Properties

Label 700.2.r.d.149.3
Level $700$
Weight $2$
Character 700.149
Analytic conductor $5.590$
Analytic rank $0$
Dimension $12$
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] = [700,2,Mod(149,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.r (of order \(6\), degree \(2\), not 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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 149.3
Root \(-1.90412 - 1.09935i\) of defining polynomial
Character \(\chi\) \(=\) 700.149
Dual form 700.2.r.d.249.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.315621 + 0.182224i) q^{3} +(-1.58850 - 2.11581i) q^{7} +(-1.43359 + 2.48305i) q^{9} +O(q^{10})\) \(q+(-0.315621 + 0.182224i) q^{3} +(-1.58850 - 2.11581i) q^{7} +(-1.43359 + 2.48305i) q^{9} +(-0.682224 - 1.18165i) q^{11} -2.63555i q^{13} +(-1.93264 + 1.11581i) q^{17} +(-3.11581 + 5.39675i) q^{19} +(0.886917 + 0.378332i) q^{21} +(-5.71237 - 3.29804i) q^{23} -2.13828i q^{27} -5.50273 q^{29} +(-2.25136 - 3.89948i) q^{31} +(0.430649 + 0.248635i) q^{33} +(-1.81289 - 1.04667i) q^{37} +(0.480261 + 0.831836i) q^{39} +9.32497 q^{41} -1.86718i q^{43} +(-5.94715 - 3.43359i) q^{47} +(-1.95333 + 6.72194i) q^{49} +(0.406656 - 0.704349i) q^{51} +(-8.78001 + 5.06914i) q^{53} -2.27110i q^{57} +(-0.817776 - 1.41643i) q^{59} +(-0.0197391 + 0.0341891i) q^{61} +(7.53092 - 0.911120i) q^{63} +(5.82739 - 3.36445i) q^{67} +2.40393 q^{69} -6.27110 q^{71} +(-3.46410 + 2.00000i) q^{73} +(-1.41643 + 3.32051i) q^{77} +(2.66248 - 4.61156i) q^{79} +(-3.91112 - 6.77426i) q^{81} -14.7738i q^{83} +(1.73678 - 1.00273i) q^{87} +(0.433589 - 0.750998i) q^{89} +(-5.57633 + 4.18658i) q^{91} +(1.42116 + 0.820506i) q^{93} +16.0988i q^{97} +3.91211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 16 q^{9} - 8 q^{11} - 4 q^{19} - 22 q^{21} + 6 q^{31} - 28 q^{39} + 44 q^{41} - 24 q^{49} + 6 q^{51} - 10 q^{59} - 34 q^{61} + 96 q^{69} - 76 q^{71} - 2 q^{79} - 46 q^{81} - 28 q^{89} + 34 q^{91} - 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.315621 + 0.182224i −0.182224 + 0.105207i −0.588337 0.808616i \(-0.700217\pi\)
0.406113 + 0.913823i \(0.366884\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.58850 2.11581i −0.600397 0.799702i
\(8\) 0 0
\(9\) −1.43359 + 2.48305i −0.477863 + 0.827683i
\(10\) 0 0
\(11\) −0.682224 1.18165i −0.205698 0.356280i 0.744657 0.667448i \(-0.232613\pi\)
−0.950355 + 0.311168i \(0.899280\pi\)
\(12\) 0 0
\(13\) 2.63555i 0.730971i −0.930817 0.365485i \(-0.880903\pi\)
0.930817 0.365485i \(-0.119097\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.93264 + 1.11581i −0.468735 + 0.270624i −0.715710 0.698398i \(-0.753897\pi\)
0.246975 + 0.969022i \(0.420563\pi\)
\(18\) 0 0
\(19\) −3.11581 + 5.39675i −0.714816 + 1.23810i 0.248214 + 0.968705i \(0.420156\pi\)
−0.963030 + 0.269393i \(0.913177\pi\)
\(20\) 0 0
\(21\) 0.886917 + 0.378332i 0.193541 + 0.0825589i
\(22\) 0 0
\(23\) −5.71237 3.29804i −1.19111 0.687688i −0.232552 0.972584i \(-0.574708\pi\)
−0.958559 + 0.284896i \(0.908041\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.13828i 0.411512i
\(28\) 0 0
\(29\) −5.50273 −1.02183 −0.510916 0.859631i \(-0.670694\pi\)
−0.510916 + 0.859631i \(0.670694\pi\)
\(30\) 0 0
\(31\) −2.25136 3.89948i −0.404357 0.700367i 0.589889 0.807484i \(-0.299171\pi\)
−0.994246 + 0.107117i \(0.965838\pi\)
\(32\) 0 0
\(33\) 0.430649 + 0.248635i 0.0749663 + 0.0432818i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.81289 1.04667i −0.298037 0.172072i 0.343524 0.939144i \(-0.388379\pi\)
−0.641561 + 0.767072i \(0.721713\pi\)
\(38\) 0 0
\(39\) 0.480261 + 0.831836i 0.0769033 + 0.133200i
\(40\) 0 0
\(41\) 9.32497 1.45632 0.728158 0.685410i \(-0.240377\pi\)
0.728158 + 0.685410i \(0.240377\pi\)
\(42\) 0 0
\(43\) 1.86718i 0.284742i −0.989813 0.142371i \(-0.954527\pi\)
0.989813 0.142371i \(-0.0454726\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.94715 3.43359i −0.867481 0.500840i −0.000970685 1.00000i \(-0.500309\pi\)
−0.866510 + 0.499159i \(0.833642\pi\)
\(48\) 0 0
\(49\) −1.95333 + 6.72194i −0.279047 + 0.960277i
\(50\) 0 0
\(51\) 0.406656 0.704349i 0.0569432 0.0986285i
\(52\) 0 0
\(53\) −8.78001 + 5.06914i −1.20603 + 0.696300i −0.961889 0.273440i \(-0.911838\pi\)
−0.244138 + 0.969740i \(0.578505\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.27110i 0.300815i
\(58\) 0 0
\(59\) −0.817776 1.41643i −0.106465 0.184403i 0.807871 0.589360i \(-0.200620\pi\)
−0.914336 + 0.404956i \(0.867287\pi\)
\(60\) 0 0
\(61\) −0.0197391 + 0.0341891i −0.00252733 + 0.00437747i −0.867286 0.497810i \(-0.834138\pi\)
0.864759 + 0.502187i \(0.167471\pi\)
\(62\) 0 0
\(63\) 7.53092 0.911120i 0.948807 0.114790i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.82739 3.36445i 0.711930 0.411033i −0.0998455 0.995003i \(-0.531835\pi\)
0.811775 + 0.583970i \(0.198502\pi\)
\(68\) 0 0
\(69\) 2.40393 0.289399
\(70\) 0 0
\(71\) −6.27110 −0.744243 −0.372122 0.928184i \(-0.621370\pi\)
−0.372122 + 0.928184i \(0.621370\pi\)
\(72\) 0 0
