Properties

Label 414.3.k.b.179.2
Level $414$
Weight $3$
Character 414.179
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 179.2
Character \(\chi\) \(=\) 414.179
Dual form 414.3.k.b.377.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.398430 + 1.35693i) q^{2} +(-1.68251 - 1.08128i) q^{4} +(0.248013 + 0.0356589i) q^{5} +(-2.43143 - 5.32409i) q^{7} +(2.13758 - 1.85223i) q^{8} +O(q^{10})\) \(q+(-0.398430 + 1.35693i) q^{2} +(-1.68251 - 1.08128i) q^{4} +(0.248013 + 0.0356589i) q^{5} +(-2.43143 - 5.32409i) q^{7} +(2.13758 - 1.85223i) q^{8} +(-0.147203 + 0.322329i) q^{10} +(3.31490 + 11.2895i) q^{11} +(-2.93599 + 6.42891i) q^{13} +(8.19317 - 1.17800i) q^{14} +(1.66166 + 3.63853i) q^{16} +(-14.1185 - 21.9688i) q^{17} +(-23.8489 - 15.3268i) q^{19} +(-0.378727 - 0.328169i) q^{20} -16.6398 q^{22} +(22.4715 - 4.90223i) q^{23} +(-23.9271 - 7.02563i) q^{25} +(-7.55379 - 6.54539i) q^{26} +(-1.66594 + 11.5869i) q^{28} +(-10.1321 - 15.7658i) q^{29} +(-30.8842 - 35.6423i) q^{31} +(-5.59928 + 0.805054i) q^{32} +(35.4352 - 10.4047i) q^{34} +(-0.413176 - 1.40715i) q^{35} +(-0.393342 - 2.73575i) q^{37} +(30.2994 - 26.2546i) q^{38} +(0.596198 - 0.383153i) q^{40} +(69.6368 + 10.0123i) q^{41} +(-13.3344 + 15.3887i) q^{43} +(6.62980 - 22.5790i) q^{44} +(-2.30134 + 32.4454i) q^{46} -35.9856i q^{47} +(9.65407 - 11.1414i) q^{49} +(19.0665 - 29.6681i) q^{50} +(11.8913 - 7.64206i) q^{52} +(-35.7151 + 16.3106i) q^{53} +(0.419567 + 2.91816i) q^{55} +(-15.0588 - 6.87713i) q^{56} +(25.4300 - 7.46693i) q^{58} +(-77.7269 - 35.4967i) q^{59} +(-45.3143 - 52.2955i) q^{61} +(60.6692 - 27.7067i) q^{62} +(1.13852 - 7.91857i) q^{64} +(-0.957412 + 1.48976i) q^{65} +(-47.8061 - 14.0372i) q^{67} +52.2286i q^{68} +2.07402 q^{70} +(-15.6758 + 53.3870i) q^{71} +(97.9254 + 62.9328i) q^{73} +(3.86894 + 0.556269i) q^{74} +(23.5534 + 51.5747i) q^{76} +(52.0465 - 45.0985i) q^{77} +(30.4262 - 66.6241i) q^{79} +(0.282368 + 0.961657i) q^{80} +(-41.3313 + 90.5030i) q^{82} +(16.3863 - 2.35600i) q^{83} +(-2.71819 - 5.95200i) q^{85} +(-15.5686 - 24.2251i) q^{86} +(27.9966 + 17.9923i) q^{88} +(8.85582 + 7.67361i) q^{89} +41.3668 q^{91} +(-43.1091 - 16.0500i) q^{92} +(48.8299 + 14.3377i) q^{94} +(-5.36831 - 4.65167i) q^{95} +(11.3739 - 79.1074i) q^{97} +(11.2716 + 17.5389i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(47\) \(235\)
\(\chi(n)\) \(-1\) \(e\left(\frac{6}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.398430 + 1.35693i −0.199215 + 0.678464i
\(3\) 0 0
\(4\) −1.68251 1.08128i −0.420627 0.270320i
\(5\) 0.248013 + 0.0356589i 0.0496027 + 0.00713179i 0.167071 0.985945i \(-0.446569\pi\)
−0.117469 + 0.993077i \(0.537478\pi\)
\(6\) 0 0
\(7\) −2.43143 5.32409i −0.347347 0.760585i −0.999996 0.00292371i \(-0.999069\pi\)
0.652648 0.757661i \(-0.273658\pi\)
\(8\) 2.13758 1.85223i 0.267198 0.231528i
\(9\) 0 0
\(10\) −0.147203 + 0.322329i −0.0147203 + 0.0322329i
\(11\) 3.31490 + 11.2895i 0.301354 + 1.02632i 0.961414 + 0.275106i \(0.0887129\pi\)
−0.660059 + 0.751213i \(0.729469\pi\)
\(12\) 0 0
\(13\) −2.93599 + 6.42891i −0.225845 + 0.494532i −0.988302 0.152507i \(-0.951265\pi\)
0.762457 + 0.647039i \(0.223993\pi\)
\(14\) 8.19317 1.17800i 0.585226 0.0841428i
\(15\) 0 0
\(16\) 1.66166 + 3.63853i 0.103854 + 0.227408i
\(17\) −14.1185 21.9688i −0.830498 1.29228i −0.953961 0.299931i \(-0.903036\pi\)
0.123463 0.992349i \(-0.460600\pi\)
\(18\) 0 0
\(19\) −23.8489 15.3268i −1.25521 0.806671i −0.267585 0.963534i \(-0.586226\pi\)
−0.987620 + 0.156863i \(0.949862\pi\)
\(20\) −0.378727 0.328169i −0.0189363 0.0164084i
\(21\) 0 0
\(22\) −16.6398 −0.756355
\(23\) 22.4715 4.90223i 0.977022 0.213141i
\(24\) 0 0
\(25\) −23.9271 7.02563i −0.957083 0.281025i
\(26\) −7.55379 6.54539i −0.290530 0.251746i
\(27\) 0 0
\(28\) −1.66594 + 11.5869i −0.0594980 + 0.413817i
\(29\) −10.1321 15.7658i −0.349382 0.543649i 0.621436 0.783465i \(-0.286549\pi\)
−0.970819 + 0.239815i \(0.922913\pi\)
\(30\) 0 0
\(31\) −30.8842 35.6423i −0.996265 1.14975i −0.988719 0.149780i \(-0.952144\pi\)
−0.00754580 0.999972i \(-0.502402\pi\)
\(32\) −5.59928 + 0.805054i −0.174977 + 0.0251579i
\(33\) 0 0
\(34\) 35.4352 10.4047i 1.04221 0.306021i
\(35\) −0.413176 1.40715i −0.0118050 0.0402042i
\(36\) 0 0
\(37\) −0.393342 2.73575i −0.0106309 0.0739393i 0.983815 0.179185i \(-0.0573461\pi\)
−0.994446 + 0.105246i \(0.966437\pi\)
\(38\) 30.2994 26.2546i 0.797353 0.690910i
\(39\) 0 0
\(40\) 0.596198 0.383153i 0.0149049 0.00957882i
\(41\) 69.6368 + 10.0123i 1.69846 + 0.244202i 0.922338 0.386383i \(-0.126276\pi\)
0.776121 + 0.630585i \(0.217185\pi\)
\(42\) 0 0
\(43\) −13.3344 + 15.3887i −0.310102 + 0.357877i −0.889312 0.457302i \(-0.848816\pi\)
0.579209 + 0.815179i \(0.303361\pi\)
\(44\) 6.62980 22.5790i 0.150677 0.513160i
\(45\) 0 0
\(46\) −2.30134 + 32.4454i −0.0500291 + 0.705335i
\(47\) 35.9856i 0.765651i −0.923821 0.382825i \(-0.874951\pi\)
0.923821 0.382825i \(-0.125049\pi\)
\(48\) 0 0
\(49\) 9.65407 11.1414i 0.197022 0.227375i
\(50\) 19.0665 29.6681i 0.381331 0.593362i
\(51\) 0 0
\(52\) 11.8913 7.64206i 0.228679 0.146963i
\(53\) −35.7151 + 16.3106i −0.673871 + 0.307746i −0.722801 0.691056i \(-0.757146\pi\)
0.0489309 + 0.998802i \(0.484419\pi\)
\(54\) 0 0
\(55\) 0.419567 + 2.91816i 0.00762850 + 0.0530574i
\(56\) −15.0588 6.87713i −0.268907 0.122806i
\(57\) 0 0
\(58\) 25.4300 7.46693i 0.438449 0.128740i
\(59\) −77.7269 35.4967i −1.31741 0.601639i −0.372211 0.928148i \(-0.621400\pi\)
−0.945194 + 0.326509i \(0.894128\pi\)
\(60\) 0 0
\(61\) −45.3143 52.2955i −0.742858 0.857304i 0.250998 0.967988i \(-0.419241\pi\)
−0.993856 + 0.110684i \(0.964696\pi\)
\(62\) 60.6692 27.7067i 0.978536 0.446882i
\(63\) 0 0
\(64\) 1.13852 7.91857i 0.0177894 0.123728i
\(65\) −0.957412 + 1.48976i −0.0147294 + 0.0229194i
\(66\) 0 0
\(67\) −47.8061 14.0372i −0.713525 0.209510i −0.0952290 0.995455i \(-0.530358\pi\)
−0.618296 + 0.785946i \(0.712177\pi\)
\(68\) 52.2286i 0.768068i
\(69\) 0 0
\(70\) 2.07402 0.0296289
\(71\) −15.6758 + 53.3870i −0.220786 + 0.751929i 0.772374 + 0.635168i \(0.219069\pi\)
−0.993160 + 0.116761i \(0.962749\pi\)
\(72\) 0 0
\(73\) 97.9254 + 62.9328i 1.34144 + 0.862094i 0.997052 0.0767321i \(-0.0244486\pi\)
0.344392 + 0.938826i \(0.388085\pi\)
\(74\) 3.86894 + 0.556269i 0.0522830 + 0.00751715i
