Properties

Label 495.2.n.d.181.2
Level $495$
Weight $2$
Character 495.181
Analytic conductor $3.953$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [495,2,Mod(91,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.2
Root \(-0.227943 - 0.701538i\) of defining polynomial
Character \(\chi\) \(=\) 495.181
Dual form 495.2.n.d.361.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.359123 - 1.10527i) q^{2} +(0.525387 - 0.381716i) q^{4} +(0.309017 - 0.951057i) q^{5} +(3.46813 - 2.51974i) q^{7} +(-2.49097 - 1.80980i) q^{8} +O(q^{10})\) \(q+(-0.359123 - 1.10527i) q^{2} +(0.525387 - 0.381716i) q^{4} +(0.309017 - 0.951057i) q^{5} +(3.46813 - 2.51974i) q^{7} +(-2.49097 - 1.80980i) q^{8} -1.16215 q^{10} +(3.15911 - 1.00996i) q^{11} +(1.59676 + 4.91433i) q^{13} +(-4.03048 - 2.92831i) q^{14} +(-0.704384 + 2.16787i) q^{16} +(-1.54508 + 4.75528i) q^{17} +(-4.53048 - 3.29158i) q^{19} +(-0.200680 - 0.617629i) q^{20} +(-2.25079 - 3.12896i) q^{22} +0.219819 q^{23} +(-0.809017 - 0.587785i) q^{25} +(4.85822 - 3.52970i) q^{26} +(0.860283 - 2.64768i) q^{28} +(5.19262 - 3.77266i) q^{29} +(-0.874813 - 2.69240i) q^{31} -3.50898 q^{32} +5.81074 q^{34} +(-1.32471 - 4.07703i) q^{35} +(-3.17784 + 2.30883i) q^{37} +(-2.01108 + 6.18947i) q^{38} +(-2.49097 + 1.80980i) q^{40} +(4.74165 + 3.44501i) q^{41} -8.90173 q^{43} +(1.27424 - 1.73650i) q^{44} +(-0.0789420 - 0.242959i) q^{46} +(-0.192447 - 0.139821i) q^{47} +(3.51569 - 10.8202i) q^{49} +(-0.359123 + 1.10527i) q^{50} +(2.71480 + 1.97242i) q^{52} +(-0.783885 - 2.41255i) q^{53} +(0.0156899 - 3.31659i) q^{55} -13.1992 q^{56} +(-6.03459 - 4.38439i) q^{58} +(-6.36725 + 4.62608i) q^{59} +(-1.50123 + 4.62030i) q^{61} +(-2.66165 + 1.93381i) q^{62} +(2.66892 + 8.21410i) q^{64} +5.16724 q^{65} +12.1280 q^{67} +(1.00340 + 3.08815i) q^{68} +(-4.03048 + 2.92831i) q^{70} +(3.08459 - 9.49339i) q^{71} +(-11.7813 + 8.55964i) q^{73} +(3.69311 + 2.68320i) q^{74} -3.63670 q^{76} +(8.41136 - 11.4628i) q^{77} +(2.47274 + 7.61030i) q^{79} +(1.84410 + 1.33982i) q^{80} +(2.10482 - 6.47797i) q^{82} +(-3.87908 + 11.9386i) q^{83} +(4.04508 + 2.93893i) q^{85} +(3.19682 + 9.83880i) q^{86} +(-9.69707 - 3.20157i) q^{88} +2.56545 q^{89} +(17.9206 + 13.0201i) q^{91} +(0.115490 - 0.0839083i) q^{92} +(-0.0854274 + 0.262919i) q^{94} +(-4.53048 + 3.29158i) q^{95} +(0.621738 + 1.91351i) q^{97} -13.2218 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8} - 10 q^{10} + 3 q^{11} + 6 q^{13} + 10 q^{14} - 20 q^{16} + 10 q^{17} + 6 q^{19} - 7 q^{20} - 25 q^{22} + 10 q^{23} - 2 q^{25} + 8 q^{26} + 31 q^{28} + 3 q^{31} - 60 q^{32} + 50 q^{34} + q^{35} - 19 q^{37} + 28 q^{38} - 5 q^{40} + 25 q^{41} - 4 q^{43} - 7 q^{44} - 6 q^{46} - 15 q^{47} + 21 q^{49} + 6 q^{52} - 7 q^{53} - 7 q^{55} - 20 q^{56} - 2 q^{58} - 35 q^{59} + 21 q^{61} + 19 q^{62} - 77 q^{64} + 6 q^{65} - 26 q^{67} + 35 q^{68} + 10 q^{70} - 25 q^{71} + q^{73} + 29 q^{74} - 14 q^{76} + 61 q^{77} + 30 q^{79} + 5 q^{80} + 57 q^{82} - 11 q^{83} + 10 q^{85} + 34 q^{86} - 85 q^{88} - 32 q^{89} + 37 q^{91} + 10 q^{92} - 39 q^{94} + 6 q^{95} + 5 q^{97} - 50 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.359123 1.10527i −0.253938 0.781542i −0.994037 0.109044i \(-0.965221\pi\)
0.740098 0.672499i \(-0.234779\pi\)
\(3\) 0 0
\(4\) 0.525387 0.381716i 0.262693 0.190858i
\(5\) 0.309017 0.951057i 0.138197 0.425325i
\(6\) 0 0
\(7\) 3.46813 2.51974i 1.31083 0.952373i 0.310831 0.950465i \(-0.399393\pi\)
0.999998 0.00190785i \(-0.000607288\pi\)
\(8\) −2.49097 1.80980i −0.880691 0.639860i
\(9\) 0 0
\(10\) −1.16215 −0.367503
\(11\) 3.15911 1.00996i 0.952508 0.304514i
\(12\) 0 0
\(13\) 1.59676 + 4.91433i 0.442863 + 1.36299i 0.884811 + 0.465950i \(0.154287\pi\)
−0.441948 + 0.897040i \(0.645713\pi\)
\(14\) −4.03048 2.92831i −1.07719 0.782624i
\(15\) 0 0
\(16\) −0.704384 + 2.16787i −0.176096 + 0.541968i
\(17\) −1.54508 + 4.75528i −0.374738 + 1.15333i 0.568917 + 0.822395i \(0.307363\pi\)
−0.943655 + 0.330930i \(0.892637\pi\)
\(18\) 0 0
\(19\) −4.53048 3.29158i −1.03936 0.755141i −0.0692013 0.997603i \(-0.522045\pi\)
−0.970161 + 0.242462i \(0.922045\pi\)
\(20\) −0.200680 0.617629i −0.0448734 0.138106i
\(21\) 0 0
\(22\) −2.25079 3.12896i −0.479869 0.667097i
\(23\) 0.219819 0.0458354 0.0229177 0.999737i \(-0.492704\pi\)
0.0229177 + 0.999737i \(0.492704\pi\)
\(24\) 0 0
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) 4.85822 3.52970i 0.952775 0.692232i
\(27\) 0 0
\(28\) 0.860283 2.64768i 0.162578 0.500364i
\(29\) 5.19262 3.77266i 0.964246 0.700566i 0.0101128 0.999949i \(-0.496781\pi\)
0.954133 + 0.299383i \(0.0967809\pi\)
\(30\) 0 0
\(31\) −0.874813 2.69240i −0.157121 0.483569i 0.841249 0.540649i \(-0.181821\pi\)
−0.998370 + 0.0570796i \(0.981821\pi\)
\(32\) −3.50898 −0.620306
\(33\) 0 0
\(34\) 5.81074 0.996533
\(35\) −1.32471 4.07703i −0.223916 0.689144i
\(36\) 0 0
\(37\) −3.17784 + 2.30883i −0.522433 + 0.379570i −0.817520 0.575901i \(-0.804652\pi\)
0.295087 + 0.955471i \(0.404652\pi\)
\(38\) −2.01108 + 6.18947i −0.326240 + 1.00406i
\(39\) 0 0
\(40\) −2.49097 + 1.80980i −0.393857 + 0.286154i
\(41\) 4.74165 + 3.44501i 0.740521 + 0.538020i 0.892874 0.450306i \(-0.148685\pi\)
−0.152353 + 0.988326i \(0.548685\pi\)
\(42\) 0 0
\(43\) −8.90173 −1.35750 −0.678751 0.734369i \(-0.737478\pi\)
−0.678751 + 0.734369i \(0.737478\pi\)
\(44\) 1.27424 1.73650i 0.192099 0.261788i
\(45\) 0 0
\(46\) −0.0789420 0.242959i −0.0116394 0.0358223i
\(47\) −0.192447 0.139821i −0.0280713 0.0203950i 0.573661 0.819093i \(-0.305523\pi\)
−0.601732 + 0.798698i \(0.705523\pi\)
\(48\) 0 0
\(49\) 3.51569 10.8202i 0.502241 1.54574i
\(50\) −0.359123 + 1.10527i −0.0507877 + 0.156308i
\(51\) 0 0
\(52\) 2.71480 + 1.97242i 0.376475 + 0.273525i
\(53\) −0.783885 2.41255i −0.107675 0.331389i 0.882674 0.469986i \(-0.155741\pi\)
−0.990349 + 0.138596i \(0.955741\pi\)
\(54\) 0 0
\(55\) 0.0156899 3.31659i 0.00211563 0.447209i
\(56\) −13.1992 −1.76382
\(57\) 0 0
\(58\) −6.03459 4.38439i −0.792381 0.575698i
\(59\) −6.36725 + 4.62608i −0.828945 + 0.602264i −0.919261 0.393649i \(-0.871212\pi\)
0.0903156 + 0.995913i \(0.471212\pi\)
\(60\) 0 0
\(61\) −1.50123 + 4.62030i −0.192212 + 0.591569i 0.807785 + 0.589477i \(0.200666\pi\)
−0.999998 + 0.00209225i \(0.999334\pi\)
