Properties

Label 700.2.k.b.43.18
Level $700$
Weight $2$
Character 700.43
Analytic conductor $5.590$
Analytic rank $0$
Dimension $36$
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] = [700,2,Mod(43,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.k (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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.18
Character \(\chi\) \(=\) 700.43
Dual form 700.2.k.b.407.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.38250 + 0.297828i) q^{2} +(0.137886 - 0.137886i) q^{3} +(1.82260 + 0.823494i) q^{4} +(0.231693 - 0.149560i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.27447 + 1.68130i) q^{8} +2.96198i q^{9} +O(q^{10})\) \(q+(1.38250 + 0.297828i) q^{2} +(0.137886 - 0.137886i) q^{3} +(1.82260 + 0.823494i) q^{4} +(0.231693 - 0.149560i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.27447 + 1.68130i) q^{8} +2.96198i q^{9} +3.12749i q^{11} +(0.364858 - 0.137762i) q^{12} +(-2.50519 - 2.50519i) q^{13} +(0.766977 + 1.18817i) q^{14} +(2.64372 + 3.00179i) q^{16} +(-2.85846 + 2.85846i) q^{17} +(-0.882160 + 4.09492i) q^{18} +3.29172 q^{19} +0.195000 q^{21} +(-0.931456 + 4.32375i) q^{22} +(6.43733 - 6.43733i) q^{23} +(0.545444 - 0.0817904i) q^{24} +(-2.71731 - 4.20954i) q^{26} +(0.822071 + 0.822071i) q^{27} +(0.706472 + 1.87107i) q^{28} -3.55957i q^{29} -8.67099i q^{31} +(2.76091 + 4.93735i) q^{32} +(0.431236 + 0.431236i) q^{33} +(-4.80314 + 3.10048i) q^{34} +(-2.43917 + 5.39849i) q^{36} +(-3.64472 + 3.64472i) q^{37} +(4.55080 + 0.980369i) q^{38} -0.690861 q^{39} +1.66648 q^{41} +(0.269587 + 0.0580765i) q^{42} +(-1.17838 + 1.17838i) q^{43} +(-2.57547 + 5.70015i) q^{44} +(10.8168 - 6.98237i) q^{46} +(-0.598252 - 0.598252i) q^{47} +(0.778435 + 0.0493739i) q^{48} +1.00000i q^{49} +0.788281i q^{51} +(-2.50295 - 6.62897i) q^{52} +(1.12536 + 1.12536i) q^{53} +(0.891674 + 1.38135i) q^{54} +(0.419438 + 2.79715i) q^{56} +(0.453882 - 0.453882i) q^{57} +(1.06014 - 4.92110i) q^{58} +10.4032 q^{59} -6.81629 q^{61} +(2.58247 - 11.9876i) q^{62} +(-2.09443 + 2.09443i) q^{63} +(2.34647 + 7.64814i) q^{64} +(0.467748 + 0.724617i) q^{66} +(-6.83728 - 6.83728i) q^{67} +(-7.56374 + 2.85589i) q^{68} -1.77523i q^{69} -3.15952i q^{71} +(-4.97997 + 6.73694i) q^{72} +(-6.00943 - 6.00943i) q^{73} +(-6.12432 + 3.95332i) q^{74} +(5.99949 + 2.71072i) q^{76} +(-2.21147 + 2.21147i) q^{77} +(-0.955113 - 0.205758i) q^{78} +0.153472 q^{79} -8.65922 q^{81} +(2.30390 + 0.496324i) q^{82} +(-8.57229 + 8.57229i) q^{83} +(0.355406 + 0.160581i) q^{84} +(-1.98006 + 1.27815i) q^{86} +(-0.490814 - 0.490814i) q^{87} +(-5.25825 + 7.11340i) q^{88} -17.4053i q^{89} -3.54288i q^{91} +(17.0338 - 6.43155i) q^{92} +(-1.19560 - 1.19560i) q^{93} +(-0.648905 - 1.00526i) q^{94} +(1.06148 + 0.300099i) q^{96} +(-2.28422 + 2.28422i) q^{97} +(-0.297828 + 1.38250i) q^{98} -9.26355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38250 + 0.297828i 0.977573 + 0.210596i
\(3\) 0.137886 0.137886i 0.0796083 0.0796083i −0.666181 0.745790i \(-0.732072\pi\)
0.745790 + 0.666181i \(0.232072\pi\)
\(4\) 1.82260 + 0.823494i 0.911298 + 0.411747i
\(5\) 0 0
\(6\) 0.231693 0.149560i 0.0945882 0.0610577i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 2.27447 + 1.68130i 0.804148 + 0.594429i
\(9\) 2.96198i 0.987325i
\(10\) 0 0
\(11\) 3.12749i 0.942974i 0.881873 + 0.471487i \(0.156283\pi\)
−0.881873 + 0.471487i \(0.843717\pi\)
\(12\) 0.364858 0.137762i 0.105325 0.0397684i
\(13\) −2.50519 2.50519i −0.694816 0.694816i 0.268472 0.963288i \(-0.413481\pi\)
−0.963288 + 0.268472i \(0.913481\pi\)
\(14\) 0.766977 + 1.18817i 0.204983 + 0.317552i
\(15\) 0 0
\(16\) 2.64372 + 3.00179i 0.660929 + 0.750449i
\(17\) −2.85846 + 2.85846i −0.693278 + 0.693278i −0.962952 0.269674i \(-0.913084\pi\)
0.269674 + 0.962952i \(0.413084\pi\)
\(18\) −0.882160 + 4.09492i −0.207927 + 0.965182i
\(19\) 3.29172 0.755173 0.377587 0.925974i \(-0.376754\pi\)
0.377587 + 0.925974i \(0.376754\pi\)
\(20\) 0 0
\(21\) 0.195000 0.0425524
\(22\) −0.931456 + 4.32375i −0.198587 + 0.921826i
\(23\) 6.43733 6.43733i 1.34228 1.34228i 0.448486 0.893790i \(-0.351964\pi\)
0.893790 0.448486i \(-0.148036\pi\)
\(24\) 0.545444 0.0817904i 0.111338 0.0166954i
\(25\) 0 0
\(26\) −2.71731 4.20954i −0.532908 0.825559i
\(27\) 0.822071 + 0.822071i 0.158208 + 0.158208i
\(28\) 0.706472 + 1.87107i 0.133511 + 0.353599i
\(29\) 3.55957i 0.660996i −0.943807 0.330498i \(-0.892783\pi\)
0.943807 0.330498i \(-0.107217\pi\)
\(30\) 0 0
\(31\) 8.67099i 1.55735i −0.627424 0.778677i \(-0.715891\pi\)
0.627424 0.778677i \(-0.284109\pi\)
\(32\) 2.76091 + 4.93735i 0.488064 + 0.872808i
\(33\) 0.431236 + 0.431236i 0.0750686 + 0.0750686i
\(34\) −4.80314 + 3.10048i −0.823732 + 0.531728i
\(35\) 0 0
\(36\) −2.43917 + 5.39849i −0.406528 + 0.899748i
\(37\) −3.64472 + 3.64472i −0.599189 + 0.599189i −0.940097 0.340908i \(-0.889266\pi\)
0.340908 + 0.940097i \(0.389266\pi\)
\(38\) 4.55080 + 0.980369i 0.738237 + 0.159037i
\(39\) −0.690861 −0.110626
\(40\) 0 0
\(41\) 1.66648 0.260260 0.130130 0.991497i \(-0.458461\pi\)
0.130130 + 0.991497i \(0.458461\pi\)
\(42\) 0.269587 + 0.0580765i 0.0415981 + 0.00896139i
\(43\) −1.17838 + 1.17838i −0.179701 + 0.179701i −0.791225 0.611525i \(-0.790557\pi\)
0.611525 + 0.791225i \(0.290557\pi\)
\(44\) −2.57547 + 5.70015i −0.388267 + 0.859331i
\(45\) 0 0
\(46\) 10.8168 6.98237i 1.59485 1.02949i
\(47\) −0.598252 0.598252i −0.0872640 0.0872640i 0.662127 0.749391i \(-0.269654\pi\)
−0.749391 + 0.662127i \(0.769654\pi\)
\(48\) 0.778435 + 0.0493739i 0.112357 + 0.00712650i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0.788281i 0.110381i
\(52\) −2.50295 6.62897i −0.347096 0.919273i
\(53\) 1.12536 + 1.12536i 0.154580 + 0.154580i 0.780160 0.625580i \(-0.215138\pi\)
−0.625580 + 0.780160i \(0.715138\pi\)
\(54\) 0.891674 + 1.38135i 0.121342 + 0.187977i
\(55\) 0 0
\(56\) 0.419438 + 2.79715i 0.0560498 + 0.373785i
\(57\) 0.453882 0.453882i 0.0601181 0.0601181i
\(58\) 1.06014 4.92110i 0.139203 0.646172i
\(59\) 10.4032 1.35438 0.677189 0.735810i \(-0.263198\pi\)
0.677189 + 0.735810i \(0.263198\pi\)
\(60\) 0 0
\(61\) −6.81629 −0.872736 −0.436368 0.899768i \(-0.643735\pi\)
−0.436368 + 0.899768i \(0.643735\pi\)
\(62\) 2.58247 11.9876i 0.327973 1.52243i
\(63\) −2.09443 + 2.09443i −0.263874 + 0.263874i
\(64\) 2.34647 + 7.64814i 0.293308 + 0.956018i
\(65\) 0 0
\(66\) 0.467748 + 0.724617i 0.0575758 + 0.0891942i
\(67\) −6.83728 6.83728i −0.835307 0.835307i 0.152930 0.988237i \(-0.451129\pi\)
−0.988237 + 0.152930i \(0.951129\pi\)
\(68\) −7.56374 + 2.85589i −0.917238 + 0.346328i
\(69\) 1.77523i 0.213713i
\(70\) 0 0
\(71\) 3.15952i 0.374966i −0.982268 0.187483i \(-0.939967\pi\)
0.982268 0.187483i \(-0.0600329\pi\)
\(72\) −4.97997 + 6.73694i −0.586895 + 0.793956i
