Properties

Label 315.2.bb.b.89.12
Level $315$
Weight $2$
Character 315.89
Analytic conductor $2.515$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(89,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.12
Character \(\chi\) \(=\) 315.89
Dual form 315.2.bb.b.269.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.28469 - 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(-1.33613 - 1.79297i) q^{5} +(2.64140 - 0.151755i) q^{7} -6.68468 q^{8} +O(q^{10})\) \(q+(1.28469 - 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(-1.33613 - 1.79297i) q^{5} +(2.64140 - 0.151755i) q^{7} -6.68468 q^{8} +(-5.70613 + 0.669669i) q^{10} +(-4.88189 + 2.81856i) q^{11} +3.53537 q^{13} +(3.05569 - 6.07244i) q^{14} +(-3.98605 + 6.90403i) q^{16} +(4.62703 - 2.67142i) q^{17} +(-1.24942 - 0.721351i) q^{19} +(-4.07109 + 9.45005i) q^{20} +14.4839i q^{22} +(1.49930 - 2.59686i) q^{23} +(-1.42951 + 4.79129i) q^{25} +(4.54184 - 7.86670i) q^{26} +(-6.68220 - 10.1772i) q^{28} +2.19404i q^{29} +(1.31899 - 0.761520i) q^{31} +(3.55696 + 6.16083i) q^{32} -13.7277i q^{34} +(-3.80134 - 4.53319i) q^{35} +(-0.946690 - 0.546572i) q^{37} +(-3.21022 + 1.85342i) q^{38} +(8.93161 + 11.9855i) q^{40} +6.52058 q^{41} -0.486125i q^{43} +(22.4649 + 12.9701i) q^{44} +(-3.85226 - 6.67231i) q^{46} +(3.68608 + 2.12816i) q^{47} +(6.95394 - 0.801688i) q^{49} +(8.82483 + 9.33618i) q^{50} +(-8.13432 - 14.0891i) q^{52} +(2.01102 + 3.48318i) q^{53} +(11.5764 + 4.98714i) q^{55} +(-17.6569 + 1.01443i) q^{56} +(4.88206 + 2.81866i) q^{58} +(-5.70978 - 9.88963i) q^{59} +(6.06957 + 3.50427i) q^{61} -3.91326i q^{62} +2.33411 q^{64} +(-4.72371 - 6.33883i) q^{65} +(2.15623 - 1.24490i) q^{67} +(-21.2921 - 12.2930i) q^{68} +(-14.9705 + 2.63479i) q^{70} +8.13849i q^{71} +(1.56901 + 2.71761i) q^{73} +(-2.43240 + 1.40435i) q^{74} +6.63886i q^{76} +(-12.4673 + 8.18578i) q^{77} +(-6.40252 + 11.0895i) q^{79} +(17.7046 - 2.07781i) q^{80} +(8.37690 - 14.5092i) q^{82} -6.77241i q^{83} +(-10.9721 - 4.72679i) q^{85} +(-1.08170 - 0.624518i) q^{86} +(32.6339 - 18.8412i) q^{88} +(-5.16513 + 8.94627i) q^{89} +(9.33831 - 0.536509i) q^{91} -13.7986 q^{92} +(9.47093 - 5.46804i) q^{94} +(0.376019 + 3.20399i) q^{95} -14.7321 q^{97} +(7.14976 - 16.5034i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} - 12 q^{10} - 36 q^{19} + 12 q^{25} - 60 q^{31} + 96 q^{40} - 24 q^{46} + 36 q^{49} + 48 q^{61} + 48 q^{64} - 48 q^{70} - 60 q^{79} - 72 q^{85} + 60 q^{91} + 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28469 2.22514i 0.908411 1.57341i 0.0921382 0.995746i \(-0.470630\pi\)
0.816272 0.577667i \(-0.196037\pi\)
\(3\) 0 0
\(4\) −2.30084 3.98517i −1.15042 1.99259i
\(5\) −1.33613 1.79297i −0.597535 0.801843i
\(6\) 0 0
\(7\) 2.64140 0.151755i 0.998354 0.0573579i
\(8\) −6.68468 −2.36339
\(9\) 0 0
\(10\) −5.70613 + 0.669669i −1.80444 + 0.211768i
\(11\) −4.88189 + 2.81856i −1.47195 + 0.849828i −0.999503 0.0315336i \(-0.989961\pi\)
−0.472442 + 0.881362i \(0.656628\pi\)
\(12\) 0 0
\(13\) 3.53537 0.980535 0.490267 0.871572i \(-0.336899\pi\)
0.490267 + 0.871572i \(0.336899\pi\)
\(14\) 3.05569 6.07244i 0.816667 1.62293i
\(15\) 0 0
\(16\) −3.98605 + 6.90403i −0.996512 + 1.72601i
\(17\) 4.62703 2.67142i 1.12222 0.647914i 0.180253 0.983620i \(-0.442308\pi\)
0.941967 + 0.335707i \(0.108975\pi\)
\(18\) 0 0
\(19\) −1.24942 0.721351i −0.286636 0.165489i 0.349788 0.936829i \(-0.386254\pi\)
−0.636424 + 0.771340i \(0.719587\pi\)
\(20\) −4.07109 + 9.45005i −0.910323 + 2.11310i
\(21\) 0 0
\(22\) 14.4839i 3.08797i
\(23\) 1.49930 2.59686i 0.312626 0.541484i −0.666304 0.745680i \(-0.732125\pi\)
0.978930 + 0.204196i \(0.0654581\pi\)
\(24\) 0 0
\(25\) −1.42951 + 4.79129i −0.285903 + 0.958259i
\(26\) 4.54184 7.86670i 0.890728 1.54279i
\(27\) 0 0
\(28\) −6.68220 10.1772i −1.26282 1.92332i
\(29\) 2.19404i 0.407423i 0.979031 + 0.203712i \(0.0653005\pi\)
−0.979031 + 0.203712i \(0.934699\pi\)
\(30\) 0 0
\(31\) 1.31899 0.761520i 0.236898 0.136773i −0.376852 0.926273i \(-0.622994\pi\)
0.613750 + 0.789500i \(0.289660\pi\)
\(32\) 3.55696 + 6.16083i 0.628787 + 1.08909i
\(33\) 0 0
\(34\) 13.7277i 2.35429i
\(35\) −3.80134 4.53319i −0.642544 0.766249i
\(36\) 0 0
\(37\) −0.946690 0.546572i −0.155635 0.0898558i 0.420160 0.907450i \(-0.361974\pi\)
−0.575795 + 0.817594i \(0.695307\pi\)
\(38\) −3.21022 + 1.85342i −0.520766 + 0.300665i
\(39\) 0 0
\(40\) 8.93161 + 11.9855i 1.41221 + 1.89507i
\(41\) 6.52058 1.01834 0.509172 0.860665i \(-0.329952\pi\)
0.509172 + 0.860665i \(0.329952\pi\)
\(42\) 0 0
\(43\) 0.486125i 0.0741333i −0.999313 0.0370667i \(-0.988199\pi\)
0.999313 0.0370667i \(-0.0118014\pi\)
\(44\) 22.4649 + 12.9701i 3.38671 + 1.95532i
\(45\) 0 0
\(46\) −3.85226 6.67231i −0.567985 0.983779i
\(47\) 3.68608 + 2.12816i 0.537671 + 0.310424i 0.744134 0.668030i \(-0.232862\pi\)
−0.206464 + 0.978454i \(0.566196\pi\)
\(48\) 0 0
\(49\) 6.95394 0.801688i 0.993420 0.114527i
\(50\) 8.82483 + 9.33618i 1.24802 + 1.32034i
\(51\) 0 0
\(52\) −8.13432 14.0891i −1.12803 1.95380i
\(53\) 2.01102 + 3.48318i 0.276235 + 0.478452i 0.970446 0.241319i \(-0.0775800\pi\)
−0.694211 + 0.719771i \(0.744247\pi\)
\(54\) 0 0
\(55\) 11.5764 + 4.98714i 1.56097 + 0.672466i
\(56\) −17.6569 + 1.01443i −2.35950 + 0.135559i
\(57\) 0 0
\(58\) 4.88206 + 2.81866i 0.641046 + 0.370108i
\(59\) −5.70978 9.88963i −0.743350 1.28752i −0.950962 0.309309i \(-0.899902\pi\)
0.207612 0.978211i \(-0.433431\pi\)
\(60\) 0 0
\(61\) 6.06957 + 3.50427i 0.777129 + 0.448676i 0.835412 0.549624i \(-0.185229\pi\)
−0.0582826 + 0.998300i \(0.518562\pi\)
\(62\) 3.91326i 0.496984i
\(63\) 0 0
\(64\) 2.33411 0.291764
\(65\) −4.72371 6.33883i −0.585904 0.786235i
\(66\) 0 0
\(67\) 2.15623 1.24490i 0.263425 0.152089i −0.362471 0.931995i \(-0.618067\pi\)
0.625896 + 0.779907i \(0.284733\pi\)
\(68\) −21.2921 12.2930i −2.58205 1.49075i
\(69\) 0 0
\(70\) −14.9705 + 2.63479i −1.78932 + 0.314918i
\(71\) 8.13849i 0.965861i 0.875659 + 0.482930i \(0.160428\pi\)
−0.875659 + 0.482930i \(0.839572\pi\)
\(72\) 0 0
\(73\) 1.56901 + 2.71761i 0.183639 + 0.318072i 0.943117 0.332461i \(-0.107879\pi\)
−0.759478 + 0.650533i \(0.774546\pi\)
