Properties

Label 845.2.l.f.699.5
Level $845$
Weight $2$
Character 845.699
Analytic conductor $6.747$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(654,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.654");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.l (of order \(6\), degree \(2\), not 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: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 699.5
Character \(\chi\) \(=\) 845.699
Dual form 845.2.l.f.654.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.165418 - 0.286513i) q^{2} +(-2.33117 + 1.34590i) q^{3} +(0.945274 - 1.63726i) q^{4} +(0.702335 - 2.12291i) q^{5} +(0.771236 + 0.445274i) q^{6} +(1.67674 - 2.90420i) q^{7} -1.28714 q^{8} +(2.12291 - 3.67698i) q^{9} +O(q^{10})\) \(q+(-0.165418 - 0.286513i) q^{2} +(-2.33117 + 1.34590i) q^{3} +(0.945274 - 1.63726i) q^{4} +(0.702335 - 2.12291i) q^{5} +(0.771236 + 0.445274i) q^{6} +(1.67674 - 2.90420i) q^{7} -1.28714 q^{8} +(2.12291 - 3.67698i) q^{9} +(-0.724419 + 0.149939i) q^{10} +(2.81095 - 1.62291i) q^{11} +5.08898i q^{12} -1.10945 q^{14} +(1.21996 + 5.89413i) q^{15} +(-1.67763 - 2.90574i) q^{16} +(1.68772 + 0.974404i) q^{17} -1.40467 q^{18} +(-1.07890 - 0.622905i) q^{19} +(-2.81185 - 3.15663i) q^{20} +9.02690i q^{21} +(-0.929966 - 0.536916i) q^{22} +(-2.33117 + 1.34590i) q^{23} +(3.00053 - 1.73236i) q^{24} +(-4.01345 - 2.98198i) q^{25} +3.35348i q^{27} +(-3.16995 - 5.49052i) q^{28} +(1.50000 + 2.59808i) q^{29} +(1.48694 - 1.32453i) q^{30} +3.78109i q^{31} +(-1.84216 + 3.19071i) q^{32} +(-4.36854 + 7.56654i) q^{33} -0.644737i q^{34} +(-4.98770 - 5.59927i) q^{35} +(-4.01345 - 6.95150i) q^{36} +(0.974404 + 1.68772i) q^{37} +0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +(2.40850 - 1.39055i) q^{41} +(2.58632 - 1.49321i) q^{42} +(-7.56654 - 4.36854i) q^{43} -6.13636i q^{44} +(-6.31489 - 7.08920i) q^{45} +(0.771236 + 0.445274i) q^{46} +6.86960 q^{47} +(7.82169 + 4.51586i) q^{48} +(-2.12291 - 3.67698i) q^{49} +(-0.190477 + 1.64318i) q^{50} -5.24581 q^{51} -12.8336i q^{53} +(0.960814 - 0.554726i) q^{54} +(-1.47104 - 7.10721i) q^{55} +(-2.15819 + 3.73809i) q^{56} +3.35348 q^{57} +(0.496255 - 0.859539i) q^{58} +(2.19562 + 1.26764i) q^{59} +(10.8034 + 3.57417i) q^{60} +(3.74581 - 6.48793i) q^{61} +(1.08333 - 0.625462i) q^{62} +(-7.11911 - 12.3307i) q^{63} -5.49162 q^{64} +2.89055 q^{66} +(2.00758 + 3.47722i) q^{67} +(3.19071 - 1.84216i) q^{68} +(3.62291 - 6.27506i) q^{69} +(-0.779207 + 2.35526i) q^{70} +(-4.54300 - 2.62291i) q^{71} +(-2.73247 + 4.73277i) q^{72} -5.46493 q^{73} +(0.322368 - 0.558359i) q^{74} +(13.3695 + 1.54979i) q^{75} +(-2.03972 + 1.17763i) q^{76} -10.8848i q^{77} -13.7811 q^{79} +(-7.34688 + 1.52065i) q^{80} +(1.85526 + 3.21341i) q^{81} +(-0.796819 - 0.460044i) q^{82} -8.61955 q^{83} +(14.7794 + 8.53289i) q^{84} +(3.25391 - 2.89851i) q^{85} +2.89055i q^{86} +(-6.99351 - 4.03771i) q^{87} +(-3.61808 + 2.08890i) q^{88} +(8.93425 - 5.15819i) q^{89} +(-0.986548 + 2.98198i) q^{90} +5.08898i q^{92} +(-5.08898 - 8.81438i) q^{93} +(-1.13636 - 1.96823i) q^{94} +(-2.08012 + 1.85292i) q^{95} -9.91745i q^{96} +(2.63304 - 4.56055i) q^{97} +(-0.702335 + 1.21648i) q^{98} -13.7811i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{4} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{4} + 12 q^{9} - 14 q^{10} - 88 q^{14} - 32 q^{16} + 4 q^{25} + 36 q^{29} - 8 q^{30} + 20 q^{35} + 4 q^{36} + 140 q^{40} - 12 q^{49} - 48 q^{51} - 52 q^{55} + 32 q^{56} + 12 q^{61} + 24 q^{64} + 8 q^{66} + 48 q^{69} + 16 q^{74} - 4 q^{75} - 208 q^{79} + 28 q^{81} - 124 q^{90} + 112 q^{94} - 40 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.165418 0.286513i −0.116968 0.202595i 0.801597 0.597865i \(-0.203984\pi\)
−0.918565 + 0.395270i \(0.870651\pi\)
\(3\) −2.33117 + 1.34590i −1.34590 + 0.777057i −0.987666 0.156574i \(-0.949955\pi\)
−0.358236 + 0.933631i \(0.616622\pi\)
\(4\) 0.945274 1.63726i 0.472637 0.818631i
\(5\) 0.702335 2.12291i 0.314094 0.949392i
\(6\) 0.771236 + 0.445274i 0.314856 + 0.181782i
\(7\) 1.67674 2.90420i 0.633748 1.09768i −0.353031 0.935611i \(-0.614849\pi\)
0.986779 0.162072i \(-0.0518176\pi\)
\(8\) −1.28714 −0.455071
\(9\) 2.12291 3.67698i 0.707635 1.22566i
\(10\) −0.724419 + 0.149939i −0.229081 + 0.0474150i
\(11\) 2.81095 1.62291i 0.847535 0.489324i −0.0122837 0.999925i \(-0.503910\pi\)
0.859818 + 0.510600i \(0.170577\pi\)
\(12\) 5.08898i 1.46906i
\(13\) 0 0
\(14\) −1.10945 −0.296514
\(15\) 1.21996 + 5.89413i 0.314992 + 1.52186i
\(16\) −1.67763 2.90574i −0.419408 0.726436i
\(17\) 1.68772 + 0.974404i 0.409332 + 0.236328i 0.690503 0.723330i \(-0.257389\pi\)
−0.281171 + 0.959658i \(0.590723\pi\)
\(18\) −1.40467 −0.331084
\(19\) −1.07890 0.622905i −0.247517 0.142904i 0.371110 0.928589i \(-0.378977\pi\)
−0.618627 + 0.785685i \(0.712311\pi\)
\(20\) −2.81185 3.15663i −0.628750 0.705844i
\(21\) 9.02690i 1.96983i
\(22\) −0.929966 0.536916i −0.198269 0.114471i
\(23\) −2.33117 + 1.34590i −0.486083 + 0.280640i −0.722948 0.690903i \(-0.757213\pi\)
0.236865 + 0.971543i \(0.423880\pi\)
\(24\) 3.00053 1.73236i 0.612481 0.353616i
\(25\) −4.01345 2.98198i −0.802690 0.596396i
\(26\) 0 0
\(27\) 3.35348i 0.645377i
\(28\) −3.16995 5.49052i −0.599065 1.03761i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 1.48694 1.32453i 0.271477 0.241825i
\(31\) 3.78109i 0.679105i 0.940587 + 0.339552i \(0.110276\pi\)
−0.940587 + 0.339552i \(0.889724\pi\)
\(32\) −1.84216 + 3.19071i −0.325650 + 0.564043i
\(33\) −4.36854 + 7.56654i −0.760466 + 1.31717i
\(34\) 0.644737i 0.110571i
\(35\) −4.98770 5.59927i −0.843076 0.946450i
\(36\) −4.01345 6.95150i −0.668909 1.15858i
\(37\) 0.974404 + 1.68772i 0.160191 + 0.277459i 0.934937 0.354813i \(-0.115456\pi\)
−0.774746 + 0.632273i \(0.782122\pi\)
\(38\) 0.412160i 0.0668611i
\(39\) 0 0
\(40\) −0.904000 + 2.73247i −0.142935 + 0.432041i
\(41\) 2.40850 1.39055i 0.376144 0.217167i −0.299995 0.953941i \(-0.596985\pi\)
0.676139 + 0.736774i \(0.263652\pi\)
\(42\) 2.58632 1.49321i 0.399078 0.230408i
\(43\) −7.56654 4.36854i −1.15389 0.666197i −0.204055 0.978959i \(-0.565412\pi\)
−0.949831 + 0.312763i \(0.898745\pi\)
\(44\) 6.13636i 0.925091i
\(45\) −6.31489 7.08920i −0.941368 1.05679i
\(46\) 0.771236 + 0.445274i 0.113713 + 0.0656520i
\(47\) 6.86960 1.00203 0.501017 0.865437i \(-0.332959\pi\)
0.501017 + 0.865437i \(0.332959\pi\)
\(48\) 7.82169 + 4.51586i 1.12896 + 0.651808i
\(49\) −2.12291 3.67698i −0.303272 0.525283i
\(50\) −0.190477 + 1.64318i −0.0269375 + 0.232381i
\(51\) −5.24581 −0.734560
\(52\) 0 0
\(53\) 12.8336i 1.76282i −0.472347 0.881412i \(-0.656593\pi\)
0.472347 0.881412i \(-0.343407\pi\)
\(54\) 0.960814 0.554726i 0.130750 0.0754887i
\(55\) −1.47104 7.10721i −0.198355 0.958336i
\(56\) −2.15819 + 3.73809i −0.288400 + 0.499524i
\(57\) 3.35348 0.444179
\(58\) 0.496255 0.859539i 0.0651614 0.112863i
\(59\) 2.19562 + 1.26764i 0.285845 + 0.165033i 0.636067 0.771634i \(-0.280560\pi\)
−0.350221 + 0.936667i \(0.613894\pi\)
\(60\) 10.8034 + 3.57417i 1.39472 + 0.461423i
\(61\) 3.74581 6.48793i 0.479602 0.830695i −0.520124 0.854090i \(-0.674114\pi\)
0.999726 + 0.0233957i \(0.00744777\pi\)
\(62\) 1.08333 0.625462i 0.137583 0.0794338i
\(63\) −7.11911 12.3307i −0.896924 1.55352i
\(64\) −5.49162 −0.686453
\(65\) 0 0
\(66\) 2.89055 0.355802
