Properties

Label 63.6.e.e.46.2
Level $63$
Weight $6$
Character 63.46
Analytic conductor $10.104$
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] = [63,6,Mod(37,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), 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: \(10.1041806482\)
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: \(\Z[a_1, \ldots, a_{7}]\)
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 46.2
Root \(0.895402 + 1.55088i\) of defining polynomial
Character \(\chi\) \(=\) 63.46
Dual form 63.6.e.e.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.395402 - 0.684857i) q^{2} +(15.6873 - 27.1712i) q^{4} +(-52.0958 - 90.2327i) q^{5} +(-7.12980 + 129.446i) q^{7} -50.1170 q^{8} +O(q^{10})\) \(q+(-0.395402 - 0.684857i) q^{2} +(15.6873 - 27.1712i) q^{4} +(-52.0958 - 90.2327i) q^{5} +(-7.12980 + 129.446i) q^{7} -50.1170 q^{8} +(-41.1977 + 71.3564i) q^{10} +(-248.830 + 430.986i) q^{11} -206.551 q^{13} +(91.4709 - 46.3002i) q^{14} +(-482.178 - 835.156i) q^{16} +(31.5793 - 54.6969i) q^{17} +(-661.977 - 1146.58i) q^{19} -3268.98 q^{20} +393.552 q^{22} +(-97.2187 - 168.388i) q^{23} +(-3865.45 + 6695.16i) q^{25} +(81.6709 + 141.458i) q^{26} +(3405.35 + 2224.38i) q^{28} -4323.14 q^{29} +(3762.66 - 6517.11i) q^{31} +(-1183.18 + 2049.33i) q^{32} -49.9461 q^{34} +(12051.7 - 6100.24i) q^{35} +(-5177.82 - 8968.25i) q^{37} +(-523.495 + 906.720i) q^{38} +(2610.89 + 4522.19i) q^{40} +4180.92 q^{41} +5960.87 q^{43} +(7806.94 + 13522.0i) q^{44} +(-76.8810 + 133.162i) q^{46} +(-2194.87 - 3801.62i) q^{47} +(-16705.3 - 1845.84i) q^{49} +6113.64 q^{50} +(-3240.24 + 5612.25i) q^{52} +(8892.39 - 15402.1i) q^{53} +51852.0 q^{55} +(357.324 - 6487.42i) q^{56} +(1709.38 + 2960.73i) q^{58} +(1750.23 - 3031.49i) q^{59} +(5316.23 + 9207.98i) q^{61} -5951.06 q^{62} -28988.0 q^{64} +(10760.5 + 18637.7i) q^{65} +(6637.37 - 11496.3i) q^{67} +(-990.789 - 1716.10i) q^{68} +(-8943.05 - 5841.61i) q^{70} -38811.1 q^{71} +(-15687.8 + 27172.1i) q^{73} +(-4094.65 + 7092.14i) q^{74} -41538.6 q^{76} +(-54015.1 - 35282.8i) q^{77} +(-19745.7 - 34200.6i) q^{79} +(-50238.9 + 87016.3i) q^{80} +(-1653.14 - 2863.33i) q^{82} +102372. q^{83} -6580.60 q^{85} +(-2356.94 - 4082.34i) q^{86} +(12470.6 - 21599.7i) q^{88} +(-56410.5 - 97705.8i) q^{89} +(1472.67 - 26737.2i) q^{91} -6100.40 q^{92} +(-1735.71 + 3006.34i) q^{94} +(-68972.6 + 119464. i) q^{95} +30334.3 q^{97} +(5341.19 + 12170.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8} - 283 q^{10} + 402 q^{11} + 924 q^{13} - 1926 q^{14} - 3273 q^{16} + 276 q^{17} - 510 q^{19} - 9438 q^{20} + 2750 q^{22} + 6900 q^{23} - 2814 q^{25} - 15138 q^{26} - 26221 q^{28} - 1080 q^{29} + 6410 q^{31} + 15519 q^{32} + 42288 q^{34} + 33108 q^{35} - 15250 q^{37} - 41250 q^{38} + 8547 q^{40} - 8616 q^{41} + 58396 q^{43} + 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 64252 q^{49} + 14604 q^{50} + 47476 q^{52} + 13692 q^{53} + 146248 q^{55} + 15921 q^{56} - 52309 q^{58} + 34830 q^{59} + 5364 q^{61} - 32058 q^{62} - 146974 q^{64} + 66864 q^{65} + 5994 q^{67} - 58272 q^{68} - 4307 q^{70} - 178536 q^{71} - 59638 q^{73} - 185442 q^{74} + 42616 q^{76} + 75660 q^{77} + 44062 q^{79} - 33381 q^{80} - 57596 q^{82} + 416892 q^{83} + 72648 q^{85} - 136968 q^{86} - 87597 q^{88} - 77520 q^{89} + 104722 q^{91} - 316512 q^{92} + 73722 q^{94} - 221376 q^{95} - 377260 q^{97} - 382479 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.828958 0.559310i \(-0.188934\pi\)
−0.898856 + 0.438244i \(0.855601\pi\)
\(3\) 0 0
\(4\) 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 \(-0.548533\pi\)
\(6\) 0 0
\(7\) −7.12980 + 129.446i −0.0549961 + 0.998487i
\(8\) −50.1170 −0.276860
\(9\) 0 0
\(10\) −41.1977 + 71.3564i −0.130278 + 0.225649i
\(11\) −248.830 + 430.986i −0.620041 + 1.07394i 0.369436 + 0.929256i \(0.379551\pi\)
−0.989477 + 0.144687i \(0.953782\pi\)
\(12\) 0 0
\(13\) −206.551 −0.338977 −0.169488 0.985532i \(-0.554211\pi\)
−0.169488 + 0.985532i \(0.554211\pi\)
\(14\) 91.4709 46.3002i 0.124728 0.0631340i
\(15\) 0 0
\(16\) −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 \(0.158230\pi\)
\(18\) 0 0
\(19\) −661.977 1146.58i −0.420687 0.728651i 0.575320 0.817929i \(-0.304878\pi\)
−0.996007 + 0.0892772i \(0.971544\pi\)
\(20\) −3268.98 −1.82741
\(21\) 0 0
\(22\) 393.552 0.173358
\(23\) −97.2187 168.388i −0.0383204 0.0663729i 0.846229 0.532819i \(-0.178867\pi\)
−0.884550 + 0.466446i \(0.845534\pi\)
\(24\) 0 0
\(25\) −3865.45 + 6695.16i −1.23695 + 2.14245i
\(26\) 81.6709 + 141.458i 0.0236938 + 0.0410388i
\(27\) 0 0
\(28\) 3405.35 + 2224.38i 0.820855 + 0.536184i
\(29\) −4323.14 −0.954562 −0.477281 0.878751i \(-0.658378\pi\)
−0.477281 + 0.878751i \(0.658378\pi\)
\(30\) 0 0
\(31\) 3762.66 6517.11i 0.703219 1.21801i −0.264112 0.964492i \(-0.585079\pi\)
0.967331 0.253518i \(-0.0815879\pi\)
\(32\) −1183.18 + 2049.33i −0.204256 + 0.353783i
\(33\) 0 0
\(34\) −49.9461 −0.00740977
\(35\) 12051.7 6100.24i 1.66294 0.841738i
\(36\) 0 0
\(37\) −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
\(39\) 0 0
\(40\) 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
\(45\) 0 0
