Properties

Label 23.5.d.a.10.5
Level $23$
Weight $5$
Character 23.10
Analytic conductor $2.378$
Analytic rank $0$
Dimension $70$
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] = [23,5,Mod(5,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.5");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 23.d (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.37750915093\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(7\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 10.5
Character \(\chi\) \(=\) 23.10
Dual form 23.5.d.a.7.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.24584 + 1.43777i) q^{2} +(-13.2108 - 8.49010i) q^{3} +(1.76196 - 12.2547i) q^{4} +(-8.32630 - 3.80249i) q^{5} +(-4.25173 - 29.5714i) q^{6} +(-1.18231 + 4.02657i) q^{7} +(45.4215 - 29.1907i) q^{8} +(68.7961 + 150.642i) q^{9} +O(q^{10})\) \(q+(1.24584 + 1.43777i) q^{2} +(-13.2108 - 8.49010i) q^{3} +(1.76196 - 12.2547i) q^{4} +(-8.32630 - 3.80249i) q^{5} +(-4.25173 - 29.5714i) q^{6} +(-1.18231 + 4.02657i) q^{7} +(45.4215 - 29.1907i) q^{8} +(68.7961 + 150.642i) q^{9} +(-4.90608 - 16.7086i) q^{10} +(-138.378 - 119.905i) q^{11} +(-127.320 + 146.936i) q^{12} +(162.336 - 47.6662i) q^{13} +(-7.26225 + 3.31656i) q^{14} +(77.7139 + 120.925i) q^{15} +(-91.5100 - 26.8698i) q^{16} +(123.573 - 17.7671i) q^{17} +(-130.881 + 286.589i) q^{18} +(519.438 + 74.6839i) q^{19} +(-61.2690 + 95.3363i) q^{20} +(49.8053 - 43.1565i) q^{21} -348.337i q^{22} +(-167.815 - 501.676i) q^{23} -847.889 q^{24} +(-354.420 - 409.022i) q^{25} +(270.777 + 174.018i) q^{26} +(189.089 - 1315.14i) q^{27} +(47.2612 + 21.5835i) q^{28} +(71.1634 + 494.952i) q^{29} +(-77.0440 + 262.388i) q^{30} +(-676.717 + 434.900i) q^{31} +(-434.244 - 950.861i) q^{32} +(810.081 + 2758.88i) q^{33} +(179.497 + 155.535i) q^{34} +(25.1552 - 29.0307i) q^{35} +(1967.29 - 577.649i) q^{36} +(1852.47 - 845.996i) q^{37} +(539.756 + 839.877i) q^{38} +(-2549.29 - 748.539i) q^{39} +(-489.190 + 70.3350i) q^{40} +(-1235.78 + 2705.98i) q^{41} +(124.098 + 17.8426i) q^{42} +(779.260 - 1212.55i) q^{43} +(-1713.21 + 1484.51i) q^{44} -1515.89i q^{45} +(512.226 - 866.285i) q^{46} -319.343 q^{47} +(980.798 + 1131.90i) q^{48} +(2005.03 + 1288.56i) q^{49} +(146.531 - 1019.15i) q^{50} +(-1783.35 - 814.427i) q^{51} +(-298.105 - 2073.37i) q^{52} +(-373.020 + 1270.39i) q^{53} +(2126.45 - 1366.59i) q^{54} +(696.235 + 1524.54i) q^{55} +(63.8360 + 217.405i) q^{56} +(-6228.14 - 5396.72i) q^{57} +(-622.970 + 718.946i) q^{58} +(2601.91 - 763.988i) q^{59} +(1618.83 - 739.295i) q^{60} +(-454.994 - 707.985i) q^{61} +(-1468.36 - 431.151i) q^{62} +(-687.911 + 98.9066i) q^{63} +(192.213 - 420.887i) q^{64} +(-1532.91 - 220.399i) q^{65} +(-2957.41 + 4601.83i) q^{66} +(4908.84 - 4253.53i) q^{67} -1545.65i q^{68} +(-2042.31 + 8052.33i) q^{69} +73.0788 q^{70} +(-136.598 - 157.642i) q^{71} +(7522.18 + 4834.21i) q^{72} +(99.6906 - 693.364i) q^{73} +(3524.22 + 1609.46i) q^{74} +(1209.55 + 8412.59i) q^{75} +(1830.46 - 6233.96i) q^{76} +(646.410 - 415.423i) q^{77} +(-2099.77 - 4597.85i) q^{78} +(362.477 + 1234.48i) q^{79} +(659.767 + 571.692i) q^{80} +(-4879.24 + 5630.94i) q^{81} +(-5430.15 + 1594.44i) q^{82} +(-4450.33 + 2032.40i) q^{83} +(-441.115 - 686.388i) q^{84} +(-1096.46 - 321.951i) q^{85} +(2714.20 - 390.243i) q^{86} +(3262.06 - 7142.92i) q^{87} +(-9785.42 - 1406.93i) q^{88} +(5270.76 - 8201.46i) q^{89} +(2179.50 - 1888.55i) q^{90} +710.014i q^{91} +(-6443.57 + 1172.58i) q^{92} +12632.3 q^{93} +(-397.848 - 459.142i) q^{94} +(-4041.01 - 2597.00i) q^{95} +(-2336.18 + 16248.5i) q^{96} +(7082.59 + 3234.51i) q^{97} +(645.293 + 4488.11i) q^{98} +(8542.92 - 29094.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 70 q - 3 q^{2} + q^{3} - 35 q^{4} - 11 q^{5} - 110 q^{6} - 11 q^{7} + 146 q^{8} - 182 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 70 q - 3 q^{2} + q^{3} - 35 q^{4} - 11 q^{5} - 110 q^{6} - 11 q^{7} + 146 q^{8} - 182 q^{9} - 11 q^{10} - 11 q^{11} + 490 q^{12} - 7 q^{13} - 11 q^{14} + 1452 q^{15} - 139 q^{16} - 506 q^{17} - 2670 q^{18} - 968 q^{19} - 3179 q^{20} - 1364 q^{21} + 356 q^{23} + 2666 q^{24} + 3432 q^{25} + 5642 q^{26} + 4924 q^{27} + 5269 q^{28} - 378 q^{29} - 1419 q^{30} - 2800 q^{31} - 5771 q^{32} - 6666 q^{33} + 12815 q^{34} + 5797 q^{35} + 2425 q^{36} - 3531 q^{37} - 10406 q^{38} - 5453 q^{39} - 24211 q^{40} - 6591 q^{41} - 24761 q^{42} - 7227 q^{43} - 6534 q^{44} + 8301 q^{46} - 4706 q^{47} + 42122 q^{48} + 28806 q^{49} + 29544 q^{50} + 17413 q^{51} + 22872 q^{52} + 7381 q^{53} + 30522 q^{54} + 22055 q^{55} + 19888 q^{56} - 13310 q^{57} - 45421 q^{58} - 17613 q^{59} - 83941 q^{60} - 22495 q^{61} - 30910 q^{62} - 27786 q^{63} - 43726 q^{64} - 27962 q^{65} - 21648 q^{66} - 2937 q^{67} - 2064 q^{69} + 730 q^{70} + 42522 q^{71} + 116359 q^{72} + 5383 q^{73} + 85492 q^{74} + 103504 q^{75} + 122166 q^{76} + 38020 q^{77} + 41808 q^{78} + 10505 q^{79} - 21362 q^{80} - 94198 q^{81} - 19388 q^{82} - 65120 q^{83} - 221221 q^{84} - 105813 q^{85} - 141053 q^{86} - 61205 q^{87} - 41283 q^{88} - 22979 q^{89} - 37246 q^{90} - 21998 q^{92} - 25744 q^{93} + 128365 q^{94} + 146512 q^{95} + 211093 q^{96} + 115852 q^{97} + 84021 q^{98} + 163768 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{3}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24584 + 1.43777i 0.311459 + 0.359443i 0.889799 0.456353i \(-0.150845\pi\)
−0.578340 + 0.815796i \(0.696299\pi\)
\(3\) −13.2108 8.49010i −1.46787 0.943344i −0.998167 0.0605204i \(-0.980724\pi\)
−0.469705 0.882824i \(-0.655640\pi\)
\(4\) 1.76196 12.2547i 0.110122 0.765918i
\(5\) −8.32630 3.80249i −0.333052 0.152100i 0.241869 0.970309i \(-0.422240\pi\)
−0.574920 + 0.818209i \(0.694967\pi\)
\(6\) −4.25173 29.5714i −0.118104 0.821429i
\(7\) −1.18231 + 4.02657i −0.0241287 + 0.0821749i −0.970677 0.240387i \(-0.922726\pi\)
0.946548 + 0.322562i \(0.104544\pi\)
\(8\) 45.4215 29.1907i 0.709712 0.456104i
\(9\) 68.7961 + 150.642i 0.849335 + 1.85978i
\(10\) −4.90608 16.7086i −0.0490608 0.167086i
\(11\) −138.378 119.905i −1.14362 0.990949i −0.999999 0.00131577i \(-0.999581\pi\)
−0.143617 0.989633i \(-0.545873\pi\)
\(12\) −127.320 + 146.936i −0.884170 + 1.02039i
\(13\) 162.336 47.6662i 0.960569 0.282049i 0.236388 0.971659i \(-0.424036\pi\)
0.724181 + 0.689610i \(0.242218\pi\)
\(14\) −7.26225 + 3.31656i −0.0370523 + 0.0169212i
\(15\) 77.7139 + 120.925i 0.345395 + 0.537445i
\(16\) −91.5100 26.8698i −0.357461 0.104960i
\(17\) 123.573 17.7671i 0.427588 0.0614779i 0.0748385 0.997196i \(-0.476156\pi\)
0.352749 + 0.935718i \(0.385247\pi\)
\(18\) −130.881 + 286.589i −0.403953 + 0.884533i
\(19\) 519.438 + 74.6839i 1.43889 + 0.206881i 0.817186 0.576374i \(-0.195533\pi\)
0.621701 + 0.783255i \(0.286442\pi\)
\(20\) −61.2690 + 95.3363i −0.153172 + 0.238341i
\(21\) 49.8053 43.1565i 0.112937 0.0978605i
\(22\) 348.337i 0.719704i
\(23\) −167.815 501.676i −0.317230 0.948349i
\(24\) −847.889 −1.47203
\(25\) −354.420 409.022i −0.567072 0.654435i
\(26\) 270.777 + 174.018i 0.400558 + 0.257423i
\(27\) 189.089 1315.14i 0.259381 1.80404i
\(28\) 47.2612 + 21.5835i 0.0602821 + 0.0275299i
\(29\) 71.1634 + 494.952i 0.0846176 + 0.588528i 0.987378 + 0.158384i \(0.0506283\pi\)
−0.902760 + 0.430145i \(0.858463\pi\)
\(30\) −77.0440 + 262.388i −0.0856044 + 0.291542i
\(31\) −676.717 + 434.900i −0.704180 + 0.452549i −0.843102 0.537754i \(-0.819273\pi\)
0.138922 + 0.990303i \(0.455636\pi\)
\(32\) −434.244 950.861i −0.424066 0.928576i
\(33\) 810.081 + 2758.88i 0.743876 + 2.53341i
\(34\) 179.497 + 155.535i 0.155274 + 0.134546i
\(35\) 25.1552 29.0307i 0.0205349 0.0236985i
\(36\) 1967.29 577.649i 1.51797 0.445717i
\(37\) 1852.47 845.996i 1.35316 0.617966i 0.398912 0.916989i \(-0.369388\pi\)
0.954246 + 0.299023i \(0.0966608\pi\)
\(38\) 539.756 + 839.877i 0.373792 + 0.581632i
\(39\) −2549.29 748.539i −1.67606 0.492136i
\(40\) −489.190 + 70.3350i −0.305744 + 0.0439594i
\(41\) −1235.78 + 2705.98i −0.735145 + 1.60974i 0.0562344 + 0.998418i \(0.482091\pi\)
−0.791379 + 0.611325i \(0.790637\pi\)
