Properties

Label 294.4.e.l.79.2
Level $294$
Weight $4$
Character 294.79
Analytic conductor $17.347$
Analytic rank $0$
Dimension $4$
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] = [294,4,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.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: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 337x^{2} + 336x + 112896 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(9.41856 - 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.4.e.l.67.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(20.8371 + 36.0910i) q^{10} +(-7.58144 - 13.1314i) q^{11} +(6.00000 - 10.3923i) q^{12} -2.16288 q^{13} +62.5114 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-59.6742 - 103.359i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(-16.7557 + 29.0217i) q^{19} -83.3485 q^{20} +30.3258 q^{22} +(-0.325758 + 0.564230i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-154.593 - 267.763i) q^{25} +(2.16288 - 3.74622i) q^{26} -27.0000 q^{27} -163.208 q^{29} +(-62.5114 + 108.273i) q^{30} +(-111.663 - 193.406i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(22.7443 - 39.3943i) q^{33} +238.697 q^{34} +36.0000 q^{36} +(-84.2670 + 145.955i) q^{37} +(-33.5114 - 58.0434i) q^{38} +(-3.24432 - 5.61932i) q^{39} +(83.3485 - 144.364i) q^{40} +323.023 q^{41} +221.557 q^{43} +(-30.3258 + 52.5258i) q^{44} +(93.7670 + 162.409i) q^{45} +(-0.651517 - 1.12846i) q^{46} +(254.023 - 439.980i) q^{47} -48.0000 q^{48} +618.371 q^{50} +(179.023 - 310.076i) q^{51} +(4.32576 + 7.49243i) q^{52} +(88.2557 + 152.863i) q^{53} +(27.0000 - 46.7654i) q^{54} -315.951 q^{55} -100.534 q^{57} +(163.208 - 282.685i) q^{58} +(227.464 + 393.979i) q^{59} +(-125.023 - 216.546i) q^{60} +(19.3258 - 33.4732i) q^{61} +446.652 q^{62} +64.0000 q^{64} +(-22.5341 + 39.0302i) q^{65} +(45.4886 + 78.7886i) q^{66} +(-70.8958 - 122.795i) q^{67} +(-238.697 + 413.435i) q^{68} -1.95455 q^{69} +602.742 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-551.150 - 954.619i) q^{73} +(-168.534 - 291.910i) q^{74} +(463.778 - 803.288i) q^{75} +134.045 q^{76} +12.9773 q^{78} +(58.1515 - 100.721i) q^{79} +(166.697 + 288.728i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-323.023 + 559.492i) q^{82} +568.928 q^{83} -2486.88 q^{85} +(-221.557 + 383.748i) q^{86} +(-244.812 - 424.028i) q^{87} +(-60.6515 - 105.052i) q^{88} +(-191.580 + 331.825i) q^{89} -375.068 q^{90} +2.60607 q^{92} +(334.989 - 580.217i) q^{93} +(508.045 + 879.961i) q^{94} +(349.140 + 604.728i) q^{95} +(48.0000 - 83.1384i) q^{96} -334.701 q^{97} +136.466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 5 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 5 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9} + 10 q^{10} - 67 q^{11} + 24 q^{12} - 82 q^{13} + 30 q^{15} - 32 q^{16} - 92 q^{17} - 36 q^{18} + 43 q^{19} - 40 q^{20} + 268 q^{22} - 148 q^{23} + 48 q^{24} - 435 q^{25} + 82 q^{26} - 108 q^{27} + 154 q^{29} - 30 q^{30} - 520 q^{31} - 64 q^{32} + 201 q^{33} + 368 q^{34} + 144 q^{36} - 7 q^{37} + 86 q^{38} - 123 q^{39} + 40 q^{40} + 852 q^{41} - 214 q^{43} - 268 q^{44} + 45 q^{45} - 296 q^{46} + 576 q^{47} - 192 q^{48} + 1740 q^{50} + 276 q^{51} + 164 q^{52} + 243 q^{53} + 108 q^{54} + 1010 q^{55} + 258 q^{57} - 154 q^{58} - 7 q^{59} - 60 q^{60} + 224 q^{61} + 2080 q^{62} + 256 q^{64} + 570 q^{65} + 402 q^{66} - 687 q^{67} - 368 q^{68} - 888 q^{69} + 944 q^{71} - 144 q^{72} - 921 q^{73} - 14 q^{74} + 1305 q^{75} - 344 q^{76} + 492 q^{78} + 526 q^{79} + 80 q^{80} - 162 q^{81} - 852 q^{82} + 442 q^{83} - 5840 q^{85} + 214 q^{86} + 231 q^{87} - 536 q^{88} + 774 q^{89} - 180 q^{90} + 1184 q^{92} + 1560 q^{93} + 1152 q^{94} + 1910 q^{95} + 192 q^{96} - 3906 q^{97} + 1206 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 10.4186 18.0455i 0.931864 1.61404i 0.151732 0.988422i \(-0.451515\pi\)
0.780132 0.625615i \(-0.215152\pi\)
\(6\) −6.00000 −0.408248
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 20.8371 + 36.0910i 0.658928 + 1.14130i
\(11\) −7.58144 13.1314i −0.207808 0.359934i 0.743216 0.669052i \(-0.233300\pi\)
−0.951024 + 0.309118i \(0.899966\pi\)
\(12\) 6.00000 10.3923i 0.144338 0.250000i
\(13\) −2.16288 −0.0461442 −0.0230721 0.999734i \(-0.507345\pi\)
−0.0230721 + 0.999734i \(0.507345\pi\)
\(14\) 0 0
\(15\) 62.5114 1.07602
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −59.6742 103.359i −0.851361 1.47460i −0.879981 0.475009i \(-0.842445\pi\)
0.0286202 0.999590i \(-0.490889\pi\)
\(18\) −9.00000 15.5885i −0.117851 0.204124i
\(19\) −16.7557 + 29.0217i −0.202317 + 0.350423i −0.949274 0.314449i \(-0.898180\pi\)
0.746958 + 0.664871i \(0.231514\pi\)
\(20\) −83.3485 −0.931864
\(21\) 0 0
\(22\) 30.3258 0.293885
\(23\) −0.325758 + 0.564230i −0.00295327 + 0.00511522i −0.867498 0.497440i \(-0.834273\pi\)
0.864545 + 0.502555i \(0.167607\pi\)
\(24\) 12.0000 + 20.7846i 0.102062 + 0.176777i
\(25\) −154.593 267.763i −1.23674 2.14210i
\(26\) 2.16288 3.74622i 0.0163144 0.0282574i
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −163.208 −1.04507 −0.522535 0.852618i \(-0.675014\pi\)
−0.522535 + 0.852618i \(0.675014\pi\)
\(30\) −62.5114 + 108.273i −0.380432 + 0.658928i
\(31\) −111.663 193.406i −0.646943 1.12054i −0.983849 0.179000i \(-0.942714\pi\)
0.336906 0.941538i \(-0.390620\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 22.7443 39.3943i 0.119978 0.207808i
\(34\) 238.697 1.20401
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) −84.2670 + 145.955i −0.374417 + 0.648509i −0.990240 0.139376i \(-0.955490\pi\)
0.615823 + 0.787885i \(0.288824\pi\)
\(38\) −33.5114 58.0434i −0.143059 0.247786i
\(39\) −3.24432 5.61932i −0.0133207 0.0230721i
\(40\) 83.3485 144.364i 0.329464 0.570648i
\(41\) 323.023 1.23043 0.615216 0.788359i \(-0.289069\pi\)
0.615216 + 0.788359i \(0.289069\pi\)
\(42\) 0 0
\(43\) 221.557 0.785746 0.392873 0.919593i \(-0.371481\pi\)
0.392873 + 0.919593i \(0.371481\pi\)
\(44\) −30.3258 + 52.5258i −0.103904 + 0.179967i
\(45\) 93.7670 + 162.409i 0.310621 + 0.538012i
\(46\) −0.651517 1.12846i −0.00208828 0.00361701i
\(47\) 254.023 439.980i 0.788362 1.36548i −0.138608 0.990347i \(-0.544263\pi\)
0.926970 0.375136i \(-0.122404\pi\)
\(48\) −48.0000 −0.144338
\(49\) 0 0
\(50\) 618.371 1.74902
\(51\) 179.023 310.076i 0.491533 0.851361i
\(52\) 4.32576 + 7.49243i 0.0115361 + 0.0199810i
\(53\) 88.2557 + 152.863i 0.228733 + 0.396177i 0.957433 0.288656i \(-0.0932084\pi\)
−0.728700 + 0.684833i \(0.759875\pi\)
\(54\) 27.0000 46.7654i 0.0680414 0.117851i
\(55\) −315.951 −0.774596
\(56\) 0 0
\(57\) −100.534 −0.233615
\(58\) 163.208 282.685i 0.369488 0.639972i
\(59\) 227.464 + 393.979i 0.501920 + 0.869351i 0.999998 + 0.00221868i \(0.000706227\pi\)
