Properties

Label 55.6.e.b.32.13
Level $55$
Weight $6$
Character 55.32
Analytic conductor $8.821$
Analytic rank $0$
Dimension $52$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,6,Mod(32,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.32");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 55.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.82111008971\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 32.13
Character \(\chi\) \(=\) 55.32
Dual form 55.6.e.b.43.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.819850 + 0.819850i) q^{2} +(-2.25487 + 2.25487i) q^{3} +30.6557i q^{4} +(5.74279 - 55.6059i) q^{5} -3.69731i q^{6} +(-88.0749 + 88.0749i) q^{7} +(-51.3683 - 51.3683i) q^{8} +232.831i q^{9} +(40.8803 + 50.2967i) q^{10} +(68.0926 - 395.493i) q^{11} +(-69.1247 - 69.1247i) q^{12} +(-741.664 - 741.664i) q^{13} -144.416i q^{14} +(112.435 + 138.334i) q^{15} -896.754 q^{16} +(-805.641 + 805.641i) q^{17} +(-190.887 - 190.887i) q^{18} -1851.56 q^{19} +(1704.64 + 176.049i) q^{20} -397.196i q^{21} +(268.419 + 380.070i) q^{22} +(-561.188 + 561.188i) q^{23} +231.658 q^{24} +(-3059.04 - 638.666i) q^{25} +1216.11 q^{26} +(-1072.94 - 1072.94i) q^{27} +(-2700.00 - 2700.00i) q^{28} +3983.79 q^{29} +(-205.593 - 21.2329i) q^{30} +4011.45 q^{31} +(2378.99 - 2378.99i) q^{32} +(738.246 + 1045.33i) q^{33} -1321.01i q^{34} +(4391.69 + 5403.28i) q^{35} -7137.60 q^{36} +(5642.57 + 5642.57i) q^{37} +(1518.00 - 1518.00i) q^{38} +3344.72 q^{39} +(-3151.38 + 2561.38i) q^{40} +14226.7i q^{41} +(325.641 + 325.641i) q^{42} +(3129.47 + 3129.47i) q^{43} +(12124.1 + 2087.42i) q^{44} +(12946.8 + 1337.10i) q^{45} -920.180i q^{46} +(-18434.0 - 18434.0i) q^{47} +(2022.07 - 2022.07i) q^{48} +1292.61i q^{49} +(3031.56 - 1984.34i) q^{50} -3633.24i q^{51} +(22736.2 - 22736.2i) q^{52} +(-2404.01 + 2404.01i) q^{53} +1759.30 q^{54} +(-21600.7 - 6057.58i) q^{55} +9048.51 q^{56} +(4175.04 - 4175.04i) q^{57} +(-3266.11 + 3266.11i) q^{58} +22820.4i q^{59} +(-4240.71 + 3446.77i) q^{60} +37872.4i q^{61} +(-3288.79 + 3288.79i) q^{62} +(-20506.6 - 20506.6i) q^{63} -24795.3i q^{64} +(-45500.1 + 36981.7i) q^{65} +(-1462.26 - 251.760i) q^{66} +(5682.77 + 5682.77i) q^{67} +(-24697.5 - 24697.5i) q^{68} -2530.82i q^{69} +(-8030.41 - 829.353i) q^{70} -3271.14 q^{71} +(11960.1 - 11960.1i) q^{72} +(-25842.3 - 25842.3i) q^{73} -9252.11 q^{74} +(8337.86 - 5457.64i) q^{75} -56760.9i q^{76} +(28835.7 + 40830.2i) q^{77} +(-2742.16 + 2742.16i) q^{78} +41319.9 q^{79} +(-5149.87 + 49864.8i) q^{80} -51739.3 q^{81} +(-11663.8 - 11663.8i) q^{82} +(-67888.9 - 67888.9i) q^{83} +12176.3 q^{84} +(40171.8 + 49425.0i) q^{85} -5131.39 q^{86} +(-8982.93 + 8982.93i) q^{87} +(-23813.6 + 16818.0i) q^{88} -86508.1i q^{89} +(-11710.6 + 9518.20i) q^{90} +130644. q^{91} +(-17203.6 - 17203.6i) q^{92} +(-9045.31 + 9045.31i) q^{93} +30226.3 q^{94} +(-10633.1 + 102958. i) q^{95} +10728.6i q^{96} +(-24593.2 - 24593.2i) q^{97} +(-1059.75 - 1059.75i) q^{98} +(92083.0 + 15854.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.819850 + 0.819850i −0.144930 + 0.144930i −0.775849 0.630919i \(-0.782678\pi\)
0.630919 + 0.775849i \(0.282678\pi\)
\(3\) −2.25487 + 2.25487i −0.144650 + 0.144650i −0.775723 0.631073i \(-0.782615\pi\)
0.631073 + 0.775723i \(0.282615\pi\)
\(4\) 30.6557i 0.957990i
\(5\) 5.74279 55.6059i 0.102730 0.994709i
\(6\) 3.69731i 0.0419284i
\(7\) −88.0749 + 88.0749i −0.679371 + 0.679371i −0.959858 0.280487i \(-0.909504\pi\)
0.280487 + 0.959858i \(0.409504\pi\)
\(8\) −51.3683 51.3683i −0.283772 0.283772i
\(9\) 232.831i 0.958153i
\(10\) 40.8803 + 50.2967i 0.129275 + 0.159052i
\(11\) 68.0926 395.493i 0.169675 0.985500i
\(12\) −69.1247 69.1247i −0.138573 0.138573i
\(13\) −741.664 741.664i −1.21716 1.21716i −0.968621 0.248542i \(-0.920049\pi\)
−0.248542 0.968621i \(-0.579951\pi\)
\(14\) 144.416i 0.196923i
\(15\) 112.435 + 138.334i 0.129025 + 0.158745i
\(16\) −896.754 −0.875736
\(17\) −805.641 + 805.641i −0.676113 + 0.676113i −0.959118 0.283005i \(-0.908669\pi\)
0.283005 + 0.959118i \(0.408669\pi\)
\(18\) −190.887 190.887i −0.138865 0.138865i
\(19\) −1851.56 −1.17667 −0.588334 0.808618i \(-0.700216\pi\)
−0.588334 + 0.808618i \(0.700216\pi\)
\(20\) 1704.64 + 176.049i 0.952922 + 0.0984145i
\(21\) 397.196i 0.196542i
\(22\) 268.419 + 380.070i 0.118238 + 0.167420i
\(23\) −561.188 + 561.188i −0.221202 + 0.221202i −0.809004 0.587803i \(-0.799993\pi\)
0.587803 + 0.809004i \(0.299993\pi\)
\(24\) 231.658 0.0820954
\(25\) −3059.04 638.666i −0.978893 0.204373i
\(26\) 1216.11 0.352808
\(27\) −1072.94 1072.94i −0.283247 0.283247i
\(28\) −2700.00 2700.00i −0.650831 0.650831i
\(29\) 3983.79 0.879632 0.439816 0.898088i \(-0.355044\pi\)
0.439816 + 0.898088i \(0.355044\pi\)
\(30\) −205.593 21.2329i −0.0417066 0.00430731i
\(31\) 4011.45 0.749717 0.374859 0.927082i \(-0.377691\pi\)
0.374859 + 0.927082i \(0.377691\pi\)
\(32\) 2378.99 2378.99i 0.410693 0.410693i
\(33\) 738.246 + 1045.33i 0.118009 + 0.167096i
\(34\) 1321.01i 0.195979i
\(35\) 4391.69 + 5403.28i 0.605985 + 0.745569i
\(36\) −7137.60 −0.917901
\(37\) 5642.57 + 5642.57i 0.677598 + 0.677598i 0.959456 0.281858i \(-0.0909507\pi\)
−0.281858 + 0.959456i \(0.590951\pi\)
\(38\) 1518.00 1518.00i 0.170535 0.170535i
\(39\) 3344.72 0.352126
\(40\) −3151.38 + 2561.38i −0.311423 + 0.253119i
\(41\) 14226.7i 1.32174i 0.750502 + 0.660868i \(0.229812\pi\)
−0.750502 + 0.660868i \(0.770188\pi\)
\(42\) 325.641 + 325.641i 0.0284849 + 0.0284849i
\(43\) 3129.47 + 3129.47i 0.258107 + 0.258107i 0.824284 0.566177i \(-0.191578\pi\)
−0.566177 + 0.824284i \(0.691578\pi\)
\(44\) 12124.1 + 2087.42i 0.944100 + 0.162547i
\(45\) 12946.8 + 1337.10i 0.953083 + 0.0984311i
\(46\) 920.180i 0.0641177i
\(47\) −18434.0 18434.0i −1.21724 1.21724i −0.968595 0.248645i \(-0.920015\pi\)
−0.248645 0.968595i \(-0.579985\pi\)
\(48\) 2022.07 2022.07i 0.126675 0.126675i
\(49\) 1292.61i 0.0769093i
\(50\) 3031.56 1984.34i 0.171491 0.112251i
\(51\) 3633.24i 0.195600i
\(52\) 22736.2 22736.2i 1.16603 1.16603i
\(53\) −2404.01 + 2404.01i −0.117557 + 0.117557i −0.763438 0.645881i \(-0.776490\pi\)
0.645881 + 0.763438i \(0.276490\pi\)
\(54\) 1759.30 0.0821022
\(55\) −21600.7 6057.58i −0.962855 0.270018i
\(56\) 9048.51 0.385573
\(57\) 4175.04 4175.04i 0.170205 0.170205i
\(58\) −3266.11 + 3266.11i −0.127485 + 0.127485i
\(59\) 22820.4i 0.853479i 0.904375 + 0.426739i \(0.140338\pi\)
−0.904375 + 0.426739i \(0.859662\pi\)
\(60\) −4240.71 + 3446.77i −0.152076 + 0.123605i
\(61\) 37872.4i 1.30316i 0.758579 + 0.651581i \(0.225894\pi\)
−0.758579 + 0.651581i \(0.774106\pi\)
\(62\) −3288.79 + 3288.79i −0.108657 + 0.108657i
\(63\) −20506.6 20506.6i −0.650941 0.650941i
\(64\) 24795.3i 0.756692i
\(65\) −45500.1 + 36981.7i −1.33576 + 1.08568i
\(66\) −1462.26 251.760i −0.0413204 0.00711420i
\(67\) 5682.77 + 5682.77i 0.154658 + 0.154658i 0.780195 0.625537i \(-0.215120\pi\)
−0.625537 + 0.780195i \(0.715120\pi\)
\(68\) −24697.5 24697.5i −0.647710 0.647710i
\(69\) 2530.82i 0.0639938i
\(70\) −8030.41 829.353i −0.195881 0.0202299i
\(71\) −3271.14 −0.0770111 −0.0385056 0.999258i \(-0.512260\pi\)
−0.0385056 + 0.999258i \(0.512260\pi\)
\(72\) 11960.1 11960.1i 0.271897 0.271897i
