Properties

Label 1300.2.y.e.101.1
Level $1300$
Weight $2$
Character 1300.101
Analytic conductor $10.381$
Analytic rank $0$
Dimension $16$
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] = [1300,2,Mod(101,1300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1300.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.y (of order \(6\), 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: \(10.3805522628\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 7x^{14} + 21x^{12} + 22x^{10} - 26x^{8} + 198x^{6} + 1701x^{4} + 5103x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.1
Root \(1.65307 + 0.517063i\) of defining polynomial
Character \(\chi\) \(=\) 1300.101
Dual form 1300.2.y.e.901.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.65307 - 2.86320i) q^{3} +(0.895580 + 0.517063i) q^{7} +(-3.96529 + 6.86809i) q^{9} +O(q^{10})\) \(q+(-1.65307 - 2.86320i) q^{3} +(0.895580 + 0.517063i) q^{7} +(-3.96529 + 6.86809i) q^{9} +(-2.96091 + 1.70948i) q^{11} +(0.455025 - 3.57672i) q^{13} +(-1.19805 + 2.07508i) q^{17} +(5.37246 + 3.10179i) q^{19} -3.41897i q^{21} +(3.62751 + 6.28304i) q^{23} +16.3012 q^{27} +(-0.902796 - 1.56369i) q^{29} +5.80053i q^{31} +(9.78921 + 5.65180i) q^{33} +(1.23585 - 0.713520i) q^{37} +(-10.9931 + 4.60975i) q^{39} +(-3.60158 + 2.07937i) q^{41} +(1.07886 - 1.86864i) q^{43} +3.50894i q^{47} +(-2.96529 - 5.13604i) q^{49} +7.92183 q^{51} -4.55382 q^{53} -20.5099i q^{57} +(5.06250 + 2.92283i) q^{59} +(-1.90280 + 3.29574i) q^{61} +(-7.10247 + 4.10061i) q^{63} +(6.59603 - 3.80822i) q^{67} +(11.9931 - 20.7726i) q^{69} +(9.49745 + 5.48336i) q^{71} -7.15345i q^{73} -3.53565 q^{77} +12.8524 q^{79} +(-15.0512 - 26.0694i) q^{81} +0.706694i q^{83} +(-2.98477 + 5.16978i) q^{87} +(-5.06250 + 2.92283i) q^{89} +(2.25690 - 2.96796i) q^{91} +(16.6081 - 9.58870i) q^{93} +(13.8528 + 7.99794i) q^{97} -27.1144i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 10 q^{9} - 6 q^{11} + 18 q^{19} - 12 q^{29} - 18 q^{39} - 48 q^{41} + 6 q^{49} + 44 q^{51} + 30 q^{59} - 28 q^{61} + 34 q^{69} - 18 q^{71} + 16 q^{79} - 44 q^{81} - 30 q^{89} - 10 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(651\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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
\(3\) −1.65307 2.86320i −0.954401 1.65307i −0.735732 0.677273i \(-0.763162\pi\)
−0.218669 0.975799i \(-0.570172\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.895580 + 0.517063i 0.338497 + 0.195432i 0.659607 0.751610i \(-0.270723\pi\)
−0.321110 + 0.947042i \(0.604056\pi\)
\(8\) 0 0
\(9\) −3.96529 + 6.86809i −1.32176 + 2.28936i
\(10\) 0 0
\(11\) −2.96091 + 1.70948i −0.892749 + 0.515429i −0.874841 0.484411i \(-0.839034\pi\)
−0.0179086 + 0.999840i \(0.505701\pi\)
\(12\) 0 0
\(13\) 0.455025 3.57672i 0.126201 0.992005i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.19805 + 2.07508i −0.290569 + 0.503280i −0.973944 0.226787i \(-0.927178\pi\)
0.683375 + 0.730067i \(0.260511\pi\)
\(18\) 0 0
\(19\) 5.37246 + 3.10179i 1.23253 + 0.711600i 0.967556 0.252656i \(-0.0813041\pi\)
0.264972 + 0.964256i \(0.414637\pi\)
\(20\) 0 0
\(21\) 3.41897i 0.746080i
\(22\) 0 0
\(23\) 3.62751 + 6.28304i 0.756389 + 1.31010i 0.944681 + 0.327991i \(0.106371\pi\)
−0.188292 + 0.982113i \(0.560295\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 16.3012 3.13717
\(28\) 0 0
\(29\) −0.902796 1.56369i −0.167645 0.290370i 0.769946 0.638109i \(-0.220283\pi\)
−0.937591 + 0.347739i \(0.886950\pi\)
\(30\) 0 0
\(31\) 5.80053i 1.04181i 0.853616 + 0.520903i \(0.174405\pi\)
−0.853616 + 0.520903i \(0.825595\pi\)
\(32\) 0 0
\(33\) 9.78921 + 5.65180i 1.70408 + 0.983852i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.23585 0.713520i 0.203173 0.117302i −0.394962 0.918698i \(-0.629242\pi\)
0.598135 + 0.801396i \(0.295909\pi\)
\(38\) 0 0
\(39\) −10.9931 + 4.60975i −1.76030 + 0.738151i
\(40\) 0 0
\(41\) −3.60158 + 2.07937i −0.562472 + 0.324744i −0.754137 0.656717i \(-0.771945\pi\)
0.191665 + 0.981460i \(0.438611\pi\)
\(42\) 0 0
\(43\) 1.07886 1.86864i 0.164525 0.284965i −0.771962 0.635669i \(-0.780724\pi\)
0.936486 + 0.350704i \(0.114058\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.50894i 0.511832i 0.966699 + 0.255916i \(0.0823770\pi\)
−0.966699 + 0.255916i \(0.917623\pi\)
\(48\) 0 0
\(49\) −2.96529 5.13604i −0.423613 0.733719i
\(50\) 0 0
\(51\) 7.92183 1.10928
\(52\) 0 0
\(53\) −4.55382 −0.625515 −0.312757 0.949833i \(-0.601253\pi\)
−0.312757 + 0.949833i \(0.601253\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 20.5099i 2.71661i
\(58\) 0 0
\(59\) 5.06250 + 2.92283i 0.659081 + 0.380520i 0.791927 0.610616i \(-0.209078\pi\)
−0.132846 + 0.991137i \(0.542412\pi\)
\(60\) 0 0
\(61\) −1.90280 + 3.29574i −0.243628 + 0.421976i −0.961745 0.273946i \(-0.911671\pi\)
0.718117 + 0.695922i \(0.245004\pi\)
\(62\) 0 0
\(63\) −7.10247 + 4.10061i −0.894827 + 0.516629i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.59603 3.80822i 0.805833 0.465248i −0.0396734 0.999213i \(-0.512632\pi\)
0.845507 + 0.533965i \(0.179298\pi\)
\(68\) 0 0
\(69\) 11.9931 20.7726i 1.44380 2.50073i
