Properties

Label 147.6.e.o.67.4
Level $147$
Weight $6$
Character 147.67
Analytic conductor $23.576$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,6,Mod(67,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.4
Root \(5.09061 + 8.81720i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.6.e.o.79.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.59061 + 7.95118i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-26.1475 + 45.2888i) q^{4} +(11.0358 + 19.1146i) q^{5} +82.6311 q^{6} -186.333 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(4.59061 + 7.95118i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-26.1475 + 45.2888i) q^{4} +(11.0358 + 19.1146i) q^{5} +82.6311 q^{6} -186.333 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-101.322 + 175.495i) q^{10} +(-208.355 + 360.881i) q^{11} +(235.327 + 407.599i) q^{12} -797.918 q^{13} +198.644 q^{15} +(-18.6623 - 32.3240i) q^{16} +(-687.775 + 1191.26i) q^{17} +(371.840 - 644.045i) q^{18} +(1156.51 + 2003.14i) q^{19} -1154.23 q^{20} -3825.91 q^{22} +(477.701 + 827.402i) q^{23} +(-838.497 + 1452.32i) q^{24} +(1318.92 - 2284.44i) q^{25} +(-3662.93 - 6344.39i) q^{26} -729.000 q^{27} -7035.29 q^{29} +(911.900 + 1579.46i) q^{30} +(630.596 - 1092.22i) q^{31} +(-2809.98 + 4867.03i) q^{32} +(1875.19 + 3247.93i) q^{33} -12629.2 q^{34} +4235.89 q^{36} +(-4888.22 - 8466.65i) q^{37} +(-10618.2 + 18391.3i) q^{38} +(-3590.63 + 6219.16i) q^{39} +(-2056.33 - 3561.67i) q^{40} +5400.95 q^{41} +19686.6 q^{43} +(-10895.9 - 18872.3i) q^{44} +(893.900 - 1548.28i) q^{45} +(-4385.88 + 7596.57i) q^{46} +(1028.28 + 1781.04i) q^{47} -335.921 q^{48} +24218.7 q^{50} +(6189.98 + 10721.4i) q^{51} +(20863.5 - 36136.7i) q^{52} +(-9011.37 + 15608.2i) q^{53} +(-3346.56 - 5796.41i) q^{54} -9197.45 q^{55} +20817.2 q^{57} +(-32296.3 - 55938.8i) q^{58} +(3717.84 - 6439.49i) q^{59} +(-5194.05 + 8996.36i) q^{60} +(1747.69 + 3027.09i) q^{61} +11579.3 q^{62} -52792.5 q^{64} +(-8805.67 - 15251.9i) q^{65} +(-17216.6 + 29820.0i) q^{66} +(-7928.21 + 13732.1i) q^{67} +(-35967.2 - 62297.0i) q^{68} +8598.62 q^{69} +58133.5 q^{71} +(7546.48 + 13070.9i) q^{72} +(19555.3 - 33870.8i) q^{73} +(44879.9 - 77734.2i) q^{74} +(-11870.3 - 20560.0i) q^{75} -120960. q^{76} -65932.8 q^{78} +(-4880.35 - 8453.01i) q^{79} +(411.906 - 713.442i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(24793.7 + 42943.9i) q^{82} +70395.7 q^{83} -30360.6 q^{85} +(90373.4 + 156531. i) q^{86} +(-31658.8 + 54834.7i) q^{87} +(38823.3 - 67243.9i) q^{88} +(72153.1 + 124973. i) q^{89} +16414.2 q^{90} -49962.7 q^{92} +(-5675.36 - 9830.01i) q^{93} +(-9440.90 + 16352.1i) q^{94} +(-25526.1 + 44212.5i) q^{95} +(25289.8 + 43803.3i) q^{96} +79328.7 q^{97} +33753.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.59061 + 7.95118i 0.811514 + 1.40558i 0.911804 + 0.410625i \(0.134689\pi\)
−0.100291 + 0.994958i \(0.531977\pi\)
\(3\) 4.50000 7.79423i 0.288675 0.500000i
\(4\) −26.1475 + 45.2888i −0.817109 + 1.41527i
\(5\) 11.0358 + 19.1146i 0.197414 + 0.341932i 0.947689 0.319194i \(-0.103412\pi\)
−0.750275 + 0.661126i \(0.770079\pi\)
\(6\) 82.6311 0.937055
\(7\) 0 0
\(8\) −186.333 −1.02935
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) −101.322 + 175.495i −0.320409 + 0.554965i
\(11\) −208.355 + 360.881i −0.519184 + 0.899254i 0.480567 + 0.876958i \(0.340431\pi\)
−0.999751 + 0.0222959i \(0.992902\pi\)
\(12\) 235.327 + 407.599i 0.471758 + 0.817109i
\(13\) −797.918 −1.30948 −0.654742 0.755853i \(-0.727223\pi\)
−0.654742 + 0.755853i \(0.727223\pi\)
\(14\) 0 0
\(15\) 198.644 0.227955
\(16\) −18.6623 32.3240i −0.0182249 0.0315664i
\(17\) −687.775 + 1191.26i −0.577197 + 0.999735i 0.418602 + 0.908170i \(0.362520\pi\)
−0.995799 + 0.0915652i \(0.970813\pi\)
\(18\) 371.840 644.045i 0.270505 0.468528i
\(19\) 1156.51 + 2003.14i 0.734965 + 1.27300i 0.954739 + 0.297446i \(0.0961347\pi\)
−0.219774 + 0.975551i \(0.570532\pi\)
\(20\) −1154.23 −0.645236
\(21\) 0 0
\(22\) −3825.91 −1.68530
\(23\) 477.701 + 827.402i 0.188294 + 0.326135i 0.944682 0.327989i \(-0.106371\pi\)
−0.756388 + 0.654124i \(0.773038\pi\)
\(24\) −838.497 + 1452.32i −0.297149 + 0.514676i
\(25\) 1318.92 2284.44i 0.422055 0.731021i
\(26\) −3662.93 6344.39i −1.06266 1.84059i
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) −7035.29 −1.55341 −0.776707 0.629862i \(-0.783111\pi\)
−0.776707 + 0.629862i \(0.783111\pi\)
\(30\) 911.900 + 1579.46i 0.184988 + 0.320409i
\(31\) 630.596 1092.22i 0.117855 0.204130i −0.801063 0.598581i \(-0.795732\pi\)
0.918917 + 0.394450i \(0.129065\pi\)
\(32\) −2809.98 + 4867.03i −0.485097 + 0.840212i
\(33\) 1875.19 + 3247.93i 0.299751 + 0.519184i
\(34\) −12629.2 −1.87361
\(35\) 0 0
\(36\) 4235.89 0.544739
\(37\) −4888.22 8466.65i −0.587012 1.01673i −0.994621 0.103578i \(-0.966971\pi\)
0.407610 0.913156i \(-0.366362\pi\)
\(38\) −10618.2 + 18391.3i −1.19287 + 2.06611i
\(39\) −3590.63 + 6219.16i −0.378015 + 0.654742i
\(40\) −2056.33 3561.67i −0.203209 0.351968i
\(41\) 5400.95 0.501777 0.250888 0.968016i \(-0.419277\pi\)
0.250888 + 0.968016i \(0.419277\pi\)
\(42\) 0 0
\(43\) 19686.6 1.62367 0.811837 0.583885i \(-0.198468\pi\)
0.811837 + 0.583885i \(0.198468\pi\)
\(44\) −10895.9 18872.3i −0.848460 1.46958i
\(45\) 893.900 1548.28i 0.0658048 0.113977i
\(46\) −4385.88 + 7596.57i −0.305606 + 0.529326i
\(47\) 1028.28 + 1781.04i 0.0678997 + 0.117606i 0.897977 0.440043i \(-0.145037\pi\)
−0.830077 + 0.557649i \(0.811704\pi\)
\(48\) −335.921 −0.0210443
\(49\) 0 0
\(50\) 24218.7 1.37001
\(51\) 6189.98 + 10721.4i 0.333245 + 0.577197i
\(52\) 20863.5 36136.7i 1.06999 1.85328i
\(53\) −9011.37 + 15608.2i −0.440658 + 0.763241i −0.997738 0.0672170i \(-0.978588\pi\)
0.557081 + 0.830458i \(0.311921\pi\)
\(54\) −3346.56 5796.41i −0.156176 0.270505i
\(55\) −9197.45 −0.409978
\(56\) 0 0
\(57\) 20817.2 0.848664
\(58\) −32296.3 55938.8i −1.26062 2.18345i
\(59\) 3717.84 6439.49i 0.139047 0.240836i −0.788089 0.615561i \(-0.788930\pi\)
0.927136 + 0.374725i \(0.122263\pi\)
\(60\) −5194.05 + 8996.36i −0.186264 + 0.322618i
\(61\) 1747.69 + 3027.09i 0.0601368 + 0.104160i 0.894526 0.447015i \(-0.147513\pi\)
−0.834390 + 0.551175i \(0.814180\pi\)
\(62\) 11579.3 0.382563
\(63\) 0 0
\(64\) −52792.5 −1.61110
\(65\) −8805.67 15251.9i −0.258511 0.447754i
\(66\) −17216.6 + 29820.0i −0.486505 + 0.842651i
\(67\) −7928.21 + 13732.1i −0.215769 + 0.373722i −0.953510 0.301361i \(-0.902559\pi\)
0.737741 + 0.675083i \(0.235892\pi\)
\(68\) −35967.2 62297.0i −0.943266 1.63378i
\(69\) 8598.62 0.217423
\(70\) 0 0
\(71\) 58133.5 1.36861 0.684306 0.729195i \(-0.260105\pi\)
0.684306 + 0.729195i \(0.260105\pi\)
\(72\) 7546.48 + 13070.9i 0.171559 + 0.297149i
\(73\) 19555.3 33870.8i 0.429495 0.743907i −0.567334 0.823488i \(-0.692025\pi\)
