Properties

Label 350.3.i.a.299.4
Level $350$
Weight $3$
Character 350.299
Analytic conductor $9.537$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,3,Mod(199,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.199");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 350.i (of order \(6\), 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: \(9.53680925261\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 299.4
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 350.299
Dual form 350.3.i.a.199.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(2.09077 + 3.62132i) q^{3} +(1.00000 + 1.73205i) q^{4} +5.91359i q^{6} +(6.63103 - 2.24264i) q^{7} +2.82843i q^{8} +(-4.24264 + 7.34847i) q^{9} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(2.09077 + 3.62132i) q^{3} +(1.00000 + 1.73205i) q^{4} +5.91359i q^{6} +(6.63103 - 2.24264i) q^{7} +2.82843i q^{8} +(-4.24264 + 7.34847i) q^{9} +(6.62132 + 11.4685i) q^{11} +(-4.18154 + 7.24264i) q^{12} -5.49333 q^{13} +(9.70711 + 1.94218i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-6.77962 - 11.7426i) q^{17} +(-10.3923 + 6.00000i) q^{18} +(0.621320 + 0.358719i) q^{19} +(21.9853 + 19.3242i) q^{21} +18.7279i q^{22} +(-1.96768 - 1.13604i) q^{23} +(-10.2426 + 5.91359i) q^{24} +(-6.72792 - 3.88437i) q^{26} +2.15232 q^{27} +(10.5154 + 9.24264i) q^{28} -20.4853 q^{29} +(21.3198 - 12.3090i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-27.6873 + 47.9558i) q^{33} -19.1757i q^{34} -16.9706 q^{36} +(-56.2407 - 32.4706i) q^{37} +(0.507306 + 0.878680i) q^{38} +(-11.4853 - 19.8931i) q^{39} -21.0308i q^{41} +(13.2621 + 39.2132i) q^{42} -6.48528i q^{43} +(-13.2426 + 22.9369i) q^{44} +(-1.60660 - 2.78272i) q^{46} +(-23.8900 + 41.3787i) q^{47} -16.7262 q^{48} +(38.9411 - 29.7420i) q^{49} +(28.3492 - 49.1023i) q^{51} +(-5.49333 - 9.51472i) q^{52} +(-19.0781 + 11.0147i) q^{53} +(2.63604 + 1.52192i) q^{54} +(6.34315 + 18.7554i) q^{56} +3.00000i q^{57} +(-25.0892 - 14.4853i) q^{58} +(72.5330 - 41.8770i) q^{59} +(57.3823 + 33.1297i) q^{61} +34.8151 q^{62} +(-11.6531 + 58.2426i) q^{63} -8.00000 q^{64} +(-67.8198 + 39.1558i) q^{66} +(80.2283 - 46.3198i) q^{67} +(13.5592 - 23.4853i) q^{68} -9.50079i q^{69} -48.4264 q^{71} +(-20.7846 - 12.0000i) q^{72} +(-65.4953 - 113.441i) q^{73} +(-45.9203 - 79.5363i) q^{74} +1.43488i q^{76} +(69.6258 + 61.1985i) q^{77} -32.4853i q^{78} +(-38.1066 + 66.0026i) q^{79} +(42.6838 + 73.9305i) q^{81} +(14.8710 - 25.7574i) q^{82} +107.981 q^{83} +(-11.4853 + 57.4039i) q^{84} +(4.58579 - 7.94282i) q^{86} +(-42.8300 - 74.1838i) q^{87} +(-32.4377 + 18.7279i) q^{88} +(145.412 + 83.9535i) q^{89} +(-36.4264 + 12.3196i) q^{91} -4.54416i q^{92} +(89.1496 + 51.4706i) q^{93} +(-58.5183 + 33.7856i) q^{94} +(-20.4853 - 11.8272i) q^{96} -25.5816 q^{97} +(68.7237 - 8.89087i) q^{98} -112.368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 36 q^{11} + 72 q^{14} - 16 q^{16} - 12 q^{19} + 108 q^{21} - 48 q^{24} + 48 q^{26} - 96 q^{29} - 84 q^{31} - 24 q^{39} - 72 q^{44} + 72 q^{46} + 40 q^{49} + 108 q^{51} + 72 q^{54} + 96 q^{56} + 156 q^{59} - 84 q^{61} - 64 q^{64} - 288 q^{66} - 48 q^{71} - 192 q^{74} - 220 q^{79} + 36 q^{81} - 24 q^{84} + 48 q^{86} + 756 q^{89} + 48 q^{91} + 24 q^{94} - 96 q^{96} - 288 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) 2.09077 + 3.62132i 0.696923 + 1.20711i 0.969528 + 0.244981i \(0.0787816\pi\)
−0.272605 + 0.962126i \(0.587885\pi\)
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 5.91359i 0.985599i
\(7\) 6.63103 2.24264i 0.947290 0.320377i
\(8\) 2.82843i 0.353553i
\(9\) −4.24264 + 7.34847i −0.471405 + 0.816497i
\(10\) 0 0
\(11\) 6.62132 + 11.4685i 0.601938 + 1.04259i 0.992527 + 0.122022i \(0.0389380\pi\)
−0.390589 + 0.920565i \(0.627729\pi\)
\(12\) −4.18154 + 7.24264i −0.348462 + 0.603553i
\(13\) −5.49333 −0.422563 −0.211282 0.977425i \(-0.567764\pi\)
−0.211282 + 0.977425i \(0.567764\pi\)
\(14\) 9.70711 + 1.94218i 0.693365 + 0.138727i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −6.77962 11.7426i −0.398801 0.690744i 0.594777 0.803891i \(-0.297240\pi\)
−0.993578 + 0.113147i \(0.963907\pi\)
\(18\) −10.3923 + 6.00000i −0.577350 + 0.333333i
\(19\) 0.621320 + 0.358719i 0.0327011 + 0.0188800i 0.516261 0.856431i \(-0.327323\pi\)
−0.483560 + 0.875311i \(0.660657\pi\)
\(20\) 0 0
\(21\) 21.9853 + 19.3242i 1.04692 + 0.920202i
\(22\) 18.7279i 0.851269i
\(23\) −1.96768 1.13604i −0.0855512 0.0493930i 0.456614 0.889665i \(-0.349062\pi\)
−0.542165 + 0.840272i \(0.682395\pi\)
\(24\) −10.2426 + 5.91359i −0.426777 + 0.246400i
\(25\) 0 0
\(26\) −6.72792 3.88437i −0.258766 0.149399i
