Properties

Label 230.6.a.h.1.5
Level $230$
Weight $6$
Character 230.1
Self dual yes
Analytic conductor $36.888$
Analytic rank $0$
Dimension $6$
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] = [230,6,Mod(1,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, 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("230.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.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: \(36.8882785570\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 1168x^{4} - 2857x^{3} + 297325x^{2} + 680040x - 8930700 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-19.8456\) of defining polynomial
Character \(\chi\) \(=\) 230.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} +21.8456 q^{3} +16.0000 q^{4} +25.0000 q^{5} +87.3823 q^{6} +7.44621 q^{7} +64.0000 q^{8} +234.229 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} +21.8456 q^{3} +16.0000 q^{4} +25.0000 q^{5} +87.3823 q^{6} +7.44621 q^{7} +64.0000 q^{8} +234.229 q^{9} +100.000 q^{10} -441.618 q^{11} +349.529 q^{12} +785.235 q^{13} +29.7848 q^{14} +546.139 q^{15} +256.000 q^{16} +632.287 q^{17} +936.917 q^{18} +2085.12 q^{19} +400.000 q^{20} +162.667 q^{21} -1766.47 q^{22} +529.000 q^{23} +1398.12 q^{24} +625.000 q^{25} +3140.94 q^{26} -191.604 q^{27} +119.139 q^{28} +3126.22 q^{29} +2184.56 q^{30} -416.399 q^{31} +1024.00 q^{32} -9647.41 q^{33} +2529.15 q^{34} +186.155 q^{35} +3747.67 q^{36} +744.963 q^{37} +8340.49 q^{38} +17153.9 q^{39} +1600.00 q^{40} -10179.3 q^{41} +650.667 q^{42} +20597.2 q^{43} -7065.89 q^{44} +5855.73 q^{45} +2116.00 q^{46} -17461.2 q^{47} +5592.47 q^{48} -16751.6 q^{49} +2500.00 q^{50} +13812.7 q^{51} +12563.8 q^{52} -30308.6 q^{53} -766.417 q^{54} -11040.5 q^{55} +476.557 q^{56} +45550.7 q^{57} +12504.9 q^{58} -20612.7 q^{59} +8738.23 q^{60} +6553.21 q^{61} -1665.60 q^{62} +1744.12 q^{63} +4096.00 q^{64} +19630.9 q^{65} -38589.6 q^{66} +29514.0 q^{67} +10116.6 q^{68} +11556.3 q^{69} +744.621 q^{70} -54219.6 q^{71} +14990.7 q^{72} -81319.3 q^{73} +2979.85 q^{74} +13653.5 q^{75} +33362.0 q^{76} -3288.38 q^{77} +68615.6 q^{78} +99309.8 q^{79} +6400.00 q^{80} -61103.4 q^{81} -40717.0 q^{82} +9250.19 q^{83} +2602.67 q^{84} +15807.2 q^{85} +82388.8 q^{86} +68294.2 q^{87} -28263.6 q^{88} +22988.9 q^{89} +23422.9 q^{90} +5847.02 q^{91} +8464.00 q^{92} -9096.47 q^{93} -69844.8 q^{94} +52128.1 q^{95} +22369.9 q^{96} -54909.5 q^{97} -67006.2 q^{98} -103440. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9} + 600 q^{10} + 151 q^{11} + 176 q^{12} + 463 q^{13} + 1464 q^{14} + 275 q^{15} + 1536 q^{16} + 644 q^{17} + 3596 q^{18} + 3431 q^{19} + 2400 q^{20} - 3846 q^{21} + 604 q^{22} + 3174 q^{23} + 704 q^{24} + 3750 q^{25} + 1852 q^{26} - 3364 q^{27} + 5856 q^{28} + 5973 q^{29} + 1100 q^{30} + 10262 q^{31} + 6144 q^{32} + 23025 q^{33} + 2576 q^{34} + 9150 q^{35} + 14384 q^{36} + 17207 q^{37} + 13724 q^{38} + 14136 q^{39} + 9600 q^{40} + 784 q^{41} - 15384 q^{42} + 13452 q^{43} + 2416 q^{44} + 22475 q^{45} + 12696 q^{46} + 24572 q^{47} + 2816 q^{48} + 28050 q^{49} + 15000 q^{50} + 26125 q^{51} + 7408 q^{52} + 17563 q^{53} - 13456 q^{54} + 3775 q^{55} + 23424 q^{56} - 41798 q^{57} + 23892 q^{58} + 62911 q^{59} + 4400 q^{60} + 32851 q^{61} + 41048 q^{62} + 138693 q^{63} + 24576 q^{64} + 11575 q^{65} + 92100 q^{66} + 54177 q^{67} + 10304 q^{68} + 5819 q^{69} + 36600 q^{70} - 14368 q^{71} + 57536 q^{72} + 33276 q^{73} + 68828 q^{74} + 6875 q^{75} + 54896 q^{76} - 143678 q^{77} + 56544 q^{78} + 74296 q^{79} + 38400 q^{80} + 150834 q^{81} + 3136 q^{82} + 65145 q^{83} - 61536 q^{84} + 16100 q^{85} + 53808 q^{86} - 790 q^{87} + 9664 q^{88} - 67562 q^{89} + 89900 q^{90} - 89487 q^{91} + 50784 q^{92} - 209450 q^{93} + 98288 q^{94} + 85775 q^{95} + 11264 q^{96} - 13201 q^{97} + 112200 q^{98} - 355951 q^{99}+O(q^{100}) \) 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
\(3\) 21.8456 1.40139 0.700697 0.713459i \(-0.252872\pi\)
0.700697 + 0.713459i \(0.252872\pi\)
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) 87.3823 0.990935
\(7\) 7.44621 0.0574368 0.0287184 0.999588i \(-0.490857\pi\)
0.0287184 + 0.999588i \(0.490857\pi\)
\(8\) 64.0000 0.353553
\(9\) 234.229 0.963906
\(10\) 100.000 0.316228
\(11\) −441.618 −1.10044 −0.550219 0.835020i \(-0.685456\pi\)
−0.550219 + 0.835020i \(0.685456\pi\)
\(12\) 349.529 0.700697
\(13\) 785.235 1.28867 0.644334 0.764744i \(-0.277135\pi\)
0.644334 + 0.764744i \(0.277135\pi\)
\(14\) 29.7848 0.0406139
\(15\) 546.139 0.626723
\(16\) 256.000 0.250000
\(17\) 632.287 0.530631 0.265315 0.964162i \(-0.414524\pi\)
0.265315 + 0.964162i \(0.414524\pi\)
\(18\) 936.917 0.681584
\(19\) 2085.12 1.32510 0.662548 0.749019i \(-0.269475\pi\)
0.662548 + 0.749019i \(0.269475\pi\)
\(20\) 400.000 0.223607
\(21\) 162.667 0.0804916
\(22\) −1766.47 −0.778127
\(23\) 529.000 0.208514
\(24\) 1398.12 0.495468
\(25\) 625.000 0.200000
\(26\) 3140.94 0.911226
\(27\) −191.604 −0.0505820
\(28\) 119.139 0.0287184
\(29\) 3126.22 0.690280 0.345140 0.938551i \(-0.387831\pi\)
0.345140 + 0.938551i \(0.387831\pi\)
\(30\) 2184.56 0.443160
\(31\) −416.399 −0.0778225 −0.0389113 0.999243i \(-0.512389\pi\)
−0.0389113 + 0.999243i \(0.512389\pi\)
\(32\) 1024.00 0.176777
\(33\) −9647.41 −1.54215
\(34\) 2529.15 0.375212
\(35\) 186.155 0.0256865
\(36\) 3747.67 0.481953
\(37\) 744.963 0.0894603 0.0447301 0.998999i \(-0.485757\pi\)
0.0447301 + 0.998999i \(0.485757\pi\)