\(67\) 2.00758 + 3.47722i 0.245264 + 0.424810i 0.962206 0.272323i \(-0.0877919\pi\)
−0.716942 + 0.697133i \(0.754459\pi\)
\(68\) 3.19071 1.84216i 0.386930 0.223394i
\(69\) 3.62291 6.27506i 0.436147 0.755428i
\(70\) −0.779207 + 2.35526i −0.0931331 + 0.281508i
\(71\) −4.54300 2.62291i −0.539155 0.311282i 0.205581 0.978640i \(-0.434092\pi\)
−0.744737 + 0.667359i \(0.767425\pi\)
\(72\) −2.73247 + 4.73277i −0.322024 + 0.557762i
\(73\) −5.46493 −0.639622 −0.319811 0.947481i \(-0.603619\pi\)
−0.319811 + 0.947481i \(0.603619\pi\)
\(74\) 0.322368 0.558359i 0.0374746 0.0649079i
\(75\) 13.3695 + 1.54979i 1.54378 + 0.178954i
\(76\) −2.03972 + 1.17763i −0.233972 + 0.135084i
\(77\) 10.8848i 1.24043i
\(78\) 0 0
\(79\) −13.7811 −1.55049 −0.775247 0.631658i \(-0.782375\pi\)
−0.775247 + 0.631658i \(0.782375\pi\)
\(80\) −7.34688 + 1.52065i −0.821406 + 0.170014i
\(81\) 1.85526 + 3.21341i 0.206140 + 0.357046i
\(82\) −0.796819 0.460044i −0.0879940 0.0508033i
\(83\) −8.61955 −0.946119 −0.473059 0.881031i \(-0.656850\pi\)
−0.473059 + 0.881031i \(0.656850\pi\)
\(84\) 14.7794 + 8.53289i 1.61257 + 0.931015i
\(85\) 3.25391 2.89851i 0.352936 0.314387i
\(86\) 2.89055i 0.311696i
\(87\) −6.99351 4.03771i −0.749783 0.432888i
\(88\) −3.61808 + 2.08890i −0.385688 + 0.222677i
\(89\) 8.93425 5.15819i 0.947028 0.546767i 0.0548717 0.998493i \(-0.482525\pi\)
0.892156 + 0.451726i \(0.149192\pi\)
\(90\) −0.986548 + 2.98198i −0.103991 + 0.314328i
\(91\) 0 0
\(92\) 5.08898i 0.530563i
\(93\) −5.08898 8.81438i −0.527703 0.914008i
\(94\) −1.13636 1.96823i −0.117206 0.203007i
\(95\) −2.08012 + 1.85292i −0.213416 + 0.190106i
\(96\) 9.91745i 1.01220i
\(97\) 2.63304 4.56055i 0.267344 0.463054i −0.700831 0.713328i \(-0.747187\pi\)
0.968175 + 0.250273i \(0.0805205\pi\)
\(98\) −0.702335 + 1.21648i −0.0709465 + 0.122883i
\(99\) 13.7811i 1.38505i
\(100\) −8.67609 + 3.75229i −0.867609 + 0.375229i
\(101\) 2.85526 + 4.94546i 0.284109 + 0.492092i 0.972393 0.233350i \(-0.0749688\pi\)
−0.688283 + 0.725442i \(0.741635\pi\)
\(102\) 0.867753 + 1.50299i 0.0859203 + 0.148818i
\(103\) 7.36863i 0.726052i 0.931779 + 0.363026i \(0.118256\pi\)
−0.931779 + 0.363026i \(0.881744\pi\)
\(104\) 0 0
\(105\) 19.1633 + 6.33991i 1.87014 + 0.618712i
\(106\) −3.67698 + 2.12291i −0.357140 + 0.206195i
\(107\) −7.42568 + 4.28722i −0.717868 + 0.414461i −0.813967 0.580911i \(-0.802697\pi\)
0.0960996 + 0.995372i \(0.469363\pi\)
\(108\) 5.49052 + 3.16995i 0.528326 + 0.305029i
\(109\) 8.49162i 0.813350i 0.913573 + 0.406675i \(0.133312\pi\)
−0.913573 + 0.406675i \(0.866688\pi\)
\(110\) −1.79297 + 1.59714i −0.170953 + 0.152281i
\(111\) −4.54300 2.62291i −0.431203 0.248955i
\(112\) −11.2518 −1.06320
\(113\) 6.35006 + 3.66621i 0.597363 + 0.344888i 0.768004 0.640446i \(-0.221250\pi\)
−0.170640 + 0.985333i \(0.554584\pi\)
\(114\) −0.554726 0.960814i −0.0519549 0.0899885i
\(115\) 1.21996 + 5.89413i 0.113762 + 0.549630i
\(116\) 5.67164 0.526599
\(117\) 0 0
\(118\) 0.838765i 0.0772145i
\(119\) 5.65972 3.26764i 0.518826 0.299544i
\(120\) −1.57025 7.58654i −0.143344 0.692553i
\(121\) −0.232358 + 0.402456i −0.0211234 + 0.0365869i
\(122\) −2.47850 −0.224393
\(123\) −3.74308 + 6.48321i −0.337502 + 0.584571i
\(124\) 6.19064 + 3.57417i 0.555936 + 0.320970i
\(125\) −9.14925 + 6.42583i −0.818333 + 0.574744i
\(126\) −2.35526 + 4.07944i −0.209824 + 0.363425i
\(127\) −7.93599 + 4.58185i −0.704205 + 0.406573i −0.808912 0.587930i \(-0.799943\pi\)
0.104707 + 0.994503i \(0.466610\pi\)
\(128\) 4.59273 + 7.95484i 0.405944 + 0.703115i
\(129\) 23.5185 2.07069
\(130\) 0 0
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) 8.25894 + 14.3049i 0.718848 + 1.24508i
\(133\) −3.61808 + 2.08890i −0.313727 + 0.181130i
\(134\) 0.664179 1.15039i 0.0573763 0.0993787i
\(135\) 7.11911 + 2.35526i 0.612716 + 0.202709i
\(136\) −2.17232 1.25419i −0.186275 0.107546i
\(137\) 8.42435 14.5914i 0.719741 1.24663i −0.241361 0.970435i \(-0.577594\pi\)
0.961102 0.276193i \(-0.0890729\pi\)
\(138\) −2.39718 −0.204061
\(139\) −0.513452 + 0.889325i −0.0435505 + 0.0754316i −0.886979 0.461810i \(-0.847200\pi\)
0.843429 + 0.537241i \(0.180534\pi\)
\(140\) −13.8822 + 2.87333i −1.17326 + 0.242841i
\(141\) −16.0142 + 9.24581i −1.34864 + 0.778638i
\(142\) 1.73551i 0.145640i
\(143\) 0 0
\(144\) −14.2458 −1.18715
\(145\) 6.56897 1.35964i 0.545523 0.112912i
\(146\) 0.904000 + 1.56577i 0.0748155 + 0.129584i
\(147\) 9.89771 + 5.71445i 0.816349 + 0.471319i
\(148\) 3.68431 0.302849
\(149\) 13.7279 + 7.92583i 1.12464 + 0.649309i 0.942581 0.333979i \(-0.108391\pi\)
0.182056 + 0.983288i \(0.441725\pi\)
\(150\) −1.76752 4.08690i −0.144318 0.333694i
\(151\) 14.5454i 1.18369i −0.806052 0.591845i \(-0.798400\pi\)
0.806052 0.591845i \(-0.201600\pi\)
\(152\) 1.38869 + 0.801763i 0.112638 + 0.0650316i
\(153\) 7.16573 4.13713i 0.579315 0.334468i
\(154\) −3.11862 + 1.80054i −0.251306 + 0.145091i
\(155\) 8.02690 + 2.65559i 0.644736 + 0.213302i
\(156\) 0 0
\(157\) 10.9210i 0.871588i −0.900047 0.435794i \(-0.856468\pi\)
0.900047 0.435794i \(-0.143532\pi\)
\(158\) 2.27964 + 3.94846i 0.181359 + 0.314123i
\(159\) 17.2727 + 29.9172i 1.36982 + 2.37259i
\(160\) 5.47976 + 6.15167i 0.433213 + 0.486332i
\(161\) 9.02690i 0.711420i
\(162\) 0.613789 1.06311i 0.0482238 0.0835261i
\(163\) 2.08890 3.61808i 0.163615 0.283390i −0.772547 0.634957i \(-0.781018\pi\)
0.936163 + 0.351567i \(0.114351\pi\)
\(164\) 5.25779i 0.410564i
\(165\) 12.9949 + 14.5882i 1.01165 + 1.13569i
\(166\) 1.42583 + 2.46961i 0.110666 + 0.191679i
\(167\) −1.67674 2.90420i −0.129750 0.224733i 0.793830 0.608140i \(-0.208084\pi\)
−0.923580 + 0.383407i \(0.874751\pi\)
\(168\) 11.6188i 0.896413i
\(169\) 0 0
\(170\) −1.36872 0.452821i −0.104976 0.0347298i
\(171\) −4.58082 + 2.64474i −0.350304 + 0.202248i
\(172\) −14.3049 + 8.25894i −1.09074 + 0.629738i
\(173\) 7.56654 + 4.36854i 0.575273 + 0.332134i 0.759253 0.650796i \(-0.225565\pi\)
−0.183979 + 0.982930i \(0.558898\pi\)
\(174\) 2.67164i 0.202537i
\(175\) −15.3898 + 6.65585i −1.16336 + 0.503135i
\(176\) −9.43149 5.44527i −0.710925 0.410453i
\(177\) −6.82449 −0.512960
\(178\) −2.95577 1.70652i −0.221545 0.127909i
\(179\) 9.00507 + 15.5972i 0.673071 + 1.16579i 0.977029 + 0.213107i \(0.0683584\pi\)
−0.303958 + 0.952685i \(0.598308\pi\)
\(180\) −17.5762 + 3.63790i −1.31005 + 0.271153i
\(181\) −1.04366 −0.0775749 −0.0387875 0.999247i \(-0.512350\pi\)
−0.0387875 + 0.999247i \(0.512350\pi\)
\(182\) 0 0
\(183\) 20.1660i 1.49071i
\(184\) 3.00053 1.73236i 0.221202 0.127711i
\(185\) 4.26722 0.883225i 0.313732 0.0649360i
\(186\) −1.68362 + 2.91612i −0.123449 + 0.213820i
\(187\) 6.32546 0.462564
\(188\) 6.49365 11.2473i 0.473598 0.820296i
\(189\) 9.73916 + 5.62291i 0.708419 + 0.409006i
\(190\) 0.874976 + 0.289474i 0.0634774 + 0.0210006i
\(191\) −12.7593 + 22.0997i −0.923228 + 1.59908i −0.128841 + 0.991665i \(0.541126\pi\)
−0.794387 + 0.607412i \(0.792208\pi\)
\(192\) 12.8019 7.39118i 0.923898 0.533413i
\(193\) 9.91035 + 17.1652i 0.713362 + 1.23558i 0.963588 + 0.267392i \(0.0861619\pi\)
−0.250225 + 0.968188i \(0.580505\pi\)
\(194\) −1.74221 −0.125083
\(195\) 0 0
\(196\) −8.02690 −0.573350
\(197\) −10.8260 18.7512i −0.771319 1.33596i −0.936840 0.349758i \(-0.886264\pi\)
0.165521 0.986206i \(-0.447070\pi\)
\(198\) −3.94846 + 2.27964i −0.280605 + 0.162007i
\(199\) −9.11453 + 15.7868i −0.646112 + 1.11910i 0.337932 + 0.941171i \(0.390273\pi\)
