Properties

Label 891.2.f.f.82.5
Level $891$
Weight $2$
Character 891.82
Analytic conductor $7.115$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(82,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.f (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 82.5
Character \(\chi\) \(=\) 891.82
Dual form 891.2.f.f.163.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0881157 + 0.271192i) q^{2} +(1.55225 - 1.12778i) q^{4} +(0.837045 - 2.57616i) q^{5} +(3.29540 - 2.39425i) q^{7} +(0.904002 + 0.656796i) q^{8} +0.772391 q^{10} +(1.82892 + 2.76678i) q^{11} +(1.19001 + 3.66248i) q^{13} +(0.939677 + 0.682715i) q^{14} +(1.08735 - 3.34653i) q^{16} +(-1.33502 + 4.10876i) q^{17} +(1.31246 + 0.953561i) q^{19} +(-1.60603 - 4.94285i) q^{20} +(-0.589172 + 0.739785i) q^{22} -1.86423 q^{23} +(-1.89087 - 1.37379i) q^{25} +(-0.888377 + 0.645443i) q^{26} +(2.41511 - 7.43295i) q^{28} +(-2.87472 + 2.08860i) q^{29} +(-1.50324 - 4.62650i) q^{31} +3.23818 q^{32} -1.23190 q^{34} +(-3.40956 - 10.4936i) q^{35} +(-6.26542 + 4.55210i) q^{37} +(-0.142950 + 0.439954i) q^{38} +(2.44870 - 1.77909i) q^{40} +(-5.55968 - 4.03935i) q^{41} +0.984991 q^{43} +(5.95925 + 2.23213i) q^{44} +(-0.164268 - 0.505566i) q^{46} +(-4.74598 - 3.44815i) q^{47} +(2.96411 - 9.12259i) q^{49} +(0.205947 - 0.633841i) q^{50} +(5.97766 + 4.34302i) q^{52} +(-0.485721 - 1.49489i) q^{53} +(8.65855 - 2.39567i) q^{55} +4.55158 q^{56} +(-0.819721 - 0.595562i) q^{58} +(-9.19245 + 6.67871i) q^{59} +(-2.65986 + 8.18620i) q^{61} +(1.12221 - 0.815335i) q^{62} +(-1.88937 - 5.81490i) q^{64} +10.4312 q^{65} -1.74056 q^{67} +(2.56148 + 7.88344i) q^{68} +(2.54534 - 1.84929i) q^{70} +(-1.77418 + 5.46036i) q^{71} +(3.27379 - 2.37855i) q^{73} +(-1.78657 - 1.29802i) q^{74} +3.11268 q^{76} +(12.6514 + 4.73875i) q^{77} +(-1.32264 - 4.07066i) q^{79} +(-7.71104 - 5.60240i) q^{80} +(0.605544 - 1.86367i) q^{82} +(-2.00867 + 6.18204i) q^{83} +(9.46735 + 6.87843i) q^{85} +(0.0867932 + 0.267122i) q^{86} +(-0.163863 + 3.70240i) q^{88} +9.26243 q^{89} +(12.6904 + 9.22014i) q^{91} +(-2.89376 + 2.10244i) q^{92} +(0.516917 - 1.59091i) q^{94} +(3.55511 - 2.58294i) q^{95} +(-2.29064 - 7.04988i) q^{97} +2.73516 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + q^{2} - 11 q^{4} + 8 q^{5} + 2 q^{7} + 3 q^{8} - 4 q^{10} + 2 q^{11} + 11 q^{13} + 10 q^{14} + 9 q^{16} - 10 q^{17} + 4 q^{19} + 45 q^{20} + 16 q^{22} - 20 q^{23} - 11 q^{25} - 6 q^{26} - 27 q^{28}+ \cdots - 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0881157 + 0.271192i 0.0623072 + 0.191762i 0.977365 0.211562i \(-0.0678549\pi\)
−0.915057 + 0.403324i \(0.867855\pi\)
\(3\) 0 0
\(4\) 1.55225 1.12778i 0.776127 0.563889i
\(5\) 0.837045 2.57616i 0.374338 1.15209i −0.569587 0.821931i \(-0.692897\pi\)
0.943924 0.330162i \(-0.107103\pi\)
\(6\) 0 0
\(7\) 3.29540 2.39425i 1.24554 0.904940i 0.247588 0.968865i \(-0.420362\pi\)
0.997955 + 0.0639253i \(0.0203619\pi\)
\(8\) 0.904002 + 0.656796i 0.319613 + 0.232212i
\(9\) 0 0
\(10\) 0.772391 0.244251
\(11\) 1.82892 + 2.76678i 0.551439 + 0.834215i
\(12\) 0 0
\(13\) 1.19001 + 3.66248i 0.330050 + 1.01579i 0.969109 + 0.246631i \(0.0793236\pi\)
−0.639060 + 0.769157i \(0.720676\pi\)
\(14\) 0.939677 + 0.682715i 0.251139 + 0.182463i
\(15\) 0 0
\(16\) 1.08735 3.34653i 0.271839 0.836633i
\(17\) −1.33502 + 4.10876i −0.323789 + 0.996520i 0.648195 + 0.761474i \(0.275524\pi\)
−0.971984 + 0.235046i \(0.924476\pi\)
\(18\) 0 0
\(19\) 1.31246 + 0.953561i 0.301100 + 0.218762i 0.728068 0.685505i \(-0.240418\pi\)
−0.426968 + 0.904267i \(0.640418\pi\)
\(20\) −1.60603 4.94285i −0.359119 1.10526i
\(21\) 0 0
\(22\) −0.589172 + 0.739785i −0.125612 + 0.157723i
\(23\) −1.86423 −0.388720 −0.194360 0.980930i \(-0.562263\pi\)
−0.194360 + 0.980930i \(0.562263\pi\)
\(24\) 0 0
\(25\) −1.89087 1.37379i −0.378173 0.274759i
\(26\) −0.888377 + 0.645443i −0.174225 + 0.126582i
\(27\) 0 0
\(28\) 2.41511 7.43295i 0.456413 1.40470i
\(29\) −2.87472 + 2.08860i −0.533821 + 0.387844i −0.821785 0.569797i \(-0.807022\pi\)
0.287964 + 0.957641i \(0.407022\pi\)
\(30\) 0 0
\(31\) −1.50324 4.62650i −0.269990 0.830944i −0.990502 0.137501i \(-0.956093\pi\)
0.720512 0.693443i \(-0.243907\pi\)
\(32\) 3.23818 0.572435
\(33\) 0 0
\(34\) −1.23190 −0.211269
\(35\) −3.40956 10.4936i −0.576321 1.77374i
\(36\) 0 0
\(37\) −6.26542 + 4.55210i −1.03003 + 0.748360i −0.968314 0.249734i \(-0.919657\pi\)
−0.0617145 + 0.998094i \(0.519657\pi\)
\(38\) −0.142950 + 0.439954i −0.0231895 + 0.0713699i
\(39\) 0 0
\(40\) 2.44870 1.77909i 0.387174 0.281298i
\(41\) −5.55968 4.03935i −0.868276 0.630840i 0.0618474 0.998086i \(-0.480301\pi\)
−0.930124 + 0.367246i \(0.880301\pi\)
\(42\) 0 0
\(43\) 0.984991 0.150210 0.0751049 0.997176i \(-0.476071\pi\)
0.0751049 + 0.997176i \(0.476071\pi\)
\(44\) 5.95925 + 2.23213i 0.898391 + 0.336506i
\(45\) 0 0
\(46\) −0.164268 0.505566i −0.0242200 0.0745416i
\(47\) −4.74598 3.44815i −0.692272 0.502965i 0.185134 0.982713i \(-0.440728\pi\)
−0.877406 + 0.479748i \(0.840728\pi\)
\(48\) 0 0
\(49\) 2.96411 9.12259i 0.423444 1.30323i
\(50\) 0.205947 0.633841i 0.0291254 0.0896386i
\(51\) 0 0
\(52\) 5.97766 + 4.34302i 0.828952 + 0.602269i
\(53\) −0.485721 1.49489i −0.0667189 0.205340i 0.912139 0.409881i \(-0.134430\pi\)
−0.978858 + 0.204541i \(0.934430\pi\)
\(54\) 0 0
\(55\) 8.65855 2.39567i 1.16752 0.323032i
\(56\) 4.55158 0.608230
\(57\) 0 0
\(58\) −0.819721 0.595562i −0.107635 0.0782011i
\(59\) −9.19245 + 6.67871i −1.19676 + 0.869494i −0.993962 0.109728i \(-0.965002\pi\)
−0.202794 + 0.979222i \(0.565002\pi\)
\(60\) 0 0
\(61\) −2.65986 + 8.18620i −0.340560 + 1.04814i 0.623358 + 0.781936i \(0.285768\pi\)
−0.963918 + 0.266199i \(0.914232\pi\)
\(62\) 1.12221 0.815335i 0.142521 0.103548i
\(63\) 0 0
\(64\) −1.88937 5.81490i −0.236172 0.726862i
\(65\) 10.4312 1.29383
\(66\) 0 0
\(67\) −1.74056 −0.212644 −0.106322 0.994332i \(-0.533907\pi\)
−0.106322 + 0.994332i \(0.533907\pi\)
\(68\) 2.56148 + 7.88344i 0.310626 + 0.956007i
\(69\) 0 0
\(70\) 2.54534 1.84929i 0.304226 0.221033i
\(71\) −1.77418 + 5.46036i −0.210556 + 0.648026i 0.788883 + 0.614543i \(0.210660\pi\)
−0.999439 + 0.0334822i \(0.989340\pi\)
\(72\) 0 0
\(73\) 3.27379 2.37855i 0.383168 0.278388i −0.379482 0.925199i \(-0.623898\pi\)
