Properties

Label 1064.2.q.n.457.5
Level $1064$
Weight $2$
Character 1064.457
Analytic conductor $8.496$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1064,2,Mod(305,1064)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1064, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1064.305");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.q (of order \(3\), degree \(2\), 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: \(8.49608277506\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + 4560 x^{6} + 1376 x^{5} + 4688 x^{4} + 736 x^{3} + 1280 x^{2} - 128 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 457.5
Root \(0.218288 + 0.378086i\) of defining polynomial
Character \(\chi\) \(=\) 1064.457
Dual form 1064.2.q.n.305.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.218288 + 0.378086i) q^{3} +(0.149820 - 0.259496i) q^{5} +(1.68999 + 2.03567i) q^{7} +(1.40470 - 2.43301i) q^{9} +O(q^{10})\) \(q+(0.218288 + 0.378086i) q^{3} +(0.149820 - 0.259496i) q^{5} +(1.68999 + 2.03567i) q^{7} +(1.40470 - 2.43301i) q^{9} +(2.59469 + 4.49414i) q^{11} -1.26174 q^{13} +0.130816 q^{15} +(-0.979458 - 1.69647i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-0.400752 + 1.08332i) q^{21} +(0.745532 - 1.29130i) q^{23} +(2.45511 + 4.25237i) q^{25} +2.53625 q^{27} -0.530372 q^{29} +(-0.974190 - 1.68735i) q^{31} +(-1.13278 + 1.96203i) q^{33} +(0.781440 - 0.133562i) q^{35} +(-2.09673 + 3.63165i) q^{37} +(-0.275423 - 0.477047i) q^{39} -2.00000 q^{41} +5.51755 q^{43} +(-0.420904 - 0.729027i) q^{45} +(4.27048 - 7.39669i) q^{47} +(-1.28787 + 6.88051i) q^{49} +(0.427608 - 0.740639i) q^{51} +(5.87784 + 10.1807i) q^{53} +1.55494 q^{55} -0.436576 q^{57} +(6.40759 + 11.0983i) q^{59} +(2.96790 - 5.14056i) q^{61} +(7.32673 - 1.25227i) q^{63} +(-0.189034 + 0.327416i) q^{65} +(-2.75386 - 4.76982i) q^{67} +0.650963 q^{69} +2.28016 q^{71} +(2.34620 + 4.06373i) q^{73} +(-1.07184 + 1.85648i) q^{75} +(-4.76356 + 12.8770i) q^{77} +(-2.84734 + 4.93174i) q^{79} +(-3.66047 - 6.34012i) q^{81} +1.46325 q^{83} -0.586969 q^{85} +(-0.115774 - 0.200526i) q^{87} +(1.92525 - 3.33463i) q^{89} +(-2.13233 - 2.56848i) q^{91} +(0.425308 - 0.736655i) q^{93} +(0.149820 + 0.259496i) q^{95} -9.69800 q^{97} +14.5791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(799\) \(913\) \(1009\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(3\) 0.218288 + 0.378086i 0.126029 + 0.218288i 0.922135 0.386869i \(-0.126444\pi\)
−0.796106 + 0.605157i \(0.793110\pi\)
\(4\) 0 0
\(5\) 0.149820 0.259496i 0.0670015 0.116050i −0.830579 0.556901i \(-0.811990\pi\)
0.897580 + 0.440851i \(0.145323\pi\)
\(6\) 0 0
\(7\) 1.68999 + 2.03567i 0.638756 + 0.769409i
\(8\) 0 0
\(9\) 1.40470 2.43301i 0.468234 0.811004i
\(10\) 0 0
\(11\) 2.59469 + 4.49414i 0.782329 + 1.35503i 0.930582 + 0.366084i \(0.119302\pi\)
−0.148253 + 0.988949i \(0.547365\pi\)
\(12\) 0 0
\(13\) −1.26174 −0.349944 −0.174972 0.984573i \(-0.555984\pi\)
−0.174972 + 0.984573i \(0.555984\pi\)
\(14\) 0 0
\(15\) 0.130816 0.0337764
\(16\) 0 0
\(17\) −0.979458 1.69647i −0.237553 0.411454i 0.722458 0.691414i \(-0.243012\pi\)
−0.960012 + 0.279960i \(0.909679\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i
\(20\) 0 0
\(21\) −0.400752 + 1.08332i −0.0874513 + 0.236401i
\(22\) 0 0
\(23\) 0.745532 1.29130i 0.155454 0.269254i −0.777770 0.628549i \(-0.783649\pi\)
0.933224 + 0.359294i \(0.116983\pi\)
\(24\) 0 0
\(25\) 2.45511 + 4.25237i 0.491022 + 0.850474i
\(26\) 0 0
\(27\) 2.53625 0.488101
\(28\) 0 0
\(29\) −0.530372 −0.0984876 −0.0492438 0.998787i \(-0.515681\pi\)
−0.0492438 + 0.998787i \(0.515681\pi\)
\(30\) 0 0
\(31\) −0.974190 1.68735i −0.174970 0.303056i 0.765181 0.643815i \(-0.222649\pi\)
−0.940151 + 0.340759i \(0.889316\pi\)
\(32\) 0 0
\(33\) −1.13278 + 1.96203i −0.197192 + 0.341546i
\(34\) 0 0
\(35\) 0.781440 0.133562i 0.132088 0.0225761i
\(36\) 0 0
\(37\) −2.09673 + 3.63165i −0.344701 + 0.597039i −0.985299 0.170837i \(-0.945353\pi\)
0.640599 + 0.767876i \(0.278686\pi\)
\(38\) 0 0
\(39\) −0.275423 0.477047i −0.0441030 0.0763887i
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 5.51755 0.841418 0.420709 0.907196i \(-0.361781\pi\)
0.420709 + 0.907196i \(0.361781\pi\)
\(44\) 0 0
\(45\) −0.420904 0.729027i −0.0627447 0.108677i
\(46\) 0 0
\(47\) 4.27048 7.39669i 0.622913 1.07892i −0.366027 0.930604i \(-0.619282\pi\)
0.988940 0.148313i \(-0.0473844\pi\)
\(48\) 0 0
\(49\) −1.28787 + 6.88051i −0.183981 + 0.982930i
\(50\) 0 0
\(51\) 0.427608 0.740639i 0.0598771 0.103710i
\(52\) 0 0
\(53\) 5.87784 + 10.1807i 0.807383 + 1.39843i 0.914671 + 0.404200i \(0.132450\pi\)
−0.107288 + 0.994228i \(0.534217\pi\)
\(54\) 0 0
\(55\) 1.55494 0.209669
\(56\) 0 0
\(57\) −0.436576 −0.0578259
\(58\) 0 0
\(59\) 6.40759 + 11.0983i 0.834198 + 1.44487i 0.894682 + 0.446704i \(0.147402\pi\)
−0.0604842 + 0.998169i \(0.519264\pi\)
\(60\) 0 0
\(61\) 2.96790 5.14056i 0.380001 0.658181i −0.611061 0.791583i \(-0.709257\pi\)
0.991062 + 0.133403i \(0.0425904\pi\)
\(62\) 0 0
\(63\) 7.32673 1.25227i 0.923081 0.157771i
\(64\) 0 0
\(65\) −0.189034 + 0.327416i −0.0234468 + 0.0406110i
\(66\) 0 0
\(67\) −2.75386 4.76982i −0.336438 0.582727i 0.647322 0.762216i \(-0.275889\pi\)
−0.983760 + 0.179489i \(0.942555\pi\)
\(68\) 0 0
