Properties

Label 414.3.k.a.35.1
Level $414$
Weight $3$
Character 414.35
Analytic conductor $11.281$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [414,3,Mod(35,414)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(414, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 20]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("414.35");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 414.k (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.2806829445\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 35.1
Character \(\chi\) \(=\) 414.35
Dual form 414.3.k.a.71.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.764582 - 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(-1.90263 - 6.47977i) q^{5} +(-7.74127 - 8.93390i) q^{7} +(2.79964 - 0.402527i) q^{8} +O(q^{10})\) \(q+(-0.764582 - 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(-1.90263 - 6.47977i) q^{5} +(-7.74127 - 8.93390i) q^{7} +(2.79964 - 0.402527i) q^{8} +(-6.25434 + 7.21790i) q^{10} +(-1.39544 + 2.17135i) q^{11} +(-15.9554 + 18.4135i) q^{13} +(-4.70994 + 16.0406i) q^{14} +(-2.61944 - 3.02300i) q^{16} +(17.1606 - 7.83698i) q^{17} +(5.09911 - 11.1655i) q^{19} +(13.3692 + 1.92220i) q^{20} +3.65021 q^{22} +(21.7442 + 7.49613i) q^{23} +(-17.3361 + 11.1412i) q^{25} +(34.1059 + 4.90369i) q^{26} +(22.6848 - 6.66086i) q^{28} +(-24.1659 + 11.0362i) q^{29} +(5.15642 + 35.8637i) q^{31} +(-1.59372 + 5.42771i) q^{32} +(-22.4444 - 14.4242i) q^{34} +(-43.1608 + 67.1596i) q^{35} +(-44.6329 - 13.1054i) q^{37} +(-17.1824 + 2.47046i) q^{38} +(-7.93497 - 17.3751i) q^{40} +(-4.50009 - 15.3259i) q^{41} +(-0.512794 + 3.56656i) q^{43} +(-2.79088 - 4.34270i) q^{44} +(-7.70694 - 31.6007i) q^{46} +79.2879i q^{47} +(-12.9139 + 89.8183i) q^{49} +(26.5097 + 12.1066i) q^{50} +(-20.2428 - 44.3254i) q^{52} +(49.7226 - 43.0849i) q^{53} +(16.7249 + 4.91086i) q^{55} +(-25.2689 - 21.8956i) q^{56} +(31.6067 + 20.3124i) q^{58} +(-38.0838 - 32.9998i) q^{59} +(0.442839 + 3.08002i) q^{61} +(38.7249 - 33.5554i) q^{62} +(7.67594 - 2.25386i) q^{64} +(149.672 + 68.3530i) q^{65} +(-59.6258 + 38.3192i) q^{67} +37.7309i q^{68} +112.901 q^{70} +(-55.4188 - 86.2333i) q^{71} +(0.255877 - 0.560292i) q^{73} +(18.5338 + 63.1204i) q^{74} +(16.0765 + 18.5533i) q^{76} +(30.2011 - 4.34227i) q^{77} +(-89.4179 + 103.194i) q^{79} +(-14.6045 + 22.7250i) q^{80} +(-14.7927 + 17.0717i) q^{82} +(-8.41661 + 28.6644i) q^{83} +(-83.4322 - 96.2858i) q^{85} +(4.63525 - 2.11685i) q^{86} +(-3.03270 + 6.64070i) q^{88} +(-139.890 - 20.1131i) q^{89} +288.019 q^{91} +(-31.7031 + 33.3303i) q^{92} +(94.3298 - 60.6221i) q^{94} +(-82.0516 - 11.7972i) q^{95} +(162.707 - 47.7750i) q^{97} +(116.732 - 53.3095i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(-1\) \(e\left(\frac{10}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.764582 1.18971i −0.382291 0.594856i
\(3\) 0 0
\(4\) −0.830830 + 1.81926i −0.207708 + 0.454816i
\(5\) −1.90263 6.47977i −0.380526 1.29595i −0.897902 0.440196i \(-0.854909\pi\)
0.517375 0.855759i \(-0.326909\pi\)
\(6\) 0 0
\(7\) −7.74127 8.93390i −1.10590 1.27627i −0.957843 0.287292i \(-0.907245\pi\)
−0.148053 0.988979i \(-0.547301\pi\)
\(8\) 2.79964 0.402527i 0.349955 0.0503159i
\(9\) 0 0
\(10\) −6.25434 + 7.21790i −0.625434 + 0.721790i
\(11\) −1.39544 + 2.17135i −0.126858 + 0.197395i −0.898873 0.438209i \(-0.855613\pi\)
0.772015 + 0.635605i \(0.219249\pi\)
\(12\) 0 0
\(13\) −15.9554 + 18.4135i −1.22733 + 1.41642i −0.349856 + 0.936803i \(0.613770\pi\)
−0.877478 + 0.479616i \(0.840776\pi\)
\(14\) −4.70994 + 16.0406i −0.336424 + 1.14576i
\(15\) 0 0
\(16\) −2.61944 3.02300i −0.163715 0.188937i
\(17\) 17.1606 7.83698i 1.00945 0.460999i 0.159123 0.987259i \(-0.449133\pi\)
0.850324 + 0.526260i \(0.176406\pi\)
\(18\) 0 0
\(19\) 5.09911 11.1655i 0.268374 0.587658i −0.726682 0.686974i \(-0.758938\pi\)
0.995056 + 0.0993168i \(0.0316657\pi\)
\(20\) 13.3692 + 1.92220i 0.668459 + 0.0961099i
\(21\) 0 0
\(22\) 3.65021 0.165919
\(23\) 21.7442 + 7.49613i 0.945398 + 0.325919i
\(24\) 0 0
\(25\) −17.3361 + 11.1412i −0.693443 + 0.445649i
\(26\) 34.1059 + 4.90369i 1.31176 + 0.188603i
\(27\) 0 0
\(28\) 22.6848 6.66086i 0.810172 0.237888i
\(29\) −24.1659 + 11.0362i −0.833306 + 0.380558i −0.785927 0.618319i \(-0.787814\pi\)
−0.0473784 + 0.998877i \(0.515087\pi\)
\(30\) 0 0
\(31\) 5.15642 + 35.8637i 0.166336 + 1.15689i 0.886378 + 0.462962i \(0.153213\pi\)
−0.720042 + 0.693931i \(0.755877\pi\)
\(32\) −1.59372 + 5.42771i −0.0498038 + 0.169616i
\(33\) 0 0
\(34\) −22.4444 14.4242i −0.660130 0.424240i
\(35\) −43.1608 + 67.1596i −1.23317 + 1.91885i
\(36\) 0 0
\(37\) −44.6329 13.1054i −1.20629 0.354200i −0.384038 0.923317i \(-0.625467\pi\)
−0.822256 + 0.569118i \(0.807285\pi\)
\(38\) −17.1824 + 2.47046i −0.452169 + 0.0650120i
\(39\) 0 0
\(40\) −7.93497 17.3751i −0.198374 0.434379i
\(41\) −4.50009 15.3259i −0.109758 0.373802i 0.886234 0.463237i \(-0.153312\pi\)
−0.995993 + 0.0894347i \(0.971494\pi\)
\(42\) 0 0
\(43\) −0.512794 + 3.56656i −0.0119254 + 0.0829432i −0.994915 0.100718i \(-0.967886\pi\)
0.982990 + 0.183661i \(0.0587950\pi\)
\(44\) −2.79088 4.34270i −0.0634292 0.0986977i
\(45\) 0 0
\(46\) −7.70694 31.6007i −0.167542 0.686971i
\(47\) 79.2879i 1.68698i 0.537147 + 0.843489i \(0.319502\pi\)
−0.537147 + 0.843489i \(0.680498\pi\)
\(48\) 0 0
\(49\) −12.9139 + 89.8183i −0.263549 + 1.83303i
\(50\) 26.5097 + 12.1066i 0.530194 + 0.242131i
\(51\) 0 0
\(52\) −20.2428 44.3254i −0.389284 0.852412i
\(53\) 49.7226 43.0849i 0.938162 0.812922i −0.0443699 0.999015i \(-0.514128\pi\)
0.982532 + 0.186093i \(0.0595826\pi\)
\(54\) 0 0
\(55\) 16.7249 + 4.91086i 0.304088 + 0.0892884i
\(56\) −25.2689 21.8956i −0.451230 0.390993i
\(57\) 0 0
\(58\) 31.6067 + 20.3124i 0.544942 + 0.350213i
\(59\) −38.0838 32.9998i −0.645489 0.559319i 0.269398 0.963029i \(-0.413175\pi\)
−0.914887 + 0.403710i \(0.867721\pi\)
\(60\) 0 0
\(61\) 0.442839 + 3.08002i 0.00725966 + 0.0504921i 0.993129 0.117023i \(-0.0373350\pi\)
−0.985870 + 0.167515i \(0.946426\pi\)
\(62\) 38.7249 33.5554i 0.624596 0.541215i
\(63\) 0 0
\(64\) 7.67594 2.25386i 0.119937 0.0352166i
\(65\) 149.672 + 68.3530i 2.30265 + 1.05158i
\(66\) 0 0
\(67\) −59.6258 + 38.3192i −0.889938 + 0.571928i −0.903790 0.427976i \(-0.859227\pi\)
