Properties

Label 432.2.v.a.35.6
Level $432$
Weight $2$
Character 432.35
Analytic conductor $3.450$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(35,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.v (of order \(12\), degree \(4\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 35.6
Character \(\chi\) \(=\) 432.35
Dual form 432.2.v.a.395.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00831 + 0.991617i) q^{2} +(0.0333930 - 1.99972i) q^{4} +(-0.473330 + 1.76649i) q^{5} +(1.40613 - 2.43549i) q^{7} +(1.94929 + 2.04946i) q^{8} +O(q^{10})\) \(q+(-1.00831 + 0.991617i) q^{2} +(0.0333930 - 1.99972i) q^{4} +(-0.473330 + 1.76649i) q^{5} +(1.40613 - 2.43549i) q^{7} +(1.94929 + 2.04946i) q^{8} +(-1.27442 - 2.25054i) q^{10} +(-1.55262 - 5.79446i) q^{11} +(0.296913 - 1.10810i) q^{13} +(0.997253 + 3.85009i) q^{14} +(-3.99777 - 0.133554i) q^{16} -0.699378i q^{17} +(-2.01481 + 2.01481i) q^{19} +(3.51668 + 1.00552i) q^{20} +(7.31141 + 4.30303i) q^{22} +(4.91498 - 2.83767i) q^{23} +(1.43368 + 0.827735i) q^{25} +(0.799424 + 1.41173i) q^{26} +(-4.82335 - 2.89320i) q^{28} +(-1.45175 - 5.41802i) q^{29} +(5.15522 - 2.97637i) q^{31} +(4.16344 - 3.82959i) q^{32} +(0.693515 + 0.705192i) q^{34} +(3.63671 + 3.63671i) q^{35} +(3.48490 - 3.48490i) q^{37} +(0.0336414 - 4.02947i) q^{38} +(-4.54301 + 2.47333i) q^{40} +(1.55998 + 2.70196i) q^{41} +(7.09570 - 1.90129i) q^{43} +(-11.6392 + 2.91131i) q^{44} +(-2.14197 + 7.73504i) q^{46} +(-2.83634 + 4.91269i) q^{47} +(-0.454420 - 0.787079i) q^{49} +(-2.26639 + 0.587044i) q^{50} +(-2.20597 - 0.630746i) q^{52} +(-4.45605 - 4.45605i) q^{53} +10.9708 q^{55} +(7.73240 - 1.86566i) q^{56} +(6.83642 + 4.02348i) q^{58} +(13.6570 + 3.65938i) q^{59} +(-13.2354 + 3.54643i) q^{61} +(-2.24666 + 8.11312i) q^{62} +(-0.400567 + 7.98997i) q^{64} +(1.81690 + 1.04899i) q^{65} +(-12.8958 - 3.45542i) q^{67} +(-1.39856 - 0.0233544i) q^{68} +(-7.27317 - 0.0607225i) q^{70} -7.21910i q^{71} +3.75535i q^{73} +(-0.0581877 + 6.96955i) q^{74} +(3.96177 + 4.09633i) q^{76} +(-16.2956 - 4.36638i) q^{77} +(2.96345 + 1.71095i) q^{79} +(2.12818 - 6.99881i) q^{80} +(-4.25226 - 1.17752i) q^{82} +(-1.15222 + 0.308735i) q^{83} +(1.23544 + 0.331036i) q^{85} +(-5.26935 + 8.95331i) q^{86} +(8.84901 - 14.4771i) q^{88} +0.391835 q^{89} +(-2.28126 - 2.28126i) q^{91} +(-5.51042 - 9.92336i) q^{92} +(-2.01158 - 7.76609i) q^{94} +(-2.60547 - 4.51280i) q^{95} +(-0.875387 + 1.51622i) q^{97} +(1.23868 + 0.343012i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00831 + 0.991617i −0.712985 + 0.701179i
\(3\) 0 0
\(4\) 0.0333930 1.99972i 0.0166965 0.999861i
\(5\) −0.473330 + 1.76649i −0.211679 + 0.789999i 0.775630 + 0.631188i \(0.217432\pi\)
−0.987309 + 0.158810i \(0.949234\pi\)
\(6\) 0 0
\(7\) 1.40613 2.43549i 0.531468 0.920530i −0.467857 0.883804i \(-0.654974\pi\)
0.999325 0.0367260i \(-0.0116929\pi\)
\(8\) 1.94929 + 2.04946i 0.689177 + 0.724593i
\(9\) 0 0
\(10\) −1.27442 2.25054i −0.403006 0.711683i
\(11\) −1.55262 5.79446i −0.468133 1.74710i −0.646288 0.763093i \(-0.723680\pi\)
0.178156 0.984002i \(-0.442987\pi\)
\(12\) 0 0
\(13\) 0.296913 1.10810i 0.0823489 0.307330i −0.912450 0.409188i \(-0.865812\pi\)
0.994799 + 0.101858i \(0.0324787\pi\)
\(14\) 0.997253 + 3.85009i 0.266527 + 1.02898i
\(15\) 0 0
\(16\) −3.99777 0.133554i −0.999442 0.0333884i
\(17\) 0.699378i 0.169624i −0.996397 0.0848120i \(-0.972971\pi\)
0.996397 0.0848120i \(-0.0270290\pi\)
\(18\) 0 0
\(19\) −2.01481 + 2.01481i −0.462228 + 0.462228i −0.899385 0.437157i \(-0.855985\pi\)
0.437157 + 0.899385i \(0.355985\pi\)
\(20\) 3.51668 + 1.00552i 0.786354 + 0.224840i
\(21\) 0 0
\(22\) 7.31141 + 4.30303i 1.55880 + 0.917409i
\(23\) 4.91498 2.83767i 1.02485 0.591695i 0.109341 0.994004i \(-0.465126\pi\)
0.915504 + 0.402310i \(0.131792\pi\)
\(24\) 0 0
\(25\) 1.43368 + 0.827735i 0.286736 + 0.165547i
\(26\) 0.799424 + 1.41173i 0.156780 + 0.276863i
\(27\) 0 0
\(28\) −4.82335 2.89320i −0.911528 0.546764i
\(29\) −1.45175 5.41802i −0.269584 1.00610i −0.959385 0.282101i \(-0.908969\pi\)
0.689801 0.723999i \(-0.257698\pi\)
\(30\) 0 0
\(31\) 5.15522 2.97637i 0.925905 0.534572i 0.0403909 0.999184i \(-0.487140\pi\)
0.885514 + 0.464612i \(0.153806\pi\)
\(32\) 4.16344 3.82959i 0.735999 0.676982i
\(33\) 0 0
\(34\) 0.693515 + 0.705192i 0.118937 + 0.120939i
\(35\) 3.63671 + 3.63671i 0.614717 + 0.614717i
\(36\) 0 0
\(37\) 3.48490 3.48490i 0.572913 0.572913i −0.360028 0.932941i \(-0.617233\pi\)
0.932941 + 0.360028i \(0.117233\pi\)
\(38\) 0.0336414 4.02947i 0.00545736 0.653666i
\(39\) 0 0
\(40\) −4.54301 + 2.47333i −0.718312 + 0.391067i
\(41\) 1.55998 + 2.70196i 0.243628 + 0.421975i 0.961745 0.273947i \(-0.0883292\pi\)
−0.718117 + 0.695922i \(0.754996\pi\)
\(42\) 0 0
\(43\) 7.09570 1.90129i 1.08208 0.289944i 0.326635 0.945151i \(-0.394085\pi\)
0.755450 + 0.655207i \(0.227419\pi\)
\(44\) −11.6392 + 2.91131i −1.75467 + 0.438897i
\(45\) 0 0
\(46\) −2.14197 + 7.73504i −0.315816 + 1.14047i
\(47\) −2.83634 + 4.91269i −0.413723 + 0.716589i −0.995293 0.0969068i \(-0.969105\pi\)
0.581570 + 0.813496i \(0.302438\pi\)
\(48\) 0 0
\(49\) −0.454420 0.787079i −0.0649172 0.112440i
\(50\) −2.26639 + 0.587044i −0.320517 + 0.0830205i
\(51\) 0 0
\(52\) −2.20597 0.630746i −0.305913 0.0874688i
\(53\) −4.45605 4.45605i −0.612086 0.612086i 0.331403 0.943489i \(-0.392478\pi\)
−0.943489 + 0.331403i \(0.892478\pi\)
\(54\) 0 0
\(55\) 10.9708 1.47930
\(56\) 7.73240 1.86566i 1.03329 0.249310i
\(57\) 0 0
\(58\) 6.83642 + 4.02348i 0.897666 + 0.528309i
\(59\) 13.6570 + 3.65938i 1.77799 + 0.476411i 0.990215 0.139552i \(-0.0445663\pi\)
0.787775 + 0.615963i \(0.211233\pi\)
\(60\) 0 0
\(61\) −13.2354 + 3.54643i −1.69463 + 0.454074i −0.971577 0.236724i \(-0.923926\pi\)
−0.723048 + 0.690797i \(0.757260\pi\)
\(62\) −2.24666 + 8.11312i −0.285327 + 1.03037i
\(63\) 0 0
\(64\) −0.400567 + 7.98997i −0.0500709 + 0.998746i
\(65\) 1.81690 + 1.04899i 0.225359 + 0.130111i
\(66\) 0 0
\(67\) −12.8958 3.45542i −1.57547 0.422146i −0.637952 0.770077i \(-0.720218\pi\)
−0.937520 + 0.347930i \(0.886885\pi\)
\(68\) −1.39856 0.0233544i −0.169600 0.00283213i
\(69\) 0 0
\(70\) −7.27317 0.0607225i −0.869310 0.00725773i
\(71\) 7.21910i 0.856749i −0.903601 0.428375i \(-0.859086\pi\)
0.903601 0.428375i \(-0.140914\pi\)
\(72\) 0 0
\(73\) 3.75535i 0.439531i 0.975553 + 0.219765i \(0.0705292\pi\)
−0.975553 + 0.219765i \(0.929471\pi\)
