Properties

Label 560.2.ci.c.33.4
Level $560$
Weight $2$
Character 560.33
Analytic conductor $4.472$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [560,2,Mod(17,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.ci (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.4
Root \(0.587308 + 2.01725i\) of defining polynomial
Character \(\chi\) \(=\) 560.33
Dual form 560.2.ci.c.17.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.80762 + 0.752300i) q^{3} +(-2.21323 - 0.318742i) q^{5} +(-0.559876 + 2.58583i) q^{7} +(4.71872 + 2.72435i) q^{9} +O(q^{10})\) \(q+(2.80762 + 0.752300i) q^{3} +(-2.21323 - 0.318742i) q^{5} +(-0.559876 + 2.58583i) q^{7} +(4.71872 + 2.72435i) q^{9} +(1.83557 + 3.17930i) q^{11} +(0.830578 - 0.830578i) q^{13} +(-5.97414 - 2.55992i) q^{15} +(-0.204036 + 0.761471i) q^{17} +(-1.09461 + 1.89593i) q^{19} +(-3.51725 + 6.83885i) q^{21} +(4.54529 - 1.21791i) q^{23} +(4.79681 + 1.41090i) q^{25} +(5.03288 + 5.03288i) q^{27} -2.62236i q^{29} +(-0.0359651 + 0.0207644i) q^{31} +(2.76180 + 10.3072i) q^{33} +(2.06335 - 5.54460i) q^{35} +(0.0664979 + 0.248174i) q^{37} +(2.95680 - 1.70711i) q^{39} -8.98026i q^{41} +(0.474569 + 0.474569i) q^{43} +(-9.57526 - 7.53368i) q^{45} +(-6.18205 + 1.65648i) q^{47} +(-6.37308 - 2.89549i) q^{49} +(-1.14571 + 1.98443i) q^{51} +(2.04824 - 7.64413i) q^{53} +(-3.04917 - 7.62161i) q^{55} +(-4.49957 + 4.49957i) q^{57} +(-5.35616 - 9.27713i) q^{59} +(1.72539 + 0.996157i) q^{61} +(-9.68662 + 10.6765i) q^{63} +(-2.10300 + 1.57352i) q^{65} +(-6.39671 - 1.71399i) q^{67} +13.6777 q^{69} -8.11777 q^{71} +(9.52910 + 2.55331i) q^{73} +(12.4062 + 7.56992i) q^{75} +(-9.24884 + 2.96647i) q^{77} +(11.6145 + 6.70563i) q^{79} +(2.17114 + 3.76053i) q^{81} +(9.73033 - 9.73033i) q^{83} +(0.694291 - 1.62028i) q^{85} +(1.97280 - 7.36260i) q^{87} +(0.715130 - 1.23864i) q^{89} +(1.68272 + 2.61276i) q^{91} +(-0.116597 + 0.0312422i) q^{93} +(3.02695 - 3.84723i) q^{95} +(-3.16693 - 3.16693i) q^{97} +20.0030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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
\(3\) 2.80762 + 0.752300i 1.62098 + 0.434341i 0.951290 0.308298i \(-0.0997593\pi\)
0.669692 + 0.742639i \(0.266426\pi\)
\(4\) 0 0
\(5\) −2.21323 0.318742i −0.989788 0.142546i
\(6\) 0 0
\(7\) −0.559876 + 2.58583i −0.211613 + 0.977353i
\(8\) 0 0
\(9\) 4.71872 + 2.72435i 1.57291 + 0.908118i
\(10\) 0 0
\(11\) 1.83557 + 3.17930i 0.553445 + 0.958596i 0.998023 + 0.0628551i \(0.0200206\pi\)
−0.444577 + 0.895741i \(0.646646\pi\)
\(12\) 0 0
\(13\) 0.830578 0.830578i 0.230361 0.230361i −0.582482 0.812843i \(-0.697918\pi\)
0.812843 + 0.582482i \(0.197918\pi\)
\(14\) 0 0
\(15\) −5.97414 2.55992i −1.54252 0.660970i
\(16\) 0 0
\(17\) −0.204036 + 0.761471i −0.0494859 + 0.184684i −0.986245 0.165292i \(-0.947143\pi\)
0.936759 + 0.349976i \(0.113810\pi\)
\(18\) 0 0
\(19\) −1.09461 + 1.89593i −0.251122 + 0.434955i −0.963835 0.266500i \(-0.914133\pi\)
0.712713 + 0.701455i \(0.247466\pi\)
\(20\) 0 0
\(21\) −3.51725 + 6.83885i −0.767526 + 1.49236i
\(22\) 0 0
\(23\) 4.54529 1.21791i 0.947759 0.253951i 0.248348 0.968671i \(-0.420112\pi\)
0.699411 + 0.714719i \(0.253446\pi\)
\(24\) 0 0
\(25\) 4.79681 + 1.41090i 0.959361 + 0.282180i
\(26\) 0 0
\(27\) 5.03288 + 5.03288i 0.968579 + 0.968579i
\(28\) 0 0
\(29\) 2.62236i 0.486960i −0.969906 0.243480i \(-0.921711\pi\)
0.969906 0.243480i \(-0.0782891\pi\)
\(30\) 0 0
\(31\) −0.0359651 + 0.0207644i −0.00645952 + 0.00372940i −0.503226 0.864155i \(-0.667854\pi\)
0.496767 + 0.867884i \(0.334520\pi\)
\(32\) 0 0
\(33\) 2.76180 + 10.3072i 0.480768 + 1.79425i
\(34\) 0 0
\(35\) 2.06335 5.54460i 0.348770 0.937208i
\(36\) 0 0
\(37\) 0.0664979 + 0.248174i 0.0109322 + 0.0407995i 0.971176 0.238362i \(-0.0766103\pi\)
−0.960244 + 0.279161i \(0.909944\pi\)
\(38\) 0 0
\(39\) 2.95680 1.70711i 0.473466 0.273356i
\(40\) 0 0
\(41\) 8.98026i 1.40248i −0.712925 0.701241i \(-0.752630\pi\)
0.712925 0.701241i \(-0.247370\pi\)
\(42\) 0 0
\(43\) 0.474569 + 0.474569i 0.0723711 + 0.0723711i 0.742366 0.669995i \(-0.233704\pi\)
−0.669995 + 0.742366i \(0.733704\pi\)
\(44\) 0 0
\(45\) −9.57526 7.53368i −1.42740 1.12306i
\(46\) 0 0
\(47\) −6.18205 + 1.65648i −0.901745 + 0.241622i −0.679766 0.733429i \(-0.737919\pi\)
−0.221980 + 0.975051i \(0.571252\pi\)
\(48\) 0 0
\(49\) −6.37308 2.89549i −0.910440 0.413642i
\(50\) 0 0
\(51\) −1.14571 + 1.98443i −0.160432 + 0.277876i
\(52\) 0 0
\(53\) 2.04824 7.64413i 0.281347 1.05000i −0.670120 0.742252i \(-0.733758\pi\)
0.951468 0.307749i \(-0.0995758\pi\)
\(54\) 0 0
\(55\) −3.04917 7.62161i −0.411150 1.02770i
\(56\) 0 0
\(57\) −4.49957 + 4.49957i −0.595982 + 0.595982i
\(58\) 0 0
\(59\) −5.35616 9.27713i −0.697312 1.20778i −0.969395 0.245506i \(-0.921046\pi\)
0.272083 0.962274i \(-0.412287\pi\)
\(60\) 0 0
\(61\) 1.72539 + 0.996157i 0.220914 + 0.127545i 0.606373 0.795180i \(-0.292624\pi\)
−0.385459 + 0.922725i \(0.625957\pi\)
\(62\) 0 0
\(63\) −9.68662 + 10.6765i −1.22040 + 1.34512i
\(64\) 0 0
\(65\) −2.10300 + 1.57352i −0.260846 + 0.195172i
\(66\) 0 0
\(67\) −6.39671 1.71399i −0.781482 0.209398i −0.154044 0.988064i \(-0.549230\pi\)
−0.627438 + 0.778666i \(0.715897\pi\)
\(68\) 0 0
\(69\) 13.6777 1.64660
\(70\) 0 0
\(71\) −8.11777 −0.963402 −0.481701 0.876336i \(-0.659981\pi\)
−0.481701 + 0.876336i \(0.659981\pi\)
\(72\) 0 0
\(73\) 9.52910 + 2.55331i 1.11530 + 0.298843i 0.768979 0.639274i \(-0.220765\pi\)
0.346318 + 0.938117i \(0.387432\pi\)
\(74\) 0 0
\(75\) 12.4062 + 7.56992i 1.43255 + 0.874099i
\(76\) 0 0
\(77\) −9.24884 + 2.96647i −1.05400 + 0.338060i
\(78\) 0 0