\(70\) 0 0
\(71\) 9.49745 + 5.48336i 1.12714 + 0.650755i 0.943214 0.332185i \(-0.107786\pi\)
0.183926 + 0.982940i \(0.441119\pi\)
\(72\) 0 0
\(73\) 7.15345i 0.837248i −0.908160 0.418624i \(-0.862513\pi\)
0.908160 0.418624i \(-0.137487\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.53565 −0.402924
\(78\) 0 0
\(79\) 12.8524 1.44601 0.723005 0.690843i \(-0.242760\pi\)
0.723005 + 0.690843i \(0.242760\pi\)
\(80\) 0 0
\(81\) −15.0512 26.0694i −1.67236 2.89660i
\(82\) 0 0
\(83\) 0.706694i 0.0775698i 0.999248 + 0.0387849i \(0.0123487\pi\)
−0.999248 + 0.0387849i \(0.987651\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.98477 + 5.16978i −0.320001 + 0.554258i
\(88\) 0 0
\(89\) −5.06250 + 2.92283i −0.536623 + 0.309820i −0.743709 0.668503i \(-0.766935\pi\)
0.207086 + 0.978323i \(0.433602\pi\)
\(90\) 0 0
\(91\) 2.25690 2.96796i 0.236588 0.311127i
\(92\) 0 0
\(93\) 16.6081 9.58870i 1.72218 0.994302i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.8528 + 7.99794i 1.40654 + 0.812068i 0.995053 0.0993461i \(-0.0316751\pi\)
0.411490 + 0.911414i \(0.365008\pi\)
\(98\) 0 0
\(99\) 27.1144i 2.72510i
\(100\) 0 0
\(101\) 2.99562 + 5.18857i 0.298076 + 0.516282i 0.975696 0.219130i \(-0.0703219\pi\)
−0.677620 + 0.735412i \(0.736989\pi\)
\(102\) 0 0
\(103\) −11.7096 −1.15378 −0.576890 0.816822i \(-0.695734\pi\)
−0.576890 + 0.816822i \(0.695734\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.78110 11.7452i −0.655554 1.13545i −0.981755 0.190152i \(-0.939102\pi\)
0.326201 0.945300i \(-0.394231\pi\)
\(108\) 0 0
\(109\) 1.39533i 0.133648i 0.997765 + 0.0668240i \(0.0212866\pi\)
−0.997765 + 0.0668240i \(0.978713\pi\)
\(110\) 0 0
\(111\) −4.08591 2.35900i −0.387817 0.223906i
\(112\) 0 0
\(113\) 2.10810 3.65133i 0.198313 0.343488i −0.749669 0.661813i \(-0.769787\pi\)
0.947982 + 0.318325i \(0.103120\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 22.7609 + 17.3079i 2.10425 + 1.60012i
\(118\) 0 0
\(119\) −2.14589 + 1.23893i −0.196714 + 0.113573i
\(120\) 0 0
\(121\) 0.344677 0.596999i 0.0313343 0.0542726i
\(122\) 0 0
\(123\) 11.9073 + 6.87471i 1.07365 + 0.619871i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.98477 + 5.16978i 0.264856 + 0.458744i 0.967526 0.252772i \(-0.0813423\pi\)
−0.702670 + 0.711516i \(0.748009\pi\)
\(128\) 0 0
\(129\) −7.13374 −0.628091
\(130\) 0 0
\(131\) 19.0556 1.66489 0.832447 0.554105i \(-0.186940\pi\)
0.832447 + 0.554105i \(0.186940\pi\)
\(132\) 0 0
\(133\) 3.20765 + 5.55581i 0.278138 + 0.481750i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.400964 + 0.231497i 0.0342567 + 0.0197781i 0.517031 0.855967i \(-0.327037\pi\)
−0.482774 + 0.875745i \(0.660371\pi\)
\(138\) 0 0
\(139\) −4.65970 + 8.07084i −0.395231 + 0.684559i −0.993131 0.117011i \(-0.962669\pi\)
0.597900 + 0.801571i \(0.296002\pi\)
\(140\) 0 0
\(141\) 10.0468 5.80053i 0.846095 0.488493i
\(142\) 0 0
\(143\) 4.76707 + 11.3682i 0.398642 + 0.950659i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −9.80368 + 16.9805i −0.808594 + 1.40053i
\(148\) 0 0
\(149\) 9.44524 + 5.45321i 0.773784 + 0.446744i 0.834223 0.551427i \(-0.185917\pi\)
−0.0604387 + 0.998172i \(0.519250\pi\)
\(150\) 0 0
\(151\) 4.85943i 0.395455i −0.980257 0.197727i \(-0.936644\pi\)
0.980257 0.197727i \(-0.0633561\pi\)
\(152\) 0 0
\(153\) −9.50121 16.4566i −0.768127 1.33044i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.80782 −0.702940 −0.351470 0.936199i \(-0.614318\pi\)
−0.351470 + 0.936199i \(0.614318\pi\)
\(158\) 0 0
\(159\) 7.52779 + 13.0385i 0.596992 + 1.03402i
\(160\) 0 0
\(161\) 7.50261i 0.591289i
\(162\) 0 0
\(163\) −16.1253 9.30996i −1.26303 0.729212i −0.289372 0.957217i \(-0.593447\pi\)
−0.973660 + 0.228004i \(0.926780\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.4508 + 7.18849i −0.963474 + 0.556262i −0.897240 0.441542i \(-0.854432\pi\)
−0.0662334 + 0.997804i \(0.521098\pi\)
\(168\) 0 0
\(169\) −12.5859 3.25499i −0.968147 0.250384i
\(170\) 0 0
\(171\) −42.6068 + 24.5990i −3.25822 + 1.88113i
\(172\) 0 0
\(173\) −10.9666 + 18.9947i −0.833773 + 1.44414i 0.0612532 + 0.998122i \(0.480490\pi\)
−0.895026 + 0.446014i \(0.852843\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 19.3266i 1.45268i
\(178\) 0 0
\(179\) 5.06250 + 8.76850i 0.378389 + 0.655388i 0.990828 0.135129i \(-0.0431450\pi\)
−0.612439 + 0.790518i \(0.709812\pi\)
\(180\) 0 0
\(181\) 0.272578 0.0202606 0.0101303 0.999949i \(-0.496775\pi\)
0.0101303 + 0.999949i \(0.496775\pi\)
\(182\) 0 0
\(183\) 12.5818 0.930076
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 8.19217i 0.599071i
\(188\) 0 0
\(189\) 14.5990 + 8.42876i 1.06192 + 0.613102i
\(190\) 0 0
\(191\) 7.39587 12.8100i 0.535147 0.926901i −0.464010 0.885830i \(-0.653590\pi\)
0.999156 0.0410710i \(-0.0130770\pi\)
\(192\) 0 0
\(193\) 6.06585 3.50212i 0.436629 0.252088i −0.265538 0.964101i \(-0.585549\pi\)
0.702167 + 0.712013i \(0.252216\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.34230 4.81643i 0.594365 0.343157i −0.172457 0.985017i \(-0.555171\pi\)
0.766821 + 0.641861i \(0.221837\pi\)
\(198\) 0 0