\(27\) 2.15232 0.0797154
\(28\) 10.5154 + 9.24264i 0.375550 + 0.330094i
\(29\) −20.4853 −0.706389 −0.353195 0.935550i \(-0.614905\pi\)
−0.353195 + 0.935550i \(0.614905\pi\)
\(30\) 0 0
\(31\) 21.3198 12.3090i 0.687736 0.397064i −0.115028 0.993362i \(-0.536696\pi\)
0.802763 + 0.596298i \(0.203362\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) −27.6873 + 47.9558i −0.839010 + 1.45321i
\(34\) 19.1757i 0.563990i
\(35\) 0 0
\(36\) −16.9706 −0.471405
\(37\) −56.2407 32.4706i −1.52002 0.877583i −0.999722 0.0235970i \(-0.992488\pi\)
−0.520296 0.853986i \(-0.674179\pi\)
\(38\) 0.507306 + 0.878680i 0.0133502 + 0.0231231i
\(39\) −11.4853 19.8931i −0.294494 0.510079i
\(40\) 0 0
\(41\) 21.0308i 0.512946i −0.966551 0.256473i \(-0.917439\pi\)
0.966551 0.256473i \(-0.0825605\pi\)
\(42\) 13.2621 + 39.2132i 0.315763 + 0.933648i
\(43\) 6.48528i 0.150820i −0.997153 0.0754102i \(-0.975973\pi\)
0.997153 0.0754102i \(-0.0240266\pi\)
\(44\) −13.2426 + 22.9369i −0.300969 + 0.521294i
\(45\) 0 0
\(46\) −1.60660 2.78272i −0.0349261 0.0604938i
\(47\) −23.8900 + 41.3787i −0.508298 + 0.880397i 0.491656 + 0.870789i \(0.336392\pi\)
−0.999954 + 0.00960801i \(0.996942\pi\)
\(48\) −16.7262 −0.348462
\(49\) 38.9411 29.7420i 0.794717 0.606980i
\(50\) 0 0
\(51\) 28.3492 49.1023i 0.555867 0.962791i
\(52\) −5.49333 9.51472i −0.105641 0.182975i
\(53\) −19.0781 + 11.0147i −0.359963 + 0.207825i −0.669065 0.743204i \(-0.733305\pi\)
0.309101 + 0.951029i \(0.399972\pi\)
\(54\) 2.63604 + 1.52192i 0.0488155 + 0.0281837i
\(55\) 0 0
\(56\) 6.34315 + 18.7554i 0.113270 + 0.334918i
\(57\) 3.00000i 0.0526316i
\(58\) −25.0892 14.4853i −0.432573 0.249746i
\(59\) 72.5330 41.8770i 1.22937 0.709779i 0.262474 0.964939i \(-0.415462\pi\)
0.966899 + 0.255160i \(0.0821282\pi\)
\(60\) 0 0
\(61\) 57.3823 + 33.1297i 0.940693 + 0.543109i 0.890177 0.455614i \(-0.150580\pi\)
0.0505153 + 0.998723i \(0.483914\pi\)
\(62\) 34.8151 0.561534
\(63\) −11.6531 + 58.2426i −0.184970 + 0.924486i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −67.8198 + 39.1558i −1.02757 + 0.593269i
\(67\) 80.2283 46.3198i 1.19744 0.691340i 0.237454 0.971399i \(-0.423687\pi\)
0.959983 + 0.280058i \(0.0903539\pi\)
\(68\) 13.5592 23.4853i 0.199400 0.345372i
\(69\) 9.50079i 0.137693i
\(70\) 0 0
\(71\) −48.4264 −0.682062 −0.341031 0.940052i \(-0.610776\pi\)
−0.341031 + 0.940052i \(0.610776\pi\)
\(72\) −20.7846 12.0000i −0.288675 0.166667i
\(73\) −65.4953 113.441i −0.897195 1.55399i −0.831064 0.556177i \(-0.812268\pi\)
−0.0661316 0.997811i \(-0.521066\pi\)
\(74\) −45.9203 79.5363i −0.620545 1.07482i
\(75\) 0 0
\(76\) 1.43488i 0.0188800i
\(77\) 69.6258 + 61.1985i 0.904231 + 0.794786i
\(78\) 32.4853i 0.416478i
\(79\) −38.1066 + 66.0026i −0.482362 + 0.835476i −0.999795 0.0202482i \(-0.993554\pi\)
0.517433 + 0.855724i \(0.326888\pi\)
\(80\) 0 0
\(81\) 42.6838 + 73.9305i 0.526960 + 0.912722i
\(82\) 14.8710 25.7574i 0.181354 0.314114i
\(83\) 107.981 1.30098 0.650491 0.759514i \(-0.274563\pi\)
0.650491 + 0.759514i \(0.274563\pi\)
\(84\) −11.4853 + 57.4039i −0.136730 + 0.683379i
\(85\) 0 0
\(86\) 4.58579 7.94282i 0.0533231 0.0923583i
\(87\) −42.8300 74.1838i −0.492299 0.852687i
\(88\) −32.4377 + 18.7279i −0.368610 + 0.212817i
\(89\) 145.412 + 83.9535i 1.63384 + 0.943297i 0.982894 + 0.184173i \(0.0589606\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(90\) 0 0
\(91\) −36.4264 + 12.3196i −0.400290 + 0.135380i
\(92\) 4.54416i 0.0493930i
\(93\) 89.1496 + 51.4706i 0.958598 + 0.553447i
\(94\) −58.5183 + 33.7856i −0.622535 + 0.359421i
\(95\) 0 0
\(96\) −20.4853 11.8272i −0.213388 0.123200i
\(97\) −25.5816 −0.263728 −0.131864 0.991268i \(-0.542096\pi\)
−0.131864 + 0.991268i \(0.542096\pi\)
\(98\) 68.7237 8.89087i 0.701263 0.0907232i
\(99\) −112.368 −1.13503
\(100\) 0 0
\(101\) 24.6838 14.2512i 0.244394 0.141101i −0.372801 0.927911i \(-0.621603\pi\)
0.617194 + 0.786811i \(0.288269\pi\)
\(102\) 69.4412 40.0919i 0.680796 0.393058i
\(103\) 28.2456 48.9228i 0.274229 0.474979i −0.695711 0.718322i \(-0.744911\pi\)
0.969940 + 0.243343i \(0.0782440\pi\)
\(104\) 15.5375i 0.149399i
\(105\) 0 0
\(106\) −31.1543 −0.293909
\(107\) −41.2316 23.8051i −0.385342 0.222477i 0.294798 0.955560i \(-0.404748\pi\)
−0.680140 + 0.733082i \(0.738081\pi\)
\(108\) 2.15232 + 3.72792i 0.0199289 + 0.0345178i
\(109\) 37.6543 + 65.2192i 0.345453 + 0.598341i 0.985436 0.170047i \(-0.0543921\pi\)
−0.639983 + 0.768389i \(0.721059\pi\)
\(110\) 0 0
\(111\) 271.554i 2.44643i
\(112\) −5.49333 + 27.4558i −0.0490475 + 0.245141i
\(113\) 85.4558i 0.756246i −0.925755 0.378123i \(-0.876570\pi\)
0.925755 0.378123i \(-0.123430\pi\)
