Properties

Label 180.7.c.b.91.14
Level $180$
Weight $7$
Character 180.91
Analytic conductor $41.410$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [180,7,Mod(91,180)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(180, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("180.91");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 180.c (of order \(2\), degree \(1\), 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: \(41.4097350516\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.14
Character \(\chi\) \(=\) 180.91
Dual form 180.7.c.b.91.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.331992 + 7.99311i) q^{2} +(-63.7796 - 5.30729i) q^{4} +55.9017 q^{5} -552.003i q^{7} +(63.5960 - 508.035i) q^{8} +O(q^{10})\) \(q+(-0.331992 + 7.99311i) q^{2} +(-63.7796 - 5.30729i) q^{4} +55.9017 q^{5} -552.003i q^{7} +(63.5960 - 508.035i) q^{8} +(-18.5589 + 446.828i) q^{10} -1284.63i q^{11} -2513.57 q^{13} +(4412.22 + 183.260i) q^{14} +(4039.67 + 676.993i) q^{16} -4597.01 q^{17} +9800.21i q^{19} +(-3565.39 - 296.687i) q^{20} +(10268.2 + 426.487i) q^{22} +15217.2i q^{23} +3125.00 q^{25} +(834.485 - 20091.2i) q^{26} +(-2929.64 + 35206.5i) q^{28} +14380.1 q^{29} +34497.8i q^{31} +(-6752.42 + 32064.7i) q^{32} +(1526.17 - 36744.4i) q^{34} -30857.9i q^{35} -71409.5 q^{37} +(-78334.2 - 3253.59i) q^{38} +(3555.13 - 28400.0i) q^{40} +37657.2 q^{41} +1535.15i q^{43} +(-6817.91 + 81933.1i) q^{44} +(-121633. - 5052.00i) q^{46} +131297. i q^{47} -187058. q^{49} +(-1037.47 + 24978.5i) q^{50} +(160314. + 13340.3i) q^{52} +228206. q^{53} -71813.0i q^{55} +(-280437. - 35105.2i) q^{56} +(-4774.07 + 114942. i) q^{58} +271199. i q^{59} -252456. q^{61} +(-275745. - 11453.0i) q^{62} +(-254055. - 64618.0i) q^{64} -140513. q^{65} +71786.4i q^{67} +(293196. + 24397.7i) q^{68} +(246651. + 10244.6i) q^{70} -193845. i q^{71} +125558. q^{73} +(23707.4 - 570784. i) q^{74} +(52012.6 - 625053. i) q^{76} -709120. q^{77} -609914. i q^{79} +(225824. + 37845.1i) q^{80} +(-12501.9 + 300998. i) q^{82} -592195. i q^{83} -256981. q^{85} +(-12270.6 - 509.657i) q^{86} +(-652637. - 81697.4i) q^{88} +154289. q^{89} +1.38750e6i q^{91} +(80762.4 - 970549. i) q^{92} +(-1.04947e6 - 43589.6i) q^{94} +547849. i q^{95} -1.46175e6 q^{97} +(62101.9 - 1.49518e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(91\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.331992 + 7.99311i −0.0414990 + 0.999139i
\(3\) 0 0
\(4\) −63.7796 5.30729i −0.996556 0.0829264i
\(5\) 55.9017 0.447214
\(6\) 0 0
\(7\) 552.003i 1.60934i −0.593723 0.804669i \(-0.702343\pi\)
0.593723 0.804669i \(-0.297657\pi\)
\(8\) 63.5960 508.035i 0.124211 0.992256i
\(9\) 0 0
\(10\) −18.5589 + 446.828i −0.0185589 + 0.446828i
\(11\) 1284.63i 0.965162i −0.875851 0.482581i \(-0.839699\pi\)
0.875851 0.482581i \(-0.160301\pi\)
\(12\) 0 0
\(13\) −2513.57 −1.14409 −0.572046 0.820221i \(-0.693850\pi\)
−0.572046 + 0.820221i \(0.693850\pi\)
\(14\) 4412.22 + 183.260i 1.60795 + 0.0667859i
\(15\) 0 0
\(16\) 4039.67 + 676.993i 0.986246 + 0.165282i
\(17\) −4597.01 −0.935684 −0.467842 0.883812i \(-0.654968\pi\)
−0.467842 + 0.883812i \(0.654968\pi\)
\(18\) 0 0
\(19\) 9800.21i 1.42881i 0.699732 + 0.714405i \(0.253303\pi\)
−0.699732 + 0.714405i \(0.746697\pi\)
\(20\) −3565.39 296.687i −0.445673 0.0370858i
\(21\) 0 0
\(22\) 10268.2 + 426.487i 0.964330 + 0.0400532i
\(23\) 15217.2i 1.25070i 0.780345 + 0.625349i \(0.215043\pi\)
−0.780345 + 0.625349i \(0.784957\pi\)
\(24\) 0 0
\(25\) 3125.00 0.200000
\(26\) 834.485 20091.2i 0.0474787 1.14311i
\(27\) 0 0
\(28\) −2929.64 + 35206.5i −0.133457 + 1.60380i
\(29\) 14380.1 0.589614 0.294807 0.955557i \(-0.404745\pi\)
0.294807 + 0.955557i \(0.404745\pi\)
\(30\) 0 0
\(31\) 34497.8i 1.15800i 0.815329 + 0.578998i \(0.196556\pi\)
−0.815329 + 0.578998i \(0.803444\pi\)
\(32\) −6752.42 + 32064.7i −0.206067 + 0.978538i
\(33\) 0 0
\(34\) 1526.17 36744.4i 0.0388299 0.934878i
\(35\) 30857.9i 0.719718i
\(36\) 0 0
\(37\) −71409.5 −1.40978 −0.704889 0.709318i \(-0.749003\pi\)
−0.704889 + 0.709318i \(0.749003\pi\)
\(38\) −78334.2 3253.59i −1.42758 0.0592942i
\(39\) 0 0
\(40\) 3555.13 28400.0i 0.0555489 0.443750i
\(41\) 37657.2 0.546383 0.273191 0.961960i \(-0.411921\pi\)
0.273191 + 0.961960i \(0.411921\pi\)
\(42\) 0 0
\(43\) 1535.15i 0.0193083i 0.999953 + 0.00965417i \(0.00307307\pi\)
−0.999953 + 0.00965417i \(0.996927\pi\)
\(44\) −6817.91 + 81933.1i −0.0800374 + 0.961837i
\(45\) 0 0
\(46\) −121633. 5052.00i −1.24962 0.0519027i
\(47\) 131297.i 1.26463i 0.774713 + 0.632313i \(0.217894\pi\)
−0.774713 + 0.632313i \(0.782106\pi\)
\(48\) 0 0
\(49\) −187058. −1.58997
\(50\) −1037.47 + 24978.5i −0.00829979 + 0.199828i
\(51\) 0 0
\(52\) 160314. + 13340.3i 1.14015 + 0.0948755i
\(53\) 228206. 1.53285 0.766424 0.642336i \(-0.222034\pi\)
0.766424 + 0.642336i \(0.222034\pi\)
\(54\) 0 0
\(55\) 71813.0i 0.431633i
\(56\) −280437. 35105.2i −1.59688 0.199898i
\(57\) 0 0
\(58\) −4774.07 + 114942.i −0.0244684 + 0.589106i
\(59\) 271199.i 1.32048i 0.751053 + 0.660241i \(0.229546\pi\)
−0.751053 + 0.660241i \(0.770454\pi\)
\(60\) 0 0
\(61\) −252456. −1.11223 −0.556116 0.831105i \(-0.687709\pi\)
−0.556116 + 0.831105i \(0.687709\pi\)
\(62\) −275745. 11453.0i −1.15700 0.0480556i
\(63\) 0 0
\(64\) −254055. 64618.0i −0.969143 0.246498i
\(65\) −140513. −0.511654
\(66\) 0 0
\(67\) 71786.4i 0.238681i 0.992853 + 0.119340i \(0.0380780\pi\)
−0.992853 + 0.119340i \(0.961922\pi\)
\(68\) 293196. + 24397.7i 0.932461 + 0.0775929i
\(69\) 0 0
\(70\) 246651. + 10244.6i 0.719098 + 0.0298676i
\(71\) 193845.i 0.541601i −0.962635 0.270801i \(-0.912712\pi\)
0.962635 0.270801i \(-0.0872884\pi\)
\(72\) 0 0
\(73\) 125558. 0.322758 0.161379 0.986893i \(-0.448406\pi\)
