Properties

Label 460.2.s.a.449.5
Level $460$
Weight $2$
Character 460.449
Analytic conductor $3.673$
Analytic rank $0$
Dimension $120$
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] = [460,2,Mod(9,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.s (of order \(22\), degree \(10\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(12\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 449.5
Character \(\chi\) \(=\) 460.449
Dual form 460.2.s.a.209.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.768762 - 0.110531i) q^{3} +(-1.82650 + 1.28992i) q^{5} +(2.41290 - 2.09079i) q^{7} +(-2.29970 - 0.675253i) q^{9} +O(q^{10})\) \(q+(-0.768762 - 0.110531i) q^{3} +(-1.82650 + 1.28992i) q^{5} +(2.41290 - 2.09079i) q^{7} +(-2.29970 - 0.675253i) q^{9} +(3.09680 + 1.99019i) q^{11} +(1.64776 + 1.42779i) q^{13} +(1.54672 - 0.789752i) q^{15} +(6.67285 - 3.04739i) q^{17} +(-1.21721 + 2.66533i) q^{19} +(-2.08604 + 1.34062i) q^{21} +(4.38042 + 1.95241i) q^{23} +(1.67223 - 4.71207i) q^{25} +(3.81273 + 1.74122i) q^{27} +(2.38433 + 5.22096i) q^{29} +(-0.218648 - 1.52073i) q^{31} +(-2.16072 - 1.87228i) q^{33} +(-1.71023 + 6.93127i) q^{35} +(0.256558 - 0.873758i) q^{37} +(-1.10892 - 1.27976i) q^{39} +(5.53126 - 1.62412i) q^{41} +(-3.96839 - 0.570568i) q^{43} +(5.07143 - 1.73307i) q^{45} +4.46950i q^{47} +(0.454481 - 3.16098i) q^{49} +(-5.46667 + 1.60516i) q^{51} +(7.82976 - 6.78453i) q^{53} +(-8.22350 + 0.359516i) q^{55} +(1.23035 - 1.91446i) q^{57} +(-0.621592 + 0.717356i) q^{59} +(-1.46762 - 10.2075i) q^{61} +(-6.96076 + 3.17887i) q^{63} +(-4.85137 - 0.482397i) q^{65} +(-3.77312 - 5.87108i) q^{67} +(-3.15170 - 1.98511i) q^{69} +(-8.76551 + 5.63325i) q^{71} +(-8.40563 - 3.83872i) q^{73} +(-1.80638 + 3.43763i) q^{75} +(11.6333 - 1.67262i) q^{77} +(3.32902 - 3.84189i) q^{79} +(3.31030 + 2.12740i) q^{81} +(-4.28961 + 14.6091i) q^{83} +(-8.25712 + 14.1735i) q^{85} +(-1.25590 - 4.27722i) q^{87} +(-1.36184 + 9.47178i) q^{89} +6.96109 q^{91} +1.19325i q^{93} +(-1.21480 - 6.43833i) q^{95} +(-0.287573 - 0.979385i) q^{97} +(-5.77783 - 6.66797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{10}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.768762 0.110531i −0.443845 0.0638152i −0.0832306 0.996530i \(-0.526524\pi\)
−0.360614 + 0.932715i \(0.617433\pi\)
\(4\) 0 0
\(5\) −1.82650 + 1.28992i −0.816837 + 0.576868i
\(6\) 0 0
\(7\) 2.41290 2.09079i 0.911991 0.790244i −0.0662318 0.997804i \(-0.521098\pi\)
0.978222 + 0.207560i \(0.0665522\pi\)
\(8\) 0 0
\(9\) −2.29970 0.675253i −0.766567 0.225084i
\(10\) 0 0
\(11\) 3.09680 + 1.99019i 0.933720 + 0.600065i 0.916608 0.399788i \(-0.130916\pi\)
0.0171124 + 0.999854i \(0.494553\pi\)
\(12\) 0 0
\(13\) 1.64776 + 1.42779i 0.457006 + 0.395998i 0.852714 0.522378i \(-0.174955\pi\)
−0.395708 + 0.918377i \(0.629501\pi\)
\(14\) 0 0
\(15\) 1.54672 0.789752i 0.399362 0.203913i
\(16\) 0 0
\(17\) 6.67285 3.04739i 1.61840 0.739101i 0.619460 0.785028i \(-0.287352\pi\)
0.998945 + 0.0459273i \(0.0146242\pi\)
\(18\) 0 0
\(19\) −1.21721 + 2.66533i −0.279248 + 0.611468i −0.996337 0.0855139i \(-0.972747\pi\)
0.717089 + 0.696982i \(0.245474\pi\)
\(20\) 0 0
\(21\) −2.08604 + 1.34062i −0.455212 + 0.292547i
\(22\) 0 0
\(23\) 4.38042 + 1.95241i 0.913381 + 0.407107i
\(24\) 0 0
\(25\) 1.67223 4.71207i 0.334447 0.942415i
\(26\) 0 0
\(27\) 3.81273 + 1.74122i 0.733760 + 0.335097i
\(28\) 0 0
\(29\) 2.38433 + 5.22096i 0.442759 + 0.969508i 0.991084 + 0.133242i \(0.0425387\pi\)
−0.548324 + 0.836266i \(0.684734\pi\)
\(30\) 0 0
\(31\) −0.218648 1.52073i −0.0392704 0.273131i 0.960720 0.277520i \(-0.0895123\pi\)
−0.999990 + 0.00438809i \(0.998603\pi\)
\(32\) 0 0
\(33\) −2.16072 1.87228i −0.376133 0.325921i
\(34\) 0 0
\(35\) −1.71023 + 6.93127i −0.289082 + 1.17160i
\(36\) 0 0
\(37\) 0.256558 0.873758i 0.0421780 0.143645i −0.935712 0.352765i \(-0.885242\pi\)
0.977890 + 0.209120i \(0.0670598\pi\)
\(38\) 0 0
\(39\) −1.10892 1.27976i −0.177569 0.204926i
\(40\) 0 0
\(41\) 5.53126 1.62412i 0.863838 0.253646i 0.180345 0.983603i \(-0.442278\pi\)
0.683492 + 0.729958i \(0.260460\pi\)
\(42\) 0 0
\(43\) −3.96839 0.570568i −0.605173 0.0870108i −0.167085 0.985943i \(-0.553435\pi\)
−0.438089 + 0.898932i \(0.644344\pi\)
\(44\) 0 0
\(45\) 5.07143 1.73307i 0.756005 0.258351i
\(46\) 0 0
\(47\) 4.46950i 0.651944i 0.945379 + 0.325972i \(0.105692\pi\)
−0.945379 + 0.325972i \(0.894308\pi\)
\(48\) 0 0
\(49\) 0.454481 3.16098i 0.0649258 0.451569i
\(50\) 0 0
\(51\) −5.46667 + 1.60516i −0.765487 + 0.224767i
\(52\) 0 0
\(53\) 7.82976 6.78453i 1.07550 0.931927i 0.0776191 0.996983i \(-0.475268\pi\)
0.997882 + 0.0650564i \(0.0207227\pi\)
\(54\) 0 0
\(55\) −8.22350 + 0.359516i −1.10886 + 0.0484771i
\(56\) 0 0
\(57\) 1.23035 1.91446i 0.162964 0.253576i
\(58\) 0 0
\(59\) −0.621592 + 0.717356i −0.0809244 + 0.0933918i −0.794768 0.606914i \(-0.792407\pi\)
0.713843 + 0.700305i \(0.246953\pi\)
\(60\) 0 0
\(61\) −1.46762 10.2075i −0.187910 1.30694i −0.837408 0.546579i \(-0.815930\pi\)
0.649498 0.760363i \(-0.274979\pi\)
\(62\) 0 0
\(63\) −6.96076 + 3.17887i −0.876974 + 0.400500i
\(64\) 0 0
\(65\) −4.85137 0.482397i −0.601738 0.0598339i
\(66\) 0 0
\(67\) −3.77312 5.87108i −0.460959 0.717267i 0.530500 0.847685i \(-0.322004\pi\)
−0.991459 + 0.130418i \(0.958368\pi\)
\(68\) 0 0
\(69\) −3.15170 1.98511i −0.379420 0.238980i
\(70\) 0 0
\(71\) −8.76551 + 5.63325i −1.04027 + 0.668544i −0.945055 0.326912i \(-0.893992\pi\)
−0.0952198 + 0.995456i \(0.530355\pi\)
\(72\) 0 0
