Properties

Label 429.2.m.b.307.4
Level $429$
Weight $2$
Character 429.307
Analytic conductor $3.426$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(109,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.m (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.4
Character \(\chi\) \(=\) 429.307
Dual form 429.2.m.b.109.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20600 + 1.20600i) q^{2} +1.00000 q^{3} -0.908895i q^{4} +(-0.200991 - 0.200991i) q^{5} +(-1.20600 + 1.20600i) q^{6} +(-3.33407 - 3.33407i) q^{7} +(-1.31588 - 1.31588i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.20600 + 1.20600i) q^{2} +1.00000 q^{3} -0.908895i q^{4} +(-0.200991 - 0.200991i) q^{5} +(-1.20600 + 1.20600i) q^{6} +(-3.33407 - 3.33407i) q^{7} +(-1.31588 - 1.31588i) q^{8} +1.00000 q^{9} +0.484791 q^{10} +(2.95091 + 1.51398i) q^{11} -0.908895i q^{12} +(2.46083 - 2.63521i) q^{13} +8.04182 q^{14} +(-0.200991 - 0.200991i) q^{15} +4.99170 q^{16} +7.25513 q^{17} +(-1.20600 + 1.20600i) q^{18} +(-1.18165 + 1.18165i) q^{19} +(-0.182679 + 0.182679i) q^{20} +(-3.33407 - 3.33407i) q^{21} +(-5.38468 + 1.73295i) q^{22} -3.26417i q^{23} +(-1.31588 - 1.31588i) q^{24} -4.91921i q^{25} +(0.210296 + 6.14585i) q^{26} +1.00000 q^{27} +(-3.03032 + 3.03032i) q^{28} +5.67492i q^{29} +0.484791 q^{30} +(-3.86547 - 3.86547i) q^{31} +(-3.38826 + 3.38826i) q^{32} +(2.95091 + 1.51398i) q^{33} +(-8.74972 + 8.74972i) q^{34} +1.34024i q^{35} -0.908895i q^{36} +(2.95704 - 2.95704i) q^{37} -2.85014i q^{38} +(2.46083 - 2.63521i) q^{39} +0.528958i q^{40} +(4.75377 - 4.75377i) q^{41} +8.04182 q^{42} -2.81887 q^{43} +(1.37605 - 2.68207i) q^{44} +(-0.200991 - 0.200991i) q^{45} +(3.93660 + 3.93660i) q^{46} +(3.39398 - 3.39398i) q^{47} +4.99170 q^{48} +15.2321i q^{49} +(5.93259 + 5.93259i) q^{50} +7.25513 q^{51} +(-2.39513 - 2.23664i) q^{52} -5.44413 q^{53} +(-1.20600 + 1.20600i) q^{54} +(-0.288811 - 0.897400i) q^{55} +8.77447i q^{56} +(-1.18165 + 1.18165i) q^{57} +(-6.84397 - 6.84397i) q^{58} +(-5.68655 + 5.68655i) q^{59} +(-0.182679 + 0.182679i) q^{60} -14.3278i q^{61} +9.32355 q^{62} +(-3.33407 - 3.33407i) q^{63} +1.81089i q^{64} +(-1.02426 + 0.0350475i) q^{65} +(-5.38468 + 1.73295i) q^{66} +(-0.748559 - 0.748559i) q^{67} -6.59415i q^{68} -3.26417i q^{69} +(-1.61633 - 1.61633i) q^{70} +(6.94874 + 6.94874i) q^{71} +(-1.31588 - 1.31588i) q^{72} +(2.84928 + 2.84928i) q^{73} +7.13242i q^{74} -4.91921i q^{75} +(1.07399 + 1.07399i) q^{76} +(-4.79085 - 14.8863i) q^{77} +(0.210296 + 6.14585i) q^{78} +3.04264i q^{79} +(-1.00328 - 1.00328i) q^{80} +1.00000 q^{81} +11.4661i q^{82} +(-4.10311 + 4.10311i) q^{83} +(-3.03032 + 3.03032i) q^{84} +(-1.45821 - 1.45821i) q^{85} +(3.39957 - 3.39957i) q^{86} +5.67492i q^{87} +(-1.89083 - 5.87525i) q^{88} +(6.08327 - 6.08327i) q^{89} +0.484791 q^{90} +(-16.9906 + 0.581376i) q^{91} -2.96679 q^{92} +(-3.86547 - 3.86547i) q^{93} +8.18631i q^{94} +0.475000 q^{95} +(-3.38826 + 3.38826i) q^{96} +(-1.76445 - 1.76445i) q^{97} +(-18.3700 - 18.3700i) q^{98} +(2.95091 + 1.51398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20600 + 1.20600i −0.852774 + 0.852774i −0.990474 0.137700i \(-0.956029\pi\)
0.137700 + 0.990474i \(0.456029\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.908895i 0.454448i
\(5\) −0.200991 0.200991i −0.0898857 0.0898857i 0.660734 0.750620i \(-0.270245\pi\)
−0.750620 + 0.660734i \(0.770245\pi\)
\(6\) −1.20600 + 1.20600i −0.492349 + 0.492349i
\(7\) −3.33407 3.33407i −1.26016 1.26016i −0.951014 0.309147i \(-0.899956\pi\)
−0.309147 0.951014i \(-0.600044\pi\)
\(8\) −1.31588 1.31588i −0.465233 0.465233i
\(9\) 1.00000 0.333333
\(10\) 0.484791 0.153304
\(11\) 2.95091 + 1.51398i 0.889733 + 0.456481i
\(12\) 0.908895i 0.262375i
\(13\) 2.46083 2.63521i 0.682512 0.730875i
\(14\) 8.04182 2.14927
\(15\) −0.200991 0.200991i −0.0518956 0.0518956i
\(16\) 4.99170 1.24792
\(17\) 7.25513 1.75963 0.879814 0.475319i \(-0.157667\pi\)
0.879814 + 0.475319i \(0.157667\pi\)
\(18\) −1.20600 + 1.20600i −0.284258 + 0.284258i
\(19\) −1.18165 + 1.18165i −0.271089 + 0.271089i −0.829538 0.558450i \(-0.811396\pi\)
0.558450 + 0.829538i \(0.311396\pi\)
\(20\) −0.182679 + 0.182679i −0.0408484 + 0.0408484i
\(21\) −3.33407 3.33407i −0.727554 0.727554i
\(22\) −5.38468 + 1.73295i −1.14802 + 0.369466i
\(23\) 3.26417i 0.680626i −0.940312 0.340313i \(-0.889467\pi\)
0.940312 0.340313i \(-0.110533\pi\)
\(24\) −1.31588 1.31588i −0.268602 0.268602i
\(25\) 4.91921i 0.983841i
\(26\) 0.210296 + 6.14585i 0.0412424 + 1.20530i
\(27\) 1.00000 0.192450
\(28\) −3.03032 + 3.03032i −0.572677 + 0.572677i
\(29\) 5.67492i 1.05381i 0.849926 + 0.526903i \(0.176647\pi\)
−0.849926 + 0.526903i \(0.823353\pi\)
\(30\) 0.484791 0.0885104
\(31\) −3.86547 3.86547i −0.694259 0.694259i 0.268907 0.963166i \(-0.413338\pi\)
−0.963166 + 0.268907i \(0.913338\pi\)
\(32\) −3.38826 + 3.38826i −0.598965 + 0.598965i
\(33\) 2.95091 + 1.51398i 0.513688 + 0.263549i
\(34\) −8.74972 + 8.74972i −1.50056 + 1.50056i
\(35\) 1.34024i 0.226541i
\(36\) 0.908895i 0.151483i
\(37\) 2.95704 2.95704i 0.486135 0.486135i −0.420949 0.907084i \(-0.638303\pi\)
0.907084 + 0.420949i \(0.138303\pi\)
\(38\) 2.85014i 0.462355i
\(39\) 2.46083 2.63521i 0.394048 0.421971i
\(40\) 0.528958i 0.0836356i
\(41\) 4.75377 4.75377i 0.742413 0.742413i −0.230628 0.973042i \(-0.574078\pi\)
0.973042 + 0.230628i \(0.0740782\pi\)
\(42\) 8.04182 1.24088
\(43\) −2.81887 −0.429873 −0.214937 0.976628i \(-0.568954\pi\)
−0.214937 + 0.976628i \(0.568954\pi\)
\(44\) 1.37605 2.68207i 0.207447 0.404337i
\(45\) −0.200991 0.200991i −0.0299619 0.0299619i
\(46\) 3.93660 + 3.93660i 0.580420 + 0.580420i
\(47\) 3.39398 3.39398i 0.495063 0.495063i −0.414834 0.909897i \(-0.636160\pi\)
0.909897 + 0.414834i \(0.136160\pi\)
\(48\) 4.99170 0.720490
\(49\) 15.2321i 2.17601i
\(50\) 5.93259 + 5.93259i 0.838994 + 0.838994i
\(51\) 7.25513 1.01592
\(52\) −2.39513 2.23664i −0.332144 0.310166i
\(53\) −5.44413 −0.747809 −0.373904 0.927467i \(-0.621981\pi\)
−0.373904 + 0.927467i \(0.621981\pi\)
\(54\) −1.20600 + 1.20600i −0.164116 + 0.164116i
\(55\) −0.288811 0.897400i −0.0389432 0.121005i
\(56\) 8.77447i 1.17254i
\(57\) −1.18165 + 1.18165i −0.156513 + 0.156513i
\(58\) −6.84397 6.84397i −0.898658 0.898658i
\(59\) −5.68655 + 5.68655i −0.740325 + 0.740325i −0.972641 0.232315i \(-0.925370\pi\)
0.232315 + 0.972641i \(0.425370\pi\)
\(60\) −0.182679 + 0.182679i −0.0235838 + 0.0235838i
\(61\) 14.3278i 1.83448i −0.398330 0.917242i \(-0.630410\pi\)
0.398330 0.917242i \(-0.369590\pi\)
\(62\) 9.32355 1.18409
\(63\) −3.33407 3.33407i −0.420054 0.420054i
\(64\) 1.81089i 0.226361i
\(65\) −1.02426 + 0.0350475i −0.127043 + 0.00434711i
\(66\) −5.38468 + 1.73295i −0.662808 + 0.213312i
\(67\) −0.748559 0.748559i −0.0914511 0.0914511i 0.659901 0.751352i \(-0.270598\pi\)
−0.751352 + 0.659901i \(0.770598\pi\)
\(68\) 6.59415i 0.799658i