\(38\) 8340.49 0.936985
\(39\) 17153.9 1.80593
\(40\) 1600.00 0.158114
\(41\) −10179.3 −0.945707 −0.472853 0.881141i \(-0.656776\pi\)
−0.472853 + 0.881141i \(0.656776\pi\)
\(42\) 650.667 0.0569161
\(43\) 20597.2 1.69878 0.849390 0.527766i \(-0.176970\pi\)
0.849390 + 0.527766i \(0.176970\pi\)
\(44\) −7065.89 −0.550219
\(45\) 5855.73 0.431072
\(46\) 2116.00 0.147442
\(47\) −17461.2 −1.15300 −0.576500 0.817097i \(-0.695582\pi\)
−0.576500 + 0.817097i \(0.695582\pi\)
\(48\) 5592.47 0.350349
\(49\) −16751.6 −0.996701
\(50\) 2500.00 0.141421
\(51\) 13812.7 0.743623
\(52\) 12563.8 0.644334
\(53\) −30308.6 −1.48210 −0.741048 0.671452i \(-0.765671\pi\)
−0.741048 + 0.671452i \(0.765671\pi\)
\(54\) −766.417 −0.0357669
\(55\) −11040.5 −0.492131
\(56\) 476.557 0.0203070
\(57\) 45550.7 1.85698
\(58\) 12504.9 0.488102
\(59\) −20612.7 −0.770913 −0.385456 0.922726i \(-0.625956\pi\)
−0.385456 + 0.922726i \(0.625956\pi\)
\(60\) 8738.23 0.313361
\(61\) 6553.21 0.225491 0.112746 0.993624i \(-0.464036\pi\)
0.112746 + 0.993624i \(0.464036\pi\)
\(62\) −1665.60 −0.0550288
\(63\) 1744.12 0.0553636
\(64\) 4096.00 0.125000
\(65\) 19630.9 0.576310
\(66\) −38589.6 −1.09046
\(67\) 29514.0 0.803233 0.401616 0.915808i \(-0.368449\pi\)
0.401616 + 0.915808i \(0.368449\pi\)
\(68\) 10116.6 0.265315
\(69\) 11556.3 0.292211
\(70\) 744.621 0.0181631
\(71\) −54219.6 −1.27647 −0.638235 0.769842i \(-0.720335\pi\)
−0.638235 + 0.769842i \(0.720335\pi\)
\(72\) 14990.7 0.340792
\(73\) −81319.3 −1.78602 −0.893010 0.450037i \(-0.851411\pi\)
−0.893010 + 0.450037i \(0.851411\pi\)
\(74\) 2979.85 0.0632580
\(75\) 13653.5 0.280279
\(76\) 33362.0 0.662548
\(77\) −3288.38 −0.0632056
\(78\) 68615.6 1.27699
\(79\) 99309.8 1.79029 0.895147 0.445771i \(-0.147070\pi\)
0.895147 + 0.445771i \(0.147070\pi\)
\(80\) 6400.00 0.111803
\(81\) −61103.4 −1.03479
\(82\) −40717.0 −0.668716
\(83\) 9250.19 0.147386 0.0736929 0.997281i \(-0.476522\pi\)
0.0736929 + 0.997281i \(0.476522\pi\)
\(84\) 2602.67 0.0402458
\(85\) 15807.2 0.237305
\(86\) 82388.8 1.20122
\(87\) 68294.2 0.967354
\(88\) −28263.6 −0.389063
\(89\) 22988.9 0.307640 0.153820 0.988099i \(-0.450842\pi\)
0.153820 + 0.988099i \(0.450842\pi\)
\(90\) 23422.9 0.304814
\(91\) 5847.02 0.0740170
\(92\) 8464.00 0.104257
\(93\) −9096.47 −0.109060
\(94\) −69844.8 −0.815294
\(95\) 52128.1 0.592601
\(96\) 22369.9 0.247734
\(97\) −54909.5 −0.592541 −0.296271 0.955104i \(-0.595743\pi\)
−0.296271 + 0.955104i \(0.595743\pi\)
\(98\) −67006.2 −0.704774
\(99\) −103440. −1.06072
\(100\) 10000.0 0.100000
\(101\) 189171. 1.84523 0.922614 0.385724i \(-0.126048\pi\)
0.922614 + 0.385724i \(0.126048\pi\)
\(102\) 55250.7 0.525821
\(103\) −25299.5 −0.234974 −0.117487 0.993074i \(-0.537484\pi\)
−0.117487 + 0.993074i \(0.537484\pi\)
\(104\) 50255.0 0.455613
\(105\) 4066.67 0.0359969
\(106\) −121234. −1.04800
\(107\) −136708. −1.15434 −0.577169 0.816624i \(-0.695843\pi\)
−0.577169 + 0.816624i \(0.695843\pi\)
\(108\) −3065.67 −0.0252910
\(109\) 85251.3 0.687282 0.343641 0.939101i \(-0.388340\pi\)
0.343641 + 0.939101i \(0.388340\pi\)
\(110\) −44161.8 −0.347989
\(111\) 16274.1 0.125369
\(112\) 1906.23 0.0143592
\(113\) 9728.45 0.0716717 0.0358358 0.999358i \(-0.488591\pi\)
0.0358358 + 0.999358i \(0.488591\pi\)
\(114\) 182203. 1.31309
\(115\) 13225.0 0.0932505
\(116\) 50019.6 0.345140
\(117\) 183925. 1.24216
\(118\) −82450.9 −0.545118
\(119\) 4708.14 0.0304777
\(120\) 34952.9 0.221580
\(121\) 33975.8 0.210963
\(122\) 26212.8 0.159446
\(123\) −222372. −1.32531
\(124\) −6662.38 −0.0389113
\(125\) 15625.0 0.0894427
\(126\) 6976.48 0.0391480
\(127\) −170675. −0.938990 −0.469495 0.882935i \(-0.655564\pi\)
−0.469495 + 0.882935i \(0.655564\pi\)
\(128\) 16384.0 0.0883883
\(129\) 449958. 2.38066
\(130\) 78523.5 0.407513
\(131\) 131578. 0.669891 0.334945 0.942238i \(-0.391282\pi\)
0.334945 + 0.942238i \(0.391282\pi\)
\(132\) −154359. −0.771074
\(133\) 15526.3 0.0761093
\(134\) 118056. 0.567971
\(135\) −4790.11 −0.0226210
\(136\) 40466.4 0.187606
\(137\) −143880. −0.654936 −0.327468 0.944862i \(-0.606195\pi\)
−0.327468 + 0.944862i \(0.606195\pi\)
\(138\) 46225.2 0.206624
\(139\) 43271.1 0.189960 0.0949798 0.995479i \(-0.469721\pi\)
0.0949798 + 0.995479i \(0.469721\pi\)
\(140\) 2978.48 0.0128433
\(141\) −381450. −1.61581
\(142\) −216878. −0.902600
\(143\) −346774. −1.41810
\(144\) 59962.7 0.240976
\(145\) 78155.6 0.308703
\(146\) −325277. −1.26291
\(147\) −365947. −1.39677
\(148\) 11919.4 0.0447301
\(149\) −371769. −1.37185 −0.685927 0.727670i \(-0.740603\pi\)
−0.685927 + 0.727670i \(0.740603\pi\)
\(150\) 54613.9 0.198187
\(151\) −224317. −0.800607 −0.400303 0.916383i \(-0.631095\pi\)
−0.400303 + 0.916383i \(0.631095\pi\)
\(152\) 133448. 0.468492
\(153\) 148100. 0.511478
\(154\) −13153.5 −0.0446931
\(155\) −10410.0 −0.0348033
\(156\) 274463. 0.902966
\(157\) −316299. −1.02412 −0.512058 0.858951i \(-0.671117\pi\)
−0.512058 + 0.858951i \(0.671117\pi\)
\(158\) 397239. 1.26593
\(159\) −662109. −2.07700
\(160\) 25600.0 0.0790569
\(161\) 3939.04 0.0119764
\(162\) −244414. −0.731708
\(163\) −486020. −1.43280 −0.716399 0.697691i \(-0.754211\pi\)
−0.716399 + 0.697691i \(0.754211\pi\)
\(164\) −162868. −0.472853
\(165\) −241185. −0.689669
\(166\) 37000.8 0.104217
\(167\) 483955. 1.34281 0.671404 0.741092i \(-0.265692\pi\)
0.671404 + 0.741092i \(0.265692\pi\)
\(168\) 10410.7 0.0284581
\(169\) 245301. 0.660666
\(170\) 63228.7 0.167800
\(171\) 488396. 1.27727
