Properties

Label 162.7.d.e.107.1
Level $162$
Weight $7$
Character 162.107
Analytic conductor $37.269$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,7,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.d (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: \(37.2687615464\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{12} \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.1
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.7.d.e.53.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-43.4287 + 25.0736i) q^{5} +(-28.1325 + 48.7269i) q^{7} -181.019i q^{8} +O(q^{10})\) \(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-43.4287 + 25.0736i) q^{5} +(-28.1325 + 48.7269i) q^{7} -181.019i q^{8} +283.675 q^{10} +(1412.94 + 815.764i) q^{11} +(-1735.09 - 3005.26i) q^{13} +(275.641 - 159.141i) q^{14} +(-512.000 + 886.810i) q^{16} +599.995i q^{17} +5353.81 q^{19} +(-1389.72 - 802.355i) q^{20} +(-4614.66 - 7992.82i) q^{22} +(817.994 - 472.269i) q^{23} +(-6555.13 + 11353.8i) q^{25} +19630.3i q^{26} -1800.48 q^{28} +(13159.6 + 7597.70i) q^{29} +(-21167.0 - 36662.3i) q^{31} +(5016.55 - 2896.31i) q^{32} +(1697.04 - 2939.36i) q^{34} -2821.53i q^{35} -53825.9 q^{37} +(-26228.2 - 15142.9i) q^{38} +(4538.81 + 7861.44i) q^{40} +(-97537.2 + 56313.1i) q^{41} +(38675.4 - 66987.7i) q^{43} +52208.9i q^{44} -5343.12 q^{46} +(164513. + 94981.5i) q^{47} +(57241.6 + 99145.4i) q^{49} +(64226.9 - 37081.4i) q^{50} +(55522.7 - 96168.2i) q^{52} +243552. i q^{53} -81816.5 q^{55} +(8820.50 + 5092.52i) q^{56} +(-42979.1 - 74442.0i) q^{58} +(-72989.8 + 42140.7i) q^{59} +(-49191.3 + 85201.9i) q^{61} +239477. i q^{62} -32768.0 q^{64} +(150705. + 87009.7i) q^{65} +(123800. + 214427. i) q^{67} +(-16627.5 + 9599.92i) q^{68} +(-7980.49 + 13822.6i) q^{70} +411915. i q^{71} +368946. q^{73} +(263692. + 152243. i) q^{74} +(85661.0 + 148369. i) q^{76} +(-79499.2 + 45898.9i) q^{77} +(-421907. + 730765. i) q^{79} -51350.7i q^{80} +637110. q^{82} +(407498. + 235269. i) q^{83} +(-15044.0 - 26057.0i) q^{85} +(-378940. + 218781. i) q^{86} +(147669. - 255770. i) q^{88} +752753. i q^{89} +195249. q^{91} +(26175.8 + 15112.6i) q^{92} +(-537296. - 930624. i) q^{94} +(-232509. + 134239. i) q^{95} +(-230930. + 399983. i) q^{97} -647615. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 128 q^{4} - 836 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 128 q^{4} - 836 q^{7} - 3840 q^{10} - 440 q^{13} - 4096 q^{16} - 13376 q^{19} - 19200 q^{22} + 39200 q^{25} - 53504 q^{28} - 160172 q^{31} + 78336 q^{34} - 301088 q^{37} - 61440 q^{40} - 90152 q^{43} + 274944 q^{46} + 202560 q^{49} + 14080 q^{52} - 269640 q^{55} - 86016 q^{58} - 584144 q^{61} - 262144 q^{64} + 766792 q^{67} + 867840 q^{70} + 3149512 q^{73} - 214016 q^{76} - 323000 q^{79} + 2081280 q^{82} + 2720520 q^{85} + 614400 q^{88} - 3921808 q^{91} - 1970688 q^{94} - 4432940 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.89898 2.82843i −0.612372 0.353553i
\(3\) 0 0
\(4\) 16.0000 + 27.7128i 0.250000 + 0.433013i
\(5\) −43.4287 + 25.0736i −0.347430 + 0.200589i −0.663553 0.748130i \(-0.730952\pi\)
0.316123 + 0.948718i \(0.397619\pi\)
\(6\) 0 0
\(7\) −28.1325 + 48.7269i −0.0820189 + 0.142061i −0.904117 0.427285i \(-0.859470\pi\)
0.822098 + 0.569346i \(0.192803\pi\)
\(8\) 181.019i 0.353553i
\(9\) 0 0
\(10\) 283.675 0.283675
\(11\) 1412.94 + 815.764i 1.06157 + 0.612896i 0.925865 0.377854i \(-0.123338\pi\)
0.135701 + 0.990750i \(0.456671\pi\)
\(12\) 0 0
\(13\) −1735.09 3005.26i −0.789752 1.36789i −0.926119 0.377233i \(-0.876876\pi\)
0.136366 0.990658i \(-0.456458\pi\)
\(14\) 275.641 159.141i 0.100452 0.0579961i
\(15\) 0 0
\(16\) −512.000 + 886.810i −0.125000 + 0.216506i
\(17\) 599.995i 0.122124i 0.998134 + 0.0610620i \(0.0194487\pi\)
−0.998134 + 0.0610620i \(0.980551\pi\)
\(18\) 0 0
\(19\) 5353.81 0.780553 0.390276 0.920698i \(-0.372379\pi\)
0.390276 + 0.920698i \(0.372379\pi\)
\(20\) −1389.72 802.355i −0.173715 0.100294i
\(21\) 0 0
\(22\) −4614.66 7992.82i −0.433383 0.750641i
\(23\) 817.994 472.269i 0.0672306 0.0388156i −0.466008 0.884781i \(-0.654308\pi\)
0.533238 + 0.845965i \(0.320975\pi\)
\(24\) 0 0
\(25\) −6555.13 + 11353.8i −0.419528 + 0.726644i
\(26\) 19630.3i 1.11688i
\(27\) 0 0
\(28\) −1800.48 −0.0820189
\(29\) 13159.6 + 7597.70i 0.539571 + 0.311522i 0.744905 0.667170i \(-0.232495\pi\)
−0.205334 + 0.978692i \(0.565828\pi\)
\(30\) 0 0
\(31\) −21167.0 36662.3i −0.710517 1.23065i −0.964663 0.263486i \(-0.915128\pi\)
0.254146 0.967166i \(-0.418206\pi\)
\(32\) 5016.55 2896.31i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 1697.04 2939.36i 0.0431773 0.0747853i
\(35\) 2821.53i 0.0658082i
\(36\) 0 0
\(37\) −53825.9 −1.06264 −0.531320 0.847171i \(-0.678304\pi\)
−0.531320 + 0.847171i \(0.678304\pi\)
\(38\) −26228.2 15142.9i −0.477989 0.275967i
\(39\) 0 0
\(40\) 4538.81 + 7861.44i 0.0709188 + 0.122835i
\(41\) −97537.2 + 56313.1i −1.41520 + 0.817068i −0.995872 0.0907662i \(-0.971068\pi\)
−0.419330 + 0.907834i \(0.637735\pi\)
\(42\) 0 0
\(43\) 38675.4 66987.7i 0.486440 0.842538i −0.513439 0.858126i \(-0.671629\pi\)
0.999879 + 0.0155879i \(0.00496197\pi\)
\(44\) 52208.9i 0.612896i
\(45\) 0 0
\(46\) −5343.12 −0.0548935
\(47\) 164513. + 94981.5i 1.58455 + 0.914840i 0.994183 + 0.107705i \(0.0343503\pi\)
0.590367 + 0.807135i \(0.298983\pi\)
\(48\) 0 0
\(49\) 57241.6 + 99145.4i 0.486546 + 0.842722i
\(50\) 64226.9 37081.4i 0.513815 0.296651i
\(51\) 0 0
\(52\) 55522.7 96168.2i 0.394876 0.683946i
\(53\) 243552.i 1.63592i 0.575272 + 0.817962i \(0.304896\pi\)
−0.575272 + 0.817962i \(0.695104\pi\)
\(54\) 0 0
\(55\) −81816.5 −0.491760
\(56\) 8820.50 + 5092.52i 0.0502261 + 0.0289980i
\(57\) 0 0
\(58\) −42979.1 74442.0i −0.220279 0.381535i
\(59\) −72989.8 + 42140.7i −0.355391 + 0.205185i −0.667057 0.745007i \(-0.732446\pi\)
0.311666 + 0.950192i \(0.399113\pi\)
\(60\) 0 0
\(61\) −49191.3 + 85201.9i −0.216720 + 0.375370i −0.953803 0.300432i \(-0.902869\pi\)
0.737083 + 0.675802i \(0.236203\pi\)
\(62\) 239477.i 1.00482i
\(63\) 0 0
\(64\) −32768.0 −0.125000
\(65\) 150705. + 87009.7i 0.548767 + 0.316831i
\(66\) 0 0
