Properties

Label 98.5.d.c.31.1
Level $98$
Weight $5$
Character 98.31
Analytic conductor $10.130$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [98,5,Mod(19,98)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(98, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("98.19");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 98.d (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.1302563822\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(-1.60021 - 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 98.31
Dual form 98.5.d.c.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41421 - 2.44949i) q^{2} +(-1.76104 - 1.01673i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(0.615721 - 0.355487i) q^{5} +5.75152i q^{6} +22.6274 q^{8} +(-38.4325 - 66.5670i) q^{9} +O(q^{10})\) \(q+(-1.41421 - 2.44949i) q^{2} +(-1.76104 - 1.01673i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(0.615721 - 0.355487i) q^{5} +5.75152i q^{6} +22.6274 q^{8} +(-38.4325 - 66.5670i) q^{9} +(-1.74152 - 1.00547i) q^{10} +(-75.8320 + 131.345i) q^{11} +(14.0883 - 8.13387i) q^{12} +260.864i q^{13} -1.44574 q^{15} +(-32.0000 - 55.4256i) q^{16} +(333.938 + 192.799i) q^{17} +(-108.704 + 188.280i) q^{18} +(337.871 - 195.070i) q^{19} +5.68779i q^{20} +428.971 q^{22} +(88.8234 + 153.847i) q^{23} +(-39.8477 - 23.0061i) q^{24} +(-312.247 + 540.828i) q^{25} +(638.984 - 368.918i) q^{26} +321.013i q^{27} -320.887 q^{29} +(2.04459 + 3.54133i) q^{30} +(1165.99 + 673.186i) q^{31} +(-90.5097 + 156.767i) q^{32} +(267.086 - 154.202i) q^{33} -1090.64i q^{34} +614.920 q^{36} +(398.544 + 690.299i) q^{37} +(-955.643 - 551.741i) q^{38} +(265.230 - 459.391i) q^{39} +(13.9322 - 8.04375i) q^{40} +815.856i q^{41} -2167.70 q^{43} +(-606.656 - 1050.76i) q^{44} +(-47.3274 - 27.3245i) q^{45} +(251.230 - 435.144i) q^{46} +(-3711.45 + 2142.80i) q^{47} +130.142i q^{48} +1766.34 q^{50} +(-392.051 - 679.052i) q^{51} +(-1807.32 - 1043.46i) q^{52} +(1585.78 - 2746.66i) q^{53} +(786.319 - 453.982i) q^{54} +107.829i q^{55} -793.337 q^{57} +(453.803 + 786.010i) q^{58} +(-4075.86 - 2353.20i) q^{59} +(5.78297 - 10.0164i) q^{60} +(-2195.18 + 1267.39i) q^{61} -3808.12i q^{62} +512.000 q^{64} +(92.7338 + 160.620i) q^{65} +(-755.432 - 436.149i) q^{66} +(2046.21 - 3544.15i) q^{67} +(-2671.50 + 1542.39i) q^{68} -361.239i q^{69} -2255.28 q^{71} +(-869.628 - 1506.24i) q^{72} +(4029.78 + 2326.60i) q^{73} +(1127.25 - 1952.46i) q^{74} +(1099.76 - 634.945i) q^{75} +3121.12i q^{76} -1500.37 q^{78} +(2096.87 + 3631.88i) q^{79} +(-39.4062 - 22.7512i) q^{80} +(-2786.65 + 4826.61i) q^{81} +(1998.43 - 1153.80i) q^{82} -7799.12i q^{83} +274.150 q^{85} +(3065.59 + 5309.76i) q^{86} +(565.094 + 326.257i) q^{87} +(-1715.88 + 2972.00i) q^{88} +(8200.49 - 4734.55i) q^{89} +154.571i q^{90} -1421.17 q^{92} +(-1368.90 - 2371.01i) q^{93} +(10497.6 + 6060.77i) q^{94} +(138.690 - 240.217i) q^{95} +(318.781 - 184.049i) q^{96} +9945.39i q^{97} +11657.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 32 q^{4} + 196 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 32 q^{4} + 196 q^{9} - 24 q^{11} + 1776 q^{15} - 256 q^{16} - 1424 q^{18} + 3296 q^{22} - 104 q^{23} - 948 q^{25} - 2816 q^{29} + 2528 q^{30} - 3136 q^{36} + 3392 q^{37} - 2200 q^{39} - 4048 q^{43} - 192 q^{44} + 2304 q^{46} + 8768 q^{50} - 18936 q^{51} + 16680 q^{53} - 12128 q^{57} - 352 q^{58} - 7104 q^{60} + 4096 q^{64} + 6048 q^{65} + 20816 q^{67} - 3968 q^{71} - 11392 q^{72} - 576 q^{74} - 24448 q^{78} + 29616 q^{79} - 30852 q^{81} - 59376 q^{85} + 18800 q^{86} - 13184 q^{88} + 1664 q^{92} - 18192 q^{93} - 7240 q^{95} + 144320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 2.44949i −0.353553 0.612372i
\(3\) −1.76104 1.01673i −0.195671 0.112970i 0.398964 0.916967i \(-0.369370\pi\)
−0.594634 + 0.803996i \(0.702703\pi\)
\(4\) −4.00000 + 6.92820i −0.250000 + 0.433013i
\(5\) 0.615721 0.355487i 0.0246289 0.0142195i −0.487635 0.873048i \(-0.662140\pi\)
0.512264 + 0.858828i \(0.328807\pi\)
\(6\) 5.75152i 0.159764i
\(7\) 0 0
\(8\) 22.6274 0.353553
\(9\) −38.4325 66.5670i −0.474475 0.821815i
\(10\) −1.74152 1.00547i −0.0174152 0.0100547i
\(11\) −75.8320 + 131.345i −0.626711 + 1.08549i 0.361497 + 0.932373i \(0.382266\pi\)
−0.988207 + 0.153121i \(0.951067\pi\)
\(12\) 14.0883 8.13387i 0.0978353 0.0564852i
\(13\) 260.864i 1.54358i 0.635880 + 0.771788i \(0.280637\pi\)
−0.635880 + 0.771788i \(0.719363\pi\)
\(14\) 0 0
\(15\) −1.44574 −0.00642552
\(16\) −32.0000 55.4256i −0.125000 0.216506i
\(17\) 333.938 + 192.799i 1.15549 + 0.667125i 0.950220 0.311580i \(-0.100858\pi\)
0.205274 + 0.978705i \(0.434191\pi\)
\(18\) −108.704 + 188.280i −0.335505 + 0.581111i
\(19\) 337.871 195.070i 0.935931 0.540360i 0.0472483 0.998883i \(-0.484955\pi\)
0.888682 + 0.458523i \(0.151621\pi\)
\(20\) 5.68779i 0.0142195i
\(21\) 0 0
\(22\) 428.971 0.886303
\(23\) 88.8234 + 153.847i 0.167908 + 0.290825i 0.937684 0.347489i \(-0.112965\pi\)
−0.769776 + 0.638314i \(0.779632\pi\)
\(24\) −39.8477 23.0061i −0.0691800 0.0399411i
\(25\) −312.247 + 540.828i −0.499596 + 0.865325i
\(26\) 638.984 368.918i 0.945243 0.545736i
\(27\) 321.013i 0.440348i
\(28\) 0 0
\(29\) −320.887 −0.381554 −0.190777 0.981633i \(-0.561101\pi\)
−0.190777 + 0.981633i \(0.561101\pi\)
\(30\) 2.04459 + 3.54133i 0.00227177 + 0.00393481i
\(31\) 1165.99 + 673.186i 1.21331 + 0.700506i 0.963479 0.267783i \(-0.0862909\pi\)
0.249833 + 0.968289i \(0.419624\pi\)
\(32\) −90.5097 + 156.767i −0.0883883 + 0.153093i
\(33\) 267.086 154.202i 0.245258 0.141600i
\(34\) 1090.64i 0.943457i
\(35\) 0 0
\(36\) 614.920 0.474475
\(37\) 398.544 + 690.299i 0.291121 + 0.504236i 0.974075 0.226225i \(-0.0726386\pi\)
−0.682954 + 0.730461i \(0.739305\pi\)
\(38\) −955.643 551.741i −0.661803 0.382092i
\(39\) 265.230 459.391i 0.174378 0.302032i
\(40\) 13.9322 8.04375i 0.00870762 0.00502734i
\(41\) 815.856i 0.485340i 0.970109 + 0.242670i \(0.0780232\pi\)
−0.970109 + 0.242670i \(0.921977\pi\)
\(42\) 0 0
\(43\) −2167.70 −1.17236 −0.586182 0.810179i \(-0.699370\pi\)
−0.586182 + 0.810179i \(0.699370\pi\)
\(44\) −606.656 1050.76i −0.313355 0.542747i
\(45\) −47.3274 27.3245i −0.0233716 0.0134936i
\(46\) 251.230 435.144i 0.118729 0.205645i
\(47\) −3711.45 + 2142.80i −1.68015 + 0.970034i −0.718589 + 0.695435i \(0.755212\pi\)
−0.961559 + 0.274598i \(0.911455\pi\)
\(48\) 130.142i 0.0564852i
\(49\) 0 0
\(50\) 1766.34 0.706535
\(51\) −392.051 679.052i −0.150731 0.261073i
\(52\) −1807.32 1043.46i −0.668388 0.385894i
\(53\) 1585.78 2746.66i 0.564536 0.977806i −0.432556 0.901607i \(-0.642388\pi\)
0.997093 0.0761987i \(-0.0242783\pi\)
\(54\) 786.319 453.982i 0.269657 0.155686i
\(55\) 107.829i 0.0356460i
\(56\) 0 0
\(57\) −793.337 −0.244179