0.0138524 + 0.999904i \(0.495590\pi\)
\(68\) 37.7309i 0.554866i
\(69\) 0 0
\(70\) 112.901 1.61287
\(71\) −55.4188 86.2333i −0.780546 1.21455i −0.972444 0.233138i \(-0.925101\pi\)
0.191898 0.981415i \(-0.438536\pi\)
\(72\) 0 0
\(73\) 0.255877 0.560292i 0.00350516 0.00767523i −0.907871 0.419249i \(-0.862293\pi\)
0.911376 + 0.411574i \(0.135021\pi\)
\(74\) 18.5338 + 63.1204i 0.250457 + 0.852979i
\(75\) 0 0
\(76\) 16.0765 + 18.5533i 0.211533 + 0.244122i
\(77\) 30.2011 4.34227i 0.392222 0.0563931i
\(78\) 0 0
\(79\) −89.4179 + 103.194i −1.13187 + 1.30625i −0.185693 + 0.982608i \(0.559453\pi\)
−0.946179 + 0.323642i \(0.895093\pi\)
\(80\) −14.6045 + 22.7250i −0.182556 + 0.284063i
\(81\) 0 0
\(82\) −14.7927 + 17.0717i −0.180399 + 0.208192i
\(83\) −8.41661 + 28.6644i −0.101405 + 0.345354i −0.994530 0.104456i \(-0.966690\pi\)
0.893125 + 0.449809i \(0.148508\pi\)
\(84\) 0 0
\(85\) −83.4322 96.2858i −0.981555 1.13277i
\(86\) 4.63525 2.11685i 0.0538983 0.0246145i
\(87\) 0 0
\(88\) −3.03270 + 6.64070i −0.0344626 + 0.0754625i
\(89\) −139.890 20.1131i −1.57180 0.225990i −0.699379 0.714751i \(-0.746540\pi\)
−0.872418 + 0.488760i \(0.837449\pi\)
\(90\) 0 0
\(91\) 288.019 3.16504
\(92\) −31.7031 + 33.3303i −0.344599 + 0.362286i
\(93\) 0 0
\(94\) 94.3298 60.6221i 1.00351 0.644916i
\(95\) −82.0516 11.7972i −0.863701 0.124181i
\(96\) 0 0
\(97\) 162.707 47.7750i 1.67739 0.492525i 0.701844 0.712331i \(-0.252360\pi\)
0.975544 + 0.219805i \(0.0705422\pi\)
\(98\) 116.732 53.3095i 1.19114 0.543975i
\(99\) 0 0
\(100\) −5.86549 40.7954i −0.0586549 0.407954i
\(101\) 8.40929 28.6394i 0.0832603 0.283558i −0.907330 0.420419i \(-0.861883\pi\)
0.990590 + 0.136861i \(0.0437012\pi\)
\(102\) 0 0
\(103\) −47.2928 30.3933i −0.459154 0.295080i 0.290543 0.956862i \(-0.406164\pi\)
−0.749696 + 0.661782i \(0.769801\pi\)
\(104\) −37.2573 + 57.9735i −0.358243 + 0.557437i
\(105\) 0 0
\(106\) −89.2756 26.2137i −0.842223 0.247299i
\(107\) 12.6115 1.81327i 0.117865 0.0169464i −0.0831299 0.996539i \(-0.526492\pi\)
0.200995 + 0.979592i \(0.435583\pi\)
\(108\) 0 0
\(109\) −37.3163 81.7113i −0.342351 0.749645i 0.657642 0.753331i \(-0.271554\pi\)
−0.999993 + 0.00368599i \(0.998827\pi\)
\(110\) −6.94501 23.6525i −0.0631364 0.215023i
\(111\) 0 0
\(112\) −6.72936 + 46.8037i −0.0600835 + 0.417890i
\(113\) −37.7071 58.6734i −0.333691 0.519233i 0.633346 0.773869i \(-0.281681\pi\)
−0.967037 + 0.254635i \(0.918045\pi\)
\(114\) 0 0
\(115\) 7.20206 155.159i 0.0626266 1.34921i
\(116\) 53.1333i 0.458045i
\(117\) 0 0
\(118\) −10.1421 + 70.5399i −0.0859500 + 0.597796i
\(119\) −202.860 92.6429i −1.70470 0.778512i
\(120\) 0 0
\(121\) 47.4977 + 104.005i 0.392543 + 0.859549i
\(122\) 3.32575 2.88177i 0.0272602 0.0236211i
\(123\) 0 0
\(124\) −69.5296 20.4157i −0.560723 0.164643i
\(125\) −22.4189 19.4261i −0.179351 0.155408i
\(126\) 0 0
\(127\) 102.639 + 65.9622i 0.808183 + 0.519388i 0.878277 0.478153i \(-0.158693\pi\)
−0.0700938 + 0.997540i \(0.522330\pi\)
\(128\) −8.55033 7.40890i −0.0667995 0.0578821i
\(129\) 0 0
\(130\) −33.1162 230.328i −0.254740 1.77176i
\(131\) 6.58012 5.70170i 0.0502299 0.0435244i −0.629384 0.777094i \(-0.716693\pi\)
0.679614 + 0.733570i \(0.262147\pi\)
\(132\) 0 0
\(133\) −139.225 + 40.8802i −1.04680 + 0.307370i
\(134\) 91.1776 + 41.6394i 0.680430 + 0.310742i
\(135\) 0 0
\(136\) 44.8889 28.8483i 0.330065 0.212120i
\(137\) 216.729i 1.58196i −0.611842 0.790980i \(-0.709571\pi\)
0.611842 0.790980i \(-0.290429\pi\)
\(138\) 0 0
\(139\) −202.996 −1.46041 −0.730203 0.683230i \(-0.760575\pi\)
−0.730203 + 0.683230i \(0.760575\pi\)
\(140\) −86.3217 134.319i −0.616584 0.959423i
\(141\) 0 0
\(142\) −60.2206 + 131.865i −0.424089 + 0.928625i
\(143\) −17.7173 60.3396i −0.123897 0.421955i
\(144\) 0 0
\(145\) 117.491 + 135.591i 0.810280 + 0.935113i
\(146\) −0.862225 + 0.123969i −0.00590565 + 0.000849104i
\(147\) 0 0
\(148\) 60.9245 70.3106i 0.411652 0.475072i
\(149\) −47.7552 + 74.3085i −0.320505 + 0.498715i −0.963700 0.266987i \(-0.913972\pi\)
0.643195 + 0.765702i \(0.277608\pi\)
\(150\) 0 0
\(151\) −166.377 + 192.009i −1.10183 + 1.27158i −0.142348 + 0.989817i \(0.545465\pi\)
−0.959483 + 0.281765i \(0.909080\pi\)
\(152\) 9.78125 33.3119i 0.0643503 0.219157i
\(153\) 0 0
\(154\) −28.2573 32.6106i −0.183489 0.211757i
\(155\) 222.578 101.648i 1.43598 0.655792i
\(156\) 0 0
\(157\) 48.4486 106.088i 0.308590 0.675718i −0.690265 0.723557i \(-0.742506\pi\)
0.998855 + 0.0478388i \(0.0152334\pi\)
\(158\) 191.138 + 27.4815i 1.20974 + 0.173934i
\(159\) 0 0
\(160\) 38.2026 0.238766
\(161\) −101.358 252.290i −0.629551 1.56702i
\(162\) 0 0
\(163\) −87.5780 + 56.2830i −0.537289 + 0.345294i −0.780978 0.624559i \(-0.785279\pi\)
0.243689 + 0.969853i \(0.421642\pi\)
\(164\) 31.6207 + 4.54636i 0.192809 + 0.0277217i
\(165\) 0 0
\(166\) 40.5375 11.9029i 0.244202 0.0717041i
\(167\) 2.25698 1.03073i 0.0135148 0.00617202i −0.408646 0.912693i \(-0.633999\pi\)
0.422161 + 0.906521i \(0.361272\pi\)
\(168\) 0 0
\(169\) −60.4310 420.307i −0.357580 2.48702i
\(170\) −50.7617 + 172.879i −0.298598 + 1.01693i
\(171\) 0 0
\(172\) −6.06247 3.89611i −0.0352469 0.0226518i
\(173\) 12.0949 18.8200i 0.0699125 0.108786i −0.804537 0.593903i \(-0.797586\pi\)
0.874449 + 0.485117i \(0.161223\pi\)
\(174\) 0 0
\(175\) 233.738 + 68.6316i 1.33564 + 0.392181i
\(176\) 10.2193 1.46931i 0.0580640 0.00834835i
\(177\) 0 0
\(178\) 83.0284 + 181.807i 0.466452 + 1.02139i
\(179\) −2.21870 7.55620i −0.0123950 0.0422134i 0.953063 0.302771i \(-0.0979118\pi\)
−0.965458 + 0.260558i \(0.916094\pi\)
\(180\) 0 0
\(181\) −1.82235 + 12.6748i −0.0100683 + 0.0700262i −0.994236 0.107213i \(-0.965807\pi\)
0.984168 + 0.177239i \(0.0567165\pi\)
\(182\) −220.214 342.659i −1.20997 1.88274i
\(183\) 0 0
\(184\) 63.8931 + 12.2338i 0.347245 + 0.0664882i
\(185\) 314.146i 1.69808i
\(186\) 0 0
\(187\) −6.92978 + 48.1977i −0.0370577 + 0.257742i
\(188\) −144.246 65.8748i −0.767264 0.350398i
\(189\) 0 0
\(190\) 48.6998 + 106.638i 0.256315 + 0.561251i
\(191\) −25.2390 + 21.8697i −0.132141 + 0.114501i −0.718424 0.695605i \(-0.755136\pi\)
0.586283 + 0.810107i \(0.300591\pi\)
\(192\) 0 0
\(193\) 168.384 + 49.4420i 0.872456 + 0.256176i 0.687160 0.726506i \(-0.258857\pi\)
0.185296 + 0.982683i \(0.440675\pi\)
\(194\) −181.241 157.046i −0.934232 0.809516i