−0.498077 + 0.867133i \(0.665960\pi\)
\(60\) −125.023 216.546i −0.269006 0.465932i
\(61\) 19.3258 33.4732i 0.0405641 0.0702591i −0.845031 0.534718i \(-0.820418\pi\)
0.885595 + 0.464459i \(0.153751\pi\)
\(62\) 446.652 0.914916
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −22.5341 + 39.0302i −0.0430001 + 0.0744784i
\(66\) 45.4886 + 78.7886i 0.0848373 + 0.146943i
\(67\) −70.8958 122.795i −0.129273 0.223908i 0.794122 0.607758i \(-0.207931\pi\)
−0.923395 + 0.383851i \(0.874598\pi\)
\(68\) −238.697 + 413.435i −0.425680 + 0.737300i
\(69\) −1.95455 −0.00341015
\(70\) 0 0
\(71\) 602.742 1.00750 0.503749 0.863850i \(-0.331954\pi\)
0.503749 + 0.863850i \(0.331954\pi\)
\(72\) −36.0000 + 62.3538i −0.0589256 + 0.102062i
\(73\) −551.150 954.619i −0.883660 1.53054i −0.847242 0.531207i \(-0.821738\pi\)
−0.0364183 0.999337i \(-0.511595\pi\)
\(74\) −168.534 291.910i −0.264753 0.458565i
\(75\) 463.778 803.288i 0.714034 1.23674i
\(76\) 134.045 0.202317
\(77\) 0 0
\(78\) 12.9773 0.0188383
\(79\) 58.1515 100.721i 0.0828172 0.143444i −0.821642 0.570004i \(-0.806942\pi\)
0.904459 + 0.426561i \(0.140275\pi\)
\(80\) 166.697 + 288.728i 0.232966 + 0.403509i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −323.023 + 559.492i −0.435023 + 0.753482i
\(83\) 568.928 0.752385 0.376193 0.926542i \(-0.377233\pi\)
0.376193 + 0.926542i \(0.377233\pi\)
\(84\) 0 0
\(85\) −2486.88 −3.17341
\(86\) −221.557 + 383.748i −0.277803 + 0.481169i
\(87\) −244.812 424.028i −0.301686 0.522535i
\(88\) −60.6515 105.052i −0.0734713 0.127256i
\(89\) −191.580 + 331.825i −0.228173 + 0.395207i −0.957267 0.289207i \(-0.906608\pi\)
0.729094 + 0.684414i \(0.239942\pi\)
\(90\) −375.068 −0.439285
\(91\) 0 0
\(92\) 2.60607 0.00295327
\(93\) 334.989 580.217i 0.373513 0.646943i
\(94\) 508.045 + 879.961i 0.557456 + 0.965543i
\(95\) 349.140 + 604.728i 0.377063 + 0.653093i
\(96\) 48.0000 83.1384i 0.0510310 0.0883883i
\(97\) −334.701 −0.350348 −0.175174 0.984538i \(-0.556049\pi\)
−0.175174 + 0.984538i \(0.556049\pi\)
\(98\) 0 0
\(99\) 136.466 0.138539
\(100\) −618.371 + 1071.05i −0.618371 + 1.07105i
\(101\) −7.37121 12.7673i −0.00726201 0.0125782i 0.862372 0.506276i \(-0.168978\pi\)
−0.869634 + 0.493698i \(0.835645\pi\)
\(102\) 358.045 + 620.153i 0.347566 + 0.602003i
\(103\) −420.710 + 728.691i −0.402464 + 0.697088i −0.994023 0.109174i \(-0.965180\pi\)
0.591559 + 0.806262i \(0.298513\pi\)
\(104\) −17.3030 −0.0163144
\(105\) 0 0
\(106\) −353.023 −0.323477
\(107\) 357.835 619.789i 0.323301 0.559974i −0.657866 0.753135i \(-0.728541\pi\)
0.981167 + 0.193161i \(0.0618739\pi\)
\(108\) 54.0000 + 93.5307i 0.0481125 + 0.0833333i
\(109\) −300.009 519.632i −0.263630 0.456621i 0.703574 0.710622i \(-0.251587\pi\)
−0.967204 + 0.254001i \(0.918253\pi\)
\(110\) 315.951 547.243i 0.273861 0.474341i
\(111\) −505.602 −0.432339
\(112\) 0 0
\(113\) 622.644 0.518349 0.259174 0.965831i \(-0.416550\pi\)
0.259174 + 0.965831i \(0.416550\pi\)
\(114\) 100.534 174.130i 0.0825954 0.143059i
\(115\) 6.78787 + 11.7569i 0.00550410 + 0.00953339i
\(116\) 326.417 + 565.370i 0.261267 + 0.452529i
\(117\) 9.73296 16.8580i 0.00769070 0.0133207i
\(118\) −909.856 −0.709822
\(119\) 0 0
\(120\) 500.091 0.380432
\(121\) 550.544 953.569i 0.413632 0.716431i
\(122\) 38.6515 + 66.9464i 0.0286831 + 0.0496807i
\(123\) 484.534 + 839.238i 0.355195 + 0.615216i
\(124\) −446.652 + 773.623i −0.323472 + 0.560269i
\(125\) −3837.90 −2.74618
\(126\) 0 0
\(127\) −180.076 −0.125820 −0.0629100 0.998019i \(-0.520038\pi\)
−0.0629100 + 0.998019i \(0.520038\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 332.335 + 575.621i 0.226825 + 0.392873i
\(130\) −45.0682 78.0604i −0.0304057 0.0526642i
\(131\) 108.930 188.672i 0.0726508 0.125835i −0.827411 0.561596i \(-0.810187\pi\)
0.900062 + 0.435761i \(0.143521\pi\)
\(132\) −181.955 −0.119978
\(133\) 0 0
\(134\) 283.583 0.182820
\(135\) −281.301 + 487.228i −0.179337 + 0.310621i
\(136\) −477.394 826.871i −0.301001 0.521350i
\(137\) 1300.93 + 2253.27i 0.811283 + 1.40518i 0.911966 + 0.410265i \(0.134564\pi\)
−0.100683 + 0.994919i \(0.532103\pi\)
\(138\) 1.95455 3.38538i 0.00120567 0.00208828i
\(139\) 2651.55 1.61800 0.808998 0.587811i \(-0.200010\pi\)
0.808998 + 0.587811i \(0.200010\pi\)
\(140\) 0 0
\(141\) 1524.14 0.910322
\(142\) −602.742 + 1043.98i −0.356204 + 0.616964i
\(143\) 16.3977 + 28.4017i 0.00958914 + 0.0166089i
\(144\) −72.0000 124.708i −0.0416667 0.0721688i
\(145\) −1700.40 + 2945.17i −0.973863 + 1.68678i
\(146\) 2204.60 1.24968
\(147\) 0 0
\(148\) 674.136 0.374417
\(149\) −290.511 + 503.180i −0.159729 + 0.276659i −0.934771 0.355251i \(-0.884395\pi\)
0.775042 + 0.631910i \(0.217729\pi\)
\(150\) 927.557 + 1606.58i 0.504898 + 0.874509i
\(151\) 307.695 + 532.943i 0.165827 + 0.287221i 0.936949 0.349467i \(-0.113637\pi\)
−0.771122 + 0.636688i \(0.780304\pi\)
\(152\) −134.045 + 232.174i −0.0715297 + 0.123893i
\(153\) 1074.14 0.567574
\(154\) 0 0
\(155\) −4653.47 −2.41145
\(156\) −12.9773 + 22.4773i −0.00666034 + 0.0115361i
\(157\) −153.466 265.811i −0.0780122 0.135121i 0.824380 0.566037i \(-0.191524\pi\)
−0.902392 + 0.430916i \(0.858191\pi\)
\(158\) 116.303 + 201.443i 0.0585606 + 0.101430i
\(159\) −264.767 + 458.590i −0.132059 + 0.228733i
\(160\) −666.788 −0.329464
\(161\) 0 0
\(162\) 162.000 0.0785674
\(163\) −1757.25 + 3043.65i −0.844408 + 1.46256i 0.0417271 + 0.999129i \(0.486714\pi\)
−0.886135 + 0.463428i \(0.846619\pi\)
\(164\) −646.045 1118.98i −0.307608 0.532792i
\(165\) −473.926 820.864i −0.223607 0.387298i
\(166\) −568.928 + 985.412i −0.266008 + 0.460740i
\(167\) −1123.30 −0.520502 −0.260251 0.965541i \(-0.583805\pi\)
−0.260251 + 0.965541i \(0.583805\pi\)
\(168\) 0 0
\(169\) −2192.32 −0.997871
\(170\) 2486.88 4307.40i 1.12197 1.94331i
\(171\) −150.801 261.195i −0.0674389 0.116808i
\(172\) −443.114 767.495i −0.196437 0.340238i
\(173\) 765.299 1325.54i 0.336327 0.582536i −0.647412 0.762141i \(-0.724148\pi\)
0.983739 + 0.179605i \(0.0574818\pi\)
\(174\) 979.250 0.426648
\(175\) 0 0
\(176\) 242.606 0.103904
\(177\) −682.392 + 1181.94i −0.289784 + 0.501920i
\(178\) −383.159 663.651i −0.161343 0.279454i
\(179\) −1706.72 2956.12i −0.712659 1.23436i −0.963856 0.266425i \(-0.914157\pi\)
0.251197 0.967936i \(-0.419176\pi\)
\(180\) 375.068 649.637i 0.155311 0.269006i
\(181\) −1286.71 −0.528399 −0.264200 0.964468i \(-0.585108\pi\)
−0.264200 + 0.964468i \(0.585108\pi\)
\(182\) 0 0
\(183\) 115.955 0.0468394
\(184\) −2.60607 + 4.51384i −0.00104414 + 0.00180850i
\(185\) 1755.88 + 3041.28i 0.697811 + 1.20864i
\(186\) 669.977 + 1160.43i 0.264114 + 0.457458i
\(187\) −904.833 + 1567.22i −0.353839 + 0.612868i
\(188\) −2032.18 −0.788362
\(189\) 0 0
\(190\) −1396.56 −0.533248