\(58\) 453.803 + 786.010i 0.134900 + 0.233653i
\(59\) −4075.86 2353.20i −1.17089 0.676012i −0.216998 0.976172i \(-0.569627\pi\)
−0.953889 + 0.300160i \(0.902960\pi\)
\(60\) 5.78297 10.0164i 0.00160638 0.00278233i
\(61\) −2195.18 + 1267.39i −0.589944 + 0.340604i −0.765075 0.643941i \(-0.777298\pi\)
0.175131 + 0.984545i \(0.443965\pi\)
\(62\) 3808.12i 0.990665i
\(63\) 0 0
\(64\) 512.000 0.125000
\(65\) 92.7338 + 160.620i 0.0219488 + 0.0380165i
\(66\) −755.432 436.149i −0.173423 0.100126i
\(67\) 2046.21 3544.15i 0.455828 0.789518i −0.542907 0.839793i \(-0.682676\pi\)
0.998735 + 0.0502748i \(0.0160097\pi\)
\(68\) −2671.50 + 1542.39i −0.577747 + 0.333562i
\(69\) 361.239i 0.0758746i
\(70\) 0 0
\(71\) −2255.28 −0.447388 −0.223694 0.974659i \(-0.571812\pi\)
−0.223694 + 0.974659i \(0.571812\pi\)
\(72\) −869.628 1506.24i −0.167752 0.290556i
\(73\) 4029.78 + 2326.60i 0.756198 + 0.436591i 0.827929 0.560833i \(-0.189519\pi\)
−0.0717308 + 0.997424i \(0.522852\pi\)
\(74\) 1127.25 1952.46i 0.205853 0.356549i
\(75\) 1099.76 634.945i 0.195512 0.112879i
\(76\) 3121.12i 0.540360i
\(77\) 0 0
\(78\) −1500.37 −0.246608
\(79\) 2096.87 + 3631.88i 0.335983 + 0.581939i 0.983673 0.179965i \(-0.0575983\pi\)
−0.647690 + 0.761904i \(0.724265\pi\)
\(80\) −39.4062 22.7512i −0.00615721 0.00355487i
\(81\) −2786.65 + 4826.61i −0.424729 + 0.735652i
\(82\) 1998.43 1153.80i 0.297209 0.171594i
\(83\) 7799.12i 1.13211i −0.824367 0.566056i \(-0.808468\pi\)
0.824367 0.566056i \(-0.191532\pi\)
\(84\) 0 0
\(85\) 274.150 0.0379447
\(86\) 3065.59 + 5309.76i 0.414493 + 0.717923i
\(87\) 565.094 + 326.257i 0.0746590 + 0.0431044i
\(88\) −1715.88 + 2972.00i −0.221576 + 0.383780i
\(89\) 8200.49 4734.55i 1.03528 0.597722i 0.116790 0.993157i \(-0.462739\pi\)
0.918494 + 0.395435i \(0.129406\pi\)
\(90\) 154.571i 0.0190828i
\(91\) 0 0
\(92\) −1421.17 −0.167908
\(93\) −1368.90 2371.01i −0.158273 0.274137i
\(94\) 10497.6 + 6060.77i 1.18804 + 0.685917i
\(95\) 138.690 240.217i 0.0153673 0.0266169i
\(96\) 318.781 184.049i 0.0345900 0.0199705i
\(97\) 9945.39i 1.05701i 0.848931 + 0.528504i \(0.177247\pi\)
−0.848931 + 0.528504i \(0.822753\pi\)
\(98\) 0 0
\(99\) 11657.7 1.18944
\(100\) −2497.98 4326.62i −0.249798 0.432662i
\(101\) −1791.21 1034.16i −0.175592 0.101378i 0.409628 0.912253i \(-0.365659\pi\)
−0.585220 + 0.810875i \(0.698992\pi\)
\(102\) −1108.89 + 1920.65i −0.106583 + 0.184607i
\(103\) 2169.19 1252.38i 0.204467 0.118049i −0.394271 0.918994i \(-0.629003\pi\)
0.598737 + 0.800946i \(0.295669\pi\)
\(104\) 5902.68i 0.545736i
\(105\) 0 0
\(106\) −8970.54 −0.798375
\(107\) −3221.70 5580.14i −0.281395 0.487391i 0.690333 0.723491i \(-0.257464\pi\)
−0.971729 + 0.236100i \(0.924131\pi\)
\(108\) −2224.05 1284.05i −0.190676 0.110087i
\(109\) −11773.0 + 20391.5i −0.990912 + 1.71631i −0.378962 + 0.925412i \(0.623719\pi\)
−0.611949 + 0.790897i \(0.709614\pi\)
\(110\) 264.126 152.493i 0.0218286 0.0126028i
\(111\) 1620.85i 0.131552i
\(112\) 0 0
\(113\) 19692.2 1.54219 0.771096 0.636719i \(-0.219709\pi\)
0.771096 + 0.636719i \(0.219709\pi\)
\(114\) 1121.95 + 1943.27i 0.0863302 + 0.149528i
\(115\) 109.381 + 63.1511i 0.00827077 + 0.00477513i
\(116\) 1283.55 2223.17i 0.0953886 0.165218i
\(117\) 17365.0 10025.7i 1.26853 0.732389i
\(118\) 13311.7i 0.956025i
\(119\) 0 0
\(120\) −32.7134 −0.00227177
\(121\) −4180.48 7240.81i −0.285533 0.494557i
\(122\) 6208.91 + 3584.72i 0.417154 + 0.240844i
\(123\) 829.509 1436.75i 0.0548291 0.0949667i
\(124\) −9327.95 + 5385.49i −0.606656 + 0.350253i
\(125\) 888.358i 0.0568549i
\(126\) 0 0
\(127\) −12550.5 −0.778135 −0.389067 0.921209i \(-0.627203\pi\)
−0.389067 + 0.921209i \(0.627203\pi\)
\(128\) −724.077 1254.14i −0.0441942 0.0765466i
\(129\) 3817.40 + 2203.98i 0.229397 + 0.132442i
\(130\) 262.291 454.301i 0.0155202 0.0268817i
\(131\) −16734.4 + 9661.63i −0.975143 + 0.562999i −0.900800 0.434234i \(-0.857019\pi\)
−0.0743429 + 0.997233i \(0.523686\pi\)
\(132\) 2467.23i 0.141600i
\(133\) 0 0
\(134\) −11575.1 −0.644639
\(135\) 114.116 + 197.655i 0.00626151 + 0.0108453i
\(136\) 7556.15 + 4362.54i 0.408529 + 0.235864i
\(137\) −1854.29 + 3211.73i −0.0987955 + 0.171119i −0.911186 0.411994i \(-0.864832\pi\)
0.812391 + 0.583113i \(0.198166\pi\)
\(138\) −884.851 + 510.869i −0.0464635 + 0.0268257i
\(139\) 1096.09i 0.0567307i 0.999598 + 0.0283653i \(0.00903018\pi\)
−0.999598 + 0.0283653i \(0.990970\pi\)
\(140\) 0 0
\(141\) 8714.65 0.438341
\(142\) 3189.45 + 5524.29i 0.158175 + 0.273968i
\(143\) −34263.2 19781.9i −1.67554 0.967375i
\(144\) −2459.68 + 4260.29i −0.118619 + 0.205454i
\(145\) −197.577 + 114.071i −0.00939725 + 0.00542551i
\(146\) 13161.2i 0.617433i
\(147\) 0 0
\(148\) −6376.71 −0.291121
\(149\) 616.908 + 1068.52i 0.0277874 + 0.0481291i 0.879585 0.475742i \(-0.157821\pi\)
−0.851797 + 0.523872i \(0.824487\pi\)
\(150\) −3110.58 1795.90i −0.138248 0.0798176i
\(151\) 21336.4 36955.7i 0.935766 1.62079i 0.162503 0.986708i \(-0.448043\pi\)
0.773262 0.634086i \(-0.218624\pi\)
\(152\) 7645.15 4413.93i 0.330901 0.191046i
\(153\) 29639.0i 1.26614i
\(154\) 0 0
\(155\) 957.236 0.0398433
\(156\) 2121.84 + 3675.13i 0.0871892 + 0.151016i
\(157\) 25881.1 + 14942.5i 1.04999 + 0.606209i 0.922645 0.385650i \(-0.126023\pi\)
0.127340 + 0.991859i \(0.459356\pi\)
\(158\) 5930.84 10272.5i 0.237576 0.411493i
\(159\) −5585.24 + 3224.64i −0.220926 + 0.127552i
\(160\) 128.700i 0.00502734i
\(161\) 0 0
\(162\) 15763.7 0.600658
\(163\) 13102.6 + 22694.4i 0.493154 + 0.854168i 0.999969 0.00788711i \(-0.00251057\pi\)
−0.506815 + 0.862055i \(0.669177\pi\)
\(164\) −5652.42 3263.43i −0.210158 0.121335i
\(165\) 109.634 189.891i 0.00402694 0.00697487i
\(166\) −19103.9 + 11029.6i −0.693275 + 0.400262i
\(167\) 35887.5i 1.28680i −0.765532 0.643398i \(-0.777524\pi\)
0.765532 0.643398i \(-0.222476\pi\)
\(168\) 0 0
\(169\) −39489.2 −1.38263
\(170\) −387.707 671.528i −0.0134155 0.0232363i
\(171\) −25970.5 14994.0i −0.888152 0.512775i
\(172\) 8670.80 15018.3i 0.293091 0.507648i
\(173\) 9502.65 5486.36i 0.317506 0.183312i −0.332774 0.943007i \(-0.607985\pi\)
0.650281 + 0.759694i \(0.274651\pi\)
\(174\) 1845.59i 0.0609588i
\(175\) 0 0
\(176\) 9706.50 0.313355
\(177\) 4785.15 + 8288.13i 0.152739 + 0.264551i
\(178\) −23194.5 13391.3i −0.732057 0.422653i
\(179\) 16922.1 29309.9i 0.528138 0.914761i −0.471324 0.881960i \(-0.656224\pi\)
0.999462 0.0328012i \(-0.0104428\pi\)
\(180\) 378.619 218.596i 0.0116858 0.00674679i
\(181\) 50094.5i 1.52909i 0.644571 + 0.764545i \(0.277036\pi\)
−0.644571 + 0.764545i \(0.722964\pi\)
\(182\) 0 0
\(183\) 5154.39 0.153913
\(184\) 2009.84 + 3481.15i 0.0593645 + 0.102822i
\(185\) 490.784 + 283.354i 0.0143399 + 0.00827917i
\(186\) −3871.84 + 6706.23i −0.111916 + 0.193844i
\(187\) −50646.3 + 29240.7i −1.44832 + 0.836189i