0.762650 + 0.646811i \(0.223898\pi\)
\(74\) −1.78657 1.29802i −0.207685 0.150892i
\(75\) 0 0
\(76\) 3.11268 0.357049
\(77\) 12.6514 + 4.73875i 1.44176 + 0.540031i
\(78\) 0 0
\(79\) −1.32264 4.07066i −0.148808 0.457985i 0.848673 0.528918i \(-0.177402\pi\)
−0.997481 + 0.0709332i \(0.977402\pi\)
\(80\) −7.71104 5.60240i −0.862120 0.626367i
\(81\) 0 0
\(82\) 0.605544 1.86367i 0.0668711 0.205808i
\(83\) −2.00867 + 6.18204i −0.220480 + 0.678567i 0.778239 + 0.627968i \(0.216113\pi\)
−0.998719 + 0.0505994i \(0.983887\pi\)
\(84\) 0 0
\(85\) 9.46735 + 6.87843i 1.02688 + 0.746071i
\(86\) 0.0867932 + 0.267122i 0.00935915 + 0.0288045i
\(87\) 0 0
\(88\) −0.163863 + 3.70240i −0.0174679 + 0.394677i
\(89\) 9.26243 0.981816 0.490908 0.871211i \(-0.336665\pi\)
0.490908 + 0.871211i \(0.336665\pi\)
\(90\) 0 0
\(91\) 12.6904 + 9.22014i 1.33032 + 0.966533i
\(92\) −2.89376 + 2.10244i −0.301696 + 0.219195i
\(93\) 0 0
\(94\) 0.516917 1.59091i 0.0533160 0.164090i
\(95\) 3.55511 2.58294i 0.364747 0.265004i
\(96\) 0 0
\(97\) −2.29064 7.04988i −0.232580 0.715807i −0.997433 0.0716026i \(-0.977189\pi\)
0.764854 0.644204i \(-0.222811\pi\)
\(98\) 2.73516 0.276293
\(99\) 0 0
\(100\) −4.48444 −0.448444
\(101\) −4.23897 13.0462i −0.421794 1.29815i −0.906031 0.423211i \(-0.860903\pi\)
0.484238 0.874936i \(-0.339097\pi\)
\(102\) 0 0
\(103\) −4.10596 + 2.98316i −0.404572 + 0.293939i −0.771401 0.636350i \(-0.780444\pi\)
0.366828 + 0.930289i \(0.380444\pi\)
\(104\) −1.32973 + 4.09248i −0.130391 + 0.401301i
\(105\) 0 0
\(106\) 0.362604 0.263447i 0.0352192 0.0255883i
\(107\) 2.24824 + 1.63344i 0.217346 + 0.157911i 0.691131 0.722730i \(-0.257113\pi\)
−0.473785 + 0.880640i \(0.657113\pi\)
\(108\) 0 0
\(109\) −17.3573 −1.66253 −0.831263 0.555879i \(-0.812382\pi\)
−0.831263 + 0.555879i \(0.812382\pi\)
\(110\) 1.41264 + 2.13703i 0.134690 + 0.203758i
\(111\) 0 0
\(112\) −4.42916 13.6316i −0.418516 1.28806i
\(113\) −0.763432 0.554666i −0.0718177 0.0521786i 0.551297 0.834309i \(-0.314133\pi\)
−0.623115 + 0.782130i \(0.714133\pi\)
\(114\) 0 0
\(115\) −1.56045 + 4.80257i −0.145513 + 0.447842i
\(116\) −2.10681 + 6.48408i −0.195612 + 0.602032i
\(117\) 0 0
\(118\) −2.62121 1.90442i −0.241302 0.175316i
\(119\) 5.43797 + 16.7364i 0.498498 + 1.53422i
\(120\) 0 0
\(121\) −4.31012 + 10.1204i −0.391829 + 0.920038i
\(122\) −2.45441 −0.222212
\(123\) 0 0
\(124\) −7.55108 5.48618i −0.678107 0.492673i
\(125\) 5.83521 4.23953i 0.521917 0.379195i
\(126\) 0 0
\(127\) 0.757216 2.33047i 0.0671920 0.206796i −0.911823 0.410583i \(-0.865325\pi\)
0.979015 + 0.203787i \(0.0653251\pi\)
\(128\) 6.64996 4.83148i 0.587779 0.427047i
\(129\) 0 0
\(130\) 0.919154 + 2.82886i 0.0806151 + 0.248108i
\(131\) 3.99737 0.349252 0.174626 0.984635i \(-0.444128\pi\)
0.174626 + 0.984635i \(0.444128\pi\)
\(132\) 0 0
\(133\) 6.60815 0.572999
\(134\) −0.153371 0.472027i −0.0132492 0.0407769i
\(135\) 0 0
\(136\) −3.90547 + 2.83749i −0.334892 + 0.243313i
\(137\) 0.336599 1.03594i 0.0287576 0.0885067i −0.935648 0.352936i \(-0.885183\pi\)
0.964405 + 0.264429i \(0.0851835\pi\)
\(138\) 0 0
\(139\) −2.33395 + 1.69572i −0.197963 + 0.143829i −0.682351 0.731025i \(-0.739042\pi\)
0.484388 + 0.874853i \(0.339042\pi\)
\(140\) −17.1269 12.4434i −1.44749 1.05166i
\(141\) 0 0
\(142\) −1.63714 −0.137386
\(143\) −7.95683 + 9.99087i −0.665383 + 0.835478i
\(144\) 0 0
\(145\) 2.97431 + 9.15398i 0.247003 + 0.760197i
\(146\) 0.933515 + 0.678238i 0.0772583 + 0.0561314i
\(147\) 0 0
\(148\) −4.59177 + 14.1320i −0.377441 + 1.16164i
\(149\) 6.23436 19.1874i 0.510739 1.57189i −0.280165 0.959952i \(-0.590389\pi\)
0.790904 0.611940i \(-0.209611\pi\)
\(150\) 0 0
\(151\) 8.96258 + 6.51169i 0.729364 + 0.529914i 0.889362 0.457203i \(-0.151149\pi\)
−0.159998 + 0.987117i \(0.551149\pi\)
\(152\) 0.560175 + 1.72404i 0.0454362 + 0.139838i
\(153\) 0 0
\(154\) −0.170330 + 3.84851i −0.0137255 + 0.310122i
\(155\) −13.1769 −1.05839
\(156\) 0 0
\(157\) −0.269228 0.195606i −0.0214867 0.0156110i 0.576990 0.816751i \(-0.304227\pi\)
−0.598477 + 0.801140i \(0.704227\pi\)
\(158\) 0.987387 0.717378i 0.0785523 0.0570716i
\(159\) 0 0
\(160\) 2.71050 8.34207i 0.214284 0.659499i
\(161\) −6.14339 + 4.46344i −0.484167 + 0.351768i
\(162\) 0 0
\(163\) 4.12168 + 12.6852i 0.322835 + 0.993584i 0.972408 + 0.233285i \(0.0749475\pi\)
−0.649574 + 0.760299i \(0.725053\pi\)
\(164\) −13.1855 −1.02962
\(165\) 0 0
\(166\) −1.85352 −0.143861
\(167\) −5.84510 17.9894i −0.452308 1.39206i −0.874267 0.485445i \(-0.838658\pi\)
0.421960 0.906615i \(-0.361342\pi\)
\(168\) 0 0
\(169\) −1.48039 + 1.07557i −0.113876 + 0.0827359i
\(170\) −1.03115 + 3.17357i −0.0790860 + 0.243402i
\(171\) 0 0
\(172\) 1.52896 1.11085i 0.116582 0.0847016i
\(173\) 1.22492 + 0.889958i 0.0931292 + 0.0676623i 0.633375 0.773845i \(-0.281669\pi\)
−0.540246 + 0.841507i \(0.681669\pi\)
\(174\) 0 0
\(175\) −9.52036 −0.719671
\(176\) 11.2478 3.11207i 0.847835 0.234581i
\(177\) 0 0
\(178\) 0.816166 + 2.51190i 0.0611742 + 0.188275i
\(179\) −10.6703 7.75244i −0.797537 0.579445i 0.112653 0.993634i \(-0.464065\pi\)
−0.910191 + 0.414190i \(0.864065\pi\)
\(180\) 0 0
\(181\) 0.864886 2.66185i 0.0642865 0.197853i −0.913754 0.406267i \(-0.866830\pi\)
0.978041 + 0.208414i \(0.0668301\pi\)
\(182\) −1.38220 + 4.25398i −0.102456 + 0.315326i
\(183\) 0 0
\(184\) −1.68527 1.22442i −0.124240 0.0902656i
\(185\) 6.48248 + 19.9510i 0.476602 + 1.46683i
\(186\) 0 0
\(187\) −13.8097 + 3.82089i −1.00986 + 0.279411i
\(188\) −11.2557 −0.820907
\(189\) 0 0
\(190\) 1.01374 + 0.736522i 0.0735441 + 0.0534329i
\(191\) 13.5442 9.84044i 0.980024 0.712029i 0.0223100 0.999751i \(-0.492898\pi\)
0.957714 + 0.287722i \(0.0928979\pi\)
\(192\) 0 0
\(193\) −6.81054 + 20.9607i −0.490233 + 1.50878i 0.334022 + 0.942565i \(0.391594\pi\)
−0.824255 + 0.566218i \(0.808406\pi\)
\(194\) 1.71003 1.24241i 0.122773 0.0891998i
\(195\) 0 0
\(196\) −5.68721 17.5034i −0.406229 1.25024i
\(197\) 18.2247 1.29845 0.649227 0.760595i \(-0.275093\pi\)
0.649227 + 0.760595i \(0.275093\pi\)
\(198\) 0 0
\(199\) −25.0958 −1.77899 −0.889497 0.456942i \(-0.848945\pi\)
−0.889497 + 0.456942i \(0.848945\pi\)
\(200\) −0.807044 2.48383i −0.0570666 0.175633i
\(201\) 0 0