\(73\) −3.46410 + 2.00000i −0.405442 + 0.234082i −0.688830 0.724923i \(-0.741875\pi\)
0.283387 + 0.959006i \(0.408542\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.41643 + 3.32051i −0.161417 + 0.378407i
\(78\) 0 0
\(79\) 2.66248 4.61156i 0.299553 0.518841i −0.676481 0.736460i \(-0.736496\pi\)
0.976034 + 0.217619i \(0.0698291\pi\)
\(80\) 0 0
\(81\) −3.91112 6.77426i −0.434569 0.752695i
\(82\) 0 0
\(83\) 14.7738i 1.62164i −0.585296 0.810819i \(-0.699022\pi\)
0.585296 0.810819i \(-0.300978\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.73678 1.00273i 0.186202 0.107504i
\(88\) 0 0
\(89\) 0.433589 0.750998i 0.0459603 0.0796056i −0.842130 0.539274i \(-0.818699\pi\)
0.888090 + 0.459669i \(0.152032\pi\)
\(90\) 0 0
\(91\) −5.57633 + 4.18658i −0.584559 + 0.438873i
\(92\) 0 0
\(93\) 1.42116 + 0.820506i 0.147367 + 0.0850825i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 16.0988i 1.63459i 0.576222 + 0.817293i \(0.304526\pi\)
−0.576222 + 0.817293i \(0.695474\pi\)
\(98\) 0 0
\(99\) 3.91211 0.393182
\(100\) 0 0
\(101\) 7.84744 + 13.5922i 0.780849 + 1.35247i 0.931448 + 0.363876i \(0.118547\pi\)
−0.150598 + 0.988595i \(0.548120\pi\)
\(102\) 0 0
\(103\) 11.5787 + 6.68495i 1.14088 + 0.658688i 0.946649 0.322267i \(-0.104445\pi\)
0.194233 + 0.980956i \(0.437778\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.67994 + 2.70196i 0.452427 + 0.261209i 0.708854 0.705355i \(-0.249212\pi\)
−0.256428 + 0.966563i \(0.582546\pi\)
\(108\) 0 0
\(109\) −7.91385 13.7072i −0.758009 1.31291i −0.943864 0.330333i \(-0.892839\pi\)
0.185855 0.982577i \(-0.440495\pi\)
\(110\) 0 0
\(111\) 0.762915 0.0724127
\(112\) 0 0
\(113\) 18.4238i 1.73316i 0.499036 + 0.866581i \(0.333688\pi\)
−0.499036 + 0.866581i \(0.666312\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 6.54420 + 3.77830i 0.605012 + 0.349304i
\(118\) 0 0
\(119\) 5.43086 + 2.31664i 0.497846 + 0.212366i
\(120\) 0 0
\(121\) 4.56914 7.91398i 0.415376 0.719453i
\(122\) 0 0
\(123\) −2.94316 + 1.69923i −0.265376 + 0.153215i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.32497i 0.472515i −0.971691 0.236257i \(-0.924079\pi\)
0.971691 0.236257i \(-0.0759208\pi\)
\(128\) 0 0
\(129\) 0.340245 + 0.589321i 0.0299569 + 0.0518868i
\(130\) 0 0
\(131\) −8.11854 + 14.0617i −0.709320 + 1.22858i 0.255789 + 0.966733i \(0.417665\pi\)
−0.965110 + 0.261846i \(0.915669\pi\)
\(132\) 0 0
\(133\) 16.3680 1.98026i 1.41928 0.171710i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.81864 + 2.20469i −0.326248 + 0.188360i −0.654174 0.756344i \(-0.726984\pi\)
0.327926 + 0.944703i \(0.393650\pi\)
\(138\) 0 0
\(139\) 22.3699 1.89739 0.948695 0.316192i \(-0.102404\pi\)
0.948695 + 0.316192i \(0.102404\pi\)
\(140\) 0 0
\(141\) 2.50273 0.210768
\(142\) 0 0
\(143\) −3.11429 + 1.79804i −0.260430 + 0.150359i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.608388 2.47753i −0.0501790 0.204343i
\(148\) 0 0
\(149\) 11.2541 19.4927i 0.921971 1.59690i 0.125610 0.992080i \(-0.459911\pi\)
0.796361 0.604822i \(-0.206756\pi\)
\(150\) 0 0
\(151\) −6.75136 11.6937i −0.549418 0.951620i −0.998314 0.0580365i \(-0.981516\pi\)
0.448896 0.893584i \(-0.351817\pi\)
\(152\) 0 0
\(153\) 6.39847i 0.517285i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 13.4724 7.77830i 1.07522 0.620776i 0.145613 0.989342i \(-0.453484\pi\)
0.929602 + 0.368566i \(0.120151\pi\)
\(158\) 0 0
\(159\) 1.84744 3.19986i 0.146511 0.253765i
\(160\) 0 0
\(161\) 2.09607 + 17.3252i 0.165194 + 1.36542i
\(162\) 0 0
\(163\) −3.81391 2.20196i −0.298729 0.172471i 0.343143 0.939283i \(-0.388508\pi\)
−0.641872 + 0.766812i \(0.721842\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.09880i 0.704087i 0.935984 + 0.352043i \(0.114513\pi\)
−0.935984 + 0.352043i \(0.885487\pi\)
\(168\) 0 0
\(169\) 6.05387 0.465682
\(170\) 0 0
\(171\) −8.93359 15.4734i −0.683169 1.18328i
\(172\) 0 0
\(173\) 17.2863 + 9.98026i 1.31425 + 0.758785i 0.982798 0.184685i \(-0.0591266\pi\)
0.331457 + 0.943470i \(0.392460\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.516215 + 0.298037i 0.0388011 + 0.0224018i
\(178\) 0 0
\(179\) −6.59607 11.4247i −0.493014 0.853925i 0.506954 0.861973i \(-0.330771\pi\)
−0.999968 + 0.00804839i \(0.997438\pi\)
\(180\) 0 0
\(181\) 10.2316 0.760511 0.380255 0.924882i \(-0.375836\pi\)
0.380255 + 0.924882i \(0.375836\pi\)
\(182\) 0 0
\(183\) 0.0143878i 0.00106357i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.63699 + 1.52247i 0.192836 + 0.111334i
\(188\) 0 0
\(189\) −4.52420 + 3.39666i −0.329087 + 0.247071i
\(190\) 0 0
\(191\) −7.00273 + 12.1291i −0.506700 + 0.877630i 0.493270 + 0.869876i \(0.335801\pi\)
−0.999970 + 0.00775353i \(0.997532\pi\)
\(192\) 0 0
\(193\) −12.4789 + 7.20469i −0.898250 + 0.518605i −0.876632 0.481161i \(-0.840215\pi\)
−0.0216183 + 0.999766i \(0.506882\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.5566i 0.823373i 0.911325 + 0.411687i \(0.135060\pi\)
−0.911325 + 0.411687i \(0.864940\pi\)
\(198\) 0 0
\(199\) −2.70469 4.68467i −0.191731 0.332087i 0.754093 0.656767i \(-0.228077\pi\)
−0.945824 + 0.324680i \(0.894743\pi\)