\(172\) 329555. 0.849390
\(173\) 162216. 0.412077 0.206039 0.978544i \(-0.433943\pi\)
0.206039 + 0.978544i \(0.433943\pi\)
\(174\) 273177. 0.684023
\(175\) 4653.88 0.0114874
\(176\) −113054. −0.275109
\(177\) −450297. −1.08035
\(178\) 91955.6 0.217535
\(179\) −285816. −0.666736 −0.333368 0.942797i \(-0.608185\pi\)
−0.333368 + 0.942797i \(0.608185\pi\)
\(180\) 93691.7 0.215536
\(181\) 46992.1 0.106617 0.0533087 0.998578i \(-0.483023\pi\)
0.0533087 + 0.998578i \(0.483023\pi\)
\(182\) 23388.1 0.0523379
\(183\) 143159. 0.316002
\(184\) 33856.0 0.0737210
\(185\) 18624.1 0.0400078
\(186\) −36385.9 −0.0771171
\(187\) −279230. −0.583926
\(188\) −279379. −0.576500
\(189\) −1426.73 −0.00290527
\(190\) 208512. 0.419032
\(191\) −511443. −1.01441 −0.507206 0.861825i \(-0.669321\pi\)
−0.507206 + 0.861825i \(0.669321\pi\)
\(192\) 89479.5 0.175174
\(193\) −502843. −0.971716 −0.485858 0.874038i \(-0.661493\pi\)
−0.485858 + 0.874038i \(0.661493\pi\)
\(194\) −219638. −0.418990
\(195\) 428848. 0.807638
\(196\) −268025. −0.498351
\(197\) 514622. 0.944763 0.472381 0.881394i \(-0.343395\pi\)
0.472381 + 0.881394i \(0.343395\pi\)
\(198\) −413760. −0.750041
\(199\) 426847. 0.764082 0.382041 0.924145i \(-0.375221\pi\)
0.382041 + 0.924145i \(0.375221\pi\)
\(200\) 40000.0 0.0707107
\(201\) 644751. 1.12565
\(202\) 756682. 1.30477
\(203\) 23278.5 0.0396474
\(204\) 221003. 0.371811
\(205\) −254482. −0.422933
\(206\) −101198. −0.166152
\(207\) 123907. 0.200988
\(208\) 201020. 0.322167
\(209\) −920828. −1.45819
\(210\) 16266.7 0.0254537
\(211\) 647680. 1.00151 0.500754 0.865589i \(-0.333056\pi\)
0.500754 + 0.865589i \(0.333056\pi\)
\(212\) −484938. −0.741048
\(213\) −1.18446e6 −1.78884
\(214\) −546830. −0.816241
\(215\) 514930. 0.759717
\(216\) −12262.7 −0.0178834
\(217\) −3100.59 −0.00446988
\(218\) 341005. 0.485981
\(219\) −1.77647e6 −2.50292
\(220\) −176647. −0.246065
\(221\) 496494. 0.683807
\(222\) 65096.5 0.0886493
\(223\) −534158. −0.719296 −0.359648 0.933088i \(-0.617103\pi\)
−0.359648 + 0.933088i \(0.617103\pi\)
\(224\) 7624.92 0.0101535
\(225\) 146393. 0.192781
\(226\) 38913.8 0.0506795
\(227\) −205929. −0.265248 −0.132624 0.991166i \(-0.542340\pi\)
−0.132624 + 0.991166i \(0.542340\pi\)
\(228\) 728811. 0.928491
\(229\) −934046. −1.17701 −0.588504 0.808494i \(-0.700283\pi\)
−0.588504 + 0.808494i \(0.700283\pi\)
\(230\) 52900.0 0.0659380
\(231\) −71836.6 −0.0885760
\(232\) 200078. 0.244051
\(233\) −529838. −0.639372 −0.319686 0.947524i \(-0.603577\pi\)
−0.319686 + 0.947524i \(0.603577\pi\)
\(234\) 735700. 0.878336
\(235\) −436530. −0.515637
\(236\) −329803. −0.385456
\(237\) 2.16948e6 2.50891
\(238\) 18832.6 0.0215510
\(239\) −796507. −0.901975 −0.450988 0.892530i \(-0.648928\pi\)
−0.450988 + 0.892530i \(0.648928\pi\)
\(240\) 139812. 0.156681
\(241\) 492031. 0.545694 0.272847 0.962057i \(-0.412035\pi\)
0.272847 + 0.962057i \(0.412035\pi\)
\(242\) 135903. 0.149174
\(243\) −1.28828e6 −1.39957
\(244\) 104851. 0.112746
\(245\) −418789. −0.445738
\(246\) −889487. −0.937134
\(247\) 1.63731e6 1.70761
\(248\) −26649.5 −0.0275144
\(249\) 202076. 0.206546
\(250\) 62500.0 0.0632456
\(251\) 1.50649e6 1.50932 0.754661 0.656115i \(-0.227801\pi\)
0.754661 + 0.656115i \(0.227801\pi\)
\(252\) 27905.9 0.0276818
\(253\) −233616. −0.229457
\(254\) −682700. −0.663966
\(255\) 345317. 0.332558
\(256\) 65536.0 0.0625000
\(257\) −512195. −0.483730 −0.241865 0.970310i \(-0.577759\pi\)
−0.241865 + 0.970310i \(0.577759\pi\)
\(258\) 1.79983e6 1.68338
\(259\) 5547.15 0.00513831
\(260\) 314094. 0.288155
\(261\) 732253. 0.665365
\(262\) 526311. 0.473684
\(263\) −1.40580e6 −1.25324 −0.626622 0.779323i \(-0.715563\pi\)
−0.626622 + 0.779323i \(0.715563\pi\)
\(264\) −617434. −0.545231
\(265\) −757715. −0.662814
\(266\) 62105.0 0.0538174
\(267\) 502206. 0.431125
\(268\) 472224. 0.401616
\(269\) 476712. 0.401675 0.200838 0.979625i \(-0.435634\pi\)
0.200838 + 0.979625i \(0.435634\pi\)
\(270\) −19160.4 −0.0159954
\(271\) 918358. 0.759607 0.379803 0.925067i \(-0.375992\pi\)
0.379803 + 0.925067i \(0.375992\pi\)
\(272\) 161866. 0.132658
\(273\) 127732. 0.103727
\(274\) −575520. −0.463110
\(275\) −276012. −0.220088
\(276\) 184901. 0.146105
\(277\) 579006. 0.453402 0.226701 0.973964i \(-0.427206\pi\)
0.226701 + 0.973964i \(0.427206\pi\)
\(278\) 173085. 0.134322
\(279\) −97532.8 −0.0750136
\(280\) 11913.9 0.00908155
\(281\) 1.30977e6 0.989531 0.494766 0.869026i \(-0.335254\pi\)
0.494766 + 0.869026i \(0.335254\pi\)
\(282\) −1.52580e6 −1.14255
\(283\) 388018. 0.287995 0.143998 0.989578i \(-0.454004\pi\)
0.143998 + 0.989578i \(0.454004\pi\)
\(284\) −867513. −0.638235
\(285\) 1.13877e6 0.830468
\(286\) −1.38710e6 −1.00275
\(287\) −75796.9 −0.0543184
\(288\) 239851. 0.170396
\(289\) −1.02007e6 −0.718431
\(290\) 312622. 0.218286
\(291\) −1.19953e6 −0.830384
\(292\) −1.30111e6 −0.893010
\(293\) 1.44959e6 0.986453 0.493227 0.869901i \(-0.335817\pi\)
0.493227 + 0.869901i \(0.335817\pi\)
\(294\) −1.46379e6 −0.987666
\(295\) −515318. −0.344763
\(296\) 47677.6 0.0316290
\(297\) 84616.0 0.0556623
\(298\) −1.48708e6 −0.970048
\(299\) 415389. 0.268706
\(300\) 218456. 0.140139
\(301\) 153371. 0.0975724
\(302\) −897267. −0.566114
\(303\) 4.13254e6 2.58589
\(304\) 533791. 0.331274
\(305\) 163830. 0.100843
\(306\) 592401. 0.361670
\(307\) 2.28279e6 1.38235 0.691177 0.722686i \(-0.257093\pi\)
0.691177 + 0.722686i \(0.257093\pi\)
\(308\) −52614.1 −0.0316028
