Properties

Label 297.2.t.a.62.8
Level $297$
Weight $2$
Character 297.62
Analytic conductor $2.372$
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] = [297,2,Mod(8,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([5, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.t (of order \(30\), degree \(8\), not 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: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{30})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 62.8
Character \(\chi\) \(=\) 297.62
Dual form 297.2.t.a.206.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.65764 - 0.738027i) q^{2} +(0.864813 - 0.960472i) q^{4} +(0.488756 - 1.09776i) q^{5} +(1.00654 - 4.73540i) q^{7} +(-0.396737 + 1.22103i) q^{8} -2.18041i q^{10} +(-1.36897 + 3.02091i) q^{11} +(3.04321 + 0.319854i) q^{13} +(-1.82638 - 8.59243i) q^{14} +(0.513703 + 4.88755i) q^{16} +(1.80866 - 1.31407i) q^{17} +(-4.34428 - 1.41154i) q^{19} +(-0.631690 - 1.41880i) q^{20} +(-0.0397341 + 6.01791i) q^{22} +(-1.72112 + 0.993689i) q^{23} +(2.37945 + 2.64264i) q^{25} +(5.28060 - 1.71577i) q^{26} +(-3.67776 - 5.06200i) q^{28} +(1.65886 + 0.352601i) q^{29} +(-0.555254 + 5.28289i) q^{31} +(3.17481 + 5.49894i) q^{32} +(2.02828 - 3.51308i) q^{34} +(-4.70641 - 3.41941i) q^{35} +(0.344857 + 1.06136i) q^{37} +(-8.24299 + 0.866373i) q^{38} +(1.14650 + 1.03231i) q^{40} +(-10.3998 + 2.21054i) q^{41} +(3.28272 + 1.89528i) q^{43} +(1.71760 + 3.92738i) q^{44} +(-2.11962 + 2.91741i) q^{46} +(-2.42651 + 2.18484i) q^{47} +(-15.0161 - 6.68560i) q^{49} +(5.89460 + 2.62445i) q^{50} +(2.93902 - 2.64630i) q^{52} +(-0.749954 + 1.03222i) q^{53} +(2.64716 + 2.97930i) q^{55} +(5.38274 + 3.10773i) q^{56} +(3.01001 - 0.639797i) q^{58} +(-0.0234836 - 0.0211447i) q^{59} +(1.18080 - 0.124107i) q^{61} +(2.97851 + 9.16690i) q^{62} +(1.36926 + 0.994827i) q^{64} +(1.83851 - 3.18440i) q^{65} +(1.05277 + 1.82345i) q^{67} +(0.302026 - 2.87359i) q^{68} +(-10.3251 - 2.19467i) q^{70} +(-2.26013 - 3.11080i) q^{71} +(6.69980 - 2.17690i) q^{73} +(1.35496 + 1.50483i) q^{74} +(-5.11273 + 2.95184i) q^{76} +(12.9273 + 9.52329i) q^{77} +(-1.55422 - 3.49084i) q^{79} +(5.61646 + 1.82490i) q^{80} +(-15.6076 + 11.3396i) q^{82} +(-0.759844 - 7.22943i) q^{83} +(-0.558543 - 2.62774i) q^{85} +(6.84032 + 0.718946i) q^{86} +(-3.14551 - 2.87006i) q^{88} -10.2875i q^{89} +(4.57775 - 14.0889i) q^{91} +(-0.534037 + 2.51244i) q^{92} +(-2.40980 + 5.41250i) q^{94} +(-3.67283 + 4.07909i) q^{95} +(13.2506 - 5.89957i) q^{97} -29.8254 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.65764 0.738027i 1.17213 0.521864i 0.274055 0.961714i \(-0.411635\pi\)
0.898071 + 0.439850i \(0.144968\pi\)
\(3\) 0 0
\(4\) 0.864813 0.960472i 0.432407 0.480236i
\(5\) 0.488756 1.09776i 0.218579 0.490935i −0.770660 0.637246i \(-0.780073\pi\)
0.989239 + 0.146311i \(0.0467400\pi\)
\(6\) 0 0
\(7\) 1.00654 4.73540i 0.380437 1.78981i −0.204641 0.978837i \(-0.565603\pi\)
0.585077 0.810977i \(-0.301064\pi\)
\(8\) −0.396737 + 1.22103i −0.140268 + 0.431700i
\(9\) 0 0
\(10\) 2.18041i 0.689506i
\(11\) −1.36897 + 3.02091i −0.412759 + 0.910840i
\(12\) 0 0
\(13\) 3.04321 + 0.319854i 0.844034 + 0.0887116i 0.516668 0.856186i \(-0.327172\pi\)
0.327366 + 0.944897i \(0.393839\pi\)
\(14\) −1.82638 8.59243i −0.488120 2.29642i
\(15\) 0 0
\(16\) 0.513703 + 4.88755i 0.128426 + 1.22189i
\(17\) 1.80866 1.31407i 0.438664 0.318708i −0.346440 0.938072i \(-0.612610\pi\)
0.785104 + 0.619364i \(0.212610\pi\)
\(18\) 0 0
\(19\) −4.34428 1.41154i −0.996645 0.323830i −0.235121 0.971966i \(-0.575549\pi\)
−0.761524 + 0.648136i \(0.775549\pi\)
\(20\) −0.631690 1.41880i −0.141250 0.317253i
\(21\) 0 0
\(22\) −0.0397341 + 6.01791i −0.00847133 + 1.28302i
\(23\) −1.72112 + 0.993689i −0.358878 + 0.207199i −0.668589 0.743632i \(-0.733101\pi\)
0.309710 + 0.950831i \(0.399768\pi\)
\(24\) 0 0
\(25\) 2.37945 + 2.64264i 0.475890 + 0.528529i
\(26\) 5.28060 1.71577i 1.03561 0.336490i
\(27\) 0 0
\(28\) −3.67776 5.06200i −0.695030 0.956627i
\(29\) 1.65886 + 0.352601i 0.308042 + 0.0654763i 0.359339 0.933207i \(-0.383002\pi\)
−0.0512972 + 0.998683i \(0.516336\pi\)
\(30\) 0 0
\(31\) −0.555254 + 5.28289i −0.0997266 + 0.948835i 0.824209 + 0.566286i \(0.191620\pi\)
−0.923935 + 0.382549i \(0.875046\pi\)
\(32\) 3.17481 + 5.49894i 0.561233 + 0.972084i
\(33\) 0 0
\(34\) 2.02828 3.51308i 0.347847 0.602489i
\(35\) −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 \(0.870759\pi\)
\(38\) −8.24299 + 0.866373i −1.33719 + 0.140544i
\(39\) 0 0
\(40\) 1.14650 + 1.03231i 0.181277 + 0.163223i
\(41\) −10.3998 + 2.21054i −1.62417 + 0.345228i −0.927981 0.372628i \(-0.878457\pi\)
−0.696191 + 0.717857i \(0.745123\pi\)
\(42\) 0 0
\(43\) 3.28272 + 1.89528i 0.500609 + 0.289027i 0.728965 0.684551i \(-0.240002\pi\)
−0.228356 + 0.973578i \(0.573335\pi\)
\(44\) 1.71760 + 3.92738i 0.258938 + 0.592075i
\(45\) 0 0
\(46\) −2.11962 + 2.91741i −0.312521 + 0.430149i
\(47\) −2.42651 + 2.18484i −0.353943 + 0.318692i −0.826852 0.562420i \(-0.809871\pi\)
0.472909 + 0.881111i \(0.343204\pi\)
\(48\) 0 0
\(49\) −15.0161 6.68560i −2.14516 0.955086i
\(50\) 5.89460 + 2.62445i 0.833623 + 0.371153i
\(51\) 0 0
\(52\) 2.93902 2.64630i 0.407569 0.366976i
\(53\) −0.749954 + 1.03222i −0.103014 + 0.141787i −0.857412 0.514631i \(-0.827929\pi\)
0.754398 + 0.656417i \(0.227929\pi\)
\(54\) 0 0
\(55\) 2.64716 + 2.97930i 0.356943 + 0.401728i
\(56\) 5.38274 + 3.10773i 0.719299 + 0.415288i
\(57\) 0 0
\(58\) 3.01001 0.639797i 0.395233 0.0840095i
\(59\) −0.0234836 0.0211447i −0.00305730 0.00275281i 0.667601 0.744520i \(-0.267321\pi\)
−0.670658 + 0.741767i \(0.733988\pi\)
\(60\) 0 0
\(61\) 1.18080 0.124107i 0.151186 0.0158903i −0.0286330 0.999590i \(-0.509115\pi\)
0.179819 + 0.983700i \(0.442449\pi\)
\(62\) 2.97851 + 9.16690i 0.378271 + 1.16420i
\(63\) 0 0
\(64\) 1.36926 + 0.994827i 0.171158 + 0.124353i
\(65\) 1.83851 3.18440i 0.228039 0.394976i
\(66\) 0 0
\(67\) 1.05277 + 1.82345i 0.128617 + 0.222770i 0.923141 0.384462i \(-0.125613\pi\)
−0.794524 + 0.607232i \(0.792280\pi\)
\(68\) 0.302026 2.87359i 0.0366261 0.348474i
\(69\) 0 0
\(70\) −10.3251 2.19467i −1.23409 0.262314i
\(71\) −2.26013 3.11080i −0.268228 0.369184i 0.653563 0.756873i \(-0.273274\pi\)
