Properties

Label 108.6.i.a.13.12
Level $108$
Weight $6$
Character 108.13
Analytic conductor $17.321$
Analytic rank $0$
Dimension $90$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [108,6,Mod(13,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.13");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), 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: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(90\)
Relative dimension: \(15\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 13.12
Character \(\chi\) \(=\) 108.13
Dual form 108.6.i.a.25.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(11.6047 + 10.4082i) q^{3} +(50.4250 + 42.3116i) q^{5} +(105.429 + 38.3730i) q^{7} +(26.3374 + 241.569i) q^{9} +O(q^{10})\) \(q+(11.6047 + 10.4082i) q^{3} +(50.4250 + 42.3116i) q^{5} +(105.429 + 38.3730i) q^{7} +(26.3374 + 241.569i) q^{9} +(15.8754 - 13.3211i) q^{11} +(66.0301 - 374.475i) q^{13} +(144.777 + 1015.85i) q^{15} +(93.8720 - 162.591i) q^{17} +(23.9773 + 41.5299i) q^{19} +(824.075 + 1542.64i) q^{21} +(-2001.53 + 728.498i) q^{23} +(209.758 + 1189.60i) q^{25} +(-2208.66 + 3077.45i) q^{27} +(192.854 + 1093.73i) q^{29} +(5304.29 - 1930.61i) q^{31} +(322.878 + 10.6484i) q^{33} +(3692.63 + 6395.82i) q^{35} +(-5133.04 + 8890.68i) q^{37} +(4663.88 - 3658.41i) q^{39} +(-632.010 + 3584.31i) q^{41} +(-4373.32 + 3669.65i) q^{43} +(-8893.08 + 13295.5i) q^{45} +(10589.0 + 3854.10i) q^{47} +(-3232.12 - 2712.07i) q^{49} +(2781.64 - 909.776i) q^{51} +40756.1 q^{53} +1364.15 q^{55} +(-154.004 + 731.502i) q^{57} +(-6950.23 - 5831.93i) q^{59} +(-37315.2 - 13581.6i) q^{61} +(-6492.99 + 26479.0i) q^{63} +(19174.2 - 16089.1i) q^{65} +(8375.85 - 47501.8i) q^{67} +(-30809.5 - 12378.4i) q^{69} +(-1152.02 + 1995.35i) q^{71} +(-17866.4 - 30945.5i) q^{73} +(-9947.41 + 15988.1i) q^{75} +(2184.90 - 795.239i) q^{77} +(-15966.2 - 90549.1i) q^{79} +(-57661.7 + 12724.6i) q^{81} +(-16547.1 - 93843.4i) q^{83} +(11613.0 - 4226.78i) q^{85} +(-9145.79 + 14699.7i) q^{87} +(-13047.3 - 22598.6i) q^{89} +(21331.2 - 36946.8i) q^{91} +(81648.9 + 32804.3i) q^{93} +(-548.141 + 3108.66i) q^{95} +(13856.1 - 11626.7i) q^{97} +(3636.07 + 3484.16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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
\(3\) 11.6047 + 10.4082i 0.744441 + 0.667688i
\(4\) 0 0
\(5\) 50.4250 + 42.3116i 0.902029 + 0.756892i 0.970586 0.240755i \(-0.0773950\pi\)
−0.0685567 + 0.997647i \(0.521839\pi\)
\(6\) 0 0
\(7\) 105.429 + 38.3730i 0.813233 + 0.295993i 0.714959 0.699167i \(-0.246446\pi\)
0.0982743 + 0.995159i \(0.468668\pi\)
\(8\) 0 0
\(9\) 26.3374 + 241.569i 0.108384 + 0.994109i
\(10\) 0 0
\(11\) 15.8754 13.3211i 0.0395589 0.0331939i −0.622794 0.782386i \(-0.714002\pi\)
0.662353 + 0.749192i \(0.269558\pi\)
\(12\) 0 0
\(13\) 66.0301 374.475i 0.108364 0.614561i −0.881460 0.472259i \(-0.843439\pi\)
0.989823 0.142302i \(-0.0454503\pi\)
\(14\) 0 0
\(15\) 144.777 + 1015.85i 0.166139 + 1.16574i
\(16\) 0 0
\(17\) 93.8720 162.591i 0.0787796 0.136450i −0.823944 0.566671i \(-0.808231\pi\)
0.902724 + 0.430221i \(0.141564\pi\)
\(18\) 0 0
\(19\) 23.9773 + 41.5299i 0.0152376 + 0.0263923i 0.873544 0.486746i \(-0.161816\pi\)
−0.858306 + 0.513138i \(0.828483\pi\)
\(20\) 0 0
\(21\) 824.075 + 1542.64i 0.407773 + 0.763335i
\(22\) 0 0
\(23\) −2001.53 + 728.498i −0.788938 + 0.287150i −0.704895 0.709312i \(-0.749006\pi\)
−0.0840437 + 0.996462i \(0.526784\pi\)
\(24\) 0 0
\(25\) 209.758 + 1189.60i 0.0671225 + 0.380671i
\(26\) 0 0
\(27\) −2208.66 + 3077.45i −0.583069 + 0.812422i
\(28\) 0 0
\(29\) 192.854 + 1093.73i 0.0425828 + 0.241499i 0.998668 0.0515884i \(-0.0164284\pi\)
−0.956086 + 0.293087i \(0.905317\pi\)
\(30\) 0 0
\(31\) 5304.29 1930.61i 0.991342 0.360819i 0.205102 0.978741i \(-0.434247\pi\)
0.786240 + 0.617922i \(0.212025\pi\)
\(32\) 0 0
\(33\) 322.878 + 10.6484i 0.0516124 + 0.00170216i
\(34\) 0 0
\(35\) 3692.63 + 6395.82i 0.509525 + 0.882524i
\(36\) 0 0
\(37\) −5133.04 + 8890.68i −0.616411 + 1.06765i 0.373725 + 0.927540i \(0.378080\pi\)
−0.990135 + 0.140115i \(0.955253\pi\)
\(38\) 0 0
\(39\) 4663.88 3658.41i 0.491005 0.385151i
\(40\) 0 0
\(41\) −632.010 + 3584.31i −0.0587171 + 0.333001i −0.999989 0.00464783i \(-0.998521\pi\)
0.941272 + 0.337649i \(0.109632\pi\)
\(42\) 0 0
\(43\) −4373.32 + 3669.65i −0.360695 + 0.302659i −0.805068 0.593183i \(-0.797871\pi\)
0.444373 + 0.895842i \(0.353427\pi\)
\(44\) 0 0
\(45\) −8893.08 + 13295.5i −0.654668 + 0.978751i
\(46\) 0 0
\(47\) 10589.0 + 3854.10i 0.699217 + 0.254494i 0.667077 0.744989i \(-0.267545\pi\)
0.0321405 + 0.999483i \(0.489768\pi\)
\(48\) 0 0
\(49\) −3232.12 2712.07i −0.192308 0.161366i
\(50\) 0 0
\(51\) 2781.64 909.776i 0.149753 0.0489789i
\(52\) 0 0
\(53\) 40756.1 1.99298 0.996490 0.0837151i \(-0.0266786\pi\)
0.996490 + 0.0837151i \(0.0266786\pi\)
\(54\) 0 0
\(55\) 1364.15 0.0608075
\(56\) 0 0
\(57\) −154.004 + 731.502i −0.00627833 + 0.0298214i
\(58\) 0 0
\(59\) −6950.23 5831.93i −0.259938 0.218113i 0.503500 0.863995i \(-0.332045\pi\)
−0.763437 + 0.645882i \(0.776490\pi\)
\(60\) 0 0
\(61\) −37315.2 13581.6i −1.28399 0.467334i −0.392240 0.919863i \(-0.628300\pi\)
−0.891750 + 0.452529i \(0.850522\pi\)
\(62\) 0 0
\(63\) −6492.99 + 26479.0i −0.206107 + 0.840523i
\(64\) 0 0
\(65\) 19174.2 16089.1i 0.562904 0.472332i
\(66\) 0 0
\(67\) 8375.85 47501.8i 0.227951 1.29278i −0.629011 0.777396i \(-0.716540\pi\)
0.856962 0.515379i \(-0.172349\pi\)
\(68\) 0 0
\(69\) −30809.5 12378.4i −0.779045 0.312999i
\(70\) 0 0
\(71\) −1152.02 + 1995.35i −0.0271215 + 0.0469758i −0.879268 0.476328i \(-0.841967\pi\)
0.852146 + 0.523304i \(0.175301\pi\)
\(72\) 0 0