\(195\) 0 0
\(196\) −152.674 98.1175i −0.778948 0.500600i
\(197\) 20.0241 + 17.3510i 0.101645 + 0.0880760i 0.704201 0.710001i \(-0.251305\pi\)
−0.602556 + 0.798077i \(0.705851\pi\)
\(198\) 0 0
\(199\) −6.93905 48.2622i −0.0348696 0.242524i 0.964931 0.262505i \(-0.0845485\pi\)
−0.999800 + 0.0199811i \(0.993639\pi\)
\(200\) −44.0501 + 38.1696i −0.220251 + 0.190848i
\(201\) 0 0
\(202\) −40.5022 + 11.8925i −0.200506 + 0.0588739i
\(203\) 285.671 + 130.461i 1.40724 + 0.642667i
\(204\) 0 0
\(205\) −90.7463 + 58.3191i −0.442665 + 0.284483i
\(206\) 79.5030i 0.385937i
\(207\) 0 0
\(208\) 97.4580 0.468548
\(209\) 17.1287 + 26.6528i 0.0819554 + 0.127525i
\(210\) 0 0
\(211\) 128.416 281.193i 0.608609 1.33267i −0.314913 0.949121i \(-0.601975\pi\)
0.923522 0.383546i \(-0.125297\pi\)
\(212\) 37.0717 + 126.255i 0.174867 + 0.595541i
\(213\) 0 0
\(214\) −11.7998 13.6177i −0.0551393 0.0636342i
\(215\) 24.0861 3.46306i 0.112029 0.0161073i
\(216\) 0 0
\(217\) 280.485 323.697i 1.29256 1.49169i
\(218\) −68.6815 + 106.871i −0.315053 + 0.490232i
\(219\) 0 0
\(220\) −22.8297 + 26.3468i −0.103771 + 0.119758i
\(221\) −129.497 + 441.028i −0.585961 + 1.99560i
\(222\) 0 0
\(223\) 66.4635 + 76.7030i 0.298043 + 0.343960i 0.884943 0.465700i \(-0.154197\pi\)
−0.586900 + 0.809659i \(0.699652\pi\)
\(224\) 60.8281 27.7792i 0.271554 0.124014i
\(225\) 0 0
\(226\) −40.9743 + 89.7212i −0.181302 + 0.396996i
\(227\) −141.483 20.3422i −0.623273 0.0896132i −0.176559 0.984290i \(-0.556497\pi\)
−0.446714 + 0.894677i \(0.647406\pi\)
\(228\) 0 0
\(229\) −386.344 −1.68709 −0.843545 0.537059i \(-0.819535\pi\)
−0.843545 + 0.537059i \(0.819535\pi\)
\(230\) −190.102 + 110.064i −0.826529 + 0.478538i
\(231\) 0 0
\(232\) −63.2133 + 40.6247i −0.272471 + 0.175107i
\(233\) 401.670 + 57.7515i 1.72391 + 0.247860i 0.931917 0.362673i \(-0.118136\pi\)
0.791991 + 0.610533i \(0.209045\pi\)
\(234\) 0 0
\(235\) 513.768 150.856i 2.18624 0.641939i
\(236\) 91.6766 41.8673i 0.388460 0.177404i
\(237\) 0 0
\(238\) 44.8844 + 312.178i 0.188590 + 1.31167i
\(239\) −22.8024 + 77.6577i −0.0954074 + 0.324928i −0.993342 0.115201i \(-0.963249\pi\)
0.897935 + 0.440128i \(0.145067\pi\)
\(240\) 0 0
\(241\) −218.000 140.100i −0.904563 0.581327i 0.00357745 0.999994i \(-0.498861\pi\)
−0.908140 + 0.418667i \(0.862498\pi\)
\(242\) 87.4207 136.029i 0.361243 0.562104i
\(243\) 0 0
\(244\) −5.97129 1.75333i −0.0244725 0.00718577i
\(245\) 606.572 87.2119i 2.47580 0.355967i
\(246\) 0 0
\(247\) 124.237 + 272.042i 0.502985 + 1.10138i
\(248\) 28.8722 + 98.3297i 0.116420 + 0.396491i
\(249\) 0 0
\(250\) −5.97037 + 41.5248i −0.0238815 + 0.166099i
\(251\) 186.120 + 289.608i 0.741513 + 1.15382i 0.983034 + 0.183421i \(0.0587173\pi\)
−0.241521 + 0.970396i \(0.577646\pi\)
\(252\) 0 0
\(253\) −46.6194 + 36.7537i −0.184266 + 0.145272i
\(254\) 172.545i 0.679310i
\(255\) 0 0
\(256\) −2.27704 + 15.8371i −0.00889468 + 0.0618638i
\(257\) −371.171 169.508i −1.44424 0.659564i −0.469509 0.882928i \(-0.655569\pi\)
−0.974735 + 0.223363i \(0.928296\pi\)
\(258\) 0 0
\(259\) 228.433 + 500.198i 0.881980 + 1.93127i
\(260\) −248.704 + 215.503i −0.956555 + 0.828859i
\(261\) 0 0
\(262\) −11.8144 3.46903i −0.0450932 0.0132406i
\(263\) 129.497 + 112.210i 0.492384 + 0.426653i 0.865332 0.501199i \(-0.167108\pi\)
−0.372948 + 0.927852i \(0.621653\pi\)
\(264\) 0 0
\(265\) −373.784 240.216i −1.41051 0.906477i
\(266\) 155.085 + 134.382i 0.583025 + 0.505194i
\(267\) 0 0
\(268\) −20.1738 140.312i −0.0752754 0.523552i
\(269\) 31.4702 27.2691i 0.116990 0.101372i −0.594401 0.804169i \(-0.702611\pi\)
0.711391 + 0.702796i \(0.248065\pi\)
\(270\) 0 0
\(271\) −346.619 + 101.777i −1.27904 + 0.375559i −0.849548 0.527512i \(-0.823125\pi\)
−0.429490 + 0.903071i \(0.641307\pi\)
\(272\) −68.6424 31.3479i −0.252362 0.115250i
\(273\) 0 0
\(274\) −257.845 + 165.707i −0.941039 + 0.604769i
\(275\) 53.1896i 0.193417i
\(276\) 0 0
\(277\) −240.875 −0.869586 −0.434793 0.900530i \(-0.643178\pi\)
−0.434793 + 0.900530i \(0.643178\pi\)
\(278\) 155.207 + 241.507i 0.558300 + 0.868731i
\(279\) 0 0
\(280\) −93.8012 + 205.396i −0.335004 + 0.733557i
\(281\) 55.9740 + 190.630i 0.199196 + 0.678399i 0.997134 + 0.0756590i \(0.0241060\pi\)
−0.797938 + 0.602740i \(0.794076\pi\)
\(282\) 0 0
\(283\) −88.3756 101.991i −0.312281 0.360392i 0.577812 0.816170i \(-0.303907\pi\)
−0.890094 + 0.455778i \(0.849361\pi\)
\(284\) 202.925 29.1762i 0.714523 0.102733i
\(285\) 0 0
\(286\) −58.2404 + 67.2130i −0.203638 + 0.235010i
\(287\) −102.084 + 158.845i −0.355692 + 0.553468i
\(288\) 0 0
\(289\) 43.8130 50.5629i 0.151602 0.174958i
\(290\) 71.4836 243.451i 0.246495 0.839486i
\(291\) 0 0
\(292\) 0.806729 + 0.931014i 0.00276277 + 0.00318841i
\(293\) −290.553 + 132.691i −0.991648 + 0.452870i −0.844101 0.536185i \(-0.819865\pi\)
−0.147547 + 0.989055i \(0.547138\pi\)
\(294\) 0 0
\(295\) −141.372 + 309.561i −0.479227 + 1.04936i
\(296\) −130.231 18.7244i −0.439970 0.0632582i
\(297\) 0 0
\(298\) 124.919 0.419190
\(299\) −484.965 + 280.782i −1.62196 + 0.939069i
\(300\) 0 0
\(301\) 35.8330 23.0284i 0.119046 0.0765064i
\(302\) 355.644 + 51.1339i 1.17763 + 0.169317i
\(303\) 0 0
\(304\) −47.1101 + 13.8328i −0.154967 + 0.0455025i
\(305\) 19.1152 8.72964i 0.0626729 0.0286218i
\(306\) 0 0
\(307\) −15.6683 108.975i −0.0510367 0.354968i −0.999298 0.0374757i \(-0.988068\pi\)
0.948261 0.317492i \(-0.102841\pi\)
\(308\) −17.1923 + 58.5515i −0.0558191 + 0.190102i
\(309\) 0 0
\(310\) −291.110 187.085i −0.939066 0.603501i
\(311\) −122.581 + 190.740i −0.394152 + 0.613313i −0.980447 0.196785i \(-0.936950\pi\)
0.586294 + 0.810098i \(0.300586\pi\)
\(312\) 0 0
\(313\) 43.4557 + 12.7598i 0.138836 + 0.0407660i 0.350412 0.936596i \(-0.386041\pi\)
−0.211576 + 0.977362i \(0.567860\pi\)
\(314\) −163.257 + 23.4728i −0.519926 + 0.0747541i
\(315\) 0 0
\(316\) −113.446 248.411i −0.359005 0.786112i
\(317\) −54.0899 184.213i −0.170631 0.581114i −0.999757 0.0220528i \(-0.992980\pi\)
0.829126 0.559061i \(-0.188838\pi\)
\(318\) 0 0
\(319\) 9.75865 67.8729i 0.0305914 0.212768i
\(320\) −29.2090 45.4501i −0.0912781 0.142032i
\(321\) 0 0
\(322\) −222.656 + 313.482i −0.691478 + 0.973548i
\(323\) 231.568i 0.716929i
\(324\) 0 0
\(325\) 71.4548 496.979i 0.219861 1.52917i
\(326\) 133.921 + 61.1597i 0.410801 + 0.187606i
