Properties

Label 891.2.k.a.161.16
Level $891$
Weight $2$
Character 891.161
Analytic conductor $7.115$
Analytic rank $0$
Dimension $80$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(161,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.k (of order \(10\), degree \(4\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 161.16
Character \(\chi\) \(=\) 891.161
Dual form 891.2.k.a.404.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.46797 + 1.06654i) q^{2} +(0.399387 + 1.22919i) q^{4} +(-0.706314 - 0.972158i) q^{5} +(-4.60425 + 1.49601i) q^{7} +(0.396737 - 1.22103i) q^{8} -2.18041i q^{10} +(-3.30067 + 0.324896i) q^{11} +(-1.79861 + 2.47557i) q^{13} +(-8.35446 - 2.71453i) q^{14} +(3.97590 - 2.88866i) q^{16} +(-1.80866 + 1.31407i) q^{17} +(-4.34428 - 1.41154i) q^{19} +(0.912871 - 1.25646i) q^{20} +(-5.19180 - 3.04337i) q^{22} +1.98738i q^{23} +(1.09887 - 3.38198i) q^{25} +(-5.28060 + 1.71577i) q^{26} +(-3.67776 - 5.06200i) q^{28} +(0.524067 + 1.61291i) q^{29} +(-4.29749 - 3.12231i) q^{31} +6.34963 q^{32} -4.05656 q^{34} +(4.70641 + 3.41941i) q^{35} +(0.344857 + 1.06136i) q^{37} +(-4.87179 - 6.70545i) q^{38} +(-1.46726 + 0.476740i) q^{40} +(-3.28550 + 10.1117i) q^{41} -3.79055i q^{43} +(-1.71760 - 3.92738i) q^{44} +(-2.11962 + 2.91741i) q^{46} +(-3.10538 - 1.00900i) q^{47} +(13.2980 - 9.66153i) q^{49} +(5.22014 - 3.79265i) q^{50} +(-3.76128 - 1.22211i) q^{52} +(0.749954 - 1.03222i) q^{53} +(2.64716 + 2.97930i) q^{55} +6.21546i q^{56} +(-0.950924 + 2.92664i) q^{58} +(-0.0300536 + 0.00976502i) q^{59} +(-0.697881 - 0.960551i) q^{61} +(-2.97851 - 9.16690i) q^{62} +(1.36926 + 0.994827i) q^{64} +3.67703 q^{65} -2.10554 q^{67} +(-2.33759 - 1.69836i) q^{68} +(3.26192 + 10.0392i) q^{70} +(2.26013 + 3.11080i) q^{71} +(6.69980 - 2.17690i) q^{73} +(-0.625746 + 1.92585i) q^{74} -5.90368i q^{76} +(14.7111 - 6.43375i) q^{77} +(-2.24604 + 3.09141i) q^{79} +(-5.61646 - 1.82490i) q^{80} +(-15.6076 + 11.3396i) q^{82} +(5.88095 - 4.27276i) q^{83} +(2.55496 + 0.830157i) q^{85} +(4.04278 - 5.56441i) q^{86} +(-0.912791 + 4.15912i) q^{88} +10.2875i q^{89} +(4.57775 - 14.0889i) q^{91} +(-2.44286 + 0.793733i) q^{92} +(-3.48246 - 4.79320i) q^{94} +(1.69618 + 5.22031i) q^{95} +(-11.7345 - 8.52561i) q^{97} +29.8254 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.46797 + 1.06654i 1.03801 + 0.754159i 0.969896 0.243519i \(-0.0783017\pi\)
0.0681144 + 0.997678i \(0.478302\pi\)
\(3\) 0 0
\(4\) 0.399387 + 1.22919i 0.199693 + 0.614593i
\(5\) −0.706314 0.972158i −0.315873 0.434762i 0.621328 0.783550i \(-0.286593\pi\)
−0.937202 + 0.348788i \(0.886593\pi\)
\(6\) 0 0
\(7\) −4.60425 + 1.49601i −1.74024 + 0.565439i −0.994866 0.101203i \(-0.967731\pi\)
−0.745378 + 0.666643i \(0.767731\pi\)
\(8\) 0.396737 1.22103i 0.140268 0.431700i
\(9\) 0 0
\(10\) 2.18041i 0.689506i
\(11\) −3.30067 + 0.324896i −0.995190 + 0.0979599i
\(12\) 0 0
\(13\) −1.79861 + 2.47557i −0.498844 + 0.686599i −0.981988 0.188941i \(-0.939494\pi\)
0.483145 + 0.875541i \(0.339494\pi\)
\(14\) −8.35446 2.71453i −2.23282 0.725488i
\(15\) 0 0
\(16\) 3.97590 2.88866i 0.993974 0.722164i
\(17\) −1.80866 + 1.31407i −0.438664 + 0.318708i −0.785104 0.619364i \(-0.787390\pi\)
0.346440 + 0.938072i \(0.387390\pi\)
\(18\) 0 0
\(19\) −4.34428 1.41154i −0.996645 0.323830i −0.235121 0.971966i \(-0.575549\pi\)
−0.761524 + 0.648136i \(0.775549\pi\)
\(20\) 0.912871 1.25646i 0.204124 0.280953i
\(21\) 0 0
\(22\) −5.19180 3.04337i −1.10690 0.648848i
\(23\) 1.98738i 0.414397i 0.978299 + 0.207199i \(0.0664346\pi\)
−0.978299 + 0.207199i \(0.933565\pi\)
\(24\) 0 0
\(25\) 1.09887 3.38198i 0.219775 0.676397i
\(26\) −5.28060 + 1.71577i −1.03561 + 0.336490i
\(27\) 0 0
\(28\) −3.67776 5.06200i −0.695030 0.956627i
\(29\) 0.524067 + 1.61291i 0.0973167 + 0.299510i 0.987851 0.155407i \(-0.0496689\pi\)
−0.890534 + 0.454917i \(0.849669\pi\)
\(30\) 0 0
\(31\) −4.29749 3.12231i −0.771852 0.560783i 0.130671 0.991426i \(-0.458287\pi\)
−0.902523 + 0.430643i \(0.858287\pi\)
\(32\) 6.34963 1.12247
\(33\) 0 0
\(34\) −4.05656 −0.695694
\(35\) 4.70641 + 3.41941i 0.795528 + 0.577985i
\(36\) 0 0
\(37\) 0.344857 + 1.06136i 0.0566941 + 0.174486i 0.975394 0.220471i \(-0.0707594\pi\)
−0.918699 + 0.394957i \(0.870759\pi\)
\(38\) −4.87179 6.70545i −0.790309 1.08777i
\(39\) 0 0
\(40\) −1.46726 + 0.476740i −0.231994 + 0.0753793i
\(41\) −3.28550 + 10.1117i −0.513109 + 1.57919i 0.273587 + 0.961847i \(0.411790\pi\)
−0.786696 + 0.617341i \(0.788210\pi\)
\(42\) 0 0
\(43\) 3.79055i 0.578054i −0.957321 0.289027i \(-0.906668\pi\)
0.957321 0.289027i \(-0.0933317\pi\)
\(44\) −1.71760 3.92738i −0.258938 0.592075i
\(45\) 0 0
\(46\) −2.11962 + 2.91741i −0.312521 + 0.430149i
\(47\) −3.10538 1.00900i −0.452967 0.147178i 0.0736436 0.997285i \(-0.476537\pi\)
−0.526610 + 0.850107i \(0.676537\pi\)
\(48\) 0 0
\(49\) 13.2980 9.66153i 1.89971 1.38022i
\(50\) 5.22014 3.79265i 0.738239 0.536362i
\(51\) 0 0
\(52\) −3.76128 1.22211i −0.521595 0.169477i
\(53\) 0.749954 1.03222i 0.103014 0.141787i −0.754398 0.656417i \(-0.772071\pi\)
0.857412 + 0.514631i \(0.172071\pi\)
\(54\) 0 0
\(55\) 2.64716 + 2.97930i 0.356943 + 0.401728i
\(56\) 6.21546i 0.830575i
\(57\) 0 0
\(58\) −0.950924 + 2.92664i −0.124862 + 0.384287i
\(59\) −0.0300536 + 0.00976502i −0.00391265 + 0.00127130i −0.310973 0.950419i \(-0.600655\pi\)
0.307060 + 0.951690i \(0.400655\pi\)
\(60\) 0 0
\(61\) −0.697881 0.960551i −0.0893545 0.122986i 0.761999 0.647578i \(-0.224218\pi\)
−0.851354 + 0.524592i \(0.824218\pi\)
\(62\) −2.97851 9.16690i −0.378271 1.16420i
\(63\) 0 0
\(64\) 1.36926 + 0.994827i 0.171158 + 0.124353i
\(65\) 3.67703 0.456079
\(66\) 0 0
\(67\) −2.10554 −0.257233 −0.128617 0.991694i \(-0.541054\pi\)
−0.128617 + 0.991694i \(0.541054\pi\)
\(68\) −2.33759 1.69836i −0.283474 0.205956i
\(69\) 0 0
\(70\) 3.26192 + 10.0392i 0.389874 + 1.19991i
\(71\) 2.26013 + 3.11080i 0.268228 + 0.369184i 0.921790 0.387688i \(-0.126726\pi\)
−0.653563 + 0.756873i \(0.726726\pi\)
\(72\) 0 0
\(73\) 6.69980 2.17690i 0.784152 0.254786i 0.110540 0.993872i \(-0.464742\pi\)
0.673612 + 0.739085i \(0.264742\pi\)
\(74\) −0.625746 + 1.92585i −0.0727414 + 0.223875i