\(62\) −2.66165 + 1.93381i −0.338031 + 0.245594i
\(63\) 0 0
\(64\) 2.66892 + 8.21410i 0.333615 + 1.02676i
\(65\) 5.16724 0.640917
\(66\) 0 0
\(67\) 12.1280 1.48167 0.740834 0.671688i \(-0.234431\pi\)
0.740834 + 0.671688i \(0.234431\pi\)
\(68\) 1.00340 + 3.08815i 0.121680 + 0.374493i
\(69\) 0 0
\(70\) −4.03048 + 2.92831i −0.481734 + 0.350000i
\(71\) 3.08459 9.49339i 0.366073 1.12666i −0.583233 0.812305i \(-0.698212\pi\)
0.949306 0.314353i \(-0.101788\pi\)
\(72\) 0 0
\(73\) −11.7813 + 8.55964i −1.37890 + 1.00183i −0.381918 + 0.924196i \(0.624736\pi\)
−0.996982 + 0.0776335i \(0.975264\pi\)
\(74\) 3.69311 + 2.68320i 0.429316 + 0.311916i
\(75\) 0 0
\(76\) −3.63670 −0.417158
\(77\) 8.41136 11.4628i 0.958564 1.30631i
\(78\) 0 0
\(79\) 2.47274 + 7.61030i 0.278205 + 0.856226i 0.988354 + 0.152174i \(0.0486275\pi\)
−0.710149 + 0.704051i \(0.751372\pi\)
\(80\) 1.84410 + 1.33982i 0.206177 + 0.149796i
\(81\) 0 0
\(82\) 2.10482 6.47797i 0.232439 0.715373i
\(83\) −3.87908 + 11.9386i −0.425784 + 1.31043i 0.476458 + 0.879197i \(0.341921\pi\)
−0.902242 + 0.431231i \(0.858079\pi\)
\(84\) 0 0
\(85\) 4.04508 + 2.93893i 0.438751 + 0.318771i
\(86\) 3.19682 + 9.83880i 0.344722 + 1.06094i
\(87\) 0 0
\(88\) −9.69707 3.20157i −1.03371 0.341288i
\(89\) 2.56545 0.271937 0.135969 0.990713i \(-0.456585\pi\)
0.135969 + 0.990713i \(0.456585\pi\)
\(90\) 0 0
\(91\) 17.9206 + 13.0201i 1.87859 + 1.36488i
\(92\) 0.115490 0.0839083i 0.0120407 0.00874805i
\(93\) 0 0
\(94\) −0.0854274 + 0.262919i −0.00881116 + 0.0271180i
\(95\) −4.53048 + 3.29158i −0.464817 + 0.337709i
\(96\) 0 0
\(97\) 0.621738 + 1.91351i 0.0631279 + 0.194288i 0.977646 0.210257i \(-0.0674300\pi\)
−0.914518 + 0.404545i \(0.867430\pi\)
\(98\) −13.2218 −1.33560
\(99\) 0 0
\(100\) −0.649414 −0.0649414
\(101\) 2.34385 + 7.21362i 0.233221 + 0.717782i 0.997352 + 0.0727205i \(0.0231681\pi\)
−0.764131 + 0.645061i \(0.776832\pi\)
\(102\) 0 0
\(103\) 13.6469 9.91508i 1.34467 0.976962i 0.345414 0.938450i \(-0.387738\pi\)
0.999258 0.0385116i \(-0.0122617\pi\)
\(104\) 4.91645 15.1313i 0.482098 1.48374i
\(105\) 0 0
\(106\) −2.38500 + 1.73281i −0.231652 + 0.168305i
\(107\) 6.27928 + 4.56216i 0.607041 + 0.441041i 0.848371 0.529402i \(-0.177584\pi\)
−0.241330 + 0.970443i \(0.577584\pi\)
\(108\) 0 0
\(109\) 4.45671 0.426876 0.213438 0.976957i \(-0.431534\pi\)
0.213438 + 0.976957i \(0.431534\pi\)
\(110\) −3.67135 + 1.17372i −0.350050 + 0.111910i
\(111\) 0 0
\(112\) 3.01958 + 9.29332i 0.285324 + 0.878136i
\(113\) −6.23952 4.53327i −0.586964 0.426455i 0.254264 0.967135i \(-0.418167\pi\)
−0.841228 + 0.540680i \(0.818167\pi\)
\(114\) 0 0
\(115\) 0.0679277 0.209060i 0.00633429 0.0194950i
\(116\) 1.28805 3.96421i 0.119593 0.368068i
\(117\) 0 0
\(118\) 7.39968 + 5.37618i 0.681196 + 0.494918i
\(119\) 6.62353 + 20.3851i 0.607178 + 1.86870i
\(120\) 0 0
\(121\) 8.95996 6.38115i 0.814542 0.580105i
\(122\) 5.64579 0.511146
\(123\) 0 0
\(124\) −1.48735 1.08062i −0.133568 0.0970426i
\(125\) −0.809017 + 0.587785i −0.0723607 + 0.0525731i
\(126\) 0 0
\(127\) 0.473149 1.45620i 0.0419852 0.129217i −0.927867 0.372912i \(-0.878359\pi\)
0.969852 + 0.243695i \(0.0783594\pi\)
\(128\) 2.44266 1.77470i 0.215903 0.156863i
\(129\) 0 0
\(130\) −1.85567 5.71118i −0.162753 0.500903i
\(131\) −2.66108 −0.232500 −0.116250 0.993220i \(-0.537087\pi\)
−0.116250 + 0.993220i \(0.537087\pi\)
\(132\) 0 0
\(133\) −24.0062 −2.08160
\(134\) −4.35544 13.4047i −0.376252 1.15799i
\(135\) 0 0
\(136\) 12.4549 9.04898i 1.06799 0.775944i
\(137\) −3.16911 + 9.75352i −0.270756 + 0.833300i 0.719556 + 0.694435i \(0.244345\pi\)
−0.990311 + 0.138865i \(0.955655\pi\)
\(138\) 0 0
\(139\) 4.28381 3.11237i 0.363348 0.263987i −0.391099 0.920348i \(-0.627905\pi\)
0.754447 + 0.656361i \(0.227905\pi\)
\(140\) −2.25225 1.63636i −0.190350 0.138297i
\(141\) 0 0
\(142\) −11.6005 −0.973491
\(143\) 10.0076 + 13.9123i 0.836880 + 1.16340i
\(144\) 0 0
\(145\) −1.98341 6.10429i −0.164713 0.506934i
\(146\) 13.6916 + 9.94756i 1.13313 + 0.823266i
\(147\) 0 0
\(148\) −0.788275 + 2.42606i −0.0647958 + 0.199421i
\(149\) −1.17068 + 3.60300i −0.0959062 + 0.295169i −0.987489 0.157689i \(-0.949596\pi\)
0.891583 + 0.452858i \(0.149596\pi\)
\(150\) 0 0
\(151\) 4.78939 + 3.47969i 0.389755 + 0.283173i 0.765355 0.643608i \(-0.222563\pi\)
−0.375600 + 0.926782i \(0.622563\pi\)
\(152\) 5.32819 + 16.3985i 0.432173 + 1.33009i
\(153\) 0 0
\(154\) −15.6902 5.18024i −1.26435 0.417436i
\(155\) −2.83095 −0.227388
\(156\) 0 0
\(157\) 6.01026 + 4.36671i 0.479671 + 0.348501i 0.801198 0.598399i \(-0.204196\pi\)
−0.321528 + 0.946900i \(0.604196\pi\)
\(158\) 7.52340 5.46607i 0.598530 0.434857i
\(159\) 0 0
\(160\) −1.08433 + 3.33724i −0.0857242 + 0.263832i
\(161\) 0.762360 0.553887i 0.0600824 0.0436524i
\(162\) 0 0
\(163\) 1.64424 + 5.06044i 0.128786 + 0.396364i 0.994572 0.104051i \(-0.0331807\pi\)
−0.865785 + 0.500415i \(0.833181\pi\)
\(164\) 3.80621 0.297215
\(165\) 0 0
\(166\) 14.5884 1.13228
\(167\) 0.609193 + 1.87490i 0.0471407 + 0.145084i 0.971856 0.235575i \(-0.0756972\pi\)
−0.924716 + 0.380659i \(0.875697\pi\)
\(168\) 0 0
\(169\) −11.0838 + 8.05285i −0.852599 + 0.619450i
\(170\) 1.79562 5.52634i 0.137717 0.423851i
\(171\) 0 0
\(172\) −4.67685 + 3.39793i −0.356607 + 0.259090i
\(173\) −1.59784 1.16090i −0.121482 0.0882617i 0.525385 0.850864i \(-0.323921\pi\)
−0.646867 + 0.762603i \(0.723921\pi\)
\(174\) 0 0
\(175\) −4.28684 −0.324055
\(176\) −0.0357642 + 7.55994i −0.00269583 + 0.569852i
\(177\) 0 0
\(178\) −0.921313 2.83551i −0.0690553 0.212530i
\(179\) −1.63676 1.18918i −0.122337 0.0888832i 0.524934 0.851143i \(-0.324090\pi\)
−0.647271 + 0.762260i \(0.724090\pi\)
\(180\) 0 0
\(181\) 6.22299 19.1524i 0.462551 1.42359i −0.399485 0.916740i \(-0.630811\pi\)
0.862036 0.506846i \(-0.169189\pi\)
\(182\) 7.95498 24.4829i 0.589662 1.81479i
\(183\) 0 0
\(184\) −0.547562 0.397827i −0.0403668 0.0293282i
\(185\) 1.21383 + 3.73577i 0.0892422 + 0.274659i
\(186\) 0 0
\(187\) −0.0784497 + 16.5829i −0.00573681 + 1.21266i
\(188\) −0.154481 −0.0112667
\(189\) 0 0
\(190\) 5.26508 + 3.82530i 0.381969 + 0.277517i
\(191\) 10.2463 7.44439i 0.741398 0.538657i −0.151751 0.988419i \(-0.548491\pi\)
0.893149 + 0.449762i \(0.148491\pi\)
\(192\) 0 0
