Properties

Label 252.2.i.b.121.6
Level $252$
Weight $2$
Character 252.121
Analytic conductor $2.012$
Analytic rank $0$
Dimension $14$
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] = [252,2,Mod(25,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.6
Root \(-1.58203 - 0.705117i\) of defining polynomial
Character \(\chi\) \(=\) 252.121
Dual form 252.2.i.b.25.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40166 - 1.01752i) q^{3} +(1.26013 + 2.18261i) q^{5} +(0.527655 + 2.59260i) q^{7} +(0.929318 - 2.85243i) q^{9} +O(q^{10})\) \(q+(1.40166 - 1.01752i) q^{3} +(1.26013 + 2.18261i) q^{5} +(0.527655 + 2.59260i) q^{7} +(0.929318 - 2.85243i) q^{9} +(0.687041 - 1.18999i) q^{11} +(-2.80008 + 4.84989i) q^{13} +(3.98712 + 1.77708i) q^{15} +(-2.69613 - 4.66983i) q^{17} +(2.44717 - 4.23863i) q^{19} +(3.37761 + 3.09705i) q^{21} +(-2.08765 - 3.61591i) q^{23} +(-0.675864 + 1.17063i) q^{25} +(-1.59981 - 4.94375i) q^{27} +(-1.56761 - 2.71518i) q^{29} +4.80121 q^{31} +(-0.247835 - 2.36704i) q^{33} +(-4.99373 + 4.41869i) q^{35} +(-2.69839 + 4.67374i) q^{37} +(1.01007 + 9.64704i) q^{39} +(-3.02991 + 5.24797i) q^{41} +(2.44717 + 4.23863i) q^{43} +(7.39682 - 1.56610i) q^{45} -5.65548 q^{47} +(-6.44316 + 2.73600i) q^{49} +(-8.53069 - 3.80217i) q^{51} +(-7.00281 - 12.1292i) q^{53} +3.46305 q^{55} +(-0.882764 - 8.43117i) q^{57} +14.2688 q^{59} -6.85721 q^{61} +(7.88558 + 0.904251i) q^{63} -14.1139 q^{65} -8.11356 q^{67} +(-6.60543 - 2.94407i) q^{69} -2.25704 q^{71} +(3.51456 + 6.08739i) q^{73} +(0.243803 + 2.32853i) q^{75} +(3.44769 + 1.15332i) q^{77} +2.75685 q^{79} +(-7.27273 - 5.30163i) q^{81} +(7.48876 + 12.9709i) q^{83} +(6.79495 - 11.7692i) q^{85} +(-4.95999 - 2.21069i) q^{87} +(2.75804 - 4.77707i) q^{89} +(-14.0513 - 4.70043i) q^{91} +(6.72968 - 4.88531i) q^{93} +12.3350 q^{95} +(0.894003 + 1.54846i) q^{97} +(-2.75589 - 3.06562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.40166 1.01752i 0.809251 0.587464i
\(4\) 0 0
\(5\) 1.26013 + 2.18261i 0.563548 + 0.976094i 0.997183 + 0.0750053i \(0.0238974\pi\)
−0.433635 + 0.901089i \(0.642769\pi\)
\(6\) 0 0
\(7\) 0.527655 + 2.59260i 0.199435 + 0.979911i
\(8\) 0 0
\(9\) 0.929318 2.85243i 0.309773 0.950811i
\(10\) 0 0
\(11\) 0.687041 1.18999i 0.207151 0.358796i −0.743665 0.668552i \(-0.766914\pi\)
0.950816 + 0.309757i \(0.100248\pi\)
\(12\) 0 0
\(13\) −2.80008 + 4.84989i −0.776603 + 1.34512i 0.157285 + 0.987553i \(0.449726\pi\)
−0.933889 + 0.357563i \(0.883608\pi\)
\(14\) 0 0
\(15\) 3.98712 + 1.77708i 1.02947 + 0.458840i
\(16\) 0 0
\(17\) −2.69613 4.66983i −0.653907 1.13260i −0.982167 0.188013i \(-0.939795\pi\)
0.328260 0.944588i \(-0.393538\pi\)
\(18\) 0 0
\(19\) 2.44717 4.23863i 0.561420 0.972408i −0.435953 0.899969i \(-0.643589\pi\)
0.997373 0.0724385i \(-0.0230781\pi\)
\(20\) 0 0
\(21\) 3.37761 + 3.09705i 0.737055 + 0.675833i
\(22\) 0 0
\(23\) −2.08765 3.61591i −0.435304 0.753969i 0.562016 0.827126i \(-0.310026\pi\)
−0.997320 + 0.0731570i \(0.976693\pi\)
\(24\) 0 0
\(25\) −0.675864 + 1.17063i −0.135173 + 0.234126i
\(26\) 0 0
\(27\) −1.59981 4.94375i −0.307883 0.951424i
\(28\) 0 0
\(29\) −1.56761 2.71518i −0.291097 0.504195i 0.682972 0.730444i \(-0.260687\pi\)
−0.974069 + 0.226249i \(0.927354\pi\)
\(30\) 0 0
\(31\) 4.80121 0.862323 0.431161 0.902275i \(-0.358104\pi\)
0.431161 + 0.902275i \(0.358104\pi\)
\(32\) 0 0
\(33\) −0.247835 2.36704i −0.0431426 0.412049i
\(34\) 0 0
\(35\) −4.99373 + 4.41869i −0.844094 + 0.746894i
\(36\) 0 0
\(37\) −2.69839 + 4.67374i −0.443612 + 0.768359i −0.997954 0.0639302i \(-0.979637\pi\)
0.554342 + 0.832289i \(0.312970\pi\)
\(38\) 0 0
\(39\) 1.01007 + 9.64704i 0.161740 + 1.54476i
\(40\) 0 0
\(41\) −3.02991 + 5.24797i −0.473193 + 0.819595i −0.999529 0.0306820i \(-0.990232\pi\)
0.526336 + 0.850277i \(0.323565\pi\)
\(42\) 0 0
\(43\) 2.44717 + 4.23863i 0.373190 + 0.646385i 0.990054 0.140685i \(-0.0449305\pi\)
−0.616864 + 0.787070i \(0.711597\pi\)
\(44\) 0 0
\(45\) 7.39682 1.56610i 1.10265 0.233460i
\(46\) 0 0
\(47\) −5.65548 −0.824936 −0.412468 0.910972i \(-0.635333\pi\)
−0.412468 + 0.910972i \(0.635333\pi\)
\(48\) 0 0
\(49\) −6.44316 + 2.73600i −0.920451 + 0.390857i
\(50\) 0 0
\(51\) −8.53069 3.80217i −1.19454 0.532411i
\(52\) 0 0
\(53\) −7.00281 12.1292i −0.961910 1.66608i −0.717696 0.696356i \(-0.754803\pi\)
−0.244214 0.969721i \(-0.578530\pi\)
\(54\) 0 0
\(55\) 3.46305 0.466958
\(56\) 0 0
\(57\) −0.882764 8.43117i −0.116925 1.11674i
\(58\) 0 0
\(59\) 14.2688 1.85765 0.928823 0.370524i \(-0.120822\pi\)
0.928823 + 0.370524i \(0.120822\pi\)
\(60\) 0 0
\(61\) −6.85721 −0.877975 −0.438988 0.898493i \(-0.644663\pi\)
−0.438988 + 0.898493i \(0.644663\pi\)
\(62\) 0 0
\(63\) 7.88558 + 0.904251i 0.993489 + 0.113925i
\(64\) 0 0
\(65\) −14.1139 −1.75061
\(66\) 0 0
\(67\) −8.11356 −0.991229 −0.495615 0.868543i \(-0.665057\pi\)
−0.495615 + 0.868543i \(0.665057\pi\)
\(68\) 0 0
\(69\) −6.60543 2.94407i −0.795200 0.354424i
\(70\) 0 0
\(71\) −2.25704 −0.267861 −0.133931 0.990991i \(-0.542760\pi\)
−0.133931 + 0.990991i \(0.542760\pi\)
\(72\) 0 0
\(73\) 3.51456 + 6.08739i 0.411348 + 0.712475i 0.995037 0.0995017i \(-0.0317249\pi\)
−0.583690 + 0.811977i \(0.698392\pi\)
\(74\) 0 0
\(75\) 0.243803 + 2.32853i 0.0281520 + 0.268876i
\(76\) 0 0
\(77\) 3.44769 + 1.15332i 0.392901 + 0.131433i
\(78\) 0 0
\(79\) 2.75685 0.310170 0.155085 0.987901i \(-0.450435\pi\)
0.155085 + 0.987901i \(0.450435\pi\)
\(80\) 0 0
\(81\) −7.27273 5.30163i −0.808082 0.589070i
\(82\) 0 0
\(83\) 7.48876 + 12.9709i 0.821998 + 1.42374i 0.904192 + 0.427127i \(0.140474\pi\)
