Properties

Label 336.2.s.d.155.3
Level $336$
Weight $2$
Character 336.155
Analytic conductor $2.683$
Analytic rank $0$
Dimension $48$
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] = [336,2,Mod(155,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.s (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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 155.3
Character \(\chi\) \(=\) 336.155
Dual form 336.2.s.d.323.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.30954 + 0.533943i) q^{2} +(1.26449 + 1.18367i) q^{3} +(1.42981 - 1.39844i) q^{4} +(1.97913 - 1.97913i) q^{5} +(-2.28791 - 0.874897i) q^{6} +1.00000 q^{7} +(-1.12571 + 2.59476i) q^{8} +(0.197870 + 2.99347i) q^{9} +O(q^{10})\) \(q+(-1.30954 + 0.533943i) q^{2} +(1.26449 + 1.18367i) q^{3} +(1.42981 - 1.39844i) q^{4} +(1.97913 - 1.97913i) q^{5} +(-2.28791 - 0.874897i) q^{6} +1.00000 q^{7} +(-1.12571 + 2.59476i) q^{8} +(0.197870 + 2.99347i) q^{9} +(-1.53501 + 3.64849i) q^{10} +(-0.735190 - 0.735190i) q^{11} +(3.46327 - 0.0758987i) q^{12} +(2.83849 - 2.83849i) q^{13} +(-1.30954 + 0.533943i) q^{14} +(4.84521 - 0.159961i) q^{15} +(0.0887163 - 3.99902i) q^{16} -3.89383i q^{17} +(-1.85746 - 3.81443i) q^{18} +(-2.65054 - 2.65054i) q^{19} +(0.0620810 - 5.59747i) q^{20} +(1.26449 + 1.18367i) q^{21} +(1.35531 + 0.570214i) q^{22} +4.59167i q^{23} +(-4.49478 + 1.94858i) q^{24} -2.83389i q^{25} +(-2.20154 + 5.23272i) q^{26} +(-3.29306 + 4.01942i) q^{27} +(1.42981 - 1.39844i) q^{28} +(6.93183 + 6.93183i) q^{29} +(-6.25961 + 2.79654i) q^{30} +6.03914i q^{31} +(2.01907 + 5.28426i) q^{32} +(-0.0594210 - 1.79986i) q^{33} +(2.07908 + 5.09914i) q^{34} +(1.97913 - 1.97913i) q^{35} +(4.46911 + 4.00338i) q^{36} +(-7.23258 - 7.23258i) q^{37} +(4.88623 + 2.05576i) q^{38} +(6.94907 - 0.229419i) q^{39} +(2.90743 + 7.36328i) q^{40} -0.424100 q^{41} +(-2.28791 - 0.874897i) q^{42} +(-1.72961 + 1.72961i) q^{43} +(-2.07930 - 0.0230613i) q^{44} +(6.31606 + 5.53284i) q^{45} +(-2.45169 - 6.01299i) q^{46} -3.45146 q^{47} +(4.84568 - 4.95171i) q^{48} +1.00000 q^{49} +(1.51313 + 3.71110i) q^{50} +(4.60899 - 4.92370i) q^{51} +(0.0890375 - 8.02798i) q^{52} +(-7.07724 + 7.07724i) q^{53} +(2.16627 - 7.02191i) q^{54} -2.91007 q^{55} +(-1.12571 + 2.59476i) q^{56} +(-0.214227 - 6.48893i) q^{57} +(-12.7787 - 5.37633i) q^{58} +(1.95980 + 1.95980i) q^{59} +(6.70404 - 7.00447i) q^{60} +(-0.0653394 + 0.0653394i) q^{61} +(-3.22455 - 7.90852i) q^{62} +(0.197870 + 2.99347i) q^{63} +(-5.46555 - 5.84190i) q^{64} -11.2355i q^{65} +(1.03884 + 2.32527i) q^{66} +(9.77673 + 9.77673i) q^{67} +(-5.44529 - 5.56743i) q^{68} +(-5.43500 + 5.80612i) q^{69} +(-1.53501 + 3.64849i) q^{70} -8.50810i q^{71} +(-7.99007 - 2.85636i) q^{72} -5.13683i q^{73} +(13.3332 + 5.60960i) q^{74} +(3.35438 - 3.58342i) q^{75} +(-7.49640 - 0.0831418i) q^{76} +(-0.735190 - 0.735190i) q^{77} +(-8.97762 + 4.01084i) q^{78} +2.65552i q^{79} +(-7.73898 - 8.09014i) q^{80} +(-8.92169 + 1.18463i) q^{81} +(0.555377 - 0.226445i) q^{82} +(0.666819 - 0.666819i) q^{83} +(3.46327 - 0.0758987i) q^{84} +(-7.70638 - 7.70638i) q^{85} +(1.34149 - 3.18851i) q^{86} +(0.560258 + 16.9702i) q^{87} +(2.73525 - 1.08003i) q^{88} -14.1865 q^{89} +(-11.2254 - 3.87309i) q^{90} +(2.83849 - 2.83849i) q^{91} +(6.42119 + 6.56522i) q^{92} +(-7.14832 + 7.63643i) q^{93} +(4.51984 - 1.84288i) q^{94} -10.4915 q^{95} +(-3.70170 + 9.07179i) q^{96} -11.9786 q^{97} +(-1.30954 + 0.533943i) q^{98} +(2.05530 - 2.34624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30954 + 0.533943i −0.925987 + 0.377554i
\(3\) 1.26449 + 1.18367i 0.730054 + 0.683390i
\(4\) 1.42981 1.39844i 0.714905 0.699221i
\(5\) 1.97913 1.97913i 0.885093 0.885093i −0.108954 0.994047i \(-0.534750\pi\)
0.994047 + 0.108954i \(0.0347502\pi\)
\(6\) −2.28791 0.874897i −0.934037 0.357175i
\(7\) 1.00000 0.377964
\(8\) −1.12571 + 2.59476i −0.397999 + 0.917386i
\(9\) 0.197870 + 2.99347i 0.0659566 + 0.997822i
\(10\) −1.53501 + 3.64849i −0.485414 + 1.15376i
\(11\) −0.735190 0.735190i −0.221668 0.221668i 0.587532 0.809201i \(-0.300099\pi\)
−0.809201 + 0.587532i \(0.800099\pi\)
\(12\) 3.46327 0.0758987i 0.999760 0.0219101i
\(13\) 2.83849 2.83849i 0.787256 0.787256i −0.193787 0.981044i \(-0.562077\pi\)
0.981044 + 0.193787i \(0.0620771\pi\)
\(14\) −1.30954 + 0.533943i −0.349990 + 0.142702i
\(15\) 4.84521 0.159961i 1.25103 0.0413018i
\(16\) 0.0887163 3.99902i 0.0221791 0.999754i
\(17\) 3.89383i 0.944391i −0.881494 0.472196i \(-0.843462\pi\)
0.881494 0.472196i \(-0.156538\pi\)
\(18\) −1.85746 3.81443i −0.437807 0.899069i
\(19\) −2.65054 2.65054i −0.608075 0.608075i 0.334367 0.942443i \(-0.391477\pi\)
−0.942443 + 0.334367i \(0.891477\pi\)
\(20\) 0.0620810 5.59747i 0.0138817 1.25163i
\(21\) 1.26449 + 1.18367i 0.275934 + 0.258297i
\(22\) 1.35531 + 0.570214i 0.288954 + 0.121570i
\(23\) 4.59167i 0.957429i 0.877971 + 0.478715i \(0.158897\pi\)
−0.877971 + 0.478715i \(0.841103\pi\)
\(24\) −4.49478 + 1.94858i −0.917493 + 0.397752i
\(25\) 2.83389i 0.566778i
\(26\) −2.20154 + 5.23272i −0.431757 + 1.02622i
\(27\) −3.29306 + 4.01942i −0.633750 + 0.773538i
\(28\) 1.42981 1.39844i 0.270209 0.264281i
\(29\) 6.93183 + 6.93183i 1.28721 + 1.28721i 0.936476 + 0.350732i \(0.114067\pi\)
0.350732 + 0.936476i \(0.385933\pi\)
\(30\) −6.25961 + 2.79654i −1.14284 + 0.510576i
\(31\) 6.03914i 1.08466i 0.840165 + 0.542331i \(0.182458\pi\)
−0.840165 + 0.542331i \(0.817542\pi\)
\(32\) 2.01907 + 5.28426i 0.356924 + 0.934133i
\(33\) −0.0594210 1.79986i −0.0103439 0.313315i
\(34\) 2.07908 + 5.09914i 0.356559 + 0.874495i
\(35\) 1.97913 1.97913i 0.334534 0.334534i
\(36\) 4.46911 + 4.00338i 0.744852 + 0.667230i
\(37\) −7.23258 7.23258i −1.18903 1.18903i −0.977336 0.211693i \(-0.932102\pi\)
−0.211693 0.977336i \(-0.567898\pi\)
\(38\) 4.88623 + 2.05576i 0.792652 + 0.333489i
\(39\) 6.94907 0.229419i 1.11274 0.0367364i
\(40\) 2.90743 + 7.36328i 0.459705 + 1.16424i
\(41\) −0.424100 −0.0662333 −0.0331166 0.999451i \(-0.510543\pi\)
−0.0331166 + 0.999451i \(0.510543\pi\)
\(42\) −2.28791 0.874897i −0.353033 0.135000i
\(43\) −1.72961 + 1.72961i −0.263763 + 0.263763i −0.826581 0.562818i \(-0.809717\pi\)
0.562818 + 0.826581i \(0.309717\pi\)
\(44\) −2.07930 0.0230613i −0.313467 0.00347663i
\(45\) 6.31606 + 5.53284i 0.941543 + 0.824788i
\(46\) −2.45169 6.01299i −0.361482 0.886567i
\(47\) −3.45146 −0.503448 −0.251724 0.967799i \(-0.580997\pi\)
−0.251724 + 0.967799i \(0.580997\pi\)
\(48\) 4.84568 4.95171i 0.699414 0.714717i
\(49\) 1.00000 0.142857
\(50\) 1.51313 + 3.71110i 0.213990 + 0.524829i
\(51\) 4.60899 4.92370i 0.645388 0.689456i
\(52\) 0.0890375 8.02798i 0.0123473 1.11328i
\(53\) −7.07724 + 7.07724i −0.972133 + 0.972133i −0.999622 0.0274890i \(-0.991249\pi\)
0.0274890 + 0.999622i \(0.491249\pi\)
\(54\) 2.16627 7.02191i 0.294792 0.955562i
\(55\) −2.91007 −0.392394
\(56\) −1.12571 + 2.59476i −0.150430 + 0.346739i
\(57\) −0.214227 6.48893i −0.0283751 0.859480i
\(58\) −12.7787 5.37633i −1.67793 0.705947i
\(59\) 1.95980 + 1.95980i 0.255144 + 0.255144i 0.823076 0.567931i \(-0.192256\pi\)
−0.567931 + 0.823076i \(0.692256\pi\)
\(60\) 6.70404 7.00447i 0.865488 0.904273i
\(61\) −0.0653394 + 0.0653394i −0.00836586 + 0.00836586i −0.711277 0.702911i \(-0.751883\pi\)
0.702911 + 0.711277i \(0.251883\pi\)
\(62\) −3.22455 7.90852i −0.409519 1.00438i
\(63\) 0.197870 + 2.99347i 0.0249293 + 0.377141i
\(64\) −5.46555 5.84190i −0.683193 0.730237i
\(65\) 11.2355i 1.39359i
\(66\) 1.03884 + 2.32527i 0.127872 + 0.286221i
\(67\) 9.77673 + 9.77673i 1.19442 + 1.19442i 0.975814 + 0.218604i \(0.0701503\pi\)
0.218604 + 0.975814i \(0.429850\pi\)