\(73\) −25842.3 25842.3i −0.567575 0.567575i 0.363873 0.931449i \(-0.381454\pi\)
−0.931449 + 0.363873i \(0.881454\pi\)
\(74\) −9252.11 −0.196409
\(75\) 8337.86 5457.64i 0.171160 0.112034i
\(76\) 56760.9i 1.12724i
\(77\) 28835.7 + 40830.2i 0.554248 + 0.784793i
\(78\) −2742.16 + 2742.16i −0.0510337 + 0.0510337i
\(79\) 41319.9 0.744889 0.372445 0.928054i \(-0.378520\pi\)
0.372445 + 0.928054i \(0.378520\pi\)
\(80\) −5149.87 + 49864.8i −0.0899645 + 0.871103i
\(81\) −51739.3 −0.876209
\(82\) −11663.8 11663.8i −0.191560 0.191560i
\(83\) −67888.9 67888.9i −1.08169 1.08169i −0.996352 0.0853401i \(-0.972802\pi\)
−0.0853401 0.996352i \(-0.527198\pi\)
\(84\) 12176.3 0.188286
\(85\) 40171.8 + 49425.0i 0.603079 + 0.741993i
\(86\) −5131.39 −0.0748151
\(87\) −8982.93 + 8982.93i −0.127239 + 0.127239i
\(88\) −23813.6 + 16818.0i −0.327807 + 0.231508i
\(89\) 86508.1i 1.15766i −0.815447 0.578831i \(-0.803509\pi\)
0.815447 0.578831i \(-0.196491\pi\)
\(90\) −11710.6 + 9518.20i −0.152396 + 0.123865i
\(91\) 130644. 1.65381
\(92\) −17203.6 17203.6i −0.211909 0.211909i
\(93\) −9045.31 + 9045.31i −0.108447 + 0.108447i
\(94\) 30226.3 0.352830
\(95\) −10633.1 + 102958.i −0.120879 + 1.17044i
\(96\) 10728.6i 0.118814i
\(97\) −24593.2 24593.2i −0.265390 0.265390i 0.561849 0.827240i \(-0.310090\pi\)
−0.827240 + 0.561849i \(0.810090\pi\)
\(98\) −1059.75 1059.75i −0.0111465 0.0111465i
\(99\) 92083.0 + 15854.1i 0.944260 + 0.162575i
\(100\) 19578.8 93777.0i 0.195788 0.937770i
\(101\) 102376.i 0.998606i 0.866427 + 0.499303i \(0.166411\pi\)
−0.866427 + 0.499303i \(0.833589\pi\)
\(102\) 2978.71 + 2978.71i 0.0283483 + 0.0283483i
\(103\) −99062.9 + 99062.9i −0.920064 + 0.920064i −0.997033 0.0769694i \(-0.975476\pi\)
0.0769694 + 0.997033i \(0.475476\pi\)
\(104\) 76196.0i 0.690794i
\(105\) −22086.4 2281.01i −0.195502 0.0201908i
\(106\) 3941.86i 0.0340750i
\(107\) 489.464 489.464i 0.00413296 0.00413296i −0.705037 0.709170i \(-0.749070\pi\)
0.709170 + 0.705037i \(0.249070\pi\)
\(108\) 32891.7 32891.7i 0.271348 0.271348i
\(109\) 134140. 1.08141 0.540706 0.841212i \(-0.318157\pi\)
0.540706 + 0.841212i \(0.318157\pi\)
\(110\) 22675.6 12743.0i 0.178681 0.100413i
\(111\) −25446.5 −0.196029
\(112\) 78981.5 78981.5i 0.594950 0.594950i
\(113\) 113964. 113964.i 0.839601 0.839601i −0.149205 0.988806i \(-0.547671\pi\)
0.988806 + 0.149205i \(0.0476715\pi\)
\(114\) 6845.80i 0.0493358i
\(115\) 27982.6 + 34428.2i 0.197307 + 0.242756i
\(116\) 122126.i 0.842679i
\(117\) 172682. 172682.i 1.16623 1.16623i
\(118\) −18709.3 18709.3i −0.123695 0.123695i
\(119\) 141914.i 0.918663i
\(120\) 1330.36 12881.5i 0.00843367 0.0816610i
\(121\) −151778. 53860.2i −0.942421 0.334430i
\(122\) −31049.7 31049.7i −0.188868 0.188868i
\(123\) −32079.4 32079.4i −0.191189 0.191189i
\(124\) 122974.i 0.718222i
\(125\) −53081.1 + 166433.i −0.303854 + 0.952719i
\(126\) 33624.6 0.188682
\(127\) −72970.4 + 72970.4i −0.401455 + 0.401455i −0.878746 0.477290i \(-0.841619\pi\)
0.477290 + 0.878746i \(0.341619\pi\)
\(128\) 96456.0 + 96456.0i 0.520361 + 0.520361i
\(129\) −14113.1 −0.0746704
\(130\) 6983.84 67622.7i 0.0362440 0.350941i
\(131\) 170832.i 0.869741i 0.900493 + 0.434871i \(0.143206\pi\)
−0.900493 + 0.434871i \(0.856794\pi\)
\(132\) −32045.2 + 22631.4i −0.160077 + 0.113052i
\(133\) 163076. 163076.i 0.799395 0.799395i
\(134\) −9318.04 −0.0448294
\(135\) −65823.4 + 53500.1i −0.310847 + 0.252651i
\(136\) 82768.7 0.383724
\(137\) 145269. + 145269.i 0.661258 + 0.661258i 0.955677 0.294418i \(-0.0951259\pi\)
−0.294418 + 0.955677i \(0.595126\pi\)
\(138\) 2074.89 + 2074.89i 0.00927464 + 0.00927464i
\(139\) −361121. −1.58532 −0.792659 0.609665i \(-0.791304\pi\)
−0.792659 + 0.609665i \(0.791304\pi\)
\(140\) −165641. + 134630.i −0.714248 + 0.580528i
\(141\) 83132.9 0.352148
\(142\) 2681.85 2681.85i 0.0111613 0.0111613i
\(143\) −343824. + 242821.i −1.40604 + 0.992992i
\(144\) 208792.i 0.839089i
\(145\) 22878.0 221522.i 0.0903647 0.874978i
\(146\) 42373.6 0.164518
\(147\) −2914.68 2914.68i −0.0111249 0.0111249i
\(148\) −172977. + 172977.i −0.649133 + 0.649133i
\(149\) 157044. 0.579505 0.289752 0.957102i \(-0.406427\pi\)
0.289752 + 0.957102i \(0.406427\pi\)
\(150\) −2361.35 + 11310.2i −0.00856904 + 0.0410434i
\(151\) 406149.i 1.44958i −0.688968 0.724792i \(-0.741936\pi\)
0.688968 0.724792i \(-0.258064\pi\)
\(152\) 95111.5 + 95111.5i 0.333906 + 0.333906i
\(153\) −187578. 187578.i −0.647819 0.647819i
\(154\) −57115.6 9833.68i −0.194068 0.0334129i
\(155\) 23036.9 223061.i 0.0770185 0.745750i
\(156\) 102535.i 0.337333i
\(157\) −294046. 294046.i −0.952063 0.952063i 0.0468397 0.998902i \(-0.485085\pi\)
−0.998902 + 0.0468397i \(0.985085\pi\)
\(158\) −33876.1 + 33876.1i −0.107957 + 0.107957i
\(159\) 10841.5i 0.0340091i
\(160\) −118624. 145948.i −0.366330 0.450711i
\(161\) 98853.2i 0.300556i
\(162\) 42418.4 42418.4i 0.126989 0.126989i
\(163\) 321782. 321782.i 0.948620 0.948620i −0.0501226 0.998743i \(-0.515961\pi\)
0.998743 + 0.0501226i \(0.0159612\pi\)
\(164\) −436130. −1.26621
\(165\) 62365.9 35047.7i 0.178335 0.100219i
\(166\) 111317. 0.313540
\(167\) −285860. + 285860.i −0.793164 + 0.793164i −0.982007 0.188843i \(-0.939526\pi\)
0.188843 + 0.982007i \(0.439526\pi\)
\(168\) −20403.2 + 20403.2i −0.0557733 + 0.0557733i
\(169\) 728838.i 1.96297i
\(170\) −73455.9 7586.28i −0.194942 0.0201329i
\(171\) 431101.i 1.12743i
\(172\) −95936.1 + 95936.1i −0.247264 + 0.247264i
\(173\) 427806. + 427806.i 1.08675 + 1.08675i 0.995861 + 0.0908942i \(0.0289725\pi\)
0.0908942 + 0.995861i \(0.471027\pi\)
\(174\) 14729.3i 0.0368815i
\(175\) 325675. 213174.i 0.803877 0.526187i
\(176\) −61062.3 + 354659.i −0.148591 + 0.863038i
\(177\) −51457.0 51457.0i −0.123456 0.123456i
\(178\) 70923.7 + 70923.7i 0.167780 + 0.167780i
\(179\) 241635.i 0.563672i −0.959463 0.281836i \(-0.909057\pi\)
0.959463 0.281836i \(-0.0909434\pi\)
\(180\) −40989.7 + 396893.i −0.0942961 + 0.913045i
\(181\) −632254. −1.43448 −0.717241 0.696825i \(-0.754595\pi\)
−0.717241 + 0.696825i \(0.754595\pi\)
\(182\) −107108. + 107108.i −0.239687 + 0.239687i
\(183\) −85397.4 85397.4i −0.188503 0.188503i
\(184\) 57654.5 0.125542
\(185\) 346164. 281356.i 0.743623 0.604404i
\(186\) 14831.6i 0.0314344i
\(187\) 263767. + 373483.i 0.551590 + 0.781029i
\(188\) 565108. 565108.i 1.16610 1.16610i
\(189\) 188998. 0.384860
\(190\) −75692.4 93127.5i −0.152114 0.187152i
\(191\) −8107.14 −0.0160799 −0.00803997 0.999968i \(-0.502559\pi\)
−0.00803997 + 0.999968i \(0.502559\pi\)
\(192\) 55910.2 + 55910.2i 0.109456 + 0.109456i
\(193\) 422534. + 422534.i 0.816522 + 0.816522i 0.985602 0.169080i \(-0.0540797\pi\)
−0.169080 + 0.985602i \(0.554080\pi\)
\(194\) 40325.4 0.0769263
\(195\) 19208.0 185986.i 0.0361739 0.350263i
\(196\) −39626.0 −0.0736783
\(197\) −96838.2 + 96838.2i −0.177779 + 0.177779i −0.790387 0.612608i \(-0.790121\pi\)
0.612608 + 0.790387i \(0.290121\pi\)
\(198\) −88492.2 + 62496.3i −0.160414 + 0.113290i
\(199\) 377063.i 0.674965i −0.941332 0.337482i \(-0.890425\pi\)
0.941332 0.337482i \(-0.109575\pi\)
\(200\) 124330. + 189945.i 0.219787 + 0.335778i
\(201\) −25627.9 −0.0447427
\(202\) −83932.9 83932.9i −0.144728 0.144728i
\(203\) −350872. + 350872.i −0.597597 + 0.597597i
\(204\) 111379. 0.187383
