Properties

Label 76.7.j.a.13.7
Level $76$
Weight $7$
Character 76.13
Analytic conductor $17.484$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,7,Mod(13,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.13");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), 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: \(17.4841103551\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 13.7
Character \(\chi\) \(=\) 76.13
Dual form 76.7.j.a.41.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6.80225 - 18.6890i) q^{3} +(-6.07240 - 34.4383i) q^{5} +(-223.008 + 386.261i) q^{7} +(255.437 + 214.337i) q^{9} +O(q^{10})\) \(q+(6.80225 - 18.6890i) q^{3} +(-6.07240 - 34.4383i) q^{5} +(-223.008 + 386.261i) q^{7} +(255.437 + 214.337i) q^{9} +(338.033 + 585.490i) q^{11} +(630.159 + 1731.35i) q^{13} +(-684.924 - 120.771i) q^{15} +(3154.66 - 2647.08i) q^{17} +(2252.47 - 6478.60i) q^{19} +(5701.88 + 6795.24i) q^{21} +(-3207.53 + 18190.8i) q^{23} +(13533.6 - 4925.82i) q^{25} +(18299.5 - 10565.2i) q^{27} +(-10737.6 + 12796.6i) q^{29} +(29439.5 + 16996.9i) q^{31} +(13241.6 - 2334.86i) q^{33} +(14656.4 + 5334.48i) q^{35} -5729.37i q^{37} +36643.7 q^{39} +(-21479.7 + 59015.1i) q^{41} +(19195.5 + 108863. i) q^{43} +(5830.30 - 10098.4i) q^{45} +(46760.9 + 39237.0i) q^{47} +(-40640.4 - 70391.2i) q^{49} +(-28012.5 - 76963.7i) q^{51} +(-15076.1 - 2658.33i) q^{53} +(18110.6 - 15196.6i) q^{55} +(-105757. - 86165.5i) q^{57} +(-124978. - 148943. i) q^{59} +(58204.5 - 330094. i) q^{61} +(-139755. + 50866.5i) q^{63} +(55798.0 - 32215.0i) q^{65} +(-63591.1 + 75785.0i) q^{67} +(318150. + 183684. i) q^{69} +(-695029. + 122552. i) q^{71} +(-175843. - 64001.5i) q^{73} -286436. i q^{75} -301536. q^{77} +(-234966. + 645565. i) q^{79} +(-30764.8 - 174476. i) q^{81} +(334822. - 579928. i) q^{83} +(-110317. - 92567.2i) q^{85} +(166116. + 287721. i) q^{87} +(-19415.8 - 53344.6i) q^{89} +(-809281. - 142698. i) q^{91} +(517911. - 434579. i) q^{93} +(-236790. - 38230.6i) q^{95} +(752838. + 897198. i) q^{97} +(-39146.2 + 222009. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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
\(3\) 6.80225 18.6890i 0.251935 0.692186i −0.747670 0.664071i \(-0.768827\pi\)
0.999605 0.0281151i \(-0.00895048\pi\)
\(4\) 0 0
\(5\) −6.07240 34.4383i −0.0485792 0.275506i 0.950836 0.309694i \(-0.100227\pi\)
−0.999415 + 0.0341878i \(0.989116\pi\)
\(6\) 0 0
\(7\) −223.008 + 386.261i −0.650168 + 1.12612i 0.332914 + 0.942957i \(0.391968\pi\)
−0.983082 + 0.183167i \(0.941365\pi\)
\(8\) 0 0
\(9\) 255.437 + 214.337i 0.350394 + 0.294016i
\(10\) 0 0
\(11\) 338.033 + 585.490i 0.253969 + 0.439888i 0.964615 0.263662i \(-0.0849305\pi\)
−0.710646 + 0.703550i \(0.751597\pi\)
\(12\) 0 0
\(13\) 630.159 + 1731.35i 0.286827 + 0.788050i 0.996506 + 0.0835249i \(0.0266178\pi\)
−0.709679 + 0.704525i \(0.751160\pi\)
\(14\) 0 0
\(15\) −684.924 120.771i −0.202940 0.0357839i
\(16\) 0 0
\(17\) 3154.66 2647.08i 0.642106 0.538791i −0.262558 0.964916i \(-0.584566\pi\)
0.904664 + 0.426126i \(0.140122\pi\)
\(18\) 0 0
\(19\) 2252.47 6478.60i 0.328396 0.944540i
\(20\) 0 0
\(21\) 5701.88 + 6795.24i 0.615687 + 0.733748i
\(22\) 0 0
\(23\) −3207.53 + 18190.8i −0.263626 + 1.49510i 0.509295 + 0.860592i \(0.329906\pi\)
−0.772920 + 0.634503i \(0.781205\pi\)
\(24\) 0 0
\(25\) 13533.6 4925.82i 0.866149 0.315252i
\(26\) 0 0
\(27\) 18299.5 10565.2i 0.929712 0.536770i
\(28\) 0 0
\(29\) −10737.6 + 12796.6i −0.440264 + 0.524686i −0.939854 0.341576i \(-0.889039\pi\)
0.499590 + 0.866262i \(0.333484\pi\)
\(30\) 0 0
\(31\) 29439.5 + 16996.9i 0.988202 + 0.570539i 0.904736 0.425972i \(-0.140068\pi\)
0.0834657 + 0.996511i \(0.473401\pi\)
\(32\) 0 0
\(33\) 13241.6 2334.86i 0.368468 0.0649708i
\(34\) 0 0
\(35\) 14656.4 + 5334.48i 0.341839 + 0.124419i
\(36\) 0 0
\(37\) 5729.37i 0.113110i −0.998399 0.0565551i \(-0.981988\pi\)
0.998399 0.0565551i \(-0.0180116\pi\)
\(38\) 0 0
\(39\) 36643.7 0.617739
\(40\) 0 0
\(41\) −21479.7 + 59015.1i −0.311657 + 0.856271i 0.680665 + 0.732595i \(0.261691\pi\)
−0.992323 + 0.123677i \(0.960531\pi\)
\(42\) 0 0
\(43\) 19195.5 + 108863.i 0.241431 + 1.36922i 0.828637 + 0.559786i \(0.189117\pi\)
−0.587206 + 0.809437i \(0.699772\pi\)
\(44\) 0 0
\(45\) 5830.30 10098.4i 0.0639813 0.110819i
\(46\) 0 0
\(47\) 46760.9 + 39237.0i 0.450390 + 0.377922i 0.839581 0.543235i \(-0.182801\pi\)
−0.389190 + 0.921157i \(0.627245\pi\)
\(48\) 0 0
\(49\) −40640.4 70391.2i −0.345437 0.598315i
\(50\) 0 0
\(51\) −28012.5 76963.7i −0.211174 0.580197i
\(52\) 0 0
\(53\) −15076.1 2658.33i −0.101266 0.0178559i 0.122786 0.992433i \(-0.460817\pi\)
−0.224051 + 0.974577i \(0.571928\pi\)
\(54\) 0 0
\(55\) 18110.6 15196.6i 0.108854 0.0913395i
\(56\) 0 0
\(57\) −105757. 86165.5i −0.571063 0.465274i
\(58\) 0 0
\(59\) −124978. 148943.i −0.608525 0.725212i 0.370527 0.928822i \(-0.379177\pi\)
−0.979052 + 0.203610i \(0.934733\pi\)
\(60\) 0 0
\(61\) 58204.5 330094.i 0.256429 1.45428i −0.535949 0.844250i \(-0.680046\pi\)
0.792378 0.610031i \(-0.208843\pi\)
\(62\) 0 0
\(63\) −139755. + 50866.5i −0.558914 + 0.203428i
\(64\) 0 0
\(65\) 55798.0 32215.0i 0.203179 0.117305i
\(66\) 0 0
\(67\) −63591.1 + 75785.0i −0.211433 + 0.251976i −0.861329 0.508047i \(-0.830368\pi\)
0.649897 + 0.760023i \(0.274812\pi\)
\(68\) 0 0
\(69\) 318150. + 183684.i 0.968467 + 0.559145i
\(70\) 0 0
\(71\) −695029. + 122552.i −1.94191 + 0.342410i −0.941927 + 0.335816i \(0.890988\pi\)
−0.999978 + 0.00659391i \(0.997901\pi\)
\(72\) 0 0
\(73\) −175843. 64001.5i −0.452018 0.164521i 0.105971 0.994369i \(-0.466205\pi\)
−0.557989 + 0.829848i \(0.688427\pi\)
\(74\) 0 0
\(75\) 286436.i 0.678959i