\(73\) −6.00943 6.00943i −0.703351 0.703351i 0.261778 0.965128i \(-0.415691\pi\)
−0.965128 + 0.261778i \(0.915691\pi\)
\(74\) −6.12432 + 3.95332i −0.711938 + 0.459564i
\(75\) 0 0
\(76\) 5.99949 + 2.71072i 0.688188 + 0.310940i
\(77\) −2.21147 + 2.21147i −0.252020 + 0.252020i
\(78\) −0.955113 0.205758i −0.108145 0.0232975i
\(79\) 0.153472 0.0172670 0.00863348 0.999963i \(-0.497252\pi\)
0.00863348 + 0.999963i \(0.497252\pi\)
\(80\) 0 0
\(81\) −8.65922 −0.962136
\(82\) 2.30390 + 0.496324i 0.254423 + 0.0548098i
\(83\) −8.57229 + 8.57229i −0.940931 + 0.940931i −0.998350 0.0574191i \(-0.981713\pi\)
0.0574191 + 0.998350i \(0.481713\pi\)
\(84\) 0.355406 + 0.160581i 0.0387780 + 0.0175208i
\(85\) 0 0
\(86\) −1.98006 + 1.27815i −0.213515 + 0.137826i
\(87\) −0.490814 0.490814i −0.0526208 0.0526208i
\(88\) −5.25825 + 7.11340i −0.560531 + 0.758291i
\(89\) 17.4053i 1.84496i −0.386047 0.922479i \(-0.626160\pi\)
0.386047 0.922479i \(-0.373840\pi\)
\(90\) 0 0
\(91\) 3.54288i 0.371395i
\(92\) 17.0338 6.43155i 1.77589 0.670536i
\(93\) −1.19560 1.19560i −0.123978 0.123978i
\(94\) −0.648905 1.00526i −0.0669295 0.103684i
\(95\) 0 0
\(96\) 1.06148 + 0.300099i 0.108337 + 0.0306287i
\(97\) −2.28422 + 2.28422i −0.231927 + 0.231927i −0.813497 0.581569i \(-0.802439\pi\)
0.581569 + 0.813497i \(0.302439\pi\)
\(98\) −0.297828 + 1.38250i −0.0300852 + 0.139653i
\(99\) −9.26355 −0.931022
\(100\) 0 0
\(101\) 5.41332 0.538645 0.269323 0.963050i \(-0.413200\pi\)
0.269323 + 0.963050i \(0.413200\pi\)
\(102\) −0.234772 + 1.08980i −0.0232459 + 0.107906i
\(103\) 10.1362 10.1362i 0.998747 0.998747i −0.00125245 0.999999i \(-0.500399\pi\)
0.999999 + 0.00125245i \(0.000398668\pi\)
\(104\) −1.48602 9.90998i −0.145716 0.971754i
\(105\) 0 0
\(106\) 1.22064 + 1.89097i 0.118559 + 0.183668i
\(107\) −6.05492 6.05492i −0.585352 0.585352i 0.351017 0.936369i \(-0.385836\pi\)
−0.936369 + 0.351017i \(0.885836\pi\)
\(108\) 0.821333 + 2.17527i 0.0790328 + 0.209316i
\(109\) 8.01732i 0.767920i 0.923350 + 0.383960i \(0.125440\pi\)
−0.923350 + 0.383960i \(0.874560\pi\)
\(110\) 0 0
\(111\) 1.00511i 0.0954009i
\(112\) −0.253200 + 3.99198i −0.0239251 + 0.377206i
\(113\) −2.96906 2.96906i −0.279306 0.279306i 0.553526 0.832832i \(-0.313282\pi\)
−0.832832 + 0.553526i \(0.813282\pi\)
\(114\) 0.762669 0.492311i 0.0714305 0.0461092i
\(115\) 0 0
\(116\) 2.93129 6.48766i 0.272163 0.602364i
\(117\) 7.42032 7.42032i 0.686009 0.686009i
\(118\) 14.3823 + 3.09836i 1.32400 + 0.285227i
\(119\) −4.04247 −0.370573
\(120\) 0 0
\(121\) 1.21880 0.110800
\(122\) −9.42350 2.03008i −0.853163 0.183795i
\(123\) 0.229783 0.229783i 0.0207188 0.0207188i
\(124\) 7.14050 15.8037i 0.641236 1.41921i
\(125\) 0 0
\(126\) −3.51933 + 2.27177i −0.313527 + 0.202385i
\(127\) 5.46545 + 5.46545i 0.484981 + 0.484981i 0.906718 0.421737i \(-0.138580\pi\)
−0.421737 + 0.906718i \(0.638580\pi\)
\(128\) 0.966151 + 11.2724i 0.0853965 + 0.996347i
\(129\) 0.324962i 0.0286113i
\(130\) 0 0
\(131\) 1.22936i 0.107410i 0.998557 + 0.0537051i \(0.0171031\pi\)
−0.998557 + 0.0537051i \(0.982897\pi\)
\(132\) 0.430849 + 1.14109i 0.0375006 + 0.0993191i
\(133\) 2.32760 + 2.32760i 0.201829 + 0.201829i
\(134\) −7.41619 11.4889i −0.640661 0.992486i
\(135\) 0 0
\(136\) −11.3074 + 1.69557i −0.969603 + 0.145394i
\(137\) 3.17885 3.17885i 0.271587 0.271587i −0.558152 0.829739i \(-0.688489\pi\)
0.829739 + 0.558152i \(0.188489\pi\)
\(138\) 0.528714 2.45425i 0.0450071 0.208920i
\(139\) 1.28774 0.109225 0.0546125 0.998508i \(-0.482608\pi\)
0.0546125 + 0.998508i \(0.482608\pi\)
\(140\) 0 0
\(141\) −0.164981 −0.0138939
\(142\) 0.940994 4.36802i 0.0789665 0.366556i
\(143\) 7.83498 7.83498i 0.655194 0.655194i
\(144\) −8.89124 + 7.83062i −0.740937 + 0.652552i
\(145\) 0 0
\(146\) −6.51824 10.0978i −0.539454 0.835700i
\(147\) 0.137886 + 0.137886i 0.0113726 + 0.0113726i
\(148\) −9.64427 + 3.64145i −0.792754 + 0.299326i
\(149\) 9.87336i 0.808857i −0.914570 0.404429i \(-0.867470\pi\)
0.914570 0.404429i \(-0.132530\pi\)
\(150\) 0 0
\(151\) 23.1711i 1.88564i 0.333308 + 0.942818i \(0.391835\pi\)
−0.333308 + 0.942818i \(0.608165\pi\)
\(152\) 7.48694 + 5.53437i 0.607271 + 0.448897i
\(153\) −8.46668 8.46668i −0.684491 0.684491i
\(154\) −3.71599 + 2.39871i −0.299443 + 0.193294i
\(155\) 0 0
\(156\) −1.25916 0.568920i −0.100814 0.0455500i
\(157\) −3.47358 + 3.47358i −0.277222 + 0.277222i −0.831999 0.554777i \(-0.812804\pi\)
0.554777 + 0.831999i \(0.312804\pi\)
\(158\) 0.212175 + 0.0457084i 0.0168797 + 0.00363636i
\(159\) 0.310342 0.0246117
\(160\) 0 0
\(161\) 9.10376 0.717477
\(162\) −11.9713 2.57896i −0.940558 0.202622i
\(163\) −1.51463 + 1.51463i −0.118635 + 0.118635i −0.763932 0.645297i \(-0.776734\pi\)
0.645297 + 0.763932i \(0.276734\pi\)
\(164\) 3.03731 + 1.37233i 0.237174 + 0.107161i
\(165\) 0 0
\(166\) −14.4042 + 9.29809i −1.11799 + 0.721672i
\(167\) 9.86696 + 9.86696i 0.763528 + 0.763528i 0.976958 0.213430i \(-0.0684636\pi\)
−0.213430 + 0.976958i \(0.568464\pi\)
\(168\) 0.443522 + 0.327853i 0.0342185 + 0.0252944i
\(169\) 0.447999i 0.0344614i
\(170\) 0 0
\(171\) 9.75001i 0.745602i
\(172\) −3.11809 + 1.17732i −0.237752 + 0.0897697i
\(173\) −9.97554 9.97554i −0.758426 0.758426i 0.217610 0.976036i \(-0.430174\pi\)
−0.976036 + 0.217610i \(0.930174\pi\)
\(174\) −0.532370 0.824727i −0.0403589 0.0625224i
\(175\) 0 0
\(176\) −9.38808 + 8.26820i −0.707654 + 0.623239i
\(177\) 1.43445 1.43445i 0.107820 0.107820i
\(178\) 5.18379 24.0628i 0.388542 1.80358i
\(179\) −4.67593 −0.349495 −0.174748 0.984613i \(-0.555911\pi\)
−0.174748 + 0.984613i \(0.555911\pi\)
\(180\) 0 0
\(181\) −18.2503 −1.35654 −0.678268 0.734815i \(-0.737269\pi\)
−0.678268 + 0.734815i \(0.737269\pi\)
\(182\) 1.05517 4.89802i 0.0782144 0.363066i
\(183\) −0.939868 + 0.939868i −0.0694770 + 0.0694770i
\(184\) 25.4646 3.81847i 1.87728 0.281501i
\(185\) 0 0
\(186\) −1.29683 2.00900i −0.0950885 0.147307i
\(187\) −8.93980 8.93980i −0.653743 0.653743i
\(188\) −0.597715 1.58303i −0.0435929 0.115454i
\(189\) 1.16258i 0.0845655i
\(190\) 0 0
\(191\) 18.6406i 1.34879i −0.738371 0.674395i \(-0.764405\pi\)
0.738371 0.674395i \(-0.235595\pi\)
\(192\) 1.37811 + 0.731025i 0.0994568 + 0.0527572i
\(193\) 7.81768 + 7.81768i 0.562729 + 0.562729i 0.930082 0.367353i \(-0.119736\pi\)
−0.367353 + 0.930082i \(0.619736\pi\)
\(194\) −3.83823 + 2.47762i −0.275569 + 0.177883i
\(195\) 0 0
\(196\) −0.823494 + 1.82260i −0.0588210 + 0.130185i
\(197\) 5.27851 5.27851i 0.376078 0.376078i −0.493607 0.869685i \(-0.664322\pi\)
0.869685 + 0.493607i \(0.164322\pi\)
\(198\) −12.8068 2.75895i −0.910142 0.196070i
\(199\) −0.716716 −0.0508067 −0.0254033 0.999677i \(-0.508087\pi\)
−0.0254033 + 0.999677i \(0.508087\pi\)
\(200\) 0 0
\(201\) −1.88553 −0.132995
\(202\) 7.48390 + 1.61224i 0.526565 + 0.113437i
