Properties

Label 60.6.h.c.59.15
Level $60$
Weight $6$
Character 60.59
Analytic conductor $9.623$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,6,Mod(59,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.59");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 60.h (of order \(2\), degree \(1\), 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: \(9.62302918878\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 59.15
Character \(\chi\) \(=\) 60.59
Dual form 60.6.h.c.59.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.28930 + 4.60223i) q^{2} +(-3.33289 - 15.2280i) q^{3} +(-10.3610 - 30.2762i) q^{4} +(-17.3746 - 53.1331i) q^{5} +(81.0456 + 34.7508i) q^{6} -121.108 q^{7} +(173.418 + 51.9042i) q^{8} +(-220.784 + 101.506i) q^{9} +O(q^{10})\) \(q+(-3.28930 + 4.60223i) q^{2} +(-3.33289 - 15.2280i) q^{3} +(-10.3610 - 30.2762i) q^{4} +(-17.3746 - 53.1331i) q^{5} +(81.0456 + 34.7508i) q^{6} -121.108 q^{7} +(173.418 + 51.9042i) q^{8} +(-220.784 + 101.506i) q^{9} +(301.681 + 94.8087i) q^{10} +442.039 q^{11} +(-426.514 + 258.684i) q^{12} +1183.35i q^{13} +(398.360 - 557.365i) q^{14} +(-751.202 + 441.668i) q^{15} +(-809.301 + 627.382i) q^{16} -1031.92 q^{17} +(259.069 - 1349.98i) q^{18} -1292.69i q^{19} +(-1428.65 + 1076.55i) q^{20} +(403.639 + 1844.23i) q^{21} +(-1454.00 + 2034.36i) q^{22} -2193.11i q^{23} +(212.412 - 2813.81i) q^{24} +(-2521.24 + 1846.34i) q^{25} +(-5446.04 - 3892.39i) q^{26} +(2281.59 + 3023.78i) q^{27} +(1254.79 + 3666.69i) q^{28} +4786.72i q^{29} +(438.277 - 4909.98i) q^{30} +6536.74i q^{31} +(-225.320 - 5788.23i) q^{32} +(-1473.27 - 6731.36i) q^{33} +(3394.31 - 4749.14i) q^{34} +(2104.20 + 6434.83i) q^{35} +(5360.77 + 5632.79i) q^{36} -4285.04i q^{37} +(5949.26 + 4252.05i) q^{38} +(18020.0 - 3943.97i) q^{39} +(-255.255 - 10116.1i) q^{40} +7103.64i q^{41} +(-9815.25 - 4208.59i) q^{42} +194.861 q^{43} +(-4579.95 - 13383.3i) q^{44} +(9229.39 + 9967.27i) q^{45} +(10093.2 + 7213.82i) q^{46} -5085.39i q^{47} +(12251.1 + 10233.0i) q^{48} -2139.91 q^{49} +(-204.121 - 17676.5i) q^{50} +(3439.28 + 15714.1i) q^{51} +(35827.3 - 12260.6i) q^{52} -15284.7 q^{53} +(-21421.0 + 554.244i) q^{54} +(-7680.27 - 23486.9i) q^{55} +(-21002.3 - 6286.00i) q^{56} +(-19685.1 + 4308.40i) q^{57} +(-22029.6 - 15745.0i) q^{58} -33964.5 q^{59} +(21155.2 + 18167.5i) q^{60} +2293.47 q^{61} +(-30083.6 - 21501.3i) q^{62} +(26738.6 - 12293.2i) q^{63} +(27379.9 + 18002.3i) q^{64} +(62874.9 - 20560.3i) q^{65} +(35825.3 + 15361.2i) q^{66} -43903.6 q^{67} +(10691.7 + 31242.7i) q^{68} +(-33396.7 + 7309.41i) q^{69} +(-36535.9 - 11482.1i) q^{70} -9415.84 q^{71} +(-43556.6 + 6143.50i) q^{72} +12782.0i q^{73} +(19720.7 + 14094.8i) q^{74} +(36519.0 + 32239.8i) q^{75} +(-39137.8 + 13393.5i) q^{76} -53534.3 q^{77} +(-41122.3 + 95905.2i) q^{78} +63342.1i q^{79} +(47396.0 + 32100.1i) q^{80} +(38441.9 - 44821.9i) q^{81} +(-32692.6 - 23366.0i) q^{82} -37815.3i q^{83} +(51654.2 - 31328.7i) q^{84} +(17929.3 + 54829.2i) q^{85} +(-640.958 + 896.795i) q^{86} +(72892.2 - 15953.6i) q^{87} +(76657.7 + 22943.7i) q^{88} -110770. i q^{89} +(-76229.9 + 9690.34i) q^{90} -143313. i q^{91} +(-66399.2 + 22722.8i) q^{92} +(99541.5 - 21786.2i) q^{93} +(23404.1 + 16727.4i) q^{94} +(-68684.6 + 22460.0i) q^{95} +(-87392.2 + 22722.7i) q^{96} +57206.3i q^{97} +(7038.80 - 9848.33i) q^{98} +(-97595.0 + 44869.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 8 q^{4} + 420 q^{6} + 1440 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 8 q^{4} + 420 q^{6} + 1440 q^{9} - 1600 q^{10} - 10608 q^{16} - 1296 q^{21} - 8568 q^{24} + 1360 q^{25} + 13260 q^{30} + 23744 q^{34} + 15312 q^{36} - 35840 q^{40} + 71760 q^{45} - 126152 q^{46} + 191888 q^{49} - 19908 q^{54} + 64800 q^{60} + 12224 q^{61} + 69856 q^{64} + 21696 q^{66} - 640176 q^{69} - 81560 q^{70} + 56640 q^{76} - 123120 q^{81} - 312 q^{84} + 117440 q^{85} + 401280 q^{90} + 558088 q^{94} + 646128 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.28930 + 4.60223i −0.581472 + 0.813566i
\(3\) −3.33289 15.2280i −0.213805 0.976876i
\(4\) −10.3610 30.2762i −0.323780 0.946132i
\(5\) −17.3746 53.1331i −0.310807 0.950473i
\(6\) 81.0456 + 34.7508i 0.919075 + 0.394082i
\(7\) −121.108 −0.934172 −0.467086 0.884212i \(-0.654696\pi\)
−0.467086 + 0.884212i \(0.654696\pi\)
\(8\) 173.418 + 51.9042i 0.958011 + 0.286733i
\(9\) −220.784 + 101.506i −0.908575 + 0.417722i
\(10\) 301.681 + 94.8087i 0.953998 + 0.299811i
\(11\) 442.039 1.10149 0.550743 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(12\) −426.514 + 258.684i −0.855028 + 0.518581i
\(13\) 1183.35i 1.94202i 0.239032 + 0.971012i \(0.423170\pi\)
−0.239032 + 0.971012i \(0.576830\pi\)
\(14\) 398.360 557.365i 0.543195 0.760011i
\(15\) −751.202 + 441.668i −0.862043 + 0.506836i
\(16\) −809.301 + 627.382i −0.790333 + 0.612678i
\(17\) −1031.92 −0.866014 −0.433007 0.901391i \(-0.642547\pi\)
−0.433007 + 0.901391i \(0.642547\pi\)
\(18\) 259.069 1349.98i 0.188466 0.982080i
\(19\) 1292.69i 0.821506i −0.911747 0.410753i \(-0.865266\pi\)
0.911747 0.410753i \(-0.134734\pi\)
\(20\) −1428.65 + 1076.55i −0.798640 + 0.601809i
\(21\) 403.639 + 1844.23i 0.199731 + 0.912571i
\(22\) −1454.00 + 2034.36i −0.640483 + 0.896131i
\(23\) 2193.11i 0.864454i −0.901765 0.432227i \(-0.857728\pi\)
0.901765 0.432227i \(-0.142272\pi\)
\(24\) 212.412 2813.81i 0.0752751 0.997163i
\(25\) −2521.24 + 1846.34i −0.806798 + 0.590828i
\(26\) −5446.04 3892.39i −1.57996 1.12923i
\(27\) 2281.59 + 3023.78i 0.602321 + 0.798254i
\(28\) 1254.79 + 3666.69i 0.302467 + 0.883850i
\(29\) 4786.72i 1.05692i 0.848957 + 0.528462i \(0.177231\pi\)
−0.848957 + 0.528462i \(0.822769\pi\)
\(30\) 438.277 4909.98i 0.0889090 0.996040i
\(31\) 6536.74i 1.22168i 0.791754 + 0.610840i \(0.209168\pi\)
−0.791754 + 0.610840i \(0.790832\pi\)
\(32\) −225.320 5788.23i −0.0388977 0.999243i
\(33\) −1473.27 6731.36i −0.235503 1.07601i
\(34\) 3394.31 4749.14i 0.503563 0.704560i
\(35\) 2104.20 + 6434.83i 0.290347 + 0.887905i
\(36\) 5360.77 + 5632.79i 0.689399 + 0.724382i
\(37\) 4285.04i 0.514577i −0.966335 0.257289i \(-0.917171\pi\)
0.966335 0.257289i \(-0.0828291\pi\)
\(38\) 5949.26 + 4252.05i 0.668350 + 0.477683i
\(39\) 18020.0 3943.97i 1.89712 0.415214i
\(40\) −255.255 10116.1i −0.0252246 0.999682i
\(41\) 7103.64i 0.659966i 0.943987 + 0.329983i \(0.107043\pi\)
−0.943987 + 0.329983i \(0.892957\pi\)
\(42\) −9815.25 4208.59i −0.858575 0.368140i
\(43\) 194.861 0.0160714 0.00803571 0.999968i \(-0.497442\pi\)
0.00803571 + 0.999968i \(0.497442\pi\)
\(44\) −4579.95 13383.3i −0.356639 1.04215i
\(45\) 9229.39 + 9967.27i 0.679425 + 0.733745i
\(46\) 10093.2 + 7213.82i 0.703290 + 0.502656i
\(47\) 5085.39i 0.335799i −0.985804 0.167900i \(-0.946302\pi\)
0.985804 0.167900i \(-0.0536985\pi\)
\(48\) 12251.1 + 10233.0i 0.767488 + 0.641064i
\(49\) −2139.91 −0.127322
\(50\) −204.121 17676.5i −0.0115468 0.999933i
\(51\) 3439.28 + 15714.1i 0.185158 + 0.845988i
\(52\) 35827.3 12260.6i 1.83741 0.628789i
\(53\) −15284.7 −0.747426 −0.373713 0.927544i \(-0.621916\pi\)
−0.373713 + 0.927544i \(0.621916\pi\)
\(54\) −21421.0 + 554.244i −0.999665 + 0.0258652i
\(55\) −7680.27 23486.9i −0.342349 1.04693i
\(56\) −21002.3 6286.00i −0.894947 0.267858i
\(57\) −19685.1 + 4308.40i −0.802510 + 0.175642i
\(58\) −22029.6 15745.0i −0.859877 0.614571i
\(59\) −33964.5 −1.27027 −0.635133 0.772402i \(-0.719055\pi\)
−0.635133 + 0.772402i \(0.719055\pi\)
\(60\) 21155.2 + 18167.5i 0.758646 + 0.651503i
\(61\) 2293.47 0.0789165 0.0394583 0.999221i \(-0.487437\pi\)
0.0394583 + 0.999221i \(0.487437\pi\)
\(62\) −30083.6 21501.3i −0.993917 0.710372i
\(63\) 26738.6 12293.2i 0.848765 0.390224i