\(114\) −2.12132 + 3.67423i −0.0186081 + 0.0322301i
\(115\) 0 0
\(116\) −20.4853 35.4815i −0.176597 0.305875i
\(117\) 23.3062 40.3675i 0.199198 0.345022i
\(118\) 118.446 1.00378
\(119\) −71.2904 62.6616i −0.599079 0.526568i
\(120\) 0 0
\(121\) −27.1838 + 47.0837i −0.224659 + 0.389121i
\(122\) 46.8524 + 81.1508i 0.384036 + 0.665170i
\(123\) 76.1592 43.9706i 0.619181 0.357484i
\(124\) 42.6396 + 24.6180i 0.343868 + 0.198532i
\(125\) 0 0
\(126\) −55.4558 + 63.0924i −0.440126 + 0.500733i
\(127\) 60.6619i 0.477653i −0.971062 0.238826i \(-0.923237\pi\)
0.971062 0.238826i \(-0.0767627\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 23.4853 13.5592i 0.182056 0.105110i
\(130\) 0 0
\(131\) −115.136 66.4738i −0.878901 0.507434i −0.00860515 0.999963i \(-0.502739\pi\)
−0.870296 + 0.492529i \(0.836072\pi\)
\(132\) −110.749 −0.839010
\(133\) 4.92447 + 0.985281i 0.0370261 + 0.00740813i
\(134\) 131.012 0.977703
\(135\) 0 0
\(136\) 33.2132 19.1757i 0.244215 0.140997i
\(137\) −101.694 + 58.7132i −0.742294 + 0.428564i −0.822903 0.568182i \(-0.807647\pi\)
0.0806089 + 0.996746i \(0.474314\pi\)
\(138\) 6.71807 11.6360i 0.0486817 0.0843191i
\(139\) 68.5857i 0.493422i −0.969089 0.246711i \(-0.920650\pi\)
0.969089 0.246711i \(-0.0793499\pi\)
\(140\) 0 0
\(141\) −199.794 −1.41698
\(142\) −59.3100 34.2426i −0.417676 0.241145i
\(143\) −36.3731 63.0000i −0.254357 0.440559i
\(144\) −16.9706 29.3939i −0.117851 0.204124i
\(145\) 0 0
\(146\) 185.249i 1.26883i
\(147\) 189.122 + 78.8345i 1.28655 + 0.536289i
\(148\) 129.882i 0.877583i
\(149\) −13.1985 + 22.8604i −0.0885804 + 0.153426i −0.906911 0.421322i \(-0.861566\pi\)
0.818331 + 0.574747i \(0.194900\pi\)
\(150\) 0 0
\(151\) 67.1066 + 116.232i 0.444415 + 0.769749i 0.998011 0.0630363i \(-0.0200784\pi\)
−0.553597 + 0.832785i \(0.686745\pi\)
\(152\) −1.01461 + 1.75736i −0.00667508 + 0.0115616i
\(153\) 115.054 0.751986
\(154\) 42.0000 + 124.185i 0.272727 + 0.806399i
\(155\) 0 0
\(156\) 22.9706 39.7862i 0.147247 0.255040i
\(157\) −113.347 196.323i −0.721958 1.25047i −0.960214 0.279265i \(-0.909909\pi\)
0.238256 0.971202i \(-0.423424\pi\)
\(158\) −93.3417 + 53.8909i −0.590770 + 0.341081i
\(159\) −79.7756 46.0585i −0.501734 0.289676i
\(160\) 0 0
\(161\) −15.5955 3.12032i −0.0968662 0.0193808i
\(162\) 120.728i 0.745234i
\(163\) −79.6550 45.9889i −0.488681 0.282140i 0.235346 0.971912i \(-0.424378\pi\)
−0.724027 + 0.689771i \(0.757711\pi\)
\(164\) 36.4264 21.0308i 0.222112 0.128237i
\(165\) 0 0
\(166\) 132.250 + 76.3544i 0.796685 + 0.459967i
\(167\) −203.482 −1.21845 −0.609227 0.792996i \(-0.708520\pi\)
−0.609227 + 0.792996i \(0.708520\pi\)
\(168\) −54.6572 + 62.1838i −0.325340 + 0.370141i
\(169\) −138.823 −0.821440
\(170\) 0 0
\(171\) −5.27208 + 3.04384i −0.0308309 + 0.0178002i
\(172\) 11.2328 6.48528i 0.0653072 0.0377051i
\(173\) 35.4051 61.3234i 0.204654 0.354470i −0.745369 0.666652i \(-0.767727\pi\)
0.950022 + 0.312182i \(0.101060\pi\)
\(174\) 121.142i 0.696216i
\(175\) 0 0
\(176\) −52.9706 −0.300969
\(177\) 303.300 + 175.110i 1.71356 + 0.989323i
\(178\) 118.728 + 205.643i 0.667012 + 1.15530i
\(179\) 54.4081 + 94.2376i 0.303956 + 0.526467i 0.977028 0.213109i \(-0.0683591\pi\)
−0.673072 + 0.739577i \(0.735026\pi\)
\(180\) 0 0
\(181\) 99.6607i 0.550611i −0.961357 0.275306i \(-0.911221\pi\)
0.961357 0.275306i \(-0.0887791\pi\)
\(182\) −53.3243 10.6690i −0.292991 0.0586211i
\(183\) 277.066i 1.51402i
\(184\) 3.21320 5.56543i 0.0174631 0.0302469i
\(185\) 0 0
\(186\) 72.7904 + 126.077i 0.391346 + 0.677831i
\(187\) 89.7800 155.504i 0.480107 0.831570i
\(188\) −95.5600 −0.508298
\(189\) 14.2721 4.82687i 0.0755136 0.0255390i
\(190\) 0 0
\(191\) −34.9523 + 60.5391i −0.182996 + 0.316959i −0.942899 0.333077i \(-0.891913\pi\)
0.759903 + 0.650036i \(0.225246\pi\)
\(192\) −16.7262 28.9706i −0.0871154 0.150888i
\(193\) 28.0056 16.1690i 0.145107 0.0837774i −0.425689 0.904870i \(-0.639968\pi\)
0.570796 + 0.821092i \(0.306635\pi\)
\(194\) −31.3310 18.0889i −0.161500 0.0932419i
\(195\) 0 0
\(196\) 90.4558 + 37.7060i 0.461509 + 0.192377i
\(197\) 277.103i 1.40661i 0.710887 + 0.703306i \(0.248294\pi\)
−0.710887 + 0.703306i \(0.751706\pi\)
\(198\) −137.622 79.4558i −0.695058 0.401292i
\(199\) −145.011 + 83.7222i −0.728699 + 0.420715i −0.817946 0.575295i \(-0.804887\pi\)
0.0892469 + 0.996010i \(0.471554\pi\)
\(200\) 0 0
\(201\) 335.478 + 193.688i 1.66904 + 0.963623i
\(202\) 40.3084 0.199547
\(203\) −135.839 + 45.9411i −0.669155 + 0.226311i
\(204\) 113.397 0.555867
\(205\) 0 0
\(206\) 69.1873 39.9453i 0.335861 0.193909i
\(207\) 16.6963 9.63961i 0.0806584 0.0465682i