−0.984044 + 0.177928i \(0.943061\pi\)
\(200\) 5.16586 + 3.83821i 0.365281 + 0.271402i
\(201\) −9.36000 5.40400i −0.660204 0.381169i
\(202\) 0.944625 1.63614i 0.0664636 0.115118i
\(203\) 10.0604 0.706104
\(204\) −4.95873 + 8.58877i −0.347180 + 0.601334i
\(205\) −1.26043 6.08964i −0.0880321 0.425319i
\(206\) 2.11121 1.21891i 0.147095 0.0849252i
\(207\) 11.4289i 0.794363i
\(208\) 0 0
\(209\) −4.04366 −0.279706
\(210\) −1.35349 6.53926i −0.0933996 0.451252i
\(211\) −9.64981 16.7140i −0.664320 1.15064i −0.979469 0.201594i \(-0.935388\pi\)
0.315149 0.949042i \(-0.397946\pi\)
\(212\) −21.0119 12.1312i −1.44310 0.833176i
\(213\) 14.1207 0.967534
\(214\) 2.45669 + 1.41837i 0.167936 + 0.0969577i
\(215\) −14.5882 + 12.9949i −0.994910 + 0.886242i
\(216\) 4.31638i 0.293692i
\(217\) 10.9810 + 6.33991i 0.745442 + 0.430381i
\(218\) 2.43296 1.40467i 0.164781 0.0951362i
\(219\) 12.7397 7.35526i 0.860868 0.497023i
\(220\) −13.0269 4.30978i −0.878274 0.290565i
\(221\) 0 0
\(222\) 1.73551i 0.116480i
\(223\) 6.18537 + 10.7134i 0.414203 + 0.717421i 0.995344 0.0963818i \(-0.0307270\pi\)
−0.581141 + 0.813803i \(0.697394\pi\)
\(224\) 6.17763 + 10.7000i 0.412760 + 0.714922i
\(225\) −19.4849 + 8.42692i −1.29899 + 0.561795i
\(226\) 2.42583i 0.161364i
\(227\) 3.08141 5.33715i 0.204520 0.354239i −0.745460 0.666551i \(-0.767770\pi\)
0.949980 + 0.312311i \(0.101103\pi\)
\(228\) 3.16995 5.49052i 0.209935 0.363619i
\(229\) 26.9832i 1.78310i −0.452920 0.891551i \(-0.649618\pi\)
0.452920 0.891551i \(-0.350382\pi\)
\(230\) 1.48694 1.32453i 0.0980459 0.0873370i
\(231\) 14.6498 + 25.3742i 0.963887 + 1.66950i
\(232\) −1.93070 3.34408i −0.126757 0.219549i
\(233\) 0.824319i 0.0540029i −0.999635 0.0270015i \(-0.991404\pi\)
0.999635 0.0270015i \(-0.00859588\pi\)
\(234\) 0 0
\(235\) 4.82476 14.5835i 0.314733 0.951323i
\(236\) 4.15092 2.39654i 0.270202 0.156001i
\(237\) 32.1261 18.5480i 2.08681 1.20482i
\(238\) −1.87244 1.08106i −0.121372 0.0700744i
\(239\) 4.00000i 0.258738i −0.991596 0.129369i \(-0.958705\pi\)
0.991596 0.129369i \(-0.0412952\pi\)
\(240\) 15.0802 13.4331i 0.973421 0.867101i
\(241\) 19.6534 + 11.3469i 1.26599 + 0.730917i 0.974226 0.225575i \(-0.0724260\pi\)
0.291760 + 0.956492i \(0.405759\pi\)
\(242\) 0.153745 0.00988310
\(243\) −17.3625 10.0242i −1.11380 0.643054i
\(244\) −7.08163 12.2657i −0.453355 0.785234i
\(245\) −9.29687 + 1.92426i −0.593955 + 0.122936i
\(246\) 2.47670 0.157908
\(247\) 0 0
\(248\) 4.86678i 0.309041i
\(249\) 20.0936 11.6011i 1.27338 0.735188i
\(250\) 3.35454 + 1.55843i 0.212159 + 0.0985635i
\(251\) 9.51345 16.4778i 0.600484 1.04007i −0.392264 0.919853i \(-0.628308\pi\)
0.992748 0.120216i \(-0.0383586\pi\)
\(252\) −26.9180 −1.69568
\(253\) −4.36854 + 7.56654i −0.274648 + 0.475704i
\(254\) 2.62552 + 1.51584i 0.164739 + 0.0951124i
\(255\) −3.68431 + 11.1364i −0.230721 + 0.697386i
\(256\) −3.97218 + 6.88001i −0.248261 + 0.430001i
\(257\) −1.82857 + 1.05573i −0.114063 + 0.0658544i −0.555946 0.831218i \(-0.687644\pi\)
0.441883 + 0.897073i \(0.354311\pi\)
\(258\) −3.89039 6.73836i −0.242205 0.419512i
\(259\) 6.53528 0.406083
\(260\) 0 0
\(261\) 12.7374 0.788427
\(262\) −1.65418 2.86513i −0.102196 0.177008i
\(263\) 25.9092 14.9587i 1.59763 0.922391i 0.605685 0.795704i \(-0.292899\pi\)
0.991943 0.126687i \(-0.0404343\pi\)
\(264\) 5.62291 9.73916i 0.346066 0.599404i
\(265\) −27.2444 9.01345i −1.67361 0.553692i
\(266\) 1.19699 + 0.691084i 0.0733923 + 0.0423731i
\(267\) −13.8848 + 24.0492i −0.849738 + 1.47179i
\(268\) 7.59083 0.463684
\(269\) 9.29455 16.0986i 0.566699 0.981551i −0.430191 0.902738i \(-0.641554\pi\)
0.996889 0.0788127i \(-0.0251129\pi\)
\(270\) −0.502818 2.42932i −0.0306006 0.147844i
\(271\) −5.04439 + 2.91238i −0.306425 + 0.176914i −0.645326 0.763908i \(-0.723278\pi\)
0.338901 + 0.940822i \(0.389945\pi\)
\(272\) 6.53876i 0.396471i
\(273\) 0 0
\(274\) −5.57417 −0.336748
\(275\) −16.1211 1.86875i −0.972139 0.112690i
\(276\) −6.84927 11.8633i −0.412278 0.714086i
\(277\) 11.7263 + 6.77017i 0.704564 + 0.406780i 0.809045 0.587747i \(-0.199985\pi\)
−0.104481 + 0.994527i \(0.533318\pi\)
\(278\) 0.339738 0.0203761
\(279\) 13.9030 + 8.02690i 0.832351 + 0.480558i
\(280\) 6.41985 + 7.20702i 0.383659 + 0.430702i
\(281\) 0.464716i 0.0277226i 0.999904 + 0.0138613i \(0.00441233\pi\)
−0.999904 + 0.0138613i \(0.995588\pi\)
\(282\) 5.29809 + 3.05885i 0.315496 + 0.182152i
\(283\) 8.71259 5.03022i 0.517910 0.299015i −0.218169 0.975911i \(-0.570009\pi\)
0.736079 + 0.676896i \(0.236675\pi\)
\(284\) −8.58877 + 4.95873i −0.509649 + 0.294246i
\(285\) 2.35526 7.11911i 0.139514 0.421700i
\(286\) 0 0
\(287\) 9.32634i 0.550516i
\(288\) 7.82145 + 13.5471i 0.460883 + 0.798273i
\(289\) −6.60107 11.4334i −0.388298 0.672553i
\(290\) −1.47618 1.65719i −0.0866844 0.0973133i
\(291\) 14.1752i 0.830967i
\(292\) −5.16586 + 8.94752i −0.302309 + 0.523614i
\(293\) 6.72506 11.6481i 0.392882 0.680492i −0.599946 0.800040i \(-0.704811\pi\)
0.992828 + 0.119548i \(0.0381447\pi\)
\(294\) 3.78109i 0.220518i
\(295\) 4.23314 3.77079i 0.246463 0.219544i
\(296\) −1.25419 2.17232i −0.0728983 0.126264i
\(297\) 5.44238 + 9.42647i 0.315799 + 0.546979i
\(298\) 5.24431i 0.303795i
\(299\) 0 0
\(300\) 15.1752 20.4244i 0.876143 1.17920i
\(301\) −25.3742 + 14.6498i −1.46255 + 0.844401i
\(302\) −4.16745 + 2.40608i −0.239810 + 0.138454i
\(303\) −13.3122 7.68581i −0.764767 0.441538i
\(304\) 4.18002i 0.239741i
\(305\) −11.1425 12.5087i −0.638015 0.716246i
\(306\) −2.37068 1.36872i −0.135523 0.0782442i
\(307\) 24.6077 1.40444 0.702219 0.711961i \(-0.252193\pi\)
0.702219 + 0.711961i \(0.252193\pi\)
\(308\) −17.8212 10.2891i −1.01546 0.586274i
\(309\) −9.91745 17.1775i −0.564184 0.977196i
\(310\) −0.566935 2.73909i −0.0321997 0.155570i
\(311\) −2.43781 −0.138236 −0.0691178 0.997609i \(-0.522018\pi\)
−0.0691178 + 0.997609i \(0.522018\pi\)
\(312\) 0 0
\(313\) 19.2965i 1.09071i 0.838207 + 0.545353i \(0.183604\pi\)
−0.838207 + 0.545353i \(0.816396\pi\)
\(314\) −3.12900 + 1.80653i −0.176579 + 0.101948i
\(315\) −31.1768 + 6.45295i −1.75662 + 0.363583i
\(316\) −13.0269 + 22.5633i −0.732821 + 1.26928i
\(317\) 28.8217 1.61879 0.809395 0.587265i \(-0.199795\pi\)
0.809395 + 0.587265i \(0.199795\pi\)
\(318\) 5.71445 9.89771i 0.320450 0.555036i
\(319\) 8.43286 + 4.86872i 0.472150 + 0.272596i
\(320\) −3.85695 + 11.6582i −0.215610 + 0.651713i
\(321\) 11.5404 19.9885i 0.644120 1.11565i
\(322\) 2.58632 1.49321i 0.144130 0.0832136i
\(323\) −1.21392 2.10258i −0.0675445 0.116990i
\(324\) 7.01492 0.389718
\(325\) 0 0
\(326\) −1.38217 −0.0765512
\(327\) −11.4289 19.7954i −0.632019 1.09469i
\(328\) −3.10006 + 1.78982i −0.171172 + 0.0988264i
\(329\) 11.5185 19.9507i 0.635037 1.09992i
\(330\) 2.03013 6.13636i 0.111755 0.337795i
\(331\) 2.57478 + 1.48655i 0.141522 + 0.0817081i 0.569089 0.822276i \(-0.307296\pi\)
−0.427567 + 0.903984i \(0.640629\pi\)
\(332\) −8.14783 + 14.1125i −0.447171 + 0.774522i
\(333\) 8.27427 0.453427
\(334\) −0.554726 + 0.960814i −0.0303533 + 0.0525734i
\(335\) 8.79180 1.81972i 0.480347 0.0994218i
\(336\) 26.2299 15.1438i 1.43096 0.826163i
\(337\) 1.90370i 0.103701i −0.998655 0.0518505i \(-0.983488\pi\)
0.998655 0.0518505i \(-0.0165119\pi\)
\(338\) 0 0
\(339\) −19.7374 −1.07199
\(340\) −1.66978 8.06738i −0.0905565 0.437515i
\(341\) 6.13636 + 10.6285i 0.332302 + 0.575565i
