Properties

Label 288.2.w.b.107.7
Level $288$
Weight $2$
Character 288.107
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(35,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 107.7
Character \(\chi\) \(=\) 288.107
Dual form 288.2.w.b.35.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.33776 - 0.458699i) q^{2} +(1.57919 - 1.22726i) q^{4} +(2.70076 + 1.11869i) q^{5} +(-1.06647 + 1.06647i) q^{7} +(1.54963 - 2.36614i) q^{8} +O(q^{10})\) \(q+(1.33776 - 0.458699i) q^{2} +(1.57919 - 1.22726i) q^{4} +(2.70076 + 1.11869i) q^{5} +(-1.06647 + 1.06647i) q^{7} +(1.54963 - 2.36614i) q^{8} +(4.12611 + 0.257702i) q^{10} +(-5.29504 - 2.19328i) q^{11} +(1.67540 + 4.04478i) q^{13} +(-0.937494 + 1.91588i) q^{14} +(0.987684 - 3.87614i) q^{16} -3.44484 q^{17} +(3.23205 - 1.33876i) q^{19} +(5.63794 - 1.54790i) q^{20} +(-8.08953 - 0.505243i) q^{22} +(-0.703083 + 0.703083i) q^{23} +(2.50711 + 2.50711i) q^{25} +(4.09662 + 4.64243i) q^{26} +(-0.375329 + 2.99300i) q^{28} +(-3.94721 - 9.52941i) q^{29} -4.23846i q^{31} +(-0.456702 - 5.63839i) q^{32} +(-4.60837 + 1.58015i) q^{34} +(-4.07335 + 1.68724i) q^{35} +(-2.04600 + 4.93947i) q^{37} +(3.70961 - 3.27347i) q^{38} +(6.83218 - 4.65683i) q^{40} +(3.53573 + 3.53573i) q^{41} +(-3.38340 + 8.16825i) q^{43} +(-11.0536 + 3.03477i) q^{44} +(-0.618051 + 1.26306i) q^{46} +4.33671i q^{47} +4.72526i q^{49} +(4.50391 + 2.20390i) q^{50} +(7.60977 + 4.33133i) q^{52} +(0.541366 - 1.30697i) q^{53} +(-11.8470 - 11.8470i) q^{55} +(0.870790 + 4.17608i) q^{56} +(-9.65155 - 10.9375i) q^{58} +(-3.66093 + 8.83827i) q^{59} +(-1.97197 + 0.816817i) q^{61} +(-1.94418 - 5.67003i) q^{62} +(-3.19728 - 7.33331i) q^{64} +12.7983i q^{65} +(-3.55849 - 8.59096i) q^{67} +(-5.44006 + 4.22771i) q^{68} +(-4.67522 + 4.12556i) q^{70} +(1.76501 + 1.76501i) q^{71} +(-1.16342 + 1.16342i) q^{73} +(-0.471315 + 7.54631i) q^{74} +(3.46102 - 6.08071i) q^{76} +(7.98610 - 3.30795i) q^{77} +14.4770 q^{79} +(7.00371 - 9.36362i) q^{80} +(6.35178 + 3.10811i) q^{82} +(-4.27230 - 10.3143i) q^{83} +(-9.30371 - 3.85372i) q^{85} +(-0.779399 + 12.4791i) q^{86} +(-13.3950 + 9.13005i) q^{88} +(7.99481 - 7.99481i) q^{89} +(-6.10044 - 2.52688i) q^{91} +(-0.247439 + 1.97317i) q^{92} +(1.98925 + 5.80147i) q^{94} +10.2267 q^{95} +12.8450 q^{97} +(2.16747 + 6.32126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{2} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52} + 16 q^{53} - 32 q^{55} - 40 q^{56} - 32 q^{58} - 32 q^{59} + 32 q^{61} + 68 q^{62} - 48 q^{64} - 16 q^{67} + 72 q^{68} - 48 q^{70} - 16 q^{71} - 60 q^{74} - 8 q^{76} + 16 q^{77} - 32 q^{79} - 96 q^{80} + 40 q^{82} + 40 q^{83} + 40 q^{86} + 40 q^{88} - 48 q^{91} + 16 q^{92} + 72 q^{94} + 80 q^{95} + 44 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33776 0.458699i 0.945937 0.324349i
\(3\) 0 0
\(4\) 1.57919 1.22726i 0.789595 0.613628i
\(5\) 2.70076 + 1.11869i 1.20782 + 0.500294i 0.893517 0.449029i \(-0.148230\pi\)
0.314300 + 0.949324i \(0.398230\pi\)
\(6\) 0 0
\(7\) −1.06647 + 1.06647i −0.403090 + 0.403090i −0.879320 0.476231i \(-0.842003\pi\)
0.476231 + 0.879320i \(0.342003\pi\)
\(8\) 1.54963 2.36614i 0.547878 0.836558i
\(9\) 0 0
\(10\) 4.12611 + 0.257702i 1.30479 + 0.0814925i
\(11\) −5.29504 2.19328i −1.59651 0.661297i −0.605596 0.795772i \(-0.707065\pi\)
−0.990917 + 0.134475i \(0.957065\pi\)
\(12\) 0 0
\(13\) 1.67540 + 4.04478i 0.464674 + 1.12182i 0.966457 + 0.256828i \(0.0826774\pi\)
−0.501783 + 0.864993i \(0.667323\pi\)
\(14\) −0.937494 + 1.91588i −0.250556 + 0.512039i
\(15\) 0 0
\(16\) 0.987684 3.87614i 0.246921 0.969036i
\(17\) −3.44484 −0.835498 −0.417749 0.908563i \(-0.637181\pi\)
−0.417749 + 0.908563i \(0.637181\pi\)
\(18\) 0 0
\(19\) 3.23205 1.33876i 0.741483 0.307132i 0.0202218 0.999796i \(-0.493563\pi\)
0.721261 + 0.692663i \(0.243563\pi\)
\(20\) 5.63794 1.54790i 1.26068 0.346121i
\(21\) 0 0
\(22\) −8.08953 0.505243i −1.72469 0.107718i
\(23\) −0.703083 + 0.703083i −0.146603 + 0.146603i −0.776599 0.629996i \(-0.783057\pi\)
0.629996 + 0.776599i \(0.283057\pi\)
\(24\) 0 0
\(25\) 2.50711 + 2.50711i 0.501422 + 0.501422i
\(26\) 4.09662 + 4.64243i 0.803414 + 0.910456i
\(27\) 0 0
\(28\) −0.375329 + 2.99300i −0.0709304 + 0.565625i
\(29\) −3.94721 9.52941i −0.732979 1.76957i −0.632405 0.774638i \(-0.717932\pi\)
−0.100574 0.994930i \(-0.532068\pi\)
\(30\) 0 0
\(31\) 4.23846i 0.761250i −0.924729 0.380625i \(-0.875709\pi\)
0.924729 0.380625i \(-0.124291\pi\)
\(32\) −0.456702 5.63839i −0.0807343 0.996736i
\(33\) 0 0
\(34\) −4.60837 + 1.58015i −0.790328 + 0.270993i
\(35\) −4.07335 + 1.68724i −0.688522 + 0.285195i
\(36\) 0 0
\(37\) −2.04600 + 4.93947i −0.336360 + 0.812044i 0.661699 + 0.749769i \(0.269836\pi\)
−0.998059 + 0.0622749i \(0.980164\pi\)
\(38\) 3.70961 3.27347i 0.601778 0.531027i
\(39\) 0 0
\(40\) 6.83218 4.65683i 1.08026 0.736310i
\(41\) 3.53573 + 3.53573i 0.552188 + 0.552188i 0.927072 0.374884i \(-0.122317\pi\)
−0.374884 + 0.927072i \(0.622317\pi\)
\(42\) 0 0
\(43\) −3.38340 + 8.16825i −0.515963 + 1.24565i 0.424400 + 0.905475i \(0.360485\pi\)
−0.940364 + 0.340171i \(0.889515\pi\)
\(44\) −11.0536 + 3.03477i −1.66639 + 0.457508i
\(45\) 0 0
\(46\) −0.618051 + 1.26306i −0.0911267 + 0.186228i
\(47\) 4.33671i 0.632575i 0.948663 + 0.316287i \(0.102436\pi\)
−0.948663 + 0.316287i \(0.897564\pi\)
\(48\) 0 0
\(49\) 4.72526i 0.675038i
\(50\) 4.50391 + 2.20390i 0.636950 + 0.311678i
\(51\) 0 0
\(52\) 7.60977 + 4.33133i 1.05529 + 0.600648i
\(53\) 0.541366 1.30697i 0.0743624 0.179527i −0.882327 0.470636i \(-0.844024\pi\)
0.956690 + 0.291110i \(0.0940244\pi\)
\(54\) 0 0
\(55\) −11.8470 11.8470i −1.59745 1.59745i
\(56\) 0.870790 + 4.17608i 0.116364 + 0.558052i
\(57\) 0 0
\(58\) −9.65155 10.9375i −1.26731 1.43616i
\(59\) −3.66093 + 8.83827i −0.476613 + 1.15064i 0.484575 + 0.874750i \(0.338974\pi\)
−0.961188 + 0.275895i \(0.911026\pi\)
\(60\) 0 0
\(61\) −1.97197 + 0.816817i −0.252485 + 0.104583i −0.505336 0.862922i \(-0.668632\pi\)
0.252851 + 0.967505i \(0.418632\pi\)
\(62\) −1.94418 5.67003i −0.246911 0.720095i
\(63\) 0 0
\(64\) −3.19728 7.33331i −0.399660 0.916663i
\(65\) 12.7983i 1.58743i
\(66\) 0 0
\(67\) −3.55849 8.59096i −0.434739 1.04955i −0.977740 0.209821i \(-0.932712\pi\)
0.543001 0.839732i \(-0.317288\pi\)