\(309\) −552683. −0.329291
\(310\) −41639.9 −0.0246096
\(311\) 2.19166e6 1.28491 0.642455 0.766323i \(-0.277916\pi\)
0.642455 + 0.766323i \(0.277916\pi\)
\(312\) 1.09785e6 0.638494
\(313\) 2.46402e6 1.42162 0.710810 0.703384i \(-0.248329\pi\)
0.710810 + 0.703384i \(0.248329\pi\)
\(314\) −1.26520e6 −0.724159
\(315\) 43603.0 0.0247594
\(316\) 1.58896e6 0.895147
\(317\) 2.25250e6 1.25897 0.629487 0.777011i \(-0.283265\pi\)
0.629487 + 0.777011i \(0.283265\pi\)
\(318\) −2.64844e6 −1.46866
\(319\) −1.38060e6 −0.759610
\(320\) 102400. 0.0559017
\(321\) −2.98646e6 −1.61768
\(322\) 15756.2 0.00846859
\(323\) 1.31840e6 0.703137
\(324\) −977654. −0.517396
\(325\) 490772. 0.257734
\(326\) −1.94408e6 −1.01314
\(327\) 1.86236e6 0.963152
\(328\) −651473. −0.334358
\(329\) −130020. −0.0662246
\(330\) −964741. −0.487670
\(331\) 743598. 0.373051 0.186525 0.982450i \(-0.440277\pi\)
0.186525 + 0.982450i \(0.440277\pi\)
\(332\) 148003. 0.0736929
\(333\) 174492. 0.0862313
\(334\) 1.93582e6 0.949509
\(335\) 737851. 0.359217
\(336\) 41642.7 0.0201229
\(337\) 3.93157e6 1.88578 0.942891 0.333103i \(-0.108096\pi\)
0.942891 + 0.333103i \(0.108096\pi\)
\(338\) 981203. 0.467162
\(339\) 212524. 0.100440
\(340\) 252915. 0.118653
\(341\) 183889. 0.0856389
\(342\) 1.95359e6 0.903165
\(343\) −249884. −0.114684
\(344\) 1.31822e6 0.600609
\(345\) 288908. 0.130681
\(346\) 648864. 0.291383
\(347\) 202520. 0.0902909 0.0451455 0.998980i \(-0.485625\pi\)
0.0451455 + 0.998980i \(0.485625\pi\)
\(348\) 1.09271e6 0.483677
\(349\) −3.94184e6 −1.73235 −0.866174 0.499742i \(-0.833428\pi\)
−0.866174 + 0.499742i \(0.833428\pi\)
\(350\) 18615.5 0.00812279
\(351\) −150454. −0.0651834
\(352\) −452217. −0.194532
\(353\) 3.29528e6 1.40752 0.703762 0.710436i \(-0.251502\pi\)
0.703762 + 0.710436i \(0.251502\pi\)
\(354\) −1.80119e6 −0.763925
\(355\) −1.35549e6 −0.570854
\(356\) 367823. 0.153820
\(357\) 102852. 0.0427113
\(358\) −1.14326e6 −0.471454
\(359\) −52181.7 −0.0213689 −0.0106845 0.999943i \(-0.503401\pi\)
−0.0106845 + 0.999943i \(0.503401\pi\)
\(360\) 374767. 0.152407
\(361\) 1.87164e6 0.755881
\(362\) 187968. 0.0753899
\(363\) 742222. 0.295643
\(364\) 93552.3 0.0370085
\(365\) −2.03298e6 −0.798732
\(366\) 572634. 0.223447
\(367\) −1.28483e6 −0.497943 −0.248972 0.968511i \(-0.580093\pi\)
−0.248972 + 0.968511i \(0.580093\pi\)
\(368\) 135424. 0.0521286
\(369\) −2.38428e6 −0.911573
\(370\) 74496.3 0.0282898
\(371\) −225684. −0.0851268
\(372\) −145544. −0.0545300
\(373\) −850905. −0.316672 −0.158336 0.987385i \(-0.550613\pi\)
−0.158336 + 0.987385i \(0.550613\pi\)
\(374\) −1.11692e6 −0.412898
\(375\) 341337. 0.125345
\(376\) −1.11752e6 −0.407647
\(377\) 2.45482e6 0.889542
\(378\) −5706.90 −0.00205433
\(379\) 4.94210e6 1.76731 0.883657 0.468135i \(-0.155074\pi\)
0.883657 + 0.468135i \(0.155074\pi\)
\(380\) 834049. 0.296301
\(381\) −3.72850e6 −1.31589
\(382\) −2.04577e6 −0.717297
\(383\) −1.31741e6 −0.458906 −0.229453 0.973320i \(-0.573694\pi\)
−0.229453 + 0.973320i \(0.573694\pi\)
\(384\) 357918. 0.123867
\(385\) −82209.6 −0.0282664
\(386\) −2.01137e6 −0.687107
\(387\) 4.82446e6 1.63746
\(388\) −878553. −0.296271
\(389\) 471710. 0.158052 0.0790262 0.996873i \(-0.474819\pi\)
0.0790262 + 0.996873i \(0.474819\pi\)
\(390\) 1.71539e6 0.571086
\(391\) 334480. 0.110644
\(392\) −1.07210e6 −0.352387
\(393\) 2.87439e6 0.938781
\(394\) 2.05849e6 0.668048
\(395\) 2.48275e6 0.800644
\(396\) −1.65504e6 −0.530359
\(397\) −1.32333e6 −0.421398 −0.210699 0.977551i \(-0.567574\pi\)
−0.210699 + 0.977551i \(0.567574\pi\)
\(398\) 1.70739e6 0.540287
\(399\) 339180. 0.106659
\(400\) 160000. 0.0500000
\(401\) −6.08132e6 −1.88859 −0.944293 0.329107i \(-0.893252\pi\)
−0.944293 + 0.329107i \(0.893252\pi\)
\(402\) 2.57900e6 0.795952
\(403\) −326971. −0.100287
\(404\) 3.02673e6 0.922614
\(405\) −1.52758e6 −0.462773
\(406\) 93114.1 0.0280350
\(407\) −328989. −0.0984454
\(408\) 884012. 0.262910
\(409\) −4.49993e6 −1.33014 −0.665070 0.746781i \(-0.731598\pi\)
−0.665070 + 0.746781i \(0.731598\pi\)
\(410\) −1.01793e6 −0.299059
\(411\) −3.14314e6 −0.917823
\(412\) −404793. −0.117487
\(413\) −153487. −0.0442787
\(414\) 495629. 0.142120
\(415\) 231255. 0.0659129
\(416\) 804081. 0.227807
\(417\) 945283. 0.266208
\(418\) −3.68331e6 −1.03109
\(419\) 5.74909e6 1.59979 0.799896 0.600138i \(-0.204888\pi\)
0.799896 + 0.600138i \(0.204888\pi\)
\(420\) 65066.7 0.0179985
\(421\) −724622. −0.199254 −0.0996268 0.995025i \(-0.531765\pi\)
−0.0996268 + 0.995025i \(0.531765\pi\)
\(422\) 2.59072e6 0.708173
\(423\) −4.08992e6 −1.11138
\(424\) −1.93975e6 −0.524000
\(425\) 395180. 0.106126
\(426\) −4.73783e6 −1.26490
\(427\) 48796.6 0.0129515
\(428\) −2.18732e6 −0.577169
\(429\) −7.57548e6 −1.98732
\(430\) 2.05972e6 0.537201
\(431\) 290206. 0.0752512 0.0376256 0.999292i \(-0.488021\pi\)
0.0376256 + 0.999292i \(0.488021\pi\)
\(432\) −49050.7 −0.0126455
\(433\) −3.11729e6 −0.799018 −0.399509 0.916729i \(-0.630819\pi\)
−0.399509 + 0.916729i \(0.630819\pi\)
\(434\) −12402.4 −0.00316068
\(435\) 1.70735e6 0.432614
\(436\) 1.36402e6 0.343641
\(437\) 1.10303e6 0.276302
\(438\) −7.10586e6 −1.76983
\(439\) 1.01002e6 0.250131 0.125065 0.992148i \(-0.460086\pi\)
0.125065 + 0.992148i \(0.460086\pi\)
\(440\) −706589. −0.173994
\(441\) −3.92370e6 −0.960726
\(442\) 1.98598e6 0.483525
\(443\) −3.15549e6 −0.763936 −0.381968 0.924175i \(-0.624754\pi\)
−0.381968 + 0.924175i \(0.624754\pi\)
\(444\) 260386. 0.0626845
