Properties

Label 552.2.j.d.323.16
Level $552$
Weight $2$
Character 552.323
Analytic conductor $4.408$
Analytic rank $0$
Dimension $42$
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] = [552,2,Mod(323,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.j (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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(42\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.16
Character \(\chi\) \(=\) 552.323
Dual form 552.2.j.d.323.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.734855 + 1.20830i) q^{2} +(-1.73179 + 0.0302019i) q^{3} +(-0.919975 - 1.77585i) q^{4} -0.871841 q^{5} +(1.23612 - 2.11471i) q^{6} -3.09231i q^{7} +(2.82181 + 0.193388i) q^{8} +(2.99818 - 0.104607i) q^{9} +O(q^{10})\) \(q+(-0.734855 + 1.20830i) q^{2} +(-1.73179 + 0.0302019i) q^{3} +(-0.919975 - 1.77585i) q^{4} -0.871841 q^{5} +(1.23612 - 2.11471i) q^{6} -3.09231i q^{7} +(2.82181 + 0.193388i) q^{8} +(2.99818 - 0.104607i) q^{9} +(0.640677 - 1.05344i) q^{10} +1.90350i q^{11} +(1.64684 + 3.04761i) q^{12} +1.23856i q^{13} +(3.73644 + 2.27240i) q^{14} +(1.50984 - 0.0263313i) q^{15} +(-2.30729 + 3.26748i) q^{16} +1.98300i q^{17} +(-2.07683 + 3.69956i) q^{18} -4.96848 q^{19} +(0.802072 + 1.54826i) q^{20} +(0.0933936 + 5.35522i) q^{21} +(-2.29999 - 1.39879i) q^{22} +1.00000 q^{23} +(-4.89261 - 0.249682i) q^{24} -4.23989 q^{25} +(-1.49655 - 0.910161i) q^{26} +(-5.18904 + 0.271707i) q^{27} +(-5.49148 + 2.84485i) q^{28} +2.31109 q^{29} +(-1.07770 + 1.84369i) q^{30} -3.48492i q^{31} +(-2.25257 - 5.18902i) q^{32} +(-0.0574892 - 3.29645i) q^{33} +(-2.39606 - 1.45722i) q^{34} +2.69600i q^{35} +(-2.94401 - 5.22808i) q^{36} +4.56655i q^{37} +(3.65112 - 6.00341i) q^{38} +(-0.0374068 - 2.14492i) q^{39} +(-2.46017 - 0.168603i) q^{40} +8.71457i q^{41} +(-6.53934 - 3.82247i) q^{42} -3.26780 q^{43} +(3.38032 - 1.75117i) q^{44} +(-2.61393 + 0.0912003i) q^{45} +(-0.734855 + 1.20830i) q^{46} -7.68114 q^{47} +(3.89705 - 5.72826i) q^{48} -2.56238 q^{49} +(3.11571 - 5.12306i) q^{50} +(-0.0598904 - 3.43414i) q^{51} +(2.19950 - 1.13944i) q^{52} -7.53051 q^{53} +(3.48489 - 6.46958i) q^{54} -1.65955i q^{55} +(0.598014 - 8.72591i) q^{56} +(8.60435 - 0.150058i) q^{57} +(-1.69832 + 2.79249i) q^{58} +12.2120i q^{59} +(-1.43578 - 2.65703i) q^{60} +10.7975i q^{61} +(4.21082 + 2.56091i) q^{62} +(-0.323476 - 9.27129i) q^{63} +(7.92520 + 1.09141i) q^{64} -1.07983i q^{65} +(4.02535 + 2.35295i) q^{66} -0.0562647 q^{67} +(3.52152 - 1.82431i) q^{68} +(-1.73179 + 0.0302019i) q^{69} +(-3.25758 - 1.98117i) q^{70} -7.84847 q^{71} +(8.48051 + 0.284630i) q^{72} -7.04796 q^{73} +(-5.51775 - 3.35575i) q^{74} +(7.34259 - 0.128053i) q^{75} +(4.57088 + 8.82328i) q^{76} +5.88620 q^{77} +(2.61919 + 1.53101i) q^{78} -5.10654i q^{79} +(2.01159 - 2.84872i) q^{80} +(8.97811 - 0.627258i) q^{81} +(-10.5298 - 6.40395i) q^{82} +0.795490i q^{83} +(9.42416 - 5.09253i) q^{84} -1.72886i q^{85} +(2.40136 - 3.94849i) q^{86} +(-4.00232 + 0.0697994i) q^{87} +(-0.368112 + 5.37130i) q^{88} +17.3867i q^{89} +(1.81066 - 3.22543i) q^{90} +3.83001 q^{91} +(-0.919975 - 1.77585i) q^{92} +(0.105251 + 6.03513i) q^{93} +(5.64452 - 9.28111i) q^{94} +4.33173 q^{95} +(4.05768 + 8.91825i) q^{96} +9.05221 q^{97} +(1.88298 - 3.09612i) q^{98} +(0.199118 + 5.70701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.734855 + 1.20830i −0.519621 + 0.854397i
\(3\) −1.73179 + 0.0302019i −0.999848 + 0.0174371i
\(4\) −0.919975 1.77585i −0.459988 0.887925i
\(5\) −0.871841 −0.389899 −0.194950 0.980813i \(-0.562454\pi\)
−0.194950 + 0.980813i \(0.562454\pi\)
\(6\) 1.23612 2.11471i 0.504644 0.863328i
\(7\) 3.09231i 1.16878i −0.811472 0.584392i \(-0.801333\pi\)
0.811472 0.584392i \(-0.198667\pi\)
\(8\) 2.82181 + 0.193388i 0.997660 + 0.0683728i
\(9\) 2.99818 0.104607i 0.999392 0.0348688i
\(10\) 0.640677 1.05344i 0.202600 0.333129i
\(11\) 1.90350i 0.573926i 0.957942 + 0.286963i \(0.0926456\pi\)
−0.957942 + 0.286963i \(0.907354\pi\)
\(12\) 1.64684 + 3.04761i 0.475401 + 0.879769i
\(13\) 1.23856i 0.343514i 0.985139 + 0.171757i \(0.0549444\pi\)
−0.985139 + 0.171757i \(0.945056\pi\)
\(14\) 3.73644 + 2.27240i 0.998605 + 0.607325i
\(15\) 1.50984 0.0263313i 0.389840 0.00679870i
\(16\) −2.30729 + 3.26748i −0.576823 + 0.816869i
\(17\) 1.98300i 0.480949i 0.970655 + 0.240474i \(0.0773030\pi\)
−0.970655 + 0.240474i \(0.922697\pi\)
\(18\) −2.07683 + 3.69956i −0.489513 + 0.871996i
\(19\) −4.96848 −1.13985 −0.569924 0.821697i \(-0.693027\pi\)
−0.569924 + 0.821697i \(0.693027\pi\)
\(20\) 0.802072 + 1.54826i 0.179349 + 0.346201i
\(21\) 0.0933936 + 5.35522i 0.0203802 + 1.16861i
\(22\) −2.29999 1.39879i −0.490360 0.298224i
\(23\) 1.00000 0.208514
\(24\) −4.89261 0.249682i −0.998700 0.0509662i
\(25\) −4.23989 −0.847979
\(26\) −1.49655 0.910161i −0.293498 0.178497i
\(27\) −5.18904 + 0.271707i −0.998632 + 0.0522900i
\(28\) −5.49148 + 2.84485i −1.03779 + 0.537626i
\(29\) 2.31109 0.429159 0.214580 0.976706i \(-0.431162\pi\)
0.214580 + 0.976706i \(0.431162\pi\)
\(30\) −1.07770 + 1.84369i −0.196760 + 0.336611i
\(31\) 3.48492i 0.625909i −0.949768 0.312955i \(-0.898681\pi\)
0.949768 0.312955i \(-0.101319\pi\)
\(32\) −2.25257 5.18902i −0.398201 0.917298i
\(33\) −0.0574892 3.29645i −0.0100076 0.573838i
\(34\) −2.39606 1.45722i −0.410921 0.249911i
\(35\) 2.69600i 0.455708i
\(36\) −2.94401 5.22808i −0.490669 0.871346i
\(37\) 4.56655i 0.750735i 0.926876 + 0.375368i \(0.122484\pi\)
−0.926876 + 0.375368i \(0.877516\pi\)
\(38\) 3.65112 6.00341i 0.592289 0.973882i
\(39\) −0.0374068 2.14492i −0.00598989 0.343462i
\(40\) −2.46017 0.168603i −0.388987 0.0266585i
\(41\) 8.71457i 1.36099i 0.732754 + 0.680493i \(0.238234\pi\)
−0.732754 + 0.680493i \(0.761766\pi\)
\(42\) −6.53934 3.82247i −1.00904 0.589819i
\(43\) −3.26780 −0.498336 −0.249168 0.968460i \(-0.580157\pi\)
−0.249168 + 0.968460i \(0.580157\pi\)
\(44\) 3.38032 1.75117i 0.509603 0.263999i
\(45\) −2.61393 + 0.0912003i −0.389662 + 0.0135953i
\(46\) −0.734855 + 1.20830i −0.108349 + 0.178154i
\(47\) −7.68114 −1.12041 −0.560205 0.828354i \(-0.689277\pi\)
−0.560205 + 0.828354i \(0.689277\pi\)
\(48\) 3.89705 5.72826i 0.562491 0.826803i
\(49\) −2.56238 −0.366054
\(50\) 3.11571 5.12306i 0.440628 0.724510i
\(51\) −0.0598904 3.43414i −0.00838634 0.480876i
\(52\) 2.19950 1.13944i 0.305015 0.158012i
\(53\) −7.53051 −1.03439 −0.517197 0.855866i \(-0.673025\pi\)
−0.517197 + 0.855866i \(0.673025\pi\)
\(54\) 3.48489 6.46958i 0.474234 0.880399i
\(55\) 1.65955i 0.223773i
\(56\) 0.598014 8.72591i 0.0799130 1.16605i
\(57\) 8.60435 0.150058i 1.13967 0.0198756i
\(58\) −1.69832 + 2.79249i −0.223000 + 0.366672i
\(59\) 12.2120i 1.58986i 0.606698 + 0.794932i \(0.292494\pi\)
−0.606698 + 0.794932i \(0.707506\pi\)
\(60\) −1.43578 2.65703i −0.185358 0.343021i
\(61\) 10.7975i 1.38248i 0.722623 + 0.691242i \(0.242936\pi\)
−0.722623 + 0.691242i \(0.757064\pi\)
\(62\) 4.21082 + 2.56091i 0.534775 + 0.325236i
\(63\) −0.323476 9.27129i −0.0407541 1.16807i
\(64\) 7.92520 + 1.09141i 0.990650 + 0.136426i
\(65\) 1.07983i 0.133936i
\(66\) 4.02535 + 2.35295i 0.495486 + 0.289628i
\(67\) −0.0562647 −0.00687383 −0.00343692 0.999994i \(-0.501094\pi\)
