Properties

Label 819.2.j.h.352.3
Level $819$
Weight $2$
Character 819.352
Analytic conductor $6.540$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(235,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.235");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.j (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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 352.3
Root \(-0.132804 + 0.230024i\) of defining polynomial
Character \(\chi\) \(=\) 819.352
Dual form 819.2.j.h.235.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.632804 - 1.09605i) q^{2} +(0.199118 + 0.344882i) q^{4} +(-1.45130 + 2.51373i) q^{5} +(-1.29536 - 2.30696i) q^{7} +3.03523 q^{8} +O(q^{10})\) \(q+(0.632804 - 1.09605i) q^{2} +(0.199118 + 0.344882i) q^{4} +(-1.45130 + 2.51373i) q^{5} +(-1.29536 - 2.30696i) q^{7} +3.03523 q^{8} +(1.83678 + 3.18139i) q^{10} +(1.01828 + 1.76372i) q^{11} +1.00000 q^{13} +(-3.34825 - 0.0400756i) q^{14} +(1.52247 - 2.63699i) q^{16} +(1.99933 + 3.46294i) q^{17} +(-3.48105 + 6.02935i) q^{19} -1.15592 q^{20} +2.57749 q^{22} +(-0.313640 + 0.543240i) q^{23} +(-1.71254 - 2.96621i) q^{25} +(0.632804 - 1.09605i) q^{26} +(0.537699 - 0.906101i) q^{28} -1.09606 q^{29} +(5.21624 + 9.03479i) q^{31} +(1.10838 + 1.91977i) q^{32} +5.06074 q^{34} +(7.67901 + 0.0919110i) q^{35} +(1.54268 - 2.67201i) q^{37} +(4.40565 + 7.63080i) q^{38} +(-4.40502 + 7.62973i) q^{40} +0.521150 q^{41} +0.329024 q^{43} +(-0.405516 + 0.702374i) q^{44} +(0.396945 + 0.687530i) q^{46} +(5.27284 - 9.13283i) q^{47} +(-3.64409 + 5.97667i) q^{49} -4.33482 q^{50} +(0.199118 + 0.344882i) q^{52} +(3.55950 + 6.16523i) q^{53} -5.91133 q^{55} +(-3.93171 - 7.00214i) q^{56} +(-0.693593 + 1.20134i) q^{58} +(1.01828 + 1.76372i) q^{59} +(-1.20041 + 2.07917i) q^{61} +13.2034 q^{62} +8.89542 q^{64} +(-1.45130 + 2.51373i) q^{65} +(-7.34709 - 12.7255i) q^{67} +(-0.796204 + 1.37907i) q^{68} +(4.96005 - 8.35841i) q^{70} -3.60141 q^{71} +(-1.48786 - 2.57706i) q^{73} +(-1.95243 - 3.38172i) q^{74} -2.77255 q^{76} +(2.74978 - 4.63378i) q^{77} +(4.38075 - 7.58769i) q^{79} +(4.41912 + 7.65414i) q^{80} +(0.329786 - 0.571206i) q^{82} -12.8039 q^{83} -11.6065 q^{85} +(0.208208 - 0.360627i) q^{86} +(3.09072 + 5.35328i) q^{88} +(-1.34049 + 2.32180i) q^{89} +(-1.29536 - 2.30696i) q^{91} -0.249805 q^{92} +(-6.67335 - 11.5586i) q^{94} +(-10.1041 - 17.5008i) q^{95} -2.32902 q^{97} +(4.24472 + 7.77617i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.632804 1.09605i 0.447460 0.775024i −0.550760 0.834664i \(-0.685662\pi\)
0.998220 + 0.0596401i \(0.0189953\pi\)
\(3\) 0 0
\(4\) 0.199118 + 0.344882i 0.0995588 + 0.172441i
\(5\) −1.45130 + 2.51373i −0.649041 + 1.12417i 0.334311 + 0.942463i \(0.391496\pi\)
−0.983352 + 0.181709i \(0.941837\pi\)
\(6\) 0 0
\(7\) −1.29536 2.30696i −0.489599 0.871948i
\(8\) 3.03523 1.07311
\(9\) 0 0
\(10\) 1.83678 + 3.18139i 0.580840 + 1.00604i
\(11\) 1.01828 + 1.76372i 0.307024 + 0.531780i 0.977710 0.209961i \(-0.0673336\pi\)
−0.670686 + 0.741741i \(0.734000\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) −3.34825 0.0400756i −0.894856 0.0107107i
\(15\) 0 0
\(16\) 1.52247 2.63699i 0.380617 0.659249i
\(17\) 1.99933 + 3.46294i 0.484909 + 0.839887i 0.999850 0.0173386i \(-0.00551934\pi\)
−0.514941 + 0.857226i \(0.672186\pi\)
\(18\) 0 0
\(19\) −3.48105 + 6.02935i −0.798608 + 1.38323i 0.121915 + 0.992540i \(0.461096\pi\)
−0.920523 + 0.390688i \(0.872237\pi\)
\(20\) −1.15592 −0.258471
\(21\) 0 0
\(22\) 2.57749 0.549523
\(23\) −0.313640 + 0.543240i −0.0653985 + 0.113273i −0.896871 0.442293i \(-0.854165\pi\)
0.831472 + 0.555566i \(0.187499\pi\)
\(24\) 0 0
\(25\) −1.71254 2.96621i −0.342509 0.593243i
\(26\) 0.632804 1.09605i 0.124103 0.214953i
\(27\) 0 0
\(28\) 0.537699 0.906101i 0.101615 0.171237i
\(29\) −1.09606 −0.203534 −0.101767 0.994808i \(-0.532450\pi\)
−0.101767 + 0.994808i \(0.532450\pi\)
\(30\) 0 0
\(31\) 5.21624 + 9.03479i 0.936864 + 1.62270i 0.771275 + 0.636502i \(0.219619\pi\)
0.165589 + 0.986195i \(0.447047\pi\)
\(32\) 1.10838 + 1.91977i 0.195935 + 0.339370i
\(33\) 0 0
\(34\) 5.06074 0.867910
\(35\) 7.67901 + 0.0919110i 1.29799 + 0.0155358i
\(36\) 0 0
\(37\) 1.54268 2.67201i 0.253616 0.439275i −0.710903 0.703290i \(-0.751713\pi\)
0.964519 + 0.264015i \(0.0850468\pi\)
\(38\) 4.40565 + 7.63080i 0.714690 + 1.23788i
\(39\) 0 0
\(40\) −4.40502 + 7.62973i −0.696496 + 1.20637i
\(41\) 0.521150 0.0813900 0.0406950 0.999172i \(-0.487043\pi\)
0.0406950 + 0.999172i \(0.487043\pi\)
\(42\) 0 0
\(43\) 0.329024 0.0501757 0.0250879 0.999685i \(-0.492013\pi\)
0.0250879 + 0.999685i \(0.492013\pi\)
\(44\) −0.405516 + 0.702374i −0.0611338 + 0.105887i
\(45\) 0 0
\(46\) 0.396945 + 0.687530i 0.0585264 + 0.101371i
\(47\) 5.27284 9.13283i 0.769123 1.33216i −0.168916 0.985630i \(-0.554027\pi\)
0.938039 0.346530i \(-0.112640\pi\)
\(48\) 0 0
\(49\) −3.64409 + 5.97667i −0.520585 + 0.853810i
\(50\) −4.33482 −0.613036
\(51\) 0 0
\(52\) 0.199118 + 0.344882i 0.0276126 + 0.0478265i
\(53\) 3.55950 + 6.16523i 0.488935 + 0.846860i 0.999919 0.0127302i \(-0.00405225\pi\)
−0.510984 + 0.859590i \(0.670719\pi\)
\(54\) 0 0
\(55\) −5.91133 −0.797084
\(56\) −3.93171 7.00214i −0.525396 0.935700i
\(57\) 0 0
\(58\) −0.693593 + 1.20134i −0.0910733 + 0.157744i
\(59\) 1.01828 + 1.76372i 0.132569 + 0.229616i 0.924666 0.380779i \(-0.124344\pi\)
−0.792097 + 0.610395i \(0.791011\pi\)
\(60\) 0 0
\(61\) −1.20041 + 2.07917i −0.153696 + 0.266210i −0.932584 0.360954i \(-0.882451\pi\)
0.778887 + 0.627164i \(0.215784\pi\)
\(62\) 13.2034 1.67684
\(63\) 0 0
\(64\) 8.89542 1.11193
\(65\) −1.45130 + 2.51373i −0.180012 + 0.311789i
\(66\) 0 0
\(67\) −7.34709 12.7255i −0.897589 1.55467i −0.830567 0.556919i \(-0.811983\pi\)
−0.0670226 0.997751i \(-0.521350\pi\)
\(68\) −0.796204 + 1.37907i −0.0965539 + 0.167236i
\(69\) 0 0
\(70\) 4.96005 8.35841i 0.592839 0.999021i
\(71\) −3.60141 −0.427409 −0.213704 0.976898i \(-0.568553\pi\)
−0.213704 + 0.976898i \(0.568553\pi\)
\(72\) 0 0