\(67\) 123800. + 214427.i 0.411618 + 0.712944i 0.995067 0.0992064i \(-0.0316304\pi\)
−0.583449 + 0.812150i \(0.698297\pi\)
\(68\) −16627.5 + 9599.92i −0.0528812 + 0.0305310i
\(69\) 0 0
\(70\) −7980.49 + 13822.6i −0.0232667 + 0.0402992i
\(71\) 411915.i 1.15089i 0.817842 + 0.575443i \(0.195170\pi\)
−0.817842 + 0.575443i \(0.804830\pi\)
\(72\) 0 0
\(73\) 368946. 0.948406 0.474203 0.880416i \(-0.342736\pi\)
0.474203 + 0.880416i \(0.342736\pi\)
\(74\) 263692. + 152243.i 0.650732 + 0.375700i
\(75\) 0 0
\(76\) 85661.0 + 148369.i 0.195138 + 0.337989i
\(77\) −79499.2 + 45898.9i −0.174137 + 0.100538i
\(78\) 0 0
\(79\) −421907. + 730765.i −0.855728 + 1.48216i 0.0202403 + 0.999795i \(0.493557\pi\)
−0.875968 + 0.482369i \(0.839776\pi\)
\(80\) 51350.7i 0.100294i
\(81\) 0 0
\(82\) 637110. 1.15551
\(83\) 407498. + 235269.i 0.712675 + 0.411463i 0.812051 0.583587i \(-0.198351\pi\)
−0.0993759 + 0.995050i \(0.531685\pi\)
\(84\) 0 0
\(85\) −15044.0 26057.0i −0.0244967 0.0424295i
\(86\) −378940. + 218781.i −0.595765 + 0.343965i
\(87\) 0 0
\(88\) 147669. 255770.i 0.216691 0.375320i
\(89\) 752753.i 1.06778i 0.845553 + 0.533891i \(0.179271\pi\)
−0.845553 + 0.533891i \(0.820729\pi\)
\(90\) 0 0
\(91\) 195249. 0.259098
\(92\) 26175.8 + 15112.6i 0.0336153 + 0.0194078i
\(93\) 0 0
\(94\) −537296. 930624.i −0.646890 1.12045i
\(95\) −232509. + 134239.i −0.271187 + 0.156570i
\(96\) 0 0
\(97\) −230930. + 399983.i −0.253026 + 0.438254i −0.964358 0.264603i \(-0.914759\pi\)
0.711331 + 0.702857i \(0.248093\pi\)
\(98\) 647615.i 0.688080i
\(99\) 0 0
\(100\) −419528. −0.419528
\(101\) −1.06425e6 614444.i −1.03295 0.596373i −0.115121 0.993352i \(-0.536725\pi\)
−0.917828 + 0.396978i \(0.870059\pi\)
\(102\) 0 0
\(103\) 273863. + 474344.i 0.250623 + 0.434092i 0.963698 0.266996i \(-0.0860311\pi\)
−0.713074 + 0.701088i \(0.752698\pi\)
\(104\) −544010. + 314084.i −0.483623 + 0.279220i
\(105\) 0 0
\(106\) 688868. 1.19315e6i 0.578387 1.00180i
\(107\) 90822.4i 0.0741381i 0.999313 + 0.0370690i \(0.0118021\pi\)
−0.999313 + 0.0370690i \(0.988198\pi\)
\(108\) 0 0
\(109\) −1.08845e6 −0.840485 −0.420242 0.907412i \(-0.638055\pi\)
−0.420242 + 0.907412i \(0.638055\pi\)
\(110\) 400818. + 231412.i 0.301140 + 0.173863i
\(111\) 0 0
\(112\) −28807.6 49896.3i −0.0205047 0.0355152i
\(113\) 2.15675e6 1.24520e6i 1.49474 0.862987i 0.494756 0.869032i \(-0.335257\pi\)
0.999982 + 0.00604466i \(0.00192409\pi\)
\(114\) 0 0
\(115\) −23683.0 + 41020.1i −0.0155719 + 0.0269714i
\(116\) 486253.i 0.311522i
\(117\) 0 0
\(118\) 476768. 0.290175
\(119\) −29235.9 16879.3i −0.0173490 0.0100165i
\(120\) 0 0
\(121\) 445162. + 771042.i 0.251282 + 0.435233i
\(122\) 481975. 278268.i 0.265427 0.153244i
\(123\) 0 0
\(124\) 677344. 1.17319e6i 0.355259 0.615326i
\(125\) 1.44099e6i 0.737788i
\(126\) 0 0
\(127\) −3.12962e6 −1.52785 −0.763924 0.645306i \(-0.776730\pi\)
−0.763924 + 0.645306i \(0.776730\pi\)
\(128\) 160530. + 92681.9i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −492201. 852517.i −0.224033 0.388037i
\(131\) −973306. + 561939.i −0.432948 + 0.249963i −0.700602 0.713553i \(-0.747085\pi\)
0.267654 + 0.963515i \(0.413752\pi\)
\(132\) 0 0
\(133\) −150616. + 260875.i −0.0640201 + 0.110886i
\(134\) 1.40063e6i 0.582116i
\(135\) 0 0
\(136\) 108611. 0.0431773
\(137\) −1.82514e6 1.05374e6i −0.709797 0.409802i 0.101189 0.994867i \(-0.467735\pi\)
−0.810986 + 0.585066i \(0.801069\pi\)
\(138\) 0 0
\(139\) −78992.8 136820.i −0.0294133 0.0509453i 0.850944 0.525256i \(-0.176031\pi\)
−0.880357 + 0.474311i \(0.842697\pi\)
\(140\) 78192.5 45144.5i 0.0284958 0.0164521i
\(141\) 0 0
\(142\) 1.16507e6 2.01796e6i 0.406900 0.704771i
\(143\) 5.66168e6i 1.93614i
\(144\) 0 0
\(145\) −762007. −0.249951
\(146\) −1.80746e6 1.04354e6i −0.580777 0.335312i
\(147\) 0 0
\(148\) −861215. 1.49167e6i −0.265660 0.460137i
\(149\) −176935. + 102154.i −0.0534879 + 0.0308812i −0.526505 0.850172i \(-0.676498\pi\)
0.473018 + 0.881053i \(0.343165\pi\)
\(150\) 0 0
\(151\) −1.48147e6 + 2.56597e6i −0.430289 + 0.745283i −0.996898 0.0787039i \(-0.974922\pi\)
0.566609 + 0.823987i \(0.308255\pi\)
\(152\) 969144.i 0.275967i
\(153\) 0 0
\(154\) 519287. 0.142182
\(155\) 1.83851e6 + 1.06147e6i 0.493710 + 0.285043i
\(156\) 0 0
\(157\) 1.30241e6 + 2.25585e6i 0.336550 + 0.582922i 0.983781 0.179372i \(-0.0574065\pi\)
−0.647231 + 0.762294i \(0.724073\pi\)
\(158\) 4.13383e6 2.38667e6i 1.04805 0.605091i
\(159\) 0 0
\(160\) −145242. + 251566.i −0.0354594 + 0.0614175i
\(161\) 53144.4i 0.0127344i
\(162\) 0 0
\(163\) 5.62696e6 1.29930 0.649652 0.760232i \(-0.274915\pi\)
0.649652 + 0.760232i \(0.274915\pi\)
\(164\) −3.12119e6 1.80202e6i −0.707601 0.408534i
\(165\) 0 0
\(166\) −1.33088e6 2.30516e6i −0.290948 0.503937i
\(167\) −1.52697e6 + 881596.i −0.327854 + 0.189287i −0.654888 0.755726i \(-0.727284\pi\)
0.327034 + 0.945013i \(0.393951\pi\)
\(168\) 0 0
\(169\) −3.60764e6 + 6.24862e6i −0.747417 + 1.29456i
\(170\) 170204.i 0.0346435i
\(171\) 0 0
\(172\) 2.47522e6 0.486440
\(173\) −6.95934e6 4.01798e6i −1.34409 0.776013i −0.356689 0.934223i \(-0.616094\pi\)
−0.987406 + 0.158210i \(0.949428\pi\)
\(174\) 0 0
\(175\) −368824. 638822.i −0.0688185 0.119197i
\(176\) −1.44686e6 + 835342.i −0.265392 + 0.153224i
\(177\) 0 0
\(178\) 2.12911e6 3.68772e6i 0.377518 0.653880i
\(179\) 9.88186e6i 1.72298i −0.507776 0.861489i \(-0.669532\pi\)
0.507776 0.861489i \(-0.330468\pi\)
\(180\) 0 0
\(181\) 3.82714e6 0.645414 0.322707 0.946499i \(-0.395407\pi\)
0.322707 + 0.946499i \(0.395407\pi\)
\(182\) −956521. 552247.i −0.158665 0.0916051i
\(183\) 0 0
\(184\) −85489.9 148073.i −0.0137234 0.0237696i
\(185\) 2.33759e6 1.34961e6i 0.369193 0.213154i
\(186\) 0 0
\(187\) −489454. + 847760.i −0.0748492 + 0.129643i
\(188\) 6.07881e6i 0.914840i
\(189\) 0 0
\(190\) 1.51874e6 0.221424
\(191\) 3.79194e6 + 2.18928e6i 0.544204 + 0.314196i 0.746781 0.665070i \(-0.231598\pi\)
−0.202577 + 0.979266i \(0.564932\pi\)
\(192\) 0 0
\(193\) 445928. + 772370.i 0.0620287 + 0.107437i 0.895372 0.445319i \(-0.146910\pi\)
−0.833343 + 0.552756i \(0.813576\pi\)
\(194\) 2.26264e6 1.30634e6i 0.309892 0.178916i
\(195\) 0 0
\(196\) −1.83173e6 + 3.17265e6i −0.243273 + 0.421361i