\(342\) 1.51550 + 0.874976i 0.0819490 + 0.0473133i
\(343\) 9.23611 0.498703
\(344\) 9.73916 + 5.62291i 0.525100 + 0.303167i
\(345\) −10.7769 12.0983i −0.580206 0.651349i
\(346\) 2.89055i 0.155397i
\(347\) 10.9420 + 6.31735i 0.587396 + 0.339133i 0.764067 0.645137i \(-0.223200\pi\)
−0.176671 + 0.984270i \(0.556533\pi\)
\(348\) −13.2216 + 7.63347i −0.708750 + 0.409197i
\(349\) 7.77093 4.48655i 0.415968 0.240159i −0.277383 0.960760i \(-0.589467\pi\)
0.693351 + 0.720600i \(0.256134\pi\)
\(350\) 4.45274 + 3.30837i 0.238009 + 0.176840i
\(351\) 0 0
\(352\) 11.9586i 0.637395i
\(353\) 17.1252 + 29.6618i 0.911484 + 1.57874i 0.811969 + 0.583701i \(0.198396\pi\)
0.0995150 + 0.995036i \(0.468271\pi\)
\(354\) 1.12890 + 1.95530i 0.0600001 + 0.103923i
\(355\) −8.75889 + 7.80221i −0.464874 + 0.414098i
\(356\) 19.5036i 1.03369i
\(357\) −8.79585 + 15.2349i −0.465526 + 0.806315i
\(358\) 2.97921 5.16014i 0.157456 0.272722i
\(359\) 22.4043i 1.18245i 0.806505 + 0.591227i \(0.201356\pi\)
−0.806505 + 0.591227i \(0.798644\pi\)
\(360\) 8.12812 + 9.12475i 0.428389 + 0.480917i
\(361\) −8.72398 15.1104i −0.459157 0.795283i
\(362\) 0.172641 + 0.299023i 0.00907381 + 0.0157163i
\(363\) 1.25092i 0.0656565i
\(364\) 0 0
\(365\) −3.83821 + 11.6015i −0.200901 + 0.607252i
\(366\) 5.77781 3.33582i 0.302011 0.174366i
\(367\) −11.4273 + 6.59753i −0.596498 + 0.344388i −0.767663 0.640854i \(-0.778580\pi\)
0.171165 + 0.985242i \(0.445247\pi\)
\(368\) 7.82169 + 4.51586i 0.407734 + 0.235405i
\(369\) 11.8080i 0.614700i
\(370\) −0.958932 1.07651i −0.0498525 0.0559652i
\(371\) −37.2712 21.5185i −1.93502 1.11719i
\(372\) −19.2419 −0.997647
\(373\) −13.2168 7.63070i −0.684338 0.395103i 0.117149 0.993114i \(-0.462624\pi\)
−0.801488 + 0.598012i \(0.795958\pi\)
\(374\) −1.04635 1.81233i −0.0541053 0.0937131i
\(375\) 12.6799 27.2937i 0.654788 1.40944i
\(376\) −8.84210 −0.455997
\(377\) 0 0
\(378\) 3.72052i 0.191363i
\(379\) −15.7868 + 9.11453i −0.810915 + 0.468182i −0.847273 0.531157i \(-0.821757\pi\)
0.0363588 + 0.999339i \(0.488424\pi\)
\(380\) 1.06744 + 5.15722i 0.0547583 + 0.264560i
\(381\) 12.3334 21.3621i 0.631861 1.09442i
\(382\) 8.44246 0.431954
\(383\) −0.720440 + 1.24784i −0.0368128 + 0.0637616i −0.883845 0.467780i \(-0.845054\pi\)
0.847032 + 0.531542i \(0.178387\pi\)
\(384\) −21.4129 12.3627i −1.09272 0.630883i
\(385\) −23.1073 7.64474i −1.17766 0.389612i
\(386\) 3.27870 5.67888i 0.166882 0.289048i
\(387\) −32.1261 + 18.5480i −1.63306 + 0.942848i
\(388\) −4.97788 8.62194i −0.252714 0.437713i
\(389\) −18.7912 −0.952754 −0.476377 0.879241i \(-0.658050\pi\)
−0.476377 + 0.879241i \(0.658050\pi\)
\(390\) 0 0
\(391\) −5.24581 −0.265292
\(392\) 2.73247 + 4.73277i 0.138010 + 0.239041i
\(393\) −23.3117 + 13.4590i −1.17592 + 0.678918i
\(394\) −3.58163 + 6.20357i −0.180440 + 0.312531i
\(395\) −9.67894 + 29.2560i −0.487000 + 1.47203i
\(396\) −22.5633 13.0269i −1.13385 0.654627i
\(397\) 8.54634 14.8027i 0.428928 0.742926i −0.567850 0.823132i \(-0.692225\pi\)
0.996778 + 0.0802063i \(0.0255579\pi\)
\(398\) 6.03084 0.302298
\(399\) 5.62291 9.73916i 0.281497 0.487568i
\(400\) −1.93177 + 16.6647i −0.0965886 + 0.833236i
\(401\) −19.2276 + 11.1011i −0.960182 + 0.554361i −0.896229 0.443592i \(-0.853704\pi\)
−0.0639527 + 0.997953i \(0.520371\pi\)
\(402\) 3.57568i 0.178339i
\(403\) 0 0
\(404\) 10.7960 0.537122
\(405\) 8.12478 1.68166i 0.403724 0.0835623i
\(406\) −1.66418 2.88244i −0.0825918 0.143053i
\(407\) 5.47801 + 3.16273i 0.271535 + 0.156771i
\(408\) 6.75207 0.334277
\(409\) −8.34221 4.81638i −0.412496 0.238155i 0.279366 0.960185i \(-0.409876\pi\)
−0.691862 + 0.722030i \(0.743209\pi\)
\(410\) −1.53626 + 1.36847i −0.0758706 + 0.0675838i
\(411\) 45.3534i 2.23712i
\(412\) 12.0644 + 6.96537i 0.594369 + 0.343159i
\(413\) 7.36296 4.25101i 0.362308 0.209178i
\(414\) 3.27452 1.89055i 0.160934 0.0929153i
\(415\) −6.05381 + 18.2985i −0.297170 + 0.898238i
\(416\) 0 0
\(417\) 2.76423i 0.135365i
\(418\) 0.668896 + 1.15856i 0.0327168 + 0.0566671i
\(419\) −0.978168 1.69424i −0.0477866 0.0827689i 0.841143 0.540813i \(-0.181883\pi\)
−0.888929 + 0.458044i \(0.848550\pi\)
\(420\) 28.4946 25.3823i 1.39039 1.23853i
\(421\) 12.0807i 0.588778i −0.955686 0.294389i \(-0.904884\pi\)
0.955686 0.294389i \(-0.0951161\pi\)
\(422\) −3.19251 + 5.52959i −0.155409 + 0.269176i
\(423\) 14.5835 25.2594i 0.709075 1.22815i
\(424\) 16.5185i 0.802210i
\(425\) −3.86792 8.94346i −0.187622 0.433822i
\(426\) −2.33582 4.04576i −0.113171 0.196018i
\(427\) −12.5615 21.7571i −0.607893 1.05290i
\(428\) 16.2104i 0.783558i
\(429\) 0 0
\(430\) 6.13636 + 2.03013i 0.295921 + 0.0979016i
\(431\) 21.2948 12.2945i 1.02573 0.592207i 0.109974 0.993934i \(-0.464923\pi\)
0.915759 + 0.401727i \(0.131590\pi\)
\(432\) 9.74434 5.62590i 0.468825 0.270676i
\(433\) 31.2400 + 18.0364i 1.50130 + 0.866775i 0.999999 + 0.00150085i \(0.000477735\pi\)
0.501299 + 0.865274i \(0.332856\pi\)
\(434\) 4.19495i 0.201364i
\(435\) −13.4835 + 12.0107i −0.646482 + 0.575871i
\(436\) 13.9030 + 8.02690i 0.665833 + 0.384419i
\(437\) 3.35348 0.160419
\(438\) −4.21475 2.43339i −0.201389 0.116272i
\(439\) −1.26764 2.19562i −0.0605013 0.104791i 0.834188 0.551480i \(-0.185937\pi\)
−0.894690 + 0.446688i \(0.852603\pi\)
\(440\) 1.89343 + 9.14794i 0.0902658 + 0.436111i
\(441\) −18.0269 −0.858424
\(442\) 0 0
\(443\) 19.3579i 0.919721i 0.887991 + 0.459860i \(0.152101\pi\)
−0.887991 + 0.459860i \(0.847899\pi\)
\(444\) −8.58877 + 4.95873i −0.407605 + 0.235331i
\(445\) −4.67552 22.5893i −0.221641 1.07084i
\(446\) 2.04635 3.54438i 0.0968973 0.167831i
\(447\) −42.6696 −2.01820
\(448\) −9.20801 + 15.9487i −0.435038 + 0.753507i
\(449\) 21.4844 + 12.4040i 1.01391 + 0.585381i 0.912334 0.409447i \(-0.134278\pi\)
0.101576 + 0.994828i \(0.467612\pi\)
\(450\) 5.63757 + 4.18869i 0.265758 + 0.197457i
\(451\) 4.51345 7.81753i 0.212530 0.368113i
\(452\) 12.0051 6.93114i 0.564672 0.326013i
\(453\) 19.5767 + 33.9079i 0.919795 + 1.59313i
\(454\) −2.03888 −0.0956896
\(455\) 0 0
\(456\) −4.31638 −0.202133
\(457\) 3.78374 + 6.55363i 0.176996 + 0.306566i 0.940850 0.338823i \(-0.110029\pi\)
−0.763854 + 0.645389i \(0.776695\pi\)
\(458\) −7.73105 + 4.46352i −0.361248 + 0.208567i
\(459\) −3.26764 + 5.65972i −0.152520 + 0.264173i
\(460\) 10.8034 + 3.57417i 0.503712 + 0.166646i
\(461\) 10.6896 + 6.17164i 0.497864 + 0.287442i 0.727831 0.685756i \(-0.240528\pi\)
−0.229967 + 0.973198i \(0.573862\pi\)
\(462\) 4.84669 8.39472i 0.225489 0.390558i
\(463\) −22.8578 −1.06229 −0.531146 0.847281i \(-0.678238\pi\)
−0.531146 + 0.847281i \(0.678238\pi\)
\(464\) 5.03289 8.71723i 0.233646 0.404687i
\(465\) −22.2863 + 4.61279i −1.03350 + 0.213913i
\(466\) −0.236178 + 0.136357i −0.0109407 + 0.00631664i
\(467\) 15.2976i 0.707889i 0.935266 + 0.353945i \(0.115160\pi\)
−0.935266 + 0.353945i \(0.884840\pi\)
\(468\) 0 0
\(469\) 13.4647 0.621743
\(470\) −4.97647 + 1.03002i −0.229547 + 0.0475115i
\(471\) 14.6985 + 25.4586i 0.677273 + 1.17307i
\(472\) −2.82606 1.63163i −0.130080 0.0751017i
\(473\) −28.3589 −1.30394
\(474\) −10.6285 6.13636i −0.488182 0.281852i
\(475\) 2.47264 + 5.71727i 0.113452 + 0.262326i
\(476\) 12.3553i 0.566303i
\(477\) −47.1887 27.2444i −2.16062 1.24744i
\(478\) −1.14605 + 0.661673i −0.0524192 + 0.0302642i
\(479\) 21.0296 12.1414i 0.960866 0.554756i 0.0644264 0.997922i \(-0.479478\pi\)
