Properties

Label 147.6.e.o.67.3
Level $147$
Weight $6$
Character 147.67
Analytic conductor $23.576$
Analytic rank $0$
Dimension $8$
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 67.3
Root \(0.895402 + 1.55088i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.6.e.o.79.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.395402 + 0.684857i) q^{2} +(4.50000 - 7.79423i) q^{3} +(15.6873 - 27.1712i) q^{4} +(-52.0958 - 90.2327i) q^{5} +7.11724 q^{6} +50.1170 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(0.395402 + 0.684857i) q^{2} +(4.50000 - 7.79423i) q^{3} +(15.6873 - 27.1712i) q^{4} +(-52.0958 - 90.2327i) q^{5} +7.11724 q^{6} +50.1170 q^{8} +(-40.5000 - 70.1481i) q^{9} +(41.1977 - 71.3564i) q^{10} +(248.830 - 430.986i) q^{11} +(-141.186 - 244.541i) q^{12} +206.551 q^{13} -937.725 q^{15} +(-482.178 - 835.156i) q^{16} +(31.5793 - 54.6969i) q^{17} +(32.0276 - 55.4734i) q^{18} +(661.977 + 1146.58i) q^{19} -3268.98 q^{20} +393.552 q^{22} +(97.2187 + 168.388i) q^{23} +(225.526 - 390.623i) q^{24} +(-3865.45 + 6695.16i) q^{25} +(81.6709 + 141.458i) q^{26} -729.000 q^{27} +4323.14 q^{29} +(-370.779 - 642.208i) q^{30} +(-3762.66 + 6517.11i) q^{31} +(1183.18 - 2049.33i) q^{32} +(-2239.47 - 3878.87i) q^{33} +49.9461 q^{34} -2541.34 q^{36} +(-5177.82 - 8968.25i) q^{37} +(-523.495 + 906.720i) q^{38} +(929.481 - 1609.91i) q^{39} +(-2610.89 - 4522.19i) q^{40} +4180.92 q^{41} +5960.87 q^{43} +(-7806.94 - 13522.0i) q^{44} +(-4219.76 + 7308.85i) q^{45} +(-76.8810 + 133.162i) q^{46} +(-2194.87 - 3801.62i) q^{47} -8679.20 q^{48} -6113.64 q^{50} +(-284.214 - 492.273i) q^{51} +(3240.24 - 5612.25i) q^{52} +(-8892.39 + 15402.1i) q^{53} +(-288.248 - 499.261i) q^{54} -51852.0 q^{55} +11915.6 q^{57} +(1709.38 + 2960.73i) q^{58} +(1750.23 - 3031.49i) q^{59} +(-14710.4 + 25479.1i) q^{60} +(-5316.23 - 9207.98i) q^{61} -5951.06 q^{62} -28988.0 q^{64} +(-10760.5 - 18637.7i) q^{65} +(1770.98 - 3067.43i) q^{66} +(6637.37 - 11496.3i) q^{67} +(-990.789 - 1716.10i) q^{68} +1749.94 q^{69} +38811.1 q^{71} +(-2029.74 - 3515.61i) q^{72} +(15687.8 - 27172.1i) q^{73} +(4094.65 - 7092.14i) q^{74} +(34789.1 + 60256.5i) q^{75} +41538.6 q^{76} +1470.08 q^{78} +(-19745.7 - 34200.6i) q^{79} +(-50238.9 + 87016.3i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(1653.14 + 2863.33i) q^{82} +102372. q^{83} -6580.60 q^{85} +(2356.94 + 4082.34i) q^{86} +(19454.1 - 33695.5i) q^{87} +(12470.6 - 21599.7i) q^{88} +(-56410.5 - 97705.8i) q^{89} -6674.02 q^{90} +6100.40 q^{92} +(33863.9 + 58654.0i) q^{93} +(1735.71 - 3006.34i) q^{94} +(68972.6 - 119464. i) q^{95} +(-10648.6 - 18444.0i) q^{96} -30334.3 q^{97} -40310.4 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.395402 + 0.684857i 0.0698979 + 0.121067i 0.898856 0.438244i \(-0.144399\pi\)
−0.828958 + 0.559310i \(0.811066\pi\)
\(3\) 4.50000 7.79423i 0.288675 0.500000i
\(4\) 15.6873 27.1712i 0.490229 0.849101i
\(5\) −52.0958 90.2327i −0.931919 1.61413i −0.780038 0.625732i \(-0.784800\pi\)
−0.151881 0.988399i \(-0.548533\pi\)
\(6\) 7.11724 0.0807112
\(7\) 0 0
\(8\) 50.1170 0.276860
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) 41.1977 71.3564i 0.130278 0.225649i
\(11\) 248.830 430.986i 0.620041 1.07394i −0.369436 0.929256i \(-0.620449\pi\)
0.989477 0.144687i \(-0.0462176\pi\)
\(12\) −141.186 244.541i −0.283034 0.490229i
\(13\) 206.551 0.338977 0.169488 0.985532i \(-0.445789\pi\)
0.169488 + 0.985532i \(0.445789\pi\)
\(14\) 0 0
\(15\) −937.725 −1.07609
\(16\) −482.178 835.156i −0.470877 0.815582i
\(17\) 31.5793 54.6969i 0.0265021 0.0459030i −0.852470 0.522776i \(-0.824896\pi\)
0.878972 + 0.476873i \(0.158230\pi\)
\(18\) 32.0276 55.4734i 0.0232993 0.0403556i
\(19\) 661.977 + 1146.58i 0.420687 + 0.728651i 0.996007 0.0892772i \(-0.0284557\pi\)
−0.575320 + 0.817929i \(0.695122\pi\)
\(20\) −3268.98 −1.82741
\(21\) 0 0
\(22\) 393.552 0.173358
\(23\) 97.2187 + 168.388i 0.0383204 + 0.0663729i 0.884550 0.466446i \(-0.154466\pi\)
−0.846229 + 0.532819i \(0.821133\pi\)
\(24\) 225.526 390.623i 0.0799225 0.138430i
\(25\) −3865.45 + 6695.16i −1.23695 + 2.14245i
\(26\) 81.6709 + 141.458i 0.0236938 + 0.0410388i
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) 4323.14 0.954562 0.477281 0.878751i \(-0.341622\pi\)
0.477281 + 0.878751i \(0.341622\pi\)
\(30\) −370.779 642.208i −0.0752163 0.130278i
\(31\) −3762.66 + 6517.11i −0.703219 + 1.21801i 0.264112 + 0.964492i \(0.414921\pi\)
−0.967331 + 0.253518i \(0.918412\pi\)
\(32\) 1183.18 2049.33i 0.204256 0.353783i
\(33\) −2239.47 3878.87i −0.357981 0.620041i
\(34\) 49.9461 0.00740977
\(35\) 0 0
\(36\) −2541.34 −0.326819
\(37\) −5177.82 8968.25i −0.621789 1.07697i −0.989152 0.146892i \(-0.953073\pi\)
0.367364 0.930077i \(-0.380260\pi\)
\(38\) −523.495 + 906.720i −0.0588103 + 0.101862i
\(39\) 929.481 1609.91i 0.0978541 0.169488i
\(40\) −2610.89 4522.19i −0.258011 0.446888i
\(41\) 4180.92 0.388429 0.194215 0.980959i \(-0.437784\pi\)
0.194215 + 0.980959i \(0.437784\pi\)
\(42\) 0 0
\(43\) 5960.87 0.491630 0.245815 0.969317i \(-0.420944\pi\)
0.245815 + 0.969317i \(0.420944\pi\)
\(44\) −7806.94 13522.0i −0.607924 1.05296i
\(45\) −4219.76 + 7308.85i −0.310640 + 0.538044i
\(46\) −76.8810 + 133.162i −0.00535703 + 0.00927866i