\(73\) −1.48786 2.57706i −0.174141 0.301622i 0.765722 0.643171i \(-0.222382\pi\)
−0.939864 + 0.341550i \(0.889048\pi\)
\(74\) −1.95243 3.38172i −0.226966 0.393117i
\(75\) 0 0
\(76\) −2.77255 −0.318034
\(77\) 2.74978 4.63378i 0.313366 0.528068i
\(78\) 0 0
\(79\) 4.38075 7.58769i 0.492873 0.853681i −0.507093 0.861891i \(-0.669280\pi\)
0.999966 + 0.00820995i \(0.00261334\pi\)
\(80\) 4.41912 + 7.65414i 0.494073 + 0.855759i
\(81\) 0 0
\(82\) 0.329786 0.571206i 0.0364188 0.0630792i
\(83\) −12.8039 −1.40541 −0.702703 0.711483i \(-0.748024\pi\)
−0.702703 + 0.711483i \(0.748024\pi\)
\(84\) 0 0
\(85\) −11.6065 −1.25890
\(86\) 0.208208 0.360627i 0.0224516 0.0388874i
\(87\) 0 0
\(88\) 3.09072 + 5.35328i 0.329471 + 0.570661i
\(89\) −1.34049 + 2.32180i −0.142092 + 0.246110i −0.928284 0.371872i \(-0.878716\pi\)
0.786192 + 0.617982i \(0.212050\pi\)
\(90\) 0 0
\(91\) −1.29536 2.30696i −0.135790 0.241835i
\(92\) −0.249805 −0.0260440
\(93\) 0 0
\(94\) −6.67335 11.5586i −0.688304 1.19218i
\(95\) −10.1041 17.5008i −1.03666 1.79554i
\(96\) 0 0
\(97\) −2.32902 −0.236477 −0.118238 0.992985i \(-0.537725\pi\)
−0.118238 + 0.992985i \(0.537725\pi\)
\(98\) 4.24472 + 7.77617i 0.428782 + 0.785512i
\(99\) 0 0
\(100\) 0.681995 1.18125i 0.0681995 0.118125i
\(101\) 0.726620 + 1.25854i 0.0723014 + 0.125230i 0.899910 0.436077i \(-0.143632\pi\)
−0.827608 + 0.561306i \(0.810299\pi\)
\(102\) 0 0
\(103\) 5.81765 10.0765i 0.573230 0.992864i −0.423001 0.906129i \(-0.639023\pi\)
0.996231 0.0867346i \(-0.0276432\pi\)
\(104\) 3.03523 0.297628
\(105\) 0 0
\(106\) 9.00987 0.875115
\(107\) 9.81297 16.9966i 0.948656 1.64312i 0.200395 0.979715i \(-0.435777\pi\)
0.748261 0.663405i \(-0.230889\pi\)
\(108\) 0 0
\(109\) 0.553378 + 0.958479i 0.0530040 + 0.0918057i 0.891310 0.453394i \(-0.149787\pi\)
−0.838306 + 0.545200i \(0.816454\pi\)
\(110\) −3.74071 + 6.47911i −0.356663 + 0.617759i
\(111\) 0 0
\(112\) −8.05557 0.0964182i −0.761180 0.00911066i
\(113\) 1.09606 0.103109 0.0515545 0.998670i \(-0.483582\pi\)
0.0515545 + 0.998670i \(0.483582\pi\)
\(114\) 0 0
\(115\) −0.910371 1.57681i −0.0848926 0.147038i
\(116\) −0.218245 0.378012i −0.0202636 0.0350975i
\(117\) 0 0
\(118\) 2.57749 0.237277
\(119\) 5.39901 9.09812i 0.494926 0.834024i
\(120\) 0 0
\(121\) 3.42620 5.93436i 0.311473 0.539487i
\(122\) 1.51925 + 2.63141i 0.137546 + 0.238237i
\(123\) 0 0
\(124\) −2.07729 + 3.59797i −0.186546 + 0.323107i
\(125\) −4.57134 −0.408873
\(126\) 0 0
\(127\) 5.18143 0.459778 0.229889 0.973217i \(-0.426164\pi\)
0.229889 + 0.973217i \(0.426164\pi\)
\(128\) 3.41231 5.91029i 0.301608 0.522400i
\(129\) 0 0
\(130\) 1.83678 + 3.18139i 0.161096 + 0.279027i
\(131\) 5.28335 9.15103i 0.461609 0.799530i −0.537433 0.843307i \(-0.680606\pi\)
0.999041 + 0.0437770i \(0.0139391\pi\)
\(132\) 0 0
\(133\) 18.4187 + 0.220455i 1.59710 + 0.0191159i
\(134\) −18.5971 −1.60654
\(135\) 0 0
\(136\) 6.06842 + 10.5108i 0.520363 + 0.901295i
\(137\) −2.93589 5.08510i −0.250830 0.434450i 0.712925 0.701241i \(-0.247370\pi\)
−0.963754 + 0.266791i \(0.914037\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 1.49733 + 2.66665i 0.126547 + 0.225373i
\(141\) 0 0
\(142\) −2.27899 + 3.94732i −0.191248 + 0.331252i
\(143\) 1.01828 + 1.76372i 0.0851530 + 0.147489i
\(144\) 0 0
\(145\) 1.59072 2.75520i 0.132102 0.228807i
\(146\) −3.76611 −0.311685
\(147\) 0 0
\(148\) 1.22870 0.100999
\(149\) −5.05271 + 8.75155i −0.413934 + 0.716955i −0.995316 0.0966760i \(-0.969179\pi\)
0.581382 + 0.813631i \(0.302512\pi\)
\(150\) 0 0
\(151\) 0.0938631 + 0.162576i 0.00763847 + 0.0132302i 0.869819 0.493370i \(-0.164235\pi\)
−0.862181 + 0.506601i \(0.830902\pi\)
\(152\) −10.5658 + 18.3005i −0.856998 + 1.48436i
\(153\) 0 0
\(154\) −3.33878 5.94616i −0.269046 0.479155i
\(155\) −30.2813 −2.43225
\(156\) 0 0
\(157\) 6.03590 + 10.4545i 0.481717 + 0.834358i 0.999780 0.0209844i \(-0.00668003\pi\)
−0.518063 + 0.855343i \(0.673347\pi\)
\(158\) −5.54432 9.60304i −0.441082 0.763977i
\(159\) 0 0
\(160\) −6.43435 −0.508680
\(161\) 1.65951 + 0.0198629i 0.130788 + 0.00156541i
\(162\) 0 0
\(163\) −7.45678 + 12.9155i −0.584060 + 1.01162i 0.410932 + 0.911666i \(0.365203\pi\)
−0.994992 + 0.0999554i \(0.968130\pi\)
\(164\) 0.103770 + 0.179735i 0.00810309 + 0.0140350i
\(165\) 0 0
\(166\) −8.10234 + 14.0337i −0.628863 + 1.08922i
\(167\) −5.05664 −0.391294 −0.195647 0.980674i \(-0.562681\pi\)
−0.195647 + 0.980674i \(0.562681\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −7.34465 + 12.7213i −0.563309 + 0.975680i
\(171\) 0 0
\(172\) 0.0655145 + 0.113474i 0.00499543 + 0.00865235i
\(173\) −0.297807 + 0.515817i −0.0226419 + 0.0392169i −0.877124 0.480263i \(-0.840541\pi\)
0.854482 + 0.519480i \(0.173874\pi\)
\(174\) 0 0
\(175\) −4.62457 + 7.79307i −0.349584 + 0.589101i
\(176\) 6.20121 0.467434
\(177\) 0 0
\(178\) 1.69654 + 2.93849i 0.127161 + 0.220249i
\(179\) 4.03832 + 6.99458i 0.301838 + 0.522799i 0.976552 0.215280i \(-0.0690664\pi\)
−0.674714 + 0.738079i \(0.735733\pi\)
\(180\) 0 0
\(181\) 1.89324 0.140724 0.0703618 0.997522i \(-0.477585\pi\)
0.0703618 + 0.997522i \(0.477585\pi\)
\(182\) −3.34825 0.0400756i −0.248188 0.00297060i
\(183\) 0 0
\(184\) −0.951968 + 1.64886i −0.0701800 + 0.121555i
\(185\) 4.47780 + 7.75577i 0.329214 + 0.570216i
\(186\) 0 0
\(187\) −4.07177 + 7.05251i −0.297757 + 0.515730i
\(188\) 4.19966 0.306292
\(189\) 0 0
\(190\) −25.5757 −1.85545
\(191\) 1.85087 3.20580i 0.133924 0.231964i −0.791262 0.611478i \(-0.790575\pi\)
0.925186 + 0.379514i \(0.123909\pi\)
\(192\) 0 0
\(193\) −6.79373 11.7671i −0.489024 0.847014i 0.510897 0.859642i \(-0.329313\pi\)
−0.999920 + 0.0126285i \(0.995980\pi\)
\(194\) −1.47382 + 2.55272i −0.105814 + 0.183275i
\(195\) 0 0
\(196\) −2.78685 0.0667218i −0.199061 0.00476585i
\(197\) 9.70258 0.691280 0.345640 0.938367i \(-0.387662\pi\)
0.345640 + 0.938367i \(0.387662\pi\)
\(198\) 0 0
\(199\) −13.1360 22.7522i −0.931185 1.61286i −0.781299 0.624156i \(-0.785443\pi\)
−0.149885 0.988703i \(-0.547891\pi\)