\(69\) 3.26417i 0.392960i
\(70\) −1.61633 1.61633i −0.193188 0.193188i
\(71\) 6.94874 + 6.94874i 0.824664 + 0.824664i 0.986773 0.162109i \(-0.0518295\pi\)
−0.162109 + 0.986773i \(0.551829\pi\)
\(72\) −1.31588 1.31588i −0.155078 0.155078i
\(73\) 2.84928 + 2.84928i 0.333483 + 0.333483i 0.853908 0.520424i \(-0.174226\pi\)
−0.520424 + 0.853908i \(0.674226\pi\)
\(74\) 7.13242i 0.829127i
\(75\) 4.91921i 0.568021i
\(76\) 1.07399 + 1.07399i 0.123196 + 0.123196i
\(77\) −4.79085 14.8863i −0.545968 1.69645i
\(78\) 0.210296 + 6.14585i 0.0238113 + 0.695880i
\(79\) 3.04264i 0.342323i 0.985243 + 0.171162i \(0.0547520\pi\)
−0.985243 + 0.171162i \(0.945248\pi\)
\(80\) −1.00328 1.00328i −0.112171 0.112171i
\(81\) 1.00000 0.111111
\(82\) 11.4661i 1.26622i
\(83\) −4.10311 + 4.10311i −0.450375 + 0.450375i −0.895479 0.445104i \(-0.853167\pi\)
0.445104 + 0.895479i \(0.353167\pi\)
\(84\) −3.03032 + 3.03032i −0.330635 + 0.330635i
\(85\) −1.45821 1.45821i −0.158165 0.158165i
\(86\) 3.39957 3.39957i 0.366585 0.366585i
\(87\) 5.67492i 0.608415i
\(88\) −1.89083 5.87525i −0.201563 0.626303i
\(89\) 6.08327 6.08327i 0.644826 0.644826i −0.306912 0.951738i \(-0.599296\pi\)
0.951738 + 0.306912i \(0.0992958\pi\)
\(90\) 0.484791 0.0511015
\(91\) −16.9906 + 0.581376i −1.78109 + 0.0609447i
\(92\) −2.96679 −0.309309
\(93\) −3.86547 3.86547i −0.400831 0.400831i
\(94\) 8.18631i 0.844354i
\(95\) 0.475000 0.0487340
\(96\) −3.38826 + 3.38826i −0.345813 + 0.345813i
\(97\) −1.76445 1.76445i −0.179153 0.179153i 0.611833 0.790987i \(-0.290432\pi\)
−0.790987 + 0.611833i \(0.790432\pi\)
\(98\) −18.3700 18.3700i −1.85565 1.85565i
\(99\) 2.95091 + 1.51398i 0.296578 + 0.152160i
\(100\) −4.47104 −0.447104
\(101\) −17.5489 −1.74618 −0.873089 0.487561i \(-0.837887\pi\)
−0.873089 + 0.487561i \(0.837887\pi\)
\(102\) −8.74972 + 8.74972i −0.866352 + 0.866352i
\(103\) 3.92179i 0.386426i 0.981157 + 0.193213i \(0.0618908\pi\)
−0.981157 + 0.193213i \(0.938109\pi\)
\(104\) −6.70576 + 0.229455i −0.657554 + 0.0224999i
\(105\) 1.34024i 0.130794i
\(106\) 6.56565 6.56565i 0.637712 0.637712i
\(107\) 0.546231i 0.0528062i −0.999651 0.0264031i \(-0.991595\pi\)
0.999651 0.0264031i \(-0.00840534\pi\)
\(108\) 0.908895i 0.0874585i
\(109\) 4.52795 4.52795i 0.433699 0.433699i −0.456186 0.889885i \(-0.650785\pi\)
0.889885 + 0.456186i \(0.150785\pi\)
\(110\) 1.43058 + 0.733962i 0.136400 + 0.0699806i
\(111\) 2.95704 2.95704i 0.280670 0.280670i
\(112\) −16.6427 16.6427i −1.57259 1.57259i
\(113\) 5.58972 0.525836 0.262918 0.964818i \(-0.415315\pi\)
0.262918 + 0.964818i \(0.415315\pi\)
\(114\) 2.85014i 0.266941i
\(115\) −0.656067 + 0.656067i −0.0611786 + 0.0611786i
\(116\) 5.15790 0.478899
\(117\) 2.46083 2.63521i 0.227504 0.243625i
\(118\) 13.7160i 1.26266i
\(119\) −24.1891 24.1891i −2.21741 2.21741i
\(120\) 0.528958i 0.0482871i
\(121\) 6.41575 + 8.93522i 0.583250 + 0.812292i
\(122\) 17.2794 + 17.2794i 1.56440 + 1.56440i
\(123\) 4.75377 4.75377i 0.428633 0.428633i
\(124\) −3.51331 + 3.51331i −0.315504 + 0.315504i
\(125\) −1.99367 + 1.99367i −0.178319 + 0.178319i
\(126\) 8.04182 0.716422
\(127\) 10.9493 0.971598 0.485799 0.874071i \(-0.338529\pi\)
0.485799 + 0.874071i \(0.338529\pi\)
\(128\) −8.96046 8.96046i −0.792000 0.792000i
\(129\) −2.81887 −0.248187
\(130\) 1.19299 1.27752i 0.104632 0.112046i
\(131\) 13.8031i 1.20598i −0.797747 0.602992i \(-0.793975\pi\)
0.797747 0.602992i \(-0.206025\pi\)
\(132\) 1.37605 2.68207i 0.119769 0.233444i
\(133\) 7.87940 0.683231
\(134\) 1.80553 0.155974
\(135\) −0.200991 0.200991i −0.0172985 0.0172985i
\(136\) −9.54686 9.54686i −0.818637 0.818637i
\(137\) −12.6531 + 12.6531i −1.08103 + 1.08103i −0.0846164 + 0.996414i \(0.526966\pi\)
−0.996414 + 0.0846164i \(0.973034\pi\)
\(138\) 3.93660 + 3.93660i 0.335106 + 0.335106i
\(139\) 16.0680i 1.36287i 0.731880 + 0.681433i \(0.238643\pi\)
−0.731880 + 0.681433i \(0.761357\pi\)
\(140\) 1.21813 0.102951
\(141\) 3.39398 3.39398i 0.285825 0.285825i
\(142\) −16.7604 −1.40650
\(143\) 11.2513 4.05062i 0.940884 0.338730i
\(144\) 4.99170 0.415975
\(145\) 1.14060 1.14060i 0.0947221 0.0947221i
\(146\) −6.87250 −0.568772
\(147\) 15.2321i 1.25632i
\(148\) −2.68764 2.68764i −0.220923 0.220923i
\(149\) −10.6538 + 10.6538i −0.872794 + 0.872794i −0.992776 0.119982i \(-0.961716\pi\)
0.119982 + 0.992776i \(0.461716\pi\)
\(150\) 5.93259 + 5.93259i 0.484394 + 0.484394i
\(151\) −2.70436 2.70436i −0.220078 0.220078i 0.588453 0.808531i \(-0.299737\pi\)
−0.808531 + 0.588453i \(0.799737\pi\)
\(152\) 3.10981 0.252239
\(153\) 7.25513 0.586543
\(154\) 23.7307 + 12.1751i 1.91227 + 0.981099i
\(155\) 1.55385i 0.124808i
\(156\) −2.39513 2.23664i −0.191764 0.179074i
\(157\) 13.0749 1.04349 0.521746 0.853101i \(-0.325281\pi\)
0.521746 + 0.853101i \(0.325281\pi\)
\(158\) −3.66943 3.66943i −0.291924 0.291924i
\(159\) −5.44413 −0.431748
\(160\) 1.36202 0.107677
\(161\) −10.8830 + 10.8830i −0.857698 + 0.857698i
\(162\) −1.20600 + 1.20600i −0.0947527 + 0.0947527i
\(163\) −3.24947 + 3.24947i −0.254518 + 0.254518i −0.822820 0.568302i \(-0.807601\pi\)
0.568302 + 0.822820i \(0.307601\pi\)
\(164\) −4.32067 4.32067i −0.337388 0.337388i
\(165\) −0.288811 0.897400i −0.0224839 0.0698625i
\(166\) 9.89674i 0.768136i
\(167\) 3.87790 + 3.87790i 0.300081 + 0.300081i 0.841046 0.540964i \(-0.181941\pi\)
−0.540964 + 0.841046i \(0.681941\pi\)
\(168\) 8.77447i 0.676965i
\(169\) −0.888616 12.9696i −0.0683551 0.997661i
\(170\) 3.51722 0.269759
\(171\) −1.18165 + 1.18165i −0.0903628 + 0.0903628i
\(172\) 2.56205i 0.195355i
\(173\) 8.75558 0.665675 0.332837 0.942984i \(-0.391994\pi\)
0.332837 + 0.942984i \(0.391994\pi\)
\(174\) −6.84397 6.84397i −0.518840 0.518840i
\(175\) −16.4010 + 16.4010i −1.23980 + 1.23980i
\(176\) 14.7301 + 7.55731i 1.11032 + 0.569654i
\(177\) −5.68655 + 5.68655i −0.427427 + 0.427427i
\(178\) 14.6729i 1.09978i
\(179\) 8.37650i 0.626089i 0.949738 + 0.313044i \(0.101349\pi\)
−0.949738 + 0.313044i \(0.898651\pi\)
\(180\) −0.182679 + 0.182679i −0.0136161 + 0.0136161i
\(181\) 8.13564i 0.604717i 0.953194 + 0.302359i \(0.0977740\pi\)
−0.953194 + 0.302359i \(0.902226\pi\)
\(182\) 19.7896 21.1918i 1.46690 1.57084i
\(183\) 14.3278i 1.05914i
\(184\) −4.29524 + 4.29524i −0.316650 + 0.316650i
\(185\) −1.18868 −0.0873932
\(186\) 9.32355 0.683636
\(187\) 21.4092 + 10.9841i 1.56560 + 0.803236i
\(188\) −3.08477 3.08477i −0.224980 0.224980i
\(189\) −3.33407 3.33407i −0.242518 0.242518i
\(190\) −0.572852 + 0.572852i −0.0415591 + 0.0415591i
\(191\) −1.28415 −0.0929180 −0.0464590 0.998920i \(-0.514794\pi\)
−0.0464590 + 0.998920i \(0.514794\pi\)
\(192\) 1.81089i 0.130690i
\(193\) 18.7908 + 18.7908i 1.35259 + 1.35259i 0.882753 + 0.469838i \(0.155688\pi\)
0.469838 + 0.882753i \(0.344312\pi\)
\(194\) 4.25588 0.305555
\(195\) −1.02426 + 0.0350475i −0.0733485 + 0.00250981i
\(196\) 13.8444 0.988884