\(74\) −0.0581877 + 6.96955i −0.00676418 + 0.810194i
\(75\) 0 0
\(76\) 3.96177 + 4.09633i 0.454446 + 0.469881i
\(77\) −16.2956 4.36638i −1.85705 0.497596i
\(78\) 0 0
\(79\) 2.96345 + 1.71095i 0.333415 + 0.192497i 0.657356 0.753580i \(-0.271675\pi\)
−0.323942 + 0.946077i \(0.605008\pi\)
\(80\) 2.12818 6.99881i 0.237938 0.782490i
\(81\) 0 0
\(82\) −4.25226 1.17752i −0.469583 0.130036i
\(83\) −1.15222 + 0.308735i −0.126472 + 0.0338881i −0.321500 0.946910i \(-0.604187\pi\)
0.195028 + 0.980798i \(0.437520\pi\)
\(84\) 0 0
\(85\) 1.23544 + 0.331036i 0.134003 + 0.0359059i
\(86\) −5.26935 + 8.95331i −0.568208 + 0.965461i
\(87\) 0 0
\(88\) 8.84901 14.4771i 0.943308 1.54326i
\(89\) 0.391835 0.0415344 0.0207672 0.999784i \(-0.493389\pi\)
0.0207672 + 0.999784i \(0.493389\pi\)
\(90\) 0 0
\(91\) −2.28126 2.28126i −0.239141 0.239141i
\(92\) −5.51042 9.92336i −0.574501 1.03458i
\(93\) 0 0
\(94\) −2.01158 7.76609i −0.207479 0.801011i
\(95\) −2.60547 4.51280i −0.267315 0.463004i
\(96\) 0 0
\(97\) −0.875387 + 1.51622i −0.0888821 + 0.153948i −0.907039 0.421047i \(-0.861663\pi\)
0.818157 + 0.574995i \(0.194996\pi\)
\(98\) 1.23868 + 0.343012i 0.125125 + 0.0346494i
\(99\) 0 0
\(100\) 1.70311 2.83932i 0.170311 0.283932i
\(101\) 0.816427 0.218761i 0.0812375 0.0217675i −0.217971 0.975955i \(-0.569944\pi\)
0.299209 + 0.954188i \(0.403277\pi\)
\(102\) 0 0
\(103\) −5.30341 9.18577i −0.522560 0.905101i −0.999655 0.0262492i \(-0.991644\pi\)
0.477095 0.878852i \(-0.341690\pi\)
\(104\) 2.84976 1.55148i 0.279442 0.152135i
\(105\) 0 0
\(106\) 8.91180 + 0.0744032i 0.865590 + 0.00722668i
\(107\) −6.39894 + 6.39894i −0.618609 + 0.618609i −0.945174 0.326566i \(-0.894109\pi\)
0.326566 + 0.945174i \(0.394109\pi\)
\(108\) 0 0
\(109\) 1.52592 + 1.52592i 0.146157 + 0.146157i 0.776399 0.630242i \(-0.217044\pi\)
−0.630242 + 0.776399i \(0.717044\pi\)
\(110\) −11.0620 + 10.8788i −1.05472 + 1.03725i
\(111\) 0 0
\(112\) −5.94666 + 9.54875i −0.561907 + 0.902272i
\(113\) −5.75213 + 3.32099i −0.541115 + 0.312413i −0.745531 0.666471i \(-0.767804\pi\)
0.204416 + 0.978884i \(0.434471\pi\)
\(114\) 0 0
\(115\) 2.68630 + 10.0254i 0.250499 + 0.934876i
\(116\) −10.8830 + 2.72218i −1.01046 + 0.252748i
\(117\) 0 0
\(118\) −17.3992 + 9.85270i −1.60173 + 0.907015i
\(119\) −1.70333 0.983418i −0.156144 0.0901498i
\(120\) 0 0
\(121\) −21.6389 + 12.4932i −1.96717 + 1.13575i
\(122\) 9.82879 16.7004i 0.889857 1.51198i
\(123\) 0 0
\(124\) −5.77976 10.4084i −0.519038 0.934701i
\(125\) −8.60659 + 8.60659i −0.769797 + 0.769797i
\(126\) 0 0
\(127\) 13.8224i 1.22654i −0.789874 0.613270i \(-0.789854\pi\)
0.789874 0.613270i \(-0.210146\pi\)
\(128\) −7.51908 8.45360i −0.664599 0.747200i
\(129\) 0 0
\(130\) −2.87220 + 0.743960i −0.251909 + 0.0652496i
\(131\) −2.40595 + 8.97914i −0.210209 + 0.784511i 0.777589 + 0.628773i \(0.216442\pi\)
−0.987798 + 0.155739i \(0.950224\pi\)
\(132\) 0 0
\(133\) 2.07396 + 7.74013i 0.179835 + 0.671154i
\(134\) 16.4295 9.30354i 1.41929 0.803703i
\(135\) 0 0
\(136\) 1.43335 1.36329i 0.122908 0.116901i
\(137\) 5.96603 10.3335i 0.509712 0.882848i −0.490224 0.871596i \(-0.663085\pi\)
0.999937 0.0112514i \(-0.00358150\pi\)
\(138\) 0 0
\(139\) −0.323448 + 1.20712i −0.0274345 + 0.102387i −0.978286 0.207262i \(-0.933545\pi\)
0.950851 + 0.309649i \(0.100211\pi\)
\(140\) 7.39385 7.15097i 0.624894 0.604367i
\(141\) 0 0
\(142\) 7.15858 + 7.27912i 0.600735 + 0.610850i
\(143\) −6.88181 −0.575486
\(144\) 0 0
\(145\) 10.2580 0.851884
\(146\) −3.72387 3.78657i −0.308190 0.313379i
\(147\) 0 0
\(148\) −6.85245 7.08519i −0.563268 0.582399i
\(149\) 0.930902 3.47417i 0.0762625 0.284615i −0.917254 0.398302i \(-0.869599\pi\)
0.993517 + 0.113687i \(0.0362661\pi\)
\(150\) 0 0
\(151\) −5.43126 + 9.40721i −0.441989 + 0.765548i −0.997837 0.0657361i \(-0.979060\pi\)
0.555848 + 0.831284i \(0.312394\pi\)
\(152\) −8.05669 0.201830i −0.653484 0.0163705i
\(153\) 0 0
\(154\) 20.7608 11.7563i 1.67295 0.947347i
\(155\) 2.81761 + 10.5155i 0.226316 + 0.844621i
\(156\) 0 0
\(157\) 2.55352 9.52986i 0.203793 0.760565i −0.786021 0.618199i \(-0.787862\pi\)
0.989814 0.142366i \(-0.0454709\pi\)
\(158\) −4.68470 + 1.21343i −0.372695 + 0.0965357i
\(159\) 0 0
\(160\) 4.79426 + 9.16734i 0.379019 + 0.724742i
\(161\) 15.9606i 1.25787i
\(162\) 0 0
\(163\) −3.66703 + 3.66703i −0.287224 + 0.287224i −0.835981 0.548758i \(-0.815101\pi\)
0.548758 + 0.835981i \(0.315101\pi\)
\(164\) 5.45526 3.02929i 0.425984 0.236548i
\(165\) 0 0
\(166\) 0.855648 1.45386i 0.0664112 0.112841i
\(167\) 17.4253 10.0605i 1.34841 0.778505i 0.360385 0.932803i \(-0.382645\pi\)
0.988024 + 0.154299i \(0.0493118\pi\)
\(168\) 0 0
\(169\) 10.1186 + 5.84198i 0.778355 + 0.449383i
\(170\) −1.57398 + 0.891299i −0.120719 + 0.0683595i
\(171\) 0 0
\(172\) −3.56510 14.2529i −0.271836 1.08677i
\(173\) 2.70826 + 10.1074i 0.205906 + 0.768450i 0.989172 + 0.146763i \(0.0468855\pi\)
−0.783266 + 0.621687i \(0.786448\pi\)
\(174\) 0 0
\(175\) 4.03189 2.32781i 0.304782 0.175966i
\(176\) 5.43315 + 23.3723i 0.409539 + 1.76175i
\(177\) 0 0
\(178\) −0.395093 + 0.388550i −0.0296135 + 0.0291231i
\(179\) 12.4542 + 12.4542i 0.930872 + 0.930872i 0.997760 0.0668885i \(-0.0213072\pi\)
−0.0668885 + 0.997760i \(0.521307\pi\)
\(180\) 0 0
\(181\) −9.12083 + 9.12083i −0.677946 + 0.677946i −0.959535 0.281589i \(-0.909139\pi\)
0.281589 + 0.959535i \(0.409139\pi\)
\(182\) 4.56236 + 0.0380904i 0.338185 + 0.00282345i
\(183\) 0 0
\(184\) 15.3964 + 4.54163i 1.13504 + 0.334814i
\(185\) 4.50653 + 7.80554i 0.331327 + 0.573875i
\(186\) 0 0
\(187\) −4.05252 + 1.08587i −0.296349 + 0.0794066i
\(188\) 9.72929 + 5.83594i 0.709582 + 0.425630i
\(189\) 0 0
\(190\) 7.10210 + 1.96670i 0.515240 + 0.142679i
\(191\) 1.76985 3.06547i 0.128062 0.221810i −0.794864 0.606788i \(-0.792458\pi\)
0.922926 + 0.384978i \(0.125791\pi\)
\(192\) 0 0
\(193\) 7.43004 + 12.8692i 0.534826 + 0.926346i 0.999172 + 0.0406916i \(0.0129561\pi\)
−0.464346 + 0.885654i \(0.653711\pi\)
\(194\) −0.620839 2.39687i −0.0445737 0.172085i
\(195\) 0 0
\(196\) −1.58911 + 0.882431i −0.113508 + 0.0630308i
\(197\) 11.9105 + 11.9105i 0.848589 + 0.848589i 0.989957 0.141368i \(-0.0451501\pi\)
−0.141368 + 0.989957i \(0.545150\pi\)
\(198\) 0 0
\(199\) 15.5983 1.10574 0.552868 0.833269i \(-0.313533\pi\)
0.552868 + 0.833269i \(0.313533\pi\)
\(200\) 1.09824 + 4.55176i 0.0776574 + 0.321858i
\(201\) 0 0