\(200\) −5.19796 9.00313i −0.367551 0.636617i
\(201\) 0 0
\(202\) 1.83923 0.129408
\(203\) 1.41979 + 2.52857i 0.0996500 + 0.177471i
\(204\) 0 0
\(205\) −0.756345 + 1.31003i −0.0528255 + 0.0914964i
\(206\) −7.36287 12.7529i −0.512995 0.888534i
\(207\) 0 0
\(208\) 1.52247 2.63699i 0.105564 0.182843i
\(209\) −14.1788 −0.980765
\(210\) 0 0
\(211\) 10.0338 0.690758 0.345379 0.938463i \(-0.387750\pi\)
0.345379 + 0.938463i \(0.387750\pi\)
\(212\) −1.41752 + 2.45521i −0.0973555 + 0.168625i
\(213\) 0 0
\(214\) −12.4194 21.5110i −0.848971 1.47046i
\(215\) −0.477513 + 0.827077i −0.0325661 + 0.0564062i
\(216\) 0 0
\(217\) 14.0860 23.7369i 0.956218 1.61137i
\(218\) 1.40072 0.0948688
\(219\) 0 0
\(220\) −1.17705 2.03871i −0.0793567 0.137450i
\(221\) 1.99933 + 3.46294i 0.134490 + 0.232943i
\(222\) 0 0
\(223\) 17.4961 1.17163 0.585813 0.810446i \(-0.300775\pi\)
0.585813 + 0.810446i \(0.300775\pi\)
\(224\) 2.99307 5.04376i 0.199983 0.337000i
\(225\) 0 0
\(226\) 0.693593 1.20134i 0.0461371 0.0799119i
\(227\) −4.75815 8.24136i −0.315810 0.546998i 0.663800 0.747910i \(-0.268943\pi\)
−0.979609 + 0.200912i \(0.935609\pi\)
\(228\) 0 0
\(229\) −10.5585 + 18.2878i −0.697725 + 1.20849i 0.271529 + 0.962430i \(0.412471\pi\)
−0.969254 + 0.246064i \(0.920863\pi\)
\(230\) −2.30435 −0.151944
\(231\) 0 0
\(232\) −3.32680 −0.218415
\(233\) 7.08938 12.2792i 0.464441 0.804435i −0.534735 0.845020i \(-0.679589\pi\)
0.999176 + 0.0405847i \(0.0129221\pi\)
\(234\) 0 0
\(235\) 15.3050 + 26.5090i 0.998385 + 1.72925i
\(236\) −0.405516 + 0.702374i −0.0263968 + 0.0457206i
\(237\) 0 0
\(238\) −6.55547 11.6749i −0.424928 0.756772i
\(239\) 16.5275 1.06907 0.534536 0.845145i \(-0.320486\pi\)
0.534536 + 0.845145i \(0.320486\pi\)
\(240\) 0 0
\(241\) 6.84450 + 11.8550i 0.440893 + 0.763649i 0.997756 0.0669552i \(-0.0213284\pi\)
−0.556863 + 0.830604i \(0.687995\pi\)
\(242\) −4.33623 7.51058i −0.278744 0.482798i
\(243\) 0 0
\(244\) −0.956089 −0.0612073
\(245\) −9.73503 17.8342i −0.621948 1.13938i
\(246\) 0 0
\(247\) −3.48105 + 6.02935i −0.221494 + 0.383639i
\(248\) 15.8325 + 27.4226i 1.00536 + 1.74134i
\(249\) 0 0
\(250\) −2.89276 + 5.01042i −0.182954 + 0.316886i
\(251\) 14.6603 0.925349 0.462674 0.886528i \(-0.346890\pi\)
0.462674 + 0.886528i \(0.346890\pi\)
\(252\) 0 0
\(253\) −1.27750 −0.0803155
\(254\) 3.27883 5.67910i 0.205732 0.356339i
\(255\) 0 0
\(256\) 4.57678 + 7.92721i 0.286049 + 0.495451i
\(257\) −0.876387 + 1.51795i −0.0546675 + 0.0946869i −0.892064 0.451909i \(-0.850743\pi\)
0.837397 + 0.546596i \(0.184077\pi\)
\(258\) 0 0
\(259\) −8.16254 0.0976985i −0.507195 0.00607069i
\(260\) −1.15592 −0.0716870
\(261\) 0 0
\(262\) −6.68666 11.5816i −0.413103 0.715515i
\(263\) 13.4708 + 23.3321i 0.830645 + 1.43872i 0.897527 + 0.440959i \(0.145361\pi\)
−0.0668823 + 0.997761i \(0.521305\pi\)
\(264\) 0 0
\(265\) −20.6636 −1.26936
\(266\) 11.8970 20.0483i 0.729454 1.22924i
\(267\) 0 0
\(268\) 2.92587 5.06775i 0.178726 0.309562i
\(269\) −11.0346 19.1124i −0.672789 1.16530i −0.977110 0.212735i \(-0.931763\pi\)
0.304321 0.952570i \(-0.401570\pi\)
\(270\) 0 0
\(271\) 4.48105 7.76141i 0.272204 0.471472i −0.697222 0.716856i \(-0.745581\pi\)
0.969426 + 0.245384i \(0.0789140\pi\)
\(272\) 12.1757 0.738259
\(273\) 0 0
\(274\) −7.43137 −0.448945
\(275\) 3.48770 6.04088i 0.210316 0.364279i
\(276\) 0 0
\(277\) 3.76463 + 6.52052i 0.226194 + 0.391780i 0.956677 0.291151i \(-0.0940382\pi\)
−0.730483 + 0.682931i \(0.760705\pi\)
\(278\) −2.53122 + 4.38420i −0.151812 + 0.262947i
\(279\) 0 0
\(280\) 23.3075 + 0.278971i 1.39289 + 0.0166717i
\(281\) −29.7762 −1.77630 −0.888151 0.459553i \(-0.848010\pi\)
−0.888151 + 0.459553i \(0.848010\pi\)
\(282\) 0 0
\(283\) −0.150726 0.261064i −0.00895970 0.0155187i 0.861511 0.507739i \(-0.169519\pi\)
−0.870470 + 0.492221i \(0.836185\pi\)
\(284\) −0.717104 1.24206i −0.0425523 0.0737027i
\(285\) 0 0
\(286\) 2.57749 0.152410
\(287\) −0.675076 1.20227i −0.0398485 0.0709678i
\(288\) 0 0
\(289\) 0.505347 0.875286i 0.0297263 0.0514874i
\(290\) −2.01322 3.48701i −0.118221 0.204764i
\(291\) 0 0
\(292\) 0.592520 1.02627i 0.0346746 0.0600582i
\(293\) 19.2471 1.12443 0.562214 0.826992i \(-0.309950\pi\)
0.562214 + 0.826992i \(0.309950\pi\)
\(294\) 0 0
\(295\) −5.91133 −0.344171
\(296\) 4.68240 8.11015i 0.272159 0.471393i
\(297\) 0 0
\(298\) 6.39475 + 11.0760i 0.370438 + 0.641618i
\(299\) −0.313640 + 0.543240i −0.0181383 + 0.0314164i
\(300\) 0 0
\(301\) −0.426204 0.759044i −0.0245660 0.0437506i
\(302\) 0.237588 0.0136716
\(303\) 0 0
\(304\) 10.5996 + 18.3590i 0.607928 + 1.05296i
\(305\) −3.48430 6.03499i −0.199511 0.345562i
\(306\) 0 0
\(307\) −3.57779 −0.204195 −0.102098 0.994774i \(-0.532555\pi\)
−0.102098 + 0.994774i \(0.532555\pi\)
\(308\) 2.14563 + 0.0256814i 0.122259 + 0.00146333i
\(309\) 0 0
\(310\) −19.1621 + 33.1898i −1.08834 + 1.88505i
\(311\) −11.9153 20.6379i −0.675655 1.17027i −0.976277 0.216526i \(-0.930527\pi\)
0.300622 0.953743i \(-0.402806\pi\)
\(312\) 0 0
\(313\) 9.04068 15.6589i 0.511009 0.885094i −0.488909 0.872335i \(-0.662605\pi\)
0.999919 0.0127596i \(-0.00406161\pi\)
\(314\) 15.2782 0.862196
\(315\) 0 0
\(316\) 3.48914 0.196279
\(317\) −13.7741 + 23.8574i −0.773630 + 1.33997i 0.161931 + 0.986802i \(0.448228\pi\)
−0.935561 + 0.353164i \(0.885106\pi\)
\(318\) 0 0
\(319\) −1.11610 1.93314i −0.0624897 0.108235i
\(320\) −12.9099 + 22.3606i −0.721687 + 1.25000i
\(321\) 0 0
\(322\) 1.07191 1.80633i 0.0597355 0.100663i
\(323\) −27.8391 −1.54901
\(324\) 0 0
\(325\) −1.71254 2.96621i −0.0949948 0.164536i
\(326\) 9.43736 + 16.3460i 0.522687 + 0.905321i
\(327\) 0 0
\(328\) 1.58181 0.0873408
\(329\) −27.8993 0.333930i −1.53814 0.0184101i
\(330\) 0 0
\(331\) 9.09069 15.7455i 0.499669 0.865453i −0.500331 0.865834i \(-0.666788\pi\)
1.00000 0.000381757i \(0.000121517\pi\)
\(332\) −2.54947 4.41582i −0.139921 0.242350i
\(333\) 0 0
\(334\) −3.19986 + 5.54232i −0.175089 + 0.303262i
\(335\) 42.6513 2.33029
\(336\) 0 0
\(337\) −17.1381 −0.933572 −0.466786 0.884370i \(-0.654588\pi\)