\(73\) −8.40563 3.83872i −0.983805 0.449289i −0.142468 0.989799i \(-0.545504\pi\)
−0.841337 + 0.540511i \(0.818231\pi\)
\(74\) 0 0
\(75\) −1.80638 + 3.43763i −0.208583 + 0.396943i
\(76\) 0 0
\(77\) 11.6333 1.67262i 1.32574 0.190613i
\(78\) 0 0
\(79\) 3.32902 3.84189i 0.374544 0.432246i −0.536916 0.843636i \(-0.680411\pi\)
0.911460 + 0.411389i \(0.134956\pi\)
\(80\) 0 0
\(81\) 3.31030 + 2.12740i 0.367811 + 0.236378i
\(82\) 0 0
\(83\) −4.28961 + 14.6091i −0.470846 + 1.60355i 0.291626 + 0.956532i \(0.405804\pi\)
−0.762472 + 0.647021i \(0.776015\pi\)
\(84\) 0 0
\(85\) −8.25712 + 14.1735i −0.895610 + 1.53733i
\(86\) 0 0
\(87\) −1.25590 4.27722i −0.134647 0.458566i
\(88\) 0 0
\(89\) −1.36184 + 9.47178i −0.144354 + 1.00401i 0.780899 + 0.624657i \(0.214761\pi\)
−0.925253 + 0.379350i \(0.876148\pi\)
\(90\) 0 0
\(91\) 6.96109 0.729721
\(92\) 0 0
\(93\) 1.19325i 0.123734i
\(94\) 0 0
\(95\) −1.21480 6.43833i −0.124636 0.660559i
\(96\) 0 0
\(97\) −0.287573 0.979385i −0.0291987 0.0994415i 0.943605 0.331075i \(-0.107411\pi\)
−0.972803 + 0.231633i \(0.925593\pi\)
\(98\) 0 0
\(99\) −5.77783 6.66797i −0.580694 0.670156i
\(100\) 0 0
\(101\) −9.95910 2.92426i −0.990967 0.290974i −0.254223 0.967146i \(-0.581820\pi\)
−0.736744 + 0.676171i \(0.763638\pi\)
\(102\) 0 0
\(103\) −6.98000 + 10.8611i −0.687760 + 1.07018i 0.305264 + 0.952268i \(0.401255\pi\)
−0.993025 + 0.117908i \(0.962381\pi\)
\(104\) 0 0
\(105\) 2.08088 5.13946i 0.203073 0.501560i
\(106\) 0 0
\(107\) 14.3127 2.05786i 1.38366 0.198941i 0.590052 0.807365i \(-0.299107\pi\)
0.793612 + 0.608424i \(0.208198\pi\)
\(108\) 0 0
\(109\) 4.88673 + 10.7004i 0.468064 + 1.02492i 0.985575 + 0.169240i \(0.0541314\pi\)
−0.517511 + 0.855677i \(0.673141\pi\)
\(110\) 0 0
\(111\) −0.293810 + 0.643354i −0.0278872 + 0.0610644i
\(112\) 0 0
\(113\) −10.9340 17.0137i −1.02859 1.60051i −0.773709 0.633542i \(-0.781601\pi\)
−0.254880 0.966973i \(-0.582036\pi\)
\(114\) 0 0
\(115\) −10.5193 + 2.08428i −0.980930 + 0.194360i
\(116\) 0 0
\(117\) −2.82523 4.39615i −0.261193 0.406424i
\(118\) 0 0
\(119\) 9.72948 21.3046i 0.891900 1.95299i
\(120\) 0 0
\(121\) 1.05973 + 2.32050i 0.0963395 + 0.210954i
\(122\) 0 0
\(123\) −4.43174 + 0.637188i −0.399596 + 0.0574533i
\(124\) 0 0
\(125\) 3.02383 + 10.7637i 0.270460 + 0.962731i
\(126\) 0 0
\(127\) 1.02268 1.59133i 0.0907485 0.141207i −0.792911 0.609337i \(-0.791436\pi\)
0.883660 + 0.468130i \(0.155072\pi\)
\(128\) 0 0
\(129\) 2.98768 + 0.877261i 0.263050 + 0.0772386i
\(130\) 0 0
\(131\) −5.84537 6.74591i −0.510712 0.589393i 0.440569 0.897719i \(-0.354777\pi\)
−0.951281 + 0.308326i \(0.900231\pi\)
\(132\) 0 0
\(133\) 2.63562 + 8.97610i 0.228537 + 0.778327i
\(134\) 0 0
\(135\) −9.20999 + 1.73776i −0.792670 + 0.149563i
\(136\) 0 0
\(137\) 8.77966i 0.750097i −0.927005 0.375049i \(-0.877626\pi\)
0.927005 0.375049i \(-0.122374\pi\)
\(138\) 0 0
\(139\) 9.00938 0.764166 0.382083 0.924128i \(-0.375207\pi\)
0.382083 + 0.924128i \(0.375207\pi\)
\(140\) 0 0
\(141\) 0.494020 3.43598i 0.0416040 0.289362i
\(142\) 0 0
\(143\) 2.26120 + 7.70094i 0.189091 + 0.643985i
\(144\) 0 0
\(145\) −11.0896 6.46051i −0.920940 0.536517i
\(146\) 0 0
\(147\) −0.698775 + 2.37981i −0.0576340 + 0.196283i
\(148\) 0 0
\(149\) −8.40420 5.40105i −0.688499 0.442471i 0.149053 0.988829i \(-0.452378\pi\)
−0.837552 + 0.546358i \(0.816014\pi\)
\(150\) 0 0
\(151\) −1.15503 + 1.33297i −0.0939949 + 0.108476i −0.800798 0.598934i \(-0.795591\pi\)
0.706803 + 0.707410i \(0.250137\pi\)
\(152\) 0 0
\(153\) −17.4033 + 2.50222i −1.40698 + 0.202293i
\(154\) 0 0
\(155\) 2.36098 + 2.49558i 0.189638 + 0.200450i
\(156\) 0 0
\(157\) −1.33762 0.610871i −0.106754 0.0487528i 0.361322 0.932441i \(-0.382325\pi\)
−0.468076 + 0.883688i \(0.655053\pi\)
\(158\) 0 0
\(159\) −6.76912 + 4.35025i −0.536827 + 0.344997i
\(160\) 0 0
\(161\) 14.6516 4.44756i 1.15471 0.350517i
\(162\) 0 0
\(163\) 2.26058 + 3.51753i 0.177062 + 0.275514i 0.918429 0.395586i \(-0.129458\pi\)
−0.741367 + 0.671100i \(0.765822\pi\)
\(164\) 0 0
\(165\) 6.36165 + 0.632571i 0.495254 + 0.0492456i
\(166\) 0 0
\(167\) −1.35417 + 0.618431i −0.104789 + 0.0478556i −0.467120 0.884194i \(-0.654708\pi\)
0.362331 + 0.932050i \(0.381981\pi\)
\(168\) 0 0
\(169\) −1.17357 8.16236i −0.0902747 0.627874i
\(170\) 0 0
\(171\) 4.59900 5.30753i 0.351694 0.405877i
\(172\) 0 0
\(173\) 5.03817 7.83954i 0.383045 0.596029i −0.595176 0.803595i \(-0.702918\pi\)
0.978221 + 0.207566i \(0.0665542\pi\)
\(174\) 0 0
\(175\) −5.81702 14.8661i −0.439725 1.12377i
\(176\) 0 0
\(177\) 0.557147 0.482770i 0.0418777 0.0362872i
\(178\) 0 0
\(179\) −6.64636 + 1.95155i −0.496772 + 0.145865i −0.520515 0.853853i \(-0.674260\pi\)
0.0237427 + 0.999718i \(0.492442\pi\)
\(180\) 0 0
\(181\) −3.24413 + 22.5635i −0.241135 + 1.67713i 0.405319 + 0.914175i \(0.367160\pi\)
−0.646454 + 0.762953i \(0.723749\pi\)
\(182\) 0 0
\(183\) 8.00939i 0.592071i
\(184\) 0 0
\(185\) 0.658469 + 1.92686i 0.0484116 + 0.141666i
\(186\) 0 0
\(187\) 26.7294 + 3.84310i 1.95465 + 0.281036i
\(188\) 0 0
\(189\) 12.8403 3.77024i 0.933991 0.274244i
\(190\) 0 0
\(191\) 17.3086 + 19.9752i 1.25241 + 1.44536i 0.847324 + 0.531076i \(0.178212\pi\)
0.405083 + 0.914280i \(0.367243\pi\)
\(192\) 0 0
\(193\) 6.17668 21.0358i 0.444607 1.51419i −0.367130 0.930170i \(-0.619659\pi\)
0.811737 0.584023i \(-0.198522\pi\)
\(194\) 0 0
\(195\) 3.67623 + 0.907076i 0.263260 + 0.0649571i
\(196\) 0 0
\(197\) 17.5555 + 15.2119i 1.25078 + 1.08380i 0.993063 + 0.117583i \(0.0375146\pi\)
0.257714 + 0.966221i \(0.417031\pi\)
\(198\) 0 0