\(208\) 10.9867 19.0294i 0.0528204 0.0914877i
\(209\) 9.50079i 0.0454583i
\(210\) 0 0
\(211\) −128.073 −0.606982 −0.303491 0.952834i \(-0.598152\pi\)
−0.303491 + 0.952834i \(0.598152\pi\)
\(212\) −38.1561 22.0294i −0.179982 0.103912i
\(213\) −101.248 175.368i −0.475345 0.823322i
\(214\) −33.6655 58.3103i −0.157315 0.272478i
\(215\) 0 0
\(216\) 6.08767i 0.0281837i
\(217\) 113.768 129.434i 0.524275 0.596470i
\(218\) 106.503i 0.488544i
\(219\) 273.871 474.359i 1.25055 2.16602i
\(220\) 0 0
\(221\) 37.2426 + 64.5061i 0.168519 + 0.291883i
\(222\) 192.018 332.584i 0.864944 1.49813i
\(223\) −417.169 −1.87071 −0.935357 0.353705i \(-0.884922\pi\)
−0.935357 + 0.353705i \(0.884922\pi\)
\(224\) −26.1421 + 29.7420i −0.116706 + 0.132777i
\(225\) 0 0
\(226\) 60.4264 104.662i 0.267373 0.463104i
\(227\) 116.130 + 201.143i 0.511586 + 0.886093i 0.999910 + 0.0134307i \(0.00427525\pi\)
−0.488324 + 0.872663i \(0.662391\pi\)
\(228\) −5.19615 + 3.00000i −0.0227901 + 0.0131579i
\(229\) 72.4188 + 41.8110i 0.316239 + 0.182581i 0.649715 0.760178i \(-0.274888\pi\)
−0.333476 + 0.942759i \(0.608222\pi\)
\(230\) 0 0
\(231\) −76.0477 + 380.089i −0.329211 + 1.64541i
\(232\) 57.9411i 0.249746i
\(233\) 189.723 + 109.537i 0.814261 + 0.470114i 0.848434 0.529302i \(-0.177546\pi\)
−0.0341721 + 0.999416i \(0.510879\pi\)
\(234\) 57.0883 32.9600i 0.243967 0.140854i
\(235\) 0 0
\(236\) 145.066 + 83.7539i 0.614687 + 0.354889i
\(237\) −318.689 −1.34468
\(238\) −43.0041 127.154i −0.180689 0.534262i
\(239\) −193.103 −0.807961 −0.403980 0.914768i \(-0.632374\pi\)
−0.403980 + 0.914768i \(0.632374\pi\)
\(240\) 0 0
\(241\) 42.8970 24.7666i 0.177996 0.102766i −0.408355 0.912823i \(-0.633897\pi\)
0.586351 + 0.810057i \(0.300564\pi\)
\(242\) −66.5864 + 38.4437i −0.275150 + 0.158858i
\(243\) −168.798 + 292.368i −0.694644 + 1.20316i
\(244\) 132.519i 0.543109i
\(245\) 0 0
\(246\) 124.368 0.505559
\(247\) −3.41311 1.97056i −0.0138183 0.00797799i
\(248\) 34.8151 + 60.3015i 0.140383 + 0.243151i
\(249\) 225.765 + 391.036i 0.906685 + 1.57042i
\(250\) 0 0
\(251\) 162.524i 0.647507i 0.946141 + 0.323754i \(0.104945\pi\)
−0.946141 + 0.323754i \(0.895055\pi\)
\(252\) −112.532 + 38.0589i −0.446557 + 0.151027i
\(253\) 30.0883i 0.118926i
\(254\) 42.8944 74.2954i 0.168876 0.292501i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 49.5798 85.8747i 0.192917 0.334143i −0.753298 0.657679i \(-0.771538\pi\)
0.946216 + 0.323536i \(0.104872\pi\)
\(258\) 38.3513 0.148648
\(259\) −445.753 89.1857i −1.72106 0.344346i
\(260\) 0 0
\(261\) 86.9117 150.535i 0.332995 0.576764i
\(262\) −94.0082 162.827i −0.358810 0.621477i
\(263\) −376.154 + 217.173i −1.43024 + 0.825751i −0.997139 0.0755923i \(-0.975915\pi\)
−0.433105 + 0.901344i \(0.642582\pi\)
\(264\) −135.640 78.3116i −0.513786 0.296635i
\(265\) 0 0
\(266\) 5.33452 + 4.68885i 0.0200546 + 0.0176272i
\(267\) 702.110i 2.62962i
\(268\) 160.457 + 92.6396i 0.598718 + 0.345670i
\(269\) 79.1619 45.7041i 0.294282 0.169904i −0.345589 0.938386i \(-0.612321\pi\)
0.639871 + 0.768482i \(0.278988\pi\)
\(270\) 0 0
\(271\) 14.8051 + 8.54772i 0.0546313 + 0.0315414i 0.527067 0.849824i \(-0.323292\pi\)
−0.472436 + 0.881365i \(0.656625\pi\)
\(272\) 54.2369 0.199400
\(273\) −120.772 106.154i −0.442389 0.388844i
\(274\) −166.066 −0.606080
\(275\) 0 0
\(276\) 16.4558 9.50079i 0.0596226 0.0344231i
\(277\) −346.766 + 200.206i −1.25186 + 0.722764i −0.971479 0.237124i \(-0.923795\pi\)
−0.280385 + 0.959888i \(0.590462\pi\)
\(278\) 48.4974 84.0000i 0.174451 0.302158i
\(279\) 208.891i 0.748712i
\(280\) 0 0
\(281\) −538.690 −1.91705 −0.958524 0.285012i \(-0.908002\pi\)
−0.958524 + 0.285012i \(0.908002\pi\)
\(282\) −244.697 141.276i −0.867718 0.500977i
\(283\) 154.604 + 267.783i 0.546306 + 0.946229i 0.998523 + 0.0543215i \(0.0172996\pi\)
−0.452218 + 0.891907i \(0.649367\pi\)
\(284\) −48.4264 83.8770i −0.170516 0.295342i
\(285\) 0 0
\(286\) 102.879i 0.359715i
\(287\) −47.1645 139.456i −0.164336 0.485909i
\(288\) 48.0000i 0.166667i
\(289\) 52.5736 91.0601i 0.181916 0.315087i
\(290\) 0 0
\(291\) −53.4853 92.6392i −0.183798 0.318348i
\(292\) 130.991 226.882i 0.448598 0.776994i
\(293\) 327.391 1.11738 0.558688 0.829378i \(-0.311305\pi\)
0.558688 + 0.829378i \(0.311305\pi\)
\(294\) 175.882 + 230.282i 0.598239 + 0.783272i
\(295\) 0 0
\(296\) 91.8406 159.073i 0.310272 0.537408i
\(297\) 14.2512 + 24.6838i 0.0479838 + 0.0831103i
\(298\) −32.3296 + 18.6655i −0.108488 + 0.0626358i
\(299\) 10.8091 + 6.24063i 0.0361508 + 0.0208717i
\(300\) 0 0
\(301\) −14.5442 43.0041i −0.0483195 0.142871i
\(302\) 189.806i 0.628497i
\(303\) 103.216 + 59.5919i 0.340647 + 0.196673i
