Properties

Label 360.3.v.b.217.2
Level $360$
Weight $3$
Character 360.217
Analytic conductor $9.809$
Analytic rank $0$
Dimension $4$
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] = [360,3,Mod(73,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.73");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 360.v (of order \(4\), 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: \(9.80928951697\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 217.2
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 360.217
Dual form 360.3.v.b.73.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.67423 + 4.22474i) q^{5} +(-5.44949 - 5.44949i) q^{7} +O(q^{10})\) \(q+(2.67423 + 4.22474i) q^{5} +(-5.44949 - 5.44949i) q^{7} +6.44949 q^{11} +(14.4495 - 14.4495i) q^{13} +(23.1464 + 23.1464i) q^{17} +16.6969i q^{19} +(6.65153 - 6.65153i) q^{23} +(-10.6969 + 22.5959i) q^{25} +0.0454077i q^{29} +4.49490 q^{31} +(8.44949 - 37.5959i) q^{35} +(35.3485 + 35.3485i) q^{37} -20.2929 q^{41} +(32.2929 - 32.2929i) q^{43} +(50.5403 + 50.5403i) q^{47} +10.3939i q^{49} +(5.50510 - 5.50510i) q^{53} +(17.2474 + 27.2474i) q^{55} -55.4393i q^{59} +47.8888 q^{61} +(99.6867 + 22.4041i) q^{65} +(-85.2827 - 85.2827i) q^{67} -48.4041 q^{71} +(-21.9898 + 21.9898i) q^{73} +(-35.1464 - 35.1464i) q^{77} -126.697i q^{79} +(-94.9444 + 94.9444i) q^{83} +(-35.8888 + 159.687i) q^{85} +71.7980i q^{89} -157.485 q^{91} +(-70.5403 + 44.6515i) q^{95} +(-37.0000 - 37.0000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{5} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{5} - 12 q^{7} + 16 q^{11} + 48 q^{13} + 24 q^{17} + 56 q^{23} + 16 q^{25} - 80 q^{31} + 24 q^{35} + 112 q^{37} + 56 q^{41} - 8 q^{43} + 16 q^{47} + 120 q^{53} + 20 q^{55} - 24 q^{61} + 144 q^{65} - 8 q^{67} - 272 q^{71} + 108 q^{73} - 72 q^{77} - 272 q^{83} + 72 q^{85} - 336 q^{91} - 96 q^{95} - 148 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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 0
\(4\) 0 0
\(5\) 2.67423 + 4.22474i 0.534847 + 0.844949i
\(6\) 0 0
\(7\) −5.44949 5.44949i −0.778499 0.778499i 0.201077 0.979575i \(-0.435556\pi\)
−0.979575 + 0.201077i \(0.935556\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.44949 0.586317 0.293159 0.956064i \(-0.405294\pi\)
0.293159 + 0.956064i \(0.405294\pi\)
\(12\) 0 0
\(13\) 14.4495 14.4495i 1.11150 1.11150i 0.118551 0.992948i \(-0.462175\pi\)
0.992948 0.118551i \(-0.0378250\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 23.1464 + 23.1464i 1.36155 + 1.36155i 0.871938 + 0.489617i \(0.162863\pi\)
0.489617 + 0.871938i \(0.337137\pi\)
\(18\) 0 0
\(19\) 16.6969i 0.878786i 0.898295 + 0.439393i \(0.144806\pi\)
−0.898295 + 0.439393i \(0.855194\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.65153 6.65153i 0.289197 0.289197i −0.547566 0.836763i \(-0.684445\pi\)
0.836763 + 0.547566i \(0.184445\pi\)
\(24\) 0 0
\(25\) −10.6969 + 22.5959i −0.427878 + 0.903837i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.0454077i 0.00156578i 1.00000 0.000782891i \(0.000249202\pi\)
−1.00000 0.000782891i \(0.999751\pi\)
\(30\) 0 0
\(31\) 4.49490 0.144997 0.0724983 0.997369i \(-0.476903\pi\)
0.0724983 + 0.997369i \(0.476903\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 8.44949 37.5959i 0.241414 1.07417i
\(36\) 0 0
\(37\) 35.3485 + 35.3485i 0.955364 + 0.955364i 0.999046 0.0436815i \(-0.0139087\pi\)
−0.0436815 + 0.999046i \(0.513909\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −20.2929 −0.494948 −0.247474 0.968895i \(-0.579600\pi\)
−0.247474 + 0.968895i \(0.579600\pi\)
\(42\) 0 0
\(43\) 32.2929 32.2929i 0.750997 0.750997i −0.223669 0.974665i \(-0.571803\pi\)
0.974665 + 0.223669i \(0.0718033\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 50.5403 + 50.5403i 1.07533 + 1.07533i 0.996922 + 0.0784040i \(0.0249824\pi\)
0.0784040 + 0.996922i \(0.475018\pi\)
\(48\) 0 0
\(49\) 10.3939i 0.212120i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.50510 5.50510i 0.103870 0.103870i −0.653262 0.757132i \(-0.726600\pi\)
0.757132 + 0.653262i \(0.226600\pi\)
\(54\) 0 0
\(55\) 17.2474 + 27.2474i 0.313590 + 0.495408i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 55.4393i 0.939649i −0.882760 0.469824i \(-0.844317\pi\)
0.882760 0.469824i \(-0.155683\pi\)
\(60\) 0 0
\(61\) 47.8888 0.785062 0.392531 0.919739i \(-0.371600\pi\)
0.392531 + 0.919739i \(0.371600\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 99.6867 + 22.4041i 1.53364 + 0.344678i
\(66\) 0 0
\(67\) −85.2827 85.2827i −1.27288 1.27288i −0.944573 0.328303i \(-0.893523\pi\)
−0.328303 0.944573i \(-0.606477\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −48.4041 −0.681748 −0.340874 0.940109i \(-0.610723\pi\)