\(188\) 34284.9i 0.970034i
\(189\) 0 0
\(190\) −784.547 −0.0217326
\(191\) −8806.47 15253.3i −0.241399 0.418115i 0.719714 0.694271i \(-0.244273\pi\)
−0.961113 + 0.276155i \(0.910940\pi\)
\(192\) −901.650 520.568i −0.0244588 0.0141213i
\(193\) −6632.12 + 11487.2i −0.178048 + 0.308389i −0.941212 0.337817i \(-0.890312\pi\)
0.763164 + 0.646205i \(0.223645\pi\)
\(194\) 24361.1 14064.9i 0.647282 0.373709i
\(195\) 377.143i 0.00991828i
\(196\) 0 0
\(197\) 5362.20 0.138169 0.0690844 0.997611i \(-0.477992\pi\)
0.0690844 + 0.997611i \(0.477992\pi\)
\(198\) −16486.4 28555.3i −0.420529 0.728377i
\(199\) 36572.8 + 21115.3i 0.923532 + 0.533202i 0.884760 0.466047i \(-0.154322\pi\)
0.0387720 + 0.999248i \(0.487655\pi\)
\(200\) −7065.35 + 12237.5i −0.176634 + 0.305939i
\(201\) −7206.91 + 4160.91i −0.178384 + 0.102990i
\(202\) 5850.08i 0.143370i
\(203\) 0 0
\(204\) 6272.81 0.150731
\(205\) 290.026 + 502.340i 0.00690128 + 0.0119534i
\(206\) −6135.38 3542.27i −0.144580 0.0834731i
\(207\) 6827.41 11825.4i 0.159336 0.275979i
\(208\) 14458.6 8347.66i 0.334194 0.192947i
\(209\) 59170.2i 1.35460i
\(210\) 0 0
\(211\) −77049.0 −1.73062 −0.865311 0.501236i \(-0.832879\pi\)
−0.865311 + 0.501236i \(0.832879\pi\)
\(212\) 12686.3 + 21973.2i 0.282268 + 0.488903i
\(213\) 3971.63 + 2293.02i 0.0875406 + 0.0505416i
\(214\) −9112.33 + 15783.0i −0.198977 + 0.344638i
\(215\) −1334.70 + 770.589i −0.0288740 + 0.0166704i
\(216\) 7263.71i 0.155686i
\(217\) 0 0
\(218\) 66598.3 1.40136
\(219\) −4731.06 8194.43i −0.0986438 0.170856i
\(220\) −747.062 431.317i −0.0154352 0.00891150i
\(221\) −50294.4 + 87112.4i −1.02976 + 1.78359i
\(222\) −3970.26 + 2292.23i −0.0805589 + 0.0465107i
\(223\) 3702.60i 0.0744555i 0.999307 + 0.0372278i \(0.0118527\pi\)
−0.999307 + 0.0372278i \(0.988147\pi\)
\(224\) 0 0
\(225\) 48001.8 0.948183
\(226\) −27849.0 48235.9i −0.545247 0.944396i
\(227\) 10408.5 + 6009.38i 0.201994 + 0.116621i 0.597585 0.801805i \(-0.296127\pi\)
−0.395591 + 0.918427i \(0.629460\pi\)
\(228\) 3173.35 5496.40i 0.0610447 0.105733i
\(229\) 28891.0 16680.2i 0.550924 0.318076i −0.198570 0.980087i \(-0.563630\pi\)
0.749495 + 0.662010i \(0.230297\pi\)
\(230\) 357.237i 0.00675305i
\(231\) 0 0
\(232\) −7260.85 −0.134900
\(233\) −27069.4 46885.7i −0.498618 0.863631i 0.501381 0.865226i \(-0.332825\pi\)
−0.999999 + 0.00159563i \(0.999492\pi\)
\(234\) −49115.5 28356.9i −0.896989 0.517877i
\(235\) −1523.48 + 2638.74i −0.0275867 + 0.0477816i
\(236\) 32606.9 18825.6i 0.585443 0.338006i
\(237\) 8527.83i 0.151824i
\(238\) 0 0
\(239\) 29165.4 0.510590 0.255295 0.966863i \(-0.417827\pi\)
0.255295 + 0.966863i \(0.417827\pi\)
\(240\) 46.2638 + 80.1312i 0.000803190 + 0.00139117i
\(241\) 86715.3 + 50065.1i 1.49301 + 0.861988i 0.999968 0.00801977i \(-0.00255280\pi\)
0.493039 + 0.870007i \(0.335886\pi\)
\(242\) −11824.2 + 20480.1i −0.201902 + 0.349705i
\(243\) 32333.2 18667.6i 0.547566 0.316138i
\(244\) 20278.2i 0.340604i
\(245\) 0 0
\(246\) −4692.41 −0.0775400
\(247\) 50886.8 + 88138.5i 0.834086 + 1.44468i
\(248\) 26383.4 + 15232.5i 0.428971 + 0.247666i
\(249\) −7929.64 + 13734.5i −0.127895 + 0.221521i
\(250\) 2176.02 1256.33i 0.0348164 0.0201012i
\(251\) 81988.2i 1.30138i 0.759344 + 0.650690i \(0.225520\pi\)
−0.759344 + 0.650690i \(0.774480\pi\)
\(252\) 0 0
\(253\) −26942.6 −0.420919
\(254\) 17749.1 + 30742.4i 0.275112 + 0.476508i
\(255\) −482.788 278.738i −0.00742465 0.00428663i
\(256\) −2048.00 + 3547.24i −0.0312500 + 0.0541266i
\(257\) 63890.8 36887.4i 0.967324 0.558485i 0.0689050 0.997623i \(-0.478049\pi\)
0.898420 + 0.439138i \(0.144716\pi\)
\(258\) 12467.6i 0.187302i
\(259\) 0 0
\(260\) −1483.74 −0.0219488
\(261\) 12332.5 + 21360.5i 0.181038 + 0.313567i
\(262\) 47332.1 + 27327.2i 0.689530 + 0.398101i
\(263\) −19621.8 + 33985.9i −0.283679 + 0.491346i −0.972288 0.233787i \(-0.924888\pi\)
0.688609 + 0.725133i \(0.258222\pi\)
\(264\) 6043.46 3489.19i 0.0867117 0.0500630i
\(265\) 2254.90i 0.0321096i
\(266\) 0 0
\(267\) −19255.1 −0.270100
\(268\) 16369.7 + 28353.2i 0.227914 + 0.394759i
\(269\) 8930.08 + 5155.78i 0.123410 + 0.0712509i 0.560434 0.828199i \(-0.310634\pi\)
−0.437024 + 0.899450i \(0.643968\pi\)
\(270\) 322.769 559.052i 0.00442756 0.00766876i
\(271\) −32016.3 + 18484.6i −0.435946 + 0.251694i −0.701877 0.712299i \(-0.747654\pi\)
0.265930 + 0.963992i \(0.414321\pi\)
\(272\) 24678.3i 0.333562i
\(273\) 0 0
\(274\) 10489.5 0.139718
\(275\) −47356.7 82024.2i −0.626204 1.08462i
\(276\) 2502.74 + 1444.96i 0.0328547 + 0.0189687i
\(277\) 46202.9 80025.8i 0.602157 1.04297i −0.390337 0.920672i \(-0.627641\pi\)
0.992494 0.122294i \(-0.0390252\pi\)
\(278\) 2684.87 1550.11i 0.0347403 0.0200573i
\(279\) 103489.i 1.32949i
\(280\) 0 0
\(281\) 21171.6 0.268128 0.134064 0.990973i \(-0.457197\pi\)
0.134064 + 0.990973i \(0.457197\pi\)
\(282\) −12324.4 21346.4i −0.154977 0.268428i
\(283\) −41625.7 24032.6i −0.519743 0.300074i 0.217087 0.976152i \(-0.430345\pi\)
−0.736829 + 0.676079i \(0.763678\pi\)
\(284\) 9021.13 15625.0i 0.111847 0.193725i
\(285\) −488.475 + 282.021i −0.00601384 + 0.00347209i
\(286\) 111903.i 1.36808i
\(287\) 0 0
\(288\) 13914.1 0.167752
\(289\) 32582.5 + 56434.5i 0.390111 + 0.675692i
\(290\) 558.833 + 322.642i 0.00664486 + 0.00383641i
\(291\) 10111.8 17514.2i 0.119411 0.206825i
\(292\) −32238.2 + 18612.8i −0.378099 + 0.218296i
\(293\) 26781.1i 0.311956i −0.987761 0.155978i \(-0.950147\pi\)
0.987761 0.155978i \(-0.0498528\pi\)
\(294\) 0 0
\(295\) −3346.12 −0.0384501
\(296\) 9018.02 + 15619.7i 0.102927 + 0.178274i
\(297\) −42163.5 24343.1i −0.477995 0.275971i
\(298\) 1744.88 3022.22i 0.0196486 0.0340324i
\(299\) −40133.1 + 23170.8i −0.448911 + 0.259179i
\(300\) 10159.1i 0.112879i
\(301\) 0 0
\(302\) −120697. −1.32337
\(303\) 2102.93 + 3642.38i 0.0229055 + 0.0396734i
\(304\) −21623.7 12484.5i −0.233983 0.135090i
\(305\) −901.081 + 1560.72i −0.00968643 + 0.0167774i
\(306\) −72600.4 + 41915.9i −0.775347 + 0.447647i
\(307\) 69996.0i 0.742671i −0.928499 0.371336i \(-0.878900\pi\)
0.928499 0.371336i \(-0.121100\pi\)
\(308\) 0 0
\(309\) −5093.35 −0.0533441
\(310\) −1353.74 2344.74i −0.0140867 0.0243990i
\(311\) −75310.9 43480.8i −0.778641 0.449549i 0.0573075 0.998357i \(-0.481748\pi\)
−0.835948 + 0.548808i \(0.815082\pi\)
\(312\) 6001.46 10394.8i 0.0616521 0.106785i
\(313\) −28720.2 + 16581.6i −0.293156 + 0.169253i −0.639364 0.768904i \(-0.720802\pi\)
0.346208 + 0.938158i \(0.387469\pi\)
\(314\) 84527.3i 0.857310i
\(315\) 0 0
\(316\) −33549.9 −0.335983
\(317\) −14603.0 25293.1i −0.145319 0.251700i 0.784173 0.620543i \(-0.213088\pi\)
−0.929492 + 0.368842i \(0.879754\pi\)
\(318\) 15797.4 + 9120.66i 0.156218 + 0.0901928i
\(319\) 24333.5 42146.9i 0.239124 0.414175i
