Properties

Label 650.6.a.j.1.1
Level $650$
Weight $6$
Character 650.1
Self dual yes
Analytic conductor $104.249$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [650,6,Mod(1,650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(650, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("650.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 650.a (trivial)

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: yes
Analytic conductor: \(104.249482878\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1458804.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 361x - 1139 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 130)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-16.6075\) of defining polynomial
Character \(\chi\) \(=\) 650.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} -9.60750 q^{3} +16.0000 q^{4} -38.4300 q^{6} -16.6832 q^{7} +64.0000 q^{8} -150.696 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} -9.60750 q^{3} +16.0000 q^{4} -38.4300 q^{6} -16.6832 q^{7} +64.0000 q^{8} -150.696 q^{9} -693.425 q^{11} -153.720 q^{12} -169.000 q^{13} -66.7328 q^{14} +256.000 q^{16} -826.423 q^{17} -602.784 q^{18} -1787.39 q^{19} +160.284 q^{21} -2773.70 q^{22} +2375.24 q^{23} -614.880 q^{24} -676.000 q^{26} +3782.43 q^{27} -266.931 q^{28} +2020.54 q^{29} +6723.34 q^{31} +1024.00 q^{32} +6662.08 q^{33} -3305.69 q^{34} -2411.14 q^{36} +2855.18 q^{37} -7149.54 q^{38} +1623.67 q^{39} -19394.3 q^{41} +641.135 q^{42} +14028.7 q^{43} -11094.8 q^{44} +9500.97 q^{46} +19989.2 q^{47} -2459.52 q^{48} -16528.7 q^{49} +7939.86 q^{51} -2704.00 q^{52} -3915.90 q^{53} +15129.7 q^{54} -1067.72 q^{56} +17172.3 q^{57} +8082.17 q^{58} -24027.0 q^{59} +34515.9 q^{61} +26893.4 q^{62} +2514.09 q^{63} +4096.00 q^{64} +26648.3 q^{66} -20445.0 q^{67} -13222.8 q^{68} -22820.1 q^{69} +43931.2 q^{71} -9644.54 q^{72} +18271.5 q^{73} +11420.7 q^{74} -28598.2 q^{76} +11568.5 q^{77} +6494.67 q^{78} -41359.0 q^{79} +279.391 q^{81} -77577.4 q^{82} -58383.5 q^{83} +2564.54 q^{84} +56114.6 q^{86} -19412.3 q^{87} -44379.2 q^{88} +48741.2 q^{89} +2819.46 q^{91} +38003.9 q^{92} -64594.5 q^{93} +79956.9 q^{94} -9838.08 q^{96} +151991. q^{97} -66114.7 q^{98} +104496. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 12 q^{2} + 22 q^{3} + 48 q^{4} + 88 q^{6} + 234 q^{7} + 192 q^{8} + 155 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 12 q^{2} + 22 q^{3} + 48 q^{4} + 88 q^{6} + 234 q^{7} + 192 q^{8} + 155 q^{9} + 48 q^{11} + 352 q^{12} - 507 q^{13} + 936 q^{14} + 768 q^{16} - 1506 q^{17} + 620 q^{18} - 360 q^{19} + 6904 q^{21} + 192 q^{22} + 2370 q^{23} + 1408 q^{24} - 2028 q^{26} + 10168 q^{27} + 3744 q^{28} - 3078 q^{29} - 5388 q^{31} + 3072 q^{32} + 22572 q^{33} - 6024 q^{34} + 2480 q^{36} + 25362 q^{37} - 1440 q^{38} - 3718 q^{39} - 15906 q^{41} + 27616 q^{42} + 39306 q^{43} + 768 q^{44} + 9480 q^{46} + 17778 q^{47} + 5632 q^{48} + 7767 q^{49} - 33972 q^{51} - 8112 q^{52} - 9246 q^{53} + 40672 q^{54} + 14976 q^{56} + 2996 q^{57} - 12312 q^{58} - 77760 q^{59} + 17982 q^{61} - 21552 q^{62} + 128762 q^{63} + 12288 q^{64} + 90288 q^{66} + 2922 q^{67} - 24096 q^{68} - 31860 q^{69} - 4944 q^{71} + 9920 q^{72} - 43278 q^{73} + 101448 q^{74} - 5760 q^{76} + 144420 q^{77} - 14872 q^{78} + 42120 q^{79} + 146519 q^{81} - 63624 q^{82} - 58098 q^{83} + 110464 q^{84} + 157224 q^{86} - 2016 q^{87} + 3072 q^{88} + 19614 q^{89} - 39546 q^{91} + 37920 q^{92} - 162796 q^{93} + 71112 q^{94} + 22528 q^{96} + 87078 q^{97} + 31068 q^{98} + 350340 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) −9.60750 −0.616321 −0.308161 0.951334i \(-0.599713\pi\)
−0.308161 + 0.951334i \(0.599713\pi\)
\(4\) 16.0000 0.500000
\(5\) 0 0
\(6\) −38.4300 −0.435805
\(7\) −16.6832 −0.128687 −0.0643434 0.997928i \(-0.520495\pi\)
−0.0643434 + 0.997928i \(0.520495\pi\)
\(8\) 64.0000 0.353553
\(9\) −150.696 −0.620148
\(10\) 0 0
\(11\) −693.425 −1.72790 −0.863948 0.503580i \(-0.832016\pi\)
−0.863948 + 0.503580i \(0.832016\pi\)
\(12\) −153.720 −0.308161
\(13\) −169.000 −0.277350
\(14\) −66.7328 −0.0909953
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) −826.423 −0.693553 −0.346777 0.937948i \(-0.612724\pi\)
−0.346777 + 0.937948i \(0.612724\pi\)
\(18\) −602.784 −0.438511
\(19\) −1787.39 −1.13588 −0.567942 0.823068i \(-0.692260\pi\)
−0.567942 + 0.823068i \(0.692260\pi\)
\(20\) 0 0
\(21\) 160.284 0.0793124
\(22\) −2773.70 −1.22181
\(23\) 2375.24 0.936242 0.468121 0.883664i \(-0.344931\pi\)
0.468121 + 0.883664i \(0.344931\pi\)
\(24\) −614.880 −0.217903
\(25\) 0 0
\(26\) −676.000 −0.196116
\(27\) 3782.43 0.998532
\(28\) −266.931 −0.0643434
\(29\) 2020.54 0.446142 0.223071 0.974802i \(-0.428392\pi\)
0.223071 + 0.974802i \(0.428392\pi\)
\(30\) 0 0
\(31\) 6723.34 1.25655 0.628277 0.777990i \(-0.283760\pi\)
0.628277 + 0.777990i \(0.283760\pi\)
\(32\) 1024.00 0.176777
\(33\) 6662.08 1.06494
\(34\) −3305.69 −0.490416
\(35\) 0 0
\(36\) −2411.14 −0.310074
\(37\) 2855.18 0.342870 0.171435 0.985195i \(-0.445160\pi\)
0.171435 + 0.985195i \(0.445160\pi\)
\(38\) −7149.54 −0.803192