\(197\) −12.3045 + 12.3045i −0.876663 + 0.876663i −0.993188 0.116525i \(-0.962824\pi\)
0.116525 + 0.993188i \(0.462824\pi\)
\(198\) −5.38468 + 1.73295i −0.382672 + 0.123155i
\(199\) 20.0985i 1.42475i 0.701801 + 0.712373i \(0.252379\pi\)
−0.701801 + 0.712373i \(0.747621\pi\)
\(200\) −6.47307 + 6.47307i −0.457715 + 0.457715i
\(201\) −0.748559 0.748559i −0.0527993 0.0527993i
\(202\) 21.1640 21.1640i 1.48910 1.48910i
\(203\) 18.9206 18.9206i 1.32796 1.32796i
\(204\) 6.59415i 0.461683i
\(205\) −1.91092 −0.133465
\(206\) −4.72970 4.72970i −0.329534 0.329534i
\(207\) 3.26417i 0.226875i
\(208\) 12.2837 13.1542i 0.851724 0.912077i
\(209\) −5.27592 + 1.69795i −0.364943 + 0.117450i
\(210\) −1.61633 1.61633i −0.111537 0.111537i
\(211\) 21.6318i 1.48919i −0.667515 0.744597i \(-0.732642\pi\)
0.667515 0.744597i \(-0.267358\pi\)
\(212\) 4.94814i 0.339840i
\(213\) 6.94874 + 6.94874i 0.476120 + 0.476120i
\(214\) 0.658758 + 0.658758i 0.0450317 + 0.0450317i
\(215\) 0.566566 + 0.566566i 0.0386395 + 0.0386395i
\(216\) −1.31588 1.31588i −0.0895341 0.0895341i
\(217\) 25.7755i 1.74976i
\(218\) 10.9215i 0.739695i
\(219\) 2.84928 + 2.84928i 0.192537 + 0.192537i
\(220\) −0.815643 + 0.262499i −0.0549906 + 0.0176976i
\(221\) 17.8537 19.1188i 1.20097 1.28607i
\(222\) 7.13242i 0.478697i
\(223\) −18.0992 18.0992i −1.21201 1.21201i −0.970363 0.241651i \(-0.922311\pi\)
−0.241651 0.970363i \(-0.577689\pi\)
\(224\) 22.5934 1.50959
\(225\) 4.91921i 0.327947i
\(226\) −6.74123 + 6.74123i −0.448420 + 0.448420i
\(227\) −0.513536 + 0.513536i −0.0340846 + 0.0340846i −0.723944 0.689859i \(-0.757672\pi\)
0.689859 + 0.723944i \(0.257672\pi\)
\(228\) 1.07399 + 1.07399i 0.0711270 + 0.0711270i
\(229\) 12.6249 12.6249i 0.834274 0.834274i −0.153824 0.988098i \(-0.549159\pi\)
0.988098 + 0.153824i \(0.0491589\pi\)
\(230\) 1.58244i 0.104343i
\(231\) −4.79085 14.8863i −0.315215 0.979444i
\(232\) 7.46749 7.46749i 0.490265 0.490265i
\(233\) 22.5952 1.48026 0.740130 0.672464i \(-0.234764\pi\)
0.740130 + 0.672464i \(0.234764\pi\)
\(234\) 0.210296 + 6.14585i 0.0137475 + 0.401766i
\(235\) −1.36432 −0.0889982
\(236\) 5.16847 + 5.16847i 0.336439 + 0.336439i
\(237\) 3.04264i 0.197640i
\(238\) 58.3444 3.78191
\(239\) −3.72061 + 3.72061i −0.240666 + 0.240666i −0.817126 0.576459i \(-0.804434\pi\)
0.576459 + 0.817126i \(0.304434\pi\)
\(240\) −1.00328 1.00328i −0.0647618 0.0647618i
\(241\) −7.81915 7.81915i −0.503676 0.503676i 0.408902 0.912578i \(-0.365912\pi\)
−0.912578 + 0.408902i \(0.865912\pi\)
\(242\) −18.5133 3.03848i −1.19008 0.195321i
\(243\) 1.00000 0.0641500
\(244\) −13.0225 −0.833677
\(245\) 3.06151 3.06151i 0.195593 0.195593i
\(246\) 11.4661i 0.731054i
\(247\) 0.206049 + 6.02172i 0.0131106 + 0.383153i
\(248\) 10.1730i 0.645984i
\(249\) −4.10311 + 4.10311i −0.260024 + 0.260024i
\(250\) 4.80874i 0.304132i
\(251\) 14.5266i 0.916911i 0.888717 + 0.458456i \(0.151597\pi\)
−0.888717 + 0.458456i \(0.848403\pi\)
\(252\) −3.03032 + 3.03032i −0.190892 + 0.190892i
\(253\) 4.94187 9.63227i 0.310693 0.605575i
\(254\) −13.2050 + 13.2050i −0.828553 + 0.828553i
\(255\) −1.45821 1.45821i −0.0913169 0.0913169i
\(256\) 17.9909 1.12443
\(257\) 2.83504i 0.176845i 0.996083 + 0.0884226i \(0.0281826\pi\)
−0.996083 + 0.0884226i \(0.971817\pi\)
\(258\) 3.39957 3.39957i 0.211648 0.211648i
\(259\) −19.7180 −1.22522
\(260\) 0.0318545 + 0.930941i 0.00197553 + 0.0577345i
\(261\) 5.67492i 0.351268i
\(262\) 16.6466 + 16.6466i 1.02843 + 1.02843i
\(263\) 14.5178i 0.895209i −0.894232 0.447604i \(-0.852277\pi\)
0.894232 0.447604i \(-0.147723\pi\)
\(264\) −1.89083 5.87525i −0.116373 0.361596i
\(265\) 1.09422 + 1.09422i 0.0672174 + 0.0672174i
\(266\) −9.50259 + 9.50259i −0.582641 + 0.582641i
\(267\) 6.08327 6.08327i 0.372290 0.372290i
\(268\) −0.680362 + 0.680362i −0.0415597 + 0.0415597i
\(269\) −23.0188 −1.40348 −0.701740 0.712433i \(-0.747593\pi\)
−0.701740 + 0.712433i \(0.747593\pi\)
\(270\) 0.484791 0.0295035
\(271\) 17.0008 + 17.0008i 1.03272 + 1.03272i 0.999446 + 0.0332760i \(0.0105940\pi\)
0.0332760 + 0.999446i \(0.489406\pi\)
\(272\) 36.2154 2.19588
\(273\) −16.9906 + 0.581376i −1.02832 + 0.0351865i
\(274\) 30.5195i 1.84375i
\(275\) 7.44756 14.5161i 0.449105 0.875356i
\(276\) −2.96679 −0.178579
\(277\) −27.4149 −1.64720 −0.823601 0.567169i \(-0.808038\pi\)
−0.823601 + 0.567169i \(0.808038\pi\)
\(278\) −19.3780 19.3780i −1.16222 1.16222i
\(279\) −3.86547 3.86547i −0.231420 0.231420i
\(280\) 1.76359 1.76359i 0.105394 0.105394i
\(281\) 3.55759 + 3.55759i 0.212228 + 0.212228i 0.805213 0.592985i \(-0.202051\pi\)
−0.592985 + 0.805213i \(0.702051\pi\)
\(282\) 8.18631i 0.487488i
\(283\) −25.2088 −1.49851 −0.749253 0.662284i \(-0.769587\pi\)
−0.749253 + 0.662284i \(0.769587\pi\)
\(284\) 6.31568 6.31568i 0.374767 0.374767i
\(285\) 0.475000 0.0281366
\(286\) −8.68410 + 18.4542i −0.513501 + 1.09122i
\(287\) −31.6988 −1.87112
\(288\) −3.38826 + 3.38826i −0.199655 + 0.199655i
\(289\) 35.6369 2.09629
\(290\) 2.75115i 0.161553i
\(291\) −1.76445 1.76445i −0.103434 0.103434i
\(292\) 2.58970 2.58970i 0.151551 0.151551i
\(293\) 14.1743 + 14.1743i 0.828069 + 0.828069i 0.987250 0.159180i \(-0.0508851\pi\)
−0.159180 + 0.987250i \(0.550885\pi\)
\(294\) −18.3700 18.3700i −1.07136 1.07136i
\(295\) 2.28588 0.133089
\(296\) −7.78222 −0.452332
\(297\) 2.95091 + 1.51398i 0.171229 + 0.0878498i
\(298\) 25.6971i 1.48859i
\(299\) −8.60175 8.03256i −0.497452 0.464535i
\(300\) −4.47104 −0.258136
\(301\) 9.39831 + 9.39831i 0.541709 + 0.541709i
\(302\) 6.52295 0.375353
\(303\) −17.5489 −1.00816
\(304\) −5.89843 + 5.89843i −0.338298 + 0.338298i
\(305\) −2.87975 + 2.87975i −0.164894 + 0.164894i
\(306\) −8.74972 + 8.74972i −0.500188 + 0.500188i
\(307\) −8.82445 8.82445i −0.503638 0.503638i 0.408929 0.912566i \(-0.365903\pi\)
−0.912566 + 0.408929i \(0.865903\pi\)
\(308\) −13.5301 + 4.35438i −0.770946 + 0.248114i
\(309\) 3.92179i 0.223103i
\(310\) −1.87395 1.87395i −0.106433 0.106433i
\(311\) 15.5102i 0.879502i 0.898120 + 0.439751i \(0.144933\pi\)
−0.898120 + 0.439751i \(0.855067\pi\)
\(312\) −6.70576 + 0.229455i −0.379639 + 0.0129903i
\(313\) 28.7631 1.62579 0.812895 0.582411i \(-0.197891\pi\)
0.812895 + 0.582411i \(0.197891\pi\)
\(314\) −15.7684 + 15.7684i −0.889863 + 0.889863i
\(315\) 1.34024i 0.0755137i
\(316\) 2.76544 0.155568
\(317\) 11.7770 + 11.7770i 0.661463 + 0.661463i 0.955725 0.294262i \(-0.0950737\pi\)
−0.294262 + 0.955725i \(0.595074\pi\)
\(318\) 6.56565 6.56565i 0.368183 0.368183i
\(319\) −8.59168 + 16.7462i −0.481042 + 0.937606i
\(320\) 0.363971 0.363971i 0.0203466 0.0203466i
\(321\) 0.546231i 0.0304877i
\(322\) 26.2498i 1.46285i
\(323\) −8.57301 + 8.57301i −0.477015 + 0.477015i
\(324\) 0.908895i 0.0504942i
\(325\) −12.9631 12.1053i −0.719064 0.671483i
\(326\) 7.83776i 0.434093i
\(327\) 4.52795 4.52795i 0.250396 0.250396i
\(328\) −12.5107 −0.690790
\(329\) −22.6316 −1.24772