\(73\) −17866.4 30945.5i −0.392401 0.679659i 0.600364 0.799727i \(-0.295022\pi\)
−0.992766 + 0.120068i \(0.961689\pi\)
\(74\) 0 0
\(75\) −9947.41 + 15988.1i −0.204201 + 0.328204i
\(76\) 0 0
\(77\) 2184.90 795.239i 0.0419957 0.0152852i
\(78\) 0 0
\(79\) −15966.2 90549.1i −0.287829 1.63236i −0.695000 0.719009i \(-0.744596\pi\)
0.407171 0.913352i \(-0.366515\pi\)
\(80\) 0 0
\(81\) −57661.7 + 12724.6i −0.976506 + 0.215492i
\(82\) 0 0
\(83\) −16547.1 93843.4i −0.263650 1.49523i −0.772853 0.634585i \(-0.781171\pi\)
0.509203 0.860646i \(-0.329940\pi\)
\(84\) 0 0
\(85\) 11613.0 4226.78i 0.174340 0.0634544i
\(86\) 0 0
\(87\) −9145.79 + 14699.7i −0.129546 + 0.208214i
\(88\) 0 0
\(89\) −13047.3 22598.6i −0.174600 0.302417i 0.765423 0.643528i \(-0.222530\pi\)
−0.940023 + 0.341111i \(0.889197\pi\)
\(90\) 0 0
\(91\) 21331.2 36946.8i 0.270030 0.467706i
\(92\) 0 0
\(93\) 81648.9 + 32804.3i 0.978910 + 0.393299i
\(94\) 0 0
\(95\) −548.141 + 3108.66i −0.00623136 + 0.0353398i
\(96\) 0 0
\(97\) 13856.1 11626.7i 0.149524 0.125466i −0.564957 0.825120i \(-0.691107\pi\)
0.714481 + 0.699655i \(0.246663\pi\)
\(98\) 0 0
\(99\) 3636.07 + 3484.16i 0.0372859 + 0.0357282i
\(100\) 0 0
\(101\) 172922. + 62938.3i 1.68673 + 0.613920i 0.994208 0.107476i \(-0.0342770\pi\)
0.692523 + 0.721396i \(0.256499\pi\)
\(102\) 0 0
\(103\) −70924.5 59512.7i −0.658724 0.552735i 0.250980 0.967992i \(-0.419247\pi\)
−0.909704 + 0.415257i \(0.863692\pi\)
\(104\) 0 0
\(105\) −23717.4 + 112655.i −0.209939 + 0.997191i
\(106\) 0 0
\(107\) 606.415 0.00512048 0.00256024 0.999997i \(-0.499185\pi\)
0.00256024 + 0.999997i \(0.499185\pi\)
\(108\) 0 0
\(109\) 81329.8 0.655667 0.327834 0.944735i \(-0.393681\pi\)
0.327834 + 0.944735i \(0.393681\pi\)
\(110\) 0 0
\(111\) −152104. + 49747.7i −1.17174 + 0.383235i
\(112\) 0 0
\(113\) 167369. + 140439.i 1.23305 + 1.03465i 0.998035 + 0.0626552i \(0.0199568\pi\)
0.235010 + 0.971993i \(0.424488\pi\)
\(114\) 0 0
\(115\) −131751. 47953.5i −0.928987 0.338124i
\(116\) 0 0
\(117\) 92200.5 + 6088.09i 0.622685 + 0.0411165i
\(118\) 0 0
\(119\) 16135.9 13539.7i 0.104454 0.0876476i
\(120\) 0 0
\(121\) −27891.6 + 158181.i −0.173185 + 0.982182i
\(122\) 0 0
\(123\) −44640.6 + 35016.6i −0.266052 + 0.208695i
\(124\) 0 0
\(125\) 63095.1 109284.i 0.361178 0.625578i
\(126\) 0 0
\(127\) −154548. 267684.i −0.850262 1.47270i −0.880972 0.473169i \(-0.843110\pi\)
0.0307091 0.999528i \(-0.490223\pi\)
\(128\) 0 0
\(129\) −88945.5 2933.39i −0.470598 0.0155201i
\(130\) 0 0
\(131\) 175212. 63772.1i 0.892045 0.324678i 0.144984 0.989434i \(-0.453687\pi\)
0.747060 + 0.664756i \(0.231465\pi\)
\(132\) 0 0
\(133\) 934.275 + 5298.53i 0.00457979 + 0.0259733i
\(134\) 0 0
\(135\) −241584. + 61728.4i −1.14086 + 0.291508i
\(136\) 0 0
\(137\) 35228.9 + 199793.i 0.160361 + 0.909451i 0.953720 + 0.300697i \(0.0972192\pi\)
−0.793359 + 0.608754i \(0.791670\pi\)
\(138\) 0 0
\(139\) −289065. + 105211.i −1.26899 + 0.461875i −0.886776 0.462199i \(-0.847060\pi\)
−0.382214 + 0.924074i \(0.624838\pi\)
\(140\) 0 0
\(141\) 82768.2 + 154939.i 0.350603 + 0.656315i
\(142\) 0 0
\(143\) −3940.16 6824.55i −0.0161129 0.0279084i
\(144\) 0 0
\(145\) −36552.8 + 63311.3i −0.144378 + 0.250070i
\(146\) 0 0
\(147\) −9279.88 65113.5i −0.0354200 0.248529i
\(148\) 0 0
\(149\) −24420.3 + 138494.i −0.0901124 + 0.511053i 0.906023 + 0.423227i \(0.139103\pi\)
−0.996136 + 0.0878254i \(0.972008\pi\)
\(150\) 0 0
\(151\) −45605.6 + 38267.6i −0.162770 + 0.136581i −0.720535 0.693419i \(-0.756104\pi\)
0.557765 + 0.829999i \(0.311659\pi\)
\(152\) 0 0
\(153\) 41749.2 + 18394.3i 0.144185 + 0.0635264i
\(154\) 0 0
\(155\) 349156. + 127082.i 1.16732 + 0.424870i
\(156\) 0 0
\(157\) 272711. + 228831.i 0.882984 + 0.740912i 0.966791 0.255570i \(-0.0822632\pi\)
−0.0838060 + 0.996482i \(0.526708\pi\)
\(158\) 0 0
\(159\) 472962. + 424199.i 1.48366 + 1.33069i
\(160\) 0 0
\(161\) −238974. −0.726585
\(162\) 0 0
\(163\) 579999. 1.70985 0.854926 0.518750i \(-0.173603\pi\)
0.854926 + 0.518750i \(0.173603\pi\)
\(164\) 0 0
\(165\) 15830.6 + 14198.4i 0.0452676 + 0.0406004i
\(166\) 0 0
\(167\) −136225. 114307.i −0.377978 0.317161i 0.433930 0.900947i \(-0.357126\pi\)
−0.811908 + 0.583785i \(0.801571\pi\)
\(168\) 0 0
\(169\) 213030. + 77536.4i 0.573750 + 0.208828i
\(170\) 0 0
\(171\) −9400.81 + 6885.95i −0.0245853 + 0.0180083i
\(172\) 0 0
\(173\) −273574. + 229555.i −0.694958 + 0.583139i −0.920334 0.391133i \(-0.872083\pi\)
0.225376 + 0.974272i \(0.427639\pi\)
\(174\) 0 0
\(175\) −23533.8 + 133467.i −0.0580894 + 0.329442i
\(176\) 0 0
\(177\) −19955.1 140017.i −0.0478763 0.335930i
\(178\) 0 0
\(179\) 133930. 231974.i 0.312426 0.541137i −0.666461 0.745540i \(-0.732192\pi\)
0.978887 + 0.204403i \(0.0655252\pi\)
\(180\) 0 0
\(181\) −316166. 547615.i −0.717329 1.24245i −0.962055 0.272857i \(-0.912031\pi\)
0.244726 0.969592i \(-0.421302\pi\)
\(182\) 0 0
\(183\) −291671. 545996.i −0.643821 1.20521i
\(184\) 0 0
\(185\) −635012. + 231125.i −1.36412 + 0.496499i
\(186\) 0 0
\(187\) −675.629 3831.68i −0.00141288 0.00801282i
\(188\) 0 0
\(189\) −350948. + 239700.i −0.714642 + 0.488104i
\(190\) 0 0
\(191\) −31083.5 176283.i −0.0616519 0.349645i −0.999992 0.00393252i \(-0.998748\pi\)
0.938340 0.345713i \(-0.112363\pi\)
\(192\) 0 0
\(193\) 399489. 145402.i 0.771990 0.280981i 0.0741616 0.997246i \(-0.476372\pi\)
0.697829 + 0.716265i \(0.254150\pi\)
\(194\) 0 0
\(195\) 389969. + 12861.0i 0.734419 + 0.0242208i
\(196\) 0 0
\(197\) −498292. 863067.i −0.914783 1.58445i −0.807219 0.590253i \(-0.799028\pi\)
−0.107564 0.994198i \(-0.534305\pi\)
\(198\) 0 0
\(199\) −57000.7 + 98728.1i −0.102035 + 0.176729i −0.912523 0.409026i \(-0.865869\pi\)
0.810488 + 0.585755i \(0.199202\pi\)