−0.921790 + 0.387688i \(0.873274\pi\)
\(72\) 0 0
\(73\) 6.69980 2.17690i 0.784152 0.254786i 0.110540 0.993872i \(-0.464742\pi\)
0.673612 + 0.739085i \(0.264742\pi\)
\(74\) 1.35496 + 1.50483i 0.157511 + 0.174934i
\(75\) 0 0
\(76\) −5.11273 + 2.95184i −0.586471 + 0.338599i
\(77\) 12.9273 + 9.52329i 1.47321 + 1.08528i
\(78\) 0 0
\(79\) −1.55422 3.49084i −0.174863 0.392750i 0.804758 0.593603i \(-0.202295\pi\)
−0.979621 + 0.200854i \(0.935628\pi\)
\(80\) 5.61646 + 1.82490i 0.627940 + 0.204030i
\(81\) 0 0
\(82\) −15.6076 + 11.3396i −1.72357 + 1.25225i
\(83\) −0.759844 7.22943i −0.0834037 0.793533i −0.953650 0.300917i \(-0.902707\pi\)
0.870247 0.492616i \(-0.163959\pi\)
\(84\) 0 0
\(85\) −0.558543 2.62774i −0.0605825 0.285018i
\(86\) 6.84032 + 0.718946i 0.737610 + 0.0775260i
\(87\) 0 0
\(88\) −3.14551 2.87006i −0.335313 0.305950i
\(89\) 10.2875i 1.09048i −0.838281 0.545238i \(-0.816439\pi\)
0.838281 0.545238i \(-0.183561\pi\)
\(90\) 0 0
\(91\) 4.57775 14.0889i 0.479879 1.47692i
\(92\) −0.534037 + 2.51244i −0.0556772 + 0.261940i
\(93\) 0 0
\(94\) −2.40980 + 5.41250i −0.248552 + 0.558257i
\(95\) −3.67283 + 4.07909i −0.376825 + 0.418506i
\(96\) 0 0
\(97\) 13.2506 5.89957i 1.34540 0.599010i 0.397506 0.917600i \(-0.369876\pi\)
0.947893 + 0.318589i \(0.103209\pi\)
\(98\) −29.8254 −3.01282
\(99\) 0 0
\(100\) 4.59597 0.459597
\(101\) 14.6950 6.54265i 1.46221 0.651018i 0.487222 0.873278i \(-0.338010\pi\)
0.974987 + 0.222260i \(0.0713435\pi\)
\(102\) 0 0
\(103\) −1.39257 + 1.54661i −0.137214 + 0.152392i −0.807835 0.589408i \(-0.799361\pi\)
0.670621 + 0.741800i \(0.266028\pi\)
\(104\) −1.59791 + 3.58896i −0.156688 + 0.351926i
\(105\) 0 0
\(106\) −0.481342 + 2.26454i −0.0467521 + 0.219951i
\(107\) 0.129361 0.398133i 0.0125058 0.0384889i −0.944609 0.328198i \(-0.893559\pi\)
0.957115 + 0.289709i \(0.0935586\pi\)
\(108\) 0 0
\(109\) 14.6788i 1.40597i 0.711205 + 0.702985i \(0.248150\pi\)
−0.711205 + 0.702985i \(0.751850\pi\)
\(110\) 6.58684 + 2.98491i 0.628030 + 0.284600i
\(111\) 0 0
\(112\) 23.6616 + 2.48694i 2.23581 + 0.234993i
\(113\) 0.664620 + 3.12679i 0.0625222 + 0.294144i 0.998289 0.0584761i \(-0.0186242\pi\)
−0.935767 + 0.352620i \(0.885291\pi\)
\(114\) 0 0
\(115\) 0.249629 + 2.37506i 0.0232780 + 0.221475i
\(116\) 1.77326 1.28835i 0.164643 0.119620i
\(117\) 0 0
\(118\) −0.0545326 0.0177187i −0.00502013 0.00163114i
\(119\) −4.40215 9.88738i −0.403544 0.906375i
\(120\) 0 0
\(121\) −7.25185 8.27107i −0.659259 0.751916i
\(122\) 1.86575 1.07719i 0.168917 0.0975241i
\(123\) 0 0
\(124\) 4.59388 + 5.10202i 0.412543 + 0.458175i
\(125\) 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 \(-0.653821\pi\)
\(128\) −9.41780 2.00181i −0.832423 0.176937i
\(129\) 0 0
\(130\) 0.697414 6.63545i 0.0611672 0.581967i
\(131\) −7.74960 13.4227i −0.677086 1.17275i −0.975855 0.218421i \(-0.929909\pi\)
0.298769 0.954326i \(-0.403424\pi\)
\(132\) 0 0
\(133\) −11.0569 + 19.1511i −0.958756 + 1.66061i
\(134\) 3.09087 + 2.24565i 0.267011 + 0.193995i
\(135\) 0 0
\(136\) 0.886955 + 2.72977i 0.0760557 + 0.234075i
\(137\) −17.0469 + 1.79170i −1.45641 + 0.153075i −0.799397 0.600803i \(-0.794848\pi\)
−0.657015 + 0.753878i \(0.728181\pi\)
\(138\) 0 0
\(139\) 7.70480 + 6.93744i 0.653513 + 0.588426i 0.927734 0.373241i \(-0.121753\pi\)
−0.274222 + 0.961667i \(0.588420\pi\)
\(140\) −7.35441 + 1.56323i −0.621561 + 0.132117i
\(141\) 0 0
\(142\) −6.04233 3.48854i −0.507061 0.292752i
\(143\) −5.13231 + 8.75541i −0.429185 + 0.732164i
\(144\) 0 0
\(145\) 1.19785 1.64870i 0.0994759 0.136917i
\(146\) 9.49922 8.55313i 0.786161 0.707862i
\(147\) 0 0
\(148\) 1.31764 + 0.586653i 0.108310 + 0.0482225i
\(149\) 0.0369600 + 0.0164557i 0.00302788 + 0.00134810i 0.408250 0.912870i \(-0.366139\pi\)
−0.405222 + 0.914218i \(0.632806\pi\)
\(150\) 0 0
\(151\) −2.04486 + 1.84120i −0.166408 + 0.149834i −0.748127 0.663555i \(-0.769047\pi\)
0.581719 + 0.813390i \(0.302380\pi\)
\(152\) 3.44707 4.74449i 0.279594 0.384829i
\(153\) 0 0
\(154\) 28.4573 + 6.24544i 2.29315 + 0.503272i
\(155\) 5.52799 + 3.19159i 0.444019 + 0.256354i
\(156\) 0 0
\(157\) −2.06376 + 0.438666i −0.164706 + 0.0350094i −0.289527 0.957170i \(-0.593498\pi\)
0.124820 + 0.992179i \(0.460165\pi\)
\(158\) −5.15266 4.63948i −0.409924 0.369097i
\(159\) 0 0
\(160\) 7.58825 0.797557i 0.599904 0.0630525i
\(161\) 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 \(0.893689\pi\)
\(164\) −6.87070 + 11.9004i −0.536512 + 0.929265i
\(165\) 0 0
\(166\) −6.59506 11.4230i −0.511876 0.886596i
\(167\) −0.0932678 + 0.887384i −0.00721728 + 0.0686678i −0.997538 0.0701322i \(-0.977658\pi\)
0.990320 + 0.138800i \(0.0443245\pi\)
\(168\) 0 0
\(169\) −3.55710 0.756085i −0.273623 0.0581604i
\(170\) −2.86520 3.94362i −0.219751 0.302461i
\(171\) 0 0
\(172\) 4.65930 1.51390i 0.355268 0.115434i
\(173\) 8.86427 + 9.84476i 0.673938 + 0.748484i 0.979003 0.203848i \(-0.0653448\pi\)
−0.305065 + 0.952332i \(0.598678\pi\)
\(174\) 0 0
\(175\) 14.9090 8.60772i 1.12701 0.650682i
\(176\) −15.4681 5.13906i −1.16595 0.387371i
\(177\) 0 0
\(178\) −7.59248 17.0530i −0.569080 1.27817i
\(179\) −19.1587 6.22502i −1.43199 0.465280i −0.512596 0.858630i \(-0.671316\pi\)
−0.919389 + 0.393350i \(0.871316\pi\)
\(180\) 0 0
\(181\) 3.63758 2.64286i 0.270379 0.196442i −0.444331 0.895863i \(-0.646559\pi\)
0.714710 + 0.699421i \(0.246559\pi\)
\(182\) −2.80973 26.7328i −0.208271 1.98156i
\(183\) 0 0
\(184\) −0.530493 2.49578i −0.0391085 0.183991i
\(185\) 1.33367 + 0.140175i 0.0980537 + 0.0103059i
\(186\) 0 0
\(187\) 1.49369 + 7.26271i 0.109229 + 0.531102i
\(188\) 4.22008i 0.307781i
\(189\) 0 0
\(190\) −3.07774 + 9.47231i −0.223283 + 0.687193i
\(191\) −3.69541 + 17.3855i −0.267390 + 1.25797i 0.615403 + 0.788212i \(0.288993\pi\)
−0.882794 + 0.469761i \(0.844340\pi\)
\(192\) 0 0
\(193\) 2.50508 5.62649i 0.180319 0.405004i −0.800659 0.599120i \(-0.795517\pi\)
0.980979 + 0.194116i \(0.0621839\pi\)
\(194\) 17.6107 19.5587i 1.26438 1.40423i
\(195\) 0 0
\(196\) −19.4075 + 8.64076i −1.38625 + 0.617197i
\(197\) 22.5100 1.60377 0.801886 0.597477i \(-0.203830\pi\)
0.801886 + 0.597477i \(0.203830\pi\)
\(198\) 0 0
\(199\) 9.30680 0.659742 0.329871 0.944026i \(-0.392995\pi\)