\(320\) 315.249 182.009i 0.00307861 0.00177743i
\(321\) 13102.4i 0.127157i
\(322\) 0 0
\(323\) 150437. 1.44195
\(324\) −22293.2 38612.9i −0.212365 0.367826i
\(325\) −141083. 81454.1i −1.33569 0.771164i
\(326\) 37059.8 64189.4i 0.348713 0.603988i
\(327\) 41465.4 23940.1i 0.387784 0.223887i
\(328\) 18460.7i 0.171594i
\(329\) 0 0
\(330\) −620.181 −0.00569496
\(331\) −83496.6 144620.i −0.762102 1.32000i −0.941765 0.336271i \(-0.890834\pi\)
0.179664 0.983728i \(-0.442499\pi\)
\(332\) 54033.9 + 31196.5i 0.490219 + 0.283028i
\(333\) 30634.1 53059.8i 0.276259 0.478495i
\(334\) −87906.0 + 50752.5i −0.787999 + 0.454951i
\(335\) 2909.61i 0.0259266i
\(336\) 0 0
\(337\) 16126.0 0.141993 0.0709964 0.997477i \(-0.477382\pi\)
0.0709964 + 0.997477i \(0.477382\pi\)
\(338\) 55846.1 + 96728.3i 0.488832 + 0.846682i
\(339\) −34678.7 20021.8i −0.301761 0.174222i
\(340\) −1096.60 + 1899.37i −0.00948617 + 0.0164305i
\(341\) −176839. + 102098.i −1.52079 + 0.878030i
\(342\) 84819.2i 0.725173i
\(343\) 0 0
\(344\) −49049.5 −0.414493
\(345\) −128.416 222.423i −0.00107890 0.00186871i
\(346\) −26877.5 15517.8i −0.224511 0.129621i
\(347\) −5035.67 + 8722.04i −0.0418214 + 0.0724368i −0.886178 0.463344i \(-0.846649\pi\)
0.844357 + 0.535781i \(0.179983\pi\)
\(348\) −4520.75 + 2610.06i −0.0373295 + 0.0215522i
\(349\) 97674.1i 0.801915i −0.916097 0.400958i \(-0.868677\pi\)
0.916097 0.400958i \(-0.131323\pi\)
\(350\) 0 0
\(351\) −83740.9 −0.679710
\(352\) −13727.1 23776.0i −0.110788 0.191890i
\(353\) −73833.2 42627.6i −0.592519 0.342091i 0.173574 0.984821i \(-0.444468\pi\)
−0.766093 + 0.642730i \(0.777802\pi\)
\(354\) 13534.5 23442.4i 0.108003 0.187066i
\(355\) −1388.63 + 801.723i −0.0110186 + 0.00636162i
\(356\) 75752.9i 0.597722i
\(357\) 0 0
\(358\) −95725.6 −0.746899
\(359\) 71119.9 + 123183.i 0.551826 + 0.955791i 0.998143 + 0.0609162i \(0.0194022\pi\)
−0.446316 + 0.894875i \(0.647264\pi\)
\(360\) −1070.90 618.283i −0.00826310 0.00477070i
\(361\) 10944.0 18955.6i 0.0839775 0.145453i
\(362\) 122706. 70844.3i 0.936372 0.540615i
\(363\) 17001.8i 0.129027i
\(364\) 0 0
\(365\) 3308.30 0.0248324
\(366\) −7289.41 12625.6i −0.0544164 0.0942520i
\(367\) 154015. + 88920.4i 1.14348 + 0.660191i 0.947291 0.320375i \(-0.103809\pi\)
0.196193 + 0.980565i \(0.437142\pi\)
\(368\) 5684.70 9846.18i 0.0419770 0.0727063i
\(369\) 54309.1 31355.4i 0.398860 0.230282i
\(370\) 1602.90i 0.0117085i
\(371\) 0 0
\(372\) 21902.5 0.158273
\(373\) 10835.4 + 18767.5i 0.0778803 + 0.134893i 0.902335 0.431035i \(-0.141851\pi\)
−0.824455 + 0.565928i \(0.808518\pi\)
\(374\) 143249. + 82705.1i 1.02412 + 0.591275i
\(375\) 903.224 1564.43i 0.00642293 0.0111248i
\(376\) −83980.4 + 48486.1i −0.594022 + 0.342959i
\(377\) 83708.0i 0.588958i
\(378\) 0 0
\(379\) 125199. 0.871608 0.435804 0.900042i \(-0.356464\pi\)
0.435804 + 0.900042i \(0.356464\pi\)
\(380\) 1109.52 + 1921.74i 0.00768363 + 0.0133084i
\(381\) 22101.9 + 12760.6i 0.152258 + 0.0879062i
\(382\) −24908.5 + 43142.7i −0.170695 + 0.295652i
\(383\) 183086. 105705.i 1.24813 0.720605i 0.277390 0.960757i \(-0.410531\pi\)
0.970735 + 0.240152i \(0.0771973\pi\)
\(384\) 2944.78i 0.0199705i
\(385\) 0 0
\(386\) 37516.9 0.251798
\(387\) 83310.2 + 144297.i 0.556258 + 0.963467i
\(388\) −68903.7 39781.5i −0.457698 0.264252i
\(389\) 19580.4 33914.2i 0.129396 0.224121i −0.794047 0.607857i \(-0.792029\pi\)
0.923443 + 0.383736i \(0.125363\pi\)
\(390\) −923.807 + 533.360i −0.00607368 + 0.00350664i
\(391\) 68500.3i 0.448063i
\(392\) 0 0
\(393\) 39293.2 0.254409
\(394\) −7583.29 13134.6i −0.0488501 0.0846108i
\(395\) 2582.17 + 1490.82i 0.0165497 + 0.00955500i
\(396\) −46630.6 + 80766.6i −0.297359 + 0.515041i
\(397\) 170195. 98262.3i 1.07986 0.623456i 0.149000 0.988837i \(-0.452395\pi\)
0.930858 + 0.365381i \(0.119061\pi\)
\(398\) 119446.i 0.754061i
\(399\) 0 0
\(400\) 39967.6 0.249798
\(401\) −106825. 185026.i −0.664330 1.15065i −0.979466 0.201608i \(-0.935383\pi\)
0.315136 0.949047i \(-0.397950\pi\)
\(402\) 20384.2 + 11768.8i 0.126137 + 0.0728251i
\(403\) −175610. + 304166.i −1.08128 + 1.87284i
\(404\) 14329.7 8273.26i 0.0877960 0.0506890i
\(405\) 3962.47i 0.0241577i
\(406\) 0 0
\(407\) −120890. −0.729794
\(408\) −8871.10 15365.2i −0.0532914 0.0923034i
\(409\) 30834.0 + 17802.0i 0.184325 + 0.106420i 0.589323 0.807898i \(-0.299395\pi\)
−0.404998 + 0.914317i \(0.632728\pi\)
\(410\) 820.318 1420.83i 0.00487994 0.00845231i
\(411\) 6530.95 3770.65i 0.0386628 0.0223220i
\(412\) 20038.1i 0.118049i
\(413\) 0 0
\(414\) −38621.7 −0.225336
\(415\) −2772.49 4802.09i −0.0160981 0.0278826i
\(416\) −40895.0 23610.7i −0.236311 0.136434i
\(417\) 1114.44 1930.26i 0.00640889 0.0111005i
\(418\) 144937. 83679.2i 0.829518 0.478922i
\(419\) 254947.i 1.45219i 0.687597 + 0.726093i \(0.258666\pi\)
−0.687597 + 0.726093i \(0.741334\pi\)
\(420\) 0 0
\(421\) 107186. 0.604748 0.302374 0.953189i \(-0.402221\pi\)
0.302374 + 0.953189i \(0.402221\pi\)
\(422\) 108964. + 188731.i 0.611867 + 1.05978i
\(423\) 285280. + 164707.i 1.59438 + 0.920514i
\(424\) 35882.2 62149.7i 0.199594 0.345707i
\(425\) −208542. + 120402.i −1.15456 + 0.666585i
\(426\) 12971.3i 0.0714766i
\(427\) 0 0
\(428\) 51547.1 0.281395
\(429\) 40225.8 + 69673.1i 0.218570 + 0.378574i
\(430\) 3775.10 + 2179.56i 0.0204170 + 0.0117878i
\(431\) −59979.2 + 103887.i −0.322884 + 0.559251i −0.981082 0.193594i \(-0.937986\pi\)
0.658198 + 0.752845i \(0.271319\pi\)
\(432\) 17792.4 10272.4i 0.0953381 0.0550435i
\(433\) 110159.i 0.587547i −0.955875 0.293773i \(-0.905089\pi\)
0.955875 0.293773i \(-0.0949111\pi\)
\(434\) 0 0
\(435\) 463.921 0.00245169
\(436\) −94184.2 163132.i −0.495456 0.858155i
\(437\) 60021.7 + 34653.5i 0.314301 + 0.181462i
\(438\) −13381.4 + 23177.4i −0.0697517 + 0.120814i
\(439\) 305096. 176148.i 1.58310 0.914003i 0.588696 0.808355i \(-0.299642\pi\)
0.994404 0.105648i \(-0.0336917\pi\)
\(440\) 2439.90i 0.0126028i
\(441\) 0 0
\(442\) 284508. 1.45630
\(443\) −142866. 247452.i −0.727984 1.26091i −0.957734 0.287656i \(-0.907124\pi\)
0.229749 0.973250i \(-0.426209\pi\)
\(444\) 11229.6 + 6483.41i 0.0569637 + 0.0328880i
\(445\) 3366.14 5830.33i 0.0169986 0.0294424i
\(446\) 9069.48 5236.27i 0.0455945 0.0263240i
\(447\) 2508.92i 0.0125566i
\(448\) 0 0
\(449\) −342184. −1.69733 −0.848667 0.528927i \(-0.822594\pi\)
−0.848667 + 0.528927i \(0.822594\pi\)
\(450\) −67884.8 117580.i −0.335233 0.580641i
\(451\) −107159. 61868.0i −0.526834 0.304168i
\(452\) −78769.0 + 136432.i −0.385548 + 0.667788i
\(453\) −75148.3 + 43386.9i −0.366204 + 0.211428i
\(454\) 33994.2i 0.164927i
\(455\) 0 0
\(456\) −17951.2 −0.0863302
\(457\) 138812. + 240430.i 0.664653 + 1.15121i 0.979379 + 0.202030i \(0.0647540\pi\)
−0.314726 + 0.949183i \(0.601913\pi\)
\(458\) −81716.2 47178.8i −0.389562 0.224914i
