Properties

Label 460.2.e.a.91.5
Level $460$
Weight $2$
Character 460.91
Analytic conductor $3.673$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(91,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.e (of order \(2\), degree \(1\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: 16.0.7465802011608416256.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.5
Root \(1.37379 - 0.335728i\) of defining polynomial
Character \(\chi\) \(=\) 460.91
Dual form 460.2.e.a.91.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.637910 - 1.26217i) q^{2} +2.87247i q^{3} +(-1.18614 + 1.61030i) q^{4} -1.00000i q^{5} +(3.62554 - 1.83238i) q^{6} -2.68161 q^{7} +(2.78912 + 0.469882i) q^{8} -5.25109 q^{9} +O(q^{10})\) \(q+(-0.637910 - 1.26217i) q^{2} +2.87247i q^{3} +(-1.18614 + 1.61030i) q^{4} -1.00000i q^{5} +(3.62554 - 1.83238i) q^{6} -2.68161 q^{7} +(2.78912 + 0.469882i) q^{8} -5.25109 q^{9} +(-1.26217 + 0.637910i) q^{10} -4.89140 q^{11} +(-4.62554 - 3.40715i) q^{12} +0.727591 q^{13} +(1.71063 + 3.38465i) q^{14} +2.87247 q^{15} +(-1.18614 - 3.82009i) q^{16} -6.34755i q^{17} +(3.34972 + 6.62776i) q^{18} +2.68161 q^{19} +(1.61030 + 1.18614i) q^{20} -7.70285i q^{21} +(3.12027 + 6.17377i) q^{22} +(2.20979 - 4.25639i) q^{23} +(-1.34972 + 8.01167i) q^{24} -1.00000 q^{25} +(-0.464138 - 0.918342i) q^{26} -6.46618i q^{27} +(3.18077 - 4.31821i) q^{28} -4.27582 q^{29} +(-1.83238 - 3.62554i) q^{30} +6.13645i q^{31} +(-4.06494 + 3.93398i) q^{32} -14.0504i q^{33} +(-8.01167 + 4.04917i) q^{34} +2.68161i q^{35} +(6.22853 - 8.45583i) q^{36} -3.87539i q^{37} +(-1.71063 - 3.38465i) q^{38} +2.08998i q^{39} +(0.469882 - 2.78912i) q^{40} -8.07172 q^{41} +(-9.72230 + 4.91373i) q^{42} -11.1319 q^{43} +(5.80189 - 7.87663i) q^{44} +5.25109i q^{45} +(-6.78193 - 0.0739292i) q^{46} -9.80928i q^{47} +(10.9731 - 3.40715i) q^{48} +0.191051 q^{49} +(0.637910 + 1.26217i) q^{50} +18.2331 q^{51} +(-0.863025 + 1.17164i) q^{52} +11.1565i q^{53} +(-8.16141 + 4.12484i) q^{54} +4.89140i q^{55} +(-7.47935 - 1.26004i) q^{56} +7.70285i q^{57} +(2.72759 + 5.39681i) q^{58} -1.87953i q^{59} +(-3.40715 + 4.62554i) q^{60} +6.93356i q^{61} +(7.74524 - 3.91451i) q^{62} +14.0814 q^{63} +(7.55842 + 2.62112i) q^{64} -0.727591i q^{65} +(-17.7340 + 8.96290i) q^{66} -10.5224 q^{67} +(10.2215 + 7.52908i) q^{68} +(12.2263 + 6.34755i) q^{69} +(3.38465 - 1.71063i) q^{70} +7.24866i q^{71} +(-14.6459 - 2.46739i) q^{72} +7.90882 q^{73} +(-4.89140 + 2.47215i) q^{74} -2.87247i q^{75} +(-3.18077 + 4.31821i) q^{76} +13.1168 q^{77} +(2.63791 - 1.33322i) q^{78} -3.67993 q^{79} +(-3.82009 + 1.18614i) q^{80} +2.82064 q^{81} +(5.14904 + 10.1879i) q^{82} +4.75372 q^{83} +(12.4039 + 9.13667i) q^{84} -6.34755 q^{85} +(7.10119 + 14.0504i) q^{86} -12.2822i q^{87} +(-13.6427 - 2.29838i) q^{88} -8.12461i q^{89} +(6.62776 - 3.34972i) q^{90} -1.95112 q^{91} +(4.23295 + 8.60710i) q^{92} -17.6268 q^{93} +(-12.3810 + 6.25744i) q^{94} -2.68161i q^{95} +(-11.3003 - 11.6764i) q^{96} -2.68434i q^{97} +(-0.121873 - 0.241138i) q^{98} +25.6852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9} - 30 q^{12} + 4 q^{13} + 4 q^{16} + 30 q^{18} + 2 q^{24} - 16 q^{25} - 54 q^{26} - 48 q^{29} + 34 q^{36} - 36 q^{41} - 40 q^{46} + 18 q^{48} + 68 q^{49} + 34 q^{52} - 40 q^{54} + 36 q^{58} + 6 q^{62} + 52 q^{64} + 40 q^{69} + 42 q^{70} - 78 q^{72} + 8 q^{73} + 72 q^{77} + 32 q^{78} + 40 q^{81} - 42 q^{82} + 12 q^{85} - 120 q^{93} + 20 q^{94} - 22 q^{96} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.637910 1.26217i −0.451071 0.892488i
\(3\) 2.87247i 1.65842i 0.558936 + 0.829211i \(0.311210\pi\)
−0.558936 + 0.829211i \(0.688790\pi\)
\(4\) −1.18614 + 1.61030i −0.593070 + 0.805151i
\(5\) 1.00000i 0.447214i
\(6\) 3.62554 1.83238i 1.48012 0.748065i
\(7\) −2.68161 −1.01355 −0.506777 0.862077i \(-0.669163\pi\)
−0.506777 + 0.862077i \(0.669163\pi\)
\(8\) 2.78912 + 0.469882i 0.986104 + 0.166128i
\(9\) −5.25109 −1.75036
\(10\) −1.26217 + 0.637910i −0.399133 + 0.201725i
\(11\) −4.89140 −1.47481 −0.737406 0.675449i \(-0.763950\pi\)
−0.737406 + 0.675449i \(0.763950\pi\)
\(12\) −4.62554 3.40715i −1.33528 0.983561i
\(13\) 0.727591 0.201797 0.100899 0.994897i \(-0.467828\pi\)
0.100899 + 0.994897i \(0.467828\pi\)
\(14\) 1.71063 + 3.38465i 0.457185 + 0.904586i
\(15\) 2.87247 0.741669
\(16\) −1.18614 3.82009i −0.296535 0.955022i
\(17\) 6.34755i 1.53951i −0.638342 0.769753i \(-0.720379\pi\)
0.638342 0.769753i \(-0.279621\pi\)
\(18\) 3.34972 + 6.62776i 0.789537 + 1.56218i
\(19\) 2.68161 0.615204 0.307602 0.951515i \(-0.400473\pi\)
0.307602 + 0.951515i \(0.400473\pi\)
\(20\) 1.61030 + 1.18614i 0.360074 + 0.265229i
\(21\) 7.70285i 1.68090i
\(22\) 3.12027 + 6.17377i 0.665245 + 1.31625i
\(23\) 2.20979 4.25639i 0.460772 0.887518i
\(24\) −1.34972 + 8.01167i −0.275511 + 1.63538i
\(25\) −1.00000 −0.200000
\(26\) −0.464138 0.918342i −0.0910249 0.180102i
\(27\) 6.46618i 1.24442i
\(28\) 3.18077 4.31821i 0.601109 0.816064i
\(29\) −4.27582 −0.794000 −0.397000 0.917819i \(-0.629949\pi\)
−0.397000 + 0.917819i \(0.629949\pi\)
\(30\) −1.83238 3.62554i −0.334545 0.661930i
\(31\) 6.13645i 1.10214i 0.834459 + 0.551070i \(0.185780\pi\)
−0.834459 + 0.551070i \(0.814220\pi\)
\(32\) −4.06494 + 3.93398i −0.718587 + 0.695437i
\(33\) 14.0504i 2.44586i
\(34\) −8.01167 + 4.04917i −1.37399 + 0.694426i
\(35\) 2.68161i 0.453275i
\(36\) 6.22853 8.45583i 1.03809 1.40930i
\(37\) 3.87539i 0.637111i −0.947904 0.318555i \(-0.896802\pi\)
0.947904 0.318555i \(-0.103198\pi\)
\(38\) −1.71063 3.38465i −0.277501 0.549063i
\(39\) 2.08998i 0.334665i
\(40\) 0.469882 2.78912i 0.0742949 0.440999i
\(41\) −8.07172 −1.26059 −0.630296 0.776355i \(-0.717066\pi\)
−0.630296 + 0.776355i \(0.717066\pi\)
\(42\) −9.72230 + 4.91373i −1.50018 + 0.758205i
\(43\) −11.1319 −1.69761 −0.848803 0.528709i \(-0.822676\pi\)
−0.848803 + 0.528709i \(0.822676\pi\)
\(44\) 5.80189 7.87663i 0.874668 1.18745i
\(45\) 5.25109i 0.782786i
\(46\) −6.78193 0.0739292i −0.999941 0.0109003i
\(47\) 9.80928i 1.43083i −0.698699 0.715416i \(-0.746237\pi\)
0.698699 0.715416i \(-0.253763\pi\)
\(48\) 10.9731 3.40715i 1.58383 0.491780i
\(49\) 0.191051 0.0272930
\(50\) 0.637910 + 1.26217i 0.0902142 + 0.178498i
\(51\) 18.2331 2.55315
\(52\) −0.863025 + 1.17164i −0.119680 + 0.162477i
\(53\) 11.1565i 1.53246i 0.642565 + 0.766231i \(0.277870\pi\)
−0.642565 + 0.766231i \(0.722130\pi\)
\(54\) −8.16141 + 4.12484i −1.11063 + 0.561320i
\(55\) 4.89140i 0.659556i
\(56\) −7.47935 1.26004i −0.999470 0.168380i
\(57\) 7.70285i 1.02027i
\(58\) 2.72759 + 5.39681i 0.358150 + 0.708636i
\(59\) 1.87953i 0.244694i −0.992487 0.122347i \(-0.960958\pi\)
0.992487 0.122347i \(-0.0390420\pi\)
\(60\) −3.40715 + 4.62554i −0.439862 + 0.597155i