\(191\) −527.648 + 913.913i −0.199891 + 0.346222i −0.948493 0.316798i \(-0.897392\pi\)
0.748602 + 0.663020i \(0.230726\pi\)
\(192\) 96.0000 + 166.277i 0.0360844 + 0.0625000i
\(193\) 2385.42 + 4131.67i 0.889670 + 1.54095i 0.840266 + 0.542175i \(0.182399\pi\)
0.0494044 + 0.998779i \(0.484268\pi\)
\(194\) 334.701 579.719i 0.123867 0.214543i
\(195\) −135.205 −0.0496523
\(196\) 0 0
\(197\) 1622.31 0.586725 0.293363 0.956001i \(-0.405226\pi\)
0.293363 + 0.956001i \(0.405226\pi\)
\(198\) −136.466 + 236.366i −0.0489809 + 0.0848373i
\(199\) −1775.07 3074.51i −0.632318 1.09521i −0.987077 0.160249i \(-0.948770\pi\)
0.354759 0.934958i \(-0.384563\pi\)
\(200\) −1236.74 2142.10i −0.437254 0.757347i
\(201\) 212.688 368.386i 0.0746359 0.129273i
\(202\) 29.4848 0.0102700
\(203\) 0 0
\(204\) −1432.18 −0.491533
\(205\) 3365.43 5829.10i 1.14659 1.98596i
\(206\) −841.420 1457.38i −0.284585 0.492916i
\(207\) −2.93183 5.07807i −0.000984425 0.00170507i
\(208\) 17.3030 29.9697i 0.00576803 0.00999051i
\(209\) 508.129 0.168172
\(210\) 0 0
\(211\) 4653.39 1.51826 0.759129 0.650941i \(-0.225625\pi\)
0.759129 + 0.650941i \(0.225625\pi\)
\(212\) 353.023 611.453i 0.114367 0.198089i
\(213\) 904.114 + 1565.97i 0.290840 + 0.503749i
\(214\) 715.670 + 1239.58i 0.228609 + 0.395962i
\(215\) 2308.30 3998.10i 0.732209 1.26822i
\(216\) −216.000 −0.0680414
\(217\) 0 0
\(218\) 1200.04 0.372829
\(219\) 1653.45 2863.86i 0.510181 0.883660i
\(220\) 631.901 + 1094.49i 0.193649 + 0.335410i
\(221\) 129.068 + 223.553i 0.0392854 + 0.0680442i
\(222\) 505.602 875.729i 0.152855 0.264753i
\(223\) 4649.53 1.39621 0.698107 0.715993i \(-0.254026\pi\)
0.698107 + 0.715993i \(0.254026\pi\)
\(224\) 0 0
\(225\) 2782.67 0.824495
\(226\) −622.644 + 1078.45i −0.183264 + 0.317423i
\(227\) 2075.86 + 3595.49i 0.606958 + 1.05128i 0.991739 + 0.128274i \(0.0409438\pi\)
−0.384780 + 0.923008i \(0.625723\pi\)
\(228\) 201.068 + 348.260i 0.0584038 + 0.101158i
\(229\) 2131.82 3692.41i 0.615172 1.06551i −0.375182 0.926951i \(-0.622420\pi\)
0.990354 0.138558i \(-0.0442468\pi\)
\(230\) −27.1515 −0.00778398
\(231\) 0 0
\(232\) −1305.67 −0.369488
\(233\) −1524.95 + 2641.29i −0.428768 + 0.742647i −0.996764 0.0803838i \(-0.974385\pi\)
0.567996 + 0.823031i \(0.307719\pi\)
\(234\) 19.4659 + 33.7159i 0.00543815 + 0.00941915i
\(235\) −5293.10 9167.92i −1.46929 2.54489i
\(236\) 909.856 1575.92i 0.250960 0.434676i
\(237\) 348.909 0.0956290
\(238\) 0 0
\(239\) 3987.20 1.07912 0.539562 0.841946i \(-0.318590\pi\)
0.539562 + 0.841946i \(0.318590\pi\)
\(240\) −500.091 + 866.183i −0.134503 + 0.232966i
\(241\) −312.324 540.961i −0.0834795 0.144591i 0.821263 0.570550i \(-0.193270\pi\)
−0.904742 + 0.425959i \(0.859937\pi\)
\(242\) 1101.09 + 1907.14i 0.292482 + 0.506593i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) −154.606 −0.0405641
\(245\) 0 0
\(246\) −1938.14 −0.502321
\(247\) 36.2405 62.7704i 0.00933574 0.0161700i
\(248\) −893.303 1547.25i −0.228729 0.396170i
\(249\) 853.392 + 1478.12i 0.217195 + 0.376193i
\(250\) 3837.90 6647.43i 0.970920 1.68168i
\(251\) 1328.78 0.334152 0.167076 0.985944i \(-0.446568\pi\)
0.167076 + 0.985944i \(0.446568\pi\)
\(252\) 0 0
\(253\) 9.87887 0.00245486
\(254\) 180.076 311.900i 0.0444841 0.0770487i
\(255\) −3730.32 6461.10i −0.916085 1.58671i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −1613.09 + 2793.96i −0.391525 + 0.678141i −0.992651 0.121013i \(-0.961386\pi\)
0.601126 + 0.799154i \(0.294719\pi\)
\(258\) −1329.34 −0.320780
\(259\) 0 0
\(260\) 180.273 0.0430001
\(261\) 734.437 1272.08i 0.174178 0.301686i
\(262\) 217.860 + 377.344i 0.0513719 + 0.0889787i
\(263\) −1625.31 2815.11i −0.381067 0.660028i 0.610148 0.792288i \(-0.291110\pi\)
−0.991215 + 0.132260i \(0.957777\pi\)
\(264\) 181.955 315.155i 0.0424187 0.0734713i
\(265\) 3677.99 0.852593
\(266\) 0 0
\(267\) −1149.48 −0.263471
\(268\) −283.583 + 491.181i −0.0646366 + 0.111954i
\(269\) 1413.02 + 2447.42i 0.320273 + 0.554729i 0.980544 0.196298i \(-0.0628921\pi\)
−0.660271 + 0.751027i \(0.729559\pi\)
\(270\) −562.602 974.456i −0.126811 0.219643i
\(271\) −1198.38 + 2075.66i −0.268622 + 0.465268i −0.968506 0.248989i \(-0.919902\pi\)
0.699884 + 0.714257i \(0.253235\pi\)
\(272\) 1909.58 0.425680
\(273\) 0 0
\(274\) −5203.71 −1.14733
\(275\) −2344.07 + 4060.05i −0.514010 + 0.890292i
\(276\) 3.90910 + 6.77076i 0.000852537 + 0.00147664i
\(277\) −910.233 1576.57i −0.197439 0.341974i 0.750258 0.661145i \(-0.229929\pi\)
−0.947697 + 0.319170i \(0.896596\pi\)
\(278\) −2651.55 + 4592.62i −0.572048 + 0.990816i
\(279\) 2009.93 0.431296
\(280\) 0 0
\(281\) 3083.81 0.654679 0.327339 0.944907i \(-0.393848\pi\)
0.327339 + 0.944907i \(0.393848\pi\)
\(282\) −1524.14 + 2639.88i −0.321848 + 0.557456i
\(283\) 1277.38 + 2212.49i 0.268313 + 0.464732i 0.968426 0.249300i \(-0.0802005\pi\)
−0.700113 + 0.714032i \(0.746867\pi\)
\(284\) −1205.48 2087.96i −0.251875 0.436259i
\(285\) −1047.42 + 1814.19i −0.217698 + 0.377063i
\(286\) −65.5910 −0.0135611
\(287\) 0 0
\(288\) 288.000 0.0589256
\(289\) −4665.53 + 8080.94i −0.949630 + 1.64481i
\(290\) −3400.79 5890.34i −0.688625 1.19273i
\(291\) −502.051 869.578i −0.101137 0.175174i
\(292\) −2204.60 + 3818.48i −0.441830 + 0.765272i
\(293\) 1846.47 0.368163 0.184081 0.982911i \(-0.441069\pi\)
0.184081 + 0.982911i \(0.441069\pi\)
\(294\) 0 0
\(295\) 9479.39 1.87089
\(296\) −674.136 + 1167.64i −0.132376 + 0.229282i
\(297\) 204.699 + 354.549i 0.0399927 + 0.0692694i
\(298\) −581.023 1006.36i −0.112945 0.195627i
\(299\) 0.704576 1.22036i 0.000136277 0.000236038i
\(300\) −3710.23 −0.714034
\(301\) 0 0
\(302\) −1230.78 −0.234515
\(303\) 22.1136 38.3019i 0.00419272 0.00726201i
\(304\) −268.091 464.347i −0.0505792 0.0876057i
\(305\) −402.693 697.485i −0.0756005 0.130944i
\(306\) −1074.14 + 1860.46i −0.200668 + 0.347566i
\(307\) −7041.50 −1.30905 −0.654527 0.756039i \(-0.727132\pi\)
−0.654527 + 0.756039i \(0.727132\pi\)
\(308\) 0 0
\(309\) −2524.26 −0.464726
\(310\) 4653.47 8060.04i 0.852578 1.47671i
\(311\) −1343.00 2326.14i −0.244869 0.424126i 0.717226 0.696841i \(-0.245412\pi\)
−0.962095 + 0.272715i \(0.912078\pi\)
\(312\) −25.9546 44.9546i −0.00470957 0.00815722i
\(313\) 1109.59 1921.87i 0.200377 0.347063i −0.748273 0.663391i \(-0.769117\pi\)
0.948650 + 0.316328i \(0.102450\pi\)
\(314\) 613.864 0.110326
\(315\) 0 0
\(316\) −465.212 −0.0828172
\(317\) −1110.63 + 1923.67i −0.196780 + 0.340833i −0.947483 0.319807i \(-0.896382\pi\)
0.750703 + 0.660640i \(0.229715\pi\)
\(318\) −529.534 917.180i −0.0933799 0.161739i
\(319\) 1237.35 + 2143.16i 0.217174 + 0.376157i
\(320\) 666.788 1154.91i 0.116483 0.201755i
\(321\) 2147.01 0.373316
\(322\) 0 0
\(323\) 3999.53 0.688978
\(324\) −162.000 + 280.592i −0.0277778 + 0.0481125i