\(42\) 124.098 + 17.8426i 0.0703505 + 0.0101149i
\(43\) 779.260 1212.55i 0.421449 0.655788i −0.563997 0.825777i \(-0.690737\pi\)
0.985446 + 0.169989i \(0.0543733\pi\)
\(44\) −1713.21 + 1484.51i −0.884924 + 0.766791i
\(45\) 1515.89i 0.748588i
\(46\) 512.226 866.285i 0.242073 0.409398i
\(47\) −319.343 −0.144564 −0.0722822 0.997384i \(-0.523028\pi\)
−0.0722822 + 0.997384i \(0.523028\pi\)
\(48\) 980.798 + 1131.90i 0.425693 + 0.491276i
\(49\) 2005.03 + 1288.56i 0.835083 + 0.536675i
\(50\) 146.531 1019.15i 0.0586126 0.407659i
\(51\) −1783.35 814.427i −0.685639 0.313121i
\(52\) −298.105 2073.37i −0.110246 0.766777i
\(53\) −373.020 + 1270.39i −0.132795 + 0.452257i −0.998863 0.0476683i \(-0.984821\pi\)
0.866069 + 0.499925i \(0.166639\pi\)
\(54\) 2126.45 1366.59i 0.729235 0.468651i
\(55\) 696.235 + 1524.54i 0.230160 + 0.503981i
\(56\) 63.8360 + 217.405i 0.0203559 + 0.0693257i
\(57\) −6228.14 5396.72i −1.91694 1.66104i
\(58\) −622.970 + 718.946i −0.185187 + 0.213718i
\(59\) 2601.91 763.988i 0.747459 0.219474i 0.114247 0.993452i \(-0.463554\pi\)
0.633212 + 0.773978i \(0.281736\pi\)
\(60\) 1618.83 739.295i 0.449675 0.205360i
\(61\) −454.994 707.985i −0.122277 0.190267i 0.774718 0.632306i \(-0.217892\pi\)
−0.896996 + 0.442039i \(0.854255\pi\)
\(62\) −1468.36 431.151i −0.381989 0.112162i
\(63\) −687.911 + 98.9066i −0.173321 + 0.0249198i
\(64\) 192.213 420.887i 0.0469269 0.102756i
\(65\) −1532.91 220.399i −0.362819 0.0521655i
\(66\) −2957.41 + 4601.83i −0.678929 + 1.05643i
\(67\) 4908.84 4253.53i 1.09353 0.947545i 0.0946763 0.995508i \(-0.469818\pi\)
0.998849 + 0.0479630i \(0.0152729\pi\)
\(68\) 1545.65i 0.334267i
\(69\) −2042.31 + 8052.33i −0.428966 + 1.69131i
\(70\) 73.0788 0.0149140
\(71\) −136.598 157.642i −0.0270974 0.0312720i 0.742039 0.670357i \(-0.233859\pi\)
−0.769136 + 0.639085i \(0.779313\pi\)
\(72\) 7522.18 + 4834.21i 1.45104 + 0.932525i
\(73\) 99.6906 693.364i 0.0187072 0.130111i −0.978328 0.207063i \(-0.933610\pi\)
0.997035 + 0.0769514i \(0.0245186\pi\)
\(74\) 3524.22 + 1609.46i 0.643576 + 0.293912i
\(75\) 1209.55 + 8412.59i 0.215031 + 1.49557i
\(76\) 1830.46 6233.96i 0.316907 1.07929i
\(77\) 646.410 415.423i 0.109025 0.0700662i
\(78\) −2099.77 4597.85i −0.345130 0.755728i
\(79\) 362.477 + 1234.48i 0.0580800 + 0.197802i 0.983422 0.181331i \(-0.0580404\pi\)
−0.925342 + 0.379133i \(0.876222\pi\)
\(80\) 659.767 + 571.692i 0.103089 + 0.0893268i
\(81\) −4879.24 + 5630.94i −0.743673 + 0.858245i
\(82\) −5430.15 + 1594.44i −0.807578 + 0.237126i
\(83\) −4450.33 + 2032.40i −0.646006 + 0.295021i −0.711346 0.702842i \(-0.751914\pi\)
0.0653401 + 0.997863i \(0.479187\pi\)
\(84\) −441.115 686.388i −0.0625163 0.0972772i
\(85\) −1096.46 321.951i −0.151760 0.0445607i
\(86\) 2714.20 390.243i 0.366982 0.0527641i
\(87\) 3262.06 7142.92i 0.430977 0.943708i
\(88\) −9785.42 1406.93i −1.26361 0.181680i
\(89\) 5270.76 8201.46i 0.665416 1.03541i −0.330384 0.943847i \(-0.607178\pi\)
0.995800 0.0915603i \(-0.0291854\pi\)
\(90\) 2179.50 1888.55i 0.269075 0.233154i
\(91\) 710.014i 0.0857402i
\(92\) −6443.57 + 1172.58i −0.761292 + 0.138538i
\(93\) 12632.3 1.46056
\(94\) −397.848 459.142i −0.0450259 0.0519626i
\(95\) −4041.01 2597.00i −0.447757 0.287756i
\(96\) −2336.18 + 16248.5i −0.253491 + 1.76307i
\(97\) 7082.59 + 3234.51i 0.752747 + 0.343768i 0.754561 0.656230i \(-0.227850\pi\)
−0.00181385 + 0.999998i \(0.500577\pi\)
\(98\) 645.293 + 4488.11i 0.0671900 + 0.467317i
\(99\) 8542.92 29094.5i 0.871638 2.96853i
\(100\) −5636.91 + 3622.62i −0.563691 + 0.362262i
\(101\) −689.872 1510.61i −0.0676279 0.148084i 0.872800 0.488079i \(-0.162302\pi\)
−0.940427 + 0.339994i \(0.889575\pi\)
\(102\) −1050.80 3578.69i −0.100999 0.343972i
\(103\) 8611.98 + 7462.33i 0.811762 + 0.703396i 0.958286 0.285811i \(-0.0922631\pi\)
−0.146524 + 0.989207i \(0.546809\pi\)
\(104\) 5982.15 6903.77i 0.553084 0.638293i
\(105\) −578.796 + 169.950i −0.0524985 + 0.0154149i
\(106\) −2291.25 + 1046.38i −0.203921 + 0.0931274i
\(107\) 2135.15 + 3322.36i 0.186493 + 0.290188i 0.921893 0.387445i \(-0.126642\pi\)
−0.735400 + 0.677633i \(0.763006\pi\)
\(108\) −15783.5 4634.45i −1.35318 0.397330i
\(109\) −17274.1 + 2483.64i −1.45392 + 0.209043i −0.823548 0.567247i \(-0.808009\pi\)
−0.630376 + 0.776290i \(0.717099\pi\)
\(110\) −1324.55 + 2900.36i −0.109467 + 0.239699i
\(111\) −31655.3 4551.35i −2.56922 0.369398i
\(112\) 216.386 336.703i 0.0172502 0.0268418i
\(113\) 7014.63 6078.21i 0.549349 0.476013i −0.335404 0.942074i \(-0.608873\pi\)
0.884752 + 0.466061i \(0.154327\pi\)
\(114\) 15678.1i 1.20638i
\(115\) −510.347 + 4815.22i −0.0385895 + 0.364100i
\(116\) 6190.87 0.460083
\(117\) 18348.7 + 21175.5i 1.34039 + 1.54690i
\(118\) 4339.99 + 2789.14i 0.311691 + 0.200312i
\(119\) −74.5607 + 518.581i −0.00526522 + 0.0366204i
\(120\) 7059.77 + 3224.09i 0.490262 + 0.223895i
\(121\) 2687.55 + 18692.3i 0.183563 + 1.27671i
\(122\) 451.072 1536.21i 0.0303058 0.103212i
\(123\) 39299.7 25256.4i 2.59764 1.66940i
\(124\) 4137.21 + 9059.23i 0.269069 + 0.589180i
\(125\) 3007.47 + 10242.5i 0.192478 + 0.655520i
\(126\) −999.229 865.837i −0.0629396 0.0545375i
\(127\) −17362.3 + 20037.2i −1.07647 + 1.24231i −0.107739 + 0.994179i \(0.534361\pi\)
−0.968727 + 0.248129i \(0.920184\pi\)
\(128\) −15203.1 + 4464.04i −0.927924 + 0.272463i
\(129\) −20589.4 + 9402.85i −1.23727 + 0.565041i
\(130\) −1592.87 2478.55i −0.0942527 0.146660i
\(131\) 1912.32 + 561.507i 0.111434 + 0.0327200i 0.336974 0.941514i \(-0.390597\pi\)
−0.225540 + 0.974234i \(0.572415\pi\)
\(132\) 35236.6 5066.26i 2.02230 0.290763i
\(133\) −914.856 + 2003.25i −0.0517189 + 0.113249i
\(134\) 12231.2 + 1758.58i 0.681176 + 0.0979384i
\(135\) −6575.23 + 10231.3i −0.360781 + 0.561386i
\(136\) 5094.24 4414.18i 0.275424 0.238656i
\(137\) 14917.2i 0.794781i −0.917650 0.397390i \(-0.869916\pi\)
0.917650 0.397390i \(-0.130084\pi\)
\(138\) −14121.8 + 7095.51i −0.741535 + 0.372585i
\(139\) −5240.17 −0.271216 −0.135608 0.990763i \(-0.543299\pi\)
−0.135608 + 0.990763i \(0.543299\pi\)
\(140\) −311.440 359.421i −0.0158898 0.0183378i
\(141\) 4218.79 + 2711.25i 0.212202 + 0.136374i
\(142\) 56.4751 392.793i 0.00280079 0.0194799i
\(143\) −28179.1 12869.0i −1.37802 0.629320i
\(144\) −2247.80 15633.8i −0.108401 0.753946i
\(145\) 1289.52 4391.72i 0.0613329 0.208881i
\(146\) 1121.10 720.485i 0.0525941 0.0338002i
\(147\) −15548.2 34045.9i −0.719525 1.57554i
\(148\) −7103.44 24192.1i −0.324299 1.10446i
\(149\) −15586.3 13505.6i −0.702054 0.608333i 0.228909 0.973448i \(-0.426484\pi\)
−0.930962 + 0.365115i \(0.881030\pi\)
\(150\) −10588.5 + 12219.8i −0.470599 + 0.543100i
\(151\) −3136.31 + 920.904i −0.137551 + 0.0403887i −0.349784 0.936831i \(-0.613745\pi\)
0.212232 + 0.977219i \(0.431927\pi\)
\(152\) 25773.7 11770.5i 1.11555 0.509456i
\(153\) 11177.8 + 17393.0i 0.477501 + 0.743006i
\(154\) 1402.60 + 411.842i 0.0591416 + 0.0173656i
\(155\) 7288.25 1047.89i 0.303361 0.0436167i
\(156\) −13664.9 + 29921.9i −0.561508 + 1.22953i
\(157\) 8546.26 + 1228.77i 0.346718 + 0.0498506i 0.313474 0.949597i \(-0.398507\pi\)
0.0332441 + 0.999447i \(0.489416\pi\)
\(158\) −1323.32 + 2059.12i −0.0530091 + 0.0824838i
\(159\) 15713.6 13615.9i 0.621559 0.538584i
\(160\) 9568.36i 0.373764i
\(161\) 2218.44 82.5813i 0.0855848 0.00318588i
\(162\) −14174.7 −0.540113
\(163\) −9951.15 11484.2i −0.374540 0.432242i 0.536919 0.843634i \(-0.319588\pi\)
−0.911458 + 0.411392i \(0.865043\pi\)
\(164\) 30983.5 + 19911.9i 1.15198 + 0.740330i
\(165\) 3745.66 26051.6i 0.137581 0.956900i
\(166\) −8466.51 3866.53i −0.307247 0.140315i
\(167\) −821.633 5714.58i −0.0294608 0.204905i 0.969775 0.244003i \(-0.0784606\pi\)
−0.999235 + 0.0390982i \(0.987551\pi\)
\(168\) 1002.47 3414.08i 0.0355182 0.120964i
\(169\) 53.9381 34.6639i 0.00188852 0.00121368i
\(170\) −903.122 1977.56i −0.0312499 0.0684278i
\(171\) 24484.7 + 83387.4i 0.837343 + 2.85173i
\(172\) −13486.4 11686.1i −0.455869 0.395013i
\(173\) 5358.73 6184.31i 0.179048 0.206633i −0.659130 0.752029i \(-0.729075\pi\)