\(199\) 3.58101 + 24.9065i 0.253851 + 1.76557i 0.574624 + 0.818418i \(0.305148\pi\)
−0.320773 + 0.947156i \(0.603943\pi\)
\(200\) 0 0
\(201\) 2.25169 + 4.93051i 0.158822 + 0.347771i
\(202\) 0 0
\(203\) 16.6691 + 7.61251i 1.16994 + 0.534294i
\(204\) 0 0
\(205\) −8.00789 + 10.1013i −0.559295 + 0.705508i
\(206\) 0 0
\(207\) −8.75528 7.44786i −0.608534 0.517662i
\(208\) 0 0
\(209\) −9.07397 + 5.83149i −0.627660 + 0.403373i
\(210\) 0 0
\(211\) 8.11401 17.7672i 0.558591 1.22314i −0.394062 0.919084i \(-0.628930\pi\)
0.952653 0.304060i \(-0.0983424\pi\)
\(212\) 0 0
\(213\) 7.36124 3.36176i 0.504384 0.230344i
\(214\) 0 0
\(215\) 7.98426 4.07674i 0.544522 0.278031i
\(216\) 0 0
\(217\) −3.70711 3.21223i −0.251655 0.218060i
\(218\) 0 0
\(219\) 6.03763 + 3.88015i 0.407985 + 0.262196i
\(220\) 0 0
\(221\) 15.3463 + 4.50608i 1.03230 + 0.303112i
\(222\) 0 0
\(223\) 19.5296 16.9225i 1.30780 1.13321i 0.325568 0.945519i \(-0.394445\pi\)
0.982228 0.187693i \(-0.0601009\pi\)
\(224\) 0 0
\(225\) −7.02748 + 9.70718i −0.468499 + 0.647145i
\(226\) 0 0
\(227\) −1.82542 0.262455i −0.121157 0.0174198i 0.0814695 0.996676i \(-0.474039\pi\)
−0.202627 + 0.979256i \(0.564948\pi\)
\(228\) 0 0
\(229\) −2.01925 −0.133436 −0.0667179 0.997772i \(-0.521253\pi\)
−0.0667179 + 0.997772i \(0.521253\pi\)
\(230\) 0 0
\(231\) −9.12814 −0.600588
\(232\) 0 0
\(233\) 2.98172 + 0.428706i 0.195339 + 0.0280855i 0.239290 0.970948i \(-0.423085\pi\)
−0.0439509 + 0.999034i \(0.513995\pi\)
\(234\) 0 0
\(235\) −5.76528 8.16356i −0.376085 0.532532i
\(236\) 0 0
\(237\) −2.98387 + 2.58554i −0.193823 + 0.167949i
\(238\) 0 0
\(239\) −17.7112 5.20047i −1.14564 0.336391i −0.346804 0.937938i \(-0.612733\pi\)
−0.798838 + 0.601547i \(0.794551\pi\)
\(240\) 0 0
\(241\) −22.4658 14.4379i −1.44715 0.930026i −0.999356 0.0358887i \(-0.988574\pi\)
−0.447793 0.894137i \(-0.647790\pi\)
\(242\) 0 0
\(243\) −11.8129 10.2359i −0.757796 0.656634i
\(244\) 0 0
\(245\) 3.24729 + 6.35979i 0.207462 + 0.406312i
\(246\) 0 0
\(247\) −5.81120 + 2.65389i −0.369758 + 0.168863i
\(248\) 0 0
\(249\) 4.91245 10.7568i 0.311314 0.681682i
\(250\) 0 0
\(251\) −22.2800 + 14.3185i −1.40630 + 0.903776i −0.999951 0.00994090i \(-0.996836\pi\)
−0.406352 + 0.913717i \(0.633199\pi\)
\(252\) 0 0
\(253\) 9.67960 + 14.7641i 0.608551 + 0.928212i
\(254\) 0 0
\(255\) 7.91437 9.98337i 0.495617 0.625183i
\(256\) 0 0
\(257\) 10.1084 + 4.61635i 0.630545 + 0.287960i 0.704938 0.709269i \(-0.250975\pi\)
−0.0743931 + 0.997229i \(0.523702\pi\)
\(258\) 0 0
\(259\) −1.20779 2.64470i −0.0750487 0.164334i
\(260\) 0 0
\(261\) −1.95778 13.6167i −0.121184 0.842851i
\(262\) 0 0
\(263\) 0.193353 + 0.167541i 0.0119227 + 0.0103310i 0.660802 0.750561i \(-0.270216\pi\)
−0.648879 + 0.760892i \(0.724762\pi\)
\(264\) 0 0
\(265\) −5.54963 + 22.4917i −0.340911 + 1.38165i
\(266\) 0 0
\(267\) 2.09386 7.13102i 0.128142 0.436411i
\(268\) 0 0
\(269\) 1.50271 + 1.73422i 0.0916221 + 0.105738i 0.799709 0.600388i \(-0.204987\pi\)
−0.708087 + 0.706125i \(0.750442\pi\)
\(270\) 0 0
\(271\) 6.10988 1.79402i 0.371149 0.108979i −0.0908384 0.995866i \(-0.528955\pi\)
0.461987 + 0.886886i \(0.347136\pi\)
\(272\) 0 0
\(273\) −5.35142 0.769418i −0.323883 0.0465673i
\(274\) 0 0
\(275\) 14.5565 11.2643i 0.877790 0.679261i
\(276\) 0 0
\(277\) 3.22244i 0.193618i −0.995303 0.0968088i \(-0.969136\pi\)
0.995303 0.0968088i \(-0.0308635\pi\)
\(278\) 0 0
\(279\) −0.524053 + 3.64487i −0.0313743 + 0.218213i
\(280\) 0 0
\(281\) −9.56173 + 2.80758i −0.570405 + 0.167486i −0.554201 0.832383i \(-0.686976\pi\)
−0.0162036 + 0.999869i \(0.505158\pi\)
\(282\) 0 0
\(283\) 1.57656 1.36610i 0.0937166 0.0812059i −0.606742 0.794898i \(-0.707524\pi\)
0.700459 + 0.713693i \(0.252979\pi\)
\(284\) 0 0
\(285\) 0.222255 + 5.08382i 0.0131652 + 0.301139i
\(286\) 0 0
\(287\) 9.95068 15.4836i 0.587370 0.913965i
\(288\) 0 0
\(289\) 24.1078 27.8218i 1.41810 1.63658i
\(290\) 0 0
\(291\) 0.112823 + 0.784700i 0.00661379 + 0.0459999i
\(292\) 0 0
\(293\) 4.60392 2.10254i 0.268964 0.122832i −0.276368 0.961052i \(-0.589131\pi\)
0.545332 + 0.838220i \(0.316404\pi\)
\(294\) 0 0
\(295\) 0.210013 2.11206i 0.0122274 0.122969i
\(296\) 0 0
\(297\) 8.34190 + 12.9803i 0.484046 + 0.753191i
\(298\) 0 0
\(299\) 4.43024 + 9.47144i 0.256207 + 0.547747i
\(300\) 0 0
\(301\) −10.7683 + 6.92034i −0.620672 + 0.398882i
\(302\) 0 0
\(303\) 7.33295 + 3.34885i 0.421267 + 0.192386i
\(304\) 0 0
\(305\) 15.8475 + 16.7510i 0.907425 + 0.959160i
\(306\) 0 0
\(307\) −22.2106 + 3.19341i −1.26763 + 0.182257i −0.743126 0.669152i \(-0.766658\pi\)
−0.524502 + 0.851409i \(0.675749\pi\)
\(308\) 0 0
\(309\) 6.56645 7.57809i 0.373552 0.431102i
\(310\) 0 0
\(311\) 8.86888 + 5.69968i 0.502908 + 0.323199i 0.767378 0.641194i \(-0.221561\pi\)
−0.264470 + 0.964394i \(0.585197\pi\)
\(312\) 0 0
\(313\) 2.17998 7.42434i 0.123220 0.419649i −0.874659 0.484738i \(-0.838915\pi\)
0.997879 + 0.0650891i \(0.0207332\pi\)
\(314\) 0 0
\(315\) 8.61338 14.7850i 0.485309 0.833042i
\(316\) 0 0
\(317\) −1.88211 6.40987i −0.105710 0.360014i 0.889602 0.456737i \(-0.150982\pi\)
−0.995311 + 0.0967232i \(0.969164\pi\)
\(318\) 0 0
\(319\) −3.00691 + 20.9135i −0.168355 + 1.17093i
\(320\) 0 0
\(321\) −11.2305 −0.626828
\(322\) 0 0
\(323\) 21.4947i 1.19599i
\(324\) 0 0
\(325\) 9.48330 5.37676i 0.526039 0.298249i
\(326\) 0 0
\(327\) −2.57400 8.76623i −0.142342 0.484774i
\(328\) 0 0
\(329\) 9.34479 + 10.7845i 0.515195 + 0.594567i
\(330\) 0 0
\(331\) −16.7120 4.90709i −0.918576 0.269718i −0.211930 0.977285i \(-0.567975\pi\)
−0.706647 + 0.707567i \(0.749793\pi\)