\(325\) 334.366 + 579.138i 0.0570685 + 0.0988455i
\(326\) −3514.50 6087.29i −0.597086 1.03418i
\(327\) 900.028 1558.89i 0.152207 0.263630i
\(328\) 2584.18 0.435023
\(329\) 0 0
\(330\) 1895.70 0.316228
\(331\) −2077.03 + 3597.52i −0.344906 + 0.597394i −0.985337 0.170622i \(-0.945422\pi\)
0.640431 + 0.768016i \(0.278756\pi\)
\(332\) −1137.86 1970.82i −0.188096 0.325792i
\(333\) −758.403 1313.59i −0.124806 0.216170i
\(334\) 1123.30 1945.62i 0.184025 0.318741i
\(335\) −2954.53 −0.481860
\(336\) 0 0
\(337\) −254.167 −0.0410841 −0.0205420 0.999789i \(-0.506539\pi\)
−0.0205420 + 0.999789i \(0.506539\pi\)
\(338\) 2192.32 3797.21i 0.352801 0.611069i
\(339\) 933.966 + 1617.68i 0.149634 + 0.259174i
\(340\) 4973.76 + 8614.80i 0.793353 + 1.37413i
\(341\) −1693.13 + 2932.59i −0.268880 + 0.465714i
\(342\) 603.205 0.0953730
\(343\) 0 0
\(344\) 1772.45 0.277803
\(345\) −20.3636 + 35.2708i −0.00317780 + 0.00550410i
\(346\) 1530.60 + 2651.07i 0.237819 + 0.411915i
\(347\) 3112.32 + 5390.69i 0.481493 + 0.833970i 0.999774 0.0212401i \(-0.00676143\pi\)
−0.518282 + 0.855210i \(0.673428\pi\)
\(348\) −979.250 + 1696.11i −0.150843 + 0.261267i
\(349\) −9732.21 −1.49270 −0.746352 0.665552i \(-0.768196\pi\)
−0.746352 + 0.665552i \(0.768196\pi\)
\(350\) 0 0
\(351\) 58.3977 0.00888046
\(352\) −242.606 + 420.206i −0.0367356 + 0.0636280i
\(353\) 712.807 + 1234.62i 0.107476 + 0.186153i 0.914747 0.404027i \(-0.132390\pi\)
−0.807271 + 0.590180i \(0.799057\pi\)
\(354\) −1364.78 2363.88i −0.204908 0.354911i
\(355\) 6279.71 10876.8i 0.938852 1.62614i
\(356\) 1532.64 0.228173
\(357\) 0 0
\(358\) 6826.86 1.00785
\(359\) 2883.25 4993.93i 0.423877 0.734177i −0.572438 0.819948i \(-0.694002\pi\)
0.996315 + 0.0857714i \(0.0273355\pi\)
\(360\) 750.136 + 1299.27i 0.109821 + 0.190216i
\(361\) 2867.99 + 4967.51i 0.418136 + 0.724233i
\(362\) 1286.71 2228.64i 0.186817 0.323577i
\(363\) 3303.26 0.477621
\(364\) 0 0
\(365\) −22968.7 −3.29381
\(366\) −115.955 + 200.839i −0.0165602 + 0.0286831i
\(367\) 5772.67 + 9998.56i 0.821065 + 1.42213i 0.904890 + 0.425646i \(0.139953\pi\)
−0.0838244 + 0.996481i \(0.526713\pi\)
\(368\) −5.21213 9.02768i −0.000738319 0.00127881i
\(369\) −1453.60 + 2517.71i −0.205072 + 0.355195i
\(370\) −7023.53 −0.986854
\(371\) 0 0
\(372\) −2679.91 −0.373513
\(373\) 3239.79 5611.47i 0.449731 0.778957i −0.548637 0.836061i \(-0.684853\pi\)
0.998368 + 0.0571033i \(0.0181864\pi\)
\(374\) −1809.67 3134.43i −0.250202 0.433363i
\(375\) −5756.85 9971.15i −0.792753 1.37309i
\(376\) 2032.18 3519.84i 0.278728 0.482771i
\(377\) 353.000 0.0482239
\(378\) 0 0
\(379\) 611.996 0.0829449 0.0414725 0.999140i \(-0.486795\pi\)
0.0414725 + 0.999140i \(0.486795\pi\)
\(380\) 1396.56 2418.91i 0.188532 0.326546i
\(381\) −270.114 467.851i −0.0363211 0.0629100i
\(382\) −1055.30 1827.83i −0.141345 0.244816i
\(383\) 2180.41 3776.57i 0.290897 0.503848i −0.683125 0.730301i \(-0.739380\pi\)
0.974022 + 0.226453i \(0.0727130\pi\)
\(384\) −384.000 −0.0510310
\(385\) 0 0
\(386\) −9541.68 −1.25818
\(387\) −997.006 + 1726.86i −0.130958 + 0.226825i
\(388\) 669.402 + 1159.44i 0.0875869 + 0.151705i
\(389\) 6573.46 + 11385.6i 0.856781 + 1.48399i 0.874983 + 0.484154i \(0.160872\pi\)
−0.0182021 + 0.999834i \(0.505794\pi\)
\(390\) 135.205 234.181i 0.0175547 0.0304057i
\(391\) 77.7575 0.0100572
\(392\) 0 0
\(393\) 653.580 0.0838899
\(394\) −1622.31 + 2809.92i −0.207439 + 0.359294i
\(395\) −1211.71 2098.74i −0.154349 0.267340i
\(396\) −272.932 472.732i −0.0346347 0.0599891i
\(397\) −4239.02 + 7342.20i −0.535895 + 0.928198i 0.463224 + 0.886241i \(0.346692\pi\)
−0.999119 + 0.0419565i \(0.986641\pi\)
\(398\) 7100.27 0.894232
\(399\) 0 0
\(400\) 4946.97 0.618371
\(401\) −1401.50 + 2427.47i −0.174533 + 0.302299i −0.939999 0.341176i \(-0.889175\pi\)
0.765467 + 0.643475i \(0.222508\pi\)
\(402\) 425.375 + 736.771i 0.0527756 + 0.0914100i
\(403\) 241.513 + 418.313i 0.0298527 + 0.0517064i
\(404\) −29.4848 + 51.0692i −0.00363100 + 0.00628908i
\(405\) −1687.81 −0.207081
\(406\) 0 0
\(407\) 2555.46 0.311227
\(408\) 1432.18 2480.61i 0.173783 0.301001i
\(409\) −3192.69 5529.91i −0.385987 0.668548i 0.605919 0.795526i \(-0.292806\pi\)
−0.991906 + 0.126978i \(0.959472\pi\)
\(410\) 6730.86 + 11658.2i 0.810765 + 1.40429i
\(411\) −3902.78 + 6759.82i −0.468395 + 0.811283i
\(412\) 3365.68 0.402464
\(413\) 0 0
\(414\) 11.7273 0.00139219
\(415\) 5927.41 10266.6i 0.701121 1.21438i
\(416\) 34.6061 + 59.9395i 0.00407861 + 0.00706436i
\(417\) 3977.32 + 6888.93i 0.467075 + 0.808998i
\(418\) −508.129 + 880.105i −0.0594579 + 0.102984i
\(419\) −4831.66 −0.563346 −0.281673 0.959510i \(-0.590889\pi\)
−0.281673 + 0.959510i \(0.590889\pi\)
\(420\) 0 0
\(421\) 7475.37 0.865385 0.432693 0.901542i \(-0.357564\pi\)
0.432693 + 0.901542i \(0.357564\pi\)
\(422\) −4653.39 + 8059.90i −0.536785 + 0.929739i
\(423\) 2286.20 + 3959.82i 0.262787 + 0.455161i
\(424\) 706.045 + 1222.91i 0.0808693 + 0.140070i
\(425\) −18450.4 + 31957.1i −2.10583 + 3.64740i
\(426\) −3616.45 −0.411309
\(427\) 0 0
\(428\) −2862.68 −0.323301
\(429\) −49.1932 + 85.2051i −0.00553630 + 0.00958914i
\(430\) 4616.61 + 7996.20i 0.517750 + 0.896769i
\(431\) −3495.97 6055.19i −0.390707 0.676725i 0.601836 0.798620i \(-0.294436\pi\)
−0.992543 + 0.121895i \(0.961103\pi\)
\(432\) 216.000 374.123i 0.0240563 0.0416667i
\(433\) 7699.26 0.854510 0.427255 0.904131i \(-0.359481\pi\)
0.427255 + 0.904131i \(0.359481\pi\)
\(434\) 0 0
\(435\) −10202.4 −1.12452
\(436\) −1200.04 + 2078.53i −0.131815 + 0.228310i
\(437\) −10.9166 18.9081i −0.00119499 0.00206979i
\(438\) 3306.90 + 5727.71i 0.360753 + 0.624842i
\(439\) 4706.16 8151.31i 0.511646 0.886198i −0.488262 0.872697i \(-0.662369\pi\)
0.999909 0.0135008i \(-0.00429758\pi\)
\(440\) −2527.61 −0.273861
\(441\) 0 0
\(442\) −516.273 −0.0555579
\(443\) 3129.09 5419.74i 0.335593 0.581263i −0.648006 0.761635i \(-0.724397\pi\)
0.983598 + 0.180372i \(0.0577301\pi\)
\(444\) 1011.20 + 1751.46i 0.108085 + 0.187208i
\(445\) 3991.97 + 6914.29i 0.425252 + 0.736559i
\(446\) −4649.53 + 8053.23i −0.493636 + 0.855003i
\(447\) −1743.07 −0.184439
\(448\) 0 0
\(449\) −11633.8 −1.22279 −0.611396 0.791325i \(-0.709392\pi\)
−0.611396 + 0.791325i \(0.709392\pi\)
\(450\) −2782.67 + 4819.73i −0.291503 + 0.504898i
\(451\) −2448.98 4241.75i −0.255694 0.442874i
\(452\) −1245.29 2156.90i −0.129587 0.224452i
\(453\) −923.085 + 1598.83i −0.0957402 + 0.165827i
\(454\) −8303.43 −0.858369
\(455\) 0 0
\(456\) −804.273 −0.0825954
\(457\) 6552.31 11348.9i 0.670688 1.16167i −0.307022 0.951703i \(-0.599332\pi\)
0.977709 0.209963i \(-0.0673343\pi\)
\(458\) 4263.63 + 7384.83i 0.434992 + 0.753429i
\(459\) 1611.20 + 2790.69i 0.163844 + 0.283787i
\(460\) 27.1515 47.0277i 0.00275205 0.00476669i