0.838178 + 0.545396i \(0.183621\pi\)
\(174\) 14333.9 4208.81i 0.473440 0.139015i
\(175\) 2065.99 943.506i 0.0674609 0.0308084i
\(176\) 9441.11 + 14690.7i 0.304788 + 0.474259i
\(177\) −40859.7 11997.5i −1.30421 0.382952i
\(178\) 18358.3 2639.53i 0.579419 0.0833079i
\(179\) −12225.2 + 26769.5i −0.381549 + 0.835476i 0.617264 + 0.786756i \(0.288241\pi\)
−0.998813 + 0.0487192i \(0.984486\pi\)
\(180\) −18576.8 2670.94i −0.573357 0.0824363i
\(181\) 27790.6 43243.0i 0.848283 1.31995i −0.0975269 0.995233i \(-0.531093\pi\)
0.945810 0.324721i \(-0.105270\pi\)
\(182\) −1020.84 + 884.561i −0.0308187 + 0.0267045i
\(183\) 13216.0i 0.394638i
\(184\) −22266.7 17888.3i −0.657687 0.528364i
\(185\) −18641.1 −0.544664
\(186\) 15737.8 + 18162.4i 0.454903 + 0.524986i
\(187\) −19230.1 12358.4i −0.549918 0.353411i
\(188\) −562.669 + 3913.45i −0.0159198 + 0.110724i
\(189\) 5071.95 + 2316.28i 0.141988 + 0.0648438i
\(190\) −1300.54 9045.48i −0.0360261 0.250567i
\(191\) −12162.2 + 41420.5i −0.333384 + 1.13540i 0.606835 + 0.794828i \(0.292439\pi\)
−0.940218 + 0.340572i \(0.889379\pi\)
\(192\) −6112.66 + 3928.37i −0.165817 + 0.106564i
\(193\) 14460.4 + 31663.9i 0.388210 + 0.850061i 0.998331 + 0.0577525i \(0.0183934\pi\)
−0.610121 + 0.792308i \(0.708879\pi\)
\(194\) 4173.26 + 14212.8i 0.110885 + 0.377639i
\(195\) 18379.8 + 15926.2i 0.483362 + 0.418835i
\(196\) 19323.7 22300.7i 0.503011 0.580505i
\(197\) 37051.3 10879.2i 0.954709 0.280328i 0.232963 0.972486i \(-0.425158\pi\)
0.721746 + 0.692158i \(0.243340\pi\)
\(198\) 52474.3 23964.2i 1.33849 0.611270i
\(199\) 38164.1 + 59384.5i 0.963716 + 1.49957i 0.863340 + 0.504622i \(0.168368\pi\)
0.100376 + 0.994950i \(0.467996\pi\)
\(200\) −28037.9 8232.67i −0.700948 0.205817i
\(201\) −100963. + 14516.3i −2.49902 + 0.359304i
\(202\) 1312.44 2873.85i 0.0321645 0.0704305i
\(203\) −2077.10 298.642i −0.0504040 0.00724700i
\(204\) −13122.7 + 20419.4i −0.315329 + 0.490662i
\(205\) 20578.9 17831.7i 0.489683 0.424313i
\(206\) 21678.9i 0.510861i
\(207\) 64028.8 59793.4i 1.49429 1.39544i
\(208\) −16136.2 −0.372970
\(209\) −62923.6 72617.7i −1.44053 1.66246i
\(210\) −965.433 620.446i −0.0218919 0.0140691i
\(211\) 608.587 4232.81i 0.0136697 0.0950746i −0.981844 0.189688i \(-0.939252\pi\)
0.995514 + 0.0946133i \(0.0301615\pi\)
\(212\) 14911.0 + 6809.62i 0.331768 + 0.151513i
\(213\) 466.175 + 3242.32i 0.0102752 + 0.0714655i
\(214\) −2116.75 + 7208.98i −0.0462212 + 0.157415i
\(215\) −11099.1 + 7132.94i −0.240110 + 0.154309i
\(216\) −29801.2 65255.5i −0.638742 1.39865i
\(217\) −951.066 3239.03i −0.0201972 0.0687853i
\(218\) −25091.6 21742.0i −0.527977 0.457494i
\(219\) −7203.72 + 8313.54i −0.150200 + 0.173339i
\(220\) 19909.5 5845.97i 0.411354 0.120784i
\(221\) 19213.5 8774.50i 0.393388 0.179654i
\(222\) −32893.5 51183.3i −0.667428 1.03854i
\(223\) 31118.9 + 9137.34i 0.625770 + 0.183743i 0.579217 0.815173i \(-0.303358\pi\)
0.0465529 + 0.998916i \(0.485176\pi\)
\(224\) 4342.12 624.303i 0.0865378 0.0124423i
\(225\) 37233.4 81529.8i 0.735475 1.61047i
\(226\) 17478.2 + 2512.98i 0.342199 + 0.0492008i
\(227\) −33687.1 + 52418.2i −0.653750 + 1.01726i 0.343203 + 0.939261i \(0.388488\pi\)
−0.996954 + 0.0779943i \(0.975148\pi\)
\(228\) −77108.8 + 66815.2i −1.48332 + 1.28530i
\(229\) 27905.6i 0.532134i −0.963955 0.266067i \(-0.914276\pi\)
0.963955 0.266067i \(-0.0857242\pi\)
\(230\) −7558.99 + 5265.21i −0.142892 + 0.0995314i
\(231\) −12066.6 −0.226131
\(232\) 17680.3 + 20404.2i 0.328484 + 0.379091i
\(233\) 38179.2 + 24536.3i 0.703258 + 0.451956i 0.842777 0.538263i \(-0.180919\pi\)
−0.139519 + 0.990219i \(0.544556\pi\)
\(234\) −7586.08 + 52762.3i −0.138543 + 0.963590i
\(235\) 2658.94 + 1214.30i 0.0481474 + 0.0219882i
\(236\) −4777.99 33231.7i −0.0857870 0.596662i
\(237\) 5692.26 19386.1i 0.101342 0.345138i
\(238\) −838.492 + 538.866i −0.0148028 + 0.00951320i
\(239\) 34947.0 + 76523.2i 0.611806 + 1.33967i 0.921332 + 0.388777i \(0.127102\pi\)
−0.309526 + 0.950891i \(0.600170\pi\)
\(240\) −3862.37 13154.0i −0.0670550 0.228368i
\(241\) −51938.0 45004.5i −0.894234 0.774858i 0.0808424 0.996727i \(-0.474239\pi\)
−0.975077 + 0.221869i \(0.928784\pi\)
\(242\) −23527.0 + 27151.6i −0.401732 + 0.463623i
\(243\) 9003.57 2643.69i 0.152476 0.0447711i
\(244\) −9477.81 + 4328.37i −0.159195 + 0.0727018i
\(245\) −11794.8 18353.0i −0.196498 0.305757i
\(246\) 85273.8 + 25038.7i 1.40911 + 0.413753i
\(247\) 87883.5 12635.7i 1.44050 0.207113i
\(248\) −18042.5 + 39507.6i −0.293355 + 0.642359i
\(249\) 76047.9 + 10934.0i 1.22656 + 0.176353i
\(250\) −10979.6 + 17084.5i −0.175673 + 0.273352i
\(251\) 40351.1 34964.5i 0.640484 0.554983i −0.272920 0.962037i \(-0.587989\pi\)
0.913404 + 0.407054i \(0.133444\pi\)
\(252\) 8604.40i 0.135494i
\(253\) −36931.7 + 89542.5i −0.576976 + 1.39891i
\(254\) −50439.5 −0.781813
\(255\) 11751.8 + 13562.3i 0.180728 + 0.208571i
\(256\) −31586.8 20299.6i −0.481977 0.309748i
\(257\) 8623.76 59979.5i 0.130566 0.908107i −0.814252 0.580511i \(-0.802853\pi\)
0.944818 0.327595i \(-0.106238\pi\)
\(258\) −39170.1 17888.4i −0.588458 0.268740i
\(259\) 1216.27 + 8459.34i 0.0181314 + 0.126106i
\(260\) −5401.85 + 18397.0i −0.0799090 + 0.272145i
\(261\) −69665.1 + 44771.0i −1.02267 + 0.657228i
\(262\) 1575.12 + 3449.02i 0.0229461 + 0.0502451i
\(263\) −34862.6 118731.i −0.504020 1.71653i −0.680967 0.732314i \(-0.738440\pi\)
0.176947 0.984220i \(-0.443378\pi\)
\(264\) 117329. + 101666.i 1.68344 + 1.45871i
\(265\) 7936.52 9159.23i 0.113016 0.130427i
\(266\) −4019.98 + 1180.37i −0.0568147 + 0.0166823i
\(267\) −139262. + 63599.0i −1.95349 + 0.892129i
\(268\) −43476.5 67650.8i −0.605320 0.941897i
\(269\) 74410.9 + 21849.0i 1.02833 + 0.301944i 0.752031 0.659128i \(-0.229074\pi\)
0.276297 + 0.961072i \(0.410893\pi\)
\(270\) −22901.9 + 3292.79i −0.314155 + 0.0451686i
\(271\) 17101.0 37446.0i 0.232854 0.509879i −0.756749 0.653706i \(-0.773213\pi\)
0.989603 + 0.143826i \(0.0459407\pi\)
\(272\) −11785.6 1694.51i −0.159299 0.0229037i
\(273\) 6028.09 9379.89i 0.0808825 0.125856i
\(274\) 21447.6 18584.4i 0.285678 0.247542i
\(275\) 99096.1i 1.31036i
\(276\) 95080.4 + 39215.7i 1.24817 + 0.514804i
\(277\) 142671. 1.85941 0.929707 0.368300i \(-0.120060\pi\)
0.929707 + 0.368300i \(0.120060\pi\)
\(278\) −6528.39 7534.17i −0.0844728 0.0974868i
\(279\) −112070. 72022.9i −1.43973 0.925257i
\(280\) 295.165 2052.92i 0.00376486 0.0261852i
\(281\) 37099.1 + 16942.6i 0.469841 + 0.214569i 0.636243 0.771489i \(-0.280488\pi\)
−0.166402 + 0.986058i \(0.553215\pi\)
\(282\) 1357.76 + 9443.42i 0.0170736 + 0.118749i
\(283\) −12027.9 + 40963.2i −0.150182 + 0.511472i −0.999875 0.0158054i \(-0.994969\pi\)
0.849693 + 0.527277i \(0.176787\pi\)
\(284\) −2172.54 + 1396.21i −0.0269359 + 0.0173106i
\(285\) 31336.4 + 68617.1i 0.385797 + 0.844778i
\(286\) −16603.9 56547.7i −0.202992 0.691326i
\(287\) −9434.74 8175.25i −0.114542 0.0992515i
\(288\) 113366. 130831.i 1.36678 1.57734i
\(289\) −65183.2 + 19139.5i −0.780441 + 0.229158i
\(290\) 7920.82 3617.32i 0.0941834 0.0430121i
\(291\) −66105.7 102863.i −0.780644 1.21471i
\(292\) −8321.30 2443.36i −0.0975946 0.0286564i
\(293\) −6332.73 + 910.509i −0.0737659 + 0.0106059i −0.179099 0.983831i \(-0.557318\pi\)
0.105333 + 0.994437i \(0.466409\pi\)
\(294\) 29579.6 64770.3i 0.342214 0.749344i
\(295\) −24569.3 3532.53i −0.282325 0.0405921i
\(296\) 59447.0 92501.3i 0.678495 1.05576i
\(297\) −183858. + 159314.i −2.08434 + 1.80609i
\(298\) 39235.3i 0.441819i
\(299\) −51155.4 73441.2i −0.572202 0.821480i
\(300\) 105225. 1.16916
\(301\) 3961.10 + 4571.35i 0.0437203 + 0.0504559i
\(302\) −5231.38 3362.00i −0.0573591 0.0368624i
\(303\) −3711.42 + 25813.5i −0.0404254 + 0.281165i
\(304\) −45527.0 20791.5i −0.492631 0.224977i
\(305\) 1096.31 + 7625.00i 0.0117851 + 0.0819672i
\(306\) −11081.5 + 37740.0i −0.118346 + 0.403050i
\(307\) −77218.6 + 49625.4i −0.819304 + 0.526535i −0.881862 0.471507i \(-0.843710\pi\)
0.0625587 + 0.998041i \(0.480074\pi\)
\(308\) −3951.93 8653.51i −0.0416589 0.0912202i
\(309\) −50415.7 171700.i −0.528018 1.79827i