\(203\) 2.51700 2.51700i 0.176659 0.176659i
\(204\) −0.649144 + 1.43672i −0.0454492 + 0.100590i
\(205\) 0 0
\(206\) 17.0321 10.9944i 1.18668 0.766015i
\(207\) 19.0672 + 19.0672i 1.32526 + 1.32526i
\(208\) 0.897056 14.1431i 0.0621996 0.980648i
\(209\) 10.2948i 0.712109i
\(210\) 0 0
\(211\) 9.81937i 0.675994i −0.941147 0.337997i \(-0.890251\pi\)
0.941147 0.337997i \(-0.109749\pi\)
\(212\) 1.12435 + 2.97781i 0.0772208 + 0.204517i
\(213\) −0.435652 0.435652i −0.0298504 0.0298504i
\(214\) −6.56759 10.1742i −0.448951 0.695497i
\(215\) 0 0
\(216\) 0.487632 + 3.25193i 0.0331792 + 0.221265i
\(217\) 6.13131 6.13131i 0.416221 0.416221i
\(218\) −2.38779 + 11.0839i −0.161721 + 0.750698i
\(219\) −1.65723 −0.111985
\(220\) 0 0
\(221\) 14.3220 0.963401
\(222\) −0.299350 + 1.38956i −0.0200911 + 0.0932613i
\(223\) −13.7246 + 13.7246i −0.919066 + 0.919066i −0.996962 0.0778955i \(-0.975180\pi\)
0.0778955 + 0.996962i \(0.475180\pi\)
\(224\) −1.53897 + 5.44349i −0.102827 + 0.363708i
\(225\) 0 0
\(226\) −3.22045 4.98899i −0.214221 0.331862i
\(227\) −8.05232 8.05232i −0.534451 0.534451i 0.387443 0.921894i \(-0.373359\pi\)
−0.921894 + 0.387443i \(0.873359\pi\)
\(228\) 1.20101 0.453474i 0.0795389 0.0300321i
\(229\) 12.7874i 0.845017i 0.906359 + 0.422508i \(0.138850\pi\)
−0.906359 + 0.422508i \(0.861150\pi\)
\(230\) 0 0
\(231\) 0.609860i 0.0401258i
\(232\) 5.98470 8.09616i 0.392915 0.531539i
\(233\) 15.5244 + 15.5244i 1.01704 + 1.01704i 0.999852 + 0.0171872i \(0.00547113\pi\)
0.0171872 + 0.999852i \(0.494529\pi\)
\(234\) 12.4686 8.04859i 0.815095 0.526153i
\(235\) 0 0
\(236\) 18.9608 + 8.56694i 1.23424 + 0.557661i
\(237\) 0.0211616 0.0211616i 0.00137459 0.00137459i
\(238\) −5.58870 1.20396i −0.362262 0.0780413i
\(239\) 2.29513 0.148459 0.0742297 0.997241i \(-0.476350\pi\)
0.0742297 + 0.997241i \(0.476350\pi\)
\(240\) 0 0
\(241\) −17.7343 −1.14236 −0.571182 0.820823i \(-0.693515\pi\)
−0.571182 + 0.820823i \(0.693515\pi\)
\(242\) 1.68498 + 0.362993i 0.108315 + 0.0233340i
\(243\) −3.66019 + 3.66019i −0.234802 + 0.234802i
\(244\) −12.4233 5.61317i −0.795323 0.359346i
\(245\) 0 0
\(246\) 0.386110 0.249238i 0.0246175 0.0158909i
\(247\) −8.24641 8.24641i −0.524707 0.524707i
\(248\) 14.5785 19.7219i 0.925737 1.25234i
\(249\) 2.36399i 0.149812i
\(250\) 0 0
\(251\) 28.4484i 1.79565i 0.440354 + 0.897824i \(0.354853\pi\)
−0.440354 + 0.897824i \(0.645147\pi\)
\(252\) −5.54206 + 2.09255i −0.349117 + 0.131818i
\(253\) 20.1327 + 20.1327i 1.26573 + 1.26573i
\(254\) 5.92821 + 9.18374i 0.371969 + 0.576239i
\(255\) 0 0
\(256\) −2.02153 + 15.8718i −0.126346 + 0.991986i
\(257\) 2.62467 2.62467i 0.163722 0.163722i −0.620491 0.784214i \(-0.713067\pi\)
0.784214 + 0.620491i \(0.213067\pi\)
\(258\) −0.0967830 + 0.449259i −0.00602545 + 0.0279697i
\(259\) −5.15442 −0.320280
\(260\) 0 0
\(261\) 10.5434 0.652618
\(262\) −0.366140 + 1.69959i −0.0226202 + 0.105001i
\(263\) −14.6752 + 14.6752i −0.904912 + 0.904912i −0.995856 0.0909438i \(-0.971012\pi\)
0.0909438 + 0.995856i \(0.471012\pi\)
\(264\) 0.255799 + 1.70587i 0.0157433 + 0.104989i
\(265\) 0 0
\(266\) 2.52468 + 3.91113i 0.154798 + 0.239807i
\(267\) −2.39994 2.39994i −0.146874 0.146874i
\(268\) −6.83115 18.0921i −0.417279 1.10515i
\(269\) 11.7355i 0.715529i −0.933812 0.357764i \(-0.883539\pi\)
0.933812 0.357764i \(-0.116461\pi\)
\(270\) 0 0
\(271\) 21.0504i 1.27872i −0.768907 0.639361i \(-0.779199\pi\)
0.768907 0.639361i \(-0.220801\pi\)
\(272\) −16.1375 1.02355i −0.978477 0.0620619i
\(273\) −0.488512 0.488512i −0.0295661 0.0295661i
\(274\) 5.34150 3.44800i 0.322692 0.208301i
\(275\) 0 0
\(276\) 1.46189 3.23553i 0.0879955 0.194756i
\(277\) −9.30733 + 9.30733i −0.559223 + 0.559223i −0.929086 0.369863i \(-0.879405\pi\)
0.369863 + 0.929086i \(0.379405\pi\)
\(278\) 1.78030 + 0.383527i 0.106775 + 0.0230024i
\(279\) 25.6832 1.53762
\(280\) 0 0
\(281\) 16.2003 0.966427 0.483214 0.875502i \(-0.339469\pi\)
0.483214 + 0.875502i \(0.339469\pi\)
\(282\) −0.228085 0.0491360i −0.0135823 0.00292600i
\(283\) 8.04576 8.04576i 0.478271 0.478271i −0.426307 0.904578i \(-0.640186\pi\)
0.904578 + 0.426307i \(0.140186\pi\)
\(284\) 2.60184 5.75852i 0.154391 0.341706i
\(285\) 0 0
\(286\) 13.1653 8.49835i 0.778481 0.502518i
\(287\) 1.17838 + 1.17838i 0.0695573 + 0.0695573i
\(288\) −14.6243 + 8.17775i −0.861745 + 0.481878i
\(289\) 0.658435i 0.0387314i
\(290\) 0 0
\(291\) 0.629922i 0.0369267i
\(292\) −6.00404 15.9015i −0.351360 0.930565i
\(293\) 18.5783 + 18.5783i 1.08536 + 1.08536i 0.996000 + 0.0893564i \(0.0284810\pi\)
0.0893564 + 0.996000i \(0.471519\pi\)
\(294\) 0.149560 + 0.231693i 0.00872253 + 0.0135126i
\(295\) 0 0
\(296\) −14.4177 + 2.16196i −0.838012 + 0.125661i
\(297\) −2.57102 + 2.57102i −0.149186 + 0.149186i
\(298\) 2.94057 13.6499i 0.170343 0.790717i
\(299\) −32.2535 −1.86527
\(300\) 0 0
\(301\) −1.66648 −0.0960540
\(302\) −6.90101 + 32.0340i −0.397108 + 1.84335i
\(303\) 0.746419 0.746419i 0.0428807 0.0428807i
\(304\) 8.70238 + 9.88108i 0.499116 + 0.566719i
\(305\) 0 0
\(306\) −9.18354 14.2268i −0.524988 0.813291i
\(307\) 11.1792 + 11.1792i 0.638033 + 0.638033i 0.950070 0.312037i \(-0.101011\pi\)
−0.312037 + 0.950070i \(0.601011\pi\)
\(308\) −5.85175 + 2.20949i −0.333434 + 0.125897i
\(309\) 2.79527i 0.159017i
\(310\) 0 0
\(311\) 3.61486i 0.204980i 0.994734 + 0.102490i \(0.0326810\pi\)
−0.994734 + 0.102490i \(0.967319\pi\)
\(312\) −1.57135 1.16154i −0.0889599 0.0657594i
\(313\) 15.5668 + 15.5668i 0.879888 + 0.879888i 0.993523 0.113635i \(-0.0362494\pi\)
−0.113635 + 0.993523i \(0.536249\pi\)
\(314\) −5.83674 + 3.76768i −0.329387 + 0.212623i
\(315\) 0 0
\(316\) 0.279718 + 0.126383i 0.0157353 + 0.00710962i
\(317\) 14.4642 14.4642i 0.812389 0.812389i −0.172602 0.984992i \(-0.555218\pi\)
0.984992 + 0.172602i \(0.0552175\pi\)
\(318\) 0.429047 + 0.0924287i 0.0240598 + 0.00518315i
\(319\) 11.1325 0.623302
\(320\) 0 0
\(321\) −1.66977 −0.0931977
\(322\) 12.5859 + 2.71136i 0.701386 + 0.151098i
\(323\) −9.40926 + 9.40926i −0.523545 + 0.523545i
\(324\) −15.7823 7.13082i −0.876793 0.396156i
\(325\) 0 0
\(326\) −2.54507 + 1.64287i −0.140958 + 0.0909902i
\(327\) 1.10547 + 1.10547i 0.0611328 + 0.0611328i
\(328\) 3.79036 + 2.80184i 0.209287 + 0.154706i
\(329\) 0.846056i 0.0466446i
\(330\) 0 0
\(331\) 20.9381i 1.15086i −0.817851 0.575430i \(-0.804835\pi\)
0.817851 0.575430i \(-0.195165\pi\)
\(332\) −22.6831 + 8.56460i −1.24489 + 0.470043i
\(333\) −10.7956 10.7956i −0.591594 0.591594i
\(334\) 10.7024 + 16.5797i 0.585608 + 0.907201i
\(335\) 0 0
\(336\) 0.515524 + 0.585349i 0.0281241 + 0.0319334i
\(337\) 6.60024 6.60024i 0.359538 0.359538i −0.504104 0.863643i \(-0.668177\pi\)
0.863643 + 0.504104i \(0.168177\pi\)
\(338\) 0.133427 0.619357i 0.00725746 0.0336886i
\(339\) −0.818781 −0.0444701
\(340\) 0 0