\(197\) 4.90719e6i 0.641850i 0.947105 + 0.320925i \(0.103994\pi\)
−0.947105 + 0.320925i \(0.896006\pi\)
\(198\) 0 0
\(199\) −8.34946e6 −1.05950 −0.529748 0.848155i \(-0.677713\pi\)
−0.529748 + 0.848155i \(0.677713\pi\)
\(200\) 2.05526e6 + 1.18661e6i 0.256908 + 0.148326i
\(201\) 0 0
\(202\) 3.47582e6 + 6.02029e6i 0.421699 + 0.730405i
\(203\) −740424. + 427484.i −0.0885101 + 0.0511013i
\(204\) 0 0
\(205\) 2.82394e6 4.89121e6i 0.327789 0.567747i
\(206\) 3.09840e6i 0.354435i
\(207\) 0 0
\(208\) 3.55346e6 0.394876
\(209\) 7.56464e6 + 4.36745e6i 0.828609 + 0.478398i
\(210\) 0 0
\(211\) 6.48355e6 + 1.12298e7i 0.690185 + 1.19544i 0.971777 + 0.235902i \(0.0758044\pi\)
−0.281592 + 0.959534i \(0.590862\pi\)
\(212\) −6.74950e6 + 3.89682e6i −0.708376 + 0.408981i
\(213\) 0 0
\(214\) 256884. 444937.i 0.0262118 0.0454001i
\(215\) 3.87892e6i 0.390297i
\(216\) 0 0
\(217\) 2.38192e6 0.233103
\(218\) 5.33230e6 + 3.07861e6i 0.514690 + 0.297156i
\(219\) 0 0
\(220\) −1.30906e6 2.26737e6i −0.122940 0.212938i
\(221\) 1.80314e6 1.04104e6i 0.167052 0.0964476i
\(222\) 0 0
\(223\) −1.88621e6 + 3.26702e6i −0.170089 + 0.294603i −0.938451 0.345413i \(-0.887739\pi\)
0.768362 + 0.640016i \(0.221072\pi\)
\(224\) 325921.i 0.0289980i
\(225\) 0 0
\(226\) −1.40878e7 −1.22045
\(227\) 4.35856e6 + 2.51641e6i 0.372619 + 0.215132i 0.674602 0.738182i \(-0.264315\pi\)
−0.301983 + 0.953313i \(0.597649\pi\)
\(228\) 0 0
\(229\) −1.43726e6 2.48941e6i −0.119682 0.207295i 0.799960 0.600054i \(-0.204854\pi\)
−0.919642 + 0.392758i \(0.871521\pi\)
\(230\) 232045. 133971.i 0.0190717 0.0110110i
\(231\) 0 0
\(232\) 1.37533e6 2.38214e6i 0.110140 0.190767i
\(233\) 2.23245e7i 1.76487i 0.470431 + 0.882437i \(0.344098\pi\)
−0.470431 + 0.882437i \(0.655902\pi\)
\(234\) 0 0
\(235\) −9.52611e6 −0.734027
\(236\) −2.33567e6 1.34850e6i −0.177695 0.102593i
\(237\) 0 0
\(238\) 95483.9 + 165383.i 0.00708271 + 0.0122676i
\(239\) −1.01660e7 + 5.86937e6i −0.744661 + 0.429930i −0.823761 0.566937i \(-0.808128\pi\)
0.0791008 + 0.996867i \(0.474795\pi\)
\(240\) 0 0
\(241\) 1.32692e7 2.29829e7i 0.947969 1.64193i 0.198273 0.980147i \(-0.436467\pi\)
0.749696 0.661783i \(-0.230200\pi\)
\(242\) 5.03643e6i 0.355367i
\(243\) 0 0
\(244\) −3.14825e6 −0.216720
\(245\) −4.97186e6 2.87051e6i −0.338081 0.195191i
\(246\) 0 0
\(247\) −9.28932e6 1.60896e7i −0.616443 1.06771i
\(248\) −6.63659e6 + 3.83164e6i −0.435101 + 0.251206i
\(249\) 0 0
\(250\) −4.07574e6 + 7.05939e6i −0.260847 + 0.451801i
\(251\) 2.64855e7i 1.67489i 0.546521 + 0.837446i \(0.315952\pi\)
−0.546521 + 0.837446i \(0.684048\pi\)
\(252\) 0 0
\(253\) 1.54104e6 0.0951596
\(254\) 1.53319e7 + 8.85189e6i 0.935612 + 0.540176i
\(255\) 0 0
\(256\) −524288. 908093.i −0.0312500 0.0541266i
\(257\) 1.93078e7 1.11473e7i 1.13745 0.656708i 0.191653 0.981463i \(-0.438615\pi\)
0.945798 + 0.324755i \(0.105282\pi\)
\(258\) 0 0
\(259\) 1.51426e6 2.62277e6i 0.0871565 0.150960i
\(260\) 5.56862e6i 0.316831i
\(261\) 0 0
\(262\) 6.35761e6 0.353501
\(263\) −1.50734e6 870261.i −0.0828596 0.0478390i 0.457998 0.888953i \(-0.348567\pi\)
−0.540857 + 0.841114i \(0.681900\pi\)
\(264\) 0 0
\(265\) −6.10671e6 1.05771e7i −0.328148 0.568369i
\(266\) 1.47573e6 852013.i 0.0784082 0.0452690i
\(267\) 0 0
\(268\) −3.96158e6 + 6.86167e6i −0.205809 + 0.356472i
\(269\) 3.21970e6i 0.165409i 0.996574 + 0.0827044i \(0.0263557\pi\)
−0.996574 + 0.0827044i \(0.973644\pi\)
\(270\) 0 0
\(271\) 8.71025e6 0.437646 0.218823 0.975765i \(-0.429778\pi\)
0.218823 + 0.975765i \(0.429778\pi\)
\(272\) −532081. 307197.i −0.0264406 0.0152655i
\(273\) 0 0
\(274\) 5.96088e6 + 1.03245e7i 0.289774 + 0.501903i
\(275\) −1.85241e7 + 1.06949e7i −0.890714 + 0.514254i
\(276\) 0 0
\(277\) −2.37163e6 + 4.10779e6i −0.111586 + 0.193272i −0.916410 0.400241i \(-0.868926\pi\)
0.804824 + 0.593513i \(0.202260\pi\)
\(278\) 893702.i 0.0415967i
\(279\) 0 0
\(280\) −510751. −0.0232667
\(281\) 6.35229e6 + 3.66750e6i 0.286294 + 0.165292i 0.636269 0.771467i \(-0.280477\pi\)
−0.349976 + 0.936759i \(0.613810\pi\)
\(282\) 0 0
\(283\) −1.93466e7 3.35093e7i −0.853581 1.47845i −0.877955 0.478743i \(-0.841093\pi\)
0.0243739 0.999703i \(-0.492241\pi\)
\(284\) −1.14153e7 + 6.59064e6i −0.498348 + 0.287722i
\(285\) 0 0
\(286\) −1.60137e7 + 2.77365e7i −0.684530 + 1.18564i
\(287\) 6.33691e6i 0.268060i
\(288\) 0 0
\(289\) 2.37776e7 0.985086
\(290\) 3.73306e6 + 2.15528e6i 0.153063 + 0.0883710i
\(291\) 0 0
\(292\) 5.90313e6 + 1.02245e7i 0.237101 + 0.410672i
\(293\) −2.03760e7 + 1.17641e7i −0.810058 + 0.467687i −0.846976 0.531631i \(-0.821579\pi\)
0.0369179 + 0.999318i \(0.488246\pi\)
\(294\) 0 0
\(295\) 2.11324e6 3.66023e6i 0.0823156 0.142575i
\(296\) 9.74353e6i 0.375700i
\(297\) 0 0
\(298\) 1.15574e6 0.0436727
\(299\) −2.83858e6 1.63886e6i −0.106191 0.0613094i
\(300\) 0 0
\(301\) 2.17607e6 + 3.76906e6i 0.0797945 + 0.138208i
\(302\) 1.45153e7 8.38043e6i 0.526995 0.304261i
\(303\) 0 0
\(304\) −2.74115e6 + 4.74781e6i −0.0975691 + 0.168995i
\(305\) 4.93361e6i 0.173886i
\(306\) 0 0
\(307\) −1.92808e7 −0.666360 −0.333180 0.942863i \(-0.608122\pi\)
−0.333180 + 0.942863i \(0.608122\pi\)
\(308\) −2.54398e6 1.46877e6i −0.0870685 0.0502690i
\(309\) 0 0
\(310\) −6.00456e6 1.04002e7i −0.201556 0.349105i
\(311\) 2.70295e7 1.56055e7i 0.898582 0.518796i 0.0218419 0.999761i \(-0.493047\pi\)
0.876740 + 0.480965i \(0.159714\pi\)
\(312\) 0 0
\(313\) 1.76015e6 3.04866e6i 0.0574005 0.0994206i −0.835897 0.548886i \(-0.815052\pi\)
0.893298 + 0.449465i \(0.148385\pi\)
\(314\) 1.47351e7i 0.475954i
\(315\) 0 0
\(316\) −2.70021e7 −0.855728
\(317\) 4.11426e7 + 2.37537e7i 1.29156 + 0.745682i 0.978931 0.204193i \(-0.0654570\pi\)
0.312629 + 0.949875i \(0.398790\pi\)
\(318\) 0 0
\(319\) 1.23959e7 + 2.14703e7i 0.381861 + 0.661402i
\(320\) 1.42307e6 821611.i 0.0434287 0.0250736i
\(321\) 0 0
\(322\) 150315. 260353.i 0.00450230 0.00779822i
\(323\) 3.21226e6i 0.0953242i
\(324\) 0 0
\(325\) 4.54948e7 1.32529
\(326\) −2.75664e7 1.59154e7i −0.795658 0.459374i
\(327\) 0 0
\(328\) 1.01938e7 + 1.76561e7i 0.288877 + 0.500350i
\(329\) −9.25630e6 + 5.34413e6i −0.259926 + 0.150068i
\(330\) 0 0
