Properties

Label 336.2.y.a.125.6
Level $336$
Weight $2$
Character 336.125
Analytic conductor $2.683$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(125,336)]
 
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([0, 3, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.y (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: \(120\)
Relative dimension: \(60\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 125.6
Character \(\chi\) \(=\) 336.125
Dual form 336.2.y.a.293.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37255 - 0.340756i) q^{2} +(1.24999 + 1.19897i) q^{3} +(1.76777 + 0.935408i) q^{4} +(-2.22287 + 2.22287i) q^{5} +(-1.30712 - 2.07158i) q^{6} +(-1.16923 - 2.37337i) q^{7} +(-2.10760 - 1.88627i) q^{8} +(0.124963 + 2.99740i) q^{9} +O(q^{10})\) \(q+(-1.37255 - 0.340756i) q^{2} +(1.24999 + 1.19897i) q^{3} +(1.76777 + 0.935408i) q^{4} +(-2.22287 + 2.22287i) q^{5} +(-1.30712 - 2.07158i) q^{6} +(-1.16923 - 2.37337i) q^{7} +(-2.10760 - 1.88627i) q^{8} +(0.124963 + 2.99740i) q^{9} +(3.80846 - 2.29354i) q^{10} +(2.89998 + 2.89998i) q^{11} +(1.08818 + 3.28875i) q^{12} +(-2.85803 + 2.85803i) q^{13} +(0.796083 + 3.65599i) q^{14} +(-5.44373 + 0.113426i) q^{15} +(2.25002 + 3.30717i) q^{16} -3.18041 q^{17} +(0.849865 - 4.15665i) q^{18} +(1.73347 - 1.73347i) q^{19} +(-6.00883 + 1.85023i) q^{20} +(1.38406 - 4.36857i) q^{21} +(-2.99217 - 4.96855i) q^{22} -7.79850 q^{23} +(-0.372911 - 4.88477i) q^{24} -4.88234i q^{25} +(4.89668 - 2.94889i) q^{26} +(-3.43757 + 3.89655i) q^{27} +(0.153140 - 5.28929i) q^{28} +(1.10738 - 1.10738i) q^{29} +(7.51042 + 1.69930i) q^{30} +9.18848i q^{31} +(-1.96132 - 5.30596i) q^{32} +(0.147977 + 7.10194i) q^{33} +(4.36527 + 1.08375i) q^{34} +(7.87476 + 2.67665i) q^{35} +(-2.58288 + 5.41560i) q^{36} +(1.36244 - 1.36244i) q^{37} +(-2.96995 + 1.78857i) q^{38} +(-6.99921 + 0.145837i) q^{39} +(8.87787 - 0.491988i) q^{40} -4.51251i q^{41} +(-3.38831 + 5.52443i) q^{42} +(-3.61139 + 3.61139i) q^{43} +(2.41383 + 7.83917i) q^{44} +(-6.94061 - 6.38506i) q^{45} +(10.7038 + 2.65739i) q^{46} +9.27141 q^{47} +(-1.15268 + 6.83164i) q^{48} +(-4.26579 + 5.55004i) q^{49} +(-1.66369 + 6.70124i) q^{50} +(-3.97549 - 3.81321i) q^{51} +(-7.72578 + 2.37892i) q^{52} +(4.39447 + 4.39447i) q^{53} +(6.04600 - 4.17682i) q^{54} -12.8926 q^{55} +(-2.01255 + 7.20761i) q^{56} +(4.24518 - 0.0884533i) q^{57} +(-1.89728 + 1.14258i) q^{58} +(0.471265 - 0.471265i) q^{59} +(-9.72936 - 4.89160i) q^{60} +(6.41637 - 6.41637i) q^{61} +(3.13103 - 12.6116i) q^{62} +(6.96783 - 3.80123i) q^{63} +(0.883963 + 7.95101i) q^{64} -12.7061i q^{65} +(2.21693 - 9.79816i) q^{66} +(9.87337 + 9.87337i) q^{67} +(-5.62224 - 2.97499i) q^{68} +(-9.74806 - 9.35013i) q^{69} +(-9.89639 - 6.35721i) q^{70} +13.3355 q^{71} +(5.39053 - 6.55303i) q^{72} +8.05789 q^{73} +(-2.33428 + 1.40576i) q^{74} +(5.85376 - 6.10289i) q^{75} +(4.68587 - 1.44287i) q^{76} +(3.49199 - 10.2735i) q^{77} +(9.65643 + 2.18486i) q^{78} -1.71738 q^{79} +(-12.3529 - 2.34992i) q^{80} +(-8.96877 + 0.749126i) q^{81} +(-1.53767 + 6.19363i) q^{82} +(-2.17510 - 2.17510i) q^{83} +(6.53310 - 6.42796i) q^{84} +(7.06966 - 7.06966i) q^{85} +(6.18741 - 3.72620i) q^{86} +(2.71192 - 0.0565061i) q^{87} +(-0.641853 - 11.5822i) q^{88} -1.76913i q^{89} +(7.35056 + 11.1288i) q^{90} +(10.1249 + 3.44148i) q^{91} +(-13.7860 - 7.29478i) q^{92} +(-11.0167 + 11.4855i) q^{93} +(-12.7254 - 3.15929i) q^{94} +7.70655i q^{95} +(3.91003 - 8.98397i) q^{96} -3.24825i q^{97} +(7.74622 - 6.16410i) q^{98} +(-8.33001 + 9.05479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 8 q^{4} - 8 q^{15} + 8 q^{16} - 32 q^{18} - 8 q^{21} + 16 q^{22} - 16 q^{30} - 8 q^{36} - 8 q^{37} - 24 q^{42} - 8 q^{43} - 24 q^{46} - 8 q^{49} - 56 q^{51} + 40 q^{58} - 96 q^{60} + 24 q^{63} - 56 q^{64} + 24 q^{67} - 80 q^{70} - 8 q^{72} + 64 q^{78} - 16 q^{79} - 8 q^{81} - 48 q^{84} - 48 q^{85} - 24 q^{88} - 8 q^{91} + 8 q^{93} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37255 0.340756i −0.970537 0.240951i
\(3\) 1.24999 + 1.19897i 0.721684 + 0.692223i
\(4\) 1.76777 + 0.935408i 0.883885 + 0.467704i
\(5\) −2.22287 + 2.22287i −0.994099 + 0.994099i −0.999983 0.00588320i \(-0.998127\pi\)
0.00588320 + 0.999983i \(0.498127\pi\)
\(6\) −1.30712 2.07158i −0.533629 0.845719i
\(7\) −1.16923 2.37337i −0.441928 0.897050i
\(8\) −2.10760 1.88627i −0.745149 0.666898i
\(9\) 0.124963 + 2.99740i 0.0416542 + 0.999132i
\(10\) 3.80846 2.29354i 1.20434 0.725281i
\(11\) 2.89998 + 2.89998i 0.874378 + 0.874378i 0.992946 0.118568i \(-0.0378304\pi\)
−0.118568 + 0.992946i \(0.537830\pi\)
\(12\) 1.08818 + 3.28875i 0.314130 + 0.949380i
\(13\) −2.85803 + 2.85803i −0.792676 + 0.792676i −0.981928 0.189252i \(-0.939394\pi\)
0.189252 + 0.981928i \(0.439394\pi\)
\(14\) 0.796083 + 3.65599i 0.212762 + 0.977104i
\(15\) −5.44373 + 0.113426i −1.40556 + 0.0292866i
\(16\) 2.25002 + 3.30717i 0.562505 + 0.826794i
\(17\) −3.18041 −0.771364 −0.385682 0.922632i \(-0.626034\pi\)
−0.385682 + 0.922632i \(0.626034\pi\)
\(18\) 0.849865 4.15665i 0.200315 0.979732i
\(19\) 1.73347 1.73347i 0.397684 0.397684i −0.479731 0.877415i \(-0.659266\pi\)
0.877415 + 0.479731i \(0.159266\pi\)
\(20\) −6.00883 + 1.85023i −1.34361 + 0.413725i
\(21\) 1.38406 4.36857i 0.302027 0.953299i
\(22\) −2.99217 4.96855i −0.637934 1.05930i
\(23\) −7.79850 −1.62610 −0.813050 0.582194i \(-0.802194\pi\)
−0.813050 + 0.582194i \(0.802194\pi\)
\(24\) −0.372911 4.88477i −0.0761202 0.997099i
\(25\) 4.88234i 0.976468i
\(26\) 4.89668 2.94889i 0.960318 0.578325i
\(27\) −3.43757 + 3.89655i −0.661561 + 0.749891i
\(28\) 0.153140 5.28929i 0.0289407 0.999581i
\(29\) 1.10738 1.10738i 0.205635 0.205635i −0.596774 0.802409i \(-0.703551\pi\)
0.802409 + 0.596774i \(0.203551\pi\)
\(30\) 7.51042 + 1.69930i 1.37121 + 0.310249i
\(31\) 9.18848i 1.65030i 0.564914 + 0.825150i \(0.308909\pi\)
−0.564914 + 0.825150i \(0.691091\pi\)
\(32\) −1.96132 5.30596i −0.346716 0.937970i
\(33\) 0.147977 + 7.10194i 0.0257595 + 1.23629i
\(34\) 4.36527 + 1.08375i 0.748637 + 0.185861i
\(35\) 7.87476 + 2.67665i 1.33108 + 0.452437i
\(36\) −2.58288 + 5.41560i −0.430481 + 0.902600i
\(37\) 1.36244 1.36244i 0.223984 0.223984i −0.586190 0.810174i \(-0.699373\pi\)
0.810174 + 0.586190i \(0.199373\pi\)
\(38\) −2.96995 + 1.78857i −0.481790 + 0.290145i
\(39\) −6.99921 + 0.145837i −1.12077 + 0.0233525i
\(40\) 8.87787 0.491988i 1.40372 0.0777902i
\(41\) 4.51251i 0.704735i −0.935862 0.352368i \(-0.885377\pi\)
0.935862 0.352368i \(-0.114623\pi\)
\(42\) −3.38831 + 5.52443i −0.522827 + 0.852439i
\(43\) −3.61139 + 3.61139i −0.550732 + 0.550732i −0.926652 0.375920i \(-0.877327\pi\)
0.375920 + 0.926652i \(0.377327\pi\)
\(44\) 2.41383 + 7.83917i 0.363899 + 1.18180i
\(45\) −6.94061 6.38506i −1.03465 0.951828i
\(46\) 10.7038 + 2.65739i 1.57819 + 0.391811i
\(47\) 9.27141 1.35237 0.676187 0.736730i \(-0.263631\pi\)
0.676187 + 0.736730i \(0.263631\pi\)
\(48\) −1.15268 + 6.83164i −0.166375 + 0.986063i
\(49\) −4.26579 + 5.55004i −0.609399 + 0.792864i
\(50\) −1.66369 + 6.70124i −0.235281 + 0.947698i
\(51\) −3.97549 3.81321i −0.556680 0.533956i
\(52\) −7.72578 + 2.37892i −1.07137 + 0.329897i
\(53\) 4.39447 + 4.39447i 0.603627 + 0.603627i 0.941273 0.337646i \(-0.109631\pi\)
−0.337646 + 0.941273i \(0.609631\pi\)
\(54\) 6.04600 4.17682i 0.822757 0.568393i
\(55\) −12.8926 −1.73844
\(56\) −2.01255 + 7.20761i −0.268938 + 0.963157i
\(57\) 4.24518 0.0884533i 0.562288 0.0117159i
\(58\) −1.89728 + 1.14258i −0.249125 + 0.150029i
\(59\) 0.471265 0.471265i 0.0613534 0.0613534i −0.675764 0.737118i \(-0.736186\pi\)
0.737118 + 0.675764i \(0.236186\pi\)
\(60\) −9.72936 4.89160i −1.25605 0.631502i
\(61\) 6.41637 6.41637i 0.821532 0.821532i −0.164796 0.986328i \(-0.552697\pi\)