−0.340874 + 0.940109i \(0.610723\pi\)
\(72\) 0 0
\(73\) −21.9898 + 21.9898i −0.301230 + 0.301230i −0.841495 0.540265i \(-0.818324\pi\)
0.540265 + 0.841495i \(0.318324\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −35.1464 35.1464i −0.456447 0.456447i
\(78\) 0 0
\(79\) 126.697i 1.60376i −0.597486 0.801879i \(-0.703834\pi\)
0.597486 0.801879i \(-0.296166\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −94.9444 + 94.9444i −1.14391 + 1.14391i −0.156180 + 0.987729i \(0.549918\pi\)
−0.987729 + 0.156180i \(0.950082\pi\)
\(84\) 0 0
\(85\) −35.8888 + 159.687i −0.422221 + 1.87867i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 71.7980i 0.806719i 0.915042 + 0.403359i \(0.132158\pi\)
−0.915042 + 0.403359i \(0.867842\pi\)
\(90\) 0 0
\(91\) −157.485 −1.73060
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −70.5403 + 44.6515i −0.742530 + 0.470016i
\(96\) 0 0
\(97\) −37.0000 37.0000i −0.381443 0.381443i 0.490179 0.871622i \(-0.336932\pi\)
−0.871622 + 0.490179i \(0.836932\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −94.3383 −0.934042 −0.467021 0.884246i \(-0.654673\pi\)
−0.467021 + 0.884246i \(0.654673\pi\)
\(102\) 0 0
\(103\) 72.6413 72.6413i 0.705256 0.705256i −0.260278 0.965534i \(-0.583814\pi\)
0.965534 + 0.260278i \(0.0838142\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.0556 + 13.0556i 0.122015 + 0.122015i 0.765478 0.643463i \(-0.222503\pi\)
−0.643463 + 0.765478i \(0.722503\pi\)
\(108\) 0 0
\(109\) 69.2827i 0.635621i −0.948154 0.317810i \(-0.897052\pi\)
0.948154 0.317810i \(-0.102948\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 102.136 102.136i 0.903860 0.903860i −0.0919072 0.995768i \(-0.529296\pi\)
0.995768 + 0.0919072i \(0.0292963\pi\)
\(114\) 0 0
\(115\) 45.8888 + 10.3133i 0.399033 + 0.0896806i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 252.272i 2.11994i
\(120\) 0 0
\(121\) −79.4041 −0.656232
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −124.068 + 15.2350i −0.992545 + 0.121880i
\(126\) 0 0
\(127\) 119.944 + 119.944i 0.944444 + 0.944444i 0.998536 0.0540920i \(-0.0172264\pi\)
−0.0540920 + 0.998536i \(0.517226\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −121.146 −0.924782 −0.462391 0.886676i \(-0.653008\pi\)
−0.462391 + 0.886676i \(0.653008\pi\)
\(132\) 0 0
\(133\) 90.9898 90.9898i 0.684134 0.684134i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −119.530 119.530i −0.872482 0.872482i 0.120260 0.992742i \(-0.461627\pi\)
−0.992742 + 0.120260i \(0.961627\pi\)
\(138\) 0 0
\(139\) 140.788i 1.01286i 0.862281 + 0.506431i \(0.169035\pi\)
−0.862281 + 0.506431i \(0.830965\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 93.1918 93.1918i 0.651691 0.651691i
\(144\) 0 0
\(145\) −0.191836 + 0.121431i −0.00132301 + 0.000837454i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 53.5301i 0.359262i 0.983734 + 0.179631i \(0.0574904\pi\)
−0.983734 + 0.179631i \(0.942510\pi\)
\(150\) 0 0
\(151\) −232.606 −1.54044 −0.770219 0.637780i \(-0.779853\pi\)
−0.770219 + 0.637780i \(0.779853\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 12.0204 + 18.9898i 0.0775510 + 0.122515i
\(156\) 0 0
\(157\) 128.631 + 128.631i 0.819306 + 0.819306i 0.986007 0.166701i \(-0.0533115\pi\)
−0.166701 + 0.986007i \(0.553311\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −72.4949 −0.450279
\(162\) 0 0
\(163\) −117.576 + 117.576i −0.721322 + 0.721322i −0.968875 0.247552i \(-0.920374\pi\)
0.247552 + 0.968875i \(0.420374\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 33.6617 + 33.6617i 0.201567 + 0.201567i 0.800671 0.599104i \(-0.204476\pi\)
−0.599104 + 0.800671i \(0.704476\pi\)
\(168\) 0 0
\(169\) 248.576i 1.47086i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −28.2474 + 28.2474i −0.163280 + 0.163280i −0.784018 0.620738i \(-0.786833\pi\)
0.620738 + 0.784018i \(0.286833\pi\)
\(174\) 0 0
\(175\) 181.429 64.8434i 1.03674 0.370534i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 45.2372i 0.252722i 0.991984 + 0.126361i \(0.0403298\pi\)
−0.991984 + 0.126361i \(0.959670\pi\)
\(180\) 0 0
\(181\) −260.656 −1.44009 −0.720045 0.693928i \(-0.755879\pi\)
−0.720045 + 0.693928i \(0.755879\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −54.8082 + 243.868i −0.296260 + 1.31821i
\(186\) 0 0
\(187\) 149.283 + 149.283i 0.798303 + 0.798303i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 51.8684 0.271562 0.135781 0.990739i \(-0.456646\pi\)
0.135781 + 0.990739i \(0.456646\pi\)
\(192\) 0 0
\(193\) 16.6163 16.6163i 0.0860950 0.0860950i −0.662748 0.748843i \(-0.730610\pi\)
0.748843 + 0.662748i \(0.230610\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −86.0908 86.0908i −0.437009 0.437009i 0.453995 0.891004i \(-0.349998\pi\)
−0.891004 + 0.453995i \(0.849998\pi\)