\(193\) −4.30526 + 13.2502i −0.309900 + 0.953773i 0.667904 + 0.744248i \(0.267192\pi\)
−0.977803 + 0.209525i \(0.932808\pi\)
\(194\) 1.89166 1.37437i 0.135813 0.0986743i
\(195\) 0 0
\(196\) −2.28314 7.02678i −0.163081 0.501913i
\(197\) −14.6060 −1.04064 −0.520319 0.853972i \(-0.674187\pi\)
−0.520319 + 0.853972i \(0.674187\pi\)
\(198\) 0 0
\(199\) −11.8748 −0.841784 −0.420892 0.907111i \(-0.638283\pi\)
−0.420892 + 0.907111i \(0.638283\pi\)
\(200\) 0.951466 + 2.92831i 0.0672788 + 0.207063i
\(201\) 0 0
\(202\) 7.13125 5.18115i 0.501753 0.364545i
\(203\) 8.50254 26.1681i 0.596762 1.83664i
\(204\) 0 0
\(205\) 4.74165 3.44501i 0.331171 0.240610i
\(206\) −15.8597 11.5228i −1.10500 0.802830i
\(207\) 0 0
\(208\) −11.7784 −0.816683
\(209\) −17.6366 5.82288i −1.21995 0.402777i
\(210\) 0 0
\(211\) −6.90710 21.2579i −0.475504 1.46345i −0.845277 0.534329i \(-0.820564\pi\)
0.369772 0.929122i \(-0.379436\pi\)
\(212\) −1.33275 0.968301i −0.0915338 0.0665032i
\(213\) 0 0
\(214\) 2.78738 8.57866i 0.190541 0.586425i
\(215\) −2.75079 + 8.46605i −0.187602 + 0.577380i
\(216\) 0 0
\(217\) −9.81811 7.13328i −0.666497 0.484238i
\(218\) −1.60051 4.92586i −0.108400 0.333621i
\(219\) 0 0
\(220\) −1.25775 1.74848i −0.0847976 0.117883i
\(221\) −25.8362 −1.73793
\(222\) 0 0
\(223\) 15.4994 + 11.2610i 1.03792 + 0.754091i 0.969878 0.243592i \(-0.0783258\pi\)
0.0680388 + 0.997683i \(0.478326\pi\)
\(224\) −12.1696 + 8.84173i −0.813115 + 0.590763i
\(225\) 0 0
\(226\) −2.76973 + 8.52434i −0.184239 + 0.567031i
\(227\) 12.4394 9.03772i 0.825629 0.599855i −0.0926901 0.995695i \(-0.529547\pi\)
0.918319 + 0.395840i \(0.129547\pi\)
\(228\) 0 0
\(229\) 2.75064 + 8.46560i 0.181767 + 0.559422i 0.999878 0.0156388i \(-0.00497820\pi\)
−0.818110 + 0.575061i \(0.804978\pi\)
\(230\) −0.255462 −0.0168447
\(231\) 0 0
\(232\) −19.7624 −1.29747
\(233\) −7.05677 21.7185i −0.462304 1.42283i −0.862342 0.506327i \(-0.831003\pi\)
0.400037 0.916499i \(-0.368997\pi\)
\(234\) 0 0
\(235\) −0.192447 + 0.139821i −0.0125539 + 0.00912092i
\(236\) −1.57942 + 4.86096i −0.102812 + 0.316422i
\(237\) 0 0
\(238\) 20.1524 14.6416i 1.30628 0.949071i
\(239\) 13.6405 + 9.91037i 0.882327 + 0.641048i 0.933866 0.357623i \(-0.116413\pi\)
−0.0515388 + 0.998671i \(0.516413\pi\)
\(240\) 0 0
\(241\) −11.9607 −0.770459 −0.385229 0.922821i \(-0.625878\pi\)
−0.385229 + 0.922821i \(0.625878\pi\)
\(242\) −10.2706 7.61154i −0.660220 0.489288i
\(243\) 0 0
\(244\) 0.974917 + 3.00049i 0.0624127 + 0.192087i
\(245\) −9.20420 6.68724i −0.588034 0.427232i
\(246\) 0 0
\(247\) 8.94184 27.5201i 0.568955 1.75106i
\(248\) −2.69356 + 8.28992i −0.171041 + 0.526410i
\(249\) 0 0
\(250\) 0.940197 + 0.683093i 0.0594633 + 0.0432026i
\(251\) −4.94533 15.2201i −0.312146 0.960687i −0.976913 0.213637i \(-0.931469\pi\)
0.664767 0.747051i \(-0.268531\pi\)
\(252\) 0 0
\(253\) 0.694432 0.222008i 0.0436586 0.0139575i
\(254\) −1.77941 −0.111650
\(255\) 0 0
\(256\) 11.1359 + 8.09073i 0.695996 + 0.505671i
\(257\) 4.42893 3.21780i 0.276269 0.200721i −0.441019 0.897498i \(-0.645383\pi\)
0.717288 + 0.696776i \(0.245383\pi\)
\(258\) 0 0
\(259\) −5.20348 + 16.0147i −0.323328 + 0.995103i
\(260\) 2.71480 1.97242i 0.168365 0.122324i
\(261\) 0 0
\(262\) 0.955657 + 2.94121i 0.0590407 + 0.181709i
\(263\) −11.9841 −0.738971 −0.369486 0.929236i \(-0.620466\pi\)
−0.369486 + 0.929236i \(0.620466\pi\)
\(264\) 0 0
\(265\) −2.53671 −0.155829
\(266\) 8.62119 + 26.5333i 0.528599 + 1.62686i
\(267\) 0 0
\(268\) 6.37188 4.62944i 0.389224 0.282788i
\(269\) −4.21700 + 12.9786i −0.257115 + 0.791318i 0.736291 + 0.676665i \(0.236576\pi\)
−0.993406 + 0.114653i \(0.963424\pi\)
\(270\) 0 0
\(271\) −9.57702 + 6.95812i −0.581763 + 0.422675i −0.839359 0.543577i \(-0.817070\pi\)
0.257596 + 0.966253i \(0.417070\pi\)
\(272\) −9.22050 6.69909i −0.559075 0.406192i
\(273\) 0 0
\(274\) 11.9184 0.720014
\(275\) −3.14941 1.03980i −0.189917 0.0627025i
\(276\) 0 0
\(277\) 3.17170 + 9.76148i 0.190569 + 0.586511i 1.00000 0.000704561i \(-0.000224269\pi\)
−0.809431 + 0.587215i \(0.800224\pi\)
\(278\) −4.97841 3.61703i −0.298585 0.216935i
\(279\) 0 0
\(280\) −4.07878 + 12.5532i −0.243754 + 0.750198i
\(281\) 0.908167 2.79505i 0.0541767 0.166739i −0.920307 0.391197i \(-0.872061\pi\)
0.974484 + 0.224458i \(0.0720612\pi\)
\(282\) 0 0
\(283\) −17.6592 12.8301i −1.04973 0.762673i −0.0775682 0.996987i \(-0.524716\pi\)
−0.972161 + 0.234314i \(0.924716\pi\)
\(284\) −2.00318 6.16514i −0.118867 0.365834i
\(285\) 0 0
\(286\) 11.7828 16.0573i 0.696731 0.949490i
\(287\) 25.1252 1.48309
\(288\) 0 0
\(289\) −6.47214 4.70228i −0.380714 0.276605i
\(290\) −6.03459 + 4.38439i −0.354363 + 0.257460i
\(291\) 0 0
\(292\) −2.92241 + 8.99424i −0.171021 + 0.526348i
\(293\) −20.0365 + 14.5574i −1.17055 + 0.850452i −0.991074 0.133311i \(-0.957439\pi\)
−0.179473 + 0.983763i \(0.557439\pi\)
\(294\) 0 0
\(295\) 2.43207 + 7.48515i 0.141601 + 0.435802i
\(296\) 12.0944 0.702974
\(297\) 0 0
\(298\) 4.40269 0.255041
\(299\) 0.350999 + 1.08026i 0.0202988 + 0.0624732i
\(300\) 0 0
\(301\) −30.8723 + 22.4301i −1.77945 + 1.29285i
\(302\) 2.12601 6.54319i 0.122338 0.376518i
\(303\) 0 0
\(304\) 10.3269 7.50295i 0.592289 0.430323i
\(305\) 3.93026 + 2.85550i 0.225046 + 0.163506i
\(306\) 0 0
\(307\) −4.94023 −0.281954 −0.140977 0.990013i \(-0.545024\pi\)
−0.140977 + 0.990013i \(0.545024\pi\)
\(308\) 0.0436798 9.23316i 0.00248889 0.526108i
\(309\) 0 0
\(310\) 1.01666 + 3.12896i 0.0577425 + 0.177713i
\(311\) −11.1722 8.11707i −0.633517 0.460277i 0.224100 0.974566i \(-0.428056\pi\)
−0.857617 + 0.514289i \(0.828056\pi\)
\(312\) 0 0
\(313\) −1.25750 + 3.87017i −0.0710779 + 0.218755i −0.980285 0.197589i \(-0.936689\pi\)
0.909207 + 0.416344i \(0.136689\pi\)
\(314\) 2.66796 8.21113i 0.150562 0.463381i
\(315\) 0 0
\(316\) 4.20412 + 3.05447i 0.236500 + 0.171827i
\(317\) −7.97880 24.5562i −0.448134 1.37921i −0.879010 0.476803i \(-0.841795\pi\)
0.430876 0.902411i \(-0.358205\pi\)
\(318\) 0 0
\(319\) 12.5938 17.1626i 0.705119 0.960921i
\(320\) 8.63682 0.482813
\(321\) 0 0
\(322\) −0.885974 0.643698i −0.0493734 0.0358719i
\(323\) 22.6524 16.4579i 1.26041 0.915743i
\(324\) 0 0
\(325\) 1.59676 4.91433i 0.0885725 0.272598i
\(326\) 5.00265 3.63464i 0.277071 0.201304i
\(327\) 0 0
\(328\) −5.57654 17.1628i −0.307913 0.947659i
