Properties

Label 1110.2.e.c.739.9
Level $1110$
Weight $2$
Character 1110.739
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(739,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.739");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} - 3018 x^{7} + 658 x^{6} - 1584 x^{5} + 16372 x^{4} - 18840 x^{3} + 10952 x^{2} + \cdots + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 739.9
Root \(2.23405 + 2.23405i\) of defining polynomial
Character \(\chi\) \(=\) 1110.739
Dual form 1110.2.e.c.739.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.23405 + 0.0950871i) q^{5} -1.00000i q^{6} +3.20752i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.23405 + 0.0950871i) q^{5} -1.00000i q^{6} +3.20752i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(2.23405 - 0.0950871i) q^{10} -3.73314 q^{11} +1.00000i q^{12} +0.424858 q^{13} -3.20752i q^{14} +(-0.0950871 - 2.23405i) q^{15} +1.00000 q^{16} -6.90738 q^{17} +1.00000 q^{18} -8.02549i q^{19} +(-2.23405 + 0.0950871i) q^{20} -3.20752 q^{21} +3.73314 q^{22} +6.34959 q^{23} -1.00000i q^{24} +(4.98192 - 0.424858i) q^{25} -0.424858 q^{26} -1.00000i q^{27} +3.20752i q^{28} +3.39355i q^{29} +(0.0950871 + 2.23405i) q^{30} +1.20338i q^{31} -1.00000 q^{32} -3.73314i q^{33} +6.90738 q^{34} +(-0.304994 - 7.16575i) q^{35} -1.00000 q^{36} +(5.90637 - 1.45421i) q^{37} +8.02549i q^{38} +0.424858i q^{39} +(2.23405 - 0.0950871i) q^{40} +5.74899 q^{41} +3.20752 q^{42} -9.31001 q^{43} -3.73314 q^{44} +(2.23405 - 0.0950871i) q^{45} -6.34959 q^{46} +2.04357i q^{47} +1.00000i q^{48} -3.28821 q^{49} +(-4.98192 + 0.424858i) q^{50} -6.90738i q^{51} +0.424858 q^{52} -11.8045i q^{53} +1.00000i q^{54} +(8.34000 - 0.354973i) q^{55} -3.20752i q^{56} +8.02549 q^{57} -3.39355i q^{58} -2.16131i q^{59} +(-0.0950871 - 2.23405i) q^{60} -1.45108i q^{61} -1.20338i q^{62} -3.20752i q^{63} +1.00000 q^{64} +(-0.949152 + 0.0403985i) q^{65} +3.73314i q^{66} -11.4940i q^{67} -6.90738 q^{68} +6.34959i q^{69} +(0.304994 + 7.16575i) q^{70} -5.59683 q^{71} +1.00000 q^{72} +12.5062i q^{73} +(-5.90637 + 1.45421i) q^{74} +(0.424858 + 4.98192i) q^{75} -8.02549i q^{76} -11.9741i q^{77} -0.424858i q^{78} +4.50480i q^{79} +(-2.23405 + 0.0950871i) q^{80} +1.00000 q^{81} -5.74899 q^{82} -7.00128i q^{83} -3.20752 q^{84} +(15.4314 - 0.656803i) q^{85} +9.31001 q^{86} -3.39355 q^{87} +3.73314 q^{88} -15.9242i q^{89} +(-2.23405 + 0.0950871i) q^{90} +1.36274i q^{91} +6.34959 q^{92} -1.20338 q^{93} -2.04357i q^{94} +(0.763120 + 17.9293i) q^{95} -1.00000i q^{96} +4.43763 q^{97} +3.28821 q^{98} +3.73314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} + 6 q^{15} + 16 q^{16} - 38 q^{17} + 16 q^{18} - 2 q^{20} + 6 q^{21} - 2 q^{22} - 20 q^{23} - 4 q^{25} - 6 q^{30} - 16 q^{32} + 38 q^{34} - 10 q^{35} - 16 q^{36} - 4 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 2 q^{44} + 2 q^{45} + 20 q^{46} - 18 q^{49} + 4 q^{50} + 20 q^{55} + 16 q^{57} + 6 q^{60} + 16 q^{64} + 12 q^{65} - 38 q^{68} + 10 q^{70} - 24 q^{71} + 16 q^{72} + 4 q^{74} - 2 q^{80} + 16 q^{81} + 6 q^{82} + 6 q^{84} + 2 q^{86} + 2 q^{87} - 2 q^{88} - 2 q^{90} - 20 q^{92} + 22 q^{93} - 16 q^{95} + 38 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) −2.23405 + 0.0950871i −0.999095 + 0.0425243i
\(6\) 1.00000i 0.408248i
\(7\) 3.20752i 1.21233i 0.795339 + 0.606165i \(0.207293\pi\)
−0.795339 + 0.606165i \(0.792707\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) 2.23405 0.0950871i 0.706467 0.0300692i
\(11\) −3.73314 −1.12558 −0.562792 0.826599i \(-0.690273\pi\)
−0.562792 + 0.826599i \(0.690273\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0.424858 0.117834 0.0589172 0.998263i \(-0.481235\pi\)
0.0589172 + 0.998263i \(0.481235\pi\)
\(14\) 3.20752i 0.857247i
\(15\) −0.0950871 2.23405i −0.0245514 0.576828i
\(16\) 1.00000 0.250000
\(17\) −6.90738 −1.67529 −0.837643 0.546218i \(-0.816067\pi\)
−0.837643 + 0.546218i \(0.816067\pi\)
\(18\) 1.00000 0.235702
\(19\) 8.02549i 1.84117i −0.390539 0.920586i \(-0.627711\pi\)
0.390539 0.920586i \(-0.372289\pi\)
\(20\) −2.23405 + 0.0950871i −0.499548 + 0.0212621i
\(21\) −3.20752 −0.699939
\(22\) 3.73314 0.795907
\(23\) 6.34959 1.32398 0.661990 0.749512i \(-0.269712\pi\)
0.661990 + 0.749512i \(0.269712\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 4.98192 0.424858i 0.996383 0.0849716i
\(26\) −0.424858 −0.0833215
\(27\) 1.00000i 0.192450i
\(28\) 3.20752i 0.606165i
\(29\) 3.39355i 0.630167i 0.949064 + 0.315084i \(0.102033\pi\)
−0.949064 + 0.315084i \(0.897967\pi\)
\(30\) 0.0950871 + 2.23405i 0.0173605 + 0.407879i
\(31\) 1.20338i 0.216134i 0.994144 + 0.108067i \(0.0344660\pi\)
−0.994144 + 0.108067i \(0.965534\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.73314i 0.649856i
\(34\) 6.90738 1.18461
\(35\) −0.304994 7.16575i −0.0515534 1.21123i
\(36\) −1.00000 −0.166667
\(37\) 5.90637 1.45421i 0.971002 0.239071i
\(38\) 8.02549i 1.30191i
\(39\) 0.424858i 0.0680317i
\(40\) 2.23405 0.0950871i 0.353234 0.0150346i
\(41\) 5.74899 0.897841 0.448921 0.893572i \(-0.351809\pi\)
0.448921 + 0.893572i \(0.351809\pi\)
\(42\) 3.20752 0.494932
\(43\) −9.31001 −1.41976 −0.709882 0.704321i \(-0.751252\pi\)
−0.709882 + 0.704321i \(0.751252\pi\)
\(44\) −3.73314 −0.562792
\(45\) 2.23405 0.0950871i 0.333032 0.0141748i
\(46\) −6.34959 −0.936196
\(47\) 2.04357i 0.298085i 0.988831 + 0.149043i \(0.0476191\pi\)
−0.988831 + 0.149043i \(0.952381\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −3.28821 −0.469744
\(50\) −4.98192 + 0.424858i −0.704549 + 0.0600840i
\(51\) 6.90738i 0.967227i
\(52\) 0.424858 0.0589172
\(53\) 11.8045i 1.62147i −0.585414 0.810734i \(-0.699068\pi\)
0.585414 0.810734i \(-0.300932\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 8.34000 0.354973i 1.12456 0.0478646i
\(56\) 3.20752i 0.428623i
\(57\) 8.02549 1.06300
\(58\) 3.39355i 0.445596i
\(59\) 2.16131i 0.281379i −0.990054 0.140689i \(-0.955068\pi\)
0.990054 0.140689i \(-0.0449318\pi\)
\(60\) −0.0950871 2.23405i −0.0122757 0.288414i
