Properties

Label 1040.2.dh.c.529.4
Level $1040$
Weight $2$
Character 1040.529
Analytic conductor $8.304$
Analytic rank $0$
Dimension $12$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1040,2,Mod(289,1040)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
 
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("1040.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.dh (of order \(6\), degree \(2\), 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: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.513226913958144.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6x^{10} + 28x^{8} - 46x^{6} + 58x^{4} - 8x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 529.4
Root \(1.75675 - 1.01426i\) of defining polynomial
Character \(\chi\) \(=\) 1040.529
Dual form 1040.2.dh.c.289.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.201864 + 0.116546i) q^{3} +(-2.11491 + 0.726062i) q^{5} +(3.71537 - 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +O(q^{10})\) \(q+(0.201864 + 0.116546i) q^{3} +(-2.11491 + 0.726062i) q^{5} +(3.71537 - 2.14507i) q^{7} +(-1.47283 - 2.55102i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-3.51351 - 0.809492i) q^{13} +(-0.511544 - 0.0999188i) q^{15} +(-3.31164 + 1.91198i) q^{17} +(-1.14207 - 1.97813i) q^{19} +1.00000 q^{21} +(-4.97295 - 2.87113i) q^{23} +(3.94567 - 3.07111i) q^{25} -1.38589i q^{27} +(-1.14207 + 1.97813i) q^{29} +6.22982 q^{31} +(-0.201864 + 0.116546i) q^{33} +(-6.30021 + 7.23421i) q^{35} +(-5.82679 - 3.36410i) q^{37} +(-0.614908 - 0.572894i) q^{39} +(-1.33076 + 2.30494i) q^{41} +(-5.97130 + 3.44753i) q^{43} +(4.96711 + 4.32581i) q^{45} -6.60840i q^{47} +(5.70265 - 9.87728i) q^{49} -0.891336 q^{51} -5.04299i q^{53} +(0.428666 - 2.19459i) q^{55} -0.532418i q^{57} +(-5.56058 - 9.63120i) q^{59} +(-2.08774 - 3.61607i) q^{61} +(-10.9442 - 6.31866i) q^{63} +(8.01848 - 0.839022i) q^{65} +(3.76176 + 2.17185i) q^{67} +(-0.669240 - 1.15916i) q^{69} +(-3.37189 - 5.84028i) q^{71} -13.5697i q^{73} +(1.15442 - 0.160094i) q^{75} +4.29014i q^{77} +11.4053 q^{79} +(-4.25698 + 7.37331i) q^{81} +10.0324i q^{83} +(5.61560 - 6.44811i) q^{85} +(-0.461087 + 0.266209i) q^{87} +(-5.56058 + 9.63120i) q^{89} +(-14.7904 + 4.52915i) q^{91} +(1.25758 + 0.726062i) q^{93} +(3.85162 + 3.35434i) q^{95} +(-12.8538 + 7.42115i) q^{97} +2.94567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{9} - 6 q^{11} - 10 q^{15} - 10 q^{19} + 12 q^{21} + 4 q^{25} - 10 q^{29} + 24 q^{31} + 6 q^{35} + 18 q^{39} + 2 q^{41} + 12 q^{45} - 4 q^{49} + 76 q^{51} + 2 q^{59} + 22 q^{61} - 40 q^{65} - 26 q^{69} + 14 q^{71} + 8 q^{75} - 8 q^{79} - 22 q^{81} + 14 q^{85} + 2 q^{89} - 58 q^{91} + 20 q^{95} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.201864 + 0.116546i 0.116546 + 0.0672881i 0.557140 0.830419i \(-0.311899\pi\)
−0.440594 + 0.897707i \(0.645232\pi\)
\(4\) 0 0
\(5\) −2.11491 + 0.726062i −0.945815 + 0.324705i
\(6\) 0 0
\(7\) 3.71537 2.14507i 1.40428 0.810760i 0.409450 0.912333i \(-0.365721\pi\)
0.994828 + 0.101573i \(0.0323874\pi\)
\(8\) 0 0
\(9\) −1.47283 2.55102i −0.490945 0.850341i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 0 0
\(13\) −3.51351 0.809492i −0.974471 0.224513i
\(14\) 0 0
\(15\) −0.511544 0.0999188i −0.132080 0.0257989i
\(16\) 0 0
\(17\) −3.31164 + 1.91198i −0.803191 + 0.463723i −0.844586 0.535420i \(-0.820153\pi\)
0.0413947 + 0.999143i \(0.486820\pi\)
\(18\) 0 0
\(19\) −1.14207 1.97813i −0.262010 0.453814i 0.704766 0.709440i \(-0.251052\pi\)
−0.966776 + 0.255626i \(0.917719\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) −4.97295 2.87113i −1.03693 0.598672i −0.117968 0.993017i \(-0.537638\pi\)
−0.918962 + 0.394345i \(0.870972\pi\)
\(24\) 0 0
\(25\) 3.94567 3.07111i 0.789134 0.614222i
\(26\) 0 0
\(27\) 1.38589i 0.266715i
\(28\) 0 0
\(29\) −1.14207 + 1.97813i −0.212078 + 0.367329i −0.952365 0.304962i \(-0.901356\pi\)
0.740287 + 0.672291i \(0.234690\pi\)
\(30\) 0 0
\(31\) 6.22982 1.11891 0.559454 0.828861i \(-0.311011\pi\)
0.559454 + 0.828861i \(0.311011\pi\)
\(32\) 0 0
\(33\) −0.201864 + 0.116546i −0.0351400 + 0.0202881i
\(34\) 0 0
\(35\) −6.30021 + 7.23421i −1.06493 + 1.22281i
\(36\) 0 0
\(37\) −5.82679 3.36410i −0.957919 0.553055i −0.0623871 0.998052i \(-0.519871\pi\)
−0.895532 + 0.444997i \(0.853205\pi\)
\(38\) 0 0
\(39\) −0.614908 0.572894i −0.0984640 0.0917364i
\(40\) 0 0
\(41\) −1.33076 + 2.30494i −0.207830 + 0.359972i −0.951031 0.309097i \(-0.899973\pi\)
0.743201 + 0.669068i \(0.233307\pi\)
\(42\) 0 0
\(43\) −5.97130 + 3.44753i −0.910615 + 0.525744i −0.880629 0.473807i \(-0.842880\pi\)
−0.0299858 + 0.999550i \(0.509546\pi\)
\(44\) 0 0
\(45\) 4.96711 + 4.32581i 0.740453 + 0.644854i
\(46\) 0 0
\(47\) 6.60840i 0.963934i −0.876189 0.481967i \(-0.839922\pi\)
0.876189 0.481967i \(-0.160078\pi\)
\(48\) 0 0
\(49\) 5.70265 9.87728i 0.814664 1.41104i
\(50\) 0 0
\(51\) −0.891336 −0.124812
\(52\) 0 0
\(53\) 5.04299i 0.692707i −0.938104 0.346354i \(-0.887420\pi\)
0.938104 0.346354i \(-0.112580\pi\)
\(54\) 0 0
\(55\) 0.428666 2.19459i 0.0578013 0.295919i
\(56\) 0 0
\(57\) 0.532418i 0.0705205i
\(58\) 0 0
\(59\) −5.56058 9.63120i −0.723925 1.25388i −0.959415 0.281998i \(-0.909003\pi\)
0.235490 0.971877i \(-0.424331\pi\)
\(60\) 0 0
\(61\) −2.08774 3.61607i −0.267308 0.462991i 0.700858 0.713301i \(-0.252801\pi\)
−0.968166 + 0.250310i \(0.919467\pi\)
\(62\) 0 0
\(63\) −10.9442 6.31866i −1.37885 0.796077i
\(64\) 0 0
\(65\) 8.01848 0.839022i 0.994570 0.104068i
\(66\) 0 0