\(74\) −2.43240 + 1.40435i −0.282761 + 0.163252i
\(75\) 0 0
\(76\) 6.63886i 0.761529i
\(77\) −12.4673 + 8.18578i −1.42078 + 0.932856i
\(78\) 0 0
\(79\) −6.40252 + 11.0895i −0.720340 + 1.24766i 0.240524 + 0.970643i \(0.422681\pi\)
−0.960864 + 0.277022i \(0.910653\pi\)
\(80\) 17.7046 2.07781i 1.97944 0.232306i
\(81\) 0 0
\(82\) 8.37690 14.5092i 0.925074 1.60228i
\(83\) 6.77241i 0.743368i −0.928359 0.371684i \(-0.878780\pi\)
0.928359 0.371684i \(-0.121220\pi\)
\(84\) 0 0
\(85\) −10.9721 4.72679i −1.19009 0.512692i
\(86\) −1.08170 0.624518i −0.116642 0.0673435i
\(87\) 0 0
\(88\) 32.6339 18.8412i 3.47878 2.00848i
\(89\) −5.16513 + 8.94627i −0.547503 + 0.948303i 0.450942 + 0.892553i \(0.351088\pi\)
−0.998445 + 0.0557494i \(0.982245\pi\)
\(90\) 0 0
\(91\) 9.33831 0.536509i 0.978921 0.0562414i
\(92\) −13.7986 −1.43860
\(93\) 0 0
\(94\) 9.47093 5.46804i 0.976852 0.563985i
\(95\) 0.376019 + 3.20399i 0.0385787 + 0.328723i
\(96\) 0 0
\(97\) −14.7321 −1.49582 −0.747908 0.663802i \(-0.768942\pi\)
−0.747908 + 0.663802i \(0.768942\pi\)
\(98\) 7.14976 16.5034i 0.722235 1.66710i
\(99\) 0 0
\(100\) 22.3832 5.32714i 2.23832 0.532714i
\(101\) 7.46683 + 12.9329i 0.742977 + 1.28687i 0.951134 + 0.308779i \(0.0999202\pi\)
−0.208157 + 0.978095i \(0.566746\pi\)
\(102\) 0 0
\(103\) −1.95755 + 3.39058i −0.192883 + 0.334084i −0.946205 0.323569i \(-0.895117\pi\)
0.753321 + 0.657653i \(0.228451\pi\)
\(104\) −23.6328 −2.31739
\(105\) 0 0
\(106\) 10.3341 1.00374
\(107\) −7.41102 + 12.8363i −0.716450 + 1.24093i 0.245948 + 0.969283i \(0.420901\pi\)
−0.962398 + 0.271645i \(0.912432\pi\)
\(108\) 0 0
\(109\) −5.51932 9.55974i −0.528655 0.915657i −0.999442 0.0334099i \(-0.989363\pi\)
0.470787 0.882247i \(-0.343970\pi\)
\(110\) 25.9692 19.3523i 2.47607 1.84517i
\(111\) 0 0
\(112\) −9.48101 + 18.8412i −0.895871 + 1.78032i
\(113\) 7.54314 0.709599 0.354799 0.934942i \(-0.384549\pi\)
0.354799 + 0.934942i \(0.384549\pi\)
\(114\) 0 0
\(115\) −6.65937 + 0.781540i −0.620990 + 0.0728790i
\(116\) 8.74363 5.04814i 0.811826 0.468708i
\(117\) 0 0
\(118\) −29.3411 −2.70107
\(119\) 11.8164 7.75844i 1.08321 0.711215i
\(120\) 0 0
\(121\) 10.3886 17.9935i 0.944415 1.63577i
\(122\) 15.5950 9.00378i 1.41191 0.815164i
\(123\) 0 0
\(124\) −6.06957 3.50427i −0.545064 0.314693i
\(125\) 10.5007 3.83871i 0.939210 0.343344i
\(126\) 0 0
\(127\) 3.93715i 0.349366i −0.984625 0.174683i \(-0.944110\pi\)
0.984625 0.174683i \(-0.0558900\pi\)
\(128\) −4.11531 + 7.12793i −0.363746 + 0.630026i
\(129\) 0 0
\(130\) −20.1733 + 2.36753i −1.76931 + 0.207646i
\(131\) −1.97399 + 3.41906i −0.172469 + 0.298724i −0.939282 0.343145i \(-0.888508\pi\)
0.766814 + 0.641870i \(0.221841\pi\)
\(132\) 0 0
\(133\) −3.40967 1.71577i −0.295656 0.148776i
\(134\) 6.39722i 0.552635i
\(135\) 0 0
\(136\) −30.9302 + 17.8576i −2.65225 + 1.53127i
\(137\) 2.83062 + 4.90279i 0.241837 + 0.418873i 0.961237 0.275722i \(-0.0889169\pi\)
−0.719401 + 0.694595i \(0.755584\pi\)
\(138\) 0 0
\(139\) 23.3015i 1.97640i 0.153158 + 0.988202i \(0.451056\pi\)
−0.153158 + 0.988202i \(0.548944\pi\)
\(140\) −9.31927 + 25.5791i −0.787622 + 2.16183i
\(141\) 0 0
\(142\) 18.1093 + 10.4554i 1.51970 + 0.877398i
\(143\) −17.2593 + 9.96465i −1.44329 + 0.833286i
\(144\) 0 0
\(145\) 3.93386 2.93153i 0.326689 0.243450i
\(146\) 8.06275 0.667278
\(147\) 0 0
\(148\) 5.03030i 0.413488i
\(149\) −4.04926 2.33784i −0.331728 0.191523i 0.324880 0.945755i \(-0.394676\pi\)
−0.656608 + 0.754232i \(0.728009\pi\)
\(150\) 0 0
\(151\) −0.930426 1.61155i −0.0757170 0.131146i 0.825681 0.564138i \(-0.190791\pi\)
−0.901398 + 0.432992i \(0.857458\pi\)
\(152\) 8.35196 + 4.82201i 0.677433 + 0.391116i
\(153\) 0 0
\(154\) 2.19799 + 38.2576i 0.177119 + 3.08289i
\(155\) −3.12773 1.34743i −0.251225 0.108228i
\(156\) 0 0
\(157\) −3.28398 5.68802i −0.262090 0.453953i 0.704707 0.709498i \(-0.251078\pi\)
−0.966797 + 0.255545i \(0.917745\pi\)
\(158\) 16.4505 + 28.4930i 1.30873 + 2.26678i
\(159\) 0 0
\(160\) 6.29365 14.6092i 0.497557 1.15496i
\(161\) 3.56616 7.08687i 0.281053 0.558524i
\(162\) 0 0
\(163\) −16.2598 9.38762i −1.27357 0.735295i −0.297910 0.954594i \(-0.596290\pi\)
−0.975658 + 0.219299i \(0.929623\pi\)
\(164\) −15.0028 25.9856i −1.17152 2.02914i
\(165\) 0 0
\(166\) −15.0696 8.70042i −1.16963 0.675284i
\(167\) 4.80581i 0.371884i 0.982561 + 0.185942i \(0.0595337\pi\)
−0.982561 + 0.185942i \(0.940466\pi\)
\(168\) 0 0
\(169\) −0.501166 −0.0385512
\(170\) −24.6135 + 18.3420i −1.88777 + 1.40677i
\(171\) 0 0
\(172\) −1.93729 + 1.11849i −0.147717 + 0.0852844i
\(173\) −2.91312 1.68189i −0.221480 0.127872i 0.385155 0.922852i \(-0.374148\pi\)
−0.606635 + 0.794980i \(0.707481\pi\)
\(174\) 0 0
\(175\) −3.04881 + 12.8726i −0.230469 + 0.973080i
\(176\) 44.9396i 3.38745i
\(177\) 0 0
\(178\) 13.2712 + 22.9863i 0.994715 + 1.72290i
\(179\) −9.63782 + 5.56440i −0.720365 + 0.415903i −0.814887 0.579620i \(-0.803201\pi\)
0.0945223 + 0.995523i \(0.469868\pi\)
\(180\) 0 0
\(181\) 2.19549i 0.163190i −0.996666 0.0815949i \(-0.973999\pi\)
0.996666 0.0815949i \(-0.0260014\pi\)
\(182\) 10.8030 21.4683i 0.800771 1.59134i
\(183\) 0 0
\(184\) −10.0223 + 17.3592i −0.738857 + 1.27974i
\(185\) 0.284911 + 2.42768i 0.0209471 + 0.178487i
\(186\) 0 0
\(187\) −15.0591 + 26.0831i −1.10123 + 1.90739i
\(188\) 19.5862i 1.42847i
\(189\) 0 0
\(190\) 7.61241 + 3.27943i 0.552262 + 0.237915i
\(191\) −8.62053 4.97707i −0.623760 0.360128i 0.154572 0.987982i \(-0.450600\pi\)
−0.778331 + 0.627854i \(0.783934\pi\)
\(192\) 0 0
\(193\) 21.6068 12.4747i 1.55529 0.897948i 0.557594 0.830114i \(-0.311725\pi\)
0.997697 0.0678339i \(-0.0216088\pi\)
\(194\) −18.9261 + 32.7810i −1.35882 + 2.35354i
\(195\) 0 0
\(196\) −19.1948 25.8681i −1.37105 1.84772i
\(197\) 19.1023 1.36098 0.680492 0.732755i \(-0.261766\pi\)
0.680492 + 0.732755i \(0.261766\pi\)
\(198\) 0 0
\(199\) 1.59632 0.921633i 0.113160 0.0653329i −0.442352 0.896842i \(-0.645856\pi\)
0.555512 + 0.831509i \(0.312522\pi\)
\(200\) 9.55586 32.0283i 0.675701 2.26474i
\(201\) 0 0
\(202\) 38.3701 2.69971
\(203\) 0.332956 + 5.79533i 0.0233689 + 0.406753i
\(204\) 0 0
\(205\) −8.71234 11.6912i −0.608496 0.816551i