\(331\) 5.44968e6 9.43912e6i 0.150275 0.260284i −0.781053 0.624464i \(-0.785317\pi\)
0.931329 + 0.364180i \(0.118651\pi\)
\(332\) 1.50572e7i 0.411463i
\(333\) 0 0
\(334\) 9.97412e6 0.267692
\(335\) −1.07529e7 6.20820e6i −0.286017 0.165132i
\(336\) 0 0
\(337\) 2.38414e7 + 4.12946e7i 0.622935 + 1.07895i 0.988936 + 0.148341i \(0.0473932\pi\)
−0.366001 + 0.930614i \(0.619273\pi\)
\(338\) 3.53475e7 2.04079e7i 0.915395 0.528504i
\(339\) 0 0
\(340\) 481409. 833825.i 0.0122483 0.0212147i
\(341\) 6.90692e7i 1.74189i
\(342\) 0 0
\(343\) −1.30609e7 −0.323661
\(344\) −1.21261e7 7.00099e6i −0.297882 0.171982i
\(345\) 0 0
\(346\) 2.27291e7 + 3.93680e7i 0.548724 + 0.950418i
\(347\) 2.23319e7 1.28933e7i 0.534487 0.308586i −0.208355 0.978053i \(-0.566811\pi\)
0.742842 + 0.669467i \(0.233477\pi\)
\(348\) 0 0
\(349\) 2.94007e7 5.09235e7i 0.691642 1.19796i −0.279658 0.960100i \(-0.590221\pi\)
0.971300 0.237859i \(-0.0764457\pi\)
\(350\) 4.17277e6i 0.0973240i
\(351\) 0 0
\(352\) 9.45082e6 0.216691
\(353\) −6.54573e7 3.77918e7i −1.48811 0.859159i −0.488199 0.872732i \(-0.662346\pi\)
−0.999908 + 0.0135736i \(0.995679\pi\)
\(354\) 0 0
\(355\) −1.03282e7 1.78889e7i −0.230855 0.399852i
\(356\) −2.08609e7 + 1.20441e7i −0.462363 + 0.266946i
\(357\) 0 0
\(358\) −2.79501e7 + 4.84110e7i −0.609165 + 1.05510i
\(359\) 4.56033e7i 0.985628i −0.870135 0.492814i \(-0.835968\pi\)
0.870135 0.492814i \(-0.164032\pi\)
\(360\) 0 0
\(361\) −1.83826e7 −0.390737
\(362\) −1.87491e7 1.08248e7i −0.395234 0.228188i
\(363\) 0 0
\(364\) 3.12398e6 + 5.41090e6i 0.0647746 + 0.112193i
\(365\) −1.60229e7 + 9.25080e6i −0.329504 + 0.190239i
\(366\) 0 0
\(367\) 1.57052e7 2.72022e7i 0.317721 0.550309i −0.662291 0.749247i \(-0.730416\pi\)
0.980012 + 0.198938i \(0.0637491\pi\)
\(368\) 967207.i 0.0194078i
\(369\) 0 0
\(370\) −1.52691e7 −0.301445
\(371\) −1.18675e7 6.85171e6i −0.232401 0.134177i
\(372\) 0 0
\(373\) −5.69047e6 9.85619e6i −0.109653 0.189925i 0.805977 0.591948i \(-0.201641\pi\)
−0.915630 + 0.402022i \(0.868307\pi\)
\(374\) 4.79565e6 2.76877e6i 0.0916712 0.0529264i
\(375\) 0 0
\(376\) 1.71935e7 2.97800e7i 0.323445 0.560223i
\(377\) 5.27307e7i 0.984100i
\(378\) 0 0
\(379\) −4.52964e7 −0.832044 −0.416022 0.909355i \(-0.636576\pi\)
−0.416022 + 0.909355i \(0.636576\pi\)
\(380\) −7.44030e6 4.29566e6i −0.135594 0.0782851i
\(381\) 0 0
\(382\) −1.23844e7 2.14505e7i −0.222170 0.384810i
\(383\) 2.83885e7 1.63901e7i 0.505297 0.291733i −0.225602 0.974220i \(-0.572435\pi\)
0.730898 + 0.682486i \(0.239101\pi\)
\(384\) 0 0
\(385\) 2.30170e6 3.98666e6i 0.0403336 0.0698598i
\(386\) 5.04510e6i 0.0877219i
\(387\) 0 0
\(388\) −1.47795e7 −0.253026
\(389\) 2.98843e7 + 1.72537e7i 0.507686 + 0.293113i 0.731882 0.681432i \(-0.238642\pi\)
−0.224196 + 0.974544i \(0.571976\pi\)
\(390\) 0 0
\(391\) 283359. + 490792.i 0.00474031 + 0.00821046i
\(392\) 1.79472e7 1.03618e7i 0.297947 0.172020i
\(393\) 0 0
\(394\) 1.38796e7 2.40402e7i 0.226928 0.393051i
\(395\) 4.23149e7i 0.686597i
\(396\) 0 0
\(397\) 5.72396e7 0.914798 0.457399 0.889262i \(-0.348781\pi\)
0.457399 + 0.889262i \(0.348781\pi\)
\(398\) 4.09038e7 + 2.36158e7i 0.648806 + 0.374588i
\(399\) 0 0
\(400\) −6.71245e6 1.16263e7i −0.104882 0.181661i
\(401\) −6.90479e7 + 3.98648e7i −1.07082 + 0.618239i −0.928406 0.371568i \(-0.878820\pi\)
−0.142416 + 0.989807i \(0.545487\pi\)
\(402\) 0 0
\(403\) −7.34532e7 + 1.27225e8i −1.12226 + 1.94382i
\(404\) 3.93244e7i 0.596373i
\(405\) 0 0
\(406\) 4.83643e6 0.0722682
\(407\) −7.60531e7 4.39092e7i −1.12806 0.651288i
\(408\) 0 0
\(409\) −2.39594e7 4.14989e7i −0.350192 0.606550i 0.636091 0.771614i \(-0.280550\pi\)
−0.986283 + 0.165064i \(0.947217\pi\)
\(410\) −2.76689e7 + 1.59746e7i −0.401458 + 0.231782i
\(411\) 0 0
\(412\) −8.76361e6 + 1.51790e7i −0.125312 + 0.217046i
\(413\) 4.74209e6i 0.0673162i
\(414\) 0 0
\(415\) −2.35962e7 −0.330139
\(416\) −1.74083e7 1.00507e7i −0.241811 0.139610i
\(417\) 0 0
\(418\) −2.47060e7 4.27921e7i −0.338278 0.585915i
\(419\) 9.53262e7 5.50366e7i 1.29590 0.748186i 0.316204 0.948691i \(-0.397592\pi\)
0.979693 + 0.200505i \(0.0642582\pi\)
\(420\) 0 0
\(421\) 1.87470e7 3.24708e7i 0.251238 0.435158i −0.712629 0.701541i \(-0.752496\pi\)
0.963867 + 0.266384i \(0.0858289\pi\)
\(422\) 7.33530e7i 0.976070i
\(423\) 0 0
\(424\) 4.40875e7 0.578387
\(425\) −6.81223e6 3.93304e6i −0.0887407 0.0512344i
\(426\) 0 0
\(427\) −2.76775e6 4.79388e6i −0.0355503 0.0615749i
\(428\) −2.51694e6 + 1.45316e6i −0.0321027 + 0.0185345i
\(429\) 0 0
\(430\) 1.09712e7 1.90028e7i 0.137991 0.239007i
\(431\) 1.35605e8i 1.69373i 0.531810 + 0.846864i \(0.321512\pi\)
−0.531810 + 0.846864i \(0.678488\pi\)
\(432\) 0 0
\(433\) 1.18161e8 1.45549 0.727746 0.685846i \(-0.240568\pi\)
0.727746 + 0.685846i \(0.240568\pi\)
\(434\) −1.16690e7 6.73709e6i −0.142746 0.0824144i
\(435\) 0 0
\(436\) −1.74152e7 3.01641e7i −0.210121 0.363941i
\(437\) 4.37939e6 2.52844e6i 0.0524770 0.0302976i
\(438\) 0 0
\(439\) −4.59907e7 + 7.96582e7i −0.543596 + 0.941535i 0.455098 + 0.890441i \(0.349604\pi\)
−0.998694 + 0.0510942i \(0.983729\pi\)
\(440\) 1.48104e7i 0.173863i
\(441\) 0 0
\(442\) −1.17781e7 −0.136398
\(443\) 1.70594e7 + 9.84924e6i 0.196224 + 0.113290i 0.594893 0.803805i \(-0.297194\pi\)
−0.398669 + 0.917095i \(0.630528\pi\)
\(444\) 0 0
\(445\) −1.88742e7 3.26911e7i −0.214185 0.370980i
\(446\) 1.84811e7 1.06700e7i 0.208316 0.120271i
\(447\) 0 0
\(448\) 921845. 1.59668e6i 0.0102524 0.0177576i
\(449\) 1.38530e7i 0.153040i 0.997068 + 0.0765199i \(0.0243809\pi\)
−0.997068 + 0.0765199i \(0.975619\pi\)
\(450\) 0 0
\(451\) −1.83753e8 −2.00311
\(452\) 6.90161e7 + 3.98465e7i 0.747369 + 0.431494i
\(453\) 0 0
\(454\) −1.42350e7 2.46557e7i −0.152121 0.263481i
\(455\) −8.47942e6 + 4.89559e6i −0.0900185 + 0.0519722i
\(456\) 0 0
\(457\) 3.69186e7 6.39448e7i 0.386809 0.669972i −0.605210 0.796066i \(-0.706911\pi\)
0.992018 + 0.126094i \(0.0402441\pi\)
\(458\) 1.62607e7i 0.169256i
\(459\) 0 0
\(460\) −1.51571e6 −0.0155719
\(461\) 4.60339e7 + 2.65777e7i 0.469867 + 0.271278i 0.716184 0.697912i \(-0.245887\pi\)
−0.246317 + 0.969189i \(0.579220\pi\)
\(462\) 0 0
\(463\) −4.74332e7 8.21567e7i −0.477903 0.827752i 0.521776 0.853082i \(-0.325270\pi\)