\(205\) 791090. + 81701.0i 1.31474 + 0.135782i
\(206\) 162433.i 0.266690i
\(207\) −130662. 130662.i −0.211945 0.211945i
\(208\) 665090. + 665090.i 1.06591 + 1.06591i
\(209\) −126078. + 732279.i −0.199651 + 1.15961i
\(210\) 19977.6 16237.5i 0.0312605 0.0254080i
\(211\) 737422.i 1.14028i −0.821549 0.570138i \(-0.806890\pi\)
0.821549 0.570138i \(-0.193110\pi\)
\(212\) −73696.6 73696.6i −0.112618 0.112618i
\(213\) 7376.01 7376.01i 0.0111397 0.0111397i
\(214\) 802.574i 0.00119798i
\(215\) 191989. 156045.i 0.283257 0.230226i
\(216\) 110230.i 0.160755i
\(217\) −353308. + 353308.i −0.509336 + 0.509336i
\(218\) −109974. + 109974.i −0.156729 + 0.156729i
\(219\) 116542. 0.164200
\(220\) 185699. 662184.i 0.258675 0.922406i
\(221\) 1.19503e6 1.64588
\(222\) 20862.3 20862.3i 0.0284106 0.0284106i
\(223\) 16331.6 16331.6i 0.0219921 0.0219921i −0.696025 0.718017i \(-0.745050\pi\)
0.718017 + 0.696025i \(0.245050\pi\)
\(224\) 419058.i 0.558026i
\(225\) 148701. 712240.i 0.195821 0.937929i
\(226\) 186867.i 0.243367i
\(227\) −355915. + 355915.i −0.458439 + 0.458439i −0.898143 0.439704i \(-0.855083\pi\)
0.439704 + 0.898143i \(0.355083\pi\)
\(228\) 127989. + 127989.i 0.163055 + 0.163055i
\(229\) 1.50015e6i 1.89036i −0.326544 0.945182i \(-0.605884\pi\)
0.326544 0.945182i \(-0.394116\pi\)
\(230\) −51167.5 5284.40i −0.0637785 0.00658682i
\(231\) −157088. 27046.1i −0.193692 0.0333483i
\(232\) −204640. 204640.i −0.249615 0.249615i
\(233\) 191449. + 191449.i 0.231028 + 0.231028i 0.813122 0.582094i \(-0.197766\pi\)
−0.582094 + 0.813122i \(0.697766\pi\)
\(234\) 283147.i 0.338044i
\(235\) −1.13091e6 + 919180.i −1.33585 + 1.08575i
\(236\) −699574. −0.817625
\(237\) −93171.1 + 93171.1i −0.107748 + 0.107748i
\(238\) 116348. + 116348.i 0.133142 + 0.133142i
\(239\) −972477. −1.10125 −0.550624 0.834754i \(-0.685610\pi\)
−0.550624 + 0.834754i \(0.685610\pi\)
\(240\) −100827. 124051.i −0.112992 0.139019i
\(241\) 169545.i 0.188037i −0.995570 0.0940186i \(-0.970029\pi\)
0.995570 0.0940186i \(-0.0299713\pi\)
\(242\) 168592. 80277.7i 0.185054 0.0881164i
\(243\) 377390. 377390.i 0.409991 0.409991i
\(244\) −1.16100e6 −1.24842
\(245\) 71877.0 + 7423.21i 0.0765024 + 0.00790090i
\(246\) 52600.6 0.0554183
\(247\) 1.37324e6 + 1.37324e6i 1.43220 + 1.43220i
\(248\) −206061. 206061.i −0.212749 0.212749i
\(249\) 306162. 0.312934
\(250\) −92931.6 179969.i −0.0940402 0.182115i
\(251\) −550651. −0.551686 −0.275843 0.961203i \(-0.588957\pi\)
−0.275843 + 0.961203i \(0.588957\pi\)
\(252\) 628643. 628643.i 0.623596 0.623596i
\(253\) 183733. + 260158.i 0.180462 + 0.255527i
\(254\) 119649.i 0.116366i
\(255\) −202029. 20864.9i −0.194565 0.0200940i
\(256\) 635291. 0.605860
\(257\) −708471. 708471.i −0.669097 0.669097i 0.288410 0.957507i \(-0.406873\pi\)
−0.957507 + 0.288410i \(0.906873\pi\)
\(258\) 11570.6 11570.6i 0.0108220 0.0108220i
\(259\) −993937. −0.920682
\(260\) −1.13370e6 1.39484e6i −1.04008 1.27965i
\(261\) 927549.i 0.842822i
\(262\) −140056. 140056.i −0.126052 0.126052i
\(263\) −463210. 463210.i −0.412942 0.412942i 0.469820 0.882762i \(-0.344319\pi\)
−0.882762 + 0.469820i \(0.844319\pi\)
\(264\) 15774.2 91618.9i 0.0139295 0.0809050i
\(265\) 119872. + 147483.i 0.104858 + 0.129011i
\(266\) 267396.i 0.231713i
\(267\) 195065. + 195065.i 0.167456 + 0.167456i
\(268\) −174209. + 174209.i −0.148161 + 0.148161i
\(269\) 657951.i 0.554387i 0.960814 + 0.277193i \(0.0894043\pi\)
−0.960814 + 0.277193i \(0.910596\pi\)
\(270\) 10103.3 97827.4i 0.00843437 0.0816678i
\(271\) 162774.i 0.134636i −0.997732 0.0673181i \(-0.978556\pi\)
0.997732 0.0673181i \(-0.0214442\pi\)
\(272\) 722461. 722461.i 0.592096 0.592096i
\(273\) −294586. + 294586.i −0.239224 + 0.239224i
\(274\) −238197. −0.191673
\(275\) −460886. + 1.16634e6i −0.367504 + 0.930022i
\(276\) 77583.9 0.0613054
\(277\) −322956. + 322956.i −0.252897 + 0.252897i −0.822157 0.569260i \(-0.807230\pi\)
0.569260 + 0.822157i \(0.307230\pi\)
\(278\) 296065. 296065.i 0.229761 0.229761i
\(279\) 933991.i 0.718343i
\(280\) 51963.7 503151.i 0.0396100 0.383533i
\(281\) 135801.i 0.102598i −0.998683 0.0512988i \(-0.983664\pi\)
0.998683 0.0512988i \(-0.0163361\pi\)
\(282\) −68156.5 + 68156.5i −0.0510369 + 0.0510369i
\(283\) −1.20597e6 1.20597e6i −0.895099 0.895099i 0.0998984 0.994998i \(-0.468148\pi\)
−0.994998 + 0.0998984i \(0.968148\pi\)
\(284\) 100279.i 0.0737759i
\(285\) −208180. 256133.i −0.151820 0.186790i
\(286\) 82807.8 480961.i 0.0598627 0.347692i
\(287\) −1.25302e6 1.25302e6i −0.897950 0.897950i
\(288\) 553902. + 553902.i 0.393506 + 0.393506i
\(289\) 121742.i 0.0857427i
\(290\) 162858. + 200371.i 0.113714 + 0.139907i
\(291\) 110909. 0.0767776
\(292\) 792213. 792213.i 0.543732 0.543732i
\(293\) 251556. + 251556.i 0.171185 + 0.171185i 0.787500 0.616315i \(-0.211375\pi\)
−0.616315 + 0.787500i \(0.711375\pi\)
\(294\) 4779.20 0.00322468
\(295\) 1.26895e6 + 131053.i 0.848963 + 0.0876780i
\(296\) 579697.i 0.384567i
\(297\) −497398. + 351280.i −0.327200 + 0.231080i
\(298\) −128753. + 128753.i −0.0839878 + 0.0839878i
\(299\) 832426. 0.538478
\(300\) 167308. + 255603.i 0.107328 + 0.163969i
\(301\) −551256. −0.350701
\(302\) 332981. + 332981.i 0.210089 + 0.210089i
\(303\) −230845. 230845.i −0.144449 0.144449i
\(304\) 1.66039e6 1.03045
\(305\) 2.10593e6 + 217493.i 1.29627 + 0.133874i
\(306\) 307572. 0.187777
\(307\) −1.73184e6 + 1.73184e6i −1.04873 + 1.04873i −0.0499766 + 0.998750i \(0.515915\pi\)
−0.998750 + 0.0499766i \(0.984085\pi\)
\(308\) −1.25168e6 + 883979.i −0.751824 + 0.530964i
\(309\) 446749.i 0.266175i
\(310\) 163989. + 201763.i 0.0969195 + 0.119244i
\(311\) 750807. 0.440177 0.220088 0.975480i \(-0.429365\pi\)
0.220088 + 0.975480i \(0.429365\pi\)
\(312\) −171812. 171812.i −0.0999235 0.0999235i
\(313\) −15556.4 + 15556.4i −0.00897526 + 0.00897526i −0.711580 0.702605i \(-0.752020\pi\)
0.702605 + 0.711580i \(0.252020\pi\)
\(314\) 482146. 0.275966
\(315\) −1.25805e6 + 1.02252e6i −0.714369 + 0.580626i
\(316\) 1.26669e6i 0.713597i
\(317\) 1.39427e6 + 1.39427e6i 0.779289 + 0.779289i 0.979710 0.200421i \(-0.0642308\pi\)
−0.200421 + 0.979710i \(0.564231\pi\)
\(318\) 8888.38 + 8888.38i 0.00492896 + 0.00492896i
\(319\) 271266. 1.57556e6i 0.149252 0.866877i
\(320\) −1.37877e6 142394.i −0.752689 0.0777351i
\(321\) 2207.36i 0.00119567i
\(322\) 81044.8 + 81044.8i 0.0435597 + 0.0435597i
\(323\) 1.49169e6 1.49169e6i 0.795561 0.795561i
\(324\) 1.58610e6i 0.839400i
\(325\) 1.79510e6 + 2.74246e6i 0.942717 + 1.44023i
\(326\) 527626.i 0.274968i
\(327\) −302468. + 302468.i −0.156426 + 0.156426i
\(328\) 730801. 730801.i 0.375072 0.375072i
\(329\) 3.24715e6 1.65391
\(330\) −22396.8 + 79864.6i −0.0113214 + 0.0403710i
\(331\) −1.98487e6 −0.995779 −0.497889 0.867241i \(-0.665891\pi\)
−0.497889 + 0.867241i \(0.665891\pi\)
\(332\) 2.08118e6 2.08118e6i 1.03625 1.03625i
\(333\) −1.31376e6 + 1.31376e6i −0.649243 + 0.649243i
\(334\) 468725.i 0.229907i
\(335\) 348631. 283361.i 0.169728 0.137952i
\(336\) 356187.i 0.172119i
\(337\) −120865. + 120865.i −0.0579729 + 0.0579729i −0.735499 0.677526i \(-0.763052\pi\)
0.677526 + 0.735499i \(0.263052\pi\)
\(338\) −597538. 597538.i −0.284494 0.284494i
\(339\) 513950.i 0.242897i
\(340\) −1.51516e6 + 1.23149e6i −0.710822 + 0.577744i
