Properties

Label 50.5.c.b.43.1
Level $50$
Weight $5$
Character 50.43
Analytic conductor $5.168$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [50,5,Mod(7,50)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(50, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("50.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 50.c (of order \(4\), degree \(2\), 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: \(5.16849815419\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 50.43
Dual form 50.5.c.b.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 - 2.00000i) q^{2} +(-9.00000 - 9.00000i) q^{3} -8.00000i q^{4} -36.0000 q^{6} +(-29.0000 + 29.0000i) q^{7} +(-16.0000 - 16.0000i) q^{8} +81.0000i q^{9} -118.000 q^{11} +(-72.0000 + 72.0000i) q^{12} +(-69.0000 - 69.0000i) q^{13} +116.000i q^{14} -64.0000 q^{16} +(271.000 - 271.000i) q^{17} +(162.000 + 162.000i) q^{18} -280.000i q^{19} +522.000 q^{21} +(-236.000 + 236.000i) q^{22} +(-269.000 - 269.000i) q^{23} +288.000i q^{24} -276.000 q^{26} +(232.000 + 232.000i) q^{28} -680.000i q^{29} +202.000 q^{31} +(-128.000 + 128.000i) q^{32} +(1062.00 + 1062.00i) q^{33} -1084.00i q^{34} +648.000 q^{36} +(651.000 - 651.000i) q^{37} +(-560.000 - 560.000i) q^{38} +1242.00i q^{39} +1682.00 q^{41} +(1044.00 - 1044.00i) q^{42} +(-1089.00 - 1089.00i) q^{43} +944.000i q^{44} -1076.00 q^{46} +(-1269.00 + 1269.00i) q^{47} +(576.000 + 576.000i) q^{48} +719.000i q^{49} -4878.00 q^{51} +(-552.000 + 552.000i) q^{52} +(611.000 + 611.000i) q^{53} +928.000 q^{56} +(-2520.00 + 2520.00i) q^{57} +(-1360.00 - 1360.00i) q^{58} -1160.00i q^{59} -5598.00 q^{61} +(404.000 - 404.000i) q^{62} +(-2349.00 - 2349.00i) q^{63} +512.000i q^{64} +4248.00 q^{66} +(751.000 - 751.000i) q^{67} +(-2168.00 - 2168.00i) q^{68} +4842.00i q^{69} +6442.00 q^{71} +(1296.00 - 1296.00i) q^{72} +(2951.00 + 2951.00i) q^{73} -2604.00i q^{74} -2240.00 q^{76} +(3422.00 - 3422.00i) q^{77} +(2484.00 + 2484.00i) q^{78} -10560.0i q^{79} +6561.00 q^{81} +(3364.00 - 3364.00i) q^{82} +(6231.00 + 6231.00i) q^{83} -4176.00i q^{84} -4356.00 q^{86} +(-6120.00 + 6120.00i) q^{87} +(1888.00 + 1888.00i) q^{88} +14480.0i q^{89} +4002.00 q^{91} +(-2152.00 + 2152.00i) q^{92} +(-1818.00 - 1818.00i) q^{93} +5076.00i q^{94} +2304.00 q^{96} +(7311.00 - 7311.00i) q^{97} +(1438.00 + 1438.00i) q^{98} -9558.00i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} - 18 q^{3} - 72 q^{6} - 58 q^{7} - 32 q^{8} - 236 q^{11} - 144 q^{12} - 138 q^{13} - 128 q^{16} + 542 q^{17} + 324 q^{18} + 1044 q^{21} - 472 q^{22} - 538 q^{23} - 552 q^{26} + 464 q^{28}+ \cdots + 2876 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).

\(n\) \(27\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 2.00000i 0.500000 0.500000i
\(3\) −9.00000 9.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(4\) 8.00000i 0.500000i
\(5\) 0 0
\(6\) −36.0000 −1.00000
\(7\) −29.0000 + 29.0000i −0.591837 + 0.591837i −0.938127 0.346291i \(-0.887441\pi\)
0.346291 + 0.938127i \(0.387441\pi\)
\(8\) −16.0000 16.0000i −0.250000 0.250000i
\(9\) 81.0000i 1.00000i
\(10\) 0 0
\(11\) −118.000 −0.975207 −0.487603 0.873065i \(-0.662129\pi\)
−0.487603 + 0.873065i \(0.662129\pi\)
\(12\) −72.0000 + 72.0000i −0.500000 + 0.500000i
\(13\) −69.0000 69.0000i −0.408284 0.408284i 0.472856 0.881140i \(-0.343223\pi\)
−0.881140 + 0.472856i \(0.843223\pi\)
\(14\) 116.000i 0.591837i
\(15\) 0 0
\(16\) −64.0000 −0.250000
\(17\) 271.000 271.000i 0.937716 0.937716i −0.0604547 0.998171i \(-0.519255\pi\)
0.998171 + 0.0604547i \(0.0192551\pi\)
\(18\) 162.000 + 162.000i 0.500000 + 0.500000i
\(19\) 280.000i 0.775623i −0.921739 0.387812i \(-0.873231\pi\)
0.921739 0.387812i \(-0.126769\pi\)
\(20\) 0 0
\(21\) 522.000 1.18367
\(22\) −236.000 + 236.000i −0.487603 + 0.487603i
\(23\) −269.000 269.000i −0.508507 0.508507i 0.405561 0.914068i \(-0.367076\pi\)
−0.914068 + 0.405561i \(0.867076\pi\)
\(24\) 288.000i 0.500000i
\(25\) 0 0
\(26\) −276.000 −0.408284
\(27\) 0 0
\(28\) 232.000 + 232.000i 0.295918 + 0.295918i
\(29\) 680.000i 0.808561i −0.914635 0.404281i \(-0.867522\pi\)
0.914635 0.404281i \(-0.132478\pi\)
\(30\) 0 0
\(31\) 202.000 0.210198 0.105099 0.994462i \(-0.466484\pi\)
0.105099 + 0.994462i \(0.466484\pi\)
\(32\) −128.000 + 128.000i −0.125000 + 0.125000i
\(33\) 1062.00 + 1062.00i 0.975207 + 0.975207i
\(34\) 1084.00i 0.937716i
\(35\) 0 0
\(36\) 648.000 0.500000
\(37\) 651.000 651.000i 0.475530 0.475530i −0.428169 0.903699i \(-0.640841\pi\)
0.903699 + 0.428169i \(0.140841\pi\)
\(38\) −560.000 560.000i −0.387812 0.387812i
\(39\) 1242.00i 0.816568i
\(40\) 0 0
\(41\) 1682.00 1.00059 0.500297 0.865854i \(-0.333224\pi\)
0.500297 + 0.865854i \(0.333224\pi\)
\(42\) 1044.00 1044.00i 0.591837 0.591837i
\(43\) −1089.00 1089.00i −0.588967 0.588967i 0.348385 0.937352i \(-0.386730\pi\)
−0.937352 + 0.348385i \(0.886730\pi\)
\(44\) 944.000i 0.487603i
\(45\) 0 0
\(46\) −1076.00 −0.508507
\(47\) −1269.00 + 1269.00i −0.574468 + 0.574468i −0.933374 0.358906i \(-0.883150\pi\)
0.358906 + 0.933374i \(0.383150\pi\)
\(48\) 576.000 + 576.000i 0.250000 + 0.250000i
\(49\) 719.000i 0.299459i
\(50\) 0 0
\(51\) −4878.00 −1.87543
\(52\) −552.000 + 552.000i −0.204142 + 0.204142i
\(53\) 611.000 + 611.000i 0.217515 + 0.217515i 0.807450 0.589935i \(-0.200847\pi\)
−0.589935 + 0.807450i \(0.700847\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 928.000 0.295918
\(57\) −2520.00 + 2520.00i −0.775623 + 0.775623i
\(58\) −1360.00 1360.00i −0.404281 0.404281i
\(59\) 1160.00i 0.333238i −0.986021 0.166619i \(-0.946715\pi\)
0.986021 0.166619i \(-0.0532849\pi\)
\(60\) 0 0
\(61\) −5598.00 −1.50443 −0.752217 0.658915i \(-0.771016\pi\)
−0.752217 + 0.658915i \(0.771016\pi\)
\(62\) 404.000 404.000i 0.105099 0.105099i
\(63\) −2349.00 2349.00i −0.591837 0.591837i
\(64\) 512.000i 0.125000i
\(65\) 0 0
\(66\) 4248.00 0.975207
\(67\) 751.000 751.000i 0.167298 0.167298i −0.618493 0.785791i \(-0.712256\pi\)
0.785791 + 0.618493i \(0.212256\pi\)
