Properties

Label 1045.6.a.e.1.7
Level $1045$
Weight $6$
Character 1045.1
Self dual yes
Analytic conductor $167.601$
Analytic rank $1$
Dimension $38$
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] = [1045,6,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.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: \(167.601091705\)
Analytic rank: \(1\)
Dimension: \(38\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-8.88488 q^{2} -24.9356 q^{3} +46.9410 q^{4} +25.0000 q^{5} +221.550 q^{6} -188.162 q^{7} -132.749 q^{8} +378.784 q^{9} +O(q^{10})\) \(q-8.88488 q^{2} -24.9356 q^{3} +46.9410 q^{4} +25.0000 q^{5} +221.550 q^{6} -188.162 q^{7} -132.749 q^{8} +378.784 q^{9} -222.122 q^{10} +121.000 q^{11} -1170.50 q^{12} +1013.16 q^{13} +1671.80 q^{14} -623.390 q^{15} -322.653 q^{16} +136.931 q^{17} -3365.45 q^{18} -361.000 q^{19} +1173.53 q^{20} +4691.94 q^{21} -1075.07 q^{22} -2499.86 q^{23} +3310.18 q^{24} +625.000 q^{25} -9001.81 q^{26} -3385.87 q^{27} -8832.53 q^{28} +6928.91 q^{29} +5538.74 q^{30} +1840.68 q^{31} +7114.70 q^{32} -3017.21 q^{33} -1216.61 q^{34} -4704.05 q^{35} +17780.5 q^{36} -10033.0 q^{37} +3207.44 q^{38} -25263.8 q^{39} -3318.73 q^{40} +11841.6 q^{41} -41687.3 q^{42} -3911.61 q^{43} +5679.86 q^{44} +9469.61 q^{45} +22211.0 q^{46} -16417.7 q^{47} +8045.54 q^{48} +18598.0 q^{49} -5553.05 q^{50} -3414.45 q^{51} +47558.8 q^{52} -35920.1 q^{53} +30083.0 q^{54} +3025.00 q^{55} +24978.4 q^{56} +9001.75 q^{57} -61562.5 q^{58} -20681.9 q^{59} -29262.6 q^{60} -2228.28 q^{61} -16354.2 q^{62} -71272.9 q^{63} -52888.4 q^{64} +25329.0 q^{65} +26807.5 q^{66} -29275.7 q^{67} +6427.66 q^{68} +62335.6 q^{69} +41794.9 q^{70} -25545.3 q^{71} -50283.3 q^{72} +31498.9 q^{73} +89142.3 q^{74} -15584.8 q^{75} -16945.7 q^{76} -22767.6 q^{77} +224465. q^{78} -92865.9 q^{79} -8066.31 q^{80} -7615.96 q^{81} -105211. q^{82} +88852.5 q^{83} +220244. q^{84} +3423.26 q^{85} +34754.2 q^{86} -172777. q^{87} -16062.7 q^{88} +127748. q^{89} -84136.3 q^{90} -190638. q^{91} -117346. q^{92} -45898.5 q^{93} +145869. q^{94} -9025.00 q^{95} -177409. q^{96} -35272.3 q^{97} -165241. q^{98} +45832.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.88488 −1.57064 −0.785320 0.619091i \(-0.787501\pi\)
−0.785320 + 0.619091i \(0.787501\pi\)
\(3\) −24.9356 −1.59962 −0.799810 0.600253i \(-0.795066\pi\)
−0.799810 + 0.600253i \(0.795066\pi\)
\(4\) 46.9410 1.46691
\(5\) 25.0000 0.447214
\(6\) 221.550 2.51243
\(7\) −188.162 −1.45140 −0.725700 0.688011i \(-0.758484\pi\)
−0.725700 + 0.688011i \(0.758484\pi\)
\(8\) −132.749 −0.733343
\(9\) 378.784 1.55878
\(10\) −222.122 −0.702411
\(11\) 121.000 0.301511
\(12\) −1170.50 −2.34649
\(13\) 1013.16 1.66272 0.831361 0.555732i \(-0.187562\pi\)
0.831361 + 0.555732i \(0.187562\pi\)
\(14\) 1671.80 2.27963
\(15\) −623.390 −0.715372
\(16\) −322.653 −0.315090
\(17\) 136.931 0.114915 0.0574577 0.998348i \(-0.481701\pi\)
0.0574577 + 0.998348i \(0.481701\pi\)
\(18\) −3365.45 −2.44829
\(19\) −361.000 −0.229416
\(20\) 1173.53 0.656021
\(21\) 4691.94 2.32169
\(22\) −1075.07 −0.473566
\(23\) −2499.86 −0.985364 −0.492682 0.870209i \(-0.663983\pi\)
−0.492682 + 0.870209i \(0.663983\pi\)
\(24\) 3310.18 1.17307
\(25\) 625.000 0.200000
\(26\) −9001.81 −2.61154
\(27\) −3385.87 −0.893842
\(28\) −8832.53 −2.12907
\(29\) 6928.91 1.52992 0.764962 0.644075i \(-0.222758\pi\)
0.764962 + 0.644075i \(0.222758\pi\)
\(30\) 5538.74 1.12359
\(31\) 1840.68 0.344013 0.172006 0.985096i \(-0.444975\pi\)
0.172006 + 0.985096i \(0.444975\pi\)
\(32\) 7114.70 1.22824
\(33\) −3017.21 −0.482304
\(34\) −1216.61 −0.180490
\(35\) −4704.05 −0.649086
\(36\) 17780.5 2.28659
\(37\) −10033.0 −1.20484 −0.602418 0.798181i \(-0.705796\pi\)
−0.602418 + 0.798181i \(0.705796\pi\)
\(38\) 3207.44 0.360329
\(39\) −25263.8 −2.65972
\(40\) −3318.73 −0.327961
\(41\) 11841.6 1.10015 0.550073 0.835117i \(-0.314600\pi\)
0.550073 + 0.835117i \(0.314600\pi\)
\(42\) −41687.3 −3.64653
\(43\) −3911.61 −0.322615 −0.161308 0.986904i \(-0.551571\pi\)
−0.161308 + 0.986904i \(0.551571\pi\)
\(44\) 5679.86 0.442289
\(45\) 9469.61 0.697109
\(46\) 22211.0 1.54765
\(47\) −16417.7 −1.08409 −0.542047 0.840348i \(-0.682351\pi\)
−0.542047 + 0.840348i \(0.682351\pi\)
\(48\) 8045.54 0.504025
\(49\) 18598.0 1.10656
\(50\) −5553.05 −0.314128
\(51\) −3414.45 −0.183821
\(52\) 47558.8 2.43906
\(53\) −35920.1 −1.75650 −0.878250 0.478202i \(-0.841289\pi\)
−0.878250 + 0.478202i \(0.841289\pi\)
\(54\) 30083.0 1.40390
\(55\) 3025.00 0.134840
\(56\) 24978.4 1.06437
\(57\) 9001.75 0.366978
\(58\) −61562.5 −2.40296
\(59\) −20681.9 −0.773502 −0.386751 0.922184i \(-0.626403\pi\)
−0.386751 + 0.922184i \(0.626403\pi\)
\(60\) −29262.6 −1.04938
\(61\) −2228.28 −0.0766734 −0.0383367 0.999265i \(-0.512206\pi\)
−0.0383367 + 0.999265i \(0.512206\pi\)
\(62\) −16354.2 −0.540320
\(63\) −71272.9 −2.26242
\(64\) −52888.4 −1.61403
\(65\) 25329.0 0.743592
\(66\) 26807.5 0.757525
\(67\) −29275.7 −0.796748 −0.398374 0.917223i \(-0.630425\pi\)
−0.398374 + 0.917223i \(0.630425\pi\)
\(68\) 6427.66 0.168570
\(69\) 62335.6 1.57621
\(70\) 41794.9 1.01948
\(71\) −25545.3 −0.601403 −0.300702 0.953718i \(-0.597221\pi\)
−0.300702 + 0.953718i \(0.597221\pi\)
\(72\) −50283.3 −1.14312
