Properties

Label 819.2.fm.f.370.6
Level $819$
Weight $2$
Character 819.370
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(370,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.370");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), 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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 370.6
Character \(\chi\) \(=\) 819.370
Dual form 819.2.fm.f.622.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.281068 + 1.04896i) q^{2} +(0.710736 - 0.410344i) q^{4} +(-1.02734 - 1.02734i) q^{5} +(-1.22381 - 2.34570i) q^{7} +(2.16598 + 2.16598i) q^{8} +O(q^{10})\) \(q+(0.281068 + 1.04896i) q^{2} +(0.710736 - 0.410344i) q^{4} +(-1.02734 - 1.02734i) q^{5} +(-1.22381 - 2.34570i) q^{7} +(2.16598 + 2.16598i) q^{8} +(0.788887 - 1.36639i) q^{10} +(-0.972198 + 0.260500i) q^{11} +(3.05530 - 1.91446i) q^{13} +(2.11656 - 1.94303i) q^{14} +(-0.842549 + 1.45934i) q^{16} +(-2.37035 - 4.10557i) q^{17} +(-0.391878 + 1.46251i) q^{19} +(-1.15173 - 0.308606i) q^{20} +(-0.546507 - 0.946578i) q^{22} +(0.337046 + 0.194594i) q^{23} -2.88914i q^{25} +(2.86693 + 2.66679i) q^{26} +(-1.83235 - 1.16499i) q^{28} +(4.30065 - 7.44895i) q^{29} +(-2.92542 - 2.92542i) q^{31} +(4.14997 + 1.11198i) q^{32} +(3.64034 - 3.64034i) q^{34} +(-1.15256 + 3.66710i) q^{35} +(9.77690 - 2.61971i) q^{37} -1.64425 q^{38} -4.45041i q^{40} +(8.64616 - 2.31673i) q^{41} +(-8.28885 + 4.78557i) q^{43} +(-0.584082 + 0.584082i) q^{44} +(-0.109388 + 0.408241i) q^{46} +(4.78928 - 4.78928i) q^{47} +(-4.00458 + 5.74137i) q^{49} +(3.03058 - 0.812042i) q^{50} +(1.38592 - 2.61440i) q^{52} -12.7329 q^{53} +(1.26640 + 0.731158i) q^{55} +(2.42998 - 7.73148i) q^{56} +(9.02241 + 2.41755i) q^{58} +(0.889636 + 0.238377i) q^{59} +(-8.36449 + 4.82924i) q^{61} +(2.24640 - 3.89088i) q^{62} +8.03588i q^{64} +(-5.10564 - 1.17203i) q^{65} +(1.71328 + 6.39405i) q^{67} +(-3.36939 - 1.94532i) q^{68} +(-4.17059 - 0.178284i) q^{70} +(2.56663 + 0.687727i) q^{71} +(2.46596 - 2.46596i) q^{73} +(5.49594 + 9.51925i) q^{74} +(0.321609 + 1.20026i) q^{76} +(1.80084 + 1.96168i) q^{77} +7.06532 q^{79} +(2.36483 - 0.633653i) q^{80} +(4.86031 + 8.41830i) q^{82} +(2.43414 + 2.43414i) q^{83} +(-1.78266 + 6.65299i) q^{85} +(-7.34959 - 7.34959i) q^{86} +(-2.67000 - 1.54152i) q^{88} +(2.79345 + 10.4253i) q^{89} +(-8.22984 - 4.82387i) q^{91} +0.319401 q^{92} +(6.36986 + 3.67764i) q^{94} +(1.90509 - 1.09990i) q^{95} +(-3.55710 + 13.2753i) q^{97} +(-7.14802 - 2.58692i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.281068 + 1.04896i 0.198745 + 0.741726i 0.991266 + 0.131881i \(0.0421016\pi\)
−0.792521 + 0.609845i \(0.791232\pi\)
\(3\) 0 0
\(4\) 0.710736 0.410344i 0.355368 0.205172i
\(5\) −1.02734 1.02734i −0.459441 0.459441i 0.439031 0.898472i \(-0.355322\pi\)
−0.898472 + 0.439031i \(0.855322\pi\)
\(6\) 0 0
\(7\) −1.22381 2.34570i −0.462557 0.886590i
\(8\) 2.16598 + 2.16598i 0.765790 + 0.765790i
\(9\) 0 0
\(10\) 0.788887 1.36639i 0.249468 0.432091i
\(11\) −0.972198 + 0.260500i −0.293129 + 0.0785436i −0.402387 0.915470i \(-0.631819\pi\)
0.109258 + 0.994013i \(0.465153\pi\)
\(12\) 0 0
\(13\) 3.05530 1.91446i 0.847387 0.530975i
\(14\) 2.11656 1.94303i 0.565676 0.519295i
\(15\) 0 0
\(16\) −0.842549 + 1.45934i −0.210637 + 0.364834i
\(17\) −2.37035 4.10557i −0.574895 0.995747i −0.996053 0.0887595i \(-0.971710\pi\)
0.421159 0.906987i \(-0.361624\pi\)
\(18\) 0 0
\(19\) −0.391878 + 1.46251i −0.0899030 + 0.335522i −0.996197 0.0871243i \(-0.972232\pi\)
0.906294 + 0.422647i \(0.138899\pi\)
\(20\) −1.15173 0.308606i −0.257535 0.0690064i
\(21\) 0 0
\(22\) −0.546507 0.946578i −0.116516 0.201811i
\(23\) 0.337046 + 0.194594i 0.0702790 + 0.0405756i 0.534728 0.845024i \(-0.320414\pi\)
−0.464449 + 0.885600i \(0.653748\pi\)
\(24\) 0 0
\(25\) 2.88914i 0.577827i
\(26\) 2.86693 + 2.66679i 0.562252 + 0.523000i
\(27\) 0 0
\(28\) −1.83235 1.16499i −0.346281 0.220162i
\(29\) 4.30065 7.44895i 0.798611 1.38324i −0.121909 0.992541i \(-0.538902\pi\)
0.920521 0.390694i \(-0.127765\pi\)
\(30\) 0 0
\(31\) −2.92542 2.92542i −0.525420 0.525420i 0.393783 0.919203i \(-0.371166\pi\)
−0.919203 + 0.393783i \(0.871166\pi\)
\(32\) 4.14997 + 1.11198i 0.733618 + 0.196572i
\(33\) 0 0
\(34\) 3.64034 3.64034i 0.624313 0.624313i
\(35\) −1.15256 + 3.66710i −0.194818 + 0.619854i
\(36\) 0 0
\(37\) 9.77690 2.61971i 1.60731 0.430678i 0.660072 0.751202i \(-0.270526\pi\)
0.947240 + 0.320524i \(0.103859\pi\)
\(38\) −1.64425 −0.266733
\(39\) 0 0
\(40\) 4.45041i 0.703671i
\(41\) 8.64616 2.31673i 1.35030 0.361813i 0.490056 0.871691i \(-0.336976\pi\)
0.860247 + 0.509878i \(0.170310\pi\)
\(42\) 0 0
\(43\) −8.28885 + 4.78557i −1.26404 + 0.729792i −0.973853 0.227179i \(-0.927050\pi\)
−0.290184 + 0.956971i \(0.593717\pi\)
\(44\) −0.584082 + 0.584082i −0.0880537 + 0.0880537i
\(45\) 0 0
\(46\) −0.109388 + 0.408241i −0.0161284 + 0.0601919i
\(47\) 4.78928 4.78928i 0.698588 0.698588i −0.265518 0.964106i \(-0.585543\pi\)
0.964106 + 0.265518i \(0.0855430\pi\)
\(48\) 0 0
\(49\) −4.00458 + 5.74137i −0.572082 + 0.820196i
\(50\) 3.03058 0.812042i 0.428589 0.114840i
\(51\) 0 0
\(52\) 1.38592 2.61440i 0.192193 0.362552i
\(53\) −12.7329 −1.74900 −0.874498 0.485029i \(-0.838809\pi\)
−0.874498 + 0.485029i \(0.838809\pi\)
\(54\) 0 0
\(55\) 1.26640 + 0.731158i 0.170762 + 0.0985893i
\(56\) 2.42998 7.73148i 0.324720 1.03316i
\(57\) 0 0
\(58\) 9.02241 + 2.41755i 1.18470 + 0.317440i
\(59\) 0.889636 + 0.238377i 0.115821 + 0.0310341i 0.316264 0.948671i \(-0.397572\pi\)
−0.200443 + 0.979705i \(0.564238\pi\)
\(60\) 0 0
\(61\) −8.36449 + 4.82924i −1.07096 + 0.618321i −0.928445 0.371471i \(-0.878854\pi\)
−0.142519 + 0.989792i \(0.545520\pi\)
\(62\) 2.24640 3.89088i 0.285293 0.494142i
\(63\) 0 0
\(64\) 8.03588i 1.00449i
\(65\) −5.10564 1.17203i −0.633277 0.145373i
\(66\) 0 0
\(67\) 1.71328 + 6.39405i 0.209311 + 0.781158i 0.988092 + 0.153863i \(0.0491713\pi\)
−0.778782 + 0.627295i \(0.784162\pi\)
\(68\) −3.36939 1.94532i −0.408598 0.235904i
\(69\) 0 0
\(70\) −4.17059 0.178284i −0.498481 0.0213090i
\(71\) 2.56663 + 0.687727i 0.304603 + 0.0816182i 0.407883 0.913034i \(-0.366267\pi\)
−0.103280 + 0.994652i \(0.532934\pi\)
\(72\) 0 0