\(64\) 27379.9 + 18002.3i 0.835569 + 0.549386i
\(65\) 62874.9 20560.3i 1.84584 0.603595i
\(66\) 35825.3 + 15361.2i 1.01235 + 0.434075i
\(67\) −43903.6 −1.19485 −0.597425 0.801925i \(-0.703809\pi\)
−0.597425 + 0.801925i \(0.703809\pi\)
\(68\) 10691.7 + 31242.7i 0.280398 + 0.819364i
\(69\) −33396.7 + 7309.41i −0.844464 + 0.184825i
\(70\) −36535.9 11482.1i −0.891199 0.280075i
\(71\) −9415.84 −0.221673 −0.110837 0.993839i \(-0.535353\pi\)
−0.110837 + 0.993839i \(0.535353\pi\)
\(72\) −43556.6 + 6143.50i −0.990199 + 0.139664i
\(73\) 12782.0i 0.280731i 0.990100 + 0.140365i \(0.0448278\pi\)
−0.990100 + 0.140365i \(0.955172\pi\)
\(74\) 19720.7 + 14094.8i 0.418643 + 0.299212i
\(75\) 36519.0 + 32239.8i 0.749663 + 0.661820i
\(76\) −39137.8 + 13393.5i −0.777253 + 0.265987i
\(77\) −53534.3 −1.02898
\(78\) −41122.3 + 95905.2i −0.765316 + 1.78487i
\(79\) 63342.1i 1.14189i 0.820988 + 0.570946i \(0.193423\pi\)
−0.820988 + 0.570946i \(0.806577\pi\)
\(80\) 47396.0 + 32100.1i 0.827975 + 0.560765i
\(81\) 38441.9 44821.9i 0.651016 0.759064i
\(82\) −32692.6 23366.0i −0.536926 0.383752i
\(83\) 37815.3i 0.602521i −0.953542 0.301260i \(-0.902593\pi\)
0.953542 0.301260i \(-0.0974073\pi\)
\(84\) 51654.2 31328.7i 0.798744 0.484444i
\(85\) 17929.3 + 54829.2i 0.269163 + 0.823123i
\(86\) −640.958 + 896.795i −0.00934508 + 0.0130752i
\(87\) 72892.2 15953.6i 1.03248 0.225975i
\(88\) 76657.7 + 22943.7i 1.05523 + 0.315832i
\(89\) 110770.i 1.48234i −0.671316 0.741171i \(-0.734271\pi\)
0.671316 0.741171i \(-0.265729\pi\)
\(90\) −76229.9 + 9690.34i −0.992017 + 0.126105i
\(91\) 143313.i 1.81418i
\(92\) −66399.2 + 22722.8i −0.817887 + 0.279893i
\(93\) 99541.5 21786.2i 1.19343 0.261201i
\(94\) 23404.1 + 16727.4i 0.273195 + 0.195258i
\(95\) −68684.6 + 22460.0i −0.780819 + 0.255330i
\(96\) −87392.2 + 22722.7i −0.967821 + 0.251641i
\(97\) 57206.3i 0.617325i 0.951172 + 0.308663i \(0.0998814\pi\)
−0.951172 + 0.308663i \(0.900119\pi\)
\(98\) 7038.80 9848.33i 0.0740344 0.103585i
\(99\) −97595.0 + 44869.8i −1.00078 + 0.460115i
\(100\) 82022.6 + 57203.9i 0.820226 + 0.572039i
\(101\) 6462.78i 0.0630400i 0.999503 + 0.0315200i \(0.0100348\pi\)
−0.999503 + 0.0315200i \(0.989965\pi\)
\(102\) −83632.7 35860.1i −0.795932 0.341280i
\(103\) −89277.9 −0.829184 −0.414592 0.910007i \(-0.636076\pi\)
−0.414592 + 0.910007i \(0.636076\pi\)
\(104\) −61420.8 + 205215.i −0.556842 + 1.86048i
\(105\) 90976.4 53489.4i 0.805296 0.473472i
\(106\) 50276.1 70343.8i 0.434607 0.608081i
\(107\) 64391.3i 0.543710i −0.962338 0.271855i \(-0.912363\pi\)
0.962338 0.271855i \(-0.0876371\pi\)
\(108\) 67909.3 100407.i 0.560235 0.828334i
\(109\) −136392. −1.09957 −0.549785 0.835306i \(-0.685291\pi\)
−0.549785 + 0.835306i \(0.685291\pi\)
\(110\) 133355. + 41909.1i 1.05082 + 0.330238i
\(111\) −65252.6 + 14281.6i −0.502678 + 0.110019i
\(112\) 98012.6 75980.9i 0.738307 0.572347i
\(113\) 6299.61 0.0464106 0.0232053 0.999731i \(-0.492613\pi\)
0.0232053 + 0.999731i \(0.492613\pi\)
\(114\) 44922.0 104767.i 0.323741 0.755026i
\(115\) −116527. + 38104.6i −0.821640 + 0.268678i
\(116\) 144924. 49595.1i 0.999989 0.342211i
\(117\) −120118. 261264.i −0.811226 1.76447i
\(118\) 111719. 156312.i 0.738625 1.03345i
\(119\) 124974. 0.809006
\(120\) −153197. + 37602.8i −0.971172 + 0.238378i
\(121\) 34347.3 0.213270
\(122\) −7543.91 + 10555.1i −0.0458878 + 0.0642038i
\(123\) 108174. 23675.6i 0.644705 0.141104i
\(124\) 197908. 67727.0i 1.15587 0.395556i
\(125\) 141907. + 101882.i 0.812324 + 0.583206i
\(126\) −31375.2 + 163493.i −0.176060 + 0.917431i
\(127\) 37809.7 0.208015 0.104007 0.994577i \(-0.466833\pi\)
0.104007 + 0.994577i \(0.466833\pi\)
\(128\) −172911. + 66793.6i −0.932822 + 0.360338i
\(129\) −649.451 2967.35i −0.00343615 0.0156998i
\(130\) −112192. + 356994.i −0.582241 + 1.85269i
\(131\) 159728. 0.813209 0.406604 0.913604i \(-0.366713\pi\)
0.406604 + 0.913604i \(0.366713\pi\)
\(132\) −188536. + 114348.i −0.941801 + 0.571209i
\(133\) 156555.i 0.767428i
\(134\) 144412. 202054.i 0.694772 0.972089i
\(135\) 121021. 173765.i 0.571514 0.820593i
\(136\) −178954. 53561.1i −0.829650 0.248315i
\(137\) −147918. −0.673316 −0.336658 0.941627i \(-0.609297\pi\)
−0.336658 + 0.941627i \(0.609297\pi\)
\(138\) 76212.4 177742.i 0.340665 0.794498i
\(139\) 115859.i 0.508620i 0.967123 + 0.254310i \(0.0818484\pi\)
−0.967123 + 0.254310i \(0.918152\pi\)
\(140\) 173021. 130378.i 0.746067 0.562193i
\(141\) −77440.4 + 16949.1i −0.328035 + 0.0717956i
\(142\) 30971.6 43333.8i 0.128897 0.180346i
\(143\) 523086.i 2.13911i
\(144\) 114997. 220665.i 0.462147 0.886803i
\(145\) 254333. 83167.6i 1.00458 0.328499i
\(146\) −58825.5 42043.7i −0.228393 0.163237i
\(147\) 7132.07 + 32586.5i 0.0272222 + 0.124378i
\(148\) −129735. + 44397.2i −0.486858 + 0.166610i
\(149\) 288615.i 1.06501i 0.846427 + 0.532505i \(0.178749\pi\)
−0.846427 + 0.532505i \(0.821251\pi\)
\(150\) −268497. + 62022.2i −0.974342 + 0.225071i
\(151\) 191668.i 0.684082i −0.939685 0.342041i \(-0.888882\pi\)
0.939685 0.342041i \(-0.111118\pi\)
\(152\) 67096.1 224176.i 0.235553 0.787011i
\(153\) 227832. 104747.i 0.786838 0.361753i
\(154\) 176091. 246377.i 0.598321 0.837141i
\(155\) 347317. 113574.i 1.16117 0.379707i
\(156\) −306114. 504715.i −1.00710 1.66049i
\(157\) 137072.i 0.443812i 0.975068 + 0.221906i \(0.0712278\pi\)
−0.975068 + 0.221906i \(0.928772\pi\)
\(158\) −291515. 208351.i −0.929005 0.663978i
\(159\) 50942.3 + 232756.i 0.159803 + 0.730143i
\(160\) −303632. + 112540.i −0.937664 + 0.347543i
\(161\) 265603.i 0.807549i
\(162\) 79833.8 + 324351.i 0.239001 + 0.971019i
\(163\) −353583. −1.04237 −0.521185 0.853444i \(-0.674510\pi\)
−0.521185 + 0.853444i \(0.674510\pi\)
\(164\) 215071. 73600.6i 0.624415 0.213684i
\(165\) −332060. + 195234.i −0.949527 + 0.558272i
\(166\) 174034. + 124386.i 0.490190 + 0.350349i
\(167\) 195975.i 0.543762i −0.962331 0.271881i \(-0.912354\pi\)
0.962331 0.271881i \(-0.0876457\pi\)
\(168\) −25724.8 + 340774.i −0.0703199 + 0.931522i
\(169\) −1.02902e6 −2.77145
\(170\) −311311. 97835.2i −0.826176 0.259641i
\(171\) 131216. + 285405.i 0.343161 + 0.746400i
\(172\) −2018.95 5899.66i −0.00520361 0.0152057i
\(173\) −345862. −0.878593 −0.439296 0.898342i \(-0.644772\pi\)
−0.439296 + 0.898342i \(0.644772\pi\)
\(174\) −166342. + 387943.i −0.416514 + 0.971392i
\(175\) 305342. 223606.i 0.753688 0.551935i
\(176\) −357742. + 277327.i −0.870540 + 0.674856i
\(177\) 113200. + 517211.i 0.271589 + 1.24089i
\(178\) 509790. + 364357.i 1.20598 + 0.861941i
\(179\) −190425. −0.444213 −0.222106 0.975022i \(-0.571293\pi\)
−0.222106 + 0.975022i \(0.571293\pi\)
\(180\) 206146. 382702.i 0.474235 0.880398i
\(181\) 652504. 1.48043 0.740213 0.672372i \(-0.234725\pi\)
0.740213 + 0.672372i \(0.234725\pi\)
\(182\) 659558. + 471399.i 1.47596 + 1.05490i
\(183\) −7643.88 34924.9i −0.0168728 0.0770917i
\(184\) 113832. 380326.i 0.247867 0.828156i
\(185\) −227677. + 74451.0i −0.489092 + 0.159934i
\(186\) −227157. + 529774.i −0.481442 + 1.12282i
\(187\) −456150. −0.953901
\(188\) −153967. + 52689.6i −0.317711 + 0.108725i
\(189\) −276318. 366204.i −0.562671 0.745707i
\(190\) 122558. 389980.i 0.246297 0.783715i
\(191\) −64257.8 −0.127451 −0.0637254 0.997967i \(-0.520298\pi\)
−0.0637254 + 0.997967i \(0.520298\pi\)
\(192\) 182885. 476941.i 0.358034 0.933709i
\(193\) 31878.7i 0.0616038i −0.999526 0.0308019i \(-0.990194\pi\)
0.999526 0.0308019i \(-0.00980610\pi\)
\(194\) −263276. 188169.i −0.502235 0.358958i
\(195\) −522647. 888934.i −0.984287 1.67411i
\(196\) 22171.5 + 64788.3i 0.0412245 + 0.120464i
\(197\) 661276. 1.21400 0.606998 0.794703i \(-0.292374\pi\)
0.606998 + 0.794703i \(0.292374\pi\)