\(73\) 31498.9 0.691812 0.345906 0.938269i \(-0.387572\pi\)
0.345906 + 0.938269i \(0.387572\pi\)
\(74\) 89142.3 1.89236
\(75\) −15584.8 −0.319924
\(76\) −16945.7 −0.336532
\(77\) −22767.6 −0.437614
\(78\) 224465. 4.17747
\(79\) −92865.9 −1.67413 −0.837063 0.547106i \(-0.815729\pi\)
−0.837063 + 0.547106i \(0.815729\pi\)
\(80\) −8066.31 −0.140913
\(81\) −7615.96 −0.128977
\(82\) −105211. −1.72793
\(83\) 88852.5 1.41571 0.707855 0.706358i \(-0.249663\pi\)
0.707855 + 0.706358i \(0.249663\pi\)
\(84\) 220244. 3.40570
\(85\) 3423.26 0.0513917
\(86\) 34754.2 0.506712
\(87\) −172777. −2.44730
\(88\) −16062.7 −0.221111
\(89\) 127748. 1.70954 0.854770 0.519007i \(-0.173698\pi\)
0.854770 + 0.519007i \(0.173698\pi\)
\(90\) −84136.3 −1.09491
\(91\) −190638. −2.41328
\(92\) −117346. −1.44544
\(93\) −45898.5 −0.550290
\(94\) 145869. 1.70272
\(95\) −9025.00 −0.102598
\(96\) −177409. −1.96471
\(97\) −35272.3 −0.380631 −0.190316 0.981723i \(-0.560951\pi\)
−0.190316 + 0.981723i \(0.560951\pi\)
\(98\) −165241. −1.73801
\(99\) 45832.9 0.469991
\(100\) 29338.1 0.293381
\(101\) −110956. −1.08230 −0.541149 0.840926i \(-0.682011\pi\)
−0.541149 + 0.840926i \(0.682011\pi\)
\(102\) 30336.9 0.288716
\(103\) 56546.7 0.525187 0.262594 0.964906i \(-0.415422\pi\)
0.262594 + 0.964906i \(0.415422\pi\)
\(104\) −134496. −1.21935
\(105\) 117298. 1.03829
\(106\) 319146. 2.75883
\(107\) 29592.8 0.249877 0.124939 0.992164i \(-0.460127\pi\)
0.124939 + 0.992164i \(0.460127\pi\)
\(108\) −158936. −1.31118
\(109\) 131250. 1.05812 0.529059 0.848585i \(-0.322545\pi\)
0.529059 + 0.848585i \(0.322545\pi\)
\(110\) −26876.8 −0.211785
\(111\) 250180. 1.92728
\(112\) 60711.0 0.457322
\(113\) 33785.7 0.248907 0.124453 0.992225i \(-0.460282\pi\)
0.124453 + 0.992225i \(0.460282\pi\)
\(114\) −79979.5 −0.576390
\(115\) −62496.6 −0.440668
\(116\) 325250. 2.24426
\(117\) 383769. 2.59183
\(118\) 183756. 1.21489
\(119\) −25765.1 −0.166788
\(120\) 82754.6 0.524613
\(121\) 14641.0 0.0909091
\(122\) 19798.0 0.120426
\(123\) −295277. −1.75981
\(124\) 86403.6 0.504635
\(125\) 15625.0 0.0894427
\(126\) 633251. 3.55344
\(127\) −154895. −0.852171 −0.426085 0.904683i \(-0.640108\pi\)
−0.426085 + 0.904683i \(0.640108\pi\)
\(128\) 242236. 1.30682
\(129\) 97538.5 0.516062
\(130\) −225045. −1.16792
\(131\) 290721. 1.48013 0.740063 0.672537i \(-0.234795\pi\)
0.740063 + 0.672537i \(0.234795\pi\)
\(132\) −141631. −0.707495
\(133\) 67926.5 0.332974
\(134\) 260111. 1.25140
\(135\) −84646.7 −0.399738
\(136\) −18177.4 −0.0842723
\(137\) 32993.2 0.150184 0.0750919 0.997177i \(-0.476075\pi\)
0.0750919 + 0.997177i \(0.476075\pi\)
\(138\) −553844. −2.47565
\(139\) 174089. 0.764247 0.382123 0.924111i \(-0.375193\pi\)
0.382123 + 0.924111i \(0.375193\pi\)
\(140\) −220813. −0.952149
\(141\) 409385. 1.73414
\(142\) 226967. 0.944588
\(143\) 122592. 0.501330
\(144\) −122216. −0.491158
\(145\) 173223. 0.684203
\(146\) −279864. −1.08659
\(147\) −463752. −1.77008
\(148\) −470961. −1.76738
\(149\) 435723. 1.60785 0.803924 0.594732i \(-0.202742\pi\)
0.803924 + 0.594732i \(0.202742\pi\)
\(150\) 138469. 0.502485
\(151\) −155989. −0.556738 −0.278369 0.960474i \(-0.589794\pi\)
−0.278369 + 0.960474i \(0.589794\pi\)
\(152\) 47922.5 0.168240
\(153\) 51867.1 0.179128
\(154\) 202287. 0.687333
\(155\) 46017.1 0.153847
\(156\) −1.18591e6 −3.90157
\(157\) −125610. −0.406702 −0.203351 0.979106i \(-0.565183\pi\)
−0.203351 + 0.979106i \(0.565183\pi\)
\(158\) 825102. 2.62945
\(159\) 895690. 2.80973
\(160\) 177868. 0.549284
\(161\) 470380. 1.43016
\(162\) 67666.9 0.202576
\(163\) 488373. 1.43974 0.719868 0.694111i \(-0.244202\pi\)
0.719868 + 0.694111i \(0.244202\pi\)
\(164\) 555856. 1.61381
\(165\) −75430.2 −0.215693
\(166\) −789443. −2.22357
\(167\) 261701. 0.726130 0.363065 0.931764i \(-0.381730\pi\)
0.363065 + 0.931764i \(0.381730\pi\)
\(168\) −622851. −1.70259
\(169\) 655201. 1.76465
\(170\) −30415.3 −0.0807178
\(171\) −136741. −0.357610
\(172\) −183615. −0.473247
\(173\) −14891.8 −0.0378297 −0.0189149 0.999821i \(-0.506021\pi\)
−0.0189149 + 0.999821i \(0.506021\pi\)
\(174\) 1.53510e6 3.84382
\(175\) −117601. −0.290280
\(176\) −39041.0 −0.0950033
\(177\) 515717. 1.23731
\(178\) −1.13503e6 −2.68507
\(179\) 456700. 1.06537 0.532683 0.846315i \(-0.321184\pi\)
0.532683 + 0.846315i \(0.321184\pi\)
\(180\) 444513. 1.02259
\(181\) −349168. −0.792206 −0.396103 0.918206i \(-0.629638\pi\)
−0.396103 + 0.918206i \(0.629638\pi\)
\(182\) 1.69380e6 3.79039
\(183\) 55563.5 0.122648
\(184\) 331855. 0.722610
\(185\) −250826. −0.538819
\(186\) 407803. 0.864307
\(187\) 16568.6 0.0346483
\(188\) −770663. −1.59027
\(189\) 637092. 1.29732
\(190\) 80186.0 0.161144
\(191\) 442443. 0.877555 0.438777 0.898596i \(-0.355412\pi\)
0.438777 + 0.898596i \(0.355412\pi\)
\(192\) 1.31880e6 2.58183
\(193\) −135166. −0.261201 −0.130601 0.991435i \(-0.541691\pi\)
−0.130601 + 0.991435i \(0.541691\pi\)
\(194\) 313390. 0.597834
\(195\) −631594. −1.18947
\(196\) 873009. 1.62322
\(197\) −476036. −0.873924 −0.436962 0.899480i \(-0.643946\pi\)
−0.436962 + 0.899480i \(0.643946\pi\)
\(198\) −407220. −0.738186
\(199\) −698847. −1.25098 −0.625489 0.780233i \(-0.715100\pi\)
−0.625489 + 0.780233i \(0.715100\pi\)
\(200\) −82968.3 −0.146669