\(61\) 6.93356i 0.887751i 0.896088 + 0.443875i \(0.146397\pi\)
−0.896088 + 0.443875i \(0.853603\pi\)
\(62\) 7.74524 3.91451i 0.983646 0.497143i
\(63\) 14.0814 1.77409
\(64\) 7.55842 + 2.62112i 0.944803 + 0.327640i
\(65\) 0.727591i 0.0902465i
\(66\) −17.7340 + 8.96290i −2.18290 + 1.10326i
\(67\) −10.5224 −1.28552 −0.642761 0.766067i \(-0.722211\pi\)
−0.642761 + 0.766067i \(0.722211\pi\)
\(68\) 10.2215 + 7.52908i 1.23953 + 0.913035i
\(69\) 12.2263 + 6.34755i 1.47188 + 0.764155i
\(70\) 3.38465 1.71063i 0.404543 0.204459i
\(71\) 7.24866i 0.860258i 0.902767 + 0.430129i \(0.141532\pi\)
−0.902767 + 0.430129i \(0.858468\pi\)
\(72\) −14.6459 2.46739i −1.72604 0.290785i
\(73\) 7.90882 0.925657 0.462829 0.886448i \(-0.346834\pi\)
0.462829 + 0.886448i \(0.346834\pi\)
\(74\) −4.89140 + 2.47215i −0.568614 + 0.287382i
\(75\) 2.87247i 0.331684i
\(76\) −3.18077 + 4.31821i −0.364859 + 0.495332i
\(77\) 13.1168 1.49480
\(78\) 2.63791 1.33322i 0.298685 0.150958i
\(79\) −3.67993 −0.414024 −0.207012 0.978338i \(-0.566374\pi\)
−0.207012 + 0.978338i \(0.566374\pi\)
\(80\) −3.82009 + 1.18614i −0.427099 + 0.132615i
\(81\) 2.82064 0.313404
\(82\) 5.14904 + 10.1879i 0.568616 + 1.12506i
\(83\) 4.75372 0.521789 0.260894 0.965367i \(-0.415983\pi\)
0.260894 + 0.965367i \(0.415983\pi\)
\(84\) 12.4039 + 9.13667i 1.35338 + 0.996892i
\(85\) −6.34755 −0.688488
\(86\) 7.10119 + 14.0504i 0.765741 + 1.51509i
\(87\) 12.2822i 1.31679i
\(88\) −13.6427 2.29838i −1.45432 0.245008i
\(89\) 8.12461i 0.861207i −0.902541 0.430603i \(-0.858301\pi\)
0.902541 0.430603i \(-0.141699\pi\)
\(90\) 6.62776 3.34972i 0.698627 0.353092i
\(91\) −1.95112 −0.204533
\(92\) 4.23295 + 8.60710i 0.441316 + 0.897352i
\(93\) −17.6268 −1.82781
\(94\) −12.3810 + 6.25744i −1.27700 + 0.645406i
\(95\) 2.68161i 0.275128i
\(96\) −11.3003 11.6764i −1.15333 1.19172i
\(97\) 2.68434i 0.272554i −0.990671 0.136277i \(-0.956486\pi\)
0.990671 0.136277i \(-0.0435137\pi\)
\(98\) −0.121873 0.241138i −0.0123111 0.0243587i
\(99\) 25.6852 2.58146
\(100\) 1.18614 1.61030i 0.118614 0.161030i
\(101\) 1.53860 0.153096 0.0765480 0.997066i \(-0.475610\pi\)
0.0765480 + 0.997066i \(0.475610\pi\)
\(102\) −11.6311 23.0133i −1.15165 2.27866i
\(103\) −18.1121 −1.78464 −0.892321 0.451401i \(-0.850924\pi\)
−0.892321 + 0.451401i \(0.850924\pi\)
\(104\) 2.02934 + 0.341882i 0.198993 + 0.0335243i
\(105\) −7.70285 −0.751722
\(106\) 14.0814 7.11684i 1.36770 0.691249i
\(107\) 11.1319 1.07617 0.538083 0.842892i \(-0.319149\pi\)
0.538083 + 0.842892i \(0.319149\pi\)
\(108\) 10.4125 + 7.66979i 1.00194 + 0.738026i
\(109\) 10.6447i 1.01958i 0.860300 + 0.509788i \(0.170276\pi\)
−0.860300 + 0.509788i \(0.829724\pi\)
\(110\) 6.17377 3.12027i 0.588646 0.297507i
\(111\) 11.1319 1.05660
\(112\) 3.18077 + 10.2440i 0.300555 + 0.967967i
\(113\) 5.41399i 0.509305i −0.967033 0.254653i \(-0.918039\pi\)
0.967033 0.254653i \(-0.0819611\pi\)
\(114\) 9.72230 4.91373i 0.910577 0.460213i
\(115\) −4.25639 2.20979i −0.396910 0.206064i
\(116\) 5.07172 6.88536i 0.470898 0.639290i
\(117\) −3.82064 −0.353218
\(118\) −2.37228 + 1.19897i −0.218386 + 0.110374i
\(119\) 17.0217i 1.56037i
\(120\) 8.01167 + 1.34972i 0.731362 + 0.123212i
\(121\) 12.9258 1.17507
\(122\) 8.75132 4.42299i 0.792307 0.400439i
\(123\) 23.1858i 2.09059i
\(124\) −9.88154 7.27870i −0.887388 0.653646i
\(125\) 1.00000i 0.0894427i
\(126\) −8.98266 17.7731i −0.800239 1.58335i
\(127\) 3.05353i 0.270957i 0.990780 + 0.135478i \(0.0432571\pi\)
−0.990780 + 0.135478i \(0.956743\pi\)
\(128\) −1.51330 11.2120i −0.133758 0.991014i
\(129\) 31.9762i 2.81535i
\(130\) −0.918342 + 0.464138i −0.0805439 + 0.0407076i
\(131\) 3.09691i 0.270578i 0.990806 + 0.135289i \(0.0431963\pi\)
−0.990806 + 0.135289i \(0.956804\pi\)
\(132\) 22.6254 + 16.6658i 1.96929 + 1.45057i
\(133\) −7.19105 −0.623543
\(134\) 6.71238 + 13.2811i 0.579861 + 1.14731i
\(135\) −6.46618 −0.556520
\(136\) 2.98260 17.7041i 0.255756 1.51811i
\(137\) 5.92579i 0.506275i 0.967430 + 0.253137i \(0.0814625\pi\)
−0.967430 + 0.253137i \(0.918538\pi\)
\(138\) 0.212359 19.4809i 0.0180772 1.65832i
\(139\) 3.32470i 0.281997i 0.990010 + 0.140999i \(0.0450313\pi\)
−0.990010 + 0.140999i \(0.954969\pi\)
\(140\) −4.31821 3.18077i −0.364955 0.268824i
\(141\) 28.1769 2.37292
\(142\) 9.14904 4.62400i 0.767770 0.388037i
\(143\) −3.55894 −0.297613
\(144\) 6.22853 + 20.0596i 0.519044 + 1.67163i
\(145\) 4.27582i 0.355088i
\(146\) −5.04512 9.98227i −0.417537 0.826138i
\(147\) 0.548788i 0.0452633i
\(148\) 6.24055 + 4.59676i 0.512970 + 0.377851i
\(149\) 14.4242i 1.18168i 0.806789 + 0.590839i \(0.201203\pi\)
−0.806789 + 0.590839i \(0.798797\pi\)
\(150\) −3.62554 + 1.83238i −0.296024 + 0.149613i
\(151\) 13.3082i 1.08300i 0.840700 + 0.541501i \(0.182144\pi\)
−0.840700 + 0.541501i \(0.817856\pi\)
\(152\) 7.47935 + 1.26004i 0.606656 + 0.102203i
\(153\) 33.3315i 2.69469i
\(154\) −8.36737 16.5557i −0.674262 1.33409i
\(155\) 6.13645 0.492892
\(156\) −3.36550 2.47901i −0.269456 0.198480i
\(157\) 3.66320i 0.292356i −0.989258 0.146178i \(-0.953303\pi\)
0.989258 0.146178i \(-0.0466971\pi\)
\(158\) 2.34746 + 4.64469i 0.186754 + 0.369512i
\(159\) −32.0467 −2.54147
\(160\) 3.93398 + 4.06494i 0.311009 + 0.321362i
\(161\) −5.92579 + 11.4140i −0.467018 + 0.899548i
\(162\) −1.79932 3.56012i −0.141368 0.279710i
\(163\) 16.6589i 1.30483i −0.757864 0.652413i \(-0.773757\pi\)
0.757864 0.652413i \(-0.226243\pi\)
\(164\) 9.57420 12.9979i 0.747620 1.01497i
\(165\) −14.0504 −1.09382
\(166\) −3.03245 6.00000i −0.235364 0.465690i
\(167\) 1.87953i 0.145442i 0.997352 + 0.0727211i \(0.0231683\pi\)
−0.997352 + 0.0727211i \(0.976832\pi\)
\(168\) 3.61943 21.4842i 0.279245 1.65754i
\(169\) −12.4706 −0.959278
\(170\) 4.04917 + 8.01167i 0.310557 + 0.614467i
\(171\) −14.0814 −1.07683
\(172\) 13.2041 17.9258i 1.00680 1.36683i
\(173\) 6.34755 0.482595 0.241297 0.970451i \(-0.422427\pi\)
0.241297 + 0.970451i \(0.422427\pi\)
\(174\) −15.5022 + 7.83492i −1.17522 + 0.593964i
\(175\) 2.68161 0.202711
\(176\) 5.80189 + 18.6856i 0.437334 + 1.40848i
\(177\) 5.39889 0.405805
\(178\) −10.2546 + 5.18277i −0.768617 + 0.388465i
\(179\) 3.09691i 0.231474i −0.993280 0.115737i \(-0.963077\pi\)
0.993280 0.115737i \(-0.0369229\pi\)
\(180\) −8.45583 6.22853i −0.630260 0.464247i
\(181\) 10.7610i 0.799860i −0.916546 0.399930i \(-0.869034\pi\)
0.916546 0.399930i \(-0.130966\pi\)
\(182\) 1.24464 + 2.46264i 0.0922587 + 0.182543i
\(183\) −19.9164 −1.47227
\(184\) 8.16337 10.8333i 0.601811 0.798638i
\(185\) −3.87539 −0.284925
\(186\) 11.2443 + 22.2480i 0.824472 + 1.63130i
\(187\) 31.0484i 2.27048i
\(188\) 15.7959 + 11.6352i 1.15203 + 0.848584i
\(189\) 17.3398i 1.26128i
\(190\) −3.38465 + 1.71063i −0.245548 + 0.124102i