\(75\) 0 0
\(76\) 5.90368i 0.677198i
\(77\) 14.7111 6.43375i 1.67648 0.733194i
\(78\) 0 0
\(79\) −2.24604 + 3.09141i −0.252700 + 0.347811i −0.916454 0.400139i \(-0.868962\pi\)
0.663755 + 0.747950i \(0.268962\pi\)
\(80\) −5.61646 1.82490i −0.627940 0.204030i
\(81\) 0 0
\(82\) −15.6076 + 11.3396i −1.72357 + 1.25225i
\(83\) 5.88095 4.27276i 0.645518 0.468996i −0.216223 0.976344i \(-0.569374\pi\)
0.861742 + 0.507348i \(0.169374\pi\)
\(84\) 0 0
\(85\) 2.55496 + 0.830157i 0.277124 + 0.0900431i
\(86\) 4.04278 5.56441i 0.435945 0.600026i
\(87\) 0 0
\(88\) −0.912791 + 4.15912i −0.0973039 + 0.443364i
\(89\) 10.2875i 1.09048i 0.838281 + 0.545238i \(0.183561\pi\)
−0.838281 + 0.545238i \(0.816439\pi\)
\(90\) 0 0
\(91\) 4.57775 14.0889i 0.479879 1.47692i
\(92\) −2.44286 + 0.793733i −0.254686 + 0.0827524i
\(93\) 0 0
\(94\) −3.48246 4.79320i −0.359189 0.494381i
\(95\) 1.69618 + 5.22031i 0.174025 + 0.535593i
\(96\) 0 0
\(97\) −11.7345 8.52561i −1.19146 0.865644i −0.198040 0.980194i \(-0.563458\pi\)
−0.993418 + 0.114549i \(0.963458\pi\)
\(98\) 29.8254 3.01282
\(99\) 0 0
\(100\) 4.59597 0.459597
\(101\) 13.0136 + 9.45494i 1.29490 + 0.940802i 0.999892 0.0146921i \(-0.00467680\pi\)
0.295011 + 0.955494i \(0.404677\pi\)
\(102\) 0 0
\(103\) −0.643116 1.97931i −0.0633681 0.195027i 0.914360 0.404902i \(-0.132694\pi\)
−0.977728 + 0.209875i \(0.932694\pi\)
\(104\) 2.30917 + 3.17830i 0.226433 + 0.311658i
\(105\) 0 0
\(106\) 2.20182 0.715414i 0.213859 0.0694871i
\(107\) −0.129361 + 0.398133i −0.0125058 + 0.0384889i −0.957115 0.289709i \(-0.906441\pi\)
0.944609 + 0.328198i \(0.106441\pi\)
\(108\) 0 0
\(109\) 14.6788i 1.40597i 0.711205 + 0.702985i \(0.248150\pi\)
−0.711205 + 0.702985i \(0.751850\pi\)
\(110\) 0.708407 + 7.19682i 0.0675440 + 0.686190i
\(111\) 0 0
\(112\) −13.9846 + 19.2481i −1.32142 + 1.81877i
\(113\) 3.04019 + 0.987818i 0.285997 + 0.0929261i 0.448503 0.893782i \(-0.351957\pi\)
−0.162505 + 0.986708i \(0.551957\pi\)
\(114\) 0 0
\(115\) 1.93205 1.40371i 0.180164 0.130897i
\(116\) −1.77326 + 1.28835i −0.164643 + 0.119620i
\(117\) 0 0
\(118\) −0.0545326 0.0177187i −0.00502013 0.00163114i
\(119\) 6.36165 8.75606i 0.583172 0.802667i
\(120\) 0 0
\(121\) 10.7889 2.14475i 0.980808 0.194977i
\(122\) 2.15438i 0.195048i
\(123\) 0 0
\(124\) 2.12154 6.52943i 0.190520 0.586360i
\(125\) −9.77817 + 3.17712i −0.874587 + 0.284170i
\(126\) 0 0
\(127\) −13.1088 18.0428i −1.16322 1.60104i −0.698567 0.715545i \(-0.746179\pi\)
−0.464654 0.885492i \(-0.653821\pi\)
\(128\) −2.97528 9.15696i −0.262980 0.809368i
\(129\) 0 0
\(130\) 5.39776 + 3.92170i 0.473415 + 0.343956i
\(131\) −15.4992 −1.35417 −0.677086 0.735904i \(-0.736757\pi\)
−0.677086 + 0.735904i \(0.736757\pi\)
\(132\) 0 0
\(133\) 22.1138 1.91751
\(134\) −3.09087 2.24565i −0.267011 0.193995i
\(135\) 0 0
\(136\) 0.886955 + 2.72977i 0.0760557 + 0.234075i
\(137\) −10.0751 13.8672i −0.860773 1.18475i −0.981385 0.192053i \(-0.938486\pi\)
0.120612 0.992700i \(-0.461514\pi\)
\(138\) 0 0
\(139\) −9.86040 + 3.20384i −0.836348 + 0.271746i −0.695717 0.718316i \(-0.744913\pi\)
−0.140631 + 0.990062i \(0.544913\pi\)
\(140\) −2.32341 + 7.15072i −0.196364 + 0.604346i
\(141\) 0 0
\(142\) 6.97708i 0.585503i
\(143\) 5.13231 8.75541i 0.429185 0.732164i
\(144\) 0 0
\(145\) 1.19785 1.64870i 0.0994759 0.136917i
\(146\) 12.1568 + 3.95000i 1.00611 + 0.326904i
\(147\) 0 0
\(148\) −1.16688 + 0.847786i −0.0959168 + 0.0696876i
\(149\) 0.0327310 0.0237805i 0.00268143 0.00194817i −0.586444 0.809990i \(-0.699472\pi\)
0.589125 + 0.808042i \(0.299472\pi\)
\(150\) 0 0
\(151\) 2.61695 + 0.850299i 0.212964 + 0.0691964i 0.413556 0.910479i \(-0.364286\pi\)
−0.200592 + 0.979675i \(0.564286\pi\)
\(152\) −3.44707 + 4.74449i −0.279594 + 0.384829i
\(153\) 0 0
\(154\) 28.4573 + 6.24544i 2.29315 + 0.503272i
\(155\) 6.38317i 0.512709i
\(156\) 0 0
\(157\) 0.651985 2.00660i 0.0520341 0.160145i −0.921663 0.387992i \(-0.873169\pi\)
0.973697 + 0.227848i \(0.0731688\pi\)
\(158\) −6.59424 + 2.14260i −0.524610 + 0.170456i
\(159\) 0 0
\(160\) −4.48483 6.17284i −0.354557 0.488006i
\(161\) −2.97314 9.15039i −0.234316 0.721152i
\(162\) 0 0
\(163\) −11.8085 8.57941i −0.924917 0.671991i 0.0198264 0.999803i \(-0.493689\pi\)
−0.944743 + 0.327812i \(0.893689\pi\)
\(164\) −13.7414 −1.07302
\(165\) 0 0
\(166\) 13.1901 1.02375
\(167\) 0.721863 + 0.524464i 0.0558594 + 0.0405843i 0.615365 0.788243i \(-0.289009\pi\)
−0.559505 + 0.828827i \(0.689009\pi\)
\(168\) 0 0
\(169\) 1.12376 + 3.45858i 0.0864432 + 0.266045i
\(170\) 2.86520 + 3.94362i 0.219751 + 0.302461i
\(171\) 0 0
\(172\) 4.65930 1.51390i 0.355268 0.115434i
\(173\) −4.09368 + 12.5991i −0.311237 + 0.957889i 0.666039 + 0.745917i \(0.267989\pi\)
−0.977276 + 0.211972i \(0.932011\pi\)
\(174\) 0 0
\(175\) 17.2154i 1.30136i
\(176\) −12.1846 + 10.8263i −0.918450 + 0.816060i
\(177\) 0 0
\(178\) −10.9721 + 15.1018i −0.822392 + 1.13193i
\(179\) 19.1587 + 6.22502i 1.43199 + 0.465280i 0.919389 0.393350i \(-0.128684\pi\)
0.512596 + 0.858630i \(0.328684\pi\)
\(180\) 0 0
\(181\) 3.63758 2.64286i 0.270379 0.196442i −0.444331 0.895863i \(-0.646559\pi\)
0.714710 + 0.699421i \(0.246559\pi\)
\(182\) 21.7464 15.7997i 1.61195 1.17115i
\(183\) 0 0
\(184\) 2.42665 + 0.788467i 0.178895 + 0.0581265i
\(185\) 0.788232 1.08491i 0.0579520 0.0797641i
\(186\) 0 0
\(187\) 5.54285 4.92493i 0.405333 0.360146i
\(188\) 4.22008i 0.307781i
\(189\) 0 0
\(190\) −3.07774 + 9.47231i −0.223283 + 0.687193i
\(191\) −16.9040 + 5.49245i −1.22313 + 0.397420i −0.848222 0.529641i \(-0.822327\pi\)
−0.374910 + 0.927061i \(0.622327\pi\)
\(192\) 0 0
\(193\) 3.62015 + 4.98270i 0.260584 + 0.358663i 0.919183 0.393831i \(-0.128851\pi\)
−0.658599 + 0.752494i \(0.728851\pi\)
\(194\) −8.13295 25.0307i −0.583912 1.79710i
\(195\) 0 0
\(196\) 17.1869 + 12.4870i 1.22763 + 0.891927i
\(197\) −22.5100 −1.60377 −0.801886 0.597477i \(-0.796170\pi\)
−0.801886 + 0.597477i \(0.796170\pi\)
\(198\) 0 0
\(199\) 9.30680 0.659742 0.329871 0.944026i \(-0.392995\pi\)
0.329871 + 0.944026i \(0.392995\pi\)
\(200\) −3.69355 2.68352i −0.261173 0.189753i
\(201\) 0 0
\(202\) 9.01948 + 27.7591i 0.634609 + 1.95312i