\(47\) −2194.87 3801.62i −0.144932 0.251029i 0.784416 0.620236i \(-0.212963\pi\)
−0.929348 + 0.369206i \(0.879630\pi\)
\(48\) −8679.20 −0.543721
\(49\) 0 0
\(50\) −6113.64 −0.345840
\(51\) −284.214 492.273i −0.0153010 0.0265021i
\(52\) 3240.24 5612.25i 0.166176 0.287825i
\(53\) −8892.39 + 15402.1i −0.434839 + 0.753164i −0.997283 0.0736720i \(-0.976528\pi\)
0.562443 + 0.826836i \(0.309862\pi\)
\(54\) −288.248 499.261i −0.0134519 0.0232993i
\(55\) −51852.0 −2.31131
\(56\) 0 0
\(57\) 11915.6 0.485768
\(58\) 1709.38 + 2960.73i 0.0667219 + 0.115566i
\(59\) 1750.23 3031.49i 0.0654585 0.113377i −0.831439 0.555616i \(-0.812482\pi\)
0.896897 + 0.442239i \(0.145816\pi\)
\(60\) −14710.4 + 25479.1i −0.527529 + 0.913706i
\(61\) −5316.23 9207.98i −0.182928 0.316840i 0.759949 0.649983i \(-0.225224\pi\)
−0.942876 + 0.333143i \(0.891891\pi\)
\(62\) −5951.06 −0.196614
\(63\) 0 0
\(64\) −28988.0 −0.884645
\(65\) −10760.5 18637.7i −0.315899 0.547153i
\(66\) 1770.98 3067.43i 0.0500443 0.0866792i
\(67\) 6637.37 11496.3i 0.180638 0.312874i −0.761460 0.648212i \(-0.775517\pi\)
0.942098 + 0.335338i \(0.108850\pi\)
\(68\) −990.789 1716.10i −0.0259842 0.0450059i
\(69\) 1749.94 0.0442486
\(70\) 0 0
\(71\) 38811.1 0.913713 0.456857 0.889540i \(-0.348975\pi\)
0.456857 + 0.889540i \(0.348975\pi\)
\(72\) −2029.74 3515.61i −0.0461433 0.0799225i
\(73\) 15687.8 27172.1i 0.344552 0.596782i −0.640720 0.767775i \(-0.721364\pi\)
0.985272 + 0.170992i \(0.0546974\pi\)
\(74\) 4094.65 7092.14i 0.0869235 0.150556i
\(75\) 34789.1 + 60256.5i 0.714151 + 1.23695i
\(76\) 41538.6 0.824931
\(77\) 0 0
\(78\) 1470.08 0.0273592
\(79\) −19745.7 34200.6i −0.355964 0.616547i 0.631319 0.775523i \(-0.282514\pi\)
−0.987282 + 0.158976i \(0.949181\pi\)
\(80\) −50238.9 + 87016.3i −0.877638 + 1.52011i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 1653.14 + 2863.33i 0.0271504 + 0.0470259i
\(83\) 102372. 1.63112 0.815559 0.578675i \(-0.196430\pi\)
0.815559 + 0.578675i \(0.196430\pi\)
\(84\) 0 0
\(85\) −6580.60 −0.0987912
\(86\) 2356.94 + 4082.34i 0.0343639 + 0.0595201i
\(87\) 19454.1 33695.5i 0.275558 0.477281i
\(88\) 12470.6 21599.7i 0.171665 0.297332i
\(89\) −56410.5 97705.8i −0.754892 1.30751i −0.945428 0.325831i \(-0.894356\pi\)
0.190536 0.981680i \(-0.438977\pi\)
\(90\) −6674.02 −0.0868523
\(91\) 0 0
\(92\) 6100.40 0.0751430
\(93\) 33863.9 + 58654.0i 0.406004 + 0.703219i
\(94\) 1735.71 3006.34i 0.0202609 0.0350929i
\(95\) 68972.6 119464.i 0.784092 1.35809i
\(96\) −10648.6 18444.0i −0.117928 0.204256i
\(97\) −30334.3 −0.327345 −0.163672 0.986515i \(-0.552334\pi\)
−0.163672 + 0.986515i \(0.552334\pi\)
\(98\) 0 0
\(99\) −40310.4 −0.413361
\(100\) 121277. + 210058.i 1.21277 + 2.10058i
\(101\) 53398.2 92488.4i 0.520862 0.902160i −0.478843 0.877900i \(-0.658944\pi\)
0.999706 0.0242599i \(-0.00772291\pi\)
\(102\) 224.758 389.292i 0.00213902 0.00370488i
\(103\) 78767.8 + 136430.i 0.731570 + 1.26712i 0.956212 + 0.292674i \(0.0945452\pi\)
−0.224643 + 0.974441i \(0.572121\pi\)
\(104\) 10351.7 0.0938490
\(105\) 0 0
\(106\) −14064.3 −0.121578
\(107\) 44662.2 + 77357.1i 0.377121 + 0.653192i 0.990642 0.136486i \(-0.0435809\pi\)
−0.613521 + 0.789678i \(0.710248\pi\)
\(108\) −11436.1 + 19807.8i −0.0943445 + 0.163410i
\(109\) −83802.3 + 145150.i −0.675600 + 1.17017i 0.300693 + 0.953721i \(0.402782\pi\)
−0.976293 + 0.216452i \(0.930551\pi\)
\(110\) −20502.4 35511.2i −0.161556 0.279823i
\(111\) −93200.8 −0.717980
\(112\) 0 0
\(113\) −115794. −0.853079 −0.426539 0.904469i \(-0.640267\pi\)
−0.426539 + 0.904469i \(0.640267\pi\)
\(114\) 4711.46 + 8160.48i 0.0339542 + 0.0588103i
\(115\) 10129.4 17544.6i 0.0714230 0.123708i
\(116\) 67818.4 117465.i 0.467954 0.810519i
\(117\) −8365.33 14489.2i −0.0564961 0.0978541i
\(118\) 2768.19 0.0183017
\(119\) 0 0
\(120\) −46995.9 −0.297925
\(121\) −43307.1 75010.0i −0.268903 0.465753i
\(122\) 4204.10 7281.72i 0.0255725 0.0442929i
\(123\) 18814.1 32587.0i 0.112130 0.194215i
\(124\) 118052. + 204472.i 0.689476 + 1.19421i
\(125\) 479898. 2.74709
\(126\) 0 0
\(127\) 201513. 1.10865 0.554325 0.832300i \(-0.312977\pi\)
0.554325 + 0.832300i \(0.312977\pi\)
\(128\) −49323.7 85431.2i −0.266091 0.460884i
\(129\) 26823.9 46460.4i 0.141921 0.245815i
\(130\) 8509.43 14738.8i 0.0441613 0.0764897i
\(131\) 19234.8 + 33315.6i 0.0979285 + 0.169617i 0.910827 0.412788i \(-0.135445\pi\)
−0.812899 + 0.582405i \(0.802112\pi\)
\(132\) −140525. −0.701970
\(133\) 0 0
\(134\) 10497.7 0.0505049
\(135\) 37977.9 + 65779.6i 0.179348 + 0.310640i
\(136\) 1582.66 2741.25i 0.00733736 0.0127087i
\(137\) 120861. 209337.i 0.550155 0.952896i −0.448108 0.893979i \(-0.647902\pi\)
0.998263 0.0589167i \(-0.0187646\pi\)
\(138\) 691.929 + 1198.46i 0.00309289 + 0.00535703i
\(139\) 53112.2 0.233162 0.116581 0.993181i \(-0.462807\pi\)
0.116581 + 0.993181i \(0.462807\pi\)
\(140\) 0 0
\(141\) −39507.6 −0.167353
\(142\) 15346.0 + 26580.1i 0.0638667 + 0.110620i
\(143\) 51396.1 89020.7i 0.210180 0.364042i
\(144\) −39056.4 + 67647.7i −0.156959 + 0.271861i
\(145\) −225218. 390088.i −0.889574 1.54079i
\(146\) 24812.0 0.0963340
\(147\) 0 0
\(148\) −324905. −1.21927
\(149\) −64531.0 111771.i −0.238124 0.412443i 0.722052 0.691839i \(-0.243199\pi\)