0.329871 + 0.944026i \(0.392995\pi\)
\(200\) −4.17077 + 1.85695i −0.294918 + 0.131306i
\(201\) 0 0
\(202\) 19.5304 21.6907i 1.37415 1.52615i
\(203\) 3.33941 7.50044i 0.234381 0.526428i
\(204\) 0 0
\(205\) −2.65630 + 12.4969i −0.185524 + 0.872823i
\(206\) −1.16694 + 3.59147i −0.0813046 + 0.250230i
\(207\) 0 0
\(208\) 15.0382i 1.04271i
\(209\) 10.2113 11.1913i 0.706332 0.774121i
\(210\) 0 0
\(211\) −13.9344 1.46456i −0.959282 0.100825i −0.388073 0.921629i \(-0.626859\pi\)
−0.571210 + 0.820804i \(0.693526\pi\)
\(212\) 0.342852 + 1.61299i 0.0235471 + 0.110781i
\(213\) 0 0
\(214\) −0.0793990 0.755431i −0.00542761 0.0516402i
\(215\) 3.68502 2.67732i 0.251316 0.182592i
\(216\) 0 0
\(217\) 24.4577 + 7.94680i 1.66030 + 0.539464i
\(218\) 10.8333 + 24.3320i 0.733725 + 1.64797i
\(219\) 0 0
\(220\) 5.15083 + 0.0340091i 0.347269 + 0.00229289i
\(221\) 5.92443 3.42047i 0.398520 0.230086i
\(222\) 0 0
\(223\) −10.7949 11.9890i −0.722881 0.802841i 0.263960 0.964534i \(-0.414971\pi\)
−0.986841 + 0.161693i \(0.948305\pi\)
\(224\) 29.2353 9.49912i 1.95336 0.634686i
\(225\) 0 0
\(226\) 3.40936 + 4.69258i 0.226787 + 0.312146i
\(227\) 14.3933 + 3.05940i 0.955320 + 0.203060i 0.659096 0.752059i \(-0.270939\pi\)
0.296224 + 0.955118i \(0.404272\pi\)
\(228\) 0 0
\(229\) −2.32043 + 22.0774i −0.153338 + 1.45892i 0.599323 + 0.800507i \(0.295436\pi\)
−0.752661 + 0.658408i \(0.771230\pi\)
\(230\) 2.16665 + 3.75275i 0.142865 + 0.247449i
\(231\) 0 0
\(232\) −1.08867 + 1.88562i −0.0714744 + 0.123797i
\(233\) 4.18134 + 3.03792i 0.273929 + 0.199021i 0.716265 0.697828i \(-0.245850\pi\)
−0.442336 + 0.896849i \(0.645850\pi\)
\(234\) 0 0
\(235\) 1.21247 + 3.73159i 0.0790927 + 0.243422i
\(236\) −0.0406178 + 0.00426911i −0.00264400 + 0.000277895i
\(237\) 0 0
\(238\) −14.5943 13.1408i −0.946009 0.851790i
\(239\) 13.3666 2.84115i 0.864612 0.183779i 0.245802 0.969320i \(-0.420949\pi\)
0.618809 + 0.785541i \(0.287615\pi\)
\(240\) 0 0
\(241\) 6.10765 + 3.52625i 0.393428 + 0.227146i 0.683645 0.729815i \(-0.260394\pi\)
−0.290216 + 0.956961i \(0.593727\pi\)
\(242\) −18.1252 8.35837i −1.16513 0.537296i
\(243\) 0 0
\(244\) 0.901971 1.24146i 0.0577428 0.0794761i
\(245\) −14.6784 + 13.2165i −0.937771 + 0.844373i
\(246\) 0 0
\(247\) −12.7691 5.68515i −0.812476 0.361737i
\(248\) −6.23028 2.77390i −0.395623 0.176143i
\(249\) 0 0
\(250\) 13.8639 12.4831i 0.876827 0.789499i
\(251\) 3.95496 5.44354i 0.249635 0.343593i −0.665748 0.746176i \(-0.731888\pi\)
0.915383 + 0.402583i \(0.131888\pi\)
\(252\) 0 0
\(253\) −0.645692 6.55969i −0.0405943 0.412404i
\(254\) −35.0457 20.2337i −2.19897 1.26957i
\(255\) 0 0
\(256\) −20.3997 + 4.33609i −1.27498 + 0.271006i
\(257\) −10.5166 9.46922i −0.656009 0.590673i 0.272422 0.962178i \(-0.412175\pi\)
−0.928431 + 0.371504i \(0.878842\pi\)
\(258\) 0 0
\(259\) 5.37308 0.564733i 0.333867 0.0350908i
\(260\) −1.46856 4.51975i −0.0910760 0.280303i
\(261\) 0 0
\(262\) −22.7523 16.5305i −1.40564 1.02126i
\(263\) −3.47292 + 6.01527i −0.214149 + 0.370917i −0.953009 0.302942i \(-0.902031\pi\)
0.738860 + 0.673859i \(0.235365\pi\)
\(264\) 0 0
\(265\) 0.766593 + 1.32778i 0.0470914 + 0.0815648i
\(266\) −4.19428 + 39.9059i −0.257168 + 2.44679i
\(267\) 0 0
\(268\) 2.66183 + 0.565789i 0.162597 + 0.0345611i
\(269\) −4.05850 5.58605i −0.247451 0.340587i 0.667165 0.744910i \(-0.267507\pi\)
−0.914617 + 0.404322i \(0.867507\pi\)
\(270\) 0 0
\(271\) −12.9581 + 4.21033i −0.787146 + 0.255759i −0.674888 0.737920i \(-0.735808\pi\)
−0.112258 + 0.993679i \(0.535808\pi\)
\(272\) 7.35168 + 8.16487i 0.445761 + 0.495068i
\(273\) 0 0
\(274\) −26.9352 + 15.5510i −1.62721 + 0.939473i
\(275\) −11.2406 + 3.57041i −0.677833 + 0.215304i
\(276\) 0 0
\(277\) −4.74062 10.6476i −0.284836 0.639753i 0.713294 0.700864i \(-0.247202\pi\)
−0.998131 + 0.0611112i \(0.980536\pi\)
\(278\) 17.8918 + 5.81339i 1.07308 + 0.348664i
\(279\) 0 0
\(280\) 6.04241 4.39007i 0.361103 0.262357i
\(281\) 2.28295 + 21.7209i 0.136190 + 1.29576i 0.822632 + 0.568574i \(0.192505\pi\)
−0.686443 + 0.727184i \(0.740829\pi\)
\(282\) 0 0
\(283\) 4.88066 + 22.9617i 0.290125 + 1.36493i 0.845786 + 0.533523i \(0.179132\pi\)
−0.555661 + 0.831409i \(0.687535\pi\)
\(284\) −4.94243 0.519470i −0.293279 0.0308249i
\(285\) 0 0
\(286\) −2.04577 + 18.3011i −0.120969 + 1.08216i
\(287\) 51.4721i 3.03830i
\(288\) 0 0
\(289\) −3.70882 + 11.4146i −0.218166 + 0.671445i
\(290\) 0.768814 3.61699i 0.0451463 0.212397i
\(291\) 0 0
\(292\) 3.70322 8.31758i 0.216715 0.486749i
\(293\) −1.13529 + 1.26087i −0.0663243 + 0.0736606i −0.775394 0.631478i \(-0.782449\pi\)
0.709069 + 0.705139i \(0.249115\pi\)
\(294\) 0 0
\(295\) −0.0346897 + 0.0154448i −0.00201971 + 0.000899233i
\(296\) −1.43277 −0.0832781
\(297\) 0 0
\(298\) 0.0734110 0.00425258
\(299\) −5.55557 + 2.47350i −0.321287 + 0.143046i
\(300\) 0 0
\(301\) 12.2791 13.6373i 0.707755 0.786042i
\(302\) −2.03077 + 4.56119i −0.116858 + 0.262467i
\(303\) 0 0
\(304\) 4.66732 21.9580i 0.267689 1.25938i
\(305\) 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 \(-0.0213877\pi\)
\(308\) 20.3266 4.18047i 1.15821 0.238205i
\(309\) 0 0
\(310\) 11.5189 + 1.21068i 0.654228 + 0.0687621i
\(311\) 2.20518 + 10.3746i 0.125044 + 0.588288i 0.995395 + 0.0958557i \(0.0305587\pi\)
−0.870351 + 0.492432i \(0.836108\pi\)
\(312\) 0 0
\(313\) 2.64814 + 25.1954i 0.149682 + 1.42413i 0.769132 + 0.639090i \(0.220689\pi\)
−0.619450 + 0.785036i \(0.712645\pi\)
\(314\) −3.09722 + 2.25026i −0.174786 + 0.126990i
\(315\) 0 0
\(316\) −4.69696 1.52614i −0.264225 0.0858518i
\(317\) −10.9056 24.4944i −0.612520 1.37574i −0.907424 0.420215i \(-0.861955\pi\)
0.294905 0.955527i \(-0.404712\pi\)
\(318\) 0 0
\(319\) −3.33610 + 4.52856i −0.186786 + 0.253551i
\(320\) 1.76132 1.01690i 0.0984609 0.0568464i
\(321\) 0 0
\(322\) 11.6816 + 12.9738i 0.650992 + 0.722999i
\(323\) −9.71216 + 3.15567i −0.540399 + 0.175586i
\(324\) 0 0
\(325\) 6.39590 + 8.80320i 0.354781 + 0.488314i
\(326\) −25.9061 5.50651i −1.43481 0.304978i
\(327\) 0 0
\(328\) 1.42684 13.5755i 0.0787839 0.749579i
\(329\) 7.90372 + 13.6896i 0.435746 + 0.754735i
\(330\) 0 0
\(331\) 8.66186 15.0028i 0.476099 0.824627i −0.523526 0.852010i \(-0.675384\pi\)