−0.0821933 + 0.996616i \(0.526192\pi\)
\(84\) 0 0
\(85\) 6.79495 11.7692i 0.737016 1.27655i
\(86\) 0 0
\(87\) −4.95999 2.21069i −0.531767 0.237011i
\(88\) 0 0
\(89\) 2.75804 4.77707i 0.292352 0.506368i −0.682014 0.731339i \(-0.738896\pi\)
0.974365 + 0.224971i \(0.0722289\pi\)
\(90\) 0 0
\(91\) −14.0513 4.70043i −1.47298 0.492739i
\(92\) 0 0
\(93\) 6.72968 4.88531i 0.697835 0.506583i
\(94\) 0 0
\(95\) 12.3350 1.26555
\(96\) 0 0
\(97\) 0.894003 + 1.54846i 0.0907722 + 0.157222i 0.907836 0.419325i \(-0.137733\pi\)
−0.817064 + 0.576547i \(0.804400\pi\)
\(98\) 0 0
\(99\) −2.75589 3.06562i −0.276977 0.308106i
\(100\) 0 0
\(101\) −6.69534 + 11.5967i −0.666211 + 1.15391i 0.312744 + 0.949837i \(0.398752\pi\)
−0.978955 + 0.204074i \(0.934582\pi\)
\(102\) 0 0
\(103\) −1.10164 1.90810i −0.108548 0.188010i 0.806634 0.591051i \(-0.201287\pi\)
−0.915182 + 0.403040i \(0.867953\pi\)
\(104\) 0 0
\(105\) −2.50343 + 11.2747i −0.244310 + 1.10030i
\(106\) 0 0
\(107\) 4.93284 8.54392i 0.476875 0.825972i −0.522774 0.852472i \(-0.675103\pi\)
0.999649 + 0.0264995i \(0.00843603\pi\)
\(108\) 0 0
\(109\) 1.54340 + 2.67325i 0.147831 + 0.256051i 0.930426 0.366481i \(-0.119438\pi\)
−0.782595 + 0.622532i \(0.786104\pi\)
\(110\) 0 0
\(111\) 0.973384 + 9.29667i 0.0923895 + 0.882401i
\(112\) 0 0
\(113\) 0.218815 0.378999i 0.0205844 0.0356532i −0.855550 0.517721i \(-0.826781\pi\)
0.876134 + 0.482067i \(0.160114\pi\)
\(114\) 0 0
\(115\) 5.26142 9.11304i 0.490630 0.849796i
\(116\) 0 0
\(117\) 11.2318 + 12.4941i 1.03838 + 1.15508i
\(118\) 0 0
\(119\) 10.6844 9.45404i 0.979435 0.866651i
\(120\) 0 0
\(121\) 4.55595 + 7.89113i 0.414177 + 0.717376i
\(122\) 0 0
\(123\) 1.09298 + 10.4389i 0.0985503 + 0.941241i
\(124\) 0 0
\(125\) 9.19461 0.822391
\(126\) 0 0
\(127\) −5.75958 −0.511080 −0.255540 0.966798i \(-0.582253\pi\)
−0.255540 + 0.966798i \(0.582253\pi\)
\(128\) 0 0
\(129\) 7.74299 + 3.45109i 0.681732 + 0.303851i
\(130\) 0 0
\(131\) 0.714865 + 1.23818i 0.0624580 + 0.108180i 0.895564 0.444934i \(-0.146773\pi\)
−0.833106 + 0.553114i \(0.813439\pi\)
\(132\) 0 0
\(133\) 12.2803 + 4.10801i 1.06484 + 0.356210i
\(134\) 0 0
\(135\) 8.77431 9.72153i 0.755172 0.836696i
\(136\) 0 0
\(137\) −5.59335 + 9.68796i −0.477872 + 0.827698i −0.999678 0.0253656i \(-0.991925\pi\)
0.521806 + 0.853064i \(0.325258\pi\)
\(138\) 0 0
\(139\) 7.87024 13.6317i 0.667545 1.15622i −0.311044 0.950396i \(-0.600679\pi\)
0.978589 0.205826i \(-0.0659881\pi\)
\(140\) 0 0
\(141\) −7.92707 + 5.75454i −0.667580 + 0.484620i
\(142\) 0 0
\(143\) 3.84755 + 6.66415i 0.321748 + 0.557284i
\(144\) 0 0
\(145\) 3.95078 6.84296i 0.328095 0.568277i
\(146\) 0 0
\(147\) −6.24721 + 10.3910i −0.515261 + 0.857033i
\(148\) 0 0
\(149\) −3.96513 6.86780i −0.324836 0.562632i 0.656643 0.754201i \(-0.271976\pi\)
−0.981479 + 0.191569i \(0.938642\pi\)
\(150\) 0 0
\(151\) 5.39683 9.34758i 0.439188 0.760696i −0.558439 0.829545i \(-0.688600\pi\)
0.997627 + 0.0688499i \(0.0219329\pi\)
\(152\) 0 0
\(153\) −15.8259 + 3.35076i −1.27945 + 0.270893i
\(154\) 0 0
\(155\) 6.05016 + 10.4792i 0.485960 + 0.841708i
\(156\) 0 0
\(157\) 21.1768 1.69009 0.845045 0.534695i \(-0.179574\pi\)
0.845045 + 0.534695i \(0.179574\pi\)
\(158\) 0 0
\(159\) −22.1573 9.87561i −1.75719 0.783187i
\(160\) 0 0
\(161\) 8.27305 7.32039i 0.652008 0.576927i
\(162\) 0 0
\(163\) 0.536552 0.929336i 0.0420260 0.0727912i −0.844247 0.535954i \(-0.819952\pi\)
0.886273 + 0.463163i \(0.153285\pi\)
\(164\) 0 0
\(165\) 4.85403 3.52371i 0.377886 0.274321i
\(166\) 0 0
\(167\) −7.71638 + 13.3652i −0.597112 + 1.03423i 0.396133 + 0.918193i \(0.370352\pi\)
−0.993245 + 0.116035i \(0.962982\pi\)
\(168\) 0 0
\(169\) −9.18094 15.9018i −0.706226 1.22322i
\(170\) 0 0
\(171\) −9.81620 10.9194i −0.750663 0.835030i
\(172\) 0 0
\(173\) 20.3620 1.54809 0.774046 0.633129i \(-0.218230\pi\)
0.774046 + 0.633129i \(0.218230\pi\)
\(174\) 0 0
\(175\) −3.39160 1.13456i −0.256381 0.0857644i
\(176\) 0 0
\(177\) 20.0001 14.5188i 1.50330 1.09130i
\(178\) 0 0
\(179\) 3.04960 + 5.28206i 0.227938 + 0.394800i 0.957197 0.289438i \(-0.0934684\pi\)
−0.729259 + 0.684238i \(0.760135\pi\)
\(180\) 0 0
\(181\) 10.0056 0.743714 0.371857 0.928290i \(-0.378721\pi\)
0.371857 + 0.928290i \(0.378721\pi\)
\(182\) 0 0
\(183\) −9.61149 + 6.97733i −0.710502 + 0.515779i
\(184\) 0 0
\(185\) −13.6013 −0.999987
\(186\) 0 0
\(187\) −7.40940 −0.541829
\(188\) 0 0
\(189\) 11.9730 6.75625i 0.870909 0.491445i
\(190\) 0 0
\(191\) −22.1987 −1.60624 −0.803120 0.595818i \(-0.796828\pi\)
−0.803120 + 0.595818i \(0.796828\pi\)
\(192\) 0 0
\(193\) −26.6160 −1.91586 −0.957930 0.287002i \(-0.907342\pi\)
−0.957930 + 0.287002i \(0.907342\pi\)
\(194\) 0 0
\(195\) −19.7829 + 14.3611i −1.41668 + 1.02842i
\(196\) 0 0
\(197\) 10.1696 0.724551 0.362276 0.932071i \(-0.382000\pi\)
0.362276 + 0.932071i \(0.382000\pi\)
\(198\) 0 0
\(199\) −1.66243 2.87941i −0.117846 0.204116i 0.801068 0.598574i \(-0.204266\pi\)
−0.918914 + 0.394458i \(0.870932\pi\)
\(200\) 0 0
\(201\) −11.3725 + 8.25569i −0.802153 + 0.582311i
\(202\) 0 0
\(203\) 6.21221 5.49686i 0.436012 0.385804i
\(204\) 0 0
\(205\) −15.2724 −1.06667
\(206\) 0 0
\(207\) −12.2542 + 2.59454i −0.851727 + 0.180333i
\(208\) 0 0
\(209\) −3.36262 5.82423i −0.232597 0.402870i
\(210\) 0 0
\(211\) −1.29535 + 2.24361i −0.0891755 + 0.154456i −0.907163 0.420780i \(-0.861757\pi\)
0.817987 + 0.575236i \(0.195090\pi\)
\(212\) 0 0
\(213\) −3.16361 + 2.29658i −0.216767 + 0.157359i
\(214\) 0 0
\(215\) −6.16752 + 10.6825i −0.420621 + 0.728538i
\(216\) 0 0
\(217\) 2.53338 + 12.4476i 0.171977 + 0.845000i