−0.466786 + 0.884370i \(0.654588\pi\)
\(338\) 0.632804 1.09605i 0.0344200 0.0596172i
\(339\) 0 0
\(340\) −2.31106 4.00288i −0.125335 0.217086i
\(341\) −10.6232 + 18.3999i −0.575279 + 0.996412i
\(342\) 0 0
\(343\) 18.5083 + 0.664840i 0.999355 + 0.0358980i
\(344\) 0.998663 0.0538443
\(345\) 0 0
\(346\) 0.376907 + 0.652823i 0.0202627 + 0.0350960i
\(347\) 11.1344 + 19.2853i 0.597725 + 1.03529i 0.993156 + 0.116794i \(0.0372619\pi\)
−0.395431 + 0.918496i \(0.629405\pi\)
\(348\) 0 0
\(349\) 19.9368 1.06719 0.533595 0.845740i \(-0.320841\pi\)
0.533595 + 0.845740i \(0.320841\pi\)
\(350\) 5.61514 + 10.0002i 0.300142 + 0.534535i
\(351\) 0 0
\(352\) −2.25728 + 3.90972i −0.120313 + 0.208389i
\(353\) 11.4576 + 19.8451i 0.609825 + 1.05625i 0.991269 + 0.131856i \(0.0420937\pi\)
−0.381444 + 0.924392i \(0.624573\pi\)
\(354\) 0 0
\(355\) 5.22673 9.05296i 0.277406 0.480481i
\(356\) −1.06766 −0.0565860
\(357\) 0 0
\(358\) 10.2219 0.540242
\(359\) 13.6157 23.5831i 0.718610 1.24467i −0.242940 0.970041i \(-0.578112\pi\)
0.961551 0.274628i \(-0.0885547\pi\)
\(360\) 0 0
\(361\) −14.7354 25.5225i −0.775548 1.34329i
\(362\) 1.19805 2.07509i 0.0629682 0.109064i
\(363\) 0 0
\(364\) 0.537699 0.906101i 0.0281831 0.0474926i
\(365\) 8.63735 0.452099
\(366\) 0 0
\(367\) 5.42822 + 9.40195i 0.283351 + 0.490778i 0.972208 0.234119i \(-0.0752206\pi\)
−0.688857 + 0.724897i \(0.741887\pi\)
\(368\) 0.955014 + 1.65413i 0.0497836 + 0.0862277i
\(369\) 0 0
\(370\) 11.3343 0.589241
\(371\) 9.61210 16.1978i 0.499035 0.840948i
\(372\) 0 0
\(373\) 1.18572 2.05373i 0.0613943 0.106338i −0.833695 0.552226i \(-0.813779\pi\)
0.895089 + 0.445888i \(0.147112\pi\)
\(374\) 5.15326 + 8.92571i 0.266469 + 0.461538i
\(375\) 0 0
\(376\) 16.0043 27.7202i 0.825357 1.42956i
\(377\) −1.09606 −0.0564501
\(378\) 0 0
\(379\) −29.2197 −1.50092 −0.750458 0.660918i \(-0.770167\pi\)
−0.750458 + 0.660918i \(0.770167\pi\)
\(380\) 4.02381 6.96944i 0.206417 0.357525i
\(381\) 0 0
\(382\) −2.34248 4.05729i −0.119852 0.207589i
\(383\) −1.53297 + 2.65519i −0.0783313 + 0.135674i −0.902530 0.430627i \(-0.858293\pi\)
0.824199 + 0.566301i \(0.191626\pi\)
\(384\) 0 0
\(385\) 7.65729 + 13.6372i 0.390252 + 0.695015i
\(386\) −17.1964 −0.875274
\(387\) 0 0
\(388\) −0.463750 0.803238i −0.0235433 0.0407782i
\(389\) 13.8705 + 24.0244i 0.703261 + 1.21808i 0.967315 + 0.253576i \(0.0816069\pi\)
−0.264054 + 0.964508i \(0.585060\pi\)
\(390\) 0 0
\(391\) −2.50828 −0.126849
\(392\) −11.0607 + 18.1405i −0.558647 + 0.916236i
\(393\) 0 0
\(394\) 6.13984 10.6345i 0.309320 0.535759i
\(395\) 12.7156 + 22.0240i 0.639790 + 1.10815i
\(396\) 0 0
\(397\) −8.61559 + 14.9226i −0.432404 + 0.748946i −0.997080 0.0763669i \(-0.975668\pi\)
0.564676 + 0.825313i \(0.309001\pi\)
\(398\) −33.2500 −1.66667
\(399\) 0 0
\(400\) −10.4292 −0.521459
\(401\) 8.32201 14.4142i 0.415582 0.719808i −0.579908 0.814682i \(-0.696911\pi\)
0.995489 + 0.0948737i \(0.0302447\pi\)
\(402\) 0 0
\(403\) 5.21624 + 9.03479i 0.259839 + 0.450055i
\(404\) −0.289366 + 0.501196i −0.0143965 + 0.0249354i
\(405\) 0 0
\(406\) 3.66989 + 0.0439254i 0.182133 + 0.00217998i
\(407\) 6.28355 0.311464
\(408\) 0 0
\(409\) 6.81689 + 11.8072i 0.337073 + 0.583828i 0.983881 0.178825i \(-0.0572296\pi\)
−0.646807 + 0.762653i \(0.723896\pi\)
\(410\) 0.957237 + 1.65798i 0.0472746 + 0.0818820i
\(411\) 0 0
\(412\) 4.63359 0.228280
\(413\) 2.74978 4.63378i 0.135308 0.228013i
\(414\) 0 0
\(415\) 18.5822 32.1854i 0.912167 1.57992i
\(416\) 1.10838 + 1.91977i 0.0543426 + 0.0941242i
\(417\) 0 0
\(418\) −8.97238 + 15.5406i −0.438853 + 0.760116i
\(419\) 10.8502 0.530066 0.265033 0.964239i \(-0.414617\pi\)
0.265033 + 0.964239i \(0.414617\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 6.34946 10.9976i 0.309087 0.535354i
\(423\) 0 0
\(424\) 10.8039 + 18.7129i 0.524683 + 0.908778i
\(425\) 6.84788 11.8609i 0.332171 0.575337i
\(426\) 0 0
\(427\) 6.35150 + 0.0760220i 0.307371 + 0.00367896i
\(428\) 7.81574 0.377788
\(429\) 0 0
\(430\) 0.604344 + 1.04676i 0.0291441 + 0.0504790i
\(431\) 0.604764 + 1.04748i 0.0291304 + 0.0504554i 0.880223 0.474560i \(-0.157393\pi\)
−0.851093 + 0.525016i \(0.824060\pi\)
\(432\) 0 0
\(433\) −5.56422 −0.267399 −0.133700 0.991022i \(-0.542686\pi\)
−0.133700 + 0.991022i \(0.542686\pi\)
\(434\) −17.1032 30.4597i −0.820979 1.46211i
\(435\) 0 0
\(436\) −0.220375 + 0.381700i −0.0105540 + 0.0182801i
\(437\) −2.18359 3.78209i −0.104455 0.180922i
\(438\) 0 0
\(439\) 9.85960 17.0773i 0.470573 0.815057i −0.528860 0.848709i \(-0.677381\pi\)
0.999434 + 0.0336522i \(0.0107139\pi\)
\(440\) −17.9422 −0.855362
\(441\) 0 0
\(442\) 5.06074 0.240715
\(443\) 11.1155 19.2526i 0.528113 0.914719i −0.471350 0.881946i \(-0.656233\pi\)
0.999463 0.0327726i \(-0.0104337\pi\)
\(444\) 0 0
\(445\) −3.89091 6.73926i −0.184447 0.319471i
\(446\) 11.0716 19.1766i 0.524256 0.908039i
\(447\) 0 0
\(448\) −11.5228 20.5213i −0.544399 0.969542i
\(449\) −18.4579 −0.871082 −0.435541 0.900169i \(-0.643443\pi\)
−0.435541 + 0.900169i \(0.643443\pi\)
\(450\) 0 0
\(451\) 0.530678 + 0.919161i 0.0249886 + 0.0432816i
\(452\) 0.218245 + 0.378012i 0.0102654 + 0.0177802i
\(453\) 0 0
\(454\) −12.0439 −0.565249
\(455\) 7.67901 + 0.0919110i 0.359997 + 0.00430886i
\(456\) 0 0
\(457\) 14.9910 25.9651i 0.701248 1.21460i −0.266781 0.963757i \(-0.585960\pi\)
0.968029 0.250840i \(-0.0807067\pi\)
\(458\) 13.3629 + 23.1452i 0.624408 + 1.08151i
\(459\) 0 0
\(460\) 0.362542 0.627941i 0.0169036 0.0292779i
\(461\) −29.1498 −1.35764 −0.678821 0.734304i \(-0.737509\pi\)
−0.678821 + 0.734304i \(0.737509\pi\)
\(462\) 0 0
\(463\) 1.55900 0.0724530 0.0362265 0.999344i \(-0.488466\pi\)
0.0362265 + 0.999344i \(0.488466\pi\)
\(464\) −1.66872 + 2.89031i −0.0774685 + 0.134179i
\(465\) 0 0
\(466\) −8.97238 15.5406i −0.415637 0.719905i
\(467\) 6.21156 10.7587i 0.287437 0.497855i −0.685760 0.727827i \(-0.740530\pi\)
0.973197 + 0.229972i \(0.0738635\pi\)
\(468\) 0 0
\(469\) −19.8401 + 33.4335i −0.916132 + 1.54382i