\(330\) 1.43058 + 0.733962i 0.0787506 + 0.0404033i
\(331\) 0.0573492 + 0.0573492i 0.00315220 + 0.00315220i 0.708681 0.705529i \(-0.249291\pi\)
−0.705529 + 0.708681i \(0.749291\pi\)
\(332\) 3.72930 + 3.72930i 0.204672 + 0.204672i
\(333\) 2.95704 2.95704i 0.162045 0.162045i
\(334\) −9.35354 −0.511803
\(335\) 0.300907i 0.0164403i
\(336\) −16.6427 16.6427i −0.907933 0.907933i
\(337\) −3.94748 −0.215033 −0.107516 0.994203i \(-0.534290\pi\)
−0.107516 + 0.994203i \(0.534290\pi\)
\(338\) 16.7131 + 14.5697i 0.909071 + 0.792488i
\(339\) 5.58972 0.303592
\(340\) −1.32536 + 1.32536i −0.0718779 + 0.0718779i
\(341\) −5.55443 17.2589i −0.300789 0.934621i
\(342\) 2.85014i 0.154118i
\(343\) 27.4464 27.4464i 1.48197 1.48197i
\(344\) 3.70928 + 3.70928i 0.199991 + 0.199991i
\(345\) −0.656067 + 0.656067i −0.0353215 + 0.0353215i
\(346\) −10.5593 + 10.5593i −0.567670 + 0.567670i
\(347\) 3.45221i 0.185324i −0.995698 0.0926622i \(-0.970462\pi\)
0.995698 0.0926622i \(-0.0295377\pi\)
\(348\) 5.15790 0.276493
\(349\) −5.50942 5.50942i −0.294912 0.294912i 0.544105 0.839017i \(-0.316869\pi\)
−0.839017 + 0.544105i \(0.816869\pi\)
\(350\) 39.5594i 2.11454i
\(351\) 2.46083 2.63521i 0.131349 0.140657i
\(352\) −15.1282 + 4.86871i −0.806335 + 0.259503i
\(353\) 7.13058 + 7.13058i 0.379522 + 0.379522i 0.870930 0.491407i \(-0.163517\pi\)
−0.491407 + 0.870930i \(0.663517\pi\)
\(354\) 13.7160i 0.728997i
\(355\) 2.79327i 0.148251i
\(356\) −5.52906 5.52906i −0.293040 0.293040i
\(357\) −24.1891 24.1891i −1.28022 1.28022i
\(358\) −10.1021 10.1021i −0.533912 0.533912i
\(359\) 16.0603 + 16.0603i 0.847632 + 0.847632i 0.989837 0.142205i \(-0.0454192\pi\)
−0.142205 + 0.989837i \(0.545419\pi\)
\(360\) 0.528958i 0.0278785i
\(361\) 16.2074i 0.853022i
\(362\) −9.81162 9.81162i −0.515687 0.515687i
\(363\) 6.41575 + 8.93522i 0.336740 + 0.468977i
\(364\) 0.528410 + 15.4426i 0.0276962 + 0.809414i
\(365\) 1.14536i 0.0599508i
\(366\) 17.2794 + 17.2794i 0.903207 + 0.903207i
\(367\) −35.5649 −1.85647 −0.928236 0.371993i \(-0.878675\pi\)
−0.928236 + 0.371993i \(0.878675\pi\)
\(368\) 16.2937i 0.849370i
\(369\) 4.75377 4.75377i 0.247471 0.247471i
\(370\) 1.43355 1.43355i 0.0745267 0.0745267i
\(371\) 18.1511 + 18.1511i 0.942360 + 0.942360i
\(372\) −3.51331 + 3.51331i −0.182156 + 0.182156i
\(373\) 21.1566i 1.09545i 0.836659 + 0.547724i \(0.184506\pi\)
−0.836659 + 0.547724i \(0.815494\pi\)
\(374\) −39.0665 + 12.5728i −2.02008 + 0.650123i
\(375\) −1.99367 + 1.99367i −0.102953 + 0.102953i
\(376\) −8.93213 −0.460639
\(377\) 14.9546 + 13.9650i 0.770199 + 0.719235i
\(378\) 8.04182 0.413626
\(379\) 12.9964 + 12.9964i 0.667579 + 0.667579i 0.957155 0.289576i \(-0.0935143\pi\)
−0.289576 + 0.957155i \(0.593514\pi\)
\(380\) 0.431725i 0.0221470i
\(381\) 10.9493 0.560952
\(382\) 1.54869 1.54869i 0.0792381 0.0792381i
\(383\) 15.7374 + 15.7374i 0.804144 + 0.804144i 0.983740 0.179596i \(-0.0574792\pi\)
−0.179596 + 0.983740i \(0.557479\pi\)
\(384\) −8.96046 8.96046i −0.457261 0.457261i
\(385\) −2.02908 + 3.95491i −0.103412 + 0.201561i
\(386\) −45.3236 −2.30691
\(387\) −2.81887 −0.143291
\(388\) −1.60370 + 1.60370i −0.0814158 + 0.0814158i
\(389\) 6.41847i 0.325429i −0.986673 0.162715i \(-0.947975\pi\)
0.986673 0.162715i \(-0.0520250\pi\)
\(390\) 1.19299 1.27752i 0.0604094 0.0646900i
\(391\) 23.6820i 1.19765i
\(392\) 20.0436 20.0436i 1.01235 1.01235i
\(393\) 13.8031i 0.696275i
\(394\) 29.6787i 1.49519i
\(395\) 0.611541 0.611541i 0.0307700 0.0307700i
\(396\) 1.37605 2.68207i 0.0691489 0.134779i
\(397\) 13.2341 13.2341i 0.664198 0.664198i −0.292168 0.956367i \(-0.594377\pi\)
0.956367 + 0.292168i \(0.0943768\pi\)
\(398\) −24.2389 24.2389i −1.21499 1.21499i
\(399\) 7.87940 0.394463
\(400\) 24.5552i 1.22776i
\(401\) 2.12792 2.12792i 0.106263 0.106263i −0.651976 0.758239i \(-0.726060\pi\)
0.758239 + 0.651976i \(0.226060\pi\)
\(402\) 1.80553 0.0900517
\(403\) −19.6986 + 0.674038i −0.981256 + 0.0335762i
\(404\) 15.9501i 0.793546i
\(405\) −0.200991 0.200991i −0.00998730 0.00998730i
\(406\) 45.6366i 2.26491i
\(407\) 13.2029 4.24908i 0.654442 0.210619i
\(408\) −9.54686 9.54686i −0.472640 0.472640i
\(409\) −5.55755 + 5.55755i −0.274803 + 0.274803i −0.831030 0.556227i \(-0.812248\pi\)
0.556227 + 0.831030i \(0.312248\pi\)
\(410\) 2.30458 2.30458i 0.113815 0.113815i
\(411\) −12.6531 + 12.6531i −0.624133 + 0.624133i
\(412\) 3.56450 0.175610
\(413\) 37.9187 1.86586
\(414\) 3.93660 + 3.93660i 0.193473 + 0.193473i
\(415\) 1.64937 0.0809646
\(416\) 0.590824 + 17.2667i 0.0289675 + 0.846569i
\(417\) 16.0680i 0.786852i
\(418\) 4.31505 8.41052i 0.211056 0.411372i
\(419\) −11.0697 −0.540791 −0.270396 0.962749i \(-0.587155\pi\)
−0.270396 + 0.962749i \(0.587155\pi\)
\(420\) 1.21813 0.0594388
\(421\) 3.62745 + 3.62745i 0.176791 + 0.176791i 0.789955 0.613164i \(-0.210104\pi\)
−0.613164 + 0.789955i \(0.710104\pi\)
\(422\) 26.0880 + 26.0880i 1.26995 + 1.26995i
\(423\) 3.39398 3.39398i 0.165021 0.165021i
\(424\) 7.16381 + 7.16381i 0.347905 + 0.347905i
\(425\) 35.6895i 1.73119i
\(426\) −16.7604 −0.812046
\(427\) −47.7699 + 47.7699i −2.31175 + 2.31175i
\(428\) −0.496467 −0.0239976
\(429\) 11.2513 4.05062i 0.543219 0.195566i
\(430\) −1.36656 −0.0659015
\(431\) −5.17800 + 5.17800i −0.249415 + 0.249415i −0.820731 0.571315i \(-0.806433\pi\)
0.571315 + 0.820731i \(0.306433\pi\)
\(432\) 4.99170 0.240163
\(433\) 29.3459i 1.41027i −0.709072 0.705137i \(-0.750886\pi\)
0.709072 0.705137i \(-0.249114\pi\)
\(434\) −31.0854 31.0854i −1.49215 1.49215i
\(435\) 1.14060 1.14060i 0.0546878 0.0546878i
\(436\) −4.11543 4.11543i −0.197093 0.197093i
\(437\) 3.85709 + 3.85709i 0.184510 + 0.184510i
\(438\) −6.87250 −0.328381
\(439\) 28.6462 1.36721 0.683604 0.729854i \(-0.260412\pi\)
0.683604 + 0.729854i \(0.260412\pi\)
\(440\) −0.800830 + 1.56091i −0.0381781 + 0.0744134i
\(441\) 15.2321i 0.725338i
\(442\) 1.52572 + 44.5889i 0.0725713 + 2.12088i
\(443\) −16.3682 −0.777679 −0.388839 0.921306i \(-0.627124\pi\)
−0.388839 + 0.921306i \(0.627124\pi\)
\(444\) −2.68764 2.68764i −0.127550 0.127550i
\(445\) −2.44536 −0.115921
\(446\) 43.6555 2.06715
\(447\) −10.6538 + 10.6538i −0.503908 + 0.503908i
\(448\) 6.03763 6.03763i 0.285251 0.285251i
\(449\) −5.62755 + 5.62755i −0.265580 + 0.265580i −0.827316 0.561736i \(-0.810134\pi\)
0.561736 + 0.827316i \(0.310134\pi\)
\(450\) 5.93259 + 5.93259i 0.279665 + 0.279665i
\(451\) 21.2250 6.83085i 0.999447 0.321652i
\(452\) 5.08047i 0.238965i
\(453\) −2.70436 2.70436i −0.127062 0.127062i
\(454\) 1.23865i 0.0581329i
\(455\) 3.53179 + 3.29809i 0.165573 + 0.154617i
\(456\) 3.10981 0.145630
\(457\) −17.4431 + 17.4431i −0.815955 + 0.815955i −0.985519 0.169564i \(-0.945764\pi\)
0.169564 + 0.985519i \(0.445764\pi\)
\(458\) 30.4513i 1.42290i
\(459\) 7.25513 0.338640
\(460\) 0.596296 + 0.596296i 0.0278024 + 0.0278024i
\(461\) 12.6607 12.6607i 0.589669 0.589669i −0.347873 0.937542i \(-0.613096\pi\)