\(67\) 3.76176 + 2.17185i 0.459572 + 0.265334i 0.711864 0.702317i \(-0.247851\pi\)
−0.252292 + 0.967651i \(0.581184\pi\)
\(68\) 0 0
\(69\) −0.669240 1.15916i −0.0805670 0.139546i
\(70\) 0 0
\(71\) −3.37189 5.84028i −0.400170 0.693114i 0.593577 0.804778i \(-0.297715\pi\)
−0.993746 + 0.111664i \(0.964382\pi\)
\(72\) 0 0
\(73\) 13.5697i 1.58821i −0.607779 0.794106i \(-0.707939\pi\)
0.607779 0.794106i \(-0.292061\pi\)
\(74\) 0 0
\(75\) 1.15442 0.160094i 0.133300 0.0184860i
\(76\) 0 0
\(77\) 4.29014i 0.488907i
\(78\) 0 0
\(79\) 11.4053 1.28320 0.641598 0.767041i \(-0.278272\pi\)
0.641598 + 0.767041i \(0.278272\pi\)
\(80\) 0 0
\(81\) −4.25698 + 7.37331i −0.472998 + 0.819256i
\(82\) 0 0
\(83\) 10.0324i 1.10120i 0.834769 + 0.550600i \(0.185601\pi\)
−0.834769 + 0.550600i \(0.814399\pi\)
\(84\) 0 0
\(85\) 5.61560 6.44811i 0.609098 0.699396i
\(86\) 0 0
\(87\) −0.461087 + 0.266209i −0.0494338 + 0.0285406i
\(88\) 0 0
\(89\) −5.56058 + 9.63120i −0.589420 + 1.02091i 0.404889 + 0.914366i \(0.367310\pi\)
−0.994309 + 0.106539i \(0.966023\pi\)
\(90\) 0 0
\(91\) −14.7904 + 4.52915i −1.55045 + 0.474784i
\(92\) 0 0
\(93\) 1.25758 + 0.726062i 0.130405 + 0.0752891i
\(94\) 0 0
\(95\) 3.85162 + 3.35434i 0.395168 + 0.344149i
\(96\) 0 0
\(97\) −12.8538 + 7.42115i −1.30511 + 0.753503i −0.981275 0.192611i \(-0.938304\pi\)
−0.323831 + 0.946115i \(0.604971\pi\)
\(98\) 0 0
\(99\) 2.94567 0.296051
\(100\) 0 0
\(101\) 9.48680 16.4316i 0.943972 1.63501i 0.186174 0.982517i \(-0.440391\pi\)
0.757797 0.652490i \(-0.226275\pi\)
\(102\) 0 0
\(103\) 17.9796i 1.77159i −0.464080 0.885793i \(-0.653615\pi\)
0.464080 0.885793i \(-0.346385\pi\)
\(104\) 0 0
\(105\) −2.11491 + 0.726062i −0.206394 + 0.0708564i
\(106\) 0 0
\(107\) 3.97459 + 2.29473i 0.384238 + 0.221840i 0.679661 0.733527i \(-0.262127\pi\)
−0.295422 + 0.955367i \(0.595460\pi\)
\(108\) 0 0
\(109\) 0.147558 0.0141335 0.00706676 0.999975i \(-0.497751\pi\)
0.00706676 + 0.999975i \(0.497751\pi\)
\(110\) 0 0
\(111\) −0.784147 1.35818i −0.0744280 0.128913i
\(112\) 0 0
\(113\) −13.9503 + 8.05419i −1.31233 + 0.757675i −0.982482 0.186359i \(-0.940331\pi\)
−0.329849 + 0.944034i \(0.606998\pi\)
\(114\) 0 0
\(115\) 12.6019 + 2.46151i 1.17514 + 0.229537i
\(116\) 0 0
\(117\) 3.10978 + 10.1553i 0.287499 + 0.938856i
\(118\) 0 0
\(119\) −8.20265 + 14.2074i −0.751936 + 1.30239i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) −0.537266 + 0.310190i −0.0484436 + 0.0279689i
\(124\) 0 0
\(125\) −6.11491 + 9.35991i −0.546934 + 0.837176i
\(126\) 0 0
\(127\) 8.98829 + 5.18939i 0.797582 + 0.460484i 0.842625 0.538501i \(-0.181009\pi\)
−0.0450429 + 0.998985i \(0.514342\pi\)
\(128\) 0 0
\(129\) −1.60719 −0.141505
\(130\) 0 0
\(131\) 17.6351 1.54079 0.770393 0.637569i \(-0.220060\pi\)
0.770393 + 0.637569i \(0.220060\pi\)
\(132\) 0 0
\(133\) −8.48645 4.89966i −0.735869 0.424854i
\(134\) 0 0
\(135\) 1.00624 + 2.93103i 0.0866036 + 0.252263i
\(136\) 0 0
\(137\) 5.56757 3.21444i 0.475670 0.274628i −0.242940 0.970041i \(-0.578112\pi\)
0.718610 + 0.695413i \(0.244779\pi\)
\(138\) 0 0
\(139\) 7.48680 + 12.9675i 0.635022 + 1.09989i 0.986511 + 0.163698i \(0.0523422\pi\)
−0.351489 + 0.936192i \(0.614324\pi\)
\(140\) 0 0
\(141\) 0.770185 1.33400i 0.0648613 0.112343i
\(142\) 0 0
\(143\) 2.45779 2.63804i 0.205531 0.220604i
\(144\) 0 0
\(145\) 0.979135 5.01278i 0.0813128 0.416289i
\(146\) 0 0
\(147\) 2.30232 1.32925i 0.189892 0.109634i
\(148\) 0 0
\(149\) 7.84472 + 13.5875i 0.642665 + 1.11313i 0.984836 + 0.173490i \(0.0555045\pi\)
−0.342171 + 0.939638i \(0.611162\pi\)
\(150\) 0 0
\(151\) 1.17548 0.0956594 0.0478297 0.998856i \(-0.484770\pi\)
0.0478297 + 0.998856i \(0.484770\pi\)
\(152\) 0 0
\(153\) 9.75500 + 5.63205i 0.788645 + 0.455324i
\(154\) 0 0
\(155\) −13.1755 + 4.52323i −1.05828 + 0.363315i
\(156\) 0 0
\(157\) 5.45560i 0.435405i −0.976015 0.217702i \(-0.930144\pi\)
0.976015 0.217702i \(-0.0698562\pi\)
\(158\) 0 0
\(159\) 0.587741 1.01800i 0.0466109 0.0807325i
\(160\) 0 0
\(161\) −24.6351 −1.94152
\(162\) 0 0
\(163\) 4.02098 2.32152i 0.314948 0.181835i −0.334191 0.942506i \(-0.608463\pi\)
0.649138 + 0.760670i \(0.275130\pi\)
\(164\) 0 0
\(165\) 0.342304 0.393051i 0.0266483 0.0305989i
\(166\) 0 0
\(167\) −2.76341 1.59545i −0.213839 0.123460i 0.389255 0.921130i \(-0.372732\pi\)
−0.603094 + 0.797670i \(0.706066\pi\)
\(168\) 0 0
\(169\) 11.6894 + 5.68831i 0.899188 + 0.437562i
\(170\) 0 0
\(171\) −3.36417 + 5.82691i −0.257264 + 0.445595i
\(172\) 0 0
\(173\) −3.00603 + 1.73553i −0.228544 + 0.131950i −0.609900 0.792478i \(-0.708790\pi\)
0.381356 + 0.924428i \(0.375457\pi\)
\(174\) 0 0
\(175\) 8.07187 19.8740i 0.610176 1.50234i
\(176\) 0 0
\(177\) 2.59226i 0.194846i
\(178\) 0 0
\(179\) −2.56058 + 4.43505i −0.191386 + 0.331491i −0.945710 0.325012i \(-0.894632\pi\)
0.754324 + 0.656503i \(0.227965\pi\)
\(180\) 0 0
\(181\) −4.14756 −0.308286 −0.154143 0.988049i \(-0.549262\pi\)
−0.154143 + 0.988049i \(0.549262\pi\)
\(182\) 0 0
\(183\) 0.973274i 0.0719465i
\(184\) 0 0
\(185\) 14.7657 + 2.88415i 1.08559 + 0.212047i
\(186\) 0 0
\(187\) 3.82395i 0.279635i
\(188\) 0 0
\(189\) −2.97283 5.14910i −0.216242 0.374542i
\(190\) 0 0
\(191\) −0.404539 0.700683i −0.0292714 0.0506996i 0.851019 0.525136i \(-0.175985\pi\)
−0.880290 + 0.474436i \(0.842652\pi\)
\(192\) 0 0
\(193\) −8.34195 4.81623i −0.600466 0.346679i 0.168759 0.985657i \(-0.446024\pi\)
−0.769225 + 0.638978i \(0.779358\pi\)
\(194\) 0 0
\(195\) 1.71643 + 0.765156i 0.122916 + 0.0547940i
\(196\) 0 0
\(197\) 14.0650 + 8.12043i 1.00209 + 0.578556i 0.908866 0.417089i \(-0.136950\pi\)