\(310\) 10586.6 + 9173.33i 0.110162 + 0.0954561i
\(311\) 19210.4 22170.0i 0.198617 0.229216i −0.647701 0.761895i \(-0.724269\pi\)
0.846317 + 0.532679i \(0.178815\pi\)
\(312\) −137643. + 40415.6i −1.41399 + 0.415184i
\(313\) −39613.4 + 18090.8i −0.404346 + 0.184659i −0.607198 0.794551i \(-0.707706\pi\)
0.202851 + 0.979210i \(0.434979\pi\)
\(314\) 8880.55 + 13818.4i 0.0900701 + 0.140152i
\(315\) 6103.84 + 1792.25i 0.0615152 + 0.0180625i
\(316\) 15766.9 2266.94i 0.157896 0.0227021i
\(317\) −18500.1 + 40509.6i −0.184101 + 0.403125i −0.979070 0.203526i \(-0.934760\pi\)
0.794969 + 0.606650i \(0.207487\pi\)
\(318\) 39153.2 + 5629.38i 0.387180 + 0.0556681i
\(319\) 49499.8 77023.1i 0.486432 0.756902i
\(320\) −3200.84 + 2773.54i −0.0312582 + 0.0270854i
\(321\) 62018.9i 0.601886i
\(322\) 2882.55 + 3086.73i 0.0278013 + 0.0297706i
\(323\) 65515.4 0.627969
\(324\) 60408.4 + 69715.1i 0.575450 + 0.664105i
\(325\) −77031.7 49505.3i −0.729294 0.468689i
\(326\) 4114.21 28614.9i 0.0387125 0.269251i
\(327\) 249291. + 113848.i 2.33137 + 1.06470i
\(328\) 22858.3 + 158983.i 0.212469 + 1.47776i
\(329\) 377.561 1285.86i 0.00348815 0.0118796i
\(330\) 42122.7 27070.6i 0.386802 0.248582i
\(331\) 13230.7 + 28971.1i 0.120761 + 0.264429i 0.960352 0.278789i \(-0.0899329\pi\)
−0.839592 + 0.543218i \(0.817206\pi\)
\(332\) 17065.1 + 58118.5i 0.154822 + 0.527276i
\(333\) 254886. + 220860.i 2.29857 + 1.99172i
\(334\) 7192.64 8300.75i 0.0644756 0.0744088i
\(335\) −57046.4 + 16750.3i −0.508322 + 0.149257i
\(336\) −5717.28 + 2611.00i −0.0506420 + 0.0231274i
\(337\) −25002.4 38904.6i −0.220152 0.342563i 0.713556 0.700598i \(-0.247083\pi\)
−0.933708 + 0.358035i \(0.883447\pi\)
\(338\) 117.037 + 34.3651i 0.00102445 + 0.000300804i
\(339\) −144274. + 20743.4i −1.25542 + 0.180502i
\(340\) −5877.33 + 12869.6i −0.0508420 + 0.111328i
\(341\) 145789. + 20961.3i 1.25376 + 0.180264i
\(342\) −89388.0 + 139090.i −0.764235 + 1.18917i
\(343\) −15173.9 + 13148.3i −0.128976 + 0.111759i
\(344\) 77823.1i 0.657645i
\(345\) 47623.8 59280.2i 0.400116 0.498049i
\(346\) 15567.7 0.130039
\(347\) −24632.7 28427.7i −0.204576 0.236093i 0.644186 0.764869i \(-0.277196\pi\)
−0.848761 + 0.528776i \(0.822651\pi\)
\(348\) −81786.7 52561.1i −0.675343 0.434016i
\(349\) −15360.1 + 106832.i −0.126108 + 0.877100i 0.824313 + 0.566134i \(0.191562\pi\)
−0.950421 + 0.310966i \(0.899348\pi\)
\(350\) 3930.43 + 1794.97i 0.0320851 + 0.0146528i
\(351\) −31991.9 222508.i −0.259672 1.80606i
\(352\) −53923.3 + 183646.i −0.435202 + 1.48216i
\(353\) −81790.2 + 52563.3i −0.656374 + 0.421826i −0.825991 0.563684i \(-0.809384\pi\)
0.169616 + 0.985510i \(0.445747\pi\)
\(354\) −33654.8 73693.8i −0.268560 0.588064i
\(355\) 537.921 + 1831.99i 0.00426837 + 0.0145367i
\(356\) −91219.5 79042.1i −0.719760 0.623675i
\(357\) 5387.81 6217.87i 0.0422743 0.0487871i
\(358\) −53719.0 + 15773.3i −0.419142 + 0.123071i
\(359\) 24295.5 11095.4i 0.188511 0.0860901i −0.318923 0.947780i \(-0.603321\pi\)
0.507434 + 0.861690i \(0.330594\pi\)
\(360\) −44249.8 68854.1i −0.341434 0.531282i
\(361\) 139196. + 40871.6i 1.06810 + 0.313623i
\(362\) 96796.1 13917.2i 0.738653 0.106202i
\(363\) 123195. 269759.i 0.934929 2.04721i
\(364\) 8701.01 + 1251.02i 0.0656700 + 0.00944191i
\(365\) −3466.56 + 5394.08i −0.0260204 + 0.0404885i
\(366\) −19001.6 + 16465.0i −0.141850 + 0.122913i
\(367\) 219889.i 1.63257i 0.577652 + 0.816283i \(0.303969\pi\)
−0.577652 + 0.816283i \(0.696031\pi\)
\(368\) 1876.79 + 50417.5i 0.0138586 + 0.372294i
\(369\) −492652. −3.61816
\(370\) −23223.8 26801.7i −0.169640 0.195776i
\(371\) −4674.29 3003.98i −0.0339600 0.0218248i
\(372\) 22257.7 154805.i 0.160840 1.11867i
\(373\) −126020. 57551.6i −0.905781 0.413656i −0.0926243 0.995701i \(-0.529526\pi\)
−0.813157 + 0.582045i \(0.802253\pi\)
\(374\) −6188.94 43045.0i −0.0442459 0.307737i
\(375\) 47228.6 160846.i 0.335848 1.14379i
\(376\) −14505.0 + 9321.82i −0.102599 + 0.0659364i
\(377\) 35144.9 + 76956.6i 0.247275 + 0.541456i
\(378\) 2988.54 + 10178.0i 0.0209158 + 0.0712327i
\(379\) −56672.3 49106.8i −0.394541 0.341872i 0.434887 0.900485i \(-0.356788\pi\)
−0.829428 + 0.558613i \(0.811334\pi\)
\(380\) −38945.5 + 44945.5i −0.269706 + 0.311257i
\(381\) 399488. 117300.i 2.75204 0.808071i
\(382\) −74705.3 + 34116.8i −0.511947 + 0.233798i
\(383\) 80558.1 + 125351.i 0.549176 + 0.854534i 0.999260 0.0384516i \(-0.0122425\pi\)
−0.450085 + 0.892986i \(0.648606\pi\)
\(384\) 238746. + 70102.2i 1.61910 + 0.475411i
\(385\) −6961.84 + 1000.96i −0.0469681 + 0.00675299i
\(386\) −27510.1 + 60238.8i −0.184637 + 0.404298i
\(387\) 236272. + 33970.8i 1.57758 + 0.226821i
\(388\) 52117.2 81095.9i 0.346192 0.538686i
\(389\) 13172.9 11414.4i 0.0870527 0.0754316i −0.610247 0.792211i \(-0.708930\pi\)
0.697300 + 0.716779i \(0.254384\pi\)
\(390\) 46267.4i 0.304191i
\(391\) −29650.7 59012.0i −0.193946 0.386000i
\(392\) 128686. 0.837448
\(393\) −20496.1 23653.8i −0.132705 0.153149i
\(394\) 61801.7 + 39717.5i 0.398114 + 0.255853i
\(395\) 1676.02 11657.0i 0.0107420 0.0747124i
\(396\) −341492. 155954.i −2.17766 0.994505i
\(397\) −23271.2 161855.i −0.147652 1.02694i −0.920050 0.391801i \(-0.871852\pi\)
0.772398 0.635139i \(-0.219057\pi\)
\(398\) −37835.1 + 128855.i −0.238852 + 0.813456i
\(399\) 29093.8 18697.5i 0.182749 0.117446i
\(400\) 21442.6 + 46952.8i 0.134016 + 0.293455i
\(401\) 4160.37 + 14168.9i 0.0258728 + 0.0881147i 0.971417 0.237378i \(-0.0762880\pi\)
−0.945545 + 0.325493i \(0.894470\pi\)
\(402\) −146654. 127076.i −0.907490 0.786345i
\(403\) −89125.6 + 102856.i −0.548773 + 0.633318i
\(404\) −19727.6 + 5792.54i −0.120868 + 0.0354900i
\(405\) 62037.6 28331.6i 0.378220 0.172727i
\(406\) −2158.34 3358.45i −0.0130939 0.0203745i
\(407\) −357780. 105054.i −2.15987 0.634194i
\(408\) −104776. + 15064.5i −0.629422 + 0.0904972i
\(409\) −91424.6 + 200192.i −0.546533 + 1.19674i 0.411849 + 0.911252i \(0.364883\pi\)
−0.958382 + 0.285488i \(0.907844\pi\)
\(410\) 51275.9 + 7372.36i 0.305032 + 0.0438570i
\(411\) −126649. + 197069.i −0.749752 + 1.16664i
\(412\) 106622. 92388.9i 0.628137 0.544284i
\(413\) 11380.0i 0.0667180i
\(414\) 165739. + 17566.0i 0.966992 + 0.102488i
\(415\) 44783.0 0.260026
\(416\) −115817. 133660.i −0.669249 0.772354i
\(417\) 69227.1 + 44489.6i 0.398111 + 0.255850i
\(418\) 26015.2 180939.i 0.148893 1.03557i
\(419\) 184786. + 84388.7i 1.05254 + 0.480680i 0.865102 0.501595i \(-0.167253\pi\)
0.187441 + 0.982276i \(0.439981\pi\)
\(420\) 1062.87 + 7392.40i 0.00602532 + 0.0419071i
\(421\) 34384.9 117104.i 0.194001 0.660706i −0.803829 0.594860i \(-0.797207\pi\)
0.997830 0.0658456i \(-0.0209745\pi\)
\(422\) 6844.02 4398.38i 0.0384314 0.0246984i
\(423\) −21969.5 48106.6i −0.122784 0.268858i
\(424\) 20140.4 + 68591.8i 0.112030 + 0.381540i
\(425\) −51063.8 44247.0i −0.282706 0.244966i
\(426\) −4080.93 + 4709.65i −0.0224875 + 0.0259519i
\(427\) 3388.69 995.010i 0.0185856 0.00545722i
\(428\) 44476.6 20311.8i 0.242797 0.110882i
\(429\) 263011. + 409253.i 1.42909 + 2.22371i
\(430\) −24083.1 7071.45i −0.130250 0.0382447i
\(431\) 292854. 42106.1i 1.57651 0.226668i 0.702181 0.711999i \(-0.252210\pi\)
0.874331 + 0.485331i \(0.161301\pi\)
\(432\) −52641.1 + 115268.i −0.282070 + 0.617648i
\(433\) −173478. 24942.4i −0.925272 0.133034i −0.336823 0.941568i \(-0.609352\pi\)
−0.588449 + 0.808534i \(0.700261\pi\)
\(434\) 3472.12 5402.72i 0.0184338 0.0286835i
\(435\) −54321.8 + 47070.1i −0.287075 + 0.248752i
\(436\) 216064.i 1.13661i
\(437\) −49702.1 273123.i −0.260263 1.43019i
\(438\) −20927.6 −0.109087
\(439\) −110150. 127120.i −0.571551 0.659605i 0.394216 0.919018i \(-0.371016\pi\)
−0.965766 + 0.259413i \(0.916471\pi\)
\(440\) 76126.5 + 48923.5i 0.393215 + 0.252704i
\(441\) −56172.9 + 390691.i −0.288835 + 2.00889i
\(442\) 36552.5 + 16693.0i 0.187100 + 0.0854456i
\(443\) −9323.24 64844.6i −0.0475072 0.330420i −0.999690 0.0248914i \(-0.992076\pi\)
0.952183 0.305528i \(-0.0988331\pi\)
\(444\) −111551. + 379907.i −0.565857 + 1.92713i
\(445\) −75071.9 + 48245.8i −0.379103 + 0.243635i