\(75\) 0 0
\(76\) 23.5534 + 51.5747i 0.309913 + 0.678615i
\(77\) 52.0465 45.0985i 0.675928 0.585695i
\(78\) 0 0
\(79\) 30.4262 66.6241i 0.385142 0.843343i −0.613421 0.789756i \(-0.710207\pi\)
0.998563 0.0535870i \(-0.0170655\pi\)
\(80\) 0.282368 + 0.961657i 0.00352960 + 0.0120207i
\(81\) 0 0
\(82\) −41.3313 + 90.5030i −0.504040 + 1.10369i
\(83\) 16.3863 2.35600i 0.197426 0.0283855i −0.0428925 0.999080i \(-0.513657\pi\)
0.240318 + 0.970694i \(0.422748\pi\)
\(84\) 0 0
\(85\) −2.71819 5.95200i −0.0319787 0.0700235i
\(86\) −15.5686 24.2251i −0.181030 0.281688i
\(87\) 0 0
\(88\) 27.9966 + 17.9923i 0.318143 + 0.204458i
\(89\) 8.85582 + 7.67361i 0.0995036 + 0.0862203i 0.703192 0.711000i \(-0.251757\pi\)
−0.603688 + 0.797220i \(0.706303\pi\)
\(90\) 0 0
\(91\) 41.3668 0.454580
\(92\) −43.1091 16.0500i −0.468578 0.174456i
\(93\) 0 0
\(94\) 48.8299 + 14.3377i 0.519467 + 0.152529i
\(95\) −5.36831 4.65167i −0.0565085 0.0489649i
\(96\) 0 0
\(97\) 11.3739 79.1074i 0.117257 0.815540i −0.843297 0.537447i \(-0.819389\pi\)
0.960554 0.278093i \(-0.0897022\pi\)
\(98\) 11.2716 + 17.5389i 0.115016 + 0.178969i
\(99\) 0 0
\(100\) 32.6608 + 37.6926i 0.326608 + 0.376926i
\(101\) 12.7182 1.82860i 0.125923 0.0181049i −0.0790653 0.996869i \(-0.525194\pi\)
0.204988 + 0.978764i \(0.434284\pi\)
\(102\) 0 0
\(103\) 64.1290 18.8300i 0.622612 0.182815i 0.0448141 0.998995i \(-0.485730\pi\)
0.577798 + 0.816180i \(0.303912\pi\)
\(104\) 5.63189 + 19.1804i 0.0541528 + 0.184427i
\(105\) 0 0
\(106\) −7.90227 54.9615i −0.0745497 0.518505i
\(107\) −109.098 + 94.5340i −1.01961 + 0.883495i −0.993231 0.116157i \(-0.962942\pi\)
−0.0263768 + 0.999652i \(0.508397\pi\)
\(108\) 0 0
\(109\) −134.216 + 86.2553i −1.23134 + 0.791333i −0.984099 0.177622i \(-0.943160\pi\)
−0.247239 + 0.968954i \(0.579523\pi\)
\(110\) −4.12690 0.593358i −0.0375172 0.00539416i
\(111\) 0 0
\(112\) 15.3316 17.6937i 0.136890 0.157979i
\(113\) −41.8294 + 142.458i −0.370172 + 1.26069i 0.538303 + 0.842751i \(0.319066\pi\)
−0.908475 + 0.417939i \(0.862753\pi\)
\(114\) 0 0
\(115\) 5.74804 0.414510i 0.0499830 0.00360444i
\(116\) 37.4818i 0.323119i
\(117\) 0 0
\(118\) 79.1352 91.3269i 0.670637 0.773956i
\(119\) −82.6356 + 128.584i −0.694417 + 1.08053i
\(120\) 0 0
\(121\) −14.6728 + 9.42965i −0.121263 + 0.0779310i
\(122\) 89.0158 40.6522i 0.729638 0.333215i
\(123\) 0 0
\(124\) 13.4236 + 93.3629i 0.108255 + 0.752927i
\(125\) −11.3817 5.19786i −0.0910539 0.0415829i
\(126\) 0 0
\(127\) −94.9042 + 27.8664i −0.747277 + 0.219420i −0.633132 0.774044i \(-0.718231\pi\)
−0.114145 + 0.993464i \(0.536413\pi\)
\(128\) 10.2913 + 4.69988i 0.0804009 + 0.0367178i
\(129\) 0 0
\(130\) −1.64004 1.89271i −0.0126157 0.0145593i
\(131\) −23.3810 + 10.6777i −0.178481 + 0.0815094i −0.502651 0.864489i \(-0.667642\pi\)
0.324171 + 0.945999i \(0.394915\pi\)
\(132\) 0 0
\(133\) −23.6141 + 164.240i −0.177550 + 1.23488i
\(134\) 38.0948 59.2767i 0.284290 0.442363i
\(135\) 0 0
\(136\) −70.8705 20.8094i −0.521106 0.153011i
\(137\) 134.738i 0.983488i 0.870740 + 0.491744i \(0.163640\pi\)
−0.870740 + 0.491744i \(0.836360\pi\)
\(138\) 0 0
\(139\) −30.5470 −0.219763 −0.109881 0.993945i \(-0.535047\pi\)
−0.109881 + 0.993945i \(0.535047\pi\)
\(140\) −0.826352 + 2.81430i −0.00590252 + 0.0201021i
\(141\) 0 0
\(142\) −66.1966 42.5420i −0.466173 0.299591i
\(143\) −82.3118 11.8346i −0.575607 0.0827598i
\(144\) 0 0
\(145\) −1.95070 4.27144i −0.0134531 0.0294582i
\(146\) −124.412 + 107.803i −0.852135 + 0.738379i
\(147\) 0 0
\(148\) −2.29632 + 5.02824i −0.0155157 + 0.0339746i
\(149\) −2.11936 7.21787i −0.0142239 0.0484421i 0.952075 0.305864i \(-0.0989452\pi\)
−0.966299 + 0.257422i \(0.917127\pi\)
\(150\) 0 0
\(151\) 108.240 237.012i 0.716820 1.56962i −0.101489 0.994837i \(-0.532361\pi\)
0.818308 0.574779i \(-0.194912\pi\)
\(152\) −79.3676 + 11.4113i −0.522155 + 0.0750746i
\(153\) 0 0
\(154\) 40.4586 + 88.5919i 0.262718 + 0.575272i
\(155\) −6.38873 9.94106i −0.0412176 0.0641359i
\(156\) 0 0
\(157\) 186.486 + 119.847i 1.18781 + 0.763359i 0.976806 0.214126i \(-0.0686902\pi\)
0.211004 + 0.977485i \(0.432327\pi\)
\(158\) 78.2814 + 67.8312i 0.495452 + 0.429311i
\(159\) 0 0
\(160\) −1.41740 −0.00885877
\(161\) −80.7379 107.721i −0.501477 0.669074i
\(162\) 0 0
\(163\) −200.588 58.8981i −1.23060 0.361338i −0.399126 0.916896i \(-0.630687\pi\)
−0.831478 + 0.555558i \(0.812505\pi\)
\(164\) −106.338 92.1427i −0.648405 0.561846i
\(165\) 0 0
\(166\) −3.33189 + 23.1738i −0.0200716 + 0.139601i
\(167\) 40.9069 + 63.6523i 0.244951 + 0.381152i 0.941859 0.336010i \(-0.109077\pi\)
−0.696907 + 0.717161i \(0.745441\pi\)
\(168\) 0 0
\(169\) 77.9606 + 89.9713i 0.461305 + 0.532374i
\(170\) 9.15944 1.31693i 0.0538790 0.00774664i
\(171\) 0 0
\(172\) 39.0747 11.4734i 0.227179 0.0667057i
\(173\) 79.2785 + 269.998i 0.458257 + 1.56068i 0.787425 + 0.616410i \(0.211414\pi\)
−0.329168 + 0.944271i \(0.606768\pi\)
\(174\) 0 0
\(175\) 20.7720 + 144.472i 0.118697 + 0.825556i
\(176\) −35.5690 + 30.8207i −0.202096 + 0.175118i
\(177\) 0 0
\(178\) −13.9410 + 8.95931i −0.0783200 + 0.0503332i
\(179\) −8.47810 1.21897i −0.0473637 0.00680987i 0.118592 0.992943i \(-0.462162\pi\)
−0.165956 + 0.986133i \(0.553071\pi\)
\(180\) 0 0
\(181\) −42.1570 + 48.6518i −0.232912 + 0.268794i −0.860159 0.510026i \(-0.829636\pi\)
0.627248 + 0.778820i \(0.284181\pi\)
\(182\) −16.4818 + 56.1317i −0.0905592 + 0.308416i
\(183\) 0 0
\(184\) 38.9546 52.1012i 0.211710 0.283159i
\(185\) 0.692530i 0.00374340i
\(186\) 0 0
\(187\) 201.215 232.215i 1.07602 1.24179i
\(188\) −38.9106 + 60.5460i −0.206971 + 0.322053i
\(189\) 0 0
\(190\) 8.45087 5.43105i 0.0444783 0.0285845i
\(191\) 178.551 81.5415i 0.934822 0.426919i 0.111034 0.993817i \(-0.464584\pi\)
0.823788 + 0.566898i \(0.191857\pi\)
\(192\) 0 0
\(193\) −19.3219 134.387i −0.100114 0.696305i −0.976629 0.214932i \(-0.931047\pi\)
0.876516 0.481374i \(-0.159862\pi\)
\(194\) 102.811 + 46.9523i 0.529955 + 0.242022i
\(195\) 0 0
\(196\) −28.2900 + 8.30670i −0.144337 + 0.0423811i
\(197\) 6.76341 + 3.08875i 0.0343320 + 0.0156789i 0.432507 0.901631i \(-0.357629\pi\)
−0.398175 + 0.917309i \(0.630356\pi\)
\(198\) 0 0
\(199\) 189.487 + 218.680i 0.952196 + 1.09889i 0.995007 + 0.0998096i \(0.0318234\pi\)