\(198\) 114518. 596744.i 0.207593 1.08175i
\(199\) 925806.i 1.65725i 0.559806 + 0.828624i \(0.310876\pi\)
−0.559806 + 0.828624i \(0.689124\pi\)
\(200\) −533063. + 189326.i −0.942331 + 0.334684i
\(201\) 146326. + 668564.i 0.255465 + 1.16722i
\(202\) −29743.2 21258.1i −0.0512872 0.0366560i
\(203\) 579710.i 0.987348i
\(204\) 440130. 266942.i 0.740466 0.449098i
\(205\) 377438. 123423.i 0.627279 0.205122i
\(206\) 293662. 410877.i 0.482147 0.674596i
\(207\) 222615. + 484204.i 0.361101 + 0.785421i
\(208\) −742412. 957685.i −1.18983 1.53484i
\(209\) 571420.i 0.904877i
\(210\) −53078.8 + 594637.i −0.0830563 + 0.930473i
\(211\) 557799.i 0.862525i −0.902226 0.431263i \(-0.858068\pi\)
0.902226 0.431263i \(-0.141932\pi\)
\(212\) 158365. + 462764.i 0.242002 + 0.707164i
\(213\) 31382.0 + 143384.i 0.0473948 + 0.216547i
\(214\) 296343. + 211802.i 0.442344 + 0.316152i
\(215\) −3385.64 10353.6i −0.00499511 0.0152754i
\(216\) 238722. + 642804.i 0.348144 + 0.937441i
\(217\) 791650.i 1.14126i
\(218\) 448635. 627708.i 0.639370 0.894574i
\(219\) 194644. 42600.9i 0.274239 0.0600217i
\(220\) −631519. + 475876.i −0.879690 + 0.662884i
\(221\) 1.22112e6i 1.68182i
\(222\) 148908. 347283.i 0.202786 0.472935i
\(223\) 1.31048e6 1.76469 0.882347 0.470599i \(-0.155962\pi\)
0.882347 + 0.470599i \(0.155962\pi\)
\(224\) 27288.0 + 701000.i 0.0363372 + 0.933465i
\(225\) 369234. 663563.i 0.486235 0.873828i
\(226\) −20721.3 + 28992.2i −0.0269865 + 0.0377581i
\(227\) 390870.i 0.503464i 0.967797 + 0.251732i \(0.0810001\pi\)
−0.967797 + 0.251732i \(0.919000\pi\)
\(228\) 334399. + 551351.i 0.426017 + 0.702411i
\(229\) −104093. −0.131170 −0.0655850 0.997847i \(-0.520891\pi\)
−0.0655850 + 0.997847i \(0.520891\pi\)
\(230\) 207926. 661621.i 0.259173 0.824687i
\(231\) 178424. + 815221.i 0.220000 + 1.00518i
\(232\) −248451. + 830106.i −0.303055 + 1.01254i
\(233\) −1108.46 −0.00133761 −0.000668804 1.00000i \(-0.500213\pi\)
−0.000668804 1.00000i \(0.500213\pi\)
\(234\) 1.59750e6 + 306569.i 1.90722 + 0.366006i
\(235\) −270203. + 88356.9i −0.319168 + 0.104369i
\(236\) 351905. + 1.02832e6i 0.411287 + 1.20184i
\(237\) 964574. 211112.i 1.11549 0.244142i
\(238\) −411077. + 575158.i −0.470414 + 0.658180i
\(239\) −1.10753e6 −1.25418 −0.627090 0.778947i \(-0.715754\pi\)
−0.627090 + 0.778947i \(0.715754\pi\)
\(240\) 330854. 828733.i 0.370773 0.928723i
\(241\) 413980. 0.459131 0.229565 0.973293i \(-0.426270\pi\)
0.229565 + 0.973293i \(0.426270\pi\)
\(242\) −112979. + 158074.i −0.124010 + 0.173509i
\(243\) −810671. 436006.i −0.880702 0.473671i
\(244\) −23762.6 69437.6i −0.0255516 0.0746655i
\(245\) 37180.1 + 113700.i 0.0395727 + 0.121016i
\(246\) −246857. + 575718.i −0.260080 + 0.606558i
\(247\) 1.52970e6 1.59538
\(248\) −339284. + 1.13359e6i −0.350296 + 1.17038i
\(249\) −575851. + 126034.i −0.588588 + 0.128822i
\(250\) −935659. + 317968.i −0.946821 + 0.321761i
\(251\) −1.55143e6 −1.55435 −0.777173 0.629287i \(-0.783347\pi\)
−0.777173 + 0.629287i \(0.783347\pi\)
\(252\) −649231. 682175.i −0.644017 0.676697i
\(253\) 969442.i 0.952183i
\(254\) −124367. + 174009.i −0.120955 + 0.169234i
\(255\) 775182. 455767.i 0.746541 0.438927i
\(256\) 261359. 1.01548e6i 0.249251 0.968439i
\(257\) 746836. 0.705331 0.352665 0.935750i \(-0.385275\pi\)
0.352665 + 0.935750i \(0.385275\pi\)
\(258\) 15792.6 + 6771.58i 0.0147708 + 0.00633345i
\(259\) 518952.i 0.480704i
\(260\) −1.27393e6 1.69059e6i −1.16873 1.55098i
\(261\) −485884. 1.05683e6i −0.441500 0.960294i
\(262\) −525393. + 735103.i −0.472858 + 0.661599i
\(263\) 728564.i 0.649499i −0.945800 0.324749i \(-0.894720\pi\)
0.945800 0.324749i \(-0.105280\pi\)
\(264\) 93894.4 1.24381e6i 0.0829144 1.09836i
\(265\) 265567. + 812125.i 0.232305 + 0.710408i
\(266\) −720501. 514957.i −0.624354 0.446238i
\(267\) −1.68681e6 + 369185.i −1.44807 + 0.316932i
\(268\) 454884. + 1.32924e6i 0.386869 + 1.13049i
\(269\) 593389.i 0.499987i −0.968247 0.249994i \(-0.919571\pi\)
0.968247 0.249994i \(-0.0804286\pi\)
\(270\) 401630. + 1.12853e6i 0.335287 + 0.942116i
\(271\) 1.37591e6i 1.13806i −0.822317 0.569030i \(-0.807319\pi\)
0.822317 0.569030i \(-0.192681\pi\)
\(272\) 835136. 647410.i 0.684439 0.530588i
\(273\) −2.18237e6 + 477646.i −1.77223 + 0.387882i
\(274\) 486546. 680751.i 0.391514 0.547787i
\(275\) −1.11449e6 + 816152.i −0.888676 + 0.650788i
\(276\) 567324. + 935395.i 0.448289 + 0.739132i
\(277\) 1.66045e6i 1.30025i 0.759826 + 0.650126i \(0.225284\pi\)
−0.759826 + 0.650126i \(0.774716\pi\)
\(278\) −533210. 381096.i −0.413796 0.295748i
\(279\) −663522. 1.44321e6i −0.510322 1.10999i
\(280\) 30913.4 + 1.22513e6i 0.0235642 + 0.933875i
\(281\) 1.23967e6i 0.936570i 0.883577 + 0.468285i \(0.155128\pi\)
−0.883577 + 0.468285i \(0.844872\pi\)
\(282\) 176721. 412149.i 0.132332 0.308625i
\(283\) −376888. −0.279735 −0.139867 0.990170i \(-0.544668\pi\)
−0.139867 + 0.990170i \(0.544668\pi\)
\(284\) 97557.2 + 285076.i 0.0717734 + 0.209732i
\(285\) 570940. + 971072.i 0.416369 + 0.708173i
\(286\) −2.40736e6 1.72059e6i −1.74031 1.24383i
\(287\) 860306.i 0.616521i
\(288\) 637290. + 1.25508e6i 0.452747 + 0.891639i
\(289\) −354993. −0.250020
\(290\) −453823. + 1.44406e6i −0.316878 + 1.00830i
\(291\) 871137. 190662.i 0.603051 0.131987i
\(292\) 386990. 132433.i 0.265609 0.0908952i
\(293\) 49206.4 0.0334852 0.0167426 0.999860i \(-0.494670\pi\)
0.0167426 + 0.999860i \(0.494670\pi\)
\(294\) −173430. 74363.4i −0.117019 0.0501754i
\(295\) 590121. + 1.80464e6i 0.394808 + 1.20735i
\(296\) 222412. 743105.i 0.147546 0.492970i
\(297\) 1.00855e6 + 1.33663e6i 0.663447 + 0.879265i
\(298\) −1.32827e6 949342.i −0.866456 0.619273i
\(299\) 2.59522e6 1.67879
\(300\) 597729. 1.43969e6i 0.383443 0.923564i
\(301\) −23599.2 −0.0150135
\(302\) 882102. + 630456.i 0.556546 + 0.397775i
\(303\) 98415.3 21539.8i 0.0615823 0.0134783i
\(304\) 811011. + 1.04618e6i 0.503319 + 0.649263i
\(305\) −39848.2 121859.i −0.0245278 0.0750081i
\(306\) −267339. + 1.39308e6i −0.163214 + 0.850494i
\(307\) −1.12986e6 −0.684191 −0.342095 0.939665i \(-0.611137\pi\)
−0.342095 + 0.939665i \(0.611137\pi\)
\(308\) 554668. + 1.62082e6i 0.333162 + 0.973548i
\(309\) 297553. + 1.35952e6i 0.177284 + 0.810010i
\(310\) −619740. + 1.97201e6i −0.366273 + 1.16548i
\(311\) 2.93775e6 1.72232 0.861159 0.508335i \(-0.169739\pi\)
0.861159 + 0.508335i \(0.169739\pi\)
\(312\) 3.32971e6 + 251358.i 1.93651 + 0.146186i
\(313\) 328381.i 0.189460i −0.995503 0.0947300i \(-0.969801\pi\)
0.995503 0.0947300i \(-0.0301988\pi\)
\(314\) −630836. 450871.i −0.361071 0.258064i
\(315\) −1.11775e6 1.20711e6i −0.634700 0.685444i
\(316\) 1.91776e6 656286.i 1.08038 0.369722i
\(317\) −2.94941e6 −1.64849 −0.824247 0.566231i \(-0.808401\pi\)
−0.824247 + 0.566231i \(0.808401\pi\)
\(318\) −1.23876e6 531157.i −0.686941 0.294547i
\(319\) 2.11592e6i 1.16419i
\(320\) 480800. 1.76756e6i 0.262476 0.964938i
\(321\) −980550. + 214609.i −0.531138 + 0.116248i
\(322\) −1.22237e6 873649.i −0.656994 0.469567i
\(323\) 1.33396e6i 0.711435i
\(324\) −1.75533e6 699476.i −0.928961 0.370178i
\(325\) −2.18486e6 2.98351e6i −1.14740 1.56682i
\(326\) 1.16304e6 1.62727e6i 0.606109 0.848037i
\(327\) 454580. + 2.07698e6i 0.235094 + 1.07414i
\(328\) −368709. + 1.23190e6i −0.189234 + 0.632254i
\(329\) 615881.i 0.313694i
\(330\) 193736. 2.17040e6i 0.0979320 1.09712i
\(331\) 2.29057e6i 1.14914i −0.818454 0.574572i \(-0.805169\pi\)
0.818454 0.574572i \(-0.194831\pi\)
\(332\) −1.14490e6 + 391803.i −0.570064 + 0.195084i
\(333\) 434959. + 946067.i 0.214950 + 0.467532i
\(334\) 901920. + 644620.i 0.442386 + 0.316182i
\(335\) 762809. + 2.33273e6i 0.371368 + 1.13567i