−0.00343692 + 0.999994i \(0.501094\pi\)
\(68\) 3.52152 1.82431i 0.427047 0.221231i
\(69\) −1.73179 + 0.0302019i −0.208483 + 0.00363588i
\(70\) −3.25758 1.98117i −0.389355 0.236795i
\(71\) −7.84847 −0.931442 −0.465721 0.884932i \(-0.654205\pi\)
−0.465721 + 0.884932i \(0.654205\pi\)
\(72\) 8.48051 + 0.284630i 0.999437 + 0.0335440i
\(73\) −7.04796 −0.824902 −0.412451 0.910980i \(-0.635327\pi\)
−0.412451 + 0.910980i \(0.635327\pi\)
\(74\) −5.51775 3.35575i −0.641426 0.390098i
\(75\) 7.34259 0.128053i 0.847850 0.0147863i
\(76\) 4.57088 + 8.82328i 0.524316 + 1.01210i
\(77\) 5.88620 0.670795
\(78\) 2.61919 + 1.53101i 0.296565 + 0.173352i
\(79\) 5.10654i 0.574531i −0.957851 0.287265i \(-0.907254\pi\)
0.957851 0.287265i \(-0.0927462\pi\)
\(80\) 2.01159 2.84872i 0.224903 0.318497i
\(81\) 8.97811 0.627258i 0.997568 0.0696953i
\(82\) −10.5298 6.40395i −1.16282 0.707198i
\(83\) 0.795490i 0.0873163i 0.999047 + 0.0436582i \(0.0139012\pi\)
−0.999047 + 0.0436582i \(0.986099\pi\)
\(84\) 9.42416 5.09253i 1.02826 0.555640i
\(85\) 1.72886i 0.187522i
\(86\) 2.40136 3.94849i 0.258946 0.425776i
\(87\) −4.00232 + 0.0697994i −0.429094 + 0.00748329i
\(88\) −0.368112 + 5.37130i −0.0392409 + 0.572582i
\(89\) 17.3867i 1.84298i 0.388399 + 0.921491i \(0.373028\pi\)
−0.388399 + 0.921491i \(0.626972\pi\)
\(90\) 1.81066 3.22543i 0.190861 0.339990i
\(91\) 3.83001 0.401494
\(92\) −0.919975 1.77585i −0.0959141 0.185145i
\(93\) 0.105251 + 6.03513i 0.0109140 + 0.625814i
\(94\) 5.64452 9.28111i 0.582188 0.957274i
\(95\) 4.33173 0.444426
\(96\) 4.05768 + 8.91825i 0.414136 + 0.910215i
\(97\) 9.05221 0.919113 0.459557 0.888149i \(-0.348008\pi\)
0.459557 + 0.888149i \(0.348008\pi\)
\(98\) 1.88298 3.09612i 0.190210 0.312756i
\(99\) 0.199118 + 5.70701i 0.0200121 + 0.573577i
\(100\) 3.90060 + 7.52942i 0.390060 + 0.752942i
\(101\) −19.5806 −1.94835 −0.974173 0.225803i \(-0.927500\pi\)
−0.974173 + 0.225803i \(0.927500\pi\)
\(102\) 4.19348 + 2.45123i 0.415216 + 0.242708i
\(103\) 2.96013i 0.291670i −0.989309 0.145835i \(-0.953413\pi\)
0.989309 0.145835i \(-0.0465869\pi\)
\(104\) −0.239522 + 3.49497i −0.0234870 + 0.342710i
\(105\) −0.0814244 4.66890i −0.00794621 0.455638i
\(106\) 5.53383 9.09911i 0.537494 0.883784i
\(107\) 8.95826i 0.866028i −0.901387 0.433014i \(-0.857450\pi\)
0.901387 0.433014i \(-0.142550\pi\)
\(108\) 5.25630 + 8.96500i 0.505788 + 0.862658i
\(109\) 9.35024i 0.895591i −0.894136 0.447795i \(-0.852209\pi\)
0.894136 0.447795i \(-0.147791\pi\)
\(110\) 2.00523 + 1.21953i 0.191191 + 0.116277i
\(111\) −0.137918 7.90829i −0.0130906 0.750621i
\(112\) 10.1041 + 7.13486i 0.954743 + 0.674181i
\(113\) 1.47151i 0.138428i 0.997602 + 0.0692140i \(0.0220491\pi\)
−0.997602 + 0.0692140i \(0.977951\pi\)
\(114\) −6.14164 + 10.5069i −0.575217 + 0.984062i
\(115\) −0.871841 −0.0812996
\(116\) −2.12615 4.10416i −0.197408 0.381062i
\(117\) 0.129561 + 3.71342i 0.0119779 + 0.343305i
\(118\) −14.7557 8.97404i −1.35838 0.826127i
\(119\) 6.13206 0.562125
\(120\) 4.26558 + 0.217683i 0.389392 + 0.0198717i
\(121\) 7.37670 0.670609
\(122\) −13.0467 7.93463i −1.18119 0.718368i
\(123\) −0.263196 15.0918i −0.0237316 1.36078i
\(124\) −6.18869 + 3.20604i −0.555761 + 0.287911i
\(125\) 8.05572 0.720525
\(126\) 11.4402 + 6.42220i 1.01917 + 0.572135i
\(127\) 6.90921i 0.613093i 0.951856 + 0.306547i \(0.0991735\pi\)
−0.951856 + 0.306547i \(0.900826\pi\)
\(128\) −7.14262 + 8.77399i −0.631325 + 0.775519i
\(129\) 5.65914 0.0986939i 0.498260 0.00868951i
\(130\) 1.30475 + 0.793516i 0.114434 + 0.0695959i
\(131\) 12.5716i 1.09839i 0.835695 + 0.549193i \(0.185065\pi\)
−0.835695 + 0.549193i \(0.814935\pi\)
\(132\) −5.80111 + 3.13474i −0.504922 + 0.272845i
\(133\) 15.3641i 1.33224i
\(134\) 0.0413464 0.0679846i 0.00357179 0.00587298i
\(135\) 4.52402 0.236885i 0.389366 0.0203878i
\(136\) −0.383488 + 5.59565i −0.0328838 + 0.479823i
\(137\) 1.78484i 0.152490i −0.997089 0.0762448i \(-0.975707\pi\)
0.997089 0.0762448i \(-0.0242930\pi\)
\(138\) 1.23612 2.11471i 0.105226 0.180016i
\(139\) 5.90847 0.501150 0.250575 0.968097i \(-0.419380\pi\)
0.250575 + 0.968097i \(0.419380\pi\)
\(140\) 4.78770 2.48026i 0.404634 0.209620i
\(141\) 13.3021 0.231985i 1.12024 0.0195367i
\(142\) 5.76749 9.48330i 0.483997 0.795821i
\(143\) −2.35759 −0.197152
\(144\) −6.57586 + 10.0378i −0.547989 + 0.836486i
\(145\) −2.01491 −0.167329
\(146\) 5.17923 8.51605i 0.428636 0.704793i
\(147\) 4.43750 0.0773888i 0.365999 0.00638292i
\(148\) 8.10950 4.20111i 0.666597 0.345329i
\(149\) 18.3640 1.50444 0.752219 0.658914i \(-0.228984\pi\)
0.752219 + 0.658914i \(0.228984\pi\)
\(150\) −5.24102 + 8.96615i −0.427927 + 0.732083i
\(151\) 5.65286i 0.460023i 0.973188 + 0.230012i \(0.0738764\pi\)
−0.973188 + 0.230012i \(0.926124\pi\)
\(152\) −14.0201 0.960843i −1.13718 0.0779346i
\(153\) 0.207435 + 5.94539i 0.0167701 + 0.480656i
\(154\) −4.32550 + 7.11229i −0.348559 + 0.573125i
\(155\) 3.03829i 0.244041i
\(156\) −3.77464 + 2.03970i −0.302213 + 0.163307i
\(157\) 17.6786i 1.41090i −0.708758 0.705451i \(-0.750744\pi\)
0.708758 0.705451i \(-0.249256\pi\)
\(158\) 6.17023 + 3.75257i 0.490877 + 0.298538i
\(159\) 13.0412 0.227436i 1.03424 0.0180368i
\(160\) 1.96388 + 4.52400i 0.155258 + 0.357654i
\(161\) 3.09231i 0.243708i
\(162\) −5.83970 + 11.3092i −0.458810 + 0.888534i
\(163\) −15.4158 −1.20746 −0.603728 0.797191i \(-0.706319\pi\)
−0.603728 + 0.797191i \(0.706319\pi\)
\(164\) 15.4758 8.01719i 1.20845 0.626037i
\(165\) 0.0501214 + 2.87398i 0.00390195 + 0.223739i
\(166\) −0.961190 0.584570i −0.0746028 0.0453714i
\(167\) 9.04899 0.700232 0.350116 0.936706i \(-0.386142\pi\)
0.350116 + 0.936706i \(0.386142\pi\)
\(168\) −0.772095 + 15.1295i −0.0595684 + 1.16726i
\(169\) 11.4660 0.881998
\(170\) 2.08898 + 1.27046i 0.160218 + 0.0974401i
\(171\) −14.8964 + 0.519736i −1.13915 + 0.0397452i
\(172\) 3.00630 + 5.80313i 0.229228 + 0.442485i
\(173\) 2.83727 0.215714 0.107857 0.994166i \(-0.465601\pi\)
0.107857 + 0.994166i \(0.465601\pi\)
\(174\) 2.85679 4.88730i 0.216573 0.370505i
\(175\) 13.1111i 0.991103i
\(176\) −6.21963 4.39192i −0.468822 0.331053i
\(177\) −0.368825 21.1486i −0.0277226 1.58962i
\(178\) −21.0083 12.7767i −1.57464 0.957653i
\(179\) 10.5834i 0.791043i −0.918457 0.395521i \(-0.870564\pi\)
0.918457 0.395521i \(-0.129436\pi\)
\(180\) 2.56671 + 4.55805i 0.191311 + 0.339737i
\(181\) 8.60505i 0.639608i −0.947484 0.319804i \(-0.896383\pi\)
0.947484 0.319804i \(-0.103617\pi\)
\(182\) −2.81450 + 4.62780i −0.208625 + 0.343035i
\(183\) −0.326106 18.6991i −0.0241065 1.38227i
\(184\) 2.82181 + 0.193388i 0.208026 + 0.0142567i
\(185\) 3.98130i 0.292711i
\(186\) −7.36959 4.30778i −0.540365 0.315861i
\(187\) −3.77464 −0.276029
\(188\) 7.06646 + 13.6406i 0.515374 + 0.994840i
\(189\) 0.840202 + 16.0461i 0.0611157 + 1.16718i
\(190\) −3.18319 + 5.23402i −0.230933 + 0.379716i
\(191\) −14.6068 −1.05691 −0.528454 0.848962i \(-0.677228\pi\)
−0.528454 + 0.848962i \(0.677228\pi\)
\(192\) −13.7577 1.65073i −0.992879 0.119131i
\(193\) −5.48507 −0.394824 −0.197412 0.980321i \(-0.563254\pi\)
−0.197412 + 0.980321i \(0.563254\pi\)
\(194\) −6.65207 + 10.9378i −0.477591 + 0.785287i
\(195\) 0.0326128 + 1.87003i 0.00233545 + 0.133916i
\(196\) 2.35733 + 4.55040i 0.168380 + 0.325029i