\(341\) 273150. 1.58650e6i 0.127208 0.738846i
\(342\) 353438. + 353438.i 0.163399 + 0.163399i
\(343\) −1.59412e6 1.59412e6i −0.731621 0.731621i
\(344\) 321511.i 0.146487i
\(345\) −140728. 14533.9i −0.0636552 0.00657409i
\(346\) −701473. −0.315007
\(347\) 1.39645e6 1.39645e6i 0.622591 0.622591i −0.323602 0.946193i \(-0.604894\pi\)
0.946193 + 0.323602i \(0.104894\pi\)
\(348\) −275378. 275378.i −0.121894 0.121894i
\(349\) 3.13019e6 1.37565 0.687824 0.725878i \(-0.258566\pi\)
0.687824 + 0.725878i \(0.258566\pi\)
\(350\) −92233.9 + 441776.i −0.0402458 + 0.192767i
\(351\) 1.59152e6i 0.689516i
\(352\) −778881. 1.10286e6i −0.335054 0.474422i
\(353\) −23224.5 + 23224.5i −0.00991995 + 0.00991995i −0.712049 0.702129i \(-0.752233\pi\)
0.702129 + 0.712049i \(0.252233\pi\)
\(354\) 84374.1 0.0357850
\(355\) −18785.5 + 181895.i −0.00791136 + 0.0766037i
\(356\) 2.65197e6 1.10903
\(357\) 319997. + 319997.i 0.132885 + 0.132885i
\(358\) 198104. + 198104.i 0.0816932 + 0.0816932i
\(359\) 690277. 0.282675 0.141338 0.989961i \(-0.454860\pi\)
0.141338 + 0.989961i \(0.454860\pi\)
\(360\) −596370. 733739.i −0.242527 0.298391i
\(361\) 952181. 0.384549
\(362\) 518353. 518353.i 0.207900 0.207900i
\(363\) 463688. 220792.i 0.184697 0.0879460i
\(364\) 4.00498e6i 1.58434i
\(365\) −1.58539e6 + 1.28858e6i −0.622880 + 0.506265i
\(366\) 140026. 0.0546395
\(367\) −84271.0 84271.0i −0.0326597 0.0326597i 0.690588 0.723248i \(-0.257352\pi\)
−0.723248 + 0.690588i \(0.757352\pi\)
\(368\) 503247. 503247.i 0.193714 0.193714i
\(369\) −3.31242e6 −1.26643
\(370\) −53132.9 + 514472.i −0.0201771 + 0.195370i
\(371\) 423466.i 0.159729i
\(372\) −277290. 277290.i −0.103891 0.103891i
\(373\) −1.52634e6 1.52634e6i −0.568042 0.568042i 0.363538 0.931579i \(-0.381569\pi\)
−0.931579 + 0.363538i \(0.881569\pi\)
\(374\) −522449. 89950.9i −0.193137 0.0332527i
\(375\) −255594. 494977.i −0.0938584 0.181763i
\(376\) 1.89385e6i 0.690837i
\(377\) −2.95463e6 2.95463e6i −1.07066 1.07066i
\(378\) −154950. + 154950.i −0.0557779 + 0.0557779i
\(379\) 2.00045e6i 0.715368i 0.933843 + 0.357684i \(0.116433\pi\)
−0.933843 + 0.357684i \(0.883567\pi\)
\(380\) −3.15624e6 325966.i −1.12127 0.115801i
\(381\) 329078.i 0.116141i
\(382\) 6646.64 6646.64i 0.00233047 0.00233047i
\(383\) −3.76908e6 + 3.76908e6i −1.31292 + 1.31292i −0.393665 + 0.919254i \(0.628793\pi\)
−0.919254 + 0.393665i \(0.871207\pi\)
\(384\) −434992. −0.150540
\(385\) 2.43600e6 1.36896e6i 0.837579 0.470694i
\(386\) −692828. −0.236678
\(387\) −728638. + 728638.i −0.247306 + 0.247306i
\(388\) 753921. 753921.i 0.254242 0.254242i
\(389\) 4.53726e6i 1.52026i −0.649768 0.760132i \(-0.725134\pi\)
0.649768 0.760132i \(-0.274866\pi\)
\(390\) 136733. + 168228.i 0.0455210 + 0.0560064i
\(391\) 904232.i 0.299115i
\(392\) 66399.3 66399.3i 0.0218247 0.0218247i
\(393\) −385204. 385204.i −0.125808 0.125808i
\(394\) 158786.i 0.0515312i
\(395\) 237291. 2.29763e6i 0.0765225 0.740948i
\(396\) −486017. + 2.82287e6i −0.155745 + 0.904592i
\(397\) 3.97395e6 + 3.97395e6i 1.26545 + 1.26545i 0.948412 + 0.317041i \(0.102689\pi\)
0.317041 + 0.948412i \(0.397311\pi\)
\(398\) 309135. + 309135.i 0.0978228 + 0.0978228i
\(399\) 735432.i 0.231265i
\(400\) 2.74321e6 + 572726.i 0.857252 + 0.178977i
\(401\) 185273. 0.0575374 0.0287687 0.999586i \(-0.490841\pi\)
0.0287687 + 0.999586i \(0.490841\pi\)
\(402\) 21011.0 21011.0i 0.00648457 0.00648457i
\(403\) −2.97515e6 2.97515e6i −0.912528 0.912528i
\(404\) −3.13840e6 −0.956655
\(405\) −297128. + 2.87701e6i −0.0900131 + 0.871573i
\(406\) 575324.i 0.173220i
\(407\) 2.61581e6 1.84738e6i 0.782745 0.552802i
\(408\) −186633. + 186633.i −0.0555058 + 0.0555058i
\(409\) 2.72097e6 0.804295 0.402148 0.915575i \(-0.368264\pi\)
0.402148 + 0.915575i \(0.368264\pi\)
\(410\) −715557. + 581592.i −0.210225 + 0.170867i
\(411\) −655126. −0.191302
\(412\) −3.03684e6 3.03684e6i −0.881413 0.881413i
\(413\) −2.00990e6 2.00990e6i −0.579829 0.579829i
\(414\) 214246. 0.0614346
\(415\) −4.16490e6 + 3.38515e6i −1.18709 + 0.964847i
\(416\) −3.52882e6 −0.999761
\(417\) 814283. 814283.i 0.229316 0.229316i
\(418\) −496994. 703723.i −0.139127 0.196998i
\(419\) 3.36223e6i 0.935604i 0.883833 + 0.467802i \(0.154954\pi\)
−0.883833 + 0.467802i \(0.845046\pi\)
\(420\) 69925.9 677075.i 0.0193426 0.187290i
\(421\) −798459. −0.219557 −0.109778 0.993956i \(-0.535014\pi\)
−0.109778 + 0.993956i \(0.535014\pi\)
\(422\) 604576. + 604576.i 0.165261 + 0.165261i
\(423\) 4.29202e6 4.29202e6i 1.16630 1.16630i
\(424\) 246980. 0.0667186
\(425\) 2.97902e6 1.94995e6i 0.800022 0.523663i
\(426\) 12094.4i 0.00322895i
\(427\) −3.33561e6 3.33561e6i −0.885330 0.885330i
\(428\) 15004.9 + 15004.9i 0.00395934 + 0.00395934i
\(429\) 227750. 1.32281e6i 0.0597469 0.347020i
\(430\) −29468.5 + 285336.i −0.00768576 + 0.0744192i
\(431\) 3.94706e6i 1.02348i −0.859139 0.511742i \(-0.829000\pi\)
0.859139 0.511742i \(-0.171000\pi\)
\(432\) 962162. + 962162.i 0.248050 + 0.248050i
\(433\) 1.70841e6 1.70841e6i 0.437897 0.437897i −0.453407 0.891304i \(-0.649792\pi\)
0.891304 + 0.453407i \(0.149792\pi\)
\(434\) 579320.i 0.147637i
\(435\) 447917. + 551091.i 0.113494 + 0.139637i
\(436\) 4.11214e6i 1.03598i
\(437\) 1.03907e6 1.03907e6i 0.260281 0.260281i
\(438\) −95547.0 + 95547.0i −0.0237975 + 0.0237975i
\(439\) −678707. −0.168082 −0.0840409 0.996462i \(-0.526783\pi\)
−0.0840409 + 0.996462i \(0.526783\pi\)
\(440\) 798423. + 1.42076e6i 0.196608 + 0.349855i
\(441\) −300961. −0.0736908
\(442\) −979745. + 979745.i −0.238538 + 0.238538i
\(443\) −1.67407e6 + 1.67407e6i −0.405289 + 0.405289i −0.880092 0.474803i \(-0.842519\pi\)
0.474803 + 0.880092i \(0.342519\pi\)
\(444\) 780081.i 0.187794i
\(445\) −4.81036e6 496798.i −1.15154 0.118927i
\(446\) 26779.0i 0.00637466i
\(447\) −354115. + 354115.i −0.0838255 + 0.0838255i
\(448\) 2.18384e6 + 2.18384e6i 0.514075 + 0.514075i
\(449\) 1.54007e6i 0.360515i 0.983619 + 0.180258i \(0.0576931\pi\)
−0.983619 + 0.180258i \(0.942307\pi\)
\(450\) 462017. + 705842.i 0.107554 + 0.164315i
\(451\) 5.62656e6 + 968733.i 1.30257 + 0.224266i
\(452\) 3.49366e6 + 3.49366e6i 0.804330 + 0.804330i
\(453\) 915815. + 915815.i 0.209683 + 0.209683i
\(454\) 583594.i 0.132884i
\(455\) 750261. 7.26458e6i 0.169896 1.64506i
\(456\) −428929. −0.0965991
\(457\) −2.37478e6 + 2.37478e6i −0.531904 + 0.531904i −0.921139 0.389235i \(-0.872739\pi\)
0.389235 + 0.921139i \(0.372739\pi\)
\(458\) 1.22990e6 + 1.22990e6i 0.273971 + 0.273971i
\(459\) 1.72881e6 0.383014
\(460\) −1.05542e6 + 857826.i −0.232558 + 0.189019i
\(461\) 4.89233e6i 1.07217i 0.844164 + 0.536084i \(0.180097\pi\)
−0.844164 + 0.536084i \(0.819903\pi\)
\(462\) 150962. 106615.i 0.0329051 0.0232387i
\(463\) −5.39140e6 + 5.39140e6i −1.16882 + 1.16882i −0.186338 + 0.982486i \(0.559662\pi\)
−0.982486 + 0.186338i \(0.940338\pi\)
\(464\) −3.57247e6 −0.770325
\(465\) 451028. + 554919.i 0.0967322 + 0.119014i
\(466\) −313919. −0.0669659
\(467\) 692307. + 692307.i 0.146895 + 0.146895i 0.776729 0.629835i \(-0.216877\pi\)
−0.629835 + 0.776729i \(0.716877\pi\)
\(468\) 5.29370e6 + 5.29370e6i 1.11724 + 1.11724i
\(469\) −1.00102e6 −0.210141
\(470\) 173583. 1.68076e6i 0.0362462 0.350963i
\(471\) 1.32607e6 0.275432