\(200\) 0 0
\(201\) −1.22617 + 2.12378i −0.0864871 + 0.149800i
\(202\) 0 0
\(203\) 8.74109 + 11.6427i 0.613504 + 0.817161i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 16.3784 9.45606i 1.13838 0.657241i
\(208\) 0 0
\(209\) 8.50273 0.588146
\(210\) 0 0
\(211\) −10.9660 −0.754929 −0.377465 0.926024i \(-0.623204\pi\)
−0.377465 + 0.926024i \(0.623204\pi\)
\(212\) 0 0
\(213\) 1.97929 1.14275i 0.135619 0.0782997i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −4.67427 + 10.9578i −0.317310 + 0.743863i
\(218\) 0 0
\(219\) 0.728896 1.26249i 0.0492542 0.0853108i
\(220\) 0 0
\(221\) 2.94078 + 5.09359i 0.197818 + 0.342632i
\(222\) 0 0
\(223\) 21.5566i 1.44354i −0.692135 0.721768i \(-0.743330\pi\)
0.692135 0.721768i \(-0.256670\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −10.7593 + 6.21189i −0.714120 + 0.412297i −0.812585 0.582843i \(-0.801940\pi\)
0.0984646 + 0.995141i \(0.468607\pi\)
\(228\) 0 0
\(229\) −4.18222 + 7.24382i −0.276369 + 0.478685i −0.970480 0.241183i \(-0.922465\pi\)
0.694110 + 0.719868i \(0.255798\pi\)
\(230\) 0 0
\(231\) −0.158021 1.30613i −0.0103970 0.0859370i
\(232\) 0 0
\(233\) −12.1291 7.00273i −0.794603 0.458764i 0.0469777 0.998896i \(-0.485041\pi\)
−0.841580 + 0.540132i \(0.818374\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.94067i 0.126060i
\(238\) 0 0
\(239\) −16.9605 −1.09708 −0.548542 0.836123i \(-0.684817\pi\)
−0.548542 + 0.836123i \(0.684817\pi\)
\(240\) 0 0
\(241\) −5.16521 8.94641i −0.332721 0.576289i 0.650324 0.759657i \(-0.274633\pi\)
−0.983044 + 0.183368i \(0.941300\pi\)
\(242\) 0 0
\(243\) 8.02428 + 4.63282i 0.514758 + 0.297196i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 14.2234 + 8.21189i 0.905014 + 0.522510i
\(248\) 0 0
\(249\) 2.69215 + 4.66294i 0.170608 + 0.295502i
\(250\) 0 0
\(251\) 19.5082 1.23135 0.615673 0.788002i \(-0.288884\pi\)
0.615673 + 0.788002i \(0.288884\pi\)
\(252\) 0 0
\(253\) 9.00000i 0.565825i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −24.6499 14.2316i −1.53762 0.887744i −0.998978 0.0452090i \(-0.985605\pi\)
−0.538641 0.842535i \(-0.681062\pi\)
\(258\) 0 0
\(259\) 0.665214 + 5.49837i 0.0413344 + 0.341652i
\(260\) 0 0
\(261\) 7.88865 13.6635i 0.488295 0.845752i
\(262\) 0 0
\(263\) −24.7355 + 14.2810i −1.52525 + 0.880606i −0.525702 + 0.850669i \(0.676197\pi\)
−0.999552 + 0.0299373i \(0.990469\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.316041i 0.0193414i
\(268\) 0 0
\(269\) −4.59880 7.96536i −0.280394 0.485657i 0.691088 0.722771i \(-0.257132\pi\)
−0.971482 + 0.237114i \(0.923798\pi\)
\(270\) 0 0
\(271\) −1.93086 + 3.34435i −0.117291 + 0.203155i −0.918693 0.394971i \(-0.870754\pi\)
0.801402 + 0.598126i \(0.204088\pi\)
\(272\) 0 0
\(273\) 0.997115 2.33752i 0.0603481 0.141473i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 9.21539 5.32051i 0.553699 0.319678i −0.196914 0.980421i \(-0.563092\pi\)
0.750613 + 0.660743i \(0.229759\pi\)
\(278\) 0 0
\(279\) 12.9101 0.772909
\(280\) 0 0
\(281\) 1.73436 0.103463 0.0517315 0.998661i \(-0.483526\pi\)
0.0517315 + 0.998661i \(0.483526\pi\)
\(282\) 0 0
\(283\) 5.12004 2.95606i 0.304355 0.175719i −0.340043 0.940410i \(-0.610442\pi\)
0.644398 + 0.764691i \(0.277108\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −14.8127 19.7299i −0.874368 1.16462i
\(288\) 0 0
\(289\) −6.00992 + 10.4095i −0.353525 + 0.612323i
\(290\) 0 0
\(291\) −2.93359 5.08112i −0.171970 0.297861i
\(292\) 0 0
\(293\) 24.3250i 1.42108i −0.703657 0.710540i \(-0.748451\pi\)
0.703657 0.710540i \(-0.251549\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2.52669 + 1.45879i −0.146614 + 0.0846474i
\(298\) 0 0
\(299\) −8.69215 + 15.0552i −0.502680 + 0.870667i
\(300\) 0 0
\(301\) −3.95060 + 2.96601i −0.227709 + 0.170958i
\(302\) 0 0
\(303\) −4.95364 2.85998i −0.284579 0.164302i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 23.5226i 1.34250i −0.741229 0.671252i \(-0.765757\pi\)
0.741229 0.671252i \(-0.234243\pi\)
\(308\) 0 0
\(309\) −4.87264 −0.277195
\(310\) 0 0
\(311\) 4.40939 + 7.63728i 0.250033 + 0.433070i 0.963535 0.267583i \(-0.0862251\pi\)
−0.713501 + 0.700654i \(0.752892\pi\)
\(312\) 0 0
\(313\) −0.0808384 0.0466721i −0.00456926 0.00263806i 0.497714 0.867341i \(-0.334173\pi\)
−0.502283 + 0.864703i \(0.667506\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.06764 1.77110i −0.172296 0.0994751i 0.411372 0.911468i \(-0.365050\pi\)
−0.583668 + 0.811992i \(0.698383\pi\)
\(318\) 0 0
\(319\) 3.75409 + 6.50228i 0.210189 + 0.364058i
\(320\) 0 0
\(321\) −1.96945 −0.109924
\(322\) 0 0
\(323\) 13.9067i 0.773787i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 4.99556 + 2.88419i 0.276255 + 0.159496i
\(328\) 0 0
\(329\) 2.18222 + 18.0373i 0.120310 + 0.994429i
\(330\) 0 0
\(331\) 9.82497 17.0173i 0.540029 0.935358i −0.458872 0.888502i \(-0.651747\pi\)
0.998902 0.0468558i \(-0.0149201\pi\)
\(332\) 0 0
\(333\) 5.19788 3.00099i 0.284842 0.164454i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 23.0449i 1.25534i −0.778480 0.627669i \(-0.784009\pi\)
