Properties

Label 297.2.n.b.91.5
Level $297$
Weight $2$
Character 297.91
Analytic conductor $2.372$
Analytic rank $0$
Dimension $72$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [297,2,Mod(37,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.n (of order \(15\), degree \(8\), 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: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 91.5
Character \(\chi\) \(=\) 297.91
Dual form 297.2.n.b.235.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.448089 + 0.199502i) q^{2} +(-1.17728 - 1.30750i) q^{4} +(-1.56050 + 0.694778i) q^{5} +(-3.33599 + 0.709088i) q^{7} +(-0.569818 - 1.75372i) q^{8} -0.837851 q^{10} +(-3.25533 + 0.634703i) q^{11} +(0.417897 + 3.97602i) q^{13} +(-1.63629 - 0.347803i) q^{14} +(-0.273277 + 2.60005i) q^{16} +(-2.67346 - 1.94238i) q^{17} +(-1.36513 - 4.20144i) q^{19} +(2.74556 + 1.22240i) q^{20} +(-1.58530 - 0.365040i) q^{22} +(3.74601 - 6.48827i) q^{23} +(-1.39322 + 1.54733i) q^{25} +(-0.605969 + 1.86498i) q^{26} +(4.85453 + 3.52702i) q^{28} +(1.65433 - 0.351639i) q^{29} +(0.407506 + 3.87716i) q^{31} +(-2.48514 + 4.30439i) q^{32} +(-0.810437 - 1.40372i) q^{34} +(4.71315 - 3.42431i) q^{35} +(0.947300 - 2.91549i) q^{37} +(0.226496 - 2.15496i) q^{38} +(2.10765 + 2.34078i) q^{40} +(0.382333 + 0.0812674i) q^{41} +(-4.80634 - 8.32483i) q^{43} +(4.66230 + 3.50912i) q^{44} +(2.97296 - 2.15999i) q^{46} +(0.722834 - 0.802788i) q^{47} +(4.23124 - 1.88387i) q^{49} +(-0.932979 + 0.415389i) q^{50} +(4.70667 - 5.22729i) q^{52} +(-10.1643 + 7.38480i) q^{53} +(4.63895 - 3.25218i) q^{55} +(3.14445 + 5.44635i) q^{56} +(0.811439 + 0.172477i) q^{58} +(2.44670 + 2.71734i) q^{59} +(0.402767 - 3.83207i) q^{61} +(-0.590902 + 1.81861i) q^{62} +(2.25785 - 1.64043i) q^{64} +(-3.41458 - 5.91423i) q^{65} +(-1.55060 + 2.68572i) q^{67} +(0.607741 + 5.78227i) q^{68} +(2.79506 - 0.594109i) q^{70} +(5.67699 + 4.12458i) q^{71} +(-4.64842 + 14.3064i) q^{73} +(1.00612 - 1.11741i) q^{74} +(-3.88624 + 6.73117i) q^{76} +(10.4097 - 4.42568i) q^{77} +(-3.65339 - 1.62659i) q^{79} +(-1.38001 - 4.24724i) q^{80} +(0.155106 + 0.112691i) q^{82} +(-0.0130625 + 0.124281i) q^{83} +(5.52145 + 1.17362i) q^{85} +(-0.492848 - 4.68913i) q^{86} +(2.96804 + 5.34727i) q^{88} +7.93327 q^{89} +(-4.21345 - 12.9677i) q^{91} +(-12.8935 + 2.74060i) q^{92} +(0.484051 - 0.215514i) q^{94} +(5.04935 + 5.60787i) q^{95} +(0.313492 + 0.139576i) q^{97} +2.27180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.448089 + 0.199502i 0.316846 + 0.141069i 0.558997 0.829169i \(-0.311186\pi\)
−0.242151 + 0.970239i \(0.577853\pi\)
\(3\) 0 0
\(4\) −1.17728 1.30750i −0.588639 0.653750i
\(5\) −1.56050 + 0.694778i −0.697876 + 0.310714i −0.724835 0.688922i \(-0.758084\pi\)
0.0269596 + 0.999637i \(0.491417\pi\)
\(6\) 0 0
\(7\) −3.33599 + 0.709088i −1.26089 + 0.268010i −0.789409 0.613868i \(-0.789613\pi\)
−0.471478 + 0.881878i \(0.656280\pi\)
\(8\) −0.569818 1.75372i −0.201461 0.620034i
\(9\) 0 0
\(10\) −0.837851 −0.264952
\(11\) −3.25533 + 0.634703i −0.981518 + 0.191370i
\(12\) 0 0
\(13\) 0.417897 + 3.97602i 0.115904 + 1.10275i 0.885635 + 0.464382i \(0.153724\pi\)
−0.769731 + 0.638368i \(0.779610\pi\)
\(14\) −1.63629 0.347803i −0.437316 0.0929543i
\(15\) 0 0
\(16\) −0.273277 + 2.60005i −0.0683191 + 0.650013i
\(17\) −2.67346 1.94238i −0.648409 0.471097i 0.214320 0.976763i \(-0.431246\pi\)
−0.862729 + 0.505667i \(0.831246\pi\)
\(18\) 0 0
\(19\) −1.36513 4.20144i −0.313182 0.963875i −0.976496 0.215534i \(-0.930851\pi\)
0.663314 0.748341i \(-0.269149\pi\)
\(20\) 2.74556 + 1.22240i 0.613927 + 0.273338i
\(21\) 0 0
\(22\) −1.58530 0.365040i −0.337987 0.0778269i
\(23\) 3.74601 6.48827i 0.781096 1.35290i −0.150208 0.988654i \(-0.547994\pi\)
0.931304 0.364244i \(-0.118672\pi\)
\(24\) 0 0
\(25\) −1.39322 + 1.54733i −0.278644 + 0.309465i
\(26\) −0.605969 + 1.86498i −0.118840 + 0.365753i
\(27\) 0 0
\(28\) 4.85453 + 3.52702i 0.917420 + 0.666544i
\(29\) 1.65433 0.351639i 0.307201 0.0652977i −0.0517316 0.998661i \(-0.516474\pi\)
0.358933 + 0.933363i \(0.383141\pi\)
\(30\) 0 0
\(31\) 0.407506 + 3.87716i 0.0731902 + 0.696358i 0.968177 + 0.250266i \(0.0805181\pi\)
−0.894987 + 0.446092i \(0.852815\pi\)
\(32\) −2.48514 + 4.30439i −0.439315 + 0.760915i
\(33\) 0 0
\(34\) −0.810437 1.40372i −0.138989 0.240736i
\(35\) 4.71315 3.42431i 0.796668 0.578813i
\(36\) 0 0
\(37\) 0.947300 2.91549i 0.155735 0.479304i −0.842499 0.538697i \(-0.818917\pi\)
0.998235 + 0.0593935i \(0.0189167\pi\)
\(38\) 0.226496 2.15496i 0.0367424 0.349581i
\(39\) 0 0
\(40\) 2.10765 + 2.34078i 0.333248 + 0.370110i
\(41\) 0.382333 + 0.0812674i 0.0597104 + 0.0126918i 0.237670 0.971346i \(-0.423616\pi\)
−0.177960 + 0.984038i \(0.556950\pi\)
\(42\) 0 0
\(43\) −4.80634 8.32483i −0.732960 1.26952i −0.955613 0.294626i \(-0.904805\pi\)
0.222652 0.974898i \(-0.428529\pi\)
\(44\) 4.66230 + 3.50912i 0.702869 + 0.529020i
\(45\) 0 0
\(46\) 2.97296 2.15999i 0.438340 0.318472i
\(47\) 0.722834 0.802788i 0.105436 0.117099i −0.688117 0.725600i \(-0.741562\pi\)
0.793553 + 0.608501i \(0.208229\pi\)
\(48\) 0 0
\(49\) 4.23124 1.88387i 0.604462 0.269124i
\(50\) −0.932979 + 0.415389i −0.131943 + 0.0587449i
\(51\) 0 0
\(52\) 4.70667 5.22729i 0.652698 0.724894i
\(53\) −10.1643 + 7.38480i −1.39618 + 1.01438i −0.401020 + 0.916069i \(0.631344\pi\)
−0.995156 + 0.0983117i \(0.968656\pi\)
\(54\) 0 0
\(55\) 4.63895 3.25218i 0.625516 0.438524i
\(56\) 3.14445 + 5.44635i 0.420195 + 0.727799i
\(57\) 0 0
\(58\) 0.811439 + 0.172477i 0.106547 + 0.0226473i
\(59\) 2.44670 + 2.71734i 0.318534 + 0.353768i 0.881054 0.473016i \(-0.156835\pi\)
−0.562520 + 0.826784i \(0.690168\pi\)
\(60\) 0 0
\(61\) 0.402767 3.83207i 0.0515690 0.490646i −0.938005 0.346621i \(-0.887329\pi\)
0.989574 0.144025i \(-0.0460045\pi\)
\(62\) −0.590902 + 1.81861i −0.0750446 + 0.230964i
\(63\) 0 0
\(64\) 2.25785 1.64043i 0.282232 0.205053i
\(65\) −3.41458 5.91423i −0.423527 0.733570i
\(66\) 0 0
\(67\) −1.55060 + 2.68572i −0.189436 + 0.328113i −0.945062 0.326890i \(-0.893999\pi\)
0.755626 + 0.655003i \(0.227333\pi\)
\(68\) 0.607741 + 5.78227i 0.0736994 + 0.701203i
\(69\) 0 0
\(70\) 2.79506 0.594109i 0.334074 0.0710097i
\(71\) 5.67699 + 4.12458i 0.673735 + 0.489497i 0.871273 0.490798i \(-0.163295\pi\)
−0.197538 + 0.980295i \(0.563295\pi\)
\(72\) 0 0
\(73\) −4.64842 + 14.3064i −0.544057 + 1.67443i 0.179165 + 0.983819i \(0.442660\pi\)
−0.723222 + 0.690615i \(0.757340\pi\)