\(46\) −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 \(0.879630\pi\)
\(48\) 0 0
\(49\) −16705.3 1845.84i −0.993951 0.109826i
\(50\) 6113.64 0.345840
\(51\) 0 0
\(52\) −3240.24 + 5612.25i −0.166176 + 0.287825i
\(53\) 8892.39 15402.1i 0.434839 0.753164i −0.562443 0.826836i \(-0.690138\pi\)
0.997283 + 0.0736720i \(0.0234718\pi\)
\(54\) 0 0
\(55\) 51852.0 2.31131
\(56\) 357.324 6487.42i 0.0152262 0.276441i
\(57\) 0 0
\(58\) 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 \(0.145816\pi\)
\(60\) 0 0
\(61\) 5316.23 + 9207.98i 0.182928 + 0.316840i 0.942876 0.333143i \(-0.108109\pi\)
−0.759949 + 0.649983i \(0.774776\pi\)
\(62\) −5951.06 −0.196614
\(63\) 0 0
\(64\) −28988.0 −0.884645
\(65\) 10760.5 + 18637.7i 0.315899 + 0.547153i
\(66\) 0 0
\(67\) 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
\(69\) 0 0
\(70\) −8943.05 5841.61i −0.218143 0.142491i
\(71\) −38811.1 −0.913713 −0.456857 0.889540i \(-0.651025\pi\)
−0.456857 + 0.889540i \(0.651025\pi\)
\(72\) 0 0
\(73\) −15687.8 + 27172.1i −0.344552 + 0.596782i −0.985272 0.170992i \(-0.945303\pi\)
0.640720 + 0.767775i \(0.278636\pi\)
\(74\) −4094.65 + 7092.14i −0.0869235 + 0.150556i
\(75\) 0 0
\(76\) −41538.6 −0.824931
\(77\) −54015.1 35282.8i −1.03822 0.678166i
\(78\) 0 0
\(79\) −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
\(81\) 0 0
\(82\) −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
\(87\) 0 0
\(88\) 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 \(-0.438977\pi\)
\(90\) 0 0
\(91\) 1472.67 26737.2i 0.0186424 0.338464i
\(92\) −6100.40 −0.0751430
\(93\) 0 0
\(94\) −1735.71 + 3006.34i −0.0202609 + 0.0350929i
\(95\) −68972.6 + 119464.i −0.784092 + 1.35809i
\(96\) 0 0
\(97\) 30334.3 0.327345 0.163672 0.986515i \(-0.447666\pi\)
0.163672 + 0.986515i \(0.447666\pi\)
\(98\) 5341.19 + 12170.6i 0.0561789 + 0.128011i
\(99\) 0 0
\(100\) 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 \(-0.00772291\pi\)
\(102\) 0 0
\(103\) −78767.8 136430.i −0.731570 1.26712i −0.956212 0.292674i \(-0.905455\pi\)
0.224643 0.974441i \(-0.427879\pi\)
\(104\) 10351.7 0.0938490
\(105\) 0 0
\(106\) −14064.3 −0.121578
\(107\) −44662.2 77357.1i −0.377121 0.653192i 0.613521 0.789678i \(-0.289752\pi\)
−0.990642 + 0.136486i \(0.956419\pi\)
\(108\) 0 0
\(109\) −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
\(111\) 0 0
\(112\) 111545. 56461.3i 0.840244 0.425310i
\(113\) 115794. 0.853079 0.426539 0.904469i \(-0.359733\pi\)
0.426539 + 0.904469i \(0.359733\pi\)
\(114\) 0 0
\(115\) −10129.4 + 17544.6i −0.0714230 + 0.123708i
\(116\) −67818.4 + 117465.i −0.467954 + 0.810519i
\(117\) 0 0
\(118\) −2768.19 −0.0183017
\(119\) 6855.13 + 4477.78i 0.0443760 + 0.0289865i
\(120\) 0 0
\(121\) −43307.1 75010.0i −0.268903 0.465753i
\(122\) 4204.10 7281.72i 0.0255725 0.0442929i
\(123\) 0 0
\(124\) −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
\(129\) 0 0
\(130\) 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 \(0.802112\pi\)
\(132\) 0 0
\(133\) 153139. 77515.2i 0.750685 0.379977i
\(134\) −10497.7 −0.0505049
\(135\) 0 0
\(136\) −1582.66 + 2741.25i −0.00733736 + 0.0127087i
\(137\) −120861. + 209337.i −0.550155 + 0.952896i 0.448108 + 0.893979i \(0.352098\pi\)
−0.998263 + 0.0589167i \(0.981235\pi\)
\(138\) 0 0
\(139\) −53112.2 −0.233162 −0.116581 0.993181i \(-0.537193\pi\)
−0.116581 + 0.993181i \(0.537193\pi\)
\(140\) 23307.1 423155.i 0.100501 1.82465i
\(141\) 0 0
\(142\) 15346.0 + 26580.1i 0.0638667 + 0.110620i
\(143\) 51396.1 89020.7i 0.210180 0.364042i
\(144\) 0 0
\(145\) 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 0.960176 0.279396i \(-0.0901342\pi\)
−0.722052 + 0.691839i \(0.756801\pi\)
\(150\) 0 0
\(151\) −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
\(153\) 0 0
\(154\) −2805.94 + 50943.5i −0.00953405 + 0.173096i
\(155\) −784075. −2.62137
\(156\) 0 0
\(157\) 75593.9 130932.i 0.244758 0.423934i −0.717305 0.696759i \(-0.754625\pi\)
0.962064 + 0.272825i \(0.0879581\pi\)
\(158\) −15615.0 + 27046.0i −0.0497622 + 0.0861907i
\(159\) 0 0
\(160\) 246555. 0.761402
\(161\) 22490.2 11384.0i 0.0683799 0.0346122i
\(162\) 0 0
\(163\) 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
\(165\) 0 0
\(166\) −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
\(171\) 0 0
\(172\) 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 \(-0.346370\pi\)
\(174\) 0 0
\(175\) −839100. 548101.i −2.07118 1.35290i
\(176\) 479921. 1.16785
\(177\) 0 0
\(178\) −44609.7 + 77266.3i −0.105531 + 0.182785i
\(179\) 1747.03 3025.94i 0.00407538 0.00705876i −0.863981 0.503525i \(-0.832036\pi\)
0.868056 + 0.496466i \(0.165369\pi\)
\(180\) 0 0
\(181\) 594611. 1.34908 0.674538 0.738240i \(-0.264343\pi\)
0.674538 + 0.738240i \(0.264343\pi\)
\(182\) −18893.4 + 9563.37i −0.0422798 + 0.0214009i
\(183\) 0 0
\(184\) 4872.30 + 8439.08i 0.0106094 + 0.0183760i
\(185\) −539486. + 934418.i −1.15891 + 2.00730i
\(186\) 0 0
\(187\) 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 \(0.140351\pi\)
−0.0825782 + 0.996585i \(0.526315\pi\)
\(192\) 0 0
\(193\) −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
\(195\) 0 0
\(196\) −312216. + 424948.i −0.580516 + 0.790125i