\(445\) 574723. 0.137581
\(446\) −2.13663e6 −0.508619
\(447\) −8.12152e6 −1.92251
\(448\) 30499.7 0.00717960
\(449\) −3.14786e6 −0.736884 −0.368442 0.929651i \(-0.620109\pi\)
−0.368442 + 0.929651i \(0.620109\pi\)
\(450\) 585573. 0.136317
\(451\) 4.49535e6 1.04069
\(452\) 155655. 0.0358358
\(453\) −4.90033e6 −1.12197
\(454\) −823715. −0.187559
\(455\) 146176. 0.0331014
\(456\) 2.91524e6 0.656543
\(457\) −1.40125e6 −0.313852 −0.156926 0.987610i \(-0.550158\pi\)
−0.156926 + 0.987610i \(0.550158\pi\)
\(458\) −3.73618e6 −0.832271
\(459\) −121149. −0.0268403
\(460\) 211600. 0.0466252
\(461\) −3.99638e6 −0.875820 −0.437910 0.899019i \(-0.644281\pi\)
−0.437910 + 0.899019i \(0.644281\pi\)
\(462\) −287346. −0.0626327
\(463\) 4.67627e6 1.01379 0.506894 0.862009i \(-0.330794\pi\)
0.506894 + 0.862009i \(0.330794\pi\)
\(464\) 800313. 0.172570
\(465\) −227412. −0.0487731
\(466\) −2.11935e6 −0.452104
\(467\) 499509. 0.105987 0.0529934 0.998595i \(-0.483124\pi\)
0.0529934 + 0.998595i \(0.483124\pi\)
\(468\) 2.94280e6 0.621078
\(469\) 219768. 0.0461351
\(470\) −1.74612e6 −0.364611
\(471\) −6.90974e6 −1.43519
\(472\) −1.31921e6 −0.272559
\(473\) −9.09610e6 −1.86940
\(474\) 8.67792e6 1.77407
\(475\) 1.30320e6 0.265019
\(476\) 75330.3 0.0152389
\(477\) −7.09916e6 −1.42860
\(478\) −3.18603e6 −0.637793
\(479\) −7.27067e6 −1.44789 −0.723945 0.689858i \(-0.757673\pi\)
−0.723945 + 0.689858i \(0.757673\pi\)
\(480\) 559247. 0.110790
\(481\) 584971. 0.115285
\(482\) 1.96812e6 0.385864
\(483\) 86050.7 0.0167837
\(484\) 543613. 0.105482
\(485\) −1.37274e6 −0.264992
\(486\) −5.15312e6 −0.989644
\(487\) 4.39818e6 0.840331 0.420165 0.907448i \(-0.361972\pi\)
0.420165 + 0.907448i \(0.361972\pi\)
\(488\) 419405. 0.0797231
\(489\) −1.06174e7 −2.00792
\(490\) −1.67516e6 −0.315185
\(491\) 6.73646e6 1.26104 0.630518 0.776174i \(-0.282842\pi\)
0.630518 + 0.776174i \(0.282842\pi\)
\(492\) −3.55795e6 −0.662654
\(493\) 1.97667e6 0.366284
\(494\) 6.54924e6 1.20746
\(495\) −2.58600e6 −0.474368
\(496\) −106598. −0.0194556
\(497\) −403730. −0.0733163
\(498\) 808303. 0.146050
\(499\) 5.10709e6 0.918168 0.459084 0.888393i \(-0.348178\pi\)
0.459084 + 0.888393i \(0.348178\pi\)
\(500\) 250000. 0.0447214
\(501\) 1.05723e7 1.88180
\(502\) 6.02596e6 1.06725
\(503\) −3.16963e6 −0.558584 −0.279292 0.960206i \(-0.590100\pi\)
−0.279292 + 0.960206i \(0.590100\pi\)
\(504\) 111624. 0.0195740
\(505\) 4.72926e6 0.825211
\(506\) −934465. −0.162251
\(507\) 5.35874e6 0.925854
\(508\) −2.73080e6 −0.469495
\(509\) −7.46538e6 −1.27720 −0.638598 0.769540i \(-0.720485\pi\)
−0.638598 + 0.769540i \(0.720485\pi\)
\(510\) 1.38127e6 0.235154
\(511\) −605520. −0.102583
\(512\) 262144. 0.0441942
\(513\) −399518. −0.0670260
\(514\) −2.04878e6 −0.342049
\(515\) −632489. −0.105084
\(516\) 7.19932e6 1.19033
\(517\) 7.71119e6 1.26880
\(518\) 22188.6 0.00363333
\(519\) 3.54370e6 0.577483
\(520\) 1.25638e6 0.203756
\(521\) −3.67478e6 −0.593112 −0.296556 0.955015i \(-0.595838\pi\)
−0.296556 + 0.955015i \(0.595838\pi\)
\(522\) 2.92901e6 0.470484
\(523\) 8.09022e6 1.29332 0.646660 0.762778i \(-0.276165\pi\)
0.646660 + 0.762778i \(0.276165\pi\)
\(524\) 2.10524e6 0.334945
\(525\) 101667. 0.0160983
\(526\) −5.62322e6 −0.886177
\(527\) −263284. −0.0412950
\(528\) −2.46974e6 −0.385537
\(529\) 279841. 0.0434783
\(530\) −3.03086e6 −0.468680
\(531\) −4.82810e6 −0.743087
\(532\) 248420. 0.0380546
\(533\) −7.99311e6 −1.21870
\(534\) 2.00882e6 0.304852
\(535\) −3.41769e6 −0.516236
\(536\) 1.88890e6 0.283986
\(537\) −6.24382e6 −0.934360
\(538\) 1.90685e6 0.284027
\(539\) 7.39780e6 1.09681
\(540\) −76641.7 −0.0113105
\(541\) −2.85957e6 −0.420056 −0.210028 0.977695i \(-0.567355\pi\)
−0.210028 + 0.977695i \(0.567355\pi\)
\(542\) 3.67343e6 0.537123
\(543\) 1.02657e6 0.149413
\(544\) 647462. 0.0938031
\(545\) 2.13128e6 0.307362
\(546\) 510926. 0.0733460
\(547\) 8.65627e6 1.23698 0.618490 0.785793i \(-0.287745\pi\)
0.618490 + 0.785793i \(0.287745\pi\)
\(548\) −2.30208e6 −0.327468
\(549\) 1.53495e6 0.217352
\(550\) −1.10405e6 −0.155625
\(551\) 6.51856e6 0.914687
\(552\) 739604. 0.103312
\(553\) 739482. 0.102829
\(554\) 2.31602e6 0.320604
\(555\) 406853. 0.0560668
\(556\) 692338. 0.0949798
\(557\) 6.77607e6 0.925422 0.462711 0.886509i \(-0.346877\pi\)
0.462711 + 0.886509i \(0.346877\pi\)
\(558\) −390131. −0.0530426
\(559\) 1.61736e7 2.18916
\(560\) 47655.7 0.00642163
\(561\) −6.09994e6 −0.818310
\(562\) 5.23908e6 0.699704
\(563\) 1.40916e7 1.87365 0.936824 0.349800i \(-0.113751\pi\)
0.936824 + 0.349800i \(0.113751\pi\)
\(564\) −6.10320e6 −0.807904
\(565\) 243211. 0.0320526
\(566\) 1.55207e6 0.203644
\(567\) −454989. −0.0594351
\(568\) −3.47005e6 −0.451300
\(569\) 5.42734e6 0.702759 0.351380 0.936233i \(-0.385713\pi\)
0.351380 + 0.936233i \(0.385713\pi\)
\(570\) 4.55507e6 0.587230
\(571\) −2.93711e6 −0.376990 −0.188495 0.982074i \(-0.560361\pi\)
−0.188495 + 0.982074i \(0.560361\pi\)
\(572\) −5.54839e6 −0.709050
\(573\) −1.11728e7 −1.42159
\(574\) −303188. −0.0384089
\(575\) 330625. 0.0417029
\(576\) 959403. 0.120488
\(577\) 4.20072e6 0.525271 0.262636 0.964895i \(-0.415408\pi\)
0.262636 + 0.964895i \(0.415408\pi\)
\(578\) −4.08028e6 −0.508008
\(579\) −1.09849e7 −1.36176
\(580\) 1.25049e6 0.154351
\(581\) 68878.9 0.00846536
\(582\) −4.79812e6 −0.587170
\(583\) 1.33848e7 1.63095
\(584\) −5.20443e6 −0.631453
\(585\) 4.59812e6 0.555509
\(586\) 5.79837e6 0.697528
\(587\) 1.44189e7 1.72718 0.863589 0.504196i \(-0.168211\pi\)