\(459\) −61891.1 + 107199.i −0.293767 + 0.508819i
\(460\) −875.047 + 505.209i −0.00413538 + 0.00238757i
\(461\) 361934.i 1.70305i 0.524315 + 0.851524i \(0.324322\pi\)
−0.524315 + 0.851524i \(0.675678\pi\)
\(462\) 0 0
\(463\) 146876. 0.685153 0.342577 0.939490i \(-0.388700\pi\)
0.342577 + 0.939490i \(0.388700\pi\)
\(464\) 10268.4 + 17785.4i 0.0476943 + 0.0826090i
\(465\) −1685.73 973.255i −0.00779617 0.00450112i
\(466\) −76564.0 + 132613.i −0.352576 + 0.610679i
\(467\) −232450. + 134205.i −1.06585 + 0.615367i −0.927044 0.374953i \(-0.877659\pi\)
−0.138803 + 0.990320i \(0.544326\pi\)
\(468\) 160411.i 0.732389i
\(469\) 0 0
\(470\) 8618.09 0.0390136
\(471\) −30385.0 52628.4i −0.136968 0.237235i
\(472\) −92226.1 53246.8i −0.413971 0.239006i
\(473\) 164381. 284716.i 0.734733 1.27259i
\(474\) −20888.8 + 12060.2i −0.0929731 + 0.0536780i
\(475\) 243640.i 1.07985i
\(476\) 0 0
\(477\) −243782. −1.07143
\(478\) −41246.1 71440.4i −0.180521 0.312671i
\(479\) 134481. + 77642.5i 0.586124 + 0.338399i 0.763563 0.645733i \(-0.223448\pi\)
−0.177440 + 0.984132i \(0.556781\pi\)
\(480\) 130.854 226.645i 0.000567941 0.000983703i
\(481\) −180074. + 103966.i −0.778326 + 0.449367i
\(482\) 283211.i 1.21903i
\(483\) 0 0
\(484\) 66887.7 0.285533
\(485\) 3535.46 + 6123.59i 0.0150301 + 0.0260329i
\(486\) −91452.2 52800.0i −0.387188 0.223543i
\(487\) 77813.9 134778.i 0.328095 0.568277i −0.654039 0.756461i \(-0.726927\pi\)
0.982134 + 0.188184i \(0.0602601\pi\)
\(488\) −49671.3 + 28677.7i −0.208577 + 0.120422i
\(489\) 53287.5i 0.222847i
\(490\) 0 0
\(491\) 37550.7 0.155760 0.0778798 0.996963i \(-0.475185\pi\)
0.0778798 + 0.996963i \(0.475185\pi\)
\(492\) 6636.07 + 11494.0i 0.0274145 + 0.0474834i
\(493\) −107156. 61866.8i −0.440884 0.254544i
\(494\) 143930. 249293.i 0.589788 1.02154i
\(495\) 7177.87 4144.14i 0.0292944 0.0169131i
\(496\) 86167.9i 0.350253i
\(497\) 0 0
\(498\) 44856.8 0.180871
\(499\) −83910.2 145337.i −0.336987 0.583679i 0.646877 0.762594i \(-0.276075\pi\)
−0.983865 + 0.178915i \(0.942741\pi\)
\(500\) −6154.72 3553.43i −0.0246189 0.0142137i
\(501\) −36488.0 + 63199.1i −0.145370 + 0.251788i
\(502\) 200829. 115949.i 0.796929 0.460107i
\(503\) 133035.i 0.525810i −0.964822 0.262905i \(-0.915319\pi\)
0.964822 0.262905i \(-0.0846806\pi\)
\(504\) 0 0
\(505\) −1470.52 −0.00576617
\(506\) 38102.6 + 65995.7i 0.148817 + 0.257759i
\(507\) 69541.8 + 40150.0i 0.270539 + 0.156196i
\(508\) 50202.1 86952.7i 0.194534 0.336942i
\(509\) −197449. + 113997.i −0.762112 + 0.440005i −0.830053 0.557684i \(-0.811690\pi\)
0.0679416 + 0.997689i \(0.478357\pi\)
\(510\) 1576.78i 0.00606220i
\(511\) 0 0
\(512\) 11585.2 0.0441942
\(513\) 62620.1 + 108461.i 0.237946 + 0.412135i
\(514\) −180711. 104333.i −0.684002 0.394909i
\(515\) 890.410 1542.23i 0.00335719 0.00581482i
\(516\) −30539.2 + 17631.8i −0.114699 + 0.0662212i
\(517\) 649973.i 2.43172i
\(518\) 0 0
\(519\) −22312.7 −0.0828355
\(520\) 2098.33 + 3634.41i 0.00776009 + 0.0134409i
\(521\) −295670. 170705.i −1.08926 0.628885i −0.155882 0.987776i \(-0.549822\pi\)
−0.933380 + 0.358890i \(0.883155\pi\)
\(522\) 34881.6 60416.7i 0.128013 0.221726i
\(523\) 54483.4 31456.0i 0.199187 0.115001i −0.397089 0.917780i \(-0.629980\pi\)
0.596276 + 0.802779i \(0.296646\pi\)
\(524\) 154586.i 0.562999i
\(525\) 0 0
\(526\) 110998. 0.401182
\(527\) 259579. + 449605.i 0.934650 + 1.61886i
\(528\) −17093.5 9868.93i −0.0613144 0.0353999i
\(529\) 124141. 215019.i 0.443614 0.768362i
\(530\) −5523.35 + 3188.91i −0.0196631 + 0.0113525i
\(531\) 361757.i 1.28300i
\(532\) 0 0
\(533\) −212828. −0.749159
\(534\) 27230.9 + 47165.2i 0.0954946 + 0.165402i
\(535\) −3967.33 2290.54i −0.0138609 0.00800259i
\(536\) 46300.5 80194.9i 0.161160 0.279137i
\(537\) −59600.7 + 34410.5i −0.206682 + 0.119328i
\(538\) 29165.5i 0.100764i
\(539\) 0 0
\(540\) −1825.86 −0.00626151
\(541\) −125601. 217548.i −0.429141 0.743294i 0.567656 0.823266i \(-0.307850\pi\)
−0.996797 + 0.0799715i \(0.974517\pi\)
\(542\) 90555.9 + 52282.5i 0.308261 + 0.177974i
\(543\) 50932.8 88218.2i 0.172742 0.299198i
\(544\) −60449.2 + 34900.4i −0.204264 + 0.117932i
\(545\) 16740.6i 0.0563610i
\(546\) 0 0
\(547\) −153431. −0.512789 −0.256395 0.966572i \(-0.582535\pi\)
−0.256395 + 0.966572i \(0.582535\pi\)
\(548\) −14834.3 25693.8i −0.0493978 0.0855594i
\(549\) 168733. + 97417.9i 0.559828 + 0.323217i
\(550\) −133945. + 231999.i −0.442793 + 0.766940i
\(551\) −108419. + 62595.5i −0.357109 + 0.206177i
\(552\) 8173.91i 0.0268257i
\(553\) 0 0
\(554\) −261363. −0.851579
\(555\) −576.192 997.994i −0.00187060 0.00323998i
\(556\) −7593.96 4384.37i −0.0245651 0.0141827i
\(557\) 237576. 411493.i 0.765758 1.32633i −0.174087 0.984730i \(-0.555697\pi\)
0.939845 0.341601i \(-0.110969\pi\)
\(558\) −253495. + 146356.i −0.814144 + 0.470046i
\(559\) 565476.i 1.80963i
\(560\) 0 0
\(561\) 118920. 0.377858
\(562\) −29941.2 51859.7i −0.0947975 0.164194i
\(563\) 34196.7 + 19743.5i 0.107887 + 0.0622884i 0.552972 0.833200i \(-0.313493\pi\)
−0.445086 + 0.895488i \(0.646827\pi\)
\(564\) −34858.6 + 60376.9i −0.109585 + 0.189807i
\(565\) 12124.9 7000.34i 0.0379824 0.0219292i
\(566\) 135949.i 0.424368i
\(567\) 0 0
\(568\) −51031.2 −0.158175
\(569\) 42653.8 + 73878.6i 0.131745 + 0.228189i 0.924349 0.381547i \(-0.124609\pi\)
−0.792604 + 0.609736i \(0.791275\pi\)
\(570\) 1381.61 + 797.676i 0.00425243 + 0.00245514i
\(571\) −44549.5 + 77162.0i −0.136638 + 0.236664i −0.926222 0.376979i \(-0.876963\pi\)
0.789584 + 0.613642i \(0.210296\pi\)
\(572\) 274105. 158255.i 0.837772 0.483688i
\(573\) 35815.4i 0.109084i
\(574\) 0 0
\(575\) −110939. −0.335545
\(576\) −19677.4 34082.3i −0.0593094 0.102727i
\(577\) −269400. 155538.i −0.809181 0.467181i 0.0374905 0.999297i \(-0.488064\pi\)
−0.846671 + 0.532116i \(0.821397\pi\)
\(578\) 92157.1 159621.i 0.275850 0.477786i
\(579\) 23358.8 13486.2i 0.0696776 0.0402284i
\(580\) 1825.14i 0.00542551i
\(581\) 0 0
\(582\) −57201.1 −0.168872
\(583\) 240506. + 416569.i 0.707602 + 1.22560i
\(584\) 91183.5 + 52644.8i 0.267356 + 0.154358i
\(585\) 7127.99 12346.0i 0.0208284 0.0360758i
\(586\) −65600.0 + 37874.2i −0.191033 + 0.110293i
\(587\) 62466.3i 0.181288i 0.995883 + 0.0906440i \(0.0288926\pi\)
−0.995883 + 0.0906440i \(0.971107\pi\)
\(588\) 0 0
\(589\) 525274. 1.51410
\(590\) 4732.13 + 8196.30i 0.0135942 + 0.0235458i
\(591\) −9443.01 5451.93i −0.0270356 0.0156090i
\(592\) 25506.8 44179.1i 0.0727802 0.126059i
\(593\) −41194.5 + 23783.7i −0.117147 + 0.0676346i −0.557428 0.830225i \(-0.688212\pi\)
0.440282 + 0.897860i \(0.354879\pi\)
\(594\) 137705.i 0.390281i
\(595\) 0 0
\(596\) −9870.52 −0.0277874
\(597\) −42937.3 74369.6i −0.120472 0.208664i
\(598\) 113513. + 65537.0i 0.317428 + 0.183267i