0.0932234 + 0.995645i \(0.470283\pi\)
\(198\) 0 0
\(199\) −2.06829 3.58239i −0.146618 0.253949i 0.783358 0.621571i \(-0.213505\pi\)
−0.929975 + 0.367622i \(0.880172\pi\)
\(200\) 0 0
\(201\) 0.506243 + 0.876839i 0.0357076 + 0.0618474i
\(202\) 0 0
\(203\) 9.79931i 0.687777i
\(204\) 0 0
\(205\) 1.14090 5.84096i 0.0796841 0.407950i
\(206\) 0 0
\(207\) 16.9148i 1.17566i
\(208\) 0 0
\(209\) 2.28415 0.157998
\(210\) 0 0
\(211\) 4.80359 8.32007i 0.330693 0.572777i −0.651955 0.758258i \(-0.726051\pi\)
0.982648 + 0.185481i \(0.0593842\pi\)
\(212\) 0 0
\(213\) 1.57192i 0.107707i
\(214\) 0 0
\(215\) 10.1256 11.6267i 0.690562 0.792937i
\(216\) 0 0
\(217\) 23.1461 13.3634i 1.57126 0.907166i
\(218\) 0 0
\(219\) 1.58150 2.73924i 0.106868 0.185100i
\(220\) 0 0
\(221\) 13.1832 4.03700i 0.886798 0.271558i
\(222\) 0 0
\(223\) −13.0447 7.53136i −0.873538 0.504337i −0.00501557 0.999987i \(-0.501597\pi\)
−0.868522 + 0.495650i \(0.834930\pi\)
\(224\) 0 0
\(225\) −13.6458 5.54226i −0.909719 0.369484i
\(226\) 0 0
\(227\) −17.4174 + 10.0559i −1.15603 + 0.667436i −0.950350 0.311183i \(-0.899275\pi\)
−0.205683 + 0.978619i \(0.565941\pi\)
\(228\) 0 0
\(229\) −12.5683 −0.830536 −0.415268 0.909699i \(-0.636312\pi\)
−0.415268 + 0.909699i \(0.636312\pi\)
\(230\) 0 0
\(231\) −0.500000 + 0.866025i −0.0328976 + 0.0569803i
\(232\) 0 0
\(233\) 11.3712i 0.744954i −0.928041 0.372477i \(-0.878508\pi\)
0.928041 0.372477i \(-0.121492\pi\)
\(234\) 0 0
\(235\) 4.79811 + 13.9762i 0.312994 + 0.911704i
\(236\) 0 0
\(237\) 2.30232 + 1.32925i 0.149552 + 0.0863438i
\(238\) 0 0
\(239\) 18.3510 1.18703 0.593513 0.804825i \(-0.297741\pi\)
0.593513 + 0.804825i \(0.297741\pi\)
\(240\) 0 0
\(241\) 0.688687 + 1.19284i 0.0443622 + 0.0768376i 0.887354 0.461089i \(-0.152541\pi\)
−0.842992 + 0.537927i \(0.819208\pi\)
\(242\) 0 0
\(243\) −5.31932 + 3.07111i −0.341234 + 0.197012i
\(244\) 0 0
\(245\) −4.88906 + 25.0300i −0.312351 + 1.59911i
\(246\) 0 0
\(247\) 2.41140 + 7.87467i 0.153434 + 0.501053i
\(248\) 0 0
\(249\) −1.16924 + 2.02518i −0.0740976 + 0.128341i
\(250\) 0 0
\(251\) −12.6149 21.8497i −0.796246 1.37914i −0.922045 0.387083i \(-0.873483\pi\)
0.125799 0.992056i \(-0.459851\pi\)
\(252\) 0 0
\(253\) 4.97295 2.87113i 0.312646 0.180507i
\(254\) 0 0
\(255\) 1.88509 0.647165i 0.118049 0.0405270i
\(256\) 0 0
\(257\) 26.3596 + 15.2187i 1.64427 + 0.949318i 0.979292 + 0.202451i \(0.0648907\pi\)
0.664974 + 0.746866i \(0.268443\pi\)
\(258\) 0 0
\(259\) −28.8649 −1.79358
\(260\) 0 0
\(261\) 6.72834 0.416474
\(262\) 0 0
\(263\) 2.80980 + 1.62224i 0.173260 + 0.100032i 0.584122 0.811666i \(-0.301439\pi\)
−0.410862 + 0.911697i \(0.634772\pi\)
\(264\) 0 0
\(265\) 3.66152 + 10.6654i 0.224925 + 0.655173i
\(266\) 0 0
\(267\) −2.24496 + 1.29613i −0.137389 + 0.0793218i
\(268\) 0 0
\(269\) −0.554332 0.960132i −0.0337982 0.0585403i 0.848632 0.528984i \(-0.177427\pi\)
−0.882430 + 0.470444i \(0.844094\pi\)
\(270\) 0 0
\(271\) −15.0877 + 26.1327i −0.916515 + 1.58745i −0.111847 + 0.993725i \(0.535677\pi\)
−0.804668 + 0.593725i \(0.797657\pi\)
\(272\) 0 0
\(273\) −3.51351 0.809492i −0.212647 0.0489927i
\(274\) 0 0
\(275\) 0.686824 + 4.95260i 0.0414170 + 0.298653i
\(276\) 0 0
\(277\) 22.4941 12.9870i 1.35154 0.780311i 0.363073 0.931761i \(-0.381727\pi\)
0.988465 + 0.151449i \(0.0483941\pi\)
\(278\) 0 0
\(279\) −9.17548 15.8924i −0.549322 0.951453i
\(280\) 0 0
\(281\) 17.7827 1.06083 0.530413 0.847740i \(-0.322037\pi\)
0.530413 + 0.847740i \(0.322037\pi\)
\(282\) 0 0
\(283\) −6.37503 3.68062i −0.378956 0.218790i 0.298408 0.954438i \(-0.403544\pi\)
−0.677364 + 0.735648i \(0.736878\pi\)
\(284\) 0 0
\(285\) 0.386568 + 1.12601i 0.0228983 + 0.0666994i
\(286\) 0 0
\(287\) 11.4183i 0.674001i
\(288\) 0 0
\(289\) −1.18869 + 2.05887i −0.0699227 + 0.121110i
\(290\) 0 0
\(291\) −3.45963 −0.202807
\(292\) 0 0
\(293\) −14.5449 + 8.39750i −0.849722 + 0.490587i −0.860557 0.509354i \(-0.829884\pi\)
0.0108351 + 0.999941i \(0.496551\pi\)
\(294\) 0 0
\(295\) 18.7530 + 16.3318i 1.09184 + 0.950873i
\(296\) 0 0
\(297\) 1.20022 + 0.692946i 0.0696437 + 0.0402088i
\(298\) 0 0
\(299\) 15.1483 + 14.1133i 0.876050 + 0.816193i
\(300\) 0 0
\(301\) −14.7904 + 25.6177i −0.852504 + 1.47658i
\(302\) 0 0
\(303\) 3.83009 2.21130i 0.220033 0.127036i
\(304\) 0 0
\(305\) 7.04087 + 6.13183i 0.403159 + 0.351108i
\(306\) 0 0
\(307\) 3.12468i 0.178335i 0.996017 + 0.0891674i \(0.0284206\pi\)
−0.996017 + 0.0891674i \(0.971579\pi\)
\(308\) 0 0
\(309\) 2.09546 3.62944i 0.119207 0.206472i
\(310\) 0 0
\(311\) 18.6072 1.05512 0.527558 0.849519i \(-0.323108\pi\)
0.527558 + 0.849519i \(0.323108\pi\)
\(312\) 0 0
\(313\) 17.5732i 0.993295i 0.867952 + 0.496647i \(0.165436\pi\)
−0.867952 + 0.496647i \(0.834564\pi\)
\(314\) 0 0
\(315\) 27.7338 + 5.41719i 1.56262 + 0.305224i
\(316\) 0 0
\(317\) 22.2633i 1.25043i −0.780453 0.625215i \(-0.785011\pi\)
0.780453 0.625215i \(-0.214989\pi\)
\(318\) 0 0
\(319\) −1.14207 1.97813i −0.0639438 0.110754i
\(320\) 0 0
\(321\) 0.534885 + 0.926448i 0.0298544 + 0.0517093i
\(322\) 0 0
\(323\) 7.56428 + 4.36724i 0.420888 + 0.243000i
\(324\) 0 0
\(325\) −16.3492 + 7.59637i −0.906888 + 0.421371i
\(326\) 0 0
\(327\) 0.0297867 + 0.0171974i 0.00164721 + 0.000951017i
\(328\) 0 0
\(329\) −14.1755 24.5527i −0.781520 1.35363i
\(330\) 0 0
\(331\) 14.2026 + 24.5997i 0.780648 + 1.35212i 0.931565 + 0.363576i \(0.118444\pi\)
−0.150916 + 0.988547i \(0.548222\pi\)
\(332\) 0 0
\(333\) 19.8190i 1.08608i
\(334\) 0 0
\(335\) −9.53268 1.86200i −0.520826 0.101732i
\(336\) 0 0