\(202\) −0.606287 + 1.03016i −0.0426582 + 0.0724819i
\(203\) −15.2369 4.08272i −1.06942 0.286551i
\(204\) 0 0
\(205\) −5.51137 + 1.47677i −0.384931 + 0.103142i
\(206\) 14.4563 + 4.00319i 1.00722 + 0.278916i
\(207\) 0 0
\(208\) −1.33498 + 4.39026i −0.0925643 + 0.304409i
\(209\) 14.8029 + 8.54648i 1.02394 + 0.591172i
\(210\) 0 0
\(211\) 15.6018 + 4.18049i 1.07407 + 0.287797i 0.752165 0.658975i \(-0.229010\pi\)
0.321907 + 0.946771i \(0.395676\pi\)
\(212\) −9.05967 + 8.76207i −0.622221 + 0.601781i
\(213\) 0 0
\(214\) 0.106844 12.7974i 0.00730368 0.874814i
\(215\) 13.4344i 0.916220i
\(216\) 0 0
\(217\) 16.7407i 1.13643i
\(218\) −3.05174 0.0254785i −0.206690 0.00172562i
\(219\) 0 0
\(220\) 0.366347 21.9385i 0.0246991 1.47909i
\(221\) −0.774977 0.207655i −0.0521306 0.0139684i
\(222\) 0 0
\(223\) −13.9254 8.03982i −0.932512 0.538386i −0.0449068 0.998991i \(-0.514299\pi\)
−0.887605 + 0.460605i \(0.847632\pi\)
\(224\) −3.47259 15.5249i −0.232023 1.03730i
\(225\) 0 0
\(226\) 2.50680 9.05251i 0.166750 0.602164i
\(227\) −10.6697 + 2.85895i −0.708176 + 0.189755i −0.594890 0.803807i \(-0.702804\pi\)
−0.113286 + 0.993562i \(0.536138\pi\)
\(228\) 0 0
\(229\) −0.390566 0.104652i −0.0258093 0.00691559i 0.245891 0.969297i \(-0.420919\pi\)
−0.271701 + 0.962382i \(0.587586\pi\)
\(230\) −12.6500 7.44499i −0.834117 0.490908i
\(231\) 0 0
\(232\) 8.27413 13.5366i 0.543223 0.888720i
\(233\) 11.6252 0.761590 0.380795 0.924659i \(-0.375650\pi\)
0.380795 + 0.924659i \(0.375650\pi\)
\(234\) 0 0
\(235\) −7.33569 7.33569i −0.478528 0.478528i
\(236\) 7.77379 27.1880i 0.506031 1.76979i
\(237\) 0 0
\(238\) 2.69267 0.697457i 0.174540 0.0452094i
\(239\) −1.55685 2.69654i −0.100704 0.174425i 0.811271 0.584671i \(-0.198776\pi\)
−0.911975 + 0.410246i \(0.865443\pi\)
\(240\) 0 0
\(241\) −7.16669 + 12.4131i −0.461647 + 0.799596i −0.999043 0.0437337i \(-0.986075\pi\)
0.537396 + 0.843330i \(0.319408\pi\)
\(242\) 9.43029 34.0545i 0.606202 2.18911i
\(243\) 0 0
\(244\) 6.64989 + 26.5856i 0.425716 + 1.70197i
\(245\) 1.60546 0.430181i 0.102569 0.0274833i
\(246\) 0 0
\(247\) 1.63437 + 2.83082i 0.103993 + 0.180121i
\(248\) 16.1489 + 4.76362i 1.02546 + 0.302490i
\(249\) 0 0
\(250\) 0.143705 17.2126i 0.00908871 1.08862i
\(251\) 3.06176 3.06176i 0.193257 0.193257i −0.603845 0.797102i \(-0.706365\pi\)
0.797102 + 0.603845i \(0.206365\pi\)
\(252\) 0 0
\(253\) −24.0739 24.0739i −1.51351 1.51351i
\(254\) 13.7065 + 13.9373i 0.860023 + 0.874505i
\(255\) 0 0
\(256\) 15.9643 + 1.06783i 0.997770 + 0.0667395i
\(257\) −2.78074 + 1.60546i −0.173458 + 0.100146i −0.584215 0.811599i \(-0.698598\pi\)
0.410757 + 0.911745i \(0.365264\pi\)
\(258\) 0 0
\(259\) −3.58722 13.3877i −0.222899 0.831870i
\(260\) 2.15836 3.59827i 0.133856 0.223155i
\(261\) 0 0
\(262\) −6.47791 11.4396i −0.400207 0.706739i
\(263\) −2.63762 1.52283i −0.162643 0.0939018i 0.416469 0.909150i \(-0.363267\pi\)
−0.579112 + 0.815248i \(0.696601\pi\)
\(264\) 0 0
\(265\) 9.98076 5.76240i 0.613113 0.353981i
\(266\) −9.76645 5.74790i −0.598819 0.352427i
\(267\) 0 0
\(268\) −7.34050 + 25.6726i −0.448393 + 1.56820i
\(269\) −1.99648 + 1.99648i −0.121727 + 0.121727i −0.765346 0.643619i \(-0.777432\pi\)
0.643619 + 0.765346i \(0.277432\pi\)
\(270\) 0 0
\(271\) 13.9357i 0.846534i 0.906005 + 0.423267i \(0.139117\pi\)
−0.906005 + 0.423267i \(0.860883\pi\)
\(272\) −0.0934044 + 2.79595i −0.00566347 + 0.169529i
\(273\) 0 0
\(274\) 4.23121 + 16.3354i 0.255617 + 0.986857i
\(275\) 2.57032 9.59256i 0.154996 0.578453i
\(276\) 0 0
\(277\) −8.09885 30.2253i −0.486613 1.81606i −0.572686 0.819774i \(-0.694099\pi\)
0.0860738 0.996289i \(-0.472568\pi\)
\(278\) −0.870867 1.53790i −0.0522311 0.0922368i
\(279\) 0 0
\(280\) −0.364301 + 14.5423i −0.0217712 + 0.869068i
\(281\) −11.3745 + 19.7012i −0.678544 + 1.17527i 0.296875 + 0.954916i \(0.404056\pi\)
−0.975419 + 0.220357i \(0.929278\pi\)
\(282\) 0 0
\(283\) 0.633463 2.36412i 0.0376555 0.140532i −0.944539 0.328399i \(-0.893491\pi\)
0.982194 + 0.187867i \(0.0601575\pi\)
\(284\) −14.4362 0.241068i −0.856630 0.0143047i
\(285\) 0 0
\(286\) 6.93902 6.82411i 0.410313 0.403518i
\(287\) 8.77415 0.517921
\(288\) 0 0
\(289\) 16.5109 0.971228
\(290\) −10.3433 + 10.1720i −0.607381 + 0.597323i
\(291\) 0 0
\(292\) 7.50966 + 0.125403i 0.439469 + 0.00733863i
\(293\) −2.01774 + 7.53030i −0.117877 + 0.439925i −0.999486 0.0320565i \(-0.989794\pi\)
0.881609 + 0.471981i \(0.156461\pi\)
\(294\) 0 0
\(295\) −12.9285 + 22.3929i −0.752728 + 1.30376i
\(296\) 13.9352 + 0.349094i 0.809968 + 0.0202907i
\(297\) 0 0
\(298\) 2.50641 + 4.42616i 0.145192 + 0.256400i
\(299\) −1.68508 6.28881i −0.0974508 0.363691i
\(300\) 0 0
\(301\) 5.34693 19.9550i 0.308192 1.15019i
\(302\) −3.85194 14.8711i −0.221654 0.855738i
\(303\) 0 0
\(304\) 8.32381 7.78564i 0.477403 0.446537i
\(305\) 25.0589i 1.43487i
\(306\) 0 0
\(307\) −24.0831 + 24.0831i −1.37450 + 1.37450i −0.520843 + 0.853652i \(0.674382\pi\)
−0.853652 + 0.520843i \(0.825618\pi\)
\(308\) −9.27571 + 32.4408i −0.528532 + 1.84848i
\(309\) 0 0
\(310\) −13.2683 7.80889i −0.753590 0.443515i
\(311\) −9.09165 + 5.24907i −0.515540 + 0.297647i −0.735108 0.677950i \(-0.762869\pi\)
0.219568 + 0.975597i \(0.429535\pi\)
\(312\) 0 0
\(313\) 19.1380 + 11.0493i 1.08174 + 0.624544i 0.931366 0.364085i \(-0.118618\pi\)
0.150376 + 0.988629i \(0.451952\pi\)
\(314\) 6.87522 + 12.1412i 0.387991 + 0.685167i
\(315\) 0 0
\(316\) 3.52038 5.86895i 0.198037 0.330154i
\(317\) 5.71597 + 21.3323i 0.321041 + 1.19814i 0.918232 + 0.396042i \(0.129617\pi\)
−0.597192 + 0.802099i \(0.703717\pi\)
\(318\) 0 0
\(319\) −29.1405 + 16.8243i −1.63155 + 0.941978i
\(320\) −13.9246 4.48949i −0.778409 0.250970i
\(321\) 0 0
\(322\) 15.8267 + 16.0932i 0.881990 + 0.896841i
\(323\) 1.40911 + 1.40911i 0.0784050 + 0.0784050i
\(324\) 0 0
\(325\) 1.34289 1.34289i 0.0744900 0.0744900i
\(326\) 0.0612287 7.33380i 0.00339114 0.406182i
\(327\) 0 0
\(328\) −2.49672 + 8.46401i −0.137858 + 0.467347i
\(329\) 7.97655 + 13.8158i 0.439761 + 0.761689i
\(330\) 0 0
\(331\) 3.16734 0.848686i 0.174093 0.0466480i −0.170720 0.985320i \(-0.554609\pi\)
0.344812 + 0.938672i \(0.387943\pi\)
\(332\) 0.578908 + 2.31442i 0.0317717 + 0.127020i
\(333\) 0 0
\(334\) −7.59401 + 27.4233i −0.415525 + 1.50054i
\(335\) 12.2079 21.1447i 0.666990 1.15526i
\(336\) 0 0
\(337\) −11.5710 20.0416i −0.630315 1.09174i −0.987487 0.157699i \(-0.949593\pi\)