\(39\) 1623.67 0.170937
\(40\) 0 0
\(41\) −19394.3 −1.80184 −0.900918 0.433989i \(-0.857106\pi\)
−0.900918 + 0.433989i \(0.857106\pi\)
\(42\) 641.135 0.0560823
\(43\) 14028.7 1.15703 0.578515 0.815672i \(-0.303632\pi\)
0.578515 + 0.815672i \(0.303632\pi\)
\(44\) −11094.8 −0.863948
\(45\) 0 0
\(46\) 9500.97 0.662023
\(47\) 19989.2 1.31993 0.659966 0.751296i \(-0.270571\pi\)
0.659966 + 0.751296i \(0.270571\pi\)
\(48\) −2459.52 −0.154080
\(49\) −16528.7 −0.983440
\(50\) 0 0
\(51\) 7939.86 0.427452
\(52\) −2704.00 −0.138675
\(53\) −3915.90 −0.191488 −0.0957441 0.995406i \(-0.530523\pi\)
−0.0957441 + 0.995406i \(0.530523\pi\)
\(54\) 15129.7 0.706069
\(55\) 0 0
\(56\) −1067.72 −0.0454977
\(57\) 17172.3 0.700070
\(58\) 8082.17 0.315470
\(59\) −24027.0 −0.898605 −0.449303 0.893380i \(-0.648327\pi\)
−0.449303 + 0.893380i \(0.648327\pi\)
\(60\) 0 0
\(61\) 34515.9 1.18767 0.593833 0.804588i \(-0.297614\pi\)
0.593833 + 0.804588i \(0.297614\pi\)
\(62\) 26893.4 0.888518
\(63\) 2514.09 0.0798049
\(64\) 4096.00 0.125000
\(65\) 0 0
\(66\) 26648.3 0.753026
\(67\) −20445.0 −0.556417 −0.278208 0.960521i \(-0.589741\pi\)
−0.278208 + 0.960521i \(0.589741\pi\)
\(68\) −13222.8 −0.346777
\(69\) −22820.1 −0.577026
\(70\) 0 0
\(71\) 43931.2 1.03426 0.517128 0.855908i \(-0.327001\pi\)
0.517128 + 0.855908i \(0.327001\pi\)
\(72\) −9644.54 −0.219255
\(73\) 18271.5 0.401297 0.200649 0.979663i \(-0.435695\pi\)
0.200649 + 0.979663i \(0.435695\pi\)
\(74\) 11420.7 0.242445
\(75\) 0 0
\(76\) −28598.2 −0.567942
\(77\) 11568.5 0.222358
\(78\) 6494.67 0.120871
\(79\) −41359.0 −0.745593 −0.372797 0.927913i \(-0.621601\pi\)
−0.372797 + 0.927913i \(0.621601\pi\)
\(80\) 0 0
\(81\) 279.391 0.00473152
\(82\) −77577.4 −1.27409
\(83\) −58383.5 −0.930240 −0.465120 0.885248i \(-0.653989\pi\)
−0.465120 + 0.885248i \(0.653989\pi\)
\(84\) 2564.54 0.0396562
\(85\) 0 0
\(86\) 56114.6 0.818144
\(87\) −19412.3 −0.274967
\(88\) −44379.2 −0.610904
\(89\) 48741.2 0.652261 0.326130 0.945325i \(-0.394255\pi\)
0.326130 + 0.945325i \(0.394255\pi\)
\(90\) 0 0
\(91\) 2819.46 0.0356913
\(92\) 38003.9 0.468121
\(93\) −64594.5 −0.774441
\(94\) 79956.9 0.933333
\(95\) 0 0
\(96\) −9838.08 −0.108951
\(97\) 151991. 1.64017 0.820084 0.572244i \(-0.193927\pi\)
0.820084 + 0.572244i \(0.193927\pi\)
\(98\) −66114.7 −0.695397
\(99\) 104496. 1.07155
\(100\) 0 0
\(101\) 116976. 1.14102 0.570512 0.821290i \(-0.306745\pi\)
0.570512 + 0.821290i \(0.306745\pi\)
\(102\) 31759.4 0.302254
\(103\) −123435. −1.14642 −0.573211 0.819408i \(-0.694302\pi\)
−0.573211 + 0.819408i \(0.694302\pi\)
\(104\) −10816.0 −0.0980581
\(105\) 0 0
\(106\) −15663.6 −0.135403
\(107\) 158700. 1.34004 0.670021 0.742342i \(-0.266285\pi\)
0.670021 + 0.742342i \(0.266285\pi\)
\(108\) 60518.9 0.499266
\(109\) −43201.2 −0.348281 −0.174140 0.984721i \(-0.555715\pi\)
−0.174140 + 0.984721i \(0.555715\pi\)
\(110\) 0 0
\(111\) −27431.1 −0.211318
\(112\) −4270.90 −0.0321717
\(113\) 6402.49 0.0471685 0.0235843 0.999722i \(-0.492492\pi\)
0.0235843 + 0.999722i \(0.492492\pi\)
\(114\) 68689.2 0.495024
\(115\) 0 0
\(116\) 32328.7 0.223071
\(117\) 25467.6 0.171998
\(118\) −96107.8 −0.635410
\(119\) 13787.4 0.0892512
\(120\) 0 0
\(121\) 319787. 1.98563
\(122\) 138063. 0.839807
\(123\) 186331. 1.11051
\(124\) 107574. 0.628277
\(125\) 0 0
\(126\) 10056.4 0.0564306
\(127\) −126776. −0.697475 −0.348737 0.937221i \(-0.613389\pi\)
−0.348737 + 0.937221i \(0.613389\pi\)
\(128\) 16384.0 0.0883883
\(129\) −134780. −0.713103
\(130\) 0 0
\(131\) −374014. −1.90419 −0.952093 0.305808i \(-0.901073\pi\)
−0.952093 + 0.305808i \(0.901073\pi\)
\(132\) 106593. 0.532470
\(133\) 29819.3 0.146173
\(134\) −81780.0 −0.393446
\(135\) 0 0
\(136\) −52891.1 −0.245208
\(137\) 360787. 1.64229 0.821144 0.570721i \(-0.193336\pi\)
0.821144 + 0.570721i \(0.193336\pi\)
\(138\) −91280.5 −0.408019
\(139\) 406503. 1.78454 0.892271 0.451499i \(-0.149111\pi\)
0.892271 + 0.451499i \(0.149111\pi\)
\(140\) 0 0
\(141\) −192047. −0.813502
\(142\) 175725. 0.731329
\(143\) 117189. 0.479232
\(144\) −38578.2 −0.155037
\(145\) 0 0
\(146\) 73085.9 0.283760
\(147\) 158799. 0.606115
\(148\) 45682.9 0.171435
\(149\) 128834. 0.475407 0.237704 0.971338i \(-0.423605\pi\)
0.237704 + 0.971338i \(0.423605\pi\)
\(150\) 0 0
\(151\) 180055. 0.642634 0.321317 0.946972i \(-0.395874\pi\)
0.321317 + 0.946972i \(0.395874\pi\)
\(152\) −114393. −0.401596
\(153\) 124539. 0.430106
\(154\) 46274.2 0.157231
\(155\) 0 0
\(156\) 25978.7 0.0854684
\(157\) −321316. −1.04036 −0.520180 0.854057i \(-0.674135\pi\)
−0.520180 + 0.854057i \(0.674135\pi\)
\(158\) −165436. −0.527214
\(159\) 37622.0 0.118018
\(160\) 0 0
\(161\) −39626.6 −0.120482
\(162\) 1117.57 0.00334569
\(163\) 135115. 0.398322 0.199161 0.979967i \(-0.436178\pi\)
0.199161 + 0.979967i \(0.436178\pi\)
\(164\) −310309. −0.900918
\(165\) 0 0
\(166\) −233534. −0.657779
\(167\) −101528. −0.281705 −0.140853 0.990031i \(-0.544984\pi\)
−0.140853 + 0.990031i \(0.544984\pi\)
\(168\) 10258.2 0.0280412
\(169\) 28561.0 0.0769231
\(170\) 0 0
\(171\) 269352. 0.704417