\(201\) 730008. 1.27449
\(202\) 985830. 1.69990
\(203\) −1.30376e6 −2.22053
\(204\) −160278. −0.269648
\(205\) 296039. 0.492000
\(206\) −502411. −0.824880
\(207\) −946910. −1.53597
\(208\) −326899. −0.523908
\(209\) −43681.0 −0.0691714
\(210\) −1.04218e6 −1.63078
\(211\) −332407. −0.514001 −0.257001 0.966411i \(-0.582734\pi\)
−0.257001 + 0.966411i \(0.582734\pi\)
\(212\) −1.68613e6 −2.57662
\(213\) 636989. 0.962017
\(214\) −262928. −0.392467
\(215\) −97790.3 −0.144278
\(216\) 449471. 0.655492
\(217\) −346347. −0.499300
\(218\) −1.16614e6 −1.66192
\(219\) −785443. −1.10664
\(220\) 141997. 0.197798
\(221\) 138733. 0.191072
\(222\) −2.22282e6 −3.02706
\(223\) 1.38186e6 1.86082 0.930408 0.366527i \(-0.119453\pi\)
0.930408 + 0.366527i \(0.119453\pi\)
\(224\) −1.33872e6 −1.78266
\(225\) 236740. 0.311757
\(226\) −300182. −0.390943
\(227\) −404074. −0.520471 −0.260235 0.965545i \(-0.583800\pi\)
−0.260235 + 0.965545i \(0.583800\pi\)
\(228\) 422552. 0.538323
\(229\) 1.34341e6 1.69286 0.846430 0.532499i \(-0.178747\pi\)
0.846430 + 0.532499i \(0.178747\pi\)
\(230\) 555275. 0.692131
\(231\) 567724. 0.700015
\(232\) −919808. −1.12196
\(233\) −1.42763e6 −1.72276 −0.861381 0.507960i \(-0.830400\pi\)
−0.861381 + 0.507960i \(0.830400\pi\)
\(234\) −3.40974e6 −4.07082
\(235\) −410442. −0.484822
\(236\) −970832. −1.13466
\(237\) 2.31567e6 2.67797
\(238\) 228920. 0.261964
\(239\) −403793. −0.457261 −0.228630 0.973513i \(-0.573425\pi\)
−0.228630 + 0.973513i \(0.573425\pi\)
\(240\) 201138. 0.225407
\(241\) −1.07591e6 −1.19325 −0.596627 0.802519i \(-0.703493\pi\)
−0.596627 + 0.802519i \(0.703493\pi\)
\(242\) −130083. −0.142785
\(243\) 1.01267e6 1.10016
\(244\) −104598. −0.112473
\(245\) 464950. 0.494870
\(246\) 2.62350e6 2.76403
\(247\) −365751. −0.381455
\(248\) −244349. −0.252279
\(249\) −2.21559e6 −2.26460
\(250\) −138826. −0.140482
\(251\) −356261. −0.356931 −0.178465 0.983946i \(-0.557113\pi\)
−0.178465 + 0.983946i \(0.557113\pi\)
\(252\) −3.34562e6 −3.31876
\(253\) −302484. −0.297099
\(254\) 1.37622e6 1.33845
\(255\) −85361.1 −0.0822072
\(256\) −459811. −0.438510
\(257\) −757207. −0.715125 −0.357562 0.933889i \(-0.616392\pi\)
−0.357562 + 0.933889i \(0.616392\pi\)
\(258\) −866617. −0.810547
\(259\) 1.88784e6 1.74870
\(260\) 1.18897e6 1.09078
\(261\) 2.62456e6 2.38482
\(262\) −2.58302e6 −2.32474
\(263\) −1.51030e6 −1.34640 −0.673199 0.739461i \(-0.735080\pi\)
−0.673199 + 0.739461i \(0.735080\pi\)
\(264\) 400532. 0.353694
\(265\) −898003. −0.785530
\(266\) −603519. −0.522982
\(267\) −3.18547e6 −2.73461
\(268\) −1.37423e6 −1.16876
\(269\) 292026. 0.246060 0.123030 0.992403i \(-0.460739\pi\)
0.123030 + 0.992403i \(0.460739\pi\)
\(270\) 752075. 0.627844
\(271\) 1.45925e6 1.20700 0.603500 0.797363i \(-0.293772\pi\)
0.603500 + 0.797363i \(0.293772\pi\)
\(272\) −44181.0 −0.0362087
\(273\) 4.75369e6 3.86032
\(274\) −293140. −0.235885
\(275\) 75625.0 0.0603023
\(276\) 2.92610e6 2.31215
\(277\) 553858. 0.433709 0.216855 0.976204i \(-0.430420\pi\)
0.216855 + 0.976204i \(0.430420\pi\)
\(278\) −1.54676e6 −1.20036
\(279\) 697222. 0.536242
\(280\) 624459. 0.476002
\(281\) 869175. 0.656662 0.328331 0.944563i \(-0.393514\pi\)
0.328331 + 0.944563i \(0.393514\pi\)
\(282\) −3.63733e6 −2.72371
\(283\) −1.26603e6 −0.939675 −0.469837 0.882753i \(-0.655687\pi\)
−0.469837 + 0.882753i \(0.655687\pi\)
\(284\) −1.19912e6 −0.882203
\(285\) 225044. 0.164118
\(286\) −1.08922e6 −0.787408
\(287\) −2.22814e6 −1.59675
\(288\) 2.69494e6 1.91455
\(289\) −1.40111e6 −0.986794
\(290\) −1.53906e6 −1.07464
\(291\) 879536. 0.608865
\(292\) 1.47859e6 1.01482
\(293\) −690423. −0.469836 −0.234918 0.972015i \(-0.575482\pi\)
−0.234918 + 0.972015i \(0.575482\pi\)
\(294\) 4.12038e6 2.78016
\(295\) −517048. −0.345920
\(296\) 1.33188e6 0.883558
\(297\) −409690. −0.269503
\(298\) −3.87135e6 −2.52535
\(299\) −2.53276e6 −1.63839
\(300\) −731564. −0.469299
\(301\) 736018. 0.468244
\(302\) 1.38594e6 0.874434
\(303\) 2.76675e6 1.73127
\(304\) 116478. 0.0722867
\(305\) −55707.0 −0.0342894
\(306\) −460833. −0.281346
\(307\) 616049. 0.373052 0.186526 0.982450i \(-0.440277\pi\)
0.186526 + 0.982450i \(0.440277\pi\)
\(308\) −1.06874e6 −0.641939
\(309\) −1.41003e6 −0.840100
\(310\) −408856. −0.241639
\(311\) 1.66166e6 0.974182 0.487091 0.873351i \(-0.338058\pi\)
0.487091 + 0.873351i \(0.338058\pi\)
\(312\) 3.35375e6 1.95049
\(313\) 1.35601e6 0.782354 0.391177 0.920315i \(-0.372068\pi\)
0.391177 + 0.920315i \(0.372068\pi\)
\(314\) 1.11603e6 0.638781
\(315\) −1.78182e6 −1.01178
\(316\) −4.35922e6 −2.45579
\(317\) 1.23272e6 0.688998 0.344499 0.938787i \(-0.388049\pi\)
0.344499 + 0.938787i \(0.388049\pi\)
\(318\) −7.95809e6 −4.41307
\(319\) 838398. 0.461290
\(320\) −1.32221e6 −0.721814
\(321\) −737914. −0.399708
\(322\) −4.17927e6 −2.24626
\(323\) −49431.9 −0.0263634
\(324\) −357501. −0.189197
\(325\) 633225. 0.332545
\(326\) −4.33914e6 −2.26131
\(327\) −3.27280e6 −1.69259
\(328\) −1.57196e6 −0.806784
\(329\) 3.08919e6 1.57346
\(330\) 670188. 0.338775
\(331\) −899915. −0.451473 −0.225736 0.974188i \(-0.572479\pi\)
−0.225736 + 0.974188i \(0.572479\pi\)
\(332\) 4.17083e6 2.07672
\(333\) −3.80036e6 −1.87808
\(334\) −2.32518e6 −1.14049
\(335\) −731893. −0.356316