\(76\) 0 0
\(77\) −301536. −0.660491
\(78\) 0 0
\(79\) −234966. + 645565.i −0.476568 + 1.30936i 0.435821 + 0.900033i \(0.356458\pi\)
−0.912389 + 0.409325i \(0.865764\pi\)
\(80\) 0 0
\(81\) −30764.8 174476.i −0.0578893 0.328307i
\(82\) 0 0
\(83\) 334822. 579928.i 0.585571 1.01424i −0.409233 0.912430i \(-0.634204\pi\)
0.994804 0.101808i \(-0.0324629\pi\)
\(84\) 0 0
\(85\) −110317. 92567.2i −0.179633 0.150730i
\(86\) 0 0
\(87\) 166116. + 287721.i 0.252262 + 0.436931i
\(88\) 0 0
\(89\) −19415.8 53344.6i −0.0275414 0.0756694i 0.925160 0.379577i \(-0.123931\pi\)
−0.952701 + 0.303908i \(0.901708\pi\)
\(90\) 0 0
\(91\) −809281. 142698.i −1.07393 0.189363i
\(92\) 0 0
\(93\) 517911. 434579.i 0.643882 0.540281i
\(94\) 0 0
\(95\) −236790. 38230.6i −0.276180 0.0445903i
\(96\) 0 0
\(97\) 752838. + 897198.i 0.824872 + 0.983044i 0.999999 0.00150162i \(-0.000477982\pi\)
−0.175127 + 0.984546i \(0.556034\pi\)
\(98\) 0 0
\(99\) −39146.2 + 222009.i −0.0403445 + 0.228805i
\(100\) 0 0
\(101\) 1.36349e6 496271.i 1.32339 0.481675i 0.418849 0.908056i \(-0.362434\pi\)
0.904544 + 0.426381i \(0.140212\pi\)
\(102\) 0 0
\(103\) −784403. + 452875.i −0.717840 + 0.414445i −0.813957 0.580925i \(-0.802691\pi\)
0.0961172 + 0.995370i \(0.469358\pi\)
\(104\) 0 0
\(105\) 199392. 237626.i 0.172243 0.205271i
\(106\) 0 0
\(107\) 1.12479e6 + 649398.i 0.918164 + 0.530102i 0.883049 0.469281i \(-0.155487\pi\)
0.0351149 + 0.999383i \(0.488820\pi\)
\(108\) 0 0
\(109\) 228120. 40223.8i 0.176151 0.0310601i −0.0848769 0.996391i \(-0.527050\pi\)
0.261028 + 0.965331i \(0.415939\pi\)
\(110\) 0 0
\(111\) −107076. 38972.6i −0.0782932 0.0284964i
\(112\) 0 0
\(113\) 1.22997e6i 0.852431i −0.904622 0.426216i \(-0.859846\pi\)
0.904622 0.426216i \(-0.140154\pi\)
\(114\) 0 0
\(115\) 645938. 0.424715
\(116\) 0 0
\(117\) −210126. + 577317.i −0.131197 + 0.360460i
\(118\) 0 0
\(119\) 318948. + 1.80884e6i 0.189269 + 1.07340i
\(120\) 0 0
\(121\) 657248. 1.13839e6i 0.370999 0.642590i
\(122\) 0 0
\(123\) 956824. + 802870.i 0.514182 + 0.431450i
\(124\) 0 0
\(125\) −525018. 909357.i −0.268809 0.465591i
\(126\) 0 0
\(127\) 460147. + 1.26424e6i 0.224639 + 0.617191i 0.999896 0.0144557i \(-0.00460154\pi\)
−0.775256 + 0.631647i \(0.782379\pi\)
\(128\) 0 0
\(129\) 2.16511e6 + 381768.i 1.00858 + 0.177840i
\(130\) 0 0
\(131\) −1.40432e6 + 1.17836e6i −0.624672 + 0.524162i −0.899268 0.437397i \(-0.855900\pi\)
0.274596 + 0.961560i \(0.411456\pi\)
\(132\) 0 0
\(133\) 2.00011e6 + 2.31482e6i 0.850157 + 0.983925i
\(134\) 0 0
\(135\) −474971. 566048.i −0.193048 0.230066i
\(136\) 0 0
\(137\) −38396.2 + 217756.i −0.0149323 + 0.0846854i −0.991363 0.131145i \(-0.958135\pi\)
0.976431 + 0.215830i \(0.0692458\pi\)
\(138\) 0 0
\(139\) −2.38012e6 + 866293.i −0.886246 + 0.322567i −0.744728 0.667368i \(-0.767421\pi\)
−0.141518 + 0.989936i \(0.545198\pi\)
\(140\) 0 0
\(141\) 1.05138e6 607015.i 0.375062 0.216542i
\(142\) 0 0
\(143\) −800672. + 954204.i −0.273808 + 0.326312i
\(144\) 0 0
\(145\) 505895. + 292079.i 0.165942 + 0.0958067i
\(146\) 0 0
\(147\) −1.59199e6 + 280711.i −0.501173 + 0.0883704i
\(148\) 0 0
\(149\) −529979. 192897.i −0.160214 0.0583131i 0.260668 0.965428i \(-0.416057\pi\)
−0.420882 + 0.907115i \(0.638279\pi\)
\(150\) 0 0
\(151\) 3.18209e6i 0.924234i −0.886819 0.462117i \(-0.847090\pi\)
0.886819 0.462117i \(-0.152910\pi\)
\(152\) 0 0
\(153\) 1.37319e6 0.383403
\(154\) 0 0
\(155\) 406576. 1.11706e6i 0.109181 0.299972i
\(156\) 0 0
\(157\) −656962. 3.72582e6i −0.169762 0.962770i −0.944017 0.329896i \(-0.892986\pi\)
0.774255 0.632874i \(-0.218125\pi\)
\(158\) 0 0
\(159\) −152233. + 263675.i −0.0378720 + 0.0655961i
\(160\) 0 0
\(161\) −6.31110e6 5.29564e6i −1.51226 1.26894i
\(162\) 0 0
\(163\) 119764. + 207437.i 0.0276543 + 0.0478986i 0.879521 0.475859i \(-0.157863\pi\)
−0.851867 + 0.523758i \(0.824530\pi\)
\(164\) 0 0
\(165\) −160817. 441841.i −0.0357997 0.0983590i
\(166\) 0 0
\(167\) 1.41774e6 + 249987.i 0.304403 + 0.0536744i 0.323763 0.946138i \(-0.395052\pi\)
−0.0193605 + 0.999813i \(0.506163\pi\)
\(168\) 0 0
\(169\) 1.09709e6 920568.i 0.227291 0.190720i
\(170\) 0 0
\(171\) 1.96397e6 1.17209e6i 0.392778 0.234408i
\(172\) 0 0
\(173\) −6.13020e6 7.30568e6i −1.18396 1.41099i −0.890482 0.455019i \(-0.849632\pi\)
−0.293476 0.955966i \(-0.594812\pi\)
\(174\) 0 0
\(175\) −1.11544e6 + 6.32598e6i −0.208129 + 1.18036i
\(176\) 0 0
\(177\) −3.63374e6 + 1.32257e6i −0.655290 + 0.238506i
\(178\) 0 0
\(179\) −3.02397e6 + 1.74589e6i −0.527253 + 0.304410i −0.739897 0.672720i \(-0.765126\pi\)
0.212644 + 0.977130i \(0.431792\pi\)
\(180\) 0 0
\(181\) −1.98204e6 + 2.36211e6i −0.334255 + 0.398349i −0.906826 0.421506i \(-0.861502\pi\)
0.572571 + 0.819855i \(0.305946\pi\)
\(182\) 0 0
\(183\) −5.77322e6 3.33317e6i −0.942030 0.543881i
\(184\) 0 0
\(185\) −197310. + 34791.0i −0.0311626 + 0.00549480i
\(186\) 0 0
\(187\) 2.61622e6 + 952226.i 0.400082 + 0.145618i
\(188\) 0 0
\(189\) 9.42452e6i 1.39596i
\(190\) 0 0
\(191\) 4.12208e6 0.591584 0.295792 0.955252i \(-0.404416\pi\)
0.295792 + 0.955252i \(0.404416\pi\)
\(192\) 0 0
\(193\) 1.72786e6 4.74725e6i 0.240346 0.660344i −0.759605 0.650385i \(-0.774608\pi\)
0.999950 0.00995941i \(-0.00317023\pi\)
\(194\) 0 0
\(195\) −222515. 1.26195e6i −0.0300093 0.170191i
\(196\) 0 0
\(197\) 4.42997e6 7.67294e6i 0.579432 1.00361i −0.416113 0.909313i \(-0.636608\pi\)
0.995545 0.0942922i \(-0.0300588\pi\)
\(198\) 0 0
\(199\) −4.69142e6 3.93657e6i −0.595312 0.499526i 0.294623 0.955614i \(-0.404806\pi\)
−0.889935 + 0.456087i \(0.849250\pi\)
\(200\) 0 0
\(201\) 983784. + 1.70396e6i 0.121147 + 0.209832i
\(202\) 0 0
\(203\) −2.54825e6 7.00125e6i −0.304616 0.836926i