\(446\) 25631.7 + 56125.5i 0.128857 + 0.282157i
\(447\) 91244.3 + 310750.i 0.456658 + 1.55523i
\(448\) 1467.48 + 1271.58i 0.00731165 + 0.00633558i
\(449\) 170144. 196357.i 0.843965 0.973987i −0.155940 0.987766i \(-0.549841\pi\)
0.999905 + 0.0137792i \(0.00438618\pi\)
\(450\) 163608. 48039.6i 0.807940 0.237233i
\(451\) 495464. 226271.i 2.43590 1.11244i
\(452\) −62127.1 96671.7i −0.304092 0.473176i
\(453\) 49251.9 + 14461.7i 0.240008 + 0.0704728i
\(454\) −117334. + 16870.1i −0.569261 + 0.0818474i
\(455\) 2699.82 5911.79i 0.0130411 0.0285559i
\(456\) −440425. 63323.6i −2.11808 0.304534i
\(457\) 45524.8 70837.9i 0.217979 0.339182i −0.714992 0.699132i \(-0.753570\pi\)
0.932972 + 0.359950i \(0.117206\pi\)
\(458\) 40121.9 34765.8i 0.191272 0.165738i
\(459\) 165876.i 0.787331i
\(460\) 58109.8 + 14738.4i 0.274621 + 0.0696520i
\(461\) −267210. −1.25734 −0.628668 0.777674i \(-0.716400\pi\)
−0.628668 + 0.777674i \(0.716400\pi\)
\(462\) −15033.0 17349.0i −0.0704307 0.0812813i
\(463\) −1921.92 1235.14i −0.00896546 0.00576175i 0.536150 0.844122i \(-0.319878\pi\)
−0.545116 + 0.838361i \(0.683514\pi\)
\(464\) 6787.09 47205.2i 0.0315244 0.219257i
\(465\) −105181. 48034.4i −0.486441 0.222150i
\(466\) 12287.4 + 85461.0i 0.0565835 + 0.393547i
\(467\) −40238.5 + 137040.i −0.184505 + 0.628367i 0.814343 + 0.580384i \(0.197097\pi\)
−0.998848 + 0.0479828i \(0.984721\pi\)
\(468\) 291829. 187547.i 1.33240 0.856284i
\(469\) 11323.4 + 24794.8i 0.0514791 + 0.112723i
\(470\) 1566.72 + 5335.76i 0.00709245 + 0.0241547i
\(471\) −102471. 88791.6i −0.461912 0.400249i
\(472\) 95881.3 110653.i 0.430378 0.496682i
\(473\) −253223. + 74353.0i −1.13183 + 0.332335i
\(474\) 34964.3 15967.7i 0.155621 0.0710698i
\(475\) −153552. 238931.i −0.680561 1.05897i
\(476\) 6223.68 + 1827.44i 0.0274684 + 0.00806545i
\(477\) −217037. + 31205.2i −0.953887 + 0.137148i
\(478\) −66484.6 + 145581.i −0.290982 + 0.637161i
\(479\) −62624.2 9004.01i −0.272943 0.0392432i 0.00448434 0.999990i \(-0.498573\pi\)
−0.277427 + 0.960747i \(0.589482\pi\)
\(480\) 81236.3 126406.i 0.352588 0.548638i
\(481\) 260398. 225636.i 1.12551 0.975256i
\(482\) 130743.i 0.562763i
\(483\) −30008.6 17743.8i −0.128633 0.0760595i
\(484\) 233804. 0.998069
\(485\) −46672.6 53863.0i −0.198417 0.228985i
\(486\) 15018.0 + 9651.48i 0.0635827 + 0.0408621i
\(487\) 38253.0 266055.i 0.161290 1.12180i −0.734916 0.678158i \(-0.762778\pi\)
0.896206 0.443638i \(-0.146313\pi\)
\(488\) −41333.1 18876.2i −0.173563 0.0792637i
\(489\) 33960.8 + 236203.i 0.142024 + 0.987795i
\(490\) 11693.1 39823.1i 0.0487010 0.165860i
\(491\) −178630. + 114798.i −0.740952 + 0.476181i −0.855868 0.517194i \(-0.826977\pi\)
0.114916 + 0.993375i \(0.463340\pi\)
\(492\) −240265. 526106.i −0.992567 2.17342i
\(493\) 17587.7 + 59898.3i 0.0723629 + 0.246446i
\(494\) 127656. + 110614.i 0.523102 + 0.453270i
\(495\) −181763. + 209765.i −0.741813 + 0.856097i
\(496\) 73612.0 21614.4i 0.299216 0.0878578i
\(497\) 796.259 363.639i 0.00322360 0.00147217i
\(498\) 79022.6 + 122962.i 0.318634 + 0.495805i
\(499\) −221630. 65076.5i −0.890077 0.261350i −0.195444 0.980715i \(-0.562615\pi\)
−0.694633 + 0.719365i \(0.744433\pi\)
\(500\) 130818. 18808.8i 0.523271 0.0752350i
\(501\) −37662.9 + 82470.2i −0.150051 + 0.328565i
\(502\) 100542. + 14455.7i 0.398969 + 0.0573631i
\(503\) −136582. + 212525.i −0.539829 + 0.839990i −0.998826 0.0484478i \(-0.984573\pi\)
0.458997 + 0.888438i \(0.348209\pi\)
\(504\) −28358.8 + 24573.1i −0.111642 + 0.0967382i
\(505\) 15201.0i 0.0596059i
\(506\) −174752. + 58456.0i −0.682531 + 0.228312i
\(507\) −1006.87 −0.00391703
\(508\) 214958. + 248075.i 0.832963 + 0.961291i
\(509\) 129909. + 83487.3i 0.501422 + 0.322244i 0.766785 0.641904i \(-0.221855\pi\)
−0.265363 + 0.964149i \(0.585492\pi\)
\(510\) −4858.68 + 33792.9i −0.0186800 + 0.129923i
\(511\) 2674.01 + 1221.18i 0.0102405 + 0.00467668i
\(512\) 25913.7 + 180234.i 0.0988531 + 0.687538i
\(513\) 196440. 669013.i 0.746441 2.54214i
\(514\) 96980.6 62325.7i 0.367078 0.235907i
\(515\) −43330.5 94880.5i −0.163373 0.357736i
\(516\) 78951.4 + 268884.i 0.296524 + 1.00987i
\(517\) 44189.9 + 38290.7i 0.165326 + 0.143256i
\(518\) −10647.3 + 12287.7i −0.0396808 + 0.0457941i
\(519\) −123299. + 36203.8i −0.457745 + 0.134406i
\(520\) −76060.7 + 34735.8i −0.281290 + 0.128461i
\(521\) 127223. + 197962.i 0.468694 + 0.729302i 0.992461 0.122559i \(-0.0391102\pi\)
−0.523767 + 0.851861i \(0.675474\pi\)
\(522\) −151162. 44385.1i −0.554755 0.162891i
\(523\) 226092. 32507.1i 0.826573 0.118843i 0.283971 0.958833i \(-0.408348\pi\)
0.542602 + 0.839990i \(0.317439\pi\)
\(524\) 10250.5 22445.5i 0.0373322 0.0817461i
\(525\) −35303.9 5075.94i −0.128087 0.0184161i
\(526\) 127275. 198044.i 0.460014 0.715796i
\(527\) −75897.0 + 65765.1i −0.273277 + 0.236796i
\(528\) 274232.i 0.983672i
\(529\) −223518. + 168377.i −0.798730 + 0.601689i
\(530\) 23056.5 0.0820808
\(531\) 294090. + 339398.i 1.04302 + 1.20371i
\(532\) 22937.3 + 14740.9i 0.0810437 + 0.0520836i
\(533\) −71627.9 + 498183.i −0.252132 + 1.75362i
\(534\) −264939. 120993.i −0.929101 0.424306i
\(535\) −5144.66 35781.9i −0.0179742 0.125013i
\(536\) 98803.6 336494.i 0.343909 1.17125i
\(537\) 388781. 249854.i 1.34821 0.866439i
\(538\) 61289.9 + 134206.i 0.211750 + 0.463668i
\(539\) −122948. 418721.i −0.423197 1.44128i
\(540\) 113796. + 98604.5i 0.390246 + 0.338150i
\(541\) −329198. + 379915.i −1.12477 + 1.29805i −0.175183 + 0.984536i \(0.556052\pi\)
−0.949584 + 0.313514i \(0.898494\pi\)
\(542\) 75143.9 22064.2i 0.255797 0.0751087i
\(543\) −734275. + 335332.i −2.49034 + 1.13730i
\(544\) −70554.8 109785.i −0.238412 0.370977i
\(545\) 153273. + 45005.0i 0.516027 + 0.151519i
\(546\) 20996.1 3018.79i 0.0704294 0.0101262i
\(547\) 178711. 391322.i 0.597277 1.30785i −0.333667 0.942691i \(-0.608286\pi\)
0.930944 0.365163i \(-0.118987\pi\)
\(548\) −182806. 26283.6i −0.608737 0.0875232i
\(549\) 75350.7 117248.i 0.250002 0.389010i
\(550\) −142478. + 123457.i −0.471000 + 0.408124i
\(551\) 262412.i 0.864331i
\(552\) 142288. + 425366.i 0.466971 + 1.39600i
\(553\) −5399.30 −0.0176558
\(554\) 177745. + 205128.i 0.579131 + 0.668353i
\(555\) 246265. + 158265.i 0.799497 + 0.513806i
\(556\) −9232.96 + 64216.7i −0.0298670 + 0.207730i
\(557\) 397413. + 181492.i 1.28095 + 0.584989i 0.935459 0.353434i \(-0.114986\pi\)
0.345488 + 0.938423i \(0.387713\pi\)
\(558\) −36068.1 250859.i −0.115839 0.805679i
\(559\) 68704.3 233985.i 0.219867 0.748799i
\(560\) −3082.00 + 1980.68i −0.00982782 + 0.00631596i
\(561\) 149121. + 326530.i 0.473821 + 1.03752i
\(562\) 21859.8 + 74447.6i 0.0692108 + 0.235710i
\(563\) −219043. 189801.i −0.691054 0.598801i 0.236884 0.971538i \(-0.423874\pi\)
−0.927937 + 0.372737i \(0.878419\pi\)
\(564\) 40658.9 46922.8i 0.127819 0.147512i
\(565\) −81518.3 + 23935.9i −0.255363 + 0.0749813i
\(566\) −73880.5 + 33740.1i −0.230620 + 0.105321i
\(567\) −16904.6 26304.1i −0.0525823 0.0818196i
\(568\) −10806.2 3172.98i −0.0334946 0.00983491i
\(569\) 169025. 24302.1i 0.522067 0.0750619i 0.123757 0.992313i \(-0.460506\pi\)
0.398310 + 0.917251i \(0.369597\pi\)
\(570\) −59615.7 + 130540.i −0.183489 + 0.401786i
\(571\) 238878. + 34345.4i 0.732661 + 0.105341i 0.498540 0.866867i \(-0.333870\pi\)
0.234121 + 0.972207i \(0.424779\pi\)
\(572\) −207356. + 322652.i −0.633758 + 0.986147i
\(573\) 512337. 443942.i 1.56044 1.35213i
\(574\) 23750.0i 0.0720842i
\(575\) −145720. + 246444.i −0.440741 + 0.745388i
\(576\) 76627.0 0.230960
\(577\) −229944. 265370.i −0.690670 0.797076i 0.296790 0.954943i \(-0.404084\pi\)
−0.987460 + 0.157867i \(0.949538\pi\)
\(578\) −108726. 69873.8i −0.325445 0.209151i
\(579\) 77795.2 541077.i 0.232057 1.61400i
\(580\) −51547.1 23540.7i −0.153231 0.0699784i
\(581\) −2921.94 20322.5i −0.00865602 0.0602040i
\(582\) 65535.9 223195.i 0.193479 0.658928i
\(583\) 203943. 131067.i 0.600030 0.385616i
\(584\) −15711.6 34403.7i −0.0460676 0.100874i
\(585\) −72256.8 246084.i −0.211138 0.719071i
\(586\) −9198.64 7970.67i −0.0267873 0.0232113i