\(74\) 1.00612 1.11741i 0.116959 0.129896i
\(75\) 0 0
\(76\) −3.88624 + 6.73117i −0.445783 + 0.772118i
\(77\) 10.4097 4.42568i 1.18629 0.504353i
\(78\) 0 0
\(79\) −3.65339 1.62659i −0.411038 0.183006i 0.190791 0.981631i \(-0.438895\pi\)
−0.601829 + 0.798625i \(0.705561\pi\)
\(80\) −1.38001 4.24724i −0.154290 0.474856i
\(81\) 0 0
\(82\) 0.155106 + 0.112691i 0.0171286 + 0.0124447i
\(83\) −0.0130625 + 0.124281i −0.00143379 + 0.0136416i −0.995215 0.0977052i \(-0.968850\pi\)
0.993782 + 0.111347i \(0.0355164\pi\)
\(84\) 0 0
\(85\) 5.52145 + 1.17362i 0.598885 + 0.127297i
\(86\) −0.492848 4.68913i −0.0531451 0.505642i
\(87\) 0 0
\(88\) 2.96804 + 5.34727i 0.316394 + 0.570021i
\(89\) 7.93327 0.840925 0.420462 0.907310i \(-0.361868\pi\)
0.420462 + 0.907310i \(0.361868\pi\)
\(90\) 0 0
\(91\) −4.21345 12.9677i −0.441690 1.35938i
\(92\) −12.8935 + 2.74060i −1.34424 + 0.285727i
\(93\) 0 0
\(94\) 0.484051 0.215514i 0.0499261 0.0222285i
\(95\) 5.04935 + 5.60787i 0.518052 + 0.575355i
\(96\) 0 0
\(97\) 0.313492 + 0.139576i 0.0318303 + 0.0141718i 0.422590 0.906321i \(-0.361121\pi\)
−0.390760 + 0.920493i \(0.627788\pi\)
\(98\) 2.27180 0.229487
\(99\) 0 0
\(100\) 3.66333 0.366333
\(101\) −6.50041 2.89417i −0.646815 0.287981i 0.0569891 0.998375i \(-0.481850\pi\)
−0.703804 + 0.710394i \(0.748517\pi\)
\(102\) 0 0
\(103\) −1.10693 1.22938i −0.109069 0.121134i 0.686138 0.727472i \(-0.259305\pi\)
−0.795207 + 0.606338i \(0.792638\pi\)
\(104\) 6.73471 2.99848i 0.660392 0.294026i
\(105\) 0 0
\(106\) −6.02779 + 1.28125i −0.585471 + 0.124446i
\(107\) −1.02187 3.14498i −0.0987876 0.304037i 0.889435 0.457062i \(-0.151098\pi\)
−0.988222 + 0.153025i \(0.951098\pi\)
\(108\) 0 0
\(109\) −5.50709 −0.527484 −0.263742 0.964593i \(-0.584957\pi\)
−0.263742 + 0.964593i \(0.584957\pi\)
\(110\) 2.72748 0.531787i 0.260055 0.0507039i
\(111\) 0 0
\(112\) −0.932016 8.86754i −0.0880672 0.837904i
\(113\) −16.0506 3.41167i −1.50992 0.320943i −0.622761 0.782412i \(-0.713989\pi\)
−0.887156 + 0.461469i \(0.847323\pi\)
\(114\) 0 0
\(115\) −1.33772 + 12.7276i −0.124743 + 1.18685i
\(116\) −2.40738 1.74906i −0.223519 0.162396i
\(117\) 0 0
\(118\) 0.554226 + 1.70573i 0.0510206 + 0.157025i
\(119\) 10.2960 + 4.58406i 0.943829 + 0.420220i
\(120\) 0 0
\(121\) 10.1943 4.13233i 0.926755 0.375667i
\(122\) 0.944980 1.63675i 0.0855545 0.148185i
\(123\) 0 0
\(124\) 4.58964 5.09731i 0.412162 0.457752i
\(125\) 3.73834 11.5054i 0.334368 1.02908i
\(126\) 0 0
\(127\) −8.73327 6.34509i −0.774952 0.563036i 0.128508 0.991709i \(-0.458981\pi\)
−0.903460 + 0.428673i \(0.858981\pi\)
\(128\) 11.0623 2.35137i 0.977780 0.207833i
\(129\) 0 0
\(130\) −0.350135 3.33131i −0.0307089 0.292175i
\(131\) −10.5778 + 18.3213i −0.924189 + 1.60074i −0.131329 + 0.991339i \(0.541925\pi\)
−0.792860 + 0.609404i \(0.791409\pi\)
\(132\) 0 0
\(133\) 7.53325 + 13.0480i 0.653216 + 1.13140i
\(134\) −1.23061 + 0.894092i −0.106309 + 0.0772378i
\(135\) 0 0
\(136\) −1.88301 + 5.79530i −0.161467 + 0.496943i
\(137\) 0.334546 3.18299i 0.0285822 0.271941i −0.970892 0.239518i \(-0.923011\pi\)
0.999474 0.0324237i \(-0.0103226\pi\)
\(138\) 0 0
\(139\) −10.0327 11.1425i −0.850963 0.945090i 0.148073 0.988976i \(-0.452693\pi\)
−0.999037 + 0.0438860i \(0.986026\pi\)
\(140\) −10.0260 2.13109i −0.847350 0.180110i
\(141\) 0 0
\(142\) 1.72094 + 2.98075i 0.144418 + 0.250139i
\(143\) −3.88399 12.6780i −0.324795 1.06019i
\(144\) 0 0
\(145\) −2.33727 + 1.69812i −0.194099 + 0.141021i
\(146\) −4.93705 + 5.48315i −0.408593 + 0.453789i
\(147\) 0 0
\(148\) −4.92724 + 2.19375i −0.405017 + 0.180325i
\(149\) −3.70089 + 1.64774i −0.303188 + 0.134988i −0.552692 0.833386i \(-0.686399\pi\)
0.249503 + 0.968374i \(0.419733\pi\)
\(150\) 0 0
\(151\) −5.21519 + 5.79206i −0.424406 + 0.471351i −0.916988 0.398915i \(-0.869387\pi\)
0.492581 + 0.870266i \(0.336053\pi\)
\(152\) −6.59027 + 4.78811i −0.534541 + 0.388367i
\(153\) 0 0
\(154\) 5.54740 + 0.0936570i 0.447022 + 0.00754709i
\(155\) −3.32968 5.76717i −0.267446 0.463230i
\(156\) 0 0
\(157\) −0.302396 0.0642763i −0.0241339 0.00512981i 0.195829 0.980638i \(-0.437260\pi\)
−0.219963 + 0.975508i \(0.570594\pi\)
\(158\) −1.31253 1.45772i −0.104419 0.115970i
\(159\) 0 0
\(160\) 0.887458 8.44360i 0.0701597 0.667525i
\(161\) −7.89590 + 24.3011i −0.622284 + 1.91519i
\(162\) 0 0
\(163\) −8.89442 + 6.46217i −0.696665 + 0.506157i −0.878844 0.477109i \(-0.841685\pi\)
0.182179 + 0.983265i \(0.441685\pi\)
\(164\) −0.343855 0.595575i −0.0268506 0.0465066i
\(165\) 0 0
\(166\) −0.0306475 + 0.0530830i −0.00237871 + 0.00412004i
\(167\) −1.83697 17.4776i −0.142149 1.35246i −0.800313 0.599582i \(-0.795333\pi\)
0.658164 0.752874i \(-0.271333\pi\)
\(168\) 0 0
\(169\) −2.91820 + 0.620282i −0.224477 + 0.0477140i
\(170\) 2.23996 + 1.62742i 0.171797 + 0.124818i
\(171\) 0 0
\(172\) −5.22631 + 16.0849i −0.398503 + 1.22646i
\(173\) −8.27429 + 9.18953i −0.629083 + 0.698667i −0.970461 0.241259i \(-0.922440\pi\)
0.341378 + 0.939926i \(0.389106\pi\)
\(174\) 0 0
\(175\) 3.55058 6.14978i 0.268398 0.464880i
\(176\) −0.760658 8.63747i −0.0573368 0.651074i
\(177\) 0 0
\(178\) 3.55481 + 1.58270i 0.266444 + 0.118628i
\(179\) −6.76200 20.8113i −0.505416 1.55551i −0.800071 0.599906i \(-0.795205\pi\)
0.294655 0.955604i \(-0.404795\pi\)
\(180\) 0 0
\(181\) 3.54364 + 2.57460i 0.263396 + 0.191369i 0.711643 0.702541i \(-0.247951\pi\)
−0.448247 + 0.893910i \(0.647951\pi\)
\(182\) 0.699075 6.65125i 0.0518189 0.493024i
\(183\) 0 0
\(184\) −13.5132 2.87231i −0.996203 0.211750i
\(185\) 0.547360 + 5.20778i 0.0402427 + 0.382884i
\(186\) 0 0
\(187\) 9.93581 + 4.62623i 0.726579 + 0.338304i
\(188\) −1.90062 −0.138617
\(189\) 0 0
\(190\) 1.14377 + 3.52018i 0.0829781 + 0.255380i
\(191\) 12.2413 2.60196i 0.885746 0.188271i 0.257493 0.966280i \(-0.417104\pi\)
0.628253 + 0.778009i \(0.283770\pi\)
\(192\) 0 0
\(193\) −11.4794 + 5.11094i −0.826302 + 0.367893i −0.775916 0.630837i \(-0.782712\pi\)
−0.0503860 + 0.998730i \(0.516045\pi\)
\(194\) 0.112627 + 0.125084i 0.00808611 + 0.00898054i
\(195\) 0 0
\(196\) −7.44450 3.31451i −0.531750 0.236750i
\(197\) 10.3453 0.737075 0.368538 0.929613i \(-0.379859\pi\)
0.368538 + 0.929613i \(0.379859\pi\)
\(198\) 0 0
\(199\) 26.4773 1.87693 0.938464 0.345376i \(-0.112249\pi\)
0.938464 + 0.345376i \(0.112249\pi\)
\(200\) 3.50746 + 1.56162i 0.248015 + 0.110423i
\(201\) 0 0
\(202\) −2.33537 2.59369i −0.164316 0.182491i
\(203\) −5.26949 + 2.34613i −0.369846 + 0.164666i
\(204\) 0 0