\(197\) −21.8619 −1.55760 −0.778798 0.627274i \(-0.784170\pi\)
−0.778798 + 0.627274i \(0.784170\pi\)
\(198\) −7.04211 3.95324i −0.500461 0.280944i
\(199\) 19.5960i 1.38912i 0.719435 + 0.694560i \(0.244401\pi\)
−0.719435 + 0.694560i \(0.755599\pi\)
\(200\) −11.9642 0.819943i −0.845994 0.0579787i
\(201\) 0.0974385 0.00169930i 0.00687279 0.000119859i
\(202\) 14.3889 23.6593i 1.01240 1.66466i
\(203\) 7.14662i 0.501594i
\(204\) −6.04342 + 3.26568i −0.423124 + 0.228643i
\(205\) 7.59772i 0.530647i
\(206\) 3.57672 + 2.17527i 0.249202 + 0.151558i
\(207\) 2.99818 0.104607i 0.208388 0.00727066i
\(208\) −4.04696 2.85771i −0.280606 0.198147i
\(209\) 9.45748i 0.654188i
\(210\) 5.70127 + 3.33258i 0.393425 + 0.229970i
\(211\) 9.82214 0.676184 0.338092 0.941113i \(-0.390218\pi\)
0.338092 + 0.941113i \(0.390218\pi\)
\(212\) 6.92788 + 13.3731i 0.475809 + 0.918465i
\(213\) 13.5919 0.237039i 0.931300 0.0162416i
\(214\) 10.8243 + 6.58302i 0.739931 + 0.450006i
\(215\) 2.84901 0.194301
\(216\) −14.6950 0.236792i −0.999870 0.0161116i
\(217\) −10.7764 −0.731552
\(218\) 11.2979 + 6.87107i 0.765190 + 0.465368i
\(219\) 12.2056 0.212862i 0.824776 0.0143839i
\(220\) −2.94710 + 1.52674i −0.198694 + 0.102933i
\(221\) −2.45607 −0.165213
\(222\) 9.65693 + 5.64480i 0.648131 + 0.378854i
\(223\) 5.37339i 0.359829i −0.983682 0.179914i \(-0.942418\pi\)
0.983682 0.179914i \(-0.0575821\pi\)
\(224\) −16.0461 + 6.96563i −1.07212 + 0.465411i
\(225\) −12.7119 + 0.443521i −0.847463 + 0.0295680i
\(226\) −1.77802 1.08135i −0.118272 0.0719301i
\(227\) 23.0536i 1.53012i −0.643957 0.765061i \(-0.722709\pi\)
0.643957 0.765061i \(-0.277291\pi\)
\(228\) −8.18227 15.1420i −0.541884 1.00280i
\(229\) 27.2263i 1.79916i −0.436752 0.899582i \(-0.643871\pi\)
0.436752 0.899582i \(-0.356129\pi\)
\(230\) 0.640677 1.05344i 0.0422450 0.0694621i
\(231\) −10.1936 + 0.177774i −0.670693 + 0.0116967i
\(232\) 6.52147 + 0.446937i 0.428155 + 0.0293428i
\(233\) 21.6173i 1.41620i −0.706114 0.708098i \(-0.749553\pi\)
0.706114 0.708098i \(-0.250447\pi\)
\(234\) −4.58213 2.57227i −0.299543 0.168155i
\(235\) 6.69673 0.436846
\(236\) 21.6867 11.2347i 1.41168 0.731318i
\(237\) 0.154227 + 8.84345i 0.0100181 + 0.574444i
\(238\) −4.50618 + 7.40936i −0.292092 + 0.480278i
\(239\) 17.6777 1.14348 0.571738 0.820436i \(-0.306270\pi\)
0.571738 + 0.820436i \(0.306270\pi\)
\(240\) −3.39761 + 4.99413i −0.219315 + 0.322370i
\(241\) −16.3445 −1.05284 −0.526419 0.850225i \(-0.676466\pi\)
−0.526419 + 0.850225i \(0.676466\pi\)
\(242\) −5.42081 + 8.91327i −0.348463 + 0.572967i
\(243\) −15.5292 + 1.35743i −0.996201 + 0.0870794i
\(244\) 19.1748 9.93348i 1.22754 0.635926i
\(245\) 2.23399 0.142724
\(246\) 18.4288 + 10.7723i 1.17498 + 0.686814i
\(247\) 6.15376i 0.391554i
\(248\) 0.673939 9.83376i 0.0427952 0.624445i
\(249\) −0.0240253 1.37762i −0.00152254 0.0873030i
\(250\) −5.91979 + 9.73372i −0.374400 + 0.615614i
\(251\) 14.1286i 0.891791i 0.895085 + 0.445896i \(0.147115\pi\)
−0.895085 + 0.445896i \(0.852885\pi\)
\(252\) −16.1668 + 9.10380i −1.01841 + 0.573486i
\(253\) 1.90350i 0.119672i
\(254\) −8.34839 5.07727i −0.523825 0.318576i
\(255\) 0.0522149 + 2.99402i 0.00326983 + 0.187493i
\(256\) −5.35282 15.0780i −0.334551 0.942378i
\(257\) 13.2937i 0.829238i −0.909995 0.414619i \(-0.863915\pi\)
0.909995 0.414619i \(-0.136085\pi\)
\(258\) −4.03940 + 6.91047i −0.251482 + 0.430227i
\(259\) 14.1212 0.877447
\(260\) −1.91761 + 0.993413i −0.118925 + 0.0616089i
\(261\) 6.92907 0.241756i 0.428898 0.0149643i
\(262\) −15.1903 9.23832i −0.938458 0.570745i
\(263\) −25.3919 −1.56573 −0.782865 0.622192i \(-0.786242\pi\)
−0.782865 + 0.622192i \(0.786242\pi\)
\(264\) 0.475269 9.31307i 0.0292508 0.573180i
\(265\) 6.56541 0.403310
\(266\) −18.5644 11.2904i −1.13826 0.692258i
\(267\) −0.525110 30.1100i −0.0321362 1.84270i
\(268\) 0.0517622 + 0.0999177i 0.00316188 + 0.00610345i
\(269\) −2.58876 −0.157840 −0.0789198 0.996881i \(-0.525147\pi\)
−0.0789198 + 0.996881i \(0.525147\pi\)
\(270\) −3.03827 + 5.64045i −0.184903 + 0.343267i
\(271\) 29.5135i 1.79282i 0.443226 + 0.896410i \(0.353834\pi\)
−0.443226 + 0.896410i \(0.646166\pi\)
\(272\) −6.47942 4.57536i −0.392872 0.277422i
\(273\) −6.63276 + 0.115673i −0.401433 + 0.00700088i
\(274\) 2.15663 + 1.31160i 0.130287 + 0.0792368i
\(275\) 8.07062i 0.486677i
\(276\) 1.64684 + 3.04761i 0.0991279 + 0.183445i
\(277\) 1.08750i 0.0653413i −0.999466 0.0326707i \(-0.989599\pi\)
0.999466 0.0326707i \(-0.0104012\pi\)
\(278\) −4.34187 + 7.13920i −0.260408 + 0.428181i
\(279\) −0.364545 10.4484i −0.0218247 0.625529i
\(280\) −0.521373 + 7.60760i −0.0311580 + 0.454641i
\(281\) 3.26761i 0.194929i −0.995239 0.0974647i \(-0.968927\pi\)
0.995239 0.0974647i \(-0.0310733\pi\)
\(282\) −9.49481 + 16.2434i −0.565408 + 0.967280i
\(283\) 6.37119 0.378728 0.189364 0.981907i \(-0.439357\pi\)
0.189364 + 0.981907i \(0.439357\pi\)
\(284\) 7.22040 + 13.9377i 0.428452 + 0.827051i
\(285\) −7.50163 + 0.130826i −0.444358 + 0.00774948i
\(286\) 1.73249 2.84868i 0.102444 0.168446i
\(287\) 26.9481 1.59070
\(288\) −7.29640 15.3220i −0.429944 0.902855i
\(289\) 13.0677 0.768688
\(290\) 1.48066 2.43461i 0.0869476 0.142965i
\(291\) −15.6765 + 0.273394i −0.918973 + 0.0160266i
\(292\) 6.48395 + 12.5161i 0.379445 + 0.732451i
\(293\) −24.5319 −1.43317 −0.716584 0.697501i \(-0.754295\pi\)
−0.716584 + 0.697501i \(0.754295\pi\)
\(294\) −3.16741 + 5.41870i −0.184727 + 0.316025i
\(295\) 10.6469i 0.619887i
\(296\) −0.883113 + 12.8859i −0.0513299 + 0.748979i
\(297\) −0.517193 9.87732i −0.0300106 0.573140i
\(298\) −13.4949 + 22.1892i −0.781738 + 1.28539i
\(299\) 1.23856i 0.0716277i
\(300\) −6.98241 12.9215i −0.403130 0.746026i
\(301\) 10.1051i 0.582446i
\(302\) −6.83035 4.15403i −0.393042 0.239038i
\(303\) 33.9095 0.591372i 1.94805 0.0339735i
\(304\) 11.4637 16.2344i 0.657490 0.931107i
\(305\) 9.41374i 0.539029i
\(306\) −7.33625 4.11836i −0.419385 0.235431i
\(307\) 6.49267 0.370556 0.185278 0.982686i \(-0.440681\pi\)
0.185278 + 0.982686i \(0.440681\pi\)
\(308\) −5.41516 10.4530i −0.308557 0.595615i
\(309\) 0.0894015 + 5.12631i 0.00508587 + 0.291626i
\(310\) −3.67117 2.23271i −0.208508 0.126809i
\(311\) −26.3522 −1.49430 −0.747149 0.664657i \(-0.768578\pi\)
−0.747149 + 0.664657i \(0.768578\pi\)
\(312\) 0.309246 6.05979i 0.0175076 0.343068i
\(313\) −33.2164 −1.87750 −0.938750 0.344599i \(-0.888015\pi\)
−0.938750 + 0.344599i \(0.888015\pi\)
\(314\) 21.3610 + 12.9912i 1.20547 + 0.733135i
\(315\) 0.282019 + 8.08309i 0.0158900 + 0.455430i
\(316\) −9.06846 + 4.69789i −0.510141 + 0.264277i
\(317\) 21.3265 1.19782 0.598908 0.800818i \(-0.295601\pi\)
0.598908 + 0.800818i \(0.295601\pi\)
\(318\) −9.30861 + 15.9249i −0.522001 + 0.893022i
\(319\) 4.39916i 0.246306i
\(320\) −6.90952 0.951532i −0.386254 0.0531922i
\(321\) 0.270556 + 15.5138i 0.0151010 + 0.865896i
\(322\) 3.73644 + 2.27240i 0.208223 + 0.126636i
\(323\) 9.85251i 0.548208i
\(324\) −9.37356 15.3667i −0.520753 0.853707i
\(325\) 5.25136i 0.291293i
\(326\) 11.3284 18.6269i 0.627419 1.03165i
\(327\) 0.282395 + 16.1926i 0.0156165 + 0.895454i
\(328\) −1.68529 + 24.5908i −0.0930545 + 1.35780i
\(329\) 23.7525i 1.30952i