\(199\) −1.96091 + 3.39640i −0.139006 + 0.240765i −0.927120 0.374763i \(-0.877724\pi\)
0.788115 + 0.615528i \(0.211057\pi\)
\(200\) 0 0
\(201\) −21.8074 12.5905i −1.53818 0.888067i
\(202\) 0 0
\(203\) 1.86721i 0.131052i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −57.5366 −3.99907
\(208\) 0 0
\(209\) −21.2099 −1.46712
\(210\) 0 0
\(211\) 7.29429 + 12.6341i 0.502160 + 0.869766i 0.999997 + 0.00249580i \(0.000794440\pi\)
−0.497837 + 0.867271i \(0.665872\pi\)
\(212\) 0 0
\(213\) 36.2575i 2.48433i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.99924 + 5.19484i −0.203602 + 0.352649i
\(218\) 0 0
\(219\) −20.4818 + 11.8252i −1.38403 + 0.799070i
\(220\) 0 0
\(221\) 6.87684 + 5.22929i 0.462586 + 0.351760i
\(222\) 0 0
\(223\) −2.60093 + 1.50165i −0.174171 + 0.100558i −0.584551 0.811357i \(-0.698729\pi\)
0.410380 + 0.911915i \(0.365396\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.1162 + 5.84058i 0.671435 + 0.387653i 0.796620 0.604480i \(-0.206619\pi\)
−0.125185 + 0.992133i \(0.539953\pi\)
\(228\) 0 0
\(229\) 18.5293i 1.22445i 0.790684 + 0.612224i \(0.209725\pi\)
−0.790684 + 0.612224i \(0.790275\pi\)
\(230\) 0 0
\(231\) 5.84468 + 10.1233i 0.384552 + 0.666063i
\(232\) 0 0
\(233\) −11.1750 −0.732097 −0.366048 0.930596i \(-0.619290\pi\)
−0.366048 + 0.930596i \(0.619290\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −21.2460 36.7991i −1.38007 2.39036i
\(238\) 0 0
\(239\) 2.16507i 0.140047i −0.997545 0.0700235i \(-0.977693\pi\)
0.997545 0.0700235i \(-0.0223074\pi\)
\(240\) 0 0
\(241\) 16.7318 + 9.66011i 1.07779 + 0.622262i 0.930299 0.366801i \(-0.119547\pi\)
0.147491 + 0.989063i \(0.452880\pi\)
\(242\) 0 0
\(243\) −25.3096 + 43.8375i −1.62361 + 2.81218i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 13.5389 17.8044i 0.861457 1.13287i
\(248\) 0 0
\(249\) 2.02341 1.16822i 0.128228 0.0740327i
\(250\) 0 0
\(251\) −3.87684 + 6.71488i −0.244704 + 0.423840i −0.962048 0.272879i \(-0.912024\pi\)
0.717344 + 0.696719i \(0.245357\pi\)
\(252\) 0 0
\(253\) −21.4815 12.4024i −1.35053 0.779730i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.90366 + 15.4216i 0.555395 + 0.961973i 0.997873 + 0.0651933i \(0.0207664\pi\)
−0.442477 + 0.896780i \(0.645900\pi\)
\(258\) 0 0
\(259\) 1.47574 0.0916980
\(260\) 0 0
\(261\) 14.3194 0.886348
\(262\) 0 0
\(263\) 8.30316 + 14.3815i 0.511995 + 0.886801i 0.999903 + 0.0139065i \(0.00442670\pi\)
−0.487908 + 0.872895i \(0.662240\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 16.7373 + 9.66330i 1.02431 + 0.591385i
\(268\) 0 0
\(269\) 2.96967 5.14362i 0.181064 0.313612i −0.761179 0.648542i \(-0.775379\pi\)
0.942243 + 0.334930i \(0.108713\pi\)
\(270\) 0 0
\(271\) −8.37246 + 4.83384i −0.508591 + 0.293635i −0.732254 0.681031i \(-0.761532\pi\)
0.223663 + 0.974666i \(0.428198\pi\)
\(272\) 0 0
\(273\) −12.2287 1.55572i −0.740115 0.0941562i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −10.3590 + 17.9423i −0.622411 + 1.07805i 0.366624 + 0.930369i \(0.380513\pi\)
−0.989035 + 0.147679i \(0.952820\pi\)
\(278\) 0 0
\(279\) −39.8386 23.0008i −2.38507 1.37702i
\(280\) 0 0
\(281\) 27.7700i 1.65662i 0.560272 + 0.828309i \(0.310697\pi\)
−0.560272 + 0.828309i \(0.689303\pi\)
\(282\) 0 0
\(283\) 12.7885 + 22.1502i 0.760194 + 1.31670i 0.942750 + 0.333500i \(0.108230\pi\)
−0.182556 + 0.983196i \(0.558437\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.30067 −0.253861
\(288\) 0 0
\(289\) 5.62937 + 9.75035i 0.331139 + 0.573550i
\(290\) 0 0
\(291\) 52.8847i 3.10016i
\(292\) 0 0
\(293\) 24.5929 + 14.1987i 1.43673 + 0.829497i 0.997621 0.0689370i \(-0.0219608\pi\)
0.439109 + 0.898434i \(0.355294\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −48.2665 + 27.8667i −2.80071 + 1.61699i
\(298\) 0 0
\(299\) 24.1233 10.1157i 1.39509 0.585005i
\(300\) 0 0
\(301\) 1.93241 1.11568i 0.111382 0.0643067i
\(302\) 0 0
\(303\) 9.90396 17.1542i 0.568968 0.985481i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 11.5519i 0.659302i −0.944103 0.329651i \(-0.893069\pi\)
0.944103 0.329651i \(-0.106931\pi\)
\(308\) 0 0
\(309\) 19.3568 + 33.5269i 1.10117 + 1.90728i
\(310\) 0 0
\(311\) −1.03807 −0.0588634 −0.0294317 0.999567i \(-0.509370\pi\)
−0.0294317 + 0.999567i \(0.509370\pi\)
\(312\) 0 0
\(313\) 29.6339 1.67501 0.837504 0.546432i \(-0.184014\pi\)
0.837504 + 0.546432i \(0.184014\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.4445i 1.14828i −0.818759 0.574138i \(-0.805337\pi\)
0.818759 0.574138i \(-0.194663\pi\)
\(318\) 0 0
\(319\) 5.34620 + 3.08663i 0.299330 + 0.172818i
\(320\) 0 0
\(321\) −22.4193 + 38.8313i −1.25132 + 2.16735i
\(322\) 0 0
\(323\) −12.8729 + 7.43219i −0.716269 + 0.413538i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 3.99510 2.30657i 0.220930 0.127554i
\(328\) 0 0
\(329\) −1.81435 + 3.14254i −0.100028 + 0.173254i
\(330\) 0 0
\(331\) 4.39587 + 2.53796i 0.241619 + 0.139499i 0.615921 0.787808i \(-0.288784\pi\)
−0.374302 + 0.927307i \(0.622118\pi\)
\(332\) 0 0
\(333\) 11.3173i 0.620182i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −10.4909 −0.571473 −0.285737 0.958308i \(-0.592238\pi\)