\(336\) −1.48370e6 1.23930e6i −0.716966 0.598864i
\(337\) 3.30109e6i 1.58337i −0.610928 0.791686i \(-0.709203\pi\)
0.610928 0.791686i \(-0.290797\pi\)
\(338\) 3.38476e6 4.73579e6i 1.61152 2.25476i
\(339\) −20995.9 95930.4i −0.00992282 0.0453374i
\(340\) 1.47426e6 1.11091e6i 0.691633 0.521175i
\(341\) 2.88949e6i 1.34566i
\(342\) −1.74511e6 334896.i −0.806784 0.154826i
\(343\) 2.29462e6 1.05311
\(344\) 33792.5 + 10114.1i 0.0153966 + 0.00460820i
\(345\) 968628. + 1.64747e6i 0.438136 + 0.745196i
\(346\) 1.13765e6 1.59174e6i 0.510877 0.714794i
\(347\) 2.61161e6i 1.16435i −0.813062 0.582177i \(-0.802201\pi\)
0.813062 0.582177i \(-0.197799\pi\)
\(348\) −1.23825e6 2.04161e6i −0.548100 0.903699i
\(349\) 3.00616e6 1.32114 0.660569 0.750765i \(-0.270315\pi\)
0.660569 + 0.750765i \(0.270315\pi\)
\(350\) 24720.7 + 2.14076e6i 0.0107867 + 0.934110i
\(351\) −3.57819e6 + 2.69991e6i −1.55023 + 1.16972i
\(352\) −99600.0 2.55862e6i −0.0428453 1.10065i
\(353\) 3.71861e6 1.58834 0.794170 0.607696i \(-0.207906\pi\)
0.794170 + 0.607696i \(0.207906\pi\)
\(354\) −2.75267e6 1.18029e6i −1.16747 0.500589i
\(355\) 163597. + 500292.i 0.0688976 + 0.210694i
\(356\) −3.35371e6 + 1.14769e6i −1.40249 + 0.479953i
\(357\) −416524. 1.90310e6i −0.172970 0.790299i
\(358\) 626365. 876378.i 0.258297 0.361397i
\(359\) −919094. −0.376378 −0.188189 0.982133i \(-0.560262\pi\)
−0.188189 + 0.982133i \(0.560262\pi\)
\(360\) 1.08320e6 + 2.20755e6i 0.440508 + 0.897749i
\(361\) 805049. 0.325128
\(362\) −2.14628e6 + 3.00297e6i −0.860827 + 1.20442i
\(363\) −114476. 523040.i −0.0455981 0.208338i
\(364\) −4.33897e6 + 1.48486e6i −1.71646 + 0.587397i
\(365\) 679145. 222082.i 0.266827 0.0872532i
\(366\) 185875. + 79699.8i 0.0725303 + 0.0310996i
\(367\) 1.96673e6 0.762217 0.381109 0.924530i \(-0.375542\pi\)
0.381109 + 0.924530i \(0.375542\pi\)
\(368\) 1.37592e6 + 1.77489e6i 0.529632 + 0.683206i
\(369\) −721065. 1.56837e6i −0.275682 0.599628i
\(370\) 406259. 1.29271e6i 0.154276 0.490906i
\(371\) 1.85110e6 0.698225
\(372\) −1.69095e6 2.78801e6i −0.633540 1.04457i
\(373\) 160117.i 0.0595889i 0.999556 + 0.0297944i \(0.00948527\pi\)
−0.999556 + 0.0297944i \(0.990515\pi\)
\(374\) 1.50041e6 2.09930e6i 0.554667 0.776062i
\(375\) 1.07850e6 2.50052e6i 0.396041 0.918233i
\(376\) 263953. 881901.i 0.0962847 0.321699i
\(377\) −5.66437e6 −2.05257
\(378\) 2.59425e6 67123.2i 0.933860 0.0241626i
\(379\) 2.75160e6i 0.983982i −0.870600 0.491991i \(-0.836269\pi\)
0.870600 0.491991i \(-0.163731\pi\)
\(380\) 1.39164e6 + 1.84680e6i 0.494390 + 0.656087i
\(381\) −126016. 575766.i −0.0444745 0.203204i
\(382\) 211363. 295729.i 0.0741090 0.103690i
\(383\) 2.27962e6i 0.794084i 0.917800 + 0.397042i \(0.129963\pi\)
−0.917800 + 0.397042i \(0.870037\pi\)
\(384\) 1.59343e6 + 2.41048e6i 0.551447 + 0.834210i
\(385\) 930140. + 2.84444e6i 0.319813 + 0.978015i
\(386\) 146713. + 104859.i 0.0501188 + 0.0358209i
\(387\) −43022.2 + 19779.7i −0.0146021 + 0.00671339i
\(388\) 1.73199e6 592712.i 0.584072 0.199878i
\(389\) 4.66990e6i 1.56471i 0.622834 + 0.782354i \(0.285981\pi\)
−0.622834 + 0.782354i \(0.714019\pi\)
\(390\) 5.81022e6 + 518635.i 1.93433 + 0.172663i
\(391\) 2.26312e6i 0.748629i
\(392\) −371099. 111070.i −0.121976 0.0365075i
\(393\) −532355. 2.43233e6i −0.173868 0.794405i
\(394\) −2.17514e6 + 3.04334e6i −0.705905 + 0.987666i
\(395\) 3.36556e6 1.10055e6i 1.08534 0.354908i
\(396\) 2.36967e6 + 2.48991e6i 0.759363 + 0.797896i
\(397\) 2.29103e6i 0.729550i 0.931096 + 0.364775i \(0.118854\pi\)
−0.931096 + 0.364775i \(0.881146\pi\)
\(398\) −4.26077e6 3.04526e6i −1.34828 0.963643i
\(399\) 2.38402e6 521780.i 0.749682 0.164080i
\(400\) 882086. 3.07602e6i 0.275652 0.961258i
\(401\) 5.11533e6i 1.58859i −0.607530 0.794297i \(-0.707839\pi\)
0.607530 0.794297i \(-0.292161\pi\)
\(402\) −3.55819e6 1.52568e6i −1.09816 0.470868i
\(403\) −7.73525e6 −2.37253
\(404\) 195669. 66960.7i 0.0596442 0.0204111i
\(405\) −3.04944e6 1.26377e6i −0.923810 0.382851i
\(406\) 2.66795e6 + 1.90684e6i 0.803273 + 0.574116i
\(407\) 1.89415e6i 0.566799i
\(408\) −219193. + 2.90363e6i −0.0651893 + 0.863557i
\(409\) −399605. −0.118120 −0.0590599 0.998254i \(-0.518810\pi\)
−0.0590599 + 0.998254i \(0.518810\pi\)
\(410\) −673487. + 2.14303e6i −0.197865 + 0.629606i
\(411\) 492994. + 2.25249e6i 0.143958 + 0.657746i
\(412\) 925006. + 2.70300e6i 0.268473 + 0.784518i
\(413\) 4.11336e6 1.18665
\(414\) −2.96066e6 568167.i −0.848962 0.162920i
\(415\) −2.00924e6 + 657027.i −0.572680 + 0.187268i
\(416\) 6.84950e6 266632.i 1.94055 0.0755403i
\(417\) 1.76430e6 386146.i 0.496859 0.108746i
\(418\) 2.62980e6 + 1.87957e6i 0.736177 + 0.526161i
\(419\) −3.34608e6 −0.931110 −0.465555 0.885019i \(-0.654145\pi\)
−0.465555 + 0.885019i \(0.654145\pi\)
\(420\) −2.56206e6 2.20022e6i −0.708706 0.608616i
\(421\) −4.59285e6 −1.26292 −0.631461 0.775407i \(-0.717545\pi\)
−0.631461 + 0.775407i \(0.717545\pi\)
\(422\) 2.56712e6 + 1.83477e6i 0.701722 + 0.501535i
\(423\) 516200. + 1.12277e6i 0.140271 + 0.305099i
\(424\) −2.65066e6 793342.i −0.716042 0.214312i
\(425\) 2.60173e6 1.90528e6i 0.698698 0.511665i
\(426\) −763112. 327208.i −0.203734 0.0873574i
\(427\) −277757. −0.0737216
\(428\) −1.94952e6 + 667156.i −0.514422 + 0.176043i
\(429\) 7.96555e6 1.74339e6i 2.08965 0.457352i
\(430\) 58785.9 + 18474.5i 0.0153321 + 0.00481839i
\(431\) −4.21176e6 −1.09212 −0.546060 0.837746i \(-0.683873\pi\)
−0.546060 + 0.837746i \(0.683873\pi\)
\(432\) −3.74356e6 1.01572e6i −0.965106 0.261858i
\(433\) 7.22457e6i 1.85179i 0.377777 + 0.925896i \(0.376688\pi\)
−0.377777 + 0.925896i \(0.623312\pi\)
\(434\) 3.64335e6 + 2.60398e6i 0.928490 + 0.663610i
\(435\) −2.11414e6 3.59580e6i −0.535687 0.911113i
\(436\) 1.41316e6 + 4.12944e6i 0.356019 + 1.04034i
\(437\) −2.83502e6 −0.710154
\(438\) −444183. + 1.03592e6i −0.110631 + 0.258013i
\(439\) 7.00983e6i 1.73599i −0.496577 0.867993i \(-0.665410\pi\)
0.496577 0.867993i \(-0.334590\pi\)
\(440\) −112833. 4.47169e6i −0.0277846 1.10113i
\(441\) 472456. 217214.i 0.115682 0.0531853i
\(442\) 5.61989e6 + 4.01665e6i 1.36827 + 0.977931i
\(443\) 2.85015e6i 0.690015i 0.938600 + 0.345007i \(0.112124\pi\)
−0.938600 + 0.345007i \(0.887876\pi\)
\(444\) 1.10847e6 + 1.82763e6i 0.266850 + 0.439978i
\(445\) −5.88557e6 + 1.92460e6i −1.40893 + 0.460722i
\(446\) −4.31058e6 + 6.03114e6i −1.02612 + 1.43570i
\(447\) 4.39503e6 961922.i 1.04038 0.227704i
\(448\) −3.31592e6 2.18022e6i −0.780565 0.513221i
\(449\) 7.50057e6i 1.75581i −0.478831 0.877907i \(-0.658939\pi\)
0.478831 0.877907i \(-0.341061\pi\)
\(450\) 1.83934e6 + 3.88196e6i 0.428185 + 0.903691i
\(451\) 3.14008e6i 0.726942i
\(452\) −65270.0 190728.i −0.0150268 0.0439106i
\(453\) −2.91873e6 + 638810.i −0.668264 + 0.146260i
\(454\) −1.79887e6 1.28569e6i −0.409601 0.292750i
\(455\) −7.61465e6 + 2.49001e6i −1.72433 + 0.563861i
\(456\) −3.63738e6 274583.i −0.819175 0.0618389i
\(457\) 964023.i 0.215922i 0.994155 + 0.107961i \(0.0344321\pi\)
−0.994155 + 0.107961i \(0.965568\pi\)
\(458\) 342395. 479061.i 0.0762717 0.106716i
\(459\) −2.35442e6 3.12031e6i −0.521618 0.691299i
\(460\) 2.36099e6 + 3.13319e6i 0.520236 + 0.690387i
\(461\) 825020.i 0.180806i 0.995905 + 0.0904028i \(0.0288154\pi\)
−0.995905 + 0.0904028i \(0.971185\pi\)
\(462\) −4.33872e6 1.86036e6i −0.945707 0.405501i
\(463\) 4.08513e6 0.885632 0.442816 0.896613i \(-0.353980\pi\)
0.442816 + 0.896613i \(0.353980\pi\)
\(464\) −3.00311e6 3.87390e6i −0.647554 0.835321i
\(465\) −2.88707e6 4.91042e6i −0.619191 1.05314i
\(466\) 3646.05 5101.37i 0.000777782 0.00108823i
\(467\) 6.08462e6i 1.29105i −0.763741 0.645523i \(-0.776640\pi\)
0.763741 0.645523i \(-0.223360\pi\)