−0.0428105 + 0.999083i \(0.513631\pi\)
\(200\) −64.1592 + 29.3005i −0.320796 + 0.146503i
\(201\) 0 0
\(202\) −2.58603 + 17.9862i −0.0128021 + 0.0890408i
\(203\) −59.3033 + 92.2777i −0.292134 + 0.454570i
\(204\) 0 0
\(205\) 16.9138 + 4.96635i 0.0825065 + 0.0242261i
\(206\) 94.5209i 0.458839i
\(207\) 0 0
\(208\) −28.2704 −0.135915
\(209\) 93.9749 320.049i 0.449641 1.53134i
\(210\) 0 0
\(211\) −55.5348 35.6901i −0.263198 0.169147i 0.402386 0.915470i \(-0.368181\pi\)
−0.665584 + 0.746323i \(0.731817\pi\)
\(212\) 77.7273 + 11.1755i 0.366638 + 0.0527146i
\(213\) 0 0
\(214\) −84.8079 185.703i −0.396298 0.867773i
\(215\) −3.85585 + 3.34112i −0.0179342 + 0.0155401i
\(216\) 0 0
\(217\) −114.670 + 251.092i −0.528433 + 1.15711i
\(218\) −63.5666 216.488i −0.291590 0.993064i
\(219\) 0 0
\(220\) 2.44942 5.36349i 0.0111337 0.0243795i
\(221\) 182.687 26.2664i 0.826637 0.118853i
\(222\) 0 0
\(223\) −40.0789 87.7605i −0.179726 0.393545i 0.798231 0.602351i \(-0.205769\pi\)
−0.977957 + 0.208807i \(0.933042\pi\)
\(224\) 17.9004 + 27.8536i 0.0799127 + 0.124347i
\(225\) 0 0
\(226\) −176.639 113.519i −0.781589 0.502297i
\(227\) −232.691 201.628i −1.02507 0.888228i −0.0312812 0.999511i \(-0.509959\pi\)
−0.993789 + 0.111282i \(0.964504\pi\)
\(228\) 0 0
\(229\) 144.063 0.629094 0.314547 0.949242i \(-0.398147\pi\)
0.314547 + 0.949242i \(0.398147\pi\)
\(230\) −1.72773 + 7.96483i −0.00751188 + 0.0346297i
\(231\) 0 0
\(232\) −50.8601 14.9339i −0.219224 0.0643701i
\(233\) −127.024 110.067i −0.545166 0.472389i 0.338199 0.941075i \(-0.390182\pi\)
−0.883365 + 0.468686i \(0.844728\pi\)
\(234\) 0 0
\(235\) 1.28321 8.92491i 0.00546046 0.0379783i
\(236\) 92.3941 + 143.768i 0.391501 + 0.609187i
\(237\) 0 0
\(238\) −141.554 163.362i −0.594765 0.686395i
\(239\) 365.030 52.4834i 1.52732 0.219596i 0.673119 0.739535i \(-0.264954\pi\)
0.854203 + 0.519939i \(0.174045\pi\)
\(240\) 0 0
\(241\) 102.771 30.1762i 0.426435 0.125213i −0.0614709 0.998109i \(-0.519579\pi\)
0.487906 + 0.872896i \(0.337761\pi\)
\(242\) −6.94926 23.6670i −0.0287160 0.0977976i
\(243\) 0 0
\(244\) 19.6955 + 136.985i 0.0807192 + 0.561414i
\(245\) 2.79163 2.41896i 0.0113944 0.00987331i
\(246\) 0 0
\(247\) 168.554 108.323i 0.682407 0.438556i
\(248\) −132.035 18.9838i −0.532400 0.0765475i
\(249\) 0 0
\(250\) 11.5879 13.3732i 0.0463518 0.0534928i
\(251\) 28.1843 95.9868i 0.112288 0.382418i −0.884104 0.467290i \(-0.845230\pi\)
0.996392 + 0.0848728i \(0.0270484\pi\)
\(252\) 0 0
\(253\) 129.835 + 237.442i 0.513180 + 0.938505i
\(254\) 139.881i 0.550712i
\(255\) 0 0
\(256\) −10.4778 + 12.0920i −0.0409288 + 0.0472343i
\(257\) 212.331 330.394i 0.826191 1.28558i −0.129610 0.991565i \(-0.541373\pi\)
0.955801 0.294013i \(-0.0949910\pi\)
\(258\) 0 0
\(259\) −13.6090 + 8.74599i −0.0525445 + 0.0337683i
\(260\) 3.22171 1.47130i 0.0123912 0.00565886i
\(261\) 0 0
\(262\) −5.17323 35.9806i −0.0197452 0.137331i
\(263\) −276.276 126.171i −1.05048 0.479738i −0.186075 0.982536i \(-0.559577\pi\)
−0.864404 + 0.502798i \(0.832304\pi\)
\(264\) 0 0
\(265\) −9.43945 + 2.77167i −0.0356206 + 0.0104591i
\(266\) −213.453 97.4807i −0.802454 0.366469i
\(267\) 0 0
\(268\) 65.2561 + 75.3095i 0.243493 + 0.281006i
\(269\) 375.195 171.346i 1.39478 0.636973i 0.430675 0.902507i \(-0.358276\pi\)
0.964101 + 0.265535i \(0.0855484\pi\)
\(270\) 0 0
\(271\) −56.9913 + 396.383i −0.210300 + 1.46267i 0.561856 + 0.827235i \(0.310087\pi\)
−0.772156 + 0.635433i \(0.780822\pi\)
\(272\) 56.4738 87.8750i 0.207624 0.323070i
\(273\) 0 0
\(274\) −182.830 53.6836i −0.667261 0.195926i
\(275\) 293.414i 1.06696i
\(276\) 0 0
\(277\) −181.276 −0.654428 −0.327214 0.944950i \(-0.606110\pi\)
−0.327214 + 0.944950i \(0.606110\pi\)
\(278\) 12.1708 41.4501i 0.0437800 0.149101i
\(279\) 0 0
\(280\) −3.48956 2.24260i −0.0124627 0.00800929i
\(281\) 201.616 + 28.9881i 0.717496 + 0.103160i 0.491387 0.870942i \(-0.336490\pi\)
0.226109 + 0.974102i \(0.427399\pi\)
\(282\) 0 0
\(283\) −228.944 501.318i −0.808991 1.77144i −0.611686 0.791101i \(-0.709508\pi\)
−0.197305 0.980342i \(-0.563219\pi\)
\(284\) 84.1011 72.8740i 0.296131 0.256599i
\(285\) 0 0
\(286\) 48.8543 106.976i 0.170819 0.374042i
\(287\) −116.011 395.097i −0.404219 1.37664i
\(288\) 0 0
\(289\) −163.240 + 357.446i −0.564845 + 1.23684i
\(290\) 6.57325 0.945091i 0.0226664 0.00325893i
\(291\) 0 0
\(292\) −96.7121 211.770i −0.331206 0.725239i
\(293\) −27.7678 43.2075i −0.0947706 0.147466i 0.790631 0.612293i \(-0.209753\pi\)
−0.885401 + 0.464827i \(0.846116\pi\)
\(294\) 0 0
\(295\) −18.0115 11.5753i −0.0610561 0.0392383i
\(296\) −5.90803 5.11934i −0.0199596 0.0172951i
\(297\) 0 0
\(298\) 10.6385 0.0356998
\(299\) −34.4600 + 158.860i −0.115251 + 0.531305i
\(300\) 0 0
\(301\) 114.353 + 33.5770i 0.379909 + 0.111551i
\(302\) 278.482 + 241.306i 0.922127 + 0.799027i
\(303\) 0 0
\(304\) 16.1381 112.243i 0.0530858 0.369220i
\(305\) −9.37376 14.5859i −0.0307336 0.0478225i
\(306\) 0 0
\(307\) −339.325 391.602i −1.10529 1.27558i −0.958089 0.286472i \(-0.907517\pi\)
−0.147206 0.989106i \(-0.547028\pi\)
\(308\) −136.333 + 19.6017i −0.442639 + 0.0636418i
\(309\) 0 0
\(310\) 16.0348 4.70823i 0.0517251 0.0151879i
\(311\) 27.0949 + 92.2766i 0.0871217 + 0.296709i 0.991515 0.129990i \(-0.0414945\pi\)
−0.904394 + 0.426699i \(0.859676\pi\)
\(312\) 0 0
\(313\) −2.33464 16.2378i −0.00745891 0.0518778i 0.985752 0.168205i \(-0.0537970\pi\)
−0.993211 + 0.116327i \(0.962888\pi\)
\(314\) −236.926 + 205.298i −0.754542 + 0.653814i
\(315\) 0 0
\(316\) −123.232 + 79.1962i −0.389974 + 0.250621i
\(317\) 420.225 + 60.4192i 1.32563 + 0.190597i 0.768511 0.639836i \(-0.220998\pi\)
0.557119 + 0.830433i \(0.311907\pi\)
\(318\) 0 0
\(319\) 144.402 166.648i 0.452670 0.522409i
\(320\) 0.564736 1.92331i 0.00176480 0.00601035i
\(321\) 0 0
\(322\) 178.338 66.6362i 0.553844 0.206945i
\(323\) 740.321i 2.29201i
\(324\) 0 0
\(325\) 115.417 133.198i 0.355128 0.409840i
\(326\) 159.841 248.717i 0.490310 0.762937i
\(327\) 0 0
\(328\) 167.399 107.581i 0.510364 0.327991i
\(329\) −191.591 + 87.4965i −0.582342 + 0.265947i
\(330\) 0 0
\(331\) 7.74573 + 53.8728i 0.0234010 + 0.162758i 0.998171 0.0604543i \(-0.0192549\pi\)
−0.974770 + 0.223212i \(0.928346\pi\)
\(332\) −30.1176 13.7543i −0.0907157 0.0414285i
\(333\) 0 0