\(337\) 8.87960i 0.483703i 0.970313 + 0.241851i \(0.0777547\pi\)
−0.970313 + 0.241851i \(0.922245\pi\)
\(338\) 0 0
\(339\) −3.75475 −0.203930
\(340\) 0 0
\(341\) −3.11491 + 5.39518i −0.168682 + 0.292165i
\(342\) 0 0
\(343\) 18.8993i 1.02047i
\(344\) 0 0
\(345\) 2.25700 + 1.96560i 0.121513 + 0.105824i
\(346\) 0 0
\(347\) 14.9652 8.64018i 0.803376 0.463829i −0.0412745 0.999148i \(-0.513142\pi\)
0.844650 + 0.535319i \(0.179808\pi\)
\(348\) 0 0
\(349\) −5.37189 + 9.30438i −0.287551 + 0.498052i −0.973225 0.229857i \(-0.926174\pi\)
0.685674 + 0.727909i \(0.259508\pi\)
\(350\) 0 0
\(351\) −1.12187 + 4.86934i −0.0598809 + 0.259906i
\(352\) 0 0
\(353\) −27.8598 16.0849i −1.48283 0.856111i −0.483017 0.875611i \(-0.660459\pi\)
−0.999810 + 0.0195003i \(0.993792\pi\)
\(354\) 0 0
\(355\) 11.3716 + 9.90346i 0.603544 + 0.525621i
\(356\) 0 0
\(357\) −3.31164 + 1.91198i −0.175271 + 0.101193i
\(358\) 0 0
\(359\) −13.8913 −0.733157 −0.366578 0.930387i \(-0.619471\pi\)
−0.366578 + 0.930387i \(0.619471\pi\)
\(360\) 0 0
\(361\) 6.89134 11.9361i 0.362702 0.628218i
\(362\) 0 0
\(363\) 2.33093i 0.122342i
\(364\) 0 0
\(365\) 9.85244 + 28.6987i 0.515700 + 1.50216i
\(366\) 0 0
\(367\) −15.6282 9.02293i −0.815784 0.470993i 0.0331762 0.999450i \(-0.489438\pi\)
−0.848961 + 0.528456i \(0.822771\pi\)
\(368\) 0 0
\(369\) 7.83996 0.408132
\(370\) 0 0
\(371\) −10.8176 18.7366i −0.561620 0.972754i
\(372\) 0 0
\(373\) 18.1267 10.4655i 0.938566 0.541882i 0.0490558 0.998796i \(-0.484379\pi\)
0.889511 + 0.456914i \(0.151045\pi\)
\(374\) 0 0
\(375\) −2.32524 + 1.17676i −0.120075 + 0.0607676i
\(376\) 0 0
\(377\) 5.61396 6.02567i 0.289134 0.310338i
\(378\) 0 0
\(379\) 12.2089 21.1464i 0.627129 1.08622i −0.360996 0.932567i \(-0.617563\pi\)
0.988125 0.153652i \(-0.0491033\pi\)
\(380\) 0 0
\(381\) 1.20961 + 2.09511i 0.0619702 + 0.107335i
\(382\) 0 0
\(383\) 25.9612 14.9887i 1.32656 0.765887i 0.341790 0.939776i \(-0.388967\pi\)
0.984765 + 0.173889i \(0.0556335\pi\)
\(384\) 0 0
\(385\) −3.11491 9.07325i −0.158750 0.462416i
\(386\) 0 0
\(387\) 17.5895 + 10.1553i 0.894123 + 0.516222i
\(388\) 0 0
\(389\) 3.80908 0.193128 0.0965640 0.995327i \(-0.469215\pi\)
0.0965640 + 0.995327i \(0.469215\pi\)
\(390\) 0 0
\(391\) 21.9582 1.11047
\(392\) 0 0
\(393\) 3.55990 + 2.05531i 0.179573 + 0.103677i
\(394\) 0 0
\(395\) −24.1212 + 8.28095i −1.21367 + 0.416660i
\(396\) 0 0
\(397\) −10.0330 + 5.79258i −0.503544 + 0.290721i −0.730176 0.683259i \(-0.760562\pi\)
0.226632 + 0.973980i \(0.427229\pi\)
\(398\) 0 0
\(399\) −1.14207 1.97813i −0.0571752 0.0990303i
\(400\) 0 0
\(401\) 9.74302 16.8754i 0.486543 0.842717i −0.513337 0.858187i \(-0.671591\pi\)
0.999880 + 0.0154696i \(0.00492431\pi\)
\(402\) 0 0
\(403\) −21.8885 5.04299i −1.09034 0.251209i
\(404\) 0 0
\(405\) 3.64964 18.6847i 0.181352 0.928450i
\(406\) 0 0
\(407\) 5.82679 3.36410i 0.288823 0.166752i
\(408\) 0 0
\(409\) −2.29811 3.98044i −0.113634 0.196820i 0.803599 0.595171i \(-0.202916\pi\)
−0.917233 + 0.398351i \(0.869583\pi\)
\(410\) 0 0
\(411\) 1.49852 0.0739167
\(412\) 0 0
\(413\) −41.3192 23.8556i −2.03318 1.17386i
\(414\) 0 0
\(415\) −7.28415 21.2176i −0.357565 1.04153i
\(416\) 0 0
\(417\) 3.49023i 0.170918i
\(418\) 0 0
\(419\) −3.38509 + 5.86315i −0.165373 + 0.286434i −0.936788 0.349899i \(-0.886216\pi\)
0.771415 + 0.636332i \(0.219549\pi\)
\(420\) 0 0
\(421\) −16.1087 −0.785088 −0.392544 0.919733i \(-0.628405\pi\)
−0.392544 + 0.919733i \(0.628405\pi\)
\(422\) 0 0
\(423\) −16.8582 + 9.73308i −0.819673 + 0.473238i
\(424\) 0 0
\(425\) −7.19475 + 17.7144i −0.348997 + 0.859276i
\(426\) 0 0
\(427\) −15.5135 8.95670i −0.750749 0.433445i
\(428\) 0 0
\(429\) 0.803594 0.246079i 0.0387979 0.0118808i
\(430\) 0 0
\(431\) −1.12887 + 1.95526i −0.0543757 + 0.0941816i −0.891932 0.452169i \(-0.850650\pi\)
0.837556 + 0.546351i \(0.183984\pi\)
\(432\) 0 0
\(433\) −8.03633 + 4.63978i −0.386201 + 0.222974i −0.680513 0.732736i \(-0.738243\pi\)
0.294312 + 0.955710i \(0.404910\pi\)
\(434\) 0 0
\(435\) 0.781873 0.897785i 0.0374879 0.0430455i
\(436\) 0 0
\(437\) 13.1162i 0.627432i
\(438\) 0 0
\(439\) 12.9659 22.4576i 0.618827 1.07184i −0.370873 0.928684i \(-0.620941\pi\)
0.989700 0.143157i \(-0.0457253\pi\)
\(440\) 0 0
\(441\) −33.5962 −1.59982
\(442\) 0 0
\(443\) 19.4318i 0.923231i 0.887080 + 0.461615i \(0.152730\pi\)
−0.887080 + 0.461615i \(0.847270\pi\)
\(444\) 0 0
\(445\) 4.76725 24.4064i 0.225990 1.15698i
\(446\) 0 0
\(447\) 3.65709i 0.172975i
\(448\) 0 0
\(449\) −12.7361 22.0595i −0.601052 1.04105i −0.992662 0.120921i \(-0.961415\pi\)
0.391610 0.920131i \(-0.371918\pi\)
\(450\) 0 0
\(451\) −1.33076 2.30494i −0.0626631 0.108536i
\(452\) 0 0
\(453\) 0.237288 + 0.136998i 0.0111488 + 0.00643674i
\(454\) 0 0
\(455\) 27.9919 20.3175i 1.31228 0.952498i
\(456\) 0 0
\(457\) −16.9321 9.77578i −0.792053 0.457292i 0.0486321 0.998817i \(-0.484514\pi\)
−0.840685 + 0.541525i \(0.817847\pi\)
\(458\) 0 0
\(459\) 2.64979 + 4.58958i 0.123682 + 0.214223i
\(460\) 0 0
\(461\) −16.1678 28.0034i −0.753008 1.30425i −0.946359 0.323118i \(-0.895269\pi\)
0.193351 0.981130i \(-0.438064\pi\)
\(462\) 0 0
\(463\) 28.8119i 1.33900i −0.742810 0.669502i \(-0.766507\pi\)
0.742810 0.669502i \(-0.233493\pi\)
\(464\) 0 0
\(465\) −3.18682 0.622476i −0.147785 0.0288666i
\(466\) 0 0
\(467\) 24.8085i 1.14800i −0.818856 0.573999i \(-0.805391\pi\)
0.818856 0.573999i \(-0.194609\pi\)
\(468\) 0 0
\(469\) 18.6351 0.860490
\(470\) 0 0
\(471\) 0.635830 1.10129i 0.0292975 0.0507448i
\(472\) 0 0
\(473\) 6.89506i 0.317035i
\(474\) 0 0