\(79\) 11.6145 + 6.70563i 1.30673 + 0.754443i 0.981550 0.191208i \(-0.0612405\pi\)
0.325184 + 0.945651i \(0.394574\pi\)
\(80\) 0 0
\(81\) 2.17114 + 3.76053i 0.241238 + 0.417836i
\(82\) 0 0
\(83\) 9.73033 9.73033i 1.06804 1.06804i 0.0705331 0.997509i \(-0.477530\pi\)
0.997509 0.0705331i \(-0.0224700\pi\)
\(84\) 0 0
\(85\) 0.694291 1.62028i 0.0753065 0.175744i
\(86\) 0 0
\(87\) 1.97280 7.36260i 0.211507 0.789354i
\(88\) 0 0
\(89\) 0.715130 1.23864i 0.0758036 0.131296i −0.825632 0.564209i \(-0.809181\pi\)
0.901435 + 0.432914i \(0.142514\pi\)
\(90\) 0 0
\(91\) 1.68272 + 2.61276i 0.176397 + 0.273892i
\(92\) 0 0
\(93\) −0.116597 + 0.0312422i −0.0120906 + 0.00323967i
\(94\) 0 0
\(95\) 3.02695 3.84723i 0.310558 0.394717i
\(96\) 0 0
\(97\) −3.16693 3.16693i −0.321553 0.321553i 0.527810 0.849363i \(-0.323013\pi\)
−0.849363 + 0.527810i \(0.823013\pi\)
\(98\) 0 0
\(99\) 20.0030i 2.01037i
\(100\) 0 0
\(101\) −0.0622734 + 0.0359536i −0.00619644 + 0.00357751i −0.503095 0.864231i \(-0.667805\pi\)
0.496899 + 0.867809i \(0.334472\pi\)
\(102\) 0 0
\(103\) 4.29116 + 16.0148i 0.422820 + 1.57799i 0.768638 + 0.639685i \(0.220935\pi\)
−0.345817 + 0.938302i \(0.612398\pi\)
\(104\) 0 0
\(105\) 9.96432 14.0149i 0.972418 1.36771i
\(106\) 0 0
\(107\) −1.18265 4.41372i −0.114331 0.426690i 0.884905 0.465772i \(-0.154223\pi\)
−0.999236 + 0.0390819i \(0.987557\pi\)
\(108\) 0 0
\(109\) −15.6773 + 9.05131i −1.50162 + 0.866958i −0.501617 + 0.865090i \(0.667261\pi\)
−0.999998 + 0.00186842i \(0.999405\pi\)
\(110\) 0 0
\(111\) 0.746804i 0.0708835i
\(112\) 0 0
\(113\) 1.52064 + 1.52064i 0.143049 + 0.143049i 0.775005 0.631955i \(-0.217747\pi\)
−0.631955 + 0.775005i \(0.717747\pi\)
\(114\) 0 0
\(115\) −10.4480 + 1.24674i −0.974281 + 0.116259i
\(116\) 0 0
\(117\) 6.18205 1.65648i 0.571531 0.153141i
\(118\) 0 0
\(119\) −1.85480 0.953932i −0.170030 0.0874468i
\(120\) 0 0
\(121\) −1.23864 + 2.14539i −0.112604 + 0.195035i
\(122\) 0 0
\(123\) 6.75585 25.2132i 0.609155 2.27340i
\(124\) 0 0
\(125\) −10.1667 4.65160i −0.909341 0.416051i
\(126\) 0 0
\(127\) 13.2527 13.2527i 1.17599 1.17599i 0.195234 0.980757i \(-0.437453\pi\)
0.980757 0.195234i \(-0.0625467\pi\)
\(128\) 0 0
\(129\) 0.975392 + 1.68943i 0.0858785 + 0.148746i
\(130\) 0 0
\(131\) −12.2929 7.09731i −1.07404 0.620095i −0.144755 0.989468i \(-0.546239\pi\)
−0.929281 + 0.369372i \(0.879573\pi\)
\(132\) 0 0
\(133\) −4.28970 3.89197i −0.371964 0.337477i
\(134\) 0 0
\(135\) −9.53476 12.7431i −0.820621 1.09675i
\(136\) 0 0
\(137\) 18.3201 + 4.90887i 1.56519 + 0.419393i 0.934303 0.356479i \(-0.116023\pi\)
0.630891 + 0.775871i \(0.282689\pi\)
\(138\) 0 0
\(139\) −8.23706 −0.698658 −0.349329 0.937000i \(-0.613591\pi\)
−0.349329 + 0.937000i \(0.613591\pi\)
\(140\) 0 0
\(141\) −18.6030 −1.56666
\(142\) 0 0
\(143\) 4.16524 + 1.11607i 0.348315 + 0.0933308i
\(144\) 0 0
\(145\) −0.835856 + 5.80390i −0.0694141 + 0.481988i
\(146\) 0 0
\(147\) −15.7149 12.9239i −1.29614 1.06595i
\(148\) 0 0
\(149\) 4.19317 + 2.42093i 0.343518 + 0.198330i 0.661826 0.749657i \(-0.269782\pi\)
−0.318309 + 0.947987i \(0.603115\pi\)
\(150\) 0 0
\(151\) 5.02292 + 8.69995i 0.408759 + 0.707992i 0.994751 0.102325i \(-0.0326282\pi\)
−0.585992 + 0.810317i \(0.699295\pi\)
\(152\) 0 0
\(153\) −3.03730 + 3.03730i −0.245551 + 0.245551i
\(154\) 0 0
\(155\) 0.0862176 0.0344930i 0.00692516 0.00277054i
\(156\) 0 0
\(157\) 6.33762 23.6523i 0.505797 1.88766i 0.0474774 0.998872i \(-0.484882\pi\)
0.458320 0.888788i \(-0.348452\pi\)
\(158\) 0 0
\(159\) 11.5014 19.9209i 0.912117 1.57983i
\(160\) 0 0
\(161\) 0.604505 + 12.4353i 0.0476417 + 0.980035i
\(162\) 0 0
\(163\) −21.2171 + 5.68510i −1.66185 + 0.445291i −0.962895 0.269875i \(-0.913018\pi\)
−0.698954 + 0.715166i \(0.746351\pi\)
\(164\) 0 0
\(165\) −2.82718 23.6925i −0.220096 1.84446i
\(166\) 0 0
\(167\) 3.14616 + 3.14616i 0.243457 + 0.243457i 0.818279 0.574821i \(-0.194928\pi\)
−0.574821 + 0.818279i \(0.694928\pi\)
\(168\) 0 0
\(169\) 11.6203i 0.893868i
\(170\) 0 0
\(171\) −10.3303 + 5.96423i −0.789981 + 0.456096i
\(172\) 0 0
\(173\) −1.35273 5.04844i −0.102846 0.383826i 0.895246 0.445572i \(-0.147000\pi\)
−0.998092 + 0.0617463i \(0.980333\pi\)
\(174\) 0 0
\(175\) −6.33397 + 11.6138i −0.478803 + 0.877922i
\(176\) 0 0
\(177\) −8.05888 30.0761i −0.605742 2.26066i
\(178\) 0 0
\(179\) −10.8847 + 6.28428i −0.813560 + 0.469709i −0.848191 0.529691i \(-0.822308\pi\)
0.0346308 + 0.999400i \(0.488974\pi\)
\(180\) 0 0
\(181\) 11.6742i 0.867740i 0.900976 + 0.433870i \(0.142852\pi\)
−0.900976 + 0.433870i \(0.857148\pi\)
\(182\) 0 0
\(183\) 4.09485 + 4.09485i 0.302700 + 0.302700i
\(184\) 0 0
\(185\) −0.0680721 0.570462i −0.00500476 0.0419412i
\(186\) 0 0
\(187\) −2.79547 + 0.749044i −0.204425 + 0.0547755i
\(188\) 0 0
\(189\) −15.8320 + 10.1964i −1.15161 + 0.741680i
\(190\) 0 0
\(191\) 7.75170 13.4263i 0.560894 0.971496i −0.436525 0.899692i \(-0.643791\pi\)
0.997419 0.0718040i \(-0.0228756\pi\)
\(192\) 0 0
\(193\) 2.32883 8.69132i 0.167633 0.625615i −0.830057 0.557679i \(-0.811692\pi\)
0.997690 0.0679359i \(-0.0216413\pi\)
\(194\) 0 0
\(195\) −7.08821 + 2.83577i −0.507597 + 0.203074i
\(196\) 0 0
\(197\) 12.1951 12.1951i 0.868865 0.868865i −0.123482 0.992347i \(-0.539406\pi\)
0.992347 + 0.123482i \(0.0394061\pi\)
\(198\) 0 0
\(199\) −4.36557 7.56140i −0.309467 0.536013i 0.668779 0.743462i \(-0.266817\pi\)
−0.978246 + 0.207448i \(0.933484\pi\)
\(200\) 0 0
\(201\) −16.6701 9.62450i −1.17582 0.678860i
\(202\) 0 0
\(203\) 6.78099 + 1.46820i 0.475932 + 0.103047i
\(204\) 0 0
\(205\) −2.86239 + 19.8754i −0.199918 + 1.38816i
\(206\) 0 0
\(207\) 24.7660 + 6.63602i 1.72135 + 0.461235i
\(208\) 0 0