\(198\) 0 0
\(199\) 28.5653i 0.143544i 0.997421 + 0.0717721i \(0.0228654\pi\)
−0.997421 + 0.0717721i \(0.977135\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.247449 0.247449i 0.00121896 0.00121896i
\(204\) 0 0
\(205\) −54.2679 85.7321i −0.264721 0.418206i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 107.687i 0.515248i
\(210\) 0 0
\(211\) −197.151 −0.934365 −0.467183 0.884161i \(-0.654731\pi\)
−0.467183 + 0.884161i \(0.654731\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 222.788 + 50.0704i 1.03622 + 0.232886i
\(216\) 0 0
\(217\) −24.4949 24.4949i −0.112880 0.112880i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 668.908 3.02673
\(222\) 0 0
\(223\) 287.338 287.338i 1.28851 1.28851i 0.352822 0.935690i \(-0.385222\pi\)
0.935690 0.352822i \(-0.114778\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 234.384 + 234.384i 1.03253 + 1.03253i 0.999453 + 0.0330743i \(0.0105298\pi\)
0.0330743 + 0.999453i \(0.489470\pi\)
\(228\) 0 0
\(229\) 284.969i 1.24441i −0.782855 0.622204i \(-0.786237\pi\)
0.782855 0.622204i \(-0.213763\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 241.530 241.530i 1.03661 1.03661i 0.0373060 0.999304i \(-0.488122\pi\)
0.999304 0.0373060i \(-0.0118776\pi\)
\(234\) 0 0
\(235\) −78.3633 + 348.677i −0.333461 + 1.48373i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 327.737i 1.37128i 0.727939 + 0.685642i \(0.240478\pi\)
−0.727939 + 0.685642i \(0.759522\pi\)
\(240\) 0 0
\(241\) 269.131 1.11672 0.558362 0.829597i \(-0.311430\pi\)
0.558362 + 0.829597i \(0.311430\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −43.9115 + 27.7957i −0.179231 + 0.113452i
\(246\) 0 0
\(247\) 241.262 + 241.262i 0.976770 + 0.976770i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −186.136 −0.741579 −0.370789 0.928717i \(-0.620913\pi\)
−0.370789 + 0.928717i \(0.620913\pi\)
\(252\) 0 0
\(253\) 42.8990 42.8990i 0.169561 0.169561i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −138.268 138.268i −0.538007 0.538007i 0.384936 0.922943i \(-0.374224\pi\)
−0.922943 + 0.384936i \(0.874224\pi\)
\(258\) 0 0
\(259\) 385.262i 1.48750i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 163.146 163.146i 0.620329 0.620329i −0.325287 0.945615i \(-0.605461\pi\)
0.945615 + 0.325287i \(0.105461\pi\)
\(264\) 0 0
\(265\) 37.9796 + 8.53572i 0.143319 + 0.0322103i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 108.227i 0.402331i −0.979557 0.201165i \(-0.935527\pi\)
0.979557 0.201165i \(-0.0644729\pi\)
\(270\) 0 0
\(271\) 324.384 1.19699 0.598494 0.801127i \(-0.295766\pi\)
0.598494 + 0.801127i \(0.295766\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −68.9898 + 145.732i −0.250872 + 0.529935i
\(276\) 0 0
\(277\) −165.864 165.864i −0.598786 0.598786i 0.341203 0.939990i \(-0.389166\pi\)
−0.939990 + 0.341203i \(0.889166\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −300.434 −1.06916 −0.534579 0.845118i \(-0.679530\pi\)
−0.534579 + 0.845118i \(0.679530\pi\)
\(282\) 0 0
\(283\) −352.161 + 352.161i −1.24439 + 1.24439i −0.286223 + 0.958163i \(0.592400\pi\)
−0.958163 + 0.286223i \(0.907600\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 110.586 + 110.586i 0.385316 + 0.385316i
\(288\) 0 0
\(289\) 782.514i 2.70766i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 109.414 109.414i 0.373428 0.373428i −0.495296 0.868724i \(-0.664941\pi\)
0.868724 + 0.495296i \(0.164941\pi\)
\(294\) 0 0
\(295\) 234.217 148.258i 0.793955 0.502568i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 192.222i 0.642884i
\(300\) 0 0
\(301\) −351.959 −1.16930
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 128.066 + 202.318i 0.419888 + 0.663337i
\(306\) 0 0
\(307\) 110.627 + 110.627i 0.360347 + 0.360347i 0.863941 0.503594i \(-0.167989\pi\)
−0.503594 + 0.863941i \(0.667989\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.38367 −0.00766454 −0.00383227 0.999993i \(-0.501220\pi\)
−0.00383227 + 0.999993i \(0.501220\pi\)
\(312\) 0 0
\(313\) 132.959 132.959i 0.424790 0.424790i −0.462059 0.886849i \(-0.652889\pi\)
0.886849 + 0.462059i \(0.152889\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 37.1464 + 37.1464i 0.117181 + 0.117181i 0.763266 0.646085i \(-0.223595\pi\)
−0.646085 + 0.763266i \(0.723595\pi\)
\(318\) 0 0
\(319\) 0.292856i 0.000918045i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −386.474 + 386.474i −1.19652 + 1.19652i
\(324\) 0 0
\(325\) 171.934 + 481.065i 0.529028 + 1.48020i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 550.838i 1.67428i
\(330\) 0 0
\(331\) 21.6459 0.0653955 0.0326978 0.999465i \(-0.489590\pi\)
0.0326978 + 0.999465i \(0.489590\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 132.232 588.363i 0.394721 1.75631i
\(336\) 0 0