0.161379 + 0.986893i \(0.448406\pi\)
\(74\) 23707.4 570784.i 0.0585043 1.40856i
\(75\) 0 0
\(76\) 52012.6 625053.i 0.118486 1.42389i
\(77\) −709120. −1.55327
\(78\) 0 0
\(79\) 609914.i 1.23705i −0.785765 0.618525i \(-0.787730\pi\)
0.785765 0.618525i \(-0.212270\pi\)
\(80\) 225824. + 37845.1i 0.441063 + 0.0739162i
\(81\) 0 0
\(82\) −12501.9 + 300998.i −0.0226743 + 0.545912i
\(83\) 592195.i 1.03569i −0.855474 0.517846i \(-0.826734\pi\)
0.855474 0.517846i \(-0.173266\pi\)
\(84\) 0 0
\(85\) −256981. −0.418451
\(86\) −12270.6 509.657i −0.0192917 0.000801276i
\(87\) 0 0
\(88\) −652637. 81697.4i −0.957687 0.119884i
\(89\) 154289. 0.218859 0.109429 0.993995i \(-0.465098\pi\)
0.109429 + 0.993995i \(0.465098\pi\)
\(90\) 0 0
\(91\) 1.38750e6i 1.84123i
\(92\) 80762.4 970549.i 0.103716 1.24639i
\(93\) 0 0
\(94\) −1.04947e6 43589.6i −1.26354 0.0524807i
\(95\) 547849.i 0.638984i
\(96\) 0 0
\(97\) −1.46175e6 −1.60162 −0.800810 0.598919i \(-0.795597\pi\)
−0.800810 + 0.598919i \(0.795597\pi\)
\(98\) 62101.9 1.49518e6i 0.0659821 1.58860i
\(99\) 0 0
\(100\) −199311. 16585.3i −0.199311 0.0165853i
\(101\) −963761. −0.935417 −0.467708 0.883883i \(-0.654920\pi\)
−0.467708 + 0.883883i \(0.654920\pi\)
\(102\) 0 0
\(103\) 1.01542e6i 0.929250i 0.885508 + 0.464625i \(0.153811\pi\)
−0.885508 + 0.464625i \(0.846189\pi\)
\(104\) −159853. + 1.27698e6i −0.142109 + 1.13523i
\(105\) 0 0
\(106\) −75762.4 + 1.82407e6i −0.0636116 + 1.53153i
\(107\) 509249.i 0.415699i 0.978161 + 0.207849i \(0.0666463\pi\)
−0.978161 + 0.207849i \(0.933354\pi\)
\(108\) 0 0
\(109\) 2.13481e6 1.64846 0.824231 0.566254i \(-0.191608\pi\)
0.824231 + 0.566254i \(0.191608\pi\)
\(110\) 574009. + 23841.3i 0.431262 + 0.0179123i
\(111\) 0 0
\(112\) 373703. 2.22991e6i 0.265994 1.58720i
\(113\) −178688. −0.123840 −0.0619200 0.998081i \(-0.519722\pi\)
−0.0619200 + 0.998081i \(0.519722\pi\)
\(114\) 0 0
\(115\) 850670.i 0.559329i
\(116\) −917156. 76319.3i −0.587583 0.0488946i
\(117\) 0 0
\(118\) −2.16773e6 90036.0i −1.31935 0.0547987i
\(119\) 2.53757e6i 1.50583i
\(120\) 0 0
\(121\) 121287. 0.0684633
\(122\) 83813.2 2.01790e6i 0.0461565 1.11127i
\(123\) 0 0
\(124\) 183090. 2.20026e6i 0.0960284 1.15401i
\(125\) 174693. 0.0894427
\(126\) 0 0
\(127\) 1.94450e6i 0.949286i −0.880178 0.474643i \(-0.842577\pi\)
0.880178 0.474643i \(-0.157423\pi\)
\(128\) 600843. 2.00924e6i 0.286504 0.958079i
\(129\) 0 0
\(130\) 46649.1 1.12313e6i 0.0212331 0.511213i
\(131\) 3.66180e6i 1.62885i 0.580270 + 0.814424i \(0.302947\pi\)
−0.580270 + 0.814424i \(0.697053\pi\)
\(132\) 0 0
\(133\) 5.40975e6 2.29944
\(134\) −573796. 23832.5i −0.238475 0.00990501i
\(135\) 0 0
\(136\) −292352. + 2.33544e6i −0.116222 + 0.928438i
\(137\) −477013. −0.185510 −0.0927552 0.995689i \(-0.529567\pi\)
−0.0927552 + 0.995689i \(0.529567\pi\)
\(138\) 0 0
\(139\) 874957.i 0.325793i −0.986643 0.162897i \(-0.947916\pi\)
0.986643 0.162897i \(-0.0520837\pi\)
\(140\) −163772. + 1.96810e6i −0.0596837 + 0.717239i
\(141\) 0 0
\(142\) 1.54942e6 + 64354.9i 0.541135 + 0.0224759i
\(143\) 3.22901e6i 1.10423i
\(144\) 0 0
\(145\) 803871. 0.263683
\(146\) −41684.3 + 1.00360e6i −0.0133941 + 0.322480i
\(147\) 0 0
\(148\) 4.55447e6 + 378991.i 1.40492 + 0.116908i
\(149\) 2.52851e6 0.764375 0.382187 0.924085i \(-0.375171\pi\)
0.382187 + 0.924085i \(0.375171\pi\)
\(150\) 0 0
\(151\) 3.24281e6i 0.941869i 0.882168 + 0.470934i \(0.156083\pi\)
−0.882168 + 0.470934i \(0.843917\pi\)
\(152\) 4.97885e6 + 623255.i 1.41775 + 0.177474i
\(153\) 0 0
\(154\) 235422. 5.66807e6i 0.0644592 1.55193i
\(155\) 1.92849e6i 0.517871i
\(156\) 0 0
\(157\) −5.96596e6 −1.54164 −0.770818 0.637056i \(-0.780152\pi\)
−0.770818 + 0.637056i \(0.780152\pi\)
\(158\) 4.87511e6 + 202487.i 1.23599 + 0.0513363i
\(159\) 0 0
\(160\) −377472. + 1.79247e6i −0.0921562 + 0.437615i
\(161\) 8.39997e6 2.01280
\(162\) 0 0
\(163\) 4.08504e6i 0.943265i 0.881795 + 0.471632i \(0.156335\pi\)
−0.881795 + 0.471632i \(0.843665\pi\)
\(164\) −2.40176e6 199858.i −0.544501 0.0453096i
\(165\) 0 0
\(166\) 4.73348e6 + 196604.i 1.03480 + 0.0429801i
\(167\) 2.47808e6i 0.532067i −0.963964 0.266034i \(-0.914287\pi\)
0.963964 0.266034i \(-0.0857132\pi\)
\(168\) 0 0
\(169\) 1.49123e6 0.308948
\(170\) 85315.5 2.05408e6i 0.0173653 0.418090i
\(171\) 0 0
\(172\) 8147.48 97911.1i 0.00160117 0.0192418i
\(173\) −8.20504e6 −1.58468 −0.792341 0.610078i \(-0.791138\pi\)
−0.792341 + 0.610078i \(0.791138\pi\)
\(174\) 0 0
\(175\) 1.72501e6i 0.321868i
\(176\) 869686. 5.18948e6i 0.159523 0.951887i
\(177\) 0 0
\(178\) −51222.6 + 1.23325e6i −0.00908241 + 0.218670i
\(179\) 3.09966e6i 0.540450i 0.962797 + 0.270225i \(0.0870981\pi\)
−0.962797 + 0.270225i \(0.912902\pi\)
\(180\) 0 0
\(181\) −2.47886e6 −0.418038 −0.209019 0.977912i \(-0.567027\pi\)
−0.209019 + 0.977912i \(0.567027\pi\)
\(182\) −1.10904e7 460638.i −1.83965 0.0764092i
\(183\) 0 0
\(184\) 7.73089e6 + 967757.i 1.24101 + 0.155351i
\(185\) −3.99191e6 −0.630472
\(186\) 0 0
\(187\) 5.90546e6i 0.903086i
\(188\) 696833. 8.37408e6i 0.104871 1.26027i
\(189\) 0 0
\(190\) −4.37901e6 181881.i −0.638433 0.0265172i
\(191\) 1.42970e6i 0.205185i 0.994723 + 0.102592i \(0.0327137\pi\)
−0.994723 + 0.102592i \(0.967286\pi\)
\(192\) 0 0
\(193\) −1.81356e6 −0.252266 −0.126133 0.992013i \(-0.540257\pi\)
−0.126133 + 0.992013i \(0.540257\pi\)
\(194\) 485291. 1.16840e7i 0.0664656 1.60024i
\(195\) 0 0
\(196\) 1.19305e7 + 992774.i 1.58449 + 0.131851i
\(197\) 8.69647e6 1.13748 0.568740 0.822517i \(-0.307431\pi\)
0.568740 + 0.822517i \(0.307431\pi\)
\(198\) 0 0
\(199\) 5.01570e6i 0.636462i −0.948013 0.318231i \(-0.896911\pi\)
0.948013 0.318231i \(-0.103089\pi\)
\(200\) 198738. 1.58761e6i 0.0248422 0.198451i