0.996828 + 0.0795812i \(0.0253583\pi\)
\(74\) 44879.9 77734.2i 0.952736 1.65019i
\(75\) −11870.3 20560.0i −0.243674 0.422055i
\(76\) −120960. −2.40218
\(77\) 0 0
\(78\) −65932.8 −1.22706
\(79\) −4880.35 8453.01i −0.0879798 0.152385i 0.818677 0.574254i \(-0.194708\pi\)
−0.906657 + 0.421868i \(0.861374\pi\)
\(80\) 411.906 713.442i 0.00719570 0.0124633i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 24793.7 + 42943.9i 0.407199 + 0.705289i
\(83\) 70395.7 1.12163 0.560816 0.827940i \(-0.310487\pi\)
0.560816 + 0.827940i \(0.310487\pi\)
\(84\) 0 0
\(85\) −30360.6 −0.455788
\(86\) 90373.4 + 156531.i 1.31763 + 2.28221i
\(87\) −31658.8 + 54834.7i −0.448432 + 0.776707i
\(88\) 38823.3 67243.9i 0.534424 0.925649i
\(89\) 72153.1 + 124973.i 0.965562 + 1.67240i 0.708098 + 0.706115i \(0.249554\pi\)
0.257464 + 0.966288i \(0.417113\pi\)
\(90\) 16414.2 0.213606
\(91\) 0 0
\(92\) −49962.7 −0.615427
\(93\) −5675.36 9830.01i −0.0680434 0.117855i
\(94\) −9440.90 + 16352.1i −0.110203 + 0.190877i
\(95\) −25526.1 + 44212.5i −0.290185 + 0.502616i
\(96\) 25289.8 + 43803.3i 0.280071 + 0.485097i
\(97\) 79328.7 0.856053 0.428027 0.903766i \(-0.359209\pi\)
0.428027 + 0.903766i \(0.359209\pi\)
\(98\) 0 0
\(99\) 33753.5 0.346123
\(100\) 68973.0 + 119465.i 0.689730 + 1.19465i
\(101\) −42416.9 + 73468.2i −0.413747 + 0.716631i −0.995296 0.0968802i \(-0.969114\pi\)
0.581549 + 0.813512i \(0.302447\pi\)
\(102\) −56831.6 + 98435.2i −0.540866 + 0.936807i
\(103\) 10166.1 + 17608.3i 0.0944197 + 0.163540i 0.909366 0.415996i \(-0.136567\pi\)
−0.814947 + 0.579536i \(0.803234\pi\)
\(104\) 148678. 1.34792
\(105\) 0 0
\(106\) −165471. −1.43040
\(107\) −3481.09 6029.43i −0.0293938 0.0509116i 0.850954 0.525240i \(-0.176024\pi\)
−0.880348 + 0.474328i \(0.842691\pi\)
\(108\) 19061.5 33015.5i 0.157253 0.272370i
\(109\) −56325.7 + 97559.0i −0.454088 + 0.786504i −0.998635 0.0522262i \(-0.983368\pi\)
0.544547 + 0.838730i \(0.316702\pi\)
\(110\) −42221.9 73130.5i −0.332703 0.576258i
\(111\) −87988.0 −0.677823
\(112\) 0 0
\(113\) 112005. 0.825167 0.412583 0.910920i \(-0.364627\pi\)
0.412583 + 0.910920i \(0.364627\pi\)
\(114\) 95563.9 + 165522.i 0.688703 + 1.19287i
\(115\) −10543.6 + 18262.1i −0.0743439 + 0.128767i
\(116\) 183955. 318620.i 1.26931 2.19851i
\(117\) 32315.7 + 55972.4i 0.218247 + 0.378015i
\(118\) 68268.7 0.451353
\(119\) 0 0
\(120\) −37014.0 −0.234646
\(121\) −6297.91 10908.3i −0.0391051 0.0677320i
\(122\) −16046.0 + 27792.4i −0.0976037 + 0.169055i
\(123\) 24304.3 42096.2i 0.144850 0.250888i
\(124\) 32977.0 + 57117.8i 0.192600 + 0.333593i
\(125\) 127195. 0.728108
\(126\) 0 0
\(127\) 82224.5 0.452368 0.226184 0.974085i \(-0.427375\pi\)
0.226184 + 0.974085i \(0.427375\pi\)
\(128\) −152431. 264018.i −0.822333 1.42432i
\(129\) 88589.5 153442.i 0.468714 0.811837i
\(130\) 80846.8 140031.i 0.419570 0.726717i
\(131\) −87905.9 152258.i −0.447548 0.775176i 0.550677 0.834718i \(-0.314369\pi\)
−0.998226 + 0.0595417i \(0.981036\pi\)
\(132\) −196126. −0.979718
\(133\) 0 0
\(134\) −145581. −0.700397
\(135\) −8045.10 13934.5i −0.0379924 0.0658048i
\(136\) 128155. 221971.i 0.594140 1.02908i
\(137\) −15665.2 + 27132.9i −0.0713072 + 0.123508i −0.899474 0.436973i \(-0.856050\pi\)
0.828167 + 0.560481i \(0.189384\pi\)
\(138\) 39472.9 + 68369.1i 0.176442 + 0.305606i
\(139\) −152234. −0.668305 −0.334152 0.942519i \(-0.608450\pi\)
−0.334152 + 0.942519i \(0.608450\pi\)
\(140\) 0 0
\(141\) 18509.1 0.0784038
\(142\) 266868. + 462229.i 1.11065 + 1.92370i
\(143\) 166250. 287953.i 0.679863 1.17756i
\(144\) −1511.64 + 2618.24i −0.00607495 + 0.0105221i
\(145\) −77640.1 134477.i −0.306666 0.531162i
\(146\) 359084. 1.39416
\(147\) 0 0
\(148\) 511259. 1.91861
\(149\) −181430. 314246.i −0.669489 1.15959i −0.978047 0.208384i \(-0.933180\pi\)
0.308558 0.951206i \(-0.400154\pi\)
\(150\) 108984. 188766.i 0.395489 0.685007i
\(151\) −102563. + 177644.i −0.366056 + 0.634027i −0.988945 0.148283i \(-0.952625\pi\)
0.622889 + 0.782310i \(0.285959\pi\)
\(152\) −215496. 373250.i −0.756538 1.31036i
\(153\) 111420. 0.384798
\(154\) 0 0
\(155\) 27836.5 0.0930648
\(156\) −187772. 325231.i −0.617759 1.06999i
\(157\) −38636.0 + 66919.5i −0.125096 + 0.216672i −0.921770 0.387736i \(-0.873257\pi\)
0.796675 + 0.604409i \(0.206591\pi\)
\(158\) 44807.6 77609.0i 0.142794 0.247326i
\(159\) 81102.3 + 140473.i 0.254414 + 0.440658i
\(160\) −124042. −0.383060
\(161\) 0 0
\(162\) −60238.0 −0.180336
\(163\) −92465.7 160155.i −0.272591 0.472141i 0.696934 0.717136i \(-0.254547\pi\)
−0.969525 + 0.244994i \(0.921214\pi\)
\(164\) −141221. + 244602.i −0.410006 + 0.710152i
\(165\) −41388.5 + 71687.0i −0.118350 + 0.204989i
\(166\) 323159. + 559728.i 0.910220 + 1.57655i
\(167\) −129262. −0.358657 −0.179329 0.983789i \(-0.557393\pi\)
−0.179329 + 0.983789i \(0.557393\pi\)
\(168\) 0 0
\(169\) 265380. 0.714746
\(170\) −139374. 241403.i −0.369878 0.640648i
\(171\) 93677.6 162254.i 0.244988 0.424332i
\(172\) −514754. + 891580.i −1.32672 + 2.29794i
\(173\) −253934. 439826.i −0.645067 1.11729i −0.984286 0.176582i \(-0.943496\pi\)
0.339219 0.940707i \(-0.389837\pi\)
\(174\) −581334. −1.45563
\(175\) 0 0
\(176\) 15553.5 0.0378483
\(177\) −33460.6 57955.4i −0.0802786 0.139047i
\(178\) −662454. + 1.14740e6i −1.56713 + 2.71435i
\(179\) 66294.5 114825.i 0.154648 0.267859i −0.778283 0.627914i \(-0.783909\pi\)
0.932931 + 0.360056i \(0.117242\pi\)
\(180\) 46746.5 + 80967.3i 0.107539 + 0.186264i
\(181\) 740060. 1.67908 0.839538 0.543301i \(-0.182826\pi\)
0.839538 + 0.543301i \(0.182826\pi\)
\(182\) 0 0
\(183\) 31458.5 0.0694400
\(184\) −89011.3 154172.i −0.193821 0.335708i
\(185\) 107891. 186873.i 0.231769 0.401436i
\(186\) 52106.8 90251.6i 0.110436 0.191281i
\(187\) −286603. 496410.i −0.599344 1.03809i
\(188\) −107548. −0.221926
\(189\) 0 0
\(190\) −468722. −0.941957
\(191\) 291366. + 504661.i 0.577904 + 1.00096i 0.995719 + 0.0924273i \(0.0294626\pi\)
−0.417815 + 0.908532i \(0.637204\pi\)
\(192\) −237566. + 411477.i −0.465085 + 0.805550i
\(193\) 200452. 347193.i 0.387362 0.670931i −0.604731 0.796429i \(-0.706720\pi\)
0.992094 + 0.125498i \(0.0400529\pi\)
\(194\) 364167. + 630756.i 0.694699 + 1.20325i
\(195\) −158502. −0.298503
\(196\) 0 0
\(197\) 671589. 1.23293 0.616464 0.787383i \(-0.288564\pi\)
0.616464 + 0.787383i \(0.288564\pi\)
\(198\) 154949. + 268380.i 0.280884 + 0.486505i
\(199\) −227511. + 394060.i −0.407258 + 0.705391i −0.994581 0.103961i \(-0.966848\pi\)
0.587324 + 0.809352i \(0.300182\pi\)
\(200\) −245758. + 425666.i −0.434443 + 0.752478i
\(201\) 71353.9 + 123589.i 0.124574 + 0.215769i
\(202\) −778878. −1.34305
\(203\) 0 0
\(204\) −647409. −1.08919
\(205\) 59603.8 + 103237.i 0.0990580 + 0.171573i
\(206\) −93337.6 + 161665.i −0.153246 + 0.265430i
\(207\) 38693.8 67019.6i 0.0627647 0.108712i