\(69\) 0.650963 0.0783667
\(70\) 0 0
\(71\) 2.28016 0.270605 0.135303 0.990804i \(-0.456799\pi\)
0.135303 + 0.990804i \(0.456799\pi\)
\(72\) 0 0
\(73\) 2.34620 + 4.06373i 0.274602 + 0.475624i 0.970035 0.242967i \(-0.0781207\pi\)
−0.695433 + 0.718591i \(0.744787\pi\)
\(74\) 0 0
\(75\) −1.07184 + 1.85648i −0.123766 + 0.214368i
\(76\) 0 0
\(77\) −4.76356 + 12.8770i −0.542858 + 1.46747i
\(78\) 0 0
\(79\) −2.84734 + 4.93174i −0.320351 + 0.554864i −0.980560 0.196217i \(-0.937134\pi\)
0.660209 + 0.751082i \(0.270468\pi\)
\(80\) 0 0
\(81\) −3.66047 6.34012i −0.406719 0.704458i
\(82\) 0 0
\(83\) 1.46325 0.160613 0.0803065 0.996770i \(-0.474410\pi\)
0.0803065 + 0.996770i \(0.474410\pi\)
\(84\) 0 0
\(85\) −0.586969 −0.0636657
\(86\) 0 0
\(87\) −0.115774 0.200526i −0.0124123 0.0214987i
\(88\) 0 0
\(89\) 1.92525 3.33463i 0.204076 0.353470i −0.745762 0.666213i \(-0.767914\pi\)
0.949838 + 0.312742i \(0.101248\pi\)
\(90\) 0 0
\(91\) −2.13233 2.56848i −0.223529 0.269250i
\(92\) 0 0
\(93\) 0.425308 0.736655i 0.0441024 0.0763876i
\(94\) 0 0
\(95\) 0.149820 + 0.259496i 0.0153712 + 0.0266237i
\(96\) 0 0
\(97\) −9.69800 −0.984683 −0.492341 0.870402i \(-0.663859\pi\)
−0.492341 + 0.870402i \(0.663859\pi\)
\(98\) 0 0
\(99\) 14.5791 1.46525
\(100\) 0 0
\(101\) −8.19033 14.1861i −0.814969 1.41157i −0.909350 0.416031i \(-0.863421\pi\)
0.0943816 0.995536i \(-0.469913\pi\)
\(102\) 0 0
\(103\) −2.43891 + 4.22431i −0.240313 + 0.416234i −0.960803 0.277231i \(-0.910583\pi\)
0.720491 + 0.693465i \(0.243917\pi\)
\(104\) 0 0
\(105\) 0.221077 + 0.266297i 0.0215749 + 0.0259879i
\(106\) 0 0
\(107\) −3.67777 + 6.37008i −0.355543 + 0.615819i −0.987211 0.159420i \(-0.949037\pi\)
0.631667 + 0.775239i \(0.282371\pi\)
\(108\) 0 0
\(109\) −2.19435 3.80073i −0.210181 0.364044i 0.741590 0.670853i \(-0.234072\pi\)
−0.951771 + 0.306809i \(0.900739\pi\)
\(110\) 0 0
\(111\) −1.83077 −0.173769
\(112\) 0 0
\(113\) 6.60321 0.621178 0.310589 0.950544i \(-0.399474\pi\)
0.310589 + 0.950544i \(0.399474\pi\)
\(114\) 0 0
\(115\) −0.223391 0.386924i −0.0208313 0.0360809i
\(116\) 0 0
\(117\) −1.77237 + 3.06983i −0.163856 + 0.283806i
\(118\) 0 0
\(119\) 1.79817 4.86087i 0.164838 0.445595i
\(120\) 0 0
\(121\) −7.96484 + 13.7955i −0.724076 + 1.25414i
\(122\) 0 0
\(123\) −0.436576 0.756172i −0.0393647 0.0681817i
\(124\) 0 0
\(125\) 2.96949 0.265600
\(126\) 0 0
\(127\) −2.94961 −0.261736 −0.130868 0.991400i \(-0.541776\pi\)
−0.130868 + 0.991400i \(0.541776\pi\)
\(128\) 0 0
\(129\) 1.20442 + 2.08611i 0.106043 + 0.183672i
\(130\) 0 0
\(131\) 6.49451 11.2488i 0.567428 0.982815i −0.429391 0.903119i \(-0.641272\pi\)
0.996819 0.0796960i \(-0.0253949\pi\)
\(132\) 0 0
\(133\) −2.60793 + 0.445742i −0.226136 + 0.0386507i
\(134\) 0 0
\(135\) 0.379980 0.658145i 0.0327035 0.0566441i
\(136\) 0 0
\(137\) −6.81620 11.8060i −0.582347 1.00866i −0.995200 0.0978576i \(-0.968801\pi\)
0.412853 0.910798i \(-0.364532\pi\)
\(138\) 0 0
\(139\) 20.6698 1.75319 0.876596 0.481226i \(-0.159809\pi\)
0.876596 + 0.481226i \(0.159809\pi\)
\(140\) 0 0
\(141\) 3.72878 0.314020
\(142\) 0 0
\(143\) −3.27383 5.67044i −0.273771 0.474186i
\(144\) 0 0
\(145\) −0.0794602 + 0.137629i −0.00659881 + 0.0114295i
\(146\) 0 0
\(147\) −2.88255 + 1.01501i −0.237749 + 0.0837165i
\(148\) 0 0
\(149\) 3.33713 5.78008i 0.273388 0.473523i −0.696339 0.717713i \(-0.745189\pi\)
0.969727 + 0.244191i \(0.0785223\pi\)
\(150\) 0 0
\(151\) −7.83236 13.5660i −0.637388 1.10399i −0.986004 0.166723i \(-0.946681\pi\)
0.348616 0.937266i \(-0.386652\pi\)
\(152\) 0 0
\(153\) −5.50338 −0.444922
\(154\) 0 0
\(155\) −0.583812 −0.0468929
\(156\) 0 0
\(157\) −2.97962 5.16085i −0.237799 0.411880i 0.722283 0.691597i \(-0.243093\pi\)
−0.960082 + 0.279717i \(0.909759\pi\)
\(158\) 0 0
\(159\) −2.56612 + 4.44466i −0.203507 + 0.352484i
\(160\) 0 0
\(161\) 3.88859 0.664629i 0.306464 0.0523801i
\(162\) 0 0
\(163\) −8.73136 + 15.1232i −0.683893 + 1.18454i 0.289890 + 0.957060i \(0.406381\pi\)
−0.973783 + 0.227478i \(0.926952\pi\)
\(164\) 0 0
\(165\) 0.339426 + 0.587903i 0.0264243 + 0.0457682i
\(166\) 0 0
\(167\) 1.72621 0.133578 0.0667892 0.997767i \(-0.478724\pi\)
0.0667892 + 0.997767i \(0.478724\pi\)
\(168\) 0 0
\(169\) −11.4080 −0.877539
\(170\) 0 0
\(171\) 1.40470 + 2.43301i 0.107420 + 0.186057i
\(172\) 0 0
\(173\) 0.439572 0.761360i 0.0334200 0.0578852i −0.848832 0.528663i \(-0.822693\pi\)
0.882252 + 0.470778i \(0.156027\pi\)
\(174\) 0 0
\(175\) −4.50730 + 12.1842i −0.340720 + 0.921042i
\(176\) 0 0
\(177\) −2.79740 + 4.84524i −0.210266 + 0.364191i
\(178\) 0 0
\(179\) −3.67088 6.35815i −0.274374 0.475231i 0.695603 0.718427i \(-0.255137\pi\)
−0.969977 + 0.243196i \(0.921804\pi\)
\(180\) 0 0
\(181\) −18.2504 −1.35654 −0.678270 0.734813i \(-0.737270\pi\)
−0.678270 + 0.734813i \(0.737270\pi\)
\(182\) 0 0
\(183\) 2.59143 0.191564
\(184\) 0 0
\(185\) 0.628264 + 1.08819i 0.0461909 + 0.0800050i
\(186\) 0 0
\(187\) 5.08278 8.80363i 0.371690 0.643785i
\(188\) 0 0
\(189\) 4.28623 + 5.16295i 0.311777 + 0.375549i
\(190\) 0 0
\(191\) 3.68604 6.38440i 0.266712 0.461959i −0.701299 0.712868i \(-0.747396\pi\)
0.968011 + 0.250909i \(0.0807293\pi\)
\(192\) 0 0
\(193\) −0.731428 1.26687i −0.0526493 0.0911913i 0.838500 0.544902i \(-0.183433\pi\)
−0.891149 + 0.453711i \(0.850100\pi\)