\(172\) 224458. 0.578515
\(173\) −309597. −0.786470 −0.393235 0.919438i \(-0.628644\pi\)
−0.393235 + 0.919438i \(0.628644\pi\)
\(174\) −77649.4 −0.194431
\(175\) 0 0
\(176\) −177517. −0.431974
\(177\) 230839. 0.553829
\(178\) 194965. 0.461218
\(179\) −191098. −0.445782 −0.222891 0.974843i \(-0.571549\pi\)
−0.222891 + 0.974843i \(0.571549\pi\)
\(180\) 0 0
\(181\) 694442. 1.57558 0.787789 0.615945i \(-0.211226\pi\)
0.787789 + 0.615945i \(0.211226\pi\)
\(182\) 11277.8 0.0252376
\(183\) −331611. −0.731984
\(184\) 152015. 0.331012
\(185\) 0 0
\(186\) −258378. −0.547612
\(187\) 573062. 1.19839
\(188\) 319828. 0.659966
\(189\) −63103.1 −0.128498
\(190\) 0 0
\(191\) −581263. −1.15289 −0.576447 0.817135i \(-0.695561\pi\)
−0.576447 + 0.817135i \(0.695561\pi\)
\(192\) −39352.3 −0.0770402
\(193\) −53201.0 −0.102808 −0.0514039 0.998678i \(-0.516370\pi\)
−0.0514039 + 0.998678i \(0.516370\pi\)
\(194\) 607963. 1.15977
\(195\) 0 0
\(196\) −264459. −0.491720
\(197\) 877908. 1.61170 0.805848 0.592122i \(-0.201710\pi\)
0.805848 + 0.592122i \(0.201710\pi\)
\(198\) 417985. 0.757702
\(199\) 1.03412e6 1.85114 0.925571 0.378574i \(-0.123585\pi\)
0.925571 + 0.378574i \(0.123585\pi\)
\(200\) 0 0
\(201\) 196425. 0.342931
\(202\) 467905. 0.806825
\(203\) −33709.1 −0.0574125
\(204\) 127038. 0.213726
\(205\) 0 0
\(206\) −493739. −0.810642
\(207\) −357939. −0.580609
\(208\) −43264.0 −0.0693375
\(209\) 1.23942e6 1.96269
\(210\) 0 0
\(211\) −46774.3 −0.0723271 −0.0361635 0.999346i \(-0.511514\pi\)
−0.0361635 + 0.999346i \(0.511514\pi\)
\(212\) −62654.4 −0.0957441
\(213\) −422069. −0.637434
\(214\) 634801. 0.947552
\(215\) 0 0
\(216\) 242076. 0.353034
\(217\) −112167. −0.161702
\(218\) −172805. −0.246272
\(219\) −175543. −0.247328
\(220\) 0 0
\(221\) 139665. 0.192357
\(222\) −109725. −0.149424
\(223\) 302978. 0.407990 0.203995 0.978972i \(-0.434607\pi\)
0.203995 + 0.978972i \(0.434607\pi\)
\(224\) −17083.6 −0.0227488
\(225\) 0 0
\(226\) 25609.9 0.0333532
\(227\) 581763. 0.749345 0.374672 0.927157i \(-0.377755\pi\)
0.374672 + 0.927157i \(0.377755\pi\)
\(228\) 274757. 0.350035
\(229\) 53955.7 0.0679905 0.0339953 0.999422i \(-0.489177\pi\)
0.0339953 + 0.999422i \(0.489177\pi\)
\(230\) 0 0
\(231\) −111145. −0.137044
\(232\) 129315. 0.157735
\(233\) −897805. −1.08341 −0.541704 0.840569i \(-0.682221\pi\)
−0.541704 + 0.840569i \(0.682221\pi\)
\(234\) 101870. 0.121621
\(235\) 0 0
\(236\) −384431. −0.449303
\(237\) 397356. 0.459525
\(238\) 55149.5 0.0631101
\(239\) −1.02657e6 −1.16250 −0.581251 0.813724i \(-0.697437\pi\)
−0.581251 + 0.813724i \(0.697437\pi\)
\(240\) 0 0
\(241\) 1.13459e6 1.25833 0.629167 0.777270i \(-0.283396\pi\)
0.629167 + 0.777270i \(0.283396\pi\)
\(242\) 1.27915e6 1.40405
\(243\) −921816. −1.00145
\(244\) 552254. 0.593833
\(245\) 0 0
\(246\) 745324. 0.785249
\(247\) 302068. 0.315038
\(248\) 430294. 0.444259
\(249\) 560919. 0.573327
\(250\) 0 0
\(251\) −697428. −0.698740 −0.349370 0.936985i \(-0.613604\pi\)
−0.349370 + 0.936985i \(0.613604\pi\)
\(252\) 40225.4 0.0399024
\(253\) −1.64705e6 −1.61773
\(254\) −507105. −0.493189
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) −1.56660e6 −1.47954 −0.739770 0.672860i \(-0.765066\pi\)
−0.739770 + 0.672860i \(0.765066\pi\)
\(258\) −539121. −0.504240
\(259\) −47633.5 −0.0441228
\(260\) 0 0
\(261\) −304487. −0.276674
\(262\) −1.49606e6 −1.34646
\(263\) 1.03876e6 0.926028 0.463014 0.886351i \(-0.346768\pi\)
0.463014 + 0.886351i \(0.346768\pi\)
\(264\) 426373. 0.376513
\(265\) 0 0
\(266\) 119277. 0.103360
\(267\) −468281. −0.402002
\(268\) −327120. −0.278208
\(269\) 107944. 0.0909532 0.0454766 0.998965i \(-0.485519\pi\)
0.0454766 + 0.998965i \(0.485519\pi\)
\(270\) 0 0
\(271\) −1.06092e6 −0.877528 −0.438764 0.898602i \(-0.644584\pi\)
−0.438764 + 0.898602i \(0.644584\pi\)
\(272\) −211564. −0.173388
\(273\) −27087.9 −0.0219973
\(274\) 1.44315e6 1.16127
\(275\) 0 0
\(276\) −365122. −0.288513
\(277\) −523617. −0.410028 −0.205014 0.978759i \(-0.565724\pi\)
−0.205014 + 0.978759i \(0.565724\pi\)
\(278\) 1.62601e6 1.26186
\(279\) −1.01318e6 −0.779249
\(280\) 0 0
\(281\) 1.24579e6 0.941192 0.470596 0.882349i \(-0.344039\pi\)
0.470596 + 0.882349i \(0.344039\pi\)
\(282\) −768186. −0.575233
\(283\) −772266. −0.573193 −0.286597 0.958051i \(-0.592524\pi\)
−0.286597 + 0.958051i \(0.592524\pi\)
\(284\) 702900. 0.517128
\(285\) 0 0
\(286\) 468755. 0.338868
\(287\) 323559. 0.231873
\(288\) −154313. −0.109628
\(289\) −736882. −0.518984
\(290\) 0 0
\(291\) −1.46025e6 −1.01087
\(292\) 292343. 0.200649
\(293\) −1.55416e6 −1.05761 −0.528806 0.848743i \(-0.677360\pi\)
−0.528806 + 0.848743i \(0.677360\pi\)
\(294\) 635197. 0.428588
\(295\) 0 0
\(296\) 182731. 0.121223
\(297\) −2.62283e6 −1.72536
\(298\) 515337. 0.336164
\(299\) −401416. −0.259667
\(300\) 0 0
\(301\) −234043. −0.148895
\(302\) 720222. 0.454411
\(303\) −1.12385e6 −0.703237
\(304\) −457571. −0.283971
\(305\) 0 0
\(306\) 498154. 0.304131
\(307\) 836762. 0.506706 0.253353 0.967374i \(-0.418467\pi\)
0.253353 + 0.967374i \(0.418467\pi\)
\(308\) 185097. 0.111179
