Properties

Label 1512.2.j.c.323.6
Level $1512$
Weight $2$
Character 1512.323
Analytic conductor $12.073$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1512,2,Mod(323,1512)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1512.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.j (of order \(2\), degree \(1\), 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: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.6
Character \(\chi\) \(=\) 1512.323
Dual form 1512.2.j.c.323.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.30241 + 0.551119i) q^{2} +(1.39253 - 1.43556i) q^{4} +3.61017 q^{5} -1.00000i q^{7} +(-1.02248 + 2.63714i) q^{8} +O(q^{10})\) \(q+(-1.30241 + 0.551119i) q^{2} +(1.39253 - 1.43556i) q^{4} +3.61017 q^{5} -1.00000i q^{7} +(-1.02248 + 2.63714i) q^{8} +(-4.70192 + 1.98963i) q^{10} +2.00899i q^{11} -1.59265i q^{13} +(0.551119 + 1.30241i) q^{14} +(-0.121693 - 3.99815i) q^{16} -7.79257i q^{17} -5.05480 q^{19} +(5.02729 - 5.18263i) q^{20} +(-1.10719 - 2.61653i) q^{22} +7.14612 q^{23} +8.03333 q^{25} +(0.877741 + 2.07428i) q^{26} +(-1.43556 - 1.39253i) q^{28} +4.94298 q^{29} +2.53252i q^{31} +(2.36195 + 5.14015i) q^{32} +(4.29463 + 10.1491i) q^{34} -3.61017i q^{35} -4.76592i q^{37} +(6.58341 - 2.78580i) q^{38} +(-3.69133 + 9.52054i) q^{40} +0.836835i q^{41} +0.151434 q^{43} +(2.88404 + 2.79759i) q^{44} +(-9.30717 + 3.93836i) q^{46} +0.795430 q^{47} -1.00000 q^{49} +(-10.4627 + 4.42732i) q^{50} +(-2.28635 - 2.21782i) q^{52} +1.05980 q^{53} +7.25280i q^{55} +(2.63714 + 1.02248i) q^{56} +(-6.43778 + 2.72417i) q^{58} -8.34506i q^{59} -10.2367i q^{61} +(-1.39572 - 3.29837i) q^{62} +(-5.90906 - 5.39286i) q^{64} -5.74974i q^{65} +0.655357 q^{67} +(-11.1867 - 10.8514i) q^{68} +(1.98963 + 4.70192i) q^{70} +11.3675 q^{71} -14.3835 q^{73} +(2.62659 + 6.20717i) q^{74} +(-7.03899 + 7.25649i) q^{76} +2.00899 q^{77} -3.81177i q^{79} +(-0.439332 - 14.4340i) q^{80} +(-0.461196 - 1.08990i) q^{82} +14.9522i q^{83} -28.1325i q^{85} +(-0.197228 + 0.0834580i) q^{86} +(-5.29800 - 2.05416i) q^{88} +0.0444167i q^{89} -1.59265 q^{91} +(9.95122 - 10.2587i) q^{92} +(-1.03597 + 0.438377i) q^{94} -18.2487 q^{95} +9.87000 q^{97} +(1.30241 - 0.551119i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30241 + 0.551119i −0.920942 + 0.389700i
\(3\) 0 0
\(4\) 1.39253 1.43556i 0.696267 0.717782i
\(5\) 3.61017 1.61452 0.807259 0.590198i \(-0.200950\pi\)
0.807259 + 0.590198i \(0.200950\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) −1.02248 + 2.63714i −0.361502 + 0.932371i
\(9\) 0 0
\(10\) −4.70192 + 1.98963i −1.48688 + 0.629178i
\(11\) 2.00899i 0.605734i 0.953033 + 0.302867i \(0.0979438\pi\)
−0.953033 + 0.302867i \(0.902056\pi\)
\(12\) 0 0
\(13\) 1.59265i 0.441722i −0.975305 0.220861i \(-0.929113\pi\)
0.975305 0.220861i \(-0.0708867\pi\)
\(14\) 0.551119 + 1.30241i 0.147293 + 0.348083i
\(15\) 0 0
\(16\) −0.121693 3.99815i −0.0304232 0.999537i
\(17\) 7.79257i 1.88998i −0.327106 0.944988i \(-0.606074\pi\)
0.327106 0.944988i \(-0.393926\pi\)
\(18\) 0 0
\(19\) −5.05480 −1.15965 −0.579825 0.814741i \(-0.696879\pi\)
−0.579825 + 0.814741i \(0.696879\pi\)
\(20\) 5.02729 5.18263i 1.12414 1.15887i
\(21\) 0 0
\(22\) −1.10719 2.61653i −0.236055 0.557846i
\(23\) 7.14612 1.49007 0.745034 0.667026i \(-0.232433\pi\)
0.745034 + 0.667026i \(0.232433\pi\)
\(24\) 0 0
\(25\) 8.03333 1.60667
\(26\) 0.877741 + 2.07428i 0.172139 + 0.406800i
\(27\) 0 0
\(28\) −1.43556 1.39253i −0.271296 0.263164i
\(29\) 4.94298 0.917889 0.458945 0.888465i \(-0.348228\pi\)
0.458945 + 0.888465i \(0.348228\pi\)
\(30\) 0 0
\(31\) 2.53252i 0.454853i 0.973795 + 0.227427i \(0.0730312\pi\)
−0.973795 + 0.227427i \(0.926969\pi\)
\(32\) 2.36195 + 5.14015i 0.417538 + 0.908660i
\(33\) 0 0
\(34\) 4.29463 + 10.1491i 0.736524 + 1.74056i
\(35\) 3.61017i 0.610230i
\(36\) 0 0
\(37\) 4.76592i 0.783512i −0.920069 0.391756i \(-0.871868\pi\)
0.920069 0.391756i \(-0.128132\pi\)
\(38\) 6.58341 2.78580i 1.06797 0.451916i
\(39\) 0 0
\(40\) −3.69133 + 9.52054i −0.583651 + 1.50533i
\(41\) 0.836835i 0.130692i 0.997863 + 0.0653458i \(0.0208151\pi\)
−0.997863 + 0.0653458i \(0.979185\pi\)
\(42\) 0 0
\(43\) 0.151434 0.0230934 0.0115467 0.999933i \(-0.496324\pi\)
0.0115467 + 0.999933i \(0.496324\pi\)
\(44\) 2.88404 + 2.79759i 0.434785 + 0.421753i
\(45\) 0 0
\(46\) −9.30717 + 3.93836i −1.37227 + 0.580680i
\(47\) 0.795430 0.116025 0.0580127 0.998316i \(-0.481524\pi\)
0.0580127 + 0.998316i \(0.481524\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) −10.4627 + 4.42732i −1.47965 + 0.626118i
\(51\) 0 0
\(52\) −2.28635 2.21782i −0.317060 0.307557i
\(53\) 1.05980 0.145575 0.0727873 0.997347i \(-0.476811\pi\)
0.0727873 + 0.997347i \(0.476811\pi\)
\(54\) 0 0
\(55\) 7.25280i 0.977968i
\(56\) 2.63714 + 1.02248i 0.352403 + 0.136635i
\(57\) 0 0
\(58\) −6.43778 + 2.72417i −0.845322 + 0.357702i
\(59\) 8.34506i 1.08643i −0.839592 0.543217i \(-0.817206\pi\)
0.839592 0.543217i \(-0.182794\pi\)
\(60\) 0 0
\(61\) 10.2367i 1.31067i −0.755336 0.655337i \(-0.772526\pi\)
0.755336 0.655337i \(-0.227474\pi\)
\(62\) −1.39572 3.29837i −0.177256 0.418893i
\(63\) 0 0
\(64\) −5.90906 5.39286i −0.738633 0.674108i
\(65\) 5.74974i 0.713168i
\(66\) 0 0
\(67\) 0.655357 0.0800646 0.0400323 0.999198i \(-0.487254\pi\)
0.0400323 + 0.999198i \(0.487254\pi\)
\(68\) −11.1867 10.8514i −1.35659 1.31593i
\(69\) 0 0
\(70\) 1.98963 + 4.70192i 0.237807 + 0.561986i
\(71\) 11.3675 1.34907 0.674536 0.738242i \(-0.264344\pi\)
0.674536 + 0.738242i \(0.264344\pi\)
\(72\) 0 0