\(73\) 2.46596 2.46596i 0.288619 0.288619i −0.547915 0.836534i \(-0.684578\pi\)
0.836534 + 0.547915i \(0.184578\pi\)
\(74\) 5.49594 + 9.51925i 0.638890 + 1.10659i
\(75\) 0 0
\(76\) 0.321609 + 1.20026i 0.0368911 + 0.137680i
\(77\) 1.80084 + 1.96168i 0.205225 + 0.223554i
\(78\) 0 0
\(79\) 7.06532 0.794911 0.397455 0.917622i \(-0.369893\pi\)
0.397455 + 0.917622i \(0.369893\pi\)
\(80\) 2.36483 0.633653i 0.264396 0.0708446i
\(81\) 0 0
\(82\) 4.86031 + 8.41830i 0.536731 + 0.929646i
\(83\) 2.43414 + 2.43414i 0.267181 + 0.267181i 0.827963 0.560782i \(-0.189499\pi\)
−0.560782 + 0.827963i \(0.689499\pi\)
\(84\) 0 0
\(85\) −1.78266 + 6.65299i −0.193357 + 0.721618i
\(86\) −7.34959 7.34959i −0.792526 0.792526i
\(87\) 0 0
\(88\) −2.67000 1.54152i −0.284623 0.164327i
\(89\) 2.79345 + 10.4253i 0.296105 + 1.10508i 0.940336 + 0.340248i \(0.110511\pi\)
−0.644231 + 0.764831i \(0.722822\pi\)
\(90\) 0 0
\(91\) −8.22984 4.82387i −0.862722 0.505679i
\(92\) 0.319401 0.0332999
\(93\) 0 0
\(94\) 6.36986 + 3.67764i 0.657001 + 0.379320i
\(95\) 1.90509 1.09990i 0.195458 0.112848i
\(96\) 0 0
\(97\) −3.55710 + 13.2753i −0.361169 + 1.34790i 0.511372 + 0.859359i \(0.329137\pi\)
−0.872541 + 0.488541i \(0.837529\pi\)
\(98\) −7.14802 2.58692i −0.722059 0.261318i
\(99\) 0 0
\(100\) −1.18554 2.05341i −0.118554 0.205341i
\(101\) 1.97748 3.42510i 0.196767 0.340810i −0.750711 0.660630i \(-0.770289\pi\)
0.947478 + 0.319820i \(0.103622\pi\)
\(102\) 0 0
\(103\) 12.7709 1.25835 0.629176 0.777263i \(-0.283393\pi\)
0.629176 + 0.777263i \(0.283393\pi\)
\(104\) 10.7644 + 2.47103i 1.05554 + 0.242305i
\(105\) 0 0
\(106\) −3.57880 13.3563i −0.347604 1.29728i
\(107\) −1.79997 + 3.11764i −0.174010 + 0.301394i −0.939818 0.341675i \(-0.889006\pi\)
0.765808 + 0.643069i \(0.222339\pi\)
\(108\) 0 0
\(109\) −0.0623175 + 0.0623175i −0.00596893 + 0.00596893i −0.710085 0.704116i \(-0.751343\pi\)
0.704116 + 0.710085i \(0.251343\pi\)
\(110\) −0.411010 + 1.53391i −0.0391882 + 0.146252i
\(111\) 0 0
\(112\) 4.45428 + 0.190411i 0.420890 + 0.0179922i
\(113\) 1.09268 + 1.89259i 0.102791 + 0.178039i 0.912834 0.408332i \(-0.133889\pi\)
−0.810042 + 0.586371i \(0.800556\pi\)
\(114\) 0 0
\(115\) −0.146347 0.546176i −0.0136470 0.0509312i
\(116\) 7.05898i 0.655410i
\(117\) 0 0
\(118\) 1.00019i 0.0920751i
\(119\) −6.72955 + 10.5846i −0.616897 + 0.970285i
\(120\) 0 0
\(121\) −8.64897 + 4.99349i −0.786270 + 0.453953i
\(122\) −7.41666 7.41666i −0.671473 0.671473i
\(123\) 0 0
\(124\) −3.27962 0.878773i −0.294519 0.0789161i
\(125\) −8.10484 + 8.10484i −0.724919 + 0.724919i
\(126\) 0 0
\(127\) −12.3666 7.13987i −1.09736 0.633561i −0.161834 0.986818i \(-0.551741\pi\)
−0.935526 + 0.353257i \(0.885074\pi\)
\(128\) −0.129367 + 0.0346639i −0.0114346 + 0.00306389i
\(129\) 0 0
\(130\) −0.205617 5.68503i −0.0180338 0.498610i
\(131\) 17.8888i 1.56295i 0.623934 + 0.781477i \(0.285533\pi\)
−0.623934 + 0.781477i \(0.714467\pi\)
\(132\) 0 0
\(133\) 3.91018 0.870606i 0.339056 0.0754912i
\(134\) −6.22555 + 3.59432i −0.537805 + 0.310502i
\(135\) 0 0
\(136\) 3.75845 14.0267i 0.322284 1.20278i
\(137\) 0.654988 2.44445i 0.0559594 0.208843i −0.932285 0.361724i \(-0.882188\pi\)
0.988245 + 0.152881i \(0.0488550\pi\)
\(138\) 0 0
\(139\) 8.86338 5.11727i 0.751782 0.434041i −0.0745556 0.997217i \(-0.523754\pi\)
0.826337 + 0.563176i \(0.190421\pi\)
\(140\) 0.685607 + 3.07929i 0.0579444 + 0.260247i
\(141\) 0 0
\(142\) 2.88559i 0.242153i
\(143\) −2.47164 + 2.65714i −0.206689 + 0.222201i
\(144\) 0 0
\(145\) −12.0709 + 3.23438i −1.00243 + 0.268601i
\(146\) 3.27979 + 1.89359i 0.271437 + 0.156714i
\(147\) 0 0
\(148\) 5.87381 5.87381i 0.482825 0.482825i
\(149\) −8.14575 2.18265i −0.667326 0.178809i −0.0907761 0.995871i \(-0.528935\pi\)
−0.576550 + 0.817062i \(0.695601\pi\)
\(150\) 0 0
\(151\) −0.453678 0.453678i −0.0369198 0.0369198i 0.688406 0.725326i \(-0.258311\pi\)
−0.725326 + 0.688406i \(0.758311\pi\)
\(152\) −4.01656 + 2.31896i −0.325786 + 0.188093i
\(153\) 0 0
\(154\) −1.55156 + 2.44037i −0.125028 + 0.196651i
\(155\) 6.01081i 0.482800i
\(156\) 0 0
\(157\) 8.10530i 0.646874i −0.946250 0.323437i \(-0.895162\pi\)
0.946250 0.323437i \(-0.104838\pi\)
\(158\) 1.98583 + 7.41123i 0.157984 + 0.589606i
\(159\) 0 0
\(160\) −3.12105 5.40583i −0.246741 0.427368i
\(161\) 0.0439771 1.02875i 0.00346588 0.0810771i
\(162\) 0 0
\(163\) 3.55525 13.2684i 0.278469 1.03926i −0.675012 0.737807i \(-0.735862\pi\)
0.953481 0.301453i \(-0.0974717\pi\)
\(164\) 5.19448 5.19448i 0.405621 0.405621i
\(165\) 0 0
\(166\) −1.86915 + 3.23746i −0.145074 + 0.251276i
\(167\) 5.75214 + 21.4673i 0.445114 + 1.66119i 0.715636 + 0.698473i \(0.246137\pi\)
−0.270523 + 0.962714i \(0.587196\pi\)
\(168\) 0 0
\(169\) 5.66969 11.6985i 0.436130 0.899884i
\(170\) −7.47975 −0.573671
\(171\) 0 0
\(172\) −3.92745 + 6.80255i −0.299466 + 0.518690i
\(173\) −6.33728 10.9765i −0.481815 0.834527i 0.517967 0.855400i \(-0.326689\pi\)
−0.999782 + 0.0208728i \(0.993355\pi\)
\(174\) 0 0
\(175\) −6.77703 + 3.53575i −0.512295 + 0.267278i
\(176\) 0.438968 1.63825i 0.0330884 0.123488i
\(177\) 0 0
\(178\) −10.1505 + 5.86042i −0.760816 + 0.439257i
\(179\) −9.48849 5.47818i −0.709203 0.409459i 0.101563 0.994829i \(-0.467616\pi\)
−0.810766 + 0.585370i \(0.800949\pi\)
\(180\) 0 0
\(181\) 4.38394 0.325856 0.162928 0.986638i \(-0.447906\pi\)
0.162928 + 0.986638i \(0.447906\pi\)
\(182\) 2.74689 9.98860i 0.203613 0.740404i
\(183\) 0 0
\(184\) 0.308549 + 1.15152i 0.0227466 + 0.0848913i
\(185\) −12.7356 7.35288i −0.936338 0.540595i
\(186\) 0 0
\(187\) 3.37395 + 3.37395i 0.246728 + 0.246728i
\(188\) 1.43866 5.36916i 0.104925 0.391586i
\(189\) 0 0
\(190\) 1.68921 + 1.68921i 0.122548 + 0.122548i
\(191\) 4.92507 + 8.53047i 0.356366 + 0.617243i 0.987351 0.158552i \(-0.0506824\pi\)
−0.630985 + 0.775795i \(0.717349\pi\)
\(192\) 0 0
\(193\) 12.2874 3.29240i 0.884465 0.236992i 0.212133 0.977241i \(-0.431959\pi\)
0.672333 + 0.740249i \(0.265292\pi\)
\(194\) −14.9250 −1.07155
\(195\) 0 0
\(196\) −0.490261 + 5.72385i −0.0350187 + 0.408847i
\(197\) 0.404048 + 1.50793i 0.0287873 + 0.107436i 0.978825 0.204701i \(-0.0656221\pi\)
−0.950037 + 0.312136i \(0.898955\pi\)
\(198\) 0 0
\(199\) 5.84499 + 10.1238i 0.414340 + 0.717659i 0.995359 0.0962317i \(-0.0306790\pi\)