\(206\) 5.02968 + 8.71167i 0.350435 + 0.606971i
\(207\) 0 0
\(208\) −14.0921 + 24.4083i −0.977114 + 1.69241i
\(209\) 8.13269 0.562550
\(210\) 0 0
\(211\) −9.77713 −0.673085 −0.336543 0.941668i \(-0.609258\pi\)
−0.336543 + 0.941668i \(0.609258\pi\)
\(212\) 9.25406 16.0285i 0.635571 1.10084i
\(213\) 0 0
\(214\) 19.0417 + 32.9811i 1.30166 + 2.25454i
\(215\) −0.871609 + 0.649526i −0.0594432 + 0.0442973i
\(216\) 0 0
\(217\) 3.36841 2.21164i 0.228663 0.150136i
\(218\) −28.3624 −1.92094
\(219\) 0 0
\(220\) −6.76093 57.6087i −0.455822 3.88398i
\(221\) 16.3583 9.44444i 1.10038 0.635302i
\(222\) 0 0
\(223\) 7.84782 0.525529 0.262765 0.964860i \(-0.415366\pi\)
0.262765 + 0.964860i \(0.415366\pi\)
\(224\) 10.3303 + 15.7334i 0.690220 + 1.05123i
\(225\) 0 0
\(226\) 9.69057 16.7846i 0.644607 1.11649i
\(227\) −0.475865 + 0.274741i −0.0315843 + 0.0182352i −0.515709 0.856764i \(-0.672471\pi\)
0.484125 + 0.874999i \(0.339138\pi\)
\(228\) 0 0
\(229\) −18.5833 10.7291i −1.22802 0.708998i −0.261406 0.965229i \(-0.584186\pi\)
−0.966616 + 0.256231i \(0.917519\pi\)
\(230\) −6.81617 + 15.8221i −0.449445 + 1.04328i
\(231\) 0 0
\(232\) 14.6665i 0.962902i
\(233\) 9.38319 16.2522i 0.614713 1.06471i −0.375722 0.926733i \(-0.622605\pi\)
0.990435 0.137982i \(-0.0440615\pi\)
\(234\) 0 0
\(235\) −1.10935 9.45256i −0.0723658 0.616617i
\(236\) −26.2746 + 45.5089i −1.71033 + 2.96238i
\(237\) 0 0
\(238\) −2.08325 36.2604i −0.135037 2.35041i
\(239\) 7.35866i 0.475992i 0.971266 + 0.237996i \(0.0764905\pi\)
−0.971266 + 0.237996i \(0.923509\pi\)
\(240\) 0 0
\(241\) 23.8467 13.7679i 1.53610 0.886868i 0.537040 0.843557i \(-0.319543\pi\)
0.999062 0.0433114i \(-0.0137908\pi\)
\(242\) −26.6921 46.2321i −1.71583 2.97191i
\(243\) 0 0
\(244\) 32.2511i 2.06466i
\(245\) −10.7288 11.3971i −0.685436 0.728133i
\(246\) 0 0
\(247\) −4.41715 2.55024i −0.281057 0.162268i
\(248\) −8.81704 + 5.09052i −0.559883 + 0.323248i
\(249\) 0 0
\(250\) 4.94842 28.2970i 0.312966 1.78966i
\(251\) 22.4204 1.41516 0.707582 0.706631i \(-0.249786\pi\)
0.707582 + 0.706631i \(0.249786\pi\)
\(252\) 0 0
\(253\) 16.9035i 1.06271i
\(254\) −8.76072 5.05801i −0.549697 0.317368i
\(255\) 0 0
\(256\) 12.9079 + 22.3571i 0.806743 + 1.39732i
\(257\) −14.8328 8.56373i −0.925246 0.534191i −0.0399409 0.999202i \(-0.512717\pi\)
−0.885305 + 0.465011i \(0.846050\pi\)
\(258\) 0 0
\(259\) −2.58353 1.30005i −0.160533 0.0807810i
\(260\) −14.3928 + 33.4094i −0.892604 + 2.07196i
\(261\) 0 0
\(262\) 5.07193 + 8.78483i 0.313345 + 0.542729i
\(263\) 0.808821 + 1.40092i 0.0498741 + 0.0863844i 0.889885 0.456186i \(-0.150785\pi\)
−0.840011 + 0.542570i \(0.817451\pi\)
\(264\) 0 0
\(265\) 3.55828 8.25969i 0.218583 0.507389i
\(266\) −8.19819 + 5.38278i −0.502664 + 0.330040i
\(267\) 0 0
\(268\) −9.92226 5.72862i −0.606099 0.349931i
\(269\) −5.84048 10.1160i −0.356101 0.616784i 0.631205 0.775616i \(-0.282561\pi\)
−0.987306 + 0.158832i \(0.949227\pi\)
\(270\) 0 0
\(271\) 5.05562 + 2.91886i 0.307107 + 0.177308i 0.645631 0.763649i \(-0.276594\pi\)
−0.338524 + 0.940958i \(0.609928\pi\)
\(272\) 42.5936i 2.58261i
\(273\) 0 0
\(274\) 14.5459 0.878748
\(275\) −6.52581 27.4197i −0.393521 1.65347i
\(276\) 0 0
\(277\) −14.3760 + 8.29998i −0.863770 + 0.498698i −0.865273 0.501301i \(-0.832855\pi\)
0.00150328 + 0.999999i \(0.499521\pi\)
\(278\) 51.8491 + 29.9351i 3.10970 + 1.79539i
\(279\) 0 0
\(280\) 25.4108 + 30.3030i 1.51858 + 1.81095i
\(281\) 20.4255i 1.21848i 0.792984 + 0.609242i \(0.208526\pi\)
−0.792984 + 0.609242i \(0.791474\pi\)
\(282\) 0 0
\(283\) 3.31643 + 5.74423i 0.197141 + 0.341459i 0.947600 0.319458i \(-0.103501\pi\)
−0.750459 + 0.660917i \(0.770168\pi\)
\(284\) 32.4333 18.7254i 1.92456 1.11115i
\(285\) 0 0
\(286\) 51.2058i 3.02786i
\(287\) 17.2234 0.989529i 1.01667 0.0584100i
\(288\) 0 0
\(289\) 5.77293 9.99901i 0.339584 0.588177i
\(290\) −1.46928 12.5195i −0.0862792 0.735170i
\(291\) 0 0
\(292\) 7.22008 12.5055i 0.422523 0.731832i
\(293\) 16.3716i 0.956437i −0.878241 0.478219i \(-0.841283\pi\)
0.878241 0.478219i \(-0.158717\pi\)
\(294\) 0 0
\(295\) −10.1028 + 23.4513i −0.588210 + 1.36539i
\(296\) 6.32832 + 3.65366i 0.367826 + 0.212365i
\(297\) 0 0
\(298\) −10.4040 + 6.00678i −0.602690 + 0.347963i
\(299\) 5.30058 9.18087i 0.306540 0.530944i
\(300\) 0 0
\(301\) −0.0737717 1.28405i −0.00425213 0.0740113i
\(302\) −4.78122 −0.275129
\(303\) 0 0
\(304\) 9.96047 5.75068i 0.571272 0.329824i
\(305\) −1.82667 15.5648i −0.104595 0.891235i
\(306\) 0 0
\(307\) 25.5071 1.45576 0.727882 0.685702i \(-0.240505\pi\)
0.727882 + 0.685702i \(0.240505\pi\)
\(308\) 61.3069 + 30.8500i 3.49329 + 1.75784i
\(309\) 0 0
\(310\) −7.01637 + 5.22862i −0.398503 + 0.296966i
\(311\) −15.5180 26.8780i −0.879946 1.52411i −0.851399 0.524519i \(-0.824245\pi\)
−0.0285476 0.999592i \(-0.509088\pi\)
\(312\) 0 0
\(313\) −7.52345 + 13.0310i −0.425251 + 0.736556i −0.996444 0.0842599i \(-0.973147\pi\)
0.571193 + 0.820816i \(0.306481\pi\)
\(314\) −16.8755 −0.952341
\(315\) 0 0
\(316\) 58.9247 3.31477
\(317\) −7.79061 + 13.4937i −0.437564 + 0.757884i −0.997501 0.0706518i \(-0.977492\pi\)
0.559937 + 0.828535i \(0.310825\pi\)
\(318\) 0 0
\(319\) −6.18404 10.7111i −0.346240 0.599705i
\(320\) −3.11867 4.18500i −0.174339 0.233949i
\(321\) 0 0
\(322\) −11.1879 17.0396i −0.623477 0.949581i
\(323\) −7.70812 −0.428891
\(324\) 0 0
\(325\) −5.05386 + 16.9390i −0.280338 + 0.939606i
\(326\) −41.7776 + 24.1203i −2.31385 + 1.33590i
\(327\) 0 0
\(328\) −43.5880 −2.40675
\(329\) 10.0594 + 5.06194i 0.554591 + 0.279074i
\(330\) 0 0
\(331\) −6.83411 + 11.8370i −0.375637 + 0.650622i −0.990422 0.138073i \(-0.955909\pi\)
0.614785 + 0.788694i \(0.289243\pi\)
\(332\) −26.9892 + 15.5822i −1.48123 + 0.855186i
\(333\) 0 0
\(334\) 10.6936 + 6.17395i 0.585128 + 0.337824i
\(335\) −5.11307 2.20271i −0.279357 0.120347i
\(336\) 0 0
\(337\) 22.8443i 1.24441i −0.782855 0.622204i \(-0.786237\pi\)
0.782855 0.622204i \(-0.213763\pi\)
\(338\) −0.643841 + 1.11516i −0.0350203 + 0.0606570i
\(339\) 0 0
\(340\) 6.40797 + 54.6012i 0.347521 + 2.96117i
\(341\) −4.29278 + 7.43531i −0.232467 + 0.402645i
\(342\) 0 0
\(343\) 18.2464 3.17287i 0.985216 0.171319i