\(200\) 0 0
\(201\) 591609. 464066.i 1.03287 0.810194i
\(202\) 0 0
\(203\) −21637.3 + 122711.i −0.0368522 + 0.208999i
\(204\) 0 0
\(205\) −183527. + 153997.i −0.305011 + 0.255934i
\(206\) 0 0
\(207\) −228697. 464320.i −0.370967 0.753168i
\(208\) 0 0
\(209\) 933.873 + 339.902i 0.00147884 + 0.000538255i
\(210\) 0 0
\(211\) 8500.53 + 7132.79i 0.0131444 + 0.0110294i 0.649336 0.760502i \(-0.275047\pi\)
−0.636192 + 0.771531i \(0.719491\pi\)
\(212\) 0 0
\(213\) −34136.9 + 11165.0i −0.0515555 + 0.0168620i
\(214\) 0 0
\(215\) −375793. −0.554437
\(216\) 0 0
\(217\) 633310. 0.912992
\(218\) 0 0
\(219\) 114754. 545071.i 0.161681 0.767968i
\(220\) 0 0
\(221\) −54687.9 45888.6i −0.0753201 0.0632011i
\(222\) 0 0
\(223\) −1.08720e6 395708.i −1.46402 0.532860i −0.517551 0.855652i \(-0.673156\pi\)
−0.946470 + 0.322792i \(0.895379\pi\)
\(224\) 0 0
\(225\) −281844. + 82001.7i −0.371153 + 0.107986i
\(226\) 0 0
\(227\) 990520. 831145.i 1.27585 1.07056i 0.282045 0.959401i \(-0.408987\pi\)
0.993802 0.111162i \(-0.0354571\pi\)
\(228\) 0 0
\(229\) −165477. + 938466.i −0.208521 + 1.18258i 0.683282 + 0.730154i \(0.260552\pi\)
−0.891803 + 0.452424i \(0.850559\pi\)
\(230\) 0 0
\(231\) 33632.1 + 13512.5i 0.0414691 + 0.0166611i
\(232\) 0 0
\(233\) 51142.1 88580.8i 0.0617147 0.106893i −0.833517 0.552493i \(-0.813676\pi\)
0.895232 + 0.445600i \(0.147010\pi\)
\(234\) 0 0
\(235\) 370879. + 642382.i 0.438090 + 0.758793i
\(236\) 0 0
\(237\) 757173. 1.21697e6i 0.875637 1.40738i
\(238\) 0 0
\(239\) −1.45627e6 + 530039.i −1.64910 + 0.600224i −0.988595 0.150596i \(-0.951881\pi\)
−0.660507 + 0.750820i \(0.729659\pi\)
\(240\) 0 0
\(241\) −71022.4 402788.i −0.0787686 0.446719i −0.998528 0.0542364i \(-0.982728\pi\)
0.919760 0.392482i \(-0.128384\pi\)
\(242\) 0 0
\(243\) −801586. 452492.i −0.870832 0.491581i
\(244\) 0 0
\(245\) −48227.6 273513.i −0.0513311 0.291113i
\(246\) 0 0
\(247\) 17135.1 6236.68i 0.0178708 0.00650446i
\(248\) 0 0
\(249\) 784720. 1.26125e6i 0.802077 1.28915i
\(250\) 0 0
\(251\) 86526.5 + 149868.i 0.0866892 + 0.150150i 0.906110 0.423043i \(-0.139038\pi\)
−0.819421 + 0.573193i \(0.805705\pi\)
\(252\) 0 0
\(253\) −22070.8 + 38227.8i −0.0216779 + 0.0375472i
\(254\) 0 0
\(255\) 178758. + 71820.1i 0.172153 + 0.0691665i
\(256\) 0 0
\(257\) −248173. + 1.40746e6i −0.234381 + 1.32924i 0.609532 + 0.792761i \(0.291357\pi\)
−0.843913 + 0.536480i \(0.819754\pi\)
\(258\) 0 0
\(259\) −882333. + 740365.i −0.817303 + 0.685799i
\(260\) 0 0
\(261\) −259132. + 75393.5i −0.235461 + 0.0685067i
\(262\) 0 0
\(263\) 252535. + 91915.4i 0.225130 + 0.0819405i 0.452122 0.891956i \(-0.350667\pi\)
−0.226992 + 0.973897i \(0.572889\pi\)
\(264\) 0 0
\(265\) 2.05512e6 + 1.72445e6i 1.79773 + 1.50847i
\(266\) 0 0
\(267\) 83801.4 398048.i 0.0719405 0.341710i
\(268\) 0 0
\(269\) −1.05143e6 −0.885927 −0.442963 0.896540i \(-0.646073\pi\)
−0.442963 + 0.896540i \(0.646073\pi\)
\(270\) 0 0
\(271\) 2.24688e6 1.85847 0.929237 0.369484i \(-0.120466\pi\)
0.929237 + 0.369484i \(0.120466\pi\)
\(272\) 0 0
\(273\) 632093. 206735.i 0.513304 0.167883i
\(274\) 0 0
\(275\) 19176.7 + 16091.2i 0.0152912 + 0.0128309i
\(276\) 0 0
\(277\) −964358. 350997.i −0.755159 0.274856i −0.0643843 0.997925i \(-0.520508\pi\)
−0.690775 + 0.723070i \(0.742731\pi\)
\(278\) 0 0
\(279\) 606075. + 1.23050e6i 0.466139 + 0.946395i
\(280\) 0 0
\(281\) 388199. 325738.i 0.293284 0.246095i −0.484258 0.874925i \(-0.660911\pi\)
0.777542 + 0.628830i \(0.216466\pi\)
\(282\) 0 0
\(283\) −295011. + 1.67309e6i −0.218964 + 1.24181i 0.654930 + 0.755690i \(0.272698\pi\)
−0.873894 + 0.486117i \(0.838413\pi\)
\(284\) 0 0
\(285\) −38716.6 + 30369.8i −0.0282349 + 0.0221478i
\(286\) 0 0
\(287\) −204173. + 353638.i −0.146317 + 0.253428i
\(288\) 0 0
\(289\) 692305. + 1.19911e6i 0.487588 + 0.844526i
\(290\) 0 0
\(291\) 281809. + 9293.94i 0.195084 + 0.00643380i
\(292\) 0 0
\(293\) −1.83054e6 + 666263.i −1.24569 + 0.453395i −0.878944 0.476925i \(-0.841751\pi\)
−0.366749 + 0.930320i \(0.619529\pi\)
\(294\) 0 0
\(295\) −103707. 588150.i −0.0693828 0.393489i
\(296\) 0 0
\(297\) 5931.45 + 78277.7i 0.00390185 + 0.0514929i
\(298\) 0 0
\(299\) 140643. + 797627.i 0.0909789 + 0.515967i
\(300\) 0 0
\(301\) −601890. + 219070.i −0.382914 + 0.139369i
\(302\) 0 0
\(303\) 1.35162e6 + 2.53019e6i 0.845764 + 1.58324i
\(304\) 0 0
\(305\) −1.30696e6 2.26372e6i −0.804474 1.39339i
\(306\) 0 0
\(307\) 940971. 1.62981e6i 0.569810 0.986941i −0.426774 0.904358i \(-0.640350\pi\)
0.996584 0.0825822i \(-0.0263167\pi\)
\(308\) 0 0
\(309\) −203634. 1.42883e6i −0.121326 0.851301i
\(310\) 0 0
\(311\) −278916. + 1.58181e6i −0.163521 + 0.927371i 0.787056 + 0.616881i \(0.211604\pi\)
−0.950577 + 0.310490i \(0.899507\pi\)
\(312\) 0 0
\(313\) 64593.6 54200.5i 0.0372674 0.0312710i −0.623964 0.781453i \(-0.714479\pi\)
0.661231 + 0.750182i \(0.270034\pi\)
\(314\) 0 0
\(315\) −1.44778e6 + 1.06047e6i −0.822100 + 0.602176i
\(316\) 0 0
\(317\) −385099. 140164.i −0.215240 0.0783411i 0.232150 0.972680i \(-0.425424\pi\)
−0.447390 + 0.894339i \(0.647646\pi\)
\(318\) 0 0
\(319\) 17631.3 + 14794.4i 0.00970081 + 0.00813995i
\(320\) 0 0
\(321\) 7037.25 + 6311.71i 0.00381189 + 0.00341888i
\(322\) 0 0
\(323\) 9003.18 0.00480164
\(324\) 0 0
\(325\) 459324. 0.241219
\(326\) 0 0
\(327\) 943807. + 846500.i 0.488106 + 0.437782i
\(328\) 0 0
\(329\) 968499. + 812667.i 0.493298 + 0.413926i
\(330\) 0 0
\(331\) −1.20156e6 437333.i −0.602804 0.219403i 0.0225477 0.999746i \(-0.492822\pi\)
−0.625352 + 0.780343i \(0.715044\pi\)
\(332\) 0 0
\(333\) −2.28290e6 1.00582e6i −1.12817 0.497062i
\(334\) 0 0
\(335\) 2.43223e6 2.04088e6i 1.18411 0.993587i
\(336\) 0 0