−0.999679 + 0.0253305i \(0.991936\pi\)
\(464\) −1.34754e7 + 7.78005e6i −0.134893 + 0.0778804i
\(465\) 0 0
\(466\) 6.31432e7 1.09367e8i 0.623977 1.08076i
\(467\) 1.90459e8i 1.87004i 0.354598 + 0.935019i \(0.384618\pi\)
−0.354598 + 0.935019i \(0.615382\pi\)
\(468\) 0 0
\(469\) −1.39311e7 −0.135042
\(470\) 4.66682e7 + 2.69439e7i 0.449498 + 0.259518i
\(471\) 0 0
\(472\) 7.62828e6 + 1.32126e7i 0.0725439 + 0.125650i
\(473\) 1.09292e8 6.30999e7i 1.03278 0.596274i
\(474\) 0 0
\(475\) −3.50949e7 + 6.07862e7i −0.327464 + 0.567184i
\(476\) 1.08028e6i 0.0100165i
\(477\) 0 0
\(478\) 6.64043e7 0.608013
\(479\) 2.45490e7 + 1.41734e7i 0.223371 + 0.128963i 0.607510 0.794312i \(-0.292168\pi\)
−0.384139 + 0.923275i \(0.625502\pi\)
\(480\) 0 0
\(481\) 9.33926e7 + 1.61761e8i 0.839223 + 1.45358i
\(482\) −1.30011e8 + 7.50620e7i −1.16102 + 0.670315i
\(483\) 0 0
\(484\) −1.42452e7 + 2.46734e7i −0.125641 + 0.217617i
\(485\) 2.31610e7i 0.203017i
\(486\) 0 0
\(487\) −6.06414e7 −0.525028 −0.262514 0.964928i \(-0.584552\pi\)
−0.262514 + 0.964928i \(0.584552\pi\)
\(488\) 1.54232e7 + 8.90458e6i 0.132713 + 0.0766221i
\(489\) 0 0
\(490\) 1.62380e7 + 2.81251e7i 0.138021 + 0.239059i
\(491\) −1.34714e8 + 7.77769e7i −1.13806 + 0.657062i −0.945951 0.324311i \(-0.894868\pi\)
−0.192114 + 0.981373i \(0.561534\pi\)
\(492\) 0 0
\(493\) −4.55858e6 + 7.89570e6i −0.0380443 + 0.0658946i
\(494\) 1.05097e8i 0.871783i
\(495\) 0 0
\(496\) 4.33500e7 0.355259
\(497\) −2.00713e7 1.15882e7i −0.163496 0.0943944i
\(498\) 0 0
\(499\) 6.46864e7 + 1.12040e8i 0.520609 + 0.901721i 0.999713 + 0.0239626i \(0.00762826\pi\)
−0.479104 + 0.877758i \(0.659038\pi\)
\(500\) 3.99340e7 2.30559e7i 0.319472 0.184447i
\(501\) 0 0
\(502\) 7.49122e7 1.29752e8i 0.592163 1.02566i
\(503\) 1.43279e8i 1.12585i −0.826509 0.562923i \(-0.809677\pi\)
0.826509 0.562923i \(-0.190323\pi\)
\(504\) 0 0
\(505\) 6.16253e7 0.478503
\(506\) −7.54953e6 4.35872e6i −0.0582731 0.0336440i
\(507\) 0 0
\(508\) −5.00739e7 8.67305e7i −0.381962 0.661577i
\(509\) −1.37466e8 + 7.93661e7i −1.04242 + 0.601841i −0.920517 0.390702i \(-0.872232\pi\)
−0.121901 + 0.992542i \(0.538899\pi\)
\(510\) 0 0
\(511\) −1.03794e7 + 1.79776e7i −0.0777871 + 0.134731i
\(512\) 5.93164e6i 0.0441942i
\(513\) 0 0
\(514\) −1.26118e8 −0.928725
\(515\) −2.37870e7 1.37335e7i −0.174148 0.100544i
\(516\) 0 0
\(517\) 1.54965e8 + 2.68407e8i 1.12140 + 1.94233i
\(518\) −1.48366e7 + 8.56592e6i −0.106745 + 0.0616290i
\(519\) 0 0
\(520\) 1.57504e7 2.72805e7i 0.112017 0.194018i
\(521\) 2.21508e8i 1.56630i 0.621831 + 0.783152i \(0.286389\pi\)
−0.621831 + 0.783152i \(0.713611\pi\)
\(522\) 0 0
\(523\) 5.17660e7 0.361859 0.180930 0.983496i \(-0.442089\pi\)
0.180930 + 0.983496i \(0.442089\pi\)
\(524\) −3.11458e7 1.79820e7i −0.216474 0.124981i
\(525\) 0 0
\(526\) 4.92294e6 + 8.52678e6i 0.0338273 + 0.0585906i
\(527\) 2.19972e7 1.27001e7i 0.150292 0.0867711i
\(528\) 0 0
\(529\) −7.35719e7 + 1.27430e8i −0.496987 + 0.860806i
\(530\) 6.90896e7i 0.464071i
\(531\) 0 0
\(532\) −9.63942e6 −0.0640201
\(533\) 3.38471e8 + 1.95416e8i 2.23532 + 1.29056i
\(534\) 0 0
\(535\) −2.27724e6 3.94430e6i −0.0148713 0.0257578i
\(536\) 3.88154e7 2.24101e7i 0.252064 0.145529i
\(537\) 0 0
\(538\) 9.10669e6 1.57733e7i 0.0584809 0.101292i
\(539\) 1.86783e8i 1.19281i
\(540\) 0 0
\(541\) 1.49689e7 0.0945361 0.0472681 0.998882i \(-0.484949\pi\)
0.0472681 + 0.998882i \(0.484949\pi\)
\(542\) −4.26713e7 2.46363e7i −0.268002 0.154731i
\(543\) 0 0
\(544\) 1.73777e6 + 3.00991e6i 0.0107943 + 0.0186963i
\(545\) 4.72701e7 2.72914e7i 0.292009 0.168592i
\(546\) 0 0
\(547\) 4.60003e7 7.96749e7i 0.281060 0.486810i −0.690586 0.723250i \(-0.742647\pi\)
0.971646 + 0.236440i \(0.0759807\pi\)
\(548\) 6.74397e7i 0.409802i
\(549\) 0 0
\(550\) 1.20999e8 0.727265
\(551\) 7.04541e7 + 4.06767e7i 0.421164 + 0.243159i
\(552\) 0 0
\(553\) −2.37386e7 4.11164e7i −0.140372 0.243131i
\(554\) 2.32372e7 1.34160e7i 0.136664 0.0789030i
\(555\) 0 0
\(556\) 2.52777e6 4.37823e6i 0.0147066 0.0254726i
\(557\) 1.53984e8i 0.891066i −0.895266 0.445533i \(-0.853014\pi\)
0.895266 0.445533i \(-0.146986\pi\)
\(558\) 0 0
\(559\) −2.68420e8 −1.53667
\(560\) 2.50216e6 + 1.44462e6i 0.0142479 + 0.00822603i
\(561\) 0 0
\(562\) −2.07465e7 3.59340e7i −0.116879 0.202440i
\(563\) −9.62471e7 + 5.55683e7i −0.539340 + 0.311388i −0.744811 0.667275i \(-0.767461\pi\)
0.205471 + 0.978663i \(0.434127\pi\)
\(564\) 0 0
\(565\) −6.24434e7 + 1.08155e8i −0.346211 + 0.599655i
\(566\) 2.18882e8i 1.20715i
\(567\) 0 0
\(568\) 7.45646e7 0.406900
\(569\) −2.79773e8 1.61527e8i −1.51869 0.876817i −0.999758 0.0220026i \(-0.992996\pi\)
−0.518934 0.854814i \(-0.673671\pi\)
\(570\) 0 0
\(571\) −2.71860e7 4.70875e7i −0.146028 0.252928i 0.783728 0.621104i \(-0.213316\pi\)
−0.929756 + 0.368176i \(0.879982\pi\)
\(572\) 1.56901e8 9.05869e7i 0.838374 0.484036i
\(573\) 0 0
\(574\) −1.79235e7 + 3.10444e7i −0.0947734 + 0.164152i
\(575\) 1.23831e7i 0.0651370i
\(576\) 0 0
\(577\) 2.74190e8 1.42733 0.713665 0.700487i \(-0.247034\pi\)
0.713665 + 0.700487i \(0.247034\pi\)
\(578\) −1.16486e8 6.72531e7i −0.603239 0.348280i
\(579\) 0 0
\(580\) −1.21921e7 2.11174e7i −0.0624877 0.108232i
\(581\) −2.29279e7 + 1.32374e7i −0.116906 + 0.0674954i
\(582\) 0 0
\(583\) −1.98681e8 + 3.44125e8i −1.00265 + 1.73664i
\(584\) 6.67863e7i 0.335312i
\(585\) 0 0
\(586\) 1.33096e8 0.661410
\(587\) 2.14847e8 + 1.24042e8i 1.06222 + 0.613274i 0.926046 0.377411i \(-0.123186\pi\)
0.136176 + 0.990685i \(0.456519\pi\)
\(588\) 0 0
\(589\) −1.13324e8 1.96283e8i −0.554596 0.960589i
\(590\) −2.07054e7 + 1.19543e7i −0.100816 + 0.0582059i
\(591\) 0 0
\(592\) 2.75589e7 4.77334e7i 0.132830 0.230068i
\(593\) 2.27716e8i 1.09202i 0.837779 + 0.546009i \(0.183854\pi\)
−0.837779 + 0.546009i \(0.816146\pi\)
\(594\) 0 0
\(595\) 1.69290e6 0.00803676
\(596\) −5.66192e6 3.26891e6i −0.0267439 0.0154406i
\(597\) 0 0
\(598\) 9.27077e6 + 1.60574e7i 0.0433523 + 0.0750884i
\(599\) −7.43379e7 + 4.29190e7i −0.345884 + 0.199696i −0.662871 0.748734i \(-0.730662\pi\)
0.316987 + 0.948430i \(0.397329\pi\)
\(600\) 0 0
\(601\) 1.73833e8 3.01088e8i 0.800774 1.38698i −0.118334 0.992974i \(-0.537755\pi\)