\(341\) 27.1184 1.46855
\(342\) −2.90383 + 13.4794i −0.157021 + 0.728880i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) −4.66139 + 0.698984i −0.251325 + 0.0376867i
\(345\) 0 0
\(346\) −10.8202 16.7622i −0.581695 0.901139i
\(347\) 9.72907 + 9.72907i 0.522284 + 0.522284i 0.918261 0.395977i \(-0.129594\pi\)
−0.395977 + 0.918261i \(0.629594\pi\)
\(348\) −0.490373 1.29874i −0.0262868 0.0696197i
\(349\) 26.2310i 1.40411i 0.712121 + 0.702057i \(0.247735\pi\)
−0.712121 + 0.702057i \(0.752265\pi\)
\(350\) 0 0
\(351\) 4.11889i 0.219850i
\(352\) −15.4415 + 8.63472i −0.823035 + 0.460232i
\(353\) −6.56094 6.56094i −0.349203 0.349203i 0.510609 0.859813i \(-0.329420\pi\)
−0.859813 + 0.510609i \(0.829420\pi\)
\(354\) 2.41034 1.55590i 0.128108 0.0826952i
\(355\) 0 0
\(356\) 14.3332 31.7228i 0.759656 1.68131i
\(357\) −0.557399 + 0.557399i −0.0295007 + 0.0295007i
\(358\) −6.46445 1.39262i −0.341657 0.0736024i
\(359\) −1.22428 −0.0646151 −0.0323076 0.999478i \(-0.510286\pi\)
−0.0323076 + 0.999478i \(0.510286\pi\)
\(360\) 0 0
\(361\) −8.16455 −0.429713
\(362\) −25.2310 5.43546i −1.32611 0.285682i
\(363\) 0.168055 0.168055i 0.00882058 0.00882058i
\(364\) 2.91754 6.45724i 0.152921 0.338451i
\(365\) 0 0
\(366\) −1.57928 + 1.01945i −0.0825505 + 0.0532873i
\(367\) −2.79961 2.79961i −0.146138 0.146138i 0.630252 0.776391i \(-0.282952\pi\)
−0.776391 + 0.630252i \(0.782952\pi\)
\(368\) 36.3420 + 2.30507i 1.89446 + 0.120160i
\(369\) 4.93606i 0.256961i
\(370\) 0 0
\(371\) 1.59150i 0.0826266i
\(372\) −1.19453 3.16368i −0.0619336 0.164029i
\(373\) −14.2337 14.2337i −0.736993 0.736993i 0.235002 0.971995i \(-0.424490\pi\)
−0.971995 + 0.235002i \(0.924490\pi\)
\(374\) −9.69672 15.0218i −0.501406 0.776758i
\(375\) 0 0
\(376\) −0.354869 2.36655i −0.0183009 0.122045i
\(377\) −8.91742 + 8.91742i −0.459271 + 0.459271i
\(378\) −0.346250 + 1.60727i −0.0178092 + 0.0826690i
\(379\) −30.5331 −1.56838 −0.784190 0.620521i \(-0.786921\pi\)
−0.784190 + 0.620521i \(0.786921\pi\)
\(380\) 0 0
\(381\) 1.50722 0.0772170
\(382\) 5.55171 25.7706i 0.284050 1.31854i
\(383\) 5.16784 5.16784i 0.264064 0.264064i −0.562639 0.826703i \(-0.690214\pi\)
0.826703 + 0.562639i \(0.190214\pi\)
\(384\) 1.68752 + 1.42108i 0.0861158 + 0.0725192i
\(385\) 0 0
\(386\) 8.47959 + 13.1363i 0.431600 + 0.668618i
\(387\) −3.49032 3.49032i −0.177423 0.177423i
\(388\) −6.04425 + 2.28217i −0.306850 + 0.115860i
\(389\) 31.5845i 1.60140i 0.599067 + 0.800699i \(0.295538\pi\)
−0.599067 + 0.800699i \(0.704462\pi\)
\(390\) 0 0
\(391\) 36.8017i 1.86114i
\(392\) −1.68130 + 2.27447i −0.0849184 + 0.114878i
\(393\) 0.169512 + 0.169512i 0.00855074 + 0.00855074i
\(394\) 8.86961 5.72543i 0.446845 0.288443i
\(395\) 0 0
\(396\) −16.8837 7.62848i −0.848439 0.383345i
\(397\) −16.7022 + 16.7022i −0.838260 + 0.838260i −0.988630 0.150370i \(-0.951954\pi\)
0.150370 + 0.988630i \(0.451954\pi\)
\(398\) −0.990858 0.213459i −0.0496672 0.0106997i
\(399\) 0.641885 0.0321345
\(400\) 0 0
\(401\) 16.6522 0.831573 0.415787 0.909462i \(-0.363506\pi\)
0.415787 + 0.909462i \(0.363506\pi\)
\(402\) −2.60673 0.561563i −0.130012 0.0280082i
\(403\) −21.7225 + 21.7225i −1.08208 + 1.08208i
\(404\) 9.86630 + 4.45784i 0.490867 + 0.221786i
\(405\) 0 0
\(406\) 4.22938 2.73011i 0.209900 0.135493i
\(407\) −11.3988 11.3988i −0.565020 0.565020i
\(408\) −1.32534 + 1.79292i −0.0656139 + 0.0887630i
\(409\) 24.1043i 1.19188i 0.803029 + 0.595940i \(0.203220\pi\)
−0.803029 + 0.595940i \(0.796780\pi\)
\(410\) 0 0
\(411\) 0.876636i 0.0432412i
\(412\) 26.8212 10.1271i 1.32139 0.498925i
\(413\) 7.35615 + 7.35615i 0.361973 + 0.361973i
\(414\) 20.6816 + 32.0391i 1.01645 + 1.57464i
\(415\) 0 0
\(416\) 5.45239 19.2856i 0.267326 0.945556i
\(417\) 0.177561 0.177561i 0.00869522 0.00869522i
\(418\) −3.06610 + 14.2326i −0.149968 + 0.696139i
\(419\) −10.7316 −0.524272 −0.262136 0.965031i \(-0.584427\pi\)
−0.262136 + 0.965031i \(0.584427\pi\)
\(420\) 0 0
\(421\) 9.45571 0.460843 0.230422 0.973091i \(-0.425989\pi\)
0.230422 + 0.973091i \(0.425989\pi\)
\(422\) 2.92449 13.5753i 0.142362 0.660833i
\(423\) 1.77201 1.77201i 0.0861580 0.0861580i
\(424\) 0.667537 + 4.45167i 0.0324184 + 0.216192i
\(425\) 0 0
\(426\) −0.472538 0.732037i −0.0228945 0.0354673i
\(427\) −4.81984 4.81984i −0.233249 0.233249i
\(428\) −6.04949 16.0219i −0.292413 0.774447i
\(429\) 2.16066i 0.104318i
\(430\) 0 0
\(431\) 33.1577i 1.59715i −0.601894 0.798576i \(-0.705587\pi\)
0.601894 0.798576i \(-0.294413\pi\)
\(432\) −0.294366 + 4.64101i −0.0141627 + 0.223291i
\(433\) −10.1337 10.1337i −0.486995 0.486995i 0.420362 0.907357i \(-0.361903\pi\)
−0.907357 + 0.420362i \(0.861903\pi\)
\(434\) 10.3026 6.65044i 0.494541 0.319231i
\(435\) 0 0
\(436\) −6.60222 + 14.6123i −0.316189 + 0.699805i
\(437\) 21.1899 21.1899i 1.01365 1.01365i
\(438\) −2.29111 0.493570i −0.109474 0.0235837i
\(439\) 39.0061 1.86166 0.930829 0.365454i \(-0.119086\pi\)
0.930829 + 0.365454i \(0.119086\pi\)
\(440\) 0 0
\(441\) −2.96198 −0.141046
\(442\) 19.8001 + 4.26550i 0.941795 + 0.202889i
\(443\) 28.9618 28.9618i 1.37601 1.37601i 0.524772 0.851243i \(-0.324151\pi\)
0.851243 0.524772i \(-0.175849\pi\)
\(444\) −0.827702 + 1.83191i −0.0392810 + 0.0869386i
\(445\) 0 0
\(446\) −23.0618 + 14.8866i −1.09201 + 0.704902i
\(447\) −1.36140 1.36140i −0.0643918 0.0643918i
\(448\) −3.74885 + 7.06726i −0.177117 + 0.333897i
\(449\) 30.0275i 1.41709i 0.705667 + 0.708544i \(0.250648\pi\)
−0.705667 + 0.708544i \(0.749352\pi\)
\(450\) 0 0
\(451\) 5.21189i 0.245418i
\(452\) −2.96639 7.85640i −0.139527 0.369534i
\(453\) 3.19496 + 3.19496i 0.150112 + 0.150112i
\(454\) −8.73410 13.5305i −0.409912 0.635019i
\(455\) 0 0
\(456\) 1.79545 0.269231i 0.0840798 0.0126079i
\(457\) −13.4226 + 13.4226i −0.627883 + 0.627883i −0.947535 0.319652i \(-0.896434\pi\)
0.319652 + 0.947535i \(0.396434\pi\)
\(458\) −3.80846 + 17.6786i −0.177958 + 0.826066i
\(459\) −4.69971 −0.219364
\(460\) 0 0
\(461\) −24.0109 −1.11830 −0.559150 0.829067i \(-0.688872\pi\)
−0.559150 + 0.829067i \(0.688872\pi\)
\(462\) −0.181634 + 0.843130i −0.00845036 + 0.0392259i
\(463\) 14.2733 14.2733i 0.663337 0.663337i −0.292828 0.956165i \(-0.594596\pi\)
0.956165 + 0.292828i \(0.0945964\pi\)
\(464\) 10.6851 9.41050i 0.496043 0.436871i
\(465\) 0 0
\(466\) 16.8389 + 26.0861i 0.780045 + 1.20842i
\(467\) 21.3140 + 21.3140i 0.986296 + 0.986296i 0.999907 0.0136114i \(-0.00433278\pi\)
−0.0136114 + 0.999907i \(0.504333\pi\)
\(468\) 19.6348 7.41367i 0.907621 0.342697i
\(469\) 9.66938i 0.446490i
\(470\) 0 0
\(471\) 0.957913i 0.0441383i
\(472\) 23.6617 + 17.4908i 1.08912 + 0.805081i
\(473\) −3.68536 3.68536i −0.169453 0.169453i
\(474\) 0.0355584 0.0229533i 0.00163325 0.00105428i
\(475\) 0 0
\(476\) −7.36779 3.32895i −0.337702 0.152582i
\(477\) −3.33329 + 3.33329i −0.152621 + 0.152621i