0.778480 0.627669i \(-0.215991\pi\)
\(338\) 0 0
\(339\) −3.35725 5.81493i −0.182341 0.315824i
\(340\) 0 0
\(341\) −3.07187 + 5.32064i −0.166351 + 0.288129i
\(342\) 0 0
\(343\) 17.3252 6.54494i 0.935475 0.353393i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −19.5393 + 11.2810i −1.04893 + 0.605597i −0.922348 0.386360i \(-0.873732\pi\)
−0.126577 + 0.991957i \(0.540399\pi\)
\(348\) 0 0
\(349\) −14.3250 −0.766798 −0.383399 0.923583i \(-0.625247\pi\)
−0.383399 + 0.923583i \(0.625247\pi\)
\(350\) 0 0
\(351\) −5.63555 −0.300804
\(352\) 0 0
\(353\) −28.3193 + 16.3502i −1.50729 + 0.870232i −0.507321 + 0.861757i \(0.669364\pi\)
−0.999964 + 0.00847467i \(0.997302\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.13624 + 0.258451i −0.113062 + 0.0136787i
\(358\) 0 0
\(359\) −13.0791 + 22.6536i −0.690287 + 1.19561i 0.281457 + 0.959574i \(0.409182\pi\)
−0.971744 + 0.236038i \(0.924151\pi\)
\(360\) 0 0
\(361\) −9.91658 17.1760i −0.521925 0.904001i
\(362\) 0 0
\(363\) 3.33043i 0.174802i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −21.8512 + 12.6158i −1.14062 + 0.658540i −0.946585 0.322454i \(-0.895492\pi\)
−0.194040 + 0.980994i \(0.562159\pi\)
\(368\) 0 0
\(369\) −13.3682 + 23.1544i −0.695919 + 1.20537i
\(370\) 0 0
\(371\) 24.6724 + 10.5245i 1.28093 + 0.546406i
\(372\) 0 0
\(373\) −4.93191 2.84744i −0.255365 0.147435i 0.366854 0.930279i \(-0.380435\pi\)
−0.622218 + 0.782844i \(0.713768\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 14.5027i 0.746929i
\(378\) 0 0
\(379\) −14.9660 −0.768751 −0.384375 0.923177i \(-0.625583\pi\)
−0.384375 + 0.923177i \(0.625583\pi\)
\(380\) 0 0
\(381\) 0.970337 + 1.68067i 0.0497119 + 0.0861035i
\(382\) 0 0
\(383\) −21.1983 12.2388i −1.08318 0.625374i −0.151428 0.988468i \(-0.548387\pi\)
−0.931753 + 0.363094i \(0.881720\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.63629 + 2.67676i 0.235676 + 0.136068i
\(388\) 0 0
\(389\) −15.6230 27.0598i −0.792118 1.37199i −0.924653 0.380810i \(-0.875645\pi\)
0.132535 0.991178i \(-0.457688\pi\)
\(390\) 0 0
\(391\) 14.7200 0.744421
\(392\) 0 0
\(393\) 5.91757i 0.298502i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.981053 + 0.566411i 0.0492376 + 0.0284274i 0.524417 0.851462i \(-0.324283\pi\)
−0.475179 + 0.879889i \(0.657617\pi\)
\(398\) 0 0
\(399\) −4.80523 + 3.60765i −0.240562 + 0.180608i
\(400\) 0 0
\(401\) 1.91112 3.31016i 0.0954368 0.165301i −0.814354 0.580368i \(-0.802909\pi\)
0.909791 + 0.415067i \(0.136242\pi\)
\(402\) 0 0
\(403\) −10.2773 + 5.93359i −0.511948 + 0.295573i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.85626i 0.141580i
\(408\) 0 0
\(409\) 16.8304 + 29.1512i 0.832211 + 1.44143i 0.896281 + 0.443487i \(0.146259\pi\)
−0.0640699 + 0.997945i \(0.520408\pi\)
\(410\) 0 0
\(411\) 0.803496 1.39170i 0.0396335 0.0686473i
\(412\) 0 0
\(413\) −1.69786 + 3.98026i −0.0835463 + 0.195856i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.06042 + 4.07633i −0.345750 + 0.199619i
\(418\) 0 0
\(419\) 0.497270 0.0242933 0.0121466 0.999926i \(-0.496134\pi\)
0.0121466 + 0.999926i \(0.496134\pi\)
\(420\) 0 0
\(421\) −1.28003 −0.0623850 −0.0311925 0.999513i \(-0.509930\pi\)
−0.0311925 + 0.999513i \(0.509930\pi\)
\(422\) 0 0
\(423\) 17.0515 9.84471i 0.829074 0.478666i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.103693 0.0125452i 0.00501808 0.000607106i
\(428\) 0 0
\(429\) 0.655291 1.13500i 0.0316377 0.0547982i
\(430\) 0 0
\(431\) 5.14548 + 8.91222i 0.247849 + 0.429287i 0.962929 0.269756i \(-0.0869430\pi\)
−0.715080 + 0.699043i \(0.753610\pi\)
\(432\) 0 0
\(433\) 29.8870i 1.43628i −0.695899 0.718139i \(-0.744994\pi\)
0.695899 0.718139i \(-0.255006\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 35.5973 20.5521i 1.70285 0.983142i
\(438\) 0 0
\(439\) −2.52420 + 4.37205i −0.120474 + 0.208666i −0.919955 0.392025i \(-0.871775\pi\)
0.799481 + 0.600692i \(0.205108\pi\)
\(440\) 0 0
\(441\) −13.8906 14.4867i −0.661459 0.689843i
\(442\) 0 0
\(443\) −10.1964 5.88692i −0.484447 0.279696i 0.237821 0.971309i \(-0.423567\pi\)
−0.722268 + 0.691613i \(0.756900\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 8.20307i 0.387992i
\(448\) 0 0
\(449\) 11.3843 0.537258 0.268629 0.963244i \(-0.413429\pi\)
0.268629 + 0.963244i \(0.413429\pi\)
\(450\) 0 0
\(451\) −6.36172 11.0188i −0.299562 0.518856i
\(452\) 0 0
\(453\) 4.26175 + 2.46052i 0.200234 + 0.115605i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −32.2607 18.6257i −1.50909 0.871275i −0.999944 0.0105968i \(-0.996627\pi\)
−0.509149 0.860678i \(-0.670040\pi\)
\(458\) 0 0
\(459\) 2.38592 + 4.13254i 0.111365 + 0.192890i
\(460\) 0 0
\(461\) −15.0449 −0.700713 −0.350356 0.936616i \(-0.613939\pi\)
−0.350356 + 0.936616i \(0.613939\pi\)
\(462\) 0 0
\(463\) 31.2031i 1.45013i 0.688681 + 0.725065i \(0.258190\pi\)
−0.688681 + 0.725065i \(0.741810\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.2539 9.38419i −0.752140 0.434248i 0.0743264 0.997234i \(-0.476319\pi\)
−0.826467 + 0.562986i \(0.809653\pi\)
\(468\) 0 0