\(218\) 0 0
\(219\) 11.1202 + 4.95635i 0.751437 + 0.334919i
\(220\) 0 0
\(221\) 30.1975 2.03131
\(222\) 0 0
\(223\) −12.4029 21.4824i −0.830556 1.43857i −0.897598 0.440816i \(-0.854689\pi\)
0.0670411 0.997750i \(-0.478644\pi\)
\(224\) 0 0
\(225\) 2.71105 + 3.01574i 0.180737 + 0.201050i
\(226\) 0 0
\(227\) −3.55125 + 6.15095i −0.235705 + 0.408253i −0.959477 0.281786i \(-0.909073\pi\)
0.723772 + 0.690039i \(0.242407\pi\)
\(228\) 0 0
\(229\) 3.23252 + 5.59889i 0.213611 + 0.369985i 0.952842 0.303467i \(-0.0981442\pi\)
−0.739231 + 0.673452i \(0.764811\pi\)
\(230\) 0 0
\(231\) 6.00602 1.89152i 0.395167 0.124453i
\(232\) 0 0
\(233\) −4.42950 + 7.67212i −0.290186 + 0.502617i −0.973854 0.227177i \(-0.927051\pi\)
0.683667 + 0.729794i \(0.260384\pi\)
\(234\) 0 0
\(235\) −7.12665 12.3437i −0.464891 0.805215i
\(236\) 0 0
\(237\) 3.86418 2.80514i 0.251005 0.182214i
\(238\) 0 0
\(239\) 8.60836 14.9101i 0.556828 0.964455i −0.440930 0.897541i \(-0.645351\pi\)
0.997759 0.0669138i \(-0.0213152\pi\)
\(240\) 0 0
\(241\) −10.1106 + 17.5120i −0.651279 + 1.12805i 0.331534 + 0.943443i \(0.392434\pi\)
−0.982813 + 0.184604i \(0.940900\pi\)
\(242\) 0 0
\(243\) −15.5884 0.0309734i −0.999998 0.00198694i
\(244\) 0 0
\(245\) −14.0909 10.6152i −0.900232 0.678180i
\(246\) 0 0
\(247\) 13.7046 + 23.7370i 0.872001 + 1.51035i
\(248\) 0 0
\(249\) 23.6949 + 10.5609i 1.50160 + 0.669271i
\(250\) 0 0
\(251\) 7.32214 0.462169 0.231085 0.972934i \(-0.425773\pi\)
0.231085 + 0.972934i \(0.425773\pi\)
\(252\) 0 0
\(253\) −5.73720 −0.360695
\(254\) 0 0
\(255\) −2.45113 23.4104i −0.153496 1.46602i
\(256\) 0 0
\(257\) −3.07308 5.32274i −0.191694 0.332023i 0.754118 0.656739i \(-0.228065\pi\)
−0.945812 + 0.324716i \(0.894731\pi\)
\(258\) 0 0
\(259\) −13.5410 4.52971i −0.841395 0.281463i
\(260\) 0 0
\(261\) −9.20166 + 1.94823i −0.569568 + 0.120592i
\(262\) 0 0
\(263\) 0.0824634 0.142831i 0.00508491 0.00880732i −0.863472 0.504397i \(-0.831715\pi\)
0.868557 + 0.495590i \(0.165048\pi\)
\(264\) 0 0
\(265\) 17.6489 30.5689i 1.08417 1.87783i
\(266\) 0 0
\(267\) −0.994903 9.50219i −0.0608871 0.581525i
\(268\) 0 0
\(269\) −1.86477 3.22988i −0.113697 0.196929i 0.803561 0.595222i \(-0.202936\pi\)
−0.917258 + 0.398293i \(0.869603\pi\)
\(270\) 0 0
\(271\) −0.393652 + 0.681825i −0.0239127 + 0.0414179i −0.877734 0.479148i \(-0.840946\pi\)
0.853821 + 0.520566i \(0.174279\pi\)
\(272\) 0 0
\(273\) −24.4780 + 7.70902i −1.48147 + 0.466571i
\(274\) 0 0
\(275\) 0.928693 + 1.60854i 0.0560023 + 0.0969988i
\(276\) 0 0
\(277\) 1.62954 2.82245i 0.0979096 0.169584i −0.812910 0.582390i \(-0.802118\pi\)
0.910819 + 0.412805i \(0.135451\pi\)
\(278\) 0 0
\(279\) 4.46185 13.6951i 0.267124 0.819906i
\(280\) 0 0
\(281\) 9.39147 + 16.2665i 0.560248 + 0.970379i 0.997474 + 0.0710269i \(0.0226276\pi\)
−0.437226 + 0.899352i \(0.644039\pi\)
\(282\) 0 0
\(283\) −12.8370 −0.763078 −0.381539 0.924353i \(-0.624606\pi\)
−0.381539 + 0.924353i \(0.624606\pi\)
\(284\) 0 0
\(285\) 17.2896 12.5511i 1.02415 0.743464i
\(286\) 0 0
\(287\) −15.2046 5.08624i −0.897501 0.300231i
\(288\) 0 0
\(289\) −6.03821 + 10.4585i −0.355189 + 0.615205i
\(290\) 0 0
\(291\) 2.82867 + 1.26075i 0.165820 + 0.0739067i
\(292\) 0 0
\(293\) −13.6293 + 23.6066i −0.796230 + 1.37911i 0.125825 + 0.992052i \(0.459842\pi\)
−0.922055 + 0.387058i \(0.873491\pi\)
\(294\) 0 0
\(295\) 17.9806 + 31.1434i 1.04687 + 1.81324i
\(296\) 0 0
\(297\) −6.98214 1.49280i −0.405145 0.0866212i
\(298\) 0 0
\(299\) 23.3823 1.35224
\(300\) 0 0
\(301\) −9.69781 + 8.58108i −0.558972 + 0.494605i
\(302\) 0 0
\(303\) 2.41520 + 23.0672i 0.138749 + 1.32518i
\(304\) 0 0
\(305\) −8.64098 14.9666i −0.494781 0.856986i
\(306\) 0 0
\(307\) 24.4623 1.39614 0.698069 0.716030i \(-0.254043\pi\)
0.698069 + 0.716030i \(0.254043\pi\)
\(308\) 0 0
\(309\) −3.48565 1.55357i −0.198292 0.0883796i
\(310\) 0 0
\(311\) −17.1783 −0.974094 −0.487047 0.873376i \(-0.661926\pi\)
−0.487047 + 0.873376i \(0.661926\pi\)
\(312\) 0 0
\(313\) 15.8645 0.896715 0.448358 0.893854i \(-0.352009\pi\)
0.448358 + 0.893854i \(0.352009\pi\)
\(314\) 0 0
\(315\) 7.96324 + 18.3506i 0.448678 + 1.03394i
\(316\) 0 0
\(317\) −22.7252 −1.27638 −0.638188 0.769880i \(-0.720316\pi\)
−0.638188 + 0.769880i \(0.720316\pi\)
\(318\) 0 0
\(319\) −4.30804 −0.241204
\(320\) 0 0
\(321\) −1.77941 16.9949i −0.0993171 0.948565i
\(322\) 0 0
\(323\) −26.3916 −1.46847
\(324\) 0 0
\(325\) −3.78495 6.55573i −0.209951 0.363646i
\(326\) 0 0
\(327\) 4.88340 + 2.17656i 0.270053 + 0.120364i
\(328\) 0 0
\(329\) −2.98414 14.6624i −0.164521 0.808364i
\(330\) 0 0
\(331\) 24.2281 1.33170 0.665848 0.746088i \(-0.268070\pi\)
0.665848 + 0.746088i \(0.268070\pi\)
\(332\) 0 0
\(333\) 10.8239 + 12.0404i 0.593145 + 0.659808i
\(334\) 0 0
\(335\) −10.2242 17.7088i −0.558605 0.967533i
\(336\) 0 0
\(337\) −2.20181 + 3.81365i −0.119940 + 0.207743i −0.919744 0.392519i \(-0.871604\pi\)
0.799803 + 0.600262i \(0.204937\pi\)
\(338\) 0 0
\(339\) −0.0789328 0.753877i −0.00428704 0.0409450i
\(340\) 0 0
\(341\) 3.29863 5.71339i 0.178631 0.309398i
\(342\) 0 0
\(343\) −10.4931 15.2609i −0.566575 0.824010i
\(344\) 0 0
\(345\) −1.89794 18.1270i −0.102182 0.975925i
\(346\) 0 0
\(347\) −12.2506 −0.657645 −0.328823 0.944392i \(-0.606652\pi\)
−0.328823 + 0.944392i \(0.606652\pi\)
\(348\) 0 0
\(349\) 7.19444 + 12.4611i 0.385110 + 0.667030i 0.991784 0.127921i \(-0.0408303\pi\)
−0.606675 + 0.794950i \(0.707497\pi\)
\(350\) 0 0
\(351\) 28.4562 + 6.08402i 1.51888 + 0.324741i
\(352\) 0 0
\(353\) 4.40835 7.63549i 0.234633 0.406396i −0.724533 0.689240i \(-0.757945\pi\)