\(587\) −195549. + 225675.i −0.567517 + 0.654950i −0.964874 0.262715i \(-0.915382\pi\)
0.397356 + 0.917664i \(0.369928\pi\)
\(588\) −444617. + 130551.i −1.28597 + 0.377595i
\(589\) −383992. + 175363.i −1.10686 + 0.505485i
\(590\) −25530.3 39726.0i −0.0733420 0.114122i
\(591\) −581845. 170845.i −1.66584 0.489133i
\(592\) −192251. + 27641.6i −0.548563 + 0.0788714i
\(593\) 13311.5 29148.1i 0.0378545 0.0828897i −0.889760 0.456428i \(-0.849128\pi\)
0.927615 + 0.373539i \(0.121856\pi\)
\(594\) −458113. 65866.7i −1.29837 0.186678i
\(595\) 2592.72 4034.34i 0.00732354 0.0113956i
\(596\) −192969. + 167209.i −0.543245 + 0.470725i
\(597\) 1.10854e6i 3.11029i
\(598\) 41860.4 165045.i 0.117058 0.461531i
\(599\) 681573. 1.89959 0.949793 0.312880i \(-0.101294\pi\)
0.949793 + 0.312880i \(0.101294\pi\)
\(600\) 300508. + 346805.i 0.834746 + 0.963348i
\(601\) −396828. 255026.i −1.09864 0.706050i −0.139848 0.990173i \(-0.544661\pi\)
−0.958788 + 0.284123i \(0.908298\pi\)
\(602\) −1637.68 + 11390.3i −0.00451893 + 0.0314299i
\(603\) 978471. + 446853.i 2.69100 + 1.22894i
\(604\) 5759.34 + 40057.1i 0.0157870 + 0.109801i
\(605\) 48700.0 165857.i 0.133051 0.453130i
\(606\) −41737.7 + 26823.2i −0.113654 + 0.0730408i
\(607\) 18713.0 + 40975.8i 0.0507887 + 0.111212i 0.933325 0.359032i \(-0.116893\pi\)
−0.882536 + 0.470244i \(0.844166\pi\)
\(608\) −154549. 526345.i −0.418079 1.42385i
\(609\) 24904.7 + 21580.1i 0.0671502 + 0.0581859i
\(610\) −9597.18 + 11075.7i −0.0257919 + 0.0297655i
\(611\) −51840.9 + 15221.9i −0.138864 + 0.0407742i
\(612\) 232841. 106335.i 0.621665 0.283905i
\(613\) 144150. + 224301.i 0.383613 + 0.596913i 0.978337 0.207016i \(-0.0663753\pi\)
−0.594725 + 0.803929i \(0.702739\pi\)
\(614\) −167552. 49197.6i −0.444438 0.130499i
\(615\) −423258. + 60855.3i −1.11906 + 0.160897i
\(616\) 17234.5 37738.3i 0.0454189 0.0994536i
\(617\) −318666. 45817.3i −0.837077 0.120353i −0.289572 0.957156i \(-0.593513\pi\)
−0.547505 + 0.836803i \(0.684422\pi\)
\(618\) 184056. 286397.i 0.481917 0.749878i
\(619\) 180851. 156708.i 0.471997 0.408988i −0.386115 0.922451i \(-0.626183\pi\)
0.858112 + 0.513463i \(0.171638\pi\)
\(620\) 91161.6i 0.237153i
\(621\) −691508. + 125839.i −1.79314 + 0.326310i
\(622\) 55808.3 0.144251
\(623\) 26792.1 + 30919.7i 0.0690288 + 0.0796635i
\(624\) 213172. + 136998.i 0.547472 + 0.351839i
\(625\) −34233.3 + 238098.i −0.0876372 + 0.609530i
\(626\) −75362.3 34416.8i −0.192312 0.0878258i
\(627\) 214743. + 1.49357e6i 0.546240 + 3.79918i
\(628\) 30116.3 102567.i 0.0763629 0.260068i
\(629\) 213885. 137455.i 0.540603 0.347424i
\(630\) 5027.54 + 11008.8i 0.0126670 + 0.0277369i
\(631\) 183422. + 624677.i 0.460672 + 1.56891i 0.782840 + 0.622223i \(0.213770\pi\)
−0.322168 + 0.946682i \(0.604412\pi\)
\(632\) 52499.7 + 45491.3i 0.131439 + 0.113892i
\(633\) −43976.9 + 50752.1i −0.109753 + 0.126662i
\(634\) −81291.6 + 23869.4i −0.202240 + 0.0593830i
\(635\) 220755. 100815.i 0.547474 0.250023i
\(636\) −139172. 216557.i −0.344064 0.535374i
\(637\) 386910. + 113607.i 0.953524 + 0.279980i
\(638\) 172410. 24788.8i 0.423566 0.0608997i
\(639\) 14350.2 31422.6i 0.0351445 0.0769557i
\(640\) 143560. + 20640.8i 0.350489 + 0.0503926i
\(641\) 330949. 514967.i 0.805462 1.25332i −0.158520 0.987356i \(-0.550672\pi\)
0.963982 0.265968i \(-0.0856914\pi\)
\(642\) 89169.0 77265.4i 0.216343 0.187463i
\(643\) 69578.6i 0.168288i 0.996454 + 0.0841441i \(0.0268156\pi\)
−0.996454 + 0.0841441i \(0.973184\pi\)
\(644\) 2896.80 27331.9i 0.00698468 0.0659018i
\(645\) 207187. 0.498017
\(646\) 81621.4 + 94196.1i 0.195587 + 0.225719i
\(647\) 632420. + 406432.i 1.51077 + 0.970911i 0.993345 + 0.115180i \(0.0367445\pi\)
0.517422 + 0.855731i \(0.326892\pi\)
\(648\) −57251.7 + 398194.i −0.136345 + 0.948299i
\(649\) −451651. 206262.i −1.07229 0.489700i
\(650\) −24791.6 172429.i −0.0586783 0.408117i
\(651\) −14935.3 + 50865.0i −0.0352413 + 0.120021i
\(652\) −158269. + 101713.i −0.372307 + 0.239267i
\(653\) −95903.0 209998.i −0.224909 0.492481i 0.763215 0.646145i \(-0.223620\pi\)
−0.988123 + 0.153664i \(0.950893\pi\)
\(654\) 146889. + 500259.i 0.343427 + 1.16961i
\(655\) −13787.4 11946.9i −0.0321366 0.0278465i
\(656\) 185795. 214419.i 0.431744 0.498259i
\(657\) 111308. 32683.1i 0.257868 0.0757168i
\(658\) 2319.15 1059.12i 0.00535644 0.00244620i
\(659\) −303229. 471833.i −0.698231 1.08647i −0.991458 0.130426i \(-0.958365\pi\)
0.293227 0.956043i \(-0.405271\pi\)
\(660\) −312655. 91803.7i −0.717756 0.210752i
\(661\) −615092. + 88436.9i −1.40779 + 0.202409i −0.803950 0.594697i \(-0.797272\pi\)
−0.603838 + 0.797107i \(0.706363\pi\)
\(662\) −25170.6 + 55116.0i −0.0574352 + 0.125766i
\(663\) −328323. 47205.7i −0.746919 0.107391i
\(664\) −142814. + 222223.i −0.323918 + 0.504026i
\(665\) 15234.7 13201.0i 0.0344501 0.0298512i
\(666\) 641623.i 1.44654i
\(667\) 236364. 118761.i 0.531287 0.266946i
\(668\) −71478.1 −0.160184
\(669\) −333531. 384915.i −0.745218 0.860027i
\(670\) −95153.6 61151.5i −0.211971 0.136225i
\(671\) −21929.8 + 152525.i −0.0487068 + 0.338763i
\(672\) −62663.5 28617.5i −0.138764 0.0633713i
\(673\) 28285.7 + 196731.i 0.0624506 + 0.434353i 0.996928 + 0.0783295i \(0.0249586\pi\)
−0.934477 + 0.356024i \(0.884132\pi\)
\(674\) 24786.9 84416.5i 0.0545635 0.185826i
\(675\) −604939. + 388771.i −1.32771 + 0.853270i
\(676\) −329.759 722.071i −0.000721611 0.00158011i
\(677\) −108362. 369046.i −0.236428 0.805199i −0.989156 0.146868i \(-0.953081\pi\)
0.752728 0.658331i \(-0.228737\pi\)
\(678\) −209566. 181590.i −0.455891 0.395032i
\(679\) −21397.8 + 24694.4i −0.0464119 + 0.0535622i
\(680\) −59201.0 + 17383.0i −0.128030 + 0.0375930i
\(681\) 890070. 406481.i 1.91924 0.876489i
\(682\) 151492. + 235726.i 0.325701 + 0.506801i
\(683\) −166766. 48966.8i −0.357491 0.104969i 0.0980550 0.995181i \(-0.468738\pi\)
−0.455546 + 0.890212i \(0.650556\pi\)
\(684\) 1.06503e6 153128.i 2.27640 0.327297i
\(685\) −56722.7 + 124205.i −0.120886 + 0.264703i
\(686\) −37808.4 5436.03i −0.0803416 0.0115514i
\(687\) −236921. + 368657.i −0.501985 + 0.781104i
\(688\) −103891. + 90022.1i −0.219483 + 0.190183i
\(689\) 224011.i 0.471879i
\(690\) 144563. 5381.33i 0.303640 0.0113029i
\(691\) −296953. −0.621916 −0.310958 0.950424i \(-0.600650\pi\)
−0.310958 + 0.950424i \(0.600650\pi\)
\(692\) −66344.9 76566.1i −0.138546 0.159891i
\(693\) 107051. + 68797.4i 0.222907 + 0.143254i
\(694\) 10184.2 70832.5i 0.0211450 0.147066i
\(695\) 43631.2 + 19925.7i 0.0903291 + 0.0412519i
\(696\) −60338.6 419664.i −0.124560 0.866331i
\(697\) −104631. + 356342.i −0.215376 + 0.733502i
\(698\) −172736. + 111010.i −0.354545 + 0.227852i
\(699\) −296064. 648290.i −0.605942 1.32683i
\(700\) −7922.18 26980.5i −0.0161677 0.0550622i
\(701\) 280057. + 242670.i 0.569914 + 0.493834i 0.891484 0.453052i \(-0.149665\pi\)
−0.321570 + 0.946886i \(0.604210\pi\)
\(702\) 280060. 323206.i 0.568298 0.655851i
\(703\) 1.02543e6 301093.i 2.07489 0.609241i
\(704\) −77064.3 + 35194.1i −0.155492 + 0.0710108i
\(705\) −24817.4 38616.6i −0.0499318 0.0776954i
\(706\) −177471. 52110.2i −0.356056 0.104547i
\(707\) 6898.21 991.813i 0.0138006 0.00198423i
\(708\) −219019. + 479584.i −0.436933 + 0.956749i
\(709\) 31051.3 + 4464.50i 0.0617714 + 0.00888138i 0.173131 0.984899i \(-0.444612\pi\)
−0.111360 + 0.993780i \(0.535521\pi\)
\(710\) −1963.82 + 3055.76i −0.00389570 + 0.00606182i
\(711\) −161029. + 139532.i −0.318540 + 0.276017i
\(712\) 526380.i 1.03834i
\(713\) 331742. + 266510.i 0.652561 + 0.524246i
\(714\) 15652.2 0.0307029
\(715\) 185693. + 214302.i 0.363232 + 0.419192i
\(716\) 306511. + 196983.i 0.597889 + 0.384240i
\(717\) 188010. 1.30764e6i 0.365715 2.54360i
\(718\) 46220.8 + 21108.3i 0.0896579 + 0.0409454i
\(719\) −133751. 930256.i −0.258725 1.79947i −0.541943 0.840415i \(-0.682311\pi\)
0.283218 0.959055i \(-0.408598\pi\)
\(720\) −40731.6 + 138719.i −0.0785718 + 0.267591i
\(721\) −40229.6 + 25854.0i −0.0773883 + 0.0497344i
\(722\) 114651. + 251051.i 0.219940 + 0.481602i
\(723\) 304052. + 1.03551e6i 0.581663 + 1.98096i
\(724\) −480964. 416758.i −0.917562 0.795072i