\(475\) −10.5813 4.29761i −0.485503 0.197188i
\(476\) 0 0
\(477\) −12.8648 + 7.42748i −0.589038 + 0.340081i
\(478\) 0 0
\(479\) −3.18945 + 5.52428i −0.145729 + 0.252411i −0.929645 0.368457i \(-0.879886\pi\)
0.783915 + 0.620868i \(0.213220\pi\)
\(480\) 0 0
\(481\) 17.7493 + 16.5365i 0.809297 + 0.754001i
\(482\) 0 0
\(483\) −4.97295 2.87113i −0.226277 0.130641i
\(484\) 0 0
\(485\) 21.7964 25.0277i 0.989723 1.13645i
\(486\) 0 0
\(487\) −15.8874 + 9.17260i −0.719927 + 0.415650i −0.814726 0.579846i \(-0.803113\pi\)
0.0947988 + 0.995496i \(0.469779\pi\)
\(488\) 0 0
\(489\) 1.08226 0.0489413
\(490\) 0 0
\(491\) 1.95963 3.39418i 0.0884369 0.153177i −0.818414 0.574629i \(-0.805146\pi\)
0.906851 + 0.421452i \(0.138480\pi\)
\(492\) 0 0
\(493\) 8.73447i 0.393381i
\(494\) 0 0
\(495\) −6.22982 + 2.13874i −0.280009 + 0.0961291i
\(496\) 0 0
\(497\) −25.0556 14.4659i −1.12390 0.648883i
\(498\) 0 0
\(499\) −23.6087 −1.05687 −0.528435 0.848974i \(-0.677221\pi\)
−0.528435 + 0.848974i \(0.677221\pi\)
\(500\) 0 0
\(501\) −0.371889 0.644130i −0.0166148 0.0287776i
\(502\) 0 0
\(503\) −15.9636 + 9.21658i −0.711781 + 0.410947i −0.811720 0.584047i \(-0.801469\pi\)
0.0999391 + 0.994994i \(0.468135\pi\)
\(504\) 0 0
\(505\) −8.13333 + 41.6393i −0.361928 + 1.85293i
\(506\) 0 0
\(507\) 1.69673 + 2.51063i 0.0753544 + 0.111501i
\(508\) 0 0
\(509\) 6.83848 11.8446i 0.303110 0.525002i −0.673729 0.738979i \(-0.735308\pi\)
0.976839 + 0.213977i \(0.0686416\pi\)
\(510\) 0 0
\(511\) −29.1079 50.4164i −1.28766 2.23029i
\(512\) 0 0
\(513\) −2.74147 + 1.58279i −0.121039 + 0.0698819i
\(514\) 0 0
\(515\) 13.0543 + 38.0253i 0.575243 + 1.67559i
\(516\) 0 0
\(517\) 5.72304 + 3.30420i 0.251699 + 0.145319i
\(518\) 0 0
\(519\) −0.809079 −0.0355146
\(520\) 0 0
\(521\) 25.9472 1.13677 0.568383 0.822764i \(-0.307569\pi\)
0.568383 + 0.822764i \(0.307569\pi\)
\(522\) 0 0
\(523\) −28.4246 16.4110i −1.24292 0.717601i −0.273234 0.961948i \(-0.588093\pi\)
−0.969688 + 0.244346i \(0.921427\pi\)
\(524\) 0 0
\(525\) 3.94567 3.07111i 0.172203 0.134034i
\(526\) 0 0
\(527\) −20.6309 + 11.9113i −0.898697 + 0.518863i
\(528\) 0 0
\(529\) 4.98680 + 8.63738i 0.216817 + 0.375538i
\(530\) 0 0
\(531\) −16.3796 + 28.3703i −0.710814 + 1.23117i
\(532\) 0 0
\(533\) 6.54147 7.02120i 0.283342 0.304122i
\(534\) 0 0
\(535\) −10.0720 1.96735i −0.435451 0.0850558i
\(536\) 0 0
\(537\) −1.03378 + 0.596851i −0.0446108 + 0.0257560i
\(538\) 0 0
\(539\) 5.70265 + 9.87728i 0.245630 + 0.425444i
\(540\) 0 0
\(541\) 22.8370 0.981839 0.490920 0.871205i \(-0.336661\pi\)
0.490920 + 0.871205i \(0.336661\pi\)
\(542\) 0 0
\(543\) −0.837243 0.483383i −0.0359296 0.0207439i
\(544\) 0 0
\(545\) −0.312072 + 0.107136i −0.0133677 + 0.00458922i
\(546\) 0 0
\(547\) 31.4513i 1.34476i −0.740207 0.672379i \(-0.765272\pi\)
0.740207 0.672379i \(-0.234728\pi\)
\(548\) 0 0
\(549\) −6.14979 + 10.6518i −0.262467 + 0.454606i
\(550\) 0 0
\(551\) 5.21733 0.222266
\(552\) 0 0
\(553\) 42.3749 24.4652i 1.80196 1.04036i
\(554\) 0 0
\(555\) 2.64452 + 2.30309i 0.112254 + 0.0977608i
\(556\) 0 0
\(557\) −15.9636 9.21658i −0.676399 0.390519i 0.122098 0.992518i \(-0.461038\pi\)
−0.798497 + 0.601999i \(0.794371\pi\)
\(558\) 0 0
\(559\) 23.7709 7.27920i 1.00540 0.307877i
\(560\) 0 0
\(561\) 0.445668 0.771919i 0.0188161 0.0325905i
\(562\) 0 0
\(563\) 8.51624 4.91685i 0.358917 0.207221i −0.309689 0.950838i \(-0.600225\pi\)
0.668605 + 0.743617i \(0.266892\pi\)
\(564\) 0 0
\(565\) 23.6557 27.1626i 0.995202 1.14274i
\(566\) 0 0
\(567\) 36.5261i 1.53395i
\(568\) 0 0
\(569\) −21.6017 + 37.4152i −0.905591 + 1.56853i −0.0854680 + 0.996341i \(0.527239\pi\)
−0.820123 + 0.572188i \(0.806095\pi\)
\(570\) 0 0
\(571\) 17.3106 0.724424 0.362212 0.932096i \(-0.382022\pi\)
0.362212 + 0.932096i \(0.382022\pi\)
\(572\) 0 0
\(573\) 0.188590i 0.00787847i
\(574\) 0 0
\(575\) −28.4392 + 3.94392i −1.18599 + 0.164473i
\(576\) 0 0
\(577\) 0.245757i 0.0102310i 0.999987 + 0.00511550i \(0.00162832\pi\)
−0.999987 + 0.00511550i \(0.998372\pi\)
\(578\) 0 0
\(579\) −1.12263 1.94445i −0.0466548 0.0808084i
\(580\) 0 0
\(581\) 21.5202 + 37.2741i 0.892809 + 1.54639i
\(582\) 0 0
\(583\) 4.36735 + 2.52149i 0.180877 + 0.104430i
\(584\) 0 0
\(585\) −13.9503 19.2196i −0.576772 0.794632i
\(586\) 0 0
\(587\) −15.9006 9.18021i −0.656287 0.378908i 0.134573 0.990904i \(-0.457034\pi\)
−0.790861 + 0.611996i \(0.790367\pi\)
\(588\) 0 0
\(589\) −7.11491 12.3234i −0.293165 0.507776i
\(590\) 0 0
\(591\) 1.89281 + 3.27845i 0.0778599 + 0.134857i
\(592\) 0 0
\(593\) 20.7514i 0.852159i 0.904686 + 0.426079i \(0.140106\pi\)
−0.904686 + 0.426079i \(0.859894\pi\)
\(594\) 0 0
\(595\) 7.03239 36.0030i 0.288300 1.47598i
\(596\) 0 0
\(597\) 0.964208i 0.0394624i
\(598\) 0 0
\(599\) 1.80908 0.0739170 0.0369585 0.999317i \(-0.488233\pi\)
0.0369585 + 0.999317i \(0.488233\pi\)
\(600\) 0 0
\(601\) 7.88585 13.6587i 0.321671 0.557150i −0.659162 0.752001i \(-0.729089\pi\)
0.980833 + 0.194851i \(0.0624223\pi\)
\(602\) 0 0
\(603\) 12.7951i 0.521058i
\(604\) 0 0
\(605\) −16.8624 14.6853i −0.685555 0.597043i
\(606\) 0 0
\(607\) 22.3330 12.8939i 0.906467 0.523349i 0.0271746 0.999631i \(-0.491349\pi\)
0.879293 + 0.476281i \(0.158016\pi\)
\(608\) 0 0
\(609\) −1.14207 + 1.97813i −0.0462792 + 0.0801579i
\(610\) 0 0
\(611\) −5.34945 + 23.2187i −0.216416 + 0.939326i
\(612\) 0 0
\(613\) 5.10085 + 2.94498i 0.206021 + 0.118946i 0.599461 0.800404i \(-0.295382\pi\)
−0.393440 + 0.919350i \(0.628715\pi\)
\(614\) 0 0
\(615\) 0.911050 1.04611i 0.0367371 0.0421833i
\(616\) 0 0