\(329\) −1.01974 −0.0562203
\(330\) 0 0
\(331\) −3.35008 −0.184137 −0.0920684 0.995753i \(-0.529348\pi\)
−0.0920684 + 0.995753i \(0.529348\pi\)
\(332\) 2.51913 + 7.75307i 0.138255 + 0.425505i
\(333\) 0 0
\(334\) 1.85349 1.34664i 0.101419 0.0736850i
\(335\) 3.74775 11.5344i 0.204761 0.630191i
\(336\) 0 0
\(337\) 22.1669 16.1052i 1.20751 0.877307i 0.212507 0.977160i \(-0.431837\pi\)
0.995002 + 0.0998530i \(0.0318372\pi\)
\(338\) 12.8810 + 9.35859i 0.700634 + 0.509040i
\(339\) 0 0
\(340\) 3.24707 0.176097
\(341\) −5.48285 7.62206i −0.296913 0.412758i
\(342\) 0 0
\(343\) −5.79826 17.8452i −0.313076 0.963550i
\(344\) 22.1739 + 16.1103i 1.19554 + 0.868610i
\(345\) 0 0
\(346\) −0.709284 + 2.18295i −0.0381313 + 0.117356i
\(347\) −4.89065 + 15.0519i −0.262544 + 0.808027i 0.729705 + 0.683762i \(0.239657\pi\)
−0.992249 + 0.124265i \(0.960343\pi\)
\(348\) 0 0
\(349\) 2.96043 + 2.15088i 0.158468 + 0.115134i 0.664194 0.747561i \(-0.268775\pi\)
−0.505725 + 0.862695i \(0.668775\pi\)
\(350\) 1.53950 + 4.73811i 0.0822900 + 0.253263i
\(351\) 0 0
\(352\) −11.0853 + 3.54393i −0.590846 + 0.188892i
\(353\) 27.4937 1.46334 0.731671 0.681658i \(-0.238741\pi\)
0.731671 + 0.681658i \(0.238741\pi\)
\(354\) 0 0
\(355\) −8.07556 5.86724i −0.428606 0.311401i
\(356\) 1.34785 0.979273i 0.0714361 0.0519014i
\(357\) 0 0
\(358\) −0.726559 + 2.23612i −0.0383998 + 0.118183i
\(359\) 0.387309 0.281397i 0.0204414 0.0148515i −0.577518 0.816378i \(-0.695979\pi\)
0.597959 + 0.801527i \(0.295979\pi\)
\(360\) 0 0
\(361\) 3.81936 + 11.7548i 0.201019 + 0.618673i
\(362\) −23.4033 −1.23005
\(363\) 0 0
\(364\) 14.3852 0.753992
\(365\) 4.50007 + 13.8498i 0.235544 + 0.724931i
\(366\) 0 0
\(367\) 20.5961 14.9639i 1.07511 0.781111i 0.0982843 0.995158i \(-0.468665\pi\)
0.976823 + 0.214047i \(0.0686645\pi\)
\(368\) −0.154837 + 0.476539i −0.00807143 + 0.0248413i
\(369\) 0 0
\(370\) 3.69311 2.68320i 0.191996 0.139493i
\(371\) −8.79762 6.39184i −0.456750 0.331848i
\(372\) 0 0
\(373\) −2.75967 −0.142890 −0.0714451 0.997445i \(-0.522761\pi\)
−0.0714451 + 0.997445i \(0.522761\pi\)
\(374\) 18.3568 5.86861i 0.949205 0.303459i
\(375\) 0 0
\(376\) 0.226333 + 0.696580i 0.0116722 + 0.0359234i
\(377\) 26.8315 + 19.4942i 1.38189 + 1.00400i
\(378\) 0 0
\(379\) −6.69130 + 20.5937i −0.343709 + 1.05783i 0.618562 + 0.785736i \(0.287716\pi\)
−0.962271 + 0.272092i \(0.912284\pi\)
\(380\) −1.12380 + 3.45871i −0.0576499 + 0.177428i
\(381\) 0 0
\(382\) −11.9077 8.65148i −0.609253 0.442648i
\(383\) −5.01518 15.4351i −0.256264 0.788699i −0.993578 0.113149i \(-0.963906\pi\)
0.737314 0.675550i \(-0.236094\pi\)
\(384\) 0 0
\(385\) −8.30253 11.5419i −0.423136 0.588229i
\(386\) 16.1912 0.824109
\(387\) 0 0
\(388\) 1.05707 + 0.768007i 0.0536647 + 0.0389897i
\(389\) −13.1802 + 9.57598i −0.668263 + 0.485522i −0.869443 0.494033i \(-0.835522\pi\)
0.201180 + 0.979554i \(0.435522\pi\)
\(390\) 0 0
\(391\) −0.339639 + 1.04530i −0.0171763 + 0.0528631i
\(392\) −28.3398 + 20.5901i −1.43138 + 1.03996i
\(393\) 0 0
\(394\) 5.24537 + 16.1436i 0.264258 + 0.813302i
\(395\) 8.00194 0.402621
\(396\) 0 0
\(397\) −19.9673 −1.00213 −0.501064 0.865410i \(-0.667058\pi\)
−0.501064 + 0.865410i \(0.667058\pi\)
\(398\) 4.26453 + 13.1249i 0.213761 + 0.657890i
\(399\) 0 0
\(400\) 1.84410 1.33982i 0.0922050 0.0669909i
\(401\) 8.44448 25.9894i 0.421697 1.29785i −0.484425 0.874833i \(-0.660971\pi\)
0.906122 0.423017i \(-0.139029\pi\)
\(402\) 0 0
\(403\) 11.8345 8.59825i 0.589517 0.428309i
\(404\) 3.98498 + 2.89526i 0.198260 + 0.144044i
\(405\) 0 0
\(406\) −31.9763 −1.58696
\(407\) −7.70731 + 10.5034i −0.382037 + 0.520632i
\(408\) 0 0
\(409\) 7.70626 + 23.7174i 0.381050 + 1.17275i 0.939305 + 0.343082i \(0.111471\pi\)
−0.558255 + 0.829669i \(0.688529\pi\)
\(410\) −5.51049 4.00361i −0.272144 0.197724i
\(411\) 0 0
\(412\) 3.38518 10.4185i 0.166776 0.513283i
\(413\) −10.4259 + 32.0876i −0.513025 + 1.57893i
\(414\) 0 0
\(415\) 10.1556 + 7.37844i 0.498517 + 0.362193i
\(416\) −5.60301 17.2443i −0.274710 0.845471i
\(417\) 0 0
\(418\) −0.102110 + 21.5843i −0.00499437 + 1.05572i
\(419\) −16.8256 −0.821986 −0.410993 0.911639i \(-0.634818\pi\)
−0.410993 + 0.911639i \(0.634818\pi\)
\(420\) 0 0
\(421\) −19.0933 13.8721i −0.930551 0.676085i 0.0155763 0.999879i \(-0.495042\pi\)
−0.946128 + 0.323793i \(0.895042\pi\)
\(422\) −21.0151 + 15.2684i −1.02300 + 0.743253i
\(423\) 0 0
\(424\) −2.41359 + 7.42826i −0.117214 + 0.360748i
\(425\) 4.04508 2.93893i 0.196215 0.142559i
\(426\) 0 0
\(427\) 6.43552 + 19.8065i 0.311437 + 0.958504i
\(428\) 5.04050 0.243642
\(429\) 0 0
\(430\) 10.3451 0.498886
\(431\) 11.6362 + 35.8126i 0.560497 + 1.72503i 0.680966 + 0.732315i \(0.261560\pi\)
−0.120469 + 0.992717i \(0.538440\pi\)
\(432\) 0 0
\(433\) 25.0594 18.2068i 1.20428 0.874961i 0.209581 0.977791i \(-0.432790\pi\)
0.994699 + 0.102831i \(0.0327900\pi\)
\(434\) −4.35827 + 13.4134i −0.209204 + 0.643862i
\(435\) 0 0
\(436\) 2.34150 1.70120i 0.112137 0.0814726i
\(437\) −0.995884 0.723552i −0.0476396 0.0346122i
\(438\) 0 0
\(439\) −28.2131 −1.34654 −0.673268 0.739399i \(-0.735110\pi\)
−0.673268 + 0.739399i \(0.735110\pi\)
\(440\) −6.04143 + 8.23313i −0.288014 + 0.392499i
\(441\) 0 0
\(442\) 9.27837 + 28.5559i 0.441327 + 1.35827i
\(443\) 11.8456 + 8.60636i 0.562803 + 0.408900i 0.832484 0.554050i \(-0.186918\pi\)
−0.269681 + 0.962950i \(0.586918\pi\)
\(444\) 0 0
\(445\) 0.792768 2.43989i 0.0375808 0.115662i
\(446\) 6.88019 21.1751i 0.325787 1.00267i
\(447\) 0 0
\(448\) 29.9536 + 21.7626i 1.41517 + 1.02818i
\(449\) −3.70749 11.4105i −0.174967 0.538493i 0.824665 0.565622i \(-0.191364\pi\)
−0.999632 + 0.0271282i \(0.991364\pi\)
\(450\) 0 0
\(451\) 18.4587 + 6.09429i 0.869187 + 0.286969i
\(452\) −5.00858 −0.235584
\(453\) 0 0
\(454\) −14.4564 10.5032i −0.678471 0.492938i
\(455\) 17.9206 13.0201i 0.840132 0.610392i
\(456\) 0 0
\(457\) 3.10367 9.55211i 0.145183 0.446829i −0.851851 0.523784i \(-0.824520\pi\)
0.997035 + 0.0769553i \(0.0245199\pi\)
\(458\) 8.36893 6.08039i 0.391055 0.284118i
\(459\) 0 0
\(460\) −0.0441132 0.135767i −0.00205679 0.00633015i
\(461\) 13.4491 0.626386 0.313193 0.949689i \(-0.398601\pi\)
0.313193 + 0.949689i \(0.398601\pi\)
\(462\) 0 0
\(463\) 18.7836 0.872946 0.436473 0.899717i \(-0.356227\pi\)