\(599\) −282017. + 488468.i −0.785999 + 1.36139i 0.142401 + 0.989809i \(0.454518\pi\)
−0.928400 + 0.371582i \(0.878815\pi\)
\(600\) 24884.7 14367.2i 0.0691240 0.0399088i
\(601\) 255637.i 0.707740i 0.935295 + 0.353870i \(0.115135\pi\)
−0.935295 + 0.353870i \(0.884865\pi\)
\(602\) 0 0
\(603\) −314565. −0.865118
\(604\) 170691. + 295646.i 0.467883 + 0.810397i
\(605\) −5148.03 2972.22i −0.0140647 0.00812025i
\(606\) 5947.98 10302.2i 0.0161966 0.0280533i
\(607\) 495972. 286350.i 1.34611 0.777176i 0.358412 0.933564i \(-0.383318\pi\)
0.987696 + 0.156388i \(0.0499850\pi\)
\(608\) 70622.8i 0.191046i
\(609\) 0 0
\(610\) 5097.28 0.0136987
\(611\) −558981. 968184.i −1.49732 2.59343i
\(612\) 205345. + 118556.i 0.548253 + 0.316534i
\(613\) −141501. + 245087.i −0.376563 + 0.652227i −0.990560 0.137082i \(-0.956228\pi\)
0.613996 + 0.789309i \(0.289561\pi\)
\(614\) −171455. + 98989.3i −0.454791 + 0.262574i
\(615\) 1179.52i 0.00311856i
\(616\) 0 0
\(617\) 248170. 0.651896 0.325948 0.945388i \(-0.394317\pi\)
0.325948 + 0.945388i \(0.394317\pi\)
\(618\) 7203.09 + 12476.1i 0.0188600 + 0.0326665i
\(619\) −49006.8 28294.1i −0.127901 0.0738438i 0.434684 0.900583i \(-0.356860\pi\)
−0.562586 + 0.826739i \(0.690193\pi\)
\(620\) −3828.94 + 6631.93i −0.00996083 + 0.0172527i
\(621\) −49386.8 + 28513.5i −0.128064 + 0.0739379i
\(622\) 245964.i 0.635758i
\(623\) 0 0
\(624\) −33949.4 −0.0871892
\(625\) −194839. 337471.i −0.498787 0.863925i
\(626\) 81232.9 + 46899.8i 0.207292 + 0.119680i
\(627\) 60160.3 104201.i 0.153029 0.265055i
\(628\) −207049. + 119540.i −0.524993 + 0.303105i
\(629\) 307356.i 0.776855i
\(630\) 0 0
\(631\) 681448. 1.71149 0.855744 0.517399i \(-0.173100\pi\)
0.855744 + 0.517399i \(0.173100\pi\)
\(632\) 47446.7 + 82180.1i 0.118788 + 0.205747i
\(633\) 135686. + 78338.3i 0.338632 + 0.195509i
\(634\) −41303.5 + 71539.8i −0.102756 + 0.177979i
\(635\) −7727.63 + 4461.55i −0.0191646 + 0.0110647i
\(636\) 51594.2i 0.127552i
\(637\) 0 0
\(638\) −137651. −0.338173
\(639\) 86676.1 + 150127.i 0.212274 + 0.367670i
\(640\) −891.660 514.800i −0.00217690 0.00125684i
\(641\) −339057. + 587264.i −0.825195 + 1.42928i 0.0765754 + 0.997064i \(0.475601\pi\)
−0.901770 + 0.432216i \(0.857732\pi\)
\(642\) 32094.3 18529.6i 0.0778677 0.0449569i
\(643\) 345520.i 0.835701i 0.908516 + 0.417851i \(0.137216\pi\)
−0.908516 + 0.417851i \(0.862784\pi\)
\(644\) 0 0
\(645\) 3133.94 0.00753305
\(646\) −212750. 368494.i −0.509806 0.883010i
\(647\) 6718.19 + 3878.75i 0.0160489 + 0.00926581i 0.508003 0.861355i \(-0.330384\pi\)
−0.491954 + 0.870621i \(0.663717\pi\)
\(648\) −63054.6 + 109214.i −0.150164 + 0.260092i
\(649\) 618161. 356895.i 1.46761 0.847328i
\(650\) 460774.i 1.09059i
\(651\) 0 0
\(652\) −209642. −0.493154
\(653\) 224236. + 388389.i 0.525872 + 0.910836i 0.999546 + 0.0301362i \(0.00959410\pi\)
−0.473674 + 0.880700i \(0.657073\pi\)
\(654\) −117282. 67712.7i −0.274205 0.158312i
\(655\) −6869.17 + 11897.7i −0.0160111 + 0.0277321i
\(656\) 45219.3 26107.4i 0.105079 0.0606675i
\(657\) 357667.i 0.828607i
\(658\) 0 0
\(659\) 583660. 1.34397 0.671984 0.740565i \(-0.265442\pi\)
0.671984 + 0.740565i \(0.265442\pi\)
\(660\) 877.069 + 1519.13i 0.00201347 + 0.00348744i
\(661\) −331589. 191443.i −0.758922 0.438164i 0.0699869 0.997548i \(-0.477704\pi\)
−0.828908 + 0.559384i \(0.811038\pi\)
\(662\) −236164. + 409048.i −0.538887 + 0.933380i
\(663\) 177140. 102272.i 0.402986 0.232664i
\(664\) 176474.i 0.400262i
\(665\) 0 0
\(666\) −173293. −0.390689
\(667\) −28502.3 49367.4i −0.0640661 0.110966i
\(668\) 248636. + 143550.i 0.557199 + 0.321699i
\(669\) 3764.56 6520.41i 0.00841128 0.0145688i
\(670\) −7127.06 + 4114.81i −0.0158767 + 0.00916643i
\(671\) 384435.i 0.853842i
\(672\) 0 0
\(673\) −323802. −0.714907 −0.357453 0.933931i \(-0.616355\pi\)
−0.357453 + 0.933931i \(0.616355\pi\)
\(674\) −22805.6 39500.4i −0.0502021 0.0869525i
\(675\) −173613. 100236.i −0.381044 0.219996i
\(676\) 157957. 273589.i 0.345656 0.598694i
\(677\) 324589. 187402.i 0.708201 0.408880i −0.102194 0.994765i \(-0.532586\pi\)
0.810395 + 0.585884i \(0.199253\pi\)
\(678\) 113260.i 0.246387i
\(679\) 0 0
\(680\) 6203.31 0.0134155
\(681\) −12219.9 21165.5i −0.0263495 0.0456387i
\(682\) 500177. + 288777.i 1.07536 + 0.620861i
\(683\) −48682.3 + 84320.1i −0.104359 + 0.180755i −0.913476 0.406892i \(-0.866612\pi\)
0.809117 + 0.587647i \(0.199946\pi\)
\(684\) 207764. 119952.i 0.444076 0.256387i
\(685\) 2636.71i 0.00561928i
\(686\) 0 0
\(687\) −67837.5 −0.143733
\(688\) 69366.4 + 120146.i 0.146545 + 0.253824i
\(689\) 716504. + 413674.i 1.50932 + 0.871404i
\(690\) −363.215 + 629.106i −0.000762896 + 0.00132137i
\(691\) −681662. + 393558.i −1.42762 + 0.824238i −0.996933 0.0782630i \(-0.975063\pi\)
−0.430689 + 0.902501i \(0.641729\pi\)
\(692\) 87781.7i 0.183312i
\(693\) 0 0
\(694\) 28486.1 0.0591444
\(695\) 389.647 + 674.888i 0.000806681 + 0.00139721i
\(696\) 12786.6 + 7382.35i 0.0263959 + 0.0152397i
\(697\) −157296. + 272445.i −0.323782 + 0.560807i
\(698\) −239252. + 138132.i −0.491071 + 0.283520i
\(699\) 110090.i 0.225316i
\(700\) 0 0
\(701\) −232522. −0.473182 −0.236591 0.971609i \(-0.576030\pi\)
−0.236591 + 0.971609i \(0.576030\pi\)
\(702\) 118428. + 205123.i 0.240314 + 0.416236i
\(703\) 269313. + 155488.i 0.544937 + 0.314620i
\(704\) −38826.0 + 67248.6i −0.0783388 + 0.135687i
\(705\) 5365.80 3097.94i 0.0107958 0.00623297i
\(706\) 241138.i 0.483790i
\(707\) 0 0
\(708\) −76562.4 −0.152739
\(709\) −75524.5 130812.i −0.150243 0.260229i 0.781073 0.624439i \(-0.214672\pi\)
−0.931317 + 0.364210i \(0.881339\pi\)
\(710\) 3927.63 + 2267.62i 0.00779136 + 0.00449834i
\(711\) 161176. 279165.i 0.318831 0.552231i
\(712\) 185556. 107131.i 0.366028 0.211327i
\(713\) 239179.i 0.470483i
\(714\) 0 0
\(715\) −28128.8 −0.0550223
\(716\) 135376. + 234479.i 0.264069 + 0.457381i
\(717\) −51361.3 29653.5i −0.0999074 0.0576816i
\(718\) 201158. 348415.i 0.390200 0.675847i
\(719\) 616705. 356055.i 1.19294 0.688746i 0.233971 0.972244i \(-0.424828\pi\)
0.958973 + 0.283497i \(0.0914947\pi\)
\(720\) 3497.54i 0.00674679i
\(721\) 0 0
\(722\) −61908.8 −0.118762
\(723\) −101806. 176333.i −0.194758 0.337331i
\(724\) −347065. 200378.i −0.662115 0.382272i
\(725\) 100196. 173545.i 0.190623 0.330169i
\(726\) 41645.6 24044.1i 0.0790126 0.0456179i
\(727\) 693160.i 1.31149i −0.754983 0.655744i \(-0.772355\pi\)
0.754983 0.655744i \(-0.227645\pi\)
\(728\) 0 0
\(729\) 375517. 0.706601
\(730\) −4678.64 8103.64i −0.00877958 0.0152067i
\(731\) −723877. 417931.i −1.35466 0.782113i
\(732\) −20617.6 + 35710.7i −0.0384782 + 0.0666463i
\(733\) −233054. + 134554.i −0.433759 + 0.250431i −0.700947 0.713214i \(-0.747239\pi\)
0.267188 + 0.963644i \(0.413906\pi\)
\(734\) 503010.i 0.933651i
\(735\) 0 0