\(337\) −136.757 136.757i −0.405808 0.405808i 0.474466 0.880274i \(-0.342641\pi\)
−0.880274 + 0.474466i \(0.842641\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 28.9898 0.0850141
\(342\) 0 0
\(343\) −210.384 + 210.384i −0.613363 + 0.613363i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −33.8480 33.8480i −0.0975445 0.0975445i 0.656650 0.754195i \(-0.271973\pi\)
−0.754195 + 0.656650i \(0.771973\pi\)
\(348\) 0 0
\(349\) 241.283i 0.691354i −0.938354 0.345677i \(-0.887649\pi\)
0.938354 0.345677i \(-0.112351\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −126.833 + 126.833i −0.359301 + 0.359301i −0.863555 0.504254i \(-0.831767\pi\)
0.504254 + 0.863555i \(0.331767\pi\)
\(354\) 0 0
\(355\) −129.444 204.495i −0.364631 0.576042i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 22.1112i 0.0615912i 0.999526 + 0.0307956i \(0.00980409\pi\)
−0.999526 + 0.0307956i \(0.990196\pi\)
\(360\) 0 0
\(361\) 82.2122 0.227735
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −151.707 34.0954i −0.415636 0.0934121i
\(366\) 0 0
\(367\) −213.944 213.944i −0.582955 0.582955i 0.352759 0.935714i \(-0.385243\pi\)
−0.935714 + 0.352759i \(0.885243\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −60.0000 −0.161725
\(372\) 0 0
\(373\) 210.025 210.025i 0.563070 0.563070i −0.367108 0.930178i \(-0.619652\pi\)
0.930178 + 0.367108i \(0.119652\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.656118 + 0.656118i 0.00174037 + 0.00174037i
\(378\) 0 0
\(379\) 124.343i 0.328081i −0.986454 0.164041i \(-0.947547\pi\)
0.986454 0.164041i \(-0.0524528\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −418.540 + 418.540i −1.09279 + 1.09279i −0.0975654 + 0.995229i \(0.531106\pi\)
−0.995229 + 0.0975654i \(0.968894\pi\)
\(384\) 0 0
\(385\) 54.4949 242.474i 0.141545 0.629804i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 369.884i 0.950859i 0.879754 + 0.475430i \(0.157707\pi\)
−0.879754 + 0.475430i \(0.842293\pi\)
\(390\) 0 0
\(391\) 307.918 0.787515
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 535.262 338.817i 1.35509 0.857765i
\(396\) 0 0
\(397\) −373.984 373.984i −0.942026 0.942026i 0.0563835 0.998409i \(-0.482043\pi\)
−0.998409 + 0.0563835i \(0.982043\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −113.151 −0.282172 −0.141086 0.989997i \(-0.545059\pi\)
−0.141086 + 0.989997i \(0.545059\pi\)
\(402\) 0 0
\(403\) 64.9490 64.9490i 0.161164 0.161164i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 227.980 + 227.980i 0.560146 + 0.560146i
\(408\) 0 0
\(409\) 90.3837i 0.220987i 0.993877 + 0.110493i \(0.0352431\pi\)
−0.993877 + 0.110493i \(0.964757\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −302.116 + 302.116i −0.731515 + 0.731515i
\(414\) 0 0
\(415\) −655.019 147.212i −1.57836 0.354728i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 334.772i 0.798978i −0.916738 0.399489i \(-0.869188\pi\)
0.916738 0.399489i \(-0.130812\pi\)
\(420\) 0 0
\(421\) 57.2735 0.136042 0.0680208 0.997684i \(-0.478332\pi\)
0.0680208 + 0.997684i \(0.478332\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −770.611 + 275.419i −1.81320 + 0.648044i
\(426\) 0 0
\(427\) −260.969 260.969i −0.611170 0.611170i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −442.656 −1.02704 −0.513522 0.858076i \(-0.671660\pi\)
−0.513522 + 0.858076i \(0.671660\pi\)
\(432\) 0 0
\(433\) −14.8684 + 14.8684i −0.0343380 + 0.0343380i −0.724067 0.689729i \(-0.757730\pi\)
0.689729 + 0.724067i \(0.257730\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 111.060 + 111.060i 0.254142 + 0.254142i
\(438\) 0 0
\(439\) 233.818i 0.532616i 0.963888 + 0.266308i \(0.0858038\pi\)
−0.963888 + 0.266308i \(0.914196\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 246.747 246.747i 0.556991 0.556991i −0.371459 0.928449i \(-0.621142\pi\)
0.928449 + 0.371459i \(0.121142\pi\)
\(444\) 0 0
\(445\) −303.328 + 192.005i −0.681636 + 0.431471i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 282.758i 0.629751i 0.949133 + 0.314875i \(0.101963\pi\)
−0.949133 + 0.314875i \(0.898037\pi\)
\(450\) 0 0
\(451\) −130.879 −0.290196
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −421.151 665.333i −0.925607 1.46227i
\(456\) 0 0
\(457\) −298.171 298.171i −0.652454 0.652454i 0.301129 0.953583i \(-0.402636\pi\)
−0.953583 + 0.301129i \(0.902636\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 264.318 0.573358 0.286679 0.958027i \(-0.407449\pi\)
0.286679 + 0.958027i \(0.407449\pi\)
\(462\) 0 0
\(463\) 135.116 135.116i 0.291827 0.291827i −0.545975 0.837802i \(-0.683841\pi\)
0.837802 + 0.545975i \(0.183841\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −558.631 558.631i −1.19621 1.19621i −0.975292 0.220920i \(-0.929094\pi\)