\(205\) −0.653093 + 0.138819i −0.0456140 + 0.00969555i
\(206\) −0.250742 0.771705i −0.0174700 0.0537672i
\(207\) 0 0
\(208\) −10.4521 −0.724721
\(209\) 7.11061 + 12.8106i 0.491851 + 0.886127i
\(210\) 0 0
\(211\) 0.761375 + 7.24400i 0.0524152 + 0.498698i 0.988964 + 0.148159i \(0.0473347\pi\)
−0.936548 + 0.350538i \(0.885999\pi\)
\(212\) 21.6219 + 4.59587i 1.48500 + 0.315646i
\(213\) 0 0
\(214\) 0.169543 1.61310i 0.0115897 0.110269i
\(215\) 13.2842 + 9.65153i 0.905974 + 0.658229i
\(216\) 0 0
\(217\) −4.10868 12.6452i −0.278916 0.858414i
\(218\) −2.46767 1.09868i −0.167131 0.0744117i
\(219\) 0 0
\(220\) −9.71357 2.23670i −0.654889 0.150799i
\(221\) 6.60572 11.4414i 0.444349 0.769635i
\(222\) 0 0
\(223\) 15.7313 17.4714i 1.05345 1.16997i 0.0684035 0.997658i \(-0.478209\pi\)
0.985042 0.172312i \(-0.0551239\pi\)
\(224\) 5.23822 16.1216i 0.349993 1.07717i
\(225\) 0 0
\(226\) −6.51148 4.73086i −0.433137 0.314692i
\(227\) −11.6617 + 2.47876i −0.774012 + 0.164521i −0.577952 0.816071i \(-0.696148\pi\)
−0.196060 + 0.980592i \(0.562815\pi\)
\(228\) 0 0
\(229\) −0.319603 3.04082i −0.0211200 0.200943i 0.978874 0.204465i \(-0.0655455\pi\)
−0.999994 + 0.00352213i \(0.998879\pi\)
\(230\) −3.13859 + 5.43620i −0.206953 + 0.358453i
\(231\) 0 0
\(232\) −1.55934 2.70086i −0.102376 0.177320i
\(233\) −19.8463 + 14.4192i −1.30017 + 0.944632i −0.999957 0.00923938i \(-0.997059\pi\)
−0.300217 + 0.953871i \(0.597059\pi\)
\(234\) 0 0
\(235\) −0.570221 + 1.75496i −0.0371971 + 0.114481i
\(236\) 0.672471 6.39814i 0.0437741 0.416483i
\(237\) 0 0
\(238\) 3.69897 + 4.10813i 0.239769 + 0.266290i
\(239\) −6.79874 1.44512i −0.439774 0.0934768i −0.0172968 0.999850i \(-0.505506\pi\)
−0.422477 + 0.906374i \(0.638839\pi\)
\(240\) 0 0
\(241\) 3.88529 + 6.72952i 0.250274 + 0.433487i 0.963601 0.267344i \(-0.0861461\pi\)
−0.713327 + 0.700831i \(0.752813\pi\)
\(242\) 5.39236 + 0.182131i 0.346634 + 0.0117078i
\(243\) 0 0
\(244\) −5.48460 + 3.98480i −0.351116 + 0.255100i
\(245\) −5.29396 + 5.87954i −0.338219 + 0.375630i
\(246\) 0 0
\(247\) 16.1345 7.18355i 1.02661 0.457078i
\(248\) 6.56725 2.92393i 0.417021 0.185670i
\(249\) 0 0
\(250\) 3.97047 4.40965i 0.251114 0.278891i
\(251\) 0.264684 0.192304i 0.0167067 0.0121381i −0.579401 0.815043i \(-0.696713\pi\)
0.596107 + 0.802905i \(0.296713\pi\)
\(252\) 0 0
\(253\) −8.07634 + 23.4990i −0.507755 + 1.47737i
\(254\) −2.64742 4.58547i −0.166114 0.287718i
\(255\) 0 0
\(256\) −0.0337447 0.00717266i −0.00210904 0.000448291i
\(257\) 9.18661 + 10.2028i 0.573045 + 0.636431i 0.958090 0.286467i \(-0.0924809\pi\)
−0.385045 + 0.922898i \(0.625814\pi\)
\(258\) 0 0
\(259\) −1.09285 + 10.3978i −0.0679064 + 0.646087i
\(260\) −3.71294 + 11.4273i −0.230267 + 0.708689i
\(261\) 0 0
\(262\) −8.39495 + 6.09928i −0.518641 + 0.376815i
\(263\) −8.42709 14.5961i −0.519637 0.900037i −0.999739 0.0228249i \(-0.992734\pi\)
0.480103 0.877212i \(-0.340599\pi\)
\(264\) 0 0
\(265\) 10.7306 18.5859i 0.659174 1.14172i
\(266\) 0.772468 + 7.34954i 0.0473631 + 0.450629i
\(267\) 0 0
\(268\) 5.33707 1.13443i 0.326013 0.0692963i
\(269\) 10.0297 + 7.28700i 0.611522 + 0.444296i 0.849950 0.526864i \(-0.176632\pi\)
−0.238428 + 0.971160i \(0.576632\pi\)
\(270\) 0 0
\(271\) 5.95460 18.3264i 0.361716 1.11325i −0.590296 0.807187i \(-0.700989\pi\)
0.952012 0.306061i \(-0.0990112\pi\)
\(272\) 5.78089 6.42032i 0.350518 0.389289i
\(273\) 0 0
\(274\) 0.784919 1.35952i 0.0474187 0.0821316i
\(275\) 3.55329 5.92133i 0.214271 0.357070i
\(276\) 0 0
\(277\) 9.45618 + 4.21016i 0.568167 + 0.252964i 0.670654 0.741770i \(-0.266013\pi\)
−0.102487 + 0.994734i \(0.532680\pi\)
\(278\) −2.27260 6.99435i −0.136302 0.419493i
\(279\) 0 0
\(280\) −8.69092 6.31432i −0.519382 0.377353i
\(281\) −1.71801 + 16.3458i −0.102488 + 0.975106i 0.815570 + 0.578659i \(0.196424\pi\)
−0.918057 + 0.396447i \(0.870243\pi\)
\(282\) 0 0
\(283\) 1.23731 + 0.262999i 0.0735505 + 0.0156336i 0.244540 0.969639i \(-0.421363\pi\)
−0.170989 + 0.985273i \(0.554696\pi\)
\(284\) −1.29052 12.2785i −0.0765781 0.728592i
\(285\) 0 0
\(286\) 0.788917 6.45573i 0.0466497 0.381736i
\(287\) −1.33309 −0.0786896
\(288\) 0 0
\(289\) −1.87876 5.78222i −0.110515 0.340130i
\(290\) −1.38608 + 0.294621i −0.0813935 + 0.0173007i
\(291\) 0 0
\(292\) 24.1781 10.7648i 1.41492 0.629961i
\(293\) 16.1176 + 17.9004i 0.941602 + 1.04575i 0.998876 + 0.0473960i \(0.0150923\pi\)
−0.0572746 + 0.998358i \(0.518241\pi\)
\(294\) 0 0
\(295\) −5.70603 2.54049i −0.332218 0.147913i
\(296\) −5.65274 −0.328559
\(297\) 0 0
\(298\) −1.98705 −0.115107
\(299\) 27.3630 + 12.1828i 1.58244 + 0.704548i
\(300\) 0 0
\(301\) 21.9370 + 24.3635i 1.26443 + 1.40429i
\(302\) −3.49240 + 1.55491i −0.200965 + 0.0894753i
\(303\) 0 0
\(304\) 11.2970 2.40125i 0.647928 0.137721i
\(305\) 2.03392 + 6.25977i 0.116462 + 0.358433i
\(306\) 0 0
\(307\) 16.2949 0.930001 0.465001 0.885310i \(-0.346054\pi\)
0.465001 + 0.885310i \(0.346054\pi\)
\(308\) −18.0417 8.40042i −1.02802 0.478658i
\(309\) 0 0
\(310\) −0.341429 3.24848i −0.0193919 0.184501i
\(311\) 20.9042 + 4.44333i 1.18537 + 0.251958i 0.758083 0.652158i \(-0.226136\pi\)
0.427287 + 0.904116i \(0.359469\pi\)
\(312\) 0 0
\(313\) −0.325724 + 3.09905i −0.0184110 + 0.175169i −0.999863 0.0165379i \(-0.994736\pi\)
0.981452 + 0.191707i \(0.0614023\pi\)
\(314\) −0.122677 0.0891301i −0.00692307 0.00502990i
\(315\) 0 0
\(316\) 2.17428 + 6.69176i 0.122313 + 0.376441i
\(317\) 16.6858 + 7.42898i 0.937166 + 0.417253i 0.817739 0.575590i \(-0.195227\pi\)
0.119428 + 0.992843i \(0.461894\pi\)
\(318\) 0 0
\(319\) −5.16220 + 2.19471i −0.289028 + 0.122880i
\(320\) −2.38364 + 4.12859i −0.133250 + 0.230795i
\(321\) 0 0
\(322\) −8.38617 + 9.31379i −0.467343 + 0.519037i
\(323\) −4.51117 + 13.8840i −0.251008 + 0.772524i
\(324\) 0 0
\(325\) −6.73442 4.89284i −0.373558 0.271406i
\(326\) −5.27470 + 1.12117i −0.292139 + 0.0620960i
\(327\) 0 0
\(328\) −0.0753401 0.716813i −0.00415996 0.0395794i
\(329\) −1.84212 + 3.19065i −0.101560 + 0.175906i
\(330\) 0 0
\(331\) −1.88308 3.26159i −0.103503 0.179273i 0.809622 0.586951i \(-0.199672\pi\)
−0.913126 + 0.407678i \(0.866339\pi\)
\(332\) 0.177876 0.129235i 0.00976222 0.00709267i
\(333\) 0 0
\(334\) 2.66369 8.19799i 0.145751 0.448574i
\(335\) 0.553729 5.26838i 0.0302534 0.287842i
\(336\) 0 0
\(337\) 3.99215 + 4.43373i 0.217466 + 0.241521i 0.842001 0.539477i \(-0.181378\pi\)
−0.624534 + 0.780997i \(0.714711\pi\)
\(338\) −1.43136 0.304245i −0.0778556 0.0165487i
\(339\) 0 0