\(191\) −4.75372 −0.343967 −0.171984 0.985100i \(-0.555018\pi\)
−0.171984 + 0.985100i \(0.555018\pi\)
\(192\) −7.52908 + 21.7113i −0.543365 + 1.56688i
\(193\) 21.3640 1.53781 0.768907 0.639360i \(-0.220801\pi\)
0.768907 + 0.639360i \(0.220801\pi\)
\(194\) −3.38809 + 1.71237i −0.243251 + 0.122941i
\(195\) 2.08998 0.149667
\(196\) −0.226613 + 0.307650i −0.0161867 + 0.0219750i
\(197\) 20.4988 1.46048 0.730238 0.683193i \(-0.239409\pi\)
0.730238 + 0.683193i \(0.239409\pi\)
\(198\) −16.3848 32.4190i −1.16442 2.30392i
\(199\) −15.2762 −1.08290 −0.541449 0.840733i \(-0.682124\pi\)
−0.541449 + 0.840733i \(0.682124\pi\)
\(200\) −2.78912 0.469882i −0.197221 0.0332257i
\(201\) 30.2254i 2.13194i
\(202\) −0.981487 1.94197i −0.0690572 0.136636i
\(203\) 11.4661 0.804762
\(204\) −21.6271 + 29.3608i −1.51420 + 2.05567i
\(205\) 8.07172i 0.563754i
\(206\) 11.5539 + 22.8606i 0.805000 + 1.59277i
\(207\) −11.6038 + 22.3507i −0.806518 + 1.55348i
\(208\) −0.863025 2.77946i −0.0598400 0.192721i
\(209\) −13.1168 −0.907311
\(210\) 4.91373 + 9.72230i 0.339080 + 0.670903i
\(211\) 26.0740i 1.79501i −0.441008 0.897503i \(-0.645379\pi\)
0.441008 0.897503i \(-0.354621\pi\)
\(212\) −17.9653 13.2332i −1.23386 0.908858i
\(213\) −20.8216 −1.42667
\(214\) −7.10119 14.0504i −0.485427 0.960466i
\(215\) 11.1319i 0.759193i
\(216\) 3.03834 18.0350i 0.206733 1.22712i
\(217\) 16.4556i 1.11708i
\(218\) 13.4354 6.79036i 0.909960 0.459901i
\(219\) 22.7179i 1.53513i
\(220\) −7.87663 5.80189i −0.531042 0.391163i
\(221\) 4.61841i 0.310668i
\(222\) −7.10119 14.0504i −0.476600 0.943001i
\(223\) 1.47929i 0.0990606i −0.998773 0.0495303i \(-0.984228\pi\)
0.998773 0.0495303i \(-0.0157724\pi\)
\(224\) 10.9006 10.5494i 0.728328 0.704863i
\(225\) 5.25109 0.350072
\(226\) −6.83337 + 3.45364i −0.454549 + 0.229733i
\(227\) 2.20064 0.146062 0.0730308 0.997330i \(-0.476733\pi\)
0.0730308 + 0.997330i \(0.476733\pi\)
\(228\) −12.4039 9.13667i −0.821469 0.605091i
\(229\) 17.4140i 1.15075i 0.817890 + 0.575374i \(0.195144\pi\)
−0.817890 + 0.575374i \(0.804856\pi\)
\(230\) −0.0739292 + 6.78193i −0.00487475 + 0.447187i
\(231\) 37.6777i 2.47901i
\(232\) −11.9258 2.00913i −0.782967 0.131906i
\(233\) −26.7931 −1.75527 −0.877637 0.479326i \(-0.840881\pi\)
−0.877637 + 0.479326i \(0.840881\pi\)
\(234\) 2.43723 + 4.82229i 0.159326 + 0.315243i
\(235\) −9.80928 −0.639887
\(236\) 3.02661 + 2.22938i 0.197015 + 0.145121i
\(237\) 10.5705i 0.686627i
\(238\) 21.4842 10.8583i 1.39261 0.703839i
\(239\) 23.5866i 1.52569i −0.646583 0.762844i \(-0.723802\pi\)
0.646583 0.762844i \(-0.276198\pi\)
\(240\) −3.40715 10.9731i −0.219931 0.708310i
\(241\) 0.212188i 0.0136683i −0.999977 0.00683413i \(-0.997825\pi\)
0.999977 0.00683413i \(-0.00217539\pi\)
\(242\) −8.24550 16.3145i −0.530041 1.04874i
\(243\) 11.2963i 0.724659i
\(244\) −11.1651 8.22417i −0.714773 0.526499i
\(245\) 0.191051i 0.0122058i
\(246\) −29.2644 + 14.7905i −1.86583 + 0.943005i
\(247\) 1.95112 0.124147
\(248\) −2.88341 + 17.1153i −0.183097 + 1.08682i
\(249\) 13.6549i 0.865346i
\(250\) 1.26217 0.637910i 0.0798266 0.0403450i
\(251\) −11.1153 −0.701589 −0.350795 0.936452i \(-0.614088\pi\)
−0.350795 + 0.936452i \(0.614088\pi\)
\(252\) −16.7025 + 22.6753i −1.05216 + 1.42841i
\(253\) −10.8089 + 20.8197i −0.679553 + 1.30892i
\(254\) 3.85407 1.94788i 0.241826 0.122221i
\(255\) 18.2331i 1.14180i
\(256\) −13.1861 + 9.06232i −0.824134 + 0.566395i
\(257\) 1.25450 0.0782533 0.0391267 0.999234i \(-0.487542\pi\)
0.0391267 + 0.999234i \(0.487542\pi\)
\(258\) −40.3594 + 20.3979i −2.51266 + 1.26992i
\(259\) 10.3923i 0.645746i
\(260\) 1.17164 + 0.863025i 0.0726620 + 0.0535225i
\(261\) 22.4527 1.38979
\(262\) 3.90882 1.97555i 0.241488 0.122050i
\(263\) −25.6760 −1.58325 −0.791625 0.611007i \(-0.790765\pi\)
−0.791625 + 0.611007i \(0.790765\pi\)
\(264\) 6.60203 39.1883i 0.406327 2.41187i
\(265\) 11.1565 0.685338
\(266\) 4.58725 + 9.07632i 0.281262 + 0.556505i
\(267\) 23.3377 1.42824
\(268\) 12.4811 16.9443i 0.762404 1.03504i
\(269\) 20.4193 1.24498 0.622492 0.782626i \(-0.286120\pi\)
0.622492 + 0.782626i \(0.286120\pi\)
\(270\) 4.12484 + 8.16141i 0.251030 + 0.496687i
\(271\) 3.08711i 0.187529i 0.995594 + 0.0937643i \(0.0298900\pi\)
−0.995594 + 0.0937643i \(0.970110\pi\)
\(272\) −24.2482 + 7.52908i −1.47026 + 0.456518i
\(273\) 5.60452i 0.339201i
\(274\) 7.47935 3.78012i 0.451844 0.228366i
\(275\) 4.89140 0.294963
\(276\) −24.7236 + 12.1590i −1.48819 + 0.731887i
\(277\) 2.96451 0.178120 0.0890602 0.996026i \(-0.471614\pi\)
0.0890602 + 0.996026i \(0.471614\pi\)
\(278\) 4.19633 2.12086i 0.251679 0.127201i
\(279\) 32.2230i 1.92914i
\(280\) −1.26004 + 7.47935i −0.0753019 + 0.446977i
\(281\) 8.93603i 0.533079i 0.963824 + 0.266539i \(0.0858802\pi\)
−0.963824 + 0.266539i \(0.914120\pi\)
\(282\) −17.9743 35.5640i −1.07036 2.11780i
\(283\) 17.2348 1.02450 0.512252 0.858835i \(-0.328811\pi\)
0.512252 + 0.858835i \(0.328811\pi\)
\(284\) −11.6725 8.59793i −0.692637 0.510194i
\(285\) 7.70285 0.456278
\(286\) 2.27028 + 4.49198i 0.134245 + 0.265616i
\(287\) 21.6452 1.27768
\(288\) 21.3454 20.6577i 1.25779 1.21727i
\(289\) −23.2913 −1.37008
\(290\) 5.39681 2.72759i 0.316911 0.160170i
\(291\) 7.71069 0.452009
\(292\) −9.38097 + 12.7356i −0.548980 + 0.745294i
\(293\) 20.3500i 1.18886i −0.804147 0.594430i \(-0.797378\pi\)
0.804147 0.594430i \(-0.202622\pi\)
\(294\) 0.692663 0.350078i 0.0403969 0.0204169i
\(295\) −1.87953 −0.109430
\(296\) 1.82098 10.8089i 0.105842 0.628257i
\(297\) 31.6286i 1.83528i
\(298\) 18.2058 9.20136i 1.05463 0.533021i
\(299\) 1.60782 3.09691i 0.0929826 0.179099i
\(300\) 4.62554 + 3.40715i 0.267056 + 0.196712i
\(301\) 29.8516 1.72062
\(302\) 16.7971 8.48941i 0.966567 0.488511i
\(303\) 4.41957i 0.253898i
\(304\) −3.18077 10.2440i −0.182430 0.587534i
\(305\) 6.93356 0.397014
\(306\) 42.0700 21.2625i 2.40498 1.21550i
\(307\) 32.9240i 1.87907i 0.342449 + 0.939537i \(0.388744\pi\)
−0.342449 + 0.939537i \(0.611256\pi\)
\(308\) −15.5584 + 21.1221i −0.886523 + 1.20354i
\(309\) 52.0266i 2.95969i
\(310\) −3.91451 7.74524i −0.222329 0.439900i
\(311\) 31.6677i 1.79571i −0.440291 0.897855i \(-0.645125\pi\)
0.440291 0.897855i \(-0.354875\pi\)
\(312\) −0.982045 + 5.82922i −0.0555973 + 0.330015i
\(313\) 5.92579i 0.334946i −0.985877 0.167473i \(-0.946439\pi\)
0.985877 0.167473i \(-0.0535606\pi\)
\(314\) −4.62358 + 2.33680i −0.260924 + 0.131873i
\(315\) 14.0814i 0.793396i
\(316\) 4.36491 5.92579i 0.245546 0.333352i
\(317\) 14.3079 0.803611 0.401806 0.915725i \(-0.368383\pi\)
0.401806 + 0.915725i \(0.368383\pi\)
\(318\) 20.4429 + 40.4483i 1.14638 + 2.26823i
\(319\) 20.9147 1.17100
\(320\) 2.62112 7.55842i 0.146525 0.422529i
\(321\) 31.9762i 1.78474i
