Properties

Label 36.6.e.a.25.1
Level $36$
Weight $6$
Character 36.25
Analytic conductor $5.774$
Analytic rank $0$
Dimension $10$
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] = [36,6,Mod(13,36)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(36, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("36.13");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 36.e (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: \(5.77381751327\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.1
Root \(-2.13639i\) of defining polynomial
Character \(\chi\) \(=\) 36.25
Dual form 36.6.e.a.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-12.2647 + 9.62174i) q^{3} +(-14.0718 - 24.3731i) q^{5} +(75.7039 - 131.123i) q^{7} +(57.8441 - 236.015i) q^{9} +O(q^{10})\) \(q+(-12.2647 + 9.62174i) q^{3} +(-14.0718 - 24.3731i) q^{5} +(75.7039 - 131.123i) q^{7} +(57.8441 - 236.015i) q^{9} +(138.873 - 240.536i) q^{11} +(-291.929 - 505.636i) q^{13} +(407.098 + 163.533i) q^{15} -1612.01 q^{17} +1368.76 q^{19} +(333.149 + 2336.58i) q^{21} +(-428.014 - 741.342i) q^{23} +(1166.47 - 2020.38i) q^{25} +(1561.44 + 3451.21i) q^{27} +(-4267.49 + 7391.50i) q^{29} +(-1469.19 - 2544.71i) q^{31} +(611.138 + 4286.30i) q^{33} -4261.17 q^{35} +4036.80 q^{37} +(8445.52 + 3392.59i) q^{39} +(-9449.81 - 16367.5i) q^{41} +(10158.6 - 17595.1i) q^{43} +(-6566.39 + 1911.32i) q^{45} +(147.890 - 256.152i) q^{47} +(-3058.67 - 5297.78i) q^{49} +(19770.7 - 15510.3i) q^{51} +3039.13 q^{53} -7816.81 q^{55} +(-16787.4 + 13169.9i) q^{57} +(8618.31 + 14927.4i) q^{59} +(-12826.2 + 22215.7i) q^{61} +(-26568.0 - 25452.0i) q^{63} +(-8215.95 + 14230.4i) q^{65} +(13140.1 + 22759.4i) q^{67} +(12382.5 + 4974.07i) q^{69} +76665.7 q^{71} +1496.33 q^{73} +(5133.25 + 36002.8i) q^{75} +(-21026.5 - 36419.0i) q^{77} +(-49637.1 + 85974.0i) q^{79} +(-52357.1 - 27304.1i) q^{81} +(-25025.7 + 43345.7i) q^{83} +(22683.8 + 39289.6i) q^{85} +(-18779.8 - 131715. i) q^{87} +136635. q^{89} -88400.8 q^{91} +(42503.6 + 17073.9i) q^{93} +(-19261.0 - 33361.0i) q^{95} +(33325.0 - 57720.5i) q^{97} +(-48737.1 - 46689.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 12 q^{3} - 21 q^{5} + 29 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 12 q^{3} - 21 q^{5} + 29 q^{7} + 12 q^{9} + 177 q^{11} - 181 q^{13} + 117 q^{15} + 2280 q^{17} - 832 q^{19} - 207 q^{21} + 399 q^{23} - 4778 q^{25} - 7128 q^{27} - 6033 q^{29} + 2759 q^{31} + 9603 q^{33} + 37146 q^{35} - 15172 q^{37} + 5529 q^{39} - 18435 q^{41} + 1469 q^{43} - 64089 q^{45} - 25155 q^{47} - 4056 q^{49} + 90612 q^{51} + 116844 q^{53} + 14778 q^{55} + 26934 q^{57} - 90537 q^{59} + 1403 q^{61} - 198255 q^{63} - 148407 q^{65} + 13907 q^{67} + 214425 q^{69} + 229368 q^{71} + 15200 q^{73} + 44640 q^{75} - 211983 q^{77} + 29993 q^{79} - 404172 q^{81} - 228951 q^{83} - 49662 q^{85} + 397323 q^{87} + 598332 q^{89} + 124930 q^{91} + 250041 q^{93} - 394764 q^{95} + 40541 q^{97} - 697239 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −12.2647 + 9.62174i −0.786779 + 0.617235i
\(4\) 0 0
\(5\) −14.0718 24.3731i −0.251724 0.435999i 0.712276 0.701899i \(-0.247664\pi\)
−0.964001 + 0.265900i \(0.914331\pi\)
\(6\) 0 0
\(7\) 75.7039 131.123i 0.583947 1.01143i −0.411059 0.911609i \(-0.634841\pi\)
0.995006 0.0998170i \(-0.0318257\pi\)
\(8\) 0 0
\(9\) 57.8441 236.015i 0.238042 0.971255i
\(10\) 0 0
\(11\) 138.873 240.536i 0.346049 0.599374i −0.639495 0.768795i \(-0.720856\pi\)
0.985544 + 0.169421i \(0.0541898\pi\)
\(12\) 0 0
\(13\) −291.929 505.636i −0.479092 0.829812i 0.520620 0.853788i \(-0.325701\pi\)
−0.999713 + 0.0239762i \(0.992367\pi\)
\(14\) 0 0
\(15\) 407.098 + 163.533i 0.467165 + 0.187662i
\(16\) 0 0
\(17\) −1612.01 −1.35283 −0.676417 0.736519i \(-0.736468\pi\)
−0.676417 + 0.736519i \(0.736468\pi\)
\(18\) 0 0
\(19\) 1368.76 0.869851 0.434925 0.900467i \(-0.356775\pi\)
0.434925 + 0.900467i \(0.356775\pi\)
\(20\) 0 0
\(21\) 333.149 + 2336.58i 0.164850 + 1.15620i
\(22\) 0 0
\(23\) −428.014 741.342i −0.168709 0.292213i 0.769257 0.638939i \(-0.220627\pi\)
−0.937966 + 0.346727i \(0.887293\pi\)
\(24\) 0 0
\(25\) 1166.47 2020.38i 0.373270 0.646522i
\(26\) 0 0
\(27\) 1561.44 + 3451.21i 0.412207 + 0.911090i
\(28\) 0 0
\(29\) −4267.49 + 7391.50i −0.942274 + 1.63207i −0.181154 + 0.983455i \(0.557983\pi\)
−0.761120 + 0.648611i \(0.775350\pi\)
\(30\) 0 0
\(31\) −1469.19 2544.71i −0.274583 0.475591i 0.695447 0.718577i \(-0.255206\pi\)
−0.970030 + 0.242986i \(0.921873\pi\)
\(32\) 0 0
\(33\) 611.138 + 4286.30i 0.0976910 + 0.685169i
\(34\) 0 0
\(35\) −4261.17 −0.587975
\(36\) 0 0
\(37\) 4036.80 0.484767 0.242383 0.970181i \(-0.422071\pi\)
0.242383 + 0.970181i \(0.422071\pi\)
\(38\) 0 0
\(39\) 8445.52 + 3392.59i 0.889129 + 0.357166i
\(40\) 0 0
\(41\) −9449.81 16367.5i −0.877937 1.52063i −0.853601 0.520928i \(-0.825586\pi\)
−0.0243361 0.999704i \(-0.507747\pi\)
\(42\) 0 0
\(43\) 10158.6 17595.1i 0.837840 1.45118i −0.0538576 0.998549i \(-0.517152\pi\)
0.891697 0.452632i \(-0.149515\pi\)
\(44\) 0 0
\(45\) −6566.39 + 1911.32i −0.483387 + 0.140703i
\(46\) 0 0
\(47\) 147.890 256.152i 0.00976546 0.0169143i −0.861101 0.508433i \(-0.830225\pi\)
0.870867 + 0.491519i \(0.163558\pi\)
\(48\) 0 0
\(49\) −3058.67 5297.78i −0.181988 0.315213i
\(50\) 0 0
\(51\) 19770.7 15510.3i 1.06438 0.835016i
\(52\) 0 0
\(53\) 3039.13 0.148614 0.0743069 0.997235i \(-0.476326\pi\)
0.0743069 + 0.997235i \(0.476326\pi\)
\(54\) 0 0
\(55\) −7816.81 −0.348436
\(56\) 0 0
\(57\) −16787.4 + 13169.9i −0.684380 + 0.536902i
\(58\) 0 0
\(59\) 8618.31 + 14927.4i 0.322324 + 0.558281i 0.980967 0.194174i \(-0.0622027\pi\)