\(68\) −2168.00 2168.00i −0.468858 0.468858i
\(69\) 4842.00i 1.01701i
\(70\) 0 0
\(71\) 6442.00 1.27792 0.638961 0.769240i \(-0.279365\pi\)
0.638961 + 0.769240i \(0.279365\pi\)
\(72\) 1296.00 1296.00i 0.250000 0.250000i
\(73\) 2951.00 + 2951.00i 0.553762 + 0.553762i 0.927525 0.373762i \(-0.121932\pi\)
−0.373762 + 0.927525i \(0.621932\pi\)
\(74\) 2604.00i 0.475530i
\(75\) 0 0
\(76\) −2240.00 −0.387812
\(77\) 3422.00 3422.00i 0.577163 0.577163i
\(78\) 2484.00 + 2484.00i 0.408284 + 0.408284i
\(79\) 10560.0i 1.69204i −0.533154 0.846018i \(-0.678993\pi\)
0.533154 0.846018i \(-0.321007\pi\)
\(80\) 0 0
\(81\) 6561.00 1.00000
\(82\) 3364.00 3364.00i 0.500297 0.500297i
\(83\) 6231.00 + 6231.00i 0.904485 + 0.904485i 0.995820 0.0913348i \(-0.0291134\pi\)
−0.0913348 + 0.995820i \(0.529113\pi\)
\(84\) 4176.00i 0.591837i
\(85\) 0 0
\(86\) −4356.00 −0.588967
\(87\) −6120.00 + 6120.00i −0.808561 + 0.808561i
\(88\) 1888.00 + 1888.00i 0.243802 + 0.243802i
\(89\) 14480.0i 1.82805i 0.405656 + 0.914026i \(0.367043\pi\)
−0.405656 + 0.914026i \(0.632957\pi\)
\(90\) 0 0
\(91\) 4002.00 0.483275
\(92\) −2152.00 + 2152.00i −0.254253 + 0.254253i
\(93\) −1818.00 1818.00i −0.210198 0.210198i
\(94\) 5076.00i 0.574468i
\(95\) 0 0
\(96\) 2304.00 0.250000
\(97\) 7311.00 7311.00i 0.777022 0.777022i −0.202301 0.979323i \(-0.564842\pi\)
0.979323 + 0.202301i \(0.0648420\pi\)
\(98\) 1438.00 + 1438.00i 0.149729 + 0.149729i
\(99\) 9558.00i 0.975207i
\(100\) 0 0
\(101\) −878.000 −0.0860700 −0.0430350 0.999074i \(-0.513703\pi\)
−0.0430350 + 0.999074i \(0.513703\pi\)
\(102\) −9756.00 + 9756.00i −0.937716 + 0.937716i
\(103\) −10429.0 10429.0i −0.983033 0.983033i 0.0168252 0.999858i \(-0.494644\pi\)
−0.999858 + 0.0168252i \(0.994644\pi\)
\(104\) 2208.00i 0.204142i
\(105\) 0 0
\(106\) 2444.00 0.217515
\(107\) 4711.00 4711.00i 0.411477 0.411477i −0.470776 0.882253i \(-0.656026\pi\)
0.882253 + 0.470776i \(0.156026\pi\)
\(108\) 0 0
\(109\) 22040.0i 1.85506i −0.373745 0.927531i \(-0.621927\pi\)
0.373745 0.927531i \(-0.378073\pi\)
\(110\) 0 0
\(111\) −11718.0 −0.951059
\(112\) 1856.00 1856.00i 0.147959 0.147959i
\(113\) 2111.00 + 2111.00i 0.165322 + 0.165322i 0.784920 0.619597i \(-0.212704\pi\)
−0.619597 + 0.784920i \(0.712704\pi\)
\(114\) 10080.0i 0.775623i
\(115\) 0 0
\(116\) −5440.00 −0.404281
\(117\) 5589.00 5589.00i 0.408284 0.408284i
\(118\) −2320.00 2320.00i −0.166619 0.166619i
\(119\) 15718.0i 1.10995i
\(120\) 0 0
\(121\) −717.000 −0.0489721
\(122\) −11196.0 + 11196.0i −0.752217 + 0.752217i
\(123\) −15138.0 15138.0i −1.00059 1.00059i
\(124\) 1616.00i 0.105099i
\(125\) 0 0
\(126\) −9396.00 −0.591837
\(127\) −5909.00 + 5909.00i −0.366359 + 0.366359i −0.866147 0.499789i \(-0.833411\pi\)
0.499789 + 0.866147i \(0.333411\pi\)
\(128\) 1024.00 + 1024.00i 0.0625000 + 0.0625000i
\(129\) 19602.0i 1.17793i
\(130\) 0 0
\(131\) −6358.00 −0.370491 −0.185246 0.982692i \(-0.559308\pi\)
−0.185246 + 0.982692i \(0.559308\pi\)
\(132\) 8496.00 8496.00i 0.487603 0.487603i
\(133\) 8120.00 + 8120.00i 0.459042 + 0.459042i
\(134\) 3004.00i 0.167298i
\(135\) 0 0
\(136\) −8672.00 −0.468858
\(137\) −20409.0 + 20409.0i −1.08738 + 1.08738i −0.0915804 + 0.995798i \(0.529192\pi\)
−0.995798 + 0.0915804i \(0.970808\pi\)
\(138\) 9684.00 + 9684.00i 0.508507 + 0.508507i
\(139\) 9400.00i 0.486517i 0.969961 + 0.243259i \(0.0782164\pi\)
−0.969961 + 0.243259i \(0.921784\pi\)
\(140\) 0 0
\(141\) 22842.0 1.14894
\(142\) 12884.0 12884.0i 0.638961 0.638961i
\(143\) 8142.00 + 8142.00i 0.398161 + 0.398161i
\(144\) 5184.00i 0.250000i
\(145\) 0 0
\(146\) 11804.0 0.553762
\(147\) 6471.00 6471.00i 0.299459 0.299459i
\(148\) −5208.00 5208.00i −0.237765 0.237765i
\(149\) 13800.0i 0.621594i −0.950476 0.310797i \(-0.899404\pi\)
0.950476 0.310797i \(-0.100596\pi\)
\(150\) 0 0
\(151\) −18998.0 −0.833209 −0.416605 0.909088i \(-0.636780\pi\)
−0.416605 + 0.909088i \(0.636780\pi\)
\(152\) −4480.00 + 4480.00i −0.193906 + 0.193906i
\(153\) 21951.0 + 21951.0i 0.937716 + 0.937716i
\(154\) 13688.0i 0.577163i
\(155\) 0 0
\(156\) 9936.00 0.408284
\(157\) 16371.0 16371.0i 0.664165 0.664165i −0.292194 0.956359i \(-0.594385\pi\)
0.956359 + 0.292194i \(0.0943853\pi\)
\(158\) −21120.0 21120.0i −0.846018 0.846018i
\(159\) 10998.0i 0.435030i
\(160\) 0 0
\(161\) 15602.0 0.601906
\(162\) 13122.0 13122.0i 0.500000 0.500000i
\(163\) −20009.0 20009.0i −0.753096 0.753096i 0.221960 0.975056i \(-0.428755\pi\)
−0.975056 + 0.221960i \(0.928755\pi\)
\(164\) 13456.0i 0.500297i
\(165\) 0 0
\(166\) 24924.0 0.904485
\(167\) −1549.00 + 1549.00i −0.0555416 + 0.0555416i −0.734332 0.678790i \(-0.762504\pi\)
0.678790 + 0.734332i \(0.262504\pi\)
\(168\) −8352.00 8352.00i −0.295918 0.295918i
\(169\) 19039.0i 0.666608i
\(170\) 0 0
\(171\) 22680.0 0.775623
\(172\) −8712.00 + 8712.00i −0.294484 + 0.294484i
\(173\) −2789.00 2789.00i −0.0931872 0.0931872i 0.658976 0.752164i \(-0.270990\pi\)
−0.752164 + 0.658976i \(0.770990\pi\)
\(174\) 24480.0i 0.808561i
\(175\) 0 0
\(176\) 7552.00 0.243802
\(177\) −10440.0 + 10440.0i −0.333238 + 0.333238i
\(178\) 28960.0 + 28960.0i 0.914026 + 0.914026i
\(179\) 2600.00i 0.0811460i 0.999177 + 0.0405730i \(0.0129183\pi\)
−0.999177 + 0.0405730i \(0.987082\pi\)
\(180\) 0 0
\(181\) −44398.0 −1.35521 −0.677604 0.735427i \(-0.736982\pi\)
−0.677604 + 0.735427i \(0.736982\pi\)
\(182\) 8004.00 8004.00i 0.241637 0.241637i
\(183\) 50382.0 + 50382.0i 1.50443 + 1.50443i
\(184\) 8608.00i 0.254253i
\(185\) 0 0
\(186\) −7272.00 −0.210198
\(187\) −31978.0 + 31978.0i −0.914467 + 0.914467i
\(188\) 10152.0 + 10152.0i 0.287234 + 0.287234i
\(189\) 0 0
\(190\) 0 0
\(191\) −14678.0 −0.402346 −0.201173 0.979556i \(-0.564475\pi\)
−0.201173 + 0.979556i \(0.564475\pi\)
\(192\) 4608.00 4608.00i 0.125000 0.125000i
\(193\) −42849.0 42849.0i −1.15034 1.15034i −0.986484 0.163855i \(-0.947607\pi\)
−0.163855 0.986484i \(-0.552393\pi\)
\(194\) 29244.0i 0.777022i
\(195\) 0 0
\(196\) 5752.00 0.149729
\(197\) 10971.0 10971.0i 0.282692 0.282692i −0.551490 0.834182i \(-0.685940\pi\)