0.863589 + 0.504196i \(0.168211\pi\)
\(588\) −5.85516e6 −0.698386
\(589\) −868243. −0.103122
\(590\) −2.06127e6 −0.243784
\(591\) 1.12422e7 1.32398
\(592\) 190710. 0.0223651
\(593\) 4.05611e6 0.473667 0.236834 0.971550i \(-0.423890\pi\)
0.236834 + 0.971550i \(0.423890\pi\)
\(594\) 338464. 0.0393592
\(595\) 117704. 0.0136300
\(596\) −5.94831e6 −0.685927
\(597\) 9.32472e6 1.07078
\(598\) 1.66156e6 0.190004
\(599\) −1.56448e7 −1.78157 −0.890787 0.454421i \(-0.849846\pi\)
−0.890787 + 0.454421i \(0.849846\pi\)
\(600\) 873823. 0.0990935
\(601\) −5.61467e6 −0.634071 −0.317036 0.948414i \(-0.602687\pi\)
−0.317036 + 0.948414i \(0.602687\pi\)
\(602\) 613484. 0.0689941
\(603\) 6.91305e6 0.774241
\(604\) −3.58907e6 −0.400303
\(605\) 849396. 0.0943456
\(606\) 1.65302e7 1.82850
\(607\) −7.89001e6 −0.869173 −0.434586 0.900630i \(-0.643105\pi\)
−0.434586 + 0.900630i \(0.643105\pi\)
\(608\) 2.13517e6 0.234246
\(609\) 508533. 0.0555617
\(610\) 655321. 0.0713065
\(611\) −1.37111e7 −1.48583
\(612\) 2.36960e6 0.255739
\(613\) 1.28240e6 0.137839 0.0689196 0.997622i \(-0.478045\pi\)
0.0689196 + 0.997622i \(0.478045\pi\)
\(614\) 9.13114e6 0.977472
\(615\) −5.55929e6 −0.592696
\(616\) −210456. −0.0223466
\(617\) 9.12950e6 0.965460 0.482730 0.875769i \(-0.339645\pi\)
0.482730 + 0.875769i \(0.339645\pi\)
\(618\) −2.21073e6 −0.232844
\(619\) 1.01828e7 1.06817 0.534087 0.845430i \(-0.320655\pi\)
0.534087 + 0.845430i \(0.320655\pi\)
\(620\) −166560. −0.0174016
\(621\) −101359. −0.0105471
\(622\) 8.76665e6 0.908569
\(623\) 171180. 0.0176699
\(624\) 4.39140e6 0.451483
\(625\) 390625. 0.0400000
\(626\) 9.85608e6 1.00524
\(627\) −2.01160e7 −2.04349
\(628\) −5.06079e6 −0.512058
\(629\) 471030. 0.0474703
\(630\) 174412. 0.0175075
\(631\) 6.18377e6 0.618273 0.309136 0.951018i \(-0.399960\pi\)
0.309136 + 0.951018i \(0.399960\pi\)
\(632\) 6.35583e6 0.632965
\(633\) 1.41490e7 1.40351
\(634\) 9.01001e6 0.890229
\(635\) −4.26688e6 −0.419929
\(636\) −1.05937e7 −1.03850
\(637\) −1.31539e7 −1.28442
\(638\) −5.52239e6 −0.537125
\(639\) −1.26998e7 −1.23040
\(640\) 409600. 0.0395285
\(641\) −1.57251e7 −1.51164 −0.755820 0.654780i \(-0.772761\pi\)
−0.755820 + 0.654780i \(0.772761\pi\)
\(642\) −1.19458e7 −1.14388
\(643\) 3.35266e6 0.319788 0.159894 0.987134i \(-0.448885\pi\)
0.159894 + 0.987134i \(0.448885\pi\)
\(644\) 63024.7 0.00598820
\(645\) 1.12489e7 1.06466
\(646\) 5.27359e6 0.497193
\(647\) −1.21032e7 −1.13669 −0.568343 0.822792i \(-0.692415\pi\)
−0.568343 + 0.822792i \(0.692415\pi\)
\(648\) −3.91062e6 −0.365854
\(649\) 9.10295e6 0.848341
\(650\) 1.96309e6 0.182245
\(651\) −67734.2 −0.00626406
\(652\) −7.77632e6 −0.716399
\(653\) −1.29405e7 −1.18759 −0.593797 0.804615i \(-0.702372\pi\)
−0.593797 + 0.804615i \(0.702372\pi\)
\(654\) 7.44945e6 0.681052
\(655\) 3.28944e6 0.299584
\(656\) −2.60589e6 −0.236427
\(657\) −1.90473e7 −1.72156
\(658\) −520079. −0.0468279
\(659\) 6.49902e6 0.582954 0.291477 0.956578i \(-0.405853\pi\)
0.291477 + 0.956578i \(0.405853\pi\)
\(660\) −3.85896e6 −0.344835
\(661\) 1.22642e7 1.09178 0.545891 0.837856i \(-0.316191\pi\)
0.545891 + 0.837856i \(0.316191\pi\)
\(662\) 2.97439e6 0.263787
\(663\) 1.08462e7 0.958283
\(664\) 592012. 0.0521087
\(665\) 388156. 0.0340371
\(666\) 697968. 0.0609747
\(667\) 1.65377e6 0.143933
\(668\) 7.74328e6 0.671404
\(669\) −1.16690e7 −1.00802
\(670\) 2.95140e6 0.254005
\(671\) −2.89402e6 −0.248139
\(672\) 166571. 0.0142290
\(673\) −7.93539e6 −0.675353 −0.337676 0.941262i \(-0.609641\pi\)
−0.337676 + 0.941262i \(0.609641\pi\)
\(674\) 1.57263e7 1.33345
\(675\) −119753. −0.0101164
\(676\) 3.92481e6 0.330333
\(677\) 8.83259e6 0.740656 0.370328 0.928901i \(-0.379245\pi\)
0.370328 + 0.928901i \(0.379245\pi\)
\(678\) 850095. 0.0710220
\(679\) −408868. −0.0340337
\(680\) 1.01166e6 0.0839001
\(681\) −4.49863e6 −0.371717
\(682\) 735558. 0.0605558
\(683\) 9.13451e6 0.749261 0.374631 0.927174i \(-0.377769\pi\)
0.374631 + 0.927174i \(0.377769\pi\)
\(684\) 7.81434e6 0.638634
\(685\) −3.59700e6 −0.292896
\(686\) −999536. −0.0810939
\(687\) −2.04048e7 −1.64945
\(688\) 5.27288e6 0.424695
\(689\) −2.37994e7 −1.90993
\(690\) 1.15563e6 0.0924052
\(691\) 4.27639e6 0.340708 0.170354 0.985383i \(-0.445509\pi\)
0.170354 + 0.985383i \(0.445509\pi\)
\(692\) 2.59546e6 0.206039
\(693\) −770235. −0.0609242
\(694\) 810080. 0.0638453
\(695\) 1.08178e6 0.0849525
\(696\) 4.37083e6 0.342011
\(697\) −6.43622e6 −0.501821
\(698\) −1.57674e7 −1.22496
\(699\) −1.15746e7 −0.896012
\(700\) 74462.1 0.00574368
\(701\) −9.09791e6 −0.699273 −0.349637 0.936885i \(-0.613695\pi\)
−0.349637 + 0.936885i \(0.613695\pi\)
\(702\) −601818. −0.0460916
\(703\) 1.55334e6 0.118543
\(704\) −1.80887e6 −0.137555
\(705\) −9.53625e6 −0.722611
\(706\) 1.31811e7 0.995270
\(707\) 1.40860e6 0.105984
\(708\) −7.20475e6 −0.540176
\(709\) 1.40966e7 1.05317 0.526584 0.850123i \(-0.323473\pi\)
0.526584 + 0.850123i \(0.323473\pi\)
\(710\) −5.42196e6 −0.403655
\(711\) 2.32613e7 1.72568
\(712\) 1.47129e6 0.108767
\(713\) −220275. −0.0162271
\(714\) 411408. 0.0302014
\(715\) −8.66935e6 −0.634193
\(716\) −4.57306e6 −0.333368
\(717\) −1.74001e7 −1.26402
\(718\) −208727. −0.0151101
\(719\) −7.26273e6 −0.523936 −0.261968 0.965077i \(-0.584371\pi\)
−0.261968 + 0.965077i \(0.584371\pi\)
\(720\) 1.49907e6 0.107768
\(721\) −188386. −0.0134961
\(722\) 7.48655e6 0.534489
\(723\) 1.07487e7 0.764733
\(724\) 751874. 0.0533087