0.999625 + 0.0273822i \(0.00871710\pi\)
\(332\) −7.60079 5.52230i −0.417148 0.303076i
\(333\) 0 0
\(334\) 0.500309 + 1.53979i 0.0273757 + 0.0842538i
\(335\) 2.51627 0.264471i 0.137479 0.0144496i
\(336\) 0 0
\(337\) 9.66376 + 8.70129i 0.526419 + 0.473989i 0.888964 0.457977i \(-0.151426\pi\)
−0.362546 + 0.931966i \(0.618092\pi\)
\(338\) −6.45439 + 1.37192i −0.351073 + 0.0746228i
\(339\) 0 0
\(340\) −3.00691 1.73604i −0.163072 0.0941499i
\(341\) −15.1990 8.90948i −0.823074 0.482476i
\(342\) 0 0
\(343\) −26.8543 + 36.9618i −1.45000 + 1.99575i
\(344\) −3.61657 + 3.25637i −0.194992 + 0.175572i
\(345\) 0 0
\(346\) 21.9594 + 9.77697i 1.18055 + 0.525613i
\(347\) 19.4186 + 8.64572i 1.04244 + 0.464126i 0.855260 0.518198i \(-0.173397\pi\)
0.187185 + 0.982325i \(0.440064\pi\)
\(348\) 0 0
\(349\) −6.93428 + 6.24365i −0.371183 + 0.334215i −0.833520 0.552490i \(-0.813678\pi\)
0.462337 + 0.886705i \(0.347011\pi\)
\(350\) 18.3610 25.2717i 0.981436 1.35083i
\(351\) 0 0
\(352\) −20.9580 + 2.06297i −1.11707 + 0.109957i
\(353\) −7.89937 4.56070i −0.420441 0.242742i 0.274825 0.961494i \(-0.411380\pi\)
−0.695266 + 0.718753i \(0.744713\pi\)
\(354\) 0 0
\(355\) −4.51958 + 0.960666i −0.239874 + 0.0509869i
\(356\) −9.88089 8.89679i −0.523686 0.471529i
\(357\) 0 0
\(358\) −36.3523 + 3.82078i −1.92128 + 0.201935i
\(359\) 2.41692 + 7.43851i 0.127560 + 0.392589i 0.994359 0.106069i \(-0.0338263\pi\)
−0.866799 + 0.498658i \(0.833826\pi\)
\(360\) 0 0
\(361\) 1.50897 + 1.09633i 0.0794193 + 0.0577015i
\(362\) 4.07929 7.06553i 0.214402 0.371356i
\(363\) 0 0
\(364\) −9.57308 16.5811i −0.501766 0.869084i
\(365\) 0.884849 8.41877i 0.0463151 0.440659i
\(366\) 0 0
\(367\) −23.9688 5.09473i −1.25116 0.265943i −0.465750 0.884916i \(-0.654215\pi\)
−0.785412 + 0.618974i \(0.787549\pi\)
\(368\) −5.74086 7.90161i −0.299263 0.411900i
\(369\) 0 0
\(370\) 2.31420 0.751929i 0.120310 0.0390909i
\(371\) 4.13313 + 4.59031i 0.214582 + 0.238317i
\(372\) 0 0
\(373\) −2.47795 + 1.43065i −0.128303 + 0.0740760i −0.562778 0.826608i \(-0.690267\pi\)
0.434475 + 0.900684i \(0.356934\pi\)
\(374\) 7.83607 + 10.9366i 0.405194 + 0.565516i
\(375\) 0 0
\(376\) −1.70507 3.82965i −0.0879324 0.197499i
\(377\) 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 \(0.0292899\pi\)
\(380\) 0.741543 + 7.05531i 0.0380404 + 0.361930i
\(381\) 0 0
\(382\) 6.70535 + 31.5462i 0.343076 + 1.61404i
\(383\) −28.3035 2.97482i −1.44624 0.152006i −0.651359 0.758769i \(-0.725801\pi\)
−0.794883 + 0.606763i \(0.792468\pi\)
\(384\) 0 0
\(385\) 16.7727 9.53660i 0.854814 0.486030i
\(386\) 11.1755i 0.568818i
\(387\) 0 0
\(388\) 5.79296 17.8289i 0.294093 0.905125i
\(389\) 2.96928 13.9694i 0.150548 0.708275i −0.836515 0.547944i \(-0.815411\pi\)
0.987063 0.160331i \(-0.0512560\pi\)
\(390\) 0 0
\(391\) −1.80714 + 4.05891i −0.0913911 + 0.205268i
\(392\) 14.1208 15.6827i 0.713207 0.792097i
\(393\) 0 0
\(394\) 37.3134 16.6130i 1.87982 0.836951i
\(395\) −4.59175 −0.231036
\(396\) 0 0
\(397\) 2.20687 0.110760 0.0553798 0.998465i \(-0.482363\pi\)
0.0553798 + 0.998465i \(0.482363\pi\)
\(398\) 15.4273 6.86867i 0.773300 0.344295i
\(399\) 0 0
\(400\) −11.6937 + 12.9872i −0.584687 + 0.649361i
\(401\) 12.8297 28.8160i 0.640684 1.43900i −0.242583 0.970131i \(-0.577995\pi\)
0.883267 0.468870i \(-0.155339\pi\)
\(402\) 0 0
\(403\) −3.37951 + 15.8993i −0.168345 + 0.792003i
\(404\) 6.42442 19.7723i 0.319627 0.983710i
\(405\) 0 0
\(406\) 14.8976i 0.739355i
\(407\) −3.67837 0.411185i −0.182330 0.0203817i
\(408\) 0 0
\(409\) 6.74107 + 0.708515i 0.333324 + 0.0350338i 0.269712 0.962941i \(-0.413071\pi\)
0.0636119 + 0.997975i \(0.479738\pi\)
\(410\) 4.81989 + 22.6758i 0.238037 + 1.11988i
\(411\) 0 0
\(412\) 0.281160 + 2.67506i 0.0138517 + 0.131791i
\(413\) −0.123766 + 0.0899212i −0.00609012 + 0.00442473i
\(414\) 0 0
\(415\) −8.30760 2.69930i −0.407804 0.132504i
\(416\) 7.90276 + 17.7499i 0.387465 + 0.870260i
\(417\) 0 0
\(418\) 8.66715 26.0874i 0.423924 1.27598i
\(419\) 24.7759 14.3044i 1.21038 0.698815i 0.247541 0.968877i \(-0.420378\pi\)
0.962843 + 0.270062i \(0.0870442\pi\)
\(420\) 0 0
\(421\) −3.74264 4.15662i −0.182405 0.202582i 0.645007 0.764177i \(-0.276854\pi\)
−0.827412 + 0.561595i \(0.810188\pi\)
\(422\) −24.1790 + 7.85624i −1.17702 + 0.382436i
\(423\) 0 0
\(424\) −0.962842 1.32524i −0.0467597 0.0643592i
\(425\) 7.77622 + 1.65289i 0.377202 + 0.0801767i
\(426\) 0 0
\(427\) 0.600828 5.71649i 0.0290761 0.276640i
\(428\) −0.270522 0.468558i −0.0130762 0.0226486i
\(429\) 0 0
\(430\) 4.13248 7.15767i 0.199286 0.345173i
\(431\) −15.7825 11.4667i −0.760216 0.552329i 0.138760 0.990326i \(-0.455688\pi\)
−0.898977 + 0.437997i \(0.855688\pi\)
\(432\) 0 0
\(433\) −6.96921 21.4490i −0.334919 1.03077i −0.966762 0.255678i \(-0.917701\pi\)
0.631843 0.775096i \(-0.282299\pi\)
\(434\) 46.4070 4.87757i 2.22761 0.234131i
\(435\) 0 0
\(436\) 14.0985 + 12.6944i 0.675198 + 0.607951i
\(437\) 8.87966 1.88743i 0.424772 0.0902880i
\(438\) 0 0
\(439\) 25.9695 + 14.9935i 1.23946 + 0.715601i 0.968983 0.247126i \(-0.0794861\pi\)
0.270474 + 0.962727i \(0.412819\pi\)
\(440\) −4.68804 + 2.05027i −0.223494 + 0.0977428i
\(441\) 0 0
\(442\) 7.29615 10.0423i 0.347043 0.477663i
\(443\) 23.4444 21.1094i 1.11388 1.00294i 0.113922 0.993490i \(-0.463659\pi\)
0.999955 0.00944948i \(-0.00300791\pi\)
\(444\) 0 0
\(445\) −11.2933 5.02810i −0.535353 0.238355i
\(446\) −26.7422 11.9064i −1.26628 0.563785i
\(447\) 0 0
\(448\) 6.08913 5.48268i 0.287684 0.259032i
\(449\) −22.3362 + 30.7432i −1.05411 + 1.45086i −0.168921 + 0.985630i \(0.554028\pi\)
−0.885190 + 0.465229i \(0.845972\pi\)
\(450\) 0 0
\(451\) 7.55911 34.4430i 0.355944 1.62186i
\(452\) 3.57797 + 2.06574i 0.168294 + 0.0971644i
\(453\) 0 0
\(454\) 26.1169 5.55131i 1.22572 0.260536i
\(455\) −13.2289 11.9113i −0.620179 0.558412i
\(456\) 0 0
\(457\) 39.0111 4.10023i 1.82486 0.191801i 0.870846 0.491555i \(-0.163571\pi\)
0.954016 + 0.299755i \(0.0969048\pi\)
\(458\) 12.4473 + 38.3088i 0.581624 + 1.79005i
\(459\) 0 0
\(460\) 2.49706 + 1.81422i 0.116426 + 0.0845885i
\(461\) 8.77604 15.2006i 0.408741 0.707960i −0.586008 0.810305i \(-0.699301\pi\)
0.994749 + 0.102345i \(0.0326346\pi\)
\(462\) 0 0