\(337\) −171503. + 972644.i −0.0822617 + 0.466530i 0.915652 + 0.401971i \(0.131675\pi\)
−0.997914 + 0.0645581i \(0.979436\pi\)
\(338\) 0 0
\(339\) 480540. + 3.37177e6i 0.227107 + 1.59352i
\(340\) 0 0
\(341\) 58490.3 101308.i 0.0272394 0.0471801i
\(342\) 0 0
\(343\) −1.17952e6 2.04299e6i −0.541341 0.937629i
\(344\) 0 0
\(345\) −1.02982e6 1.92778e6i −0.465815 0.871987i
\(346\) 0 0
\(347\) −22562.9 + 8212.24i −0.0100594 + 0.00366132i −0.347045 0.937848i \(-0.612815\pi\)
0.336986 + 0.941510i \(0.390593\pi\)
\(348\) 0 0
\(349\) −226.526 1284.69i −9.95530e−5 0.000564593i 0.984758 0.173930i \(-0.0556468\pi\)
−0.984857 + 0.173366i \(0.944536\pi\)
\(350\) 0 0
\(351\) 1.00659e6 + 1.03029e6i 0.436099 + 0.446369i
\(352\) 0 0
\(353\) 580092. + 3.28987e6i 0.247777 + 1.40521i 0.813955 + 0.580928i \(0.197310\pi\)
−0.566178 + 0.824283i \(0.691579\pi\)
\(354\) 0 0
\(355\) −142517. + 51872.0i −0.0600200 + 0.0218455i
\(356\) 0 0
\(357\) 328176. + 10823.1i 0.136281 + 0.00449451i
\(358\) 0 0
\(359\) −1.03014e6 1.78425e6i −0.421850 0.730666i 0.574270 0.818666i \(-0.305286\pi\)
−0.996121 + 0.0879996i \(0.971953\pi\)
\(360\) 0 0
\(361\) 1.23690e6 2.14237e6i 0.499536 0.865221i
\(362\) 0 0
\(363\) −1.97006e6 + 1.54534e6i −0.784717 + 0.615542i
\(364\) 0 0
\(365\) 408441. 2.31638e6i 0.160471 0.910078i
\(366\) 0 0
\(367\) −613458. + 514752.i −0.237749 + 0.199495i −0.753876 0.657017i \(-0.771818\pi\)
0.516126 + 0.856512i \(0.327374\pi\)
\(368\) 0 0
\(369\) −882501. 58272.5i −0.337403 0.0222791i
\(370\) 0 0
\(371\) 4.29687e6 + 1.56393e6i 1.62076 + 0.589907i
\(372\) 0 0
\(373\) 357268. + 299783.i 0.132960 + 0.111567i 0.706843 0.707371i \(-0.250119\pi\)
−0.573882 + 0.818938i \(0.694563\pi\)
\(374\) 0 0
\(375\) 1.86965e6 611497.i 0.686567 0.224552i
\(376\) 0 0
\(377\) 422309. 0.153030
\(378\) 0 0
\(379\) −3.64393e6 −1.30308 −0.651541 0.758613i \(-0.725877\pi\)
−0.651541 + 0.758613i \(0.725877\pi\)
\(380\) 0 0
\(381\) 992644. 4.71496e6i 0.350333 1.66405i
\(382\) 0 0
\(383\) 2.96855e6 + 2.49091e6i 1.03406 + 0.867683i 0.991329 0.131404i \(-0.0419485\pi\)
0.0427349 + 0.999086i \(0.486393\pi\)
\(384\) 0 0
\(385\) 143821. + 52346.7i 0.0494506 + 0.0179986i
\(386\) 0 0
\(387\) −1.00165e6 959807.i −0.339970 0.325766i
\(388\) 0 0
\(389\) −327734. + 275001.i −0.109811 + 0.0921427i −0.696040 0.718003i \(-0.745056\pi\)
0.586229 + 0.810146i \(0.300612\pi\)
\(390\) 0 0
\(391\) −69440.5 + 393817.i −0.0229705 + 0.130272i
\(392\) 0 0
\(393\) 2.69704e6 + 1.08360e6i 0.880858 + 0.353905i
\(394\) 0 0
\(395\) 3.02618e6 5.24149e6i 0.975892 1.69029i
\(396\) 0 0
\(397\) −698113. 1.20917e6i −0.222305 0.385044i 0.733202 0.680011i \(-0.238025\pi\)
−0.955508 + 0.294967i \(0.904691\pi\)
\(398\) 0 0
\(399\) −44306.4 + 71212.0i −0.0139327 + 0.0223934i
\(400\) 0 0
\(401\) −1.70691e6 + 621263.i −0.530089 + 0.192937i −0.593178 0.805071i \(-0.702127\pi\)
0.0630889 + 0.998008i \(0.479905\pi\)
\(402\) 0 0
\(403\) −372721. 2.11381e6i −0.114320 0.648339i
\(404\) 0 0
\(405\) −3.44599e6 1.79812e6i −1.04394 0.544730i
\(406\) 0 0
\(407\) 36944.2 + 209521.i 0.0110550 + 0.0626963i
\(408\) 0 0
\(409\) −2.94043e6 + 1.07023e6i −0.869166 + 0.316351i −0.737829 0.674987i \(-0.764149\pi\)
−0.131337 + 0.991338i \(0.541927\pi\)
\(410\) 0 0
\(411\) −1.67067e6 + 2.68521e6i −0.487851 + 0.784103i
\(412\) 0 0
\(413\) −508967. 881556.i −0.146830 0.254317i
\(414\) 0 0
\(415\) 3.13627e6 5.43218e6i 0.893910 1.54830i
\(416\) 0 0
\(417\) −4.44957e6 1.78771e6i −1.25308 0.503452i
\(418\) 0 0
\(419\) 379779. 2.15383e6i 0.105681 0.599345i −0.885266 0.465086i \(-0.846023\pi\)
0.990946 0.134259i \(-0.0428654\pi\)
\(420\) 0 0
\(421\) 689302. 578393.i 0.189541 0.159044i −0.543079 0.839682i \(-0.682742\pi\)
0.732620 + 0.680638i \(0.238297\pi\)
\(422\) 0 0
\(423\) −652141. + 2.65949e6i −0.177211 + 0.722681i
\(424\) 0 0
\(425\) 213108. + 77564.9i 0.0572305 + 0.0208302i
\(426\) 0 0
\(427\) −3.41294e6 2.86380e6i −0.905855 0.760103i
\(428\) 0 0
\(429\) 25307.3 120207.i 0.00663899 0.0315345i
\(430\) 0 0
\(431\) −1.40307e6 −0.363820 −0.181910 0.983315i \(-0.558228\pi\)
−0.181910 + 0.983315i \(0.558228\pi\)
\(432\) 0 0
\(433\) −516851. −0.132479 −0.0662393 0.997804i \(-0.521100\pi\)
−0.0662393 + 0.997804i \(0.521100\pi\)
\(434\) 0 0
\(435\) −1.08314e6 + 354258.i −0.274450 + 0.0897628i
\(436\) 0 0
\(437\) −78245.8 65656.0i −0.0196001 0.0164464i
\(438\) 0 0
\(439\) −3.95225e6 1.43850e6i −0.978775 0.356245i −0.197411 0.980321i \(-0.563253\pi\)
−0.781364 + 0.624076i \(0.785476\pi\)
\(440\) 0 0
\(441\) 570026. 852208.i 0.139572 0.208665i
\(442\) 0 0
\(443\) 768945. 645221.i 0.186160 0.156207i −0.544945 0.838472i \(-0.683449\pi\)
0.731105 + 0.682265i \(0.239005\pi\)
\(444\) 0 0
\(445\) 298272. 1.69158e6i 0.0714022 0.404942i
\(446\) 0 0
\(447\) −1.72487e6 + 1.35301e6i −0.408307 + 0.320282i
\(448\) 0 0
\(449\) −27453.5 + 47550.8i −0.00642661 + 0.0111312i −0.869221 0.494424i \(-0.835379\pi\)
0.862794 + 0.505555i \(0.168712\pi\)
\(450\) 0 0
\(451\) 37713.4 + 65321.5i 0.00873081 + 0.0151222i
\(452\) 0 0
\(453\) −927536. 30589.8i −0.212366 0.00700375i
\(454\) 0 0
\(455\) 2.63890e6 960482.i 0.597579 0.217501i
\(456\) 0 0
\(457\) −373230. 2.11669e6i −0.0835962 0.474098i −0.997651 0.0685062i \(-0.978177\pi\)
0.914055 0.405591i \(-0.132934\pi\)
\(458\) 0 0
\(459\) 293034. + 647995.i 0.0649212 + 0.143562i
\(460\) 0 0
\(461\) −247406. 1.40311e6i −0.0542198 0.307496i 0.945622 0.325267i \(-0.105454\pi\)
−0.999842 + 0.0177712i \(0.994343\pi\)
\(462\) 0 0
\(463\) 2.90834e6 1.05855e6i 0.630510 0.229487i −0.00694314 0.999976i \(-0.502210\pi\)
0.637453 + 0.770489i \(0.279988\pi\)
\(464\) 0 0
\(465\) 2.72914e6 + 5.10885e6i 0.585320 + 1.09570i
\(466\) 0 0