\(309\) 1.18590e6 0.706564
\(310\) 0 0
\(311\) 2.18576e6 1.28145 0.640724 0.767772i \(-0.278634\pi\)
0.640724 + 0.767772i \(0.278634\pi\)
\(312\) 103915. 0.0604353
\(313\) −1.05261e6 −0.607307 −0.303654 0.952782i \(-0.598207\pi\)
−0.303654 + 0.952782i \(0.598207\pi\)
\(314\) −1.28526e6 −0.735645
\(315\) 0 0
\(316\) −661744. −0.372797
\(317\) 1.09831e6 0.613872 0.306936 0.951730i \(-0.400696\pi\)
0.306936 + 0.951730i \(0.400696\pi\)
\(318\) 150488. 0.0834515
\(319\) −1.40109e6 −0.770887
\(320\) 0 0
\(321\) −1.52471e6 −0.825896
\(322\) −158506. −0.0851936
\(323\) 1.47714e6 0.787797
\(324\) 4470.26 0.00236576
\(325\) 0 0
\(326\) 540460. 0.281656
\(327\) 415055. 0.214653
\(328\) −1.24124e6 −0.637045
\(329\) −333484. −0.169858
\(330\) 0 0
\(331\) 2.32534e6 1.16659 0.583293 0.812262i \(-0.301764\pi\)
0.583293 + 0.812262i \(0.301764\pi\)
\(332\) −934136. −0.465120
\(333\) −430264. −0.212630
\(334\) −406112. −0.199196
\(335\) 0 0
\(336\) 41032.6 0.0198281
\(337\) 2.86939e6 1.37630 0.688152 0.725567i \(-0.258422\pi\)
0.688152 + 0.725567i \(0.258422\pi\)
\(338\) 114244. 0.0543928
\(339\) −61511.9 −0.0290710
\(340\) 0 0
\(341\) −4.66214e6 −2.17120
\(342\) 1.07741e6 0.498098
\(343\) 556145. 0.255242
\(344\) 897834. 0.409072
\(345\) 0 0
\(346\) −1.23839e6 −0.556118
\(347\) 3.31346e6 1.47726 0.738632 0.674109i \(-0.235472\pi\)
0.738632 + 0.674109i \(0.235472\pi\)
\(348\) −310598. −0.137483
\(349\) −3.47506e6 −1.52721 −0.763605 0.645684i \(-0.776572\pi\)
−0.763605 + 0.645684i \(0.776572\pi\)
\(350\) 0 0
\(351\) −639231. −0.276943
\(352\) −710067. −0.305452
\(353\) 2.82052e6 1.20474 0.602368 0.798218i \(-0.294224\pi\)
0.602368 + 0.798218i \(0.294224\pi\)
\(354\) 923356. 0.391617
\(355\) 0 0
\(356\) 779859. 0.326130
\(357\) −132462. −0.0550074
\(358\) −764390. −0.315215
\(359\) −2.32351e6 −0.951500 −0.475750 0.879580i \(-0.657823\pi\)
−0.475750 + 0.879580i \(0.657823\pi\)
\(360\) 0 0
\(361\) 718647. 0.290234
\(362\) 2.77777e6 1.11410
\(363\) −3.07236e6 −1.22378
\(364\) 45111.3 0.0178456
\(365\) 0 0
\(366\) −1.32644e6 −0.517591
\(367\) 2.12636e6 0.824084 0.412042 0.911165i \(-0.364816\pi\)
0.412042 + 0.911165i \(0.364816\pi\)
\(368\) 608062. 0.234061
\(369\) 2.92265e6 1.11741
\(370\) 0 0
\(371\) 65329.7 0.0246420
\(372\) −1.03351e6 −0.387221
\(373\) −3.90096e6 −1.45178 −0.725888 0.687813i \(-0.758571\pi\)
−0.725888 + 0.687813i \(0.758571\pi\)
\(374\) 2.29225e6 0.847389
\(375\) 0 0
\(376\) 1.27931e6 0.466666
\(377\) −341471. −0.123737
\(378\) −252412. −0.0908617
\(379\) −3.71050e6 −1.32689 −0.663444 0.748226i \(-0.730906\pi\)
−0.663444 + 0.748226i \(0.730906\pi\)
\(380\) 0 0
\(381\) 1.21800e6 0.429868
\(382\) −2.32505e6 −0.815219
\(383\) 3.60895e6 1.25714 0.628571 0.777752i \(-0.283640\pi\)
0.628571 + 0.777752i \(0.283640\pi\)
\(384\) −157409. −0.0544756
\(385\) 0 0
\(386\) −212804. −0.0726961
\(387\) −2.11406e6 −0.717530
\(388\) 2.43185e6 0.820084
\(389\) −1.65714e6 −0.555245 −0.277622 0.960690i \(-0.589546\pi\)
−0.277622 + 0.960690i \(0.589546\pi\)
\(390\) 0 0
\(391\) −1.96295e6 −0.649334
\(392\) −1.05783e6 −0.347698
\(393\) 3.59334e6 1.17359
\(394\) 3.51163e6 1.13964
\(395\) 0 0
\(396\) 1.67194e6 0.535776
\(397\) 2.10413e6 0.670035 0.335017 0.942212i \(-0.391258\pi\)
0.335017 + 0.942212i \(0.391258\pi\)
\(398\) 4.13649e6 1.30896
\(399\) −286489. −0.0900897
\(400\) 0 0
\(401\) 2.98174e6 0.925994 0.462997 0.886360i \(-0.346774\pi\)
0.462997 + 0.886360i \(0.346774\pi\)
\(402\) 785701. 0.242489
\(403\) −1.13625e6 −0.348505
\(404\) 1.87162e6 0.570512
\(405\) 0 0
\(406\) −134836. −0.0405968
\(407\) −1.97985e6 −0.592443
\(408\) 508151. 0.151127
\(409\) 2.98041e6 0.880983 0.440491 0.897757i \(-0.354804\pi\)
0.440491 + 0.897757i \(0.354804\pi\)
\(410\) 0 0
\(411\) −3.46626e6 −1.01218
\(412\) −1.97496e6 −0.573211
\(413\) 400846. 0.115639
\(414\) −1.43176e6 −0.410552
\(415\) 0 0
\(416\) −173056. −0.0490290
\(417\) −3.90548e6 −1.09985
\(418\) 4.95767e6 1.38783
\(419\) −7.06233e6 −1.96523 −0.982614 0.185663i \(-0.940557\pi\)
−0.982614 + 0.185663i \(0.940557\pi\)
\(420\) 0 0
\(421\) 299952. 0.0824795 0.0412398 0.999149i \(-0.486869\pi\)
0.0412398 + 0.999149i \(0.486869\pi\)
\(422\) −187097. −0.0511430
\(423\) −3.01230e6 −0.818553
\(424\) −250618. −0.0677013
\(425\) 0 0
\(426\) −1.68828e6 −0.450734
\(427\) −575835. −0.152837
\(428\) 2.53920e6 0.670021
\(429\) −1.12589e6 −0.295361
\(430\) 0 0
\(431\) −1.29958e6 −0.336983 −0.168492 0.985703i \(-0.553890\pi\)
−0.168492 + 0.985703i \(0.553890\pi\)
\(432\) 968303. 0.249633
\(433\) 5.44298e6 1.39514 0.697569 0.716518i \(-0.254265\pi\)
0.697569 + 0.716518i \(0.254265\pi\)
\(434\) −448667. −0.114341
\(435\) 0 0
\(436\) −691219. −0.174140
\(437\) −4.24547e6 −1.06346
\(438\) −702172. −0.174887
\(439\) −4.35230e6 −1.07785 −0.538924 0.842355i \(-0.681169\pi\)
−0.538924 + 0.842355i \(0.681169\pi\)
\(440\) 0 0
\(441\) 2.49080e6 0.609878
\(442\) 558662. 0.136017
\(443\) 2.75827e6 0.667771 0.333886 0.942614i \(-0.391640\pi\)
0.333886 + 0.942614i \(0.391640\pi\)
\(444\) −438898. −0.105659
\(445\) 0 0
\(446\) 1.21191e6 0.288493