0.834182 + 0.551490i \(0.185940\pi\)
\(198\) −19116.0 19116.0i −0.487603 0.487603i
\(199\) 38160.0i 0.963612i 0.876278 + 0.481806i \(0.160019\pi\)
−0.876278 + 0.481806i \(0.839981\pi\)
\(200\) 0 0
\(201\) −13518.0 −0.334596
\(202\) −1756.00 + 1756.00i −0.0430350 + 0.0430350i
\(203\) 19720.0 + 19720.0i 0.478536 + 0.478536i
\(204\) 39024.0i 0.937716i
\(205\) 0 0
\(206\) −41716.0 −0.983033
\(207\) 21789.0 21789.0i 0.508507 0.508507i
\(208\) 4416.00 + 4416.00i 0.102071 + 0.102071i
\(209\) 33040.0i 0.756393i
\(210\) 0 0
\(211\) 72842.0 1.63613 0.818063 0.575128i \(-0.195048\pi\)
0.818063 + 0.575128i \(0.195048\pi\)
\(212\) 4888.00 4888.00i 0.108758 0.108758i
\(213\) −57978.0 57978.0i −1.27792 1.27792i
\(214\) 18844.0i 0.411477i
\(215\) 0 0
\(216\) 0 0
\(217\) −5858.00 + 5858.00i −0.124403 + 0.124403i
\(218\) −44080.0 44080.0i −0.927531 0.927531i
\(219\) 53118.0i 1.10752i
\(220\) 0 0
\(221\) −37398.0 −0.765709
\(222\) −23436.0 + 23436.0i −0.475530 + 0.475530i
\(223\) 30891.0 + 30891.0i 0.621187 + 0.621187i 0.945835 0.324648i \(-0.105246\pi\)
−0.324648 + 0.945835i \(0.605246\pi\)
\(224\) 7424.00i 0.147959i
\(225\) 0 0
\(226\) 8444.00 0.165322
\(227\) 54911.0 54911.0i 1.06563 1.06563i 0.0679438 0.997689i \(-0.478356\pi\)
0.997689 0.0679438i \(-0.0216439\pi\)
\(228\) 20160.0 + 20160.0i 0.387812 + 0.387812i
\(229\) 50280.0i 0.958792i 0.877599 + 0.479396i \(0.159144\pi\)
−0.877599 + 0.479396i \(0.840856\pi\)
\(230\) 0 0
\(231\) −61596.0 −1.15433
\(232\) −10880.0 + 10880.0i −0.202140 + 0.202140i
\(233\) 2391.00 + 2391.00i 0.0440421 + 0.0440421i 0.728785 0.684743i \(-0.240085\pi\)
−0.684743 + 0.728785i \(0.740085\pi\)
\(234\) 22356.0i 0.408284i
\(235\) 0 0
\(236\) −9280.00 −0.166619
\(237\) −95040.0 + 95040.0i −1.69204 + 1.69204i
\(238\) 31436.0 + 31436.0i 0.554975 + 0.554975i
\(239\) 17760.0i 0.310919i 0.987842 + 0.155459i \(0.0496858\pi\)
−0.987842 + 0.155459i \(0.950314\pi\)
\(240\) 0 0
\(241\) −28238.0 −0.486183 −0.243092 0.970003i \(-0.578162\pi\)
−0.243092 + 0.970003i \(0.578162\pi\)
\(242\) −1434.00 + 1434.00i −0.0244860 + 0.0244860i
\(243\) −59049.0 59049.0i −1.00000 1.00000i
\(244\) 44784.0i 0.752217i
\(245\) 0 0
\(246\) −60552.0 −1.00059
\(247\) −19320.0 + 19320.0i −0.316675 + 0.316675i
\(248\) −3232.00 3232.00i −0.0525494 0.0525494i
\(249\) 112158.i 1.80897i
\(250\) 0 0
\(251\) 121002. 1.92064 0.960318 0.278907i \(-0.0899722\pi\)
0.960318 + 0.278907i \(0.0899722\pi\)
\(252\) −18792.0 + 18792.0i −0.295918 + 0.295918i
\(253\) 31742.0 + 31742.0i 0.495899 + 0.495899i
\(254\) 23636.0i 0.366359i
\(255\) 0 0
\(256\) 4096.00 0.0625000
\(257\) 72431.0 72431.0i 1.09663 1.09663i 0.101823 0.994803i \(-0.467533\pi\)
0.994803 0.101823i \(-0.0324674\pi\)
\(258\) 39204.0 + 39204.0i 0.588967 + 0.588967i
\(259\) 37758.0i 0.562872i
\(260\) 0 0
\(261\) 55080.0 0.808561
\(262\) −12716.0 + 12716.0i −0.185246 + 0.185246i
\(263\) 14771.0 + 14771.0i 0.213549 + 0.213549i 0.805773 0.592224i \(-0.201750\pi\)
−0.592224 + 0.805773i \(0.701750\pi\)
\(264\) 33984.0i 0.487603i
\(265\) 0 0
\(266\) 32480.0 0.459042
\(267\) 130320. 130320.i 1.82805 1.82805i
\(268\) −6008.00 6008.00i −0.0836489 0.0836489i
\(269\) 89720.0i 1.23989i −0.784644 0.619947i \(-0.787154\pi\)
0.784644 0.619947i \(-0.212846\pi\)
\(270\) 0 0
\(271\) 68202.0 0.928664 0.464332 0.885661i \(-0.346294\pi\)
0.464332 + 0.885661i \(0.346294\pi\)
\(272\) −17344.0 + 17344.0i −0.234429 + 0.234429i
\(273\) −36018.0 36018.0i −0.483275 0.483275i
\(274\) 81636.0i 1.08738i
\(275\) 0 0
\(276\) 38736.0 0.508507
\(277\) −18549.0 + 18549.0i −0.241747 + 0.241747i −0.817573 0.575826i \(-0.804681\pi\)
0.575826 + 0.817573i \(0.304681\pi\)
\(278\) 18800.0 + 18800.0i 0.243259 + 0.243259i
\(279\) 16362.0i 0.210198i
\(280\) 0 0
\(281\) 2322.00 0.0294069 0.0147035 0.999892i \(-0.495320\pi\)
0.0147035 + 0.999892i \(0.495320\pi\)
\(282\) 45684.0 45684.0i 0.574468 0.574468i
\(283\) 91711.0 + 91711.0i 1.14511 + 1.14511i 0.987501 + 0.157613i \(0.0503797\pi\)
0.157613 + 0.987501i \(0.449620\pi\)
\(284\) 51536.0i 0.638961i
\(285\) 0 0
\(286\) 32568.0 0.398161
\(287\) −48778.0 + 48778.0i −0.592189 + 0.592189i
\(288\) −10368.0 10368.0i −0.125000 0.125000i
\(289\) 63361.0i 0.758624i
\(290\) 0 0
\(291\) −131598. −1.55404
\(292\) 23608.0 23608.0i 0.276881 0.276881i
\(293\) 4851.00 + 4851.00i 0.0565062 + 0.0565062i 0.734795 0.678289i \(-0.237278\pi\)
−0.678289 + 0.734795i \(0.737278\pi\)
\(294\) 25884.0i 0.299459i
\(295\) 0 0
\(296\) −20832.0 −0.237765
\(297\) 0 0
\(298\) −27600.0 27600.0i −0.310797 0.310797i
\(299\) 37122.0i 0.415230i
\(300\) 0 0
\(301\) 63162.0 0.697145
\(302\) −37996.0 + 37996.0i −0.416605 + 0.416605i
\(303\) 7902.00 + 7902.00i 0.0860700 + 0.0860700i
\(304\) 17920.0i 0.193906i
\(305\) 0 0
\(306\) 87804.0 0.937716
\(307\) −42849.0 + 42849.0i −0.454636 + 0.454636i −0.896890 0.442254i \(-0.854179\pi\)
0.442254 + 0.896890i \(0.354179\pi\)
\(308\) −27376.0 27376.0i −0.288582 0.288582i
\(309\) 187722.i 1.96607i
\(310\) 0 0
\(311\) −72278.0 −0.747283 −0.373642 0.927573i \(-0.621891\pi\)
−0.373642 + 0.927573i \(0.621891\pi\)
\(312\) 19872.0 19872.0i 0.204142 0.204142i
\(313\) −18249.0 18249.0i −0.186273 0.186273i 0.607810 0.794083i \(-0.292048\pi\)
−0.794083 + 0.607810i \(0.792048\pi\)
\(314\) 65484.0i 0.664165i
\(315\) 0 0
\(316\) −84480.0 −0.846018
\(317\) −25149.0 + 25149.0i −0.250266 + 0.250266i −0.821080 0.570814i \(-0.806628\pi\)
0.570814 + 0.821080i \(0.306628\pi\)
\(318\) −21996.0 21996.0i −0.217515 0.217515i
\(319\) 80240.0i 0.788514i
\(320\) 0 0
\(321\) −84798.0 −0.822954
\(322\) 31204.0 31204.0i 0.300953 0.300953i
\(323\) −75880.0 75880.0i −0.727315 0.727315i
\(324\) 52488.0i 0.500000i
\(325\) 0 0
\(326\) −80036.0 −0.753096
\(327\) −198360. + 198360.i −1.85506 + 1.85506i
\(328\) −26912.0 26912.0i −0.250149 0.250149i
\(329\) 73602.0i 0.679983i
\(330\) 0 0
\(331\) −54038.0 −0.493223 −0.246611 0.969114i \(-0.579317\pi\)
−0.246611 + 0.969114i \(0.579317\pi\)