−0.960176 + 0.279396i \(0.909866\pi\)
\(150\) −27511.4 + 47651.1i −0.0998353 + 0.172920i
\(151\) −76603.2 + 132681.i −0.273404 + 0.473549i −0.969731 0.244175i \(-0.921483\pi\)
0.696327 + 0.717724i \(0.254816\pi\)
\(152\) 33176.3 + 57463.0i 0.116471 + 0.201734i
\(153\) −5115.85 −0.0176681
\(154\) 0 0
\(155\) 784075. 2.62137
\(156\) −29162.1 50510.3i −0.0959418 0.166176i
\(157\) −75593.9 + 130932.i −0.244758 + 0.423934i −0.962064 0.272825i \(-0.912042\pi\)
0.717305 + 0.696759i \(0.245375\pi\)
\(158\) 15615.0 27046.0i 0.0497622 0.0861907i
\(159\) 80031.5 + 138619.i 0.251055 + 0.434839i
\(160\) −246555. −0.761402
\(161\) 0 0
\(162\) −5188.47 −0.0155329
\(163\) 16458.3 + 28506.7i 0.0485196 + 0.0840384i 0.889265 0.457392i \(-0.151216\pi\)
−0.840746 + 0.541430i \(0.817883\pi\)
\(164\) 65587.3 113601.i 0.190419 0.329816i
\(165\) −233334. + 404146.i −0.667219 + 1.15566i
\(166\) 40478.1 + 70110.1i 0.114012 + 0.197474i
\(167\) −217586. −0.603725 −0.301862 0.953352i \(-0.597608\pi\)
−0.301862 + 0.953352i \(0.597608\pi\)
\(168\) 0 0
\(169\) −328630. −0.885095
\(170\) −2601.99 4506.77i −0.00690530 0.0119603i
\(171\) 53620.2 92872.9i 0.140229 0.242884i
\(172\) 93510.0 161964.i 0.241011 0.417443i
\(173\) −210621. 364807.i −0.535041 0.926718i −0.999161 0.0409458i \(-0.986963\pi\)
0.464121 0.885772i \(-0.346370\pi\)
\(174\) 30768.8 0.0770438
\(175\) 0 0
\(176\) −479921. −1.16785
\(177\) −15752.1 27283.4i −0.0377925 0.0654585i
\(178\) 44609.7 77266.3i 0.105531 0.182785i
\(179\) −1747.03 + 3025.94i −0.00407538 + 0.00705876i −0.868056 0.496466i \(-0.834631\pi\)
0.863981 + 0.503525i \(0.167964\pi\)
\(180\) 132394. + 229312.i 0.304569 + 0.527529i
\(181\) −594611. −1.34908 −0.674538 0.738240i \(-0.735657\pi\)
−0.674538 + 0.738240i \(0.735657\pi\)
\(182\) 0 0
\(183\) −95692.2 −0.211227
\(184\) 4872.30 + 8439.08i 0.0106094 + 0.0183760i
\(185\) −539486. + 934418.i −1.15891 + 2.00730i
\(186\) −26779.8 + 46383.9i −0.0567576 + 0.0983071i
\(187\) −15715.7 27220.5i −0.0328648 0.0569235i
\(188\) −137726. −0.284199
\(189\) 0 0
\(190\) 109088. 0.219226
\(191\) −414322. 717627.i −0.821778 1.42336i −0.904357 0.426777i \(-0.859649\pi\)
0.0825782 0.996585i \(-0.473685\pi\)
\(192\) −130446. + 225939.i −0.255375 + 0.442322i
\(193\) −109869. + 190299.i −0.212316 + 0.367743i −0.952439 0.304729i \(-0.901434\pi\)
0.740123 + 0.672472i \(0.234767\pi\)
\(194\) −11994.3 20774.7i −0.0228807 0.0396306i
\(195\) −193688. −0.364768
\(196\) 0 0
\(197\) 475612. 0.873146 0.436573 0.899669i \(-0.356192\pi\)
0.436573 + 0.899669i \(0.356192\pi\)
\(198\) −15938.8 27606.9i −0.0288931 0.0500443i
\(199\) 313778. 543479.i 0.561681 0.972859i −0.435669 0.900107i \(-0.643488\pi\)
0.997350 0.0727525i \(-0.0231783\pi\)
\(200\) −193725. + 335541.i −0.342460 + 0.593159i
\(201\) −59736.4 103466.i −0.104291 0.180638i
\(202\) 84455.1 0.145629
\(203\) 0 0
\(204\) −17834.2 −0.0300039
\(205\) −217808. 377255.i −0.361984 0.626975i
\(206\) −62290.0 + 107889.i −0.102270 + 0.177138i
\(207\) 7874.71 13639.4i 0.0127735 0.0221243i
\(208\) −99594.5 172503.i −0.159616 0.276463i
\(209\) 658879. 1.04337
\(210\) 0 0
\(211\) 570989. 0.882920 0.441460 0.897281i \(-0.354461\pi\)
0.441460 + 0.897281i \(0.354461\pi\)
\(212\) 278995. + 483234.i 0.426341 + 0.738445i
\(213\) 174650. 302502.i 0.263766 0.456857i
\(214\) −35319.1 + 61174.4i −0.0527199 + 0.0913136i
\(215\) −310536. 537865.i −0.458159 0.793555i
\(216\) −36535.3 −0.0532817
\(217\) 0 0
\(218\) −132543. −0.188892
\(219\) −141190. 244549.i −0.198927 0.344552i
\(220\) −813419. + 1.40888e6i −1.13307 + 1.96254i
\(221\) 6522.75 11297.7i 0.00898359 0.0155600i
\(222\) −36851.8 63829.3i −0.0501853 0.0869235i
\(223\) −4233.11 −0.00570029 −0.00285015 0.999996i \(-0.500907\pi\)
−0.00285015 + 0.999996i \(0.500907\pi\)
\(224\) 0 0
\(225\) 626204. 0.824630
\(226\) −45785.2 79302.2i −0.0596285 0.103280i
\(227\) 564931. 978490.i 0.727664 1.26035i −0.230204 0.973142i \(-0.573939\pi\)
0.957868 0.287209i \(-0.0927274\pi\)
\(228\) 186924. 323761.i 0.238137 0.412466i
\(229\) 402322. + 696842.i 0.506973 + 0.878103i 0.999967 + 0.00807048i \(0.00256894\pi\)
−0.492994 + 0.870032i \(0.664098\pi\)
\(230\) 16020.7 0.0199693
\(231\) 0 0
\(232\) 216663. 0.264280
\(233\) −584636. 1.01262e6i −0.705498 1.22196i −0.966511 0.256624i \(-0.917390\pi\)
0.261013 0.965335i \(-0.415943\pi\)
\(234\) 6615.34 11458.1i 0.00789792 0.0136796i
\(235\) −228687. + 396098.i −0.270130 + 0.467878i
\(236\) −54912.9 95112.0i −0.0641792 0.111162i
\(237\) −355423. −0.411031
\(238\) 0 0
\(239\) −1.70554e6 −1.93138 −0.965689 0.259700i \(-0.916376\pi\)
−0.965689 + 0.259700i \(0.916376\pi\)
\(240\) 452150. + 783147.i 0.506704 + 0.877638i
\(241\) 475598. 823760.i 0.527470 0.913604i −0.472018 0.881589i \(-0.656474\pi\)
0.999487 0.0320153i \(-0.0101925\pi\)
\(242\) 34247.4 59318.3i 0.0375915 0.0651104i
\(243\) 29524.5 + 51137.9i 0.0320750 + 0.0555556i
\(244\) −333590. −0.358705
\(245\) 0 0
\(246\) 29756.6 0.0313506
\(247\) 136732. + 236827.i 0.142603 + 0.246996i
\(248\) −188573. + 326618.i −0.194693 + 0.337218i
\(249\) 460673. 797909.i 0.470863 0.815559i
\(250\) 189753. + 328661.i 0.192016 + 0.332582i