−0.581019 + 0.813890i \(0.697346\pi\)
\(200\) 6.25781 6.25781i 0.442494 0.442494i
\(201\) 0 0
\(202\) 4.14860 + 1.11161i 0.291894 + 0.0782128i
\(203\) −22.7362 0.971923i −1.59577 0.0682156i
\(204\) 0 0
\(205\) −11.2626 6.50249i −0.786617 0.454153i
\(206\) 3.58948 + 13.3961i 0.250091 + 0.933351i
\(207\) 0 0
\(208\) 0.219604 + 6.07174i 0.0152268 + 0.420999i
\(209\) 1.52393i 0.105413i
\(210\) 0 0
\(211\) −11.0809 + 19.1926i −0.762838 + 1.32127i 0.178544 + 0.983932i \(0.442861\pi\)
−0.941382 + 0.337343i \(0.890472\pi\)
\(212\) −9.04972 + 5.22486i −0.621537 + 0.358845i
\(213\) 0 0
\(214\) −3.77619 1.01183i −0.258135 0.0691670i
\(215\) 13.4319 + 3.59907i 0.916048 + 0.245454i
\(216\) 0 0
\(217\) −3.28198 + 10.4423i −0.222795 + 0.708869i
\(218\) −0.0828838 0.0478530i −0.00561360 0.00324101i
\(219\) 0 0
\(220\) 1.20010 0.0809110
\(221\) −15.1021 8.00580i −1.01588 0.538528i
\(222\) 0 0
\(223\) −13.2842 + 3.55949i −0.889575 + 0.238361i −0.674534 0.738244i \(-0.735655\pi\)
−0.215041 + 0.976605i \(0.568989\pi\)
\(224\) −2.47041 11.0954i −0.165061 0.741344i
\(225\) 0 0
\(226\) −1.67813 + 1.67813i −0.111627 + 0.111627i
\(227\) 1.04021 3.88213i 0.0690413 0.257666i −0.922775 0.385339i \(-0.874084\pi\)
0.991816 + 0.127674i \(0.0407510\pi\)
\(228\) 0 0
\(229\) 1.36272 1.36272i 0.0900509 0.0900509i −0.660646 0.750697i \(-0.729718\pi\)
0.750697 + 0.660646i \(0.229718\pi\)
\(230\) 0.531783 0.307025i 0.0350647 0.0202446i
\(231\) 0 0
\(232\) 25.4494 6.81915i 1.67084 0.447699i
\(233\) 1.13013i 0.0740376i −0.999315 0.0370188i \(-0.988214\pi\)
0.999315 0.0370188i \(-0.0117861\pi\)
\(234\) 0 0
\(235\) −9.84046 −0.641921
\(236\) 0.730113 0.195633i 0.0475263 0.0127346i
\(237\) 0 0
\(238\) −12.9942 4.08405i −0.842290 0.264729i
\(239\) −3.62833 + 3.62833i −0.234697 + 0.234697i −0.814650 0.579953i \(-0.803071\pi\)
0.579953 + 0.814650i \(0.303071\pi\)
\(240\) 0 0
\(241\) −9.46780 2.53689i −0.609875 0.163415i −0.0593540 0.998237i \(-0.518904\pi\)
−0.550521 + 0.834822i \(0.685571\pi\)
\(242\) −7.66890 7.66890i −0.492976 0.492976i
\(243\) 0 0
\(244\) −3.96330 + 6.86463i −0.253724 + 0.439463i
\(245\) 10.0124 1.78428i 0.639671 0.113994i
\(246\) 0 0
\(247\) 1.60261 + 5.21863i 0.101972 + 0.332054i
\(248\) 12.6728i 0.804723i
\(249\) 0 0
\(250\) −10.7797 6.22363i −0.681765 0.393617i
\(251\) 14.1820 + 24.5639i 0.895158 + 1.55046i 0.833610 + 0.552354i \(0.186270\pi\)
0.0615480 + 0.998104i \(0.480396\pi\)
\(252\) 0 0
\(253\) −0.378367 0.101383i −0.0237878 0.00637391i
\(254\) 4.01357 14.9789i 0.251834 0.939857i
\(255\) 0 0
\(256\) 7.96316 + 13.7926i 0.497698 + 0.862037i
\(257\) 3.32083 5.75185i 0.207148 0.358790i −0.743667 0.668550i \(-0.766915\pi\)
0.950815 + 0.309760i \(0.100249\pi\)
\(258\) 0 0
\(259\) −18.1101 19.7276i −1.12531 1.22581i
\(260\) −4.10970 + 1.26206i −0.254873 + 0.0782698i
\(261\) 0 0
\(262\) −18.7646 + 5.02797i −1.15928 + 0.310629i
\(263\) 6.24723 10.8205i 0.385221 0.667222i −0.606579 0.795023i \(-0.707459\pi\)
0.991800 + 0.127801i \(0.0407920\pi\)
\(264\) 0 0
\(265\) 13.0810 + 13.0810i 0.803561 + 0.803561i
\(266\) 2.01226 + 3.85692i 0.123379 + 0.236483i
\(267\) 0 0
\(268\) 3.84145 + 3.84145i 0.234654 + 0.234654i
\(269\) −7.27737 + 4.20159i −0.443709 + 0.256176i −0.705170 0.709038i \(-0.749129\pi\)
0.261460 + 0.965214i \(0.415796\pi\)
\(270\) 0 0
\(271\) 0.0939748 + 0.350719i 0.00570857 + 0.0213047i 0.968721 0.248151i \(-0.0798229\pi\)
−0.963013 + 0.269456i \(0.913156\pi\)
\(272\) 7.98855 0.484377
\(273\) 0 0
\(274\) 2.74822 0.166026
\(275\) 0.752619 + 2.80881i 0.0453846 + 0.169378i
\(276\) 0 0
\(277\) 13.5251 7.80875i 0.812647 0.469182i −0.0352270 0.999379i \(-0.511215\pi\)
0.847874 + 0.530197i \(0.177882\pi\)
\(278\) 7.85901 + 7.85901i 0.471352 + 0.471352i
\(279\) 0 0
\(280\) −10.4393 + 5.44645i −0.623867 + 0.325488i
\(281\) 0.848694 + 0.848694i 0.0506289 + 0.0506289i 0.731968 0.681339i \(-0.238602\pi\)
−0.681339 + 0.731968i \(0.738602\pi\)
\(282\) 0 0
\(283\) 11.9723 20.7366i 0.711678 1.23266i −0.252549 0.967584i \(-0.581269\pi\)
0.964227 0.265078i \(-0.0853976\pi\)
\(284\) 2.10640 0.564409i 0.124992 0.0334915i
\(285\) 0 0
\(286\) −3.48193 1.84581i −0.205891 0.109145i
\(287\) −16.0156 17.4460i −0.945371 1.02981i
\(288\) 0 0
\(289\) −2.73713 + 4.74084i −0.161007 + 0.278873i
\(290\) −6.78546 11.7528i −0.398456 0.690146i
\(291\) 0 0
\(292\) 0.740755 2.76454i 0.0433494 0.161782i
\(293\) 18.6502 + 4.99730i 1.08956 + 0.291946i 0.758505 0.651667i \(-0.225930\pi\)
0.331051 + 0.943613i \(0.392597\pi\)
\(294\) 0 0
\(295\) −0.669066 1.15886i −0.0389545 0.0674712i
\(296\) 26.8508 + 15.5023i 1.56067 + 0.901055i
\(297\) 0 0
\(298\) 9.15803i 0.530510i
\(299\) 1.40232 0.0507193i 0.0810982 0.00293317i
\(300\) 0 0
\(301\) 21.3695 + 13.5865i 1.23172 + 0.783112i
\(302\) 0.348375 0.603403i 0.0200467 0.0347220i
\(303\) 0 0
\(304\) −1.80412 1.80412i −0.103473 0.103473i
\(305\) 13.5545 + 3.63191i 0.776127 + 0.207963i
\(306\) 0 0
\(307\) 17.1942 17.1942i 0.981322 0.981322i −0.0185063 0.999829i \(-0.505891\pi\)
0.999829 + 0.0185063i \(0.00589106\pi\)
\(308\) 2.08488 + 0.655273i 0.118797 + 0.0373377i
\(309\) 0 0
\(310\) −6.30509 + 1.68944i −0.358105 + 0.0959539i
\(311\) −14.0638 −0.797487 −0.398744 0.917062i \(-0.630554\pi\)
−0.398744 + 0.917062i \(0.630554\pi\)
\(312\) 0 0
\(313\) 18.8063i 1.06300i −0.847060 0.531498i \(-0.821629\pi\)
0.847060 0.531498i \(-0.178371\pi\)
\(314\) 8.50213 2.27814i 0.479803 0.128563i
\(315\) 0 0
\(316\) 5.02158 2.89921i 0.282486 0.163093i
\(317\) 1.67207 1.67207i 0.0939128 0.0939128i −0.658590 0.752502i \(-0.728847\pi\)
0.752502 + 0.658590i \(0.228847\pi\)
\(318\) 0 0
\(319\) −2.24064 + 8.36218i −0.125452 + 0.468192i
\(320\) 8.25560 8.25560i 0.461502 0.461502i
\(321\) 0 0
\(322\) 1.09148 0.243019i 0.0608258 0.0135429i
\(323\) 6.93332 1.85778i 0.385780 0.103369i
\(324\) 0 0
\(325\) −5.53113 8.82717i −0.306812 0.489643i
\(326\) 14.9172 0.826190
\(327\) 0 0
\(328\) 23.7454 + 13.7094i 1.31112 + 0.756976i
\(329\) −17.0954 5.37302i −0.942497 0.296224i
\(330\) 0 0
\(331\) −33.2290 8.90368i −1.82643 0.489391i −0.828886 0.559418i \(-0.811025\pi\)
−0.997545 + 0.0700274i \(0.977691\pi\)
\(332\) 2.72886 + 0.731196i 0.149766 + 0.0401296i
\(333\) 0 0