\(209\) −8.03696 −0.555928
\(210\) 0 0
\(211\) 11.1745 0.769288 0.384644 0.923065i \(-0.374324\pi\)
0.384644 + 0.923065i \(0.374324\pi\)
\(212\) 0 0
\(213\) −22.7916 6.10700i −1.56166 0.418445i
\(214\) 0 0
\(215\) −0.899067 1.20160i −0.0613158 0.0819482i
\(216\) 0 0
\(217\) −0.0335574 0.104625i −0.00227803 0.00710242i
\(218\) 0 0
\(219\) 24.8333 + 14.3375i 1.67808 + 0.968838i
\(220\) 0 0
\(221\) 0.462994 + 0.801929i 0.0311443 + 0.0539436i
\(222\) 0 0
\(223\) −0.746804 + 0.746804i −0.0500097 + 0.0500097i −0.731669 0.681660i \(-0.761258\pi\)
0.681660 + 0.731669i \(0.261258\pi\)
\(224\) 0 0
\(225\) 18.7910 + 19.7258i 1.25273 + 1.31506i
\(226\) 0 0
\(227\) 0.807609 3.01404i 0.0536029 0.200049i −0.933932 0.357452i \(-0.883646\pi\)
0.987534 + 0.157403i \(0.0503122\pi\)
\(228\) 0 0
\(229\) 4.21091 7.29350i 0.278264 0.481968i −0.692689 0.721236i \(-0.743574\pi\)
0.970954 + 0.239268i \(0.0769075\pi\)
\(230\) 0 0
\(231\) −28.1989 + 1.37081i −1.85535 + 0.0901928i
\(232\) 0 0
\(233\) 22.0201 5.90027i 1.44259 0.386540i 0.549148 0.835725i \(-0.314952\pi\)
0.893439 + 0.449186i \(0.148286\pi\)
\(234\) 0 0
\(235\) 14.2103 1.69569i 0.926979 0.110615i
\(236\) 0 0
\(237\) 27.5645 + 27.5645i 1.79051 + 1.79051i
\(238\) 0 0
\(239\) 23.9971i 1.55224i 0.630585 + 0.776120i \(0.282815\pi\)
−0.630585 + 0.776120i \(0.717185\pi\)
\(240\) 0 0
\(241\) −21.4666 + 12.3937i −1.38278 + 0.798350i −0.992488 0.122340i \(-0.960960\pi\)
−0.390295 + 0.920690i \(0.627627\pi\)
\(242\) 0 0
\(243\) −2.25979 8.43364i −0.144965 0.541018i
\(244\) 0 0
\(245\) 13.1822 + 8.43977i 0.842179 + 0.539197i
\(246\) 0 0
\(247\) 0.665553 + 2.48388i 0.0423481 + 0.158045i
\(248\) 0 0
\(249\) 34.6392 19.9990i 2.19517 1.26738i
\(250\) 0 0
\(251\) 11.1158i 0.701623i 0.936446 + 0.350811i \(0.114094\pi\)
−0.936446 + 0.350811i \(0.885906\pi\)
\(252\) 0 0
\(253\) 12.2153 + 12.2153i 0.767970 + 0.767970i
\(254\) 0 0
\(255\) 3.16825 4.02682i 0.198403 0.252169i
\(256\) 0 0
\(257\) −24.4314 + 6.54637i −1.52399 + 0.408351i −0.921052 0.389439i \(-0.872669\pi\)
−0.602935 + 0.797790i \(0.706002\pi\)
\(258\) 0 0
\(259\) −0.678966 + 0.0330060i −0.0421889 + 0.00205090i
\(260\) 0 0
\(261\) 7.14424 12.3742i 0.442217 0.765943i
\(262\) 0 0
\(263\) −2.93659 + 10.9595i −0.181078 + 0.675792i 0.814358 + 0.580363i \(0.197089\pi\)
−0.995436 + 0.0954297i \(0.969577\pi\)
\(264\) 0 0
\(265\) −6.96973 + 16.2654i −0.428147 + 0.999174i
\(266\) 0 0
\(267\) 2.93964 2.93964i 0.179903 0.179903i
\(268\) 0 0
\(269\) −4.03346 6.98616i −0.245924 0.425954i 0.716467 0.697621i \(-0.245758\pi\)
−0.962391 + 0.271668i \(0.912425\pi\)
\(270\) 0 0
\(271\) −7.27419 4.19976i −0.441876 0.255117i 0.262517 0.964927i \(-0.415447\pi\)
−0.704393 + 0.709810i \(0.748781\pi\)
\(272\) 0 0
\(273\) 2.75885 + 8.60155i 0.166974 + 0.520590i
\(274\) 0 0
\(275\) 4.31920 + 17.8403i 0.260458 + 1.07581i
\(276\) 0 0
\(277\) −5.48646 1.47009i −0.329650 0.0883293i 0.0901983 0.995924i \(-0.471250\pi\)
−0.419848 + 0.907594i \(0.637917\pi\)
\(278\) 0 0
\(279\) −0.226279 −0.0135470
\(280\) 0 0
\(281\) 7.27627 0.434066 0.217033 0.976164i \(-0.430362\pi\)
0.217033 + 0.976164i \(0.430362\pi\)
\(282\) 0 0
\(283\) 7.44729 + 1.99550i 0.442696 + 0.118620i 0.473280 0.880912i \(-0.343070\pi\)
−0.0305840 + 0.999532i \(0.509737\pi\)
\(284\) 0 0
\(285\) 11.3928 8.52440i 0.674851 0.504942i
\(286\) 0 0
\(287\) 23.2215 + 5.02784i 1.37072 + 0.296784i
\(288\) 0 0
\(289\) 14.1842 + 8.18927i 0.834366 + 0.481721i
\(290\) 0 0
\(291\) −6.50906 11.2740i −0.381568 0.660895i
\(292\) 0 0
\(293\) 3.35198 3.35198i 0.195824 0.195824i −0.602383 0.798207i \(-0.705782\pi\)
0.798207 + 0.602383i \(0.205782\pi\)
\(294\) 0 0
\(295\) 8.89741 + 22.2397i 0.518027 + 1.29485i
\(296\) 0 0
\(297\) −6.76284 + 25.2393i −0.392420 + 1.46453i
\(298\) 0 0
\(299\) 2.76365 4.78679i 0.159826 0.276827i
\(300\) 0 0
\(301\) −1.49286 + 0.961456i −0.0860468 + 0.0554174i
\(302\) 0 0
\(303\) −0.201888 + 0.0540958i −0.0115982 + 0.00310772i
\(304\) 0 0
\(305\) −3.50118 2.75468i −0.200477 0.157733i
\(306\) 0 0
\(307\) 1.06546 + 1.06546i 0.0608089 + 0.0608089i 0.736857 0.676048i \(-0.236309\pi\)
−0.676048 + 0.736857i \(0.736309\pi\)
\(308\) 0 0
\(309\) 48.1918i 2.74154i
\(310\) 0 0
\(311\) −11.9584 + 6.90417i −0.678097 + 0.391500i −0.799138 0.601148i \(-0.794710\pi\)
0.121040 + 0.992648i \(0.461377\pi\)
\(312\) 0 0
\(313\) 6.04266 + 22.5515i 0.341551 + 1.27469i 0.896590 + 0.442863i \(0.146037\pi\)
−0.555038 + 0.831825i \(0.687296\pi\)
\(314\) 0 0
\(315\) 24.8418 20.5421i 1.39968 1.15742i
\(316\) 0 0
\(317\) 3.41352 + 12.7394i 0.191722 + 0.715518i 0.993091 + 0.117347i \(0.0374390\pi\)
−0.801369 + 0.598171i \(0.795894\pi\)
\(318\) 0 0
\(319\) 8.33728 4.81353i 0.466798 0.269506i
\(320\) 0 0
\(321\) 13.2818i 0.741316i
\(322\) 0 0
\(323\) −1.22035 1.22035i −0.0679023 0.0679023i
\(324\) 0 0
\(325\) 5.15599 2.81226i 0.286003 0.155996i
\(326\) 0 0
\(327\) −50.8253 + 13.6186i −2.81065 + 0.753111i
\(328\) 0 0
\(329\) −0.822187 16.9132i −0.0453286 0.932454i
\(330\) 0 0
\(331\) −9.54799 + 16.5376i −0.524805 + 0.908989i 0.474778 + 0.880106i \(0.342528\pi\)
−0.999583 + 0.0288830i \(0.990805\pi\)
\(332\) 0 0
\(333\) −0.362328 + 1.35222i −0.0198554 + 0.0741015i
\(334\) 0 0
\(335\) 13.6111 + 5.83237i 0.743653 + 0.318656i
\(336\) 0 0
\(337\) 0.488226 0.488226i 0.0265953 0.0265953i −0.693684 0.720279i \(-0.744014\pi\)
0.720279 + 0.693684i \(0.244014\pi\)
\(338\) 0 0
\(339\) 3.12540 + 5.41335i 0.169748 + 0.294013i
\(340\) 0 0
\(341\) −0.132033 0.0762292i −0.00714998 0.00412804i
\(342\) 0 0
\(343\) 11.0554 14.8586i 0.596936 0.802289i
\(344\) 0 0