\(334\) −102.670 + 30.1467i −0.307396 + 0.0902595i
\(335\) −11.3560 5.18612i −0.0338986 0.0154810i
\(336\) 0 0
\(337\) 6.56118 + 7.57200i 0.0194694 + 0.0224688i 0.765401 0.643554i \(-0.222541\pi\)
−0.745931 + 0.666023i \(0.767995\pi\)
\(338\) −153.146 + 69.9396i −0.453096 + 0.206922i
\(339\) 0 0
\(340\) −1.86242 + 12.9534i −0.00547770 + 0.0380982i
\(341\) 300.006 466.818i 0.879783 1.36897i
\(342\) 0 0
\(343\) −357.972 105.110i −1.04365 0.306443i
\(344\) 57.5930i 0.167421i
\(345\) 0 0
\(346\) −397.955 −1.15016
\(347\) 61.5995 209.789i 0.177520 0.604579i −0.821870 0.569675i \(-0.807069\pi\)
0.999391 0.0349041i \(-0.0111126\pi\)
\(348\) 0 0
\(349\) 364.372 + 234.168i 1.04405 + 0.670968i 0.945984 0.324212i \(-0.105099\pi\)
0.0980623 + 0.995180i \(0.468736\pi\)
\(350\) −204.315 29.3760i −0.583756 0.0839315i
\(351\) 0 0
\(352\) −27.6497 60.5444i −0.0785503 0.172001i
\(353\) 68.6870 59.5176i 0.194581 0.168605i −0.552121 0.833764i \(-0.686182\pi\)
0.746702 + 0.665159i \(0.231636\pi\)
\(354\) 0 0
\(355\) −5.79154 + 12.6817i −0.0163142 + 0.0357231i
\(356\) −6.60264 22.4865i −0.0185467 0.0631644i
\(357\) 0 0
\(358\) 5.03198 11.0185i 0.0140558 0.0307779i
\(359\) −158.132 + 22.7359i −0.440479 + 0.0633313i −0.358987 0.933343i \(-0.616878\pi\)
−0.0814922 + 0.996674i \(0.525969\pi\)
\(360\) 0 0
\(361\) 183.896 + 402.675i 0.509406 + 1.11544i
\(362\) −49.2203 76.5883i −0.135968 0.211570i
\(363\) 0 0
\(364\) −69.5999 44.7291i −0.191209 0.122882i
\(365\) 22.0427 + 19.1001i 0.0603909 + 0.0523291i
\(366\) 0 0
\(367\) −459.664 −1.25249 −0.626245 0.779627i \(-0.715409\pi\)
−0.626245 + 0.779627i \(0.715409\pi\)
\(368\) 55.1769 + 73.6173i 0.149937 + 0.200047i
\(369\) 0 0
\(370\) 0.939713 + 0.275925i 0.00253976 + 0.000745742i
\(371\) 173.678 + 150.493i 0.468134 + 0.405641i
\(372\) 0 0
\(373\) −96.2313 + 669.303i −0.257993 + 1.79438i 0.289091 + 0.957302i \(0.406647\pi\)
−0.547084 + 0.837078i \(0.684262\pi\)
\(374\) 234.929 + 365.556i 0.628151 + 0.977422i
\(375\) 0 0
\(376\) −66.6534 76.9222i −0.177270 0.204580i
\(377\) 131.105 18.8500i 0.347758 0.0500001i
\(378\) 0 0
\(379\) 603.001 177.057i 1.59103 0.467169i 0.637999 0.770038i \(-0.279763\pi\)
0.953032 + 0.302869i \(0.0979444\pi\)
\(380\) 4.00246 + 13.6311i 0.0105328 + 0.0358714i
\(381\) 0 0
\(382\) 39.5059 + 274.769i 0.103419 + 0.719292i
\(383\) −407.510 + 353.109i −1.06399 + 0.921956i −0.997123 0.0758058i \(-0.975847\pi\)
−0.0668712 + 0.997762i \(0.521302\pi\)
\(384\) 0 0
\(385\) 14.5164 9.32911i 0.0377049 0.0242315i
\(386\) 190.052 + 27.3253i 0.492362 + 0.0707910i
\(387\) 0 0
\(388\) −104.674 + 120.800i −0.269778 + 0.311341i
\(389\) 21.6957 73.8886i 0.0557729 0.189945i −0.926895 0.375322i \(-0.877532\pi\)
0.982668 + 0.185377i \(0.0593505\pi\)
\(390\) 0 0
\(391\) −424.959 424.459i −1.08685 1.08557i
\(392\) 41.6972i 0.106370i
\(393\) 0 0
\(394\) −6.88595 + 7.94682i −0.0174770 + 0.0201696i
\(395\) 9.92185 15.4387i 0.0251186 0.0390853i
\(396\) 0 0
\(397\) −305.603 + 196.399i −0.769781 + 0.494708i −0.865628 0.500688i \(-0.833080\pi\)
0.0958468 + 0.995396i \(0.469444\pi\)
\(398\) −372.230 + 169.992i −0.935251 + 0.427115i
\(399\) 0 0
\(400\) −14.1957 98.7336i −0.0354894 0.246834i
\(401\) −451.483 206.185i −1.12589 0.514178i −0.236641 0.971597i \(-0.576047\pi\)
−0.889251 + 0.457419i \(0.848774\pi\)
\(402\) 0 0
\(403\) 319.817 93.9067i 0.793590 0.233019i
\(404\) −23.3757 10.6753i −0.0578606 0.0264240i
\(405\) 0 0
\(406\) −101.586 117.237i −0.250212 0.288760i
\(407\) 29.5814 13.5094i 0.0726816 0.0331926i
\(408\) 0 0
\(409\) 104.579 727.360i 0.255693 1.77839i −0.306989 0.951713i \(-0.599321\pi\)
0.562682 0.826673i \(-0.309770\pi\)
\(410\) −13.4780 + 20.9721i −0.0328731 + 0.0511515i
\(411\) 0 0
\(412\) −128.258 37.6600i −0.311306 0.0914077i
\(413\) 500.133i 1.21098i
\(414\) 0 0
\(415\) 4.14804 0.00999528
\(416\) 11.2638 38.3609i 0.0270764 0.0922137i
\(417\) 0 0
\(418\) 396.841 + 255.034i 0.949381 + 0.610130i
\(419\) −322.760 46.4058i −0.770309 0.110754i −0.254056 0.967190i \(-0.581765\pi\)
−0.516254 + 0.856436i \(0.672674\pi\)
\(420\) 0 0
\(421\) −286.687 627.756i −0.680966 1.49111i −0.861616 0.507560i \(-0.830548\pi\)
0.180651 0.983547i \(-0.442180\pi\)
\(422\) 70.5556 61.1368i 0.167193 0.144874i
\(423\) 0 0
\(424\) −46.1332 + 101.018i −0.108805 + 0.238249i
\(425\) 183.469 + 624.839i 0.431693 + 1.47021i
\(426\) 0 0
\(427\) −168.248 + 368.411i −0.394022 + 0.862788i
\(428\) 285.776 41.0884i 0.667701 0.0960009i
\(429\) 0 0
\(430\) −2.99737 6.56332i −0.00697062 0.0152635i
\(431\) −404.454 629.343i −0.938409 1.46019i −0.887136 0.461508i \(-0.847309\pi\)
−0.0512725 0.998685i \(-0.516328\pi\)
\(432\) 0 0
\(433\) 116.184 + 74.6671i 0.268324 + 0.172441i 0.667883 0.744266i \(-0.267201\pi\)
−0.399559 + 0.916707i \(0.630837\pi\)
\(434\) −295.026 255.642i −0.679784 0.589036i
\(435\) 0 0
\(436\) 319.085 0.731847
\(437\) −611.056 227.502i −1.39830 0.520600i
\(438\) 0 0
\(439\) 109.115 + 32.0391i 0.248554 + 0.0729819i 0.403636 0.914920i \(-0.367746\pi\)
−0.155083 + 0.987902i \(0.549564\pi\)
\(440\) 6.30194 + 5.46067i 0.0143226 + 0.0124106i
\(441\) 0 0
\(442\) −37.1463 + 258.358i −0.0840414 + 0.584521i
\(443\) 255.608 + 397.734i 0.576994 + 0.897820i 0.999965 0.00832306i \(-0.00264934\pi\)
−0.422972 + 0.906143i \(0.639013\pi\)
\(444\) 0 0
\(445\) 1.92273 + 2.21895i 0.00432074 + 0.00498640i
\(446\) 135.053 19.4177i 0.302810 0.0435375i
\(447\) 0 0
\(448\) −44.9274 + 13.1919i −0.100284 + 0.0294462i
\(449\) 160.811 + 547.671i 0.358153 + 1.21976i 0.919802 + 0.392382i \(0.128349\pi\)
−0.561649 + 0.827376i \(0.689833\pi\)
\(450\) 0 0
\(451\) 117.805 + 819.355i 0.261210 + 1.81675i
\(452\) 224.416 194.457i 0.496495 0.430215i
\(453\) 0 0
\(454\) 366.305 235.410i 0.806840 0.518525i
\(455\) 10.2595 + 1.47510i 0.0225484 + 0.00324197i
\(456\) 0 0
\(457\) 243.799 281.359i 0.533476 0.615665i −0.423477 0.905907i \(-0.639190\pi\)
0.956953 + 0.290242i \(0.0937359\pi\)
\(458\) −57.3989 + 195.483i −0.125325 + 0.426818i
\(459\) 0 0
\(460\) −10.1193 5.51783i −0.0219985 0.0119953i
\(461\) 345.649i 0.749782i 0.927069 + 0.374891i \(0.122320\pi\)
−0.927069 + 0.374891i \(0.877680\pi\)
\(462\) 0 0
\(463\) 239.183 276.032i 0.516594 0.596182i −0.436181 0.899859i \(-0.643669\pi\)
0.952775 + 0.303678i \(0.0982146\pi\)