\(68\) −5.44006 + 4.22771i −0.659705 + 0.512685i
\(69\) 0 0
\(70\) −4.67522 + 4.12556i −0.558796 + 0.493098i
\(71\) 1.76501 + 1.76501i 0.209468 + 0.209468i 0.804041 0.594574i \(-0.202679\pi\)
−0.594574 + 0.804041i \(0.702679\pi\)
\(72\) 0 0
\(73\) −1.16342 + 1.16342i −0.136168 + 0.136168i −0.771905 0.635737i \(-0.780696\pi\)
0.635737 + 0.771905i \(0.280696\pi\)
\(74\) −0.471315 + 7.54631i −0.0547893 + 0.877241i
\(75\) 0 0
\(76\) 3.46102 6.08071i 0.397006 0.697505i
\(77\) 7.98610 3.30795i 0.910100 0.376976i
\(78\) 0 0
\(79\) 14.4770 1.62879 0.814393 0.580314i \(-0.197070\pi\)
0.814393 + 0.580314i \(0.197070\pi\)
\(80\) 7.00371 9.36362i 0.783039 1.04689i
\(81\) 0 0
\(82\) 6.35178 + 3.10811i 0.701437 + 0.343233i
\(83\) −4.27230 10.3143i −0.468946 1.13214i −0.964624 0.263630i \(-0.915080\pi\)
0.495678 0.868507i \(-0.334920\pi\)
\(84\) 0 0
\(85\) −9.30371 3.85372i −1.00913 0.417995i
\(86\) −0.779399 + 12.4791i −0.0840448 + 1.34566i
\(87\) 0 0
\(88\) −13.3950 + 9.13005i −1.42791 + 0.973267i
\(89\) 7.99481 7.99481i 0.847448 0.847448i −0.142366 0.989814i \(-0.545471\pi\)
0.989814 + 0.142366i \(0.0454709\pi\)
\(90\) 0 0
\(91\) −6.10044 2.52688i −0.639500 0.264889i
\(92\) −0.247439 + 1.97317i −0.0257973 + 0.205717i
\(93\) 0 0
\(94\) 1.98925 + 5.80147i 0.205175 + 0.598376i
\(95\) 10.2267 1.04923
\(96\) 0 0
\(97\) 12.8450 1.30421 0.652107 0.758127i \(-0.273885\pi\)
0.652107 + 0.758127i \(0.273885\pi\)
\(98\) 2.16747 + 6.32126i 0.218948 + 0.638543i
\(99\) 0 0
\(100\) 7.03607 + 0.882337i 0.703607 + 0.0882337i
\(101\) 0.195046 + 0.0807908i 0.0194078 + 0.00803898i 0.392366 0.919809i \(-0.371657\pi\)
−0.372958 + 0.927848i \(0.621657\pi\)
\(102\) 0 0
\(103\) 7.52990 7.52990i 0.741943 0.741943i −0.231009 0.972952i \(-0.574203\pi\)
0.972952 + 0.231009i \(0.0742026\pi\)
\(104\) 12.1668 + 2.30368i 1.19305 + 0.225894i
\(105\) 0 0
\(106\) 0.124709 1.99674i 0.0121128 0.193940i
\(107\) 6.43177 + 2.66413i 0.621783 + 0.257551i 0.671257 0.741225i \(-0.265755\pi\)
−0.0494744 + 0.998775i \(0.515755\pi\)
\(108\) 0 0
\(109\) −4.89484 11.8172i −0.468840 1.13188i −0.964670 0.263461i \(-0.915136\pi\)
0.495830 0.868420i \(-0.334864\pi\)
\(110\) −21.2827 10.4142i −2.02922 0.992958i
\(111\) 0 0
\(112\) 3.08047 + 5.18715i 0.291077 + 0.490139i
\(113\) 0.983568 0.0925263 0.0462631 0.998929i \(-0.485269\pi\)
0.0462631 + 0.998929i \(0.485269\pi\)
\(114\) 0 0
\(115\) −2.68539 + 1.11233i −0.250414 + 0.103725i
\(116\) −17.9284 10.2045i −1.66461 0.947465i
\(117\) 0 0
\(118\) −0.843332 + 13.5027i −0.0776350 + 1.24303i
\(119\) 3.67384 3.67384i 0.336780 0.336780i
\(120\) 0 0
\(121\) 15.4488 + 15.4488i 1.40443 + 1.40443i
\(122\) −2.26335 + 1.99724i −0.204914 + 0.180822i
\(123\) 0 0
\(124\) −5.20168 6.69334i −0.467125 0.601079i
\(125\) −1.62704 3.92802i −0.145527 0.351333i
\(126\) 0 0
\(127\) 5.32766i 0.472754i 0.971661 + 0.236377i \(0.0759600\pi\)
−0.971661 + 0.236377i \(0.924040\pi\)
\(128\) −7.64097 8.34360i −0.675372 0.737477i
\(129\) 0 0
\(130\) 5.87055 + 17.1210i 0.514882 + 1.50161i
\(131\) −17.7023 + 7.33252i −1.54666 + 0.640646i −0.982707 0.185165i \(-0.940718\pi\)
−0.563948 + 0.825811i \(0.690718\pi\)
\(132\) 0 0
\(133\) −2.01915 + 4.87465i −0.175082 + 0.422686i
\(134\) −8.70107 9.86034i −0.751658 0.851804i
\(135\) 0 0
\(136\) −5.33824 + 8.15100i −0.457750 + 0.698943i
\(137\) 10.0787 + 10.0787i 0.861079 + 0.861079i 0.991464 0.130384i \(-0.0416211\pi\)
−0.130384 + 0.991464i \(0.541621\pi\)
\(138\) 0 0
\(139\) −4.57378 + 11.0421i −0.387943 + 0.936578i 0.602432 + 0.798170i \(0.294198\pi\)
−0.990375 + 0.138408i \(0.955802\pi\)
\(140\) −4.36192 + 7.66352i −0.368650 + 0.647685i
\(141\) 0 0
\(142\) 3.17076 + 1.55154i 0.266084 + 0.130203i
\(143\) 25.0919i 2.09829i
\(144\) 0 0
\(145\) 30.1524i 2.50402i
\(146\) −1.02271 + 2.09003i −0.0846404 + 0.172972i
\(147\) 0 0
\(148\) 2.83098 + 10.3113i 0.232705 + 0.847586i
\(149\) 2.47497 5.97511i 0.202758 0.489500i −0.789492 0.613761i \(-0.789656\pi\)
0.992250 + 0.124261i \(0.0396559\pi\)
\(150\) 0 0
\(151\) −5.28519 5.28519i −0.430103 0.430103i 0.458560 0.888663i \(-0.348365\pi\)
−0.888663 + 0.458560i \(0.848365\pi\)
\(152\) 1.84079 9.72208i 0.149308 0.788565i
\(153\) 0 0
\(154\) 9.16611 8.08845i 0.738626 0.651786i
\(155\) 4.74153 11.4471i 0.380849 0.919451i
\(156\) 0 0
\(157\) 19.9431 8.26070i 1.59163 0.659276i 0.601431 0.798924i \(-0.294597\pi\)
0.990201 + 0.139649i \(0.0445973\pi\)
\(158\) 19.3667 6.64057i 1.54073 0.528295i
\(159\) 0 0
\(160\) 5.07418 15.7389i 0.401149 1.24427i
\(161\) 1.49964i 0.118188i
\(162\) 0 0
\(163\) 4.75817 + 11.4872i 0.372689 + 0.899751i 0.993293 + 0.115626i \(0.0368875\pi\)
−0.620604 + 0.784124i \(0.713112\pi\)
\(164\) 9.92283 + 1.24434i 0.774843 + 0.0971668i
\(165\) 0 0
\(166\) −10.4464 11.8383i −0.810801 0.918828i
\(167\) 13.4711 + 13.4711i 1.04243 + 1.04243i 0.999059 + 0.0433679i \(0.0138088\pi\)
0.0433679 + 0.999059i \(0.486191\pi\)
\(168\) 0 0
\(169\) −4.36092 + 4.36092i −0.335455 + 0.335455i
\(170\) −14.2138 0.887743i −1.09015 0.0680868i
\(171\) 0 0
\(172\) 4.68150 + 17.0515i 0.356961 + 1.30017i
\(173\) 1.48659 0.615768i 0.113024 0.0468160i −0.325455 0.945558i \(-0.605517\pi\)
0.438479 + 0.898742i \(0.355517\pi\)
\(174\) 0 0
\(175\) −5.34754 −0.404236
\(176\) −13.7313 + 18.3581i −1.03503 + 1.38379i
\(177\) 0 0
\(178\) 7.02791 14.3623i 0.526764 1.07650i
\(179\) −0.188898 0.456040i −0.0141189 0.0340860i 0.916663 0.399661i \(-0.130872\pi\)
−0.930782 + 0.365575i \(0.880872\pi\)
\(180\) 0 0
\(181\) −20.2286 8.37896i −1.50358 0.622803i −0.529358 0.848398i \(-0.677567\pi\)
−0.974221 + 0.225596i \(0.927567\pi\)
\(182\) −9.31999 0.582093i −0.690843 0.0431476i
\(183\) 0 0
\(184\) 0.574076 + 2.75312i 0.0423215 + 0.202963i
\(185\) −11.0515 + 11.0515i −0.812522 + 0.812522i
\(186\) 0 0
\(187\) 18.2406 + 7.55549i 1.33388 + 0.552512i
\(188\) 5.32226 + 6.84850i 0.388166 + 0.499478i
\(189\) 0 0
\(190\) 13.6808 4.69096i 0.992509 0.340318i
\(191\) 23.3059 1.68636 0.843180 0.537632i \(-0.180681\pi\)
0.843180 + 0.537632i \(0.180681\pi\)
\(192\) 0 0
\(193\) −27.0699 −1.94854 −0.974268 0.225392i \(-0.927634\pi\)
−0.974268 + 0.225392i \(0.927634\pi\)
\(194\) 17.1835 5.89200i 1.23371 0.423021i
\(195\) 0 0