\(336\) −1.51387e6 −0.731542
\(337\) −3.37808e6 −1.62030 −0.810150 0.586223i \(-0.800614\pi\)
−0.810150 + 0.586223i \(0.800614\pi\)
\(338\) −5.82138e6 −2.77162
\(339\) −842467. −0.398156
\(340\) 160691. 0.0753868
\(341\) 222723. 0.103724
\(342\) 1.21493e6 0.561675
\(343\) −336997. −0.154665
\(344\) 519264. 0.236588
\(345\) 1.55839e6 0.704902
\(346\) 132312. 0.0594169
\(347\) −3.33946e6 −1.48886 −0.744428 0.667703i \(-0.767278\pi\)
−0.744428 + 0.667703i \(0.767278\pi\)
\(348\) −8.11031e6 −3.58996
\(349\) 3.42925e6 1.50708 0.753538 0.657404i \(-0.228345\pi\)
0.753538 + 0.657404i \(0.228345\pi\)
\(350\) 1.04487e6 0.455925
\(351\) −3.43043e6 −1.48621
\(352\) 860879. 0.370327
\(353\) 790575. 0.337681 0.168840 0.985643i \(-0.445998\pi\)
0.168840 + 0.985643i \(0.445998\pi\)
\(354\) −4.58208e6 −1.94337
\(355\) −638634. −0.268956
\(356\) 5.99662e6 2.50774
\(357\) 642469. 0.266798
\(358\) −4.05773e6 −1.67330
\(359\) −3.75551e6 −1.53792 −0.768959 0.639299i \(-0.779225\pi\)
−0.768959 + 0.639299i \(0.779225\pi\)
\(360\) −1.25708e6 −0.511220
\(361\) 130321. 0.0526316
\(362\) 3.10232e6 1.24427
\(363\) −365082. −0.145420
\(364\) −8.94877e6 −3.54005
\(365\) 787472. 0.309388
\(366\) −493675. −0.192636
\(367\) −96283.1 −0.0373151 −0.0186576 0.999826i \(-0.505939\pi\)
−0.0186576 + 0.999826i \(0.505939\pi\)
\(368\) 806588. 0.310479
\(369\) 4.48541e6 1.71489
\(370\) 2.22856e6 0.846290
\(371\) 6.75881e6 2.54938
\(372\) −2.15453e6 −0.807224
\(373\) 1.32162e6 0.491852 0.245926 0.969289i \(-0.420908\pi\)
0.245926 + 0.969289i \(0.420908\pi\)
\(374\) −147210. −0.0544199
\(375\) −389619. −0.143074
\(376\) 2.17943e6 0.795013
\(377\) 7.02010e6 2.54384
\(378\) −5.66048e6 −2.03762
\(379\) 784562. 0.280562 0.140281 0.990112i \(-0.455199\pi\)
0.140281 + 0.990112i \(0.455199\pi\)
\(380\) −423643. −0.150502
\(381\) 3.86239e6 1.36315
\(382\) −3.93105e6 −1.37832
\(383\) 3.13193e6 1.09098 0.545489 0.838118i \(-0.316344\pi\)
0.545489 + 0.838118i \(0.316344\pi\)
\(384\) −6.04031e6 −2.09041
\(385\) −569190. −0.195707
\(386\) 1.20094e6 0.410253
\(387\) −1.48166e6 −0.502887
\(388\) −1.65572e6 −0.558351
\(389\) −2.33290e6 −0.781669 −0.390834 0.920461i \(-0.627813\pi\)
−0.390834 + 0.920461i \(0.627813\pi\)
\(390\) 5.61164e6 1.86822
\(391\) −342308. −0.113233
\(392\) −2.46887e6 −0.811490
\(393\) −7.24932e6 −2.36764
\(394\) 4.22952e6 1.37262
\(395\) −2.32165e6 −0.748692
\(396\) 2.15144e6 0.689433
\(397\) 4.61021e6 1.46806 0.734031 0.679116i \(-0.237637\pi\)
0.734031 + 0.679116i \(0.237637\pi\)
\(398\) 6.20917e6 1.96483
\(399\) −1.69379e6 −0.532632
\(400\) −201658. −0.0630181
\(401\) 2.26692e6 0.704005 0.352002 0.935999i \(-0.385501\pi\)
0.352002 + 0.935999i \(0.385501\pi\)
\(402\) −6.48603e6 −2.00177
\(403\) 1.86491e6 0.571998
\(404\) −5.20839e6 −1.58763
\(405\) −190399. −0.0576803
\(406\) 1.15837e7 3.48766
\(407\) −1.21400e6 −0.363272
\(408\) 453265. 0.134804
\(409\) −5.53987e6 −1.63754 −0.818769 0.574124i \(-0.805343\pi\)
−0.818769 + 0.574124i \(0.805343\pi\)
\(410\) −2.63027e6 −0.772754
\(411\) −822705. −0.240237
\(412\) 2.65436e6 0.770401
\(413\) 3.89156e6 1.12266
\(414\) 8.41318e6 2.41245
\(415\) 2.22131e6 0.633125
\(416\) 7.20834e6 2.04222
\(417\) −4.34101e6 −1.22250
\(418\) 388100. 0.108643
\(419\) 5.61196e6 1.56164 0.780818 0.624759i \(-0.214803\pi\)
0.780818 + 0.624759i \(0.214803\pi\)
\(420\) 5.50611e6 1.52308
\(421\) −4.63665e6 −1.27497 −0.637483 0.770464i \(-0.720024\pi\)
−0.637483 + 0.770464i \(0.720024\pi\)
\(422\) 2.95340e6 0.807311
\(423\) −6.21876e6 −1.68987
\(424\) 4.76837e6 1.28812
\(425\) 85581.6 0.0229831
\(426\) −5.65956e6 −1.51098
\(427\) 419278. 0.111284
\(428\) 1.38912e6 0.366547
\(429\) −3.05692e6 −0.801937
\(430\) 868855. 0.226608
\(431\) −2.50316e6 −0.649076 −0.324538 0.945873i \(-0.605209\pi\)
−0.324538 + 0.945873i \(0.605209\pi\)
\(432\) 1.09246e6 0.281641
\(433\) −2.77523e6 −0.711344 −0.355672 0.934611i \(-0.615748\pi\)
−0.355672 + 0.934611i \(0.615748\pi\)
\(434\) 3.07725e6 0.784221
\(435\) −4.31942e6 −1.09446
\(436\) 6.16102e6 1.55216
\(437\) 902451. 0.226058
\(438\) 6.97857e6 1.73812
\(439\) 6.81783e6 1.68844 0.844219 0.535999i \(-0.180065\pi\)
0.844219 + 0.535999i \(0.180065\pi\)
\(440\) −401566. −0.0988839
\(441\) 7.04463e6 1.72489
\(442\) −1.23262e6 −0.300106
\(443\) 427517. 0.103501 0.0517505 0.998660i \(-0.483520\pi\)
0.0517505 + 0.998660i \(0.483520\pi\)
\(444\) 1.17437e7 2.82714
\(445\) 3.19370e6 0.764529
\(446\) −1.22777e7 −2.92267
\(447\) −1.08650e7 −2.57195
\(448\) 9.95159e6 2.34260
\(449\) −8.49047e6 −1.98754 −0.993770 0.111448i \(-0.964451\pi\)
−0.993770 + 0.111448i \(0.964451\pi\)
\(450\) −2.10341e6 −0.489657
\(451\) 1.43283e6 0.331706
\(452\) 1.58594e6 0.365123
\(453\) 3.88967e6 0.890569
\(454\) 3.59015e6 0.817472
\(455\) −4.76596e6 −1.07925
\(456\) −1.19498e6 −0.269121
\(457\) 6.49877e6 1.45560 0.727798 0.685792i \(-0.240544\pi\)
0.727798 + 0.685792i \(0.240544\pi\)
\(458\) −1.19361e7 −2.65887
\(459\) −463629. −0.102716
\(460\) −2.93366e6 −0.646420
\(461\) 4.71758e6 1.03387 0.516937 0.856024i \(-0.327072\pi\)
0.516937 + 0.856024i \(0.327072\pi\)
\(462\) −5.04416e6 −1.09947
\(463\) 5.90781e6 1.28078 0.640389 0.768051i \(-0.278773\pi\)
0.640389 + 0.768051i \(0.278773\pi\)