−0.658643 + 0.752455i \(0.728869\pi\)
\(60\) 0 0
\(61\) −12826.2 + 22215.7i −0.441342 + 0.764426i −0.997789 0.0664565i \(-0.978831\pi\)
0.556448 + 0.830883i \(0.312164\pi\)
\(62\) 0 0
\(63\) −26568.0 25452.0i −0.843349 0.807923i
\(64\) 0 0
\(65\) −8215.95 + 14230.4i −0.241198 + 0.417768i
\(66\) 0 0
\(67\) 13140.1 + 22759.4i 0.357613 + 0.619403i 0.987561 0.157233i \(-0.0502575\pi\)
−0.629949 + 0.776637i \(0.716924\pi\)
\(68\) 0 0
\(69\) 12382.5 + 4974.07i 0.313101 + 0.125774i
\(70\) 0 0
\(71\) 76665.7 1.80491 0.902454 0.430786i \(-0.141764\pi\)
0.902454 + 0.430786i \(0.141764\pi\)
\(72\) 0 0
\(73\) 1496.33 0.0328640 0.0164320 0.999865i \(-0.494769\pi\)
0.0164320 + 0.999865i \(0.494769\pi\)
\(74\) 0 0
\(75\) 5133.25 + 36002.8i 0.105375 + 0.739065i
\(76\) 0 0
\(77\) −21026.5 36419.0i −0.404148 0.700006i
\(78\) 0 0
\(79\) −49637.1 + 85974.0i −0.894826 + 1.54988i −0.0608070 + 0.998150i \(0.519367\pi\)
−0.834019 + 0.551735i \(0.813966\pi\)
\(80\) 0 0
\(81\) −52357.1 27304.1i −0.886672 0.462398i
\(82\) 0 0
\(83\) −25025.7 + 43345.7i −0.398740 + 0.690639i −0.993571 0.113213i \(-0.963886\pi\)
0.594830 + 0.803851i \(0.297219\pi\)
\(84\) 0 0
\(85\) 22683.8 + 39289.6i 0.340541 + 0.589834i
\(86\) 0 0
\(87\) −18779.8 131715.i −0.266008 1.86568i
\(88\) 0 0
\(89\) 136635. 1.82847 0.914235 0.405185i \(-0.132793\pi\)
0.914235 + 0.405185i \(0.132793\pi\)
\(90\) 0 0
\(91\) −88400.8 −1.11906
\(92\) 0 0
\(93\) 42503.6 + 17073.9i 0.509588 + 0.204703i
\(94\) 0 0
\(95\) −19261.0 33361.0i −0.218963 0.379254i
\(96\) 0 0
\(97\) 33325.0 57720.5i 0.359617 0.622875i −0.628280 0.777987i \(-0.716241\pi\)
0.987897 + 0.155113i \(0.0495740\pi\)
\(98\) 0 0
\(99\) −48737.1 46689.8i −0.499771 0.478778i
\(100\) 0 0
\(101\) 12338.7 21371.2i 0.120355 0.208462i −0.799552 0.600596i \(-0.794930\pi\)
0.919908 + 0.392135i \(0.128263\pi\)
\(102\) 0 0
\(103\) −57883.5 100257.i −0.537603 0.931155i −0.999032 0.0439785i \(-0.985997\pi\)
0.461430 0.887177i \(-0.347337\pi\)
\(104\) 0 0
\(105\) 52261.8 40999.9i 0.462606 0.362919i
\(106\) 0 0
\(107\) 84364.3 0.712360 0.356180 0.934417i \(-0.384079\pi\)
0.356180 + 0.934417i \(0.384079\pi\)
\(108\) 0 0
\(109\) 198400. 1.59947 0.799735 0.600354i \(-0.204973\pi\)
0.799735 + 0.600354i \(0.204973\pi\)
\(110\) 0 0
\(111\) −49510.0 + 38841.1i −0.381404 + 0.299215i
\(112\) 0 0
\(113\) −114453. 198238.i −0.843199 1.46046i −0.887176 0.461430i \(-0.847336\pi\)
0.0439777 0.999033i \(-0.485997\pi\)
\(114\) 0 0
\(115\) −12045.9 + 20864.1i −0.0849364 + 0.147114i
\(116\) 0 0
\(117\) −136224. + 39651.6i −0.920003 + 0.267791i
\(118\) 0 0
\(119\) −122035. + 211371.i −0.789983 + 1.36829i
\(120\) 0 0
\(121\) 41953.8 + 72666.2i 0.260500 + 0.451200i
\(122\) 0 0
\(123\) 273383. + 109819.i 1.62933 + 0.654507i
\(124\) 0 0
\(125\) −153606. −0.879293
\(126\) 0 0
\(127\) −246629. −1.35686 −0.678430 0.734665i \(-0.737339\pi\)
−0.678430 + 0.734665i \(0.737339\pi\)
\(128\) 0 0
\(129\) 44704.6 + 313542.i 0.236525 + 1.65890i
\(130\) 0 0
\(131\) 84612.6 + 146553.i 0.430781 + 0.746135i 0.996941 0.0781606i \(-0.0249047\pi\)
−0.566159 + 0.824296i \(0.691571\pi\)
\(132\) 0 0
\(133\) 103621. 179477.i 0.507947 0.879789i
\(134\) 0 0
\(135\) 62144.3 86621.8i 0.293472 0.409065i
\(136\) 0 0
\(137\) −49985.3 + 86577.0i −0.227531 + 0.394095i −0.957076 0.289838i \(-0.906399\pi\)
0.729545 + 0.683933i \(0.239732\pi\)
\(138\) 0 0
\(139\) 18699.4 + 32388.2i 0.0820899 + 0.142184i 0.904147 0.427221i \(-0.140507\pi\)
−0.822058 + 0.569404i \(0.807174\pi\)
\(140\) 0 0
\(141\) 650.815 + 4564.58i 0.00275683 + 0.0193354i
\(142\) 0 0
\(143\) −162165. −0.663158
\(144\) 0 0
\(145\) 240205. 0.948773
\(146\) 0 0
\(147\) 88487.5 + 35545.7i 0.337745 + 0.135673i
\(148\) 0 0
\(149\) −127267. 220433.i −0.469623 0.813411i 0.529774 0.848139i \(-0.322277\pi\)
−0.999397 + 0.0347281i \(0.988943\pi\)
\(150\) 0 0
\(151\) 118363. 205010.i 0.422448 0.731701i −0.573731 0.819044i \(-0.694504\pi\)
0.996178 + 0.0873434i \(0.0278377\pi\)
\(152\) 0 0
\(153\) −93245.0 + 380457.i −0.322031 + 1.31395i
\(154\) 0 0
\(155\) −41348.3 + 71617.4i −0.138238 + 0.239436i
\(156\) 0 0
\(157\) −127406. 220673.i −0.412515 0.714497i 0.582649 0.812724i \(-0.302016\pi\)
−0.995164 + 0.0982266i \(0.968683\pi\)
\(158\) 0 0
\(159\) −37273.9 + 29241.7i −0.116926 + 0.0917297i
\(160\) 0 0
\(161\) −129609. −0.394069
\(162\) 0 0
\(163\) 215050. 0.633973 0.316987 0.948430i \(-0.397329\pi\)
0.316987 + 0.948430i \(0.397329\pi\)
\(164\) 0 0
\(165\) 95870.5 75211.3i 0.274142 0.215067i
\(166\) 0 0
\(167\) −96168.5 166569.i −0.266834 0.462171i 0.701208 0.712956i \(-0.252644\pi\)
−0.968043 + 0.250786i \(0.919311\pi\)
\(168\) 0 0
\(169\) 15201.2 26329.2i 0.0409411 0.0709121i
\(170\) 0 0
\(171\) 79174.9 323049.i 0.207061 0.844847i
\(172\) 0 0
\(173\) 4150.57 7189.00i 0.0105437 0.0182622i −0.860705 0.509103i \(-0.829977\pi\)
0.871249 + 0.490841i \(0.163310\pi\)
\(174\) 0 0
\(175\) −176612. 305902.i −0.435939 0.755069i
\(176\) 0 0
\(177\) −249328. 100156.i −0.598188 0.240294i
\(178\) 0 0
\(179\) 574496. 1.34015 0.670077 0.742292i \(-0.266261\pi\)
0.670077 + 0.742292i \(0.266261\pi\)
\(180\) 0 0
\(181\) −224707. −0.509823 −0.254912 0.966964i \(-0.582046\pi\)
−0.254912 + 0.966964i \(0.582046\pi\)
\(182\) 0 0
\(183\) −56444.2 395879.i −0.124592 0.873846i
\(184\) 0 0
\(185\) −56805.1 98389.3i −0.122028 0.211358i
\(186\) 0 0
\(187\) −223865. + 387745.i −0.468147 + 0.810854i
\(188\) 0 0
\(189\) 570740. + 56529.5i 1.16221 + 0.115112i
\(190\) 0 0
\(191\) 239041. 414031.i 0.474121 0.821201i −0.525440 0.850830i \(-0.676099\pi\)