\(332\) 49848.0 49848.0i 0.452243 0.452243i
\(333\) 52731.0 + 52731.0i 0.475530 + 0.475530i
\(334\) 6196.00i 0.0555416i
\(335\) 0 0
\(336\) −33408.0 −0.295918
\(337\) −8529.00 + 8529.00i −0.0750997 + 0.0750997i −0.743659 0.668559i \(-0.766911\pi\)
0.668559 + 0.743659i \(0.266911\pi\)
\(338\) −38078.0 38078.0i −0.333304 0.333304i
\(339\) 37998.0i 0.330645i
\(340\) 0 0
\(341\) −23836.0 −0.204986
\(342\) 45360.0 45360.0i 0.387812 0.387812i
\(343\) −90480.0 90480.0i −0.769067 0.769067i
\(344\) 34848.0i 0.294484i
\(345\) 0 0
\(346\) −11156.0 −0.0931872
\(347\) 56551.0 56551.0i 0.469658 0.469658i −0.432146 0.901804i \(-0.642244\pi\)
0.901804 + 0.432146i \(0.142244\pi\)
\(348\) 48960.0 + 48960.0i 0.404281 + 0.404281i
\(349\) 22520.0i 0.184892i 0.995718 + 0.0924459i \(0.0294685\pi\)
−0.995718 + 0.0924459i \(0.970531\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 15104.0 15104.0i 0.121901 0.121901i
\(353\) 44511.0 + 44511.0i 0.357205 + 0.357205i 0.862782 0.505576i \(-0.168720\pi\)
−0.505576 + 0.862782i \(0.668720\pi\)
\(354\) 41760.0i 0.333238i
\(355\) 0 0
\(356\) 115840. 0.914026
\(357\) 141462. 141462.i 1.10995 1.10995i
\(358\) 5200.00 + 5200.00i 0.0405730 + 0.0405730i
\(359\) 9680.00i 0.0751080i 0.999295 + 0.0375540i \(0.0119566\pi\)
−0.999295 + 0.0375540i \(0.988043\pi\)
\(360\) 0 0
\(361\) 51921.0 0.398409
\(362\) −88796.0 + 88796.0i −0.677604 + 0.677604i
\(363\) 6453.00 + 6453.00i 0.0489721 + 0.0489721i
\(364\) 32016.0i 0.241637i
\(365\) 0 0
\(366\) 201528. 1.50443
\(367\) 14971.0 14971.0i 0.111152 0.111152i −0.649343 0.760496i \(-0.724956\pi\)
0.760496 + 0.649343i \(0.224956\pi\)
\(368\) 17216.0 + 17216.0i 0.127127 + 0.127127i
\(369\) 136242.i 1.00059i
\(370\) 0 0
\(371\) −35438.0 −0.257467
\(372\) −14544.0 + 14544.0i −0.105099 + 0.105099i
\(373\) 13811.0 + 13811.0i 0.0992676 + 0.0992676i 0.754996 0.655729i \(-0.227639\pi\)
−0.655729 + 0.754996i \(0.727639\pi\)
\(374\) 127912.i 0.914467i
\(375\) 0 0
\(376\) 40608.0 0.287234
\(377\) −46920.0 + 46920.0i −0.330123 + 0.330123i
\(378\) 0 0
\(379\) 251080.i 1.74797i −0.485954 0.873984i \(-0.661528\pi\)
0.485954 0.873984i \(-0.338472\pi\)
\(380\) 0 0
\(381\) 106362. 0.732717
\(382\) −29356.0 + 29356.0i −0.201173 + 0.201173i
\(383\) 86091.0 + 86091.0i 0.586895 + 0.586895i 0.936789 0.349894i \(-0.113783\pi\)
−0.349894 + 0.936789i \(0.613783\pi\)
\(384\) 18432.0i 0.125000i
\(385\) 0 0
\(386\) −171396. −1.15034
\(387\) 88209.0 88209.0i 0.588967 0.588967i
\(388\) −58488.0 58488.0i −0.388511 0.388511i
\(389\) 75000.0i 0.495635i 0.968807 + 0.247818i \(0.0797134\pi\)
−0.968807 + 0.247818i \(0.920287\pi\)
\(390\) 0 0
\(391\) −145798. −0.953670
\(392\) 11504.0 11504.0i 0.0748646 0.0748646i
\(393\) 57222.0 + 57222.0i 0.370491 + 0.370491i
\(394\) 43884.0i 0.282692i
\(395\) 0 0
\(396\) −76464.0 −0.487603
\(397\) −29149.0 + 29149.0i −0.184945 + 0.184945i −0.793507 0.608562i \(-0.791747\pi\)
0.608562 + 0.793507i \(0.291747\pi\)
\(398\) 76320.0 + 76320.0i 0.481806 + 0.481806i
\(399\) 146160.i 0.918085i
\(400\) 0 0
\(401\) −45918.0 −0.285558 −0.142779 0.989755i \(-0.545604\pi\)
−0.142779 + 0.989755i \(0.545604\pi\)
\(402\) −27036.0 + 27036.0i −0.167298 + 0.167298i
\(403\) −13938.0 13938.0i −0.0858204 0.0858204i
\(404\) 7024.00i 0.0430350i
\(405\) 0 0
\(406\) 78880.0 0.478536
\(407\) −76818.0 + 76818.0i −0.463740 + 0.463740i
\(408\) 78048.0 + 78048.0i 0.468858 + 0.468858i
\(409\) 78720.0i 0.470585i −0.971925 0.235293i \(-0.924395\pi\)
0.971925 0.235293i \(-0.0756049\pi\)
\(410\) 0 0
\(411\) 367362. 2.17476
\(412\) −83432.0 + 83432.0i −0.491517 + 0.491517i
\(413\) 33640.0 + 33640.0i 0.197222 + 0.197222i
\(414\) 87156.0i 0.508507i
\(415\) 0 0
\(416\) 17664.0 0.102071
\(417\) 84600.0 84600.0i 0.486517 0.486517i
\(418\) 66080.0 + 66080.0i 0.378196 + 0.378196i
\(419\) 14760.0i 0.0840733i 0.999116 + 0.0420367i \(0.0133846\pi\)
−0.999116 + 0.0420367i \(0.986615\pi\)
\(420\) 0 0
\(421\) 221282. 1.24848 0.624240 0.781232i \(-0.285409\pi\)
0.624240 + 0.781232i \(0.285409\pi\)
\(422\) 145684. 145684.i 0.818063 0.818063i
\(423\) −102789. 102789.i −0.574468 0.574468i
\(424\) 19552.0i 0.108758i
\(425\) 0 0
\(426\) −231912. −1.27792
\(427\) 162342. 162342.i 0.890379 0.890379i
\(428\) −37688.0 37688.0i −0.205738 0.205738i
\(429\) 146556.i 0.796323i
\(430\) 0 0
\(431\) 212522. 1.14406 0.572031 0.820232i \(-0.306156\pi\)
0.572031 + 0.820232i \(0.306156\pi\)
\(432\) 0 0
\(433\) −145409. 145409.i −0.775560 0.775560i 0.203512 0.979072i \(-0.434764\pi\)
−0.979072 + 0.203512i \(0.934764\pi\)
\(434\) 23432.0i 0.124403i
\(435\) 0 0
\(436\) −176320. −0.927531
\(437\) −75320.0 + 75320.0i −0.394410 + 0.394410i
\(438\) −106236. 106236.i −0.553762 0.553762i
\(439\) 299440.i 1.55375i 0.629656 + 0.776874i \(0.283196\pi\)
−0.629656 + 0.776874i \(0.716804\pi\)
\(440\) 0 0
\(441\) −58239.0 −0.299459
\(442\) −74796.0 + 74796.0i −0.382855 + 0.382855i
\(443\) −240609. 240609.i −1.22604 1.22604i −0.965450 0.260590i \(-0.916083\pi\)
−0.260590 0.965450i \(-0.583917\pi\)
\(444\) 93744.0i 0.475530i
\(445\) 0 0
\(446\) 123564. 0.621187
\(447\) −124200. + 124200.i −0.621594 + 0.621594i
\(448\) −14848.0 14848.0i −0.0739796 0.0739796i
\(449\) 82480.0i 0.409125i 0.978854 + 0.204562i \(0.0655772\pi\)
−0.978854 + 0.204562i \(0.934423\pi\)
\(450\) 0 0
\(451\) −198476. −0.975787
\(452\) 16888.0 16888.0i 0.0826611 0.0826611i
\(453\) 170982. + 170982.i 0.833209 + 0.833209i
\(454\) 219644.i 1.06563i
\(455\) 0 0
\(456\) 80640.0 0.387812
\(457\) 188151. 188151.i 0.900895 0.900895i −0.0946187 0.995514i \(-0.530163\pi\)
0.995514 + 0.0946187i \(0.0301632\pi\)
\(458\) 100560. + 100560.i 0.479396 + 0.479396i
\(459\) 0 0
\(460\) 0 0
\(461\) −326158. −1.53471 −0.767355 0.641223i \(-0.778427\pi\)
−0.767355 + 0.641223i \(0.778427\pi\)
\(462\) −123192. + 123192.i −0.577163 + 0.577163i
\(463\) 218731. + 218731.i 1.02035 + 1.02035i 0.999789 + 0.0205595i \(0.00654474\pi\)
0.0205595 + 0.999789i \(0.493455\pi\)
\(464\) 43520.0i 0.202140i
\(465\) 0 0