\(68\) −5.44529 5.56743i −0.660339 0.675150i
\(69\) −5.43500 + 5.80612i −0.654297 + 0.698975i
\(70\) −1.53501 + 3.64849i −0.183469 + 0.436078i
\(71\) 8.50810i 1.00973i −0.863200 0.504863i \(-0.831543\pi\)
0.863200 0.504863i \(-0.168457\pi\)
\(72\) −7.99007 2.85636i −0.941639 0.336625i
\(73\) 5.13683i 0.601221i −0.953747 0.300610i \(-0.902810\pi\)
0.953747 0.300610i \(-0.0971904\pi\)
\(74\) 13.3332 + 5.60960i 1.54995 + 0.652103i
\(75\) 3.35438 3.58342i 0.387330 0.413778i
\(76\) −7.49640 0.0831418i −0.859896 0.00953701i
\(77\) −0.735190 0.735190i −0.0837827 0.0837827i
\(78\) −8.97762 + 4.01084i −1.01652 + 0.454138i
\(79\) 2.65552i 0.298769i 0.988779 + 0.149384i \(0.0477292\pi\)
−0.988779 + 0.149384i \(0.952271\pi\)
\(80\) −7.73898 8.09014i −0.865244 0.904505i
\(81\) −8.92169 + 1.18463i −0.991299 + 0.131626i
\(82\) 0.555377 0.226445i 0.0613312 0.0250067i
\(83\) 0.666819 0.666819i 0.0731929 0.0731929i −0.669563 0.742756i \(-0.733518\pi\)
0.742756 + 0.669563i \(0.233518\pi\)
\(84\) 3.46327 0.0758987i 0.377874 0.00828123i
\(85\) −7.70638 7.70638i −0.835874 0.835874i
\(86\) 1.34149 3.18851i 0.144656 0.343826i
\(87\) 0.560258 + 16.9702i 0.0600660 + 1.81940i
\(88\) 2.73525 1.08003i 0.291579 0.115131i
\(89\) −14.1865 −1.50376 −0.751882 0.659298i \(-0.770854\pi\)
−0.751882 + 0.659298i \(0.770854\pi\)
\(90\) −11.2254 3.87309i −1.18326 0.408259i
\(91\) 2.83849 2.83849i 0.297555 0.297555i
\(92\) 6.42119 + 6.56522i 0.669455 + 0.684471i
\(93\) −7.14832 + 7.63643i −0.741246 + 0.791861i
\(94\) 4.51984 1.84288i 0.466186 0.190079i
\(95\) −10.4915 −1.07641
\(96\) −3.70170 + 9.07179i −0.377804 + 0.925886i
\(97\) −11.9786 −1.21625 −0.608123 0.793843i \(-0.708077\pi\)
−0.608123 + 0.793843i \(0.708077\pi\)
\(98\) −1.30954 + 0.533943i −0.132284 + 0.0539364i
\(99\) 2.05530 2.34624i 0.206565 0.235806i
\(100\) −3.96303 4.05192i −0.396303 0.405192i
\(101\) 12.3027 12.3027i 1.22416 1.22416i 0.258027 0.966138i \(-0.416928\pi\)
0.966138 0.258027i \(-0.0830723\pi\)
\(102\) −3.40670 + 8.90874i −0.337313 + 0.882097i
\(103\) −8.78406 −0.865519 −0.432760 0.901509i \(-0.642460\pi\)
−0.432760 + 0.901509i \(0.642460\pi\)
\(104\) 4.16988 + 10.5605i 0.408890 + 1.03555i
\(105\) 4.84521 0.159961i 0.472844 0.0156106i
\(106\) 5.48911 13.0468i 0.533150 1.26722i
\(107\) −11.7876 11.7876i −1.13955 1.13955i −0.988531 0.151021i \(-0.951744\pi\)
−0.151021 0.988531i \(-0.548256\pi\)
\(108\) 0.912477 + 10.3522i 0.0878032 + 0.996138i
\(109\) 0.978979 0.978979i 0.0937692 0.0937692i −0.658666 0.752435i \(-0.728879\pi\)
0.752435 + 0.658666i \(0.228879\pi\)
\(110\) 3.81086 1.55381i 0.363352 0.148150i
\(111\) −0.584567 17.7065i −0.0554846 1.68063i
\(112\) 0.0887163 3.99902i 0.00838290 0.377871i
\(113\) 7.35599i 0.691993i −0.938236 0.345997i \(-0.887541\pi\)
0.938236 0.345997i \(-0.112459\pi\)
\(114\) 3.74526 + 8.38316i 0.350776 + 0.785155i
\(115\) 9.08750 + 9.08750i 0.847413 + 0.847413i
\(116\) 19.6050 + 0.217437i 1.82027 + 0.0201885i
\(117\) 9.05859 + 7.93528i 0.837467 + 0.733617i
\(118\) −3.61287 1.52002i −0.332591 0.139930i
\(119\) 3.89383i 0.356946i
\(120\) −5.03925 + 12.7522i −0.460019 + 1.16411i
\(121\) 9.91899i 0.901726i
\(122\) 0.0506773 0.120452i 0.00458811 0.0109052i
\(123\) −0.536270 0.501992i −0.0483538 0.0452631i
\(124\) 8.44539 + 8.63482i 0.758418 + 0.775430i
\(125\) 4.28701 + 4.28701i 0.383442 + 0.383442i
\(126\) −1.85746 3.81443i −0.165476 0.339816i
\(127\) 20.2328i 1.79537i 0.440639 + 0.897684i \(0.354752\pi\)
−0.440639 + 0.897684i \(0.645248\pi\)
\(128\) 10.2766 + 4.73194i 0.908333 + 0.418248i
\(129\) −4.23435 + 0.139794i −0.372814 + 0.0123082i
\(130\) 5.99910 + 14.7134i 0.526156 + 1.29045i
\(131\) 6.06303 6.06303i 0.529729 0.529729i −0.390762 0.920492i \(-0.627789\pi\)
0.920492 + 0.390762i \(0.127789\pi\)
\(132\) −2.60196 2.49036i −0.226472 0.216758i
\(133\) −2.65054 2.65054i −0.229831 0.229831i
\(134\) −18.0233 7.58284i −1.55697 0.655058i
\(135\) 1.43756 + 14.4723i 0.123725 + 1.24558i
\(136\) 10.1035 + 4.38332i 0.866371 + 0.375867i
\(137\) −17.4916 −1.49441 −0.747205 0.664594i \(-0.768605\pi\)
−0.747205 + 0.664594i \(0.768605\pi\)
\(138\) 4.01724 10.5053i 0.341970 0.894275i
\(139\) −1.84549 + 1.84549i −0.156532 + 0.156532i −0.781028 0.624496i \(-0.785305\pi\)
0.624496 + 0.781028i \(0.285305\pi\)
\(140\) 0.0620810 5.59747i 0.00524680 0.473073i
\(141\) −4.36434 4.08538i −0.367544 0.344051i
\(142\) 4.54284 + 11.1417i 0.381226 + 0.934993i
\(143\) −4.17366 −0.349019
\(144\) 11.9885 0.525716i 0.999040 0.0438096i
\(145\) 27.4379 2.27860
\(146\) 2.74277 + 6.72691i 0.226994 + 0.556723i
\(147\) 1.26449 + 1.18367i 0.104293 + 0.0976271i
\(148\) −20.4556 0.226871i −1.68144 0.0186487i
\(149\) 2.57107 2.57107i 0.210630 0.210630i −0.593905 0.804535i \(-0.702414\pi\)
0.804535 + 0.593905i \(0.202414\pi\)
\(150\) −2.47936 + 6.48370i −0.202439 + 0.529392i
\(151\) −2.94402 −0.239581 −0.119790 0.992799i \(-0.538222\pi\)
−0.119790 + 0.992799i \(0.538222\pi\)
\(152\) 9.86125 3.89377i 0.799853 0.315826i
\(153\) 11.6560 0.770471i 0.942335 0.0622889i
\(154\) 1.35531 + 0.570214i 0.109214 + 0.0459492i
\(155\) 11.9522 + 11.9522i 0.960026 + 0.960026i
\(156\) 9.61503 10.0459i 0.769819 0.804316i
\(157\) 6.36388 6.36388i 0.507893 0.507893i −0.405986 0.913879i \(-0.633072\pi\)
0.913879 + 0.405986i \(0.133072\pi\)
\(158\) −1.41789 3.47751i −0.112802 0.276656i
\(159\) −17.3262 + 0.572011i −1.37406 + 0.0453634i
\(160\) 14.4542 + 6.46222i 1.14271 + 0.510884i
\(161\) 4.59167i 0.361874i
\(162\) 11.0508 6.31500i 0.868235 0.496154i
\(163\) −10.4613 10.4613i −0.819389 0.819389i 0.166631 0.986019i \(-0.446711\pi\)
−0.986019 + 0.166631i \(0.946711\pi\)
\(164\) −0.606382 + 0.593079i −0.0473505 + 0.0463117i
\(165\) −3.67975 3.44455i −0.286468 0.268158i
\(166\) −0.517186 + 1.22927i −0.0401414 + 0.0954100i
\(167\) 5.87517i 0.454635i 0.973821 + 0.227317i \(0.0729954\pi\)
−0.973821 + 0.227317i \(0.927005\pi\)
\(168\) −4.49478 + 1.94858i −0.346780 + 0.150336i
\(169\) 3.11409i 0.239545i
\(170\) 14.2066 + 5.97708i 1.08960 + 0.458421i
\(171\) 7.40984 8.45877i 0.566645 0.646858i
\(172\) −0.0542542 + 4.89177i −0.00413684 + 0.372994i
\(173\) 5.65527 + 5.65527i 0.429962 + 0.429962i 0.888615 0.458653i \(-0.151668\pi\)
−0.458653 + 0.888615i \(0.651668\pi\)
\(174\) −9.79479 21.9241i −0.742541 1.66206i
\(175\) 2.83389i 0.214222i
\(176\) −3.00526 + 2.87481i −0.226530 + 0.216697i
\(177\) 0.158399 + 4.79790i 0.0119060 + 0.360632i
\(178\) 18.5778 7.57477i 1.39247 0.567753i
\(179\) −9.77837 + 9.77837i −0.730870 + 0.730870i −0.970792 0.239922i \(-0.922878\pi\)
0.239922 + 0.970792i \(0.422878\pi\)
\(180\) 16.7681 0.921734i 1.24982 0.0687020i
\(181\) 17.5393 + 17.5393i 1.30369 + 1.30369i 0.925887 + 0.377801i \(0.123320\pi\)
0.377801 + 0.925887i \(0.376680\pi\)
\(182\) −2.20154 + 5.23272i −0.163189 + 0.387875i
\(183\) −0.159961 + 0.00528100i −0.0118247 + 0.000390383i
\(184\) −11.9143 5.16889i −0.878332 0.381056i
\(185\) −28.6284 −2.10480
\(186\) 5.28363 13.8170i 0.387414 1.01311i
\(187\) −2.86270 + 2.86270i −0.209341 + 0.209341i
\(188\) −4.93494 + 4.82667i −0.359917 + 0.352021i
\(189\) −3.29306 + 4.01942i −0.239535 + 0.292370i
\(190\) 13.7391 5.60186i 0.996739 0.406402i
\(191\) −10.8068 −0.781954 −0.390977 0.920400i \(-0.627863\pi\)
−0.390977 + 0.920400i \(0.627863\pi\)
\(192\) 0.00372809 13.8564i 0.000269052 1.00000i
\(193\) 0.865334 0.0622881 0.0311441 0.999515i \(-0.490085\pi\)
0.0311441 + 0.999515i \(0.490085\pi\)
\(194\) 15.6866 6.39590i 1.12623 0.459199i
\(195\) 13.2991 14.2072i 0.952365 1.01740i
\(196\) 1.42981 1.39844i 0.102129 0.0998888i
\(197\) −8.43635 + 8.43635i −0.601065 + 0.601065i −0.940595 0.339530i \(-0.889732\pi\)