\(332\) 0 0
\(333\) −1.18002 + 1.83614i −0.0646645 + 0.100620i
\(334\) 0 0
\(335\) 14.4648 + 5.85655i 0.790297 + 0.319978i
\(336\) 0 0
\(337\) −12.9348 + 1.85974i −0.704604 + 0.101307i −0.485297 0.874349i \(-0.661289\pi\)
−0.219307 + 0.975656i \(0.570379\pi\)
\(338\) 0 0
\(339\) 6.52513 + 14.2880i 0.354396 + 0.776020i
\(340\) 0 0
\(341\) 2.34944 5.14455i 0.127229 0.278593i
\(342\) 0 0
\(343\) 6.57048 + 10.2239i 0.354773 + 0.552037i
\(344\) 0 0
\(345\) 8.31722 0.439602i 0.447784 0.0236674i
\(346\) 0 0
\(347\) −12.7765 19.8807i −0.685881 1.06725i −0.993287 0.115673i \(-0.963098\pi\)
0.307407 0.951578i \(-0.400539\pi\)
\(348\) 0 0
\(349\) 1.62905 3.56713i 0.0872012 0.190944i −0.861007 0.508593i \(-0.830166\pi\)
0.948209 + 0.317649i \(0.102893\pi\)
\(350\) 0 0
\(351\) 3.79637 + 8.31289i 0.202635 + 0.443709i
\(352\) 0 0
\(353\) −7.61551 + 1.09494i −0.405333 + 0.0582780i −0.341966 0.939712i \(-0.611093\pi\)
−0.0633665 + 0.997990i \(0.520184\pi\)
\(354\) 0 0
\(355\) 8.74382 21.5959i 0.464074 1.14619i
\(356\) 0 0
\(357\) −9.83447 + 15.3027i −0.520496 + 0.809907i
\(358\) 0 0
\(359\) −1.56025 0.458130i −0.0823466 0.0241792i 0.240300 0.970699i \(-0.422754\pi\)
−0.322646 + 0.946520i \(0.604572\pi\)
\(360\) 0 0
\(361\) 6.82000 + 7.87070i 0.358947 + 0.414247i
\(362\) 0 0
\(363\) −0.558196 1.90104i −0.0292977 0.0997788i
\(364\) 0 0
\(365\) 20.3046 3.83111i 1.06279 0.200530i
\(366\) 0 0
\(367\) 33.4403i 1.74557i 0.488107 + 0.872784i \(0.337688\pi\)
−0.488107 + 0.872784i \(0.662312\pi\)
\(368\) 0 0
\(369\) −13.8169 −0.719281
\(370\) 0 0
\(371\) 4.70741 32.7408i 0.244397 1.69982i
\(372\) 0 0
\(373\) −8.48815 28.9080i −0.439500 1.49680i −0.820187 0.572095i \(-0.806131\pi\)
0.380687 0.924704i \(-0.375687\pi\)
\(374\) 0 0
\(375\) −1.13489 8.60892i −0.0586052 0.444563i
\(376\) 0 0
\(377\) −3.52564 + 12.0072i −0.181579 + 0.618403i
\(378\) 0 0
\(379\) −19.6894 12.6536i −1.01138 0.649972i −0.0736275 0.997286i \(-0.523458\pi\)
−0.937749 + 0.347314i \(0.887094\pi\)
\(380\) 0 0
\(381\) −0.962091 + 1.11031i −0.0492894 + 0.0568830i
\(382\) 0 0
\(383\) −37.3856 + 5.37523i −1.91031 + 0.274662i −0.992490 0.122326i \(-0.960965\pi\)
−0.917824 + 0.396988i \(0.870055\pi\)
\(384\) 0 0
\(385\) −19.0908 + 18.0611i −0.972957 + 0.920478i
\(386\) 0 0
\(387\) 8.74082 + 3.99180i 0.444321 + 0.202915i
\(388\) 0 0
\(389\) −20.0087 + 12.8588i −1.01448 + 0.651969i −0.938550 0.345144i \(-0.887830\pi\)
−0.0759336 + 0.997113i \(0.524194\pi\)
\(390\) 0 0
\(391\) 35.1797 0.320672i 1.77911 0.0162171i
\(392\) 0 0
\(393\) 3.74806 + 5.83209i 0.189065 + 0.294190i
\(394\) 0 0
\(395\) −1.12475 + 11.3114i −0.0565922 + 0.569137i
\(396\) 0 0
\(397\) −32.4878 + 14.8367i −1.63052 + 0.744632i −0.999515 0.0311480i \(-0.990084\pi\)
−0.631003 + 0.775780i \(0.717356\pi\)
\(398\) 0 0
\(399\) −1.03403 7.19180i −0.0517660 0.360040i
\(400\) 0 0
\(401\) 11.1034 12.8140i 0.554478 0.639902i −0.407443 0.913231i \(-0.633579\pi\)
0.961921 + 0.273329i \(0.0881248\pi\)
\(402\) 0 0
\(403\) 1.81101 2.81798i 0.0902127 0.140374i
\(404\) 0 0
\(405\) −8.79044 + 0.384302i −0.436800 + 0.0190961i
\(406\) 0 0
\(407\) 2.53346 2.19525i 0.125579 0.108815i
\(408\) 0 0
\(409\) −34.3665 + 10.0909i −1.69932 + 0.498964i −0.980547 0.196284i \(-0.937112\pi\)
−0.718769 + 0.695249i \(0.755294\pi\)
\(410\) 0 0
\(411\) −0.970427 + 6.74947i −0.0478676 + 0.332927i
\(412\) 0 0
\(413\) 3.03053i 0.149123i
\(414\) 0 0
\(415\) −11.0095 32.2168i −0.540434 1.58146i
\(416\) 0 0
\(417\) −6.92607 0.995818i −0.339171 0.0487654i
\(418\) 0 0
\(419\) −20.8646 + 6.12638i −1.01930 + 0.299293i −0.748353 0.663301i \(-0.769155\pi\)
−0.270947 + 0.962594i \(0.587337\pi\)
\(420\) 0 0
\(421\) −5.27609 6.08893i −0.257141 0.296756i 0.612470 0.790494i \(-0.290176\pi\)
−0.869611 + 0.493737i \(0.835630\pi\)
\(422\) 0 0
\(423\) 3.01805 10.2785i 0.146742 0.499759i
\(424\) 0 0
\(425\) −3.20095 36.5389i −0.155269 1.77240i
\(426\) 0 0
\(427\) −24.8831 21.5613i −1.20418 1.04342i
\(428\) 0 0
\(429\) −0.887130 6.17012i −0.0428310 0.297896i
\(430\) 0 0
\(431\) −7.29150 15.9662i −0.351219 0.769062i −0.999968 0.00805955i \(-0.997435\pi\)
0.648748 0.761003i \(-0.275293\pi\)
\(432\) 0 0
\(433\) −1.18017 0.538964i −0.0567152 0.0259010i 0.386856 0.922140i \(-0.373561\pi\)
−0.443571 + 0.896239i \(0.646288\pi\)
\(434\) 0 0
\(435\) 7.81116 + 6.19234i 0.374517 + 0.296900i
\(436\) 0 0
\(437\) −10.5357 + 9.29874i −0.503992 + 0.444819i
\(438\) 0 0
\(439\) 20.5621 13.2145i 0.981378 0.630693i 0.0515431 0.998671i \(-0.483586\pi\)
0.929835 + 0.367978i \(0.119950\pi\)
\(440\) 0 0
\(441\) −3.17964 + 6.96243i −0.151411 + 0.331544i
\(442\) 0 0
\(443\) −2.21511 + 1.01161i −0.105243 + 0.0480628i −0.467341 0.884077i \(-0.654788\pi\)
0.362098 + 0.932140i \(0.382061\pi\)
\(444\) 0 0
\(445\) −9.73040 19.0569i −0.461265 0.903384i
\(446\) 0 0
\(447\) 5.86384 + 5.08105i 0.277350 + 0.240325i
\(448\) 0 0
\(449\) 21.3361 + 13.7119i 1.00691 + 0.647103i 0.936592 0.350421i \(-0.113962\pi\)
0.0703202 + 0.997524i \(0.477598\pi\)
\(450\) 0 0
\(451\) 20.3615 + 5.97868i 0.958787 + 0.281525i
\(452\) 0 0
\(453\) 1.03528 0.897073i 0.0486416 0.0421482i
\(454\) 0 0
\(455\) −12.7145 + 8.97922i −0.596063 + 0.420952i
\(456\) 0 0
\(457\) −24.9433 3.58631i −1.16680 0.167760i −0.468432 0.883500i \(-0.655181\pi\)
−0.698368 + 0.715739i \(0.746090\pi\)
\(458\) 0 0
\(459\) 30.7480 1.43519
\(460\) 0 0
\(461\) 7.45005 0.346983 0.173492 0.984835i \(-0.444495\pi\)
0.173492 + 0.984835i \(0.444495\pi\)
\(462\) 0 0