\(201\) 0 0
\(202\) 319961. 7.70344e6i 0.0388188 0.934611i
\(203\) 7.93785e6i 0.948888i
\(204\) 0 0
\(205\) 2.10510e6 0.244350
\(206\) −8.11634e6 337110.i −0.928450 0.0385629i
\(207\) 0 0
\(208\) −1.01540e7 1.70167e6i −1.12836 0.189097i
\(209\) 1.25896e7 1.37903
\(210\) 0 0
\(211\) 6.77795e6i 0.721525i 0.932658 + 0.360762i \(0.117483\pi\)
−0.932658 + 0.360762i \(0.882517\pi\)
\(212\) −1.45549e7 1.21115e6i −1.52757 0.127114i
\(213\) 0 0
\(214\) −4.07048e6 169066.i −0.415340 0.0172511i
\(215\) 85817.4i 0.00863495i
\(216\) 0 0
\(217\) 1.90429e7 1.86361
\(218\) −708738. + 1.70637e7i −0.0684095 + 1.64704i
\(219\) 0 0
\(220\) −381133. + 4.58020e6i −0.0357938 + 0.430147i
\(221\) 1.15549e7 1.07051
\(222\) 0 0
\(223\) 1.21767e7i 1.09803i −0.835812 0.549016i \(-0.815003\pi\)
0.835812 0.549016i \(-0.184997\pi\)
\(224\) 1.76998e7 + 3.72736e6i 1.57480 + 0.331632i
\(225\) 0 0
\(226\) 59323.1 1.42828e6i 0.00513923 0.123733i
\(227\) 8.92756e6i 0.763230i 0.924321 + 0.381615i \(0.124632\pi\)
−0.924321 + 0.381615i \(0.875368\pi\)
\(228\) 0 0
\(229\) −1.61284e7 −1.34302 −0.671512 0.740994i \(-0.734355\pi\)
−0.671512 + 0.740994i \(0.734355\pi\)
\(230\) −6.79950e6 282415.i −0.558847 0.0232116i
\(231\) 0 0
\(232\) 914517. 7.30559e6i 0.0732365 0.585048i
\(233\) −5.66976e6 −0.448226 −0.224113 0.974563i \(-0.571948\pi\)
−0.224113 + 0.974563i \(0.571948\pi\)
\(234\) 0 0
\(235\) 7.33974e6i 0.565558i
\(236\) 1.43933e6 1.72970e7i 0.109503 1.31593i
\(237\) 0 0
\(238\) −2.02830e7 842451.i −1.50453 0.0624905i
\(239\) 1.01650e7i 0.744583i −0.928116 0.372291i \(-0.878572\pi\)
0.928116 0.372291i \(-0.121428\pi\)
\(240\) 0 0
\(241\) −1.87229e7 −1.33759 −0.668795 0.743447i \(-0.733189\pi\)
−0.668795 + 0.743447i \(0.733189\pi\)
\(242\) −40266.2 + 969459.i −0.00284115 + 0.0684043i
\(243\) 0 0
\(244\) 1.61015e7 + 1.33986e6i 1.10840 + 0.0922335i
\(245\) −1.04569e7 −0.711057
\(246\) 0 0
\(247\) 2.46335e7i 1.63469i
\(248\) 1.75261e7 + 2.19393e6i 1.14903 + 0.143836i
\(249\) 0 0
\(250\) −57996.6 + 1.39634e6i −0.00371178 + 0.0893657i
\(251\) 3.39034e6i 0.214398i 0.994238 + 0.107199i \(0.0341883\pi\)
−0.994238 + 0.107199i \(0.965812\pi\)
\(252\) 0 0
\(253\) 1.95485e7 1.20713
\(254\) 1.55426e7 + 645559.i 0.948468 + 0.0393944i
\(255\) 0 0
\(256\) 1.58606e7 + 5.46965e6i 0.945364 + 0.326017i
\(257\) −2.79800e7 −1.64835 −0.824173 0.566338i \(-0.808360\pi\)
−0.824173 + 0.566338i \(0.808360\pi\)
\(258\) 0 0
\(259\) 3.94183e7i 2.26881i
\(260\) 8.96185e6 + 745743.i 0.509891 + 0.0424296i
\(261\) 0 0
\(262\) −2.92692e7 1.21569e6i −1.62745 0.0675955i
\(263\) 2.67037e7i 1.46793i 0.679189 + 0.733963i \(0.262331\pi\)
−0.679189 + 0.733963i \(0.737669\pi\)
\(264\) 0 0
\(265\) 1.27571e7 0.685510
\(266\) −1.79599e6 + 4.32407e7i −0.0954244 + 2.29746i
\(267\) 0 0
\(268\) 380991. 4.57850e6i 0.0197929 0.237859i
\(269\) −2.74962e7 −1.41259 −0.706295 0.707917i \(-0.749635\pi\)
−0.706295 + 0.707917i \(0.749635\pi\)
\(270\) 0 0
\(271\) 7.82244e6i 0.393038i −0.980500 0.196519i \(-0.937036\pi\)
0.980500 0.196519i \(-0.0629637\pi\)
\(272\) −1.85704e7 3.11215e6i −0.922815 0.154651i
\(273\) 0 0
\(274\) 158364. 3.81281e6i 0.00769849 0.185351i
\(275\) 4.01447e6i 0.193032i
\(276\) 0 0
\(277\) −3.48863e7 −1.64140 −0.820702 0.571356i \(-0.806418\pi\)
−0.820702 + 0.571356i \(0.806418\pi\)
\(278\) 6.99362e6 + 290478.i 0.325513 + 0.0135201i
\(279\) 0 0
\(280\) −1.56769e7 1.96244e6i −0.714144 0.0893969i
\(281\) 2.43392e6 0.109695 0.0548476 0.998495i \(-0.482533\pi\)
0.0548476 + 0.998495i \(0.482533\pi\)
\(282\) 0 0
\(283\) 3.82558e7i 1.68787i −0.536447 0.843934i \(-0.680234\pi\)
0.536447 0.843934i \(-0.319766\pi\)
\(284\) −1.02879e6 + 1.23634e7i −0.0449131 + 0.539736i
\(285\) 0 0
\(286\) −2.58098e7 1.07200e6i −1.10328 0.0458246i
\(287\) 2.07869e7i 0.879315i
\(288\) 0 0
\(289\) −3.00503e6 −0.124496
\(290\) −266879. + 6.42543e6i −0.0109426 + 0.263456i
\(291\) 0 0
\(292\) −8.00805e6 666374.i −0.321646 0.0267651i
\(293\) −2.04358e7 −0.812436 −0.406218 0.913776i \(-0.633153\pi\)
−0.406218 + 0.913776i \(0.633153\pi\)
\(294\) 0 0
\(295\) 1.51605e7i 0.590538i
\(296\) −4.54136e6 + 3.62785e7i −0.175110 + 1.39886i
\(297\) 0 0
\(298\) −839445. + 2.02107e7i −0.0317208 + 0.763716i
\(299\) 3.82496e7i 1.43091i
\(300\) 0 0
\(301\) 847407. 0.0310737
\(302\) −2.59201e7 1.07659e6i −0.941058 0.0390866i
\(303\) 0 0
\(304\) −6.63468e6 + 3.95896e7i −0.236156 + 1.40916i
\(305\) −1.41127e7 −0.497405
\(306\) 0 0
\(307\) 9.54158e6i 0.329765i 0.986313 + 0.164883i \(0.0527246\pi\)
−0.986313 + 0.164883i \(0.947275\pi\)
\(308\) 4.52273e7 + 3.76351e6i 1.54792 + 0.128807i
\(309\) 0 0
\(310\) −1.54146e7 640242.i −0.517425 0.0214911i
\(311\) 2.91657e6i 0.0969595i 0.998824 + 0.0484798i \(0.0154376\pi\)
−0.998824 + 0.0484798i \(0.984562\pi\)
\(312\) 0 0
\(313\) 1.93741e7 0.631814 0.315907 0.948790i \(-0.397691\pi\)
0.315907 + 0.948790i \(0.397691\pi\)
\(314\) 1.98065e6 4.76866e7i 0.0639763 1.54031i
\(315\) 0 0
\(316\) −3.23699e6 + 3.89001e7i −0.102584 + 1.23279i
\(317\) −6.50536e6 −0.204218 −0.102109 0.994773i \(-0.532559\pi\)
−0.102109 + 0.994773i \(0.532559\pi\)
\(318\) 0 0
\(319\) 1.84731e7i 0.569072i
\(320\) −1.42021e7 3.61226e6i −0.433414 0.110237i
\(321\) 0 0
\(322\) −2.78872e6 + 6.71419e7i −0.0835290 + 2.01106i
\(323\) 4.50517e7i 1.33692i
\(324\) 0 0
\(325\) −7.85491e6 −0.228818
\(326\) −3.26522e7 1.35620e6i −0.942452 0.0391445i
\(327\) 0 0
\(328\) 2.39485e6 1.91312e7i 0.0678668 0.542151i
\(329\) 7.24765e7 2.03521
\(330\) 0 0
\(331\) 2.30862e7i 0.636603i −0.947990 0.318301i \(-0.896888\pi\)
0.947990 0.318301i \(-0.103112\pi\)
\(332\) −3.14295e6 + 3.77699e7i −0.0858862 + 1.03212i
\(333\) 0 0
\(334\) 1.98076e7 + 822703.i 0.531609 + 0.0220802i