\(197\) −475612. −0.873146 −0.436573 0.899669i \(-0.643808\pi\)
−0.436573 + 0.899669i \(0.643808\pi\)
\(198\) 0 0
\(199\) −313778. + 543479.i −0.561681 + 0.972859i 0.435669 + 0.900107i \(0.356512\pi\)
−0.997350 + 0.0727525i \(0.976822\pi\)
\(200\) 193725. 335541.i 0.342460 0.593159i
\(201\) 0 0
\(202\) −84455.1 −0.145629
\(203\) 30823.1 559611.i 0.0524972 0.953117i
\(204\) 0 0
\(205\) −217808. 377255.i −0.361984 0.626975i
\(206\) −62290.0 + 107889.i −0.102270 + 0.177138i
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) −35319.1 + 61174.4i −0.0527199 + 0.0913136i
\(215\) −310536. 537865.i −0.458159 0.793555i
\(216\) 0 0
\(217\) 816785. + 533525.i 1.17749 + 0.769140i
\(218\) 132543. 0.188892
\(219\) 0 0
\(220\) 813419. 1.40888e6i 1.13307 1.96254i
\(221\) −6522.75 + 11297.7i −0.00898359 + 0.0155600i
\(222\) 0 0
\(223\) 4233.11 0.00570029 0.00285015 0.999996i \(-0.499093\pi\)
0.00285015 + 0.999996i \(0.499093\pi\)
\(224\) −256841. 167769.i −0.342014 0.223404i
\(225\) 0 0
\(226\) −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 \(-0.0927274\pi\)
\(228\) 0 0
\(229\) −402322. 696842.i −0.506973 0.878103i −0.999967 0.00807048i \(-0.997431\pi\)
0.492994 0.870032i \(-0.335902\pi\)
\(230\) 16020.7 0.0199693
\(231\) 0 0
\(232\) 216663. 0.264280
\(233\) 584636. + 1.01262e6i 0.705498 + 1.22196i 0.966511 + 0.256624i \(0.0826101\pi\)
−0.261013 + 0.965335i \(0.584057\pi\)
\(234\) 0 0
\(235\) −228687. + 396098.i −0.270130 + 0.467878i
\(236\) −54912.9 95112.0i −0.0641792 0.111162i
\(237\) 0 0
\(238\) 356.106 6465.31i 0.000407508 0.00739855i
\(239\) 1.70554e6 1.93138 0.965689 0.259700i \(-0.0836238\pi\)
0.965689 + 0.259700i \(0.0836238\pi\)
\(240\) 0 0
\(241\) −475598. + 823760.i −0.527470 + 0.913604i 0.472018 + 0.881589i \(0.343526\pi\)
−0.999487 + 0.0320153i \(0.989807\pi\)
\(242\) −34247.4 + 59318.3i −0.0375915 + 0.0651104i
\(243\) 0 0
\(244\) 333590. 0.358705
\(245\) 703723. + 1.60353e6i 0.749008 + 1.70672i
\(246\) 0 0
\(247\) 136732. + 236827.i 0.142603 + 0.246996i
\(248\) −188573. + 326618.i −0.194693 + 0.337218i
\(249\) 0 0
\(250\) −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
\(255\) 0 0
\(256\) −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 \(0.644528\pi\)
\(258\) 0 0
\(259\) 1.19782e6 606305.i 1.10954 0.561619i
\(260\) 675211. 0.619450
\(261\) 0 0
\(262\) 15211.0 26346.2i 0.0136900 0.0237118i
\(263\) 224158. 388253.i 0.199832 0.346119i −0.748642 0.662975i \(-0.769294\pi\)
0.948474 + 0.316856i \(0.102627\pi\)
\(264\) 0 0
\(265\) −1.85303e6 −1.62094
\(266\) −113639. 74228.9i −0.0984740 0.0643234i
\(267\) 0 0
\(268\) −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 \(0.0646925\pi\)
\(270\) 0 0
\(271\) 116319. + 201470.i 0.0962114 + 0.166643i 0.910114 0.414359i \(-0.135994\pi\)
−0.813902 + 0.581002i \(0.802661\pi\)
\(272\) −60907.3 −0.0499169
\(273\) 0 0
\(274\) 191155. 0.153819
\(275\) −1.92368e6 3.33191e6i −1.53391 2.65682i
\(276\) 0 0
\(277\) 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
\(279\) 0 0
\(280\) −603992. + 305725.i −0.460401 + 0.233043i
\(281\) −2.51704e6 −1.90163 −0.950813 0.309766i \(-0.899749\pi\)
−0.950813 + 0.309766i \(0.899749\pi\)
\(282\) 0 0
\(283\) −130497. + 226028.i −0.0968579 + 0.167763i −0.910382 0.413768i \(-0.864213\pi\)
0.813525 + 0.581530i \(0.197546\pi\)
\(284\) −608842. + 1.05454e6i −0.447928 + 0.775835i
\(285\) 0 0
\(286\) −81288.6 −0.0587645
\(287\) −29809.1 + 541201.i −0.0213621 + 0.387841i
\(288\) 0 0
\(289\) 707934. + 1.22618e6i 0.498595 + 0.863592i
\(290\) 178103. 308484.i 0.124359 0.215396i
\(291\) 0 0
\(292\) 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
\(297\) 0 0
\(298\) 51031.5 88389.1i 0.0332887 0.0576578i
\(299\) 20080.6 + 34780.7i 0.0129897 + 0.0224989i
\(300\) 0 0
\(301\) −42499.8 + 771608.i −0.0270377 + 0.490886i
\(302\) 121156. 0.0764414
\(303\) 0 0
\(304\) −638381. + 1.10571e6i −0.396183 + 0.686210i
\(305\) 553907. 959395.i 0.340947 0.590538i
\(306\) 0 0
\(307\) −2.35599e6 −1.42668 −0.713342 0.700816i \(-0.752819\pi\)
−0.713342 + 0.700816i \(0.752819\pi\)
\(308\) −1.80603e6 + 914165.i −1.08480 + 0.549096i
\(309\) 0 0
\(310\) 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 \(0.953443\pi\)
\(312\) 0 0
\(313\) 93756.8 + 162392.i 0.0540931 + 0.0936920i 0.891804 0.452422i \(-0.149440\pi\)
−0.837711 + 0.546114i \(0.816107\pi\)
\(314\) −119560. −0.0684324
\(315\) 0 0
\(316\) −1.23903e6 −0.698014
\(317\) −502705. 870711.i −0.280974 0.486661i 0.690651 0.723188i \(-0.257324\pi\)
−0.971625 + 0.236527i \(0.923991\pi\)
\(318\) 0 0
\(319\) 1.07573e6 1.86321e6i 0.591868 1.02515i
\(320\) 1.51016e6 + 2.61567e6i 0.824417 + 1.42793i
\(321\) 0 0
\(322\) −16689.1 10901.3i −0.00897000 0.00585922i
\(323\) −83619.1 −0.0445964
\(324\) 0 0
\(325\) 798415. 1.38290e6i 0.419296 0.726241i
\(326\) 13015.3 22543.2i 0.00678284 0.0117482i
\(327\) 0 0
\(328\) −209535. −0.107540
\(329\) 507753. 257011.i 0.258620 0.130907i
\(330\) 0 0
\(331\) −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
\(333\) 0 0
\(334\) 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
\(339\) 0 0