\(203\) −4.82587 6.64224i −0.338710 0.466194i
\(204\) 0 0
\(205\) 12.1508 3.94804i 0.848649 0.275743i
\(206\) 1.16694 3.59147i 0.0813046 0.250230i
\(207\) 0 0
\(208\) 15.0382i 1.04271i
\(209\) 14.7976 + 3.24760i 1.02357 + 0.224641i
\(210\) 0 0
\(211\) 8.23554 11.3352i 0.566958 0.780351i −0.425232 0.905084i \(-0.639808\pi\)
0.992190 + 0.124734i \(0.0398076\pi\)
\(212\) 1.56832 + 0.509577i 0.107712 + 0.0349979i
\(213\) 0 0
\(214\) −0.614523 + 0.446477i −0.0420079 + 0.0305206i
\(215\) −3.68502 + 2.67732i −0.251316 + 0.182592i
\(216\) 0 0
\(217\) 24.4577 + 7.94680i 1.66030 + 0.539464i
\(218\) −15.6555 + 21.5480i −1.06032 + 1.45941i
\(219\) 0 0
\(220\) −2.60487 + 4.44375i −0.175620 + 0.299597i
\(221\) 6.84094i 0.460172i
\(222\) 0 0
\(223\) −4.98529 + 15.3432i −0.333840 + 1.02745i 0.633451 + 0.773783i \(0.281638\pi\)
−0.967291 + 0.253671i \(0.918362\pi\)
\(224\) −29.2353 + 9.49912i −1.95336 + 0.634686i
\(225\) 0 0
\(226\) 3.40936 + 4.69258i 0.226787 + 0.312146i
\(227\) 4.54715 + 13.9947i 0.301805 + 0.928861i 0.980850 + 0.194764i \(0.0623942\pi\)
−0.679045 + 0.734097i \(0.737606\pi\)
\(228\) 0 0
\(229\) −17.9594 13.0482i −1.18679 0.862252i −0.193867 0.981028i \(-0.562103\pi\)
−0.992921 + 0.118775i \(0.962103\pi\)
\(230\) 4.33330 0.285729
\(231\) 0 0
\(232\) 2.17733 0.142949
\(233\) −4.18134 3.03792i −0.273929 0.199021i 0.442336 0.896849i \(-0.354150\pi\)
−0.716265 + 0.697828i \(0.754150\pi\)
\(234\) 0 0
\(235\) 1.21247 + 3.73159i 0.0790927 + 0.243422i
\(236\) −0.0240061 0.0330415i −0.00156266 0.00215082i
\(237\) 0 0
\(238\) 18.6774 6.06866i 1.21068 0.393373i
\(239\) 4.22278 12.9964i 0.273149 0.840665i −0.716555 0.697531i \(-0.754282\pi\)
0.989703 0.143134i \(-0.0457180\pi\)
\(240\) 0 0
\(241\) 7.05251i 0.454292i −0.973861 0.227146i \(-0.927061\pi\)
0.973861 0.227146i \(-0.0729395\pi\)
\(242\) 18.1252 + 8.35837i 1.16513 + 0.537296i
\(243\) 0 0
\(244\) 0.901971 1.24146i 0.0577428 0.0794761i
\(245\) −18.7851 6.10364i −1.20013 0.389947i
\(246\) 0 0
\(247\) 11.3080 8.21575i 0.719512 0.522756i
\(248\) −5.51741 + 4.00863i −0.350356 + 0.254548i
\(249\) 0 0
\(250\) −17.7426 5.76492i −1.12214 0.364605i
\(251\) −3.95496 + 5.44354i −0.249635 + 0.343593i −0.915383 0.402583i \(-0.868112\pi\)
0.665748 + 0.746176i \(0.268112\pi\)
\(252\) 0 0
\(253\) −0.645692 6.55969i −0.0405943 0.412404i
\(254\) 40.4673i 2.53915i
\(255\) 0 0
\(256\) 6.44469 19.8347i 0.402793 1.23967i
\(257\) −13.4589 + 4.37306i −0.839543 + 0.272784i −0.697060 0.717013i \(-0.745509\pi\)
−0.142483 + 0.989797i \(0.545509\pi\)
\(258\) 0 0
\(259\) −3.17561 4.37086i −0.197323 0.271592i
\(260\) 1.46856 + 4.51975i 0.0910760 + 0.280303i
\(261\) 0 0
\(262\) −22.7523 16.5305i −1.40564 1.02126i
\(263\) −6.94583 −0.428298 −0.214149 0.976801i \(-0.568698\pi\)
−0.214149 + 0.976801i \(0.568698\pi\)
\(264\) 0 0
\(265\) −1.53319 −0.0941829
\(266\) 32.4624 + 23.5853i 1.99040 + 1.44611i
\(267\) 0 0
\(268\) −0.840926 2.58811i −0.0513678 0.158094i
\(269\) 4.05850 + 5.58605i 0.247451 + 0.340587i 0.914617 0.404322i \(-0.132493\pi\)
−0.667165 + 0.744910i \(0.732493\pi\)
\(270\) 0 0
\(271\) −12.9581 + 4.21033i −0.787146 + 0.255759i −0.674888 0.737920i \(-0.735808\pi\)
−0.112258 + 0.993679i \(0.535808\pi\)
\(272\) −3.39514 + 10.4492i −0.205861 + 0.633575i
\(273\) 0 0
\(274\) 31.1021i 1.87895i
\(275\) −2.52823 + 11.5198i −0.152458 + 0.694673i
\(276\) 0 0
\(277\) −6.85079 + 9.42931i −0.411624 + 0.566552i −0.963614 0.267299i \(-0.913869\pi\)
0.551989 + 0.833851i \(0.313869\pi\)
\(278\) −17.8918 5.81339i −1.07308 0.348664i
\(279\) 0 0
\(280\) 6.04241 4.39007i 0.361103 0.262357i
\(281\) −17.6693 + 12.8375i −1.05406 + 0.765823i −0.972981 0.230885i \(-0.925838\pi\)
−0.0810832 + 0.996707i \(0.525838\pi\)
\(282\) 0 0
\(283\) −22.3258 7.25408i −1.32713 0.431210i −0.442191 0.896921i \(-0.645799\pi\)
−0.884937 + 0.465711i \(0.845799\pi\)
\(284\) −2.92109 + 4.02053i −0.173335 + 0.238575i
\(285\) 0 0
\(286\) 16.8721 7.37884i 0.997667 0.436320i
\(287\) 51.4721i 3.03830i
\(288\) 0 0
\(289\) −3.70882 + 11.4146i −0.218166 + 0.671445i
\(290\) 3.51681 1.14268i 0.206514 0.0671005i
\(291\) 0 0
\(292\) 5.35162 + 7.36588i 0.313180 + 0.431055i
\(293\) 0.524298 + 1.61362i 0.0306298 + 0.0942689i 0.965203 0.261503i \(-0.0842181\pi\)
−0.934573 + 0.355772i \(0.884218\pi\)
\(294\) 0 0
\(295\) 0.0307205 + 0.0223197i 0.00178861 + 0.00129950i
\(296\) 1.43277 0.0832781
\(297\) 0 0
\(298\) 0.0734110 0.00425258
\(299\) −4.91989 3.57451i −0.284525 0.206719i
\(300\) 0 0
\(301\) 5.67071 + 17.4527i 0.326855 + 1.00595i
\(302\) 2.93472 + 4.03930i 0.168874 + 0.232436i
\(303\) 0 0
\(304\) −21.3498 + 6.93699i −1.22450 + 0.397863i
\(305\) −0.440884 + 1.35690i −0.0252449 + 0.0776959i
\(306\) 0 0
\(307\) 2.35281i 0.134282i −0.997743 0.0671410i \(-0.978612\pi\)
0.997743 0.0671410i \(-0.0213877\pi\)
\(308\) 13.7837 + 15.5131i 0.785399 + 0.883941i
\(309\) 0 0
\(310\) −6.80792 + 9.37029i −0.386664 + 0.532197i
\(311\) 10.0872 + 3.27754i 0.571995 + 0.185852i 0.580711 0.814110i \(-0.302775\pi\)
−0.00871654 + 0.999962i \(0.502775\pi\)
\(312\) 0 0
\(313\) 20.4957 14.8910i 1.15849 0.841691i 0.168902 0.985633i \(-0.445978\pi\)
0.989586 + 0.143942i \(0.0459779\pi\)
\(314\) 3.09722 2.25026i 0.174786 0.126990i
\(315\) 0 0
\(316\) −4.69696 1.52614i −0.264225 0.0858518i
\(317\) 15.7600 21.6917i 0.885168 1.21833i −0.0897951 0.995960i \(-0.528621\pi\)
0.974963 0.222368i \(-0.0713788\pi\)
\(318\) 0 0
\(319\) −2.25380 5.15343i −0.126189 0.288536i
\(320\) 2.03380i 0.113693i
\(321\) 0 0
\(322\) 5.39479 16.6035i 0.300640 0.925275i
\(323\) 9.71216 3.15567i 0.540399 0.175586i
\(324\) 0 0
\(325\) 6.39590 + 8.80320i 0.354781 + 0.488314i
\(326\) −8.18427 25.1886i −0.453285 1.39507i
\(327\) 0 0
\(328\) 11.0433 + 8.02340i 0.609762 + 0.443018i
\(329\) 15.8074 0.871492
\(330\) 0 0
\(331\) −17.3237 −0.952198 −0.476099 0.879392i \(-0.657950\pi\)
−0.476099 + 0.879392i \(0.657950\pi\)
\(332\) 7.60079 + 5.52230i 0.417148 + 0.303076i
\(333\) 0 0
\(334\) 0.500309 + 1.53979i 0.0273757 + 0.0842538i
\(335\) 1.48717 + 2.04692i 0.0812530 + 0.111835i
\(336\) 0 0