0.896439 + 0.443166i \(0.146145\pi\)
\(480\) −21.0538 6.96537i −0.960971 0.317924i
\(481\) 0 0
\(482\) 7.50793i 0.341977i
\(483\) −12.1493 21.0433i −0.552814 0.957501i
\(484\) 0.439284 + 0.760862i 0.0199674 + 0.0345846i
\(485\) −7.83235 8.79272i −0.355649 0.399257i
\(486\) 6.63276i 0.300868i
\(487\) 18.4441 31.9462i 0.835783 1.44762i −0.0576081 0.998339i \(-0.518347\pi\)
0.893391 0.449280i \(-0.148319\pi\)
\(488\) −4.82136 + 8.35085i −0.218253 + 0.378025i
\(489\) 11.2458i 0.508553i
\(490\) 2.08920 + 2.34537i 0.0943803 + 0.105953i
\(491\) −17.6767 30.6170i −0.797739 1.38172i −0.921085 0.389361i \(-0.872696\pi\)
0.123346 0.992364i \(-0.460637\pi\)
\(492\) 7.07647 + 12.2568i 0.319032 + 0.552580i
\(493\) 5.84642i 0.263310i
\(494\) 0 0
\(495\) −29.2560 9.67894i −1.31496 0.435036i
\(496\) 10.9869 6.34328i 0.493326 0.284822i
\(497\) −15.2349 + 8.79585i −0.683377 + 0.394548i
\(498\) −6.64771 3.83806i −0.297891 0.171988i
\(499\) 16.2189i 0.726058i −0.931778 0.363029i \(-0.881743\pi\)
0.931778 0.363029i \(-0.118257\pi\)
\(500\) 1.87223 + 21.0539i 0.0837286 + 0.941558i
\(501\) 7.81753 + 4.51345i 0.349261 + 0.201646i
\(502\) −6.29480 −0.280950
\(503\) 17.5270 + 10.1192i 0.781489 + 0.451193i 0.836958 0.547268i \(-0.184332\pi\)
−0.0554688 + 0.998460i \(0.517665\pi\)
\(504\) 9.16326 + 15.8712i 0.408164 + 0.706961i
\(505\) 12.5041 2.58808i 0.556425 0.115168i
\(506\) 2.89055 0.128500
\(507\) 0 0
\(508\) 17.3244i 0.768646i
\(509\) 17.3526 10.0185i 0.769140 0.444063i −0.0634276 0.997986i \(-0.520203\pi\)
0.832568 + 0.553923i \(0.186870\pi\)
\(510\) 3.80016 0.786554i 0.168274 0.0348292i
\(511\) −9.16326 + 15.8712i −0.405359 + 0.702102i
\(512\) 20.9992 0.928042
\(513\) 2.08890 3.61808i 0.0922271 0.159742i
\(514\) 0.604959 + 0.349273i 0.0266836 + 0.0154058i
\(515\) 15.6429 + 5.17524i 0.689308 + 0.228048i
\(516\) 22.2314 38.5060i 0.978685 1.69513i
\(517\) 19.3101 11.1487i 0.849259 0.490320i
\(518\) −1.08106 1.87244i −0.0474988 0.0822704i
\(519\) −23.5185 −1.03235
\(520\) 0 0
\(521\) 16.0269 0.702151 0.351076 0.936347i \(-0.385816\pi\)
0.351076 + 0.936347i \(0.385816\pi\)
\(522\) −2.10700 3.64944i −0.0922210 0.159732i
\(523\) 10.1654 5.86898i 0.444501 0.256633i −0.261004 0.965338i \(-0.584054\pi\)
0.705505 + 0.708705i \(0.250720\pi\)
\(524\) 9.45274 16.3726i 0.412945 0.715241i
\(525\) 26.9180 36.2291i 1.17480 1.58117i
\(526\) −8.57170 4.94887i −0.373744 0.215781i
\(527\) −3.68431 + 6.38142i −0.160491 + 0.277979i
\(528\) 29.3152 1.27578
\(529\) −7.87709 + 13.6435i −0.342482 + 0.593197i
\(530\) 1.92426 + 9.29687i 0.0835844 + 0.403830i
\(531\) 9.32219 5.38217i 0.404548 0.233566i
\(532\) 7.89832i 0.342436i
\(533\) 0 0
\(534\) 9.18722 0.397570
\(535\) 3.88605 + 18.7751i 0.168008 + 0.811718i
\(536\) −2.58402 4.47565i −0.111613 0.193319i
\(537\) −41.9847 24.2399i −1.81177 1.04603i
\(538\) −6.14995 −0.265143
\(539\) −11.9348 6.89055i −0.514067 0.296797i
\(540\) 10.5857 9.42949i 0.455536 0.405780i
\(541\) 21.8080i 0.937599i 0.883305 + 0.468800i \(0.155313\pi\)
−0.883305 + 0.468800i \(0.844687\pi\)
\(542\) 1.66887 + 0.963521i 0.0716840 + 0.0413868i
\(543\) 2.43296 1.40467i 0.104408 0.0602801i
\(544\) −6.21808 + 3.59001i −0.266598 + 0.153920i
\(545\) 18.0269 + 5.96396i 0.772188 + 0.255468i
\(546\) 0 0
\(547\) 6.30924i 0.269764i −0.990862 0.134882i \(-0.956935\pi\)
0.990862 0.134882i \(-0.0430655\pi\)
\(548\) −15.9266 27.5858i −0.680352 1.17840i
\(549\) −15.9040 27.5465i −0.678766 1.17566i
\(550\) 2.13130 + 4.92803i 0.0908790 + 0.210132i
\(551\) 3.73743i 0.159220i
\(552\) −4.66317 + 8.07684i −0.198478 + 0.343773i
\(553\) −23.1073 + 40.0230i −0.982622 + 1.70195i
\(554\) 4.47964i 0.190322i
\(555\) −8.75889 + 7.80221i −0.371794 + 0.331185i
\(556\) 0.970706 + 1.68131i 0.0411671 + 0.0713035i
\(557\) −17.9189 31.0364i −0.759247 1.31506i −0.943235 0.332126i \(-0.892234\pi\)
0.183987 0.982929i \(-0.441099\pi\)
\(558\) 5.31119i 0.224840i
\(559\) 0 0
\(560\) −7.90253 + 23.8865i −0.333943 + 1.00939i
\(561\) −14.7457 + 8.51345i −0.622565 + 0.359438i
\(562\) 0.133147 0.0768725i 0.00561647 0.00324267i
\(563\) −4.33196 2.50106i −0.182570 0.105407i 0.405929 0.913904i \(-0.366948\pi\)
−0.588500 + 0.808497i \(0.700281\pi\)
\(564\) 34.9593i 1.47205i
\(565\) 12.2429 10.9057i 0.515062 0.458805i
\(566\) −2.88244 1.66418i −0.121158 0.0699507i
\(567\) 12.4432 0.522564
\(568\) 5.84746 + 3.37603i 0.245354 + 0.141655i
\(569\) 6.58402 + 11.4039i 0.276017 + 0.478075i 0.970391 0.241539i \(-0.0776522\pi\)
−0.694375 + 0.719614i \(0.744319\pi\)
\(570\) −2.42932 + 0.502818i −0.101753 + 0.0210607i
\(571\) −19.8349 −0.830065 −0.415032 0.909807i \(-0.636230\pi\)
−0.415032 + 0.909807i \(0.636230\pi\)
\(572\) 0 0
\(573\) 68.6909i 2.86960i
\(574\) −2.67212 + 1.54275i −0.111532 + 0.0643930i
\(575\) 13.3695 + 1.54979i 0.557547 + 0.0646307i
\(576\) −11.6582 + 20.1926i −0.485758 + 0.841357i
\(577\) −10.9210 −0.454646 −0.227323 0.973819i \(-0.572997\pi\)
−0.227323 + 0.973819i \(0.572997\pi\)
\(578\) −2.18388 + 3.78258i −0.0908373 + 0.157335i
\(579\) −46.2054 26.6767i −1.92023 1.10865i
\(580\) 3.98339 12.0404i 0.165401 0.499949i
\(581\) −14.4527 + 25.0329i −0.599601 + 1.03854i
\(582\) 4.06139 2.34484i 0.168350 0.0971969i
\(583\) −20.8276 36.0745i −0.862593 1.49406i
\(584\) 7.03411 0.291073
\(585\) 0 0
\(586\) −4.44979 −0.183819
\(587\) 20.2247 + 35.0303i 0.834764 + 1.44585i 0.894222 + 0.447624i \(0.147730\pi\)
−0.0594576 + 0.998231i \(0.518937\pi\)
\(588\) 18.7121 10.8034i 0.771673 0.445526i
\(589\) 2.35526 4.07944i 0.0970469 0.168090i
\(590\) −1.78062 0.589093i −0.0733069 0.0242526i
\(591\) 50.4744 + 29.1414i 2.07624 + 1.19872i
\(592\) 3.26938 5.66274i 0.134371 0.232737i
\(593\) −1.47709 −0.0606569 −0.0303284 0.999540i \(-0.509655\pi\)
−0.0303284 + 0.999540i \(0.509655\pi\)
\(594\) 1.80054 3.11862i 0.0738769 0.127959i
\(595\) −2.96188 14.3100i −0.121425 0.586654i
\(596\) 25.9533 14.9842i 1.06309 0.613775i
\(597\) 49.0690i 2.00826i
\(598\) 0 0
\(599\) −2.27271 −0.0928606 −0.0464303 0.998922i \(-0.514785\pi\)
−0.0464303 + 0.998922i \(0.514785\pi\)
\(600\) −17.2083 1.99479i −0.702528 0.0814369i
\(601\) −3.70215 6.41231i −0.151014 0.261563i 0.780587 0.625048i \(-0.214920\pi\)
−0.931600 + 0.363484i \(0.881587\pi\)
\(602\) 8.39472 + 4.84669i 0.342143 + 0.197536i
\(603\) 17.0476 0.694231
\(604\) −23.8147 13.7494i −0.969005 0.559456i
\(605\) 0.691182 + 0.775932i 0.0281006 + 0.0315461i
\(606\) 5.08549i 0.206584i
\(607\) 9.26059 + 5.34661i 0.375876 + 0.217012i 0.676022 0.736881i \(-0.263702\pi\)
−0.300146 + 0.953893i \(0.597036\pi\)
\(608\) 3.97502 2.29498i 0.161208 0.0930736i
\(609\) −23.4526 + 13.5404i −0.950347 + 0.548683i
\(610\) −1.74074 + 5.26162i −0.0704804 + 0.213037i
\(611\) 0 0
\(612\) 15.6429i 0.632327i
\(613\) −3.04075 5.26673i −0.122815 0.212721i 0.798062 0.602575i \(-0.205859\pi\)
−0.920877 + 0.389854i \(0.872525\pi\)
\(614\) −4.07057 7.05043i −0.164275 0.284532i
\(615\) 11.1343 + 12.4996i 0.448980 + 0.504032i
\(616\) 14.0101i 0.564485i
\(617\) 15.9194 27.5732i 0.640892 1.11006i −0.344342 0.938844i \(-0.611898\pi\)
0.985234 0.171213i \(-0.0547685\pi\)
\(618\) −3.28106 + 5.68295i −0.131983 + 0.228602i
\(619\) 26.4043i 1.06128i −0.847598 0.530639i \(-0.821952\pi\)
0.847598 0.530639i \(-0.178048\pi\)
\(620\) 11.9355 10.6319i 0.479342 0.426987i
\(621\) −4.51345 7.81753i −0.181119 0.313707i