\(73\) −14.3835 −1.68346 −0.841728 0.539901i \(-0.818462\pi\)
−0.841728 + 0.539901i \(0.818462\pi\)
\(74\) 2.62659 + 6.20717i 0.305335 + 0.721569i
\(75\) 0 0
\(76\) −7.03899 + 7.25649i −0.807427 + 0.832377i
\(77\) 2.00899 0.228946
\(78\) 0 0
\(79\) 3.81177i 0.428858i −0.976740 0.214429i \(-0.931211\pi\)
0.976740 0.214429i \(-0.0687890\pi\)
\(80\) −0.439332 14.4340i −0.0491188 1.61377i
\(81\) 0 0
\(82\) −0.461196 1.08990i −0.0509306 0.120359i
\(83\) 14.9522i 1.64121i 0.571494 + 0.820606i \(0.306364\pi\)
−0.571494 + 0.820606i \(0.693636\pi\)
\(84\) 0 0
\(85\) 28.1325i 3.05140i
\(86\) −0.197228 + 0.0834580i −0.0212677 + 0.00899951i
\(87\) 0 0
\(88\) −5.29800 2.05416i −0.564769 0.218974i
\(89\) 0.0444167i 0.00470816i 0.999997 + 0.00235408i \(0.000749328\pi\)
−0.999997 + 0.00235408i \(0.999251\pi\)
\(90\) 0 0
\(91\) −1.59265 −0.166955
\(92\) 9.95122 10.2587i 1.03749 1.06955i
\(93\) 0 0
\(94\) −1.03597 + 0.438377i −0.106853 + 0.0452151i
\(95\) −18.2487 −1.87228
\(96\) 0 0
\(97\) 9.87000 1.00215 0.501073 0.865405i \(-0.332939\pi\)
0.501073 + 0.865405i \(0.332939\pi\)
\(98\) 1.30241 0.551119i 0.131563 0.0556715i
\(99\) 0 0
\(100\) 11.1867 11.5324i 1.11867 1.15324i
\(101\) −4.43029 −0.440830 −0.220415 0.975406i \(-0.570741\pi\)
−0.220415 + 0.975406i \(0.570741\pi\)
\(102\) 0 0
\(103\) 11.2939i 1.11282i 0.830906 + 0.556412i \(0.187823\pi\)
−0.830906 + 0.556412i \(0.812177\pi\)
\(104\) 4.20005 + 1.62846i 0.411849 + 0.159683i
\(105\) 0 0
\(106\) −1.38029 + 0.584076i −0.134066 + 0.0567304i
\(107\) 8.60018i 0.831411i 0.909499 + 0.415705i \(0.136465\pi\)
−0.909499 + 0.415705i \(0.863535\pi\)
\(108\) 0 0
\(109\) 19.9155i 1.90756i 0.300512 + 0.953778i \(0.402842\pi\)
−0.300512 + 0.953778i \(0.597158\pi\)
\(110\) −3.99716 9.44611i −0.381114 0.900651i
\(111\) 0 0
\(112\) −3.99815 + 0.121693i −0.377790 + 0.0114989i
\(113\) 3.81372i 0.358764i −0.983779 0.179382i \(-0.942590\pi\)
0.983779 0.179382i \(-0.0574098\pi\)
\(114\) 0 0
\(115\) 25.7987 2.40574
\(116\) 6.88328 7.09597i 0.639096 0.658845i
\(117\) 0 0
\(118\) 4.59912 + 10.8687i 0.423384 + 1.00054i
\(119\) −7.79257 −0.714343
\(120\) 0 0
\(121\) 6.96395 0.633086
\(122\) 5.64164 + 13.3324i 0.510770 + 1.20706i
\(123\) 0 0
\(124\) 3.63559 + 3.52662i 0.326486 + 0.316700i
\(125\) 10.9508 0.979472
\(126\) 0 0
\(127\) 15.9943i 1.41926i −0.704574 0.709630i \(-0.748862\pi\)
0.704574 0.709630i \(-0.251138\pi\)
\(128\) 10.6681 + 3.76711i 0.942938 + 0.332969i
\(129\) 0 0
\(130\) 3.16879 + 7.48851i 0.277922 + 0.656786i
\(131\) 19.8839i 1.73726i 0.495460 + 0.868631i \(0.335000\pi\)
−0.495460 + 0.868631i \(0.665000\pi\)
\(132\) 0 0
\(133\) 5.05480i 0.438307i
\(134\) −0.853543 + 0.361180i −0.0737348 + 0.0312012i
\(135\) 0 0
\(136\) 20.5501 + 7.96776i 1.76216 + 0.683229i
\(137\) 8.93576i 0.763433i −0.924279 0.381717i \(-0.875333\pi\)
0.924279 0.381717i \(-0.124667\pi\)
\(138\) 0 0
\(139\) 1.20344 0.102074 0.0510372 0.998697i \(-0.483747\pi\)
0.0510372 + 0.998697i \(0.483747\pi\)
\(140\) −5.18263 5.02729i −0.438012 0.424883i
\(141\) 0 0
\(142\) −14.8051 + 6.26484i −1.24242 + 0.525733i
\(143\) 3.19962 0.267566
\(144\) 0 0
\(145\) 17.8450 1.48195
\(146\) 18.7331 7.92700i 1.55037 0.656044i
\(147\) 0 0
\(148\) −6.84179 6.63671i −0.562391 0.545534i
\(149\) −12.6791 −1.03871 −0.519355 0.854559i \(-0.673828\pi\)
−0.519355 + 0.854559i \(0.673828\pi\)
\(150\) 0 0
\(151\) 17.5094i 1.42489i −0.701727 0.712446i \(-0.747588\pi\)
0.701727 0.712446i \(-0.252412\pi\)
\(152\) 5.16844 13.3302i 0.419216 1.08123i
\(153\) 0 0
\(154\) −2.61653 + 1.10719i −0.210846 + 0.0892203i
\(155\) 9.14281i 0.734368i
\(156\) 0 0
\(157\) 15.2891i 1.22020i −0.792324 0.610100i \(-0.791129\pi\)
0.792324 0.610100i \(-0.208871\pi\)
\(158\) 2.10074 + 4.96448i 0.167126 + 0.394953i
\(159\) 0 0
\(160\) 8.52704 + 18.5568i 0.674122 + 1.46705i
\(161\) 7.14612i 0.563193i
\(162\) 0 0
\(163\) 17.5634 1.37567 0.687835 0.725867i \(-0.258561\pi\)
0.687835 + 0.725867i \(0.258561\pi\)
\(164\) 1.20133 + 1.16532i 0.0938082 + 0.0909964i
\(165\) 0 0
\(166\) −8.24042 19.4738i −0.639581 1.51146i
\(167\) −4.20290 −0.325230 −0.162615 0.986690i \(-0.551993\pi\)
−0.162615 + 0.986690i \(0.551993\pi\)
\(168\) 0 0
\(169\) 10.4635 0.804882
\(170\) 15.5044 + 36.6400i 1.18913 + 2.81016i
\(171\) 0 0
\(172\) 0.210877 0.217393i 0.0160792 0.0165761i
\(173\) 18.0074 1.36907 0.684537 0.728978i \(-0.260005\pi\)
0.684537 + 0.728978i \(0.260005\pi\)
\(174\) 0 0
\(175\) 8.03333i 0.607263i
\(176\) 8.03225 0.244480i 0.605454 0.0184284i
\(177\) 0 0
\(178\) −0.0244789 0.0578487i −0.00183477 0.00433594i
\(179\) 0.886091i 0.0662295i 0.999452 + 0.0331148i \(0.0105427\pi\)
−0.999452 + 0.0331148i \(0.989457\pi\)
\(180\) 0 0
\(181\) 8.47338i 0.629821i 0.949121 + 0.314911i \(0.101975\pi\)
−0.949121 + 0.314911i \(0.898025\pi\)
\(182\) 2.07428 0.877741i 0.153756 0.0650625i
\(183\) 0 0
\(184\) −7.30678 + 18.8454i −0.538663 + 1.38930i
\(185\) 17.2058i 1.26499i
\(186\) 0 0
\(187\) 15.6552 1.14482
\(188\) 1.10766 1.14189i 0.0807847 0.0832809i
\(189\) 0 0
\(190\) 23.7672 10.0572i 1.72426 0.729626i
\(191\) −20.6102 −1.49130 −0.745652 0.666335i \(-0.767862\pi\)
−0.745652 + 0.666335i \(0.767862\pi\)
\(192\) 0 0
\(193\) 18.2972 1.31706 0.658530 0.752555i \(-0.271179\pi\)
0.658530 + 0.752555i \(0.271179\pi\)
\(194\) −12.8548 + 5.43955i −0.922918 + 0.390537i
\(195\) 0 0
\(196\) −1.39253 + 1.43556i −0.0994668 + 0.102540i
\(197\) 10.6580 0.759353 0.379677 0.925119i \(-0.376035\pi\)
0.379677 + 0.925119i \(0.376035\pi\)
\(198\) 0 0