\(447\) −1.23778e6 −0.293004
\(448\) −68334.3 −0.0160858
\(449\) 720400. 0.168639 0.0843195 0.996439i \(-0.473128\pi\)
0.0843195 + 0.996439i \(0.473128\pi\)
\(450\) 0 0
\(451\) 1.34485e7 3.11339
\(452\) 102440. 0.0235843
\(453\) −1.72988e6 −0.396069
\(454\) 2.32705e6 0.529867
\(455\) 0 0
\(456\) 1.09903e6 0.247512
\(457\) 6.87411e6 1.53966 0.769832 0.638247i \(-0.220340\pi\)
0.769832 + 0.638247i \(0.220340\pi\)
\(458\) 215823. 0.0480766
\(459\) −3.12589e6 −0.692535
\(460\) 0 0
\(461\) 3.25115e6 0.712501 0.356250 0.934391i \(-0.384055\pi\)
0.356250 + 0.934391i \(0.384055\pi\)
\(462\) −444579. −0.0969045
\(463\) 1.41176e6 0.306061 0.153031 0.988221i \(-0.451097\pi\)
0.153031 + 0.988221i \(0.451097\pi\)
\(464\) 517259. 0.111535
\(465\) 0 0
\(466\) −3.59122e6 −0.766085
\(467\) −9.07019e6 −1.92453 −0.962264 0.272117i \(-0.912276\pi\)
−0.962264 + 0.272117i \(0.912276\pi\)
\(468\) 407482. 0.0859991
\(469\) 341088. 0.0716035
\(470\) 0 0
\(471\) 3.08704e6 0.641196
\(472\) −1.53773e6 −0.317705
\(473\) −9.72782e6 −1.99923
\(474\) 1.58943e6 0.324933
\(475\) 0 0
\(476\) 220598. 0.0446256
\(477\) 590110. 0.118751
\(478\) −4.10628e6 −0.822013
\(479\) −3.57727e6 −0.712382 −0.356191 0.934413i \(-0.615925\pi\)
−0.356191 + 0.934413i \(0.615925\pi\)
\(480\) 0 0
\(481\) −482525. −0.0950949
\(482\) 4.53836e6 0.889777
\(483\) 380713. 0.0742556
\(484\) 5.11660e6 0.992814
\(485\) 0 0
\(486\) −3.68726e6 −0.708131
\(487\) −9.72962e6 −1.85898 −0.929488 0.368853i \(-0.879751\pi\)
−0.929488 + 0.368853i \(0.879751\pi\)
\(488\) 2.20902e6 0.419903
\(489\) −1.29812e6 −0.245495
\(490\) 0 0
\(491\) −292730. −0.0547978 −0.0273989 0.999625i \(-0.508722\pi\)
−0.0273989 + 0.999625i \(0.508722\pi\)
\(492\) 2.98130e6 0.555255
\(493\) −1.66982e6 −0.309423
\(494\) 1.20827e6 0.222765
\(495\) 0 0
\(496\) 1.72118e6 0.314138
\(497\) −732913. −0.133095
\(498\) 2.24368e6 0.405403
\(499\) 1.95009e6 0.350594 0.175297 0.984516i \(-0.443911\pi\)
0.175297 + 0.984516i \(0.443911\pi\)
\(500\) 0 0
\(501\) 975431. 0.173621
\(502\) −2.78971e6 −0.494083
\(503\) 3.52987e6 0.622069 0.311034 0.950399i \(-0.399325\pi\)
0.311034 + 0.950399i \(0.399325\pi\)
\(504\) 160902. 0.0282153
\(505\) 0 0
\(506\) −6.58821e6 −1.14391
\(507\) −274400. −0.0474093
\(508\) −2.02842e6 −0.348737
\(509\) 80297.4 0.0137375 0.00686874 0.999976i \(-0.497814\pi\)
0.00686874 + 0.999976i \(0.497814\pi\)
\(510\) 0 0
\(511\) −304826. −0.0516417
\(512\) 262144. 0.0441942
\(513\) −6.76067e6 −1.13422
\(514\) −6.26642e6 −1.04619
\(515\) 0 0
\(516\) −2.15648e6 −0.356551
\(517\) −1.38610e7 −2.28071
\(518\) −190534. −0.0311995
\(519\) 2.97446e6 0.484718
\(520\) 0 0
\(521\) 6.04030e6 0.974909 0.487455 0.873148i \(-0.337925\pi\)
0.487455 + 0.873148i \(0.337925\pi\)
\(522\) −1.21795e6 −0.195638
\(523\) 2.72218e6 0.435174 0.217587 0.976041i \(-0.430181\pi\)
0.217587 + 0.976041i \(0.430181\pi\)
\(524\) −5.98422e6 −0.952093
\(525\) 0 0
\(526\) 4.15502e6 0.654801
\(527\) −5.55632e6 −0.871487
\(528\) 1.70549e6 0.266235
\(529\) −794572. −0.123451
\(530\) 0 0
\(531\) 3.62077e6 0.557268
\(532\) 477109. 0.0730867
\(533\) 3.27764e6 0.499740
\(534\) −1.87312e6 −0.284258
\(535\) 0 0
\(536\) −1.30848e6 −0.196723
\(537\) 1.83597e6 0.274745
\(538\) 431776. 0.0643136
\(539\) 1.14614e7 1.69928
\(540\) 0 0
\(541\) −3.59202e6 −0.527650 −0.263825 0.964571i \(-0.584984\pi\)
−0.263825 + 0.964571i \(0.584984\pi\)
\(542\) −4.24370e6 −0.620506
\(543\) −6.67185e6 −0.971062
\(544\) −846257. −0.122604
\(545\) 0 0
\(546\) −108352. −0.0155544
\(547\) 5.06329e6 0.723543 0.361772 0.932267i \(-0.382172\pi\)
0.361772 + 0.932267i \(0.382172\pi\)
\(548\) 5.77259e6 0.821144
\(549\) −5.20140e6 −0.736529
\(550\) 0 0
\(551\) −3.61149e6 −0.506765
\(552\) −1.46049e6 −0.204009
\(553\) 690000. 0.0959480
\(554\) −2.09447e6 −0.289934
\(555\) 0 0
\(556\) 6.50405e6 0.892271
\(557\) 1.11450e7 1.52209 0.761046 0.648698i \(-0.224686\pi\)
0.761046 + 0.648698i \(0.224686\pi\)
\(558\) −4.05272e6 −0.551013
\(559\) −2.37084e6 −0.320903
\(560\) 0 0
\(561\) −5.50570e6 −0.738593
\(562\) 4.98315e6 0.665524
\(563\) −2.52470e6 −0.335691 −0.167845 0.985813i \(-0.553681\pi\)
−0.167845 + 0.985813i \(0.553681\pi\)
\(564\) −3.07274e6 −0.406751
\(565\) 0 0
\(566\) −3.08906e6 −0.405309
\(567\) −4661.14 −0.000608884 0
\(568\) 2.81160e6 0.365664
\(569\) −1.14153e7 −1.47811 −0.739057 0.673643i \(-0.764729\pi\)
−0.739057 + 0.673643i \(0.764729\pi\)
\(570\) 0 0
\(571\) −1.30087e7 −1.66972 −0.834862 0.550460i \(-0.814452\pi\)
−0.834862 + 0.550460i \(0.814452\pi\)
\(572\) 1.87502e6 0.239616
\(573\) 5.58448e6 0.710553
\(574\) 1.29424e6 0.163959
\(575\) 0 0
\(576\) −617251. −0.0775185
\(577\) 3.66964e6 0.458864 0.229432 0.973325i \(-0.426313\pi\)
0.229432 + 0.973325i \(0.426313\pi\)
\(578\) −2.94753e6 −0.366977
\(579\) 511128. 0.0633627
\(580\) 0 0
\(581\) 974023. 0.119710
\(582\) −5.84101e6 −0.714793
\(583\) 2.71538e6 0.330872
\(584\) 1.16937e6 0.141880
\(585\) 0 0
\(586\) −6.21663e6 −0.747844
\(587\) −9.50908e6 −1.13905 −0.569526 0.821974i \(-0.692873\pi\)
−0.569526 + 0.821974i \(0.692873\pi\)