0.986328 + 0.164796i \(0.0526966\pi\)
\(62\) 3.13103 12.6116i 0.397642 1.60168i
\(63\) 6.96783 3.80123i 0.877864 0.478910i
\(64\) 0.883963 + 7.95101i 0.110495 + 0.993877i
\(65\) 12.7061i 1.57600i
\(66\) 2.21693 9.79816i 0.272885 1.20607i
\(67\) 9.87337 + 9.87337i 1.20622 + 1.20622i 0.972240 + 0.233984i \(0.0751764\pi\)
0.233984 + 0.972240i \(0.424824\pi\)
\(68\) −5.62224 2.97499i −0.681797 0.360770i
\(69\) −9.74806 9.35013i −1.17353 1.12562i
\(70\) −9.89639 6.35721i −1.18285 0.759832i
\(71\) 13.3355 1.58264 0.791318 0.611405i \(-0.209395\pi\)
0.791318 + 0.611405i \(0.209395\pi\)
\(72\) 5.39053 6.55303i 0.635280 0.772282i
\(73\) 8.05789 0.943104 0.471552 0.881838i \(-0.343694\pi\)
0.471552 + 0.881838i \(0.343694\pi\)
\(74\) −2.33428 + 1.40576i −0.271355 + 0.163416i
\(75\) 5.85376 6.10289i 0.675933 0.704701i
\(76\) 4.68587 1.44287i 0.537506 0.165509i
\(77\) 3.49199 10.2735i 0.397949 1.17077i
\(78\) 9.65643 + 2.18486i 1.09338 + 0.247386i
\(79\) −1.71738 −0.193220 −0.0966101 0.995322i \(-0.530800\pi\)
−0.0966101 + 0.995322i \(0.530800\pi\)
\(80\) −12.3529 2.34992i −1.38110 0.262729i
\(81\) −8.96877 + 0.749126i −0.996530 + 0.0832362i
\(82\) −1.53767 + 6.19363i −0.169807 + 0.683972i
\(83\) −2.17510 2.17510i −0.238748 0.238748i 0.577583 0.816332i \(-0.303996\pi\)
−0.816332 + 0.577583i \(0.803996\pi\)
\(84\) 6.53310 6.42796i 0.712819 0.701348i
\(85\) 7.06966 7.06966i 0.766812 0.766812i
\(86\) 6.18741 3.72620i 0.667206 0.401807i
\(87\) 2.71192 0.0565061i 0.290749 0.00605809i
\(88\) −0.641853 11.5822i −0.0684217 1.23466i
\(89\) 1.76913i 0.187528i −0.995594 0.0937638i \(-0.970110\pi\)
0.995594 0.0937638i \(-0.0298899\pi\)
\(90\) 7.35056 + 11.1288i 0.774817 + 1.17308i
\(91\) 10.1249 + 3.44148i 1.06138 + 0.360765i
\(92\) −13.7860 7.29478i −1.43728 0.760533i
\(93\) −11.0167 + 11.4855i −1.14238 + 1.19099i
\(94\) −12.7254 3.15929i −1.31253 0.325856i
\(95\) 7.70655i 0.790675i
\(96\) 3.91003 8.98397i 0.399066 0.916922i
\(97\) 3.24825i 0.329810i −0.986309 0.164905i \(-0.947268\pi\)
0.986309 0.164905i \(-0.0527317\pi\)
\(98\) 7.74622 6.16410i 0.782486 0.622668i
\(99\) −8.33001 + 9.05479i −0.837197 + 0.910040i
\(100\) 4.56698 8.63085i 0.456698 0.863085i
\(101\) −3.17797 + 3.17797i −0.316220 + 0.316220i −0.847313 0.531093i \(-0.821781\pi\)
0.531093 + 0.847313i \(0.321781\pi\)
\(102\) 4.15718 + 6.58848i 0.411622 + 0.652357i
\(103\) 0.232663 0.0229249 0.0114625 0.999934i \(-0.496351\pi\)
0.0114625 + 0.999934i \(0.496351\pi\)
\(104\) 11.4146 0.632568i 1.11930 0.0620284i
\(105\) 6.63418 + 12.7874i 0.647430 + 1.24792i
\(106\) −4.53417 7.52906i −0.440398 0.731287i
\(107\) 3.24753 + 3.24753i 0.313950 + 0.313950i 0.846438 0.532488i \(-0.178743\pi\)
−0.532488 + 0.846438i \(0.678743\pi\)
\(108\) −9.72170 + 3.67267i −0.935471 + 0.353403i
\(109\) −6.57591 6.57591i −0.629858 0.629858i 0.318174 0.948032i \(-0.396930\pi\)
−0.948032 + 0.318174i \(0.896930\pi\)
\(110\) 17.6957 + 4.39323i 1.68722 + 0.418878i
\(111\) 3.33657 0.0695213i 0.316693 0.00659867i
\(112\) 5.21836 9.20699i 0.493089 0.869979i
\(113\) 2.85308i 0.268395i −0.990955 0.134197i \(-0.957154\pi\)
0.990955 0.134197i \(-0.0428456\pi\)
\(114\) −5.85685 1.32517i −0.548545 0.124113i
\(115\) 17.3351 17.3351i 1.61650 1.61650i
\(116\) 2.99344 0.921740i 0.277934 0.0855814i
\(117\) −8.92381 8.20951i −0.825006 0.758970i
\(118\) −0.807419 + 0.486246i −0.0743290 + 0.0447626i
\(119\) 3.71864 + 7.54831i 0.340887 + 0.691952i
\(120\) 11.6872 + 10.0293i 1.06689 + 0.915544i
\(121\) 5.81980i 0.529073i
\(122\) −10.9932 + 6.62035i −0.995276 + 0.599378i
\(123\) 5.41034 5.64060i 0.487834 0.508596i
\(124\) −8.59498 + 16.2431i −0.771852 + 1.45868i
\(125\) −0.261548 0.261548i −0.0233935 0.0233935i
\(126\) −10.8590 + 2.84304i −0.967394 + 0.253278i
\(127\) 0.963414 0.0854891 0.0427446 0.999086i \(-0.486390\pi\)
0.0427446 + 0.999086i \(0.486390\pi\)
\(128\) 1.49608 11.2144i 0.132236 0.991218i
\(129\) −8.84415 + 0.184278i −0.778684 + 0.0162248i
\(130\) −4.32969 + 17.4397i −0.379739 + 1.52956i
\(131\) 7.55453 + 7.55453i 0.660043 + 0.660043i 0.955390 0.295347i \(-0.0954354\pi\)
−0.295347 + 0.955390i \(0.595435\pi\)
\(132\) −6.38162 + 12.6930i −0.555449 + 1.10478i
\(133\) −6.14098 2.08734i −0.532491 0.180995i
\(134\) −10.1873 16.9161i −0.880045 1.46133i
\(135\) −1.02025 16.3028i −0.0878088 1.40312i
\(136\) 6.70304 + 5.99912i 0.574781 + 0.514420i
\(137\) −0.360233 −0.0307768 −0.0153884 0.999882i \(-0.504898\pi\)
−0.0153884 + 0.999882i \(0.504898\pi\)
\(138\) 10.1936 + 16.1552i 0.867733 + 1.37522i
\(139\) −7.40390 7.40390i −0.627991 0.627991i 0.319571 0.947562i \(-0.396461\pi\)
−0.947562 + 0.319571i \(0.896461\pi\)
\(140\) 11.4170 + 12.0978i 0.964913 + 1.02245i
\(141\) 11.5892 + 11.1161i 0.975986 + 0.936145i
\(142\) −18.3036 4.54417i −1.53601 0.381338i
\(143\) −16.5765 −1.38620
\(144\) −9.63174 + 7.15748i −0.802645 + 0.596457i
\(145\) 4.92313i 0.408844i
\(146\) −11.0598 2.74578i −0.915318 0.227242i
\(147\) −11.9865 + 1.82297i −0.988632 + 0.150356i
\(148\) 3.68293 1.13405i 0.302735 0.0932180i
\(149\) 8.67794 + 8.67794i 0.710925 + 0.710925i 0.966729 0.255804i \(-0.0823401\pi\)
−0.255804 + 0.966729i \(0.582340\pi\)
\(150\) −10.1142 + 6.38179i −0.825817 + 0.521071i
\(151\) 7.62482i 0.620499i 0.950655 + 0.310250i \(0.100413\pi\)
−0.950655 + 0.310250i \(0.899587\pi\)
\(152\) −6.92324 + 0.383667i −0.561549 + 0.0311195i
\(153\) −0.397433 9.53296i −0.0321306 0.770694i
\(154\) −8.29368 + 12.9109i −0.668323 + 1.04039i
\(155\) −20.4248 20.4248i −1.64056 1.64056i
\(156\) −12.5094 6.28931i −1.00155 0.503548i
\(157\) 3.32883 3.32883i 0.265670 0.265670i −0.561683 0.827353i \(-0.689846\pi\)
0.827353 + 0.561683i \(0.189846\pi\)
\(158\) 2.35718 + 0.585208i 0.187527 + 0.0465567i
\(159\) 0.224236 + 10.7619i 0.0177831 + 0.853472i
\(160\) 16.1543 + 7.43472i 1.27711 + 0.587766i
\(161\) 9.11825 + 18.5087i 0.718619 + 1.45869i
\(162\) 12.5653 + 2.02796i 0.987225 + 0.159331i
\(163\) 6.16429 + 6.16429i 0.482825 + 0.482825i 0.906033 0.423208i \(-0.139096\pi\)
−0.423208 + 0.906033i \(0.639096\pi\)
\(164\) 4.22104 7.97707i 0.329608 0.622905i
\(165\) −16.1156 15.4578i −1.25460 1.20339i
\(166\) 2.24425 + 3.72661i 0.174188 + 0.289241i
\(167\) 13.1283i 1.01590i 0.861387 + 0.507949i \(0.169596\pi\)
−0.861387 + 0.507949i \(0.830404\pi\)
\(168\) −11.1573 + 6.59648i −0.860808 + 0.508929i
\(169\) 3.33672i 0.256671i
\(170\) −12.1125 + 7.29441i −0.928984 + 0.559455i
\(171\) 5.41250 + 4.97926i 0.413904 + 0.380774i
\(172\) −9.76224 + 3.00599i −0.744364 + 0.229204i
\(173\) 6.31691 + 6.31691i 0.480266 + 0.480266i 0.905217 0.424951i \(-0.139709\pi\)
−0.424951 + 0.905217i \(0.639709\pi\)
\(174\) −3.74150 0.846549i −0.283642 0.0641767i
\(175\) −11.5876 + 5.70858i −0.875941 + 0.431528i
\(176\) −3.06572 + 16.1158i −0.231088 + 1.21477i
\(177\) 1.15411 0.0240472i 0.0867480 0.00180750i
\(178\) −0.602843 + 2.42822i −0.0451850 + 0.182003i
\(179\) 6.90667 6.90667i 0.516229 0.516229i −0.400199 0.916428i \(-0.631059\pi\)
0.916428 + 0.400199i \(0.131059\pi\)
\(180\) −6.29677 17.7796i −0.469333 1.32521i
\(181\) −0.796484 0.796484i −0.0592022 0.0592022i 0.676886 0.736088i \(-0.263329\pi\)
−0.736088 + 0.676886i \(0.763329\pi\)
\(182\) −12.7242 8.17371i −0.943178 0.605875i
\(183\) 15.7134 0.327407i 1.16157 0.0242026i
\(184\) 16.4361 + 14.7101i 1.21169 + 1.08444i
\(185\) 6.05708i 0.445326i
\(186\) 19.0347 12.0104i 1.39569 0.880647i
\(187\) −9.22314 9.22314i −0.674463 0.674463i
\(188\) 16.3897 + 8.67256i 1.19534 + 0.632511i
\(189\) 13.2673 + 3.60267i 0.965053 + 0.262056i
\(190\) 2.62606 10.5776i 0.190514 0.767380i
\(191\) 0.749474i 0.0542300i −0.999632 0.0271150i \(-0.991368\pi\)
0.999632 0.0271150i \(-0.00863204\pi\)