\(464\) −2.23563e6 −0.482065
\(465\) −1.14746e6 −0.246097
\(466\) 1.26843e7 2.70584
\(467\) 5.03866e6 1.06911 0.534556 0.845133i \(-0.320479\pi\)
0.534556 + 0.845133i \(0.320479\pi\)
\(468\) 1.80145e7 3.80197
\(469\) 5.50859e6 1.15640
\(470\) 3.64673e6 0.761480
\(471\) 3.13217e6 0.650568
\(472\) 2.74551e6 0.567242
\(473\) −473305. −0.0972721
\(474\) −2.05744e7 −4.20612
\(475\) −225625. −0.0458831
\(476\) −1.20944e6 −0.244663
\(477\) −1.36060e7 −2.73800
\(478\) 3.58765e6 0.718191
\(479\) −1.78762e6 −0.355989 −0.177995 0.984031i \(-0.556961\pi\)
−0.177995 + 0.984031i \(0.556961\pi\)
\(480\) −4.43524e6 −0.878645
\(481\) −1.01651e7 −2.00331
\(482\) 9.55932e6 1.87417
\(483\) −1.17292e7 −2.28771
\(484\) 687264. 0.133355
\(485\) −881808. −0.170224
\(486\) −8.99749e6 −1.72795
\(487\) 3.29188e6 0.628958 0.314479 0.949264i \(-0.398170\pi\)
0.314479 + 0.949264i \(0.398170\pi\)
\(488\) 295802. 0.0562279
\(489\) −1.21779e7 −2.30303
\(490\) −4.13102e6 −0.777262
\(491\) −1.03906e7 −1.94508 −0.972541 0.232733i \(-0.925233\pi\)
−0.972541 + 0.232733i \(0.925233\pi\)
\(492\) −1.38606e7 −2.58148
\(493\) 948779. 0.175812
\(494\) 3.24965e6 0.599128
\(495\) 1.14582e6 0.210186
\(496\) −593901. −0.108395
\(497\) 4.80667e6 0.872877
\(498\) 1.96852e7 3.55687
\(499\) −3.54549e6 −0.637419 −0.318710 0.947852i \(-0.603250\pi\)
−0.318710 + 0.947852i \(0.603250\pi\)
\(500\) 733454. 0.131204
\(501\) −6.52567e6 −1.16153
\(502\) 3.16533e6 0.560609
\(503\) 3.87983e6 0.683743 0.341872 0.939747i \(-0.388939\pi\)
0.341872 + 0.939747i \(0.388939\pi\)
\(504\) 9.46142e6 1.65913
\(505\) −2.77390e6 −0.484019
\(506\) 2.68753e6 0.466635
\(507\) −1.63378e7 −2.82277
\(508\) −7.27091e6 −1.25006
\(509\) −6.20042e6 −1.06078 −0.530392 0.847753i \(-0.677955\pi\)
−0.530392 + 0.847753i \(0.677955\pi\)
\(510\) 758423. 0.129118
\(511\) −5.92689e6 −1.00410
\(512\) −3.66620e6 −0.618075
\(513\) 1.22230e6 0.205061
\(514\) 6.72769e6 1.12320
\(515\) 1.41367e6 0.234871
\(516\) 4.57856e6 0.757015
\(517\) −1.98654e6 −0.326867
\(518\) −1.67732e7 −2.74658
\(519\) 371337. 0.0605132
\(520\) −3.36241e6 −0.545308
\(521\) −1.15408e7 −1.86269 −0.931347 0.364132i \(-0.881366\pi\)
−0.931347 + 0.364132i \(0.881366\pi\)
\(522\) −2.33189e7 −3.74569
\(523\) −4.76148e6 −0.761181 −0.380591 0.924744i \(-0.624279\pi\)
−0.380591 + 0.924744i \(0.624279\pi\)
\(524\) 1.36468e7 2.17121
\(525\) 2.93246e6 0.464338
\(526\) 1.34188e7 2.11471
\(527\) 252046. 0.0395324
\(528\) 973510. 0.151969
\(529\) −187022. −0.0290572
\(530\) 7.97864e6 1.23378
\(531\) −7.83400e6 −1.20572
\(532\) 3.18854e6 0.488442
\(533\) 1.19974e7 1.82924
\(534\) 2.83025e7 4.29509
\(535\) 739820. 0.111748
\(536\) 3.88633e6 0.584289
\(537\) −1.13881e7 −1.70418
\(538\) −2.59462e6 −0.386472
\(539\) 2.25036e6 0.333641
\(540\) −3.97340e6 −0.586379
\(541\) −2.61622e6 −0.384309 −0.192154 0.981365i \(-0.561547\pi\)
−0.192154 + 0.981365i \(0.561547\pi\)
\(542\) −1.29653e7 −1.89576
\(543\) 8.70672e6 1.26723
\(544\) 974220. 0.141143
\(545\) 3.28126e6 0.473205
\(546\) −4.22359e7 −6.06318
\(547\) −3.57422e6 −0.510756 −0.255378 0.966841i \(-0.582200\pi\)
−0.255378 + 0.966841i \(0.582200\pi\)
\(548\) 1.54873e6 0.220306
\(549\) −844037. −0.119517
\(550\) −671919. −0.0947131
\(551\) −2.50134e6 −0.350989
\(552\) −8.27501e6 −1.15590
\(553\) 1.74738e7 2.42983
\(554\) −4.92096e6 −0.681201
\(555\) 6.25449e6 0.861906
\(556\) 8.17190e6 1.12108
\(557\) 1.23683e7 1.68917 0.844585 0.535422i \(-0.179847\pi\)
0.844585 + 0.535422i \(0.179847\pi\)
\(558\) −6.19473e6 −0.842242
\(559\) −3.96309e6 −0.536420
\(560\) 1.51777e6 0.204521
\(561\) −413148. −0.0554241
\(562\) −7.72252e6 −1.03138
\(563\) −6.02685e6 −0.801345 −0.400672 0.916221i \(-0.631223\pi\)
−0.400672 + 0.916221i \(0.631223\pi\)
\(564\) 1.92169e7 2.54382
\(565\) 844643. 0.111315
\(566\) 1.12485e7 1.47589
\(567\) 1.43304e6 0.187197
\(568\) 3.39112e6 0.441035
\(569\) 1.27503e7 1.65097 0.825487 0.564421i \(-0.190901\pi\)
0.825487 + 0.564421i \(0.190901\pi\)
\(570\) −1.99949e6 −0.257769
\(571\) 2.46819e6 0.316802 0.158401 0.987375i \(-0.449366\pi\)
0.158401 + 0.987375i \(0.449366\pi\)
\(572\) 5.75461e6 0.735404
\(573\) −1.10326e7 −1.40375
\(574\) 1.97967e7 2.50792
\(575\) −1.56242e6 −0.197073
\(576\) −2.00333e7 −2.51592
\(577\) 139823. 0.0174839 0.00874197 0.999962i \(-0.497217\pi\)
0.00874197 + 0.999962i \(0.497217\pi\)
\(578\) 1.24487e7 1.54990
\(579\) 3.37045e6 0.417823
\(580\) 8.13126e6 1.00366
\(581\) −1.67187e7 −2.05476
\(582\) −7.81457e6 −0.956308
\(583\) −4.34633e6 −0.529604
\(584\) −4.18145e6 −0.507335
\(585\) 9.59424e6 1.15910
\(586\) 6.13432e6 0.737943
\(587\) 5.33599e6 0.639175 0.319588 0.947557i \(-0.396456\pi\)
0.319588 + 0.947557i \(0.396456\pi\)
\(588\) −2.17690e7 −2.59654
\(589\) −664487. −0.0789220
\(590\) 4.59391e6 0.543316
\(591\) 1.18702e7 1.39795
\(592\) 3.23718e6 0.379632
\(593\) −1.22305e7 −1.42826 −0.714130 0.700013i \(-0.753177\pi\)
−0.714130 + 0.700013i \(0.753177\pi\)
\(594\) 3.64004e6 0.423293
\(595\) −644128. −0.0745899
\(596\) 2.04533e7 2.35856
\(597\) 1.74262e7 2.00109
\(598\) 2.25033e7 2.57332
\(599\) −1.15256e7 −1.31249 −0.656247 0.754546i \(-0.727857\pi\)
−0.656247 + 0.754546i \(0.727857\pi\)
\(600\) 2.06886e6 0.234614