\(61\) 1.45108i 0.185791i −0.995676 0.0928957i \(-0.970388\pi\)
0.995676 0.0928957i \(-0.0296123\pi\)
\(62\) 1.20338i 0.152829i
\(63\) 3.20752i 0.404110i
\(64\) 1.00000 0.125000
\(65\) −0.949152 + 0.0403985i −0.117728 + 0.00501082i
\(66\) 3.73314i 0.459517i
\(67\) 11.4940i 1.40422i −0.712069 0.702109i \(-0.752242\pi\)
0.712069 0.702109i \(-0.247758\pi\)
\(68\) −6.90738 −0.837643
\(69\) 6.34959i 0.764401i
\(70\) 0.304994 + 7.16575i 0.0364538 + 0.856471i
\(71\) −5.59683 −0.664222 −0.332111 0.943240i \(-0.607761\pi\)
−0.332111 + 0.943240i \(0.607761\pi\)
\(72\) 1.00000 0.117851
\(73\) 12.5062i 1.46374i 0.681444 + 0.731870i \(0.261352\pi\)
−0.681444 + 0.731870i \(0.738648\pi\)
\(74\) −5.90637 + 1.45421i −0.686602 + 0.169049i
\(75\) 0.424858 + 4.98192i 0.0490584 + 0.575262i
\(76\) 8.02549i 0.920586i
\(77\) 11.9741i 1.36458i
\(78\) 0.424858i 0.0481057i
\(79\) 4.50480i 0.506830i 0.967358 + 0.253415i \(0.0815538\pi\)
−0.967358 + 0.253415i \(0.918446\pi\)
\(80\) −2.23405 + 0.0950871i −0.249774 + 0.0106311i
\(81\) 1.00000 0.111111
\(82\) −5.74899 −0.634870
\(83\) 7.00128i 0.768491i −0.923231 0.384245i \(-0.874462\pi\)
0.923231 0.384245i \(-0.125538\pi\)
\(84\) −3.20752 −0.349969
\(85\) 15.4314 0.656803i 1.67377 0.0712403i
\(86\) 9.31001 1.00392
\(87\) −3.39355 −0.363827
\(88\) 3.73314 0.397954
\(89\) 15.9242i 1.68796i −0.536373 0.843981i \(-0.680206\pi\)
0.536373 0.843981i \(-0.319794\pi\)
\(90\) −2.23405 + 0.0950871i −0.235489 + 0.0100231i
\(91\) 1.36274i 0.142854i
\(92\) 6.34959 0.661990
\(93\) −1.20338 −0.124785
\(94\) 2.04357i 0.210778i
\(95\) 0.763120 + 17.9293i 0.0782945 + 1.83951i
\(96\) 1.00000i 0.102062i
\(97\) 4.43763 0.450573 0.225286 0.974293i \(-0.427668\pi\)
0.225286 + 0.974293i \(0.427668\pi\)
\(98\) 3.28821 0.332159
\(99\) 3.73314 0.375194
\(100\) 4.98192 0.424858i 0.498192 0.0424858i
\(101\) 13.0171 1.29525 0.647623 0.761961i \(-0.275763\pi\)
0.647623 + 0.761961i \(0.275763\pi\)
\(102\) 6.90738i 0.683933i
\(103\) −7.17254 −0.706732 −0.353366 0.935485i \(-0.614963\pi\)
−0.353366 + 0.935485i \(0.614963\pi\)
\(104\) −0.424858 −0.0416608
\(105\) 7.16575 0.304994i 0.699306 0.0297644i
\(106\) 11.8045i 1.14655i
\(107\) 3.80308i 0.367658i −0.982958 0.183829i \(-0.941151\pi\)
0.982958 0.183829i \(-0.0588492\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 4.93476i 0.472664i −0.971672 0.236332i \(-0.924055\pi\)
0.971672 0.236332i \(-0.0759454\pi\)
\(110\) −8.34000 + 0.354973i −0.795187 + 0.0338454i
\(111\) 1.45421 + 5.90637i 0.138028 + 0.560608i
\(112\) 3.20752i 0.303082i
\(113\) −9.29880 −0.874758 −0.437379 0.899277i \(-0.644093\pi\)
−0.437379 + 0.899277i \(0.644093\pi\)
\(114\) −8.02549 −0.751656
\(115\) −14.1853 + 0.603764i −1.32278 + 0.0563013i
\(116\) 3.39355i 0.315084i
\(117\) −0.424858 −0.0392781
\(118\) 2.16131i 0.198965i
\(119\) 22.1556i 2.03100i
\(120\) 0.0950871 + 2.23405i 0.00868023 + 0.203940i
\(121\) 2.93631 0.266937
\(122\) 1.45108i 0.131374i
\(123\) 5.74899i 0.518369i
\(124\) 1.20338i 0.108067i
\(125\) −11.0894 + 1.42287i −0.991869 + 0.127265i
\(126\) 3.20752i 0.285749i
\(127\) 14.3747i 1.27555i −0.770222 0.637776i \(-0.779855\pi\)
0.770222 0.637776i \(-0.220145\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 9.31001i 0.819701i
\(130\) 0.949152 0.0403985i 0.0832461 0.00354319i
\(131\) 12.3237i 1.07672i 0.842714 + 0.538362i \(0.180957\pi\)
−0.842714 + 0.538362i \(0.819043\pi\)
\(132\) 3.73314i 0.324928i
\(133\) 25.7419 2.23211
\(134\) 11.4940i 0.992933i
\(135\) 0.0950871 + 2.23405i 0.00818380 + 0.192276i
\(136\) 6.90738 0.592303
\(137\) 17.4773i 1.49319i −0.665280 0.746594i \(-0.731688\pi\)
0.665280 0.746594i \(-0.268312\pi\)
\(138\) 6.34959i 0.540513i
\(139\) −0.125741 −0.0106652 −0.00533261 0.999986i \(-0.501697\pi\)
−0.00533261 + 0.999986i \(0.501697\pi\)
\(140\) −0.304994 7.16575i −0.0257767 0.605617i
\(141\) −2.04357 −0.172100
\(142\) 5.59683 0.469676
\(143\) −1.58605 −0.132632
\(144\) −1.00000 −0.0833333
\(145\) −0.322683 7.58136i −0.0267974 0.629597i
\(146\) 12.5062i 1.03502i
\(147\) 3.28821i 0.271207i
\(148\) 5.90637 1.45421i 0.485501 0.119536i
\(149\) 2.43147 0.199194 0.0995968 0.995028i \(-0.468245\pi\)
0.0995968 + 0.995028i \(0.468245\pi\)
\(150\) −0.424858 4.98192i −0.0346895 0.406772i
\(151\) −15.1683 −1.23438 −0.617188 0.786816i \(-0.711728\pi\)
−0.617188 + 0.786816i \(0.711728\pi\)
\(152\) 8.02549i 0.650953i
\(153\) 6.90738 0.558429
\(154\) 11.9741i 0.964902i
\(155\) −0.114426 2.68841i −0.00919092 0.215938i
\(156\) 0.424858i 0.0340159i
\(157\) 19.1941i 1.53185i −0.642928 0.765927i \(-0.722281\pi\)
0.642928 0.765927i \(-0.277719\pi\)
\(158\) 4.50480i 0.358383i
\(159\) 11.8045 0.936156
\(160\) 2.23405 0.0950871i 0.176617 0.00751730i
\(161\) 20.3665i 1.60510i
\(162\) −1.00000 −0.0785674
\(163\) 7.14619 0.559733 0.279867 0.960039i \(-0.409710\pi\)
0.279867 + 0.960039i \(0.409710\pi\)
\(164\) 5.74899 0.448921
\(165\) 0.354973 + 8.34000i 0.0276346 + 0.649268i
\(166\) 7.00128i 0.543405i
\(167\) −12.6692 −0.980373 −0.490187 0.871618i \(-0.663071\pi\)
−0.490187 + 0.871618i \(0.663071\pi\)
\(168\) 3.20752 0.247466
\(169\) −12.8195 −0.986115
\(170\) −15.4314 + 0.656803i −1.18353 + 0.0503745i
\(171\) 8.02549i 0.613724i
\(172\) −9.31001 −0.709882
\(173\) 19.7245i 1.49963i 0.661649 + 0.749814i \(0.269857\pi\)
−0.661649 + 0.749814i \(0.730143\pi\)
\(174\) 3.39355 0.257265
\(175\) 1.36274 + 15.9796i 0.103014 + 1.20795i
\(176\) −3.73314 −0.281396
\(177\) 2.16131 0.162454
\(178\) 15.9242i 1.19357i
\(179\) 3.19619i 0.238895i −0.992841 0.119447i \(-0.961888\pi\)
0.992841 0.119447i \(-0.0381123\pi\)
\(180\) 2.23405 0.0950871i 0.166516 0.00708738i
\(181\) −11.3735 −0.845387 −0.422694 0.906273i \(-0.638915\pi\)
−0.422694 + 0.906273i \(0.638915\pi\)
\(182\) 1.36274i 0.101013i
\(183\) 1.45108 0.107267
\(184\) −6.34959 −0.468098
\(185\) −13.0568 + 3.81040i −0.959957 + 0.280146i
\(186\) 1.20338 0.0882361
\(187\) 25.7862 1.88567
\(188\) 2.04357i 0.149043i
\(189\) 3.20752 0.233313
\(190\) −0.763120 17.9293i −0.0553626 1.30073i