0.339530 + 0.940595i \(0.389732\pi\)
\(198\) −1.43874 + 4.16991i −0.102247 + 0.296343i
\(199\) 15.9750 1.13244 0.566218 0.824256i \(-0.308406\pi\)
0.566218 + 0.824256i \(0.308406\pi\)
\(200\) 7.35326 + 3.19014i 0.519954 + 0.225577i
\(201\) 0.790195 + 23.9350i 0.0557361 + 1.68824i
\(202\) −9.54199 + 22.6799i −0.671372 + 1.59575i
\(203\) 6.93183 + 6.93183i 0.486519 + 0.486519i
\(204\) −0.295536 13.4854i −0.0206917 0.944165i
\(205\) −0.839347 + 0.839347i −0.0586226 + 0.0586226i
\(206\) 11.5031 4.69018i 0.801460 0.326781i
\(207\) −13.7450 + 0.908553i −0.955344 + 0.0631488i
\(208\) −11.0994 11.6030i −0.769602 0.804523i
\(209\) 3.89730i 0.269582i
\(210\) −6.25961 + 2.79654i −0.431954 + 0.192980i
\(211\) 0.568585 + 0.568585i 0.0391430 + 0.0391430i 0.726407 0.687264i \(-0.241189\pi\)
−0.687264 + 0.726407i \(0.741189\pi\)
\(212\) −0.221998 + 20.0162i −0.0152469 + 1.37472i
\(213\) 10.0707 10.7584i 0.690036 0.737154i
\(214\) 21.7303 + 9.14249i 1.48545 + 0.624968i
\(215\) 6.84623i 0.466909i
\(216\) −6.72239 13.0694i −0.457401 0.889261i
\(217\) 6.03914i 0.409963i
\(218\) −0.759297 + 1.80473i −0.0514261 + 0.122232i
\(219\) 6.08030 6.49548i 0.410868 0.438924i
\(220\) −4.16085 + 4.06956i −0.280524 + 0.274370i
\(221\) −11.0526 11.0526i −0.743478 0.743478i
\(222\) 10.2198 + 22.8753i 0.685906 + 1.53529i
\(223\) 10.5154i 0.704163i −0.935969 0.352081i \(-0.885474\pi\)
0.935969 0.352081i \(-0.114526\pi\)
\(224\) 2.01907 + 5.28426i 0.134905 + 0.353069i
\(225\) 8.48316 0.560741i 0.565544 0.0373828i
\(226\) 3.92768 + 9.63299i 0.261265 + 0.640777i
\(227\) 18.4341 18.4341i 1.22352 1.22352i 0.257144 0.966373i \(-0.417219\pi\)
0.966373 0.257144i \(-0.0827814\pi\)
\(228\) −9.38071 8.97836i −0.621252 0.594606i
\(229\) 8.85041 + 8.85041i 0.584851 + 0.584851i 0.936232 0.351381i \(-0.114288\pi\)
−0.351381 + 0.936232i \(0.614288\pi\)
\(230\) −16.7527 7.04827i −1.10464 0.464749i
\(231\) −0.0594210 1.79986i −0.00390962 0.118422i
\(232\) −25.7897 + 10.1832i −1.69317 + 0.668558i
\(233\) −2.34164 −0.153406 −0.0767030 0.997054i \(-0.524439\pi\)
−0.0767030 + 0.997054i \(0.524439\pi\)
\(234\) −16.0996 5.55484i −1.05246 0.363131i
\(235\) −6.83089 + 6.83089i −0.445598 + 0.445598i
\(236\) 5.54281 + 0.0614748i 0.360806 + 0.00400167i
\(237\) −3.14324 + 3.35787i −0.204176 + 0.218117i
\(238\) 2.07908 + 5.09914i 0.134767 + 0.330528i
\(239\) −4.23101 −0.273681 −0.136841 0.990593i \(-0.543695\pi\)
−0.136841 + 0.990593i \(0.543695\pi\)
\(240\) −0.209838 19.3903i −0.0135450 1.25164i
\(241\) −7.44279 −0.479432 −0.239716 0.970843i \(-0.577054\pi\)
−0.239716 + 0.970843i \(0.577054\pi\)
\(242\) 5.29617 + 12.9894i 0.340451 + 0.834987i
\(243\) −12.6836 9.06235i −0.813654 0.581350i
\(244\) −0.00204956 + 0.184796i −0.000131210 + 0.0118304i
\(245\) 1.97913 1.97913i 0.126442 0.126442i
\(246\) 0.970304 + 0.371044i 0.0618643 + 0.0236569i
\(247\) −15.0471 −0.957423
\(248\) −15.6701 6.79833i −0.995053 0.431694i
\(249\) 1.63248 0.0538950i 0.103454 0.00341546i
\(250\) −7.90304 3.32501i −0.499832 0.210292i
\(251\) 2.89305 + 2.89305i 0.182607 + 0.182607i 0.792491 0.609884i \(-0.208784\pi\)
−0.609884 + 0.792491i \(0.708784\pi\)
\(252\) 4.46911 + 4.00338i 0.281527 + 0.252189i
\(253\) 3.37575 3.37575i 0.212231 0.212231i
\(254\) −10.8031 26.4957i −0.677849 1.66249i
\(255\) −0.622861 18.8664i −0.0390050 1.18146i
\(256\) −15.9843 0.709556i −0.999016 0.0443472i
\(257\) 17.5346i 1.09378i 0.837206 + 0.546888i \(0.184188\pi\)
−0.837206 + 0.546888i \(0.815812\pi\)
\(258\) 5.47043 2.44397i 0.340574 0.152155i
\(259\) −7.23258 7.23258i −0.449411 0.449411i
\(260\) −15.7122 16.0646i −0.974428 0.996285i
\(261\) −19.3786 + 22.1218i −1.19950 + 1.36930i
\(262\) −4.70249 + 11.1771i −0.290521 + 0.690524i
\(263\) 27.4008i 1.68961i −0.535077 0.844803i \(-0.679717\pi\)
0.535077 0.844803i \(-0.320283\pi\)
\(264\) 4.73709 + 1.87194i 0.291548 + 0.115210i
\(265\) 28.0135i 1.72086i
\(266\) 4.88623 + 2.05576i 0.299594 + 0.126047i
\(267\) −17.9387 16.7921i −1.09783 1.02766i
\(268\) 27.6511 + 0.306675i 1.68906 + 0.0187332i
\(269\) 16.5057 + 16.5057i 1.00637 + 1.00637i 0.999980 + 0.00638853i \(0.00203354\pi\)
0.00638853 + 0.999980i \(0.497966\pi\)
\(270\) −9.60994 18.1846i −0.584843 1.10668i
\(271\) 19.7618i 1.20044i −0.799833 0.600222i \(-0.795079\pi\)
0.799833 0.600222i \(-0.204921\pi\)
\(272\) −15.5715 0.345446i −0.944159 0.0209457i
\(273\) 6.94907 0.229419i 0.420577 0.0138850i
\(274\) 22.9060 9.33952i 1.38380 0.564221i
\(275\) −2.08345 + 2.08345i −0.125637 + 0.125637i
\(276\) 0.348502 + 15.9022i 0.0209773 + 0.957199i
\(277\) −0.876958 0.876958i −0.0526913 0.0526913i 0.680270 0.732961i \(-0.261862\pi\)
−0.732961 + 0.680270i \(0.761862\pi\)
\(278\) 1.43136 3.40214i 0.0858476 0.204047i
\(279\) −18.0780 + 1.19496i −1.08230 + 0.0715406i
\(280\) 2.90743 + 7.36328i 0.173752 + 0.440040i
\(281\) 25.1587 1.50084 0.750422 0.660959i \(-0.229851\pi\)
0.750422 + 0.660959i \(0.229851\pi\)
\(282\) 7.89666 + 3.01968i 0.470239 + 0.179819i
\(283\) −23.1011 + 23.1011i −1.37322 + 1.37322i −0.517589 + 0.855629i \(0.673170\pi\)
−0.855629 + 0.517589i \(0.826830\pi\)
\(284\) −11.8981 12.1650i −0.706022 0.721858i
\(285\) −13.2664 12.4184i −0.785834 0.735605i
\(286\) 5.46560 2.22850i 0.323187 0.131774i
\(287\) −0.424100 −0.0250338
\(288\) −15.4187 + 7.08961i −0.908558 + 0.417759i
\(289\) 1.83812 0.108125
\(290\) −35.9312 + 14.6503i −2.10995 + 0.860294i
\(291\) −15.1469 14.1787i −0.887925 0.831170i
\(292\) −7.18357 7.34470i −0.420387 0.429816i
\(293\) 14.2144 14.2144i 0.830415 0.830415i −0.157158 0.987573i \(-0.550233\pi\)
0.987573 + 0.157158i \(0.0502333\pi\)
\(294\) −2.28791 0.874897i −0.133434 0.0510251i
\(295\) 7.75739 0.451653
\(296\) 26.9086 10.6250i 1.56403 0.617566i
\(297\) 5.37606 0.534013i 0.311951 0.0309866i
\(298\) −1.99412 + 4.73973i −0.115517 + 0.274565i
\(299\) 13.0334 + 13.0334i 0.753742 + 0.753742i
\(300\) −0.215089 9.81452i −0.0124181 0.566642i
\(301\) −1.72961 + 1.72961i −0.0996930 + 0.0996930i
\(302\) 3.85532 1.57194i 0.221849 0.0904549i
\(303\) 30.1189 0.994354i 1.73029 0.0571242i
\(304\) −10.8347 + 10.3644i −0.621412 + 0.594439i
\(305\) 0.258630i 0.0148091i
\(306\) −14.8527 + 7.23262i −0.849073 + 0.413462i
\(307\) −3.47944 3.47944i −0.198582 0.198582i 0.600810 0.799392i \(-0.294845\pi\)
−0.799392 + 0.600810i \(0.794845\pi\)
\(308\) −2.07930 0.0230613i −0.118479 0.00131404i
\(309\) −11.1074 10.3974i −0.631875 0.591487i
\(310\) −22.0338 9.27016i −1.25143 0.526510i
\(311\) 13.6519i 0.774127i −0.922053 0.387064i \(-0.873489\pi\)
0.922053 0.387064i \(-0.126511\pi\)
\(312\) −7.22737 + 18.2894i −0.409169 + 1.03544i
\(313\) 4.68752i 0.264954i −0.991186 0.132477i \(-0.957707\pi\)
0.991186 0.132477i \(-0.0422931\pi\)
\(314\) −4.93583 + 11.7317i −0.278545 + 0.662060i
\(315\) 6.31606 + 5.53284i 0.355870 + 0.311740i
\(316\) 3.71359 + 3.79688i 0.208906 + 0.213591i
\(317\) 14.0564 + 14.0564i 0.789488 + 0.789488i 0.981410 0.191922i \(-0.0614720\pi\)
−0.191922 + 0.981410i \(0.561472\pi\)
\(318\) 22.3840 10.0003i 1.25523 0.560787i
\(319\) 10.1924i 0.570666i
\(320\) −22.3789 0.744850i −1.25102 0.0416384i
\(321\) −0.952723 28.8579i −0.0531758 1.61069i
\(322\) −2.45169 6.01299i −0.136627 0.335091i
\(323\) −10.3207 + 10.3207i −0.574261 + 0.574261i
\(324\) −11.0997 + 14.1703i −0.616649 + 0.787238i
\(325\) −8.04398 8.04398i −0.446199 0.446199i
\(326\) 19.2852 + 8.11376i 1.06811 + 0.449380i
\(327\) 2.39669 0.0791250i 0.132537 0.00437562i
\(328\) 0.477414 1.10044i 0.0263608 0.0607615i
\(329\) −3.45146 −0.190285
\(330\) 6.65799 + 2.54601i 0.366510 + 0.140153i