\(192\) −8.42804 + 10.9985i −0.608242 + 0.793752i
\(193\) 4.00979 0.288631 0.144316 0.989532i \(-0.453902\pi\)
0.144316 + 0.989532i \(0.453902\pi\)
\(194\) −1.10686 + 4.45837i −0.0794680 + 0.320092i
\(195\) 15.2342 15.8825i 1.09094 1.13737i
\(196\) −12.7325 + 5.82094i −0.909464 + 0.415782i
\(197\) 3.14044 + 3.14044i 0.223747 + 0.223747i 0.810074 0.586327i \(-0.199427\pi\)
−0.586327 + 0.810074i \(0.699427\pi\)
\(198\) 14.5188 9.58962i 1.03181 0.681504i
\(199\) −20.8169 −1.47567 −0.737834 0.674982i \(-0.764151\pi\)
−0.737834 + 0.674982i \(0.764151\pi\)
\(200\) −9.20941 + 10.2900i −0.651204 + 0.727614i
\(201\) 0.503808 + 24.1795i 0.0355358 + 1.70549i
\(202\) 5.44483 3.27900i 0.383097 0.230710i
\(203\) −3.92301 1.33344i −0.275341 0.0935892i
\(204\) −3.46085 10.4596i −0.242308 0.732317i
\(205\) 10.0307 + 10.0307i 0.700577 + 0.700577i
\(206\) −0.319341 0.0792814i −0.0222495 0.00552379i
\(207\) −0.974521 23.3752i −0.0677339 1.62469i
\(208\) −15.8827 3.02138i −1.10126 0.209495i
\(209\) 10.0540 0.695452
\(210\) −4.74834 19.8119i −0.327667 1.36715i
\(211\) 2.27906 + 2.27906i 0.156897 + 0.156897i 0.781190 0.624293i \(-0.214613\pi\)
−0.624293 + 0.781190i \(0.714613\pi\)
\(212\) 3.65779 + 11.8790i 0.251218 + 0.815855i
\(213\) 16.6693 + 15.9888i 1.14216 + 1.09554i
\(214\) −3.35077 5.56400i −0.229054 0.380347i
\(215\) 16.0553i 1.09497i
\(216\) 14.5950 1.72818i 0.993063 0.117587i
\(217\) 21.8077 10.7435i 1.48040 0.729314i
\(218\) 6.78496 + 11.2665i 0.459536 + 0.763066i
\(219\) 10.0723 + 9.66113i 0.680623 + 0.652839i
\(220\) −22.7911 12.0598i −1.53658 0.813074i
\(221\) 9.08973 9.08973i 0.611441 0.611441i
\(222\) −4.60329 1.04154i −0.308952 0.0699033i
\(223\) 5.90307i 0.395299i −0.980273 0.197649i \(-0.936669\pi\)
0.980273 0.197649i \(-0.0633308\pi\)
\(224\) −10.2998 + 10.8588i −0.688183 + 0.725537i
\(225\) 14.6343 0.610110i 0.975620 0.0406740i
\(226\) −0.972204 + 3.91598i −0.0646701 + 0.260487i
\(227\) −9.96279 9.96279i −0.661253 0.661253i 0.294422 0.955676i \(-0.404873\pi\)
−0.955676 + 0.294422i \(0.904873\pi\)
\(228\) 7.58725 + 3.81462i 0.502478 + 0.252629i
\(229\) −14.6759 14.6759i −0.969811 0.969811i 0.0297465 0.999557i \(-0.490530\pi\)
−0.999557 + 0.0297465i \(0.990530\pi\)
\(230\) −29.7002 + 17.8862i −1.95838 + 1.17938i
\(231\) 16.6825 8.65501i 1.09763 0.569458i
\(232\) −4.42273 + 0.245096i −0.290366 + 0.0160913i
\(233\) −13.3284 −0.873174 −0.436587 0.899662i \(-0.643813\pi\)
−0.436587 + 0.899662i \(0.643813\pi\)
\(234\) 9.45090 + 14.3088i 0.617825 + 0.935395i
\(235\) −20.6092 + 20.6092i −1.34439 + 1.34439i
\(236\) 1.27391 0.392263i 0.0829246 0.0255341i
\(237\) −2.14671 2.05908i −0.139444 0.133752i
\(238\) −2.53187 11.6276i −0.164117 0.753702i
\(239\) 15.8337i 1.02420i 0.858927 + 0.512098i \(0.171132\pi\)
−0.858927 + 0.512098i \(0.828868\pi\)
\(240\) −12.6236 17.7481i −0.814851 1.14564i
\(241\) 4.77361i 0.307495i 0.988110 + 0.153748i \(0.0491343\pi\)
−0.988110 + 0.153748i \(0.950866\pi\)
\(242\) 1.98313 7.98795i 0.127481 0.513485i
\(243\) −12.1091 9.81684i −0.776797 0.629751i
\(244\) 17.3446 5.34074i 1.11037 0.341906i
\(245\) −2.85473 21.8194i −0.182382 1.39399i
\(246\) −9.34802 + 5.89838i −0.596008 + 0.376067i
\(247\) 9.90860i 0.630469i
\(248\) 17.3320 19.3656i 1.10058 1.22972i
\(249\) −0.110989 5.32673i −0.00703362 0.337568i
\(250\) 0.269862 + 0.448110i 0.0170676 + 0.0283410i
\(251\) −6.90611 + 6.90611i −0.435910 + 0.435910i −0.890633 0.454723i \(-0.849738\pi\)
0.454723 + 0.890633i \(0.349738\pi\)
\(252\) 15.8732 0.201943i 0.999919 0.0127212i
\(253\) −22.6155 22.6155i −1.42182 1.42182i
\(254\) −1.32233 0.328289i −0.0829704 0.0205987i
\(255\) 17.3133 0.360743i 1.08420 0.0225906i
\(256\) −5.87480 + 14.8824i −0.367175 + 0.930152i
\(257\) −26.4573 −1.65036 −0.825179 0.564871i \(-0.808926\pi\)
−0.825179 + 0.564871i \(0.808926\pi\)
\(258\) 12.2018 + 2.76077i 0.759651 + 0.171878i
\(259\) −4.82660 1.64057i −0.299910 0.101940i
\(260\) 11.8854 22.4615i 0.737101 1.39300i
\(261\) 3.45763 + 3.18087i 0.214022 + 0.196891i
\(262\) −7.79469 12.9432i −0.481558 0.799634i
\(263\) −13.4804 −0.831236 −0.415618 0.909539i \(-0.636435\pi\)
−0.415618 + 0.909539i \(0.636435\pi\)
\(264\) 13.0843 15.2472i 0.805283 0.938399i
\(265\) −19.5367 −1.20013
\(266\) 7.71751 + 4.95755i 0.473191 + 0.303967i
\(267\) 2.12113 2.21140i 0.129811 0.135336i
\(268\) 8.21822 + 26.6895i 0.502008 + 1.63032i
\(269\) 16.8300 + 16.8300i 1.02614 + 1.02614i 0.999649 + 0.0264934i \(0.00843410\pi\)
0.0264934 + 0.999649i \(0.491566\pi\)
\(270\) −4.15496 + 22.7241i −0.252863 + 1.38294i
\(271\) 16.2786i 0.988856i −0.869219 0.494428i \(-0.835378\pi\)
0.869219 0.494428i \(-0.164622\pi\)
\(272\) −7.15600 10.5182i −0.433896 0.637758i
\(273\) 8.52982 + 16.4412i 0.516248 + 0.995067i
\(274\) 0.494436 + 0.122752i 0.0298700 + 0.00741570i
\(275\) 14.1587 14.1587i 0.853801 0.853801i
\(276\) −8.48614 25.6473i −0.510806 1.54379i
\(277\) 18.1892 18.1892i 1.09288 1.09288i 0.0976637 0.995219i \(-0.468863\pi\)
0.995219 0.0976637i \(-0.0311369\pi\)
\(278\) 7.63928 + 12.6851i 0.458173 + 0.760804i
\(279\) −27.5415 + 1.14822i −1.64887 + 0.0687420i
\(280\) −11.5480 20.4953i −0.690123 1.22483i
\(281\) −14.1329 −0.843099 −0.421550 0.906805i \(-0.638514\pi\)
−0.421550 + 0.906805i \(0.638514\pi\)
\(282\) −12.1188 19.2065i −0.721666 1.14373i
\(283\) 14.3799 + 14.3799i 0.854799 + 0.854799i 0.990720 0.135921i \(-0.0433992\pi\)
−0.135921 + 0.990720i \(0.543399\pi\)
\(284\) 23.5741 + 12.4742i 1.39887 + 0.740206i
\(285\) −9.23989 + 9.63313i −0.547324 + 0.570617i
\(286\) 22.7520 + 5.64855i 1.34536 + 0.334006i
\(287\) −10.7099 + 5.27617i −0.632183 + 0.311442i
\(288\) 15.6590 6.54190i 0.922714 0.385485i
\(289\) −6.88497 −0.404998
\(290\) 1.67759 6.75722i 0.0985113 0.396798i
\(291\) 3.89454 4.06028i 0.228302 0.238018i
\(292\) 14.2445 + 7.53741i 0.833596 + 0.441094i
\(293\) 15.2285 15.2285i 0.889657 0.889657i −0.104833 0.994490i \(-0.533431\pi\)
0.994490 + 0.104833i \(0.0334309\pi\)
\(294\) 17.0733 + 1.58237i 0.995733 + 0.0922856i
\(295\) 2.09512i 0.121983i
\(296\) −5.44143 + 0.301549i −0.316277 + 0.0175272i
\(297\) −21.2688 + 1.33102i −1.23414 + 0.0772338i
\(298\) −8.95382 14.8680i −0.518681 0.861277i
\(299\) 22.2884 22.2884i 1.28897 1.28897i
\(300\) 16.0568 5.31285i 0.927039 0.306737i
\(301\) 12.7937 + 4.34863i 0.737419 + 0.250651i
\(302\) 2.59821 10.4654i 0.149510 0.602218i
\(303\) −7.78272 + 0.162162i −0.447105 + 0.00931596i
\(304\) 9.63321 + 1.83254i 0.552502 + 0.105103i
\(305\) 28.5255i 1.63337i
\(306\) −2.70292 + 13.2199i −0.154516 + 0.755729i
\(307\) −18.3375 + 18.3375i −1.04658 + 1.04658i −0.0477172 + 0.998861i \(0.515195\pi\)
−0.998861 + 0.0477172i \(0.984805\pi\)
\(308\) 15.7829 14.8947i 0.899317 0.848706i
\(309\) 0.290827 + 0.278955i 0.0165446 + 0.0158692i
\(310\) 21.0741 + 34.9939i 1.19693 + 1.98752i
\(311\) 29.4211i 1.66832i −0.551525 0.834158i \(-0.685954\pi\)
0.551525 0.834158i \(-0.314046\pi\)
\(312\) 15.0266 + 12.8950i 0.850715 + 0.730038i
\(313\) 12.3284 0.696841 0.348420 0.937338i \(-0.386718\pi\)
0.348420 + 0.937338i \(0.386718\pi\)
\(314\) −5.70330 + 3.43466i −0.321856 + 0.193829i
\(315\) −7.03894 + 23.9383i −0.396599 + 1.34877i
\(316\) −3.03593 1.60645i −0.170785 0.0903699i
\(317\) −0.0346918 + 0.0346918i −0.00194848 + 0.00194848i −0.708080 0.706132i \(-0.750439\pi\)
0.706132 + 0.708080i \(0.250439\pi\)
\(318\) 3.35940 14.8476i 0.188386 0.832611i
\(319\) 6.42276 0.359606
\(320\) −19.6390 15.7092i −1.09786 0.878169i
\(321\) 0.165711 + 7.95306i 0.00924910 + 0.443896i
\(322\) −6.20825 28.5112i −0.345972 1.58887i
\(323\) −5.51314 + 5.51314i −0.306759 + 0.306759i
\(324\) −16.5555 7.06518i −0.919748 0.392510i
\(325\) 13.9539 + 13.9539i 0.774022 + 0.774022i