\(251\) −1.14498e6 −1.14713 −0.573566 0.819159i \(-0.694440\pi\)
−0.573566 + 0.819159i \(0.694440\pi\)
\(252\) 0 0
\(253\) 96763.6 0.0950409
\(254\) 79678.8 + 138008.i 0.0774923 + 0.134221i
\(255\) −29612.7 + 51290.7i −0.0285186 + 0.0493956i
\(256\) −424803. + 735781.i −0.405124 + 0.701695i
\(257\) 591869. + 1.02515e6i 0.558976 + 0.968175i 0.997582 + 0.0694955i \(0.0221389\pi\)
−0.438606 + 0.898679i \(0.644528\pi\)
\(258\) 42425.0 0.0396800
\(259\) 0 0
\(260\) −675211. −0.619450
\(261\) −175087. 303260.i −0.159094 0.275558i
\(262\) −15211.0 + 26346.2i −0.0136900 + 0.0237118i
\(263\) −224158. + 388253.i −0.199832 + 0.346119i −0.948474 0.316856i \(-0.897373\pi\)
0.748642 + 0.662975i \(0.230706\pi\)
\(264\) −112235. 194397.i −0.0991106 0.171665i
\(265\) 1.85303e6 1.62094
\(266\) 0 0
\(267\) −1.01539e6 −0.871674
\(268\) −208245. 360691.i −0.177108 0.306760i
\(269\) 373737. 647332.i 0.314909 0.545439i −0.664509 0.747280i \(-0.731359\pi\)
0.979418 + 0.201841i \(0.0646925\pi\)
\(270\) −30033.1 + 52018.8i −0.0250721 + 0.0434261i
\(271\) −116319. 201470.i −0.0962114 0.166643i 0.813902 0.581002i \(-0.197339\pi\)
−0.910114 + 0.414359i \(0.864006\pi\)
\(272\) −60907.3 −0.0499169
\(273\) 0 0
\(274\) 191155. 0.153819
\(275\) 1.92368e6 + 3.33191e6i 1.53391 + 2.65682i
\(276\) 27451.8 47547.9i 0.0216919 0.0375715i
\(277\) 1.21462e6 2.10379e6i 0.951134 1.64741i 0.208157 0.978095i \(-0.433253\pi\)
0.742977 0.669317i \(-0.233413\pi\)
\(278\) 21000.7 + 36374.3i 0.0162975 + 0.0282282i
\(279\) 609550. 0.468812
\(280\) 0 0
\(281\) 2.51704e6 1.90163 0.950813 0.309766i \(-0.100251\pi\)
0.950813 + 0.309766i \(0.100251\pi\)
\(282\) −15621.4 27057.1i −0.0116976 0.0202609i
\(283\) 130497. 226028.i 0.0968579 0.167763i −0.813525 0.581530i \(-0.802454\pi\)
0.910382 + 0.413768i \(0.135787\pi\)
\(284\) 608842. 1.05454e6i 0.447928 0.775835i
\(285\) −620753. 1.07518e6i −0.452696 0.784092i
\(286\) 81288.6 0.0587645
\(287\) 0 0
\(288\) −191675. −0.136171
\(289\) 707934. + 1.22618e6i 0.498595 + 0.863592i
\(290\) 178103. 308484.i 0.124359 0.215396i
\(291\) −136505. + 236433.i −0.0944963 + 0.163672i
\(292\) −492199. 852514.i −0.337819 0.585119i
\(293\) −65011.7 −0.0442408 −0.0221204 0.999755i \(-0.507042\pi\)
−0.0221204 + 0.999755i \(0.507042\pi\)
\(294\) 0 0
\(295\) −364720. −0.244008
\(296\) −259497. 449462.i −0.172148 0.298170i
\(297\) −181397. + 314189.i −0.119327 + 0.206680i
\(298\) 51031.5 88389.1i 0.0332887 0.0576578i
\(299\) 20080.6 + 34780.7i 0.0129897 + 0.0224989i
\(300\) 2.18299e6 1.40039
\(301\) 0 0
\(302\) −121156. −0.0764414
\(303\) −480584. 832395.i −0.300720 0.520862i
\(304\) 638381. 1.10571e6i 0.396183 0.686210i
\(305\) −553907. + 959395.i −0.340947 + 0.590538i
\(306\) −2022.82 3503.62i −0.00123496 0.00213902i
\(307\) 2.35599e6 1.42668 0.713342 0.700816i \(-0.247181\pi\)
0.713342 + 0.700816i \(0.247181\pi\)
\(308\) 0 0
\(309\) 1.41782e6 0.844744
\(310\) 310025. + 536980.i 0.183228 + 0.317361i
\(311\) −1.05903e6 + 1.83429e6i −0.620878 + 1.07539i 0.368445 + 0.929650i \(0.379890\pi\)
−0.989323 + 0.145742i \(0.953443\pi\)
\(312\) 46582.8 80683.7i 0.0270919 0.0469245i
\(313\) −93756.8 162392.i −0.0540931 0.0936920i 0.837711 0.546114i \(-0.183893\pi\)
−0.891804 + 0.452422i \(0.850560\pi\)
\(314\) −119560. −0.0684324
\(315\) 0 0
\(316\) −1.23903e6 −0.698014
\(317\) 502705. + 870711.i 0.280974 + 0.486661i 0.971625 0.236527i \(-0.0760093\pi\)
−0.690651 + 0.723188i \(0.742676\pi\)
\(318\) −63289.3 + 109620.i −0.0350964 + 0.0607888i
\(319\) 1.07573e6 1.86321e6i 0.591868 1.02515i
\(320\) 1.51016e6 + 2.61567e6i 0.824417 + 1.42793i
\(321\) 803919. 0.435461
\(322\) 0 0
\(323\) 83619.1 0.0445964
\(324\) 102924. + 178270.i 0.0544698 + 0.0943445i
\(325\) −798415. + 1.38290e6i −0.419296 + 0.726241i
\(326\) −13015.3 + 22543.2i −0.00678284 + 0.0117482i
\(327\) 754220. + 1.30635e6i 0.390058 + 0.675600i
\(328\) 209535. 0.107540
\(329\) 0 0
\(330\) −369043. −0.186549
\(331\) −839920. 1.45478e6i −0.421374 0.729841i 0.574700 0.818364i \(-0.305119\pi\)
−0.996074 + 0.0885229i \(0.971785\pi\)
\(332\) 1.60594e6 2.78157e6i 0.799620 1.38498i
\(333\) −419404. + 726429.i −0.207263 + 0.358990i
\(334\) −86033.9 149015.i −0.0421991 0.0730910i
\(335\) −1.38312e6 −0.673360
\(336\) 0 0
\(337\) −995036. −0.477270 −0.238635 0.971109i \(-0.576700\pi\)
−0.238635 + 0.971109i \(0.576700\pi\)
\(338\) −129941. 225064.i −0.0618663 0.107156i
\(339\) −521072. + 902523.i −0.246263 + 0.426539i
\(340\) −103232. + 178803.i −0.0484303 + 0.0838837i
\(341\) 1.87252e6 + 3.24330e6i 0.872049 + 1.51043i
\(342\) 84806.2 0.0392069
\(343\) 0 0
\(344\) 298741. 0.136113
\(345\) −91164.4 157901.i −0.0412361 0.0714230i
\(346\) 166560. 288491.i 0.0747965 0.129551i
\(347\) −2.02833e6 + 3.51317e6i −0.904304 + 1.56630i −0.0824546 + 0.996595i \(0.526276\pi\)
−0.821849 + 0.569705i \(0.807057\pi\)
\(348\) −610366. 1.05718e6i −0.270173 0.467954i
\(349\) −2.86202e6 −1.25779 −0.628897 0.777488i \(-0.716493\pi\)
−0.628897 + 0.777488i \(0.716493\pi\)
\(350\) 0 0
\(351\) −150576. −0.0652361
\(352\) −588821. 1.01987e6i −0.253295 0.438720i
\(353\) 416343. 721126.i 0.177834 0.308017i −0.763305 0.646039i \(-0.776424\pi\)
0.941138 + 0.338022i \(0.109758\pi\)
\(354\) 12456.8 21575.9i 0.00528323 0.00915083i