\(461\) 2594.63 0.262134 0.131067 0.991373i \(-0.458160\pi\)
0.131067 + 0.991373i \(0.458160\pi\)
\(462\) 0 0
\(463\) −14136.2 −1.41893 −0.709465 0.704741i \(-0.751063\pi\)
−0.709465 + 0.704741i \(0.751063\pi\)
\(464\) 1305.67 2261.48i 0.130634 0.226264i
\(465\) −6980.20 12090.1i −0.696127 1.20573i
\(466\) −3049.90 5282.58i −0.303184 0.525131i
\(467\) 7795.12 13501.5i 0.772409 1.33785i −0.163830 0.986489i \(-0.552385\pi\)
0.936239 0.351363i \(-0.114282\pi\)
\(468\) −77.8637 −0.00769070
\(469\) 0 0
\(470\) 21172.4 2.07789
\(471\) 460.398 797.432i 0.0450404 0.0780122i
\(472\) 1819.71 + 3151.83i 0.177456 + 0.307362i
\(473\) −1679.72 2909.36i −0.163285 0.282817i
\(474\) −348.909 + 604.328i −0.0338100 + 0.0585606i
\(475\) 10361.2 1.00085
\(476\) 0 0
\(477\) −1588.60 −0.152489
\(478\) −3987.20 + 6906.04i −0.381528 + 0.660826i
\(479\) −4226.75 7320.95i −0.403184 0.698336i 0.590924 0.806727i \(-0.298763\pi\)
−0.994108 + 0.108391i \(0.965430\pi\)
\(480\) −1000.18 1732.37i −0.0951080 0.164732i
\(481\) 182.259 315.683i 0.0172772 0.0299249i
\(482\) 1249.30 0.118058
\(483\) 0 0
\(484\) −4404.35 −0.413632
\(485\) −3487.10 + 6039.83i −0.326476 + 0.565474i
\(486\) 243.000 + 420.888i 0.0226805 + 0.0392837i
\(487\) 2005.53 + 3473.69i 0.186611 + 0.323219i 0.944118 0.329607i \(-0.106916\pi\)
−0.757507 + 0.652827i \(0.773583\pi\)
\(488\) 154.606 267.786i 0.0143416 0.0248403i
\(489\) −10543.5 −0.975038
\(490\) 0 0
\(491\) 13927.9 1.28016 0.640079 0.768309i \(-0.278902\pi\)
0.640079 + 0.768309i \(0.278902\pi\)
\(492\) 1938.14 3356.95i 0.177597 0.307608i
\(493\) 9739.33 + 16869.0i 0.889731 + 1.54106i
\(494\) 72.4810 + 125.541i 0.00660137 + 0.0114339i
\(495\) 1421.78 2462.59i 0.129099 0.223607i
\(496\) 3573.21 0.323472
\(497\) 0 0
\(498\) −3413.57 −0.307160
\(499\) 1973.77 3418.68i 0.177071 0.306695i −0.763805 0.645447i \(-0.776671\pi\)
0.940876 + 0.338751i \(0.110005\pi\)
\(500\) 7675.80 + 13294.9i 0.686544 + 1.18913i
\(501\) −1684.95 2918.43i −0.150256 0.260251i
\(502\) −1328.78 + 2301.52i −0.118141 + 0.204625i
\(503\) 13725.3 1.21666 0.608331 0.793684i \(-0.291839\pi\)
0.608331 + 0.793684i \(0.291839\pi\)
\(504\) 0 0
\(505\) −307.190 −0.0270688
\(506\) −9.87887 + 17.1107i −0.000867924 + 0.00150329i
\(507\) −3288.48 5695.82i −0.288060 0.498935i
\(508\) 360.152 + 623.801i 0.0314550 + 0.0544817i
\(509\) 3915.05 6781.07i 0.340926 0.590502i −0.643679 0.765296i \(-0.722593\pi\)
0.984605 + 0.174794i \(0.0559259\pi\)
\(510\) 14921.3 1.29554
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 452.403 783.586i 0.0389359 0.0674389i
\(514\) −3226.18 5587.91i −0.276850 0.479518i
\(515\) 8766.39 + 15183.8i 0.750084 + 1.29918i
\(516\) 1329.34 2302.49i 0.113413 0.196437i
\(517\) −7703.43 −0.655312
\(518\) 0 0
\(519\) 4591.80 0.388357
\(520\) −180.273 + 312.241i −0.0152028 + 0.0263321i
\(521\) −2953.69 5115.95i −0.248376 0.430199i 0.714700 0.699431i \(-0.246563\pi\)
−0.963075 + 0.269232i \(0.913230\pi\)
\(522\) 1468.87 + 2544.17i 0.123163 + 0.213324i
\(523\) 3954.03 6848.58i 0.330588 0.572595i −0.652039 0.758185i \(-0.726086\pi\)
0.982627 + 0.185590i \(0.0594196\pi\)
\(524\) −871.439 −0.0726508
\(525\) 0 0
\(526\) 6501.23 0.538911
\(527\) −13326.8 + 23082.7i −1.10156 + 1.90797i
\(528\) 363.909 + 630.309i 0.0299945 + 0.0519520i
\(529\) 6083.29 + 10536.6i 0.499983 + 0.865995i
\(530\) −3677.99 + 6370.46i −0.301437 + 0.522104i
\(531\) −4094.35 −0.334613
\(532\) 0 0
\(533\) −698.659 −0.0567773
\(534\) 1149.48 1990.95i 0.0931512 0.161343i
\(535\) −7456.26 12914.6i −0.602546 1.04364i
\(536\) −567.167 982.362i −0.0457050 0.0791633i
\(537\) 5120.15 8868.36i 0.411454 0.712659i
\(538\) −5652.08 −0.452934
\(539\) 0 0
\(540\) 2250.41 0.179337
\(541\) 1970.52 3413.04i 0.156598 0.271235i −0.777042 0.629449i \(-0.783281\pi\)
0.933640 + 0.358214i \(0.116614\pi\)
\(542\) −2396.77 4151.33i −0.189945 0.328994i
\(543\) −1930.06 3342.97i −0.152536 0.264200i
\(544\) −1909.58 + 3307.48i −0.150501 + 0.260675i
\(545\) −12502.7 −0.982670
\(546\) 0 0
\(547\) −1828.71 −0.142943 −0.0714717 0.997443i \(-0.522770\pi\)
−0.0714717 + 0.997443i \(0.522770\pi\)
\(548\) 5203.71 9013.09i 0.405642 0.702592i
\(549\) 173.932 + 301.259i 0.0135214 + 0.0234197i
\(550\) −4688.14 8120.10i −0.363460 0.629532i
\(551\) 2734.67 4736.58i 0.211435 0.366216i
\(552\) −15.6364 −0.00120567
\(553\) 0 0
\(554\) 3640.93 0.279221
\(555\) −5267.65 + 9123.83i −0.402881 + 0.697811i
\(556\) −5303.10 9185.24i −0.404499 0.700613i
\(557\) −11266.0 19513.3i −0.857011 1.48439i −0.874767 0.484544i \(-0.838985\pi\)
0.0177556 0.999842i \(-0.494348\pi\)
\(558\) −2009.93 + 3481.30i −0.152486 + 0.264114i
\(559\) −479.201 −0.0362577
\(560\) 0 0
\(561\) −5429.00 −0.408579
\(562\) −3083.81 + 5341.32i −0.231464 + 0.400907i
\(563\) 11677.9 + 20226.6i 0.874179 + 1.51412i 0.857635 + 0.514260i \(0.171933\pi\)
0.0165446 + 0.999863i \(0.494733\pi\)
\(564\) −3048.27 5279.76i −0.227581 0.394181i
\(565\) 6487.05 11235.9i 0.483031 0.836634i
\(566\) −5109.54 −0.379452
\(567\) 0 0
\(568\) 4821.94 0.356204
\(569\) 10443.8 18089.2i 0.769468 1.33276i −0.168384 0.985721i \(-0.553855\pi\)
0.937852 0.347036i \(-0.112812\pi\)
\(570\) −2094.84 3628.37i −0.153935 0.266624i
\(571\) −11872.6 20564.0i −0.870147 1.50714i −0.861844 0.507173i \(-0.830690\pi\)
−0.00830301 0.999966i \(-0.502643\pi\)
\(572\) 65.5910 113.607i 0.00479457 0.00830444i
\(573\) −3165.89 −0.230815
\(574\) 0 0
\(575\) 201.440 0.0146098
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) 1227.20 + 2125.57i 0.0885422 + 0.153360i 0.906895 0.421356i \(-0.138446\pi\)
−0.818353 + 0.574716i \(0.805113\pi\)
\(578\) −9331.06 16161.9i −0.671490 1.16305i
\(579\) −7156.26 + 12395.0i −0.513651 + 0.889670i
\(580\) 13603.2 0.973863
\(581\) 0 0
\(582\) 2008.20 0.143029
\(583\) 1338.21 2317.85i 0.0950652 0.164658i
\(584\) −4409.20 7636.95i −0.312421 0.541129i
\(585\) −202.807 351.272i −0.0143334 0.0248261i
\(586\) −1846.47 + 3198.17i −0.130165 + 0.225453i
\(587\) −18567.5 −1.30556 −0.652780 0.757547i \(-0.726397\pi\)
−0.652780 + 0.757547i \(0.726397\pi\)
\(588\) 0 0
\(589\) 7483.95 0.523550
\(590\) −9479.39 + 16418.8i −0.661458 + 1.14568i
\(591\) 2433.47 + 4214.89i 0.169373 + 0.293363i
\(592\) −1348.27 2335.28i −0.0936042 0.162127i
\(593\) 8556.47 14820.2i 0.592533 1.02630i −0.401357 0.915922i \(-0.631461\pi\)
0.993890 0.110375i \(-0.0352053\pi\)
\(594\) −818.795 −0.0565582
\(595\) 0 0
\(596\) 2324.09 0.159729
\(597\) 5325.20 9223.52i 0.365069 0.632318i
\(598\) 1.40915 + 2.44072i 9.63621e−5 + 0.000166904i
\(599\) −11632.4 20147.9i −0.793469 1.37433i −0.923807 0.382859i \(-0.874940\pi\)
0.130338 0.991470i \(-0.458394\pi\)
\(600\) 3710.23 6426.30i 0.252449 0.437254i
\(601\) −25322.3 −1.71867 −0.859334 0.511416i \(-0.829121\pi\)