\(322\) 18.1865 + 0.198249i 1.01349 + 0.0110480i
\(323\) 17.0217i 0.947111i
\(324\) −3.34568 + 4.54208i −0.185871 + 0.252338i
\(325\) −0.727591 −0.0403595
\(326\) −21.0263 + 10.6269i −1.16454 + 0.588569i
\(327\) −30.5766 −1.69089
\(328\) −22.5130 3.79276i −1.24307 0.209420i
\(329\) 26.3047i 1.45023i
\(330\) 8.96290 + 17.7340i 0.493391 + 0.976223i
\(331\) 15.1629i 0.833430i −0.909037 0.416715i \(-0.863181\pi\)
0.909037 0.416715i \(-0.136819\pi\)
\(332\) −5.63858 + 7.65492i −0.309457 + 0.420119i
\(333\) 20.3500i 1.11517i
\(334\) 2.37228 1.19897i 0.129805 0.0656047i
\(335\) 10.5224i 0.574903i
\(336\) −29.4256 + 9.13667i −1.60530 + 0.498446i
\(337\) 11.5520i 0.629276i 0.949212 + 0.314638i \(0.101883\pi\)
−0.949212 + 0.314638i \(0.898117\pi\)
\(338\) 7.95513 + 15.7400i 0.432702 + 0.856144i
\(339\) 15.5515 0.844643
\(340\) 7.52908 10.2215i 0.408322 0.554337i
\(341\) 30.0158i 1.62545i
\(342\) 8.98266 + 17.7731i 0.485727 + 0.961058i
\(343\) 18.2590 0.985892
\(344\) −31.0484 5.23070i −1.67402 0.282021i
\(345\) 6.34755 12.2263i 0.341740 0.658245i
\(346\) −4.04917 8.01167i −0.217684 0.430710i
\(347\) 3.94249i 0.211644i −0.994385 0.105822i \(-0.966253\pi\)
0.994385 0.105822i \(-0.0337474\pi\)
\(348\) 19.7780 + 14.5684i 1.06021 + 0.780947i
\(349\) −14.2826 −0.764532 −0.382266 0.924052i \(-0.624856\pi\)
−0.382266 + 0.924052i \(0.624856\pi\)
\(350\) −1.71063 3.38465i −0.0914370 0.180917i
\(351\) 4.70473i 0.251120i
\(352\) 19.8833 19.2427i 1.05978 1.02564i
\(353\) −24.2520 −1.29080 −0.645402 0.763843i \(-0.723310\pi\)
−0.645402 + 0.763843i \(0.723310\pi\)
\(354\) −3.44401 6.81431i −0.183047 0.362176i
\(355\) 7.24866 0.384719
\(356\) 13.0831 + 9.63693i 0.693401 + 0.510756i
\(357\) −48.8942 −2.58776
\(358\) −3.90882 + 1.97555i −0.206588 + 0.104411i
\(359\) 35.2093 1.85828 0.929138 0.369734i \(-0.120551\pi\)
0.929138 + 0.369734i \(0.120551\pi\)
\(360\) −2.46739 + 14.6459i −0.130043 + 0.771908i
\(361\) −11.8089 −0.621524
\(362\) −13.5822 + 6.86457i −0.713866 + 0.360794i
\(363\) 37.1290i 1.94876i
\(364\) 2.31430 3.14189i 0.121302 0.164680i
\(365\) 7.90882i 0.413967i
\(366\) 12.7049 + 25.1379i 0.664096 + 1.31398i
\(367\) 4.51174 0.235511 0.117755 0.993043i \(-0.462430\pi\)
0.117755 + 0.993043i \(0.462430\pi\)
\(368\) −18.8809 3.39290i −0.984235 0.176867i
\(369\) 42.3853 2.20649
\(370\) 2.47215 + 4.89140i 0.128521 + 0.254292i
\(371\) 29.9174i 1.55323i
\(372\) 20.9078 28.3844i 1.08402 1.47166i
\(373\) 1.05569i 0.0546617i −0.999626 0.0273309i \(-0.991299\pi\)
0.999626 0.0273309i \(-0.00870077\pi\)
\(374\) 39.1883 19.8061i 2.02638 1.02415i
\(375\) −2.87247 −0.148334
\(376\) 4.60921 27.3593i 0.237702 1.41095i
\(377\) −3.11105 −0.160227
\(378\) 21.8857 11.0612i 1.12568 0.568928i
\(379\) 6.48253 0.332985 0.166493 0.986043i \(-0.446756\pi\)
0.166493 + 0.986043i \(0.446756\pi\)
\(380\) 4.31821 + 3.18077i 0.221519 + 0.163170i
\(381\) −8.77117 −0.449361
\(382\) 3.03245 + 6.00000i 0.155154 + 0.306987i
\(383\) −1.34915 −0.0689383 −0.0344692 0.999406i \(-0.510974\pi\)
−0.0344692 + 0.999406i \(0.510974\pi\)
\(384\) 32.2063 4.34692i 1.64352 0.221828i
\(385\) 13.1168i 0.668496i
\(386\) −13.6283 26.9650i −0.693663 1.37248i
\(387\) 58.4548 2.97143
\(388\) 4.32260 + 3.18401i 0.219447 + 0.161643i
\(389\) 10.3846i 0.526519i −0.964725 0.263259i \(-0.915203\pi\)
0.964725 0.263259i \(-0.0847975\pi\)
\(390\) −1.33322 2.63791i −0.0675103 0.133576i
\(391\) −27.0176 14.0267i −1.36634 0.709362i
\(392\) 0.532865 + 0.0897714i 0.0269137 + 0.00453414i
\(393\) −8.89578 −0.448733
\(394\) −13.0764 25.8729i −0.658778 1.30346i
\(395\) 3.67993i 0.185157i
\(396\) −30.4662 + 41.3608i −1.53098 + 2.07846i
\(397\) −23.4623 −1.17754 −0.588770 0.808300i \(-0.700388\pi\)
−0.588770 + 0.808300i \(0.700388\pi\)
\(398\) 9.74483 + 19.2811i 0.488464 + 0.966474i
\(399\) 20.6561i 1.03410i
\(400\) 1.18614 + 3.82009i 0.0593070 + 0.191004i
\(401\) 26.3500i 1.31586i −0.753080 0.657929i \(-0.771433\pi\)
0.753080 0.657929i \(-0.228567\pi\)
\(402\) −38.1496 + 19.2811i −1.90273 + 0.961654i
\(403\) 4.46482i 0.222409i
\(404\) −1.82499 + 2.47760i −0.0907967 + 0.123265i
\(405\) 2.82064i 0.140159i
\(406\) −7.31434 14.4722i −0.363005 0.718241i
\(407\) 18.9561i 0.939619i
\(408\) 50.8545 + 8.56742i 2.51767 + 0.424151i
\(409\) 18.3538 0.907535 0.453768 0.891120i \(-0.350080\pi\)
0.453768 + 0.891120i \(0.350080\pi\)
\(410\) 10.1879 5.14904i 0.503144 0.254293i
\(411\) −17.0217 −0.839617
\(412\) 21.4836 29.1660i 1.05842 1.43691i
\(413\) 5.04017i 0.248010i
\(414\) 35.6125 + 0.388208i 1.75026 + 0.0190794i
\(415\) 4.75372i 0.233351i
\(416\) −2.95762 + 2.86233i −0.145009 + 0.140337i
\(417\) −9.55010 −0.467670
\(418\) 8.36737 + 16.5557i 0.409261 + 0.809764i
\(419\) −20.3386 −0.993606 −0.496803 0.867863i \(-0.665493\pi\)
−0.496803 + 0.867863i \(0.665493\pi\)
\(420\) 9.13667 12.4039i 0.445824 0.605249i
\(421\) 9.22242i 0.449473i 0.974420 + 0.224737i \(0.0721522\pi\)
−0.974420 + 0.224737i \(0.927848\pi\)
\(422\) −32.9098 + 16.6329i −1.60202 + 0.809675i
\(423\) 51.5094i 2.50447i
\(424\) −5.24224 + 31.1168i −0.254585 + 1.51117i
\(425\) 6.34755i 0.307901i
\(426\) 13.2823 + 26.2803i 0.643529 + 1.27329i
\(427\) 18.5931i 0.899784i
\(428\) −13.2041 + 17.9258i −0.638242 + 0.866476i
\(429\) 10.2229i 0.493568i
\(430\) 14.0504 7.10119i 0.677570 0.342450i
\(431\) 10.2805 0.495192 0.247596 0.968863i \(-0.420359\pi\)
0.247596 + 0.968863i \(0.420359\pi\)
\(432\) −24.7014 + 7.66979i −1.18844 + 0.369013i
\(433\) 17.8095i 0.855868i −0.903810 0.427934i \(-0.859242\pi\)
0.903810 0.427934i \(-0.140758\pi\)
\(434\) −20.7697 + 10.4972i −0.996979 + 0.503881i
\(435\) −12.2822 −0.588885
\(436\) −17.1412 12.6261i −0.820913 0.604681i
\(437\) 5.92579 11.4140i 0.283469 0.546005i
\(438\) 28.6738 14.4920i 1.37009 0.692452i
\(439\) 14.9756i 0.714746i 0.933962 + 0.357373i \(0.116328\pi\)
−0.933962 + 0.357373i \(0.883672\pi\)
\(440\) −2.29838 + 13.6427i −0.109571 + 0.650391i
\(441\) −1.00322 −0.0477726
\(442\) −5.82922 + 2.94613i −0.277268 + 0.140133i
\(443\) 14.0082i 0.665548i 0.943007 + 0.332774i \(0.107985\pi\)
−0.943007 + 0.332774i \(0.892015\pi\)
\(444\) −13.2041 + 17.9258i −0.626637 + 0.850720i
\(445\) −8.12461 −0.385143
\(446\) −1.86711 + 0.943654i −0.0884104 + 0.0446833i
\(447\) −41.4332 −1.95972
\(448\) −20.2688 7.02882i −0.957609 0.332081i
\(449\) −28.3872 −1.33967 −0.669837 0.742508i \(-0.733636\pi\)
−0.669837 + 0.742508i \(0.733636\pi\)
\(450\) −3.34972 6.62776i −0.157907 0.312435i
\(451\) 39.4820 1.85914
\(452\) 8.71815 + 6.42175i 0.410067 + 0.302054i
\(453\) −38.2273 −1.79607
\(454\) −1.40381 2.77758i −0.0658841 0.130358i
\(455\) 1.95112i 0.0914698i
\(456\) −3.61943 + 21.4842i −0.169495 + 1.00609i
\(457\) 35.6394i 1.66714i 0.552413 + 0.833570i \(0.313707\pi\)