\(725\) 1.95389e6 0.138056
\(726\) 2.96889e6 0.209051
\(727\) −1.58378e7 −1.11137 −0.555687 0.831392i \(-0.687545\pi\)
−0.555687 + 0.831392i \(0.687545\pi\)
\(728\) 374209. 0.0261689
\(729\) −1.32951e7 −0.926556
\(730\) −8.13193e6 −0.564789
\(731\) 1.30233e7 0.901424
\(732\) 2.29054e6 0.158001
\(733\) 1.99229e7 1.36959 0.684797 0.728734i \(-0.259891\pi\)
0.684797 + 0.728734i \(0.259891\pi\)
\(734\) −5.13931e6 −0.352099
\(735\) −9.14868e6 −0.624655
\(736\) 541696. 0.0368605
\(737\) −1.30339e7 −0.883908
\(738\) −9.53712e6 −0.644579
\(739\) 2.55968e7 1.72415 0.862073 0.506784i \(-0.169166\pi\)
0.862073 + 0.506784i \(0.169166\pi\)
\(740\) 297985. 0.0200039
\(741\) 3.57680e7 2.39304
\(742\) −902737. −0.0601938
\(743\) −1.10625e7 −0.735162 −0.367581 0.929992i \(-0.619814\pi\)
−0.367581 + 0.929992i \(0.619814\pi\)
\(744\) −582174. −0.0385586
\(745\) −9.29424e6 −0.613512
\(746\) −3.40362e6 −0.223921
\(747\) 2.16667e6 0.142066
\(748\) −4.46768e6 −0.291963
\(749\) −1.01795e6 −0.0663015
\(750\) 1.36535e6 0.0886320
\(751\) −1.11013e7 −0.718248 −0.359124 0.933290i \(-0.616925\pi\)
−0.359124 + 0.933290i \(0.616925\pi\)
\(752\) −4.47007e6 −0.288250
\(753\) 3.29101e7 2.11516
\(754\) 9.81928e6 0.629001
\(755\) −5.60792e6 −0.358042
\(756\) −22827.6 −0.00145263
\(757\) 6.41568e6 0.406914 0.203457 0.979084i \(-0.434782\pi\)
0.203457 + 0.979084i \(0.434782\pi\)
\(758\) 1.97684e7 1.24968
\(759\) −5.10348e6 −0.321560
\(760\) 3.33620e6 0.209516
\(761\) 1.71384e7 1.07278 0.536389 0.843971i \(-0.319788\pi\)
0.536389 + 0.843971i \(0.319788\pi\)
\(762\) −1.49140e7 −0.930478
\(763\) 634799. 0.0394752
\(764\) −8.18309e6 −0.507206
\(765\) 3.70250e6 0.228740
\(766\) −5.26964e6 −0.324496
\(767\) −1.61858e7 −0.993451
\(768\) 1.43167e6 0.0875871
\(769\) −6.53211e6 −0.398325 −0.199163 0.979966i \(-0.563822\pi\)
−0.199163 + 0.979966i \(0.563822\pi\)
\(770\) −328838. −0.0199874
\(771\) −1.11892e7 −0.677896
\(772\) −8.04550e6 −0.485858
\(773\) −2.94949e6 −0.177541 −0.0887705 0.996052i \(-0.528294\pi\)
−0.0887705 + 0.996052i \(0.528294\pi\)
\(774\) 1.92979e7 1.15786
\(775\) −260249. −0.0155645
\(776\) −3.51421e6 −0.209495
\(777\) 121181. 0.00720080
\(778\) 1.88684e6 0.111760
\(779\) −2.12250e7 −1.25315
\(780\) 6.86156e6 0.403819
\(781\) 2.39444e7 1.40467
\(782\) 1.33792e6 0.0782372
\(783\) −598998. −0.0349157
\(784\) −4.28840e6 −0.249175
\(785\) −7.90748e6 −0.457998
\(786\) 1.14976e7 0.663818
\(787\) 4.59906e6 0.264687 0.132343 0.991204i \(-0.457750\pi\)
0.132343 + 0.991204i \(0.457750\pi\)
\(788\) 8.23395e6 0.472381
\(789\) −3.07106e7 −1.75629
\(790\) 9.93098e6 0.566141
\(791\) 72440.1 0.00411659
\(792\) −6.62015e6 −0.375021
\(793\) 5.14581e6 0.290583
\(794\) −5.29333e6 −0.297973
\(795\) −1.65527e7 −0.928863
\(796\) 6.82956e6 0.382041
\(797\) 6.06291e6 0.338092 0.169046 0.985608i \(-0.445931\pi\)
0.169046 + 0.985608i \(0.445931\pi\)
\(798\) 1.35672e6 0.0754194
\(799\) −1.10405e7 −0.611817
\(800\) 640000. 0.0353553
\(801\) 5.38467e6 0.296536
\(802\) −2.43253e7 −1.33543
\(803\) 3.59121e7 1.96540
\(804\) 1.03160e7 0.562823
\(805\) 98476.1 0.00535601
\(806\) −1.30788e6 −0.0709139
\(807\) 1.04140e7 0.562905
\(808\) 1.21069e7 0.652387
\(809\) 2.38764e7 1.28262 0.641310 0.767282i \(-0.278391\pi\)
0.641310 + 0.767282i \(0.278391\pi\)
\(810\) −6.11034e6 −0.327230
\(811\) −2.78099e6 −0.148473 −0.0742366 0.997241i \(-0.523652\pi\)
−0.0742366 + 0.997241i \(0.523652\pi\)
\(812\) 372456. 0.0198237
\(813\) 2.00621e7 1.06451
\(814\) −1.31596e6 −0.0696114
\(815\) −1.21505e7 −0.640767
\(816\) 3.53605e6 0.185906
\(817\) 4.29477e7 2.25105
\(818\) −1.79997e7 −0.940551
\(819\) 1.36954e6 0.0713454
\(820\) −4.07170e6 −0.211467
\(821\) −1.59900e7 −0.827925 −0.413963 0.910294i \(-0.635856\pi\)
−0.413963 + 0.910294i \(0.635856\pi\)
\(822\) −1.25726e7 −0.648999
\(823\) 3.19956e7 1.64661 0.823304 0.567600i \(-0.192128\pi\)
0.823304 + 0.567600i \(0.192128\pi\)
\(824\) −1.61917e6 −0.0830758
\(825\) −6.02963e6 −0.308429
\(826\) −613946. −0.0313098
\(827\) −2.56186e7 −1.30254 −0.651271 0.758846i \(-0.725764\pi\)
−0.651271 + 0.758846i \(0.725764\pi\)
\(828\) 1.98252e6 0.100494
\(829\) 2.44926e7 1.23779 0.618897 0.785473i \(-0.287580\pi\)
0.618897 + 0.785473i \(0.287580\pi\)
\(830\) 925019. 0.0466075
\(831\) 1.26487e7 0.635395
\(832\) 3.21632e6 0.161084
\(833\) −1.05918e7 −0.528880
\(834\) 3.78113e6 0.188238
\(835\) 1.20989e7 0.600522
\(836\) −1.47333e7 −0.729093
\(837\) 79783.8 0.00393642
\(838\) 2.29963e7 1.13122
\(839\) −3.75328e7 −1.84080 −0.920398 0.390982i \(-0.872136\pi\)
−0.920398 + 0.390982i \(0.872136\pi\)
\(840\) 260267. 0.0127268
\(841\) −1.07379e7 −0.523514
\(842\) −2.89849e6 −0.140894
\(843\) 2.86127e7 1.38672
\(844\) 1.03629e7 0.500754
\(845\) 6.13252e6 0.295459
\(846\) −1.63597e7 −0.785867
\(847\) 252991. 0.0121170
\(848\) −7.75901e6 −0.370524
\(849\) 8.47647e6 0.403595
\(850\) 1.58072e6 0.0750425
\(851\) 394085. 0.0186538
\(852\) −1.89513e7 −0.894418
\(853\) −2.48528e7 −1.16951 −0.584754 0.811210i \(-0.698809\pi\)
−0.584754 + 0.811210i \(0.698809\pi\)
\(854\) 195186. 0.00915808
\(855\) 1.22099e7 0.571212
\(856\) −8.74929e6 −0.408120
\(857\) −1.82652e7 −0.849516 −0.424758 0.905307i \(-0.639641\pi\)
−0.424758 + 0.905307i \(0.639641\pi\)
\(858\) −3.03019e7 −1.40524
\(859\) 3.03679e7 1.40421 0.702104 0.712075i \(-0.252244\pi\)
0.702104 + 0.712075i \(0.252244\pi\)
\(860\) 8.23888e6 0.379859
\(861\) −1.65583e6 −0.0761214
\(862\) 1.16082e6 0.0532106