\(199\) 26.1305i 1.85234i −0.377108 0.926169i \(-0.623081\pi\)
0.377108 0.926169i \(-0.376919\pi\)
\(200\) −8.21393 + 21.1850i −0.580813 + 1.49801i
\(201\) 0 0
\(202\) 5.77004 2.44162i 0.405979 0.171792i
\(203\) 4.94298i 0.346929i
\(204\) 0 0
\(205\) 3.02112i 0.211004i
\(206\) −6.22431 14.7093i −0.433668 1.02485i
\(207\) 0 0
\(208\) −6.36766 + 0.193814i −0.441518 + 0.0134386i
\(209\) 10.1551i 0.702440i
\(210\) 0 0
\(211\) −21.1542 −1.45632 −0.728159 0.685409i \(-0.759624\pi\)
−0.728159 + 0.685409i \(0.759624\pi\)
\(212\) 1.47581 1.52141i 0.101359 0.104491i
\(213\) 0 0
\(214\) −4.73972 11.2009i −0.324001 0.765681i
\(215\) 0.546701 0.0372847
\(216\) 0 0
\(217\) 2.53252 0.171918
\(218\) −10.9758 25.9381i −0.743375 1.75675i
\(219\) 0 0
\(220\) 10.4119 + 10.0998i 0.701968 + 0.680927i
\(221\) −12.4108 −0.834844
\(222\) 0 0
\(223\) 6.04274i 0.404652i 0.979318 + 0.202326i \(0.0648500\pi\)
−0.979318 + 0.202326i \(0.935150\pi\)
\(224\) 5.14015 2.36195i 0.343441 0.157814i
\(225\) 0 0
\(226\) 2.10181 + 4.96702i 0.139811 + 0.330401i
\(227\) 20.0726i 1.33227i 0.745832 + 0.666134i \(0.232052\pi\)
−0.745832 + 0.666134i \(0.767948\pi\)
\(228\) 0 0
\(229\) 18.5176i 1.22368i 0.790983 + 0.611838i \(0.209570\pi\)
−0.790983 + 0.611838i \(0.790430\pi\)
\(230\) −33.6005 + 14.2182i −2.21555 + 0.937518i
\(231\) 0 0
\(232\) −5.05411 + 13.0354i −0.331819 + 0.855814i
\(233\) 17.1203i 1.12159i 0.827956 + 0.560793i \(0.189504\pi\)
−0.827956 + 0.560793i \(0.810496\pi\)
\(234\) 0 0
\(235\) 2.87164 0.187325
\(236\) −11.9799 11.6208i −0.779823 0.756449i
\(237\) 0 0
\(238\) 10.1491 4.29463i 0.657869 0.278380i
\(239\) −3.95612 −0.255900 −0.127950 0.991781i \(-0.540840\pi\)
−0.127950 + 0.991781i \(0.540840\pi\)
\(240\) 0 0
\(241\) −15.3726 −0.990235 −0.495117 0.868826i \(-0.664875\pi\)
−0.495117 + 0.868826i \(0.664875\pi\)
\(242\) −9.06991 + 3.83797i −0.583036 + 0.246714i
\(243\) 0 0
\(244\) −14.6954 14.2550i −0.940779 0.912580i
\(245\) −3.61017 −0.230645
\(246\) 0 0
\(247\) 8.05054i 0.512243i
\(248\) −6.67861 2.58945i −0.424092 0.164430i
\(249\) 0 0
\(250\) −14.2625 + 6.03522i −0.902037 + 0.381701i
\(251\) 13.1732i 0.831482i −0.909483 0.415741i \(-0.863522\pi\)
0.909483 0.415741i \(-0.136478\pi\)
\(252\) 0 0
\(253\) 14.3565i 0.902585i
\(254\) 8.81474 + 20.8310i 0.553086 + 1.30706i
\(255\) 0 0
\(256\) −15.9704 + 0.973093i −0.998149 + 0.0608183i
\(257\) 26.9072i 1.67843i 0.543802 + 0.839213i \(0.316984\pi\)
−0.543802 + 0.839213i \(0.683016\pi\)
\(258\) 0 0
\(259\) −4.76592 −0.296140
\(260\) −8.25413 8.00672i −0.511899 0.496556i
\(261\) 0 0
\(262\) −10.9584 25.8969i −0.677011 1.59992i
\(263\) 8.15057 0.502586 0.251293 0.967911i \(-0.419144\pi\)
0.251293 + 0.967911i \(0.419144\pi\)
\(264\) 0 0
\(265\) 3.82605 0.235033
\(266\) −2.78580 6.58341i −0.170808 0.403655i
\(267\) 0 0
\(268\) 0.912608 0.940808i 0.0557464 0.0574690i
\(269\) −3.84304 −0.234314 −0.117157 0.993113i \(-0.537378\pi\)
−0.117157 + 0.993113i \(0.537378\pi\)
\(270\) 0 0
\(271\) 12.8705i 0.781829i 0.920427 + 0.390914i \(0.127841\pi\)
−0.920427 + 0.390914i \(0.872159\pi\)
\(272\) −31.1558 + 0.948300i −1.88910 + 0.0574991i
\(273\) 0 0
\(274\) 4.92467 + 11.6380i 0.297510 + 0.703078i
\(275\) 16.1389i 0.973212i
\(276\) 0 0
\(277\) 2.72420i 0.163682i −0.996645 0.0818408i \(-0.973920\pi\)
0.996645 0.0818408i \(-0.0260799\pi\)
\(278\) −1.56737 + 0.663239i −0.0940046 + 0.0397784i
\(279\) 0 0
\(280\) 9.52054 + 3.69133i 0.568961 + 0.220599i
\(281\) 8.91234i 0.531666i −0.964019 0.265833i \(-0.914353\pi\)
0.964019 0.265833i \(-0.0856469\pi\)
\(282\) 0 0
\(283\) 4.90080 0.291322 0.145661 0.989335i \(-0.453469\pi\)
0.145661 + 0.989335i \(0.453469\pi\)
\(284\) 15.8296 16.3188i 0.939315 0.968340i
\(285\) 0 0
\(286\) −4.16722 + 1.76338i −0.246413 + 0.104271i
\(287\) 0.836835 0.0493968
\(288\) 0 0
\(289\) −43.7241 −2.57201
\(290\) −23.2415 + 9.83473i −1.36479 + 0.577515i
\(291\) 0 0
\(292\) −20.0295 + 20.6484i −1.17214 + 1.20836i
\(293\) 26.1386 1.52704 0.763518 0.645786i \(-0.223470\pi\)
0.763518 + 0.645786i \(0.223470\pi\)
\(294\) 0 0
\(295\) 30.1271i 1.75407i
\(296\) 12.5684 + 4.87307i 0.730525 + 0.283241i
\(297\) 0 0
\(298\) 16.5133 6.98768i 0.956592 0.404786i
\(299\) 11.3813i 0.658196i
\(300\) 0 0
\(301\) 0.151434i 0.00872849i
\(302\) 9.64975 + 22.8043i 0.555280 + 1.31224i
\(303\) 0 0
\(304\) 0.615133 + 20.2098i 0.0352803 + 1.15911i
\(305\) 36.9562i 2.11611i
\(306\) 0 0
\(307\) −23.4257 −1.33697 −0.668487 0.743724i \(-0.733058\pi\)
−0.668487 + 0.743724i \(0.733058\pi\)
\(308\) 2.79759 2.88404i 0.159408 0.164333i
\(309\) 0 0
\(310\) −5.03878 11.9077i −0.286184 0.676310i
\(311\) −15.4333 −0.875143 −0.437571 0.899184i \(-0.644161\pi\)
−0.437571 + 0.899184i \(0.644161\pi\)
\(312\) 0 0
\(313\) −31.1894 −1.76293 −0.881464 0.472251i \(-0.843442\pi\)
−0.881464 + 0.472251i \(0.843442\pi\)
\(314\) 8.42610 + 19.9126i 0.475513 + 1.12373i
\(315\) 0 0
\(316\) −5.47205 5.30803i −0.307827 0.298600i
\(317\) 30.7471 1.72693 0.863466 0.504407i \(-0.168289\pi\)
0.863466 + 0.504407i \(0.168289\pi\)
\(318\) 0 0
\(319\) 9.93042i 0.555997i
\(320\) −21.3327 19.4692i −1.19254 1.08836i
\(321\) 0 0
\(322\) 3.93836 + 9.30717i 0.219476 + 0.518668i
\(323\) 39.3899i 2.19171i
\(324\) 0 0
\(325\) 12.7943i 0.709700i
\(326\) −22.8747 + 9.67952i −1.26691 + 0.536099i
\(327\) 0 0
\(328\) −2.20685 0.855648i −0.121853 0.0472453i
\(329\) 0.795430i 0.0438535i
\(330\) 0 0
\(331\) 1.00125 0.0550339 0.0275169 0.999621i \(-0.491240\pi\)
0.0275169 + 0.999621i \(0.491240\pi\)
\(332\) 21.4648 + 20.8214i 1.17803 + 1.14272i