0.959166 + 0.282844i \(0.0912779\pi\)
\(354\) 0 0
\(355\) −2.84417 4.92624i −0.150953 0.261458i
\(356\) 0 0
\(357\) 5.35625 24.1229i 0.283483 1.27672i
\(358\) 0 0
\(359\) −3.04909 + 5.28118i −0.160925 + 0.278730i −0.935201 0.354118i \(-0.884781\pi\)
0.774276 + 0.632848i \(0.218114\pi\)
\(360\) 0 0
\(361\) −2.47731 4.29083i −0.130385 0.225833i
\(362\) 0 0
\(363\) 14.4153 + 6.42496i 0.756605 + 0.337223i
\(364\) 0 0
\(365\) −8.85761 + 15.3418i −0.463628 + 0.803028i
\(366\) 0 0
\(367\) 3.45814 5.98967i 0.180513 0.312658i −0.761542 0.648115i \(-0.775557\pi\)
0.942055 + 0.335457i \(0.108891\pi\)
\(368\) 0 0
\(369\) 12.1537 + 13.5197i 0.632697 + 0.703805i
\(370\) 0 0
\(371\) 27.7512 24.5556i 1.44077 1.27486i
\(372\) 0 0
\(373\) 11.9489 + 20.6961i 0.618691 + 1.07160i 0.989725 + 0.142985i \(0.0456701\pi\)
−0.371034 + 0.928619i \(0.620997\pi\)
\(374\) 0 0
\(375\) 12.8877 9.35567i 0.665520 0.483125i
\(376\) 0 0
\(377\) 17.5577 0.904269
\(378\) 0 0
\(379\) 34.6719 1.78097 0.890487 0.455008i \(-0.150364\pi\)
0.890487 + 0.455008i \(0.150364\pi\)
\(380\) 0 0
\(381\) −8.07299 + 5.86047i −0.413592 + 0.300241i
\(382\) 0 0
\(383\) −9.71507 16.8270i −0.496417 0.859820i 0.503574 0.863952i \(-0.332018\pi\)
−0.999991 + 0.00413220i \(0.998685\pi\)
\(384\) 0 0
\(385\) 1.82730 + 8.97831i 0.0931277 + 0.457577i
\(386\) 0 0
\(387\) 14.3646 3.04136i 0.730194 0.154601i
\(388\) 0 0
\(389\) 16.3172 28.2623i 0.827317 1.43295i −0.0728190 0.997345i \(-0.523200\pi\)
0.900136 0.435610i \(-0.143467\pi\)
\(390\) 0 0
\(391\) −11.2571 + 19.4979i −0.569297 + 0.986051i
\(392\) 0 0
\(393\) 2.26187 + 1.00813i 0.114096 + 0.0508533i
\(394\) 0 0
\(395\) 3.47400 + 6.01714i 0.174796 + 0.302755i
\(396\) 0 0
\(397\) −3.11807 + 5.40065i −0.156491 + 0.271051i −0.933601 0.358314i \(-0.883352\pi\)
0.777110 + 0.629365i \(0.216685\pi\)
\(398\) 0 0
\(399\) 21.3929 6.73741i 1.07098 0.337292i
\(400\) 0 0
\(401\) 12.3672 + 21.4207i 0.617591 + 1.06970i 0.989924 + 0.141599i \(0.0452245\pi\)
−0.372333 + 0.928099i \(0.621442\pi\)
\(402\) 0 0
\(403\) −13.4438 + 23.2853i −0.669683 + 1.15992i
\(404\) 0 0
\(405\) 2.40681 22.5543i 0.119595 1.12073i
\(406\) 0 0
\(407\) 3.70781 + 6.42211i 0.183789 + 0.318332i
\(408\) 0 0
\(409\) −23.1499 −1.14469 −0.572344 0.820014i \(-0.693966\pi\)
−0.572344 + 0.820014i \(0.693966\pi\)
\(410\) 0 0
\(411\) 2.01768 + 19.2706i 0.0995247 + 0.950548i
\(412\) 0 0
\(413\) 7.52903 + 36.9934i 0.370480 + 1.82033i
\(414\) 0 0
\(415\) −18.8737 + 32.6901i −0.926471 + 1.60470i
\(416\) 0 0
\(417\) −2.83902 27.1151i −0.139027 1.32783i
\(418\) 0 0
\(419\) −0.703260 + 1.21808i −0.0343565 + 0.0595072i −0.882692 0.469951i \(-0.844271\pi\)
0.848336 + 0.529458i \(0.177605\pi\)
\(420\) 0 0
\(421\) −0.663904 1.14992i −0.0323567 0.0560435i 0.849394 0.527760i \(-0.176968\pi\)
−0.881750 + 0.471716i \(0.843635\pi\)
\(422\) 0 0
\(423\) −5.25574 + 16.1319i −0.255543 + 0.784358i
\(424\) 0 0
\(425\) 7.28886 0.353562
\(426\) 0 0
\(427\) −3.61824 17.7780i −0.175099 0.860338i
\(428\) 0 0
\(429\) 12.1738 + 5.42594i 0.587759 + 0.261967i
\(430\) 0 0
\(431\) −2.83378 4.90825i −0.136498 0.236422i 0.789670 0.613531i \(-0.210252\pi\)
−0.926169 + 0.377109i \(0.876918\pi\)
\(432\) 0 0
\(433\) 1.60371 0.0770696 0.0385348 0.999257i \(-0.487731\pi\)
0.0385348 + 0.999257i \(0.487731\pi\)
\(434\) 0 0
\(435\) −1.42516 13.6115i −0.0683311 0.652622i
\(436\) 0 0
\(437\) −20.4353 −0.977554
\(438\) 0 0
\(439\) −0.454645 −0.0216990 −0.0108495 0.999941i \(-0.503454\pi\)
−0.0108495 + 0.999941i \(0.503454\pi\)
\(440\) 0 0
\(441\) 1.81651 + 20.9213i 0.0865003 + 0.996252i
\(442\) 0 0
\(443\) 18.6288 0.885083 0.442542 0.896748i \(-0.354077\pi\)
0.442542 + 0.896748i \(0.354077\pi\)
\(444\) 0 0
\(445\) 13.9020 0.659017
\(446\) 0 0
\(447\) −12.5459 5.59176i −0.593400 0.264481i
\(448\) 0 0
\(449\) −14.2330 −0.671696 −0.335848 0.941916i \(-0.609023\pi\)
−0.335848 + 0.941916i \(0.609023\pi\)
\(450\) 0 0
\(451\) 4.16335 + 7.21114i 0.196045 + 0.339559i
\(452\) 0 0
\(453\) −1.94679 18.5935i −0.0914681 0.873600i
\(454\) 0 0
\(455\) −7.44727 36.5917i −0.349134 1.71545i
\(456\) 0 0
\(457\) 29.3458 1.37274 0.686370 0.727252i \(-0.259203\pi\)
0.686370 + 0.727252i \(0.259203\pi\)
\(458\) 0 0
\(459\) −18.7732 + 20.7998i −0.876256 + 0.970851i
\(460\) 0 0
\(461\) −12.6587 21.9254i −0.589572 1.02117i −0.994288 0.106727i \(-0.965963\pi\)
0.404716 0.914442i \(-0.367370\pi\)
\(462\) 0 0
\(463\) −11.6503 + 20.1789i −0.541435 + 0.937793i 0.457387 + 0.889268i \(0.348785\pi\)
−0.998822 + 0.0485250i \(0.984548\pi\)
\(464\) 0 0
\(465\) 19.1430 + 8.53214i 0.887736 + 0.395669i
\(466\) 0 0
\(467\) −20.8409 + 36.0976i −0.964403 + 1.67040i −0.253194 + 0.967416i \(0.581481\pi\)
−0.711210 + 0.702980i \(0.751852\pi\)
\(468\) 0 0
\(469\) −4.28116 21.0352i −0.197686 0.971316i
\(470\) 0 0
\(471\) 29.6827 21.5477i 1.36771 0.992866i
\(472\) 0 0
\(473\) 6.72524 0.309227
\(474\) 0 0
\(475\) 3.30791 + 5.72947i 0.151777 + 0.262886i
\(476\) 0 0
\(477\) −41.1056 + 8.70313i −1.88210 + 0.398489i
\(478\) 0 0
\(479\) −2.76946 + 4.79684i −0.126540 + 0.219173i −0.922334 0.386394i \(-0.873720\pi\)
0.795794 + 0.605567i \(0.207054\pi\)
\(480\) 0 0
\(481\) −15.1114 26.1737i −0.689021 1.19342i
\(482\) 0 0
\(483\) 4.14741 18.6787i 0.188714 0.849910i
\(484\) 0 0
\(485\) −2.25312 + 3.90252i −0.102309 + 0.177204i
\(486\) 0 0
\(487\) 12.3357 + 21.3661i 0.558985 + 0.968190i 0.997582 + 0.0695061i \(0.0221423\pi\)
−0.438597 + 0.898684i \(0.644524\pi\)
\(488\) 0 0
\(489\) −0.193549 1.84857i −0.00875261 0.0835951i
\(490\) 0 0