−0.552413 + 0.833570i \(0.686293\pi\)
\(458\) 21.9794 11.1086i 1.02703 0.519069i
\(459\) −41.0443 −1.91579
\(460\) 8.60710 4.23295i 0.401308 0.197362i
\(461\) −1.09286 −0.0508997 −0.0254498 0.999676i \(-0.508102\pi\)
−0.0254498 + 0.999676i \(0.508102\pi\)
\(462\) 47.5557 24.0350i 2.21249 1.11821i
\(463\) 20.3766i 0.946980i 0.880799 + 0.473490i \(0.157006\pi\)
−0.880799 + 0.473490i \(0.842994\pi\)
\(464\) 5.07172 + 16.3340i 0.235449 + 0.758287i
\(465\) 17.6268i 0.817422i
\(466\) 17.0916 + 33.8174i 0.791753 + 1.56656i
\(467\) −30.8277 −1.42654 −0.713268 0.700892i \(-0.752786\pi\)
−0.713268 + 0.700892i \(0.752786\pi\)
\(468\) 4.53182 6.15238i 0.209483 0.284394i
\(469\) 28.2171 1.30295
\(470\) 6.25744 + 12.3810i 0.288634 + 0.571092i
\(471\) 10.5224 0.484849
\(472\) 0.883156 5.24224i 0.0406506 0.241293i
\(473\) 54.4508 2.50365
\(474\) −13.3417 + 6.74302i −0.612806 + 0.309717i
\(475\) −2.68161 −0.123041
\(476\) −27.4100 20.1901i −1.25634 0.925411i
\(477\) 58.5837i 2.68236i
\(478\) −29.7702 + 15.0461i −1.36166 + 0.688193i
\(479\) −14.5699 −0.665715 −0.332858 0.942977i \(-0.608013\pi\)
−0.332858 + 0.942977i \(0.608013\pi\)
\(480\) −11.6764 + 11.3003i −0.532954 + 0.515784i
\(481\) 2.81970i 0.128567i
\(482\) −0.267818 + 0.135357i −0.0121988 + 0.00616535i
\(483\) −32.7863 17.0217i −1.49183 0.774513i
\(484\) −15.3318 + 20.8144i −0.696900 + 0.946110i
\(485\) −2.68434 −0.121890
\(486\) −14.2579 + 7.20604i −0.646750 + 0.326873i
\(487\) 2.18374i 0.0989549i −0.998775 0.0494774i \(-0.984244\pi\)
0.998775 0.0494774i \(-0.0157556\pi\)
\(488\) −3.25795 + 19.3385i −0.147481 + 0.875415i
\(489\) 47.8522 2.16395
\(490\) −0.241138 + 0.121873i −0.0108935 + 0.00550568i
\(491\) 7.55568i 0.340983i 0.985359 + 0.170491i \(0.0545355\pi\)
−0.985359 + 0.170491i \(0.945464\pi\)
\(492\) 37.3361 + 27.5016i 1.68324 + 1.23987i
\(493\) 27.1410i 1.22237i
\(494\) −1.24464 2.46264i −0.0559989 0.110799i
\(495\) 25.6852i 1.15446i
\(496\) 23.4418 7.27870i 1.05257 0.326823i
\(497\) 19.4381i 0.871919i
\(498\) 17.2348 8.71062i 0.772311 0.390332i
\(499\) 10.0079i 0.448015i −0.974587 0.224007i \(-0.928086\pi\)
0.974587 0.224007i \(-0.0719140\pi\)
\(500\) −1.61030 1.18614i −0.0720149 0.0530458i
\(501\) −5.39889 −0.241204
\(502\) 7.09054 + 14.0293i 0.316466 + 0.626160i
\(503\) 32.7697 1.46113 0.730563 0.682845i \(-0.239258\pi\)
0.730563 + 0.682845i \(0.239258\pi\)
\(504\) 39.2747 + 6.61659i 1.74943 + 0.294726i
\(505\) 1.53860i 0.0684666i
\(506\) 33.1731 + 0.361617i 1.47472 + 0.0160758i
\(507\) 35.8215i 1.59089i
\(508\) −4.91710 3.62191i −0.218161 0.160696i
\(509\) −4.89723 −0.217066 −0.108533 0.994093i \(-0.534615\pi\)
−0.108533 + 0.994093i \(0.534615\pi\)
\(510\) −23.0133 + 11.6311i −1.01905 + 0.515034i
\(511\) −21.2084 −0.938204
\(512\) 19.8498 + 10.8622i 0.877244 + 0.480045i
\(513\) 17.3398i 0.765570i
\(514\) −0.800256 1.58339i −0.0352978 0.0698402i
\(515\) 18.1121i 0.798116i
\(516\) 51.4913 + 37.9283i 2.26678 + 1.66970i
\(517\) 47.9811i 2.11021i
\(518\) 13.1168 6.62936i 0.576321 0.291277i
\(519\) 18.2331i 0.800346i
\(520\) 0.341882 2.02934i 0.0149925 0.0889924i
\(521\) 31.5065i 1.38033i 0.723654 + 0.690163i \(0.242461\pi\)
−0.723654 + 0.690163i \(0.757539\pi\)
\(522\) −14.3228 28.3391i −0.626892 1.24037i
\(523\) −29.1444 −1.27440 −0.637198 0.770700i \(-0.719906\pi\)
−0.637198 + 0.770700i \(0.719906\pi\)
\(524\) −4.98696 3.67337i −0.217856 0.160472i
\(525\) 7.70285i 0.336180i
\(526\) 16.3790 + 32.4075i 0.714158 + 1.41303i
\(527\) 38.9514 1.69675
\(528\) −53.6738 + 16.6658i −2.33585 + 0.725284i
\(529\) −13.2337 18.8114i −0.575378 0.817888i
\(530\) −7.11684 14.0814i −0.309136 0.611656i
\(531\) 9.86956i 0.428302i
\(532\) 8.52960 11.5798i 0.369805 0.502046i
\(533\) −5.87291 −0.254384
\(534\) −14.8874 29.4561i −0.644239 1.27469i
\(535\) 11.1319i 0.481276i
\(536\) −29.3484 4.94431i −1.26766 0.213562i
\(537\) 8.89578 0.383881
\(538\) −13.0257 25.7726i −0.561576 1.11113i
\(539\) −0.934506 −0.0402520
\(540\) 7.66979 10.4125i 0.330055 0.448082i
\(541\) 10.0459 0.431906 0.215953 0.976404i \(-0.430714\pi\)
0.215953 + 0.976404i \(0.430714\pi\)
\(542\) 3.89645 1.96930i 0.167367 0.0845886i
\(543\) 30.9107 1.32651
\(544\) 24.9711 + 25.8024i 1.07063 + 1.10627i
\(545\) 10.6447 0.455968
\(546\) −7.07386 + 3.57518i −0.302733 + 0.153004i
\(547\) 40.9194i 1.74959i −0.484495 0.874794i \(-0.660997\pi\)
0.484495 0.874794i \(-0.339003\pi\)
\(548\) −9.54231 7.02882i −0.407627 0.300256i
\(549\) 36.4087i 1.55389i
\(550\) −3.12027 6.17377i −0.133049 0.263251i
\(551\) −11.4661 −0.488472
\(552\) 31.1182 + 23.4490i 1.32448 + 0.998057i
\(553\) 9.86814 0.419636
\(554\) −1.89109 3.74172i −0.0803449 0.158970i
\(555\) 11.1319i 0.472525i
\(556\) −5.35377 3.94356i −0.227050 0.167244i
\(557\) 5.20180i 0.220407i 0.993909 + 0.110204i \(0.0351503\pi\)
−0.993909 + 0.110204i \(0.964850\pi\)
\(558\) −40.6709 + 20.5554i −1.72174 + 0.870180i
\(559\) −8.09950 −0.342572
\(560\) 10.2440 3.18077i 0.432888 0.134412i
\(561\) −89.1856 −3.76542
\(562\) 11.2788 5.70038i 0.475766 0.240456i
\(563\) 22.2639 0.938311 0.469156 0.883115i \(-0.344558\pi\)
0.469156 + 0.883115i \(0.344558\pi\)
\(564\) −33.4217 + 45.3733i −1.40731 + 1.91056i
\(565\) −5.41399 −0.227768
\(566\) −10.9943 21.7533i −0.462124 0.914358i
\(567\) −7.56387 −0.317652
\(568\) −3.40602 + 20.2174i −0.142913 + 0.848304i
\(569\) 33.1614i 1.39020i −0.718913 0.695100i \(-0.755360\pi\)
0.718913 0.695100i \(-0.244640\pi\)
\(570\) −4.91373 9.72230i −0.205814 0.407222i
\(571\) −3.20810 −0.134255 −0.0671274 0.997744i \(-0.521383\pi\)
−0.0671274 + 0.997744i \(0.521383\pi\)
\(572\) 4.22140 5.73096i 0.176506 0.239623i
\(573\) 13.6549i 0.570443i
\(574\) −13.8077 27.3200i −0.576323 1.14031i
\(575\) −2.20979 + 4.25639i −0.0921545 + 0.177504i
\(576\) −39.6899 13.7637i −1.65375 0.573488i
\(577\) 12.3249 0.513091 0.256545 0.966532i \(-0.417416\pi\)
0.256545 + 0.966532i \(0.417416\pi\)
\(578\) 14.8578 + 29.3976i 0.618002 + 1.22278i
\(579\) 61.3675i 2.55034i
\(580\) −6.88536 5.07172i −0.285899 0.210592i
\(581\) −12.7476 −0.528861
\(582\) −4.91873 9.73219i −0.203888 0.403412i
\(583\) 54.5709i 2.26009i
\(584\) 22.0587 + 3.71621i 0.912795 + 0.153778i
\(585\) 3.82064i 0.157964i
\(586\) −25.6852 + 12.9815i −1.06104 + 0.536260i
\(587\) 8.83980i 0.364857i 0.983219 + 0.182429i \(0.0583959\pi\)
−0.983219 + 0.182429i \(0.941604\pi\)
\(588\) −0.883714 0.650940i −0.0364438 0.0268443i
\(589\) 16.4556i 0.678041i
\(590\) 1.19897 + 2.37228i 0.0493608 + 0.0976653i
\(591\) 58.8821i 2.42208i
\(592\) −14.8043 + 4.59676i −0.608455 + 0.188926i
\(593\) 2.38210 0.0978212 0.0489106 0.998803i \(-0.484425\pi\)
0.0489106 + 0.998803i \(0.484425\pi\)
\(594\) 39.9207 20.1762i 1.63797 0.827841i