\(333\) 0 0
\(334\) 5.47389 2.31630i 0.299518 0.126742i
\(335\) 2.36595 0.129266
\(336\) 0 0
\(337\) 28.1818 1.53516 0.767580 0.640953i \(-0.221461\pi\)
0.767580 + 0.640953i \(0.221461\pi\)
\(338\) −13.6277 + 5.76662i −0.741249 + 0.313663i
\(339\) 0 0
\(340\) −40.3860 39.1755i −2.19024 2.12459i
\(341\) −5.08780 −0.275520
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −0.154838 + 0.399352i −0.00834831 + 0.0215316i
\(345\) 0 0
\(346\) −23.4529 + 9.92420i −1.26084 + 0.533528i
\(347\) 19.6496i 1.05485i −0.849602 0.527424i \(-0.823158\pi\)
0.849602 0.527424i \(-0.176842\pi\)
\(348\) 0 0
\(349\) 11.2275i 0.600993i −0.953783 0.300497i \(-0.902848\pi\)
0.953783 0.300497i \(-0.0971524\pi\)
\(350\) 4.42732 + 10.4627i 0.236650 + 0.559253i
\(351\) 0 0
\(352\) −10.3265 + 4.74514i −0.550406 + 0.252917i
\(353\) 32.2047i 1.71408i −0.515249 0.857041i \(-0.672300\pi\)
0.515249 0.857041i \(-0.327700\pi\)
\(354\) 0 0
\(355\) 41.0385 2.17810
\(356\) 0.0637631 + 0.0618518i 0.00337944 + 0.00327814i
\(357\) 0 0
\(358\) −0.488342 1.15405i −0.0258097 0.0609935i
\(359\) −20.1918 −1.06568 −0.532842 0.846215i \(-0.678876\pi\)
−0.532842 + 0.846215i \(0.678876\pi\)
\(360\) 0 0
\(361\) 6.55100 0.344790
\(362\) −4.66984 11.0358i −0.245442 0.580029i
\(363\) 0 0
\(364\) −2.21782 + 2.28635i −0.116246 + 0.119838i
\(365\) −51.9267 −2.71797
\(366\) 0 0
\(367\) 1.42641i 0.0744578i 0.999307 + 0.0372289i \(0.0118531\pi\)
−0.999307 + 0.0372289i \(0.988147\pi\)
\(368\) −0.869632 28.5712i −0.0453327 1.48938i
\(369\) 0 0
\(370\) 9.48244 + 22.4090i 0.492969 + 1.16499i
\(371\) 1.05980i 0.0550220i
\(372\) 0 0
\(373\) 9.80760i 0.507818i 0.967228 + 0.253909i \(0.0817165\pi\)
−0.967228 + 0.253909i \(0.918284\pi\)
\(374\) −20.3895 + 8.62789i −1.05431 + 0.446137i
\(375\) 0 0
\(376\) −0.813312 + 2.09766i −0.0419434 + 0.108179i
\(377\) 7.87245i 0.405452i
\(378\) 0 0
\(379\) −17.5378 −0.900857 −0.450428 0.892813i \(-0.648729\pi\)
−0.450428 + 0.892813i \(0.648729\pi\)
\(380\) −25.4119 + 26.1972i −1.30360 + 1.34389i
\(381\) 0 0
\(382\) 26.8429 11.3587i 1.37340 0.581162i
\(383\) −8.32355 −0.425313 −0.212657 0.977127i \(-0.568212\pi\)
−0.212657 + 0.977127i \(0.568212\pi\)
\(384\) 0 0
\(385\) 7.25280 0.369637
\(386\) −23.8304 + 10.0839i −1.21293 + 0.513258i
\(387\) 0 0
\(388\) 13.7443 14.1690i 0.697762 0.719323i
\(389\) −8.79829 −0.446091 −0.223045 0.974808i \(-0.571600\pi\)
−0.223045 + 0.974808i \(0.571600\pi\)
\(390\) 0 0
\(391\) 55.6866i 2.81619i
\(392\) 1.02248 2.63714i 0.0516431 0.133196i
\(393\) 0 0
\(394\) −13.8811 + 5.87385i −0.699320 + 0.295920i
\(395\) 13.7611i 0.692398i
\(396\) 0 0
\(397\) 31.5495i 1.58342i 0.610896 + 0.791711i \(0.290810\pi\)
−0.610896 + 0.791711i \(0.709190\pi\)
\(398\) 14.4010 + 34.0325i 0.721857 + 1.70590i
\(399\) 0 0
\(400\) −0.977599 32.1184i −0.0488800 1.60592i
\(401\) 8.99955i 0.449416i 0.974426 + 0.224708i \(0.0721428\pi\)
−0.974426 + 0.224708i \(0.927857\pi\)
\(402\) 0 0
\(403\) 4.03341 0.200919
\(404\) −6.16933 + 6.35996i −0.306936 + 0.316420i
\(405\) 0 0
\(406\) 2.72417 + 6.43778i 0.135199 + 0.319502i
\(407\) 9.57470 0.474600
\(408\) 0 0
\(409\) −35.7330 −1.76688 −0.883441 0.468542i \(-0.844779\pi\)
−0.883441 + 0.468542i \(0.844779\pi\)
\(410\) −1.66500 3.93473i −0.0822283 0.194322i
\(411\) 0 0
\(412\) 16.2132 + 15.7272i 0.798766 + 0.774824i
\(413\) −8.34506 −0.410633
\(414\) 0 0
\(415\) 53.9798i 2.64976i
\(416\) 8.18648 3.76176i 0.401375 0.184436i
\(417\) 0 0
\(418\) 5.59665 + 13.2260i 0.273741 + 0.646906i
\(419\) 35.1521i 1.71729i 0.512569 + 0.858646i \(0.328694\pi\)
−0.512569 + 0.858646i \(0.671306\pi\)
\(420\) 0 0
\(421\) 22.7156i 1.10709i 0.832819 + 0.553546i \(0.186726\pi\)
−0.832819 + 0.553546i \(0.813274\pi\)
\(422\) 27.5514 11.6585i 1.34118 0.567527i
\(423\) 0 0
\(424\) −1.08362 + 2.79484i −0.0526255 + 0.135730i
\(425\) 62.6002i 3.03656i
\(426\) 0 0
\(427\) −10.2367 −0.495388
\(428\) 12.3461 + 11.9760i 0.596772 + 0.578884i
\(429\) 0 0
\(430\) −0.712028 + 0.301298i −0.0343371 + 0.0145299i
\(431\) −1.00587 −0.0484511 −0.0242256 0.999707i \(-0.507712\pi\)
−0.0242256 + 0.999707i \(0.507712\pi\)
\(432\) 0 0
\(433\) −33.8256 −1.62555 −0.812776 0.582576i \(-0.802045\pi\)
−0.812776 + 0.582576i \(0.802045\pi\)
\(434\) −3.29837 + 1.39572i −0.158327 + 0.0669966i
\(435\) 0 0
\(436\) 28.5899 + 27.7330i 1.36921 + 1.32817i
\(437\) −36.1222 −1.72796
\(438\) 0 0
\(439\) 11.9514i 0.570411i −0.958466 0.285206i \(-0.907938\pi\)
0.958466 0.285206i \(-0.0920619\pi\)
\(440\) −19.1267 7.41586i −0.911829 0.353537i
\(441\) 0 0
\(442\) 16.1640 6.83986i 0.768842 0.325339i
\(443\) 17.6849i 0.840234i 0.907470 + 0.420117i \(0.138011\pi\)
−0.907470 + 0.420117i \(0.861989\pi\)
\(444\) 0 0
\(445\) 0.160352i 0.00760141i
\(446\) −3.33027 7.87011i −0.157693 0.372661i
\(447\) 0 0
\(448\) −5.39286 + 5.90906i −0.254789 + 0.279177i
\(449\) 33.4546i 1.57882i 0.613867 + 0.789409i \(0.289613\pi\)
−0.613867 + 0.789409i \(0.710387\pi\)
\(450\) 0 0
\(451\) −1.68120 −0.0791644
\(452\) −5.47484 5.31073i −0.257515 0.249796i
\(453\) 0 0
\(454\) −11.0624 26.1428i −0.519185 1.22694i
\(455\) −5.74974 −0.269552
\(456\) 0 0
\(457\) 34.7127 1.62379 0.811896 0.583802i \(-0.198436\pi\)
0.811896 + 0.583802i \(0.198436\pi\)
\(458\) −10.2054 24.1174i −0.476867 1.12693i
\(459\) 0 0
\(460\) 35.9256 37.0357i 1.67504 1.72680i
\(461\) 9.30870 0.433549 0.216775 0.976222i \(-0.430446\pi\)
0.216775 + 0.976222i \(0.430446\pi\)
\(462\) 0 0
\(463\) 1.56421i 0.0726950i 0.999339 + 0.0363475i \(0.0115723\pi\)