\(491\) −10.0509 + 17.4087i −0.453590 + 0.785642i −0.998606 0.0527842i \(-0.983190\pi\)
0.545015 + 0.838426i \(0.316524\pi\)
\(492\) 0 0
\(493\) −8.45294 + 14.6409i −0.380701 + 0.659394i
\(494\) 0 0
\(495\) 3.21828 9.87812i 0.144651 0.443988i
\(496\) 0 0
\(497\) −1.19094 5.85160i −0.0534209 0.262480i
\(498\) 0 0
\(499\) −17.7587 30.7589i −0.794987 1.37696i −0.922848 0.385166i \(-0.874144\pi\)
0.127861 0.991792i \(-0.459189\pi\)
\(500\) 0 0
\(501\) 2.78352 + 26.5850i 0.124358 + 1.18773i
\(502\) 0 0
\(503\) 24.2236 1.08008 0.540039 0.841640i \(-0.318410\pi\)
0.540039 + 0.841640i \(0.318410\pi\)
\(504\) 0 0
\(505\) −33.7480 −1.50177
\(506\) 0 0
\(507\) −29.0490 12.9473i −1.29011 0.575009i
\(508\) 0 0
\(509\) 3.86723 + 6.69824i 0.171412 + 0.296894i 0.938914 0.344153i \(-0.111834\pi\)
−0.767502 + 0.641047i \(0.778500\pi\)
\(510\) 0 0
\(511\) −13.9277 + 12.3239i −0.616125 + 0.545177i
\(512\) 0 0
\(513\) −24.8697 5.31721i −1.09802 0.234761i
\(514\) 0 0
\(515\) 2.77642 4.80891i 0.122344 0.211906i
\(516\) 0 0
\(517\) −3.88555 + 6.72997i −0.170886 + 0.295984i
\(518\) 0 0
\(519\) 28.5406 20.7187i 1.25279 0.909448i
\(520\) 0 0
\(521\) −14.9050 25.8161i −0.652998 1.13103i −0.982392 0.186833i \(-0.940178\pi\)
0.329394 0.944193i \(-0.393156\pi\)
\(522\) 0 0
\(523\) −1.76218 + 3.05219i −0.0770547 + 0.133463i −0.901978 0.431782i \(-0.857885\pi\)
0.824923 + 0.565245i \(0.191218\pi\)
\(524\) 0 0
\(525\) −5.90831 + 1.86075i −0.257860 + 0.0812097i
\(526\) 0 0
\(527\) −12.9447 22.4208i −0.563879 0.976667i
\(528\) 0 0
\(529\) 2.78347 4.82110i 0.121020 0.209613i
\(530\) 0 0
\(531\) 13.2603 40.7009i 0.575448 1.76627i
\(532\) 0 0
\(533\) −16.9680 29.3895i −0.734967 1.27300i
\(534\) 0 0
\(535\) 24.8641 1.07497
\(536\) 0 0
\(537\) 9.64910 + 4.30065i 0.416389 + 0.185587i
\(538\) 0 0
\(539\) −1.17090 + 9.54704i −0.0504344 + 0.411220i
\(540\) 0 0
\(541\) 13.8435 23.9777i 0.595180 1.03088i −0.398342 0.917237i \(-0.630414\pi\)
0.993521 0.113645i \(-0.0362525\pi\)
\(542\) 0 0
\(543\) 14.0245 10.1809i 0.601851 0.436905i
\(544\) 0 0
\(545\) −3.88977 + 6.73729i −0.166620 + 0.288594i
\(546\) 0 0
\(547\) −16.6136 28.7756i −0.710347 1.23036i −0.964727 0.263253i \(-0.915205\pi\)
0.254380 0.967104i \(-0.418129\pi\)
\(548\) 0 0
\(549\) −6.37253 + 19.5597i −0.271973 + 0.834788i
\(550\) 0 0
\(551\) −15.3448 −0.653712
\(552\) 0 0
\(553\) 1.45467 + 7.14741i 0.0618587 + 0.303939i
\(554\) 0 0
\(555\) −19.0644 + 13.8395i −0.809240 + 0.587456i
\(556\) 0 0
\(557\) 7.80873 + 13.5251i 0.330866 + 0.573078i 0.982682 0.185300i \(-0.0593257\pi\)
−0.651816 + 0.758378i \(0.725992\pi\)
\(558\) 0 0
\(559\) −27.4092 −1.15928
\(560\) 0 0
\(561\) −10.3855 + 7.53919i −0.438476 + 0.318305i
\(562\) 0 0
\(563\) −19.5118 −0.822326 −0.411163 0.911562i \(-0.634877\pi\)
−0.411163 + 0.911562i \(0.634877\pi\)
\(564\) 0 0
\(565\) 1.10294 0.0464012
\(566\) 0 0
\(567\) 9.90753 21.6527i 0.416077 0.909329i
\(568\) 0 0
\(569\) 7.18361 0.301153 0.150576 0.988598i \(-0.451887\pi\)
0.150576 + 0.988598i \(0.451887\pi\)
\(570\) 0 0
\(571\) 29.5773 1.23777 0.618886 0.785481i \(-0.287584\pi\)
0.618886 + 0.785481i \(0.287584\pi\)
\(572\) 0 0
\(573\) −31.1151 + 22.5875i −1.29985 + 0.943607i
\(574\) 0 0
\(575\) 5.64386 0.235365
\(576\) 0 0
\(577\) 5.18911 + 8.98780i 0.216025 + 0.374167i 0.953589 0.301110i \(-0.0973573\pi\)
−0.737564 + 0.675277i \(0.764024\pi\)
\(578\) 0 0
\(579\) −37.3066 + 27.0822i −1.55041 + 1.12550i
\(580\) 0 0
\(581\) −29.6769 + 26.2595i −1.23121 + 1.08943i
\(582\) 0 0
\(583\) −19.2449 −0.797042
\(584\) 0 0
\(585\) −13.1163 + 40.2589i −0.542292 + 1.66450i
\(586\) 0 0
\(587\) 14.4563 + 25.0391i 0.596677 + 1.03348i 0.993308 + 0.115497i \(0.0368461\pi\)
−0.396630 + 0.917978i \(0.629821\pi\)
\(588\) 0 0
\(589\) 11.7494 20.3505i 0.484125 0.838530i
\(590\) 0 0
\(591\) 14.2543 10.3477i 0.586343 0.425647i
\(592\) 0 0
\(593\) −10.2645 + 17.7786i −0.421512 + 0.730080i −0.996088 0.0883714i \(-0.971834\pi\)
0.574576 + 0.818451i \(0.305167\pi\)
\(594\) 0 0
\(595\) 34.0982 + 11.4065i 1.39789 + 0.467622i
\(596\) 0 0
\(597\) −5.26001 2.34441i −0.215278 0.0959504i
\(598\) 0 0
\(599\) 7.83304 0.320049 0.160025 0.987113i \(-0.448843\pi\)
0.160025 + 0.987113i \(0.448843\pi\)
\(600\) 0 0
\(601\) −7.27021 12.5924i −0.296558 0.513654i 0.678788 0.734334i \(-0.262505\pi\)
−0.975346 + 0.220681i \(0.929172\pi\)
\(602\) 0 0
\(603\) −7.54008 + 23.1434i −0.307056 + 0.942471i
\(604\) 0 0
\(605\) −11.4822 + 19.8877i −0.466817 + 0.808551i
\(606\) 0 0
\(607\) 15.2755 + 26.4579i 0.620013 + 1.07389i 0.989483 + 0.144651i \(0.0462060\pi\)
−0.369470 + 0.929243i \(0.620461\pi\)
\(608\) 0 0
\(609\) 3.11428 14.0258i 0.126197 0.568353i
\(610\) 0 0
\(611\) 15.8358 27.4284i 0.640648 1.10964i
\(612\) 0 0
\(613\) −14.4646 25.0534i −0.584220 1.01190i −0.994972 0.100152i \(-0.968067\pi\)
0.410752 0.911747i \(-0.365266\pi\)
\(614\) 0 0
\(615\) −21.4067 + 15.5399i −0.863202 + 0.626629i
\(616\) 0 0
\(617\) 20.2106 35.0059i 0.813650 1.40928i −0.0966430 0.995319i \(-0.530811\pi\)
0.910293 0.413964i \(-0.135856\pi\)
\(618\) 0 0
\(619\) 9.05857 15.6899i 0.364095 0.630631i −0.624536 0.780996i \(-0.714712\pi\)
0.988630 + 0.150366i \(0.0480451\pi\)
\(620\) 0 0
\(621\) −14.5363 + 16.1055i −0.583322 + 0.646293i
\(622\) 0 0
\(623\) 13.8403 + 4.62985i 0.554501 + 0.185491i
\(624\) 0 0
\(625\) 14.9657 + 25.9214i 0.598629 + 1.03686i
\(626\) 0 0
\(627\) −10.6395 4.74208i −0.424901 0.189380i
\(628\) 0 0
\(629\) 29.1008 1.16032
\(630\) 0 0
\(631\) 8.50373 0.338528 0.169264 0.985571i \(-0.445861\pi\)
0.169264 + 0.985571i \(0.445861\pi\)
\(632\) 0 0