\(472\) 1.17224e6 1.17224e6i 0.242194 0.242194i
\(473\) 1.45078e6 1.02459e6i 0.298159 0.210570i
\(474\) 152773.i 0.0312320i
\(475\) 5.66400e6 + 1.18253e6i 1.15183 + 0.240480i
\(476\) 4.35046e6 0.880071
\(477\) −559729. 559729.i −0.112637 0.112637i
\(478\) 797285. 797285.i 0.159604 0.159604i
\(479\) 6.45641e6 1.28574 0.642869 0.765976i \(-0.277744\pi\)
0.642869 + 0.765976i \(0.277744\pi\)
\(480\) 596575. + 61612.2i 0.118185 + 0.0122057i
\(481\) 8.36978e6i 1.64950i
\(482\) 139002. + 139002.i 0.0272523 + 0.0272523i
\(483\) 222901. + 222901.i 0.0434755 + 0.0434755i
\(484\) 1.65112e6 4.65285e6i 0.320380 0.902830i
\(485\) −1.50876e6 + 1.22629e6i −0.291250 + 0.236723i
\(486\) 618806.i 0.118840i
\(487\) 1.03959e6 + 1.03959e6i 0.198627 + 0.198627i 0.799411 0.600784i \(-0.205145\pi\)
−0.600784 + 0.799411i \(0.705145\pi\)
\(488\) 1.94544e6 1.94544e6i 0.369801 0.369801i
\(489\) 1.45115e6i 0.274436i
\(490\) −65014.3 + 52842.4i −0.0122326 + 0.00994243i
\(491\) 2.84028e6i 0.531689i −0.964016 0.265844i \(-0.914349\pi\)
0.964016 0.265844i \(-0.0856507\pi\)
\(492\) 983417. 983417.i 0.183158 0.183158i
\(493\) −3.20950e6 + 3.20950e6i −0.594730 + 0.594730i
\(494\) −2.25170e6 −0.415138
\(495\) 1.41039e6 5.02931e6i 0.258718 0.922562i
\(496\) −3.59728e6 −0.656554
\(497\) 288106. 288106.i 0.0523192 0.0523192i
\(498\) −251007. + 251007.i −0.0453536 + 0.0453536i
\(499\) 3.97737e6i 0.715064i −0.933901 0.357532i \(-0.883618\pi\)
0.933901 0.357532i \(-0.116382\pi\)
\(500\) −5.10212e6 1.62724e6i −0.912695 0.291089i
\(501\) 1.28916e6i 0.229463i
\(502\) 451451. 451451.i 0.0799560 0.0799560i
\(503\) 6.10079e6 + 6.10079e6i 1.07514 + 1.07514i 0.996937 + 0.0782056i \(0.0249191\pi\)
0.0782056 + 0.996937i \(0.475081\pi\)
\(504\) 2.10677e6i 0.369438i
\(505\) 5.69271e6 + 587923.i 0.993323 + 0.102587i
\(506\) −363924. 62657.4i −0.0631880 0.0108792i
\(507\) −1.64344e6 1.64344e6i −0.283944 0.283944i
\(508\) −2.23696e6 2.23696e6i −0.384590 0.384590i
\(509\) 1.28443e6i 0.219743i −0.993946 0.109871i \(-0.964956\pi\)
0.993946 0.109871i \(-0.0350439\pi\)
\(510\) 182740. 148528.i 0.0311106 0.0252861i
\(511\) 4.55211e6 0.771189
\(512\) −3.60744e6 + 3.60744e6i −0.608168 + 0.608168i
\(513\) 1.98661e6 + 1.98661e6i 0.333288 + 0.333288i
\(514\) 1.16168e6 0.193945
\(515\) 4.93959e6 + 6.07738e6i 0.820678 + 1.00971i
\(516\) 432647.i 0.0715336i
\(517\) −8.54575e6 + 6.03531e6i −1.40612 + 0.993054i
\(518\) 814879. 814879.i 0.133435 0.133435i
\(519\) −1.92930e6 −0.314399
\(520\) 4.23695e6 + 437577.i 0.687139 + 0.0709654i
\(521\) −6.78721e6 −1.09546 −0.547731 0.836655i \(-0.684508\pi\)
−0.547731 + 0.836655i \(0.684508\pi\)
\(522\) −760451. 760451.i −0.122150 0.122150i
\(523\) −2.29263e6 2.29263e6i −0.366506 0.366506i 0.499695 0.866201i \(-0.333445\pi\)
−0.866201 + 0.499695i \(0.833445\pi\)
\(524\) −5.23696e6 −0.833204
\(525\) −253675. + 1.21504e6i −0.0401680 + 0.192394i
\(526\) 759526. 0.119696
\(527\) −3.23179e6 + 3.23179e6i −0.506893 + 0.506893i
\(528\) −662024. 937400.i −0.103345 0.146332i
\(529\) 5.80648e6i 0.902139i
\(530\) −219191. 22637.2i −0.0338947 0.00350053i
\(531\) −5.31329e6 −0.817763
\(532\) 4.99921e6 + 4.99921e6i 0.765813 + 0.765813i
\(533\) 1.05514e7 1.05514e7i 1.60877 1.60877i
\(534\) −319848. −0.0485389
\(535\) −24406.2 30028.0i −0.00368652 0.00453568i
\(536\) 583828.i 0.0877755i
\(537\) 544855. + 544855.i 0.0815353 + 0.0815353i
\(538\) −539421. 539421.i −0.0803475 0.0803475i
\(539\) 511219. + 88017.4i 0.0757941 + 0.0130496i
\(540\) −1.64008e6 2.01786e6i −0.242037 0.297788i
\(541\) 2.13626e6i 0.313805i 0.987614 + 0.156903i \(0.0501509\pi\)
−0.987614 + 0.156903i \(0.949849\pi\)
\(542\) 133450. + 133450.i 0.0195129 + 0.0195129i
\(543\) 1.42565e6 1.42565e6i 0.207498 0.207498i
\(544\) 3.83322e6i 0.555350i
\(545\) 770336. 7.45896e6i 0.111094 1.07569i
\(546\) 483032.i 0.0693417i
\(547\) −3.51247e6 + 3.51247e6i −0.501932 + 0.501932i −0.912038 0.410106i \(-0.865492\pi\)
0.410106 + 0.912038i \(0.365492\pi\)
\(548\) −4.45332e6 + 4.45332e6i −0.633479 + 0.633479i
\(549\) −8.81787e6 −1.24863
\(550\) −578366. 1.33408e6i −0.0815260 0.188051i
\(551\) −7.37622e6 −1.03504
\(552\) −130004. + 130004.i −0.0181597 + 0.0181597i
\(553\) −3.63925e6 + 3.63925e6i −0.506056 + 0.506056i
\(554\) 529550.i 0.0733049i
\(555\) −146134. + 1.41498e6i −0.0201381 + 0.194992i
\(556\) 1.10704e7i 1.51872i
\(557\) −1.23335e6 + 1.23335e6i −0.168442 + 0.168442i −0.786294 0.617852i \(-0.788003\pi\)
0.617852 + 0.786294i \(0.288003\pi\)
\(558\) −765732. 765732.i −0.104110 0.104110i
\(559\) 4.64203e6i 0.628317i
\(560\) −3.93827e6 4.84542e6i −0.530683 0.652921i
\(561\) −1.43692e6 247396.i −0.192764 0.0331884i
\(562\) 111336. + 111336.i 0.0148695 + 0.0148695i
\(563\) 4.59650e6 + 4.59650e6i 0.611161 + 0.611161i 0.943249 0.332087i \(-0.107753\pi\)
−0.332087 + 0.943249i \(0.607753\pi\)
\(564\) 2.54850e6i 0.337354i
\(565\) −5.68262e6 6.99157e6i −0.748907 0.921411i
\(566\) 1.97743e6 0.259454
\(567\) 4.55693e6 4.55693e6i 0.595271 0.595271i
\(568\) 168033. + 168033.i 0.0218536 + 0.0218536i
\(569\) −1.33573e7 −1.72957 −0.864785 0.502143i \(-0.832545\pi\)
−0.864785 + 0.502143i \(0.832545\pi\)
\(570\) 380667. + 39314.0i 0.0490748 + 0.00506828i
\(571\) 9.47840e6i 1.21659i −0.793711 0.608296i \(-0.791854\pi\)
0.793711 0.608296i \(-0.208146\pi\)
\(572\) −7.44384e6 1.05402e7i −0.951277 1.34697i
\(573\) 18280.6 18280.6i 0.00232597 0.00232597i
\(574\) 2.05457e6 0.260280
\(575\) 2.07511e6 1.35829e6i 0.261741 0.171325i
\(576\) 5.77312e6 0.725027
\(577\) 6.28321e6 + 6.28321e6i 0.785674 + 0.785674i 0.980782 0.195108i \(-0.0625057\pi\)
−0.195108 + 0.980782i \(0.562506\pi\)
\(578\) −99810.5 99810.5i −0.0124267 0.0124267i
\(579\) −1.90552e6 −0.236220
\(580\) 6.79091e6 + 701342.i 0.838220 + 0.0865685i
\(581\) 1.19586e7 1.46974
\(582\) −90928.7 + 90928.7i −0.0111274 + 0.0111274i
\(583\) 787073. + 1.11446e6i 0.0959056 + 0.135798i
\(584\) 2.65494e6i 0.322124i
\(585\) −8.61049e6 1.05938e7i −1.04025 1.27986i
\(586\) −412476. −0.0496198
\(587\) 4.86606e6 + 4.86606e6i 0.582884 + 0.582884i 0.935695 0.352811i \(-0.114774\pi\)
−0.352811 + 0.935695i \(0.614774\pi\)
\(588\) 89351.6 89351.6i 0.0106576 0.0106576i
\(589\) −7.42745e6 −0.882168
\(590\) −1.14779e6 + 932904.i −0.135748 + 0.110333i
\(591\) 436716.i 0.0514316i
\(592\) −5.05999e6 5.05999e6i −0.593397 0.593397i
\(593\) 6.68231e6 + 6.68231e6i 0.780351 + 0.780351i 0.979890 0.199539i \(-0.0639445\pi\)
−0.199539 + 0.979890i \(0.563945\pi\)
\(594\) 119795. 695789.i 0.0139307 0.0809117i
\(595\) −7.89124e6 814979.i −0.913803 0.0943744i
\(596\) 4.81431e6i 0.555160i
\(597\) 850229. + 850229.i 0.0976337 + 0.0976337i
\(598\) −682464. + 682464.i −0.0780417 + 0.0780417i
\(599\) 9.73065e6i 1.10809i 0.832487 + 0.554045i \(0.186916\pi\)
−0.832487 + 0.554045i \(0.813084\pi\)
\(600\) −708651. 147952.i −0.0803626 0.0167781i
\(601\) 1.28500e6i 0.145117i −0.997364 0.0725584i \(-0.976884\pi\)
0.997364 0.0725584i \(-0.0231164\pi\)
\(602\) 451947. 451947.i 0.0508272 0.0508272i
\(603\) −1.32313e6 + 1.32313e6i −0.148186 + 0.148186i
\(604\) 1.24508e7 1.38869
\(605\) −3.86658e6 + 8.13044e6i −0.429475 + 0.903079i
\(606\) 378516. 0.0418700
\(607\) −2.93816e6 + 2.93816e6i −0.323671 + 0.323671i −0.850174 0.526502i \(-0.823503\pi\)