\(191\) 12.4830i 0.903235i 0.892212 + 0.451617i \(0.149153\pi\)
−0.892212 + 0.451617i \(0.850847\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −12.1559 −0.874999 −0.437499 0.899219i \(-0.644136\pi\)
−0.437499 + 0.899219i \(0.644136\pi\)
\(194\) −4.43763 −0.318603
\(195\) −0.0403985 0.949152i −0.00289300 0.0679702i
\(196\) −3.28821 −0.234872
\(197\) 8.89921i 0.634042i −0.948418 0.317021i \(-0.897317\pi\)
0.948418 0.317021i \(-0.102683\pi\)
\(198\) −3.73314 −0.265302
\(199\) 10.3470i 0.733481i −0.930323 0.366740i \(-0.880474\pi\)
0.930323 0.366740i \(-0.119526\pi\)
\(200\) −4.98192 + 0.424858i −0.352275 + 0.0300420i
\(201\) 11.4940 0.810726
\(202\) −13.0171 −0.915878
\(203\) −10.8849 −0.763971
\(204\) 6.90738i 0.483613i
\(205\) −12.8435 + 0.546655i −0.897029 + 0.0381800i
\(206\) 7.17254 0.499735
\(207\) −6.34959 −0.441327
\(208\) 0.424858 0.0294586
\(209\) 29.9602i 2.07239i
\(210\) −7.16575 + 0.304994i −0.494484 + 0.0210466i
\(211\) 5.52374 0.380270 0.190135 0.981758i \(-0.439107\pi\)
0.190135 + 0.981758i \(0.439107\pi\)
\(212\) 11.8045i 0.810734i
\(213\) 5.59683i 0.383489i
\(214\) 3.80308i 0.259973i
\(215\) 20.7990 0.885263i 1.41848 0.0603744i
\(216\) 1.00000i 0.0680414i
\(217\) −3.85987 −0.262025
\(218\) 4.93476i 0.334224i
\(219\) −12.5062 −0.845091
\(220\) 8.34000 0.354973i 0.562282 0.0239323i
\(221\) −2.93466 −0.197406
\(222\) −1.45421 5.90637i −0.0976005 0.396410i
\(223\) 3.24704i 0.217438i −0.994073 0.108719i \(-0.965325\pi\)
0.994073 0.108719i \(-0.0346748\pi\)
\(224\) 3.20752i 0.214312i
\(225\) −4.98192 + 0.424858i −0.332128 + 0.0283239i
\(226\) 9.29880 0.618547
\(227\) −3.24282 −0.215234 −0.107617 0.994192i \(-0.534322\pi\)
−0.107617 + 0.994192i \(0.534322\pi\)
\(228\) 8.02549 0.531501
\(229\) −23.2392 −1.53569 −0.767845 0.640636i \(-0.778671\pi\)
−0.767845 + 0.640636i \(0.778671\pi\)
\(230\) 14.1853 0.603764i 0.935349 0.0398110i
\(231\) 11.9741 0.787839
\(232\) 3.39355i 0.222798i
\(233\) 23.5036i 1.53977i −0.638181 0.769886i \(-0.720313\pi\)
0.638181 0.769886i \(-0.279687\pi\)
\(234\) 0.424858 0.0277738
\(235\) −0.194317 4.56543i −0.0126759 0.297815i
\(236\) 2.16131i 0.140689i
\(237\) −4.50480 −0.292618
\(238\) 22.1556i 1.43613i
\(239\) 6.75627i 0.437027i 0.975834 + 0.218514i \(0.0701208\pi\)
−0.975834 + 0.218514i \(0.929879\pi\)
\(240\) −0.0950871 2.23405i −0.00613785 0.144207i
\(241\) 27.0533i 1.74266i 0.490699 + 0.871329i \(0.336741\pi\)
−0.490699 + 0.871329i \(0.663259\pi\)
\(242\) −2.93631 −0.188753
\(243\) 1.00000i 0.0641500i
\(244\) 1.45108i 0.0928957i
\(245\) 7.34600 0.312666i 0.469319 0.0199755i
\(246\) 5.74899i 0.366542i
\(247\) 3.40969i 0.216953i
\(248\) 1.20338i 0.0764147i
\(249\) 7.00128 0.443688
\(250\) 11.0894 1.42287i 0.701357 0.0899901i
\(251\) 12.9375i 0.816609i 0.912846 + 0.408305i \(0.133880\pi\)
−0.912846 + 0.408305i \(0.866120\pi\)
\(252\) 3.20752i 0.202055i
\(253\) −23.7039 −1.49025
\(254\) 14.3747i 0.901951i
\(255\) 0.656803 + 15.4314i 0.0411306 + 0.966352i
\(256\) 1.00000 0.0625000
\(257\) −14.5960 −0.910473 −0.455237 0.890370i \(-0.650445\pi\)
−0.455237 + 0.890370i \(0.650445\pi\)
\(258\) 9.31001i 0.579616i
\(259\) 4.66443 + 18.9448i 0.289833 + 1.17717i
\(260\) −0.949152 + 0.0403985i −0.0588639 + 0.00250541i
\(261\) 3.39355i 0.210056i
\(262\) 12.3237i 0.761358i
\(263\) 12.2500i 0.755370i −0.925934 0.377685i \(-0.876720\pi\)
0.925934 0.377685i \(-0.123280\pi\)
\(264\) 3.73314i 0.229759i
\(265\) 1.12245 + 26.3717i 0.0689518 + 1.62000i
\(266\) −25.7419 −1.57834
\(267\) 15.9242 0.974545
\(268\) 11.4940i 0.702109i
\(269\) 14.1886 0.865094 0.432547 0.901611i \(-0.357615\pi\)
0.432547 + 0.901611i \(0.357615\pi\)
\(270\) −0.0950871 2.23405i −0.00578682 0.135960i
\(271\) −8.82413 −0.536028 −0.268014 0.963415i \(-0.586367\pi\)
−0.268014 + 0.963415i \(0.586367\pi\)
\(272\) −6.90738 −0.418821
\(273\) −1.36274 −0.0824769
\(274\) 17.4773i 1.05584i
\(275\) −18.5982 + 1.58605i −1.12151 + 0.0956426i
\(276\) 6.34959i 0.382200i
\(277\) 12.6061 0.757426 0.378713 0.925514i \(-0.376367\pi\)
0.378713 + 0.925514i \(0.376367\pi\)
\(278\) 0.125741 0.00754145
\(279\) 1.20338i 0.0720445i
\(280\) 0.304994 + 7.16575i 0.0182269 + 0.428236i
\(281\) 15.8731i 0.946908i −0.880819 0.473454i \(-0.843007\pi\)
0.880819 0.473454i \(-0.156993\pi\)
\(282\) 2.04357 0.121693
\(283\) −29.1588 −1.73331 −0.866656 0.498906i \(-0.833735\pi\)
−0.866656 + 0.498906i \(0.833735\pi\)
\(284\) −5.59683 −0.332111
\(285\) −17.9293 + 0.763120i −1.06204 + 0.0452034i
\(286\) 1.58605 0.0937853
\(287\) 18.4400i 1.08848i
\(288\) 1.00000 0.0589256
\(289\) 30.7119 1.80658
\(290\) 0.322683 + 7.58136i 0.0189486 + 0.445193i
\(291\) 4.43763i 0.260138i
\(292\) 12.5062i 0.731870i
\(293\) 28.4275i 1.66075i 0.557204 + 0.830376i \(0.311874\pi\)
−0.557204 + 0.830376i \(0.688126\pi\)
\(294\) 3.28821i 0.191772i
\(295\) 0.205513 + 4.82846i 0.0119654 + 0.281124i
\(296\) −5.90637 + 1.45421i −0.343301 + 0.0845245i
\(297\) 3.73314i 0.216619i
\(298\) −2.43147 −0.140851
\(299\) 2.69767 0.156010
\(300\) 0.424858 + 4.98192i 0.0245292 + 0.287631i
\(301\) 29.8621i 1.72122i
\(302\) 15.1683 0.872835
\(303\) 13.0171i 0.747811i
\(304\) 8.02549i 0.460293i
\(305\) 0.137979 + 3.24177i 0.00790064 + 0.185623i
\(306\) −6.90738 −0.394869
\(307\) 20.6139i 1.17650i 0.808680 + 0.588249i \(0.200182\pi\)
−0.808680 + 0.588249i \(0.799818\pi\)
\(308\) 11.9741i 0.682289i
\(309\) 7.17254i 0.408032i
\(310\) 0.114426 + 2.68841i 0.00649896 + 0.152691i
\(311\) 15.0056i 0.850887i 0.904985 + 0.425443i \(0.139882\pi\)
−0.904985 + 0.425443i \(0.860118\pi\)
\(312\) 0.424858i 0.0240528i
\(313\) 28.8720 1.63194 0.815972 0.578092i \(-0.196202\pi\)
0.815972 + 0.578092i \(0.196202\pi\)
\(314\) 19.1941i 1.08318i
\(315\) 0.304994 + 7.16575i 0.0171845 + 0.403744i
\(316\) 4.50480i 0.253415i
\(317\) 14.7214i 0.826837i −0.910541 0.413419i \(-0.864335\pi\)
0.910541 0.413419i \(-0.135665\pi\)
\(318\) −11.8045 −0.661962
\(319\) 12.6686i 0.709306i
\(320\) −2.23405 + 0.0950871i −0.124887 + 0.00531553i