\(467\) 1.84631e6 + 3.19790e6i 0.391753 + 0.678536i 0.992681 0.120767i \(-0.0385355\pi\)
−0.600928 + 0.799303i \(0.705202\pi\)
\(468\) 0 0
\(469\) 2.70584e6 4.68666e6i 0.568029 0.983856i
\(470\) 0 0
\(471\) 782991. + 5.49395e6i 0.162631 + 1.14112i
\(472\) 0 0
\(473\) −20544.7 + 116515.i −0.00422227 + 0.0239457i
\(474\) 0 0
\(475\) −44374.3 + 37234.5i −0.00902397 + 0.00757201i
\(476\) 0 0
\(477\) 1.07341e6 + 9.84539e6i 0.216008 + 1.98124i
\(478\) 0 0
\(479\) 3.93158e6 + 1.43098e6i 0.782939 + 0.284966i 0.702398 0.711785i \(-0.252113\pi\)
0.0805413 + 0.996751i \(0.474335\pi\)
\(480\) 0 0
\(481\) 2.99041e6 + 2.50925e6i 0.589342 + 0.494517i
\(482\) 0 0
\(483\) −2.77322e6 2.48730e6i −0.540899 0.485132i
\(484\) 0 0
\(485\) 1.19064e6 0.229840
\(486\) 0 0
\(487\) −4.17953e6 −0.798556 −0.399278 0.916830i \(-0.630739\pi\)
−0.399278 + 0.916830i \(0.630739\pi\)
\(488\) 0 0
\(489\) 6.73071e6 + 6.03677e6i 1.27288 + 1.14165i
\(490\) 0 0
\(491\) 4.58207e6 + 3.84481e6i 0.857745 + 0.719733i 0.961481 0.274872i \(-0.0886353\pi\)
−0.103736 + 0.994605i \(0.533080\pi\)
\(492\) 0 0
\(493\) 195934. + 71314.3i 0.0363073 + 0.0132148i
\(494\) 0 0
\(495\) 35928.3 + 329537.i 0.00659057 + 0.0604493i
\(496\) 0 0
\(497\) −198024. + 166162.i −0.0359606 + 0.0301745i
\(498\) 0 0
\(499\) −696332. + 3.94909e6i −0.125189 + 0.709980i 0.856007 + 0.516964i \(0.172938\pi\)
−0.981196 + 0.193016i \(0.938173\pi\)
\(500\) 0 0
\(501\) −391122. 2.74435e6i −0.0696174 0.488479i
\(502\) 0 0
\(503\) −31468.3 + 54504.6i −0.00554565 + 0.00960535i −0.868785 0.495190i \(-0.835099\pi\)
0.863239 + 0.504795i \(0.168432\pi\)
\(504\) 0 0
\(505\) 6.05655e6 + 1.04902e7i 1.05681 + 1.83045i
\(506\) 0 0
\(507\) 1.66512e6 + 3.11705e6i 0.287691 + 0.538547i
\(508\) 0 0
\(509\) −8.67397e6 + 3.15707e6i −1.48396 + 0.540119i −0.951853 0.306555i \(-0.900824\pi\)
−0.532111 + 0.846674i \(0.678601\pi\)
\(510\) 0 0
\(511\) −696165. 3.94815e6i −0.117940 0.668869i
\(512\) 0 0
\(513\) −180764. 17936.6i −0.0303262 0.00300917i
\(514\) 0 0
\(515\) −1.05829e6 6.00186e6i −0.175827 0.997166i
\(516\) 0 0
\(517\) 219446. 79872.0i 0.0361079 0.0131422i
\(518\) 0 0
\(519\) −5.56400e6 183499.i −0.906711 0.0299030i
\(520\) 0 0
\(521\) 2.62625e6 + 4.54879e6i 0.423878 + 0.734179i 0.996315 0.0857702i \(-0.0273351\pi\)
−0.572437 + 0.819949i \(0.694002\pi\)
\(522\) 0 0
\(523\) −2.99299e6 + 5.18400e6i −0.478465 + 0.828726i −0.999695 0.0246901i \(-0.992140\pi\)
0.521230 + 0.853416i \(0.325473\pi\)
\(524\) 0 0
\(525\) −1.66226e6 + 1.30390e6i −0.263208 + 0.206464i
\(526\) 0 0
\(527\) 184025. 1.04366e6i 0.0288637 0.163694i
\(528\) 0 0
\(529\) −1.45510e6 + 1.22098e6i −0.226076 + 0.189700i
\(530\) 0 0
\(531\) 1.22576e6 1.83255e6i 0.188655 0.282046i
\(532\) 0 0
\(533\) 1.30050e6 + 473344.i 0.198287 + 0.0721704i
\(534\) 0 0
\(535\) 30578.5 + 25658.4i 0.00461882 + 0.00387565i
\(536\) 0 0
\(537\) 3.96866e6 1.29801e6i 0.593893 0.194242i
\(538\) 0 0
\(539\) −87439.2 −0.0129639
\(540\) 0 0
\(541\) 584809. 0.0859054 0.0429527 0.999077i \(-0.486324\pi\)
0.0429527 + 0.999077i \(0.486324\pi\)
\(542\) 0 0
\(543\) 2.03070e6 9.64562e6i 0.295560 1.40388i
\(544\) 0 0
\(545\) 4.10105e6 + 3.44119e6i 0.591431 + 0.496270i
\(546\) 0 0
\(547\) −2.12856e6 774732.i −0.304171 0.110709i 0.185426 0.982658i \(-0.440634\pi\)
−0.489596 + 0.871949i \(0.662856\pi\)
\(548\) 0 0
\(549\) 2.29811e6 9.37189e6i 0.325417 1.32708i
\(550\) 0 0
\(551\) −40798.4 + 34233.9i −0.00572485 + 0.00480372i
\(552\) 0 0
\(553\) 1.79134e6 1.01592e7i 0.249095 1.41269i
\(554\) 0 0
\(555\) −9.77472e6 3.92721e6i −1.34701 0.541193i
\(556\) 0 0
\(557\) −6.87071e6 + 1.19004e7i −0.938348 + 1.62527i −0.169796 + 0.985479i \(0.554311\pi\)
−0.768552 + 0.639787i \(0.779022\pi\)
\(558\) 0 0
\(559\) 1.08542e6 + 1.88001e6i 0.146916 + 0.254466i
\(560\) 0 0
\(561\) 32040.6 51497.5i 0.00429826 0.00690843i
\(562\) 0 0
\(563\) −6.28717e6 + 2.28834e6i −0.835957 + 0.304264i −0.724301 0.689483i \(-0.757838\pi\)
−0.111656 + 0.993747i \(0.535615\pi\)
\(564\) 0 0
\(565\) 2.49737e6 + 1.41633e7i 0.329126 + 1.86657i
\(566\) 0 0
\(567\) −6.56749e6 871115.i −0.857911 0.113794i
\(568\) 0 0
\(569\) −781637. 4.43288e6i −0.101210 0.573992i −0.992667 0.120885i \(-0.961427\pi\)
0.891456 0.453107i \(-0.149684\pi\)
\(570\) 0 0
\(571\) −1.78221e6 + 648672.i −0.228754 + 0.0832598i −0.453854 0.891076i \(-0.649951\pi\)
0.225100 + 0.974336i \(0.427729\pi\)
\(572\) 0 0
\(573\) 1.47408e6 2.36924e6i 0.187558 0.301455i
\(574\) 0 0
\(575\) −1.28646e6 2.22821e6i −0.162265 0.281051i
\(576\) 0 0
\(577\) −5.65512e6 + 9.79495e6i −0.707134 + 1.22479i 0.258781 + 0.965936i \(0.416679\pi\)
−0.965916 + 0.258857i \(0.916654\pi\)
\(578\) 0 0
\(579\) 6.14933e6 + 2.47063e6i 0.762309 + 0.306275i
\(580\) 0 0
\(581\) 1.85651e6 1.05288e7i 0.228169 1.29401i
\(582\) 0 0
\(583\) 647021. 542915.i 0.0788401 0.0661547i
\(584\) 0 0
\(585\) 4.39161e6 + 4.20814e6i 0.530560 + 0.508394i
\(586\) 0 0
\(587\) −1.04029e7 3.78633e6i −1.24611 0.453548i −0.367026 0.930211i \(-0.619624\pi\)
−0.879086 + 0.476663i \(0.841846\pi\)
\(588\) 0 0
\(589\) 207360. + 173996.i 0.0246285 + 0.0206657i
\(590\) 0 0
\(591\) 3.20048e6 1.52020e7i 0.376918 1.79032i
\(592\) 0 0
\(593\) 1.05137e7 1.22777 0.613885 0.789396i \(-0.289606\pi\)
0.613885 + 0.789396i \(0.289606\pi\)
\(594\) 0 0
\(595\) 1.38654e6 0.160561
\(596\) 0 0
\(597\) −1.68906e6 + 552432.i −0.193959 + 0.0634370i
\(598\) 0 0
\(599\) 3.84673e6 + 3.22779e6i 0.438051 + 0.367569i 0.834980 0.550281i \(-0.185479\pi\)
−0.396928 + 0.917850i \(0.629924\pi\)
\(600\) 0 0
\(601\) 1.01180e7 + 3.68265e6i 1.14264 + 0.415886i 0.842865 0.538124i \(-0.180867\pi\)
0.299773 + 0.954011i \(0.403089\pi\)
\(602\) 0 0