\(331\) 12.4869 12.4869i 0.686342 0.686342i −0.275080 0.961421i \(-0.588704\pi\)
0.961421 + 0.275080i \(0.0887043\pi\)
\(332\) 0.0209167 1.88593i 0.00114795 0.103504i
\(333\) 20.2194 23.0816i 1.10802 1.26486i
\(334\) −3.13701 7.69380i −0.171649 0.420986i
\(335\) 38.6988 2.11434
\(336\) 4.84568 4.95171i 0.264354 0.270138i
\(337\) −9.96314 −0.542727 −0.271363 0.962477i \(-0.587474\pi\)
−0.271363 + 0.962477i \(0.587474\pi\)
\(338\) 1.66274 + 4.07803i 0.0904414 + 0.221816i
\(339\) 8.70704 9.30158i 0.472901 0.505192i
\(340\) −21.7956 0.241733i −1.18203 0.0131098i
\(341\) 4.43991 4.43991i 0.240435 0.240435i
\(342\) −5.18702 + 15.0336i −0.280482 + 0.812922i
\(343\) 1.00000 0.0539949
\(344\) −2.54088 6.43496i −0.136995 0.346950i
\(345\) 0.734488 + 22.2476i 0.0395435 + 1.19777i
\(346\) −10.4254 4.38623i −0.560473 0.235805i
\(347\) 6.06219 + 6.06219i 0.325435 + 0.325435i 0.850848 0.525412i \(-0.176089\pi\)
−0.525412 + 0.850848i \(0.676089\pi\)
\(348\) 24.5329 + 23.4807i 1.31510 + 1.25870i
\(349\) 7.31976 7.31976i 0.391818 0.391818i −0.483517 0.875335i \(-0.660641\pi\)
0.875335 + 0.483517i \(0.160641\pi\)
\(350\) 1.51313 + 3.71110i 0.0808804 + 0.198367i
\(351\) 2.06177 + 20.7564i 0.110049 + 1.10790i
\(352\) 2.40053 5.36933i 0.127949 0.286186i
\(353\) 15.5092i 0.825472i 0.910851 + 0.412736i \(0.135427\pi\)
−0.910851 + 0.412736i \(0.864573\pi\)
\(354\) −2.76923 6.19848i −0.147183 0.329446i
\(355\) −16.8386 16.8386i −0.893701 0.893701i
\(356\) −20.2840 + 19.8390i −1.07505 + 1.05146i
\(357\) 4.60899 4.92370i 0.243934 0.260590i
\(358\) 7.58412 18.0263i 0.400833 0.952719i
\(359\) 17.0316i 0.898894i 0.893307 + 0.449447i \(0.148379\pi\)
−0.893307 + 0.449447i \(0.851621\pi\)
\(360\) −21.4665 + 10.1603i −1.13138 + 0.535493i
\(361\) 4.94928i 0.260489i
\(362\) −32.3335 13.6035i −1.69941 0.714985i
\(363\) 11.7408 12.5425i 0.616231 0.658309i
\(364\) 0.0890375 8.02798i 0.00466683 0.420780i
\(365\) −10.1664 10.1664i −0.532136 0.532136i
\(366\) 0.206656 0.0923258i 0.0108021 0.00482594i
\(367\) 23.1877i 1.21039i 0.796078 + 0.605194i \(0.206905\pi\)
−0.796078 + 0.605194i \(0.793095\pi\)
\(368\) 18.3622 + 0.407356i 0.957194 + 0.0212349i
\(369\) −0.0839166 1.26953i −0.00436852 0.0660890i
\(370\) 37.4901 15.2859i 1.94902 0.794677i
\(371\) −7.07724 + 7.07724i −0.367432 + 0.367432i
\(372\) 0.458363 + 20.9152i 0.0237650 + 1.08440i
\(373\) 19.3034 + 19.3034i 0.999491 + 0.999491i 1.00000 0.000509216i \(-0.000162088\pi\)
−0.000509216 1.00000i \(0.500162\pi\)
\(374\) 2.22031 5.27735i 0.114810 0.272885i
\(375\) 0.346493 + 10.4953i 0.0178928 + 0.541973i
\(376\) 3.88535 8.95572i 0.200372 0.461856i
\(377\) 39.3519 2.02672
\(378\) 2.16627 7.02191i 0.111421 0.361168i
\(379\) 5.35540 5.35540i 0.275088 0.275088i −0.556056 0.831145i \(-0.687686\pi\)
0.831145 + 0.556056i \(0.187686\pi\)
\(380\) −15.0009 + 14.6718i −0.769528 + 0.752646i
\(381\) −23.9489 + 25.5841i −1.22694 + 1.31072i
\(382\) 14.1520 5.77022i 0.724080 0.295230i
\(383\) 11.4760 0.586394 0.293197 0.956052i \(-0.405281\pi\)
0.293197 + 0.956052i \(0.405281\pi\)
\(384\) 7.39364 + 18.1476i 0.377305 + 0.926089i
\(385\) −2.91007 −0.148311
\(386\) −1.13319 + 0.462039i −0.0576780 + 0.0235172i
\(387\) −5.51977 4.83529i −0.280586 0.245792i
\(388\) −17.1272 + 16.7514i −0.869501 + 0.850425i
\(389\) 13.4649 13.4649i 0.682699 0.682699i −0.277909 0.960608i \(-0.589641\pi\)
0.960608 + 0.277909i \(0.0896413\pi\)
\(390\) −9.82989 + 25.7058i −0.497756 + 1.30166i
\(391\) 17.8792 0.904188
\(392\) −1.12571 + 2.59476i −0.0568570 + 0.131055i
\(393\) 14.8432 0.490038i 0.748742 0.0247192i
\(394\) 6.54325 15.5523i 0.329644 0.783514i
\(395\) 5.25560 + 5.25560i 0.264438 + 0.264438i
\(396\) −0.342398 6.22889i −0.0172062 0.313013i
\(397\) −12.0340 + 12.0340i −0.603969 + 0.603969i −0.941363 0.337395i \(-0.890454\pi\)
0.337395 + 0.941363i \(0.390454\pi\)
\(398\) −20.9199 + 8.52972i −1.04862 + 0.427556i
\(399\) −0.214227 6.48893i −0.0107248 0.324853i
\(400\) −11.3328 0.251412i −0.566638 0.0125706i
\(401\) 25.5890i 1.27786i −0.769267 0.638928i \(-0.779378\pi\)
0.769267 0.638928i \(-0.220622\pi\)
\(402\) −13.8147 30.9220i −0.689014 1.54225i
\(403\) 17.1421 + 17.1421i 0.853906 + 0.853906i
\(404\) 0.385909 34.7952i 0.0191997 1.73112i
\(405\) −15.3126 + 20.0017i −0.760891 + 0.993893i
\(406\) −12.7787 5.37633i −0.634198 0.266823i
\(407\) 10.6346i 0.527140i
\(408\) 7.58743 + 17.5019i 0.375634 + 0.866472i
\(409\) 15.7110i 0.776860i −0.921478 0.388430i \(-0.873018\pi\)
0.921478 0.388430i \(-0.126982\pi\)
\(410\) 0.650999 1.54733i 0.0321505 0.0764170i
\(411\) −22.1180 20.7042i −1.09100 1.02126i
\(412\) −12.5595 + 12.2840i −0.618764 + 0.605189i
\(413\) 1.95980 + 1.95980i 0.0964355 + 0.0964355i
\(414\) 17.5146 8.52884i 0.860795 0.419169i
\(415\) 2.63944i 0.129565i
\(416\) 20.7304 + 9.26822i 1.01639 + 0.454412i
\(417\) −4.51805 + 0.149160i −0.221250 + 0.00730440i
\(418\) −2.08093 5.10369i −0.101782 0.249629i
\(419\) −24.2201 + 24.2201i −1.18323 + 1.18323i −0.204324 + 0.978903i \(0.565500\pi\)
−0.978903 + 0.204324i \(0.934500\pi\)
\(420\) 6.70404 7.00447i 0.327124 0.341783i
\(421\) −10.2110 10.2110i −0.497652 0.497652i 0.413054 0.910706i \(-0.364462\pi\)
−0.910706 + 0.413054i \(0.864462\pi\)
\(422\) −1.04818 0.440995i −0.0510245 0.0214673i
\(423\) −0.682941 10.3318i −0.0332057 0.502352i
\(424\) −10.3968 26.3306i −0.504913 1.27873i
\(425\) −11.0347 −0.535260
\(426\) −7.44372 + 19.4658i −0.360649 + 0.943122i
\(427\) −0.0653394 + 0.0653394i −0.00316200 + 0.00316200i
\(428\) −33.3384 0.369752i −1.61147 0.0178726i
\(429\) −5.27756 4.94022i −0.254803 0.238516i
\(430\) −3.65550 8.96544i −0.176284 0.432352i
\(431\) −4.69315 −0.226061 −0.113031 0.993592i \(-0.536056\pi\)
−0.113031 + 0.993592i \(0.536056\pi\)
\(432\) 15.7816 + 13.5256i 0.759292 + 0.650750i
\(433\) 22.8408 1.09766 0.548829 0.835935i \(-0.315074\pi\)
0.548829 + 0.835935i \(0.315074\pi\)
\(434\) −3.22455 7.90852i −0.154784 0.379621i
\(435\) 34.6950 + 32.4773i 1.66350 + 1.55717i
\(436\) 0.0307085 2.76880i 0.00147067 0.132601i
\(437\) 12.1704 12.1704i 0.582189 0.582189i
\(438\) −4.49420 + 11.7526i −0.214741 + 0.561563i
\(439\) −10.3738 −0.495113 −0.247556 0.968873i \(-0.579628\pi\)
−0.247556 + 0.968873i \(0.579628\pi\)
\(440\) 3.27590 7.55093i 0.156172 0.359976i
\(441\) 0.197870 + 2.99347i 0.00942238 + 0.142546i
\(442\) 20.3753 + 8.57241i 0.969155 + 0.407748i
\(443\) −23.7210 23.7210i −1.12702 1.12702i −0.990660 0.136359i \(-0.956460\pi\)
−0.136359 0.990660i \(-0.543540\pi\)
\(444\) −25.5973 24.4994i −1.21480 1.16269i
\(445\) −28.0769 + 28.0769i −1.33097 + 1.33097i
\(446\) 5.61462 + 13.7704i 0.265860 + 0.652046i
\(447\) 6.29438 0.207804i 0.297714 0.00982881i
\(448\) −5.46555 5.84190i −0.258223 0.276004i
\(449\) 7.24900i 0.342101i 0.985262 + 0.171051i \(0.0547162\pi\)
−0.985262 + 0.171051i \(0.945284\pi\)
\(450\) −10.8097 + 5.26383i −0.509572 + 0.248140i
\(451\) 0.311794 + 0.311794i 0.0146818 + 0.0146818i
\(452\) −10.2869 10.5177i −0.483857 0.494710i
\(453\) −3.72268 3.48474i −0.174907 0.163727i
\(454\) −14.2975 + 33.9831i −0.671017 + 1.59491i
\(455\) 11.2355i 0.526727i
\(456\) 17.0784 + 6.74880i 0.799768 + 0.316041i
\(457\) 10.4702i 0.489775i 0.969551 + 0.244888i \(0.0787511\pi\)
−0.969551 + 0.244888i \(0.921249\pi\)
\(458\) −16.3156 6.86439i −0.762378 0.320752i
\(459\) 15.6509 + 12.8226i 0.730523 + 0.598508i
\(460\) 25.7017 + 0.285055i 1.19835 + 0.0132908i
\(461\) 0.786465 + 0.786465i 0.0366293 + 0.0366293i 0.725184 0.688555i \(-0.241755\pi\)
−0.688555 + 0.725184i \(0.741755\pi\)
\(462\) 1.03884 + 2.32527i 0.0483310 + 0.108181i
\(463\) 11.7932i 0.548076i −0.961719 0.274038i \(-0.911641\pi\)