\(304\) −2.48528 + 1.43488i −0.00817527 + 0.00471999i
\(305\) 0 0
\(306\) 140.912 + 81.3554i 0.460496 + 0.265867i
\(307\) −256.140 −0.834331 −0.417165 0.908831i \(-0.636976\pi\)
−0.417165 + 0.908831i \(0.636976\pi\)
\(308\) −36.3731 + 181.794i −0.118094 + 0.590240i
\(309\) 236.220 0.764467
\(310\) 0 0
\(311\) 187.349 108.166i 0.602409 0.347801i −0.167580 0.985859i \(-0.553595\pi\)
0.769989 + 0.638057i \(0.220262\pi\)
\(312\) 56.2662 32.4853i 0.180340 0.104119i
\(313\) 78.4092 135.809i 0.250509 0.433893i −0.713157 0.701004i \(-0.752736\pi\)
0.963666 + 0.267110i \(0.0860689\pi\)
\(314\) 320.595i 1.02100i
\(315\) 0 0
\(316\) −152.426 −0.482362
\(317\) 388.005 + 224.015i 1.22399 + 0.706671i 0.965766 0.259414i \(-0.0835294\pi\)
0.258224 + 0.966085i \(0.416863\pi\)
\(318\) −65.1365 112.820i −0.204832 0.354779i
\(319\) −135.640 234.935i −0.425203 0.736472i
\(320\) 0 0
\(321\) 199.084i 0.620199i
\(322\) −16.8941 14.8492i −0.0524660 0.0461157i
\(323\) 9.72792i 0.0301174i
\(324\) −85.3675 + 147.861i −0.263480 + 0.456361i
\(325\) 0 0
\(326\) −65.0381 112.649i −0.199503 0.345550i
\(327\) −157.453 + 272.717i −0.481508 + 0.833996i
\(328\) 59.4841 0.181354
\(329\) −65.6177 + 327.960i −0.199446 + 0.996839i
\(330\) 0 0
\(331\) 27.5036 47.6376i 0.0830924 0.143920i −0.821484 0.570231i \(-0.806854\pi\)
0.904577 + 0.426311i \(0.140187\pi\)
\(332\) 107.981 + 187.029i 0.325245 + 0.563342i
\(333\) 477.218 275.522i 1.43309 0.827393i
\(334\) −249.213 143.883i −0.746147 0.430788i
\(335\) 0 0
\(336\) −110.912 + 37.5108i −0.330094 + 0.111639i
\(337\) 111.632i 0.331254i −0.986189 0.165627i \(-0.947035\pi\)
0.986189 0.165627i \(-0.0529647\pi\)
\(338\) −170.023 98.1630i −0.503027 0.290423i
\(339\) 309.463 178.669i 0.912870 0.527046i
\(340\) 0 0
\(341\) 282.331 + 163.004i 0.827949 + 0.478016i
\(342\) −8.60927 −0.0251733
\(343\) 191.519 284.551i 0.558365 0.829596i
\(344\) 18.3431 0.0533231
\(345\) 0 0
\(346\) 86.7244 50.0703i 0.250648 0.144712i
\(347\) 326.714 188.628i 0.941539 0.543598i 0.0510967 0.998694i \(-0.483728\pi\)
0.890442 + 0.455096i \(0.150395\pi\)
\(348\) 85.6600 148.368i 0.246150 0.426343i
\(349\) 204.034i 0.584624i 0.956323 + 0.292312i \(0.0944246\pi\)
−0.956323 + 0.292312i \(0.905575\pi\)
\(350\) 0 0
\(351\) −11.8234 −0.0336848
\(352\) −64.8754 37.4558i −0.184305 0.106409i
\(353\) 208.538 + 361.198i 0.590759 + 1.02323i 0.994130 + 0.108189i \(0.0345051\pi\)
−0.403371 + 0.915036i \(0.632162\pi\)
\(354\) 247.643 + 428.931i 0.699557 + 1.21167i
\(355\) 0 0
\(356\) 335.814i 0.943297i
\(357\) 77.8658 389.176i 0.218112 1.09013i
\(358\) 153.889i 0.429859i
\(359\) −89.4153 + 154.872i −0.249068 + 0.431398i −0.963267 0.268544i \(-0.913457\pi\)
0.714200 + 0.699942i \(0.246791\pi\)
\(360\) 0 0
\(361\) −180.243 312.189i −0.499287 0.864791i
\(362\) 70.4707 122.059i 0.194671 0.337179i
\(363\) −227.340 −0.626281
\(364\) −57.7645 50.7728i −0.158694 0.139486i
\(365\) 0 0
\(366\) −195.915 + 339.335i −0.535288 + 0.927145i
\(367\) −314.497 544.724i −0.856939 1.48426i −0.874835 0.484422i \(-0.839030\pi\)
0.0178960 0.999840i \(-0.494303\pi\)
\(368\) 7.87071 4.54416i 0.0213878 0.0123482i
\(369\) 154.544 + 89.2261i 0.418819 + 0.241805i
\(370\) 0 0
\(371\) −101.805 + 115.824i −0.274407 + 0.312194i
\(372\) 205.882i 0.553447i
\(373\) −221.320 127.779i −0.593351 0.342572i 0.173070 0.984910i \(-0.444631\pi\)
−0.766422 + 0.642338i \(0.777965\pi\)
\(374\) 219.915 126.968i 0.588009 0.339487i
\(375\) 0 0
\(376\) −117.037 67.5711i −0.311267 0.179710i
\(377\) 112.532 0.298494
\(378\) 20.8928 + 4.18019i 0.0552719 + 0.0110587i
\(379\) −219.750 −0.579816 −0.289908 0.957055i \(-0.593625\pi\)
−0.289908 + 0.957055i \(0.593625\pi\)
\(380\) 0 0
\(381\) 219.676 126.830i 0.576578 0.332887i
\(382\) −85.6152 + 49.4300i −0.224124 + 0.129398i
\(383\) −8.51785 + 14.7534i −0.0222398 + 0.0385205i −0.876931 0.480616i \(-0.840413\pi\)
0.854691 + 0.519137i \(0.173746\pi\)
\(384\) 47.3087i 0.123200i
\(385\) 0 0
\(386\) 45.7330 0.118479
\(387\) 47.6569 + 27.5147i 0.123144 + 0.0710975i
\(388\) −25.5816 44.3087i −0.0659320 0.114198i
\(389\) −76.1102 131.827i −0.195656 0.338886i 0.751459 0.659779i \(-0.229350\pi\)
−0.947115 + 0.320893i \(0.896017\pi\)
\(390\) 0 0
\(391\) 30.8076i 0.0787919i
\(392\) 84.1232 + 110.142i 0.214600 + 0.280975i
\(393\) 555.926i 1.41457i
\(394\) −195.941 + 339.380i −0.497313 + 0.861371i
\(395\) 0 0
\(396\) −112.368 194.626i −0.283756 0.491480i
\(397\) 186.361 322.786i 0.469423 0.813064i −0.529966 0.848019i \(-0.677795\pi\)
0.999389 + 0.0349549i \(0.0111287\pi\)
\(398\) −236.802 −0.594980