\(321\) 3.80308 0.212267
\(322\) 20.3665i 1.13498i
\(323\) 55.4351i 3.08449i
\(324\) 1.00000 0.0555556
\(325\) 2.11661 0.180504i 0.117408 0.0100126i
\(326\) −7.14619 −0.395791
\(327\) 4.93476 0.272893
\(328\) −5.74899 −0.317435
\(329\) −6.55479 −0.361378
\(330\) −0.354973 8.34000i −0.0195406 0.459102i
\(331\) 8.15238i 0.448095i 0.974578 + 0.224048i \(0.0719271\pi\)
−0.974578 + 0.224048i \(0.928073\pi\)
\(332\) 7.00128i 0.384245i
\(333\) −5.90637 + 1.45421i −0.323667 + 0.0796904i
\(334\) 12.6692 0.693228
\(335\) 1.09293 + 25.6782i 0.0597134 + 1.40295i
\(336\) −3.20752 −0.174985
\(337\) 28.0034i 1.52544i 0.646726 + 0.762722i \(0.276138\pi\)
−0.646726 + 0.762722i \(0.723862\pi\)
\(338\) 12.8195 0.697289
\(339\) 9.29880i 0.505042i
\(340\) 15.4314 0.656803i 0.836885 0.0356201i
\(341\) 4.49238i 0.243276i
\(342\) 8.02549i 0.433969i
\(343\) 11.9057i 0.642846i
\(344\) 9.31001 0.501962
\(345\) −0.603764 14.1853i −0.0325056 0.763709i
\(346\) 19.7245i 1.06040i
\(347\) 6.82853 0.366575 0.183287 0.983059i \(-0.441326\pi\)
0.183287 + 0.983059i \(0.441326\pi\)
\(348\) −3.39355 −0.181914
\(349\) −5.65418 −0.302662 −0.151331 0.988483i \(-0.548356\pi\)
−0.151331 + 0.988483i \(0.548356\pi\)
\(350\) −1.36274 15.9796i −0.0728416 0.854146i
\(351\) 0.424858i 0.0226772i
\(352\) 3.73314 0.198977
\(353\) 12.7850 0.680476 0.340238 0.940339i \(-0.389492\pi\)
0.340238 + 0.940339i \(0.389492\pi\)
\(354\) −2.16131 −0.114872
\(355\) 12.5036 0.532187i 0.663621 0.0282456i
\(356\) 15.9242i 0.843981i
\(357\) 22.1556 1.17260
\(358\) 3.19619i 0.168924i
\(359\) 11.3292 0.597933 0.298966 0.954264i \(-0.403358\pi\)
0.298966 + 0.954264i \(0.403358\pi\)
\(360\) −2.23405 + 0.0950871i −0.117745 + 0.00501153i
\(361\) −45.4084 −2.38992
\(362\) 11.3735 0.597779
\(363\) 2.93631i 0.154116i
\(364\) 1.36274i 0.0714271i
\(365\) −1.18918 27.9394i −0.0622445 1.46242i
\(366\) −1.45108 −0.0758490
\(367\) 10.0590i 0.525075i 0.964922 + 0.262538i \(0.0845594\pi\)
−0.964922 + 0.262538i \(0.915441\pi\)
\(368\) 6.34959 0.330995
\(369\) −5.74899 −0.299280
\(370\) 13.0568 3.81040i 0.678792 0.198093i
\(371\) 37.8631 1.96576
\(372\) −1.20338 −0.0623924
\(373\) 9.39169i 0.486283i −0.969991 0.243142i \(-0.921822\pi\)
0.969991 0.243142i \(-0.0781780\pi\)
\(374\) −25.7862 −1.33337
\(375\) −1.42287 11.0894i −0.0734766 0.572656i
\(376\) 2.04357i 0.105389i
\(377\) 1.44178i 0.0742554i
\(378\) −3.20752 −0.164977
\(379\) −10.7371 −0.551526 −0.275763 0.961226i \(-0.588930\pi\)
−0.275763 + 0.961226i \(0.588930\pi\)
\(380\) 0.763120 + 17.9293i 0.0391473 + 0.919754i
\(381\) 14.3747 0.736440
\(382\) 12.4830i 0.638683i
\(383\) −11.2412 −0.574399 −0.287199 0.957871i \(-0.592724\pi\)
−0.287199 + 0.957871i \(0.592724\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 1.13859 + 26.7507i 0.0580277 + 1.36334i
\(386\) 12.1559 0.618717
\(387\) 9.31001 0.473255
\(388\) 4.43763 0.225286
\(389\) 7.80757i 0.395860i 0.980216 + 0.197930i \(0.0634218\pi\)
−0.980216 + 0.197930i \(0.936578\pi\)
\(390\) 0.0403985 + 0.949152i 0.00204566 + 0.0480622i
\(391\) −43.8590 −2.21805
\(392\) 3.28821 0.166079
\(393\) −12.3237 −0.621646
\(394\) 8.89921i 0.448336i
\(395\) −0.428349 10.0639i −0.0215526 0.506371i
\(396\) 3.73314 0.187597
\(397\) 33.1348i 1.66299i −0.555534 0.831494i \(-0.687486\pi\)
0.555534 0.831494i \(-0.312514\pi\)
\(398\) 10.3470i 0.518649i
\(399\) 25.7419i 1.28871i
\(400\) 4.98192 0.424858i 0.249096 0.0212429i
\(401\) 33.2206i 1.65896i −0.558540 0.829478i \(-0.688638\pi\)
0.558540 0.829478i \(-0.311362\pi\)
\(402\) −11.4940 −0.573270
\(403\) 0.511266i 0.0254680i
\(404\) 13.0171 0.647623
\(405\) −2.23405 + 0.0950871i −0.111011 + 0.00472492i
\(406\) 10.8849 0.540209
\(407\) −22.0493 + 5.42878i −1.09294 + 0.269095i
\(408\) 6.90738i 0.341966i
\(409\) 18.4622i 0.912899i −0.889749 0.456449i \(-0.849121\pi\)
0.889749 0.456449i \(-0.150879\pi\)
\(410\) 12.8435 0.546655i 0.634295 0.0269974i
\(411\) 17.4773 0.862092
\(412\) −7.17254 −0.353366
\(413\) 6.93245 0.341124
\(414\) 6.34959 0.312065
\(415\) 0.665732 + 15.6412i 0.0326795 + 0.767796i
\(416\) −0.424858 −0.0208304
\(417\) 0.125741i 0.00615757i
\(418\) 29.9602i 1.46540i
\(419\) 0.759460 0.0371021 0.0185510 0.999828i \(-0.494095\pi\)
0.0185510 + 0.999828i \(0.494095\pi\)
\(420\) 7.16575 0.304994i 0.349653 0.0148822i
\(421\) 27.6679i 1.34845i −0.738525 0.674227i \(-0.764477\pi\)
0.738525 0.674227i \(-0.235523\pi\)
\(422\) −5.52374 −0.268891
\(423\) 2.04357i 0.0993617i
\(424\) 11.8045i 0.573276i
\(425\) −34.4120 + 2.93466i −1.66923 + 0.142352i
\(426\) 5.59683i 0.271168i
\(427\) 4.65437 0.225241
\(428\) 3.80308i 0.183829i
\(429\) 1.58605i 0.0765754i
\(430\) −20.7990 + 0.885263i −1.00302 + 0.0426911i
\(431\) 4.94514i 0.238199i 0.992882 + 0.119100i \(0.0380008\pi\)
−0.992882 + 0.119100i \(0.961999\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 3.83656i 0.184373i 0.995742 + 0.0921867i \(0.0293857\pi\)
−0.995742 + 0.0921867i \(0.970614\pi\)
\(434\) 3.85987 0.185280
\(435\) 7.58136 0.322683i 0.363498 0.0154715i
\(436\) 4.93476i 0.236332i
\(437\) 50.9585i 2.43768i
\(438\) 12.5062 0.597569
\(439\) 27.6321i 1.31881i −0.751789 0.659404i \(-0.770809\pi\)
0.751789 0.659404i \(-0.229191\pi\)
\(440\) −8.34000 + 0.354973i −0.397594 + 0.0169227i
\(441\) 3.28821 0.156581
\(442\) 2.93466 0.139587
\(443\) 17.7327i 0.842504i 0.906944 + 0.421252i \(0.138409\pi\)
−0.906944 + 0.421252i \(0.861591\pi\)
\(444\) 1.45421 + 5.90637i 0.0690139 + 0.280304i
\(445\) 1.51419 + 35.5754i 0.0717793 + 1.68643i
\(446\) 3.24704i 0.153752i
\(447\) 2.43147i 0.115004i
\(448\) 3.20752i 0.151541i
\(449\) 25.3794i 1.19773i −0.800850 0.598864i \(-0.795619\pi\)
0.800850 0.598864i \(-0.204381\pi\)
\(450\) 4.98192 0.424858i 0.234850 0.0200280i
\(451\) −21.4618 −1.01059
\(452\) −9.29880 −0.437379
\(453\) 15.1683i 0.712667i
\(454\) 3.24282 0.152193
\(455\) −0.129579 3.04443i −0.00607477 0.142725i
\(456\) −8.02549 −0.375828
\(457\) 41.8627 1.95826 0.979128 0.203243i \(-0.0651480\pi\)