\(340\) −103232. + 178803.i −0.0484303 + 0.0838837i
\(341\) 1.87252e6 + 3.24330e6i 0.872049 + 1.51043i
\(342\) 0 0
\(343\) 358042. 2.14927e6i 0.164323 0.986407i
\(344\) −298741. −0.136113
\(345\) 0 0
\(346\) −166560. + 288491.i −0.0747965 + 0.129551i
\(347\) 2.02833e6 3.51317e6i 0.904304 1.56630i 0.0824546 0.996595i \(-0.473724\pi\)
0.821849 0.569705i \(-0.192943\pi\)
\(348\) 0 0
\(349\) 2.86202e6 1.25779 0.628897 0.777488i \(-0.283507\pi\)
0.628897 + 0.777488i \(0.283507\pi\)
\(350\) −43589.0 + 791384.i −0.0190198 + 0.345316i
\(351\) 0 0
\(352\) −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 \(0.109758\pi\)
\(354\) 0 0
\(355\) 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 \(-0.980407\pi\)
0.445779 0.895143i \(-0.352927\pi\)
\(360\) 0 0
\(361\) 361621. 626346.i 0.146045 0.252957i
\(362\) −235110. 407223.i −0.0942976 0.163328i
\(363\) 0 0
\(364\) −703379. 459449.i −0.278251 0.181754i
\(365\) 3.26908e6 1.28438
\(366\) 0 0
\(367\) −727411. + 1.25991e6i −0.281913 + 0.488287i −0.971856 0.235576i \(-0.924302\pi\)
0.689943 + 0.723864i \(0.257636\pi\)
\(368\) −93753.3 + 162386.i −0.0360884 + 0.0625069i
\(369\) 0 0
\(370\) 853257. 0.324023
\(371\) 1.93033e6 + 1.26089e6i 0.728110 + 0.475602i
\(372\) 0 0
\(373\) 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
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) 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 \(-0.402578\pi\)
\(384\) 0 0
\(385\) −369694. + 6.71201e6i −0.127113 + 2.30782i
\(386\) 173771. 0.0593619
\(387\) 0 0
\(388\) 475864. 824221.i 0.160474 0.277949i
\(389\) 1.41901e6 2.45780e6i 0.475458 0.823517i −0.524147 0.851628i \(-0.675616\pi\)
0.999605 + 0.0281111i \(0.00894921\pi\)
\(390\) 0 0
\(391\) −12280.4 −0.00406228
\(392\) 837221. + 92508.0i 0.275185 + 0.0304063i
\(393\) 0 0
\(394\) 188058. + 325726.i 0.0610311 + 0.105709i
\(395\) −2.05734e6 + 3.56342e6i −0.663458 + 1.14914i
\(396\) 0 0
\(397\) −2.17133e6 3.76085e6i −0.691432 1.19760i −0.971369 0.237577i \(-0.923647\pi\)
0.279937 0.960018i \(-0.409686\pi\)
\(398\) 496274. 0.157041
\(399\) 0 0
\(400\) 7.45534e6 2.32979
\(401\) 1.70152e6 + 2.94712e6i 0.528417 + 0.915244i 0.999451 + 0.0331296i \(0.0105474\pi\)
−0.471034 + 0.882115i \(0.656119\pi\)
\(402\) 0 0
\(403\) −777182. + 1.34612e6i −0.238375 + 0.412877i
\(404\) −1.67535e6 2.90179e6i −0.510683 0.884529i
\(405\) 0 0
\(406\) −395441. + 200162.i −0.119060 + 0.0602653i
\(407\) 5.15359e6 1.54214
\(408\) 0 0
\(409\) 2.64716e6 4.58501e6i 0.782477 1.35529i −0.148018 0.988985i \(-0.547289\pi\)
0.930495 0.366305i \(-0.119377\pi\)
\(410\) −172244. + 298335.i −0.0506039 + 0.0876486i
\(411\) 0 0
\(412\) −4.94262e6 −1.43455
\(413\) 379935. + 248174.i 0.109606 + 0.0715947i
\(414\) 0 0
\(415\) −5.33315e6 9.23728e6i −1.52007 2.63284i
\(416\) 244387. 423291.i 0.0692382 0.119924i
\(417\) 0 0
\(418\) −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
\(423\) 0 0
\(424\) −445660. + 771905.i −0.120390 + 0.208521i
\(425\) 244137. + 422857.i 0.0655633 + 0.113559i
\(426\) 0 0
\(427\) −1.22984e6 + 622512.i −0.326421 + 0.165226i
\(428\) −2.80252e6 −0.739501
\(429\) 0 0
\(430\) −245574. + 425346.i −0.0640488 + 0.110936i
\(431\) −1.21432e6 + 2.10326e6i −0.314876 + 0.545380i −0.979411 0.201876i \(-0.935296\pi\)
0.664535 + 0.747257i \(0.268629\pi\)
\(432\) 0 0
\(433\) 956219. 0.245097 0.122548 0.992463i \(-0.460893\pi\)
0.122548 + 0.992463i \(0.460893\pi\)
\(434\) 42429.8 770338.i 0.0108130 0.196317i
\(435\) 0 0
\(436\) 2.62927e6 + 4.55402e6i 0.662397 + 1.14730i
\(437\) −128713. + 222938.i −0.0322418 + 0.0558444i
\(438\) 0 0
\(439\) −1.32102e6 2.28808e6i −0.327152 0.566644i 0.654794 0.755808i \(-0.272756\pi\)
−0.981946 + 0.189164i \(0.939422\pi\)
\(440\) −2.59867e6 −0.639910
\(441\) 0 0
\(442\) 10316.4 0.00251174
\(443\) −1.71983e6 2.97883e6i −0.416366 0.721168i 0.579205 0.815182i \(-0.303363\pi\)
−0.995571 + 0.0940147i \(0.970030\pi\)
\(444\) 0 0
\(445\) −5.87750e6 + 1.01801e7i −1.40700 + 2.43699i
\(446\) −1673.78 2899.07i −0.000398439 0.000690116i
\(447\) 0 0
\(448\) 206679. 3.75237e6i 0.0486520 0.883306i
\(449\) −4.39903e6 −1.02977 −0.514886 0.857259i \(-0.672166\pi\)
−0.514886 + 0.857259i \(0.672166\pi\)
\(450\) 0 0
\(451\) −1.04034e6 + 1.80192e6i −0.240842 + 0.417151i
\(452\) 1.81649e6 3.14626e6i 0.418204 0.724350i
\(453\) 0 0
\(454\) −893501. −0.203449
\(455\) −2.48929e6 + 1.26001e6i −0.563698 + 0.285329i
\(456\) 0 0
\(457\) 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
\(459\) 0 0
\(460\) 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
\(465\) 0 0
\(466\) 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 \(0.869452\pi\)
\(468\) 0 0
\(469\) 1.44082e6 + 941145.i 0.302466 + 0.197572i
\(470\) 361694. 0.0755260
\(471\) 0 0
\(472\) −87716.4 + 151929.i −0.0181228 + 0.0313896i
\(473\) −1.48324e6 + 2.56905e6i −0.304831 + 0.527983i
\(474\) 0 0
\(475\) 1.02354e7 2.08147
\(476\) 229205. 116018.i 0.0463668 0.0234697i
\(477\) 0 0
\(478\) −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 \(0.975023\pi\)
\(480\) 0 0
\(481\) 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
\(486\) 0 0