\(399\) 6.72792 + 19.8931i 0.0168620 + 0.0498574i
\(400\) 0 0
\(401\) −325.786 + 564.279i −0.812435 + 1.40718i 0.0987205 + 0.995115i \(0.468525\pi\)
−0.911155 + 0.412063i \(0.864808\pi\)
\(402\) 273.916 + 474.437i 0.681384 + 1.18019i
\(403\) −117.117 + 67.6173i −0.290612 + 0.167785i
\(404\) 49.3675 + 28.5024i 0.122197 + 0.0705504i
\(405\) 0 0
\(406\) −198.853 39.7862i −0.489785 0.0979955i
\(407\) 859.992i 2.11300i
\(408\) 138.882 + 80.1838i 0.340398 + 0.196529i
\(409\) −462.081 + 266.782i −1.12978 + 0.652280i −0.943880 0.330289i \(-0.892854\pi\)
−0.185902 + 0.982568i \(0.559521\pi\)
\(410\) 0 0
\(411\) −425.239 245.512i −1.03464 0.597352i
\(412\) 112.982 0.274229
\(413\) 387.054 440.353i 0.937176 1.06623i
\(414\) 27.2649 0.0658573
\(415\) 0 0
\(416\) 26.9117 15.5375i 0.0646916 0.0373497i
\(417\) 248.371 143.397i 0.595614 0.343878i
\(418\) −6.71807 + 11.6360i −0.0160719 + 0.0278374i
\(419\) 534.252i 1.27507i −0.770423 0.637533i \(-0.779955\pi\)
0.770423 0.637533i \(-0.220045\pi\)
\(420\) 0 0
\(421\) 157.220 0.373445 0.186723 0.982413i \(-0.440213\pi\)
0.186723 + 0.982413i \(0.440213\pi\)
\(422\) −156.857 90.5614i −0.371699 0.214600i
\(423\) −202.713 351.110i −0.479228 0.830047i
\(424\) −31.1543 53.9609i −0.0734772 0.127266i
\(425\) 0 0
\(426\) 286.374i 0.672239i
\(427\) 454.801 + 90.9960i 1.06511 + 0.213105i
\(428\) 95.2203i 0.222477i
\(429\) 152.095 263.437i 0.354535 0.614072i
\(430\) 0 0
\(431\) 114.268 + 197.918i 0.265123 + 0.459207i 0.967596 0.252504i \(-0.0812541\pi\)
−0.702473 + 0.711711i \(0.747921\pi\)
\(432\) −4.30463 + 7.45584i −0.00996443 + 0.0172589i
\(433\) −47.5549 −0.109827 −0.0549133 0.998491i \(-0.517488\pi\)
−0.0549133 + 0.998491i \(0.517488\pi\)
\(434\) 230.860 78.0778i 0.531935 0.179903i
\(435\) 0 0
\(436\) −75.3087 + 130.438i −0.172726 + 0.299171i
\(437\) −0.815039 1.41169i −0.00186508 0.00323041i
\(438\) 670.844 387.312i 1.53161 0.884274i
\(439\) 63.9594 + 36.9270i 0.145693 + 0.0841161i 0.571075 0.820898i \(-0.306527\pi\)
−0.425381 + 0.905014i \(0.639860\pi\)
\(440\) 0 0
\(441\) 53.3452 + 412.342i 0.120964 + 0.935017i
\(442\) 105.338i 0.238321i
\(443\) 203.204 + 117.320i 0.458699 + 0.264830i 0.711497 0.702689i \(-0.248017\pi\)
−0.252798 + 0.967519i \(0.581351\pi\)
\(444\) 470.345 271.554i 1.05934 0.611608i
\(445\) 0 0
\(446\) −510.926 294.983i −1.14557 0.661397i
\(447\) −110.380 −0.246935
\(448\) −53.0482 + 17.9411i −0.118411 + 0.0400472i
\(449\) 255.161 0.568288 0.284144 0.958782i \(-0.408291\pi\)
0.284144 + 0.958782i \(0.408291\pi\)
\(450\) 0 0
\(451\) 241.191 139.252i 0.534791 0.308762i
\(452\) 148.014 85.4558i 0.327464 0.189062i
\(453\) −280.609 + 486.029i −0.619446 + 1.07291i
\(454\) 328.465i 0.723492i
\(455\) 0 0
\(456\) −8.48528 −0.0186081
\(457\) 126.210 + 72.8675i 0.276171 + 0.159448i 0.631689 0.775222i \(-0.282362\pi\)
−0.355518 + 0.934670i \(0.615695\pi\)
\(458\) 59.1297 + 102.416i 0.129104 + 0.223615i
\(459\) −14.5919 25.2739i −0.0317906 0.0550629i
\(460\) 0 0
\(461\) 888.329i 1.92696i −0.267777 0.963481i \(-0.586289\pi\)
0.267777 0.963481i \(-0.413711\pi\)
\(462\) −361.903 + 411.739i −0.783339 + 0.891209i
\(463\) 234.014i 0.505430i −0.967541 0.252715i \(-0.918676\pi\)
0.967541 0.252715i \(-0.0813236\pi\)
\(464\) 40.9706 70.9631i 0.0882986 0.152938i
\(465\) 0 0
\(466\) 154.908 + 268.309i 0.332421 + 0.575770i
\(467\) −393.309 + 681.231i −0.842204 + 1.45874i 0.0458237 + 0.998950i \(0.485409\pi\)
−0.888028 + 0.459790i \(0.847925\pi\)
\(468\) 93.2248 0.199198
\(469\) 428.117 487.071i 0.912830 1.03853i
\(470\) 0 0
\(471\) 473.967 820.934i 1.00630 1.74296i
\(472\) 118.446 + 205.154i 0.250945 + 0.434649i
\(473\) 74.3762 42.9411i 0.157244 0.0907846i
\(474\) −390.312 225.347i −0.823444 0.475415i
\(475\) 0 0
\(476\) 37.2426 186.140i 0.0782408 0.391051i
\(477\) 186.926i 0.391878i
\(478\) −236.501 136.544i −0.494773 0.285657i
\(479\) −638.202 + 368.466i −1.33236 + 0.769240i −0.985661 0.168735i \(-0.946032\pi\)
−0.346702 + 0.937975i \(0.612698\pi\)
\(480\) 0 0
\(481\) 308.948 + 178.371i 0.642304 + 0.370834i
\(482\) 70.0505 0.145333
\(483\) −21.3068 63.0000i −0.0441136 0.130435i
\(484\) −108.735 −0.224659
\(485\) 0 0
\(486\) −413.470 + 238.717i −0.850762 + 0.491187i
\(487\) 234.432 135.349i 0.481379 0.277925i −0.239612 0.970869i \(-0.577020\pi\)
0.720991 + 0.692944i \(0.243687\pi\)
\(488\) −93.7048 + 162.302i −0.192018 + 0.332585i
\(489\) 384.609i 0.786520i
\(490\) 0 0
\(491\) 760.161 1.54819 0.774094 0.633070i \(-0.218206\pi\)
0.774094 + 0.633070i \(0.218206\pi\)
\(492\) 152.318 + 87.9411i 0.309590 + 0.178742i
\(493\) 138.882 + 240.551i 0.281709 + 0.487934i