\(469\) −16.3754 6.98525i −0.756144 0.322549i
\(470\) 0 0
\(471\) −2.83479 + 4.90999i −0.130620 + 0.226241i
\(472\) 0 0
\(473\) −2.20634 + 1.27383i −0.101448 + 0.0585709i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 29.0683i 1.33094i
\(478\) 0 0
\(479\) −0.357254 0.618782i −0.0163234 0.0282729i 0.857748 0.514070i \(-0.171863\pi\)
−0.874072 + 0.485797i \(0.838529\pi\)
\(480\) 0 0
\(481\) −2.75856 + 4.77796i −0.125779 + 0.217856i
\(482\) 0 0
\(483\) −3.81864 5.08626i −0.173754 0.231433i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 14.4582 8.34744i 0.655163 0.378259i −0.135268 0.990809i \(-0.543190\pi\)
0.790432 + 0.612550i \(0.209856\pi\)
\(488\) 0 0
\(489\) 1.60500 0.0725807
\(490\) 0 0
\(491\) 6.19761 0.279694 0.139847 0.990173i \(-0.455339\pi\)
0.139847 + 0.990173i \(0.455339\pi\)
\(492\) 0 0
\(493\) 10.6348 6.14002i 0.478968 0.276532i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9.96166 + 13.2685i 0.446841 + 0.595173i
\(498\) 0 0
\(499\) 7.23436 12.5303i 0.323854 0.560932i −0.657426 0.753519i \(-0.728355\pi\)
0.981280 + 0.192588i \(0.0616879\pi\)
\(500\) 0 0
\(501\) −1.65802 2.87178i −0.0740749 0.128301i
\(502\) 0 0
\(503\) 30.6949i 1.36862i 0.729193 + 0.684308i \(0.239896\pi\)
−0.729193 + 0.684308i \(0.760104\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.91073 + 1.10316i −0.0848585 + 0.0489930i
\(508\) 0 0
\(509\) 22.2371 38.5158i 0.985641 1.70718i 0.346591 0.938016i \(-0.387339\pi\)
0.639051 0.769165i \(-0.279327\pi\)
\(510\) 0 0
\(511\) 9.73436 + 4.15239i 0.430623 + 0.183691i
\(512\) 0 0
\(513\) 11.5398 + 6.66248i 0.509493 + 0.294156i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 9.36991i 0.412088i
\(518\) 0 0
\(519\) −7.27457 −0.319318
\(520\) 0 0
\(521\) 6.32497 + 10.9552i 0.277102 + 0.479955i 0.970663 0.240443i \(-0.0772927\pi\)
−0.693561 + 0.720398i \(0.743959\pi\)
\(522\) 0 0
\(523\) 8.89504 + 5.13555i 0.388953 + 0.224562i 0.681706 0.731626i \(-0.261238\pi\)
−0.292753 + 0.956188i \(0.594572\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.70218 + 5.02420i 0.379073 + 0.218858i
\(528\) 0 0
\(529\) 10.2541 + 17.7606i 0.445830 + 0.772201i
\(530\) 0 0
\(531\) 4.68942 0.203503
\(532\) 0 0
\(533\) 24.5764i 1.06452i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.16372 + 2.40393i 0.179678 + 0.103737i
\(538\) 0 0
\(539\) 9.27557 2.27773i 0.399527 0.0981087i
\(540\) 0 0
\(541\) 1.06914 1.85181i 0.0459660 0.0796154i −0.842127 0.539279i \(-0.818697\pi\)
0.888093 + 0.459664i \(0.152030\pi\)
\(542\) 0 0
\(543\) −3.22932 + 1.86445i −0.138583 + 0.0800111i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 32.0198i 1.36907i 0.728980 + 0.684535i \(0.239995\pi\)
−0.728980 + 0.684535i \(0.760005\pi\)
\(548\) 0 0
\(549\) −0.0565955 0.0980263i −0.00241544 0.00418366i
\(550\) 0 0
\(551\) 17.1455 29.6968i 0.730422 1.26513i
\(552\) 0 0
\(553\) −13.9866 + 1.69215i −0.594769 + 0.0719574i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.21436 4.16521i 0.305682 0.176486i −0.339310 0.940674i \(-0.610194\pi\)
0.644993 + 0.764189i \(0.276860\pi\)
\(558\) 0 0
\(559\) −4.92104 −0.208138
\(560\) 0 0
\(561\) −1.10972 −0.0468525
\(562\) 0 0
\(563\) −16.8557 + 9.73163i −0.710382 + 0.410139i −0.811202 0.584766i \(-0.801187\pi\)
0.100821 + 0.994905i \(0.467853\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −8.12024 + 19.0361i −0.341018 + 0.799442i
\(568\) 0 0
\(569\) 9.44624 16.3614i 0.396007 0.685904i −0.597222 0.802076i \(-0.703729\pi\)
0.993229 + 0.116172i \(0.0370622\pi\)
\(570\) 0 0
\(571\) 9.31505 + 16.1341i 0.389823 + 0.675192i 0.992425 0.122849i \(-0.0392030\pi\)
−0.602603 + 0.798041i \(0.705870\pi\)
\(572\) 0 0
\(573\) 5.10426i 0.213234i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 16.1017 9.29630i 0.670321 0.387010i −0.125877 0.992046i \(-0.540175\pi\)
0.796198 + 0.605036i \(0.206841\pi\)
\(578\) 0 0
\(579\) 2.62574 4.54791i 0.109122 0.189005i
\(580\) 0 0
\(581\) −31.2587 + 23.4683i −1.29683 + 0.973627i
\(582\) 0 0
\(583\) 11.9799 + 6.91658i 0.496155 + 0.286455i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10.1383i 0.418452i −0.977867 0.209226i \(-0.932906\pi\)
0.977867 0.209226i \(-0.0670944\pi\)
\(588\) 0 0
\(589\) 28.0593 1.15616
\(590\) 0 0
\(591\) −2.10589 3.64751i −0.0866247 0.150038i
\(592\) 0 0
\(593\) 14.7272 + 8.50273i 0.604772 + 0.349165i 0.770917 0.636936i \(-0.219799\pi\)
−0.166145 + 0.986101i \(0.553132\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.70732 + 0.985720i 0.0698758 + 0.0403428i
\(598\) 0 0
\(599\) −4.09334 7.08988i −0.167250 0.289685i 0.770202 0.637800i \(-0.220155\pi\)
−0.937452 + 0.348115i \(0.886822\pi\)
\(600\) 0 0
\(601\) −35.3359 −1.44138 −0.720690 0.693257i \(-0.756175\pi\)
−0.720690 + 0.693257i \(0.756175\pi\)
\(602\) 0 0
\(603\) 19.2929i 0.785669i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 24.4493 + 14.1158i 0.992367 + 0.572943i 0.905981 0.423319i \(-0.139135\pi\)
0.0863858 + 0.996262i \(0.472468\pi\)
\(608\) 0 0
\(609\) −4.88046 2.08186i −0.197766 0.0843613i
\(610\) 0 0