\(326\) −6.36026 10.5613i −0.352262 0.584937i
\(327\) −0.335548 16.1041i −0.0185559 0.890561i
\(328\) −8.51181 + 9.51056i −0.469986 + 0.525133i
\(329\) −10.8404 22.0045i −0.597652 1.21315i
\(330\) 16.8521 + 26.7080i 0.927680 + 1.47023i
\(331\) 7.94426 7.94426i 0.436656 0.436656i −0.454229 0.890885i \(-0.650085\pi\)
0.890885 + 0.454229i \(0.150085\pi\)
\(332\) −1.81047 5.87969i −0.0993625 0.322690i
\(333\) 4.25404 + 3.91353i 0.233120 + 0.214460i
\(334\) 4.47356 18.0192i 0.244782 0.985968i
\(335\) −43.8945 −2.39821
\(336\) 17.5618 5.25204i 0.958074 0.286522i
\(337\) −34.5423 −1.88164 −0.940819 0.338909i \(-0.889942\pi\)
−0.940819 + 0.338909i \(0.889942\pi\)
\(338\) −1.13701 + 4.57980i −0.0618451 + 0.249108i
\(339\) 3.42074 3.56632i 0.185789 0.193696i
\(340\) 19.1105 5.88451i 1.03642 0.319132i
\(341\) −26.6464 + 26.6464i −1.44299 + 1.44299i
\(342\) −5.73219 8.67862i −0.309962 0.469286i
\(343\) 18.1600 + 3.63503i 0.980549 + 0.196273i
\(344\) 14.4234 0.799309i 0.777660 0.0430959i
\(345\) 42.4529 0.884555i 2.28559 0.0476228i
\(346\) −6.51773 10.8228i −0.350395 0.581837i
\(347\) 16.1082 + 16.1082i 0.864732 + 0.864732i 0.991883 0.127152i \(-0.0405835\pi\)
−0.127152 + 0.991883i \(0.540583\pi\)
\(348\) 4.84692 + 2.43687i 0.259822 + 0.130630i
\(349\) 0.472415 0.472415i 0.0252878 0.0252878i −0.694350 0.719638i \(-0.744308\pi\)
0.719638 + 0.694350i \(0.244308\pi\)
\(350\) 17.8498 3.88675i 0.954110 0.207755i
\(351\) −1.31177 20.9612i −0.0700171 1.11882i
\(352\) 9.69940 21.0750i 0.516980 1.12330i
\(353\) 25.5518 1.35998 0.679991 0.733220i \(-0.261983\pi\)
0.679991 + 0.733220i \(0.261983\pi\)
\(354\) −1.59226 0.360264i −0.0846277 0.0191478i
\(355\) −29.6432 + 29.6432i −1.57330 + 1.57330i
\(356\) 1.65486 3.12742i 0.0877075 0.165753i
\(357\) −4.40189 + 13.8938i −0.232973 + 0.735340i
\(358\) −11.8332 + 7.12624i −0.625405 + 0.376633i
\(359\) 0.233640 0.0123310 0.00616552 0.999981i \(-0.498037\pi\)
0.00616552 + 0.999981i \(0.498037\pi\)
\(360\) 2.58409 + 26.5490i 0.136193 + 1.39926i
\(361\) 12.9902i 0.683695i
\(362\) 0.821804 + 1.36462i 0.0431931 + 0.0717227i
\(363\) −6.97774 + 7.27471i −0.366236 + 0.381823i
\(364\) 14.6793 + 15.5546i 0.769403 + 0.815285i
\(365\) −17.9117 + 17.9117i −0.937539 + 0.937539i
\(366\) −21.6790 4.90507i −1.13318 0.256392i
\(367\) 24.9794i 1.30391i 0.758257 + 0.651956i \(0.226051\pi\)
−0.758257 + 0.651956i \(0.773949\pi\)
\(368\) −17.5468 25.7910i −0.914690 1.34445i
\(369\) 13.5258 0.563895i 0.704123 0.0293552i
\(370\) 2.06399 8.31363i 0.107302 0.432205i
\(371\) 5.29156 15.5679i 0.274724 0.808243i
\(372\) −30.2186 + 9.99869i −1.56676 + 0.518408i
\(373\) −11.1769 + 11.1769i −0.578718 + 0.578718i −0.934550 0.355832i \(-0.884197\pi\)
0.355832 + 0.934550i \(0.384197\pi\)
\(374\) 9.51635 + 15.8020i 0.492079 + 0.817104i
\(375\) −0.0133460 0.640519i −0.000689182 0.0330763i
\(376\) −19.5404 17.4884i −1.00772 0.901895i
\(377\) 6.32985i 0.326004i
\(378\) −16.9823 9.46575i −0.873477 0.486866i
\(379\) 13.0511 13.0511i 0.670389 0.670389i −0.287417 0.957806i \(-0.592796\pi\)
0.957806 + 0.287417i \(0.0927964\pi\)
\(380\) −7.20877 + 13.6234i −0.369802 + 0.698866i
\(381\) 1.20426 + 1.15510i 0.0616961 + 0.0591776i
\(382\) −0.255388 + 1.02869i −0.0130668 + 0.0526323i
\(383\) 14.0708 0.718984 0.359492 0.933148i \(-0.382950\pi\)
0.359492 + 0.933148i \(0.382950\pi\)
\(384\) 15.3157 12.2241i 0.781577 0.623809i
\(385\) 15.0744 + 30.5989i 0.768264 + 1.55947i
\(386\) −5.50363 1.36636i −0.280127 0.0695460i
\(387\) −11.2761 10.3735i −0.573195 0.527314i
\(388\) 3.03844 5.74215i 0.154253 0.291514i
\(389\) 13.8414 + 13.8414i 0.701787 + 0.701787i 0.964794 0.263007i \(-0.0847142\pi\)
−0.263007 + 0.964794i \(0.584714\pi\)
\(390\) −26.3217 + 16.6084i −1.33285 + 0.840998i
\(391\) 24.8024 1.25431
\(392\) 19.4595 3.65083i 0.982852 0.184395i
\(393\) 0.385484 + 18.5007i 0.0194451 + 0.933239i
\(394\) −3.24027 5.38052i −0.163243 0.271067i
\(395\) 3.81752 3.81752i 0.192080 0.192080i
\(396\) −23.1955 + 8.21482i −1.16562 + 0.412810i
\(397\) −14.4891 + 14.4891i −0.727185 + 0.727185i −0.970058 0.242873i \(-0.921910\pi\)
0.242873 + 0.970058i \(0.421910\pi\)
\(398\) 28.5721 + 7.09348i 1.43219 + 0.355564i
\(399\) −5.17354 9.97198i −0.259001 0.499223i
\(400\) 16.1467 10.9854i 0.807337 0.549268i
\(401\) 27.8553i 1.39103i −0.718514 0.695513i \(-0.755177\pi\)
0.718514 0.695513i \(-0.244823\pi\)
\(402\) 7.54781 33.3591i 0.376451 1.66380i
\(403\) −26.2610 26.2610i −1.30815 1.30815i
\(404\) −8.59062 + 2.64522i −0.427399 + 0.131605i
\(405\) 18.2712 21.6017i 0.907905 1.07339i
\(406\) 4.93013 + 3.16700i 0.244678 + 0.157176i
\(407\) 7.90213 0.391694
\(408\) 1.18601 + 15.5356i 0.0587163 + 0.769126i
\(409\) −8.40568 −0.415634 −0.207817 0.978168i \(-0.566636\pi\)
−0.207817 + 0.978168i \(0.566636\pi\)
\(410\) −10.3496 17.1857i −0.511131 0.848741i
\(411\) −0.450288 0.431907i −0.0222111 0.0213044i
\(412\) 0.411294 + 0.217635i 0.0202630 + 0.0107221i
\(413\) −1.66950 0.567469i −0.0821509 0.0279233i
\(414\) −6.62767 + 32.4156i −0.325732 + 1.59314i
\(415\) 9.66996 0.474679
\(416\) 20.7701 + 9.55910i 1.01834 + 0.468673i
\(417\) −0.377798 18.1319i −0.0185009 0.887921i
\(418\) −13.7996 3.42598i −0.674962 0.167570i
\(419\) 15.2311 + 15.2311i 0.744086 + 0.744086i 0.973361 0.229276i \(-0.0736358\pi\)
−0.229276 + 0.973361i \(0.573636\pi\)
\(420\) −0.233707 + 28.8108i −0.0114037 + 1.40582i
\(421\) −27.3478 + 27.3478i −1.33285 + 1.33285i −0.430039 + 0.902810i \(0.641500\pi\)
−0.902810 + 0.430039i \(0.858500\pi\)
\(422\) −2.35152 3.90473i −0.114470 0.190079i
\(423\) 1.15858 + 27.7901i 0.0563321 + 1.35120i
\(424\) −0.972627 17.5509i −0.0472349 0.852349i
\(425\) 15.5279i 0.753212i
\(426\) −17.4311 27.6256i −0.844540 1.33847i
\(427\) −22.7306 7.72621i −1.10001 0.373897i
\(428\) 2.70312 + 8.77865i 0.130660 + 0.424332i
\(429\) −20.7205 19.8747i −1.00040 0.959557i
\(430\) −5.47096 + 22.0367i −0.263833 + 1.06270i
\(431\) 21.9259i 1.05613i 0.849203 + 0.528067i \(0.177083\pi\)
−0.849203 + 0.528067i \(0.822917\pi\)
\(432\) −20.6212 2.60133i −0.992137 0.125157i
\(433\) 36.1727i 1.73835i −0.494504 0.869175i \(-0.664650\pi\)
0.494504 0.869175i \(-0.335350\pi\)
\(434\) −33.5930 + 7.31480i −1.61251 + 0.351121i
\(435\) −5.90266 + 6.15387i −0.283011 + 0.295056i
\(436\) −5.47354 17.7759i −0.262135 0.851309i
\(437\) −13.5184 + 13.5184i −0.646674 + 0.646674i
\(438\) −10.5326 16.6926i −0.503267 0.797601i
\(439\) 24.2387 1.15685 0.578425 0.815736i \(-0.303668\pi\)
0.578425 + 0.815736i \(0.303668\pi\)
\(440\) 27.1724 + 24.3189i 1.29540 + 1.15936i
\(441\) −17.1687 12.0927i −0.817559 0.575844i
\(442\) −15.5735 + 9.37870i −0.740754 + 0.446099i
\(443\) −17.1906 17.1906i −0.816751 0.816751i 0.168885 0.985636i \(-0.445983\pi\)
−0.985636 + 0.168885i \(0.945983\pi\)
\(444\) 5.96332 + 2.99816i 0.283006 + 0.142286i
\(445\) 3.93256 + 3.93256i 0.186421 + 0.186421i
\(446\) −2.01151 + 8.10224i −0.0952477 + 0.383652i
\(447\) 0.442809 + 21.2519i 0.0209441 + 1.00518i
\(448\) 17.8372 11.3945i 0.842727 0.538342i
\(449\) 17.0216i 0.803299i −0.915793 0.401650i \(-0.868437\pi\)
0.915793 0.401650i \(-0.131563\pi\)
\(450\) −20.2942 4.14933i −0.956676 0.195601i
\(451\) 13.0862 13.0862i 0.616205 0.616205i
\(452\) 2.66879 5.04358i 0.125529 0.237230i
\(453\) −9.14190 + 9.53097i −0.429524 + 0.447804i
\(454\) 10.2795 + 17.0693i 0.482441 + 0.801101i
\(455\) −30.1563 + 14.8564i −1.41375 + 0.696478i
\(456\) −9.11400 7.82114i −0.426802 0.366259i
\(457\) 18.4609i 0.863565i −0.901978 0.431783i \(-0.857885\pi\)
0.901978 0.431783i \(-0.142115\pi\)
\(458\) 15.1425 + 25.1443i 0.707561 + 1.17491i
\(459\) 10.9329 12.3926i 0.510304 0.578439i
\(460\) 46.8598 14.4291i 2.18485 0.672758i