\(478\) 3.17301 + 0.683554i 0.145130 + 0.0312650i
\(479\) 41.3956 1.89142 0.945708 0.325019i \(-0.105371\pi\)
0.945708 + 0.325019i \(0.105371\pi\)
\(480\) 0 0
\(481\) 18.2615 0.832652
\(482\) −24.5176 5.28177i −1.11674 0.240578i
\(483\) 1.25528 1.25528i 0.0571171 0.0571171i
\(484\) 2.22138 + 1.00367i 0.100972 + 0.0456215i
\(485\) 0 0
\(486\) −6.15032 + 3.97010i −0.278984 + 0.180087i
\(487\) 1.60723 + 1.60723i 0.0728304 + 0.0728304i 0.742584 0.669753i \(-0.233600\pi\)
−0.669753 + 0.742584i \(0.733600\pi\)
\(488\) −15.5035 11.4602i −0.701809 0.518780i
\(489\) 0.417691i 0.0188887i
\(490\) 0 0
\(491\) 20.1931i 0.911303i 0.890158 + 0.455652i \(0.150594\pi\)
−0.890158 + 0.455652i \(0.849406\pi\)
\(492\) 0.608027 0.229577i 0.0274120 0.0103501i
\(493\) 10.1749 + 10.1749i 0.458254 + 0.458254i
\(494\) −8.94462 13.8567i −0.402438 0.623440i
\(495\) 0 0
\(496\) 26.0285 22.9236i 1.16871 1.02930i
\(497\) 2.23412 2.23412i 0.100214 0.100214i
\(498\) −0.704064 + 3.26821i −0.0315499 + 0.146452i
\(499\) −27.6768 −1.23898 −0.619492 0.785003i \(-0.712661\pi\)
−0.619492 + 0.785003i \(0.712661\pi\)
\(500\) 0 0
\(501\) 2.72102 0.121566
\(502\) −8.47275 + 39.3299i −0.378157 + 1.75538i
\(503\) 1.13993 1.13993i 0.0508271 0.0508271i −0.681236 0.732063i \(-0.738557\pi\)
0.732063 + 0.681236i \(0.238557\pi\)
\(504\) −8.28510 + 1.24237i −0.369048 + 0.0553394i
\(505\) 0 0
\(506\) 21.8373 + 33.8295i 0.970786 + 1.50390i
\(507\) −0.0617726 0.0617726i −0.00274342 0.00274342i
\(508\) 5.46055 + 14.4621i 0.242273 + 0.641651i
\(509\) 11.8542i 0.525429i −0.964874 0.262714i \(-0.915382\pi\)
0.964874 0.262714i \(-0.0846177\pi\)
\(510\) 0 0
\(511\) 8.49862i 0.375957i
\(512\) −7.52183 + 21.3406i −0.332421 + 0.943131i
\(513\) 2.70603 + 2.70603i 0.119474 + 0.119474i
\(514\) 4.41030 2.84690i 0.194530 0.125571i
\(515\) 0 0
\(516\) −0.267604 + 0.592275i −0.0117806 + 0.0260735i
\(517\) 1.87103 1.87103i 0.0822877 0.0822877i
\(518\) −7.12597 1.53513i −0.313097 0.0674499i
\(519\) −2.75097 −0.120754
\(520\) 0 0
\(521\) −5.91845 −0.259292 −0.129646 0.991560i \(-0.541384\pi\)
−0.129646 + 0.991560i \(0.541384\pi\)
\(522\) 14.5762 + 3.14011i 0.637982 + 0.137439i
\(523\) −12.7321 + 12.7321i −0.556737 + 0.556737i −0.928377 0.371640i \(-0.878796\pi\)
0.371640 + 0.928377i \(0.378796\pi\)
\(524\) −1.01237 + 2.24064i −0.0442258 + 0.0978827i
\(525\) 0 0
\(526\) −24.6591 + 15.9177i −1.07519 + 0.694047i
\(527\) 24.7856 + 24.7856i 1.07968 + 1.07968i
\(528\) −0.154416 + 2.43455i −0.00672011 + 0.105950i
\(529\) 59.8784i 2.60341i
\(530\) 0 0
\(531\) 30.8139i 1.33721i
\(532\) 2.32551 + 6.15904i 0.100824 + 0.267028i
\(533\) −4.17485 4.17485i −0.180833 0.180833i
\(534\) −2.60314 4.03268i −0.112649 0.174511i
\(535\) 0 0
\(536\) −4.05571 27.0467i −0.175180 1.16824i
\(537\) −0.644743 + 0.644743i −0.0278227 + 0.0278227i
\(538\) 3.49518 16.2244i 0.150688 0.699482i
\(539\) −3.12749 −0.134711
\(540\) 0 0
\(541\) −17.3293 −0.745043 −0.372521 0.928024i \(-0.621507\pi\)
−0.372521 + 0.928024i \(0.621507\pi\)
\(542\) 6.26941 29.1021i 0.269294 1.25004i
\(543\) −2.51646 + 2.51646i −0.107991 + 0.107991i
\(544\) −22.0051 6.22125i −0.943463 0.266734i
\(545\) 0 0
\(546\) −0.529874 0.820860i −0.0226765 0.0351296i
\(547\) 0.00989653 + 0.00989653i 0.000423145 + 0.000423145i 0.707318 0.706895i \(-0.249905\pi\)
−0.706895 + 0.707318i \(0.749905\pi\)
\(548\) 8.41152 3.17600i 0.359323 0.135672i
\(549\) 20.1897i 0.861674i
\(550\) 0 0
\(551\) 11.7171i 0.499167i
\(552\) 2.98469 4.03772i 0.127037 0.171857i
\(553\) 0.108521 + 0.108521i 0.00461479 + 0.00461479i
\(554\) −15.6394 + 10.0954i −0.664452 + 0.428911i
\(555\) 0 0
\(556\) 2.34704 + 1.06045i 0.0995366 + 0.0449731i
\(557\) 7.03769 7.03769i 0.298196 0.298196i −0.542111 0.840307i \(-0.682375\pi\)
0.840307 + 0.542111i \(0.182375\pi\)
\(558\) 35.5070 + 7.64920i 1.50313 + 0.323816i
\(559\) 5.90412 0.249718
\(560\) 0 0
\(561\) −2.46534 −0.104087
\(562\) 22.3968 + 4.82490i 0.944753 + 0.203526i
\(563\) −10.2569 + 10.2569i −0.432276 + 0.432276i −0.889402 0.457126i \(-0.848879\pi\)
0.457126 + 0.889402i \(0.348879\pi\)
\(564\) −0.300693 0.135861i −0.0126615 0.00572076i
\(565\) 0 0
\(566\) 13.5195 8.72699i 0.568267 0.366823i
\(567\) −6.12299 6.12299i −0.257142 0.257142i
\(568\) 5.31209 7.18624i 0.222890 0.301528i
\(569\) 20.3219i 0.851939i −0.904738 0.425969i \(-0.859933\pi\)
0.904738 0.425969i \(-0.140067\pi\)
\(570\) 0 0
\(571\) 9.32953i 0.390429i 0.980761 + 0.195214i \(0.0625403\pi\)
−0.980761 + 0.195214i \(0.937460\pi\)
\(572\) 20.7321 7.82794i 0.866851 0.327303i
\(573\) −2.57028 2.57028i −0.107375 0.107375i
\(574\) 1.27815 + 1.98006i 0.0533488 + 0.0826459i
\(575\) 0 0
\(576\) −22.6536 + 6.95018i −0.943900 + 0.289591i
\(577\) −22.8297 + 22.8297i −0.950412 + 0.950412i −0.998827 0.0484150i \(-0.984583\pi\)
0.0484150 + 0.998827i \(0.484583\pi\)
\(578\) −0.196101 + 0.910284i −0.00815671 + 0.0378628i
\(579\) 2.15589 0.0895958
\(580\) 0 0
\(581\) −12.1230 −0.502949
\(582\) −0.187609 + 0.870866i −0.00777663 + 0.0360985i
\(583\) −3.51956 + 3.51956i −0.145765 + 0.145765i
\(584\) −3.56465 23.7719i −0.147506 0.983690i
\(585\) 0 0
\(586\) 20.1513 + 31.2176i 0.832443 + 1.28959i
\(587\) −19.2388 19.2388i −0.794070 0.794070i 0.188083 0.982153i \(-0.439773\pi\)
−0.982153 + 0.188083i \(0.939773\pi\)
\(588\) 0.137762 + 0.364858i 0.00568120 + 0.0150465i
\(589\) 28.5425i 1.17607i
\(590\) 0 0
\(591\) 1.45566i 0.0598779i
\(592\) −20.5763 1.30510i −0.845682 0.0536392i
\(593\) 16.3324 + 16.3324i 0.670691 + 0.670691i 0.957875 0.287184i \(-0.0927192\pi\)
−0.287184 + 0.957875i \(0.592719\pi\)
\(594\) −4.32015 + 2.78870i −0.177258 + 0.114422i
\(595\) 0 0
\(596\) 8.13065 17.9952i 0.333045 0.737110i
\(597\) −0.0988249 + 0.0988249i −0.00404463 + 0.00404463i
\(598\) −44.5904 9.60602i −1.82344 0.392819i
\(599\) 13.2232 0.540283 0.270142 0.962821i \(-0.412929\pi\)
0.270142 + 0.962821i \(0.412929\pi\)
\(600\) 0 0
\(601\) 3.28661 0.134064 0.0670318 0.997751i \(-0.478647\pi\)
0.0670318 + 0.997751i \(0.478647\pi\)
\(602\) −2.30390 0.496324i −0.0938998 0.0202286i
\(603\) 20.2519 20.2519i 0.824720 0.824720i
\(604\) −19.0812 + 42.2315i −0.776405 + 1.71838i
\(605\) 0 0
\(606\) 1.25423 0.809617i 0.0509495 0.0328885i
\(607\) −16.4028 16.4028i −0.665770 0.665770i 0.290964 0.956734i \(-0.406024\pi\)
−0.956734 + 0.290964i \(0.906024\pi\)
\(608\) 9.08816 + 16.2524i 0.368573 + 0.659121i
\(609\) 0.694116i 0.0281270i
\(610\) 0 0
\(611\) 2.99748i 0.121265i
\(612\) −8.45908 22.4036i −0.341938 0.905612i
\(613\) −25.4438 25.4438i −1.02767 1.02767i −0.999606 0.0280588i \(-0.991067\pi\)
−0.0280588 0.999606i \(-0.508933\pi\)
\(614\) 12.1258 + 18.7848i 0.489356 + 0.758091i
\(615\) 0 0
\(616\) −8.74808 + 1.31179i −0.352470 + 0.0528535i