\(340\) −4.96577 8.60097i −0.269307 0.466453i
\(341\) −3.78741 12.3628i −0.205100 0.669482i
\(342\) 0 0
\(343\) 6.53464 4.74769i 0.352837 0.256351i
\(344\) −11.8607 + 13.1726i −0.639485 + 0.710220i
\(345\) 0 0
\(346\) −5.54095 + 2.46699i −0.297883 + 0.132626i
\(347\) −22.2442 + 9.90376i −1.19413 + 0.531662i −0.904911 0.425600i \(-0.860063\pi\)
−0.289221 + 0.957262i \(0.593396\pi\)
\(348\) 0 0
\(349\) 11.2024 12.4416i 0.599652 0.665981i −0.364539 0.931188i \(-0.618773\pi\)
0.964192 + 0.265207i \(0.0854402\pi\)
\(350\) 2.81787 2.04730i 0.150621 0.109433i
\(351\) 0 0
\(352\) 5.35793 15.5895i 0.285579 0.830924i
\(353\) −4.01566 6.95533i −0.213732 0.370195i 0.739148 0.673544i \(-0.235229\pi\)
−0.952880 + 0.303349i \(0.901895\pi\)
\(354\) 0 0
\(355\) −11.7246 2.49214i −0.622277 0.132269i
\(356\) −9.33967 10.3728i −0.495001 0.549755i
\(357\) 0 0
\(358\) 1.12192 10.6743i 0.0592952 0.564156i
\(359\) 8.90742 27.4142i 0.470116 1.44687i −0.382317 0.924031i \(-0.624874\pi\)
0.852433 0.522836i \(-0.175126\pi\)
\(360\) 0 0
\(361\) −0.417162 + 0.303086i −0.0219559 + 0.0159519i
\(362\) 1.07422 + 1.86061i 0.0564600 + 0.0977916i
\(363\) 0 0
\(364\) −11.9948 + 20.7756i −0.628700 + 1.08894i
\(365\) −2.68591 25.5547i −0.140587 1.33759i
\(366\) 0 0
\(367\) −21.8551 + 4.64545i −1.14083 + 0.242491i −0.739313 0.673362i \(-0.764850\pi\)
−0.401515 + 0.915852i \(0.631516\pi\)
\(368\) 15.8462 + 11.5129i 0.826038 + 0.600152i
\(369\) 0 0
\(370\) −0.793696 + 2.44275i −0.0412623 + 0.126992i
\(371\) 28.6716 31.8431i 1.48856 1.65321i
\(372\) 0 0
\(373\) −3.53936 + 6.13036i −0.183261 + 0.317418i −0.942989 0.332823i \(-0.891999\pi\)
0.759728 + 0.650241i \(0.225332\pi\)
\(374\) 3.52918 + 4.05517i 0.182490 + 0.209688i
\(375\) 0 0
\(376\) −1.81975 0.810205i −0.0938465 0.0417831i
\(377\) 2.08946 + 6.43070i 0.107613 + 0.331198i
\(378\) 0 0
\(379\) 19.6964 + 14.3103i 1.01174 + 0.735070i 0.964573 0.263818i \(-0.0849817\pi\)
0.0471638 + 0.998887i \(0.484982\pi\)
\(380\) 1.38780 13.2040i 0.0711927 0.677353i
\(381\) 0 0
\(382\) 6.00426 + 1.27625i 0.307205 + 0.0652984i
\(383\) −1.84366 17.5413i −0.0942067 0.896317i −0.934925 0.354845i \(-0.884534\pi\)
0.840719 0.541472i \(-0.182133\pi\)
\(384\) 0 0
\(385\) −13.1694 + 14.1387i −0.671176 + 0.720574i
\(386\) −6.16341 −0.313709
\(387\) 0 0
\(388\) −0.186572 0.574210i −0.00947177 0.0291511i
\(389\) −17.4922 + 3.71808i −0.886890 + 0.188514i −0.628763 0.777597i \(-0.716439\pi\)
−0.258127 + 0.966111i \(0.583105\pi\)
\(390\) 0 0
\(391\) −22.6175 + 10.0700i −1.14382 + 0.509259i
\(392\) −5.71481 6.34694i −0.288642 0.320569i
\(393\) 0 0
\(394\) 4.63563 + 2.06392i 0.233540 + 0.103979i
\(395\) 6.83122 0.343716
\(396\) 0 0
\(397\) −21.9395 −1.10111 −0.550556 0.834798i \(-0.685584\pi\)
−0.550556 + 0.834798i \(0.685584\pi\)
\(398\) 11.8642 + 5.28228i 0.594698 + 0.264777i
\(399\) 0 0
\(400\) −3.64239 4.04529i −0.182120 0.202264i
\(401\) −4.94005 + 2.19945i −0.246694 + 0.109835i −0.526359 0.850262i \(-0.676443\pi\)
0.279665 + 0.960098i \(0.409777\pi\)
\(402\) 0 0
\(403\) −15.2454 + 3.24051i −0.759426 + 0.161421i
\(404\) 3.86867 + 11.9065i 0.192473 + 0.592372i
\(405\) 0 0
\(406\) −2.82926 −0.140414
\(407\) −1.23330 + 10.0921i −0.0611324 + 0.500248i
\(408\) 0 0
\(409\) −2.46898 23.4907i −0.122083 1.16154i −0.868369 0.495918i \(-0.834832\pi\)
0.746286 0.665625i \(-0.231835\pi\)
\(410\) −0.320338 0.0680899i −0.0158204 0.00336272i
\(411\) 0 0
\(412\) −0.304238 + 2.89464i −0.0149888 + 0.142608i
\(413\) −10.0890 7.33011i −0.496449 0.360691i
\(414\) 0 0
\(415\) −0.0659639 0.203016i −0.00323804 0.00996567i
\(416\) −18.1529 8.08218i −0.890017 0.396261i
\(417\) 0 0
\(418\) 0.630444 + 7.15886i 0.0308360 + 0.350151i
\(419\) −9.06566 + 15.7022i −0.442886 + 0.767102i −0.997902 0.0647380i \(-0.979379\pi\)
0.555016 + 0.831840i \(0.312712\pi\)
\(420\) 0 0
\(421\) −8.57303 + 9.52132i −0.417824 + 0.464041i −0.914908 0.403662i \(-0.867737\pi\)
0.497084 + 0.867702i \(0.334404\pi\)
\(422\) −1.10403 + 3.39785i −0.0537432 + 0.165405i
\(423\) 0 0
\(424\) 18.7427 + 13.6174i 0.910226 + 0.661318i
\(425\) 6.73020 1.43055i 0.326463 0.0693918i
\(426\) 0 0
\(427\) 1.37364 + 13.0694i 0.0664753 + 0.632470i
\(428\) −2.90904 + 5.03861i −0.140614 + 0.243551i
\(429\) 0 0
\(430\) 4.02700 + 6.97496i 0.194199 + 0.336362i
\(431\) −5.32265 + 3.86713i −0.256383 + 0.186273i −0.708551 0.705660i \(-0.750651\pi\)
0.452168 + 0.891933i \(0.350651\pi\)
\(432\) 0 0
\(433\) 4.32555 13.3127i 0.207873 0.639767i −0.791710 0.610897i \(-0.790809\pi\)
0.999583 0.0288700i \(-0.00919089\pi\)
\(434\) 0.681693 6.48587i 0.0327223 0.311332i
\(435\) 0 0
\(436\) 6.48339 + 7.20053i 0.310498 + 0.344843i
\(437\) −32.3738 6.88127i −1.54865 0.329176i
\(438\) 0 0
\(439\) −12.5891 21.8050i −0.600846 1.04070i −0.992693 0.120665i \(-0.961497\pi\)
0.391848 0.920030i \(-0.371836\pi\)
\(440\) −8.34678 6.28227i −0.397917 0.299495i
\(441\) 0 0
\(442\) 5.24254 3.80893i 0.249362 0.181172i
\(443\) −17.9477 + 19.9330i −0.852723 + 0.947045i −0.999110 0.0421828i \(-0.986569\pi\)
0.146387 + 0.989227i \(0.453235\pi\)
\(444\) 0 0
\(445\) −12.3798 + 5.51186i −0.586861 + 0.261287i
\(446\) 10.5346 4.69030i 0.498827 0.222092i
\(447\) 0 0
\(448\) −6.36898 + 7.07347i −0.300906 + 0.334190i
\(449\) 11.4685 8.33234i 0.541231 0.393228i −0.283311 0.959028i \(-0.591433\pi\)
0.824542 + 0.565801i \(0.191433\pi\)
\(450\) 0 0
\(451\) −1.29620 0.0218838i −0.0610357 0.00103047i
\(452\) 14.4353 + 25.0027i 0.678981 + 1.17603i
\(453\) 0 0
\(454\) −5.71997 1.21582i −0.268452 0.0570612i
\(455\) 15.5847 + 17.3086i 0.730623 + 0.811439i
\(456\) 0 0
\(457\) −2.57572 + 24.5063i −0.120487 + 1.14636i 0.752493 + 0.658600i \(0.228851\pi\)
−0.872980 + 0.487756i \(0.837816\pi\)
\(458\) 0.463439 1.42632i 0.0216551 0.0666475i
\(459\) 0 0
\(460\) 18.2162 13.2348i 0.849334 0.617077i
\(461\) −13.1227 22.7292i −0.611185 1.05860i −0.991041 0.133558i \(-0.957360\pi\)
0.379856 0.925046i \(-0.375973\pi\)
\(462\) 0 0
\(463\) −6.34609 + 10.9917i −0.294928 + 0.510830i −0.974968 0.222345i \(-0.928629\pi\)
0.680040 + 0.733175i \(0.261962\pi\)
\(464\) 0.462189 + 4.39744i 0.0214566 + 0.204146i
\(465\) 0 0
\(466\) −11.7696 + 2.50170i −0.545214 + 0.115889i
\(467\) −22.4130 16.2840i −1.03715 0.753534i −0.0674235 0.997724i \(-0.521478\pi\)
−0.969727 + 0.244190i \(0.921478\pi\)
\(468\) 0 0
\(469\) 3.26838 10.0591i 0.150920 0.464484i
\(470\) −0.605627 + 0.672617i −0.0279355 + 0.0310255i
\(471\) 0 0
\(472\) 3.37128 5.83923i 0.155176 0.268772i