\(204\) 0 0
\(205\) 2.16281e6 + 381362.i 0.251048 + 0.0442666i
\(206\) 0 0
\(207\) −4.71830e6 + 3.95912e6i −0.531954 + 0.446363i
\(208\) 0 0
\(209\) 4.55457e6 871180.i 0.498894 0.0954266i
\(210\) 0 0
\(211\) 5.25470e6 + 6.26231e6i 0.559372 + 0.666634i 0.969414 0.245433i \(-0.0789302\pi\)
−0.410041 + 0.912067i \(0.634486\pi\)
\(212\) 0 0
\(213\) −2.43738e6 + 1.38231e7i −0.252223 + 1.43043i
\(214\) 0 0
\(215\) 3.63249e6 1.32212e6i 0.365501 0.133032i
\(216\) 0 0
\(217\) −1.31305e7 + 7.58089e6i −1.28500 + 0.741892i
\(218\) 0 0
\(219\) −2.39225e6 + 2.85097e6i −0.227758 + 0.271432i
\(220\) 0 0
\(221\) 6.57095e6 + 3.79374e6i 0.608767 + 0.351472i
\(222\) 0 0
\(223\) 3.74211e6 659835.i 0.337444 0.0595005i −0.00235853 0.999997i \(-0.500751\pi\)
0.339803 + 0.940497i \(0.389640\pi\)
\(224\) 0 0
\(225\) 4.51277e6 + 1.64251e6i 0.396183 + 0.144199i
\(226\) 0 0
\(227\) 1.55988e7i 1.33356i −0.745254 0.666780i \(-0.767672\pi\)
0.745254 0.666780i \(-0.232328\pi\)
\(228\) 0 0
\(229\) 2.04778e7 1.70521 0.852603 0.522559i \(-0.175023\pi\)
0.852603 + 0.522559i \(0.175023\pi\)
\(230\) 0 0
\(231\) −2.05112e6 + 5.63541e6i −0.166401 + 0.457183i
\(232\) 0 0
\(233\) −1.88321e6 1.06802e7i −0.148878 0.844330i −0.964171 0.265281i \(-0.914535\pi\)
0.815293 0.579049i \(-0.196576\pi\)
\(234\) 0 0
\(235\) 1.06731e6 1.84863e6i 0.0822404 0.142445i
\(236\) 0 0
\(237\) 1.04667e7 + 8.78258e6i 0.786256 + 0.659747i
\(238\) 0 0
\(239\) −1.01761e6 1.76255e6i −0.0745395 0.129106i 0.826346 0.563162i \(-0.190415\pi\)
−0.900886 + 0.434056i \(0.857082\pi\)
\(240\) 0 0
\(241\) 6.25488e6 + 1.71851e7i 0.446856 + 1.22773i 0.934901 + 0.354909i \(0.115488\pi\)
−0.488045 + 0.872819i \(0.662290\pi\)
\(242\) 0 0
\(243\) 1.17000e7 + 2.06303e6i 0.815396 + 0.143776i
\(244\) 0 0
\(245\) −2.17737e6 + 1.82703e6i −0.148059 + 0.124236i
\(246\) 0 0
\(247\) 1.26361e7 182737.i 0.838538 0.0121265i
\(248\) 0 0
\(249\) −8.56075e6 1.02023e7i −0.554516 0.660846i
\(250\) 0 0
\(251\) 2.56964e6 1.45732e7i 0.162499 0.921579i −0.789106 0.614257i \(-0.789456\pi\)
0.951605 0.307322i \(-0.0994330\pi\)
\(252\) 0 0
\(253\) −1.17348e7 + 4.27112e6i −0.724627 + 0.263743i
\(254\) 0 0
\(255\) −2.48039e6 + 1.43206e6i −0.149589 + 0.0863654i
\(256\) 0 0
\(257\) 1.29411e7 1.54226e7i 0.762379 0.908568i −0.235617 0.971846i \(-0.575711\pi\)
0.997996 + 0.0632783i \(0.0201556\pi\)
\(258\) 0 0
\(259\) 2.21303e6 + 1.27769e6i 0.127376 + 0.0735406i
\(260\) 0 0
\(261\) −5.48557e6 + 967254.i −0.308532 + 0.0544025i
\(262\) 0 0
\(263\) 3.77771e6 + 1.37497e6i 0.207664 + 0.0755835i 0.443758 0.896147i \(-0.353645\pi\)
−0.236094 + 0.971730i \(0.575867\pi\)
\(264\) 0 0
\(265\) 535339.i 0.0287668i
\(266\) 0 0
\(267\) −1.12903e6 −0.0593159
\(268\) 0 0
\(269\) −4.28982e6 + 1.17862e7i −0.220385 + 0.605503i −0.999779 0.0210316i \(-0.993305\pi\)
0.779394 + 0.626534i \(0.215527\pi\)
\(270\) 0 0
\(271\) 4.64876e6 + 2.63644e7i 0.233577 + 1.32468i 0.845590 + 0.533832i \(0.179249\pi\)
−0.612014 + 0.790847i \(0.709640\pi\)
\(272\) 0 0
\(273\) −8.17182e6 + 1.41540e7i −0.401634 + 0.695651i
\(274\) 0 0
\(275\) 7.45882e6 + 6.25869e6i 0.358651 + 0.300944i
\(276\) 0 0
\(277\) 4.74114e6 + 8.21189e6i 0.223071 + 0.386370i 0.955739 0.294216i \(-0.0950585\pi\)
−0.732668 + 0.680586i \(0.761725\pi\)
\(278\) 0 0
\(279\) 3.87688e6 + 1.06516e7i 0.178513 + 0.490460i
\(280\) 0 0
\(281\) −3.58733e7 6.32543e6i −1.61678 0.285083i −0.709217 0.704990i \(-0.750951\pi\)
−0.907567 + 0.419907i \(0.862063\pi\)
\(282\) 0 0
\(283\) 2.21487e7 1.85850e7i 0.977214 0.819980i −0.00645240 0.999979i \(-0.502054\pi\)
0.983667 + 0.179999i \(0.0576094\pi\)
\(284\) 0 0
\(285\) −2.32520e6 + 4.16532e6i −0.100444 + 0.179934i
\(286\) 0 0
\(287\) −1.80051e7 2.14576e7i −0.761638 0.907685i
\(288\) 0 0
\(289\) −1.24656e6 + 7.06958e6i −0.0516439 + 0.292887i
\(290\) 0 0
\(291\) 2.18887e7 7.96685e6i 0.888264 0.323302i
\(292\) 0 0
\(293\) −1.36327e7 + 7.87085e6i −0.541975 + 0.312910i −0.745879 0.666081i \(-0.767970\pi\)
0.203904 + 0.978991i \(0.434637\pi\)
\(294\) 0 0
\(295\) −4.37044e6 + 5.20848e6i −0.170239 + 0.202883i
\(296\) 0 0
\(297\) 1.23717e7 + 7.14280e6i 0.472237 + 0.272646i
\(298\) 0 0
\(299\) −3.35159e7 + 5.90975e6i −1.25383 + 0.221083i
\(300\) 0 0
\(301\) −4.63302e7 1.68628e7i −1.69889 0.618344i
\(302\) 0 0
\(303\) 2.88581e7i 1.03738i
\(304\) 0 0
\(305\) −1.17213e7 −0.413121
\(306\) 0 0
\(307\) 5.75649e6 1.58158e7i 0.198949 0.546609i −0.799595 0.600539i \(-0.794953\pi\)
0.998545 + 0.0539304i \(0.0171749\pi\)
\(308\) 0 0
\(309\) 3.12809e6 + 1.77403e7i 0.106024 + 0.601292i
\(310\) 0 0
\(311\) 2.74940e7 4.76210e7i 0.914023 1.58313i 0.105697 0.994398i \(-0.466293\pi\)
0.808326 0.588736i \(-0.200374\pi\)
\(312\) 0 0
\(313\) −1.65303e7 1.38706e7i −0.539074 0.452337i 0.332147 0.943228i \(-0.392227\pi\)
−0.871221 + 0.490891i \(0.836671\pi\)
\(314\) 0 0
\(315\) 2.60040e6 + 4.50403e6i 0.0831973 + 0.144102i
\(316\) 0 0
\(317\) −1.11556e7 3.06496e7i −0.350198 0.962161i −0.982306 0.187281i \(-0.940033\pi\)
0.632108 0.774880i \(-0.282190\pi\)
\(318\) 0 0
\(319\) −1.11219e7 1.96110e6i −0.342616 0.0604125i
\(320\) 0 0
\(321\) 1.97877e7 1.66039e7i 0.598247 0.501989i
\(322\) 0 0
\(323\) −1.00436e7 2.64003e7i −0.298044 0.783431i
\(324\) 0 0
\(325\) 1.70566e7 + 2.03273e7i 0.496869 + 0.592146i
\(326\) 0 0
\(327\) 799988. 4.53696e6i 0.0228792 0.129754i
\(328\) 0 0
\(329\) −2.55838e7 + 9.31173e6i −0.718417 + 0.261482i
\(330\) 0 0
\(331\) −2.59223e7 + 1.49662e7i −0.714808 + 0.412695i −0.812839 0.582489i \(-0.802079\pi\)
0.0980306 + 0.995183i \(0.468746\pi\)
\(332\) 0 0
\(333\) 1.22802e6 1.46350e6i 0.0332562 0.0396331i
\(334\) 0 0