\(208\) 14891.0 + 25791.9i 0.0238652 + 0.0413357i
\(209\) −963860. −1.52633
\(210\) 0 0
\(211\) −1.19545e6 −1.84852 −0.924260 0.381764i \(-0.875317\pi\)
−0.924260 + 0.381764i \(0.875317\pi\)
\(212\) −471249. 816228.i −0.720130 1.24730i
\(213\) 261601. 453105.i 0.395084 0.684306i
\(214\) 31960.7 55357.6i 0.0477070 0.0826310i
\(215\) 217257. + 376300.i 0.320537 + 0.555186i
\(216\) 135837. 0.198099
\(217\) 0 0
\(218\) −1.03428e6 −1.47400
\(219\) −175998. 304837.i −0.247969 0.429495i
\(220\) 240490. 416541.i 0.334997 0.580231i
\(221\) 548788. 950529.i 0.755830 1.30914i
\(222\) −403919. 699608.i −0.550062 0.952736i
\(223\) −296529. −0.399305 −0.199653 0.979867i \(-0.563981\pi\)
−0.199653 + 0.979867i \(0.563981\pi\)
\(224\) 0 0
\(225\) −213665. −0.281370
\(226\) 514172. + 890573.i 0.669634 + 1.15984i
\(227\) 109073. 188920.i 0.140492 0.243340i −0.787190 0.616711i \(-0.788465\pi\)
0.927682 + 0.373371i \(0.121798\pi\)
\(228\) −544318. + 942787.i −0.693451 + 1.20109i
\(229\) −614602. 1.06452e6i −0.774471 1.34142i −0.935091 0.354407i \(-0.884683\pi\)
0.160620 0.987016i \(-0.448651\pi\)
\(230\) −193607. −0.241324
\(231\) 0 0
\(232\) 1.31090e6 1.59901
\(233\) 31472.1 + 54511.3i 0.0379784 + 0.0657805i 0.884390 0.466749i \(-0.154575\pi\)
−0.846411 + 0.532530i \(0.821242\pi\)
\(234\) −296698. + 513895.i −0.354221 + 0.613529i
\(235\) −22695.8 + 39310.4i −0.0268088 + 0.0464341i
\(236\) 194424. + 336753.i 0.227233 + 0.393578i
\(237\) −87846.2 −0.101590
\(238\) 0 0
\(239\) 219330. 0.248372 0.124186 0.992259i \(-0.460368\pi\)
0.124186 + 0.992259i \(0.460368\pi\)
\(240\) −3707.15 6420.98i −0.00415444 0.00719570i
\(241\) 216932. 375737.i 0.240592 0.416717i −0.720291 0.693672i \(-0.755992\pi\)
0.960883 + 0.276955i \(0.0893252\pi\)
\(242\) 57822.6 100152.i 0.0634686 0.109931i
\(243\) 29524.5 + 51137.9i 0.0320750 + 0.0555556i
\(244\) −182791. −0.196553
\(245\) 0 0
\(246\) 446286. 0.470193
\(247\) −922803. 1.59834e6i −0.962424 1.66697i
\(248\) −117501. + 203517.i −0.121314 + 0.210122i
\(249\) 316780. 548680.i 0.323787 0.560816i
\(250\) 583904. + 1.01135e6i 0.590870 + 1.02342i
\(251\) 1.71109e6 1.71431 0.857155 0.515059i \(-0.172230\pi\)
0.857155 + 0.515059i \(0.172230\pi\)
\(252\) 0 0
\(253\) −398125. −0.391037
\(254\) 377461. + 653782.i 0.367103 + 0.635841i
\(255\) −136623. + 236638.i −0.131575 + 0.227894i
\(256\) 554822. 960979.i 0.529119 0.916461i
\(257\) 492029. + 852219.i 0.464684 + 0.804856i 0.999187 0.0403103i \(-0.0128346\pi\)
−0.534503 + 0.845166i \(0.679501\pi\)
\(258\) 1.62672e6 1.52147
\(259\) 0 0
\(260\) 920984. 0.844926
\(261\) 284929. + 493512.i 0.258902 + 0.448432i
\(262\) 807084. 1.39791e6i 0.726383 1.25813i
\(263\) −273548. + 473799.i −0.243862 + 0.422381i −0.961811 0.273714i \(-0.911748\pi\)
0.717949 + 0.696096i \(0.245081\pi\)
\(264\) −349410. 605196.i −0.308550 0.534424i
\(265\) −397791. −0.347969
\(266\) 0 0
\(267\) 1.29876e6 1.11493
\(268\) −414605. 718118.i −0.352613 0.610743i
\(269\) −320556. + 555219.i −0.270099 + 0.467825i −0.968887 0.247504i \(-0.920390\pi\)
0.698788 + 0.715329i \(0.253723\pi\)
\(270\) 73863.9 127936.i 0.0616627 0.106803i
\(271\) −274006. 474593.i −0.226640 0.392552i 0.730170 0.683265i \(-0.239441\pi\)
−0.956810 + 0.290713i \(0.906107\pi\)
\(272\) 51341.8 0.0420774
\(273\) 0 0
\(274\) −287651. −0.231467
\(275\) 549607. + 951948.i 0.438249 + 0.759069i
\(276\) −224832. + 389421.i −0.177658 + 0.307713i
\(277\) −837070. + 1.44985e6i −0.655485 + 1.13533i 0.326287 + 0.945271i \(0.394202\pi\)
−0.981772 + 0.190062i \(0.939131\pi\)
\(278\) −698847. 1.21044e6i −0.542338 0.939358i
\(279\) −102157. −0.0785698
\(280\) 0 0
\(281\) 1.81078e6 1.36804 0.684021 0.729462i \(-0.260230\pi\)
0.684021 + 0.729462i \(0.260230\pi\)
\(282\) 84968.1 + 147169.i 0.0636258 + 0.110203i
\(283\) 1.25657e6 2.17645e6i 0.932657 1.61541i 0.153898 0.988087i \(-0.450817\pi\)
0.778759 0.627323i \(-0.215849\pi\)
\(284\) −1.52004e6 + 2.63279e6i −1.11830 + 1.93696i
\(285\) 229735. + 397913.i 0.167539 + 0.290185i
\(286\) 3.05276e6 2.20687
\(287\) 0 0
\(288\) 455217. 0.323398
\(289\) −236142. 409009.i −0.166314 0.288064i
\(290\) 712831. 1.23466e6i 0.497728 0.862090i
\(291\) 356979. 618306.i 0.247121 0.428027i
\(292\) 1.02265e6 + 1.77127e6i 0.701888 + 1.21571i
\(293\) −107228. −0.0729691 −0.0364845 0.999334i \(-0.511616\pi\)
−0.0364845 + 0.999334i \(0.511616\pi\)
\(294\) 0 0
\(295\) 164117. 0.109799
\(296\) 910836. + 1.57761e6i 0.604242 + 1.04658i
\(297\) 151891. 263082.i 0.0999171 0.173061i
\(298\) 1.66575e6 2.88517e6i 1.08660 1.88205i
\(299\) −381166. 660199.i −0.246568 0.427068i
\(300\) 1.24151e6 0.796431
\(301\) 0 0
\(302\) −1.88330e6 −1.18824
\(303\) 381752. + 661214.i 0.238877 + 0.413747i
\(304\) 43166.3 74766.2i 0.0267893 0.0464004i
\(305\) −38574.4 + 66812.8i −0.0237437 + 0.0411254i
\(306\) 511485. + 885917.i 0.312269 + 0.540866i
\(307\) −1.49622e6 −0.906042 −0.453021 0.891500i \(-0.649654\pi\)
−0.453021 + 0.891500i \(0.649654\pi\)
\(308\) 0 0
\(309\) 182990. 0.109027
\(310\) 127787. + 221333.i 0.0755234 + 0.130810i
\(311\) 430601. 745823.i 0.252449 0.437255i −0.711750 0.702433i \(-0.752097\pi\)
0.964200 + 0.265178i \(0.0854306\pi\)
\(312\) 669052. 1.15883e6i 0.389111 0.673960i
\(313\) −251969. 436422.i −0.145374 0.251794i 0.784139 0.620586i \(-0.213105\pi\)
−0.929512 + 0.368791i \(0.879772\pi\)
\(314\) −709452. −0.406068
\(315\) 0 0
\(316\) 510435. 0.287556
\(317\) 240004. + 415700.i 0.134144 + 0.232344i 0.925270 0.379309i \(-0.123838\pi\)
−0.791126 + 0.611653i \(0.790505\pi\)
\(318\) −744619. + 1.28972e6i −0.412921 + 0.715199i
\(319\) 1.46584e6 2.53890e6i 0.806508 1.39691i
\(320\) −582608. 1.00911e6i −0.318055 0.550887i
\(321\) −62659.7 −0.0339411
\(322\) 0 0
\(323\) −3.18168e6 −1.69688
\(324\) −171554. 297140.i −0.0907899 0.157253i
\(325\) −1.05239e6 + 1.82280e6i −0.552674 + 0.957259i
\(326\) 848948. 1.47042e6i 0.442423 0.766298i
\(327\) 506931. + 878031.i 0.262168 + 0.454088i
\(328\) −1.00637e6 −0.516505
\(329\) 0 0
\(330\) −759995. −0.384172
\(331\) 1.09961e6 + 1.90458e6i 0.551656 + 0.955497i 0.998155 + 0.0607125i \(0.0193373\pi\)
−0.446499 + 0.894784i \(0.647329\pi\)
\(332\) −1.84067e6 + 3.18813e6i −0.916496 + 1.58742i
\(333\) −395946. + 685799.i −0.195671 + 0.338911i
\(334\) −593392. 1.02778e6i −0.291055 0.504122i
\(335\) −349977. −0.170383
\(336\) 0 0
\(337\) −1.35725e6 −0.651008 −0.325504 0.945541i \(-0.605534\pi\)
−0.325504 + 0.945541i \(0.605534\pi\)
\(338\) 1.21826e6 + 2.11008e6i 0.580026 + 1.00463i
\(339\) 504023. 872993.i 0.238205 0.412583i
\(340\) 793854. 1.37499e6i 0.372429 0.645065i
\(341\) 262775. + 455140.i 0.122377 + 0.211963i
\(342\) 1.72015e6 0.795245
\(343\) 0 0
\(344\) −3.66825e6 −1.67133
\(345\) 94892.6 + 164359.i 0.0429225 + 0.0743439i