\(463\) 7.30867 + 1.05083i 0.339663 + 0.0488361i 0.310036 0.950725i \(-0.399659\pi\)
0.0296270 + 0.999561i \(0.490568\pi\)
\(464\) 0 0
\(465\) −1.53919 2.17947i −0.0713782 0.101071i
\(466\) 0 0
\(467\) −22.8606 + 19.8088i −1.05786 + 0.916643i −0.996675 0.0814831i \(-0.974034\pi\)
−0.0611878 + 0.998126i \(0.519489\pi\)
\(468\) 0 0
\(469\) −21.3793 6.27754i −0.987207 0.289870i
\(470\) 0 0
\(471\) 0.960792 + 0.617464i 0.0442710 + 0.0284512i
\(472\) 0 0
\(473\) −11.1538 9.66478i −0.512850 0.444387i
\(474\) 0 0
\(475\) 10.5237 + 10.1926i 0.482862 + 0.467671i
\(476\) 0 0
\(477\) −22.5874 + 10.3153i −1.03421 + 0.472306i
\(478\) 0 0
\(479\) 7.24263 15.8591i 0.330924 0.724623i −0.668900 0.743352i \(-0.733235\pi\)
0.999825 + 0.0187291i \(0.00596201\pi\)
\(480\) 0 0
\(481\) 1.67029 1.07343i 0.0761587 0.0489442i
\(482\) 0 0
\(483\) −11.7552 + 1.79965i −0.534880 + 0.0818870i
\(484\) 0 0
\(485\) 1.78858 + 1.41791i 0.0812151 + 0.0643838i
\(486\) 0 0
\(487\) −25.8165 11.7900i −1.16986 0.534255i −0.266788 0.963755i \(-0.585963\pi\)
−0.903067 + 0.429500i \(0.858690\pi\)
\(488\) 0 0
\(489\) −1.34905 2.95401i −0.0610061 0.133585i
\(490\) 0 0
\(491\) 4.59013 + 31.9251i 0.207150 + 1.44076i 0.782398 + 0.622779i \(0.213996\pi\)
−0.575248 + 0.817979i \(0.695095\pi\)
\(492\) 0 0
\(493\) 31.8206 + 27.5727i 1.43313 + 1.24181i
\(494\) 0 0
\(495\) 19.1543 + 4.72616i 0.860924 + 0.212425i
\(496\) 0 0
\(497\) −9.37235 + 31.9193i −0.420408 + 1.43178i
\(498\) 0 0
\(499\) −19.7792 22.8265i −0.885440 1.02185i −0.999597 0.0283895i \(-0.990962\pi\)
0.114157 0.993463i \(-0.463583\pi\)
\(500\) 0 0
\(501\) 1.10939 0.325747i 0.0495640 0.0145533i
\(502\) 0 0
\(503\) −16.5342 2.37726i −0.737225 0.105997i −0.236534 0.971623i \(-0.576012\pi\)
−0.500691 + 0.865626i \(0.666921\pi\)
\(504\) 0 0
\(505\) 21.9624 7.50523i 0.977313 0.333978i
\(506\) 0 0
\(507\) 6.40463i 0.284440i
\(508\) 0 0
\(509\) 1.60299 11.1490i 0.0710512 0.494172i −0.922960 0.384895i \(-0.874238\pi\)
0.994011 0.109276i \(-0.0348534\pi\)
\(510\) 0 0
\(511\) −28.3079 + 8.31195i −1.25227 + 0.367699i
\(512\) 0 0
\(513\) −9.28181 + 8.04274i −0.409802 + 0.355095i
\(514\) 0 0
\(515\) −1.26089 28.8415i −0.0555616 1.27091i
\(516\) 0 0
\(517\) −8.89517 + 13.8411i −0.391209 + 0.608733i
\(518\) 0 0
\(519\) −4.73966 + 5.46986i −0.208048 + 0.240100i
\(520\) 0 0
\(521\) −3.31750 23.0737i −0.145342 1.01088i −0.923717 0.383077i \(-0.874865\pi\)
0.778374 0.627800i \(-0.216045\pi\)
\(522\) 0 0
\(523\) 36.0672 16.4713i 1.57711 0.720241i 0.581472 0.813567i \(-0.302477\pi\)
0.995636 + 0.0933260i \(0.0297499\pi\)
\(524\) 0 0
\(525\) 2.82874 + 12.0714i 0.123456 + 0.526840i
\(526\) 0 0
\(527\) −6.09327 9.48131i −0.265427 0.413012i
\(528\) 0 0
\(529\) 15.3762 + 17.1048i 0.668528 + 0.743687i
\(530\) 0 0
\(531\) 1.91387 1.22997i 0.0830551 0.0533762i
\(532\) 0 0
\(533\) 11.4331 + 5.22132i 0.495222 + 0.226161i
\(534\) 0 0
\(535\) −23.4878 + 22.2209i −1.01547 + 0.960694i
\(536\) 0 0
\(537\) 5.32517 0.765644i 0.229798 0.0330400i
\(538\) 0 0
\(539\) 7.69840 8.88443i 0.331594 0.382679i
\(540\) 0 0
\(541\) 15.7029 + 10.0916i 0.675120 + 0.433873i 0.832768 0.553622i \(-0.186755\pi\)
−0.157648 + 0.987495i \(0.550391\pi\)
\(542\) 0 0
\(543\) 4.98793 16.9873i 0.214053 0.728996i
\(544\) 0 0
\(545\) −22.7283 13.2409i −0.973574 0.567180i
\(546\) 0 0
\(547\) −5.04687 17.1881i −0.215789 0.734908i −0.994237 0.107200i \(-0.965811\pi\)
0.778449 0.627708i \(-0.216007\pi\)
\(548\) 0 0
\(549\) −3.51758 + 24.4653i −0.150127 + 1.04415i
\(550\) 0 0
\(551\) −16.8178 −0.716462
\(552\) 0 0
\(553\) 16.2304i 0.690185i
\(554\) 0 0
\(555\) −0.293227 1.55408i −0.0124468 0.0659670i
\(556\) 0 0
\(557\) 4.39006 + 14.9512i 0.186013 + 0.633501i 0.998708 + 0.0508124i \(0.0161811\pi\)
−0.812696 + 0.582689i \(0.802001\pi\)
\(558\) 0 0
\(559\) −5.72429 6.60619i −0.242112 0.279412i
\(560\) 0 0
\(561\) −20.1237 5.90886i −0.849625 0.249472i
\(562\) 0 0
\(563\) −4.06489 + 6.32509i −0.171315 + 0.266571i −0.916285 0.400527i \(-0.868827\pi\)
0.744971 + 0.667097i \(0.232464\pi\)
\(564\) 0 0
\(565\) 41.9173 + 16.9716i 1.76347 + 0.714001i
\(566\) 0 0
\(567\) 12.4354 1.78794i 0.522236 0.0750862i
\(568\) 0 0
\(569\) −2.68047 5.86941i −0.112371 0.246059i 0.845088 0.534627i \(-0.179548\pi\)
−0.957459 + 0.288569i \(0.906821\pi\)
\(570\) 0 0
\(571\) 8.17890 17.9093i 0.342277 0.749481i −0.657716 0.753266i \(-0.728477\pi\)
0.999993 + 0.00378471i \(0.00120471\pi\)
\(572\) 0 0
\(573\) −11.0983 17.2693i −0.463639 0.721436i
\(574\) 0 0
\(575\) 16.5250 17.3760i 0.689141 0.724628i
\(576\) 0 0
\(577\) 19.9870 + 31.1004i 0.832070 + 1.29473i 0.953277 + 0.302099i \(0.0976872\pi\)
−0.121207 + 0.992627i \(0.538676\pi\)
\(578\) 0 0
\(579\) −7.07351 + 15.4888i −0.293965 + 0.643694i
\(580\) 0 0
\(581\) 20.1941 + 44.2189i 0.837792 + 1.83451i
\(582\) 0 0
\(583\) 37.7497 5.42759i 1.56343 0.224788i
\(584\) 0 0
\(585\) 10.8310 + 4.38527i 0.447805 + 0.181309i
\(586\) 0 0
\(587\) 9.31110 14.4883i 0.384310 0.597998i −0.594170 0.804339i \(-0.702519\pi\)
0.978480 + 0.206341i \(0.0661557\pi\)
\(588\) 0 0
\(589\) 4.31939 + 1.26829i 0.177977 + 0.0522588i
\(590\) 0 0
\(591\) −11.8146 13.6348i −0.485988 0.560859i
\(592\) 0 0
\(593\) −12.1264 41.2986i −0.497970 1.69593i −0.697964 0.716133i \(-0.745910\pi\)
0.199994 0.979797i \(-0.435908\pi\)
\(594\) 0 0
\(595\) 9.71019 + 51.4631i 0.398079 + 2.10978i
\(596\) 0 0
\(597\) 19.5430i 0.799840i
\(598\) 0 0
\(599\) 34.4873 1.40911 0.704556 0.709648i \(-0.251146\pi\)
0.704556 + 0.709648i \(0.251146\pi\)
\(600\) 0 0