\(461\) 0.625538 + 0.625538i 0.0291342 + 0.0291342i 0.721524 0.692390i \(-0.243442\pi\)
−0.692390 + 0.721524i \(0.743442\pi\)
\(462\) −25.8468 + 6.19474i −1.20250 + 0.288205i
\(463\) 33.6057 1.56179 0.780895 0.624662i \(-0.214763\pi\)
0.780895 + 0.624662i \(0.214763\pi\)
\(464\) 6.15392 + 1.17067i 0.285689 + 0.0543469i
\(465\) −1.04222 50.0196i −0.0483316 2.31960i
\(466\) 18.2939 + 4.54175i 0.847448 + 0.210392i
\(467\) −13.9953 13.9953i −0.647626 0.647626i 0.304793 0.952419i \(-0.401413\pi\)
−0.952419 + 0.304793i \(0.901413\pi\)
\(468\) −8.09599 22.8599i −0.374237 1.05670i
\(469\) 11.8889 34.9775i 0.548980 1.61511i
\(470\) 35.3098 21.2644i 1.62872 0.980852i
\(471\) 8.15217 0.169860i 0.375632 0.00782673i
\(472\) −1.88217 + 0.104305i −0.0866339 + 0.00480102i
\(473\) −20.9460 −0.963096
\(474\) 2.24482 + 3.55769i 0.103108 + 0.163410i
\(475\) −8.46336 8.46336i −0.388326 0.388326i
\(476\) −0.487048 + 16.8221i −0.0223238 + 0.771040i
\(477\) −12.6228 + 13.7211i −0.577959 + 0.628246i
\(478\) 5.39543 21.7325i 0.246781 0.994020i
\(479\) 35.3621 1.61574 0.807868 0.589364i \(-0.200621\pi\)
0.807868 + 0.589364i \(0.200621\pi\)
\(480\) 11.2787 + 28.6617i 0.514801 + 1.30822i
\(481\) 7.78782i 0.355094i
\(482\) 1.62664 6.55200i 0.0740913 0.298435i
\(483\) −10.7936 + 34.0683i −0.491126 + 1.55016i
\(484\) −5.44389 + 10.2881i −0.247450 + 0.467639i
\(485\) 7.22044 + 7.22044i 0.327863 + 0.327863i
\(486\) 13.2751 + 17.6003i 0.602171 + 0.798367i
\(487\) 10.2503i 0.464484i −0.972658 0.232242i \(-0.925394\pi\)
0.972658 0.232242i \(-0.0746061\pi\)
\(488\) −25.6261 + 1.42013i −1.16004 + 0.0642864i
\(489\) 0.314545 + 15.0961i 0.0142242 + 0.682669i
\(490\) −3.51685 + 30.9209i −0.158875 + 1.39686i
\(491\) 1.50660 + 1.50660i 0.0679920 + 0.0679920i 0.740285 0.672293i \(-0.234691\pi\)
−0.672293 + 0.740285i \(0.734691\pi\)
\(492\) 14.8405 4.91040i 0.669061 0.221378i
\(493\) −3.52192 + 3.52192i −0.158619 + 0.158619i
\(494\) 3.37642 13.6000i 0.151912 0.611894i
\(495\) −1.61109 38.6442i −0.0724133 1.73693i
\(496\) −30.3879 + 20.6743i −1.36446 + 0.928303i
\(497\) −15.5923 31.6502i −0.699411 1.41970i
\(498\) −1.66278 + 7.34901i −0.0745110 + 0.329317i
\(499\) 15.9716 + 15.9716i 0.714987 + 0.714987i 0.967574 0.252587i \(-0.0812814\pi\)
−0.252587 + 0.967574i \(0.581281\pi\)
\(500\) −0.217702 0.707010i −0.00973594 0.0316184i
\(501\) −15.7404 + 16.4103i −0.703229 + 0.733157i
\(502\) 11.8323 7.12566i 0.528100 0.318034i
\(503\) 13.4898i 0.601482i −0.953706 0.300741i \(-0.902766\pi\)
0.953706 0.300741i \(-0.0972339\pi\)
\(504\) −21.8556 5.13173i −0.973524 0.228585i
\(505\) 14.1285i 0.628708i
\(506\) 23.3345 + 38.7472i 1.03734 + 1.72252i
\(507\) 4.00061 4.17087i 0.177673 0.185235i
\(508\) 1.70309 + 0.901185i 0.0755626 + 0.0399836i
\(509\) −15.0378 15.0378i −0.666538 0.666538i 0.290375 0.956913i \(-0.406220\pi\)
−0.956913 + 0.290375i \(0.906220\pi\)
\(510\) −23.8862 5.40448i −1.05770 0.239314i
\(511\) −9.42154 19.1244i −0.416784 0.846012i
\(512\) 13.1347 18.4250i 0.580478 0.814276i
\(513\) 0.795619 + 12.7134i 0.0351275 + 0.561312i
\(514\) 36.3138 + 9.01548i 1.60173 + 0.397656i
\(515\) −0.517180 + 0.517180i −0.0227897 + 0.0227897i
\(516\) −15.8068 7.94713i −0.695856 0.349853i
\(517\) 26.8869 + 26.8869i 1.18249 + 1.18249i
\(518\) 6.06570 + 3.89646i 0.266511 + 0.171201i
\(519\) 0.322332 + 15.4699i 0.0141488 + 0.679051i
\(520\) −23.9671 + 26.7794i −1.05103 + 1.17435i
\(521\) 12.8211i 0.561704i −0.959751 0.280852i \(-0.909383\pi\)
0.959751 0.280852i \(-0.0906170\pi\)
\(522\) −3.66186 5.54411i −0.160275 0.242659i
\(523\) 20.0902 + 20.0902i 0.878485 + 0.878485i 0.993378 0.114893i \(-0.0366526\pi\)
−0.114893 + 0.993378i \(0.536653\pi\)
\(524\) 6.28810 + 20.4212i 0.274697 + 0.892106i
\(525\) −21.3288 6.75745i −0.930866 0.294920i
\(526\) 18.5025 + 4.59353i 0.806746 + 0.200287i
\(527\) 29.2232i 1.27298i
\(528\) −23.1544 + 16.4689i −1.00767 + 0.716717i
\(529\) 37.8166 1.64420
\(530\) 26.8150 + 6.65726i 1.16477 + 0.289173i
\(531\) 1.47146 + 1.35368i 0.0638558 + 0.0587445i
\(532\) −8.90333 9.43426i −0.386008 0.409027i
\(533\) 12.8969 + 12.8969i 0.558627 + 0.558627i
\(534\) −3.66490 + 2.31247i −0.158596 + 0.100070i
\(535\) −14.4377 −0.624196
\(536\) −2.18527 39.4330i −0.0943894 1.70325i
\(537\) 16.9142 0.352426i 0.729900 0.0152083i
\(538\) −17.3650 28.8349i −0.748659 1.24316i
\(539\) −28.4658 + 3.72430i −1.22611 + 0.160417i
\(540\) 13.4462 29.7740i 0.578634 1.28127i
\(541\) 0.677305 + 0.677305i 0.0291196 + 0.0291196i 0.721517 0.692397i \(-0.243445\pi\)
−0.692397 + 0.721517i \(0.743445\pi\)
\(542\) −5.54705 + 22.3432i −0.238266 + 0.959722i
\(543\) −0.0406421 1.95056i −0.00174412 0.0837063i
\(544\) 6.23781 + 16.8752i 0.267444 + 0.723516i
\(545\) 29.2348 1.25228
\(546\) −6.10513 25.4729i −0.261275 1.09014i
\(547\) 2.69994 + 2.69994i 0.115441 + 0.115441i 0.762467 0.647027i \(-0.223988\pi\)
−0.647027 + 0.762467i \(0.723988\pi\)
\(548\) −0.636808 0.336965i −0.0272031 0.0143944i
\(549\) 20.0342 + 18.4306i 0.855039 + 0.786598i
\(550\) −24.2581 + 14.6088i −1.03437 + 0.622922i
\(551\) 3.83921i 0.163556i
\(552\) 2.90815 + 38.0938i 0.123779 + 1.62138i
\(553\) 2.00801 + 4.07598i 0.0853895 + 0.173328i
\(554\) −31.1636 + 18.7674i −1.32402 + 0.797352i
\(555\) −7.26223 + 7.57131i −0.308265 + 0.321384i
\(556\) −6.16273 20.0141i −0.261358 0.848786i
\(557\) −7.69062 + 7.69062i −0.325862 + 0.325862i −0.851011 0.525148i \(-0.824010\pi\)
0.525148 + 0.851011i \(0.324010\pi\)
\(558\) 38.1933 + 7.80897i 1.61685 + 0.330580i
\(559\) 20.6430i 0.873105i
\(560\) 8.86623 + 32.0657i 0.374667 + 1.35502i
\(561\) −0.470628 22.5871i −0.0198699 0.953628i
\(562\) 19.3981 + 4.81588i 0.818259 + 0.203146i
\(563\) 16.2002 + 16.2002i 0.682758 + 0.682758i 0.960621 0.277863i \(-0.0896261\pi\)
−0.277863 + 0.960621i \(0.589626\pi\)
\(564\) 10.0889 + 30.4913i 0.424821 + 1.28392i
\(565\) 6.34203 + 6.34203i 0.266811 + 0.266811i
\(566\) −14.8371 24.6372i −0.623649 1.03558i
\(567\) 12.2645 + 20.4103i 0.515062 + 0.857153i
\(568\) −28.1060 25.1544i −1.17930 1.05546i
\(569\) −43.9239 −1.84139 −0.920693 0.390287i \(-0.872376\pi\)
−0.920693 + 0.390287i \(0.872376\pi\)
\(570\) 15.9647 10.0734i 0.668689 0.421927i
\(571\) 10.2306 10.2306i 0.428136 0.428136i −0.459857 0.887993i \(-0.652099\pi\)
0.887993 + 0.459857i \(0.152099\pi\)
\(572\) −29.3034 15.5058i −1.22524 0.648330i
\(573\) 0.898594 0.936837i 0.0375393 0.0391369i
\(574\) 16.4977 3.59233i 0.688599 0.149941i
\(575\) 38.0749i 1.58783i
\(576\) −23.7219 + 3.64317i −0.988411 + 0.151799i
\(577\) 47.0721i 1.95964i −0.199887 0.979819i \(-0.564057\pi\)
0.199887 0.979819i \(-0.435943\pi\)
\(578\) 9.44994 + 2.34610i 0.393066 + 0.0975848i
\(579\) 5.01221 + 4.80760i 0.208300 + 0.199797i
\(580\) −4.60514 + 8.70296i −0.191218 + 0.361371i
\(581\) −2.61913 + 7.70553i −0.108660 + 0.319679i
\(582\) −6.72900 + 4.24584i −0.278926 + 0.175996i
\(583\) 25.4878i 1.05560i
\(584\) −16.9828 15.1994i −0.702754 0.628954i
\(585\) 38.0852 1.58779i 1.57463 0.0656470i
\(586\) −26.0910 + 15.7126i −1.07781 + 0.649081i
\(587\) 2.19342 2.19342i 0.0905321 0.0905321i −0.660390 0.750922i \(-0.729609\pi\)
0.750922 + 0.660390i \(0.229609\pi\)
\(588\) −22.8946 7.98970i −0.944159 0.329490i
\(589\) 15.9279 + 15.9279i 0.656298 + 0.656298i
\(590\) 0.713927 2.87566i 0.0293919 0.118389i
\(591\) 0.160247 + 7.69080i 0.00659167 + 0.316357i
\(592\) 7.57137 + 1.44031i 0.311181 + 0.0591964i
\(593\) −14.4280 −0.592486 −0.296243 0.955113i \(-0.595734\pi\)
−0.296243 + 0.955113i \(0.595734\pi\)
\(594\) 29.6460 + 5.42060i 1.21639 + 0.222410i
\(595\) −25.0450 8.51286i −1.02674 0.348993i
\(596\) 7.22319 + 23.4580i 0.295873 + 0.960878i
\(597\) −26.0209 24.9587i −1.06496 1.02149i
\(598\) −38.1867 + 22.9969i −1.56157 + 0.940414i