\(464\) 40.5283 63.0633i 0.0873456 0.135912i
\(465\) 0 0
\(466\) 199.963 128.508i 0.429104 0.275769i
\(467\) −101.065 + 46.1549i −0.216414 + 0.0988328i −0.520672 0.853757i \(-0.674319\pi\)
0.304258 + 0.952590i \(0.401591\pi\)
\(468\) 0 0
\(469\) 41.5023 + 288.655i 0.0884910 + 0.615469i
\(470\) 11.5992 + 5.29717i 0.0246791 + 0.0112706i
\(471\) 0 0
\(472\) −231.896 + 68.0907i −0.491304 + 0.144260i
\(473\) −217.933 99.5268i −0.460747 0.210416i
\(474\) 0 0
\(475\) 462.955 + 534.278i 0.974641 + 1.12480i
\(476\) 278.070 126.990i 0.584181 0.266786i
\(477\) 0 0
\(478\) −74.2227 + 516.230i −0.155278 + 1.07998i
\(479\) −50.0209 + 77.8340i −0.104428 + 0.162493i −0.889535 0.456867i \(-0.848971\pi\)
0.785107 + 0.619360i \(0.212608\pi\)
\(480\) 0 0
\(481\) 18.7428 + 5.50337i 0.0389663 + 0.0114415i
\(482\) 151.476i 0.314265i
\(483\) 0 0
\(484\) 34.8832 0.0720728
\(485\) 5.64177 19.2141i 0.0116325 0.0396167i
\(486\) 0 0
\(487\) 84.9796 + 54.6131i 0.174496 + 0.112142i 0.624973 0.780646i \(-0.285110\pi\)
−0.450477 + 0.892788i \(0.648746\pi\)
\(488\) −193.726 27.8536i −0.396980 0.0570771i
\(489\) 0 0
\(490\) 2.17009 + 4.75183i 0.00442875 + 0.00969761i
\(491\) 182.534 158.167i 0.371760 0.322132i −0.448864 0.893600i \(-0.648171\pi\)
0.820624 + 0.571468i \(0.193626\pi\)
\(492\) 0 0
\(493\) −203.306 + 445.179i −0.412386 + 0.902999i
\(494\) 79.8298 + 271.875i 0.161599 + 0.550355i
\(495\) 0 0
\(496\) 78.3664 171.598i 0.157997 0.345965i
\(497\) 322.352 46.3472i 0.648596 0.0932540i
\(498\) 0 0
\(499\) −116.394 254.868i −0.233255 0.510758i 0.756420 0.654086i \(-0.226947\pi\)
−0.989675 + 0.143329i \(0.954219\pi\)
\(500\) 13.5295 + 21.0523i 0.0270590 + 0.0421046i
\(501\) 0 0
\(502\) 119.018 + 76.4881i 0.237087 + 0.152367i
\(503\) −57.4722 49.7999i −0.114259 0.0990059i 0.595858 0.803090i \(-0.296812\pi\)
−0.710116 + 0.704084i \(0.751358\pi\)
\(504\) 0 0
\(505\) 3.21949 0.00637522
\(506\) −373.921 + 81.5722i −0.738975 + 0.161210i
\(507\) 0 0
\(508\) 189.808 + 55.7328i 0.373639 + 0.109710i
\(509\) −154.516 133.889i −0.303567 0.263043i 0.489734 0.871872i \(-0.337094\pi\)
−0.793301 + 0.608829i \(0.791639\pi\)
\(510\) 0 0
\(511\) 96.9613 674.381i 0.189748 1.31973i
\(512\) −12.2333 19.0354i −0.0238932 0.0371785i
\(513\) 0 0
\(514\) 363.721 + 419.757i 0.707629 + 0.816647i
\(515\) 16.5763 2.38331i 0.0321870 0.00462779i
\(516\) 0 0
\(517\) 406.260 119.289i 0.785802 0.230732i
\(518\) −6.44543 21.9511i −0.0124429 0.0423767i
\(519\) 0 0
\(520\) 0.712829 + 4.95783i 0.00137082 + 0.00953430i
\(521\) 20.9885 18.1866i 0.0402850 0.0349072i −0.634486 0.772935i \(-0.718788\pi\)
0.674771 + 0.738028i \(0.264243\pi\)
\(522\) 0 0
\(523\) 67.6338 43.4656i 0.129319 0.0831083i −0.474382 0.880319i \(-0.657328\pi\)
0.603701 + 0.797211i \(0.293692\pi\)
\(524\) 50.8843 + 7.31605i 0.0971074 + 0.0139619i
\(525\) 0 0
\(526\) 281.282 324.616i 0.534756 0.617141i
\(527\) −346.979 + 1181.70i −0.658404 + 2.24232i
\(528\) 0 0
\(529\) 480.936 220.321i 0.909142 0.416486i
\(530\) 13.9130i 0.0262509i
\(531\) 0 0
\(532\) 217.320 250.801i 0.408497 0.471430i
\(533\) −268.821 + 418.293i −0.504354 + 0.784790i
\(534\) 0 0
\(535\) −30.4288 + 19.5554i −0.0568762 + 0.0365521i
\(536\) −128.190 + 58.5422i −0.239160 + 0.109221i
\(537\) 0 0
\(538\) 83.0149 + 577.381i 0.154303 + 1.07320i
\(539\) 157.783 + 72.0572i 0.292733 + 0.133687i
\(540\) 0 0
\(541\) −808.277 + 237.332i −1.49404 + 0.438690i −0.923829 0.382806i \(-0.874958\pi\)
−0.570214 + 0.821496i \(0.693140\pi\)
\(542\) −515.156 235.264i −0.950472 0.434066i
\(543\) 0 0
\(544\) 96.7392 + 111.643i 0.177829 + 0.205226i
\(545\) −36.3631 + 16.6065i −0.0667213 + 0.0304706i
\(546\) 0 0
\(547\) 46.3826 322.598i 0.0847945 0.589759i −0.902480 0.430732i \(-0.858255\pi\)
0.987274 0.159027i \(-0.0508355\pi\)
\(548\) 145.690 226.697i 0.265857 0.413682i
\(549\) 0 0
\(550\) 398.142 + 116.905i 0.723895 + 0.212555i
\(551\) 531.290i 0.964228i
\(552\) 0 0
\(553\) −428.692 −0.775212
\(554\) 72.2260 245.979i 0.130372 0.444006i
\(555\) 0 0
\(556\) 51.3956 + 33.0299i 0.0924381 + 0.0594064i
\(557\) 682.683 + 98.1550i 1.22564 + 0.176221i 0.724580 0.689190i \(-0.242034\pi\)
0.501062 + 0.865411i \(0.332943\pi\)
\(558\) 0 0
\(559\) −59.7831 130.907i −0.106947 0.234180i
\(560\) 4.43339 3.84156i 0.00791677 0.00685992i
\(561\) 0 0
\(562\) −119.665 + 262.029i −0.212926 + 0.466244i
\(563\) −193.920 660.430i −0.344440 1.17306i −0.931570 0.363562i \(-0.881560\pi\)
0.587130 0.809493i \(-0.300258\pi\)
\(564\) 0 0
\(565\) −15.4542 + 33.8399i −0.0273525 + 0.0598936i
\(566\) 771.471 110.921i 1.36302 0.195973i
\(567\) 0 0
\(568\) 65.3764 + 143.154i 0.115099 + 0.252032i
\(569\) −341.617 531.567i −0.600382 0.934212i −0.999847 0.0174639i \(-0.994441\pi\)
0.399466 0.916748i \(-0.369196\pi\)
\(570\) 0 0
\(571\) 20.6197 + 13.2515i 0.0361116 + 0.0232075i 0.558572 0.829456i \(-0.311349\pi\)
−0.522460 + 0.852663i \(0.674986\pi\)
\(572\) 125.694 + 108.914i 0.219744 + 0.190409i
\(573\) 0 0
\(574\) 582.340 1.01453
\(575\) −572.119 40.5801i −0.994989 0.0705742i
\(576\) 0 0
\(577\) −188.124 55.2381i −0.326037 0.0957332i 0.114618 0.993410i \(-0.463436\pi\)
−0.440655 + 0.897676i \(0.645254\pi\)
\(578\) −419.989 363.923i −0.726625 0.629624i
\(579\) 0 0
\(580\) −1.33656 + 9.29598i −0.00230441 + 0.0160276i
\(581\) −52.3858 81.5139i −0.0901649 0.140299i
\(582\) 0 0
\(583\) −302.530 349.139i −0.518920 0.598865i
\(584\) 325.889 46.8558i 0.558030 0.0802326i
\(585\) 0 0
\(586\) 69.6930 20.4637i 0.118930 0.0349210i
\(587\) 32.4899 + 110.650i 0.0553491 + 0.188502i 0.982527 0.186119i \(-0.0595911\pi\)
−0.927178 + 0.374621i \(0.877773\pi\)
\(588\) 0 0
\(589\) 190.274 + 1323.38i 0.323046 + 2.24683i
\(590\) 22.8832 19.8284i 0.0387851 0.0336075i
\(591\) 0 0
\(592\) 9.30051 5.97708i 0.0157103 0.0100964i
\(593\) −523.582 75.2798i −0.882938 0.126947i −0.314093 0.949392i \(-0.601700\pi\)
−0.568845 + 0.822445i \(0.692610\pi\)
\(594\) 0 0
\(595\) −25.0799 + 28.9437i −0.0421511 + 0.0486449i
\(596\) −4.23871 + 14.4357i −0.00711194 + 0.0242210i
\(597\) 0 0
\(598\) −201.832 110.054i −0.337512 0.184037i
\(599\) 167.467i 0.279578i −0.990181 0.139789i \(-0.955358\pi\)
0.990181 0.139789i \(-0.0446425\pi\)
\(600\) 0 0
\(601\) 719.126 829.915i 1.19655 1.38089i 0.290959 0.956735i \(-0.406026\pi\)