\(335\) 4.01298e6i 0.106741i
\(336\) 0 0
\(337\) −4.43828e7 −1.15965 −0.579823 0.814743i \(-0.696878\pi\)
−0.579823 + 0.814743i \(0.696878\pi\)
\(338\) −495076. + 1.19196e7i −0.0128210 + 0.308681i
\(339\) 0 0
\(340\) 1.63901e7 + 1.36387e6i 0.417009 + 0.0347006i
\(341\) 4.43170e7 1.11765
\(342\) 0 0
\(343\) 3.83142e7i 0.949463i
\(344\) 779909. + 97629.4i 0.0191588 + 0.00239831i
\(345\) 0 0
\(346\) 2.72400e6 6.55838e7i 0.0657627 1.58332i
\(347\) 2.62548e7i 0.628376i −0.949361 0.314188i \(-0.898268\pi\)
0.949361 0.314188i \(-0.101732\pi\)
\(348\) 0 0
\(349\) 7.54811e7 1.77567 0.887834 0.460164i \(-0.152209\pi\)
0.887834 + 0.460164i \(0.152209\pi\)
\(350\) 1.37882e7 + 572689.i 0.321590 + 0.0133572i
\(351\) 0 0
\(352\) 4.11913e7 + 8.67436e6i 0.944447 + 0.198888i
\(353\) 7.31900e6 0.166390 0.0831951 0.996533i \(-0.473488\pi\)
0.0831951 + 0.996533i \(0.473488\pi\)
\(354\) 0 0
\(355\) 1.08363e7i 0.242211i
\(356\) −9.84046e6 818855.i −0.218105 0.0181492i
\(357\) 0 0
\(358\) −2.47759e7 1.02906e6i −0.539984 0.0224281i
\(359\) 4.02979e7i 0.870961i 0.900198 + 0.435480i \(0.143421\pi\)
−0.900198 + 0.435480i \(0.856579\pi\)
\(360\) 0 0
\(361\) −4.89983e7 −1.04150
\(362\) 822960. 1.98138e7i 0.0173482 0.417678i
\(363\) 0 0
\(364\) 7.36386e6 8.84941e7i 0.152687 1.83489i
\(365\) 7.01892e6 0.144342
\(366\) 0 0
\(367\) 2.15750e7i 0.436469i −0.975896 0.218234i \(-0.929970\pi\)
0.975896 0.218234i \(-0.0700297\pi\)
\(368\) −1.03020e7 + 6.14726e7i −0.206717 + 1.23350i
\(369\) 0 0
\(370\) 1.32528e6 3.19078e7i 0.0261639 0.629929i
\(371\) 1.25970e8i 2.46687i
\(372\) 0 0
\(373\) 5.20071e7 1.00216 0.501079 0.865401i \(-0.332937\pi\)
0.501079 + 0.865401i \(0.332937\pi\)
\(374\) −4.72030e7 1.96056e6i −0.902308 0.0374771i
\(375\) 0 0
\(376\) 6.67036e7 + 8.34999e6i 1.25483 + 0.157081i
\(377\) −3.61454e7 −0.674573
\(378\) 0 0
\(379\) 9.39645e6i 0.172602i −0.996269 0.0863010i \(-0.972495\pi\)
0.996269 0.0863010i \(-0.0275047\pi\)
\(380\) 2.90759e6 3.49415e7i 0.0529886 0.636783i
\(381\) 0 0
\(382\) −1.14277e7 474649.i −0.205008 0.00851495i
\(383\) 1.54516e7i 0.275028i −0.990500 0.137514i \(-0.956089\pi\)
0.990500 0.137514i \(-0.0439112\pi\)
\(384\) 0 0
\(385\) −3.96410e7 −0.694644
\(386\) 602086. 1.44960e7i 0.0104688 0.252049i
\(387\) 0 0
\(388\) 9.32301e7 + 7.75796e6i 1.59610 + 0.132817i
\(389\) 5.51480e7 0.936873 0.468437 0.883497i \(-0.344817\pi\)
0.468437 + 0.883497i \(0.344817\pi\)
\(390\) 0 0
\(391\) 6.99539e7i 1.17026i
\(392\) −1.18962e7 + 9.50322e7i −0.197492 + 1.57766i
\(393\) 0 0
\(394\) −2.88715e6 + 6.95118e7i −0.0472043 + 1.13650i
\(395\) 3.40952e7i 0.553226i
\(396\) 0 0
\(397\) −9.29579e7 −1.48564 −0.742822 0.669489i \(-0.766513\pi\)
−0.742822 + 0.669489i \(0.766513\pi\)
\(398\) 4.00910e7 + 1.66517e6i 0.635914 + 0.0264125i
\(399\) 0 0
\(400\) 1.26240e7 + 2.11560e6i 0.197249 + 0.0330563i
\(401\) −1.17915e8 −1.82867 −0.914334 0.404960i \(-0.867285\pi\)
−0.914334 + 0.404960i \(0.867285\pi\)
\(402\) 0 0
\(403\) 8.67128e7i 1.32485i
\(404\) 6.14682e7 + 5.11496e6i 0.932195 + 0.0775708i
\(405\) 0 0
\(406\) 6.34481e7 + 2.63530e6i 0.948071 + 0.0393779i
\(407\) 9.17348e7i 1.36066i
\(408\) 0 0
\(409\) 6.08808e7 0.889836 0.444918 0.895571i \(-0.353233\pi\)
0.444918 + 0.895571i \(0.353233\pi\)
\(410\) −698877. + 1.68263e7i −0.0101403 + 0.244139i
\(411\) 0 0
\(412\) 5.38911e6 6.47628e7i 0.0770594 0.926050i
\(413\) 1.49703e8 2.12510
\(414\) 0 0
\(415\) 3.31047e7i 0.463175i
\(416\) 1.69727e7 8.05970e7i 0.235760 1.11954i
\(417\) 0 0
\(418\) −4.17966e6 + 1.00630e8i −0.0572285 + 1.37785i
\(419\) 3.24991e7i 0.441803i 0.975296 + 0.220902i \(0.0709000\pi\)
−0.975296 + 0.220902i \(0.929100\pi\)
\(420\) 0 0
\(421\) 4.14006e7 0.554830 0.277415 0.960750i \(-0.410522\pi\)
0.277415 + 0.960750i \(0.410522\pi\)
\(422\) −5.41769e7 2.25022e6i −0.720903 0.0299425i
\(423\) 0 0
\(424\) 1.45130e7 1.15936e8i 0.190397 1.52098i
\(425\) −1.43657e7 −0.187137
\(426\) 0 0
\(427\) 1.39356e8i 1.78996i
\(428\) 2.70273e6 3.24797e7i 0.0344724 0.414267i
\(429\) 0 0
\(430\) −685948. 28490.7i −0.00862752 0.000358342i
\(431\) 2.64521e7i 0.330391i 0.986261 + 0.165196i \(0.0528255\pi\)
−0.986261 + 0.165196i \(0.947174\pi\)
\(432\) 0 0
\(433\) −2.52090e7 −0.310521 −0.155261 0.987874i \(-0.549622\pi\)
−0.155261 + 0.987874i \(0.549622\pi\)
\(434\) −6.32209e6 + 1.52212e8i −0.0773377 + 1.86200i
\(435\) 0 0
\(436\) −1.36157e8 1.13300e7i −1.64278 0.136701i
\(437\) −1.49132e8 −1.78701
\(438\) 0 0
\(439\) 1.58533e8i 1.87381i 0.349589 + 0.936903i \(0.386321\pi\)
−0.349589 + 0.936903i \(0.613679\pi\)
\(440\) −3.64835e7 4.56702e6i −0.428291 0.0536136i
\(441\) 0 0
\(442\) −3.83614e6 + 9.23598e7i −0.0444250 + 1.06959i
\(443\) 1.05332e8i 1.21157i −0.795627 0.605787i \(-0.792858\pi\)
0.795627 0.605787i \(-0.207142\pi\)
\(444\) 0 0
\(445\) 8.62500e6 0.0978766
\(446\) 9.73297e7 + 4.04256e6i 1.09709 + 0.0455672i
\(447\) 0 0
\(448\) −3.56694e7 + 1.40239e8i −0.396699 + 1.55968i
\(449\) 1.45273e8 1.60490 0.802448 0.596722i \(-0.203530\pi\)
0.802448 + 0.596722i \(0.203530\pi\)
\(450\) 0 0
\(451\) 4.83756e7i 0.527348i
\(452\) 1.13967e7 + 948351.i 0.123413 + 0.0102696i
\(453\) 0 0
\(454\) −7.13590e7 2.96388e6i −0.762572 0.0316732i
\(455\) 7.75636e7i 0.823424i
\(456\) 0 0
\(457\) 1.00926e8 1.05744 0.528718 0.848797i \(-0.322673\pi\)
0.528718 + 0.848797i \(0.322673\pi\)
\(458\) 5.35448e6 1.28916e8i 0.0557341 1.34187i
\(459\) 0 0
\(460\) 4.51475e6 5.42554e7i 0.0463832 0.557403i
\(461\) 1.04798e8 1.06968 0.534838 0.844955i \(-0.320373\pi\)
0.534838 + 0.844955i \(0.320373\pi\)
\(462\) 0 0
\(463\) 8.32165e7i 0.838430i −0.907887 0.419215i \(-0.862305\pi\)
0.907887 0.419215i \(-0.137695\pi\)
\(464\) 5.80907e7 + 9.73523e6i 0.581504 + 0.0974523i