\(330\) −3.50946 2.05140i −0.193189 0.112926i
\(331\) −7.14989 −0.392994 −0.196497 0.980504i \(-0.562957\pi\)
−0.196497 + 0.980504i \(0.562957\pi\)
\(332\) 1.41267 0.731831i 0.0775304 0.0401644i
\(333\) 0.477691 + 13.6913i 0.0261773 + 0.750279i
\(334\) −6.64970 + 10.9339i −0.363855 + 0.598276i
\(335\) 0.0490539 0.00268010
\(336\) −17.7136 12.0509i −0.966354 0.657430i
\(337\) 7.67027 0.417826 0.208913 0.977934i \(-0.433007\pi\)
0.208913 + 0.977934i \(0.433007\pi\)
\(338\) −8.42583 + 13.8543i −0.458305 + 0.753576i
\(339\) −0.0444424 2.54834i −0.00241378 0.138407i
\(340\) −3.07020 + 1.59051i −0.166505 + 0.0862576i
\(341\) 6.63352 0.359225
\(342\) 10.3187 18.3812i 0.557971 0.993943i
\(343\) 13.7225i 0.740945i
\(344\) −9.22112 0.631953i −0.497169 0.0340726i
\(345\) 1.50984 0.0263313i 0.0812872 0.00141763i
\(346\) −2.08498 + 3.42827i −0.112089 + 0.184305i
\(347\) 27.3593i 1.46872i 0.678759 + 0.734361i \(0.262518\pi\)
−0.678759 + 0.734361i \(0.737482\pi\)
\(348\) 3.80599 + 7.04332i 0.204023 + 0.377561i
\(349\) 6.07938i 0.325422i 0.986674 + 0.162711i \(0.0520238\pi\)
−0.986674 + 0.162711i \(0.947976\pi\)
\(350\) −15.8421 9.63474i −0.846795 0.514998i
\(351\) −0.336525 6.42693i −0.0179624 0.343044i
\(352\) 9.87728 4.28775i 0.526461 0.228538i
\(353\) 25.6872i 1.36719i 0.729861 + 0.683595i \(0.239585\pi\)
−0.729861 + 0.683595i \(0.760415\pi\)
\(354\) 25.8248 + 15.0955i 1.37257 + 0.802316i
\(355\) 6.84262 0.363168
\(356\) 30.8761 15.9953i 1.63643 0.847749i
\(357\) −10.6194 + 0.185200i −0.562039 + 0.00980181i
\(358\) 12.7880 + 7.77729i 0.675864 + 0.411042i
\(359\) −17.9590 −0.947838 −0.473919 0.880568i \(-0.657161\pi\)
−0.473919 + 0.880568i \(0.657161\pi\)
\(360\) −7.39365 0.248152i −0.389680 0.0130788i
\(361\) 5.68581 0.299253
\(362\) 10.3975 + 6.32347i 0.546479 + 0.332354i
\(363\) −12.7749 + 0.222790i −0.670508 + 0.0116935i
\(364\) −3.52351 6.80152i −0.184682 0.356497i
\(365\) 6.14470 0.321628
\(366\) 22.8337 + 13.3471i 1.19354 + 0.697662i
\(367\) 22.5647i 1.17787i −0.808180 0.588935i \(-0.799547\pi\)
0.808180 0.588935i \(-0.200453\pi\)
\(368\) −2.30729 + 3.26748i −0.120276 + 0.170329i
\(369\) 0.911601 + 26.1278i 0.0474560 + 1.36016i
\(370\) 4.81060 + 2.92568i 0.250091 + 0.152099i
\(371\) 23.2867i 1.20898i
\(372\) 10.6207 5.73908i 0.550656 0.297558i
\(373\) 19.6359i 1.01671i 0.861147 + 0.508355i \(0.169746\pi\)
−0.861147 + 0.508355i \(0.830254\pi\)
\(374\) 2.77381 4.56089i 0.143430 0.235838i
\(375\) −13.9508 + 0.243298i −0.720416 + 0.0125639i
\(376\) −21.6747 1.48544i −1.11779 0.0766055i
\(377\) 2.86243i 0.147422i
\(378\) −20.0060 10.7764i −1.02900 0.554277i
\(379\) −13.9167 −0.714855 −0.357428 0.933941i \(-0.616346\pi\)
−0.357428 + 0.933941i \(0.616346\pi\)
\(380\) −3.98508 7.69250i −0.204430 0.394617i
\(381\) −0.208671 11.9653i −0.0106905 0.613000i
\(382\) 10.7339 17.6493i 0.549192 0.903019i
\(383\) 27.2328 1.39153 0.695766 0.718269i \(-0.255065\pi\)
0.695766 + 0.718269i \(0.255065\pi\)
\(384\) 12.1045 15.4104i 0.617706 0.786409i
\(385\) −5.13183 −0.261542
\(386\) 4.03073 6.62761i 0.205159 0.337336i
\(387\) −9.79745 + 0.341834i −0.498032 + 0.0173764i
\(388\) −8.32781 16.0754i −0.422781 0.816104i
\(389\) 0.198260 0.0100522 0.00502608 0.999987i \(-0.498400\pi\)
0.00502608 + 0.999987i \(0.498400\pi\)
\(390\) −2.28352 1.33479i −0.115631 0.0675900i
\(391\) 1.98300i 0.100285i
\(392\) −7.23055 0.495532i −0.365198 0.0250282i
\(393\) −0.379687 21.7714i −0.0191527 1.09822i
\(394\) 16.0653 26.4157i 0.809360 1.33081i
\(395\) 4.45209i 0.224009i
\(396\) 9.95162 5.60392i 0.500088 0.281607i
\(397\) 12.8510i 0.644971i −0.946574 0.322485i \(-0.895482\pi\)
0.946574 0.322485i \(-0.104518\pi\)
\(398\) −23.6778 14.4002i −1.18686 0.721816i
\(399\) −0.464025 26.6073i −0.0232303 1.33203i
\(400\) 9.78267 13.8538i 0.489133 0.692688i
\(401\) 23.3200i 1.16454i 0.812994 + 0.582272i \(0.197836\pi\)
−0.812994 + 0.582272i \(0.802164\pi\)
\(402\) −0.0695500 + 0.118984i −0.00346884 + 0.00593437i
\(403\) 4.31627 0.215009
\(404\) 18.0137 + 34.7723i 0.896215 + 1.72999i
\(405\) −7.82749 + 0.546869i −0.388951 + 0.0271741i
\(406\) 8.63526 + 5.25173i 0.428561 + 0.260639i
\(407\) −8.69240 −0.430866
\(408\) 0.495120 9.70206i 0.0245121 0.480324i
\(409\) 2.90989 0.143885 0.0719425 0.997409i \(-0.477080\pi\)
0.0719425 + 0.997409i \(0.477080\pi\)
\(410\) 9.18032 + 5.58322i 0.453383 + 0.275736i
\(411\) 0.0539057 + 3.09097i 0.00265897 + 0.152466i
\(412\) −5.25674 + 2.72324i −0.258981 + 0.134165i
\(413\) 37.7632 1.85821
\(414\) −2.07683 + 3.69956i −0.102071 + 0.181824i
\(415\) 0.693540i 0.0340446i
\(416\) 6.42691 2.78994i 0.315105 0.136788i
\(417\) −10.2322 + 0.178447i −0.501074 + 0.00873859i
\(418\) 11.4275 + 6.94988i 0.558936 + 0.339930i
\(419\) 15.9445i 0.778941i 0.921039 + 0.389470i \(0.127342\pi\)
−0.921039 + 0.389470i \(0.872658\pi\)
\(420\) −8.21637 + 4.43987i −0.400918 + 0.216644i
\(421\) 30.6791i 1.49521i −0.664144 0.747604i \(-0.731204\pi\)
0.664144 0.747604i \(-0.268796\pi\)
\(422\) −7.21785 + 11.8681i −0.351360 + 0.577730i
\(423\) −23.0294 + 0.803497i −1.11973 + 0.0390674i
\(424\) −21.2497 1.45631i −1.03197 0.0707245i
\(425\) 8.40772i 0.407834i
\(426\) −9.70165 + 16.5972i −0.470047 + 0.804139i
\(427\) 33.3894 1.61582
\(428\) −15.9085 + 8.24138i −0.768968 + 0.398362i
\(429\) 4.08285 0.0712037i 0.197122 0.00343775i
\(430\) −2.09361 + 3.44245i −0.100963 + 0.166010i
\(431\) 35.6205 1.71578 0.857890 0.513833i \(-0.171775\pi\)
0.857890 + 0.513833i \(0.171775\pi\)
\(432\) 11.0848 17.5820i 0.533319 0.845914i
\(433\) 3.15606 0.151670 0.0758352 0.997120i \(-0.475838\pi\)
0.0758352 + 0.997120i \(0.475838\pi\)
\(434\) 7.91912 13.0212i 0.380130 0.625036i
\(435\) 3.48939 0.0608540i 0.167303 0.00291773i
\(436\) −16.6046 + 8.60199i −0.795218 + 0.411961i
\(437\) −4.96848 −0.237675
\(438\) −8.71213 + 14.9044i −0.416282 + 0.712160i
\(439\) 27.8197i 1.32776i 0.747839 + 0.663880i \(0.231092\pi\)
−0.747839 + 0.663880i \(0.768908\pi\)
\(440\) 0.320935 4.68292i 0.0153000 0.223249i
\(441\) −7.68247 + 0.268042i −0.365832 + 0.0127639i
\(442\) 1.80485 2.96766i 0.0858481 0.141157i
\(443\) 6.53287i 0.310386i 0.987884 + 0.155193i \(0.0496000\pi\)
−0.987884 + 0.155193i \(0.950400\pi\)
\(444\) −13.9171 + 7.52035i −0.660474 + 0.356900i
\(445\) 15.1584i 0.718577i
\(446\) 6.49267 + 3.94867i 0.307437 + 0.186975i
\(447\) −31.8025 + 0.554628i −1.50421 + 0.0262330i
\(448\) 3.37496 24.5072i 0.159452 1.15786i
\(449\) 25.4871i 1.20281i −0.798943 0.601406i \(-0.794607\pi\)
0.798943 0.601406i \(-0.205393\pi\)
\(450\) 8.80554 15.6858i 0.415097 0.739434i
\(451\) −16.5881 −0.781105
\(452\) 2.61318 1.35375i 0.122914 0.0636752i
\(453\) −0.170727 9.78955i −0.00802146 0.459953i
\(454\) 27.8557 + 16.9411i 1.30733 + 0.795084i
\(455\) −3.33916 −0.156542
\(456\) 24.3089 + 1.24054i 1.13837 + 0.0580937i
\(457\) 2.40286 0.112401 0.0562004 0.998420i \(-0.482101\pi\)
0.0562004 + 0.998420i \(0.482101\pi\)
\(458\) 32.8975 + 20.0074i 1.53720 + 0.934884i
\(459\) −0.538796 10.2899i −0.0251488 0.480291i
\(460\) 0.802072 + 1.54826i 0.0373968 + 0.0721880i
\(461\) −14.0637 −0.655013 −0.327506 0.944849i \(-0.606208\pi\)
−0.327506 + 0.944849i \(0.606208\pi\)
\(462\) 7.27605 12.4476i 0.338512 0.579115i