\(335\) 2.99606e6 + 1.72977e6i 0.0796921 + 0.0460103i
\(336\) 0 0
\(337\) −581576. + 102548.i −0.0151956 + 0.00267939i −0.181241 0.983439i \(-0.558011\pi\)
0.166045 + 0.986118i \(0.446900\pi\)
\(338\) 0 0
\(339\) −2.29869e7 8.36656e6i −0.590041 0.214757i
\(340\) 0 0
\(341\) 2.29821e7i 0.579597i
\(342\) 0 0
\(343\) −1.62208e7 −0.401967
\(344\) 0 0
\(345\) 4.39383e6 1.20720e7i 0.107001 0.293982i
\(346\) 0 0
\(347\) 9.17242e6 + 5.20194e7i 0.219531 + 1.24502i 0.872869 + 0.487955i \(0.162257\pi\)
−0.653338 + 0.757066i \(0.726632\pi\)
\(348\) 0 0
\(349\) −2.33494e6 + 4.04424e6i −0.0549288 + 0.0951395i −0.892182 0.451675i \(-0.850827\pi\)
0.837254 + 0.546815i \(0.184160\pi\)
\(350\) 0 0
\(351\) 2.98237e7 + 2.50250e7i 0.689668 + 0.578700i
\(352\) 0 0
\(353\) −1.73778e7 3.00992e7i −0.395067 0.684276i 0.598043 0.801464i \(-0.295945\pi\)
−0.993110 + 0.117188i \(0.962612\pi\)
\(354\) 0 0
\(355\) 8.44099e6 + 2.31914e7i 0.188672 + 0.518373i
\(356\) 0 0
\(357\) 3.59750e7 + 6.34337e6i 0.790673 + 0.139417i
\(358\) 0 0
\(359\) 1.44752e7 1.21461e7i 0.312853 0.262515i −0.472817 0.881161i \(-0.656763\pi\)
0.785670 + 0.618646i \(0.212318\pi\)
\(360\) 0 0
\(361\) −3.68986e7 2.91857e7i −0.784312 0.620367i
\(362\) 0 0
\(363\) −1.68046e7 2.00269e7i −0.351324 0.418691i
\(364\) 0 0
\(365\) −1.13632e6 + 6.44437e6i −0.0233679 + 0.132526i
\(366\) 0 0
\(367\) 1.25663e7 4.57375e6i 0.254219 0.0925282i −0.211767 0.977320i \(-0.567922\pi\)
0.465986 + 0.884792i \(0.345700\pi\)
\(368\) 0 0
\(369\) −1.81359e7 + 1.04708e7i −0.360960 + 0.208400i
\(370\) 0 0
\(371\) 4.38890e6 5.23049e6i 0.0859476 0.102428i
\(372\) 0 0
\(373\) 8.03291e7 + 4.63780e7i 1.54791 + 0.893688i 0.998301 + 0.0582673i \(0.0185576\pi\)
0.549611 + 0.835420i \(0.314776\pi\)
\(374\) 0 0
\(375\) −2.05663e7 + 3.62639e6i −0.389998 + 0.0687672i
\(376\) 0 0
\(377\) −2.89217e7 1.05266e7i −0.539759 0.196456i
\(378\) 0 0
\(379\) 4.63765e7i 0.851884i 0.904750 + 0.425942i \(0.140057\pi\)
−0.904750 + 0.425942i \(0.859943\pi\)
\(380\) 0 0
\(381\) 2.67575e7 0.483805
\(382\) 0 0
\(383\) 3.18755e7 8.75773e7i 0.567363 1.55882i −0.241242 0.970465i \(-0.577555\pi\)
0.808605 0.588352i \(-0.200223\pi\)
\(384\) 0 0
\(385\) 1.83105e6 + 1.03844e7i 0.0320861 + 0.181969i
\(386\) 0 0
\(387\) −1.84302e7 + 3.19220e7i −0.317977 + 0.550753i
\(388\) 0 0
\(389\) 6.54686e7 + 5.49346e7i 1.11220 + 0.933249i 0.998185 0.0602298i \(-0.0191834\pi\)
0.114018 + 0.993479i \(0.463628\pi\)
\(390\) 0 0
\(391\) 3.80338e7 + 6.58765e7i 0.636268 + 1.10205i
\(392\) 0 0
\(393\) 1.24699e7 + 3.42609e7i 0.205441 + 0.564444i
\(394\) 0 0
\(395\) 2.36590e7 + 4.17171e6i 0.383888 + 0.0676898i
\(396\) 0 0
\(397\) −2.41889e7 + 2.02969e7i −0.386584 + 0.324383i −0.815281 0.579066i \(-0.803417\pi\)
0.428696 + 0.903449i \(0.358973\pi\)
\(398\) 0 0
\(399\) 5.68669e7 2.16341e7i 0.895243 0.340581i
\(400\) 0 0
\(401\) −4.07945e7 4.86170e7i −0.632658 0.753972i 0.350534 0.936550i \(-0.386000\pi\)
−0.983191 + 0.182578i \(0.941556\pi\)
\(402\) 0 0
\(403\) −1.08760e7 + 6.16808e7i −0.166170 + 0.942399i
\(404\) 0 0
\(405\) −5.82183e6 + 2.11897e6i −0.0876383 + 0.0318977i
\(406\) 0 0
\(407\) 3.35449e6 1.93672e6i 0.0497557 0.0287265i
\(408\) 0 0
\(409\) 6.50643e7 7.75406e7i 0.950983 1.13334i −0.0399793 0.999201i \(-0.512729\pi\)
0.990963 0.134137i \(-0.0428264\pi\)
\(410\) 0 0
\(411\) 3.80846e6 + 2.19882e6i 0.0548560 + 0.0316711i
\(412\) 0 0
\(413\) 8.54021e7 1.50587e7i 1.21232 0.213765i
\(414\) 0 0
\(415\) −2.20049e7 8.00913e6i −0.307876 0.112058i
\(416\) 0 0
\(417\) 5.03748e7i 0.694713i
\(418\) 0 0
\(419\) −1.11157e8 −1.51110 −0.755549 0.655092i \(-0.772630\pi\)
−0.755549 + 0.655092i \(0.772630\pi\)
\(420\) 0 0
\(421\) 2.36936e7 6.50975e7i 0.317529 0.872405i −0.673551 0.739141i \(-0.735232\pi\)
0.991081 0.133264i \(-0.0425459\pi\)
\(422\) 0 0
\(423\) 3.53451e6 + 2.00452e7i 0.0466991 + 0.264844i
\(424\) 0 0
\(425\) 2.96549e7 5.13637e7i 0.386304 0.669098i
\(426\) 0 0
\(427\) 1.14522e8 + 9.60957e7i 1.47098 + 1.23430i
\(428\) 0 0
\(429\) 1.23868e7 + 2.14545e7i 0.156887 + 0.271736i
\(430\) 0 0
\(431\) −2.34585e7 6.44518e7i −0.293001 0.805014i −0.995624 0.0934512i \(-0.970210\pi\)
0.702623 0.711562i \(-0.252012\pi\)
\(432\) 0 0
\(433\) −1.00887e8 1.77891e7i −1.24271 0.219124i −0.486636 0.873605i \(-0.661776\pi\)
−0.756079 + 0.654481i \(0.772887\pi\)
\(434\) 0 0
\(435\) 8.89989e6 7.46789e6i 0.108123 0.0907257i
\(436\) 0 0
\(437\) 1.10626e8 + 6.17546e7i 1.32560 + 0.739989i
\(438\) 0 0
\(439\) −7.19709e7 8.57716e7i −0.850675 1.01379i −0.999688 0.0249595i \(-0.992054\pi\)
0.149014 0.988835i \(-0.452390\pi\)
\(440\) 0 0
\(441\) 4.70640e6 2.66913e7i 0.0548748 0.311210i
\(442\) 0 0
\(443\) −5.83127e7 + 2.12241e7i −0.670737 + 0.244128i −0.654865 0.755746i \(-0.727275\pi\)
−0.0158716 + 0.999874i \(0.505052\pi\)
\(444\) 0 0
\(445\) −1.71920e6 + 992578.i −0.0195095 + 0.0112638i
\(446\) 0 0
\(447\) −7.21010e6 + 8.59266e6i −0.0807270 + 0.0962067i
\(448\) 0 0
\(449\) −6.52284e7 3.76596e7i −0.720606 0.416042i 0.0943698 0.995537i \(-0.469916\pi\)
−0.814976 + 0.579495i \(0.803250\pi\)
\(450\) 0 0
\(451\) −4.18136e7 + 7.37287e6i −0.455815 + 0.0803724i
\(452\) 0 0
\(453\) −5.94702e7 2.16454e7i −0.639742 0.232847i
\(454\) 0 0
\(455\) 2.87368e7i 0.305073i
\(456\) 0 0
\(457\) 1.52194e8 1.59459 0.797296 0.603589i \(-0.206263\pi\)
0.797296 + 0.603589i \(0.206263\pi\)
\(458\) 0 0
\(459\) 2.97619e7 8.17700e7i 0.307767 0.845583i
\(460\) 0 0
\(461\) 6.75401e6 + 3.83039e7i 0.0689380 + 0.390967i 0.999680 + 0.0252907i \(0.00805114\pi\)
−0.930742 + 0.365676i \(0.880838\pi\)
\(462\) 0 0
\(463\) −4.28131e7 + 7.41545e7i −0.431354 + 0.747127i −0.996990 0.0775277i \(-0.975297\pi\)