0.919108 0.394007i \(-0.128911\pi\)
\(602\) 2.46194e7i 0.112846i
\(603\) 0 0
\(604\) −9.48138e7 −0.430289
\(605\) −3.86656e7 2.23236e7i −0.174606 0.100809i
\(606\) 0 0
\(607\) −4.35211e7 7.53807e7i −0.194596 0.337050i 0.752172 0.658967i \(-0.229006\pi\)
−0.946768 + 0.321917i \(0.895673\pi\)
\(608\) 2.68577e7 1.55063e7i 0.119497 0.0689918i
\(609\) 0 0
\(610\) −1.39544e7 + 2.41697e7i −0.0614781 + 0.106483i
\(611\) 6.59204e8i 2.88999i
\(612\) 0 0
\(613\) 3.18298e8 1.38182 0.690912 0.722939i \(-0.257209\pi\)
0.690912 + 0.722939i \(0.257209\pi\)
\(614\) 9.44560e7 + 5.45342e7i 0.408061 + 0.235594i
\(615\) 0 0
\(616\) 8.30859e6 + 1.43909e7i 0.0355455 + 0.0615667i
\(617\) 1.18589e8 6.84674e7i 0.504881 0.291493i −0.225846 0.974163i \(-0.572515\pi\)
0.730727 + 0.682670i \(0.239181\pi\)
\(618\) 0 0
\(619\) −8.03059e7 + 1.39094e8i −0.338591 + 0.586457i −0.984168 0.177238i \(-0.943284\pi\)
0.645577 + 0.763695i \(0.276617\pi\)
\(620\) 6.79338e7i 0.285043i
\(621\) 0 0
\(622\) −1.76556e8 −0.733689
\(623\) −3.66793e7 2.11768e7i −0.151690 0.0875783i
\(624\) 0 0
\(625\) −6.62930e7 1.14823e8i −0.271536 0.470315i
\(626\) −1.72458e7 + 9.95689e6i −0.0703010 + 0.0405883i
\(627\) 0 0
\(628\) −4.16772e7 + 7.21870e7i −0.168275 + 0.291461i
\(629\) 3.22953e7i 0.129774i
\(630\) 0 0
\(631\) −4.09279e8 −1.62904 −0.814519 0.580136i \(-0.802999\pi\)
−0.814519 + 0.580136i \(0.802999\pi\)
\(632\) 1.32283e8 + 7.63734e7i 0.524024 + 0.302545i
\(633\) 0 0
\(634\) −1.34371e8 2.32738e8i −0.527277 0.913271i
\(635\) 1.35915e8 7.84708e7i 0.530820 0.306469i
\(636\) 0 0
\(637\) 1.98638e8 3.44052e8i 0.768501 1.33108i
\(638\) 1.40243e8i 0.540032i
\(639\) 0 0
\(640\) −9.29547e6 −0.0354594
\(641\) −6.47552e7 3.73865e7i −0.245867 0.141952i 0.372003 0.928231i \(-0.378671\pi\)
−0.617870 + 0.786280i \(0.712004\pi\)
\(642\) 0 0
\(643\) −1.35130e8 2.34052e8i −0.508298 0.880399i −0.999954 0.00960888i \(-0.996941\pi\)
0.491655 0.870790i \(-0.336392\pi\)
\(644\) −1.47278e6 + 850310.i −0.00551417 + 0.00318361i
\(645\) 0 0
\(646\) 9.08564e6 1.57368e7i 0.0337022 0.0583739i
\(647\) 2.04687e8i 0.755749i −0.925857 0.377874i \(-0.876655\pi\)
0.925857 0.377874i \(-0.123345\pi\)
\(648\) 0 0
\(649\) −1.37507e8 −0.503028
\(650\) −2.22878e8 1.28679e8i −0.811573 0.468562i
\(651\) 0 0
\(652\) 9.00313e7 + 1.55939e8i 0.324826 + 0.562615i
\(653\) −1.10498e8 + 6.37963e7i −0.396841 + 0.229116i −0.685120 0.728430i \(-0.740250\pi\)
0.288279 + 0.957546i \(0.406917\pi\)
\(654\) 0 0
\(655\) 2.81796e7 4.88086e7i 0.100279 0.173689i
\(656\) 1.15329e8i 0.408534i
\(657\) 0 0
\(658\) 6.04619e7 0.212229
\(659\) −2.79267e8 1.61235e8i −0.975807 0.563383i −0.0748056 0.997198i \(-0.523834\pi\)
−0.901002 + 0.433816i \(0.857167\pi\)
\(660\) 0 0
\(661\) 2.17389e8 + 3.76529e8i 0.752721 + 1.30375i 0.946500 + 0.322705i \(0.104592\pi\)
−0.193779 + 0.981045i \(0.562074\pi\)
\(662\) −5.33957e7 + 3.08280e7i −0.184049 + 0.106260i
\(663\) 0 0
\(664\) 4.25883e7 7.37650e7i 0.145474 0.251969i
\(665\) 1.51059e7i 0.0513668i
\(666\) 0 0
\(667\) 1.43526e7 0.0483676
\(668\) −4.88630e7 2.82111e7i −0.163927 0.0946434i
\(669\) 0 0
\(670\) 3.51189e7 + 6.08277e7i 0.116766 + 0.202245i
\(671\) −1.39009e8 + 8.02570e7i −0.460125 + 0.265654i
\(672\) 0 0
\(673\) 4.31783e7 7.47869e7i 0.141651 0.245347i −0.786467 0.617632i \(-0.788092\pi\)
0.928119 + 0.372285i \(0.121426\pi\)
\(674\) 2.69735e8i 0.880963i
\(675\) 0 0
\(676\) −2.30889e8 −0.747417
\(677\) −4.92732e8 2.84479e8i −1.58798 0.916820i −0.993640 0.112606i \(-0.964080\pi\)
−0.594340 0.804214i \(-0.702587\pi\)
\(678\) 0 0
\(679\) −1.29933e7 2.25050e7i −0.0415058 0.0718902i
\(680\) −4.71682e6 + 2.72326e6i −0.0150011 + 0.00866089i
\(681\) 0 0
\(682\) −1.95357e8 + 3.38368e8i −0.615852 + 1.06669i
\(683\) 1.34652e8i 0.422622i 0.977419 + 0.211311i \(0.0677733\pi\)
−0.977419 + 0.211311i \(0.932227\pi\)
\(684\) 0 0
\(685\) 1.05685e8 0.328806
\(686\) 6.39851e7 + 3.69418e7i 0.198201 + 0.114432i
\(687\) 0 0
\(688\) 3.96036e7 + 6.85954e7i 0.121610 + 0.210635i
\(689\) 7.31935e8 4.22583e8i 2.23777 1.29198i
\(690\) 0 0
\(691\) 5.35612e7 9.27707e7i 0.162336 0.281175i −0.773370 0.633955i \(-0.781430\pi\)
0.935706 + 0.352780i \(0.114764\pi\)
\(692\) 2.57151e8i 0.776013i
\(693\) 0 0
\(694\) −1.45871e8 −0.436407
\(695\) 6.86112e6 + 3.96127e6i 0.0204381 + 0.0117999i
\(696\) 0 0
\(697\) −3.37876e7 5.85218e7i −0.0997835 0.172830i
\(698\) −2.88067e8 + 1.66315e8i −0.847085 + 0.489065i
\(699\) 0 0
\(700\) 1.18024e7 2.04423e7i 0.0344092 0.0595985i
\(701\) 2.39134e8i 0.694204i −0.937827 0.347102i \(-0.887166\pi\)
0.937827 0.347102i \(-0.112834\pi\)
\(702\) 0 0
\(703\) −2.88174e8 −0.829447
\(704\) −4.62994e7 2.67310e7i −0.132696 0.0766120i
\(705\) 0 0
\(706\) 2.13783e8 + 3.70282e8i 0.607517 + 1.05225i
\(707\) 5.98798e7 3.45716e7i 0.169443 0.0978277i
\(708\) 0 0
\(709\) 1.85010e8 3.20446e8i 0.519106 0.899118i −0.480648 0.876914i \(-0.659598\pi\)
0.999753 0.0222038i \(-0.00706826\pi\)
\(710\) 1.16850e8i 0.326478i
\(711\) 0 0
\(712\) 1.36263e8 0.377518
\(713\) −3.46290e7 1.99931e7i −0.0955369 0.0551583i
\(714\) 0 0
\(715\) 1.41959e8 + 2.45880e8i 0.388368 + 0.672674i
\(716\) 2.73854e8 1.58110e8i 0.746071 0.430744i
\(717\) 0 0
\(718\) −1.28986e8 + 2.23410e8i −0.348472 + 0.603571i
\(719\) 1.59561e8i 0.429279i −0.976693 0.214639i \(-0.931142\pi\)
0.976693 0.214639i \(-0.0688576\pi\)
\(720\) 0 0
\(721\) −3.08177e7 −0.0822233
\(722\) 9.00558e7 + 5.19938e7i 0.239277 + 0.138146i
\(723\) 0 0
\(724\) 6.12342e7 + 1.06061e8i 0.161354 + 0.279473i
\(725\) −1.72526e8 + 9.96079e7i −0.452731 + 0.261384i
\(726\) 0 0
\(727\) 1.24125e8 2.14991e8i 0.323040 0.559522i −0.658073 0.752954i \(-0.728628\pi\)
0.981114 + 0.193432i \(0.0619617\pi\)
\(728\) 3.53438e7i 0.0916051i
\(729\) 0 0
\(730\) 1.04661e8 0.269039
\(731\) 4.01923e7 + 2.32050e7i 0.102894 + 0.0594059i
\(732\) 0 0
\(733\) −2.13730e8 3.70190e8i −0.542691 0.939968i −0.998748 0.0500180i \(-0.984072\pi\)
0.456057 0.889950i \(-0.349261\pi\)
\(734\) −1.53879e8 + 8.88422e7i −0.389127 + 0.224663i
\(735\) 0 0
\(736\) 2.73568e6 4.73833e6i 0.00686169 0.0118848i
\(737\) 4.03965e8i 1.00912i