0.526502 + 0.850174i \(0.323503\pi\)
\(608\) −4.40484e6 + 4.40484e6i −0.483249 + 0.483249i
\(609\) 1.58234e6i 0.172885i
\(610\) −1.90486e6 + 1.54823e6i −0.207271 + 0.168466i
\(611\) 2.73437e7i 2.96316i
\(612\) 5.75034e6 5.75034e6i 0.620605 0.620605i
\(613\) −2.21322e6 2.21322e6i −0.237889 0.237889i 0.578087 0.815975i \(-0.303800\pi\)
−0.815975 + 0.578087i \(0.803800\pi\)
\(614\) 2.83970e6i 0.303985i
\(615\) −1.96803e6 + 1.59958e6i −0.209819 + 0.170537i
\(616\) 616136. 3.57862e6i 0.0654222 0.379983i
\(617\) 1.25927e6 + 1.25927e6i 0.133170 + 0.133170i 0.770550 0.637380i \(-0.219982\pi\)
−0.637380 + 0.770550i \(0.719982\pi\)
\(618\) 366267. + 366267.i 0.0385768 + 0.0385768i
\(619\) 1.33220e7i 1.39747i −0.715380 0.698735i \(-0.753746\pi\)
0.715380 0.698735i \(-0.246254\pi\)
\(620\) 6.83808e6 + 706213.i 0.714422 + 0.0737830i
\(621\) 1.20424e6 0.125310
\(622\) −615549. + 615549.i −0.0637950 + 0.0637950i
\(623\) 7.61920e6 + 7.61920e6i 0.786482 + 0.786482i
\(624\) −2.99939e6 −0.308369
\(625\) 8.94984e6 + 3.90741e6i 0.916463 + 0.400119i
\(626\) 25507.8i 0.00260158i
\(627\) −1.36691e6 1.93548e6i −0.138858 0.196617i
\(628\) 9.01417e6 9.01417e6i 0.912067 0.912067i
\(629\) −9.09176e6 −0.916266
\(630\) 193099. 1.86973e6i 0.0193834 0.187684i
\(631\) −9.67806e6 −0.967642 −0.483821 0.875167i \(-0.660751\pi\)
−0.483821 + 0.875167i \(0.660751\pi\)
\(632\) −2.12253e6 2.12253e6i −0.211379 0.211379i
\(633\) 1.66279e6 + 1.66279e6i 0.164941 + 0.164941i
\(634\) −2.28618e6 −0.225885
\(635\) 3.63853e6 + 4.47664e6i 0.358090 + 0.440573i
\(636\) 332353. 0.0325804
\(637\) 958685. 958685.i 0.0936111 0.0936111i
\(638\) 1.06932e6 + 1.51412e6i 0.104006 + 0.147268i
\(639\) 761624.i 0.0737884i
\(640\) 5.91745e6 4.80960e6i 0.571064 0.464151i
\(641\) −4.75399e6 −0.456997 −0.228498 0.973544i \(-0.573382\pi\)
−0.228498 + 0.973544i \(0.573382\pi\)
\(642\) −1809.70 1809.70i −0.000173288 0.000173288i
\(643\) 8.80966e6 8.80966e6i 0.840295 0.840295i −0.148602 0.988897i \(-0.547477\pi\)
0.988897 + 0.148602i \(0.0474774\pi\)
\(644\) 3.03041e6 0.287930
\(645\) −81048.7 + 784773.i −0.00767090 + 0.0742754i
\(646\) 2.44593e6i 0.230602i
\(647\) −4.90324e6 4.90324e6i −0.460492 0.460492i 0.438325 0.898817i \(-0.355572\pi\)
−0.898817 + 0.438325i \(0.855572\pi\)
\(648\) 2.65776e6 + 2.65776e6i 0.248644 + 0.248644i
\(649\) 9.02529e6 + 1.55390e6i 0.841103 + 0.144814i
\(650\) −3.72012e6 776686.i −0.345361 0.0721045i
\(651\) 1.59333e6i 0.147351i
\(652\) 9.86444e6 + 9.86444e6i 0.908769 + 0.908769i
\(653\) −9.36700e6 + 9.36700e6i −0.859642 + 0.859642i −0.991296 0.131653i \(-0.957971\pi\)
0.131653 + 0.991296i \(0.457971\pi\)
\(654\) 495957.i 0.0453419i
\(655\) 9.49925e6 + 981050.i 0.865140 + 0.0893486i
\(656\) 1.27579e7i 1.15749i
\(657\) 6.01688e6 6.01688e6i 0.543824 0.543824i
\(658\) −2.66218e6 + 2.66218e6i −0.239702 + 0.239702i
\(659\) 1.65001e7 1.48004 0.740020 0.672585i \(-0.234816\pi\)
0.740020 + 0.672585i \(0.234816\pi\)
\(660\) 1.07441e6 + 1.91187e6i 0.0960089 + 0.170844i
\(661\) 3.06152e6 0.272542 0.136271 0.990672i \(-0.456488\pi\)
0.136271 + 0.990672i \(0.456488\pi\)
\(662\) 1.62730e6 1.62730e6i 0.144319 0.144319i
\(663\) −2.69464e6 + 2.69464e6i −0.238077 + 0.238077i
\(664\) 6.97467e6i 0.613908i
\(665\) −8.13149e6 1.00045e7i −0.713044 0.877287i
\(666\) 2.15418e6i 0.188190i
\(667\) −2.23565e6 + 2.23565e6i −0.194576 + 0.194576i
\(668\) −8.76325e6 8.76325e6i −0.759843 0.759843i
\(669\) 73651.5i 0.00636233i
\(670\) −53511.5 + 518138.i −0.00460533 + 0.0445922i
\(671\) 1.49783e7 + 2.57883e6i 1.28427 + 0.221114i
\(672\) −944923. 944923.i −0.0807185 0.0807185i
\(673\) −1.46489e6 1.46489e6i −0.124672 0.124672i 0.642018 0.766690i \(-0.278098\pi\)
−0.766690 + 0.642018i \(0.778098\pi\)
\(674\) 198182.i 0.0168041i
\(675\) 2.59691e6 + 3.96741e6i 0.219381 + 0.335157i
\(676\) −2.23430e7 −1.88051
\(677\) 1.01776e6 1.01776e6i 0.0853441 0.0853441i −0.663146 0.748490i \(-0.730779\pi\)
0.748490 + 0.663146i \(0.230779\pi\)
\(678\) −421362. 421362.i −0.0352031 0.0352031i
\(679\) 4.33208e6 0.360597
\(680\) 475323. 4.60243e6i 0.0394200 0.381694i
\(681\) 1.60509e6i 0.132627i
\(682\) 1.07675e6 + 1.52463e6i 0.0886449 + 0.125518i
\(683\) 1.70844e7 1.70844e7i 1.40136 1.40136i 0.605548 0.795809i \(-0.292954\pi\)
0.795809 0.605548i \(-0.207046\pi\)
\(684\) 1.32157e7 1.08007
\(685\) 8.91206e6 7.24357e6i 0.725691 0.589829i
\(686\) 2.61388e6 0.212068
\(687\) 3.38264e6 + 3.38264e6i 0.273441 + 0.273441i
\(688\) −2.80636e6 2.80636e6i −0.226034 0.226034i
\(689\) 3.56594e6 0.286171
\(690\) 127292. 103460.i 0.0101784 0.00827279i
\(691\) 1.82141e6 0.145115 0.0725577 0.997364i \(-0.476884\pi\)
0.0725577 + 0.997364i \(0.476884\pi\)
\(692\) −1.31147e7 + 1.31147e7i −1.04110 + 1.04110i
\(693\) −9.50655e6 + 6.71386e6i −0.751951 + 0.531054i
\(694\) 2.28977e6i 0.180465i
\(695\) −2.07384e6 + 2.00805e7i −0.162860 + 1.57693i
\(696\) 922875. 0.0722137
\(697\) −1.14616e7 1.14616e7i −0.893643 0.893643i
\(698\) −2.56629e6 + 2.56629e6i −0.199373 + 0.199373i
\(699\) −863388. −0.0668364
\(700\) 6.53501e6 + 9.98380e6i 0.504082 + 0.770107i
\(701\) 1.47651e7i 1.13486i 0.823422 + 0.567429i \(0.192062\pi\)
−0.823422 + 0.567429i \(0.807938\pi\)
\(702\) −1.30481e6 1.30481e6i −0.0999318 0.0999318i
\(703\) −1.04476e7 1.04476e7i −0.797309 0.797309i
\(704\) −9.80636e6 1.68838e6i −0.745720 0.128392i
\(705\) 477414. 4.62268e6i 0.0361762 0.350285i
\(706\) 38081.2i 0.00287540i
\(707\) −9.01675e6 9.01675e6i −0.678425 0.678425i
\(708\) 1.57745e6 1.57745e6i 0.118270 0.118270i
\(709\) 1.67676e7i 1.25273i 0.779532 + 0.626363i \(0.215457\pi\)
−0.779532 + 0.626363i \(0.784543\pi\)
\(710\) −133725. 164528.i −0.00995560 0.0122488i
\(711\) 9.62056e6i 0.713717i
\(712\) −4.44377e6 + 4.44377e6i −0.328512 + 0.328512i
\(713\) −2.25118e6 + 2.25118e6i −0.165839 + 0.165839i
\(714\) −524699. −0.0385181
\(715\) 1.15278e7 + 2.05131e7i 0.843296 + 1.50061i
\(716\) 7.40748e6 0.539993
\(717\) 2.19281e6 2.19281e6i 0.159296 0.159296i
\(718\) −565924. + 565924.i −0.0409682 + 0.0409682i
\(719\) 1.39297e7i 1.00489i 0.864609 + 0.502445i \(0.167566\pi\)
−0.864609 + 0.502445i \(0.832434\pi\)
\(720\) −1.16101e7 1.19905e6i −0.834649 0.0861997i
\(721\) 1.74499e7i 1.25013i
\(722\) −780646. + 780646.i −0.0557328 + 0.0557328i
\(723\) 382304. + 382304.i 0.0271996 + 0.0271996i
\(724\) 1.93822e7i 1.37422i
\(725\) −1.21866e7 2.54431e6i −0.861065 0.179773i
\(726\) −199138. + 561170.i −0.0140221 + 0.0395142i
\(727\) 8.02094e6 + 8.02094e6i 0.562846 + 0.562846i 0.930115 0.367269i \(-0.119707\pi\)
−0.367269 + 0.930115i \(0.619707\pi\)
\(728\) −6.71095e6 6.71095e6i −0.469306 0.469306i
\(729\) 1.08707e7i 0.757599i
\(730\) 243342. 2.35622e6i 0.0169009 0.163647i
\(731\) −5.04246e6 −0.349019
\(732\) 2.61792e6 2.61792e6i 0.180584 0.180584i
\(733\) −1.26801e7 1.26801e7i −0.871691 0.871691i 0.120966 0.992657i \(-0.461401\pi\)
−0.992657 + 0.120966i \(0.961401\pi\)
\(734\) 138179. 0.00946677
\(735\) −178812. + 145335.i −0.0122089 + 0.00992321i
\(736\) 2.67012e6i 0.181692i
\(737\) 2.63445e6 1.86054e6i 0.178657 0.126174i
\(738\) 2.71569e6 2.71569e6i 0.183543 0.183543i
\(739\) 8.77406e6 0.591002 0.295501 0.955342i \(-0.404513\pi\)