\(465\) 0 0
\(466\) 1.88231e6 4.53190e7i 0.0186009 0.447840i
\(467\) 7.13276e6i 0.0700337i 0.999387 + 0.0350168i \(0.0111485\pi\)
−0.999387 + 0.0350168i \(0.988852\pi\)
\(468\) 0 0
\(469\) 3.96263e7 0.384118
\(470\) −5.86673e7 2.43673e6i −0.565071 0.0234701i
\(471\) 0 0
\(472\) 1.37779e8 + 1.72472e7i 1.31026 + 0.164019i
\(473\) 1.97210e6 0.0186357
\(474\) 0 0
\(475\) 3.06257e7i 0.285762i
\(476\) 1.34676e7 1.61845e8i 0.124873 1.50065i
\(477\) 0 0
\(478\) 8.12498e7 + 3.37469e6i 0.743941 + 0.0308994i
\(479\) 1.02247e8i 0.930346i 0.885220 + 0.465173i \(0.154008\pi\)
−0.885220 + 0.465173i \(0.845992\pi\)
\(480\) 0 0
\(481\) 1.79493e8 1.61292
\(482\) 6.21586e6 1.49654e8i 0.0555086 1.33644i
\(483\) 0 0
\(484\) −7.73562e6 643705.i −0.0682274 0.00567741i
\(485\) −8.17146e7 −0.716266
\(486\) 0 0
\(487\) 7.59619e6i 0.0657671i 0.999459 + 0.0328836i \(0.0104691\pi\)
−0.999459 + 0.0328836i \(0.989531\pi\)
\(488\) −1.60552e7 + 1.28256e8i −0.138152 + 1.10362i
\(489\) 0 0
\(490\) 3.47160e6 8.35830e7i 0.0295081 0.710444i
\(491\) 4.78138e7i 0.403932i 0.979393 + 0.201966i \(0.0647331\pi\)
−0.979393 + 0.201966i \(0.935267\pi\)
\(492\) 0 0
\(493\) −6.61055e7 −0.551692
\(494\) 1.96899e8 + 8.17813e6i 1.63328 + 0.0678380i
\(495\) 0 0
\(496\) −2.33548e7 + 1.39360e8i −0.191395 + 1.14207i
\(497\) −1.07003e8 −0.871620
\(498\) 0 0
\(499\) 7.03458e7i 0.566157i 0.959097 + 0.283078i \(0.0913556\pi\)
−0.959097 + 0.283078i \(0.908644\pi\)
\(500\) −1.11418e7 927146.i −0.0891346 0.00741717i
\(501\) 0 0
\(502\) −2.70993e7 1.12556e6i −0.214214 0.00889731i
\(503\) 1.29972e7i 0.102128i −0.998695 0.0510639i \(-0.983739\pi\)
0.998695 0.0510639i \(-0.0162612\pi\)
\(504\) 0 0
\(505\) −5.38759e7 −0.418331
\(506\) −6.48995e6 + 1.56254e8i −0.0500945 + 1.20609i
\(507\) 0 0
\(508\) −1.03200e7 + 1.24019e8i −0.0787209 + 0.946017i
\(509\) −1.39419e8 −1.05723 −0.528616 0.848861i \(-0.677289\pi\)
−0.528616 + 0.848861i \(0.677289\pi\)
\(510\) 0 0
\(511\) 6.93085e7i 0.519426i
\(512\) −4.89851e7 + 1.24959e8i −0.364968 + 0.931020i
\(513\) 0 0
\(514\) 9.28913e6 2.23647e8i 0.0684047 1.64693i
\(515\) 5.67635e7i 0.415573i
\(516\) 0 0
\(517\) 1.68668e8 1.22057
\(518\) −3.15074e8 1.30865e7i −2.26686 0.0941533i
\(519\) 0 0
\(520\) −8.93606e6 + 7.13855e7i −0.0635530 + 0.507691i
\(521\) 1.76371e6 0.0124714 0.00623570 0.999981i \(-0.498015\pi\)
0.00623570 + 0.999981i \(0.498015\pi\)
\(522\) 0 0
\(523\) 2.26098e8i 1.58049i 0.612792 + 0.790244i \(0.290046\pi\)
−0.612792 + 0.790244i \(0.709954\pi\)
\(524\) 1.94342e7 2.33548e8i 0.135075 1.62324i
\(525\) 0 0
\(526\) −2.13446e8 8.86541e6i −1.46666 0.0609174i
\(527\) 1.58587e8i 1.08352i
\(528\) 0 0
\(529\) −8.35287e7 −0.564246
\(530\) −4.23525e6 + 1.01969e8i −0.0284480 + 0.684920i
\(531\) 0 0
\(532\) −3.45031e8 2.87111e7i −2.29152 0.190684i
\(533\) −9.46542e7 −0.625112
\(534\) 0 0
\(535\) 2.84679e7i 0.185906i
\(536\) 3.64700e7 + 4.56533e6i 0.236832 + 0.0296468i
\(537\) 0 0
\(538\) 9.12852e6 2.19780e8i 0.0586210 1.41137i
\(539\) 2.40301e8i 1.53458i
\(540\) 0 0
\(541\) 1.06341e8 0.671596 0.335798 0.941934i \(-0.390994\pi\)
0.335798 + 0.941934i \(0.390994\pi\)
\(542\) 6.25256e7 + 2.59699e6i 0.392699 + 0.0163107i
\(543\) 0 0
\(544\) 3.10410e7 1.47402e8i 0.192814 0.915602i
\(545\) 1.19339e8 0.737215
\(546\) 0 0
\(547\) 1.70542e7i 0.104200i −0.998642 0.0521002i \(-0.983408\pi\)
0.998642 0.0521002i \(-0.0165915\pi\)
\(548\) 3.04237e7 + 2.53165e6i 0.184871 + 0.0153837i
\(549\) 0 0
\(550\) 3.20881e7 + 1.33277e6i 0.192866 + 0.00801064i
\(551\) 1.40928e8i 0.842446i
\(552\) 0 0
\(553\) −3.36675e8 −1.99083
\(554\) 1.15820e7 2.78850e8i 0.0681166 1.63999i
\(555\) 0 0
\(556\) −4.64365e6 + 5.58043e7i −0.0270169 + 0.324671i
\(557\) 1.31701e8 0.762118 0.381059 0.924551i \(-0.375559\pi\)
0.381059 + 0.924551i \(0.375559\pi\)
\(558\) 0 0
\(559\) 3.85871e6i 0.0220905i
\(560\) 2.08906e7 1.24656e8i 0.118956 0.709819i
\(561\) 0 0
\(562\) −808042. + 1.94546e7i −0.00455224 + 0.109601i
\(563\) 9.70061e7i 0.543593i 0.962355 + 0.271797i \(0.0876178\pi\)
−0.962355 + 0.271797i \(0.912382\pi\)
\(564\) 0 0
\(565\) −9.98898e6 −0.0553829
\(566\) 3.05783e8 + 1.27006e7i 1.68641 + 0.0700448i
\(567\) 0 0
\(568\) −9.84801e7 1.23278e7i −0.537407 0.0672728i
\(569\) −2.37401e8 −1.28868 −0.644341 0.764738i \(-0.722868\pi\)
−0.644341 + 0.764738i \(0.722868\pi\)
\(570\) 0 0
\(571\) 8.85844e7i 0.475827i 0.971286 + 0.237913i \(0.0764635\pi\)
−0.971286 + 0.237913i \(0.923537\pi\)
\(572\) 1.71373e7 2.05945e8i 0.0915702 1.10043i
\(573\) 0 0
\(574\) 1.66152e8 + 6.90108e6i 0.878557 + 0.0364907i
\(575\) 4.75539e7i 0.250140i
\(576\) 0 0
\(577\) −2.33160e8 −1.21374 −0.606871 0.794800i \(-0.707576\pi\)
−0.606871 + 0.794800i \(0.707576\pi\)
\(578\) 997644. 2.40195e7i 0.00516645 0.124389i
\(579\) 0 0
\(580\) −5.12706e7 4.26638e6i −0.262775 0.0218663i
\(581\) −3.26893e8 −1.66678
\(582\) 0 0
\(583\) 2.93160e8i 1.47945i
\(584\) 7.98500e6 6.37880e7i 0.0400901 0.320258i
\(585\) 0 0
\(586\) 6.78452e6 1.63346e8i 0.0337152 0.811736i
\(587\) 3.20487e8i 1.58451i 0.610187 + 0.792257i \(0.291094\pi\)
−0.610187 + 0.792257i \(0.708906\pi\)
\(588\) 0 0
\(589\) −3.38086e8 −1.65456
\(590\) −1.21180e8 5.03316e6i −0.590029 0.0245067i
\(591\) 0 0
\(592\) −2.88470e8 4.83438e7i −1.39039 0.233010i
\(593\) 2.06932e8 0.992345 0.496173 0.868224i \(-0.334738\pi\)
0.496173 + 0.868224i \(0.334738\pi\)
\(594\) 0 0
\(595\) 1.41854e8i 0.673429i
\(596\) −1.61267e8 1.34196e7i −0.761742 0.0633869i
\(597\) 0 0
\(598\) 3.05733e8 + 1.26986e7i 1.42968 + 0.0593815i
\(599\) 1.70428e8i 0.792976i 0.918040 + 0.396488i \(0.129771\pi\)
−0.918040 + 0.396488i \(0.870229\pi\)
\(600\) 0 0
\(601\) −2.51778e8 −1.15983 −0.579914 0.814678i \(-0.696914\pi\)