\(463\) 35.7689i 1.66232i 0.556031 + 0.831161i \(0.312323\pi\)
−0.556031 + 0.831161i \(0.687677\pi\)
\(464\) −5.33237 + 7.55145i −0.247549 + 0.350567i
\(465\) −0.0917622 5.26168i −0.00425537 0.244004i
\(466\) 26.1202 + 15.8856i 1.20999 + 0.735886i
\(467\) 39.3360i 1.82025i −0.414331 0.910126i \(-0.635985\pi\)
0.414331 0.910126i \(-0.364015\pi\)
\(468\) 6.47528 3.64633i 0.299320 0.168552i
\(469\) 0.173988i 0.00803402i
\(470\) −4.92113 + 8.09165i −0.226995 + 0.373240i
\(471\) 0.533926 + 30.6155i 0.0246020 + 1.41069i
\(472\) −2.36165 + 34.4599i −0.108704 + 1.58614i
\(473\) 6.22025i 0.286007i
\(474\) −10.7989 6.31230i −0.496008 0.289934i
\(475\) 21.0658 0.966567
\(476\) −5.64134 10.8896i −0.258571 0.499125i
\(477\) −22.5778 + 0.787740i −1.03377 + 0.0360682i
\(478\) −12.9906 + 21.3600i −0.594174 + 0.976982i
\(479\) 2.16149 0.0987611 0.0493805 0.998780i \(-0.484275\pi\)
0.0493805 + 0.998780i \(0.484275\pi\)
\(480\) −3.53766 7.77530i −0.161471 0.354892i
\(481\) −5.65593 −0.257888
\(482\) 12.0108 19.7490i 0.547077 0.899542i
\(483\) 0.0933936 + 5.35522i 0.00424956 + 0.243671i
\(484\) −6.78639 13.0999i −0.308472 0.595451i
\(485\) −7.89209 −0.358361
\(486\) 9.77156 19.7615i 0.443247 0.896400i
\(487\) 28.2115i 1.27839i 0.769046 + 0.639193i \(0.220732\pi\)
−0.769046 + 0.639193i \(0.779268\pi\)
\(488\) −2.08811 + 30.4686i −0.0945244 + 1.37925i
\(489\) 26.6968 0.465585i 1.20727 0.0210545i
\(490\) −1.64166 + 2.69933i −0.0741625 + 0.121943i
\(491\) 5.65453i 0.255185i −0.991827 0.127593i \(-0.959275\pi\)
0.991827 0.127593i \(-0.0407250\pi\)
\(492\) −26.5586 + 14.3515i −1.19735 + 0.647014i
\(493\) 4.58291i 0.206404i
\(494\) 7.43558 + 4.52212i 0.334543 + 0.203460i
\(495\) −0.173599 4.97561i −0.00780271 0.223637i
\(496\) 11.3869 + 8.04071i 0.511286 + 0.361039i
\(497\) 24.2699i 1.08865i
\(498\) 1.68223 + 0.983321i 0.0753826 + 0.0440637i
\(499\) 31.1605 1.39494 0.697468 0.716616i \(-0.254310\pi\)
0.697468 + 0.716616i \(0.254310\pi\)
\(500\) −7.41106 14.3057i −0.331433 0.639773i
\(501\) −15.6709 + 0.273297i −0.700125 + 0.0122100i
\(502\) −17.0716 10.3825i −0.761944 0.463394i
\(503\) −0.784770 −0.0349912 −0.0174956 0.999847i \(-0.505569\pi\)
−0.0174956 + 0.999847i \(0.505569\pi\)
\(504\) 0.880165 26.2244i 0.0392057 1.16813i
\(505\) 17.0712 0.759658
\(506\) −2.29999 1.39879i −0.102247 0.0621840i
\(507\) −19.8566 + 0.346294i −0.881864 + 0.0153795i
\(508\) 12.2697 6.35630i 0.544381 0.282015i
\(509\) 1.62618 0.0720790 0.0360395 0.999350i \(-0.488526\pi\)
0.0360395 + 0.999350i \(0.488526\pi\)
\(510\) −3.65605 2.13708i −0.161892 0.0946316i
\(511\) 21.7945i 0.964131i
\(512\) 22.1523 + 4.61237i 0.979004 + 0.203840i
\(513\) 25.7817 1.34997i 1.13829 0.0596027i
\(514\) 16.0628 + 9.76895i 0.708499 + 0.430890i
\(515\) 2.58076i 0.113722i
\(516\) −5.38154 9.95900i −0.236909 0.438420i
\(517\) 14.6210i 0.643031i
\(518\) −10.3770 + 17.0626i −0.455940 + 0.749688i
\(519\) −4.91355 + 0.0856910i −0.215681 + 0.00376142i
\(520\) 0.208825 3.04706i 0.00915758 0.133623i
\(521\) 22.0363i 0.965429i 0.875778 + 0.482715i \(0.160349\pi\)
−0.875778 + 0.482715i \(0.839651\pi\)
\(522\) −4.79975 + 8.55004i −0.210079 + 0.374225i
\(523\) −0.873026 −0.0381748 −0.0190874 0.999818i \(-0.506076\pi\)
−0.0190874 + 0.999818i \(0.506076\pi\)
\(524\) 22.3253 11.5656i 0.975286 0.505244i
\(525\) −0.395979 22.7056i −0.0172819 0.990953i
\(526\) 18.6593 30.6810i 0.813586 1.33775i
\(527\) 6.91060 0.301030
\(528\) 10.9037 + 7.41802i 0.474524 + 0.322828i
\(529\) 1.00000 0.0434783
\(530\) −4.82462 + 7.93298i −0.209568 + 0.344586i
\(531\) 1.27745 + 36.6137i 0.0554368 + 1.58890i
\(532\) 27.2843 14.1346i 1.18293 0.612812i
\(533\) −10.7935 −0.467518
\(534\) 36.7678 + 21.4920i 1.59110 + 0.930050i
\(535\) 7.81018i 0.337663i
\(536\) −0.158768 0.0108809i −0.00685774 0.000469983i
\(537\) 0.319640 + 18.3282i 0.0137935 + 0.790922i
\(538\) 1.90236 3.12800i 0.0820168 0.134858i
\(539\) 4.87748i 0.210088i
\(540\) −4.58266 7.81606i −0.197206 0.336350i
\(541\) 40.4127i 1.73748i −0.495269 0.868739i \(-0.664931\pi\)
0.495269 0.868739i \(-0.335069\pi\)
\(542\) −35.6612 21.6882i −1.53178 0.931587i
\(543\) 0.259889 + 14.9021i 0.0111529 + 0.639511i
\(544\) 10.2898 4.46685i 0.441173 0.191514i
\(545\) 8.15192i 0.349190i
\(546\) 4.73435 8.09936i 0.202611 0.346621i
\(547\) 26.3268 1.12565 0.562825 0.826576i \(-0.309714\pi\)
0.562825 + 0.826576i \(0.309714\pi\)
\(548\) −3.16962 + 1.64201i −0.135399 + 0.0701433i
\(549\) 1.12949 + 32.3729i 0.0482056 + 1.38164i
\(550\) 9.75172 + 5.93074i 0.415815 + 0.252887i
\(551\) −11.4826 −0.489176
\(552\) −4.89261 0.249682i −0.208243 0.0106272i
\(553\) −15.7910 −0.671502
\(554\) 1.31402 + 0.799152i 0.0558274 + 0.0339527i
\(555\) 0.120243 + 6.89477i 0.00510402 + 0.292667i
\(556\) −5.43565 10.4926i −0.230523 0.444984i
\(557\) 26.7166 1.13202 0.566009 0.824399i \(-0.308487\pi\)
0.566009 + 0.824399i \(0.308487\pi\)
\(558\) 12.8927 + 7.23758i 0.545790 + 0.306391i
\(559\) 4.04737i 0.171185i
\(560\) −8.80913 6.22046i −0.372254 0.262862i
\(561\) 6.53687 0.114001i 0.275987 0.00481313i
\(562\) 3.94825 + 2.40122i 0.166547 + 0.101289i
\(563\) 13.0343i 0.549330i −0.961540 0.274665i \(-0.911433\pi\)
0.961540 0.274665i \(-0.0885669\pi\)
\(564\) −12.6496 23.4091i −0.532643 0.985702i
\(565\) 1.28292i 0.0539729i
\(566\) −4.68191 + 7.69831i −0.196795 + 0.323584i
\(567\) −1.93967 27.7631i −0.0814587 1.16594i
\(568\) −22.1469 1.51780i −0.929262 0.0636853i
\(569\) 38.2253i 1.60249i −0.598338 0.801244i \(-0.704172\pi\)
0.598338 0.801244i \(-0.295828\pi\)
\(570\) 5.35453 9.16035i 0.224277 0.383685i
\(571\) 25.1413 1.05213 0.526066 0.850444i \(-0.323667\pi\)
0.526066 + 0.850444i \(0.323667\pi\)
\(572\) 2.16893 + 4.18673i 0.0906873 + 0.175056i
\(573\) 25.2958 0.441152i 1.05675 0.0184294i
\(574\) −19.8030 + 32.5614i −0.826561 + 1.35909i
\(575\) −4.23989 −0.176816
\(576\) 23.8753 + 2.44320i 0.994805 + 0.101800i
\(577\) −20.3082 −0.845442 −0.422721 0.906260i \(-0.638925\pi\)
−0.422721 + 0.906260i \(0.638925\pi\)
\(578\) −9.60287 + 15.7897i −0.399427 + 0.656765i
\(579\) 9.49898 0.165660i 0.394764 0.00688458i
\(580\) 1.85366 + 3.57817i 0.0769692 + 0.148576i
\(581\) 2.45990 0.102054
\(582\) 11.1896 19.1428i 0.463825 0.793496i
\(583\) 14.3343i 0.593666i
\(584\) −19.8880 1.36299i −0.822971 0.0564009i
\(585\) −0.112957 3.23751i −0.00467019 0.133854i
\(586\) 18.0274 29.6419i 0.744705 1.22449i
\(587\) 15.5366i 0.641263i 0.947204 + 0.320631i \(0.103895\pi\)
−0.947204 + 0.320631i \(0.896105\pi\)
\(588\) −4.21982 7.80914i −0.174022 0.322043i
\(589\) 17.3147i 0.713441i
\(590\) 12.8647 + 7.82394i 0.529629 + 0.322106i
\(591\) 37.8602 0.660271i 1.55736 0.0271599i
\(592\) −14.9211 10.5363i −0.613253 0.433041i
\(593\) 6.77501i 0.278216i −0.990277 0.139108i \(-0.955576\pi\)
0.990277 0.139108i \(-0.0444236\pi\)
\(594\) 12.3148 + 6.63348i 0.505283 + 0.272175i
\(595\) −5.34618 −0.219172
\(596\) −16.8944 32.6117i −0.692023 1.33583i
\(597\) −0.591835 33.9360i −0.0242222 1.38891i
\(598\) −1.49655 0.910161i −0.0611985 0.0372193i
\(599\) −32.7522 −1.33822 −0.669109 0.743164i \(-0.733324\pi\)
−0.669109 + 0.743164i \(0.733324\pi\)
\(600\) 20.7442 + 1.05863i 0.846877 + 0.0432182i