\(327\) 0 0
\(328\) −18.7677 41.0955i −0.0572186 0.125291i
\(329\) 708.351 613.789i 2.15304 1.86562i
\(330\) 0 0
\(331\) 513.135 + 150.670i 1.55026 + 0.455196i 0.941177 0.337914i \(-0.109721\pi\)
0.609078 + 0.793110i \(0.291539\pi\)
\(332\) −45.1552 39.1272i −0.136010 0.117853i
\(333\) 0 0
\(334\) −2.95191 1.89708i −0.00883806 0.00567988i
\(335\) 361.746 + 313.454i 1.07984 + 0.935685i
\(336\) 0 0
\(337\) −35.8224 249.150i −0.106298 0.739318i −0.971353 0.237641i \(-0.923626\pi\)
0.865055 0.501677i \(-0.167283\pi\)
\(338\) −453.839 + 393.254i −1.34272 + 1.16347i
\(339\) 0 0
\(340\) 244.487 71.7879i 0.719080 0.211141i
\(341\) −85.0681 38.8493i −0.249466 0.113928i
\(342\) 0 0
\(343\) 415.109 266.774i 1.21023 0.777768i
\(344\) 10.1915i 0.0296264i
\(345\) 0 0
\(346\) −31.6379 −0.0914389
\(347\) 82.1344 + 127.804i 0.236698 + 0.368310i 0.939199 0.343373i \(-0.111570\pi\)
−0.702501 + 0.711683i \(0.747933\pi\)
\(348\) 0 0
\(349\) 63.8389 139.788i 0.182920 0.400538i −0.795852 0.605491i \(-0.792977\pi\)
0.978772 + 0.204953i \(0.0657041\pi\)
\(350\) −97.0598 330.555i −0.277314 0.944444i
\(351\) 0 0
\(352\) −9.56152 11.0346i −0.0271634 0.0313482i
\(353\) 408.145 58.6824i 1.15622 0.166239i 0.462590 0.886572i \(-0.346920\pi\)
0.693628 + 0.720333i \(0.256011\pi\)
\(354\) 0 0
\(355\) −453.330 + 523.171i −1.27699 + 1.47372i
\(356\) 152.816 237.786i 0.429258 0.667939i
\(357\) 0 0
\(358\) −7.29333 + 8.41695i −0.0203724 + 0.0235110i
\(359\) −81.0080 + 275.888i −0.225649 + 0.768490i 0.766370 + 0.642400i \(0.222061\pi\)
−0.992019 + 0.126090i \(0.959757\pi\)
\(360\) 0 0
\(361\) 137.737 + 158.957i 0.381544 + 0.440325i
\(362\) 16.4726 7.52280i 0.0455045 0.0207812i
\(363\) 0 0
\(364\) −239.295 + 523.982i −0.657403 + 1.43951i
\(365\) −4.11740 0.591993i −0.0112806 0.00162190i
\(366\) 0 0
\(367\) 156.483 0.426383 0.213192 0.977010i \(-0.431614\pi\)
0.213192 + 0.977010i \(0.431614\pi\)
\(368\) −34.2968 85.3682i −0.0931978 0.231979i
\(369\) 0 0
\(370\) 373.743 240.190i 1.01012 0.649162i
\(371\) −769.832 110.685i −2.07502 0.298343i
\(372\) 0 0
\(373\) −496.117 + 145.673i −1.33007 + 0.390545i −0.868117 0.496359i \(-0.834670\pi\)
−0.461955 + 0.886903i \(0.652852\pi\)
\(374\) 62.6398 28.6066i 0.167486 0.0764883i
\(375\) 0 0
\(376\) 31.9155 + 221.977i 0.0848818 + 0.590366i
\(377\) 182.361 621.063i 0.483715 1.64738i
\(378\) 0 0
\(379\) 135.588 + 87.1370i 0.357751 + 0.229913i 0.707154 0.707060i \(-0.249979\pi\)
−0.349402 + 0.936973i \(0.613615\pi\)
\(380\) 89.6332 139.472i 0.235877 0.367032i
\(381\) 0 0
\(382\) 45.3160 + 13.3060i 0.118628 + 0.0348324i
\(383\) −36.4286 + 5.23764i −0.0951137 + 0.0136753i −0.189707 0.981841i \(-0.560754\pi\)
0.0945936 + 0.995516i \(0.469845\pi\)
\(384\) 0 0
\(385\) −85.5985 187.435i −0.222334 0.486843i
\(386\) −69.9216 238.131i −0.181144 0.616920i
\(387\) 0 0
\(388\) −48.2663 + 335.699i −0.124398 + 0.865204i
\(389\) 228.536 + 355.609i 0.587496 + 0.914161i 0.999995 + 0.00320307i \(0.00101957\pi\)
−0.412499 + 0.910958i \(0.635344\pi\)
\(390\) 0 0
\(391\) 431.890 41.7705i 1.10458 0.106830i
\(392\) 256.657i 0.654737i
\(393\) 0 0
\(394\) 5.33261 37.0891i 0.0135346 0.0941349i
\(395\) 838.801 + 383.068i 2.12355 + 0.969792i
\(396\) 0 0
\(397\) 90.9337 + 199.117i 0.229052 + 0.501554i 0.988907 0.148539i \(-0.0474571\pi\)
−0.759854 + 0.650093i \(0.774730\pi\)
\(398\) −52.1126 + 45.1559i −0.130936 + 0.113457i
\(399\) 0 0
\(400\) 79.0908 + 23.2231i 0.197727 + 0.0580579i
\(401\) −274.287 237.671i −0.684009 0.592697i 0.241965 0.970285i \(-0.422208\pi\)
−0.925974 + 0.377588i \(0.876754\pi\)
\(402\) 0 0
\(403\) −742.647 477.270i −1.84280 1.18429i
\(404\) 45.1160 + 39.0932i 0.111673 + 0.0967653i
\(405\) 0 0
\(406\) −63.2070 439.614i −0.155682 1.08279i
\(407\) 90.7390 78.6258i 0.222946 0.193184i
\(408\) 0 0
\(409\) −613.916 + 180.262i −1.50102 + 0.440738i −0.926038 0.377430i \(-0.876808\pi\)
−0.574979 + 0.818168i \(0.694990\pi\)
\(410\) 138.766 + 63.3722i 0.338453 + 0.154566i
\(411\) 0 0
\(412\) 94.5857 60.7865i 0.229577 0.147540i
\(413\) 595.698i 1.44237i
\(414\) 0 0
\(415\) 201.752 0.486150
\(416\) −74.5146 115.947i −0.179122 0.278719i
\(417\) 0 0
\(418\) 18.6128 40.7564i 0.0445283 0.0975034i
\(419\) −78.2230 266.403i −0.186690 0.635807i −0.998643 0.0520841i \(-0.983414\pi\)
0.811953 0.583723i \(-0.198405\pi\)
\(420\) 0 0
\(421\) −525.911 606.933i −1.24919 1.44165i −0.851689 0.524047i \(-0.824422\pi\)
−0.397505 0.917600i \(-0.630124\pi\)
\(422\) −432.723 + 62.2162i −1.02541 + 0.147432i
\(423\) 0 0
\(424\) 121.862 140.637i 0.287411 0.331690i
\(425\) −210.184 + 327.053i −0.494550 + 0.769535i
\(426\) 0 0
\(427\) 24.0884 27.7995i 0.0564132 0.0651043i
\(428\) −7.17924 + 24.4502i −0.0167739 + 0.0571267i
\(429\) 0 0
\(430\) −22.5359 26.0078i −0.0524090 0.0604832i
\(431\) −133.179 + 60.8209i −0.309001 + 0.141116i −0.563879 0.825857i \(-0.690692\pi\)
0.254879 + 0.966973i \(0.417964\pi\)
\(432\) 0 0
\(433\) −17.0209 + 37.2706i −0.0393093 + 0.0860753i −0.928268 0.371912i \(-0.878702\pi\)
0.888959 + 0.457987i \(0.151430\pi\)
\(434\) −599.561 86.2038i −1.38148 0.198626i
\(435\) 0 0
\(436\) 179.658 0.412059
\(437\) 194.574 204.561i 0.445249 0.468102i
\(438\) 0 0
\(439\) −270.086 + 173.574i −0.615230 + 0.395384i −0.810815 0.585303i \(-0.800976\pi\)
0.195585 + 0.980687i \(0.437339\pi\)
\(440\) 48.8003 + 7.01643i 0.110910 + 0.0159464i
\(441\) 0 0
\(442\) 623.707 183.137i 1.41110 0.414337i
\(443\) −68.0622 + 31.0829i −0.153639 + 0.0701647i −0.490751 0.871300i \(-0.663277\pi\)
0.337111 + 0.941465i \(0.390550\pi\)
\(444\) 0 0
\(445\) 135.831 + 944.723i 0.305237 + 2.12297i
\(446\) 40.4377 137.718i 0.0906675 0.308785i
\(447\) 0 0
\(448\) −79.5573 51.1284i −0.177583 0.114126i
\(449\) 301.243 468.743i 0.670919 1.04397i −0.324267 0.945966i \(-0.605118\pi\)
0.995186 0.0980046i \(-0.0312460\pi\)
\(450\) 0 0
\(451\) 39.5575 + 11.6151i 0.0877106 + 0.0257542i
\(452\) 138.071 19.8515i 0.305466 0.0439193i
\(453\) 0 0
\(454\) 83.9740 + 183.877i 0.184965 + 0.405016i
\(455\) −547.994 1866.30i −1.20438 4.10175i
\(456\) 0 0
\(457\) −43.6023 + 303.260i −0.0954098 + 0.663590i 0.884850 + 0.465876i \(0.154261\pi\)
−0.980260 + 0.197714i \(0.936648\pi\)
\(458\) 295.391 + 459.638i 0.644959 + 1.00358i
\(459\) 0 0