\(194\) 0 0
\(195\) −0.165055 −0.0118199
\(196\) 0 0
\(197\) 2.41230 0.171870 0.0859348 0.996301i \(-0.472612\pi\)
0.0859348 + 0.996301i \(0.472612\pi\)
\(198\) 0 0
\(199\) −7.97857 13.8193i −0.565586 0.979623i −0.996995 0.0774670i \(-0.975317\pi\)
0.431409 0.902156i \(-0.358017\pi\)
\(200\) 0 0
\(201\) 1.20227 2.08239i 0.0848016 0.146881i
\(202\) 0 0
\(203\) −0.896323 1.07966i −0.0629096 0.0757773i
\(204\) 0 0
\(205\) −0.299640 + 0.518991i −0.0209277 + 0.0362479i
\(206\) 0 0
\(207\) −2.09450 3.62778i −0.145578 0.252148i
\(208\) 0 0
\(209\) −5.18938 −0.358957
\(210\) 0 0
\(211\) 13.2835 0.914474 0.457237 0.889345i \(-0.348839\pi\)
0.457237 + 0.889345i \(0.348839\pi\)
\(212\) 0 0
\(213\) 0.497732 + 0.862097i 0.0341040 + 0.0590699i
\(214\) 0 0
\(215\) 0.826638 1.43178i 0.0563763 0.0976465i
\(216\) 0 0
\(217\) 1.78850 4.83472i 0.121411 0.328202i
\(218\) 0 0
\(219\) −1.02429 + 1.77413i −0.0692154 + 0.119885i
\(220\) 0 0
\(221\) 1.23582 + 2.14051i 0.0831304 + 0.143986i
\(222\) 0 0
\(223\) −28.1602 −1.88574 −0.942872 0.333154i \(-0.891887\pi\)
−0.942872 + 0.333154i \(0.891887\pi\)
\(224\) 0 0
\(225\) 13.7948 0.919651
\(226\) 0 0
\(227\) −9.03880 15.6557i −0.599926 1.03910i −0.992831 0.119523i \(-0.961863\pi\)
0.392905 0.919579i \(-0.371470\pi\)
\(228\) 0 0
\(229\) −3.60996 + 6.25264i −0.238553 + 0.413186i −0.960299 0.278972i \(-0.910006\pi\)
0.721746 + 0.692158i \(0.243340\pi\)
\(230\) 0 0
\(231\) −5.90843 + 1.00985i −0.388746 + 0.0664435i
\(232\) 0 0
\(233\) 2.38604 4.13274i 0.156314 0.270744i −0.777222 0.629226i \(-0.783372\pi\)
0.933537 + 0.358481i \(0.116705\pi\)
\(234\) 0 0
\(235\) −1.27960 2.21634i −0.0834722 0.144578i
\(236\) 0 0
\(237\) −2.48616 −0.161494
\(238\) 0 0
\(239\) 3.62602 0.234548 0.117274 0.993100i \(-0.462584\pi\)
0.117274 + 0.993100i \(0.462584\pi\)
\(240\) 0 0
\(241\) −8.66741 15.0124i −0.558317 0.967033i −0.997637 0.0687027i \(-0.978114\pi\)
0.439320 0.898331i \(-0.355219\pi\)
\(242\) 0 0
\(243\) 5.40244 9.35731i 0.346567 0.600271i
\(244\) 0 0
\(245\) 1.59251 + 1.36503i 0.101742 + 0.0872087i
\(246\) 0 0
\(247\) 0.630871 1.09270i 0.0401414 0.0695269i
\(248\) 0 0
\(249\) 0.319411 + 0.553236i 0.0202418 + 0.0350599i
\(250\) 0 0
\(251\) 9.71280 0.613067 0.306533 0.951860i \(-0.400831\pi\)
0.306533 + 0.951860i \(0.400831\pi\)
\(252\) 0 0
\(253\) 7.73770 0.486465
\(254\) 0 0
\(255\) −0.128128 0.221925i −0.00802370 0.0138975i
\(256\) 0 0
\(257\) 3.59148 6.22062i 0.224030 0.388032i −0.731998 0.681307i \(-0.761412\pi\)
0.956028 + 0.293275i \(0.0947452\pi\)
\(258\) 0 0
\(259\) −10.9363 + 1.86920i −0.679547 + 0.116147i
\(260\) 0 0
\(261\) −0.745014 + 1.29040i −0.0461152 + 0.0798739i
\(262\) 0 0
\(263\) −1.37024 2.37333i −0.0844928 0.146346i 0.820682 0.571385i \(-0.193594\pi\)
−0.905175 + 0.425039i \(0.860260\pi\)
\(264\) 0 0
\(265\) 3.52247 0.216383
\(266\) 0 0
\(267\) 1.68104 0.102878
\(268\) 0 0
\(269\) −10.2040 17.6738i −0.622148 1.07759i −0.989085 0.147346i \(-0.952927\pi\)
0.366937 0.930246i \(-0.380406\pi\)
\(270\) 0 0
\(271\) 7.35452 12.7384i 0.446755 0.773803i −0.551417 0.834230i \(-0.685913\pi\)
0.998173 + 0.0604265i \(0.0192461\pi\)
\(272\) 0 0
\(273\) 0.505646 1.36687i 0.0306031 0.0827270i
\(274\) 0 0
\(275\) −12.7405 + 22.0672i −0.768281 + 1.33070i
\(276\) 0 0
\(277\) −10.0509 17.4087i −0.603901 1.04599i −0.992224 0.124463i \(-0.960279\pi\)
0.388324 0.921523i \(-0.373054\pi\)
\(278\) 0 0
\(279\) −5.47378 −0.327707
\(280\) 0 0
\(281\) 15.1058 0.901136 0.450568 0.892742i \(-0.351222\pi\)
0.450568 + 0.892742i \(0.351222\pi\)
\(282\) 0 0
\(283\) 2.52706 + 4.37700i 0.150218 + 0.260186i 0.931308 0.364234i \(-0.118669\pi\)
−0.781089 + 0.624419i \(0.785336\pi\)
\(284\) 0 0
\(285\) −0.0654078 + 0.113290i −0.00387442 + 0.00671070i
\(286\) 0 0
\(287\) −3.37998 4.07133i −0.199514 0.240323i
\(288\) 0 0
\(289\) 6.58133 11.3992i 0.387137 0.670541i
\(290\) 0 0
\(291\) −2.11696 3.66668i −0.124098 0.214944i
\(292\) 0 0
\(293\) −13.5367 −0.790823 −0.395411 0.918504i \(-0.629398\pi\)
−0.395411 + 0.918504i \(0.629398\pi\)
\(294\) 0 0
\(295\) 3.83994 0.223570
\(296\) 0 0
\(297\) 6.58077 + 11.3982i 0.381855 + 0.661393i
\(298\) 0 0
\(299\) −0.940668 + 1.62929i −0.0544003 + 0.0942240i
\(300\) 0 0
\(301\) 9.32460 + 11.2319i 0.537461 + 0.647395i
\(302\) 0 0
\(303\) 3.57571 6.19330i 0.205419 0.355796i
\(304\) 0 0
\(305\) −0.889301 1.54031i −0.0509212 0.0881982i
\(306\) 0 0
\(307\) 0.853123 0.0486903 0.0243452 0.999704i \(-0.492250\pi\)
0.0243452 + 0.999704i \(0.492250\pi\)
\(308\) 0 0
\(309\) −2.12954 −0.121145
\(310\) 0 0
\(311\) −8.69648 15.0627i −0.493132 0.854130i 0.506837 0.862042i \(-0.330815\pi\)
−0.999969 + 0.00791223i \(0.997481\pi\)
\(312\) 0 0
\(313\) −12.0278 + 20.8328i −0.679853 + 1.17754i 0.295172 + 0.955444i \(0.404623\pi\)
−0.975025 + 0.222096i \(0.928710\pi\)
\(314\) 0 0
\(315\) 0.772732 2.08887i 0.0435385 0.117694i
\(316\) 0 0
\(317\) −3.72778 + 6.45671i −0.209373 + 0.362645i −0.951517 0.307596i \(-0.900476\pi\)
0.742144 + 0.670240i \(0.233809\pi\)
\(318\) 0 0
\(319\) −1.37615 2.38356i −0.0770497 0.133454i
\(320\) 0 0
\(321\) −3.21125 −0.179235
\(322\) 0 0
\(323\) 1.95892 0.108997
\(324\) 0 0
\(325\) −3.09771 5.36540i −0.171830 0.297619i
\(326\) 0 0
\(327\) 0.958002 1.65931i 0.0529776 0.0917600i