\(487\) 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
\(489\) 0 0
\(490\) 819933. 1.11599e6i 0.154272 0.209976i
\(491\) −5.60132e6 −1.04854 −0.524272 0.851551i \(-0.675662\pi\)
−0.524272 + 0.851551i \(0.675662\pi\)
\(492\) 0 0
\(493\) −136522. + 236462.i −0.0252979 + 0.0438172i
\(494\) 108129. 187284.i 0.0199353 0.0345290i
\(495\) 0 0
\(496\) −7.25708e6 −1.32452
\(497\) 276715. 5.02392e6i 0.0502507 0.912330i
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) 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
\(507\) 0 0
\(508\) 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 \(0.745684\pi\)
\(510\) 0 0
\(511\) −3.40546e6 2.22445e6i −0.576930 0.376852i
\(512\) 3.82859e6 0.645452
\(513\) 0 0
\(514\) 468053. 810692.i 0.0781425 0.135347i
\(515\) −8.20695e6 + 1.42149e7i −1.36353 + 2.36170i
\(516\) 0 0
\(517\) 2.18460e6 0.359455
\(518\) −888852. 580600.i −0.145548 0.0950720i
\(519\) 0 0
\(520\) −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 \(0.995155\pi\)
\(522\) 0 0
\(523\) 3.61094e6 + 6.25433e6i 0.577252 + 0.999830i 0.995793 + 0.0916321i \(0.0292084\pi\)
−0.418541 + 0.908198i \(0.637458\pi\)
\(524\) 1.20697e6 0.192029
\(525\) 0 0
\(526\) −354531. −0.0558714
\(527\) −237644. 411612.i −0.0372735 0.0645597i
\(528\) 0 0
\(529\) 3.19927e6 5.54130e6i 0.497063 0.860939i
\(530\) 732691. + 1.26906e6i 0.113300 + 0.196242i
\(531\) 0 0
\(532\) 296162. 5.37699e6i 0.0453680 0.823683i
\(533\) −863574. −0.131668
\(534\) 0 0
\(535\) −4.65343e6 + 8.05997e6i −0.702892 + 1.21744i
\(536\) −332645. + 576158.i −0.0500114 + 0.0866223i
\(537\) 0 0
\(538\) −591106. −0.0880461
\(539\) 4.95232e6 6.74046e6i 0.734237 0.999350i
\(540\) 0 0
\(541\) 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
\(543\) 0 0
\(544\) 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
\(549\) 0 0
\(550\) −1.52126e6 + 2.63489e6i −0.214435 + 0.371412i
\(551\) 2.86182e6 + 4.95682e6i 0.401572 + 0.695543i
\(552\) 0 0
\(553\) 4.56790e6 2.31216e6i 0.635191 0.321517i
\(554\) −1.92106e6 −0.265929
\(555\) 0 0
\(556\) −833188. + 1.44312e6i −0.114303 + 0.197978i
\(557\) 4.82306e6 8.35379e6i 0.658696 1.14089i −0.322258 0.946652i \(-0.604442\pi\)
0.980953 0.194243i \(-0.0622249\pi\)
\(558\) 0 0
\(559\) −1.23123e6 −0.166651
\(560\) −1.09057e7 7.12362e6i −1.46955 0.959910i
\(561\) 0 0
\(562\) 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 \(0.100699\pi\)
\(564\) 0 0
\(565\) −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 \(-0.872805\pi\)
0.123685 0.992322i \(-0.460529\pi\)
\(570\) 0 0
\(571\) 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
\(573\) 0 0
\(574\) 382432. 193577.i 0.0484479 0.0245231i
\(575\) 1.50318e6 0.189601
\(576\) 0 0
\(577\) 4.52525e6 7.83796e6i 0.565852 0.980084i −0.431118 0.902296i \(-0.641881\pi\)
0.996970 0.0777887i \(-0.0247859\pi\)
\(578\) 559838. 969667.i 0.0697016 0.120727i
\(579\) 0 0
\(580\) 1.41322e7 1.74438
\(581\) −729890. + 1.32516e7i −0.0897051 + 1.62865i
\(582\) 0 0
\(583\) 4.42538e6 + 7.66499e6i 0.539237 + 0.933986i
\(584\) 786226. 1.36178e6i 0.0953927 0.165225i
\(585\) 0 0
\(586\) 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
\(591\) 0 0
\(592\) −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 \(0.972866\pi\)
\(594\) 0 0
\(595\) 46918.4 851830.i 0.00543313 0.0986417i
\(596\) 4.04927e6 0.466941
\(597\) 0 0
\(598\) 15879.9 27504.8i 0.00181591 0.00314525i
\(599\) −1.10282e6 + 1.91015e6i −0.125585 + 0.217520i −0.921962 0.387281i \(-0.873414\pi\)
0.796376 + 0.604802i \(0.206748\pi\)
\(600\) 0 0
\(601\) −1.00121e7 −1.13067 −0.565336 0.824860i \(-0.691254\pi\)
−0.565336 + 0.824860i \(0.691254\pi\)
\(602\) 545246. 275990.i 0.0613199 0.0310385i
\(603\) 0 0
\(604\) 2.40340e6 + 4.16280e6i 0.268061 + 0.464295i
\(605\) −4.51224e6 + 7.81542e6i −0.501191 + 0.868088i
\(606\) 0 0
\(607\) −3.16069e6 5.47448e6i −0.348185 0.603075i 0.637742 0.770250i \(-0.279869\pi\)
−0.985927 + 0.167175i \(0.946535\pi\)
\(608\) 3.13295e6 0.343712
\(609\) 0 0
\(610\) −876065. −0.0953261
\(611\) 453353. + 785231.i 0.0491285 + 0.0850931i
\(612\) 0 0
\(613\) −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
\(615\) 0 0
\(616\) 2.70707e6 + 1.76827e6i 0.287441 + 0.187757i
\(617\) −1.73991e7 −1.83999 −0.919993 0.391936i \(-0.871806\pi\)
−0.919993 + 0.391936i \(0.871806\pi\)
\(618\) 0 0
\(619\) −4.13368e6 + 7.15975e6i −0.433621 + 0.751054i −0.997182 0.0750208i \(-0.976098\pi\)
0.563561 + 0.826074i \(0.309431\pi\)
\(620\) −1.23000e7 + 2.13043e7i −1.28507 + 2.22581i
\(621\) 0 0
\(622\) 1.67497e6 0.173592
\(623\) 1.30498e7 6.60547e6i 1.34705 0.681841i
\(624\) 0 0
\(625\) −1.29211e7 2.23800e7i −1.32312 2.29172i
\(626\) 74143.4 128420.i 0.00756200 0.0130978i
\(627\) 0 0
\(628\) −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
\(633\) 0 0
\(634\) −397542. + 688563.i −0.0392790 + 0.0680331i
\(635\) −1.04980e7 1.81831e7i −1.03317 1.78951i
\(636\) 0 0
\(637\) 3.45051e6 + 381261.i 0.336926 + 0.0372284i
\(638\) −1.70138e6 −0.165481
\(639\) 0 0
\(640\) 5.13912e6 8.90122e6i 0.495951 0.859012i
\(641\) −1.78588e6 + 3.09324e6i −0.171675 + 0.297350i −0.939006 0.343902i \(-0.888251\pi\)
0.767330 + 0.641252i \(0.221585\pi\)