0.961719 0.274038i \(-0.0883594\pi\)
\(464\) 28.3354 27.1055i 1.31544 1.25834i
\(465\) 0.966027 + 29.2609i 0.0447984 + 1.35694i
\(466\) 3.06648 1.25030i 0.142052 0.0579191i
\(467\) −12.7443 + 12.7443i −0.589734 + 0.589734i −0.937559 0.347826i \(-0.886920\pi\)
0.347826 + 0.937559i \(0.386920\pi\)
\(468\) 24.0491 1.32196i 1.11167 0.0611078i
\(469\) 9.77673 + 9.77673i 0.451447 + 0.451447i
\(470\) 5.29804 12.5926i 0.244381 0.580856i
\(471\) 15.5798 0.514355i 0.717878 0.0237002i
\(472\) −7.29138 + 2.87904i −0.335613 + 0.132519i
\(473\) 2.54318 0.116936
\(474\) 2.32330 6.07559i 0.106713 0.279061i
\(475\) −7.51134 + 7.51134i −0.344644 + 0.344644i
\(476\) −5.44529 5.56743i −0.249585 0.255183i
\(477\) −22.5858 19.7851i −1.03413 0.905898i
\(478\) 5.54069 2.25912i 0.253425 0.103330i
\(479\) 12.4359 0.568213 0.284106 0.958793i \(-0.408303\pi\)
0.284106 + 0.958793i \(0.408303\pi\)
\(480\) 10.6281 + 25.2804i 0.485103 + 1.15389i
\(481\) −41.0593 −1.87214
\(482\) 9.74666 3.97402i 0.443948 0.181012i
\(483\) −5.43500 + 5.80612i −0.247301 + 0.264188i
\(484\) −13.8711 14.1823i −0.630506 0.644649i
\(485\) −23.7072 + 23.7072i −1.07649 + 1.07649i
\(486\) 21.4485 + 5.09523i 0.972924 + 0.231124i
\(487\) 5.45746 0.247301 0.123651 0.992326i \(-0.460540\pi\)
0.123651 + 0.992326i \(0.460540\pi\)
\(488\) −0.0959867 0.243093i −0.00434511 0.0110043i
\(489\) −0.845521 25.6108i −0.0382358 1.15816i
\(490\) −1.53501 + 3.64849i −0.0693448 + 0.164822i
\(491\) 15.9959 + 15.9959i 0.721886 + 0.721886i 0.968989 0.247103i \(-0.0794787\pi\)
−0.247103 + 0.968989i \(0.579479\pi\)
\(492\) −1.46877 + 0.0321886i −0.0662174 + 0.00145118i
\(493\) 26.9913 26.9913i 1.21563 1.21563i
\(494\) 19.7048 8.03428i 0.886561 0.361479i
\(495\) −0.575815 8.71120i −0.0258810 0.391539i
\(496\) 24.1506 + 0.535770i 1.08439 + 0.0240568i
\(497\) 8.50810i 0.381640i
\(498\) −2.10902 + 0.942227i −0.0945076 + 0.0422222i
\(499\) 15.9973 + 15.9973i 0.716137 + 0.716137i 0.967812 0.251675i \(-0.0809813\pi\)
−0.251675 + 0.967812i \(0.580981\pi\)
\(500\) 12.1247 + 0.134474i 0.542235 + 0.00601387i
\(501\) −6.95424 + 7.42910i −0.310693 + 0.331908i
\(502\) −5.33329 2.24385i −0.238036 0.100148i
\(503\) 22.2817i 0.993490i −0.867897 0.496745i \(-0.834528\pi\)
0.867897 0.496745i \(-0.165472\pi\)
\(504\) −7.99007 2.85636i −0.355906 0.127232i
\(505\) 48.6972i 2.16700i
\(506\) −2.61823 + 6.22315i −0.116395 + 0.276653i
\(507\) 3.68604 3.93773i 0.163703 0.174881i
\(508\) 28.2944 + 28.9290i 1.25536 + 1.28352i
\(509\) 22.7995 + 22.7995i 1.01057 + 1.01057i 0.999944 + 0.0106261i \(0.00338245\pi\)
0.0106261 + 0.999944i \(0.496618\pi\)
\(510\) 10.8892 + 24.3738i 0.482184 + 1.07929i
\(511\) 5.13683i 0.227240i
\(512\) 21.3110 7.60548i 0.941820 0.336118i
\(513\) 19.3820 1.92525i 0.855737 0.0850017i
\(514\) −9.36245 22.9623i −0.412960 1.01282i
\(515\) −17.3848 + 17.3848i −0.766065 + 0.766065i
\(516\) −5.85883 + 6.12138i −0.257921 + 0.269479i
\(517\) 2.53748 + 2.53748i 0.111598 + 0.111598i
\(518\) 13.3332 + 5.60960i 0.585826 + 0.246472i
\(519\) 0.457082 + 13.8450i 0.0200637 + 0.607727i
\(520\) 29.1534 + 12.6479i 1.27846 + 0.554647i
\(521\) −25.3376 −1.11006 −0.555030 0.831831i \(-0.687293\pi\)
−0.555030 + 0.831831i \(0.687293\pi\)
\(522\) 13.5654 39.3165i 0.593739 1.72084i
\(523\) 18.0986 18.0986i 0.791395 0.791395i −0.190326 0.981721i \(-0.560955\pi\)
0.981721 + 0.190326i \(0.0609545\pi\)
\(524\) 0.190184 17.1478i 0.00830824 0.749104i
\(525\) 3.35438 3.58342i 0.146397 0.156393i
\(526\) 14.6305 + 35.8826i 0.637919 + 1.56455i
\(527\) 23.5153 1.02434
\(528\) −7.20294 + 0.0779489i −0.313468 + 0.00339229i
\(529\) 1.91658 0.0833295
\(530\) −14.9576 36.6849i −0.649717 1.59349i
\(531\) −5.47882 + 6.25439i −0.237760 + 0.271417i
\(532\) −7.49640 0.0831418i −0.325010 0.00360465i
\(533\) −1.20380 + 1.20380i −0.0521426 + 0.0521426i
\(534\) 32.4575 + 12.4117i 1.40457 + 0.537108i
\(535\) −46.6584 −2.01722
\(536\) −36.3740 + 14.3625i −1.57112 + 0.620365i
\(537\) −23.9390 + 0.790327i −1.03304 + 0.0341051i
\(538\) −30.4280 12.8018i −1.31184 0.551925i
\(539\) −0.735190 0.735190i −0.0316669 0.0316669i
\(540\) 22.2942 + 18.6823i 0.959388 + 0.803960i
\(541\) 3.85585 3.85585i 0.165776 0.165776i −0.619344 0.785120i \(-0.712601\pi\)
0.785120 + 0.619344i \(0.212601\pi\)
\(542\) 10.5517 + 25.8790i 0.453233 + 1.11160i
\(543\) 1.41760 + 42.9390i 0.0608350 + 1.84269i
\(544\) 20.5760 7.86190i 0.882188 0.337076i
\(545\) 3.87505i 0.165989i
\(546\) −8.97762 + 4.01084i −0.384207 + 0.171648i
\(547\) 3.89933 + 3.89933i 0.166723 + 0.166723i 0.785537 0.618814i \(-0.212387\pi\)
−0.618814 + 0.785537i \(0.712387\pi\)
\(548\) −25.0097 + 24.4610i −1.06836 + 1.04492i
\(549\) −0.208520 0.182663i −0.00889942 0.00779586i
\(550\) 1.61592 3.84081i 0.0689032 0.163773i
\(551\) 36.7462i 1.56544i
\(552\) −8.94723 20.6385i −0.380820 0.878434i
\(553\) 2.65552i 0.112924i
\(554\) 1.61666 + 0.680170i 0.0686853 + 0.0288976i
\(555\) −36.2003 33.8865i −1.53662 1.43840i
\(556\) −0.0578891 + 5.21951i −0.00245504 + 0.221357i
\(557\) −13.6931 13.6931i −0.580195 0.580195i 0.354762 0.934957i \(-0.384562\pi\)
−0.934957 + 0.354762i \(0.884562\pi\)
\(558\) 23.0358 11.2175i 0.975185 0.474873i
\(559\) 9.81897i 0.415298i
\(560\) −7.73898 8.09014i −0.327032 0.341871i
\(561\) −7.00834 + 0.231375i −0.295892 + 0.00976867i
\(562\) −32.9464 + 13.4333i −1.38976 + 0.566650i
\(563\) −11.5660 + 11.5660i −0.487450 + 0.487450i −0.907501 0.420050i \(-0.862012\pi\)
0.420050 + 0.907501i \(0.362012\pi\)
\(564\) −11.9534 + 0.261962i −0.503327 + 0.0110306i
\(565\) −14.5584 14.5584i −0.612478 0.612478i
\(566\) 17.9173 42.5866i 0.753118 1.79005i
\(567\) −8.92169 + 1.18463i −0.374676 + 0.0497500i
\(568\) 22.0765 + 9.57767i 0.926308 + 0.401870i
\(569\) 5.95769 0.249759 0.124880 0.992172i \(-0.460146\pi\)
0.124880 + 0.992172i \(0.460146\pi\)
\(570\) 24.0037 + 9.17899i 1.00540 + 0.384466i
\(571\) 11.7621 11.7621i 0.492228 0.492228i −0.416779 0.909008i \(-0.636841\pi\)
0.909008 + 0.416779i \(0.136841\pi\)
\(572\) −5.96755 + 5.83663i −0.249516 + 0.244042i
\(573\) −13.6651 12.7917i −0.570869 0.534380i
\(574\) 0.555377 0.226445i 0.0231810 0.00945163i
\(575\) 13.0123 0.542650
\(576\) 16.4061 17.5169i 0.683586 0.729870i
\(577\) 4.01062 0.166964 0.0834821 0.996509i \(-0.473396\pi\)
0.0834821 + 0.996509i \(0.473396\pi\)
\(578\) −2.40710 + 0.981451i −0.100122 + 0.0408230i
\(579\) 1.09421 + 1.02427i 0.0454737 + 0.0425671i
\(580\) 39.2310 38.3704i 1.62898 1.59324i
\(581\) 0.666819 0.666819i 0.0276643 0.0276643i
\(582\) 27.4061 + 10.4801i 1.13602 + 0.434413i
\(583\) 10.4062 0.430982
\(584\) 13.3288 + 5.78259i 0.551552 + 0.239285i
\(585\) 33.6330 2.22316i 1.39056 0.0919165i
\(586\) −11.0247 + 26.2041i −0.455427 + 1.08248i
\(587\) −21.7757 21.7757i −0.898780 0.898780i 0.0965487 0.995328i \(-0.469220\pi\)
−0.995328 + 0.0965487i \(0.969220\pi\)
\(588\) 3.46327 0.0758987i 0.142823 0.00313001i
\(589\) 16.0070 16.0070i 0.659556 0.659556i
\(590\) −10.1586 + 4.14200i −0.418225 + 0.170524i
\(591\) −20.6535 + 0.681860i −0.849572 + 0.0280480i
\(592\) −29.5649 + 28.2816i −1.21511 + 1.16236i
\(593\) 13.0247i 0.534858i 0.963578 + 0.267429i \(0.0861742\pi\)
−0.963578 + 0.267429i \(0.913826\pi\)
\(594\) −6.75506 + 3.56982i −0.277163 + 0.146472i
\(595\) −7.70638 7.70638i −0.315931 0.315931i
\(596\) 0.0806490 7.27164i 0.00330351 0.297858i
\(597\) 20.2002 + 18.9090i 0.826739 + 0.773895i
\(598\) −24.0269 10.1087i −0.982534 0.413377i
\(599\) 21.4927i 0.878167i −0.898446 0.439084i \(-0.855303\pi\)
0.898446 0.439084i \(-0.144697\pi\)
\(600\) 5.52206 + 12.7377i 0.225437 + 0.520015i