\(328\) 0 0
\(329\) 22.2742 3.80706i 1.22802 0.209890i
\(330\) 0 0
\(331\) −16.9634 + 29.3815i −0.932393 + 1.61495i −0.153176 + 0.988199i \(0.548950\pi\)
−0.779217 + 0.626754i \(0.784383\pi\)
\(332\) 0 0
\(333\) 5.89056 + 10.2028i 0.322801 + 0.559108i
\(334\) 0 0
\(335\) −1.65033 −0.0901672
\(336\) 0 0
\(337\) −16.1792 −0.881336 −0.440668 0.897670i \(-0.645258\pi\)
−0.440668 + 0.897670i \(0.645258\pi\)
\(338\) 0 0
\(339\) 1.44140 + 2.49658i 0.0782862 + 0.135596i
\(340\) 0 0
\(341\) 5.05544 8.75628i 0.273768 0.474179i
\(342\) 0 0
\(343\) −16.1829 + 9.00632i −0.873794 + 0.486296i
\(344\) 0 0
\(345\) 0.0975271 0.168922i 0.00525068 0.00909445i
\(346\) 0 0
\(347\) 14.2507 + 24.6829i 0.765016 + 1.32505i 0.940238 + 0.340518i \(0.110602\pi\)
−0.175222 + 0.984529i \(0.556064\pi\)
\(348\) 0 0
\(349\) −24.1291 −1.29160 −0.645801 0.763506i \(-0.723476\pi\)
−0.645801 + 0.763506i \(0.723476\pi\)
\(350\) 0 0
\(351\) −3.20009 −0.170808
\(352\) 0 0
\(353\) −12.2268 21.1775i −0.650768 1.12716i −0.982937 0.183943i \(-0.941114\pi\)
0.332169 0.943220i \(-0.392220\pi\)
\(354\) 0 0
\(355\) 0.341613 0.591692i 0.0181310 0.0314037i
\(356\) 0 0
\(357\) 2.23035 0.381205i 0.118042 0.0201755i
\(358\) 0 0
\(359\) −14.8696 + 25.7549i −0.784789 + 1.35929i 0.144336 + 0.989529i \(0.453895\pi\)
−0.929125 + 0.369765i \(0.879438\pi\)
\(360\) 0 0
\(361\) −0.500000 0.866025i −0.0263158 0.0455803i
\(362\) 0 0
\(363\) −6.95452 −0.365018
\(364\) 0 0
\(365\) 1.40603 0.0735949
\(366\) 0 0
\(367\) −12.1623 21.0657i −0.634865 1.09962i −0.986544 0.163498i \(-0.947722\pi\)
0.351679 0.936121i \(-0.385611\pi\)
\(368\) 0 0
\(369\) −2.80940 + 4.86603i −0.146252 + 0.253315i
\(370\) 0 0
\(371\) −10.7910 + 29.1706i −0.560243 + 1.51446i
\(372\) 0 0
\(373\) 12.5850 21.7979i 0.651628 1.12865i −0.331100 0.943596i \(-0.607420\pi\)
0.982728 0.185057i \(-0.0592471\pi\)
\(374\) 0 0
\(375\) 0.648205 + 1.12272i 0.0334732 + 0.0579772i
\(376\) 0 0
\(377\) 0.669192 0.0344652
\(378\) 0 0
\(379\) 5.07880 0.260880 0.130440 0.991456i \(-0.458361\pi\)
0.130440 + 0.991456i \(0.458361\pi\)
\(380\) 0 0
\(381\) −0.643865 1.11521i −0.0329862 0.0571338i
\(382\) 0 0
\(383\) −2.07557 + 3.59500i −0.106057 + 0.183696i −0.914169 0.405332i \(-0.867156\pi\)
0.808113 + 0.589028i \(0.200489\pi\)
\(384\) 0 0
\(385\) 2.62784 + 3.16535i 0.133927 + 0.161321i
\(386\) 0 0
\(387\) 7.75050 13.4243i 0.393980 0.682394i
\(388\) 0 0
\(389\) 3.91951 + 6.78879i 0.198727 + 0.344205i 0.948116 0.317925i \(-0.102986\pi\)
−0.749389 + 0.662130i \(0.769653\pi\)
\(390\) 0 0
\(391\) −2.92087 −0.147715
\(392\) 0 0
\(393\) 5.67070 0.286049
\(394\) 0 0
\(395\) 0.853177 + 1.47775i 0.0429280 + 0.0743534i
\(396\) 0 0
\(397\) −1.53879 + 2.66526i −0.0772295 + 0.133765i −0.902054 0.431624i \(-0.857941\pi\)
0.824824 + 0.565389i \(0.191274\pi\)
\(398\) 0 0
\(399\) −0.737809 0.888723i −0.0369367 0.0444918i
\(400\) 0 0
\(401\) 18.7483 32.4730i 0.936246 1.62163i 0.163850 0.986485i \(-0.447609\pi\)
0.772396 0.635141i \(-0.219058\pi\)
\(402\) 0 0
\(403\) 1.22918 + 2.12900i 0.0612296 + 0.106053i
\(404\) 0 0
\(405\) −2.19364 −0.109003
\(406\) 0 0
\(407\) −21.7615 −1.07868
\(408\) 0 0
\(409\) 17.3776 + 30.0988i 0.859265 + 1.48829i 0.872631 + 0.488380i \(0.162412\pi\)
−0.0133656 + 0.999911i \(0.504255\pi\)
\(410\) 0 0
\(411\) 2.97579 5.15422i 0.146785 0.254239i
\(412\) 0 0
\(413\) −11.7636 + 31.7997i −0.578850 + 1.56476i
\(414\) 0 0
\(415\) 0.219225 0.379708i 0.0107613 0.0186391i
\(416\) 0 0
\(417\) 4.51198 + 7.81498i 0.220953 + 0.382701i
\(418\) 0 0
\(419\) 21.5451 1.05255 0.526274 0.850315i \(-0.323589\pi\)
0.526274 + 0.850315i \(0.323589\pi\)
\(420\) 0 0
\(421\) 2.66307 0.129790 0.0648951 0.997892i \(-0.479329\pi\)
0.0648951 + 0.997892i \(0.479329\pi\)
\(422\) 0 0
\(423\) −11.9975 20.7803i −0.583338 1.01037i
\(424\) 0 0
\(425\) 4.80935 8.33004i 0.233288 0.404066i
\(426\) 0 0
\(427\) 15.4802 2.64583i 0.749138 0.128041i
\(428\) 0 0
\(429\) 1.42928 2.47558i 0.0690061 0.119522i
\(430\) 0 0
\(431\) 12.3588 + 21.4060i 0.595302 + 1.03109i 0.993504 + 0.113795i \(0.0363008\pi\)
−0.398202 + 0.917298i \(0.630366\pi\)
\(432\) 0 0
\(433\) −7.26963 −0.349356 −0.174678 0.984626i \(-0.555888\pi\)
−0.174678 + 0.984626i \(0.555888\pi\)
\(434\) 0 0
\(435\) −0.0693809 −0.00332656
\(436\) 0 0
\(437\) 0.745532 + 1.29130i 0.0356636 + 0.0617712i
\(438\) 0 0
\(439\) 17.5101 30.3283i 0.835710 1.44749i −0.0577412 0.998332i \(-0.518390\pi\)
0.893451 0.449160i \(-0.148277\pi\)
\(440\) 0 0
\(441\) 14.9313 + 12.7985i 0.711014 + 0.609450i
\(442\) 0 0
\(443\) 3.05984 5.29981i 0.145378 0.251801i −0.784136 0.620589i \(-0.786894\pi\)
0.929514 + 0.368787i \(0.120227\pi\)
\(444\) 0 0
\(445\) −0.576881 0.999188i −0.0273468 0.0473660i
\(446\) 0 0
\(447\) 2.91382 0.137819
\(448\) 0 0
\(449\) 34.7695 1.64087 0.820436 0.571738i \(-0.193731\pi\)
0.820436 + 0.571738i \(0.193731\pi\)
\(450\) 0 0
\(451\) −5.18938 8.98827i −0.244358 0.423241i
\(452\) 0 0
\(453\) 3.41942 5.92261i 0.160658 0.278268i
\(454\) 0 0
\(455\) −0.985976 + 0.168521i −0.0462233 + 0.00790037i
\(456\) 0 0
\(457\) 11.2863 19.5485i 0.527953 0.914442i −0.471516 0.881858i \(-0.656293\pi\)
0.999469 0.0325841i \(-0.0103737\pi\)
\(458\) 0 0
\(459\) −2.48415 4.30267i −0.115950 0.200831i