\(601\) −7.83996 −0.319799 −0.159899 0.987133i \(-0.551117\pi\)
−0.159899 + 0.987133i \(0.551117\pi\)
\(602\) −12.2099 7.42576i −0.497640 0.302651i
\(603\) −0.168692 + 0.00588566i −0.00686965 + 0.000239683i
\(604\) 10.0386 5.20049i 0.408466 0.211605i
\(605\) −6.43131 −0.261470
\(606\) −24.2040 + 41.4074i −0.983221 + 1.68206i
\(607\) 11.1151i 0.451147i 0.974226 + 0.225574i \(0.0724256\pi\)
−0.974226 + 0.225574i \(0.927574\pi\)
\(608\) 11.1918 + 25.7816i 0.453889 + 1.04558i
\(609\) 0.215841 + 12.3764i 0.00874634 + 0.501518i
\(610\) 11.3746 + 6.91774i 0.460545 + 0.280091i
\(611\) 9.51354i 0.384877i
\(612\) 10.3673 5.83799i 0.419073 0.235987i
\(613\) 2.83979i 0.114698i −0.998354 0.0573490i \(-0.981735\pi\)
0.998354 0.0573490i \(-0.0182648\pi\)
\(614\) −4.77117 + 7.84509i −0.192549 + 0.316602i
\(615\) 0.229465 + 13.1576i 0.00925294 + 0.530567i
\(616\) 16.6097 + 1.13832i 0.669225 + 0.0458641i
\(617\) 2.11914i 0.0853133i −0.999090 0.0426566i \(-0.986418\pi\)
0.999090 0.0426566i \(-0.0135822\pi\)
\(618\) −6.25982 3.65907i −0.251807 0.147190i
\(619\) −19.2856 −0.775154 −0.387577 0.921837i \(-0.626688\pi\)
−0.387577 + 0.921837i \(0.626688\pi\)
\(620\) 5.39555 2.79515i 0.216691 0.112256i
\(621\) −5.18904 + 0.271707i −0.208229 + 0.0109032i
\(622\) 19.3651 31.8414i 0.776469 1.27672i
\(623\) 53.7649 2.15405
\(624\) 7.09479 + 4.82673i 0.284019 + 0.193224i
\(625\) 14.1762 0.567047
\(626\) 24.4092 40.1353i 0.975589 1.60413i
\(627\) 0.285634 + 16.3784i 0.0114071 + 0.654088i
\(628\) −31.3945 + 16.2638i −1.25278 + 0.648998i
\(629\) −9.05547 −0.361065
\(630\) −9.97403 5.59914i −0.397375 0.223075i
\(631\) 12.4518i 0.495696i 0.968799 + 0.247848i \(0.0797234\pi\)
−0.968799 + 0.247848i \(0.920277\pi\)
\(632\) 0.987542 14.4097i 0.0392823 0.573186i
\(633\) −17.0099 + 0.296647i −0.676081 + 0.0117907i
\(634\) −15.6719 + 25.7688i −0.622411 + 1.02341i
\(635\) 6.02373i 0.239044i
\(636\) −12.4015 22.9501i −0.491752 0.910029i
\(637\) 3.17366i 0.125745i
\(638\) −5.31550 3.23274i −0.210443 0.127986i
\(639\) −23.5311 + 0.821001i −0.930875 + 0.0324783i
\(640\) 6.22723 7.64953i 0.246153 0.302374i
\(641\) 18.3406i 0.724411i 0.932098 + 0.362205i \(0.117976\pi\)
−0.932098 + 0.362205i \(0.882024\pi\)
\(642\) −18.9441 11.0735i −0.747665 0.437036i
\(643\) 42.8115 1.68832 0.844160 0.536091i \(-0.180100\pi\)
0.844160 + 0.536091i \(0.180100\pi\)
\(644\) −5.49148 + 2.84485i −0.216395 + 0.112103i
\(645\) −4.93387 + 0.0860454i −0.194271 + 0.00338803i
\(646\) 11.9048 + 7.24017i 0.468388 + 0.284861i
\(647\) −24.2136 −0.951935 −0.475968 0.879463i \(-0.657902\pi\)
−0.475968 + 0.879463i \(0.657902\pi\)
\(648\) 25.4558 0.0337447i 0.999999 0.00132562i
\(649\) −23.2455 −0.912464
\(650\) 6.34521 + 3.85899i 0.248880 + 0.151362i
\(651\) 18.6625 0.325469i 0.731441 0.0127561i
\(652\) 14.1821 + 27.3761i 0.555415 + 1.07213i
\(653\) −37.6716 −1.47420 −0.737101 0.675782i \(-0.763806\pi\)
−0.737101 + 0.675782i \(0.763806\pi\)
\(654\) −19.7731 11.5580i −0.773188 0.451954i
\(655\) 10.9604i 0.428260i
\(656\) −28.4747 20.1070i −1.11175 0.785048i
\(657\) −21.1310 + 0.737263i −0.824400 + 0.0287634i
\(658\) −28.7001 17.4546i −1.11885 0.680452i
\(659\) 24.6271i 0.959337i −0.877450 0.479669i \(-0.840757\pi\)
0.877450 0.479669i \(-0.159243\pi\)
\(660\) 5.05765 2.73300i 0.196869 0.106382i
\(661\) 43.8276i 1.70470i −0.522976 0.852348i \(-0.675178\pi\)
0.522976 0.852348i \(-0.324822\pi\)
\(662\) 5.25414 8.63921i 0.204208 0.335773i
\(663\) 4.25338 0.0741778i 0.165188 0.00288083i
\(664\) −0.153838 + 2.24472i −0.00597006 + 0.0871120i
\(665\) 13.3950i 0.519437i
\(666\) −16.8942 9.48394i −0.654638 0.367495i
\(667\) 2.31109 0.0894859
\(668\) −8.32484 16.0696i −0.322098 0.621753i
\(669\) 0.162287 + 9.30557i 0.00627436 + 0.359774i
\(670\) −0.0360475 + 0.0592718i −0.00139264 + 0.00228987i
\(671\) −20.5531 −0.793443
\(672\) 27.5780 12.5476i 1.06384 0.484035i
\(673\) −33.5022 −1.29142 −0.645708 0.763584i \(-0.723438\pi\)
−0.645708 + 0.763584i \(0.723438\pi\)
\(674\) −5.63654 + 9.26799i −0.217111 + 0.356989i
\(675\) 22.0010 1.15201i 0.846819 0.0443408i
\(676\) −10.5484 20.3619i −0.405708 0.783148i
\(677\) −14.9572 −0.574850 −0.287425 0.957803i \(-0.592799\pi\)
−0.287425 + 0.957803i \(0.592799\pi\)
\(678\) 3.11182 + 1.81896i 0.119509 + 0.0698568i
\(679\) 27.9923i 1.07424i
\(680\) 0.334341 4.87852i 0.0128214 0.187083i
\(681\) 0.696263 + 39.9240i 0.0266809 + 1.52989i
\(682\) −4.87468 + 8.01528i −0.186661 + 0.306921i
\(683\) 4.05767i 0.155262i −0.996982 0.0776312i \(-0.975264\pi\)
0.996982 0.0776312i \(-0.0247357\pi\)
\(684\) 14.6273 + 25.9756i 0.559288 + 0.993202i
\(685\) 1.55610i 0.0594555i
\(686\) 16.5809 + 10.0840i 0.633061 + 0.385011i
\(687\) 0.822286 + 47.1502i 0.0313722 + 1.79889i
\(688\) 7.53978 10.6775i 0.287451 0.407075i
\(689\) 9.32698i 0.355329i
\(690\) −1.07770 + 1.84369i −0.0410273 + 0.0701882i
\(691\) −23.0400 −0.876485 −0.438242 0.898857i \(-0.644399\pi\)
−0.438242 + 0.898857i \(0.644399\pi\)
\(692\) −2.61022 5.03857i −0.0992257 0.191538i
\(693\) 17.6479 0.615735i 0.670387 0.0233898i
\(694\) −33.0582 20.1051i −1.25487 0.763179i
\(695\) −5.15125 −0.195398
\(696\) −11.3073 0.577039i −0.428602 0.0218726i
\(697\) −17.2810 −0.654565
\(698\) −7.34572 4.46747i −0.278040 0.169096i
\(699\) 0.652884 + 37.4366i 0.0246943 + 1.41598i
\(700\) 23.2833 12.0619i 0.880026 0.455895i
\(701\) 22.3112 0.842683 0.421342 0.906902i \(-0.361559\pi\)
0.421342 + 0.906902i \(0.361559\pi\)
\(702\) 8.01296 + 4.31624i 0.302430 + 0.162906i
\(703\) 22.6888i 0.855724i
\(704\) −2.07749 + 15.0856i −0.0782982 + 0.568560i
\(705\) −11.5973 + 0.202254i −0.436780 + 0.00761732i
\(706\) −31.0378 18.8764i −1.16812 0.710421i
\(707\) 60.5494i 2.27719i
\(708\) −37.2174 + 20.1111i −1.39871 + 0.755823i
\(709\) 17.9668i 0.674758i 0.941369 + 0.337379i \(0.109540\pi\)
−0.941369 + 0.337379i \(0.890460\pi\)
\(710\) −5.02833 + 8.26793i −0.188710 + 0.310290i
\(711\) −0.534178 15.3103i −0.0200332 0.574182i
\(712\) −3.36236 + 49.0618i −0.126010 + 1.83867i
\(713\) 3.48492i 0.130511i
\(714\) 7.57996 12.9675i 0.283673 0.485298i
\(715\) 2.05544 0.0768693
\(716\) −18.7946 + 9.73649i −0.702387 + 0.363870i
\(717\) −30.6140 + 0.533900i −1.14330 + 0.0199389i
\(718\) 13.1972 21.6998i 0.492517 0.809830i
\(719\) 34.2271 1.27646 0.638228 0.769848i \(-0.279668\pi\)
0.638228 + 0.769848i \(0.279668\pi\)
\(720\) 5.73311 8.75139i 0.213660 0.326145i
\(721\) −9.15363 −0.340899
\(722\) −4.17825 + 6.87016i −0.155498 + 0.255681i
\(723\) 28.3051 0.493634i 1.05268 0.0183584i
\(724\) −15.2813 + 7.91644i −0.567925 + 0.294212i
\(725\) −9.79879 −0.363918
\(726\) 9.11849 15.5996i 0.338419 0.578956i
\(727\) 19.2864i 0.715293i 0.933857 + 0.357646i \(0.116421\pi\)
−0.933857 + 0.357646i \(0.883579\pi\)
\(728\) 10.8075 + 0.740676i 0.400554 + 0.0274513i
\(729\) 26.8524 2.81980i 0.994532 0.104437i
\(730\) −4.51547 + 7.42464i −0.167125 + 0.274798i
\(731\) 6.48007i 0.239674i
\(732\) −32.9067 + 17.7818i −1.21627 + 0.657234i
\(733\) 13.7227i 0.506860i 0.967354 + 0.253430i \(0.0815587\pi\)
−0.967354 + 0.253430i \(0.918441\pi\)
\(734\) 27.2650 + 16.5818i 1.00637 + 0.612046i
\(735\) −3.86879 + 0.0674707i −0.142703 + 0.00248869i
\(736\) −2.25257 5.18902i −0.0830307 0.191270i