\(617\) 11.2348 11.2348i 0.452295 0.452295i −0.443820 0.896116i \(-0.646377\pi\)
0.896116 + 0.443820i \(0.146377\pi\)
\(618\) 0.832509 3.86445i 0.0334884 0.155451i
\(619\) −23.1057 −0.928696 −0.464348 0.885653i \(-0.653711\pi\)
−0.464348 + 0.885653i \(0.653711\pi\)
\(620\) 0 0
\(621\) 10.5839 0.424716
\(622\) −1.07661 + 4.99753i −0.0431681 + 0.200383i
\(623\) 12.3074 12.3074i 0.493086 0.493086i
\(624\) −1.82644 2.07382i −0.0731161 0.0830193i
\(625\) 0 0
\(626\) 16.8848 + 26.1573i 0.674853 + 1.04546i
\(627\) 1.41951 + 1.41951i 0.0566898 + 0.0566898i
\(628\) −9.19140 + 3.47046i −0.366777 + 0.138487i
\(629\) 20.8366i 0.830809i
\(630\) 0 0
\(631\) 24.2657i 0.966003i −0.875619 0.483002i \(-0.839546\pi\)
0.875619 0.483002i \(-0.160454\pi\)
\(632\) 0.349068 + 0.258032i 0.0138852 + 0.0102640i
\(633\) −1.35395 1.35395i −0.0538147 0.0538147i
\(634\) 24.3045 15.6888i 0.965256 0.623084i
\(635\) 0 0
\(636\) 0.565629 + 0.255565i 0.0224286 + 0.0101338i
\(637\) 2.50519 2.50519i 0.0992594 0.0992594i
\(638\) 15.3907 + 3.31558i 0.609323 + 0.131265i
\(639\) 9.35841 0.370213
\(640\) 0 0
\(641\) −36.6994 −1.44954 −0.724770 0.688991i \(-0.758054\pi\)
−0.724770 + 0.688991i \(0.758054\pi\)
\(642\) −2.30846 0.497306i −0.0911076 0.0196271i
\(643\) −16.3697 + 16.3697i −0.645558 + 0.645558i −0.951916 0.306358i \(-0.900889\pi\)
0.306358 + 0.951916i \(0.400889\pi\)
\(644\) 16.5925 + 7.49689i 0.653835 + 0.295419i
\(645\) 0 0
\(646\) −15.8106 + 10.2059i −0.622060 + 0.401547i
\(647\) 6.53001 + 6.53001i 0.256721 + 0.256721i 0.823719 0.566998i \(-0.191895\pi\)
−0.566998 + 0.823719i \(0.691895\pi\)
\(648\) −19.6952 14.5587i −0.773700 0.571921i
\(649\) 32.5358i 1.27714i
\(650\) 0 0
\(651\) 1.69084i 0.0662692i
\(652\) −4.00785 + 1.51327i −0.156959 + 0.0592643i
\(653\) −8.77757 8.77757i −0.343493 0.343493i 0.514186 0.857679i \(-0.328094\pi\)
−0.857679 + 0.514186i \(0.828094\pi\)
\(654\) 1.19907 + 1.85756i 0.0468875 + 0.0726362i
\(655\) 0 0
\(656\) 4.40569 + 5.00242i 0.172013 + 0.195312i
\(657\) 17.7998 17.7998i 0.694436 0.694436i
\(658\) 0.251980 1.16967i 0.00982319 0.0455985i
\(659\) 16.8433 0.656122 0.328061 0.944657i \(-0.393605\pi\)
0.328061 + 0.944657i \(0.393605\pi\)
\(660\) 0 0
\(661\) −44.5785 −1.73390 −0.866952 0.498392i \(-0.833924\pi\)
−0.866952 + 0.498392i \(0.833924\pi\)
\(662\) 6.23595 28.9468i 0.242367 1.12505i
\(663\) 1.97480 1.97480i 0.0766947 0.0766947i
\(664\) −33.9100 + 5.08487i −1.31596 + 0.197331i
\(665\) 0 0
\(666\) −11.7096 18.1401i −0.453739 0.702914i
\(667\) −22.9141 22.9141i −0.887239 0.887239i
\(668\) 9.85810 + 26.1089i 0.381421 + 1.01018i
\(669\) 3.78485i 0.146331i
\(670\) 0 0
\(671\) 21.3179i 0.822967i
\(672\) 0.538377 + 0.962781i 0.0207683 + 0.0371401i
\(673\) 7.02160 + 7.02160i 0.270663 + 0.270663i 0.829367 0.558704i \(-0.188701\pi\)
−0.558704 + 0.829367i \(0.688701\pi\)
\(674\) 11.0906 7.15908i 0.427192 0.275757i
\(675\) 0 0
\(676\) 0.368924 0.816521i 0.0141894 0.0314046i
\(677\) −3.51482 + 3.51482i −0.135085 + 0.135085i −0.771416 0.636331i \(-0.780451\pi\)
0.636331 + 0.771416i \(0.280451\pi\)
\(678\) −1.13196 0.243856i −0.0434728 0.00936525i
\(679\) −3.23037 −0.123970
\(680\) 0 0
\(681\) −2.22060 −0.0850935
\(682\) 37.4912 + 8.07664i 1.43561 + 0.309271i
\(683\) 9.24465 9.24465i 0.353737 0.353737i −0.507761 0.861498i \(-0.669527\pi\)
0.861498 + 0.507761i \(0.169527\pi\)
\(684\) −8.02907 + 17.7703i −0.306999 + 0.679465i
\(685\) 0 0
\(686\) −1.18817 + 0.766977i −0.0453645 + 0.0292833i
\(687\) 1.76320 + 1.76320i 0.0672704 + 0.0672704i
\(688\) −6.65253 0.421951i −0.253625 0.0160867i
\(689\) 5.63850i 0.214810i
\(690\) 0 0
\(691\) 8.40931i 0.319905i −0.987125 0.159953i \(-0.948866\pi\)
0.987125 0.159953i \(-0.0511342\pi\)
\(692\) −9.96659 26.3962i −0.378873 1.00343i
\(693\) −6.55032 6.55032i −0.248826 0.248826i
\(694\) 10.5528 + 16.3480i 0.400579 + 0.620562i
\(695\) 0 0
\(696\) −0.291139 1.94155i −0.0110356 0.0735942i
\(697\) −4.76355 + 4.76355i −0.180432 + 0.180432i
\(698\) −7.81234 + 36.2643i −0.295701 + 1.37262i
\(699\) 4.28119 0.161930
\(700\) 0 0
\(701\) −13.1276 −0.495822 −0.247911 0.968783i \(-0.579744\pi\)
−0.247911 + 0.968783i \(0.579744\pi\)
\(702\) 1.22672 5.69436i 0.0462997 0.214920i
\(703\) −11.9974 + 11.9974i −0.452492 + 0.452492i
\(704\) −23.9195 + 7.33856i −0.901500 + 0.276582i
\(705\) 0 0
\(706\) −7.11644 11.0245i −0.267831 0.414913i
\(707\) 3.82779 + 3.82779i 0.143959 + 0.143959i
\(708\) 3.79568 1.43316i 0.142650 0.0538615i
\(709\) 7.84217i 0.294519i −0.989098 0.147259i \(-0.952955\pi\)
0.989098 0.147259i \(-0.0470452\pi\)
\(710\) 0 0
\(711\) 0.454581i 0.0170481i
\(712\) 29.2635 39.5879i 1.09670 1.48362i
\(713\) −55.8180 55.8180i −2.09040 2.09040i
\(714\) −0.936611 + 0.604593i −0.0350518 + 0.0226263i
\(715\) 0 0
\(716\) −8.52233 3.85060i −0.318494 0.143904i
\(717\) 0.316465 0.316465i 0.0118186 0.0118186i
\(718\) −1.69257 0.364626i −0.0631660 0.0136077i
\(719\) −34.9463 −1.30328 −0.651639 0.758529i \(-0.725918\pi\)
−0.651639 + 0.758529i \(0.725918\pi\)
\(720\) 0 0
\(721\) 14.3347 0.533853
\(722\) −11.2875 2.43163i −0.420076 0.0904961i
\(723\) −2.44530 + 2.44530i −0.0909417 + 0.0909417i
\(724\) −33.2630 15.0290i −1.23621 0.558549i
\(725\) 0 0
\(726\) 0.282387 0.182284i 0.0104803 0.00676518i
\(727\) 8.74837 + 8.74837i 0.324459 + 0.324459i 0.850475 0.526016i \(-0.176315\pi\)
−0.526016 + 0.850475i \(0.676315\pi\)
\(728\) 5.95664 8.05819i 0.220768 0.298656i
\(729\) 24.9683i 0.924751i
\(730\) 0 0
\(731\) 6.73668i 0.249165i
\(732\) −2.48698 + 0.939024i −0.0919213 + 0.0347073i
\(733\) −22.6984 22.6984i −0.838385 0.838385i 0.150261 0.988646i \(-0.451989\pi\)
−0.988646 + 0.150261i \(0.951989\pi\)
\(734\) −3.03665 4.70426i −0.112085 0.173637i
\(735\) 0 0
\(736\) 49.5562 + 14.0104i 1.82667 + 0.516431i
\(737\) 21.3835 21.3835i 0.787673 0.787673i
\(738\) −1.47010 + 6.82409i −0.0541151 + 0.251198i
\(739\) 0.138193 0.00508353 0.00254176 0.999997i \(-0.499191\pi\)
0.00254176 + 0.999997i \(0.499191\pi\)
\(740\) 0 0
\(741\) −2.27412 −0.0835420
\(742\) −0.473994 + 2.20025i −0.0174009 + 0.0807735i
\(743\) 6.26844 6.26844i 0.229967 0.229967i −0.582712 0.812679i \(-0.698008\pi\)
0.812679 + 0.582712i \(0.198008\pi\)
\(744\) −0.709203 4.72954i −0.0260007 0.173393i
\(745\) 0 0
\(746\) −15.4388 23.9172i −0.565256 0.875673i
\(747\) −25.3909 25.3909i −0.929005 0.929005i
\(748\) −8.93178 23.6555i −0.326578 0.864932i
\(749\) 8.56296i 0.312884i
\(750\) 0 0
\(751\) 0.0302132i 0.00110249i 1.00000 0.000551247i \(0.000175468\pi\)
−1.00000 0.000551247i \(0.999825\pi\)
\(752\) 0.214221 3.37744i 0.00781184 0.123163i
\(753\) 3.92263 + 3.92263i 0.142948 + 0.142948i
\(754\) −14.9842 + 9.67245i −0.545691 + 0.352250i
\(755\) 0 0
\(756\) −0.957380 + 2.11892i −0.0348196 + 0.0770644i
\(757\) −37.2066 + 37.2066i −1.35230 + 1.35230i −0.469213 + 0.883085i \(0.655462\pi\)