\(611\) −9.04940 + 15.6740i −0.366100 + 0.634103i
\(612\) 0 0
\(613\) 26.9837 15.5791i 1.08986 0.629232i 0.156323 0.987706i \(-0.450036\pi\)
0.933540 + 0.358474i \(0.116703\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 39.1527i 1.57623i 0.615530 + 0.788114i \(0.288942\pi\)
−0.615530 + 0.788114i \(0.711058\pi\)
\(618\) 0 0
\(619\) −19.6921 34.1078i −0.791494 1.37091i −0.925042 0.379866i \(-0.875970\pi\)
0.133547 0.991042i \(-0.457363\pi\)
\(620\) 0 0
\(621\) −7.05213 + 12.2146i −0.282992 + 0.490157i
\(622\) 0 0
\(623\) −2.27773 + 0.275568i −0.0912552 + 0.0110404i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.68364 + 1.54940i −0.107174 + 0.0618771i
\(628\) 0 0
\(629\) 4.67156 0.186267
\(630\) 0 0
\(631\) 22.7003 0.903686 0.451843 0.892097i \(-0.350767\pi\)
0.451843 + 0.892097i \(0.350767\pi\)
\(632\) 0 0
\(633\) 3.46110 1.99827i 0.137566 0.0794239i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 17.7160 + 5.14810i 0.701935 + 0.203975i
\(638\) 0 0
\(639\) 8.99018 15.5715i 0.355646 0.615997i
\(640\) 0 0
\(641\) −4.20643 7.28575i −0.166144 0.287770i 0.770917 0.636936i \(-0.219798\pi\)
−0.937061 + 0.349166i \(0.886465\pi\)
\(642\) 0 0
\(643\) 29.7398i 1.17282i 0.810013 + 0.586412i \(0.199460\pi\)
−0.810013 + 0.586412i \(0.800540\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.7806 + 10.8430i −0.738341 + 0.426281i −0.821466 0.570258i \(-0.806843\pi\)
0.0831249 + 0.996539i \(0.473510\pi\)
\(648\) 0 0
\(649\) −1.11581 + 1.93264i −0.0437995 + 0.0758629i
\(650\) 0 0
\(651\) −0.521474 4.31028i −0.0204382 0.168933i
\(652\) 0 0
\(653\) 26.0416 + 15.0351i 1.01909 + 0.588370i 0.913839 0.406076i \(-0.133103\pi\)
0.105247 + 0.994446i \(0.466437\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 11.4687i 0.447437i
\(658\) 0 0
\(659\) −2.37537 −0.0925311 −0.0462656 0.998929i \(-0.514732\pi\)
−0.0462656 + 0.998929i \(0.514732\pi\)
\(660\) 0 0
\(661\) 7.23163 + 12.5255i 0.281278 + 0.487187i 0.971700 0.236220i \(-0.0759085\pi\)
−0.690422 + 0.723407i \(0.742575\pi\)
\(662\) 0 0
\(663\) −1.85635 1.07176i −0.0720946 0.0416238i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 31.4336 + 18.1482i 1.21711 + 0.702701i
\(668\) 0 0
\(669\) 3.92813 + 6.80372i 0.151870 + 0.263047i
\(670\) 0 0
\(671\) 0.0538660 0.00207947
\(672\) 0 0
\(673\) 8.99653i 0.346791i −0.984852 0.173395i \(-0.944526\pi\)
0.984852 0.173395i \(-0.0554738\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.48810 3.74591i −0.249358 0.143967i 0.370112 0.928987i \(-0.379319\pi\)
−0.619470 + 0.785020i \(0.712653\pi\)
\(678\) 0 0
\(679\) 34.0621 25.5730i 1.30718 0.981400i
\(680\) 0 0
\(681\) 2.26391 3.92121i 0.0867532 0.150261i
\(682\) 0 0
\(683\) 36.6545 21.1625i 1.40255 0.809760i 0.407892 0.913030i \(-0.366264\pi\)
0.994653 + 0.103270i \(0.0329306\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 3.04841i 0.116304i
\(688\) 0 0
\(689\) 13.3600 + 23.1402i 0.508975 + 0.881570i
\(690\) 0 0
\(691\) −14.3232 + 24.8086i −0.544882 + 0.943763i 0.453733 + 0.891138i \(0.350092\pi\)
−0.998614 + 0.0526247i \(0.983241\pi\)
\(692\) 0 0
\(693\) −6.21440 8.27730i −0.236066 0.314429i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −18.0219 + 10.4049i −0.682626 + 0.394114i
\(698\) 0 0
\(699\) 5.10426 0.193061
\(700\) 0 0
\(701\) −20.4292 −0.771601 −0.385801 0.922582i \(-0.626075\pi\)
−0.385801 + 0.922582i \(0.626075\pi\)
\(702\) 0 0
\(703\) 11.2972 6.52247i 0.426084 0.246000i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16.2928 38.1949i 0.612754 1.43647i
\(708\) 0 0
\(709\) 14.4138 24.9655i 0.541323 0.937600i −0.457505 0.889207i \(-0.651257\pi\)
0.998828 0.0483927i \(-0.0154099\pi\)
\(710\) 0 0
\(711\) 7.63382 + 13.2222i 0.286291 + 0.495870i
\(712\) 0 0
\(713\) 29.7003i 1.11229i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 5.35310 3.09061i 0.199915 0.115421i
\(718\) 0 0
\(719\) 15.6553 27.1158i 0.583844 1.01125i −0.411175 0.911557i \(-0.634881\pi\)
0.995018 0.0996906i \(-0.0317853\pi\)
\(720\) 0 0
\(721\) −4.24864 35.1174i −0.158227 1.30784i
\(722\) 0 0
\(723\) 3.26050 + 1.88245i 0.121259 + 0.0700092i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 8.17230i 0.303094i −0.988450 0.151547i \(-0.951575\pi\)
0.988450 0.151547i \(-0.0484255\pi\)
\(728\) 0 0
\(729\) 20.0899 0.744069
\(730\) 0 0
\(731\) 2.08342 + 3.60859i 0.0770581 + 0.133469i
\(732\) 0 0
\(733\) −18.5488 10.7092i −0.685116 0.395552i 0.116664 0.993171i \(-0.462780\pi\)
−0.801780 + 0.597620i \(0.796113\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.95118 4.59061i −0.292885 0.169097i
\(738\) 0 0
\(739\) 2.17503 + 3.76726i 0.0800098 + 0.138581i 0.903254 0.429107i \(-0.141172\pi\)
−0.823244 + 0.567688i \(0.807838\pi\)
\(740\) 0 0
\(741\) −5.98561 −0.219887
\(742\) 0 0
\(743\) 6.53328i 0.239683i −0.992793 0.119841i \(-0.961761\pi\)
0.992793 0.119841i \(-0.0382386\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 36.6841 + 21.1796i 1.34220 + 0.774921i
\(748\) 0 0
\(749\) −1.71724 14.1939i −0.0627465 0.518635i
\(750\) 0 0