0.937542 + 0.347873i \(0.113096\pi\)
\(462\) 23.7307 + 12.1751i 1.10405 + 0.566438i
\(463\) 14.2561 14.2561i 0.662535 0.662535i −0.293442 0.955977i \(-0.594801\pi\)
0.955977 + 0.293442i \(0.0948007\pi\)
\(464\) 28.3275i 1.31507i
\(465\) 1.55385i 0.0720579i
\(466\) −27.2499 + 27.2499i −1.26233 + 1.26233i
\(467\) 3.80081i 0.175880i −0.996126 0.0879402i \(-0.971972\pi\)
0.996126 0.0879402i \(-0.0280285\pi\)
\(468\) −2.39513 2.23664i −0.110715 0.103389i
\(469\) 4.99150i 0.230486i
\(470\) 1.64537 1.64537i 0.0758954 0.0758954i
\(471\) 13.0749 0.602461
\(472\) 14.9656 0.688847
\(473\) −8.31822 4.26769i −0.382472 0.196229i
\(474\) −3.66943 3.66943i −0.168543 0.168543i
\(475\) 5.81277 + 5.81277i 0.266708 + 0.266708i
\(476\) −21.9854 + 21.9854i −1.00770 + 1.00770i
\(477\) −5.44413 −0.249270
\(478\) 8.97415i 0.410468i
\(479\) 15.4257 + 15.4257i 0.704818 + 0.704818i 0.965441 0.260623i \(-0.0839279\pi\)
−0.260623 + 0.965441i \(0.583928\pi\)
\(480\) 1.36202 0.0621673
\(481\) −0.515632 15.0692i −0.0235108 0.687097i
\(482\) 18.8599 0.859044
\(483\) −10.8830 + 10.8830i −0.495192 + 0.495192i
\(484\) 8.12117 5.83125i 0.369144 0.265057i
\(485\) 0.709278i 0.0322066i
\(486\) −1.20600 + 1.20600i −0.0547055 + 0.0547055i
\(487\) −7.87086 7.87086i −0.356663 0.356663i 0.505918 0.862581i \(-0.331154\pi\)
−0.862581 + 0.505918i \(0.831154\pi\)
\(488\) −18.8536 + 18.8536i −0.853463 + 0.853463i
\(489\) −3.24947 + 3.24947i −0.146946 + 0.146946i
\(490\) 7.38439i 0.333593i
\(491\) −33.4183 −1.50815 −0.754074 0.656789i \(-0.771914\pi\)
−0.754074 + 0.656789i \(0.771914\pi\)
\(492\) −4.32067 4.32067i −0.194791 0.194791i
\(493\) 41.1722i 1.85430i
\(494\) −7.51072 7.01373i −0.337923 0.315562i
\(495\) −0.288811 0.897400i −0.0129811 0.0403352i
\(496\) −19.2953 19.2953i −0.866383 0.866383i
\(497\) 46.3353i 2.07842i
\(498\) 9.89674i 0.443484i
\(499\) −13.6017 13.6017i −0.608896 0.608896i 0.333761 0.942658i \(-0.391682\pi\)
−0.942658 + 0.333761i \(0.891682\pi\)
\(500\) 1.81203 + 1.81203i 0.0810367 + 0.0810367i
\(501\) 3.87790 + 3.87790i 0.173252 + 0.173252i
\(502\) −17.5192 17.5192i −0.781918 0.781918i
\(503\) 12.4724i 0.556117i −0.960564 0.278058i \(-0.910309\pi\)
0.960564 0.278058i \(-0.0896909\pi\)
\(504\) 8.77447i 0.390846i
\(505\) 3.52716 + 3.52716i 0.156957 + 0.156957i
\(506\) 5.65664 + 17.5765i 0.251468 + 0.781370i
\(507\) −0.888616 12.9696i −0.0394648 0.576000i
\(508\) 9.95181i 0.441540i
\(509\) 22.4584 + 22.4584i 0.995450 + 0.995450i 0.999990 0.00454003i \(-0.00144514\pi\)
−0.00454003 + 0.999990i \(0.501445\pi\)
\(510\) 3.51722 0.155745
\(511\) 18.9994i 0.840485i
\(512\) −3.77624 + 3.77624i −0.166888 + 0.166888i
\(513\) −1.18165 + 1.18165i −0.0521710 + 0.0521710i
\(514\) −3.41908 3.41908i −0.150809 0.150809i
\(515\) 0.788243 0.788243i 0.0347342 0.0347342i
\(516\) 2.56205i 0.112788i
\(517\) 15.1537 4.87693i 0.666461 0.214487i
\(518\) 23.7800 23.7800i 1.04483 1.04483i
\(519\) 8.75558 0.384327
\(520\) 1.39391 + 1.30168i 0.0611272 + 0.0570823i
\(521\) 40.1278 1.75803 0.879014 0.476795i \(-0.158202\pi\)
0.879014 + 0.476795i \(0.158202\pi\)
\(522\) −6.84397 6.84397i −0.299553 0.299553i
\(523\) 22.0859i 0.965747i −0.875690 0.482874i \(-0.839593\pi\)
0.875690 0.482874i \(-0.160407\pi\)
\(524\) −12.5456 −0.548057
\(525\) −16.4010 + 16.4010i −0.715798 + 0.715798i
\(526\) 17.5086 + 17.5086i 0.763411 + 0.763411i
\(527\) −28.0445 28.0445i −1.22164 1.22164i
\(528\) 14.7301 + 7.55731i 0.641044 + 0.328890i
\(529\) 12.3452 0.536748
\(530\) −2.63927 −0.114642
\(531\) −5.68655 + 5.68655i −0.246775 + 0.246775i
\(532\) 7.16155i 0.310492i
\(533\) −0.828933 24.2254i −0.0359051 1.04932i
\(534\) 14.6729i 0.634959i
\(535\) −0.109787 + 0.109787i −0.00474652 + 0.00474652i
\(536\) 1.97002i 0.0850921i
\(537\) 8.37650i 0.361473i
\(538\) 27.7608 27.7608i 1.19685 1.19685i
\(539\) −23.0610 + 44.9486i −0.993308 + 1.93607i
\(540\) −0.182679 + 0.182679i −0.00786127 + 0.00786127i
\(541\) 8.27698 + 8.27698i 0.355855 + 0.355855i 0.862283 0.506427i \(-0.169034\pi\)
−0.506427 + 0.862283i \(0.669034\pi\)
\(542\) −41.0060 −1.76136
\(543\) 8.13564i 0.349134i
\(544\) −24.5823 + 24.5823i −1.05396 + 1.05396i
\(545\) −1.82015 −0.0779667
\(546\) 19.7896 21.1918i 0.846915 0.906927i
\(547\) 13.3885i 0.572451i −0.958162 0.286225i \(-0.907599\pi\)
0.958162 0.286225i \(-0.0924006\pi\)
\(548\) 11.5004 + 11.5004i 0.491271 + 0.491271i
\(549\) 14.3278i 0.611495i
\(550\) 8.52474 + 26.4883i 0.363496 + 1.12947i
\(551\) −6.70575 6.70575i −0.285674 0.285674i
\(552\) −4.29524 + 4.29524i −0.182818 + 0.182818i
\(553\) 10.1444 10.1444i 0.431383 0.431383i
\(554\) 33.0625 33.0625i 1.40469 1.40469i
\(555\) −1.18868 −0.0504565
\(556\) 14.6041 0.619351
\(557\) 1.84660 + 1.84660i 0.0782429 + 0.0782429i 0.745145 0.666902i \(-0.232380\pi\)
−0.666902 + 0.745145i \(0.732380\pi\)
\(558\) 9.32355 0.394697
\(559\) −6.93675 + 7.42829i −0.293393 + 0.314183i
\(560\) 6.69005i 0.282706i
\(561\) 21.4092 + 10.9841i 0.903899 + 0.463749i
\(562\) −8.58094 −0.361965
\(563\) 13.1782 0.555396 0.277698 0.960668i \(-0.410429\pi\)
0.277698 + 0.960668i \(0.410429\pi\)
\(564\) −3.08477 3.08477i −0.129892 0.129892i
\(565\) −1.12348 1.12348i −0.0472652 0.0472652i
\(566\) 30.4019 30.4019i 1.27789 1.27789i
\(567\) −3.33407 3.33407i −0.140018 0.140018i
\(568\) 18.2874i 0.767322i
\(569\) 4.97172 0.208426 0.104213 0.994555i \(-0.466768\pi\)
0.104213 + 0.994555i \(0.466768\pi\)
\(570\) −0.572852 + 0.572852i −0.0239941 + 0.0239941i
\(571\) −17.0888 −0.715145 −0.357572 0.933885i \(-0.616395\pi\)
−0.357572 + 0.933885i \(0.616395\pi\)
\(572\) −3.68159 10.2263i −0.153935 0.427582i
\(573\) −1.28415 −0.0536462
\(574\) 38.2289 38.2289i 1.59564 1.59564i
\(575\) −16.0571 −0.669628
\(576\) 1.81089i 0.0754536i
\(577\) 4.06432 + 4.06432i 0.169200 + 0.169200i 0.786628 0.617428i \(-0.211825\pi\)
−0.617428 + 0.786628i \(0.711825\pi\)
\(578\) −42.9783 + 42.9783i −1.78766 + 1.78766i
\(579\) 18.7908 + 18.7908i 0.780919 + 0.780919i
\(580\) −1.03669 1.03669i −0.0430462 0.0430462i
\(581\) 27.3602 1.13509
\(582\) 4.25588 0.176412
\(583\) −16.0651 8.24228i −0.665350 0.341360i
\(584\) 7.49861i 0.310295i
\(585\) −1.02426 + 0.0350475i −0.0423478 + 0.00144904i
\(586\) −34.1885 −1.41231
\(587\) −4.92139 4.92139i −0.203127 0.203127i 0.598211 0.801339i \(-0.295878\pi\)
−0.801339 + 0.598211i \(0.795878\pi\)
\(588\) 13.8444 0.570932
\(589\) 9.13525 0.376411
\(590\) −2.75679 + 2.75679i −0.113495 + 0.113495i
\(591\) −12.3045 + 12.3045i −0.506141 + 0.506141i
\(592\) 14.7607 14.7607i 0.606660 0.606660i
\(593\) −8.10376 8.10376i −0.332781 0.332781i 0.520860 0.853642i \(-0.325611\pi\)
−0.853642 + 0.520860i \(0.825611\pi\)
\(594\) −5.38468 + 1.73295i −0.220936 + 0.0711038i
\(595\) 9.72358i 0.398628i
\(596\) 9.68319 + 9.68319i 0.396639 + 0.396639i
\(597\) 20.0985i 0.822577i
\(598\) 20.0611 0.686441i 0.820358 0.0280707i