\(601\) −0.382751 + 2.66209i −0.0156127 + 0.108589i −0.996138 0.0878062i \(-0.972014\pi\)
0.980525 + 0.196395i \(0.0629235\pi\)
\(602\) 0 0
\(603\) 4.71257 + 16.0495i 0.191911 + 0.653588i
\(604\) 0 0
\(605\) −4.92885 2.87143i −0.200386 0.116740i
\(606\) 0 0
\(607\) 4.40031 14.9861i 0.178603 0.608266i −0.820715 0.571338i \(-0.806425\pi\)
0.999318 0.0369279i \(-0.0117572\pi\)
\(608\) 0 0
\(609\) −11.9731 7.69466i −0.485176 0.311804i
\(610\) 0 0
\(611\) −6.38152 + 7.36466i −0.258169 + 0.297942i
\(612\) 0 0
\(613\) 34.8103 5.00497i 1.40598 0.202149i 0.602801 0.797892i \(-0.294051\pi\)
0.803175 + 0.595743i \(0.203142\pi\)
\(614\) 0 0
\(615\) 7.27267 6.88039i 0.293262 0.277444i
\(616\) 0 0
\(617\) −10.7410 4.90523i −0.432415 0.197477i 0.187303 0.982302i \(-0.440026\pi\)
−0.619717 + 0.784825i \(0.712753\pi\)
\(618\) 0 0
\(619\) −6.60273 + 4.24332i −0.265386 + 0.170553i −0.666566 0.745446i \(-0.732237\pi\)
0.401180 + 0.915999i \(0.368600\pi\)
\(620\) 0 0
\(621\) 13.3018 + 15.0713i 0.533782 + 0.604790i
\(622\) 0 0
\(623\) 16.5175 + 25.7018i 0.661761 + 1.02972i
\(624\) 0 0
\(625\) −19.4073 15.7594i −0.776290 0.630375i
\(626\) 0 0
\(627\) 7.62029 3.48007i 0.304325 0.138981i
\(628\) 0 0
\(629\) −0.950704 6.61229i −0.0379071 0.263649i
\(630\) 0 0
\(631\) 8.27577 9.55075i 0.329453 0.380209i −0.566722 0.823909i \(-0.691789\pi\)
0.896176 + 0.443699i \(0.146334\pi\)
\(632\) 0 0
\(633\) −8.20157 + 12.7619i −0.325983 + 0.507240i
\(634\) 0 0
\(635\) 0.184741 + 4.22574i 0.00733124 + 0.167693i
\(636\) 0 0
\(637\) 5.26210 4.55964i 0.208492 0.180659i
\(638\) 0 0
\(639\) 23.9619 7.03586i 0.947919 0.278334i
\(640\) 0 0
\(641\) 3.60512 25.0742i 0.142394 0.990371i −0.785855 0.618411i \(-0.787777\pi\)
0.928249 0.371960i \(-0.121314\pi\)
\(642\) 0 0
\(643\) 10.6136i 0.418561i 0.977856 + 0.209280i \(0.0671122\pi\)
−0.977856 + 0.209280i \(0.932888\pi\)
\(644\) 0 0
\(645\) −6.58860 + 2.25153i −0.259426 + 0.0886539i
\(646\) 0 0
\(647\) −5.76579 0.828995i −0.226676 0.0325912i 0.0280406 0.999607i \(-0.491073\pi\)
−0.254717 + 0.967016i \(0.581982\pi\)
\(648\) 0 0
\(649\) −3.35262 + 0.984419i −0.131602 + 0.0386418i
\(650\) 0 0
\(651\) 2.49483 + 2.87919i 0.0977801 + 0.112844i
\(652\) 0 0
\(653\) −1.40767 + 4.79410i −0.0550865 + 0.187607i −0.982440 0.186579i \(-0.940260\pi\)
0.927353 + 0.374187i \(0.122078\pi\)
\(654\) 0 0
\(655\) 19.3782 + 4.78141i 0.757171 + 0.186825i
\(656\) 0 0
\(657\) 16.7383 + 14.5038i 0.653025 + 0.565849i
\(658\) 0 0
\(659\) 1.09083 + 7.58690i 0.0424928 + 0.295544i 0.999975 + 0.00705195i \(0.00224473\pi\)
−0.957482 + 0.288492i \(0.906846\pi\)
\(660\) 0 0
\(661\) 4.67286 + 10.2321i 0.181753 + 0.397984i 0.978476 0.206361i \(-0.0661621\pi\)
−0.796723 + 0.604345i \(0.793435\pi\)
\(662\) 0 0
\(663\) −11.2996 5.16035i −0.438839 0.200411i
\(664\) 0 0
\(665\) −16.3924 12.9952i −0.635670 0.503931i
\(666\) 0 0
\(667\) 0.250900 + 27.5252i 0.00971487 + 1.06578i
\(668\) 0 0
\(669\) −16.8840 + 10.8507i −0.652774 + 0.419513i
\(670\) 0 0
\(671\) 15.7700 34.5316i 0.608795 1.33308i
\(672\) 0 0
\(673\) 13.0032 5.93836i 0.501236 0.228907i −0.148719 0.988880i \(-0.547515\pi\)
0.649955 + 0.759973i \(0.274788\pi\)
\(674\) 0 0
\(675\) 14.5805 15.0541i 0.561204 0.579434i
\(676\) 0 0
\(677\) −17.1504 14.8609i −0.659143 0.571151i 0.259741 0.965678i \(-0.416363\pi\)
−0.918884 + 0.394528i \(0.870908\pi\)
\(678\) 0 0
\(679\) −2.74157 1.76190i −0.105212 0.0676156i
\(680\) 0 0
\(681\) 1.37430 + 0.403531i 0.0526633 + 0.0154634i
\(682\) 0 0
\(683\) −1.69345 + 1.46738i −0.0647981 + 0.0561479i −0.686658 0.726981i \(-0.740923\pi\)
0.621860 + 0.783129i \(0.286377\pi\)
\(684\) 0 0
\(685\) 11.3250 + 16.0361i 0.432707 + 0.612708i
\(686\) 0 0
\(687\) 1.55232 + 0.223190i 0.0592247 + 0.00851523i
\(688\) 0 0
\(689\) 22.5885 0.860552
\(690\) 0 0
\(691\) 9.43181 0.358803 0.179402 0.983776i \(-0.442584\pi\)
0.179402 + 0.983776i \(0.442584\pi\)
\(692\) 0 0
\(693\) −27.8827 4.00892i −1.05917 0.152286i
\(694\) 0 0
\(695\) −16.4557 + 11.6213i −0.624199 + 0.440823i
\(696\) 0 0
\(697\) 31.9600 27.6935i 1.21057 1.04896i
\(698\) 0 0
\(699\) −2.24485 0.659146i −0.0849079 0.0249312i
\(700\) 0 0
\(701\) −32.9491 21.1751i −1.24447 0.799773i −0.258390 0.966041i \(-0.583192\pi\)
−0.986081 + 0.166268i \(0.946828\pi\)
\(702\) 0 0
\(703\) 2.01656 + 1.74736i 0.0760561 + 0.0659030i
\(704\) 0 0
\(705\) 3.52980 + 6.91308i 0.132940 + 0.260362i
\(706\) 0 0
\(707\) −30.1443 + 13.7664i −1.13369 + 0.517740i
\(708\) 0 0
\(709\) −15.6485 + 34.2655i −0.587693 + 1.28687i 0.349133 + 0.937073i \(0.386476\pi\)
−0.936826 + 0.349795i \(0.886251\pi\)
\(710\) 0 0
\(711\) −10.2500 + 6.58727i −0.384405 + 0.247042i
\(712\) 0 0
\(713\) 2.01133 7.08833i 0.0753248 0.265460i
\(714\) 0 0
\(715\) −14.0637 11.1490i −0.525951 0.416951i
\(716\) 0 0
\(717\) 13.0409 + 5.95557i 0.487020 + 0.222415i
\(718\) 0 0
\(719\) 12.0653 + 26.4193i 0.449960 + 0.985275i 0.989662 + 0.143419i \(0.0458096\pi\)
−0.539702 + 0.841856i \(0.681463\pi\)
\(720\) 0 0
\(721\) 5.86622 + 40.8005i 0.218469 + 1.51949i
\(722\) 0 0
\(723\) 15.6750 + 13.5825i 0.582960 + 0.505137i
\(724\) 0 0
\(725\) 28.5887 2.50448i 1.06176 0.0930139i
\(726\) 0 0
\(727\) −5.94251 + 20.2383i −0.220396 + 0.750598i 0.772852 + 0.634586i \(0.218829\pi\)
−0.993248 + 0.116012i \(0.962989\pi\)
\(728\) 0 0
\(729\) 0.219350 + 0.253143i 0.00812407 + 0.00937567i
\(730\) 0 0
\(731\) −28.2192 + 8.28591i −1.04372 + 0.306465i
\(732\) 0 0
\(733\) 12.1863 + 1.75212i 0.450111 + 0.0647162i 0.363643 0.931538i \(-0.381533\pi\)
0.0864682 + 0.996255i \(0.472442\pi\)