0.999561 + 0.0296294i \(0.00943271\pi\)
\(192\) 0 0
\(193\) 263025. + 455572.i 0.508281 + 0.880368i 0.999954 + 0.00958824i \(0.00305208\pi\)
−0.491673 + 0.870780i \(0.663615\pi\)
\(194\) 0 0
\(195\) −36155.8 253583.i −0.0680912 0.477567i
\(196\) 0 0
\(197\) −222278. −0.408067 −0.204034 0.978964i \(-0.565405\pi\)
−0.204034 + 0.978964i \(0.565405\pi\)
\(198\) 0 0
\(199\) −109696. −0.196363 −0.0981813 0.995169i \(-0.531303\pi\)
−0.0981813 + 0.995169i \(0.531303\pi\)
\(200\) 0 0
\(201\) −380144. 152705.i −0.663679 0.266602i
\(202\) 0 0
\(203\) 646131. + 1.11913e6i 1.10048 + 1.90608i
\(204\) 0 0
\(205\) −265952. + 460642.i −0.441996 + 0.765560i
\(206\) 0 0
\(207\) −199726. + 58135.5i −0.323973 + 0.0943008i
\(208\) 0 0
\(209\) 190085. 329237.i 0.301011 0.521366i
\(210\) 0 0
\(211\) 309436. + 535959.i 0.478482 + 0.828754i 0.999696 0.0246717i \(-0.00785404\pi\)
−0.521214 + 0.853426i \(0.674521\pi\)
\(212\) 0 0
\(213\) −940279. + 737657.i −1.42006 + 1.11405i
\(214\) 0 0
\(215\) −571797. −0.843618
\(216\) 0 0
\(217\) −444893. −0.641367
\(218\) 0 0
\(219\) −18352.0 + 14397.3i −0.0258567 + 0.0202848i
\(220\) 0 0
\(221\) 470592. + 815089.i 0.648132 + 1.12260i
\(222\) 0 0
\(223\) −231653. + 401234.i −0.311943 + 0.540301i −0.978783 0.204900i \(-0.934313\pi\)
0.666840 + 0.745201i \(0.267646\pi\)
\(224\) 0 0
\(225\) −409367. 392171.i −0.539084 0.516439i
\(226\) 0 0
\(227\) 573326. 993029.i 0.738477 1.27908i −0.214704 0.976679i \(-0.568879\pi\)
0.953181 0.302400i \(-0.0977878\pi\)
\(228\) 0 0
\(229\) 175527. + 304022.i 0.221185 + 0.383104i 0.955168 0.296064i \(-0.0956741\pi\)
−0.733983 + 0.679168i \(0.762341\pi\)
\(230\) 0 0
\(231\) 608298. + 244355.i 0.750043 + 0.301295i
\(232\) 0 0
\(233\) 814275. 0.982610 0.491305 0.870988i \(-0.336520\pi\)
0.491305 + 0.870988i \(0.336520\pi\)
\(234\) 0 0
\(235\) −8324.30 −0.00983281
\(236\) 0 0
\(237\) −218437. 1.53204e6i −0.252613 1.77173i
\(238\) 0 0
\(239\) 357452. + 619124.i 0.404783 + 0.701105i 0.994296 0.106654i \(-0.0340137\pi\)
−0.589513 + 0.807759i \(0.700680\pi\)
\(240\) 0 0
\(241\) −22648.5 + 39228.3i −0.0251186 + 0.0435068i −0.878311 0.478089i \(-0.841330\pi\)
0.853193 + 0.521596i \(0.174663\pi\)
\(242\) 0 0
\(243\) 904856. 168891.i 0.983023 0.183480i
\(244\) 0 0
\(245\) −86082.2 + 149099.i −0.0916216 + 0.158693i
\(246\) 0 0
\(247\) −399582. 692097.i −0.416739 0.721813i
\(248\) 0 0
\(249\) −110130. 772411.i −0.112566 0.789496i
\(250\) 0 0
\(251\) −1.35110e6 −1.35364 −0.676822 0.736147i \(-0.736643\pi\)
−0.676822 + 0.736147i \(0.736643\pi\)
\(252\) 0 0
\(253\) −237759. −0.233526
\(254\) 0 0
\(255\) −656244. 263615.i −0.631997 0.253875i
\(256\) 0 0
\(257\) −600097. 1.03940e6i −0.566747 0.981634i −0.996885 0.0788708i \(-0.974869\pi\)
0.430138 0.902763i \(-0.358465\pi\)
\(258\) 0 0
\(259\) 305602. 529318.i 0.283078 0.490306i
\(260\) 0 0
\(261\) 1.49766e6 + 1.43475e6i 1.36085 + 1.30369i
\(262\) 0 0
\(263\) 656802. 1.13761e6i 0.585525 1.01416i −0.409285 0.912407i \(-0.634222\pi\)
0.994810 0.101752i \(-0.0324449\pi\)
\(264\) 0 0
\(265\) −42766.1 74073.0i −0.0374097 0.0647956i
\(266\) 0 0
\(267\) −1.67579e6 + 1.31467e6i −1.43860 + 1.12860i
\(268\) 0 0
\(269\) 321363. 0.270779 0.135389 0.990792i \(-0.456771\pi\)
0.135389 + 0.990792i \(0.456771\pi\)
\(270\) 0 0
\(271\) 384928. 0.318388 0.159194 0.987247i \(-0.449110\pi\)
0.159194 + 0.987247i \(0.449110\pi\)
\(272\) 0 0
\(273\) 1.08421e6 850570.i 0.880451 0.690722i
\(274\) 0 0
\(275\) −323983. 561155.i −0.258339 0.447457i
\(276\) 0 0
\(277\) 847964. 1.46872e6i 0.664015 1.15011i −0.315536 0.948913i \(-0.602184\pi\)
0.979551 0.201194i \(-0.0644822\pi\)
\(278\) 0 0
\(279\) −685573. + 199554.i −0.527283 + 0.153479i
\(280\) 0 0
\(281\) −530669. + 919146.i −0.400920 + 0.694415i −0.993837 0.110849i \(-0.964643\pi\)
0.592917 + 0.805264i \(0.297976\pi\)
\(282\) 0 0
\(283\) 192313. + 333096.i 0.142739 + 0.247231i 0.928527 0.371265i \(-0.121076\pi\)
−0.785788 + 0.618496i \(0.787742\pi\)
\(284\) 0 0
\(285\) 557221. + 223838.i 0.406364 + 0.163238i
\(286\) 0 0
\(287\) −2.86155e6 −2.05067
\(288\) 0 0
\(289\) 1.17871e6 0.830158
\(290\) 0 0
\(291\) 146653. + 1.02857e6i 0.101521 + 0.712033i
\(292\) 0 0
\(293\) 667643. + 1.15639e6i 0.454334 + 0.786929i 0.998650 0.0519513i \(-0.0165441\pi\)
−0.544316 + 0.838880i \(0.683211\pi\)
\(294\) 0 0
\(295\) 242551. 420110.i 0.162273 0.281066i
\(296\) 0 0
\(297\) 1.04698e6 + 103699.i 0.688728 + 0.0682158i
\(298\) 0 0
\(299\) −249900. + 432839.i −0.161655 + 0.279994i
\(300\) 0 0
\(301\) −1.53809e6 2.66404e6i −0.978508 1.69483i
\(302\) 0 0
\(303\) 54298.7 + 380831.i 0.0339768 + 0.238301i
\(304\) 0 0
\(305\) 721954. 0.444386
\(306\) 0 0
\(307\) 636269. 0.385296 0.192648 0.981268i \(-0.438292\pi\)
0.192648 + 0.981268i \(0.438292\pi\)
\(308\) 0 0
\(309\) 1.67457e6 + 672680.i 0.997716 + 0.400786i
\(310\) 0 0
\(311\) 269890. + 467464.i 0.158229 + 0.274061i 0.934230 0.356671i \(-0.116088\pi\)
−0.776001 + 0.630732i \(0.782755\pi\)
\(312\) 0 0
\(313\) −976605. + 1.69153e6i −0.563454 + 0.975931i 0.433738 + 0.901039i \(0.357194\pi\)
−0.997192 + 0.0748915i \(0.976139\pi\)
\(314\) 0 0
\(315\) −246483. + 1.00570e6i −0.139962 + 0.571073i
\(316\) 0 0
\(317\) −781983. + 1.35443e6i −0.437068 + 0.757024i −0.997462 0.0712021i \(-0.977316\pi\)
0.560394 + 0.828226i \(0.310650\pi\)
\(318\) 0 0
\(319\) 1.18528e6 + 2.05297e6i 0.652146 + 1.12955i
\(320\) 0 0
\(321\) −1.03470e6 + 811732.i −0.560469 + 0.439693i
\(322\) 0 0
\(323\) −2.20646e6 −1.17676
\(324\) 0 0
\(325\) −1.36210e6 −0.715323
\(326\) 0 0