−0.859334 + 0.511416i \(0.829121\pi\)
\(602\) 0 0
\(603\) 1276.13 0.0861821
\(604\) 1230.78 2131.77i 0.0829135 0.143610i
\(605\) −11471.7 19869.6i −0.770897 1.33523i
\(606\) 44.2272 + 76.6038i 0.00296470 + 0.00513501i
\(607\) −10867.2 + 18822.5i −0.726665 + 1.25862i 0.231620 + 0.972806i \(0.425597\pi\)
−0.958285 + 0.285814i \(0.907736\pi\)
\(608\) 1072.36 0.0715297
\(609\) 0 0
\(610\) 1610.77 0.106915
\(611\) −549.420 + 951.624i −0.0363784 + 0.0630092i
\(612\) −2148.27 3720.92i −0.141893 0.245767i
\(613\) 6786.19 + 11754.0i 0.447131 + 0.774454i 0.998198 0.0600072i \(-0.0191124\pi\)
−0.551067 + 0.834461i \(0.685779\pi\)
\(614\) 7041.50 12196.2i 0.462820 0.801628i
\(615\) 20192.6 1.32397
\(616\) 0 0
\(617\) −8497.12 −0.554427 −0.277213 0.960808i \(-0.589411\pi\)
−0.277213 + 0.960808i \(0.589411\pi\)
\(618\) 2524.26 4372.15i 0.164305 0.284585i
\(619\) −11491.5 19903.8i −0.746173 1.29241i −0.949645 0.313329i \(-0.898556\pi\)
0.203472 0.979081i \(-0.434777\pi\)
\(620\) 9306.93 + 16120.1i 0.602863 + 1.04419i
\(621\) 8.79548 15.2342i 0.000568358 0.000984425i
\(622\) 5371.98 0.346297
\(623\) 0 0
\(624\) 103.818 0.00666034
\(625\) −20661.3 + 35786.4i −1.32232 + 2.29033i
\(626\) 2219.19 + 3843.75i 0.141688 + 0.245411i
\(627\) 762.193 + 1320.16i 0.0485471 + 0.0840861i
\(628\) −613.864 + 1063.24i −0.0390061 + 0.0675605i
\(629\) 20114.3 1.27505
\(630\) 0 0
\(631\) −15717.9 −0.991635 −0.495817 0.868427i \(-0.665131\pi\)
−0.495817 + 0.868427i \(0.665131\pi\)
\(632\) 465.212 805.771i 0.0292803 0.0507150i
\(633\) 6980.08 + 12089.9i 0.438283 + 0.759129i
\(634\) −2221.26 3847.34i −0.139144 0.241005i
\(635\) −1876.13 + 3249.55i −0.117247 + 0.203078i
\(636\) 2118.14 0.132059
\(637\) 0 0
\(638\) −4949.42 −0.307131
\(639\) −2712.34 + 4697.91i −0.167916 + 0.290840i
\(640\) 1333.58 + 2309.82i 0.0823660 + 0.142662i
\(641\) −14553.7 25207.7i −0.896780 1.55327i −0.831587 0.555395i \(-0.812567\pi\)
−0.0651930 0.997873i \(-0.520766\pi\)
\(642\) −2147.01 + 3718.73i −0.131987 + 0.228609i
\(643\) 3112.26 0.190880 0.0954398 0.995435i \(-0.469574\pi\)
0.0954398 + 0.995435i \(0.469574\pi\)
\(644\) 0 0
\(645\) 13849.8 0.845482
\(646\) −3999.53 + 6927.39i −0.243590 + 0.421911i
\(647\) −3928.80 6804.87i −0.238728 0.413489i 0.721622 0.692288i \(-0.243397\pi\)
−0.960349 + 0.278799i \(0.910064\pi\)
\(648\) −324.000 561.184i −0.0196419 0.0340207i
\(649\) 3449.01 5973.86i 0.208606 0.361317i
\(650\) −1337.46 −0.0807071
\(651\) 0 0
\(652\) 14058.0 0.844408
\(653\) 9761.01 16906.6i 0.584958 1.01318i −0.409923 0.912120i \(-0.634444\pi\)
0.994881 0.101057i \(-0.0322224\pi\)
\(654\) 1800.06 + 3117.79i 0.107627 + 0.186415i
\(655\) −2269.79 3931.38i −0.135401 0.234522i
\(656\) −2584.18 + 4475.93i −0.153804 + 0.266396i
\(657\) 9920.69 0.589107
\(658\) 0 0
\(659\) 664.061 0.0392536 0.0196268 0.999807i \(-0.493752\pi\)
0.0196268 + 0.999807i \(0.493752\pi\)
\(660\) −1895.70 + 3283.46i −0.111803 + 0.193649i
\(661\) 7960.82 + 13788.5i 0.468442 + 0.811365i 0.999349 0.0360650i \(-0.0114823\pi\)
−0.530908 + 0.847430i \(0.678149\pi\)
\(662\) −4154.06 7195.04i −0.243885 0.422422i
\(663\) −387.205 + 670.658i −0.0226814 + 0.0392854i
\(664\) 4551.42 0.266008
\(665\) 0 0
\(666\) 3033.61 0.176502
\(667\) 53.1665 92.0870i 0.00308638 0.00534576i
\(668\) 2246.61 + 3891.24i 0.130125 + 0.225384i
\(669\) 6974.30 + 12079.8i 0.403052 + 0.698107i
\(670\) 2954.53 5117.40i 0.170363 0.295078i
\(671\) −586.068 −0.0337182
\(672\) 0 0
\(673\) 24631.0 1.41078 0.705391 0.708819i \(-0.250771\pi\)
0.705391 + 0.708819i \(0.250771\pi\)
\(674\) 254.167 440.230i 0.0145254 0.0251588i
\(675\) 4174.01 + 7229.59i 0.238011 + 0.412247i
\(676\) 4384.64 + 7594.43i 0.249468 + 0.432091i
\(677\) 8546.39 14802.8i 0.485177 0.840350i −0.514678 0.857383i \(-0.672089\pi\)
0.999855 + 0.0170329i \(0.00542200\pi\)
\(678\) −3735.86 −0.211615
\(679\) 0 0
\(680\) −19895.0 −1.12197
\(681\) −6227.57 + 10786.5i −0.350428 + 0.606958i
\(682\) −3386.26 5865.18i −0.190127 0.329310i
\(683\) 9581.79 + 16596.1i 0.536804 + 0.929771i 0.999074 + 0.0430322i \(0.0137018\pi\)
−0.462270 + 0.886739i \(0.652965\pi\)
\(684\) −603.205 + 1044.78i −0.0337194 + 0.0584038i
\(685\) 54215.2 3.02402
\(686\) 0 0
\(687\) 12790.9 0.710339
\(688\) −1772.45 + 3069.98i −0.0982183 + 0.170119i
\(689\) −190.886 330.625i −0.0105547 0.0182813i
\(690\) −40.7272 70.5416i −0.00224704 0.00389199i
\(691\) 4047.94 7011.23i 0.222852 0.385991i −0.732821 0.680422i \(-0.761797\pi\)
0.955673 + 0.294431i \(0.0951300\pi\)
\(692\) −6122.39 −0.336327
\(693\) 0 0
\(694\) −12449.3 −0.680934
\(695\) 27625.3 47848.5i 1.50775 2.61150i
\(696\) −1958.50 3392.22i −0.106662 0.184744i
\(697\) −19276.1 33387.2i −1.04754 1.81439i
\(698\) 9732.21 16856.7i 0.527750 0.914090i
\(699\) −9149.70 −0.495098
\(700\) 0 0
\(701\) 12354.7 0.665664 0.332832 0.942986i \(-0.391996\pi\)
0.332832 + 0.942986i \(0.391996\pi\)
\(702\) −58.3977 + 101.148i −0.00313972 + 0.00543815i
\(703\) −2823.90 4891.14i −0.151501 0.262408i
\(704\) −485.212 840.412i −0.0259760 0.0449918i
\(705\) 15879.3 27503.8i 0.848297 1.46929i
\(706\) −2851.23 −0.151993
\(707\) 0 0
\(708\) 5459.14 0.289784
\(709\) −1914.41 + 3315.85i −0.101406 + 0.175641i −0.912264 0.409602i \(-0.865668\pi\)
0.810858 + 0.585243i \(0.199001\pi\)
\(710\) 12559.4 + 21753.5i 0.663868 + 1.14985i
\(711\) 523.364 + 906.492i 0.0276057 + 0.0478145i
\(712\) −1532.64 + 2654.60i −0.0806713 + 0.139727i
\(713\) 145.500 0.00764241
\(714\) 0 0
\(715\) 683.363 0.0357431
\(716\) −6826.86 + 11824.5i −0.356329 + 0.617181i
\(717\) 5980.81 + 10359.1i 0.311516 + 0.539562i
\(718\) 5766.49 + 9987.86i 0.299726 + 0.519141i
\(719\) 611.500 1059.15i 0.0317178 0.0549368i −0.849731 0.527217i \(-0.823236\pi\)
0.881449 + 0.472280i \(0.156569\pi\)
\(720\) −3000.55 −0.155311
\(721\) 0 0
\(722\) −11472.0 −0.591333
\(723\) 936.972 1622.88i 0.0481969 0.0834795i
\(724\) 2573.42 + 4457.29i 0.132100 + 0.228804i
\(725\) 25230.8 + 43701.1i 1.29248 + 2.23864i
\(726\) −3303.26 + 5721.42i −0.168864 + 0.292482i
\(727\) −6368.21 −0.324875 −0.162437 0.986719i \(-0.551936\pi\)
−0.162437 + 0.986719i \(0.551936\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 22968.7 39783.0i 1.16454 2.01704i
\(731\) −13221.2 22899.9i −0.668954 1.15866i
\(732\) −231.909 401.678i −0.0117098 0.0202820i
\(733\) −12577.0 + 21784.0i −0.633753 + 1.09769i 0.353024 + 0.935614i \(0.385153\pi\)
−0.986778 + 0.162079i \(0.948180\pi\)
\(734\) −23090.7 −1.16116
\(735\) 0 0
\(736\) 20.8485 0.00104414
\(737\) −1074.98 + 1861.93i −0.0537281 + 0.0930597i
\(738\) −2907.20 5035.43i −0.145008 0.251161i
\(739\) 5369.55 + 9300.34i 0.267283 + 0.462948i 0.968159 0.250335i \(-0.0805408\pi\)
−0.700876 + 0.713283i \(0.747207\pi\)