0.357172 0.934038i \(-0.383741\pi\)
\(338\) −15.9957 + 4.14323i −0.870054 + 0.225362i
\(339\) 0 0
\(340\) 0.703236 2.45949i 0.0381383 0.133385i
\(341\) −25.2506 25.2506i −1.36739 1.36739i
\(342\) 0 0
\(343\) 17.1300 0.924931
\(344\) 17.7282 + 10.8362i 0.955839 + 0.584249i
\(345\) 0 0
\(346\) −12.7534 7.50585i −0.685628 0.403517i
\(347\) −7.59002 2.03374i −0.407454 0.109177i 0.0492700 0.998785i \(-0.484311\pi\)
−0.456724 + 0.889609i \(0.650977\pi\)
\(348\) 0 0
\(349\) 20.9793 5.62138i 1.12299 0.300905i 0.350900 0.936413i \(-0.385876\pi\)
0.772095 + 0.635508i \(0.219209\pi\)
\(350\) −1.75711 + 6.34525i −0.0939216 + 0.339168i
\(351\) 0 0
\(352\) −28.6547 18.1790i −1.52730 0.968943i
\(353\) 0.108858 + 0.0628489i 0.00579390 + 0.00334511i 0.502894 0.864348i \(-0.332269\pi\)
−0.497100 + 0.867693i \(0.665602\pi\)
\(354\) 0 0
\(355\) 12.7525 + 3.41701i 0.676831 + 0.181356i
\(356\) 0.0130846 0.783561i 0.000693481 0.0415287i
\(357\) 0 0
\(358\) −24.9076 0.207949i −1.31641 0.0109905i
\(359\) 4.07414i 0.215025i 0.994204 + 0.107512i \(0.0342886\pi\)
−0.994204 + 0.107512i \(0.965711\pi\)
\(360\) 0 0
\(361\) 10.8811i 0.572691i
\(362\) 0.152291 18.2410i 0.00800426 0.958727i
\(363\) 0 0
\(364\) −4.63806 + 4.48571i −0.243100 + 0.235115i
\(365\) −6.63379 1.77752i −0.347229 0.0930396i
\(366\) 0 0
\(367\) 4.96310 + 2.86545i 0.259072 + 0.149575i 0.623911 0.781495i \(-0.285543\pi\)
−0.364839 + 0.931071i \(0.618876\pi\)
\(368\) −20.0280 + 10.6879i −1.04403 + 0.557147i
\(369\) 0 0
\(370\) −12.2841 3.40168i −0.638620 0.176845i
\(371\) −17.1185 + 4.58689i −0.888748 + 0.238139i
\(372\) 0 0
\(373\) 19.7409 + 5.28955i 1.02214 + 0.273882i 0.730695 0.682704i \(-0.239196\pi\)
0.291448 + 0.956587i \(0.405863\pi\)
\(374\) 3.00944 5.11344i 0.155615 0.264410i
\(375\) 0 0
\(376\) −15.5972 + 3.76327i −0.804364 + 0.194076i
\(377\) −6.43473 −0.331405
\(378\) 0 0
\(379\) −2.85273 2.85273i −0.146535 0.146535i 0.630033 0.776568i \(-0.283041\pi\)
−0.776568 + 0.630033i \(0.783041\pi\)
\(380\) −9.11135 + 5.05951i −0.467402 + 0.259547i
\(381\) 0 0
\(382\) 1.25521 + 4.84597i 0.0642220 + 0.247941i
\(383\) −7.78731 13.4880i −0.397913 0.689206i 0.595555 0.803314i \(-0.296932\pi\)
−0.993468 + 0.114109i \(0.963599\pi\)
\(384\) 0 0
\(385\) 15.4263 26.7192i 0.786200 1.36174i
\(386\) −20.2531 5.60845i −1.03086 0.285462i
\(387\) 0 0
\(388\) 3.00278 + 1.80116i 0.152443 + 0.0914401i
\(389\) 26.9587 7.22357i 1.36686 0.366250i 0.500531 0.865719i \(-0.333138\pi\)
0.866332 + 0.499469i \(0.166471\pi\)
\(390\) 0 0
\(391\) −1.98460 3.43743i −0.100366 0.173838i
\(392\) 0.727291 2.46556i 0.0367337 0.124529i
\(393\) 0 0
\(394\) −23.8202 0.198871i −1.20004 0.0100190i
\(395\) −4.42507 + 4.42507i −0.222649 + 0.222649i
\(396\) 0 0
\(397\) 27.4204 + 27.4204i 1.37619 + 1.37619i 0.850961 + 0.525230i \(0.176021\pi\)
0.525230 + 0.850961i \(0.323979\pi\)
\(398\) −15.7280 + 15.4676i −0.788374 + 0.775319i
\(399\) 0 0
\(400\) −5.62097 3.50057i −0.281049 0.175028i
\(401\) 14.6316 8.44757i 0.730669 0.421852i −0.0879981 0.996121i \(-0.528047\pi\)
0.818667 + 0.574269i \(0.194714\pi\)
\(402\) 0 0
\(403\) −1.76745 6.59620i −0.0880428 0.328580i
\(404\) −0.410198 1.63993i −0.0204081 0.0815896i
\(405\) 0 0
\(406\) 19.4121 10.9925i 0.963405 0.545549i
\(407\) −25.6038 14.7824i −1.26913 0.732735i
\(408\) 0 0
\(409\) −14.9737 + 8.64508i −0.740402 + 0.427471i −0.822216 0.569176i \(-0.807262\pi\)
0.0818133 + 0.996648i \(0.473929\pi\)
\(410\) 4.09280 6.95421i 0.202129 0.343444i
\(411\) 0 0
\(412\) −18.5461 + 10.2986i −0.913700 + 0.507375i
\(413\) 28.1160 28.1160i 1.38350 1.38350i
\(414\) 0 0
\(415\) 2.18151i 0.107086i
\(416\) −3.00737 5.75054i −0.147449 0.281944i
\(417\) 0 0
\(418\) −23.4008 + 6.06131i −1.14457 + 0.296468i
\(419\) −0.788205 + 2.94162i −0.0385063 + 0.143708i −0.982503 0.186248i \(-0.940367\pi\)
0.943996 + 0.329956i \(0.107034\pi\)
\(420\) 0 0
\(421\) −2.38357 8.89561i −0.116168 0.433546i 0.883203 0.468990i \(-0.155382\pi\)
−0.999372 + 0.0354445i \(0.988715\pi\)
\(422\) −19.8769 + 11.2558i −0.967595 + 0.547922i
\(423\) 0 0
\(424\) 0.446378 17.8186i 0.0216780 0.865349i
\(425\) 0.578900 1.00268i 0.0280808 0.0486373i
\(426\) 0 0
\(427\) −9.97350 + 37.2216i −0.482651 + 1.80128i
\(428\) 12.5824 + 13.0098i 0.608194 + 0.628851i
\(429\) 0 0
\(430\) −13.3218 13.5461i −0.642434 0.653252i
\(431\) −7.28002 −0.350666 −0.175333 0.984509i \(-0.556100\pi\)
−0.175333 + 0.984509i \(0.556100\pi\)
\(432\) 0 0
\(433\) −19.9763 −0.960002 −0.480001 0.877268i \(-0.659364\pi\)
−0.480001 + 0.877268i \(0.659364\pi\)
\(434\) 16.6003 + 16.8799i 0.796842 + 0.810259i
\(435\) 0 0
\(436\) 3.10237 3.00046i 0.148577 0.143696i
\(437\) −4.18539 + 15.6201i −0.200214 + 0.747210i
\(438\) 0 0
\(439\) 15.3133 26.5235i 0.730866 1.26590i −0.225647 0.974209i \(-0.572450\pi\)
0.956513 0.291688i \(-0.0942170\pi\)
\(440\) 21.3852 + 22.4841i 1.01950 + 1.07189i
\(441\) 0 0
\(442\) 0.987334 0.559099i 0.0469627 0.0265937i
\(443\) −7.70884 28.7698i −0.366258 1.36689i −0.865708 0.500550i \(-0.833131\pi\)
0.499450 0.866343i \(-0.333536\pi\)
\(444\) 0 0
\(445\) −0.185467 + 0.692173i −0.00879199 + 0.0328121i
\(446\) 22.0136 5.70197i 1.04237 0.269996i
\(447\) 0 0
\(448\) 18.8963 + 12.2105i 0.892764 + 0.576893i
\(449\) 26.8028i 1.26490i 0.774599 + 0.632452i \(0.217952\pi\)
−0.774599 + 0.632452i \(0.782048\pi\)
\(450\) 0 0
\(451\) 13.2344 13.2344i 0.623181 0.623181i
\(452\) 6.44898 + 11.6136i 0.303335 + 0.546256i
\(453\) 0 0
\(454\) 7.92347 13.4630i 0.371867 0.631851i
\(455\) 5.10961 2.95004i 0.239542 0.138300i
\(456\) 0 0
\(457\) −3.25342 1.87837i −0.152189 0.0878662i 0.421972 0.906609i \(-0.361338\pi\)
−0.574161 + 0.818743i \(0.694671\pi\)
\(458\) 0.497588 0.281770i 0.0232507 0.0131662i
\(459\) 0 0
\(460\) 20.1378 5.03708i 0.938928 0.234855i
\(461\) −1.05208 3.92641i −0.0490002 0.182871i 0.937088 0.349092i \(-0.113510\pi\)
−0.986088 + 0.166221i \(0.946843\pi\)
\(462\) 0 0
\(463\) 20.2888 11.7137i 0.942899 0.544383i 0.0520310 0.998645i \(-0.483431\pi\)
0.890868 + 0.454263i \(0.150097\pi\)
\(464\) 5.08018 + 21.8539i 0.235842 + 1.01454i
\(465\) 0 0
\(466\) −11.7218 + 11.5277i −0.543003 + 0.534011i
\(467\) −13.2570 13.2570i −0.613463 0.613463i 0.330384 0.943847i \(-0.392822\pi\)
−0.943847 + 0.330384i \(0.892822\pi\)
\(468\) 0 0
\(469\) −26.5489 + 26.5489i −1.22591 + 1.22591i
\(470\) 14.6709 + 0.122485i 0.676717 + 0.00564980i