\(601\) 3.52237e6 0.397786 0.198893 0.980021i \(-0.436265\pi\)
0.198893 + 0.980021i \(0.436265\pi\)
\(602\) −6.53943e6 −0.735442
\(603\) −1.10892e7 −1.24196
\(604\) −7.32227e6 −0.816682
\(605\) 366025. 0.0406558
\(606\) −2.45823e7 −2.71919
\(607\) −3.87019e6 −0.426344 −0.213172 0.977015i \(-0.568380\pi\)
−0.213172 + 0.977015i \(0.568380\pi\)
\(608\) −2.56841e6 −0.281777
\(609\) 3.25100e7 3.55201
\(610\) 494950. 0.0538563
\(611\) −1.66337e7 −1.80255
\(612\) 2.43470e6 0.262764
\(613\) 5.31523e6 0.571309 0.285655 0.958333i \(-0.407789\pi\)
0.285655 + 0.958333i \(0.407789\pi\)
\(614\) −5.47352e6 −0.585930
\(615\) −7.38192e6 −0.787013
\(616\) 3.02238e6 0.320921
\(617\) −5.68939e6 −0.601663 −0.300831 0.953677i \(-0.597264\pi\)
−0.300831 + 0.953677i \(0.597264\pi\)
\(618\) 1.25279e7 1.31949
\(619\) −1.27931e6 −0.134199 −0.0670997 0.997746i \(-0.521375\pi\)
−0.0670997 + 0.997746i \(0.521375\pi\)
\(620\) 2.16009e6 0.225680
\(621\) 8.46421e6 0.880760
\(622\) −1.47636e7 −1.53009
\(623\) −2.40373e7 −2.48123
\(624\) 8.15142e6 0.838054
\(625\) 390625. 0.0400000
\(626\) −1.20480e7 −1.22880
\(627\) 1.08921e6 0.110648
\(628\) −5.89627e6 −0.596593
\(629\) −1.37383e6 −0.138454
\(630\) 1.58313e7 1.58915
\(631\) 3.51100e6 0.351041 0.175521 0.984476i \(-0.443839\pi\)
0.175521 + 0.984476i \(0.443839\pi\)
\(632\) 1.23279e7 1.22771
\(633\) 8.28878e6 0.822207
\(634\) −1.09526e7 −1.08217
\(635\) −3.87236e6 −0.381102
\(636\) 4.20446e7 4.12162
\(637\) 1.88428e7 1.83991
\(638\) −7.44907e6 −0.724520
\(639\) −9.67618e6 −0.937458
\(640\) 6.05591e6 0.584425
\(641\) −1.25302e6 −0.120452 −0.0602258 0.998185i \(-0.519182\pi\)
−0.0602258 + 0.998185i \(0.519182\pi\)
\(642\) 6.55628e6 0.627798
\(643\) 1.36373e7 1.30077 0.650386 0.759604i \(-0.274607\pi\)
0.650386 + 0.759604i \(0.274607\pi\)
\(644\) 2.20801e7 2.09791
\(645\) 2.43846e6 0.230790
\(646\) 439196. 0.0414074
\(647\) −4.55963e6 −0.428222 −0.214111 0.976809i \(-0.568685\pi\)
−0.214111 + 0.976809i \(0.568685\pi\)
\(648\) 1.01101e6 0.0945843
\(649\) −2.50251e6 −0.233220
\(650\) −5.62613e6 −0.522308
\(651\) 8.63637e6 0.798691
\(652\) 2.29248e7 2.11196
\(653\) −1.74990e7 −1.60594 −0.802971 0.596019i \(-0.796748\pi\)
−0.802971 + 0.596019i \(0.796748\pi\)
\(654\) 2.90785e7 2.65844
\(655\) 7.26804e6 0.661933
\(656\) −3.82072e6 −0.346645
\(657\) 1.19313e7 1.07838
\(658\) −2.74470e7 −2.47133
\(659\) 1.41476e7 1.26902 0.634512 0.772913i \(-0.281201\pi\)
0.634512 + 0.772913i \(0.281201\pi\)
\(660\) −3.54077e6 −0.316401
\(661\) −9.25386e6 −0.823795 −0.411897 0.911230i \(-0.635134\pi\)
−0.411897 + 0.911230i \(0.635134\pi\)
\(662\) 7.99563e6 0.709101
\(663\) −3.45938e6 −0.305643
\(664\) −1.17951e7 −1.03820
\(665\) 1.69816e6 0.148911
\(666\) 3.37657e7 2.94978
\(667\) −1.73213e7 −1.50753
\(668\) 1.22845e7 1.06517
\(669\) −3.44576e7 −2.97660
\(670\) 6.50278e6 0.559644
\(671\) −269622. −0.0231179
\(672\) 3.33817e7 2.85158
\(673\) 1.31201e7 1.11660 0.558301 0.829638i \(-0.311453\pi\)
0.558301 + 0.829638i \(0.311453\pi\)
\(674\) 3.00138e7 2.54491
\(675\) −2.11617e6 −0.178768
\(676\) 3.07558e7 2.58857
\(677\) 1.75189e7 1.46904 0.734521 0.678586i \(-0.237407\pi\)
0.734521 + 0.678586i \(0.237407\pi\)
\(678\) 7.48522e6 0.625360
\(679\) 6.63691e6 0.552448
\(680\) −454435. −0.0376877
\(681\) 1.00758e7 0.832555
\(682\) −1.97886e6 −0.162913
\(683\) −6.94169e6 −0.569395 −0.284698 0.958617i \(-0.591893\pi\)
−0.284698 + 0.958617i \(0.591893\pi\)
\(684\) −6.41877e6 −0.524580
\(685\) 824830. 0.0671642
\(686\) 2.99418e6 0.242922
\(687\) −3.34989e7 −2.70793
\(688\) 1.26209e6 0.101653
\(689\) −3.63928e7 −2.92057
\(690\) −1.38461e7 −1.10715
\(691\) −743833. −0.0592625 −0.0296313 0.999561i \(-0.509433\pi\)
−0.0296313 + 0.999561i \(0.509433\pi\)
\(692\) −699039. −0.0554927
\(693\) −8.62402e6 −0.682145
\(694\) 2.96707e7 2.33846
\(695\) 4.35222e6 0.341782
\(696\) 2.29360e7 1.79471
\(697\) 1.62147e6 0.126424
\(698\) −3.04684e7 −2.36707
\(699\) 3.55988e7 2.75576
\(700\) −5.52033e6 −0.425814
\(701\) 2.12345e6 0.163210 0.0816049 0.996665i \(-0.473995\pi\)
0.0816049 + 0.996665i \(0.473995\pi\)
\(702\) 3.04789e7 2.33430
\(703\) 3.62193e6 0.276408
\(704\) −6.39949e6 −0.486647
\(705\) 1.02346e7 0.775531
\(706\) −7.02416e6 −0.530375
\(707\) 2.08777e7 1.57085
\(708\) 2.42083e7 1.81502
\(709\) −1.34560e7 −1.00531 −0.502654 0.864488i \(-0.667643\pi\)
−0.502654 + 0.864488i \(0.667643\pi\)
\(710\) 5.67418e6 0.422432
\(711\) −3.51761e7 −2.60960
\(712\) −1.69585e7 −1.25368
\(713\) −4.60146e6 −0.338978
\(714\) −5.70826e6 −0.419043
\(715\) 3.06481e6 0.224202
\(716\) 2.14380e7 1.56279
\(717\) 1.00688e7 0.731443
\(718\) 3.33673e7 2.41551
\(719\) 791399. 0.0570917 0.0285459 0.999592i \(-0.490912\pi\)
0.0285459 + 0.999592i \(0.490912\pi\)
\(720\) −3.05539e6 −0.219652
\(721\) −1.06400e7 −0.762257
\(722\) −1.15789e6 −0.0826652
\(723\) 2.68284e7 1.90875
\(724\) −1.63903e7 −1.16209
\(725\) 4.33057e6 0.305985
\(726\) 3.24371e6 0.228402
\(727\) −532721. −0.0373821 −0.0186911 0.999825i \(-0.505950\pi\)
−0.0186911 + 0.999825i \(0.505950\pi\)
\(728\) 2.53071e7 1.76976
\(729\) −2.34010e7 −1.63085
\(730\) −6.99659e6 −0.485936
\(731\) −535619. −0.0370734
\(732\) 2.60821e6 0.179914
\(733\) −5.86911e6 −0.403471 −0.201735 0.979440i \(-0.564658\pi\)