\(466\) 9564.00 0.0440421
\(467\) −59249.0 + 59249.0i −0.271673 + 0.271673i −0.829774 0.558100i \(-0.811530\pi\)
0.558100 + 0.829774i \(0.311530\pi\)
\(468\) −44712.0 44712.0i −0.204142 0.204142i
\(469\) 43558.0i 0.198026i
\(470\) 0 0
\(471\) −294678. −1.32833
\(472\) −18560.0 + 18560.0i −0.0833094 + 0.0833094i
\(473\) 128502. + 128502.i 0.574365 + 0.574365i
\(474\) 380160.i 1.69204i
\(475\) 0 0
\(476\) 125744. 0.554975
\(477\) −49491.0 + 49491.0i −0.217515 + 0.217515i
\(478\) 35520.0 + 35520.0i 0.155459 + 0.155459i
\(479\) 273440.i 1.19177i −0.803071 0.595883i \(-0.796802\pi\)
0.803071 0.595883i \(-0.203198\pi\)
\(480\) 0 0
\(481\) −89838.0 −0.388302
\(482\) −56476.0 + 56476.0i −0.243092 + 0.243092i
\(483\) −140418. 140418.i −0.601906 0.601906i
\(484\) 5736.00i 0.0244860i
\(485\) 0 0
\(486\) −236196. −1.00000
\(487\) 123651. 123651.i 0.521362 0.521362i −0.396620 0.917983i \(-0.629817\pi\)
0.917983 + 0.396620i \(0.129817\pi\)
\(488\) 89568.0 + 89568.0i 0.376109 + 0.376109i
\(489\) 360162.i 1.50619i
\(490\) 0 0
\(491\) 198442. 0.823134 0.411567 0.911379i \(-0.364982\pi\)
0.411567 + 0.911379i \(0.364982\pi\)
\(492\) −121104. + 121104.i −0.500297 + 0.500297i
\(493\) −184280. 184280.i −0.758201 0.758201i
\(494\) 77280.0i 0.316675i
\(495\) 0 0
\(496\) −12928.0 −0.0525494
\(497\) −186818. + 186818.i −0.756321 + 0.756321i
\(498\) −224316. 224316.i −0.904485 0.904485i
\(499\) 269240.i 1.08128i −0.841254 0.540640i \(-0.818182\pi\)
0.841254 0.540640i \(-0.181818\pi\)
\(500\) 0 0
\(501\) 27882.0 0.111083
\(502\) 242004. 242004.i 0.960318 0.960318i
\(503\) −109869. 109869.i −0.434249 0.434249i 0.455822 0.890071i \(-0.349345\pi\)
−0.890071 + 0.455822i \(0.849345\pi\)
\(504\) 75168.0i 0.295918i
\(505\) 0 0
\(506\) 126968. 0.495899
\(507\) −171351. + 171351.i −0.666608 + 0.666608i
\(508\) 47272.0 + 47272.0i 0.183179 + 0.183179i
\(509\) 211000.i 0.814417i 0.913335 + 0.407209i \(0.133498\pi\)
−0.913335 + 0.407209i \(0.866502\pi\)
\(510\) 0 0
\(511\) −171158. −0.655474
\(512\) 8192.00 8192.00i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 289724.i 1.09663i
\(515\) 0 0
\(516\) 156816. 0.588967
\(517\) 149742. 149742.i 0.560225 0.560225i
\(518\) 75516.0 + 75516.0i 0.281436 + 0.281436i
\(519\) 50202.0i 0.186374i
\(520\) 0 0
\(521\) 297282. 1.09520 0.547600 0.836740i \(-0.315542\pi\)
0.547600 + 0.836740i \(0.315542\pi\)
\(522\) 110160. 110160.i 0.404281 0.404281i
\(523\) 25071.0 + 25071.0i 0.0916576 + 0.0916576i 0.751449 0.659791i \(-0.229355\pi\)
−0.659791 + 0.751449i \(0.729355\pi\)
\(524\) 50864.0i 0.185246i
\(525\) 0 0
\(526\) 59084.0 0.213549
\(527\) 54742.0 54742.0i 0.197106 0.197106i
\(528\) −67968.0 67968.0i −0.243802 0.243802i
\(529\) 135119.i 0.482842i
\(530\) 0 0
\(531\) 93960.0 0.333238
\(532\) 64960.0 64960.0i 0.229521 0.229521i
\(533\) −116058. 116058.i −0.408527 0.408527i
\(534\) 521280.i 1.82805i
\(535\) 0 0
\(536\) −24032.0 −0.0836489
\(537\) 23400.0 23400.0i 0.0811460 0.0811460i
\(538\) −179440. 179440.i −0.619947 0.619947i
\(539\) 84842.0i 0.292034i
\(540\) 0 0
\(541\) −142478. −0.486803 −0.243402 0.969926i \(-0.578263\pi\)
−0.243402 + 0.969926i \(0.578263\pi\)
\(542\) 136404. 136404.i 0.464332 0.464332i
\(543\) 399582. + 399582.i 1.35521 + 1.35521i
\(544\) 69376.0i 0.234429i
\(545\) 0 0
\(546\) −144072. −0.483275
\(547\) −291009. + 291009.i −0.972594 + 0.972594i −0.999634 0.0270399i \(-0.991392\pi\)
0.0270399 + 0.999634i \(0.491392\pi\)
\(548\) 163272. + 163272.i 0.543689 + 0.543689i
\(549\) 453438.i 1.50443i
\(550\) 0 0
\(551\) −190400. −0.627139
\(552\) 77472.0 77472.0i 0.254253 0.254253i
\(553\) 306240. + 306240.i 1.00141 + 1.00141i
\(554\) 74196.0i 0.241747i
\(555\) 0 0
\(556\) 75200.0 0.243259
\(557\) 83091.0 83091.0i 0.267820 0.267820i −0.560401 0.828221i \(-0.689353\pi\)
0.828221 + 0.560401i \(0.189353\pi\)
\(558\) 32724.0 + 32724.0i 0.105099 + 0.105099i
\(559\) 150282.i 0.480932i
\(560\) 0 0
\(561\) 575604. 1.82893
\(562\) 4644.00 4644.00i 0.0147035 0.0147035i
\(563\) −43449.0 43449.0i −0.137076 0.137076i 0.635239 0.772316i \(-0.280902\pi\)
−0.772316 + 0.635239i \(0.780902\pi\)
\(564\) 182736.i 0.574468i
\(565\) 0 0
\(566\) 366844. 1.14511
\(567\) −190269. + 190269.i −0.591837 + 0.591837i
\(568\) −103072. 103072.i −0.319480 0.319480i
\(569\) 270560.i 0.835678i 0.908521 + 0.417839i \(0.137212\pi\)
−0.908521 + 0.417839i \(0.862788\pi\)
\(570\) 0 0
\(571\) 57482.0 0.176303 0.0881515 0.996107i \(-0.471904\pi\)
0.0881515 + 0.996107i \(0.471904\pi\)
\(572\) 65136.0 65136.0i 0.199081 0.199081i
\(573\) 132102. + 132102.i 0.402346 + 0.402346i
\(574\) 195112.i 0.592189i
\(575\) 0 0
\(576\) −41472.0 −0.125000
\(577\) −195889. + 195889.i −0.588381 + 0.588381i −0.937193 0.348812i \(-0.886585\pi\)
0.348812 + 0.937193i \(0.386585\pi\)
\(578\) −126722. 126722.i −0.379312 0.379312i
\(579\) 771282.i 2.30068i
\(580\) 0 0
\(581\) −361398. −1.07062
\(582\) −263196. + 263196.i −0.777022 + 0.777022i
\(583\) −72098.0 72098.0i −0.212122 0.212122i
\(584\) 94432.0i 0.276881i
\(585\) 0 0
\(586\) 19404.0 0.0565062
\(587\) 404631. 404631.i 1.17431 1.17431i 0.193139 0.981171i \(-0.438133\pi\)
0.981171 0.193139i \(-0.0618669\pi\)
\(588\) −51768.0 51768.0i −0.149729 0.149729i
\(589\) 56560.0i 0.163034i
\(590\) 0 0
\(591\) −197478. −0.565384
\(592\) −41664.0 + 41664.0i −0.118882 + 0.118882i
\(593\) 210991. + 210991.i 0.600005 + 0.600005i 0.940314 0.340309i \(-0.110532\pi\)
−0.340309 + 0.940314i \(0.610532\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −110400. −0.310797
\(597\) 343440. 343440.i 0.963612 0.963612i
\(598\) 74244.0 + 74244.0i 0.207615 + 0.207615i
\(599\) 300560.i 0.837679i −0.908060 0.418839i \(-0.862437\pi\)
0.908060 0.418839i \(-0.137563\pi\)
\(600\) 0 0
\(601\) 367442. 1.01728 0.508639 0.860980i \(-0.330149\pi\)
0.508639 + 0.860980i \(0.330149\pi\)
\(602\) 126324. 126324.i 0.348572 0.348572i
\(603\) 60831.0 + 60831.0i 0.167298 + 0.167298i
\(604\) 151984.i 0.416605i
\(605\) 0 0
\(606\) 31608.0 0.0860700