\(470\) 38.7402 1.78695
\(471\) 0 0
\(472\) 3.09072 + 5.35328i 0.142262 + 0.246405i
\(473\) 0.335039 + 0.580305i 0.0154051 + 0.0266825i
\(474\) 0 0
\(475\) 23.8458 1.09412
\(476\) 4.21281 + 0.0504237i 0.193094 + 0.00231117i
\(477\) 0 0
\(478\) 10.4587 18.1149i 0.478368 0.828557i
\(479\) 18.0279 + 31.2252i 0.823716 + 1.42672i 0.902897 + 0.429857i \(0.141436\pi\)
−0.0791811 + 0.996860i \(0.525231\pi\)
\(480\) 0 0
\(481\) 1.54268 2.67201i 0.0703404 0.121833i
\(482\) 17.3249 0.789128
\(483\) 0 0
\(484\) 2.72887 0.124040
\(485\) 3.38011 5.85453i 0.153483 0.265840i
\(486\) 0 0
\(487\) −3.65002 6.32202i −0.165398 0.286478i 0.771398 0.636352i \(-0.219558\pi\)
−0.936797 + 0.349874i \(0.886224\pi\)
\(488\) −3.64351 + 6.31074i −0.164934 + 0.285674i
\(489\) 0 0
\(490\) −25.7075 0.615481i −1.16135 0.0278046i
\(491\) −4.49178 −0.202711 −0.101356 0.994850i \(-0.532318\pi\)
−0.101356 + 0.994850i \(0.532318\pi\)
\(492\) 0 0
\(493\) −2.19139 3.79560i −0.0986954 0.170945i
\(494\) 4.40565 + 7.63080i 0.198219 + 0.343326i
\(495\) 0 0
\(496\) 31.7663 1.42635
\(497\) 4.66512 + 8.30829i 0.209259 + 0.372678i
\(498\) 0 0
\(499\) −5.68369 + 9.84443i −0.254437 + 0.440697i −0.964742 0.263196i \(-0.915223\pi\)
0.710306 + 0.703893i \(0.248557\pi\)
\(500\) −0.910235 1.57657i −0.0407069 0.0705065i
\(501\) 0 0
\(502\) 9.27709 16.0684i 0.414057 0.717167i
\(503\) −17.1080 −0.762806 −0.381403 0.924409i \(-0.624559\pi\)
−0.381403 + 0.924409i \(0.624559\pi\)
\(504\) 0 0
\(505\) −4.21818 −0.187706
\(506\) −0.808405 + 1.40020i −0.0359380 + 0.0622464i
\(507\) 0 0
\(508\) 1.03171 + 1.78698i 0.0457749 + 0.0792845i
\(509\) 1.64142 2.84303i 0.0727547 0.126015i −0.827353 0.561682i \(-0.810154\pi\)
0.900108 + 0.435667i \(0.143488\pi\)
\(510\) 0 0
\(511\) −4.01784 + 6.77065i −0.177739 + 0.299516i
\(512\) 25.2340 1.11520
\(513\) 0 0
\(514\) 1.10916 + 1.92113i 0.0489231 + 0.0847373i
\(515\) 16.8863 + 29.2479i 0.744100 + 1.28882i
\(516\) 0 0
\(517\) 21.4770 0.944555
\(518\) −5.27237 + 8.88472i −0.231655 + 0.390372i
\(519\) 0 0
\(520\) −4.40502 + 7.62973i −0.193173 + 0.334586i
\(521\) −2.38530 4.13147i −0.104502 0.181003i 0.809033 0.587764i \(-0.199992\pi\)
−0.913535 + 0.406761i \(0.866658\pi\)
\(522\) 0 0
\(523\) −12.7562 + 22.0944i −0.557789 + 0.966119i 0.439892 + 0.898051i \(0.355017\pi\)
−0.997681 + 0.0680682i \(0.978316\pi\)
\(524\) 4.20803 0.183829
\(525\) 0 0
\(526\) 34.0975 1.48672
\(527\) −20.8580 + 36.1271i −0.908588 + 1.57372i
\(528\) 0 0
\(529\) 11.3033 + 19.5778i 0.491446 + 0.851210i
\(530\) −13.0760 + 22.6483i −0.567986 + 0.983780i
\(531\) 0 0
\(532\) 3.59145 + 6.39616i 0.155709 + 0.277309i
\(533\) 0.521150 0.0225735
\(534\) 0 0
\(535\) 28.4831 + 49.3342i 1.23143 + 2.13290i
\(536\) −22.3001 38.6249i −0.963216 1.66834i
\(537\) 0 0
\(538\) −27.9309 −1.20418
\(539\) −14.2519 0.341214i −0.613871 0.0146971i
\(540\) 0 0
\(541\) 8.25784 14.3030i 0.355032 0.614934i −0.632091 0.774894i \(-0.717803\pi\)
0.987123 + 0.159960i \(0.0511366\pi\)
\(542\) −5.67125 9.82290i −0.243601 0.421930i
\(543\) 0 0
\(544\) −4.43203 + 7.67649i −0.190022 + 0.329127i
\(545\) −3.21247 −0.137607
\(546\) 0 0
\(547\) 23.3317 0.997591 0.498796 0.866720i \(-0.333776\pi\)
0.498796 + 0.866720i \(0.333776\pi\)
\(548\) 1.16917 2.02507i 0.0499446 0.0865066i
\(549\) 0 0
\(550\) −4.41407 7.64539i −0.188216 0.326001i
\(551\) 3.81545 6.60855i 0.162544 0.281534i
\(552\) 0 0
\(553\) −23.1791 0.277434i −0.985676 0.0117977i
\(554\) 9.52909 0.404852
\(555\) 0 0
\(556\) −0.796470 1.37953i −0.0337779 0.0585050i
\(557\) −10.0235 17.3613i −0.424711 0.735621i 0.571682 0.820475i \(-0.306291\pi\)
−0.996393 + 0.0848540i \(0.972958\pi\)
\(558\) 0 0
\(559\) 0.329024 0.0139162
\(560\) 11.9334 20.1096i 0.504279 0.849784i
\(561\) 0 0
\(562\) −18.8425 + 32.6362i −0.794824 + 1.37668i
\(563\) −20.2642 35.0986i −0.854034 1.47923i −0.877539 0.479506i \(-0.840816\pi\)
0.0235047 0.999724i \(-0.492518\pi\)
\(564\) 0 0
\(565\) −1.59072 + 2.75520i −0.0669219 + 0.115912i
\(566\) −0.381519 −0.0160364
\(567\) 0 0
\(568\) −10.9311 −0.458659
\(569\) −10.7252 + 18.5766i −0.449623 + 0.778770i −0.998361 0.0572245i \(-0.981775\pi\)
0.548739 + 0.835994i \(0.315108\pi\)
\(570\) 0 0
\(571\) 5.47793 + 9.48806i 0.229244 + 0.397063i 0.957584 0.288153i \(-0.0930412\pi\)
−0.728340 + 0.685216i \(0.759708\pi\)
\(572\) −0.405516 + 0.702374i −0.0169555 + 0.0293677i
\(573\) 0 0
\(574\) −1.74494 0.0208854i −0.0728323 0.000871740i
\(575\) 2.14849 0.0895982
\(576\) 0 0
\(577\) −17.3708 30.0870i −0.723154 1.25254i −0.959729 0.280927i \(-0.909358\pi\)
0.236575 0.971613i \(-0.423975\pi\)
\(578\) −0.639571 1.10777i −0.0266027 0.0460771i
\(579\) 0 0
\(580\) 1.26696 0.0526076
\(581\) 16.5856 + 29.5380i 0.688086 + 1.22544i
\(582\) 0 0
\(583\) −7.24915 + 12.5559i −0.300229 + 0.520012i
\(584\) −4.51600 7.82195i −0.186874 0.323675i
\(585\) 0 0
\(586\) 12.1796 21.0958i 0.503136 0.871458i
\(587\) 22.8463 0.942967 0.471483 0.881875i \(-0.343719\pi\)
0.471483 + 0.881875i \(0.343719\pi\)
\(588\) 0 0
\(589\) −72.6320 −2.99275
\(590\) −3.74071 + 6.47911i −0.154003 + 0.266741i
\(591\) 0 0
\(592\) −4.69738 8.13610i −0.193061 0.334392i
\(593\) 8.79676 15.2364i 0.361240 0.625686i −0.626925 0.779079i \(-0.715687\pi\)
0.988165 + 0.153394i \(0.0490202\pi\)
\(594\) 0 0
\(595\) 15.0346 + 26.7757i 0.616359 + 1.09770i
\(596\) −4.02433 −0.164843
\(597\) 0 0
\(598\) 0.396945 + 0.687530i 0.0162323 + 0.0281152i
\(599\) 15.5036 + 26.8531i 0.633461 + 1.09719i 0.986839 + 0.161706i \(0.0516997\pi\)
−0.353378 + 0.935481i \(0.614967\pi\)
\(600\) 0 0
\(601\) −1.43754 −0.0586385 −0.0293193 0.999570i \(-0.509334\pi\)
−0.0293193 + 0.999570i \(0.509334\pi\)
\(602\) −1.10165 0.0131858i −0.0449001 0.000537415i
\(603\) 0 0
\(604\) −0.0373796 + 0.0647433i −0.00152095 + 0.00263437i
\(605\) 9.94490 + 17.2251i 0.404318 + 0.700299i
\(606\) 0 0
\(607\) 16.5085 28.5936i 0.670061 1.16058i −0.307826 0.951443i \(-0.599601\pi\)
0.977887 0.209136i \(-0.0670652\pi\)