0.436473 + 0.899717i \(0.356227\pi\)
\(464\) 4.52104 + 13.9143i 0.209884 + 0.645957i
\(465\) 0 0
\(466\) −21.4705 + 15.5992i −0.994602 + 0.722620i
\(467\) −8.20470 + 25.2515i −0.379668 + 1.16850i 0.560607 + 0.828082i \(0.310568\pi\)
−0.940275 + 0.340416i \(0.889432\pi\)
\(468\) 0 0
\(469\) 42.0614 30.5594i 1.94221 1.41110i
\(470\) 0.223652 + 0.162493i 0.0103163 + 0.00749522i
\(471\) 0 0
\(472\) 24.2329 1.11541
\(473\) −28.1216 + 8.99039i −1.29303 + 0.413379i
\(474\) 0 0
\(475\) 1.73049 + 5.32589i 0.0794002 + 0.244369i
\(476\) 11.2613 + 8.18178i 0.516159 + 0.375011i
\(477\) 0 0
\(478\) 6.05501 18.6354i 0.276950 0.852363i
\(479\) −3.33214 + 10.2553i −0.152249 + 0.468575i −0.997872 0.0652062i \(-0.979229\pi\)
0.845623 + 0.533781i \(0.179229\pi\)
\(480\) 0 0
\(481\) −16.4206 11.9303i −0.748716 0.543974i
\(482\) 4.29538 + 13.2198i 0.195649 + 0.602146i
\(483\) 0 0
\(484\) 2.27166 6.77273i 0.103257 0.307851i
\(485\) 2.01199 0.0913596
\(486\) 0 0
\(487\) −5.51018 4.00338i −0.249690 0.181410i 0.455899 0.890031i \(-0.349318\pi\)
−0.705589 + 0.708621i \(0.749318\pi\)
\(488\) 12.1013 8.79212i 0.547801 0.398001i
\(489\) 0 0
\(490\) −4.08575 + 12.5746i −0.184575 + 0.568064i
\(491\) 21.1116 15.3385i 0.952754 0.692216i 0.00129727 0.999999i \(-0.499587\pi\)
0.951457 + 0.307783i \(0.0995871\pi\)
\(492\) 0 0
\(493\) 9.91703 + 30.5215i 0.446640 + 1.37462i
\(494\) −33.6283 −1.51301
\(495\) 0 0
\(496\) 6.45297 0.289747
\(497\) −13.2231 40.6967i −0.593139 1.82549i
\(498\) 0 0
\(499\) −15.6815 + 11.3933i −0.702000 + 0.510033i −0.880583 0.473892i \(-0.842849\pi\)
0.178583 + 0.983925i \(0.442849\pi\)
\(500\) −0.200680 + 0.617629i −0.00897468 + 0.0276212i
\(501\) 0 0
\(502\) −15.0464 + 10.9318i −0.671552 + 0.487911i
\(503\) 15.2437 + 11.0752i 0.679683 + 0.493819i 0.873253 0.487268i \(-0.162007\pi\)
−0.193570 + 0.981087i \(0.562007\pi\)
\(504\) 0 0
\(505\) 7.58484 0.337521
\(506\) −0.494765 0.687805i −0.0219950 0.0305767i
\(507\) 0 0
\(508\) −0.307270 0.945678i −0.0136329 0.0419577i
\(509\) −4.16741 3.02780i −0.184717 0.134205i 0.491584 0.870830i \(-0.336418\pi\)
−0.676301 + 0.736625i \(0.736418\pi\)
\(510\) 0 0
\(511\) −19.2911 + 59.3718i −0.853387 + 2.62645i
\(512\) 6.80928 20.9568i 0.300930 0.926168i
\(513\) 0 0
\(514\) −5.14707 3.73956i −0.227027 0.164945i
\(515\) −5.21267 16.0429i −0.229698 0.706936i
\(516\) 0 0
\(517\) −0.749175 0.247346i −0.0329487 0.0108783i
\(518\) 19.5692 0.859820
\(519\) 0 0
\(520\) −12.8714 9.35164i −0.564450 0.410097i
\(521\) −33.5759 + 24.3944i −1.47099 + 1.06874i −0.490663 + 0.871349i \(0.663246\pi\)
−0.980326 + 0.197387i \(0.936754\pi\)
\(522\) 0 0
\(523\) −2.13926 + 6.58397i −0.0935434 + 0.287897i −0.986871 0.161508i \(-0.948364\pi\)
0.893328 + 0.449405i \(0.148364\pi\)
\(524\) −1.39810 + 1.01578i −0.0610762 + 0.0443745i
\(525\) 0 0
\(526\) 4.30377 + 13.2456i 0.187653 + 0.577537i
\(527\) 14.1548 0.616592
\(528\) 0 0
\(529\) −22.9517 −0.997899
\(530\) 0.910990 + 2.80374i 0.0395709 + 0.121787i
\(531\) 0 0
\(532\) −12.6125 + 9.16355i −0.546823 + 0.397290i
\(533\) −9.35863 + 28.8029i −0.405367 + 1.24759i
\(534\) 0 0
\(535\) 6.27928 4.56216i 0.271477 0.197239i
\(536\) −30.2104 21.9492i −1.30489 0.948059i
\(537\) 0 0
\(538\) 15.8592 0.683740
\(539\) 0.178505 37.7329i 0.00768874 1.62527i
\(540\) 0 0
\(541\) −8.78173 27.0274i −0.377556 1.16200i −0.941738 0.336348i \(-0.890808\pi\)
0.564182 0.825651i \(-0.309192\pi\)
\(542\) 11.1299 + 8.08635i 0.478071 + 0.347339i
\(543\) 0 0
\(544\) 5.42167 16.6862i 0.232452 0.715415i
\(545\) 1.37720 4.23858i 0.0589928 0.181561i
\(546\) 0 0
\(547\) −20.9205 15.1996i −0.894496 0.649889i 0.0425503 0.999094i \(-0.486452\pi\)
−0.937046 + 0.349205i \(0.886452\pi\)
\(548\) 2.05807 + 6.33407i 0.0879162 + 0.270578i
\(549\) 0 0
\(550\) −0.0182340 + 3.85436i −0.000777501 + 0.164351i
\(551\) −35.9431 −1.53123
\(552\) 0 0
\(553\) 27.7518 + 20.1628i 1.18012 + 0.857411i
\(554\) 9.65002 7.01115i 0.409990 0.297875i
\(555\) 0 0
\(556\) 1.06262 3.27039i 0.0450649 0.138696i
\(557\) −6.52399 + 4.73996i −0.276430 + 0.200838i −0.717359 0.696704i \(-0.754649\pi\)
0.440929 + 0.897542i \(0.354649\pi\)
\(558\) 0 0
\(559\) −14.2140 43.7461i −0.601186 1.85026i
\(560\) 9.77157 0.412924
\(561\) 0 0
\(562\) −3.41542 −0.144071
\(563\) −9.16284 28.2003i −0.386168 1.18850i −0.935630 0.352983i \(-0.885167\pi\)
0.549462 0.835519i \(-0.314833\pi\)
\(564\) 0 0
\(565\) −6.23952 + 4.53327i −0.262498 + 0.190716i
\(566\) −7.83892 + 24.1257i −0.329494 + 1.01408i
\(567\) 0 0
\(568\) −24.8647 + 18.0653i −1.04330 + 0.758002i
\(569\) −34.0618 24.7473i −1.42794 1.03746i −0.990395 0.138266i \(-0.955847\pi\)
−0.437548 0.899195i \(-0.644153\pi\)
\(570\) 0 0
\(571\) −26.6823 −1.11662 −0.558311 0.829632i \(-0.688550\pi\)
−0.558311 + 0.829632i \(0.688550\pi\)
\(572\) 10.5684 + 3.48924i 0.441887 + 0.145893i
\(573\) 0 0
\(574\) −9.02304 27.7700i −0.376614 1.15910i
\(575\) −0.177837 0.129206i −0.00741632 0.00538827i
\(576\) 0 0
\(577\) −1.02228 + 3.14627i −0.0425582 + 0.130981i −0.970078 0.242793i \(-0.921936\pi\)
0.927520 + 0.373774i \(0.121936\pi\)
\(578\) −2.87299 + 8.84214i −0.119500 + 0.367785i
\(579\) 0 0
\(580\) −3.37216 2.45002i −0.140021 0.101731i
\(581\) 16.6290 + 51.1788i 0.689887 + 2.12325i
\(582\) 0 0
\(583\) −4.91296 6.82982i −0.203474 0.282862i
\(584\) 44.8381 1.85542
\(585\) 0 0
\(586\) 23.2854 + 16.9178i 0.961911 + 0.698869i
\(587\) −6.89906 + 5.01246i −0.284755 + 0.206886i −0.720989 0.692947i \(-0.756312\pi\)
0.436234 + 0.899833i \(0.356312\pi\)
\(588\) 0 0
\(589\) −4.89893 + 15.0774i −0.201857 + 0.621252i
\(590\) 7.39968 5.37618i 0.304640 0.221334i
\(591\) 0 0
\(592\) −2.76684 8.51544i −0.113716 0.349983i
\(593\) 23.4343 0.962333 0.481167 0.876629i \(-0.340213\pi\)
0.481167 + 0.876629i \(0.340213\pi\)
\(594\) 0 0
\(595\) 21.4342 0.878717
\(596\) 0.760259 + 2.33984i 0.0311414 + 0.0958434i
\(597\) 0 0
\(598\) 1.06793 0.775895i 0.0436708 0.0317287i
\(599\) −5.82017 + 17.9126i −0.237805 + 0.731890i 0.758931 + 0.651171i \(0.225722\pi\)
−0.996737 + 0.0807194i \(0.974278\pi\)
\(600\) 0 0
\(601\) 30.4664 22.1351i 1.24275 0.902911i 0.244971 0.969530i \(-0.421221\pi\)
0.997778 + 0.0666198i \(0.0212214\pi\)
\(602\) 35.8782 + 26.0670i 1.46229 + 1.06241i
\(603\) 0 0