−0.999339 + 0.0363475i \(0.988428\pi\)
\(464\) −0.601526 19.7628i −0.0279252 0.917464i
\(465\) 0 0
\(466\) −9.43531 22.2976i −0.437082 1.03292i
\(467\) 2.47725i 0.114633i 0.998356 + 0.0573167i \(0.0182545\pi\)
−0.998356 + 0.0573167i \(0.981746\pi\)
\(468\) 0 0
\(469\) 0.655357i 0.0302616i
\(470\) −3.74004 + 1.58261i −0.172515 + 0.0730006i
\(471\) 0 0
\(472\) 22.0071 + 8.53267i 1.01296 + 0.392748i
\(473\) 0.304229i 0.0139885i
\(474\) 0 0
\(475\) −40.6069 −1.86317
\(476\) −10.8514 + 11.1867i −0.497374 + 0.512743i
\(477\) 0 0
\(478\) 5.15248 2.18029i 0.235669 0.0997243i
\(479\) −4.20750 −0.192245 −0.0961227 0.995369i \(-0.530644\pi\)
−0.0961227 + 0.995369i \(0.530644\pi\)
\(480\) 0 0
\(481\) −7.59045 −0.346095
\(482\) 20.0214 8.47212i 0.911949 0.385895i
\(483\) 0 0
\(484\) 9.69754 9.99720i 0.440797 0.454418i
\(485\) 35.6324 1.61798
\(486\) 0 0
\(487\) 29.7159i 1.34656i 0.739389 + 0.673278i \(0.235114\pi\)
−0.739389 + 0.673278i \(0.764886\pi\)
\(488\) 26.9956 + 10.4668i 1.22204 + 0.473811i
\(489\) 0 0
\(490\) 4.70192 1.98963i 0.212411 0.0898825i
\(491\) 6.98629i 0.315287i −0.987496 0.157643i \(-0.949610\pi\)
0.987496 0.157643i \(-0.0503896\pi\)
\(492\) 0 0
\(493\) 38.5185i 1.73479i
\(494\) −4.43681 10.4851i −0.199621 0.471746i
\(495\) 0 0
\(496\) 10.1254 0.308189i 0.454643 0.0138381i
\(497\) 11.3675i 0.509901i
\(498\) 0 0
\(499\) 9.65859 0.432378 0.216189 0.976352i \(-0.430637\pi\)
0.216189 + 0.976352i \(0.430637\pi\)
\(500\) 15.2494 15.7206i 0.681975 0.703048i
\(501\) 0 0
\(502\) 7.25998 + 17.1568i 0.324029 + 0.765747i
\(503\) −33.8339 −1.50858 −0.754290 0.656542i \(-0.772019\pi\)
−0.754290 + 0.656542i \(0.772019\pi\)
\(504\) 0 0
\(505\) −15.9941 −0.711728
\(506\) −7.91214 18.6980i −0.351738 0.831229i
\(507\) 0 0
\(508\) −22.9608 22.2726i −1.01872 0.988185i
\(509\) 12.8961 0.571611 0.285806 0.958288i \(-0.407739\pi\)
0.285806 + 0.958288i \(0.407739\pi\)
\(510\) 0 0
\(511\) 14.3835i 0.636287i
\(512\) 20.2637 10.0690i 0.895536 0.444989i
\(513\) 0 0
\(514\) −14.8291 35.0442i −0.654083 1.54573i
\(515\) 40.7730i 1.79667i
\(516\) 0 0
\(517\) 1.59801i 0.0702805i
\(518\) 6.20717 2.62659i 0.272728 0.115406i
\(519\) 0 0
\(520\) 15.1629 + 5.87901i 0.664937 + 0.257811i
\(521\) 15.4735i 0.677905i 0.940803 + 0.338953i \(0.110073\pi\)
−0.940803 + 0.338953i \(0.889927\pi\)
\(522\) 0 0
\(523\) −20.0632 −0.877301 −0.438651 0.898658i \(-0.644543\pi\)
−0.438651 + 0.898658i \(0.644543\pi\)
\(524\) 28.5446 + 27.6890i 1.24698 + 1.20960i
\(525\) 0 0
\(526\) −10.6154 + 4.49194i −0.462852 + 0.195858i
\(527\) 19.7348 0.859661
\(528\) 0 0
\(529\) 28.0670 1.22031
\(530\) −4.98309 + 2.10861i −0.216451 + 0.0915923i
\(531\) 0 0
\(532\) 7.25649 + 7.03899i 0.314609 + 0.305179i
\(533\) 1.33279 0.0577294
\(534\) 0 0
\(535\) 31.0481i 1.34233i
\(536\) −0.670091 + 1.72827i −0.0289435 + 0.0746500i
\(537\) 0 0
\(538\) 5.00520 2.11797i 0.215790 0.0913123i
\(539\) 2.00899i 0.0865334i
\(540\) 0 0
\(541\) 18.5169i 0.796103i −0.917363 0.398052i \(-0.869687\pi\)
0.917363 0.398052i \(-0.130313\pi\)
\(542\) −7.09320 16.7627i −0.304679 0.720019i
\(543\) 0 0
\(544\) 40.0550 18.4057i 1.71734 0.789136i
\(545\) 71.8982i 3.07978i
\(546\) 0 0
\(547\) −24.8132 −1.06094 −0.530468 0.847705i \(-0.677984\pi\)
−0.530468 + 0.847705i \(0.677984\pi\)
\(548\) −12.8279 12.4434i −0.547979 0.531554i
\(549\) 0 0
\(550\) −8.89446 21.0194i −0.379261 0.896272i
\(551\) −24.9858 −1.06443
\(552\) 0 0
\(553\) −3.81177 −0.162093
\(554\) 1.50136 + 3.54803i 0.0637867 + 0.150741i
\(555\) 0 0
\(556\) 1.67583 1.72762i 0.0710711 0.0732672i
\(557\) −19.4177 −0.822756 −0.411378 0.911465i \(-0.634952\pi\)
−0.411378 + 0.911465i \(0.634952\pi\)
\(558\) 0 0
\(559\) 0.241181i 0.0102009i
\(560\) −14.4340 + 0.439332i −0.609948 + 0.0185652i
\(561\) 0 0
\(562\) 4.91176 + 11.6075i 0.207190 + 0.489633i
\(563\) 14.6696i 0.618252i −0.951021 0.309126i \(-0.899964\pi\)
0.951021 0.309126i \(-0.100036\pi\)
\(564\) 0 0
\(565\) 13.7682i 0.579231i
\(566\) −6.38284 + 2.70093i −0.268291 + 0.113528i
\(567\) 0 0
\(568\) −11.6230 + 29.9777i −0.487692 + 1.25784i
\(569\) 17.3133i 0.725809i 0.931826 + 0.362905i \(0.118215\pi\)
−0.931826 + 0.362905i \(0.881785\pi\)
\(570\) 0 0
\(571\) 11.7082 0.489975 0.244987 0.969526i \(-0.421216\pi\)
0.244987 + 0.969526i \(0.421216\pi\)
\(572\) 4.45559 4.59327i 0.186298 0.192054i
\(573\) 0 0
\(574\) −1.08990 + 0.461196i −0.0454916 + 0.0192499i
\(575\) 57.4071 2.39404
\(576\) 0 0
\(577\) 4.79465 0.199604 0.0998020 0.995007i \(-0.468179\pi\)
0.0998020 + 0.995007i \(0.468179\pi\)
\(578\) 56.9466 24.0972i 2.36867 1.00231i
\(579\) 0 0
\(580\) 24.8498 25.6177i 1.03183 1.06372i
\(581\) 14.9522 0.620320
\(582\) 0 0
\(583\) 2.12913i 0.0881795i
\(584\) 14.7068 37.9313i 0.608573 1.56961i
\(585\) 0 0
\(586\) −34.0432 + 14.4055i −1.40631 + 0.595086i
\(587\) 30.1643i 1.24501i 0.782615 + 0.622506i \(0.213886\pi\)
−0.782615 + 0.622506i \(0.786114\pi\)
\(588\) 0 0
\(589\) 12.8014i 0.527471i
\(590\) 16.6036 + 39.2378i 0.683560 + 1.61539i
\(591\) 0 0
\(592\) −19.0549 + 0.579979i −0.783150 + 0.0238370i
\(593\) 2.60974i 0.107169i −0.998563 0.0535847i \(-0.982935\pi\)
0.998563 0.0535847i \(-0.0170647\pi\)
\(594\) 0 0
\(595\) −28.1325 −1.15332
\(596\) −17.6561 + 18.2016i −0.723220 + 0.745568i
\(597\) 0 0
\(598\) 6.27244 + 14.8231i 0.256499 + 0.606160i
\(599\) 27.6903 1.13139 0.565697 0.824613i \(-0.308607\pi\)
0.565697 + 0.824613i \(0.308607\pi\)
\(600\) 0 0
\(601\) 16.3291 0.666079 0.333039 0.942913i \(-0.391926\pi\)
0.333039 + 0.942913i \(0.391926\pi\)