\(468\) −6.66556e6 + 6.34366e6i −1.40677 + 1.33883i
\(469\) 5.31707e6 1.11619
\(470\) 482140. 1.53417e6i 0.100676 0.320352i
\(471\) 2.08733e6 456845.i 0.433550 0.0948893i
\(472\) −5.89007e6 1.76290e6i −1.21693 0.364227i
\(473\) 86136.2 0.0177024
\(474\) −2.20119e6 + 5.13360e6i −0.449999 + 1.04948i
\(475\) 2.38674e6 + 3.25919e6i 0.485368 + 0.662789i
\(476\) −1.29485e6 3.78374e6i −0.261940 0.765427i
\(477\) 3.37462e6 1.55150e6i 0.679093 0.312216i
\(478\) 3.64299e6 5.09709e6i 0.729271 1.02036i
\(479\) 6.70686e6 1.33561 0.667807 0.744335i \(-0.267233\pi\)
0.667807 + 0.744335i \(0.267233\pi\)
\(480\) 2.72574e6 + 4.24862e6i 0.539984 + 0.841675i
\(481\) 5.07070e6 0.999321
\(482\) −1.36170e6 + 1.90523e6i −0.266972 + 0.373533i
\(483\) 4.04460e6 885226.i 0.788875 0.172658i
\(484\) −355871. 1.03991e6i −0.0690525 0.201781i
\(485\) 3.03954e6 993938.i 0.586751 0.191869i
\(486\) 4.67314e6 2.29673e6i 0.897466 0.441083i
\(487\) −9.58647e6 −1.83162 −0.915812 0.401606i \(-0.868452\pi\)
−0.915812 + 0.401606i \(0.868452\pi\)
\(488\) 397730. + 119041.i 0.0756029 + 0.0226280i
\(489\) 1.17845e6 + 5.38435e6i 0.222864 + 1.01827i
\(490\) −645569. 202882.i −0.121465 0.0381727i
\(491\) −7.35723e6 −1.37724 −0.688622 0.725121i \(-0.741784\pi\)
−0.688622 + 0.725121i \(0.741784\pi\)
\(492\) −1.83760e6 3.02980e6i −0.342246 0.564289i
\(493\) 4.93953e6i 0.915310i
\(494\) −5.03166e6 + 7.04005e6i −0.927671 + 1.29795i
\(495\) 4.07975e6 + 4.40592e6i 0.748377 + 0.808209i
\(496\) −4.10104e6 5.29019e6i −0.748496 0.965533i
\(497\) 1.14033e6 0.207081
\(498\) 1.31411e6 3.06476e6i 0.237442 0.553762i
\(499\) 4.94817e6i 0.889598i −0.895631 0.444799i \(-0.853275\pi\)
0.895631 0.444799i \(-0.146725\pi\)
\(500\) 1.61431e6 5.35201e6i 0.288776 0.957397i
\(501\) −2.98430e6 + 653162.i −0.531188 + 0.116259i
\(502\) 5.10312e6 7.14003e6i 0.903809 1.26456i
\(503\) 2.65554e6i 0.467985i −0.972238 0.233993i \(-0.924821\pi\)
0.972238 0.233993i \(-0.0751792\pi\)
\(504\) 5.27504e6 744025.i 0.925016 0.130470i
\(505\) 343388. 112289.i 0.0599178 0.0195933i
\(506\) 4.46159e6 + 3.18879e6i 0.774664 + 0.553668i
\(507\) 3.42962e6 + 1.56699e7i 0.592551 + 2.70737i
\(508\) −391745. 1.14473e6i −0.0673510 0.196809i
\(509\) 3.31880e6i 0.567788i 0.958856 + 0.283894i \(0.0916264\pi\)
−0.958856 + 0.283894i \(0.908374\pi\)
\(510\) −452268. + 5.06672e6i −0.0769964 + 0.862584i
\(511\) 1.54799e6i 0.262251i
\(512\) 3.81379e6 + 4.54306e6i 0.642956 + 0.765903i
\(513\) 3.90882e6 2.94939e6i 0.655771 0.494810i
\(514\) −2.45657e6 + 3.43711e6i −0.410130 + 0.573833i
\(515\) 1.55117e6 + 4.74361e6i 0.257716 + 0.788117i
\(516\) −83111.1 + 50407.5i −0.0137415 + 0.00833433i
\(517\) 2.24794e6i 0.369878i
\(518\) −2.38833e6 1.70699e6i −0.391084 0.279516i
\(519\) 1.15272e6 + 5.26679e6i 0.187848 + 0.858277i
\(520\) 1.19708e7 302056.i 1.94141 0.0489868i
\(521\) 3.67823e6i 0.593668i −0.954929 0.296834i \(-0.904069\pi\)
0.954929 0.296834i \(-0.0959309\pi\)
\(522\) 6.46199e6 + 1.24009e6i 1.03798 + 0.199194i
\(523\) 515191. 0.0823596 0.0411798 0.999152i \(-0.486888\pi\)
0.0411798 + 0.999152i \(0.486888\pi\)
\(524\) −1.65493e6 4.83595e6i −0.263301 0.769403i
\(525\) −4.42274e6 3.90450e6i −0.700314 0.618254i
\(526\) 3.35302e6 + 2.39647e6i 0.528410 + 0.377665i
\(527\) 6.74541e6i 1.05799i
\(528\) 5.41545e6 + 4.52340e6i 0.845376 + 0.706122i
\(529\) 1.62659e6 0.252720
\(530\) −4.61111e6 1.44913e6i −0.713043 0.224087i
\(531\) 7.49880e6 3.44761e6i 1.15413 0.530619i
\(532\) 4.73989e6 1.62206e6i 0.726088 0.248478i
\(533\) −8.40608e6 −1.28167
\(534\) 3.84936e6 8.97744e6i 0.584164 1.36238i
\(535\) −3.42130e6 + 1.11878e6i −0.516782 + 0.168989i
\(536\) −7.61369e6 2.27878e6i −1.14468 0.342603i
\(537\) 634665. + 2.89979e6i 0.0949749 + 0.433941i
\(538\) 2.73091e6 + 1.95184e6i 0.406773 + 0.290729i
\(539\) −945922. −0.140244
\(540\) −6.51484e6 1.86369e6i −0.961434 0.275036i
\(541\) −7.93761e6 −1.16599 −0.582997 0.812474i \(-0.698120\pi\)
−0.582997 + 0.812474i \(0.698120\pi\)
\(542\) 6.33223e6 + 4.52577e6i 0.925887 + 0.661750i
\(543\) −2.17472e6 9.93633e6i −0.316523 1.44619i
\(544\) 232512. + 5.97301e6i 0.0336860 + 0.865358i
\(545\) 2.36977e6 + 7.24693e6i 0.341754 + 1.04511i
\(546\) 4.98023e6 1.16149e7i 0.714937 1.66737i
\(547\) −45039.6 −0.00643615 −0.00321808 0.999995i \(-0.501024\pi\)
−0.00321808 + 0.999995i \(0.501024\pi\)
\(548\) 1.53257e6 + 4.47839e6i 0.218006 + 0.637046i
\(549\) −506360. + 232802.i −0.0717016 + 0.0329652i
\(550\) −90229.5 7.81369e6i −0.0127187 1.10141i
\(551\) 6.18776e6 0.868269
\(552\) −6.17100e6 465844.i −0.862001 0.0650718i
\(553\) 7.67122e6i 1.06672i
\(554\) −7.64179e6 5.46174e6i −1.05784 0.756060i
\(555\) 1.89256e6 + 3.21893e6i 0.260806 + 0.443587i
\(556\) 3.50778e6 1.20041e6i 0.481222 0.164681i
\(557\) 455969. 0.0622727 0.0311363 0.999515i \(-0.490087\pi\)
0.0311363 + 0.999515i \(0.490087\pi\)
\(558\) 8.82449e6 + 1.69347e6i 1.19979 + 0.230245i
\(559\) 230589.i 0.0312111i
\(560\) −5.74003e6 3.88757e6i −0.773471 0.523851i
\(561\) 1.52030e6 + 6.94625e6i 0.203949 + 0.931844i
\(562\) −5.70524e6 4.07765e6i −0.761962 0.544590i
\(563\) 3.79787e6i 0.504974i −0.967600 0.252487i \(-0.918751\pi\)
0.967600 0.252487i \(-0.0812485\pi\)
\(564\) 1.31551e6 + 2.16899e6i 0.174139 + 0.287118i
\(565\) −109453. 334717.i −0.0144247 0.0441120i
\(566\) 1.23970e6 1.73452e6i 0.162658 0.227583i
\(567\) −4.65561e6 + 5.42829e6i −0.608161 + 0.709096i
\(568\) −1.63288e6 488722.i −0.212365 0.0635610i
\(569\) 5.75280e6i 0.744902i 0.928052 + 0.372451i \(0.121482\pi\)
−0.928052 + 0.372451i \(0.878518\pi\)
\(570\) −6.34709e6 566557.i −0.818253 0.0730393i
\(571\) 2.47760e6i 0.318011i 0.987278 + 0.159005i \(0.0508287\pi\)
−0.987278 + 0.159005i \(0.949171\pi\)
\(572\) 1.58371e7 5.41968e6i 2.02388 0.692602i
\(573\) 214164. + 978517.i 0.0272496 + 0.124504i
\(574\) 3.95932e6 + 2.82981e6i 0.501581 + 0.358490i
\(575\) 4.04923e6 + 5.52938e6i 0.510743 + 0.697439i
\(576\) −7.87239e6 1.19537e6i −0.988667 0.150123i
\(577\) 9.56094e6i 1.19553i 0.801671 + 0.597766i \(0.203945\pi\)
−0.801671 + 0.597766i \(0.796055\pi\)
\(578\) 1.16768e6 1.63376e6i 0.145380 0.203408i
\(579\) −485449. + 106248.i −0.0601793 + 0.0131712i
\(580\) −5.15314e6 6.83856e6i −0.636066 0.844101i
\(581\) 4.57972e6i 0.562858i
\(582\) −1.98796e6 + 4.63631e6i −0.243277 + 0.567369i
\(583\) −6.75645e6 −0.823279
\(584\) −663437. + 2.21663e6i −0.0804948 + 0.268943i
\(585\) −1.17948e7 + 1.09216e7i −1.42495 + 1.31946i
\(586\) −161855. + 226459.i −0.0194707 + 0.0272424i
\(587\) 5.40537e6i 0.647486i 0.946145 + 0.323743i \(0.104941\pi\)
−0.946145 + 0.323743i \(0.895059\pi\)
\(588\) 912701. 553560.i 0.108864 0.0660270i
\(589\) 8.44999e6 1.00362
\(590\) −1.02464e7 3.22013e6i −1.21183 0.380841i
\(591\) −2.20396e6 1.00699e7i −0.259558 1.18592i
\(592\) 2.68836e6 + 3.46789e6i 0.315270 + 0.406687i
\(593\) −1.04976e7 −1.22589 −0.612945 0.790125i \(-0.710015\pi\)
−0.612945 + 0.790125i \(0.710015\pi\)
\(594\) −9.46890e6 + 244997.i −1.10112 + 0.0284902i
\(595\) −2.17138e6 6.64024e6i −0.251445 0.768938i
\(596\) 8.73818e6 2.99033e6i 1.00764 0.344829i
\(597\) 1.40982e7 3.08561e6i 1.61893 0.354328i
\(598\) −8.53646e6 + 1.19438e7i −0.976169 + 1.36581i
\(599\) −3.31460e6 −0.377453 −0.188727 0.982030i \(-0.560436\pi\)
−0.188727 + 0.982030i \(0.560436\pi\)
\(600\) 4.65969e6 + 7.48647e6i 0.528419 + 0.848983i
\(601\) −1.12802e7 −1.27389 −0.636945 0.770909i \(-0.719802\pi\)
−0.636945 + 0.770909i \(0.719802\pi\)
\(602\) 77624.9 108609.i 0.00872992 0.0122145i
\(603\) 9.69320e6 4.45650e6i 1.08561 0.499115i
\(604\) −5.80300e6 + 1.98587e6i −0.647232 + 0.221492i
\(605\) −596772. 1.82498e6i −0.0662857 0.202707i
\(606\) −224587. + 523780.i −0.0248429 + 0.0579385i