−0.579914 + 0.814678i \(0.696914\pi\)
\(602\) −281332. + 6.77342e6i −0.00128953 + 0.0310469i
\(603\) 0 0
\(604\) 1.72105e7 2.06825e8i 0.0781058 0.938625i
\(605\) 6.78014e6 0.0306177
\(606\) 0 0
\(607\) 3.60842e8i 1.61343i −0.590940 0.806716i \(-0.701243\pi\)
0.590940 0.806716i \(-0.298757\pi\)
\(608\) −3.14241e8 6.61751e7i −1.39815 0.294431i
\(609\) 0 0
\(610\) 4.68530e6 1.12804e8i 0.0206418 0.496977i
\(611\) 3.30025e8i 1.44685i
\(612\) 0 0
\(613\) 2.76049e6 0.0119841 0.00599203 0.999982i \(-0.498093\pi\)
0.00599203 + 0.999982i \(0.498093\pi\)
\(614\) −7.62669e7 3.16773e6i −0.329481 0.0136849i
\(615\) 0 0
\(616\) −4.50972e7 + 3.60258e8i −0.192933 + 1.54124i
\(617\) 5.86892e7 0.249863 0.124932 0.992165i \(-0.460129\pi\)
0.124932 + 0.992165i \(0.460129\pi\)
\(618\) 0 0
\(619\) 2.86112e8i 1.20632i 0.797619 + 0.603161i \(0.206093\pi\)
−0.797619 + 0.603161i \(0.793907\pi\)
\(620\) 1.02350e7 1.22998e8i 0.0429452 0.516087i
\(621\) 0 0
\(622\) −2.33124e7 968275.i −0.0968760 0.00402372i
\(623\) 8.51678e7i 0.352218i
\(624\) 0 0
\(625\) 9.76562e6 0.0400000
\(626\) −6.43205e6 + 1.54859e8i −0.0262196 + 0.631269i
\(627\) 0 0
\(628\) 3.80507e8 + 3.16631e7i 1.53633 + 0.127842i
\(629\) 3.28270e8 1.31911
\(630\) 0 0
\(631\) 2.43261e8i 0.968244i 0.875001 + 0.484122i \(0.160861\pi\)
−0.875001 + 0.484122i \(0.839139\pi\)
\(632\) −3.09858e8 3.87881e7i −1.22747 0.153655i
\(633\) 0 0
\(634\) 2.15972e6 5.19980e7i 0.00847482 0.204042i
\(635\) 1.08701e8i 0.424534i
\(636\) 0 0
\(637\) 4.70185e8 1.81907
\(638\) 1.47657e8 + 6.13291e6i 0.568582 + 0.0236159i
\(639\) 0 0
\(640\) 3.35882e7 1.12320e8i 0.128129 0.428466i
\(641\) −1.54539e8 −0.586766 −0.293383 0.955995i \(-0.594781\pi\)
−0.293383 + 0.955995i \(0.594781\pi\)
\(642\) 0 0
\(643\) 1.73101e8i 0.651130i −0.945520 0.325565i \(-0.894445\pi\)
0.945520 0.325565i \(-0.105555\pi\)
\(644\) −5.35746e8 4.45811e7i −2.00586 0.166914i
\(645\) 0 0
\(646\) 3.60103e8 + 1.49568e7i 1.33576 + 0.0554806i
\(647\) 2.97783e8i 1.09948i −0.835336 0.549740i \(-0.814727\pi\)
0.835336 0.549740i \(-0.185273\pi\)
\(648\) 0 0
\(649\) 3.48391e8 1.27448
\(650\) 2.60777e6 6.27851e7i 0.00949573 0.228621i
\(651\) 0 0
\(652\) 2.16805e7 2.60542e8i 0.0782216 0.940016i
\(653\) 4.67892e8 1.68038 0.840188 0.542296i \(-0.182445\pi\)
0.840188 + 0.542296i \(0.182445\pi\)
\(654\) 0 0
\(655\) 2.04701e8i 0.728443i
\(656\) 1.52123e8 + 2.54937e7i 0.538868 + 0.0903070i
\(657\) 0 0
\(658\) −2.40616e7 + 5.79313e8i −0.0844592 + 2.03346i
\(659\) 3.65042e8i 1.27552i −0.770236 0.637759i \(-0.779862\pi\)
0.770236 0.637759i \(-0.220138\pi\)
\(660\) 0 0
\(661\) 2.50270e7 0.0866573 0.0433287 0.999061i \(-0.486204\pi\)
0.0433287 + 0.999061i \(0.486204\pi\)
\(662\) 1.84530e8 + 7.66443e6i 0.636054 + 0.0264183i
\(663\) 0 0
\(664\) −3.00856e8 3.76612e7i −1.02767 0.128644i
\(665\) 3.02414e8 1.02834
\(666\) 0 0
\(667\) 2.18825e8i 0.737429i
\(668\) −1.31519e7 + 1.58051e8i −0.0441224 + 0.530234i
\(669\) 0 0
\(670\) −3.20762e7 1.33228e6i −0.106649 0.00442965i
\(671\) 3.24312e8i 1.07348i
\(672\) 0 0
\(673\) −4.07582e8 −1.33712 −0.668559 0.743659i \(-0.733088\pi\)
−0.668559 + 0.743659i \(0.733088\pi\)
\(674\) 1.47347e7 3.54757e8i 0.0481241 1.15865i
\(675\) 0 0
\(676\) −9.51101e7 7.91440e6i −0.307883 0.0256199i
\(677\) 3.08100e8 0.992946 0.496473 0.868052i \(-0.334628\pi\)
0.496473 + 0.868052i \(0.334628\pi\)
\(678\) 0 0
\(679\) 8.06893e8i 2.57755i
\(680\) −1.63430e7 + 1.30555e8i −0.0519762 + 0.415210i
\(681\) 0 0
\(682\) −1.47129e7 + 3.54230e8i −0.0463814 + 1.11669i
\(683\) 2.86032e8i 0.897744i 0.893596 + 0.448872i \(0.148174\pi\)
−0.893596 + 0.448872i \(0.851826\pi\)
\(684\) 0 0
\(685\) −2.66658e7 −0.0829628
\(686\) −3.06250e8 1.27200e7i −0.948645 0.0394017i
\(687\) 0 0
\(688\) −1.03929e6 + 6.20149e6i −0.00319131 + 0.0190428i
\(689\) −5.73611e8 −1.75372
\(690\) 0 0
\(691\) 6.17632e8i 1.87196i −0.352059 0.935978i \(-0.614518\pi\)
0.352059 0.935978i \(-0.385482\pi\)
\(692\) 5.23314e8 + 4.35465e7i 1.57922 + 0.131412i
\(693\) 0 0
\(694\) 2.09857e8 + 8.71636e6i 0.627835 + 0.0260770i
\(695\) 4.89116e7i 0.145699i
\(696\) 0 0
\(697\) −1.73111e8 −0.511241
\(698\) −2.50591e7 + 6.03328e8i −0.0736884 + 1.77414i
\(699\) 0 0
\(700\) −9.15513e6 + 1.10020e8i −0.0266913 + 0.320759i
\(701\) 2.90668e8 0.843808 0.421904 0.906641i \(-0.361362\pi\)
0.421904 + 0.906641i \(0.361362\pi\)
\(702\) 0 0
\(703\) 6.99828e8i 2.01431i
\(704\) −8.30103e7 + 3.26367e8i −0.237911 + 0.935380i
\(705\) 0 0
\(706\) −2.42985e6 + 5.85016e7i −0.00690502 + 0.166247i
\(707\) 5.31999e8i 1.50540i
\(708\) 0 0
\(709\) 5.33660e7 0.149736 0.0748679 0.997193i \(-0.476146\pi\)
0.0748679 + 0.997193i \(0.476146\pi\)
\(710\) 8.66155e7 + 3.59755e6i 0.242003 + 0.0100515i
\(711\) 0 0
\(712\) 9.81215e6 7.83840e7i 0.0271847 0.217164i
\(713\) −5.24962e8 −1.44830
\(714\) 0 0
\(715\) 1.80507e8i 0.493828i
\(716\) 1.64508e7 1.97695e8i 0.0448176 0.538588i
\(717\) 0 0
\(718\) −3.22105e8 1.33786e7i −0.870210 0.0361440i
\(719\) 8.54538e7i 0.229903i 0.993371 + 0.114951i \(0.0366713\pi\)
−0.993371 + 0.114951i \(0.963329\pi\)
\(720\) 0 0
\(721\) 5.60513e8 1.49548
\(722\) 1.62670e7 3.91649e8i 0.0432212 1.04060i
\(723\) 0 0
\(724\) 1.58100e8 + 1.31560e7i 0.416598 + 0.0346664i
\(725\) 4.49378e7 0.117923
\(726\) 0 0
\(727\) 4.69711e8i 1.22244i −0.791461 0.611220i \(-0.790679\pi\)
0.791461 0.611220i \(-0.209321\pi\)
\(728\) 7.04898e8 + 8.82395e7i 1.82697 + 0.228701i
\(729\) 0 0
\(730\) −2.33022e6 + 5.61030e7i −0.00599003 + 0.144217i
\(731\) 7.05710e6i 0.0180665i
\(732\) 0 0
\(733\) 3.65700e8 0.928567 0.464283 0.885687i \(-0.346312\pi\)
0.464283 + 0.885687i \(0.346312\pi\)
\(734\) 1.72452e8 + 7.16273e6i 0.436093 + 0.0181130i
\(735\) 0 0