\(608\) −15.4333 −0.625901
\(609\) 0 0
\(610\) −8.81953 −0.357092
\(611\) 5.27284 9.13283i 0.213316 0.369475i
\(612\) 0 0
\(613\) 21.5829 + 37.3826i 0.871723 + 1.50987i 0.860213 + 0.509935i \(0.170331\pi\)
0.0115102 + 0.999934i \(0.496336\pi\)
\(614\) −2.26404 + 3.92143i −0.0913692 + 0.158256i
\(615\) 0 0
\(616\) 8.34619 14.0646i 0.336278 0.566677i
\(617\) −2.45772 −0.0989441 −0.0494721 0.998776i \(-0.515754\pi\)
−0.0494721 + 0.998776i \(0.515754\pi\)
\(618\) 0 0
\(619\) −18.8894 32.7175i −0.759231 1.31503i −0.943243 0.332102i \(-0.892242\pi\)
0.184013 0.982924i \(-0.441091\pi\)
\(620\) −6.02954 10.4435i −0.242152 0.419420i
\(621\) 0 0
\(622\) −30.1602 −1.20932
\(623\) 7.09271 + 0.0848936i 0.284163 + 0.00340119i
\(624\) 0 0
\(625\) 15.1971 26.3222i 0.607884 1.05289i
\(626\) −11.4420 19.8181i −0.457313 0.792089i
\(627\) 0 0
\(628\) −2.40371 + 4.16334i −0.0959183 + 0.166135i
\(629\) 12.3374 0.491922
\(630\) 0 0
\(631\) −28.4828 −1.13388 −0.566942 0.823758i \(-0.691874\pi\)
−0.566942 + 0.823758i \(0.691874\pi\)
\(632\) 13.2966 23.0303i 0.528909 0.916098i
\(633\) 0 0
\(634\) 17.4326 + 30.1942i 0.692337 + 1.19916i
\(635\) −7.51981 + 13.0247i −0.298415 + 0.516869i
\(636\) 0 0
\(637\) −3.64409 + 5.97667i −0.144384 + 0.236804i
\(638\) −2.82509 −0.111847
\(639\) 0 0
\(640\) 9.90456 + 17.1552i 0.391512 + 0.678119i
\(641\) −13.5961 23.5492i −0.537014 0.930136i −0.999063 0.0432812i \(-0.986219\pi\)
0.462049 0.886854i \(-0.347114\pi\)
\(642\) 0 0
\(643\) −37.1664 −1.46570 −0.732849 0.680391i \(-0.761810\pi\)
−0.732849 + 0.680391i \(0.761810\pi\)
\(644\) 0.323587 + 0.576289i 0.0127511 + 0.0227090i
\(645\) 0 0
\(646\) −17.6167 + 30.5130i −0.693120 + 1.20052i
\(647\) 9.41593 + 16.3089i 0.370178 + 0.641168i 0.989593 0.143896i \(-0.0459632\pi\)
−0.619414 + 0.785064i \(0.712630\pi\)
\(648\) 0 0
\(649\) −2.07380 + 3.59192i −0.0814036 + 0.140995i
\(650\) −4.33482 −0.170026
\(651\) 0 0
\(652\) −5.93910 −0.232593
\(653\) −13.0092 + 22.5326i −0.509090 + 0.881770i 0.490854 + 0.871242i \(0.336685\pi\)
−0.999945 + 0.0105286i \(0.996649\pi\)
\(654\) 0 0
\(655\) 15.3355 + 26.5618i 0.599206 + 1.03786i
\(656\) 0.793435 1.37427i 0.0309784 0.0536562i
\(657\) 0 0
\(658\) −18.0208 + 30.3676i −0.702523 + 1.18385i
\(659\) 33.3339 1.29851 0.649253 0.760573i \(-0.275082\pi\)
0.649253 + 0.760573i \(0.275082\pi\)
\(660\) 0 0
\(661\) −3.14920 5.45458i −0.122490 0.212159i 0.798259 0.602314i \(-0.205755\pi\)
−0.920749 + 0.390156i \(0.872421\pi\)
\(662\) −11.5053 19.9277i −0.447164 0.774511i
\(663\) 0 0
\(664\) −38.8626 −1.50816
\(665\) −27.2852 + 45.9795i −1.05807 + 1.78301i
\(666\) 0 0
\(667\) 0.343769 0.595426i 0.0133108 0.0230550i
\(668\) −1.00687 1.74394i −0.0389568 0.0674752i
\(669\) 0 0
\(670\) 26.9899 46.7479i 1.04271 1.80603i
\(671\) −4.88941 −0.188754
\(672\) 0 0
\(673\) 18.3188 0.706137 0.353068 0.935598i \(-0.385138\pi\)
0.353068 + 0.935598i \(0.385138\pi\)
\(674\) −10.8451 + 18.7842i −0.417736 + 0.723541i
\(675\) 0 0
\(676\) 0.199118 + 0.344882i 0.00765837 + 0.0132647i
\(677\) 12.1696 21.0783i 0.467715 0.810106i −0.531604 0.846993i \(-0.678411\pi\)
0.999319 + 0.0368866i \(0.0117440\pi\)
\(678\) 0 0
\(679\) 3.01692 + 5.37296i 0.115779 + 0.206195i
\(680\) −35.2284 −1.35095
\(681\) 0 0
\(682\) 13.4448 + 23.2871i 0.514829 + 0.891709i
\(683\) 5.88409 + 10.1916i 0.225149 + 0.389969i 0.956364 0.292178i \(-0.0943799\pi\)
−0.731215 + 0.682147i \(0.761047\pi\)
\(684\) 0 0
\(685\) 17.0434 0.651195
\(686\) 12.4408 19.8653i 0.474994 0.758461i
\(687\) 0 0
\(688\) 0.500929 0.867635i 0.0190977 0.0330783i
\(689\) 3.55950 + 6.16523i 0.135606 + 0.234877i
\(690\) 0 0
\(691\) −0.588923 + 1.02004i −0.0224037 + 0.0388043i −0.877010 0.480472i \(-0.840465\pi\)
0.854606 + 0.519277i \(0.173799\pi\)
\(692\) −0.237195 −0.00901679
\(693\) 0 0
\(694\) 28.1835 1.06983
\(695\) 5.80520 10.0549i 0.220204 0.381404i
\(696\) 0 0
\(697\) 1.04195 + 1.80471i 0.0394668 + 0.0683584i
\(698\) 12.6161 21.8517i 0.477525 0.827097i
\(699\) 0 0
\(700\) −3.60852 0.0431908i −0.136389 0.00163246i
\(701\) 31.2867 1.18168 0.590841 0.806788i \(-0.298796\pi\)
0.590841 + 0.806788i \(0.298796\pi\)
\(702\) 0 0
\(703\) 10.7403 + 18.6028i 0.405079 + 0.701617i
\(704\) 9.05804 + 15.6890i 0.341388 + 0.591301i
\(705\) 0 0
\(706\) 29.0016 1.09149
\(707\) 1.96217 3.30654i 0.0737950 0.124355i
\(708\) 0 0
\(709\) −7.68738 + 13.3149i −0.288706 + 0.500053i −0.973501 0.228682i \(-0.926558\pi\)
0.684795 + 0.728735i \(0.259892\pi\)
\(710\) −6.61499 11.4575i −0.248256 0.429992i
\(711\) 0 0
\(712\) −4.06870 + 7.04719i −0.152481 + 0.264105i
\(713\) −6.54409 −0.245078
\(714\) 0 0
\(715\) −5.91133 −0.221071
\(716\) −1.60820 + 2.78549i −0.0601013 + 0.104098i
\(717\) 0 0
\(718\) −17.2322 29.8470i −0.643099 1.11388i
\(719\) −5.57087 + 9.64904i −0.207759 + 0.359848i −0.951008 0.309166i \(-0.899950\pi\)
0.743250 + 0.669014i \(0.233283\pi\)
\(720\) 0 0
\(721\) −30.7819 0.368433i −1.14638 0.0137211i
\(722\) −37.2985 −1.38811
\(723\) 0 0
\(724\) 0.376978 + 0.652945i 0.0140103 + 0.0242665i
\(725\) 1.87706 + 3.25116i 0.0697121 + 0.120745i
\(726\) 0 0
\(727\) −6.24735 −0.231702 −0.115851 0.993267i \(-0.536959\pi\)
−0.115851 + 0.993267i \(0.536959\pi\)
\(728\) −3.93171 7.00214i −0.145719 0.259516i
\(729\) 0 0
\(730\) 5.46575 9.46696i 0.202296 0.350388i
\(731\) 0.657828 + 1.13939i 0.0243307 + 0.0421419i
\(732\) 0 0
\(733\) −15.4834 + 26.8181i −0.571894 + 0.990550i 0.424477 + 0.905439i \(0.360458\pi\)
−0.996371 + 0.0851111i \(0.972875\pi\)
\(734\) 13.7400 0.507153
\(735\) 0 0
\(736\) −1.39053 −0.0512554
\(737\) 14.9628 25.9163i 0.551162 0.954641i
\(738\) 0 0
\(739\) −1.16872 2.02429i −0.0429921 0.0744646i 0.843729 0.536770i \(-0.180356\pi\)
−0.886721 + 0.462305i \(0.847022\pi\)
\(740\) −1.78322 + 3.08862i −0.0655523 + 0.113540i
\(741\) 0 0
\(742\) −11.6710 20.7854i −0.428456 0.763055i
\(743\) −24.3612 −0.893726 −0.446863 0.894603i \(-0.647459\pi\)
−0.446863 + 0.894603i \(0.647459\pi\)
\(744\) 0 0
\(745\) −14.6660 25.4022i −0.537321 0.930666i