−0.285737 + 0.958308i \(0.592238\pi\)
\(338\) 0 0
\(339\) −13.9393 −0.757081
\(340\) 0 0
\(341\) −9.91593 17.1749i −0.536977 0.930072i
\(342\) 0 0
\(343\) 13.3719i 0.722012i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.9491 + 27.6247i −0.856193 + 1.48297i 0.0193399 + 0.999813i \(0.493844\pi\)
−0.875533 + 0.483158i \(0.839490\pi\)
\(348\) 0 0
\(349\) 28.4661 16.4349i 1.52376 0.879741i 0.524151 0.851625i \(-0.324383\pi\)
0.999605 0.0281153i \(-0.00895056\pi\)
\(350\) 0 0
\(351\) 7.41745 58.3049i 0.395914 3.11209i
\(352\) 0 0
\(353\) −23.6988 + 13.6825i −1.26136 + 0.728245i −0.973337 0.229379i \(-0.926330\pi\)
−0.288021 + 0.957624i \(0.592997\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 7.09463 + 4.09609i 0.375488 + 0.216788i
\(358\) 0 0
\(359\) 0.625579i 0.0330168i 0.999864 + 0.0165084i \(0.00525502\pi\)
−0.999864 + 0.0165084i \(0.994745\pi\)
\(360\) 0 0
\(361\) 9.74225 + 16.8741i 0.512750 + 0.888109i
\(362\) 0 0
\(363\) −2.27911 −0.119622
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.98891 3.44490i −0.103820 0.179822i 0.809435 0.587209i \(-0.199773\pi\)
−0.913256 + 0.407387i \(0.866440\pi\)
\(368\) 0 0
\(369\) 32.9813i 1.71694i
\(370\) 0 0
\(371\) −4.07831 2.35461i −0.211735 0.122245i
\(372\) 0 0
\(373\) 14.1246 24.4645i 0.731343 1.26672i −0.224966 0.974367i \(-0.572227\pi\)
0.956309 0.292357i \(-0.0944396\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.00368 + 2.51754i −0.309205 + 0.129660i
\(378\) 0 0
\(379\) 14.1642 8.17771i 0.727567 0.420061i −0.0899646 0.995945i \(-0.528675\pi\)
0.817531 + 0.575884i \(0.195342\pi\)
\(380\) 0 0
\(381\) 9.86809 17.0920i 0.505557 0.875651i
\(382\) 0 0
\(383\) −18.0708 10.4332i −0.923376 0.533111i −0.0386654 0.999252i \(-0.512311\pi\)
−0.884710 + 0.466141i \(0.845644\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8.55600 + 14.8194i 0.434926 + 0.753314i
\(388\) 0 0
\(389\) 3.54177 0.179575 0.0897874 0.995961i \(-0.471381\pi\)
0.0897874 + 0.995961i \(0.471381\pi\)
\(390\) 0 0
\(391\) −17.3837 −0.879133
\(392\) 0 0
\(393\) −31.5002 54.5600i −1.58898 2.75219i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −23.9705 13.8394i −1.20305 0.694578i −0.241814 0.970323i \(-0.577742\pi\)
−0.961231 + 0.275744i \(0.911076\pi\)
\(398\) 0 0
\(399\) 10.6049 18.3683i 0.530911 0.919565i
\(400\) 0 0
\(401\) 10.6799 6.16604i 0.533328 0.307917i −0.209043 0.977907i \(-0.567035\pi\)
0.742371 + 0.669989i \(0.233701\pi\)
\(402\) 0 0
\(403\) 20.7469 + 2.63939i 1.03348 + 0.131477i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.43950 + 4.22534i −0.120922 + 0.209442i
\(408\) 0 0
\(409\) −31.2917 18.0663i −1.54728 0.893321i −0.998348 0.0574521i \(-0.981702\pi\)
−0.548929 0.835869i \(-0.684964\pi\)
\(410\) 0 0
\(411\) 1.53072i 0.0755049i
\(412\) 0 0
\(413\) 3.02258 + 5.23526i 0.148731 + 0.257610i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 30.8113 1.50883
\(418\) 0 0
\(419\) −6.26566 10.8524i −0.306097 0.530176i 0.671408 0.741088i \(-0.265690\pi\)
−0.977505 + 0.210912i \(0.932357\pi\)
\(420\) 0 0
\(421\) 7.74907i 0.377667i 0.982009 + 0.188833i \(0.0604706\pi\)
−0.982009 + 0.188833i \(0.939529\pi\)
\(422\) 0 0
\(423\) −24.0997 13.9140i −1.17177 0.676521i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.40821 + 1.96773i −0.164935 + 0.0952252i
\(428\) 0 0
\(429\) 24.6693 32.4416i 1.19104 1.56629i
\(430\) 0 0
\(431\) −18.9375 + 10.9336i −0.912188 + 0.526652i −0.881134 0.472866i \(-0.843219\pi\)
−0.0310532 + 0.999518i \(0.509886\pi\)
\(432\) 0 0
\(433\) −0.126574 + 0.219232i −0.00608275 + 0.0105356i −0.869051 0.494723i \(-0.835270\pi\)
0.862968 + 0.505259i \(0.168603\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 45.0072i 2.15299i
\(438\) 0 0
\(439\) −6.98432 12.0972i −0.333344 0.577368i 0.649822 0.760087i \(-0.274844\pi\)
−0.983165 + 0.182719i \(0.941510\pi\)
\(440\) 0 0
\(441\) 47.0330 2.23967
\(442\) 0 0
\(443\) −28.5957 −1.35862 −0.679310 0.733851i \(-0.737721\pi\)
−0.679310 + 0.733851i \(0.737721\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 36.0582i 1.70549i
\(448\) 0 0
\(449\) −15.7293 9.08129i −0.742309 0.428572i 0.0805990 0.996747i \(-0.474317\pi\)
−0.822908 + 0.568174i \(0.807650\pi\)
\(450\) 0 0
\(451\) 7.10932 12.3137i 0.334765 0.579829i
\(452\) 0 0
\(453\) −13.9135 + 8.03298i −0.653715 + 0.377422i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.86337 4.53992i 0.367833 0.212368i −0.304678 0.952455i \(-0.598549\pi\)
0.672511 + 0.740087i \(0.265216\pi\)
\(458\) 0 0
\(459\) −19.5296 + 33.8263i −0.911564 + 1.57888i
\(460\) 0 0
\(461\) −32.7734 18.9217i −1.52641 0.881273i −0.999509 0.0313456i \(-0.990021\pi\)
−0.526900 0.849927i \(-0.676646\pi\)
\(462\) 0 0
\(463\) 15.5694i 0.723570i −0.932262 0.361785i \(-0.882167\pi\)
0.932262 0.361785i \(-0.117833\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.19255 0.194008 0.0970040 0.995284i \(-0.469074\pi\)
0.0970040 + 0.995284i \(0.469074\pi\)
\(468\) 0 0
\(469\) 7.87636 0.363697
\(470\) 0 0
\(471\) 14.5599 + 25.2186i 0.670887 + 1.16201i
\(472\) 0 0
\(473\) 7.37719i 0.339204i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 18.0572 31.2760i 0.826783 1.43203i