\(463\) −2.53619 4.39282i −0.117867 0.204151i 0.801055 0.598590i \(-0.204272\pi\)
−0.918922 + 0.394439i \(0.870939\pi\)
\(464\) −0.871196 + 8.28888i −0.0404443 + 0.384802i
\(465\) 0 0
\(466\) 9.17322 + 1.94983i 0.424941 + 0.0903240i
\(467\) 9.96792 + 13.7197i 0.461260 + 0.634870i 0.974770 0.223214i \(-0.0716548\pi\)
−0.513509 + 0.858084i \(0.671655\pi\)
\(468\) 0 0
\(469\) 9.69445 3.14992i 0.447648 0.145450i
\(470\) 4.76385 + 5.29079i 0.219740 + 0.244046i
\(471\) 0 0
\(472\) 0.0351352 0.0202853i 0.00161723 0.000933706i
\(473\) −10.2194 + 7.32223i −0.469889 + 0.336677i
\(474\) 0 0
\(475\) −6.60678 14.8391i −0.303140 0.680863i
\(476\) −13.3036 4.32260i −0.609769 0.198126i
\(477\) 0 0
\(478\) 20.0601 14.5745i 0.917526 0.666622i
\(479\) −1.88983 17.9805i −0.0863485 0.821551i −0.948899 0.315580i \(-0.897801\pi\)
0.862550 0.505971i \(-0.168866\pi\)
\(480\) 0 0
\(481\) 0.709991 + 3.34024i 0.0323728 + 0.152302i
\(482\) 12.7267 + 1.33763i 0.579687 + 0.0609276i
\(483\) 0 0
\(484\) −14.2156 0.187729i −0.646165 0.00853315i
\(485\) 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 \(0.899472\pi\)
\(488\) −0.316929 + 1.49103i −0.0143467 + 0.0674959i
\(489\) 0 0
\(490\) −14.5774 + 32.7413i −0.658538 + 1.47910i
\(491\) −4.90602 + 5.44869i −0.221406 + 0.245896i −0.843607 0.536962i \(-0.819572\pi\)
0.622201 + 0.782858i \(0.286239\pi\)
\(492\) 0 0
\(493\) 3.46364 1.54211i 0.155995 0.0694532i
\(494\) −25.3622 −1.14110
\(495\) 0 0
\(496\) −26.1057 −1.17218
\(497\) −17.0058 + 7.57147i −0.762815 + 0.339627i
\(498\) 0 0
\(499\) −6.30257 + 6.99971i −0.282142 + 0.313350i −0.867512 0.497416i \(-0.834282\pi\)
0.585371 + 0.810766i \(0.300949\pi\)
\(500\) 5.40476 12.1393i 0.241708 0.542885i
\(501\) 0 0
\(502\) 2.53841 11.9423i 0.113295 0.533010i
\(503\) 10.3211 31.7652i 0.460196 1.41634i −0.404728 0.914437i \(-0.632634\pi\)
0.864925 0.501902i \(-0.167366\pi\)
\(504\) 0 0
\(505\) 19.3294i 0.860149i
\(506\) −5.91155 10.3970i −0.262800 0.462205i
\(507\) 0 0
\(508\) −28.6663 3.01295i −1.27186 0.133678i
\(509\) 4.26297 + 20.0557i 0.188953 + 0.888953i 0.965805 + 0.259270i \(0.0834819\pi\)
−0.776852 + 0.629683i \(0.783185\pi\)
\(510\) 0 0
\(511\) −3.56486 33.9174i −0.157700 1.50042i
\(512\) −15.0364 + 10.9246i −0.664521 + 0.482803i
\(513\) 0 0
\(514\) −24.4213 7.93496i −1.07718 0.349996i
\(515\) 1.01718 + 2.28463i 0.0448225 + 0.100673i
\(516\) 0 0
\(517\) −3.27840 10.3213i −0.144184 0.453929i
\(518\) 8.48982 4.90160i 0.373021 0.215364i
\(519\) 0 0
\(520\) 3.15884 + 3.50825i 0.138524 + 0.153847i
\(521\) 12.4115 4.03273i 0.543757 0.176677i −0.0242430 0.999706i \(-0.507718\pi\)
0.568000 + 0.823029i \(0.307718\pi\)
\(522\) 0 0
\(523\) −4.85832 6.68690i −0.212439 0.292398i 0.689478 0.724307i \(-0.257840\pi\)
−0.901917 + 0.431909i \(0.857840\pi\)
\(524\) −19.5941 4.16485i −0.855972 0.181942i
\(525\) 0 0
\(526\) −1.31740 + 12.5342i −0.0574414 + 0.546519i
\(527\) 5.93780 + 10.2846i 0.258655 + 0.448003i
\(528\) 0 0
\(529\) −9.52516 + 16.4981i −0.414138 + 0.717307i
\(530\) 2.25067 + 1.63521i 0.0977628 + 0.0710289i
\(531\) 0 0
\(532\) 8.83197 + 27.1820i 0.382915 + 1.17849i
\(533\) −32.3557 + 3.40073i −1.40148 + 0.147302i
\(534\) 0 0
\(535\) −0.373830 0.336598i −0.0161621 0.0145524i
\(536\) −2.64417 + 0.562035i −0.114211 + 0.0242762i
\(537\) 0 0
\(538\) −10.8502 6.26435i −0.467784 0.270075i
\(539\) 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 \(0.132741\pi\)
\(542\) −18.3724 + 16.5426i −0.789163 + 0.710565i
\(543\) 0 0
\(544\) 12.9681 + 5.77378i 0.556003 + 0.247549i
\(545\) 16.1138 + 7.17434i 0.690240 + 0.307315i
\(546\) 0 0
\(547\) −5.78545 + 5.20924i −0.247368 + 0.222731i −0.783482 0.621414i \(-0.786558\pi\)
0.536114 + 0.844146i \(0.319892\pi\)
\(548\) −13.0215 + 17.9225i −0.556250 + 0.765613i
\(549\) 0 0
\(550\) −15.9978 + 14.2143i −0.682147 + 0.606100i
\(551\) −6.70882 3.87334i −0.285805 0.165010i
\(552\) 0 0
\(553\) −18.0949 + 3.84619i −0.769474 + 0.163557i
\(554\) −15.7165 14.1512i −0.667729 0.601225i
\(555\) 0 0
\(556\) 13.3264 1.40066i 0.565167 0.0594014i
\(557\) −1.09093 3.35755i −0.0462244 0.142264i 0.925281 0.379283i \(-0.123829\pi\)
−0.971505 + 0.237019i \(0.923829\pi\)
\(558\) 0 0
\(559\) 9.38378 + 6.81772i 0.396892 + 0.288359i
\(560\) 14.2948 24.7594i 0.604067 1.04627i
\(561\) 0 0
\(562\) 19.8149 + 34.3204i 0.835841 + 1.44772i
\(563\) 0.157070 1.49442i 0.00661970 0.0629822i −0.990713 0.135967i \(-0.956586\pi\)
0.997333 + 0.0729849i \(0.0232525\pi\)
\(564\) 0 0
\(565\) 3.75732 + 0.798643i 0.158072 + 0.0335992i
\(566\) 25.0367 + 34.4601i 1.05237 + 1.44847i
\(567\) 0 0
\(568\) 4.69506 1.52552i 0.197000 0.0640093i
\(569\) 9.92854 + 11.0268i 0.416226 + 0.462266i 0.914400 0.404811i \(-0.132663\pi\)
−0.498174 + 0.867077i \(0.665996\pi\)
\(570\) 0 0
\(571\) 25.8594 14.9299i 1.08218 0.624798i 0.150697 0.988580i \(-0.451848\pi\)
0.931484 + 0.363782i \(0.118515\pi\)
\(572\) 3.97084 + 12.5012i 0.166029 + 0.522703i
\(573\) 0 0
\(574\) 37.9878 + 85.3221i 1.58558 + 3.56128i
\(575\) −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 \(0.478196\pi\)
\(578\) 2.27639 + 21.6584i 0.0946854 + 0.900871i
\(579\) 0 0
\(580\) −0.547613 2.57632i −0.0227384 0.106976i
\(581\) −34.9991 3.67855i −1.45201 0.152612i
\(582\) 0 0
\(583\) −2.09159 3.67863i −0.0866250 0.152353i
\(584\) 9.04432i 0.374256i
\(585\) 0 0
\(586\) −0.951344 + 2.92793i −0.0392996 + 0.120952i
\(587\) −4.91248 + 23.1114i −0.202760 + 0.953910i 0.752603 + 0.658475i \(0.228798\pi\)
−0.955363 + 0.295436i \(0.904535\pi\)
\(588\) 0 0
\(589\) 9.86919 22.1666i 0.406653 0.913358i
\(590\) −0.0461042 + 0.0512039i −0.00189808 + 0.00210803i
\(591\) 0 0
\(592\) −5.01030 + 2.23073i −0.205922 + 0.0916824i
\(593\) 10.1681 0.417553 0.208777 0.977963i \(-0.433052\pi\)
0.208777 + 0.977963i \(0.433052\pi\)
\(594\) 0 0
\(595\) −13.0056 −0.533178
\(596\) 0.0477687 0.0212680i 0.00195668 0.000871171i
\(597\) 0 0
\(598\) −7.38360 + 8.20032i −0.301938 + 0.335336i
\(599\) −2.47923 + 5.56843i −0.101298 + 0.227520i −0.957084 0.289811i \(-0.906408\pi\)
0.855786 + 0.517331i \(0.173074\pi\)
\(600\) 0 0
\(601\) −2.91575 + 13.7175i −0.118936 + 0.559550i 0.877815 + 0.479001i \(0.159001\pi\)
−0.996751 + 0.0805495i \(0.974333\pi\)
\(602\) 10.2896 31.6680i 0.419371 1.29069i