\(337\) −12.3674 + 4.01842i −0.673696 + 0.218897i −0.625833 0.779957i \(-0.715241\pi\)
−0.0478628 + 0.998854i \(0.515241\pi\)
\(338\) −2.03908 + 6.27563i −0.110911 + 0.341349i
\(339\) 0 0
\(340\) 3.47208i 0.188300i
\(341\) 15.1990 + 8.90948i 0.823074 + 0.482476i
\(342\) 0 0
\(343\) −26.8543 + 36.9618i −1.45000 + 1.99575i
\(344\) −4.62838 1.50385i −0.249546 0.0810823i
\(345\) 0 0
\(346\) −19.4468 + 14.1289i −1.04547 + 0.759577i
\(347\) 17.1967 12.4941i 0.923168 0.670721i −0.0211427 0.999776i \(-0.506730\pi\)
0.944310 + 0.329056i \(0.106730\pi\)
\(348\) 0 0
\(349\) 8.87430 + 2.88343i 0.475030 + 0.154347i 0.536740 0.843747i \(-0.319655\pi\)
−0.0617102 + 0.998094i \(0.519655\pi\)
\(350\) −18.3610 + 25.2717i −0.981436 + 1.35083i
\(351\) 0 0
\(352\) −20.9580 + 2.06297i −1.11707 + 0.109957i
\(353\) 9.12141i 0.485483i −0.970091 0.242742i \(-0.921953\pi\)
0.970091 0.242742i \(-0.0780468\pi\)
\(354\) 0 0
\(355\) 1.42783 4.39440i 0.0757813 0.233231i
\(356\) −12.6453 + 4.10870i −0.670199 + 0.217761i
\(357\) 0 0
\(358\) 21.4851 + 29.5716i 1.13552 + 1.56291i
\(359\) −2.41692 7.43851i −0.127560 0.392589i 0.866799 0.498658i \(-0.166174\pi\)
−0.994359 + 0.106069i \(0.966174\pi\)
\(360\) 0 0
\(361\) 1.50897 + 1.09633i 0.0794193 + 0.0577015i
\(362\) 8.15857 0.428805
\(363\) 0 0
\(364\) 19.1462 1.00353
\(365\) −6.84845 4.97569i −0.358464 0.260439i
\(366\) 0 0
\(367\) 7.57224 + 23.3050i 0.395268 + 1.21651i 0.928753 + 0.370700i \(0.120882\pi\)
−0.533485 + 0.845810i \(0.679118\pi\)
\(368\) 5.74086 + 7.90161i 0.299263 + 0.411900i
\(369\) 0 0
\(370\) 2.31420 0.751929i 0.120310 0.0390909i
\(371\) −1.90876 + 5.87455i −0.0990978 + 0.304992i
\(372\) 0 0
\(373\) 2.86129i 0.148152i −0.997253 0.0740760i \(-0.976399\pi\)
0.997253 0.0740760i \(-0.0236007\pi\)
\(374\) 13.3894 1.31796i 0.692348 0.0681501i
\(375\) 0 0
\(376\) −2.46404 + 3.39146i −0.127073 + 0.174901i
\(377\) −4.93546 1.60363i −0.254189 0.0825911i
\(378\) 0 0
\(379\) 23.6747 17.2007i 1.21609 0.883540i 0.220320 0.975428i \(-0.429290\pi\)
0.995769 + 0.0918872i \(0.0292899\pi\)
\(380\) −5.73931 + 4.16985i −0.294420 + 0.213909i
\(381\) 0 0
\(382\) −30.6725 9.96610i −1.56934 0.509910i
\(383\) −16.7280 + 23.0242i −0.854762 + 1.17648i 0.128031 + 0.991770i \(0.459134\pi\)
−0.982793 + 0.184709i \(0.940866\pi\)
\(384\) 0 0
\(385\) −16.6453 9.75724i −0.848321 0.497275i
\(386\) 11.1755i 0.568818i
\(387\) 0 0
\(388\) 5.79296 17.8289i 0.294093 0.905125i
\(389\) 13.5825 4.41321i 0.688658 0.223759i 0.0562761 0.998415i \(-0.482077\pi\)
0.632382 + 0.774657i \(0.282077\pi\)
\(390\) 0 0
\(391\) −2.61155 3.59449i −0.132072 0.181781i
\(392\) −6.52124 20.0703i −0.329372 1.01370i
\(393\) 0 0
\(394\) −33.0440 24.0079i −1.66473 1.20950i
\(395\) 4.59175 0.231036
\(396\) 0 0
\(397\) 2.20687 0.110760 0.0553798 0.998465i \(-0.482363\pi\)
0.0553798 + 0.998465i \(0.482363\pi\)
\(398\) 13.6621 + 9.92609i 0.684819 + 0.497550i
\(399\) 0 0
\(400\) −5.40039 16.6207i −0.270019 0.831034i
\(401\) −18.5405 25.5188i −0.925869 1.27435i −0.961449 0.274983i \(-0.911328\pi\)
0.0355802 0.999367i \(-0.488672\pi\)
\(402\) 0 0
\(403\) 15.4590 5.02293i 0.770067 0.250210i
\(404\) −6.42442 + 19.7723i −0.319627 + 0.983710i
\(405\) 0 0
\(406\) 14.8976i 0.739355i
\(407\) −1.48309 3.39116i −0.0735141 0.168093i
\(408\) 0 0
\(409\) −3.98413 + 5.48368i −0.197002 + 0.271150i −0.896077 0.443898i \(-0.853595\pi\)
0.699075 + 0.715048i \(0.253595\pi\)
\(410\) 22.0477 + 7.16375i 1.08886 + 0.353792i
\(411\) 0 0
\(412\) 2.17609 1.58102i 0.107208 0.0778913i
\(413\) 0.123766 0.0899212i 0.00609012 0.00442473i
\(414\) 0 0
\(415\) −8.30760 2.69930i −0.407804 0.132504i
\(416\) −11.4205 + 15.7189i −0.559935 + 0.770685i
\(417\) 0 0
\(418\) 18.2588 + 20.5497i 0.893066 + 1.00512i
\(419\) 28.6088i 1.39763i −0.715302 0.698815i \(-0.753711\pi\)
0.715302 0.698815i \(-0.246289\pi\)
\(420\) 0 0
\(421\) −1.72842 + 5.31954i −0.0842381 + 0.259258i −0.984300 0.176504i \(-0.943521\pi\)
0.900062 + 0.435762i \(0.143521\pi\)
\(422\) 24.1790 7.85624i 1.17702 0.382436i
\(423\) 0 0
\(424\) −0.962842 1.32524i −0.0467597 0.0643592i
\(425\) 2.45667 + 7.56084i 0.119166 + 0.366755i
\(426\) 0 0
\(427\) 4.65021 + 3.37858i 0.225040 + 0.163501i
\(428\) −0.541044 −0.0261524
\(429\) 0 0
\(430\) −8.26497 −0.398572
\(431\) 15.7825 + 11.4667i 0.760216 + 0.552329i 0.898977 0.437997i \(-0.144312\pi\)
−0.138760 + 0.990326i \(0.544312\pi\)
\(432\) 0 0
\(433\) −6.96921 21.4490i −0.334919 1.03077i −0.966762 0.255678i \(-0.917701\pi\)
0.631843 0.775096i \(-0.282299\pi\)
\(434\) 27.4276 + 37.7508i 1.31657 + 1.81210i
\(435\) 0 0
\(436\) −18.0429 + 5.86250i −0.864099 + 0.280763i
\(437\) 2.80527 8.63372i 0.134194 0.413007i
\(438\) 0 0
\(439\) 29.9870i 1.43120i −0.698509 0.715601i \(-0.746153\pi\)
0.698509 0.715601i \(-0.253847\pi\)
\(440\) 4.68804 2.05027i 0.223494 0.0977428i
\(441\) 0 0
\(442\) 7.29615 10.0423i 0.347043 0.477663i
\(443\) 30.0035 + 9.74873i 1.42551 + 0.463176i 0.917348 0.398086i \(-0.130325\pi\)
0.508161 + 0.861262i \(0.330325\pi\)
\(444\) 0 0
\(445\) 10.0011 7.26623i 0.474098 0.344452i
\(446\) −23.6824 + 17.2063i −1.12139 + 0.814740i
\(447\) 0 0
\(448\) −7.79270 2.53200i −0.368171 0.119626i
\(449\) 22.3362 30.7432i 1.05411 1.45086i 0.168921 0.985630i \(-0.445972\pi\)
0.885190 0.465229i \(-0.154028\pi\)
\(450\) 0 0
\(451\) 7.55911 34.4430i 0.355944 1.62186i
\(452\) 4.13148i 0.194329i
\(453\) 0 0
\(454\) −8.25085 + 25.3935i −0.387232 + 1.19178i
\(455\) −16.9300 + 5.50087i −0.793688 + 0.257885i
\(456\) 0 0
\(457\) −23.0565 31.7345i −1.07854 1.48448i −0.861123 0.508397i \(-0.830238\pi\)
−0.217413 0.976080i \(-0.569762\pi\)
\(458\) −12.4473 38.3088i −0.581624 1.79005i
\(459\) 0 0
\(460\) 2.49706 + 1.81422i 0.116426 + 0.0845885i
\(461\) 17.5521 0.817482 0.408741 0.912650i \(-0.365968\pi\)
0.408741 + 0.912650i \(0.365968\pi\)
\(462\) 0 0
\(463\) 5.07239 0.235734 0.117867 0.993029i \(-0.462394\pi\)
0.117867 + 0.993029i \(0.462394\pi\)
\(464\) 6.74278 + 4.89892i 0.313026 + 0.227427i
\(465\) 0 0
\(466\) −2.89801 8.91915i −0.134248 0.413172i
\(467\) −9.96792 13.7197i −0.461260 0.634870i 0.513509 0.858084i \(-0.328345\pi\)
−0.974770 + 0.223214i \(0.928345\pi\)