\(736\) −32157.5 −0.0593645
\(737\) 310337. + 537519.i 0.571345 + 0.989599i
\(738\) −153609. 88686.5i −0.282036 0.162834i
\(739\) −43092.6 + 74638.5i −0.0789066 + 0.136670i −0.902778 0.430106i \(-0.858476\pi\)
0.823872 + 0.566776i \(0.191810\pi\)
\(740\) −3926.28 + 2266.84i −0.00716997 + 0.00413958i
\(741\) 206953.i 0.376908i
\(742\) 0 0
\(743\) −457439. −0.828620 −0.414310 0.910136i \(-0.635977\pi\)
−0.414310 + 0.910136i \(0.635977\pi\)
\(744\) −30974.7 53649.8i −0.0559580 0.0969220i
\(745\) 759.686 + 438.605i 0.00136874 + 0.000790244i
\(746\) 30647.2 53082.4i 0.0550697 0.0953835i
\(747\) −519165. + 299740.i −0.930388 + 0.537160i
\(748\) 467851.i 0.836189i
\(749\) 0 0
\(750\) −5109.41 −0.00908339
\(751\) 290721. + 503543.i 0.515462 + 0.892806i 0.999839 + 0.0179464i \(0.00571284\pi\)
−0.484377 + 0.874859i \(0.660954\pi\)
\(752\) 237533. + 137139.i 0.420037 + 0.242508i
\(753\) 83360.2 144384.i 0.147017 0.254642i
\(754\) −205042. + 118381.i −0.360662 + 0.208228i
\(755\) 30339.2i 0.0532244i
\(756\) 0 0
\(757\) 398071. 0.694655 0.347327 0.937744i \(-0.387089\pi\)
0.347327 + 0.937744i \(0.387089\pi\)
\(758\) −177058. 306673.i −0.308160 0.533749i
\(759\) 47446.9 + 27393.5i 0.0823615 + 0.0475514i
\(760\) 3138.19 5435.50i 0.00543315 0.00941049i
\(761\) 280562. 161982.i 0.484462 0.279704i −0.237812 0.971311i \(-0.576430\pi\)
0.722274 + 0.691607i \(0.243097\pi\)
\(762\) 72184.6i 0.124318i
\(763\) 0 0
\(764\) 140904. 0.241399
\(765\) −10536.3 18249.4i −0.0180038 0.0311835i
\(766\) −517846. 298979.i −0.882558 0.509545i
\(767\) 613865. 1.06325e6i 1.04348 1.80735i
\(768\) 7213.20 4164.54i 0.0122294 0.00706065i
\(769\) 318602.i 0.538760i 0.963034 + 0.269380i \(0.0868187\pi\)
−0.963034 + 0.269380i \(0.913181\pi\)
\(770\) 0 0
\(771\) −150019. −0.252369
\(772\) −53057.0 91897.4i −0.0890242 0.154194i
\(773\) 443418. + 256007.i 0.742086 + 0.428443i 0.822827 0.568292i \(-0.192395\pi\)
−0.0807415 + 0.996735i \(0.525729\pi\)
\(774\) 235637. 408135.i 0.393334 0.681274i
\(775\) −728156. + 420401.i −1.21233 + 0.699940i
\(776\) 225038.i 0.373709i
\(777\) 0 0
\(778\) −110763. −0.182994
\(779\) 159149. + 275654.i 0.262258 + 0.454244i
\(780\) 2612.92 + 1508.57i 0.00429474 + 0.00247957i
\(781\) 171023. 296220.i 0.280383 0.485637i
\(782\) 167791. 96874.0i 0.274381 0.158414i
\(783\) 103009.i 0.168017i
\(784\) 0 0
\(785\) 21247.4 0.0344799
\(786\) −55569.0 96248.4i −0.0899472 0.155793i
\(787\) −558516. 322460.i −0.901751 0.520626i −0.0239830 0.999712i \(-0.507635\pi\)
−0.877768 + 0.479086i \(0.840968\pi\)
\(788\) −21448.8 + 37150.4i −0.0345422 + 0.0598289i
\(789\) 69109.3 39900.3i 0.111015 0.0640946i
\(790\) 8433.34i 0.0135128i
\(791\) 0 0
\(792\) 263783. 0.420529
\(793\) −330617. 572645.i −0.525749 0.910623i
\(794\) −481385. 277928.i −0.763575 0.440850i
\(795\) −2292.63 + 3970.96i −0.00362744 + 0.00628291i
\(796\) −292582. + 168923.i −0.461766 + 0.266601i
\(797\) 278844.i 0.438980i −0.975615 0.219490i \(-0.929561\pi\)
0.975615 0.219490i \(-0.0704393\pi\)
\(798\) 0 0
\(799\) −1.65252e6 −2.58853
\(800\) −56522.8 97900.3i −0.0883169 0.152969i
\(801\) −630331. 363922.i −0.982434 0.567208i
\(802\) −302147. + 523333.i −0.469753 + 0.813635i
\(803\) −611173. + 352861.i −0.947835 + 0.547233i
\(804\) 66574.6i 0.102990i
\(805\) 0 0
\(806\) 993402. 1.52917
\(807\) −10484.1 18159.0i −0.0160985 0.0278834i
\(808\) −40530.5 23400.3i −0.0620811 0.0358426i
\(809\) −331260. + 573759.i −0.506142 + 0.876663i 0.493833 + 0.869557i \(0.335595\pi\)
−0.999975 + 0.00710632i \(0.997738\pi\)
\(810\) 9706.02 5603.77i 0.0147935 0.00854104i
\(811\) 586078.i 0.891073i 0.895264 + 0.445537i \(0.146987\pi\)
−0.895264 + 0.445537i \(0.853013\pi\)
\(812\) 0 0
\(813\) 75175.9 0.113736
\(814\) 170964. + 296118.i 0.258021 + 0.446906i
\(815\) 16135.1 + 9315.61i 0.0242916 + 0.0140248i
\(816\) −25091.2 + 43459.3i −0.0376827 + 0.0652683i
\(817\) −732403. + 422853.i −1.09725 + 0.633498i
\(818\) 100704.i 0.150501i
\(819\) 0 0
\(820\) −4640.42 −0.00690128
\(821\) −395267. 684623.i −0.586414 1.01570i −0.994698 0.102844i \(-0.967206\pi\)
0.408284 0.912855i \(-0.366127\pi\)
\(822\) −18472.3 10665.0i −0.0273387 0.0157840i
\(823\) 578225. 1.00151e6i 0.853684 1.47862i −0.0241766 0.999708i \(-0.507696\pi\)
0.877861 0.478916i \(-0.158970\pi\)
\(824\) 49083.1 28338.1i 0.0722899 0.0417366i
\(825\) 192597.i 0.282970i
\(826\) 0 0
\(827\) 390408. 0.570832 0.285416 0.958404i \(-0.407868\pi\)
0.285416 + 0.958404i \(0.407868\pi\)
\(828\) 54619.3 + 94603.4i 0.0796682 + 0.137989i
\(829\) 460055. + 265613.i 0.669423 + 0.386492i 0.795858 0.605483i \(-0.207020\pi\)
−0.126435 + 0.991975i \(0.540353\pi\)
\(830\) −7841.78 + 13582.4i −0.0113830 + 0.0197160i
\(831\) −162730. + 93952.1i −0.235649 + 0.136052i
\(832\) 133562.i 0.192947i
\(833\) 0 0
\(834\) −6304.20 −0.00906354
\(835\) −12757.5 22096.7i −0.0182976 0.0316923i
\(836\) −409943. 236681.i −0.586558 0.338649i
\(837\) −216102. + 374300.i −0.308466 + 0.534279i
\(838\) 624490. 360550.i 0.889278 0.513425i
\(839\) 263842.i 0.374817i −0.982282 0.187409i \(-0.939991\pi\)
0.982282 0.187409i \(-0.0600089\pi\)
\(840\) 0 0
\(841\) −604312. −0.854416
\(842\) −151584. 262552.i −0.213811 0.370331i
\(843\) −37284.0 21525.9i −0.0524647 0.0302905i
\(844\) 308196. 533811.i 0.432655 0.749381i
\(845\) −24314.3 + 14037.9i −0.0340525 + 0.0196602i
\(846\) 931722.i 1.30180i
\(847\) 0 0
\(848\) −202980. −0.282268
\(849\) 48869.5 + 84644.5i 0.0677989 + 0.117431i
\(850\) 589847. + 340548.i 0.816397 + 0.471347i
\(851\) −70800.1 + 122629.i −0.0977630 + 0.169331i
\(852\) −31773.0 + 18344.2i −0.0437703 + 0.0252708i
\(853\) 1.17089e6i 1.60923i 0.593798 + 0.804614i \(0.297628\pi\)
−0.593798 + 0.804614i \(0.702372\pi\)
\(854\) 0 0
\(855\) −21320.8 −0.0291656
\(856\) −72898.6 126264.i −0.0994883 0.172319i
\(857\) 367922. + 212420.i 0.500950 + 0.289223i 0.729106 0.684401i \(-0.239936\pi\)
−0.228156 + 0.973625i \(0.573270\pi\)
\(858\) 113776. 197065.i 0.154552 0.267692i
\(859\) −353490. + 204087.i −0.479061 + 0.276586i −0.720025 0.693948i \(-0.755870\pi\)
0.240964 + 0.970534i \(0.422536\pi\)
\(860\) 12329.4i 0.0166704i
\(861\) 0 0
\(862\) 339294. 0.456627
\(863\) 441370. + 764476.i 0.592627 + 1.02646i 0.993877 + 0.110492i \(0.0352425\pi\)
−0.401250 + 0.915969i \(0.631424\pi\)
\(864\) −50324.4 29054.8i −0.0674142 0.0389216i
\(865\) 3900.66 6756.13i 0.00521321 0.00902955i
\(866\) −269832. + 155788.i −0.359797 + 0.207729i
\(867\) 132511.i 0.176284i
\(868\) 0 0
\(869\) −636039. −0.842256
\(870\) −656.083 1136.37i −0.000866802 0.00150135i
\(871\) 924541. + 533784.i 1.21868 + 0.703606i
\(872\) −266393. + 461406.i −0.350340 + 0.606807i
\(873\) 662035. 382226.i 0.868665 0.501524i
\(874\) 196030.i 0.256625i
\(875\) 0 0