\(473\) 20.9300 + 24.0494i 0.962363 + 1.10579i
\(474\) 0 0
\(475\) 8.40291 + 3.74122i 0.385552 + 0.171659i
\(476\) −6.12756 18.8587i −0.280856 0.864386i
\(477\) 0 0
\(478\) −2.75813 2.00390i −0.126154 0.0916563i
\(479\) −1.63297 + 15.5366i −0.0746121 + 0.709886i 0.891720 + 0.452588i \(0.149499\pi\)
−0.966332 + 0.257299i \(0.917168\pi\)
\(480\) 0 0
\(481\) 11.9879 + 2.54811i 0.546603 + 0.116184i
\(482\) 0.398402 + 3.79055i 0.0181467 + 0.172655i
\(483\) 0 0
\(484\) −17.4046 8.46415i −0.791117 0.384734i
\(485\) −0.586177 −0.0266169
\(486\) 0 0
\(487\) 8.32090 + 25.6091i 0.377056 + 1.16046i 0.942081 + 0.335386i \(0.108867\pi\)
−0.565025 + 0.825074i \(0.691133\pi\)
\(488\) −6.94988 + 1.47724i −0.314606 + 0.0668716i
\(489\) 0 0
\(490\) −3.54514 + 1.57840i −0.160153 + 0.0713048i
\(491\) −26.0959 28.9825i −1.17769 1.30796i −0.941797 0.336182i \(-0.890864\pi\)
−0.235895 0.971778i \(-0.575802\pi\)
\(492\) 0 0
\(493\) −5.10580 2.27325i −0.229954 0.102382i
\(494\) 8.66283 0.389759
\(495\) 0 0
\(496\) −10.1922 −0.457642
\(497\) −21.8631 9.73408i −0.980694 0.436633i
\(498\) 0 0
\(499\) −16.0826 17.8616i −0.719958 0.799594i 0.266461 0.963846i \(-0.414146\pi\)
−0.986418 + 0.164252i \(0.947479\pi\)
\(500\) −19.4444 + 8.65722i −0.869582 + 0.387163i
\(501\) 0 0
\(502\) 0.156967 0.0333644i 0.00700578 0.00148912i
\(503\) 7.41223 + 22.8125i 0.330495 + 1.01716i 0.968899 + 0.247457i \(0.0795949\pi\)
−0.638404 + 0.769701i \(0.720405\pi\)
\(504\) 0 0
\(505\) 12.1547 0.540876
\(506\) −8.30702 + 8.91841i −0.369292 + 0.396472i
\(507\) 0 0
\(508\) 1.98528 + 18.8887i 0.0880827 + 0.838050i
\(509\) 3.61803 + 0.769037i 0.160367 + 0.0340870i 0.287395 0.957812i \(-0.407211\pi\)
−0.127029 + 0.991899i \(0.540544\pi\)
\(510\) 0 0
\(511\) 5.36264 51.0221i 0.237229 2.25709i
\(512\) −18.3128 13.3050i −0.809318 0.588004i
\(513\) 0 0
\(514\) 2.08094 + 6.40449i 0.0917865 + 0.282490i
\(515\) 2.58151 + 1.14936i 0.113755 + 0.0506470i
\(516\) 0 0
\(517\) −1.84353 + 3.07212i −0.0810783 + 0.135112i
\(518\) −2.56407 + 4.44110i −0.112659 + 0.195131i
\(519\) 0 0
\(520\) −8.42621 + 9.35825i −0.369514 + 0.410387i
\(521\) 1.98178 6.09929i 0.0868234 0.267215i −0.898213 0.439560i \(-0.855134\pi\)
0.985037 + 0.172345i \(0.0551344\pi\)
\(522\) 0 0
\(523\) 2.21554 + 1.60969i 0.0968790 + 0.0703867i 0.635170 0.772372i \(-0.280930\pi\)
−0.538291 + 0.842759i \(0.680930\pi\)
\(524\) 36.4082 7.73880i 1.59050 0.338071i
\(525\) 0 0
\(526\) −0.864124 8.22159i −0.0376776 0.358478i
\(527\) 6.44147 11.1570i 0.280595 0.486005i
\(528\) 0 0
\(529\) −16.5651 28.6916i −0.720222 1.24746i
\(530\) 8.51617 6.18736i 0.369919 0.268762i
\(531\) 0 0
\(532\) 8.19149 25.2108i 0.355146 1.09303i
\(533\) −0.163345 + 1.55413i −0.00707527 + 0.0673167i
\(534\) 0 0
\(535\) 3.77969 + 4.19777i 0.163410 + 0.181485i
\(536\) 5.59356 + 1.18895i 0.241605 + 0.0513547i
\(537\) 0 0
\(538\) 3.04042 + 5.26617i 0.131082 + 0.227041i
\(539\) −12.5784 + 8.81819i −0.541788 + 0.379826i
\(540\) 0 0
\(541\) −16.9114 + 12.2869i −0.727079 + 0.528254i −0.888638 0.458609i \(-0.848348\pi\)
0.161559 + 0.986863i \(0.448348\pi\)
\(542\) 6.32434 7.02389i 0.271654 0.301702i
\(543\) 0 0
\(544\) 15.0047 6.68051i 0.643320 0.286424i
\(545\) 8.59381 3.82621i 0.368118 0.163897i
\(546\) 0 0
\(547\) −28.0208 + 31.1202i −1.19808 + 1.33060i −0.267925 + 0.963440i \(0.586338\pi\)
−0.930156 + 0.367164i \(0.880329\pi\)
\(548\) −4.55562 + 3.30985i −0.194606 + 0.141390i
\(549\) 0 0
\(550\) 2.77350 1.94439i 0.118263 0.0829092i
\(551\) −3.73576 6.47053i −0.159149 0.275654i
\(552\) 0 0
\(553\) 13.3411 + 2.83573i 0.567320 + 0.120588i
\(554\) 3.39727 + 3.77305i 0.144336 + 0.160302i
\(555\) 0 0
\(556\) −2.75747 + 26.2355i −0.116943 + 1.11263i
\(557\) 3.87025 11.9114i 0.163988 0.504702i −0.834973 0.550291i \(-0.814517\pi\)
0.998960 + 0.0455895i \(0.0145166\pi\)
\(558\) 0 0
\(559\) 31.0911 22.5890i 1.31502 0.955415i
\(560\) 7.61538 + 13.1902i 0.321809 + 0.557389i
\(561\) 0 0
\(562\) −4.03083 + 6.98160i −0.170030 + 0.294501i
\(563\) −1.51658 14.4293i −0.0639161 0.608121i −0.978859 0.204537i \(-0.934431\pi\)
0.914943 0.403584i \(-0.132236\pi\)
\(564\) 0 0
\(565\) 27.4173 5.82774i 1.15346 0.245175i
\(566\) 0.501956 + 0.364693i 0.0210988 + 0.0153292i
\(567\) 0 0
\(568\) 3.99850 12.3061i 0.167773 0.516353i
\(569\) 18.7172 20.7876i 0.784666 0.871460i −0.209667 0.977773i \(-0.567238\pi\)
0.994333 + 0.106313i \(0.0339046\pi\)
\(570\) 0 0
\(571\) −4.52443 + 7.83654i −0.189341 + 0.327949i −0.945031 0.326981i \(-0.893969\pi\)
0.755689 + 0.654930i \(0.227302\pi\)
\(572\) −12.0040 + 20.0039i −0.501911 + 0.836404i
\(573\) 0 0
\(574\) −0.597341 0.265953i −0.0249325 0.0111007i
\(575\) 4.82046 + 14.8359i 0.201027 + 0.618698i
\(576\) 0 0
\(577\) −31.0234 22.5398i −1.29152 0.938346i −0.291687 0.956514i \(-0.594217\pi\)
−0.999835 + 0.0181683i \(0.994217\pi\)
\(578\) 0.311714 2.96576i 0.0129656 0.123359i
\(579\) 0 0
\(580\) 4.97191 + 1.05681i 0.206447 + 0.0438817i
\(581\) −0.0445499 0.423864i −0.00184824 0.0175848i
\(582\) 0 0
\(583\) 28.4010 30.4913i 1.17625 1.26282i
\(584\) 27.7381 1.14781
\(585\) 0 0
\(586\) 3.65095 + 11.2365i 0.150819 + 0.464175i
\(587\) −0.706826 + 0.150241i −0.0291738 + 0.00620109i −0.222475 0.974938i \(-0.571414\pi\)
0.193302 + 0.981139i \(0.438080\pi\)
\(588\) 0 0
\(589\) 15.7333 7.00493i 0.648281 0.288633i
\(590\) −2.04997 2.27673i −0.0843961 0.0937313i
\(591\) 0 0
\(592\) 7.32155 + 3.25977i 0.300914 + 0.133976i
\(593\) 39.6596 1.62863 0.814313 0.580426i \(-0.197114\pi\)
0.814313 + 0.580426i \(0.197114\pi\)
\(594\) 0 0
\(595\) −19.2517 −0.789244
\(596\) 6.51139 + 2.89906i 0.266717 + 0.118750i
\(597\) 0 0
\(598\) 9.83054 + 10.9179i 0.402001 + 0.446467i
\(599\) 18.6151 8.28799i 0.760594 0.338638i 0.0104783 0.999945i \(-0.496665\pi\)
0.750115 + 0.661307i \(0.229998\pi\)
\(600\) 0 0
\(601\) 47.3147 10.0570i 1.93001 0.410235i 0.931032 0.364936i \(-0.118909\pi\)
0.998973 0.0452991i \(-0.0144241\pi\)
\(602\) 4.96914 + 15.2935i 0.202527 + 0.623315i
\(603\) 0 0
\(604\) 13.7129 0.557968
\(605\) −13.0371 + 13.5313i −0.530035 + 0.550125i
\(606\) 0 0
\(607\) 2.05945 + 19.5944i 0.0835905 + 0.795310i 0.953357 + 0.301846i \(0.0976029\pi\)
−0.869766 + 0.493464i \(0.835730\pi\)
\(608\) 21.4771 + 4.56511i 0.871013 + 0.185140i
\(609\) 0 0
\(610\) −0.337458 + 3.21070i −0.0136633 + 0.129997i
\(611\) 3.49397 + 2.53852i 0.141351 + 0.102698i
\(612\) 0 0
\(613\) 1.76690 + 5.43796i 0.0713644 + 0.219637i 0.980377 0.197131i \(-0.0631626\pi\)