\(196\) 5.79911 + 7.46209i 0.414222 + 0.533006i
\(197\) −0.234504 0.0971345i −0.0167077 0.00692055i 0.374314 0.927302i \(-0.377878\pi\)
−0.391022 + 0.920381i \(0.627878\pi\)
\(198\) 0 0
\(199\) −2.87064 + 2.87064i −0.203494 + 0.203494i −0.801495 0.598001i \(-0.795962\pi\)
0.598001 + 0.801495i \(0.295962\pi\)
\(200\) 9.81728 2.04709i 0.694187 0.144751i
\(201\) 0 0
\(202\) 0.297983 + 0.0186110i 0.0209660 + 0.00130946i
\(203\) 14.3725 + 5.95328i 1.00875 + 0.417838i
\(204\) 0 0
\(205\) 5.59377 + 13.5045i 0.390686 + 0.943199i
\(206\) 6.61922 13.5271i 0.461183 0.942480i
\(207\) 0 0
\(208\) 17.3329 2.49914i 1.20182 0.173284i
\(209\) −20.0501 −1.38689
\(210\) 0 0
\(211\) 21.3966 8.86277i 1.47300 0.610138i 0.505462 0.862849i \(-0.331322\pi\)
0.967542 + 0.252710i \(0.0813219\pi\)
\(212\) −0.749072 2.72836i −0.0514465 0.187384i
\(213\) 0 0
\(214\) 9.82618 + 0.613708i 0.671704 + 0.0419522i
\(215\) −18.2755 + 18.2755i −1.24638 + 1.24638i
\(216\) 0 0
\(217\) 4.52021 + 4.52021i 0.306852 + 0.306852i
\(218\) −11.9686 13.5633i −0.810618 0.918620i
\(219\) 0 0
\(220\) −33.2481 4.16937i −2.24158 0.281099i
\(221\) −5.77151 13.9337i −0.388234 0.937279i
\(222\) 0 0
\(223\) 6.32748i 0.423720i −0.977300 0.211860i \(-0.932048\pi\)
0.977300 0.211860i \(-0.0679520\pi\)
\(224\) 6.50026 + 5.52614i 0.434317 + 0.369231i
\(225\) 0 0
\(226\) 1.31578 0.451162i 0.0875241 0.0300108i
\(227\) 6.62883 2.74575i 0.439971 0.182242i −0.151691 0.988428i \(-0.548472\pi\)
0.591662 + 0.806186i \(0.298472\pi\)
\(228\) 0 0
\(229\) −2.56839 + 6.20065i −0.169724 + 0.409751i −0.985739 0.168280i \(-0.946179\pi\)
0.816015 + 0.578031i \(0.196179\pi\)
\(230\) −3.08218 + 2.71981i −0.203233 + 0.179339i
\(231\) 0 0
\(232\) −28.6647 5.42741i −1.88193 0.356327i
\(233\) −4.72679 4.72679i −0.309662 0.309662i 0.535116 0.844779i \(-0.320268\pi\)
−0.844779 + 0.535116i \(0.820268\pi\)
\(234\) 0 0
\(235\) −4.85145 + 11.7124i −0.316474 + 0.764035i
\(236\) 5.06552 + 18.4502i 0.329737 + 1.20101i
\(237\) 0 0
\(238\) 3.22952 6.59989i 0.209339 0.427808i
\(239\) 5.76879i 0.373152i 0.982441 + 0.186576i \(0.0597390\pi\)
−0.982441 + 0.186576i \(0.940261\pi\)
\(240\) 0 0
\(241\) 20.1679i 1.29913i −0.760308 0.649563i \(-0.774952\pi\)
0.760308 0.649563i \(-0.225048\pi\)
\(242\) 27.7530 + 13.5804i 1.78403 + 0.872979i
\(243\) 0 0
\(244\) −2.11167 + 3.71002i −0.135186 + 0.237510i
\(245\) −5.28612 + 12.7618i −0.337718 + 0.815322i
\(246\) 0 0
\(247\) 10.8300 + 10.8300i 0.689095 + 0.689095i
\(248\) −10.0288 6.56806i −0.636830 0.417072i
\(249\) 0 0
\(250\) −3.97836 4.50842i −0.251614 0.285137i
\(251\) −0.288817 + 0.697266i −0.0182300 + 0.0440110i −0.932732 0.360569i \(-0.882582\pi\)
0.914502 + 0.404580i \(0.132582\pi\)
\(252\) 0 0
\(253\) 5.26491 2.18080i 0.331002 0.137105i
\(254\) 2.44379 + 7.12712i 0.153337 + 0.447195i
\(255\) 0 0
\(256\) −14.0490 7.65681i −0.878060 0.478550i
\(257\) 6.89560i 0.430136i −0.976599 0.215068i \(-0.931003\pi\)
0.976599 0.215068i \(-0.0689973\pi\)
\(258\) 0 0
\(259\) −3.08582 7.44983i −0.191743 0.462910i
\(260\) 15.7068 + 20.2109i 0.974091 + 1.25343i
\(261\) 0 0
\(262\) −20.3179 + 17.9292i −1.25525 + 1.10767i
\(263\) −3.11571 3.11571i −0.192123 0.192123i 0.604490 0.796613i \(-0.293377\pi\)
−0.796613 + 0.604490i \(0.793377\pi\)
\(264\) 0 0
\(265\) 2.92420 2.92420i 0.179632 0.179632i
\(266\) −0.465130 + 7.44728i −0.0285190 + 0.456622i
\(267\) 0 0
\(268\) −16.1628 9.19958i −0.987303 0.561954i
\(269\) −12.4085 + 5.13977i −0.756560 + 0.313378i −0.727415 0.686198i \(-0.759279\pi\)
−0.0291452 + 0.999575i \(0.509279\pi\)
\(270\) 0 0
\(271\) 5.94627 0.361210 0.180605 0.983556i \(-0.442194\pi\)
0.180605 + 0.983556i \(0.442194\pi\)
\(272\) −3.40242 + 13.3527i −0.206302 + 0.809627i
\(273\) 0 0
\(274\) 18.1059 + 8.85974i 1.09382 + 0.535237i
\(275\) −7.77645 18.7740i −0.468938 1.13212i
\(276\) 0 0
\(277\) −8.48544 3.51479i −0.509841 0.211183i 0.112907 0.993606i \(-0.463984\pi\)
−0.622748 + 0.782423i \(0.713984\pi\)
\(278\) −1.05362 + 16.8696i −0.0631917 + 1.01177i
\(279\) 0 0
\(280\) −2.31995 + 12.2527i −0.138643 + 0.732241i
\(281\) −12.5190 + 12.5190i −0.746823 + 0.746823i −0.973881 0.227058i \(-0.927089\pi\)
0.227058 + 0.973881i \(0.427089\pi\)
\(282\) 0 0
\(283\) −16.8466 6.97810i −1.00143 0.414805i −0.179107 0.983830i \(-0.557321\pi\)
−0.822321 + 0.569024i \(0.807321\pi\)
\(284\) 4.95340 + 0.621166i 0.293930 + 0.0368594i
\(285\) 0 0
\(286\) −11.5096 33.5669i −0.680579 1.98485i
\(287\) −7.54153 −0.445162
\(288\) 0 0
\(289\) −5.13305 −0.301944
\(290\) −13.8309 40.3366i −0.812177 2.36865i
\(291\) 0 0
\(292\) −0.409447 + 3.26508i −0.0239611 + 0.191074i
\(293\) −1.86190 0.771224i −0.108773 0.0450554i 0.327633 0.944805i \(-0.393749\pi\)
−0.436406 + 0.899750i \(0.643749\pi\)
\(294\) 0 0
\(295\) −19.7746 + 19.7746i −1.15132 + 1.15132i
\(296\) 8.51696 + 12.4955i 0.495038 + 0.726285i
\(297\) 0 0
\(298\) 0.570135 9.12852i 0.0330270 0.528801i
\(299\) −4.02177 1.66587i −0.232585 0.0963398i
\(300\) 0 0
\(301\) −5.10292 12.3195i −0.294127 0.710086i
\(302\) −9.49462 4.64599i −0.546354 0.267347i
\(303\) 0 0
\(304\) −1.99698 13.8502i −0.114534 0.794361i
\(305\) −6.23959 −0.357278
\(306\) 0 0
\(307\) −3.70099 + 1.53300i −0.211227 + 0.0874930i −0.485788 0.874077i \(-0.661467\pi\)
0.274561 + 0.961570i \(0.411467\pi\)
\(308\) 8.55186 15.0249i 0.487288 0.856121i
\(309\) 0 0
\(310\) 1.09226 17.4884i 0.0620362 0.993272i
\(311\) −9.17785 + 9.17785i −0.520428 + 0.520428i −0.917701 0.397273i \(-0.869957\pi\)
0.397273 + 0.917701i \(0.369957\pi\)
\(312\) 0 0
\(313\) −8.66154 8.66154i −0.489579 0.489579i 0.418594 0.908173i \(-0.362523\pi\)
−0.908173 + 0.418594i \(0.862523\pi\)
\(314\) 22.8899 20.1987i 1.29175 1.13988i
\(315\) 0 0
\(316\) 22.8619 17.7669i 1.28608 0.999469i
\(317\) 7.41379 + 17.8985i 0.416400 + 1.00528i 0.983382 + 0.181548i \(0.0581108\pi\)
−0.566982 + 0.823730i \(0.691889\pi\)
\(318\) 0 0
\(319\) 59.1159i 3.30986i
\(320\) −0.431378 23.3823i −0.0241148 1.30711i
\(321\) 0 0
\(322\) −0.687884 2.00616i −0.0383343 0.111799i
\(323\) −11.1339 + 4.61182i −0.619507 + 0.256608i
\(324\) 0 0
\(325\) −5.94030 + 14.3411i −0.329508 + 0.795503i
\(326\) 11.6345 + 13.1846i 0.644374 + 0.730226i
\(327\) 0 0
\(328\) 13.8451 2.88697i 0.764469 0.159406i