\(334\) −20.9015 + 12.0675i −1.14368 + 0.660304i
\(335\) 4.80875 8.32901i 0.262730 0.455062i
\(336\) 0 0
\(337\) 3.43766i 0.187261i −0.995607 0.0936305i \(-0.970153\pi\)
0.995607 0.0936305i \(-0.0298472\pi\)
\(338\) 13.8648 + 2.65921i 0.754145 + 0.144642i
\(339\) 0 0
\(340\) 1.46301 + 5.46002i 0.0793428 + 0.296111i
\(341\) 3.60616 + 2.08201i 0.195284 + 0.112747i
\(342\) 0 0
\(343\) 18.3684 + 2.36717i 0.991798 + 0.127815i
\(344\) −28.3189 7.58803i −1.52685 0.409119i
\(345\) 0 0
\(346\) 9.73268 9.73268i 0.523232 0.523232i
\(347\) 9.46705 + 16.3974i 0.508218 + 0.880259i 0.999955 + 0.00951518i \(0.00302882\pi\)
−0.491737 + 0.870744i \(0.663638\pi\)
\(348\) 0 0
\(349\) 8.44404 + 31.5136i 0.451999 + 1.68688i 0.696764 + 0.717300i \(0.254623\pi\)
−0.244765 + 0.969582i \(0.578711\pi\)
\(350\) −5.61366 6.11504i −0.300063 0.326863i
\(351\) 0 0
\(352\) −4.32426 −0.230484
\(353\) −31.7685 + 8.51233i −1.69086 + 0.453066i −0.970613 0.240647i \(-0.922640\pi\)
−0.720251 + 0.693713i \(0.755974\pi\)
\(354\) 0 0
\(355\) −1.93028 3.34334i −0.102449 0.177446i
\(356\) 6.26336 + 6.26336i 0.331957 + 0.331957i
\(357\) 0 0
\(358\) 3.07948 11.4928i 0.162756 0.607412i
\(359\) 1.45164 + 1.45164i 0.0766146 + 0.0766146i 0.744376 0.667761i \(-0.232747\pi\)
−0.667761 + 0.744376i \(0.732747\pi\)
\(360\) 0 0
\(361\) 14.4691 + 8.35375i 0.761533 + 0.439671i
\(362\) 1.23218 + 4.59857i 0.0647622 + 0.241696i
\(363\) 0 0
\(364\) −7.82869 0.0514311i −0.410335 0.00269572i
\(365\) −5.06677 −0.265207
\(366\) 0 0
\(367\) 0.400843 + 0.231427i 0.0209238 + 0.0120804i 0.510425 0.859922i \(-0.329488\pi\)
−0.489502 + 0.872002i \(0.662821\pi\)
\(368\) −0.567956 + 0.327909i −0.0296067 + 0.0170935i
\(369\) 0 0
\(370\) 4.13331 15.4257i 0.214881 0.801946i
\(371\) 15.5826 + 29.8675i 0.809010 + 1.55064i
\(372\) 0 0
\(373\) 5.17460 + 8.96266i 0.267930 + 0.464069i 0.968327 0.249685i \(-0.0803269\pi\)
−0.700397 + 0.713754i \(0.746994\pi\)
\(374\) −2.59083 + 4.48744i −0.133968 + 0.232040i
\(375\) 0 0
\(376\) 20.7470 1.06994
\(377\) −1.12093 30.9922i −0.0577309 1.59618i
\(378\) 0 0
\(379\) 3.99214 + 14.8989i 0.205062 + 0.765303i 0.989431 + 0.145007i \(0.0463206\pi\)
−0.784368 + 0.620295i \(0.787013\pi\)
\(380\) 0.902677 1.56348i 0.0463064 0.0802050i
\(381\) 0 0
\(382\) −7.56383 + 7.56383i −0.386999 + 0.386999i
\(383\) 8.40301 31.3605i 0.429374 1.60245i −0.324808 0.945780i \(-0.605300\pi\)
0.754182 0.656665i \(-0.228034\pi\)
\(384\) 0 0
\(385\) 0.165238 3.86539i 0.00842128 0.196999i
\(386\) 6.90717 + 11.9636i 0.351566 + 0.608930i
\(387\) 0 0
\(388\) 2.91927 + 10.8948i 0.148203 + 0.553102i
\(389\) 37.3829i 1.89539i 0.319179 + 0.947694i \(0.396593\pi\)
−0.319179 + 0.947694i \(0.603407\pi\)
\(390\) 0 0
\(391\) 1.84502i 0.0933068i
\(392\) −21.1095 + 3.76186i −1.06619 + 0.190003i
\(393\) 0 0
\(394\) −1.46819 + 0.847660i −0.0739664 + 0.0427045i
\(395\) −7.25850 7.25850i −0.365215 0.365215i
\(396\) 0 0
\(397\) 34.9889 + 9.37524i 1.75604 + 0.470530i 0.985899 0.167343i \(-0.0535187\pi\)
0.770142 + 0.637873i \(0.220185\pi\)
\(398\) −8.97663 + 8.97663i −0.449958 + 0.449958i
\(399\) 0 0
\(400\) 4.21622 + 2.43424i 0.210811 + 0.121712i
\(401\) 33.6403 9.01390i 1.67992 0.450133i 0.712161 0.702016i \(-0.247716\pi\)
0.967758 + 0.251883i \(0.0810498\pi\)
\(402\) 0 0
\(403\) −14.5386 3.33743i −0.724220 0.166249i
\(404\) 3.24579i 0.161484i
\(405\) 0 0
\(406\) −5.37089 24.1225i −0.266553 1.19718i
\(407\) −8.82265 + 5.09376i −0.437323 + 0.252488i
\(408\) 0 0
\(409\) −2.97572 + 11.1055i −0.147140 + 0.549134i 0.852511 + 0.522709i \(0.175079\pi\)
−0.999651 + 0.0264241i \(0.991588\pi\)
\(410\) 3.65528 13.6417i 0.180521 0.673715i
\(411\) 0 0
\(412\) 9.07672 5.24044i 0.447178 0.258178i
\(413\) −0.529585 2.37854i −0.0260592 0.117040i
\(414\) 0 0
\(415\) 5.00138i 0.245508i
\(416\) 14.8082 4.54751i 0.726034 0.222960i
\(417\) 0 0
\(418\) 1.59854 0.428328i 0.0781872 0.0209502i
\(419\) 25.3323 + 14.6256i 1.23756 + 0.714507i 0.968595 0.248642i \(-0.0799844\pi\)
0.268967 + 0.963149i \(0.413318\pi\)
\(420\) 0 0
\(421\) −8.84750 + 8.84750i −0.431201 + 0.431201i −0.889037 0.457836i \(-0.848625\pi\)
0.457836 + 0.889037i \(0.348625\pi\)
\(422\) −23.2467 6.22894i −1.13163 0.303220i
\(423\) 0 0
\(424\) −27.5792 27.5792i −1.33936 1.33936i
\(425\) −11.8615 + 6.84826i −0.575369 + 0.332190i
\(426\) 0 0
\(427\) 21.5645 + 13.7105i 1.04358 + 0.663497i
\(428\) 2.95443i 0.142808i
\(429\) 0 0
\(430\) 15.1011i 0.728239i
\(431\) 3.91058 + 14.5945i 0.188366 + 0.702992i 0.993885 + 0.110422i \(0.0352201\pi\)
−0.805519 + 0.592570i \(0.798113\pi\)
\(432\) 0 0
\(433\) −16.6099 28.7692i −0.798222 1.38256i −0.920773 0.390100i \(-0.872441\pi\)
0.122550 0.992462i \(-0.460893\pi\)
\(434\) −11.8760 0.507674i −0.570066 0.0243691i
\(435\) 0 0
\(436\) −0.0187197 + 0.0698628i −0.000896511 + 0.00334582i
\(437\) −0.416676 + 0.416676i −0.0199323 + 0.0199323i
\(438\) 0 0
\(439\) 3.12262 5.40854i 0.149035 0.258135i −0.781836 0.623484i \(-0.785717\pi\)
0.930871 + 0.365348i \(0.119050\pi\)
\(440\) 1.15933 + 4.32668i 0.0552689 + 0.206266i
\(441\) 0 0
\(442\) 4.15304 18.0916i 0.197540 0.860530i
\(443\) 17.0915 0.812043 0.406022 0.913863i \(-0.366916\pi\)
0.406022 + 0.913863i \(0.366916\pi\)
\(444\) 0 0
\(445\) 7.84051 13.5802i 0.371676 0.643762i
\(446\) −7.46751 12.9341i −0.353597 0.612448i
\(447\) 0 0
\(448\) 18.8497 9.83440i 0.890566 0.464632i
\(449\) 9.60577 35.8492i 0.453324 1.69183i −0.239644 0.970861i \(-0.577031\pi\)
0.692968 0.720968i \(-0.256303\pi\)
\(450\) 0 0
\(451\) −7.80227 + 4.50464i −0.367395 + 0.212115i
\(452\) 1.55322 + 0.896753i 0.0730574 + 0.0421797i
\(453\) 0 0
\(454\) 4.36456 0.204839
\(455\) 3.49911 + 13.4106i 0.164041 + 0.628700i
\(456\) 0 0
\(457\) 2.07001 + 7.72540i 0.0968312 + 0.361379i 0.997291 0.0735609i \(-0.0234363\pi\)
−0.900460 + 0.434940i \(0.856770\pi\)
\(458\) 1.81245 + 1.04642i 0.0846902 + 0.0488959i
\(459\) 0 0
\(460\) −0.328134 0.328134i −0.0152993 0.0152993i
\(461\) 2.87961 10.7469i 0.134117 0.500531i −0.865883 0.500247i \(-0.833243\pi\)
1.00000 0.000284720i \(-9.06291e-5\pi\)
\(462\) 0 0
\(463\) 24.2312 + 24.2312i 1.12612 + 1.12612i 0.990803 + 0.135316i \(0.0432049\pi\)
0.135316 + 0.990803i \(0.456795\pi\)
\(464\) 7.24702 + 12.5522i 0.336435 + 0.582722i