\(746\) −1.50066 2.59922i −0.0549430 0.0951641i
\(747\) 0 0
\(748\) −3.24304 −0.118577
\(749\) −51.9216 0.621457i −1.89718 0.0227075i
\(750\) 0 0
\(751\) 6.01266 10.4142i 0.219405 0.380021i −0.735221 0.677827i \(-0.762922\pi\)
0.954626 + 0.297806i \(0.0962550\pi\)
\(752\) −16.0555 27.8089i −0.585483 1.01409i
\(753\) 0 0
\(754\) −0.693593 + 1.20134i −0.0252592 + 0.0437502i
\(755\) −0.544894 −0.0198307
\(756\) 0 0
\(757\) 25.9905 0.944641 0.472321 0.881427i \(-0.343416\pi\)
0.472321 + 0.881427i \(0.343416\pi\)
\(758\) −18.4904 + 32.0263i −0.671600 + 1.16325i
\(759\) 0 0
\(760\) −30.6682 53.1189i −1.11245 1.92683i
\(761\) 6.66350 11.5415i 0.241552 0.418380i −0.719605 0.694384i \(-0.755677\pi\)
0.961156 + 0.276004i \(0.0890103\pi\)
\(762\) 0 0
\(763\) 1.49435 2.51819i 0.0540990 0.0911647i
\(764\) 1.47416 0.0533334
\(765\) 0 0
\(766\) 1.94014 + 3.36043i 0.0701002 + 0.121417i
\(767\) 1.01828 + 1.76372i 0.0367680 + 0.0636841i
\(768\) 0 0
\(769\) 9.24486 0.333378 0.166689 0.986010i \(-0.446692\pi\)
0.166689 + 0.986010i \(0.446692\pi\)
\(770\) 19.7926 + 0.236900i 0.713275 + 0.00853728i
\(771\) 0 0
\(772\) 2.70550 4.68607i 0.0973732 0.168655i
\(773\) −5.07097 8.78317i −0.182390 0.315909i 0.760304 0.649568i \(-0.225050\pi\)
−0.942694 + 0.333659i \(0.891717\pi\)
\(774\) 0 0
\(775\) 17.8661 30.9450i 0.641768 1.11158i
\(776\) −7.06912 −0.253766
\(777\) 0 0
\(778\) 35.1092 1.25873
\(779\) −1.81415 + 3.14220i −0.0649987 + 0.112581i
\(780\) 0 0
\(781\) −3.66725 6.35186i −0.131225 0.227288i
\(782\) −1.58725 + 2.74920i −0.0567600 + 0.0983112i
\(783\) 0 0
\(784\) 10.2124 + 18.7088i 0.364729 + 0.668170i
\(785\) −35.0396 −1.25062
\(786\) 0 0
\(787\) −22.6411 39.2156i −0.807070 1.39789i −0.914885 0.403715i \(-0.867719\pi\)
0.107815 0.994171i \(-0.465614\pi\)
\(788\) 1.93195 + 3.34624i 0.0688230 + 0.119205i
\(789\) 0 0
\(790\) 32.1859 1.14512
\(791\) −1.41979 2.52857i −0.0504821 0.0899056i
\(792\) 0 0
\(793\) −1.20041 + 2.07917i −0.0426277 + 0.0738334i
\(794\) 10.9040 + 18.8862i 0.386967 + 0.670247i
\(795\) 0 0
\(796\) 5.23121 9.06072i 0.185415 0.321149i
\(797\) −27.0784 −0.959165 −0.479583 0.877497i \(-0.659212\pi\)
−0.479583 + 0.877497i \(0.659212\pi\)
\(798\) 0 0
\(799\) 42.1686 1.49182
\(800\) 3.79629 6.57536i 0.134219 0.232474i
\(801\) 0 0
\(802\) −10.5324 18.2427i −0.371912 0.644171i
\(803\) 3.03013 5.24834i 0.106931 0.185210i
\(804\) 0 0
\(805\) −2.45837 + 4.14272i −0.0866463 + 0.146012i
\(806\) 13.2034 0.465071
\(807\) 0 0
\(808\) 2.20546 + 3.81996i 0.0775877 + 0.134386i
\(809\) −12.8899 22.3260i −0.453185 0.784939i 0.545397 0.838178i \(-0.316379\pi\)
−0.998582 + 0.0532388i \(0.983046\pi\)
\(810\) 0 0
\(811\) −25.7829 −0.905362 −0.452681 0.891673i \(-0.649532\pi\)
−0.452681 + 0.891673i \(0.649532\pi\)
\(812\) −0.589352 + 0.993144i −0.0206822 + 0.0348525i
\(813\) 0 0
\(814\) 3.97626 6.88708i 0.139368 0.241392i
\(815\) −21.6440 37.4886i −0.758158 1.31317i
\(816\) 0 0
\(817\) −1.14535 + 1.98380i −0.0400707 + 0.0694045i
\(818\) 17.2550 0.603308
\(819\) 0 0
\(820\) −0.602407 −0.0210370
\(821\) −0.855366 + 1.48154i −0.0298525 + 0.0517060i −0.880566 0.473924i \(-0.842837\pi\)
0.850713 + 0.525630i \(0.176170\pi\)
\(822\) 0 0
\(823\) 20.1887 + 34.9678i 0.703733 + 1.21890i 0.967147 + 0.254218i \(0.0818181\pi\)
−0.263414 + 0.964683i \(0.584849\pi\)
\(824\) 17.6579 30.5844i 0.615142 1.06546i
\(825\) 0 0
\(826\) −3.33878 5.94616i −0.116171 0.206893i
\(827\) −19.5698 −0.680509 −0.340254 0.940333i \(-0.610513\pi\)
−0.340254 + 0.940333i \(0.610513\pi\)
\(828\) 0 0
\(829\) −20.7871 36.0043i −0.721966 1.25048i −0.960211 0.279277i \(-0.909905\pi\)
0.238244 0.971205i \(-0.423428\pi\)
\(830\) −23.5178 40.7341i −0.816316 1.41390i
\(831\) 0 0
\(832\) 8.89542 0.308393
\(833\) −27.9826 0.669951i −0.969540 0.0232124i
\(834\) 0 0
\(835\) 7.33870 12.7110i 0.253966 0.439882i
\(836\) −2.82324 4.89000i −0.0976438 0.169124i
\(837\) 0 0
\(838\) 6.86604 11.8923i 0.237183 0.410814i
\(839\) −45.8480 −1.58285 −0.791425 0.611266i \(-0.790660\pi\)
−0.791425 + 0.611266i \(0.790660\pi\)
\(840\) 0 0
\(841\) −27.7986 −0.958574
\(842\) −6.32804 + 10.9605i −0.218079 + 0.377723i
\(843\) 0 0
\(844\) 1.99791 + 3.46049i 0.0687710 + 0.119115i
\(845\) −1.45130 + 2.51373i −0.0499262 + 0.0864748i
\(846\) 0 0
\(847\) −18.1285 0.216982i −0.622902 0.00745559i
\(848\) 21.6769 0.744388
\(849\) 0 0
\(850\) −8.66674 15.0112i −0.297267 0.514881i
\(851\) 0.967695 + 1.67610i 0.0331722 + 0.0574559i
\(852\) 0 0
\(853\) 40.0236 1.37038 0.685191 0.728364i \(-0.259719\pi\)
0.685191 + 0.728364i \(0.259719\pi\)
\(854\) 4.10258 6.91345i 0.140387 0.236573i
\(855\) 0 0
\(856\) 29.7846 51.5884i 1.01802 1.76326i
\(857\) 16.4351 + 28.4664i 0.561412 + 0.972395i 0.997374 + 0.0724294i \(0.0230752\pi\)
−0.435961 + 0.899966i \(0.643591\pi\)
\(858\) 0 0
\(859\) 17.0252 29.4885i 0.580891 1.00613i −0.414483 0.910057i \(-0.636037\pi\)
0.995374 0.0960762i \(-0.0306292\pi\)
\(860\) −0.380325 −0.0129690
\(861\) 0 0
\(862\) 1.53079 0.0521388
\(863\) −7.03208 + 12.1799i −0.239375 + 0.414609i −0.960535 0.278159i \(-0.910276\pi\)
0.721160 + 0.692768i \(0.243609\pi\)
\(864\) 0 0
\(865\) −0.864415 1.49721i −0.0293910 0.0509067i
\(866\) −3.52106 + 6.09866i −0.119651 + 0.207241i
\(867\) 0 0
\(868\) 10.9912 + 0.131555i 0.373066 + 0.00446527i
\(869\) 17.8434 0.605295
\(870\) 0 0
\(871\) −7.34709 12.7255i −0.248947 0.431188i
\(872\) 1.67963 + 2.90920i 0.0568794 + 0.0985180i
\(873\) 0 0
\(874\) −5.52715 −0.186959
\(875\) 5.92153 + 10.5459i 0.200184 + 0.356516i
\(876\) 0 0
\(877\) −25.5335 + 44.2252i −0.862204 + 1.49338i 0.00759373 + 0.999971i \(0.497583\pi\)
−0.869797 + 0.493409i \(0.835751\pi\)
\(878\) −12.4784 21.6132i −0.421125 0.729411i
\(879\) 0 0
\(880\) −8.99982 + 15.5881i −0.303384 + 0.525476i
\(881\) 18.4203 0.620597 0.310298 0.950639i \(-0.399571\pi\)
0.310298 + 0.950639i \(0.399571\pi\)
\(882\) 0 0
\(883\) 0.126678 0.00426305 0.00213153 0.999998i \(-0.499322\pi\)