\(345\) −30.2720 4.35966i −1.62979 0.234716i
\(346\) 0 0
\(347\) 3.68015 + 0.986094i 0.197561 + 0.0529363i 0.356243 0.934393i \(-0.384058\pi\)
−0.158682 + 0.987330i \(0.550724\pi\)
\(348\) 0 0
\(349\) −7.91303 −0.423575 −0.211787 0.977316i \(-0.567928\pi\)
−0.211787 + 0.977316i \(0.567928\pi\)
\(350\) 0 0
\(351\) 8.36041 0.446246
\(352\) 0 0
\(353\) −24.9004 6.67203i −1.32531 0.355116i −0.474347 0.880338i \(-0.657316\pi\)
−0.850965 + 0.525222i \(0.823982\pi\)
\(354\) 0 0
\(355\) 17.9665 + 2.58747i 0.953564 + 0.137329i
\(356\) 0 0
\(357\) −4.48995 4.07365i −0.237633 0.215601i
\(358\) 0 0
\(359\) −8.99497 5.19325i −0.474737 0.274089i 0.243484 0.969905i \(-0.421710\pi\)
−0.718220 + 0.695816i \(0.755043\pi\)
\(360\) 0 0
\(361\) 7.10364 + 12.3039i 0.373876 + 0.647572i
\(362\) 0 0
\(363\) −5.09161 + 5.09161i −0.267240 + 0.267240i
\(364\) 0 0
\(365\) −20.2763 8.68840i −1.06131 0.454772i
\(366\) 0 0
\(367\) 2.24811 8.39004i 0.117350 0.437957i −0.882102 0.471059i \(-0.843872\pi\)
0.999452 + 0.0331020i \(0.0105386\pi\)
\(368\) 0 0
\(369\) 24.4654 42.3753i 1.27362 2.20597i
\(370\) 0 0
\(371\) 18.6197 + 9.57617i 0.966686 + 0.497170i
\(372\) 0 0
\(373\) −12.8560 + 3.44476i −0.665660 + 0.178363i −0.575799 0.817591i \(-0.695309\pi\)
−0.0898611 + 0.995954i \(0.528642\pi\)
\(374\) 0 0
\(375\) −25.0450 20.7084i −1.29332 1.06938i
\(376\) 0 0
\(377\) −2.17808 2.17808i −0.112177 0.112177i
\(378\) 0 0
\(379\) 25.3453i 1.30190i −0.759121 0.650949i \(-0.774371\pi\)
0.759121 0.650949i \(-0.225629\pi\)
\(380\) 0 0
\(381\) 47.1788 27.2387i 2.41704 1.39548i
\(382\) 0 0
\(383\) −4.76251 17.7739i −0.243353 0.908205i −0.974204 0.225668i \(-0.927543\pi\)
0.730851 0.682537i \(-0.239123\pi\)
\(384\) 0 0
\(385\) 21.4154 3.61749i 1.09143 0.184364i
\(386\) 0 0
\(387\) 0.946464 + 3.53225i 0.0481114 + 0.179554i
\(388\) 0 0
\(389\) −19.3621 + 11.1787i −0.981699 + 0.566784i −0.902783 0.430097i \(-0.858479\pi\)
−0.0789164 + 0.996881i \(0.525146\pi\)
\(390\) 0 0
\(391\) 3.70961i 0.187603i
\(392\) 0 0
\(393\) −29.1745 29.1745i −1.47166 1.47166i
\(394\) 0 0
\(395\) −23.5682 18.5432i −1.18585 0.933008i
\(396\) 0 0
\(397\) −15.2461 + 4.08518i −0.765181 + 0.205029i −0.620241 0.784411i \(-0.712965\pi\)
−0.144939 + 0.989441i \(0.546299\pi\)
\(398\) 0 0
\(399\) −9.11594 14.1543i −0.456368 0.708603i
\(400\) 0 0
\(401\) −6.98528 + 12.0989i −0.348828 + 0.604188i −0.986042 0.166499i \(-0.946754\pi\)
0.637213 + 0.770687i \(0.280087\pi\)
\(402\) 0 0
\(403\) −0.0126253 + 0.0471183i −0.000628911 + 0.00234713i
\(404\) 0 0
\(405\) −3.60661 9.01496i −0.179214 0.447957i
\(406\) 0 0
\(407\) −0.666957 + 0.666957i −0.0330598 + 0.0330598i
\(408\) 0 0
\(409\) −0.156681 0.271379i −0.00774737 0.0134188i 0.862126 0.506694i \(-0.169133\pi\)
−0.869873 + 0.493276i \(0.835799\pi\)
\(410\) 0 0
\(411\) 47.7431 + 27.5645i 2.35499 + 1.35966i
\(412\) 0 0
\(413\) 26.9879 8.65608i 1.32799 0.425938i
\(414\) 0 0
\(415\) −24.6370 + 18.4340i −1.20938 + 0.904891i
\(416\) 0 0
\(417\) −23.1266 6.19675i −1.13251 0.303456i
\(418\) 0 0
\(419\) −31.6254 −1.54500 −0.772501 0.635014i \(-0.780994\pi\)
−0.772501 + 0.635014i \(0.780994\pi\)
\(420\) 0 0
\(421\) 24.2137 1.18011 0.590053 0.807365i \(-0.299107\pi\)
0.590053 + 0.807365i \(0.299107\pi\)
\(422\) 0 0
\(423\) −33.6842 9.02565i −1.63778 0.438842i
\(424\) 0 0
\(425\) −2.05308 + 3.36476i −0.0995890 + 0.163215i
\(426\) 0 0
\(427\) −3.54190 + 3.90386i −0.171405 + 0.188921i
\(428\) 0 0
\(429\) 10.8548 + 6.26703i 0.524075 + 0.302575i
\(430\) 0 0
\(431\) 0.779037 + 1.34933i 0.0375249 + 0.0649950i 0.884178 0.467150i \(-0.154719\pi\)
−0.846653 + 0.532145i \(0.821386\pi\)
\(432\) 0 0
\(433\) 6.28166 6.28166i 0.301877 0.301877i −0.539871 0.841748i \(-0.681527\pi\)
0.841748 + 0.539871i \(0.181527\pi\)
\(434\) 0 0
\(435\) −6.71305 + 15.6663i −0.321866 + 0.751144i
\(436\) 0 0
\(437\) −2.66628 + 9.95068i −0.127545 + 0.476006i
\(438\) 0 0
\(439\) −11.9571 + 20.7103i −0.570681 + 0.988449i 0.425815 + 0.904810i \(0.359988\pi\)
−0.996496 + 0.0836389i \(0.973346\pi\)
\(440\) 0 0
\(441\) −22.1844 31.0255i −1.05640 1.47741i
\(442\) 0 0
\(443\) 12.4238 3.32895i 0.590272 0.158163i 0.0486946 0.998814i \(-0.484494\pi\)
0.541578 + 0.840651i \(0.317827\pi\)
\(444\) 0 0
\(445\) −1.97756 + 2.51346i −0.0937451 + 0.119149i
\(446\) 0 0
\(447\) 9.95157 + 9.95157i 0.470693 + 0.470693i
\(448\) 0 0
\(449\) 17.8932i 0.844435i −0.906495 0.422217i \(-0.861252\pi\)
0.906495 0.422217i \(-0.138748\pi\)
\(450\) 0 0
\(451\) 28.5510 16.4839i 1.34441 0.776197i
\(452\) 0 0
\(453\) 7.55749 + 28.2049i 0.355082 + 1.32518i
\(454\) 0 0
\(455\) −2.89145 6.31900i −0.135553 0.296239i
\(456\) 0 0
\(457\) 8.85449 + 33.0454i 0.414196 + 1.54580i 0.786442 + 0.617665i \(0.211921\pi\)
−0.372246 + 0.928134i \(0.621412\pi\)
\(458\) 0 0
\(459\) −4.85928 + 2.80551i −0.226812 + 0.130950i
\(460\) 0 0
\(461\) 23.3471i 1.08738i 0.839286 + 0.543690i \(0.182973\pi\)
−0.839286 + 0.543690i \(0.817027\pi\)
\(462\) 0 0
\(463\) −3.98510 3.98510i −0.185203 0.185203i 0.608415 0.793619i \(-0.291805\pi\)
−0.793619 + 0.608415i \(0.791805\pi\)
\(464\) 0 0
\(465\) 0.268016 0.0319818i 0.0124289 0.00148312i
\(466\) 0 0
\(467\) 4.71932 1.26454i 0.218384 0.0585159i −0.147968 0.988992i \(-0.547273\pi\)
0.366352 + 0.930476i \(0.380607\pi\)
\(468\) 0 0
\(469\) 8.01347 15.5812i 0.370028 0.719473i
\(470\) 0 0
\(471\) 35.5873 61.6390i 1.63978 2.84017i
\(472\) 0 0
\(473\) −0.637693 + 2.37990i −0.0293212 + 0.109428i
\(474\) 0 0
\(475\) −7.92561 + 7.55000i −0.363652 + 0.346418i
\(476\) 0 0
\(477\) 30.4904 30.4904i 1.39606 1.39606i
\(478\) 0 0
\(479\) 8.55572 + 14.8189i 0.390921 + 0.677094i 0.992571 0.121665i \(-0.0388234\pi\)