\(344\) 3.24959i 0.175206i
\(345\) 0 0
\(346\) −7.48488 + 4.32140i −0.402390 + 0.232320i
\(347\) 9.81241 + 16.9956i 0.526758 + 0.912372i 0.999514 + 0.0311781i \(0.00992591\pi\)
−0.472756 + 0.881193i \(0.656741\pi\)
\(348\) 0 0
\(349\) 6.14050i 0.328693i −0.986403 0.164347i \(-0.947448\pi\)
0.986403 0.164347i \(-0.0525516\pi\)
\(350\) 24.7267 + 23.3213i 1.32170 + 1.24658i
\(351\) 0 0
\(352\) −34.7293 20.0510i −1.85108 1.06872i
\(353\) 20.7882 12.0021i 1.10644 0.638805i 0.168537 0.985695i \(-0.446096\pi\)
0.937906 + 0.346890i \(0.112762\pi\)
\(354\) 0 0
\(355\) 14.5921 10.8741i 0.774468 0.577136i
\(356\) 47.5366 2.51943
\(357\) 0 0
\(358\) 28.5940i 1.51124i
\(359\) −14.6798 8.47541i −0.774773 0.447315i 0.0598018 0.998210i \(-0.480953\pi\)
−0.834575 + 0.550895i \(0.814286\pi\)
\(360\) 0 0
\(361\) −8.45930 14.6519i −0.445227 0.771155i
\(362\) −4.88529 2.82052i −0.256765 0.148243i
\(363\) 0 0
\(364\) −23.6240 35.9803i −1.23824 1.88588i
\(365\) 2.77620 6.44427i 0.145313 0.337308i
\(366\) 0 0
\(367\) −17.5018 30.3140i −0.913587 1.58238i −0.808956 0.587869i \(-0.799967\pi\)
−0.104631 0.994511i \(-0.533366\pi\)
\(368\) 11.9526 + 20.7024i 0.623070 + 1.07919i
\(369\) 0 0
\(370\) 5.76796 + 2.48484i 0.299862 + 0.129181i
\(371\) 5.84048 + 8.89529i 0.303223 + 0.461820i
\(372\) 0 0
\(373\) −5.18881 2.99576i −0.268667 0.155115i 0.359615 0.933101i \(-0.382908\pi\)
−0.628282 + 0.777986i \(0.716241\pi\)
\(374\) 38.6924 + 67.0173i 2.00074 + 3.46538i
\(375\) 0 0
\(376\) −24.6403 14.2261i −1.27073 0.733655i
\(377\) 7.75675i 0.399493i
\(378\) 0 0
\(379\) −3.12842 −0.160696 −0.0803481 0.996767i \(-0.525603\pi\)
−0.0803481 + 0.996767i \(0.525603\pi\)
\(380\) 11.9033 8.87037i 0.610626 0.455040i
\(381\) 0 0
\(382\) −22.1494 + 12.7879i −1.13326 + 0.654288i
\(383\) −14.6929 8.48295i −0.750772 0.433459i 0.0752006 0.997168i \(-0.476040\pi\)
−0.825973 + 0.563710i \(0.809374\pi\)
\(384\) 0 0
\(385\) 31.3348 + 11.4162i 1.59697 + 0.581825i
\(386\) 64.1043i 3.26282i
\(387\) 0 0
\(388\) 33.8961 + 58.7099i 1.72082 + 2.98054i
\(389\) 0.389255 0.224737i 0.0197360 0.0113946i −0.490100 0.871666i \(-0.663040\pi\)
0.509836 + 0.860272i \(0.329706\pi\)
\(390\) 0 0
\(391\) 16.0210i 0.810218i
\(392\) −46.4849 + 5.35903i −2.34784 + 0.270672i
\(393\) 0 0
\(394\) 24.5405 42.5054i 1.23633 2.14139i
\(395\) 28.4378 3.33744i 1.43086 0.167925i
\(396\) 0 0
\(397\) −11.3663 + 19.6870i −0.570459 + 0.988064i 0.426060 + 0.904695i \(0.359901\pi\)
−0.996519 + 0.0833689i \(0.973432\pi\)
\(398\) 4.73604i 0.237396i
\(399\) 0 0
\(400\) −27.3811 28.9677i −1.36906 1.44839i
\(401\) −8.41308 4.85729i −0.420129 0.242562i 0.275004 0.961443i \(-0.411321\pi\)
−0.695132 + 0.718882i \(0.744654\pi\)
\(402\) 0 0
\(403\) 4.66312 2.69225i 0.232287 0.134111i
\(404\) 34.3599 59.5132i 1.70947 2.96089i
\(405\) 0 0
\(406\) 13.3232 + 6.70431i 0.661219 + 0.332729i
\(407\) 6.16218 0.305448
\(408\) 0 0
\(409\) 3.51628 2.03013i 0.173869 0.100383i −0.410540 0.911843i \(-0.634660\pi\)
0.584409 + 0.811459i \(0.301326\pi\)
\(410\) −37.2073 + 4.36663i −1.83754 + 0.215652i
\(411\) 0 0
\(412\) 18.0161 0.887587
\(413\) −16.5826 25.2559i −0.815976 1.24276i
\(414\) 0 0
\(415\) −12.1428 + 9.04882i −0.596064 + 0.444189i
\(416\) 12.5752 + 21.7808i 0.616548 + 1.06789i
\(417\) 0 0
\(418\) 10.4480 18.0964i 0.511026 0.885124i
\(419\) 20.9314 1.02257 0.511283 0.859412i \(-0.329170\pi\)
0.511283 + 0.859412i \(0.329170\pi\)
\(420\) 0 0
\(421\) −19.7795 −0.963992 −0.481996 0.876173i \(-0.660088\pi\)
−0.481996 + 0.876173i \(0.660088\pi\)
\(422\) −12.5605 + 21.7555i −0.611438 + 1.05904i
\(423\) 0 0
\(424\) −13.4430 23.2840i −0.652851 1.13077i
\(425\) 6.18513 + 25.9883i 0.300023 + 1.26062i
\(426\) 0 0
\(427\) 16.5639 + 8.33508i 0.801585 + 0.403363i
\(428\) 68.2062 3.29687
\(429\) 0 0
\(430\) 0.325542 + 2.77389i 0.0156991 + 0.133769i
\(431\) −9.23148 + 5.32980i −0.444665 + 0.256727i −0.705574 0.708636i \(-0.749311\pi\)
0.260910 + 0.965363i \(0.415978\pi\)
\(432\) 0 0
\(433\) −21.2351 −1.02050 −0.510248 0.860028i \(-0.670446\pi\)
−0.510248 + 0.860028i \(0.670446\pi\)
\(434\) −0.593855 10.3365i −0.0285060 0.496166i
\(435\) 0 0
\(436\) −25.3981 + 43.9908i −1.21635 + 2.10678i
\(437\) −3.74650 + 2.16304i −0.179220 + 0.103472i
\(438\) 0 0
\(439\) 18.5707 + 10.7218i 0.886333 + 0.511725i 0.872741 0.488183i \(-0.162340\pi\)
0.0135918 + 0.999908i \(0.495673\pi\)
\(440\) −77.3849 33.3375i −3.68918 1.58930i
\(441\) 0 0
\(442\) 48.5326i 2.30846i
\(443\) 0.0854851 0.148064i 0.00406152 0.00703475i −0.863988 0.503513i \(-0.832041\pi\)
0.868049 + 0.496478i \(0.165374\pi\)
\(444\) 0 0
\(445\) 22.9417 2.69243i 1.08754 0.127633i
\(446\) 10.0820 17.4625i 0.477396 0.826874i
\(447\) 0 0
\(448\) 6.16531 0.354212i 0.291283 0.0167350i
\(449\) 9.38752i 0.443025i 0.975158 + 0.221512i \(0.0710993\pi\)
−0.975158 + 0.221512i \(0.928901\pi\)
\(450\) 0 0
\(451\) −31.8328 + 18.3786i −1.49895 + 0.865417i
\(452\) −17.3556 30.0607i −0.816337 1.41394i
\(453\) 0 0
\(454\) 1.41182i 0.0662602i
\(455\) −13.4391 16.0265i −0.630036 0.751334i
\(456\) 0 0
\(457\) 14.6293 + 8.44623i 0.684330 + 0.395098i 0.801484 0.598016i \(-0.204044\pi\)
−0.117155 + 0.993114i \(0.537377\pi\)
\(458\) −47.7475 + 27.5670i −2.23110 + 1.28812i
\(459\) 0 0
\(460\) 18.4367 + 24.7405i 0.859616 + 1.15353i
\(461\) −31.0360 −1.44549 −0.722746 0.691113i \(-0.757120\pi\)
−0.722746 + 0.691113i \(0.757120\pi\)
\(462\) 0 0
\(463\) 11.9434i 0.555055i −0.960718 0.277528i \(-0.910485\pi\)
0.960718 0.277528i \(-0.0895150\pi\)
\(464\) −15.1477 8.74555i −0.703216 0.406002i
\(465\) 0 0
\(466\) −24.1089 41.7579i −1.11682 1.93440i
\(467\) −29.9304 17.2803i −1.38501 0.799638i −0.392265 0.919852i \(-0.628308\pi\)
−0.992748 + 0.120215i \(0.961642\pi\)
\(468\) 0 0
\(469\) 5.50653 3.61549i 0.254268 0.166948i
\(470\) −22.4584 9.67512i −1.03593 0.446280i
\(471\) 0 0
\(472\) 38.1681 + 66.1090i 1.75683 + 3.04292i
\(473\) 1.37017 + 2.37321i 0.0630006 + 0.109120i
\(474\) 0 0
\(475\) 5.24227 4.95514i 0.240532 0.227357i
\(476\) −58.1064 29.2395i −2.66330 1.34019i
\(477\) 0 0
\(478\) 16.3741 + 9.45357i 0.748932 + 0.432396i