\(725\) 177225. 204528.i 0.337170 0.389114i
\(726\) 541332. 158949.i 1.02705 0.301568i
\(727\) −564117. + 257624.i −1.06733 + 0.487435i −0.870077 0.492916i \(-0.835931\pi\)
−0.197258 + 0.980352i \(0.563204\pi\)
\(728\) 20725.8 + 32250.0i 0.0391064 + 0.0608508i
\(729\) 437679. + 128514.i 0.823570 + 0.241822i
\(730\) −12074.2 + 1736.01i −0.0226576 + 0.00325767i
\(731\) 74751.9 163684.i 0.139890 0.306317i
\(732\) 161958. + 23286.1i 0.302260 + 0.0434584i
\(733\) −21722.8 + 33801.4i −0.0404304 + 0.0629109i −0.860880 0.508807i \(-0.830087\pi\)
0.820450 + 0.571718i \(0.193723\pi\)
\(734\) −316150. + 273945.i −0.586814 + 0.508477i
\(735\) 342598.i 0.634176i
\(736\) −404152. + 377418.i −0.746087 + 0.696735i
\(737\) −1.18929e6 −2.18954
\(738\) −613763. 708321.i −1.12691 1.30052i
\(739\) −467858. 300674.i −0.856692 0.550563i 0.0369630 0.999317i \(-0.488232\pi\)
−0.893655 + 0.448754i \(0.851868\pi\)
\(740\) −32844.9 + 228441.i −0.0599797 + 0.417168i
\(741\) −1.26829e6 579210.i −2.30985 1.05487i
\(742\) −1504.36 10463.0i −0.00273239 0.0190042i
\(743\) 125935. 428895.i 0.228123 0.776914i −0.763280 0.646068i \(-0.776412\pi\)
0.991403 0.130847i \(-0.0417695\pi\)
\(744\) 573780. 368746.i 1.03657 0.666165i
\(745\) 78421.2 + 171718.i 0.141293 + 0.309389i
\(746\) −74254.7 252888.i −0.133428 0.454413i
\(747\) −612331. 530588.i −1.09735 0.950860i
\(748\) −185331. + 213884.i −0.331242 + 0.382274i
\(749\) −15902.1 + 4669.29i −0.0283460 + 0.00832314i
\(750\) 290099. 132484.i 0.515731 0.235526i
\(751\) 169199. + 263279.i 0.299998 + 0.466806i 0.958226 0.286013i \(-0.0923300\pi\)
−0.658228 + 0.752819i \(0.728694\pi\)
\(752\) 29223.0 + 8580.66i 0.0516761 + 0.0151735i
\(753\) −829924. + 119325.i −1.46369 + 0.210447i
\(754\) −66861.2 + 146406.i −0.117607 + 0.257522i
\(755\) 29615.6 + 4258.08i 0.0519549 + 0.00746998i
\(756\) 37321.9 58074.0i 0.0653011 0.101610i
\(757\) −141538. + 122643.i −0.246991 + 0.214019i −0.769554 0.638582i \(-0.779521\pi\)
0.522563 + 0.852601i \(0.324976\pi\)
\(758\) 142661.i 0.248294i
\(759\) 1.24812e6 869379.i 2.16658 1.50913i
\(760\) −259357. −0.449025
\(761\) 475001. + 548180.i 0.820210 + 0.946573i 0.999306 0.0372589i \(-0.0118626\pi\)
−0.179096 + 0.983832i \(0.557317\pi\)
\(762\) 666348. + 428236.i 1.14760 + 0.737519i
\(763\) 10422.7 72491.7i 0.0179033 0.124520i
\(764\) 486167. + 222025.i 0.832911 + 0.380378i
\(765\) −26933.0 187323.i −0.0460216 0.320087i
\(766\) −79863.6 + 271991.i −0.136110 + 0.463550i
\(767\) 385967. 248046.i 0.656084 0.421640i
\(768\) 244943. + 536350.i 0.415281 + 0.909339i
\(769\) 224445. + 764388.i 0.379539 + 1.29259i 0.898944 + 0.438063i \(0.144335\pi\)
−0.519405 + 0.854528i \(0.673846\pi\)
\(770\) −10112.5 8762.50i −0.0170559 0.0147791i
\(771\) −623159. + 719164.i −1.04831 + 1.20982i
\(772\) 413510. 121417.i 0.693827 0.203726i
\(773\) 199664. 91183.3i 0.334149 0.152601i −0.241273 0.970457i \(-0.577565\pi\)
0.575422 + 0.817857i \(0.304838\pi\)
\(774\) 245514. + 382027.i 0.409821 + 0.637693i
\(775\) 417725. + 122655.i 0.695484 + 0.204213i
\(776\) 416120. 59829.0i 0.691027 0.0993547i
\(777\) 55752.6 122081.i 0.0923471 0.202212i
\(778\) 32822.6 + 4719.17i 0.0542267 + 0.00779662i
\(779\) −844003. + 1.31329e6i −1.39081 + 2.16415i
\(780\) 227555. 197178.i 0.374022 0.324092i
\(781\) 38192.9i 0.0626154i
\(782\) 47905.9 116150.i 0.0783386 0.189936i
\(783\) 664389. 1.08367
\(784\) −148857. 171791.i −0.242180 0.279491i
\(785\) −66486.3 42728.2i −0.107893 0.0693386i
\(786\) 8473.91 58937.4i 0.0137164 0.0953994i
\(787\) −209858. 95838.8i −0.338825 0.154736i 0.238734 0.971085i \(-0.423267\pi\)
−0.577559 + 0.816349i \(0.695995\pi\)
\(788\) −68038.9 473221.i −0.109573 0.762099i
\(789\) −547473. + 1.86452e6i −0.879446 + 2.99512i
\(790\) 18848.2 12113.0i 0.0302005 0.0194087i
\(791\) 16180.9 + 35431.2i 0.0258613 + 0.0566283i
\(792\) −461256. 1.57089e6i −0.735345 2.50436i
\(793\) −107609. 93243.7i −0.171120 0.148277i
\(794\) 203718. 235103.i 0.323139 0.372922i
\(795\) −182611. + 53619.4i −0.288930 + 0.0848375i
\(796\) 794983. 363056.i 1.25468 0.572991i
\(797\) 308046. + 479329.i 0.484952 + 0.754600i 0.994375 0.105916i \(-0.0337775\pi\)
−0.509423 + 0.860516i \(0.670141\pi\)
\(798\) 63128.8 + 18536.3i 0.0991338 + 0.0291083i
\(799\) −39462.1 + 5673.79i −0.0618140 + 0.00888751i
\(800\) −235019. + 514619.i −0.367217 + 0.804093i
\(801\) 1.59810e6 + 229771.i 2.49079 + 0.358122i
\(802\) −15188.5 + 23633.8i −0.0236139 + 0.0367439i
\(803\) −96932.6 + 83992.6i −0.150328 + 0.130260i
\(804\) 1.26284e6i 1.95361i
\(805\) −18785.4 7748.02i −0.0289888 0.0119564i
\(806\) −258920. −0.398562
\(807\) −797530. 920399.i −1.22462 1.41328i
\(808\) −75430.7 48476.4i −0.115538 0.0742519i
\(809\) −129991. + 904104.i −0.198616 + 1.38141i 0.609688 + 0.792642i \(0.291295\pi\)
−0.808304 + 0.588765i \(0.799614\pi\)
\(810\) 118023. + 53899.3i 0.179886 + 0.0821511i
\(811\) 30383.5 + 211322.i 0.0461951 + 0.321294i 0.999796 + 0.0202190i \(0.00643634\pi\)
−0.953600 + 0.301075i \(0.902655\pi\)
\(812\) −7319.52 + 24928.0i −0.0111012 + 0.0378073i
\(813\) −543840. + 349504.i −0.822791 + 0.528776i
\(814\) −294692. 645285.i −0.444753 0.973873i
\(815\) 39187.5 + 133460.i 0.0589973 + 0.200926i
\(816\) 141311. + 122446.i 0.212224 + 0.183893i
\(817\) 495335. 571647.i 0.742087 0.856415i
\(818\) −401730. + 117959.i −0.600382 + 0.176288i
\(819\) −106958. + 48846.2i −0.159458 + 0.0728221i
\(820\) −182263. 283607.i −0.271064 0.421783i
\(821\) −393065. 115414.i −0.583148 0.171228i −0.0231646 0.999732i \(-0.507374\pi\)
−0.559983 + 0.828504i \(0.689192\pi\)
\(822\) −441124. + 63424.1i −0.652856 + 0.0938665i
\(823\) 294050. 643879.i 0.434132 0.950615i −0.558507 0.829500i \(-0.688626\pi\)
0.992638 0.121116i \(-0.0386472\pi\)
\(824\) 609000. + 87561.0i 0.896939 + 0.128960i
\(825\) 841336. 1.30914e6i 1.23612 1.92344i
\(826\) −16361.9 + 14177.6i −0.0239813 + 0.0207799i
\(827\) 959377.i 1.40274i −0.712796 0.701372i \(-0.752571\pi\)
0.712796 0.701372i \(-0.247429\pi\)
\(828\) −619934. 890007.i −0.904242 1.29817i
\(829\) −612065. −0.890612 −0.445306 0.895379i \(-0.646905\pi\)
−0.445306 + 0.895379i \(0.646905\pi\)
\(830\) 55792.2 + 64387.7i 0.0809874 + 0.0934645i
\(831\) −1.88480e6 1.21129e6i −2.72938 1.75407i
\(832\) 11141.0 77487.3i 0.0160945 0.111940i
\(833\) 270662. + 123607.i 0.390065 + 0.178137i
\(834\) 22279.8 + 154959.i 0.0320316 + 0.222785i
\(835\) −14888.5 + 50705.6i −0.0213539 + 0.0727248i
\(836\) −1.00078e6 + 643160.i −1.43194 + 0.920251i
\(837\) 443995. + 972214.i 0.633764 + 1.38775i
\(838\) 108881. + 370814.i 0.155047 + 0.528041i
\(839\) 918131. + 795565.i 1.30431 + 1.13019i 0.983078 + 0.183190i \(0.0586422\pi\)
0.321232 + 0.947001i \(0.395903\pi\)
\(840\) −21328.8 + 24614.8i −0.0302280 + 0.0348849i
\(841\) 438718. 128819.i 0.620288 0.182133i
\(842\) 211207. 96455.0i 0.297909 0.136051i
\(843\) −346266. 538801.i −0.487253 0.758181i
\(844\) −50799.5 14916.1i −0.0713140 0.0209397i
\(845\) −580.914 + 83.5228i −0.000813577 + 0.000116975i
\(846\) 41795.8 91520.1i 0.0583972 0.127872i
\(847\) −78443.4 11278.5i −0.109343 0.0157211i
\(848\) 68270.1 106230.i 0.0949377 0.147726i
\(849\) 506680. 439041.i 0.702941 0.609102i
\(850\) 128543.i 0.177914i
\(851\) −735288. 787371.i −1.01531 1.08723i
\(852\) 40555.0 0.0558683
\(853\) 483667. + 558182.i 0.664735 + 0.767145i 0.983543 0.180674i \(-0.0578280\pi\)
−0.318808 + 0.947819i \(0.603283\pi\)
\(854\) 5652.35 + 3632.55i 0.00775021 + 0.00498076i
\(855\) 113213. 787411.i 0.154868 1.07713i
\(856\) 193964. + 88580.4i 0.264712 + 0.120890i
\(857\) −44524.0 309671.i −0.0606223 0.421637i −0.997421 0.0717691i \(-0.977136\pi\)
0.936799 0.349868i \(-0.113774\pi\)
\(858\) −260744. + 888012.i −0.354193 + 1.20627i
\(859\) 439534. 282472.i 0.595671 0.382814i −0.207789 0.978174i \(-0.566627\pi\)
0.803460 + 0.595359i \(0.202990\pi\)
\(860\) 67855.8 + 148584.i 0.0917467 + 0.200897i
\(861\) 55232.3 + 188104.i 0.0745052 + 0.253741i
\(862\) 425387. + 368600.i 0.572493 + 0.496068i