\(468\) 0 0
\(469\) 9.69445 3.14992i 0.447648 0.145450i
\(470\) −2.20004 + 6.77101i −0.101480 + 0.312324i
\(471\) 0 0
\(472\) 0.0405706i 0.00186741i
\(473\) 1.23154 + 12.5114i 0.0566261 + 0.575274i
\(474\) 0 0
\(475\) −9.54762 + 13.1412i −0.438075 + 0.602958i
\(476\) 13.3036 + 4.32260i 0.609769 + 0.198126i
\(477\) 0 0
\(478\) 20.0601 14.5745i 0.917526 0.666622i
\(479\) 14.6267 10.6269i 0.668310 0.485556i −0.201149 0.979561i \(-0.564468\pi\)
0.869459 + 0.494005i \(0.164468\pi\)
\(480\) 0 0
\(481\) −3.24773 1.05525i −0.148084 0.0481153i
\(482\) 7.52180 10.3529i 0.342608 0.471560i
\(483\) 0 0
\(484\) 6.94524 + 12.4050i 0.315693 + 0.563862i
\(485\) 17.4295i 0.791435i
\(486\) 0 0
\(487\) −8.03498 + 24.7291i −0.364100 + 1.12058i 0.586443 + 0.809991i \(0.300528\pi\)
−0.950543 + 0.310594i \(0.899472\pi\)
\(488\) −1.44974 + 0.471048i −0.0656265 + 0.0213234i
\(489\) 0 0
\(490\) −21.0661 28.9950i −0.951670 1.30986i
\(491\) 2.26569 + 6.97309i 0.102249 + 0.314691i 0.989075 0.147413i \(-0.0470947\pi\)
−0.886826 + 0.462104i \(0.847095\pi\)
\(492\) 0 0
\(493\) −3.06733 2.22854i −0.138146 0.100369i
\(494\) 25.3622 1.14110
\(495\) 0 0
\(496\) −26.1057 −1.17218
\(497\) −15.0600 10.9417i −0.675533 0.490804i
\(498\) 0 0
\(499\) −2.91064 8.95804i −0.130298 0.401017i 0.864531 0.502580i \(-0.167616\pi\)
−0.994829 + 0.101563i \(0.967616\pi\)
\(500\) −7.81055 10.7503i −0.349298 0.480768i
\(501\) 0 0
\(502\) −11.6115 + 3.77281i −0.518247 + 0.168389i
\(503\) −10.3211 + 31.7652i −0.460196 + 1.41634i 0.404728 + 0.914437i \(0.367366\pi\)
−0.864925 + 0.501902i \(0.832634\pi\)
\(504\) 0 0
\(505\) 19.3294i 0.860149i
\(506\) 6.04832 10.3181i 0.268881 0.458694i
\(507\) 0 0
\(508\) 16.9424 23.3193i 0.751699 1.03462i
\(509\) 19.5002 + 6.33601i 0.864332 + 0.280839i 0.707437 0.706777i \(-0.249851\pi\)
0.156895 + 0.987615i \(0.449851\pi\)
\(510\) 0 0
\(511\) −27.5909 + 20.0459i −1.22055 + 0.886781i
\(512\) 15.0364 10.9246i 0.664521 0.482803i
\(513\) 0 0
\(514\) −24.4213 7.93496i −1.07718 0.349996i
\(515\) −1.46996 + 2.02322i −0.0647741 + 0.0891539i
\(516\) 0 0
\(517\) 10.5777 + 2.32145i 0.465206 + 0.102097i
\(518\) 9.80320i 0.430728i
\(519\) 0 0
\(520\) 1.45881 4.48976i 0.0639732 0.196889i
\(521\) −12.4115 + 4.03273i −0.543757 + 0.176677i −0.568000 0.823029i \(-0.692282\pi\)
0.0242430 + 0.999706i \(0.492282\pi\)
\(522\) 0 0
\(523\) −4.85832 6.68690i −0.212439 0.292398i 0.689478 0.724307i \(-0.257840\pi\)
−0.901917 + 0.431909i \(0.857840\pi\)
\(524\) −6.19018 19.0514i −0.270419 0.832265i
\(525\) 0 0
\(526\) −10.1963 7.40802i −0.444578 0.323005i
\(527\) 11.8756 0.517310
\(528\) 0 0
\(529\) 19.0503 0.828275
\(530\) −2.25067 1.63521i −0.0977628 0.0710289i
\(531\) 0 0
\(532\) 8.83197 + 27.1820i 0.382915 + 1.17849i
\(533\) −19.1230 26.3205i −0.828308 1.14007i
\(534\) 0 0
\(535\) 0.478417 0.155447i 0.0206838 0.00672057i
\(536\) −0.835347 + 2.57093i −0.0360815 + 0.111047i
\(537\) 0 0
\(538\) 12.5287i 0.540151i
\(539\) −40.7532 + 36.2100i −1.75537 + 1.55968i
\(540\) 0 0
\(541\) 5.73469 7.89312i 0.246554 0.339352i −0.667747 0.744388i \(-0.732741\pi\)
0.914301 + 0.405036i \(0.132741\pi\)
\(542\) −23.5125 7.63968i −1.00995 0.328152i
\(543\) 0 0
\(544\) −11.4843 + 8.34383i −0.492385 + 0.357739i
\(545\) 14.2701 10.3678i 0.611263 0.444108i
\(546\) 0 0
\(547\) 7.40406 + 2.40572i 0.316575 + 0.102861i 0.462994 0.886361i \(-0.346775\pi\)
−0.146420 + 0.989223i \(0.546775\pi\)
\(548\) 13.0215 17.9225i 0.556250 0.765613i
\(549\) 0 0
\(550\) −15.9978 + 14.2143i −0.682147 + 0.606100i
\(551\) 7.74667i 0.330019i
\(552\) 0 0
\(553\) 5.71655 17.5937i 0.243093 0.748162i
\(554\) −20.1135 + 6.53527i −0.854541 + 0.277657i
\(555\) 0 0
\(556\) −7.87623 10.8407i −0.334026 0.459748i
\(557\) 1.09093 + 3.35755i 0.0462244 + 0.142264i 0.971505 0.237019i \(-0.0761705\pi\)
−0.925281 + 0.379283i \(0.876171\pi\)
\(558\) 0 0
\(559\) 9.38378 + 6.81772i 0.396892 + 0.288359i
\(560\) 28.5897 1.20813
\(561\) 0 0
\(562\) −39.6298 −1.67168
\(563\) −1.21567 0.883235i −0.0512343 0.0372239i 0.561873 0.827223i \(-0.310081\pi\)
−0.613108 + 0.789999i \(0.710081\pi\)
\(564\) 0 0
\(565\) −1.18702 3.65326i −0.0499381 0.153694i
\(566\) −25.0367 34.4601i −1.05237 1.44847i
\(567\) 0 0
\(568\) 4.69506 1.52552i 0.197000 0.0640093i
\(569\) −4.58518 + 14.1117i −0.192221 + 0.591595i 0.807777 + 0.589488i \(0.200671\pi\)
−0.999998 + 0.00210682i \(0.999329\pi\)
\(570\) 0 0
\(571\) 29.8598i 1.24960i 0.780787 + 0.624798i \(0.214819\pi\)
−0.780787 + 0.624798i \(0.785181\pi\)
\(572\) 12.8118 + 2.81177i 0.535688 + 0.117566i
\(573\) 0 0
\(574\) 54.8972 75.5595i 2.29136 3.15379i
\(575\) 6.72128 + 2.18388i 0.280297 + 0.0910740i
\(576\) 0 0
\(577\) −20.6394 + 14.9954i −0.859228 + 0.624266i −0.927675 0.373389i \(-0.878196\pi\)
0.0684465 + 0.997655i \(0.478196\pi\)
\(578\) −17.6185 + 12.8006i −0.732835 + 0.532436i
\(579\) 0 0
\(580\) 2.50496 + 0.813911i 0.104013 + 0.0337958i
\(581\) −20.6853 + 28.4708i −0.858170 + 1.18117i
\(582\) 0 0
\(583\) −2.13999 + 3.65069i −0.0886292 + 0.151196i
\(584\) 9.04432i 0.374256i
\(585\) 0 0
\(586\) −0.951344 + 2.92793i −0.0392996 + 0.120952i
\(587\) −22.4713 + 7.30137i −0.927491 + 0.301360i −0.733536 0.679651i \(-0.762131\pi\)
−0.193955 + 0.981011i \(0.562131\pi\)
\(588\) 0 0
\(589\) 14.2622 + 19.6303i 0.587664 + 0.808851i
\(590\) 0.0212918 + 0.0655293i 0.000876568 + 0.00269780i
\(591\) 0 0
\(592\) 4.43702 + 3.22368i 0.182360 + 0.132493i
\(593\) −10.1681 −0.417553 −0.208777 0.977963i \(-0.566948\pi\)
−0.208777 + 0.977963i \(0.566948\pi\)
\(594\) 0 0
\(595\) −13.0056 −0.533178
\(596\) 0.0423030 + 0.0307349i 0.00173280 + 0.00125895i
\(597\) 0 0
\(598\) −3.40988 10.4945i −0.139441 0.429154i
\(599\) 3.58279 + 4.93129i 0.146389 + 0.201487i 0.875914 0.482467i \(-0.160259\pi\)
−0.729525 + 0.683954i \(0.760259\pi\)
\(600\) 0 0
\(601\) 13.3376 4.33365i 0.544053 0.176773i −0.0240806 0.999710i \(-0.507666\pi\)
0.568133 + 0.822937i \(0.307666\pi\)
\(602\) −10.2896 + 31.6680i −0.419371 + 1.29069i
\(603\) 0 0
\(604\) 3.55632i 0.144705i
\(605\) −9.70538 8.97363i −0.394580 0.364830i
\(606\) 0 0