\(346\) 2.33142e6 4.03814e6i 1.04696 1.81339i
\(347\) −1.89970e6 + 3.29038e6i −0.846959 + 1.46698i 0.0369507 + 0.999317i \(0.488236\pi\)
−0.883909 + 0.467658i \(0.845098\pi\)
\(348\) −1.65560e6 2.86758e6i −0.732835 1.26931i
\(349\) 1.31753e6 0.579024 0.289512 0.957174i \(-0.406507\pi\)
0.289512 + 0.957174i \(0.406507\pi\)
\(350\) 0 0
\(351\) 581682. 0.252010
\(352\) −1.17095e6 2.02814e6i −0.503710 0.872451i
\(353\) −1.71253e6 + 2.96618e6i −0.731477 + 1.26695i 0.224775 + 0.974411i \(0.427835\pi\)
−0.956252 + 0.292544i \(0.905498\pi\)
\(354\) 307209. 532102.i 0.130294 0.225677i
\(355\) 641549. + 1.11120e6i 0.270184 + 0.467972i
\(356\) −7.54649e6 −3.15588
\(357\) 0 0
\(358\) 1.21733e6 0.501997
\(359\) −735419. 1.27378e6i −0.301161 0.521626i 0.675238 0.737600i \(-0.264041\pi\)
−0.976399 + 0.215974i \(0.930707\pi\)
\(360\) −166563. + 288495.i −0.0677364 + 0.117323i
\(361\) −1.43700e6 + 2.48895e6i −0.580347 + 1.00519i
\(362\) 3.39733e6 + 5.88435e6i 1.36259 + 2.36008i
\(363\) −113362. −0.0451547
\(364\) 0 0
\(365\) 863235. 0.339154
\(366\) 144414. + 250132.i 0.0563515 + 0.0976037i
\(367\) −2.49039e6 + 4.31349e6i −0.965168 + 1.67172i −0.256006 + 0.966675i \(0.582407\pi\)
−0.709163 + 0.705045i \(0.750927\pi\)
\(368\) 17830.0 30882.4i 0.00686326 0.0118875i
\(369\) −218738. 378866.i −0.0836295 0.144850i
\(370\) 1.98114e6 0.752335
\(371\) 0 0
\(372\) 593586. 0.222396
\(373\) −1.98024e6 3.42987e6i −0.736962 1.27646i −0.953857 0.300261i \(-0.902926\pi\)
0.216895 0.976195i \(-0.430407\pi\)
\(374\) 2.63136e6 4.55766e6i 0.972751 1.68485i
\(375\) 572379. 991389.i 0.210187 0.364054i
\(376\) −191603. 331866.i −0.0698927 0.121058i
\(377\) 5.61359e6 2.03417
\(378\) 0 0
\(379\) −1.75155e6 −0.626359 −0.313179 0.949694i \(-0.601394\pi\)
−0.313179 + 0.949694i \(0.601394\pi\)
\(380\) −1.33489e6 2.31209e6i −0.474226 0.821384i
\(381\) 370010. 640876.i 0.130587 0.226184i
\(382\) −2.67510e6 + 4.63341e6i −0.937954 + 1.62458i
\(383\) 1.56917e6 + 2.71788e6i 0.546604 + 0.946745i 0.998504 + 0.0546771i \(0.0174129\pi\)
−0.451900 + 0.892068i \(0.649254\pi\)
\(384\) −2.74375e6 −0.949549
\(385\) 0 0
\(386\) 3.68079e6 1.25740
\(387\) −797306. 1.38097e6i −0.270612 0.468714i
\(388\) −2.07425e6 + 3.59270e6i −0.699489 + 1.21155i
\(389\) 526262. 911512.i 0.176331 0.305414i −0.764290 0.644872i \(-0.776911\pi\)
0.940621 + 0.339459i \(0.110244\pi\)
\(390\) −727622. 1.26028e6i −0.242239 0.419570i
\(391\) −1.31420e6 −0.434731
\(392\) 0 0
\(393\) −1.58231e6 −0.516784
\(394\) 3.08301e6 + 5.33992e6i 1.00054 + 1.73298i
\(395\) 107717. 186571.i 0.0347370 0.0601662i
\(396\) −882568. + 1.52865e6i −0.282820 + 0.489859i
\(397\) 227362. + 393803.i 0.0724005 + 0.125401i 0.899953 0.435987i \(-0.143601\pi\)
−0.827552 + 0.561389i \(0.810267\pi\)
\(398\) −4.17766e6 −1.32198
\(399\) 0 0
\(400\) −98456.3 −0.0307676
\(401\) 1.44216e6 + 2.49789e6i 0.447870 + 0.775733i 0.998247 0.0591831i \(-0.0188496\pi\)
−0.550378 + 0.834916i \(0.685516\pi\)
\(402\) −655116. + 1.13469e6i −0.202187 + 0.350198i
\(403\) −503164. + 871505.i −0.154329 + 0.267305i
\(404\) −2.21819e6 3.84202e6i −0.676153 1.17113i
\(405\) −144812. −0.0438699
\(406\) 0 0
\(407\) 4.07394e6 1.21907
\(408\) −1.15340e6 1.99774e6i −0.343027 0.594140i
\(409\) −112957. + 195647.i −0.0333891 + 0.0578317i −0.882237 0.470805i \(-0.843963\pi\)
0.848848 + 0.528637i \(0.177297\pi\)
\(410\) −547236. + 947841.i −0.160774 + 0.278468i
\(411\) 140986. + 244196.i 0.0411692 + 0.0713072i
\(412\) −1.06328e6 −0.308605
\(413\) 0 0
\(414\) 710513. 0.203738
\(415\) 776873. + 1.34558e6i 0.221426 + 0.383522i
\(416\) 2.24213e6 3.88349e6i 0.635226 1.10024i
\(417\) −685053. + 1.18655e6i −0.192923 + 0.334152i
\(418\) −4.42471e6 7.66382e6i −1.23864 2.14538i
\(419\) −4.31027e6 −1.19941 −0.599707 0.800220i \(-0.704716\pi\)
−0.599707 + 0.800220i \(0.704716\pi\)
\(420\) 0 0
\(421\) 1.25088e6 0.343962 0.171981 0.985100i \(-0.444983\pi\)
0.171981 + 0.985100i \(0.444983\pi\)
\(422\) −5.48784e6 9.50521e6i −1.50010 2.59825i
\(423\) 83290.9 144264.i 0.0226332 0.0392019i
\(424\) 1.67911e6 2.90831e6i 0.453592 0.785644i
\(425\) 1.81424e6 + 3.14236e6i 0.487218 + 0.843887i
\(426\) 4.80363e6 1.28246
\(427\) 0 0
\(428\) 364087. 0.0960719
\(429\) −1.49625e6 2.59158e6i −0.392519 0.679863i
\(430\) −1.99469e6 + 3.45490e6i −0.520240 + 0.901081i
\(431\) 2.20397e6 3.81738e6i 0.571494 0.989857i −0.424919 0.905231i \(-0.639697\pi\)
0.996413 0.0846252i \(-0.0269693\pi\)
\(432\) 13604.8 + 23564.2i 0.00350738 + 0.00607495i
\(433\) 1.60951e6 0.412549 0.206274 0.978494i \(-0.433866\pi\)
0.206274 + 0.978494i \(0.433866\pi\)
\(434\) 0 0
\(435\) −1.39752e6 −0.354108
\(436\) −2.94555e6 5.10184e6i −0.742079 1.28532i
\(437\) −1.10493e6 + 1.91380e6i −0.276779 + 0.479395i
\(438\) 1.61588e6 2.79878e6i 0.402460 0.697082i
\(439\) −2.21226e6 3.83175e6i −0.547867 0.948933i −0.998420 0.0561836i \(-0.982107\pi\)
0.450554 0.892749i \(-0.351227\pi\)
\(440\) 1.71379e6 0.422012
\(441\) 0 0
\(442\) 1.00771e7 2.45347
\(443\) 1.80719e6 + 3.13015e6i 0.437517 + 0.757801i 0.997497 0.0707044i \(-0.0225247\pi\)
−0.559980 + 0.828506i \(0.689191\pi\)
\(444\) 2.30066e6 3.98487e6i 0.553855 0.959305i
\(445\) −1.59254e6 + 2.75835e6i −0.381232 + 0.660313i
\(446\) −1.36125e6 2.35776e6i −0.324042 0.561257i
\(447\) −3.26574e6 −0.773060
\(448\) 0 0
\(449\) −467024. −0.109326 −0.0546630 0.998505i \(-0.517408\pi\)
−0.0546630 + 0.998505i \(0.517408\pi\)
\(450\) −980855. 1.69889e6i −0.228336 0.395489i
\(451\) −1.12531e6 + 1.94910e6i −0.260515 + 0.451225i
\(452\) −2.92865e6 + 5.07257e6i −0.674251 + 1.16784i
\(453\) 923065. + 1.59880e6i 0.211342 + 0.366056i
\(454\) 2.00285e6 0.456046
\(455\) 0 0
\(456\) −3.87893e6 −0.873575
\(457\) 300626. + 520699.i 0.0673342 + 0.116626i 0.897727 0.440552i \(-0.145217\pi\)
−0.830393 + 0.557178i \(0.811884\pi\)
\(458\) 5.64280e6 9.77362e6i 1.25699 2.17717i
\(459\) 501388. 868430.i 0.111082 0.192399i
\(460\) −551379. 955016.i −0.121494 0.210434i
\(461\) −2.87193e6 −0.629392 −0.314696 0.949192i \(-0.601903\pi\)
−0.314696 + 0.949192i \(0.601903\pi\)
\(462\) 0 0
\(463\) −2.91502e6 −0.631959 −0.315979 0.948766i \(-0.602333\pi\)
−0.315979 + 0.948766i \(0.602333\pi\)
\(464\) 131294. + 227409.i 0.0283107 + 0.0490357i
\(465\) 125264. 216964.i 0.0268655 0.0465324i
\(466\) −288953. + 500481.i −0.0616399 + 0.106763i
\(467\) −3.59688e6 6.22998e6i −0.763192 1.32189i −0.941197 0.337857i \(-0.890298\pi\)
0.178006 0.984029i \(-0.443035\pi\)
\(468\) −3.37989e6 −0.713327
\(469\) 0 0
\(470\) −416751. −0.0870227
\(471\) 347724. + 602275.i 0.0722241 + 0.125096i
\(472\) −692755. + 1.19989e6i −0.143128 + 0.247905i
\(473\) −4.10179e6 + 7.10451e6i −0.842986 + 1.46009i
\(474\) −403268. 698481.i −0.0824419 0.142794i
\(475\) 6.10140e6 1.24078
\(476\) 0 0