−0.220920 0.975292i \(-0.570906\pi\)
\(468\) 0 0
\(469\) 929.494i 1.98186i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 208.272 208.272i 0.440322 0.440322i
\(474\) 0 0
\(475\) −377.283 178.606i −0.794279 0.376013i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 456.141i 0.952277i 0.879370 + 0.476139i \(0.157964\pi\)
−0.879370 + 0.476139i \(0.842036\pi\)
\(480\) 0 0
\(481\) 1021.53 2.12377
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 57.3689 255.262i 0.118286 0.526314i
\(486\) 0 0
\(487\) 11.9444 + 11.9444i 0.0245265 + 0.0245265i 0.719264 0.694737i \(-0.244479\pi\)
−0.694737 + 0.719264i \(0.744479\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −822.468 −1.67509 −0.837544 0.546370i \(-0.816009\pi\)
−0.837544 + 0.546370i \(0.816009\pi\)
\(492\) 0 0
\(493\) −1.05103 + 1.05103i −0.00213190 + 0.00213190i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 263.778 + 263.778i 0.530740 + 0.530740i
\(498\) 0 0
\(499\) 312.474i 0.626201i 0.949720 + 0.313101i \(0.101368\pi\)
−0.949720 + 0.313101i \(0.898632\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 371.530 371.530i 0.738628 0.738628i −0.233684 0.972313i \(-0.575078\pi\)
0.972313 + 0.233684i \(0.0750782\pi\)
\(504\) 0 0
\(505\) −252.283 398.555i −0.499570 0.789218i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 171.228i 0.336401i −0.985753 0.168200i \(-0.946204\pi\)
0.985753 0.168200i \(-0.0537956\pi\)
\(510\) 0 0
\(511\) 239.666 0.469014
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 501.151 + 112.631i 0.973109 + 0.218701i
\(516\) 0 0
\(517\) 325.959 + 325.959i 0.630482 + 0.630482i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 206.313 0.395995 0.197997 0.980203i \(-0.436556\pi\)
0.197997 + 0.980203i \(0.436556\pi\)
\(522\) 0 0
\(523\) −135.526 + 135.526i −0.259131 + 0.259131i −0.824701 0.565570i \(-0.808656\pi\)
0.565570 + 0.824701i \(0.308656\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 104.041 + 104.041i 0.197421 + 0.197421i
\(528\) 0 0
\(529\) 440.514i 0.832730i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −293.221 + 293.221i −0.550134 + 0.550134i
\(534\) 0 0
\(535\) −20.2429 + 90.0704i −0.0378371 + 0.168356i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 67.0352i 0.124370i
\(540\) 0 0
\(541\) 303.485 0.560970 0.280485 0.959858i \(-0.409505\pi\)
0.280485 + 0.959858i \(0.409505\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 292.702 185.278i 0.537067 0.339960i
\(546\) 0 0
\(547\) −71.3939 71.3939i −0.130519 0.130519i 0.638829 0.769348i \(-0.279419\pi\)
−0.769348 + 0.638829i \(0.779419\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.758169 −0.00137599
\(552\) 0 0
\(553\) −690.434 + 690.434i −1.24852 + 1.24852i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −753.019 753.019i −1.35192 1.35192i −0.883513 0.468407i \(-0.844828\pi\)
−0.468407 0.883513i \(-0.655172\pi\)
\(558\) 0 0
\(559\) 933.231i 1.66946i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −703.464 + 703.464i −1.24949 + 1.24949i −0.293548 + 0.955944i \(0.594836\pi\)
−0.955944 + 0.293548i \(0.905164\pi\)
\(564\) 0 0
\(565\) 704.636 + 158.363i 1.24714 + 0.280289i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 434.504i 0.763628i −0.924239 0.381814i \(-0.875300\pi\)
0.924239 0.381814i \(-0.124700\pi\)
\(570\) 0 0
\(571\) −131.040 −0.229492 −0.114746 0.993395i \(-0.536605\pi\)
−0.114746 + 0.993395i \(0.536605\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 79.1464 + 221.448i 0.137646 + 0.385128i
\(576\) 0 0
\(577\) 290.444 + 290.444i 0.503369 + 0.503369i 0.912483 0.409114i \(-0.134162\pi\)
−0.409114 + 0.912483i \(0.634162\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1034.80 1.78106
\(582\) 0 0
\(583\) 35.5051 35.5051i 0.0609007 0.0609007i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −180.288 180.288i −0.307135 0.307135i 0.536662 0.843797i \(-0.319685\pi\)
−0.843797 + 0.536662i \(0.819685\pi\)
\(588\) 0 0
\(589\) 75.0510i 0.127421i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 25.0556 25.0556i 0.0422523 0.0422523i −0.685665 0.727917i \(-0.740488\pi\)
0.727917 + 0.685665i \(0.240488\pi\)
\(594\) 0 0
\(595\) 1065.79 674.636i 1.79124 1.13384i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 509.807i 0.851097i −0.904936 0.425549i \(-0.860081\pi\)
0.904936 0.425549i \(-0.139919\pi\)
\(600\) 0 0
\(601\) 179.757 0.299097 0.149548 0.988754i \(-0.452218\pi\)
0.149548 + 0.988754i \(0.452218\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −212.345 335.462i −0.350984 0.554483i
\(606\) 0 0
\(607\) 33.1566 + 33.1566i 0.0546238 + 0.0546238i 0.733891 0.679267i \(-0.237702\pi\)
−0.679267 + 0.733891i \(0.737702\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1460.56 2.39045