\(471\) 0 0
\(472\) 19.1216 + 35.1226i 0.880145 + 1.61665i
\(473\) −22.0339 38.1638i −1.01312 1.75477i
\(474\) 0 0
\(475\) −4.55631 + 1.22086i −0.209058 + 0.0560169i
\(476\) −2.02344 + 3.37335i −0.0927443 + 0.154617i
\(477\) 0 0
\(478\) 4.24372 + 1.17516i 0.194103 + 0.0537506i
\(479\) −17.6429 + 30.5584i −0.806124 + 1.39625i 0.109405 + 0.993997i \(0.465105\pi\)
−0.915529 + 0.402251i \(0.868228\pi\)
\(480\) 0 0
\(481\) −2.82689 4.89631i −0.128895 0.223252i
\(482\) −5.08274 19.6229i −0.231512 0.893798i
\(483\) 0 0
\(484\) 24.2603 + 43.6889i 1.10274 + 1.98586i
\(485\) −2.26403 2.26403i −0.102804 0.102804i
\(486\) 0 0
\(487\) −12.1433 −0.550266 −0.275133 0.961406i \(-0.588722\pi\)
−0.275133 + 0.961406i \(0.588722\pi\)
\(488\) −33.0679 20.2125i −1.49692 0.914977i
\(489\) 0 0
\(490\) −1.19223 + 2.02576i −0.0538595 + 0.0915143i
\(491\) 0.746514 + 0.200028i 0.0336897 + 0.00902713i 0.275625 0.961265i \(-0.411115\pi\)
−0.241935 + 0.970293i \(0.577782\pi\)
\(492\) 0 0
\(493\) −3.78924 + 1.01532i −0.170659 + 0.0457279i
\(494\) −4.45505 1.23368i −0.200442 0.0555059i
\(495\) 0 0
\(496\) −21.0069 + 11.2103i −0.943237 + 0.503359i
\(497\) −17.5821 10.1510i −0.788664 0.455335i
\(498\) 0 0
\(499\) 0.785369 + 0.210439i 0.0351579 + 0.00942054i 0.276355 0.961056i \(-0.410873\pi\)
−0.241197 + 0.970476i \(0.577540\pi\)
\(500\) 16.9234 + 17.4982i 0.756837 + 0.782543i
\(501\) 0 0
\(502\) −0.0511225 + 6.12331i −0.00228171 + 0.273297i
\(503\) 5.40486i 0.240991i 0.992714 + 0.120495i \(0.0384483\pi\)
−0.992714 + 0.120495i \(0.961552\pi\)
\(504\) 0 0
\(505\) 1.54576i 0.0687852i
\(506\) 48.1460 + 0.401964i 2.14035 + 0.0178695i
\(507\) 0 0
\(508\) −27.6409 0.461572i −1.22637 0.0204789i
\(509\) 27.7030 + 7.42301i 1.22792 + 0.329019i 0.813768 0.581191i \(-0.197413\pi\)
0.414148 + 0.910210i \(0.364080\pi\)
\(510\) 0 0
\(511\) 9.14614 + 5.28052i 0.404601 + 0.233597i
\(512\) −17.1559 + 14.7538i −0.758192 + 0.652031i
\(513\) 0 0
\(514\) 1.21186 4.37624i 0.0534528 0.193028i
\(515\) 18.7368 5.02052i 0.825644 0.221231i
\(516\) 0 0
\(517\) 32.8701 + 8.80753i 1.44563 + 0.387355i
\(518\) 16.8925 + 9.94183i 0.742213 + 0.436819i
\(519\) 0 0
\(520\) 1.39180 + 5.76845i 0.0610345 + 0.252963i
\(521\) 12.8208 0.561689 0.280845 0.959753i \(-0.409385\pi\)
0.280845 + 0.959753i \(0.409385\pi\)
\(522\) 0 0
\(523\) −2.08204 2.08204i −0.0910411 0.0910411i 0.660120 0.751161i \(-0.270506\pi\)
−0.751161 + 0.660120i \(0.770506\pi\)
\(524\) 17.8754 + 5.11108i 0.780892 + 0.223278i
\(525\) 0 0
\(526\) 4.16962 1.08002i 0.181804 0.0470910i
\(527\) −2.08161 3.60545i −0.0906762 0.157056i
\(528\) 0 0
\(529\) 4.60471 7.97560i 0.200205 0.346765i
\(530\) −4.34965 + 15.7074i −0.188937 + 0.682285i
\(531\) 0 0
\(532\) 15.5474 3.88888i 0.674063 0.168604i
\(533\) 3.45721 0.926356i 0.149748 0.0401249i
\(534\) 0 0
\(535\) −8.27485 14.3325i −0.357753 0.619647i
\(536\) −18.0559 33.1650i −0.779894 1.43251i
\(537\) 0 0
\(538\) 0.0333354 3.99281i 0.00143719 0.172142i
\(539\) −3.85515 + 3.85515i −0.166053 + 0.166053i
\(540\) 0 0
\(541\) 22.7002 + 22.7002i 0.975956 + 0.975956i 0.999718 0.0237613i \(-0.00756417\pi\)
−0.0237613 + 0.999718i \(0.507564\pi\)
\(542\) −13.8189 14.0516i −0.593572 0.603566i
\(543\) 0 0
\(544\) −2.67833 2.91182i −0.114833 0.124843i
\(545\) −3.41779 + 1.97326i −0.146402 + 0.0845253i
\(546\) 0 0
\(547\) −5.33444 19.9084i −0.228084 0.851222i −0.981145 0.193271i \(-0.938090\pi\)
0.753061 0.657951i \(-0.228576\pi\)
\(548\) −20.4648 12.2755i −0.874214 0.524382i
\(549\) 0 0
\(550\) 6.92045 + 12.2211i 0.295089 + 0.521109i
\(551\) 13.8413 + 7.99125i 0.589657 + 0.340439i
\(552\) 0 0
\(553\) 8.33402 4.81165i 0.354399 0.204612i
\(554\) 38.1381 + 22.4456i 1.62033 + 0.953624i
\(555\) 0 0
\(556\) 2.40311 + 0.687115i 0.101915 + 0.0291402i
\(557\) 10.7551 10.7551i 0.455708 0.455708i −0.441535 0.897244i \(-0.645566\pi\)
0.897244 + 0.441535i \(0.145566\pi\)
\(558\) 0 0
\(559\) 8.42723i 0.356434i
\(560\) −14.0530 15.0244i −0.593849 0.634898i
\(561\) 0 0
\(562\) −8.06697 31.1441i −0.340285 1.31373i
\(563\) 5.56420 20.7659i 0.234503 0.875177i −0.743869 0.668325i \(-0.767012\pi\)
0.978372 0.206852i \(-0.0663218\pi\)
\(564\) 0 0
\(565\) −3.14385 11.7330i −0.132263 0.493611i
\(566\) 1.70557 + 3.01192i 0.0716904 + 0.126601i
\(567\) 0 0
\(568\) 14.7953 14.0721i 0.620795 0.590452i
\(569\) −1.88272 + 3.26097i −0.0789277 + 0.136707i −0.902788 0.430087i \(-0.858483\pi\)
0.823860 + 0.566794i \(0.191816\pi\)
\(570\) 0 0
\(571\) −4.37466 + 16.3264i −0.183074 + 0.683241i 0.811961 + 0.583712i \(0.198400\pi\)
−0.995035 + 0.0995287i \(0.968266\pi\)
\(572\) −0.229804 + 13.7617i −0.00960861 + 0.575405i
\(573\) 0 0
\(574\) −8.84709 + 8.70059i −0.369270 + 0.363156i
\(575\) 9.39535 0.391813
\(576\) 0 0
\(577\) −9.76787 −0.406642 −0.203321 0.979112i \(-0.565173\pi\)
−0.203321 + 0.979112i \(0.565173\pi\)
\(578\) −16.6481 + 16.3725i −0.692471 + 0.681004i
\(579\) 0 0
\(580\) 0.342547 20.5132i 0.0142235 0.851765i
\(581\) −0.868246 + 3.24034i −0.0360209 + 0.134432i
\(582\) 0 0
\(583\) −18.9019 + 32.7390i −0.782835 + 1.35591i
\(584\) −7.69644 + 7.32026i −0.318481 + 0.302914i
\(585\) 0 0
\(586\) −5.43266 9.59372i −0.224421 0.396313i
\(587\) 5.94132 + 22.1733i 0.245224 + 0.915190i 0.973271 + 0.229662i \(0.0737620\pi\)
−0.728046 + 0.685528i \(0.759571\pi\)
\(588\) 0 0
\(589\) −4.38996 + 16.3836i −0.180885 + 0.675073i
\(590\) −9.16912 35.3992i −0.377487 1.45736i
\(591\) 0 0
\(592\) −14.3972 + 13.4664i −0.591723 + 0.553465i
\(593\) 1.37926i 0.0566394i 0.999599 + 0.0283197i \(0.00901564\pi\)
−0.999599 + 0.0283197i \(0.990984\pi\)
\(594\) 0 0
\(595\) 2.54344 2.54344i 0.104271 0.104271i
\(596\) −6.91629 1.97756i −0.283302 0.0810039i
\(597\) 0 0
\(598\) 7.93518 + 4.67014i 0.324494 + 0.190976i
\(599\) −26.6820 + 15.4049i −1.09020 + 0.629425i −0.933629 0.358242i \(-0.883376\pi\)
−0.156568 + 0.987667i \(0.550043\pi\)
\(600\) 0 0
\(601\) 2.43951 + 1.40845i 0.0995098 + 0.0574520i 0.548929 0.835869i \(-0.315036\pi\)
−0.449419 + 0.893321i \(0.648369\pi\)
\(602\) 14.3963 + 25.4230i 0.586751 + 1.03616i
\(603\) 0 0
\(604\) 18.6304 + 11.1751i 0.758062 + 0.454710i
\(605\) −11.8268 44.1382i −0.480828 1.79447i
\(606\) 0 0
\(607\) 26.2297 15.1437i 1.06463 0.614666i 0.137922 0.990443i \(-0.455958\pi\)
0.926710 + 0.375777i \(0.122624\pi\)
\(608\) −0.672641 + 16.1044i −0.0272792 + 0.653120i
\(609\) 0 0