\(736\) −4.87937e8 1.02753e8i −1.22386 0.257728i
\(737\) 9.22189e7 0.230366
\(738\) 0 0
\(739\) 4.87643e8i 1.20828i 0.796877 + 0.604142i \(0.206484\pi\)
−0.796877 + 0.604142i \(0.793516\pi\)
\(740\) 2.54602e8 + 2.11862e7i 0.628300 + 0.0522828i
\(741\) 0 0
\(742\) 1.00689e9 + 4.18211e7i 2.46474 + 0.102373i
\(743\) 7.13753e8i 1.74013i −0.492939 0.870064i \(-0.664077\pi\)
0.492939 0.870064i \(-0.335923\pi\)
\(744\) 0 0
\(745\) 1.41348e8 0.341839
\(746\) −1.72659e7 + 4.15699e8i −0.0415885 + 1.00129i
\(747\) 0 0
\(748\) 3.13420e7 3.76648e8i 0.0748897 0.899975i
\(749\) 2.81107e8 0.669000
\(750\) 0 0
\(751\) 3.91873e8i 0.925180i 0.886572 + 0.462590i \(0.153080\pi\)
−0.886572 + 0.462590i \(0.846920\pi\)
\(752\) −8.88874e7 + 5.30397e8i −0.209019 + 1.24723i
\(753\) 0 0
\(754\) 1.20000e7 2.88914e8i 0.0279941 0.673991i
\(755\) 1.81279e8i 0.421217i
\(756\) 0 0
\(757\) 2.04521e7 0.0471466 0.0235733 0.999722i \(-0.492496\pi\)
0.0235733 + 0.999722i \(0.492496\pi\)
\(758\) 7.51068e7 + 3.11954e6i 0.172453 + 0.00716281i
\(759\) 0 0
\(760\) 2.78326e8 + 3.48410e7i 0.634035 + 0.0793688i
\(761\) −5.17521e8 −1.17429 −0.587143 0.809483i \(-0.699748\pi\)
−0.587143 + 0.809483i \(0.699748\pi\)
\(762\) 0 0
\(763\) 1.17842e9i 2.65293i
\(764\) 7.58784e6 9.11857e7i 0.0170152 0.204478i
\(765\) 0 0
\(766\) 1.23506e8 + 5.12980e6i 0.274791 + 0.0114134i
\(767\) 6.81679e8i 1.51075i
\(768\) 0 0
\(769\) −2.63067e8 −0.578478 −0.289239 0.957257i \(-0.593402\pi\)
−0.289239 + 0.957257i \(0.593402\pi\)
\(770\) 1.31605e7 3.16855e8i 0.0288270 0.694046i
\(771\) 0 0
\(772\) 1.15668e8 + 9.62508e6i 0.251397 + 0.0209196i
\(773\) −5.41479e8 −1.17231 −0.586155 0.810199i \(-0.699359\pi\)
−0.586155 + 0.810199i \(0.699359\pi\)
\(774\) 0 0
\(775\) 1.07806e8i 0.231599i
\(776\) −9.29618e7 + 7.42623e8i −0.198939 + 1.58922i
\(777\) 0 0
\(778\) −1.83087e7 + 4.40804e8i −0.0388793 + 0.936066i
\(779\) 3.69049e8i 0.780678i
\(780\) 0 0
\(781\) −2.49019e8 −0.522733
\(782\) 5.59149e8 + 2.32241e7i 1.16925 + 0.0485645i
\(783\) 0 0
\(784\) −7.55654e8 1.26637e8i −1.56810 0.262793i
\(785\) −3.33508e8 −0.689440
\(786\) 0 0
\(787\) 2.07996e7i 0.0426709i 0.999772 + 0.0213354i \(0.00679179\pi\)
−0.999772 + 0.0213354i \(0.993208\pi\)
\(788\) −5.54657e8 4.61547e7i −1.13356 0.0943272i
\(789\) 0 0
\(790\) 2.72527e8 + 1.13193e7i 0.552749 + 0.0229583i
\(791\) 9.86365e7i 0.199300i
\(792\) 0 0
\(793\) 6.34565e8 1.27250
\(794\) 3.08613e7 7.43023e8i 0.0616527 1.48436i
\(795\) 0 0
\(796\) −2.66198e7 + 3.19899e8i −0.0527795 + 0.634270i
\(797\) −6.81937e8 −1.34701 −0.673503 0.739185i \(-0.735211\pi\)
−0.673503 + 0.739185i \(0.735211\pi\)
\(798\) 0 0
\(799\) 6.03575e8i 1.18329i
\(800\) −2.11013e7 + 1.00202e8i −0.0412135 + 0.195708i
\(801\) 0 0
\(802\) 3.91467e7 9.42505e8i 0.0758879 1.82709i
\(803\) 1.61296e8i 0.311513i
\(804\) 0 0
\(805\) 4.69572e8 0.900150
\(806\) 6.93105e8 + 2.87879e7i 1.32371 + 0.0549801i
\(807\) 0 0
\(808\) −6.12914e7 + 4.89624e8i −0.116189 + 0.928173i
\(809\) 7.38152e7 0.139412 0.0697060 0.997568i \(-0.477794\pi\)
0.0697060 + 0.997568i \(0.477794\pi\)
\(810\) 0 0
\(811\) 1.60157e8i 0.300250i −0.988667 0.150125i \(-0.952032\pi\)
0.988667 0.150125i \(-0.0479675\pi\)
\(812\) −4.21285e7 + 5.06273e8i −0.0786879 + 0.945620i
\(813\) 0 0
\(814\) −7.33246e8 3.04552e7i −1.35949 0.0564661i
\(815\) 2.28361e8i 0.421841i
\(816\) 0 0
\(817\) −1.50448e7 −0.0275880
\(818\) −2.02119e7 + 4.86626e8i −0.0369273 + 0.889070i
\(819\) 0 0
\(820\) −1.34263e8 1.11724e7i −0.243508 0.0202631i
\(821\) 7.70613e8 1.39254 0.696269 0.717781i \(-0.254842\pi\)
0.696269 + 0.717781i \(0.254842\pi\)
\(822\) 0 0
\(823\) 8.88839e8i 1.59450i 0.603652 + 0.797248i \(0.293712\pi\)
−0.603652 + 0.797248i \(0.706288\pi\)
\(824\) 5.15867e8 + 6.45765e7i 0.922054 + 0.115423i
\(825\) 0 0
\(826\) −4.97001e7 + 1.19659e9i −0.0881896 + 2.12327i
\(827\) 7.22792e8i 1.27790i −0.769248 0.638950i \(-0.779369\pi\)
0.769248 0.638950i \(-0.220631\pi\)
\(828\) 0 0
\(829\) 7.80531e8 1.37002 0.685009 0.728534i \(-0.259798\pi\)
0.685009 + 0.728534i \(0.259798\pi\)
\(830\) 2.64609e8 + 1.09905e7i 0.462776 + 0.0192213i
\(831\) 0 0
\(832\) 6.38586e8 + 1.62422e8i 1.10879 + 0.282017i
\(833\) 8.59910e8 1.48771
\(834\) 0 0
\(835\) 1.38529e8i 0.237948i
\(836\) −8.02962e8 6.68169e7i −1.37428 0.114358i
\(837\) 0 0
\(838\) −2.59769e8 1.07894e7i −0.441423 0.0183344i
\(839\) 3.58594e8i 0.607180i −0.952803 0.303590i \(-0.901815\pi\)
0.952803 0.303590i \(-0.0981853\pi\)
\(840\) 0 0
\(841\) −3.88036e8 −0.652356
\(842\) −1.37446e7 + 3.30919e8i −0.0230249 + 0.554352i
\(843\) 0 0
\(844\) 3.59726e7 4.32295e8i 0.0598335 0.719039i
\(845\) 8.33623e7 0.138166
\(846\) 0 0
\(847\) 6.69507e7i 0.110181i
\(848\) 9.21875e8 + 1.54494e8i 1.51176 + 0.253351i
\(849\) 0 0
\(850\) 4.76928e6 1.14826e8i 0.00776598 0.186976i
\(851\) 1.08666e9i 1.76321i
\(852\) 0 0
\(853\) 7.64679e8 1.23206 0.616031 0.787722i \(-0.288740\pi\)
0.616031 + 0.787722i \(0.288740\pi\)
\(854\) −1.11389e9 4.62651e7i −1.78842 0.0742814i
\(855\) 0 0
\(856\) 2.58716e8 + 3.23862e7i 0.412479 + 0.0516343i
\(857\) 7.39540e8 1.17495 0.587474 0.809243i \(-0.300122\pi\)
0.587474 + 0.809243i \(0.300122\pi\)
\(858\) 0 0
\(859\) 2.38366e8i 0.376067i 0.982163 + 0.188034i \(0.0602114\pi\)
−0.982163 + 0.188034i \(0.939789\pi\)
\(860\) 455458. 5.47340e6i 0.000716066 0.00860521i
\(861\) 0 0
\(862\) −2.11435e8 8.78188e6i −0.330107 0.0137109i
\(863\) 1.16251e9i 1.80870i −0.426794 0.904349i \(-0.640357\pi\)
0.426794 0.904349i \(-0.359643\pi\)
\(864\) 0 0
\(865\) −4.58676e8 −0.708692
\(866\) 8.36917e6 2.01498e8i 0.0128863 0.310254i
\(867\) 0 0
\(868\) −1.21455e9 1.01066e8i −1.85719 0.154542i
\(869\) −7.83514e8 −1.19395
\(870\) 0 0
\(871\) 1.80440e8i 0.273073i