\(465\) 0 0
\(466\) 1.18546 0.317644i 0.0549156 0.0147146i
\(467\) 10.5574 0.488538 0.244269 0.969707i \(-0.421452\pi\)
0.244269 + 0.969707i \(0.421452\pi\)
\(468\) 0 0
\(469\) 12.9018 11.8439i 0.595748 0.546902i
\(470\) −2.76583 10.3222i −0.127578 0.476129i
\(471\) 0 0
\(472\) 1.41061 + 2.44325i 0.0649287 + 0.112460i
\(473\) 6.81176 6.81176i 0.313205 0.313205i
\(474\) 0 0
\(475\) 4.22539 + 1.13219i 0.193874 + 0.0519484i
\(476\) −0.439630 + 10.2843i −0.0201504 + 0.471378i
\(477\) 0 0
\(478\) −4.82578 2.78616i −0.220726 0.127436i
\(479\) 2.28082 + 8.51215i 0.104214 + 0.388930i 0.998255 0.0590545i \(-0.0188086\pi\)
−0.894041 + 0.447985i \(0.852142\pi\)
\(480\) 0 0
\(481\) 24.8560 26.7215i 1.13334 1.21839i
\(482\) 10.6444i 0.484838i
\(483\) 0 0
\(484\) −4.09809 + 7.09810i −0.186277 + 0.322641i
\(485\) 17.2926 9.98389i 0.785217 0.453345i
\(486\) 0 0
\(487\) 19.8298 + 5.31338i 0.898574 + 0.240772i 0.678404 0.734689i \(-0.262672\pi\)
0.220170 + 0.975461i \(0.429339\pi\)
\(488\) −28.5774 7.65728i −1.29364 0.346629i
\(489\) 0 0
\(490\) 4.68581 + 10.0011i 0.211683 + 0.451804i
\(491\) 2.72329 + 1.57229i 0.122900 + 0.0709565i 0.560190 0.828364i \(-0.310728\pi\)
−0.437290 + 0.899321i \(0.644062\pi\)
\(492\) 0 0
\(493\) −40.7762 −1.83647
\(494\) −5.02369 + 3.14786i −0.226026 + 0.141629i
\(495\) 0 0
\(496\) 6.73398 1.80436i 0.302364 0.0810183i
\(497\) −1.52787 6.86219i −0.0685345 0.307811i
\(498\) 0 0
\(499\) −10.7019 + 10.7019i −0.479082 + 0.479082i −0.904838 0.425756i \(-0.860008\pi\)
0.425756 + 0.904838i \(0.360008\pi\)
\(500\) −2.43463 + 9.08617i −0.108880 + 0.406346i
\(501\) 0 0
\(502\) −21.7804 + 21.7804i −0.972107 + 0.972107i
\(503\) −22.4889 + 12.9840i −1.00273 + 0.578926i −0.909055 0.416677i \(-0.863195\pi\)
−0.0936745 + 0.995603i \(0.529861\pi\)
\(504\) 0 0
\(505\) −5.55031 + 1.48720i −0.246985 + 0.0661795i
\(506\) 0.425387i 0.0189108i
\(507\) 0 0
\(508\) −11.7192 −0.519955
\(509\) 31.8249 8.52745i 1.41061 0.377973i 0.528469 0.848952i \(-0.322766\pi\)
0.882144 + 0.470980i \(0.156100\pi\)
\(510\) 0 0
\(511\) −8.80225 2.76652i −0.389389 0.122384i
\(512\) −12.4191 + 12.4191i −0.548851 + 0.548851i
\(513\) 0 0
\(514\) 6.96683 + 1.86676i 0.307294 + 0.0823391i
\(515\) −13.1201 13.1201i −0.578139 0.578139i
\(516\) 0 0
\(517\) −3.40852 + 5.90373i −0.149907 + 0.259646i
\(518\) 15.6033 24.5416i 0.685568 1.07829i
\(519\) 0 0
\(520\) −8.52012 13.5973i −0.373632 0.596282i
\(521\) 26.4544i 1.15899i −0.814976 0.579495i \(-0.803250\pi\)
0.814976 0.579495i \(-0.196750\pi\)
\(522\) 0 0
\(523\) −9.23888 5.33407i −0.403988 0.233243i 0.284215 0.958761i \(-0.408267\pi\)
−0.688203 + 0.725518i \(0.741600\pi\)
\(524\) 7.34057 + 12.7142i 0.320674 + 0.555424i
\(525\) 0 0
\(526\) 13.1062 + 3.51179i 0.571456 + 0.153121i
\(527\) −5.07623 + 18.9448i −0.221124 + 0.825247i
\(528\) 0 0
\(529\) −11.4243 19.7874i −0.496707 0.860322i
\(530\) −10.0448 + 17.3981i −0.436318 + 0.755726i
\(531\) 0 0
\(532\) 2.42186 2.22329i 0.105001 0.0963919i
\(533\) 21.9813 23.6310i 0.952116 1.02357i
\(534\) 0 0
\(535\) 5.05207 1.35370i 0.218420 0.0585255i
\(536\) −10.1385 + 17.5603i −0.437915 + 0.758490i
\(537\) 0 0
\(538\) −6.45273 6.45273i −0.278197 0.278197i
\(539\) 2.39762 6.62494i 0.103273 0.285357i
\(540\) 0 0
\(541\) 3.42225 + 3.42225i 0.147134 + 0.147134i 0.776836 0.629702i \(-0.216823\pi\)
−0.629702 + 0.776836i \(0.716823\pi\)
\(542\) −0.341476 + 0.197151i −0.0146677 + 0.00846838i
\(543\) 0 0
\(544\) −5.27157 19.6738i −0.226017 0.843506i
\(545\) 0.128043 0.00548475
\(546\) 0 0
\(547\) −19.6406 −0.839770 −0.419885 0.907577i \(-0.637930\pi\)
−0.419885 + 0.907577i \(0.637930\pi\)
\(548\) −0.537540 2.00613i −0.0229626 0.0856975i
\(549\) 0 0
\(550\) −2.73479 + 1.57893i −0.116612 + 0.0673259i
\(551\) 9.20882 + 9.20882i 0.392309 + 0.392309i
\(552\) 0 0
\(553\) −8.64661 16.5731i −0.367691 0.704759i
\(554\) 11.9925 + 11.9925i 0.509514 + 0.509514i
\(555\) 0 0
\(556\) 4.19968 7.27406i 0.178106 0.308489i
\(557\) 34.1973 9.16315i 1.44899 0.388255i 0.553316 0.832971i \(-0.313362\pi\)
0.895672 + 0.444716i \(0.146695\pi\)
\(558\) 0 0
\(559\) −16.1631 + 30.4900i −0.683627 + 1.28959i
\(560\) −4.38045 4.77169i −0.185108 0.201641i
\(561\) 0 0
\(562\) −0.651705 + 1.12879i −0.0274905 + 0.0476149i
\(563\) −15.9428 27.6137i −0.671908 1.16378i −0.977362 0.211572i \(-0.932142\pi\)
0.305455 0.952207i \(-0.401192\pi\)
\(564\) 0 0
\(565\) 0.821772 3.06689i 0.0345722 0.129025i
\(566\) 25.1168 + 6.73003i 1.05574 + 0.282884i
\(567\) 0 0
\(568\) 4.06967 + 7.04888i 0.170760 + 0.295764i
\(569\) −23.6253 13.6401i −0.990426 0.571823i −0.0850245 0.996379i \(-0.527097\pi\)
−0.905402 + 0.424556i \(0.860430\pi\)
\(570\) 0 0
\(571\) 33.0144i 1.38161i 0.723042 + 0.690804i \(0.242743\pi\)
−0.723042 + 0.690804i \(0.757257\pi\)
\(572\) −0.666344 + 2.90275i −0.0278612 + 0.121370i
\(573\) 0 0
\(574\) 13.7987 21.7032i 0.575946 0.905874i
\(575\) 0.562208 0.973772i 0.0234457 0.0406091i
\(576\) 0 0
\(577\) −18.3031 18.3031i −0.761967 0.761967i 0.214711 0.976678i \(-0.431119\pi\)
−0.976678 + 0.214711i \(0.931119\pi\)
\(578\) −5.74226 1.53863i −0.238847 0.0639988i
\(579\) 0 0
\(580\) −7.25199 + 7.25199i −0.301123 + 0.301123i
\(581\) 2.73082 8.68866i 0.113294 0.360467i
\(582\) 0 0
\(583\) 12.3789 3.31691i 0.512681 0.137373i
\(584\) 10.6824 0.442042
\(585\) 0 0
\(586\) 20.9678i 0.866174i
\(587\) −30.3048 + 8.12014i −1.25081 + 0.335154i −0.822650 0.568548i \(-0.807505\pi\)
−0.428162 + 0.903702i \(0.640839\pi\)
\(588\) 0 0
\(589\) 5.42485 3.13204i 0.223527 0.129053i
\(590\) 1.02754 1.02754i 0.0423031 0.0423031i
\(591\) 0 0
\(592\) −4.41447 + 16.4750i −0.181434 + 0.677120i
\(593\) 14.5568 14.5568i 0.597777 0.597777i −0.341943 0.939721i \(-0.611085\pi\)
0.939721 + 0.341943i \(0.111085\pi\)
\(594\) 0 0
\(595\) 17.7875 3.96041i 0.729217 0.162361i
\(596\) −6.68512 + 1.79127i −0.273833 + 0.0733733i
\(597\) 0 0
\(598\) 0.447349 + 1.45672i 0.0182934 + 0.0595696i
\(599\) −17.9695 −0.734214 −0.367107 0.930179i \(-0.619652\pi\)
−0.367107 + 0.930179i \(0.619652\pi\)
\(600\) 0 0
\(601\) −15.4598 8.92570i −0.630617 0.364087i 0.150374 0.988629i \(-0.451952\pi\)
−0.780991 + 0.624542i \(0.785286\pi\)
\(602\) −8.24539 + 26.2344i −0.336057 + 1.06923i