\(602\) 0.0834580 + 0.197228i 0.00340150 + 0.00803843i
\(603\) 0 0
\(604\) −25.1358 24.3824i −1.02276 0.992105i
\(605\) 25.1410 1.02213
\(606\) 0 0
\(607\) 12.9385i 0.525159i 0.964910 + 0.262580i \(0.0845732\pi\)
−0.964910 + 0.262580i \(0.915427\pi\)
\(608\) −11.9392 25.9825i −0.484198 1.05373i
\(609\) 0 0
\(610\) 20.3673 + 48.1321i 0.824647 + 1.94881i
\(611\) 1.26684i 0.0512509i
\(612\) 0 0
\(613\) 21.7992i 0.880463i 0.897884 + 0.440231i \(0.145104\pi\)
−0.897884 + 0.440231i \(0.854896\pi\)
\(614\) 30.5098 12.9103i 1.23127 0.521019i
\(615\) 0 0
\(616\) −2.05416 + 5.29800i −0.0827644 + 0.213463i
\(617\) 41.8226i 1.68371i −0.539700 0.841857i \(-0.681462\pi\)
0.539700 0.841857i \(-0.318538\pi\)
\(618\) 0 0
\(619\) −4.82763 −0.194039 −0.0970193 0.995282i \(-0.530931\pi\)
−0.0970193 + 0.995282i \(0.530931\pi\)
\(620\) 13.1251 + 12.7317i 0.527117 + 0.511317i
\(621\) 0 0
\(622\) 20.1005 8.50560i 0.805955 0.341043i
\(623\) 0.0444167 0.00177952
\(624\) 0 0
\(625\) −0.632276 −0.0252911
\(626\) 40.6213 17.1891i 1.62355 0.687014i
\(627\) 0 0
\(628\) −21.9485 21.2906i −0.875839 0.849586i
\(629\) −37.1388 −1.48082
\(630\) 0 0
\(631\) 20.3929i 0.811830i 0.913911 + 0.405915i \(0.133047\pi\)
−0.913911 + 0.405915i \(0.866953\pi\)
\(632\) 10.0522 + 3.89747i 0.399855 + 0.155033i
\(633\) 0 0
\(634\) −40.0453 + 16.9453i −1.59040 + 0.672986i
\(635\) 57.7420i 2.29142i
\(636\) 0 0
\(637\) 1.59265i 0.0631032i
\(638\) −5.47285 12.9335i −0.216672 0.512041i
\(639\) 0 0
\(640\) 38.5137 + 13.5999i 1.52239 + 0.537584i
\(641\) 9.42755i 0.372366i −0.982515 0.186183i \(-0.940388\pi\)
0.982515 0.186183i \(-0.0596117\pi\)
\(642\) 0 0
\(643\) −27.2077 −1.07297 −0.536484 0.843911i \(-0.680248\pi\)
−0.536484 + 0.843911i \(0.680248\pi\)
\(644\) −10.2587 9.95122i −0.404250 0.392133i
\(645\) 0 0
\(646\) −21.7085 51.3017i −0.854110 2.01844i
\(647\) −7.24081 −0.284666 −0.142333 0.989819i \(-0.545460\pi\)
−0.142333 + 0.989819i \(0.545460\pi\)
\(648\) 0 0
\(649\) 16.7652 0.658090
\(650\) 7.05118 + 16.6634i 0.276570 + 0.653592i
\(651\) 0 0
\(652\) 24.4576 25.2134i 0.957834 0.987432i
\(653\) 30.0954 1.17772 0.588861 0.808234i \(-0.299576\pi\)
0.588861 + 0.808234i \(0.299576\pi\)
\(654\) 0 0
\(655\) 71.7842i 2.80484i
\(656\) 3.34579 0.101837i 0.130631 0.00397606i
\(657\) 0 0
\(658\) 0.438377 + 1.03597i 0.0170897 + 0.0403865i
\(659\) 41.9316i 1.63342i 0.577045 + 0.816712i \(0.304206\pi\)
−0.577045 + 0.816712i \(0.695794\pi\)
\(660\) 0 0
\(661\) 0.735053i 0.0285903i 0.999898 + 0.0142951i \(0.00455044\pi\)
−0.999898 + 0.0142951i \(0.995450\pi\)
\(662\) −1.30404 + 0.551810i −0.0506830 + 0.0214467i
\(663\) 0 0
\(664\) −39.4310 15.2883i −1.53022 0.593301i
\(665\) 18.2487i 0.707654i
\(666\) 0 0
\(667\) 35.3232 1.36772
\(668\) −5.85268 + 6.03353i −0.226447 + 0.233444i
\(669\) 0 0
\(670\) −3.08143 + 1.30392i −0.119046 + 0.0503749i
\(671\) 20.5654 0.793920
\(672\) 0 0
\(673\) −21.6142 −0.833165 −0.416582 0.909098i \(-0.636772\pi\)
−0.416582 + 0.909098i \(0.636772\pi\)
\(674\) −36.7042 + 15.5315i −1.41379 + 0.598252i
\(675\) 0 0
\(676\) 14.5707 15.0210i 0.560413 0.577730i
\(677\) −0.631879 −0.0242851 −0.0121425 0.999926i \(-0.503865\pi\)
−0.0121425 + 0.999926i \(0.503865\pi\)
\(678\) 0 0
\(679\) 9.87000i 0.378776i
\(680\) 74.1894 + 28.7650i 2.84504 + 1.10309i
\(681\) 0 0
\(682\) 6.62640 2.80399i 0.253738 0.107370i
\(683\) 22.4241i 0.858033i −0.903297 0.429017i \(-0.858860\pi\)
0.903297 0.429017i \(-0.141140\pi\)
\(684\) 0 0
\(685\) 32.2596i 1.23258i
\(686\) −0.551119 1.30241i −0.0210418 0.0497262i
\(687\) 0 0
\(688\) −0.0184284 0.605454i −0.000702576 0.0230827i
\(689\) 1.68789i 0.0643035i
\(690\) 0 0
\(691\) −2.69349 −0.102465 −0.0512325 0.998687i \(-0.516315\pi\)
−0.0512325 + 0.998687i \(0.516315\pi\)
\(692\) 25.0759 25.8507i 0.953241 0.982697i
\(693\) 0 0
\(694\) 10.8293 + 25.5918i 0.411074 + 0.971453i
\(695\) 4.34462 0.164801
\(696\) 0 0
\(697\) 6.52109 0.247004
\(698\) 6.18768 + 14.6228i 0.234207 + 0.553480i
\(699\) 0 0
\(700\) −11.5324 11.1867i −0.435882 0.422817i
\(701\) −28.4555 −1.07475 −0.537375 0.843344i \(-0.680584\pi\)
−0.537375 + 0.843344i \(0.680584\pi\)
\(702\) 0 0
\(703\) 24.0908i 0.908601i
\(704\) 10.8342 11.8713i 0.408330 0.447415i
\(705\) 0 0
\(706\) 17.7486 + 41.9436i 0.667978 + 1.57857i
\(707\) 4.43029i 0.166618i
\(708\) 0 0
\(709\) 13.4255i 0.504204i 0.967701 + 0.252102i \(0.0811218\pi\)
−0.967701 + 0.252102i \(0.918878\pi\)
\(710\) −53.4489 + 22.6171i −2.00590 + 0.848806i
\(711\) 0 0
\(712\) −0.117133 0.0454153i −0.00438976 0.00170201i
\(713\) 18.0977i 0.677763i
\(714\) 0 0
\(715\) 11.5512 0.431990
\(716\) 1.27204 + 1.23391i 0.0475384 + 0.0461135i
\(717\) 0 0
\(718\) 26.2980 11.1281i 0.981433 0.415297i
\(719\) −49.4437 −1.84394 −0.921969 0.387264i \(-0.873420\pi\)
−0.921969 + 0.387264i \(0.873420\pi\)
\(720\) 0 0
\(721\) 11.2939 0.420608
\(722\) −8.53208 + 3.61039i −0.317531 + 0.134365i
\(723\) 0 0
\(724\) 12.1641 + 11.7995i 0.452075 + 0.438524i
\(725\) 39.7086 1.47474
\(726\) 0 0
\(727\) 5.65644i 0.209786i −0.994484 0.104893i \(-0.966550\pi\)
0.994484 0.104893i \(-0.0334500\pi\)
\(728\) 1.62846 4.20005i 0.0603546 0.155664i
\(729\) 0 0
\(730\) 67.6298 28.6178i 2.50309 1.05919i
\(731\) 1.18006i 0.0436460i
\(732\) 0 0
\(733\) 42.3705i 1.56499i 0.622656 + 0.782495i \(0.286054\pi\)
−0.622656 + 0.782495i \(0.713946\pi\)
\(734\) −0.786120 1.85776i −0.0290162 0.0685713i
\(735\) 0 0
\(736\) 16.8788 + 36.7322i 0.622160 + 1.35397i
\(737\) 1.31661i 0.0484979i
\(738\) 0 0