\(612\) 0 0
\(613\) −261.712 + 261.712i −0.426936 + 0.426936i −0.887583 0.460647i \(-0.847617\pi\)
0.460647 + 0.887583i \(0.347617\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 762.075 + 762.075i 1.23513 + 1.23513i 0.961968 + 0.273161i \(0.0880693\pi\)
0.273161 + 0.961968i \(0.411931\pi\)
\(618\) 0 0
\(619\) 81.6367i 0.131885i −0.997823 0.0659424i \(-0.978995\pi\)
0.997823 0.0659424i \(-0.0210054\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 391.262 391.262i 0.628029 0.628029i
\(624\) 0 0
\(625\) −396.151 483.414i −0.633842 0.773463i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1636.38i 2.60156i
\(630\) 0 0
\(631\) −16.4133 −0.0260115 −0.0130057 0.999915i \(-0.504140\pi\)
−0.0130057 + 0.999915i \(0.504140\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −185.975 + 827.494i −0.292874 + 1.30314i
\(636\) 0 0
\(637\) 150.186 + 150.186i 0.235771 + 0.235771i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 546.041 0.851858 0.425929 0.904757i \(-0.359947\pi\)
0.425929 + 0.904757i \(0.359947\pi\)
\(642\) 0 0
\(643\) −142.879 + 142.879i −0.222206 + 0.222206i −0.809427 0.587221i \(-0.800222\pi\)
0.587221 + 0.809427i \(0.300222\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 649.691 + 649.691i 1.00416 + 1.00416i 0.999991 + 0.00416838i \(0.00132684\pi\)
0.00416838 + 0.999991i \(0.498673\pi\)
\(648\) 0 0
\(649\) 357.555i 0.550932i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 150.904 150.904i 0.231093 0.231093i −0.582056 0.813149i \(-0.697752\pi\)
0.813149 + 0.582056i \(0.197752\pi\)
\(654\) 0 0
\(655\) −323.974 511.813i −0.494617 0.781394i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 268.802i 0.407893i 0.978982 + 0.203947i \(0.0653769\pi\)
−0.978982 + 0.203947i \(0.934623\pi\)
\(660\) 0 0
\(661\) 311.162 0.470745 0.235372 0.971905i \(-0.424369\pi\)
0.235372 + 0.971905i \(0.424369\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 627.737 + 141.081i 0.943965 + 0.212151i
\(666\) 0 0
\(667\) 0.302031 + 0.302031i 0.000452820 + 0.000452820i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 308.858 0.460295
\(672\) 0 0
\(673\) −547.756 + 547.756i −0.813902 + 0.813902i −0.985216 0.171314i \(-0.945199\pi\)
0.171314 + 0.985216i \(0.445199\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −696.257 696.257i −1.02844 1.02844i −0.999583 0.0288606i \(-0.990812\pi\)
−0.0288606 0.999583i \(-0.509188\pi\)
\(678\) 0 0
\(679\) 403.262i 0.593906i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 84.0250 84.0250i 0.123023 0.123023i −0.642915 0.765938i \(-0.722275\pi\)
0.765938 + 0.642915i \(0.222275\pi\)
\(684\) 0 0
\(685\) 185.333 824.636i 0.270559 1.20385i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 159.092i 0.230903i
\(690\) 0 0
\(691\) 1157.06 1.67447 0.837236 0.546842i \(-0.184170\pi\)
0.837236 + 0.546842i \(0.184170\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −594.792 + 376.499i −0.855816 + 0.541726i
\(696\) 0 0
\(697\) −469.707 469.707i −0.673898 0.673898i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −843.691 −1.20355 −0.601777 0.798664i \(-0.705540\pi\)
−0.601777 + 0.798664i \(0.705540\pi\)
\(702\) 0 0
\(703\) −590.211 + 590.211i −0.839561 + 0.839561i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 514.095 + 514.095i 0.727150 + 0.727150i
\(708\) 0 0
\(709\) 170.686i 0.240741i −0.992729 0.120371i \(-0.961592\pi\)
0.992729 0.120371i \(-0.0384083\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 29.8979 29.8979i 0.0419326 0.0419326i
\(714\) 0 0
\(715\) 642.929 + 144.495i 0.899201 + 0.202091i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 605.435i 0.842051i 0.907049 + 0.421026i \(0.138330\pi\)
−0.907049 + 0.421026i \(0.861670\pi\)
\(720\) 0 0
\(721\) −791.716 −1.09808
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.02603 0.485723i −0.00141521 0.000669963i
\(726\) 0 0
\(727\) −50.8025 50.8025i −0.0698797 0.0698797i 0.671303 0.741183i \(-0.265735\pi\)
−0.741183 + 0.671303i \(0.765735\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1494.93 2.04505
\(732\) 0 0
\(733\) 516.529 516.529i 0.704678 0.704678i −0.260733 0.965411i \(-0.583964\pi\)
0.965411 + 0.260733i \(0.0839642\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −550.030 550.030i −0.746309 0.746309i
\(738\) 0 0
\(739\) 650.109i 0.879715i 0.898068 + 0.439857i \(0.144971\pi\)
−0.898068 + 0.439857i \(0.855029\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −90.6811 + 90.6811i −0.122047 + 0.122047i −0.765492 0.643445i \(-0.777504\pi\)
0.643445 + 0.765492i \(0.277504\pi\)
\(744\) 0 0
\(745\) −226.151 + 143.152i −0.303558 + 0.192150i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 142.293i 0.189977i
\(750\) 0 0
\(751\) −300.050 −0.399534 −0.199767 0.979843i \(-0.564019\pi\)
