789\) −23.3718 40.4812i −0.832060 1.44117i
\(790\)