\(739\) −41.5942 −1.53007 −0.765034 0.643989i \(-0.777278\pi\)
−0.765034 + 0.643989i \(0.777278\pi\)
\(740\) −24.7000 23.9597i −0.907991 0.880774i
\(741\) 0 0
\(742\) 0.584076 + 1.38029i 0.0214421 + 0.0506721i
\(743\) −16.5821 −0.608338 −0.304169 0.952618i \(-0.598379\pi\)
−0.304169 + 0.952618i \(0.598379\pi\)
\(744\) 0 0
\(745\) −45.7736 −1.67702
\(746\) −5.40516 12.7735i −0.197897 0.467671i
\(747\) 0 0
\(748\) 21.8004 22.4741i 0.797102 0.821733i
\(749\) 8.60018 0.314244
\(750\) 0 0
\(751\) 4.26395i 0.155594i −0.996969 0.0777968i \(-0.975211\pi\)
0.996969 0.0777968i \(-0.0247886\pi\)
\(752\) −0.0967982 3.18025i −0.00352987 0.115972i
\(753\) 0 0
\(754\) 4.33866 + 10.2531i 0.158005 + 0.373398i
\(755\) 63.2118i 2.30051i
\(756\) 0 0
\(757\) 19.5706i 0.711305i 0.934618 + 0.355653i \(0.115741\pi\)
−0.934618 + 0.355653i \(0.884259\pi\)
\(758\) 22.8414 9.66542i 0.829636 0.351064i
\(759\) 0 0
\(760\) 18.6589 48.1244i 0.676831 1.74566i
\(761\) 22.1256i 0.802053i −0.916066 0.401027i \(-0.868653\pi\)
0.916066 0.401027i \(-0.131347\pi\)
\(762\) 0 0
\(763\) 19.9155 0.720988
\(764\) −28.7005 + 29.5873i −1.03835 + 1.07043i
\(765\) 0 0
\(766\) 10.8407 4.58727i 0.391689 0.165745i
\(767\) −13.2908 −0.479902
\(768\) 0 0
\(769\) −16.1961 −0.584046 −0.292023 0.956411i \(-0.594328\pi\)
−0.292023 + 0.956411i \(0.594328\pi\)
\(770\) −9.44611 + 3.99716i −0.340414 + 0.144048i
\(771\) 0 0
\(772\) 25.4794 26.2668i 0.917025 0.945362i
\(773\) −2.34825 −0.0844608 −0.0422304 0.999108i \(-0.513446\pi\)
−0.0422304 + 0.999108i \(0.513446\pi\)
\(774\) 0 0
\(775\) 20.3445i 0.730797i
\(776\) −10.0919 + 26.0286i −0.362278 + 0.934373i
\(777\) 0 0
\(778\) 11.4590 4.84891i 0.410824 0.173842i
\(779\) 4.23003i 0.151557i
\(780\) 0 0
\(781\) 22.8372i 0.817179i
\(782\) 30.6900 + 72.5267i 1.09747 + 2.59355i
\(783\) 0 0
\(784\) 0.121693 + 3.99815i 0.00434618 + 0.142791i
\(785\) 55.1962i 1.97004i
\(786\) 0 0
\(787\) 10.9012 0.388586 0.194293 0.980943i \(-0.437759\pi\)
0.194293 + 0.980943i \(0.437759\pi\)
\(788\) 14.8417 15.3003i 0.528713 0.545050i
\(789\) 0 0
\(790\) 7.58403 + 17.9226i 0.269828 + 0.637659i
\(791\) −3.81372 −0.135600
\(792\) 0 0
\(793\) −16.3035 −0.578954
\(794\) −17.3875 41.0903i −0.617060 1.45824i
\(795\) 0 0
\(796\) −37.5120 36.3876i −1.32958 1.28972i
\(797\) 5.08600 0.180155 0.0900776 0.995935i \(-0.471288\pi\)
0.0900776 + 0.995935i \(0.471288\pi\)
\(798\) 0 0
\(799\) 6.19844i 0.219285i
\(800\) 18.9743 + 41.2925i 0.670844 + 1.45991i
\(801\) 0 0
\(802\) −4.95982 11.7211i −0.175137 0.413886i
\(803\) 28.8963i 1.01973i
\(804\) 0 0
\(805\) 25.7987i 0.909285i
\(806\) −5.25315 + 2.22289i −0.185034 + 0.0782981i
\(807\) 0 0
\(808\) 4.52989 11.6833i 0.159361 0.411017i
\(809\) 26.8140i 0.942729i 0.881938 + 0.471365i \(0.156238\pi\)
−0.881938 + 0.471365i \(0.843762\pi\)
\(810\) 0 0
\(811\) 38.8383 1.36380 0.681899 0.731446i \(-0.261154\pi\)
0.681899 + 0.731446i \(0.261154\pi\)
\(812\) −7.09597 6.88328i −0.249020 0.241556i
\(813\) 0 0
\(814\) −12.4702 + 5.27680i −0.437079 + 0.184952i
\(815\) 63.4068 2.22104
\(816\) 0 0
\(817\) −0.765467 −0.0267803
\(818\) 46.5389 19.6931i 1.62720 0.688554i
\(819\) 0 0
\(820\) 4.33701 + 4.20701i 0.151455 + 0.146915i
\(821\) −29.3421 −1.02405 −0.512023 0.858972i \(-0.671104\pi\)
−0.512023 + 0.858972i \(0.671104\pi\)
\(822\) 0 0
\(823\) 23.9770i 0.835784i −0.908497 0.417892i \(-0.862769\pi\)
0.908497 0.417892i \(-0.137231\pi\)
\(824\) −29.7837 11.5478i −1.03757 0.402288i
\(825\) 0 0
\(826\) 10.8687 4.59912i 0.378169 0.160024i
\(827\) 4.92468i 0.171248i 0.996328 + 0.0856239i \(0.0272883\pi\)
−0.996328 + 0.0856239i \(0.972712\pi\)
\(828\) 0 0
\(829\) 8.00324i 0.277964i −0.990295 0.138982i \(-0.955617\pi\)
0.990295 0.138982i \(-0.0443830\pi\)
\(830\) −29.7493 70.3038i −1.03261 2.44028i
\(831\) 0 0
\(832\) −8.58895 + 9.41108i −0.297768 + 0.326270i
\(833\) 7.79257i 0.269996i
\(834\) 0 0
\(835\) −15.1732 −0.525089
\(836\) −14.5782 14.1413i −0.504199 0.489086i
\(837\) 0 0
\(838\) −19.3730 45.7824i −0.669229 1.58153i
\(839\) −31.4595 −1.08610 −0.543051 0.839700i \(-0.682731\pi\)
−0.543051 + 0.839700i \(0.682731\pi\)
\(840\) 0 0
\(841\) −4.56691 −0.157479
\(842\) −12.5190 29.5850i −0.431434 1.01957i
\(843\) 0 0
\(844\) −29.4580 + 30.3683i −1.01399 + 1.04532i
\(845\) 37.7749 1.29950
\(846\) 0 0
\(847\) 6.96395i 0.239284i
\(848\) −0.128970 4.23723i −0.00442885 0.145507i
\(849\) 0 0
\(850\) 34.5002 + 81.5311i 1.18335 + 2.79649i
\(851\) 34.0578i 1.16749i
\(852\) 0 0
\(853\) 1.31213i 0.0449263i −0.999748 0.0224632i \(-0.992849\pi\)
0.999748 0.0224632i \(-0.00715085\pi\)
\(854\) 13.3324 5.64164i 0.456224 0.193053i
\(855\) 0 0
\(856\) −22.6799 8.79352i −0.775183 0.300556i
\(857\) 24.2200i 0.827341i 0.910427 + 0.413670i \(0.135753\pi\)
−0.910427 + 0.413670i \(0.864247\pi\)
\(858\) 0 0
\(859\) 8.49401 0.289812 0.144906 0.989445i \(-0.453712\pi\)
0.144906 + 0.989445i \(0.453712\pi\)
\(860\) 0.761301 0.784825i 0.0259601 0.0267623i
\(861\) 0 0
\(862\) 1.31006 0.554355i 0.0446207 0.0188814i
\(863\) 30.8759 1.05103 0.525513 0.850785i \(-0.323873\pi\)
0.525513 + 0.850785i \(0.323873\pi\)
\(864\) 0 0
\(865\) 65.0096 2.21039
\(866\) 44.0547 18.6419i 1.49704 0.633478i
\(867\) 0 0
\(868\) 3.52662 3.63559i 0.119701 0.123400i
\(869\) 7.65782 0.259774
\(870\) 0 0
\(871\) 1.04376i 0.0353663i
\(872\) −52.5200 20.3632i −1.77855 0.689585i
\(873\) 0 0
\(874\) 47.0459 19.9076i 1.59135 0.673386i
\(875\) 10.9508i 0.370206i
\(876\) 0 0
\(877\) 33.4689i 1.13016i 0.825035 + 0.565082i \(0.191155\pi\)
−0.825035 + 0.565082i \(0.808845\pi\)