\(327\) −2.43331e6 + 1.90896e6i −1.25843 + 0.987249i
\(328\) 0 0
\(329\) −22391.6 38783.5i −0.0114050 0.0197541i
\(330\) 0 0
\(331\) 1.28000e6 2.21702e6i 0.642154 1.11224i −0.342796 0.939410i \(-0.611374\pi\)
0.984951 0.172834i \(-0.0552925\pi\)
\(332\) 0 0
\(333\) 233505. 952745.i 0.115395 0.470832i
\(334\) 0 0
\(335\) 369811. 640532.i 0.180040 0.311838i
\(336\) 0 0
\(337\) 299646. + 519002.i 0.143725 + 0.248940i 0.928897 0.370339i \(-0.120758\pi\)
−0.785171 + 0.619279i \(0.787425\pi\)
\(338\) 0 0
\(339\) 3.31112e6 + 1.33009e6i 1.56486 + 0.628609i
\(340\) 0 0
\(341\) −816125. −0.380076
\(342\) 0 0
\(343\) 1.61850e6 0.742808
\(344\) 0 0
\(345\) −53010.1 371793.i −0.0239779 0.168172i
\(346\) 0 0
\(347\) −1.34386e6 2.32764e6i −0.599144 1.03775i −0.992948 0.118553i \(-0.962174\pi\)
0.393804 0.919195i \(-0.371159\pi\)
\(348\) 0 0
\(349\) −335807. + 581635.i −0.147580 + 0.255615i −0.930332 0.366717i \(-0.880482\pi\)
0.782753 + 0.622333i \(0.213815\pi\)
\(350\) 0 0
\(351\) 1.28923e6 1.79703e6i 0.558549 0.778550i
\(352\) 0 0
\(353\) 764881. 1.32481e6i 0.326706 0.565871i −0.655150 0.755499i \(-0.727395\pi\)
0.981856 + 0.189627i \(0.0607280\pi\)
\(354\) 0 0
\(355\) −1.07883e6 1.86858e6i −0.454339 0.786939i
\(356\) 0 0
\(357\) −537038. 3.76659e6i −0.223015 1.56415i
\(358\) 0 0
\(359\) 3.27210e6 1.33996 0.669978 0.742381i \(-0.266303\pi\)
0.669978 + 0.742381i \(0.266303\pi\)
\(360\) 0 0
\(361\) −602583. −0.243360
\(362\) 0 0
\(363\) −1.21372e6 487557.i −0.483452 0.194204i
\(364\) 0 0
\(365\) −21056.1 36470.2i −0.00827267 0.0143287i
\(366\) 0 0
\(367\) −313571. + 543121.i −0.121526 + 0.210490i −0.920370 0.391049i \(-0.872112\pi\)
0.798843 + 0.601539i \(0.205446\pi\)
\(368\) 0 0
\(369\) −4.40960e6 + 1.28353e6i −1.68591 + 0.490727i
\(370\) 0 0
\(371\) 230074. 398500.i 0.0867826 0.150312i
\(372\) 0 0
\(373\) −66186.8 114639.i −0.0246320 0.0426638i 0.853447 0.521180i \(-0.174508\pi\)
−0.878079 + 0.478516i \(0.841175\pi\)
\(374\) 0 0
\(375\) 1.88393e6 1.47796e6i 0.691809 0.542730i
\(376\) 0 0
\(377\) 4.98322e6 1.80574
\(378\) 0 0
\(379\) −163225. −0.0583700 −0.0291850 0.999574i \(-0.509291\pi\)
−0.0291850 + 0.999574i \(0.509291\pi\)
\(380\) 0 0
\(381\) 3.02482e6 2.37300e6i 1.06755 0.837501i
\(382\) 0 0
\(383\) 398301. + 689877.i 0.138744 + 0.240312i 0.927021 0.375008i \(-0.122360\pi\)
−0.788277 + 0.615320i \(0.789027\pi\)
\(384\) 0 0
\(385\) −591763. + 1.02496e6i −0.203468 + 0.352417i
\(386\) 0 0
\(387\) −3.56510e6 3.41535e6i −1.21003 1.15920i
\(388\) 0 0
\(389\) −2.04745e6 + 3.54629e6i −0.686024 + 1.18823i 0.287089 + 0.957904i \(0.407312\pi\)
−0.973114 + 0.230325i \(0.926021\pi\)
\(390\) 0 0
\(391\) 689961. + 1.19505e6i 0.228235 + 0.395315i
\(392\) 0 0
\(393\) −2.44784e6 983307.i −0.799470 0.321150i
\(394\) 0 0
\(395\) 2.79394e6 0.900998
\(396\) 0 0
\(397\) −5.58867e6 −1.77964 −0.889820 0.456312i \(-0.849170\pi\)
−0.889820 + 0.456312i \(0.849170\pi\)
\(398\) 0 0
\(399\) 456002. + 3.19823e6i 0.143395 + 1.00572i
\(400\) 0 0
\(401\) −1.11676e6 1.93429e6i −0.346817 0.600705i 0.638865 0.769319i \(-0.279404\pi\)
−0.985682 + 0.168614i \(0.946071\pi\)
\(402\) 0 0
\(403\) −857798. + 1.48575e6i −0.263101 + 0.455704i
\(404\) 0 0
\(405\) 71273.1 + 1.66032e6i 0.0215918 + 0.502985i
\(406\) 0 0
\(407\) 560604. 970995.i 0.167753 0.290557i
\(408\) 0 0
\(409\) 2.30256e6 + 3.98815e6i 0.680617 + 1.17886i 0.974793 + 0.223111i \(0.0716214\pi\)
−0.294176 + 0.955751i \(0.595045\pi\)
\(410\) 0 0
\(411\) −219969. 1.54278e6i −0.0642329 0.450506i
\(412\) 0 0
\(413\) 2.60976e6 0.752880
\(414\) 0 0
\(415\) 1.40863e6 0.401491
\(416\) 0 0
\(417\) −540973. 217310.i −0.152347 0.0611985i
\(418\) 0 0
\(419\) −571064. 989112.i −0.158909 0.275239i 0.775566 0.631266i \(-0.217464\pi\)
−0.934476 + 0.356027i \(0.884131\pi\)
\(420\) 0 0
\(421\) −962383. + 1.66690e6i −0.264632 + 0.458356i −0.967467 0.252996i \(-0.918584\pi\)
0.702835 + 0.711353i \(0.251917\pi\)
\(422\) 0 0
\(423\) −51901.2 49721.0i −0.0141035 0.0135111i
\(424\) 0 0
\(425\) −1.88035e6 + 3.25687e6i −0.504972 + 0.874637i
\(426\) 0 0
\(427\) 1.94199e6 + 3.36363e6i 0.515440 + 0.892769i
\(428\) 0 0
\(429\) 1.98890e6 1.56031e6i 0.521758 0.409324i
\(430\) 0 0
\(431\) 2.21303e6 0.573843 0.286922 0.957954i \(-0.407368\pi\)
0.286922 + 0.957954i \(0.407368\pi\)
\(432\) 0 0
\(433\) 3.00235e6 0.769558 0.384779 0.923009i \(-0.374278\pi\)
0.384779 + 0.923009i \(0.374278\pi\)
\(434\) 0 0
\(435\) −2.94604e6 + 2.31119e6i −0.746474 + 0.585616i
\(436\) 0 0
\(437\) −585851. 1.01472e6i −0.146752 0.254181i
\(438\) 0 0
\(439\) −960857. + 1.66425e6i −0.237956 + 0.412153i −0.960128 0.279562i \(-0.909811\pi\)
0.722171 + 0.691714i \(0.243144\pi\)
\(440\) 0 0
\(441\) −1.42728e6 + 415447.i −0.349472 + 0.101723i
\(442\) 0 0
\(443\) 924258. 1.60086e6i 0.223761 0.387565i −0.732186 0.681105i \(-0.761500\pi\)
0.955947 + 0.293540i \(0.0948332\pi\)
\(444\) 0 0
\(445\) −1.92271e6 3.33022e6i −0.460270 0.797211i
\(446\) 0 0
\(447\) 3.68183e6 + 1.47900e6i 0.871555 + 0.350107i
\(448\) 0 0
\(449\) 3.45640e6 0.809110 0.404555 0.914514i \(-0.367426\pi\)
0.404555 + 0.914514i \(0.367426\pi\)
\(450\) 0 0
\(451\) −5.24931e6 −1.21524
\(452\) 0 0
\(453\) 520877. + 3.65324e6i 0.119259 + 0.836436i
\(454\) 0 0
\(455\) 1.24396e6 + 2.15460e6i 0.281694 + 0.487908i
\(456\) 0 0
\(457\) −1.79319e6 + 3.10589e6i −0.401638 + 0.695658i −0.993924 0.110070i \(-0.964892\pi\)
0.592286 + 0.805728i \(0.298226\pi\)
\(458\) 0 0
\(459\) −2.51704e6 5.56336e6i −0.557647 1.23255i
\(460\) 0 0
\(461\) −4.21775e6 + 7.30536e6i −0.924333 + 1.60099i −0.131703 + 0.991289i \(0.542045\pi\)