\(610\) 24.8488 + 25.2673i 1.00610 + 1.02304i
\(611\) 4.60158 + 4.60158i 0.186160 + 0.186160i
\(612\) 0 0
\(613\) 3.66344 3.66344i 0.147965 0.147965i −0.629243 0.777208i \(-0.716635\pi\)
0.777208 + 0.629243i \(0.216635\pi\)
\(614\) 0.402118 48.1645i 0.0162282 1.94376i
\(615\) 0 0
\(616\) −22.8160 41.9084i −0.919282 1.68854i
\(617\) 13.2053 + 22.8722i 0.531624 + 0.920799i 0.999319 + 0.0369091i \(0.0117512\pi\)
−0.467695 + 0.883890i \(0.654915\pi\)
\(618\) 0 0
\(619\) 47.2262 12.6542i 1.89818 0.508617i 0.900981 0.433858i \(-0.142848\pi\)
0.997202 0.0747583i \(-0.0238185\pi\)
\(620\) 21.1221 5.28329i 0.848282 0.212182i
\(621\) 0 0
\(622\) 3.96218 14.3081i 0.158869 0.573704i
\(623\) 0.550972 0.954312i 0.0220742 0.0382337i
\(624\) 0 0
\(625\) −6.99103 12.1088i −0.279641 0.484353i
\(626\) −30.2538 + 7.83636i −1.20918 + 0.313204i
\(627\) 0 0
\(628\) −18.9718 5.42455i −0.757057 0.216463i
\(629\) −2.43726 2.43726i −0.0971799 0.0971799i
\(630\) 0 0
\(631\) −36.5500 −1.45503 −0.727516 0.686090i \(-0.759325\pi\)
−0.727516 + 0.686090i \(0.759325\pi\)
\(632\) 2.27009 + 9.40861i 0.0902995 + 0.374254i
\(633\) 0 0
\(634\) −26.9169 15.8416i −1.06901 0.629150i
\(635\) 24.4171 + 6.54255i 0.968964 + 0.259633i
\(636\) 0 0
\(637\) −1.00708 + 0.269847i −0.0399020 + 0.0106917i
\(638\) 12.6995 45.8603i 0.502779 1.81563i
\(639\) 0 0
\(640\) 18.4922 9.28105i 0.730969 0.366866i
\(641\) 5.95425 + 3.43769i 0.235179 + 0.135780i 0.612959 0.790115i \(-0.289979\pi\)
−0.377780 + 0.925895i \(0.623312\pi\)
\(642\) 0 0
\(643\) 28.3564 + 7.59808i 1.11827 + 0.299639i 0.770183 0.637823i \(-0.220165\pi\)
0.348086 + 0.937463i \(0.386832\pi\)
\(644\) −31.9167 0.532971i −1.25769 0.0210020i
\(645\) 0 0
\(646\) −2.81812 0.0235281i −0.110878 0.000925699i
\(647\) 1.90726i 0.0749821i −0.999297 0.0374911i \(-0.988063\pi\)
0.999297 0.0374911i \(-0.0119366\pi\)
\(648\) 0 0
\(649\) 84.8166i 3.32934i
\(650\) −0.0224223 + 2.68568i −0.000879476 + 0.105341i
\(651\) 0 0
\(652\) 7.21058 + 7.45548i 0.282388 + 0.291979i
\(653\) 22.1710 + 5.94070i 0.867618 + 0.232478i 0.665057 0.746792i \(-0.268407\pi\)
0.202560 + 0.979270i \(0.435074\pi\)
\(654\) 0 0
\(655\) −14.7228 8.50019i −0.575266 0.332130i
\(656\) −5.87558 11.0102i −0.229403 0.429874i
\(657\) 0 0
\(658\) −21.7428 6.02097i −0.847624 0.234722i
\(659\) 14.4059 3.86006i 0.561175 0.150366i 0.0329291 0.999458i \(-0.489516\pi\)
0.528246 + 0.849091i \(0.322850\pi\)
\(660\) 0 0
\(661\) −36.4336 9.76236i −1.41710 0.379712i −0.532648 0.846337i \(-0.678803\pi\)
−0.884455 + 0.466625i \(0.845470\pi\)
\(662\) −2.35210 + 3.99653i −0.0914170 + 0.155329i
\(663\) 0 0
\(664\) −2.87874 1.75961i −0.111717 0.0682860i
\(665\) −14.6545 −0.568278
\(666\) 0 0
\(667\) −22.5099 22.5099i −0.871586 0.871586i
\(668\) −19.5363 35.1817i −0.755882 1.36122i
\(669\) 0 0
\(670\) 8.65806 + 33.4261i 0.334490 + 1.29136i
\(671\) 41.0993 + 71.1860i 1.58662 + 2.74811i
\(672\) 0 0
\(673\) −11.2966 + 19.5664i −0.435454 + 0.754228i −0.997333 0.0729916i \(-0.976745\pi\)
0.561879 + 0.827220i \(0.310079\pi\)
\(674\) 31.5409 + 8.73421i 1.21491 + 0.336429i
\(675\) 0 0
\(676\) 12.0202 20.0393i 0.462317 0.770743i
\(677\) −30.3860 + 8.14191i −1.16783 + 0.312919i −0.790089 0.612992i \(-0.789966\pi\)
−0.377741 + 0.925911i \(0.623299\pi\)
\(678\) 0 0
\(679\) 2.46182 + 4.26400i 0.0944760 + 0.163637i
\(680\) 1.72979 + 3.17728i 0.0663344 + 0.121843i
\(681\) 0 0
\(682\) 50.4993 + 0.421611i 1.93372 + 0.0161443i
\(683\) 24.1502 24.1502i 0.924081 0.924081i −0.0732336 0.997315i \(-0.523332\pi\)
0.997315 + 0.0732336i \(0.0233319\pi\)
\(684\) 0 0
\(685\) 15.4301 + 15.4301i 0.589553 + 0.589553i
\(686\) −17.2724 + 16.9864i −0.659462 + 0.648542i
\(687\) 0 0
\(688\) −28.6209 + 6.65326i −1.09116 + 0.253653i
\(689\) −6.26079 + 3.61467i −0.238517 + 0.137708i
\(690\) 0 0
\(691\) −10.7138 39.9843i −0.407571 1.52108i −0.799264 0.600980i \(-0.794777\pi\)
0.391693 0.920096i \(-0.371889\pi\)
\(692\) 20.3024 5.07826i 0.771781 0.193046i
\(693\) 0 0
\(694\) 9.66981 5.47574i 0.367061 0.207856i
\(695\) −1.97928 1.14273i −0.0750782 0.0433464i
\(696\) 0 0
\(697\) 1.88969 1.09101i 0.0715772 0.0413251i
\(698\) −15.5794 + 26.4715i −0.589690 + 1.00196i
\(699\) 0 0
\(700\) −4.52034 8.14039i −0.170853 0.307678i
\(701\) −21.1814 + 21.1814i −0.800009 + 0.800009i −0.983097 0.183088i \(-0.941391\pi\)
0.183088 + 0.983097i \(0.441391\pi\)
\(702\) 0 0
\(703\) 14.0428i 0.529633i
\(704\) 46.9195 10.0843i 1.76834 0.380067i
\(705\) 0 0
\(706\) −0.172085 + 0.0445735i −0.00647649 + 0.00167755i
\(707\) 0.615214 2.29601i 0.0231375 0.0863503i
\(708\) 0 0
\(709\) 4.24787 + 15.8532i 0.159532 + 0.595381i 0.998675 + 0.0514698i \(0.0163906\pi\)
−0.839143 + 0.543911i \(0.816943\pi\)
\(710\) −16.2469 + 9.20014i −0.609734 + 0.345275i
\(711\) 0 0
\(712\) 0.763799 + 0.803050i 0.0286246 + 0.0300956i
\(713\) 16.8919 29.2576i 0.632606 1.09571i
\(714\) 0 0
\(715\) 3.25736 12.1566i 0.121819 0.454633i
\(716\) 25.3208 24.4891i 0.946284 0.915200i
\(717\) 0 0
\(718\) −4.03999 4.10801i −0.150771 0.153310i
\(719\) −23.3461 −0.870664 −0.435332 0.900270i \(-0.643369\pi\)
−0.435332 + 0.900270i \(0.643369\pi\)
\(720\) 0 0
\(721\) −29.8292 −1.11090
\(722\) −10.7899 10.9716i −0.401558 0.408320i
\(723\) 0 0
\(724\) 17.9345 + 18.5437i 0.666532 + 0.689171i
\(725\) 2.40334 8.96937i 0.0892576 0.333114i
\(726\) 0 0
\(727\) −2.90255 + 5.02736i −0.107650 + 0.186454i −0.914818 0.403867i \(-0.867666\pi\)
0.807168 + 0.590322i \(0.200999\pi\)
\(728\) 0.228521 9.12218i 0.00846956 0.338090i
\(729\) 0 0
\(730\) 8.45156 4.78588i 0.312806 0.177133i
\(731\) −1.32972 4.96258i −0.0491814 0.183548i
\(732\) 0 0
\(733\) −0.240792 + 0.898647i −0.00889384 + 0.0331923i −0.970230 0.242185i \(-0.922136\pi\)
0.961336 + 0.275377i \(0.0888027\pi\)
\(734\) −7.84579 + 2.03222i −0.289593 + 0.0750107i
\(735\) 0 0
\(736\) 9.59614 30.6368i 0.353718 1.12929i
\(737\) 80.0891i 2.95012i
\(738\) 0 0
\(739\) 5.91328 5.91328i 0.217523 0.217523i −0.589931 0.807454i \(-0.700845\pi\)
0.807454 + 0.589931i \(0.200845\pi\)
\(740\) 15.7594 8.75116i 0.579327 0.321699i
\(741\) 0 0
\(742\) 12.7124 21.6000i 0.466686 0.792961i
\(743\) −20.3899 + 11.7721i −0.748032 + 0.431876i −0.824982 0.565158i \(-0.808815\pi\)
0.0769504 + 0.997035i \(0.475482\pi\)
\(744\) 0 0
\(745\) 5.69647 + 3.28886i 0.208703 + 0.120494i
\(746\) −25.1502 + 14.2418i −0.920814 + 0.521431i
\(747\) 0 0