0.979128 + 0.203243i \(0.0651480\pi\)
\(458\) 23.2392 1.08590
\(459\) 6.90738i 0.322409i
\(460\) −14.1853 + 0.603764i −0.661392 + 0.0281506i
\(461\) 9.86731i 0.459567i −0.973242 0.229783i \(-0.926198\pi\)
0.973242 0.229783i \(-0.0738017\pi\)
\(462\) −11.9741 −0.557087
\(463\) −2.13573 −0.0992558 −0.0496279 0.998768i \(-0.515804\pi\)
−0.0496279 + 0.998768i \(0.515804\pi\)
\(464\) 3.39355i 0.157542i
\(465\) 2.68841 0.114426i 0.124672 0.00530638i
\(466\) 23.5036i 1.08878i
\(467\) −23.1295 −1.07031 −0.535154 0.844755i \(-0.679746\pi\)
−0.535154 + 0.844755i \(0.679746\pi\)
\(468\) −0.424858 −0.0196391
\(469\) 36.8674 1.70238
\(470\) 0.194317 + 4.56543i 0.00896318 + 0.210587i
\(471\) 19.1941 0.884416
\(472\) 2.16131i 0.0994823i
\(473\) 34.7556 1.59806
\(474\) 4.50480 0.206912
\(475\) −3.40969 39.9823i −0.156447 1.83451i
\(476\) 22.1556i 1.01550i
\(477\) 11.8045i 0.540490i
\(478\) 6.75627i 0.309025i
\(479\) 42.3018i 1.93282i −0.257006 0.966410i \(-0.582736\pi\)
0.257006 0.966410i \(-0.417264\pi\)
\(480\) 0.0950871 + 2.23405i 0.00434011 + 0.101970i
\(481\) 2.50937 0.617834i 0.114417 0.0281708i
\(482\) 27.0533i 1.23225i
\(483\) −20.3665 −0.926706
\(484\) 2.93631 0.133469
\(485\) −9.91386 + 0.421961i −0.450165 + 0.0191603i
\(486\) 1.00000i 0.0453609i
\(487\) −10.2364 −0.463858 −0.231929 0.972733i \(-0.574504\pi\)
−0.231929 + 0.972733i \(0.574504\pi\)
\(488\) 1.45108i 0.0656872i
\(489\) 7.14619i 0.323162i
\(490\) −7.34600 + 0.312666i −0.331859 + 0.0141248i
\(491\) −30.2449 −1.36494 −0.682468 0.730916i \(-0.739093\pi\)
−0.682468 + 0.730916i \(0.739093\pi\)
\(492\) 5.74899i 0.259184i
\(493\) 23.4406i 1.05571i
\(494\) 3.40969i 0.153409i
\(495\) −8.34000 + 0.354973i −0.374855 + 0.0159549i
\(496\) 1.20338i 0.0540334i
\(497\) 17.9520i 0.805256i
\(498\) −7.00128 −0.313735
\(499\) 5.43439i 0.243277i 0.992574 + 0.121638i \(0.0388148\pi\)
−0.992574 + 0.121638i \(0.961185\pi\)
\(500\) −11.0894 + 1.42287i −0.495934 + 0.0636326i
\(501\) 12.6692i 0.566019i
\(502\) 12.9375i 0.577430i
\(503\) −1.52679 −0.0680760 −0.0340380 0.999421i \(-0.510837\pi\)
−0.0340380 + 0.999421i \(0.510837\pi\)
\(504\) 3.20752i 0.142874i
\(505\) −29.0807 + 1.23776i −1.29407 + 0.0550794i
\(506\) 23.7039 1.05377
\(507\) 12.8195i 0.569334i
\(508\) 14.3747i 0.637776i
\(509\) 10.8171 0.479459 0.239729 0.970840i \(-0.422941\pi\)
0.239729 + 0.970840i \(0.422941\pi\)
\(510\) −0.656803 15.4314i −0.0290837 0.683314i
\(511\) −40.1139 −1.77454
\(512\) −1.00000 −0.0441942
\(513\) −8.02549 −0.354334
\(514\) 14.5960 0.643802
\(515\) 16.0238 0.682016i 0.706092 0.0300532i
\(516\) 9.31001i 0.409850i
\(517\) 7.62892i 0.335520i
\(518\) −4.66443 18.9448i −0.204943 0.832388i
\(519\) −19.7245 −0.865811
\(520\) 0.949152 0.0403985i 0.0416231 0.00177159i
\(521\) −39.8552 −1.74609 −0.873044 0.487642i \(-0.837857\pi\)
−0.873044 + 0.487642i \(0.837857\pi\)
\(522\) 3.39355i 0.148532i
\(523\) −17.5477 −0.767309 −0.383654 0.923477i \(-0.625335\pi\)
−0.383654 + 0.923477i \(0.625335\pi\)
\(524\) 12.3237i 0.538362i
\(525\) −15.9796 + 1.36274i −0.697408 + 0.0594749i
\(526\) 12.2500i 0.534127i
\(527\) 8.31221i 0.362085i
\(528\) 3.73314i 0.162464i
\(529\) 17.3173 0.752925
\(530\) −1.12245 26.3717i −0.0487563 1.14551i
\(531\) 2.16131i 0.0937928i
\(532\) 25.7419 1.11605
\(533\) 2.44250 0.105797
\(534\) −15.9242 −0.689107
\(535\) 0.361624 + 8.49625i 0.0156344 + 0.367325i
\(536\) 11.4940i 0.496466i
\(537\) 3.19619 0.137926
\(538\) −14.1886 −0.611714
\(539\) 12.2753 0.528736
\(540\) 0.0950871 + 2.23405i 0.00409190 + 0.0961380i
\(541\) 23.3560i 1.00415i −0.864824 0.502076i \(-0.832570\pi\)
0.864824 0.502076i \(-0.167430\pi\)
\(542\) 8.82413 0.379029
\(543\) 11.3735i 0.488085i
\(544\) 6.90738 0.296152
\(545\) 0.469232 + 11.0245i 0.0200997 + 0.472237i
\(546\) 1.36274 0.0583200
\(547\) −15.6858 −0.670675 −0.335337 0.942098i \(-0.608850\pi\)
−0.335337 + 0.942098i \(0.608850\pi\)
\(548\) 17.4773i 0.746594i
\(549\) 1.45108i 0.0619305i
\(550\) 18.5982 1.58605i 0.793029 0.0676295i
\(551\) 27.2349 1.16025
\(552\) 6.34959i 0.270256i
\(553\) −14.4493 −0.614445
\(554\) −12.6061 −0.535581
\(555\) −3.81040 13.0568i −0.161742 0.554232i
\(556\) −0.125741 −0.00533261
\(557\) 39.5638 1.67637 0.838186 0.545384i \(-0.183616\pi\)
0.838186 + 0.545384i \(0.183616\pi\)
\(558\) 1.20338i 0.0509432i
\(559\) −3.95543 −0.167297
\(560\) −0.304994 7.16575i −0.0128884 0.302808i
\(561\) 25.7862i 1.08869i
\(562\) 15.8731i 0.669565i
\(563\) 32.4565 1.36788 0.683939 0.729540i \(-0.260266\pi\)
0.683939 + 0.729540i \(0.260266\pi\)
\(564\) −2.04357 −0.0860498
\(565\) 20.7739 0.884197i 0.873967 0.0371984i
\(566\) 29.1588 1.22564
\(567\) 3.20752i 0.134703i
\(568\) 5.59683 0.234838
\(569\) 3.24636i 0.136094i 0.997682 + 0.0680472i \(0.0216769\pi\)
−0.997682 + 0.0680472i \(0.978323\pi\)
\(570\) 17.9293 0.763120i 0.750976 0.0319636i
\(571\) 28.9822 1.21287 0.606433 0.795134i \(-0.292600\pi\)
0.606433 + 0.795134i \(0.292600\pi\)
\(572\) −1.58605 −0.0663162
\(573\) −12.4830 −0.521483
\(574\) 18.4400i 0.769671i
\(575\) 31.6331 2.69767i 1.31919 0.112501i
\(576\) −1.00000 −0.0416667
\(577\) −14.3774 −0.598538 −0.299269 0.954169i \(-0.596743\pi\)
−0.299269 + 0.954169i \(0.596743\pi\)
\(578\) −30.7119 −1.27745
\(579\) 12.1559i 0.505181i
\(580\) −0.322683 7.58136i −0.0133987 0.314799i
\(581\) 22.4568 0.931664
\(582\) 4.43763i 0.183946i
\(583\) 44.0677i 1.82510i
\(584\) 12.5062i 0.517510i
\(585\) 0.949152 0.0403985i 0.0392426 0.00167027i
\(586\) 28.4275i 1.17433i
\(587\) 11.8386 0.488632 0.244316 0.969696i \(-0.421437\pi\)
0.244316 + 0.969696i \(0.421437\pi\)
\(588\) 3.28821i 0.135603i
\(589\) 9.65771 0.397939
\(590\) −0.205513 4.82846i −0.00846082 0.198785i
\(591\) 8.89921 0.366064
\(592\) 5.90637 1.45421i 0.242751 0.0597678i
\(593\) 1.69514i 0.0696112i 0.999394 + 0.0348056i \(0.0110812\pi\)
−0.999394 + 0.0348056i \(0.988919\pi\)
\(594\) 3.73314i 0.153172i
\(595\) 2.10671 + 49.4966i 0.0863667 + 2.02916i
\(596\) 2.43147 0.0995968
\(597\) 10.3470 0.423475