\(595\) 17.0217 0.697820
\(596\) −23.2273 17.1092i −0.951429 0.700818i
\(597\) 43.8803i 1.79590i
\(598\) −4.93447 0.0537902i −0.201785 0.00219964i
\(599\) 8.38036i 0.342412i 0.985235 + 0.171206i \(0.0547664\pi\)
−0.985235 + 0.171206i \(0.945234\pi\)
\(600\) 1.34972 8.01167i 0.0551022 0.327075i
\(601\) 29.2981 1.19509 0.597547 0.801834i \(-0.296142\pi\)
0.597547 + 0.801834i \(0.296142\pi\)
\(602\) −19.0426 37.6777i −0.776120 1.53563i
\(603\) 55.2543 2.25013
\(604\) −21.4301 15.7853i −0.871980 0.642297i
\(605\) 12.9258i 0.525508i
\(606\) 5.57825 2.81929i 0.226601 0.114526i
\(607\) 6.58224i 0.267165i 0.991038 + 0.133582i \(0.0426481\pi\)
−0.991038 + 0.133582i \(0.957352\pi\)
\(608\) −10.9006 + 10.5494i −0.442078 + 0.427836i
\(609\) 32.9360i 1.33464i
\(610\) −4.42299 8.75132i −0.179082 0.354331i
\(611\) 7.13714i 0.288738i
\(612\) −53.6738 39.5359i −2.16963 1.59814i
\(613\) 31.7187i 1.28111i −0.767914 0.640553i \(-0.778705\pi\)
0.767914 0.640553i \(-0.221295\pi\)
\(614\) 41.5557 21.0026i 1.67705 0.847595i
\(615\) −23.1858 −0.934941
\(616\) 36.5845 + 6.16337i 1.47403 + 0.248329i
\(617\) 41.9737i 1.68980i −0.534925 0.844899i \(-0.679660\pi\)
0.534925 0.844899i \(-0.320340\pi\)
\(618\) −65.6663 + 33.1883i −2.64149 + 1.33503i
\(619\) 40.4232 1.62474 0.812372 0.583139i \(-0.198176\pi\)
0.812372 + 0.583139i \(0.198176\pi\)
\(620\) −7.27870 + 9.88154i −0.292319 + 0.396852i
\(621\) −27.5226 14.2889i −1.10444 0.573392i
\(622\) −39.9700 + 20.2011i −1.60265 + 0.809992i
\(623\) 21.7871i 0.872880i
\(624\) 7.98391 2.47901i 0.319612 0.0992399i
\(625\) 1.00000 0.0400000
\(626\) −7.47935 + 3.78012i −0.298935 + 0.151084i
\(627\) 37.6777i 1.50470i
\(628\) 5.89886 + 4.34508i 0.235390 + 0.173387i
\(629\) −24.5992 −0.980836
\(630\) −17.7731 + 8.98266i −0.708096 + 0.357878i
\(631\) 3.27191 0.130253 0.0651263 0.997877i \(-0.479255\pi\)
0.0651263 + 0.997877i \(0.479255\pi\)
\(632\) −10.2638 1.72913i −0.408271 0.0687812i
\(633\) 74.8967 2.97688
\(634\) −9.12715 18.0590i −0.362486 0.717214i
\(635\) 3.05353 0.121176
\(636\) 38.0119 51.6048i 1.50727 2.04627i
\(637\) 0.139007 0.00550765
\(638\) −13.3417 26.3979i −0.528204 1.04510i
\(639\) 38.0633i 1.50576i
\(640\) −11.2120 + 1.51330i −0.443195 + 0.0598185i
\(641\) 2.70337i 0.106777i 0.998574 + 0.0533884i \(0.0170021\pi\)
−0.998574 + 0.0533884i \(0.982998\pi\)
\(642\) 40.3594 20.3979i 1.59286 0.805043i
\(643\) −3.81007 −0.150254 −0.0751272 0.997174i \(-0.523936\pi\)
−0.0751272 + 0.997174i \(0.523936\pi\)
\(644\) −11.3511 23.0809i −0.447297 0.909515i
\(645\) −31.9762 −1.25906
\(646\) −21.4842 + 10.8583i −0.845285 + 0.427214i
\(647\) 5.11436i 0.201066i −0.994934 0.100533i \(-0.967945\pi\)
0.994934 0.100533i \(-0.0320548\pi\)
\(648\) 7.86711 + 1.32537i 0.309049 + 0.0520654i
\(649\) 9.19352i 0.360877i
\(650\) 0.464138 + 0.918342i 0.0182050 + 0.0360203i
\(651\) 47.2682 1.85259
\(652\) 26.8258 + 19.7598i 1.05058 + 0.773853i
\(653\) −27.5197 −1.07693 −0.538465 0.842648i \(-0.680996\pi\)
−0.538465 + 0.842648i \(0.680996\pi\)
\(654\) 19.5051 + 38.5928i 0.762710 + 1.50910i
\(655\) 3.09691 0.121006
\(656\) 9.57420 + 30.8347i 0.373810 + 1.20389i
\(657\) −41.5299 −1.62024
\(658\) 33.2010 16.7800i 1.29431 0.654154i
\(659\) 31.4372 1.22462 0.612310 0.790618i \(-0.290241\pi\)
0.612310 + 0.790618i \(0.290241\pi\)
\(660\) 16.6658 22.6254i 0.648713 0.880692i
\(661\) 0.251685i 0.00978943i −0.999988 0.00489471i \(-0.998442\pi\)
0.999988 0.00489471i \(-0.00155804\pi\)
\(662\) −19.1382 + 9.67259i −0.743826 + 0.375936i
\(663\) 13.2663 0.515219
\(664\) 13.2587 + 2.23369i 0.514538 + 0.0866839i
\(665\) 7.19105i 0.278857i
\(666\) 25.6852 12.9815i 0.995280 0.503022i
\(667\) −9.44865 + 18.1996i −0.365853 + 0.704690i
\(668\) −3.02661 2.22938i −0.117103 0.0862575i
\(669\) 4.24921 0.164284
\(670\) 13.2811 6.71238i 0.513094 0.259322i
\(671\) 33.9148i 1.30927i
\(672\) 30.3029 + 31.3117i 1.16896 + 1.20787i
\(673\) −9.56375 −0.368655 −0.184328 0.982865i \(-0.559011\pi\)
−0.184328 + 0.982865i \(0.559011\pi\)
\(674\) 14.5805 7.36912i 0.561621 0.283848i
\(675\) 6.46618i 0.248883i
\(676\) 14.7919 20.0814i 0.568919 0.772363i
\(677\) 48.6951i 1.87150i 0.352658 + 0.935752i \(0.385278\pi\)
−0.352658 + 0.935752i \(0.614722\pi\)
\(678\) −9.92048 19.6286i −0.380994 0.753834i
\(679\) 7.19837i 0.276248i
\(680\) −17.7041 2.98260i −0.678921 0.114377i
\(681\) 6.32127i 0.242232i
\(682\) −37.8851 + 19.1474i −1.45069 + 0.733193i
\(683\) 23.9040i 0.914662i −0.889297 0.457331i \(-0.848805\pi\)
0.889297 0.457331i \(-0.151195\pi\)
\(684\) 16.7025 22.6753i 0.638636 0.867010i
\(685\) 5.92579 0.226413
\(686\) −11.6476 23.0459i −0.444707 0.879897i
\(687\) −50.0212 −1.90843
\(688\) 13.2041 + 42.5250i 0.503400 + 1.62125i
\(689\) 8.11736i 0.309247i
\(690\) −19.4809 0.212359i −0.741625 0.00808438i
\(691\) 32.6562i 1.24230i 0.783691 + 0.621150i \(0.213334\pi\)
−0.783691 + 0.621150i \(0.786666\pi\)
\(692\) −7.52908 + 10.2215i −0.286213 + 0.388562i
\(693\) −68.8777 −2.61645
\(694\) −4.97609 + 2.51495i −0.188890 + 0.0954664i
\(695\) 3.32470 0.126113
\(696\) 5.77117 34.2565i 0.218756 1.29849i
\(697\) 51.2356i 1.94069i
\(698\) 9.11105 + 18.0271i 0.344858 + 0.682336i
\(699\) 76.9624i 2.91098i
\(700\) −3.18077 + 4.31821i −0.120222 + 0.163213i
\(701\) 6.51180i 0.245947i 0.992410 + 0.122974i \(0.0392431\pi\)
−0.992410 + 0.122974i \(0.960757\pi\)
\(702\) −5.93816 + 3.00119i −0.224121 + 0.113273i
\(703\) 10.3923i 0.391953i
\(704\) −36.9713 12.8209i −1.39341 0.483207i
\(705\) 28.1769i 1.06120i
\(706\) 15.4706 + 30.6101i 0.582244 + 1.15203i
\(707\) −4.12592 −0.155171
\(708\) −6.40384 + 8.69384i −0.240671 + 0.326734i
\(709\) 8.35583i 0.313810i 0.987614 + 0.156905i \(0.0501516\pi\)
−0.987614 + 0.156905i \(0.949848\pi\)
\(710\) −4.62400 9.14904i −0.173536 0.343357i
\(711\) 19.3236 0.724692
\(712\) 3.81761 22.6605i 0.143071 0.849239i
\(713\) 26.1191 + 13.5602i 0.978169 + 0.507835i
\(714\) 31.1901 + 61.7128i 1.16726 + 2.30954i
\(715\) 3.55894i 0.133097i
\(716\) 4.98696 + 3.67337i 0.186371 + 0.137280i
\(717\) 67.7517 2.53023
\(718\) −22.4604 44.4401i −0.838214 1.65849i
\(719\) 3.98961i 0.148787i −0.997229 0.0743937i \(-0.976298\pi\)
0.997229 0.0743937i \(-0.0237021\pi\)
\(720\) 20.0596 6.22853i 0.747577 0.232123i
\(721\) 48.5698 1.80883
\(722\) 7.53305 + 14.9049i 0.280351 + 0.554703i
\(723\) 0.609505 0.0226677
\(724\) 17.3285 + 12.7641i 0.644008 + 0.474373i
\(725\) 4.27582 0.158800
\(726\) 46.8630 23.6849i 1.73925 0.879031i
\(727\) 26.1403 0.969490 0.484745 0.874656i \(-0.338912\pi\)
0.484745 + 0.874656i \(0.338912\pi\)
\(728\) −5.44191 0.916794i −0.201690 0.0339787i
\(729\) 40.9103 1.51520
\(730\) −9.98227 + 5.04512i −0.369460 + 0.186728i