\(460\) 276.292 + 142.014i 0.600636 + 0.308725i
\(461\) 646.978i 1.40342i −0.712461 0.701712i \(-0.752419\pi\)
0.712461 0.701712i \(-0.247581\pi\)
\(462\) 0 0
\(463\) 95.3539 663.201i 0.205948 1.43240i −0.580257 0.814433i \(-0.697048\pi\)
0.786205 0.617966i \(-0.212043\pi\)
\(464\) 96.6634 + 44.1447i 0.208326 + 0.0951395i
\(465\) 0 0
\(466\) −238.402 522.028i −0.511593 1.12023i
\(467\) −545.660 + 472.817i −1.16844 + 1.01246i −0.168796 + 0.985651i \(0.553988\pi\)
−0.999641 + 0.0268049i \(0.991467\pi\)
\(468\) 0 0
\(469\) 803.920 + 236.052i 1.71411 + 0.503309i
\(470\) −572.292 495.894i −1.21764 1.05509i
\(471\) 0 0
\(472\) −119.904 77.0578i −0.254035 0.163258i
\(473\) −7.02867 6.09038i −0.0148598 0.0128761i
\(474\) 0 0
\(475\) 35.9987 + 250.376i 0.0757867 + 0.527108i
\(476\) 337.084 292.085i 0.708159 0.613623i
\(477\) 0 0
\(478\) 109.825 32.2474i 0.229759 0.0674632i
\(479\) −106.456 48.6166i −0.222245 0.101496i 0.301181 0.953567i \(-0.402619\pi\)
−0.523426 + 0.852071i \(0.675346\pi\)
\(480\) 0 0
\(481\) 953.449 612.744i 1.98222 1.27390i
\(482\) 366.475i 0.760321i
\(483\) 0 0
\(484\) −228.676 −0.472471
\(485\) −619.142 963.403i −1.27658 1.98640i
\(486\) 0 0
\(487\) 195.527 428.145i 0.401494 0.879148i −0.595623 0.803264i \(-0.703095\pi\)
0.997117 0.0758843i \(-0.0241780\pi\)
\(488\) 2.47958 + 8.44467i 0.00508111 + 0.0173047i
\(489\) 0 0
\(490\) −567.531 654.966i −1.15823 1.33666i
\(491\) −421.318 + 60.5764i −0.858082 + 0.123374i −0.557292 0.830317i \(-0.688160\pi\)
−0.300790 + 0.953690i \(0.597250\pi\)
\(492\) 0 0
\(493\) −328.210 + 378.775i −0.665741 + 0.768306i
\(494\) 228.662 355.805i 0.462878 0.720252i
\(495\) 0 0
\(496\) 94.9089 109.531i 0.191349 0.220828i
\(497\) −341.388 + 1162.66i −0.686897 + 2.33936i
\(498\) 0 0
\(499\) 165.717 + 191.248i 0.332098 + 0.383262i 0.897100 0.441828i \(-0.145670\pi\)
−0.565002 + 0.825090i \(0.691124\pi\)
\(500\) 53.9674 24.6461i 0.107935 0.0492922i
\(501\) 0 0
\(502\) 202.246 442.858i 0.402881 0.882187i
\(503\) −416.854 59.9345i −0.828735 0.119154i −0.285123 0.958491i \(-0.592035\pi\)
−0.543612 + 0.839337i \(0.682944\pi\)
\(504\) 0 0
\(505\) −201.577 −0.399162
\(506\) 79.3707 + 27.3624i 0.156859 + 0.0540760i
\(507\) 0 0
\(508\) −205.278 + 131.924i −0.404091 + 0.259694i
\(509\) −207.447 29.8263i −0.407557 0.0585979i −0.0645124 0.997917i \(-0.520549\pi\)
−0.343045 + 0.939319i \(0.611458\pi\)
\(510\) 0 0
\(511\) −6.98640 + 2.05139i −0.0136720 + 0.00401447i
\(512\) 20.5826 9.39977i 0.0402004 0.0183589i
\(513\) 0 0
\(514\) 82.1246 + 571.189i 0.159776 + 1.11126i
\(515\) −106.960 + 364.274i −0.207690 + 0.707328i
\(516\) 0 0
\(517\) −172.162 110.642i −0.333002 0.214007i
\(518\) 420.436 654.212i 0.811653 1.26296i
\(519\) 0 0
\(520\) 446.542 + 131.116i 0.858734 + 0.252147i
\(521\) 18.4825 2.65738i 0.0354750 0.00510054i −0.124554 0.992213i \(-0.539750\pi\)
0.160030 + 0.987112i \(0.448841\pi\)
\(522\) 0 0
\(523\) −74.0594 162.168i −0.141605 0.310072i 0.825520 0.564373i \(-0.190882\pi\)
−0.967125 + 0.254301i \(0.918155\pi\)
\(524\) 4.90594 + 16.7081i 0.00936249 + 0.0318857i
\(525\) 0 0
\(526\) 34.4863 239.858i 0.0655634 0.456003i
\(527\) 369.550 + 575.031i 0.701234 + 1.09114i
\(528\) 0 0
\(529\) 416.616 + 325.994i 0.787554 + 0.616245i
\(530\) 628.360i 1.18559i
\(531\) 0 0
\(532\) 41.3005 287.252i 0.0776326 0.539947i
\(533\) 354.003 + 161.668i 0.664171 + 0.303317i
\(534\) 0 0
\(535\) −35.7447 78.2699i −0.0668125 0.146299i
\(536\) −151.506 + 131.281i −0.282661 + 0.244927i
\(537\) 0 0
\(538\) −56.5040 16.5911i −0.105026 0.0308384i
\(539\) −177.006 153.377i −0.328397 0.284558i
\(540\) 0 0
\(541\) 447.711 + 287.726i 0.827562 + 0.531842i 0.884502 0.466536i \(-0.154498\pi\)
−0.0569402 + 0.998378i \(0.518134\pi\)
\(542\) 386.104 + 334.561i 0.712368 + 0.617271i
\(543\) 0 0
\(544\) 15.1877 + 105.633i 0.0279186 + 0.194178i
\(545\) −458.471 + 397.267i −0.841231 + 0.728931i
\(546\) 0 0
\(547\) 213.747 62.7616i 0.390761 0.114738i −0.0804490 0.996759i \(-0.525635\pi\)
0.471210 + 0.882021i \(0.343817\pi\)
\(548\) 394.286 + 180.065i 0.719501 + 0.328585i
\(549\) 0 0
\(550\) −63.2803 + 40.6678i −0.115055 + 0.0739415i
\(551\) 326.099i 0.591830i
\(552\) 0 0
\(553\) 1614.13 2.91886
\(554\) 184.169 + 286.572i 0.332435 + 0.517278i
\(555\) 0 0
\(556\) 168.656 369.304i 0.303337 0.664216i
\(557\) −166.060 565.548i −0.298133 1.01535i −0.963250 0.268607i \(-0.913437\pi\)
0.665117 0.746739i \(-0.268382\pi\)
\(558\) 0 0
\(559\) −57.4909 66.3480i −0.102846 0.118690i
\(560\) 316.081 45.4455i 0.564430 0.0811528i
\(561\) 0 0
\(562\) 183.998 212.345i 0.327399 0.377838i
\(563\) 263.079 409.359i 0.467281 0.727104i −0.525001 0.851101i \(-0.675935\pi\)
0.992282 + 0.123998i \(0.0395716\pi\)
\(564\) 0 0
\(565\) −308.447 + 355.967i −0.545924 + 0.630030i
\(566\) −53.7695 + 183.122i −0.0949990 + 0.323537i
\(567\) 0 0
\(568\) −189.864 219.114i −0.334267 0.385765i
\(569\) 544.396 248.617i 0.956759 0.436937i 0.125051 0.992150i \(-0.460091\pi\)
0.831708 + 0.555213i \(0.187363\pi\)
\(570\) 0 0
\(571\) −6.24388 + 13.6722i −0.0109350 + 0.0239443i −0.915021 0.403407i \(-0.867826\pi\)
0.904086 + 0.427351i \(0.140553\pi\)
\(572\) 124.494 + 17.8995i 0.217646 + 0.0312928i
\(573\) 0 0
\(574\) 267.031 0.465211
\(575\) −460.474 + 112.303i −0.800825 + 0.195309i
\(576\) 0 0
\(577\) −279.044 + 179.331i −0.483611 + 0.310798i −0.759632 0.650354i \(-0.774621\pi\)
0.276020 + 0.961152i \(0.410984\pi\)
\(578\) −93.6540 13.4654i −0.162031 0.0232966i
\(579\) 0 0
\(580\) −344.291 + 101.093i −0.593606 + 0.174298i
\(581\) 321.240 146.705i 0.552908 0.252505i
\(582\) 0 0
\(583\) 24.1673 + 168.088i 0.0414534 + 0.288315i
\(584\) 0.490829 1.67161i 0.000840461 0.00286235i
\(585\) 0 0
\(586\) 380.015 + 244.221i 0.648491 + 0.416760i
\(587\) 152.124 236.710i 0.259155 0.403254i −0.687156 0.726510i \(-0.741141\pi\)
0.946312 + 0.323256i \(0.104778\pi\)
\(588\) 0 0
\(589\) 426.729 + 125.299i 0.724497 + 0.212732i
\(590\) 476.379 68.4930i 0.807422 0.116090i
\(591\) 0 0
\(592\) 77.2957 + 169.254i 0.130567 + 0.285902i
\(593\) 273.298 + 930.766i 0.460873 + 1.56959i 0.782455 + 0.622707i \(0.213967\pi\)
−0.321582 + 0.946882i \(0.604215\pi\)
\(594\) 0 0
\(595\) −214.337 + 1490.75i −0.360231 + 2.50546i
\(596\) −95.5104 148.617i −0.160252 0.249358i
\(597\) 0 0