\(478\) 0 0
\(479\) 10.7058 6.18102i 0.489162 0.282418i −0.235064 0.971980i \(-0.575530\pi\)
0.724227 + 0.689562i \(0.242197\pi\)
\(480\) 0 0
\(481\) −1.98972 4.74497i −0.0907234 0.216352i
\(482\) 0 0
\(483\) 21.4815 12.4024i 0.977443 0.564327i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.20427 + 0.695283i 0.0545705 + 0.0315063i 0.527037 0.849842i \(-0.323303\pi\)
−0.472467 + 0.881349i \(0.656636\pi\)
\(488\) 0 0
\(489\) 61.5601i 2.78384i
\(490\) 0 0
\(491\) −2.90025 5.02338i −0.130886 0.226702i 0.793132 0.609050i \(-0.208449\pi\)
−0.924019 + 0.382348i \(0.875116\pi\)
\(492\) 0 0
\(493\) 4.32637 0.194850
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.67049 + 9.82157i 0.254356 + 0.440558i
\(498\) 0 0
\(499\) 27.8242i 1.24558i −0.782388 0.622792i \(-0.785998\pi\)
0.782388 0.622792i \(-0.214002\pi\)
\(500\) 0 0
\(501\) 41.1642 + 23.7662i 1.83908 + 1.06179i
\(502\) 0 0
\(503\) 5.02953 8.71140i 0.224256 0.388422i −0.731840 0.681476i \(-0.761338\pi\)
0.956096 + 0.293054i \(0.0946716\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 11.4857 + 41.4168i 0.510097 + 1.83938i
\(508\) 0 0
\(509\) −2.00505 + 1.15762i −0.0888724 + 0.0513105i −0.543778 0.839229i \(-0.683006\pi\)
0.454905 + 0.890540i \(0.349673\pi\)
\(510\) 0 0
\(511\) 3.69878 6.40648i 0.163625 0.283406i
\(512\) 0 0
\(513\) 87.5777 + 50.5630i 3.86665 + 2.23241i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −5.99849 10.3897i −0.263813 0.456938i
\(518\) 0 0
\(519\) 72.5141 3.18301
\(520\) 0 0
\(521\) −2.78299 −0.121925 −0.0609626 0.998140i \(-0.519417\pi\)
−0.0609626 + 0.998140i \(0.519417\pi\)
\(522\) 0 0
\(523\) 13.6300 + 23.6078i 0.595997 + 1.03230i 0.993405 + 0.114655i \(0.0365763\pi\)
−0.397408 + 0.917642i \(0.630090\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12.0366 6.94931i −0.524321 0.302717i
\(528\) 0 0
\(529\) −14.8177 + 25.6650i −0.644248 + 1.11587i
\(530\) 0 0
\(531\) −40.1485 + 23.1798i −1.74230 + 1.00592i
\(532\) 0 0
\(533\) 5.79854 + 13.8280i 0.251162 + 0.598958i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 16.7373 28.9899i 0.722269 1.25101i
\(538\) 0 0
\(539\) 17.5599 + 10.1382i 0.756361 + 0.436685i
\(540\) 0 0
\(541\) 22.5466i 0.969353i −0.874693 0.484677i \(-0.838937\pi\)
0.874693 0.484677i \(-0.161063\pi\)
\(542\) 0 0
\(543\) −0.450591 0.780447i −0.0193367 0.0334922i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.51141 0.0646233 0.0323117 0.999478i \(-0.489713\pi\)
0.0323117 + 0.999478i \(0.489713\pi\)
\(548\) 0 0
\(549\) −15.0903 26.1371i −0.644038 1.11551i
\(550\) 0 0
\(551\) 11.2011i 0.477185i
\(552\) 0 0
\(553\) 11.5104 + 6.64551i 0.489470 + 0.282596i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 30.3618 17.5294i 1.28647 0.742745i 0.308449 0.951241i \(-0.400190\pi\)
0.978023 + 0.208496i \(0.0668567\pi\)
\(558\) 0 0
\(559\) −6.19271 4.70907i −0.261924 0.199172i
\(560\) 0 0
\(561\) −23.4559 + 13.5422i −0.990307 + 0.571754i
\(562\) 0 0
\(563\) −10.6460 + 18.4393i −0.448674 + 0.777125i −0.998300 0.0582852i \(-0.981437\pi\)
0.549626 + 0.835411i \(0.314770\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 31.1297i 1.30732i
\(568\) 0 0
\(569\) −0.488701 0.846455i −0.0204874 0.0354853i 0.855600 0.517638i \(-0.173188\pi\)
−0.876087 + 0.482152i \(0.839855\pi\)
\(570\) 0 0
\(571\) −24.5468 −1.02725 −0.513625 0.858015i \(-0.671698\pi\)
−0.513625 + 0.858015i \(0.671698\pi\)
\(572\) 0 0
\(573\) −48.9036 −2.04298
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 23.8270i 0.991932i −0.868342 0.495966i \(-0.834814\pi\)
0.868342 0.495966i \(-0.165186\pi\)
\(578\) 0 0
\(579\) −20.0546 11.5785i −0.833439 0.481186i
\(580\) 0 0
\(581\) −0.365406 + 0.632901i −0.0151596 + 0.0262572i
\(582\) 0 0
\(583\) 13.4835 7.78468i 0.558428 0.322409i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13.2172 7.63094i 0.545532 0.314963i −0.201786 0.979430i \(-0.564675\pi\)
0.747318 + 0.664467i \(0.231341\pi\)
\(588\) 0 0
\(589\) −17.9921 + 31.1632i −0.741350 + 1.28406i
\(590\) 0 0
\(591\) −27.5809 15.9238i −1.13452 0.655018i
\(592\) 0 0
\(593\) 35.9654i 1.47692i 0.674296 + 0.738461i \(0.264447\pi\)
−0.674296 + 0.738461i \(0.735553\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 12.9661 0.530668
\(598\) 0 0
\(599\) −6.60243 −0.269768 −0.134884 0.990861i \(-0.543066\pi\)
−0.134884 + 0.990861i \(0.543066\pi\)
\(600\) 0 0
\(601\) −14.9409 25.8783i −0.609451 1.05560i −0.991331 0.131388i \(-0.958057\pi\)
0.381881 0.924212i \(-0.375277\pi\)
\(602\) 0 0
\(603\) 60.4028i 2.45979i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −12.2450 + 21.2089i −0.497008 + 0.860843i −0.999994 0.00345162i \(-0.998901\pi\)
0.502986 + 0.864294i \(0.332235\pi\)
\(608\) 0 0
\(609\) −5.34620 + 3.08663i −0.216639 + 0.125077i
\(610\) 0 0
\(611\) 12.5505 + 1.59666i 0.507740 + 0.0645938i
\(612\) 0 0
\(613\) 28.3242 16.3530i 1.14400 0.660490i 0.196584 0.980487i \(-0.437015\pi\)
0.947419 + 0.319997i \(0.103682\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.4429 7.18390i −0.500932 0.289213i 0.228167 0.973622i \(-0.426727\pi\)