\(603\) 0 0
\(604\) −0.508609 0.136281i −0.0206950 0.00554521i
\(605\) 14.0155 + 3.75543i 0.569810 + 0.152680i
\(606\) 0 0
\(607\) 22.2125 12.8244i 0.901578 0.520526i 0.0238664 0.999715i \(-0.492402\pi\)
0.877712 + 0.479189i \(0.159069\pi\)
\(608\) −3.25256 + 5.63361i −0.131909 + 0.228473i
\(609\) 0 0
\(610\) 15.2389i 0.617005i
\(611\) 5.46380 23.8015i 0.221042 0.962907i
\(612\) 0 0
\(613\) 0.916231 + 3.41942i 0.0370062 + 0.138109i 0.981957 0.189102i \(-0.0605578\pi\)
−0.944951 + 0.327211i \(0.893891\pi\)
\(614\) 22.8687 + 13.2032i 0.922905 + 0.532839i
\(615\) 0 0
\(616\) −0.348376 + 8.14954i −0.0140365 + 0.328354i
\(617\) 5.87829 + 1.57508i 0.236651 + 0.0634105i 0.375195 0.926946i \(-0.377576\pi\)
−0.138544 + 0.990356i \(0.544242\pi\)
\(618\) 0 0
\(619\) −34.1674 + 34.1674i −1.37331 + 1.37331i −0.517810 + 0.855496i \(0.673253\pi\)
−0.855496 + 0.517810i \(0.826747\pi\)
\(620\) 2.46650 + 4.27210i 0.0990569 + 0.171572i
\(621\) 0 0
\(622\) −3.95289 14.7524i −0.158496 0.591517i
\(623\) 21.0359 19.3112i 0.842786 0.773685i
\(624\) 0 0
\(625\) 2.20722 0.0882889
\(626\) 19.7270 5.28584i 0.788451 0.211265i
\(627\) 0 0
\(628\) −3.32596 5.76073i −0.132720 0.229878i
\(629\) −33.9301 33.9301i −1.35288 1.35288i
\(630\) 0 0
\(631\) 2.80135 10.4548i 0.111520 0.416199i −0.887483 0.460841i \(-0.847548\pi\)
0.999003 + 0.0446417i \(0.0142146\pi\)
\(632\) 15.3033 + 15.3033i 0.608734 + 0.608734i
\(633\) 0 0
\(634\) 2.22390 + 1.28397i 0.0883222 + 0.0509928i
\(635\) 5.36966 + 20.0398i 0.213088 + 0.795257i
\(636\) 0 0
\(637\) −1.24355 + 25.2082i −0.0492714 + 0.998785i
\(638\) −9.40135 −0.372203
\(639\) 0 0
\(640\) 0.168516 + 0.0972930i 0.00666120 + 0.00384584i
\(641\) −26.3470 + 15.2114i −1.04064 + 0.600815i −0.920015 0.391883i \(-0.871824\pi\)
−0.120627 + 0.992698i \(0.538490\pi\)
\(642\) 0 0
\(643\) −5.55469 + 20.7304i −0.219056 + 0.817527i 0.765644 + 0.643265i \(0.222421\pi\)
−0.984699 + 0.174262i \(0.944246\pi\)
\(644\) −0.390886 0.749218i −0.0154031 0.0295233i
\(645\) 0 0
\(646\) 3.89746 + 6.75060i 0.153344 + 0.265599i
\(647\) −3.76958 + 6.52911i −0.148198 + 0.256686i −0.930561 0.366136i \(-0.880681\pi\)
0.782364 + 0.622822i \(0.214014\pi\)
\(648\) 0 0
\(649\) −0.927000 −0.0363879
\(650\) 7.70471 8.28296i 0.302204 0.324884i
\(651\) 0 0
\(652\) −2.91775 10.8892i −0.114268 0.426454i
\(653\) 11.4217 19.7830i 0.446966 0.774167i −0.551221 0.834359i \(-0.685838\pi\)
0.998187 + 0.0601918i \(0.0191712\pi\)
\(654\) 0 0
\(655\) 18.3779 18.3779i 0.718086 0.718086i
\(656\) −3.90392 + 14.5696i −0.152422 + 0.568848i
\(657\) 0 0
\(658\) 0.831126 19.4425i 0.0324007 0.757947i
\(659\) −13.0916 22.6753i −0.509975 0.883303i −0.999933 0.0115568i \(-0.996321\pi\)
0.489958 0.871746i \(-0.337012\pi\)
\(660\) 0 0
\(661\) 4.50623 + 16.8175i 0.175272 + 0.654124i 0.996505 + 0.0835312i \(0.0266198\pi\)
−0.821233 + 0.570593i \(0.806713\pi\)
\(662\) 37.3584i 1.45197i
\(663\) 0 0
\(664\) 10.5446i 0.409209i
\(665\) −4.91151 3.12269i −0.190460 0.121093i
\(666\) 0 0
\(667\) 2.89904 1.67376i 0.112251 0.0648083i
\(668\) 12.8972 + 12.8972i 0.499008 + 0.499008i
\(669\) 0 0
\(670\) 10.0884 + 2.70317i 0.389748 + 0.104433i
\(671\) 6.87393 6.87393i 0.265365 0.265365i
\(672\) 0 0
\(673\) 13.2813 + 7.66796i 0.511957 + 0.295578i 0.733638 0.679541i \(-0.237821\pi\)
−0.221681 + 0.975119i \(0.571154\pi\)
\(674\) 3.60596 0.966213i 0.138896 0.0372172i
\(675\) 0 0
\(676\) −0.770743 10.6411i −0.0296440 0.409271i
\(677\) 4.31369i 0.165789i 0.996558 + 0.0828943i \(0.0264164\pi\)
−0.996558 + 0.0828943i \(0.973584\pi\)
\(678\) 0 0
\(679\) 35.4930 7.90254i 1.36210 0.303272i
\(680\) −18.2714 + 10.5490i −0.700678 + 0.404537i
\(681\) 0 0
\(682\) −1.17037 + 4.36789i −0.0448159 + 0.167255i
\(683\) 2.11067 7.87714i 0.0807627 0.301410i −0.913715 0.406355i \(-0.866800\pi\)
0.994478 + 0.104944i \(0.0334664\pi\)
\(684\) 0 0
\(685\) −3.18418 + 1.83839i −0.121661 + 0.0702412i
\(686\) 2.67969 + 19.9330i 0.102311 + 0.761045i
\(687\) 0 0
\(688\) 16.1283i 0.614886i
\(689\) −38.9028 + 24.3766i −1.48208 + 0.928674i
\(690\) 0 0
\(691\) 8.79665 2.35706i 0.334640 0.0896666i −0.0875862 0.996157i \(-0.527915\pi\)
0.422227 + 0.906490i \(0.361249\pi\)
\(692\) −9.00827 5.20093i −0.342443 0.197710i
\(693\) 0 0
\(694\) −14.5393 + 14.5393i −0.551905 + 0.551905i
\(695\) −14.3629 3.84853i −0.544816 0.145983i
\(696\) 0 0
\(697\) −30.0059 30.0059i −1.13656 1.13656i
\(698\) −30.6831 + 17.7149i −1.16137 + 0.670518i
\(699\) 0 0
\(700\) −3.36581 + 5.29390i −0.127216 + 0.200091i
\(701\) 42.0549i 1.58839i 0.607663 + 0.794195i \(0.292107\pi\)
−0.607663 + 0.794195i \(0.707893\pi\)
\(702\) 0 0
\(703\) 15.3254i 0.578009i
\(704\) −2.09335 7.81247i −0.0788959 0.294444i
\(705\) 0 0
\(706\) −17.8582 30.9312i −0.672101 1.16411i
\(707\) −10.4543 0.446900i −0.393175 0.0168074i
\(708\) 0 0
\(709\) 4.70279 17.5510i 0.176617 0.659143i −0.819654 0.572859i \(-0.805834\pi\)
0.996271 0.0862837i \(-0.0274991\pi\)
\(710\) 2.96449 2.96449i 0.111255 0.111255i
\(711\) 0 0
\(712\) −16.5304 + 28.6315i −0.619504 + 1.07301i
\(713\) −0.416733 1.55527i −0.0156068 0.0582453i
\(714\) 0 0
\(715\) 5.26901 0.190570i 0.197050 0.00712693i
\(716\) −8.99175 −0.336038
\(717\) 0 0
\(718\) −1.11470 + 1.93072i −0.0416003 + 0.0720538i
\(719\) −22.3307 38.6778i −0.832793 1.44244i −0.895815 0.444427i \(-0.853407\pi\)
0.0630222 0.998012i \(-0.479926\pi\)
\(720\) 0 0
\(721\) −15.6291 29.9566i −0.582059 1.11564i
\(722\) −4.69594 + 17.5255i −0.174765 + 0.652231i
\(723\) 0 0
\(724\) 3.11583 1.79892i 0.115799 0.0668565i
\(725\) −21.5210 12.4252i −0.799271 0.461459i
\(726\) 0 0
\(727\) −21.6855 −0.804272 −0.402136 0.915580i \(-0.631732\pi\)
−0.402136 + 0.915580i \(0.631732\pi\)
\(728\) −7.37728 28.2741i −0.273420 1.04791i
\(729\) 0 0
\(730\) −1.42410 5.31483i −0.0527085 0.196711i
\(731\) 39.2949 + 22.6869i 1.45338 + 0.839107i
\(732\) 0 0
\(733\) −36.4440 36.4440i −1.34609 1.34609i −0.889865 0.456223i \(-0.849202\pi\)
−0.456223 0.889865i \(-0.650798\pi\)
\(734\) −0.130093 + 0.485514i −0.00480183 + 0.0179207i
\(735\) 0 0
\(736\) 1.18235 + 1.18235i 0.0435819 + 0.0435819i
\(737\) −3.33130 5.76998i −0.122710 0.212540i
\(738\) 0 0
\(739\) −6.28312 + 1.68356i −0.231128 + 0.0619307i −0.372524 0.928022i \(-0.621508\pi\)