−0.601651 + 0.798759i \(0.705490\pi\)
\(480\) 0 0
\(481\) 0.261359 + 0.150896i 0.0119170 + 0.00688026i
\(482\) 0 0
\(483\) −7.65783 + 35.3683i −0.348443 + 1.60931i
\(484\) 0 0
\(485\) 5.99972 + 8.01859i 0.272433 + 0.364105i
\(486\) 0 0
\(487\) 0.125860 + 0.0337240i 0.00570325 + 0.00152818i 0.261670 0.965158i \(-0.415727\pi\)
−0.255966 + 0.966686i \(0.582394\pi\)
\(488\) 0 0
\(489\) −63.8465 −2.88724
\(490\) 0 0
\(491\) −26.9895 −1.21802 −0.609011 0.793162i \(-0.708433\pi\)
−0.609011 + 0.793162i \(0.708433\pi\)
\(492\) 0 0
\(493\) 1.99685 + 0.535055i 0.0899337 + 0.0240977i
\(494\) 0 0
\(495\) 6.37579 44.2713i 0.286570 1.98985i
\(496\) 0 0
\(497\) 4.54495 20.9912i 0.203869 0.941584i
\(498\) 0 0
\(499\) 0.0833977 + 0.0481497i 0.00373339 + 0.00215548i 0.501866 0.864946i \(-0.332647\pi\)
−0.498132 + 0.867101i \(0.665981\pi\)
\(500\) 0 0
\(501\) 6.46638 + 11.2001i 0.288897 + 0.500384i
\(502\) 0 0
\(503\) 13.6334 13.6334i 0.607883 0.607883i −0.334509 0.942392i \(-0.608571\pi\)
0.942392 + 0.334509i \(0.108571\pi\)
\(504\) 0 0
\(505\) 0.149286 0.0597245i 0.00664312 0.00265771i
\(506\) 0 0
\(507\) −8.74194 + 32.6254i −0.388243 + 1.44894i
\(508\) 0 0
\(509\) −6.16366 + 10.6758i −0.273199 + 0.473195i −0.969679 0.244381i \(-0.921415\pi\)
0.696480 + 0.717576i \(0.254749\pi\)
\(510\) 0 0
\(511\) −11.9376 + 23.2111i −0.528087 + 1.02680i
\(512\) 0 0
\(513\) −15.0510 + 4.03291i −0.664520 + 0.178057i
\(514\) 0 0
\(515\) −4.39274 36.8123i −0.193567 1.62214i
\(516\) 0 0
\(517\) −16.6140 16.6140i −0.730684 0.730684i
\(518\) 0 0
\(519\) 15.1918i 0.666845i
\(520\) 0 0
\(521\) 14.1415 8.16461i 0.619551 0.357698i −0.157143 0.987576i \(-0.550228\pi\)
0.776694 + 0.629878i \(0.216895\pi\)
\(522\) 0 0
\(523\) 7.09270 + 26.4703i 0.310142 + 1.15747i 0.928428 + 0.371512i \(0.121161\pi\)
−0.618286 + 0.785953i \(0.712173\pi\)
\(524\) 0 0
\(525\) −26.5205 + 27.8422i −1.15745 + 1.21513i
\(526\) 0 0
\(527\) −0.00847337 0.0316231i −0.000369106 0.00137752i
\(528\) 0 0
\(529\) −0.742186 + 0.428501i −0.0322689 + 0.0186305i
\(530\) 0 0
\(531\) 58.3682i 2.53297i
\(532\) 0 0
\(533\) −7.45881 7.45881i −0.323077 0.323077i
\(534\) 0 0
\(535\) 1.21065 + 10.1456i 0.0523409 + 0.438630i
\(536\) 0 0
\(537\) −35.2878 + 9.45533i −1.52278 + 0.408028i
\(538\) 0 0
\(539\) −2.49258 25.5768i −0.107363 1.10167i
\(540\) 0 0
\(541\) 20.5773 35.6410i 0.884689 1.53233i 0.0386200 0.999254i \(-0.487704\pi\)
0.846069 0.533073i \(-0.178963\pi\)
\(542\) 0 0
\(543\) −8.78254 + 32.7769i −0.376895 + 1.40659i
\(544\) 0 0
\(545\) 37.5826 15.0356i 1.60986 0.644056i
\(546\) 0 0
\(547\) −8.06541 + 8.06541i −0.344852 + 0.344852i −0.858188 0.513336i \(-0.828410\pi\)
0.513336 + 0.858188i \(0.328410\pi\)
\(548\) 0 0
\(549\) 5.42777 + 9.40117i 0.231651 + 0.401232i
\(550\) 0 0
\(551\) 4.97180 + 2.87047i 0.211806 + 0.122286i
\(552\) 0 0
\(553\) −23.8423 + 26.2788i −1.01388 + 1.11749i
\(554\) 0 0
\(555\) 0.238038 1.65285i 0.0101041 0.0701597i
\(556\) 0 0
\(557\) 24.7826 + 6.64049i 1.05007 + 0.281367i 0.742282 0.670087i \(-0.233743\pi\)
0.307792 + 0.951454i \(0.400410\pi\)
\(558\) 0 0
\(559\) 0.788333 0.0333429
\(560\) 0 0
\(561\) −8.41213 −0.355160
\(562\) 0 0
\(563\) 12.3749 + 3.31584i 0.521539 + 0.139746i 0.509978 0.860187i \(-0.329653\pi\)
0.0115606 + 0.999933i \(0.496320\pi\)
\(564\) 0 0
\(565\) −2.88083 3.85022i −0.121198 0.161980i
\(566\) 0 0
\(567\) −10.9397 + 3.50878i −0.459423 + 0.147355i
\(568\) 0 0
\(569\) −29.8291 17.2218i −1.25050 0.721977i −0.279292 0.960206i \(-0.590100\pi\)
−0.971209 + 0.238229i \(0.923433\pi\)
\(570\) 0 0
\(571\) −4.11985 7.13579i −0.172410 0.298623i 0.766852 0.641824i \(-0.221822\pi\)
−0.939262 + 0.343201i \(0.888489\pi\)
\(572\) 0 0
\(573\) 31.8645 31.8645i 1.33116 1.33116i
\(574\) 0 0
\(575\) 23.5212 + 0.570889i 0.980904 + 0.0238077i
\(576\) 0 0
\(577\) −0.910086 + 3.39649i −0.0378874 + 0.141398i −0.982279 0.187426i \(-0.939985\pi\)
0.944391 + 0.328824i \(0.106652\pi\)
\(578\) 0 0
\(579\) 13.0770 22.6500i 0.543460 0.941301i
\(580\) 0 0
\(581\) 19.7132 + 30.6088i 0.817843 + 1.26987i
\(582\) 0 0
\(583\) 28.0627 7.51937i 1.16224 0.311421i
\(584\) 0 0
\(585\) −14.2103 + 1.69569i −0.587524 + 0.0701081i
\(586\) 0 0
\(587\) 5.37485 + 5.37485i 0.221844 + 0.221844i 0.809275 0.587431i \(-0.199861\pi\)
−0.587431 + 0.809275i \(0.699861\pi\)
\(588\) 0 0
\(589\) 0.0909162i 0.00374613i
\(590\) 0 0
\(591\) 43.4136 25.0649i 1.78580 1.03103i
\(592\) 0 0
\(593\) 0.190155 + 0.709668i 0.00780872 + 0.0291426i 0.969720 0.244218i \(-0.0785314\pi\)
−0.961912 + 0.273361i \(0.911865\pi\)
\(594\) 0 0
\(595\) 3.80106 + 2.70248i 0.155828 + 0.110791i
\(596\) 0 0
\(597\) −6.56845 24.5138i −0.268829 1.00328i
\(598\) 0 0
\(599\) −7.23778 + 4.17873i −0.295727 + 0.170738i −0.640522 0.767940i \(-0.721282\pi\)
0.344794 + 0.938678i \(0.387949\pi\)
\(600\) 0 0
\(601\) 39.9236i 1.62852i −0.580501 0.814259i \(-0.697143\pi\)
0.580501 0.814259i \(-0.302857\pi\)
\(602\) 0 0
\(603\) −25.5147 25.5147i −1.03904 1.03904i
\(604\) 0 0
\(605\) 3.42523 4.35344i 0.139255 0.176993i
\(606\) 0 0
\(607\) −33.2758 + 8.91623i −1.35062 + 0.361899i −0.860365 0.509678i \(-0.829765\pi\)
−0.490259 + 0.871577i \(0.663098\pi\)
\(608\) 0 0
\(609\) 17.9339 + 9.22349i 0.726720 + 0.373755i
\(610\) 0 0
\(611\) −3.75885 + 6.51051i −0.152067 + 0.263387i
\(612\) 0 0
\(613\) −8.46832 + 31.6042i −0.342032 + 1.27648i 0.554009 + 0.832510i \(0.313097\pi\)
−0.896041 + 0.443971i \(0.853569\pi\)
\(614\) 0 0
\(615\) −22.9888 + 53.6493i −0.926997 + 2.16335i
\(616\) 0 0
\(617\) −15.5005 + 15.5005i −0.624025 + 0.624025i −0.946558 0.322533i \(-0.895466\pi\)