\(734\) 0 0
\(735\) −1.79344 5.24809i −0.0661520 0.193579i
\(736\) 0 0
\(737\) 25.6908i 0.946332i
\(738\) 0 0
\(739\) 4.21781 29.3355i 0.155155 1.07912i −0.752253 0.658874i \(-0.771033\pi\)
0.907408 0.420251i \(-0.138058\pi\)
\(740\) 0 0
\(741\) 4.76077 1.39789i 0.174891 0.0513527i
\(742\) 0 0
\(743\) −25.6786 + 22.2506i −0.942056 + 0.816296i −0.983139 0.182859i \(-0.941465\pi\)
0.0410829 + 0.999156i \(0.486919\pi\)
\(744\) 0 0
\(745\) 22.3172 0.975667i 0.817639 0.0357457i
\(746\) 0 0
\(747\) 19.7296 30.6999i 0.721870 1.12325i
\(748\) 0 0
\(749\) 30.2327 34.8903i 1.10468 1.27487i
\(750\) 0 0
\(751\) 4.50302 + 31.3192i 0.164317 + 1.14285i 0.890378 + 0.455222i \(0.150440\pi\)
−0.726061 + 0.687631i \(0.758651\pi\)
\(752\) 0 0
\(753\) 18.7107 8.54488i 0.681855 0.311393i
\(754\) 0 0
\(755\) 0.390240 3.92457i 0.0142023 0.142830i
\(756\) 0 0
\(757\) 3.80980 + 5.92817i 0.138470 + 0.215463i 0.903562 0.428458i \(-0.140943\pi\)
−0.765092 + 0.643921i \(0.777307\pi\)
\(758\) 0 0
\(759\) −5.80941 12.4200i −0.210868 0.450817i
\(760\) 0 0
\(761\) −11.7822 + 7.57199i −0.427106 + 0.274484i −0.736484 0.676455i \(-0.763515\pi\)
0.309378 + 0.950939i \(0.399879\pi\)
\(762\) 0 0
\(763\) 34.1636 + 15.6020i 1.23680 + 0.564830i
\(764\) 0 0
\(765\) 28.5596 27.0192i 1.03257 0.976880i
\(766\) 0 0
\(767\) −2.04847 + 0.294525i −0.0739660 + 0.0106347i
\(768\) 0 0
\(769\) 16.3550 18.8746i 0.589775 0.680637i −0.379902 0.925027i \(-0.624042\pi\)
0.969677 + 0.244390i \(0.0785876\pi\)
\(770\) 0 0
\(771\) −7.26071 4.66617i −0.261488 0.168048i
\(772\) 0 0
\(773\) 5.56405 18.9494i 0.200125 0.681563i −0.796874 0.604146i \(-0.793515\pi\)
0.996999 0.0774170i \(-0.0246673\pi\)
\(774\) 0 0
\(775\) −7.53143 1.51273i −0.270537 0.0543390i
\(776\) 0 0
\(777\) 0.636184 + 2.16664i 0.0228230 + 0.0777279i
\(778\) 0 0
\(779\) −2.40390 + 16.7195i −0.0861288 + 0.599039i
\(780\) 0 0
\(781\) −38.3563 −1.37250
\(782\) 0 0
\(783\) 24.0577i 0.859753i
\(784\) 0 0
\(785\) 3.23114 0.609660i 0.115324 0.0217597i
\(786\) 0 0
\(787\) 4.79327 + 16.3244i 0.170862 + 0.581901i 0.999747 + 0.0224829i \(0.00715713\pi\)
−0.828886 + 0.559418i \(0.811025\pi\)
\(788\) 0 0
\(789\) −0.130124 0.150171i −0.00463253 0.00534623i
\(790\) 0 0
\(791\) −61.9548 18.1916i −2.20286 0.646818i
\(792\) 0 0
\(793\) 12.1560 18.9150i 0.431671 0.671693i
\(794\) 0 0
\(795\) 6.75238 16.6774i 0.239482 0.591485i
\(796\) 0 0
\(797\) 28.4130 4.08517i 1.00644 0.144704i 0.380668 0.924712i \(-0.375694\pi\)
0.625770 + 0.780008i \(0.284785\pi\)
\(798\) 0 0
\(799\) 13.6203 + 29.8243i 0.481852 + 1.05511i
\(800\) 0 0
\(801\) 9.52767 20.8627i 0.336644 0.737147i
\(802\) 0 0
\(803\) −18.3908 28.6166i −0.648996 1.00986i
\(804\) 0 0
\(805\) −21.0242 + 27.0228i −0.741007 + 0.952429i
\(806\) 0 0
\(807\) −0.963543 1.49930i −0.0339183 0.0527779i
\(808\) 0 0
\(809\) 0.817377 1.78981i 0.0287374 0.0629262i −0.894719 0.446630i \(-0.852624\pi\)
0.923456 + 0.383703i \(0.125351\pi\)
\(810\) 0 0
\(811\) −5.70383 12.4896i −0.200288 0.438571i 0.782661 0.622449i \(-0.213862\pi\)
−0.982949 + 0.183878i \(0.941135\pi\)
\(812\) 0 0
\(813\) −4.89534 + 0.703844i −0.171687 + 0.0246849i
\(814\) 0 0
\(815\) −8.66627 3.50883i −0.303566 0.122909i
\(816\) 0 0
\(817\) 6.35112 9.88254i 0.222198 0.345746i
\(818\) 0 0
\(819\) −16.0084 4.70050i −0.559380 0.164249i
\(820\) 0 0
\(821\) 24.1536 + 27.8747i 0.842965 + 0.972833i 0.999891 0.0147769i \(-0.00470381\pi\)
−0.156926 + 0.987610i \(0.550158\pi\)
\(822\) 0 0
\(823\) −0.797104 2.71469i −0.0277853 0.0946280i 0.944433 0.328704i \(-0.106612\pi\)
−0.972218 + 0.234076i \(0.924794\pi\)
\(824\) 0 0
\(825\) −12.4355 + 7.05059i −0.432950 + 0.245470i
\(826\) 0 0
\(827\) 35.9069i 1.24861i 0.781182 + 0.624303i \(0.214617\pi\)
−0.781182 + 0.624303i \(0.785383\pi\)
\(828\) 0 0
\(829\) −30.7867 −1.06927 −0.534633 0.845084i \(-0.679550\pi\)
−0.534633 + 0.845084i \(0.679550\pi\)
\(830\) 0 0
\(831\) −0.356180 + 2.47729i −0.0123558 + 0.0859362i
\(832\) 0 0
\(833\) −6.60007 22.4778i −0.228679 0.778809i
\(834\) 0 0
\(835\) 1.67568 2.87634i 0.0579894 0.0995398i
\(836\) 0 0
\(837\) 1.81427 6.17885i 0.0627105 0.213572i
\(838\) 0 0
\(839\) 8.19217 + 5.26479i 0.282825 + 0.181761i 0.674360 0.738402i \(-0.264419\pi\)
−0.391535 + 0.920163i \(0.628056\pi\)
\(840\) 0 0
\(841\) −2.58240 + 2.98025i −0.0890484 + 0.102767i
\(842\) 0 0
\(843\) 7.66101 1.10149i 0.263859 0.0379372i
\(844\) 0 0
\(845\) 12.6723 + 13.3948i 0.435940 + 0.460795i
\(846\) 0 0
\(847\) 7.40870 + 3.38344i 0.254566 + 0.116256i
\(848\) 0 0
\(849\) −1.36299 + 0.875943i −0.0467778 + 0.0300623i
\(850\) 0 0
\(851\) 2.82977 3.32652i 0.0970033 0.114032i
\(852\) 0 0
\(853\) −5.28655 8.22603i −0.181008 0.281654i 0.738878 0.673839i \(-0.235356\pi\)
−0.919886 + 0.392185i \(0.871719\pi\)
\(854\) 0 0
\(855\) −1.55383 + 15.6265i −0.0531398 + 0.534416i
\(856\) 0 0
\(857\) −18.7031 + 8.54143i −0.638886 + 0.291770i −0.708400 0.705811i \(-0.750583\pi\)
0.0695135 + 0.997581i \(0.477855\pi\)
\(858\) 0 0
\(859\) −3.21722 22.3763i −0.109770 0.763468i −0.968135 0.250429i \(-0.919428\pi\)
0.858365 0.513040i \(-0.171481\pi\)
\(860\) 0 0
\(861\) −9.36112 + 10.8033i −0.319026 + 0.368176i
\(862\) 0 0
\(863\) −23.6002 + 36.7227i −0.803361 + 1.25005i 0.161390 + 0.986891i \(0.448402\pi\)
−0.964751 + 0.263164i \(0.915234\pi\)
\(864\) 0 0
\(865\) 0.910113 + 20.8178i 0.0309448 + 0.707825i
\(866\) 0 0
\(867\) −21.6083 + 18.7237i −0.733857 + 0.635891i
\(868\) 0 0
\(869\) 17.9554 5.27218i 0.609095 0.178846i
\(870\) 0 0
\(871\) 2.16550 15.0614i 0.0733750 0.510334i