\(494\) −2.78680 4.82687i −0.00564129 0.00977100i
\(495\) 0 0
\(496\) 98.4720i 0.198532i
\(497\) −321.117 + 108.603i −0.646111 + 0.218517i
\(498\) 638.558i 1.28225i
\(499\) 62.7462 108.680i 0.125744 0.217795i −0.796280 0.604929i \(-0.793202\pi\)
0.922023 + 0.387134i \(0.126535\pi\)
\(500\) 0 0
\(501\) −425.434 736.873i −0.849169 1.47080i
\(502\) −114.922 + 199.051i −0.228928 + 0.396516i
\(503\) −117.083 −0.232770 −0.116385 0.993204i \(-0.537131\pi\)
−0.116385 + 0.993204i \(0.537131\pi\)
\(504\) −164.735 32.9600i −0.326855 0.0653967i
\(505\) 0 0
\(506\) 21.2756 36.8505i 0.0420467 0.0728271i
\(507\) −290.248 502.724i −0.572481 0.991566i
\(508\) 105.070 60.6619i 0.206830 0.119413i
\(509\) 574.110 + 331.463i 1.12792 + 0.651204i 0.943410 0.331627i \(-0.107598\pi\)
0.184507 + 0.982831i \(0.440931\pi\)
\(510\) 0 0
\(511\) −688.709 605.349i −1.34777 1.18464i
\(512\) 22.6274i 0.0441942i
\(513\) 1.33728 + 0.772078i 0.00260678 + 0.00150503i
\(514\) 121.445 70.1164i 0.236275 0.136413i
\(515\) 0 0
\(516\) 46.9706 + 27.1185i 0.0910282 + 0.0525552i
\(517\) −632.733 −1.22386
\(518\) −482.870 424.425i −0.932182 0.819353i
\(519\) 296.095 0.570511
\(520\) 0 0
\(521\) −40.8229 + 23.5691i −0.0783550 + 0.0452383i −0.538666 0.842520i \(-0.681071\pi\)
0.460311 + 0.887758i \(0.347738\pi\)
\(522\) 212.889 122.912i 0.407834 0.235463i
\(523\) 249.735 432.554i 0.477506 0.827064i −0.522162 0.852846i \(-0.674874\pi\)
0.999668 + 0.0257824i \(0.00820770\pi\)
\(524\) 265.895i 0.507434i
\(525\) 0 0
\(526\) −614.257 −1.16779
\(527\) −289.080 166.901i −0.548539 0.316699i
\(528\) −110.749 191.823i −0.209752 0.363302i
\(529\) −261.919 453.657i −0.495121 0.857574i
\(530\) 0 0
\(531\) 710.675i 1.33837i
\(532\) 3.21792 + 9.51472i 0.00604871 + 0.0178848i
\(533\) 115.529i 0.216752i
\(534\) −496.467 + 859.905i −0.929713 + 1.61031i
\(535\) 0 0
\(536\) 131.012 + 226.920i 0.244426 + 0.423358i
\(537\) −227.510 + 394.058i −0.423668 + 0.733815i
\(538\) 129.271 0.240280
\(539\) 598.937 + 249.663i 1.11120 + 0.463197i
\(540\) 0 0
\(541\) −249.405 + 431.981i −0.461007 + 0.798487i −0.999011 0.0444550i \(-0.985845\pi\)
0.538005 + 0.842942i \(0.319178\pi\)
\(542\) 12.0883 + 20.9376i 0.0223031 + 0.0386302i
\(543\) 360.903 208.368i 0.664647 0.383734i
\(544\) 66.4264 + 38.3513i 0.122107 + 0.0704987i
\(545\) 0 0
\(546\) −72.8528 215.411i −0.133430 0.394525i
\(547\) 279.897i 0.511694i −0.966717 0.255847i \(-0.917646\pi\)
0.966717 0.255847i \(-0.0823543\pi\)
\(548\) −203.389 117.426i −0.371147 0.214282i
\(549\) −486.905 + 281.114i −0.886894 + 0.512048i
\(550\) 0 0
\(551\) −12.7279 7.34847i −0.0230997 0.0133366i
\(552\) 26.8723 0.0486817
\(553\) −104.666 + 523.124i −0.189269 + 0.945976i
\(554\) −566.267 −1.02214
\(555\) 0 0
\(556\) 118.794 68.5857i 0.213658 0.123356i
\(557\) −226.708 + 130.890i −0.407016 + 0.234991i −0.689507 0.724279i \(-0.742173\pi\)
0.282491 + 0.959270i \(0.408839\pi\)
\(558\) −147.708 + 255.838i −0.264710 + 0.458490i
\(559\) 35.6258i 0.0637312i
\(560\) 0 0
\(561\) 750.838 1.33839
\(562\) −659.758 380.912i −1.17395 0.677779i
\(563\) 242.531 + 420.076i 0.430784 + 0.746139i 0.996941 0.0781581i \(-0.0249039\pi\)
−0.566157 + 0.824297i \(0.691571\pi\)
\(564\) −199.794 346.053i −0.354245 0.613570i
\(565\) 0 0
\(566\) 437.287i 0.772593i
\(567\) 448.837 + 394.511i 0.791599 + 0.695786i
\(568\) 136.971i 0.241145i
\(569\) −227.000 + 393.175i −0.398945 + 0.690993i −0.993596 0.112991i \(-0.963957\pi\)
0.594651 + 0.803984i \(0.297290\pi\)
\(570\) 0 0
\(571\) 115.769 + 200.517i 0.202747 + 0.351168i 0.949413 0.314032i \(-0.101680\pi\)
−0.746666 + 0.665200i \(0.768346\pi\)
\(572\) 72.7461 126.000i 0.127179 0.220280i
\(573\) −292.309 −0.510137
\(574\) 40.8457 204.148i 0.0711597 0.355659i
\(575\) 0 0
\(576\) 33.9411 58.7878i 0.0589256 0.102062i
\(577\) 325.634 + 564.014i 0.564356 + 0.977494i 0.997109 + 0.0759812i \(0.0242089\pi\)
−0.432753 + 0.901513i \(0.642458\pi\)
\(578\) 128.778 74.3503i 0.222800 0.128634i
\(579\) 117.107 + 67.6115i 0.202257 + 0.116773i
\(580\) 0 0
\(581\) 716.029 242.164i 1.23241 0.416805i
\(582\) 151.279i 0.259930i
\(583\) −252.644 145.864i −0.433351 0.250195i
\(584\) 320.860 185.249i 0.549418 0.317206i
\(585\) 0 0
\(586\) 400.971 + 231.500i 0.684250 + 0.395052i
\(587\) 823.029 1.40209 0.701046 0.713116i \(-0.252717\pi\)
0.701046 + 0.713116i \(0.252717\pi\)
\(588\) 52.5770 + 406.404i 0.0894166 + 0.691163i
\(589\) 17.6619 0.0299863
\(590\) 0 0
\(591\) −1003.48 + 579.358i −1.69793 + 0.980301i
\(592\) 224.963 129.882i 0.380004 0.219396i
\(593\) −404.209 + 700.110i −0.681634 + 1.18062i 0.292848 + 0.956159i \(0.405397\pi\)