\(617\) −5.07106 + 2.92778i −0.204153 + 0.117868i −0.598591 0.801055i \(-0.704273\pi\)
0.394438 + 0.918923i \(0.370939\pi\)
\(618\) 0 0
\(619\) 29.6740 1.19270 0.596350 0.802725i \(-0.296617\pi\)
0.596350 + 0.802725i \(0.296617\pi\)
\(620\) 0 0
\(621\) −3.97908 + 6.89196i −0.159675 + 0.276565i
\(622\) 0 0
\(623\) 47.7113i 1.91151i
\(624\) 0 0
\(625\) 6.13659 24.2351i 0.245464 0.969406i
\(626\) 0 0
\(627\) 0.461087 + 0.266209i 0.0184141 + 0.0106314i
\(628\) 0 0
\(629\) 25.7283 1.02586
\(630\) 0 0
\(631\) 15.1483 + 26.2377i 0.603045 + 1.04450i 0.992357 + 0.123399i \(0.0393794\pi\)
−0.389312 + 0.921106i \(0.627287\pi\)
\(632\) 0 0
\(633\) 1.93935 1.11968i 0.0770821 0.0445034i
\(634\) 0 0
\(635\) −22.7772 4.44903i −0.903887 0.176554i
\(636\) 0 0
\(637\) −28.0319 + 30.0876i −1.11066 + 1.19212i
\(638\) 0 0
\(639\) −9.93246 + 17.2035i −0.392922 + 0.680561i
\(640\) 0 0
\(641\) 8.98604 + 15.5643i 0.354927 + 0.614752i 0.987105 0.160071i \(-0.0511723\pi\)
−0.632178 + 0.774823i \(0.717839\pi\)
\(642\) 0 0
\(643\) −23.1517 + 13.3666i −0.913014 + 0.527129i −0.881400 0.472371i \(-0.843398\pi\)
−0.0316144 + 0.999500i \(0.510065\pi\)
\(644\) 0 0
\(645\) 3.39905 1.16692i 0.133838 0.0459474i
\(646\) 0 0
\(647\) 19.8974 + 11.4878i 0.782248 + 0.451631i 0.837227 0.546856i \(-0.184176\pi\)
−0.0549781 + 0.998488i \(0.517509\pi\)
\(648\) 0 0
\(649\) 11.1212 0.436543
\(650\) 0 0
\(651\) 6.22982 0.244166
\(652\) 0 0
\(653\) 15.4153 + 8.90006i 0.603249 + 0.348286i 0.770319 0.637659i \(-0.220097\pi\)
−0.167070 + 0.985945i \(0.553430\pi\)
\(654\) 0 0
\(655\) −37.2966 + 12.8042i −1.45730 + 0.500301i
\(656\) 0 0
\(657\) −34.6166 + 19.9859i −1.35052 + 0.779725i
\(658\) 0 0
\(659\) −16.3587 28.3341i −0.637244 1.10374i −0.986035 0.166538i \(-0.946741\pi\)
0.348791 0.937200i \(-0.386592\pi\)
\(660\) 0 0
\(661\) 4.10095 7.10305i 0.159508 0.276276i −0.775183 0.631737i \(-0.782342\pi\)
0.934691 + 0.355460i \(0.115676\pi\)
\(662\) 0 0
\(663\) 3.13171 + 0.721529i 0.121626 + 0.0280219i
\(664\) 0 0
\(665\) 21.5055 + 4.20063i 0.833948 + 0.162893i
\(666\) 0 0
\(667\) 11.3589 6.55809i 0.439820 0.253930i
\(668\) 0 0
\(669\) −1.75551 3.04062i −0.0678718 0.117557i
\(670\) 0 0
\(671\) 4.17548 0.161193
\(672\) 0 0
\(673\) 7.36805 + 4.25395i 0.284017 + 0.163978i 0.635241 0.772314i \(-0.280901\pi\)
−0.351223 + 0.936292i \(0.614234\pi\)
\(674\) 0 0
\(675\) −4.25622 5.46827i −0.163822 0.210474i
\(676\) 0 0
\(677\) 12.9710i 0.498518i −0.968437 0.249259i \(-0.919813\pi\)
0.968437 0.249259i \(-0.0801870\pi\)
\(678\) 0 0
\(679\) −31.8378 + 55.1446i −1.22182 + 2.11626i
\(680\) 0 0
\(681\) −4.68793 −0.179642
\(682\) 0 0
\(683\) 25.3910 14.6595i 0.971561 0.560931i 0.0718490 0.997416i \(-0.477110\pi\)
0.899712 + 0.436485i \(0.143777\pi\)
\(684\) 0 0
\(685\) −9.44102 + 10.8406i −0.360723 + 0.414200i
\(686\) 0 0
\(687\) −2.53709 1.46479i −0.0967959 0.0558852i
\(688\) 0 0
\(689\) −4.08226 + 17.7186i −0.155522 + 0.675023i
\(690\) 0 0
\(691\) 18.6079 32.2299i 0.707880 1.22608i −0.257763 0.966208i \(-0.582985\pi\)
0.965642 0.259875i \(-0.0836814\pi\)
\(692\) 0 0
\(693\) 10.9442 6.31866i 0.415738 0.240026i
\(694\) 0 0
\(695\) −25.2491 21.9892i −0.957753 0.834098i
\(696\) 0 0
\(697\) 10.1775i 0.385502i
\(698\) 0 0
\(699\) 1.32528 2.29544i 0.0501265 0.0868217i
\(700\) 0 0
\(701\) −49.9472 −1.88648 −0.943240 0.332113i \(-0.892238\pi\)
−0.943240 + 0.332113i \(0.892238\pi\)
\(702\) 0 0
\(703\) 15.3682i 0.579623i
\(704\) 0 0
\(705\) −0.660304 + 3.38049i −0.0248685 + 0.127317i
\(706\) 0 0
\(707\) 81.3994i 3.06134i
\(708\) 0 0
\(709\) −15.2438 26.4030i −0.572492 0.991585i −0.996309 0.0858376i \(-0.972643\pi\)
0.423817 0.905748i \(-0.360690\pi\)
\(710\) 0 0
\(711\) −16.7981 29.0952i −0.629978 1.09115i
\(712\) 0 0
\(713\) −30.9805 17.8866i −1.16023 0.669859i
\(714\) 0 0
\(715\) −3.28263 + 7.36372i −0.122763 + 0.275387i
\(716\) 0 0
\(717\) 3.70440 + 2.13874i 0.138343 + 0.0798726i
\(718\) 0 0
\(719\) 0.816798 + 1.41474i 0.0304614 + 0.0527607i 0.880854 0.473388i \(-0.156969\pi\)
−0.850393 + 0.526148i \(0.823636\pi\)
\(720\) 0 0
\(721\) −38.5676 66.8010i −1.43633 2.48780i
\(722\) 0 0
\(723\) 0.321056i 0.0119402i
\(724\) 0 0
\(725\) 1.56881 + 11.3125i 0.0582640 + 0.420135i
\(726\) 0 0
\(727\) 17.7936i 0.659928i 0.943993 + 0.329964i \(0.107037\pi\)
−0.943993 + 0.329964i \(0.892963\pi\)
\(728\) 0 0
\(729\) 24.1102 0.892970
\(730\) 0 0
\(731\) 13.1832 22.8340i 0.487598 0.844545i
\(732\) 0 0
\(733\) 22.1438i 0.817901i 0.912557 + 0.408950i \(0.134105\pi\)
−0.912557 + 0.408950i \(0.865895\pi\)
\(734\) 0 0
\(735\) −3.90408 + 4.48286i −0.144004 + 0.165353i
\(736\) 0 0
\(737\) −3.76176 + 2.17185i −0.138566 + 0.0800013i
\(738\) 0 0
\(739\) 8.99228 15.5751i 0.330786 0.572939i −0.651880 0.758322i \(-0.726019\pi\)
0.982666 + 0.185383i \(0.0593527\pi\)
\(740\) 0 0
\(741\) −0.430988 + 1.87065i −0.0158327 + 0.0687202i
\(742\) 0 0
\(743\) 13.2873 + 7.67144i 0.487465 + 0.281438i 0.723522 0.690301i \(-0.242522\pi\)
−0.236057 + 0.971739i \(0.575855\pi\)
\(744\) 0 0
\(745\) −26.4562 23.0405i −0.969280 0.844137i
\(746\) 0 0
\(747\) 25.5929 14.7761i 0.936395 0.540628i
\(748\) 0 0
\(749\) 19.6894 0.719437
\(750\) 0 0
\(751\) 19.1762 33.2142i 0.699751 1.21200i −0.268802 0.963196i \(-0.586628\pi\)
0.968553 0.248809i \(-0.0800391\pi\)
\(752\) 0 0
\(753\) 5.88088i 0.214311i
\(754\) 0 0
\(755\) −2.48604 + 0.853474i −0.0904762 + 0.0310611i
\(756\) 0 0
\(757\) −2.29135 1.32291i −0.0832806 0.0480821i 0.457781 0.889065i \(-0.348644\pi\)
−0.541062 + 0.840983i \(0.681978\pi\)