\(460\) 0 0
\(461\) 25.1756 1.17254 0.586272 0.810115i \(-0.300595\pi\)
0.586272 + 0.810115i \(0.300595\pi\)
\(462\) 0 0
\(463\) −7.74829 −0.360093 −0.180047 0.983658i \(-0.557625\pi\)
−0.180047 + 0.983658i \(0.557625\pi\)
\(464\) 0 0
\(465\) −0.127439 0.220731i −0.00590985 0.0102362i
\(466\) 0 0
\(467\) −15.5390 + 26.9144i −0.719060 + 1.24545i 0.242312 + 0.970198i \(0.422094\pi\)
−0.961372 + 0.275251i \(0.911239\pi\)
\(468\) 0 0
\(469\) 5.05577 13.6669i 0.233454 0.631078i
\(470\) 0 0
\(471\) 1.30083 2.25310i 0.0599390 0.103817i
\(472\) 0 0
\(473\) 14.3163 + 24.7966i 0.658266 + 1.14015i
\(474\) 0 0
\(475\) −4.91022 −0.225296
\(476\) 0 0
\(477\) 33.0264 1.51217
\(478\) 0 0
\(479\) 13.6603 + 23.6603i 0.624154 + 1.08107i 0.988704 + 0.149882i \(0.0478895\pi\)
−0.364550 + 0.931184i \(0.618777\pi\)
\(480\) 0 0
\(481\) 2.64554 4.58220i 0.120626 0.208930i
\(482\) 0 0
\(483\) 1.10012 + 1.32514i 0.0500572 + 0.0602961i
\(484\) 0 0
\(485\) −1.45295 + 2.51659i −0.0659752 + 0.114272i
\(486\) 0 0
\(487\) −12.5451 21.7288i −0.568475 0.984627i −0.996717 0.0809632i \(-0.974200\pi\)
0.428242 0.903664i \(-0.359133\pi\)
\(488\) 0 0
\(489\) −7.62381 −0.344761
\(490\) 0 0
\(491\) 29.4362 1.32844 0.664219 0.747538i \(-0.268764\pi\)
0.664219 + 0.747538i \(0.268764\pi\)
\(492\) 0 0
\(493\) 0.519477 + 0.899760i 0.0233961 + 0.0405232i
\(494\) 0 0
\(495\) 2.18423 3.78320i 0.0981739 0.170042i
\(496\) 0 0
\(497\) 3.85345 + 4.64164i 0.172851 + 0.208206i
\(498\) 0 0
\(499\) −21.1239 + 36.5877i −0.945637 + 1.63789i −0.191166 + 0.981558i \(0.561227\pi\)
−0.754471 + 0.656333i \(0.772107\pi\)
\(500\) 0 0
\(501\) 0.376812 + 0.652657i 0.0168347 + 0.0291586i
\(502\) 0 0
\(503\) −9.25390 −0.412611 −0.206305 0.978488i \(-0.566144\pi\)
−0.206305 + 0.978488i \(0.566144\pi\)
\(504\) 0 0
\(505\) −4.90830 −0.218416
\(506\) 0 0
\(507\) −2.49023 4.31321i −0.110595 0.191556i
\(508\) 0 0
\(509\) 11.9025 20.6157i 0.527568 0.913774i −0.471916 0.881643i \(-0.656438\pi\)
0.999484 0.0321303i \(-0.0102292\pi\)
\(510\) 0 0
\(511\) −4.30735 + 11.6437i −0.190546 + 0.515089i
\(512\) 0 0
\(513\) −1.26812 + 2.19645i −0.0559890 + 0.0969758i
\(514\) 0 0
\(515\) 0.730793 + 1.26577i 0.0322026 + 0.0557766i
\(516\) 0 0
\(517\) 44.3223 1.94929
\(518\) 0 0
\(519\) 0.383813 0.0168475
\(520\) 0 0
\(521\) −16.0422 27.7860i −0.702823 1.21733i −0.967471 0.252981i \(-0.918589\pi\)
0.264648 0.964345i \(-0.414744\pi\)
\(522\) 0 0
\(523\) −8.77620 + 15.2008i −0.383756 + 0.664685i −0.991596 0.129374i \(-0.958703\pi\)
0.607839 + 0.794060i \(0.292036\pi\)
\(524\) 0 0
\(525\) −5.59058 + 0.955529i −0.243993 + 0.0417027i
\(526\) 0 0
\(527\) −1.90836 + 3.30537i −0.0831293 + 0.143984i
\(528\) 0 0
\(529\) 10.3884 + 17.9932i 0.451668 + 0.782312i
\(530\) 0 0
\(531\) 36.0030 1.56240
\(532\) 0 0
\(533\) 2.52348 0.109304
\(534\) 0 0
\(535\) 1.10201 + 1.90873i 0.0476439 + 0.0825216i
\(536\) 0 0
\(537\) 1.60262 2.77582i 0.0691581 0.119785i
\(538\) 0 0
\(539\) −34.2636 + 12.0649i −1.47584 + 0.519674i
\(540\) 0 0
\(541\) −16.6885 + 28.9053i −0.717495 + 1.24274i 0.244495 + 0.969651i \(0.421378\pi\)
−0.961989 + 0.273087i \(0.911955\pi\)
\(542\) 0 0
\(543\) −3.98384 6.90021i −0.170963 0.296116i
\(544\) 0 0
\(545\) −1.31503 −0.0563297
\(546\) 0 0
\(547\) 39.4470 1.68663 0.843316 0.537418i \(-0.180600\pi\)
0.843316 + 0.537418i \(0.180600\pi\)
\(548\) 0 0
\(549\) −8.33803 14.4419i −0.355858 0.616365i
\(550\) 0 0
\(551\) 0.265186 0.459316i 0.0112973 0.0195675i
\(552\) 0 0
\(553\) −14.8514 + 2.53836i −0.631544 + 0.107942i
\(554\) 0 0
\(555\) −0.274285 + 0.475076i −0.0116428 + 0.0201659i
\(556\) 0 0
\(557\) 17.7422 + 30.7304i 0.751760 + 1.30209i 0.946969 + 0.321325i \(0.104128\pi\)
−0.195209 + 0.980762i \(0.562538\pi\)
\(558\) 0 0
\(559\) −6.96172 −0.294449
\(560\) 0 0
\(561\) 4.43804 0.187374
\(562\) 0 0
\(563\) 22.3555 + 38.7208i 0.942170 + 1.63189i 0.761320 + 0.648376i \(0.224551\pi\)
0.180850 + 0.983511i \(0.442115\pi\)
\(564\) 0 0
\(565\) 0.989292 1.71350i 0.0416198 0.0720876i
\(566\) 0 0
\(567\) 6.72020 18.1662i 0.282222 0.762910i
\(568\) 0 0
\(569\) 4.51888 7.82692i 0.189441 0.328122i −0.755623 0.655007i \(-0.772666\pi\)
0.945064 + 0.326885i \(0.105999\pi\)
\(570\) 0 0
\(571\) −8.48214 14.6915i −0.354966 0.614820i 0.632146 0.774849i \(-0.282174\pi\)
−0.987112 + 0.160030i \(0.948841\pi\)
\(572\) 0 0
\(573\) 3.21847 0.134454
\(574\) 0 0
\(575\) 7.32144 0.305325
\(576\) 0 0
\(577\) 8.83382 + 15.3006i 0.367757 + 0.636973i 0.989214 0.146474i \(-0.0467926\pi\)
−0.621458 + 0.783448i \(0.713459\pi\)
\(578\) 0 0
\(579\) 0.319324 0.553086i 0.0132707 0.0229855i
\(580\) 0 0
\(581\) 2.47289 + 2.97870i 0.102593 + 0.123577i
\(582\) 0 0
\(583\) −30.5023 + 52.8316i −1.26328 + 2.18806i
\(584\) 0 0
\(585\) 0.531072 + 0.919844i 0.0219571 + 0.0380309i
\(586\) 0 0
\(587\) −15.6759 −0.647014 −0.323507 0.946226i \(-0.604862\pi\)
−0.323507 + 0.946226i \(0.604862\pi\)
\(588\) 0 0
\(589\) 1.94838 0.0802816
\(590\) 0 0
\(591\) 0.526577 + 0.912059i 0.0216605 + 0.0375171i
\(592\) 0 0
\(593\) 8.29460 14.3667i 0.340619 0.589969i −0.643929 0.765085i \(-0.722697\pi\)
0.984548 + 0.175116i \(0.0560302\pi\)
\(594\) 0 0
\(595\) −0.991971 1.19487i −0.0406669 0.0489850i
\(596\) 0 0
\(597\) 3.48325 6.03317i 0.142560 0.246921i