\(355\) −2.02190e6 3.50203e6i −0.851507 1.47485i
\(356\) −3.53972e6 −1.48028
\(357\) 0 0
\(358\) −2763.12 −0.00113944
\(359\) 1.34875e6 + 2.33611e6i 0.552327 + 0.956659i 0.998106 + 0.0615157i \(0.0195934\pi\)
−0.445779 + 0.895143i \(0.647073\pi\)
\(360\) −211482. + 366297.i −0.0860036 + 0.148963i
\(361\) 361621. 626346.i 0.146045 0.252957i
\(362\) −235110. 407223.i −0.0942976 0.163328i
\(363\) −779527. −0.310502
\(364\) 0 0
\(365\) −3.26908e6 −1.28438
\(366\) −37836.9 65535.5i −0.0147643 0.0255725i
\(367\) 727411. 1.25991e6i 0.281913 0.488287i −0.689943 0.723864i \(-0.742364\pi\)
0.971856 + 0.235576i \(0.0756978\pi\)
\(368\) 93753.3 162386.i 0.0360884 0.0625069i
\(369\) −169327. 293283.i −0.0647382 0.112130i
\(370\) −853257. −0.324023
\(371\) 0 0
\(372\) 2.12494e6 0.796138
\(373\) 1.02344e6 + 1.77265e6i 0.380883 + 0.659708i 0.991189 0.132457i \(-0.0422868\pi\)
−0.610306 + 0.792166i \(0.708953\pi\)
\(374\) 12428.1 21526.1i 0.00459436 0.00795767i
\(375\) 2.15954e6 3.74043e6i 0.793018 1.37355i
\(376\) −110000. 190526.i −0.0401258 0.0694999i
\(377\) 892950. 0.323574
\(378\) 0 0
\(379\) −416898. −0.149084 −0.0745421 0.997218i \(-0.523750\pi\)
−0.0745421 + 0.997218i \(0.523750\pi\)
\(380\) −2.16399e6 3.74814e6i −0.768769 1.33155i
\(381\) 906810. 1.57064e6i 0.320040 0.554325i
\(382\) 327648. 567503.i 0.114881 0.198980i
\(383\) −1.93813e6 3.35694e6i −0.675127 1.16935i −0.976432 0.215827i \(-0.930755\pi\)
0.301305 0.953528i \(-0.402578\pi\)
\(384\) −887827. −0.307256
\(385\) 0 0
\(386\) −173771. −0.0593619
\(387\) −241415. 418143.i −0.0819383 0.141921i
\(388\) −475864. + 824221.i −0.160474 + 0.277949i
\(389\) −1.41901e6 + 2.45780e6i −0.475458 + 0.823517i −0.999605 0.0281111i \(-0.991051\pi\)
0.524147 + 0.851628i \(0.324384\pi\)
\(390\) −76584.9 132649.i −0.0254966 0.0441613i
\(391\) 12280.4 0.00406228
\(392\) 0 0
\(393\) 346226. 0.113078
\(394\) 188058. + 325726.i 0.0610311 + 0.105709i
\(395\) −2.05734e6 + 3.56342e6i −0.663458 + 1.14914i
\(396\) −632362. + 1.09528e6i −0.202641 + 0.350985i
\(397\) 2.17133e6 + 3.76085e6i 0.691432 + 1.19760i 0.971369 + 0.237577i \(0.0763532\pi\)
−0.279937 + 0.960018i \(0.590314\pi\)
\(398\) 496274. 0.157041
\(399\) 0 0
\(400\) 7.45534e6 2.32979
\(401\) −1.70152e6 2.94712e6i −0.528417 0.915244i −0.999451 0.0331296i \(-0.989453\pi\)
0.471034 0.882115i \(-0.343881\pi\)
\(402\) 47239.8 81821.8i 0.0145795 0.0252525i
\(403\) −777182. + 1.34612e6i −0.238375 + 0.412877i
\(404\) −1.67535e6 2.90179e6i −0.510683 0.884529i
\(405\) 683602. 0.207093
\(406\) 0 0
\(407\) −5.15359e6 −1.54214
\(408\) −14243.9 24671.2i −0.00423623 0.00733736i
\(409\) −2.64716e6 + 4.58501e6i −0.782477 + 1.35529i 0.148018 + 0.988985i \(0.452711\pi\)
−0.930495 + 0.366305i \(0.880623\pi\)
\(410\) 172244. 298335.i 0.0506039 0.0876486i
\(411\) −1.08775e6 1.88404e6i −0.317632 0.550155i
\(412\) 4.94262e6 1.43455
\(413\) 0 0
\(414\) 12454.7 0.00357136
\(415\) −5.33315e6 9.23728e6i −1.52007 2.63284i
\(416\) 244387. 423291.i 0.0692382 0.119924i
\(417\) 239005. 413969.i 0.0673080 0.116581i
\(418\) 260522. + 451238.i 0.0729297 + 0.126318i
\(419\) −2.87267e6 −0.799376 −0.399688 0.916651i \(-0.630881\pi\)
−0.399688 + 0.916651i \(0.630881\pi\)
\(420\) 0 0
\(421\) 2.08688e6 0.573843 0.286921 0.957954i \(-0.407368\pi\)
0.286921 + 0.957954i \(0.407368\pi\)
\(422\) 225770. + 391046.i 0.0617143 + 0.106892i
\(423\) −177784. + 307932.i −0.0483106 + 0.0836765i
\(424\) −445660. + 771905.i −0.120390 + 0.208521i
\(425\) 244137. + 422857.i 0.0655633 + 0.113559i
\(426\) 276228. 0.0737469
\(427\) 0 0
\(428\) 2.80252e6 0.739501
\(429\) −462565. 801187.i −0.121347 0.210180i
\(430\) 245574. 425346.i 0.0640488 0.110936i
\(431\) 1.21432e6 2.10326e6i 0.314876 0.545380i −0.664535 0.747257i \(-0.731371\pi\)
0.979411 + 0.201876i \(0.0647039\pi\)
\(432\) 351508. + 608829.i 0.0906202 + 0.156959i
\(433\) −956219. −0.245097 −0.122548 0.992463i \(-0.539107\pi\)
−0.122548 + 0.992463i \(0.539107\pi\)
\(434\) 0 0
\(435\) −4.05392e6 −1.02719
\(436\) 2.62927e6 + 4.55402e6i 0.662397 + 1.14730i
\(437\) −128713. + 222938.i −0.0322418 + 0.0558444i
\(438\) 111654. 193390.i 0.0278092 0.0481670i
\(439\) 1.32102e6 + 2.28808e6i 0.327152 + 0.566644i 0.981946 0.189164i \(-0.0605778\pi\)
−0.654794 + 0.755808i \(0.727244\pi\)
\(440\) −2.59867e6 −0.639910
\(441\) 0 0
\(442\) 10316.4 0.00251174
\(443\) 1.71983e6 + 2.97883e6i 0.416366 + 0.721168i 0.995571 0.0940147i \(-0.0299701\pi\)
−0.579205 + 0.815182i \(0.696637\pi\)
\(444\) −1.46207e6 + 2.53238e6i −0.351974 + 0.609637i
\(445\) −5.87750e6 + 1.01801e7i −1.40700 + 2.43699i
\(446\) −1673.78 2899.07i −0.000398439 0.000690116i
\(447\) −1.16156e6 −0.274962
\(448\) 0 0
\(449\) 4.39903e6 1.02977 0.514886 0.857259i \(-0.327834\pi\)
0.514886 + 0.857259i \(0.327834\pi\)
\(450\) 247602. + 428860.i 0.0576400 + 0.0998353i
\(451\) 1.04034e6 1.80192e6i 0.240842 0.417151i
\(452\) −1.81649e6 + 3.14626e6i −0.418204 + 0.724350i
\(453\) 689429. + 1.19413e6i 0.157850 + 0.273404i
\(454\) 893501. 0.203449
\(455\) 0 0
\(456\) 597173. 0.134490
\(457\) 1.12555e6 + 1.94951e6i 0.252101 + 0.436652i 0.964104 0.265524i \(-0.0855451\pi\)
−0.712003 + 0.702176i \(0.752212\pi\)