−0.792630 + 0.609703i \(0.791289\pi\)
\(462\) 0 0
\(463\) −2.47237e6 4.28227e6i −0.535995 0.928370i −0.999114 0.0420745i \(-0.986603\pi\)
0.463120 0.886296i \(-0.346730\pi\)
\(464\) 0 0
\(465\) −181961. 1.27621e6i −0.0390252 0.273709i
\(466\) 0 0
\(467\) −4.12589e6 −0.875438 −0.437719 0.899112i \(-0.644213\pi\)
−0.437719 + 0.899112i \(0.644213\pi\)
\(468\) 0 0
\(469\) 3.97904e6 0.835307
\(470\) 0 0
\(471\) 3.68585e6 + 1.48062e6i 0.765571 + 0.307532i
\(472\) 0 0
\(473\) −2.82151e6 4.88700e6i −0.579867 1.00436i
\(474\) 0 0
\(475\) 1.59662e6 2.76543e6i 0.324689 0.562378i
\(476\) 0 0
\(477\) 175796. 717280.i 0.0353763 0.144342i
\(478\) 0 0
\(479\) 561301. 972203.i 0.111778 0.193606i −0.804709 0.593669i \(-0.797679\pi\)
0.916487 + 0.400064i \(0.131012\pi\)
\(480\) 0 0
\(481\) −1.17846e6 2.04115e6i −0.232248 0.402265i
\(482\) 0 0
\(483\) 1.58962e6 1.24707e6i 0.310045 0.243233i
\(484\) 0 0
\(485\) −1.87577e6 −0.362097
\(486\) 0 0
\(487\) 8.11380e6 1.55025 0.775126 0.631807i \(-0.217687\pi\)
0.775126 + 0.631807i \(0.217687\pi\)
\(488\) 0 0
\(489\) −2.63752e6 + 2.06916e6i −0.498797 + 0.391310i
\(490\) 0 0
\(491\) 1.66481e6 + 2.88353e6i 0.311645 + 0.539786i 0.978719 0.205207i \(-0.0657866\pi\)
−0.667073 + 0.744992i \(0.732453\pi\)
\(492\) 0 0
\(493\) 6.87921e6 1.19151e7i 1.27474 2.20791i
\(494\) 0 0
\(495\) −452156. + 1.84488e6i −0.0829422 + 0.338420i
\(496\) 0 0
\(497\) 5.80389e6 1.00526e7i 1.05397 1.82553i
\(498\) 0 0
\(499\) −940630. 1.62922e6i −0.169109 0.292906i 0.768998 0.639252i \(-0.220756\pi\)
−0.938107 + 0.346346i \(0.887422\pi\)
\(500\) 0 0
\(501\) 2.78216e6 + 1.11760e6i 0.495207 + 0.198926i
\(502\) 0 0
\(503\) −7.96749e6 −1.40411 −0.702056 0.712122i \(-0.747734\pi\)
−0.702056 + 0.712122i \(0.747734\pi\)
\(504\) 0 0
\(505\) −694511. −0.121186
\(506\) 0 0
\(507\) 66895.5 + 469180.i 0.0115578 + 0.0810625i
\(508\) 0 0
\(509\) −5.40561e6 9.36279e6i −0.924805 1.60181i −0.791874 0.610684i \(-0.790894\pi\)
−0.132931 0.991125i \(-0.542439\pi\)
\(510\) 0 0
\(511\) 113278. 196204.i 0.0191908 0.0332395i
\(512\) 0 0
\(513\) 2.13724e6 + 4.72389e6i 0.358558 + 0.792512i
\(514\) 0 0
\(515\) −1.62905e6 + 2.82160e6i −0.270655 + 0.468789i
\(516\) 0 0
\(517\) −41075.9 71145.5i −0.00675865 0.0117063i
\(518\) 0 0
\(519\) 18265.4 + 128106.i 0.00297653 + 0.0208763i
\(520\) 0 0
\(521\) −1.19670e6 −0.193148 −0.0965740 0.995326i \(-0.530788\pi\)
−0.0965740 + 0.995326i \(0.530788\pi\)
\(522\) 0 0
\(523\) −6.43371e6 −1.02851 −0.514254 0.857638i \(-0.671931\pi\)
−0.514254 + 0.857638i \(0.671931\pi\)
\(524\) 0 0
\(525\) 5.10940e6 + 2.05246e6i 0.809043 + 0.324995i
\(526\) 0 0
\(527\) 2.36834e6 + 4.10209e6i 0.371465 + 0.643396i
\(528\) 0 0
\(529\) 2.85178e6 4.93943e6i 0.443074 0.767427i
\(530\) 0 0
\(531\) 4.02160e6 1.17059e6i 0.618960 0.180164i
\(532\) 0 0
\(533\) −5.51735e6 + 9.55633e6i −0.841226 + 1.45705i
\(534\) 0 0
\(535\) −1.18716e6 2.05622e6i −0.179318 0.310588i
\(536\) 0 0
\(537\) −7.04600e6 + 5.52765e6i −1.05440 + 0.827190i
\(538\) 0 0
\(539\) −1.69907e6 −0.251907
\(540\) 0 0
\(541\) 5.85989e6 0.860788 0.430394 0.902641i \(-0.358375\pi\)
0.430394 + 0.902641i \(0.358375\pi\)
\(542\) 0 0
\(543\) 2.75595e6 2.16207e6i 0.401118 0.314681i
\(544\) 0 0
\(545\) −2.79185e6 4.83563e6i −0.402625 0.697368i
\(546\) 0 0
\(547\) −2.59436e6 + 4.49357e6i −0.370734 + 0.642130i −0.989679 0.143305i \(-0.954227\pi\)
0.618945 + 0.785434i \(0.287560\pi\)
\(548\) 0 0
\(549\) 4.50132e6 + 4.31223e6i 0.637395 + 0.610621i
\(550\) 0 0
\(551\) −5.84118e6 + 1.01172e7i −0.819637 + 1.41965i
\(552\) 0 0
\(553\) 7.51545e6 + 1.30171e7i 1.04506 + 1.81010i
\(554\) 0 0
\(555\) 1.64337e6 + 660148.i 0.226466 + 0.0909723i
\(556\) 0 0
\(557\) 5.07405e6 0.692973 0.346487 0.938055i \(-0.387375\pi\)
0.346487 + 0.938055i \(0.387375\pi\)
\(558\) 0 0
\(559\) −1.18623e7 −1.60561
\(560\) 0 0
\(561\) −985158. 6.90954e6i −0.132160 0.926919i
\(562\) 0 0
\(563\) 3.05439e6 + 5.29036e6i 0.406119 + 0.703419i 0.994451 0.105200i \(-0.0335484\pi\)
−0.588332 + 0.808620i \(0.700215\pi\)
\(564\) 0 0
\(565\) −3.22111e6 + 5.57913e6i −0.424507 + 0.735268i
\(566\) 0 0
\(567\) −7.54384e6 + 4.79819e6i −0.985451 + 0.626787i
\(568\) 0 0
\(569\) 5.40483e6 9.36143e6i 0.699844 1.21216i −0.268677 0.963230i \(-0.586586\pi\)
0.968520 0.248934i \(-0.0800803\pi\)
\(570\) 0 0
\(571\) −6.02796e6 1.04407e7i −0.773714 1.34011i −0.935515 0.353288i \(-0.885063\pi\)
0.161801 0.986823i \(-0.448270\pi\)
\(572\) 0 0
\(573\) 1.05194e6 + 7.37794e6i 0.133846 + 0.938747i
\(574\) 0 0
\(575\) −1.99706e6 −0.251896
\(576\) 0 0
\(577\) 1.22323e7 1.52957 0.764786 0.644285i \(-0.222845\pi\)
0.764786 + 0.644285i \(0.222845\pi\)
\(578\) 0 0
\(579\) −7.60931e6 3.05669e6i −0.943298 0.378926i
\(580\) 0 0
\(581\) 3.78908e6 + 6.56288e6i 0.465686 + 0.806593i
\(582\) 0 0
\(583\) 422054. 731019.i 0.0514277 0.0890754i
\(584\) 0 0
\(585\) 2.88335e6 + 2.76223e6i 0.348344 + 0.333711i
\(586\) 0 0
\(587\) 4.29817e6 7.44465e6i 0.514859 0.891762i −0.484992 0.874519i \(-0.661177\pi\)
0.999851 0.0172439i \(-0.00548917\pi\)
\(588\) 0 0
\(589\) −2.01097e6 3.48311e6i −0.238846 0.413693i
\(590\) 0 0
\(591\) 2.72617e6 2.13871e6i 0.321059 0.251874i
\(592\) 0 0
\(593\) −5.78455e6 −0.675511 −0.337756 0.941234i \(-0.609668\pi\)
−0.337756 + 0.941234i \(0.609668\pi\)
\(594\) 0 0
\(595\) 6.86903e6 0.795432
\(596\) 0 0
\(597\) 1.34539e6 1.05547e6i 0.154494 0.121202i
\(598\) 0 0
\(599\) 2.62557e6 + 4.54761e6i 0.298989 + 0.517865i 0.975905 0.218196i \(-0.0700172\pi\)
−0.676916 + 0.736061i \(0.736684\pi\)
\(600\) 0 0