\(599\) −2.15985 −0.0882491 −0.0441245 0.999026i \(-0.514050\pi\)
−0.0441245 + 0.999026i \(0.514050\pi\)
\(600\) −23.8491 + 1.82068i −0.973635 + 0.0743289i
\(601\) −37.1400 −1.51497 −0.757486 0.652852i \(-0.773572\pi\)
−0.757486 + 0.652852i \(0.773572\pi\)
\(602\) −16.0782 10.3282i −0.655298 0.420948i
\(603\) −28.3606 + 30.8282i −1.15493 + 1.25542i
\(604\) −7.13232 + 13.4789i −0.290210 + 0.548450i
\(605\) −12.9367 12.9367i −0.525951 0.525951i
\(606\) 10.7374 + 2.42944i 0.436177 + 0.0986891i
\(607\) 23.9590i 0.972466i −0.873829 0.486233i \(-0.838371\pi\)
0.873829 0.486233i \(-0.161629\pi\)
\(608\) −12.5976 5.79782i −0.510899 0.235133i
\(609\) −3.30498 6.37034i −0.133924 0.258139i
\(610\) 9.72027 39.1527i 0.393562 1.58524i
\(611\) −26.4980 + 26.4980i −1.07199 + 1.07199i
\(612\) 8.21464 17.2238i 0.332057 0.696233i
\(613\) −17.2986 + 17.2986i −0.698684 + 0.698684i −0.964127 0.265443i \(-0.914482\pi\)
0.265443 + 0.964127i \(0.414482\pi\)
\(614\) 31.4178 18.9205i 1.26792 0.763569i
\(615\) 0.511837 + 24.5648i 0.0206393 + 0.990550i
\(616\) −26.7383 + 15.0656i −1.07732 + 0.607010i
\(617\) 33.2050 1.33678 0.668392 0.743809i \(-0.266983\pi\)
0.668392 + 0.743809i \(0.266983\pi\)
\(618\) −0.304118 0.481980i −0.0122334 0.0193881i
\(619\) −14.3872 14.3872i −0.578269 0.578269i 0.356157 0.934426i \(-0.384087\pi\)
−0.934426 + 0.356157i \(0.884087\pi\)
\(620\) −17.0008 55.2120i −0.682770 2.21737i
\(621\) 26.8079 30.3872i 1.07576 1.21940i
\(622\) −10.0254 + 40.3818i −0.401983 + 1.61916i
\(623\) −4.19881 + 2.06853i −0.168222 + 0.0828737i
\(624\) −16.2307 22.8195i −0.649747 0.913509i
\(625\) 25.5745 1.02298
\(626\) −16.9213 4.20097i −0.676310 0.167905i
\(627\) 12.5675 + 12.0544i 0.501897 + 0.481408i
\(628\) 8.99843 2.77079i 0.359076 0.110567i
\(629\) −4.33314 + 4.33314i −0.172773 + 0.172773i
\(630\) 17.8184 30.4578i 0.709902 1.21347i
\(631\) 27.6812i 1.10197i −0.834515 0.550985i \(-0.814252\pi\)
0.834515 0.550985i \(-0.185748\pi\)
\(632\) 3.61955 + 3.23944i 0.143978 + 0.128858i
\(633\) 0.116294 + 5.58133i 0.00462225 + 0.221838i
\(634\) 0.0594375 0.0357946i 0.00236056 0.00142159i
\(635\) −2.14155 + 2.14155i −0.0849847 + 0.0849847i
\(636\) −9.67035 + 19.2343i −0.383454 + 0.762688i
\(637\) −3.67043 28.0540i −0.145428 1.11154i
\(638\) −8.81554 2.18860i −0.349011 0.0866474i
\(639\) 1.66644 + 39.9719i 0.0659235 + 1.58126i
\(640\) 21.6025 + 28.2537i 0.853914 + 1.11683i
\(641\) 13.2304i 0.522570i 0.965262 + 0.261285i \(0.0841462\pi\)
−0.965262 + 0.261285i \(0.915854\pi\)
\(642\) 2.48261 10.9724i 0.0979808 0.433047i
\(643\) 7.38127 7.38127i 0.291089 0.291089i −0.546421 0.837510i \(-0.684010\pi\)
0.837510 + 0.546421i \(0.184010\pi\)
\(644\) −1.19426 + 41.2485i −0.0470605 + 1.62542i
\(645\) 19.2498 20.0691i 0.757961 0.790219i
\(646\) 9.44567 5.68840i 0.371635 0.223807i
\(647\) 28.9588i 1.13849i 0.822169 + 0.569244i \(0.192764\pi\)
−0.822169 + 0.569244i \(0.807236\pi\)
\(648\) 20.3156 + 15.3387i 0.798074 + 0.602560i
\(649\) 2.73332 0.107292
\(650\) −14.3975 23.9072i −0.564716 0.937719i
\(651\) 40.1405 + 12.7174i 1.57323 + 0.498435i
\(652\) 5.13092 + 16.6632i 0.200942 + 0.652581i
\(653\) 23.4762 23.4762i 0.918695 0.918695i −0.0782393 0.996935i \(-0.524930\pi\)
0.996935 + 0.0782393i \(0.0249298\pi\)
\(654\) −5.02703 + 22.2180i −0.196572 + 0.868793i
\(655\) −33.5855 −1.31230
\(656\) 14.9236 10.1532i 0.582670 0.396417i
\(657\) 1.00694 + 24.1527i 0.0392843 + 0.942286i
\(658\) 7.38082 + 33.8962i 0.287734 + 1.32141i
\(659\) 10.7532 10.7532i 0.418885 0.418885i −0.465934 0.884819i \(-0.654282\pi\)
0.884819 + 0.465934i \(0.154282\pi\)
\(660\) −14.0294 42.4005i −0.546094 1.65044i
\(661\) 31.4992 + 31.4992i 1.22518 + 1.22518i 0.965768 + 0.259409i \(0.0835277\pi\)
0.259409 + 0.965768i \(0.416472\pi\)
\(662\) −13.6109 + 8.19681i −0.529004 + 0.318578i
\(663\) 22.2604 0.463821i 0.864521 0.0180133i
\(664\) 0.481415 + 8.68708i 0.0186825 + 0.337124i
\(665\) 18.2905 9.01074i 0.709276 0.349422i
\(666\) −4.50531 6.82109i −0.174577 0.264312i
\(667\) −8.63589 + 8.63589i −0.334383 + 0.334383i
\(668\) −12.2803 + 23.2078i −0.475140 + 0.897938i
\(669\) 7.07758 7.37879i 0.273635 0.285281i
\(670\) 60.2473 + 14.9573i 2.32756 + 0.577853i
\(671\) 37.2147 1.43666
\(672\) −25.8940 + 1.22438i −0.998884 + 0.0472315i
\(673\) 20.2590 0.780926 0.390463 0.920619i \(-0.372315\pi\)
0.390463 + 0.920619i \(0.372315\pi\)
\(674\) 47.4109 + 11.7705i 1.82620 + 0.453383i
\(675\) 19.0243 + 16.7834i 0.732244 + 0.645993i
\(676\) 3.12119 5.89855i 0.120046 0.226867i
\(677\) 1.04757 1.04757i 0.0402613 0.0402613i −0.686690 0.726951i \(-0.740937\pi\)
0.726951 + 0.686690i \(0.240937\pi\)
\(678\) −5.91037 + 3.72931i −0.226987 + 0.143223i
\(679\) −7.70930 + 3.79795i −0.295856 + 0.145752i
\(680\) −28.2353 + 1.56473i −1.08277 + 0.0600045i
\(681\) −0.508370 24.3985i −0.0194808 0.934951i
\(682\) 45.6534 27.4935i 1.74816 1.05278i
\(683\) 2.84341 + 2.84341i 0.108800 + 0.108800i 0.759411 0.650611i \(-0.225487\pi\)
−0.650611 + 0.759411i \(0.725487\pi\)
\(684\) 4.91041 + 13.8651i 0.187754 + 0.530145i
\(685\) 0.800752 0.800752i 0.0305952 0.0305952i
\(686\) −23.6868 11.1774i −0.904367 0.426755i
\(687\) −0.748866 35.9407i −0.0285710 1.37122i
\(688\) −20.0692 3.81779i −0.765132 0.145552i
\(689\) −25.1191 −0.956961
\(690\) −58.5700 13.2520i −2.22972 0.504495i
\(691\) −20.4173 + 20.4173i −0.776709 + 0.776709i −0.979270 0.202560i \(-0.935074\pi\)
0.202560 + 0.979270i \(0.435074\pi\)
\(692\) 5.25795 + 17.0757i 0.199877 + 0.649122i
\(693\) 31.2301 + 9.18307i 1.18633 + 0.348836i
\(694\) −16.6203 27.5982i −0.630896 1.04761i
\(695\) 32.9159 1.24857
\(696\) −5.82224 4.99633i −0.220691 0.189386i
\(697\) 14.3516i 0.543607i
\(698\) −0.809390 + 0.487433i −0.0306359 + 0.0184496i
\(699\) −16.6604 15.9803i −0.630155 0.604431i
\(700\) −25.8241 0.747681i −0.976059 0.0282597i
\(701\) 15.5364 15.5364i 0.586803 0.586803i −0.349961 0.936764i \(-0.613805\pi\)
0.936764 + 0.349961i \(0.113805\pi\)
\(702\) −5.34219 + 29.2172i −0.201628 + 1.10273i
\(703\) 4.72350i 0.178150i
\(704\) −20.4943 + 25.6213i −0.772409 + 0.965638i
\(705\) −50.4710 + 1.05162i −1.90085 + 0.0396064i
\(706\) −35.0710 8.70693i −1.31991 0.327689i
\(707\) 11.2583 + 3.82672i 0.423412 + 0.143919i
\(708\) 2.06269 + 1.03705i 0.0775206 + 0.0389748i
\(709\) 12.0126 12.0126i 0.451143 0.451143i −0.444591 0.895734i \(-0.646651\pi\)
0.895734 + 0.444591i \(0.146651\pi\)
\(710\) 50.7878 30.5856i 1.90603 1.14786i
\(711\) −0.214608 5.14767i −0.00804844 0.193053i
\(712\) −3.33706 + 3.72863i −0.125062 + 0.139736i
\(713\) 71.6563i 2.68355i
\(714\) 10.7762 17.5700i 0.403290 0.657540i
\(715\) 36.8475 36.8475i 1.37802 1.37802i
\(716\) 18.6700 5.74885i 0.697730 0.214845i
\(717\) −18.9840 + 19.7920i −0.708972 + 0.739145i
\(718\) −0.320682 0.0796143i −0.0119677 0.00297118i
\(719\) −13.2223 −0.493110 −0.246555 0.969129i \(-0.579299\pi\)
−0.246555 + 0.969129i \(0.579299\pi\)
\(720\) 5.49997 37.3203i 0.204972 1.39085i
\(721\) −0.272037 0.552196i −0.0101312 0.0205648i
\(722\) 4.42649 17.8297i 0.164737 0.663551i
\(723\) −5.72339 + 5.96697i −0.212855 + 0.221914i
\(724\) −0.662962 2.15304i −0.0246388 0.0800170i
\(725\) −5.40660 5.40660i −0.200796 0.200796i
\(726\) 12.0562 7.60716i 0.447447 0.282328i
\(727\) 27.4097 1.01657 0.508284 0.861190i \(-0.330280\pi\)
0.508284 + 0.861190i \(0.330280\pi\)
\(728\) −14.8477 26.3515i −0.550291 0.976653i
\(729\) −3.36619 26.7893i −0.124674 0.992198i
\(730\) 30.6881 18.4811i 1.13582 0.684016i
\(731\) 11.4857 11.4857i 0.424815 0.424815i
\(732\) 28.0840 + 14.1197i 1.03801 + 0.521878i
\(733\) 7.60650 7.60650i 0.280953 0.280953i −0.552536 0.833489i \(-0.686340\pi\)
0.833489 + 0.552536i \(0.186340\pi\)
\(734\) 8.51188 34.2853i 0.314179 1.26550i