\(458\) −318158. + 551066.i −0.0708727 + 0.122755i
\(459\) −23021.3 + 39874.1i −0.00510033 + 0.00883403i
\(460\) −317805. 550455.i −0.0700272 0.121291i
\(461\) −1.85307e6 −0.406107 −0.203053 0.979168i \(-0.565087\pi\)
−0.203053 + 0.979168i \(0.565087\pi\)
\(462\) 0 0
\(463\) −3.01089e6 −0.652744 −0.326372 0.945241i \(-0.605826\pi\)
−0.326372 + 0.945241i \(0.605826\pi\)
\(464\) −2.08452e6 3.61050e6i −0.449481 0.778524i
\(465\) 3.52834e6 6.11126e6i 0.756725 1.31069i
\(466\) 462333. 800785.i 0.0986258 0.170825i
\(467\) −533627. 924270.i −0.113226 0.196113i 0.803843 0.594841i \(-0.202785\pi\)
−0.917069 + 0.398728i \(0.869452\pi\)
\(468\) −524918. −0.110784
\(469\) 0 0
\(470\) −361694. −0.0755260
\(471\) 680345. + 1.17839e6i 0.141311 + 0.244758i
\(472\) 87716.4 151929.i 0.0181228 0.0313896i
\(473\) 1.48324e6 2.56905e6i 0.304831 0.527983i
\(474\) −140535. 243414.i −0.0287302 0.0497622i
\(475\) −1.02354e7 −2.08147
\(476\) 0 0
\(477\) 1.44057e6 0.289893
\(478\) −674375. 1.16805e6i −0.134999 0.233826i
\(479\) −2.84394e6 + 4.92585e6i −0.566346 + 0.980939i 0.430577 + 0.902554i \(0.358310\pi\)
−0.996923 + 0.0783858i \(0.975023\pi\)
\(480\) −1.10950e6 + 1.92171e6i −0.219798 + 0.380701i
\(481\) −1.06949e6 1.85240e6i −0.210772 0.365068i
\(482\) 752211. 0.147476
\(483\) 0 0
\(484\) −2.71749e6 −0.527295
\(485\) 1.58029e6 + 2.73715e6i 0.305059 + 0.528377i
\(486\) −23348.1 + 40440.1i −0.00448396 + 0.00776644i
\(487\) 3.42239e6 5.92775e6i 0.653893 1.13258i −0.328277 0.944582i \(-0.606468\pi\)
0.982170 0.187995i \(-0.0601987\pi\)
\(488\) −266433. 461476.i −0.0506453 0.0877202i
\(489\) 296250. 0.0560256
\(490\) 0 0
\(491\) 5.60132e6 1.04854 0.524272 0.851551i \(-0.324338\pi\)
0.524272 + 0.851551i \(0.324338\pi\)
\(492\) −590286. 1.02241e6i −0.109939 0.190419i
\(493\) 136522. 236462.i 0.0252979 0.0438172i
\(494\) −108129. + 187284.i −0.0199353 + 0.0345290i
\(495\) 2.10001e6 + 3.63732e6i 0.385219 + 0.667219i
\(496\) 7.25708e6 1.32452
\(497\) 0 0
\(498\) 728605. 0.131649
\(499\) 1.16764e6 + 2.02242e6i 0.209923 + 0.363596i 0.951690 0.307061i \(-0.0993455\pi\)
−0.741767 + 0.670657i \(0.766012\pi\)
\(500\) 7.52830e6 1.30394e7i 1.34670 2.33256i
\(501\) −979135. + 1.69591e6i −0.174280 + 0.301862i
\(502\) −452728. 784147.i −0.0801822 0.138880i
\(503\) 1.08278e7 1.90819 0.954093 0.299510i \(-0.0968233\pi\)
0.954093 + 0.299510i \(0.0968233\pi\)
\(504\) 0 0
\(505\) −1.11273e7 −1.94161
\(506\) 38260.6 + 66269.3i 0.00664317 + 0.0115063i
\(507\) −1.47883e6 + 2.56141e6i −0.255505 + 0.442547i
\(508\) 3.16120e6 5.47536e6i 0.543492 0.941355i
\(509\) 1.58924e6 + 2.75264e6i 0.271890 + 0.470928i 0.969346 0.245700i \(-0.0790178\pi\)
−0.697455 + 0.716628i \(0.745684\pi\)
\(510\) −46835.7 −0.00797356
\(511\) 0 0
\(512\) −3.82859e6 −0.645452
\(513\) −482582. 835856.i −0.0809613 0.140229i
\(514\) −468053. + 810692.i −0.0781425 + 0.135347i
\(515\) 8.20695e6 1.42149e7i 1.36353 2.36170i
\(516\) −841590. 1.45768e6i −0.139148 0.241011i
\(517\) −2.18460e6 −0.359455
\(518\) 0 0
\(519\) −3.79118e6 −0.617812
\(520\) −539282. 934064.i −0.0874596 0.151485i
\(521\) −3.17918e6 + 5.50651e6i −0.513123 + 0.888755i 0.486761 + 0.873535i \(0.338178\pi\)
−0.999884 + 0.0152197i \(0.995155\pi\)
\(522\) 138460. 239819.i 0.0222406 0.0385219i
\(523\) −3.61094e6 6.25433e6i −0.577252 0.999830i −0.995793 0.0916321i \(-0.970792\pi\)
0.418541 0.908198i \(-0.362542\pi\)
\(524\) 1.20697e6 0.192029
\(525\) 0 0
\(526\) −354531. −0.0558714
\(527\) 237644. + 411612.i 0.0372735 + 0.0645597i
\(528\) −2.15964e6 + 3.74061e6i −0.337130 + 0.583926i
\(529\) 3.19927e6 5.54130e6i 0.497063 0.860939i
\(530\) 732691. + 1.26906e6i 0.113300 + 0.196242i
\(531\) −283538. −0.0436390
\(532\) 0 0
\(533\) 863574. 0.131668
\(534\) −401487. 695396.i −0.0609282 0.105531i
\(535\) 4.65343e6 8.05997e6i 0.702892 1.21744i
\(536\) 332645. 576158.i 0.0500114 0.0866223i
\(537\) 15723.3 + 27233.5i 0.00235292 + 0.00407538i
\(538\) 591106. 0.0880461
\(539\) 0 0
\(540\) 2.38308e6 0.351686
\(541\) 4.71583e6 + 8.16805e6i 0.692731 + 1.19985i 0.970940 + 0.239325i \(0.0769260\pi\)
−0.278209 + 0.960521i \(0.589741\pi\)
\(542\) 91985.4 159323.i 0.0134500 0.0232960i
\(543\) −2.67575e6 + 4.63453e6i −0.389444 + 0.674538i
\(544\) −74728.0 129433.i −0.0108264 0.0187520i
\(545\) 1.74630e7 2.51842
\(546\) 0 0
\(547\) 9.91568e6 1.41695 0.708474 0.705737i \(-0.249384\pi\)
0.708474 + 0.705737i \(0.249384\pi\)
\(548\) −3.79197e6 6.56788e6i −0.539403 0.934274i
\(549\) −430615. + 745847.i −0.0609759 + 0.105613i
\(550\) −1.52126e6 + 2.63489e6i −0.214435 + 0.371412i
\(551\) 2.86182e6 + 4.95682e6i 0.401572 + 0.695543i
\(552\) 87701.5 0.0122507
\(553\) 0 0
\(554\) 1.92106e6 0.265929
\(555\) 4.85538e6 + 8.40976e6i 0.669099 + 1.15891i
\(556\) 833188. 1.44312e6i 0.114303 0.197978i
\(557\) −4.82306e6 + 8.35379e6i −0.658696 + 1.14089i 0.322258 + 0.946652i \(0.395558\pi\)
−0.980953 + 0.194243i \(0.937775\pi\)
\(558\) 241018. + 417455.i 0.0327690 + 0.0567576i
\(559\) 1.23123e6 0.166651
\(560\) 0 0
\(561\) −282883. −0.0379490
\(562\) 995245. + 1.72382e6i 0.132920 + 0.230224i
\(563\) 1.54752e6 2.68038e6i 0.205762 0.356390i −0.744613 0.667496i \(-0.767366\pi\)
0.950375 + 0.311106i \(0.100699\pi\)