\(607\) −146469. + 146469.i −0.397529 + 0.397529i −0.877360 0.479832i \(-0.840698\pi\)
0.479832 + 0.877360i \(0.340698\pi\)
\(608\) 35840.0 + 35840.0i 0.0969529 + 0.0969529i
\(609\) 354960.i 0.957072i
\(610\) 0 0
\(611\) 175122. 0.469092
\(612\) 175608. 175608.i 0.468858 0.468858i
\(613\) −160989. 160989.i −0.428425 0.428425i 0.459666 0.888092i \(-0.347969\pi\)
−0.888092 + 0.459666i \(0.847969\pi\)
\(614\) 171396.i 0.454636i
\(615\) 0 0
\(616\) −109504. −0.288582
\(617\) −320409. + 320409.i −0.841656 + 0.841656i −0.989074 0.147419i \(-0.952904\pi\)
0.147419 + 0.989074i \(0.452904\pi\)
\(618\) 375444. + 375444.i 0.983033 + 0.983033i
\(619\) 341160.i 0.890383i −0.895435 0.445191i \(-0.853136\pi\)
0.895435 0.445191i \(-0.146864\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −144556. + 144556.i −0.373642 + 0.373642i
\(623\) −419920. 419920.i −1.08191 1.08191i
\(624\) 79488.0i 0.204142i
\(625\) 0 0
\(626\) −72996.0 −0.186273
\(627\) 297360. 297360.i 0.756393 0.756393i
\(628\) −130968. 130968.i −0.332082 0.332082i
\(629\) 352842.i 0.891824i
\(630\) 0 0
\(631\) −390998. −0.982010 −0.491005 0.871157i \(-0.663370\pi\)
−0.491005 + 0.871157i \(0.663370\pi\)
\(632\) −168960. + 168960.i −0.423009 + 0.423009i
\(633\) −655578. 655578.i −1.63613 1.63613i
\(634\) 100596.i 0.250266i
\(635\) 0 0
\(636\) −87984.0 −0.217515
\(637\) 49611.0 49611.0i 0.122264 0.122264i
\(638\) 160480. + 160480.i 0.394257 + 0.394257i
\(639\) 521802.i 1.27792i
\(640\) 0 0
\(641\) −585038. −1.42386 −0.711931 0.702249i \(-0.752179\pi\)
−0.711931 + 0.702249i \(0.752179\pi\)
\(642\) −169596. + 169596.i −0.411477 + 0.411477i
\(643\) 31911.0 + 31911.0i 0.0771824 + 0.0771824i 0.744644 0.667462i \(-0.232619\pi\)
−0.667462 + 0.744644i \(0.732619\pi\)
\(644\) 124816.i 0.300953i
\(645\) 0 0
\(646\) −303520. −0.727315
\(647\) 280931. 280931.i 0.671106 0.671106i −0.286865 0.957971i \(-0.592613\pi\)
0.957971 + 0.286865i \(0.0926131\pi\)
\(648\) −104976. 104976.i −0.250000 0.250000i
\(649\) 136880.i 0.324975i
\(650\) 0 0
\(651\) 105444. 0.248805
\(652\) −160072. + 160072.i −0.376548 + 0.376548i
\(653\) −523989. 523989.i −1.22884 1.22884i −0.964402 0.264439i \(-0.914813\pi\)
−0.264439 0.964402i \(-0.585187\pi\)
\(654\) 793440.i 1.85506i
\(655\) 0 0
\(656\) −107648. −0.250149
\(657\) −239031. + 239031.i −0.553762 + 0.553762i
\(658\) −147204. 147204.i −0.339991 0.339991i
\(659\) 404360.i 0.931102i 0.885021 + 0.465551i \(0.154144\pi\)
−0.885021 + 0.465551i \(0.845856\pi\)
\(660\) 0 0
\(661\) −5278.00 −0.0120800 −0.00603999 0.999982i \(-0.501923\pi\)
−0.00603999 + 0.999982i \(0.501923\pi\)
\(662\) −108076. + 108076.i −0.246611 + 0.246611i
\(663\) 336582. + 336582.i 0.765709 + 0.765709i
\(664\) 199392.i 0.452243i
\(665\) 0 0
\(666\) 210924. 0.475530
\(667\) −182920. + 182920.i −0.411159 + 0.411159i
\(668\) 12392.0 + 12392.0i 0.0277708 + 0.0277708i
\(669\) 556038.i 1.24237i
\(670\) 0 0
\(671\) 660564. 1.46713
\(672\) −66816.0 + 66816.0i −0.147959 + 0.147959i
\(673\) 332111. + 332111.i 0.733252 + 0.733252i 0.971263 0.238011i \(-0.0764953\pi\)
−0.238011 + 0.971263i \(0.576495\pi\)
\(674\) 34116.0i 0.0750997i
\(675\) 0 0
\(676\) −152312. −0.333304
\(677\) −578309. + 578309.i −1.26178 + 1.26178i −0.311546 + 0.950231i \(0.600847\pi\)
−0.950231 + 0.311546i \(0.899153\pi\)
\(678\) −75996.0 75996.0i −0.165322 0.165322i
\(679\) 424038.i 0.919740i
\(680\) 0 0
\(681\) −988398. −2.13127
\(682\) −47672.0 + 47672.0i −0.102493 + 0.102493i
\(683\) 349311. + 349311.i 0.748809 + 0.748809i 0.974255 0.225447i \(-0.0723842\pi\)
−0.225447 + 0.974255i \(0.572384\pi\)
\(684\) 181440.i 0.387812i
\(685\) 0 0
\(686\) −361920. −0.769067
\(687\) 452520. 452520.i 0.958792 0.958792i
\(688\) 69696.0 + 69696.0i 0.147242 + 0.147242i
\(689\) 84318.0i 0.177616i
\(690\) 0 0
\(691\) 282762. 0.592195 0.296098 0.955158i \(-0.404315\pi\)
0.296098 + 0.955158i \(0.404315\pi\)
\(692\) −22312.0 + 22312.0i −0.0465936 + 0.0465936i
\(693\) 277182. + 277182.i 0.577163 + 0.577163i
\(694\) 226204.i 0.469658i
\(695\) 0 0
\(696\) 195840. 0.404281
\(697\) 455822. 455822.i 0.938274 0.938274i
\(698\) 45040.0 + 45040.0i 0.0924459 + 0.0924459i
\(699\) 43038.0i 0.0880841i
\(700\) 0 0
\(701\) 270242. 0.549942 0.274971 0.961453i \(-0.411332\pi\)
0.274971 + 0.961453i \(0.411332\pi\)
\(702\) 0 0
\(703\) −182280. 182280.i −0.368832 0.368832i
\(704\) 60416.0i 0.121901i
\(705\) 0 0
\(706\) 178044. 0.357205
\(707\) 25462.0 25462.0i 0.0509394 0.0509394i
\(708\) 83520.0 + 83520.0i 0.166619 + 0.166619i
\(709\) 297800.i 0.592423i 0.955122 + 0.296212i \(0.0957234\pi\)
−0.955122 + 0.296212i \(0.904277\pi\)
\(710\) 0 0
\(711\) 855360. 1.69204
\(712\) 231680. 231680.i 0.457013 0.457013i
\(713\) −54338.0 54338.0i −0.106887 0.106887i
\(714\) 565848.i 1.10995i
\(715\) 0 0
\(716\) 20800.0 0.0405730
\(717\) 159840. 159840.i 0.310919 0.310919i
\(718\) 19360.0 + 19360.0i 0.0375540 + 0.0375540i
\(719\) 913760.i 1.76756i −0.467902 0.883780i \(-0.654990\pi\)
0.467902 0.883780i \(-0.345010\pi\)
\(720\) 0 0
\(721\) 604882. 1.16359
\(722\) 103842. 103842.i 0.199204 0.199204i
\(723\) 254142. + 254142.i 0.486183 + 0.486183i
\(724\) 355184.i 0.677604i
\(725\) 0 0
\(726\) 25812.0 0.0489721
\(727\) 417651. 417651.i 0.790214 0.790214i −0.191315 0.981529i \(-0.561275\pi\)
0.981529 + 0.191315i \(0.0612751\pi\)
\(728\) −64032.0 64032.0i −0.120819 0.120819i
\(729\) 531441.i 1.00000i
\(730\) 0 0
\(731\) −590238. −1.10457
\(732\) 403056. 403056.i 0.752217 0.752217i
\(733\) −394549. 394549.i −0.734333 0.734333i 0.237142 0.971475i \(-0.423789\pi\)
−0.971475 + 0.237142i \(0.923789\pi\)
\(734\) 59884.0i 0.111152i
\(735\) 0 0
\(736\) 68864.0 0.127127
\(737\) −88618.0 + 88618.0i −0.163150 + 0.163150i
\(738\) 272484. + 272484.i 0.500297 + 0.500297i
\(739\) 109880.i 0.201201i −0.994927 0.100600i \(-0.967924\pi\)
0.994927 0.100600i \(-0.0320764\pi\)
\(740\) 0 0
\(741\) 347760. 0.633349
\(742\) −70876.0 + 70876.0i −0.128733 + 0.128733i