\(633\) 0.467269 + 4.46282i 0.0185723 + 0.177381i
\(634\) 0 0
\(635\) −7.25783 12.5709i −0.288018 0.498862i
\(636\) 0 0
\(637\) 4.77210 38.9096i 0.189077 1.54166i
\(638\) 0 0
\(639\) −2.09751 + 6.43805i −0.0829762 + 0.254685i
\(640\) 0 0
\(641\) −11.0020 + 19.0561i −0.434554 + 0.752669i −0.997259 0.0739883i \(-0.976427\pi\)
0.562705 + 0.826658i \(0.309761\pi\)
\(642\) 0 0
\(643\) 13.1156 22.7170i 0.517230 0.895869i −0.482569 0.875858i \(-0.660296\pi\)
0.999800 0.0200115i \(-0.00637029\pi\)
\(644\) 0 0
\(645\) 2.22480 + 21.2488i 0.0876013 + 0.836669i
\(646\) 0 0
\(647\) 19.5845 + 33.9214i 0.769946 + 1.33359i 0.937591 + 0.347739i \(0.113050\pi\)
−0.167645 + 0.985847i \(0.553616\pi\)
\(648\) 0 0
\(649\) 9.80329 16.9798i 0.384813 0.666515i
\(650\) 0 0
\(651\) 16.2166 + 14.8696i 0.635579 + 0.582786i
\(652\) 0 0
\(653\) −6.83467 11.8380i −0.267461 0.463257i 0.700744 0.713413i \(-0.252851\pi\)
−0.968206 + 0.250156i \(0.919518\pi\)
\(654\) 0 0
\(655\) −1.80165 + 3.12054i −0.0703962 + 0.121930i
\(656\) 0 0
\(657\) 20.6300 4.36791i 0.804853 0.170408i
\(658\) 0 0
\(659\) −3.06683 5.31191i −0.119467 0.206923i 0.800090 0.599880i \(-0.204785\pi\)
−0.919557 + 0.392958i \(0.871452\pi\)
\(660\) 0 0
\(661\) −44.6236 −1.73566 −0.867828 0.496865i \(-0.834484\pi\)
−0.867828 + 0.496865i \(0.834484\pi\)
\(662\) 0 0
\(663\) 42.3268 30.7265i 1.64384 1.19332i
\(664\) 0 0
\(665\) 6.50865 + 31.9798i 0.252395 + 1.24013i
\(666\) 0 0
\(667\) −6.54522 + 11.3367i −0.253432 + 0.438957i
\(668\) 0 0
\(669\) −39.2433 17.4909i −1.51723 0.676238i
\(670\) 0 0
\(671\) −4.71119 + 8.16001i −0.181873 + 0.315014i
\(672\) 0 0
\(673\) −16.3833 28.3767i −0.631531 1.09384i −0.987239 0.159246i \(-0.949094\pi\)
0.355708 0.934597i \(-0.384240\pi\)
\(674\) 0 0
\(675\) 6.86855 + 1.46852i 0.264371 + 0.0565232i
\(676\) 0 0
\(677\) 27.1527 1.04356 0.521782 0.853079i \(-0.325267\pi\)
0.521782 + 0.853079i \(0.325267\pi\)
\(678\) 0 0
\(679\) −3.54281 + 3.13484i −0.135961 + 0.120304i
\(680\) 0 0
\(681\) 1.28104 + 12.2350i 0.0490895 + 0.468847i
\(682\) 0 0
\(683\) −19.0334 32.9668i −0.728293 1.26144i −0.957604 0.288087i \(-0.906981\pi\)
0.229312 0.973353i \(-0.426353\pi\)
\(684\) 0 0
\(685\) −28.1934 −1.07721
\(686\) 0 0
\(687\) 10.2279 + 4.55861i 0.390217 + 0.173922i
\(688\) 0 0
\(689\) 78.4338 2.98809
\(690\) 0 0
\(691\) −12.7570 −0.485297 −0.242649 0.970114i \(-0.578016\pi\)
−0.242649 + 0.970114i \(0.578016\pi\)
\(692\) 0 0
\(693\) 6.49377 8.76250i 0.246678 0.332860i
\(694\) 0 0
\(695\) 39.6701 1.50477
\(696\) 0 0
\(697\) 32.6761 1.23770
\(698\) 0 0
\(699\) 1.59784 + 15.2608i 0.0604360 + 0.577217i
\(700\) 0 0
\(701\) 40.6428 1.53506 0.767528 0.641015i \(-0.221486\pi\)
0.767528 + 0.641015i \(0.221486\pi\)
\(702\) 0 0
\(703\) 13.2068 + 22.8749i 0.498105 + 0.862744i
\(704\) 0 0
\(705\) −22.5491 10.0502i −0.849248 0.378514i
\(706\) 0 0
\(707\) −33.5984 11.2393i −1.26360 0.422697i
\(708\) 0 0
\(709\) −7.49104 −0.281332 −0.140666 0.990057i \(-0.544924\pi\)
−0.140666 + 0.990057i \(0.544924\pi\)
\(710\) 0 0
\(711\) 2.56199 7.86373i 0.0960822 0.294913i
\(712\) 0 0
\(713\) −10.0232 17.3607i −0.375373 0.650165i
\(714\) 0 0
\(715\) −9.69683 + 16.7954i −0.362641 + 0.628112i
\(716\) 0 0
\(717\) −3.10528 29.6581i −0.115969 1.10760i
\(718\) 0 0
\(719\) −1.64056 + 2.84154i −0.0611827 + 0.105972i −0.894994 0.446078i \(-0.852821\pi\)
0.833812 + 0.552049i \(0.186154\pi\)
\(720\) 0 0
\(721\) 4.36565 3.86293i 0.162585 0.143863i
\(722\) 0 0
\(723\) 3.64716 + 34.8336i 0.135639 + 1.29548i
\(724\) 0 0
\(725\) 4.23796 0.157394
\(726\) 0 0
\(727\) 8.01088 + 13.8753i 0.297107 + 0.514605i 0.975473 0.220120i \(-0.0706448\pi\)
−0.678366 + 0.734724i \(0.737311\pi\)
\(728\) 0 0
\(729\) −21.8812 + 15.8181i −0.810416 + 0.585855i
\(730\) 0 0
\(731\) 13.1958 22.8558i 0.488064 0.845351i
\(732\) 0 0
\(733\) −14.8123 25.6556i −0.547104 0.947611i −0.998471 0.0552733i \(-0.982397\pi\)
0.451368 0.892338i \(-0.350936\pi\)
\(734\) 0 0
\(735\) −30.5518 0.541247i −1.12692 0.0199642i
\(736\) 0 0
\(737\) −5.57435 + 9.65506i −0.205334 + 0.355649i
\(738\) 0 0
\(739\) −22.2867 38.6017i −0.819829 1.41998i −0.905808 0.423688i \(-0.860735\pi\)
0.0859797 0.996297i \(-0.472598\pi\)
\(740\) 0 0
\(741\) 43.3620 + 19.3267i 1.59294 + 0.709983i
\(742\) 0 0
\(743\) −5.67364 + 9.82704i −0.208146 + 0.360519i −0.951130 0.308789i \(-0.900076\pi\)
0.742985 + 0.669308i \(0.233410\pi\)
\(744\) 0 0
\(745\) 9.99317 17.3087i 0.366121 0.634141i
\(746\) 0 0
\(747\) 43.9581 9.30707i 1.60834 0.340528i
\(748\) 0 0
\(749\) 24.7538 + 8.28063i 0.904485 + 0.302568i
\(750\) 0 0
\(751\) −17.5928 30.4716i −0.641970 1.11192i −0.984992 0.172597i \(-0.944784\pi\)
0.343023 0.939327i \(-0.388549\pi\)
\(752\) 0 0
\(753\) 10.2632 7.45040i 0.374011 0.271508i
\(754\) 0 0
\(755\) 27.2029 0.990014
\(756\) 0 0
\(757\) 40.9186 1.48721 0.743605 0.668619i \(-0.233114\pi\)
0.743605 + 0.668619i \(0.233114\pi\)
\(758\) 0 0
\(759\) −8.04162 + 5.83770i −0.291892 + 0.211895i
\(760\) 0 0
\(761\) −5.72243 9.91155i −0.207438 0.359293i 0.743469 0.668771i \(-0.233179\pi\)
−0.950907 + 0.309477i \(0.899846\pi\)
\(762\) 0 0
\(763\) −6.11628 + 5.41197i −0.221424 + 0.195927i
\(764\) 0 0
\(765\) −27.2562 30.3195i −0.985449 1.09620i
\(766\) 0 0
\(767\) −39.9540 + 69.2023i −1.44265 + 2.49875i
\(768\) 0 0
\(769\) −14.9723 + 25.9328i −0.539916 + 0.935162i 0.458992 + 0.888440i \(0.348211\pi\)
−0.998908 + 0.0467217i \(0.985123\pi\)
\(770\) 0 0
\(771\) −9.72340 4.33377i −0.350180 0.156077i
\(772\) 0 0
\(773\) −3.96578 6.86893i −0.142639 0.247058i 0.785851 0.618416i \(-0.212225\pi\)