\(863\) 6.46938e6 0.295689 0.147845 0.989011i \(-0.452766\pi\)
0.147845 + 0.989011i \(0.452766\pi\)
\(864\) −196203. −0.00894172
\(865\) 4.05540e6 0.184287
\(866\) −1.24691e7 −0.564991
\(867\) −2.22840e7 −1.00681
\(868\) −49609.5 −0.00223494
\(869\) −4.38570e7 −1.97011
\(870\) 6.82942e6 0.305904
\(871\) 2.31754e7 1.03510
\(872\) 5.45608e6 0.242991
\(873\) −1.28614e7 −0.571154
\(874\) 4.41212e6 0.195375
\(875\) 116347. 0.00513730
\(876\) −2.84235e7 −1.25146
\(877\) 7.87858e6 0.345899 0.172949 0.984931i \(-0.444670\pi\)
0.172949 + 0.984931i \(0.444670\pi\)
\(878\) 4.04007e6 0.176869
\(879\) 3.16672e7 1.38241
\(880\) −2.82636e6 −0.123033
\(881\) 1.58782e7 0.689227 0.344614 0.938745i \(-0.388010\pi\)
0.344614 + 0.938745i \(0.388010\pi\)
\(882\) −1.56948e7 −0.679336
\(883\) −3.52265e7 −1.52044 −0.760218 0.649668i \(-0.774908\pi\)
−0.760218 + 0.649668i \(0.774908\pi\)
\(884\) 7.94391e6 0.341903
\(885\) −1.12574e7 −0.483148
\(886\) −1.26219e7 −0.540185
\(887\) 3.57175e6 0.152431 0.0762154 0.997091i \(-0.475716\pi\)
0.0762154 + 0.997091i \(0.475716\pi\)
\(888\) 1.04154e6 0.0443247
\(889\) −1.27088e6 −0.0539325
\(890\) 2.29889e6 0.0972844
\(891\) 2.69844e7 1.13872
\(892\) −8.54653e6 −0.359648
\(893\) −3.64087e7 −1.52784
\(894\) −3.24861e7 −1.35942
\(895\) −7.14540e6 −0.298173
\(896\) 121999. 0.00507674
\(897\) 9.07442e6 0.376563
\(898\) −1.25914e7 −0.521056
\(899\) −1.30176e6 −0.0537193
\(900\) 2.34229e6 0.0963906
\(901\) −1.91638e7 −0.786446
\(902\) 1.79814e7 0.735880
\(903\) 3.35048e6 0.136737
\(904\) 622621. 0.0253398
\(905\) 1.17480e6 0.0476808
\(906\) −1.96013e7 −0.793349
\(907\) −4.42353e7 −1.78546 −0.892732 0.450588i \(-0.851214\pi\)
−0.892732 + 0.450588i \(0.851214\pi\)
\(908\) −3.29486e6 −0.132624
\(909\) 4.43093e7 1.77863
\(910\) 584702. 0.0234062
\(911\) −3.38099e7 −1.34973 −0.674867 0.737939i \(-0.735799\pi\)
−0.674867 + 0.737939i \(0.735799\pi\)
\(912\) 1.16610e7 0.464246
\(913\) −4.08506e6 −0.162189
\(914\) −5.60499e6 −0.221927
\(915\) 3.57897e6 0.141320
\(916\) −1.49447e7 −0.588504
\(917\) 979755. 0.0384764
\(918\) −484596. −0.0189790
\(919\) −2.23014e7 −0.871052 −0.435526 0.900176i \(-0.643438\pi\)
−0.435526 + 0.900176i \(0.643438\pi\)
\(920\) 846400. 0.0329690
\(921\) 4.98688e7 1.93722
\(922\) −1.59855e7 −0.619298
\(923\) −4.25751e7 −1.64495
\(924\) −1.14939e6 −0.0442880
\(925\) 465602. 0.0178921
\(926\) 1.87051e7 0.716856
\(927\) −5.92589e6 −0.226493
\(928\) 3.20125e6 0.122025
\(929\) −3.58441e7 −1.36263 −0.681316 0.731989i \(-0.738592\pi\)
−0.681316 + 0.731989i \(0.738592\pi\)
\(930\) −909647. −0.0344878
\(931\) −3.49290e7 −1.32073
\(932\) −8.47741e6 −0.319686
\(933\) 4.78781e7 1.80067
\(934\) 1.99804e6 0.0749439
\(935\) −6.98075e6 −0.261140
\(936\) 1.17712e7 0.439168
\(937\) 1.21031e7 0.450348 0.225174 0.974319i \(-0.427705\pi\)
0.225174 + 0.974319i \(0.427705\pi\)
\(938\) 879070. 0.0326224
\(939\) 5.38279e7 1.99225
\(940\) −6.98448e6 −0.257819
\(941\) −4.13064e7 −1.52070 −0.760350 0.649513i \(-0.774973\pi\)
−0.760350 + 0.649513i \(0.774973\pi\)
\(942\) −2.76389e7 −1.01483
\(943\) −5.38483e6 −0.197194
\(944\) −5.27685e6 −0.192728
\(945\) −35668.1 −0.00129927
\(946\) −3.63844e7 −1.32187
\(947\) −5.16814e6 −0.187266 −0.0936331 0.995607i \(-0.529848\pi\)
−0.0936331 + 0.995607i \(0.529848\pi\)
\(948\) 3.47117e7 1.25445
\(949\) −6.38547e7 −2.30159
\(950\) 5.21281e6 0.187397
\(951\) 4.92072e7 1.76432
\(952\) 301321. 0.0107755
\(953\) 3.52996e7 1.25903 0.629516 0.776987i \(-0.283253\pi\)
0.629516 + 0.776987i \(0.283253\pi\)
\(954\) −2.83966e7 −1.01017
\(955\) −1.27861e7 −0.453658
\(956\) −1.27441e7 −0.450988
\(957\) −3.01600e7 −1.06451
\(958\) −2.90827e7 −1.02381
\(959\) −1.07136e6 −0.0376174
\(960\) 2.23699e6 0.0783403
\(961\) −2.84558e7 −0.993944
\(962\) 2.33988e6 0.0815185
\(963\) −3.20209e7 −1.11267
\(964\) 7.87249e6 0.272847
\(965\) −1.25711e7 −0.434565
\(966\) 344203. 0.0118678
\(967\) 2.21489e7 0.761704 0.380852 0.924636i \(-0.375631\pi\)
0.380852 + 0.924636i \(0.375631\pi\)
\(968\) 2.17445e6 0.0745868
\(969\) 2.88011e7 0.985372
\(970\) −5.49095e6 −0.187378
\(971\) −272621. −0.00927922 −0.00463961 0.999989i \(-0.501477\pi\)
−0.00463961 + 0.999989i \(0.501477\pi\)
\(972\) −2.06125e7 −0.699784
\(973\) 322206. 0.0109107
\(974\) 1.75927e7 0.594204
\(975\) 1.07212e7 0.361187
\(976\) 1.67762e6 0.0563728
\(977\) 2.78738e7 0.934244 0.467122 0.884193i \(-0.345291\pi\)
0.467122 + 0.884193i \(0.345291\pi\)
\(978\) −4.24695e7 −1.41981
\(979\) −1.01523e7 −0.338539
\(980\) −6.70062e6 −0.222869
\(981\) 1.99683e7 0.662475
\(982\) 2.69458e7 0.891688
\(983\) −3.91324e7 −1.29167 −0.645837 0.763475i \(-0.723492\pi\)
−0.645837 + 0.763475i \(0.723492\pi\)
\(984\) −1.42318e7 −0.468567
\(985\) 1.28655e7 0.422511
\(986\) 7.90669e6 0.259002
\(987\) −2.84035e6 −0.0928068
\(988\) 2.61970e7 0.853805
\(989\) 1.08959e7 0.354220
\(990\) −1.03440e7 −0.335429
\(991\) −2.03186e7 −0.657217 −0.328608 0.944466i \(-0.606580\pi\)
−0.328608 + 0.944466i \(0.606580\pi\)
\(992\) −426393. −0.0137572
\(993\) 1.62443e7 0.522791
\(994\) −1.61492e6 −0.0518424
\(995\) 1.06712e7 0.341708
\(996\) 3.23321e6 0.103273
\(997\) 2.54600e7 0.811186 0.405593 0.914054i \(-0.367065\pi\)
0.405593 + 0.914054i \(0.367065\pi\)
\(998\) 2.04284e7 0.649243
\(999\) −142738. −0.00452508
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 230.6.a.h.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.6.a.h.1.5 6 1.1 even 1 trivial