\(202\) 3.16451 2.29915i 0.222654 0.161768i
\(203\) −4.47270 + 13.7656i −0.313922 + 0.966153i
\(204\) 0 0
\(205\) −15.0597 + 10.9415i −1.05181 + 0.764188i
\(206\) −1.17081 0.850642i −0.0815741 0.0592670i
\(207\) 0 0
\(208\) 13.5506 0.939563
\(209\) −0.237902 + 5.37528i −0.0164560 + 0.371816i
\(210\) 0 0
\(211\) 2.55558 + 7.86526i 0.175933 + 0.541467i 0.999675 0.0254986i \(-0.00811733\pi\)
−0.823742 + 0.566965i \(0.808117\pi\)
\(212\) −2.43987 1.77267i −0.167571 0.121747i
\(213\) 0 0
\(214\) −0.244872 + 0.753637i −0.0167391 + 0.0515176i
\(215\) 0.824482 2.53749i 0.0562292 0.173056i
\(216\) 0 0
\(217\) −16.0308 11.6470i −1.08824 0.790652i
\(218\) −1.52945 4.70716i −0.103587 0.318809i
\(219\) 0 0
\(220\) 10.7385 13.4836i 0.723988 0.909064i
\(221\) −16.6369 −1.11912
\(222\) 0 0
\(223\) 5.94796 + 4.32145i 0.398305 + 0.289385i 0.768850 0.639429i \(-0.220829\pi\)
−0.370545 + 0.928814i \(0.620829\pi\)
\(224\) 10.6711 7.75301i 0.712993 0.518020i
\(225\) 0 0
\(226\) 0.0831507 0.255912i 0.00553110 0.0170230i
\(227\) 15.3237 11.1334i 1.01707 0.738947i 0.0513921 0.998679i \(-0.483634\pi\)
0.965681 + 0.259732i \(0.0836342\pi\)
\(228\) 0 0
\(229\) −2.42870 7.47478i −0.160493 0.493947i 0.838183 0.545389i \(-0.183618\pi\)
−0.998676 + 0.0514422i \(0.983618\pi\)
\(230\) −1.43992 −0.0949454
\(231\) 0 0
\(232\) −3.97054 −0.260678
\(233\) −2.03006 6.24789i −0.132994 0.409313i 0.862279 0.506434i \(-0.169037\pi\)
−0.995273 + 0.0971212i \(0.969037\pi\)
\(234\) 0 0
\(235\) −12.8556 + 9.34013i −0.838606 + 0.609283i
\(236\) −6.73691 + 20.7341i −0.438536 + 1.34967i
\(237\) 0 0
\(238\) −4.05960 + 2.94947i −0.263145 + 0.191186i
\(239\) 20.6674 + 15.0157i 1.33686 + 0.971287i 0.999553 + 0.0298925i \(0.00951648\pi\)
0.337308 + 0.941394i \(0.390484\pi\)
\(240\) 0 0
\(241\) −2.98198 −0.192086 −0.0960432 0.995377i \(-0.530619\pi\)
−0.0960432 + 0.995377i \(0.530619\pi\)
\(242\) −3.12437 0.277103i −0.200842 0.0178129i
\(243\) 0 0
\(244\) 5.10344 + 15.7068i 0.326714 + 1.00552i
\(245\) −21.0201 15.2720i −1.34293 0.975694i
\(246\) 0 0
\(247\) −1.93055 + 5.94161i −0.122838 + 0.378056i
\(248\) 1.67973 5.16969i 0.106663 0.328276i
\(249\) 0 0
\(250\) 1.66390 + 1.20889i 0.105234 + 0.0764572i
\(251\) 3.60577 + 11.0974i 0.227594 + 0.700463i 0.998018 + 0.0629308i \(0.0200447\pi\)
−0.770424 + 0.637532i \(0.779955\pi\)
\(252\) 0 0
\(253\) −3.40953 5.15792i −0.214355 0.324276i
\(254\) 0.698728 0.0438421
\(255\) 0 0
\(256\) −7.99667 5.80992i −0.499792 0.363120i
\(257\) −16.7664 + 12.1815i −1.04586 + 0.759863i −0.971421 0.237363i \(-0.923717\pi\)
−0.0744403 + 0.997225i \(0.523717\pi\)
\(258\) 0 0
\(259\) −9.74822 + 30.0019i −0.605725 + 1.86423i
\(260\) 16.1919 11.7641i 1.00418 0.729578i
\(261\) 0 0
\(262\) 0.352231 + 1.08406i 0.0217609 + 0.0669732i
\(263\) 9.08545 0.560233 0.280117 0.959966i \(-0.409627\pi\)
0.280117 + 0.959966i \(0.409627\pi\)
\(264\) 0 0
\(265\) −4.25766 −0.261546
\(266\) 0.582281 + 1.79208i 0.0357020 + 0.109879i
\(267\) 0 0
\(268\) −2.70179 + 1.96297i −0.165038 + 0.119907i
\(269\) 2.45399 7.55261i 0.149623 0.460491i −0.847954 0.530070i \(-0.822166\pi\)
0.997576 + 0.0695792i \(0.0221656\pi\)
\(270\) 0 0
\(271\) −3.01249 + 2.18870i −0.182995 + 0.132954i −0.675512 0.737349i \(-0.736077\pi\)
0.492516 + 0.870303i \(0.336077\pi\)
\(272\) 12.2985 + 8.93536i 0.745704 + 0.541786i
\(273\) 0 0
\(274\) 0.310600 0.0187640
\(275\) 0.342746 7.74416i 0.0206683 0.466991i
\(276\) 0 0
\(277\) −1.20536 3.70973i −0.0724232 0.222896i 0.908292 0.418336i \(-0.137386\pi\)
−0.980716 + 0.195440i \(0.937386\pi\)
\(278\) −0.665523 0.483531i −0.0399154 0.0290003i
\(279\) 0 0
\(280\) 3.80987 11.7256i 0.227684 0.700738i
\(281\) 0.0122442 0.0376838i 0.000730428 0.00224803i −0.950691 0.310141i \(-0.899624\pi\)
0.951421 + 0.307893i \(0.0996238\pi\)
\(282\) 0 0
\(283\) −5.17275 3.75822i −0.307488 0.223403i 0.423330 0.905976i \(-0.360861\pi\)
−0.730818 + 0.682572i \(0.760861\pi\)
\(284\) 3.40410 + 10.4767i 0.201996 + 0.621680i
\(285\) 0 0
\(286\) −3.41057 1.27748i −0.201671 0.0755388i
\(287\) −27.9925 −1.65235
\(288\) 0 0
\(289\) −1.34634 0.978174i −0.0791965 0.0575397i
\(290\) −2.22041 + 1.61322i −0.130387 + 0.0947315i
\(291\) 0 0
\(292\) 2.39928 7.38421i 0.140407 0.432128i
\(293\) 18.9370 13.7585i 1.10631 0.803782i 0.124233 0.992253i \(-0.460353\pi\)
0.982079 + 0.188471i \(0.0603531\pi\)
\(294\) 0 0
\(295\) 9.51092 + 29.2716i 0.553747 + 1.70426i
\(296\) −8.65375 −0.502989
\(297\) 0 0
\(298\) 5.75282 0.333252
\(299\) −2.21846 6.82772i −0.128297 0.394857i
\(300\) 0 0
\(301\) 3.24594 2.35831i 0.187093 0.135931i
\(302\) −0.976177 + 3.00436i −0.0561727 + 0.172882i
\(303\) 0 0
\(304\) 4.61824 3.35534i 0.264874 0.192442i
\(305\) 18.8625 + 13.7044i 1.08007 + 0.784713i
\(306\) 0 0
\(307\) 29.1494 1.66365 0.831823 0.555042i \(-0.187298\pi\)
0.831823 + 0.555042i \(0.187298\pi\)
\(308\) 24.9824 6.91218i 1.42350 0.393858i
\(309\) 0 0
\(310\) −1.16109 3.57347i −0.0659455 0.202959i
\(311\) 15.9423 + 11.5827i 0.904003 + 0.656797i 0.939491 0.342573i \(-0.111299\pi\)
−0.0354879 + 0.999370i \(0.511299\pi\)
\(312\) 0 0
\(313\) 0.413581 1.27287i 0.0233770 0.0719470i −0.938687 0.344769i \(-0.887957\pi\)
0.962064 + 0.272822i \(0.0879571\pi\)
\(314\) 0.0293235 0.0902485i 0.00165482 0.00509302i
\(315\) 0 0
\(316\) −6.64387 4.82706i −0.373747 0.271543i
\(317\) 1.23634 + 3.80507i 0.0694400 + 0.213714i 0.979754 0.200203i \(-0.0641602\pi\)
−0.910314 + 0.413917i \(0.864160\pi\)
\(318\) 0 0
\(319\) −11.0363 4.13382i −0.617915 0.231449i
\(320\) −16.5616 −0.925821
\(321\) 0 0
\(322\) −1.75178 1.27274i −0.0976228 0.0709271i
\(323\) −5.67011 + 4.11958i −0.315493 + 0.229219i
\(324\) 0 0
\(325\) 2.78134 8.56008i 0.154281 0.474828i
\(326\) −3.07695 + 2.23554i −0.170417 + 0.123815i
\(327\) 0 0
\(328\) −2.37294 7.30315i −0.131024 0.403249i
\(329\) −23.8956 −1.31741
\(330\) 0 0
\(331\) 3.18033 0.174807 0.0874034 0.996173i \(-0.472143\pi\)
0.0874034 + 0.996173i \(0.472143\pi\)
\(332\) 3.85401 + 11.8614i 0.211516 + 0.650980i
\(333\) 0 0
\(334\) 4.36353 3.17029i 0.238762 0.173471i
\(335\) −1.45693 + 4.48397i −0.0796006 + 0.244985i
\(336\) 0 0
\(337\) 14.7223 10.6964i 0.801977 0.582670i −0.109517 0.993985i \(-0.534930\pi\)