0.295501 + 0.955342i \(0.404513\pi\)
\(740\) 8.62517e6 + 1.06119e7i 0.579013 + 0.712384i
\(741\) −6.19295e6 −0.414335
\(742\) 347179. + 347179.i 0.0231496 + 0.0231496i
\(743\) −9.85338e6 9.85338e6i −0.654807 0.654807i 0.299340 0.954147i \(-0.403234\pi\)
−0.954147 + 0.299340i \(0.903234\pi\)
\(744\) 929284. 0.0615483
\(745\) 901873. 8.73261e6i 0.0595326 0.576439i
\(746\) 2.50275e6 0.164653
\(747\) 1.58066e7 1.58066e7i 1.03643 1.03643i
\(748\) −1.14494e7 + 8.08596e6i −0.748218 + 0.528418i
\(749\) 86219.0i 0.00561563i
\(750\) 615355. + 196257.i 0.0399460 + 0.0127401i
\(751\) −3.38585e6 −0.219063 −0.109531 0.993983i \(-0.534935\pi\)
−0.109531 + 0.993983i \(0.534935\pi\)
\(752\) 1.65308e7 + 1.65308e7i 1.06598 + 1.06598i
\(753\) 1.24165e6 1.24165e6i 0.0798015 0.0798015i
\(754\) 4.84471e6 0.310341
\(755\) −2.25843e7 2.33243e6i −1.44191 0.148916i
\(756\) 5.79386e6i 0.368692i
\(757\) −1.13440e7 1.13440e7i −0.719494 0.719494i 0.249007 0.968502i \(-0.419896\pi\)
−0.968502 + 0.249007i \(0.919896\pi\)
\(758\) −1.64007e6 1.64007e6i −0.103678 0.103678i
\(759\) −1.00092e6 172330.i −0.0630659 0.0108581i
\(760\) 5.83497e6 4.74256e6i 0.366441 0.297837i
\(761\) 1.02068e7i 0.638891i −0.947605 0.319446i \(-0.896503\pi\)
0.947605 0.319446i \(-0.103497\pi\)
\(762\) 269794. + 269794.i 0.0168324 + 0.0168324i
\(763\) −1.18143e7 + 1.18143e7i −0.734680 + 0.734680i
\(764\) 248530.i 0.0154044i
\(765\) −1.15077e7 + 9.35324e6i −0.710942 + 0.577841i
\(766\) 6.18015e6i 0.380563i
\(767\) 1.69251e7 1.69251e7i 1.03882 1.03882i
\(768\) −1.43250e6 + 1.43250e6i −0.0876378 + 0.0876378i
\(769\) −3.02499e7 −1.84462 −0.922312 0.386447i \(-0.873702\pi\)
−0.922312 + 0.386447i \(0.873702\pi\)
\(770\) −874814. + 3.11950e6i −0.0531727 + 0.189608i
\(771\) 3.19502e6 0.193570
\(772\) −1.29531e7 + 1.29531e7i −0.782220 + 0.782220i
\(773\) −6.66230e6 + 6.66230e6i −0.401028 + 0.401028i −0.878595 0.477567i \(-0.841519\pi\)
0.477567 + 0.878595i \(0.341519\pi\)
\(774\) 1.19475e6i 0.0716843i
\(775\) −1.22712e7 2.56198e6i −0.733893 0.153222i
\(776\) 2.52662e6i 0.150621i
\(777\) 2.24120e6 2.24120e6i 0.133177 0.133177i
\(778\) 3.71987e6 + 3.71987e6i 0.220333 + 0.220333i
\(779\) 2.63416e7i 1.55525i
\(780\) 5.70153e6 + 588834.i 0.335548 + 0.0346543i
\(781\) −222740. + 1.29371e6i −0.0130669 + 0.0758945i
\(782\) 741335. + 741335.i 0.0433508 + 0.0433508i
\(783\) −4.27436e6 4.27436e6i −0.249153 0.249153i
\(784\) 1.15916e6i 0.0673522i
\(785\) −1.80393e7 + 1.46620e7i −1.04483 + 0.849220i
\(786\) 631618. 0.0364669
\(787\) 1.23587e6 1.23587e6i 0.0711273 0.0711273i −0.670648 0.741776i \(-0.733984\pi\)
0.741776 + 0.670648i \(0.233984\pi\)
\(788\) −2.96864e6 2.96864e6i −0.170311 0.170311i
\(789\) 2.08896e6 0.119464
\(790\) 1.68917e6 + 2.07826e6i 0.0962954 + 0.118476i
\(791\) 2.00748e7i 1.14080i
\(792\) −3.91575e6 5.54454e6i −0.221820 0.314089i
\(793\) 2.80886e7 2.80886e7i 1.58616 1.58616i
\(794\) −6.51608e6 −0.366805
\(795\) −602851. 62260.3i −0.0338292 0.00349376i
\(796\) 1.15591e7 0.646610
\(797\) 1.75174e7 + 1.75174e7i 0.976840 + 0.976840i 0.999738 0.0228981i \(-0.00728933\pi\)
−0.0228981 + 0.999738i \(0.507289\pi\)
\(798\) −602944. 602944.i −0.0335173 0.0335173i
\(799\) 2.97024e7 1.64598
\(800\) −8.79680e6 + 5.75804e6i −0.485959 + 0.318090i
\(801\) 2.01418e7 1.10922
\(802\) −151896. + 151896.i −0.00833891 + 0.00833891i
\(803\) −1.19801e7 + 8.46076e6i −0.655649 + 0.463042i
\(804\) 785640.i 0.0428631i
\(805\) −5.49682e6 567693.i −0.298966 0.0308762i
\(806\) 4.87835e6 0.264506
\(807\) −1.48360e6 1.48360e6i −0.0801922 0.0801922i
\(808\) 5.25887e6 5.25887e6i 0.283377 0.283377i
\(809\) 3.44189e6 0.184895 0.0924477 0.995718i \(-0.470531\pi\)
0.0924477 + 0.995718i \(0.470531\pi\)
\(810\) −2.11512e6 2.60232e6i −0.113272 0.139363i
\(811\) 1.27797e7i 0.682291i −0.940010 0.341146i \(-0.889185\pi\)
0.940010 0.341146i \(-0.110815\pi\)
\(812\) −1.07562e7 1.07562e7i −0.572492 0.572492i
\(813\) 367035. + 367035.i 0.0194752 + 0.0194752i
\(814\) −630000. + 3.65914e6i −0.0333257 + 0.193561i
\(815\) −1.60451e7 1.97409e7i −0.846150 1.04105i
\(816\) 3.25812e6i 0.171294i
\(817\) −5.79441e6 5.79441e6i −0.303706 0.303706i
\(818\) −2.23079e6 + 2.23079e6i −0.116567 + 0.116567i
\(819\) 3.04180e7i 1.58460i
\(820\) −2.50460e6 + 2.42514e7i −0.130078 + 1.25951i
\(821\) 2.66295e7i 1.37881i 0.724374 + 0.689407i \(0.242129\pi\)
−0.724374 + 0.689407i \(0.757871\pi\)
\(822\) 537105. 537105.i 0.0277255 0.0277255i
\(823\) −1.61359e7 + 1.61359e7i −0.830410 + 0.830410i −0.987573 0.157163i \(-0.949765\pi\)
0.157163 + 0.987573i \(0.449765\pi\)
\(824\) 1.01774e7 0.522177
\(825\) −1.59071e6 3.66919e6i −0.0813684 0.187687i
\(826\) 3.29564e6 0.168070
\(827\) 2.40113e7 2.40113e7i 1.22082 1.22082i 0.253478 0.967341i \(-0.418426\pi\)
0.967341 0.253478i \(-0.0815745\pi\)
\(828\) 4.00554e6 4.00554e6i 0.203041 0.203041i
\(829\) 7.97873e6i 0.403225i 0.979465 + 0.201612i \(0.0646181\pi\)
−0.979465 + 0.201612i \(0.935382\pi\)
\(830\) 639272. 6.18991e6i 0.0322100 0.311881i
\(831\) 1.45645e6i 0.0731631i
\(832\) −1.83898e7 + 1.83898e7i −0.921018 + 0.921018i
\(833\) −1.04138e6 1.04138e6i −0.0519994 0.0519994i
\(834\) 1.33518e6i 0.0664698i
\(835\) 1.42539e7 + 1.75372e7i 0.707485 + 0.870449i
\(836\) −2.24485e7 3.86500e6i −1.11089 0.191264i
\(837\) −4.30404e6 4.30404e6i −0.212355 0.212355i
\(838\) −2.75652e6 2.75652e6i −0.135597 0.135597i
\(839\) 1.69830e7i 0.832931i −0.909152 0.416465i \(-0.863269\pi\)
0.909152 0.416465i \(-0.136731\pi\)
\(840\) 1.01737e6 + 1.25171e6i 0.0497486 + 0.0612078i
\(841\) −4.64060e6 −0.226248
\(842\) 654616. 654616.i 0.0318205 0.0318205i
\(843\) 306214. + 306214.i 0.0148408 + 0.0148408i
\(844\) 2.26062e7 1.09237
\(845\) 4.05277e7 + 4.18556e6i 1.95259 + 0.201656i
\(846\) 7.03762e6i 0.338065i
\(847\) 1.81116e7 8.62409e6i 0.867455 0.413052i
\(848\) 2.15581e6 2.15581e6i 0.102948 0.102948i
\(849\) 5.43863e6 0.258953
\(850\) −843684. + 4.04102e6i −0.0400528 + 0.191842i
\(851\) −6.33308e6 −0.299772
\(852\) 226117. + 226117.i 0.0106717 + 0.0106717i
\(853\) 2.49281e7 + 2.49281e7i 1.17305 + 1.17305i 0.981479 + 0.191569i \(0.0613575\pi\)
0.191569 + 0.981479i \(0.438642\pi\)
\(854\) 5.46940e6 0.256622
\(855\) −2.39718e7 2.47572e6i −1.12146 0.115821i
\(856\) −50285.8 −0.00234564
\(857\) 1.77081e7 1.77081e7i 0.823609 0.823609i −0.163015 0.986624i \(-0.552122\pi\)
0.986624 + 0.163015i \(0.0521218\pi\)
\(858\) 897785. + 1.27123e6i 0.0416346 + 0.0589529i
\(859\) 2.11987e7i 0.980225i −0.871659 0.490113i \(-0.836956\pi\)
0.871659 0.490113i \(-0.163044\pi\)
\(860\) 4.78368e6 + 5.88556e6i 0.220554 + 0.271357i
\(861\) 5.65079e6 0.259777
\(862\) 3.23600e6 + 3.23600e6i 0.148334 + 0.148334i
\(863\) 1.53434e7 1.53434e7i 0.701286 0.701286i −0.263400 0.964687i \(-0.584844\pi\)
0.964687 + 0.263400i \(0.0848440\pi\)
\(864\) −5.10502e6 −0.232655
\(865\) 2.62454e7 2.13318e7i 1.19265 0.969363i
\(866\) 2.80127e6i 0.126929i
\(867\) −274514. 274514.i −0.0124027 0.0124027i
\(868\) −1.08309e7 1.08309e7i −0.487939 0.487939i
\(869\) 2.81358e6 1.63417e7i 0.126389 0.734088i
\(870\) −819037. 84587.3i −0.0366864 0.00378885i
\(871\) 8.42942e6i 0.376489i
\(872\) −6.89052e6 6.89052e6i −0.306875 0.306875i
\(873\) 5.72606e6 5.72606e6i 0.254285 0.254285i