−0.883085 + 0.469213i \(0.844538\pi\)
\(758\) −42.2119 9.09362i −1.53321 0.330295i
\(759\) 5.55202 0.201525
\(760\) 0 0
\(761\) −37.6576 −1.36509 −0.682543 0.730846i \(-0.739126\pi\)
−0.682543 + 0.730846i \(0.739126\pi\)
\(762\) 2.08372 + 0.448892i 0.0754852 + 0.0162616i
\(763\) −5.66910 + 5.66910i −0.205235 + 0.205235i
\(764\) 15.3505 33.9744i 0.555360 1.22915i
\(765\) 0 0
\(766\) 8.68366 5.60540i 0.313753 0.202531i
\(767\) −26.0620 26.0620i −0.941043 0.941043i
\(768\) 1.90975 + 2.46723i 0.0689122 + 0.0890285i
\(769\) 1.80452i 0.0650727i 0.999471 + 0.0325364i \(0.0103585\pi\)
−0.999471 + 0.0325364i \(0.989642\pi\)
\(770\) 0 0
\(771\) 0.723809i 0.0260673i
\(772\) 7.81067 + 20.6863i 0.281112 + 0.744516i
\(773\) −0.171122 0.171122i −0.00615481 0.00615481i 0.704023 0.710177i \(-0.251385\pi\)
−0.710177 + 0.704023i \(0.751385\pi\)
\(774\) −3.78584 5.86487i −0.136079 0.210809i
\(775\) 0 0
\(776\) −9.03586 + 1.35494i −0.324368 + 0.0486396i
\(777\) −0.710720 + 0.710720i −0.0254970 + 0.0254970i
\(778\) −9.40676 + 43.6655i −0.337249 + 1.56548i
\(779\) 5.48558 0.196541
\(780\) 0 0
\(781\) 9.88136 0.353583
\(782\) −10.9606 + 50.8782i −0.391950 + 1.81940i
\(783\) 2.92622 2.92622i 0.104575 0.104575i
\(784\) −3.00179 + 2.64372i −0.107207 + 0.0944184i
\(785\) 0 0
\(786\) 0.183864 + 0.284835i 0.00655822 + 0.0101597i
\(787\) 5.77212 + 5.77212i 0.205754 + 0.205754i 0.802460 0.596706i \(-0.203524\pi\)
−0.596706 + 0.802460i \(0.703524\pi\)
\(788\) 13.9674 5.27377i 0.497568 0.187870i
\(789\) 4.04700i 0.144077i
\(790\) 0 0
\(791\) 4.19888i 0.149295i
\(792\) −21.0697 15.5748i −0.748680 0.553426i
\(793\) 17.0761 + 17.0761i 0.606391 + 0.606391i
\(794\) −28.0652 + 18.1164i −0.995995 + 0.642926i
\(795\) 0 0
\(796\) −1.30628 0.590212i −0.0463000 0.0209195i
\(797\) −18.3814 + 18.3814i −0.651103 + 0.651103i −0.953259 0.302156i \(-0.902294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(798\) 0.887405 + 0.191172i 0.0314138 + 0.00676741i
\(799\) 3.42016 0.120996
\(800\) 0 0
\(801\) 51.5541 1.82157
\(802\) 23.0217 + 4.95951i 0.812923 + 0.175126i
\(803\) 18.7944 18.7944i 0.663242 0.663242i
\(804\) −3.43655 1.55272i −0.121198 0.0547602i
\(805\) 0 0
\(806\) −36.5009 + 23.5617i −1.28569 + 0.829926i
\(807\) −1.61816 1.61816i −0.0569620 0.0569620i
\(808\) 12.3125 + 9.10141i 0.433151 + 0.320186i
\(809\) 5.64567i 0.198491i −0.995063 0.0992456i \(-0.968357\pi\)
0.995063 0.0992456i \(-0.0316429\pi\)
\(810\) 0 0
\(811\) 24.0723i 0.845294i −0.906294 0.422647i \(-0.861101\pi\)
0.906294 0.422647i \(-0.138899\pi\)
\(812\) 6.66020 2.51474i 0.233727 0.0882500i
\(813\) −2.90255 2.90255i −0.101797 0.101797i
\(814\) −12.3640 19.1538i −0.433357 0.671339i
\(815\) 0 0
\(816\) −2.36626 + 2.08399i −0.0828355 + 0.0729542i
\(817\) −3.87889 + 3.87889i −0.135705 + 0.135705i
\(818\) −7.17894 + 33.3241i −0.251006 + 1.16515i
\(819\) 10.4939 0.366687
\(820\) 0 0
\(821\) 40.7779 1.42316 0.711579 0.702606i \(-0.247980\pi\)
0.711579 + 0.702606i \(0.247980\pi\)
\(822\) 0.261087 1.21195i 0.00910645 0.0422715i
\(823\) 18.8337 18.8337i 0.656501 0.656501i −0.298049 0.954551i \(-0.596336\pi\)
0.954551 + 0.298049i \(0.0963359\pi\)
\(824\) 40.0964 6.01253i 1.39682 0.209456i
\(825\) 0 0
\(826\) 7.97899 + 12.3607i 0.277624 + 0.430085i
\(827\) −15.8664 15.8664i −0.551730 0.551730i 0.375210 0.926940i \(-0.377571\pi\)
−0.926940 + 0.375210i \(0.877571\pi\)
\(828\) 19.0501 + 50.4535i 0.662037 + 1.75338i
\(829\) 3.75621i 0.130459i 0.997870 + 0.0652293i \(0.0207779\pi\)
−0.997870 + 0.0652293i \(0.979222\pi\)
\(830\) 0 0
\(831\) 2.56670i 0.0890377i
\(832\) 13.2817 25.0384i 0.460461 0.868052i
\(833\) −2.85846 2.85846i −0.0990397 0.0990397i
\(834\) 0.298361 0.192595i 0.0103314 0.00666903i
\(835\) 0 0
\(836\) −8.47774 + 18.7633i −0.293209 + 0.648944i
\(837\) 7.12816 7.12816i 0.246385 0.246385i
\(838\) −14.8364 3.19617i −0.512514 0.110410i
\(839\) 12.2357 0.422424 0.211212 0.977440i \(-0.432259\pi\)
0.211212 + 0.977440i \(0.432259\pi\)
\(840\) 0 0
\(841\) 16.3294 0.563084
\(842\) 13.0725 + 2.81618i 0.450508 + 0.0970520i
\(843\) 2.23378 2.23378i 0.0769356 0.0769356i
\(844\) 8.08619 17.8968i 0.278338 0.616032i
\(845\) 0 0
\(846\) 2.97755 1.92204i 0.102370 0.0660811i
\(847\) 0.861820 + 0.861820i 0.0296125 + 0.0296125i
\(848\) −0.402967 + 6.35324i −0.0138380 + 0.218171i
\(849\) 2.21879i 0.0761487i
\(850\) 0 0
\(851\) 46.9246i 1.60855i
\(852\) −0.435261 1.15277i −0.0149118 0.0394934i
\(853\) 30.8929 + 30.8929i 1.05775 + 1.05775i 0.998227 + 0.0595275i \(0.0189594\pi\)
0.0595275 + 0.998227i \(0.481041\pi\)
\(854\) −5.22793 8.09890i −0.178896 0.277139i
\(855\) 0 0
\(856\) −3.59163 23.9519i −0.122759 0.818659i
\(857\) 13.2977 13.2977i 0.454242 0.454242i −0.442517 0.896760i \(-0.645915\pi\)
0.896760 + 0.442517i \(0.145915\pi\)
\(858\) 0.643506 2.98711i 0.0219689 0.101978i
\(859\) −20.8029 −0.709785 −0.354892 0.934907i \(-0.615483\pi\)
−0.354892 + 0.934907i \(0.615483\pi\)
\(860\) 0 0
\(861\) 0.324962 0.0110747
\(862\) 9.87532 45.8405i 0.336355 1.56133i
\(863\) 1.63985 1.63985i 0.0558210 0.0558210i −0.678645 0.734466i \(-0.737433\pi\)
0.734466 + 0.678645i \(0.237433\pi\)
\(864\) −1.78918 + 6.32851i −0.0608693 + 0.215300i
\(865\) 0 0
\(866\) −10.9917 17.0279i −0.373514 0.578632i
\(867\) 0.0907887 + 0.0907887i 0.00308334 + 0.00308334i
\(868\) 16.2240 6.12581i 0.550679 0.207924i
\(869\) 0.479983i 0.0162823i
\(870\) 0 0
\(871\) 34.2575i 1.16077i
\(872\) −13.4795 + 18.2352i −0.456474 + 0.617522i
\(873\) −6.76580 6.76580i −0.228988 0.228988i
\(874\) 35.6060 22.9840i 1.20439 0.777447i
\(875\) 0 0
\(876\) −3.02046 1.36472i −0.102052 0.0461095i
\(877\) −1.43888 + 1.43888i −0.0485874 + 0.0485874i −0.730983 0.682396i \(-0.760938\pi\)
0.682396 + 0.730983i \(0.260938\pi\)
\(878\) 53.9258 + 11.6171i 1.81991 + 0.392059i
\(879\) 5.12336 0.172807
\(880\) 0 0
\(881\) −20.5420 −0.692078 −0.346039 0.938220i \(-0.612474\pi\)
−0.346039 + 0.938220i \(0.612474\pi\)
\(882\) −4.09492 0.882160i −0.137883 0.0297039i
\(883\) 1.94396 1.94396i 0.0654196 0.0654196i −0.673640 0.739060i \(-0.735270\pi\)
0.739060 + 0.673640i \(0.235270\pi\)
\(884\) 26.1032 + 11.7941i 0.877946 + 0.396677i
\(885\) 0 0
\(886\) 48.6652 31.4139i 1.63494 1.05537i
\(887\) 18.7634 + 18.7634i 0.630015 + 0.630015i 0.948072 0.318057i \(-0.103030\pi\)
−0.318057 + 0.948072i \(0.603030\pi\)
\(888\) −1.68989 + 2.28610i −0.0567090 + 0.0767164i
\(889\) 7.72932i 0.259233i
\(890\) 0 0
\(891\) 27.0816i 0.907269i
\(892\) −36.3165 + 13.7123i −1.21597 + 0.459121i
\(893\) −1.96928 1.96928i −0.0658995 0.0658995i
\(894\) −1.47666 2.28759i −0.0493870 0.0765083i
\(895\) 0 0
\(896\) −7.28760 + 8.65395i −0.243462 + 0.289108i
\(897\) −4.44730 + 4.44730i −0.148491 + 0.148491i
\(898\) −8.94306 + 41.5130i −0.298434 + 1.38531i