\(731\) 70.6606i 2.61348i
\(732\) 23.6237 32.0715i 0.873157 1.18540i
\(733\) 46.1008i 1.70277i 0.524540 + 0.851386i \(0.324237\pi\)
−0.524540 + 0.851386i \(0.675763\pi\)
\(734\) −2.87808 5.69458i −0.106232 0.210191i
\(735\) 0.548788 0.0202424
\(736\) 7.76190 + 25.9952i 0.286108 + 0.958198i
\(737\) 51.4695 1.89590
\(738\) −27.0380 53.4974i −0.995284 1.96927i
\(739\) 32.2296i 1.18559i 0.805355 + 0.592793i \(0.201975\pi\)
−0.805355 + 0.592793i \(0.798025\pi\)
\(740\) 4.59676 6.24055i 0.168980 0.229407i
\(741\) 5.60452i 0.205887i
\(742\) −37.7608 + 19.0846i −1.38624 + 0.700619i
\(743\) −33.3792 −1.22456 −0.612281 0.790640i \(-0.709748\pi\)
−0.612281 + 0.790640i \(0.709748\pi\)
\(744\) −49.1633 8.28250i −1.80241 0.303651i
\(745\) 14.4242 0.528463
\(746\) −1.33246 + 0.673438i −0.0487850 + 0.0246563i
\(747\) −24.9622 −0.913319
\(748\) −49.9973 36.8278i −1.82808 1.34656i
\(749\) −29.8516 −1.09075
\(750\) 1.83238 + 3.62554i 0.0669090 + 0.132386i
\(751\) −1.95865 −0.0714723 −0.0357362 0.999361i \(-0.511378\pi\)
−0.0357362 + 0.999361i \(0.511378\pi\)
\(752\) −37.4723 + 11.6352i −1.36648 + 0.424292i
\(753\) 31.9283i 1.16353i
\(754\) 1.98457 + 3.92667i 0.0722737 + 0.143001i
\(755\) 13.3082 0.484333
\(756\) −27.9223 20.5674i −1.01552 0.748030i
\(757\) 16.8031i 0.610721i −0.952237 0.305360i \(-0.901223\pi\)
0.952237 0.305360i \(-0.0987769\pi\)
\(758\) −4.13528 8.18205i −0.150200 0.297186i
\(759\) −59.8040 31.0484i −2.17075 1.12698i
\(760\) 1.26004 7.47935i 0.0457065 0.271305i
\(761\) −44.9975 −1.63116 −0.815579 0.578646i \(-0.803581\pi\)
−0.815579 + 0.578646i \(0.803581\pi\)
\(762\) 5.59522 + 11.0707i 0.202693 + 0.401049i
\(763\) 28.5449i 1.03340i
\(764\) 5.63858 7.65492i 0.203997 0.276945i
\(765\) 33.3315 1.20510
\(766\) 0.860637 + 1.70285i 0.0310961 + 0.0615266i
\(767\) 1.36753i 0.0493785i
\(768\) −26.0313 37.8768i −0.939322 1.36676i
\(769\) 19.8146i 0.714531i 0.934003 + 0.357266i \(0.116291\pi\)
−0.934003 + 0.357266i \(0.883709\pi\)
\(770\) −16.5557 + 8.36737i −0.596625 + 0.301539i
\(771\) 3.60350i 0.129777i
\(772\) −25.3407 + 34.4025i −0.912032 + 1.23817i
\(773\) 47.4024i 1.70494i 0.522772 + 0.852472i \(0.324898\pi\)
−0.522772 + 0.852472i \(0.675102\pi\)
\(774\) −37.2889 73.7798i −1.34032 2.65196i
\(775\) 6.13645i 0.220428i
\(776\) 1.26132 7.48696i 0.0452789 0.268766i
\(777\) −29.8516 −1.07092
\(778\) −13.1071 + 6.62443i −0.469912 + 0.237497i
\(779\) −21.6452 −0.775521
\(780\) −2.47901 + 3.36550i −0.0887629 + 0.120504i
\(781\) 35.4561i 1.26872i
\(782\) −0.469269 + 43.0486i −0.0167810 + 1.53941i
\(783\) 27.6482i 0.988066i
\(784\) −0.226613 0.729831i −0.00809333 0.0260654i
\(785\) −3.66320 −0.130745
\(786\) 5.67471 + 11.2280i 0.202410 + 0.400488i
\(787\) 28.8128 1.02706 0.513532 0.858070i \(-0.328337\pi\)
0.513532 + 0.858070i \(0.328337\pi\)
\(788\) −24.3144 + 33.0092i −0.866165 + 1.17590i
\(789\) 73.7536i 2.62570i
\(790\) 4.64469 2.34746i 0.165251 0.0835190i
\(791\) 14.5182i 0.516209i
\(792\) 71.6391 + 12.0690i 2.54558 + 0.428853i
\(793\) 5.04479i 0.179146i
\(794\) 14.9669 + 29.6134i 0.531154 + 1.05094i
\(795\) 32.0467i 1.13658i
\(796\) 18.1197 24.5992i 0.642235 0.871897i
\(797\) 29.1492i 1.03252i −0.856432 0.516260i \(-0.827324\pi\)
0.856432 0.516260i \(-0.172676\pi\)
\(798\) −26.0715 + 13.1767i −0.922920 + 0.466451i
\(799\) −62.2649 −2.20277
\(800\) 4.06494 3.93398i 0.143717 0.139087i
\(801\) 42.6630i 1.50742i
\(802\) −33.2582 + 16.8089i −1.17439 + 0.593545i
\(803\) −38.6852 −1.36517
\(804\) 48.6720 + 35.8516i 1.71653 + 1.26439i
\(805\) 11.4140 + 5.92579i 0.402290 + 0.208857i
\(806\) 5.63536 2.84816i 0.198497 0.100322i
\(807\) 58.6537i 2.06471i
\(808\) 4.29134 + 0.722959i 0.150969 + 0.0254336i
\(809\) −39.3289 −1.38273 −0.691365 0.722506i \(-0.742990\pi\)
−0.691365 + 0.722506i \(0.742990\pi\)
\(810\) −3.56012 + 1.79932i −0.125090 + 0.0632215i
\(811\) 25.2461i 0.886510i −0.896396 0.443255i \(-0.853824\pi\)
0.896396 0.443255i \(-0.146176\pi\)
\(812\) −13.6004 + 18.4639i −0.477281 + 0.647955i
\(813\) −8.86763 −0.311001
\(814\) 23.9258 12.0923i 0.838599 0.423835i
\(815\) −16.6589 −0.583536
\(816\) −21.6271 69.6522i −0.757099 2.43831i
\(817\) −29.8516 −1.04437
\(818\) −11.7081 23.1656i −0.409363 0.809965i
\(819\) 10.2455 0.358006
\(820\) −12.9979 9.57420i −0.453907 0.334346i
\(821\) 11.0606 0.386019 0.193009 0.981197i \(-0.438175\pi\)
0.193009 + 0.981197i \(0.438175\pi\)
\(822\) 10.8583 + 21.4842i 0.378727 + 0.749348i
\(823\) 9.36041i 0.326283i −0.986603 0.163142i \(-0.947837\pi\)
0.986603 0.163142i \(-0.0521628\pi\)
\(824\) −50.5170 8.51057i −1.75984 0.296480i
\(825\) 14.0504i 0.489172i
\(826\) 6.36154 3.21517i 0.221346 0.111870i
\(827\) −50.8347 −1.76770 −0.883848 0.467775i \(-0.845056\pi\)
−0.883848 + 0.467775i \(0.845056\pi\)
\(828\) −22.2276 45.1966i −0.772462 1.57069i
\(829\) 6.23369 0.216505 0.108252 0.994123i \(-0.465475\pi\)
0.108252 + 0.994123i \(0.465475\pi\)
\(830\) −6.00000 + 3.03245i −0.208263 + 0.105258i
\(831\) 8.51548i 0.295399i
\(832\) 5.49944 + 1.90710i 0.190659 + 0.0661168i
\(833\) 1.21270i 0.0420177i
\(834\) 6.09211 + 12.0538i 0.210952 + 0.417390i
\(835\) 1.87953 0.0650437
\(836\) 15.5584 21.1221i 0.538099 0.730522i
\(837\) 39.6794 1.37152
\(838\) 12.9742 + 25.6708i 0.448187 + 0.886782i
\(839\) −14.6079 −0.504320 −0.252160 0.967686i \(-0.581141\pi\)
−0.252160 + 0.967686i \(0.581141\pi\)
\(840\) −21.4842 3.61943i −0.741276 0.124882i
\(841\) −10.7174 −0.369564
\(842\) 11.6403 5.88308i 0.401150 0.202744i
\(843\) −25.6685 −0.884069
\(844\) 41.9869 + 30.9274i 1.44525 + 1.06456i
\(845\) 12.4706i 0.429002i
\(846\) 65.0135 32.8584i 2.23521 1.12969i
\(847\) −34.6620 −1.19100
\(848\) 42.6188 13.2332i 1.46354 0.454429i
\(849\) 49.5065i 1.69906i
\(850\) 8.01167 4.04917i 0.274798 0.138885i
\(851\) −16.4952 8.56379i −0.565447 0.293563i
\(852\) 24.6973 33.5290i 0.846116 1.14868i
\(853\) 33.5602 1.14908 0.574541 0.818476i \(-0.305181\pi\)
0.574541 + 0.818476i \(0.305181\pi\)
\(854\) −23.4677 + 11.8607i −0.803047 + 0.405866i
\(855\) 14.0814i 0.481573i
\(856\) 31.0484 + 5.23070i 1.06121 + 0.178782i
\(857\) −51.6052 −1.76280 −0.881400 0.472372i \(-0.843398\pi\)
−0.881400 + 0.472372i \(0.843398\pi\)
\(858\) −12.9031 + 6.52132i −0.440504 + 0.222634i
\(859\) 27.1505i 0.926365i 0.886263 + 0.463182i \(0.153292\pi\)
−0.886263 + 0.463182i \(0.846708\pi\)
\(860\) −17.9258 13.2041i −0.611264 0.450255i
\(861\) 62.1753i 2.11893i
\(862\) −6.55801 12.9757i −0.223367 0.441953i
\(863\) 8.73671i 0.297401i 0.988882 + 0.148701i \(0.0475091\pi\)
−0.988882 + 0.148701i \(0.952491\pi\)
\(864\) 25.4378 + 26.2846i 0.865412 + 0.894222i
\(865\) 6.34755i 0.215823i
\(866\) −22.4786 + 11.3608i −0.763852 + 0.386057i
\(867\) 66.9037i 2.27217i