\(604\) 3.84453 0.156432
\(605\) −3.30005 10.4933i −0.134166 0.426614i
\(606\) 0 0
\(607\) −9.07520 27.9306i −0.368351 1.13367i −0.947856 0.318699i \(-0.896754\pi\)
0.579505 0.814969i \(-0.303246\pi\)
\(608\) 15.8973 + 11.5501i 0.644723 + 0.468418i
\(609\) 0 0
\(610\) 1.74465 5.36947i 0.0706387 0.217403i
\(611\) 0.379834 1.16901i 0.0153665 0.0472931i
\(612\) 0 0
\(613\) 10.4453 + 7.58894i 0.421881 + 0.306515i 0.778394 0.627776i \(-0.216035\pi\)
−0.356513 + 0.934290i \(0.616035\pi\)
\(614\) 1.77415 + 5.46027i 0.0715989 + 0.220359i
\(615\) 0 0
\(616\) −41.6978 + 13.3307i −1.68005 + 0.537109i
\(617\) −41.6041 −1.67492 −0.837459 0.546500i \(-0.815960\pi\)
−0.837459 + 0.546500i \(0.815960\pi\)
\(618\) 0 0
\(619\) −3.45545 2.51053i −0.138886 0.100907i 0.516173 0.856484i \(-0.327356\pi\)
−0.655059 + 0.755578i \(0.727356\pi\)
\(620\) −1.48735 + 1.08062i −0.0597333 + 0.0433988i
\(621\) 0 0
\(622\) −4.95935 + 15.2633i −0.198852 + 0.612002i
\(623\) 8.89731 6.46427i 0.356463 0.258986i
\(624\) 0 0
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) 4.72918 0.189016
\(627\) 0 0
\(628\) 4.82455 0.192521
\(629\) −6.06913 18.6789i −0.241992 0.744775i
\(630\) 0 0
\(631\) 22.2892 16.1941i 0.887319 0.644675i −0.0478586 0.998854i \(-0.515240\pi\)
0.935178 + 0.354179i \(0.115240\pi\)
\(632\) 7.61358 23.4322i 0.302852 0.932082i
\(633\) 0 0
\(634\) −24.2758 + 17.6374i −0.964116 + 0.700471i
\(635\) −1.23872 0.899983i −0.0491571 0.0357147i
\(636\) 0 0
\(637\) 58.7877 2.32925
\(638\) −23.4920 7.75607i −0.930057 0.307066i
\(639\) 0 0
\(640\) −0.933014 2.87152i −0.0368806 0.113507i
\(641\) 7.41712 + 5.38885i 0.292958 + 0.212847i 0.724550 0.689222i \(-0.242048\pi\)
−0.431591 + 0.902069i \(0.642048\pi\)
\(642\) 0 0
\(643\) −1.05346 + 3.24223i −0.0415446 + 0.127861i −0.969678 0.244387i \(-0.921413\pi\)
0.928133 + 0.372249i \(0.121413\pi\)
\(644\) 0.189106 0.582010i 0.00745184 0.0229344i
\(645\) 0 0
\(646\) −26.3254 19.1265i −1.03576 0.752523i
\(647\) −6.90986 21.2663i −0.271654 0.836066i −0.990085 0.140468i \(-0.955139\pi\)
0.718431 0.695598i \(-0.244861\pi\)
\(648\) 0 0
\(649\) −15.4427 + 21.0450i −0.606179 + 0.826087i
\(650\) −6.00509 −0.235539
\(651\) 0 0
\(652\) 2.79551 + 2.03106i 0.109481 + 0.0795423i
\(653\) −11.9699 + 8.69667i −0.468420 + 0.340327i −0.796825 0.604210i \(-0.793489\pi\)
0.328405 + 0.944537i \(0.393489\pi\)
\(654\) 0 0
\(655\) −0.822320 + 2.53084i −0.0321307 + 0.0988882i
\(656\) −10.8083 + 7.85267i −0.421992 + 0.306595i
\(657\) 0 0
\(658\) 0.366214 + 1.12709i 0.0142765 + 0.0439385i
\(659\) 47.4724 1.84926 0.924631 0.380864i \(-0.124373\pi\)
0.924631 + 0.380864i \(0.124373\pi\)
\(660\) 0 0
\(661\) −21.6525 −0.842184 −0.421092 0.907018i \(-0.638353\pi\)
−0.421092 + 0.907018i \(0.638353\pi\)
\(662\) 1.20309 + 3.70273i 0.0467594 + 0.143911i
\(663\) 0 0
\(664\) 31.2690 22.7183i 1.21347 0.881641i
\(665\) −7.41833 + 22.8313i −0.287670 + 0.885358i
\(666\) 0 0
\(667\) 1.14144 0.829302i 0.0441966 0.0321107i
\(668\) 1.03574 + 0.752510i 0.0400740 + 0.0291155i
\(669\) 0 0
\(670\) −14.0945 −0.544518
\(671\) −0.0762228 + 16.1122i −0.00294255 + 0.622005i
\(672\) 0 0
\(673\) −11.8639 36.5133i −0.457319 1.40748i −0.868391 0.495880i \(-0.834846\pi\)
0.411072 0.911603i \(-0.365154\pi\)
\(674\) −25.7612 18.7166i −0.992285 0.720937i
\(675\) 0 0
\(676\) −2.74938 + 8.46172i −0.105745 + 0.325451i
\(677\) 7.08677 21.8108i 0.272367 0.838259i −0.717537 0.696520i \(-0.754731\pi\)
0.989904 0.141739i \(-0.0452693\pi\)
\(678\) 0 0
\(679\) 6.97782 + 5.06969i 0.267784 + 0.194557i
\(680\) −4.75733 14.6416i −0.182435 0.561478i
\(681\) 0 0
\(682\) −6.45540 + 8.79727i −0.247190 + 0.336865i
\(683\) −25.9084 −0.991359 −0.495680 0.868505i \(-0.665081\pi\)
−0.495680 + 0.868505i \(0.665081\pi\)
\(684\) 0 0
\(685\) 8.29684 + 6.02801i 0.317006 + 0.230318i
\(686\) −17.6414 + 12.8173i −0.673553 + 0.489365i
\(687\) 0 0
\(688\) 6.27024 19.2978i 0.239050 0.735722i
\(689\) 10.6044 7.70454i 0.403995 0.293520i
\(690\) 0 0
\(691\) 4.57824 + 14.0904i 0.174165 + 0.536023i 0.999594 0.0284814i \(-0.00906715\pi\)
−0.825430 + 0.564505i \(0.809067\pi\)
\(692\) −1.28262 −0.0487579
\(693\) 0 0
\(694\) 18.3927 0.698177
\(695\) −1.63627 5.03592i −0.0620672 0.191023i
\(696\) 0 0
\(697\) −23.7082 + 17.2250i −0.898014 + 0.652445i
\(698\) 1.31414 4.04450i 0.0497409 0.153087i
\(699\) 0 0
\(700\) −2.25225 + 1.63636i −0.0851271 + 0.0618484i
\(701\) 4.45471 + 3.23653i 0.168252 + 0.122242i 0.668725 0.743510i \(-0.266840\pi\)
−0.500473 + 0.865752i \(0.666840\pi\)
\(702\) 0 0
\(703\) 21.9968 0.829626
\(704\) 16.7273 + 23.2538i 0.630435 + 0.876409i
\(705\) 0 0
\(706\) −9.87362 30.3879i −0.371599 1.14366i
\(707\) 26.3052 + 19.1119i 0.989309 + 0.718775i
\(708\) 0 0
\(709\) −5.53161 + 17.0245i −0.207744 + 0.639370i 0.791846 + 0.610721i \(0.209120\pi\)
−0.999590 + 0.0286488i \(0.990880\pi\)
\(710\) −3.58475 + 11.0327i −0.134533 + 0.414050i
\(711\) 0 0
\(712\) −6.39046 4.64294i −0.239493 0.174002i
\(713\) −0.192300 0.591840i −0.00720171 0.0221646i
\(714\) 0 0
\(715\) 16.3239 5.21870i 0.610478 0.195168i
\(716\) −1.31386 −0.0491012
\(717\) 0 0
\(718\) −0.450110 0.327024i −0.0167980 0.0122044i
\(719\) 26.3673 19.1570i 0.983334 0.714434i 0.0248831 0.999690i \(-0.492079\pi\)
0.958451 + 0.285256i \(0.0920786\pi\)
\(720\) 0 0
\(721\) 22.3459 68.7735i 0.832204 2.56126i
\(722\) 11.6206 8.44284i 0.432473 0.314210i
\(723\) 0 0
\(724\) −4.04130 12.4378i −0.150194 0.462248i
\(725\) −6.41843 −0.238375
\(726\) 0 0
\(727\) −43.0199 −1.59552 −0.797759 0.602976i \(-0.793982\pi\)
−0.797759 + 0.602976i \(0.793982\pi\)
\(728\) −21.0760 64.8654i −0.781130 2.40407i
\(729\) 0 0
\(730\) 13.6916 9.94756i 0.506750 0.368176i
\(731\) 13.7539 42.3302i 0.508708 1.56564i
\(732\) 0 0
\(733\) −32.9323 + 23.9267i −1.21638 + 0.883755i −0.995795 0.0916123i \(-0.970798\pi\)
−0.220589 + 0.975367i \(0.570798\pi\)
\(734\) −23.9357 17.3903i −0.883483 0.641888i
\(735\) 0 0
\(736\) −0.771340 −0.0284320
\(737\) 38.3136 12.2488i 1.41130 0.451189i
\(738\) 0 0
\(739\) 11.7810 + 36.2581i 0.433370 + 1.33377i 0.894748 + 0.446571i \(0.147355\pi\)
−0.461379 + 0.887203i \(0.652645\pi\)
\(740\) 2.06373 + 1.49939i 0.0758643 + 0.0551186i
\(741\) 0 0
\(742\) −3.90527 + 12.0192i −0.143367 + 0.441238i