\(599\) −8.72506 −0.356496 −0.178248 0.983986i \(-0.557043\pi\)
−0.178248 + 0.983986i \(0.557043\pi\)
\(600\) −6.47307 + 6.47307i −0.264262 + 0.264262i
\(601\) 13.9440i 0.568786i 0.958708 + 0.284393i \(0.0917921\pi\)
−0.958708 + 0.284393i \(0.908208\pi\)
\(602\) −22.6688 −0.923911
\(603\) −0.748559 0.748559i −0.0304837 0.0304837i
\(604\) −2.45798 + 2.45798i −0.100014 + 0.100014i
\(605\) 0.506388 3.08540i 0.0205876 0.125439i
\(606\) 21.1640 21.1640i 0.859730 0.859730i
\(607\) 45.9267i 1.86411i 0.362323 + 0.932053i \(0.381984\pi\)
−0.362323 + 0.932053i \(0.618016\pi\)
\(608\) 8.00745i 0.324745i
\(609\) 18.9206 18.9206i 0.766701 0.766701i
\(610\) 6.94598i 0.281235i
\(611\) −0.591822 17.2959i −0.0239426 0.699715i
\(612\) 6.59415i 0.266553i
\(613\) −3.85718 + 3.85718i −0.155790 + 0.155790i −0.780698 0.624908i \(-0.785136\pi\)
0.624908 + 0.780698i \(0.285136\pi\)
\(614\) 21.2847 0.858979
\(615\) −1.91092 −0.0770559
\(616\) −13.2843 + 25.8927i −0.535241 + 1.04325i
\(617\) 3.08121 + 3.08121i 0.124045 + 0.124045i 0.766404 0.642359i \(-0.222044\pi\)
−0.642359 + 0.766404i \(0.722044\pi\)
\(618\) −4.72970 4.72970i −0.190256 0.190256i
\(619\) −18.4046 + 18.4046i −0.739743 + 0.739743i −0.972528 0.232785i \(-0.925216\pi\)
0.232785 + 0.972528i \(0.425216\pi\)
\(620\) 1.41228 0.0567187
\(621\) 3.26417i 0.130987i
\(622\) −18.7054 18.7054i −0.750017 0.750017i
\(623\) −40.5642 −1.62517
\(624\) 12.2837 13.1542i 0.491743 0.526588i
\(625\) −23.7946 −0.951784
\(626\) −34.6885 + 34.6885i −1.38643 + 1.38643i
\(627\) −5.27592 + 1.69795i −0.210700 + 0.0678096i
\(628\) 11.8837i 0.474213i
\(629\) 21.4537 21.4537i 0.855417 0.855417i
\(630\) −1.61633 1.61633i −0.0643961 0.0643961i
\(631\) −17.6559 + 17.6559i −0.702872 + 0.702872i −0.965026 0.262154i \(-0.915567\pi\)
0.262154 + 0.965026i \(0.415567\pi\)
\(632\) 4.00374 4.00374i 0.159260 0.159260i
\(633\) 21.6318i 0.859786i
\(634\) −28.4063 −1.12816
\(635\) −2.20072 2.20072i −0.0873328 0.0873328i
\(636\) 4.94814i 0.196207i
\(637\) 40.1397 + 37.4836i 1.59039 + 1.48515i
\(638\) −9.83435 30.5576i −0.389346 1.20979i
\(639\) 6.94874 + 6.94874i 0.274888 + 0.274888i
\(640\) 3.60194i 0.142379i
\(641\) 7.41695i 0.292952i −0.989214 0.146476i \(-0.953207\pi\)
0.989214 0.146476i \(-0.0467931\pi\)
\(642\) 0.658758 + 0.658758i 0.0259991 + 0.0259991i
\(643\) −23.3090 23.3090i −0.919217 0.919217i 0.0777551 0.996972i \(-0.475225\pi\)
−0.996972 + 0.0777551i \(0.975225\pi\)
\(644\) 9.89148 + 9.89148i 0.389779 + 0.389779i
\(645\) 0.566566 + 0.566566i 0.0223085 + 0.0223085i
\(646\) 20.6782i 0.813572i
\(647\) 23.8718i 0.938499i −0.883066 0.469249i \(-0.844525\pi\)
0.883066 0.469249i \(-0.155475\pi\)
\(648\) −1.31588 1.31588i −0.0516926 0.0516926i
\(649\) −25.3898 + 8.17120i −0.996636 + 0.320748i
\(650\) 30.2327 1.03449i 1.18582 0.0405760i
\(651\) 25.7755i 1.01022i
\(652\) 2.95343 + 2.95343i 0.115665 + 0.115665i
\(653\) −31.2998 −1.22486 −0.612429 0.790526i \(-0.709807\pi\)
−0.612429 + 0.790526i \(0.709807\pi\)
\(654\) 10.9215i 0.427063i
\(655\) −2.77430 + 2.77430i −0.108401 + 0.108401i
\(656\) 23.7294 23.7294i 0.926476 0.926476i
\(657\) 2.84928 + 2.84928i 0.111161 + 0.111161i
\(658\) 27.2938 27.2938i 1.06402 1.06402i
\(659\) 33.7688i 1.31544i 0.753261 + 0.657722i \(0.228480\pi\)
−0.753261 + 0.657722i \(0.771520\pi\)
\(660\) −0.815643 + 0.262499i −0.0317489 + 0.0102177i
\(661\) 4.49941 4.49941i 0.175007 0.175007i −0.614168 0.789175i \(-0.710508\pi\)
0.789175 + 0.614168i \(0.210508\pi\)
\(662\) −0.138327 −0.00537623
\(663\) 17.8537 19.1188i 0.693378 0.742511i
\(664\) 10.7984 0.419059
\(665\) −1.58369 1.58369i −0.0614127 0.0614127i
\(666\) 7.13242i 0.276376i
\(667\) 18.5239 0.717247
\(668\) 3.52461 3.52461i 0.136371 0.136371i
\(669\) −18.0992 18.0992i −0.699757 0.699757i
\(670\) −0.362895 0.362895i −0.0140199 0.0140199i
\(671\) 21.6919 42.2800i 0.837407 1.63220i
\(672\) 22.5934 0.871560
\(673\) −26.4783 −1.02066 −0.510332 0.859977i \(-0.670478\pi\)
−0.510332 + 0.859977i \(0.670478\pi\)
\(674\) 4.76068 4.76068i 0.183374 0.183374i
\(675\) 4.91921i 0.189340i
\(676\) −11.7880 + 0.807659i −0.453385 + 0.0310638i
\(677\) 45.1205i 1.73412i −0.498201 0.867062i \(-0.666006\pi\)
0.498201 0.867062i \(-0.333994\pi\)
\(678\) −6.74123 + 6.74123i −0.258895 + 0.258895i
\(679\) 11.7656i 0.451524i
\(680\) 3.83766i 0.147168i
\(681\) −0.513536 + 0.513536i −0.0196787 + 0.0196787i
\(682\) 27.5130 + 14.1156i 1.05353 + 0.540515i
\(683\) 18.7464 18.7464i 0.717310 0.717310i −0.250744 0.968053i \(-0.580675\pi\)
0.968053 + 0.250744i \(0.0806752\pi\)
\(684\) 1.07399 + 1.07399i 0.0410652 + 0.0410652i
\(685\) 5.08632 0.194338
\(686\) 66.2010i 2.52757i
\(687\) 12.6249 12.6249i 0.481668 0.481668i
\(688\) −14.0709 −0.536449
\(689\) −13.3971 + 14.3464i −0.510388 + 0.546555i
\(690\) 1.58244i 0.0602425i
\(691\) 24.0218 + 24.0218i 0.913834 + 0.913834i 0.996571 0.0827376i \(-0.0263663\pi\)
−0.0827376 + 0.996571i \(0.526366\pi\)
\(692\) 7.95791i 0.302514i
\(693\) −4.79085 14.8863i −0.181989 0.565482i
\(694\) 4.16338 + 4.16338i 0.158040 + 0.158040i
\(695\) 3.22951 3.22951i 0.122502 0.122502i
\(696\) 7.46749 7.46749i 0.283055 0.283055i
\(697\) 34.4892 34.4892i 1.30637 1.30637i
\(698\) 13.2888 0.502987
\(699\) 22.5952 0.854629
\(700\) 14.9068 + 14.9068i 0.563423 + 0.563423i
\(701\) 3.82750 0.144563 0.0722814 0.997384i \(-0.476972\pi\)
0.0722814 + 0.997384i \(0.476972\pi\)
\(702\) 0.210296 + 6.14585i 0.00793711 + 0.231960i
\(703\) 6.98837i 0.263571i
\(704\) −2.74164 + 5.34377i −0.103329 + 0.201401i
\(705\) −1.36432 −0.0513831
\(706\) −17.1990 −0.647294
\(707\) 58.5092 + 58.5092i 2.20047 + 2.20047i
\(708\) 5.16847 + 5.16847i 0.194243 + 0.194243i
\(709\) 17.0851 17.0851i 0.641643 0.641643i −0.309317 0.950959i \(-0.600100\pi\)
0.950959 + 0.309317i \(0.100100\pi\)
\(710\) 3.36869 + 3.36869i 0.126425 + 0.126425i
\(711\) 3.04264i 0.114108i
\(712\) −16.0097 −0.599989
\(713\) −12.6175 + 12.6175i −0.472531 + 0.472531i
\(714\) 58.3444 2.18349
\(715\) −3.07555 1.44728i −0.115019 0.0541251i
\(716\) 7.61336 0.284525
\(717\) −3.72061 + 3.72061i −0.138949 + 0.138949i
\(718\) −38.7377 −1.44568
\(719\) 50.3816i 1.87892i −0.342663 0.939459i \(-0.611329\pi\)
0.342663 0.939459i \(-0.388671\pi\)
\(720\) −1.00328 1.00328i −0.0373902 0.0373902i
\(721\) 13.0755 13.0755i 0.486959 0.486959i
\(722\) −19.5462 19.5462i −0.727435 0.727435i
\(723\) −7.81915 7.81915i −0.290797 0.290797i
\(724\) 7.39444 0.274812
\(725\) 27.9161 1.03678
\(726\) −18.5133 3.03848i −0.687095 0.112769i
\(727\) 14.1485i 0.524740i 0.964967 + 0.262370i \(0.0845041\pi\)
−0.964967 + 0.262370i \(0.915496\pi\)
\(728\) 23.1225 + 21.5925i 0.856978 + 0.800271i
\(729\) 1.00000 0.0370370
\(730\) 1.38131 + 1.38131i 0.0511245 + 0.0511245i
\(731\) −20.4512 −0.756416
\(732\) −13.0225 −0.481324
\(733\) −7.13792 + 7.13792i −0.263645 + 0.263645i −0.826533 0.562888i \(-0.809690\pi\)