−0.199767 + 0.979843i \(0.564019\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −622.043 982.702i −0.823898 1.30159i
\(756\) 0 0
\(757\) 523.176 + 523.176i 0.691118 + 0.691118i 0.962478 0.271360i \(-0.0874735\pi\)
−0.271360 + 0.962478i \(0.587473\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 724.130 0.951550 0.475775 0.879567i \(-0.342168\pi\)
0.475775 + 0.879567i \(0.342168\pi\)
\(762\) 0 0
\(763\) −377.555 + 377.555i −0.494830 + 0.494830i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −801.069 801.069i −1.04442 1.04442i
\(768\) 0 0
\(769\) 13.7775i 0.0179162i −0.999960 0.00895809i \(-0.997149\pi\)
0.999960 0.00895809i \(-0.00285149\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 564.207 564.207i 0.729892 0.729892i −0.240706 0.970598i \(-0.577379\pi\)
0.970598 + 0.240706i \(0.0773789\pi\)
\(774\) 0 0
\(775\) −48.0816 + 101.566i −0.0620408 + 0.131053i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 338.829i 0.434953i
\(780\) 0 0
\(781\) −312.182 −0.399720
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −199.444 + 887.423i −0.254069 + 1.13048i
\(786\) 0 0
\(787\) −212.424 212.424i −0.269917 0.269917i 0.559150 0.829067i \(-0.311128\pi\)
−0.829067 + 0.559150i \(0.811128\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1113.18 −1.40731
\(792\) 0 0
\(793\) 691.968 691.968i 0.872596 0.872596i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15.6617 + 15.6617i 0.0196509 + 0.0196509i 0.716864 0.697213i \(-0.245577\pi\)
−0.697213 + 0.716864i \(0.745577\pi\)
\(798\) 0 0
\(799\) 2339.66i 2.92823i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −141.823 + 141.823i −0.176616 + 0.176616i
\(804\) 0 0
\(805\) −193.868 306.272i −0.240830 0.380463i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 816.788i 1.00963i 0.863229 + 0.504813i \(0.168439\pi\)
−0.863229 + 0.504813i \(0.831561\pi\)
\(810\) 0 0
\(811\) 830.504 1.02405 0.512025 0.858971i \(-0.328896\pi\)
0.512025 + 0.858971i \(0.328896\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −811.151 182.302i −0.995277 0.223683i
\(816\) 0 0
\(817\) 539.192 + 539.192i 0.659966 + 0.659966i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −569.217 −0.693321 −0.346661 0.937991i \(-0.612684\pi\)
−0.346661 + 0.937991i \(0.612684\pi\)
\(822\) 0 0
\(823\) 497.095 497.095i 0.604004 0.604004i −0.337369 0.941373i \(-0.609537\pi\)
0.941373 + 0.337369i \(0.109537\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −874.070 874.070i −1.05692 1.05692i −0.998279 0.0586377i \(-0.981324\pi\)
−0.0586377 0.998279i \(-0.518676\pi\)
\(828\) 0 0
\(829\) 1548.77i 1.86824i −0.356954 0.934122i \(-0.616185\pi\)
0.356954 0.934122i \(-0.383815\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −240.581 + 240.581i −0.288813 + 0.288813i
\(834\) 0 0
\(835\) −52.1929 + 232.232i −0.0625064 + 0.278122i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 731.523i 0.871899i −0.899971 0.435950i \(-0.856413\pi\)
0.899971 0.435950i \(-0.143587\pi\)
\(840\) 0 0
\(841\) 840.998 0.999998
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1050.17 664.749i 1.24280 0.786685i
\(846\) 0 0
\(847\) 432.712 + 432.712i 0.510876 + 0.510876i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 470.243 0.552577
\(852\) 0 0
\(853\) −554.166 + 554.166i −0.649667 + 0.649667i −0.952912 0.303246i \(-0.901930\pi\)
0.303246 + 0.952912i \(0.401930\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −687.206 687.206i −0.801874 0.801874i 0.181515 0.983388i \(-0.441900\pi\)
−0.983388 + 0.181515i \(0.941900\pi\)
\(858\) 0 0
\(859\) 1285.29i 1.49627i −0.663549 0.748133i \(-0.730951\pi\)
0.663549 0.748133i \(-0.269049\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 712.985 712.985i 0.826171 0.826171i −0.160814 0.986985i \(-0.551412\pi\)
0.986985 + 0.160814i \(0.0514120\pi\)
\(864\) 0 0
\(865\) −194.879 43.7980i −0.225293 0.0506335i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 817.131i 0.940311i
\(870\) 0 0
\(871\) −2464.58 −2.82960
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 759.131 + 593.085i 0.867578 + 0.677812i
\(876\) 0 0
\(877\) −474.297 474.297i −0.540818 0.540818i 0.382951 0.923769i \(-0.374908\pi\)
−0.923769 + 0.382951i \(0.874908\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1652.71 −1.87594 −0.937972 0.346712i \(-0.887298\pi\)
−0.937972 + 0.346712i \(0.887298\pi\)
\(882\) 0 0
\(883\) 18.9286 18.9286i 0.0214367 0.0214367i −0.696307 0.717744i \(-0.745175\pi\)
0.717744 + 0.696307i \(0.245175\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 382.338 + 382.338i 0.431047 + 0.431047i 0.888984 0.457938i \(-0.151412\pi\)
−0.457938 + 0.888984i \(0.651412\pi\)
\(888\) 0 0