\(477\) 1.45984e6 0.293772
\(478\) 1.00686e6 + 1.74393e6i 0.201557 + 0.349108i
\(479\) −1.39824e6 + 2.42183e6i −0.278448 + 0.482286i −0.970999 0.239083i \(-0.923153\pi\)
0.692551 + 0.721369i \(0.256487\pi\)
\(480\) −558187. + 966808.i −0.110580 + 0.191530i
\(481\) 3.90040e6 + 6.75569e6i 0.768682 + 1.33140i
\(482\) 3.98340e6 0.780974
\(483\) 0 0
\(484\) 658698. 0.127812
\(485\) 875456. + 1.51633e6i 0.168997 + 0.292712i
\(486\) −271071. + 469509.i −0.0520586 + 0.0901682i
\(487\) 1.46624e6 2.53960e6i 0.280144 0.485224i −0.691276 0.722591i \(-0.742951\pi\)
0.971420 + 0.237367i \(0.0762843\pi\)
\(488\) −325652. 564046.i −0.0619020 0.107217i
\(489\) −1.66438e6 −0.314761
\(490\) 0 0
\(491\) −3.06121e6 −0.573046 −0.286523 0.958073i \(-0.592499\pi\)
−0.286523 + 0.958073i \(0.592499\pi\)
\(492\) 1.27099e6 + 2.20142e6i 0.236717 + 0.410006i
\(493\) 4.83870e6 8.38087e6i 0.896626 1.55300i
\(494\) 8.47246e6 1.46747e7i 1.56204 2.70553i
\(495\) 372497. + 645183.i 0.0683297 + 0.118350i
\(496\) −47073.4 −0.00859154
\(497\) 0 0
\(498\) 5.81687e6 1.05103
\(499\) 3.27577e6 + 5.67380e6i 0.588928 + 1.02005i 0.994373 + 0.105934i \(0.0337831\pi\)
−0.405445 + 0.914119i \(0.632884\pi\)
\(500\) −3.32583e6 + 5.76052e6i −0.594943 + 1.03047i
\(501\) −581679. + 1.00750e6i −0.103535 + 0.179329i
\(502\) 7.85497e6 + 1.36052e7i 1.39119 + 2.40960i
\(503\) 1.58524e6 0.279367 0.139684 0.990196i \(-0.455391\pi\)
0.139684 + 0.990196i \(0.455391\pi\)
\(504\) 0 0
\(505\) −1.87242e6 −0.326719
\(506\) −1.82764e6 3.16556e6i −0.317332 0.549635i
\(507\) 1.19421e6 2.06843e6i 0.206329 0.357373i
\(508\) −2.14996e6 + 3.72385e6i −0.369634 + 0.640225i
\(509\) 3.38991e6 + 5.87149e6i 0.579953 + 1.00451i 0.995484 + 0.0949297i \(0.0302626\pi\)
−0.415530 + 0.909579i \(0.636404\pi\)
\(510\) −2.50873e6 −0.427099
\(511\) 0 0
\(512\) 432315. 0.0728829
\(513\) −843098. 1.46029e6i −0.141444 0.244988i
\(514\) −4.51743e6 + 7.82441e6i −0.754195 + 1.30630i
\(515\) −224383. + 388643.i −0.0372796 + 0.0645702i
\(516\) 4.63279e6 + 8.02422e6i 0.765981 + 1.32672i
\(517\) −856990. −0.141010
\(518\) 0 0
\(519\) −4.57081e6 −0.744859
\(520\) 1.64078e6 + 2.84192e6i 0.266099 + 0.460897i
\(521\) −5.06918e6 + 8.78008e6i −0.818170 + 1.41711i 0.0888599 + 0.996044i \(0.471678\pi\)
−0.907029 + 0.421067i \(0.861656\pi\)
\(522\) −2.61600e6 + 4.53105e6i −0.420205 + 0.727817i
\(523\) 49998.6 + 86600.2i 0.00799289 + 0.0138441i 0.869994 0.493062i \(-0.164122\pi\)
−0.862001 + 0.506906i \(0.830789\pi\)
\(524\) 9.19408e6 1.46278
\(525\) 0 0
\(526\) −5.02301e6 −0.791589
\(527\) 867416. + 1.50241e6i 0.136051 + 0.235647i
\(528\) 69990.7 121227.i 0.0109259 0.0189241i
\(529\) 2.76178e6 4.78354e6i 0.429091 0.743207i
\(530\) −1.82610e6 3.16291e6i −0.282381 0.489099i
\(531\) −602290. −0.0926978
\(532\) 0 0
\(533\) −4.30952e6 −0.657068
\(534\) 5.96209e6 + 1.03266e7i 0.904785 + 1.56713i
\(535\) 76833.3 133079.i 0.0116055 0.0201014i
\(536\) 1.47729e6 2.55873e6i 0.222102 0.384692i
\(537\) −596651. 1.03343e6i −0.0892862 0.154648i
\(538\) −5.88620e6 −0.876756
\(539\) 0 0
\(540\) 841436. 0.124176
\(541\) 59871.4 + 103700.i 0.00879481 + 0.0152331i 0.870389 0.492364i \(-0.163867\pi\)
−0.861595 + 0.507597i \(0.830534\pi\)
\(542\) 2.51571e6 4.35734e6i 0.367843 0.637123i
\(543\) 3.33027e6 5.76820e6i 0.484708 0.839538i
\(544\) −3.86527e6 6.69485e6i −0.559993 0.969937i
\(545\) −2.48640e6 −0.358574
\(546\) 0 0
\(547\) 236568. 0.0338056 0.0169028 0.999857i \(-0.494619\pi\)
0.0169028 + 0.999857i \(0.494619\pi\)
\(548\) −819209. 1.41891e6i −0.116531 0.201838i
\(549\) 141563. 245194.i 0.0200456 0.0347200i
\(550\) −5.04607e6 + 8.74005e6i −0.711290 + 1.23199i
\(551\) −8.13641e6 1.40927e7i −1.14170 1.97749i
\(552\) −1.60220e6 −0.223805
\(553\) 0 0
\(554\) −1.53707e7 −2.12774
\(555\) −971018. 1.68185e6i −0.133812 0.231769i
\(556\) 3.98054e6 6.89449e6i 0.546078 0.945834i
\(557\) 2.41833e6 4.18867e6i 0.330277 0.572056i −0.652289 0.757970i \(-0.726191\pi\)
0.982566 + 0.185914i \(0.0595247\pi\)
\(558\) −468961. 812264.i −0.0637604 0.110436i
\(559\) −1.57083e7 −2.12617
\(560\) 0 0
\(561\) −5.15885e6 −0.692063
\(562\) 8.31258e6 + 1.43978e7i 1.11018 + 1.92290i
\(563\) −2.74147e6 + 4.74837e6i −0.364513 + 0.631355i −0.988698 0.149922i \(-0.952098\pi\)
0.624185 + 0.781277i \(0.285431\pi\)
\(564\) −483966. + 838254.i −0.0640644 + 0.110963i
\(565\) 1.23607e6 + 2.14093e6i 0.162900 + 0.282151i
\(566\) 2.30738e7 3.02746
\(567\) 0 0
\(568\) −1.08322e7 −1.40878
\(569\) 3.48830e6 + 6.04191e6i 0.451682 + 0.782336i 0.998491 0.0549213i \(-0.0174908\pi\)
−0.546809 + 0.837258i \(0.684157\pi\)
\(570\) −2.10925e6 + 3.65333e6i −0.271920 + 0.470979i
\(571\) 5.88573e6 1.01944e7i 0.755458 1.30849i −0.189689 0.981844i \(-0.560748\pi\)
0.945146 0.326647i \(-0.105919\pi\)
\(572\) 8.69404e6 + 1.50585e7i 1.11104 + 1.92439i
\(573\) 5.24459e6 0.667306
\(574\) 0 0
\(575\) 2.52020e6 0.317882
\(576\) 2.13810e6 + 3.70329e6i 0.268517 + 0.465085i
\(577\) 3.38646e6 5.86552e6i 0.423454 0.733444i −0.572820 0.819681i \(-0.694151\pi\)
0.996275 + 0.0862365i \(0.0274841\pi\)
\(578\) 2.16807e6 3.75521e6i 0.269932 0.467535i
\(579\) −1.80407e6 3.12474e6i −0.223644 0.387362i
\(580\) 8.12037e6 1.00232
\(581\) 0 0
\(582\) 6.55501e6 0.802169
\(583\) −3.75512e6 6.50407e6i −0.457565 0.792526i
\(584\) −3.64380e6 + 6.31124e6i −0.442102 + 0.765743i
\(585\) −713259. + 1.23540e6i −0.0861703 + 0.149251i
\(586\) −492242. 852588.i −0.0592154 0.102564i
\(587\) 1.05020e7 1.25799 0.628996 0.777408i \(-0.283466\pi\)
0.628996 + 0.777408i \(0.283466\pi\)
\(588\) 0 0
\(589\) 2.91717e6 0.346476
\(590\) 753400. + 1.30493e6i 0.0891036 + 0.154332i
\(591\) 3.02215e6 5.23452e6i 0.355916 0.616464i
\(592\) −182451. + 316014.i −0.0213964 + 0.0370597i
\(593\) −3.79537e6 6.57378e6i −0.443218 0.767676i 0.554708 0.832045i \(-0.312830\pi\)
−0.997926 + 0.0643687i \(0.979497\pi\)
\(594\) 2.78909e6 0.324336
\(595\) 0 0
\(596\) 1.89758e7 2.18818
\(597\) 2.04760e6 + 3.54654e6i 0.235130 + 0.407258i
\(598\) 3.49957e6 6.06144e6i 0.400186 0.693143i
\(599\) 6.50992e6 1.12755e7i 0.741325 1.28401i −0.210567 0.977580i \(-0.567531\pi\)
0.951892 0.306434i \(-0.0991358\pi\)
\(600\) 2.21183e6 + 3.83099e6i 0.250826 + 0.434443i
\(601\) −1.41821e7 −1.60160 −0.800801 0.598931i \(-0.795592\pi\)
−0.800801 + 0.598931i \(0.795592\pi\)
\(602\) 0 0
\(603\) 1.28437e6 0.143846
\(604\) −5.36352e6 9.28988e6i −0.598215 1.03614i
\(605\) 139005. 240764.i 0.0154398 0.0267426i
\(606\) −3.50495e6 + 6.07075e6i −0.387704 + 0.671523i
\(607\) 6.03862e6 + 1.04592e7i 0.665221 + 1.15220i 0.979225 + 0.202775i \(0.0649961\pi\)
−0.314004 + 0.949422i \(0.601671\pi\)
\(608\) −1.29991e7 −1.42612
\(609\) 0 0
\(610\) −708320. −0.0770735
\(611\) −820485. 1.42112e6i −0.0889135 0.154003i