−0.729098 + 0.684409i \(0.760060\pi\)
\(618\) 0 0
\(619\) 11.1681i 0.448883i −0.974488 0.224442i \(-0.927944\pi\)
0.974488 0.224442i \(-0.0720558\pi\)
\(620\) 0 0
\(621\) 59.1329 + 102.421i 2.37292 + 4.11002i
\(622\) 0 0
\(623\) −6.04516 −0.242194
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 35.0614 + 60.7282i 1.40022 + 2.42525i
\(628\) 0 0
\(629\) 3.41932i 0.136337i
\(630\) 0 0
\(631\) 36.0259 + 20.7996i 1.43417 + 0.828018i 0.997435 0.0715729i \(-0.0228019\pi\)
0.436734 + 0.899591i \(0.356135\pi\)
\(632\) 0 0
\(633\) 24.1160 41.7701i 0.958524 1.66021i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −19.7195 + 8.26901i −0.781313 + 0.327630i
\(638\) 0 0
\(639\) −75.3203 + 43.4862i −2.97963 + 1.72029i
\(640\) 0 0
\(641\) 2.68565 4.65169i 0.106077 0.183731i −0.808101 0.589044i \(-0.799504\pi\)
0.914178 + 0.405314i \(0.132838\pi\)
\(642\) 0 0
\(643\) −15.2046 8.77839i −0.599612 0.346186i 0.169277 0.985568i \(-0.445857\pi\)
−0.768889 + 0.639383i \(0.779190\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.8732 32.6893i −0.741982 1.28515i −0.951592 0.307365i \(-0.900553\pi\)
0.209610 0.977785i \(-0.432781\pi\)
\(648\) 0 0
\(649\) −19.9862 −0.784525
\(650\) 0 0
\(651\) 19.8319 0.777272
\(652\) 0 0
\(653\) 6.35766 + 11.0118i 0.248794 + 0.430925i 0.963192 0.268816i \(-0.0866323\pi\)
−0.714397 + 0.699741i \(0.753299\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 49.1305 + 28.3655i 1.91676 + 1.10664i
\(658\) 0 0
\(659\) −11.0625 + 19.1608i −0.430934 + 0.746399i −0.996954 0.0779923i \(-0.975149\pi\)
0.566020 + 0.824391i \(0.308482\pi\)
\(660\) 0 0
\(661\) 0.612035 0.353359i 0.0238054 0.0137441i −0.488050 0.872816i \(-0.662292\pi\)
0.511855 + 0.859072i \(0.328958\pi\)
\(662\) 0 0
\(663\) 3.60463 28.3342i 0.139992 1.10041i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.54981 11.3446i 0.253610 0.439265i
\(668\) 0 0
\(669\) 8.59903 + 4.96466i 0.332458 + 0.191945i
\(670\) 0 0
\(671\) 13.0112i 0.502292i
\(672\) 0 0
\(673\) −13.4663 23.3244i −0.519090 0.899090i −0.999754 0.0221849i \(-0.992938\pi\)
0.480664 0.876905i \(-0.340396\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 21.5208 0.827111 0.413556 0.910479i \(-0.364287\pi\)
0.413556 + 0.910479i \(0.364287\pi\)
\(678\) 0 0
\(679\) 8.27088 + 14.3256i 0.317407 + 0.549766i
\(680\) 0 0
\(681\) 38.6196i 1.47991i
\(682\) 0 0
\(683\) −17.8031 10.2786i −0.681215 0.393300i 0.119098 0.992883i \(-0.462000\pi\)
−0.800313 + 0.599583i \(0.795333\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 53.0531 30.6302i 2.02410 1.16862i
\(688\) 0 0
\(689\) −2.07210 + 16.2877i −0.0789407 + 0.620514i
\(690\) 0 0
\(691\) 17.2344 9.95031i 0.655629 0.378528i −0.134980 0.990848i \(-0.543097\pi\)
0.790610 + 0.612321i \(0.209764\pi\)
\(692\) 0 0
\(693\) 14.0199 24.2831i 0.532571 0.922440i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 9.96475i 0.377442i
\(698\) 0 0
\(699\) 18.4730 + 31.9962i 0.698714 + 1.21021i
\(700\) 0 0
\(701\) 2.37131 0.0895631 0.0447816 0.998997i \(-0.485741\pi\)
0.0447816 + 0.998997i \(0.485741\pi\)
\(702\) 0 0
\(703\) 8.85276 0.333888
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.19571i 0.233014i
\(708\) 0 0
\(709\) 0.916777 + 0.529301i 0.0344303 + 0.0198783i 0.517116 0.855915i \(-0.327005\pi\)
−0.482686 + 0.875793i \(0.660339\pi\)
\(710\) 0 0
\(711\) −50.9636 + 88.2715i −1.91128 + 3.31044i
\(712\) 0 0
\(713\) −36.4450 + 21.0415i −1.36487 + 0.788011i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.19905 + 3.57902i −0.231508 + 0.133661i
\(718\) 0 0
\(719\) 5.60426 9.70687i 0.209004 0.362005i −0.742397 0.669960i \(-0.766311\pi\)
0.951401 + 0.307955i \(0.0996446\pi\)
\(720\) 0 0
\(721\) −10.4869 6.05460i −0.390551 0.225485i
\(722\) 0 0
\(723\) 63.8754i 2.37555i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 38.9060 1.44294 0.721472 0.692443i \(-0.243466\pi\)
0.721472 + 0.692443i \(0.243466\pi\)
\(728\) 0 0
\(729\) 77.0471 2.85360
\(730\) 0 0
\(731\) 2.58505 + 4.47745i 0.0956117 + 0.165604i
\(732\) 0 0
\(733\) 24.7392i 0.913765i −0.889527 0.456882i \(-0.848966\pi\)
0.889527 0.456882i \(-0.151034\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −13.0202 + 22.5516i −0.479605 + 0.830700i
\(738\) 0 0
\(739\) −0.302370 + 0.174574i −0.0111229 + 0.00642179i −0.505551 0.862797i \(-0.668711\pi\)
0.494428 + 0.869218i \(0.335377\pi\)
\(740\) 0 0
\(741\) −73.3584 9.33253i −2.69489 0.342839i
\(742\) 0 0
\(743\) 6.68184 3.85776i 0.245133 0.141528i −0.372401 0.928072i \(-0.621465\pi\)
0.617534 + 0.786544i \(0.288132\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −4.85364 2.80225i −0.177585 0.102529i
\(748\) 0 0
\(749\) 14.0250i 0.512463i
\(750\) 0 0
\(751\) 1.71161 + 2.96460i 0.0624575 + 0.108180i 0.895563 0.444934i \(-0.146773\pi\)
−0.833106 + 0.553114i \(0.813440\pi\)
\(752\) 0 0
\(753\) 25.6348 0.934183
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −5.63976 9.76835i −0.204981 0.355037i 0.745146 0.666901i \(-0.232380\pi\)
−0.950127 + 0.311865i \(0.899046\pi\)
\(758\) 0 0
\(759\) 82.0079i 2.97670i
\(760\) 0 0