\(642\) 0 0
\(643\) −5.96911e6 −0.569354 −0.284677 0.958624i \(-0.591886\pi\)
−0.284677 + 0.958624i \(0.591886\pi\)
\(644\) 43494.6 789670.i 0.00413258 0.0750293i
\(645\) 0 0
\(646\) 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 \(0.191845\pi\)
\(648\) 0 0
\(649\) 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 \(0.118866\pi\)
−0.149608 + 0.988745i \(0.547801\pi\)
\(654\) 0 0
\(655\) 2.00411e6 3.47121e6i 0.182523 0.316139i
\(656\) −2.01594e6 3.49172e6i −0.182902 0.316796i
\(657\) 0 0
\(658\) −376783. 246115.i −0.0339255 0.0221602i
\(659\) 1.99303e7 1.78772 0.893862 0.448342i \(-0.147985\pi\)
0.893862 + 0.448342i \(0.147985\pi\)
\(660\) 0 0
\(661\) −4.77867e6 + 8.27691e6i −0.425406 + 0.736825i −0.996458 0.0840888i \(-0.973202\pi\)
0.571052 + 0.820914i \(0.306535\pi\)
\(662\) −664213. + 1.15045e6i −0.0589064 + 0.102029i
\(663\) 0 0
\(664\) −5.13056e6 −0.451591
\(665\) −1.49723e7 9.77995e6i −1.31291 0.857595i
\(666\) 0 0
\(667\) 420290. + 727963.i 0.0365792 + 0.0633570i
\(668\) −3.41333e6 + 5.91207e6i −0.295963 + 0.512623i
\(669\) 0 0
\(670\) 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
\(675\) 0 0
\(676\) −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 \(-0.374238\pi\)
\(678\) 0 0
\(679\) −216278. + 3.92665e6i −0.0180027 + 0.326849i
\(680\) 329800. 0.0273513
\(681\) 0 0
\(682\) 1.48080e6 2.56482e6i 0.121909 0.211152i
\(683\) 1.34392e6 2.32774e6i 0.110236 0.190934i −0.805629 0.592420i \(-0.798173\pi\)
0.915865 + 0.401486i \(0.131506\pi\)
\(684\) 0 0
\(685\) 2.51854e7 2.05080
\(686\) −1.61351e6 + 604620.i −0.130907 + 0.0490537i
\(687\) 0 0
\(688\) −2.87420e6 4.97826e6i −0.231497 0.400965i
\(689\) −1.83674e6 + 3.18132e6i −0.147400 + 0.255305i
\(690\) 0 0
\(691\) −2.33814e6 4.04977e6i −0.186284 0.322653i 0.757725 0.652574i \(-0.226311\pi\)
−0.944008 + 0.329922i \(0.892978\pi\)
\(692\) −1.32163e7 −1.04917
\(693\) 0 0
\(694\) −3.20802e6 −0.252836
\(695\) 2.76693e6 + 4.79246e6i 0.217288 + 0.376354i
\(696\) 0 0
\(697\) 132030. 228683.i 0.0102942 0.0178301i
\(698\) −1.13165e6 1.96008e6i −0.0879172 0.152277i
\(699\) 0 0
\(700\) −2.80558e7 + 1.42011e7i −2.16410 + 1.09541i
\(701\) −6.34801e6 −0.487913 −0.243957 0.969786i \(-0.578445\pi\)
−0.243957 + 0.969786i \(0.578445\pi\)
\(702\) 0 0
\(703\) −6.85520e6 + 1.18736e7i −0.523157 + 0.906135i
\(704\) 7.21309e6 1.24934e7i 0.548516 0.950058i
\(705\) 0 0
\(706\) −658492. −0.0497208
\(707\) 1.15915e7 + 7.57158e6i 0.872150 + 0.569690i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) 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
\(717\) 0 0
\(718\) −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 \(0.747982\pi\)
\(720\) 0 0
\(721\) 1.82218e7 9.22343e6i 1.30543 0.660776i
\(722\) −571944. −0.0408329
\(723\) 0 0
\(724\) 9.32784e6 1.61563e7i 0.661355 1.14550i
\(725\) 1.67109e7 2.89441e7i 1.18074 2.04510i
\(726\) 0 0
\(727\) 1.57839e7 1.10759 0.553793 0.832655i \(-0.313180\pi\)
0.553793 + 0.832655i \(0.313180\pi\)
\(728\) −73805.7 + 1.33999e6i −0.00516133 + 0.0937069i
\(729\) 0 0
\(730\) −1.29260e6 2.23885e6i −0.0897755 0.155496i
\(731\) 188240. 326041.i 0.0130292 0.0225673i
\(732\) 0 0
\(733\) −6.76835e6 1.17231e7i −0.465289 0.805905i 0.533925 0.845532i \(-0.320716\pi\)
−0.999215 + 0.0396269i \(0.987383\pi\)
\(734\) 1.15048e6 0.0788205
\(735\) 0 0
\(736\) 460109. 0.0313088
\(737\) 3.30315e6 + 5.72123e6i 0.224006 + 0.387990i
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) 100276. 1.82056e6i 0.00668629 0.121394i
\(743\) −1.20844e7 −0.803068 −0.401534 0.915844i \(-0.631523\pi\)
−0.401534 + 0.915844i \(0.631523\pi\)
\(744\) 0 0
\(745\) 6.72360e6 1.16456e7i 0.443824 0.768726i
\(746\) 809343. 1.40182e6i 0.0532459 0.0922245i
\(747\) 0 0
\(748\) 986151. 0.0644450
\(749\) 1.03320e7 5.22978e6i 0.672944 0.340627i
\(750\) 0 0
\(751\) −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
\(753\) 0 0
\(754\) −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
\(759\) 0 0
\(760\) 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 \(0.677806\pi\)
\(762\) 0 0
\(763\) −1.81915e7 1.18827e7i −1.13125 0.738932i
\(764\) 2.59984e7 1.61144
\(765\) 0 0
\(766\) −1.53268e6 + 2.65468e6i −0.0943800 + 0.163471i
\(767\) −361513. + 626159.i −0.0221889 + 0.0384323i
\(768\) 0 0
\(769\) −1.85606e7 −1.13181 −0.565907 0.824469i \(-0.691474\pi\)
−0.565907 + 0.824469i \(0.691474\pi\)
\(770\) 4.74295e6 2.40076e6i 0.288285 0.145922i
\(771\) 0 0
\(772\) 3.44711e6 + 5.97057e6i 0.208167 + 0.360556i
\(773\) 6.13802e6 1.06314e7i 0.369470 0.639941i −0.620013 0.784592i \(-0.712872\pi\)
0.989483 + 0.144651i \(0.0462058\pi\)
\(774\) 0 0
\(775\) 2.90888e7 + 5.03832e7i 1.73969 + 3.01323i
\(776\) −1.52027e6 −0.0906286
\(777\) 0 0
\(778\) −2.24432e6 −0.132934
\(779\) −2.76767e6 4.79375e6i −0.163407 0.283029i
\(780\) 0 0
\(781\) 9.65736e6 1.67270e7i 0.566540 0.981276i
\(782\) 4855.70 + 8410.31i 0.000283945 + 0.000491808i
\(783\) 0 0
\(784\) 6.51337e6 + 1.48416e7i 0.378456 + 0.862363i
\(785\) −1.57525e7 −0.912380
\(786\) 0 0
\(787\) −2.63496e6 + 4.56388e6i −0.151648 + 0.262662i −0.931833 0.362886i \(-0.881791\pi\)