\(598\) 704.845 + 362.288i 1.17867 + 0.605834i
\(599\) 1084.33i 1.81023i −0.425163 0.905117i \(-0.639783\pi\)
0.425163 0.905117i \(-0.360217\pi\)
\(600\) 0 0
\(601\) 113.207 787.370i 0.188364 1.31010i −0.647880 0.761742i \(-0.724344\pi\)
0.836244 0.548357i \(-0.184747\pi\)
\(602\) −54.7944 25.0238i −0.0910207 0.0415677i
\(603\) 0 0
\(604\) −211.084 462.210i −0.349477 0.765248i
\(605\) 583.561 505.658i 0.964564 0.835799i
\(606\) 0 0
\(607\) 102.403 + 30.0682i 0.168703 + 0.0495357i 0.364993 0.931010i \(-0.381071\pi\)
−0.196290 + 0.980546i \(0.562889\pi\)
\(608\) 52.4765 + 45.4712i 0.0863101 + 0.0747881i
\(609\) 0 0
\(610\) −25.0009 16.0671i −0.0409851 0.0263395i
\(611\) −1459.96 1265.07i −2.38947 2.07049i
\(612\) 0 0
\(613\) −82.8421 576.179i −0.135142 0.939934i −0.938707 0.344717i \(-0.887975\pi\)
0.803565 0.595217i \(-0.202934\pi\)
\(614\) −117.669 + 101.961i −0.191644 + 0.166060i
\(615\) 0 0
\(616\) 82.8043 24.3135i 0.134423 0.0394700i
\(617\) −263.016 120.115i −0.426282 0.194677i 0.190709 0.981647i \(-0.438921\pi\)
−0.616991 + 0.786970i \(0.711649\pi\)
\(618\) 0 0
\(619\) −802.141 + 515.505i −1.29587 + 0.832802i −0.992755 0.120153i \(-0.961662\pi\)
−0.303111 + 0.952955i \(0.598025\pi\)
\(620\) 489.380i 0.789322i
\(621\) 0 0
\(622\) 320.650 0.515514
\(623\) 903.237 + 1405.46i 1.44982 + 2.25596i
\(624\) 0 0
\(625\) −297.238 + 650.859i −0.475580 + 1.04138i
\(626\) −18.0450 61.4557i −0.0288259 0.0981720i
\(627\) 0 0
\(628\) 152.749 + 176.282i 0.243231 + 0.280703i
\(629\) −868.633 + 124.891i −1.38098 + 0.198554i
\(630\) 0 0
\(631\) −254.531 + 293.745i −0.403378 + 0.465523i −0.920702 0.390267i \(-0.872383\pi\)
0.517324 + 0.855790i \(0.326928\pi\)
\(632\) −208.799 + 324.898i −0.330379 + 0.514080i
\(633\) 0 0
\(634\) −177.805 + 205.197i −0.280449 + 0.323655i
\(635\) 232.135 790.581i 0.365568 1.24501i
\(636\) 0 0
\(637\) −1447.82 1670.87i −2.27287 2.62303i
\(638\) −88.2105 + 40.2844i −0.138261 + 0.0631417i
\(639\) 0 0
\(640\) −31.7399 + 69.5006i −0.0495935 + 0.108595i
\(641\) −426.469 61.3170i −0.665319 0.0956584i −0.198623 0.980076i \(-0.563647\pi\)
−0.466696 + 0.884418i \(0.654556\pi\)
\(642\) 0 0
\(643\) 317.314 0.493490 0.246745 0.969080i \(-0.420639\pi\)
0.246745 + 0.969080i \(0.420639\pi\)
\(644\) 543.193 + 25.2134i 0.843467 + 0.0391513i
\(645\) 0 0
\(646\) −275.499 + 177.053i −0.426470 + 0.274075i
\(647\) 328.012 + 47.1610i 0.506974 + 0.0728918i 0.391056 0.920367i \(-0.372110\pi\)
0.115918 + 0.993259i \(0.463019\pi\)
\(648\) 0 0
\(649\) 124.798 36.6440i 0.192293 0.0564622i
\(650\) −645.895 + 294.971i −0.993685 + 0.453801i
\(651\) 0 0
\(652\) −29.6311 206.089i −0.0454465 0.316088i
\(653\) 187.341 638.024i 0.286892 0.977065i −0.682364 0.731012i \(-0.739048\pi\)
0.969256 0.246053i \(-0.0791337\pi\)
\(654\) 0 0
\(655\) −49.4653 31.7894i −0.0755195 0.0485334i
\(656\) −34.5424 + 53.7491i −0.0526561 + 0.0819345i
\(657\) 0 0
\(658\) −1271.82 373.441i −1.93286 0.567540i
\(659\) 440.547 63.3410i 0.668508 0.0961169i 0.200299 0.979735i \(-0.435809\pi\)
0.468209 + 0.883618i \(0.344900\pi\)
\(660\) 0 0
\(661\) −356.750 781.173i −0.539712 1.18180i −0.961423 0.275074i \(-0.911298\pi\)
0.421711 0.906730i \(-0.361430\pi\)
\(662\) −213.079 725.682i −0.321872 1.09620i
\(663\) 0 0
\(664\) −12.0253 + 83.6377i −0.0181104 + 0.125960i
\(665\) 529.788 + 824.366i 0.796674 + 1.23965i
\(666\) 0 0
\(667\) −608.195 + 58.8220i −0.911836 + 0.0881889i
\(668\) 4.96240i 0.00742874i
\(669\) 0 0
\(670\) 96.3364 670.035i 0.143786 1.00005i
\(671\) −7.30575 3.33642i −0.0108879 0.00497232i
\(672\) 0 0
\(673\) 531.985 + 1164.88i 0.790467 + 1.73088i 0.675309 + 0.737535i \(0.264010\pi\)
0.115158 + 0.993347i \(0.463262\pi\)
\(674\) −269.028 + 233.114i −0.399151 + 0.345867i
\(675\) 0 0
\(676\) 814.856 + 239.263i 1.20541 + 0.353940i
\(677\) −787.832 682.660i −1.16371 1.00836i −0.999760 0.0218924i \(-0.993031\pi\)
−0.163950 0.986469i \(-0.552424\pi\)
\(678\) 0 0
\(679\) −1686.37 1083.77i −2.48361 1.59612i
\(680\) −272.337 235.982i −0.400496 0.347032i
\(681\) 0 0
\(682\) 18.8220 + 130.910i 0.0275983 + 0.191950i
\(683\) 112.099 97.1342i 0.164127 0.142217i −0.568925 0.822389i \(-0.692641\pi\)
0.733052 + 0.680172i \(0.238095\pi\)
\(684\) 0 0
\(685\) −1404.35 + 412.355i −2.05015 + 0.601978i
\(686\) −634.769 289.889i −0.925320 0.422579i
\(687\) 0 0
\(688\) 12.1249 7.79222i 0.0176234 0.0113259i
\(689\) 1603.00i 2.32656i
\(690\) 0 0
\(691\) −202.656 −0.293279 −0.146639 0.989190i \(-0.546846\pi\)
−0.146639 + 0.989190i \(0.546846\pi\)
\(692\) 24.1897 + 37.6399i 0.0349562 + 0.0543930i
\(693\) 0 0
\(694\) 89.2510 195.433i 0.128604 0.281603i
\(695\) 386.228 + 1315.37i 0.555723 + 1.89262i
\(696\) 0 0
\(697\) −197.333 227.734i −0.283118 0.326735i
\(698\) −215.117 + 30.9292i −0.308191 + 0.0443112i
\(699\) 0 0
\(700\) −319.055 + 368.210i −0.455794 + 0.526014i
\(701\) −299.347 + 465.793i −0.427029 + 0.664469i −0.986384 0.164459i \(-0.947412\pi\)
0.559355 + 0.828928i \(0.311049\pi\)
\(702\) 0 0
\(703\) −373.916 + 431.522i −0.531886 + 0.613830i
\(704\) −5.81741 + 19.8123i −0.00826337 + 0.0281425i
\(705\) 0 0
\(706\) −381.875 440.708i −0.540900 0.624232i
\(707\) −320.960 + 146.578i −0.453975 + 0.207323i
\(708\) 0 0
\(709\) 103.353 226.312i 0.145773 0.319199i −0.822635 0.568570i \(-0.807497\pi\)
0.968408 + 0.249372i \(0.0802240\pi\)
\(710\) 969.031 + 139.326i 1.36483 + 0.196233i
\(711\) 0 0
\(712\) −399.737 −0.561429
\(713\) −156.717 + 818.478i −0.219799 + 1.14794i
\(714\) 0 0
\(715\) −357.277 + 229.608i −0.499688 + 0.321130i
\(716\) 15.5901 + 2.24152i 0.0217739 + 0.00313061i
\(717\) 0 0
\(718\) 390.165 114.563i 0.543405 0.159558i
\(719\) 1034.62 472.496i 1.43897 0.657157i 0.465311 0.885148i \(-0.345943\pi\)
0.973663 + 0.227990i \(0.0732154\pi\)
\(720\) 0 0
\(721\) 94.5762 + 657.792i 0.131174 + 0.912333i
\(722\) 83.8021 285.404i 0.116069 0.395296i
\(723\) 0 0
\(724\) −21.5447 13.8459i −0.0297578 0.0191242i
\(725\) 295.985 460.561i 0.408255 0.635257i
\(726\) 0 0
\(727\) 1171.05 + 343.851i 1.61080 + 0.472973i 0.958524 0.285011i \(-0.0919971\pi\)
0.652274 + 0.757984i \(0.273815\pi\)
\(728\) 806.348 115.935i 1.10762 0.159252i
\(729\) 0 0
\(730\) 2.44379 + 5.35115i 0.00334765 + 0.00733034i
\(731\) 19.1512 + 65.2230i 0.0261986 + 0.0892244i
\(732\) 0 0