\(622\) 0.403259 + 0.698464i 0.0161692 + 0.0280059i
\(623\) 34.5957i 1.38605i
\(624\) 0 0
\(625\) 7.21560 + 23.9361i 0.288624 + 0.957443i
\(626\) 5.52871 3.19200i 0.220972 0.127578i
\(627\) 9.42647 5.44238i 0.376457 0.217348i
\(628\) −17.8805 10.3233i −0.713509 0.411944i
\(629\) 3.79785i 0.151430i
\(630\) 7.00607 + 7.86513i 0.279129 + 0.313354i
\(631\) 30.4564 + 17.5840i 1.21245 + 0.700009i 0.963293 0.268454i \(-0.0865127\pi\)
0.249158 + 0.968463i \(0.419846\pi\)
\(632\) 17.7381 0.705585
\(633\) 44.9907 + 25.9754i 1.78822 + 1.03243i
\(634\) −4.76764 8.25780i −0.189347 0.327959i
\(635\) 4.15310 + 20.0653i 0.164811 + 0.796269i
\(636\) 65.3098 2.58970
\(637\) 0 0
\(638\) 3.22150i 0.127540i
\(639\) −19.2887 + 11.1364i −0.763051 + 0.440547i
\(640\) 20.1130 4.16297i 0.795036 0.164556i
\(641\) 2.76257 4.78491i 0.109115 0.188993i −0.806297 0.591511i \(-0.798532\pi\)
0.915412 + 0.402518i \(0.131865\pi\)
\(642\) −7.63594 −0.301367
\(643\) 16.0776 27.8472i 0.634039 1.09819i −0.352679 0.935744i \(-0.614729\pi\)
0.986718 0.162444i \(-0.0519375\pi\)
\(644\) 14.7794 + 8.53289i 0.582390 + 0.336243i
\(645\) 16.5179 49.9276i 0.650391 1.96590i
\(646\) −0.401610 + 0.695609i −0.0158011 + 0.0273684i
\(647\) 11.9376 6.89216i 0.469314 0.270959i −0.246638 0.969108i \(-0.579326\pi\)
0.715953 + 0.698149i \(0.245993\pi\)
\(648\) −2.38797 4.13609i −0.0938085 0.162481i
\(649\) 8.22905 0.323019
\(650\) 0 0
\(651\) −34.1316 −1.33772
\(652\) −3.94916 6.84015i −0.154661 0.267881i
\(653\) −7.36296 + 4.25101i −0.288135 + 0.166355i −0.637100 0.770781i \(-0.719866\pi\)
0.348965 + 0.937136i \(0.386533\pi\)
\(654\) −3.78109 + 6.54905i −0.147852 + 0.256088i
\(655\) 7.02335 21.2291i 0.274425 0.829488i
\(656\) −8.08115 4.66565i −0.315516 0.182163i
\(657\) −11.6015 + 20.0944i −0.452619 + 0.783959i
\(658\) −7.62150 −0.297117
\(659\) 2.02183 3.50192i 0.0787594 0.136415i −0.823956 0.566654i \(-0.808237\pi\)
0.902715 + 0.430239i \(0.141571\pi\)
\(660\) 36.1685 7.48611i 1.40786 0.291397i
\(661\) −27.0830 + 15.6364i −1.05341 + 0.608184i −0.923601 0.383356i \(-0.874768\pi\)
−0.129805 + 0.991540i \(0.541435\pi\)
\(662\) 0.983609i 0.0382290i
\(663\) 0 0
\(664\) 11.0945 0.430551
\(665\) 1.89343 + 9.14794i 0.0734241 + 0.354742i
\(666\) −1.36872 2.37068i −0.0530366 0.0918622i
\(667\) −6.99351 4.03771i −0.270790 0.156341i
\(668\) −6.33991 −0.245298
\(669\) −28.8383 16.6498i −1.11495 0.643719i
\(670\) −1.97570 2.21795i −0.0763278 0.0856869i
\(671\) 24.3164i 0.938723i
\(672\) −28.8022 16.6290i −1.11107 0.641477i
\(673\) −27.7768 + 16.0370i −1.07072 + 0.618179i −0.928377 0.371639i \(-0.878796\pi\)
−0.142340 + 0.989818i \(0.545463\pi\)
\(674\) −0.545433 + 0.314906i −0.0210093 + 0.0121297i
\(675\) 10.0000 13.4590i 0.384900 0.518038i
\(676\) 0 0
\(677\) 14.2382i 0.547220i 0.961841 + 0.273610i \(0.0882177\pi\)
−0.961841 + 0.273610i \(0.911782\pi\)
\(678\) 3.26493 + 5.65503i 0.125389 + 0.217180i
\(679\) −8.82983 15.2937i −0.338858 0.586919i
\(680\) −4.18822 + 3.73077i −0.160611 + 0.143068i
\(681\) 16.5891i 0.635695i
\(682\) 2.03013 3.51629i 0.0777377 0.134646i
\(683\) −12.8923 + 22.3302i −0.493311 + 0.854440i −0.999970 0.00770647i \(-0.997547\pi\)
0.506659 + 0.862146i \(0.330880\pi\)
\(684\) 10.0000i 0.382360i
\(685\) −25.0595 28.1322i −0.957473 1.07487i
\(686\) −1.52782 2.64626i −0.0583325 0.101035i
\(687\) 36.3168 + 62.9025i 1.38557 + 2.39988i
\(688\) 29.3152i 1.11763i
\(689\) 0 0
\(690\) −1.68362 + 5.08898i −0.0640944 + 0.193734i
\(691\) −0.0378138 + 0.0218318i −0.00143851 + 0.000830522i −0.500719 0.865610i \(-0.666931\pi\)
0.499281 + 0.866440i \(0.333598\pi\)
\(692\) 14.3049 8.25894i 0.543791 0.313958i
\(693\) −40.0230 23.1073i −1.52035 0.877774i
\(694\) 4.18002i 0.158671i
\(695\) 1.52734 + 1.71461i 0.0579352 + 0.0650390i
\(696\) 9.00160 + 5.19707i 0.341205 + 0.196995i
\(697\) 5.41982 0.205290
\(698\) −2.57091 1.48431i −0.0973103 0.0561821i
\(699\) 1.10945 + 1.92163i 0.0419634 + 0.0726827i
\(700\) −3.65016 + 31.4887i −0.137963 + 1.19016i
\(701\) 14.5454 0.549373 0.274687 0.961534i \(-0.411426\pi\)
0.274687 + 0.961534i \(0.411426\pi\)
\(702\) 0 0
\(703\) 2.42785i 0.0915679i
\(704\) −15.4367 + 8.91238i −0.581792 + 0.335898i
\(705\) 8.38064 + 40.4903i 0.315633 + 1.52495i
\(706\) 5.66565 9.81320i 0.213230 0.369325i
\(707\) 19.1501 0.720214
\(708\) −6.45101 + 11.1735i −0.242444 + 0.419925i
\(709\) −17.0025 9.81638i −0.638541 0.368662i 0.145511 0.989357i \(-0.453517\pi\)
−0.784052 + 0.620695i \(0.786851\pi\)
\(710\) 3.68431 + 1.21891i 0.138270 + 0.0457447i
\(711\) −29.2560 + 50.6728i −1.09718 + 1.90038i
\(712\) −11.4996 + 6.63929i −0.430965 + 0.248818i
\(713\) −5.08898 8.81438i −0.190584 0.330101i
\(714\) 5.81998 0.217807
\(715\) 0 0
\(716\) 34.0490 1.27247
\(717\) 5.38361 + 9.32468i 0.201055 + 0.348237i
\(718\) 6.41912 3.70608i 0.239559 0.138310i
\(719\) −23.7156 + 41.0766i −0.884443 + 1.53190i −0.0380914 + 0.999274i \(0.512128\pi\)
−0.846351 + 0.532625i \(0.821206\pi\)
\(720\) −10.0053 + 30.2425i −0.372876 + 1.12707i
\(721\) 21.3999 + 12.3553i 0.796976 + 0.460134i
\(722\) −2.88621 + 4.99906i −0.107414 + 0.186046i
\(723\) −61.0872 −2.27186
\(724\) −0.986548 + 1.70875i −0.0366648 + 0.0635052i
\(725\) 1.72723 14.9002i 0.0641477 0.553380i
\(726\) −0.358406 + 0.206926i −0.0133017 + 0.00767973i
\(727\) 34.0951i 1.26452i −0.774757 0.632259i \(-0.782128\pi\)
0.774757 0.632259i \(-0.217872\pi\)
\(728\) 0 0
\(729\) 42.8349 1.58648
\(730\) 3.95890 0.819409i 0.146525 0.0303277i
\(731\) −8.51345 14.7457i −0.314881 0.545391i
\(732\) 33.0170 + 19.0624i 1.22034 + 0.704565i
\(733\) −14.3920 −0.531580 −0.265790 0.964031i \(-0.585633\pi\)
−0.265790 + 0.964031i \(0.585633\pi\)
\(734\) 3.78055 + 2.18270i 0.139543 + 0.0805651i
\(735\) 19.0827 16.9984i 0.703877 0.626997i
\(736\) 9.91745i 0.365562i
\(737\) 11.2864 + 6.51621i 0.415740 + 0.240028i
\(738\) −3.38314 + 1.95326i −0.124535 + 0.0719004i
\(739\) −29.8328 + 17.2240i −1.09742 + 0.633594i −0.935541 0.353217i \(-0.885088\pi\)
−0.161876 + 0.986811i \(0.551754\pi\)
\(740\) 2.58762 7.82145i 0.0951228 0.287522i
\(741\) 0 0
\(742\) 14.2382i 0.522702i
\(743\) −20.3567 35.2589i −0.746816 1.29352i −0.949342 0.314246i \(-0.898248\pi\)
0.202526 0.979277i \(-0.435085\pi\)
\(744\) 6.55021 + 11.3453i 0.240142 + 0.415939i
\(745\) 26.4674 23.5765i 0.969690 0.863777i
\(746\) 5.04903i 0.184858i
\(747\) −18.2985 + 31.6939i −0.669507 + 1.15962i
\(748\) 5.97929 10.3564i 0.218625 0.378669i
\(749\) 28.7542i 1.05066i
\(750\) −9.91748 + 0.881918i −0.362135 + 0.0322031i
\(751\) 16.2509 + 28.1474i 0.593003 + 1.02711i 0.993825 + 0.110956i \(0.0353912\pi\)
−0.400822 + 0.916156i \(0.631275\pi\)
\(752\) −11.5247 19.9613i −0.420261 0.727914i
\(753\) 51.2167i 1.86644i
\(754\) 0 0
\(755\) −30.8786 10.2158i −1.12379 0.371790i
\(756\) 18.4123 10.6304i 0.669650 0.386623i
\(757\) −11.2864 + 6.51621i −0.410211 + 0.236836i −0.690881 0.722969i \(-0.742777\pi\)
0.280669 + 0.959805i \(0.409444\pi\)
\(758\) 5.22286 + 3.01542i 0.189703 + 0.109525i
\(759\) 23.5185i 0.853668i
\(760\) 2.67739 2.38496i 0.0971193 0.0865116i
\(761\) −3.45532 1.99493i −0.125255 0.0723161i 0.436063 0.899916i \(-0.356372\pi\)
−0.561318 + 0.827600i \(0.689706\pi\)
\(762\) −8.16070 −0.295631
\(763\) 24.6613 + 14.2382i 0.892800 + 0.515458i
\(764\) 24.1220 + 41.7805i 0.872703 + 1.51157i