\(607\) 1.09061e7 1.20143 0.600713 0.799464i \(-0.294883\pi\)
0.600713 + 0.799464i \(0.294883\pi\)
\(608\) −7.48240e6 + 291269.i −0.820884 + 0.0319547i
\(609\) −8.82781e6 + 1.93211e6i −0.964517 + 0.211100i
\(610\) 691895. + 217441.i 0.0752863 + 0.0236601i
\(611\) 6.01780e6 0.652130
\(612\) −5.53190e6 5.81261e6i −0.597029 0.627325i
\(613\) 1.42777e7i 1.53464i 0.641265 + 0.767320i \(0.278410\pi\)
−0.641265 + 0.767320i \(0.721590\pi\)
\(614\) 3.71644e6 5.19985e6i 0.397838 0.556635i
\(615\) −3.13745e6 5.33627e6i −0.334494 0.568918i
\(616\) −9.28384e6 2.77866e6i −0.985771 0.295041i
\(617\) 1.13743e7 1.20285 0.601427 0.798928i \(-0.294599\pi\)
0.601427 + 0.798928i \(0.294599\pi\)
\(618\) −7.23558e6 3.10248e6i −0.762083 0.326766i
\(619\) 1.53471e7i 1.60990i 0.593344 + 0.804949i \(0.297808\pi\)
−0.593344 + 0.804949i \(0.702192\pi\)
\(620\) −7.03712e6 9.33872e6i −0.735218 0.975682i
\(621\) 6.63150e6 5.00378e6i 0.690054 0.520678i
\(622\) −9.66314e6 + 1.35202e7i −1.00148 + 1.40122i
\(623\) 1.34151e7i 1.38476i
\(624\) −1.21092e7 + 1.44973e7i −1.24496 + 1.49048i
\(625\) 2.94771e6 9.31012e6i 0.301846 0.953357i
\(626\) 1.51128e6 + 1.08015e6i 0.154138 + 0.110166i
\(627\) −8.70157e6 + 1.90448e6i −0.883953 + 0.193467i
\(628\) 4.15002e6 1.42020e6i 0.419905 0.143698i
\(629\) 4.42183e6i 0.445631i
\(630\) 9.23203e6 1.17358e6i 0.926715 0.117804i
\(631\) 3.59843e6i 0.359783i 0.983686 + 0.179891i \(0.0575746\pi\)
−0.983686 + 0.179891i \(0.942425\pi\)
\(632\) −3.28772e6 + 1.09847e7i −0.327418 + 1.09394i
\(633\) −8.49417e6 + 1.85908e6i −0.842581 + 0.184412i
\(634\) 9.70151e6 1.35739e7i 0.958553 1.34116i
\(635\) −656930. 2.00894e6i −0.0646524 0.197712i
\(636\) 6.51916e6 3.95392e6i 0.639071 0.387601i
\(637\) 2.53226e6i 0.247263i
\(638\) −9.73793e6 6.95990e6i −0.947142 0.676941i
\(639\) 2.07886e6 955769.i 0.201407 0.0925978i
\(640\) 6.55322e6 + 8.02680e6i 0.632419 + 0.774627i
\(641\) 598498.i 0.0575330i −0.999586 0.0287665i \(-0.990842\pi\)
0.999586 0.0287665i \(-0.00915793\pi\)
\(642\) 2.23765e6 5.21863e6i 0.214266 0.499711i
\(643\) 1.29874e7 1.23878 0.619390 0.785083i \(-0.287380\pi\)
0.619390 + 0.785083i \(0.287380\pi\)
\(644\) 8.04146e6 2.75191e6i 0.764048 0.261468i
\(645\) −146380. + 86063.9i −0.0138542 + 0.00814557i
\(646\) −6.13917e6 4.38779e6i −0.578800 0.413680i
\(647\) 7.73712e6i 0.726639i −0.931665 0.363320i \(-0.881643\pi\)
0.931665 0.363320i \(-0.118357\pi\)
\(648\) 8.99298e6 5.77766e6i 0.841329 0.540523i
\(649\) −1.50136e7 −1.39918
\(650\) 2.09175e7 241547.i 1.94189 0.0224242i
\(651\) −1.20552e7 + 2.63848e6i −1.11487 + 0.244007i
\(652\) 3.66346e6 + 1.07051e7i 0.337499 + 0.986220i
\(653\) 200322. 0.0183843 0.00919213 0.999958i \(-0.497074\pi\)
0.00919213 + 0.999958i \(0.497074\pi\)
\(654\) −1.10540e7 4.73973e6i −1.01059 0.433321i
\(655\) −2.77521e6 8.48682e6i −0.252751 0.772933i
\(656\) −4.45670e6 5.74898e6i −0.404346 0.521592i
\(657\) −1.29745e6 2.82205e6i −0.117268 0.255065i
\(658\) −2.83442e6 2.02582e6i −0.255211 0.182405i
\(659\) 7.58469e6 0.680337 0.340169 0.940364i \(-0.389516\pi\)
0.340169 + 0.940364i \(0.389516\pi\)
\(660\) 9.35143e6 + 8.03073e6i 0.835638 + 0.717621i
\(661\) 1.39690e7 1.24355 0.621775 0.783196i \(-0.286412\pi\)
0.621775 + 0.783196i \(0.286412\pi\)
\(662\) 1.05417e7 + 7.53439e6i 0.934904 + 0.668195i
\(663\) −1.85953e7 + 4.06987e6i −1.64293 + 0.359581i
\(664\) 1.96277e6 6.55786e6i 0.172762 0.577221i
\(665\) 8.31824e6 2.72009e6i 0.729420 0.238522i
\(666\) −5.78473e6 1.11012e6i −0.505356 0.0969805i
\(667\) 1.04978e7 0.913661
\(668\) −5.93337e6 + 2.03049e6i −0.514471 + 0.176059i
\(669\) −4.36770e6 1.99560e7i −0.377301 1.72389i
\(670\) −1.32449e7 4.16244e6i −1.13988 0.358229i
\(671\) 1.01380e6 0.0869254
\(672\) 1.05839e7 2.75190e6i 0.904111 0.235076i
\(673\) 6.91285e6i 0.588328i −0.955755 0.294164i \(-0.904959\pi\)
0.955755 0.294164i \(-0.0950412\pi\)
\(674\) 1.51924e7 + 1.08583e7i 1.28818 + 0.920687i
\(675\) −1.13354e7 3.41112e6i −0.957582 0.288162i
\(676\) 1.06617e7 + 3.11549e7i 0.897342 + 2.62216i
\(677\) −7.18646e6 −0.602620 −0.301310 0.953526i \(-0.597424\pi\)
−0.301310 + 0.953526i \(0.597424\pi\)
\(678\) 510555. + 218916.i 0.0426549 + 0.0182896i
\(679\) 6.92812e6i 0.576688i
\(680\) 263404. + 1.04390e7i 0.0218449 + 0.865738i
\(681\) 5.95217e6 1.30273e6i 0.491822 0.107643i
\(682\) −1.32981e7 9.50442e6i −1.09478 0.782465i
\(683\) 1.32532e6i 0.108710i −0.998522 0.0543551i \(-0.982690\pi\)
0.998522 0.0543551i \(-0.0173103\pi\)
\(684\) 7.28146e6 6.92981e6i 0.595084 0.566345i
\(685\) 2.57002e6 + 7.85932e6i 0.209271 + 0.639969i
\(686\) −7.54769e6 + 1.05603e7i −0.612356 + 0.856777i
\(687\) 346932. + 1.58513e6i 0.0280448 + 0.128137i
\(688\) −157701. + 122252.i −0.0127018 + 0.00984660i
\(689\) 1.80872e7i 1.45152i
\(690\) −1.07681e7 961192.i −0.861030 0.0768577i
\(691\) 7.66746e6i 0.610881i 0.952211 + 0.305440i \(0.0988037\pi\)
−0.952211 + 0.305440i \(0.901196\pi\)
\(692\) 3.58347e6 + 1.04714e7i 0.284471 + 0.831265i
\(693\) 1.18195e7 5.43408e6i 0.934902 0.429826i
\(694\) 1.20192e7 + 8.59038e6i 0.947279 + 0.677039i
\(695\) 6.15595e6 2.01301e6i 0.483430 0.158083i
\(696\) 1.34689e7 + 1.01676e6i 1.05392 + 0.0795600i
\(697\) 7.33041e6i 0.571539i
\(698\) −9.88816e6 + 1.38350e7i −0.768205 + 1.07483i
\(699\) 3694.36 + 16879.6i 0.000285987 + 0.00130668i
\(700\) −9.93358e6 6.92784e6i −0.766233 0.534383i
\(701\) 7.13545e6i 0.548436i 0.961668 + 0.274218i \(0.0884190\pi\)
−0.961668 + 0.274218i \(0.911581\pi\)
\(702\) −655864. 2.53485e7i −0.0502309 1.94137i
\(703\) −5.53923e6 −0.422728
\(704\) 1.21030e7 + 7.95771e6i 0.920366 + 0.605141i
\(705\) 2.24605e6 + 3.82016e6i 0.170195 + 0.289473i
\(706\) −1.22316e7 + 1.71139e7i −0.923575 + 1.29222i
\(707\) 782693.i 0.0588902i
\(708\) 1.44863e7 8.78607e6i 1.08611 0.658736i
\(709\) 4.78165e6 0.357242 0.178621 0.983918i \(-0.442836\pi\)
0.178621 + 0.983918i \(0.442836\pi\)
\(710\) −2.84058e6 892704.i −0.211476 0.0664602i
\(711\) −6.42964e6 1.39849e7i −0.476993 1.03749i
\(712\) 5.74944e6 1.92096e7i 0.425036 1.42010i
\(713\) 1.43358e7 1.05608
\(714\) 1.01286e7 + 4.34294e6i 0.743537 + 0.318815i
\(715\) 2.77932e7 9.08844e6i 2.03317 0.664851i
\(716\) 1.97299e6 + 5.76535e6i 0.143827 + 0.420284i
\(717\) 3.69127e6 + 1.68654e7i 0.268150 + 1.22518i
\(718\) 3.02318e6 4.22988e6i 0.218853 0.306208i
\(719\) −2.03561e7 −1.46849 −0.734247 0.678882i \(-0.762465\pi\)
−0.734247 + 0.678882i \(0.762465\pi\)
\(720\) −1.37226e7 2.27617e6i −0.986521 0.163634i
\(721\) 1.08122e7 0.774601
\(722\) −2.64805e6 + 3.70502e6i −0.189053 + 0.264513i
\(723\) −1.37975e6 6.30408e6i −0.0981644 0.448514i
\(724\) −6.76057e6 1.97554e7i −0.479333 1.40068i
\(725\) −8.83790e6 1.20685e7i −0.624459 0.852723i
\(726\) 2.78370e6 + 1.19359e6i 0.196011 + 0.0840457i
\(727\) −2.08208e7 −1.46104 −0.730520 0.682891i \(-0.760722\pi\)
−0.730520 + 0.682891i \(0.760722\pi\)
\(728\) 7.43853e6 2.48531e7i 0.520186 1.73801i
\(729\) −3.93762e6 + 1.37981e7i −0.274420 + 0.961610i
\(730\) −1.21184e6 + 3.85607e6i −0.0841663 + 0.267817i
\(731\) −201082. −0.0139181
\(732\) −978197. + 593284.i −0.0674759 + 0.0409246i
\(733\) 1.74635e7i 1.20053i −0.799802 0.600264i \(-0.795062\pi\)
0.799802 0.600264i \(-0.204938\pi\)
\(734\) −6.46916e6 + 9.05132e6i −0.443208 + 0.620114i
\(735\) 1.60750e6 945127.i 0.109757 0.0645315i
\(736\) −1.26943e7 + 494152.i −0.863799 + 0.0336253i
\(737\) −1.94071e7 −1.31611
\(738\) 9.58978e6 + 1.84033e6i 0.648139 + 0.124381i
\(739\) 3.13917e6i 0.211448i −0.994395 0.105724i \(-0.966284\pi\)
0.994395 0.105724i \(-0.0337161\pi\)
\(740\) 4.61305e6 + 6.12182e6i 0.309677 + 0.410962i