0.322533 + 0.946558i \(0.395466\pi\)
\(618\) 0 0
\(619\) −4.31138 7.46752i −0.173289 0.300145i 0.766279 0.642508i \(-0.222106\pi\)
−0.939568 + 0.342363i \(0.888773\pi\)
\(620\) 0 0
\(621\) 29.0055 + 16.7463i 1.16395 + 0.672008i
\(622\) 0 0
\(623\) 2.80254 + 2.54269i 0.112281 + 0.101871i
\(624\) 0 0
\(625\) 21.0187 + 13.5356i 0.840749 + 0.541425i
\(626\) 0 0
\(627\) −22.5648 6.04621i −0.901150 0.241462i
\(628\) 0 0
\(629\) −0.202545 −0.00807600
\(630\) 0 0
\(631\) 4.13675 0.164682 0.0823408 0.996604i \(-0.473760\pi\)
0.0823408 + 0.996604i \(0.473760\pi\)
\(632\) 0 0
\(633\) 31.3739 + 8.40662i 1.24700 + 0.334133i
\(634\) 0 0
\(635\) −33.5556 + 25.1072i −1.33161 + 0.996349i
\(636\) 0 0
\(637\) −7.69827 + 2.88840i −0.305017 + 0.114443i
\(638\) 0 0
\(639\) −38.3055 22.1157i −1.51534 0.874882i
\(640\) 0 0
\(641\) −5.42807 9.40169i −0.214396 0.371345i 0.738690 0.674046i \(-0.235445\pi\)
−0.953086 + 0.302701i \(0.902112\pi\)
\(642\) 0 0
\(643\) 8.06230 8.06230i 0.317946 0.317946i −0.530032 0.847978i \(-0.677820\pi\)
0.847978 + 0.530032i \(0.177820\pi\)
\(644\) 0 0
\(645\) −1.62028 4.05000i −0.0637984 0.159469i
\(646\) 0 0
\(647\) 2.69865 10.0715i 0.106095 0.395951i −0.892372 0.451300i \(-0.850960\pi\)
0.998467 + 0.0553490i \(0.0176271\pi\)
\(648\) 0 0
\(649\) 19.6632 34.0577i 0.771848 1.33688i
\(650\) 0 0
\(651\) −0.0155070 0.318994i −0.000607766 0.0125023i
\(652\) 0 0
\(653\) 6.41946 1.72009i 0.251213 0.0673123i −0.131015 0.991380i \(-0.541824\pi\)
0.382228 + 0.924068i \(0.375157\pi\)
\(654\) 0 0
\(655\) 24.9449 + 19.6263i 0.974677 + 0.766862i
\(656\) 0 0
\(657\) 38.0090 + 38.0090i 1.48287 + 1.48287i
\(658\) 0 0
\(659\) 22.0345i 0.858343i −0.903223 0.429172i \(-0.858806\pi\)
0.903223 0.429172i \(-0.141194\pi\)
\(660\) 0 0
\(661\) −9.94278 + 5.74047i −0.386729 + 0.223278i −0.680742 0.732523i \(-0.738343\pi\)
0.294013 + 0.955802i \(0.405009\pi\)
\(662\) 0 0
\(663\) 0.696621 + 2.59983i 0.0270545 + 0.100969i
\(664\) 0 0
\(665\) 8.25358 + 9.98115i 0.320060 + 0.387053i
\(666\) 0 0
\(667\) −3.19379 11.9194i −0.123664 0.461521i
\(668\) 0 0
\(669\) −2.65857 + 1.53492i −0.102786 + 0.0593436i
\(670\) 0 0
\(671\) 7.31407i 0.282356i
\(672\) 0 0
\(673\) −15.2073 15.2073i −0.586198 0.586198i 0.350402 0.936600i \(-0.386045\pi\)
−0.936600 + 0.350402i \(0.886045\pi\)
\(674\) 0 0
\(675\) 17.0409 + 31.2427i 0.655903 + 1.20253i
\(676\) 0 0
\(677\) −5.54296 + 1.48523i −0.213033 + 0.0570821i −0.363757 0.931494i \(-0.618506\pi\)
0.150724 + 0.988576i \(0.451840\pi\)
\(678\) 0 0
\(679\) 9.96224 6.41606i 0.382316 0.246226i
\(680\) 0 0
\(681\) 4.53492 7.85472i 0.173779 0.300993i
\(682\) 0 0
\(683\) −5.02900 + 18.7685i −0.192430 + 0.718157i 0.800488 + 0.599349i \(0.204574\pi\)
−0.992917 + 0.118808i \(0.962093\pi\)
\(684\) 0 0
\(685\) −38.9821 16.7039i −1.48943 0.638222i
\(686\) 0 0
\(687\) 17.3095 17.3095i 0.660400 0.660400i
\(688\) 0 0
\(689\) −4.64782 8.05027i −0.177068 0.306691i
\(690\) 0 0
\(691\) −19.0914 11.0224i −0.726270 0.419312i 0.0907861 0.995870i \(-0.471062\pi\)
−0.817056 + 0.576558i \(0.804395\pi\)
\(692\) 0 0
\(693\) −51.7244 11.1992i −1.96485 0.425422i
\(694\) 0 0
\(695\) 18.2305 + 2.62550i 0.691524 + 0.0995908i
\(696\) 0 0
\(697\) 6.83821 + 1.83229i 0.259016 + 0.0694031i
\(698\) 0 0
\(699\) 66.2630 2.50630
\(700\) 0 0
\(701\) −18.0270 −0.680870 −0.340435 0.940268i \(-0.610574\pi\)
−0.340435 + 0.940268i \(0.610574\pi\)
\(702\) 0 0
\(703\) −0.543308 0.145579i −0.0204913 0.00549062i
\(704\) 0 0
\(705\) 41.1729 + 5.92957i 1.55066 + 0.223321i
\(706\) 0 0
\(707\) −0.0581046 0.181158i −0.00218525 0.00681316i
\(708\) 0 0
\(709\) −37.0614 21.3974i −1.39187 0.803597i −0.398349 0.917234i \(-0.630417\pi\)
−0.993522 + 0.113637i \(0.963750\pi\)
\(710\) 0 0
\(711\) 36.5370 + 63.2840i 1.37025 + 2.37334i
\(712\) 0 0
\(713\) −0.138183 + 0.138183i −0.00517498 + 0.00517498i
\(714\) 0 0
\(715\) −8.86292 3.79777i −0.331454 0.142029i
\(716\) 0 0
\(717\) −18.0530 + 67.3747i −0.674202 + 2.51615i
\(718\) 0 0
\(719\) 2.72691 4.72315i 0.101697 0.176144i −0.810687 0.585480i \(-0.800906\pi\)
0.912384 + 0.409336i \(0.134240\pi\)
\(720\) 0 0
\(721\) −43.8142 + 2.12990i −1.63172 + 0.0793217i
\(722\) 0 0
\(723\) −69.5938 + 18.6476i −2.58822 + 0.693512i
\(724\) 0 0
\(725\) 3.69989 12.5790i 0.137411 0.467171i
\(726\) 0 0
\(727\) −16.6781 16.6781i −0.618555 0.618555i 0.326606 0.945161i \(-0.394095\pi\)
−0.945161 + 0.326606i \(0.894095\pi\)
\(728\) 0 0
\(729\) 38.4054i 1.42242i
\(730\) 0 0
\(731\) −0.458200 + 0.264542i −0.0169471 + 0.00978443i
\(732\) 0 0
\(733\) −8.79960 32.8405i −0.325021 1.21299i −0.914291 0.405057i \(-0.867252\pi\)
0.589271 0.807936i \(-0.299415\pi\)
\(734\) 0 0
\(735\) 30.6614 + 33.6127i 1.13096 + 1.23982i
\(736\) 0 0
\(737\) −6.29231 23.4832i −0.231780 0.865016i
\(738\) 0 0
\(739\) −25.0733 + 14.4761i −0.922335 + 0.532510i −0.884379 0.466769i \(-0.845418\pi\)
−0.0379557 + 0.999279i \(0.512085\pi\)
\(740\) 0 0
\(741\) 7.47449i 0.274582i
\(742\) 0 0
\(743\) −34.0351 34.0351i −1.24863 1.24863i −0.956327 0.292300i \(-0.905579\pi\)
−0.292300 0.956327i \(-0.594421\pi\)
\(744\) 0 0
\(745\) −8.50881 6.69461i −0.311739 0.245272i
\(746\) 0 0
\(747\) 72.4235 19.4058i 2.64984 0.710022i
\(748\) 0 0
\(749\) 12.0753 0.587006i 0.441221 0.0214487i
\(750\) 0 0
\(751\) −9.30569 + 16.1179i −0.339569 + 0.588151i −0.984352 0.176215i \(-0.943615\pi\)
0.644782 + 0.764366i \(0.276948\pi\)
\(752\) 0 0
\(753\) −8.36242 + 31.2090i −0.304743 + 1.13732i
\(754\) 0 0
\(755\) −8.34385 20.8560i −0.303664 0.759029i
\(756\) 0 0
\(757\) 29.7422 29.7422i 1.08100 1.08100i 0.0845825 0.996416i \(-0.473044\pi\)