\(479\) 1.48615 + 2.57409i 0.0679040 + 0.117613i 0.897978 0.440039i \(-0.145036\pi\)
−0.830074 + 0.557653i \(0.811702\pi\)
\(480\) 0 0
\(481\) −3.34690 1.93233i −0.152605 0.0881068i
\(482\) 70.7498i 3.22256i
\(483\) 0 0
\(484\) −95.6097 −4.34589
\(485\) 19.6840 + 26.4142i 0.893803 + 1.19941i
\(486\) 0 0
\(487\) −19.6695 + 11.3562i −0.891310 + 0.514598i −0.874371 0.485258i \(-0.838726\pi\)
−0.0169394 + 0.999857i \(0.505392\pi\)
\(488\) −40.5732 23.4249i −1.83666 1.06040i
\(489\) 0 0
\(490\) −39.1432 + 9.23138i −1.76831 + 0.417031i
\(491\) 13.0036i 0.586846i −0.955983 0.293423i \(-0.905206\pi\)
0.955983 0.293423i \(-0.0947944\pi\)
\(492\) 0 0
\(493\) 5.86120 + 10.1519i 0.263975 + 0.457219i
\(494\) −11.3493 + 6.55253i −0.510630 + 0.294812i
\(495\) 0 0
\(496\) 12.1418i 0.545184i
\(497\) 1.23505 + 21.4970i 0.0553997 + 0.964271i
\(498\) 0 0
\(499\) 10.8039 18.7129i 0.483648 0.837702i −0.516176 0.856483i \(-0.672645\pi\)
0.999824 + 0.0187802i \(0.00597826\pi\)
\(500\) −39.4583 33.0148i −1.76463 1.47647i
\(501\) 0 0
\(502\) 28.8032 49.8886i 1.28555 2.22664i
\(503\) 32.4125i 1.44520i 0.691265 + 0.722601i \(0.257054\pi\)
−0.691265 + 0.722601i \(0.742946\pi\)
\(504\) 0 0
\(505\) 13.2118 30.6679i 0.587915 1.36470i
\(506\) 37.6126 + 21.7157i 1.67209 + 0.965379i
\(507\) 0 0
\(508\) −15.6902 + 9.05875i −0.696141 + 0.401917i
\(509\) 18.2802 31.6622i 0.810255 1.40340i −0.102430 0.994740i \(-0.532662\pi\)
0.912685 0.408663i \(-0.134005\pi\)
\(510\) 0 0
\(511\) 4.55679 + 6.94017i 0.201580 + 0.307015i
\(512\) 49.8691 2.20392
\(513\) 0 0
\(514\) −38.1110 + 22.0034i −1.68101 + 0.970529i
\(515\) 8.69477 1.02041i 0.383137 0.0449648i
\(516\) 0 0
\(517\) −23.9934 −1.05523
\(518\) −6.21181 + 4.07856i −0.272931 + 0.179202i
\(519\) 0 0
\(520\) 31.5765 + 42.3731i 1.38472 + 1.85818i
\(521\) 9.43608 + 16.3438i 0.413402 + 0.716033i 0.995259 0.0972577i \(-0.0310071\pi\)
−0.581857 + 0.813291i \(0.697674\pi\)
\(522\) 0 0
\(523\) 14.1124 24.4434i 0.617092 1.06884i −0.372921 0.927863i \(-0.621644\pi\)
0.990014 0.140972i \(-0.0450229\pi\)
\(524\) 18.1674 0.793645
\(525\) 0 0
\(526\) 4.15633 0.181225
\(527\) 4.06867 7.04715i 0.177234 0.306979i
\(528\) 0 0
\(529\) 7.00420 + 12.1316i 0.304530 + 0.527462i
\(530\) −13.8077 18.5288i −0.599769 0.804839i
\(531\) 0 0
\(532\) 1.00748 + 17.5358i 0.0436797 + 0.760275i
\(533\) 23.0527 0.998521
\(534\) 0 0
\(535\) 32.9172 3.86314i 1.42313 0.167018i
\(536\) −14.4137 + 8.32175i −0.622577 + 0.359445i
\(537\) 0 0
\(538\) −30.0128 −1.29394
\(539\) −31.6888 + 23.5139i −1.36493 + 1.01281i
\(540\) 0 0
\(541\) −14.2269 + 24.6417i −0.611661 + 1.05943i 0.379299 + 0.925274i \(0.376165\pi\)
−0.990960 + 0.134154i \(0.957168\pi\)
\(542\) 12.9898 7.49965i 0.557959 0.322138i
\(543\) 0 0
\(544\) 32.9163 + 19.0042i 1.41127 + 0.814799i
\(545\) −9.76584 + 22.6690i −0.418323 + 0.971035i
\(546\) 0 0
\(547\) 21.9338i 0.937820i 0.883246 + 0.468910i \(0.155353\pi\)
−0.883246 + 0.468910i \(0.844647\pi\)
\(548\) 13.0256 22.5610i 0.556427 0.963760i
\(549\) 0 0
\(550\) −69.3965 20.7049i −2.95907 0.882860i
\(551\) 1.58268 2.74127i 0.0674242 0.116782i
\(552\) 0 0
\(553\) −15.2287 + 30.2633i −0.647590 + 1.28693i
\(554\) 42.6515i 1.81209i
\(555\) 0 0
\(556\) 92.8603 53.6129i 3.93815 2.27369i
\(557\) 12.2168 + 21.1601i 0.517643 + 0.896583i 0.999790 + 0.0204933i \(0.00652367\pi\)
−0.482147 + 0.876090i \(0.660143\pi\)
\(558\) 0 0
\(559\) 1.71863i 0.0726903i
\(560\) 46.4496 8.17507i 1.96285 0.345460i
\(561\) 0 0
\(562\) 45.4497 + 26.2404i 1.91718 + 1.10688i
\(563\) −18.4585 + 10.6570i −0.777932 + 0.449139i −0.835697 0.549191i \(-0.814936\pi\)
0.0577647 + 0.998330i \(0.481603\pi\)
\(564\) 0 0
\(565\) −10.0786 13.5247i −0.424010 0.568987i
\(566\) 17.0423 0.716341
\(567\) 0 0
\(568\) 54.4032i 2.28271i
\(569\) 24.1707 + 13.9549i 1.01329 + 0.585022i 0.912152 0.409851i \(-0.134419\pi\)
0.101135 + 0.994873i \(0.467753\pi\)
\(570\) 0 0
\(571\) 23.1936 + 40.1725i 0.970622 + 1.68117i 0.693685 + 0.720279i \(0.255986\pi\)
0.276937 + 0.960888i \(0.410681\pi\)
\(572\) 79.4217 + 45.8541i 3.32079 + 1.91726i
\(573\) 0 0
\(574\) 19.9249 39.5958i 0.831648 1.65270i
\(575\) 10.2991 + 10.8958i 0.429501 + 0.454388i
\(576\) 0 0
\(577\) −16.2167 28.0881i −0.675108 1.16932i −0.976437 0.215801i \(-0.930764\pi\)
0.301329 0.953520i \(-0.402570\pi\)
\(578\) −14.8328 25.6912i −0.616964 1.06861i
\(579\) 0 0
\(580\) −20.7338 8.93214i −0.860925 0.370887i
\(581\) −1.02774 17.8886i −0.0426380 0.742145i
\(582\) 0 0
\(583\) −19.6351 11.3363i −0.813204 0.469504i
\(584\) −10.4883 18.1663i −0.434011 0.751728i
\(585\) 0 0
\(586\) −36.4291 21.0323i −1.50487 0.868838i
\(587\) 0.790380i 0.0326225i −0.999867 0.0163112i \(-0.994808\pi\)
0.999867 0.0163112i \(-0.00519226\pi\)
\(588\) 0 0
\(589\) −2.19729 −0.0905379
\(590\) 39.2035 + 52.6079i 1.61398 + 2.16583i
\(591\) 0 0
\(592\) 7.54710 4.35732i 0.310184 0.179085i
\(593\) 17.5672 + 10.1424i 0.721397 + 0.416499i 0.815267 0.579086i \(-0.196590\pi\)
−0.0938695 + 0.995585i \(0.529924\pi\)
\(594\) 0 0
\(595\) −29.6989 10.8202i −1.21754 0.443587i
\(596\) 21.5160i 0.881328i
\(597\) 0 0
\(598\) −13.6192 23.5891i −0.556929 0.964630i
\(599\) −8.77781 + 5.06787i −0.358652 + 0.207068i −0.668489 0.743722i \(-0.733059\pi\)
0.309837 + 0.950790i \(0.399725\pi\)
\(600\) 0 0
\(601\) 35.6657i 1.45483i 0.686196 + 0.727417i \(0.259279\pi\)
−0.686196 + 0.727417i \(0.740721\pi\)
\(602\) −2.95196 1.48545i −0.120313 0.0605423i
\(603\) 0 0
\(604\) −4.28152 + 7.41581i −0.174213 + 0.301745i
\(605\) −46.1424 + 5.41525i −1.87596 + 0.220161i
\(606\) 0 0
\(607\) −13.1333 + 22.7475i −0.533063 + 0.923292i 0.466192 + 0.884684i \(0.345626\pi\)
−0.999254 + 0.0386080i \(0.987708\pi\)
\(608\) 10.2633i 0.416230i
\(609\) 0 0
\(610\) −36.9805 15.9312i −1.49730 0.645036i
\(611\) 13.0317 + 7.52384i 0.527205 + 0.304382i
\(612\) 0 0
\(613\) 22.4144 12.9410i 0.905310 0.522681i 0.0263906 0.999652i \(-0.491599\pi\)
0.878919 + 0.476971i \(0.158265\pi\)
\(614\) 32.7686 56.7568i 1.32243 2.29052i
\(615\) 0 0
\(616\) 83.3398 54.7194i 3.35786 2.20471i
\(617\) −16.1754 −0.651198 −0.325599 0.945508i \(-0.605566\pi\)
−0.325599 + 0.945508i \(0.605566\pi\)