\(607\) −0.497560 + 0.684833i −0.0201953 + 0.0277965i −0.818995 0.573800i \(-0.805469\pi\)
0.798800 + 0.601597i \(0.205469\pi\)
\(608\) −27.5845 8.96276i −1.11870 0.363488i
\(609\) 0 0
\(610\) −2.09439 + 1.52167i −0.0847996 + 0.0616105i
\(611\) 8.08321 5.87280i 0.327012 0.237588i
\(612\) 0 0
\(613\) −24.1513 7.84724i −0.975462 0.316947i −0.222443 0.974946i \(-0.571403\pi\)
−0.753019 + 0.657999i \(0.771403\pi\)
\(614\) 2.50937 3.45385i 0.101270 0.139386i
\(615\) 0 0
\(616\) −2.01938 20.5152i −0.0813631 0.826581i
\(617\) 10.0839i 0.405962i 0.979183 + 0.202981i \(0.0650630\pi\)
−0.979183 + 0.202981i \(0.934937\pi\)
\(618\) 0 0
\(619\) −8.05024 + 24.7761i −0.323566 + 0.995835i 0.648517 + 0.761200i \(0.275389\pi\)
−0.972084 + 0.234635i \(0.924611\pi\)
\(620\) −7.84611 + 2.54935i −0.315107 + 0.102385i
\(621\) 0 0
\(622\) 11.3121 + 15.5698i 0.453574 + 0.624291i
\(623\) −15.3903 47.3664i −0.616598 1.89769i
\(624\) 0 0
\(625\) −4.38931 3.18902i −0.175573 0.127561i
\(626\) 45.9690 1.83729
\(627\) 0 0
\(628\) 2.72689 0.108815
\(629\) −2.01842 1.46647i −0.0804798 0.0584720i
\(630\) 0 0
\(631\) 3.44605 + 10.6058i 0.137185 + 0.422212i 0.995923 0.0902022i \(-0.0287513\pi\)
−0.858739 + 0.512414i \(0.828751\pi\)
\(632\) 2.88362 + 3.96897i 0.114704 + 0.157877i
\(633\) 0 0
\(634\) 46.2703 15.0341i 1.83763 0.597081i
\(635\) −8.28146 + 25.4877i −0.328640 + 1.01145i
\(636\) 0 0
\(637\) 50.2973i 1.99285i
\(638\) 2.18783 9.96884i 0.0866172 0.394670i
\(639\) 0 0
\(640\) −6.80053 + 9.36013i −0.268815 + 0.369991i
\(641\) 10.4988 + 3.41127i 0.414679 + 0.134737i 0.508923 0.860812i \(-0.330044\pi\)
−0.0942448 + 0.995549i \(0.530044\pi\)
\(642\) 0 0
\(643\) −29.7234 + 21.5953i −1.17218 + 0.851637i −0.991268 0.131863i \(-0.957904\pi\)
−0.180909 + 0.983500i \(0.557904\pi\)
\(644\) 10.0601 7.30909i 0.396424 0.288019i
\(645\) 0 0
\(646\) 17.6228 + 5.72600i 0.693360 + 0.225286i
\(647\) 1.59821 2.19975i 0.0628321 0.0864810i −0.776445 0.630186i \(-0.782979\pi\)
0.839277 + 0.543705i \(0.182979\pi\)
\(648\) 0 0
\(649\) 0.0960246 0.0419955i 0.00376930 0.00164847i
\(650\) 19.7443i 0.774436i
\(651\) 0 0
\(652\) 5.82952 17.9414i 0.228301 0.702640i
\(653\) 42.0798 13.6726i 1.64671 0.535048i 0.668686 0.743545i \(-0.266857\pi\)
0.978023 + 0.208496i \(0.0668570\pi\)
\(654\) 0 0
\(655\) 10.9473 + 15.0677i 0.427747 + 0.588743i
\(656\) 16.1465 + 49.6939i 0.630416 + 1.94022i
\(657\) 0 0
\(658\) 23.2048 + 16.8593i 0.904618 + 0.657244i
\(659\) −9.17428 −0.357379 −0.178690 0.983905i \(-0.557186\pi\)
−0.178690 + 0.983905i \(0.557186\pi\)
\(660\) 0 0
\(661\) −9.89631 −0.384922 −0.192461 0.981305i \(-0.561647\pi\)
−0.192461 + 0.981305i \(0.561647\pi\)
\(662\) −25.4307 18.4765i −0.988391 0.718108i
\(663\) 0 0
\(664\) −2.88398 8.87599i −0.111920 0.344455i
\(665\) −15.6193 21.4981i −0.605691 0.833662i
\(666\) 0 0
\(667\) −3.20547 + 1.04152i −0.124116 + 0.0403278i
\(668\) −0.356362 + 1.09677i −0.0137880 + 0.0424352i
\(669\) 0 0
\(670\) 4.59095i 0.177364i
\(671\) 2.61556 + 2.94372i 0.100972 + 0.113641i
\(672\) 0 0
\(673\) −10.3937 + 14.3057i −0.400649 + 0.551446i −0.960907 0.276872i \(-0.910702\pi\)
0.560258 + 0.828318i \(0.310702\pi\)
\(674\) −22.4408 7.29146i −0.864387 0.280856i
\(675\) 0 0
\(676\) −3.80243 + 2.76263i −0.146247 + 0.106255i
\(677\) −9.62387 + 6.99215i −0.369875 + 0.268730i −0.757159 0.653230i \(-0.773413\pi\)
0.387284 + 0.921961i \(0.373413\pi\)
\(678\) 0 0
\(679\) 66.7830 + 21.6991i 2.56290 + 0.832735i
\(680\) 2.02729 2.79033i 0.0777432 0.107004i
\(681\) 0 0
\(682\) 12.8094 + 29.2892i 0.490496 + 1.12154i
\(683\) 18.2564i 0.698561i −0.937018 0.349280i \(-0.886426\pi\)
0.937018 0.349280i \(-0.113574\pi\)
\(684\) 0 0
\(685\) −6.36490 + 19.5892i −0.243190 + 0.748463i
\(686\) −78.8425 + 25.6175i −3.01022 + 0.978080i
\(687\) 0 0
\(688\) −10.9496 15.0708i −0.417450 0.574571i
\(689\) 1.20647 + 3.71312i 0.0459627 + 0.141459i
\(690\) 0 0
\(691\) −14.5818 10.5943i −0.554719 0.403027i 0.274804 0.961500i \(-0.411387\pi\)
−0.829522 + 0.558474i \(0.811387\pi\)
\(692\) −17.1216 −0.650864
\(693\) 0 0
\(694\) 38.5698 1.46409
\(695\) 10.0792 + 7.32295i 0.382325 + 0.277775i
\(696\) 0 0
\(697\) −7.34515 22.6060i −0.278217 0.856265i
\(698\) 9.95189 + 13.6976i 0.376684 + 0.518462i
\(699\) 0 0
\(700\) −21.1610 + 6.87562i −0.799810 + 0.259874i
\(701\) −2.60431 + 8.01524i −0.0983635 + 0.302732i −0.988116 0.153712i \(-0.950877\pi\)
0.889752 + 0.456444i \(0.150877\pi\)
\(702\) 0 0
\(703\) 5.09762i 0.192260i
\(704\) −4.84270 2.83873i −0.182516 0.106989i
\(705\) 0 0
\(706\) 9.72836 13.3899i 0.366132 0.503937i
\(707\) −74.0626 24.0644i −2.78541 0.905035i
\(708\) 0 0
\(709\) −16.7573 + 12.1749i −0.629333 + 0.457237i −0.856169 0.516696i \(-0.827162\pi\)
0.226836 + 0.973933i \(0.427162\pi\)
\(710\) 6.78282 4.92801i 0.254555 0.184945i
\(711\) 0 0
\(712\) 12.5614 + 4.08144i 0.470758 + 0.152959i
\(713\) 6.20521 8.54074i 0.232387 0.319853i
\(714\) 0 0
\(715\) −12.1367 + 1.19465i −0.453885 + 0.0446774i
\(716\) 26.0358i 0.973002i
\(717\) 0 0
\(718\) 4.38552 13.4972i 0.163666 0.503712i
\(719\) −34.3009 + 11.1450i −1.27921 + 0.415640i −0.868301 0.496038i \(-0.834788\pi\)
−0.410906 + 0.911678i \(0.634788\pi\)
\(720\) 0 0
\(721\) 5.92214 + 8.15112i 0.220552 + 0.303564i
\(722\) 1.04584 + 3.21875i 0.0389220 + 0.119790i
\(723\) 0 0
\(724\) 4.70137 + 3.41574i 0.174725 + 0.126945i
\(725\) 6.03072 0.223975
\(726\) 0 0
\(727\) −20.9857 −0.778316 −0.389158 0.921171i \(-0.627234\pi\)
−0.389158 + 0.921171i \(0.627234\pi\)
\(728\) −15.3868 11.1792i −0.570273 0.414327i
\(729\) 0 0
\(730\) −4.74653 14.6083i −0.175677 0.540678i
\(731\) 4.98104 + 6.85581i 0.184230 + 0.253571i
\(732\) 0 0
\(733\) 38.6350 12.5533i 1.42701 0.463665i 0.509191 0.860653i \(-0.329945\pi\)
0.917824 + 0.396988i \(0.129945\pi\)
\(734\) −13.7399 + 42.2871i −0.507149 + 1.56084i
\(735\) 0 0
\(736\) 12.6191i 0.465147i
\(737\) 6.94971 0.684083i 0.255996 0.0251985i
\(738\) 0 0
\(739\) −0.159730 + 0.219850i −0.00587578 + 0.00808731i −0.811945 0.583734i \(-0.801591\pi\)
0.806069 + 0.591822i \(0.201591\pi\)
\(740\) 1.64836 + 0.535586i 0.0605951 + 0.0196885i
\(741\) 0 0
\(742\) −9.06745 + 6.58789i −0.332877 + 0.241849i