\(740\) 7023.53 12165.1i 0.348906 0.604322i
\(741\) 217.443 0.0107800
\(742\) 0 0
\(743\) 28166.3 1.39074 0.695370 0.718652i \(-0.255240\pi\)
0.695370 + 0.718652i \(0.255240\pi\)
\(744\) 2679.91 4641.74i 0.132057 0.228729i
\(745\) 6053.42 + 10484.8i 0.297691 + 0.515617i
\(746\) 6479.57 + 11222.9i 0.318008 + 0.550806i
\(747\) −2560.18 + 4434.36i −0.125398 + 0.217195i
\(748\) 7238.67 0.353839
\(749\) 0 0
\(750\) 23027.4 1.12112
\(751\) −14328.5 + 24817.7i −0.696211 + 1.20587i 0.273559 + 0.961855i \(0.411799\pi\)
−0.969771 + 0.244018i \(0.921534\pi\)
\(752\) 4064.36 + 7039.68i 0.197091 + 0.341371i
\(753\) 1993.18 + 3452.28i 0.0964613 + 0.167076i
\(754\) −353.000 + 611.414i −0.0170497 + 0.0295310i
\(755\) 12823.0 0.618113
\(756\) 0 0
\(757\) −23604.1 −1.13330 −0.566648 0.823960i \(-0.691760\pi\)
−0.566648 + 0.823960i \(0.691760\pi\)
\(758\) −611.996 + 1060.01i −0.0293255 + 0.0507932i
\(759\) 14.8183 + 25.6661i 0.000708657 + 0.00122743i
\(760\) 2793.12 + 4837.83i 0.133312 + 0.230903i
\(761\) 2315.48 4010.54i 0.110297 0.191041i −0.805593 0.592470i \(-0.798153\pi\)
0.915890 + 0.401429i \(0.131486\pi\)
\(762\) 1080.45 0.0513658
\(763\) 0 0
\(764\) 4221.18 0.199891
\(765\) 11191.0 19383.3i 0.528902 0.916085i
\(766\) 4360.81 + 7553.15i 0.205695 + 0.356274i
\(767\) −491.977 852.129i −0.0231607 0.0401155i
\(768\) 384.000 665.108i 0.0180422 0.0312500i
\(769\) −33276.8 −1.56046 −0.780228 0.625495i \(-0.784897\pi\)
−0.780228 + 0.625495i \(0.784897\pi\)
\(770\) 0 0
\(771\) −9678.55 −0.452094
\(772\) 9541.68 16526.7i 0.444835 0.770477i
\(773\) −11469.4 19865.6i −0.533668 0.924340i −0.999227 0.0393231i \(-0.987480\pi\)
0.465558 0.885017i \(-0.345853\pi\)
\(774\) −1994.01 3453.73i −0.0926011 0.160390i
\(775\) −34524.6 + 59798.3i −1.60020 + 2.77164i
\(776\) −2677.61 −0.123867
\(777\) 0 0
\(778\) −26293.8 −1.21167
\(779\) −5412.47 + 9374.67i −0.248937 + 0.431171i
\(780\) 270.409 + 468.362i 0.0124131 + 0.0215001i
\(781\) −4569.66 7914.88i −0.209366 0.362633i
\(782\) −77.7575 + 134.680i −0.00355576 + 0.00615876i
\(783\) 4406.62 0.201124
\(784\) 0 0
\(785\) −6395.58 −0.290787
\(786\) −653.580 + 1132.03i −0.0296596 + 0.0513719i
\(787\) −6757.23 11703.9i −0.306060 0.530112i 0.671437 0.741062i \(-0.265678\pi\)
−0.977497 + 0.210950i \(0.932344\pi\)
\(788\) −3244.62 5619.85i −0.146681 0.254059i
\(789\) 4875.92 8445.34i 0.220009 0.381067i
\(790\) 4846.84 0.218282
\(791\) 0 0
\(792\) 1091.73 0.0489809
\(793\) −41.7993 + 72.3985i −0.00187180 + 0.00324205i
\(794\) −8478.04 14684.4i −0.378935 0.656335i
\(795\) 5516.98 + 9555.69i 0.246122 + 0.426296i
\(796\) −7100.27 + 12298.0i −0.316159 + 0.547603i
\(797\) −10473.4 −0.465480 −0.232740 0.972539i \(-0.574769\pi\)
−0.232740 + 0.972539i \(0.574769\pi\)
\(798\) 0 0
\(799\) −60634.5 −2.68472
\(800\) −4946.97 + 8568.40i −0.218627 + 0.378673i
\(801\) −1724.22 2986.43i −0.0760576 0.131736i
\(802\) −2803.00 4854.94i −0.123413 0.213758i
\(803\) −8357.02 + 14474.8i −0.367264 + 0.636119i
\(804\) −1701.50 −0.0746359
\(805\) 0 0
\(806\) −966.053 −0.0422181
\(807\) −4239.06 + 7342.27i −0.184910 + 0.320273i
\(808\) −58.9697 102.138i −0.00256751 0.00444705i
\(809\) −11784.0 20410.5i −0.512117 0.887013i −0.999901 0.0140486i \(-0.995528\pi\)
0.487784 0.872964i \(-0.337805\pi\)
\(810\) 1687.81 2923.37i 0.0732142 0.126811i
\(811\) 6704.22 0.290280 0.145140 0.989411i \(-0.453637\pi\)
0.145140 + 0.989411i \(0.453637\pi\)
\(812\) 0 0
\(813\) −7190.31 −0.310178
\(814\) −2555.46 + 4426.19i −0.110035 + 0.190587i
\(815\) 36616.0 + 63420.8i 1.57375 + 2.72581i
\(816\) 2864.36 + 4961.22i 0.122883 + 0.212840i
\(817\) −3712.34 + 6429.95i −0.158970 + 0.275343i
\(818\) 12770.8 0.545867
\(819\) 0 0
\(820\) −26923.5 −1.14659
\(821\) −12269.7 + 21251.8i −0.521579 + 0.903401i 0.478106 + 0.878302i \(0.341323\pi\)
−0.999685 + 0.0250988i \(0.992010\pi\)
\(822\) −7805.57 13519.6i −0.331205 0.573664i
\(823\) 15558.5 + 26948.1i 0.658973 + 1.14137i 0.980882 + 0.194604i \(0.0623421\pi\)
−0.321909 + 0.946771i \(0.604325\pi\)
\(824\) −3365.68 + 5829.53i −0.142293 + 0.246458i
\(825\) −14064.4 −0.593528
\(826\) 0 0
\(827\) 31244.9 1.31377 0.656887 0.753989i \(-0.271873\pi\)
0.656887 + 0.753989i \(0.271873\pi\)
\(828\) −11.7273 + 20.3123i −0.000492212 + 0.000852537i
\(829\) 2115.75 + 3664.58i 0.0886405 + 0.153530i 0.906937 0.421267i \(-0.138414\pi\)
−0.818296 + 0.574797i \(0.805081\pi\)
\(830\) 11854.8 + 20533.2i 0.495767 + 0.858694i
\(831\) 2730.70 4729.71i 0.113991 0.197439i
\(832\) −138.424 −0.00576803
\(833\) 0 0
\(834\) −15909.3 −0.660544
\(835\) −11703.2 + 20270.5i −0.485037 + 0.840109i
\(836\) −1016.26 1760.21i −0.0420431 0.0728207i
\(837\) 3014.90 + 5221.96i 0.124504 + 0.215648i
\(838\) 4831.66 8368.68i 0.199173 0.344978i
\(839\) 38670.4 1.59124 0.795621 0.605795i \(-0.207145\pi\)
0.795621 + 0.605795i \(0.207145\pi\)
\(840\) 0 0
\(841\) 2247.96 0.0921710
\(842\) −7475.37 + 12947.7i −0.305960 + 0.529938i
\(843\) 4625.72 + 8011.97i 0.188989 + 0.327339i
\(844\) −9306.77 16119.8i −0.379564 0.657425i
\(845\) −22840.8 + 39561.5i −0.929880 + 1.61060i
\(846\) −9144.82 −0.371637
\(847\) 0 0
\(848\) −2824.18 −0.114367
\(849\) −3832.15 + 6637.48i −0.154911 + 0.268313i
\(850\) −36900.8 63914.1i −1.48904 2.57910i
\(851\) −54.9014 95.0920i −0.00221151 0.00383045i
\(852\) 3616.45 6263.88i 0.145420 0.251875i
\(853\) 19944.4 0.800565 0.400282 0.916392i \(-0.368912\pi\)
0.400282 + 0.916392i \(0.368912\pi\)
\(854\) 0 0
\(855\) −6284.52 −0.251376
\(856\) 2862.68 4958.31i 0.114304 0.197981i
\(857\) 6941.10 + 12022.3i 0.276667 + 0.479201i 0.970554 0.240882i \(-0.0774368\pi\)
−0.693887 + 0.720084i \(0.744103\pi\)
\(858\) −98.3864 170.410i −0.00391475 0.00678055i
\(859\) −2078.58 + 3600.21i −0.0825614 + 0.143000i −0.904349 0.426793i \(-0.859643\pi\)
0.821788 + 0.569793i \(0.192977\pi\)
\(860\) −18466.4 −0.732209
\(861\) 0 0
\(862\) 13983.9 0.552543
\(863\) 8118.96 14062.5i 0.320246 0.554683i −0.660292 0.751009i \(-0.729568\pi\)
0.980539 + 0.196326i \(0.0629009\pi\)
\(864\) 432.000 + 748.246i 0.0170103 + 0.0294628i
\(865\) −15946.6 27620.4i −0.626823 1.08569i
\(866\) −7699.26 + 13335.5i −0.302115 + 0.523278i
\(867\) −27993.2 −1.09654
\(868\) 0 0
\(869\) −1763.49 −0.0688403
\(870\) 10202.4 17671.0i 0.397578 0.688625i
\(871\) 153.339 + 265.591i 0.00596521 + 0.0103320i
\(872\) −2400.08 4157.05i −0.0932074 0.161440i
\(873\) 1506.15 2608.73i 0.0583913 0.101137i
\(874\) 43.6664 0.00168998
\(875\) 0 0
\(876\) −13227.6 −0.510181
\(877\) 8244.70 14280.2i 0.317450 0.549840i −0.662505 0.749057i \(-0.730507\pi\)
0.979955 + 0.199218i \(0.0638401\pi\)
\(878\) 9412.32 + 16302.6i 0.361789 + 0.626636i
\(879\) 2769.70 + 4797.26i 0.106279 + 0.184081i
\(880\) 2527.61 4377.94i 0.0968245 0.167705i