0.911493 + 0.411315i \(0.134930\pi\)
\(338\) −0.422131 0.306696i −0.0229609 0.0166821i
\(339\) 0 0
\(340\) 22.4531 1.21769
\(341\) 10.0512 12.6206i 0.544303 0.683445i
\(342\) 0 0
\(343\) −3.26270 10.0416i −0.176169 0.542193i
\(344\) 0.890434 + 0.646938i 0.0480090 + 0.0348806i
\(345\) 0 0
\(346\) −0.133415 + 0.410609i −0.00717243 + 0.0220745i
\(347\) −8.47142 + 26.0724i −0.454770 + 1.39964i 0.416635 + 0.909074i \(0.363209\pi\)
−0.871405 + 0.490564i \(0.836791\pi\)
\(348\) 0 0
\(349\) −18.5310 13.4635i −0.991940 0.720686i −0.0315945 0.999501i \(-0.510059\pi\)
−0.960345 + 0.278815i \(0.910059\pi\)
\(350\) −0.838893 2.58185i −0.0448407 0.138006i
\(351\) 0 0
\(352\) 5.92237 + 8.95933i 0.315663 + 0.477534i
\(353\) −29.7047 −1.58102 −0.790511 0.612448i \(-0.790185\pi\)
−0.790511 + 0.612448i \(0.790185\pi\)
\(354\) 0 0
\(355\) 12.5817 + 9.14113i 0.667767 + 0.485161i
\(356\) 14.3776 10.4460i 0.762013 0.553635i
\(357\) 0 0
\(358\) 1.16218 3.57682i 0.0614231 0.189041i
\(359\) 29.8183 21.6643i 1.57375 1.14340i 0.650299 0.759678i \(-0.274644\pi\)
0.923450 0.383718i \(-0.125356\pi\)
\(360\) 0 0
\(361\) −5.05804 15.5670i −0.266213 0.819318i
\(362\) 0.798082 0.0419462
\(363\) 0 0
\(364\) 30.0970 1.57751
\(365\) −3.38721 10.4247i −0.177294 0.545656i
\(366\) 0 0
\(367\) 20.1127 14.6127i 1.04987 0.762777i 0.0776846 0.996978i \(-0.475247\pi\)
0.972188 + 0.234201i \(0.0752473\pi\)
\(368\) −2.02708 + 6.23872i −0.105669 + 0.325216i
\(369\) 0 0
\(370\) −4.83936 + 3.51600i −0.251586 + 0.182788i
\(371\) −5.17979 3.76334i −0.268921 0.195383i
\(372\) 0 0
\(373\) 18.2790 0.946453 0.473227 0.880941i \(-0.343089\pi\)
0.473227 + 0.880941i \(0.343089\pi\)
\(374\) −2.25304 3.40839i −0.116502 0.176244i
\(375\) 0 0
\(376\) −2.02564 6.23428i −0.104464 0.321508i
\(377\) −11.0704 8.04312i −0.570155 0.414242i
\(378\) 0 0
\(379\) −9.72145 + 29.9196i −0.499357 + 1.53686i 0.310697 + 0.950509i \(0.399438\pi\)
−0.810054 + 0.586355i \(0.800562\pi\)
\(380\) 2.60545 8.01876i 0.133657 0.411354i
\(381\) 0 0
\(382\) 3.86211 + 2.80598i 0.197603 + 0.143567i
\(383\) −3.84163 11.8233i −0.196298 0.604143i −0.999959 0.00905578i \(-0.997117\pi\)
0.803661 0.595087i \(-0.202883\pi\)
\(384\) 0 0
\(385\) 22.7975 28.6254i 1.16187 1.45888i
\(386\) −6.28449 −0.319872
\(387\) 0 0
\(388\) −11.5064 8.35986i −0.584147 0.424408i
\(389\) −5.92175 + 4.30240i −0.300244 + 0.218140i −0.727699 0.685896i \(-0.759410\pi\)
0.427455 + 0.904037i \(0.359410\pi\)
\(390\) 0 0
\(391\) 2.48878 7.65969i 0.125863 0.387367i
\(392\) 8.67124 6.30003i 0.437964 0.318199i
\(393\) 0 0
\(394\) 1.60588 + 4.94239i 0.0809030 + 0.248994i
\(395\) −11.5938 −0.583346
\(396\) 0 0
\(397\) 34.2087 1.71688 0.858442 0.512911i \(-0.171433\pi\)
0.858442 + 0.512911i \(0.171433\pi\)
\(398\) −2.21133 6.80578i −0.110844 0.341143i
\(399\) 0 0
\(400\) −6.65349 + 4.83404i −0.332675 + 0.241702i
\(401\) 2.31014 7.10988i 0.115363 0.355051i −0.876660 0.481111i \(-0.840233\pi\)
0.992023 + 0.126061i \(0.0402334\pi\)
\(402\) 0 0
\(403\) 15.1556 11.0112i 0.754953 0.548505i
\(404\) −21.2932 15.4704i −1.05938 0.769682i
\(405\) 0 0
\(406\) −4.12723 −0.204831
\(407\) −24.0536 9.00962i −1.19229 0.446590i
\(408\) 0 0
\(409\) 0.744792 + 2.29224i 0.0368276 + 0.113344i 0.967780 0.251796i \(-0.0810212\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(410\) −4.29425 3.11995i −0.212078 0.154084i
\(411\) 0 0
\(412\) −3.00915 + 9.26122i −0.148250 + 0.456268i
\(413\) −14.3023 + 44.0180i −0.703771 + 2.16598i
\(414\) 0 0
\(415\) 14.2446 + 10.3493i 0.699239 + 0.508027i
\(416\) 3.85347 + 11.8598i 0.188932 + 0.581473i
\(417\) 0 0
\(418\) −1.47870 + 0.409129i −0.0723254 + 0.0200112i
\(419\) −11.2018 −0.547242 −0.273621 0.961838i \(-0.588221\pi\)
−0.273621 + 0.961838i \(0.588221\pi\)
\(420\) 0 0
\(421\) 5.58615 + 4.05858i 0.272252 + 0.197803i 0.715531 0.698581i \(-0.246185\pi\)
−0.443279 + 0.896384i \(0.646185\pi\)
\(422\) −1.90781 + 1.38611i −0.0928708 + 0.0674746i
\(423\) 0 0
\(424\) 0.542748 1.67041i 0.0263582 0.0811222i
\(425\) 8.16893 5.93507i 0.396251 0.287893i
\(426\) 0 0
\(427\) 10.8345 + 33.3451i 0.524318 + 1.61368i
\(428\) 5.33200 0.257732
\(429\) 0 0
\(430\) 0.760798 0.0366890
\(431\) −9.01729 27.7524i −0.434348 1.33678i −0.893754 0.448558i \(-0.851938\pi\)
0.459406 0.888226i \(-0.348062\pi\)
\(432\) 0 0
\(433\) 29.5582 21.4753i 1.42048 1.03204i 0.428785 0.903407i \(-0.358942\pi\)
0.991693 0.128630i \(-0.0410581\pi\)
\(434\) 1.74602 5.37370i 0.0838117 0.257946i
\(435\) 0 0
\(436\) −26.9429 + 19.5752i −1.29033 + 0.937480i
\(437\) −2.44674 1.77766i −0.117043 0.0850370i
\(438\) 0 0
\(439\) −21.4975 −1.02602 −0.513009 0.858383i \(-0.671469\pi\)
−0.513009 + 0.858383i \(0.671469\pi\)
\(440\) 9.40081 + 3.52121i 0.448166 + 0.167867i
\(441\) 0 0
\(442\) −1.46597 4.51180i −0.0697293 0.214605i
\(443\) 27.0576 + 19.6585i 1.28554 + 0.934002i 0.999705 0.0242753i \(-0.00772784\pi\)
0.285839 + 0.958278i \(0.407728\pi\)
\(444\) 0 0
\(445\) 7.75307 23.8615i 0.367531 1.13114i
\(446\) −0.647834 + 1.99383i −0.0306758 + 0.0944105i
\(447\) 0 0
\(448\) −20.1485 14.6388i −0.951929 0.691617i
\(449\) 12.2165 + 37.5984i 0.576530 + 1.77438i 0.630908 + 0.775858i \(0.282682\pi\)
−0.0543777 + 0.998520i \(0.517318\pi\)
\(450\) 0 0
\(451\) 1.00777 22.7700i 0.0474540 1.07220i
\(452\) −1.81058 −0.0851625
\(453\) 0 0
\(454\) 4.36954 + 3.17466i 0.205073 + 0.148994i
\(455\) 34.3750 24.9749i 1.61152 1.17084i
\(456\) 0 0
\(457\) 11.5919 35.6763i 0.542248 1.66887i −0.185196 0.982702i \(-0.559292\pi\)
0.727444 0.686167i \(-0.240708\pi\)
\(458\) 1.81309 1.31729i 0.0847204 0.0615529i
\(459\) 0 0
\(460\) 2.99402 + 9.21464i 0.139597 + 0.429635i
\(461\) 19.3653 0.901932 0.450966 0.892541i \(-0.351080\pi\)
0.450966 + 0.892541i \(0.351080\pi\)
\(462\) 0 0
\(463\) −14.3493 −0.666867 −0.333434 0.942774i \(-0.608207\pi\)
−0.333434 + 0.942774i \(0.608207\pi\)
\(464\) 3.86375 + 11.8914i 0.179370 + 0.552044i
\(465\) 0 0
\(466\) 1.51550 1.10107i 0.0702041 0.0510063i
\(467\) −6.89755 + 21.2285i −0.319180 + 0.982336i 0.654819 + 0.755786i \(0.272745\pi\)
−0.973999 + 0.226551i \(0.927255\pi\)
\(468\) 0 0
\(469\) −5.73585 + 4.16734i −0.264857 + 0.192430i
\(470\) −3.66575 2.66332i −0.169088 0.122850i
\(471\) 0 0