\(588\) 2.54079e6 0.303057
\(589\) −1.20172e7 −1.42730
\(590\) 0 0
\(591\) −8.43450e6 −0.993323
\(592\) 730926. 0.0857174
\(593\) 966817. 0.112904 0.0564518 0.998405i \(-0.482021\pi\)
0.0564518 + 0.998405i \(0.482021\pi\)
\(594\) −1.04913e7 −1.22001
\(595\) 0 0
\(596\) 2.06135e6 0.237704
\(597\) −9.93534e6 −1.14090
\(598\) −1.60566e6 −0.183612
\(599\) 272872. 0.0310737 0.0155368 0.999879i \(-0.495054\pi\)
0.0155368 + 0.999879i \(0.495054\pi\)
\(600\) 0 0
\(601\) 1.15123e6 0.130010 0.0650050 0.997885i \(-0.479294\pi\)
0.0650050 + 0.997885i \(0.479294\pi\)
\(602\) −936171. −0.105284
\(603\) 3.08098e6 0.345061
\(604\) 2.88089e6 0.321317
\(605\) 0 0
\(606\) −4.49540e6 −0.497264
\(607\) 3.34458e6 0.368443 0.184221 0.982885i \(-0.441024\pi\)
0.184221 + 0.982885i \(0.441024\pi\)
\(608\) −1.83028e6 −0.200798
\(609\) 323860. 0.0353846
\(610\) 0 0
\(611\) −3.37818e6 −0.366083
\(612\) 1.99262e6 0.215053
\(613\) 9.25214e6 0.994469 0.497234 0.867616i \(-0.334349\pi\)
0.497234 + 0.867616i \(0.334349\pi\)
\(614\) 3.34705e6 0.358295
\(615\) 0 0
\(616\) 740387. 0.0786153
\(617\) −2.23244e6 −0.236084 −0.118042 0.993009i \(-0.537662\pi\)
−0.118042 + 0.993009i \(0.537662\pi\)
\(618\) 4.74360e6 0.499616
\(619\) −1.14222e7 −1.19818 −0.599092 0.800680i \(-0.704472\pi\)
−0.599092 + 0.800680i \(0.704472\pi\)
\(620\) 0 0
\(621\) 8.98419e6 0.934867
\(622\) 8.74302e6 0.906120
\(623\) −813159. −0.0839373
\(624\) 415659. 0.0427342
\(625\) 0 0
\(626\) −4.21046e6 −0.429431
\(627\) −1.19077e7 −1.20965
\(628\) −5.14106e6 −0.520180
\(629\) −2.35958e6 −0.237798
\(630\) 0 0
\(631\) −1.66436e6 −0.166408 −0.0832040 0.996533i \(-0.526515\pi\)
−0.0832040 + 0.996533i \(0.526515\pi\)
\(632\) −2.64697e6 −0.263607
\(633\) 449384. 0.0445767
\(634\) 4.39325e6 0.434073
\(635\) 0 0
\(636\) 601952. 0.0590091
\(637\) 2.79335e6 0.272757
\(638\) −5.60438e6 −0.545099
\(639\) −6.62026e6 −0.641391
\(640\) 0 0
\(641\) −5.71944e6 −0.549804 −0.274902 0.961472i \(-0.588645\pi\)
−0.274902 + 0.961472i \(0.588645\pi\)
\(642\) −6.09885e6 −0.583997
\(643\) −2.71308e6 −0.258783 −0.129391 0.991594i \(-0.541302\pi\)
−0.129391 + 0.991594i \(0.541302\pi\)
\(644\) −634026. −0.0602410
\(645\) 0 0
\(646\) 5.90854e6 0.557056
\(647\) −5.29299e6 −0.497096 −0.248548 0.968620i \(-0.579953\pi\)
−0.248548 + 0.968620i \(0.579953\pi\)
\(648\) 17881.0 0.00167284
\(649\) 1.66609e7 1.55270
\(650\) 0 0
\(651\) 1.07764e6 0.0996603
\(652\) 2.16184e6 0.199161
\(653\) −8.54020e6 −0.783764 −0.391882 0.920016i \(-0.628176\pi\)
−0.391882 + 0.920016i \(0.628176\pi\)
\(654\) 1.66022e6 0.151782
\(655\) 0 0
\(656\) −4.96495e6 −0.450459
\(657\) −2.75344e6 −0.248864
\(658\) −1.33394e6 −0.120108
\(659\) 8.44994e6 0.757950 0.378975 0.925407i \(-0.376277\pi\)
0.378975 + 0.925407i \(0.376277\pi\)
\(660\) 0 0
\(661\) 1.35980e7 1.21052 0.605258 0.796029i \(-0.293070\pi\)
0.605258 + 0.796029i \(0.293070\pi\)
\(662\) 9.30137e6 0.824901
\(663\) −1.34184e6 −0.118554
\(664\) −3.73654e6 −0.328889
\(665\) 0 0
\(666\) −1.72106e6 −0.150352
\(667\) 4.79927e6 0.417697
\(668\) −1.62445e6 −0.140853
\(669\) −2.91087e6 −0.251453
\(670\) 0 0
\(671\) −2.39342e7 −2.05216
\(672\) 164131. 0.0140206
\(673\) 2.95663e6 0.251629 0.125814 0.992054i \(-0.459846\pi\)
0.125814 + 0.992054i \(0.459846\pi\)
\(674\) 1.14775e7 0.973194
\(675\) 0 0
\(676\) 456976. 0.0384615
\(677\) 1.47847e7 1.23977 0.619886 0.784692i \(-0.287179\pi\)
0.619886 + 0.784692i \(0.287179\pi\)
\(678\) −246047. −0.0205563
\(679\) −2.53569e6 −0.211068
\(680\) 0 0
\(681\) −5.58929e6 −0.461837
\(682\) −1.86485e7 −1.53527
\(683\) −7.10311e6 −0.582636 −0.291318 0.956626i \(-0.594094\pi\)
−0.291318 + 0.956626i \(0.594094\pi\)
\(684\) 4.30963e6 0.352208
\(685\) 0 0
\(686\) 2.22458e6 0.180484
\(687\) −518379. −0.0419040
\(688\) 3.59133e6 0.289258
\(689\) 661787. 0.0531093
\(690\) 0 0
\(691\) 1.42091e6 0.113206 0.0566032 0.998397i \(-0.481973\pi\)
0.0566032 + 0.998397i \(0.481973\pi\)
\(692\) −4.95356e6 −0.393235
\(693\) −1.74333e6 −0.137895
\(694\) 1.32538e7 1.04458
\(695\) 0 0
\(696\) −1.24239e6 −0.0972154
\(697\) 1.60279e7 1.24967
\(698\) −1.39002e7 −1.07990
\(699\) 8.62566e6 0.667728
\(700\) 0 0
\(701\) 2.53557e7 1.94886 0.974431 0.224685i \(-0.0721353\pi\)
0.974431 + 0.224685i \(0.0721353\pi\)
\(702\) −2.55693e6 −0.195828
\(703\) −5.10331e6 −0.389460
\(704\) −2.84027e6 −0.215987
\(705\) 0 0
\(706\) 1.12821e7 0.851877
\(707\) −1.95154e6 −0.146835
\(708\) 3.69342e6 0.276915
\(709\) −1.46662e7 −1.09572 −0.547862 0.836569i \(-0.684558\pi\)
−0.547862 + 0.836569i \(0.684558\pi\)
\(710\) 0 0
\(711\) 6.23263e6 0.462378
\(712\) 3.11944e6 0.230609
\(713\) 1.59696e7 1.17644
\(714\) −529848. −0.0388961
\(715\) 0 0
\(716\) −3.05756e6 −0.222891
\(717\) 9.86277e6 0.716475
\(718\) −9.29405e6 −0.672812
\(719\) 4.43789e6 0.320150 0.160075 0.987105i \(-0.448826\pi\)
0.160075 + 0.987105i \(0.448826\pi\)
\(720\) 0 0
\(721\) 2.05928e6 0.147529
\(722\) 2.87459e6 0.205226
\(723\) −1.09006e7 −0.775538
\(724\) 1.11111e7 0.787789
\(725\) 0 0
\(726\) −1.22894e7 −0.865347
\(727\) −1.07950e7 −0.757505 −0.378752 0.925498i \(-0.623647\pi\)