\(564\) −619769. + 1.07347e6i −0.0820412 + 0.142100i
\(565\) 6.03238e6 + 1.04484e7i 0.795000 + 1.37698i
\(566\) 206396. 0.0270807
\(567\) 0 0
\(568\) 1.94509e6 0.252970
\(569\) 6.15927e6 + 1.06682e7i 0.797533 + 1.38137i 0.921218 + 0.389046i \(0.127195\pi\)
−0.123685 + 0.992322i \(0.539471\pi\)
\(570\) 490895. 850254.i 0.0632850 0.109613i
\(571\) 1.61755e6 2.80168e6i 0.207619 0.359607i −0.743345 0.668908i \(-0.766762\pi\)
0.950964 + 0.309302i \(0.100095\pi\)
\(572\) −1.61253e6 2.79299e6i −0.206072 0.356927i
\(573\) −7.45780e6 −0.948908
\(574\) 0 0
\(575\) −1.50318e6 −0.189601
\(576\) 1.17402e6 + 2.03345e6i 0.147441 + 0.255375i
\(577\) −4.52525e6 + 7.83796e6i −0.565852 + 0.980084i 0.431118 + 0.902296i \(0.358119\pi\)
−0.996970 + 0.0777887i \(0.975214\pi\)
\(578\) −559838. + 969667.i −0.0697016 + 0.120727i
\(579\) 988825. + 1.71269e6i 0.122581 + 0.212316i
\(580\) −1.41322e7 −1.74438
\(581\) 0 0
\(582\) −215897. −0.0264204
\(583\) 4.42538e6 + 7.66499e6i 0.539237 + 0.933986i
\(584\) 786226. 1.36178e6i 0.0953927 0.165225i
\(585\) −871598. + 1.50965e6i −0.105300 + 0.182384i
\(586\) −25705.8 44523.8i −0.00309234 0.00535609i
\(587\) 2.13170e6 0.255347 0.127673 0.991816i \(-0.459249\pi\)
0.127673 + 0.991816i \(0.459249\pi\)
\(588\) 0 0
\(589\) −9.96318e6 −1.18334
\(590\) −144211. 249781.i −0.0170557 0.0295413i
\(591\) 2.14025e6 3.70703e6i 0.252056 0.436573i
\(592\) −4.99326e6 + 8.64858e6i −0.585572 + 1.01424i
\(593\) −3.63467e6 6.29543e6i −0.424451 0.735171i 0.571918 0.820311i \(-0.306200\pi\)
−0.996369 + 0.0851397i \(0.972866\pi\)
\(594\) −286899. −0.0333629
\(595\) 0 0
\(596\) −4.04927e6 −0.466941
\(597\) −2.82400e6 4.89131e6i −0.324286 0.561681i
\(598\) −15879.9 + 27504.8i −0.00181591 + 0.00314525i
\(599\) 1.10282e6 1.91015e6i 0.125585 0.217520i −0.796376 0.604802i \(-0.793252\pi\)
0.921962 + 0.387281i \(0.126586\pi\)
\(600\) 1.74352e6 + 3.01987e6i 0.197720 + 0.342460i
\(601\) 1.00121e7 1.13067 0.565336 0.824860i \(-0.308746\pi\)
0.565336 + 0.824860i \(0.308746\pi\)
\(602\) 0 0
\(603\) −1.07525e6 −0.120425
\(604\) 2.40340e6 + 4.16280e6i 0.268061 + 0.464295i
\(605\) −4.51224e6 + 7.81542e6i −0.501191 + 0.868088i
\(606\) 380048. 658262.i 0.0420394 0.0728144i
\(607\) 3.16069e6 + 5.47448e6i 0.348185 + 0.603075i 0.985927 0.167175i \(-0.0534646\pi\)
−0.637742 + 0.770250i \(0.720131\pi\)
\(608\) 3.13295e6 0.343712
\(609\) 0 0
\(610\) −876065. −0.0953261
\(611\) −453353. 785231.i −0.0491285 0.0850931i
\(612\) −80253.9 + 139004.i −0.00866139 + 0.0150020i
\(613\) −7.15392e6 + 1.23910e7i −0.768941 + 1.33185i 0.169196 + 0.985582i \(0.445883\pi\)
−0.938138 + 0.346263i \(0.887451\pi\)
\(614\) 931565. + 1.61352e6i 0.0997223 + 0.172724i
\(615\) −3.92055e6 −0.417984
\(616\) 0 0
\(617\) 1.73991e7 1.83999 0.919993 0.391936i \(-0.128194\pi\)
0.919993 + 0.391936i \(0.128194\pi\)
\(618\) 560610. + 971004.i 0.0590459 + 0.102270i
\(619\) 4.13368e6 7.15975e6i 0.433621 0.751054i −0.563561 0.826074i \(-0.690569\pi\)
0.997182 + 0.0750208i \(0.0239023\pi\)
\(620\) 1.23000e7 2.13043e7i 1.28507 2.22581i
\(621\) −70872.4 122755.i −0.00737476 0.0127735i
\(622\) −1.67497e6 −0.173592
\(623\) 0 0
\(624\) −1.79270e6 −0.184309
\(625\) −1.29211e7 2.23800e7i −1.32312 2.29172i
\(626\) 74143.4 128420.i 0.00756200 0.0130978i
\(627\) 2.96495e6 5.13545e6i 0.301196 0.521687i
\(628\) 2.37173e6 + 4.10796e6i 0.239975 + 0.415649i
\(629\) −654048. −0.0659148
\(630\) 0 0
\(631\) 2.83238e6 0.283190 0.141595 0.989925i \(-0.454777\pi\)
0.141595 + 0.989925i \(0.454777\pi\)
\(632\) −989596. 1.71403e6i −0.0985520 0.170697i
\(633\) 2.56945e6 4.45041e6i 0.254877 0.441460i
\(634\) −397542. + 688563.i −0.0392790 + 0.0680331i
\(635\) −1.04980e7 1.81831e7i −1.03317 1.78951i
\(636\) 5.02192e6 0.492297
\(637\) 0 0
\(638\) 1.70138e6 0.165481
\(639\) −1.57185e6 2.72252e6i −0.152286 0.263766i
\(640\) −5.13912e6 + 8.90122e6i −0.495951 + 0.859012i
\(641\) 1.78588e6 3.09324e6i 0.171675 0.297350i −0.767330 0.641252i \(-0.778415\pi\)
0.939006 + 0.343902i \(0.111749\pi\)
\(642\) 317872. + 550570.i 0.0304379 + 0.0527199i
\(643\) 5.96911e6 0.569354 0.284677 0.958624i \(-0.408114\pi\)
0.284677 + 0.958624i \(0.408114\pi\)
\(644\) 0 0
\(645\) −5.58966e6 −0.529037
\(646\) 33063.2 + 57267.2i 0.00311719 + 0.00539914i
\(647\) −841379. + 1.45731e6i −0.0790189 + 0.136865i −0.902827 0.430004i \(-0.858512\pi\)
0.823808 + 0.566869i \(0.191845\pi\)
\(648\) −164409. + 284764.i −0.0153811 + 0.0266408i
\(649\) −871021. 1.50865e6i −0.0811739 0.140597i
\(650\) −1.26278e6 −0.117232
\(651\) 0 0
\(652\) 1.03275e6 0.0951427
\(653\) −8.51526e6 1.47489e7i −0.781475 1.35355i −0.931082 0.364809i \(-0.881134\pi\)
0.149608 0.988745i \(-0.452199\pi\)
\(654\) −596441. + 1.03307e6i −0.0545285 + 0.0944461i
\(655\) 2.00411e6 3.47121e6i 0.182523 0.316139i
\(656\) −2.01594e6 3.49172e6i −0.182902 0.316796i
\(657\) −2.54143e6 −0.229702
\(658\) 0 0
\(659\) −1.99303e7 −1.78772 −0.893862 0.448342i \(-0.852015\pi\)
−0.893862 + 0.448342i \(0.852015\pi\)
\(660\) 7.32077e6 + 1.26799e7i 0.654179 + 1.13307i
\(661\) 4.77867e6 8.27691e6i 0.425406 0.736825i −0.571052 0.820914i \(-0.693465\pi\)
0.996458 + 0.0840888i \(0.0267979\pi\)
\(662\) 664213. 1.15045e6i 0.0589064 0.102029i