0.996416 0.0845825i \(-0.0269557\pi\)
\(758\) 0 0
\(759\) 25.1064 + 43.4856i 0.911305 + 1.57843i
\(760\) 0 0
\(761\) 17.6474 + 10.1887i 0.639718 + 0.369341i 0.784506 0.620122i \(-0.212917\pi\)
−0.144788 + 0.989463i \(0.546250\pi\)
\(762\) 0 0
\(763\) −14.6278 45.6066i −0.529563 1.65107i
\(764\) 0 0
\(765\) 7.69038 5.75415i 0.278046 0.208042i
\(766\) 0 0
\(767\) −12.1541 3.25668i −0.438859 0.117592i
\(768\) 0 0
\(769\) 40.9728 1.47752 0.738759 0.673970i \(-0.235412\pi\)
0.738759 + 0.673970i \(0.235412\pi\)
\(770\) 0 0
\(771\) −73.5189 −2.64772
\(772\) 0 0
\(773\) 23.8577 + 6.39265i 0.858101 + 0.229928i 0.660936 0.750443i \(-0.270160\pi\)
0.197166 + 0.980370i \(0.436826\pi\)
\(774\) 0 0
\(775\) −0.201814 + 0.0488599i −0.00724938 + 0.00175510i
\(776\) 0 0
\(777\) −1.93111 0.418118i −0.0692783 0.0149999i
\(778\) 0 0
\(779\) 17.0259 + 9.82991i 0.610017 + 0.352193i
\(780\) 0 0
\(781\) −14.9007 25.8088i −0.533190 0.923513i
\(782\) 0 0
\(783\) 13.1980 13.1980i 0.471659 0.471659i
\(784\) 0 0
\(785\) −21.5656 + 50.3280i −0.769710 + 1.79628i
\(786\) 0 0
\(787\) −2.12442 + 7.92843i −0.0757273 + 0.282618i −0.993397 0.114725i \(-0.963401\pi\)
0.917670 + 0.397343i \(0.130068\pi\)
\(788\) 0 0
\(789\) −16.4897 + 28.5610i −0.587048 + 1.01680i
\(790\) 0 0
\(791\) −4.78348 + 3.08075i −0.170081 + 0.109539i
\(792\) 0 0
\(793\) 2.26046 0.605689i 0.0802713 0.0215086i
\(794\) 0 0
\(795\) −31.8048 + 40.4237i −1.12800 + 1.43368i
\(796\) 0 0
\(797\) 11.7928 + 11.7928i 0.417722 + 0.417722i 0.884418 0.466696i \(-0.154556\pi\)
−0.466696 + 0.884418i \(0.654556\pi\)
\(798\) 0 0
\(799\) 5.04544i 0.178495i
\(800\) 0 0
\(801\) 6.74899 3.89653i 0.238464 0.137677i
\(802\) 0 0
\(803\) 9.37358 + 34.9827i 0.330786 + 1.23451i
\(804\) 0 0
\(805\) 2.62573 27.7148i 0.0925447 0.976819i
\(806\) 0 0
\(807\) −6.06875 22.6489i −0.213630 0.797278i
\(808\) 0 0
\(809\) −28.8498 + 16.6564i −1.01430 + 0.585609i −0.912449 0.409191i \(-0.865811\pi\)
−0.101855 + 0.994799i \(0.532478\pi\)
\(810\) 0 0
\(811\) 55.2368i 1.93963i −0.243850 0.969813i \(-0.578410\pi\)
0.243850 0.969813i \(-0.421590\pi\)
\(812\) 0 0
\(813\) −17.2637 17.2637i −0.605465 0.605465i
\(814\) 0 0
\(815\) 48.7704 5.81968i 1.70835 0.203855i
\(816\) 0 0
\(817\) −1.41922 + 0.380278i −0.0496521 + 0.0133042i
\(818\) 0 0
\(819\) 0.822187 + 16.9132i 0.0287295 + 0.590995i
\(820\) 0 0
\(821\) −9.31457 + 16.1333i −0.325081 + 0.563056i −0.981529 0.191315i \(-0.938725\pi\)
0.656448 + 0.754371i \(0.272058\pi\)
\(822\) 0 0
\(823\) 4.37130 16.3139i 0.152374 0.568668i −0.846942 0.531685i \(-0.821559\pi\)
0.999316 0.0369821i \(-0.0117745\pi\)
\(824\) 0 0
\(825\) −1.29458 + 53.3382i −0.0450716 + 1.85700i
\(826\) 0 0
\(827\) 5.62716 5.62716i 0.195675 0.195675i −0.602468 0.798143i \(-0.705816\pi\)
0.798143 + 0.602468i \(0.205816\pi\)
\(828\) 0 0
\(829\) 3.29757 + 5.71155i 0.114529 + 0.198370i 0.917591 0.397525i \(-0.130131\pi\)
−0.803062 + 0.595895i \(0.796797\pi\)
\(830\) 0 0
\(831\) −14.2980 8.25494i −0.495991 0.286361i
\(832\) 0 0
\(833\) 3.50517 4.26213i 0.121447 0.147674i
\(834\) 0 0
\(835\) −5.96038 7.96601i −0.206268 0.275675i
\(836\) 0 0
\(837\) −0.285513 0.0765030i −0.00986877 0.00264433i
\(838\) 0 0
\(839\) −46.0930 −1.59131 −0.795654 0.605752i \(-0.792872\pi\)
−0.795654 + 0.605752i \(0.792872\pi\)
\(840\) 0 0
\(841\) 22.1232 0.762870
\(842\) 0 0
\(843\) 20.4290 + 5.47394i 0.703613 + 0.188533i
\(844\) 0 0
\(845\) 3.70387 25.7184i 0.127417 0.884740i
\(846\) 0 0
\(847\) −4.85413 4.40407i −0.166790 0.151326i
\(848\) 0 0
\(849\) 19.4080 + 11.2052i 0.666080 + 0.384562i
\(850\) 0 0
\(851\) 0.604505 + 1.04703i 0.0207222 + 0.0358918i
\(852\) 0 0
\(853\) 14.9594 14.9594i 0.512200 0.512200i −0.403000 0.915200i \(-0.632032\pi\)
0.915200 + 0.403000i \(0.132032\pi\)
\(854\) 0 0
\(855\) 24.7645 9.90752i 0.846929 0.338830i
\(856\) 0 0
\(857\) 3.12136 11.6491i 0.106623 0.397924i −0.891901 0.452231i \(-0.850628\pi\)
0.998524 + 0.0543068i \(0.0172949\pi\)
\(858\) 0 0
\(859\) 2.90061 5.02401i 0.0989677 0.171417i −0.812290 0.583254i \(-0.801779\pi\)
0.911258 + 0.411837i \(0.135113\pi\)
\(860\) 0 0
\(861\) 61.4147 + 31.5858i 2.09301 + 1.07644i
\(862\) 0 0
\(863\) −2.90586 + 0.778623i −0.0989167 + 0.0265046i −0.307938 0.951406i \(-0.599639\pi\)
0.209021 + 0.977911i \(0.432972\pi\)
\(864\) 0 0
\(865\) 1.38475 + 11.6046i 0.0470829 + 0.394567i
\(866\) 0 0
\(867\) 33.6632 + 33.6632i 1.14326 + 1.14326i
\(868\) 0 0
\(869\) 49.2347i 1.67017i
\(870\) 0 0
\(871\) −6.73657 + 3.88936i −0.228260 + 0.131786i
\(872\) 0 0
\(873\) −6.31601 23.5717i −0.213765 0.797780i
\(874\) 0 0
\(875\) 17.7204 23.6852i 0.599058 0.800706i
\(876\) 0 0
\(877\) 9.07228 + 33.8582i 0.306349 + 1.14331i 0.931778 + 0.363030i \(0.118258\pi\)
−0.625428 + 0.780282i \(0.715076\pi\)
\(878\) 0 0
\(879\) 11.9328 6.88939i 0.402483 0.232373i
\(880\) 0 0
\(881\) 23.7116i 0.798864i −0.916763 0.399432i \(-0.869207\pi\)
0.916763 0.399432i \(-0.130793\pi\)
\(882\) 0 0
\(883\) 7.95370 + 7.95370i 0.267663 + 0.267663i 0.828158 0.560495i \(-0.189389\pi\)
−0.560495 + 0.828158i \(0.689389\pi\)
\(884\) 0 0
\(885\) 8.24965 + 69.1342i 0.277309 + 2.32392i
\(886\) 0 0
\(887\) 19.6954 5.27738i 0.661308 0.177197i 0.0874718 0.996167i \(-0.472121\pi\)
0.573836 + 0.818970i \(0.305455\pi\)
\(888\) 0 0
\(889\) 26.8495 + 41.6893i 0.900503 + 1.39821i
\(890\) 0 0
\(891\) −7.97057 + 13.8054i −0.267024 + 0.462499i
\(892\) 0 0
\(893\) 3.62640 13.5339i 0.121353 0.452895i
\(894\) 0 0
\(895\) 26.0934 10.4392i 0.872207 0.348943i
\(896\) 0 0
\(897\) 11.3604 11.3604i 0.379313 0.379313i
\(898\) 0 0
\(899\) 0.0544519 + 0.0943134i 0.00181607 + 0.00314553i