\(603\) 0 0
\(604\) 3.55632i 0.144705i
\(605\) −12.6241 + 3.91829i −0.513242 + 0.159301i
\(606\) 0 0
\(607\) 0.841863 + 0.0884833i 0.0341701 + 0.00359143i 0.121598 0.992579i \(-0.461198\pi\)
−0.0874280 + 0.996171i \(0.527865\pi\)
\(608\) −6.03029 28.3703i −0.244561 1.15057i
\(609\) 0 0
\(610\) −0.270605 2.57463i −0.0109565 0.104244i
\(611\) −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 \(0.771403\pi\)
\(614\) −1.73644 3.90011i −0.0700770 0.157395i
\(615\) 0 0
\(616\) −16.7570 + 12.0064i −0.675158 + 0.483753i
\(617\) −8.73291 + 5.04195i −0.351574 + 0.202981i −0.665378 0.746507i \(-0.731730\pi\)
0.313805 + 0.949488i \(0.398396\pi\)
\(618\) 0 0
\(619\) −17.4316 19.3597i −0.700635 0.778134i 0.282842 0.959166i \(-0.408723\pi\)
−0.983477 + 0.181033i \(0.942056\pi\)
\(620\) 7.84611 2.54935i 0.315107 0.102385i
\(621\) 0 0
\(622\) 11.3121 + 15.5698i 0.453574 + 0.624291i
\(623\) −48.7156 10.3548i −1.95175 0.414857i
\(624\) 0 0
\(625\) −0.567118 + 5.39577i −0.0226847 + 0.215831i
\(626\) 22.9845 + 39.8103i 0.918646 + 1.59114i
\(627\) 0 0
\(628\) −1.36344 + 2.36155i −0.0544073 + 0.0942362i
\(629\) 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 \(0.828751\pi\)
\(632\) 4.87904 0.512807i 0.194078 0.0203984i
\(633\) 0 0
\(634\) −36.1551 32.5542i −1.43590 1.29289i
\(635\) −26.2137 + 5.57190i −1.04026 + 0.221114i
\(636\) 0 0
\(637\) −43.5588 25.1487i −1.72586 0.996426i
\(638\) −2.18783 + 9.96884i −0.0866172 + 0.394670i
\(639\) 0 0
\(640\) −6.80053 + 9.36013i −0.268815 + 0.369991i
\(641\) 8.20366 7.38661i 0.324025 0.291754i −0.491023 0.871146i \(-0.663377\pi\)
0.815048 + 0.579393i \(0.196710\pi\)
\(642\) 0 0
\(643\) 33.5638 + 14.9436i 1.32363 + 0.589317i 0.942190 0.335078i \(-0.108763\pi\)
0.381437 + 0.924395i \(0.375429\pi\)
\(644\) 11.3599 + 5.05776i 0.447643 + 0.199304i
\(645\) 0 0
\(646\) −13.7703 + 12.3988i −0.541784 + 0.487824i
\(647\) −1.59821 + 2.19975i −0.0628321 + 0.0864810i −0.839277 0.543705i \(-0.817021\pi\)
0.776445 + 0.630186i \(0.217021\pi\)
\(648\) 0 0
\(649\) 0.0960246 0.0419955i 0.00376930 0.00164847i
\(650\) 17.0991 + 9.87215i 0.670681 + 0.387218i
\(651\) 0 0
\(652\) −18.4525 + 3.92219i −0.722655 + 0.153605i
\(653\) 32.8807 + 29.6059i 1.28672 + 1.15857i 0.978272 + 0.207327i \(0.0664764\pi\)
0.308448 + 0.951241i \(0.400190\pi\)
\(654\) 0 0
\(655\) −18.5226 + 1.94681i −0.723739 + 0.0760681i
\(656\) −16.1465 49.6939i −0.630416 1.94022i
\(657\) 0 0
\(658\) 23.2048 + 16.8593i 0.904618 + 0.657244i
\(659\) −4.58714 + 7.94516i −0.178690 + 0.309499i −0.941432 0.337203i \(-0.890519\pi\)
0.762742 + 0.646702i \(0.223852\pi\)
\(660\) 0 0
\(661\) 4.94816 + 8.57046i 0.192461 + 0.333352i 0.946065 0.323976i \(-0.105020\pi\)
−0.753604 + 0.657328i \(0.771686\pi\)
\(662\) 3.28575 31.2618i 0.127704 1.21503i
\(663\) 0 0
\(664\) 9.12882 + 1.94039i 0.354267 + 0.0753018i
\(665\) 15.6193 + 21.4981i 0.605691 + 0.833662i
\(666\) 0 0
\(667\) −3.20547 + 1.04152i −0.124116 + 0.0403278i
\(668\) 0.771649 + 0.857003i 0.0298560 + 0.0331584i
\(669\) 0 0
\(670\) 3.97588 2.29547i 0.153602 0.0886819i
\(671\) −1.24156 + 3.73700i −0.0479300 + 0.144265i
\(672\) 0 0
\(673\) −7.19227 16.1541i −0.277242 0.622695i 0.720232 0.693733i \(-0.244035\pi\)
−0.997474 + 0.0710383i \(0.977369\pi\)
\(674\) 22.4408 + 7.29146i 0.864387 + 0.280856i
\(675\) 0 0
\(676\) −3.80243 + 2.76263i −0.146247 + 0.106255i
\(677\) 1.24345 + 11.8306i 0.0477895 + 0.454687i 0.992083 + 0.125583i \(0.0400800\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(678\) 0 0
\(679\) −14.5995 68.6853i −0.560278 2.63590i
\(680\) 3.43015 + 0.360523i 0.131540 + 0.0138254i
\(681\) 0 0
\(682\) −31.7699 3.55138i −1.21653 0.135989i
\(683\) 18.2564i 0.698561i 0.937018 + 0.349280i \(0.113574\pi\)
−0.937018 + 0.349280i \(0.886426\pi\)
\(684\) 0 0
\(685\) −6.36490 + 19.5892i −0.243190 + 0.748463i
\(686\) −17.2359 + 81.0883i −0.658068 + 3.09597i
\(687\) 0 0
\(688\) −7.57693 + 17.0181i −0.288868 + 0.648808i
\(689\) −2.61243 + 2.90139i −0.0995255 + 0.110534i
\(690\) 0 0
\(691\) 16.4659 7.33107i 0.626391 0.278887i −0.0688913 0.997624i \(-0.521946\pi\)
0.695282 + 0.718737i \(0.255279\pi\)
\(692\) 17.1216 0.650864
\(693\) 0 0
\(694\) 38.5698 1.46409
\(695\) 11.3814 5.06735i 0.431723 0.192215i
\(696\) 0 0
\(697\) −15.9048 + 17.6641i −0.602438 + 0.669075i
\(698\) −6.88652 + 15.4674i −0.260659 + 0.585449i
\(699\) 0 0
\(700\) 4.62603 21.7638i 0.174847 0.822593i
\(701\) 2.60431 8.01524i 0.0983635 0.302732i −0.889752 0.456444i \(-0.849123\pi\)
0.988116 + 0.153712i \(0.0491229\pi\)
\(702\) 0 0
\(703\) 5.09762i 0.192260i
\(704\) −4.87977 + 2.77454i −0.183913 + 0.104569i
\(705\) 0 0
\(706\) −16.4602 1.73004i −0.619488 0.0651108i
\(707\) −16.1909 76.1723i −0.608923 2.86476i
\(708\) 0 0
\(709\) −2.16511 20.5997i −0.0813126 0.773637i −0.956869 0.290521i \(-0.906171\pi\)
0.875556 0.483116i \(-0.160495\pi\)
\(710\) −6.78282 + 4.92801i −0.254555 + 0.184945i
\(711\) 0 0
\(712\) 12.5614 + 4.08144i 0.470758 + 0.152959i
\(713\) −4.29389 9.64424i −0.160808 0.361180i
\(714\) 0 0
\(715\) 7.10293 + 9.91333i 0.265634 + 0.370738i
\(716\) −22.5476 + 13.0179i −0.842644 + 0.486501i
\(717\) 0 0
\(718\) 9.49619 + 10.5466i 0.354395 + 0.393595i
\(719\) 34.3009 11.1450i 1.27921 0.415640i 0.410906 0.911678i \(-0.365212\pi\)
0.868301 + 0.496038i \(0.165212\pi\)
\(720\) 0 0
\(721\) 5.92214 + 8.15112i 0.220552 + 0.303564i
\(722\) 3.31044 + 0.703656i 0.123202 + 0.0261874i
\(723\) 0 0
\(724\) 0.607437 5.77937i 0.0225752 0.214789i
\(725\) 3.01536 + 5.22276i 0.111988 + 0.193968i
\(726\) 0 0
\(727\) 10.4928 18.1741i 0.389158 0.674042i −0.603178 0.797606i \(-0.706099\pi\)
0.992337 + 0.123565i \(0.0394327\pi\)
\(728\) 15.3868 + 11.1792i 0.570273 + 0.414327i
\(729\) 0 0
\(730\) −4.74653 14.6083i −0.175677 0.540678i
\(731\) 8.42783 0.885800i 0.311714 0.0327625i
\(732\) 0 0
\(733\) −30.1889 27.1822i −1.11505 1.00400i −0.999943 0.0106457i \(-0.996611\pi\)
−0.115110 0.993353i \(-0.536722\pi\)
\(734\) −43.4916 + 9.24443i −1.60531 + 0.341218i
\(735\) 0 0
\(736\) −10.9285 6.30956i −0.402829 0.232573i
\(737\) −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 \(0.201591\pi\)
\(740\) 1.28801 1.15973i 0.0473483 0.0426326i