\(751\) −17.2415 + 29.8632i −0.629153 + 1.08973i 0.358569 + 0.933503i \(0.383265\pi\)
−0.987722 + 0.156222i \(0.950069\pi\)
\(752\) 0 0
\(753\) −6.15720 + 3.55486i −0.224381 + 0.129546i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 44.2425i 1.60802i −0.594614 0.804011i \(-0.702695\pi\)
0.594614 0.804011i \(-0.297305\pi\)
\(758\) 0 0
\(759\) −1.64002 2.84059i −0.0595288 0.103107i
\(760\) 0 0
\(761\) 11.9094 20.6277i 0.431715 0.747752i −0.565306 0.824881i \(-0.691242\pi\)
0.997021 + 0.0771290i \(0.0245753\pi\)
\(762\) 0 0
\(763\) −16.4307 + 38.5181i −0.594831 + 1.39445i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.73307 + 2.15529i −0.134793 + 0.0778230i
\(768\) 0 0
\(769\) 0.158128 0.00570225 0.00285113 0.999996i \(-0.499092\pi\)
0.00285113 + 0.999996i \(0.499092\pi\)
\(770\) 0 0
\(771\) 10.3734 0.373588
\(772\) 0 0
\(773\) 15.4145 8.89957i 0.554421 0.320095i −0.196482 0.980507i \(-0.562952\pi\)
0.750903 + 0.660412i \(0.229618\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.21189 1.61419i −0.0434764 0.0579086i
\(778\) 0 0
\(779\) −29.0549 + 50.3245i −1.04100 + 1.80306i
\(780\) 0 0
\(781\) 4.27830 + 7.41023i 0.153090 + 0.265159i
\(782\) 0 0
\(783\) 11.7664i 0.420496i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −35.9596 + 20.7613i −1.28182 + 0.740060i −0.977181 0.212407i \(-0.931870\pi\)
−0.304640 + 0.952467i \(0.598536\pi\)
\(788\) 0 0
\(789\) 5.20469 9.01479i 0.185292 0.320935i
\(790\) 0 0
\(791\) 38.9813 29.2662i 1.38601 1.04059i
\(792\) 0 0
\(793\) 0.0901072 + 0.0520234i 0.00319980 + 0.00184741i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 25.0933i 0.888852i 0.895816 + 0.444426i \(0.146592\pi\)
−0.895816 + 0.444426i \(0.853408\pi\)
\(798\) 0 0
\(799\) 15.3250 0.542158
\(800\) 0 0
\(801\) 1.24318 + 2.15324i 0.0439255 + 0.0760811i
\(802\) 0 0
\(803\) 4.72659 + 2.72890i 0.166798 + 0.0963007i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.90296 + 1.67602i 0.102189 + 0.0589989i
\(808\) 0 0
\(809\) 6.34744 + 10.9941i 0.223164 + 0.386531i 0.955767 0.294125i \(-0.0950281\pi\)
−0.732603 + 0.680656i \(0.761695\pi\)
\(810\) 0 0
\(811\) 17.9749 0.631184 0.315592 0.948895i \(-0.397797\pi\)
0.315592 + 0.948895i \(0.397797\pi\)
\(812\) 0 0
\(813\) 1.40740i 0.0493595i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 10.0767 + 5.81778i 0.352539 + 0.203538i
\(818\) 0 0
\(819\) −2.40130 19.8481i −0.0839084 0.693550i
\(820\) 0 0
\(821\) −10.0341 + 17.3796i −0.350193 + 0.606553i −0.986283 0.165062i \(-0.947217\pi\)
0.636090 + 0.771615i \(0.280551\pi\)
\(822\) 0 0
\(823\) 9.18893 5.30523i 0.320306 0.184929i −0.331223 0.943553i \(-0.607461\pi\)
0.651529 + 0.758624i \(0.274128\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 34.7793i 1.20939i 0.796455 + 0.604697i \(0.206706\pi\)
−0.796455 + 0.604697i \(0.793294\pi\)
\(828\) 0 0
\(829\) −13.1141 22.7142i −0.455471 0.788898i 0.543244 0.839575i \(-0.317196\pi\)
−0.998715 + 0.0506761i \(0.983862\pi\)
\(830\) 0 0
\(831\) −1.93905 + 3.35853i −0.0672648 + 0.116506i
\(832\) 0 0
\(833\) −3.72534 15.1707i −0.129075 0.525633i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −8.33818 + 4.81405i −0.288210 + 0.166398i
\(838\) 0 0
\(839\) −33.9210 −1.17108 −0.585542 0.810642i \(-0.699118\pi\)
−0.585542 + 0.810642i \(0.699118\pi\)
\(840\) 0 0
\(841\) 1.28003 0.0441391
\(842\) 0 0
\(843\) −0.547399 + 0.316041i −0.0188534 + 0.0108850i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −24.0026 + 2.90393i −0.824739 + 0.0997801i
\(848\) 0 0
\(849\) −1.07733 + 1.86599i −0.0369738 + 0.0640406i
\(850\) 0 0
\(851\) 6.90393 + 11.9580i 0.236664 + 0.409913i
\(852\) 0 0
\(853\) 57.6698i 1.97458i 0.158942 + 0.987288i \(0.449192\pi\)
−0.158942 + 0.987288i \(0.550808\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 30.6607 17.7020i 1.04735 0.604688i 0.125443 0.992101i \(-0.459965\pi\)
0.921906 + 0.387413i \(0.126631\pi\)
\(858\) 0 0
\(859\) −6.72170 + 11.6423i −0.229342 + 0.397231i −0.957613 0.288057i \(-0.906991\pi\)
0.728272 + 0.685289i \(0.240324\pi\)
\(860\) 0 0
\(861\) 8.27047 + 3.52794i 0.281857 + 0.120232i
\(862\) 0 0
\(863\) −6.11828 3.53239i −0.208269 0.120244i 0.392238 0.919864i \(-0.371701\pi\)
−0.600507 + 0.799620i \(0.705034\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 4.38061i 0.148773i
\(868\) 0 0
\(869\) −7.26564 −0.246470
\(870\) 0 0
\(871\) −8.86718 15.3584i −0.300453 0.520400i
\(872\) 0 0
\(873\) −39.9741 23.0791i −1.35292 0.781108i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −12.9951 7.50273i −0.438814 0.253349i 0.264281 0.964446i \(-0.414865\pi\)
−0.703094 + 0.711097i \(0.748199\pi\)
\(878\) 0 0
\(879\) 4.43259 + 7.67748i 0.149508 + 0.258955i
\(880\) 0 0
\(881\) −39.3699 −1.32641 −0.663203 0.748440i \(-0.730803\pi\)
−0.663203 + 0.748440i \(0.730803\pi\)
\(882\) 0 0
\(883\) 58.2229i 1.95936i −0.200574 0.979679i \(-0.564281\pi\)
0.200574 0.979679i \(-0.435719\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −21.8637 12.6230i −0.734111 0.423839i 0.0858133 0.996311i \(-0.472651\pi\)