\(603\) 1.16955e7 + 772268.i 1.30987 + 0.0864918i
\(604\) 0 0
\(605\) −8.09934e6 + 6.79615e6i −0.899624 + 0.754874i
\(606\) 0 0
\(607\) −1.16395e6 + 6.60111e6i −0.128222 + 0.727186i 0.851119 + 0.524973i \(0.175924\pi\)
−0.979342 + 0.202213i \(0.935187\pi\)
\(608\) 0 0
\(609\) −1.52830e6 + 1.19882e6i −0.166981 + 0.130982i
\(610\) 0 0
\(611\) 2.14246e6 3.71085e6i 0.232172 0.402133i
\(612\) 0 0
\(613\) −3.05972e6 5.29959e6i −0.328875 0.569628i 0.653414 0.757001i \(-0.273336\pi\)
−0.982289 + 0.187373i \(0.940003\pi\)
\(614\) 0 0
\(615\) −3.73261e6 123100.i −0.397947 0.0131241i
\(616\) 0 0
\(617\) −6.73684e6 + 2.45201e6i −0.712432 + 0.259304i −0.672709 0.739907i \(-0.734870\pi\)
−0.0397223 + 0.999211i \(0.512647\pi\)
\(618\) 0 0
\(619\) −1.72523e6 9.78426e6i −0.180976 1.02636i −0.931018 0.364974i \(-0.881078\pi\)
0.750042 0.661390i \(-0.230033\pi\)
\(620\) 0 0
\(621\) 2.17879e6 7.76863e6i 0.226719 0.808380i
\(622\) 0 0
\(623\) −508387. 2.88321e6i −0.0524776 0.297616i
\(624\) 0 0
\(625\) 1.13527e7 4.13206e6i 1.16252 0.423123i
\(626\) 0 0
\(627\) 7299.52 + 13664.4i 0.000741525 + 0.00138811i
\(628\) 0 0
\(629\) 963696. + 1.66917e6i 0.0971211 + 0.168219i
\(630\) 0 0
\(631\) −1.84921e6 + 3.20292e6i −0.184890 + 0.320238i −0.943539 0.331261i \(-0.892526\pi\)
0.758650 + 0.651499i \(0.225859\pi\)
\(632\) 0 0
\(633\) 24406.2 + 171249.i 0.00242098 + 0.0169871i
\(634\) 0 0
\(635\) 3.53309e6 2.00371e7i 0.347712 1.97197i
\(636\) 0 0
\(637\) −1.22902e6 + 1.03127e6i −0.120008 + 0.100699i
\(638\) 0 0
\(639\) −512356. 225739.i −0.0496386 0.0218703i
\(640\) 0 0
\(641\) −4.21072e6 1.53258e6i −0.404773 0.147325i 0.131607 0.991302i \(-0.457986\pi\)
−0.536380 + 0.843977i \(0.680209\pi\)
\(642\) 0 0
\(643\) −6.76660e6 5.67785e6i −0.645421 0.541572i 0.260257 0.965539i \(-0.416193\pi\)
−0.905678 + 0.423967i \(0.860637\pi\)
\(644\) 0 0
\(645\) −4.36096e6 3.91134e6i −0.412746 0.370191i
\(646\) 0 0
\(647\) −9.74262e6 −0.914987 −0.457494 0.889213i \(-0.651253\pi\)
−0.457494 + 0.889213i \(0.651253\pi\)
\(648\) 0 0
\(649\) −188026. −0.0175229
\(650\) 0 0
\(651\) 7.34936e6 + 6.59163e6i 0.679668 + 0.609594i
\(652\) 0 0
\(653\) −1.36921e7 1.14890e7i −1.25657 1.05439i −0.996038 0.0889232i \(-0.971657\pi\)
−0.260532 0.965465i \(-0.583898\pi\)
\(654\) 0 0
\(655\) 1.15334e7 + 4.19781e6i 1.05040 + 0.382313i
\(656\) 0 0
\(657\) 7.00491e6 5.13099e6i 0.633125 0.463754i
\(658\) 0 0
\(659\) −1.13956e7 + 9.56204e6i −1.02217 + 0.857703i −0.989899 0.141776i \(-0.954719\pi\)
−0.0322720 + 0.999479i \(0.510274\pi\)
\(660\) 0 0
\(661\) 2.40722e6 1.36520e7i 0.214295 1.21533i −0.667830 0.744314i \(-0.732777\pi\)
0.882125 0.471015i \(-0.156112\pi\)
\(662\) 0 0
\(663\) −157017. 1.10173e6i −0.0138727 0.0973398i
\(664\) 0 0
\(665\) −177079. + 306709.i −0.0155279 + 0.0268951i
\(666\) 0 0
\(667\) −1.18279e6 2.04864e6i −0.102942 0.178300i
\(668\) 0 0
\(669\) −8.49799e6 1.59079e7i −0.734093 1.37419i
\(670\) 0 0
\(671\) −773318. + 281465.i −0.0663058 + 0.0241333i
\(672\) 0 0
\(673\) 3.04279e6 + 1.72565e7i 0.258961 + 1.46864i 0.785696 + 0.618613i \(0.212305\pi\)
−0.526735 + 0.850030i \(0.676584\pi\)
\(674\) 0 0
\(675\) −4.12421e6 1.98190e6i −0.348402 0.167426i
\(676\) 0 0
\(677\) 963707. + 5.46545e6i 0.0808115 + 0.458305i 0.998182 + 0.0602706i \(0.0191964\pi\)
−0.917371 + 0.398034i \(0.869693\pi\)
\(678\) 0 0
\(679\) 1.90699e6 694086.i 0.158735 0.0577749i
\(680\) 0 0
\(681\) 2.01454e7 + 664388.i 1.66460 + 0.0548977i
\(682\) 0 0
\(683\) 1.72992e6 + 2.99631e6i 0.141898 + 0.245774i 0.928211 0.372054i \(-0.121346\pi\)
−0.786314 + 0.617828i \(0.788013\pi\)
\(684\) 0 0
\(685\) −6.67714e6 + 1.15652e7i −0.543706 + 0.941727i
\(686\) 0 0
\(687\) −1.16881e7 + 9.16828e6i −0.944825 + 0.741133i
\(688\) 0 0
\(689\) 2.69113e6 1.52621e7i 0.215967 1.22481i
\(690\) 0 0
\(691\) 1.67902e7 1.40887e7i 1.33771 1.12247i 0.355501 0.934676i \(-0.384310\pi\)
0.982208 0.187796i \(-0.0601342\pi\)
\(692\) 0 0
\(693\) 249649. + 506859.i 0.0197468 + 0.0400917i
\(694\) 0 0
\(695\) −1.90277e7 6.92552e6i −1.49426 0.543864i
\(696\) 0 0
\(697\) 523448. + 439225.i 0.0408124 + 0.0342456i
\(698\) 0 0
\(699\) 1.51546e6 495653.i 0.117314 0.0383693i
\(700\) 0 0
\(701\) −2.30263e6 −0.176982 −0.0884911 0.996077i \(-0.528204\pi\)
−0.0884911 + 0.996077i \(0.528204\pi\)
\(702\) 0 0
\(703\) −492305. −0.0375704
\(704\) 0 0
\(705\) −2.38212e6 + 1.13148e7i −0.180506 + 0.857384i
\(706\) 0 0
\(707\) 1.58158e7 + 1.32710e7i 1.18999 + 0.998519i
\(708\) 0 0
\(709\) 1.75353e7 + 6.38232e6i 1.31008 + 0.476829i 0.900266 0.435341i \(-0.143372\pi\)
0.409812 + 0.912170i \(0.365594\pi\)
\(710\) 0 0
\(711\) 2.14533e7 6.24177e6i 1.59155 0.463056i
\(712\) 0 0
\(713\) −9.21028e6 + 7.72834e6i −0.678498 + 0.569328i
\(714\) 0 0
\(715\) 90075.3 510842.i 0.00658932 0.0373699i
\(716\) 0 0
\(717\) −2.24163e7 9.00627e6i −1.62842 0.654255i
\(718\) 0 0
\(719\) −6.34649e6 + 1.09924e7i −0.457837 + 0.792997i −0.998846 0.0480194i \(-0.984709\pi\)
0.541009 + 0.841017i \(0.318042\pi\)
\(720\) 0 0
\(721\) −5.19382e6 8.99596e6i −0.372090 0.644480i
\(722\) 0 0
\(723\) 3.36812e6 5.41345e6i 0.239630 0.385149i
\(724\) 0 0
\(725\) −1.26064e6 + 458837.i −0.0890733 + 0.0324200i
\(726\) 0 0
\(727\) 3.35493e6 + 1.90267e7i 0.235422 + 1.33515i 0.841723 + 0.539910i \(0.181542\pi\)
−0.606301 + 0.795235i \(0.707347\pi\)
\(728\) 0 0
\(729\) −4.59251e6 1.35941e7i −0.320060 0.947397i
\(730\) 0 0
\(731\) 186120. + 1.05554e6i 0.0128825 + 0.0730602i
\(732\) 0 0
\(733\) −2.02668e7 + 7.37652e6i −1.39324 + 0.507097i −0.926164 0.377121i \(-0.876914\pi\)
−0.467074 + 0.884218i \(0.654692\pi\)
\(734\) 0 0
\(735\) 2.28712e6 3.67599e6i 0.156160 0.250990i
\(736\) 0 0
\(737\) −499805. 865687.i −0.0338947 0.0587073i