\(743\) 5.57409 17.1553i 0.204493 0.629366i −0.795240 0.606294i \(-0.792655\pi\)
0.999734 0.0230717i \(-0.00734459\pi\)
\(744\) 0 0
\(745\) 3.06489 + 2.22677i 0.112289 + 0.0815827i
\(746\) 0.991061 + 3.05017i 0.0362853 + 0.111675i
\(747\) 0 0
\(748\) 6.28875 + 8.74240i 0.229940 + 0.319654i
\(749\) 33.2728 1.21576
\(750\) 0 0
\(751\) 14.1861 + 10.3068i 0.517657 + 0.376100i 0.815720 0.578446i \(-0.196341\pi\)
−0.298064 + 0.954546i \(0.596341\pi\)
\(752\) 0.438670 0.318713i 0.0159967 0.0116223i
\(753\) 0 0
\(754\) 11.9105 36.6568i 0.433756 1.33496i
\(755\) 4.78939 3.47969i 0.174304 0.126639i
\(756\) 0 0
\(757\) −8.02236 24.6903i −0.291578 0.897383i −0.984350 0.176227i \(-0.943611\pi\)
0.692772 0.721157i \(-0.256389\pi\)
\(758\) 25.1646 0.914019
\(759\) 0 0
\(760\) 17.2424 0.625447
\(761\) −8.65430 26.6352i −0.313718 0.965525i −0.976279 0.216517i \(-0.930530\pi\)
0.662561 0.749008i \(-0.269470\pi\)
\(762\) 0 0
\(763\) 15.4564 11.2298i 0.559561 0.406545i
\(764\) 2.54164 7.82237i 0.0919534 0.283003i
\(765\) 0 0
\(766\) −15.2589 + 11.0862i −0.551326 + 0.400562i
\(767\) −32.9011 23.9040i −1.18799 0.863124i
\(768\) 0 0
\(769\) 22.9537 0.827732 0.413866 0.910338i \(-0.364178\pi\)
0.413866 + 0.910338i \(0.364178\pi\)
\(770\) −9.77524 + 13.3215i −0.352275 + 0.480073i
\(771\) 0 0
\(772\) 2.79590 + 8.60489i 0.100627 + 0.309697i
\(773\) −19.0347 13.8295i −0.684631 0.497414i 0.190259 0.981734i \(-0.439067\pi\)
−0.874891 + 0.484320i \(0.839067\pi\)
\(774\) 0 0
\(775\) −0.874813 + 2.69240i −0.0314242 + 0.0967138i
\(776\) 1.91434 5.89172i 0.0687207 0.211500i
\(777\) 0 0
\(778\) 15.3173 + 11.1287i 0.549153 + 0.398983i
\(779\) −10.1424 31.2151i −0.363389 1.11840i
\(780\) 0 0
\(781\) 0.156616 33.1060i 0.00560416 1.18463i
\(782\) 1.27731 0.0456765
\(783\) 0 0
\(784\) 20.9804 + 15.2431i 0.749298 + 0.544397i
\(785\) 6.01026 4.36671i 0.214515 0.155854i
\(786\) 0 0
\(787\) −7.80964 + 24.0356i −0.278384 + 0.856777i 0.709921 + 0.704282i \(0.248731\pi\)
−0.988304 + 0.152495i \(0.951269\pi\)
\(788\) −7.67383 + 5.57536i −0.273369 + 0.198614i
\(789\) 0 0
\(790\) −2.87368 8.84429i −0.102241 0.314666i
\(791\) −33.0621 −1.17555
\(792\) 0 0
\(793\) −25.1028 −0.891427
\(794\) 7.17071 + 22.0692i 0.254479 + 0.783205i
\(795\) 0 0
\(796\) −6.23888 + 4.53281i −0.221131 + 0.160661i
\(797\) −2.67499 + 8.23277i −0.0947530 + 0.291620i −0.987189 0.159554i \(-0.948994\pi\)
0.892436 + 0.451173i \(0.148994\pi\)
\(798\) 0 0
\(799\) 0.962236 0.699105i 0.0340414 0.0247326i
\(800\) 2.83882 + 2.06253i 0.100368 + 0.0729213i
\(801\) 0 0
\(802\) −31.7579 −1.12141
\(803\) −28.5736 + 38.9395i −1.00834 + 1.37415i
\(804\) 0 0
\(805\) −0.291195 0.896208i −0.0102633 0.0315872i
\(806\) −13.7534 9.99243i −0.484443 0.351968i
\(807\) 0 0
\(808\) 7.21672 22.2108i 0.253883 0.781373i
\(809\) 3.15582 9.71261i 0.110953 0.341477i −0.880129 0.474735i \(-0.842544\pi\)
0.991081 + 0.133258i \(0.0425438\pi\)
\(810\) 0 0
\(811\) 38.5273 + 27.9917i 1.35288 + 0.982923i 0.998862 + 0.0476835i \(0.0151839\pi\)
0.354015 + 0.935240i \(0.384816\pi\)
\(812\) −5.52167 16.9940i −0.193773 0.596371i
\(813\) 0 0
\(814\) 14.3769 + 4.74664i 0.503910 + 0.166370i
\(815\) 5.32086 0.186381
\(816\) 0 0
\(817\) 40.3291 + 29.3008i 1.41094 + 1.02510i
\(818\) 23.4466 17.0350i 0.819792 0.595613i
\(819\) 0 0
\(820\) 1.17618 3.61993i 0.0410742 0.126413i
\(821\) −38.4767 + 27.9550i −1.34285 + 0.975635i −0.343512 + 0.939148i \(0.611617\pi\)
−0.999334 + 0.0364868i \(0.988383\pi\)
\(822\) 0 0
\(823\) −7.64384 23.5253i −0.266448 0.820041i −0.991356 0.131196i \(-0.958118\pi\)
0.724909 0.688845i \(-0.241882\pi\)
\(824\) −51.9384 −1.80936
\(825\) 0 0
\(826\) 39.2096 1.36428
\(827\) 0.482580 + 1.48523i 0.0167810 + 0.0516465i 0.959096 0.283080i \(-0.0913561\pi\)
−0.942315 + 0.334726i \(0.891356\pi\)
\(828\) 0 0
\(829\) −34.1365 + 24.8016i −1.18561 + 0.861396i −0.992793 0.119839i \(-0.961762\pi\)
−0.192817 + 0.981235i \(0.561762\pi\)
\(830\) 4.50806 13.8744i 0.156477 0.481587i
\(831\) 0 0
\(832\) −36.1052 + 26.2320i −1.25172 + 0.909430i
\(833\) 46.0210 + 33.4362i 1.59453 + 1.15850i
\(834\) 0 0
\(835\) 1.97139 0.0682227
\(836\) −11.4887 + 3.67292i −0.397346 + 0.127031i
\(837\) 0 0
\(838\) 6.04247 + 18.5968i 0.208734 + 0.642416i
\(839\) −5.09236 3.69982i −0.175808 0.127732i 0.496401 0.868093i \(-0.334654\pi\)
−0.672209 + 0.740361i \(0.734654\pi\)
\(840\) 0 0
\(841\) 3.76886 11.5994i 0.129961 0.399978i
\(842\) −8.47554 + 26.0850i −0.292086 + 0.898949i
\(843\) 0 0
\(844\) −11.7434 8.53205i −0.404223 0.293685i
\(845\) 4.23363 + 13.0298i 0.145641 + 0.448238i
\(846\) 0 0
\(847\) 14.9954 44.7074i 0.515249 1.53617i
\(848\) 5.78225 0.198563
\(849\) 0 0
\(850\) −4.70098 3.41546i −0.161242 0.117149i
\(851\) −0.698548 + 0.507525i −0.0239459 + 0.0173977i
\(852\) 0 0
\(853\) −2.24692 + 6.91532i −0.0769332 + 0.236776i −0.982126 0.188225i \(-0.939726\pi\)
0.905193 + 0.425002i \(0.139726\pi\)
\(854\) 19.5803 14.2259i 0.670025 0.486802i
\(855\) 0 0
\(856\) −7.38491 22.7284i −0.252411 0.776841i
\(857\) −39.8590 −1.36156 −0.680779 0.732489i \(-0.738359\pi\)
−0.680779 + 0.732489i \(0.738359\pi\)
\(858\) 0 0
\(859\) 13.5278 0.461564 0.230782 0.973006i \(-0.425872\pi\)
0.230782 + 0.973006i \(0.425872\pi\)
\(860\) 1.78640 + 5.49797i 0.0609157 + 0.187479i
\(861\) 0 0
\(862\) 35.4037 25.7223i 1.20585 0.876104i
\(863\) −15.5472 + 47.8493i −0.529232 + 1.62881i 0.226560 + 0.973997i \(0.427252\pi\)
−0.755792 + 0.654812i \(0.772748\pi\)
\(864\) 0 0
\(865\) −1.59784 + 1.16090i −0.0543283 + 0.0394718i
\(866\) −29.1228 21.1589i −0.989632 0.719010i
\(867\) 0 0
\(868\) −7.88119 −0.267505
\(869\) 15.4977 + 21.5444i 0.525725 + 0.730844i
\(870\) 0 0
\(871\) 19.3655 + 59.6009i 0.656175 + 2.01950i
\(872\) −11.1015 8.06574i −0.375946 0.273140i
\(873\) 0 0
\(874\) −0.442073 + 1.36056i −0.0149534 + 0.0460217i
\(875\) −1.32471 + 4.07703i −0.0447833 + 0.137829i
\(876\) 0 0
\(877\) 0.976773 + 0.709667i 0.0329833 + 0.0239638i 0.604155 0.796867i \(-0.293511\pi\)
−0.571171 + 0.820831i \(0.693511\pi\)
\(878\) 10.1320 + 31.1830i 0.341937 + 1.05237i
\(879\) 0 0
\(880\) 7.17888 + 2.37016i 0.242000 + 0.0798982i
\(881\) −1.91816 −0.0646245 −0.0323123 0.999478i \(-0.510287\pi\)
−0.0323123 + 0.999478i \(0.510287\pi\)
\(882\) 0 0