\(741\) 0 0
\(742\) 10.2390 + 4.55870i 0.375886 + 0.167355i
\(743\) 18.7849 + 8.36360i 0.689153 + 0.306831i 0.721271 0.692653i \(-0.243558\pi\)
−0.0321177 + 0.999484i \(0.510225\pi\)
\(744\) 0 0
\(745\) 0.0361289 0.0325306i 0.00132366 0.00119183i
\(746\) −3.05169 + 4.20029i −0.111730 + 0.153783i
\(747\) 0 0
\(748\) 8.26740 + 4.84624i 0.302286 + 0.177196i
\(749\) −1.75511 1.01331i −0.0641304 0.0370257i
\(750\) 0 0
\(751\) 50.9801 10.8362i 1.86029 0.395417i 0.865814 0.500366i \(-0.166801\pi\)
0.994478 + 0.104949i \(0.0334678\pi\)
\(752\) −11.9250 10.7374i −0.434861 0.391551i
\(753\) 0 0
\(754\) 9.36473 0.984272i 0.341043 0.0358451i
\(755\) 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 \(0.462535\pi\)
\(758\) 26.5495 45.9851i 0.964322 1.67025i
\(759\) 0 0
\(760\) −3.52355 6.10297i −0.127813 0.221378i
\(761\) 4.66624 44.3963i 0.169151 1.60936i −0.499856 0.866109i \(-0.666614\pi\)
0.669007 0.743256i \(-0.266720\pi\)
\(762\) 0 0
\(763\) 69.5098 + 14.7748i 2.51642 + 0.534883i
\(764\) 13.5025 + 18.5846i 0.488503 + 0.672367i
\(765\) 0 0
\(766\) −49.1124 + 15.9576i −1.77450 + 0.576571i
\(767\) −0.0647022 0.0718591i −0.00233626 0.00259468i
\(768\) 0 0
\(769\) 19.3337 11.1623i 0.697192 0.402524i −0.109109 0.994030i \(-0.534800\pi\)
0.806301 + 0.591506i \(0.201466\pi\)
\(770\) 20.7647 28.1869i 0.748308 1.01579i
\(771\) 0 0
\(772\) −3.23767 7.27192i −0.116526 0.261722i
\(773\) −19.1268 6.21468i −0.687944 0.223526i −0.0558738 0.998438i \(-0.517794\pi\)
−0.632070 + 0.774911i \(0.717794\pi\)
\(774\) 0 0
\(775\) −15.2820 + 11.1030i −0.548946 + 0.398832i
\(776\) 1.94653 + 18.5200i 0.0698765 + 0.664830i
\(777\) 0 0
\(778\) −5.38778 25.3475i −0.193161 0.908753i
\(779\) 48.2998 + 5.07651i 1.73052 + 0.181885i
\(780\) 0 0
\(781\) 12.4915 2.56907i 0.446981 0.0919285i
\(782\) 8.06192i 0.288294i
\(783\) 0 0
\(784\) 24.9624 76.8265i 0.891516 2.74380i
\(785\) −0.527125 + 2.47993i −0.0188139 + 0.0885124i
\(786\) 0 0
\(787\) −14.1620 + 31.8083i −0.504820 + 1.13384i 0.463946 + 0.885864i \(0.346433\pi\)
−0.968765 + 0.247980i \(0.920233\pi\)
\(788\) 19.4670 21.6203i 0.693482 0.770190i
\(789\) 0 0
\(790\) −7.61146 + 3.38884i −0.270803 + 0.120569i
\(791\) 15.4756 0.550249
\(792\) 0 0
\(793\) 3.63312 0.129016
\(794\) 3.65819 1.62873i 0.129824 0.0578014i
\(795\) 0 0
\(796\) 8.04865 8.93893i 0.285277 0.316832i
\(797\) −0.319992 + 0.718713i −0.0113347 + 0.0254581i −0.919124 0.393968i \(-0.871102\pi\)
0.907789 + 0.419426i \(0.137769\pi\)
\(798\) 0 0
\(799\) −1.51770 + 7.14022i −0.0536924 + 0.252603i
\(800\) −6.97744 + 21.4743i −0.246690 + 0.759233i
\(801\) 0 0
\(802\) 57.2351i 2.02104i
\(803\) −2.59559 + 23.2196i −0.0915964 + 0.819402i
\(804\) 0 0
\(805\) 11.4981 + 1.20850i 0.405255 + 0.0425941i
\(806\) 6.13215 + 28.8495i 0.215996 + 1.01618i
\(807\) 0 0
\(808\) 2.15871 + 20.5388i 0.0759433 + 0.722552i
\(809\) −24.9035 + 18.0934i −0.875560 + 0.636131i −0.932073 0.362270i \(-0.882002\pi\)
0.0565132 + 0.998402i \(0.482002\pi\)
\(810\) 0 0
\(811\) 41.4535 + 13.4691i 1.45563 + 0.472963i 0.926732 0.375723i \(-0.122606\pi\)
0.528898 + 0.848686i \(0.322606\pi\)
\(812\) −4.31600 9.69390i −0.151462 0.340189i
\(813\) 0 0
\(814\) −6.40087 + 2.03315i −0.224351 + 0.0712617i
\(815\) −15.1897 + 8.76976i −0.532071 + 0.307191i
\(816\) 0 0
\(817\) −11.5858 12.8673i −0.405335 0.450170i
\(818\) 11.6971 3.80063i 0.408981 0.132886i
\(819\) 0 0
\(820\) 9.70574 + 13.3588i 0.338939 + 0.466510i
\(821\) 38.1089 + 8.10030i 1.33001 + 0.282702i 0.817475 0.575964i \(-0.195373\pi\)
0.512535 + 0.858666i \(0.328706\pi\)
\(822\) 0 0
\(823\) −3.92819 + 37.3742i −0.136928 + 1.30278i 0.683042 + 0.730379i \(0.260656\pi\)
−0.819971 + 0.572406i \(0.806010\pi\)
\(824\) −1.33597 2.31397i −0.0465408 0.0806111i
\(825\) 0 0
\(826\) −0.138795 + 0.240399i −0.00482928 + 0.00836456i
\(827\) −36.8905 26.8025i −1.28281 0.932015i −0.283175 0.959068i \(-0.591388\pi\)
−0.999634 + 0.0270532i \(0.991388\pi\)
\(828\) 0 0
\(829\) 8.83146 + 27.1804i 0.306729 + 0.944016i 0.979026 + 0.203734i \(0.0653078\pi\)
−0.672297 + 0.740282i \(0.734692\pi\)
\(830\) −15.7631 + 1.65677i −0.547146 + 0.0575074i
\(831\) 0 0
\(832\) 3.84875 + 3.46543i 0.133431 + 0.120142i
\(833\) −35.9443 + 7.64020i −1.24540 + 0.264717i
\(834\) 0 0
\(835\) 0.928554 + 0.536101i 0.0321339 + 0.0185525i
\(836\) −1.91808 19.4861i −0.0663382 0.673941i
\(837\) 0 0
\(838\) 30.5125 41.9968i 1.05404 1.45076i
\(839\) −4.22962 + 3.80837i −0.146023 + 0.131480i −0.738905 0.673810i \(-0.764657\pi\)
0.592882 + 0.805289i \(0.297990\pi\)
\(840\) 0 0
\(841\) −23.8653 10.6255i −0.822943 0.366398i
\(842\) −9.27164 4.12800i −0.319522 0.142260i
\(843\) 0 0
\(844\) −13.4573 + 12.1170i −0.463220 + 0.417085i
\(845\) −2.56856 + 3.53532i −0.0883612 + 0.121619i
\(846\) 0 0
\(847\) −46.4662 + 26.0153i −1.59660 + 0.893895i
\(848\) −5.43030 3.13518i −0.186477 0.107663i
\(849\) 0 0
\(850\) 14.1100 2.99918i 0.483969 0.102871i
\(851\) −1.64820 1.48405i −0.0564996 0.0508725i
\(852\) 0 0
\(853\) −24.9261 + 2.61983i −0.853452 + 0.0897014i −0.521143 0.853469i \(-0.674494\pi\)
−0.332309 + 0.943171i \(0.607828\pi\)
\(854\) −3.22297 9.91929i −0.110288 0.339431i
\(855\) 0 0
\(856\) 0.434810 + 0.315908i 0.0148615 + 0.0107975i
\(857\) 17.9582 31.1045i 0.613440 1.06251i −0.377216 0.926126i \(-0.623118\pi\)
0.990656 0.136385i \(-0.0435483\pi\)
\(858\) 0 0
\(859\) 7.86620 + 13.6247i 0.268391 + 0.464868i 0.968447 0.249221i \(-0.0801746\pi\)
−0.700055 + 0.714089i \(0.746841\pi\)
\(860\) 0.615358 5.85474i 0.0209835 0.199645i
\(861\) 0 0
\(862\) −34.6244 7.35963i −1.17931 0.250670i
\(863\) −16.0883 22.1436i −0.547652 0.753778i 0.442039 0.896996i \(-0.354255\pi\)
−0.989691 + 0.143217i \(0.954255\pi\)
\(864\) 0 0
\(865\) 15.1397 4.91919i 0.514765 0.167257i
\(866\) −27.3824 30.4112i −0.930491 1.03342i
\(867\) 0 0
\(868\) 28.7841 16.6185i 0.976995 0.564068i
\(869\) 12.6732 + 0.0836764i 0.429909 + 0.00283853i
\(870\) 0 0
\(871\) 2.62057 + 5.88589i 0.0887945 + 0.199436i
\(872\) −17.9232 5.82361i −0.606957 0.197212i
\(873\) 0 0
\(874\) 13.3263 9.68210i 0.450768 0.327502i
\(875\) −5.20282 49.5015i −0.175887 1.67346i
\(876\) 0 0
\(877\) −10.8203 50.9056i −0.365376 1.71896i −0.649665 0.760221i \(-0.725091\pi\)