\(741\) −5.09834e6 2.32943e7i −0.341101 1.55849i
\(742\) −6.08883e6 + 8.51918e6i −0.405998 + 0.568052i
\(743\) 9.57557e6i 0.636345i 0.948033 + 0.318172i \(0.103069\pi\)
−0.948033 + 0.318172i \(0.896931\pi\)
\(744\) 1.83931e7 + 1.38848e6i 1.21821 + 0.0919620i
\(745\) 1.53350e7 5.01458e6i 1.01226 0.331012i
\(746\) −736894. 526673.i −0.0484795 0.0346493i
\(747\) 3.83849e6 + 8.34899e6i 0.251686 + 0.547435i
\(748\) 4.72615e6 + 1.38105e7i 0.308854 + 0.902517i
\(749\) 7.79828e6i 0.507919i
\(750\) 7.96047e6 + 1.31885e7i 0.516756 + 0.856133i
\(751\) 3.08190e7i 1.99397i 0.0776065 + 0.996984i \(0.475272\pi\)
−0.0776065 + 0.996984i \(0.524728\pi\)
\(752\) 3.19049e6 + 4.11561e6i 0.205737 + 0.265393i
\(753\) 5.17074e6 + 2.36252e7i 0.332327 + 1.51840i
\(754\) 1.86318e7 2.60687e7i 1.19351 1.66990i
\(755\) −1.01839e7 + 3.33017e6i −0.650202 + 0.212618i
\(756\) −8.22434e6 + 1.21601e7i −0.523356 + 0.773807i
\(757\) 1.21868e7i 0.772949i −0.922300 0.386474i \(-0.873693\pi\)
0.922300 0.386474i \(-0.126307\pi\)
\(758\) 1.26635e7 + 9.05084e6i 0.800534 + 0.572158i
\(759\) −1.47627e7 + 3.23104e6i −0.930165 + 0.203581i
\(760\) −1.30769e7 + 329966.i −0.821244 + 0.0207222i
\(761\) 5.95806e6i 0.372944i −0.982460 0.186472i \(-0.940295\pi\)
0.982460 0.186472i \(-0.0597053\pi\)
\(762\) 3.06431e6 + 1.31392e6i 0.191181 + 0.0819748i
\(763\) 1.65182e7 1.02719
\(764\) 665773. + 1.94548e6i 0.0412660 + 0.120585i
\(765\) −9.52401e6 1.02855e7i −0.588391 0.635433i
\(766\) −1.04913e7 7.49838e6i −0.646040 0.461738i
\(767\) 4.01918e7i 2.46689i
\(768\) −1.63348e7 595486.i −0.999336 0.0364308i
\(769\) −1.64484e7 −1.00302 −0.501509 0.865153i \(-0.667221\pi\)
−0.501509 + 0.865153i \(0.667221\pi\)
\(770\) −1.61503e7 5.07552e6i −0.981642 0.308499i
\(771\) −2.48912e6 1.13728e7i −0.150803 0.689021i
\(772\) −965167. + 330294.i −0.0582853 + 0.0199461i
\(773\) 2.24908e7 1.35380 0.676902 0.736073i \(-0.263322\pi\)
0.676902 + 0.736073i \(0.263322\pi\)
\(774\) 50482.4 263059.i 0.00302892 0.0157834i
\(775\) −1.20690e7 1.64807e7i −0.721802 0.985648i
\(776\) −2.96924e6 + 9.92062e6i −0.177007 + 0.591404i
\(777\) 7.90259e6 1.72961e6i 0.469588 0.102777i
\(778\) −2.14919e7 1.53607e7i −1.27299 0.909834i
\(779\) 9.18281e6 0.542166
\(780\) −2.14985e7 + 2.50340e7i −1.26523 + 1.47331i
\(781\) −4.16217e6 −0.244170
\(782\) −1.04154e7 7.44410e6i −0.609059 0.435307i
\(783\) −1.44740e7 + 1.09213e7i −0.843693 + 0.636607i
\(784\) 1.73183e6 1.34254e6i 0.100627 0.0780076i
\(785\) 7.28305e6 2.38157e6i 0.421831 0.137940i
\(786\) 1.29452e7 + 5.55066e6i 0.747400 + 0.320471i
\(787\) 2.28411e7 1.31456 0.657279 0.753647i \(-0.271707\pi\)
0.657279 + 0.753647i \(0.271707\pi\)
\(788\) −6.85146e6 2.00210e7i −0.393068 1.14860i
\(789\) −1.10946e7 + 2.42822e6i −0.634480 + 0.138866i
\(790\) −6.00538e6 + 1.91091e7i −0.342352 + 1.08936i
\(791\) −762931. −0.0433555
\(792\) −1.92537e7 + 2.71566e6i −1.09069 + 0.153838i
\(793\) 2.71397e6i 0.153258i
\(794\) −1.05439e7 7.53590e6i −0.593537 0.424213i
\(795\) 1.14819e7 6.75077e6i 0.644313 0.378822i
\(796\) 2.80299e7 9.59225e6i 1.56798 0.536584i
\(797\) −1.44455e7 −0.805541 −0.402771 0.915301i \(-0.631953\pi\)
−0.402771 + 0.915301i \(0.631953\pi\)
\(798\) −5.44041e6 + 1.26881e7i −0.302429 + 0.705324i
\(799\) 5.24773e6i 0.290807i
\(800\) 1.12551e7 + 1.41775e7i 0.621763 + 0.783205i
\(801\) 1.12439e7 + 2.44563e7i 0.619207 + 1.34682i
\(802\) 2.35419e7 + 1.68259e7i 1.29243 + 0.923723i
\(803\) 5.65012e6i 0.309221i
\(804\) 1.87255e7 1.13572e7i 1.02163 0.619626i
\(805\) 1.41123e7 4.61476e6i 0.767553 0.250992i
\(806\) 2.54436e7 3.55994e7i 1.37956 1.93021i
\(807\) −9.03613e6 + 1.97770e6i −0.488426 + 0.106900i
\(808\) −335446. + 1.12077e6i −0.0180756 + 0.0603930i
\(809\) 2.89302e7i 1.55410i −0.629436 0.777052i \(-0.716714\pi\)
0.629436 0.777052i \(-0.283286\pi\)
\(810\) 1.58467e7 9.87730e6i 0.848645 0.528963i
\(811\) 2.47943e6i 0.132373i −0.997807 0.0661867i \(-0.978917\pi\)
0.997807 0.0661867i \(-0.0210833\pi\)
\(812\) −1.75514e7 + 6.00635e6i −0.934162 + 0.319684i
\(813\) −2.09523e7 + 4.58574e6i −1.11174 + 0.243323i
\(814\) 8.71732e6 + 6.23045e6i 0.461129 + 0.329578i
\(815\) 6.14337e6 + 1.87869e7i 0.323976 + 0.990744i
\(816\) −1.26422e7 1.05597e7i −0.664655 0.555170i
\(817\) 251895.i 0.0132028i
\(818\) 1.31442e6 1.83907e6i 0.0686834 0.0960983i
\(819\) 1.45472e7 + 3.16411e7i 0.757825 + 1.64832i
\(820\) −7.64741e6 1.01486e7i −0.397173 0.527075i
\(821\) 5.66176e6i 0.293152i 0.989199 + 0.146576i \(0.0468254\pi\)
−0.989199 + 0.146576i \(0.953175\pi\)
\(822\) −1.19881e7 5.14026e6i −0.618828 0.265342i
\(823\) −62728.0 −0.00322821 −0.00161410 0.999999i \(-0.500514\pi\)
−0.00161410 + 0.999999i \(0.500514\pi\)
\(824\) −1.54824e7 4.63390e6i −0.794367 0.237754i
\(825\) 1.61428e7 + 1.42513e7i 0.825743 + 0.728985i
\(826\) −1.35301e7 + 1.89306e7i −0.690003 + 0.965417i
\(827\) 2.62578e7i 1.33504i 0.744591 + 0.667521i \(0.232645\pi\)
−0.744591 + 0.667521i \(0.767355\pi\)
\(828\) 1.23534e7 1.17568e7i 0.626194 0.595953i
\(829\) −3.28939e7 −1.66238 −0.831188 0.555992i \(-0.812338\pi\)
−0.831188 + 0.555992i \(0.812338\pi\)
\(830\) 3.58522e6 1.14081e7i 0.180643 0.574804i
\(831\) 2.52854e7 5.53411e6i 1.27019 0.278000i
\(832\) −2.13030e7 + 3.24000e7i −1.06692 + 1.62269i
\(833\) 2.20822e6 0.110263
\(834\) −4.02620e6 + 9.38987e6i −0.200438 + 0.467460i
\(835\) −1.04127e7 + 3.40499e6i −0.516831 + 0.169005i
\(836\) −1.73004e7 + 5.92046e6i −0.856133 + 0.292981i
\(837\) −1.97657e7 + 1.49142e7i −0.975211 + 0.735843i
\(838\) 1.10063e7 1.53994e7i 0.541415 0.757520i
\(839\) 1.61524e7 0.792196 0.396098 0.918208i \(-0.370364\pi\)
0.396098 + 0.918208i \(0.370364\pi\)
\(840\) 1.85533e7 4.55399e6i 0.907242 0.222686i
\(841\) −2.40158e6 −0.117087
\(842\) 1.51073e7 2.11373e7i 0.734355 1.02747i
\(843\) 1.88777e7 4.13169e6i 0.914913 0.200243i
\(844\) −1.68881e7 + 5.77934e6i −0.816063 + 0.279269i
\(845\) 1.78789e7 + 5.46751e7i 0.861388 + 2.63419i
\(846\) −6.86519e6 1.31747e6i −0.329782 0.0632869i
\(847\) −4.15972e6 −0.199231
\(848\) 1.23699e7 9.58937e6i 0.590715 0.457932i
\(849\) 1.25613e6 + 5.73925e6i 0.0598087 + 0.273266i
\(850\) 210637. + 1.82408e7i 0.00999972 + 0.865956i
\(851\) −9.39758e6 −0.444828
\(852\) 4.01599e6 2.43573e6i 0.189537 0.114956i
\(853\) 3.14182e7i 1.47846i 0.673455 + 0.739228i \(0.264810\pi\)
−0.673455 + 0.739228i \(0.735190\pi\)
\(854\) 913626. 1.27830e6i 0.0428671 0.0599774i
\(855\) 1.28846e7 1.19307e7i 0.602776 0.558152i
\(856\) 3.34218e6 1.11666e7i 0.155900 0.520880i
\(857\) −2.02060e7 −0.939783 −0.469891 0.882724i \(-0.655707\pi\)
−0.469891 + 0.882724i \(0.655707\pi\)
\(858\) −1.81777e7 + 4.23938e7i −0.842984 + 1.96600i
\(859\) 2.66482e7i 1.23221i 0.787663 + 0.616106i \(0.211291\pi\)
−0.787663 + 0.616106i \(0.788709\pi\)
\(860\) −278389. + 209778.i −0.0128353 + 0.00967192i
\(861\) −1.31007e7 + 2.86731e6i −0.602265 + 0.131815i
\(862\) 1.38538e7 1.93835e7i 0.635038 0.888513i
\(863\) 1.42426e6i 0.0650971i −0.999470 0.0325485i \(-0.989638\pi\)
0.999470 0.0325485i \(-0.0103624\pi\)
\(864\) 1.69883e7 1.38877e7i 0.774221 0.632915i
\(865\) 6.00923e6 + 1.83767e7i 0.273073 + 0.835079i
\(866\) −3.32491e7 2.37638e7i −1.50656 1.07677i
\(867\) 1.18315e6 + 5.40583e6i 0.0534556 + 0.244239i
\(868\) −2.39682e7 + 8.20227e6i −1.07978 + 0.369517i
\(869\) 2.79997e7i 1.25778i
\(870\) 2.35027e7 + 2.09791e6i 1.05274 + 0.0939700i
\(871\) 5.19533e7i 2.32043i
\(872\) −2.36529e7 7.07933e6i −1.05340 0.315283i
\(873\) −5.80681e6 1.26302e7i −0.257870 0.560886i
\(874\) 9.32524e6 1.30474e7i 0.412935 0.577757i
\(875\) −1.71861e7 1.23387e7i −0.758851 0.544815i
\(876\) −3.30649e6 5.45169e6i −0.145582 0.240033i