\(601\) 3.11169e6 5.38960e6i 0.351407 0.608654i −0.635090 0.772439i \(-0.719037\pi\)
0.986496 + 0.163784i \(0.0523701\pi\)
\(602\) 0 0
\(603\) 6.13163e6 1.78477e6i 0.686725 0.199889i
\(604\) 0 0
\(605\) 1.18073e6 2.04509e6i 0.131148 0.227156i
\(606\) 0 0
\(607\) 7.94049e6 + 1.37533e7i 0.874733 + 1.51508i 0.857046 + 0.515239i \(0.172297\pi\)
0.0176871 + 0.999844i \(0.494370\pi\)
\(608\) 0 0
\(609\) −1.86926e7 7.50887e6i −2.04233 0.820411i
\(610\) 0 0
\(611\) −172693. −0.0187142
\(612\) 0 0
\(613\) −1.28661e7 −1.38292 −0.691458 0.722417i \(-0.743031\pi\)
−0.691458 + 0.722417i \(0.743031\pi\)
\(614\) 0 0
\(615\) −1.17037e6 8.20854e6i −0.124777 0.875142i
\(616\) 0 0
\(617\) 3.43797e6 + 5.95473e6i 0.363571 + 0.629723i 0.988546 0.150922i \(-0.0482242\pi\)
−0.624975 + 0.780645i \(0.714891\pi\)
\(618\) 0 0
\(619\) −6.52408e6 + 1.13000e7i −0.684373 + 1.18537i 0.289261 + 0.957250i \(0.406591\pi\)
−0.973633 + 0.228118i \(0.926743\pi\)
\(620\) 0 0
\(621\) 1.89021e6 2.63472e6i 0.196689 0.274161i
\(622\) 0 0
\(623\) 1.03438e7 1.79160e7i 1.06773 1.84936i
\(624\) 0 0
\(625\) −1.48369e6 2.56983e6i −0.151930 0.263151i
\(626\) 0 0
\(627\) 836504. + 5.86693e6i 0.0849765 + 0.595994i
\(628\) 0 0
\(629\) −6.50734e6 −0.655809
\(630\) 0 0
\(631\) −1.52784e7 −1.52758 −0.763790 0.645464i \(-0.776664\pi\)
−0.763790 + 0.645464i \(0.776664\pi\)
\(632\) 0 0
\(633\) −8.95200e6 3.59605e6i −0.887995 0.356711i
\(634\) 0 0
\(635\) 3.47052e6 + 6.01111e6i 0.341554 + 0.591590i
\(636\) 0 0
\(637\) −1.78583e6 + 3.09315e6i −0.174378 + 0.302032i
\(638\) 0 0
\(639\) 4.43466e6 1.80942e7i 0.429643 1.75303i
\(640\) 0 0
\(641\) 5.96157e6 1.03257e7i 0.573080 0.992604i −0.423167 0.906052i \(-0.639082\pi\)
0.996247 0.0865524i \(-0.0275850\pi\)
\(642\) 0 0
\(643\) 3.00302e6 + 5.20137e6i 0.286438 + 0.496125i 0.972957 0.230987i \(-0.0741955\pi\)
−0.686519 + 0.727112i \(0.740862\pi\)
\(644\) 0 0
\(645\) 7.01291e6 5.50169e6i 0.663741 0.520711i
\(646\) 0 0
\(647\) 1.19440e7 1.12173 0.560864 0.827908i \(-0.310469\pi\)
0.560864 + 0.827908i \(0.310469\pi\)
\(648\) 0 0
\(649\) 4.78742e6 0.446159
\(650\) 0 0
\(651\) 5.45647e6 4.28065e6i 0.504614 0.395874i
\(652\) 0 0
\(653\) 1.53297e6 + 2.65518e6i 0.140686 + 0.243675i 0.927755 0.373190i \(-0.121736\pi\)
−0.787069 + 0.616864i \(0.788403\pi\)
\(654\) 0 0
\(655\) 2.38131e6 4.12454e6i 0.216876 0.375641i
\(656\) 0 0
\(657\) 86553.9 353157.i 0.00782300 0.0319193i
\(658\) 0 0
\(659\) 1.55065e6 2.68581e6i 0.139092 0.240914i −0.788061 0.615597i \(-0.788915\pi\)
0.927153 + 0.374683i \(0.122248\pi\)
\(660\) 0 0
\(661\) −6.48853e6 1.12385e7i −0.577621 1.00047i −0.995751 0.0920819i \(-0.970648\pi\)
0.418130 0.908387i \(-0.362685\pi\)
\(662\) 0 0
\(663\) −1.36142e7 5.46888e6i −1.20284 0.483186i
\(664\) 0 0
\(665\) −5.83253e6 −0.511450
\(666\) 0 0
\(667\) 7.30618e6 0.635881
\(668\) 0 0
\(669\) −1.01943e6 7.14991e6i −0.0880627 0.617640i
\(670\) 0 0
\(671\) 3.56245e6 + 6.17034e6i 0.305452 + 0.529058i
\(672\) 0 0
\(673\) −1.10703e7 + 1.91743e7i −0.942154 + 1.63186i −0.180801 + 0.983520i \(0.557869\pi\)
−0.761352 + 0.648338i \(0.775464\pi\)
\(674\) 0 0
\(675\) 8.79412e6 + 871023.i 0.742904 + 0.0735817i
\(676\) 0 0
\(677\) −799850. + 1.38538e6i −0.0670713 + 0.116171i −0.897611 0.440789i \(-0.854699\pi\)
0.830540 + 0.556960i \(0.188032\pi\)
\(678\) 0 0
\(679\) −5.04566e6 8.73934e6i −0.419994 0.727452i
\(680\) 0 0
\(681\) 2.52302e6 + 1.76956e7i 0.208475 + 1.46217i
\(682\) 0 0
\(683\) 1.36986e7 1.12363 0.561816 0.827262i \(-0.310103\pi\)
0.561816 + 0.827262i \(0.310103\pi\)
\(684\) 0 0
\(685\) 2.81353e6 0.229100
\(686\) 0 0
\(687\) −5.07801e6 2.03985e6i −0.410489 0.164895i
\(688\) 0 0
\(689\) −887210. 1.53669e6i −0.0711998 0.123322i
\(690\) 0 0
\(691\) 2.09107e6 3.62183e6i 0.166599 0.288558i −0.770623 0.637291i \(-0.780055\pi\)
0.937222 + 0.348733i \(0.113388\pi\)
\(692\) 0 0
\(693\) −9.81170e6 + 2.85595e6i −0.776088 + 0.225901i
\(694\) 0 0
\(695\) 526268. 911522.i 0.0413280 0.0715822i
\(696\) 0 0
\(697\) 1.52331e7 + 2.63846e7i 1.18770 + 2.05716i
\(698\) 0 0
\(699\) −9.98681e6 + 7.83474e6i −0.773097 + 0.606501i
\(700\) 0 0
\(701\) −1.47134e7 −1.13089 −0.565443 0.824788i \(-0.691295\pi\)
−0.565443 + 0.824788i \(0.691295\pi\)
\(702\) 0 0
\(703\) 5.52543e6 0.421675
\(704\) 0 0
\(705\) 102095. 80094.2i 0.00773625 0.00606916i
\(706\) 0 0
\(707\) −1.86818e6 3.23577e6i −0.140562 0.243461i
\(708\) 0 0
\(709\) 4.25908e6 7.37694e6i 0.318200 0.551139i −0.661913 0.749581i \(-0.730255\pi\)
0.980113 + 0.198442i \(0.0635883\pi\)
\(710\) 0 0
\(711\) 1.74199e7 + 1.66882e7i 1.29233 + 1.23804i
\(712\) 0 0
\(713\) −1.25767e6 + 2.17834e6i −0.0926493 + 0.160473i
\(714\) 0 0
\(715\) 2.28195e6 + 3.95246e6i 0.166933 + 0.289136i
\(716\) 0 0
\(717\) −1.03411e7 4.15404e6i −0.751221 0.301768i
\(718\) 0 0
\(719\) −1.20183e7 −0.867003 −0.433502 0.901153i \(-0.642722\pi\)
−0.433502 + 0.901153i \(0.642722\pi\)
\(720\) 0 0
\(721\) −1.75280e7 −1.25573
\(722\) 0 0
\(723\) −99668.7 699040.i −0.00709109 0.0497343i
\(724\) 0 0
\(725\) 9.95577e6 + 1.72439e7i 0.703445 + 1.21840i
\(726\) 0 0
\(727\) −1.49257e6 + 2.58521e6i −0.104737 + 0.181409i −0.913631 0.406545i \(-0.866733\pi\)
0.808894 + 0.587955i \(0.200067\pi\)
\(728\) 0 0
\(729\) −9.47274e6 + 1.07777e7i −0.660171 + 0.751115i
\(730\) 0 0
\(731\) −1.63757e7 + 2.83635e7i −1.13346 + 1.96321i
\(732\) 0 0
\(733\) −1.05675e7 1.83035e7i −0.726464 1.25827i −0.958369 0.285534i \(-0.907829\pi\)
0.231905 0.972739i \(-0.425504\pi\)
\(734\) 0 0
\(735\) −378820. 2.65691e6i −0.0258651 0.181409i
\(736\) 0 0
\(737\) 7.29926e6 0.495006
\(738\) 0 0