\(738\) 0 0
\(739\) −4.82686e6 + 8.36037e6i −0.325127 + 0.563137i −0.981538 0.191266i \(-0.938741\pi\)
0.656411 + 0.754404i \(0.272074\pi\)
\(740\) 0 0
\(741\) 263761. + 105972.i 0.0176467 + 0.00708998i
\(742\) 0 0
\(743\) 3.02349e6 1.71470e7i 0.200926 1.13951i −0.702797 0.711390i \(-0.748066\pi\)
0.903723 0.428117i \(-0.140823\pi\)
\(744\) 0 0
\(745\) −7.09130e6 + 5.95030e6i −0.468096 + 0.392779i
\(746\) 0 0
\(747\) 2.22338e7 6.46885e6i 1.45785 0.424156i
\(748\) 0 0
\(749\) 63933.7 + 23270.0i 0.00416414 + 0.00151562i
\(750\) 0 0
\(751\) 2.11243e6 + 1.77254e6i 0.136673 + 0.114682i 0.708561 0.705649i \(-0.249345\pi\)
−0.571888 + 0.820331i \(0.693789\pi\)
\(752\) 0 0
\(753\) −555752. + 2.63976e6i −0.0357185 + 0.169659i
\(754\) 0 0
\(755\) −3.91882e6 −0.250200
\(756\) 0 0
\(757\) −1.48248e7 −0.940264 −0.470132 0.882596i \(-0.655794\pi\)
−0.470132 + 0.882596i \(0.655794\pi\)
\(758\) 0 0
\(759\) −654009. + 213903.i −0.0412078 + 0.0134776i
\(760\) 0 0
\(761\) 1.77510e7 + 1.48949e7i 1.11112 + 0.932342i 0.998122 0.0612528i \(-0.0195096\pi\)
0.113000 + 0.993595i \(0.463954\pi\)
\(762\) 0 0
\(763\) 8.57452e6 + 3.12087e6i 0.533210 + 0.194073i
\(764\) 0 0
\(765\) 1.32691e6 + 2.69401e6i 0.0819763 + 0.166435i
\(766\) 0 0
\(767\) −2.64284e6 + 2.21761e6i −0.162212 + 0.136112i
\(768\) 0 0
\(769\) 1.40904e6 7.99108e6i 0.0859228 0.487292i −0.911231 0.411896i \(-0.864867\pi\)
0.997154 0.0753963i \(-0.0240222\pi\)
\(770\) 0 0
\(771\) −1.75292e7 + 1.37501e7i −1.06200 + 0.833048i
\(772\) 0 0
\(773\) 4.32621e6 7.49321e6i 0.260411 0.451044i −0.705940 0.708271i \(-0.749475\pi\)
0.966351 + 0.257227i \(0.0828087\pi\)
\(774\) 0 0
\(775\) 3.40926e6 + 5.90501e6i 0.203894 + 0.353156i
\(776\) 0 0
\(777\) −1.79451e7 591822.i −1.06633 0.0351673i
\(778\) 0 0
\(779\) −164010. + 59694.7i −0.00968336 + 0.00352445i
\(780\) 0 0
\(781\) 8291.47 + 47023.3i 0.000486412 + 0.00275858i
\(782\) 0 0
\(783\) −3.79185e6 1.82218e6i −0.221028 0.106216i
\(784\) 0 0
\(785\) 4.06921e6 + 2.30776e7i 0.235687 + 1.33665i
\(786\) 0 0
\(787\) −1.59758e6 + 581473.i −0.0919448 + 0.0334652i −0.387583 0.921835i \(-0.626690\pi\)
0.295638 + 0.955300i \(0.404468\pi\)
\(788\) 0 0
\(789\) 1.97392e6 + 3.69510e6i 0.112885 + 0.211316i
\(790\) 0 0
\(791\) 1.22565e7 + 2.12288e7i 0.696505 + 1.20638i
\(792\) 0 0
\(793\) −7.54991e6 + 1.30768e7i −0.426343 + 0.738447i
\(794\) 0 0
\(795\) 5.90055e6 + 4.14020e7i 0.331112 + 2.32329i
\(796\) 0 0
\(797\) 3.03888e6 1.72344e7i 0.169460 0.961057i −0.774885 0.632102i \(-0.782192\pi\)
0.944345 0.328955i \(-0.106697\pi\)
\(798\) 0 0
\(799\) 1.62066e6 1.35989e6i 0.0898098 0.0753594i
\(800\) 0 0
\(801\) 5.11547e6 3.74700e6i 0.281711 0.206349i
\(802\) 0 0
\(803\) −695865. 253274.i −0.0380835 0.0138612i
\(804\) 0 0
\(805\) −1.20503e7 1.01114e7i −0.655401 0.549947i
\(806\) 0 0
\(807\) −1.22015e7 1.09435e7i −0.659520 0.591523i
\(808\) 0 0
\(809\) 3.00572e7 1.61465 0.807323 0.590110i \(-0.200916\pi\)
0.807323 + 0.590110i \(0.200916\pi\)
\(810\) 0 0
\(811\) 2.59135e7 1.38348 0.691741 0.722146i \(-0.256844\pi\)
0.691741 + 0.722146i \(0.256844\pi\)
\(812\) 0 0
\(813\) 2.60743e7 + 2.33860e7i 1.38352 + 1.24088i
\(814\) 0 0
\(815\) 2.92464e7 + 2.45407e7i 1.54234 + 1.29417i
\(816\) 0 0
\(817\) −257260. 93635.1i −0.0134840 0.00490776i
\(818\) 0 0
\(819\) 9.48699e6 + 4.17987e6i 0.494218 + 0.217748i
\(820\) 0 0
\(821\) 2.33044e7 1.95548e7i 1.20665 1.01250i 0.207234 0.978291i \(-0.433554\pi\)
0.999415 0.0342072i \(-0.0108906\pi\)
\(822\) 0 0
\(823\) −2.81266e6 + 1.59514e7i −0.144750 + 0.820916i 0.822818 + 0.568305i \(0.192401\pi\)
−0.967568 + 0.252612i \(0.918711\pi\)
\(824\) 0 0
\(825\) 55059.0 + 386328.i 0.00281639 + 0.0197616i
\(826\) 0 0
\(827\) −1.62710e7 + 2.81821e7i −0.827274 + 1.43288i 0.0728953 + 0.997340i \(0.476776\pi\)
−0.900169 + 0.435541i \(0.856557\pi\)
\(828\) 0 0
\(829\) −1.12068e7 1.94107e7i −0.566362 0.980968i −0.996922 0.0784058i \(-0.975017\pi\)
0.430559 0.902562i \(-0.358316\pi\)
\(830\) 0 0
\(831\) −7.53780e6 1.41105e7i −0.378654 0.708825i
\(832\) 0 0
\(833\) −744365. + 270927.i −0.0371683 + 0.0135282i
\(834\) 0 0
\(835\) −2.03266e6 1.15278e7i −0.100890 0.572177i
\(836\) 0 0
\(837\) −5.77406e6 + 2.05878e7i −0.284884 + 1.01577i
\(838\) 0 0
\(839\) −2.71713e6 1.54096e7i −0.133262 0.755765i −0.976054 0.217527i \(-0.930201\pi\)
0.842793 0.538239i \(-0.180910\pi\)
\(840\) 0 0
\(841\) 1.81151e7 6.59336e6i 0.883184 0.321453i
\(842\) 0 0
\(843\) 7.89528e6 + 260383.i 0.382647 + 0.0126196i
\(844\) 0 0
\(845\) 7.46132e6 + 1.29234e7i 0.359479 + 0.622636i
\(846\) 0 0
\(847\) −9.01048e6 + 1.56066e7i −0.431558 + 0.747481i
\(848\) 0 0
\(849\) −2.08375e7 + 1.63452e7i −0.992146 + 0.778252i
\(850\) 0 0
\(851\) 3.79709e6 2.15344e7i 0.179733 1.01932i
\(852\) 0 0
\(853\) 1.40573e7 1.17955e7i 0.661500 0.555064i −0.249036 0.968494i \(-0.580114\pi\)
0.910536 + 0.413430i \(0.135669\pi\)
\(854\) 0 0
\(855\) −765391. 50539.5i −0.0358070 0.00236437i
\(856\) 0 0
\(857\) −2.62701e7 9.56155e6i −1.22183 0.444709i −0.351037 0.936361i \(-0.614171\pi\)
−0.870792 + 0.491652i \(0.836393\pi\)
\(858\) 0 0
\(859\) −2.28653e7 1.91863e7i −1.05729 0.887171i −0.0634481 0.997985i \(-0.520210\pi\)
−0.993841 + 0.110814i \(0.964654\pi\)
\(860\) 0 0
\(861\) −6.05011e6 + 1.97878e6i −0.278135 + 0.0909680i
\(862\) 0 0
\(863\) −2.00275e7 −0.915378 −0.457689 0.889112i \(-0.651323\pi\)
−0.457689 + 0.889112i \(0.651323\pi\)
\(864\) 0 0
\(865\) −2.35078e7 −1.06825
\(866\) 0 0
\(867\) −4.44661e6 + 2.11209e7i −0.200900 + 0.954257i
\(868\) 0 0
\(869\) −1.45968e6 1.22482e6i −0.0655706 0.0550203i
\(870\) 0 0
\(871\) −1.72352e7 6.27310e6i −0.769787 0.280180i
\(872\) 0 0