0.141396 + 0.989953i \(0.454841\pi\)
\(740\) −12.0688 −0.443659
\(741\) 0 0
\(742\) −26.9500 + 24.7403i −0.989364 + 0.908246i
\(743\) −6.75798 25.2211i −0.247926 0.925273i −0.971890 0.235435i \(-0.924348\pi\)
0.723964 0.689838i \(-0.242318\pi\)
\(744\) 0 0
\(745\) 6.12615 + 10.6108i 0.224445 + 0.388750i
\(746\) −7.94705 + 7.94705i −0.290962 + 0.290962i
\(747\) 0 0
\(748\) 3.78247 + 1.01351i 0.138301 + 0.0370576i
\(749\) 9.51586 + 0.406783i 0.347702 + 0.0148635i
\(750\) 0 0
\(751\) 31.8018 + 18.3608i 1.16046 + 0.669993i 0.951415 0.307912i \(-0.0996303\pi\)
0.209048 + 0.977905i \(0.432964\pi\)
\(752\) 2.95397 + 11.0244i 0.107720 + 0.402017i
\(753\) 0 0
\(754\) 32.1945 9.88671i 1.17245 0.360053i
\(755\) 0.932165i 0.0339250i
\(756\) 0 0
\(757\) 25.3385 43.8875i 0.920943 1.59512i 0.122984 0.992409i \(-0.460754\pi\)
0.797959 0.602711i \(-0.205913\pi\)
\(758\) −14.5062 + 8.37517i −0.526890 + 0.304200i
\(759\) 0 0
\(760\) 6.50876 + 1.74402i 0.236097 + 0.0632621i
\(761\) −25.8358 6.92269i −0.936548 0.250947i −0.241903 0.970300i \(-0.577772\pi\)
−0.694645 + 0.719353i \(0.744438\pi\)
\(762\) 0 0
\(763\) 0.222443 + 0.0699131i 0.00805296 + 0.00253102i
\(764\) 7.00085 + 4.04194i 0.253282 + 0.146232i
\(765\) 0 0
\(766\) 35.2576 1.27391
\(767\) 3.17447 0.974858i 0.114623 0.0352001i
\(768\) 0 0
\(769\) −22.6180 + 6.06047i −0.815626 + 0.218546i −0.642433 0.766342i \(-0.722075\pi\)
−0.173193 + 0.984888i \(0.555408\pi\)
\(770\) 4.10108 0.913110i 0.147793 0.0329062i
\(771\) 0 0
\(772\) 7.38208 7.38208i 0.265687 0.265687i
\(773\) −3.07578 + 11.4790i −0.110628 + 0.412869i −0.998923 0.0464045i \(-0.985224\pi\)
0.888295 + 0.459274i \(0.151890\pi\)
\(774\) 0 0
\(775\) −8.45192 + 8.45192i −0.303602 + 0.303602i
\(776\) −36.4586 + 21.0494i −1.30879 + 0.755628i
\(777\) 0 0
\(778\) −39.2131 + 10.5071i −1.40586 + 0.376699i
\(779\) 13.5530i 0.485585i
\(780\) 0 0
\(781\) −2.67443 −0.0956986
\(782\) 1.93535 0.518576i 0.0692080 0.0185442i
\(783\) 0 0
\(784\) −5.00455 10.6814i −0.178734 0.381479i
\(785\) −8.32692 + 8.32692i −0.297201 + 0.297201i
\(786\) 0 0
\(787\) 1.37868 + 0.369415i 0.0491445 + 0.0131682i 0.283308 0.959029i \(-0.408568\pi\)
−0.234163 + 0.972197i \(0.575235\pi\)
\(788\) 0.905941 + 0.905941i 0.0322728 + 0.0322728i
\(789\) 0 0
\(790\) 5.57374 9.65400i 0.198305 0.343474i
\(791\) 3.10219 4.87927i 0.110301 0.173487i
\(792\) 0 0
\(793\) −16.3106 + 30.7683i −0.579208 + 1.09261i
\(794\) 39.3369i 1.39602i
\(795\) 0 0
\(796\) 8.30849 + 4.79691i 0.294487 + 0.170022i
\(797\) 15.8960 + 27.5327i 0.563065 + 0.975258i 0.997227 + 0.0744227i \(0.0237114\pi\)
−0.434161 + 0.900835i \(0.642955\pi\)
\(798\) 0 0
\(799\) −31.0150 8.31044i −1.09723 0.294002i
\(800\) 3.21266 11.9898i 0.113585 0.423904i
\(801\) 0 0
\(802\) 18.9104 + 32.7538i 0.667750 + 1.15658i
\(803\) −1.75502 + 3.03978i −0.0619333 + 0.107272i
\(804\) 0 0
\(805\) −1.10206 + 1.01170i −0.0388426 + 0.0356578i
\(806\) −0.585506 16.1884i −0.0206236 0.570213i
\(807\) 0 0
\(808\) 11.7019 3.13551i 0.411671 0.110307i
\(809\) −7.21908 + 12.5038i −0.253809 + 0.439611i −0.964571 0.263822i \(-0.915017\pi\)
0.710762 + 0.703432i \(0.248350\pi\)
\(810\) 0 0
\(811\) 16.5212 + 16.5212i 0.580138 + 0.580138i 0.934941 0.354803i \(-0.115452\pi\)
−0.354803 + 0.934941i \(0.615452\pi\)
\(812\) −16.5582 + 8.63886i −0.581080 + 0.303164i
\(813\) 0 0
\(814\) −7.82291 7.82291i −0.274193 0.274193i
\(815\) −17.2836 + 9.97871i −0.605419 + 0.349539i
\(816\) 0 0
\(817\) −3.75072 13.9979i −0.131221 0.489723i
\(818\) −12.4856 −0.436550
\(819\) 0 0
\(820\) −10.6730 −0.372718
\(821\) 7.38477 + 27.5603i 0.257730 + 0.961862i 0.966551 + 0.256474i \(0.0825607\pi\)
−0.708821 + 0.705388i \(0.750773\pi\)
\(822\) 0 0
\(823\) 0.0527072 0.0304305i 0.00183726 0.00106074i −0.499081 0.866555i \(-0.666329\pi\)
0.500918 + 0.865495i \(0.332996\pi\)
\(824\) 27.6614 + 27.6614i 0.963632 + 0.963632i
\(825\) 0 0
\(826\) 2.34614 1.22404i 0.0816328 0.0425900i
\(827\) 37.2665 + 37.2665i 1.29588 + 1.29588i 0.931087 + 0.364798i \(0.118862\pi\)
0.364798 + 0.931087i \(0.381138\pi\)
\(828\) 0 0
\(829\) 2.17299 3.76373i 0.0754711 0.130720i −0.825820 0.563934i \(-0.809287\pi\)
0.901291 + 0.433214i \(0.142621\pi\)
\(830\) 5.24624 1.40573i 0.182100 0.0487935i
\(831\) 0 0
\(832\) 15.3844 + 24.5520i 0.533357 + 0.851188i
\(833\) 33.0638 + 2.83200i 1.14559 + 0.0981228i
\(834\) 0 0
\(835\) 16.1448 27.9636i 0.558714 0.967722i
\(836\) −0.625336 1.08311i −0.0216277 0.0374603i
\(837\) 0 0
\(838\) −8.22156 + 30.6833i −0.284009 + 1.05994i
\(839\) −46.4621 12.4495i −1.60405 0.429804i −0.657788 0.753203i \(-0.728508\pi\)
−0.946263 + 0.323399i \(0.895174\pi\)
\(840\) 0 0
\(841\) −22.4912 38.9560i −0.775560 1.34331i
\(842\) −11.7674 6.79392i −0.405532 0.234134i
\(843\) 0 0
\(844\) 18.1879i 0.626052i
\(845\) −17.8431 + 6.19363i −0.613820 + 0.213067i
\(846\) 0 0
\(847\) 22.2979 + 14.1768i 0.766165 + 0.487120i
\(848\) 10.7281 18.5816i 0.368404 0.638094i
\(849\) 0 0
\(850\) −10.5174 10.5174i −0.360745 0.360745i
\(851\) 3.80505 + 1.01956i 0.130435 + 0.0349500i
\(852\) 0 0
\(853\) 3.74166 3.74166i 0.128112 0.128112i −0.640143 0.768255i \(-0.721125\pi\)
0.768255 + 0.640143i \(0.221125\pi\)
\(854\) −8.32064 + 26.4738i −0.284727 + 0.905915i
\(855\) 0 0
\(856\) −10.6514 + 2.85405i −0.364059 + 0.0975493i
\(857\) −10.1411 −0.346413 −0.173207 0.984885i \(-0.555413\pi\)
−0.173207 + 0.984885i \(0.555413\pi\)
\(858\) 0 0
\(859\) 32.3015i 1.10211i −0.834468 0.551056i \(-0.814225\pi\)
0.834468 0.551056i \(-0.185775\pi\)
\(860\) 11.0234 2.95371i 0.375894 0.100721i
\(861\) 0 0
\(862\) −14.2099 + 8.20407i −0.483990 + 0.279432i
\(863\) −30.9883 + 30.9883i −1.05486 + 1.05486i −0.0564495 + 0.998405i \(0.517978\pi\)
−0.998405 + 0.0564495i \(0.982022\pi\)
\(864\) 0 0
\(865\) −4.76606 + 17.7872i −0.162051 + 0.604782i
\(866\) 25.5092 25.5092i 0.866839 0.866839i
\(867\) 0 0
\(868\) 1.95230 + 8.76845i 0.0662655 + 0.297621i
\(869\) −6.86889 + 1.84051i −0.233011 + 0.0624352i
\(870\) 0 0
\(871\) 17.4757 + 16.2557i 0.592143 + 0.550804i
\(872\) −0.269957 −0.00914189
\(873\) 0 0
\(874\) −0.554190 0.319962i −0.0187458 0.0108229i
\(875\) 28.9303 + 9.09271i 0.978022 + 0.307390i
\(876\) 0 0