0.00213153 + 0.999998i \(0.499322\pi\)
\(884\) −0.796204 + 1.37907i −0.0267792 + 0.0463830i
\(885\) 0 0
\(886\) −14.0679 24.3663i −0.472619 0.818601i
\(887\) 1.93735 3.35559i 0.0650498 0.112670i −0.831666 0.555276i \(-0.812613\pi\)
0.896716 + 0.442606i \(0.145946\pi\)
\(888\) 0 0
\(889\) −6.71181 11.9533i −0.225107 0.400902i
\(890\) −9.84874 −0.330131
\(891\) 0 0
\(892\) 3.48378 + 6.03409i 0.116646 + 0.202036i
\(893\) 36.7100 + 63.5837i 1.22845 + 2.12775i
\(894\) 0 0
\(895\) −23.4433 −0.783622
\(896\) −18.0549 0.216102i −0.603173 0.00721945i
\(897\) 0 0
\(898\) −11.6802 + 20.2308i −0.389775 + 0.675109i
\(899\) −5.71733 9.90270i −0.190684 0.330274i
\(900\) 0 0
\(901\) −14.2332 + 24.6527i −0.474178 + 0.821300i
\(902\) 1.34326 0.0447257
\(903\) 0 0
\(904\) 3.32680 0.110648
\(905\) −2.74766 + 4.75909i −0.0913355 + 0.158198i
\(906\) 0 0
\(907\) 23.3871 + 40.5076i 0.776555 + 1.34503i 0.933916 + 0.357491i \(0.116368\pi\)
−0.157362 + 0.987541i \(0.550299\pi\)
\(908\) 1.89486 3.28200i 0.0628832 0.108917i
\(909\) 0 0
\(910\) 4.96005 8.35841i 0.164424 0.277079i
\(911\) −5.93675 −0.196693 −0.0983467 0.995152i \(-0.531355\pi\)
−0.0983467 + 0.995152i \(0.531355\pi\)
\(912\) 0 0
\(913\) −13.0379 22.5824i −0.431493 0.747368i
\(914\) −18.9727 32.8617i −0.627561 1.08697i
\(915\) 0 0
\(916\) −8.40952 −0.277858
\(917\) −27.9549 0.334595i −0.923151 0.0110493i
\(918\) 0 0
\(919\) 4.29351 7.43657i 0.141630 0.245310i −0.786481 0.617615i \(-0.788099\pi\)
0.928110 + 0.372305i \(0.121432\pi\)
\(920\) −2.76318 4.78597i −0.0910995 0.157789i
\(921\) 0 0
\(922\) −18.4461 + 31.9496i −0.607490 + 1.05220i
\(923\) −3.60141 −0.118542
\(924\) 0 0
\(925\) −10.5677 −0.347463
\(926\) 0.986543 1.70874i 0.0324198 0.0561528i
\(927\) 0 0
\(928\) −1.21485 2.10418i −0.0398794 0.0690732i
\(929\) −4.22972 + 7.32610i −0.138773 + 0.240361i −0.927032 0.374981i \(-0.877649\pi\)
0.788260 + 0.615343i \(0.210982\pi\)
\(930\) 0 0
\(931\) −23.3502 42.7766i −0.765271 1.40195i
\(932\) 5.64648 0.184957
\(933\) 0 0
\(934\) −7.86141 13.6164i −0.257233 0.445541i
\(935\) −11.8187 20.4706i −0.386513 0.669460i
\(936\) 0 0
\(937\) −33.3596 −1.08981 −0.544905 0.838498i \(-0.683434\pi\)
−0.544905 + 0.838498i \(0.683434\pi\)
\(938\) 24.0899 + 42.9026i 0.786562 + 1.40082i
\(939\) 0 0
\(940\) −6.09497 + 10.5568i −0.198796 + 0.344325i
\(941\) −6.70187 11.6080i −0.218475 0.378409i 0.735867 0.677126i \(-0.236775\pi\)
−0.954342 + 0.298717i \(0.903441\pi\)
\(942\) 0 0
\(943\) −0.163454 + 0.283110i −0.00532278 + 0.00921933i
\(944\) 6.20121 0.201832
\(945\) 0 0
\(946\) 0.848057 0.0275727
\(947\) 21.5397 37.3078i 0.699946 1.21234i −0.268539 0.963269i \(-0.586541\pi\)
0.968485 0.249073i \(-0.0801259\pi\)
\(948\) 0 0
\(949\) −1.48786 2.57706i −0.0482981 0.0836548i
\(950\) 15.0897 26.1362i 0.489575 0.847969i
\(951\) 0 0
\(952\) 16.3872 27.6149i 0.531113 0.895003i
\(953\) −16.7332 −0.542040 −0.271020 0.962574i \(-0.587361\pi\)
−0.271020 + 0.962574i \(0.587361\pi\)
\(954\) 0 0
\(955\) 5.37234 + 9.30517i 0.173845 + 0.301108i
\(956\) 3.29091 + 5.70002i 0.106436 + 0.184352i
\(957\) 0 0
\(958\) 45.6325 1.47432
\(959\) −7.92809 + 13.3600i −0.256011 + 0.431417i
\(960\) 0 0
\(961\) −38.9183 + 67.4085i −1.25543 + 2.17447i
\(962\) −1.95243 3.38172i −0.0629490 0.109031i
\(963\) 0 0
\(964\) −2.72572 + 4.72109i −0.0877896 + 0.152056i
\(965\) 39.4390 1.26959
\(966\) 0 0
\(967\) 44.7594 1.43937 0.719683 0.694303i \(-0.244287\pi\)
0.719683 + 0.694303i \(0.244287\pi\)
\(968\) 10.3993 18.0121i 0.334246 0.578932i
\(969\) 0 0
\(970\) −4.27790 7.40954i −0.137355 0.237906i
\(971\) −2.10129 + 3.63955i −0.0674337 + 0.116799i −0.897771 0.440463i \(-0.854814\pi\)
0.830337 + 0.557261i \(0.188148\pi\)
\(972\) 0 0
\(973\) 5.18143 + 9.22783i 0.166109 + 0.295830i
\(974\) −9.23899 −0.296036
\(975\) 0 0
\(976\) 3.65517 + 6.33093i 0.116999 + 0.202648i
\(977\) −12.8449 22.2481i −0.410946 0.711779i 0.584048 0.811719i \(-0.301468\pi\)
−0.994993 + 0.0999403i \(0.968135\pi\)
\(978\) 0 0
\(979\) −5.45999 −0.174502
\(980\) 4.21227 6.90854i 0.134556 0.220685i
\(981\) 0 0
\(982\) −2.84242 + 4.92321i −0.0907051 + 0.157106i
\(983\) −15.9122 27.5607i −0.507520 0.879051i −0.999962 0.00870538i \(-0.997229\pi\)
0.492442 0.870345i \(-0.336104\pi\)
\(984\) 0 0
\(985\) −14.0814 + 24.3896i −0.448669 + 0.777118i
\(986\) −5.54689 −0.176649
\(987\) 0 0
\(988\) −2.77255 −0.0882067
\(989\) −0.103195 + 0.178739i −0.00328141 + 0.00568358i
\(990\) 0 0
\(991\) −4.73739 8.20540i −0.150488 0.260653i 0.780919 0.624632i \(-0.214751\pi\)
−0.931407 + 0.363979i \(0.881418\pi\)
\(992\) −11.5631 + 20.0279i −0.367129 + 0.635887i
\(993\) 0 0
\(994\) 12.0584 + 0.144329i 0.382469 + 0.00457783i
\(995\) 76.2570 2.41751
\(996\) 0 0
\(997\) −10.9755 19.0102i −0.347599 0.602059i 0.638224 0.769851i \(-0.279670\pi\)
−0.985822 + 0.167792i \(0.946336\pi\)
\(998\) 7.19332 + 12.4592i 0.227701 + 0.394389i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 819.2.j.h.352.3 10
3.2 odd 2 91.2.e.c.79.3 yes 10
7.2 even 3 5733.2.a.bl.1.3 5
7.4 even 3 inner 819.2.j.h.235.3 10
7.5 odd 6 5733.2.a.bm.1.3 5
12.11 even 2 1456.2.r.p.625.1 10
21.2 odd 6 637.2.a.l.1.3 5
21.5 even 6 637.2.a.k.1.3 5
21.11 odd 6 91.2.e.c.53.3 10
21.17 even 6 637.2.e.m.508.3 10
21.20 even 2 637.2.e.m.79.3 10
39.38 odd 2 1183.2.e.f.170.3 10
84.11 even 6 1456.2.r.p.417.1 10
273.116 odd 6 1183.2.e.f.508.3 10
273.194 even 6 8281.2.a.bx.1.3 5
273.233 odd 6 8281.2.a.bw.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.3 10 21.11 odd 6
91.2.e.c.79.3 yes 10 3.2 odd 2
637.2.a.k.1.3 5 21.5 even 6
637.2.a.l.1.3 5 21.2 odd 6
637.2.e.m.79.3 10 21.20 even 2
637.2.e.m.508.3 10 21.17 even 6
819.2.j.h.235.3 10 7.4 even 3 inner
819.2.j.h.352.3 10 1.1 even 1 trivial
1183.2.e.f.170.3 10 39.38 odd 2
1183.2.e.f.508.3 10 273.116 odd 6
1456.2.r.p.417.1 10 84.11 even 6
1456.2.r.p.625.1 10 12.11 even 2
5733.2.a.bl.1.3 5 7.2 even 3
5733.2.a.bm.1.3 5 7.5 odd 6
8281.2.a.bw.1.3 5 273.233 odd 6
8281.2.a.bx.1.3 5 273.194 even 6