\(876\) 75696.9 0.0986438
\(877\) 297696. + 515624.i 0.387056 + 0.670400i 0.992052 0.125828i \(-0.0401588\pi\)
−0.604996 + 0.796228i \(0.706825\pi\)
\(878\) −862943. 498220.i −1.11942 0.646298i
\(879\) −27229.2 + 47162.4i −0.0352418 + 0.0610405i
\(880\) 5976.50 3450.53i 0.00771759 0.00445575i
\(881\) 238444.i 0.307209i 0.988132 + 0.153605i \(0.0490882\pi\)
−0.988132 + 0.153605i \(0.950912\pi\)
\(882\) 0 0
\(883\) 189523. 0.243076 0.121538 0.992587i \(-0.461217\pi\)
0.121538 + 0.992587i \(0.461217\pi\)
\(884\) −402355. 696899.i −0.514879 0.891796i
\(885\) 5892.64 + 3402.12i 0.00752356 + 0.00434373i
\(886\) −404087. + 699899.i −0.514763 + 0.891595i
\(887\) 709753. 409776.i 0.902111 0.520834i 0.0242268 0.999706i \(-0.492288\pi\)
0.877885 + 0.478872i \(0.158954\pi\)
\(888\) 36675.7i 0.0465107i
\(889\) 0 0
\(890\) −19041.8 −0.0240396
\(891\) −422634. 732024.i −0.532365 0.922082i
\(892\) −25652.4 14810.4i −0.0322402 0.0186139i
\(893\) −835993. + 1.44798e6i −1.04833 + 1.81577i
\(894\) −6145.58 + 3548.15i −0.00768932 + 0.00443943i
\(895\) 24062.3i 0.0300394i
\(896\) 0 0
\(897\) 94234.3 0.117118
\(898\) 483922. + 838177.i 0.600098 + 1.03940i
\(899\) −374152. 216017.i −0.462945 0.267281i
\(900\) −192007. + 332566.i −0.237046 + 0.410575i
\(901\) 1.05911e6 611475.i 1.30464 0.753232i
\(902\) 349978.i 0.430158i
\(903\) 0 0
\(904\) 445585. 0.545247
\(905\) 17807.9 + 30844.3i 0.0217429 + 0.0376597i
\(906\) 212551. + 122717.i 0.258945 + 0.149502i
\(907\) 328809. 569515.i 0.399696 0.692294i −0.593992 0.804471i \(-0.702449\pi\)
0.993688 + 0.112177i \(0.0357824\pi\)
\(908\) −83268.4 + 48075.0i −0.100997 + 0.0583106i
\(909\) 158981.i 0.192406i
\(910\) 0 0
\(911\) 1.32632e6 1.59812 0.799061 0.601250i \(-0.205330\pi\)
0.799061 + 0.601250i \(0.205330\pi\)
\(912\) 25386.8 + 43971.2i 0.0305223 + 0.0528663i
\(913\) 1.02437e6 + 591423.i 1.22890 + 0.709507i
\(914\) 392620. 680038.i 0.469981 0.814031i
\(915\) 3173.67 1832.32i 0.00379070 0.00218856i
\(916\) 266884.i 0.318076i
\(917\) 0 0
\(918\) 350109. 0.415449
\(919\) 118155. + 204651.i 0.139901 + 0.242316i 0.927459 0.373925i \(-0.121988\pi\)
−0.787558 + 0.616241i \(0.788655\pi\)
\(920\) 2475.01 + 1428.95i 0.00292416 + 0.00168826i
\(921\) −71167.3 + 123265.i −0.0838999 + 0.145319i
\(922\) 886553. 511852.i 1.04290 0.602119i
\(923\) 588322.i 0.690577i
\(924\) 0 0
\(925\) −497777. −0.581770
\(926\) −207713. 359770.i −0.242238 0.419569i
\(927\) −166735. 96264.2i −0.194029 0.112023i
\(928\) 29043.4 50304.6i 0.0337250 0.0584134i
\(929\) 305501. 176381.i 0.353982 0.204372i −0.312456 0.949932i \(-0.601152\pi\)
0.666438 + 0.745561i \(0.267818\pi\)
\(930\) 5505.56i 0.00636554i
\(931\) 0 0
\(932\) 433111. 0.498618
\(933\) 88416.8 + 153142.i 0.101571 + 0.175927i
\(934\) 657467. + 379589.i 0.753668 + 0.435130i
\(935\) −20789.4 + 36008.2i −0.0237803 + 0.0411887i
\(936\) 392924. 226855.i 0.448495 0.258938i
\(937\) 113445.i 0.129213i −0.997911 0.0646066i \(-0.979421\pi\)
0.997911 0.0646066i \(-0.0205793\pi\)
\(938\) 0 0
\(939\) 67436.3 0.0764826
\(940\) −12187.8 21109.9i −0.0137934 0.0238908i
\(941\) 1.01629e6 + 586757.i 1.14773 + 0.662642i 0.948333 0.317277i \(-0.102769\pi\)
0.199396 + 0.979919i \(0.436102\pi\)
\(942\) −85941.8 + 148856.i −0.0968507 + 0.167750i
\(943\) −125517. + 72467.1i −0.141149 + 0.0814925i
\(944\) 301209.i 0.338006i
\(945\) 0 0
\(946\) −929880. −1.03907
\(947\) −135979. 235522.i −0.151625 0.262622i 0.780200 0.625530i \(-0.215117\pi\)
−0.931825 + 0.362908i \(0.881784\pi\)
\(948\) 59082.5 + 34111.3i 0.0657419 + 0.0379561i
\(949\) −606925. + 1.05123e6i −0.673912 + 1.16725i
\(950\) 596794. 344559.i 0.661268 0.381783i
\(951\) 59389.5i 0.0656672i
\(952\) 0 0
\(953\) 465476. 0.512520 0.256260 0.966608i \(-0.417510\pi\)
0.256260 + 0.966608i \(0.417510\pi\)
\(954\) 344760. + 597142.i 0.378809 + 0.656117i
\(955\) −10844.7 6261.17i −0.0118908 0.00686513i
\(956\) −116662. + 202064.i −0.127647 + 0.221092i
\(957\) −85704.4 + 49481.5i −0.0935792 + 0.0540280i
\(958\) 439212.i 0.478568i
\(959\) 0 0
\(960\) −740.220 −0.000803190
\(961\) 444600. + 770069.i 0.481418 + 0.833840i
\(962\) 509327. + 294060.i 0.550360 + 0.317750i
\(963\) −247636. + 428918.i −0.267030 + 0.462510i
\(964\) −693722. + 400521.i −0.746503 + 0.430994i
\(965\) 9430.53i 0.0101270i
\(966\) 0 0
\(967\) −1.49573e6 −1.59956 −0.799782 0.600291i \(-0.795051\pi\)
−0.799782 + 0.600291i \(0.795051\pi\)
\(968\) −94593.6 163841.i −0.100951 0.174852i
\(969\) −264925. 152955.i −0.282147 0.162898i
\(970\) 9999.78 17320.1i 0.0106279 0.0184080i
\(971\) 350328. 202262.i 0.371567 0.214524i −0.302576 0.953125i \(-0.597847\pi\)
0.674143 + 0.738601i \(0.264513\pi\)
\(972\) 298682.i 0.316138i
\(973\) 0 0
\(974\) −440182. −0.463996
\(975\) 165634. + 286887.i 0.174237 + 0.301788i
\(976\) 140492. + 81112.9i 0.147486 + 0.0851511i
\(977\) 825968. 1.43062e6i 0.865315 1.49877i −0.00141922 0.999999i \(-0.500452\pi\)
0.866734 0.498770i \(-0.166215\pi\)
\(978\) −130527. + 75359.9i −0.136466 + 0.0787884i
\(979\) 1.43612e6i 1.49839i
\(980\) 0 0
\(981\) 1.80987e6 1.88065
\(982\) −53104.7 91980.0i −0.0550693 0.0953829i
\(983\) −847459. 489281.i −0.877025 0.506350i −0.00734850 0.999973i \(-0.502339\pi\)
−0.869676 + 0.493623i \(0.835672\pi\)
\(984\) 18769.6 32510.0i 0.0193850 0.0335758i
\(985\) 3301.62 1906.19i 0.00340294 0.00196469i
\(986\) 349971.i 0.359980i
\(987\) 0 0
\(988\) −814188. −0.834086
\(989\) −192543. 333493.i −0.196849 0.340953i
\(990\) −20302.1 11721.4i −0.0207143 0.0119594i
\(991\) −634268. + 1.09859e6i −0.645841 + 1.11863i 0.338265 + 0.941051i \(0.390160\pi\)
−0.984107 + 0.177579i \(0.943173\pi\)
\(992\) −211067. + 121860.i −0.214485 + 0.123833i
\(993\) 339575.i 0.344380i
\(994\) 0 0
\(995\) 30024.9 0.0303274
\(996\) −63437.1 109876.i −0.0639476 0.110761i
\(997\) −1793.83 1035.67i −0.00180464 0.00104191i 0.499097 0.866546i \(-0.333665\pi\)
−0.500902 + 0.865504i \(0.666998\pi\)
\(998\) −237334. + 411074.i −0.238286 + 0.412724i
\(999\) −221595. + 127938.i −0.222039 + 0.128194i
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 98.5.d.c.31.1 8
7.2 even 3 inner 98.5.d.c.19.2 8
7.3 odd 6 98.5.b.a.97.3 4
7.4 even 3 98.5.b.a.97.4 yes 4
7.5 odd 6 inner 98.5.d.c.19.1 8
7.6 odd 2 inner 98.5.d.c.31.2 8
21.11 odd 6 882.5.c.c.685.1 4
21.17 even 6 882.5.c.c.685.2 4
28.3 even 6 784.5.c.a.97.3 4
28.11 odd 6 784.5.c.a.97.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
98.5.b.a.97.3 4 7.3 odd 6
98.5.b.a.97.4 yes 4 7.4 even 3
98.5.d.c.19.1 8 7.5 odd 6 inner
98.5.d.c.19.2 8 7.2 even 3 inner
98.5.d.c.31.1 8 1.1 even 1 trivial
98.5.d.c.31.2 8 7.6 odd 2 inner
784.5.c.a.97.2 4 28.11 odd 6
784.5.c.a.97.3 4 28.3 even 6
882.5.c.c.685.1 4 21.11 odd 6
882.5.c.c.685.2 4 21.17 even 6