−0.909013 + 0.416768i \(0.863163\pi\)
\(614\) 7.30158 + 3.25087i 0.294668 + 0.131194i
\(615\) 0 0
\(616\) −13.6930 15.7339i −0.551708 0.633935i
\(617\) 3.05346 5.28875i 0.122928 0.212917i −0.797993 0.602666i \(-0.794105\pi\)
0.920921 + 0.389749i \(0.127438\pi\)
\(618\) 0 0
\(619\) −1.19087 + 1.32260i −0.0478653 + 0.0531598i −0.766602 0.642123i \(-0.778054\pi\)
0.718737 + 0.695282i \(0.244721\pi\)
\(620\) −3.62062 + 11.1431i −0.145408 + 0.447519i
\(621\) 0 0
\(622\) 8.48050 + 6.16144i 0.340037 + 0.247051i
\(623\) −26.4653 + 5.62538i −1.06031 + 0.225376i
\(624\) 0 0
\(625\) 1.07184 + 10.1979i 0.0428737 + 0.407916i
\(626\) −0.764220 + 1.32367i −0.0305444 + 0.0529044i
\(627\) 0 0
\(628\) 0.271963 + 0.471055i 0.0108525 + 0.0187971i
\(629\) −8.19556 + 5.95442i −0.326778 + 0.237418i
\(630\) 0 0
\(631\) −13.8566 + 42.6461i −0.551621 + 1.69771i 0.153084 + 0.988213i \(0.451079\pi\)
−0.704705 + 0.709501i \(0.748921\pi\)
\(632\) −0.770822 + 7.33388i −0.0306617 + 0.291726i
\(633\) 0 0
\(634\) 5.99461 + 6.65768i 0.238076 + 0.264410i
\(635\) 18.0367 + 3.83381i 0.715764 + 0.152140i
\(636\) 0 0
\(637\) 9.25852 + 16.0362i 0.366836 + 0.635379i
\(638\) −2.75097 0.0464448i −0.108912 0.00183877i
\(639\) 0 0
\(640\) −15.6290 + 11.3552i −0.617792 + 0.448852i
\(641\) 18.0729 20.0720i 0.713837 0.792797i −0.271677 0.962389i \(-0.587578\pi\)
0.985514 + 0.169592i \(0.0542449\pi\)
\(642\) 0 0
\(643\) −29.7427 + 13.2423i −1.17294 + 0.522225i −0.898325 0.439331i \(-0.855216\pi\)
−0.274610 + 0.961556i \(0.588549\pi\)
\(644\) 41.0694 18.2853i 1.61836 0.720540i
\(645\) 0 0
\(646\) −4.79128 + 5.32126i −0.188510 + 0.209362i
\(647\) −25.4705 + 18.5054i −1.00135 + 0.727523i −0.962377 0.271717i \(-0.912408\pi\)
−0.0389724 + 0.999240i \(0.512408\pi\)
\(648\) 0 0
\(649\) −9.68953 7.29290i −0.380347 0.286271i
\(650\) −2.04149 3.53596i −0.0800736 0.138692i
\(651\) 0 0
\(652\) 18.9205 + 4.02168i 0.740984 + 0.157501i
\(653\) 3.11800 + 3.46289i 0.122017 + 0.135513i 0.801058 0.598587i \(-0.204271\pi\)
−0.679041 + 0.734100i \(0.737604\pi\)
\(654\) 0 0
\(655\) 3.77741 35.9396i 0.147596 1.40428i
\(656\) −0.315782 + 0.971878i −0.0123292 + 0.0379455i
\(657\) 0 0
\(658\) −1.46197 + 1.06219i −0.0569937 + 0.0414084i
\(659\) −16.0209 27.7490i −0.624086 1.08095i −0.988717 0.149797i \(-0.952138\pi\)
0.364631 0.931152i \(-0.381195\pi\)
\(660\) 0 0
\(661\) 20.3527 35.2519i 0.791627 1.37114i −0.133331 0.991072i \(-0.542567\pi\)
0.924959 0.380067i \(-0.124099\pi\)
\(662\) −0.193093 1.83716i −0.00750478 0.0714032i
\(663\) 0 0
\(664\) 0.225398 0.0479098i 0.00874713 0.00185926i
\(665\) −20.8211 15.1274i −0.807406 0.586615i
\(666\) 0 0
\(667\) 3.91560 12.0510i 0.151613 0.466616i
\(668\) −20.6893 + 22.9778i −0.800495 + 0.889039i
\(669\) 0 0
\(670\) 1.29917 2.25023i 0.0501914 0.0869340i
\(671\) 1.12109 + 12.7303i 0.0432792 + 0.491447i
\(672\) 0 0
\(673\) −34.4987 15.3598i −1.32983 0.592077i −0.385994 0.922501i \(-0.626142\pi\)
−0.943833 + 0.330424i \(0.892808\pi\)
\(674\) 0.904299 + 2.78315i 0.0348323 + 0.107203i
\(675\) 0 0
\(676\) 4.24655 + 3.08530i 0.163329 + 0.118665i
\(677\) 1.97566 18.7971i 0.0759307 0.722432i −0.888640 0.458606i \(-0.848349\pi\)
0.964570 0.263826i \(-0.0849845\pi\)
\(678\) 0 0
\(679\) −1.14478 0.243330i −0.0439326 0.00933815i
\(680\) −1.08802 10.3518i −0.0417237 0.396974i
\(681\) 0 0
\(682\) 0.769301 6.29521i 0.0294581 0.241056i
\(683\) −31.1053 −1.19021 −0.595105 0.803648i \(-0.702890\pi\)
−0.595105 + 0.803648i \(0.702890\pi\)
\(684\) 0 0
\(685\) 1.68941 + 5.19948i 0.0645492 + 0.198662i
\(686\) 3.87527 0.823714i 0.147959 0.0314496i
\(687\) 0 0
\(688\) 22.9585 10.2218i 0.875283 0.389701i
\(689\) −33.6098 37.3274i −1.28043 1.42206i
\(690\) 0 0
\(691\) 20.2911 + 9.03419i 0.771911 + 0.343677i 0.754610 0.656173i \(-0.227826\pi\)
0.0173008 + 0.999850i \(0.494493\pi\)
\(692\) 21.7565 0.827057
\(693\) 0 0
\(694\) −11.9432 −0.453358
\(695\) 23.3975 + 10.4173i 0.887520 + 0.395149i
\(696\) 0 0
\(697\) −0.864299 0.959901i −0.0327377 0.0363589i
\(698\) 7.50180 3.34001i 0.283947 0.126421i
\(699\) 0 0
\(700\) −12.2209 + 2.59762i −0.461905 + 0.0981810i
\(701\) 9.25374 + 28.4801i 0.349509 + 1.07568i 0.959125 + 0.282981i \(0.0913235\pi\)
−0.609616 + 0.792697i \(0.708677\pi\)
\(702\) 0 0
\(703\) −13.5424 −0.510763
\(704\) −6.30886 + 6.77319i −0.237774 + 0.255274i
\(705\) 0 0
\(706\) −0.411770 3.91773i −0.0154972 0.147446i
\(707\) 23.7375 + 5.04557i 0.892742 + 0.189758i
\(708\) 0 0
\(709\) −1.79849 + 17.1115i −0.0675436 + 0.642635i 0.907413 + 0.420240i \(0.138054\pi\)
−0.974957 + 0.222395i \(0.928613\pi\)
\(710\) −4.75647 3.45578i −0.178507 0.129693i
\(711\) 0 0
\(712\) −4.52052 13.9127i −0.169414 0.521402i
\(713\) 26.6826 + 11.8799i 0.999271 + 0.444904i
\(714\) 0 0
\(715\) 14.8694 + 17.0855i 0.556082 + 0.638961i
\(716\) −19.2500 + 33.3420i −0.719407 + 1.24605i
\(717\) 0 0
\(718\) 9.46050 10.5070i 0.353063 0.392116i
\(719\) −1.46013 + 4.49382i −0.0544537 + 0.167591i −0.974585 0.224020i \(-0.928082\pi\)
0.920131 + 0.391611i \(0.128082\pi\)
\(720\) 0 0
\(721\) 4.56446 + 3.31628i 0.169989 + 0.123505i
\(722\) −0.247392 + 0.0525847i −0.00920696 + 0.00195700i
\(723\) 0 0
\(724\) −0.805554 7.66433i −0.0299382 0.284843i
\(725\) −1.76074 + 3.04969i −0.0653923 + 0.113263i
\(726\) 0 0
\(727\) −2.60044 4.50410i −0.0964450 0.167048i 0.813766 0.581193i \(-0.197414\pi\)
−0.910211 + 0.414145i \(0.864081\pi\)
\(728\) −20.3408 + 14.7784i −0.753879 + 0.547725i
\(729\) 0 0
\(730\) 3.89468 11.9866i 0.144149 0.443644i
\(731\) −3.32043 + 31.5918i −0.122811 + 1.16847i
\(732\) 0 0
\(733\) −32.8297 36.4610i −1.21259 1.34672i −0.920702 0.390267i \(-0.872383\pi\)
−0.291890 0.956452i \(-0.594284\pi\)
\(734\) −10.7198 2.27857i −0.395676 0.0841034i
\(735\) 0 0
\(736\) 18.6187 + 32.2485i 0.686294 + 1.18870i
\(737\) 3.34308 9.72706i 0.123144 0.358301i
\(738\) 0 0
\(739\) 12.6160 9.16603i 0.464086 0.337178i −0.331046 0.943615i \(-0.607402\pi\)
0.795132 + 0.606437i \(0.207402\pi\)
\(740\) 6.16478 6.84668i 0.226622 0.251689i
\(741\) 0 0
\(742\) 19.2002 8.54847i 0.704861 0.313824i
\(743\) −10.1718 + 4.52879i −0.373168 + 0.166145i −0.584747 0.811216i \(-0.698806\pi\)
0.211579 + 0.977361i \(0.432139\pi\)
\(744\) 0 0
\(745\) 4.63041 5.14259i 0.169645 0.188410i
\(746\) −2.80897 + 2.04083i −0.102844 + 0.0747202i
\(747\) 0 0
\(748\) −5.64842 18.4374i −0.206527 0.674140i
\(749\) 5.63901 + 9.76705i 0.206045 + 0.356880i