\(738\) 0 0
\(739\) 2.68169e8 0.664469 0.332234 0.943197i \(-0.392197\pi\)
0.332234 + 0.943197i \(0.392197\pi\)
\(740\) 7.48029e7 + 4.31875e7i 0.184596 + 0.106577i
\(741\) 0 0
\(742\) 3.87591e7 + 6.71327e7i 0.0948772 + 0.164332i
\(743\) 1.46273e8 8.44510e7i 0.356614 0.205891i −0.310980 0.950416i \(-0.600657\pi\)
0.667595 + 0.744525i \(0.267324\pi\)
\(744\) 0 0
\(745\) 5.12271e6 8.87280e6i 0.0123889 0.0214581i
\(746\) 6.43803e7i 0.155073i
\(747\) 0 0
\(748\) −3.13251e7 −0.0748492
\(749\) −4.42549e6 2.55506e6i −0.0105321 0.00608072i
\(750\) 0 0
\(751\) −1.90204e8 3.29444e8i −0.449056 0.777788i 0.549269 0.835646i \(-0.314906\pi\)
−0.998325 + 0.0578577i \(0.981573\pi\)
\(752\) −1.68461e8 + 9.72610e7i −0.396137 + 0.228710i
\(753\) 0 0
\(754\) −1.49145e8 + 2.58326e8i −0.347932 + 0.602636i
\(755\) 1.48583e8i 0.345245i
\(756\) 0 0
\(757\) 5.93762e8 1.36875 0.684376 0.729129i \(-0.260075\pi\)
0.684376 + 0.729129i \(0.260075\pi\)
\(758\) 2.21906e8 + 1.28118e8i 0.509521 + 0.294172i
\(759\) 0 0
\(760\) 2.42999e7 + 4.20887e7i 0.0553559 + 0.0958792i
\(761\) 2.02904e8 1.17147e8i 0.460401 0.265813i −0.251812 0.967776i \(-0.581026\pi\)
0.712213 + 0.701964i \(0.247693\pi\)
\(762\) 0 0
\(763\) 3.06208e7 5.30368e7i 0.0689356 0.119400i
\(764\) 1.40114e8i 0.314196i
\(765\) 0 0
\(766\) −1.85433e8 −0.412573
\(767\) 2.53287e8 + 1.46235e8i 0.561342 + 0.324091i
\(768\) 0 0
\(769\) 1.58571e8 + 2.74653e8i 0.348694 + 0.603956i 0.986018 0.166640i \(-0.0532919\pi\)
−0.637324 + 0.770596i \(0.719959\pi\)
\(770\) −2.25520e7 + 1.30204e7i −0.0493983 + 0.0285201i
\(771\) 0 0
\(772\) −1.42697e7 + 2.47158e7i −0.0310144 + 0.0537184i
\(773\) 3.31391e8i 0.717468i −0.933440 0.358734i \(-0.883209\pi\)
0.933440 0.358734i \(-0.116791\pi\)
\(774\) 0 0
\(775\) 5.55010e8 1.19233
\(776\) 7.24046e7 + 4.18028e7i 0.154946 + 0.0894582i
\(777\) 0 0
\(778\) −9.76019e7 1.69051e8i −0.207262 0.358988i
\(779\) −5.22196e8 + 3.01490e8i −1.10464 + 0.637765i
\(780\) 0 0
\(781\) −3.36025e8 + 5.82013e8i −0.705373 + 1.22174i
\(782\) 3.20584e6i 0.00670381i
\(783\) 0 0
\(784\) −1.17231e8 −0.243273
\(785\) −1.13124e8 6.53123e7i −0.233855 0.135016i
\(786\) 0 0
\(787\) 9.60758e7 + 1.66408e8i 0.197101 + 0.341390i 0.947587 0.319497i \(-0.103514\pi\)
−0.750486 + 0.660886i \(0.770181\pi\)
\(788\) −1.35992e8 + 7.85150e7i −0.277929 + 0.160463i
\(789\) 0 0
\(790\) −1.19685e8 + 2.07300e8i −0.242749 + 0.420453i
\(791\) 1.40122e8i 0.283125i
\(792\) 0 0
\(793\) 3.41405e8 0.684621
\(794\) −2.80416e8 1.61898e8i −0.560197 0.323430i
\(795\) 0 0
\(796\) −1.33591e8 2.31387e8i −0.264874 0.458775i
\(797\) −1.18277e8 + 6.82872e7i −0.233628 + 0.134885i −0.612245 0.790668i \(-0.709733\pi\)
0.378617 + 0.925554i \(0.376400\pi\)
\(798\) 0 0
\(799\) −5.69884e7 + 9.87068e7i −0.111724 + 0.193511i
\(800\) 7.59427e7i 0.148326i
\(801\) 0 0
\(802\) 4.51019e8 0.874322
\(803\) 5.21300e8 + 3.00973e8i 1.00680 + 0.581274i
\(804\) 0 0
\(805\) −1.33252e6 2.30799e6i −0.00255439 0.00442433i
\(806\) 7.19691e8 4.15514e8i 1.37449 0.793561i
\(807\) 0 0
\(808\) −1.11226e8 + 1.92649e8i −0.210850 + 0.365202i
\(809\) 6.82631e8i 1.28926i 0.764495 + 0.644630i \(0.222989\pi\)
−0.764495 + 0.644630i \(0.777011\pi\)
\(810\) 0 0
\(811\) −8.02342e7 −0.150417 −0.0752085 0.997168i \(-0.523962\pi\)
−0.0752085 + 0.997168i \(0.523962\pi\)
\(812\) −2.36936e7 1.36795e7i −0.0442550 0.0255507i
\(813\) 0 0
\(814\) 2.48388e8 + 4.30221e8i 0.460530 + 0.797661i
\(815\) −2.44372e8 + 1.41088e8i −0.451417 + 0.260626i
\(816\) 0 0
\(817\) 2.07061e8 3.58640e8i 0.379692 0.657646i
\(818\) 2.71070e8i 0.495246i
\(819\) 0 0
\(820\) 1.80732e8 0.327789
\(821\) 7.33039e8 + 4.23220e8i 1.32464 + 0.764781i 0.984465 0.175582i \(-0.0561806\pi\)
0.340174 + 0.940362i \(0.389514\pi\)
\(822\) 0 0
\(823\) −3.00433e8 5.20365e8i −0.538949 0.933487i −0.998961 0.0455745i \(-0.985488\pi\)
0.460012 0.887913i \(-0.347845\pi\)
\(824\) 8.58655e7 4.95745e7i 0.153475 0.0886087i
\(825\) 0 0
\(826\) −1.34126e7 + 2.32314e7i −0.0237999 + 0.0412226i
\(827\) 8.30480e8i 1.46829i 0.678991 + 0.734146i \(0.262417\pi\)
−0.678991 + 0.734146i \(0.737583\pi\)
\(828\) 0 0
\(829\) −9.87908e8 −1.73402 −0.867008 0.498294i \(-0.833960\pi\)
−0.867008 + 0.498294i \(0.833960\pi\)
\(830\) 1.15597e8 + 6.67401e7i 0.202168 + 0.116722i
\(831\) 0 0
\(832\) 5.68553e7 + 9.84762e7i 0.0987190 + 0.170986i
\(833\) −5.94867e7 + 3.43447e7i −0.102917 + 0.0594189i
\(834\) 0 0
\(835\) 4.42096e7 7.65732e7i 0.0759376 0.131528i
\(836\) 2.79517e8i 0.478398i
\(837\) 0 0
\(838\) −6.22668e8 −1.05810
\(839\) −3.20618e8 1.85109e8i −0.542878 0.313431i 0.203367 0.979103i \(-0.434812\pi\)
−0.746245 + 0.665672i \(0.768145\pi\)
\(840\) 0 0
\(841\) −1.81961e8 3.15167e8i −0.305908 0.529849i
\(842\) −1.83683e8 + 1.06049e8i −0.307703 + 0.177652i
\(843\) 0 0
\(844\) −2.07474e8 + 3.59355e8i −0.345093 + 0.597718i
\(845\) 3.61826e8i 0.599694i
\(846\) 0 0
\(847\) −5.00940e7 −0.0824395
\(848\) −2.15984e8 1.24698e8i −0.354188 0.204491i
\(849\) 0 0
\(850\) 2.22487e7 + 3.85358e7i 0.0362282 + 0.0627491i
\(851\) −4.40293e7 + 2.54203e7i −0.0714419 + 0.0412470i
\(852\) 0 0
\(853\) −1.82273e7 + 3.15707e7i −0.0293681 + 0.0508671i −0.880336 0.474351i \(-0.842683\pi\)
0.850968 + 0.525218i \(0.176016\pi\)
\(854\) 3.13135e7i 0.0502757i
\(855\) 0 0
\(856\) 1.64406e7 0.0262118
\(857\) −2.18436e8 1.26114e8i −0.347042 0.200365i 0.316339 0.948646i \(-0.397546\pi\)
−0.663382 + 0.748281i \(0.730879\pi\)
\(858\) 0 0
\(859\) −7.74242e7 1.34103e8i −0.122151 0.211572i 0.798465 0.602042i \(-0.205646\pi\)
−0.920616 + 0.390470i \(0.872313\pi\)
\(860\) −1.07496e8 + 6.20627e7i −0.169004 + 0.0975743i
\(861\) 0 0
\(862\) 3.83549e8 6.64326e8i 0.598823 1.03719i
\(863\) 8.16338e8i 1.27010i 0.772472 + 0.635049i \(0.219020\pi\)
−0.772472 + 0.635049i \(0.780980\pi\)
\(864\) 0 0
\(865\) 4.02981e8 0.622638
\(866\) −5.78868e8 3.34209e8i −0.891304 0.514594i
\(867\) 0 0
\(868\) 3.81107e7 + 6.60097e7i 0.0582758 + 0.100937i
\(869\) −1.19226e9 + 6.88353e8i −1.81682 + 1.04894i
\(870\) 0 0
\(871\) 4.29606e8 7.44099e8i 0.650153 1.12610i
\(872\) 1.97031e8i 0.297156i
\(873\) 0 0
\(874\) −2.86060e7 −0.0428473