\(872\) 0 0
\(873\) 2.44648i 0.0828007i
\(874\) 0 0
\(875\) 29.8008 + 19.6494i 1.00745 + 0.664272i
\(876\) 0 0
\(877\) −25.3560 3.64564i −0.856212 0.123105i −0.299791 0.954005i \(-0.596917\pi\)
−0.556421 + 0.830900i \(0.687826\pi\)
\(878\) 0 0
\(879\) −3.77171 + 1.10748i −0.127217 + 0.0373542i
\(880\) 0 0
\(881\) 20.8333 + 24.0429i 0.701891 + 0.810025i 0.989007 0.147871i \(-0.0472420\pi\)
−0.287116 + 0.957896i \(0.592697\pi\)
\(882\) 0 0
\(883\) −3.15624 + 10.7492i −0.106216 + 0.361739i −0.995399 0.0958124i \(-0.969455\pi\)
0.889183 + 0.457551i \(0.151273\pi\)
\(884\) 0 0
\(885\) −0.394898 + 1.60045i −0.0132743 + 0.0537987i
\(886\) 0 0
\(887\) 13.0124 + 11.2753i 0.436913 + 0.378587i 0.845362 0.534194i \(-0.179385\pi\)
−0.408449 + 0.912781i \(0.633930\pi\)
\(888\) 0 0
\(889\) −0.859496 5.97793i −0.0288266 0.200493i
\(890\) 0 0
\(891\) 6.01739 + 13.1763i 0.201590 + 0.441421i
\(892\) 0 0
\(893\) −11.9127 5.44034i −0.398643 0.182054i
\(894\) 0 0
\(895\) 9.62227 12.1377i 0.321637 0.405720i
\(896\) 0 0
\(897\) −2.35891 7.77096i −0.0787616 0.259465i
\(898\) 0 0
\(899\) 7.41835 4.76748i 0.247416 0.159004i
\(900\) 0 0
\(901\) 31.5718 69.1325i 1.05181 2.30314i
\(902\) 0 0
\(903\) 9.04314 4.12986i 0.300937 0.137433i
\(904\) 0 0
\(905\) −23.1795 45.3969i −0.770513 1.50904i
\(906\) 0 0
\(907\) −7.51496 6.51175i −0.249530 0.216219i 0.521110 0.853489i \(-0.325518\pi\)
−0.770640 + 0.637270i \(0.780063\pi\)
\(908\) 0 0
\(909\) 20.9283 + 13.4498i 0.694149 + 0.446103i
\(910\) 0 0
\(911\) 32.0890 + 9.42218i 1.06316 + 0.312171i 0.766121 0.642696i \(-0.222184\pi\)
0.297034 + 0.954867i \(0.404002\pi\)
\(912\) 0 0
\(913\) −42.3589 + 36.7042i −1.40188 + 1.21473i
\(914\) 0 0
\(915\) −10.3314 14.6292i −0.341547 0.483626i
\(916\) 0 0
\(917\) −28.2086 4.05578i −0.931529 0.133934i
\(918\) 0 0
\(919\) −22.2273 −0.733211 −0.366605 0.930377i \(-0.619480\pi\)
−0.366605 + 0.930377i \(0.619480\pi\)
\(920\) 0 0
\(921\) 17.4277 0.574261
\(922\) 0 0
\(923\) −22.4866 3.23308i −0.740154 0.106418i
\(924\) 0 0
\(925\) −3.68818 2.67005i −0.121267 0.0877907i
\(926\) 0 0
\(927\) 23.3859 20.2640i 0.768094 0.665557i
\(928\) 0 0
\(929\) 24.2736 + 7.12736i 0.796390 + 0.233841i 0.654521 0.756044i \(-0.272871\pi\)
0.141869 + 0.989885i \(0.454689\pi\)
\(930\) 0 0
\(931\) 7.87185 + 5.05893i 0.257990 + 0.165800i
\(932\) 0 0
\(933\) −6.18806 5.36199i −0.202588 0.175544i
\(934\) 0 0
\(935\) −53.7786 + 27.4592i −1.75875 + 0.898012i
\(936\) 0 0
\(937\) 33.8406 15.4545i 1.10552 0.504876i 0.222846 0.974854i \(-0.428465\pi\)
0.882678 + 0.469978i \(0.155738\pi\)
\(938\) 0 0
\(939\) −2.49651 + 5.46660i −0.0814705 + 0.178396i
\(940\) 0 0
\(941\) −30.4104 + 19.5436i −0.991351 + 0.637103i −0.932502 0.361164i \(-0.882379\pi\)
−0.0588490 + 0.998267i \(0.518743\pi\)
\(942\) 0 0
\(943\) 27.4002 + 3.68497i 0.892274 + 0.119999i
\(944\) 0 0
\(945\) −18.5895 + 23.4492i −0.604716 + 0.762802i
\(946\) 0 0
\(947\) −10.7265 4.89862i −0.348564 0.159184i 0.233437 0.972372i \(-0.425003\pi\)
−0.582001 + 0.813188i \(0.697730\pi\)
\(948\) 0 0
\(949\) −8.36956 18.3268i −0.271687 0.594913i
\(950\) 0 0
\(951\) 0.738401 + 5.13569i 0.0239443 + 0.166536i
\(952\) 0 0
\(953\) −29.7913 25.8144i −0.965036 0.836209i 0.0214969 0.999769i \(-0.493157\pi\)
−0.986533 + 0.163560i \(0.947702\pi\)
\(954\) 0 0
\(955\) −57.3806 14.1581i −1.85679 0.458147i
\(956\) 0 0
\(957\) 4.62320 15.7452i 0.149447 0.508969i
\(958\) 0 0
\(959\) −18.3564 21.1844i −0.592760 0.684082i
\(960\) 0 0
\(961\) 27.4795 8.06870i 0.886434 0.260281i
\(962\) 0 0
\(963\) −34.3046 4.93226i −1.10545 0.158940i
\(964\) 0 0
\(965\) 15.8527 + 46.3895i 0.510318 + 1.49333i
\(966\) 0 0
\(967\) 1.22009i 0.0392356i 0.999808 + 0.0196178i \(0.00624494\pi\)
−0.999808 + 0.0196178i \(0.993755\pi\)
\(968\) 0 0
\(969\) 2.37583 16.5243i 0.0763227 0.530836i
\(970\) 0 0
\(971\) 57.9124 17.0046i 1.85850 0.545704i 0.859070 0.511858i \(-0.171043\pi\)
0.999427 0.0338457i \(-0.0107755\pi\)
\(972\) 0 0
\(973\) 21.7387 18.8367i 0.696912 0.603878i
\(974\) 0 0
\(975\) −7.88470 + 3.08525i −0.252512 + 0.0988069i
\(976\) 0 0
\(977\) 17.7715 27.6530i 0.568561 0.884699i −0.431285 0.902216i \(-0.641940\pi\)
0.999847 + 0.0175168i \(0.00557605\pi\)
\(978\) 0 0
\(979\) −23.0680 + 26.6219i −0.737257 + 0.850839i
\(980\) 0 0
\(981\) −4.01251 27.9076i −0.128110 0.891021i
\(982\) 0 0
\(983\) −39.2541 + 17.9267i −1.25201 + 0.571774i −0.927399 0.374073i \(-0.877961\pi\)
−0.324611 + 0.945847i \(0.605234\pi\)
\(984\) 0 0
\(985\) −51.6873 5.13953i −1.64689 0.163759i
\(986\) 0 0
\(987\) −5.99190 9.32357i −0.190724 0.296773i
\(988\) 0 0
\(989\) −16.2692 10.2473i −0.517331 0.325844i
\(990\) 0 0
\(991\) −5.07042 + 3.25856i −0.161067 + 0.103512i −0.618691 0.785634i \(-0.712337\pi\)
0.457624 + 0.889146i \(0.348701\pi\)
\(992\) 0 0
\(993\) 12.3052 + 5.61959i 0.390493 + 0.178332i
\(994\) 0 0
\(995\) −38.6680 40.8726i −1.22586 1.29575i
\(996\) 0 0
\(997\) 15.7560 2.26537i 0.498997 0.0717449i 0.111779 0.993733i \(-0.464345\pi\)
0.387218 + 0.921988i \(0.373436\pi\)
\(998\) 0 0
\(999\) 2.49959 2.88468i 0.0790835 0.0912672i
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 460.2.s.a.449.5 yes 120
5.4 even 2 inner 460.2.s.a.449.8 yes 120
23.2 even 11 inner 460.2.s.a.209.8 yes 120
115.94 even 22 inner 460.2.s.a.209.5 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.s.a.209.5 120 115.94 even 22 inner
460.2.s.a.209.8 yes 120 23.2 even 11 inner
460.2.s.a.449.5 yes 120 1.1 even 1 trivial
460.2.s.a.449.8 yes 120 5.4 even 2 inner