\(329\) −4.62500 4.62500i −0.254984 0.254984i
\(330\) 0 0
\(331\) −3.96293 + 9.56736i −0.217822 + 0.525870i −0.994585 0.103923i \(-0.966860\pi\)
0.776763 + 0.629793i \(0.216860\pi\)
\(332\) −19.4050 11.0450i −1.06499 0.606171i
\(333\) 0 0
\(334\) 24.2003 + 11.8419i 1.32418 + 0.647960i
\(335\) 27.1830i 1.48517i
\(336\) 0 0
\(337\) 7.50723i 0.408945i 0.978872 + 0.204472i \(0.0655479\pi\)
−0.978872 + 0.204472i \(0.934452\pi\)
\(338\) −3.83350 + 7.83420i −0.208515 + 0.426124i
\(339\) 0 0
\(340\) −19.4218 + 5.33227i −1.05330 + 0.289183i
\(341\) −9.29611 + 22.4428i −0.503413 + 1.21535i
\(342\) 0 0
\(343\) −12.5047 12.5047i −0.675190 0.675190i
\(344\) 14.0842 + 20.6634i 0.759371 + 1.11410i
\(345\) 0 0
\(346\) 1.70625 1.50565i 0.0917286 0.0809441i
\(347\) −1.18203 + 2.85368i −0.0634548 + 0.153194i −0.952426 0.304769i \(-0.901421\pi\)
0.888971 + 0.457963i \(0.151421\pi\)
\(348\) 0 0
\(349\) 3.41473 1.41443i 0.182786 0.0757126i −0.289413 0.957204i \(-0.593460\pi\)
0.472200 + 0.881492i \(0.343460\pi\)
\(350\) −7.15371 + 2.45291i −0.382382 + 0.131114i
\(351\) 0 0
\(352\) −9.94829 + 30.8571i −0.530245 + 1.64469i
\(353\) 6.81226i 0.362580i 0.983430 + 0.181290i \(0.0580273\pi\)
−0.983430 + 0.181290i \(0.941973\pi\)
\(354\) 0 0
\(355\) 2.79236 + 6.74136i 0.148203 + 0.357794i
\(356\) 2.81365 22.4370i 0.149123 1.18916i
\(357\) 0 0
\(358\) −0.461884 0.523423i −0.0244114 0.0276638i
\(359\) −5.31414 5.31414i −0.280469 0.280469i 0.552827 0.833296i \(-0.313549\pi\)
−0.833296 + 0.552827i \(0.813549\pi\)
\(360\) 0 0
\(361\) −4.78116 + 4.78116i −0.251640 + 0.251640i
\(362\) −30.9044 1.93018i −1.62430 0.101448i
\(363\) 0 0
\(364\) −12.7349 + 3.49637i −0.667489 + 0.183260i
\(365\) −4.44363 + 1.84061i −0.232590 + 0.0963420i
\(366\) 0 0
\(367\) 29.3775 1.53349 0.766745 0.641951i \(-0.221875\pi\)
0.766745 + 0.641951i \(0.221875\pi\)
\(368\) 2.03083 + 3.41968i 0.105864 + 0.178263i
\(369\) 0 0
\(370\) −9.71491 + 19.8535i −0.505054 + 1.03214i
\(371\) 0.816501 + 1.97121i 0.0423906 + 0.102340i
\(372\) 0 0
\(373\) 14.6798 + 6.08058i 0.760092 + 0.314840i 0.728852 0.684671i \(-0.240054\pi\)
0.0312402 + 0.999512i \(0.490054\pi\)
\(374\) 27.8672 + 1.74048i 1.44098 + 0.0899982i
\(375\) 0 0
\(376\) 10.2613 + 6.72031i 0.529186 + 0.346574i
\(377\) 31.9312 31.9312i 1.64454 1.64454i
\(378\) 0 0
\(379\) −1.25001 0.517769i −0.0642085 0.0265960i 0.350348 0.936620i \(-0.386063\pi\)
−0.414557 + 0.910024i \(0.636063\pi\)
\(380\) 16.1498 12.5507i 0.828469 0.643839i
\(381\) 0 0
\(382\) 31.1777 10.6904i 1.59519 0.546969i
\(383\) −35.2581 −1.80160 −0.900802 0.434230i \(-0.857020\pi\)
−0.900802 + 0.434230i \(0.857020\pi\)
\(384\) 0 0
\(385\) 25.2691 1.28783
\(386\) −36.2130 + 12.4170i −1.84319 + 0.632006i
\(387\) 0 0
\(388\) 20.2847 15.7641i 1.02980 0.800303i
\(389\) −3.34556 1.38578i −0.169627 0.0702616i 0.296254 0.955109i \(-0.404262\pi\)
−0.465881 + 0.884848i \(0.654262\pi\)
\(390\) 0 0
\(391\) 2.42201 2.42201i 0.122486 0.122486i
\(392\) 11.1807 + 7.32242i 0.564708 + 0.369838i
\(393\) 0 0
\(394\) −0.358264 0.0223759i −0.0180491 0.00112728i
\(395\) 39.0988 + 16.1953i 1.96728 + 0.814872i
\(396\) 0 0
\(397\) −2.21822 5.35526i −0.111329 0.268773i 0.858389 0.513000i \(-0.171466\pi\)
−0.969718 + 0.244227i \(0.921466\pi\)
\(398\) −2.52346 + 5.15698i −0.126490 + 0.258496i
\(399\) 0 0
\(400\) 12.1941 7.24168i 0.609707 0.362084i
\(401\) 5.97617 0.298436 0.149218 0.988804i \(-0.452324\pi\)
0.149218 + 0.988804i \(0.452324\pi\)
\(402\) 0 0
\(403\) 17.1437 7.10114i 0.853987 0.353733i
\(404\) 0.407166 0.111788i 0.0202573 0.00556164i
\(405\) 0 0
\(406\) 21.9577 + 1.37140i 1.08974 + 0.0680612i
\(407\) 21.6672 21.6672i 1.07401 1.07401i
\(408\) 0 0
\(409\) −5.91961 5.91961i −0.292706 0.292706i 0.545443 0.838148i \(-0.316362\pi\)
−0.838148 + 0.545443i \(0.816362\pi\)
\(410\) 13.6776 + 15.5000i 0.675490 + 0.765488i
\(411\) 0 0
\(412\) 2.65003 21.1323i 0.130557 1.04111i
\(413\) −5.52150 13.3301i −0.271695 0.655931i
\(414\) 0 0
\(415\) 32.6357i 1.60203i
\(416\) 22.0409 11.2938i 1.08064 0.553726i
\(417\) 0 0
\(418\) −26.8222 + 9.19696i −1.31191 + 0.449838i
\(419\) 30.7382 12.7322i 1.50166 0.622007i 0.527841 0.849343i \(-0.323002\pi\)
0.973816 + 0.227336i \(0.0730017\pi\)
\(420\) 0 0
\(421\) 7.98264 19.2718i 0.389050 0.939249i −0.601092 0.799180i \(-0.705267\pi\)
0.990142 0.140069i \(-0.0447326\pi\)
\(422\) 24.5582 21.6709i 1.19547 1.05492i
\(423\) 0 0
\(424\) −2.25357 3.30628i −0.109443 0.160567i
\(425\) −8.63660 8.63660i −0.418937 0.418937i
\(426\) 0 0
\(427\) 1.23194 2.97417i 0.0596179 0.143930i
\(428\) 13.4266 3.68627i 0.648997 0.178183i
\(429\) 0 0
\(430\) −16.0652 + 32.8312i −0.774735 + 1.58326i
\(431\) 29.2128i 1.40713i 0.710630 + 0.703565i \(0.248410\pi\)
−0.710630 + 0.703565i \(0.751590\pi\)
\(432\) 0 0
\(433\) 17.9410i 0.862190i 0.902306 + 0.431095i \(0.141873\pi\)
−0.902306 + 0.431095i \(0.858127\pi\)
\(434\) 8.12037 + 3.97353i 0.389790 + 0.190736i
\(435\) 0 0
\(436\) −22.2326 12.6544i −1.06475 0.606034i
\(437\) −1.33114 + 3.21366i −0.0636771 + 0.153730i
\(438\) 0 0
\(439\) −8.96708 8.96708i −0.427975 0.427975i 0.459963 0.887938i \(-0.347863\pi\)
−0.887938 + 0.459963i \(0.847863\pi\)
\(440\) −46.3903 + 9.67325i −2.21157 + 0.461154i
\(441\) 0 0
\(442\) −14.1122 15.9925i −0.671251 0.760684i
\(443\) −6.09257 + 14.7088i −0.289467 + 0.698835i −0.999988 0.00484090i \(-0.998459\pi\)
0.710522 + 0.703675i \(0.248459\pi\)
\(444\) 0 0
\(445\) 30.5358 12.6484i 1.44754 0.599589i
\(446\) −2.90241 8.46464i −0.137433 0.400812i
\(447\) 0 0
\(448\) 11.2306 + 4.41097i 0.530596 + 0.208399i
\(449\) 3.66413i 0.172921i 0.996255 + 0.0864604i \(0.0275556\pi\)
−0.996255 + 0.0864604i \(0.972444\pi\)
\(450\) 0 0
\(451\) −10.9670 26.4766i −0.516415 1.24674i
\(452\) 1.55324 1.20709i 0.0730583 0.0567767i
\(453\) 0 0
\(454\) 7.60829 6.71379i 0.357075 0.315094i
\(455\) −13.6490 13.6490i −0.639876 0.639876i
\(456\) 0 0
\(457\) −13.9728 + 13.9728i −0.653622 + 0.653622i −0.953863 0.300241i \(-0.902933\pi\)
0.300241 + 0.953863i \(0.402933\pi\)
\(458\) −0.591655 + 9.47309i −0.0276462 + 0.442648i
\(459\) 0 0
\(460\) −2.87564 + 5.05224i −0.134077 + 0.235562i
\(461\) −2.25638 + 0.934623i −0.105090 + 0.0435297i −0.434609 0.900619i \(-0.643113\pi\)