\(735\) 22.5923 30.6968i 0.833329 1.13227i
\(736\) 15.2953 + 41.3785i 0.563794 + 1.52523i
\(737\) 57.2652i 2.10939i
\(738\) −18.7569 3.83502i −0.690451 0.141169i
\(739\) −11.0649 11.0649i −0.407030 0.407030i 0.473672 0.880702i \(-0.342928\pi\)
−0.880702 + 0.473672i \(0.842928\pi\)
\(740\) −5.66585 + 10.7075i −0.208281 + 0.393617i
\(741\) −11.8801 + 12.3857i −0.436426 + 0.454999i
\(742\) −12.5678 + 19.5645i −0.461377 + 0.718235i
\(743\) −37.0603 −1.35961 −0.679805 0.733392i \(-0.737936\pi\)
−0.679805 + 0.733392i \(0.737936\pi\)
\(744\) 44.8836 3.42649i 1.64551 0.125621i
\(745\) −38.5800 −1.41346
\(746\) 19.1494 11.5322i 0.701110 0.422224i
\(747\) 6.24784 6.79145i 0.228596 0.248486i
\(748\) −7.67699 24.9318i −0.280699 0.911597i
\(749\) 3.91048 11.5047i 0.142886 0.420373i
\(750\) −0.199943 + 0.883690i −0.00730089 + 0.0322678i
\(751\) 26.5089 0.967324 0.483662 0.875255i \(-0.339306\pi\)
0.483662 + 0.875255i \(0.339306\pi\)
\(752\) 20.8609 + 30.6622i 0.760718 + 1.11813i
\(753\) −16.9128 + 0.352398i −0.616336 + 0.0128421i
\(754\) 2.15694 8.68802i 0.0785511 0.316399i
\(755\) −16.9490 16.9490i −0.616838 0.616838i
\(756\) 20.0835 + 18.7790i 0.730431 + 0.682986i
\(757\) −10.4760 + 10.4760i −0.380755 + 0.380755i −0.871374 0.490619i \(-0.836771\pi\)
0.490619 + 0.871374i \(0.336771\pi\)
\(758\) −22.3605 + 13.4660i −0.812168 + 0.489106i
\(759\) −1.15400 55.3844i −0.0418875 2.01033i
\(760\) 14.5366 16.2423i 0.527299 0.589171i
\(761\) 2.06229i 0.0747578i −0.999301 0.0373789i \(-0.988099\pi\)
0.999301 0.0373789i \(-0.0119008\pi\)
\(762\) −1.25930 1.99579i −0.0456195 0.0722998i
\(763\) −7.91832 + 23.2959i −0.286663 + 0.843366i
\(764\) 0.701064 1.32490i 0.0253636 0.0479331i
\(765\) 22.0740 + 20.3071i 0.798088 + 0.734206i
\(766\) −19.3128 4.79472i −0.697801 0.173240i
\(767\) 2.69378i 0.0972668i
\(768\) −25.1870 + 11.5592i −0.908857 + 0.417108i
\(769\) 29.0064i 1.04600i −0.852333 0.522999i \(-0.824813\pi\)
0.852333 0.522999i \(-0.175187\pi\)
\(770\) −10.2636 47.1352i −0.369874 1.69863i
\(771\) −33.0714 31.7213i −1.19104 1.14242i
\(772\) 7.08839 + 3.75079i 0.255117 + 0.134994i
\(773\) 26.8815 26.8815i 0.966861 0.966861i −0.0326072 0.999468i \(-0.510381\pi\)
0.999468 + 0.0326072i \(0.0103810\pi\)
\(774\) 11.9421 + 18.0805i 0.429250 + 0.649890i
\(775\) 44.8613 1.61146
\(776\) −6.12707 + 6.84601i −0.219949 + 0.245757i
\(777\) −4.06622 7.83763i −0.145875 0.281174i
\(778\) −14.2814 23.7145i −0.512014 0.850207i
\(779\) −7.82227 7.82227i −0.280262 0.280262i
\(780\) 41.7872 13.8265i 1.49622 0.495067i
\(781\) 38.6728 + 38.6728i 1.38382 + 1.38382i
\(782\) −34.0425 8.45159i −1.21736 0.302228i
\(783\) 0.508261 + 8.12165i 0.0181638 + 0.290244i
\(784\) −27.9531 1.62000i −0.998325 0.0578572i
\(785\) 14.7991i 0.528204i
\(786\) 5.77515 25.5245i 0.205993 0.910428i
\(787\) 30.9792 30.9792i 1.10429 1.10429i 0.110401 0.993887i \(-0.464786\pi\)
0.993887 0.110401i \(-0.0352136\pi\)
\(788\) 2.61398 + 8.48916i 0.0931191 + 0.302414i
\(789\) −16.8504 16.1625i −0.599889 0.575401i
\(790\) −6.54057 + 3.93888i −0.232703 + 0.140139i
\(791\) −6.77141 + 3.33591i −0.240764 + 0.118611i
\(792\) 34.6361 3.37122i 1.23074 0.119791i
\(793\) 36.6764i 1.30242i
\(794\) 24.8242 14.9497i 0.880977 0.530544i
\(795\) −24.4207 23.4238i −0.866114 0.830758i
\(796\) −36.7994 19.4723i −1.30432 0.690176i
\(797\) 4.29020 + 4.29020i 0.151967 + 0.151967i 0.778996 0.627029i \(-0.215729\pi\)
−0.627029 + 0.778996i \(0.715729\pi\)
\(798\) 3.70290 + 15.4499i 0.131081 + 0.546921i
\(799\) −29.4869 −1.04317
\(800\) −25.9055 + 9.57583i −0.915898 + 0.338557i
\(801\) 5.30279 0.221076i 0.187365 0.00781132i
\(802\) −9.49186 + 38.2326i −0.335169 + 1.35004i
\(803\) 23.3677 + 23.3677i 0.824629 + 0.824629i
\(804\) −21.7271 + 43.2150i −0.766255 + 1.52408i
\(805\) −61.4113 20.8739i −2.16446 0.735707i
\(806\) 27.0958 + 44.9930i 0.954410 + 1.58481i
\(807\) 0.858782 + 41.2159i 0.0302306 + 1.45087i
\(808\) 12.6924 0.703379i 0.446517 0.0247448i
\(809\) −14.1148 −0.496251 −0.248126 0.968728i \(-0.579815\pi\)
−0.248126 + 0.968728i \(0.579815\pi\)
\(810\) −32.4390 + 23.4232i −1.13979 + 0.823009i
\(811\) 29.4702 + 29.4702i 1.03484 + 1.03484i 0.999371 + 0.0354672i \(0.0112919\pi\)
0.0354672 + 0.999371i \(0.488708\pi\)
\(812\) −5.68766 6.02683i −0.199598 0.211500i
\(813\) 19.5175 20.3482i 0.684509 0.713641i
\(814\) −10.8460 2.69270i −0.380154 0.0943791i
\(815\) −27.4049 −0.959952
\(816\) 3.66599 21.7274i 0.128335 0.760613i
\(817\) 12.5205i 0.438035i
\(818\) 11.5372 + 2.86429i 0.403388 + 0.100148i
\(819\) −9.05023 + 30.7783i −0.316241 + 1.07548i
\(820\) 8.34920 + 27.1149i 0.291567 + 0.946892i
\(821\) −16.6585 16.6585i −0.581385 0.581385i 0.353899 0.935284i \(-0.384856\pi\)
−0.935284 + 0.353899i \(0.884856\pi\)
\(822\) 0.470867 + 0.746251i 0.0164234 + 0.0260285i
\(823\) 9.83628i 0.342871i −0.985195 0.171436i \(-0.945159\pi\)
0.985195 0.171436i \(-0.0548406\pi\)
\(824\) −0.490360 0.438865i −0.0170825 0.0152886i
\(825\) 34.6741 0.722474i 1.20720 0.0251533i
\(826\) 2.09810 + 1.34777i 0.0730024 + 0.0468950i
\(827\) 25.6159 + 25.6159i 0.890750 + 0.890750i 0.994594 0.103843i \(-0.0331140\pi\)
−0.103843 + 0.994594i \(0.533114\pi\)
\(828\) 20.1426 42.2335i 0.700004 1.46772i
\(829\) −25.5631 + 25.5631i −0.887842 + 0.887842i −0.994316 0.106473i \(-0.966044\pi\)
0.106473 + 0.994316i \(0.466044\pi\)
\(830\) −13.2725 3.29510i −0.460694 0.114375i
\(831\) 44.5446 0.928138i 1.54523 0.0321968i
\(832\) −25.2507 20.1979i −0.875409 0.700235i
\(833\) 13.5670 17.6514i 0.470068 0.611586i
\(834\) −5.66000 + 25.0156i −0.195990 + 0.866218i
\(835\) −29.1826 29.1826i −1.00990 1.00990i
\(836\) 17.7732 + 9.40463i 0.614700 + 0.325266i
\(837\) −35.8034 31.5861i −1.23755 1.09177i
\(838\) −15.7153 26.0954i −0.542874 0.901451i
\(839\) 39.8283i 1.37502i 0.726173 + 0.687512i \(0.241297\pi\)
−0.726173 + 0.687512i \(0.758703\pi\)
\(840\) 10.1382 39.4645i 0.349802 1.36166i
\(841\) 26.5474i 0.915428i
\(842\) 46.8550 28.2172i 1.61473 0.972428i
\(843\) −17.6660 16.9449i −0.608451 0.583613i
\(844\) 1.89700 + 6.16072i 0.0652976 + 0.212061i
\(845\) 7.41710 + 7.41710i 0.255156 + 0.255156i
\(846\) 7.87945 38.5380i 0.270901 1.32496i
\(847\) 13.8126 6.80469i 0.474605 0.233812i
\(848\) −4.64562 + 24.4209i −0.159531 + 0.838618i
\(849\) 0.733764 + 35.2159i 0.0251827 + 1.20861i
\(850\) 5.29122 21.3127i 0.181487 0.731020i
\(851\) −10.6250 + 10.6250i −0.364221 + 0.364221i
\(852\) 14.5114 + 43.8572i 0.497153 + 1.50252i
\(853\) 39.2358 + 39.2358i 1.34341 + 1.34341i 0.892641 + 0.450768i \(0.148850\pi\)
0.450768 + 0.892641i \(0.351150\pi\)
\(854\) 28.5661 + 18.3502i 0.977513 + 0.627931i
\(855\) −23.0996 + 0.963031i −0.789989 + 0.0329350i
\(856\) −0.718775 12.9702i −0.0245672 0.443313i
\(857\) 26.6809i 0.911403i 0.890133 + 0.455701i \(0.150612\pi\)
−0.890133 + 0.455701i \(0.849388\pi\)
\(858\) 21.6674 + 34.3395i 0.739714 + 1.17233i
\(859\) −12.1110 12.1110i −0.413223 0.413223i 0.469637 0.882860i \(-0.344385\pi\)
−0.882860 + 0.469637i \(0.844385\pi\)
\(860\) 15.0183 28.3822i 0.512120 0.967824i
\(861\) −19.7132 6.24558i −0.671823 0.212849i
\(862\) 7.47139 30.0943i 0.254477 1.02502i
\(863\) 4.01605i 0.136708i −0.997661 0.0683539i \(-0.978225\pi\)
0.997661 0.0683539i \(-0.0217747\pi\)
\(864\) 27.4171 + 10.5972i 0.932749 + 0.360526i
\(865\) −28.0834 −0.954864
\(866\) −12.3261 + 49.6488i −0.418858 + 1.68713i
\(867\) −8.60616 8.25484i −0.292281 0.280349i
\(868\) 48.6005 + 1.40712i 1.64961 + 0.0477609i
\(869\) −4.98037 4.98037i −0.168947 0.168947i
\(870\) 10.1987 6.43511i 0.345767 0.218171i
\(871\) −56.4369 −1.91229
\(872\) 1.45544 + 26.2633i 0.0492876 + 0.889389i
\(873\) 9.73628 0.405910i 0.329523 0.0137380i
\(874\) 23.1612 13.9482i 0.783438 0.471804i