\(598\) −2.69767 −0.110316
\(599\) 44.7372 1.82791 0.913956 0.405813i \(-0.133012\pi\)
0.913956 + 0.405813i \(0.133012\pi\)
\(600\) −0.424858 4.98192i −0.0173448 0.203386i
\(601\) 6.63433 0.270620 0.135310 0.990803i \(-0.456797\pi\)
0.135310 + 0.990803i \(0.456797\pi\)
\(602\) 29.8621i 1.21709i
\(603\) 11.4940i 0.468073i
\(604\) −15.1683 −0.617188
\(605\) −6.55985 + 0.279205i −0.266696 + 0.0113513i
\(606\) 13.0171i 0.528782i
\(607\) −29.4488 −1.19529 −0.597645 0.801760i \(-0.703897\pi\)
−0.597645 + 0.801760i \(0.703897\pi\)
\(608\) 8.02549i 0.325476i
\(609\) 10.8849i 0.441079i
\(610\) −0.137979 3.24177i −0.00558660 0.131256i
\(611\) 0.868226i 0.0351247i
\(612\) 6.90738 0.279214
\(613\) 47.2277i 1.90751i −0.300590 0.953754i \(-0.597183\pi\)
0.300590 0.953754i \(-0.402817\pi\)
\(614\) 20.6139i 0.831910i
\(615\) −0.546655 12.8435i −0.0220433 0.517900i
\(616\) 11.9741i 0.482451i
\(617\) 39.6156i 1.59487i 0.603408 + 0.797433i \(0.293809\pi\)
−0.603408 + 0.797433i \(0.706191\pi\)
\(618\) 7.17254i 0.288522i
\(619\) −21.3347 −0.857512 −0.428756 0.903420i \(-0.641048\pi\)
−0.428756 + 0.903420i \(0.641048\pi\)
\(620\) −0.114426 2.68841i −0.00459546 0.107969i
\(621\) 6.34959i 0.254800i
\(622\) 15.0056i 0.601668i
\(623\) 51.0772 2.04637
\(624\) 0.424858i 0.0170079i
\(625\) 24.6390 4.23321i 0.985560 0.169329i
\(626\) −28.8720 −1.15396
\(627\) −29.9602 −1.19650
\(628\) 19.1941i 0.765927i
\(629\) −40.7976 + 10.0448i −1.62671 + 0.400513i
\(630\) −0.304994 7.16575i −0.0121513 0.285490i
\(631\) 13.9231i 0.554269i −0.960831 0.277134i \(-0.910615\pi\)
0.960831 0.277134i \(-0.0893847\pi\)
\(632\) 4.50480i 0.179191i
\(633\) 5.52374i 0.219549i
\(634\) 14.7214i 0.584662i
\(635\) 1.36685 + 32.1138i 0.0542419 + 1.27440i
\(636\) 11.8045 0.468078
\(637\) −1.39702 −0.0553520
\(638\) 12.6686i 0.501555i
\(639\) 5.59683 0.221407
\(640\) 2.23405 0.0950871i 0.0883084 0.00375865i
\(641\) 25.1770 0.994431 0.497216 0.867627i \(-0.334356\pi\)
0.497216 + 0.867627i \(0.334356\pi\)
\(642\) −3.80308 −0.150096
\(643\) −6.70070 −0.264250 −0.132125 0.991233i \(-0.542180\pi\)
−0.132125 + 0.991233i \(0.542180\pi\)
\(644\) 20.3665i 0.802551i
\(645\) 0.885263 + 20.7990i 0.0348572 + 0.818959i
\(646\) 55.4351i 2.18106i
\(647\) 2.02361 0.0795562 0.0397781 0.999209i \(-0.487335\pi\)
0.0397781 + 0.999209i \(0.487335\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 8.06846i 0.316715i
\(650\) −2.11661 + 0.180504i −0.0830202 + 0.00707996i
\(651\) 3.85987i 0.151280i
\(652\) 7.14619 0.279867
\(653\) 17.8433 0.698262 0.349131 0.937074i \(-0.386477\pi\)
0.349131 + 0.937074i \(0.386477\pi\)
\(654\) −4.93476 −0.192964
\(655\) −1.17182 27.5316i −0.0457869 1.07575i
\(656\) 5.74899 0.224460
\(657\) 12.5062i 0.487913i
\(658\) 6.55479 0.255532
\(659\) −28.2166 −1.09916 −0.549582 0.835440i \(-0.685213\pi\)
−0.549582 + 0.835440i \(0.685213\pi\)
\(660\) 0.354973 + 8.34000i 0.0138173 + 0.324634i
\(661\) 14.9551i 0.581687i −0.956771 0.290843i \(-0.906064\pi\)
0.956771 0.290843i \(-0.0939358\pi\)
\(662\) 8.15238i 0.316851i
\(663\) 2.93466i 0.113973i
\(664\) 7.00128i 0.271703i
\(665\) −57.5086 + 2.44773i −2.23009 + 0.0949188i
\(666\) 5.90637 1.45421i 0.228867 0.0563496i
\(667\) 21.5477i 0.834329i
\(668\) −12.6692 −0.490187
\(669\) 3.24704 0.125538
\(670\) −1.09293 25.6782i −0.0422237 0.992035i
\(671\) 5.41707i 0.209124i
\(672\) 3.20752 0.123733
\(673\) 26.7443i 1.03092i 0.856915 + 0.515458i \(0.172378\pi\)
−0.856915 + 0.515458i \(0.827622\pi\)
\(674\) 28.0034i 1.07865i
\(675\) −0.424858 4.98192i −0.0163528 0.191754i
\(676\) −12.8195 −0.493058
\(677\) 23.3020i 0.895569i 0.894141 + 0.447785i \(0.147787\pi\)
−0.894141 + 0.447785i \(0.852213\pi\)
\(678\) 9.29880i 0.357118i
\(679\) 14.2338i 0.546243i
\(680\) −15.4314 + 0.656803i −0.591767 + 0.0251872i
\(681\) 3.24282i 0.124265i
\(682\) 4.49238i 0.172022i
\(683\) −0.507613 −0.0194233 −0.00971163 0.999953i \(-0.503091\pi\)
−0.00971163 + 0.999953i \(0.503091\pi\)
\(684\) 8.02549i 0.306862i
\(685\) 1.66187 + 39.0451i 0.0634967 + 1.49184i
\(686\) 11.9057i 0.454560i
\(687\) 23.2392i 0.886631i
\(688\) −9.31001 −0.354941
\(689\) 5.01522i 0.191065i
\(690\) 0.603764 + 14.1853i 0.0229849 + 0.540024i
\(691\) −25.1513 −0.956801 −0.478401 0.878142i \(-0.658783\pi\)
−0.478401 + 0.878142i \(0.658783\pi\)
\(692\) 19.7245i 0.749814i
\(693\) 11.9741i 0.454859i
\(694\) −6.82853 −0.259208
\(695\) 0.280911 0.0119564i 0.0106556 0.000453531i
\(696\) 3.39355 0.128632
\(697\) −39.7105 −1.50414
\(698\) 5.65418 0.214014
\(699\) 23.5036 0.888988
\(700\) 1.36274 + 15.9796i 0.0515068 + 0.603973i
\(701\) 13.4801i 0.509136i 0.967055 + 0.254568i \(0.0819332\pi\)
−0.967055 + 0.254568i \(0.918067\pi\)
\(702\) 0.424858i 0.0160352i
\(703\) −11.6708 47.4015i −0.440172 1.78778i
\(704\) −3.73314 −0.140698
\(705\) 4.56543 0.194317i 0.171944 0.00731841i
\(706\) −12.7850 −0.481169
\(707\) 41.7525i 1.57027i
\(708\) 2.16131 0.0812270
\(709\) 16.0914i 0.604326i −0.953256 0.302163i \(-0.902291\pi\)
0.953256 0.302163i \(-0.0977086\pi\)
\(710\) −12.5036 + 0.532187i −0.469251 + 0.0199726i
\(711\) 4.50480i 0.168943i
\(712\) 15.9242i 0.596785i
\(713\) 7.64097i 0.286157i
\(714\) −22.1556 −0.829152
\(715\) 3.54331 0.150813i 0.132512 0.00564010i
\(716\) 3.19619i 0.119447i
\(717\) −6.75627 −0.252318
\(718\) −11.3292 −0.422802
\(719\) −32.6719 −1.21845 −0.609227 0.792996i \(-0.708520\pi\)
−0.609227 + 0.792996i \(0.708520\pi\)
\(720\) 2.23405 0.0950871i 0.0832580 0.00354369i
\(721\) 23.0061i 0.856792i
\(722\) 45.4084 1.68993
\(723\) −27.0533 −1.00612
\(724\) −11.3735 −0.422694
\(725\) 1.44178 + 16.9064i 0.0535463 + 0.627888i
\(726\) 2.93631i 0.108977i
\(727\) 31.3272 1.16186 0.580931 0.813953i \(-0.302689\pi\)
0.580931 + 0.813953i \(0.302689\pi\)
\(728\) 1.36274i 0.0505066i
\(729\) −1.00000 −0.0370370
\(730\) 1.18918 + 27.9394i 0.0440135 + 1.03408i
\(731\) 64.3078 2.37851
\(732\) 1.45108 0.0536334
\(733\) 28.4514i 1.05088i −0.850831 0.525439i \(-0.823901\pi\)
0.850831 0.525439i \(-0.176099\pi\)