\(761\) −33.1329 19.1293i −1.20107 0.693435i −0.240273 0.970705i \(-0.577237\pi\)
−0.960792 + 0.277270i \(0.910570\pi\)
\(762\) 0 0
\(763\) −0.721472 + 1.24963i −0.0261190 + 0.0452395i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.7577 16.7772i 0.460655 0.605789i
\(768\) 0 0
\(769\) −33.7503 + 19.4857i −1.21707 + 0.702674i −0.964289 0.264851i \(-0.914677\pi\)
−0.252777 + 0.967525i \(0.581344\pi\)
\(770\) 0 0
\(771\) 29.4368 50.9860i 1.06014 1.83622i
\(772\) 0 0
\(773\) −25.0126 14.4410i −0.899640 0.519407i −0.0225567 0.999746i \(-0.507181\pi\)
−0.877083 + 0.480338i \(0.840514\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −2.43950 4.22534i −0.0875167 0.151583i
\(778\) 0 0
\(779\) −25.7991 −0.924350
\(780\) 0 0
\(781\) −37.4949 −1.34167
\(782\) 0 0
\(783\) −14.7167 25.4900i −0.525931 0.910939i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 2.63389 + 1.52068i 0.0938879 + 0.0542062i 0.546209 0.837649i \(-0.316070\pi\)
−0.452321 + 0.891855i \(0.649404\pi\)
\(788\) 0 0
\(789\) 27.4514 47.5473i 0.977297 1.69273i
\(790\) 0 0
\(791\) 3.77594 2.18004i 0.134257 0.0775132i
\(792\) 0 0
\(793\) 10.9221 + 8.30542i 0.387856 + 0.294934i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21.1457 + 36.6254i −0.749018 + 1.29734i 0.199275 + 0.979944i \(0.436141\pi\)
−0.948294 + 0.317394i \(0.897192\pi\)
\(798\) 0 0
\(799\) −7.28133 4.20388i −0.257595 0.148723i
\(800\) 0 0
\(801\) 46.3595i 1.63803i
\(802\) 0 0
\(803\) 12.2287 + 21.1807i 0.431542 + 0.747452i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −19.6363 −0.691230
\(808\) 0 0
\(809\) −17.6250 30.5274i −0.619662 1.07329i −0.989547 0.144208i \(-0.953936\pi\)
0.369886 0.929077i \(-0.379397\pi\)
\(810\) 0 0
\(811\) 30.1607i 1.05908i 0.848284 + 0.529542i \(0.177636\pi\)
−0.848284 + 0.529542i \(0.822364\pi\)
\(812\) 0 0
\(813\) 27.6806 + 15.9814i 0.970800 + 0.560492i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 11.5923 6.69281i 0.405563 0.234152i
\(818\) 0 0
\(819\) 11.4350 + 27.2694i 0.399570 + 0.952872i
\(820\) 0 0
\(821\) 3.92434 2.26572i 0.136960 0.0790741i −0.429954 0.902851i \(-0.641470\pi\)
0.566915 + 0.823777i \(0.308137\pi\)
\(822\) 0 0
\(823\) −9.97249 + 17.2729i −0.347619 + 0.602094i −0.985826 0.167771i \(-0.946343\pi\)
0.638207 + 0.769865i \(0.279676\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 12.3377i 0.429025i 0.976721 + 0.214512i \(0.0688163\pi\)
−0.976721 + 0.214512i \(0.931184\pi\)
\(828\) 0 0
\(829\) −18.7968 32.5570i −0.652840 1.13075i −0.982431 0.186628i \(-0.940244\pi\)
0.329591 0.944124i \(-0.393089\pi\)
\(830\) 0 0
\(831\) 68.4966 2.37612
\(832\) 0 0
\(833\) 14.2102 0.492355
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 94.5557i 3.26832i
\(838\) 0 0
\(839\) 20.7606 + 11.9861i 0.716736 + 0.413808i 0.813550 0.581495i \(-0.197532\pi\)
−0.0968144 + 0.995302i \(0.530865\pi\)
\(840\) 0 0
\(841\) 12.8699 22.2914i 0.443790 0.768667i
\(842\) 0 0
\(843\) 79.5111 45.9058i 2.73851 1.58108i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0.617372 0.356440i 0.0212132 0.0122474i
\(848\) 0 0
\(849\) 42.2804 73.2319i 1.45106 2.51331i
\(850\) 0 0
\(851\) 8.96614 + 5.17660i 0.307355 + 0.177452i
\(852\) 0 0
\(853\) 38.8952i 1.33175i 0.746065 + 0.665873i \(0.231941\pi\)
−0.746065 + 0.665873i \(0.768059\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 44.4570 1.51862 0.759312 0.650727i \(-0.225536\pi\)
0.759312 + 0.650727i \(0.225536\pi\)
\(858\) 0 0
\(859\) 46.8129 1.59724 0.798618 0.601838i \(-0.205565\pi\)
0.798618 + 0.601838i \(0.205565\pi\)
\(860\) 0 0
\(861\) 7.10932 + 12.3137i 0.242285 + 0.419650i
\(862\) 0 0
\(863\) 28.9384i 0.985073i 0.870292 + 0.492537i \(0.163930\pi\)
−0.870292 + 0.492537i \(0.836070\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 18.6115 32.2361i 0.632079 1.09479i
\(868\) 0 0
\(869\) −38.0549 + 21.9710i −1.29092 + 0.745315i
\(870\) 0 0
\(871\) −10.6196 25.3250i −0.359831 0.858105i
\(872\) 0 0
\(873\) −109.861 + 63.4283i −3.71824 + 2.14672i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −1.58011 0.912276i −0.0533565 0.0308054i 0.473084 0.881017i \(-0.343141\pi\)
−0.526441 + 0.850212i \(0.676474\pi\)
\(878\) 0 0
\(879\) 93.8858i 3.16669i
\(880\) 0 0
\(881\) −5.47740 9.48714i −0.184538 0.319630i 0.758882 0.651228i \(-0.225746\pi\)
−0.943421 + 0.331598i \(0.892412\pi\)
\(882\) 0 0
\(883\) 15.8747 0.534227 0.267113 0.963665i \(-0.413930\pi\)
0.267113 + 0.963665i \(0.413930\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.97769 + 5.15751i 0.0999811 + 0.173172i 0.911677 0.410908i \(-0.134788\pi\)
−0.811695 + 0.584081i \(0.801455\pi\)
\(888\) 0 0
\(889\) 6.17327i 0.207045i
\(890\) 0 0
\(891\) 89.1306 + 51.4596i 2.98599 + 1.72396i
\(892\) 0 0
\(893\) −10.8840 + 18.8517i −0.364220 + 0.630847i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −68.8408 52.3480i −2.29853 1.74785i
\(898\) 0 0
\(899\) 9.07023 5.23670i 0.302509 0.174654i
\(900\) 0 0
\(901\) 5.45569 9.44953i 0.181755 0.314809i
\(902\) 0 0
\(903\) −6.38884 3.68860i −0.212607 0.122749i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 19.0943 + 33.0723i 0.634015 + 1.09815i 0.986723 + 0.162413i \(0.0519278\pi\)