0.284289 0.958739i \(-0.408242\pi\)
\(878\) 54.1137 + 5.68757i 1.82625 + 0.191946i
\(879\) 0 0
\(880\) −13.2016 + 14.4686i −0.445027 + 0.487737i
\(881\) 39.9758i 1.34682i −0.739270 0.673409i \(-0.764829\pi\)
0.739270 0.673409i \(-0.235171\pi\)
\(882\) 0 0
\(883\) −5.74452 + 17.6798i −0.193318 + 0.594973i 0.806674 + 0.590997i \(0.201266\pi\)
−0.999992 + 0.00397571i \(0.998734\pi\)
\(884\) 1.83826 8.64832i 0.0618273 0.290875i
\(885\) 0 0
\(886\) 23.2830 52.2944i 0.782206 1.75686i
\(887\) −36.4857 + 40.5215i −1.22507 + 1.36058i −0.313419 + 0.949615i \(0.601474\pi\)
−0.911652 + 0.410964i \(0.865192\pi\)
\(888\) 0 0
\(889\) −98.6344 + 43.9149i −3.30809 + 1.47286i
\(890\) −22.4310 −0.751890
\(891\) 0 0
\(892\) −20.8507 −0.698132
\(893\) 13.6254 6.06643i 0.455958 0.203005i
\(894\) 0 0
\(895\) −16.1975 + 17.9892i −0.541424 + 0.601312i
\(896\) −18.9588 + 42.5822i −0.633369 + 1.42257i
\(897\) 0 0
\(898\) −14.3360 + 67.4457i −0.478399 + 2.25069i
\(899\) −2.78384 + 8.56777i −0.0928461 + 0.285751i
\(900\) 0 0
\(901\) 2.85243i 0.0950281i
\(902\) −12.8896 62.6728i −0.429177 2.08678i
\(903\) 0 0
\(904\) −4.08159 0.428993i −0.135752 0.0142681i
\(905\) −1.12334 5.28492i −0.0373412 0.175677i
\(906\) 0 0
\(907\) 1.29961 + 12.3650i 0.0431530 + 0.410573i 0.994680 + 0.103009i \(0.0328471\pi\)
−0.951527 + 0.307564i \(0.900486\pi\)
\(908\) 15.3860 11.1786i 0.510603 0.370975i
\(909\) 0 0
\(910\) −30.7195 9.98139i −1.01834 0.330880i
\(911\) 18.2983 + 41.0986i 0.606249 + 1.36166i 0.912253 + 0.409628i \(0.134341\pi\)
−0.306004 + 0.952030i \(0.598992\pi\)
\(912\) 0 0
\(913\) 22.8797 + 7.60144i 0.757208 + 0.251571i
\(914\) 61.6402 35.5880i 2.03887 1.17715i
\(915\) 0 0
\(916\) 19.1980 + 21.3215i 0.634319 + 0.704483i
\(917\) −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 \(0.675187\pi\)
\(920\) −2.99906 0.637469i −0.0988760 0.0210167i
\(921\) 0 0
\(922\) 3.32907 31.6740i 0.109637 1.04313i
\(923\) −5.88304 10.1897i −0.193643 0.335399i
\(924\) 0 0
\(925\) −1.98423 + 3.43678i −0.0652410 + 0.113001i
\(926\) −7.44610 5.40991i −0.244694 0.177781i
\(927\) 0 0
\(928\) 3.32763 + 10.2414i 0.109235 + 0.336190i
\(929\) 11.5041 1.20913i 0.377438 0.0396703i 0.0860898 0.996287i \(-0.472563\pi\)
0.291348 + 0.956617i \(0.405896\pi\)
\(930\) 0 0
\(931\) 55.7971 + 50.2400i 1.82868 + 1.64655i
\(932\) 6.53392 1.38883i 0.214026 0.0454926i
\(933\) 0 0
\(934\) 26.6487 + 15.3856i 0.871971 + 0.503433i
\(935\) 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 \(0.0616326\pi\)
\(938\) 13.7451 12.3762i 0.448795 0.404097i
\(939\) 0 0
\(940\) 4.63265 + 2.06259i 0.151100 + 0.0672743i
\(941\) −54.0436 24.0617i −1.76177 0.784391i −0.988670 0.150107i \(-0.952038\pi\)
−0.773100 0.634284i \(-0.781295\pi\)
\(942\) 0 0
\(943\) 15.7027 14.1387i 0.511349 0.460421i
\(944\) 0.0912824 0.125639i 0.00297099 0.00408921i
\(945\) 0 0
\(946\) −11.5361 + 19.6798i −0.375069 + 0.639845i
\(947\) −0.104615 0.0603997i −0.00339954 0.00196272i 0.498299 0.867005i \(-0.333958\pi\)
−0.501699 + 0.865042i \(0.667291\pi\)
\(948\) 0 0
\(949\) 21.0852 4.48179i 0.684454 0.145485i
\(950\) −21.9033 19.7218i −0.710636 0.639860i
\(951\) 0 0
\(952\) 13.8193 1.45247i 0.447886 0.0470747i
\(953\) 2.50261 + 7.70223i 0.0810674 + 0.249500i 0.983373 0.181597i \(-0.0581267\pi\)
−0.902306 + 0.431097i \(0.858127\pi\)
\(954\) 0 0
\(955\) 17.2791 + 12.5540i 0.559138 + 0.406237i
\(956\) 8.83074 15.2953i 0.285607 0.494685i
\(957\) 0 0
\(958\) −16.4028 28.4104i −0.529949 0.917899i
\(959\) −8.67396 + 82.5272i −0.280097 + 2.66494i
\(960\) 0 0
\(961\) 2.72196 + 0.578570i 0.0878050 + 0.0186635i
\(962\) 3.64210 + 5.01292i 0.117426 + 0.161623i
\(963\) 0 0
\(964\) 8.66885 2.81668i 0.279205 0.0907192i
\(965\) −4.95219 5.49997i −0.159417 0.177050i
\(966\) 0 0
\(967\) −8.61320 + 4.97284i −0.276982 + 0.159916i −0.632056 0.774922i \(-0.717789\pi\)
0.355074 + 0.934838i \(0.384456\pi\)
\(968\) 12.9763 5.57330i 0.417075 0.179133i
\(969\) 0 0
\(970\) −12.8635 28.8918i −0.413021 0.927661i
\(971\) 36.6171 + 11.8976i 1.17510 + 0.381813i 0.830544 0.556953i \(-0.188030\pi\)
0.344555 + 0.938766i \(0.388030\pi\)
\(972\) 0 0
\(973\) 40.6068 29.5025i 1.30179 0.945808i
\(974\) 4.93170 + 46.9220i 0.158022 + 1.50348i
\(975\) 0 0
\(976\) 1.21316 + 5.70748i 0.0388324 + 0.182692i
\(977\) 20.2002 + 2.12313i 0.646263 + 0.0679250i 0.421989 0.906601i \(-0.361332\pi\)
0.224274 + 0.974526i \(0.427999\pi\)
\(978\) 0 0
\(979\) 31.0777 + 14.0833i 0.993249 + 0.450104i
\(980\) 25.5281i 0.815464i
\(981\) 0 0
\(982\) −4.11112 + 12.6527i −0.131191 + 0.403765i
\(983\) −2.02155 + 9.51064i −0.0644774 + 0.303342i −0.998556 0.0537258i \(-0.982890\pi\)
0.934078 + 0.357068i \(0.116224\pi\)
\(984\) 0 0
\(985\) 11.0019 24.7107i 0.350550 0.787349i
\(986\) 4.60334 5.11252i 0.146600 0.162816i
\(987\) 0 0
\(988\) −16.5033 + 7.34773i −0.525039 + 0.233763i
\(989\) −7.53327 −0.239544
\(990\) 0 0
\(991\) −22.9196 −0.728065 −0.364032 0.931386i \(-0.618600\pi\)
−0.364032 + 0.931386i \(0.618600\pi\)
\(992\) −30.8131 + 13.7189i −0.978317 + 0.435575i
\(993\) 0 0
\(994\) −22.6015 + 25.1015i −0.716876 + 0.796171i
\(995\) 4.54876 10.2167i 0.144205 0.323891i
\(996\) 0 0
\(997\) 4.47047 21.0319i 0.141581 0.666087i −0.848913 0.528532i \(-0.822743\pi\)
0.990494 0.137554i \(-0.0439242\pi\)
\(998\) −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 297.2.t.a.62.8 80
3.2 odd 2 99.2.p.a.29.3 80
9.2 odd 6 891.2.k.a.161.16 80
9.4 even 3 99.2.p.a.95.3 yes 80
9.5 odd 6 inner 297.2.t.a.260.8 80
9.7 even 3 891.2.k.a.161.5 80
11.8 odd 10 inner 297.2.t.a.8.8 80
33.8 even 10 99.2.p.a.74.3 yes 80
99.41 even 30 inner 297.2.t.a.206.8 80
99.52 odd 30 891.2.k.a.404.16 80
99.74 even 30 891.2.k.a.404.5 80
99.85 odd 30 99.2.p.a.41.3 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.29.3 80 3.2 odd 2
99.2.p.a.41.3 yes 80 99.85 odd 30
99.2.p.a.74.3 yes 80 33.8 even 10
99.2.p.a.95.3 yes 80 9.4 even 3
297.2.t.a.8.8 80 11.8 odd 10 inner
297.2.t.a.62.8 80 1.1 even 1 trivial
297.2.t.a.206.8 80 99.41 even 30 inner
297.2.t.a.260.8 80 9.5 odd 6 inner
891.2.k.a.161.5 80 9.7 even 3
891.2.k.a.161.16 80 9.2 odd 6
891.2.k.a.404.5 80 99.74 even 30
891.2.k.a.404.16 80 99.52 odd 30