0.329519 + 0.944149i \(0.393113\pi\)
\(462\) 0 0
\(463\) 16.4302 0.763575 0.381788 0.924250i \(-0.375309\pi\)
0.381788 + 0.924250i \(0.375309\pi\)
\(464\) −40.8360 + 5.88791i −1.89576 + 0.273339i
\(465\) 0 0
\(466\) −8.49148 4.15513i −0.393360 0.192482i
\(467\) 8.14599 + 19.6662i 0.376951 + 0.910041i 0.992534 + 0.121969i \(0.0389208\pi\)
−0.615582 + 0.788072i \(0.711079\pi\)
\(468\) 0 0
\(469\) 12.9571 + 5.36700i 0.598303 + 0.247825i
\(470\) −1.11758 + 17.8938i −0.0515501 + 0.825377i
\(471\) 0 0
\(472\) 15.2395 + 22.3584i 0.701456 + 1.02913i
\(473\) 35.8304 35.8304i 1.64748 1.64748i
\(474\) 0 0
\(475\) 11.4595 + 4.74669i 0.525799 + 0.217793i
\(476\) 1.29295 10.3104i 0.0592622 0.472578i
\(477\) 0 0
\(478\) 2.64614 + 7.71724i 0.121032 + 0.352978i
\(479\) −4.35772 −0.199109 −0.0995545 0.995032i \(-0.531742\pi\)
−0.0995545 + 0.995032i \(0.531742\pi\)
\(480\) 0 0
\(481\) −23.4070 −1.06727
\(482\) −9.25098 26.9797i −0.421370 1.22889i
\(483\) 0 0
\(484\) 43.3562 + 5.43695i 1.97073 + 0.247134i
\(485\) 34.6914 + 14.3696i 1.57525 + 0.652491i
\(486\) 0 0
\(487\) 10.1865 10.1865i 0.461594 0.461594i −0.437584 0.899178i \(-0.644166\pi\)
0.899178 + 0.437584i \(0.144166\pi\)
\(488\) −1.12312 + 5.93174i −0.0508414 + 0.268517i
\(489\) 0 0
\(490\) −1.21771 + 19.4969i −0.0550105 + 0.880782i
\(491\) −28.0848 11.6331i −1.26745 0.524994i −0.355260 0.934768i \(-0.615608\pi\)
−0.912187 + 0.409774i \(0.865608\pi\)
\(492\) 0 0
\(493\) 13.5975 + 32.8273i 0.612402 + 1.47847i
\(494\) 19.4556 + 9.52019i 0.875349 + 0.428333i
\(495\) 0 0
\(496\) −16.4289 4.18626i −0.737679 0.187969i
\(497\) −3.76467 −0.168869
\(498\) 0 0
\(499\) −20.5327 + 8.50493i −0.919170 + 0.380733i −0.791560 0.611092i \(-0.790731\pi\)
−0.127610 + 0.991824i \(0.540731\pi\)
\(500\) −7.39009 4.20630i −0.330495 0.188111i
\(501\) 0 0
\(502\) −0.0665318 + 1.06525i −0.00296946 + 0.0475446i
\(503\) −6.66355 + 6.66355i −0.297113 + 0.297113i −0.839882 0.542769i \(-0.817376\pi\)
0.542769 + 0.839882i \(0.317376\pi\)
\(504\) 0 0
\(505\) 0.436393 + 0.436393i 0.0194192 + 0.0194192i
\(506\) 6.04284 5.33238i 0.268637 0.237053i
\(507\) 0 0
\(508\) 6.53841 + 8.41339i 0.290095 + 0.373284i
\(509\) −4.13590 9.98494i −0.183320 0.442575i 0.805327 0.592831i \(-0.201990\pi\)
−0.988647 + 0.150257i \(0.951990\pi\)
\(510\) 0 0
\(511\) 2.48152i 0.109776i
\(512\) −22.3063 3.79870i −0.985807 0.167881i
\(513\) 0 0
\(514\) −3.16301 9.22464i −0.139514 0.406882i
\(515\) 28.7601 11.9128i 1.26732 0.524942i
\(516\) 0 0
\(517\) 9.51161 22.9631i 0.418320 1.00991i
\(518\) −7.54531 8.55060i −0.331522 0.375692i
\(519\) 0 0
\(520\) 30.2825 + 19.8326i 1.32798 + 0.869717i
\(521\) 2.91587 + 2.91587i 0.127746 + 0.127746i 0.768089 0.640343i \(-0.221208\pi\)
−0.640343 + 0.768089i \(0.721208\pi\)
\(522\) 0 0
\(523\) 14.2159 34.3201i 0.621616 1.50071i −0.228189 0.973617i \(-0.573280\pi\)
0.849805 0.527097i \(-0.176720\pi\)
\(524\) −18.9564 + 33.3047i −0.828113 + 1.45492i
\(525\) 0 0
\(526\) −5.59724 2.73889i −0.244051 0.119421i
\(527\) 14.6008i 0.636023i
\(528\) 0 0
\(529\) 22.0113i 0.957015i
\(530\) 2.57055 5.25320i 0.111657 0.228185i
\(531\) 0 0
\(532\) 2.79383 + 10.1760i 0.121128 + 0.441186i
\(533\) −8.37748 + 20.2250i −0.362869 + 0.876043i
\(534\) 0 0
\(535\) 14.3903 + 14.3903i 0.622149 + 0.622149i
\(536\) −25.8418 4.89292i −1.11620 0.211342i
\(537\) 0 0
\(538\) −14.2420 + 12.5675i −0.614015 + 0.541825i
\(539\) 10.3638 25.0204i 0.446401 1.07771i
\(540\) 0 0
\(541\) −29.5435 + 12.2373i −1.27017 + 0.526123i −0.913017 0.407921i \(-0.866254\pi\)
−0.357157 + 0.934044i \(0.616254\pi\)
\(542\) 7.95467 2.72755i 0.341682 0.117158i
\(543\) 0 0
\(544\) 1.57327 + 19.4234i 0.0674533 + 0.832770i
\(545\) 37.3912i 1.60166i
\(546\) 0 0
\(547\) −11.8740 28.6664i −0.507696 1.22569i −0.945206 0.326474i \(-0.894140\pi\)
0.437510 0.899213i \(-0.355860\pi\)
\(548\) 28.2853 + 3.54703i 1.20829 + 0.151521i
\(549\) 0 0
\(550\) −19.0146 21.5480i −0.810787 0.918811i
\(551\) −25.5152 25.5152i −1.08698 1.08698i
\(552\) 0 0
\(553\) −15.4393 + 15.4393i −0.656546 + 0.656546i
\(554\) −12.9637 0.809665i −0.550775 0.0343994i
\(555\) 0 0
\(556\) 6.32860 + 23.0508i 0.268392 + 0.977570i
\(557\) 16.2393 6.72656i 0.688083 0.285013i −0.0111181 0.999938i \(-0.503539\pi\)
0.699201 + 0.714925i \(0.253539\pi\)
\(558\) 0 0
\(559\) −38.7074 −1.63715
\(560\) 2.51679 + 17.4553i 0.106354 + 0.737623i
\(561\) 0 0
\(562\) −11.0050 + 22.4899i −0.464216 + 0.948679i
\(563\) 15.7698 + 38.0718i 0.664620 + 1.60453i 0.790481 + 0.612486i \(0.209830\pi\)
−0.125862 + 0.992048i \(0.540170\pi\)
\(564\) 0 0
\(565\) 2.65638 + 1.10031i 0.111755 + 0.0462904i
\(566\) −25.7375 1.60747i −1.08183 0.0675672i
\(567\) 0 0
\(568\) 6.91137 1.44115i 0.289995 0.0604693i
\(569\) −11.0276 + 11.0276i −0.462302 + 0.462302i −0.899409 0.437107i \(-0.856003\pi\)
0.437107 + 0.899409i \(0.356003\pi\)
\(570\) 0 0
\(571\) −31.3409 12.9818i −1.31157 0.543272i −0.386231 0.922402i \(-0.626223\pi\)
−0.925343 + 0.379130i \(0.876223\pi\)
\(572\) −30.7942 39.6249i −1.28757 1.65680i
\(573\) 0 0
\(574\) −10.0887 + 3.45929i −0.421096 + 0.144388i
\(575\) −3.52541 −0.147020
\(576\) 0 0
\(577\) −2.28631 −0.0951802 −0.0475901 0.998867i \(-0.515154\pi\)
−0.0475901 + 0.998867i \(0.515154\pi\)
\(578\) −6.86677 + 2.35452i −0.285620 + 0.0979353i
\(579\) 0 0
\(580\) −37.0047 47.6164i −1.53654 1.97716i
\(581\) 15.5562 + 6.44359i 0.645380 + 0.267325i
\(582\) 0 0
\(583\) −5.73311 + 5.73311i −0.237441 + 0.237441i
\(584\) 0.949947 + 4.55569i 0.0393091 + 0.188516i
\(585\) 0 0
\(586\) −2.84453 0.177659i −0.117506 0.00733903i
\(587\) 5.89005 + 2.43974i 0.243108 + 0.100699i 0.500911 0.865499i \(-0.332998\pi\)
−0.257803 + 0.966198i \(0.582998\pi\)
\(588\) 0 0
\(589\) −5.67428 13.6989i −0.233805 0.564454i
\(590\) −17.3830 + 35.5242i −0.715648 + 1.46251i
\(591\) 0 0
\(592\) 17.1253 + 12.8092i 0.703845 + 0.526455i
\(593\) 10.9801 0.450897 0.225449 0.974255i \(-0.427615\pi\)
0.225449 + 0.974255i \(0.427615\pi\)
\(594\) 0 0
\(595\) 14.0321 5.81227i 0.575259 0.238280i
\(596\) −3.42454 12.4733i −0.140275 0.510925i
\(597\) 0 0
\(598\) −6.14429 0.383750i −0.251259 0.0156927i
\(599\) −3.54515 + 3.54515i −0.144851 + 0.144851i −0.775813 0.630962i \(-0.782660\pi\)