0.565636 + 0.824655i \(0.308631\pi\)
\(464\) 0 0
\(465\) −1.81111e7 1.51970e7i −0.180130 0.151147i
\(466\) 0 0
\(467\) 7.27398e7 + 1.25989e8i 0.714202 + 1.23703i 0.963266 + 0.268548i \(0.0865438\pi\)
−0.249064 + 0.968487i \(0.580123\pi\)
\(468\) 0 0
\(469\) −1.50914e7 4.14634e7i −0.146289 0.401926i
\(470\) 0 0
\(471\) −7.41007e7 1.30660e7i −0.709185 0.125049i
\(472\) 0 0
\(473\) −5.72495e7 + 4.80380e7i −0.540988 + 0.453943i
\(474\) 0 0
\(475\) −1.42841e6 9.87739e7i −0.0133283 0.921640i
\(476\) 0 0
\(477\) −3.28123e6 3.91042e6i −0.0302330 0.0360303i
\(478\) 0 0
\(479\) −3.23849e7 + 1.83664e8i −0.294670 + 1.67116i 0.373872 + 0.927480i \(0.378030\pi\)
−0.668542 + 0.743675i \(0.733081\pi\)
\(480\) 0 0
\(481\) 9.91952e6 3.61041e6i 0.0891365 0.0324430i
\(482\) 0 0
\(483\) −1.41900e8 + 8.19260e7i −1.25933 + 0.727077i
\(484\) 0 0
\(485\) 2.63264e7 3.13746e7i 0.230763 0.275013i
\(486\) 0 0
\(487\) −1.44836e8 8.36209e7i −1.25397 0.723983i −0.282078 0.959391i \(-0.591024\pi\)
−0.971896 + 0.235409i \(0.924357\pi\)
\(488\) 0 0
\(489\) 4.69145e6 827229.i 0.0401218 0.00707456i
\(490\) 0 0
\(491\) −1.82318e8 6.63584e7i −1.54023 0.560598i −0.574129 0.818765i \(-0.694659\pi\)
−0.966100 + 0.258167i \(0.916881\pi\)
\(492\) 0 0
\(493\) 6.87922e7i 0.574114i
\(494\) 0 0
\(495\) 7.88334e6 0.0649972
\(496\) 0 0
\(497\) 1.07660e8 2.95793e8i 0.876969 2.40945i
\(498\) 0 0
\(499\) −1.90633e7 1.08113e8i −0.153425 0.870116i −0.960212 0.279273i \(-0.909906\pi\)
0.806787 0.590843i \(-0.201205\pi\)
\(500\) 0 0
\(501\) 1.43158e7 2.47958e7i 0.113842 0.197181i
\(502\) 0 0
\(503\) 1.12783e8 + 9.46364e7i 0.886218 + 0.743625i 0.967448 0.253070i \(-0.0814403\pi\)
−0.0812298 + 0.996695i \(0.525885\pi\)
\(504\) 0 0
\(505\) −2.53704e7 4.39428e7i −0.196994 0.341204i
\(506\) 0 0
\(507\) −9.74183e6 2.67655e7i −0.0747510 0.205377i
\(508\) 0 0
\(509\) −7.11515e7 1.25459e7i −0.539549 0.0951370i −0.102769 0.994705i \(-0.532770\pi\)
−0.436780 + 0.899568i \(0.643881\pi\)
\(510\) 0 0
\(511\) 6.39355e7 5.36483e7i 0.479159 0.402062i
\(512\) 0 0
\(513\) −2.72288e7 1.42353e8i −0.201686 1.05442i
\(514\) 0 0
\(515\) 2.03595e7 + 2.42635e7i 0.149054 + 0.177636i
\(516\) 0 0
\(517\) −7.16619e6 + 4.06415e7i −0.0518581 + 0.294102i
\(518\) 0 0
\(519\) −1.78235e8 + 6.48723e7i −1.27494 + 0.464042i
\(520\) 0 0
\(521\) −1.18148e8 + 6.82127e7i −0.835435 + 0.482338i −0.855710 0.517456i \(-0.826879\pi\)
0.0202752 + 0.999794i \(0.493546\pi\)
\(522\) 0 0
\(523\) 4.25515e7 5.07109e7i 0.297447 0.354484i −0.596534 0.802588i \(-0.703456\pi\)
0.893982 + 0.448104i \(0.147900\pi\)
\(524\) 0 0
\(525\) 1.10639e8 + 6.38774e7i 0.764593 + 0.441438i
\(526\) 0 0
\(527\) 1.37864e8 2.43091e7i 0.941931 0.166088i
\(528\) 0 0
\(529\) −1.81510e8 6.60641e7i −1.22612 0.446271i
\(530\) 0 0
\(531\) 6.48332e7i 0.433026i
\(532\) 0 0
\(533\) −1.15711e8 −0.764177
\(534\) 0 0
\(535\) 1.55340e7 4.26793e7i 0.101443 0.278712i
\(536\) 0 0
\(537\) 1.20592e7 + 6.83911e7i 0.0778745 + 0.441648i
\(538\) 0 0
\(539\) 2.74756e7 4.75891e7i 0.175461 0.303907i
\(540\) 0 0
\(541\) 1.79778e8 + 1.50851e8i 1.13539 + 0.952703i 0.999278 0.0379907i \(-0.0120957\pi\)
0.136109 + 0.990694i \(0.456540\pi\)
\(542\) 0 0
\(543\) 3.06631e7 + 5.31101e7i 0.191521 + 0.331724i
\(544\) 0 0
\(545\) −2.77048e6 7.61182e6i −0.0171145 0.0470218i
\(546\) 0 0
\(547\) 1.35585e8 + 2.39073e7i 0.828418 + 0.146072i 0.571751 0.820427i \(-0.306264\pi\)
0.256667 + 0.966500i \(0.417376\pi\)
\(548\) 0 0
\(549\) 8.56192e7 7.18430e7i 0.517433 0.434178i
\(550\) 0 0
\(551\) 5.87177e7 + 9.83885e7i 0.351006 + 0.588152i
\(552\) 0 0
\(553\) −1.96957e8 2.34724e8i −1.16465 1.38798i
\(554\) 0 0
\(555\) −691939. + 3.92418e6i −0.00404752 + 0.0229546i
\(556\) 0 0
\(557\) −1.42537e8 + 5.18791e7i −0.824824 + 0.300211i −0.719733 0.694251i \(-0.755736\pi\)
−0.105091 + 0.994463i \(0.533513\pi\)
\(558\) 0 0
\(559\) −1.76383e8 + 1.01835e8i −1.00977 + 0.582990i
\(560\) 0 0
\(561\) 3.55923e7 4.24173e7i 0.201590 0.240245i
\(562\) 0 0
\(563\) 2.86415e8 + 1.65362e8i 1.60499 + 0.926639i 0.990469 + 0.137736i \(0.0439825\pi\)
0.614517 + 0.788903i \(0.289351\pi\)
\(564\) 0 0
\(565\) −4.23581e7 + 7.46887e6i −0.234850 + 0.0414104i
\(566\) 0 0
\(567\) 7.42538e7 + 2.70262e7i 0.407352 + 0.148264i
\(568\) 0 0
\(569\) 1.84830e7i 0.100331i 0.998741 + 0.0501656i \(0.0159749\pi\)
−0.998741 + 0.0501656i \(0.984025\pi\)
\(570\) 0 0
\(571\) 1.28016e8 0.687632 0.343816 0.939037i \(-0.388280\pi\)
0.343816 + 0.939037i \(0.388280\pi\)
\(572\) 0 0
\(573\) 2.80394e7 7.70376e7i 0.149041 0.409486i
\(574\) 0 0
\(575\) 4.61953e7 + 2.61987e8i 0.242993 + 1.37808i
\(576\) 0 0
\(577\) 3.89897e7 6.75322e7i 0.202966 0.351547i −0.746517 0.665366i \(-0.768275\pi\)
0.949483 + 0.313819i \(0.101609\pi\)
\(578\) 0 0
\(579\) −7.69682e7 6.45840e7i −0.396530 0.332728i
\(580\) 0 0
\(581\) 1.49336e8 + 2.58657e8i 0.761439 + 1.31885i
\(582\) 0 0
\(583\) −3.53980e6 9.72553e6i −0.0178638 0.0490803i
\(584\) 0 0
\(585\) 2.11578e7 + 3.73069e6i 0.105682 + 0.0186347i
\(586\) 0 0
\(587\) 1.31639e8 1.10458e8i 0.650836 0.546116i −0.256489 0.966547i \(-0.582566\pi\)
0.907324 + 0.420431i \(0.138121\pi\)
\(588\) 0 0
\(589\) 1.76428e8 1.52442e8i 0.863419 0.746033i
\(590\) 0 0
\(591\) −1.13266e8 1.34985e8i −0.548702 0.653918i
\(592\) 0 0
\(593\) −2.31073e7 + 1.31048e8i −0.110812 + 0.628444i 0.877927 + 0.478794i \(0.158926\pi\)
−0.988739 + 0.149650i \(0.952185\pi\)
\(594\) 0 0
\(595\) 6.03566e7 2.19680e7i 0.286533 0.104289i
\(596\) 0 0
\(597\) −1.05483e8 + 6.09005e7i −0.495745 + 0.286219i
\(598\) 0 0
\(599\) 6.10976e6 7.28133e6i 0.0284278 0.0338790i −0.751643 0.659570i \(-0.770738\pi\)
0.780071 + 0.625691i \(0.215183\pi\)