\(743\) 466451. + 466451.i 0.844945 + 0.844945i 0.989497 0.144552i \(-0.0461742\pi\)
−0.144552 + 0.989497i \(0.546174\pi\)
\(744\) 58176.0i 0.105099i
\(745\) 0 0
\(746\) 55244.0 0.0992676
\(747\) −504711. + 504711.i −0.904485 + 0.904485i
\(748\) 255824. + 255824.i 0.457234 + 0.457234i
\(749\) 273238.i 0.487054i
\(750\) 0 0
\(751\) 1.01092e6 1.79241 0.896206 0.443638i \(-0.146313\pi\)
0.896206 + 0.443638i \(0.146313\pi\)
\(752\) 81216.0 81216.0i 0.143617 0.143617i
\(753\) −1.08902e6 1.08902e6i −1.92064 1.92064i
\(754\) 187680.i 0.330123i
\(755\) 0 0
\(756\) 0 0
\(757\) −313269. + 313269.i −0.546671 + 0.546671i −0.925476 0.378806i \(-0.876335\pi\)
0.378806 + 0.925476i \(0.376335\pi\)
\(758\) −502160. 502160.i −0.873984 0.873984i
\(759\) 571356.i 0.991798i
\(760\) 0 0
\(761\) 142082. 0.245341 0.122670 0.992447i \(-0.460854\pi\)
0.122670 + 0.992447i \(0.460854\pi\)
\(762\) 212724. 212724.i 0.366359 0.366359i
\(763\) 639160. + 639160.i 1.09789 + 1.09789i
\(764\) 117424.i 0.201173i
\(765\) 0 0
\(766\) 344364. 0.586895
\(767\) −80040.0 + 80040.0i −0.136056 + 0.136056i
\(768\) −36864.0 36864.0i −0.0625000 0.0625000i
\(769\) 13280.0i 0.0224567i −0.999937 0.0112283i \(-0.996426\pi\)
0.999937 0.0112283i \(-0.00357417\pi\)
\(770\) 0 0
\(771\) −1.30376e6 −2.19325
\(772\) −342792. + 342792.i −0.575170 + 0.575170i
\(773\) 782211. + 782211.i 1.30908 + 1.30908i 0.922082 + 0.386994i \(0.126487\pi\)
0.386994 + 0.922082i \(0.373513\pi\)
\(774\) 352836.i 0.588967i
\(775\) 0 0
\(776\) −233952. −0.388511
\(777\) 339822. 339822.i 0.562872 0.562872i
\(778\) 150000. + 150000.i 0.247818 + 0.247818i
\(779\) 470960.i 0.776085i
\(780\) 0 0
\(781\) −760156. −1.24624
\(782\) −291596. + 291596.i −0.476835 + 0.476835i
\(783\) 0 0
\(784\) 46016.0i 0.0748646i
\(785\) 0 0
\(786\) 228888. 0.370491
\(787\) −201409. + 201409.i −0.325184 + 0.325184i −0.850752 0.525568i \(-0.823853\pi\)
0.525568 + 0.850752i \(0.323853\pi\)
\(788\) −87768.0 87768.0i −0.141346 0.141346i
\(789\) 265878.i 0.427099i
\(790\) 0 0
\(791\) −122438. −0.195688
\(792\) −152928. + 152928.i −0.243802 + 0.243802i
\(793\) 386262. + 386262.i 0.614236 + 0.614236i
\(794\) 116596.i 0.184945i
\(795\) 0 0
\(796\) 305280. 0.481806
\(797\) 36291.0 36291.0i 0.0571324 0.0571324i −0.677963 0.735096i \(-0.737137\pi\)
0.735096 + 0.677963i \(0.237137\pi\)
\(798\) −292320. 292320.i −0.459042 0.459042i
\(799\) 687798.i 1.07738i
\(800\) 0 0
\(801\) −1.17288e6 −1.82805
\(802\) −91836.0 + 91836.0i −0.142779 + 0.142779i
\(803\) −348218. 348218.i −0.540033 0.540033i
\(804\) 108144.i 0.167298i
\(805\) 0 0
\(806\) −55752.0 −0.0858204
\(807\) −807480. + 807480.i −1.23989 + 1.23989i
\(808\) 14048.0 + 14048.0i 0.0215175 + 0.0215175i
\(809\) 71600.0i 0.109400i 0.998503 + 0.0546998i \(0.0174202\pi\)
−0.998503 + 0.0546998i \(0.982580\pi\)
\(810\) 0 0
\(811\) −103318. −0.157085 −0.0785424 0.996911i \(-0.525027\pi\)
−0.0785424 + 0.996911i \(0.525027\pi\)
\(812\) 157760. 157760.i 0.239268 0.239268i
\(813\) −613818. 613818.i −0.928664 0.928664i
\(814\) 307272.i 0.463740i
\(815\) 0 0
\(816\) 312192. 0.468858
\(817\) −304920. + 304920.i −0.456817 + 0.456817i
\(818\) −157440. 157440.i −0.235293 0.235293i
\(819\) 324162.i 0.483275i
\(820\) 0 0
\(821\) −157438. −0.233573 −0.116787 0.993157i \(-0.537259\pi\)
−0.116787 + 0.993157i \(0.537259\pi\)
\(822\) 734724. 734724.i 1.08738 1.08738i
\(823\) −791309. 791309.i −1.16828 1.16828i −0.982613 0.185666i \(-0.940556\pi\)
−0.185666 0.982613i \(-0.559444\pi\)
\(824\) 333728.i 0.491517i
\(825\) 0 0
\(826\) 134560. 0.197222
\(827\) 889671. 889671.i 1.30082 1.30082i 0.372987 0.927837i \(-0.378334\pi\)
0.927837 0.372987i \(-0.121666\pi\)
\(828\) −174312. 174312.i −0.254253 0.254253i
\(829\) 618280.i 0.899655i 0.893115 + 0.449828i \(0.148515\pi\)
−0.893115 + 0.449828i \(0.851485\pi\)
\(830\) 0 0
\(831\) 333882. 0.483494
\(832\) 35328.0 35328.0i 0.0510355 0.0510355i
\(833\) 194849. + 194849.i 0.280807 + 0.280807i
\(834\) 338400.i 0.486517i
\(835\) 0 0
\(836\) 264320. 0.378196
\(837\) 0 0
\(838\) 29520.0 + 29520.0i 0.0420367 + 0.0420367i
\(839\) 821360.i 1.16684i 0.812172 + 0.583418i \(0.198285\pi\)
−0.812172 + 0.583418i \(0.801715\pi\)
\(840\) 0 0
\(841\) 244881. 0.346229
\(842\) 442564. 442564.i 0.624240 0.624240i
\(843\) −20898.0 20898.0i −0.0294069 0.0294069i
\(844\) 582736.i 0.818063i
\(845\) 0 0
\(846\) −411156. −0.574468
\(847\) 20793.0 20793.0i 0.0289835 0.0289835i
\(848\) −39104.0 39104.0i −0.0543788 0.0543788i
\(849\) 1.65080e6i 2.29023i
\(850\) 0 0
\(851\) −350238. −0.483620
\(852\) −463824. + 463824.i −0.638961 + 0.638961i
\(853\) 698291. + 698291.i 0.959706 + 0.959706i 0.999219 0.0395127i \(-0.0125806\pi\)
−0.0395127 + 0.999219i \(0.512581\pi\)
\(854\) 649368.i 0.890379i
\(855\) 0 0
\(856\) −150752. −0.205738
\(857\) −144489. + 144489.i −0.196731 + 0.196731i −0.798597 0.601866i \(-0.794424\pi\)
0.601866 + 0.798597i \(0.294424\pi\)
\(858\) −293112. 293112.i −0.398161 0.398161i
\(859\) 943480.i 1.27863i 0.768943 + 0.639317i \(0.220783\pi\)
−0.768943 + 0.639317i \(0.779217\pi\)
\(860\) 0 0
\(861\) 878004. 1.18438
\(862\) 425044. 425044.i 0.572031 0.572031i
\(863\) −438149. 438149.i −0.588302 0.588302i 0.348869 0.937171i \(-0.386566\pi\)
−0.937171 + 0.348869i \(0.886566\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −581636. −0.775560
\(867\) −570249. + 570249.i −0.758624 + 0.758624i
\(868\) 46864.0 + 46864.0i 0.0622014 + 0.0622014i
\(869\) 1.24608e6i 1.65009i
\(870\) 0 0
\(871\) −103638. −0.136610
\(872\) −352640. + 352640.i −0.463766 + 0.463766i
\(873\) 592191. + 592191.i 0.777022 + 0.777022i
\(874\) 301280.i 0.394410i
\(875\) 0 0
\(876\) −424944. −0.553762
\(877\) −281469. + 281469.i −0.365958 + 0.365958i −0.866001 0.500043i \(-0.833318\pi\)
0.500043 + 0.866001i \(0.333318\pi\)
\(878\) 598880. + 598880.i 0.776874 + 0.776874i
\(879\) 87318.0i 0.113012i
\(880\) 0 0
\(881\) 876722. 1.12956 0.564781 0.825241i \(-0.308961\pi\)
0.564781 + 0.825241i \(0.308961\pi\)