\(743\) 16.6356 12.0864i 0.610300 0.443409i −0.239220 0.970965i \(-0.576892\pi\)
0.849520 + 0.527557i \(0.176892\pi\)
\(744\) 0 0
\(745\) −0.0462368 0.0150232i −0.00169398 0.000550409i
\(746\) 3.05169 4.20029i 0.111730 0.153783i
\(747\) 0 0
\(748\) 8.26740 + 4.84624i 0.302286 + 0.177196i
\(749\) 2.02663i 0.0740514i
\(750\) 0 0
\(751\) −16.1057 + 49.5682i −0.587705 + 1.80877i 0.000422486 1.00000i \(0.499866\pi\)
−0.588127 + 0.808769i \(0.700134\pi\)
\(752\) −15.2613 + 4.95871i −0.556524 + 0.180825i
\(753\) 0 0
\(754\) −5.53477 7.61795i −0.201564 0.277430i
\(755\) −1.02176 3.14467i −0.0371858 0.114446i
\(756\) 0 0
\(757\) 30.2153 + 21.9527i 1.09819 + 0.797884i 0.980764 0.195197i \(-0.0625347\pi\)
0.117429 + 0.993081i \(0.462535\pi\)
\(758\) 53.0990 1.92864
\(759\) 0 0
\(760\) 7.04711 0.255625
\(761\) −36.1152 26.2392i −1.30918 0.951171i −1.00000 0.000166228i \(-0.999947\pi\)
−0.309175 0.951005i \(-0.600053\pi\)
\(762\) 0 0
\(763\) −21.9596 67.5847i −0.794991 2.44673i
\(764\) −13.5025 18.5846i −0.488503 0.672367i
\(765\) 0 0
\(766\) −49.1124 + 15.9576i −1.77450 + 0.576571i
\(767\) 0.0298807 0.0919633i 0.00107893 0.00332060i
\(768\) 0 0
\(769\) 22.3246i 0.805047i 0.915410 + 0.402524i \(0.131867\pi\)
−0.915410 + 0.402524i \(0.868133\pi\)
\(770\) −14.0282 32.0762i −0.505542 1.15595i
\(771\) 0 0
\(772\) −4.67883 + 6.43986i −0.168395 + 0.231776i
\(773\) 19.1268 + 6.21468i 0.687944 + 0.223526i 0.632070 0.774911i \(-0.282206\pi\)
0.0558738 + 0.998438i \(0.482206\pi\)
\(774\) 0 0
\(775\) −15.2820 + 11.1030i −0.548946 + 0.398832i
\(776\) −15.0655 + 10.9458i −0.540822 + 0.392930i
\(777\) 0 0
\(778\) 24.6455 + 8.00781i 0.883584 + 0.287094i
\(779\) 28.5463 39.2906i 1.02278 1.40773i
\(780\) 0 0
\(781\) −8.47063 9.53343i −0.303103 0.341133i
\(782\) 8.06192i 0.288294i
\(783\) 0 0
\(784\) 24.9624 76.8265i 0.891516 2.74380i
\(785\) −2.41124 + 0.783461i −0.0860610 + 0.0279629i
\(786\) 0 0
\(787\) −20.4658 28.1688i −0.729527 1.00411i −0.999153 0.0411431i \(-0.986900\pi\)
0.269626 0.962965i \(-0.413100\pi\)
\(788\) −8.99021 27.6690i −0.320263 0.985668i
\(789\) 0 0
\(790\) 6.74055 + 4.89730i 0.239818 + 0.174238i
\(791\) −15.4756 −0.550249
\(792\) 0 0
\(793\) 3.63312 0.129016
\(794\) 3.23961 + 2.35372i 0.114970 + 0.0835303i
\(795\) 0 0
\(796\) 3.71701 + 11.4398i 0.131746 + 0.405473i
\(797\) 0.462428 + 0.636478i 0.0163800 + 0.0225452i 0.817128 0.576456i \(-0.195565\pi\)
−0.800748 + 0.599001i \(0.795565\pi\)
\(798\) 0 0
\(799\) 6.94247 2.25574i 0.245607 0.0798025i
\(800\) 6.97744 21.4743i 0.246690 0.759233i
\(801\) 0 0
\(802\) 57.2351i 2.02104i
\(803\) −21.4066 + 9.36196i −0.755421 + 0.330376i
\(804\) 0 0
\(805\) −6.79565 + 9.35341i −0.239515 + 0.329665i
\(806\) 28.0505 + 9.11415i 0.988036 + 0.321032i
\(807\) 0 0
\(808\) 16.7078 12.1389i 0.587777 0.427045i
\(809\) 24.9035 18.0934i 0.875560 0.636131i −0.0565132 0.998402i \(-0.517998\pi\)
0.932073 + 0.362270i \(0.117998\pi\)
\(810\) 0 0
\(811\) 41.4535 + 13.4691i 1.45563 + 0.472963i 0.926732 0.375723i \(-0.122606\pi\)
0.528898 + 0.848686i \(0.322606\pi\)
\(812\) 6.23716 8.58472i 0.218881 0.301264i
\(813\) 0 0
\(814\) 1.43968 6.55989i 0.0504608 0.229924i
\(815\) 17.5395i 0.614383i
\(816\) 0 0
\(817\) −5.35052 + 16.4672i −0.187191 + 0.576115i
\(818\) −11.6971 + 3.80063i −0.408981 + 0.132886i
\(819\) 0 0
\(820\) 9.70574 + 13.3588i 0.338939 + 0.466510i
\(821\) 12.0394 + 37.0534i 0.420178 + 1.29317i 0.907537 + 0.419972i \(0.137960\pi\)
−0.487359 + 0.873202i \(0.662040\pi\)
\(822\) 0 0
\(823\) −30.4030 22.0890i −1.05978 0.769975i −0.0857325 0.996318i \(-0.527323\pi\)
−0.974048 + 0.226343i \(0.927323\pi\)
\(824\) −2.67195 −0.0930816
\(825\) 0 0
\(826\) 0.277589 0.00965857
\(827\) 36.8905 + 26.8025i 1.28281 + 0.932015i 0.999634 0.0270532i \(-0.00861234\pi\)
0.283175 + 0.959068i \(0.408612\pi\)
\(828\) 0 0
\(829\) 8.83146 + 27.1804i 0.306729 + 0.944016i 0.979026 + 0.203734i \(0.0653078\pi\)
−0.672297 + 0.740282i \(0.734692\pi\)
\(830\) −9.31637 12.8229i −0.323376 0.445089i
\(831\) 0 0
\(832\) −4.92553 + 1.60040i −0.170762 + 0.0554839i
\(833\) −11.3556 + 34.9488i −0.393447 + 1.21090i
\(834\) 0 0
\(835\) 1.07220i 0.0371051i
\(836\) 1.91808 + 19.4861i 0.0663382 + 0.673941i
\(837\) 0 0
\(838\) 30.5125 41.9968i 1.05404 1.45076i
\(839\) −5.41296 1.75878i −0.186876 0.0607197i 0.214084 0.976815i \(-0.431323\pi\)
−0.400960 + 0.916096i \(0.631323\pi\)
\(840\) 0 0
\(841\) 21.1347 15.3552i 0.728781 0.529491i
\(842\) −8.21078 + 5.96548i −0.282962 + 0.205584i
\(843\) 0 0
\(844\) 17.2223 + 5.59587i 0.592816 + 0.192618i
\(845\) 2.56856 3.53532i 0.0883612 0.121619i
\(846\) 0 0
\(847\) −46.4662 + 26.0153i −1.59660 + 0.893895i
\(848\) 6.27037i 0.215325i
\(849\) 0 0
\(850\) −4.45764 + 13.7192i −0.152896 + 0.470565i
\(851\) −2.10932 + 0.685361i −0.0723067 + 0.0234939i
\(852\) 0 0
\(853\) 14.7319 + 20.2767i 0.504410 + 0.694261i 0.982964 0.183797i \(-0.0588390\pi\)
−0.478554 + 0.878058i \(0.658839\pi\)
\(854\) 3.22297 + 9.91929i 0.110288 + 0.339431i
\(855\) 0 0
\(856\) 0.434810 + 0.315908i 0.0148615 + 0.0107975i
\(857\) 35.9164 1.22688 0.613440 0.789741i \(-0.289785\pi\)
0.613440 + 0.789741i \(0.289785\pi\)
\(858\) 0 0
\(859\) −15.7324 −0.536783 −0.268391 0.963310i \(-0.586492\pi\)
−0.268391 + 0.963310i \(0.586492\pi\)
\(860\) −4.76268 3.46029i −0.162406 0.117995i
\(861\) 0 0
\(862\) 10.9385 + 33.6654i 0.372568 + 1.14665i
\(863\) 16.0883 + 22.1436i 0.547652 + 0.753778i 0.989691 0.143217i \(-0.0457448\pi\)
−0.442039 + 0.896996i \(0.645745\pi\)
\(864\) 0 0
\(865\) 15.1397 4.91919i 0.514765 0.167257i
\(866\) 12.6457 38.9194i 0.429718 1.32254i
\(867\) 0 0
\(868\) 33.2370i 1.12814i
\(869\) 6.40906 10.9335i 0.217413 0.370893i
\(870\) 0 0
\(871\) 3.78704 5.21242i 0.128319 0.176616i
\(872\) 17.9232 + 5.82361i 0.606957 + 0.197212i
\(873\) 0 0
\(874\) 13.3263 9.68210i 0.450768 0.327502i
\(875\) 40.2682 29.2565i 1.36131 0.989051i
\(876\) 0 0
\(877\) 49.4957 + 16.0821i 1.67135 + 0.543055i 0.983203 0.182516i \(-0.0584242\pi\)
0.688147 + 0.725571i \(0.258424\pi\)
\(878\) 31.9824 44.0200i 1.07935 1.48560i
\(879\) 0 0
\(880\) 19.1310 + 4.19863i 0.644906 + 0.141536i