\(600\) 0 0
\(601\) 2.32996e8 + 1.34521e8i 1.07331 + 0.619677i 0.929084 0.369868i \(-0.120597\pi\)
0.144227 + 0.989545i \(0.453930\pi\)
\(602\) 0 0
\(603\) −3.24871e7 + 5.72836e6i −0.148170 + 0.0261263i
\(604\) 0 0
\(605\) −4.31952e7 1.57218e7i −0.195060 0.0709962i
\(606\) 0 0
\(607\) 1.24763e8i 0.557854i 0.960312 + 0.278927i \(0.0899788\pi\)
−0.960312 + 0.278927i \(0.910021\pi\)
\(608\) 0 0
\(609\) −1.48180e8 −0.656052
\(610\) 0 0
\(611\) −3.84661e7 + 1.05685e8i −0.168638 + 0.463328i
\(612\) 0 0
\(613\) 7.19266e7 + 4.07916e8i 0.312254 + 1.77088i 0.587221 + 0.809427i \(0.300222\pi\)
−0.274967 + 0.961454i \(0.588667\pi\)
\(614\) 0 0
\(615\) 2.18393e7 3.78267e7i 0.0938886 0.162620i
\(616\) 0 0
\(617\) 1.78802e8 + 1.50033e8i 0.761234 + 0.638751i 0.938448 0.345421i \(-0.112264\pi\)
−0.177214 + 0.984172i \(0.556708\pi\)
\(618\) 0 0
\(619\) −8.87719e7 1.53757e8i −0.374286 0.648282i 0.615934 0.787798i \(-0.288779\pi\)
−0.990220 + 0.139516i \(0.955445\pi\)
\(620\) 0 0
\(621\) 1.33494e8 + 3.66772e8i 0.557426 + 1.53151i
\(622\) 0 0
\(623\) 2.49348e7 + 4.39668e6i 0.103120 + 0.0181828i
\(624\) 0 0
\(625\) 1.44257e8 1.21046e8i 0.590876 0.495804i
\(626\) 0 0
\(627\) 1.46998e7 9.10464e7i 0.0596360 0.369369i
\(628\) 0 0
\(629\) −1.51661e7 1.80742e7i −0.0609427 0.0726286i
\(630\) 0 0
\(631\) 1.00033e7 5.67314e7i 0.0398157 0.225806i −0.958407 0.285406i \(-0.907871\pi\)
0.998222 + 0.0596002i \(0.0189826\pi\)
\(632\) 0 0
\(633\) 1.52780e8 5.56075e7i 0.602360 0.219241i
\(634\) 0 0
\(635\) 4.07442e7 2.35237e7i 0.159127 0.0918722i
\(636\) 0 0
\(637\) 9.62617e7 1.14720e8i 0.372422 0.443835i
\(638\) 0 0
\(639\) −2.03804e8 1.17666e8i −0.781107 0.450972i
\(640\) 0 0
\(641\) −4.17444e8 + 7.36066e7i −1.58498 + 0.279475i −0.895578 0.444904i \(-0.853238\pi\)
−0.689402 + 0.724379i \(0.742127\pi\)
\(642\) 0 0
\(643\) −3.15666e8 1.14893e8i −1.18740 0.432176i −0.328587 0.944474i \(-0.606572\pi\)
−0.858808 + 0.512297i \(0.828795\pi\)
\(644\) 0 0
\(645\) 7.68810e7i 0.286510i
\(646\) 0 0
\(647\) 4.54236e8 1.67714 0.838570 0.544795i \(-0.183392\pi\)
0.838570 + 0.544795i \(0.183392\pi\)
\(648\) 0 0
\(649\) 4.49581e7 1.23521e8i 0.164465 0.451864i
\(650\) 0 0
\(651\) 5.23626e7 + 2.96963e8i 0.189792 + 1.07636i
\(652\) 0 0
\(653\) 1.53576e8 2.66002e8i 0.551550 0.955312i −0.446613 0.894727i \(-0.647370\pi\)
0.998163 0.0605852i \(-0.0192967\pi\)
\(654\) 0 0
\(655\) 4.91085e7 + 4.12069e7i 0.174756 + 0.146638i
\(656\) 0 0
\(657\) −3.11989e7 5.40381e7i −0.110013 0.190548i
\(658\) 0 0
\(659\) −5.48749e7 1.50768e8i −0.191742 0.526807i 0.806149 0.591712i \(-0.201548\pi\)
−0.997891 + 0.0649050i \(0.979326\pi\)
\(660\) 0 0
\(661\) −2.86882e8 5.05850e7i −0.993342 0.175153i −0.346724 0.937967i \(-0.612706\pi\)
−0.646618 + 0.762814i \(0.723817\pi\)
\(662\) 0 0
\(663\) 1.15598e8 9.69986e7i 0.396654 0.332832i
\(664\) 0 0
\(665\) 6.75729e7 8.29369e7i 0.229778 0.282022i
\(666\) 0 0
\(667\) −1.98339e8 2.36371e8i −0.668391 0.796557i
\(668\) 0 0
\(669\) 1.31231e7 7.44248e7i 0.0438286 0.248565i
\(670\) 0 0
\(671\) 2.12942e8 7.75046e7i 0.704845 0.256543i
\(672\) 0 0
\(673\) −4.66525e8 + 2.69348e8i −1.53049 + 0.883627i −0.531147 + 0.847279i \(0.678239\pi\)
−0.999339 + 0.0363475i \(0.988428\pi\)
\(674\) 0 0
\(675\) 1.95616e8 2.33126e8i 0.636051 0.758016i
\(676\) 0 0
\(677\) 4.40832e8 + 2.54515e8i 1.42072 + 0.820251i 0.996360 0.0852450i \(-0.0271673\pi\)
0.424356 + 0.905496i \(0.360501\pi\)
\(678\) 0 0
\(679\) −5.14441e8 + 9.07098e7i −1.64334 + 0.289764i
\(680\) 0 0
\(681\) −2.91526e8 1.06107e8i −0.923072 0.335971i
\(682\) 0 0
\(683\) 2.66985e8i 0.837962i −0.907995 0.418981i \(-0.862387\pi\)
0.907995 0.418981i \(-0.137613\pi\)
\(684\) 0 0
\(685\) 7.73230e6 0.0240568
\(686\) 0 0
\(687\) 1.39295e8 3.82710e8i 0.429601 1.18032i
\(688\) 0 0
\(689\) −4.89786e6 2.77772e7i −0.0149744 0.0849240i
\(690\) 0 0
\(691\) 8.28318e7 1.43469e8i 0.251051 0.434834i −0.712764 0.701404i \(-0.752557\pi\)
0.963816 + 0.266570i \(0.0858903\pi\)
\(692\) 0 0
\(693\) −7.70236e7 6.46304e7i −0.231432 0.194195i
\(694\) 0 0
\(695\) 4.42867e7 + 7.67068e7i 0.131922 + 0.228496i
\(696\) 0 0
\(697\) 8.84562e7 + 2.43031e8i 0.261234 + 0.717735i
\(698\) 0 0
\(699\) −2.12413e8 3.74541e7i −0.621941 0.109665i
\(700\) 0 0
\(701\) −3.64789e8 + 3.06094e8i −1.05898 + 0.888588i −0.994009 0.109299i \(-0.965139\pi\)
−0.0649695 + 0.997887i \(0.520695\pi\)
\(702\) 0 0
\(703\) −3.71183e7 1.29052e7i −0.106837 0.0371450i
\(704\) 0 0
\(705\) −2.72890e7 3.25217e7i −0.0778789 0.0928124i
\(706\) 0 0
\(707\) −1.12379e8 + 6.37336e8i −0.318001 + 1.80347i
\(708\) 0 0
\(709\) −3.06996e8 + 1.11737e8i −0.861378 + 0.313516i −0.734671 0.678424i \(-0.762663\pi\)
−0.126708 + 0.991940i \(0.540441\pi\)
\(710\) 0 0
\(711\) −1.98388e8 + 1.14539e8i −0.551959 + 0.318673i
\(712\) 0 0
\(713\) −4.03616e8 + 4.81011e8i −1.11353 + 1.32705i
\(714\) 0 0
\(715\) 3.77232e7 + 2.17795e7i 0.103202 + 0.0595840i
\(716\) 0 0
\(717\) −3.98623e7 + 7.02880e6i −0.108145 + 0.0190688i
\(718\) 0 0
\(719\) −5.27355e8 1.91942e8i −1.41879 0.516396i −0.485090 0.874464i \(-0.661213\pi\)
−0.933695 + 0.358069i \(0.883435\pi\)
\(720\) 0 0
\(721\) 4.03979e8i 1.07784i
\(722\) 0 0
\(723\) 3.63721e8 0.962394
\(724\) 0 0
\(725\) −8.22845e7 + 2.26075e8i −0.215926 + 0.593251i
\(726\) 0 0
\(727\) −3.76851e7 2.13723e8i −0.0980769 0.556222i −0.993761 0.111531i \(-0.964425\pi\)
0.895684 0.444691i \(-0.146686\pi\)
\(728\) 0 0
\(729\) 1.82720e8 3.16480e8i 0.471633 0.816891i
\(730\) 0 0
\(731\) 3.48724e8 + 2.92614e8i 0.892749 + 0.749105i
\(732\) 0 0
\(733\) −3.18782e7 5.52146e7i −0.0809434 0.140198i 0.822712 0.568458i \(-0.192460\pi\)
−0.903655 + 0.428260i \(0.859127\pi\)