\(872\) 1.35765e8 1.08456e9i 0.204757 1.63570i
\(873\) 0 0
\(874\) 4.95107e7 1.19203e9i 0.0741591 1.78547i
\(875\) 9.64310e7i 0.143944i
\(876\) 0 0
\(877\) 1.18584e8 0.175803 0.0879016 0.996129i \(-0.471984\pi\)
0.0879016 + 0.996129i \(0.471984\pi\)
\(878\) −1.26717e9 5.26315e7i −1.87219 0.0777610i
\(879\) 0 0
\(880\) 4.86169e7 2.90100e8i 0.0713411 0.425697i
\(881\) 5.84028e8 0.854095 0.427047 0.904229i \(-0.359554\pi\)
0.427047 + 0.904229i \(0.359554\pi\)
\(882\) 0 0
\(883\) 3.76901e8i 0.547451i −0.961808 0.273725i \(-0.911744\pi\)
0.961808 0.273725i \(-0.0882560\pi\)
\(884\) −7.36968e8 6.13253e7i −1.06682 0.0887735i
\(885\) 0 0
\(886\) 8.41932e8 + 3.49694e7i 1.21053 + 0.0502791i
\(887\) 9.41273e8i 1.34879i −0.738370 0.674395i \(-0.764404\pi\)
0.738370 0.674395i \(-0.235596\pi\)
\(888\) 0 0
\(889\) −1.07337e9 −1.52772
\(890\) −2.86343e6 + 6.89405e7i −0.00406178 + 0.0977923i
\(891\) 0 0
\(892\) −6.46253e7 + 7.76625e8i −0.0910559 + 1.09425i
\(893\) −1.28674e9 −1.80691
\(894\) 0 0
\(895\) 1.73276e8i 0.241697i
\(896\) −1.10911e9 3.31667e8i −1.54187 0.461082i
\(897\) 0 0
\(898\) −4.82295e7 + 1.16119e9i −0.0666015 + 1.60351i
\(899\) 4.96082e8i 0.682770i
\(900\) 0 0
\(901\) −1.04906e9 −1.43426
\(902\) 3.86672e8 + 1.60603e7i 0.526893 + 0.0218844i
\(903\) 0 0
\(904\) −1.13639e7 + 9.07799e7i −0.0153823 + 0.122881i
\(905\) −1.38572e8 −0.186952
\(906\) 0 0
\(907\) 1.10117e9i 1.47582i −0.674902 0.737908i \(-0.735814\pi\)
0.674902 0.737908i \(-0.264186\pi\)
\(908\) 4.73812e7 5.69396e8i 0.0632919 0.760601i
\(909\) 0 0
\(910\) −6.19974e8 2.57505e7i −0.822715 0.0341712i
\(911\) 5.43788e8i 0.719241i 0.933099 + 0.359621i \(0.117094\pi\)
−0.933099 + 0.359621i \(0.882906\pi\)
\(912\) 0 0
\(913\) −7.60751e8 −0.999609
\(914\) −3.35066e7 + 8.06712e8i −0.0438825 + 1.05653i
\(915\) 0 0
\(916\) 1.02866e9 + 8.55979e7i 1.33840 + 0.111372i
\(917\) 2.02132e9 2.62137
\(918\) 0 0
\(919\) 1.23288e9i 1.58845i 0.607626 + 0.794224i \(0.292122\pi\)
−0.607626 + 0.794224i \(0.707878\pi\)
\(920\) 4.32170e8 + 5.40992e7i 0.554998 + 0.0694749i
\(921\) 0 0
\(922\) −3.47922e7 + 8.37665e8i −0.0443904 + 1.06875i
\(923\) 4.87243e8i 0.619642i
\(924\) 0 0
\(925\) −2.23155e8 −0.281956
\(926\) 6.65159e8 + 2.76272e7i 0.837707 + 0.0347940i
\(927\) 0 0
\(928\) −9.71004e7 + 4.61094e8i −0.121500 + 0.576959i
\(929\) −5.78905e8 −0.722038 −0.361019 0.932558i \(-0.617571\pi\)
−0.361019 + 0.932558i \(0.617571\pi\)
\(930\) 0 0
\(931\) 1.83321e9i 2.27177i
\(932\) 3.61615e8 + 3.00911e7i 0.446682 + 0.0371698i
\(933\) 0 0
\(934\) −5.70129e7 2.36802e6i −0.0699733 0.00290633i
\(935\) 3.30125e8i 0.403872i
\(936\) 0 0
\(937\) −7.59361e8 −0.923059 −0.461529 0.887125i \(-0.652699\pi\)
−0.461529 + 0.887125i \(0.652699\pi\)
\(938\) −1.31556e7 + 3.16737e8i −0.0159405 + 0.383787i
\(939\) 0 0
\(940\) 3.89541e7 4.68125e8i 0.0468997 0.563610i
\(941\) −5.09200e8 −0.611110 −0.305555 0.952174i \(-0.598842\pi\)
−0.305555 + 0.952174i \(0.598842\pi\)
\(942\) 0 0
\(943\) 5.73040e8i 0.683360i
\(944\) −1.83600e8 + 1.09556e9i −0.218252 + 1.30232i
\(945\) 0 0
\(946\) −654720. + 1.57632e7i −0.000773361 + 0.0186196i
\(947\) 5.18817e8i 0.610892i 0.952209 + 0.305446i \(0.0988055\pi\)
−0.952209 + 0.305446i \(0.901194\pi\)
\(948\) 0 0
\(949\) −3.15599e8 −0.369265
\(950\) −2.44794e8 1.01675e7i −0.285516 0.0118588i
\(951\) 0 0
\(952\) 1.28917e9 + 1.61379e8i 1.49417 + 0.187041i
\(953\) −1.67690e9 −1.93745 −0.968723 0.248146i \(-0.920179\pi\)
−0.968723 + 0.248146i \(0.920179\pi\)
\(954\) 0 0
\(955\) 7.99227e7i 0.0917614i
\(956\) −5.39485e7 + 6.48318e8i −0.0617456 + 0.742018i
\(957\) 0 0
\(958\) −8.17272e8 3.39452e7i −0.929544 0.0386084i
\(959\) 2.63312e8i 0.298549i
\(960\) 0 0
\(961\) −3.02597e8 −0.340953
\(962\) −5.95901e7 + 1.43471e9i −0.0669344 + 1.61153i
\(963\) 0 0
\(964\) 1.19414e9 + 9.93681e7i 1.33298 + 0.110922i
\(965\) −1.01381e8 −0.112817
\(966\) 0 0
\(967\) 1.67789e9i 1.85560i 0.373082 + 0.927798i \(0.378301\pi\)
−0.373082 + 0.927798i \(0.621699\pi\)
\(968\) 7.71336e6 6.16180e7i 0.00850389 0.0679331i
\(969\) 0 0
\(970\) 2.71286e7 6.53154e8i 0.0297243 0.715649i
\(971\) 5.10919e8i 0.558078i −0.960280 0.279039i \(-0.909984\pi\)
0.960280 0.279039i \(-0.0900158\pi\)
\(972\) 0 0
\(973\) −4.82979e8 −0.524312
\(974\) −6.07172e7 2.52187e6i −0.0657105 0.00272927i
\(975\) 0 0
\(976\) −1.01984e9 1.70911e8i −1.09694 0.183832i
\(977\) −3.24832e7 −0.0348318 −0.0174159 0.999848i \(-0.505544\pi\)
−0.0174159 + 0.999848i \(0.505544\pi\)
\(978\) 0 0
\(979\) 1.98204e8i 0.211234i
\(980\) 6.66936e8 + 5.54977e7i 0.708607 + 0.0589654i
\(981\) 0 0
\(982\) −3.82181e8 1.58738e7i −0.403584 0.0167628i
\(983\) 7.49859e8i 0.789439i 0.918802 + 0.394720i \(0.129158\pi\)
−0.918802 + 0.394720i \(0.870842\pi\)
\(984\) 0 0
\(985\) 4.86147e8 0.508697
\(986\) 2.19465e7 5.28388e8i 0.0228946 0.551217i
\(987\) 0 0
\(988\) −1.30737e8 + 1.57112e9i −0.135559 + 1.62906i
\(989\) −2.33607e7 −0.0241489
\(990\) 0 0
\(991\) 6.65908e8i 0.684216i 0.939661 + 0.342108i \(0.111141\pi\)
−0.939661 + 0.342108i \(0.888859\pi\)
\(992\) −1.10616e9 2.32944e8i −1.13314 0.238625i
\(993\) 0 0
\(994\) 3.55241e7 8.55287e8i 0.0361713 0.870869i
\(995\) 2.80386e8i 0.284634i
\(996\) 0 0
\(997\) −6.37105e8 −0.642873 −0.321437 0.946931i \(-0.604166\pi\)
−0.321437 + 0.946931i \(0.604166\pi\)
\(998\) −5.62282e8 2.33542e7i −0.565669 0.0234949i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 180.7.c.b.91.14 24
3.2 odd 2 60.7.c.a.31.11 24
4.3 odd 2 inner 180.7.c.b.91.13 24
12.11 even 2 60.7.c.a.31.12 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.7.c.a.31.11 24 3.2 odd 2
60.7.c.a.31.12 yes 24 12.11 even 2
180.7.c.b.91.13 24 4.3 odd 2 inner
180.7.c.b.91.14 24 1.1 even 1 trivial