0.562888 + 0.826533i \(0.309690\pi\)
\(734\) 42.8914 42.8914i 1.58315 1.58315i
\(735\) 3.06151 3.06151i 0.112925 0.112925i
\(736\) 11.0598 + 11.0598i 0.407671 + 0.407671i
\(737\) −1.07563 3.34223i −0.0396214 0.123113i
\(738\) 11.4661i 0.422074i
\(739\) 6.21124 + 6.21124i 0.228484 + 0.228484i 0.812059 0.583575i \(-0.198347\pi\)
−0.583575 + 0.812059i \(0.698347\pi\)
\(740\) 1.08038i 0.0397156i
\(741\) 0.206049 + 6.02172i 0.00756938 + 0.221213i
\(742\) −43.7807 −1.60724
\(743\) 22.0058 22.0058i 0.807314 0.807314i −0.176913 0.984227i \(-0.556611\pi\)
0.984227 + 0.176913i \(0.0566111\pi\)
\(744\) 10.1730i 0.372959i
\(745\) 4.28263 0.156903
\(746\) −25.5150 25.5150i −0.934170 0.934170i
\(747\) −4.10311 + 4.10311i −0.150125 + 0.150125i
\(748\) 9.98339 19.4588i 0.365029 0.711483i
\(749\) −1.82118 + 1.82118i −0.0665443 + 0.0665443i
\(750\) 4.80874i 0.175591i
\(751\) 30.0145i 1.09525i −0.836725 0.547623i \(-0.815533\pi\)
0.836725 0.547623i \(-0.184467\pi\)
\(752\) 16.9417 16.9417i 0.617801 0.617801i
\(753\) 14.5266i 0.529379i
\(754\) −34.8771 + 1.19341i −1.27015 + 0.0434615i
\(755\) 1.08710i 0.0395637i
\(756\) −3.03032 + 3.03032i −0.110212 + 0.110212i
\(757\) −42.5187 −1.54537 −0.772684 0.634790i \(-0.781086\pi\)
−0.772684 + 0.634790i \(0.781086\pi\)
\(758\) −31.3474 −1.13859
\(759\) 4.94187 9.63227i 0.179378 0.349629i
\(760\) −0.625042 0.625042i −0.0226727 0.0226727i
\(761\) −5.20061 5.20061i −0.188522 0.188522i 0.606535 0.795057i \(-0.292559\pi\)
−0.795057 + 0.606535i \(0.792559\pi\)
\(762\) −13.2050 + 13.2050i −0.478366 + 0.478366i
\(763\) −30.1930 −1.09306
\(764\) 1.16716i 0.0422264i
\(765\) −1.45821 1.45821i −0.0527218 0.0527218i
\(766\) −37.9588 −1.37151
\(767\) 0.991586 + 28.9788i 0.0358041 + 1.04637i
\(768\) 17.9909 0.649192
\(769\) 4.65425 4.65425i 0.167836 0.167836i −0.618191 0.786028i \(-0.712134\pi\)
0.786028 + 0.618191i \(0.212134\pi\)
\(770\) −2.32256 7.21673i −0.0836993 0.260073i
\(771\) 2.83504i 0.102102i
\(772\) 17.0789 17.0789i 0.614682 0.614682i
\(773\) −13.3308 13.3308i −0.479476 0.479476i 0.425488 0.904964i \(-0.360102\pi\)
−0.904964 + 0.425488i \(0.860102\pi\)
\(774\) 3.39957 3.39957i 0.122195 0.122195i
\(775\) −19.0150 + 19.0150i −0.683041 + 0.683041i
\(776\) 4.64361i 0.166696i
\(777\) −19.7180 −0.707380
\(778\) 7.74070 + 7.74070i 0.277518 + 0.277518i
\(779\) 11.2345i 0.402519i
\(780\) 0.0318545 + 0.930941i 0.00114058 + 0.0333330i
\(781\) 9.98490 + 31.0254i 0.357288 + 1.11017i
\(782\) 28.5606 + 28.5606i 1.02132 + 1.02132i
\(783\) 5.67492i 0.202805i
\(784\) 76.0340i 2.71550i
\(785\) −2.62794 2.62794i −0.0937951 0.0937951i
\(786\) 16.6466 + 16.6466i 0.593766 + 0.593766i
\(787\) −11.1342 11.1342i −0.396890 0.396890i 0.480244 0.877135i \(-0.340548\pi\)
−0.877135 + 0.480244i \(0.840548\pi\)
\(788\) 11.1835 + 11.1835i 0.398397 + 0.398397i
\(789\) 14.5178i 0.516849i
\(790\) 1.47504i 0.0524797i
\(791\) −18.6365 18.6365i −0.662639 0.662639i
\(792\) −1.89083 5.87525i −0.0671878 0.208768i
\(793\) −37.7566 35.2583i −1.34078 1.25206i
\(794\) 31.9207i 1.13282i
\(795\) 1.09422 + 1.09422i 0.0388080 + 0.0388080i
\(796\) 18.2674 0.647472
\(797\) 19.7275i 0.698784i 0.936977 + 0.349392i \(0.113612\pi\)
−0.936977 + 0.349392i \(0.886388\pi\)
\(798\) −9.50259 + 9.50259i −0.336388 + 0.336388i
\(799\) 24.6238 24.6238i 0.871126 0.871126i
\(800\) 16.6675 + 16.6675i 0.589287 + 0.589287i
\(801\) 6.08327 6.08327i 0.214942 0.214942i
\(802\) 5.13256i 0.181237i
\(803\) 4.09423 + 12.7217i 0.144482 + 0.448940i
\(804\) −0.680362 + 0.680362i −0.0239945 + 0.0239945i
\(805\) 4.37475 0.154190
\(806\) 22.9437 24.5695i 0.808157 0.865423i
\(807\) −23.0188 −0.810300
\(808\) 23.0922 + 23.0922i 0.812380 + 0.812380i
\(809\) 3.53428i 0.124259i 0.998068 + 0.0621294i \(0.0197891\pi\)
−0.998068 + 0.0621294i \(0.980211\pi\)
\(810\) 0.484791 0.0170338
\(811\) 11.8959 11.8959i 0.417723 0.417723i −0.466695 0.884418i \(-0.654556\pi\)
0.884418 + 0.466695i \(0.154556\pi\)
\(812\) −17.1968 17.1968i −0.603490 0.603490i
\(813\) 17.0008 + 17.0008i 0.596242 + 0.596242i
\(814\) −10.7983 + 21.0471i −0.378481 + 0.737702i
\(815\) 1.30623 0.0457552
\(816\) 36.2154 1.26779
\(817\) 3.33091 3.33091i 0.116534 0.116534i
\(818\) 13.4049i 0.468690i
\(819\) −16.9906 + 0.581376i −0.593698 + 0.0203149i
\(820\) 1.73683i 0.0606527i
\(821\) −21.4198 + 21.4198i −0.747556 + 0.747556i −0.974020 0.226464i \(-0.927284\pi\)
0.226464 + 0.974020i \(0.427284\pi\)
\(822\) 30.5195i 1.06449i
\(823\) 43.7848i 1.52624i −0.646255 0.763122i \(-0.723666\pi\)
0.646255 0.763122i \(-0.276334\pi\)
\(824\) 5.16060 5.16060i 0.179778 0.179778i
\(825\) 7.44756 14.5161i 0.259291 0.505387i
\(826\) −45.7302 + 45.7302i −1.59116 + 1.59116i
\(827\) 16.0478 + 16.0478i 0.558036 + 0.558036i 0.928748 0.370712i \(-0.120886\pi\)
−0.370712 + 0.928748i \(0.620886\pi\)
\(828\) −2.96679 −0.103103
\(829\) 42.1586i 1.46423i 0.681182 + 0.732114i \(0.261466\pi\)
−0.681182 + 0.732114i \(0.738534\pi\)
\(830\) −1.98915 + 1.98915i −0.0690445 + 0.0690445i
\(831\) −27.4149 −0.951013
\(832\) 4.77206 + 4.45629i 0.165441 + 0.154494i
\(833\) 110.511i 3.82897i
\(834\) −19.3780 19.3780i −0.671007 0.671007i
\(835\) 1.55884i 0.0539460i
\(836\) 1.54326 + 4.79526i 0.0533747 + 0.165848i
\(837\) −3.86547 3.86547i −0.133610 0.133610i
\(838\) 13.3501 13.3501i 0.461173 0.461173i
\(839\) 13.9581 13.9581i 0.481887 0.481887i −0.423847 0.905734i \(-0.639321\pi\)
0.905734 + 0.423847i \(0.139321\pi\)
\(840\) 1.76359 1.76359i 0.0608495 0.0608495i
\(841\) −3.20466 −0.110506
\(842\) −8.74943 −0.301525
\(843\) 3.55759 + 3.55759i 0.122530 + 0.122530i
\(844\) −19.6610 −0.676760
\(845\) −2.42816 + 2.78537i −0.0835314 + 0.0958197i
\(846\) 8.18631i 0.281451i
\(847\) 8.40007 51.1813i 0.288630 1.75861i
\(848\) −27.1755 −0.933209
\(849\) −25.2088 −0.865163
\(850\) 43.0417 + 43.0417i 1.47632 + 1.47632i
\(851\) −9.65229 9.65229i −0.330876 0.330876i
\(852\) 6.31568 6.31568i 0.216372 0.216372i
\(853\) 40.7704 + 40.7704i 1.39595 + 1.39595i 0.811248 + 0.584702i \(0.198789\pi\)
0.584702 + 0.811248i \(0.301211\pi\)
\(854\) 115.221i 3.94280i
\(855\) 0.475000 0.0162447
\(856\) −0.718774 + 0.718774i −0.0245672 + 0.0245672i
\(857\) 31.5605 1.07809 0.539043 0.842278i \(-0.318786\pi\)
0.539043 + 0.842278i \(0.318786\pi\)
\(858\) −8.68410 + 18.4542i −0.296470 + 0.630017i
\(859\) 31.4713 1.07379 0.536894 0.843650i \(-0.319598\pi\)
0.536894 + 0.843650i \(0.319598\pi\)
\(860\) 0.514949 0.514949i 0.0175596 0.0175596i
\(861\) −31.6988 −1.08029
\(862\) 12.4894i 0.425390i
\(863\) 16.5706 + 16.5706i 0.564070 + 0.564070i 0.930461 0.366391i \(-0.119407\pi\)
−0.366391 + 0.930461i \(0.619407\pi\)
\(864\) −3.38826 + 3.38826i −0.115271 + 0.115271i
\(865\) −1.75979 1.75979i −0.0598347 0.0598347i
\(866\) 35.3913 + 35.3913i 1.20264 + 1.20264i
\(867\) 35.6369 1.21029
\(868\) 23.4272 0.795173
\(869\) −4.60648 + 8.97855i −0.156264 + 0.304576i