\(734\) 0 0
\(735\) 1.93344e7 + 5.31208e7i 0.0486932 + 0.133783i
\(736\) 0 0
\(737\) −6.58673e7 1.16142e7i −0.164538 0.0290126i
\(738\) 0 0
\(739\) 3.46050e8 2.90370e8i 0.857443 0.719480i −0.103973 0.994580i \(-0.533156\pi\)
0.961416 + 0.275100i \(0.0887111\pi\)
\(740\) 0 0
\(741\) 8.25388e7 2.37400e8i 0.202863 0.583479i
\(742\) 0 0
\(743\) −3.07292e8 3.66216e8i −0.749177 0.892834i 0.247935 0.968777i \(-0.420248\pi\)
−0.997112 + 0.0759422i \(0.975804\pi\)
\(744\) 0 0
\(745\) −3.42479e6 + 1.94229e7i −0.00828256 + 0.0469727i
\(746\) 0 0
\(747\) 2.09826e8 7.63705e7i 0.503383 0.183216i
\(748\) 0 0
\(749\) −5.01674e8 + 2.89641e8i −1.19392 + 0.689311i
\(750\) 0 0
\(751\) 3.41730e8 4.07258e8i 0.806795 0.961501i −0.193011 0.981197i \(-0.561825\pi\)
0.999806 + 0.0196960i \(0.00626984\pi\)
\(752\) 0 0
\(753\) −2.54879e8 1.47154e8i −0.596965 0.344658i
\(754\) 0 0
\(755\) −1.09586e8 + 1.93229e7i −0.254632 + 0.0448986i
\(756\) 0 0
\(757\) 7.26422e8 + 2.64396e8i 1.67456 + 0.609491i 0.992549 0.121848i \(-0.0388820\pi\)
0.682014 + 0.731339i \(0.261104\pi\)
\(758\) 0 0
\(759\) 2.48365e8i 0.568022i
\(760\) 0 0
\(761\) −4.59652e8 −1.04298 −0.521489 0.853258i \(-0.674623\pi\)
−0.521489 + 0.853258i \(0.674623\pi\)
\(762\) 0 0
\(763\) −3.53357e7 + 9.70842e7i −0.0795501 + 0.218562i
\(764\) 0 0
\(765\) −8.33855e6 4.72902e7i −0.0186254 0.105630i
\(766\) 0 0
\(767\) 1.79116e8 3.10239e8i 0.396962 0.687559i
\(768\) 0 0
\(769\) −3.08851e8 2.59157e8i −0.679156 0.569880i 0.236603 0.971606i \(-0.423966\pi\)
−0.915760 + 0.401726i \(0.868410\pi\)
\(770\) 0 0
\(771\) −2.00204e8 3.46764e8i −0.436828 0.756608i
\(772\) 0 0
\(773\) −5.32298e7 1.46248e8i −0.115243 0.316629i 0.868639 0.495446i \(-0.164995\pi\)
−0.983882 + 0.178817i \(0.942773\pi\)
\(774\) 0 0
\(775\) 4.82146e8 + 8.50153e7i 1.03579 + 0.182638i
\(776\) 0 0
\(777\) 3.89324e7 3.26682e7i 0.0829943 0.0696405i
\(778\) 0 0
\(779\) 3.33953e8 + 2.72088e8i 0.706435 + 0.575569i
\(780\) 0 0
\(781\) −3.06696e8 3.65506e8i −0.643806 0.767259i
\(782\) 0 0
\(783\) −6.12942e7 + 3.47616e8i −0.127683 + 0.724128i
\(784\) 0 0
\(785\) −1.24322e8 + 4.52493e7i −0.257002 + 0.0935412i
\(786\) 0 0
\(787\) −5.65510e8 + 3.26498e8i −1.16016 + 0.669816i −0.951341 0.308139i \(-0.900294\pi\)
−0.208815 + 0.977955i \(0.566961\pi\)
\(788\) 0 0
\(789\) 5.13938e7 6.12488e7i 0.104636 0.124700i
\(790\) 0 0
\(791\) 4.75089e8 + 2.74293e8i 0.959944 + 0.554224i
\(792\) 0 0
\(793\) 6.08185e8 1.07240e8i 1.21960 0.215048i
\(794\) 0 0
\(795\) 1.00050e7 + 3.64151e6i 0.0199119 + 0.00724736i
\(796\) 0 0
\(797\) 1.18018e8i 0.233117i 0.993184 + 0.116558i \(0.0371862\pi\)
−0.993184 + 0.116558i \(0.962814\pi\)
\(798\) 0 0
\(799\) 2.51378e8 0.492819
\(800\) 0 0
\(801\) 6.47421e6 1.77877e7i 0.0125976 0.0346117i
\(802\) 0 0
\(803\) −2.19684e7 1.24589e8i −0.0424279 0.240620i
\(804\) 0 0
\(805\) −1.44049e8 + 2.49501e8i −0.276136 + 0.478282i
\(806\) 0 0
\(807\) 1.91092e8 + 1.60345e8i 0.363598 + 0.305095i
\(808\) 0 0
\(809\) 5.14574e8 + 8.91268e8i 0.971857 + 1.68331i 0.689940 + 0.723866i \(0.257637\pi\)
0.281917 + 0.959439i \(0.409030\pi\)
\(810\) 0 0
\(811\) 3.23069e7 + 8.87624e7i 0.0605665 + 0.166405i 0.966285 0.257474i \(-0.0828903\pi\)
−0.905719 + 0.423879i \(0.860668\pi\)
\(812\) 0 0
\(813\) 5.24348e8 + 9.24567e7i 0.975771 + 0.172055i
\(814\) 0 0
\(815\) 6.41651e6 5.38409e6i 0.0118529 0.00994580i
\(816\) 0 0
\(817\) 7.48516e8 + 1.20851e8i 1.37257 + 0.221607i
\(818\) 0 0
\(819\) −1.76135e8 2.09910e8i −0.320623 0.382103i
\(820\) 0 0
\(821\) 6.43559e7 3.64980e8i 0.116294 0.659538i −0.869807 0.493392i \(-0.835757\pi\)
0.986101 0.166146i \(-0.0531322\pi\)
\(822\) 0 0
\(823\) −6.87342e8 + 2.50172e8i −1.23303 + 0.448786i −0.874634 0.484784i \(-0.838898\pi\)
−0.358395 + 0.933570i \(0.616676\pi\)
\(824\) 0 0
\(825\) 1.67705e8 9.68248e7i 0.298666 0.172435i
\(826\) 0 0
\(827\) 9.92893e7 1.18328e8i 0.175544 0.209205i −0.671097 0.741369i \(-0.734177\pi\)
0.846641 + 0.532164i \(0.178621\pi\)
\(828\) 0 0
\(829\) −2.39830e8 1.38466e8i −0.420959 0.243041i 0.274528 0.961579i \(-0.411478\pi\)
−0.695488 + 0.718538i \(0.744812\pi\)
\(830\) 0 0
\(831\) 1.85723e8 3.27479e7i 0.323640 0.0570664i
\(832\) 0 0
\(833\) −3.14538e8 1.14482e8i −0.544174 0.198063i
\(834\) 0 0
\(835\) 5.03427e7i 0.0864723i
\(836\) 0 0
\(837\) 7.18306e8 1.22499
\(838\) 0 0
\(839\) 2.02876e8 5.57398e8i 0.343515 0.943799i −0.640851 0.767665i \(-0.721419\pi\)
0.984366 0.176134i \(-0.0563592\pi\)
\(840\) 0 0
\(841\) 5.48338e7 + 3.10978e8i 0.0921850 + 0.522807i
\(842\) 0 0
\(843\) −3.62235e8 + 6.27409e8i −0.604655 + 1.04729i
\(844\) 0 0
\(845\) −3.83648e7 3.21919e7i −0.0635861 0.0533551i
\(846\) 0 0
\(847\) 2.93143e8 + 5.07738e8i 0.482424 + 0.835583i
\(848\) 0 0
\(849\) −1.96674e8 5.40358e8i −0.321384 0.882996i
\(850\) 0 0
\(851\) 1.04222e8 + 1.83771e7i 0.169110 + 0.0298187i
\(852\) 0 0
\(853\) −6.21353e7 + 5.21377e7i −0.100113 + 0.0840050i −0.691470 0.722405i \(-0.743037\pi\)
0.591357 + 0.806410i \(0.298592\pi\)
\(854\) 0 0
\(855\) −5.22907e7 6.05185e7i −0.0836617 0.0968255i
\(856\) 0 0
\(857\) 6.51435e8 + 7.76349e8i 1.03497 + 1.23343i 0.971893 + 0.235422i \(0.0756473\pi\)
0.0630781 + 0.998009i \(0.479908\pi\)
\(858\) 0 0
\(859\) −1.24825e8 + 7.07918e8i −0.196935 + 1.11687i 0.712702 + 0.701467i \(0.247471\pi\)
−0.909637 + 0.415405i \(0.863640\pi\)
\(860\) 0 0
\(861\) −5.23496e8 + 1.90537e8i −0.820171 + 0.298518i
\(862\) 0 0
\(863\) 5.55263e8 3.20581e8i 0.863905 0.498776i −0.00141285 0.999999i \(-0.500450\pi\)
0.865318 + 0.501223i \(0.167116\pi\)
\(864\) 0 0
\(865\) −2.14370e8 + 2.55477e8i −0.331220 + 0.394732i
\(866\) 0 0