\(472\) −12.6965 −0.584406
\(473\) 1.80147 + 2.72525i 0.0828316 + 0.125307i
\(474\) 0 0
\(475\) −1.17170 3.60611i −0.0537611 0.165460i
\(476\) 27.3160 + 19.8462i 1.25203 + 0.909651i
\(477\) 0 0
\(478\) −2.25103 + 6.92795i −0.102960 + 0.316877i
\(479\) −7.18824 + 22.1231i −0.328439 + 1.01083i 0.641425 + 0.767186i \(0.278343\pi\)
−0.969864 + 0.243646i \(0.921657\pi\)
\(480\) 0 0
\(481\) −24.1279 17.5299i −1.10014 0.799296i
\(482\) −0.262760 0.808691i −0.0119684 0.0368349i
\(483\) 0 0
\(484\) 4.72319 + 20.5703i 0.214690 + 0.935014i
\(485\) −20.0790 −0.911740
\(486\) 0 0
\(487\) −0.219083 0.159173i −0.00992760 0.00721282i 0.582810 0.812608i \(-0.301953\pi\)
−0.592738 + 0.805395i \(0.701953\pi\)
\(488\) −7.78118 + 5.65336i −0.352237 + 0.255915i
\(489\) 0 0
\(490\) 2.28945 7.04621i 0.103427 0.318315i
\(491\) 3.40318 2.47255i 0.153583 0.111585i −0.508340 0.861157i \(-0.669741\pi\)
0.661923 + 0.749572i \(0.269741\pi\)
\(492\) 0 0
\(493\) −4.74377 14.5998i −0.213649 0.657544i
\(494\) −1.78143 −0.0801504
\(495\) 0 0
\(496\) −17.1173 −0.768589
\(497\) 7.22682 + 22.2419i 0.324167 + 0.997685i
\(498\) 0 0
\(499\) 12.4299 9.03087i 0.556440 0.404277i −0.273714 0.961811i \(-0.588252\pi\)
0.830154 + 0.557534i \(0.188252\pi\)
\(500\) 4.27647 13.1616i 0.191250 0.588606i
\(501\) 0 0
\(502\) −2.69181 + 1.95571i −0.120141 + 0.0872878i
\(503\) −3.16786 2.30159i −0.141248 0.102623i 0.514917 0.857240i \(-0.327823\pi\)
−0.656165 + 0.754617i \(0.727823\pi\)
\(504\) 0 0
\(505\) −37.1573 −1.65348
\(506\) 1.09836 1.37913i 0.0488279 0.0613099i
\(507\) 0 0
\(508\) −1.45286 4.47145i −0.0644604 0.198389i
\(509\) −23.0969 16.7809i −1.02375 0.743801i −0.0567047 0.998391i \(-0.518059\pi\)
−0.967049 + 0.254590i \(0.918059\pi\)
\(510\) 0 0
\(511\) 5.09361 15.6765i 0.225328 0.693488i
\(512\) 5.95109 18.3156i 0.263004 0.809442i
\(513\) 0 0
\(514\) −4.78092 3.47354i −0.210877 0.153211i
\(515\) 4.24821 + 13.0746i 0.187198 + 0.576138i
\(516\) 0 0
\(517\) 0.860274 19.4375i 0.0378348 0.854858i
\(518\) −8.99526 −0.395229
\(519\) 0 0
\(520\) 9.42984 + 6.85118i 0.413526 + 0.300444i
\(521\) 11.5485 8.39049i 0.505950 0.367594i −0.305335 0.952245i \(-0.598768\pi\)
0.811285 + 0.584651i \(0.198768\pi\)
\(522\) 0 0
\(523\) −10.2462 + 31.5345i −0.448034 + 1.37891i 0.431088 + 0.902310i \(0.358130\pi\)
−0.879122 + 0.476597i \(0.841870\pi\)
\(524\) 6.20494 4.50815i 0.271064 0.196939i
\(525\) 0 0
\(526\) 0.800571 + 2.46390i 0.0349066 + 0.107431i
\(527\) 21.0160 0.915472
\(528\) 0 0
\(529\) −19.5246 −0.848897
\(530\) −0.375166 1.15464i −0.0162962 0.0501545i
\(531\) 0 0
\(532\) 10.2575 7.45252i 0.444720 0.323108i
\(533\) 8.17793 25.1691i 0.354225 1.09019i
\(534\) 0 0
\(535\) 6.08988 4.42456i 0.263289 0.191290i
\(536\) −1.57347 1.14320i −0.0679637 0.0493785i
\(537\) 0 0
\(538\) 2.26444 0.0976271
\(539\) 30.6613 8.48344i 1.32068 0.365407i
\(540\) 0 0
\(541\) −8.79490 27.0679i −0.378122 1.16374i −0.941348 0.337437i \(-0.890440\pi\)
0.563226 0.826303i \(-0.309560\pi\)
\(542\) −0.859005 0.624104i −0.0368974 0.0268076i
\(543\) 0 0
\(544\) −4.32303 + 13.3049i −0.185348 + 0.570443i
\(545\) −14.5288 + 44.7151i −0.622346 + 1.91539i
\(546\) 0 0
\(547\) 24.8745 + 18.0724i 1.06356 + 0.772721i 0.974744 0.223327i \(-0.0716919\pi\)
0.0888154 + 0.996048i \(0.471692\pi\)
\(548\) −0.645829 1.98766i −0.0275884 0.0849085i
\(549\) 0 0
\(550\) 2.13036 0.589432i 0.0908388 0.0251335i
\(551\) −5.76457 −0.245579
\(552\) 0 0
\(553\) −14.1048 10.2477i −0.599796 0.435778i
\(554\) 0.899837 0.653770i 0.0382304 0.0277760i
\(555\) 0 0
\(556\) −1.71050 + 5.26436i −0.0725412 + 0.223259i
\(557\) 5.90145 4.28765i 0.250052 0.181674i −0.455698 0.890135i \(-0.650610\pi\)
0.705750 + 0.708461i \(0.250610\pi\)
\(558\) 0 0
\(559\) 1.17215 + 3.60751i 0.0495767 + 0.152581i
\(560\) −38.8245 −1.64063
\(561\) 0 0
\(562\) 0.0112985 0.000476597
\(563\) −11.3018 34.7834i −0.476315 1.46595i −0.844176 0.536065i \(-0.819910\pi\)
0.367862 0.929881i \(-0.380090\pi\)
\(564\) 0 0
\(565\) −2.06793 + 1.50244i −0.0869987 + 0.0632082i
\(566\) 0.563400 1.73397i 0.0236815 0.0728841i
\(567\) 0 0
\(568\) −5.19020 + 3.77090i −0.217776 + 0.158224i
\(569\) −0.122553 0.0890399i −0.00513769 0.00373275i 0.585213 0.810879i \(-0.301011\pi\)
−0.590351 + 0.807147i \(0.701011\pi\)
\(570\) 0 0
\(571\) 43.2254 1.80893 0.904463 0.426552i \(-0.140272\pi\)
0.904463 + 0.426552i \(0.140272\pi\)
\(572\) −1.08353 + 24.4819i −0.0453048 + 1.02364i
\(573\) 0 0
\(574\) −2.46658 7.59136i −0.102953 0.316857i
\(575\) 3.52502 + 2.56108i 0.147003 + 0.106804i
\(576\) 0 0
\(577\) 9.00017 27.6997i 0.374682 1.15315i −0.569011 0.822330i \(-0.692674\pi\)
0.943693 0.330822i \(-0.107326\pi\)
\(578\) 0.146639 0.451310i 0.00609940 0.0187720i
\(579\) 0 0
\(580\) 14.9405 + 10.8549i 0.620372 + 0.450727i
\(581\) 8.18198 + 25.1815i 0.339446 + 1.04471i
\(582\) 0 0
\(583\) 3.24770 4.07792i 0.134506 0.168890i
\(584\) 4.52173 0.187111
\(585\) 0 0
\(586\) 5.39985 + 3.92322i 0.223066 + 0.162067i
\(587\) 18.3605 13.3397i 0.757821 0.550589i −0.140420 0.990092i \(-0.544845\pi\)
0.898241 + 0.439503i \(0.144845\pi\)
\(588\) 0 0
\(589\) 2.43870 7.50554i 0.100485 0.309261i
\(590\) −7.10017 + 5.15857i −0.292309 + 0.212375i
\(591\) 0 0
\(592\) 8.42100 + 25.9172i 0.346101 + 1.06519i
\(593\) −22.9308 −0.941656 −0.470828 0.882225i \(-0.656045\pi\)
−0.470828 + 0.882225i \(0.656045\pi\)
\(594\) 0 0
\(595\) 47.6673 1.95417
\(596\) −11.9618 36.8147i −0.489975 1.50799i
\(597\) 0 0
\(598\) 1.65614 1.20326i 0.0677247 0.0492049i
\(599\) −3.86293 + 11.8889i −0.157835 + 0.485766i −0.998437 0.0558871i \(-0.982201\pi\)
0.840602 + 0.541653i \(0.182201\pi\)
\(600\) 0 0
\(601\) −18.1858 + 13.2127i −0.741812 + 0.538958i −0.893278 0.449504i \(-0.851601\pi\)
0.151466 + 0.988462i \(0.451601\pi\)
\(602\) 0.925574 + 0.672469i 0.0377236 + 0.0274078i
\(603\) 0 0
\(604\) 21.2559 0.864892
\(605\) 22.4640 + 19.5748i 0.913293 + 0.795829i
\(606\) 0 0
\(607\) 8.25222 + 25.3977i 0.334947 + 1.03086i 0.966748 + 0.255731i \(0.0823161\pi\)
−0.631801 + 0.775131i \(0.717684\pi\)
\(608\) 4.25000 + 3.08780i 0.172360 + 0.125227i
\(609\) 0 0
\(610\) −2.05445 + 6.32295i −0.0831822 + 0.256009i
\(611\) 6.98102 21.4854i 0.282422 0.869205i
\(612\) 0 0