\(758\) 0 0
\(759\) 1.33848 0.0485837
\(760\) 0 0
\(761\) −12.3176 21.3346i −0.446511 0.773380i 0.551645 0.834079i \(-0.314000\pi\)
−0.998156 + 0.0606991i \(0.980667\pi\)
\(762\) 0 0
\(763\) 0.548233 0.316523i 0.0198474 0.0114589i
\(764\) 0 0
\(765\) −24.7201 4.82853i −0.893758 0.174576i
\(766\) 0 0
\(767\) 11.7407 + 38.3405i 0.423933 + 1.38440i
\(768\) 0 0
\(769\) −7.05509 + 12.2198i −0.254413 + 0.440656i −0.964736 0.263220i \(-0.915216\pi\)
0.710323 + 0.703876i \(0.248549\pi\)
\(770\) 0 0
\(771\) 3.54737 + 6.14423i 0.127755 + 0.221279i
\(772\) 0 0
\(773\) 13.1130 7.57081i 0.471643 0.272303i −0.245284 0.969451i \(-0.578881\pi\)
0.716927 + 0.697148i \(0.245548\pi\)
\(774\) 0 0
\(775\) 24.5808 19.1324i 0.882968 0.687257i
\(776\) 0 0
\(777\) −5.82679 3.36410i −0.209035 0.120686i
\(778\) 0 0
\(779\) 6.07930 0.217814
\(780\) 0 0
\(781\) 6.74378 0.241311
\(782\) 0 0
\(783\) 2.74147 + 1.58279i 0.0979722 + 0.0565643i
\(784\) 0 0
\(785\) 3.96111 + 11.5381i 0.141378 + 0.411812i
\(786\) 0 0
\(787\) 27.7617 16.0282i 0.989597 0.571344i 0.0844431 0.996428i \(-0.473089\pi\)
0.905154 + 0.425084i \(0.139756\pi\)
\(788\) 0 0
\(789\) 0.378132 + 0.654944i 0.0134619 + 0.0233166i
\(790\) 0 0
\(791\) −34.5536 + 59.8486i −1.22859 + 2.12797i
\(792\) 0 0
\(793\) 4.40811 + 14.3951i 0.156537 + 0.511185i
\(794\) 0 0
\(795\) −0.503889 + 2.57971i −0.0178711 + 0.0914928i
\(796\) 0 0
\(797\) −37.4537 + 21.6239i −1.32668 + 0.765957i −0.984784 0.173781i \(-0.944401\pi\)
−0.341893 + 0.939739i \(0.611068\pi\)
\(798\) 0 0
\(799\) 12.6351 + 21.8847i 0.446998 + 0.774224i
\(800\) 0 0
\(801\) 32.7592 1.15749
\(802\) 0 0
\(803\) 11.7517 + 6.78485i 0.414709 + 0.239432i
\(804\) 0 0
\(805\) 52.1010 17.8866i 1.83632 0.630421i
\(806\) 0 0
\(807\) 0.258422i 0.00909687i
\(808\) 0 0
\(809\) −5.87737 + 10.1799i −0.206637 + 0.357907i −0.950653 0.310256i \(-0.899585\pi\)
0.744016 + 0.668162i \(0.232919\pi\)
\(810\) 0 0
\(811\) −32.4068 −1.13796 −0.568979 0.822352i \(-0.692661\pi\)
−0.568979 + 0.822352i \(0.692661\pi\)
\(812\) 0 0
\(813\) −6.09135 + 3.51684i −0.213633 + 0.123341i
\(814\) 0 0
\(815\) −6.81845 + 7.82928i −0.238840 + 0.274248i
\(816\) 0 0
\(817\) 13.6393 + 7.87467i 0.477180 + 0.275500i
\(818\) 0 0
\(819\) 33.3378 + 31.0599i 1.16492 + 1.08532i
\(820\) 0 0
\(821\) −16.0877 + 27.8648i −0.561466 + 0.972488i 0.435903 + 0.899994i \(0.356429\pi\)
−0.997369 + 0.0724940i \(0.976904\pi\)
\(822\) 0 0
\(823\) 22.9608 13.2564i 0.800363 0.462090i −0.0432348 0.999065i \(-0.513766\pi\)
0.843598 + 0.536975i \(0.180433\pi\)
\(824\) 0 0
\(825\) −0.438563 + 1.07980i −0.0152688 + 0.0375938i
\(826\) 0 0
\(827\) 50.5431i 1.75756i −0.477229 0.878779i \(-0.658359\pi\)
0.477229 0.878779i \(-0.341641\pi\)
\(828\) 0 0
\(829\) 3.44567 5.96807i 0.119673 0.207280i −0.799965 0.600047i \(-0.795149\pi\)
0.919638 + 0.392767i \(0.128482\pi\)
\(830\) 0 0
\(831\) 6.05433 0.210022
\(832\) 0 0
\(833\) 43.6133i 1.51111i
\(834\) 0 0
\(835\) 7.00275 + 1.36783i 0.242340 + 0.0473358i
\(836\) 0 0
\(837\) 8.63385i 0.298429i
\(838\) 0 0
\(839\) −23.1134 40.0336i −0.797964 1.38211i −0.920940 0.389705i \(-0.872577\pi\)
0.122975 0.992410i \(-0.460756\pi\)
\(840\) 0 0
\(841\) 11.8913 + 20.5964i 0.410046 + 0.710221i
\(842\) 0 0
\(843\) 3.58968 + 2.07250i 0.123635 + 0.0713809i
\(844\) 0 0
\(845\) −28.8522 3.54299i −0.992545 0.121882i
\(846\) 0 0
\(847\) 37.1537 + 21.4507i 1.27662 + 0.737055i
\(848\) 0 0
\(849\) −0.857926 1.48597i −0.0294440 0.0509984i
\(850\) 0 0
\(851\) 19.3176 + 33.4590i 0.662197 + 1.14696i
\(852\) 0 0
\(853\) 17.3274i 0.593280i −0.954989 0.296640i \(-0.904134\pi\)
0.954989 0.296640i \(-0.0958661\pi\)
\(854\) 0 0
\(855\) 2.88421 14.7660i 0.0986378 0.504986i
\(856\) 0 0
\(857\) 0.186033i 0.00635478i −0.999995 0.00317739i \(-0.998989\pi\)
0.999995 0.00317739i \(-0.00101140\pi\)
\(858\) 0 0
\(859\) 22.0947 0.753863 0.376931 0.926241i \(-0.376979\pi\)
0.376931 + 0.926241i \(0.376979\pi\)
\(860\) 0 0
\(861\) −1.33076 + 2.30494i −0.0453522 + 0.0785523i
\(862\) 0 0
\(863\) 17.5388i 0.597027i 0.954405 + 0.298514i \(0.0964908\pi\)
−0.954405 + 0.298514i \(0.903509\pi\)
\(864\) 0 0
\(865\) 5.09737 5.85305i 0.173316 0.199010i
\(866\) 0 0
\(867\) −0.479906 + 0.277074i −0.0162985 + 0.00940993i
\(868\) 0 0
\(869\) −5.70265 + 9.87728i −0.193449 + 0.335064i
\(870\) 0 0
\(871\) −11.4589 10.6759i −0.388269 0.361740i
\(872\) 0 0
\(873\) 37.8630 + 21.8602i 1.28147 + 0.739857i
\(874\) 0 0
\(875\) −2.64148 + 47.8924i −0.0892985 + 1.61906i
\(876\) 0 0
\(877\) 10.7590 6.21170i 0.363305 0.209754i −0.307224 0.951637i \(-0.599400\pi\)
0.670530 + 0.741883i \(0.266067\pi\)
\(878\) 0 0
\(879\) −3.91479 −0.132043
\(880\) 0 0
\(881\) 3.93171 6.80991i 0.132463 0.229432i −0.792163 0.610310i \(-0.791045\pi\)
0.924625 + 0.380878i \(0.124378\pi\)
\(882\) 0 0
\(883\) 18.9717i 0.638450i −0.947679 0.319225i \(-0.896577\pi\)
0.947679 0.319225i \(-0.103423\pi\)
\(884\) 0 0
\(885\) 1.88214 + 5.48239i 0.0632675 + 0.184288i
\(886\) 0 0
\(887\) 10.2459 + 5.91546i 0.344023 + 0.198622i 0.662049 0.749460i \(-0.269687\pi\)
−0.318027 + 0.948082i \(0.603020\pi\)
\(888\) 0 0
\(889\) 44.5264 1.49337
\(890\) 0 0
\(891\) −4.25698 7.37331i −0.142614 0.247015i
\(892\) 0 0
\(893\) −13.0723 + 7.54728i −0.437447 + 0.252560i
\(894\) 0 0
\(895\) 2.19526 11.2389i 0.0733795 0.375673i
\(896\) 0 0
\(897\) 1.41305 + 4.61445i 0.0471803 + 0.154072i
\(898\) 0 0
\(899\) −7.11491 + 12.3234i −0.237295 + 0.411008i
\(900\) 0 0
\(901\) 9.64207 + 16.7006i 0.321224 + 0.556376i
\(902\) 0 0