\(601\) 23.8156i 0.971457i 0.874110 + 0.485729i \(0.161446\pi\)
−0.874110 + 0.485729i \(0.838554\pi\)
\(602\) 1.34149 3.18851i 0.0546749 0.129954i
\(603\) −27.3318 + 31.2008i −1.11304 + 1.27060i
\(604\) −4.20939 + 4.11704i −0.171278 + 0.167520i
\(605\) −19.6309 19.6309i −0.798111 0.798111i
\(606\) −38.9111 + 17.3839i −1.58066 + 0.706174i
\(607\) 5.27673i 0.214176i 0.994250 + 0.107088i \(0.0341527\pi\)
−0.994250 + 0.107088i \(0.965847\pi\)
\(608\) 8.65451 19.3577i 0.350987 0.785060i
\(609\) 0.560258 + 16.9702i 0.0227028 + 0.687667i
\(610\) −0.138094 0.338687i −0.00559125 0.0137131i
\(611\) −9.79696 + 9.79696i −0.396342 + 0.396342i
\(612\) 15.5885 17.4019i 0.630127 0.703431i
\(613\) 7.64313 + 7.64313i 0.308703 + 0.308703i 0.844406 0.535703i \(-0.179953\pi\)
−0.535703 + 0.844406i \(0.679953\pi\)
\(614\) 6.41430 + 2.69866i 0.258860 + 0.108909i
\(615\) −2.05485 + 0.0678395i −0.0828597 + 0.00273555i
\(616\) 2.73525 1.08003i 0.110206 0.0435156i
\(617\) 18.4206 0.741587 0.370793 0.928715i \(-0.379086\pi\)
0.370793 + 0.928715i \(0.379086\pi\)
\(618\) 20.0972 + 7.68515i 0.808427 + 0.309142i
\(619\) 16.6942 16.6942i 0.670998 0.670998i −0.286948 0.957946i \(-0.592641\pi\)
0.957946 + 0.286948i \(0.0926406\pi\)
\(620\) 33.8039 + 0.374916i 1.35760 + 0.0150570i
\(621\) −18.4559 15.1206i −0.740608 0.606771i
\(622\) 7.28932 + 17.8777i 0.292275 + 0.716832i
\(623\) −14.1865 −0.568369
\(624\) −0.300953 27.8098i −0.0120477 1.11328i
\(625\) 31.1385 1.24554
\(626\) 2.50287 + 6.13852i 0.100035 + 0.245345i
\(627\) −4.61310 + 4.92810i −0.184230 + 0.196809i
\(628\) 0.199621 17.9987i 0.00796576 0.718225i
\(629\) −28.1624 + 28.1624i −1.12291 + 1.12291i
\(630\) −11.2254 3.87309i −0.447230 0.154307i
\(631\) 32.8077 1.30605 0.653027 0.757335i \(-0.273499\pi\)
0.653027 + 0.757335i \(0.273499\pi\)
\(632\) −6.89042 2.98934i −0.274086 0.118910i
\(633\) 0.0459553 + 1.39198i 0.00182656 + 0.0553264i
\(634\) −25.9129 10.9022i −1.02913 0.432981i
\(635\) 40.0432 + 40.0432i 1.58907 + 1.58907i
\(636\) −23.9732 + 25.0475i −0.950600 + 0.993199i
\(637\) 2.83849 2.83849i 0.112465 0.112465i
\(638\) 5.44217 + 13.3474i 0.215457 + 0.528429i
\(639\) 25.4687 1.68350i 1.00753 0.0665981i
\(640\) 29.7038 10.9736i 1.17415 0.433771i
\(641\) 25.4996i 1.00718i 0.863944 + 0.503588i \(0.167987\pi\)
−0.863944 + 0.503588i \(0.832013\pi\)
\(642\) 16.6561 + 37.2820i 0.657364 + 1.47140i
\(643\) −24.4964 24.4964i −0.966043 0.966043i 0.0333995 0.999442i \(-0.489367\pi\)
−0.999442 + 0.0333995i \(0.989367\pi\)
\(644\) 6.42119 + 6.56522i 0.253030 + 0.258706i
\(645\) −8.10365 + 8.65699i −0.319081 + 0.340869i
\(646\) 8.00478 19.0261i 0.314944 0.748574i
\(647\) 4.04326i 0.158957i −0.996837 0.0794785i \(-0.974674\pi\)
0.996837 0.0794785i \(-0.0253255\pi\)
\(648\) 6.96941 24.4832i 0.273784 0.961791i
\(649\) 2.88165i 0.113115i
\(650\) 14.8290 + 6.23892i 0.581640 + 0.244710i
\(651\) −7.14832 + 7.63643i −0.280165 + 0.299295i
\(652\) −29.5871 0.328147i −1.15872 0.0128512i
\(653\) −14.0814 14.0814i −0.551046 0.551046i 0.375697 0.926743i \(-0.377403\pi\)
−0.926743 + 0.375697i \(0.877403\pi\)
\(654\) −3.09633 + 1.38331i −0.121076 + 0.0540919i
\(655\) 23.9990i 0.937719i
\(656\) −0.0376246 + 1.69598i −0.00146899 + 0.0662170i
\(657\) 15.3769 1.01642i 0.599912 0.0396545i
\(658\) 4.51984 1.84288i 0.176202 0.0718431i
\(659\) 2.27824 2.27824i 0.0887476 0.0887476i −0.661339 0.750087i \(-0.730012\pi\)
0.750087 + 0.661339i \(0.230012\pi\)
\(660\) −10.0784 + 0.220871i −0.392299 + 0.00859738i
\(661\) −22.1991 22.1991i −0.863443 0.863443i 0.128293 0.991736i \(-0.459050\pi\)
−0.991736 + 0.128293i \(0.959050\pi\)
\(662\) −9.68485 + 23.0194i −0.376412 + 0.894675i
\(663\) −0.893316 27.0585i −0.0346935 1.05086i
\(664\) 0.979589 + 2.48088i 0.0380154 + 0.0962769i
\(665\) −10.4915 −0.406843
\(666\) −14.1539 + 41.0224i −0.548453 + 1.58958i
\(667\) −31.8286 + 31.8286i −1.23241 + 1.23241i
\(668\) 8.21609 + 8.40039i 0.317890 + 0.325021i
\(669\) 12.4467 13.2966i 0.481218 0.514077i
\(670\) −50.6778 + 20.6629i −1.95785 + 0.798279i
\(671\) 0.0960738 0.00370889
\(672\) −3.70170 + 9.07179i −0.142796 + 0.349952i
\(673\) −40.3728 −1.55626 −0.778128 0.628105i \(-0.783831\pi\)
−0.778128 + 0.628105i \(0.783831\pi\)
\(674\) 13.0472 5.31974i 0.502558 0.204909i
\(675\) 11.3906 + 9.33217i 0.438424 + 0.359195i
\(676\) −4.35487 4.45256i −0.167495 0.171252i
\(677\) 17.2627 17.2627i 0.663460 0.663460i −0.292734 0.956194i \(-0.594565\pi\)
0.956194 + 0.292734i \(0.0945651\pi\)
\(678\) −6.43574 + 16.8299i −0.247163 + 0.646348i
\(679\) −11.9786 −0.459698
\(680\) 28.6713 11.3210i 1.09950 0.434142i
\(681\) 45.1297 1.48992i 1.72937 0.0570939i
\(682\) −3.44360 + 8.18492i −0.131862 + 0.313417i
\(683\) 6.43982 + 6.43982i 0.246413 + 0.246413i 0.819497 0.573084i \(-0.194253\pi\)
−0.573084 + 0.819497i \(0.694253\pi\)
\(684\) −1.23443 22.4567i −0.0471996 0.858652i
\(685\) −34.6181 + 34.6181i −1.32269 + 1.32269i
\(686\) −1.30954 + 0.533943i −0.0499986 + 0.0203860i
\(687\) 0.715326 + 21.6672i 0.0272914 + 0.826654i
\(688\) 6.76329 + 7.07018i 0.257848 + 0.269548i
\(689\) 40.1774i 1.53064i
\(690\) −12.8408 28.7420i −0.488841 1.09419i
\(691\) 34.9424 + 34.9424i 1.32927 + 1.32927i 0.906005 + 0.423267i \(0.139117\pi\)
0.423267 + 0.906005i \(0.360883\pi\)
\(692\) 15.9945 + 0.177394i 0.608020 + 0.00674349i
\(693\) 2.05530 2.34624i 0.0780742 0.0891263i
\(694\) −11.1756 4.70184i −0.424219 0.178479i
\(695\) 7.30492i 0.277091i
\(696\) −44.6642 17.6498i −1.69299 0.669014i
\(697\) 1.65137i 0.0625501i
\(698\) −5.67721 + 13.4939i −0.214886 + 0.510751i
\(699\) −2.96098 2.77172i −0.111995 0.104836i
\(700\) −3.96303 4.05192i −0.149789 0.153148i
\(701\) 23.3170 + 23.3170i 0.880671 + 0.880671i 0.993603 0.112931i \(-0.0360240\pi\)
−0.112931 + 0.993603i \(0.536024\pi\)
\(702\) −13.7827 26.0806i −0.520195 0.984349i
\(703\) 38.3405i 1.44604i
\(704\) −0.276691 + 8.31312i −0.0104282 + 0.313313i
\(705\) −16.7231 + 0.552100i −0.629827 + 0.0207933i
\(706\) −8.28103 20.3100i −0.311661 0.764377i
\(707\) 12.3027 12.3027i 0.462691 0.462691i
\(708\) 6.93607 + 6.63858i 0.260673 + 0.249493i
\(709\) −16.6951 16.6951i −0.626999 0.626999i 0.320313 0.947312i \(-0.396212\pi\)
−0.947312 + 0.320313i \(0.896212\pi\)
\(710\) 31.0418 + 13.0601i 1.16498 + 0.490135i
\(711\) −7.94920 + 0.525447i −0.298118 + 0.0197058i
\(712\) 15.9699 36.8105i 0.598497 1.37953i
\(713\) −27.7297 −1.03849
\(714\) −3.40670 + 8.90874i −0.127492 + 0.333401i
\(715\) −8.26021 + 8.26021i −0.308914 + 0.308914i
\(716\) −0.306727 + 27.6557i −0.0114629 + 1.03354i
\(717\) −5.35007 5.00810i −0.199802 0.187031i
\(718\) −9.09390 22.3036i −0.339381 0.832365i
\(719\) −23.6741 −0.882896 −0.441448 0.897287i \(-0.645535\pi\)
−0.441448 + 0.897287i \(0.645535\pi\)
\(720\) 22.6863 24.7672i 0.845467 0.923018i
\(721\) −8.78406 −0.327135
\(722\) 2.64263 + 6.48130i 0.0983486 + 0.241209i
\(723\) −9.41133 8.80978i −0.350011 0.327639i
\(724\) 49.6057 + 0.550171i 1.84358 + 0.0204470i
\(725\) 19.6440 19.6440i 0.729561 0.729561i
\(726\) −8.67810 + 22.6938i −0.322074 + 0.842246i
\(727\) 15.9011 0.589738 0.294869 0.955538i \(-0.404724\pi\)
0.294869 + 0.955538i \(0.404724\pi\)
\(728\) 4.16988 + 10.5605i 0.154546 + 0.391399i
\(729\) −5.31150 26.4724i −0.196722 0.980459i
\(730\) 18.7417 + 7.88511i 0.693662 + 0.291841i
\(731\) 6.73480 + 6.73480i 0.249095 + 0.249095i
\(732\) −0.221329 + 0.231247i −0.00818055 + 0.00854714i
\(733\) 3.64880 3.64880i 0.134771 0.134771i −0.636503 0.771274i \(-0.719620\pi\)
0.771274 + 0.636503i \(0.219620\pi\)
\(734\) −12.3809 30.3653i −0.456987 1.12080i
\(735\) 4.84521 0.159961i 0.178718 0.00590025i
\(736\) −24.2636 + 9.27089i −0.894367 + 0.341729i