\(733\) −112.591 + 783.085i −0.153603 + 1.06833i 0.756514 + 0.653977i \(0.226901\pi\)
−0.910117 + 0.414352i \(0.864008\pi\)
\(734\) −119.644 186.169i −0.163002 0.253637i
\(735\) 0 0
\(736\) −75.3409 + 106.074i −0.102365 + 0.144123i
\(737\) 182.941i 0.248224i
\(738\) 0 0
\(739\) 156.219 1086.52i 0.211392 1.47026i −0.557123 0.830430i \(-0.688095\pi\)
0.768515 0.639832i \(-0.220996\pi\)
\(740\) −571.514 261.002i −0.772316 0.352705i
\(741\) 0 0
\(742\) 456.916 + 1000.51i 0.615790 + 1.34839i
\(743\) −850.931 + 737.336i −1.14526 + 0.992377i −0.145268 + 0.989392i \(0.546405\pi\)
−0.999996 + 0.00298450i \(0.999050\pi\)
\(744\) 0 0
\(745\) 572.363 + 168.061i 0.768272 + 0.225585i
\(746\) 552.631 + 478.857i 0.740792 + 0.641900i
\(747\) 0 0
\(748\) −81.9269 52.6512i −0.109528 0.0703893i
\(749\) −113.829 98.6333i −0.151975 0.131687i
\(750\) 0 0
\(751\) 38.0101 + 264.366i 0.0506127 + 0.352019i 0.999353 + 0.0359627i \(0.0114498\pi\)
−0.948740 + 0.316056i \(0.897641\pi\)
\(752\) 239.687 207.690i 0.318733 0.276184i
\(753\) 0 0
\(754\) −878.316 + 257.897i −1.16488 + 0.342038i
\(755\) 1560.73 + 712.760i 2.06719 + 0.944053i
\(756\) 0 0
\(757\) −331.202 + 212.850i −0.437519 + 0.281176i −0.740801 0.671725i \(-0.765554\pi\)
0.303282 + 0.952901i \(0.401917\pi\)
\(758\) 227.934i 0.300704i
\(759\) 0 0
\(760\) −234.463 −0.308504
\(761\) 120.836 + 188.025i 0.158786 + 0.247076i 0.911526 0.411241i \(-0.134905\pi\)
−0.752740 + 0.658318i \(0.771268\pi\)
\(762\) 0 0
\(763\) −441.125 + 965.929i −0.578145 + 1.26596i
\(764\) −18.8175 64.0865i −0.0246302 0.0838828i
\(765\) 0 0
\(766\) 34.0839 + 39.3349i 0.0444959 + 0.0513510i
\(767\) 1215.28 174.731i 1.58446 0.227811i
\(768\) 0 0
\(769\) 282.593 326.130i 0.367481 0.424096i −0.541651 0.840603i \(-0.682201\pi\)
0.909132 + 0.416508i \(0.136746\pi\)
\(770\) −157.546 + 245.147i −0.204605 + 0.318372i
\(771\) 0 0
\(772\) −229.847 + 265.257i −0.297729 + 0.343597i
\(773\) 108.577 369.778i 0.140461 0.478367i −0.858972 0.512022i \(-0.828897\pi\)
0.999434 + 0.0336548i \(0.0107147\pi\)
\(774\) 0 0
\(775\) −488.957 564.287i −0.630913 0.728112i
\(776\) 436.289 199.246i 0.562228 0.256761i
\(777\) 0 0
\(778\) 248.338 543.784i 0.319200 0.698951i
\(779\) −194.068 27.9027i −0.249124 0.0358186i
\(780\) 0 0
\(781\) 264.576 0.338766
\(782\) −379.910 481.887i −0.485818 0.616224i
\(783\) 0 0
\(784\) 305.348 196.235i 0.389474 0.250300i
\(785\) −779.604 112.090i −0.993126 0.142790i
\(786\) 0 0
\(787\) 1132.28 332.467i 1.43873 0.422448i 0.532929 0.846160i \(-0.321091\pi\)
0.905797 + 0.423712i \(0.139273\pi\)
\(788\) −48.2026 + 22.0134i −0.0611708 + 0.0279358i
\(789\) 0 0
\(790\) −185.592 1290.82i −0.234926 1.63395i
\(791\) −232.281 + 791.078i −0.293655 + 1.00010i
\(792\) 0 0
\(793\) −63.7794 40.9885i −0.0804280 0.0516879i
\(794\) 167.366 260.426i 0.210788 0.327993i
\(795\) 0 0
\(796\) 93.5668 + 27.4737i 0.117546 + 0.0345147i
\(797\) 1305.24 187.665i 1.63769 0.235464i 0.738890 0.673826i \(-0.235350\pi\)
0.898799 + 0.438362i \(0.144441\pi\)
\(798\) 0 0
\(799\) 621.378 + 1360.63i 0.777695 + 1.70291i
\(800\) −32.8425 111.851i −0.0410531 0.139814i
\(801\) 0 0
\(802\) −73.0455 + 508.042i −0.0910791 + 0.633469i
\(803\) 0.859528 + 1.33745i 0.00107040 + 0.00166557i
\(804\) 0 0
\(805\) −1441.93 + 1136.79i −1.79122 + 1.41216i
\(806\) 1248.45i 1.54894i
\(807\) 0 0
\(808\) 12.0148 83.5649i 0.0148698 0.103422i
\(809\) −129.775 59.2663i −0.160414 0.0732587i 0.333590 0.942718i \(-0.391740\pi\)
−0.494004 + 0.869460i \(0.664467\pi\)
\(810\) 0 0
\(811\) 340.546 + 745.692i 0.419909 + 0.919473i 0.994858 + 0.101283i \(0.0322948\pi\)
−0.574949 + 0.818190i \(0.694978\pi\)
\(812\) −474.687 + 411.319i −0.584590 + 0.506551i
\(813\) 0 0
\(814\) −162.919 47.8374i −0.200147 0.0587684i
\(815\) 531.330 + 460.400i 0.651938 + 0.564908i
\(816\) 0 0
\(817\) 37.2076 + 23.9119i 0.0455417 + 0.0292679i
\(818\) 683.849 + 592.558i 0.836001 + 0.724399i
\(819\) 0 0
\(820\) −30.7031 213.545i −0.0374428 0.260420i
\(821\) 1188.87 1030.16i 1.44808 1.25477i 0.536338 0.844003i \(-0.319807\pi\)
0.911741 0.410765i \(-0.134738\pi\)
\(822\) 0 0
\(823\) 405.529 119.074i 0.492745 0.144683i −0.0259142 0.999664i \(-0.508250\pi\)
0.518659 + 0.854981i \(0.326431\pi\)
\(824\) −144.637 66.0535i −0.175530 0.0801620i
\(825\) 0 0
\(826\) 708.709 455.460i 0.858001 0.551404i
\(827\) 743.481i 0.899009i 0.893278 + 0.449505i \(0.148399\pi\)
−0.893278 + 0.449505i \(0.851601\pi\)
\(828\) 0 0
\(829\) 204.499 0.246681 0.123341 0.992364i \(-0.460639\pi\)
0.123341 + 0.992364i \(0.460639\pi\)
\(830\) −154.256 240.027i −0.185851 0.289189i
\(831\) 0 0
\(832\) −80.9710 + 177.302i −0.0973209 + 0.213103i
\(833\) 482.294 + 1642.54i 0.578984 + 1.97184i
\(834\) 0 0
\(835\) −10.9731 12.6636i −0.0131414 0.0151660i
\(836\) −62.7194 + 9.01769i −0.0750232 + 0.0107867i
\(837\) 0 0
\(838\) −257.135 + 296.750i −0.306844 + 0.354117i
\(839\) 414.268 644.614i 0.493764 0.768312i −0.501537 0.865136i \(-0.667232\pi\)
0.995302 + 0.0968238i \(0.0308683\pi\)
\(840\) 0 0
\(841\) −88.5462 + 102.188i −0.105287 + 0.121507i
\(842\) −319.974 + 1089.73i −0.380017 + 1.29422i
\(843\) 0 0
\(844\) 404.872 + 467.247i 0.479706 + 0.553610i
\(845\) −2608.51 + 1191.27i −3.08700 + 1.40978i
\(846\) 0 0
\(847\) 561.482 1229.47i 0.662907 1.45156i
\(848\) −260.491 37.4530i −0.307183 0.0441662i
\(849\) 0 0
\(850\) 549.801 0.646825
\(851\) −872.264 619.539i −1.02499 0.728013i
\(852\) 0 0
\(853\) 514.895 330.903i 0.603628 0.387928i −0.202835 0.979213i \(-0.565015\pi\)
0.806463 + 0.591285i \(0.201379\pi\)
\(854\) −51.4910 7.40329i −0.0602939 0.00866895i
\(855\) 0 0
\(856\) 34.5779 10.1530i 0.0403947 0.0118610i
\(857\) −1237.48 + 565.140i −1.44397 + 0.659440i −0.974680 0.223604i \(-0.928218\pi\)
−0.469291 + 0.883044i \(0.655490\pi\)
\(858\) 0 0
\(859\) −234.463 1630.73i −0.272949 1.89840i −0.417120 0.908851i \(-0.636961\pi\)
0.144171 0.989553i \(-0.453948\pi\)
\(860\) −13.7113 + 46.6963i −0.0159433 + 0.0542980i
\(861\) 0 0
\(862\) 174.186 + 111.942i 0.202072 + 0.129864i
\(863\) 917.140 1427.10i 1.06273 1.65365i 0.376220 0.926530i \(-0.377224\pi\)
0.686514 0.727117i \(-0.259140\pi\)
\(864\) 0 0
\(865\) −144.961 42.5644i −0.167585 0.0492074i
\(866\) 57.3552 8.24643i 0.0662300 0.00952244i
\(867\) 0 0