\(750\) 0 0
\(751\) 7.90852 + 1.68101i 0.288586 + 0.0613409i 0.349930 0.936776i \(-0.386205\pi\)
−0.0613440 + 0.998117i \(0.519539\pi\)
\(752\) 1.88976 + 2.09879i 0.0689124 + 0.0765350i
\(753\) 0 0
\(754\) −0.346673 + 3.29838i −0.0126251 + 0.120120i
\(755\) 4.11410 12.6619i 0.149727 0.460814i
\(756\) 0 0
\(757\) −24.1585 + 17.5522i −0.878056 + 0.637945i −0.932737 0.360559i \(-0.882586\pi\)
0.0546803 + 0.998504i \(0.482586\pi\)
\(758\) 5.97081 + 10.3417i 0.216869 + 0.375629i
\(759\) 0 0
\(760\) 6.95742 12.0506i 0.252372 0.437121i
\(761\) 3.64727 + 34.7014i 0.132213 + 1.25793i 0.836483 + 0.547993i \(0.184608\pi\)
−0.704269 + 0.709933i \(0.748725\pi\)
\(762\) 0 0
\(763\) 18.3716 3.90501i 0.665098 0.141371i
\(764\) −17.8134 12.9422i −0.644468 0.468233i
\(765\) 0 0
\(766\) 2.67339 8.22786i 0.0965936 0.297284i
\(767\) −9.78174 + 10.8637i −0.353198 + 0.392266i
\(768\) 0 0
\(769\) 2.80362 4.85600i 0.101101 0.175112i −0.811038 0.584994i \(-0.801097\pi\)
0.912139 + 0.409882i \(0.134430\pi\)
\(770\) −8.72177 + 3.70806i −0.314311 + 0.133629i
\(771\) 0 0
\(772\) 20.1969 + 8.99226i 0.726904 + 0.323639i
\(773\) 3.34979 + 10.3096i 0.120483 + 0.370810i 0.993051 0.117683i \(-0.0375467\pi\)
−0.872568 + 0.488493i \(0.837547\pi\)
\(774\) 0 0
\(775\) −6.56697 4.77118i −0.235893 0.171386i
\(776\) 0.0661431 0.629310i 0.00237440 0.0225909i
\(777\) 0 0
\(778\) −8.57982 1.82370i −0.307601 0.0653827i
\(779\) −0.180494 1.71729i −0.00646688 0.0615282i
\(780\) 0 0
\(781\) −21.0984 9.82364i −0.754958 0.351517i
\(782\) −12.1436 −0.434255
\(783\) 0 0
\(784\) 3.74186 + 11.5163i 0.133638 + 0.411295i
\(785\) 0.516546 0.109795i 0.0184363 0.00391876i
\(786\) 0 0
\(787\) −2.26233 + 1.00726i −0.0806434 + 0.0359048i −0.446662 0.894703i \(-0.647387\pi\)
0.366019 + 0.930608i \(0.380721\pi\)
\(788\) −12.1794 13.5265i −0.433872 0.481863i
\(789\) 0 0
\(790\) 3.06099 + 1.36284i 0.108905 + 0.0484877i
\(791\) 55.9640 1.98985
\(792\) 0 0
\(793\) 15.4047 0.547037
\(794\) −9.83084 4.37697i −0.348883 0.155333i
\(795\) 0 0
\(796\) −31.1712 34.6191i −1.10483 1.22704i
\(797\) 8.84284 3.93708i 0.313229 0.139459i −0.244100 0.969750i \(-0.578493\pi\)
0.557330 + 0.830291i \(0.311826\pi\)
\(798\) 0 0
\(799\) −3.49179 + 0.742202i −0.123531 + 0.0262572i
\(800\) −3.19795 9.84226i −0.113064 0.347977i
\(801\) 0 0
\(802\) −2.65237 −0.0936586
\(803\) 6.05183 49.5223i 0.213564 1.74760i
\(804\) 0 0
\(805\) −4.56233 43.4077i −0.160801 1.52992i
\(806\) −7.47777 1.58945i −0.263393 0.0559859i
\(807\) 0 0
\(808\) −1.37151 + 13.0491i −0.0482496 + 0.459064i
\(809\) −6.36318 4.62312i −0.223717 0.162540i 0.470281 0.882517i \(-0.344153\pi\)
−0.693998 + 0.719976i \(0.744153\pi\)
\(810\) 0 0
\(811\) 12.2076 + 37.5712i 0.428668 + 1.31930i 0.899438 + 0.437048i \(0.143976\pi\)
−0.470770 + 0.882256i \(0.656024\pi\)
\(812\) 9.27123 + 4.12782i 0.325356 + 0.144858i
\(813\) 0 0
\(814\) −2.56603 + 4.27612i −0.0899392 + 0.149878i
\(815\) 9.38994 16.2639i 0.328915 0.569698i
\(816\) 0 0
\(817\) −28.4149 + 31.5580i −0.994113 + 1.10407i
\(818\) 3.58013 11.0185i 0.125176 0.385253i
\(819\) 0 0
\(820\) 0.950378 + 0.690490i 0.0331886 + 0.0241130i
\(821\) −3.28033 + 0.697257i −0.114484 + 0.0243344i −0.264798 0.964304i \(-0.585305\pi\)
0.150313 + 0.988638i \(0.451972\pi\)
\(822\) 0 0
\(823\) −1.68310 16.0136i −0.0586691 0.558199i −0.983891 0.178772i \(-0.942788\pi\)
0.925221 0.379428i \(-0.123879\pi\)
\(824\) −1.52523 + 2.64177i −0.0531339 + 0.0920306i
\(825\) 0 0
\(826\) −3.05841 5.29732i −0.106416 0.184317i
\(827\) 12.3703 8.98751i 0.430156 0.312526i −0.351555 0.936167i \(-0.614347\pi\)
0.781711 + 0.623641i \(0.214347\pi\)
\(828\) 0 0
\(829\) −13.0239 + 40.0835i −0.452340 + 1.39216i 0.421890 + 0.906647i \(0.361367\pi\)
−0.874230 + 0.485512i \(0.838633\pi\)
\(830\) 0.0109444 0.104129i 0.000379886 0.00361438i
\(831\) 0 0
\(832\) 7.46592 + 8.29174i 0.258834 + 0.287464i
\(833\) −14.9712 3.18223i −0.518722 0.110258i
\(834\) 0 0
\(835\) 15.0096 + 25.9975i 0.519430 + 0.899679i
\(836\) 8.37869 24.3788i 0.289783 0.843157i
\(837\) 0 0
\(838\) −7.19483 + 5.22735i −0.248541 + 0.180576i
\(839\) −1.77145 + 1.96739i −0.0611573 + 0.0679220i −0.772947 0.634471i \(-0.781218\pi\)
0.711790 + 0.702393i \(0.247885\pi\)
\(840\) 0 0
\(841\) −23.8797 + 10.6319i −0.823437 + 0.366618i
\(842\) −5.74100 + 2.55606i −0.197848 + 0.0880876i
\(843\) 0 0
\(844\) 8.57518 9.52371i 0.295170 0.327819i
\(845\) 4.12288 2.99545i 0.141831 0.103047i
\(846\) 0 0
\(847\) −31.0780 + 21.0141i −1.06785 + 0.722053i
\(848\) −16.4232 28.4458i −0.563976 0.976834i
\(849\) 0 0
\(850\) 3.30112 + 0.701676i 0.113228 + 0.0240673i
\(851\) −15.3679 17.0678i −0.526805 0.585076i
\(852\) 0 0
\(853\) −0.969018 + 9.21959i −0.0331785 + 0.315673i 0.965328 + 0.261040i \(0.0840654\pi\)
−0.998507 + 0.0546327i \(0.982601\pi\)
\(854\) −1.99185 + 6.13027i −0.0681596 + 0.209774i
\(855\) 0 0
\(856\) −4.93314 + 3.58414i −0.168611 + 0.122503i
\(857\) −10.2678 17.7844i −0.350742 0.607502i 0.635638 0.771987i \(-0.280737\pi\)
−0.986380 + 0.164485i \(0.947404\pi\)
\(858\) 0 0
\(859\) −18.0139 + 31.2010i −0.614626 + 1.06456i 0.375824 + 0.926691i \(0.377360\pi\)
−0.990450 + 0.137872i \(0.955974\pi\)
\(860\) −3.01982 28.7316i −0.102975 0.979740i
\(861\) 0 0
\(862\) −3.15652 + 0.670939i −0.107511 + 0.0228523i
\(863\) 3.49209 + 2.53715i 0.118872 + 0.0863656i 0.645633 0.763648i \(-0.276594\pi\)
−0.526761 + 0.850014i \(0.676594\pi\)
\(864\) 0 0
\(865\) 6.52733 20.0890i 0.221936 0.683048i
\(866\) 4.59414 5.10230i 0.156115 0.173383i
\(867\) 0 0
\(868\) −11.6966 + 20.2591i −0.397008 + 0.687637i
\(869\) 12.9254 + 2.97627i 0.438463 + 0.100963i
\(870\) 0 0
\(871\) −11.3265 5.04287i −0.383783 0.170871i
\(872\) 3.13804 + 9.65790i 0.106268 + 0.327058i
\(873\) 0 0
\(874\) −13.1335 9.54206i −0.444248 0.322765i
\(875\) −4.31273 + 41.0329i −0.145797 + 1.38716i
\(876\) 0 0
\(877\) −30.4360 6.46938i −1.02775 0.218455i −0.336968 0.941516i \(-0.609401\pi\)
−0.690785 + 0.723061i \(0.742735\pi\)
\(878\) −1.29090 12.2821i −0.0435658 0.414501i
\(879\) 0 0
\(880\) 7.18813 + 12.9503i 0.242312 + 0.436553i
\(881\) −43.9267 −1.47993 −0.739964 0.672647i \(-0.765157\pi\)
−0.739964 + 0.672647i \(0.765157\pi\)
\(882\) 0 0
\(883\) −1.81685 5.59170i −0.0611420 0.188176i 0.915820 0.401589i \(-0.131542\pi\)
−0.976962 + 0.213413i \(0.931542\pi\)
\(884\) −22.7365 + 4.83279i −0.764710 + 0.162544i
\(885\) 0 0
\(886\) −12.0188 + 5.35113i −0.403781 + 0.179775i