\(877\) 8.98989e6i 0.394689i −0.980334 0.197345i \(-0.936768\pi\)
0.980334 0.197345i \(-0.0632318\pi\)
\(878\) 3.22608e7 + 2.30574e7i 1.41234 + 1.00943i
\(879\) −164000. 749315.i −0.00715930 0.0327109i
\(880\) 2.09509e7 + 1.41895e7i 0.912002 + 0.617675i
\(881\) 4.12652e6i 0.179120i 0.995981 + 0.0895600i \(0.0285461\pi\)
−0.995981 + 0.0895600i \(0.971454\pi\)
\(882\) −554383. + 2.88884e6i −0.0239960 + 0.125041i
\(883\) −3.78957e7 −1.63564 −0.817820 0.575474i \(-0.804818\pi\)
−0.817820 + 0.575474i \(0.804818\pi\)
\(884\) −3.69710e7 + 1.26520e7i −1.59122 + 0.544540i
\(885\) 2.55142e7 1.50010e7i 1.09502 0.643817i
\(886\) −1.31170e7 9.37501e6i −0.561373 0.401224i
\(887\) 3.04873e7i 1.30110i −0.759465 0.650548i \(-0.774539\pi\)
0.759465 0.650548i \(-0.225461\pi\)
\(888\) −1.20573e7 910195.i −0.513117 0.0387348i
\(889\) −4.57905e6 −0.194321
\(890\) 1.05020e7 3.34173e7i 0.444423 1.41415i
\(891\) 1.69928e7 1.98130e7i 0.717085 0.836097i
\(892\) −1.35779e7 3.96765e7i −0.571373 1.66963i
\(893\) −6.57384e6 −0.275861
\(894\) −1.00296e7 + 2.33910e7i −0.419701 + 0.978824i
\(895\) 3.30856e6 + 1.01179e7i 0.138064 + 0.422212i
\(896\) 2.09409e7 8.08922e6i 0.871416 0.336617i
\(897\) −8.64958e6 3.95200e7i −0.358933 1.63997i
\(898\) 3.45193e7 + 2.46717e7i 1.42847 + 1.02096i
\(899\) −3.12896e7 −1.29122
\(900\) −2.39158e7 4.30387e6i −0.984190 0.177114i
\(901\) 1.57727e7 0.647281
\(902\) −1.44514e7 1.03287e7i −0.591416 0.422697i
\(903\) 78653.6 + 359369.i 0.00320996 + 0.0146663i
\(904\) 1.09247e6 + 326976.i 0.0444619 + 0.0133074i
\(905\) −1.13370e7 3.46695e7i −0.460127 1.40711i
\(906\) 6.66063e6 1.55339e7i 0.269584 0.628723i
\(907\) −4.26769e6 −0.172256 −0.0861280 0.996284i \(-0.527449\pi\)
−0.0861280 + 0.996284i \(0.527449\pi\)
\(908\) 1.18341e7 4.04980e6i 0.476343 0.163012i
\(909\) −656014. 1.42688e6i −0.0263332 0.0572766i
\(910\) 1.35873e7 4.32347e7i 0.543913 1.73073i
\(911\) −5.34648e6 −0.213438 −0.106719 0.994289i \(-0.534035\pi\)
−0.106719 + 0.994289i \(0.534035\pi\)
\(912\) 1.32281e7 1.58369e7i 0.526638 0.630496i
\(913\) 1.67158e7i 0.663667i
\(914\) −4.43665e6 3.17096e6i −0.175667 0.125553i
\(915\) −1.72286e6 + 1.01295e6i −0.0680294 + 0.0399977i
\(916\) 1.07851e6 + 3.15156e6i 0.0424703 + 0.124104i
\(917\) −1.93443e7 −0.759677
\(918\) 2.21048e7 571937.i 0.865724 0.0223996i
\(919\) 2.59878e7i 1.01503i 0.861642 + 0.507516i \(0.169436\pi\)
−0.861642 + 0.507516i \(0.830564\pi\)
\(920\) −2.21857e7 + 559804.i −0.864179 + 0.0218055i
\(921\) 3.76569e6 + 1.72054e7i 0.146283 + 0.668370i
\(922\) −3.79693e6 2.71374e6i −0.147097 0.105133i
\(923\) 1.11422e7i 0.430495i
\(924\) 2.28332e7 1.38485e7i 0.879804 0.533608i
\(925\) 7.91162e6 + 1.08036e7i 0.304026 + 0.415160i
\(926\) −1.34372e7 + 1.88007e7i −0.514970 + 0.720520i
\(927\) 1.97111e7 9.06229e6i 0.753376 0.346369i
\(928\) 2.77067e7 1.07854e6i 1.05612 0.0411119i
\(929\) 566032.i 0.0215180i −0.999942 0.0107590i \(-0.996575\pi\)
0.999942 0.0107590i \(-0.00342476\pi\)
\(930\) 3.20953e7 + 2.86491e6i 1.21684 + 0.108618i
\(931\) 2.76624e6i 0.104596i
\(932\) 11484.7 + 33559.9i 0.000433091 + 0.00126555i
\(933\) −9.79119e6 4.47360e7i −0.368240 1.68249i
\(934\) 2.80028e7 + 2.00142e7i 1.05035 + 0.750707i
\(935\) 7.92544e6 + 2.42366e7i 0.296479 + 0.906657i
\(936\) −7.26990e6 5.15426e7i −0.271231 1.92299i
\(937\) 2.24464e7i 0.835213i 0.908628 + 0.417606i \(0.137131\pi\)
−0.908628 + 0.417606i \(0.862869\pi\)
\(938\) −1.74894e7 + 2.44703e7i −0.649036 + 0.908099i
\(939\) −5.00059e6 + 1.09446e6i −0.185079 + 0.0405075i
\(940\) 5.47467e6 + 7.26525e6i 0.202087 + 0.268183i
\(941\) 1.65433e7i 0.609043i 0.952505 + 0.304522i \(0.0984966\pi\)
−0.952505 + 0.304522i \(0.901503\pi\)
\(942\) −4.76335e6 + 1.11091e7i −0.174898 + 0.407897i
\(943\) 1.55791e7 0.570510
\(944\) 2.74875e7 2.13087e7i 1.00393 0.778265i
\(945\) −1.46566e7 + 2.10443e7i −0.533892 + 0.766575i
\(946\) −283328. + 396418.i −0.0102935 + 0.0144021i
\(947\) 3.74336e7i 1.35640i 0.734879 + 0.678199i \(0.237239\pi\)
−0.734879 + 0.678199i \(0.762761\pi\)
\(948\) −1.63856e7 2.70163e7i −0.592163 0.976350i
\(949\) −1.51255e7 −0.545186
\(950\) −2.28502e7 + 263866.i −0.821451 + 0.00948580i
\(951\) 9.83007e6 + 4.49136e7i 0.352456 + 1.61037i
\(952\) 2.16728e7 + 6.48667e6i 0.775036 + 0.231969i
\(953\) 2.57737e7 0.919271 0.459636 0.888108i \(-0.347980\pi\)
0.459636 + 0.888108i \(0.347980\pi\)
\(954\) −3.95980e6 + 2.06341e7i −0.140865 + 0.734032i
\(955\) 1.11646e6 + 3.41421e6i 0.0396126 + 0.121138i
\(956\) 1.14751e7 + 3.35318e7i 0.406079 + 1.18662i
\(957\) 3.22212e7 7.05212e6i 1.13727 0.248909i
\(958\) −2.20609e7 + 3.08665e7i −0.776622 + 1.08661i
\(959\) 1.79140e7 0.628993
\(960\) −2.85189e7 1.43054e6i −0.998744 0.0500981i
\(961\) −1.40999e7 −0.492500
\(962\) −1.66791e7 + 2.33365e7i −0.581077 + 0.813014i
\(963\) 6.53613e6 + 1.42165e7i 0.227120 + 0.494001i
\(964\) −4.28923e6 1.25337e7i −0.148657 0.434398i
\(965\) −1.69381e6 + 553881.i −0.0585527 + 0.0191469i
\(966\) −9.22992e6 + 2.15260e7i −0.318240 + 0.742198i
\(967\) 4.39195e6 0.151040 0.0755199 0.997144i \(-0.475938\pi\)
0.0755199 + 0.997144i \(0.475938\pi\)
\(968\) 5.95645e6 + 1.78277e6i 0.204315 + 0.0611514i
\(969\) 2.03135e7 4.44593e6i 0.694984 0.152108i
\(970\) −5.42365e6 + 1.72580e7i −0.185081 + 0.588928i
\(971\) 3.71092e7 1.26309 0.631544 0.775340i \(-0.282421\pi\)
0.631544 + 0.775340i \(0.282421\pi\)
\(972\) −4.80128e6 + 2.90615e7i −0.163002 + 0.986626i
\(973\) 1.40315e7i 0.475139i
\(974\) 3.15328e7 4.41191e7i 1.06504 1.49015i
\(975\) −3.81510e7 + 4.32147e7i −1.28527 + 1.45586i
\(976\) −1.85611e6 + 1.43888e6i −0.0623703 + 0.0483504i
\(977\) 5.66630e7 1.89917 0.949584 0.313514i \(-0.101506\pi\)
0.949584 + 0.313514i \(0.101506\pi\)
\(978\) −2.86563e7 1.22873e7i −0.958016 0.410779i
\(979\) 4.89648e7i 1.63278i
\(980\) 3.05718e6 2.30371e6i 0.101685 0.0766237i
\(981\) 3.01132e7 1.38447e7i 0.999042 0.459315i
\(982\) 2.42002e7 3.38596e7i 0.800829 1.12048i
\(983\) 4.13391e7i 1.36451i −0.731114 0.682255i \(-0.760999\pi\)
0.731114 0.682255i \(-0.239001\pi\)
\(984\) 1.99883e7 + 1.50890e6i 0.658093 + 0.0496790i
\(985\) −1.14894e7 3.51356e7i −0.377319 1.15387i
\(986\) 2.27328e7 + 1.62476e7i 0.744665 + 0.532227i
\(987\) 9.37863e6 2.05266e6i 0.306441 0.0670695i
\(988\) −1.58492e7 4.63137e7i −0.516554 1.50944i
\(989\) 427353.i 0.0138930i
\(990\) −3.36966e7 + 4.28351e6i −1.09269 + 0.138903i
\(991\) 1.73484e7i 0.561147i −0.959833 0.280573i \(-0.909475\pi\)
0.959833 0.280573i \(-0.0905246\pi\)
\(992\) 3.78362e7 1.47286e6i 1.22075 0.0475205i
\(993\) −3.48808e7 + 7.63423e6i −1.12257 + 0.245693i
\(994\) −3.75090e6 + 5.24806e6i −0.120412 + 0.168474i
\(995\) 4.91909e7 1.60856e7i 1.57517 0.515084i
\(996\) 9.78221e6 + 1.61288e7i 0.312456 + 0.515172i
\(997\) 2.58508e7i 0.823639i 0.911265 + 0.411819i \(0.135107\pi\)
−0.911265 + 0.411819i \(0.864893\pi\)
\(998\) 2.27726e7 + 1.62760e7i 0.723747 + 0.517276i
\(999\) 1.29570e7 9.77669e6i 0.410763 0.309940i
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 60.6.h.c.59.15 yes 48
3.2 odd 2 inner 60.6.h.c.59.33 yes 48
4.3 odd 2 inner 60.6.h.c.59.14 yes 48
5.4 even 2 inner 60.6.h.c.59.34 yes 48
12.11 even 2 inner 60.6.h.c.59.36 yes 48
15.14 odd 2 inner 60.6.h.c.59.16 yes 48
20.19 odd 2 inner 60.6.h.c.59.35 yes 48
60.59 even 2 inner 60.6.h.c.59.13 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.6.h.c.59.13 48 60.59 even 2 inner
60.6.h.c.59.14 yes 48 4.3 odd 2 inner
60.6.h.c.59.15 yes 48 1.1 even 1 trivial
60.6.h.c.59.16 yes 48 15.14 odd 2 inner
60.6.h.c.59.33 yes 48 3.2 odd 2 inner
60.6.h.c.59.34 yes 48 5.4 even 2 inner
60.6.h.c.59.35 yes 48 20.19 odd 2 inner
60.6.h.c.59.36 yes 48 12.11 even 2 inner