0.780185 + 0.625548i \(0.215125\pi\)
\(788\) −7.46107e6 + 1.29230e7i −0.428041 + 0.741389i
\(789\) 0 0
\(790\) 3.25391e6 0.185497
\(791\) −825586. + 1.49890e7i −0.0469160 + 0.851788i
\(792\) 0 0
\(793\) −1.09807e6 1.90192e6i −0.0620082 0.107401i
\(794\) −1.71710e6 + 2.97410e6i −0.0966593 + 0.167419i
\(795\) 0 0
\(796\) 9.84466e6 + 1.70514e7i 0.550704 + 0.953847i
\(797\) −1.11889e7 −0.623940 −0.311970 0.950092i \(-0.600989\pi\)
−0.311970 + 0.950092i \(0.600989\pi\)
\(798\) 0 0
\(799\) −277250. −0.0153640
\(800\) −9.14706e6 1.58432e7i −0.505308 0.875220i
\(801\) 0 0
\(802\) 1.34557e6 2.33060e6i 0.0738705 0.127947i
\(803\) −7.80719e6 1.35225e7i −0.427274 0.740059i
\(804\) 0 0
\(805\) −2.19885e6 1.43629e6i −0.119593 0.0781184i
\(806\) 1.22920e6 0.0666476
\(807\) 0 0
\(808\) −2.67616e6 + 4.63524e6i −0.144206 + 0.249772i
\(809\) 3.52526e6 6.10592e6i 0.189374 0.328005i −0.755668 0.654955i \(-0.772688\pi\)
0.945042 + 0.326950i \(0.106021\pi\)
\(810\) 0 0
\(811\) −2.54873e7 −1.36073 −0.680364 0.732875i \(-0.738178\pi\)
−0.680364 + 0.732875i \(0.738178\pi\)
\(812\) −1.47218e7 9.61630e6i −0.783557 0.511821i
\(813\) 0 0
\(814\) −2.03774e6 3.52947e6i −0.107792 0.186702i
\(815\) 1.71482e6 2.97016e6i 0.0904326 0.156634i
\(816\) 0 0
\(817\) −3.94596e6 6.83460e6i −0.206822 0.358227i
\(818\) −4.18677e6 −0.218774
\(819\) 0 0
\(820\) −1.36673e7 −0.709820
\(821\) −1.17439e7 2.03411e7i −0.608073 1.05321i −0.991558 0.129666i \(-0.958610\pi\)
0.383485 0.923547i \(-0.374724\pi\)
\(822\) 0 0
\(823\) 6.04517e6 1.04705e7i 0.311107 0.538852i −0.667496 0.744614i \(-0.732634\pi\)
0.978602 + 0.205761i \(0.0659671\pi\)
\(824\) 3.94760e6 + 6.83745e6i 0.202542 + 0.350813i
\(825\) 0 0
\(826\) 19736.6 358330.i 0.00100652 0.0182740i
\(827\) −3.33335e6 −0.169480 −0.0847398 0.996403i \(-0.527006\pi\)
−0.0847398 + 0.996403i \(0.527006\pi\)
\(828\) 0 0
\(829\) 3.85267e6 6.67302e6i 0.194704 0.337238i −0.752099 0.659050i \(-0.770959\pi\)
0.946804 + 0.321812i \(0.104292\pi\)
\(830\) −4.21748e6 + 7.30489e6i −0.212499 + 0.368060i
\(831\) 0 0
\(832\) 5.98752e6 0.299874
\(833\) −628505. + 855440.i −0.0313831 + 0.0427147i
\(834\) 0 0
\(835\) 1.13353e7 + 1.96333e7i 0.562622 + 0.974490i
\(836\) 1.03360e7 1.79025e7i 0.511492 0.885929i
\(837\) 0 0
\(838\) 1.13586e6 + 1.96737e6i 0.0558747 + 0.0967779i
\(839\) −2.40843e7 −1.18121 −0.590607 0.806959i \(-0.701112\pi\)
−0.590607 + 0.806959i \(0.701112\pi\)
\(840\) 0 0
\(841\) −1.82163e6 −0.0888116
\(842\) −825159. 1.42922e6i −0.0401104 0.0694733i
\(843\) 0 0
\(844\) 8.95728e6 1.55145e7i 0.432832 0.749688i
\(845\) 1.71202e7 + 2.96531e7i 0.824837 + 1.42866i
\(846\) 0 0
\(847\) 1.00185e7 5.07110e6i 0.479837 0.242881i
\(848\) −1.71509e7 −0.819023
\(849\) 0 0
\(850\) 193064. 334398.i 0.00916548 0.0158751i
\(851\) −1.00676e6 + 1.74376e6i −0.0476544 + 0.0825398i
\(852\) 0 0
\(853\) −2.82938e7 −1.33143 −0.665716 0.746206i \(-0.731874\pi\)
−0.665716 + 0.746206i \(0.731874\pi\)
\(854\) 912612. + 596120.i 0.0428195 + 0.0279698i
\(855\) 0 0
\(856\) 2.23833e6 + 3.87690e6i 0.104410 + 0.180843i
\(857\) 1.08088e7 1.87214e7i 0.502719 0.870734i −0.497276 0.867592i \(-0.665666\pi\)
0.999995 0.00314220i \(-0.00100019\pi\)
\(858\) 0 0
\(859\) −1.62691e7 2.81789e7i −0.752282 1.30299i −0.946714 0.322075i \(-0.895620\pi\)
0.194432 0.980916i \(-0.437714\pi\)
\(860\) −1.94859e7 −0.898411
\(861\) 0 0
\(862\) 1.92058e6 0.0880366
\(863\) 4.03192e6 + 6.98349e6i 0.184283 + 0.319187i 0.943335 0.331843i \(-0.107670\pi\)
−0.759052 + 0.651030i \(0.774337\pi\)
\(864\) 0 0
\(865\) −2.19450e7 + 3.80098e7i −0.997229 + 1.72725i
\(866\) −378091. 654874.i −0.0171318 0.0296731i
\(867\) 0 0
\(868\) 2.73097e7 1.38235e7i 1.23032 0.622756i
\(869\) 1.96533e7 0.882849
\(870\) 0 0
\(871\) −1.37096e6 + 2.37457e6i −0.0612321 + 0.106057i
\(872\) 4.19992e6 7.27447e6i 0.187046 0.323974i
\(873\) 0 0
\(874\) 203574. 0.00901454
\(875\) −3.42157e6 + 6.21206e7i −0.151080 + 2.74294i
\(876\) 0 0
\(877\) −8.51559e6 1.47494e7i −0.373866 0.647555i 0.616291 0.787519i \(-0.288635\pi\)
−0.990157 + 0.139964i \(0.955301\pi\)
\(878\) −1.04467e6 + 1.80943e6i −0.0457345 + 0.0792145i
\(879\) 0 0
\(880\) −2.50019e7 4.33045e7i −1.08834 1.88507i
\(881\) −1.24740e7 −0.541459 −0.270729 0.962655i \(-0.587265\pi\)
−0.270729 + 0.962655i \(0.587265\pi\)
\(882\) 0 0
\(883\) 7.28955e6 0.314629 0.157315 0.987549i \(-0.449716\pi\)
0.157315 + 0.987549i \(0.449716\pi\)
\(884\) 204649. + 354462.i 0.00880802 + 0.0152559i
\(885\) 0 0
\(886\) −1.36005e6 + 2.35567e6i −0.0582063 + 0.100816i
\(887\) 9.38377e6 + 1.62532e7i 0.400469 + 0.693632i 0.993782 0.111339i \(-0.0355140\pi\)
−0.593314 + 0.804971i \(0.702181\pi\)
\(888\) 0 0
\(889\) −1.43675e6 + 2.60850e7i −0.0609714 + 1.10697i
\(890\) 9.29592e6 0.393385
\(891\) 0 0
\(892\) 66406.1 115019.i 0.00279445 0.00484012i
\(893\) −2.90591e6 + 5.03318e6i −0.121942 + 0.211210i
\(894\) 0 0
\(895\) −364052. −0.0151917
\(896\) −1.14104e7 + 5.77563e6i −0.474820 + 0.240342i
\(897\) 0 0
\(898\) 1.73939e6 + 3.01271e6i 0.0719790 + 0.124671i
\(899\) −1.62665e7 + 2.81744e7i −0.671266 + 1.16267i
\(900\) 0 0
\(901\) −561631. 972773.i −0.0230483 0.0399208i