\(867\) 1.23644e8 + 7.13860e7i 0.189721 + 0.109536i
\(868\) 0 0
\(869\) −4.57398e8 + 8.06517e7i −0.697004 + 0.122901i
\(870\) 0 0
\(871\) −1.71283e8 6.23417e7i −0.259214 0.0943462i
\(872\) 0 0
\(873\) 3.90539e8i 0.586979i
\(874\) 0 0
\(875\) 4.68332e8 0.699085
\(876\) 0 0
\(877\) 2.05304e8 5.64068e8i 0.304368 0.836244i −0.689360 0.724419i \(-0.742108\pi\)
0.993728 0.111825i \(-0.0356696\pi\)
\(878\) 0 0
\(879\) 5.43654e7 + 3.08322e8i 0.0800490 + 0.453981i
\(880\) 0 0
\(881\) 5.93538e8 1.02804e9i 0.868002 1.50342i 0.00396761 0.999992i \(-0.498737\pi\)
0.864035 0.503432i \(-0.167930\pi\)
\(882\) 0 0
\(883\) −2.42884e8 2.03804e8i −0.352790 0.296026i 0.449119 0.893472i \(-0.351738\pi\)
−0.801909 + 0.597446i \(0.796182\pi\)
\(884\) 0 0
\(885\) 6.76127e7 + 1.17109e8i 0.0975435 + 0.168950i
\(886\) 0 0
\(887\) 5.54042e7 + 1.52222e8i 0.0793911 + 0.218125i 0.973038 0.230646i \(-0.0740840\pi\)
−0.893647 + 0.448771i \(0.851862\pi\)
\(888\) 0 0
\(889\) −5.90944e8 1.04199e8i −0.841087 0.148306i
\(890\) 0 0
\(891\) 9.17543e7 7.69910e7i 0.129716 0.108845i
\(892\) 0 0
\(893\) 3.59529e8 2.14565e8i 0.504869 0.301303i
\(894\) 0 0
\(895\) 7.84883e7 + 9.35387e7i 0.109480 + 0.130474i
\(896\) 0 0
\(897\) −1.17536e8 + 6.66578e8i −0.162852 + 0.923579i
\(898\) 0 0
\(899\) −5.33612e8 + 1.94219e8i −0.734424 + 0.267308i
\(900\) 0 0
\(901\) −5.45969e7 + 3.15215e7i −0.0746438 + 0.0430956i
\(902\) 0 0
\(903\) −6.30299e8 + 7.51161e8i −0.856018 + 1.02016i
\(904\) 0 0
\(905\) 9.33827e7 + 5.39145e7i 0.125986 + 0.0727378i
\(906\) 0 0
\(907\) 8.47053e8 1.49358e8i 1.13524 0.200174i 0.425719 0.904855i \(-0.360021\pi\)
0.709524 + 0.704681i \(0.248910\pi\)
\(908\) 0 0
\(909\) 4.54657e8 + 1.65481e8i 0.605329 + 0.220322i
\(910\) 0 0
\(911\) 5.52488e8i 0.730748i −0.930861 0.365374i \(-0.880941\pi\)
0.930861 0.365374i \(-0.119059\pi\)
\(912\) 0 0
\(913\) 4.52723e8 0.594868
\(914\) 0 0
\(915\) −7.97313e7 + 2.19060e8i −0.104080 + 0.285956i
\(916\) 0 0
\(917\) −1.41982e8 8.05218e8i −0.184130 1.04425i
\(918\) 0 0
\(919\) −2.29474e8 + 3.97461e8i −0.295656 + 0.512092i −0.975137 0.221601i \(-0.928872\pi\)
0.679481 + 0.733693i \(0.262205\pi\)
\(920\) 0 0
\(921\) −2.56425e8 2.15166e8i −0.328233 0.275420i
\(922\) 0 0
\(923\) −6.50159e8 1.12611e9i −0.826827 1.43211i
\(924\) 0 0
\(925\) −2.82218e7 7.75388e7i −0.0356582 0.0979702i
\(926\) 0 0
\(927\) −2.97434e8 5.24457e7i −0.373380 0.0658370i
\(928\) 0 0
\(929\) −7.66549e8 + 6.43211e8i −0.956077 + 0.802244i −0.980310 0.197462i \(-0.936730\pi\)
0.0242333 + 0.999706i \(0.492286\pi\)
\(930\) 0 0
\(931\) −5.47578e8 + 1.04739e8i −0.678573 + 0.129795i
\(932\) 0 0
\(933\) −7.02969e8 8.37766e8i −0.865549 1.03152i
\(934\) 0 0
\(935\) 1.69063e7 9.58804e7i 0.0206830 0.117299i
\(936\) 0 0
\(937\) 7.40992e8 2.69699e8i 0.900730 0.327839i 0.150185 0.988658i \(-0.452013\pi\)
0.750545 + 0.660819i \(0.229791\pi\)
\(938\) 0 0
\(939\) −3.71671e8 + 2.14584e8i −0.448913 + 0.259180i
\(940\) 0 0
\(941\) 3.53611e8 4.21417e8i 0.424382 0.505759i −0.510911 0.859634i \(-0.670692\pi\)
0.935293 + 0.353875i \(0.115136\pi\)
\(942\) 0 0
\(943\) −1.00464e9 5.80027e8i −1.19805 0.691692i
\(944\) 0 0
\(945\) 3.24564e8 5.72294e7i 0.384596 0.0678147i
\(946\) 0 0
\(947\) −4.29502e8 1.56326e8i −0.505726 0.184069i 0.0765415 0.997066i \(-0.475612\pi\)
−0.582268 + 0.812997i \(0.697834\pi\)
\(948\) 0 0
\(949\) 3.44776e8i 0.403402i
\(950\) 0 0
\(951\) −6.48695e8 −0.754221
\(952\) 0 0
\(953\) 4.32818e8 1.18916e9i 0.500065 1.37392i −0.391147 0.920328i \(-0.627921\pi\)
0.891211 0.453588i \(-0.149856\pi\)
\(954\) 0 0
\(955\) −2.50309e7 1.41957e8i −0.0287387 0.162985i
\(956\) 0 0
\(957\) −1.12305e8 + 1.94518e8i −0.128134 + 0.221934i
\(958\) 0 0
\(959\) −7.55479e7 6.33922e7i −0.0856577 0.0718754i
\(960\) 0 0
\(961\) 1.34039e8 + 2.32162e8i 0.151029 + 0.261590i
\(962\) 0 0
\(963\) 1.48123e8 + 4.06965e8i 0.165861 + 0.455699i
\(964\) 0 0
\(965\) −1.73980e8 3.06773e7i −0.193605 0.0341378i
\(966\) 0 0
\(967\) 1.98276e8 1.66373e8i 0.219275 0.183994i −0.526532 0.850155i \(-0.676508\pi\)
0.745808 + 0.666161i \(0.232064\pi\)
\(968\) 0 0
\(969\) −5.61714e8 + 8.12321e6i −0.617368 + 0.00892804i
\(970\) 0 0
\(971\) −1.14728e8 1.36728e8i −0.125318 0.149348i 0.699737 0.714400i \(-0.253300\pi\)
−0.825055 + 0.565052i \(0.808856\pi\)
\(972\) 0 0
\(973\) 1.96170e8 1.11254e9i 0.212958 1.20775i
\(974\) 0 0
\(975\) 4.95920e8 1.80500e8i 0.535054 0.194744i
\(976\) 0 0
\(977\) 1.02575e9 5.92216e8i 1.09991 0.635033i 0.163713 0.986508i \(-0.447653\pi\)
0.936197 + 0.351475i \(0.114320\pi\)
\(978\) 0 0
\(979\) 2.46695e7 2.94000e7i 0.0262914 0.0313328i
\(980\) 0 0
\(981\) 6.68920e7 + 3.86201e7i 0.0708544 + 0.0409078i
\(982\) 0 0
\(983\) −5.92242e8 + 1.04428e8i −0.623503 + 0.109940i −0.476469 0.879191i \(-0.658084\pi\)
−0.147034 + 0.989131i \(0.546973\pi\)
\(984\) 0 0
\(985\) −2.91143e8 1.05968e8i −0.304648 0.110883i
\(986\) 0 0
\(987\) 5.41476e8i 0.563155i
\(988\) 0 0
\(989\) −2.04187e9 −2.11077
\(990\) 0 0
\(991\) −6.54552e8 + 1.79837e9i −0.672548 + 1.84781i −0.164749 + 0.986335i \(0.552682\pi\)
−0.507799 + 0.861476i \(0.669541\pi\)
\(992\) 0 0
\(993\) 1.03375e8 + 5.86267e8i 0.105576 + 0.598753i
\(994\) 0 0
\(995\) −1.07080e8 + 1.85469e8i −0.108703 + 0.188279i
\(996\) 0 0
\(997\) 9.61974e8 + 8.07192e8i 0.970684 + 0.814501i 0.982658 0.185428i \(-0.0593671\pi\)
−0.0119739 + 0.999928i \(0.503812\pi\)
\(998\) 0 0
\(999\) −6.05321e7 1.04845e8i −0.0607141 0.105160i
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 76.7.j.a.13.7 60
19.3 odd 18 inner 76.7.j.a.41.7 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.7.j.a.13.7 60 1.1 even 1 trivial
76.7.j.a.41.7 yes 60 19.3 odd 18 inner