\(882\) −116478. + 116478.i −0.149729 + 0.149729i
\(883\) 327431. + 327431.i 0.419951 + 0.419951i 0.885187 0.465236i \(-0.154031\pi\)
−0.465236 + 0.885187i \(0.654031\pi\)
\(884\) 299184.i 0.382855i
\(885\) 0 0
\(886\) −962436. −1.22604
\(887\) 477171. 477171.i 0.606494 0.606494i −0.335534 0.942028i \(-0.608917\pi\)
0.942028 + 0.335534i \(0.108917\pi\)
\(888\) 187488. + 187488.i 0.237765 + 0.237765i
\(889\) 342722.i 0.433649i
\(890\) 0 0
\(891\) −774198. −0.975207
\(892\) 247128. 247128.i 0.310593 0.310593i
\(893\) 355320. + 355320.i 0.445571 + 0.445571i
\(894\) 496800.i 0.621594i
\(895\) 0 0
\(896\) −59392.0 −0.0739796
\(897\) 334098. 334098.i 0.415230 0.415230i
\(898\) 164960. + 164960.i 0.204562 + 0.204562i
\(899\) 137360.i 0.169958i
\(900\) 0 0
\(901\) 331162. 0.407935
\(902\) −396952. + 396952.i −0.487893 + 0.487893i
\(903\) −568458. 568458.i −0.697145 0.697145i
\(904\) 67552.0i 0.0826611i
\(905\) 0 0
\(906\) 683928. 0.833209
\(907\) −1.11209e6 + 1.11209e6i −1.35184 + 1.35184i −0.468235 + 0.883604i \(0.655110\pi\)
−0.883604 + 0.468235i \(0.844890\pi\)
\(908\) −439288. 439288.i −0.532816 0.532816i
\(909\) 71118.0i 0.0860700i
\(910\) 0 0
\(911\) −883958. −1.06511 −0.532556 0.846395i \(-0.678768\pi\)
−0.532556 + 0.846395i \(0.678768\pi\)
\(912\) 161280. 161280.i 0.193906 0.193906i
\(913\) −735258. 735258.i −0.882060 0.882060i
\(914\) 752604.i 0.900895i
\(915\) 0 0
\(916\) 402240. 0.479396
\(917\) 184382. 184382.i 0.219270 0.219270i
\(918\) 0 0
\(919\) 1.24040e6i 1.46869i −0.678775 0.734346i \(-0.737489\pi\)
0.678775 0.734346i \(-0.262511\pi\)
\(920\) 0 0
\(921\) 771282. 0.909272
\(922\) −652316. + 652316.i −0.767355 + 0.767355i
\(923\) −444498. 444498.i −0.521755 0.521755i
\(924\) 492768.i 0.577163i
\(925\) 0 0
\(926\) 874924. 1.02035
\(927\) 844749. 844749.i 0.983033 0.983033i
\(928\) 87040.0 + 87040.0i 0.101070 + 0.101070i
\(929\) 1.22744e6i 1.42223i −0.703077 0.711113i \(-0.748191\pi\)
0.703077 0.711113i \(-0.251809\pi\)
\(930\) 0 0
\(931\) 201320. 0.232267
\(932\) 19128.0 19128.0i 0.0220210 0.0220210i
\(933\) 650502. + 650502.i 0.747283 + 0.747283i
\(934\) 236996.i 0.271673i
\(935\) 0 0
\(936\) −178848. −0.204142
\(937\) 1.07047e6 1.07047e6i 1.21926 1.21926i 0.251366 0.967892i \(-0.419120\pi\)
0.967892 0.251366i \(-0.0808799\pi\)
\(938\) 87116.0 + 87116.0i 0.0990130 + 0.0990130i
\(939\) 328482.i 0.372546i
\(940\) 0 0
\(941\) 558642. 0.630891 0.315446 0.948944i \(-0.397846\pi\)
0.315446 + 0.948944i \(0.397846\pi\)
\(942\) −589356. + 589356.i −0.664165 + 0.664165i
\(943\) −452458. 452458.i −0.508809 0.508809i
\(944\) 74240.0i 0.0833094i
\(945\) 0 0
\(946\) 514008. 0.574365
\(947\) 191711. 191711.i 0.213770 0.213770i −0.592097 0.805867i \(-0.701700\pi\)
0.805867 + 0.592097i \(0.201700\pi\)
\(948\) 760320. + 760320.i 0.846018 + 0.846018i
\(949\) 407238.i 0.452185i
\(950\) 0 0
\(951\) 452682. 0.500532
\(952\) 251488. 251488.i 0.277487 0.277487i
\(953\) 630231. + 630231.i 0.693927 + 0.693927i 0.963094 0.269166i \(-0.0867482\pi\)
−0.269166 + 0.963094i \(0.586748\pi\)
\(954\) 197964.i 0.217515i
\(955\) 0 0
\(956\) 142080. 0.155459
\(957\) 722160. 722160.i 0.788514 0.788514i
\(958\) −546880. 546880.i −0.595883 0.595883i
\(959\) 1.18372e6i 1.28710i
\(960\) 0 0
\(961\) −882717. −0.955817
\(962\) −179676. + 179676.i −0.194151 + 0.194151i
\(963\) 381591. + 381591.i 0.411477 + 0.411477i
\(964\) 225904.i 0.243092i
\(965\) 0 0
\(966\) −561672. −0.601906
\(967\) 345491. 345491.i 0.369474 0.369474i −0.497811 0.867285i \(-0.665863\pi\)
0.867285 + 0.497811i \(0.165863\pi\)
\(968\) 11472.0 + 11472.0i 0.0122430 + 0.0122430i
\(969\) 1.36584e6i 1.45463i
\(970\) 0 0
\(971\) 1.08308e6 1.14874 0.574372 0.818595i \(-0.305247\pi\)
0.574372 + 0.818595i \(0.305247\pi\)
\(972\) −472392. + 472392.i −0.500000 + 0.500000i
\(973\) −272600. 272600.i −0.287939 0.287939i
\(974\) 494604.i 0.521362i
\(975\) 0 0
\(976\) 358272. 0.376109
\(977\) 146751. 146751.i 0.153742 0.153742i −0.626045 0.779787i \(-0.715327\pi\)
0.779787 + 0.626045i \(0.215327\pi\)
\(978\) 720324. + 720324.i 0.753096 + 0.753096i
\(979\) 1.70864e6i 1.78273i
\(980\) 0 0
\(981\) 1.78524e6 1.85506
\(982\) 396884. 396884.i 0.411567 0.411567i
\(983\) −466909. 466909.i −0.483198 0.483198i 0.422953 0.906151i \(-0.360993\pi\)
−0.906151 + 0.422953i \(0.860993\pi\)
\(984\) 484416.i 0.500297i
\(985\) 0 0
\(986\) −737120. −0.758201
\(987\) −662418. + 662418.i −0.679983 + 0.679983i
\(988\) 154560. + 154560.i 0.158337 + 0.158337i
\(989\) 585882.i 0.598987i
\(990\) 0 0
\(991\) −901238. −0.917682 −0.458841 0.888518i \(-0.651735\pi\)
−0.458841 + 0.888518i \(0.651735\pi\)
\(992\) −25856.0 + 25856.0i −0.0262747 + 0.0262747i
\(993\) 486342. + 486342.i 0.493223 + 0.493223i
\(994\) 747272.i 0.756321i
\(995\) 0 0
\(996\) −897264. −0.904485
\(997\) −152149. + 152149.i −0.153066 + 0.153066i −0.779486 0.626420i \(-0.784520\pi\)
0.626420 + 0.779486i \(0.284520\pi\)
\(998\) −538480. 538480.i −0.540640 0.540640i
\(999\) 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 50.5.c.b.43.1 2
3.2 odd 2 450.5.g.a.343.1 2
4.3 odd 2 400.5.p.c.193.1 2
5.2 odd 4 inner 50.5.c.b.7.1 2
5.3 odd 4 10.5.c.a.7.1 yes 2
5.4 even 2 10.5.c.a.3.1 2
15.2 even 4 450.5.g.a.307.1 2
15.8 even 4 90.5.g.b.37.1 2
15.14 odd 2 90.5.g.b.73.1 2
20.3 even 4 80.5.p.b.17.1 2
20.7 even 4 400.5.p.c.257.1 2
20.19 odd 2 80.5.p.b.33.1 2
40.3 even 4 320.5.p.i.257.1 2
40.13 odd 4 320.5.p.b.257.1 2
40.19 odd 2 320.5.p.i.193.1 2
40.29 even 2 320.5.p.b.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.5.c.a.3.1 2 5.4 even 2
10.5.c.a.7.1 yes 2 5.3 odd 4
50.5.c.b.7.1 2 5.2 odd 4 inner
50.5.c.b.43.1 2 1.1 even 1 trivial
80.5.p.b.17.1 2 20.3 even 4
80.5.p.b.33.1 2 20.19 odd 2
90.5.g.b.37.1 2 15.8 even 4
90.5.g.b.73.1 2 15.14 odd 2
320.5.p.b.193.1 2 40.29 even 2
320.5.p.b.257.1 2 40.13 odd 4
320.5.p.i.193.1 2 40.19 odd 2
320.5.p.i.257.1 2 40.3 even 4
400.5.p.c.193.1 2 4.3 odd 2
400.5.p.c.257.1 2 20.7 even 4
450.5.g.a.307.1 2 15.2 even 4
450.5.g.a.343.1 2 3.2 odd 2