\(737\) 0.107100i 0.00394507i
\(738\) −32.2401 18.0987i −1.18677 0.666221i
\(739\) −21.1541 −0.778167 −0.389083 0.921203i \(-0.627208\pi\)
−0.389083 + 0.921203i \(0.627208\pi\)
\(740\) −7.07020 + 3.66270i −0.259906 + 0.134643i
\(741\) 0.185855 + 10.6570i 0.00682756 + 0.391495i
\(742\) −28.1373 17.1123i −1.03295 0.628213i
\(743\) −26.8675 −0.985673 −0.492837 0.870122i \(-0.664040\pi\)
−0.492837 + 0.870122i \(0.664040\pi\)
\(744\) −0.870121 + 17.0503i −0.0319002 + 0.625096i
\(745\) −16.0105 −0.586579
\(746\) −23.7261 14.4296i −0.868674 0.528304i
\(747\) 0.0832134 + 2.38502i 0.00304462 + 0.0872632i
\(748\) 3.47257 + 6.70319i 0.126970 + 0.245093i
\(749\) −27.7017 −1.01220
\(750\) 9.95784 17.0355i 0.363609 0.622049i
\(751\) 6.80908i 0.248467i 0.992253 + 0.124233i \(0.0396472\pi\)
−0.992253 + 0.124233i \(0.960353\pi\)
\(752\) 17.7226 25.0979i 0.646277 0.915228i
\(753\) −0.426711 24.4678i −0.0155502 0.891656i
\(754\) −3.45867 2.10347i −0.125957 0.0766038i
\(755\) 4.92839i 0.179363i
\(756\) 27.7226 16.2541i 1.00826 0.591157i
\(757\) 5.76958i 0.209699i −0.994488 0.104849i \(-0.966564\pi\)
0.994488 0.104849i \(-0.0334361\pi\)
\(758\) 10.2268 16.8156i 0.371454 0.610770i
\(759\) −0.0574892 3.29645i −0.00208673 0.119654i
\(760\) 12.2233 + 0.837702i 0.443386 + 0.0303866i
\(761\) 39.7502i 1.44095i −0.693483 0.720473i \(-0.743925\pi\)
0.693483 0.720473i \(-0.256075\pi\)
\(762\) 14.6110 + 8.54061i 0.529300 + 0.309394i
\(763\) −28.9138 −1.04675
\(764\) 13.4379 + 25.9394i 0.486165 + 0.938455i
\(765\) −0.180850 5.18343i −0.00653866 0.187407i
\(766\) −20.0122 + 32.9054i −0.723069 + 1.18892i
\(767\) −15.1253 −0.546141
\(768\) 9.72533 + 25.9503i 0.350933 + 0.936401i
\(769\) 44.3637 1.59980 0.799898 0.600136i \(-0.204887\pi\)
0.799898 + 0.600136i \(0.204887\pi\)
\(770\) 3.77115 6.20079i 0.135903 0.223461i
\(771\) 0.401495 + 23.0219i 0.0144595 + 0.829112i
\(772\) 5.04613 + 9.74067i 0.181614 + 0.350574i
\(773\) 20.9167 0.752321 0.376161 0.926554i \(-0.377244\pi\)
0.376161 + 0.926554i \(0.377244\pi\)
\(774\) 6.78667 12.0895i 0.243942 0.434546i
\(775\) 14.7757i 0.530758i
\(776\) 25.5436 + 1.75059i 0.916962 + 0.0628424i
\(777\) −24.4549 + 0.426486i −0.877314 + 0.0153001i
\(778\) −0.145692 + 0.239557i −0.00522332 + 0.00858854i
\(779\) 43.2982i 1.55132i
\(780\) 3.29089 1.77830i 0.117833 0.0636732i
\(781\) 14.9395i 0.534578i
\(782\) −2.39606 1.45722i −0.0856830 0.0521101i
\(783\) −11.9924 + 0.627940i −0.428572 + 0.0224408i
\(784\) 5.91216 8.37252i 0.211148 0.299019i
\(785\) 15.4129i 0.550110i
\(786\) 26.5853 + 15.5400i 0.948268 + 0.554294i
\(787\) −52.1207 −1.85790 −0.928951 0.370202i \(-0.879289\pi\)
−0.928951 + 0.370202i \(0.879289\pi\)
\(788\) 20.1124 + 38.8235i 0.716475 + 1.38303i
\(789\) 43.9733 0.766883i 1.56549 0.0273017i
\(790\) −5.37946 3.27164i −0.191393 0.116400i
\(791\) 4.55036 0.161792
\(792\) −0.541793 + 16.1426i −0.0192518 + 0.573603i
\(793\) −13.3734 −0.474903
\(794\) 15.5278 + 9.44359i 0.551061 + 0.335140i
\(795\) −11.3699 + 0.198288i −0.403248 + 0.00703254i
\(796\) 34.7995 18.0278i 1.23343 0.638978i
\(797\) 35.1231 1.24412 0.622062 0.782968i \(-0.286295\pi\)
0.622062 + 0.782968i \(0.286295\pi\)
\(798\) 32.4906 + 18.9919i 1.15016 + 0.672304i
\(799\) 15.2317i 0.538859i
\(800\) 9.55064 + 22.0009i 0.337666 + 0.777849i
\(801\) 1.81876 + 52.1283i 0.0642627 + 1.84186i
\(802\) −28.1775 17.1368i −0.994983 0.605122i
\(803\) 13.4158i 0.473432i
\(804\) −0.0926588 0.171473i −0.00326782 0.00604739i
\(805\) 2.69600i 0.0950216i
\(806\) −3.17184 + 5.21535i −0.111723 + 0.183703i
\(807\) 4.48318 0.0781855i 0.157816 0.00275226i
\(808\) −55.2528 3.78665i −1.94379 0.133214i
\(809\) 11.2110i 0.394157i −0.980388 0.197078i \(-0.936855\pi\)
0.980388 0.197078i \(-0.0631454\pi\)
\(810\) 5.09129 9.85982i 0.178890 0.346439i
\(811\) −23.2309 −0.815746 −0.407873 0.913039i \(-0.633729\pi\)
−0.407873 + 0.913039i \(0.633729\pi\)
\(812\) −12.6913 + 6.57471i −0.445378 + 0.230727i
\(813\) −0.891365 51.1112i −0.0312615 1.79255i
\(814\) 6.38766 10.5030i 0.223887 0.368131i
\(815\) 13.4401 0.470786
\(816\) 11.3592 + 7.72787i 0.397650 + 0.270529i
\(817\) 16.2360 0.568027
\(818\) −2.13835 + 3.51602i −0.0747657 + 0.122935i
\(819\) 11.4830 0.400644i 0.401250 0.0139996i
\(820\) −13.4924 + 6.98971i −0.471175 + 0.244091i
\(821\) −8.28219 −0.289050 −0.144525 0.989501i \(-0.546165\pi\)
−0.144525 + 0.989501i \(0.546165\pi\)
\(822\) −3.77443 2.20628i −0.131648 0.0769529i
\(823\) 17.0583i 0.594616i 0.954782 + 0.297308i \(0.0960889\pi\)
−0.954782 + 0.297308i \(0.903911\pi\)
\(824\) 0.572452 8.35291i 0.0199423 0.290987i
\(825\) 0.243748 + 13.9766i 0.00848622 + 0.486603i
\(826\) −27.7505 + 45.6293i −0.965564 + 1.58765i
\(827\) 11.3622i 0.395101i 0.980293 + 0.197551i \(0.0632987\pi\)
−0.980293 + 0.197551i \(0.936701\pi\)
\(828\) −2.94401 5.22808i −0.102312 0.181688i
\(829\) 33.5403i 1.16490i 0.812865 + 0.582452i \(0.197906\pi\)
−0.812865 + 0.582452i \(0.802094\pi\)
\(830\) 0.838004 + 0.509652i 0.0290876 + 0.0176903i
\(831\) 0.0328444 + 1.88331i 0.00113936 + 0.0653314i
\(832\) −1.35177 + 9.81583i −0.0468642 + 0.340303i
\(833\) 5.08121i 0.176053i
\(834\) 7.30358 12.4947i 0.252902 0.432657i
\(835\) −7.88928 −0.273020
\(836\) −16.7951 + 8.70065i −0.580870 + 0.300918i
\(837\) 0.946876 + 18.0834i 0.0327288 + 0.625053i
\(838\) −19.2658 11.7169i −0.665524 0.404754i
\(839\) −0.880528 −0.0303992 −0.0151996 0.999884i \(-0.504838\pi\)
−0.0151996 + 0.999884i \(0.504838\pi\)
\(840\) 0.673144 13.1905i 0.0232257 0.455115i
\(841\) −23.6588 −0.815822
\(842\) 37.0696 + 22.5447i 1.27750 + 0.776942i
\(843\) 0.0986881 + 5.65881i 0.00339900 + 0.194900i
\(844\) −9.03613 17.4427i −0.311036 0.600401i
\(845\) −9.99650 −0.343890
\(846\) 15.9524 28.4169i 0.548455 0.976992i
\(847\) 22.8111i 0.783797i
\(848\) 17.3751 24.6058i 0.596662 0.844966i
\(849\) −11.0336 + 0.192422i −0.378671 + 0.00660391i
\(850\) 10.1590 + 6.17846i 0.348452 + 0.211919i
\(851\) 4.56655i 0.156539i
\(852\) −12.9251 23.9191i −0.442808 0.819454i
\(853\) 51.3054i 1.75666i 0.478052 + 0.878331i \(0.341343\pi\)
−0.478052 + 0.878331i \(0.658657\pi\)
\(854\) −24.5363 + 40.3443i −0.839617 + 1.38056i
\(855\) 12.9873 0.453127i 0.444155 0.0154966i
\(856\) 1.73242 25.2785i 0.0592128 0.864001i
\(857\) 20.2353i 0.691224i 0.938378 + 0.345612i \(0.112329\pi\)
−0.938378 + 0.345612i \(0.887671\pi\)
\(858\) −2.91427 + 4.98563i −0.0994914 + 0.170206i
\(859\) −23.4886 −0.801421 −0.400710 0.916205i \(-0.631237\pi\)
−0.400710 + 0.916205i \(0.631237\pi\)
\(860\) −2.62101 5.05941i −0.0893759 0.172524i
\(861\) −46.6685 + 0.813885i −1.59046 + 0.0277371i
\(862\) −26.1759 + 43.0403i −0.891556 + 1.46596i
\(863\) 4.02794 0.137113 0.0685563 0.997647i \(-0.478161\pi\)
0.0685563 + 0.997647i \(0.478161\pi\)
\(864\) 13.0986 + 26.3140i 0.445622 + 0.895221i
\(865\) −2.47365 −0.0841066
\(866\) −2.31924 + 3.81346i −0.0788111 + 0.129587i
\(867\) −22.6305 + 0.394669i −0.768571 + 0.0134037i
\(868\) 9.91406 + 19.1373i 0.336505 + 0.649564i
\(869\) 9.72028 0.329738
\(870\) −2.49067 + 4.26095i −0.0844415 + 0.144460i
\(871\) 0.0696872i 0.00236126i
\(872\) 1.80822 26.3846i 0.0612341 0.893495i
\(873\) 27.1401 0.946921i 0.918554 0.0320484i