\(873\) 3.17357e6 + 3.04099e6i 0.140933 + 0.135045i
\(874\) 0 0
\(875\) 1.08456e7 9.10055e6i 0.478888 0.401835i
\(876\) 0 0
\(877\) 7.13000e6 4.04362e7i 0.313033 1.77530i −0.270009 0.962858i \(-0.587027\pi\)
0.583042 0.812442i \(-0.301862\pi\)
\(878\) 0 0
\(879\) −2.81775e7 1.13209e7i −1.23007 0.494209i
\(880\) 0 0
\(881\) 1.79921e7 3.11632e7i 0.780984 1.35270i −0.150385 0.988627i \(-0.548051\pi\)
0.931369 0.364076i \(-0.118615\pi\)
\(882\) 0 0
\(883\) 2.86566e6 + 4.96347e6i 0.123687 + 0.214231i 0.921219 0.389045i \(-0.127195\pi\)
−0.797532 + 0.603276i \(0.793862\pi\)
\(884\) 0 0
\(885\) 4.91812e6 7.90470e6i 0.211077 0.339256i
\(886\) 0 0
\(887\) −2.87802e7 + 1.04751e7i −1.22824 + 0.447044i −0.872995 0.487729i \(-0.837826\pi\)
−0.355247 + 0.934772i \(0.615603\pi\)
\(888\) 0 0
\(889\) −6.02194e6 3.41521e7i −0.255554 1.44932i
\(890\) 0 0
\(891\) −745900. + 970124.i −0.0314765 + 0.0409386i
\(892\) 0 0
\(893\) 93836.4 + 532172.i 0.00393770 + 0.0223318i
\(894\) 0 0
\(895\) 1.65686e7 6.03049e6i 0.691400 0.251649i
\(896\) 0 0
\(897\) −6.66977e6 + 1.07201e7i −0.276777 + 0.444853i
\(898\) 0 0
\(899\) 3.13452e6 + 5.42915e6i 0.129352 + 0.224043i
\(900\) 0 0
\(901\) 3.82585e6 6.62657e6i 0.157006 0.271942i
\(902\) 0 0
\(903\) −9.26487e6 3.72237e6i −0.378112 0.151915i
\(904\) 0 0
\(905\) 7.22781e6 4.09909e7i 0.293349 1.66367i
\(906\) 0 0
\(907\) −1.18768e7 + 9.96584e6i −0.479383 + 0.402250i −0.850203 0.526455i \(-0.823521\pi\)
0.370820 + 0.928705i \(0.379077\pi\)
\(908\) 0 0
\(909\) −1.06496e7 + 4.34300e7i −0.427488 + 1.74333i
\(910\) 0 0
\(911\) −5.77900e6 2.10338e6i −0.230705 0.0839697i 0.224081 0.974571i \(-0.428062\pi\)
−0.454786 + 0.890601i \(0.650284\pi\)
\(912\) 0 0
\(913\) −1.51279e6 1.26938e6i −0.0600622 0.0503982i
\(914\) 0 0
\(915\) 8.39447e6 3.98729e7i 0.331467 1.57444i
\(916\) 0 0
\(917\) 2.09196e7 0.821542
\(918\) 0 0
\(919\) 3.34851e7 1.30786 0.653932 0.756553i \(-0.273118\pi\)
0.653932 + 0.756553i \(0.273118\pi\)
\(920\) 0 0
\(921\) 2.78831e7 9.11958e6i 1.08316 0.354263i
\(922\) 0 0
\(923\) 671143. + 563156.i 0.0259305 + 0.0217583i
\(924\) 0 0
\(925\) −1.16530e7 4.24135e6i −0.447800 0.162986i
\(926\) 0 0
\(927\) 1.25084e7 1.87005e7i 0.478083 0.714751i
\(928\) 0 0
\(929\) −1.36347e7 + 1.14409e7i −0.518330 + 0.434930i −0.864049 0.503408i \(-0.832079\pi\)
0.345719 + 0.938338i \(0.387635\pi\)
\(930\) 0 0
\(931\) 35134.5 199258.i 0.00132850 0.00753427i
\(932\) 0 0
\(933\) −1.97006e7 + 1.54534e7i −0.740926 + 0.581192i
\(934\) 0 0
\(935\) 128056. 221799.i 0.00479039 0.00829719i
\(936\) 0 0
\(937\) −1.50774e7 2.61148e7i −0.561018 0.971712i −0.997408 0.0719540i \(-0.977077\pi\)
0.436390 0.899758i \(-0.356257\pi\)
\(938\) 0 0
\(939\) 1.31372e6 + 43325.9i 0.0486226 + 0.00160356i
\(940\) 0 0
\(941\) −7.97047e6 + 2.90101e6i −0.293434 + 0.106801i −0.484542 0.874768i \(-0.661014\pi\)
0.191109 + 0.981569i \(0.438792\pi\)
\(942\) 0 0
\(943\) −1.34617e6 7.63453e6i −0.0492971 0.279578i
\(944\) 0 0
\(945\) −2.78386e7 2.76233e6i −1.01407 0.100623i
\(946\) 0 0
\(947\) −2.85012e6 1.61638e7i −0.103273 0.585692i −0.991896 0.127053i \(-0.959448\pi\)
0.888623 0.458639i \(-0.151663\pi\)
\(948\) 0 0
\(949\) −1.27681e7 + 4.64720e6i −0.460214 + 0.167504i
\(950\) 0 0
\(951\) −3.01008e6 5.63476e6i −0.107926 0.202034i
\(952\) 0 0
\(953\) 6.40183e6 + 1.10883e7i 0.228335 + 0.395487i 0.957315 0.289048i \(-0.0933386\pi\)
−0.728980 + 0.684535i \(0.760005\pi\)
\(954\) 0 0
\(955\) 5.89144e6 1.02043e7i 0.209032 0.362054i
\(956\) 0 0
\(957\) 50622.0 + 355196.i 0.00178673 + 0.0125368i
\(958\) 0 0
\(959\) −3.95252e6 + 2.24158e7i −0.138780 + 0.787061i
\(960\) 0 0
\(961\) 2.47710e6 2.07854e6i 0.0865239 0.0726021i
\(962\) 0 0
\(963\) 15971.4 + 146491.i 0.000554979 + 0.00509031i
\(964\) 0 0
\(965\) 2.62964e7 + 9.57112e6i 0.909031 + 0.330860i
\(966\) 0 0
\(967\) 1.28518e7 + 1.07839e7i 0.441974 + 0.370860i 0.836447 0.548047i \(-0.184629\pi\)
−0.394473 + 0.918907i \(0.629073\pi\)
\(968\) 0 0
\(969\) 104479. + 93707.2i 0.00357454 + 0.00320600i
\(970\) 0 0
\(971\) 3.79370e7 1.29126 0.645632 0.763648i \(-0.276594\pi\)
0.645632 + 0.763648i \(0.276594\pi\)
\(972\) 0 0
\(973\) −3.45131e7 −1.16870
\(974\) 0 0
\(975\) 5.33032e6 + 4.78076e6i 0.179573 + 0.161059i
\(976\) 0 0
\(977\) 1.75585e7 + 1.47334e7i 0.588507 + 0.493816i 0.887728 0.460368i \(-0.152282\pi\)
−0.299221 + 0.954184i \(0.596727\pi\)
\(978\) 0 0
\(979\) −508168. 184958.i −0.0169454 0.00616761i
\(980\) 0 0
\(981\) 2.14201e6 + 1.96467e7i 0.0710641 + 0.651805i
\(982\) 0 0
\(983\) 2.42875e7 2.03796e7i 0.801676 0.672686i −0.146929 0.989147i \(-0.546939\pi\)
0.948606 + 0.316461i \(0.102495\pi\)
\(984\) 0 0
\(985\) 1.13914e7 6.46036e7i 0.374098 2.12161i
\(986\) 0 0
\(987\) 2.78070e6 + 1.95111e7i 0.0908575 + 0.637513i
\(988\) 0 0
\(989\) 6.08000e6 1.05309e7i 0.197657 0.342353i
\(990\) 0 0
\(991\) 1.41122e7 + 2.44430e7i 0.456467 + 0.790624i 0.998771 0.0495580i \(-0.0157813\pi\)
−0.542304 + 0.840182i \(0.682448\pi\)
\(992\) 0 0
\(993\) −9.39188e6 1.75812e7i −0.302259 0.565818i
\(994\) 0 0
\(995\) −7.05160e6 + 2.56657e6i −0.225803 + 0.0821856i
\(996\) 0 0
\(997\) 4.86069e6 + 2.75663e7i 0.154867 + 0.878297i 0.958907 + 0.283721i \(0.0915689\pi\)
−0.804039 + 0.594576i \(0.797320\pi\)
\(998\) 0 0
\(999\) −1.60235e7 3.54332e7i −0.507976 1.12330i
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 108.6.i.a.13.12 90
3.2 odd 2 324.6.i.a.253.3 90
27.2 odd 18 324.6.i.a.73.3 90
27.25 even 9 inner 108.6.i.a.25.12 yes 90
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.6.i.a.13.12 90 1.1 even 1 trivial
108.6.i.a.25.12 yes 90 27.25 even 9 inner
324.6.i.a.73.3 90 27.2 odd 18
324.6.i.a.253.3 90 3.2 odd 2