\(739\) 1.33961e7 0.902337 0.451168 0.892439i \(-0.351007\pi\)
0.451168 + 0.892439i \(0.351007\pi\)
\(740\) 0 0
\(741\) 1.15599e7 + 4.64366e6i 0.773409 + 0.310681i
\(742\) 0 0
\(743\) −5.95418e6 1.03129e7i −0.395685 0.685347i 0.597503 0.801867i \(-0.296160\pi\)
−0.993188 + 0.116519i \(0.962826\pi\)
\(744\) 0 0
\(745\) −3.58175e6 + 6.20377e6i −0.236431 + 0.409511i
\(746\) 0 0
\(747\) 8.78265e6 + 8.41372e6i 0.575869 + 0.551679i
\(748\) 0 0
\(749\) 6.38671e6 1.10621e7i 0.415980 0.720499i
\(750\) 0 0
\(751\) −2.33184e6 4.03886e6i −0.150868 0.261312i 0.780679 0.624933i \(-0.214874\pi\)
−0.931547 + 0.363621i \(0.881540\pi\)
\(752\) 0 0
\(753\) 1.65708e7 1.30000e7i 1.06502 0.835517i
\(754\) 0 0
\(755\) −6.66232e6 −0.425361
\(756\) 0 0
\(757\) 138599. 0.00879065 0.00439532 0.999990i \(-0.498601\pi\)
0.00439532 + 0.999990i \(0.498601\pi\)
\(758\) 0 0
\(759\) 2.91604e6 2.28766e6i 0.183734 0.144141i
\(760\) 0 0
\(761\) −1.19856e6 2.07597e6i −0.0750237 0.129945i 0.826073 0.563563i \(-0.190570\pi\)
−0.901097 + 0.433618i \(0.857237\pi\)
\(762\) 0 0
\(763\) 1.50197e7 2.60148e7i 0.934005 1.61774i
\(764\) 0 0
\(765\) 1.05851e7 3.08106e6i 0.653942 0.190347i
\(766\) 0 0
\(767\) 5.03188e6 8.71546e6i 0.308846 0.534936i
\(768\) 0 0
\(769\) −399739. 692369.i −0.0243759 0.0422203i 0.853580 0.520962i \(-0.174427\pi\)
−0.877956 + 0.478741i \(0.841093\pi\)
\(770\) 0 0
\(771\) 1.73608e7 + 6.97390e6i 1.05180 + 0.422513i
\(772\) 0 0
\(773\) 1.07743e6 0.0648546 0.0324273 0.999474i \(-0.489676\pi\)
0.0324273 + 0.999474i \(0.489676\pi\)
\(774\) 0 0
\(775\) −6.85505e6 −0.409974
\(776\) 0 0
\(777\) 1.34486e6 + 9.43232e6i 0.0799140 + 0.560488i
\(778\) 0 0
\(779\) −1.29346e7 2.24033e7i −0.763674 1.32272i
\(780\) 0 0
\(781\) 1.06468e7 1.84408e7i 0.624586 1.08182i
\(782\) 0 0
\(783\) −3.21730e7 3.18661e6i −1.87537 0.185748i
\(784\) 0 0
\(785\) −3.58566e6 + 6.21055e6i −0.207680 + 0.359713i
\(786\) 0 0
\(787\) −1.53546e6 2.65949e6i −0.0883692 0.153060i 0.818453 0.574574i \(-0.194832\pi\)
−0.906822 + 0.421514i \(0.861499\pi\)
\(788\) 0 0
\(789\) 2.89038e6 + 2.02721e7i 0.165296 + 1.15932i
\(790\) 0 0
\(791\) −3.46581e7 −1.96953
\(792\) 0 0
\(793\) 1.49774e7 0.845774
\(794\) 0 0
\(795\) 1.23722e6 + 496996.i 0.0694273 + 0.0278892i
\(796\) 0 0
\(797\) −7.49242e6 1.29772e7i −0.417808 0.723664i 0.577911 0.816100i \(-0.303868\pi\)
−0.995719 + 0.0924359i \(0.970535\pi\)
\(798\) 0 0
\(799\) −238399. + 412919.i −0.0132110 + 0.0228822i
\(800\) 0 0
\(801\) 7.90354e6 3.22480e7i 0.435252 1.77591i
\(802\) 0 0
\(803\) 207801. 359921.i 0.0113726 0.0196978i
\(804\) 0 0
\(805\) 1.82384e6 + 3.15898e6i 0.0991967 + 0.171814i
\(806\) 0 0
\(807\) −3.94141e6 + 3.09207e6i −0.213043 + 0.167134i
\(808\) 0 0
\(809\) −3.11069e6 −0.167103 −0.0835516 0.996503i \(-0.526626\pi\)
−0.0835516 + 0.996503i \(0.526626\pi\)
\(810\) 0 0
\(811\) 1.12694e7 0.601659 0.300830 0.953678i \(-0.402736\pi\)
0.300830 + 0.953678i \(0.402736\pi\)
\(812\) 0 0
\(813\) −4.72102e6 + 3.70368e6i −0.250501 + 0.196520i
\(814\) 0 0
\(815\) −3.02615e6 5.24144e6i −0.159586 0.276412i
\(816\) 0 0
\(817\) 1.39047e7 2.40836e7i 0.728795 1.26231i
\(818\) 0 0
\(819\) −5.11346e6 + 2.08639e7i −0.266382 + 1.08689i
\(820\) 0 0
\(821\) −1.04769e7 + 1.81465e7i −0.542467 + 0.939580i 0.456295 + 0.889829i \(0.349176\pi\)
−0.998762 + 0.0497515i \(0.984157\pi\)
\(822\) 0 0
\(823\) −974079. 1.68715e6i −0.0501296 0.0868271i 0.839872 0.542785i \(-0.182630\pi\)
−0.890001 + 0.455958i \(0.849297\pi\)
\(824\) 0 0
\(825\) 9.37283e6 + 3.76510e6i 0.479442 + 0.192593i
\(826\) 0 0
\(827\) 3.11807e7 1.58534 0.792671 0.609650i \(-0.208690\pi\)
0.792671 + 0.609650i \(0.208690\pi\)
\(828\) 0 0
\(829\) −1.67293e7 −0.845455 −0.422727 0.906257i \(-0.638927\pi\)
−0.422727 + 0.906257i \(0.638927\pi\)
\(830\) 0 0
\(831\) 3.73162e6 + 2.61722e7i 0.187454 + 1.31473i
\(832\) 0 0
\(833\) 4.93060e6 + 8.54005e6i 0.246199 + 0.426430i
\(834\) 0 0
\(835\) −2.70653e6 + 4.68785e6i −0.134337 + 0.232679i
\(836\) 0 0
\(837\) 6.48827e6 9.04387e6i 0.320122 0.446212i
\(838\) 0 0
\(839\) 4.13660e6 7.16481e6i 0.202880 0.351398i −0.746575 0.665301i \(-0.768303\pi\)
0.949455 + 0.313903i \(0.101637\pi\)
\(840\) 0 0
\(841\) −2.61673e7 4.53231e7i −1.27576 2.20968i
\(842\) 0 0
\(843\) −2.33531e6 1.63790e7i −0.113181 0.793813i
\(844\) 0 0
\(845\) −855632. −0.0412235
\(846\) 0 0
\(847\) 1.27043e7 0.608473
\(848\) 0 0
\(849\) −5.56362e6 2.23492e6i −0.264904 0.106413i
\(850\) 0 0
\(851\) −1.72781e6 2.99265e6i −0.0817846 0.141655i
\(852\) 0 0
\(853\) −1.73469e7 + 3.00458e7i −0.816300 + 1.41387i 0.0920905 + 0.995751i \(0.470645\pi\)
−0.908391 + 0.418123i \(0.862688\pi\)
\(854\) 0 0
\(855\) −8.98784e6 + 2.61615e6i −0.420475 + 0.122390i
\(856\) 0 0
\(857\) −2.51863e6 + 4.36239e6i −0.117142 + 0.202895i −0.918634 0.395110i \(-0.870707\pi\)
0.801492 + 0.598005i \(0.204040\pi\)
\(858\) 0 0
\(859\) 2.13910e7 + 3.70502e7i 0.989116 + 1.71320i 0.621984 + 0.783030i \(0.286327\pi\)
0.367132 + 0.930169i \(0.380340\pi\)
\(860\) 0 0
\(861\) 3.50960e7 2.75331e7i 1.61343 1.26575i
\(862\) 0 0
\(863\) 1.50904e6 0.0689721 0.0344861 0.999405i \(-0.489021\pi\)
0.0344861 + 0.999405i \(0.489021\pi\)
\(864\) 0 0
\(865\) −233624. −0.0106164
\(866\) 0 0
\(867\) −1.44564e7 + 1.13412e7i −0.653151 + 0.512403i
\(868\) 0 0
\(869\) 1.37866e7 + 2.38790e7i 0.619307 + 1.07267i
\(870\) 0 0
\(871\) 7.67198e6 1.32883e7i 0.342659 0.593503i
\(872\) 0 0
\(873\) −1.16953e7 1.12040e7i −0.519367 0.497550i
\(874\) 0 0
\(875\) −1.16286e7 + 2.01413e7i −0.513460 + 0.889339i
\(876\) 0 0
\(877\) 1.64700e7 + 2.85268e7i 0.723092 + 1.25243i 0.959755 + 0.280840i \(0.0906131\pi\)