−0.352707 + 0.935734i \(0.614739\pi\)
\(908\) 0 0
\(909\) −47.5141 −1.57594
\(910\) 0 0
\(911\) 33.7516 1.11824 0.559121 0.829086i \(-0.311139\pi\)
0.559121 + 0.829086i \(0.311139\pi\)
\(912\) 0 0
\(913\) −1.20808 2.09246i −0.0399817 0.0692504i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 17.0658 + 9.85294i 0.563562 + 0.325373i
\(918\) 0 0
\(919\) 10.5062 18.1973i 0.346568 0.600273i −0.639070 0.769149i \(-0.720680\pi\)
0.985637 + 0.168876i \(0.0540137\pi\)
\(920\) 0 0
\(921\) −33.0755 + 19.0961i −1.08987 + 0.629239i
\(922\) 0 0
\(923\) 23.9340 31.4747i 0.787798 1.03600i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 46.4319 80.4225i 1.52502 2.64142i
\(928\) 0 0
\(929\) 33.3099 + 19.2315i 1.09286 + 0.630965i 0.934337 0.356390i \(-0.115992\pi\)
0.158526 + 0.987355i \(0.449326\pi\)
\(930\) 0 0
\(931\) 36.7909i 1.20577i
\(932\) 0 0
\(933\) 1.71600 + 2.97220i 0.0561793 + 0.0973054i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −45.7434 −1.49437 −0.747186 0.664615i \(-0.768596\pi\)
−0.747186 + 0.664615i \(0.768596\pi\)
\(938\) 0 0
\(939\) −48.9870 84.8479i −1.59863 2.76891i
\(940\) 0 0
\(941\) 58.6037i 1.91043i −0.295917 0.955214i \(-0.595625\pi\)
0.295917 0.955214i \(-0.404375\pi\)
\(942\) 0 0
\(943\) −26.1296 15.0859i −0.850896 0.491265i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −35.2500 + 20.3516i −1.14547 + 0.661338i −0.947780 0.318926i \(-0.896678\pi\)
−0.197692 + 0.980264i \(0.563345\pi\)
\(948\) 0 0
\(949\) −25.5859 3.25499i −0.830554 0.105662i
\(950\) 0 0
\(951\) −58.5367 + 33.7962i −1.89818 + 1.09592i
\(952\) 0 0
\(953\) −1.50581 + 2.60814i −0.0487779 + 0.0844859i −0.889384 0.457162i \(-0.848866\pi\)
0.840606 + 0.541648i \(0.182199\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 20.4097i 0.659752i
\(958\) 0 0
\(959\) 0.239397 + 0.414647i 0.00773052 + 0.0133897i
\(960\) 0 0
\(961\) −2.64620 −0.0853612
\(962\) 0 0
\(963\) 107.556 3.46595
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 37.8156i 1.21607i 0.793912 + 0.608033i \(0.208041\pi\)
−0.793912 + 0.608033i \(0.791959\pi\)
\(968\) 0 0
\(969\) 42.5597 + 24.5719i 1.36722 + 0.789362i
\(970\) 0 0
\(971\) −12.8681 + 22.2882i −0.412957 + 0.715262i −0.995212 0.0977445i \(-0.968837\pi\)
0.582255 + 0.813006i \(0.302171\pi\)
\(972\) 0 0
\(973\) −8.34626 + 4.81872i −0.267569 + 0.154481i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −20.8908 + 12.0613i −0.668355 + 0.385875i −0.795453 0.606015i \(-0.792767\pi\)
0.127098 + 0.991890i \(0.459434\pi\)
\(978\) 0 0
\(979\) 9.99308 17.3085i 0.319380 0.553183i
\(980\) 0 0
\(981\) −9.58322 5.53288i −0.305969 0.176651i
\(982\) 0 0
\(983\) 22.5964i 0.720715i 0.932814 + 0.360357i \(0.117345\pi\)
−0.932814 + 0.360357i \(0.882655\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 11.9970 0.381868
\(988\) 0 0
\(989\) 15.6543 0.497779
\(990\) 0 0
\(991\) −7.57562 13.1214i −0.240648 0.416814i 0.720251 0.693713i \(-0.244026\pi\)
−0.960899 + 0.276899i \(0.910693\pi\)
\(992\) 0 0
\(993\) 16.7817i 0.532552i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 26.7679 46.3633i 0.847747 1.46834i −0.0354673 0.999371i \(-0.511292\pi\)
0.883214 0.468970i \(-0.155375\pi\)
\(998\) 0 0
\(999\) 20.1459 11.6312i 0.637388 0.367996i
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 1300.2.y.e.101.1 16
5.2 odd 4 260.2.z.a.49.1 16
5.3 odd 4 260.2.z.a.49.8 yes 16
5.4 even 2 inner 1300.2.y.e.101.8 16
13.4 even 6 inner 1300.2.y.e.901.1 16
15.2 even 4 2340.2.cr.a.829.3 16
15.8 even 4 2340.2.cr.a.829.6 16
20.3 even 4 1040.2.df.d.49.1 16
20.7 even 4 1040.2.df.d.49.8 16
65.2 even 12 3380.2.c.e.2029.2 16
65.3 odd 12 3380.2.d.d.1689.15 16
65.4 even 6 inner 1300.2.y.e.901.8 16
65.17 odd 12 260.2.z.a.69.8 yes 16
65.23 odd 12 3380.2.d.d.1689.16 16
65.28 even 12 3380.2.c.e.2029.16 16
65.37 even 12 3380.2.c.e.2029.1 16
65.42 odd 12 3380.2.d.d.1689.2 16
65.43 odd 12 260.2.z.a.69.1 yes 16
65.62 odd 12 3380.2.d.d.1689.1 16
65.63 even 12 3380.2.c.e.2029.15 16
195.17 even 12 2340.2.cr.a.1369.6 16
195.173 even 12 2340.2.cr.a.1369.3 16
260.43 even 12 1040.2.df.d.849.8 16
260.147 even 12 1040.2.df.d.849.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.z.a.49.1 16 5.2 odd 4
260.2.z.a.49.8 yes 16 5.3 odd 4
260.2.z.a.69.1 yes 16 65.43 odd 12
260.2.z.a.69.8 yes 16 65.17 odd 12
1040.2.df.d.49.1 16 20.3 even 4
1040.2.df.d.49.8 16 20.7 even 4
1040.2.df.d.849.1 16 260.147 even 12
1040.2.df.d.849.8 16 260.43 even 12
1300.2.y.e.101.1 16 1.1 even 1 trivial
1300.2.y.e.101.8 16 5.4 even 2 inner
1300.2.y.e.901.1 16 13.4 even 6 inner
1300.2.y.e.901.8 16 65.4 even 6 inner
2340.2.cr.a.829.3 16 15.2 even 4
2340.2.cr.a.829.6 16 15.8 even 4
2340.2.cr.a.1369.3 16 195.173 even 12
2340.2.cr.a.1369.6 16 195.17 even 12
3380.2.c.e.2029.1 16 65.37 even 12
3380.2.c.e.2029.2 16 65.2 even 12
3380.2.c.e.2029.15 16 65.63 even 12
3380.2.c.e.2029.16 16 65.28 even 12
3380.2.d.d.1689.1 16 65.62 odd 12
3380.2.d.d.1689.2 16 65.42 odd 12
3380.2.d.d.1689.15 16 65.3 odd 12
3380.2.d.d.1689.16 16 65.23 odd 12