−0.378752 + 0.925498i \(0.623647\pi\)
\(728\) 180445. 0.0126188
\(729\) 8.78845e6 0.612482
\(730\) 0 0
\(731\) −1.15936e7 −0.802463
\(732\) −5.30578e6 −0.365992
\(733\) −1.67123e7 −1.14889 −0.574444 0.818544i \(-0.694782\pi\)
−0.574444 + 0.818544i \(0.694782\pi\)
\(734\) 8.50544e6 0.582716
\(735\) 0 0
\(736\) 2.43225e6 0.165506
\(737\) 1.41771e7 0.961430
\(738\) 1.16906e7 0.790125
\(739\) −8.52029e6 −0.573909 −0.286955 0.957944i \(-0.592643\pi\)
−0.286955 + 0.957944i \(0.592643\pi\)
\(740\) 0 0
\(741\) −2.90212e6 −0.194164
\(742\) 261319. 0.0174245
\(743\) 1.57051e7 1.04369 0.521843 0.853042i \(-0.325245\pi\)
0.521843 + 0.853042i \(0.325245\pi\)
\(744\) −4.13405e6 −0.273806
\(745\) 0 0
\(746\) −1.56039e7 −1.02656
\(747\) 8.79816e6 0.576886
\(748\) 9.16900e6 0.599194
\(749\) −2.64763e6 −0.172446
\(750\) 0 0
\(751\) −3.79051e6 −0.245243 −0.122622 0.992453i \(-0.539130\pi\)
−0.122622 + 0.992453i \(0.539130\pi\)
\(752\) 5.11724e6 0.329983
\(753\) 6.70054e6 0.430648
\(754\) −1.36589e6 −0.0874956
\(755\) 0 0
\(756\) −1.00965e6 −0.0642489
\(757\) 5.62004e6 0.356451 0.178226 0.983990i \(-0.442964\pi\)
0.178226 + 0.983990i \(0.442964\pi\)
\(758\) −1.48420e7 −0.938251
\(759\) 1.58240e7 0.997041
\(760\) 0 0
\(761\) −1.97957e6 −0.123911 −0.0619554 0.998079i \(-0.519734\pi\)
−0.0619554 + 0.998079i \(0.519734\pi\)
\(762\) 4.87201e6 0.303963
\(763\) 720734. 0.0448191
\(764\) −9.30021e6 −0.576447
\(765\) 0 0
\(766\) 1.44358e7 0.888934
\(767\) 4.06056e6 0.249228
\(768\) −629637. −0.0385201
\(769\) 3.06187e7 1.86711 0.933557 0.358429i \(-0.116688\pi\)
0.933557 + 0.358429i \(0.116688\pi\)
\(770\) 0 0
\(771\) 1.50512e7 0.911872
\(772\) −851215. −0.0514039
\(773\) −7.23639e6 −0.435585 −0.217793 0.975995i \(-0.569886\pi\)
−0.217793 + 0.975995i \(0.569886\pi\)
\(774\) −8.45624e6 −0.507370
\(775\) 0 0
\(776\) 9.72742e6 0.579887
\(777\) 457639. 0.0271938
\(778\) −6.62855e6 −0.392617
\(779\) 3.46652e7 2.04668
\(780\) 0 0
\(781\) −3.04630e7 −1.78709
\(782\) −7.85181e6 −0.459148
\(783\) 7.64256e6 0.445487
\(784\) −4.23134e6 −0.245860
\(785\) 0 0
\(786\) 1.43734e7 0.829854
\(787\) −1.68586e7 −0.970255 −0.485127 0.874444i \(-0.661227\pi\)
−0.485127 + 0.874444i \(0.661227\pi\)
\(788\) 1.40465e7 0.805848
\(789\) −9.97985e6 −0.570731
\(790\) 0 0
\(791\) −106814. −0.00606997
\(792\) 6.68777e6 0.378851
\(793\) −5.83318e6 −0.329399
\(794\) 8.41654e6 0.473786
\(795\) 0 0
\(796\) 1.65460e7 0.925571
\(797\) 1.33831e7 0.746293 0.373147 0.927772i \(-0.378279\pi\)
0.373147 + 0.927772i \(0.378279\pi\)
\(798\) −1.14596e6 −0.0637031
\(799\) −1.65196e7 −0.915443
\(800\) 0 0
\(801\) −7.34510e6 −0.404498
\(802\) 1.19269e7 0.654777
\(803\) −1.26699e7 −0.693400
\(804\) 3.14280e6 0.171466
\(805\) 0 0
\(806\) −4.54498e6 −0.246430
\(807\) −1.03707e6 −0.0560564
\(808\) 7.48648e6 0.403413
\(809\) 6.55526e6 0.352142 0.176071 0.984377i \(-0.443661\pi\)
0.176071 + 0.984377i \(0.443661\pi\)
\(810\) 0 0
\(811\) 1.94125e7 1.03640 0.518202 0.855258i \(-0.326602\pi\)
0.518202 + 0.855258i \(0.326602\pi\)
\(812\) −539345. −0.0287063
\(813\) 1.01928e7 0.540839
\(814\) −7.91941e6 −0.418921
\(815\) 0 0
\(816\) 2.03260e6 0.106863
\(817\) −2.50746e7 −1.31425
\(818\) 1.19216e7 0.622949
\(819\) −424881. −0.0221339
\(820\) 0 0
\(821\) 7.46292e6 0.386412 0.193206 0.981158i \(-0.438111\pi\)
0.193206 + 0.981158i \(0.438111\pi\)
\(822\) −1.38650e7 −0.715718
\(823\) 2.21232e7 1.13854 0.569271 0.822150i \(-0.307225\pi\)
0.569271 + 0.822150i \(0.307225\pi\)
\(824\) −7.89982e6 −0.405321
\(825\) 0 0
\(826\) 1.60339e6 0.0817688
\(827\) −8.40565e6 −0.427374 −0.213687 0.976902i \(-0.568547\pi\)
−0.213687 + 0.976902i \(0.568547\pi\)
\(828\) −5.72703e6 −0.290304
\(829\) 7.27092e6 0.367454 0.183727 0.982977i \(-0.441184\pi\)
0.183727 + 0.982977i \(0.441184\pi\)
\(830\) 0 0
\(831\) 5.03065e6 0.252709
\(832\) −692224. −0.0346688
\(833\) 1.36597e7 0.682068
\(834\) −1.56219e7 −0.777713
\(835\) 0 0
\(836\) 1.98307e7 0.981346
\(837\) 2.54306e7 1.25471
\(838\) −2.82493e7 −1.38963
\(839\) 2.59125e7 1.27088 0.635441 0.772150i \(-0.280818\pi\)
0.635441 + 0.772150i \(0.280818\pi\)
\(840\) 0 0
\(841\) −1.64286e7 −0.800958
\(842\) 1.19981e6 0.0583218
\(843\) −1.19689e7 −0.580077
\(844\) −748388. −0.0361635
\(845\) 0 0
\(846\) −1.20492e7 −0.578804
\(847\) −5.33507e6 −0.255524
\(848\) −1.00247e6 −0.0478720
\(849\) 7.41955e6 0.353271
\(850\) 0 0
\(851\) 6.78174e6 0.321009
\(852\) −6.75311e6 −0.318717
\(853\) 3.64342e7 1.71450 0.857248 0.514903i \(-0.172172\pi\)
0.857248 + 0.514903i \(0.172172\pi\)
\(854\) −2.30334e6 −0.108072
\(855\) 0 0
\(856\) 1.01568e7 0.473776
\(857\) 2.62890e7 1.22271 0.611353 0.791358i \(-0.290625\pi\)
0.611353 + 0.791358i \(0.290625\pi\)
\(858\) −4.50357e6 −0.208852
\(859\) 1.81329e7 0.838465 0.419233 0.907879i \(-0.362299\pi\)
0.419233 + 0.907879i \(0.362299\pi\)
\(860\) 0 0
\(861\) −3.10860e6 −0.142908
\(862\) −5.19831e6 −0.238283
\(863\) 4.85495e6 0.221900 0.110950 0.993826i \(-0.464611\pi\)
0.110950 + 0.993826i \(0.464611\pi\)
\(864\) 3.87321e6 0.176517
\(865\) 0 0