0.905589 0.424156i \(-0.139429\pi\)
\(602\) −91.1230 + 141.790i −0.151367 + 0.235532i
\(603\) 0 0
\(604\) −438.391 + 281.737i −0.725813 + 0.466452i
\(605\) −3.97531 + 1.81546i −0.00657076 + 0.00300076i
\(606\) 0 0
\(607\) 24.1168 + 167.736i 0.0397312 + 0.276337i 0.999996 0.00275321i \(-0.000876375\pi\)
−0.960265 + 0.279090i \(0.909967\pi\)
\(608\) 145.875 + 66.6191i 0.239927 + 0.109571i
\(609\) 0 0
\(610\) 23.5267 6.90807i 0.0385684 0.0113247i
\(611\) 231.348 + 105.653i 0.378639 + 0.172919i
\(612\) 0 0
\(613\) −146.654 169.248i −0.239240 0.276098i 0.623414 0.781892i \(-0.285745\pi\)
−0.862654 + 0.505794i \(0.831200\pi\)
\(614\) 666.574 304.414i 1.08562 0.495788i
\(615\) 0 0
\(616\) 27.7210 192.804i 0.0450016 0.312993i
\(617\) −572.084 + 890.180i −0.927202 + 1.44276i −0.0307942 + 0.999526i \(0.509804\pi\)
−0.896408 + 0.443229i \(0.853833\pi\)
\(618\) 0 0
\(619\) −715.915 210.211i −1.15657 0.339598i −0.353469 0.935446i \(-0.614998\pi\)
−0.803097 + 0.595848i \(0.796816\pi\)
\(620\) 23.6339i 0.0381192i
\(621\) 0 0
\(622\) −136.008 −0.218663
\(623\) 19.3227 65.8071i 0.0310156 0.105629i
\(624\) 0 0
\(625\) 521.826 + 335.357i 0.834921 + 0.536571i
\(626\) 22.9637 + 3.30168i 0.0366832 + 0.00527424i
\(627\) 0 0
\(628\) −184.176 403.288i −0.293273 0.642179i
\(629\) −54.5477 + 47.2659i −0.0867213 + 0.0751444i
\(630\) 0 0
\(631\) 219.733 481.147i 0.348229 0.762516i −0.651762 0.758423i \(-0.725970\pi\)
0.999992 0.00409245i \(-0.00130267\pi\)
\(632\) −58.3643 198.771i −0.0923486 0.314511i
\(633\) 0 0
\(634\) −249.415 + 546.142i −0.393398 + 0.861422i
\(635\) −24.5312 + 3.52705i −0.0386318 + 0.00555442i
\(636\) 0 0
\(637\) 43.2828 + 94.7762i 0.0679479 + 0.148785i
\(638\) 168.596 + 262.340i 0.264257 + 0.411192i
\(639\) 0 0
\(640\) 2.38479 + 1.53261i 0.00372623 + 0.00239471i
\(641\) 110.976 + 96.1616i 0.173130 + 0.150018i 0.737116 0.675766i \(-0.236187\pi\)
−0.563986 + 0.825785i \(0.690733\pi\)
\(642\) 0 0
\(643\) 877.046 1.36399 0.681995 0.731357i \(-0.261113\pi\)
0.681995 + 0.731357i \(0.261113\pi\)
\(644\) 19.3654 + 268.541i 0.0300705 + 0.416990i
\(645\) 0 0
\(646\) −1004.56 294.966i −1.55505 0.456604i
\(647\) −161.200 139.681i −0.249150 0.215890i 0.521328 0.853356i \(-0.325437\pi\)
−0.770478 + 0.637467i \(0.779982\pi\)
\(648\) 0 0
\(649\) 143.083 995.167i 0.220467 1.53338i
\(650\) 134.755 + 209.682i 0.207315 + 0.322588i
\(651\) 0 0
\(652\) 273.806 + 315.989i 0.419948 + 0.484646i
\(653\) 118.699 17.0663i 0.181774 0.0261352i −0.0508266 0.998707i \(-0.516186\pi\)
0.232601 + 0.972572i \(0.425276\pi\)
\(654\) 0 0
\(655\) −6.17955 + 1.81448i −0.00943442 + 0.00277020i
\(656\) 79.2828 + 270.012i 0.120858 + 0.411604i
\(657\) 0 0
\(658\) −42.3910 294.836i −0.0644240 0.448079i
\(659\) 818.482 709.219i 1.24201 1.07620i 0.247790 0.968814i \(-0.420296\pi\)
0.994217 0.107391i \(-0.0342496\pi\)
\(660\) 0 0
\(661\) −836.948 + 537.874i −1.26618 + 0.813727i −0.989118 0.147123i \(-0.952999\pi\)
−0.277067 + 0.960851i \(0.589362\pi\)
\(662\) −76.1876 10.9541i −0.115087 0.0165470i
\(663\) 0 0
\(664\) 30.6633 35.3873i 0.0461797 0.0532942i
\(665\) −11.7132 + 39.8916i −0.0176139 + 0.0599874i
\(666\) 0 0
\(667\) −304.971 304.612i −0.457228 0.456690i
\(668\) 151.327i 0.226538i
\(669\) 0 0
\(670\) 11.5618 13.3430i 0.0172564 0.0199149i
\(671\) 440.178 684.931i 0.656004 1.02076i
\(672\) 0 0
\(673\) −898.310 + 577.309i −1.33478 + 0.857814i −0.996529 0.0832407i \(-0.973473\pi\)
−0.338255 + 0.941055i \(0.609837\pi\)
\(674\) −12.8888 + 5.88613i −0.0191229 + 0.00873313i
\(675\) 0 0
\(676\) −33.8849 235.675i −0.0501256 0.348631i
\(677\) 788.242 + 359.978i 1.16432 + 0.531725i 0.901355 0.433081i \(-0.142574\pi\)
0.262961 + 0.964806i \(0.415301\pi\)
\(678\) 0 0
\(679\) −448.830 + 131.788i −0.661016 + 0.194092i
\(680\) −16.8348 7.68819i −0.0247570 0.0113062i
\(681\) 0 0
\(682\) 513.908 + 593.081i 0.753530 + 0.869620i
\(683\) −289.641 + 132.275i −0.424072 + 0.193667i −0.616008 0.787740i \(-0.711251\pi\)
0.191935 + 0.981408i \(0.438524\pi\)
\(684\) 0 0
\(685\) −4.80461 + 33.4168i −0.00701403 + 0.0487837i
\(686\) 285.253 443.863i 0.415821 0.647030i
\(687\) 0 0
\(688\) −78.1495 22.9468i −0.113589 0.0333528i
\(689\) 277.497i 0.402753i
\(690\) 0 0
\(691\) −1036.93 −1.50062 −0.750312 0.661084i \(-0.770097\pi\)
−0.750312 + 0.661084i \(0.770097\pi\)
\(692\) 158.557 539.996i 0.229129 0.780341i
\(693\) 0 0
\(694\) 260.125 + 167.172i 0.374820 + 0.240882i
\(695\) −7.57607 1.08927i −0.0109008 0.00156730i
\(696\) 0 0
\(697\) −763.208 1671.19i −1.09499 2.39769i
\(698\) −462.926 + 401.127i −0.663217 + 0.574681i
\(699\) 0 0
\(700\) 121.266 265.536i 0.173238 0.379337i
\(701\) −263.223 896.455i −0.375496 1.27882i −0.903136 0.429355i \(-0.858741\pi\)
0.527640 0.849468i \(-0.323077\pi\)
\(702\) 0 0
\(703\) −32.5494 + 71.2733i −0.0463008 + 0.101385i
\(704\) 93.1709 13.3959i 0.132345 0.0190283i
\(705\) 0 0
\(706\) 53.3942 + 116.917i 0.0756291 + 0.165605i
\(707\) −40.6590 63.2667i −0.0575092 0.0894861i
\(708\) 0 0
\(709\) −664.681 427.165i −0.937491 0.602489i −0.0198089 0.999804i \(-0.506306\pi\)
−0.917682 + 0.397315i \(0.869942\pi\)
\(710\) −14.9006 12.9115i −0.0209868 0.0181852i
\(711\) 0 0
\(712\) 33.1433 0.0465496
\(713\) −868.741 649.534i −1.21843 0.910987i
\(714\) 0 0
\(715\) −19.9924 5.87030i −0.0279614 0.00821021i
\(716\) 12.9464 + 11.2181i 0.0180816 + 0.0156678i
\(717\) 0 0
\(718\) 32.1535 223.632i 0.0447820 0.311466i
\(719\) 528.349 + 822.127i 0.734839 + 1.14343i 0.984549 + 0.175111i \(0.0560284\pi\)
−0.249710 + 0.968321i \(0.580335\pi\)
\(720\) 0 0
\(721\) −256.178 295.645i −0.355309 0.410049i
\(722\) −619.671 + 89.0952i −0.858270 + 0.123401i
\(723\) 0 0
\(724\) 123.536 36.2733i 0.170629 0.0501013i
\(725\) 131.666 + 448.415i 0.181609 + 0.618503i
\(726\) 0 0
\(727\) −8.91804 62.0263i −0.0122669 0.0853182i 0.982768 0.184842i \(-0.0591772\pi\)
−0.995035 + 0.0995235i \(0.968268\pi\)
\(728\) 88.4249 76.6206i 0.121463 0.105248i
\(729\) 0 0
\(730\) −34.6999 + 22.3003i −0.0475342 + 0.0305484i
\(731\) 526.332 + 75.6751i 0.720016 + 0.103523i
\(732\) 0 0
\(733\) 391.076 451.326i 0.533528 0.615724i −0.423438 0.905925i \(-0.639177\pi\)
0.956966 + 0.290201i \(0.0937221\pi\)
\(734\) 183.144 623.730i 0.249515 0.849769i