\(734\) 10.0590i 0.371284i
\(735\) 0.312666 + 7.34600i 0.0115329 + 0.270961i
\(736\) −6.34959 −0.234049
\(737\) 42.9088i 1.58057i
\(738\) 5.74899 0.211623
\(739\) 15.5668 0.572635 0.286318 0.958135i \(-0.407569\pi\)
0.286318 + 0.958135i \(0.407569\pi\)
\(740\) −13.0568 + 3.81040i −0.479979 + 0.140073i
\(741\) 3.40969 0.125258
\(742\) −37.8631 −1.39000
\(743\) 50.7985i 1.86362i 0.362950 + 0.931809i \(0.381770\pi\)
−0.362950 + 0.931809i \(0.618230\pi\)
\(744\) 1.20338 0.0441181
\(745\) −5.43201 + 0.231201i −0.199013 + 0.00847056i
\(746\) 9.39169i 0.343854i
\(747\) 7.00128i 0.256164i
\(748\) 25.7862 0.942837
\(749\) 12.1985 0.445722
\(750\) 1.42287 + 11.0894i 0.0519558 + 0.404929i
\(751\) −33.5086 −1.22275 −0.611373 0.791342i \(-0.709383\pi\)
−0.611373 + 0.791342i \(0.709383\pi\)
\(752\) 2.04357i 0.0745213i
\(753\) −12.9375 −0.471470
\(754\) 1.44178i 0.0525065i
\(755\) 33.8866 1.44231i 1.23326 0.0524909i
\(756\) 3.20752 0.116656
\(757\) −26.5221 −0.963964 −0.481982 0.876181i \(-0.660083\pi\)
−0.481982 + 0.876181i \(0.660083\pi\)
\(758\) 10.7371 0.389988
\(759\) 23.7039i 0.860396i
\(760\) −0.763120 17.9293i −0.0276813 0.650364i
\(761\) 31.0909 1.12704 0.563521 0.826102i \(-0.309446\pi\)
0.563521 + 0.826102i \(0.309446\pi\)
\(762\) −14.3747 −0.520742
\(763\) 15.8284 0.573025
\(764\) 12.4830i 0.451617i
\(765\) −15.4314 + 0.656803i −0.557924 + 0.0237468i
\(766\) 11.2412 0.406161
\(767\) 0.918249i 0.0331561i
\(768\) 1.00000i 0.0360844i
\(769\) 6.61015i 0.238368i 0.992872 + 0.119184i \(0.0380278\pi\)
−0.992872 + 0.119184i \(0.961972\pi\)
\(770\) −1.13859 26.7507i −0.0410318 0.964030i
\(771\) 14.5960i 0.525662i
\(772\) −12.1559 −0.437499
\(773\) 35.7529i 1.28594i −0.765890 0.642971i \(-0.777702\pi\)
0.765890 0.642971i \(-0.222298\pi\)
\(774\) −9.31001 −0.334642
\(775\) 0.511266 + 5.99514i 0.0183652 + 0.215352i
\(776\) −4.43763 −0.159302
\(777\) −18.9448 + 4.66443i −0.679642 + 0.167335i
\(778\) 7.80757i 0.279915i
\(779\) 46.1384i 1.65308i
\(780\) −0.0403985 0.949152i −0.00144650 0.0339851i
\(781\) 20.8937 0.747637
\(782\) 43.8590 1.56840
\(783\) 3.39355 0.121276
\(784\) −3.28821 −0.117436
\(785\) 1.82511 + 42.8804i 0.0651409 + 1.53047i
\(786\) 12.3237 0.439570
\(787\) 21.9895i 0.783840i −0.919999 0.391920i \(-0.871811\pi\)
0.919999 0.391920i \(-0.128189\pi\)
\(788\) 8.89921i 0.317021i
\(789\) 12.2500 0.436113
\(790\) 0.428349 + 10.0639i 0.0152400 + 0.358059i
\(791\) 29.8261i 1.06050i
\(792\) −3.73314 −0.132651
\(793\) 0.616502i 0.0218926i
\(794\) 33.1348i 1.17591i
\(795\) −26.3717 + 1.12245i −0.935309 + 0.0398093i
\(796\) 10.3470i 0.366740i
\(797\) −16.6230 −0.588817 −0.294409 0.955680i \(-0.595123\pi\)
−0.294409 + 0.955680i \(0.595123\pi\)
\(798\) 25.7419i 0.911255i
\(799\) 14.1157i 0.499378i
\(800\) −4.98192 + 0.424858i −0.176137 + 0.0150210i
\(801\) 15.9242i 0.562654i
\(802\) 33.2206i 1.17306i
\(803\) 46.6874i 1.64756i
\(804\) 11.4940 0.405363
\(805\) −1.93659 45.4996i −0.0682557 1.60365i
\(806\) 0.511266i 0.0180086i
\(807\) 14.1886i 0.499462i
\(808\) −13.0171 −0.457939
\(809\) 37.6802i 1.32476i 0.749166 + 0.662382i \(0.230454\pi\)
−0.749166 + 0.662382i \(0.769546\pi\)
\(810\) 2.23405 0.0950871i 0.0784964 0.00334102i
\(811\) 9.23902 0.324426 0.162213 0.986756i \(-0.448137\pi\)
0.162213 + 0.986756i \(0.448137\pi\)
\(812\) −10.8849 −0.381985
\(813\) 8.82413i 0.309476i
\(814\) 22.0493 5.42878i 0.772828 0.190279i
\(815\) −15.9649 + 0.679511i −0.559227 + 0.0238022i
\(816\) 6.90738i 0.241807i
\(817\) 74.7174i 2.61403i
\(818\) 18.4622i 0.645517i
\(819\) 1.36274i 0.0476181i
\(820\) −12.8435 + 0.546655i −0.448514 + 0.0190900i
\(821\) −2.02441 −0.0706525 −0.0353262 0.999376i \(-0.511247\pi\)
−0.0353262 + 0.999376i \(0.511247\pi\)
\(822\) −17.4773 −0.609591
\(823\) 21.4801i 0.748748i 0.927278 + 0.374374i \(0.122142\pi\)
−0.927278 + 0.374374i \(0.877858\pi\)
\(824\) 7.17254 0.249867
\(825\) −1.58605 18.5982i −0.0552193 0.647505i
\(826\) −6.93245 −0.241211
\(827\) 46.1615 1.60519 0.802597 0.596522i \(-0.203451\pi\)
0.802597 + 0.596522i \(0.203451\pi\)
\(828\) −6.34959 −0.220663
\(829\) 7.43600i 0.258263i 0.991627 + 0.129131i \(0.0412189\pi\)
−0.991627 + 0.129131i \(0.958781\pi\)
\(830\) −0.665732 15.6412i −0.0231079 0.542913i
\(831\) 12.6061i 0.437300i
\(832\) 0.424858 0.0147293
\(833\) 22.7129 0.786955
\(834\) 0.125741i 0.00435406i
\(835\) 28.3036 1.20468i 0.979486 0.0416896i
\(836\) 29.9602i 1.03620i
\(837\) 1.20338 0.0415949
\(838\) −0.759460 −0.0262351
\(839\) −31.3881 −1.08364 −0.541819 0.840495i \(-0.682264\pi\)
−0.541819 + 0.840495i \(0.682264\pi\)
\(840\) −7.16575 + 0.304994i −0.247242 + 0.0105233i
\(841\) 17.4838 0.602889
\(842\) 27.6679i 0.953500i
\(843\) 15.8731 0.546698
\(844\) 5.52374 0.190135
\(845\) 28.6393 1.21897i 0.985223 0.0419338i
\(846\) 2.04357i 0.0702593i
\(847\) 9.41828i 0.323616i
\(848\) 11.8045i 0.405367i
\(849\) 29.1588i 1.00073i
\(850\) 34.4120 2.93466i 1.18032 0.100658i
\(851\) 37.5030 9.23366i 1.28559 0.316526i
\(852\) 5.59683i 0.191744i
\(853\) 29.1070 0.996605 0.498302 0.867003i \(-0.333957\pi\)
0.498302 + 0.867003i \(0.333957\pi\)
\(854\) −4.65437 −0.159269
\(855\) −0.763120 17.9293i −0.0260982 0.613169i
\(856\) 3.80308i 0.129987i
\(857\) −26.4364 −0.903050 −0.451525 0.892259i \(-0.649120\pi\)
−0.451525 + 0.892259i \(0.649120\pi\)
\(858\) 1.58605i 0.0541470i
\(859\) 3.12912i 0.106764i 0.998574 + 0.0533821i \(0.0170001\pi\)
−0.998574 + 0.0533821i \(0.983000\pi\)
\(860\) 20.7990 0.885263i 0.709240 0.0301872i
\(861\) −18.4400 −0.628434
\(862\) 4.94514i 0.168432i
\(863\) 40.9780i 1.39491i −0.716631 0.697453i \(-0.754317\pi\)
0.716631 0.697453i \(-0.245683\pi\)
\(864\) 1.00000i 0.0340207i
\(865\) −1.87555 44.0655i −0.0637706 1.49827i
\(866\) 3.83656i 0.130372i
\(867\) 30.7119i 1.04303i
\(868\) −3.85987 −0.131013
\(869\) 16.8170i 0.570479i
\(870\) −7.58136 + 0.322683i −0.257032 + 0.0109400i
\(871\) 4.88333i 0.165465i
\(872\) 4.93476i 0.167112i
\(873\) −4.43763 −0.150191
\(874\) 50.9585i 1.72370i