\(887\) 5.14903 + 5.71858i 0.172887 + 0.192011i 0.823361 0.567518i \(-0.192096\pi\)
−0.650474 + 0.759529i \(0.725430\pi\)
\(888\) 0 0
\(889\) 33.6334 + 14.9745i 1.12803 + 0.502230i
\(890\) −6.64689 −0.222804
\(891\) 0 0
\(892\) −41.3640 −1.38497
\(893\) −4.35963 1.94103i −0.145889 0.0649541i
\(894\) 0 0
\(895\) 25.0113 + 27.7779i 0.836036 + 0.928512i
\(896\) −35.2365 + 15.6883i −1.17717 + 0.524109i
\(897\) 0 0
\(898\) 6.80121 1.44564i 0.226959 0.0482417i
\(899\) 2.03751 + 6.27081i 0.0679547 + 0.209143i
\(900\) 0 0
\(901\) 41.5180 1.38316
\(902\) −0.576446 0.268400i −0.0191936 0.00893675i
\(903\) 0 0
\(904\) 3.16284 + 30.0924i 0.105194 + 1.00086i
\(905\) −7.31861 1.55562i −0.243279 0.0517105i
\(906\) 0 0
\(907\) 1.98505 18.8865i 0.0659126 0.627117i −0.910842 0.412756i \(-0.864566\pi\)
0.976754 0.214361i \(-0.0687669\pi\)
\(908\) 16.9700 + 12.3294i 0.563170 + 0.409167i
\(909\) 0 0
\(910\) 3.53024 + 10.8650i 0.117026 + 0.360170i
\(911\) −45.7095 20.3512i −1.51442 0.674265i −0.529667 0.848206i \(-0.677683\pi\)
−0.984756 + 0.173941i \(0.944350\pi\)
\(912\) 0 0
\(913\) −0.0363591 0.412867i −0.00120331 0.0136639i
\(914\) −6.04320 + 10.4671i −0.199891 + 0.346222i
\(915\) 0 0
\(916\) −3.59961 + 3.99778i −0.118935 + 0.132090i
\(917\) 22.2961 68.6205i 0.736284 2.26605i
\(918\) 0 0
\(919\) −2.48708 1.80697i −0.0820411 0.0596063i 0.546009 0.837780i \(-0.316147\pi\)
−0.628050 + 0.778173i \(0.716147\pi\)
\(920\) 23.0829 4.90641i 0.761019 0.161760i
\(921\) 0 0
\(922\) −1.34562 12.8027i −0.0443155 0.421634i
\(923\) −14.0270 + 24.2955i −0.461705 + 0.799696i
\(924\) 0 0
\(925\) 3.19142 + 5.52769i 0.104933 + 0.181749i
\(926\) −5.03648 + 3.65922i −0.165509 + 0.120249i
\(927\) 0 0
\(928\) −2.59765 + 7.99474i −0.0852720 + 0.262440i
\(929\) −0.0946583 + 0.900613i −0.00310564 + 0.0295482i −0.995965 0.0897428i \(-0.971395\pi\)
0.992859 + 0.119291i \(0.0380621\pi\)
\(930\) 0 0
\(931\) −13.6911 15.2055i −0.448709 0.498342i
\(932\) 42.2177 + 8.97365i 1.38289 + 0.293942i
\(933\) 0 0
\(934\) −6.79433 11.7681i −0.222317 0.385065i
\(935\) −18.7190 0.316034i −0.612177 0.0103354i
\(936\) 0 0
\(937\) 17.8423 12.9632i 0.582881 0.423488i −0.256881 0.966443i \(-0.582695\pi\)
0.839762 + 0.542955i \(0.182695\pi\)
\(938\) 3.47133 3.85530i 0.113343 0.125880i
\(939\) 0 0
\(940\) 2.96592 1.32051i 0.0967376 0.0430703i
\(941\) −4.98880 + 2.22116i −0.162630 + 0.0724077i −0.486437 0.873715i \(-0.661704\pi\)
0.323807 + 0.946123i \(0.395037\pi\)
\(942\) 0 0
\(943\) 1.95951 2.17625i 0.0638103 0.0708685i
\(944\) −7.73386 + 5.61898i −0.251716 + 0.182882i
\(945\) 0 0
\(946\) 4.58059 + 14.9519i 0.148928 + 0.486127i
\(947\) 16.2203 + 28.0944i 0.527089 + 0.912945i 0.999502 + 0.0315677i \(0.0100500\pi\)
−0.472412 + 0.881378i \(0.656617\pi\)
\(948\) 0 0
\(949\) −58.8250 12.5036i −1.90954 0.405885i
\(950\) 3.01887 + 3.35279i 0.0979450 + 0.108779i
\(951\) 0 0
\(952\) 2.17233 20.6683i 0.0704055 0.669864i
\(953\) 16.6278 51.1752i 0.538628 1.65773i −0.197049 0.980394i \(-0.563136\pi\)
0.735677 0.677333i \(-0.236864\pi\)
\(954\) 0 0
\(955\) −17.2947 + 12.5653i −0.559642 + 0.406604i
\(956\) 6.11452 + 10.5907i 0.197758 + 0.342527i
\(957\) 0 0
\(958\) −3.83130 + 6.63600i −0.123784 + 0.214400i
\(959\) 1.14098 + 10.8557i 0.0368440 + 0.350548i
\(960\) 0 0
\(961\) 15.4563 3.28533i 0.498589 0.105978i
\(962\) 4.86330 + 3.53339i 0.156799 + 0.113921i
\(963\) 0 0
\(964\) 4.22478 13.0025i 0.136071 0.418784i
\(965\) 14.3625 15.9512i 0.462346 0.513487i
\(966\) 0 0
\(967\) 14.4075 24.9546i 0.463315 0.802486i −0.535809 0.844340i \(-0.679993\pi\)
0.999124 + 0.0418540i \(0.0133264\pi\)
\(968\) −13.0559 15.5233i −0.419631 0.498937i
\(969\) 0 0
\(970\) −0.262659 0.116943i −0.00843348 0.00375483i
\(971\) −1.66685 5.13005i −0.0534919 0.164631i 0.920742 0.390173i \(-0.127585\pi\)
−0.974233 + 0.225542i \(0.927585\pi\)
\(972\) 0 0
\(973\) 41.3700 + 30.0571i 1.32626 + 0.963586i
\(974\) −1.38056 + 13.1352i −0.0442361 + 0.420878i
\(975\) 0 0
\(976\) 9.85351 + 2.09443i 0.315403 + 0.0670410i
\(977\) −0.346236 3.29421i −0.0110771 0.105391i 0.987586 0.157077i \(-0.0502072\pi\)
−0.998663 + 0.0516860i \(0.983540\pi\)
\(978\) 0 0
\(979\) −25.8254 + 5.03527i −0.825383 + 0.160928i
\(980\) 13.9200 0.444657
\(981\) 0 0
\(982\) −5.91123 18.1929i −0.188635 0.580559i
\(983\) 33.1319 7.04241i 1.05674 0.224618i 0.353404 0.935471i \(-0.385024\pi\)
0.703341 + 0.710853i \(0.251691\pi\)
\(984\) 0 0
\(985\) −16.1439 + 7.18772i −0.514387 + 0.229020i
\(986\) −1.83433 2.03723i −0.0584170 0.0648787i
\(987\) 0 0
\(988\) −28.3873 12.6389i −0.903121 0.402095i
\(989\) −72.0183 −2.29005
\(990\) 0 0
\(991\) 8.66640 0.275297 0.137649 0.990481i \(-0.456046\pi\)
0.137649 + 0.990481i \(0.456046\pi\)
\(992\) −17.7015 7.88122i −0.562023 0.250229i
\(993\) 0 0
\(994\) −7.85464 8.72346i −0.249134 0.276691i
\(995\) −41.3178 + 18.3959i −1.30986 + 0.583189i
\(996\) 0 0
\(997\) 29.6040 6.29253i 0.937569 0.199286i 0.286306 0.958138i \(-0.407573\pi\)
0.651263 + 0.758852i \(0.274239\pi\)
\(998\) −3.64303 11.2121i −0.115318 0.354912i
\(999\) 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 297.2.n.b.91.5 72
3.2 odd 2 99.2.m.b.58.5 yes 72
9.2 odd 6 99.2.m.b.25.5 yes 72
9.4 even 3 891.2.f.e.487.5 36
9.5 odd 6 891.2.f.f.487.5 36
9.7 even 3 inner 297.2.n.b.289.5 72
11.4 even 5 inner 297.2.n.b.37.5 72
33.2 even 10 1089.2.e.o.364.9 36
33.20 odd 10 1089.2.e.p.364.10 36
33.26 odd 10 99.2.m.b.4.5 72
99.2 even 30 1089.2.e.o.727.9 36
99.4 even 15 891.2.f.e.730.5 36
99.13 odd 30 9801.2.a.cn.1.9 18
99.20 odd 30 1089.2.e.p.727.10 36
99.31 even 15 9801.2.a.cp.1.10 18
99.59 odd 30 891.2.f.f.730.5 36
99.68 even 30 9801.2.a.co.1.10 18
99.70 even 15 inner 297.2.n.b.235.5 72
99.86 odd 30 9801.2.a.cm.1.9 18
99.92 odd 30 99.2.m.b.70.5 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.5 72 33.26 odd 10
99.2.m.b.25.5 yes 72 9.2 odd 6
99.2.m.b.58.5 yes 72 3.2 odd 2
99.2.m.b.70.5 yes 72 99.92 odd 30
297.2.n.b.37.5 72 11.4 even 5 inner
297.2.n.b.91.5 72 1.1 even 1 trivial
297.2.n.b.235.5 72 99.70 even 15 inner
297.2.n.b.289.5 72 9.7 even 3 inner
891.2.f.e.487.5 36 9.4 even 3
891.2.f.e.730.5 36 99.4 even 15
891.2.f.f.487.5 36 9.5 odd 6
891.2.f.f.730.5 36 99.59 odd 30
1089.2.e.o.364.9 36 33.2 even 10
1089.2.e.o.727.9 36 99.2 even 30
1089.2.e.p.364.10 36 33.20 odd 10
1089.2.e.p.727.10 36 99.20 odd 30
9801.2.a.cm.1.9 18 99.86 odd 30
9801.2.a.cn.1.9 18 99.13 odd 30
9801.2.a.co.1.10 18 99.68 even 30
9801.2.a.cp.1.10 18 99.31 even 15