\(883\) −46.9950 34.1439i −1.58151 1.14903i −0.914941 0.403587i \(-0.867763\pi\)
−0.666566 0.745446i \(-0.732237\pi\)
\(884\) −13.5740 + 9.86208i −0.456543 + 0.331698i
\(885\) 0 0
\(886\) 5.25828 16.1833i 0.176656 0.543690i
\(887\) 24.4668 17.7762i 0.821516 0.596866i −0.0956306 0.995417i \(-0.530487\pi\)
0.917146 + 0.398551i \(0.130487\pi\)
\(888\) 0 0
\(889\) −2.02832 6.24251i −0.0680275 0.209367i
\(890\) −2.98143 −0.0999378
\(891\) 0 0
\(892\) 12.4417 0.416578
\(893\) 0.411644 + 1.26691i 0.0137752 + 0.0423956i
\(894\) 0 0
\(895\) −1.63676 + 1.18918i −0.0547109 + 0.0397498i
\(896\) 3.99968 12.3098i 0.133620 0.411240i
\(897\) 0 0
\(898\) −11.2802 + 8.19553i −0.376425 + 0.273488i
\(899\) −14.7001 10.6802i −0.490275 0.356206i
\(900\) 0 0
\(901\) 12.6835 0.422550
\(902\) 0.106870 22.5904i 0.00355837 0.752179i
\(903\) 0 0
\(904\) 7.33815 + 22.5845i 0.244063 + 0.751149i
\(905\) −16.2920 11.8368i −0.541564 0.393469i
\(906\) 0 0
\(907\) −9.87830 + 30.4023i −0.328004 + 1.00949i 0.642063 + 0.766652i \(0.278079\pi\)
−0.970066 + 0.242839i \(0.921921\pi\)
\(908\) 3.08563 9.49660i 0.102400 0.315156i
\(909\) 0 0
\(910\) −20.8264 15.1313i −0.690389 0.501597i
\(911\) 16.0211 + 49.3079i 0.530803 + 1.63364i 0.752547 + 0.658538i \(0.228825\pi\)
−0.221745 + 0.975105i \(0.571175\pi\)
\(912\) 0 0
\(913\) −0.196955 + 41.6330i −0.00651826 + 1.37785i
\(914\) −11.6722 −0.386083
\(915\) 0 0
\(916\) 4.67660 + 3.39775i 0.154519 + 0.112265i
\(917\) −9.22898 + 6.70525i −0.304768 + 0.221427i
\(918\) 0 0
\(919\) −10.5710 + 32.5341i −0.348704 + 1.07320i 0.610866 + 0.791734i \(0.290821\pi\)
−0.959571 + 0.281468i \(0.909179\pi\)
\(920\) −0.547562 + 0.397827i −0.0180526 + 0.0131160i
\(921\) 0 0
\(922\) −4.82988 14.8648i −0.159064 0.489547i
\(923\) 51.5790 1.69774
\(924\) 0 0
\(925\) 3.92802 0.129153
\(926\) −6.74561 20.7609i −0.221675 0.682244i
\(927\) 0 0
\(928\) −18.2208 + 13.2382i −0.598127 + 0.434565i
\(929\) −5.66990 + 17.4502i −0.186023 + 0.572521i −0.999964 0.00842624i \(-0.997318\pi\)
0.813941 + 0.580947i \(0.197318\pi\)
\(930\) 0 0
\(931\) −51.5433 + 37.4484i −1.68926 + 1.22732i
\(932\) −11.9978 8.71693i −0.393002 0.285533i
\(933\) 0 0
\(934\) 30.8561 1.00964
\(935\) 15.7471 + 5.19902i 0.514984 + 0.170026i
\(936\) 0 0
\(937\) 1.04576 + 3.21852i 0.0341635 + 0.105144i 0.966684 0.255972i \(-0.0823956\pi\)
−0.932521 + 0.361117i \(0.882396\pi\)
\(938\) −48.8815 35.5145i −1.59604 1.15959i
\(939\) 0 0
\(940\) −0.0477373 + 0.146920i −0.00155702 + 0.00479201i
\(941\) 10.8465 33.3822i 0.353587 1.08823i −0.603237 0.797562i \(-0.706123\pi\)
0.956824 0.290668i \(-0.0938774\pi\)
\(942\) 0 0
\(943\) 1.04230 + 0.757278i 0.0339421 + 0.0246604i
\(944\) −5.54375 17.0619i −0.180434 0.555318i
\(945\) 0 0
\(946\) 20.0359 + 27.8532i 0.651423 + 0.905585i
\(947\) 39.0512 1.26899 0.634497 0.772925i \(-0.281207\pi\)
0.634497 + 0.772925i \(0.281207\pi\)
\(948\) 0 0
\(949\) −60.8769 44.2297i −1.97615 1.43576i
\(950\) 5.26508 3.82530i 0.170822 0.124109i
\(951\) 0 0
\(952\) 20.3939 62.7660i 0.660971 2.03426i
\(953\) 19.9652 14.5055i 0.646735 0.469881i −0.215422 0.976521i \(-0.569113\pi\)
0.862158 + 0.506640i \(0.169113\pi\)
\(954\) 0 0
\(955\) −3.91375 12.0453i −0.126646 0.389776i
\(956\) 10.9495 0.354131
\(957\) 0 0
\(958\) 12.5315 0.404873
\(959\) 13.5855 + 41.8118i 0.438698 + 1.35017i
\(960\) 0 0
\(961\) 18.5958 13.5107i 0.599865 0.435827i
\(962\) −7.28913 + 22.4336i −0.235011 + 0.723290i
\(963\) 0 0
\(964\) −6.28401 + 4.56560i −0.202394 + 0.147048i
\(965\) 11.2713 + 8.18910i 0.362837 + 0.263616i
\(966\) 0 0
\(967\) 1.20724 0.0388222 0.0194111 0.999812i \(-0.493821\pi\)
0.0194111 + 0.999812i \(0.493821\pi\)
\(968\) −33.8676 0.320445i −1.08855 0.0102995i
\(969\) 0 0
\(970\) −0.722551 2.22378i −0.0231997 0.0714014i
\(971\) 40.7599 + 29.6138i 1.30805 + 0.950353i 0.999999 0.00101751i \(-0.000323883\pi\)
0.308049 + 0.951370i \(0.400324\pi\)
\(972\) 0 0
\(973\) 7.01442 21.5882i 0.224872 0.692085i
\(974\) −2.44597 + 7.52793i −0.0783740 + 0.241210i
\(975\) 0 0
\(976\) −8.95877 6.50893i −0.286763 0.208346i
\(977\) 1.81804 + 5.59535i 0.0581642 + 0.179011i 0.975917 0.218140i \(-0.0699989\pi\)
−0.917753 + 0.397151i \(0.869999\pi\)
\(978\) 0 0
\(979\) 8.10454 2.59100i 0.259022 0.0828088i
\(980\) −7.38839 −0.236013
\(981\) 0 0
\(982\) −24.5348 17.8256i −0.782937 0.568837i
\(983\) 29.5210 21.4482i 0.941573 0.684093i −0.00722580 0.999974i \(-0.502300\pi\)
0.948799 + 0.315881i \(0.102300\pi\)
\(984\) 0 0
\(985\) −4.51352 + 13.8912i −0.143813 + 0.442610i
\(986\) 30.1730 21.9219i 0.960903 0.698137i
\(987\) 0 0
\(988\) −5.80695 17.8720i −0.184744 0.568583i
\(989\) −1.95677 −0.0622216
\(990\) 0 0
\(991\) −36.8404 −1.17027 −0.585137 0.810934i \(-0.698959\pi\)
−0.585137 + 0.810934i \(0.698959\pi\)
\(992\) 3.06970 + 9.44757i 0.0974631 + 0.299961i
\(993\) 0 0
\(994\) −40.2320 + 29.2302i −1.27608 + 0.927127i
\(995\) −3.66952 + 11.2936i −0.116332 + 0.358032i
\(996\) 0 0
\(997\) −28.2099 + 20.4957i −0.893417 + 0.649105i −0.936767 0.349955i \(-0.886197\pi\)
0.0433498 + 0.999060i \(0.486197\pi\)
\(998\) 18.2242 + 13.2406i 0.576877 + 0.419125i
\(999\) 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 495.2.n.d.181.2 8
3.2 odd 2 165.2.m.a.16.1 8
11.3 even 5 5445.2.a.be.1.3 4
11.8 odd 10 5445.2.a.bv.1.2 4
11.9 even 5 inner 495.2.n.d.361.2 8
15.2 even 4 825.2.bx.h.49.2 16
15.8 even 4 825.2.bx.h.49.3 16
15.14 odd 2 825.2.n.k.676.2 8
33.8 even 10 1815.2.a.o.1.3 4
33.14 odd 10 1815.2.a.x.1.2 4
33.20 odd 10 165.2.m.a.31.1 yes 8
165.14 odd 10 9075.2.a.cl.1.3 4
165.53 even 20 825.2.bx.h.724.2 16
165.74 even 10 9075.2.a.dj.1.2 4
165.119 odd 10 825.2.n.k.526.2 8
165.152 even 20 825.2.bx.h.724.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.a.16.1 8 3.2 odd 2
165.2.m.a.31.1 yes 8 33.20 odd 10
495.2.n.d.181.2 8 1.1 even 1 trivial
495.2.n.d.361.2 8 11.9 even 5 inner
825.2.n.k.526.2 8 165.119 odd 10
825.2.n.k.676.2 8 15.14 odd 2
825.2.bx.h.49.2 16 15.2 even 4
825.2.bx.h.49.3 16 15.8 even 4
825.2.bx.h.724.2 16 165.53 even 20
825.2.bx.h.724.3 16 165.152 even 20
1815.2.a.o.1.3 4 33.8 even 10
1815.2.a.x.1.2 4 33.14 odd 10
5445.2.a.be.1.3 4 11.3 even 5
5445.2.a.bv.1.2 4 11.8 odd 10
9075.2.a.cl.1.3 4 165.14 odd 10
9075.2.a.dj.1.2 4 165.74 even 10