−0.928490 + 0.371358i \(0.878892\pi\)
\(774\) 0 0
\(775\) −3.24496 + 5.62044i −0.116563 + 0.201892i
\(776\) 0 0
\(777\) −23.5889 + 7.42903i −0.846248 + 0.266515i
\(778\) 0 0
\(779\) 14.8295 + 25.6854i 0.531320 + 0.920274i
\(780\) 0 0
\(781\) −1.55068 + 2.68586i −0.0554877 + 0.0961075i
\(782\) 0 0
\(783\) −10.9153 + 12.0936i −0.390080 + 0.432190i
\(784\) 0 0
\(785\) 26.6855 + 46.2207i 0.952447 + 1.64969i
\(786\) 0 0
\(787\) 43.2074 1.54018 0.770089 0.637936i \(-0.220212\pi\)
0.770089 + 0.637936i \(0.220212\pi\)
\(788\) 0 0
\(789\) −0.0297469 0.284108i −0.00105902 0.0101145i
\(790\) 0 0
\(791\) 1.09805 + 0.367320i 0.0390422 + 0.0130604i
\(792\) 0 0
\(793\) 19.2008 33.2567i 0.681839 1.18098i
\(794\) 0 0
\(795\) −6.36647 60.8053i −0.225795 2.15654i
\(796\) 0 0
\(797\) −8.34385 + 14.4520i −0.295554 + 0.511915i −0.975114 0.221706i \(-0.928838\pi\)
0.679559 + 0.733620i \(0.262171\pi\)
\(798\) 0 0
\(799\) 15.2479 + 26.4101i 0.539432 + 0.934323i
\(800\) 0 0
\(801\) −11.0632 12.3065i −0.390897 0.434830i
\(802\) 0 0
\(803\) 9.65858 0.340844
\(804\) 0 0
\(805\) 26.4027 + 8.83221i 0.930573 + 0.311295i
\(806\) 0 0
\(807\) −5.90024 2.62977i −0.207698 0.0925722i
\(808\) 0 0
\(809\) −2.54846 4.41407i −0.0895992 0.155190i 0.817743 0.575584i \(-0.195225\pi\)
−0.907342 + 0.420394i \(0.861892\pi\)
\(810\) 0 0
\(811\) 10.2996 0.361666 0.180833 0.983514i \(-0.442121\pi\)
0.180833 + 0.983514i \(0.442121\pi\)
\(812\) 0 0
\(813\) 0.142001 + 1.35624i 0.00498021 + 0.0475653i
\(814\) 0 0
\(815\) 2.70451 0.0947347
\(816\) 0 0
\(817\) 23.9546 0.838066
\(818\) 0 0
\(819\) −26.4658 + 35.7122i −0.924790 + 1.24788i
\(820\) 0 0
\(821\) −25.2738 −0.882063 −0.441031 0.897492i \(-0.645387\pi\)
−0.441031 + 0.897492i \(0.645387\pi\)
\(822\) 0 0
\(823\) 8.88782 0.309810 0.154905 0.987929i \(-0.450493\pi\)
0.154905 + 0.987929i \(0.450493\pi\)
\(824\) 0 0
\(825\) 2.93843 + 1.30967i 0.102303 + 0.0455970i
\(826\) 0 0
\(827\) −13.1680 −0.457895 −0.228947 0.973439i \(-0.573528\pi\)
−0.228947 + 0.973439i \(0.573528\pi\)
\(828\) 0 0
\(829\) −11.3459 19.6516i −0.394058 0.682529i 0.598922 0.800807i \(-0.295596\pi\)
−0.992981 + 0.118278i \(0.962263\pi\)
\(830\) 0 0
\(831\) −0.587821 5.61421i −0.0203913 0.194755i
\(832\) 0 0
\(833\) 30.1482 + 22.7119i 1.04457 + 0.786919i
\(834\) 0 0
\(835\) −38.8946 −1.34600
\(836\) 0 0
\(837\) −7.68101 23.7360i −0.265494 0.820435i
\(838\) 0 0
\(839\) −14.9632 25.9171i −0.516588 0.894757i −0.999814 0.0192618i \(-0.993868\pi\)
0.483226 0.875496i \(-0.339465\pi\)
\(840\) 0 0
\(841\) 9.58522 16.6021i 0.330525 0.572486i
\(842\) 0 0
\(843\) 29.7151 + 13.2442i 1.02344 + 0.456154i
\(844\) 0 0
\(845\) 23.1384 40.0768i 0.795984 1.37869i
\(846\) 0 0
\(847\) −18.0546 + 15.9756i −0.620363 + 0.548927i
\(848\) 0 0
\(849\) −17.9931 + 13.0618i −0.617522 + 0.448281i
\(850\) 0 0
\(851\) 22.5331 0.772425
\(852\) 0 0
\(853\) 6.46929 + 11.2051i 0.221504 + 0.383657i 0.955265 0.295751i \(-0.0955699\pi\)
−0.733761 + 0.679408i \(0.762237\pi\)
\(854\) 0 0
\(855\) 11.4632 35.1849i 0.392032 1.20330i
\(856\) 0 0
\(857\) 4.12252 7.14042i 0.140823 0.243912i −0.786984 0.616973i \(-0.788359\pi\)
0.927807 + 0.373061i \(0.121692\pi\)
\(858\) 0 0
\(859\) −1.73399 3.00336i −0.0591630 0.102473i 0.834927 0.550361i \(-0.185510\pi\)
−0.894090 + 0.447888i \(0.852177\pi\)
\(860\) 0 0
\(861\) −26.4871 + 8.34177i −0.902678 + 0.284287i
\(862\) 0 0
\(863\) −0.256394 + 0.444087i −0.00872775 + 0.0151169i −0.870356 0.492423i \(-0.836111\pi\)
0.861629 + 0.507539i \(0.169445\pi\)
\(864\) 0 0
\(865\) 25.6588 + 44.4423i 0.872424 + 1.51108i
\(866\) 0 0
\(867\) 2.17815 + 20.8032i 0.0739739 + 0.706515i
\(868\) 0 0
\(869\) 1.89407 3.28063i 0.0642519 0.111288i
\(870\) 0 0
\(871\) 22.7186 39.3499i 0.769792 1.33332i
\(872\) 0 0
\(873\) 5.24768 1.11107i 0.177607 0.0376041i
\(874\) 0 0
\(875\) 4.85158 + 23.8379i 0.164013 + 0.805870i
\(876\) 0 0
\(877\) −18.1880 31.5026i −0.614166 1.06377i −0.990530 0.137295i \(-0.956159\pi\)
0.376365 0.926472i \(-0.377174\pi\)
\(878\) 0 0
\(879\) 4.91646 + 46.9565i 0.165828 + 1.58380i
\(880\) 0 0
\(881\) −23.3999 −0.788363 −0.394181 0.919033i \(-0.628972\pi\)
−0.394181 + 0.919033i \(0.628972\pi\)
\(882\) 0 0
\(883\) −22.8345 −0.768442 −0.384221 0.923241i \(-0.625530\pi\)
−0.384221 + 0.923241i \(0.625530\pi\)
\(884\) 0 0
\(885\) 56.8917 + 25.3569i 1.91239 + 0.852363i
\(886\) 0 0
\(887\) −22.0791 38.2421i −0.741344 1.28405i −0.951883 0.306460i \(-0.900855\pi\)
0.210539 0.977585i \(-0.432478\pi\)
\(888\) 0 0
\(889\) −3.03907 14.9323i −0.101927 0.500813i
\(890\) 0 0
\(891\) −11.3056 + 5.01204i −0.378751 + 0.167910i
\(892\) 0 0
\(893\) −13.8399 + 23.9715i −0.463136 + 0.802175i
\(894\) 0 0
\(895\) −7.68579 + 13.3122i −0.256908 + 0.444977i
\(896\) 0 0
\(897\) 32.7742 23.7919i 1.09430 0.794389i
\(898\) 0 0
\(899\) −7.52641 13.0361i −0.251020 0.434779i
\(900\) 0 0
\(901\) −37.7610 + 65.4039i −1.25800 + 2.17892i
\(902\) 0 0
\(903\) −4.86167 + 21.8955i −0.161786 + 0.728635i
\(904\) 0 0
\(905\) 12.6084 + 21.8384i 0.419118 + 0.725934i
\(906\) 0 0
\(907\) −3.53884 + 6.12946i −0.117505 + 0.203525i −0.918778 0.394773i \(-0.870823\pi\)
0.801273 + 0.598299i \(0.204156\pi\)
\(908\) 0 0
\(909\) 26.8566 + 29.8750i 0.890777 + 0.990891i
\(910\) 0 0
\(911\) −23.6764 41.0088i −0.784435 1.35868i −0.929336 0.369235i \(-0.879620\pi\)
0.144901 0.989446i \(-0.453714\pi\)
\(912\) 0 0
\(913\) 20.5804 0.681110
\(914\) 0 0
\(915\) −27.3405 12.1858i −0.903850 0.402851i
\(916\) 0 0
\(917\) −2.83291 + 2.50669i −0.0935509 + 0.0827783i
\(918\) 0 0