\(875\) −0.314940 + 0.926560i −0.0106469 + 0.0313234i
\(876\) 8.76840 + 26.5004i 0.296257 + 0.895364i
\(877\) −34.9566 34.9566i −1.18040 1.18040i −0.979640 0.200762i \(-0.935658\pi\)
−0.200762 0.979640i \(-0.564342\pi\)
\(878\) −33.2687 8.25949i −1.12277 0.278744i
\(879\) 37.2939 0.777061i 1.25789 0.0262096i
\(880\) −29.0086 42.6380i −0.977880 1.43733i
\(881\) −48.8805 −1.64683 −0.823413 0.567442i \(-0.807933\pi\)
−0.823413 + 0.567442i \(0.807933\pi\)
\(882\) 19.4442 + 22.4482i 0.654722 + 0.755870i
\(883\) 16.8127 + 16.8127i 0.565794 + 0.565794i 0.930947 0.365154i \(-0.118984\pi\)
−0.365154 + 0.930947i \(0.618984\pi\)
\(884\) 24.5712 7.56594i 0.826418 0.254470i
\(885\) −2.51198 + 2.61889i −0.0844393 + 0.0880330i
\(886\) 17.7371 + 29.4527i 0.595890 + 0.989484i
\(887\) 21.7785i 0.731252i −0.930762 0.365626i \(-0.880855\pi\)
0.930762 0.365626i \(-0.119145\pi\)
\(888\) −7.16329 6.14715i −0.240384 0.206285i
\(889\) −1.12645 2.28654i −0.0377800 0.0766881i
\(890\) −4.05758 6.73767i −0.136010 0.225847i
\(891\) −28.1817 23.8368i −0.944123 0.798564i
\(892\) 5.52178 10.4353i 0.184883 0.349399i
\(893\) 16.0717 16.0717i 0.537818 0.537818i
\(894\) 6.63395 29.3201i 0.221873 0.980612i
\(895\) 30.7053i 1.02637i
\(896\) −28.3651 + 9.56143i −0.947612 + 0.319425i
\(897\) 54.5833 1.13731i 1.82248 0.0379736i
\(898\) −5.80022 + 23.3630i −0.193556 + 0.779632i
\(899\) 10.1751 + 10.1751i 0.339360 + 0.339360i
\(900\) 26.4408 + 12.6105i 0.881359 + 0.420351i
\(901\) −13.9762 13.9762i −0.465616 0.465616i
\(902\) −22.4206 + 13.5022i −0.746525 + 0.449574i
\(903\) 10.7782 + 20.7750i 0.358677 + 0.691349i
\(904\) −5.38167 + 6.01315i −0.178992 + 0.199994i
\(905\) 3.54097 0.117706
\(906\) 15.7954 9.96654i 0.524768 0.331116i
\(907\) 18.0784 18.0784i 0.600282 0.600282i −0.340105 0.940387i \(-0.610463\pi\)
0.940387 + 0.340105i \(0.110463\pi\)
\(908\) −8.29264 26.9312i −0.275201 0.893743i
\(909\) −9.92276 9.12851i −0.329117 0.302774i
\(910\) 46.4534 10.1151i 1.53991 0.335313i
\(911\) 9.05700i 0.300072i −0.988681 0.150036i \(-0.952061\pi\)
0.988681 0.150036i \(-0.0479389\pi\)
\(912\) 9.84429 + 13.8405i 0.325977 + 0.458306i
\(913\) 12.6155i 0.417513i
\(914\) −6.29068 + 25.3385i −0.208077 + 0.838122i
\(915\) −34.2012 + 35.6567i −1.13066 + 1.17877i
\(916\) −12.2157 39.6716i −0.403617 1.31079i
\(917\) 9.09672 26.7627i 0.300400 0.883783i
\(918\) −19.2288 + 13.2840i −0.634645 + 0.438438i
\(919\) 48.0828i 1.58611i −0.609152 0.793053i \(-0.708490\pi\)
0.609152 0.793053i \(-0.291510\pi\)
\(920\) −69.2341 + 3.83677i −2.28258 + 0.126495i
\(921\) −44.9078 + 0.935707i −1.47976 + 0.0308326i
\(922\) −0.645424 1.07174i −0.0212559 0.0352958i
\(923\) −38.1134 + 38.1134i −1.25452 + 1.25452i
\(924\) 37.5868 + 0.304897i 1.23652 + 0.0100304i
\(925\) −6.65191 6.65191i −0.218714 0.218714i
\(926\) −46.1254 11.4514i −1.51578 0.376315i
\(927\) 0.0290742 + 0.697383i 0.000954921 + 0.0229051i
\(928\) −8.04763 3.70379i −0.264177 0.121583i
\(929\) 23.0115 0.754981 0.377491 0.926013i \(-0.376787\pi\)
0.377491 + 0.926013i \(0.376787\pi\)
\(930\) −15.6140 + 69.0093i −0.512003 + 2.26291i
\(931\) 2.22620 + 17.0154i 0.0729609 + 0.557658i
\(932\) −23.5616 12.4675i −0.771785 0.408387i
\(933\) 35.2749 36.7761i 1.15485 1.20400i
\(934\) 14.4402 + 23.9782i 0.472499 + 0.784591i
\(935\) 41.0038 1.34097
\(936\) 3.32246 + 34.1351i 0.108598 + 1.11574i
\(937\) 45.2201 1.47728 0.738638 0.674102i \(-0.235469\pi\)
0.738638 + 0.674102i \(0.235469\pi\)
\(938\) −28.2369 + 43.9570i −0.921968 + 1.43525i
\(939\) 15.4104 + 14.7813i 0.502899 + 0.482369i
\(940\) −55.7103 + 17.1543i −1.81707 + 0.559511i
\(941\) 5.39416 + 5.39416i 0.175845 + 0.175845i 0.789542 0.613697i \(-0.210318\pi\)
−0.613697 + 0.789542i \(0.710318\pi\)
\(942\) −11.2471 2.54476i −0.366451 0.0829129i
\(943\) 35.1908i 1.14597i
\(944\) 2.61891 + 0.498198i 0.0852382 + 0.0162150i
\(945\) −37.4998 + 21.4832i −1.21987 + 0.698849i
\(946\) 28.7493 + 7.13747i 0.934721 + 0.232059i
\(947\) −22.9646 + 22.9646i −0.746249 + 0.746249i −0.973773 0.227523i \(-0.926937\pi\)
0.227523 + 0.973773i \(0.426937\pi\)
\(948\) −1.86881 5.64803i −0.0606962 0.183439i
\(949\) −23.0297 + 23.0297i −0.747576 + 0.747576i
\(950\) 8.73242 + 14.5003i 0.283317 + 0.470452i
\(951\) −0.0849587 + 0.00177021i −0.00275497 + 5.74031e-5i
\(952\) 6.40074 22.9232i 0.207449 0.742945i
\(953\) 25.7600 0.834447 0.417224 0.908804i \(-0.363003\pi\)
0.417224 + 0.908804i \(0.363003\pi\)
\(954\) 22.0010 14.5316i 0.712308 0.470477i
\(955\) 1.66599 + 1.66599i 0.0539101 + 0.0539101i
\(956\) −14.8110 + 27.9903i −0.479021 + 0.905272i
\(957\) 8.02840 + 7.70067i 0.259521 + 0.248927i
\(958\) −48.5361 12.0499i −1.56813 0.389314i
\(959\) 0.421195 + 0.854966i 0.0136011 + 0.0276083i
\(960\) −5.71391 43.1829i −0.184416 1.39372i
\(961\) −53.4282 −1.72349
\(962\) 2.65375 10.6892i 0.0855604 0.344632i
\(963\) −9.32831 + 10.1399i −0.300600 + 0.326755i
\(964\) −4.46527 + 8.43864i −0.143817 + 0.271790i
\(965\) −8.91326 + 8.91326i −0.286928 + 0.286928i
\(966\) 26.4237 43.0823i 0.850169 1.38615i
\(967\) 27.5218i 0.885040i 0.896759 + 0.442520i \(0.145915\pi\)
−0.896759 + 0.442520i \(0.854085\pi\)
\(968\) 10.9777 12.2658i 0.352837 0.394238i
\(969\) −13.5014 + 0.281318i −0.433729 + 0.00903724i
\(970\) −7.44998 12.3708i −0.239205 0.397203i
\(971\) 26.0683 26.0683i 0.836572 0.836572i −0.151834 0.988406i \(-0.548518\pi\)
0.988406 + 0.151834i \(0.0485179\pi\)
\(972\) −12.2233 28.6808i −0.392062 0.919939i
\(973\) −8.91534 + 26.2291i −0.285813 + 0.840866i
\(974\) −3.49285 + 14.0690i −0.111918 + 0.450799i
\(975\) 0.712024 + 34.1725i 0.0228030 + 1.09440i
\(976\) 35.6570 + 6.78308i 1.14135 + 0.217121i
\(977\) 23.8813i 0.764029i −0.924156 0.382015i \(-0.875230\pi\)
0.924156 0.382015i \(-0.124770\pi\)
\(978\) 4.71237 20.8273i 0.150685 0.665983i
\(979\) 5.13045 5.13045i 0.163970 0.163970i
\(980\) 15.3635 41.2420i 0.490770 1.31743i
\(981\) 18.8889 20.5324i 0.603075 0.655548i
\(982\) −1.55450 2.58127i −0.0496060 0.0823716i
\(983\) 27.8116i 0.887053i 0.896261 + 0.443526i \(0.146273\pi\)
−0.896261 + 0.443526i \(0.853727\pi\)
\(984\) −22.0425 + 1.68276i −0.702690 + 0.0536445i
\(985\) −13.9616 −0.444853
\(986\) 6.03412 3.63389i 0.192166 0.115727i
\(987\) 12.8322 40.5028i 0.408453 1.28922i
\(988\) −9.26859 + 17.5161i −0.294873 + 0.557262i
\(989\) 28.1634 28.1634i 0.895545 0.895545i
\(990\) −10.9570 + 53.5900i −0.348235 + 1.70320i
\(991\) −0.829975 −0.0263650 −0.0131825 0.999913i \(-0.504196\pi\)
−0.0131825 + 0.999913i \(0.504196\pi\)
\(992\) 48.7537 18.0215i 1.54793 0.572185i
\(993\) 19.4552 0.405371i 0.617391 0.0128641i
\(994\) 10.6162 + 48.7545i 0.336725 + 1.54640i
\(995\) 46.2732 46.2732i 1.46696 1.46696i
\(996\) 4.78647 9.52026i 0.151665 0.301661i
\(997\) 1.19522 + 1.19522i 0.0378528 + 0.0378528i 0.725780 0.687927i \(-0.241479\pi\)
−0.687927 + 0.725780i \(0.741479\pi\)
\(998\) −16.4794 27.3642i −0.521645 0.866199i
\(999\) 0.625330 + 9.99233i 0.0197846 + 0.316143i
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.y.a.125.6 yes 120
3.2 odd 2 inner 336.2.y.a.125.55 yes 120
7.6 odd 2 inner 336.2.y.a.125.5 120
16.5 even 4 inner 336.2.y.a.293.56 yes 120
21.20 even 2 inner 336.2.y.a.125.56 yes 120
48.5 odd 4 inner 336.2.y.a.293.5 yes 120
112.69 odd 4 inner 336.2.y.a.293.55 yes 120
336.293 even 4 inner 336.2.y.a.293.6 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.y.a.125.5 120 7.6 odd 2 inner
336.2.y.a.125.6 yes 120 1.1 even 1 trivial
336.2.y.a.125.55 yes 120 3.2 odd 2 inner
336.2.y.a.125.56 yes 120 21.20 even 2 inner
336.2.y.a.293.5 yes 120 48.5 odd 4 inner
336.2.y.a.293.6 yes 120 336.293 even 4 inner
336.2.y.a.293.55 yes 120 112.69 odd 4 inner
336.2.y.a.293.56 yes 120 16.5 even 4 inner