−0.819924 + 0.572472i \(0.805984\pi\)
\(888\) 0 0
\(889\) −11.2666 + 8.45872i −0.377871 + 0.283696i
\(890\) 0 0
\(891\) −5.33652 + 9.24312i −0.178780 + 0.309656i
\(892\) 0 0
\(893\) 37.0604 21.3968i 1.24018 0.716018i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 6.33567i 0.211542i
\(898\) 0 0
\(899\) 12.3887 + 21.4578i 0.413185 + 0.715657i
\(900\) 0 0
\(901\) 11.3124 19.5937i 0.376872 0.652761i
\(902\) 0 0
\(903\) 0.706414 1.65603i 0.0235080 0.0551093i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 23.5444 13.5933i 0.781778 0.451360i −0.0552822 0.998471i \(-0.517606\pi\)
0.837060 + 0.547111i \(0.184273\pi\)
\(908\) 0 0
\(909\) −45.0000 −1.49256
\(910\) 0 0
\(911\) −40.7882 −1.35137 −0.675687 0.737189i \(-0.736153\pi\)
−0.675687 + 0.737189i \(0.736153\pi\)
\(912\) 0 0
\(913\) −17.4575 + 10.0791i −0.577757 + 0.333568i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 42.6483 5.15976i 1.40837 0.170390i
\(918\) 0 0
\(919\) −23.5369 + 40.7670i −0.776409 + 1.34478i 0.157590 + 0.987505i \(0.449628\pi\)
−0.933999 + 0.357276i \(0.883706\pi\)
\(920\) 0 0
\(921\) 4.28638 + 7.42423i 0.141241 + 0.244637i
\(922\) 0 0
\(923\) 16.5278i 0.544020i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −33.1981 + 19.1669i −1.09037 + 0.629525i
\(928\) 0 0
\(929\) 8.99554 15.5807i 0.295134 0.511187i −0.679882 0.733321i \(-0.737969\pi\)
0.975016 + 0.222134i \(0.0713024\pi\)
\(930\) 0 0
\(931\) −30.1904 31.4859i −0.989451 1.03191i
\(932\) 0 0
\(933\) −2.78339 1.60699i −0.0911242 0.0526106i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 37.7003i 1.23162i −0.787896 0.615808i \(-0.788830\pi\)
0.787896 0.615808i \(-0.211170\pi\)
\(938\) 0 0
\(939\) 0.0340191 0.00111017
\(940\) 0 0
\(941\) −2.41658 4.18564i −0.0787782 0.136448i 0.823945 0.566670i \(-0.191769\pi\)
−0.902723 + 0.430222i \(0.858435\pi\)
\(942\) 0 0
\(943\) −53.2677 30.7541i −1.73463 1.00149i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.45659 1.41831i −0.0798285 0.0460890i 0.459554 0.888150i \(-0.348009\pi\)
−0.539383 + 0.842061i \(0.681342\pi\)
\(948\) 0 0
\(949\) 5.27110 + 9.12982i 0.171107 + 0.296366i
\(950\) 0 0
\(951\) 1.29095 0.0418619
\(952\) 0 0
\(953\) 17.7991i 0.576571i 0.957545 + 0.288285i \(0.0930852\pi\)
−0.957545 + 0.288285i \(0.906915\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −2.36974 1.36817i −0.0766029 0.0442267i
\(958\) 0 0
\(959\) 10.7306 + 4.57737i 0.346510 + 0.147811i
\(960\) 0 0
\(961\) 5.36271 9.28849i 0.172991 0.299629i
\(962\) 0 0
\(963\) −13.4182 + 7.74701i −0.432396 + 0.249644i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 15.1581i 0.487453i 0.969844 + 0.243726i \(0.0783698\pi\)
−0.969844 + 0.243726i \(0.921630\pi\)
\(968\) 0 0
\(969\) 2.53413 + 4.38924i 0.0814079 + 0.141003i
\(970\) 0 0
\(971\) 23.6921 41.0360i 0.760317 1.31691i −0.182370 0.983230i \(-0.558377\pi\)
0.942687 0.333678i \(-0.108290\pi\)
\(972\) 0 0
\(973\) −35.5346 47.3305i −1.13919 1.51735i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −20.5421 + 11.8600i −0.657200 + 0.379434i −0.791209 0.611546i \(-0.790548\pi\)
0.134009 + 0.990980i \(0.457215\pi\)
\(978\) 0 0
\(979\) −1.18322 −0.0378158
\(980\) 0 0
\(981\) 45.3808 1.44890
\(982\) 0 0
\(983\) 29.8383 17.2272i 0.951695 0.549461i 0.0580876 0.998311i \(-0.481500\pi\)
0.893607 + 0.448850i \(0.148166\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −3.97559 5.29531i −0.126544 0.168551i
\(988\) 0 0
\(989\) −6.15802 + 10.6660i −0.195814 + 0.339159i
\(990\) 0 0
\(991\) 20.8304 + 36.0794i 0.661700 + 1.14610i 0.980169 + 0.198165i \(0.0634982\pi\)
−0.318468 + 0.947934i \(0.603168\pi\)
\(992\) 0 0
\(993\) 7.16138i 0.227260i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −21.4672 + 12.3941i −0.679874 + 0.392525i −0.799808 0.600256i \(-0.795065\pi\)
0.119934 + 0.992782i \(0.461732\pi\)
\(998\) 0 0
\(999\) −2.23808 + 3.87647i −0.0708097 + 0.122646i
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 700.2.r.d.149.3 12
5.2 odd 4 700.2.i.e.401.2 yes 6
5.3 odd 4 700.2.i.d.401.2 6
5.4 even 2 inner 700.2.r.d.149.4 12
7.2 even 3 4900.2.e.t.2549.3 6
7.4 even 3 inner 700.2.r.d.249.4 12
7.5 odd 6 4900.2.e.s.2549.4 6
35.2 odd 12 4900.2.a.ba.1.2 3
35.4 even 6 inner 700.2.r.d.249.3 12
35.9 even 6 4900.2.e.t.2549.4 6
35.12 even 12 4900.2.a.bd.1.2 3
35.18 odd 12 700.2.i.d.501.2 yes 6
35.19 odd 6 4900.2.e.s.2549.3 6
35.23 odd 12 4900.2.a.bc.1.2 3
35.32 odd 12 700.2.i.e.501.2 yes 6
35.33 even 12 4900.2.a.bb.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.2.i.d.401.2 6 5.3 odd 4
700.2.i.d.501.2 yes 6 35.18 odd 12
700.2.i.e.401.2 yes 6 5.2 odd 4
700.2.i.e.501.2 yes 6 35.32 odd 12
700.2.r.d.149.3 12 1.1 even 1 trivial
700.2.r.d.149.4 12 5.4 even 2 inner
700.2.r.d.249.3 12 35.4 even 6 inner
700.2.r.d.249.4 12 7.4 even 3 inner
4900.2.a.ba.1.2 3 35.2 odd 12
4900.2.a.bb.1.2 3 35.33 even 12
4900.2.a.bc.1.2 3 35.23 odd 12
4900.2.a.bd.1.2 3 35.12 even 12
4900.2.e.s.2549.3 6 35.19 odd 6
4900.2.e.s.2549.4 6 7.5 odd 6
4900.2.e.t.2549.3 6 7.2 even 3
4900.2.e.t.2549.4 6 35.9 even 6