\(881\) 39.9758i 1.34682i 0.739270 + 0.673409i \(0.235171\pi\)
−0.739270 + 0.673409i \(0.764829\pi\)
\(882\) 0 0
\(883\) −5.74452 + 17.6798i −0.193318 + 0.594973i 0.806674 + 0.590997i \(0.201266\pi\)
−0.999992 + 0.00397571i \(0.998734\pi\)
\(884\) 8.40880 2.73218i 0.282818 0.0918933i
\(885\) 0 0
\(886\) 33.6468 + 46.3108i 1.13039 + 1.55584i
\(887\) 16.8498 + 51.8583i 0.565760 + 1.74123i 0.665681 + 0.746236i \(0.268141\pi\)
−0.0999207 + 0.994995i \(0.531859\pi\)
\(888\) 0 0
\(889\) 87.3486 + 63.4625i 2.92958 + 2.12846i
\(890\) 22.4310 0.751890
\(891\) 0 0
\(892\) −20.8507 −0.698132
\(893\) 12.0664 + 8.76675i 0.403787 + 0.293368i
\(894\) 0 0
\(895\) −7.48032 23.0221i −0.250040 0.769543i
\(896\) 27.3978 + 37.7099i 0.915297 + 1.25980i
\(897\) 0 0
\(898\) 65.5777 21.3075i 2.18836 0.711040i
\(899\) 2.78384 8.56777i 0.0928461 0.285751i
\(900\) 0 0
\(901\) 2.85243i 0.0950281i
\(902\) 47.8314 42.4991i 1.59261 1.41507i
\(903\) 0 0
\(904\) 2.41231 3.32027i 0.0802324 0.110430i
\(905\) −5.13855 1.66962i −0.170811 0.0554999i
\(906\) 0 0
\(907\) 10.0586 7.30800i 0.333990 0.242658i −0.408132 0.912923i \(-0.633820\pi\)
0.742122 + 0.670265i \(0.233820\pi\)
\(908\) −15.3860 + 11.1786i −0.510603 + 0.370975i
\(909\) 0 0
\(910\) −30.7195 9.98139i −1.01834 0.330880i
\(911\) −26.4433 + 36.3961i −0.876106 + 1.20586i 0.101379 + 0.994848i \(0.467675\pi\)
−0.977484 + 0.211008i \(0.932325\pi\)
\(912\) 0 0
\(913\) −18.0229 + 16.0137i −0.596471 + 0.529976i
\(914\) 71.1759i 2.35429i
\(915\) 0 0
\(916\) 8.86599 27.2867i 0.292941 0.901578i
\(917\) 71.3622 23.1870i 2.35659 0.765702i
\(918\) 0 0
\(919\) 13.6185 + 18.7442i 0.449232 + 0.618315i 0.972232 0.234017i \(-0.0751872\pi\)
−0.523000 + 0.852333i \(0.675187\pi\)
\(920\) −0.947464 2.91599i −0.0312370 0.0961375i
\(921\) 0 0
\(922\) 25.7659 + 18.7200i 0.848555 + 0.616512i
\(923\) −11.7661 −0.387285
\(924\) 0 0
\(925\) 3.96846 0.130482
\(926\) 7.44610 + 5.40991i 0.244694 + 0.177781i
\(927\) 0 0
\(928\) 3.32763 + 10.2414i 0.109235 + 0.336190i
\(929\) 6.79920 + 9.35830i 0.223075 + 0.307036i 0.905855 0.423588i \(-0.139229\pi\)
−0.682781 + 0.730624i \(0.739229\pi\)
\(930\) 0 0
\(931\) −71.4077 + 23.2018i −2.34029 + 0.760407i
\(932\) 2.06420 6.35296i 0.0676151 0.208098i
\(933\) 0 0
\(934\) 30.7712i 1.00687i
\(935\) −8.70280 1.90998i −0.284612 0.0624630i
\(936\) 0 0
\(937\) 15.1544 20.8582i 0.495071 0.681407i −0.486242 0.873824i \(-0.661633\pi\)
0.981313 + 0.192417i \(0.0616326\pi\)
\(938\) 17.5907 + 5.71555i 0.574356 + 0.186619i
\(939\) 0 0
\(940\) −4.10258 + 2.98070i −0.133811 + 0.0972197i
\(941\) −47.8599 + 34.7722i −1.56019 + 1.13354i −0.624331 + 0.781160i \(0.714628\pi\)
−0.935856 + 0.352383i \(0.885372\pi\)
\(942\) 0 0
\(943\) −20.0959 6.52954i −0.654411 0.212631i
\(944\) −0.0912824 + 0.125639i −0.00297099 + 0.00408921i
\(945\) 0 0
\(946\) −11.5361 + 19.6798i −0.375069 + 0.639845i
\(947\) 0.120799i 0.00392545i −0.999998 0.00196272i \(-0.999375\pi\)
0.999998 0.00196272i \(-0.000624755\pi\)
\(948\) 0 0
\(949\) −6.66124 + 20.5012i −0.216233 + 0.665497i
\(950\) −28.0312 + 9.10789i −0.909453 + 0.295499i
\(951\) 0 0
\(952\) −8.16752 11.2416i −0.264711 0.364343i
\(953\) −2.50261 7.70223i −0.0810674 0.249500i 0.902306 0.431097i \(-0.141873\pi\)
−0.983373 + 0.181597i \(0.941873\pi\)
\(954\) 0 0
\(955\) 17.2791 + 12.5540i 0.559138 + 0.406237i
\(956\) 17.6615 0.571213
\(957\) 0 0
\(958\) 32.8055 1.05990
\(959\) 67.1337 + 48.7755i 2.16786 + 1.57504i
\(960\) 0 0
\(961\) −0.859922 2.64657i −0.0277394 0.0853732i
\(962\) −3.64210 5.01292i −0.117426 0.161623i
\(963\) 0 0
\(964\) 8.66885 2.81668i 0.279205 0.0907192i
\(965\) 2.28702 7.03871i 0.0736216 0.226584i
\(966\) 0 0
\(967\) 9.94567i 0.319831i −0.987131 0.159916i \(-0.948878\pi\)
0.987131 0.159916i \(-0.0511222\pi\)
\(968\) 1.66154 14.0245i 0.0534040 0.450763i
\(969\) 0 0
\(970\) −18.5893 + 25.5860i −0.596867 + 0.821518i
\(971\) −36.6171 11.8976i −1.17510 0.381813i −0.344555 0.938766i \(-0.611970\pi\)
−0.830544 + 0.556953i \(0.811970\pi\)
\(972\) 0 0
\(973\) 40.6068 29.5025i 1.30179 0.945808i
\(974\) −38.1698 + 27.7320i −1.22304 + 0.888589i
\(975\) 0 0
\(976\) −5.54940 1.80311i −0.177632 0.0577161i
\(977\) 11.9388 16.4324i 0.381956 0.525718i −0.574145 0.818753i \(-0.694666\pi\)
0.956101 + 0.293036i \(0.0946656\pi\)
\(978\) 0 0
\(979\) −3.34238 33.9558i −0.106823 1.08523i
\(980\) 25.5281i 0.815464i
\(981\) 0 0
\(982\) −4.11112 + 12.6527i −0.131191 + 0.403765i
\(983\) −9.24723 + 3.00461i −0.294941 + 0.0958321i −0.452750 0.891638i \(-0.649557\pi\)
0.157809 + 0.987470i \(0.449557\pi\)
\(984\) 0 0
\(985\) 15.8991 + 21.8833i 0.506589 + 0.697260i
\(986\) −2.12591 6.54287i −0.0677027 0.208367i
\(987\) 0 0
\(988\) 14.6150 + 10.6184i 0.464964 + 0.337816i
\(989\) 7.53327 0.239544
\(990\) 0 0
\(991\) −22.9196 −0.728065 −0.364032 0.931386i \(-0.618600\pi\)
−0.364032 + 0.931386i \(0.618600\pi\)
\(992\) −27.2875 19.8255i −0.866378 0.629460i
\(993\) 0 0
\(994\) −10.4378 32.1242i −0.331067 1.01892i
\(995\) −6.57352 9.04768i −0.208395 0.286831i
\(996\) 0 0
\(997\) −20.4494 + 6.64441i −0.647639 + 0.210431i −0.614373 0.789016i \(-0.710591\pi\)
−0.0332659 + 0.999447i \(0.510591\pi\)
\(998\) 5.28139 16.2544i 0.167179 0.514525i
\(999\) 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 891.2.k.a.161.16 80
3.2 odd 2 inner 891.2.k.a.161.5 80
9.2 odd 6 99.2.p.a.95.3 yes 80
9.4 even 3 99.2.p.a.29.3 80
9.5 odd 6 297.2.t.a.62.8 80
9.7 even 3 297.2.t.a.260.8 80
11.8 odd 10 inner 891.2.k.a.404.5 80
33.8 even 10 inner 891.2.k.a.404.16 80
99.41 even 30 297.2.t.a.8.8 80
99.52 odd 30 297.2.t.a.206.8 80
99.74 even 30 99.2.p.a.41.3 yes 80
99.85 odd 30 99.2.p.a.74.3 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.29.3 80 9.4 even 3
99.2.p.a.41.3 yes 80 99.74 even 30
99.2.p.a.74.3 yes 80 99.85 odd 30
99.2.p.a.95.3 yes 80 9.2 odd 6
297.2.t.a.8.8 80 99.41 even 30
297.2.t.a.62.8 80 9.5 odd 6
297.2.t.a.206.8 80 99.52 odd 30
297.2.t.a.260.8 80 9.7 even 3
891.2.k.a.161.5 80 3.2 odd 2 inner
891.2.k.a.161.16 80 1.1 even 1 trivial
891.2.k.a.404.5 80 11.8 odd 10 inner
891.2.k.a.404.16 80 33.8 even 10 inner