\(598\) 0 0
\(599\) −24.3146 42.1142i −0.993469 1.72074i −0.595552 0.803317i \(-0.703067\pi\)
−0.397916 0.917422i \(-0.630267\pi\)
\(600\) 0 0
\(601\) −23.2984 −0.950362 −0.475181 0.879888i \(-0.657617\pi\)
−0.475181 + 0.879888i \(0.657617\pi\)
\(602\) 0 0
\(603\) −15.4734 −0.630125
\(604\) 0 0
\(605\) 2.38658 + 4.13368i 0.0970283 + 0.168058i
\(606\) 0 0
\(607\) −14.5411 + 25.1860i −0.590206 + 1.02227i 0.403998 + 0.914760i \(0.367620\pi\)
−0.994204 + 0.107507i \(0.965713\pi\)
\(608\) 0 0
\(609\) 0.212548 0.574564i 0.00861287 0.0232825i
\(610\) 0 0
\(611\) −5.38824 + 9.33271i −0.217985 + 0.377561i
\(612\) 0 0
\(613\) 5.52670 + 9.57253i 0.223221 + 0.386631i 0.955784 0.294068i \(-0.0950094\pi\)
−0.732563 + 0.680699i \(0.761676\pi\)
\(614\) 0 0
\(615\) −0.261631 −0.0105500
\(616\) 0 0
\(617\) −37.7605 −1.52018 −0.760090 0.649817i \(-0.774845\pi\)
−0.760090 + 0.649817i \(0.774845\pi\)
\(618\) 0 0
\(619\) −0.314476 0.544689i −0.0126399 0.0218929i 0.859636 0.510907i \(-0.170690\pi\)
−0.872276 + 0.489014i \(0.837357\pi\)
\(620\) 0 0
\(621\) 1.89085 3.27505i 0.0758773 0.131423i
\(622\) 0 0
\(623\) 10.0418 1.71633i 0.402318 0.0687632i
\(624\) 0 0
\(625\) −11.8307 + 20.4913i −0.473226 + 0.819652i
\(626\) 0 0
\(627\) −1.13278 1.96203i −0.0452389 0.0783560i
\(628\) 0 0
\(629\) 8.21464 0.327539
\(630\) 0 0
\(631\) 17.1786 0.683870 0.341935 0.939724i \(-0.388918\pi\)
0.341935 + 0.939724i \(0.388918\pi\)
\(632\) 0 0
\(633\) 2.89963 + 5.02231i 0.115250 + 0.199619i
\(634\) 0 0
\(635\) −0.441911 + 0.765412i −0.0175367 + 0.0303744i
\(636\) 0 0
\(637\) 1.62496 8.68143i 0.0643831 0.343971i
\(638\) 0 0
\(639\) 3.20294 5.54766i 0.126706 0.219462i
\(640\) 0 0
\(641\) −4.06894 7.04762i −0.160714 0.278364i 0.774411 0.632683i \(-0.218046\pi\)
−0.935125 + 0.354318i \(0.884713\pi\)
\(642\) 0 0
\(643\) 9.21363 0.363350 0.181675 0.983359i \(-0.441848\pi\)
0.181675 + 0.983359i \(0.441848\pi\)
\(644\) 0 0
\(645\) 0.721781 0.0284201
\(646\) 0 0
\(647\) 9.65112 + 16.7162i 0.379425 + 0.657183i 0.990979 0.134020i \(-0.0427885\pi\)
−0.611554 + 0.791203i \(0.709455\pi\)
\(648\) 0 0
\(649\) −33.2515 + 57.5932i −1.30523 + 2.26073i
\(650\) 0 0
\(651\) 2.21835 0.379155i 0.0869440 0.0148603i
\(652\) 0 0
\(653\) −2.37203 + 4.10848i −0.0928248 + 0.160777i −0.908699 0.417453i \(-0.862923\pi\)
0.815874 + 0.578230i \(0.196256\pi\)
\(654\) 0 0
\(655\) −1.94601 3.37060i −0.0760371 0.131700i
\(656\) 0 0
\(657\) 13.1828 0.514311
\(658\) 0 0
\(659\) 15.2932 0.595738 0.297869 0.954607i \(-0.403724\pi\)
0.297869 + 0.954607i \(0.403724\pi\)
\(660\) 0 0
\(661\) −1.95467 3.38560i −0.0760280 0.131684i 0.825505 0.564395i \(-0.190891\pi\)
−0.901533 + 0.432711i \(0.857557\pi\)
\(662\) 0 0
\(663\) −0.539531 + 0.934495i −0.0209536 + 0.0362928i
\(664\) 0 0
\(665\) −0.275052 + 0.743528i −0.0106661 + 0.0288328i
\(666\) 0 0
\(667\) −0.395409 + 0.684869i −0.0153103 + 0.0265182i
\(668\) 0 0
\(669\) −6.14703 10.6470i −0.237658 0.411636i
\(670\) 0 0
\(671\) 30.8031 1.18914
\(672\) 0 0
\(673\) −1.12569 −0.0433923 −0.0216962 0.999765i \(-0.506907\pi\)
−0.0216962 + 0.999765i \(0.506907\pi\)
\(674\) 0 0
\(675\) 6.22676 + 10.7851i 0.239668 + 0.415117i
\(676\) 0 0
\(677\) 20.5143 35.5319i 0.788430 1.36560i −0.138499 0.990363i \(-0.544228\pi\)
0.926929 0.375238i \(-0.122439\pi\)
\(678\) 0 0
\(679\) −16.3895 19.7419i −0.628972 0.757624i
\(680\) 0 0
\(681\) 3.94612 6.83489i 0.151216 0.261913i
\(682\) 0 0
\(683\) 2.86946 + 4.97006i 0.109797 + 0.190174i 0.915688 0.401890i \(-0.131647\pi\)
−0.805891 + 0.592064i \(0.798313\pi\)
\(684\) 0 0
\(685\) −4.08481 −0.156073
\(686\) 0 0
\(687\) −3.15205 −0.120258
\(688\) 0 0
\(689\) −7.41631 12.8454i −0.282539 0.489372i
\(690\) 0 0
\(691\) −2.18435 + 3.78341i −0.0830968 + 0.143928i −0.904579 0.426307i \(-0.859814\pi\)
0.821482 + 0.570235i \(0.193148\pi\)
\(692\) 0 0
\(693\) 24.6385 + 29.6781i 0.935938 + 1.12738i
\(694\) 0 0
\(695\) 3.09675 5.36373i 0.117466 0.203458i
\(696\) 0 0
\(697\) 1.95892 + 3.39294i 0.0741992 + 0.128517i
\(698\) 0 0
\(699\) 2.08337 0.0788004
\(700\) 0 0
\(701\) 36.2974 1.37093 0.685466 0.728105i \(-0.259598\pi\)
0.685466 + 0.728105i \(0.259598\pi\)
\(702\) 0 0
\(703\) −2.09673 3.63165i −0.0790798 0.136970i
\(704\) 0 0
\(705\) 0.558645 0.967601i 0.0210398 0.0364420i
\(706\) 0 0
\(707\) 15.0365 40.6471i 0.565507 1.52869i
\(708\) 0 0
\(709\) −4.94144 + 8.55882i −0.185580 + 0.321433i −0.943772 0.330598i \(-0.892750\pi\)
0.758192 + 0.652031i \(0.226083\pi\)
\(710\) 0 0
\(711\) 7.99933 + 13.8552i 0.299998 + 0.519612i
\(712\) 0 0
\(713\) −2.90516 −0.108799
\(714\) 0 0
\(715\) −1.96194 −0.0733723
\(716\) 0 0
\(717\) 0.791518 + 1.37095i 0.0295598 + 0.0511990i
\(718\) 0 0
\(719\) 13.9771 24.2090i 0.521257 0.902844i −0.478437 0.878122i \(-0.658796\pi\)
0.999694 0.0247225i \(-0.00787022\pi\)
\(720\) 0 0
\(721\) −12.7210 + 2.17424i −0.473755 + 0.0809731i
\(722\) 0 0
\(723\) 3.78398 6.55405i 0.140728 0.243748i
\(724\) 0 0
\(725\) −1.30212 2.25534i −0.0483595 0.0837612i
\(726\) 0 0
\(727\) 32.8007 1.21651 0.608255 0.793742i \(-0.291870\pi\)
0.608255 + 0.793742i \(0.291870\pi\)
\(728\) 0 0
\(729\) −17.2457 −0.638728
\(730\) 0 0
\(731\) −5.40420 9.36036i −0.199882 0.346205i
\(732\) 0 0
\(733\) −12.0931 + 20.9458i −0.446668 + 0.773651i −0.998167 0.0605246i \(-0.980723\pi\)