\(877\) −17.0303 4.56327i −0.575074 0.154091i −0.0404512 0.999182i \(-0.512880\pi\)
−0.534623 + 0.845091i \(0.679546\pi\)
\(878\) 6.55100 + 1.75533i 0.221086 + 0.0592397i
\(879\) 0 0
\(880\) −2.13401 + 1.23207i −0.0719376 + 0.0415332i
\(881\) −2.42023 + 4.19196i −0.0815396 + 0.141231i −0.903911 0.427720i \(-0.859317\pi\)
0.822372 + 0.568950i \(0.192650\pi\)
\(882\) 0 0
\(883\) 23.3796i 0.786785i 0.919371 + 0.393393i \(0.128699\pi\)
−0.919371 + 0.393393i \(0.871301\pi\)
\(884\) −14.0187 + 0.507031i −0.471500 + 0.0170533i
\(885\) 0 0
\(886\) 4.80387 + 17.9283i 0.161389 + 0.602313i
\(887\) 43.5357 + 25.1353i 1.46178 + 0.843962i 0.999094 0.0425584i \(-0.0135509\pi\)
0.462690 + 0.886520i \(0.346884\pi\)
\(888\) 0 0
\(889\) −1.61357 + 37.7462i −0.0541174 + 1.26597i
\(890\) 16.4487 + 4.40743i 0.551363 + 0.147737i
\(891\) 0 0
\(892\) −7.98094 + 7.98094i −0.267222 + 0.267222i
\(893\) 5.12755 + 8.88117i 0.171587 + 0.297197i
\(894\) 0 0
\(895\) 4.11996 + 15.3759i 0.137715 + 0.513960i
\(896\) 0.239632 + 0.261035i 0.00800555 + 0.00872056i
\(897\) 0 0
\(898\) 40.3042 1.34497
\(899\) −34.3725 + 9.21008i −1.14639 + 0.307173i
\(900\) 0 0
\(901\) 30.1814 + 52.2757i 1.00549 + 1.74156i
\(902\) −6.91815 6.91815i −0.230349 0.230349i
\(903\) 0 0
\(904\) −1.73257 + 6.46604i −0.0576244 + 0.215057i
\(905\) −4.50381 4.50381i −0.149712 0.149712i
\(906\) 0 0
\(907\) −31.7089 18.3071i −1.05288 0.607878i −0.129422 0.991590i \(-0.541312\pi\)
−0.923453 + 0.383712i \(0.874646\pi\)
\(908\) −0.853689 3.18601i −0.0283307 0.105732i
\(909\) 0 0
\(910\) −13.0837 + 7.43971i −0.433721 + 0.246624i
\(911\) −40.8424 −1.35317 −0.676585 0.736365i \(-0.736541\pi\)
−0.676585 + 0.736365i \(0.736541\pi\)
\(912\) 0 0
\(913\) −3.00056 1.73237i −0.0993039 0.0573331i
\(914\) −7.52181 + 4.34272i −0.248799 + 0.143644i
\(915\) 0 0
\(916\) 0.409350 1.52772i 0.0135253 0.0504771i
\(917\) 41.9617 21.8925i 1.38570 0.722955i
\(918\) 0 0
\(919\) 12.1413 + 21.0293i 0.400504 + 0.693693i 0.993787 0.111301i \(-0.0355018\pi\)
−0.593283 + 0.804994i \(0.702168\pi\)
\(920\) 0.866021 1.49999i 0.0285519 0.0494533i
\(921\) 0 0
\(922\) 12.0824 0.397912
\(923\) 9.15845 2.81250i 0.301454 0.0925746i
\(924\) 0 0
\(925\) −7.56871 28.2468i −0.248858 0.928749i
\(926\) −18.6069 + 32.2281i −0.611461 + 1.05908i
\(927\) 0 0
\(928\) 26.1307 26.1307i 0.857781 0.857781i
\(929\) −0.812091 + 3.03077i −0.0266438 + 0.0994362i −0.977967 0.208758i \(-0.933058\pi\)
0.951324 + 0.308194i \(0.0997246\pi\)
\(930\) 0 0
\(931\) −6.82750 8.10665i −0.223762 0.265685i
\(932\) −0.463744 0.803228i −0.0151904 0.0263106i
\(933\) 0 0
\(934\) 2.96734 + 11.0743i 0.0970944 + 0.362361i
\(935\) 6.93241i 0.226714i
\(936\) 0 0
\(937\) 39.6319i 1.29472i −0.762185 0.647359i \(-0.775874\pi\)
0.762185 0.647359i \(-0.224126\pi\)
\(938\) 16.0501 + 10.2045i 0.524053 + 0.333188i
\(939\) 0 0
\(940\) −6.99397 + 4.03797i −0.228118 + 0.131704i
\(941\) −9.63423 9.63423i −0.314067 0.314067i 0.532416 0.846483i \(-0.321284\pi\)
−0.846483 + 0.532416i \(0.821284\pi\)
\(942\) 0 0
\(943\) 3.36498 + 0.901643i 0.109579 + 0.0293615i
\(944\) −1.09743 + 1.09743i −0.0357185 + 0.0357185i
\(945\) 0 0
\(946\) 9.05982 + 5.23069i 0.294560 + 0.170064i
\(947\) −51.2831 + 13.7413i −1.66648 + 0.446531i −0.964157 0.265331i \(-0.914519\pi\)
−0.702319 + 0.711862i \(0.747852\pi\)
\(948\) 0 0
\(949\) 2.81326 12.2552i 0.0913224 0.397821i
\(950\) 4.75047i 0.154126i
\(951\) 0 0
\(952\) −37.5020 + 8.34986i −1.21545 + 0.270621i
\(953\) 28.0071 16.1699i 0.907238 0.523794i 0.0276968 0.999616i \(-0.491183\pi\)
0.879542 + 0.475822i \(0.157849\pi\)
\(954\) 0 0
\(955\) 3.70398 13.8234i 0.119858 0.447316i
\(956\) −1.08992 + 4.06765i −0.0352506 + 0.131557i
\(957\) 0 0
\(958\) −8.28783 + 4.78498i −0.267768 + 0.154596i
\(959\) −6.53551 + 1.45514i −0.211043 + 0.0469889i
\(960\) 0 0
\(961\) 13.8839i 0.447867i
\(962\) 35.0159 + 18.5624i 1.12896 + 0.598475i
\(963\) 0 0
\(964\) −7.77010 + 2.08199i −0.250258 + 0.0670565i
\(965\) −16.0058 9.24094i −0.515244 0.297476i
\(966\) 0 0
\(967\) 5.38328 5.38328i 0.173115 0.173115i −0.615232 0.788346i \(-0.710938\pi\)
0.788346 + 0.615232i \(0.210938\pi\)
\(968\) −29.5493 7.91771i −0.949750 0.254485i
\(969\) 0 0
\(970\) 15.3331 + 15.3331i 0.492316 + 0.492316i
\(971\) 36.0969 20.8405i 1.15840 0.668804i 0.207483 0.978239i \(-0.433473\pi\)
0.950921 + 0.309434i \(0.100140\pi\)
\(972\) 0 0
\(973\) −22.8507 14.5282i −0.732558 0.465753i
\(974\) 22.2941i 0.714348i
\(975\) 0 0
\(976\) 16.2755i 0.520966i
\(977\) 2.38909 + 8.91619i 0.0764336 + 0.285254i 0.993555 0.113355i \(-0.0361597\pi\)
−0.917121 + 0.398609i \(0.869493\pi\)
\(978\) 0 0
\(979\) −5.43157 9.40776i −0.173594 0.300673i
\(980\) 6.38402 5.37669i 0.203930 0.171752i
\(981\) 0 0
\(982\) −0.883840 + 3.29853i −0.0282045 + 0.105260i
\(983\) 23.8714 23.8714i 0.761380 0.761380i −0.215192 0.976572i \(-0.569038\pi\)
0.976572 + 0.215192i \(0.0690378\pi\)
\(984\) 0 0
\(985\) 1.13406 1.96426i 0.0361343 0.0625864i
\(986\) −11.4609 42.7726i −0.364989 1.36216i
\(987\) 0 0
\(988\) 3.28047 + 3.05145i 0.104365 + 0.0970796i
\(989\) −3.72497 −0.118447
\(990\) 0 0
\(991\) −2.66281 + 4.61212i −0.0845869 + 0.146509i −0.905215 0.424954i \(-0.860290\pi\)
0.820628 + 0.571462i \(0.193624\pi\)
\(992\) −8.88738 15.3934i −0.282175 0.488741i
\(993\) 0 0
\(994\) 6.76871 3.53141i 0.214691 0.112010i
\(995\) 4.39582 16.4054i 0.139357 0.520087i
\(996\) 0 0
\(997\) 28.6452 16.5383i 0.907203 0.523774i 0.0276726 0.999617i \(-0.491190\pi\)
0.879530 + 0.475843i \(0.157857\pi\)
\(998\) −14.2338 8.21788i −0.450563 0.260132i
\(999\) 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 819.2.fm.f.370.6 32
3.2 odd 2 273.2.by.c.97.3 yes 32
7.6 odd 2 819.2.fm.e.370.6 32
13.11 odd 12 819.2.fm.e.622.6 32
21.20 even 2 273.2.by.d.97.3 yes 32
39.11 even 12 273.2.by.d.76.3 yes 32
91.76 even 12 inner 819.2.fm.f.622.6 32
273.167 odd 12 273.2.by.c.76.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.by.c.76.3 32 273.167 odd 12
273.2.by.c.97.3 yes 32 3.2 odd 2
273.2.by.d.76.3 yes 32 39.11 even 12
273.2.by.d.97.3 yes 32 21.20 even 2
819.2.fm.e.370.6 32 7.6 odd 2
819.2.fm.e.622.6 32 13.11 odd 12
819.2.fm.f.370.6 32 1.1 even 1 trivial
819.2.fm.f.622.6 32 91.76 even 12 inner