−0.236663 + 0.971592i \(0.576054\pi\)
\(878\) 0 0
\(879\) −1.93149e7 7.75886e6i −0.843180 0.338708i
\(880\) 0 0
\(881\) 2.62885e7 1.14110 0.570552 0.821261i \(-0.306729\pi\)
0.570552 + 0.821261i \(0.306729\pi\)
\(882\) 0 0
\(883\) −2.07499e7 −0.895602 −0.447801 0.894133i \(-0.647793\pi\)
−0.447801 + 0.894133i \(0.647793\pi\)
\(884\) 0 0
\(885\) 1.06739e6 + 7.48627e6i 0.0458104 + 0.321297i
\(886\) 0 0
\(887\) −1.64291e7 2.84561e7i −0.701140 1.21441i −0.968066 0.250694i \(-0.919341\pi\)
0.266926 0.963717i \(-0.413992\pi\)
\(888\) 0 0
\(889\) −1.86708e7 + 3.23387e7i −0.792334 + 1.37236i
\(890\) 0 0
\(891\) −1.38386e7 + 8.80194e6i −0.583982 + 0.371436i
\(892\) 0 0
\(893\) 202426. 350612.i 0.00849449 0.0147129i
\(894\) 0 0
\(895\) −8.08420e6 1.40022e7i −0.337349 0.584306i
\(896\) 0 0
\(897\) −1.09973e6 7.71310e6i −0.0456357 0.320072i
\(898\) 0 0
\(899\) 2.50790e7 1.03493
\(900\) 0 0
\(901\) −4.89909e6 −0.201050
\(902\) 0 0
\(903\) 4.44968e7 + 1.78745e7i 1.81597 + 0.729483i
\(904\) 0 0
\(905\) 3.16203e6 + 5.47680e6i 0.128335 + 0.222283i
\(906\) 0 0
\(907\) −2.35836e7 + 4.08480e7i −0.951900 + 1.64874i −0.210593 + 0.977574i \(0.567540\pi\)
−0.741307 + 0.671166i \(0.765794\pi\)
\(908\) 0 0
\(909\) −4.33021e6 4.14832e6i −0.173820 0.166518i
\(910\) 0 0
\(911\) −1.90246e7 + 3.29516e7i −0.759486 + 1.31547i 0.183627 + 0.982996i \(0.441216\pi\)
−0.943113 + 0.332472i \(0.892117\pi\)
\(912\) 0 0
\(913\) 6.95080e6 + 1.20391e7i 0.275967 + 0.477990i
\(914\) 0 0
\(915\) −8.85453e6 + 6.94646e6i −0.349633 + 0.274290i
\(916\) 0 0
\(917\) 2.56220e7 1.00621
\(918\) 0 0
\(919\) 2.54292e7 0.993215 0.496607 0.867975i \(-0.334579\pi\)
0.496607 + 0.867975i \(0.334579\pi\)
\(920\) 0 0
\(921\) −7.80363e6 + 6.12202e6i −0.303143 + 0.237818i
\(922\) 0 0
\(923\) −2.23809e7 3.87649e7i −0.864717 1.49773i
\(924\) 0 0
\(925\) 4.70880e6 8.15588e6i 0.180949 0.313412i
\(926\) 0 0
\(927\) −2.70104e7 + 7.86208e6i −1.03236 + 0.300496i
\(928\) 0 0
\(929\) 7.00472e6 1.21325e7i 0.266288 0.461224i −0.701612 0.712559i \(-0.747536\pi\)
0.967900 + 0.251335i \(0.0808695\pi\)
\(930\) 0 0
\(931\) −4.18660e6 7.25141e6i −0.158302 0.274188i
\(932\) 0 0
\(933\) −7.80793e6 3.13647e6i −0.293651 0.117961i
\(934\) 0 0
\(935\) 1.26007e7 0.471375
\(936\) 0 0
\(937\) −1.29313e7 −0.481164 −0.240582 0.970629i \(-0.577338\pi\)
−0.240582 + 0.970629i \(0.577338\pi\)
\(938\) 0 0
\(939\) −4.29773e6 3.01427e7i −0.159065 1.11562i
\(940\) 0 0
\(941\) 4.79973e6 + 8.31337e6i 0.176702 + 0.306058i 0.940749 0.339103i \(-0.110124\pi\)
−0.764047 + 0.645161i \(0.776790\pi\)
\(942\) 0 0
\(943\) −8.08930e6 + 1.40111e7i −0.296232 + 0.513089i
\(944\) 0 0
\(945\) −6.65354e6 1.47062e7i −0.242367 0.535698i
\(946\) 0 0
\(947\) 7.16687e6 1.24134e7i 0.259690 0.449796i −0.706469 0.707744i \(-0.749713\pi\)
0.966159 + 0.257948i \(0.0830464\pi\)
\(948\) 0 0
\(949\) −436823. 756599.i −0.0157449 0.0272710i
\(950\) 0 0
\(951\) −3.44126e6 2.41357e7i −0.123386 0.865384i
\(952\) 0 0
\(953\) 3.14184e7 1.12060 0.560302 0.828289i \(-0.310685\pi\)
0.560302 + 0.828289i \(0.310685\pi\)
\(954\) 0 0
\(955\) −1.34550e7 −0.477391
\(956\) 0 0
\(957\) −3.42902e7 1.37745e7i −1.21029 0.486178i
\(958\) 0 0
\(959\) 7.56817e6 + 1.31084e7i 0.265732 + 0.460262i
\(960\) 0 0
\(961\) 9.99755e6 1.73163e7i 0.349209 0.604847i
\(962\) 0 0
\(963\) 4.87998e6 1.99112e7i 0.169571 0.691883i
\(964\) 0 0
\(965\) 7.40248e6 1.28215e7i 0.255893 0.443220i
\(966\) 0 0
\(967\) 6.76319e6 + 1.17142e7i 0.232587 + 0.402852i 0.958569 0.284862i \(-0.0919477\pi\)
−0.725982 + 0.687714i \(0.758614\pi\)
\(968\) 0 0
\(969\) 2.70614e7 2.12300e7i 0.925852 0.726339i
\(970\) 0 0
\(971\) 3.90534e7 1.32926 0.664632 0.747171i \(-0.268588\pi\)
0.664632 + 0.747171i \(0.268588\pi\)
\(972\) 0 0
\(973\) 5.66246e6 0.191744
\(974\) 0 0
\(975\) 1.67058e7 1.31058e7i 0.562801 0.441522i
\(976\) 0 0
\(977\) −9.45244e6 1.63721e7i −0.316816 0.548742i 0.663006 0.748614i \(-0.269280\pi\)
−0.979822 + 0.199873i \(0.935947\pi\)
\(978\) 0 0
\(979\) 1.89750e7 3.28657e7i 0.632740 1.09594i
\(980\) 0 0
\(981\) 1.14763e7 4.68254e7i 0.380740 1.55349i
\(982\) 0 0
\(983\) 2.95013e6 5.10977e6i 0.0973771 0.168662i −0.813221 0.581955i \(-0.802288\pi\)
0.910598 + 0.413293i \(0.135621\pi\)
\(984\) 0 0
\(985\) 3.12786e6 + 5.41762e6i 0.102720 + 0.177917i
\(986\) 0 0
\(987\) 647790. + 260220.i 0.0211661 + 0.00850251i
\(988\) 0 0
\(989\) −1.73920e7 −0.565405
\(990\) 0 0
\(991\) −3.67515e7 −1.18875 −0.594375 0.804188i \(-0.702601\pi\)
−0.594375 + 0.804188i \(0.702601\pi\)
\(992\) 0 0
\(993\) 5.63287e6 + 3.95069e7i 0.181283 + 1.27145i
\(994\) 0 0
\(995\) 1.54362e6 + 2.67364e6i 0.0494293 + 0.0856140i
\(996\) 0 0
\(997\) −1.46074e7 + 2.53008e7i −0.465410 + 0.806114i −0.999220 0.0394905i \(-0.987427\pi\)
0.533810 + 0.845605i \(0.320760\pi\)
\(998\) 0 0
\(999\) 6.30321e6 + 1.39318e7i 0.199824 + 0.441666i
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 36.6.e.a.25.1 yes 10
3.2 odd 2 108.6.e.a.73.4 10
4.3 odd 2 144.6.i.d.97.5 10
9.2 odd 6 324.6.a.d.1.2 5
9.4 even 3 inner 36.6.e.a.13.1 10
9.5 odd 6 108.6.e.a.37.4 10
9.7 even 3 324.6.a.e.1.4 5
12.11 even 2 432.6.i.d.289.4 10
36.23 even 6 432.6.i.d.145.4 10
36.31 odd 6 144.6.i.d.49.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.6.e.a.13.1 10 9.4 even 3 inner
36.6.e.a.25.1 yes 10 1.1 even 1 trivial
108.6.e.a.37.4 10 9.5 odd 6
108.6.e.a.73.4 10 3.2 odd 2
144.6.i.d.49.5 10 36.31 odd 6
144.6.i.d.97.5 10 4.3 odd 2
324.6.a.d.1.2 5 9.2 odd 6
324.6.a.e.1.4 5 9.7 even 3
432.6.i.d.145.4 10 36.23 even 6
432.6.i.d.289.4 10 12.11 even 2