\(899\) −30.8650 −1.02941
\(900\) 0 0
\(901\) −6.43359 −0.214334
\(902\) −1.55225 + 7.20542i −0.0516842 + 0.239914i
\(903\) −0.229783 + 0.229783i −0.00764670 + 0.00764670i
\(904\) −1.76117 11.7449i −0.0585758 0.390630i
\(905\) 0 0
\(906\) 3.46547 + 5.36857i 0.115133 + 0.178359i
\(907\) −5.74477 5.74477i −0.190752 0.190752i 0.605269 0.796021i \(-0.293066\pi\)
−0.796021 + 0.605269i \(0.793066\pi\)
\(908\) −8.04509 21.3072i −0.266986 0.707103i
\(909\) 16.0341i 0.531818i
\(910\) 0 0
\(911\) 23.4232i 0.776045i −0.921650 0.388023i \(-0.873158\pi\)
0.921650 0.388023i \(-0.126842\pi\)
\(912\) 2.56239 + 0.162525i 0.0848493 + 0.00538175i
\(913\) −26.8098 26.8098i −0.887274 0.887274i
\(914\) −22.5543 + 14.5591i −0.746031 + 0.481571i
\(915\) 0 0
\(916\) −10.5304 + 23.3063i −0.347933 + 0.770062i
\(917\) −0.869292 + 0.869292i −0.0287066 + 0.0287066i
\(918\) −6.49733 1.39971i −0.214444 0.0461972i
\(919\) 6.14477 0.202697 0.101349 0.994851i \(-0.467684\pi\)
0.101349 + 0.994851i \(0.467684\pi\)
\(920\) 0 0
\(921\) 3.08291 0.101585
\(922\) −33.1950 7.15113i −1.09322 0.235510i
\(923\) −7.91521 + 7.91521i −0.260532 + 0.260532i
\(924\) −0.502216 + 1.11153i −0.0165217 + 0.0365666i
\(925\) 0 0
\(926\) 23.9838 15.4818i 0.788157 0.508764i
\(927\) 30.0231 + 30.0231i 0.986088 + 0.986088i
\(928\) 17.5748 9.82766i 0.576922 0.322609i
\(929\) 29.7457i 0.975926i −0.872864 0.487963i \(-0.837740\pi\)
0.872864 0.487963i \(-0.162260\pi\)
\(930\) 0 0
\(931\) 3.29172i 0.107882i
\(932\) 15.5105 + 41.0791i 0.508063 + 1.34559i
\(933\) 0.498437 + 0.498437i 0.0163181 + 0.0163181i
\(934\) 23.1187 + 35.8145i 0.756466 + 1.17189i
\(935\) 0 0
\(936\) 29.3531 4.40155i 0.959437 0.143869i
\(937\) −19.4310 + 19.4310i −0.634784 + 0.634784i −0.949264 0.314480i \(-0.898170\pi\)
0.314480 + 0.949264i \(0.398170\pi\)
\(938\) 2.87982 13.3679i 0.0940293 0.436477i
\(939\) 4.29288 0.140093
\(940\) 0 0
\(941\) 30.1110 0.981591 0.490796 0.871275i \(-0.336706\pi\)
0.490796 + 0.871275i \(0.336706\pi\)
\(942\) −0.285294 + 1.32431i −0.00929538 + 0.0431484i
\(943\) 10.7276 10.7276i 0.349340 0.349340i
\(944\) 27.5030 + 31.2282i 0.895147 + 1.01639i
\(945\) 0 0
\(946\) −3.99740 6.19261i −0.129967 0.201339i
\(947\) 20.1763 + 20.1763i 0.655643 + 0.655643i 0.954346 0.298703i \(-0.0965541\pi\)
−0.298703 + 0.954346i \(0.596554\pi\)
\(948\) 0.0559955 0.0211426i 0.00181865 0.000686680i
\(949\) 30.1096i 0.977399i
\(950\) 0 0
\(951\) 3.98881i 0.129346i
\(952\) −9.19450 6.79660i −0.297995 0.220279i
\(953\) −19.5573 19.5573i −0.633523 0.633523i 0.315427 0.948950i \(-0.397852\pi\)
−0.948950 + 0.315427i \(0.897852\pi\)
\(954\) −5.60101 + 3.61552i −0.181340 + 0.117057i
\(955\) 0 0
\(956\) 4.18309 + 1.89002i 0.135291 + 0.0611277i
\(957\) 1.53502 1.53502i 0.0496200 0.0496200i
\(958\) 57.2294 + 12.3288i 1.84900 + 0.398325i
\(959\) 4.49557 0.145170
\(960\) 0 0
\(961\) −44.1860 −1.42535
\(962\) 25.2465 + 5.43879i 0.813979 + 0.175354i
\(963\) 17.9345 17.9345i 0.577932 0.577932i
\(964\) −32.3224 14.6041i −1.04103 0.470365i
\(965\) 0 0
\(966\) 2.10927 1.36156i 0.0678648 0.0438075i
\(967\) 7.95857 + 7.95857i 0.255930 + 0.255930i 0.823397 0.567466i \(-0.192076\pi\)
−0.567466 + 0.823397i \(0.692076\pi\)
\(968\) 2.77212 + 2.04916i 0.0890994 + 0.0658626i
\(969\) 2.59480i 0.0833571i
\(970\) 0 0
\(971\) 33.0681i 1.06121i 0.847620 + 0.530603i \(0.178035\pi\)
−0.847620 + 0.530603i \(0.821965\pi\)
\(972\) −9.68521 + 3.65691i −0.310653 + 0.117295i
\(973\) 0.910573 + 0.910573i 0.0291916 + 0.0291916i
\(974\) 1.74331 + 2.70067i 0.0558592 + 0.0865349i
\(975\) 0 0
\(976\) −18.0203 20.4611i −0.576816 0.654943i
\(977\) −20.5925 + 20.5925i −0.658813 + 0.658813i −0.955099 0.296286i \(-0.904252\pi\)
0.296286 + 0.955099i \(0.404252\pi\)
\(978\) −0.124400 + 0.577457i −0.00397789 + 0.0184650i
\(979\) 54.4349 1.73975
\(980\) 0 0
\(981\) −23.7471 −0.758187
\(982\) −6.01409 + 27.9170i −0.191917 + 0.890866i
\(983\) −26.6037 + 26.6037i −0.848528 + 0.848528i −0.989949 0.141422i \(-0.954833\pi\)
0.141422 + 0.989949i \(0.454833\pi\)
\(984\) 0.908969 0.136302i 0.0289769 0.00434514i
\(985\) 0 0
\(986\) 11.0364 + 17.0971i 0.351470 + 0.544483i
\(987\) −0.116659 0.116659i −0.00371330 0.00371330i
\(988\) −8.23901 21.8208i −0.262118 0.694211i
\(989\) 15.1712i 0.482416i
\(990\) 0 0
\(991\) 14.3981i 0.457370i 0.973500 + 0.228685i \(0.0734426\pi\)
−0.973500 + 0.228685i \(0.926557\pi\)
\(992\) 42.8116 23.9398i 1.35927 0.760090i
\(993\) −2.88706 2.88706i −0.0916180 0.0916180i
\(994\) 3.75404 2.42328i 0.119071 0.0768616i
\(995\) 0 0
\(996\) −1.94673 + 4.30860i −0.0616846 + 0.136523i
\(997\) 5.81745 5.81745i 0.184241 0.184241i −0.608960 0.793201i \(-0.708413\pi\)
0.793201 + 0.608960i \(0.208413\pi\)
\(998\) −38.2631 8.24294i −1.21120 0.260926i
\(999\) −5.99244 −0.189593
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 700.2.k.b.43.18 36
4.3 odd 2 inner 700.2.k.b.43.9 36
5.2 odd 4 inner 700.2.k.b.407.9 36
5.3 odd 4 140.2.k.a.127.10 yes 36
5.4 even 2 140.2.k.a.43.1 36
20.3 even 4 140.2.k.a.127.1 yes 36
20.7 even 4 inner 700.2.k.b.407.18 36
20.19 odd 2 140.2.k.a.43.10 yes 36
35.3 even 12 980.2.x.l.667.15 72
35.4 even 6 980.2.x.k.863.14 72
35.9 even 6 980.2.x.k.263.11 72
35.13 even 4 980.2.k.l.687.10 36
35.18 odd 12 980.2.x.k.667.15 72
35.19 odd 6 980.2.x.l.263.11 72
35.23 odd 12 980.2.x.k.67.3 72
35.24 odd 6 980.2.x.l.863.14 72
35.33 even 12 980.2.x.l.67.3 72
35.34 odd 2 980.2.k.l.883.1 36
140.3 odd 12 980.2.x.l.667.11 72
140.19 even 6 980.2.x.l.263.15 72
140.23 even 12 980.2.x.k.67.14 72
140.39 odd 6 980.2.x.k.863.3 72
140.59 even 6 980.2.x.l.863.3 72
140.79 odd 6 980.2.x.k.263.15 72
140.83 odd 4 980.2.k.l.687.1 36
140.103 odd 12 980.2.x.l.67.14 72
140.123 even 12 980.2.x.k.667.11 72
140.139 even 2 980.2.k.l.883.10 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.k.a.43.1 36 5.4 even 2
140.2.k.a.43.10 yes 36 20.19 odd 2
140.2.k.a.127.1 yes 36 20.3 even 4
140.2.k.a.127.10 yes 36 5.3 odd 4
700.2.k.b.43.9 36 4.3 odd 2 inner
700.2.k.b.43.18 36 1.1 even 1 trivial
700.2.k.b.407.9 36 5.2 odd 4 inner
700.2.k.b.407.18 36 20.7 even 4 inner
980.2.k.l.687.1 36 140.83 odd 4
980.2.k.l.687.10 36 35.13 even 4
980.2.k.l.883.1 36 35.34 odd 2
980.2.k.l.883.10 36 140.139 even 2
980.2.x.k.67.3 72 35.23 odd 12
980.2.x.k.67.14 72 140.23 even 12
980.2.x.k.263.11 72 35.9 even 6
980.2.x.k.263.15 72 140.79 odd 6
980.2.x.k.667.11 72 140.123 even 12
980.2.x.k.667.15 72 35.18 odd 12
980.2.x.k.863.3 72 140.39 odd 6
980.2.x.k.863.14 72 35.4 even 6
980.2.x.l.67.3 72 35.33 even 12
980.2.x.l.67.14 72 140.103 odd 12
980.2.x.l.263.11 72 35.19 odd 6
980.2.x.l.263.15 72 140.19 even 6
980.2.x.l.667.11 72 140.3 odd 12
980.2.x.l.667.15 72 35.3 even 12
980.2.x.l.863.3 72 140.59 even 6
980.2.x.l.863.14 72 35.24 odd 6