\(748\) 2.03611 + 8.14017i 0.0744475 + 0.297634i
\(749\) 6.58682 + 24.5823i 0.240677 + 0.898219i
\(750\) 0 0
\(751\) −13.0649 + 7.54301i −0.476744 + 0.275248i −0.719059 0.694949i \(-0.755427\pi\)
0.242315 + 0.970198i \(0.422093\pi\)
\(752\) 11.9951 19.2610i 0.437418 0.702376i
\(753\) 0 0
\(754\) 6.48822 6.38078i 0.236287 0.232374i
\(755\) −14.0470 14.0470i −0.511222 0.511222i
\(756\) 0 0
\(757\) 4.48920 4.48920i 0.163163 0.163163i −0.620803 0.783966i \(-0.713193\pi\)
0.783966 + 0.620803i \(0.213193\pi\)
\(758\) 5.70527 + 0.0476324i 0.207225 + 0.00173009i
\(759\) 0 0
\(760\) 4.17000 14.1365i 0.151262 0.512786i
\(761\) −19.0628 33.0177i −0.691025 1.19689i −0.971502 0.237030i \(-0.923826\pi\)
0.280477 0.959861i \(-0.409507\pi\)
\(762\) 0 0
\(763\) 5.86202 1.57072i 0.212219 0.0568640i
\(764\) −6.07099 3.64157i −0.219641 0.131747i
\(765\) 0 0
\(766\) 21.2270 + 5.87813i 0.766963 + 0.212385i
\(767\) 8.10989 14.0467i 0.292831 0.507198i
\(768\) 0 0
\(769\) 17.5683 + 30.4291i 0.633528 + 1.09730i 0.986825 + 0.161791i \(0.0517271\pi\)
−0.353297 + 0.935511i \(0.614940\pi\)
\(770\) 10.9406 + 42.2384i 0.394273 + 1.52217i
\(771\) 0 0
\(772\) 25.9829 14.4283i 0.935146 0.519285i
\(773\) 23.4773 + 23.4773i 0.844420 + 0.844420i 0.989430 0.145010i \(-0.0463216\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(774\) 0 0
\(775\) 9.85458 0.353987
\(776\) −4.81380 + 1.16147i −0.172805 + 0.0416942i
\(777\) 0 0
\(778\) −20.0199 + 34.0164i −0.717747 + 1.21955i
\(779\) −8.58698 2.30087i −0.307660 0.0824374i
\(780\) 0 0
\(781\) −41.8308 + 11.2085i −1.49682 + 0.401073i
\(782\) 5.40972 + 1.49805i 0.193451 + 0.0535700i
\(783\) 0 0
\(784\) 1.71155 + 3.20725i 0.0611268 + 0.114545i
\(785\) 15.6257 + 9.02153i 0.557707 + 0.321992i
\(786\) 0 0
\(787\) −0.208763 0.0559379i −0.00744160 0.00199397i 0.255096 0.966916i \(-0.417893\pi\)
−0.262538 + 0.964922i \(0.584559\pi\)
\(788\) 24.2154 23.4200i 0.862639 0.834302i
\(789\) 0 0
\(790\) 0.0738858 8.84983i 0.00262874 0.314863i
\(791\) 18.6790i 0.664150i
\(792\) 0 0
\(793\) 15.7191i 0.558202i
\(794\) −54.8389 0.457841i −1.94616 0.0162482i
\(795\) 0 0
\(796\) 0.520876 31.1923i 0.0184619 1.10558i
\(797\) 2.95273 + 0.791183i 0.104591 + 0.0280251i 0.310735 0.950497i \(-0.399425\pi\)
−0.206144 + 0.978522i \(0.566091\pi\)
\(798\) 0 0
\(799\) 3.43583 + 1.98367i 0.121551 + 0.0701774i
\(800\) 9.13893 2.04418i 0.323110 0.0722727i
\(801\) 0 0
\(802\) −6.37652 + 23.0268i −0.225163 + 0.813103i
\(803\) 21.7602 5.83064i 0.767902 0.205759i
\(804\) 0 0
\(805\) 28.1942 + 7.55460i 0.993714 + 0.266265i
\(806\) 8.32304 + 4.89841i 0.293167 + 0.172539i
\(807\) 0 0
\(808\) 2.03979 + 1.24681i 0.0717596 + 0.0438625i
\(809\) −42.5506 −1.49600 −0.748000 0.663699i \(-0.768986\pi\)
−0.748000 + 0.663699i \(0.768986\pi\)
\(810\) 0 0
\(811\) 15.1448 + 15.1448i 0.531806 + 0.531806i 0.921109 0.389304i \(-0.127284\pi\)
−0.389304 + 0.921109i \(0.627284\pi\)
\(812\) −8.67310 + 30.3332i −0.304366 + 1.06449i
\(813\) 0 0
\(814\) 40.4751 10.4839i 1.41865 0.367461i
\(815\) −4.74206 8.21348i −0.166107 0.287706i
\(816\) 0 0
\(817\) −10.4657 + 18.1272i −0.366150 + 0.634190i
\(818\) 6.52560 23.5651i 0.228162 0.823935i
\(819\) 0 0
\(820\) 2.76908 + 11.0705i 0.0967006 + 0.386599i
\(821\) −26.6973 + 7.15352i −0.931742 + 0.249660i −0.692598 0.721324i \(-0.743534\pi\)
−0.239145 + 0.970984i \(0.576867\pi\)
\(822\) 0 0
\(823\) −10.1921 17.6532i −0.355273 0.615350i 0.631892 0.775057i \(-0.282279\pi\)
−0.987165 + 0.159706i \(0.948945\pi\)
\(824\) 8.48801 28.7748i 0.295694 1.00242i
\(825\) 0 0
\(826\) −0.469455 + 56.2300i −0.0163344 + 1.95649i
\(827\) −8.34698 + 8.34698i −0.290253 + 0.290253i −0.837180 0.546927i \(-0.815797\pi\)
0.546927 + 0.837180i \(0.315797\pi\)
\(828\) 0 0
\(829\) −2.48126 2.48126i −0.0861778 0.0861778i 0.662704 0.748882i \(-0.269409\pi\)
−0.748882 + 0.662704i \(0.769409\pi\)
\(830\) 2.16322 + 2.19965i 0.0750866 + 0.0763509i
\(831\) 0 0
\(832\) 8.73471 + 2.81619i 0.302822 + 0.0976339i
\(833\) −0.550465 + 0.317811i −0.0190725 + 0.0110115i
\(834\) 0 0
\(835\) 9.52386 + 35.5435i 0.329587 + 1.23004i
\(836\) 17.5849 29.3164i 0.608186 1.01393i
\(837\) 0 0
\(838\) −2.12220 3.74767i −0.0733103 0.129461i
\(839\) 17.7430 + 10.2439i 0.612558 + 0.353660i 0.773966 0.633227i \(-0.218270\pi\)
−0.161408 + 0.986888i \(0.551604\pi\)
\(840\) 0 0
\(841\) −2.13260 + 1.23126i −0.0735380 + 0.0424572i
\(842\) 11.2244 + 6.60598i 0.386819 + 0.227657i
\(843\) 0 0
\(844\) 8.88080 31.0596i 0.305690 1.06912i
\(845\) −15.1092 + 15.1092i −0.519774 + 0.519774i
\(846\) 0 0
\(847\) 70.2684i 2.41445i
\(848\) 17.2192 + 18.4094i 0.591308 + 0.632182i
\(849\) 0 0
\(850\) 0.410565 + 1.58507i 0.0140823 + 0.0543673i
\(851\) 7.23923 27.0172i 0.248158 0.926137i
\(852\) 0 0
\(853\) 4.06296 + 15.1632i 0.139113 + 0.519177i 0.999947 + 0.0102909i \(0.00327574\pi\)
−0.860834 + 0.508886i \(0.830058\pi\)
\(854\) −26.8531 47.4209i −0.918896 1.62271i
\(855\) 0 0
\(856\) −25.5877 0.641003i −0.874570 0.0219090i
\(857\) −0.102894 + 0.178217i −0.00351478 + 0.00608778i −0.867777 0.496953i \(-0.834452\pi\)
0.864263 + 0.503041i \(0.167785\pi\)
\(858\) 0 0
\(859\) −0.733242 + 2.73650i −0.0250179 + 0.0933681i −0.977306 0.211833i \(-0.932057\pi\)
0.952288 + 0.305201i \(0.0987235\pi\)
\(860\) 26.8651 + 0.448616i 0.916093 + 0.0152977i
\(861\) 0 0
\(862\) 7.34054 7.21898i 0.250020 0.245880i
\(863\) 26.9928 0.918846 0.459423 0.888218i \(-0.348056\pi\)
0.459423 + 0.888218i \(0.348056\pi\)
\(864\) 0 0
\(865\) −19.1365 −0.650660
\(866\) 20.1424 19.8089i 0.684467 0.673133i
\(867\) 0 0
\(868\) −33.4767 0.559022i −1.13627 0.0189744i
\(869\) 5.31292 19.8281i 0.180228 0.672621i
\(870\) 0 0
\(871\) −7.65786 + 13.2638i −0.259477 + 0.449427i
\(872\) −0.152857 + 6.10177i −0.00517638 + 0.206632i
\(873\) 0 0
\(874\) −11.2689 19.9002i −0.381178 0.673136i
\(875\) 8.85929 + 33.0633i 0.299499 + 1.11774i
\(876\) 0 0
\(877\) −13.9344 + 52.0038i −0.470531 + 1.75604i 0.167338 + 0.985900i \(0.446483\pi\)
−0.637869 + 0.770145i \(0.720184\pi\)
\(878\) 10.8605 + 41.9290i 0.366524 + 1.41503i
\(879\) 0 0
\(880\) −43.8586 1.46518i −1.47847 0.0493913i
\(881\) 27.9049i 0.940139i −0.882629 0.470069i \(-0.844229\pi\)
0.882629 0.470069i \(-0.155771\pi\)
\(882\) 0 0
\(883\) 3.83601 3.83601i 0.129092 0.129092i −0.639609 0.768701i \(-0.720904\pi\)
0.768701 + 0.639609i \(0.220904\pi\)