\(863\) 181094. 208993.i 0.243154 0.280615i −0.621034 0.783784i \(-0.713287\pi\)
0.864188 + 0.503169i \(0.167833\pi\)
\(864\) −1.33263e6 + 391295.i −1.78518 + 0.524176i
\(865\) −68134.2 + 31115.8i −0.0910611 + 0.0415862i
\(866\) −180264. 280496.i −0.240366 0.374017i
\(867\) 1.02362e6 + 300562.i 1.36176 + 0.399849i
\(868\) −41369.1 + 5947.98i −0.0549081 + 0.00789459i
\(869\) 97862.0 214288.i 0.129591 0.283764i
\(870\) −135352. 19460.7i −0.178824 0.0257111i
\(871\) 594132. 924488.i 0.783153 1.21861i
\(872\) −712116. + 617052.i −0.936522 + 0.811501i
\(873\) 1.28946e6i 1.69192i
\(874\) 330767. 411726.i 0.433012 0.538996i
\(875\) −44797.9 −0.0585116
\(876\) 89187.2 + 102927.i 0.116224 + 0.134129i
\(877\) 326501. + 209829.i 0.424507 + 0.272814i 0.735403 0.677630i \(-0.236993\pi\)
−0.310896 + 0.950444i \(0.600629\pi\)
\(878\) 45540.4 316740.i 0.0590755 0.410879i
\(879\) 91391.0 + 41736.9i 0.118284 + 0.0540184i
\(880\) −22748.4 158219.i −0.0293755 0.204311i
\(881\) 404874. 1.37888e6i 0.521637 1.77653i −0.101962 0.994788i \(-0.532512\pi\)
0.623599 0.781744i \(-0.285670\pi\)
\(882\) −631707. + 405973.i −0.812041 + 0.521867i
\(883\) −347115. 760075.i −0.445196 0.974844i −0.990615 0.136680i \(-0.956357\pi\)
0.545419 0.838164i \(-0.316371\pi\)
\(884\) −73675.4 250915.i −0.0942797 0.321087i
\(885\) 294590. + 255263.i 0.376124 + 0.325913i
\(886\) 81616.4 94190.3i 0.103970 0.119988i
\(887\) −1.19888e6 + 352024.i −1.52381 + 0.447430i −0.933148 0.359492i \(-0.882950\pi\)
−0.590658 + 0.806922i \(0.701132\pi\)
\(888\) −1.57069e6 + 717310.i −1.99189 + 0.909664i
\(889\) −60153.5 93600.7i −0.0761128 0.118434i
\(890\) −162894. 47829.9i −0.205648 0.0603836i
\(891\) 1.35035e6 194152.i 1.70095 0.244560i
\(892\) 166806. 365253.i 0.209643 0.459055i
\(893\) −165879. 23849.8i −0.208012 0.0299076i
\(894\) −333111. + 518331.i −0.416787 + 0.648533i
\(895\) 203581. 176404.i 0.254151 0.220223i
\(896\) 66494.3i 0.0828263i
\(897\) 52283.6 + 1.40453e6i 0.0649801 + 1.74561i
\(898\) 494288. 0.612953
\(899\) −263412. 303994.i −0.325924 0.376136i
\(900\) −933519. 599936.i −1.15249 0.740662i
\(901\) −23524.0 + 163613.i −0.0289776 + 0.201544i
\(902\) 942592. + 430467.i 1.15854 + 0.529087i
\(903\) −13518.3 94021.6i −0.0165785 0.115306i
\(904\) 141188. 480844.i 0.172768 0.588392i
\(905\) −395824. + 254381.i −0.483287 + 0.310590i
\(906\) 40567.2 + 88829.8i 0.0494218 + 0.108219i
\(907\) −316347. 1.07738e6i −0.384547 1.30965i −0.893581 0.448901i \(-0.851816\pi\)
0.509034 0.860746i \(-0.330003\pi\)
\(908\) 583013. + 505184.i 0.707142 + 0.612742i
\(909\) 180101. 207848.i 0.217966 0.251546i
\(910\) 11863.3 3483.39i 0.0143260 0.00420648i
\(911\) −476952. + 217817.i −0.574696 + 0.262455i −0.681491 0.731826i \(-0.738668\pi\)
0.106795 + 0.994281i \(0.465941\pi\)
\(912\) 424929. + 661202.i 0.510889 + 0.794959i
\(913\) 859521. + 252378.i 1.03113 + 0.302768i
\(914\) 158565. 22798.2i 0.189808 0.0272903i
\(915\) 50253.8 110040.i 0.0600242 0.131435i
\(916\) −341975. 49168.6i −0.407571 0.0585998i
\(917\) −4521.90 + 7036.21i −0.00537752 + 0.00836758i
\(918\) 238491. 206654.i 0.283000 0.245221i
\(919\) 876506.i 1.03782i 0.854828 + 0.518912i \(0.173663\pi\)
−0.854828 + 0.518912i \(0.826337\pi\)
\(920\) 117379. + 233612.i 0.138680 + 0.276007i
\(921\) 1.44145e6 1.69934
\(922\) −332900. 384187.i −0.391608 0.451940i
\(923\) −29689.0 19080.0i −0.0348492 0.0223962i
\(924\) −21260.9 + 147872.i −0.0249021 + 0.173198i
\(925\) −1.00258e6 457865.i −1.17176 0.535123i
\(926\) −618.543 4302.06i −0.000721353 0.00501712i
\(927\) −531672. + 1.81071e6i −0.618706 + 2.10712i
\(928\) 439729. 282597.i 0.510610 0.328149i
\(929\) 28566.0 + 62550.8i 0.0330993 + 0.0724773i 0.925459 0.378847i \(-0.123679\pi\)
−0.892360 + 0.451324i \(0.850952\pi\)
\(930\) −61975.3 211069.i −0.0716561 0.244038i
\(931\) 945256. + 819069.i 1.09056 + 0.944977i
\(932\) 367954. 424642.i 0.423606 0.488867i
\(933\) −442011. + 129786.i −0.507773 + 0.149096i
\(934\) −247162. + 112875.i −0.283328 + 0.129391i
\(935\) 113123. + 176022.i 0.129398 + 0.201346i
\(936\) 1.45155e6 + 426214.i 1.65684 + 0.486492i
\(937\) −1.26116e6 + 181327.i −1.43645 + 0.206530i −0.816151 0.577838i \(-0.803896\pi\)
−0.620295 + 0.784368i \(0.712987\pi\)
\(938\) −21542.1 + 47170.6i −0.0244840 + 0.0536125i
\(939\) 676920. + 97326.4i 0.767726 + 0.110382i
\(940\) 19565.8 30445.0i 0.0221433 0.0344556i
\(941\) −1.08249e6 + 937979.i −1.22248 + 1.05929i −0.226118 + 0.974100i \(0.572603\pi\)
−0.996365 + 0.0851874i \(0.972851\pi\)
\(942\) 257950.i 0.290692i
\(943\) 1.56491e6 + 165859.i 1.75981 + 0.186515i
\(944\) −258629. −0.290223
\(945\) −33422.9 38572.1i −0.0374267 0.0431927i
\(946\) −422377. 271445.i −0.471973 0.303319i
\(947\) −203617. + 1.41618e6i −0.227046 + 1.57914i 0.483409 + 0.875394i \(0.339398\pi\)
−0.710455 + 0.703743i \(0.751511\pi\)
\(948\) −227541. 103914.i −0.253187 0.115627i
\(949\) −16866.6 117310.i −0.0187282 0.130257i
\(950\) 152228. 518441.i 0.168674 0.574450i
\(951\) 588332. 378098.i 0.650522 0.418065i
\(952\) 11751.1 + 25731.2i 0.0129659 + 0.0283914i
\(953\) −462098. 1.57376e6i −0.508802 1.73282i −0.666663 0.745359i \(-0.732278\pi\)
0.157862 0.987461i \(-0.449540\pi\)
\(954\) −315258. 273173.i −0.346394 0.300152i
\(955\) 258767. 298633.i 0.283728 0.327440i
\(956\) 999343. 293434.i 1.09345 0.321066i
\(957\) −1.30787e6 + 597283.i −1.42804 + 0.652163i
\(958\) −65073.8 101257.i −0.0709047 0.110330i
\(959\) 60065.3 + 17636.8i 0.0653110 + 0.0191770i
\(960\) 65833.4 9465.42i 0.0714339 0.0102706i
\(961\) −114836. + 251457.i −0.124346 + 0.272280i
\(962\) 648826. + 93287.1i 0.701097 + 0.100803i
\(963\) −353599. + 550211.i −0.381293 + 0.593303i
\(964\) −643029. + 557188.i −0.691953 + 0.599581i
\(965\) 318629.i 0.342161i
\(966\) −11874.3 65251.5i −0.0127249 0.0699256i
\(967\) 143760. 0.153739 0.0768695 0.997041i \(-0.475508\pi\)
0.0768695 + 0.997041i \(0.475508\pi\)
\(968\) 667713. + 770582.i 0.712589 + 0.822372i
\(969\) −865514. 556232.i −0.921778 0.592391i
\(970\) 19296.3 134209.i 0.0205084 0.142639i
\(971\) −750352. 342674.i −0.795842 0.363449i −0.0243626 0.999703i \(-0.507756\pi\)
−0.771479 + 0.636254i \(0.780483\pi\)
\(972\) −16533.7 114994.i −0.0174999 0.121715i
\(973\) 6195.50 21099.9i 0.00654411 0.0222872i
\(974\) 430184. 276462.i 0.453457 0.291419i
\(975\) 597349. + 1.30801e6i 0.628375 + 1.37595i
\(976\) 22613.1 + 77013.2i 0.0237389 + 0.0808473i
\(977\) 108450. + 93972.1i 0.113616 + 0.0984487i 0.709816 0.704387i \(-0.248778\pi\)
−0.596200 + 0.802836i \(0.703324\pi\)
\(978\) −297296. + 343098.i −0.310821 + 0.358707i
\(979\) −1.71275e6 + 502908.i −1.78702 + 0.524715i
\(980\) −245693. + 112204.i −0.255823 + 0.116831i
\(981\) −1.56253e6 2.43134e6i −1.62364 2.52644i
\(982\) −387597. 113809.i −0.401936 0.118019i
\(983\) 1.50259e6 216039.i 1.55501 0.223576i 0.689431 0.724352i \(-0.257861\pi\)
0.865577 + 0.500775i \(0.166952\pi\)
\(984\) 1.04780e6 2.29437e6i 1.08215 2.36959i
\(985\) −349868. 50303.5i −0.360605 0.0518472i
\(986\) −64208.7 + 99910.6i −0.0660450 + 0.102768i
\(987\) −15904.9 + 13781.7i −0.0163267 + 0.0141471i
\(988\) 1.09925e6i 1.12611i
\(989\) −739080. 187452.i −0.755612 0.191645i
\(990\) −528041. −0.538762
\(991\) 856691. + 988674.i 0.872322 + 1.00671i 0.999889 + 0.0148833i \(0.00473767\pi\)
−0.127567 + 0.991830i \(0.540717\pi\)
\(992\) 707389. + 454612.i 0.718845 + 0.461974i
\(993\) 71179.3 495063.i 0.0721864 0.502067i
\(994\) 1514.84 + 691.803i 0.00153318 + 0.000700180i
\(995\) −91956.6 639572.i −0.0928831 0.646016i
\(996\) 267987. 912679.i 0.270143 0.920024i
\(997\) 18946.6 12176.3i 0.0190608 0.0122496i −0.531076 0.847324i \(-0.678212\pi\)
0.550137 + 0.835075i \(0.314576\pi\)
\(998\) −182550. 399728.i −0.183282 0.401332i
\(999\) −762323. 2.59623e6i −0.763850 2.60143i
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 23.5.d.a.10.5 yes 70
23.7 odd 22 inner 23.5.d.a.7.5 70
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.5.d.a.7.5 70 23.7 odd 22 inner
23.5.d.a.10.5 yes 70 1.1 even 1 trivial