\(870\) 2.75115i 0.0932727i
\(871\) −3.81469 + 0.130529i −0.129256 + 0.00442282i
\(872\) −11.9165 −0.403542
\(873\) −1.76445 1.76445i −0.0597177 0.0597177i
\(874\) −9.30335 −0.314690
\(875\) 13.2941 0.449422
\(876\) 2.58970 2.58970i 0.0874978 0.0874978i
\(877\) −14.7471 + 14.7471i −0.497973 + 0.497973i −0.910807 0.412833i \(-0.864539\pi\)
0.412833 + 0.910807i \(0.364539\pi\)
\(878\) −34.5474 + 34.5474i −1.16592 + 1.16592i
\(879\) 14.1743 + 14.1743i 0.478086 + 0.478086i
\(880\) −1.44166 4.47955i −0.0485982 0.151006i
\(881\) 25.4247i 0.856579i 0.903642 + 0.428289i \(0.140884\pi\)
−0.903642 + 0.428289i \(0.859116\pi\)
\(882\) −18.3700 18.3700i −0.618549 0.618549i
\(883\) 16.4770i 0.554494i −0.960799 0.277247i \(-0.910578\pi\)
0.960799 0.277247i \(-0.0894221\pi\)
\(884\) −17.3769 16.2271i −0.584450 0.545776i
\(885\) 2.28588 0.0768392
\(886\) 19.7402 19.7402i 0.663184 0.663184i
\(887\) 4.46850i 0.150037i 0.997182 + 0.0750187i \(0.0239017\pi\)
−0.997182 + 0.0750187i \(0.976098\pi\)
\(888\) −7.78222 −0.261154
\(889\) −36.5059 36.5059i −1.22437 1.22437i
\(890\) 2.94912 2.94912i 0.0988547 0.0988547i
\(891\) 2.95091 + 1.51398i 0.0988592 + 0.0507201i
\(892\) −16.4503 + 16.4503i −0.550797 + 0.550797i
\(893\) 8.02098i 0.268412i
\(894\) 25.6971i 0.859439i
\(895\) 1.68360 1.68360i 0.0562765 0.0562765i
\(896\) 59.7496i 1.99610i
\(897\) −8.60175 8.03256i −0.287204 0.268200i
\(898\) 13.5737i 0.452960i
\(899\) 21.9362 21.9362i 0.731614 0.731614i
\(900\) −4.47104 −0.149035
\(901\) −39.4979 −1.31587
\(902\) −17.3594 + 33.8355i −0.578006 + 1.12660i
\(903\) 9.39831 + 9.39831i 0.312756 + 0.312756i
\(904\) −7.35539 7.35539i −0.244637 0.244637i
\(905\) 1.63519 1.63519i 0.0543555 0.0543555i
\(906\) 6.52295 0.216710
\(907\) 26.6927i 0.886316i −0.896443 0.443158i \(-0.853858\pi\)
0.896443 0.443158i \(-0.146142\pi\)
\(908\) 0.466751 + 0.466751i 0.0154897 + 0.0154897i
\(909\) −17.5489 −0.582059
\(910\) −8.23688 + 0.281846i −0.273050 + 0.00934310i
\(911\) −24.1348 −0.799622 −0.399811 0.916598i \(-0.630924\pi\)
−0.399811 + 0.916598i \(0.630924\pi\)
\(912\) −5.89843 + 5.89843i −0.195317 + 0.195317i
\(913\) −18.3199 + 5.89591i −0.606301 + 0.195126i
\(914\) 42.0730i 1.39165i
\(915\) −2.87975 + 2.87975i −0.0952016 + 0.0952016i
\(916\) −11.4747 11.4747i −0.379134 0.379134i
\(917\) −46.0206 + 46.0206i −1.51973 + 1.51973i
\(918\) −8.74972 + 8.74972i −0.288784 + 0.288784i
\(919\) 41.7170i 1.37612i −0.725655 0.688059i \(-0.758463\pi\)
0.725655 0.688059i \(-0.241537\pi\)
\(920\) 1.72661 0.0569246
\(921\) −8.82445 8.82445i −0.290775 0.290775i
\(922\) 30.5378i 1.00571i
\(923\) 35.4111 1.21168i 1.16557 0.0398829i
\(924\) −13.5301 + 4.35438i −0.445106 + 0.143249i
\(925\) −14.5463 14.5463i −0.478280 0.478280i
\(926\) 34.3857i 1.12999i
\(927\) 3.92179i 0.128809i
\(928\) −19.2281 19.2281i −0.631193 0.631193i
\(929\) −26.8941 26.8941i −0.882367 0.882367i 0.111408 0.993775i \(-0.464464\pi\)
−0.993775 + 0.111408i \(0.964464\pi\)
\(930\) −1.87395 1.87395i −0.0614491 0.0614491i
\(931\) −17.9990 17.9990i −0.589892 0.589892i
\(932\) 20.5367i 0.672701i
\(933\) 15.5102i 0.507781i
\(934\) 4.58379 + 4.58379i 0.149986 + 0.149986i
\(935\) −2.09536 6.51076i −0.0685255 0.212925i
\(936\) −6.70576 + 0.229455i −0.219185 + 0.00749997i
\(937\) 36.3852i 1.18865i −0.804224 0.594326i \(-0.797419\pi\)
0.804224 0.594326i \(-0.202581\pi\)
\(938\) −6.01978 6.01978i −0.196553 0.196553i
\(939\) 28.7631 0.938650
\(940\) 1.24002i 0.0404450i
\(941\) −35.8119 + 35.8119i −1.16743 + 1.16743i −0.184626 + 0.982809i \(0.559107\pi\)
−0.982809 + 0.184626i \(0.940893\pi\)
\(942\) −15.7684 + 15.7684i −0.513763 + 0.513763i
\(943\) −15.5171 15.5171i −0.505306 0.505306i
\(944\) −28.3855 + 28.3855i −0.923870 + 0.923870i
\(945\) 1.34024i 0.0435979i
\(946\) 15.1787 4.88496i 0.493501 0.158824i
\(947\) −35.8340 + 35.8340i −1.16445 + 1.16445i −0.180956 + 0.983491i \(0.557919\pi\)
−0.983491 + 0.180956i \(0.942081\pi\)
\(948\) 2.76544 0.0898172
\(949\) 14.5200 0.496841i 0.471341 0.0161281i
\(950\) −14.0204 −0.454883
\(951\) 11.7770 + 11.7770i 0.381896 + 0.381896i
\(952\) 63.6599i 2.06323i
\(953\) −56.4922 −1.82996 −0.914981 0.403497i \(-0.867794\pi\)
−0.914981 + 0.403497i \(0.867794\pi\)
\(954\) 6.56565 6.56565i 0.212571 0.212571i
\(955\) 0.258103 + 0.258103i 0.00835200 + 0.00835200i
\(956\) 3.38165 + 3.38165i 0.109370 + 0.109370i
\(957\) −8.59168 + 16.7462i −0.277730 + 0.541327i
\(958\) −37.2069 −1.20210
\(959\) 84.3729 2.72454
\(960\) 0.363971 0.363971i 0.0117471 0.0117471i
\(961\) 1.11628i 0.0360089i
\(962\) 18.7954 + 17.5517i 0.605988 + 0.565889i
\(963\) 0.546231i 0.0176021i
\(964\) −7.10679 + 7.10679i −0.228894 + 0.228894i
\(965\) 7.55355i 0.243157i
\(966\) 26.2498i 0.844575i
\(967\) 41.1339 41.1339i 1.32278 1.32278i 0.411257 0.911520i \(-0.365090\pi\)
0.911520 0.411257i \(-0.134910\pi\)
\(968\) 3.31530 20.2000i 0.106558 0.649253i
\(969\) −8.57301 + 8.57301i −0.275405 + 0.275405i
\(970\) −0.855392 0.855392i −0.0274650 0.0274650i
\(971\) 28.2094 0.905281 0.452641 0.891693i \(-0.350482\pi\)
0.452641 + 0.891693i \(0.350482\pi\)
\(972\) 0.908895i 0.0291528i
\(973\) 53.5718 53.5718i 1.71743 1.71743i
\(974\) 18.9846 0.608306
\(975\) −12.9631 12.1053i −0.415152 0.387681i
\(976\) 71.5200i 2.28930i
\(977\) −35.5051 35.5051i −1.13591 1.13591i −0.989176 0.146732i \(-0.953124\pi\)
−0.146732 0.989176i \(-0.546876\pi\)
\(978\) 7.83776i 0.250624i
\(979\) 27.1611 8.74127i 0.868074 0.279372i
\(980\) −2.78259 2.78259i −0.0888866 0.0888866i
\(981\) 4.52795 4.52795i 0.144566 0.144566i
\(982\) 40.3027 40.3027i 1.28611 1.28611i
\(983\) 0.418033 0.418033i 0.0133332 0.0133332i −0.700409 0.713742i \(-0.746999\pi\)
0.713742 + 0.700409i \(0.246999\pi\)
\(984\) −12.5107 −0.398828
\(985\) 4.94620 0.157599
\(986\) −49.6539 49.6539i −1.58130 1.58130i
\(987\) −22.6316 −0.720371
\(988\) 5.47311 0.187277i 0.174123 0.00595806i
\(989\) 9.20125i 0.292583i
\(990\) 1.43058 + 0.733962i 0.0454667 + 0.0233269i
\(991\) 18.9713 0.602644 0.301322 0.953522i \(-0.402572\pi\)
0.301322 + 0.953522i \(0.402572\pi\)
\(992\) 26.1944 0.831674
\(993\) 0.0573492 + 0.0573492i 0.00181992 + 0.00181992i
\(994\) 55.8805 + 55.8805i 1.77242 + 1.77242i
\(995\) 4.03961 4.03961i 0.128064 0.128064i
\(996\) 3.72930 + 3.72930i 0.118167 + 0.118167i
\(997\) 14.2729i 0.452029i −0.974124 0.226014i \(-0.927430\pi\)
0.974124 0.226014i \(-0.0725696\pi\)
\(998\) 32.8075 1.03850
\(999\) 2.95704 2.95704i 0.0935568 0.0935568i
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 429.2.m.b.307.4 yes 28
11.10 odd 2 inner 429.2.m.b.307.11 yes 28
13.5 odd 4 inner 429.2.m.b.109.11 yes 28
143.109 even 4 inner 429.2.m.b.109.4 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.m.b.109.4 28 143.109 even 4 inner
429.2.m.b.109.11 yes 28 13.5 odd 4 inner
429.2.m.b.307.4 yes 28 1.1 even 1 trivial
429.2.m.b.307.11 yes 28 11.10 odd 2 inner