\(613\) 35.1797 + 25.5595i 1.42089 + 1.03234i 0.991623 + 0.129163i \(0.0412289\pi\)
0.429269 + 0.903176i \(0.358771\pi\)
\(614\) 2.56852 + 7.90510i 0.103657 + 0.319024i
\(615\) 0 0
\(616\) 8.32446 + 12.5932i 0.335402 + 0.507395i
\(617\) 41.4255 1.66773 0.833864 0.551969i \(-0.186123\pi\)
0.833864 + 0.551969i \(0.186123\pi\)
\(618\) 0 0
\(619\) −7.20976 5.23820i −0.289785 0.210541i 0.433389 0.901207i \(-0.357318\pi\)
−0.723174 + 0.690666i \(0.757318\pi\)
\(620\) −20.4539 + 14.8606i −0.821446 + 0.596816i
\(621\) 0 0
\(622\) −1.73638 + 5.34404i −0.0696227 + 0.214277i
\(623\) 30.5234 22.1765i 1.22289 0.888485i
\(624\) 0 0
\(625\) −9.64859 29.6953i −0.385944 1.18781i
\(626\) 0.381636 0.0152532
\(627\) 0 0
\(628\) −0.638510 −0.0254793
\(629\) −10.3390 31.8202i −0.412244 1.26876i
\(630\) 0 0
\(631\) 4.58752 3.33303i 0.182626 0.132686i −0.492716 0.870190i \(-0.663996\pi\)
0.675342 + 0.737504i \(0.263996\pi\)
\(632\) 1.47793 4.54859i 0.0587888 0.180933i
\(633\) 0 0
\(634\) −0.922965 + 0.670573i −0.0366556 + 0.0266319i
\(635\) −5.36984 3.90142i −0.213096 0.154823i
\(636\) 0 0
\(637\) 36.9386 1.46356
\(638\) 0.148586 3.35722i 0.00588257 0.132914i
\(639\) 0 0
\(640\) −6.88034 21.1755i −0.271970 0.837036i
\(641\) −21.6964 15.7633i −0.856955 0.622615i 0.0700995 0.997540i \(-0.477668\pi\)
−0.927055 + 0.374925i \(0.877668\pi\)
\(642\) 0 0
\(643\) 4.36902 13.4465i 0.172297 0.530277i −0.827202 0.561904i \(-0.810069\pi\)
0.999500 + 0.0316272i \(0.0100689\pi\)
\(644\) −4.50234 + 13.8568i −0.177417 + 0.546033i
\(645\) 0 0
\(646\) −1.61682 1.17469i −0.0636130 0.0462176i
\(647\) −0.393698 1.21168i −0.0154779 0.0476360i 0.943019 0.332738i \(-0.107973\pi\)
−0.958497 + 0.285102i \(0.907973\pi\)
\(648\) 0 0
\(649\) −35.2907 13.2187i −1.38528 0.518878i
\(650\) 2.56651 0.100667
\(651\) 0 0
\(652\) 20.7040 + 15.0423i 0.810832 + 0.589104i
\(653\) 3.90620 2.83802i 0.152861 0.111060i −0.508726 0.860929i \(-0.669883\pi\)
0.661587 + 0.749868i \(0.269883\pi\)
\(654\) 0 0
\(655\) 3.34598 10.2979i 0.130738 0.402371i
\(656\) −19.5632 + 14.2135i −0.763813 + 0.554942i
\(657\) 0 0
\(658\) −2.10558 6.48030i −0.0820840 0.252628i
\(659\) −22.1777 −0.863921 −0.431961 0.901892i \(-0.642178\pi\)
−0.431961 + 0.901892i \(0.642178\pi\)
\(660\) 0 0
\(661\) −27.3975 −1.06564 −0.532820 0.846229i \(-0.678868\pi\)
−0.532820 + 0.846229i \(0.678868\pi\)
\(662\) 0.280237 + 0.862481i 0.0108917 + 0.0335213i
\(663\) 0 0
\(664\) −5.87618 + 4.26930i −0.228040 + 0.165681i
\(665\) 5.53132 17.0236i 0.214495 0.660148i
\(666\) 0 0
\(667\) 5.35915 3.89365i 0.207507 0.150763i
\(668\) −29.3611 21.3321i −1.13602 0.825363i
\(669\) 0 0
\(670\) −1.34440 −0.0519385
\(671\) −27.5141 + 7.61265i −1.06217 + 0.293883i
\(672\) 0 0
\(673\) 10.8909 + 33.5186i 0.419812 + 1.29205i 0.907876 + 0.419239i \(0.137703\pi\)
−0.488064 + 0.872808i \(0.662297\pi\)
\(674\) 4.19805 + 3.05006i 0.161703 + 0.117484i
\(675\) 0 0
\(676\) −1.08494 + 3.33910i −0.0417285 + 0.128427i
\(677\) −13.6122 + 41.8940i −0.523159 + 1.61012i 0.244769 + 0.969581i \(0.421288\pi\)
−0.767928 + 0.640536i \(0.778712\pi\)
\(678\) 0 0
\(679\) −24.4277 17.7478i −0.937450 0.681098i
\(680\) 4.04078 + 12.4362i 0.154957 + 0.476908i
\(681\) 0 0
\(682\) 4.30828 + 1.61373i 0.164973 + 0.0617929i
\(683\) 42.2845 1.61797 0.808985 0.587829i \(-0.200017\pi\)
0.808985 + 0.587829i \(0.200017\pi\)
\(684\) 0 0
\(685\) −2.38701 1.73426i −0.0912029 0.0662628i
\(686\) 2.43570 1.76964i 0.0929954 0.0675651i
\(687\) 0 0
\(688\) 1.07103 3.29631i 0.0408328 0.125670i
\(689\) 4.89701 3.55788i 0.186561 0.135545i
\(690\) 0 0
\(691\) −2.61641 8.05248i −0.0995329 0.306331i 0.888876 0.458149i \(-0.151487\pi\)
−0.988408 + 0.151818i \(0.951487\pi\)
\(692\) 2.90507 0.110434
\(693\) 0 0
\(694\) −7.81709 −0.296733
\(695\) 2.41481 + 7.43203i 0.0915990 + 0.281913i
\(696\) 0 0
\(697\) 24.0190 17.4508i 0.909783 0.660996i
\(698\) 2.01834 6.21180i 0.0763952 0.235120i
\(699\) 0 0
\(700\) −14.7780 + 10.7368i −0.558556 + 0.405815i
\(701\) −35.2342 25.5991i −1.33078 0.966865i −0.999730 0.0232503i \(-0.992599\pi\)
−0.331046 0.943615i \(-0.607401\pi\)
\(702\) 0 0
\(703\) −12.5638 −0.473854
\(704\) 12.6330 15.8624i 0.476125 0.597839i
\(705\) 0 0
\(706\) −2.61745 8.05569i −0.0985091 0.303180i
\(707\) −45.2050 32.8433i −1.70011 1.23520i
\(708\) 0 0
\(709\) −1.86253 + 5.73229i −0.0699489 + 0.215281i −0.979920 0.199391i \(-0.936104\pi\)
0.909971 + 0.414672i \(0.136104\pi\)
\(710\) −1.37036 + 4.21753i −0.0514287 + 0.158281i
\(711\) 0 0
\(712\) 8.37326 + 6.08353i 0.313801 + 0.227990i
\(713\) 2.80239 + 8.62488i 0.104950 + 0.323004i
\(714\) 0 0
\(715\) 19.0778 + 28.8609i 0.713471 + 1.07933i
\(716\) −25.3061 −0.945732
\(717\) 0 0
\(718\) 8.50264 + 6.17753i 0.317316 + 0.230543i
\(719\) −32.6897 + 23.7504i −1.21912 + 0.885741i −0.996027 0.0890560i \(-0.971615\pi\)
−0.223092 + 0.974797i \(0.571615\pi\)
\(720\) 0 0
\(721\) −6.38836 + 19.6614i −0.237915 + 0.732227i
\(722\) 3.77597 2.74340i 0.140527 0.102099i
\(723\) 0 0
\(724\) −1.65945 5.10726i −0.0616729 0.189810i
\(725\) 8.30501 0.308441
\(726\) 0 0
\(727\) 18.7206 0.694310 0.347155 0.937808i \(-0.387148\pi\)
0.347155 + 0.937808i \(0.387148\pi\)
\(728\) 5.41643 + 16.6700i 0.200746 + 0.617833i
\(729\) 0 0
\(730\) 2.52864 1.83717i 0.0935893 0.0679966i
\(731\) −1.31498 + 4.04709i −0.0486363 + 0.149687i
\(732\) 0 0
\(733\) −0.456440 + 0.331623i −0.0168590 + 0.0122488i −0.596183 0.802849i \(-0.703317\pi\)
0.579324 + 0.815097i \(0.303317\pi\)
\(734\) 5.73510 + 4.16679i 0.211686 + 0.153799i
\(735\) 0 0
\(736\) −6.03673 −0.222517
\(737\) −3.18335 4.81575i −0.117260 0.177391i
\(738\) 0 0
\(739\) 0.602004 + 1.85278i 0.0221451 + 0.0681555i 0.961518 0.274741i \(-0.0885921\pi\)
−0.939373 + 0.342896i \(0.888592\pi\)
\(740\) 32.5628 + 23.6582i 1.19703 + 0.869694i
\(741\) 0 0
\(742\) 0.564167 1.73633i 0.0207112 0.0637426i
\(743\) −8.42464 + 25.9284i −0.309070 + 0.951220i 0.669057 + 0.743211i \(0.266698\pi\)
−0.978127 + 0.208009i \(0.933302\pi\)
\(744\) 0 0
\(745\) −44.2113 32.1214i −1.61978 1.17684i
\(746\) 1.61067 + 4.95714i 0.0589709 + 0.181494i
\(747\) 0 0
\(748\) −17.1270 + 21.5052i −0.626224 + 0.786308i
\(749\) 11.3197 0.413613
\(750\) 0 0