\(874\) 3.65112 6.00341i 0.123501 0.203068i
\(875\) 24.9108i 0.842138i
\(876\) −11.6068 21.4794i −0.392159 0.725723i
\(877\) 37.8678i 1.27870i 0.768914 + 0.639352i \(0.220798\pi\)
−0.768914 + 0.639352i \(0.779202\pi\)
\(878\) −33.6145 20.4434i −1.13443 0.689933i
\(879\) 42.4840 0.740910i 1.43295 0.0249903i
\(880\) 5.42253 + 3.82905i 0.182793 + 0.129077i
\(881\) 48.6628i 1.63949i 0.572727 + 0.819746i \(0.305885\pi\)
−0.572727 + 0.819746i \(0.694115\pi\)
\(882\) 5.32163 9.47969i 0.179188 0.319198i
\(883\) −6.80087 −0.228868 −0.114434 0.993431i \(-0.536505\pi\)
−0.114434 + 0.993431i \(0.536505\pi\)
\(884\) 2.25952 + 4.36160i 0.0759959 + 0.146697i
\(885\) 0.321557 + 18.4382i 0.0108090 + 0.619793i
\(886\) −7.89367 4.80072i −0.265193 0.161283i
\(887\) −2.86430 −0.0961737 −0.0480869 0.998843i \(-0.515312\pi\)
−0.0480869 + 0.998843i \(0.515312\pi\)
\(888\) 1.14019 22.3423i 0.0382621 0.749760i
\(889\) 21.3654 0.716573
\(890\) 18.3159 + 11.1392i 0.613950 + 0.373388i
\(891\) 1.19398 + 17.0898i 0.0399999 + 0.572530i
\(892\) −9.54234 + 4.94339i −0.319501 + 0.165517i
\(893\) 38.1636 1.27710
\(894\) 22.7001 38.8346i 0.759205 1.29882i
\(895\) 9.22707i 0.308427i
\(896\) 27.1319 + 22.0872i 0.906413 + 0.737882i
\(897\) −0.0374068 2.14492i −0.00124898 0.0716168i
\(898\) 30.7961 + 18.7294i 1.02768 + 0.625007i
\(899\) 8.05397i 0.268615i
\(900\) 12.4823 + 22.1665i 0.416077 + 0.738883i
\(901\) 14.9330i 0.497491i
\(902\) 12.1899 20.0434i 0.405879 0.667374i
\(903\) −0.305192 17.4998i −0.0101562 0.582358i
\(904\) −0.284572 + 4.15232i −0.00946471 + 0.138104i
\(905\) 7.50224i 0.249383i
\(906\) 11.9542 + 6.98761i 0.397151 + 0.232148i
\(907\) −19.3695 −0.643153 −0.321576 0.946884i \(-0.604213\pi\)
−0.321576 + 0.946884i \(0.604213\pi\)
\(908\) −40.9398 + 21.2088i −1.35863 + 0.703838i
\(909\) −58.7062 + 2.04826i −1.94716 + 0.0679366i
\(910\) 2.45380 4.03470i 0.0813426 0.133749i
\(911\) −22.5365 −0.746668 −0.373334 0.927697i \(-0.621785\pi\)
−0.373334 + 0.927697i \(0.621785\pi\)
\(912\) −19.3624 + 28.4608i −0.641154 + 0.942430i
\(913\) −1.51421 −0.0501131
\(914\) −1.76575 + 2.90337i −0.0584059 + 0.0960349i
\(915\) 0.284313 + 16.3026i 0.00939909 + 0.538947i
\(916\) −48.3498 + 25.0475i −1.59752 + 0.827593i
\(917\) 38.8753 1.28378
\(918\) 12.8292 + 6.91055i 0.423427 + 0.228082i
\(919\) 47.7774i 1.57603i −0.615656 0.788015i \(-0.711109\pi\)
0.615656 0.788015i \(-0.288891\pi\)
\(920\) −2.46017 0.168603i −0.0811093 0.00555868i
\(921\) −11.2439 + 0.196091i −0.370500 + 0.00646142i
\(922\) 10.3348 16.9932i 0.340359 0.559641i
\(923\) 9.72079i 0.319964i
\(924\) 9.69360 + 17.9388i 0.318896 + 0.590145i
\(925\) 19.3617i 0.636608i
\(926\) −43.2196 26.2850i −1.42028 0.863778i
\(927\) −0.309649 8.87498i −0.0101702 0.291493i
\(928\) −5.20589 11.9923i −0.170892 0.393667i
\(929\) 40.9144i 1.34236i −0.741295 0.671179i \(-0.765788\pi\)
0.741295 0.671179i \(-0.234212\pi\)
\(930\) 6.42511 + 3.75569i 0.210688 + 0.123154i
\(931\) 12.7311 0.417246
\(932\) −38.3891 + 19.8874i −1.25748 + 0.651433i
\(933\) 45.6365 0.795887i 1.49407 0.0260562i
\(934\) 47.5296 + 28.9063i 1.55522 + 0.945842i
\(935\) 3.29088 0.107623
\(936\) −0.352531 + 10.5036i −0.0115228 + 0.343321i
\(937\) 27.6662 0.903814 0.451907 0.892065i \(-0.350744\pi\)
0.451907 + 0.892065i \(0.350744\pi\)
\(938\) −0.210230 0.127856i −0.00686424 0.00417465i
\(939\) 57.5237 1.00320i 1.87721 0.0327381i
\(940\) −6.16083 11.8924i −0.200944 0.387887i
\(941\) −6.59325 −0.214934 −0.107467 0.994209i \(-0.534274\pi\)
−0.107467 + 0.994209i \(0.534274\pi\)
\(942\) −37.3851 21.8528i −1.21807 0.712004i
\(943\) 8.71457i 0.283785i
\(944\) −39.9024 28.1766i −1.29871 0.917070i
\(945\) −0.732522 13.9897i −0.0238290 0.455084i
\(946\) 7.51593 + 4.57099i 0.244364 + 0.148616i
\(947\) 48.2638i 1.56836i 0.620531 + 0.784182i \(0.286917\pi\)
−0.620531 + 0.784182i \(0.713083\pi\)
\(948\) 15.5628 8.40964i 0.505455 0.273132i
\(949\) 8.72931i 0.283366i
\(950\) −15.4803 + 25.4538i −0.502249 + 0.825831i
\(951\) −36.9330 + 0.644101i −1.19763 + 0.0208864i
\(952\) 17.3035 + 1.18586i 0.560809 + 0.0384341i
\(953\) 48.2640i 1.56342i −0.623640 0.781712i \(-0.714347\pi\)
0.623640 0.781712i \(-0.285653\pi\)
\(954\) 15.6396 27.8596i 0.506350 0.901988i
\(955\) 12.7348 0.412087
\(956\) −16.2630 31.3930i −0.525985 1.01532i
\(957\) −0.132863 7.61841i −0.00429485 0.246268i
\(958\) −1.58838 + 2.61173i −0.0513184 + 0.0843812i
\(959\) −5.51929 −0.178227
\(960\) 11.9946 + 1.43917i 0.387122 + 0.0464490i
\(961\) 18.8554 0.608237
\(962\) 4.15629 6.83406i 0.134004 0.220339i
\(963\) −0.937092 26.8584i −0.0301974 0.865501i
\(964\) 15.0365 + 29.0253i 0.484293 + 0.934842i
\(965\) 4.78211 0.153942
\(966\) −6.53934 3.82247i −0.210400 0.122986i
\(967\) 51.1796i 1.64583i 0.568168 + 0.822913i \(0.307652\pi\)
−0.568168 + 0.822913i \(0.692348\pi\)
\(968\) 20.8156 + 1.42656i 0.669040 + 0.0458515i
\(969\) 0.297565 + 17.0625i 0.00955915 + 0.548125i
\(970\) 5.79954 9.53601i 0.186212 0.306183i
\(971\) 31.6471i 1.01560i −0.861474 0.507802i \(-0.830458\pi\)
0.861474 0.507802i \(-0.169542\pi\)
\(972\) 16.6971 + 26.3288i 0.535560 + 0.844497i
\(973\) 18.2708i 0.585736i
\(974\) −34.0880 20.7314i −1.09225 0.664277i
\(975\) 0.158601 + 9.09423i 0.00507929 + 0.291249i
\(976\) −35.2807 24.9131i −1.12931 0.797448i
\(977\) 25.9886i 0.831448i −0.909491 0.415724i \(-0.863528\pi\)
0.909491 0.415724i \(-0.136472\pi\)
\(978\) −19.0557 + 32.5999i −0.609335 + 1.04243i
\(979\) −33.0954 −1.05773
\(980\) −2.05521 3.96723i −0.0656514 0.126728i
\(981\) −0.978096 28.0337i −0.0312282 0.895046i
\(982\) 6.83236 + 4.15526i 0.218029 + 0.132600i
\(983\) 39.6637 1.26507 0.632537 0.774530i \(-0.282014\pi\)
0.632537 + 0.774530i \(0.282014\pi\)
\(984\) 2.17587 42.6370i 0.0693643 1.35922i
\(985\) 19.0601 0.607305
\(986\) −5.53752 3.36777i −0.176351 0.107252i
\(987\) −0.717369 41.1342i −0.0228341 1.30932i
\(988\) −10.9282 + 5.66130i −0.347671 + 0.180110i
\(989\) −3.26780 −0.103910
\(990\) 6.13960 + 3.44659i 0.195129 + 0.109540i
\(991\) 13.4539i 0.427378i 0.976902 + 0.213689i \(0.0685480\pi\)
−0.976902 + 0.213689i \(0.931452\pi\)
\(992\) −18.0833 + 7.85000i −0.574145 + 0.249238i
\(993\) 12.3821 0.215940i 0.392934 0.00685266i
\(994\) −29.3253 17.8349i −0.930142 0.565687i
\(995\) 17.0846i 0.541617i
\(996\) −2.42434 + 1.31004i −0.0768182 + 0.0415102i
\(997\) 57.2452i 1.81297i 0.422234 + 0.906487i \(0.361246\pi\)
−0.422234 + 0.906487i \(0.638754\pi\)
\(998\) −22.8985 + 37.6512i −0.724838 + 1.19183i
\(999\) −1.24076 23.6960i −0.0392560 0.749708i
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 552.2.j.d.323.16 yes 42
3.2 odd 2 552.2.j.c.323.27 42
4.3 odd 2 2208.2.j.d.47.41 42
8.3 odd 2 552.2.j.c.323.28 yes 42
8.5 even 2 2208.2.j.c.47.41 42
12.11 even 2 2208.2.j.c.47.42 42
24.5 odd 2 2208.2.j.d.47.42 42
24.11 even 2 inner 552.2.j.d.323.15 yes 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.j.c.323.27 42 3.2 odd 2
552.2.j.c.323.28 yes 42 8.3 odd 2
552.2.j.d.323.15 yes 42 24.11 even 2 inner
552.2.j.d.323.16 yes 42 1.1 even 1 trivial
2208.2.j.c.47.41 42 8.5 even 2
2208.2.j.c.47.42 42 12.11 even 2
2208.2.j.d.47.41 42 4.3 odd 2
2208.2.j.d.47.42 42 24.5 odd 2