\(612\) −2.91334e6 + 5.04606e6i −0.314422 + 0.544595i
\(613\) 1.36265e6 2.36018e6i 0.146465 0.253684i −0.783454 0.621450i \(-0.786544\pi\)
0.929918 + 0.367766i \(0.119877\pi\)
\(614\) −6.86855e6 1.18967e7i −0.735266 1.27352i
\(615\) 1.07287e6 0.114382
\(616\) 0 0
\(617\) 8.47094e6 0.895816 0.447908 0.894080i \(-0.352169\pi\)
0.447908 + 0.894080i \(0.352169\pi\)
\(618\) 840038. + 1.45499e6i 0.0884765 + 0.153246i
\(619\) 8.69174e6 1.50545e7i 0.911759 1.57921i 0.100180 0.994969i \(-0.468058\pi\)
0.811578 0.584243i \(-0.198609\pi\)
\(620\) −727855. + 1.26068e6i −0.0760441 + 0.131712i
\(621\) −348244. 603176.i −0.0362372 0.0627647i
\(622\) 7.90690e6 0.819464
\(623\) 0 0
\(624\) 268037. 0.0275571
\(625\) −2.71793e6 4.70759e6i −0.278316 0.482058i
\(626\) 2.31338e6 4.00689e6i 0.235945 0.408669i
\(627\) −4.33737e6 + 7.51255e6i −0.440613 + 0.763165i
\(628\) −2.02047e6 3.49955e6i −0.204434 0.354090i
\(629\) 1.34480e7 1.35529
\(630\) 0 0
\(631\) −6.45149e6 −0.645040 −0.322520 0.946563i \(-0.604530\pi\)
−0.322520 + 0.946563i \(0.604530\pi\)
\(632\) 909368. + 1.57507e6i 0.0905622 + 0.156858i
\(633\) −5.37951e6 + 9.31759e6i −0.533622 + 0.924260i
\(634\) −2.20353e6 + 3.81663e6i −0.217719 + 0.377101i
\(635\) 907413. + 1.57169e6i 0.0893040 + 0.154679i
\(636\) −8.48249e6 −0.831535
\(637\) 0 0
\(638\) 2.69164e7 2.61797
\(639\) −2.35440e6 4.07795e6i −0.228102 0.395084i
\(640\) 3.36439e6 5.82730e6i 0.324681 0.562364i
\(641\) −8.88581e6 + 1.53907e7i −0.854185 + 1.47949i 0.0232142 + 0.999731i \(0.492610\pi\)
−0.877399 + 0.479761i \(0.840723\pi\)
\(642\) −287647. 498218.i −0.0275437 0.0477070i
\(643\) 9.34806e6 0.891649 0.445825 0.895120i \(-0.352910\pi\)
0.445825 + 0.895120i \(0.352910\pi\)
\(644\) 0 0
\(645\) 3.91063e6 0.370124
\(646\) −1.46059e7 2.52981e7i −1.37704 2.38510i
\(647\) 2.67193e6 4.62792e6i 0.250937 0.434635i −0.712847 0.701319i \(-0.752595\pi\)
0.963784 + 0.266684i \(0.0859280\pi\)
\(648\) 611265. 1.05874e6i 0.0571863 0.0990495i
\(649\) 1.54926e6 + 2.68340e6i 0.144382 + 0.250077i
\(650\) −1.93245e7 −1.79401
\(651\) 0 0
\(652\) 9.67098e6 0.890946
\(653\) 598506. + 1.03664e6i 0.0549270 + 0.0951363i 0.892182 0.451677i \(-0.149174\pi\)
−0.837255 + 0.546813i \(0.815841\pi\)
\(654\) −4.65425e6 + 8.06140e6i −0.425506 + 0.736998i
\(655\) 1.94022e6 3.36057e6i 0.176705 0.306062i
\(656\) −100794. 174580.i −0.00914481 0.0158393i
\(657\) −3.16796e6 −0.286330
\(658\) 0 0
\(659\) −1.17541e7 −1.05433 −0.527163 0.849764i \(-0.676744\pi\)
−0.527163 + 0.849764i \(0.676744\pi\)
\(660\) −2.16441e6 3.74887e6i −0.193410 0.334997i
\(661\) −9.00573e6 + 1.55984e7i −0.801706 + 1.38860i 0.116787 + 0.993157i \(0.462741\pi\)
−0.918493 + 0.395438i \(0.870593\pi\)
\(662\) −1.00958e7 + 1.74864e7i −0.895353 + 1.55080i
\(663\) −4.93910e6 8.55476e6i −0.436379 0.755830i
\(664\) −1.31170e7 −1.15456
\(665\) 0 0
\(666\) −7.27054e6 −0.635157
\(667\) −3.36076e6 5.82102e6i −0.292498 0.506622i
\(668\) 3.37987e6 5.85411e6i 0.293062 0.507598i
\(669\) −1.33438e6 + 2.31122e6i −0.115270 + 0.199653i
\(670\) −1.60661e6 2.78273e6i −0.138268 0.239488i
\(671\) −1.45656e6 −0.124888
\(672\) 0 0
\(673\) 1.40977e7 1.19981 0.599904 0.800072i \(-0.295206\pi\)
0.599904 + 0.800072i \(0.295206\pi\)
\(674\) −6.23063e6 1.07918e7i −0.528302 0.915046i
\(675\) −961494. + 1.66536e6i −0.0812245 + 0.140685i
\(676\) −6.93902e6 + 1.20187e7i −0.584025 + 1.01156i
\(677\) 3.82793e6 + 6.63018e6i 0.320991 + 0.555973i 0.980693 0.195555i \(-0.0626507\pi\)
−0.659702 + 0.751527i \(0.729317\pi\)
\(678\) 9.25510e6 0.773227
\(679\) 0 0
\(680\) 5.65718e6 0.469167
\(681\) −981657. 1.70028e6i −0.0811133 0.140492i
\(682\) −2.41260e6 + 4.17874e6i −0.198621 + 0.344021i
\(683\) 5.43378e6 9.41158e6i 0.445708 0.771988i −0.552394 0.833583i \(-0.686285\pi\)
0.998101 + 0.0615953i \(0.0196188\pi\)
\(684\) 4.89886e6 + 8.48508e6i 0.400364 + 0.693451i
\(685\) −691510. −0.0563083
\(686\) 0 0
\(687\) −1.10628e7 −0.894283
\(688\) −367396. 636348.i −0.0295912 0.0512535i
\(689\) 7.19034e6 1.24540e7i 0.577034 0.999452i
\(690\) −871231. + 1.50902e6i −0.0696643 + 0.120662i
\(691\) −7.30588e6 1.26542e7i −0.582073 1.00818i −0.995233 0.0975219i \(-0.968908\pi\)
0.413160 0.910658i \(-0.364425\pi\)
\(692\) 2.65589e7 2.10836
\(693\) 0 0
\(694\) −3.48832e7 −2.74927
\(695\) −1.68002e6 2.90989e6i −0.131933 0.228515i
\(696\) 5.89907e6 1.02175e7i 0.461594 0.799505i
\(697\) −3.71464e6 + 6.43395e6i −0.289624 + 0.501644i
\(698\) 6.04827e6 + 1.04759e7i 0.469886 + 0.813867i
\(699\) 566498. 0.0438536
\(700\) 0 0
\(701\) 1.90104e7 1.46115 0.730577 0.682830i \(-0.239251\pi\)
0.730577 + 0.682830i \(0.239251\pi\)
\(702\) 2.67028e6 + 4.62506e6i 0.204510 + 0.354221i
\(703\) 1.13066e7 1.95836e7i 0.862866 1.49453i
\(704\) 1.09996e7 1.90518e7i 0.836458 1.44879i
\(705\) 204263. + 353793.i 0.0154780 + 0.0268088i
\(706\) −3.14462e7 −2.37441
\(707\) 0 0
\(708\) 3.49964e6 0.262386
\(709\) 5.79644e6 + 1.00397e7i 0.433058 + 0.750078i 0.997135 0.0756440i \(-0.0241013\pi\)
−0.564077 + 0.825722i \(0.690768\pi\)
\(710\) −5.89021e6 + 1.02021e7i −0.438516 + 0.759531i
\(711\) −395308. + 684693.i −0.0293266 + 0.0507951i
\(712\) −1.34445e7 2.32865e7i −0.993904 1.72149i
\(713\) 1.20494e6 0.0887653
\(714\) 0 0
\(715\) 7.33881e6 0.536859
\(716\) 3.46687e6 + 6.00479e6i 0.252729 + 0.437739i
\(717\) 986984. 1.70951e6i 0.0716989 0.124186i
\(718\) 6.75205e6 1.16949e7i 0.488792 0.846613i
\(719\) −5.14304e6 8.90800e6i −0.371020 0.642626i 0.618703 0.785625i \(-0.287659\pi\)
−0.989723 + 0.142999i \(0.954325\pi\)
\(720\) −66728.8 −0.00479713
\(721\) 0 0
\(722\) −2.63868e7 −1.88384
\(723\) −1.95239e6 3.38163e6i −0.138906 0.240592i
\(724\) −1.93507e7 + 3.35164e7i −1.37199 + 2.37635i
\(725\) −9.27900e6 + 1.60717e7i −0.655626 + 1.13558i
\(726\) −520403. 901365.i −0.0366436 0.0634686i
\(727\) −1.00970e7 −0.708526 −0.354263 0.935146i \(-0.615268\pi\)
−0.354263 + 0.935146i \(0.615268\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 3.96278e6 + 6.86373e6i 0.275228 + 0.476709i
\(731\) −1.35399e7 + 2.34518e7i −0.937180 + 1.62324i
\(732\) −822560. + 1.42471e6i −0.0567400 + 0.0982766i
\(733\) 962010. + 1.66625e6i 0.0661332 + 0.114546i 0.897196 0.441632i \(-0.145600\pi\)
−0.831063 + 0.556178i \(0.812267\pi\)
\(734\) −4.57298e7 −3.13299
\(735\) 0 0
\(736\) −5.36932e6 −0.365363
\(737\) −3.30376e6 5.72228e6i −0.224047 0.388061i
\(738\) 2.00829e6 3.47846e6i 0.135733 0.235096i
\(739\) −2.10136e6 + 3.63967e6i −0.141543 + 0.245161i −0.928078 0.372386i \(-0.878540\pi\)
0.786535 + 0.617546i \(0.211873\pi\)
\(740\) 5.64215e6 + 9.77249e6i 0.378761 + 0.656034i
\(741\) −1.66104e7 −1.11131
\(742\) 0 0
\(743\) −1.99659e7 −1.32684 −0.663418 0.748249i \(-0.730895\pi\)
−0.663418 + 0.748249i \(0.730895\pi\)
\(744\) 1.05751e6 + 1.83165e6i 0.0700407 + 0.121314i