\(751\) −24.5183 17.8136i −0.894685 0.650027i 0.0424105 0.999100i \(-0.486496\pi\)
−0.937095 + 0.349074i \(0.886496\pi\)
\(752\) −16.6999 + 12.1332i −0.608983 + 0.442452i
\(753\) 0 0
\(754\) 1.20576 3.71093i 0.0439110 0.135144i
\(755\) 24.2772 17.6384i 0.883539 0.641929i
\(756\) 0 0
\(757\) 3.43224 + 10.5634i 0.124747 + 0.383931i 0.993855 0.110691i \(-0.0353064\pi\)
−0.869108 + 0.494622i \(0.835306\pi\)
\(758\) −8.97056 −0.325826
\(759\) 0 0
\(760\) 4.91030 0.178115
\(761\) −10.3029 31.7091i −0.373481 1.14945i −0.944498 0.328517i \(-0.893451\pi\)
0.571017 0.820938i \(-0.306549\pi\)
\(762\) 0 0
\(763\) −57.1992 + 41.5576i −2.07075 + 1.50449i
\(764\) 9.92620 30.5497i 0.359117 1.10525i
\(765\) 0 0
\(766\) 2.86788 2.08364i 0.103621 0.0752849i
\(767\) −35.3997 25.7194i −1.27821 0.928674i
\(768\) 0 0
\(769\) −51.9401 −1.87301 −0.936504 0.350656i \(-0.885959\pi\)
−0.936504 + 0.350656i \(0.885959\pi\)
\(770\) 9.77180 + 3.66017i 0.352151 + 0.131903i
\(771\) 0 0
\(772\) 13.0673 + 40.2171i 0.470303 + 1.44744i
\(773\) 6.24784 + 4.53932i 0.224719 + 0.163268i 0.694448 0.719542i \(-0.255648\pi\)
−0.469729 + 0.882811i \(0.655648\pi\)
\(774\) 0 0
\(775\) −3.51343 + 10.8132i −0.126206 + 0.388423i
\(776\) 2.55959 7.87759i 0.0918838 0.282789i
\(777\) 0 0
\(778\) −1.68858 1.22682i −0.0605384 0.0439837i
\(779\) −3.44512 10.6030i −0.123434 0.379891i
\(780\) 0 0
\(781\) −18.3524 + 5.07779i −0.656702 + 0.181698i
\(782\) 2.29655 0.0821244
\(783\) 0 0
\(784\) −27.3060 19.8390i −0.975215 0.708535i
\(785\) −0.729267 + 0.529844i −0.0260287 + 0.0189109i
\(786\) 0 0
\(787\) −6.08959 + 18.7418i −0.217070 + 0.668074i 0.781930 + 0.623367i \(0.214236\pi\)
−0.999000 + 0.0447073i \(0.985764\pi\)
\(788\) 28.2893 20.5534i 1.00776 0.732184i
\(789\) 0 0
\(790\) −1.02159 3.14414i −0.0363467 0.111864i
\(791\) −3.84382 −0.136670
\(792\) 0 0
\(793\) −33.1470 −1.17709
\(794\) 3.01432 + 9.27712i 0.106974 + 0.329233i
\(795\) 0 0
\(796\) −38.9550 + 28.3025i −1.38072 + 1.00315i
\(797\) 4.33420 13.3393i 0.153525 0.472502i −0.844483 0.535582i \(-0.820092\pi\)
0.998008 + 0.0630799i \(0.0200923\pi\)
\(798\) 0 0
\(799\) 20.5036 14.8967i 0.725365 0.527008i
\(800\) −6.12297 4.44860i −0.216480 0.157282i
\(801\) 0 0
\(802\) 2.13170 0.0752731
\(803\) 12.5684 + 4.70768i 0.443529 + 0.166130i
\(804\) 0 0
\(805\) 6.35623 + 19.5625i 0.224028 + 0.689486i
\(806\) 4.32159 + 3.13982i 0.152221 + 0.110595i
\(807\) 0 0
\(808\) 4.73666 14.5779i 0.166635 0.512850i
\(809\) −6.46767 + 19.9055i −0.227391 + 0.699839i 0.770649 + 0.637260i \(0.219932\pi\)
−0.998040 + 0.0625783i \(0.980068\pi\)
\(810\) 0 0
\(811\) −1.57186 1.14203i −0.0551956 0.0401019i 0.559845 0.828597i \(-0.310861\pi\)
−0.615041 + 0.788495i \(0.710861\pi\)
\(812\) 8.58173 + 26.4118i 0.301160 + 0.926874i
\(813\) 0 0
\(814\) 0.323842 7.31703i 0.0113506 0.256462i
\(815\) 36.1292 1.26555
\(816\) 0 0
\(817\) 1.29276 + 0.939249i 0.0452281 + 0.0328601i
\(818\) −0.556008 + 0.403964i −0.0194404 + 0.0141243i
\(819\) 0 0
\(820\) −11.0369 + 33.9680i −0.385424 + 1.18621i
\(821\) −8.77117 + 6.37263i −0.306116 + 0.222406i −0.730228 0.683203i \(-0.760586\pi\)
0.424112 + 0.905610i \(0.360586\pi\)
\(822\) 0 0
\(823\) 14.7302 + 45.3348i 0.513461 + 1.58027i 0.786065 + 0.618144i \(0.212115\pi\)
−0.272604 + 0.962126i \(0.587885\pi\)
\(824\) −5.67112 −0.197563
\(825\) 0 0
\(826\) −13.1976 −0.459203
\(827\) 11.5619 + 35.5838i 0.402046 + 1.23737i 0.923337 + 0.383991i \(0.125451\pi\)
−0.521291 + 0.853379i \(0.674549\pi\)
\(828\) 0 0
\(829\) −8.66207 + 6.29336i −0.300846 + 0.218578i −0.727959 0.685621i \(-0.759531\pi\)
0.427113 + 0.904198i \(0.359531\pi\)
\(830\) −1.55148 + 4.77496i −0.0538526 + 0.165741i
\(831\) 0 0
\(832\) 19.0486 13.8396i 0.660390 0.479801i
\(833\) 33.5254 + 24.3576i 1.16159 + 0.843941i
\(834\) 0 0
\(835\) −51.2361 −1.77310
\(836\) 5.69284 + 8.61209i 0.196891 + 0.297856i
\(837\) 0 0
\(838\) −0.987051 3.03783i −0.0340971 0.104940i
\(839\) −12.4277 9.02927i −0.429053 0.311725i 0.352217 0.935918i \(-0.385428\pi\)
−0.781270 + 0.624193i \(0.785428\pi\)
\(840\) 0 0
\(841\) −5.05976 + 15.5724i −0.174475 + 0.536978i
\(842\) −0.608427 + 1.87255i −0.0209678 + 0.0645322i
\(843\) 0 0
\(844\) 12.8372 + 9.32675i 0.441874 + 0.321040i
\(845\) 1.53168 + 4.71402i 0.0526913 + 0.162167i
\(846\) 0 0
\(847\) 10.0272 + 43.6703i 0.344539 + 1.50053i
\(848\) −5.53087 −0.189931
\(849\) 0 0
\(850\) 2.32936 + 1.69238i 0.0798963 + 0.0580480i
\(851\) 11.6802 8.48617i 0.400393 0.290902i
\(852\) 0 0
\(853\) 12.8132 39.4348i 0.438714 1.35022i −0.450518 0.892767i \(-0.648761\pi\)
0.889232 0.457456i \(-0.151239\pi\)
\(854\) −8.08825 + 5.87646i −0.276774 + 0.201088i
\(855\) 0 0
\(856\) 0.959576 + 2.95327i 0.0327976 + 0.100941i
\(857\) 18.4055 0.628719 0.314359 0.949304i \(-0.398210\pi\)
0.314359 + 0.949304i \(0.398210\pi\)
\(858\) 0 0
\(859\) −15.0485 −0.513449 −0.256725 0.966485i \(-0.582643\pi\)
−0.256725 + 0.966485i \(0.582643\pi\)
\(860\) −1.58192 4.86866i −0.0539432 0.166020i
\(861\) 0 0
\(862\) 6.73166 4.89084i 0.229281 0.166583i
\(863\) −4.45906 + 13.7236i −0.151788 + 0.467155i −0.997821 0.0659746i \(-0.978984\pi\)
0.846033 + 0.533130i \(0.178984\pi\)
\(864\) 0 0
\(865\) 3.31799 2.41066i 0.112815 0.0819649i
\(866\) 8.42848 + 6.12365i 0.286411 + 0.208090i
\(867\) 0 0
\(868\) −38.0191 −1.29045
\(869\) 8.84362 11.1044i 0.299999 0.376689i
\(870\) 0 0
\(871\) −2.07129 6.37477i −0.0701830 0.216001i
\(872\) −15.6910 11.4002i −0.531365 0.386059i
\(873\) 0 0
\(874\) 0.266492 0.820177i 0.00901421 0.0277429i
\(875\) 9.07885 27.9418i 0.306921 0.944607i
\(876\) 0 0
\(877\) 19.4774 + 14.1511i 0.657704 + 0.477850i 0.865887 0.500240i \(-0.166755\pi\)
−0.208183 + 0.978090i \(0.566755\pi\)
\(878\) −1.89426 5.82994i −0.0639283 0.196751i
\(879\) 0 0
\(880\) 1.39773 31.5811i 0.0471176 1.06460i
\(881\) −10.0956 −0.340129 −0.170064 0.985433i \(-0.554398\pi\)
−0.170064 + 0.985433i \(0.554398\pi\)
\(882\) 0 0
\(883\) −41.0332 29.8124i −1.38088 1.00327i −0.996798 0.0799659i \(-0.974519\pi\)
−0.384079 0.923300i \(-0.625481\pi\)
\(884\) −25.8247 + 18.7628i −0.868579 + 0.631060i
\(885\) 0 0
\(886\) −2.94703 + 9.07002i −0.0990074 + 0.304713i
\(887\) 2.08136 1.51220i 0.0698854 0.0507747i −0.552294 0.833649i \(-0.686247\pi\)