\(735\) 0 0
\(736\) −121.878 + 45.5397i −0.165594 + 0.0618746i
\(737\) 586.240i 0.795441i
\(738\) 0 0
\(739\) −274.830 + 317.170i −0.371894 + 0.429189i −0.910590 0.413312i \(-0.864372\pi\)
0.538695 + 0.842501i \(0.318917\pi\)
\(740\) −0.748820 + 1.16519i −0.00101192 + 0.00157458i
\(741\) 0 0
\(742\) −273.406 + 175.708i −0.368472 + 0.236803i
\(743\) 327.809 149.705i 0.441197 0.201488i −0.182416 0.983222i \(-0.558392\pi\)
0.623612 + 0.781734i \(0.285664\pi\)
\(744\) 0 0
\(745\) −0.268247 1.86570i −0.000360064 0.00250430i
\(746\) −869.855 397.250i −1.16603 0.532506i
\(747\) 0 0
\(748\) −589.636 + 173.133i −0.788283 + 0.231461i
\(749\) 768.572 + 350.995i 1.02613 + 0.468618i
\(750\) 0 0
\(751\) 197.194 + 227.574i 0.262575 + 0.303028i 0.871693 0.490052i \(-0.163022\pi\)
−0.609118 + 0.793079i \(0.708477\pi\)
\(752\) 130.935 59.7958i 0.174115 0.0795157i
\(753\) 0 0
\(754\) −26.6580 + 185.410i −0.0353554 + 0.245902i
\(755\) 35.2965 54.9224i 0.0467503 0.0727450i
\(756\) 0 0
\(757\) −1284.30 377.105i −1.69657 0.498158i −0.716630 0.697454i \(-0.754316\pi\)
−0.979939 + 0.199296i \(0.936134\pi\)
\(758\) 888.773i 1.17252i
\(759\) 0 0
\(760\) −20.0911 −0.0264357
\(761\) 12.4545 42.4160i 0.0163659 0.0557372i −0.950905 0.309482i \(-0.899844\pi\)
0.967271 + 0.253745i \(0.0816624\pi\)
\(762\) 0 0
\(763\) 785.568 + 504.854i 1.02958 + 0.661669i
\(764\) −388.583 55.8698i −0.508616 0.0731280i
\(765\) 0 0
\(766\) −316.780 693.650i −0.413550 0.905549i
\(767\) 456.410 395.482i 0.595059 0.515622i
\(768\) 0 0
\(769\) 131.544 288.042i 0.171059 0.374567i −0.804614 0.593798i \(-0.797628\pi\)
0.975673 + 0.219231i \(0.0703550\pi\)
\(770\) 6.87517 + 23.4147i 0.00892879 + 0.0304087i
\(771\) 0 0
\(772\) −112.801 + 246.999i −0.146115 + 0.319947i
\(773\) −405.508 + 58.3032i −0.524590 + 0.0754246i −0.399522 0.916724i \(-0.630824\pi\)
−0.125068 + 0.992148i \(0.539915\pi\)
\(774\) 0 0
\(775\) 488.560 + 1069.80i 0.630400 + 1.38038i
\(776\) −122.212 190.166i −0.157490 0.245059i
\(777\) 0 0
\(778\) 91.6173 + 58.8789i 0.117760 + 0.0756798i
\(779\) −1507.31 1306.09i −1.93492 1.67662i
\(780\) 0 0
\(781\) −654.677 −0.838255
\(782\) 745.276 407.522i 0.953039 0.521127i
\(783\) 0 0
\(784\) 56.5801 + 16.6134i 0.0721684 + 0.0211906i
\(785\) 41.9775 + 36.3737i 0.0534745 + 0.0463359i
\(786\) 0 0
\(787\) 7.93411 55.1829i 0.0100815 0.0701181i −0.984160 0.177285i \(-0.943269\pi\)
0.994241 + 0.107167i \(0.0341778\pi\)
\(788\) −8.03969 12.5100i −0.0102026 0.0158756i
\(789\) 0 0
\(790\) 16.9960 + 19.6145i 0.0215140 + 0.0248284i
\(791\) 860.165 123.673i 1.08744 0.156350i
\(792\) 0 0
\(793\) 469.246 137.783i 0.591735 0.173749i
\(794\) −144.738 492.933i −0.182290 0.620822i
\(795\) 0 0
\(796\) −82.3589 572.819i −0.103466 0.719622i
\(797\) −340.720 + 295.236i −0.427503 + 0.370434i −0.841874 0.539675i \(-0.818547\pi\)
0.414370 + 0.910108i \(0.364002\pi\)
\(798\) 0 0
\(799\) −790.559 + 508.061i −0.989435 + 0.635871i
\(800\) 139.630 + 20.0758i 0.174538 + 0.0250948i
\(801\) 0 0
\(802\) 459.663 530.479i 0.573146 0.661446i
\(803\) −385.868 + 1314.15i −0.480533 + 1.63655i
\(804\) 0 0
\(805\) −16.1829 29.5952i −0.0201029 0.0367643i
\(806\) 471.384i 0.584843i
\(807\) 0 0
\(808\) 23.7992 27.4657i 0.0294545 0.0339923i
\(809\) 709.205 1103.54i 0.876644 1.36408i −0.0541477 0.998533i \(-0.517244\pi\)
0.930791 0.365551i \(-0.119119\pi\)
\(810\) 0 0
\(811\) 153.446 98.6135i 0.189205 0.121595i −0.442609 0.896715i \(-0.645947\pi\)
0.631814 + 0.775120i \(0.282311\pi\)
\(812\) 199.556 91.1344i 0.245759 0.112234i
\(813\) 0 0
\(814\) 6.54513 + 45.5224i 0.00804071 + 0.0559243i
\(815\) −47.6484 21.7603i −0.0584643 0.0266997i
\(816\) 0 0
\(817\) 553.870 162.631i 0.677931 0.199059i
\(818\) 945.308 + 431.708i 1.15563 + 0.527760i
\(819\) 0 0
\(820\) −23.0876 26.6445i −0.0281556 0.0324933i
\(821\) 1137.57 519.512i 1.38559 0.632780i 0.423600 0.905849i \(-0.360766\pi\)
0.961994 + 0.273070i \(0.0880389\pi\)
\(822\) 0 0
\(823\) −183.845 + 1278.67i −0.223383 + 1.55367i 0.501722 + 0.865029i \(0.332700\pi\)
−0.725106 + 0.688638i \(0.758209\pi\)
\(824\) 102.204 159.032i 0.124034 0.193000i
\(825\) 0 0
\(826\) −678.644 199.268i −0.821603 0.241245i
\(827\) 892.421i 1.07911i −0.841952 0.539553i \(-0.818593\pi\)
0.841952 0.539553i \(-0.181407\pi\)
\(828\) 0 0
\(829\) 960.904 1.15911 0.579556 0.814932i \(-0.303226\pi\)
0.579556 + 0.814932i \(0.303226\pi\)
\(830\) −1.65270 + 5.62859i −0.00199121 + 0.00678144i
\(831\) 0 0
\(832\) 47.5651 + 30.5683i 0.0571696 + 0.0367407i
\(833\) −381.063 54.7886i −0.457459 0.0657726i
\(834\) 0 0
\(835\) 7.87568 + 17.2453i 0.00943195 + 0.0206531i
\(836\) −504.177 + 436.871i −0.603082 + 0.522574i
\(837\) 0 0
\(838\) 191.566 419.472i 0.228600 0.500563i
\(839\) −55.8484 190.202i −0.0665655 0.226701i 0.919491 0.393110i \(-0.128601\pi\)
−0.986057 + 0.166409i \(0.946783\pi\)
\(840\) 0 0
\(841\) 203.462 445.519i 0.241928 0.529749i
\(842\) 966.044 138.896i 1.14732 0.164960i
\(843\) 0 0
\(844\) 54.8467 + 120.098i 0.0649843 + 0.142296i
\(845\) 16.1270 + 25.0941i 0.0190852 + 0.0296971i
\(846\) 0 0
\(847\) 85.8803 + 55.1919i 0.101393 + 0.0651616i
\(848\) −118.693 102.848i −0.139968 0.121283i
\(849\) 0 0
\(850\) −920.962 −1.08348
\(851\) −22.2503 59.5482i −0.0261460 0.0699744i
\(852\) 0 0
\(853\) 1143.34 + 335.716i 1.34038 + 0.393571i 0.871805 0.489853i \(-0.162950\pi\)
0.468575 + 0.883424i \(0.344768\pi\)
\(854\) −432.872 375.086i −0.506876 0.439210i
\(855\) 0 0
\(856\) −58.1078 + 404.148i −0.0678829 + 0.472136i
\(857\) −60.6228 94.3309i −0.0707384 0.110071i 0.804082 0.594518i \(-0.202657\pi\)
−0.874821 + 0.484447i \(0.839021\pi\)
\(858\) 0 0
\(859\) −528.669 610.117i −0.615447 0.710264i 0.359388 0.933188i \(-0.382985\pi\)
−0.974836 + 0.222924i \(0.928440\pi\)
\(860\) 10.1002 1.45219i 0.0117444 0.00168859i
\(861\) 0 0
\(862\) 1015.12 298.066i 1.17763 0.345784i
\(863\) 379.258 + 1291.63i 0.439464 + 1.49668i 0.820245 + 0.572012i \(0.193837\pi\)
−0.380781 + 0.924665i \(0.624345\pi\)
\(864\) 0 0
\(865\) 10.0343 + 69.7901i 0.0116003 + 0.0806822i
\(866\) −147.609 + 127.904i −0.170449 + 0.147695i
\(867\) 0 0
\(868\) 464.435 298.474i 0.535063 0.343864i
\(869\) 853.013 + 122.645i 0.981603 + 0.141133i
\(870\) 0 0
\(871\) 230.602 266.129i 0.264755 0.305544i