0.551499 + 0.834175i \(0.314056\pi\)
\(734\) 0 0
\(735\) −0.168473 + 0.900078i −0.00621422 + 0.0331999i
\(736\) 0 0
\(737\) 14.2908 24.7524i 0.526409 0.911768i
\(738\) 0 0
\(739\) −13.2300 22.9150i −0.486673 0.842943i 0.513210 0.858263i \(-0.328456\pi\)
−0.999883 + 0.0153208i \(0.995123\pi\)
\(740\) 0 0
\(741\) 0.550846 0.0202358
\(742\) 0 0
\(743\) 33.3257 1.22260 0.611301 0.791398i \(-0.290646\pi\)
0.611301 + 0.791398i \(0.290646\pi\)
\(744\) 0 0
\(745\) −0.999937 1.73194i −0.0366348 0.0634534i
\(746\) 0 0
\(747\) 2.05543 3.56012i 0.0752044 0.130258i
\(748\) 0 0
\(749\) −19.1827 + 3.27867i −0.700922 + 0.119800i
\(750\) 0 0
\(751\) 2.32153 4.02100i 0.0847138 0.146729i −0.820555 0.571567i \(-0.806336\pi\)
0.905269 + 0.424838i \(0.139669\pi\)
\(752\) 0 0
\(753\) 2.12019 + 3.67228i 0.0772640 + 0.133825i
\(754\) 0 0
\(755\) −4.69377 −0.170824
\(756\) 0 0
\(757\) 45.0481 1.63730 0.818651 0.574291i \(-0.194722\pi\)
0.818651 + 0.574291i \(0.194722\pi\)
\(758\) 0 0
\(759\) 1.68905 + 2.92551i 0.0613085 + 0.106189i
\(760\) 0 0
\(761\) −7.50637 + 13.0014i −0.272106 + 0.471301i −0.969401 0.245483i \(-0.921053\pi\)
0.697295 + 0.716784i \(0.254387\pi\)
\(762\) 0 0
\(763\) 4.02858 10.8902i 0.145844 0.394250i
\(764\) 0 0
\(765\) −0.824515 + 1.42810i −0.0298104 + 0.0516332i
\(766\) 0 0
\(767\) −8.08473 14.0032i −0.291923 0.505625i
\(768\) 0 0
\(769\) 4.05311 0.146159 0.0730794 0.997326i \(-0.476717\pi\)
0.0730794 + 0.997326i \(0.476717\pi\)
\(770\) 0 0
\(771\) 3.13591 0.112937
\(772\) 0 0
\(773\) −6.19701 10.7335i −0.222891 0.386058i 0.732794 0.680451i \(-0.238216\pi\)
−0.955685 + 0.294392i \(0.904883\pi\)
\(774\) 0 0
\(775\) 4.78348 8.28524i 0.171828 0.297614i
\(776\) 0 0
\(777\) −3.09398 3.72683i −0.110996 0.133699i
\(778\) 0 0
\(779\) 1.00000 1.73205i 0.0358287 0.0620572i
\(780\) 0 0
\(781\) 5.91631 + 10.2474i 0.211702 + 0.366679i
\(782\) 0 0
\(783\) −1.34515 −0.0480719
\(784\) 0 0
\(785\) −1.78562 −0.0637316
\(786\) 0 0
\(787\) 10.7116 + 18.5530i 0.381826 + 0.661343i 0.991323 0.131446i \(-0.0419619\pi\)
−0.609497 + 0.792788i \(0.708629\pi\)
\(788\) 0 0
\(789\) 0.598215 1.03614i 0.0212970 0.0368875i
\(790\) 0 0
\(791\) 11.1594 + 13.4419i 0.396781 + 0.477940i
\(792\) 0 0
\(793\) −3.74473 + 6.48605i −0.132979 + 0.230327i
\(794\) 0 0
\(795\) 0.768912 + 1.33180i 0.0272705 + 0.0472339i
\(796\) 0 0
\(797\) −37.1622 −1.31635 −0.658175 0.752865i \(-0.728672\pi\)
−0.658175 + 0.752865i \(0.728672\pi\)
\(798\) 0 0
\(799\) −16.7310 −0.591901
\(800\) 0 0
\(801\) −5.40880 9.36832i −0.191111 0.331013i
\(802\) 0 0
\(803\) −12.1753 + 21.0883i −0.429658 + 0.744189i
\(804\) 0 0
\(805\) 0.410120 1.10865i 0.0144548 0.0390747i
\(806\) 0 0
\(807\) 4.45482 7.71597i 0.156817 0.271615i
\(808\) 0 0
\(809\) −1.04208 1.80494i −0.0366376 0.0634582i 0.847125 0.531393i \(-0.178331\pi\)
−0.883763 + 0.467935i \(0.844998\pi\)
\(810\) 0 0
\(811\) −11.2776 −0.396009 −0.198005 0.980201i \(-0.563446\pi\)
−0.198005 + 0.980201i \(0.563446\pi\)
\(812\) 0 0
\(813\) 6.42162 0.225216
\(814\) 0 0
\(815\) 2.61626 + 4.53150i 0.0916437 + 0.158731i
\(816\) 0 0
\(817\) −2.75877 + 4.77834i −0.0965173 + 0.167173i
\(818\) 0 0
\(819\) −9.24444 + 1.58004i −0.323027 + 0.0552110i
\(820\) 0 0
\(821\) 21.2873 36.8707i 0.742931 1.28679i −0.208224 0.978081i \(-0.566768\pi\)
0.951155 0.308714i \(-0.0998985\pi\)
\(822\) 0 0
\(823\) −10.8342 18.7654i −0.377657 0.654121i 0.613064 0.790033i \(-0.289937\pi\)
−0.990721 + 0.135913i \(0.956603\pi\)
\(824\) 0 0
\(825\) −11.1244 −0.387302
\(826\) 0 0
\(827\) −31.7162 −1.10288 −0.551440 0.834215i \(-0.685921\pi\)
−0.551440 + 0.834215i \(0.685921\pi\)
\(828\) 0 0
\(829\) −9.14498 15.8396i −0.317618 0.550131i 0.662372 0.749175i \(-0.269550\pi\)
−0.979991 + 0.199044i \(0.936216\pi\)
\(830\) 0 0
\(831\) 4.38799 7.60022i 0.152218 0.263649i
\(832\) 0 0
\(833\) 12.9340 4.55434i 0.448136 0.157798i
\(834\) 0 0
\(835\) 0.258621 0.447945i 0.00894995 0.0155018i
\(836\) 0 0
\(837\) −2.47079 4.27953i −0.0854028 0.147922i
\(838\) 0 0
\(839\) −29.8422 −1.03027 −0.515134 0.857109i \(-0.672258\pi\)
−0.515134 + 0.857109i \(0.672258\pi\)
\(840\) 0 0
\(841\) −28.7187 −0.990300
\(842\) 0 0
\(843\) 3.29741 + 5.71129i 0.113569 + 0.196707i
\(844\) 0 0
\(845\) −1.70915 + 2.96033i −0.0587964 + 0.101838i
\(846\) 0 0
\(847\) −41.5435 + 7.10052i −1.42745 + 0.243977i
\(848\) 0 0
\(849\) −1.10326 + 1.91089i −0.0378636 + 0.0655817i
\(850\) 0 0
\(851\) 3.12636 + 5.41502i 0.107170 + 0.185624i
\(852\) 0 0
\(853\) −17.2641 −0.591111 −0.295555 0.955326i \(-0.595505\pi\)
−0.295555 + 0.955326i \(0.595505\pi\)
\(854\) 0 0
\(855\) 0.841808 0.0287892
\(856\) 0 0
\(857\) 5.35965 + 9.28319i 0.183082 + 0.317108i 0.942929 0.332995i \(-0.108059\pi\)
−0.759846 + 0.650103i \(0.774726\pi\)
\(858\) 0 0
\(859\) 15.0515 26.0700i 0.513551 0.889496i −0.486326 0.873778i \(-0.661663\pi\)
0.999876 0.0157186i \(-0.00500360\pi\)
\(860\) 0 0
\(861\) 0.801504 2.16665i 0.0273152 0.0738391i
\(862\) 0 0
\(863\) −18.7628 + 32.4981i −0.638693 + 1.10625i 0.347027 + 0.937855i \(0.387191\pi\)
−0.985720 + 0.168393i \(0.946142\pi\)
\(864\) 0 0
\(865\) −0.131713 0.228134i −0.00447838 0.00775678i
\(866\) 0 0
\(867\) 5.74650 0.195161
\(868\) 0 0
\(869\) −29.5519 −1.00248