0.622179 + 0.782875i \(0.286247\pi\)
\(888\) 0 0
\(889\) −3.08439 9.49279i −0.103447 0.318378i
\(890\) 7.15422 0.239810
\(891\) 0 0
\(892\) 14.1064 0.472316
\(893\) −2.94090 9.05115i −0.0984134 0.302885i
\(894\) 0 0
\(895\) −28.9031 + 20.9993i −0.966123 + 0.701929i
\(896\) 10.3465 31.8433i 0.345653 1.06381i
\(897\) 0 0
\(898\) −9.11993 + 6.62602i −0.304336 + 0.221113i
\(899\) 13.9843 + 10.1602i 0.466403 + 0.338862i
\(900\) 0 0
\(901\) 6.79061 0.226228
\(902\) 6.26386 1.73310i 0.208564 0.0577059i
\(903\) 0 0
\(904\) −0.325842 1.00284i −0.0108373 0.0333539i
\(905\) −6.13339 4.45617i −0.203881 0.148128i
\(906\) 0 0
\(907\) 3.18129 9.79100i 0.105633 0.325105i −0.884246 0.467022i \(-0.845327\pi\)
0.989878 + 0.141917i \(0.0453268\pi\)
\(908\) 11.2304 34.5636i 0.372693 1.14703i
\(909\) 0 0
\(910\) 9.80197 + 7.12155i 0.324932 + 0.236077i
\(911\) −4.82145 14.8389i −0.159742 0.491635i 0.838869 0.544334i \(-0.183218\pi\)
−0.998610 + 0.0526992i \(0.983218\pi\)
\(912\) 0 0
\(913\) −20.7780 + 5.74891i −0.687652 + 0.190261i
\(914\) 10.6966 0.353811
\(915\) 0 0
\(916\) −12.1999 8.86371i −0.403094 0.292865i
\(917\) 13.1729 9.57070i 0.435009 0.316052i
\(918\) 0 0
\(919\) 3.46483 10.6637i 0.114294 0.351761i −0.877505 0.479568i \(-0.840794\pi\)
0.991799 + 0.127806i \(0.0407935\pi\)
\(920\) −4.56495 + 3.31663i −0.150502 + 0.109346i
\(921\) 0 0
\(922\) 1.70639 + 5.25172i 0.0561968 + 0.172956i
\(923\) −22.1097 −0.727751
\(924\) 0 0
\(925\) 18.1007 0.595148
\(926\) −1.26440 3.89141i −0.0415506 0.127880i
\(927\) 0 0
\(928\) −9.30886 + 6.76328i −0.305578 + 0.222016i
\(929\) 7.27040 22.3760i 0.238534 0.734132i −0.758099 0.652140i \(-0.773872\pi\)
0.996633 0.0819927i \(-0.0261284\pi\)
\(930\) 0 0
\(931\) 12.5892 9.14661i 0.412595 0.299768i
\(932\) −10.1974 7.40884i −0.334027 0.242685i
\(933\) 0 0
\(934\) −6.36478 −0.208262
\(935\) −1.71609 + 38.7741i −0.0561221 + 1.26805i
\(936\) 0 0
\(937\) 5.76486 + 17.7424i 0.188330 + 0.579619i 0.999990 0.00451068i \(-0.00143580\pi\)
−0.811660 + 0.584130i \(0.801436\pi\)
\(938\) −1.63557 1.18831i −0.0534032 0.0387997i
\(939\) 0 0
\(940\) −9.42153 + 28.9965i −0.307296 + 0.945761i
\(941\) −10.0408 + 30.9023i −0.327320 + 1.00739i 0.643063 + 0.765814i \(0.277663\pi\)
−0.970383 + 0.241574i \(0.922337\pi\)
\(942\) 0 0
\(943\) 10.3646 + 7.53029i 0.337516 + 0.245220i
\(944\) 12.3551 + 38.0250i 0.402123 + 1.23761i
\(945\) 0 0
\(946\) −0.580329 + 0.728681i −0.0188681 + 0.0236915i
\(947\) −3.84273 −0.124872 −0.0624360 0.998049i \(-0.519887\pi\)
−0.0624360 + 0.998049i \(0.519887\pi\)
\(948\) 0 0
\(949\) 12.6072 + 9.15968i 0.409247 + 0.297336i
\(950\) 0.874704 0.635510i 0.0283792 0.0206187i
\(951\) 0 0
\(952\) −6.07643 + 18.7013i −0.196938 + 0.606114i
\(953\) −15.4434 + 11.2203i −0.500262 + 0.363461i −0.809117 0.587648i \(-0.800054\pi\)
0.308855 + 0.951109i \(0.400054\pi\)
\(954\) 0 0
\(955\) −14.0134 43.1289i −0.453464 1.39562i
\(956\) 49.0154 1.58527
\(957\) 0 0
\(958\) −6.63302 −0.214303
\(959\) −1.37108 4.21975i −0.0442745 0.136263i
\(960\) 0 0
\(961\) 5.93476 4.31185i 0.191444 0.139092i
\(962\) 2.62793 8.08795i 0.0847280 0.260766i
\(963\) 0 0
\(964\) −4.62879 + 3.36302i −0.149083 + 0.108315i
\(965\) 48.2973 + 35.0901i 1.55475 + 1.12959i
\(966\) 0 0
\(967\) 26.5627 0.854198 0.427099 0.904205i \(-0.359536\pi\)
0.427099 + 0.904205i \(0.359536\pi\)
\(968\) −10.5434 + 6.31801i −0.338878 + 0.203069i
\(969\) 0 0
\(970\) −1.76927 5.44526i −0.0568079 0.174837i
\(971\) 41.3472 + 30.0405i 1.32689 + 0.964045i 0.999819 + 0.0190472i \(0.00606329\pi\)
0.327076 + 0.944998i \(0.393937\pi\)
\(972\) 0 0
\(973\) −3.63134 + 11.1761i −0.116415 + 0.358290i
\(974\) 0.0238619 0.0734393i 0.000764584 0.00235315i
\(975\) 0 0
\(976\) 24.5032 + 17.8026i 0.784328 + 0.569847i
\(977\) −6.54331 20.1382i −0.209339 0.644279i −0.999507 0.0313890i \(-0.990007\pi\)
0.790168 0.612890i \(-0.209993\pi\)
\(978\) 0 0
\(979\) 16.9402 + 25.6271i 0.541412 + 0.819046i
\(980\) −49.8521 −1.59247
\(981\) 0 0
\(982\) 0.970410 + 0.705044i 0.0309670 + 0.0224989i
\(983\) −41.1267 + 29.8803i −1.31174 + 0.953034i −0.311743 + 0.950166i \(0.600913\pi\)
−0.999996 + 0.00286753i \(0.999087\pi\)
\(984\) 0 0
\(985\) 15.2549 46.9496i 0.486060 1.49594i
\(986\) 3.54136 2.57295i 0.112780 0.0819394i
\(987\) 0 0
\(988\) 3.70412 + 11.4001i 0.117844 + 0.362686i
\(989\) −1.83625 −0.0583895
\(990\) 0 0
\(991\) −13.1480 −0.417662 −0.208831 0.977952i \(-0.566966\pi\)
−0.208831 + 0.977952i \(0.566966\pi\)
\(992\) −4.86777 14.9815i −0.154552 0.475662i
\(993\) 0 0
\(994\) −5.39503 + 3.91972i −0.171120 + 0.124326i
\(995\) −21.0063 + 64.6507i −0.665944 + 2.04957i
\(996\) 0 0
\(997\) 30.1024 21.8707i 0.953354 0.692652i 0.00175626 0.999998i \(-0.499441\pi\)
0.951598 + 0.307346i \(0.0994410\pi\)
\(998\) 3.54437 + 2.57514i 0.112195 + 0.0815146i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 891.2.f.f.82.5 36
3.2 odd 2 891.2.f.e.82.5 36
9.2 odd 6 297.2.n.b.280.5 72
9.4 even 3 99.2.m.b.16.5 72
9.5 odd 6 297.2.n.b.181.5 72
9.7 even 3 99.2.m.b.49.5 yes 72
11.3 even 5 9801.2.a.cm.1.10 18
11.8 odd 10 9801.2.a.co.1.9 18
11.9 even 5 inner 891.2.f.f.163.5 36
33.8 even 10 9801.2.a.cn.1.10 18
33.14 odd 10 9801.2.a.cp.1.9 18
33.20 odd 10 891.2.f.e.163.5 36
99.20 odd 30 297.2.n.b.64.5 72
99.25 even 15 1089.2.e.p.364.9 36
99.31 even 15 99.2.m.b.97.5 yes 72
99.52 odd 30 1089.2.e.o.364.10 36
99.58 even 15 1089.2.e.p.727.9 36
99.85 odd 30 1089.2.e.o.727.10 36
99.86 odd 30 297.2.n.b.262.5 72
99.97 even 15 99.2.m.b.31.5 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.16.5 72 9.4 even 3
99.2.m.b.31.5 yes 72 99.97 even 15
99.2.m.b.49.5 yes 72 9.7 even 3
99.2.m.b.97.5 yes 72 99.31 even 15
297.2.n.b.64.5 72 99.20 odd 30
297.2.n.b.181.5 72 9.5 odd 6
297.2.n.b.262.5 72 99.86 odd 30
297.2.n.b.280.5 72 9.2 odd 6
891.2.f.e.82.5 36 3.2 odd 2
891.2.f.e.163.5 36 33.20 odd 10
891.2.f.f.82.5 36 1.1 even 1 trivial
891.2.f.f.163.5 36 11.9 even 5 inner
1089.2.e.o.364.10 36 99.52 odd 30
1089.2.e.o.727.10 36 99.85 odd 30
1089.2.e.p.364.9 36 99.25 even 15
1089.2.e.p.727.9 36 99.58 even 15
9801.2.a.cm.1.10 18 11.3 even 5
9801.2.a.cn.1.10 18 33.8 even 10
9801.2.a.co.1.9 18 11.8 odd 10
9801.2.a.cp.1.9 18 33.14 odd 10