\(868\) 26.4985 + 19.5186i 0.899417 + 0.662506i
\(869\) 18.0000 0.610608
\(870\) 7.83492 + 15.5022i 0.265629 + 0.525573i
\(871\) −7.65603 −0.259415
\(872\) −5.00175 + 29.6894i −0.169381 + 1.00541i
\(873\) 14.0957i 0.477067i
\(874\) −18.1865 0.198249i −0.615168 0.00670589i
\(875\) 2.68161i 0.0906551i
\(876\) −36.5826 26.9466i −1.23601 0.910440i
\(877\) 15.0426 0.507954 0.253977 0.967210i \(-0.418261\pi\)
0.253977 + 0.967210i \(0.418261\pi\)
\(878\) 18.9017 9.55309i 0.637903 0.322401i
\(879\) 58.4548 1.97163
\(880\) 18.6856 5.80189i 0.629891 0.195582i
\(881\) 18.6951i 0.629854i 0.949116 + 0.314927i \(0.101980\pi\)
−0.949116 + 0.314927i \(0.898020\pi\)
\(882\) 0.639967 + 1.26624i 0.0215488 + 0.0426365i
\(883\) 0.220695i 0.00742699i −0.999993 0.00371350i \(-0.998818\pi\)
0.999993 0.00371350i \(-0.00118205\pi\)
\(884\) 7.43704 + 5.47809i 0.250135 + 0.184248i
\(885\) 5.39889i 0.181482i
\(886\) 17.6807 8.93595i 0.593994 0.300209i
\(887\) 36.1252i 1.21297i −0.795096 0.606483i \(-0.792580\pi\)
0.795096 0.606483i \(-0.207420\pi\)
\(888\) 31.0484 + 5.23070i 1.04192 + 0.175531i
\(889\) 8.18838i 0.274630i
\(890\) 5.18277 + 10.2546i 0.173727 + 0.343736i
\(891\) −13.7969 −0.462213
\(892\) 2.38210 + 1.75465i 0.0797587 + 0.0587499i
\(893\) 26.3047i 0.880254i
\(894\) 26.4306 + 52.2956i 0.883973 + 1.74903i
\(895\) −3.09691 −0.103518
\(896\) 4.05809 + 30.0664i 0.135571 + 1.00445i
\(897\) 8.89578 + 4.61841i 0.297021 + 0.154204i
\(898\) 18.1085 + 35.8294i 0.604288 + 1.19564i
\(899\) 26.2384i 0.875099i
\(900\) −6.22853 + 8.45583i −0.207618 + 0.281861i
\(901\) 70.8164 2.35924
\(902\) −25.1860 49.8330i −0.838602 1.65926i
\(903\) 85.7478i 2.85351i
\(904\) 2.54394 15.1003i 0.0846100 0.502228i
\(905\) −10.7610 −0.357708
\(906\) 24.3856 + 48.2493i 0.810157 + 1.60298i
\(907\) 17.3062 0.574642 0.287321 0.957834i \(-0.407235\pi\)
0.287321 + 0.957834i \(0.407235\pi\)
\(908\) −2.61027 + 3.54369i −0.0866248 + 0.117602i
\(909\) −8.07930 −0.267974
\(910\) 2.46264 1.24464i 0.0816357 0.0412593i
\(911\) 36.3949 1.20582 0.602909 0.797810i \(-0.294008\pi\)
0.602909 + 0.797810i \(0.294008\pi\)
\(912\) 29.4256 9.13667i 0.974378 0.302545i
\(913\) −23.2524 −0.769541
\(914\) 44.9829 22.7347i 1.48790 0.751998i
\(915\) 19.9164i 0.658417i
\(916\) −28.0418 20.6554i −0.926526 0.682475i
\(917\) 8.30471i 0.274246i
\(918\) 26.1826 + 51.8049i 0.864155 + 1.70982i
\(919\) 11.5400 0.380668 0.190334 0.981719i \(-0.439043\pi\)
0.190334 + 0.981719i \(0.439043\pi\)
\(920\) −10.8333 8.16337i −0.357162 0.269138i
\(921\) −94.5733 −3.11630
\(922\) 0.697148 + 1.37938i 0.0229594 + 0.0454274i
\(923\) 5.27406i 0.173598i
\(924\) −60.6725 44.6911i −1.99598 1.47023i
\(925\) 3.87539i 0.127422i
\(926\) 25.7187 12.9984i 0.845169 0.427155i
\(927\) 95.1084 3.12377
\(928\) 17.3810 16.8210i 0.570558 0.552177i
\(929\) 14.6414 0.480368 0.240184 0.970727i \(-0.422792\pi\)
0.240184 + 0.970727i \(0.422792\pi\)
\(930\) 22.2480 11.2443i 0.729540 0.368715i
\(931\) 0.512325 0.0167908
\(932\) 31.7804 43.1450i 1.04100 1.41326i
\(933\) 90.9645 2.97804
\(934\) 19.6653 + 38.9098i 0.643468 + 1.27317i
\(935\) 31.0484 1.01539
\(936\) −10.6562 1.79525i −0.348310 0.0586796i
\(937\) 10.9207i 0.356762i 0.983961 + 0.178381i \(0.0570860\pi\)
−0.983961 + 0.178381i \(0.942914\pi\)
\(938\) −18.0000 35.6148i −0.587721 1.16286i
\(939\) 17.0217 0.555481
\(940\) 11.6352 15.7959i 0.379498 0.515206i
\(941\) 24.4113i 0.795786i 0.917432 + 0.397893i \(0.130259\pi\)
−0.917432 + 0.397893i \(0.869741\pi\)
\(942\) −6.71238 13.2811i −0.218701 0.432722i
\(943\) −17.8368 + 34.3564i −0.580846 + 1.11880i
\(944\) −7.17996 + 2.22938i −0.233688 + 0.0725603i
\(945\) 17.3398 0.564063
\(946\) −34.7347 68.7261i −1.12932 2.23448i
\(947\) 11.9194i 0.387327i −0.981068 0.193664i \(-0.937963\pi\)
0.981068 0.193664i \(-0.0620371\pi\)
\(948\) 17.0217 + 12.5381i 0.552838 + 0.407218i
\(949\) 5.75438 0.186795
\(950\) 1.71063 + 3.38465i 0.0555001 + 0.109813i
\(951\) 41.0990i 1.33273i
\(952\) −7.99817 + 47.4755i −0.259222 + 1.53869i
\(953\) 56.4533i 1.82870i −0.404923 0.914351i \(-0.632702\pi\)
0.404923 0.914351i \(-0.367298\pi\)
\(954\) −73.9425 + 37.3712i −2.39398 + 1.20994i
\(955\) 4.75372i 0.153827i
\(956\) 37.9815 + 27.9770i 1.22841 + 0.904840i
\(957\) 60.0770i 1.94201i
\(958\) 9.29429 + 18.3897i 0.300285 + 0.594143i
\(959\) 15.8907i 0.513137i
\(960\) 21.7113 + 7.52908i 0.700731 + 0.243000i
\(961\) −6.65605 −0.214711
\(962\) −3.55894 + 1.79872i −0.114745 + 0.0579929i
\(963\) −58.4548 −1.88368
\(964\) 0.341687 + 0.251685i 0.0110050 + 0.00810624i
\(965\) 21.3640i 0.687732i
\(966\) −0.569466 + 52.2402i −0.0183223 + 1.68080i
\(967\) 23.1460i 0.744324i −0.928168 0.372162i \(-0.878617\pi\)
0.928168 0.372162i \(-0.121383\pi\)
\(968\) 36.0516 + 6.07360i 1.15874 + 0.195213i
\(969\) 48.8942 1.57071
\(970\) 1.71237 + 3.38809i 0.0549809 + 0.108785i
\(971\) −9.18083 −0.294627 −0.147313 0.989090i \(-0.547063\pi\)
−0.147313 + 0.989090i \(0.547063\pi\)
\(972\) 18.1905 + 13.3990i 0.583460 + 0.429774i
\(973\) 8.91556i 0.285820i
\(974\) −2.75625 + 1.39303i −0.0883161 + 0.0446356i
\(975\) 2.08998i 0.0669330i
\(976\) 26.4868 8.22417i 0.847822 0.263249i
\(977\) 56.3849i 1.80391i −0.431827 0.901956i \(-0.642131\pi\)
0.431827 0.901956i \(-0.357869\pi\)
\(978\) −30.5254 60.3975i −0.976095 1.93130i
\(979\) 39.7407i 1.27012i
\(980\) 0.307650 + 0.226613i 0.00982750 + 0.00723889i
\(981\) 55.8962i 1.78463i
\(982\) 9.53654 4.81984i 0.304323 0.153807i
\(983\) −22.0549 −0.703441 −0.351721 0.936105i \(-0.614403\pi\)
−0.351721 + 0.936105i \(0.614403\pi\)
\(984\) 10.8946 64.6680i 0.347307 2.06154i
\(985\) 20.4988i 0.653145i
\(986\) 34.2565 17.3135i 1.09095 0.551374i
\(987\) −75.5595 −2.40509
\(988\) −2.31430 + 3.14189i −0.0736276 + 0.0999567i
\(989\) −24.5992 + 47.3819i −0.782210 + 1.50666i
\(990\) −32.4190 + 16.3848i −1.03034 + 0.520744i
\(991\) 14.4702i 0.459661i −0.973231 0.229830i \(-0.926183\pi\)
0.973231 0.229830i \(-0.0738171\pi\)
\(992\) −24.1407 24.9443i −0.766468 0.791984i
\(993\) 43.5550 1.38218
\(994\) −24.5342 + 12.3998i −0.778177 + 0.393297i
\(995\) 15.2762i 0.484287i
\(996\) −21.9885 16.1967i −0.696734 0.513211i
\(997\) −33.2358 −1.05259 −0.526294 0.850303i \(-0.676419\pi\)
−0.526294 + 0.850303i \(0.676419\pi\)
\(998\) −12.6316 + 6.38414i −0.399848 + 0.202086i
\(999\) −25.0590 −0.792831
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 460.2.e.a.91.5 16
4.3 odd 2 inner 460.2.e.a.91.7 yes 16
23.22 odd 2 inner 460.2.e.a.91.6 yes 16
92.91 even 2 inner 460.2.e.a.91.8 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.e.a.91.5 16 1.1 even 1 trivial
460.2.e.a.91.6 yes 16 23.22 odd 2 inner
460.2.e.a.91.7 yes 16 4.3 odd 2 inner
460.2.e.a.91.8 yes 16 92.91 even 2 inner