\(878\) 6.58667 + 15.5657i 0.222289 + 0.525316i
\(879\) 0 0
\(880\) 28.9978 0.882615i 0.977515 0.0297529i
\(881\) 33.7535i 1.13719i −0.822619 0.568593i \(-0.807488\pi\)
0.822619 0.568593i \(-0.192512\pi\)
\(882\) 0 0
\(883\) 1.59496 0.0536746 0.0268373 0.999640i \(-0.491456\pi\)
0.0268373 + 0.999640i \(0.491456\pi\)
\(884\) −17.2825 + 17.8166i −0.581275 + 0.599236i
\(885\) 0 0
\(886\) −9.74649 23.0329i −0.327440 0.773807i
\(887\) 17.9639 0.603167 0.301584 0.953440i \(-0.402485\pi\)
0.301584 + 0.953440i \(0.402485\pi\)
\(888\) 0 0
\(889\) −15.9943 −0.536430
\(890\) −0.0883730 0.208844i −0.00296227 0.00700045i
\(891\) 0 0
\(892\) 8.67474 + 8.41473i 0.290452 + 0.281746i
\(893\) −4.02074 −0.134549
\(894\) 0 0
\(895\) 3.19894i 0.106929i
\(896\) 3.76711 10.6681i 0.125850 0.356397i
\(897\) 0 0
\(898\) −18.4375 43.5715i −0.615266 1.45400i
\(899\) 12.5182i 0.417505i
\(900\) 0 0
\(901\) 8.25855i 0.275132i
\(902\) 2.18960 0.926539i 0.0729058 0.0308504i
\(903\) 0 0
\(904\) 10.0573 + 3.89945i 0.334502 + 0.129694i
\(905\) 30.5903i 1.01686i
\(906\) 0 0
\(907\) 52.9653 1.75868 0.879342 0.476190i \(-0.157983\pi\)
0.879342 + 0.476190i \(0.157983\pi\)
\(908\) 28.8156 + 27.9518i 0.956278 + 0.927614i
\(909\) 0 0
\(910\) 7.48851 3.16879i 0.248242 0.105045i
\(911\) 52.6435 1.74416 0.872079 0.489365i \(-0.162771\pi\)
0.872079 + 0.489365i \(0.162771\pi\)
\(912\) 0 0
\(913\) −30.0388 −0.994138
\(914\) −45.2101 + 19.1308i −1.49542 + 0.632792i
\(915\) 0 0
\(916\) 26.5832 + 25.7864i 0.878333 + 0.852006i
\(917\) 19.8839 0.656623
\(918\) 0 0
\(919\) 36.5794i 1.20664i −0.797498 0.603322i \(-0.793843\pi\)
0.797498 0.603322i \(-0.206157\pi\)
\(920\) −26.3787 + 68.0349i −0.869680 + 2.24304i
\(921\) 0 0
\(922\) −12.1237 + 5.13020i −0.399274 + 0.168954i
\(923\) 18.1044i 0.595915i
\(924\) 0 0
\(925\) 38.2862i 1.25884i
\(926\) −0.862067 2.03724i −0.0283293 0.0669479i
\(927\) 0 0
\(928\) 11.6751 + 25.4077i 0.383253 + 0.834049i
\(929\) 24.8413i 0.815018i 0.913201 + 0.407509i \(0.133602\pi\)
−0.913201 + 0.407509i \(0.866398\pi\)
\(930\) 0 0
\(931\) 5.05480 0.165664
\(932\) 24.5773 + 23.8406i 0.805055 + 0.780924i
\(933\) 0 0
\(934\) −1.36526 3.22639i −0.0446727 0.105571i
\(935\) 56.5180 1.84833
\(936\) 0 0
\(937\) 0.904448 0.0295470 0.0147735 0.999891i \(-0.495297\pi\)
0.0147735 + 0.999891i \(0.495297\pi\)
\(938\) 0.361180 + 0.853543i 0.0117929 + 0.0278692i
\(939\) 0 0
\(940\) 3.99885 4.12242i 0.130428 0.134459i
\(941\) −8.11337 −0.264488 −0.132244 0.991217i \(-0.542218\pi\)
−0.132244 + 0.991217i \(0.542218\pi\)
\(942\) 0 0
\(943\) 5.98012i 0.194740i
\(944\) −33.3648 + 1.01553i −1.08593 + 0.0330528i
\(945\) 0 0
\(946\) −0.167667 0.396231i −0.00545131 0.0128826i
\(947\) 34.2396i 1.11264i 0.830969 + 0.556319i \(0.187787\pi\)
−0.830969 + 0.556319i \(0.812213\pi\)
\(948\) 0 0
\(949\) 22.9078i 0.743620i
\(950\) 52.8867 22.3792i 1.71587 0.726078i
\(951\) 0 0
\(952\) 7.96776 20.5501i 0.258236 0.666033i
\(953\) 5.47739i 0.177430i 0.996057 + 0.0887151i \(0.0282761\pi\)
−0.996057 + 0.0887151i \(0.971724\pi\)
\(954\) 0 0
\(955\) −74.4065 −2.40774
\(956\) −5.50903 + 5.67926i −0.178175 + 0.183680i
\(957\) 0 0
\(958\) 5.47988 2.31883i 0.177047 0.0749181i
\(959\) −8.93576 −0.288551
\(960\) 0 0
\(961\) 24.5864 0.793109
\(962\) 9.88587 4.18324i 0.318733 0.134873i
\(963\) 0 0
\(964\) −21.4069 + 22.0683i −0.689468 + 0.710773i
\(965\) 66.0559 2.12641
\(966\) 0 0
\(967\) 45.0597i 1.44902i −0.689262 0.724512i \(-0.742065\pi\)
0.689262 0.724512i \(-0.257935\pi\)
\(968\) −7.12051 + 18.3649i −0.228862 + 0.590272i
\(969\) 0 0
\(970\) −46.4079 + 19.6377i −1.49007 + 0.630528i
\(971\) 28.4013i 0.911442i −0.890123 0.455721i \(-0.849382\pi\)
0.890123 0.455721i \(-0.150618\pi\)
\(972\) 0 0
\(973\) 1.20344i 0.0385805i
\(974\) −16.3770 38.7022i −0.524753 1.24010i
\(975\) 0 0
\(976\) −40.9278 + 1.24573i −1.31007 + 0.0398750i
\(977\) 4.06448i 0.130034i −0.997884 0.0650171i \(-0.979290\pi\)
0.997884 0.0650171i \(-0.0207102\pi\)
\(978\) 0 0
\(979\) −0.0892328 −0.00285189
\(980\) −5.02729 + 5.18263i −0.160591 + 0.165553i
\(981\) 0 0
\(982\) 3.85028 + 9.09900i 0.122867 + 0.290361i
\(983\) 13.0487 0.416189 0.208094 0.978109i \(-0.433274\pi\)
0.208094 + 0.978109i \(0.433274\pi\)
\(984\) 0 0
\(985\) 38.4773 1.22599
\(986\) 21.2283 + 50.1669i 0.676047 + 1.59764i
\(987\) 0 0
\(988\) 11.5571 + 11.2107i 0.367679 + 0.356658i
\(989\) 1.08216 0.0344108
\(990\) 0 0
\(991\) 0.598647i 0.0190166i −0.999955 0.00950832i \(-0.996973\pi\)
0.999955 0.00950832i \(-0.00302664\pi\)
\(992\) −13.0175 + 5.98168i −0.413307 + 0.189918i
\(993\) 0 0
\(994\) 6.26484 + 14.8051i 0.198709 + 0.469589i
\(995\) 94.3354i 2.99063i
\(996\) 0 0
\(997\) 4.04553i 0.128123i −0.997946 0.0640616i \(-0.979595\pi\)
0.997946 0.0640616i \(-0.0204054\pi\)
\(998\) −12.5794 + 5.32304i −0.398195 + 0.168498i
\(999\) 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 1512.2.j.c.323.6 yes 32
3.2 odd 2 inner 1512.2.j.c.323.27 yes 32
4.3 odd 2 6048.2.j.c.5615.32 32
8.3 odd 2 inner 1512.2.j.c.323.28 yes 32
8.5 even 2 6048.2.j.c.5615.2 32
12.11 even 2 6048.2.j.c.5615.1 32
24.5 odd 2 6048.2.j.c.5615.31 32
24.11 even 2 inner 1512.2.j.c.323.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.j.c.323.5 32 24.11 even 2 inner
1512.2.j.c.323.6 yes 32 1.1 even 1 trivial
1512.2.j.c.323.27 yes 32 3.2 odd 2 inner
1512.2.j.c.323.28 yes 32 8.3 odd 2 inner
6048.2.j.c.5615.1 32 12.11 even 2
6048.2.j.c.5615.2 32 8.5 even 2
6048.2.j.c.5615.31 32 24.5 odd 2
6048.2.j.c.5615.32 32 4.3 odd 2