\(745\) 4.00445e6 6.93592e6i 0.264334 0.457839i
\(746\) 1.81810e7 3.14904e7i 1.19611 2.07172i
\(747\) −2.85102e6 4.93812e6i −0.186939 0.323787i
\(748\) 2.99757e7 1.95892
\(749\) 0 0
\(750\) 1.05103e7 0.682277
\(751\) 1.81988e6 + 3.15212e6i 0.117745 + 0.203940i 0.918874 0.394552i \(-0.129100\pi\)
−0.801129 + 0.598492i \(0.795767\pi\)
\(752\) 38380.1 66476.4i 0.00247492 0.00428670i
\(753\) 7.69992e6 1.33366e7i 0.494878 0.857155i
\(754\) 2.57698e7 + 4.46346e7i 1.65076 + 2.85919i
\(755\) −4.52745e6 −0.289059
\(756\) 0 0
\(757\) 1.73429e7 1.09997 0.549986 0.835174i \(-0.314633\pi\)
0.549986 + 0.835174i \(0.314633\pi\)
\(758\) −8.04067e6 1.39268e7i −0.508299 0.880399i
\(759\) −1.79156e6 + 3.10308e6i −0.112883 + 0.195519i
\(760\) 4.75635e6 8.23824e6i 0.298703 0.517369i
\(761\) −5.17841e6 8.96927e6i −0.324142 0.561430i 0.657196 0.753719i \(-0.271742\pi\)
−0.981338 + 0.192289i \(0.938409\pi\)
\(762\) 6.79430e6 0.423894
\(763\) 0 0
\(764\) −3.04740e7 −1.88884
\(765\) 1.22960e6 + 2.12974e6i 0.0759647 + 0.131575i
\(766\) −1.44069e7 + 2.49535e7i −0.887153 + 1.53659i
\(767\) −2.96653e6 + 5.13818e6i −0.182079 + 0.315371i
\(768\) −4.99339e6 8.64881e6i −0.305487 0.529119i
\(769\) 1.81548e7 1.10707 0.553534 0.832826i \(-0.313279\pi\)
0.553534 + 0.832826i \(0.313279\pi\)
\(770\) 0 0
\(771\) 8.85652e6 0.536571
\(772\) 1.04826e7 + 1.81565e7i 0.633034 + 1.09645i
\(773\) −8.17830e6 + 1.41652e7i −0.492282 + 0.852658i −0.999960 0.00888861i \(-0.997171\pi\)
0.507678 + 0.861547i \(0.330504\pi\)
\(774\) 7.32025e6 1.26790e7i 0.439211 0.760736i
\(775\) −1.66341e6 2.88112e6i −0.0994823 0.172308i
\(776\) −1.47815e7 −0.881181
\(777\) 0 0
\(778\) 9.66346e6 0.572379
\(779\) 6.24627e6 + 1.08189e7i 0.368788 + 0.638760i
\(780\) 4.14443e6 7.17836e6i 0.243909 0.422463i
\(781\) −1.21124e7 + 2.09793e7i −0.710562 + 1.23073i
\(782\) −6.03300e6 1.04495e7i −0.352790 0.611051i
\(783\) 5.12873e6 0.298955
\(784\) 0 0
\(785\) −1.70552e6 −0.0987829
\(786\) −7.26376e6 1.25812e7i −0.419378 0.726383i
\(787\) −2.22364e6 + 3.85146e6i −0.127976 + 0.221661i −0.922892 0.385058i \(-0.874181\pi\)
0.794916 + 0.606719i \(0.207515\pi\)
\(788\) −1.75604e7 + 3.04154e7i −1.00744 + 1.74493i
\(789\) 2.46193e6 + 4.26419e6i 0.140794 + 0.243862i
\(790\) 1.97795e6 0.112758
\(791\) 0 0
\(792\) −6.28938e6 −0.356283
\(793\) −1.39452e6 2.41537e6i −0.0787481 0.136396i
\(794\) −2.08746e6 + 3.61559e6i −0.117508 + 0.203530i
\(795\) −1.79006e6 + 3.10047e6i −0.100450 + 0.173984i
\(796\) −1.18977e7 2.06074e7i −0.665548 1.15276i
\(797\) 9.15303e6 0.510410 0.255205 0.966887i \(-0.417857\pi\)
0.255205 + 0.966887i \(0.417857\pi\)
\(798\) 0 0
\(799\) −2.82891e6 −0.156766
\(800\) 7.41229e6 + 1.28385e7i 0.409475 + 0.709232i
\(801\) 5.84440e6 1.01228e7i 0.321854 0.557467i
\(802\) −1.32408e7 + 2.29337e7i −0.726905 + 1.25904i
\(803\) 8.14889e6 + 1.41143e7i 0.445974 + 0.772450i
\(804\) −7.46290e6 −0.407162
\(805\) 0 0
\(806\) −9.23932e6 −0.500959
\(807\) 2.88500e6 + 4.99697e6i 0.155942 + 0.270099i
\(808\) 7.90365e6 1.36895e7i 0.425892 0.737666i
\(809\) −1.25962e7 + 2.18172e7i −0.676654 + 1.17200i 0.299328 + 0.954150i \(0.403237\pi\)
−0.975982 + 0.217849i \(0.930096\pi\)
\(810\) −664775. 1.15142e6i −0.0356010 0.0616627i
\(811\) 8.90585e6 0.475470 0.237735 0.971330i \(-0.423595\pi\)
0.237735 + 0.971330i \(0.423595\pi\)
\(812\) 0 0
\(813\) −4.93211e6 −0.261702
\(814\) 1.87019e7 + 3.23926e7i 0.989291 + 1.71350i
\(815\) 2.04087e6 3.53488e6i 0.107627 0.186415i
\(816\) 231038. 400170.i 0.0121467 0.0210387i
\(817\) 2.27678e7 + 3.94349e7i 1.19334 + 2.06693i
\(818\) −2.07417e6 −0.108383
\(819\) 0 0
\(820\) −6.23396e6 −0.323765
\(821\) −1.67745e7 2.90543e7i −0.868543 1.50436i −0.863485 0.504374i \(-0.831723\pi\)
−0.00505812 0.999987i \(-0.501610\pi\)
\(822\) −1.29443e6 + 2.24202e6i −0.0668188 + 0.115734i
\(823\) 7.30006e6 1.26441e7i 0.375688 0.650710i −0.614742 0.788728i \(-0.710740\pi\)
0.990430 + 0.138018i \(0.0440732\pi\)
\(824\) −1.89428e6 3.28100e6i −0.0971912 0.168340i
\(825\) 9.89293e6 0.506046
\(826\) 0 0
\(827\) 1.97530e7 1.00431 0.502156 0.864777i \(-0.332540\pi\)
0.502156 + 0.864777i \(0.332540\pi\)
\(828\) 2.02349e6 + 3.50479e6i 0.102571 + 0.177658i
\(829\) −2.03127e6 + 3.51827e6i −0.102655 + 0.177804i −0.912778 0.408456i \(-0.866067\pi\)
0.810122 + 0.586261i \(0.199401\pi\)
\(830\) −7.13264e6 + 1.23541e7i −0.359381 + 0.622467i
\(831\) 7.53363e6 + 1.30486e7i 0.378444 + 0.655485i
\(832\) 4.21241e7 2.10971
\(833\) 0 0
\(834\) −1.25793e7 −0.626239
\(835\) −1.42651e6 2.47079e6i −0.0708041 0.122636i
\(836\) 2.52025e7 4.36520e7i 1.24718 2.16017i
\(837\) −459704. + 796231.i −0.0226811 + 0.0392849i
\(838\) −1.97868e7 3.42717e7i −0.973341 1.68588i
\(839\) 1.60509e7 0.787217 0.393609 0.919278i \(-0.371227\pi\)
0.393609 + 0.919278i \(0.371227\pi\)
\(840\) 0 0
\(841\) 2.89842e7 1.41309
\(842\) 5.74231e6 + 9.94597e6i 0.279130 + 0.483467i
\(843\) 8.14850e6 1.41136e7i 0.394920 0.684021i
\(844\) 3.12579e7 5.41403e7i 1.51044 2.61616i
\(845\) 2.92868e6 + 5.07263e6i 0.141101 + 0.244394i
\(846\) 1.52943e6 0.0734687
\(847\) 0 0
\(848\) 672690. 0.0321237
\(849\) −1.13092e7 1.95881e7i −0.538470 0.932657i
\(850\) −1.66570e7 + 2.88508e7i −0.790768 + 1.36965i
\(851\) 4.67022e6 8.08905e6i 0.221061 0.382890i
\(852\) 1.36804e7 + 2.36951e7i 0.645654 + 1.11830i
\(853\) 1.23887e7 0.582979 0.291489 0.956574i \(-0.405849\pi\)
0.291489 + 0.956574i \(0.405849\pi\)
\(854\) 0 0
\(855\) 4.13523e6 0.193457
\(856\) 648642. + 1.12348e6i 0.0302566 + 0.0524060i
\(857\) 1.31760e7 2.28214e7i 0.612816 1.06143i −0.377948 0.925827i \(-0.623370\pi\)
0.990764 0.135601i \(-0.0432966\pi\)
\(858\) 1.37374e7 2.37939e7i 0.637070 1.10344i
\(859\) −6.06245e6 1.05005e7i −0.280327 0.485541i 0.691138 0.722723i \(-0.257110\pi\)
−0.971465 + 0.237182i \(0.923776\pi\)
\(860\) −2.27229e7 −1.04765
\(861\) 0 0
\(862\) 4.04702e7 1.85510
\(863\) −1.27976e6 2.21661e6i −0.0584927 0.101312i 0.835296 0.549800i \(-0.185296\pi\)
−0.893789 + 0.448488i \(0.851963\pi\)
\(864\) 2.04848e6 3.54806e6i 0.0933569 0.161699i
\(865\) 5.60472e6 9.70766e6i 0.254691 0.441138i
\(866\) 7.38866e6 + 1.27975e7i 0.334789 + 0.579871i
\(867\) −4.25055e6 −0.192042
\(868\) 0 0
\(869\) 4.06737e6 0.182711
\(870\) −6.41548e6 1.11119e7i −0.287363 0.497728i
\(871\) 6.32606e6 1.09571e7i 0.282545 0.489383i
\(872\) 1.04953e7 1.81784e7i 0.467417 0.809590i
\(873\) −3.21281e6 5.56475e6i −0.142676 0.247121i
\(874\) −2.02893e7 −0.898439
\(875\) 0 0
\(876\) 1.84076e7 0.810471
\(877\) −1.32910e7 2.30207e7i −0.583523 1.01069i −0.995058 0.0992977i \(-0.968340\pi\)
0.411535 0.911394i \(-0.364993\pi\)
\(878\) 2.03113e7 3.51801e7i 0.889203 1.54014i
\(879\) −482526. + 835759.i −0.0210644 + 0.0364845i
\(880\) 171645. + 297298.i 0.00747179 + 0.0129415i