\(618\) 0 0
\(619\) 5.29108 3.05481i 0.212667 0.122783i −0.389883 0.920864i \(-0.627485\pi\)
0.602550 + 0.798081i \(0.294151\pi\)
\(620\) 1.82667 + 15.5648i 0.0733609 + 0.625095i
\(621\) 0 0
\(622\) −79.7432 −3.19741
\(623\) −12.2855 + 24.4145i −0.492209 + 0.978145i
\(624\) 0 0
\(625\) −20.9130 13.6984i −0.836519 0.547938i
\(626\) 19.3306 + 33.4815i 0.772605 + 1.33819i
\(627\) 0 0
\(628\) −15.1118 + 26.1744i −0.603027 + 1.04447i
\(629\) −5.84048 −0.232875
\(630\) 0 0
\(631\) 1.89949 0.0756174 0.0378087 0.999285i \(-0.487962\pi\)
0.0378087 + 0.999285i \(0.487962\pi\)
\(632\) 42.7988 74.1297i 1.70245 2.94872i
\(633\) 0 0
\(634\) 20.0170 + 34.6704i 0.794976 + 1.37694i
\(635\) −7.05921 + 5.26055i −0.280136 + 0.208758i
\(636\) 0 0
\(637\) 24.5847 2.83426i 0.974083 0.112298i
\(638\) −31.7782 −1.25811
\(639\) 0 0
\(640\) 18.2788 2.14519i 0.722532 0.0847960i
\(641\) 9.82533 5.67266i 0.388077 0.224057i −0.293249 0.956036i \(-0.594737\pi\)
0.681327 + 0.731979i \(0.261403\pi\)
\(642\) 0 0
\(643\) 18.2255 0.718742 0.359371 0.933195i \(-0.382991\pi\)
0.359371 + 0.933195i \(0.382991\pi\)
\(644\) −36.4476 + 2.09400i −1.43623 + 0.0825152i
\(645\) 0 0
\(646\) −9.90252 + 17.1517i −0.389609 + 0.674823i
\(647\) 21.2533 12.2706i 0.835552 0.482406i −0.0201980 0.999796i \(-0.506430\pi\)
0.855750 + 0.517390i \(0.173096\pi\)
\(648\) 0 0
\(649\) 55.7490 + 32.1867i 2.18834 + 1.26344i
\(650\) 31.1990 + 33.0069i 1.22373 + 1.29464i
\(651\) 0 0
\(652\) 86.3976i 3.38359i
\(653\) −4.37656 + 7.58043i −0.171268 + 0.296645i −0.938863 0.344290i \(-0.888120\pi\)
0.767595 + 0.640935i \(0.221453\pi\)
\(654\) 0 0
\(655\) 8.76779 1.02898i 0.342586 0.0402057i
\(656\) −25.9913 + 45.0183i −1.01479 + 1.75767i
\(657\) 0 0
\(658\) 24.1867 15.8805i 0.942894 0.619087i
\(659\) 2.51324i 0.0979020i −0.998801 0.0489510i \(-0.984412\pi\)
0.998801 0.0489510i \(-0.0155878\pi\)
\(660\) 0 0
\(661\) −34.5393 + 19.9413i −1.34342 + 0.775626i −0.987308 0.158815i \(-0.949233\pi\)
−0.356116 + 0.934442i \(0.615899\pi\)
\(662\) 17.5594 + 30.4137i 0.682465 + 1.18206i
\(663\) 0 0
\(664\) 45.2714i 1.75687i
\(665\) 1.47944 + 8.40595i 0.0573700 + 0.325969i
\(666\) 0 0
\(667\) 5.69763 + 3.28953i 0.220613 + 0.127371i
\(668\) 19.1520 11.0574i 0.741011 0.427823i
\(669\) 0 0
\(670\) −11.4700 + 8.54751i −0.443127 + 0.330219i
\(671\) −39.5080 −1.52519
\(672\) 0 0
\(673\) 36.0634i 1.39014i −0.718941 0.695071i \(-0.755373\pi\)
0.718941 0.695071i \(-0.244627\pi\)
\(674\) −50.8318 29.3478i −1.95797 1.13043i
\(675\) 0 0
\(676\) 1.15310 + 1.99723i 0.0443501 + 0.0768166i
\(677\) −6.84487 3.95189i −0.263070 0.151883i 0.362664 0.931920i \(-0.381867\pi\)
−0.625734 + 0.780036i \(0.715200\pi\)
\(678\) 0 0
\(679\) −38.9132 + 2.23566i −1.49335 + 0.0857968i
\(680\) 73.3450 + 31.5971i 2.81265 + 1.21169i
\(681\) 0 0
\(682\) 11.0298 + 19.1041i 0.422351 + 0.731534i
\(683\) 12.6430 + 21.8984i 0.483772 + 0.837918i 0.999826 0.0186377i \(-0.00593291\pi\)
−0.516054 + 0.856556i \(0.672600\pi\)
\(684\) 0 0
\(685\) 5.00849 11.6260i 0.191365 0.444206i
\(686\) 16.3809 44.6771i 0.625425 1.70578i
\(687\) 0 0
\(688\) 3.35622 + 1.93772i 0.127955 + 0.0738747i
\(689\) 7.10969 + 12.3143i 0.270858 + 0.469139i
\(690\) 0 0
\(691\) −13.1380 7.58522i −0.499792 0.288555i 0.228835 0.973465i \(-0.426508\pi\)
−0.728628 + 0.684910i \(0.759842\pi\)
\(692\) 15.4790i 0.588424i
\(693\) 0 0
\(694\) 50.4235 1.91405
\(695\) 41.7789 31.1338i 1.58476 1.18097i
\(696\) 0 0
\(697\) 30.1709 17.4192i 1.14280 0.659799i
\(698\) −13.6635 7.88861i −0.517170 0.298588i
\(699\) 0 0
\(700\) 58.3145 17.4678i 2.20408 0.660222i
\(701\) 34.6815i 1.30990i −0.755671 0.654951i \(-0.772689\pi\)
0.755671 0.654951i \(-0.227311\pi\)
\(702\) 0 0
\(703\) 0.788541 + 1.36579i 0.0297404 + 0.0515118i
\(704\) −11.3949 + 6.57883i −0.429460 + 0.247949i
\(705\) 0 0
\(706\) 61.6755i 2.32119i
\(707\) 21.6855 + 33.0278i 0.815566 + 1.24214i
\(708\) 0 0
\(709\) −17.2311 + 29.8451i −0.647126 + 1.12086i 0.336680 + 0.941619i \(0.390696\pi\)
−0.983806 + 0.179237i \(0.942637\pi\)
\(710\) −5.45009 46.4393i −0.204538 1.74284i
\(711\) 0 0
\(712\) 34.5273 59.8030i 1.29396 2.24121i
\(713\) 4.56699i 0.171035i
\(714\) 0 0
\(715\) 40.9270 + 17.6314i 1.53058 + 0.659376i
\(716\) 44.3502 + 25.6056i 1.65744 + 0.956925i
\(717\) 0 0
\(718\) −37.7180 + 21.7765i −1.40762 + 0.812692i
\(719\) −13.4825 + 23.3523i −0.502812 + 0.870895i 0.497183 + 0.867646i \(0.334368\pi\)
−0.999995 + 0.00324951i \(0.998966\pi\)
\(720\) 0 0
\(721\) −4.65613 + 9.25293i −0.173403 + 0.344597i
\(722\) −43.4702 −1.61779
\(723\) 0 0
\(724\) −8.74942 + 5.05148i −0.325170 + 0.187737i
\(725\) −10.5123 3.13642i −0.390417 0.116484i
\(726\) 0 0
\(727\) −10.4196 −0.386442 −0.193221 0.981155i \(-0.561894\pi\)
−0.193221 + 0.981155i \(0.561894\pi\)
\(728\) −62.4236 + 3.58639i −2.31357 + 0.132921i
\(729\) 0 0
\(730\) −10.7729 14.4563i −0.398722 0.535052i
\(731\) −1.29864 2.24931i −0.0480320 0.0831938i
\(732\) 0 0
\(733\) −11.3541 + 19.6659i −0.419374 + 0.726377i −0.995877 0.0907181i \(-0.971084\pi\)
0.576503 + 0.817095i \(0.304417\pi\)
\(734\) −89.9374 −3.31965
\(735\) 0 0
\(736\) 21.3318 0.786300
\(737\) −7.01764 + 12.1549i −0.258498 + 0.447732i
\(738\) 0 0
\(739\) −14.8897 25.7898i −0.547728 0.948692i −0.998430 0.0560176i \(-0.982160\pi\)
0.450702 0.892674i \(-0.351174\pi\)
\(740\) 9.01919 6.72113i 0.331552 0.247074i
\(741\) 0 0
\(742\) 27.2965 1.56825i 1.00209 0.0575723i
\(743\) −34.8044 −1.27685 −0.638424 0.769684i \(-0.720414\pi\)
−0.638424 + 0.769684i \(0.720414\pi\)
\(744\) 0 0
\(745\) 1.21865 + 10.3839i 0.0446477 + 0.380435i
\(746\) −13.3320 + 7.69723i −0.488119 + 0.281816i
\(747\) 0 0
\(748\) 138.594 5.06751
\(749\) −17.6275 + 35.0303i −0.644093 + 1.27998i
\(750\) 0 0
\(751\) −3.74522 + 6.48691i −0.136665 + 0.236711i −0.926232 0.376953i \(-0.876972\pi\)
0.789567 + 0.613664i \(0.210305\pi\)
\(752\) −29.3858 + 16.9659i −1.07159 + 0.618683i
\(753\) 0 0
\(754\) 17.2599 + 9.96499i 0.628568 + 0.362904i
\(755\) −1.64629 + 3.82146i −0.0599146 + 0.139077i
\(756\) 0 0
\(757\) 2.66139i 0.0967300i −0.998830 0.0483650i \(-0.984599\pi\)
0.998830 0.0483650i \(-0.0154011\pi\)