\(868\) 355.855 + 779.214i 0.409972 + 0.897712i
\(869\) −99.2923 338.158i −0.114260 0.389135i
\(870\) 0 0
\(871\) 245.762 1709.31i 0.282161 1.96247i
\(872\) −137.363 213.741i −0.157526 0.245116i
\(873\) 0 0
\(874\) −392.136 75.0835i −0.448668 0.0859079i
\(875\) 350.670i 0.400766i
\(876\) 0 0
\(877\) −213.219 + 1482.97i −0.243123 + 1.69096i 0.393137 + 0.919480i \(0.371390\pi\)
−0.636259 + 0.771475i \(0.719519\pi\)
\(878\) 413.005 + 188.613i 0.470393 + 0.214821i
\(879\) 0 0
\(880\) −28.9643 63.4230i −0.0329140 0.0720715i
\(881\) −911.751 + 790.037i −1.03490 + 0.896750i −0.994739 0.102443i \(-0.967334\pi\)
−0.0401659 + 0.999193i \(0.512789\pi\)
\(882\) 0 0
\(883\) −119.197 34.9993i −0.134990 0.0396368i 0.213539 0.976934i \(-0.431501\pi\)
−0.348530 + 0.937298i \(0.613319\pi\)
\(884\) −694.755 602.009i −0.785922 0.681006i
\(885\) 0 0
\(886\) 89.0188 + 57.2089i 0.100473 + 0.0645699i
\(887\) −1060.70 919.102i −1.19583 1.03619i −0.998438 0.0558663i \(-0.982208\pi\)
−0.197390 0.980325i \(-0.563247\pi\)
\(888\) 0 0
\(889\) −205.258 1427.60i −0.230886 1.60585i
\(890\) 1020.09 883.917i 1.14617 0.993165i
\(891\) 0 0
\(892\) −194.763 + 57.1876i −0.218344 + 0.0641116i
\(893\) 885.289 + 404.298i 0.991365 + 0.452741i
\(894\) 0 0
\(895\) −44.7411 + 28.7533i −0.0499900 + 0.0321266i
\(896\) 133.742i 0.149266i
\(897\) 0 0
\(898\) −787.993 −0.877498
\(899\) −520.407 809.770i −0.578873 0.900745i
\(900\) 0 0
\(901\) 515.614 1129.04i 0.572269 1.25309i
\(902\) −16.4263 55.9427i −0.0182109 0.0620208i
\(903\) 0 0
\(904\) −129.184 149.086i −0.142902 0.164918i
\(905\) 85.5968 12.3070i 0.0945820 0.0135988i
\(906\) 0 0
\(907\) 85.7957 99.0135i 0.0945929 0.109166i −0.706479 0.707734i \(-0.749718\pi\)
0.801072 + 0.598568i \(0.204263\pi\)
\(908\) 154.556 240.494i 0.170216 0.264861i
\(909\) 0 0
\(910\) −1801.37 + 2078.89i −1.97953 + 2.28449i
\(911\) 295.223 1005.44i 0.324064 1.10366i −0.622894 0.782306i \(-0.714043\pi\)
0.946959 0.321356i \(-0.104138\pi\)
\(912\) 0 0
\(913\) −50.4954 58.2748i −0.0553072 0.0638279i
\(914\) 394.130 179.993i 0.431215 0.196929i
\(915\) 0 0
\(916\) 320.986 702.861i 0.350421 0.767315i
\(917\) −101.877 14.6477i −0.111098 0.0159735i
\(918\) 0 0
\(919\) 1235.85 1.34478 0.672389 0.740198i \(-0.265268\pi\)
0.672389 + 0.740198i \(0.265268\pi\)
\(920\) −42.2927 437.289i −0.0459704 0.475315i
\(921\) 0 0
\(922\) −769.718 + 494.668i −0.834835 + 0.536516i
\(923\) 2472.08 + 355.431i 2.67831 + 0.385083i
\(924\) 0 0
\(925\) 919.769 270.069i 0.994345 0.291966i
\(926\) −861.924 + 393.628i −0.930803 + 0.425084i
\(927\) 0 0
\(928\) −21.3876 148.754i −0.0230470 0.160295i
\(929\) 167.180 569.363i 0.179957 0.612877i −0.819264 0.573416i \(-0.805618\pi\)
0.999221 0.0394607i \(-0.0125640\pi\)
\(930\) 0 0
\(931\) 937.016 + 602.183i 1.00646 + 0.646814i
\(932\) −438.785 + 682.763i −0.470799 + 0.732578i
\(933\) 0 0
\(934\) 979.718 + 287.671i 1.04895 + 0.307999i
\(935\) 325.495 46.7991i 0.348123 0.0500525i
\(936\) 0 0
\(937\) −534.327 1170.01i −0.570253 1.24868i −0.946663 0.322226i \(-0.895569\pi\)
0.376410 0.926453i \(-0.377158\pi\)
\(938\) −333.828 1136.91i −0.355893 1.21206i
\(939\) 0 0
\(940\) −152.407 + 1060.01i −0.162135 + 1.12767i
\(941\) −852.394 1326.35i −0.905838 1.40951i −0.912296 0.409532i \(-0.865692\pi\)
0.00645768 0.999979i \(-0.497944\pi\)
\(942\) 0 0
\(943\) 17.0342 366.982i 0.0180639 0.389164i
\(944\) 201.569i 0.213526i
\(945\) 0 0
\(946\) −1.87180 + 13.0187i −0.00197865 + 0.0137618i
\(947\) 645.532 + 294.805i 0.681660 + 0.311304i 0.725982 0.687713i \(-0.241385\pi\)
−0.0443219 + 0.999017i \(0.514113\pi\)
\(948\) 0 0
\(949\) 6.23431 + 13.6512i 0.00656934 + 0.0143849i
\(950\) 270.352 234.261i 0.284581 0.246591i
\(951\) 0 0
\(952\) −605.225 177.710i −0.635740 0.186670i
\(953\) −232.035 201.060i −0.243479 0.210975i 0.524569 0.851368i \(-0.324226\pi\)
−0.768048 + 0.640392i \(0.778772\pi\)
\(954\) 0 0
\(955\) 189.731 + 121.933i 0.198672 + 0.127679i
\(956\) −122.335 106.004i −0.127965 0.110883i
\(957\) 0 0
\(958\) 23.5542 + 163.823i 0.0245868 + 0.171005i
\(959\) −1936.23 + 1677.75i −2.01901 + 1.74948i
\(960\) 0 0
\(961\) −337.542 + 99.1112i −0.351240 + 0.103133i
\(962\) −1457.98 665.837i −1.51557 0.692138i
\(963\) 0 0
\(964\) 435.999 280.200i 0.452281 0.290664i
\(965\) 1185.16i 1.22814i
\(966\) 0 0
\(967\) −330.476 −0.341754 −0.170877 0.985292i \(-0.554660\pi\)
−0.170877 + 0.985292i \(0.554660\pi\)
\(968\) 174.841 + 272.059i 0.180621 + 0.281052i
\(969\) 0 0
\(970\) −672.788 + 1473.20i −0.693596 + 1.51876i
\(971\) 247.172 + 841.789i 0.254554 + 0.866930i 0.983276 + 0.182121i \(0.0582963\pi\)
−0.728722 + 0.684809i \(0.759886\pi\)
\(972\) 0 0
\(973\) 1571.45 + 1813.55i 1.61506 + 1.86387i
\(974\) −658.866 + 94.7307i −0.676454 + 0.0972594i
\(975\) 0 0
\(976\) 8.15089 9.40663i 0.00835132 0.00963794i
\(977\) 372.880 580.213i 0.381659 0.593872i −0.596277 0.802779i \(-0.703354\pi\)
0.977936 + 0.208906i \(0.0669904\pi\)
\(978\) 0 0
\(979\) 238.881 275.683i 0.244005 0.281597i
\(980\) −345.297 + 1175.97i −0.352344 + 1.19997i
\(981\) 0 0
\(982\) 394.201 + 454.932i 0.401427 + 0.463271i
\(983\) 1025.01 468.107i 1.04274 0.476203i 0.180962 0.983490i \(-0.442079\pi\)
0.861777 + 0.507288i \(0.169352\pi\)
\(984\) 0 0
\(985\) 74.3319 162.764i 0.0754638 0.165243i
\(986\) 701.577 + 100.871i 0.711538 + 0.102304i
\(987\) 0 0
\(988\) −598.136 −0.605400
\(989\) −37.8856 + 73.7078i −0.0383070 + 0.0745276i
\(990\) 0 0
\(991\) −481.780 + 309.621i −0.486155 + 0.312433i −0.760657 0.649153i \(-0.775123\pi\)
0.274502 + 0.961586i \(0.411487\pi\)
\(992\) −202.876 29.1691i −0.204512 0.0294043i
\(993\) 0 0
\(994\) 1644.25 482.796i 1.65418 0.485710i
\(995\) −299.525 + 136.789i −0.301031 + 0.137476i
\(996\) 0 0
\(997\) 141.087 + 981.283i 0.141512 + 0.984235i 0.929573 + 0.368638i \(0.120176\pi\)
−0.788061 + 0.615597i \(0.788915\pi\)
\(998\) 100.825 343.380i 0.101027 0.344068i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 414.3.k.a.35.1 80
3.2 odd 2 inner 414.3.k.a.35.8 yes 80
23.2 even 11 inner 414.3.k.a.71.8 yes 80
69.2 odd 22 inner 414.3.k.a.71.1 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
414.3.k.a.35.1 80 1.1 even 1 trivial
414.3.k.a.35.8 yes 80 3.2 odd 2 inner
414.3.k.a.71.1 yes 80 69.2 odd 22 inner
414.3.k.a.71.8 yes 80 23.2 even 11 inner