\(881\) 8.32262e6 0.361260 0.180630 0.983551i \(-0.442186\pi\)
0.180630 + 0.983551i \(0.442186\pi\)
\(882\) 0 0
\(883\) 1.81133e7 0.781798 0.390899 0.920434i \(-0.372164\pi\)
0.390899 + 0.920434i \(0.372164\pi\)
\(884\) 2.86989e7 + 4.97079e7i 1.23519 + 2.13941i
\(885\) 738528. 1.27917e6i 0.0316963 0.0548996i
\(886\) −1.65922e7 + 2.87386e7i −0.710102 + 1.22993i
\(887\) −1.02128e7 1.76890e7i −0.435847 0.754909i 0.561517 0.827465i \(-0.310218\pi\)
−0.997364 + 0.0725558i \(0.976884\pi\)
\(888\) 1.63950e7 0.697718
\(889\) 0 0
\(890\) −2.92429e7 −1.23750
\(891\) −1.36702e6 2.36774e6i −0.0576872 0.0999171i
\(892\) 7.75349e6 1.34294e7i 0.326276 0.565127i
\(893\) −2.37844e6 + 4.11959e6i −0.0998078 + 0.172872i
\(894\) −1.49918e7 2.59665e7i −0.627348 1.08660i
\(895\) 2.92645e6 0.122119
\(896\) 0 0
\(897\) −6.86099e6 −0.284712
\(898\) −2.14393e6 3.71339e6i −0.0887195 0.153667i
\(899\) −4.43642e6 + 7.68411e6i −0.183077 + 0.317099i
\(900\) 5.58681e6 9.67664e6i 0.229910 0.398216i
\(901\) −1.23956e7 2.14698e7i −0.508693 0.881082i
\(902\) −2.06635e7 −0.845645
\(903\) 0 0
\(904\) −2.08702e7 −0.849388
\(905\) 8.16715e6 + 1.41459e7i 0.331474 + 0.574130i
\(906\) −8.47487e6 + 1.46789e7i −0.343015 + 0.594119i
\(907\) 1.00599e7 1.74242e7i 0.406044 0.703290i −0.588398 0.808571i \(-0.700241\pi\)
0.994442 + 0.105282i \(0.0335745\pi\)
\(908\) 5.70397e6 + 9.87957e6i 0.229595 + 0.397670i
\(909\) 6.87153e6 0.275832
\(910\) 0 0
\(911\) 3.17075e7 1.26580 0.632902 0.774232i \(-0.281863\pi\)
0.632902 + 0.774232i \(0.281863\pi\)
\(912\) −388497. 672896.i −0.0154668 0.0267893i
\(913\) −1.46673e7 + 2.54045e7i −0.582334 + 1.00863i
\(914\) −2.76012e6 + 4.78066e6i −0.109285 + 0.189288i
\(915\) 347169. + 601315.i 0.0137085 + 0.0237437i
\(916\) 6.42812e7 2.53131
\(917\) 0 0
\(918\) 9.20672e6 0.360577
\(919\) 4.35364e6 + 7.54072e6i 0.170045 + 0.294526i 0.938435 0.345455i \(-0.112275\pi\)
−0.768390 + 0.639981i \(0.778942\pi\)
\(920\) 1.96462e6 3.40283e6i 0.0765261 0.132547i
\(921\) −6.73297e6 + 1.16619e7i −0.261552 + 0.453021i
\(922\) −1.31839e7 2.28352e7i −0.510760 0.884663i
\(923\) −4.63857e7 −1.79217
\(924\) 0 0
\(925\) −2.57887e7 −0.991005
\(926\) −1.33817e7 2.31778e7i −0.512843 0.888270i
\(927\) 823457. 1.42627e6i 0.0314732 0.0545133i
\(928\) 1.97690e7 3.42410e7i 0.753556 1.30520i
\(929\) 1.62021e7 + 2.80629e7i 0.615931 + 1.06682i 0.990220 + 0.139512i \(0.0445534\pi\)
−0.374289 + 0.927312i \(0.622113\pi\)
\(930\) 2.30016e6 0.0872069
\(931\) 0 0
\(932\) −3.29167e6 −0.124130
\(933\) −3.87541e6 6.71241e6i −0.145752 0.252449i
\(934\) 3.30238e7 5.71988e7i 1.23868 2.14546i
\(935\) 6.32578e6 1.09566e7i 0.236638 0.409869i
\(936\) −6.02147e6 1.04295e7i −0.224653 0.389111i
\(937\) 2.19155e7 0.815458 0.407729 0.913103i \(-0.366321\pi\)
0.407729 + 0.913103i \(0.366321\pi\)
\(938\) 0 0
\(939\) −4.53544e6 −0.167863
\(940\) −1.18688e6 2.05573e6i −0.0438113 0.0758835i
\(941\) 7.30095e6 1.26456e7i 0.268785 0.465550i −0.699763 0.714375i \(-0.746711\pi\)
0.968548 + 0.248825i \(0.0800444\pi\)
\(942\) −3.19253e6 + 5.52963e6i −0.117222 + 0.203034i
\(943\) 2.58004e6 + 4.46876e6i 0.0944815 + 0.163647i
\(944\) −277533. −0.0101364
\(945\) 0 0
\(946\) −7.53189e7 −2.73638
\(947\) 1.04189e7 + 1.80461e7i 0.377527 + 0.653895i 0.990702 0.136052i \(-0.0434414\pi\)
−0.613175 + 0.789947i \(0.710108\pi\)
\(948\) 2.29696e6 3.97845e6i 0.0830103 0.143778i
\(949\) −1.56035e7 + 2.70261e7i −0.562416 + 0.974134i
\(950\) 2.80092e7 + 4.85133e7i 1.00691 + 1.74402i
\(951\) 4.32008e6 0.154896
\(952\) 0 0
\(953\) −942012. −0.0335988 −0.0167994 0.999859i \(-0.505348\pi\)
−0.0167994 + 0.999859i \(0.505348\pi\)
\(954\) 6.70157e6 + 1.16075e7i 0.238400 + 0.412921i
\(955\) −6.43092e6 + 1.11387e7i −0.228173 + 0.395208i
\(956\) −5.73492e6 + 9.93318e6i −0.202947 + 0.351515i
\(957\) −1.31925e7 2.28501e7i −0.465638 0.806508i
\(958\) −2.56752e7 −0.903857
\(959\) 0 0
\(960\) −1.04869e7 −0.367258
\(961\) 1.35193e7 + 2.34161e7i 0.472221 + 0.817910i
\(962\) −3.58105e7 + 6.20256e7i −1.24759 + 2.16089i
\(963\) −281969. + 488384.i −0.00979795 + 0.0169705i
\(964\) 1.13444e7 + 1.96492e7i 0.393179 + 0.681006i
\(965\) 8.84860e6 0.305884
\(966\) 0 0
\(967\) −2.56570e7 −0.882346 −0.441173 0.897422i \(-0.645438\pi\)
−0.441173 + 0.897422i \(0.645438\pi\)
\(968\) 1.17351e6 + 2.03257e6i 0.0402529 + 0.0697201i
\(969\) −1.43176e7 + 2.47988e7i −0.489847 + 0.848439i
\(970\) −8.03776e6 + 1.39218e7i −0.274287 + 0.475079i
\(971\) −1.07137e7 1.85566e7i −0.364662 0.631613i 0.624060 0.781377i \(-0.285482\pi\)
−0.988722 + 0.149763i \(0.952149\pi\)
\(972\) −3.08797e6 −0.104835
\(973\) 0 0
\(974\) 2.69237e7 0.909364
\(975\) 9.47153e6 + 1.64052e7i 0.319086 + 0.552674i
\(976\) 65231.8 112985.i 0.00219197 0.00379660i
\(977\) 1.02420e7 1.77397e7i 0.343281 0.594580i −0.641759 0.766906i \(-0.721795\pi\)
0.985040 + 0.172326i \(0.0551283\pi\)
\(978\) −7.64054e6 1.32338e7i −0.255433 0.442423i
\(979\) −6.01338e7 −2.00522
\(980\) 0 0
\(981\) 9.12476e6 0.302726
\(982\) −1.40528e7 2.43402e7i −0.465035 0.805464i
\(983\) 1.38825e7 2.40452e7i 0.458230 0.793677i −0.540638 0.841255i \(-0.681817\pi\)
0.998868 + 0.0475784i \(0.0151504\pi\)
\(984\) −4.52868e6 + 7.84391e6i −0.149102 + 0.258253i
\(985\) 7.41152e6 + 1.28371e7i 0.243398 + 0.421578i
\(986\) 8.88504e7 2.91050
\(987\) 0 0
\(988\) 9.65159e7 3.14562
\(989\) 9.40429e6 + 1.62887e7i 0.305728 + 0.529536i
\(990\) −3.41998e6 + 5.92357e6i −0.110901 + 0.192086i
\(991\) −1.73416e7 + 3.00366e7i −0.560926 + 0.971552i 0.436490 + 0.899709i \(0.356221\pi\)
−0.997416 + 0.0718429i \(0.977112\pi\)
\(992\) 3.54392e6 + 6.13826e6i 0.114342 + 0.198046i
\(993\) 1.97930e7 0.636998
\(994\) 0 0
\(995\) −1.00431e7 −0.321594
\(996\) 1.65660e7 + 2.86932e7i 0.529139 + 0.916496i
\(997\) −7.42861e6 + 1.28667e7i −0.236685 + 0.409950i −0.959761 0.280818i \(-0.909394\pi\)
0.723076 + 0.690768i \(0.242727\pi\)
\(998\) −3.00756e7 + 5.20925e7i −0.955846 + 1.65557i
\(999\) 3.56351e6 + 6.17219e6i 0.112970 + 0.195671i
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 147.6.e.o.67.4 8
7.2 even 3 inner 147.6.e.o.79.4 8
7.3 odd 6 147.6.a.m.1.1 4
7.4 even 3 147.6.a.l.1.1 4
7.5 odd 6 21.6.e.c.16.4 yes 8
7.6 odd 2 21.6.e.c.4.4 8
21.5 even 6 63.6.e.e.37.1 8
21.11 odd 6 441.6.a.v.1.4 4
21.17 even 6 441.6.a.w.1.4 4
21.20 even 2 63.6.e.e.46.1 8
28.19 even 6 336.6.q.j.289.3 8
28.27 even 2 336.6.q.j.193.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.e.c.4.4 8 7.6 odd 2
21.6.e.c.16.4 yes 8 7.5 odd 6
63.6.e.e.37.1 8 21.5 even 6
63.6.e.e.46.1 8 21.20 even 2
147.6.a.l.1.1 4 7.4 even 3
147.6.a.m.1.1 4 7.3 odd 6
147.6.e.o.67.4 8 1.1 even 1 trivial
147.6.e.o.79.4 8 7.2 even 3 inner
336.6.q.j.193.3 8 28.27 even 2
336.6.q.j.289.3 8 28.19 even 6
441.6.a.v.1.4 4 21.11 odd 6
441.6.a.w.1.4 4 21.17 even 6