\(874\) 1.70377e6i 0.0754453i
\(875\) −9.98347e6 1.93337e7i −0.440820 0.853679i
\(876\) 3.57268e6i 0.157302i
\(877\) −3.15258e7 + 3.15258e7i −1.38410 + 1.38410i −0.546907 + 0.837193i \(0.684195\pi\)
−0.837193 + 0.546907i \(0.815805\pi\)
\(878\) 556438. 556438.i 0.0243602 0.0243602i
\(879\) −1.13445e6 −0.0495239
\(880\) 1.93705e7 + 5.43216e6i 0.843207 + 0.236464i
\(881\) −2.91839e7 −1.26679 −0.633394 0.773829i \(-0.718339\pi\)
−0.633394 + 0.773829i \(0.718339\pi\)
\(882\) 246743. 246743.i 0.0106800 0.0106800i
\(883\) −757927. + 757927.i −0.0327134 + 0.0327134i −0.723274 0.690561i \(-0.757364\pi\)
0.690561 + 0.723274i \(0.257364\pi\)
\(884\) 3.66345e7i 1.57674i
\(885\) −3.15682e6 + 2.56581e6i −0.135485 + 0.110120i
\(886\) 2.74498e6i 0.117477i
\(887\) 1.51267e7 1.51267e7i 0.645558 0.645558i −0.306358 0.951916i \(-0.599111\pi\)
0.951916 + 0.306358i \(0.0991106\pi\)
\(888\) 1.30714e6 + 1.30714e6i 0.0556277 + 0.0556277i
\(889\) 1.28537e7i 0.545475i
\(890\) 4.35108e6 3.53648e6i 0.184129 0.149657i
\(891\) −3.52306e6 + 2.04625e7i −0.148671 + 0.863504i
\(892\) 500658. + 500658.i 0.0210683 + 0.0210683i
\(893\) 3.41318e7 + 3.41318e7i 1.43229 + 1.43229i
\(894\) 580643.i 0.0242977i
\(895\) −1.34363e7 1.38766e6i −0.560690 0.0579061i
\(896\) −1.69907e7 −0.707036
\(897\) −1.87701e6 + 1.87701e6i −0.0778909 + 0.0778909i
\(898\) −1.26262e6 1.26262e6i −0.0522496 0.0522496i
\(899\) 1.59808e7 0.659475
\(900\) 2.18342e7 + 4.55854e6i 0.898527 + 0.187594i
\(901\) 3.87354e6i 0.158963i
\(902\) −5.40715e6 + 3.81872e6i −0.221285 + 0.156279i
\(903\) 1.24301e6 1.24301e6i 0.0507290 0.0507290i
\(904\) −1.17083e7 −0.476511
\(905\) −3.63090e6 + 3.51571e7i −0.147365 + 1.42689i
\(906\) −1.50166e6 −0.0607787
\(907\) 2.81619e7 + 2.81619e7i 1.13670 + 1.13670i 0.989039 + 0.147657i \(0.0471731\pi\)
0.147657 + 0.989039i \(0.452827\pi\)
\(908\) −1.09108e7 1.09108e7i −0.439180 0.439180i
\(909\) −2.38363e7 −0.956817
\(910\) 5.34077e6 + 6.57097e6i 0.213796 + 0.263042i
\(911\) 4.14771e7 1.65582 0.827908 0.560864i \(-0.189531\pi\)
0.827908 + 0.560864i \(0.189531\pi\)
\(912\) −3.74398e6 + 3.74398e6i −0.149055 + 0.149055i
\(913\) −3.14723e7 + 2.22268e7i −1.24954 + 0.882471i
\(914\) 3.89393e6i 0.154178i
\(915\) −5.23902e6 + 4.25819e6i −0.206870 + 0.168140i
\(916\) 4.59881e7 1.81095
\(917\) −1.50460e7 1.50460e7i −0.590877 0.590877i
\(918\) −1.41736e6 + 1.41736e6i −0.0555104 + 0.0555104i
\(919\) −1.89628e7 −0.740650 −0.370325 0.928902i \(-0.620754\pi\)
−0.370325 + 0.928902i \(0.620754\pi\)
\(920\) 331098. 3.20593e6i 0.0128969 0.124878i
\(921\) 7.81017e6i 0.303397i
\(922\) −4.01097e6 4.01097e6i −0.155390 0.155390i
\(923\) 2.42609e6 + 2.42609e6i 0.0937351 + 0.0937351i
\(924\) 829116. 4.81564e6i 0.0319474 0.185556i
\(925\) −1.36571e7 2.08646e7i −0.524813 0.801779i
\(926\) 8.84028e6i 0.338796i
\(927\) −2.30649e7 2.30649e7i −0.881562 0.881562i
\(928\) 9.47737e6 9.47737e6i 0.361259 0.361259i
\(929\) 1.78035e7i 0.676810i 0.941001 + 0.338405i \(0.109887\pi\)
−0.941001 + 0.338405i \(0.890113\pi\)
\(930\) −824725. 85174.7i −0.0312681 0.00322926i
\(931\) 2.39335e6i 0.0904967i
\(932\) −5.86901e6 + 5.86901e6i −0.221322 + 0.221322i
\(933\) −1.69297e6 + 1.69297e6i −0.0636716 + 0.0636716i
\(934\) −1.13518e6 −0.0425790
\(935\) 2.22826e7 1.25222e7i 0.833561 0.468436i
\(936\) −1.77408e7 −0.661886
\(937\) −1.04846e7 + 1.04846e7i −0.390123 + 0.390123i −0.874731 0.484608i \(-0.838962\pi\)
0.484608 + 0.874731i \(0.338962\pi\)
\(938\) 820686. 820686.i 0.0304558 0.0304558i
\(939\) 70155.2i 0.00259655i
\(940\) −2.81781e7 3.46687e7i −1.04014 1.27973i
\(941\) 1.69543e7i 0.624173i −0.950054 0.312086i \(-0.898972\pi\)
0.950054 0.312086i \(-0.101028\pi\)
\(942\) −1.08718e6 + 1.08718e6i −0.0399185 + 0.0399185i
\(943\) −7.98386e6 7.98386e6i −0.292371 0.292371i
\(944\) 2.04643e7i 0.747422i
\(945\) 1.08538e6 1.05094e7i 0.0395367 0.382824i
\(946\) −349410. + 2.02943e6i −0.0126942 + 0.0737303i
\(947\) 1.12252e7 + 1.12252e7i 0.406741 + 0.406741i 0.880600 0.473860i \(-0.157140\pi\)
−0.473860 + 0.880600i \(0.657140\pi\)
\(948\) −2.85623e6 2.85623e6i −0.103222 0.103222i
\(949\) 3.83326e7i 1.38166i
\(950\) −5.61313e6 + 3.67413e6i −0.201788 + 0.132083i
\(951\) −6.28780e6 −0.225449
\(952\) −7.28985e6 + 7.28985e6i −0.260691 + 0.260691i
\(953\) −1.49848e7 1.49848e7i −0.534464 0.534464i 0.387434 0.921898i \(-0.373362\pi\)
−0.921898 + 0.387434i \(0.873362\pi\)
\(954\) 917787. 0.0326491
\(955\) −46557.6 + 450805.i −0.00165189 + 0.0159949i
\(956\) 2.98120e7i 1.05498i
\(957\) 2.94101e6 + 4.16435e6i 0.103805 + 0.146983i
\(958\) −5.29329e6 + 5.29329e6i −0.186342 + 0.186342i
\(959\) −2.55891e7 −0.898480
\(960\) 3.43002e6 2.78786e6i 0.120121 0.0976322i
\(961\) −1.25374e7 −0.437924
\(962\) 6.86196e6 + 6.86196e6i 0.239062 + 0.239062i
\(963\) 113962. + 113962.i 0.00396001 + 0.00396001i
\(964\) 5.19753e6 0.180138
\(965\) 2.59219e7 2.10689e7i 0.896083 0.728321i
\(966\) −365491. −0.0126018
\(967\) −3.17757e7 + 3.17757e7i −1.09277 + 1.09277i −0.0975384 + 0.995232i \(0.531097\pi\)
−0.995232 + 0.0975384i \(0.968903\pi\)
\(968\) 5.02986e6 + 1.05633e7i 0.172531 + 0.362335i
\(969\) 6.72716e6i 0.230156i
\(970\) 231580. 2.24233e6i 0.00790264 0.0765193i
\(971\) −9.35785e6 −0.318514 −0.159257 0.987237i \(-0.550910\pi\)
−0.159257 + 0.987237i \(0.550910\pi\)
\(972\) 1.15691e7 + 1.15691e7i 0.392767 + 0.392767i
\(973\) 3.18057e7 3.18057e7i 1.07702 1.07702i
\(974\) −1.70461e6 −0.0575742
\(975\) −1.02316e7 2.13616e6i −0.344693 0.0719651i
\(976\) 3.39622e7i 1.14123i
\(977\) 1.40931e6 + 1.40931e6i 0.0472355 + 0.0472355i 0.730330 0.683094i \(-0.239366\pi\)
−0.683094 + 0.730330i \(0.739366\pi\)
\(978\) −1.18973e6 1.18973e6i −0.0397741 0.0397741i
\(979\) −3.42133e7 5.89056e6i −1.14088 0.196426i
\(980\) −227564. + 2.20344e6i −0.00756899 + 0.0732885i
\(981\) 3.12319e7i 1.03616i
\(982\) 2.32860e6 + 2.32860e6i 0.0770578 + 0.0770578i
\(983\) 2.12347e6 2.12347e6i 0.0700910 0.0700910i −0.671192 0.741283i \(-0.734218\pi\)
0.741283 + 0.671192i \(0.234218\pi\)
\(984\) 3.29573e6i 0.108508i
\(985\) 4.82866e6 + 5.94090e6i 0.158575 + 0.195102i
\(986\) 5.26262e6i 0.172389i
\(987\) −7.32192e6 + 7.32192e6i −0.239239 + 0.239239i
\(988\) −4.20975e7 + 4.20975e7i −1.37203 + 1.37203i
\(989\) −3.51244e6 −0.114188
\(990\) 2.96697e6 + 5.27959e6i 0.0962111 + 0.171203i
\(991\) 7.24962e6 0.234494 0.117247 0.993103i \(-0.462593\pi\)
0.117247 + 0.993103i \(0.462593\pi\)
\(992\) 9.54319e6 9.54319e6i 0.307903 0.307903i
\(993\) 4.47564e6 4.47564e6i 0.144040 0.144040i
\(994\) 472407.i 0.0151653i
\(995\) −2.09669e7 2.16539e6i −0.671394 0.0693392i
\(996\) 9.38560e6i 0.299788i
\(997\) −1.80710e7 + 1.80710e7i −0.575764 + 0.575764i −0.933733 0.357970i \(-0.883469\pi\)
0.357970 + 0.933733i \(0.383469\pi\)
\(998\) 3.26085e6 + 3.26085e6i 0.103634 + 0.103634i
\(999\) 1.21083e7i 0.383856i
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 55.6.e.b.32.13 52
5.3 odd 4 inner 55.6.e.b.43.14 yes 52
11.10 odd 2 inner 55.6.e.b.32.14 yes 52
55.43 even 4 inner 55.6.e.b.43.13 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.6.e.b.32.13 52 1.1 even 1 trivial
55.6.e.b.32.14 yes 52 11.10 odd 2 inner
55.6.e.b.43.13 yes 52 55.43 even 4 inner
55.6.e.b.43.14 yes 52 5.3 odd 4 inner