\(758\) −4.01904 + 6.96118i −0.145978 + 0.252842i
\(759\) 0 0
\(760\) −2.51357 21.4177i −0.0911767 0.776901i
\(761\) 2.78479 4.82340i 0.100949 0.174848i −0.811127 0.584870i \(-0.801146\pi\)
0.912076 + 0.410022i \(0.134479\pi\)
\(762\) 0 0
\(763\) −16.0294 24.4135i −0.580304 0.883827i
\(764\) 45.8057i 1.65719i
\(765\) 0 0
\(766\) −37.7516 + 21.7959i −1.36402 + 0.787517i
\(767\) −20.1862 34.9635i −0.728881 1.26246i
\(768\) 0 0
\(769\) 11.5002i 0.414709i 0.978266 + 0.207355i \(0.0664854\pi\)
−0.978266 + 0.207355i \(0.933515\pi\)
\(770\) 65.6581 55.0581i 2.36615 1.98416i
\(771\) 0 0
\(772\) −99.4275 57.4045i −3.57847 2.06603i
\(773\) 21.9748 12.6872i 0.790378 0.456325i −0.0497174 0.998763i \(-0.515832\pi\)
0.840096 + 0.542438i \(0.182499\pi\)
\(774\) 0 0
\(775\) 1.76315 + 7.40828i 0.0633341 + 0.266113i
\(776\) 98.4793 3.53520
\(777\) 0 0
\(778\) 1.15486i 0.0414039i
\(779\) −8.14692 4.70363i −0.291894 0.168525i
\(780\) 0 0
\(781\) −22.9388 39.7312i −0.820816 1.42169i
\(782\) −35.6491 20.5820i −1.27481 0.736011i
\(783\) 0 0
\(784\) −22.1838 + 51.2058i −0.792280 + 1.82878i
\(785\) −5.81065 + 13.4880i −0.207391 + 0.481408i
\(786\) 0 0
\(787\) −11.9967 20.7789i −0.427636 0.740688i 0.569026 0.822319i \(-0.307320\pi\)
−0.996663 + 0.0816315i \(0.973987\pi\)
\(788\) −43.9514 76.1260i −1.56570 2.71188i
\(789\) 0 0
\(790\) 29.1073 67.5656i 1.03559 2.40388i
\(791\) 19.9244 1.14471i 0.708431 0.0407011i
\(792\) 0 0
\(793\) 21.4582 + 12.3889i 0.762002 + 0.439942i
\(794\) 29.2043 + 50.5833i 1.03642 + 1.79514i
\(795\) 0 0
\(796\) −7.34573 4.24106i −0.260363 0.150320i
\(797\) 28.1188i 0.996020i −0.867171 0.498010i \(-0.834064\pi\)
0.867171 0.498010i \(-0.165936\pi\)
\(798\) 0 0
\(799\) 22.7408 0.804513
\(800\) −34.6031 + 8.23542i −1.22340 + 0.291166i
\(801\) 0 0
\(802\) −21.6163 + 12.4802i −0.763299 + 0.440691i
\(803\) −15.3195 8.84470i −0.540612 0.312123i
\(804\) 0 0
\(805\) −17.4714 + 3.07495i −0.615787 + 0.108378i
\(806\) 13.8348i 0.487310i
\(807\) 0 0
\(808\) −49.9134 86.4525i −1.75595 3.04139i
\(809\) −24.2977 + 14.0283i −0.854263 + 0.493209i −0.862087 0.506761i \(-0.830843\pi\)
0.00782425 + 0.999969i \(0.497509\pi\)
\(810\) 0 0
\(811\) 43.4980i 1.52742i −0.645559 0.763710i \(-0.723376\pi\)
0.645559 0.763710i \(-0.276624\pi\)
\(812\) 22.3293 14.6610i 0.783605 0.514501i
\(813\) 0 0
\(814\) 7.91647 13.7117i 0.277472 0.480596i
\(815\) 4.89348 + 41.6965i 0.171411 + 1.46057i
\(816\) 0 0
\(817\) −0.350667 + 0.607373i −0.0122683 + 0.0212493i
\(818\) 10.4323i 0.364757i
\(819\) 0 0
\(820\) −26.5459 + 61.6198i −0.927022 + 2.15186i
\(821\) −31.5875 18.2371i −1.10241 0.636477i −0.165558 0.986200i \(-0.552942\pi\)
−0.936853 + 0.349723i \(0.886276\pi\)
\(822\) 0 0
\(823\) −39.9277 + 23.0523i −1.39179 + 0.803551i −0.993514 0.113713i \(-0.963725\pi\)
−0.398278 + 0.917265i \(0.630392\pi\)
\(824\) 13.0856 22.6650i 0.455859 0.789571i
\(825\) 0 0
\(826\) −77.5015 + 4.45265i −2.69662 + 0.154928i
\(827\) −20.1533 −0.700800 −0.350400 0.936600i \(-0.613954\pi\)
−0.350400 + 0.936600i \(0.613954\pi\)
\(828\) 0 0
\(829\) 6.13818 3.54388i 0.213188 0.123084i −0.389604 0.920982i \(-0.627388\pi\)
0.602792 + 0.797898i \(0.294055\pi\)
\(830\) 4.53527 + 38.6443i 0.157422 + 1.34136i
\(831\) 0 0
\(832\) 8.25194 0.286085
\(833\) 30.0344 22.2863i 1.04063 0.772175i
\(834\) 0 0
\(835\) 8.61669 6.42118i 0.298193 0.222214i
\(836\) −18.7120 32.4102i −0.647169 1.12093i
\(837\) 0 0
\(838\) 26.8903 46.5754i 0.928911 1.60892i
\(839\) 33.0805 1.14206 0.571032 0.820928i \(-0.306543\pi\)
0.571032 + 0.820928i \(0.306543\pi\)
\(840\) 0 0
\(841\) 24.1862 0.834006
\(842\) −25.4104 + 44.0121i −0.875701 + 1.51676i
\(843\) 0 0
\(844\) 22.4956 + 38.9635i 0.774331 + 1.34118i
\(845\) 0.669622 + 0.898577i 0.0230357 + 0.0309120i
\(846\) 0 0
\(847\) 24.7097 49.1045i 0.849036 1.68725i
\(848\) −32.0640 −1.10108
\(849\) 0 0
\(850\) 65.7736 + 19.6240i 2.25602 + 0.673098i
\(851\) −2.83875 + 1.63895i −0.0973109 + 0.0561825i
\(852\) 0 0
\(853\) 38.1187 1.30516 0.652580 0.757719i \(-0.273686\pi\)
0.652580 + 0.757719i \(0.273686\pi\)
\(854\) 39.8262 26.1492i 1.36282 0.894806i
\(855\) 0 0
\(856\) 49.5403 85.8063i 1.69325 2.93280i
\(857\) 6.09347 3.51807i 0.208149 0.120175i −0.392302 0.919837i \(-0.628321\pi\)
0.600451 + 0.799662i \(0.294988\pi\)
\(858\) 0 0
\(859\) 22.2343 + 12.8370i 0.758624 + 0.437992i 0.828802 0.559543i \(-0.189023\pi\)
−0.0701772 + 0.997535i \(0.522356\pi\)
\(860\) 4.59390 + 1.97906i 0.156651 + 0.0674853i
\(861\) 0 0
\(862\) 27.3885i 0.932855i
\(863\) 25.4929 44.1550i 0.867788 1.50305i 0.00353683 0.999994i \(-0.498874\pi\)
0.864252 0.503060i \(-0.167792\pi\)
\(864\) 0 0
\(865\) 0.876718 + 7.47036i 0.0298093 + 0.254000i
\(866\) −27.2805 + 47.2512i −0.927029 + 1.60566i
\(867\) 0 0
\(868\) −16.5639 8.33508i −0.562217 0.282911i
\(869\) 72.1835i 2.44866i
\(870\) 0 0
\(871\) 7.62306 4.40117i 0.258297 0.149128i
\(872\) 36.8949 + 63.9038i 1.24942 + 2.16406i
\(873\) 0 0
\(874\) 11.1153i 0.375982i
\(875\) 27.1539 11.7331i 0.917970 0.396650i
\(876\) 0 0
\(877\) 33.3881 + 19.2766i 1.12743 + 0.650925i 0.943289 0.331974i \(-0.107715\pi\)
0.184146 + 0.982899i \(0.441048\pi\)
\(878\) 47.7152 27.5484i 1.61031 0.929712i
\(879\) 0 0
\(880\) −80.5756 + 60.0452i −2.71620 + 2.02412i
\(881\) −34.4764 −1.16154 −0.580770 0.814068i \(-0.697248\pi\)
−0.580770 + 0.814068i \(0.697248\pi\)
\(882\) 0 0
\(883\) 25.5869i 0.861068i 0.902574 + 0.430534i \(0.141675\pi\)
−0.902574 + 0.430534i \(0.858325\pi\)
\(884\) −75.2754 43.4603i −2.53179 1.46173i
\(885\) 0 0
\(886\) −0.219643 0.380433i −0.00737905 0.0127809i
\(887\) 20.6076 + 11.8978i 0.691936 + 0.399489i 0.804337 0.594174i \(-0.202521\pi\)
−0.112401 + 0.993663i \(0.535854\pi\)
\(888\) 0 0
\(889\) −0.597481 10.3996i −0.0200389 0.348791i
\(890\) 23.4819 54.5075i 0.787114 1.82710i
\(891\) 0 0
\(892\) −18.0566 31.2749i −0.604579 1.04716i
\(893\) −3.07031 5.31792i −0.102744 0.177958i
\(894\) 0 0
\(895\) 22.8542 + 9.84561i 0.763932 + 0.329102i
\(896\) −9.78847 + 19.4522i −0.327010 + 0.649852i
\(897\) 0 0
\(898\) 20.8886 + 12.0600i 0.697061 + 0.402448i
\(899\) 1.67081 + 2.89392i 0.0557245 + 0.0965177i