\(765\) −3.75001 18.1178i −0.135582 0.655051i
\(766\) 0.476696 0.0172237
\(767\) 0 0
\(768\) 21.3847i 0.771652i
\(769\) −5.77367 + 3.33343i −0.208204 + 0.120207i −0.600476 0.799642i \(-0.705022\pi\)
0.392272 + 0.919849i \(0.371689\pi\)
\(770\) 1.63205 + 7.88512i 0.0588151 + 0.284160i
\(771\) 2.84181 4.92216i 0.102345 0.177267i
\(772\) 37.4720 1.34865
\(773\) −24.1675 + 41.8593i −0.869244 + 1.50557i −0.00647254 + 0.999979i \(0.502060\pi\)
−0.862771 + 0.505595i \(0.831273\pi\)
\(774\) 10.6285 + 6.13636i 0.382033 + 0.220567i
\(775\) 11.2751 15.1752i 0.405015 0.545111i
\(776\) −3.38907 + 5.87005i −0.121661 + 0.210723i
\(777\) −15.2349 + 8.79585i −0.546548 + 0.315549i
\(778\) 3.10841 + 5.38393i 0.111442 + 0.193023i
\(779\) −3.46472 −0.124136
\(780\) 0 0
\(781\) −17.0269 −0.609271
\(782\) 0.867753 + 1.50299i 0.0310308 + 0.0537469i
\(783\) −8.71259 + 5.03022i −0.311363 + 0.179765i
\(784\) −7.12291 + 12.3372i −0.254389 + 0.440615i
\(785\) −23.1842 7.67017i −0.827478 0.273760i
\(786\) 7.71236 + 4.45274i 0.275091 + 0.158824i
\(787\) 13.9806 24.2151i 0.498355 0.863176i −0.501643 0.865074i \(-0.667271\pi\)
0.999998 + 0.00189876i \(0.000604394\pi\)
\(788\) −40.9341 −1.45822
\(789\) −40.2658 + 69.7424i −1.43350 + 2.48290i
\(790\) 9.98328 2.06633i 0.355189 0.0735167i
\(791\) 21.2948 12.2945i 0.757155 0.437144i
\(792\) 17.7381i 0.630297i
\(793\) 0 0
\(794\) −5.65488 −0.200684
\(795\) 75.6426 15.6564i 2.68277 0.555277i
\(796\) 17.2314 + 29.8457i 0.610752 + 1.05785i
\(797\) 32.2529 + 18.6212i 1.14246 + 0.659597i 0.947038 0.321123i \(-0.104060\pi\)
0.195418 + 0.980720i \(0.437393\pi\)
\(798\) −3.72052 −0.131705
\(799\) 11.5939 + 6.69377i 0.410164 + 0.236808i
\(800\) 16.9080 7.31249i 0.597789 0.258535i
\(801\) 43.8014i 1.54765i
\(802\) 6.36120 + 3.67264i 0.224622 + 0.129685i
\(803\) −15.3617 + 8.86907i −0.542102 + 0.312983i
\(804\) −17.6955 + 10.2165i −0.624073 + 0.360309i
\(805\) 19.1633 + 6.33991i 0.675416 + 0.223452i
\(806\) 0 0
\(807\) 50.0382i 1.76143i
\(808\) −3.67511 6.36548i −0.129290 0.223937i
\(809\) 7.26434 + 12.5822i 0.255400 + 0.442367i 0.965004 0.262234i \(-0.0844594\pi\)
−0.709604 + 0.704601i \(0.751126\pi\)
\(810\) −1.82580 2.04968i −0.0641522 0.0720183i
\(811\) 44.0538i 1.54694i 0.633834 + 0.773469i \(0.281480\pi\)
−0.633834 + 0.773469i \(0.718520\pi\)
\(812\) 9.50986 16.4716i 0.333731 0.578039i
\(813\) 7.83955 13.5785i 0.274945 0.476219i
\(814\) 2.09269i 0.0733489i
\(815\) −6.21373 6.97563i −0.217657 0.244346i
\(816\) 8.80054 + 15.2430i 0.308080 + 0.533611i
\(817\) 5.44238 + 9.42647i 0.190405 + 0.329790i
\(818\) 3.18687i 0.111426i
\(819\) 0 0
\(820\) −11.1618 3.69273i −0.389787 0.128956i
\(821\) 23.4060 13.5135i 0.816875 0.471623i −0.0324629 0.999473i \(-0.510335\pi\)
0.849337 + 0.527850i \(0.177002\pi\)
\(822\) 12.9943 7.50229i 0.453230 0.261672i
\(823\) 34.2914 + 19.7981i 1.19532 + 0.690120i 0.959509 0.281679i \(-0.0908912\pi\)
0.235814 + 0.971798i \(0.424225\pi\)
\(824\) 9.48442i 0.330405i
\(825\) 40.0962 17.3410i 1.39597 0.603737i
\(826\) −2.43594 1.40639i −0.0847571 0.0489345i
\(827\) −26.5639 −0.923716 −0.461858 0.886954i \(-0.652817\pi\)
−0.461858 + 0.886954i \(0.652817\pi\)
\(828\) 18.7121 + 10.8034i 0.650290 + 0.375445i
\(829\) −6.99162 12.1098i −0.242829 0.420592i 0.718690 0.695331i \(-0.244742\pi\)
−0.961519 + 0.274738i \(0.911409\pi\)
\(830\) 6.24416 1.29241i 0.216738 0.0448602i
\(831\) −36.4480 −1.26437
\(832\) 0 0
\(833\) 8.27427i 0.286686i
\(834\) −0.791986 + 0.457254i −0.0274242 + 0.0158334i
\(835\) −7.34297 + 1.51984i −0.254114 + 0.0525962i
\(836\) −3.82237 + 6.62054i −0.132199 + 0.228976i
\(837\) −12.6798 −0.438278
\(838\) −0.323614 + 0.560515i −0.0111791 + 0.0193627i
\(839\) −12.4657 7.19707i −0.430364 0.248471i 0.269138 0.963102i \(-0.413261\pi\)
−0.699502 + 0.714631i \(0.746595\pi\)
\(840\) −24.6657 8.16032i −0.851048 0.281558i
\(841\) 10.0000 17.3205i 0.344828 0.597259i
\(842\) −3.46128 + 1.99837i −0.119284 + 0.0688684i
\(843\) −0.625462 1.08333i −0.0215421 0.0373119i
\(844\) −36.4868 −1.25593
\(845\) 0 0
\(846\) −9.64952 −0.331757
\(847\) 0.779207 + 1.34963i 0.0267739 + 0.0463737i
\(848\) −37.2910 + 21.5300i −1.28058 + 0.739343i
\(849\) −13.5404 + 23.4526i −0.464704 + 0.804891i
\(850\) −1.92259 + 2.58762i −0.0659444 + 0.0887547i
\(851\) −4.54300 2.62291i −0.155732 0.0899120i
\(852\) 13.3479 23.1193i 0.457292 0.792053i
\(853\) 27.2633 0.933478 0.466739 0.884395i \(-0.345429\pi\)
0.466739 + 0.884395i \(0.345429\pi\)
\(854\) −4.15580 + 7.19806i −0.142209 + 0.246312i
\(855\) 2.39726 + 11.5821i 0.0819845 + 0.396101i
\(856\) 9.55786 5.51823i 0.326681 0.188609i
\(857\) 50.6201i 1.72915i 0.502503 + 0.864575i \(0.332413\pi\)
−0.502503 + 0.864575i \(0.667587\pi\)
\(858\) 0 0
\(859\) −1.27992 −0.0436702 −0.0218351 0.999762i \(-0.506951\pi\)
−0.0218351 + 0.999762i \(0.506951\pi\)
\(860\) 7.48611 + 36.1685i 0.255274 + 1.23333i
\(861\) 12.5523 + 21.7413i 0.427782 + 0.740941i
\(862\) −7.04509 4.06749i −0.239957 0.138539i
\(863\) 8.38448 0.285411 0.142706 0.989765i \(-0.454420\pi\)
0.142706 + 0.989765i \(0.454420\pi\)
\(864\) −10.7000 6.17763i −0.364020 0.210167i
\(865\) 14.5882 12.9949i 0.496015 0.441839i
\(866\) 11.9342i 0.405541i
\(867\) 30.7765 + 17.7688i 1.04522 + 0.603460i
\(868\) 20.7602 11.9859i 0.704646 0.406828i
\(869\) −38.7380 + 22.3654i −1.31410 + 0.758695i
\(870\) 5.67164 + 1.87639i 0.192287 + 0.0636155i
\(871\) 0 0
\(872\) 10.9299i 0.370132i
\(873\) −11.1794 19.3632i −0.378365 0.655347i
\(874\) −0.554726 0.960814i −0.0187639 0.0325000i
\(875\) 3.32098 + 37.3456i 0.112270 + 1.26251i
\(876\) 27.8109i 0.939645i
\(877\) −27.9431 + 48.3989i −0.943572 + 1.63431i −0.184985 + 0.982741i \(0.559224\pi\)
−0.758586 + 0.651573i \(0.774110\pi\)
\(878\) −0.419382 + 0.726391i −0.0141535 + 0.0245145i
\(879\) 36.2051i 1.22117i
\(880\) −18.1839 + 16.1978i −0.612978 + 0.546026i
\(881\) 12.5975 + 21.8195i 0.424420 + 0.735116i 0.996366 0.0851746i \(-0.0271448\pi\)
−0.571946 + 0.820291i \(0.693811\pi\)
\(882\) 2.98198 + 5.16494i 0.100408 + 0.173913i
\(883\) 30.7868i 1.03606i −0.855363 0.518029i \(-0.826666\pi\)
0.855363 0.518029i \(-0.173334\pi\)
\(884\) 0 0
\(885\) −4.79307 + 14.4877i −0.161117 + 0.487000i
\(886\) 5.54628 3.20215i 0.186331 0.107578i
\(887\) −10.8011 + 6.23603i −0.362666 + 0.209385i −0.670250 0.742136i \(-0.733813\pi\)
0.307584 + 0.951521i \(0.400480\pi\)
\(888\) 5.84746 + 3.37603i 0.196228 + 0.113292i
\(889\) 30.7302i 1.03066i
\(890\) −5.69872 + 5.07628i −0.191021 + 0.170157i
\(891\) 10.4301 + 6.02183i 0.349422 + 0.201739i
\(892\) 23.3875 0.783071
\(893\) −7.41163 4.27911i −0.248021 0.143195i
\(894\) 7.05833 + 12.2254i 0.236066 + 0.408878i
\(895\) 39.4360 8.16243i 1.31820 0.272840i
\(896\) 30.8032 1.02906
\(897\) 0 0
\(898\) 8.20739i 0.273884i
\(899\) −9.82357 + 5.67164i −0.327634 + 0.189160i
\(900\) −4.62144 + 39.8676i −0.154048 + 1.32892i
\(901\) 12.5051 21.6594i 0.416604 0.721580i
\(902\) −2.98643 −0.0994372
\(903\) 39.4344 68.3024i 1.31230 2.27296i
\(904\) −8.17338 4.71891i −0.271843 0.156948i
\(905\) −0.733001 + 2.21560i −0.0243658 + 0.0736490i
\(906\) 6.47670 11.2180i 0.215174 0.372692i
\(907\) 33.6807 19.4455i 1.11835 0.645678i 0.177369 0.984144i \(-0.443241\pi\)
0.940979 + 0.338466i \(0.109908\pi\)
\(908\) −5.82555 10.0901i −0.193328 0.334853i
\(909\) 24.2458 0.804183
\(910\) 0 0