\(872\) −127.133 + 432.976i −0.145795 + 0.496532i
\(873\) 0 0
\(874\) 552.167 738.515i 0.631770 0.844983i
\(875\) 73.2356i 0.0836979i
\(876\) 0 0
\(877\) 500.650 577.781i 0.570866 0.658815i −0.394749 0.918789i \(-0.629169\pi\)
0.965616 + 0.259974i \(0.0837140\pi\)
\(878\) −86.9494 + 135.296i −0.0990312 + 0.154096i
\(879\) 0 0
\(880\) −9.92061 + 6.37559i −0.0112734 + 0.00724499i
\(881\) −870.676 + 397.624i −0.988282 + 0.451333i −0.842916 0.538045i \(-0.819163\pi\)
−0.145365 + 0.989378i \(0.546436\pi\)
\(882\) 0 0
\(883\) 57.8501 + 402.356i 0.0655154 + 0.455670i 0.996001 + 0.0893414i \(0.0284762\pi\)
−0.930486 + 0.366328i \(0.880615\pi\)
\(884\) −335.773 153.343i −0.379834 0.173464i
\(885\) 0 0
\(886\) −641.539 + 188.373i −0.724084 + 0.212610i
\(887\) −466.605 213.091i −0.526048 0.240238i 0.134645 0.990894i \(-0.457010\pi\)
−0.660694 + 0.750656i \(0.729738\pi\)
\(888\) 0 0
\(889\) 379.116 + 437.524i 0.426453 + 0.492152i
\(890\) −3.77702 + 1.72491i −0.00424385 + 0.00193810i
\(891\) 0 0
\(892\) −27.4608 + 190.994i −0.0307857 + 0.214119i
\(893\) −551.542 + 858.217i −0.617629 + 0.961049i
\(894\) 0 0
\(895\) −2.05922 0.604640i −0.00230080 0.000675576i
\(896\) 66.2193i 0.0739055i
\(897\) 0 0
\(898\) −807.222 −0.898911
\(899\) −249.009 + 848.046i −0.276984 + 0.943322i
\(900\) 0 0
\(901\) 862.565 + 554.337i 0.957342 + 0.615247i
\(902\) −1158.74 166.602i −1.28464 0.184703i
\(903\) 0 0
\(904\) 174.451 + 381.993i 0.192976 + 0.422559i
\(905\) −12.1904 + 10.5630i −0.0134700 + 0.0116718i
\(906\) 0 0
\(907\) −109.448 + 239.657i −0.120670 + 0.264231i −0.960322 0.278895i \(-0.910032\pi\)
0.839651 + 0.543126i \(0.182759\pi\)
\(908\) 173.488 + 590.845i 0.191066 + 0.650710i
\(909\) 0 0
\(910\) −6.08930 + 13.3337i −0.00669154 + 0.0146524i
\(911\) 857.198 123.246i 0.940942 0.135287i 0.345260 0.938507i \(-0.387791\pi\)
0.595682 + 0.803220i \(0.296882\pi\)
\(912\) 0 0
\(913\) 80.9171 + 177.184i 0.0886277 + 0.194068i
\(914\) 284.647 + 442.919i 0.311430 + 0.484594i
\(915\) 0 0
\(916\) −242.386 155.772i −0.264614 0.170057i
\(917\) 113.698 + 98.5202i 0.123990 + 0.107438i
\(918\) 0 0
\(919\) −874.158 −0.951206 −0.475603 0.879660i \(-0.657770\pi\)
−0.475603 + 0.879660i \(0.657770\pi\)
\(920\) 11.5191 11.5327i 0.0125208 0.0125356i
\(921\) 0 0
\(922\) −469.021 137.717i −0.508700 0.149368i
\(923\) −297.196 257.522i −0.321990 0.279006i
\(924\) 0 0
\(925\) −9.80885 + 68.2221i −0.0106042 + 0.0737536i
\(926\) 279.258 + 434.534i 0.301574 + 0.469259i
\(927\) 0 0
\(928\) 69.4247 + 80.1204i 0.0748111 + 0.0863366i
\(929\) 557.468 80.1518i 0.600073 0.0862775i 0.164417 0.986391i \(-0.447426\pi\)
0.435656 + 0.900113i \(0.356517\pi\)
\(930\) 0 0
\(931\) −401.000 + 117.744i −0.430720 + 0.126471i
\(932\) 94.7052 + 322.536i 0.101615 + 0.346069i
\(933\) 0 0
\(934\) −22.3615 155.528i −0.0239417 0.166518i
\(935\) 58.1846 50.4172i 0.0622295 0.0539222i
\(936\) 0 0
\(937\) 1161.84 746.671i 1.23996 0.796874i 0.254548 0.967060i \(-0.418073\pi\)
0.985412 + 0.170186i \(0.0544370\pi\)
\(938\) −408.219 58.6931i −0.435202 0.0625726i
\(939\) 0 0
\(940\) −11.8093 + 13.6287i −0.0125631 + 0.0144986i
\(941\) 471.861 1607.01i 0.501447 1.70777i −0.186891 0.982381i \(-0.559841\pi\)
0.688338 0.725390i \(-0.258341\pi\)
\(942\) 0 0
\(943\) 1613.93 116.385i 1.71148 0.123420i
\(944\) 341.795i 0.362071i
\(945\) 0 0
\(946\) 221.882 256.065i 0.234547 0.270682i
\(947\) 637.355 991.743i 0.673025 1.04725i −0.321914 0.946769i \(-0.604326\pi\)
0.994939 0.100478i \(-0.0320374\pi\)
\(948\) 0 0
\(949\) −692.097 + 444.784i −0.729291 + 0.468687i
\(950\) −909.432 + 415.324i −0.957297 + 0.437183i
\(951\) 0 0
\(952\) 61.5253 + 427.918i 0.0646274 + 0.449493i
\(953\) −1381.39 630.861i −1.44952 0.661974i −0.473728 0.880671i \(-0.657092\pi\)
−0.975793 + 0.218697i \(0.929819\pi\)
\(954\) 0 0
\(955\) 47.1907 13.8564i 0.0494144 0.0145094i
\(956\) −670.915 306.397i −0.701794 0.320498i
\(957\) 0 0
\(958\) −85.6854 98.8862i −0.0894419 0.103221i
\(959\) 717.357 327.606i 0.748026 0.341612i
\(960\) 0 0
\(961\) −179.773 + 1250.35i −0.187069 + 1.30109i
\(962\) −14.9354 + 23.2399i −0.0155253 + 0.0241579i
\(963\) 0 0
\(964\) −205.542 60.3525i −0.213217 0.0626063i
\(965\) 34.0188i 0.0352526i
\(966\) 0 0
\(967\) 1603.98 1.65872 0.829359 0.558716i \(-0.188706\pi\)
0.829359 + 0.558716i \(0.188706\pi\)
\(968\) −13.8985 + 47.3340i −0.0143580 + 0.0488988i
\(969\) 0 0
\(970\) 23.8243 + 15.3109i 0.0245611 + 0.0157845i
\(971\) 1210.01 + 173.973i 1.24615 + 0.179169i 0.733655 0.679522i \(-0.237813\pi\)
0.512493 + 0.858691i \(0.328722\pi\)
\(972\) 0 0
\(973\) 74.2730 + 162.635i 0.0763340 + 0.167148i
\(974\) −107.964 + 93.5517i −0.110846 + 0.0960490i
\(975\) 0 0
\(976\) 114.982 251.775i 0.117809 0.257966i
\(977\) −314.727 1071.86i −0.322136 1.09709i −0.948293 0.317398i \(-0.897191\pi\)
0.626156 0.779697i \(-0.284627\pi\)
\(978\) 0 0
\(979\) −57.2752 + 125.415i −0.0585037 + 0.128105i
\(980\) −7.31251 + 1.05138i −0.00746175 + 0.00107284i
\(981\) 0 0
\(982\) 141.894 + 310.704i 0.144495 + 0.316399i
\(983\) −344.552 536.134i −0.350511 0.545406i 0.620571 0.784150i \(-0.286901\pi\)
−0.971083 + 0.238744i \(0.923264\pi\)
\(984\) 0 0
\(985\) 1.56728 + 1.00723i 0.00159114 + 0.00102257i
\(986\) −523.072 453.245i −0.530499 0.459680i
\(987\) 0 0
\(988\) −400.722 −0.405589
\(989\) −224.205 + 411.176i −0.226698 + 0.415749i
\(990\) 0 0
\(991\) −75.3659 22.1294i −0.0760504 0.0223304i 0.243486 0.969904i \(-0.421709\pi\)
−0.319536 + 0.947574i \(0.603527\pi\)
\(992\) 201.623 + 174.708i 0.203249 + 0.176116i
\(993\) 0 0
\(994\) −65.5449 + 455.875i −0.0659405 + 0.458626i
\(995\) 39.1974 + 60.9924i 0.0393944 + 0.0612989i
\(996\) 0 0
\(997\) 338.699 + 390.879i 0.339718 + 0.392055i 0.899743 0.436420i \(-0.143754\pi\)
−0.560025 + 0.828476i \(0.689209\pi\)
\(998\) 392.213 56.3917i 0.392999 0.0565047i
\(999\) 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.b.179.2 80
3.2 odd 2 inner 414.3.k.b.179.7 yes 80
23.9 even 11 inner 414.3.k.b.377.7 yes 80
69.32 odd 22 inner 414.3.k.b.377.2 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
414.3.k.b.179.2 80 1.1 even 1 trivial
414.3.k.b.179.7 yes 80 3.2 odd 2 inner
414.3.k.b.377.2 yes 80 69.32 odd 22 inner
414.3.k.b.377.7 yes 80 23.9 even 11 inner