\(900\) 0 0
\(901\) 18.6101 + 10.7445i 0.619991 + 0.357952i
\(902\) 94.4432i 3.14461i
\(903\) 0 0
\(904\) −50.4235 −1.67706
\(905\) −3.93646 + 2.93346i −0.130852 + 0.0975116i
\(906\) 0 0
\(907\) 33.5806 19.3878i 1.11503 0.643760i 0.174899 0.984586i \(-0.444040\pi\)
0.940126 + 0.340826i \(0.110707\pi\)
\(908\) 2.18978 + 1.26427i 0.0726704 + 0.0419563i
\(909\) 0 0
\(910\) −52.9263 + 9.31496i −1.75449 + 0.308788i
\(911\) 31.4438i 1.04178i −0.853624 0.520889i \(-0.825600\pi\)
0.853624 0.520889i \(-0.174400\pi\)
\(912\) 0 0
\(913\) 19.0884 + 33.0622i 0.631735 + 1.09420i
\(914\) 37.5881 21.7015i 1.24330 0.717822i
\(915\) 0 0
\(916\) 98.7437i 3.26258i
\(917\) −4.69524 + 9.33064i −0.155050 + 0.308125i
\(918\) 0 0
\(919\) −13.9872 + 24.2266i −0.461396 + 0.799161i −0.999031 0.0440170i \(-0.985984\pi\)
0.537635 + 0.843178i \(0.319318\pi\)
\(920\) 44.5158 5.22435i 1.46764 0.172242i
\(921\) 0 0
\(922\) −39.8716 + 69.0596i −1.31310 + 2.27436i
\(923\) 28.7726i 0.947060i
\(924\) 0 0
\(925\) 3.97209 3.75454i 0.130602 0.123448i
\(926\) −26.5757 15.3435i −0.873332 0.504218i
\(927\) 0 0
\(928\) −13.5171 + 7.80411i −0.443721 + 0.256183i
\(929\) −11.2452 + 19.4772i −0.368943 + 0.639027i −0.989400 0.145212i \(-0.953613\pi\)
0.620458 + 0.784240i \(0.286947\pi\)
\(930\) 0 0
\(931\) −9.26667 4.01459i −0.303703 0.131573i
\(932\) −86.3568 −2.82871
\(933\) 0 0
\(934\) −76.9023 + 44.3996i −2.51632 + 1.45280i
\(935\) 66.8873 7.84986i 2.18745 0.256718i
\(936\) 0 0
\(937\) −32.0994 −1.04864 −0.524321 0.851521i \(-0.675681\pi\)
−0.524321 + 0.851521i \(0.675681\pi\)
\(938\) −0.970808 16.8976i −0.0316980 0.551725i
\(939\) 0 0
\(940\) −35.1176 + 26.1698i −1.14541 + 0.853563i
\(941\) −5.10912 8.84925i −0.166552 0.288477i 0.770653 0.637255i \(-0.219930\pi\)
−0.937206 + 0.348778i \(0.886597\pi\)
\(942\) 0 0
\(943\) 9.77631 16.9331i 0.318360 0.551416i
\(944\) 91.0378 2.96303
\(945\) 0 0
\(946\) 7.04097 0.228922
\(947\) 5.14953 8.91925i 0.167337 0.289837i −0.770146 0.637868i \(-0.779816\pi\)
0.937483 + 0.348031i \(0.113150\pi\)
\(948\) 0 0
\(949\) 5.54703 + 9.60774i 0.180064 + 0.311880i
\(950\) −4.29123 18.0306i −0.139226 0.584990i
\(951\) 0 0
\(952\) −78.9890 + 51.8627i −2.56005 + 1.68088i
\(953\) −0.930159 −0.0301308 −0.0150654 0.999887i \(-0.504796\pi\)
−0.0150654 + 0.999887i \(0.504796\pi\)
\(954\) 0 0
\(955\) 2.59440 + 22.1064i 0.0839527 + 0.715346i
\(956\) 29.3255 16.9311i 0.948455 0.547591i
\(957\) 0 0
\(958\) 7.63696 0.246739
\(959\) 8.22082 + 12.5206i 0.265464 + 0.404312i
\(960\) 0 0
\(961\) −14.3402 + 24.8379i −0.462586 + 0.801223i
\(962\) −8.59943 + 4.96488i −0.277257 + 0.160074i
\(963\) 0 0
\(964\) −109.735 63.3555i −3.53432 2.04054i
\(965\) −51.2363 22.0726i −1.64935 0.710543i
\(966\) 0 0
\(967\) 4.22117i 0.135744i −0.997694 0.0678719i \(-0.978379\pi\)
0.997694 0.0678719i \(-0.0216209\pi\)
\(968\) −69.4443 + 120.281i −2.23202 + 3.86598i
\(969\) 0 0
\(970\) 84.0632 9.86561i 2.69911 0.316766i
\(971\) 2.28935 3.96527i 0.0734688 0.127252i −0.826951 0.562275i \(-0.809926\pi\)
0.900419 + 0.435023i \(0.143260\pi\)
\(972\) 0 0
\(973\) 3.53610 + 61.5483i 0.113362 + 1.97315i
\(974\) 58.3566i 1.86987i
\(975\) 0 0
\(976\) −48.3872 + 27.9364i −1.54884 + 0.894221i
\(977\) −22.7556 39.4138i −0.728015 1.26096i −0.957721 0.287698i \(-0.907110\pi\)
0.229707 0.973260i \(-0.426223\pi\)
\(978\) 0 0
\(979\) 58.2329i 1.86113i
\(980\) −20.7341 + 68.9788i −0.662327 + 2.20345i
\(981\) 0 0
\(982\) −28.9350 16.7056i −0.923351 0.533097i
\(983\) −9.10765 + 5.25831i −0.290489 + 0.167714i −0.638162 0.769902i \(-0.720305\pi\)
0.347673 + 0.937616i \(0.386972\pi\)
\(984\) 0 0
\(985\) −25.5232 34.2500i −0.813236 1.09130i
\(986\) 30.1192 0.959192
\(987\) 0 0
\(988\) 23.4708i 0.746706i
\(989\) −1.26240 0.728847i −0.0401420 0.0231760i
\(990\) 0 0
\(991\) 13.9539 + 24.1689i 0.443262 + 0.767752i 0.997929 0.0643204i \(-0.0204880\pi\)
−0.554668 + 0.832072i \(0.687155\pi\)
\(992\) 9.38319 + 5.41739i 0.297916 + 0.172002i
\(993\) 0 0
\(994\) 49.4205 + 24.8687i 1.56752 + 0.788787i
\(995\) −3.78535 1.63073i −0.120004 0.0516977i
\(996\) 0 0
\(997\) 19.4567 + 33.7000i 0.616201 + 1.06729i 0.990173 + 0.139851i \(0.0446623\pi\)
−0.373972 + 0.927440i \(0.622004\pi\)
\(998\) −27.7592 48.0803i −0.878701 1.52196i
\(999\) 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 315.2.bb.b.89.12 yes 24
3.2 odd 2 inner 315.2.bb.b.89.1 24
5.2 odd 4 1575.2.bk.i.26.12 24
5.3 odd 4 1575.2.bk.i.26.2 24
5.4 even 2 inner 315.2.bb.b.89.2 yes 24
7.2 even 3 2205.2.g.b.2204.4 24
7.3 odd 6 inner 315.2.bb.b.269.11 yes 24
7.5 odd 6 2205.2.g.b.2204.3 24
15.2 even 4 1575.2.bk.i.26.1 24
15.8 even 4 1575.2.bk.i.26.11 24
15.14 odd 2 inner 315.2.bb.b.89.11 yes 24
21.2 odd 6 2205.2.g.b.2204.22 24
21.5 even 6 2205.2.g.b.2204.21 24
21.17 even 6 inner 315.2.bb.b.269.2 yes 24
35.3 even 12 1575.2.bk.i.1151.11 24
35.9 even 6 2205.2.g.b.2204.24 24
35.17 even 12 1575.2.bk.i.1151.1 24
35.19 odd 6 2205.2.g.b.2204.23 24
35.24 odd 6 inner 315.2.bb.b.269.1 yes 24
105.17 odd 12 1575.2.bk.i.1151.12 24
105.38 odd 12 1575.2.bk.i.1151.2 24
105.44 odd 6 2205.2.g.b.2204.2 24
105.59 even 6 inner 315.2.bb.b.269.12 yes 24
105.89 even 6 2205.2.g.b.2204.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bb.b.89.1 24 3.2 odd 2 inner
315.2.bb.b.89.2 yes 24 5.4 even 2 inner
315.2.bb.b.89.11 yes 24 15.14 odd 2 inner
315.2.bb.b.89.12 yes 24 1.1 even 1 trivial
315.2.bb.b.269.1 yes 24 35.24 odd 6 inner
315.2.bb.b.269.2 yes 24 21.17 even 6 inner
315.2.bb.b.269.11 yes 24 7.3 odd 6 inner
315.2.bb.b.269.12 yes 24 105.59 even 6 inner
1575.2.bk.i.26.1 24 15.2 even 4
1575.2.bk.i.26.2 24 5.3 odd 4
1575.2.bk.i.26.11 24 15.8 even 4
1575.2.bk.i.26.12 24 5.2 odd 4
1575.2.bk.i.1151.1 24 35.17 even 12
1575.2.bk.i.1151.2 24 105.38 odd 12
1575.2.bk.i.1151.11 24 35.3 even 12
1575.2.bk.i.1151.12 24 105.17 odd 12
2205.2.g.b.2204.1 24 105.89 even 6
2205.2.g.b.2204.2 24 105.44 odd 6
2205.2.g.b.2204.3 24 7.5 odd 6
2205.2.g.b.2204.4 24 7.2 even 3
2205.2.g.b.2204.21 24 21.5 even 6
2205.2.g.b.2204.22 24 21.2 odd 6
2205.2.g.b.2204.23 24 35.19 odd 6
2205.2.g.b.2204.24 24 35.9 even 6