\(911\) 0.165096 0.00546989 0.00273494 0.999996i \(-0.499129\pi\)
0.00273494 + 0.999996i \(0.499129\pi\)
\(912\) −5.62590 9.74434i −0.186292 0.322667i
\(913\) −24.2292 + 13.9887i −0.801868 + 0.462959i
\(914\) 1.25180 2.16818i 0.0414059 0.0717171i
\(915\) 42.8105 + 14.1633i 1.41527 + 0.468223i
\(916\) −44.1786 25.5065i −1.45970 0.842760i
\(917\) 16.7674 29.0420i 0.553708 0.959050i
\(918\) 2.16211 0.0713603
\(919\) 0.447663 0.775375i 0.0147670 0.0255773i −0.858547 0.512734i \(-0.828633\pi\)
0.873314 + 0.487157i \(0.161966\pi\)
\(920\) −1.57025 7.58654i −0.0517697 0.250121i
\(921\) −57.3648 + 33.1196i −1.89024 + 1.09133i
\(922\) 4.08361i 0.134486i
\(923\) 0 0
\(924\) 55.3923 1.82227
\(925\) 1.12201 9.67923i 0.0368916 0.318251i
\(926\) 3.78109 + 6.54905i 0.124254 + 0.215215i
\(927\) 27.0943 + 15.6429i 0.889893 + 0.513780i
\(928\) −11.0529 −0.362831
\(929\) −10.6430 6.14474i −0.349185 0.201602i 0.315141 0.949045i \(-0.397948\pi\)
−0.664326 + 0.747443i \(0.731282\pi\)
\(930\) 5.00818 + 5.62226i 0.164225 + 0.184361i
\(931\) 5.28947i 0.173356i
\(932\) −1.34963 0.779207i −0.0442085 0.0255238i
\(933\) 5.68295 3.28106i 0.186052 0.107417i
\(934\) 4.38296 2.53051i 0.143415 0.0828007i
\(935\) 4.44259 13.4284i 0.145288 0.439154i
\(936\) 0 0
\(937\) 5.77242i 0.188577i −0.995545 0.0942884i \(-0.969942\pi\)
0.995545 0.0942884i \(-0.0300576\pi\)
\(938\) −2.22731 3.85781i −0.0727242 0.125962i
\(939\) −25.9713 44.9835i −0.847540 1.46798i
\(940\) −19.3163 21.6848i −0.630029 0.707280i
\(941\) 55.8887i 1.82192i −0.412495 0.910960i \(-0.635342\pi\)
0.412495 0.910960i \(-0.364658\pi\)
\(942\) 4.86282 8.42264i 0.158439 0.274425i
\(943\) −3.74308 + 6.48321i −0.121891 + 0.211122i
\(944\) 8.50655i 0.276864i
\(945\) 18.7770 16.7261i 0.610817 0.544102i
\(946\) 4.69108 + 8.12520i 0.152520 + 0.264173i
\(947\) 0.948188 + 1.64231i 0.0308120 + 0.0533679i 0.881020 0.473079i \(-0.156857\pi\)
−0.850208 + 0.526447i \(0.823524\pi\)
\(948\) 70.1318i 2.27777i
\(949\) 0 0
\(950\) 1.22905 1.65418i 0.0398757 0.0536688i
\(951\) −67.1884 + 38.7912i −2.17873 + 1.25789i
\(952\) −7.28483 + 4.20590i −0.236103 + 0.136314i
\(953\) −29.1438 16.8262i −0.944059 0.545053i −0.0528285 0.998604i \(-0.516824\pi\)
−0.891230 + 0.453551i \(0.850157\pi\)
\(954\) 18.0269i 0.583643i
\(955\) 37.9543 + 42.6081i 1.22817 + 1.37877i
\(956\) −6.54905 3.78109i −0.211811 0.122289i
\(957\) −26.2113 −0.847290
\(958\) −6.95735 4.01683i −0.224782 0.129778i
\(959\) −28.2509 48.9320i −0.912269 1.58010i
\(960\) −6.69956 32.3683i −0.216227 1.04468i
\(961\) 16.7033 0.538817
\(962\) 0 0
\(963\) 36.4054i 1.17315i
\(964\) 37.1556 21.4518i 1.19670 0.690917i
\(965\) 43.4005 8.98300i 1.39711 0.289173i
\(966\) −4.01944 + 6.96188i −0.129323 + 0.223995i
\(967\) 23.0493 0.741216 0.370608 0.928789i \(-0.379149\pi\)
0.370608 + 0.928789i \(0.379149\pi\)
\(968\) 0.299076 0.518015i 0.00961267 0.0166496i
\(969\) 5.65972 + 3.26764i 0.181816 + 0.104972i
\(970\) −1.22361 + 3.69855i −0.0392879 + 0.118753i
\(971\) −7.45964 + 12.9205i −0.239391 + 0.414638i −0.960540 0.278143i \(-0.910281\pi\)
0.721148 + 0.692781i \(0.243615\pi\)
\(972\) −32.8246 + 18.9513i −1.05285 + 0.607862i
\(973\) 1.72185 + 2.98233i 0.0552000 + 0.0956092i
\(974\) −12.2040 −0.391041
\(975\) 0 0
\(976\) −25.1364 −0.804595
\(977\) −11.6821 20.2339i −0.373742 0.647341i 0.616396 0.787437i \(-0.288592\pi\)
−0.990138 + 0.140096i \(0.955259\pi\)
\(978\) 3.22207 1.86026i 0.103030 0.0594846i
\(979\) 16.7425 28.9989i 0.535093 0.926808i
\(980\) −5.63757 + 17.0404i −0.180086 + 0.544334i
\(981\) 31.2235 + 18.0269i 0.996890 + 0.575555i
\(982\) −5.84810 + 10.1292i −0.186620 + 0.323236i
\(983\) −5.31119 −0.169401 −0.0847003 0.996406i \(-0.526993\pi\)
−0.0847003 + 0.996406i \(0.526993\pi\)
\(984\) 4.81785 8.34476i 0.153587 0.266021i
\(985\) −47.4104 + 9.81295i −1.51062 + 0.312667i
\(986\) 1.67508 0.967105i 0.0533453 0.0307989i
\(987\) 62.0112i 1.97384i
\(988\) 0 0
\(989\) 23.5185 0.747846
\(990\) 2.06633 + 9.98328i 0.0656723 + 0.317289i
\(991\) 12.0440 + 20.8607i 0.382589 + 0.662663i 0.991432 0.130628i \(-0.0416992\pi\)
−0.608843 + 0.793291i \(0.708366\pi\)
\(992\) −12.0644 6.96537i −0.383044 0.221151i
\(993\) −8.00299 −0.253967
\(994\) 5.04025 + 2.90999i 0.159867 + 0.0922993i
\(995\) 27.1125 + 30.4369i 0.859523 + 0.964915i
\(996\) 43.8648i 1.38991i
\(997\) −17.6755 10.2050i −0.559790 0.323195i 0.193271 0.981145i \(-0.438090\pi\)
−0.753061 + 0.657951i \(0.771424\pi\)
\(998\) −4.64692 + 2.68290i −0.147096 + 0.0849258i
\(999\) −5.65972 + 3.26764i −0.179066 + 0.103384i
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 845.2.l.f.699.5 24
5.4 even 2 inner 845.2.l.f.699.8 24
13.2 odd 12 845.2.b.d.339.3 6
13.3 even 3 845.2.d.d.844.7 12
13.4 even 6 inner 845.2.l.f.654.8 24
13.5 odd 4 65.2.n.a.29.3 yes 12
13.6 odd 12 65.2.n.a.9.4 yes 12
13.7 odd 12 845.2.n.e.529.3 12
13.8 odd 4 845.2.n.e.484.4 12
13.9 even 3 inner 845.2.l.f.654.6 24
13.10 even 6 845.2.d.d.844.5 12
13.11 odd 12 845.2.b.e.339.4 6
13.12 even 2 inner 845.2.l.f.699.7 24
39.5 even 4 585.2.bs.a.289.4 12
39.32 even 12 585.2.bs.a.334.3 12
52.19 even 12 1040.2.dh.a.529.1 12
52.31 even 4 1040.2.dh.a.289.6 12
65.2 even 12 4225.2.a.br.1.4 6
65.4 even 6 inner 845.2.l.f.654.5 24
65.9 even 6 inner 845.2.l.f.654.7 24
65.18 even 4 325.2.e.e.276.4 12
65.19 odd 12 65.2.n.a.9.3 12
65.24 odd 12 845.2.b.e.339.3 6
65.28 even 12 4225.2.a.br.1.3 6
65.29 even 6 845.2.d.d.844.6 12
65.32 even 12 325.2.e.e.126.3 12
65.34 odd 4 845.2.n.e.484.3 12
65.37 even 12 4225.2.a.bq.1.3 6
65.44 odd 4 65.2.n.a.29.4 yes 12
65.49 even 6 845.2.d.d.844.8 12
65.54 odd 12 845.2.b.d.339.4 6
65.57 even 4 325.2.e.e.276.3 12
65.58 even 12 325.2.e.e.126.4 12
65.59 odd 12 845.2.n.e.529.4 12
65.63 even 12 4225.2.a.bq.1.4 6
65.64 even 2 inner 845.2.l.f.699.6 24
195.44 even 4 585.2.bs.a.289.3 12
195.149 even 12 585.2.bs.a.334.4 12
260.19 even 12 1040.2.dh.a.529.6 12
260.239 even 4 1040.2.dh.a.289.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.n.a.9.3 12 65.19 odd 12
65.2.n.a.9.4 yes 12 13.6 odd 12
65.2.n.a.29.3 yes 12 13.5 odd 4
65.2.n.a.29.4 yes 12 65.44 odd 4
325.2.e.e.126.3 12 65.32 even 12
325.2.e.e.126.4 12 65.58 even 12
325.2.e.e.276.3 12 65.57 even 4
325.2.e.e.276.4 12 65.18 even 4
585.2.bs.a.289.3 12 195.44 even 4
585.2.bs.a.289.4 12 39.5 even 4
585.2.bs.a.334.3 12 39.32 even 12
585.2.bs.a.334.4 12 195.149 even 12
845.2.b.d.339.3 6 13.2 odd 12
845.2.b.d.339.4 6 65.54 odd 12
845.2.b.e.339.3 6 65.24 odd 12
845.2.b.e.339.4 6 13.11 odd 12
845.2.d.d.844.5 12 13.10 even 6
845.2.d.d.844.6 12 65.29 even 6
845.2.d.d.844.7 12 13.3 even 3
845.2.d.d.844.8 12 65.49 even 6
845.2.l.f.654.5 24 65.4 even 6 inner
845.2.l.f.654.6 24 13.9 even 3 inner
845.2.l.f.654.7 24 65.9 even 6 inner
845.2.l.f.654.8 24 13.4 even 6 inner
845.2.l.f.699.5 24 1.1 even 1 trivial
845.2.l.f.699.6 24 65.64 even 2 inner
845.2.l.f.699.7 24 13.12 even 2 inner
845.2.l.f.699.8 24 5.4 even 2 inner
845.2.n.e.484.3 12 65.34 odd 4
845.2.n.e.484.4 12 13.8 odd 4
845.2.n.e.529.3 12 13.7 odd 12
845.2.n.e.529.4 12 65.59 odd 12
1040.2.dh.a.289.1 12 260.239 even 4
1040.2.dh.a.289.6 12 52.31 even 4
1040.2.dh.a.529.1 12 52.19 even 12
1040.2.dh.a.529.6 12 260.19 even 12
4225.2.a.bq.1.3 6 65.37 even 12
4225.2.a.bq.1.4 6 65.63 even 12
4225.2.a.br.1.3 6 65.28 even 12
4225.2.a.br.1.4 6 65.2 even 12