\(900\) 0 0
\(901\) 5.40287 + 3.11935i 0.179996 + 0.103921i
\(902\) 0 0
\(903\) −4.91468 + 1.57633i −0.163550 + 0.0524570i
\(904\) 0 0
\(905\) 3.72107 25.8378i 0.123693 0.858879i
\(906\) 0 0
\(907\) −6.29276 1.68614i −0.208948 0.0559874i 0.152827 0.988253i \(-0.451162\pi\)
−0.361775 + 0.932266i \(0.617829\pi\)
\(908\) 0 0
\(909\) −0.391801 −0.0129952
\(910\) 0 0
\(911\) 24.2528 0.803531 0.401765 0.915743i \(-0.368397\pi\)
0.401765 + 0.915743i \(0.368397\pi\)
\(912\) 0 0
\(913\) 48.7964 + 13.0749i 1.61492 + 0.432718i
\(914\) 0 0
\(915\) −7.75766 10.3681i −0.256460 0.342757i
\(916\) 0 0
\(917\) 25.2350 27.8138i 0.833333 0.918493i
\(918\) 0 0
\(919\) 31.2542 + 18.0446i 1.03098 + 0.595236i 0.917265 0.398277i \(-0.130392\pi\)
0.113714 + 0.993513i \(0.463725\pi\)
\(920\) 0 0
\(921\) 2.18986 + 3.79295i 0.0721583 + 0.124982i
\(922\) 0 0
\(923\) −6.74244 + 6.74244i −0.221930 + 0.221930i
\(924\) 0 0
\(925\) −0.0311706 + 1.28426i −0.00102488 + 0.0422263i
\(926\) 0 0
\(927\) −23.3813 + 87.2600i −0.767941 + 2.86600i
\(928\) 0 0
\(929\) −21.2041 + 36.7266i −0.695685 + 1.20496i 0.274264 + 0.961654i \(0.411566\pi\)
−0.969949 + 0.243307i \(0.921768\pi\)
\(930\) 0 0
\(931\) 12.4657 8.91344i 0.408547 0.292126i
\(932\) 0 0
\(933\) −38.7686 + 10.3880i −1.26923 + 0.340089i
\(934\) 0 0
\(935\) 6.42578 0.766776i 0.210145 0.0250762i
\(936\) 0 0
\(937\) 4.06709 + 4.06709i 0.132866 + 0.132866i 0.770412 0.637546i \(-0.220050\pi\)
−0.637546 + 0.770412i \(0.720050\pi\)
\(938\) 0 0
\(939\) 67.8621i 2.21460i
\(940\) 0 0
\(941\) −17.4071 + 10.0500i −0.567455 + 0.327621i −0.756132 0.654419i \(-0.772913\pi\)
0.188677 + 0.982039i \(0.439580\pi\)
\(942\) 0 0
\(943\) −10.9371 40.8179i −0.356162 1.32921i
\(944\) 0 0
\(945\) 38.2899 17.5207i 1.24557 0.569949i
\(946\) 0 0
\(947\) 15.2583 + 56.9449i 0.495830 + 1.85046i 0.525333 + 0.850897i \(0.323941\pi\)
−0.0295030 + 0.999565i \(0.509392\pi\)
\(948\) 0 0
\(949\) 10.0354 5.79393i 0.325762 0.188079i
\(950\) 0 0
\(951\) 38.3355i 1.24311i
\(952\) 0 0
\(953\) −31.1044 31.1044i −1.00757 1.00757i −0.999971 0.00759828i \(-0.997581\pi\)
−0.00759828 0.999971i \(-0.502419\pi\)
\(954\) 0 0
\(955\) −21.4359 + 27.2448i −0.693648 + 0.881622i
\(956\) 0 0
\(957\) 27.0292 7.24244i 0.873729 0.234115i
\(958\) 0 0
\(959\) −22.9505 + 44.6245i −0.741111 + 1.44100i
\(960\) 0 0
\(961\) −15.4991 + 26.8453i −0.499972 + 0.865977i
\(962\) 0 0
\(963\) 6.44392 24.0491i 0.207653 0.774970i
\(964\) 0 0
\(965\) −7.92454 + 18.4936i −0.255100 + 0.595331i
\(966\) 0 0
\(967\) 21.5036 21.5036i 0.691510 0.691510i −0.271054 0.962564i \(-0.587372\pi\)
0.962564 + 0.271054i \(0.0873721\pi\)
\(968\) 0 0
\(969\) −2.50822 4.34437i −0.0805756 0.139561i
\(970\) 0 0
\(971\) 45.3034 + 26.1559i 1.45385 + 0.839384i 0.998697 0.0510273i \(-0.0162496\pi\)
0.455158 + 0.890411i \(0.349583\pi\)
\(972\) 0 0
\(973\) 4.61174 21.2997i 0.147845 0.682836i
\(974\) 0 0
\(975\) 16.5917 4.01692i 0.531361 0.128644i
\(976\) 0 0
\(977\) −54.6658 14.6477i −1.74891 0.468620i −0.764520 0.644599i \(-0.777024\pi\)
−0.984394 + 0.175979i \(0.943691\pi\)
\(978\) 0 0
\(979\) 5.25068 0.167813
\(980\) 0 0
\(981\) −98.6358 −3.14920
\(982\) 0 0
\(983\) −14.9514 4.00621i −0.476875 0.127778i 0.0123723 0.999923i \(-0.496062\pi\)
−0.489247 + 0.872145i \(0.662728\pi\)
\(984\) 0 0
\(985\) −30.8777 + 23.1035i −0.983845 + 0.736139i
\(986\) 0 0
\(987\) 10.4154 48.1044i 0.331526 1.53118i
\(988\) 0 0
\(989\) 2.73504 + 1.57907i 0.0869691 + 0.0502116i
\(990\) 0 0
\(991\) −26.8648 46.5311i −0.853388 1.47811i −0.878133 0.478417i \(-0.841211\pi\)
0.0247453 0.999694i \(-0.492123\pi\)
\(992\) 0 0
\(993\) −39.2484 + 39.2484i −1.24551 + 1.24551i
\(994\) 0 0
\(995\) 7.25190 + 18.1266i 0.229901 + 0.574653i
\(996\) 0 0
\(997\) 9.97217 37.2167i 0.315822 1.17866i −0.607400 0.794396i \(-0.707787\pi\)
0.923222 0.384267i \(-0.125546\pi\)
\(998\) 0 0
\(999\) −0.914352 + 1.58370i −0.0289288 + 0.0501062i
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 560.2.ci.c.33.4 16
4.3 odd 2 70.2.k.a.33.1 yes 16
5.2 odd 4 inner 560.2.ci.c.257.4 16
7.3 odd 6 inner 560.2.ci.c.353.4 16
12.11 even 2 630.2.bv.c.523.4 16
20.3 even 4 350.2.o.c.257.2 16
20.7 even 4 70.2.k.a.47.3 yes 16
20.19 odd 2 350.2.o.c.243.4 16
28.3 even 6 70.2.k.a.3.3 16
28.11 odd 6 490.2.l.c.423.4 16
28.19 even 6 490.2.g.c.293.1 16
28.23 odd 6 490.2.g.c.293.4 16
28.27 even 2 490.2.l.c.313.2 16
35.17 even 12 inner 560.2.ci.c.17.4 16
60.47 odd 4 630.2.bv.c.397.1 16
84.59 odd 6 630.2.bv.c.73.1 16
140.3 odd 12 350.2.o.c.157.4 16
140.27 odd 4 490.2.l.c.117.4 16
140.47 odd 12 490.2.g.c.97.4 16
140.59 even 6 350.2.o.c.143.2 16
140.67 even 12 490.2.l.c.227.2 16
140.87 odd 12 70.2.k.a.17.1 yes 16
140.107 even 12 490.2.g.c.97.1 16
420.227 even 12 630.2.bv.c.577.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.k.a.3.3 16 28.3 even 6
70.2.k.a.17.1 yes 16 140.87 odd 12
70.2.k.a.33.1 yes 16 4.3 odd 2
70.2.k.a.47.3 yes 16 20.7 even 4
350.2.o.c.143.2 16 140.59 even 6
350.2.o.c.157.4 16 140.3 odd 12
350.2.o.c.243.4 16 20.19 odd 2
350.2.o.c.257.2 16 20.3 even 4
490.2.g.c.97.1 16 140.107 even 12
490.2.g.c.97.4 16 140.47 odd 12
490.2.g.c.293.1 16 28.19 even 6
490.2.g.c.293.4 16 28.23 odd 6
490.2.l.c.117.4 16 140.27 odd 4
490.2.l.c.227.2 16 140.67 even 12
490.2.l.c.313.2 16 28.27 even 2
490.2.l.c.423.4 16 28.11 odd 6
560.2.ci.c.17.4 16 35.17 even 12 inner
560.2.ci.c.33.4 16 1.1 even 1 trivial
560.2.ci.c.257.4 16 5.2 odd 4 inner
560.2.ci.c.353.4 16 7.3 odd 6 inner
630.2.bv.c.73.1 16 84.59 odd 6
630.2.bv.c.397.1 16 60.47 odd 4
630.2.bv.c.523.4 16 12.11 even 2
630.2.bv.c.577.4 16 420.227 even 12