\(875\) −4.56388 35.5696i −0.154287 1.20247i
\(876\) −12.5062 −0.422545
\(877\) 52.0228i 1.75669i −0.478030 0.878343i \(-0.658649\pi\)
0.478030 0.878343i \(-0.341351\pi\)
\(878\) 27.6321i 0.932538i
\(879\) −28.4275 −0.958836
\(880\) 8.34000 0.354973i 0.281141 0.0119661i
\(881\) −12.4748 −0.420288 −0.210144 0.977670i \(-0.567393\pi\)
−0.210144 + 0.977670i \(0.567393\pi\)
\(882\) −3.28821 −0.110720
\(883\) 5.68269 0.191238 0.0956189 0.995418i \(-0.469517\pi\)
0.0956189 + 0.995418i \(0.469517\pi\)
\(884\) −2.93466 −0.0987032
\(885\) −4.82846 + 0.205513i −0.162307 + 0.00690823i
\(886\) 17.7327i 0.595740i
\(887\) 45.8573i 1.53974i −0.638203 0.769868i \(-0.720322\pi\)
0.638203 0.769868i \(-0.279678\pi\)
\(888\) −1.45421 5.90637i −0.0488002 0.198205i
\(889\) 46.1073 1.54639
\(890\) −1.51419 35.5754i −0.0507556 1.19249i
\(891\) −3.73314 −0.125065
\(892\) 3.24704i 0.108719i
\(893\) 16.4006 0.548826
\(894\) 2.43147i 0.0813204i
\(895\) 0.303917 + 7.14044i 0.0101588 + 0.238678i
\(896\) 3.20752i 0.107156i
\(897\) 2.69767i 0.0900727i
\(898\) 25.3794i 0.846922i
\(899\) −4.08374 −0.136200
\(900\) −4.98192 + 0.424858i −0.166064 + 0.0141619i
\(901\) 81.5380i 2.71642i
\(902\) 21.4618 0.714598
\(903\) 29.8621 0.993748
\(904\) 9.29880 0.309274
\(905\) 25.4090 1.08148i 0.844623 0.0359495i
\(906\) 15.1683i 0.503932i
\(907\) −56.7099 −1.88302 −0.941510 0.336985i \(-0.890593\pi\)
−0.941510 + 0.336985i \(0.890593\pi\)
\(908\) −3.24282 −0.107617
\(909\) −13.0171 −0.431749
\(910\) 0.129579 + 3.04443i 0.00429551 + 0.100922i
\(911\) 36.6773i 1.21517i 0.794254 + 0.607586i \(0.207862\pi\)
−0.794254 + 0.607586i \(0.792138\pi\)
\(912\) 8.02549 0.265750
\(913\) 26.1367i 0.865000i
\(914\) −41.8627 −1.38470
\(915\) −3.24177 + 0.137979i −0.107170 + 0.00456144i
\(916\) −23.2392 −0.767845
\(917\) −39.5284 −1.30534
\(918\) 6.90738i 0.227978i
\(919\) 9.37210i 0.309157i −0.987981 0.154578i \(-0.950598\pi\)
0.987981 0.154578i \(-0.0494019\pi\)
\(920\) 14.1853 0.603764i 0.467674 0.0199055i
\(921\) −20.6139 −0.679251
\(922\) 9.86731i 0.324963i
\(923\) −2.37786 −0.0782682
\(924\) 11.9741 0.393920
\(925\) 28.8072 9.75414i 0.947176 0.320714i
\(926\) 2.13573 0.0701844
\(927\) 7.17254 0.235577
\(928\) 3.39355i 0.111399i
\(929\) −50.0310 −1.64146 −0.820732 0.571314i \(-0.806434\pi\)
−0.820732 + 0.571314i \(0.806434\pi\)
\(930\) −2.68841 + 0.114426i −0.0881563 + 0.00375218i
\(931\) 26.3894i 0.864879i
\(932\) 23.5036i 0.769886i
\(933\) −15.0056 −0.491260
\(934\) 23.1295 0.756822
\(935\) −57.6075 + 2.45194i −1.88397 + 0.0801869i
\(936\) 0.424858 0.0138869
\(937\) 32.5441i 1.06317i 0.847005 + 0.531585i \(0.178403\pi\)
−0.847005 + 0.531585i \(0.821597\pi\)
\(938\) −36.8674 −1.20376
\(939\) 28.8720i 0.942203i
\(940\) −0.194317 4.56543i −0.00633793 0.148908i
\(941\) −23.1571 −0.754900 −0.377450 0.926030i \(-0.623199\pi\)
−0.377450 + 0.926030i \(0.623199\pi\)
\(942\) −19.1941 −0.625376
\(943\) 36.5037 1.18872
\(944\) 2.16131i 0.0703446i
\(945\) −7.16575 + 0.304994i −0.233102 + 0.00992146i
\(946\) −34.7556 −1.13000
\(947\) 18.7484 0.609242 0.304621 0.952474i \(-0.401470\pi\)
0.304621 + 0.952474i \(0.401470\pi\)
\(948\) −4.50480 −0.146309
\(949\) 5.31336i 0.172479i
\(950\) 3.40969 + 39.9823i 0.110625 + 1.29720i
\(951\) 14.7214 0.477375
\(952\) 22.1556i 0.718067i
\(953\) 17.1259i 0.554763i −0.960760 0.277382i \(-0.910533\pi\)
0.960760 0.277382i \(-0.0894666\pi\)
\(954\) 11.8045i 0.382184i
\(955\) −1.18697 27.8875i −0.0384094 0.902418i
\(956\) 6.75627i 0.218514i
\(957\) 12.6686 0.409518
\(958\) 42.3018i 1.36671i
\(959\) 56.0589 1.81024
\(960\) −0.0950871 2.23405i −0.00306892 0.0721035i
\(961\) 29.5519 0.953286
\(962\) −2.50937 + 0.617834i −0.0809053 + 0.0199198i
\(963\) 3.80308i 0.122553i
\(964\) 27.0533i 0.871329i
\(965\) 27.1568 1.15587i 0.874207 0.0372087i
\(966\) 20.3665 0.655280
\(967\) −22.1462 −0.712175 −0.356087 0.934453i \(-0.615889\pi\)
−0.356087 + 0.934453i \(0.615889\pi\)
\(968\) −2.93631 −0.0943766
\(969\) −55.4351 −1.78083
\(970\) 9.91386 0.421961i 0.318315 0.0135484i
\(971\) −7.32119 −0.234948 −0.117474 0.993076i \(-0.537480\pi\)
−0.117474 + 0.993076i \(0.537480\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 0.403318i 0.0129298i
\(974\) 10.2364 0.327997
\(975\) 0.180504 + 2.11661i 0.00578076 + 0.0677857i
\(976\) 1.45108i 0.0464479i
\(977\) 51.6787 1.65335 0.826675 0.562680i \(-0.190230\pi\)
0.826675 + 0.562680i \(0.190230\pi\)
\(978\) 7.14619i 0.228510i
\(979\) 59.4472i 1.89994i
\(980\) 7.34600 0.312666i 0.234659 0.00998775i
\(981\) 4.93476i 0.157555i
\(982\) 30.2449 0.965155
\(983\) 37.3050i 1.18985i 0.803783 + 0.594923i \(0.202817\pi\)
−0.803783 + 0.594923i \(0.797183\pi\)
\(984\) 5.74899i 0.183271i
\(985\) 0.846200 + 19.8812i 0.0269622 + 0.633469i
\(986\) 23.4406i 0.746500i
\(987\) 6.55479i 0.208641i
\(988\) 3.40969i 0.108477i
\(989\) −59.1147 −1.87974
\(990\) 8.34000 0.354973i 0.265062 0.0112818i
\(991\) 25.2376i 0.801699i 0.916144 + 0.400850i \(0.131285\pi\)
−0.916144 + 0.400850i \(0.868715\pi\)
\(992\) 1.20338i 0.0382074i
\(993\) −8.15238 −0.258708
\(994\) 17.9520i 0.569402i
\(995\) 0.983869 + 23.1157i 0.0311907 + 0.732817i
\(996\) 7.00128 0.221844
\(997\) 45.6991 1.44731 0.723653 0.690164i \(-0.242462\pi\)
0.723653 + 0.690164i \(0.242462\pi\)
\(998\) 5.43439i 0.172023i
\(999\) −1.45421 5.90637i −0.0460093 0.186869i
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 1110.2.e.c.739.9 yes 16
3.2 odd 2 3330.2.e.f.739.15 16
5.4 even 2 1110.2.e.d.739.8 yes 16
15.14 odd 2 3330.2.e.e.739.1 16
37.36 even 2 1110.2.e.d.739.16 yes 16
111.110 odd 2 3330.2.e.e.739.2 16
185.184 even 2 inner 1110.2.e.c.739.1 16
555.554 odd 2 3330.2.e.f.739.16 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.e.c.739.1 16 185.184 even 2 inner
1110.2.e.c.739.9 yes 16 1.1 even 1 trivial
1110.2.e.d.739.8 yes 16 5.4 even 2
1110.2.e.d.739.16 yes 16 37.36 even 2
3330.2.e.e.739.1 16 15.14 odd 2
3330.2.e.e.739.2 16 111.110 odd 2
3330.2.e.f.739.15 16 3.2 odd 2
3330.2.e.f.739.16 16 555.554 odd 2