\(881\) −45411.7 −1.73662 −0.868309 0.496023i \(-0.834793\pi\)
−0.868309 + 0.496023i \(0.834793\pi\)
\(882\) 0 0
\(883\) −2206.85 −0.0841070 −0.0420535 0.999115i \(-0.513390\pi\)
−0.0420535 + 0.999115i \(0.513390\pi\)
\(884\) 516.273 894.211i 0.0196427 0.0340221i
\(885\) 14219.1 + 24628.2i 0.540078 + 0.935443i
\(886\) 6258.18 + 10839.5i 0.237300 + 0.411015i
\(887\) 14073.1 24375.3i 0.532727 0.922710i −0.466543 0.884498i \(-0.654501\pi\)
0.999270 0.0382111i \(-0.0121659\pi\)
\(888\) −4044.82 −0.152855
\(889\) 0 0
\(890\) −15967.9 −0.601398
\(891\) −614.097 + 1063.65i −0.0230898 + 0.0399927i
\(892\) −9299.07 16106.5i −0.349054 0.604579i
\(893\) 8512.65 + 14744.3i 0.318998 + 0.552520i
\(894\) 1743.07 3019.08i 0.0652091 0.112945i
\(895\) −71126.1 −2.65641
\(896\) 0 0
\(897\) 4.22746 0.000157359
\(898\) 11633.8 20150.4i 0.432322 0.748804i
\(899\) 18224.3 + 31565.4i 0.676101 + 1.17104i
\(900\) −5565.34 9639.45i −0.206124 0.357017i
\(901\) 10533.2 18244.0i 0.389469 0.674579i
\(902\) 9795.91 0.361605
\(903\) 0 0
\(904\) 4981.15 0.183264
\(905\) −13405.6 + 23219.3i −0.492396 + 0.852856i
\(906\) −1846.17 3197.66i −0.0676986 0.117257i
\(907\) 2521.12 + 4366.71i 0.0922960 + 0.159861i 0.908477 0.417935i \(-0.137246\pi\)
−0.816181 + 0.577797i \(0.803913\pi\)
\(908\) 8303.43 14382.0i 0.303479 0.525641i
\(909\) 132.682 0.00484134
\(910\) 0 0
\(911\) 29647.3 1.07822 0.539110 0.842235i \(-0.318761\pi\)
0.539110 + 0.842235i \(0.318761\pi\)
\(912\) 804.273 1393.04i 0.0292019 0.0505792i
\(913\) −4313.29 7470.84i −0.156352 0.270809i
\(914\) 13104.6 + 22697.9i 0.474248 + 0.821421i
\(915\) 1208.08 2092.46i 0.0436480 0.0756005i
\(916\) −17054.5 −0.615172
\(917\) 0 0
\(918\) −6444.82 −0.231711
\(919\) 5945.64 10298.1i 0.213415 0.369646i −0.739366 0.673304i \(-0.764875\pi\)
0.952781 + 0.303658i \(0.0982080\pi\)
\(920\) 54.3029 + 94.0554i 0.00194599 + 0.00337056i
\(921\) −10562.2 18294.3i −0.377891 0.654527i
\(922\) −2594.63 + 4494.03i −0.0926785 + 0.160524i
\(923\) −1303.66 −0.0464902
\(924\) 0 0
\(925\) 52108.3 1.85223
\(926\) 14136.2 24484.6i 0.501667 0.868913i
\(927\) −3786.39 6558.22i −0.134155 0.232363i
\(928\) 2611.33 + 4522.96i 0.0923720 + 0.159993i
\(929\) −19594.3 + 33938.3i −0.691999 + 1.19858i 0.279183 + 0.960238i \(0.409937\pi\)
−0.971182 + 0.238340i \(0.923397\pi\)
\(930\) 27920.8 0.984472
\(931\) 0 0
\(932\) 12199.6 0.428768
\(933\) 4028.99 6978.41i 0.141375 0.244869i
\(934\) 15590.2 + 27003.1i 0.546176 + 0.946004i
\(935\) 18854.1 + 32656.3i 0.659461 + 1.14222i
\(936\) 77.8637 134.864i 0.00271907 0.00470957i
\(937\) −9716.23 −0.338757 −0.169379 0.985551i \(-0.554176\pi\)
−0.169379 + 0.985551i \(0.554176\pi\)
\(938\) 0 0
\(939\) 6657.57 0.231375
\(940\) −21172.4 + 36671.7i −0.734647 + 1.27245i
\(941\) −3497.93 6058.60i −0.121179 0.209888i 0.799054 0.601259i \(-0.205334\pi\)
−0.920233 + 0.391371i \(0.872001\pi\)
\(942\) 920.795 + 1594.86i 0.0318483 + 0.0551629i
\(943\) −105.227 + 182.259i −0.00363380 + 0.00629393i
\(944\) −7278.85 −0.250960
\(945\) 0 0
\(946\) 6718.88 0.230919
\(947\) −7489.62 + 12972.4i −0.257001 + 0.445139i −0.965437 0.260636i \(-0.916068\pi\)
0.708436 + 0.705775i \(0.249401\pi\)
\(948\) −697.818 1208.66i −0.0239073 0.0414086i
\(949\) 1192.07 + 2064.73i 0.0407758 + 0.0706258i
\(950\) −10361.2 + 17946.2i −0.353855 + 0.612896i
\(951\) −6663.78 −0.227222
\(952\) 0 0
\(953\) 29393.3 0.999100 0.499550 0.866285i \(-0.333499\pi\)
0.499550 + 0.866285i \(0.333499\pi\)
\(954\) 1588.60 2751.54i 0.0539129 0.0933799i
\(955\) 10994.7 + 19043.3i 0.372543 + 0.645264i
\(956\) −7974.41 13812.1i −0.269781 0.467275i
\(957\) −3712.06 + 6429.48i −0.125386 + 0.217174i
\(958\) 16907.0 0.570189
\(959\) 0 0
\(960\) 4000.73 0.134503
\(961\) −10041.7 + 17392.7i −0.337072 + 0.583825i
\(962\) 364.519 + 631.365i 0.0122168 + 0.0211601i
\(963\) 3220.52 + 5578.10i 0.107767 + 0.186658i
\(964\) −1249.30 + 2163.84i −0.0417397 + 0.0722953i
\(965\) 99410.6 3.31621
\(966\) 0 0
\(967\) −7133.95 −0.237241 −0.118621 0.992940i \(-0.537847\pi\)
−0.118621 + 0.992940i \(0.537847\pi\)
\(968\) 4404.35 7628.56i 0.146241 0.253297i
\(969\) 5999.30 + 10391.1i 0.198891 + 0.344489i
\(970\) −6974.20 12079.7i −0.230854 0.399850i
\(971\) −4844.06 + 8390.16i −0.160096 + 0.277295i −0.934903 0.354903i \(-0.884514\pi\)
0.774807 + 0.632198i \(0.217847\pi\)
\(972\) −972.000 −0.0320750
\(973\) 0 0
\(974\) −8022.14 −0.263907
\(975\) −1003.10 + 1737.41i −0.0329485 + 0.0570685i
\(976\) 309.212 + 535.571i 0.0101410 + 0.0175648i
\(977\) −10652.8 18451.3i −0.348838 0.604205i 0.637205 0.770694i \(-0.280090\pi\)
−0.986043 + 0.166489i \(0.946757\pi\)
\(978\) 10543.5 18261.9i 0.344728 0.597086i
\(979\) 5809.79 0.189665
\(980\) 0 0
\(981\) 5400.17 0.175753
\(982\) −13927.9 + 24123.8i −0.452604 + 0.783933i
\(983\) −18640.4 32286.1i −0.604818 1.04758i −0.992080 0.125606i \(-0.959913\pi\)
0.387262 0.921970i \(-0.373421\pi\)
\(984\) 3876.27 + 6713.90i 0.125580 + 0.217512i
\(985\) 16902.1 29275.4i 0.546748 0.946996i
\(986\) −38957.3 −1.25827
\(987\) 0 0
\(988\) −289.924 −0.00933574
\(989\) −72.1740 + 125.009i −0.00232052 + 0.00401927i
\(990\) 2843.56 + 4925.18i 0.0912870 + 0.158114i
\(991\) 25698.5 + 44511.2i 0.823755 + 1.42678i 0.902867 + 0.429919i \(0.141458\pi\)
−0.0791128 + 0.996866i \(0.525209\pi\)
\(992\) −3573.21 + 6188.98i −0.114365 + 0.198085i
\(993\) −12462.2 −0.398263
\(994\) 0 0
\(995\) −73974.6 −2.35694
\(996\) 3413.57 5912.47i 0.108597 0.188096i
\(997\) −17186.9 29768.6i −0.545953 0.945618i −0.998546 0.0539007i \(-0.982835\pi\)
0.452594 0.891717i \(-0.350499\pi\)
\(998\) 3947.55 + 6837.36i 0.125208 + 0.216866i
\(999\) 2275.21 3940.78i 0.0720565 0.124806i
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 294.4.e.l.79.2 4
3.2 odd 2 882.4.g.bf.667.1 4
7.2 even 3 294.4.a.m.1.1 2
7.3 odd 6 42.4.e.c.25.1 4
7.4 even 3 inner 294.4.e.l.67.2 4
7.5 odd 6 294.4.a.n.1.2 2
7.6 odd 2 42.4.e.c.37.1 yes 4
21.2 odd 6 882.4.a.z.1.2 2
21.5 even 6 882.4.a.v.1.1 2
21.11 odd 6 882.4.g.bf.361.1 4
21.17 even 6 126.4.g.g.109.2 4
21.20 even 2 126.4.g.g.37.2 4
28.3 even 6 336.4.q.j.193.1 4
28.19 even 6 2352.4.a.bq.1.2 2
28.23 odd 6 2352.4.a.ca.1.1 2
28.27 even 2 336.4.q.j.289.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.e.c.25.1 4 7.3 odd 6
42.4.e.c.37.1 yes 4 7.6 odd 2
126.4.g.g.37.2 4 21.20 even 2
126.4.g.g.109.2 4 21.17 even 6
294.4.a.m.1.1 2 7.2 even 3
294.4.a.n.1.2 2 7.5 odd 6
294.4.e.l.67.2 4 7.4 even 3 inner
294.4.e.l.79.2 4 1.1 even 1 trivial
336.4.q.j.193.1 4 28.3 even 6
336.4.q.j.289.1 4 28.27 even 2
882.4.a.v.1.1 2 21.5 even 6
882.4.a.z.1.2 2 21.2 odd 6
882.4.g.bf.361.1 4 21.11 odd 6
882.4.g.bf.667.1 4 3.2 odd 2
2352.4.a.bq.1.2 2 28.19 even 6
2352.4.a.ca.1.1 2 28.23 odd 6