−0.201735 + 0.979440i \(0.564658\pi\)
\(734\) 855464. 0.0586086
\(735\) −1.15938e7 −0.791603
\(736\) −1.77858e7 −1.21026
\(737\) −3.54236e6 −0.240228
\(738\) −3.98523e7 −2.69347
\(739\) −1.14369e7 −0.770368 −0.385184 0.922840i \(-0.625862\pi\)
−0.385184 + 0.922840i \(0.625862\pi\)
\(740\) −1.17740e7 −0.790398
\(741\) 9.12022e6 0.610183
\(742\) −6.00511e7 −4.00416
\(743\) −1.57238e7 −1.04492 −0.522462 0.852662i \(-0.674986\pi\)
−0.522462 + 0.852662i \(0.674986\pi\)
\(744\) 6.09300e6 0.403551
\(745\) 1.08931e7 0.719052
\(746\) −1.17424e7 −0.772522
\(747\) 3.36559e7 2.20679
\(748\) 777747. 0.0508258
\(749\) −5.56824e6 −0.362672
\(750\) 3.46172e6 0.224718
\(751\) 1.38162e7 0.893902 0.446951 0.894558i \(-0.352510\pi\)
0.446951 + 0.894558i \(0.352510\pi\)
\(752\) 5.29721e6 0.341588
\(753\) 8.88358e6 0.570953
\(754\) −6.23727e7 −3.99546
\(755\) −3.89972e6 −0.248981
\(756\) 2.99058e7 1.90305
\(757\) −1.29929e6 −0.0824073 −0.0412037 0.999151i \(-0.513119\pi\)
−0.0412037 + 0.999151i \(0.513119\pi\)
\(758\) −6.97074e6 −0.440662
\(759\) 7.54261e6 0.475245
\(760\) 1.19806e6 0.0752394
\(761\) −1.25864e7 −0.787843 −0.393922 0.919144i \(-0.628882\pi\)
−0.393922 + 0.919144i \(0.628882\pi\)
\(762\) −3.43168e7 −2.14102
\(763\) −2.46963e7 −1.53575
\(764\) 2.07687e7 1.28729
\(765\) 1.29668e6 0.0801085
\(766\) −2.78268e7 −1.71353
\(767\) −2.09541e7 −1.28612
\(768\) 1.14657e7 0.701449
\(769\) −5.78962e6 −0.353048 −0.176524 0.984296i \(-0.556485\pi\)
−0.176524 + 0.984296i \(0.556485\pi\)
\(770\) 5.05719e6 0.307385
\(771\) 1.88814e7 1.14393
\(772\) −6.34485e6 −0.383158
\(773\) 2.03165e6 0.122293 0.0611464 0.998129i \(-0.480524\pi\)
0.0611464 + 0.998129i \(0.480524\pi\)
\(774\) 1.31644e7 0.789854
\(775\) 1.15043e6 0.0688026
\(776\) 4.68237e6 0.279133
\(777\) −4.70744e7 −2.79725
\(778\) 2.07276e7 1.22772
\(779\) −4.27481e6 −0.252391
\(780\) −2.96477e7 −1.74483
\(781\) −3.09099e6 −0.181330
\(782\) 3.04136e6 0.177849
\(783\) −2.34604e7 −1.36751
\(784\) −6.00069e6 −0.348667
\(785\) −3.14026e6 −0.181882
\(786\) 6.44093e7 3.71871
\(787\) 1.29592e7 0.745833 0.372917 0.927865i \(-0.378358\pi\)
0.372917 + 0.927865i \(0.378358\pi\)
\(788\) −2.23456e7 −1.28197
\(789\) 3.76602e7 2.15372
\(790\) 2.06275e7 1.17593
\(791\) −6.35719e6 −0.361263
\(792\) −6.08428e6 −0.344664
\(793\) −2.25760e6 −0.127487
\(794\) −4.09611e7 −2.30579
\(795\) 2.23922e7 1.25655
\(796\) −3.28046e7 −1.83507
\(797\) −2.70442e6 −0.150810 −0.0754048 0.997153i \(-0.524025\pi\)
−0.0754048 + 0.997153i \(0.524025\pi\)
\(798\) 1.50491e7 0.836572
\(799\) −2.24808e6 −0.124579
\(800\) 4.44669e6 0.245647
\(801\) 4.83890e7 2.66480
\(802\) −2.01413e7 −1.10574
\(803\) 3.81136e6 0.208589
\(804\) 3.42673e7 1.86956
\(805\) 1.17595e7 0.639586
\(806\) −1.65695e7 −0.898403
\(807\) −7.28186e6 −0.393603
\(808\) 1.47293e7 0.793696
\(809\) 1.45890e7 0.783708 0.391854 0.920027i \(-0.371834\pi\)
0.391854 + 0.920027i \(0.371834\pi\)
\(810\) 1.69167e6 0.0905949
\(811\) 1.41263e7 0.754181 0.377090 0.926177i \(-0.376925\pi\)
0.377090 + 0.926177i \(0.376925\pi\)
\(812\) −6.11998e7 −3.25732
\(813\) −3.63874e7 −1.93074
\(814\) 1.07862e7 0.570569
\(815\) 1.22093e7 0.643870
\(816\) 1.10168e6 0.0579202
\(817\) 1.41209e6 0.0740130
\(818\) 4.92211e7 2.57198
\(819\) −7.22109e7 −3.76178
\(820\) 1.38964e7 0.721718
\(821\) 6.20587e6 0.321325 0.160663 0.987009i \(-0.448637\pi\)
0.160663 + 0.987009i \(0.448637\pi\)
\(822\) 7.30964e6 0.377326
\(823\) 1.55160e6 0.0798512 0.0399256 0.999203i \(-0.487288\pi\)
0.0399256 + 0.999203i \(0.487288\pi\)
\(824\) −7.50653e6 −0.385142
\(825\) −1.88576e6 −0.0964607
\(826\) −3.45760e7 −1.76329
\(827\) 2.67852e7 1.36186 0.680928 0.732350i \(-0.261577\pi\)
0.680928 + 0.732350i \(0.261577\pi\)
\(828\) −4.44489e7 −2.25313
\(829\) 2.26034e7 1.14232 0.571160 0.820839i \(-0.306493\pi\)
0.571160 + 0.820839i \(0.306493\pi\)
\(830\) −1.97361e7 −0.994411
\(831\) −1.38108e7 −0.693770
\(832\) −5.35844e7 −2.68368
\(833\) 2.54663e6 0.127161
\(834\) 3.85693e7 1.92011
\(835\) 6.54253e6 0.324735
\(836\) −2.05043e6 −0.101468
\(837\) −6.23231e6 −0.307493
\(838\) −4.98616e7 −2.45277
\(839\) −3.86543e7 −1.89580 −0.947901 0.318565i \(-0.896799\pi\)
−0.947901 + 0.318565i \(0.896799\pi\)
\(840\) −1.55713e7 −0.761423
\(841\) 2.74987e7 1.34067
\(842\) 4.11960e7 2.00251
\(843\) −2.16734e7 −1.05041
\(844\) −1.56035e7 −0.753992
\(845\) 1.63800e7 0.789174
\(846\) 5.52529e7 2.65417
\(847\) −2.75488e6 −0.131945
\(848\) 1.15897e7 0.553456
\(849\) 3.15692e7 1.50312
\(850\) −760382. −0.0360981
\(851\) 2.50812e7 1.18720
\(852\) 2.99009e7 1.41119
\(853\) 2.27225e7 1.06926 0.534631 0.845086i \(-0.320451\pi\)
0.534631 + 0.845086i \(0.320451\pi\)
\(854\) −3.72523e6 −0.174787
\(855\) −3.41853e6 −0.159928
\(856\) −3.92842e6 −0.183246
\(857\) −2.68485e6 −0.124873 −0.0624365 0.998049i \(-0.519887\pi\)
−0.0624365 + 0.998049i \(0.519887\pi\)
\(858\) 2.71603e7 1.25955
\(859\) 2.12982e7 0.984827 0.492413 0.870361i \(-0.336115\pi\)
0.492413 + 0.870361i \(0.336115\pi\)
\(860\) −4.59038e6 −0.211642
\(861\) 5.55599e7 2.55419
\(862\) 2.22403e7 1.01946
\(863\) −4.00704e7 −1.83146 −0.915729 0.401796i \(-0.868386\pi\)
−0.915729 + 0.401796i \(0.868386\pi\)
\(864\) −2.40894e7 −1.09785
\(865\) −372296. −0.0169180