\(903\) −5.97130 + 3.44753i −0.198712 + 0.114727i
\(904\) 0 0
\(905\) 8.77170 3.01138i 0.291581 0.100102i
\(906\) 0 0
\(907\) −5.16917 2.98442i −0.171640 0.0990962i 0.411719 0.911311i \(-0.364928\pi\)
−0.583359 + 0.812215i \(0.698262\pi\)
\(908\) 0 0
\(909\) −55.8899 −1.85375
\(910\) 0 0
\(911\) −29.7952 −0.987158 −0.493579 0.869701i \(-0.664312\pi\)
−0.493579 + 0.869701i \(0.664312\pi\)
\(912\) 0 0
\(913\) −8.68832 5.01620i −0.287541 0.166012i
\(914\) 0 0
\(915\) 0.706658 + 2.05839i 0.0233614 + 0.0680481i
\(916\) 0 0
\(917\) 65.5210 37.8285i 2.16369 1.24921i
\(918\) 0 0
\(919\) 12.0070 + 20.7967i 0.396074 + 0.686021i 0.993238 0.116099i \(-0.0370389\pi\)
−0.597163 + 0.802120i \(0.703706\pi\)
\(920\) 0 0
\(921\) −0.364170 + 0.630760i −0.0119998 + 0.0207843i
\(922\) 0 0
\(923\) 7.11949 + 23.2494i 0.234341 + 0.765263i
\(924\) 0 0
\(925\) −33.3221 + 4.62109i −1.09562 + 0.151940i
\(926\) 0 0
\(927\) −45.8665 + 26.4810i −1.50645 + 0.869751i
\(928\) 0 0
\(929\) 0.350207 + 0.606577i 0.0114899 + 0.0199011i 0.871713 0.490016i \(-0.163009\pi\)
−0.860223 + 0.509918i \(0.829676\pi\)
\(930\) 0 0
\(931\) −26.0514 −0.853800
\(932\) 0 0
\(933\) 3.75612 + 2.16860i 0.122970 + 0.0709968i
\(934\) 0 0
\(935\) 2.77643 + 8.08731i 0.0907989 + 0.264483i
\(936\) 0 0
\(937\) 2.65849i 0.0868491i −0.999057 0.0434246i \(-0.986173\pi\)
0.999057 0.0434246i \(-0.0138268\pi\)
\(938\) 0 0
\(939\) −2.04809 + 3.54739i −0.0668369 + 0.115765i
\(940\) 0 0
\(941\) −26.8370 −0.874861 −0.437431 0.899252i \(-0.644111\pi\)
−0.437431 + 0.899252i \(0.644111\pi\)
\(942\) 0 0
\(943\) 13.2356 7.64158i 0.431010 0.248844i
\(944\) 0 0
\(945\) 10.0258 + 8.73141i 0.326140 + 0.284033i
\(946\) 0 0
\(947\) −0.0871459 0.0503137i −0.00283186 0.00163498i 0.498583 0.866842i \(-0.333854\pi\)
−0.501415 + 0.865207i \(0.667187\pi\)
\(948\) 0 0
\(949\) −10.9846 + 47.6772i −0.356574 + 1.54767i
\(950\) 0 0
\(951\) 2.59470 4.49416i 0.0841390 0.145733i
\(952\) 0 0
\(953\) 47.4924 27.4197i 1.53843 0.888212i 0.539497 0.841987i \(-0.318614\pi\)
0.998931 0.0462245i \(-0.0147190\pi\)
\(954\) 0 0
\(955\) 1.36430 + 1.18816i 0.0441478 + 0.0384479i
\(956\) 0 0
\(957\) 0.532418i 0.0172106i
\(958\) 0 0
\(959\) 13.7904 23.8857i 0.445315 0.771308i
\(960\) 0 0
\(961\) 7.81060 0.251955
\(962\) 0 0
\(963\) 13.5190i 0.435645i
\(964\) 0 0
\(965\) 21.1393 + 4.12910i 0.680499 + 0.132920i
\(966\) 0 0
\(967\) 57.0788i 1.83553i 0.397123 + 0.917765i \(0.370009\pi\)
−0.397123 + 0.917765i \(0.629991\pi\)
\(968\) 0 0
\(969\) 1.01797 + 1.76318i 0.0327019 + 0.0566414i
\(970\) 0 0
\(971\) −2.46735 4.27357i −0.0791810 0.137146i 0.823716 0.567003i \(-0.191897\pi\)
−0.902897 + 0.429857i \(0.858564\pi\)
\(972\) 0 0
\(973\) 55.6324 + 32.1194i 1.78349 + 1.02970i
\(974\) 0 0
\(975\) −4.18564 0.372000i −0.134048 0.0119135i
\(976\) 0 0
\(977\) 8.99957 + 5.19590i 0.287922 + 0.166232i 0.637004 0.770860i \(-0.280173\pi\)
−0.349083 + 0.937092i \(0.613507\pi\)
\(978\) 0 0
\(979\) −5.56058 9.63120i −0.177717 0.307814i
\(980\) 0 0
\(981\) −0.217329 0.376424i −0.00693877 0.0120183i
\(982\) 0 0
\(983\) 45.8531i 1.46249i 0.682117 + 0.731243i \(0.261059\pi\)
−0.682117 + 0.731243i \(0.738941\pi\)
\(984\) 0 0
\(985\) −35.6421 6.96189i −1.13565 0.221824i
\(986\) 0 0
\(987\) 6.60840i 0.210348i
\(988\) 0 0
\(989\) 39.5933 1.25899
\(990\) 0 0
\(991\) −14.0070 + 24.2608i −0.444947 + 0.770671i −0.998049 0.0624430i \(-0.980111\pi\)
0.553101 + 0.833114i \(0.313444\pi\)
\(992\) 0 0
\(993\) 6.62107i 0.210113i
\(994\) 0 0
\(995\) 6.97529 + 6.07472i 0.221132 + 0.192581i
\(996\) 0 0
\(997\) −10.4998 + 6.06204i −0.332531 + 0.191987i −0.656964 0.753922i \(-0.728160\pi\)
0.324433 + 0.945909i \(0.394826\pi\)
\(998\) 0 0
\(999\) −4.66228 + 8.07530i −0.147508 + 0.255491i
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 1040.2.dh.c.529.4 12
4.3 odd 2 260.2.ba.a.9.3 12
5.4 even 2 inner 1040.2.dh.c.529.3 12
12.11 even 2 2340.2.de.a.2089.5 12
13.3 even 3 inner 1040.2.dh.c.289.3 12
20.3 even 4 1300.2.i.i.1101.4 12
20.7 even 4 1300.2.i.i.1101.3 12
20.19 odd 2 260.2.ba.a.9.4 yes 12
52.3 odd 6 260.2.ba.a.29.4 yes 12
52.7 even 12 3380.2.d.c.1689.7 12
52.19 even 12 3380.2.d.c.1689.8 12
52.35 odd 6 3380.2.c.a.2029.4 6
52.43 odd 6 3380.2.c.b.2029.4 6
60.59 even 2 2340.2.de.a.2089.6 12
65.29 even 6 inner 1040.2.dh.c.289.4 12
156.107 even 6 2340.2.de.a.289.5 12
260.3 even 12 1300.2.i.i.601.4 12
260.19 even 12 3380.2.d.c.1689.5 12
260.59 even 12 3380.2.d.c.1689.6 12
260.107 even 12 1300.2.i.i.601.3 12
260.139 odd 6 3380.2.c.a.2029.3 6
260.159 odd 6 260.2.ba.a.29.3 yes 12
260.199 odd 6 3380.2.c.b.2029.3 6
780.419 even 6 2340.2.de.a.289.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.ba.a.9.3 12 4.3 odd 2
260.2.ba.a.9.4 yes 12 20.19 odd 2
260.2.ba.a.29.3 yes 12 260.159 odd 6
260.2.ba.a.29.4 yes 12 52.3 odd 6
1040.2.dh.c.289.3 12 13.3 even 3 inner
1040.2.dh.c.289.4 12 65.29 even 6 inner
1040.2.dh.c.529.3 12 5.4 even 2 inner
1040.2.dh.c.529.4 12 1.1 even 1 trivial
1300.2.i.i.601.3 12 260.107 even 12
1300.2.i.i.601.4 12 260.3 even 12
1300.2.i.i.1101.3 12 20.7 even 4
1300.2.i.i.1101.4 12 20.3 even 4
2340.2.de.a.289.5 12 156.107 even 6
2340.2.de.a.289.6 12 780.419 even 6
2340.2.de.a.2089.5 12 12.11 even 2
2340.2.de.a.2089.6 12 60.59 even 2
3380.2.c.a.2029.3 6 260.139 odd 6
3380.2.c.a.2029.4 6 52.35 odd 6
3380.2.c.b.2029.3 6 260.199 odd 6
3380.2.c.b.2029.4 6 52.43 odd 6
3380.2.d.c.1689.5 12 260.19 even 12
3380.2.d.c.1689.6 12 260.59 even 12
3380.2.d.c.1689.7 12 52.7 even 12
3380.2.d.c.1689.8 12 52.19 even 12