\(870\) 0 0
\(871\) 3.47466 + 6.01829i 0.117734 + 0.203922i
\(872\) 0 0
\(873\) −13.6228 + 23.5954i −0.461061 + 0.798582i
\(874\) 0 0
\(875\) 5.01842 + 6.04490i 0.169653 + 0.204355i
\(876\) 0 0
\(877\) −17.0926 + 29.6052i −0.577175 + 0.999696i 0.418627 + 0.908158i \(0.362511\pi\)
−0.995802 + 0.0915375i \(0.970822\pi\)
\(878\) 0 0
\(879\) −2.95490 5.11804i −0.0996664 0.172627i
\(880\) 0 0
\(881\) −49.6527 −1.67284 −0.836420 0.548089i \(-0.815356\pi\)
−0.836420 + 0.548089i \(0.815356\pi\)
\(882\) 0 0
\(883\) −19.4134 −0.653314 −0.326657 0.945143i \(-0.605922\pi\)
−0.326657 + 0.945143i \(0.605922\pi\)
\(884\) 0 0
\(885\) 0.838213 + 1.45183i 0.0281762 + 0.0488026i
\(886\) 0 0
\(887\) −20.1285 + 34.8636i −0.675849 + 1.17060i 0.300371 + 0.953822i \(0.402889\pi\)
−0.976220 + 0.216782i \(0.930444\pi\)
\(888\) 0 0
\(889\) −4.98482 6.00442i −0.167185 0.201382i
\(890\) 0 0
\(891\) 18.9956 32.9013i 0.636376 1.10223i
\(892\) 0 0
\(893\) 4.27048 + 7.39669i 0.142906 + 0.247521i
\(894\) 0 0
\(895\) −2.19988 −0.0735340
\(896\) 0 0
\(897\) −0.821347 −0.0274240
\(898\) 0 0
\(899\) 0.516683 + 0.894921i 0.0172323 + 0.0298473i
\(900\) 0 0
\(901\) 11.5142 19.9431i 0.383593 0.664403i
\(902\) 0 0
\(903\) −2.21117 + 5.97729i −0.0735831 + 0.198912i
\(904\) 0 0
\(905\) −2.73427 + 4.73589i −0.0908902 + 0.157426i
\(906\) 0 0
\(907\) −16.3124 28.2539i −0.541645 0.938156i −0.998810 0.0487743i \(-0.984468\pi\)
0.457165 0.889382i \(-0.348865\pi\)
\(908\) 0 0
\(909\) −46.0199 −1.52638
\(910\) 0 0
\(911\) 21.6499 0.717292 0.358646 0.933474i \(-0.383238\pi\)
0.358646 + 0.933474i \(0.383238\pi\)
\(912\) 0 0
\(913\) 3.79669 + 6.57606i 0.125652 + 0.217636i
\(914\) 0 0
\(915\) 0.388248 0.672465i 0.0128351 0.0222310i
\(916\) 0 0
\(917\) 33.8745 5.78975i 1.11864 0.191194i
\(918\) 0 0
\(919\) −7.82521 + 13.5537i −0.258130 + 0.447094i −0.965741 0.259508i \(-0.916440\pi\)
0.707611 + 0.706602i \(0.249773\pi\)
\(920\) 0 0
\(921\) 0.186227 + 0.322554i 0.00613638 + 0.0106285i
\(922\) 0 0
\(923\) −2.87697 −0.0946967
\(924\) 0 0
\(925\) −20.5908 −0.677022
\(926\) 0 0
\(927\) 6.85187 + 11.8678i 0.225045 + 0.389789i
\(928\) 0 0
\(929\) 18.7667 32.5049i 0.615717 1.06645i −0.374542 0.927210i \(-0.622200\pi\)
0.990258 0.139243i \(-0.0444668\pi\)
\(930\) 0 0
\(931\) −5.31476 4.55558i −0.174184 0.149303i
\(932\) 0 0
\(933\) 3.79668 6.57604i 0.124298 0.215290i
\(934\) 0 0
\(935\) −1.52300 2.63792i −0.0498075 0.0862691i
\(936\) 0 0
\(937\) 47.1876 1.54155 0.770776 0.637106i \(-0.219869\pi\)
0.770776 + 0.637106i \(0.219869\pi\)
\(938\) 0 0
\(939\) −10.5021 −0.342724
\(940\) 0 0
\(941\) −27.6250 47.8479i −0.900550 1.55980i −0.826782 0.562523i \(-0.809831\pi\)
−0.0737682 0.997275i \(-0.523502\pi\)
\(942\) 0 0
\(943\) −1.49106 + 2.58260i −0.0485557 + 0.0841009i
\(944\) 0 0
\(945\) 1.98192 0.338746i 0.0644720 0.0110194i
\(946\) 0 0
\(947\) 22.0575 38.2047i 0.716772 1.24149i −0.245500 0.969397i \(-0.578952\pi\)
0.962272 0.272089i \(-0.0877145\pi\)
\(948\) 0 0
\(949\) −2.96030 5.12738i −0.0960953 0.166442i
\(950\) 0 0
\(951\) −3.25492 −0.105548
\(952\) 0 0
\(953\) −27.9855 −0.906540 −0.453270 0.891373i \(-0.649743\pi\)
−0.453270 + 0.891373i \(0.649743\pi\)
\(954\) 0 0
\(955\) −1.10448 1.91302i −0.0357402 0.0619039i
\(956\) 0 0
\(957\) 0.600795 1.04061i 0.0194209 0.0336381i
\(958\) 0 0
\(959\) 12.5138 33.8275i 0.404091 1.09235i
\(960\) 0 0
\(961\) 13.6019 23.5592i 0.438771 0.759974i
\(962\) 0 0
\(963\) 10.3323 + 17.8961i 0.332955 + 0.576694i
\(964\) 0 0
\(965\) −0.438330 −0.0141103
\(966\) 0 0
\(967\) −50.3705 −1.61981 −0.809904 0.586563i \(-0.800481\pi\)
−0.809904 + 0.586563i \(0.800481\pi\)
\(968\) 0 0
\(969\) 0.427608 + 0.740639i 0.0137367 + 0.0237927i
\(970\) 0 0
\(971\) 5.36711 9.29611i 0.172239 0.298327i −0.766963 0.641691i \(-0.778233\pi\)
0.939202 + 0.343364i \(0.111567\pi\)
\(972\) 0 0
\(973\) 34.9318 + 42.0769i 1.11986 + 1.34892i
\(974\) 0 0
\(975\) 1.35239 2.34240i 0.0433111 0.0750170i
\(976\) 0 0
\(977\) −22.8592 39.5932i −0.731329 1.26670i −0.956315 0.292337i \(-0.905567\pi\)
0.224986 0.974362i \(-0.427766\pi\)
\(978\) 0 0
\(979\) 19.9817 0.638618
\(980\) 0 0
\(981\) −12.3296 −0.393655
\(982\) 0 0
\(983\) 16.2010 + 28.0609i 0.516731 + 0.895005i 0.999811 + 0.0194288i \(0.00618476\pi\)
−0.483080 + 0.875576i \(0.660482\pi\)
\(984\) 0 0
\(985\) 0.361411 0.625982i 0.0115155 0.0199455i
\(986\) 0 0
\(987\) 6.30160 + 7.59054i 0.200582 + 0.241610i
\(988\) 0 0
\(989\) 4.11351 7.12480i 0.130802 0.226556i
\(990\) 0 0
\(991\) 8.21739 + 14.2329i 0.261034 + 0.452124i 0.966517 0.256603i \(-0.0826032\pi\)
−0.705483 + 0.708727i \(0.749270\pi\)
\(992\) 0 0
\(993\) −14.8116 −0.470033
\(994\) 0 0
\(995\) −4.78139 −0.151580
\(996\) 0 0
\(997\) −5.42064 9.38882i −0.171673 0.297347i 0.767332 0.641250i \(-0.221584\pi\)
−0.939005 + 0.343903i \(0.888251\pi\)
\(998\) 0 0
\(999\) −5.31783 + 9.21075i −0.168249 + 0.291415i
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 1064.2.q.n.457.5 yes 16
7.2 even 3 7448.2.a.bq.1.4 8
7.4 even 3 inner 1064.2.q.n.305.5 16
7.5 odd 6 7448.2.a.br.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.q.n.305.5 16 7.4 even 3 inner
1064.2.q.n.457.5 yes 16 1.1 even 1 trivial
7448.2.a.bq.1.4 8 7.2 even 3
7448.2.a.br.1.5 8 7.5 odd 6