\(737\) 14.3755i 0.529529i
\(738\) 0.787748 + 1.61770i 0.0289974 + 0.0595483i
\(739\) −27.0346 27.0346i −0.994483 0.994483i 0.00550198 0.999985i \(-0.498249\pi\)
−0.999985 + 0.00550198i \(0.998249\pi\)
\(740\) −40.9332 + 40.0352i −1.50473 + 1.47172i
\(741\) −19.0269 17.8107i −0.698970 0.654293i
\(742\) 5.48911 13.0468i 0.201512 0.478963i
\(743\) 2.47482i 0.0907924i −0.998969 0.0453962i \(-0.985545\pi\)
0.998969 0.0453962i \(-0.0144550\pi\)
\(744\) −11.7677 27.1446i −0.431426 0.995169i
\(745\) 10.1769i 0.372855i
\(746\) −35.5855 14.9717i −1.30288 0.548154i
\(747\) 2.12805 + 1.86416i 0.0778611 + 0.0682060i
\(748\) −0.0897968 + 8.09644i −0.00328330 + 0.296035i
\(749\) −11.7876 11.7876i −0.430710 0.430710i
\(750\) −6.05762 13.5590i −0.221193 0.495105i
\(751\) 34.4337i 1.25650i −0.778010 0.628252i \(-0.783771\pi\)
0.778010 0.628252i \(-0.216229\pi\)
\(752\) −0.306201 + 13.8025i −0.0111660 + 0.503324i
\(753\) 0.233828 + 7.08263i 0.00852116 + 0.258105i
\(754\) −51.5330 + 21.0116i −1.87672 + 0.765199i
\(755\) −5.82659 + 5.82659i −0.212051 + 0.212051i
\(756\) 0.912477 + 10.3522i 0.0331865 + 0.376505i
\(757\) −18.3886 18.3886i −0.668346 0.668346i 0.288987 0.957333i \(-0.406681\pi\)
−0.957333 + 0.288987i \(0.906681\pi\)
\(758\) −4.15366 + 9.87261i −0.150868 + 0.358589i
\(759\) 8.26436 0.272842i 0.299977 0.00990353i
\(760\) 11.8104 27.2229i 0.428409 0.987480i
\(761\) 12.2689 0.444749 0.222374 0.974961i \(-0.428619\pi\)
0.222374 + 0.974961i \(0.428619\pi\)
\(762\) 17.7016 46.2909i 0.641261 1.67694i
\(763\) 0.978979 0.978979i 0.0354414 0.0354414i
\(764\) −15.4517 + 15.1127i −0.559023 + 0.546759i
\(765\) 21.5439 24.5936i 0.778922 0.889185i
\(766\) −15.0283 + 6.12750i −0.542993 + 0.221396i
\(767\) 11.1258 0.401728
\(768\) −19.3721 19.8172i −0.699029 0.715093i
\(769\) 12.0880 0.435903 0.217952 0.975960i \(-0.430062\pi\)
0.217952 + 0.975960i \(0.430062\pi\)
\(770\) 3.81086 1.55381i 0.137334 0.0559954i
\(771\) −20.7551 + 22.1723i −0.747476 + 0.798515i
\(772\) 1.23726 1.21012i 0.0445301 0.0435532i
\(773\) 10.7162 10.7162i 0.385434 0.385434i −0.487622 0.873055i \(-0.662135\pi\)
0.873055 + 0.487622i \(0.162135\pi\)
\(774\) 9.81015 + 3.38479i 0.352618 + 0.121664i
\(775\) 17.1142 0.614762
\(776\) 13.4845 31.0817i 0.484065 1.11577i
\(777\) −0.584567 17.7065i −0.0209712 0.635217i
\(778\) −10.4434 + 24.8224i −0.374415 + 0.889927i
\(779\) 1.12409 + 1.12409i 0.0402748 + 0.0402748i
\(780\) −0.852759 38.9115i −0.0305337 1.39326i
\(781\) −6.25507 + 6.25507i −0.223824 + 0.223824i
\(782\) −23.4135 + 9.54644i −0.837267 + 0.341380i
\(783\) −50.6889 + 5.03500i −1.81147 + 0.179936i
\(784\) 0.0887163 3.99902i 0.00316844 0.142822i
\(785\) 25.1899i 0.899065i
\(786\) −19.1762 + 8.56716i −0.683993 + 0.305581i
\(787\) −18.9226 18.9226i −0.674519 0.674519i 0.284235 0.958755i \(-0.408260\pi\)
−0.958755 + 0.284235i \(0.908260\pi\)
\(788\) −0.264630 + 23.8601i −0.00942707 + 0.849982i
\(789\) 32.4334 34.6481i 1.15466 1.23350i
\(790\) −9.68864 4.07625i −0.344706 0.145027i
\(791\) 7.35599i 0.261549i
\(792\) 3.77426 + 7.97418i 0.134112 + 0.283350i
\(793\) 0.370931i 0.0131721i
\(794\) 9.33358 22.1845i 0.331236 0.787299i
\(795\) −33.1586 + 35.4228i −1.17602 + 1.25632i
\(796\) 22.8412 22.3401i 0.809584 0.791823i
\(797\) −34.1544 34.1544i −1.20981 1.20981i −0.971088 0.238722i \(-0.923272\pi\)
−0.238722 0.971088i \(-0.576728\pi\)
\(798\) 3.74526 + 8.38316i 0.132581 + 0.296761i
\(799\) 13.4394i 0.475452i
\(800\) 14.9750 5.72181i 0.529446 0.202297i
\(801\) −2.80708 42.4668i −0.0991832 1.50049i
\(802\) 13.6631 + 33.5100i 0.482460 + 1.18328i
\(803\) −3.77655 + 3.77655i −0.133272 + 0.133272i
\(804\) 34.6015 + 33.1174i 1.22030 + 1.16796i
\(805\) 9.08750 + 9.08750i 0.320292 + 0.320292i
\(806\) −31.6011 13.2954i −1.11310 0.468310i
\(807\) 1.33405 + 40.4084i 0.0469610 + 1.42244i
\(808\) 18.0733 + 45.7718i 0.635815 + 1.61025i
\(809\) −30.0240 −1.05559 −0.527793 0.849373i \(-0.676981\pi\)
−0.527793 + 0.849373i \(0.676981\pi\)
\(810\) 9.37279 34.3692i 0.329326 1.20761i
\(811\) 37.2987 37.2987i 1.30974 1.30974i 0.388132 0.921604i \(-0.373120\pi\)
0.921604 0.388132i \(-0.126880\pi\)
\(812\) 19.6050 + 0.217437i 0.687999 + 0.00763053i
\(813\) 23.3914 24.9886i 0.820372 0.876389i
\(814\) −5.67829 13.9265i −0.199024 0.488125i
\(815\) −41.4083 −1.45047
\(816\) −19.2811 18.8682i −0.674973 0.660520i
\(817\) 9.16880 0.320776
\(818\) 8.38878 + 20.5743i 0.293307 + 0.719362i
\(819\) 9.05859 + 7.93528i 0.316533 + 0.277281i
\(820\) −0.0263285 + 2.37389i −0.000919432 + 0.0828997i
\(821\) −36.8810 + 36.8810i −1.28716 + 1.28716i −0.350651 + 0.936506i \(0.614040\pi\)
−0.936506 + 0.350651i \(0.885960\pi\)
\(822\) 40.0193 + 15.3034i 1.39583 + 0.533766i
\(823\) −27.6092 −0.962395 −0.481198 0.876612i \(-0.659798\pi\)
−0.481198 + 0.876612i \(0.659798\pi\)
\(824\) 9.88832 22.7925i 0.344476 0.794015i
\(825\) −5.10060 + 0.168393i −0.177580 + 0.00586268i
\(826\) −3.61287 1.52002i −0.125708 0.0528884i
\(827\) −36.5603 36.5603i −1.27133 1.27133i −0.945392 0.325935i \(-0.894321\pi\)
−0.325935 0.945392i \(-0.605679\pi\)
\(828\) −18.3822 + 20.5207i −0.638826 + 0.713143i
\(829\) 7.72180 7.72180i 0.268189 0.268189i −0.560181 0.828370i \(-0.689268\pi\)
0.828370 + 0.560181i \(0.189268\pi\)
\(830\) 1.40931 + 3.45646i 0.0489179 + 0.119976i
\(831\) −0.0708793 2.14693i −0.00245878 0.0744762i
\(832\) −32.0961 1.06827i −1.11273 0.0370358i
\(833\) 3.89383i 0.134913i
\(834\) 5.83694 2.60771i 0.202117 0.0902976i
\(835\) 11.6277 + 11.6277i 0.402394 + 0.402394i
\(836\) 5.45015 + 5.57240i 0.188497 + 0.192725i
\(837\) −24.2738 19.8872i −0.839027 0.687404i
\(838\) 18.7851 44.6494i 0.648921 1.54239i
\(839\) 42.6397i 1.47209i 0.676935 + 0.736043i \(0.263308\pi\)
−0.676935 + 0.736043i \(0.736692\pi\)
\(840\) −5.03925 + 12.7522i −0.173871 + 0.439994i
\(841\) 67.1004i 2.31381i
\(842\) 18.8238 + 7.91964i 0.648710 + 0.272929i
\(843\) 31.8129 + 29.7795i 1.09570 + 1.02566i
\(844\) 1.60810 + 0.0178353i 0.0553532 + 0.000613916i
\(845\) −6.16318 6.16318i −0.212020 0.212020i
\(846\) 6.41095 + 13.1654i 0.220413 + 0.452634i
\(847\) 9.91899i 0.340821i
\(848\) 27.6741 + 28.9298i 0.950333 + 0.993455i
\(849\) −56.5551 + 1.86713i −1.94097 + 0.0640796i
\(850\) 14.4504 5.89188i 0.495644 0.202090i
\(851\) 33.2096 33.2096i 1.13841 1.13841i
\(852\) −0.645754 29.4659i −0.0221232 1.00948i
\(853\) −17.8281 17.8281i −0.610422 0.610422i 0.332634 0.943056i \(-0.392063\pi\)
−0.943056 + 0.332634i \(0.892063\pi\)
\(854\) 0.0506773 0.120452i 0.00173414 0.00412179i
\(855\) −2.07595 31.4060i −0.0709961 1.07406i
\(856\) 43.8555 17.3166i 1.49895 0.591868i
\(857\) 24.8082 0.847431 0.423715 0.905795i \(-0.360726\pi\)
0.423715 + 0.905795i \(0.360726\pi\)
\(858\) 9.54899 + 3.65153i 0.325997 + 0.124661i
\(859\) −21.5648 + 21.5648i −0.735783 + 0.735783i −0.971759 0.235976i \(-0.924171\pi\)
0.235976 + 0.971759i \(0.424171\pi\)
\(860\) 9.57407 + 9.78882i 0.326473 + 0.333796i
\(861\) −0.536270 0.501992i −0.0182760 0.0171079i
\(862\) 6.14589 2.50587i 0.209330 0.0853504i
\(863\) 23.1129 0.786774 0.393387 0.919373i \(-0.371303\pi\)
0.393387 + 0.919373i \(0.371303\pi\)
\(864\) −27.8886 9.28590i −0.948788 0.315913i
\(865\) 22.3850 0.761112
\(866\) −29.9110 + 12.1957i −1.01642 + 0.414426i
\(867\) 2.32429 + 2.17572i 0.0789369 + 0.0738914i
\(868\) 8.44539 + 8.63482i 0.286655 + 0.293085i
\(869\) 1.95231 1.95231i 0.0662275 0.0662275i
\(870\) −62.7756 24.0054i −2.12829 0.813858i
\(871\) 55.5024 1.88063
\(872\) 1.43817 + 3.64226i 0.0487024 + 0.123343i
\(873\) −2.37021 35.8577i −0.0802195 1.21360i
\(874\) −9.43938 + 22.4360i −0.319292 + 0.758908i