\(919\) 12.9752 22.4736i 0.428011 0.741337i −0.568685 0.822555i \(-0.692548\pi\)
0.996696 + 0.0812182i \(0.0258811\pi\)
\(920\) 0 0
\(921\) 34.2879 24.8908i 1.12983 0.820181i
\(922\) 0 0
\(923\) 6.31990 10.9464i 0.208022 0.360305i
\(924\) 0 0
\(925\) −3.64748 6.31763i −0.119929 0.207722i
\(926\) 0 0
\(927\) −6.46649 + 1.36912i −0.212387 + 0.0449680i
\(928\) 0 0
\(929\) −5.32221 −0.174616 −0.0873080 0.996181i \(-0.527826\pi\)
−0.0873080 + 0.996181i \(0.527826\pi\)
\(930\) 0 0
\(931\) −4.17064 + 34.0056i −0.136687 + 1.11449i
\(932\) 0 0
\(933\) −24.0782 + 17.4792i −0.788286 + 0.572245i
\(934\) 0 0
\(935\) −9.33682 16.1719i −0.305347 0.528876i
\(936\) 0 0
\(937\) −30.4266 −0.993994 −0.496997 0.867752i \(-0.665564\pi\)
−0.496997 + 0.867752i \(0.665564\pi\)
\(938\) 0 0
\(939\) 22.2367 16.1424i 0.725667 0.526788i
\(940\) 0 0
\(941\) 21.7637 0.709476 0.354738 0.934966i \(-0.384570\pi\)
0.354738 + 0.934966i \(0.384570\pi\)
\(942\) 0 0
\(943\) 25.3016 0.823932
\(944\) 0 0
\(945\) 29.8339 + 17.6187i 0.970495 + 0.573135i
\(946\) 0 0
\(947\) −34.8784 −1.13339 −0.566697 0.823926i \(-0.691779\pi\)
−0.566697 + 0.823926i \(0.691779\pi\)
\(948\) 0 0
\(949\) −39.3642 −1.27782
\(950\) 0 0
\(951\) −31.8531 + 23.1233i −1.03291 + 0.749825i
\(952\) 0 0
\(953\) 27.3744 0.886742 0.443371 0.896338i \(-0.353782\pi\)
0.443371 + 0.896338i \(0.353782\pi\)
\(954\) 0 0
\(955\) −27.9732 48.4511i −0.905193 1.56784i
\(956\) 0 0
\(957\) −6.03843 + 4.38351i −0.195195 + 0.141699i
\(958\) 0 0
\(959\) −28.0684 9.38941i −0.906375 0.303200i
\(960\) 0 0
\(961\) −7.94838 −0.256399
\(962\) 0 0
\(963\) −19.7868 22.0106i −0.637620 0.709282i
\(964\) 0 0
\(965\) −33.5396 58.0924i −1.07968 1.87006i
\(966\) 0 0
\(967\) 7.21327 12.4937i 0.231963 0.401772i −0.726423 0.687248i \(-0.758819\pi\)
0.958386 + 0.285476i \(0.0921518\pi\)
\(968\) 0 0
\(969\) −36.9921 + 26.8539i −1.18836 + 0.862670i
\(970\) 0 0
\(971\) −13.2592 + 22.9657i −0.425509 + 0.737004i −0.996468 0.0839752i \(-0.973238\pi\)
0.570959 + 0.820979i \(0.306572\pi\)
\(972\) 0 0
\(973\) 39.4942 + 13.2116i 1.26613 + 0.423544i
\(974\) 0 0
\(975\) −11.9758 5.33767i −0.383532 0.170942i
\(976\) 0 0
\(977\) −40.3733 −1.29166 −0.645829 0.763482i \(-0.723488\pi\)
−0.645829 + 0.763482i \(0.723488\pi\)
\(978\) 0 0
\(979\) −3.78978 6.56408i −0.121122 0.209789i
\(980\) 0 0
\(981\) 9.05957 1.91815i 0.289250 0.0612417i
\(982\) 0 0
\(983\) 10.7299 18.5847i 0.342230 0.592759i −0.642617 0.766188i \(-0.722151\pi\)
0.984846 + 0.173429i \(0.0554846\pi\)
\(984\) 0 0
\(985\) 12.8150 + 22.1962i 0.408319 + 0.707230i
\(986\) 0 0
\(987\) −19.1020 17.5153i −0.608023 0.557519i
\(988\) 0 0
\(989\) 10.2177 17.6975i 0.324903 0.562748i
\(990\) 0 0
\(991\) 7.25341 + 12.5633i 0.230412 + 0.399085i 0.957929 0.287004i \(-0.0926593\pi\)
−0.727517 + 0.686089i \(0.759326\pi\)
\(992\) 0 0
\(993\) 33.9596 24.6525i 1.07768 0.782323i
\(994\) 0 0
\(995\) 4.18975 7.25687i 0.132824 0.230058i
\(996\) 0 0
\(997\) −18.2204 + 31.5587i −0.577047 + 0.999475i 0.418769 + 0.908093i \(0.362462\pi\)
−0.995816 + 0.0913822i \(0.970871\pi\)
\(998\) 0 0
\(999\) 27.4227 + 5.86305i 0.867616 + 0.185499i
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 252.2.i.b.121.6 yes 14
3.2 odd 2 756.2.i.b.37.1 14
4.3 odd 2 1008.2.q.j.625.2 14
7.2 even 3 1764.2.j.g.589.5 14
7.3 odd 6 1764.2.l.i.949.6 14
7.4 even 3 252.2.l.b.193.2 yes 14
7.5 odd 6 1764.2.j.h.589.3 14
7.6 odd 2 1764.2.i.i.373.2 14
9.2 odd 6 756.2.l.b.289.7 14
9.4 even 3 2268.2.k.e.1297.7 14
9.5 odd 6 2268.2.k.f.1297.1 14
9.7 even 3 252.2.l.b.205.2 yes 14
12.11 even 2 3024.2.q.j.2305.1 14
21.2 odd 6 5292.2.j.h.1765.1 14
21.5 even 6 5292.2.j.g.1765.7 14
21.11 odd 6 756.2.l.b.361.7 14
21.17 even 6 5292.2.l.i.361.1 14
21.20 even 2 5292.2.i.i.1549.7 14
28.11 odd 6 1008.2.t.j.193.6 14
36.7 odd 6 1008.2.t.j.961.6 14
36.11 even 6 3024.2.t.j.289.7 14
63.2 odd 6 5292.2.j.h.3529.1 14
63.4 even 3 2268.2.k.e.1621.7 14
63.11 odd 6 756.2.i.b.613.1 14
63.16 even 3 1764.2.j.g.1177.5 14
63.20 even 6 5292.2.l.i.3313.1 14
63.25 even 3 inner 252.2.i.b.25.6 14
63.32 odd 6 2268.2.k.f.1621.1 14
63.34 odd 6 1764.2.l.i.961.6 14
63.38 even 6 5292.2.i.i.2125.7 14
63.47 even 6 5292.2.j.g.3529.7 14
63.52 odd 6 1764.2.i.i.1537.2 14
63.61 odd 6 1764.2.j.h.1177.3 14
84.11 even 6 3024.2.t.j.1873.7 14
252.11 even 6 3024.2.q.j.2881.1 14
252.151 odd 6 1008.2.q.j.529.2 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.i.b.25.6 14 63.25 even 3 inner
252.2.i.b.121.6 yes 14 1.1 even 1 trivial
252.2.l.b.193.2 yes 14 7.4 even 3
252.2.l.b.205.2 yes 14 9.7 even 3
756.2.i.b.37.1 14 3.2 odd 2
756.2.i.b.613.1 14 63.11 odd 6
756.2.l.b.289.7 14 9.2 odd 6
756.2.l.b.361.7 14 21.11 odd 6
1008.2.q.j.529.2 14 252.151 odd 6
1008.2.q.j.625.2 14 4.3 odd 2
1008.2.t.j.193.6 14 28.11 odd 6
1008.2.t.j.961.6 14 36.7 odd 6
1764.2.i.i.373.2 14 7.6 odd 2
1764.2.i.i.1537.2 14 63.52 odd 6
1764.2.j.g.589.5 14 7.2 even 3
1764.2.j.g.1177.5 14 63.16 even 3
1764.2.j.h.589.3 14 7.5 odd 6
1764.2.j.h.1177.3 14 63.61 odd 6
1764.2.l.i.949.6 14 7.3 odd 6
1764.2.l.i.961.6 14 63.34 odd 6
2268.2.k.e.1297.7 14 9.4 even 3
2268.2.k.e.1621.7 14 63.4 even 3
2268.2.k.f.1297.1 14 9.5 odd 6
2268.2.k.f.1621.1 14 63.32 odd 6
3024.2.q.j.2305.1 14 12.11 even 2
3024.2.q.j.2881.1 14 252.11 even 6
3024.2.t.j.289.7 14 36.11 even 6
3024.2.t.j.1873.7 14 84.11 even 6
5292.2.i.i.1549.7 14 21.20 even 2
5292.2.i.i.2125.7 14 63.38 even 6
5292.2.j.g.1765.7 14 21.5 even 6
5292.2.j.g.3529.7 14 63.47 even 6
5292.2.j.h.1765.1 14 21.2 odd 6
5292.2.j.h.3529.1 14 63.2 odd 6
5292.2.l.i.361.1 14 21.17 even 6
5292.2.l.i.3313.1 14 63.20 even 6