0.630962 + 0.775813i \(0.282660\pi\)
\(600\) 0 0
\(601\) 0.844578 + 0.844578i 0.0344511 + 0.0344511i 0.724122 0.689671i \(-0.242245\pi\)
−0.689671 + 0.724122i \(0.742245\pi\)
\(602\) −12.4774 14.1398i −0.508542 0.576297i
\(603\) 0 0
\(604\) −14.8326 1.86004i −0.603531 0.0756839i
\(605\) 24.4410 + 59.0059i 0.993669 + 2.39893i
\(606\) 0 0
\(607\) 17.9859i 0.730024i −0.931003 0.365012i \(-0.881065\pi\)
0.931003 0.365012i \(-0.118935\pi\)
\(608\) −9.02453 17.6121i −0.365993 0.714266i
\(609\) 0 0
\(610\) −8.34706 + 2.86210i −0.337963 + 0.115883i
\(611\) −17.5411 + 7.26575i −0.709636 + 0.293941i
\(612\) 0 0
\(613\) −6.72419 + 16.2336i −0.271588 + 0.655671i −0.999552 0.0299448i \(-0.990467\pi\)
0.727964 + 0.685615i \(0.240467\pi\)
\(614\) −4.24784 + 3.74843i −0.171429 + 0.151274i
\(615\) 0 0
\(616\) 4.54842 24.0224i 0.183261 0.967888i
\(617\) 8.70935 + 8.70935i 0.350625 + 0.350625i 0.860342 0.509717i \(-0.170250\pi\)
−0.509717 + 0.860342i \(0.670250\pi\)
\(618\) 0 0
\(619\) −3.38639 + 8.17546i −0.136110 + 0.328600i −0.977208 0.212284i \(-0.931910\pi\)
0.841098 + 0.540883i \(0.181910\pi\)
\(620\) −6.56071 23.8962i −0.263485 0.959694i
\(621\) 0 0
\(622\) −8.06786 + 16.4876i −0.323492 + 0.661093i
\(623\) 17.0525i 0.683195i
\(624\) 0 0
\(625\) 30.1567i 1.20627i
\(626\) −15.5601 7.61400i −0.621906 0.304317i
\(627\) 0 0
\(628\) 21.3559 37.5205i 0.852195 1.49723i
\(629\) 7.04814 17.0157i 0.281028 0.678461i
\(630\) 0 0
\(631\) 2.69060 + 2.69060i 0.107111 + 0.107111i 0.758631 0.651520i \(-0.225868\pi\)
−0.651520 + 0.758631i \(0.725868\pi\)
\(632\) 22.4340 34.2546i 0.892375 1.36257i
\(633\) 0 0
\(634\) 18.1279 + 20.5431i 0.719949 + 0.815871i
\(635\) −5.96002 + 14.3888i −0.236516 + 0.571000i
\(636\) 0 0
\(637\) −19.1127 + 7.91673i −0.757272 + 0.313672i
\(638\) 27.1164 + 79.0827i 1.07355 + 3.13092i
\(639\) 0 0
\(640\) −11.3025 31.0820i −0.446771 1.22862i
\(641\) 37.2166i 1.46997i −0.678084 0.734984i \(-0.737189\pi\)
0.678084 0.734984i \(-0.262811\pi\)
\(642\) 0 0
\(643\) −11.0037 26.5652i −0.433942 1.04763i −0.978005 0.208583i \(-0.933115\pi\)
0.544063 0.839044i \(-0.316885\pi\)
\(644\) −1.84044 2.36822i −0.0725237 0.0933209i
\(645\) 0 0
\(646\) −12.7790 + 11.2766i −0.502784 + 0.443672i
\(647\) 30.0988 + 30.0988i 1.18331 + 1.18331i 0.978882 + 0.204426i \(0.0655327\pi\)
0.204426 + 0.978882i \(0.434467\pi\)
\(648\) 0 0
\(649\) 38.7695 38.7695i 1.52184 1.52184i
\(650\) −1.36841 + 21.9098i −0.0536733 + 0.859372i
\(651\) 0 0
\(652\) 21.6119 + 12.3011i 0.846386 + 0.481746i
\(653\) −4.00245 + 1.65787i −0.156628 + 0.0648775i −0.459620 0.888116i \(-0.652014\pi\)
0.302992 + 0.952993i \(0.402014\pi\)
\(654\) 0 0
\(655\) −56.0125 −2.18859
\(656\) 17.1972 10.2128i 0.671436 0.398743i
\(657\) 0 0
\(658\) −8.30861 4.06564i −0.323903 0.158495i
\(659\) −2.32569 5.61472i −0.0905962 0.218719i 0.872086 0.489352i \(-0.162767\pi\)
−0.962682 + 0.270634i \(0.912767\pi\)
\(660\) 0 0
\(661\) 37.0965 + 15.3659i 1.44288 + 0.597662i 0.960496 0.278295i \(-0.0897692\pi\)
0.482389 + 0.875957i \(0.339769\pi\)
\(662\) −0.912900 + 14.6166i −0.0354809 + 0.568090i
\(663\) 0 0
\(664\) −31.0255 5.87441i −1.20402 0.227971i
\(665\) −10.9065 + 10.9065i −0.422935 + 0.422935i
\(666\) 0 0
\(667\) 9.47519 + 3.92475i 0.366881 + 0.151967i
\(668\) 37.8060 + 4.74095i 1.46276 + 0.183433i
\(669\) 0 0
\(670\) −12.4688 36.3643i −0.481712 1.40487i
\(671\) 12.2332 0.472256
\(672\) 0 0
\(673\) −13.6208 −0.525043 −0.262521 0.964926i \(-0.584554\pi\)
−0.262521 + 0.964926i \(0.584554\pi\)
\(674\) 3.44356 + 10.0429i 0.132641 + 0.386836i
\(675\) 0 0
\(676\) −1.53475 + 12.2387i −0.0590290 + 0.470718i
\(677\) −11.5314 4.77647i −0.443189 0.183575i 0.149918 0.988698i \(-0.452099\pi\)
−0.593107 + 0.805124i \(0.702099\pi\)
\(678\) 0 0
\(679\) −13.6989 + 13.6989i −0.525715 + 0.525715i
\(680\) −23.5358 + 16.0421i −0.902556 + 0.615185i
\(681\) 0 0
\(682\) −2.14145 + 34.2872i −0.0820004 + 1.31292i
\(683\) −37.0003 15.3260i −1.41578 0.586435i −0.461982 0.886889i \(-0.652862\pi\)
−0.953796 + 0.300454i \(0.902862\pi\)
\(684\) 0 0
\(685\) 15.9452 + 38.4950i 0.609233 + 1.47082i
\(686\) −22.4641 10.9924i −0.857685 0.419690i
\(687\) 0 0
\(688\) 28.3196 + 21.1822i 1.07967 + 0.807563i
\(689\) 6.19344 0.235951
\(690\) 0 0
\(691\) 6.40367 2.65249i 0.243607 0.100905i −0.257539 0.966268i \(-0.582912\pi\)
0.501147 + 0.865362i \(0.332912\pi\)
\(692\) 1.59191 2.79685i 0.0605154 0.106320i
\(693\) 0 0
\(694\) −0.272293 + 4.35973i −0.0103361 + 0.165493i
\(695\) −24.7054 + 24.7054i −0.937129 + 0.937129i
\(696\) 0 0
\(697\) −12.1800 12.1800i −0.461352 0.461352i
\(698\) 3.91929 3.45850i 0.148347 0.130906i
\(699\) 0 0
\(700\) −8.44478 + 6.56280i −0.319183 + 0.248051i
\(701\) −7.95095 19.1953i −0.300303 0.724996i −0.999945 0.0105021i \(-0.996657\pi\)
0.699642 0.714494i \(-0.253343\pi\)
\(702\) 0 0
\(703\) 18.7037i 0.705424i
\(704\) 0.845748 + 45.8426i 0.0318753 + 1.72776i
\(705\) 0 0
\(706\) 3.12478 + 9.11315i 0.117603 + 0.342978i
\(707\) −0.294173 + 0.121850i −0.0110635 + 0.00458266i
\(708\) 0 0
\(709\) 0.602133 1.45368i 0.0226136 0.0545940i −0.912169 0.409813i \(-0.865594\pi\)
0.934783 + 0.355219i \(0.115594\pi\)
\(710\) 6.82776 + 7.73745i 0.256241 + 0.290381i
\(711\) 0 0
\(712\) −6.52786 31.3059i −0.244642 1.17324i
\(713\) 2.97999 + 2.97999i 0.111602 + 0.111602i
\(714\) 0 0
\(715\) 28.0701 67.7673i 1.04976 2.53435i
\(716\) −0.857983 0.488347i −0.0320643 0.0182504i
\(717\) 0 0
\(718\) −9.54662 4.67144i −0.356277 0.174337i
\(719\) 36.1660i 1.34877i −0.738382 0.674383i \(-0.764410\pi\)
0.738382 0.674383i \(-0.235590\pi\)
\(720\) 0 0
\(721\) 16.0609i 0.598139i
\(722\) −4.20292 + 8.58915i −0.156416 + 0.319655i
\(723\) 0 0
\(724\) −42.2279 + 11.5937i −1.56939 + 0.430876i
\(725\) 13.9952 33.7874i 0.519768 1.25483i
\(726\) 0 0
\(727\) −3.48345 3.48345i −0.129194 0.129194i 0.639553 0.768747i \(-0.279119\pi\)
−0.768747 + 0.639553i \(0.779119\pi\)
\(728\) −15.4324 + 10.5188i −0.571963 + 0.389852i
\(729\) 0 0
\(730\) −5.10021 + 4.50058i −0.188767 + 0.166574i
\(731\) 11.6553 28.1383i 0.431086 1.04073i
\(732\) 0 0
\(733\) −9.32567 + 3.86282i −0.344452 + 0.142677i −0.548201 0.836347i \(-0.684687\pi\)
0.203750 + 0.979023i \(0.434687\pi\)
\(734\) 39.2999 13.4754i 1.45059 0.497387i