\(875\) 7.02150e7 + 4.05387e7i 0.104811 + 0.0605125i
\(876\) 0 0
\(877\) 1.75984e7 + 3.04813e7i 0.0260900 + 0.0451892i 0.878776 0.477235i \(-0.158361\pi\)
−0.852686 + 0.522424i \(0.825028\pi\)
\(878\) 4.50615e8 2.60162e8i 0.665766 0.384380i
\(879\) 0 0
\(880\) 4.18901e7 7.25557e7i 0.0614700 0.106469i
\(881\) 1.48112e8i 0.216602i 0.994118 + 0.108301i \(0.0345410\pi\)
−0.994118 + 0.108301i \(0.965459\pi\)
\(882\) 0 0
\(883\) −1.03227e9 −1.49937 −0.749686 0.661794i \(-0.769795\pi\)
−0.749686 + 0.661794i \(0.769795\pi\)
\(884\) 5.77004e7 + 3.33134e7i 0.0835261 + 0.0482238i
\(885\) 0 0
\(886\) −5.57157e7 9.65025e7i −0.0801081 0.138751i
\(887\) 2.13506e8 1.23268e8i 0.305943 0.176636i −0.339167 0.940726i \(-0.610145\pi\)
0.645109 + 0.764090i \(0.276812\pi\)
\(888\) 0 0
\(889\) 8.80439e7 1.52496e8i 0.125312 0.217047i
\(890\) 2.13538e8i 0.302904i
\(891\) 0 0
\(892\) −1.20718e8 −0.170089
\(893\) 8.80770e8 + 5.08513e8i 1.23683 + 0.714081i
\(894\) 0 0
\(895\) 2.47774e8 + 4.29157e8i 0.345610 + 0.598614i
\(896\) −9.03220e6 + 5.21474e6i −0.0125565 + 0.00724951i
\(897\) 0 0
\(898\) 3.91822e7 6.78655e7i 0.0541078 0.0937174i
\(899\) 6.43283e8i 0.885366i
\(900\) 0 0
\(901\) −1.46130e8 −0.199786
\(902\) 9.00201e8 + 5.19732e8i 1.22665 + 0.708206i
\(903\) 0 0
\(904\) −2.25406e8 3.90414e8i −0.305112 0.528470i
\(905\) −1.66208e8 + 9.59601e7i −0.224236 + 0.129463i
\(906\) 0 0
\(907\) −3.47798e8 + 6.02404e8i −0.466128 + 0.807357i −0.999252 0.0386800i \(-0.987685\pi\)
0.533124 + 0.846037i \(0.321018\pi\)
\(908\) 1.61050e8i 0.215132i
\(909\) 0 0
\(910\) 5.53873e7 0.0734998
\(911\) 8.66691e8 + 5.00385e8i 1.14633 + 0.661833i 0.947990 0.318300i \(-0.103112\pi\)
0.198339 + 0.980133i \(0.436445\pi\)
\(912\) 0 0
\(913\) 3.83848e8 + 6.64845e8i 0.504368 + 0.873590i
\(914\) −3.61726e8 + 2.08843e8i −0.473742 + 0.273515i
\(915\) 0 0
\(916\) 4.59923e7 7.96610e7i 0.0598410 0.103648i
\(917\) 6.32349e7i 0.0820066i
\(918\) 0 0
\(919\) 3.63664e8 0.468548 0.234274 0.972171i \(-0.424729\pi\)
0.234274 + 0.972171i \(0.424729\pi\)
\(920\) 7.42543e6 + 4.28708e6i 0.00953583 + 0.00550551i
\(921\) 0 0
\(922\) −1.50346e8 2.60407e8i −0.191822 0.332246i
\(923\) 1.23791e9 7.14708e8i 1.57429 0.908915i
\(924\) 0 0
\(925\) 3.52836e8 6.11130e8i 0.445808 0.772162i
\(926\) 5.36645e8i 0.675856i
\(927\) 0 0
\(928\) 8.80212e7 0.110140
\(929\) −3.37250e8 1.94711e8i −0.420634 0.242853i 0.274715 0.961526i \(-0.411417\pi\)
−0.695349 + 0.718673i \(0.744750\pi\)
\(930\) 0 0
\(931\) 3.06461e8 + 5.30806e8i 0.379775 + 0.657789i
\(932\) −6.18674e8 + 3.57192e8i −0.764213 + 0.441218i
\(933\) 0 0
\(934\) 5.38699e8 9.33054e8i 0.661158 1.14516i
\(935\) 4.90895e7i 0.0600556i
\(936\) 0 0
\(937\) −7.33744e8 −0.891920 −0.445960 0.895053i \(-0.647138\pi\)
−0.445960 + 0.895053i \(0.647138\pi\)
\(938\) 6.82484e7 + 3.94032e7i 0.0826959 + 0.0477445i
\(939\) 0 0
\(940\) −1.52418e8 2.63995e8i −0.183507 0.317843i
\(941\) −2.41096e8 + 1.39197e8i −0.289348 + 0.167055i −0.637648 0.770328i \(-0.720092\pi\)
0.348300 + 0.937383i \(0.386759\pi\)
\(942\) 0 0
\(943\) −5.31899e7 + 9.21276e7i −0.0634299 + 0.109864i
\(944\) 8.63042e7i 0.102593i
\(945\) 0 0
\(946\) −7.13894e8 −0.843258
\(947\) −7.22272e8 4.17004e8i −0.850454 0.491010i 0.0103502 0.999946i \(-0.496705\pi\)
−0.860804 + 0.508937i \(0.830039\pi\)
\(948\) 0 0
\(949\) −6.40153e8 1.10878e9i −0.749006 1.29732i
\(950\) 3.43859e8 1.98527e8i 0.401060 0.231552i
\(951\) 0 0
\(952\) −3.05549e6 + 5.29226e6i −0.00354135 + 0.00613381i
\(953\) 1.27101e8i 0.146849i 0.997301 + 0.0734245i \(0.0233928\pi\)
−0.997301 + 0.0734245i \(0.976607\pi\)
\(954\) 0 0
\(955\) −2.19572e8 −0.252097
\(956\) −3.25313e8 1.87820e8i −0.372330 0.214965i
\(957\) 0 0
\(958\) −8.01766e7 1.38870e8i −0.0911908 0.157947i
\(959\) 1.02691e8 5.92889e7i 0.116434 0.0672229i
\(960\) 0 0
\(961\) −4.52333e8 + 7.83464e8i −0.509669 + 0.882772i
\(962\) 1.05662e9i 1.18684i
\(963\) 0 0
\(964\) 8.49229e8 0.947969
\(965\) −3.87322e7 2.23620e7i −0.0431013 0.0248845i
\(966\) 0 0
\(967\) 1.78470e8 + 3.09120e8i 0.197373 + 0.341859i 0.947676 0.319235i \(-0.103426\pi\)
−0.750303 + 0.661094i \(0.770092\pi\)
\(968\) 1.39574e8 8.05828e7i 0.153878 0.0888416i
\(969\) 0 0
\(970\) −6.55092e7 + 1.13465e8i −0.0717773 + 0.124322i
\(971\) 2.79662e8i 0.305476i −0.988267 0.152738i \(-0.951191\pi\)
0.988267 0.152738i \(-0.0488090\pi\)
\(972\) 0 0
\(973\) 8.88905e6 0.00964977
\(974\) 2.97081e8 + 1.71520e8i 0.321513 + 0.185625i
\(975\) 0 0
\(976\) −5.03719e7 8.72467e7i −0.0541800 0.0938425i
\(977\) 7.08671e7 4.09152e7i 0.0759908 0.0438733i −0.461523 0.887128i \(-0.652697\pi\)
0.537514 + 0.843255i \(0.319364\pi\)
\(978\) 0 0
\(979\) −6.14069e8 + 1.06360e9i −0.654439 + 1.13352i
\(980\) 1.83712e8i 0.195191i
\(981\) 0 0
\(982\) 8.79946e8 0.929226
\(983\) −7.65774e8 4.42120e8i −0.806195 0.465457i 0.0394375 0.999222i \(-0.487443\pi\)
−0.845633 + 0.533765i \(0.820777\pi\)
\(984\) 0 0
\(985\) −1.23041e8 2.13113e8i −0.128748 0.222998i
\(986\) 4.46648e7 2.57872e7i 0.0465945 0.0269013i
\(987\) 0 0
\(988\) 2.97258e8 5.14867e8i 0.308222 0.533856i
\(989\) 7.30607e7i 0.0755258i
\(990\) 0 0
\(991\) 1.35522e9 1.39248 0.696239 0.717810i \(-0.254855\pi\)
0.696239 + 0.717810i \(0.254855\pi\)
\(992\) −2.12371e8 1.22612e8i −0.217551 0.125603i
\(993\) 0 0
\(994\) 6.55527e7 + 1.13541e8i 0.0667469 + 0.115609i
\(995\) 3.62606e8 2.09351e8i 0.368100 0.212523i
\(996\) 0 0
\(997\) −4.59348e8 + 7.95613e8i −0.463507 + 0.802817i −0.999133 0.0416381i \(-0.986742\pi\)
0.535626 + 0.844455i \(0.320076\pi\)
\(998\) 7.31843e8i 0.736252i
\(999\) 0 0
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 162.7.d.e.107.1 8
3.2 odd 2 inner 162.7.d.e.107.4 8
9.2 odd 6 54.7.b.c.53.2 4
9.4 even 3 inner 162.7.d.e.53.4 8
9.5 odd 6 inner 162.7.d.e.53.1 8
9.7 even 3 54.7.b.c.53.3 yes 4
36.7 odd 6 432.7.e.h.161.2 4
36.11 even 6 432.7.e.h.161.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.7.b.c.53.2 4 9.2 odd 6
54.7.b.c.53.3 yes 4 9.7 even 3
162.7.d.e.53.1 8 9.5 odd 6 inner
162.7.d.e.53.4 8 9.4 even 3 inner
162.7.d.e.107.1 8 1.1 even 1 trivial
162.7.d.e.107.4 8 3.2 odd 2 inner
432.7.e.h.161.2 4 36.7 odd 6
432.7.e.h.161.3 4 36.11 even 6