\(866\) 2.46576e7 1.11726
\(867\) 3.49375e7 1.57850
\(868\) −1.62579e7 −0.732427
\(869\) −1.12368e7 −0.504768
\(870\) 3.83775e7 1.71901
\(871\) −2.96610e7 −1.32477
\(872\) −1.74234e7 −0.775963
\(873\) −1.33606e7 −0.593322
\(874\) −8.01817e6 −0.355056
\(875\) −2.94003e6 −0.129817
\(876\) −3.68695e7 −1.62333
\(877\) 1.13767e7 0.499479 0.249739 0.968313i \(-0.419655\pi\)
0.249739 + 0.968313i \(0.419655\pi\)
\(878\) −6.05756e7 −2.65193
\(879\) 1.72161e7 0.751559
\(880\) −976024. −0.0424868
\(881\) −3.26303e7 −1.41639 −0.708193 0.706019i \(-0.750489\pi\)
−0.708193 + 0.706019i \(0.750489\pi\)
\(882\) −6.25907e7 −2.70918
\(883\) 1.50901e7 0.651315 0.325657 0.945488i \(-0.394414\pi\)
0.325657 + 0.945488i \(0.394414\pi\)
\(884\) 6.51225e6 0.280285
\(885\) 1.28929e7 0.553341
\(886\) −3.79844e6 −0.162563
\(887\) 1.37870e7 0.588384 0.294192 0.955746i \(-0.404950\pi\)
0.294192 + 0.955746i \(0.404950\pi\)
\(888\) −3.32112e7 −1.41336
\(889\) 2.91453e7 1.23684
\(890\) −2.83756e7 −1.20080
\(891\) −921531. −0.0388880
\(892\) 6.48661e7 2.72964
\(893\) 5.92678e6 0.248708
\(894\) 9.65344e7 4.03960
\(895\) 1.14175e7 0.476446
\(896\) −4.55797e7 −1.89671
\(897\) 6.31560e7 2.62080
\(898\) 7.54368e7 3.12171
\(899\) 1.27539e7 0.526314
\(900\) 1.11128e7 0.457318
\(901\) −4.91856e6 −0.201849
\(902\) −1.27305e7 −0.520991
\(903\) −1.83530e7 −0.749012
\(904\) −4.48503e6 −0.182534
\(905\) −8.72921e6 −0.354285
\(906\) −3.45592e7 −1.39876
\(907\) 2.49739e7 1.00802 0.504009 0.863698i \(-0.331858\pi\)
0.504009 + 0.863698i \(0.331858\pi\)
\(908\) −1.89676e7 −0.763482
\(909\) −4.20284e7 −1.68707
\(910\) 4.23450e7 1.69511
\(911\) 2.39786e7 0.957256 0.478628 0.878018i \(-0.341134\pi\)
0.478628 + 0.878018i \(0.341134\pi\)
\(912\) −2.90444e6 −0.115631
\(913\) 1.07512e7 0.426853
\(914\) −5.77408e7 −2.28622
\(915\) 1.38909e6 0.0548500
\(916\) 6.30613e7 2.48327
\(917\) −5.47028e7 −2.14826
\(918\) 4.11928e6 0.161330
\(919\) 6.14797e6 0.240128 0.120064 0.992766i \(-0.461690\pi\)
0.120064 + 0.992766i \(0.461690\pi\)
\(920\) 8.29638e6 0.323161
\(921\) −1.53616e7 −0.596741
\(922\) −4.19151e7 −1.62384
\(923\) −2.58815e7 −0.999967
\(924\) 2.66496e7 1.02686
\(925\) −6.27065e6 −0.240967
\(926\) −5.24902e7 −2.01164
\(927\) 2.14190e7 0.818654
\(928\) 4.92972e7 1.87911
\(929\) 3.50835e7 1.33372 0.666858 0.745185i \(-0.267639\pi\)
0.666858 + 0.745185i \(0.267639\pi\)
\(930\) 1.01951e7 0.386530
\(931\) −6.71388e6 −0.253863
\(932\) −6.70143e7 −2.52713
\(933\) −4.14344e7 −1.55832
\(934\) −4.47679e7 −1.67919
\(935\) 414215. 0.0154952
\(936\) −5.09451e7 −1.90070
\(937\) 2.05030e7 0.762902 0.381451 0.924389i \(-0.375424\pi\)
0.381451 + 0.924389i \(0.375424\pi\)
\(938\) −4.89431e7 −1.81629
\(939\) −3.38130e7 −1.25147
\(940\) −1.92666e7 −0.711189
\(941\) 2.06647e7 0.760774 0.380387 0.924827i \(-0.375791\pi\)
0.380387 + 0.924827i \(0.375791\pi\)
\(942\) −2.78289e7 −1.02181
\(943\) −2.96023e7 −1.08404
\(944\) 6.67308e6 0.243723
\(945\) 1.59273e7 0.580180
\(946\) 4.20526e6 0.152779
\(947\) −1.98587e6 −0.0719573 −0.0359786 0.999353i \(-0.511455\pi\)
−0.0359786 + 0.999353i \(0.511455\pi\)
\(948\) 1.08700e8 3.92833
\(949\) 3.19134e7 1.15029
\(950\) 2.00465e6 0.0720659
\(951\) −3.07387e7 −1.10213
\(952\) 3.42030e6 0.122313
\(953\) −5.07140e7 −1.80882 −0.904410 0.426664i \(-0.859689\pi\)
−0.904410 + 0.426664i \(0.859689\pi\)
\(954\) 1.20887e8 4.30041
\(955\) 1.10611e7 0.392454
\(956\) −1.89544e7 −0.670759
\(957\) −2.09060e7 −0.737888
\(958\) 1.58828e7 0.559131
\(959\) −6.20807e6 −0.217977
\(960\) 3.29701e7 1.15463
\(961\) −2.52410e7 −0.881655
\(962\) 9.03154e7 3.14647
\(963\) 1.12093e7 0.389504
\(964\) −5.05043e7 −1.75039
\(965\) −3.37916e6 −0.116813
\(966\) 1.04213e8 3.59317
\(967\) 2.75220e7 0.946486 0.473243 0.880932i \(-0.343083\pi\)
0.473243 + 0.880932i \(0.343083\pi\)
\(968\) −1.94358e6 −0.0666675
\(969\) 1.23261e6 0.0421714
\(970\) 7.83475e6 0.267360
\(971\) −3.59377e6 −0.122321 −0.0611607 0.998128i \(-0.519480\pi\)
−0.0611607 + 0.998128i \(0.519480\pi\)
\(972\) 4.75360e7 1.61383
\(973\) −3.27569e7 −1.10923
\(974\) −2.92480e7 −0.987867
\(975\) −1.57899e7 −0.531945
\(976\) 718960. 0.0241591
\(977\) −4.51616e7 −1.51368 −0.756838 0.653603i \(-0.773257\pi\)
−0.756838 + 0.653603i \(0.773257\pi\)
\(978\) 1.08199e8 3.61723
\(979\) 1.54575e7 0.515446
\(980\) 2.18252e7 0.725928
\(981\) 4.97156e7 1.64938
\(982\) 9.23194e7 3.05502
\(983\) 1.42881e7 0.471619 0.235810 0.971799i \(-0.424226\pi\)
0.235810 + 0.971799i \(0.424226\pi\)
\(984\) 3.91978e7 1.29055
\(985\) −1.19009e7 −0.390831
\(986\) −8.42979e6 −0.276137
\(987\) −7.70307e7 −2.51693
\(988\) −1.71687e7 −0.559559
\(989\) 9.77850e6 0.317893
\(990\) −1.01805e7 −0.330127
\(991\) 3.52970e7 1.14171 0.570853 0.821053i \(-0.306613\pi\)
0.570853 + 0.821053i \(0.306613\pi\)
\(992\) 1.30959e7 0.422529
\(993\) 2.24399e7 0.722185
\(994\) −4.27066e7 −1.37097
\(995\) −1.74712e7 −0.559454
\(996\) −1.04002e8 −3.32196
\(997\) 3.52946e7 1.12453 0.562264 0.826958i \(-0.309931\pi\)
0.562264 + 0.826958i \(0.309931\pi\)
\(998\) 3.15013e7 1.00116
\(999\) 3.39705e7 1.07693
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 1045.6.a.e.1.7 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.e.1.7 38 1.1 even 1 trivial