\(866\) 2.17719e7 0.986512
\(867\) 7.07960e6 0.319861
\(868\) −1.79467e6 −0.0808509
\(869\) 2.86794e7 1.28831
\(870\) 0 0
\(871\) 3.45520e6 0.154322
\(872\) −2.76488e6 −0.123136
\(873\) −2.29044e7 −1.01715
\(874\) −1.69819e7 −0.751982
\(875\) 0 0
\(876\) −2.80869e6 −0.123664
\(877\) 3.52512e7 1.54766 0.773828 0.633395i \(-0.218339\pi\)
0.773828 + 0.633395i \(0.218339\pi\)
\(878\) −1.74092e7 −0.762153
\(879\) 1.49316e7 0.651829
\(880\) 0 0
\(881\) −3.12586e6 −0.135684 −0.0678422 0.997696i \(-0.521611\pi\)
−0.0678422 + 0.997696i \(0.521611\pi\)
\(882\) 9.96322e6 0.431249
\(883\) 1.58054e7 0.682188 0.341094 0.940029i \(-0.389202\pi\)
0.341094 + 0.940029i \(0.389202\pi\)
\(884\) 2.23465e6 0.0961786
\(885\) 0 0
\(886\) 1.10331e7 0.472186
\(887\) 1.75515e7 0.749038 0.374519 0.927219i \(-0.377808\pi\)
0.374519 + 0.927219i \(0.377808\pi\)
\(888\) −1.75559e6 −0.0747122
\(889\) 2.11503e6 0.0897558
\(890\) 0 0
\(891\) −193737. −0.00817557
\(892\) 4.84766e6 0.203995
\(893\) −3.57285e7 −1.49929
\(894\) −4.95110e6 −0.207185
\(895\) 0 0
\(896\) −273337. −0.0113744
\(897\) 3.85660e6 0.160038
\(898\) 2.88160e6 0.119246
\(899\) 1.35848e7 0.560601
\(900\) 0 0
\(901\) 3.23619e6 0.132807
\(902\) 5.37941e7 2.20150
\(903\) 2.24856e6 0.0917669
\(904\) 409759. 0.0166766
\(905\) 0 0
\(906\) −6.91953e6 −0.280063
\(907\) 403972. 0.0163055 0.00815273 0.999967i \(-0.497405\pi\)
0.00815273 + 0.999967i \(0.497405\pi\)
\(908\) 9.30821e6 0.374672
\(909\) −1.76279e7 −0.707603
\(910\) 0 0
\(911\) 1.17873e6 0.0470564 0.0235282 0.999723i \(-0.492510\pi\)
0.0235282 + 0.999723i \(0.492510\pi\)
\(912\) 4.39611e6 0.175017
\(913\) 4.04846e7 1.60736
\(914\) 2.74964e7 1.08871
\(915\) 0 0
\(916\) 863291. 0.0339953
\(917\) 6.23974e6 0.245044
\(918\) −1.25036e7 −0.489696
\(919\) 5.16739e6 0.201828 0.100914 0.994895i \(-0.467823\pi\)
0.100914 + 0.994895i \(0.467823\pi\)
\(920\) 0 0
\(921\) −8.03919e6 −0.312294
\(922\) 1.30046e7 0.503814
\(923\) −7.42438e6 −0.286851
\(924\) −1.77832e6 −0.0685218
\(925\) 0 0
\(926\) 5.64704e6 0.216418
\(927\) 1.86011e7 0.710951
\(928\) 2.06903e6 0.0788674
\(929\) 1.58742e7 0.603467 0.301733 0.953392i \(-0.402435\pi\)
0.301733 + 0.953392i \(0.402435\pi\)
\(930\) 0 0
\(931\) 2.95431e7 1.11707
\(932\) −1.43649e7 −0.541704
\(933\) −2.09996e7 −0.789783
\(934\) −3.62808e7 −1.36085
\(935\) 0 0
\(936\) 1.62993e6 0.0608105
\(937\) 3.42717e7 1.27522 0.637612 0.770358i \(-0.279922\pi\)
0.637612 + 0.770358i \(0.279922\pi\)
\(938\) 1.36435e6 0.0506313
\(939\) 1.01130e7 0.374297
\(940\) 0 0
\(941\) −557810. −0.0205358 −0.0102679 0.999947i \(-0.503268\pi\)
−0.0102679 + 0.999947i \(0.503268\pi\)
\(942\) 1.23482e7 0.453394
\(943\) −4.60662e7 −1.68696
\(944\) −6.15090e6 −0.224651
\(945\) 0 0
\(946\) −3.89113e7 −1.41367
\(947\) 3.22519e7 1.16864 0.584319 0.811524i \(-0.301362\pi\)
0.584319 + 0.811524i \(0.301362\pi\)
\(948\) 6.35770e6 0.229763
\(949\) −3.08788e6 −0.111300
\(950\) 0 0
\(951\) −1.05520e7 −0.378342
\(952\) 882392. 0.0315551
\(953\) 2.42726e7 0.865732 0.432866 0.901458i \(-0.357502\pi\)
0.432866 + 0.901458i \(0.357502\pi\)
\(954\) 2.36044e6 0.0839696
\(955\) 0 0
\(956\) −1.64251e7 −0.581251
\(957\) 1.34610e7 0.475114
\(958\) −1.43091e7 −0.503730
\(959\) −6.01908e6 −0.211341
\(960\) 0 0
\(961\) 1.65742e7 0.578928
\(962\) −1.93010e6 −0.0672423
\(963\) −2.39155e7 −0.831024
\(964\) 1.81534e7 0.629167
\(965\) 0 0
\(966\) 1.52285e6 0.0525067
\(967\) 4.36346e7 1.50060 0.750300 0.661097i \(-0.229909\pi\)
0.750300 + 0.661097i \(0.229909\pi\)
\(968\) 2.04664e7 0.702026
\(969\) −1.41916e7 −0.485536
\(970\) 0 0
\(971\) −2.49001e7 −0.847526 −0.423763 0.905773i \(-0.639291\pi\)
−0.423763 + 0.905773i \(0.639291\pi\)
\(972\) −1.47490e7 −0.500724
\(973\) −6.78177e6 −0.229647
\(974\) −3.89185e7 −1.31449
\(975\) 0 0
\(976\) 8.83606e6 0.296916
\(977\) −4.31252e7 −1.44542 −0.722711 0.691150i \(-0.757104\pi\)
−0.722711 + 0.691150i \(0.757104\pi\)
\(978\) −5.19247e6 −0.173591
\(979\) −3.37984e7 −1.12704
\(980\) 0 0
\(981\) 6.51024e6 0.215986
\(982\) −1.17092e6 −0.0387479
\(983\) −2.51180e7 −0.829089 −0.414544 0.910029i \(-0.636059\pi\)
−0.414544 + 0.910029i \(0.636059\pi\)
\(984\) 1.19252e7 0.392625
\(985\) 0 0
\(986\) −6.67929e6 −0.218795
\(987\) 3.20395e6 0.104687
\(988\) 4.83309e6 0.157519
\(989\) 3.33214e7 1.08326
\(990\) 0 0
\(991\) −1.35160e7 −0.437182 −0.218591 0.975817i \(-0.570146\pi\)
−0.218591 + 0.975817i \(0.570146\pi\)
\(992\) 6.88470e6 0.222129
\(993\) −2.23407e7 −0.718992
\(994\) −2.93165e6 −0.0941124
\(995\) 0 0
\(996\) 8.97471e6 0.286663
\(997\) −3.69725e7 −1.17799 −0.588994 0.808138i \(-0.700476\pi\)
−0.588994 + 0.808138i \(0.700476\pi\)
\(998\) 7.80038e6 0.247907
\(999\) 1.07995e7 0.342366
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 650.6.a.j.1.1 3
5.2 odd 4 650.6.b.j.599.6 6
5.3 odd 4 650.6.b.j.599.1 6
5.4 even 2 130.6.a.f.1.3 3
20.19 odd 2 1040.6.a.l.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.6.a.f.1.3 3 5.4 even 2
650.6.a.j.1.1 3 1.1 even 1 trivial
650.6.b.j.599.1 6 5.3 odd 4
650.6.b.j.599.6 6 5.2 odd 4
1040.6.a.l.1.1 3 20.19 odd 2