\(663\) −58704.7 101680.i −0.00518668 0.00898359i
\(664\) 5.13056e6 0.451591
\(665\) 0 0
\(666\) −663333. −0.0579490
\(667\) 420290. + 727963.i 0.0365792 + 0.0633570i
\(668\) −3.41333e6 + 5.91207e6i −0.295963 + 0.512623i
\(669\) −19049.0 + 32993.8i −0.00164553 + 0.00285015i
\(670\) −546889. 947239.i −0.0470665 0.0815216i
\(671\) −5.29135e6 −0.453691
\(672\) 0 0
\(673\) 1.80397e7 1.53530 0.767648 0.640872i \(-0.221427\pi\)
0.767648 + 0.640872i \(0.221427\pi\)
\(674\) −393440. 681457.i −0.0333602 0.0577815i
\(675\) 2.81792e6 4.88077e6i 0.238050 0.412315i
\(676\) −5.15531e6 + 8.92927e6i −0.433899 + 0.751535i
\(677\) −7.23704e6 1.25349e7i −0.606861 1.05111i −0.991754 0.128153i \(-0.959095\pi\)
0.384894 0.922961i \(-0.374238\pi\)
\(678\) −824133. −0.0688530
\(679\) 0 0
\(680\) −329800. −0.0273513
\(681\) −5.08438e6 8.80641e6i −0.420117 0.727664i
\(682\) −1.48080e6 + 2.56482e6i −0.121909 + 0.211152i
\(683\) −1.34392e6 + 2.32774e6i −0.110236 + 0.190934i −0.915865 0.401486i \(-0.868494\pi\)
0.805629 + 0.592420i \(0.201827\pi\)
\(684\) −1.68231e6 2.91385e6i −0.137489 0.238137i
\(685\) −2.51854e7 −2.05080
\(686\) 0 0
\(687\) 7.24179e6 0.585402
\(688\) −2.87420e6 4.97826e6i −0.231497 0.400965i
\(689\) −1.83674e6 + 3.18132e6i −0.147400 + 0.255305i
\(690\) 72093.3 124869.i 0.00576464 0.00998464i
\(691\) 2.33814e6 + 4.04977e6i 0.186284 + 0.322653i 0.944008 0.329922i \(-0.107022\pi\)
−0.757725 + 0.652574i \(0.773689\pi\)
\(692\) −1.32163e7 −1.04917
\(693\) 0 0
\(694\) −3.20802e6 −0.252836
\(695\) −2.76693e6 4.79246e6i −0.217288 0.376354i
\(696\) 974982. 1.68872e6i 0.0762910 0.132140i
\(697\) 132030. 228683.i 0.0102942 0.0178301i
\(698\) −1.13165e6 1.96008e6i −0.0879172 0.152277i
\(699\) −1.05235e7 −0.814639
\(700\) 0 0
\(701\) 6.34801e6 0.487913 0.243957 0.969786i \(-0.421555\pi\)
0.243957 + 0.969786i \(0.421555\pi\)
\(702\) −59538.1 103123.i −0.00455987 0.00789792i
\(703\) 6.85520e6 1.18736e7i 0.523157 0.906135i
\(704\) −7.21309e6 + 1.24934e7i −0.548516 + 0.950058i
\(705\) 2.05818e6 + 3.56488e6i 0.155959 + 0.270130i
\(706\) 658492. 0.0497208
\(707\) 0 0
\(708\) −988433. −0.0741078
\(709\) 3.20526e6 + 5.55168e6i 0.239468 + 0.414771i 0.960562 0.278067i \(-0.0896936\pi\)
−0.721094 + 0.692838i \(0.756360\pi\)
\(710\) 1.59893e6 2.76942e6i 0.119037 0.206178i
\(711\) −1.59940e6 + 2.77025e6i −0.118655 + 0.205516i
\(712\) −2.82712e6 4.89672e6i −0.208999 0.361997i
\(713\) −1.46320e6 −0.107790
\(714\) 0 0
\(715\) −1.07101e7 −0.783481
\(716\) 54812.4 + 94937.9i 0.00399573 + 0.00692081i
\(717\) −7.67493e6 + 1.32934e7i −0.557541 + 0.965689i
\(718\) −1.06660e6 + 1.84741e6i −0.0772131 + 0.133737i
\(719\) 3.67253e6 + 6.36100e6i 0.264937 + 0.458885i 0.967547 0.252691i \(-0.0813155\pi\)
−0.702610 + 0.711575i \(0.747982\pi\)
\(720\) 8.13870e6 0.585092
\(721\) 0 0
\(722\) 571944. 0.0408329
\(723\) −4.28038e6 7.41384e6i −0.304535 0.527470i
\(724\) −9.32784e6 + 1.61563e7i −0.661355 + 1.14550i
\(725\) −1.67109e7 + 2.89441e7i −1.18074 + 2.04510i
\(726\) −308227. 533865.i −0.0217035 0.0375915i
\(727\) −1.57839e7 −1.10759 −0.553793 0.832655i \(-0.686820\pi\)
−0.553793 + 0.832655i \(0.686820\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −1.29260e6 2.23885e6i −0.0897755 0.155496i
\(731\) 188240. 326041.i 0.0130292 0.0225673i
\(732\) −1.50115e6 + 2.60007e6i −0.103549 + 0.179353i
\(733\) 6.76835e6 + 1.17231e7i 0.465289 + 0.805905i 0.999215 0.0396269i \(-0.0126170\pi\)
−0.533925 + 0.845532i \(0.679284\pi\)
\(734\) 1.15048e6 0.0788205
\(735\) 0 0
\(736\) 460109. 0.0313088
\(737\) −3.30315e6 5.72123e6i −0.224006 0.387990i
\(738\) 133905. 231930.i 0.00905013 0.0156753i
\(739\) 3.66851e6 6.35405e6i 0.247103 0.427996i −0.715617 0.698492i \(-0.753855\pi\)
0.962721 + 0.270497i \(0.0871879\pi\)
\(740\) 1.69262e7 + 2.93170e7i 1.13626 + 1.96807i
\(741\) 2.46118e6 0.164664
\(742\) 0 0
\(743\) 1.20844e7 0.803068 0.401534 0.915844i \(-0.368477\pi\)
0.401534 + 0.915844i \(0.368477\pi\)
\(744\) 1.69716e6 + 2.93956e6i 0.112406 + 0.194693i
\(745\) −6.72360e6 + 1.16456e7i −0.443824 + 0.768726i
\(746\) −809343. + 1.40182e6i −0.0532459 + 0.0922245i
\(747\) −4.14606e6 7.18118e6i −0.271853 0.470863i
\(748\) −986151. −0.0644450
\(749\) 0 0
\(750\) 3.41555e6 0.221721
\(751\) −4.39088e6 7.60523e6i −0.284087 0.492054i 0.688300 0.725426i \(-0.258357\pi\)
−0.972387 + 0.233372i \(0.925024\pi\)
\(752\) −2.11663e6 + 3.66612e6i −0.136490 + 0.236408i
\(753\) −5.15241e6 + 8.92423e6i −0.331148 + 0.573566i
\(754\) 353075. + 611543.i 0.0226172 + 0.0391741i
\(755\) 1.59628e7 1.01916
\(756\) 0 0
\(757\) 465874. 0.0295480 0.0147740 0.999891i \(-0.495297\pi\)
0.0147740 + 0.999891i \(0.495297\pi\)
\(758\) −164842. 285516.i −0.0104207 0.0180491i
\(759\) 435436. 754198.i 0.0274360 0.0475205i
\(760\) 3.45670e6 5.98717e6i 0.217084 0.376000i
\(761\) 7.49891e6 + 1.29885e7i 0.469393 + 0.813013i 0.999388 0.0349882i \(-0.0111394\pi\)
−0.529995 + 0.848001i \(0.677806\pi\)
\(762\) 1.43422e6 0.0894804
\(763\) 0 0
\(764\) −2.59984e7 −1.61144
\(765\) 266514. + 461616.i 0.0164652 + 0.0285186i
\(766\) 1.53268e6 2.65468e6i 0.0943800 0.163471i
\(767\) 361513. 626159.i 0.0221889 0.0384323i
\(768\) 3.82323e6 + 6.62203e6i 0.233898 + 0.405124i
\(769\) 1.85606e7 1.131