\(735\) 0 0
\(736\) 4.28536 + 3.64316i 0.157960 + 0.134289i
\(737\) 53.2942i 1.96312i
\(738\) 0 0
\(739\) 18.2859 + 44.1460i 0.672657 + 1.62394i 0.777078 + 0.629404i \(0.216701\pi\)
−0.104421 + 0.994533i \(0.533299\pi\)
\(740\) −3.88940 + 31.0154i −0.142977 + 1.14015i
\(741\) 0 0
\(742\) 1.99647 + 2.26247i 0.0732928 + 0.0830579i
\(743\) −26.3660 26.3660i −0.967273 0.967273i 0.0322079 0.999481i \(-0.489746\pi\)
−0.999481 + 0.0322079i \(0.989746\pi\)
\(744\) 0 0
\(745\) 13.3686 13.3686i 0.489789 0.489789i
\(746\) 22.4272 + 1.40072i 0.821118 + 0.0512841i
\(747\) 0 0
\(748\) 38.0779 10.4543i 1.39226 0.382247i
\(749\) −9.70055 + 4.01810i −0.354450 + 0.146818i
\(750\) 0 0
\(751\) 31.9193 1.16475 0.582377 0.812919i \(-0.302123\pi\)
0.582377 + 0.812919i \(0.302123\pi\)
\(752\) 16.8097 + 4.28330i 0.612988 + 0.156196i
\(753\) 0 0
\(754\) 28.0694 57.3631i 1.02223 2.08904i
\(755\) −8.36155 20.1866i −0.304308 0.734664i
\(756\) 0 0
\(757\) 25.8156 + 10.6932i 0.938284 + 0.388650i 0.798815 0.601577i \(-0.205461\pi\)
0.139469 + 0.990226i \(0.455461\pi\)
\(758\) −1.90970 0.119273i −0.0693636 0.00433220i
\(759\) 0 0
\(760\) 15.8476 24.1977i 0.574851 0.877745i
\(761\) −14.4436 + 14.4436i −0.523579 + 0.523579i −0.918650 0.395072i \(-0.870720\pi\)
0.395072 + 0.918650i \(0.370720\pi\)
\(762\) 0 0
\(763\) 17.8229 + 7.38250i 0.645234 + 0.267265i
\(764\) 36.8045 28.6024i 1.33154 1.03480i
\(765\) 0 0
\(766\) −47.1668 + 16.1729i −1.70420 + 0.584349i
\(767\) −41.8824 −1.51229
\(768\) 0 0
\(769\) 21.6737 0.781574 0.390787 0.920481i \(-0.372203\pi\)
0.390787 + 0.920481i \(0.372203\pi\)
\(770\) 33.8040 11.5909i 1.21821 0.417708i
\(771\) 0 0
\(772\) −42.7486 + 33.2217i −1.53855 + 1.19568i
\(773\) 5.45257 + 2.25853i 0.196115 + 0.0812336i 0.478580 0.878044i \(-0.341152\pi\)
−0.282464 + 0.959278i \(0.591152\pi\)
\(774\) 0 0
\(775\) 10.6263 10.6263i 0.381708 0.381708i
\(776\) 19.9051 30.3932i 0.714550 1.09105i
\(777\) 0 0
\(778\) −5.11120 0.319227i −0.183245 0.0114448i
\(779\) 16.1611 + 6.69416i 0.579033 + 0.239843i
\(780\) 0 0
\(781\) −5.47463 13.2169i −0.195898 0.472939i
\(782\) 2.12909 4.35104i 0.0761361 0.155593i
\(783\) 0 0
\(784\) 18.3158 + 4.66707i 0.654135 + 0.166681i
\(785\) 63.1027 2.25223
\(786\) 0 0
\(787\) −38.9288 + 16.1249i −1.38766 + 0.574789i −0.946519 0.322647i \(-0.895427\pi\)
−0.441144 + 0.897436i \(0.645427\pi\)
\(788\) −0.489535 + 0.134402i −0.0174389 + 0.00478787i
\(789\) 0 0
\(790\) 59.7335 + 3.73074i 2.12522 + 0.132734i
\(791\) −1.04895 + 1.04895i −0.0372964 + 0.0372964i
\(792\) 0 0
\(793\) −6.60770 6.60770i −0.234646 0.234646i
\(794\) −5.42390 6.14654i −0.192487 0.218133i
\(795\) 0 0
\(796\) −1.01028 + 8.05630i −0.0358083 + 0.285548i
\(797\) 13.4105 + 32.3759i 0.475025 + 1.14681i 0.961915 + 0.273349i \(0.0881312\pi\)
−0.486890 + 0.873463i \(0.661869\pi\)
\(798\) 0 0
\(799\) 14.9393i 0.528515i
\(800\) 12.9911 15.2811i 0.459303 0.540267i
\(801\) 0 0
\(802\) 7.99467 2.74126i 0.282301 0.0967974i
\(803\) 8.71205 3.60865i 0.307442 0.127346i
\(804\) 0 0
\(805\) 1.67764 4.05017i 0.0591289 0.142750i
\(806\) 19.6768 17.3634i 0.693085 0.611599i
\(807\) 0 0
\(808\) 0.493412 0.336311i 0.0173582 0.0118314i
\(809\) −23.3959 23.3959i −0.822557 0.822557i 0.163917 0.986474i \(-0.447587\pi\)
−0.986474 + 0.163917i \(0.947587\pi\)
\(810\) 0 0
\(811\) −14.5916 + 35.2272i −0.512380 + 1.23699i 0.430115 + 0.902774i \(0.358473\pi\)
−0.942495 + 0.334221i \(0.891527\pi\)
\(812\) 30.0031 8.23736i 1.05290 0.289075i
\(813\) 0 0
\(814\) 19.0468 38.9243i 0.667589 1.36429i
\(815\) 36.3473i 1.27319i
\(816\) 0 0
\(817\) 30.9297i 1.08209i
\(818\) −10.6343 5.20368i −0.371820 0.181942i
\(819\) 0 0
\(820\) 25.4072 + 14.4613i 0.887257 + 0.505009i
\(821\) 6.11371 14.7598i 0.213370 0.515120i −0.780567 0.625072i \(-0.785070\pi\)
0.993937 + 0.109952i \(0.0350696\pi\)
\(822\) 0 0
\(823\) 17.5536 + 17.5536i 0.611879 + 0.611879i 0.943435 0.331557i \(-0.107574\pi\)
−0.331557 + 0.943435i \(0.607574\pi\)
\(824\) −6.14825 29.4854i −0.214185 1.02717i
\(825\) 0 0
\(826\) −13.5009 15.2997i −0.469757 0.532345i
\(827\) −4.15220 + 10.0243i −0.144386 + 0.348579i −0.979484 0.201522i \(-0.935411\pi\)
0.835098 + 0.550102i \(0.185411\pi\)
\(828\) 0 0
\(829\) 3.68500 1.52638i 0.127985 0.0530132i −0.317772 0.948167i \(-0.602935\pi\)
0.445757 + 0.895154i \(0.352935\pi\)
\(830\) −14.9700 43.6587i −0.519616 1.51542i
\(831\) 0 0
\(832\) 24.3049 25.2186i 0.842621 0.874297i
\(833\) 16.2778i 0.563992i
\(834\) 0 0
\(835\) 21.3123 + 51.4524i 0.737541 + 1.78058i
\(836\) −31.6629 + 24.6066i −1.09508 + 0.851037i
\(837\) 0 0
\(838\) 35.2800 31.1321i 1.21873 1.07544i
\(839\) 4.96619 + 4.96619i 0.171452 + 0.171452i 0.787617 0.616165i \(-0.211315\pi\)
−0.616165 + 0.787617i \(0.711315\pi\)
\(840\) 0 0
\(841\) −54.7231 + 54.7231i −1.88700 + 1.88700i
\(842\) 1.83888 29.4426i 0.0633719 1.01466i
\(843\) 0 0
\(844\) 22.9124 40.2551i 0.788679 1.38564i
\(845\) −16.6563 + 6.89927i −0.572995 + 0.237342i
\(846\) 0 0
\(847\) −32.9514 −1.13223
\(848\) −4.53132 3.38929i −0.155606 0.116389i
\(849\) 0 0
\(850\) −15.5153 7.59208i −0.532170 0.260406i
\(851\) −2.03435 4.91137i −0.0697368 0.168359i
\(852\) 0 0
\(853\) −7.27599 3.01381i −0.249125 0.103191i 0.254627 0.967039i \(-0.418047\pi\)
−0.503752 + 0.863848i \(0.668047\pi\)
\(854\) 0.283790 4.54381i 0.00971110 0.155486i
\(855\) 0 0
\(856\) 16.2706 11.0901i 0.556117 0.379051i
\(857\) −36.1746 + 36.1746i −1.23570 + 1.23570i −0.273961 + 0.961741i \(0.588334\pi\)
−0.961741 + 0.273961i \(0.911666\pi\)
\(858\) 0 0
\(859\) −28.2133 11.6863i −0.962627 0.398733i −0.154664 0.987967i \(-0.549430\pi\)
−0.807962 + 0.589234i \(0.799430\pi\)
\(860\) −6.43177 + 51.2892i −0.219322 + 1.74895i
\(861\) 0 0
\(862\) 13.3999 + 39.0796i 0.456402 + 1.33106i
\(863\) 6.56021 0.223312 0.111656 0.993747i \(-0.464384\pi\)
0.111656 + 0.993747i \(0.464384\pi\)
\(864\) 0 0
\(865\) 4.70379 0.159934
\(866\) 8.22953 + 24.0007i 0.279651 + 0.815578i
\(867\) 0 0
\(868\) 12.6857 + 1.59082i 0.430582 + 0.0539958i
\(869\) −76.6560 31.7520i −2.60038 1.07711i
\(870\) 0 0
\(871\) 28.7867 28.7867i 0.975399 0.975399i
\(872\) −35.5463 6.73039i −1.20375 0.227920i
\(873\) 0 0
\(874\) −0.306642 + 4.90969i −0.0103723 + 0.166073i