\(884\) −0.441130 + 1.54280i −0.0148368 + 0.0518901i
\(885\) 0 0
\(886\) 36.3015 + 21.3647i 1.21957 + 0.717763i
\(887\) 44.3036 25.5787i 1.48757 0.858849i 0.487671 0.873028i \(-0.337847\pi\)
0.999899 + 0.0141788i \(0.00451340\pi\)
\(888\) 0 0
\(889\) −33.6644 19.4361i −1.12907 0.651867i
\(890\) −0.499361 0.881840i −0.0167386 0.0295593i
\(891\) 0 0
\(892\) −16.5424 + 27.5784i −0.553881 + 0.923393i
\(893\) −4.18343 15.6128i −0.139993 0.522462i
\(894\) 0 0
\(895\) −27.8952 + 16.1053i −0.932434 + 0.538341i
\(896\) −31.1615 + 6.42580i −1.04103 + 0.214671i
\(897\) 0 0
\(898\) −26.5781 27.0257i −0.886924 0.901858i
\(899\) −23.6101 23.6101i −0.787442 0.787442i
\(900\) 0 0
\(901\) −3.11647 + 3.11647i −0.103825 + 0.103825i
\(902\) −0.220975 + 26.4678i −0.00735767 + 0.881281i
\(903\) 0 0
\(904\) −18.0188 5.31519i −0.599296 0.176781i
\(905\) −11.7947 20.4290i −0.392069 0.679084i
\(906\) 0 0
\(907\) −9.99802 + 2.67896i −0.331979 + 0.0889535i −0.420958 0.907080i \(-0.638306\pi\)
0.0889794 + 0.996033i \(0.471639\pi\)
\(908\) 5.36081 + 21.4320i 0.177905 + 0.711246i
\(909\) 0 0
\(910\) −2.22679 + 8.04134i −0.0738173 + 0.266568i
\(911\) 5.69107 9.85722i 0.188553 0.326584i −0.756215 0.654324i \(-0.772953\pi\)
0.944768 + 0.327739i \(0.106287\pi\)
\(912\) 0 0
\(913\) 3.57791 + 6.19712i 0.118411 + 0.205095i
\(914\) 5.14309 1.33217i 0.170118 0.0440642i
\(915\) 0 0
\(916\) −0.222317 + 0.777528i −0.00734555 + 0.0256903i
\(917\) 18.4856 + 18.4856i 0.610447 + 0.610447i
\(918\) 0 0
\(919\) 11.8316 0.390288 0.195144 0.980775i \(-0.437483\pi\)
0.195144 + 0.980775i \(0.437483\pi\)
\(920\) −15.3103 + 25.0479i −0.504766 + 0.825805i
\(921\) 0 0
\(922\) 4.95432 + 2.91579i 0.163162 + 0.0960266i
\(923\) −7.99945 2.14345i −0.263305 0.0705524i
\(924\) 0 0
\(925\) 7.88080 2.11165i 0.259119 0.0694307i
\(926\) −8.84192 + 31.9298i −0.290563 + 1.04928i
\(927\) 0 0
\(928\) −26.7931 16.9980i −0.879526 0.557986i
\(929\) −35.7139 20.6194i −1.17174 0.676502i −0.217647 0.976027i \(-0.569838\pi\)
−0.954088 + 0.299525i \(0.903172\pi\)
\(930\) 0 0
\(931\) 2.50138 + 0.670242i 0.0819794 + 0.0219663i
\(932\) 0.388200 23.2471i 0.0127159 0.761484i
\(933\) 0 0
\(934\) 26.5132 + 0.221354i 0.867537 + 0.00724293i
\(935\) 7.67271i 0.250924i
\(936\) 0 0
\(937\) 15.6750i 0.512081i −0.966666 0.256041i \(-0.917582\pi\)
0.966666 0.256041i \(-0.0824181\pi\)
\(938\) 0.443289 53.0959i 0.0144739 1.73364i
\(939\) 0 0
\(940\) −14.9143 + 14.4244i −0.486451 + 0.470471i
\(941\) −9.63753 2.58237i −0.314174 0.0841828i 0.0982863 0.995158i \(-0.468664\pi\)
−0.412461 + 0.910975i \(0.635331\pi\)
\(942\) 0 0
\(943\) 15.3345 + 8.85340i 0.499361 + 0.288306i
\(944\) −54.1088 16.4533i −1.76109 0.535509i
\(945\) 0 0
\(946\) 60.0609 + 16.6319i 1.95275 + 0.540750i
\(947\) 2.28712 0.612832i 0.0743214 0.0199144i −0.221467 0.975168i \(-0.571084\pi\)
0.295788 + 0.955254i \(0.404418\pi\)
\(948\) 0 0
\(949\) 4.16129 + 1.11501i 0.135081 + 0.0361949i
\(950\) 3.38357 5.74912i 0.109777 0.186526i
\(951\) 0 0
\(952\) −1.30480 5.40787i −0.0422889 0.175270i
\(953\) −43.1152 −1.39664 −0.698320 0.715786i \(-0.746069\pi\)
−0.698320 + 0.715786i \(0.746069\pi\)
\(954\) 0 0
\(955\) 4.57740 + 4.57740i 0.148121 + 0.148121i
\(956\) −5.44432 + 3.02322i −0.176082 + 0.0977778i
\(957\) 0 0
\(958\) −12.5126 48.3074i −0.404265 1.56074i
\(959\) −16.7781 29.0605i −0.541792 0.938411i
\(960\) 0 0
\(961\) 2.21754 3.84089i 0.0715334 0.123900i
\(962\) 7.70565 + 2.13383i 0.248440 + 0.0687974i
\(963\) 0 0
\(964\) 24.5834 + 14.7459i 0.791777 + 0.474933i
\(965\) −26.2502 + 7.03372i −0.845023 + 0.226423i
\(966\) 0 0
\(967\) −21.1271 36.5932i −0.679401 1.17676i −0.975162 0.221495i \(-0.928906\pi\)
0.295761 0.955262i \(-0.404427\pi\)
\(968\) −67.7846 19.9951i −2.17868 0.642668i
\(969\) 0 0
\(970\) 4.52791 + 0.0378028i 0.145382 + 0.00121377i
\(971\) −11.0093 + 11.0093i −0.353305 + 0.353305i −0.861338 0.508033i \(-0.830373\pi\)
0.508033 + 0.861338i \(0.330373\pi\)
\(972\) 0 0
\(973\) 2.48513 + 2.48513i 0.0796697 + 0.0796697i
\(974\) 12.2443 12.0415i 0.392331 0.385835i
\(975\) 0 0
\(976\) 53.3859 12.4102i 1.70884 0.397240i
\(977\) −30.5197 + 17.6206i −0.976413 + 0.563732i −0.901185 0.433434i \(-0.857302\pi\)
−0.0752275 + 0.997166i \(0.523968\pi\)
\(978\) 0 0
\(979\) −0.608371 2.27047i −0.0194436 0.0725646i
\(980\) −0.806631 3.22483i −0.0257669 0.103013i
\(981\) 0 0
\(982\) −0.951071 + 0.538565i −0.0303499 + 0.0171863i
\(983\) 33.9109 + 19.5785i 1.08159 + 0.624456i 0.931325 0.364190i \(-0.118654\pi\)
0.150264 + 0.988646i \(0.451987\pi\)
\(984\) 0 0
\(985\) −26.6774 + 15.4022i −0.850013 + 0.490755i
\(986\) 2.81393 4.78124i 0.0896139 0.152266i
\(987\) 0 0
\(988\) 5.71542 3.17376i 0.181832 0.100971i
\(989\) 29.4801 29.4801i 0.937411 0.937411i
\(990\) 0 0
\(991\) 15.1164i 0.480188i −0.970750 0.240094i \(-0.922822\pi\)
0.970750 0.240094i \(-0.0771783\pi\)
\(992\) 10.0652 32.1343i 0.319570 1.02027i
\(993\) 0 0
\(994\) 27.7942 7.19927i 0.881577 0.228347i
\(995\) −7.38315 + 27.5543i −0.234062 + 0.873530i
\(996\) 0 0
\(997\) −10.3875 38.7668i −0.328976 1.22776i −0.910254 0.414051i \(-0.864113\pi\)
0.581277 0.813706i \(-0.302553\pi\)
\(998\) −1.00057 + 0.566596i −0.0316726 + 0.0179353i
\(999\) 0 0
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 432.2.v.a.35.6 88
3.2 odd 2 144.2.u.a.83.17 yes 88
4.3 odd 2 1728.2.z.a.1007.6 88
9.4 even 3 144.2.u.a.131.10 yes 88
9.5 odd 6 inner 432.2.v.a.179.13 88
12.11 even 2 576.2.y.a.47.18 88
16.5 even 4 1728.2.z.a.143.6 88
16.11 odd 4 inner 432.2.v.a.251.13 88
36.23 even 6 1728.2.z.a.1583.6 88
36.31 odd 6 576.2.y.a.239.16 88
48.5 odd 4 576.2.y.a.335.16 88
48.11 even 4 144.2.u.a.11.10 88
144.5 odd 12 1728.2.z.a.719.6 88
144.59 even 12 inner 432.2.v.a.395.6 88
144.85 even 12 576.2.y.a.527.18 88
144.139 odd 12 144.2.u.a.59.17 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.10 88 48.11 even 4
144.2.u.a.59.17 yes 88 144.139 odd 12
144.2.u.a.83.17 yes 88 3.2 odd 2
144.2.u.a.131.10 yes 88 9.4 even 3
432.2.v.a.35.6 88 1.1 even 1 trivial
432.2.v.a.179.13 88 9.5 odd 6 inner
432.2.v.a.251.13 88 16.11 odd 4 inner
432.2.v.a.395.6 88 144.59 even 12 inner
576.2.y.a.47.18 88 12.11 even 2
576.2.y.a.239.16 88 36.31 odd 6
576.2.y.a.335.16 88 48.5 odd 4
576.2.y.a.527.18 88 144.85 even 12
1728.2.z.a.143.6 88 16.5 even 4
1728.2.z.a.719.6 88 144.5 odd 12
1728.2.z.a.1007.6 88 4.3 odd 2
1728.2.z.a.1583.6 88 36.23 even 6