\(902\) 1.64541e6 0.0673375
\(903\) 0 0
\(904\) −5.80323e6 −0.236183
\(905\) −3.09767e7 5.36533e7i −1.25723 2.17758i
\(906\) 0 0
\(907\) −631833. + 1.09437e6i −0.0255026 + 0.0441718i −0.878495 0.477751i \(-0.841452\pi\)
0.852992 + 0.521923i \(0.174785\pi\)
\(908\) −1.77245e7 3.06998e7i −0.713444 1.23572i
\(909\) 0 0
\(910\) 1.84720e6 + 1.20659e6i 0.0739452 + 0.0483011i
\(911\) 2.47718e7 0.988921 0.494461 0.869200i \(-0.335366\pi\)
0.494461 + 0.869200i \(0.335366\pi\)
\(912\) 0 0
\(913\) −2.54732e7 + 4.41208e7i −1.01136 + 1.75173i
\(914\) 890092. 1.54168e6i 0.0352427 0.0610422i
\(915\) 0 0
\(916\) −2.52454e7 −0.994130
\(917\) −4.44970e6 + 2.25233e6i −0.174746 + 0.0884520i
\(918\) 0 0
\(919\) 4.68338e6 + 8.11185e6i 0.182924 + 0.316834i 0.942875 0.333147i \(-0.108110\pi\)
−0.759951 + 0.649980i \(0.774777\pi\)
\(920\) 507654. 879282.i 0.0197742 0.0342498i
\(921\) 0 0
\(922\) 732710. + 1.26909e6i 0.0283860 + 0.0491661i
\(923\) 8.01648e6 0.309727
\(924\) 0 0
\(925\) 8.00586e7 3.07648
\(926\) 1.19051e6 + 2.06203e6i 0.0456255 + 0.0790256i
\(927\) 0 0
\(928\) 5.11505e6 8.85953e6i 0.194975 0.337707i
\(929\) −3.43675e6 5.95263e6i −0.130650 0.226292i 0.793277 0.608860i \(-0.208373\pi\)
−0.923927 + 0.382568i \(0.875040\pi\)
\(930\) 0 0
\(931\) 8.94215e6 + 2.03759e7i 0.338118 + 0.770446i
\(932\) 3.66855e7 1.38342
\(933\) 0 0
\(934\) −421995. + 730917.i −0.0158285 + 0.0274158i
\(935\) 1.63745e6 2.83615e6i 0.0612546 0.106096i
\(936\) 0 0
\(937\) −4.26197e7 −1.58585 −0.792923 0.609322i \(-0.791442\pi\)
−0.792923 + 0.609322i \(0.791442\pi\)
\(938\) 74846.7 1.35889e6i 0.00277758 0.0504285i
\(939\) 0 0
\(940\) 7.17497e6 + 1.24274e7i 0.264850 + 0.458734i
\(941\) 2.25113e6 3.89907e6i 0.0828755 0.143545i −0.821608 0.570052i \(-0.806923\pi\)
0.904484 + 0.426508i \(0.140256\pi\)
\(942\) 0 0
\(943\) −406463. 704015.i −0.0148848 0.0257812i
\(944\) −3.37569e6 −0.123291
\(945\) 0 0
\(946\) 2.34591e6 0.0852282
\(947\) 1.68863e7 + 2.92479e7i 0.611870 + 1.05979i 0.990925 + 0.134415i \(0.0429156\pi\)
−0.379055 + 0.925374i \(0.623751\pi\)
\(948\) 0 0
\(949\) 3.24034e6 5.61243e6i 0.116795 0.202295i
\(950\) −4.04709e6 7.00977e6i −0.145490 0.251997i
\(951\) 0 0
\(952\) −343558. 224413.i −0.0122859 0.00802519i
\(953\) −4.81813e7 −1.71849 −0.859244 0.511566i \(-0.829066\pi\)
−0.859244 + 0.511566i \(0.829066\pi\)
\(954\) 0 0
\(955\) 4.31689e7 7.47708e7i 1.53166 2.65292i
\(956\) 2.67554e7 4.63416e7i 0.946817 1.63993i
\(957\) 0 0
\(958\) 4.49800e6 0.158346
\(959\) −2.62361e7 1.71375e7i −0.921198 0.601728i
\(960\) 0 0
\(961\) −1.40006e7 2.42498e7i −0.489033 0.847030i
\(962\) 845755. 1.46489e6i 0.0294650 0.0510349i
\(963\) 0 0
\(964\) 1.49217e7 + 2.58452e7i 0.517161 + 0.895750i
\(965\) 2.28950e7 0.791446
\(966\) 0 0
\(967\) −3.54640e7 −1.21961 −0.609805 0.792551i \(-0.708752\pi\)
−0.609805 + 0.792551i \(0.708752\pi\)
\(968\) 2.17042e6 + 3.75927e6i 0.0744483 + 0.128948i
\(969\) 0 0
\(970\) −1.24970e6 + 2.16455e6i −0.0426459 + 0.0738649i
\(971\) −3.92148e6 6.79221e6i −0.133476 0.231187i 0.791538 0.611119i \(-0.209280\pi\)
−0.925014 + 0.379933i \(0.875947\pi\)
\(972\) 0 0
\(973\) 378679. 6.87514e6i 0.0128230 0.232809i
\(974\) −5.41288e6 −0.182823
\(975\) 0 0
\(976\) 5.12674e6 8.87977e6i 0.172273 0.298385i
\(977\) −1.23767e7 + 2.14371e7i −0.414829 + 0.718505i −0.995410 0.0956975i \(-0.969492\pi\)
0.580582 + 0.814202i \(0.302825\pi\)
\(978\) 0 0
\(979\) 5.61464e7 1.87226
\(980\) 5.46093e7 + 6.03401e6i 1.81636 + 0.200697i
\(981\) 0 0
\(982\) 2.21477e6 + 3.83610e6i 0.0732910 + 0.126944i
\(983\) 2.26564e7 3.92421e7i 0.747838 1.29529i −0.201018 0.979587i \(-0.564425\pi\)
0.948857 0.315707i \(-0.102242\pi\)
\(984\) 0 0
\(985\) 2.47774e7 + 4.29157e7i 0.813701 + 1.40937i
\(986\) 215924. 0.00707308
\(987\) 0 0
\(988\) 8.57985e6 0.279632
\(989\) −579508. 1.00374e6i −0.0188395 0.0326309i
\(990\) 0 0
\(991\) 1.87071e7 3.24017e7i 0.605095 1.04805i −0.386942 0.922104i \(-0.626469\pi\)
0.992037 0.125951i \(-0.0401981\pi\)
\(992\) 8.90380e6 + 1.54218e7i 0.287274 + 0.497573i
\(993\) 0 0
\(994\) −3.55008e6 + 1.79696e6i −0.113965 + 0.0576863i
\(995\) 6.53861e7 2.09376
\(996\) 0 0
\(997\) −2.32639e7 + 4.02943e7i −0.741216 + 1.28382i 0.210726 + 0.977545i \(0.432417\pi\)
−0.951942 + 0.306279i \(0.900916\pi\)
\(998\) 923379. 1.59934e6i 0.0293463 0.0508293i
\(999\) 0 0
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 63.6.e.e.46.2 8
3.2 odd 2 21.6.e.c.4.3 8
7.2 even 3 inner 63.6.e.e.37.2 8
7.3 odd 6 441.6.a.v.1.3 4
7.4 even 3 441.6.a.w.1.3 4
12.11 even 2 336.6.q.j.193.4 8
21.2 odd 6 21.6.e.c.16.3 yes 8
21.5 even 6 147.6.e.o.79.3 8
21.11 odd 6 147.6.a.m.1.2 4
21.17 even 6 147.6.a.l.1.2 4
21.20 even 2 147.6.e.o.67.3 8
84.23 even 6 336.6.q.j.289.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.e.c.4.3 8 3.2 odd 2
21.6.e.c.16.3 yes 8 21.2 odd 6
63.6.e.e.37.2 8 7.2 even 3 inner
63.6.e.e.46.2 8 1.1 even 1 trivial
147.6.a.l.1.2 4 21.17 even 6
147.6.a.m.1.2 4 21.11 odd 6
147.6.e.o.67.3 8 21.20 even 2
147.6.e.o.79.3 8 21.5 even 6
336.6.q.j.193.4 8 12.11 even 2
336.6.q.j.289.4 8 84.23 even 6
441.6.a.v.1.3 4 7.3 odd 6
441.6.a.w.1.3 4 7.4 even 3