\(875\) 5.92433 + 2.45394i 0.200279 + 0.0829582i
\(876\) 0 0
\(877\) −9.62481 23.2364i −0.325007 0.784636i −0.998948 0.0458511i \(-0.985400\pi\)
0.673941 0.738785i \(-0.264600\pi\)
\(878\) −16.1090 7.88259i −0.543651 0.266024i
\(879\) 0 0
\(880\) −57.6219 + 34.2197i −1.94243 + 1.15354i
\(881\) −36.6081 −1.23336 −0.616679 0.787215i \(-0.711522\pi\)
−0.616679 + 0.787215i \(0.711522\pi\)
\(882\) 0 0
\(883\) 1.40699 0.582794i 0.0473489 0.0196126i −0.358883 0.933382i \(-0.616842\pi\)
0.406232 + 0.913770i \(0.366842\pi\)
\(884\) −26.2145 14.9208i −0.881688 0.501840i
\(885\) 0 0
\(886\) −1.40348 + 22.4714i −0.0471510 + 0.754942i
\(887\) 32.4795 32.4795i 1.09056 1.09056i 0.0950860 0.995469i \(-0.469687\pi\)
0.995469 0.0950860i \(-0.0303126\pi\)
\(888\) 0 0
\(889\) −5.68182 5.68182i −0.190562 0.190562i
\(890\) 35.0477 30.9272i 1.17480 1.03668i
\(891\) 0 0
\(892\) −7.76545 9.99230i −0.260006 0.334567i
\(893\) 5.80581 + 14.0165i 0.194284 + 0.469044i
\(894\) 0 0
\(895\) 1.44297i 0.0482333i
\(896\) 17.0471 + 0.749338i 0.569505 + 0.0250336i
\(897\) 0 0
\(898\) 1.68073 + 4.90171i 0.0560867 + 0.163572i
\(899\) −40.3901 + 16.7301i −1.34708 + 0.557980i
\(900\) 0 0
\(901\) −1.86492 + 4.50232i −0.0621296 + 0.149994i
\(902\) −26.8160 30.3888i −0.892874 1.01184i
\(903\) 0 0
\(904\) 1.52417 2.32726i 0.0506931 0.0774036i
\(905\) −45.2591 45.2591i −1.50446 1.50446i
\(906\) 0 0
\(907\) 10.6402 25.6878i 0.353303 0.852950i −0.642905 0.765946i \(-0.722271\pi\)
0.996208 0.0870037i \(-0.0277292\pi\)
\(908\) 7.09844 12.4713i 0.235570 0.413876i
\(909\) 0 0
\(910\) −24.5199 11.9983i −0.812826 0.397739i
\(911\) 9.64671i 0.319610i −0.987149 0.159805i \(-0.948914\pi\)
0.987149 0.159805i \(-0.0510865\pi\)
\(912\) 0 0
\(913\) 63.9847i 2.11758i
\(914\) −12.2830 + 25.1016i −0.406284 + 0.830288i
\(915\) 0 0
\(916\) 3.55381 + 12.9441i 0.117421 + 0.427685i
\(917\) 11.0591 26.6990i 0.365203 0.881678i
\(918\) 0 0
\(919\) 36.1191 + 36.1191i 1.19146 + 1.19146i 0.976657 + 0.214803i \(0.0689110\pi\)
0.214803 + 0.976657i \(0.431089\pi\)
\(920\) −1.52945 + 8.07773i −0.0504244 + 0.266315i
\(921\) 0 0
\(922\) −2.58978 + 2.28530i −0.0852898 + 0.0752623i
\(923\) −4.18197 + 10.0962i −0.137651 + 0.332320i
\(924\) 0 0
\(925\) −17.5133 + 7.25426i −0.575835 + 0.238519i
\(926\) 21.9796 7.53651i 0.722295 0.247665i
\(927\) 0 0
\(928\) −51.9278 + 26.6080i −1.70461 + 0.873451i
\(929\) 16.6303i 0.545622i −0.962068 0.272811i \(-0.912047\pi\)
0.962068 0.272811i \(-0.0879534\pi\)
\(930\) 0 0
\(931\) 6.32599 + 15.2723i 0.207326 + 0.500529i
\(932\) −13.2655 1.66352i −0.434526 0.0544903i
\(933\) 0 0
\(934\) 19.9182 + 22.5720i 0.651744 + 0.738578i
\(935\) 40.8112 + 40.8112i 1.33467 + 1.33467i
\(936\) 0 0
\(937\) 39.4807 39.4807i 1.28978 1.28978i 0.354860 0.934920i \(-0.384529\pi\)
0.934920 0.354860i \(-0.115471\pi\)
\(938\) 19.7953 + 1.23634i 0.646339 + 0.0403680i
\(939\) 0 0
\(940\) 6.71280 + 24.4501i 0.218947 + 0.797475i
\(941\) 38.4855 15.9412i 1.25459 0.519669i 0.346347 0.938107i \(-0.387422\pi\)
0.908246 + 0.418437i \(0.137422\pi\)
\(942\) 0 0
\(943\) −4.97182 −0.161905
\(944\) 30.6426 + 22.9197i 0.997330 + 0.745973i
\(945\) 0 0
\(946\) 31.4970 64.3678i 1.02406 2.09278i
\(947\) −1.88812 4.55832i −0.0613556 0.148125i 0.890228 0.455515i \(-0.150545\pi\)
−0.951584 + 0.307389i \(0.900545\pi\)
\(948\) 0 0
\(949\) −6.65498 2.75658i −0.216030 0.0894825i
\(950\) 17.5074 + 1.09345i 0.568014 + 0.0354761i
\(951\) 0 0
\(952\) −2.99974 14.3859i −0.0972220 0.466251i
\(953\) −3.89115 + 3.89115i −0.126047 + 0.126047i −0.767316 0.641269i \(-0.778408\pi\)
0.641269 + 0.767316i \(0.278408\pi\)
\(954\) 0 0
\(955\) 62.9438 + 26.0722i 2.03681 + 0.843676i
\(956\) 7.07978 + 9.11001i 0.228976 + 0.294639i
\(957\) 0 0
\(958\) −5.82957 + 1.99888i −0.188345 + 0.0645809i
\(959\) −21.4973 −0.694184
\(960\) 0 0
\(961\) 13.0354 0.420498
\(962\) −31.3129 + 10.7368i −1.00957 + 0.346167i
\(963\) 0 0
\(964\) −24.7511 31.8489i −0.797180 1.02578i
\(965\) −73.1094 30.2829i −2.35348 0.974842i
\(966\) 0 0
\(967\) 11.3033 11.3033i 0.363488 0.363488i −0.501607 0.865095i \(-0.667258\pi\)
0.865095 + 0.501607i \(0.167258\pi\)
\(968\) 60.4939 12.6141i 1.94435 0.405433i
\(969\) 0 0
\(970\) 53.0000 + 3.31019i 1.70173 + 0.106284i
\(971\) 19.3675 + 8.02226i 0.621531 + 0.257447i 0.671150 0.741322i \(-0.265801\pi\)
−0.0496188 + 0.998768i \(0.515801\pi\)
\(972\) 0 0
\(973\) −6.89828 16.6539i −0.221149 0.533900i
\(974\) 8.95451 18.2996i 0.286921 0.586356i
\(975\) 0 0
\(976\) 1.21842 + 8.45040i 0.0390006 + 0.270491i
\(977\) 2.98023 0.0953461 0.0476730 0.998863i \(-0.484819\pi\)
0.0476730 + 0.998863i \(0.484819\pi\)
\(978\) 0 0
\(979\) −59.8676 + 24.7980i −1.91338 + 0.792547i
\(980\) 7.31423 + 26.6407i 0.233645 + 0.851007i
\(981\) 0 0
\(982\) −42.9067 2.67980i −1.36921 0.0855157i
\(983\) 35.5614 35.5614i 1.13423 1.13423i 0.144767 0.989466i \(-0.453757\pi\)
0.989466 0.144767i \(-0.0462432\pi\)
\(984\) 0 0
\(985\) −0.524675 0.524675i −0.0167175 0.0167175i
\(986\) 33.2481 + 37.6779i 1.05883 + 1.19991i
\(987\) 0 0
\(988\) 30.3938 + 3.81144i 0.966955 + 0.121258i
\(989\) −3.36415 8.12177i −0.106974 0.258257i
\(990\) 0 0
\(991\) 7.45023i 0.236664i −0.992974 0.118332i \(-0.962245\pi\)
0.992974 0.118332i \(-0.0377548\pi\)
\(992\) −23.8981 + 1.93571i −0.758765 + 0.0614590i
\(993\) 0 0
\(994\) −5.03622 + 1.72685i −0.159739 + 0.0547724i
\(995\) −10.9643 + 4.54156i −0.347591 + 0.143977i
\(996\) 0 0
\(997\) 0.482816 1.16562i 0.0152909 0.0369156i −0.916050 0.401065i \(-0.868640\pi\)
0.931341 + 0.364149i \(0.118640\pi\)
\(998\) −23.5666 + 20.7959i −0.745987 + 0.658282i
\(999\) 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 288.2.w.b.107.7 yes 32
3.2 odd 2 288.2.w.a.107.2 yes 32
4.3 odd 2 1152.2.w.a.719.7 32
12.11 even 2 1152.2.w.b.719.2 32
32.3 odd 8 288.2.w.a.35.2 32
32.29 even 8 1152.2.w.b.431.2 32
96.29 odd 8 1152.2.w.a.431.7 32
96.35 even 8 inner 288.2.w.b.35.7 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.w.a.35.2 32 32.3 odd 8
288.2.w.a.107.2 yes 32 3.2 odd 2
288.2.w.b.35.7 yes 32 96.35 even 8 inner
288.2.w.b.107.7 yes 32 1.1 even 1 trivial
1152.2.w.a.431.7 32 96.29 odd 8
1152.2.w.a.719.7 32 4.3 odd 2
1152.2.w.b.431.2 32 32.29 even 8
1152.2.w.b.719.2 32 12.11 even 2