\(875\) 4.28701 + 4.28701i 0.144927 + 0.144927i
\(876\) −0.389879 17.7902i −0.0131728 0.601077i
\(877\) 4.01492 4.01492i 0.135574 0.135574i −0.636063 0.771637i \(-0.719438\pi\)
0.771637 + 0.636063i \(0.219438\pi\)
\(878\) 13.5849 5.53900i 0.458468 0.186932i
\(879\) 34.7991 1.14887i 1.17375 0.0387503i
\(880\) −0.258170 + 11.6374i −0.00870292 + 0.392297i
\(881\) 38.8398i 1.30855i 0.756259 + 0.654273i \(0.227025\pi\)
−0.756259 + 0.654273i \(0.772975\pi\)
\(882\) −1.85746 3.81443i −0.0625439 0.128438i
\(883\) 25.1588 + 25.1588i 0.846663 + 0.846663i 0.989715 0.143053i \(-0.0456918\pi\)
−0.143053 + 0.989715i \(0.545692\pi\)
\(884\) −31.2595 0.346696i −1.05137 0.0116607i
\(885\) 9.80915 + 9.18216i 0.329731 + 0.308655i
\(886\) 43.7293 + 18.3980i 1.46912 + 0.618094i
\(887\) 2.52225i 0.0846890i 0.999103 + 0.0423445i \(0.0134827\pi\)
−0.999103 + 0.0423445i \(0.986517\pi\)
\(888\) 46.6021 + 18.4156i 1.56386 + 0.617987i
\(889\) 20.2328i 0.678586i
\(890\) 21.7764 51.7593i 0.729948 1.73498i
\(891\) 7.43007 + 5.68821i 0.248917 + 0.190562i
\(892\) −14.7052 15.0350i −0.492366 0.503410i
\(893\) 9.14824 + 9.14824i 0.306134 + 0.306134i
\(894\) −8.13181 + 3.63297i −0.271968 + 0.121505i
\(895\) 38.7053i 1.29377i
\(896\) 10.2766 + 4.73194i 0.343318 + 0.158083i
\(897\) 1.05341 + 31.9078i 0.0351725 + 1.06537i
\(898\) −3.87055 9.49288i −0.129162 0.316782i
\(899\) −41.8622 + 41.8622i −1.39618 + 1.39618i
\(900\) 11.3451 12.6650i 0.378171 0.422165i
\(901\) 27.5575 + 27.5575i 0.918074 + 0.918074i
\(902\) −0.574788 0.241828i −0.0191383 0.00805198i
\(903\) −4.23435 + 0.139794i −0.140910 + 0.00465205i
\(904\) 19.0870 + 8.28072i 0.634825 + 0.275413i
\(905\) 69.4251 2.30777
\(906\) 6.73567 + 2.57572i 0.223778 + 0.0855724i
\(907\) 26.2356 26.2356i 0.871140 0.871140i −0.121457 0.992597i \(-0.538757\pi\)
0.992597 + 0.121457i \(0.0387566\pi\)
\(908\) 0.578240 52.1364i 0.0191896 1.73021i
\(909\) 39.2621 + 34.3934i 1.30224 + 1.14076i
\(910\) 5.99910 + 14.7134i 0.198868 + 0.487743i
\(911\) 7.24925 0.240178 0.120089 0.992763i \(-0.461682\pi\)
0.120089 + 0.992763i \(0.461682\pi\)
\(912\) −25.9684 + 0.281025i −0.859898 + 0.00930566i
\(913\) −0.980478 −0.0324491
\(914\) −5.59049 13.7112i −0.184917 0.453526i
\(915\) −0.306132 + 0.327035i −0.0101204 + 0.0108114i
\(916\) 25.0312 + 0.277618i 0.827054 + 0.00917277i
\(917\) 6.06303 6.06303i 0.200219 0.200219i
\(918\) −27.3421 8.43507i −0.902424 0.278399i
\(919\) −30.7140 −1.01316 −0.506581 0.862192i \(-0.669091\pi\)
−0.506581 + 0.862192i \(0.669091\pi\)
\(920\) −33.8098 + 13.3500i −1.11467 + 0.440135i
\(921\) −0.281222 8.51821i −0.00926659 0.280684i
\(922\) −1.44984 0.609984i −0.0477479 0.0200887i
\(923\) −24.1502 24.1502i −0.794913 0.794913i
\(924\) −2.60196 2.49036i −0.0855982 0.0819269i
\(925\) −20.4963 + 20.4963i −0.673915 + 0.673915i
\(926\) 6.29689 + 15.4437i 0.206929 + 0.507511i
\(927\) −1.73810 26.2948i −0.0570867 0.863634i
\(928\) −22.6337 + 50.6254i −0.742988 + 1.66186i
\(929\) 14.4699i 0.474742i 0.971419 + 0.237371i \(0.0762856\pi\)
−0.971419 + 0.237371i \(0.923714\pi\)
\(930\) −16.8887 37.8026i −0.553802 1.23960i
\(931\) −2.65054 2.65054i −0.0868679 0.0868679i
\(932\) −3.34810 + 3.27465i −0.109671 + 0.107265i
\(933\) 16.1593 17.2627i 0.529031 0.565154i
\(934\) 9.88446 23.4939i 0.323429 0.768743i
\(935\) 11.3313i 0.370573i
\(936\) −30.7875 + 14.5720i −1.00632 + 0.476301i
\(937\) 12.6716i 0.413963i 0.978345 + 0.206981i \(0.0663639\pi\)
−0.978345 + 0.206981i \(0.933636\pi\)
\(938\) −18.0233 7.58284i −0.588481 0.247589i
\(939\) 5.54846 5.92733i 0.181067 0.193431i
\(940\) −0.214270 + 19.3195i −0.00698873 + 0.630132i
\(941\) −23.3569 23.3569i −0.761414 0.761414i 0.215164 0.976578i \(-0.430971\pi\)
−0.976578 + 0.215164i \(0.930971\pi\)
\(942\) −20.1278 + 8.99227i −0.655798 + 0.292984i
\(943\) 1.94733i 0.0634137i
\(944\) 8.01114 7.66341i 0.260741 0.249423i
\(945\) 1.43756 + 14.4723i 0.0467638 + 0.470785i
\(946\) −3.33041 + 1.35791i −0.108281 + 0.0441496i
\(947\) 31.4379 31.4379i 1.02160 1.02160i 0.0218345 0.999762i \(-0.493049\pi\)
0.999762 0.0218345i \(-0.00695068\pi\)
\(948\) 0.201550 + 9.19677i 0.00654605 + 0.298697i
\(949\) −14.5809 14.5809i −0.473315 0.473315i
\(950\) 5.82580 13.8470i 0.189014 0.449257i
\(951\) 1.13610 + 34.4124i 0.0368405 + 1.11590i
\(952\) 10.1035 + 4.38332i 0.327458 + 0.142064i
\(953\) −55.1556 −1.78667 −0.893333 0.449395i \(-0.851639\pi\)
−0.893333 + 0.449395i \(0.851639\pi\)
\(954\) 40.1413 + 13.8499i 1.29962 + 0.448408i
\(955\) −21.3881 + 21.3881i −0.692102 + 0.692102i
\(956\) −6.04954 + 5.91682i −0.195656 + 0.191364i
\(957\) 12.0644 12.8882i 0.389987 0.416617i
\(958\) −16.2854 + 6.64008i −0.526158 + 0.214531i
\(959\) −17.4916 −0.564834
\(960\) −27.4162 27.4310i −0.884854 0.885331i
\(961\) −5.47118 −0.176490
\(962\) 53.7689 21.9233i 1.73358 0.706835i
\(963\) 32.9534 37.6182i 1.06191 1.21223i
\(964\) −10.6418 + 10.4083i −0.342749 + 0.335229i
\(965\) 1.71261 1.71261i 0.0551308 0.0551308i
\(966\) 4.01724 10.5053i 0.129253 0.338004i
\(967\) 9.50752 0.305741 0.152871 0.988246i \(-0.451148\pi\)
0.152871 + 0.988246i \(0.451148\pi\)
\(968\) 25.7374 + 11.1659i 0.827231 + 0.358886i
\(969\) −25.2668 + 0.834164i −0.811686 + 0.0267972i
\(970\) 18.3874 43.7040i 0.590383 1.40325i
\(971\) 39.2171 + 39.2171i 1.25854 + 1.25854i 0.951792 + 0.306746i \(0.0992401\pi\)
0.306746 + 0.951792i \(0.400760\pi\)
\(972\) −30.8083 + 4.77985i −0.988178 + 0.153314i
\(973\) −1.84549 + 1.84549i −0.0591637 + 0.0591637i
\(974\) −7.14679 + 2.91397i −0.228998 + 0.0933697i
\(975\) −0.650147 19.6929i −0.0208214 0.630678i
\(976\) 0.255497 + 0.267090i 0.00817825 + 0.00854935i
\(977\) 34.1054i 1.09113i 0.838069 + 0.545564i \(0.183684\pi\)
−0.838069 + 0.545564i \(0.816316\pi\)
\(978\) 14.7819 + 33.0870i 0.472674 + 1.05801i
\(979\) 10.4298 + 10.4298i 0.333337 + 0.333337i
\(980\) 0.0620810 5.59747i 0.00198310 0.178805i
\(981\) 3.12425 + 2.73683i 0.0997497 + 0.0873803i
\(982\) −29.4883 12.4065i −0.941008 0.395906i
\(983\) 31.2049i 0.995282i −0.867383 0.497641i \(-0.834200\pi\)
0.867383 0.497641i \(-0.165800\pi\)
\(984\) 1.90623 0.826393i 0.0607685 0.0263444i
\(985\) 33.3932i 1.06400i
\(986\) −20.9345 + 49.7581i −0.666690 + 1.58462i
\(987\) −4.36434 4.08538i −0.138919 0.130039i
\(988\) −21.5145 + 21.0425i −0.684466 + 0.669450i
\(989\) −7.94179 7.94179i −0.252534 0.252534i
\(990\) 5.40533 + 11.1002i 0.171793 + 0.352789i
\(991\) 27.0130i 0.858095i 0.903282 + 0.429048i \(0.141151\pi\)
−0.903282 + 0.429048i \(0.858849\pi\)
\(992\) −31.9124 + 12.1934i −1.01322 + 0.387142i
\(993\) 30.5699 1.00924i 0.970105 0.0320273i
\(994\) 4.54284 + 11.1417i 0.144090 + 0.353394i
\(995\) 31.6165 31.6165i 1.00231 1.00231i
\(996\) 2.25876 2.35999i 0.0715717 0.0747790i
\(997\) 25.0482 + 25.0482i 0.793283 + 0.793283i 0.982026 0.188743i \(-0.0604414\pi\)
−0.188743 + 0.982026i \(0.560441\pi\)
\(998\) −29.4908 12.4075i −0.933515 0.392753i
\(999\) 52.8881 5.25346i 1.67331 0.166212i
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 336.2.s.d.155.3 48
3.2 odd 2 inner 336.2.s.d.155.22 yes 48
4.3 odd 2 1344.2.s.d.911.7 48
12.11 even 2 1344.2.s.d.911.8 48
16.3 odd 4 inner 336.2.s.d.323.22 yes 48
16.13 even 4 1344.2.s.d.239.8 48
48.29 odd 4 1344.2.s.d.239.7 48
48.35 even 4 inner 336.2.s.d.323.3 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.s.d.155.3 48 1.1 even 1 trivial
336.2.s.d.155.22 yes 48 3.2 odd 2 inner
336.2.s.d.323.3 yes 48 48.35 even 4 inner
336.2.s.d.323.22 yes 48 16.3 odd 4 inner
1344.2.s.d.239.7 48 48.29 odd 4
1344.2.s.d.239.8 48 16.13 even 4
1344.2.s.d.911.7 48 4.3 odd 2
1344.2.s.d.911.8 48 12.11 even 2