\(889\) 1307.27i 1.47050i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −843.868 + 843.868i −0.944981 + 0.944981i
\(894\) 0 0
\(895\) −191.116 + 120.975i −0.213537 + 0.135168i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0.204103i 0.000227033i
\(900\) 0 0
\(901\) 254.847 0.282849
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −697.056 1101.21i −0.770227 1.21680i
\(906\) 0 0
\(907\) 725.485 + 725.485i 0.799873 + 0.799873i 0.983075 0.183202i \(-0.0586464\pi\)
−0.183202 + 0.983075i \(0.558646\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 154.474 0.169566 0.0847829 0.996399i \(-0.472980\pi\)
0.0847829 + 0.996399i \(0.472980\pi\)
\(912\) 0 0
\(913\) −612.343 + 612.343i −0.670693 + 0.670693i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 660.186 + 660.186i 0.719941 + 0.719941i
\(918\) 0 0
\(919\) 659.079i 0.717169i 0.933497 + 0.358585i \(0.116741\pi\)
−0.933497 + 0.358585i \(0.883259\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −699.414 + 699.414i −0.757762 + 0.757762i
\(924\) 0 0
\(925\) −1176.85 + 420.611i −1.27227 + 0.454714i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 368.556i 0.396723i −0.980129 0.198362i \(-0.936438\pi\)
0.980129 0.198362i \(-0.0635621\pi\)
\(930\) 0 0
\(931\) −173.546 −0.186408
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −231.464 + 1029.90i −0.247555 + 1.10150i
\(936\) 0 0
\(937\) −820.898 820.898i −0.876092 0.876092i 0.117036 0.993128i \(-0.462661\pi\)
−0.993128 + 0.117036i \(0.962661\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1758.50 −1.86875 −0.934377 0.356286i \(-0.884043\pi\)
−0.934377 + 0.356286i \(0.884043\pi\)
\(942\) 0 0
\(943\) −134.979 + 134.979i −0.143137 + 0.143137i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 118.080 + 118.080i 0.124688 + 0.124688i 0.766697 0.642009i \(-0.221899\pi\)
−0.642009 + 0.766697i \(0.721899\pi\)
\(948\) 0 0
\(949\) 635.483i 0.669634i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 217.955 217.955i 0.228704 0.228704i −0.583447 0.812151i \(-0.698297\pi\)
0.812151 + 0.583447i \(0.198297\pi\)
\(954\) 0 0
\(955\) 138.708 + 219.131i 0.145244 + 0.229456i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1302.76i 1.35845i
\(960\) 0 0
\(961\) −940.796 −0.978976
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 114.636 + 25.7638i 0.118793 + 0.0266982i
\(966\) 0 0
\(967\) −323.983 323.983i −0.335039 0.335039i 0.519457 0.854497i \(-0.326134\pi\)
−0.854497 + 0.519457i \(0.826134\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −743.743 −0.765956 −0.382978 0.923757i \(-0.625102\pi\)
−0.382978 + 0.923757i \(0.625102\pi\)
\(972\) 0 0
\(973\) 767.221 767.221i 0.788511 0.788511i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1050.52 + 1050.52i 1.07525 + 1.07525i 0.996928 + 0.0783226i \(0.0249564\pi\)
0.0783226 + 0.996928i \(0.475044\pi\)
\(978\) 0 0
\(979\) 463.060i 0.472993i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −72.9648 + 72.9648i −0.0742267 + 0.0742267i −0.743245 0.669019i \(-0.766715\pi\)
0.669019 + 0.743245i \(0.266715\pi\)
\(984\) 0 0
\(985\) 133.485 593.939i 0.135517 0.602984i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 429.594i 0.434372i
\(990\) 0 0
\(991\) 444.624 0.448662 0.224331 0.974513i \(-0.427980\pi\)
0.224331 + 0.974513i \(0.427980\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −120.681 + 76.3903i −0.121288 + 0.0767742i
\(996\) 0 0
\(997\) 12.6424 + 12.6424i 0.0126804 + 0.0126804i 0.713419 0.700738i \(-0.247146\pi\)
−0.700738 + 0.713419i \(0.747146\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 360.3.v.b.217.2 4
3.2 odd 2 120.3.u.a.97.1 yes 4
4.3 odd 2 720.3.bh.g.577.2 4
5.2 odd 4 1800.3.v.n.793.2 4
5.3 odd 4 inner 360.3.v.b.73.2 4
5.4 even 2 1800.3.v.n.1657.2 4
12.11 even 2 240.3.bg.c.97.2 4
15.2 even 4 600.3.u.e.193.2 4
15.8 even 4 120.3.u.a.73.1 4
15.14 odd 2 600.3.u.e.457.2 4
20.3 even 4 720.3.bh.g.433.2 4
24.5 odd 2 960.3.bg.c.577.2 4
24.11 even 2 960.3.bg.d.577.1 4
60.23 odd 4 240.3.bg.c.193.2 4
60.47 odd 4 1200.3.bg.e.193.1 4
60.59 even 2 1200.3.bg.e.1057.1 4
120.53 even 4 960.3.bg.c.193.2 4
120.83 odd 4 960.3.bg.d.193.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.3.u.a.73.1 4 15.8 even 4
120.3.u.a.97.1 yes 4 3.2 odd 2
240.3.bg.c.97.2 4 12.11 even 2
240.3.bg.c.193.2 4 60.23 odd 4
360.3.v.b.73.2 4 5.3 odd 4 inner
360.3.v.b.217.2 4 1.1 even 1 trivial
600.3.u.e.193.2 4 15.2 even 4
600.3.u.e.457.2 4 15.14 odd 2
720.3.bh.g.433.2 4 20.3 even 4
720.3.bh.g.577.2 4 4.3 odd 2
960.3.bg.c.193.2 4 120.53 even 4
960.3.bg.c.577.2 4 24.5 odd 2
960.3.bg.d.193.1 4 120.83 odd 4
960.3.bg.d.577.1 4 24.11 even 2
1200.3.bg.e.193.1 4 60.47 odd 4
1200.3.bg.e.1057.1 4 60.59 even 2
1800.3.v.n.793.2 4 5.2 odd 4
1800.3.v.n.1657.2 4 5.4 even 2