−0.974482 + 0.224465i \(0.927936\pi\)
\(594\) 40.3084i 0.0678593i
\(595\) 0 0
\(596\) −52.7939 −0.0885804
\(597\) −606.370 350.088i −1.01570 0.586412i
\(598\) 8.82559 + 15.2864i 0.0147585 + 0.0255625i
\(599\) 265.422 + 459.725i 0.443109 + 0.767488i 0.997918 0.0644900i \(-0.0205421\pi\)
−0.554809 + 0.831978i \(0.687209\pi\)
\(600\) 0 0
\(601\) 936.503i 1.55824i 0.626874 + 0.779121i \(0.284334\pi\)
−0.626874 + 0.779121i \(0.715666\pi\)
\(602\) 12.5956 62.9533i 0.0209229 0.104574i
\(603\) 786.073i 1.30360i
\(604\) −134.213 + 232.464i −0.222207 + 0.384874i
\(605\) 0 0
\(606\) 84.2756 + 145.970i 0.139069 + 0.240874i
\(607\) −301.060 + 521.452i −0.495981 + 0.859064i −0.999989 0.00463474i \(-0.998525\pi\)
0.504008 + 0.863699i \(0.331858\pi\)
\(608\) −4.05845 −0.00667508
\(609\) −450.375 395.862i −0.739531 0.650020i
\(610\) 0 0
\(611\) 131.235 227.307i 0.214788 0.372024i
\(612\) 115.054 + 199.279i 0.187997 + 0.325620i
\(613\) −949.940 + 548.448i −1.54966 + 0.894695i −0.551491 + 0.834181i \(0.685941\pi\)
−0.998167 + 0.0605142i \(0.980726\pi\)
\(614\) −313.706 181.118i −0.510921 0.294981i
\(615\) 0 0
\(616\) −173.095 + 196.932i −0.280999 + 0.319694i
\(617\) 432.956i 0.701712i −0.936429 0.350856i \(-0.885891\pi\)
0.936429 0.350856i \(-0.114109\pi\)
\(618\) 289.310 + 167.033i 0.468139 + 0.270280i
\(619\) −194.951 + 112.555i −0.314946 + 0.181834i −0.649137 0.760671i \(-0.724870\pi\)
0.334192 + 0.942505i \(0.391537\pi\)
\(620\) 0 0
\(621\) −4.23506 2.44512i −0.00681975 0.00393738i
\(622\) 305.940 0.491865
\(623\) 1152.51 + 230.592i 1.84993 + 0.370131i
\(624\) 91.8823 0.147247
\(625\) 0 0
\(626\) 192.062 110.887i 0.306809 0.177136i
\(627\) −34.4054 + 19.8640i −0.0548730 + 0.0316810i
\(628\) 226.695 392.647i 0.360979 0.625234i
\(629\) 880.552i 1.39992i
\(630\) 0 0
\(631\) 750.514 1.18940 0.594702 0.803946i \(-0.297270\pi\)
0.594702 + 0.803946i \(0.297270\pi\)
\(632\) −186.683 107.782i −0.295385 0.170541i
\(633\) −267.772 463.794i −0.423020 0.732692i
\(634\) 316.805 + 548.722i 0.499692 + 0.865492i
\(635\) 0 0
\(636\) 184.234i 0.289676i
\(637\) −213.916 + 163.383i −0.335818 + 0.256488i
\(638\) 383.647i 0.601327i
\(639\) 205.456 355.860i 0.321527 0.556901i
\(640\) 0 0
\(641\) 580.926 + 1006.19i 0.906281 + 1.56973i 0.819188 + 0.573525i \(0.194425\pi\)
0.0870937 + 0.996200i \(0.472242\pi\)
\(642\) 140.774 243.827i 0.219273 0.379793i
\(643\) −121.957 −0.189669 −0.0948347 0.995493i \(-0.530232\pi\)
−0.0948347 + 0.995493i \(0.530232\pi\)
\(644\) −10.1909 30.1324i −0.0158244 0.0467895i
\(645\) 0 0
\(646\) 6.87868 11.9142i 0.0106481 0.0184431i
\(647\) −79.3877 137.504i −0.122701 0.212525i 0.798131 0.602484i \(-0.205822\pi\)
−0.920832 + 0.389959i \(0.872489\pi\)
\(648\) −209.107 + 120.728i −0.322696 + 0.186309i
\(649\) 960.529 + 554.561i 1.48001 + 0.854486i
\(650\) 0 0
\(651\) 706.584 + 141.372i 1.08538 + 0.217162i
\(652\) 183.955i 0.282140i
\(653\) −338.565 195.471i −0.518476 0.299342i 0.217835 0.975986i \(-0.430101\pi\)
−0.736311 + 0.676643i \(0.763434\pi\)
\(654\) −385.680 + 222.672i −0.589724 + 0.340478i
\(655\) 0 0
\(656\) 72.8528 + 42.0616i 0.111056 + 0.0641183i
\(657\) 1111.49 1.69177
\(658\) −312.268 + 355.269i −0.474571 + 0.539922i
\(659\) 331.955 0.503726 0.251863 0.967763i \(-0.418957\pi\)
0.251863 + 0.967763i \(0.418957\pi\)
\(660\) 0 0
\(661\) 561.029 323.910i 0.848758 0.490031i −0.0114736 0.999934i \(-0.503652\pi\)
0.860232 + 0.509904i \(0.170319\pi\)
\(662\) 67.3697 38.8959i 0.101767 0.0587552i
\(663\) −155.732 + 269.735i −0.234889 + 0.406840i
\(664\) 305.418i 0.459967i
\(665\) 0 0
\(666\) 779.294 1.17011
\(667\) 40.3084 + 23.2721i 0.0604324 + 0.0348907i
\(668\) −203.482 352.441i −0.304613 0.527606i
\(669\) −872.205 1510.70i −1.30374 2.25815i
\(670\) 0 0
\(671\) 877.448i 1.30767i
\(672\) −162.363 32.4853i −0.241611 0.0483412i
\(673\) 100.956i 0.150009i −0.997183 0.0750047i \(-0.976103\pi\)
0.997183 0.0750047i \(-0.0238972\pi\)
\(674\) 78.9361 136.721i 0.117116 0.202851i
\(675\) 0 0
\(676\) −138.823 240.449i −0.205360 0.355694i
\(677\) −371.588 + 643.610i −0.548875 + 0.950679i 0.449477 + 0.893292i \(0.351610\pi\)
−0.998352 + 0.0573873i \(0.981723\pi\)
\(678\) 505.351 0.745355
\(679\) −169.632 + 57.3704i −0.249827 + 0.0844924i
\(680\) 0 0
\(681\) −485.603 + 841.088i −0.713073 + 1.23508i
\(682\) 230.522 + 399.276i 0.338009 + 0.585448i
\(683\) −3.84032 + 2.21721i −0.00562272 + 0.00324628i −0.502809 0.864398i \(-0.667700\pi\)
0.497186 + 0.867644i \(0.334367\pi\)
\(684\) −10.5442 6.08767i −0.0154154 0.00890010i
\(685\) 0 0
\(686\) 435.770 213.078i 0.635233 0.310610i
\(687\) 349.669i 0.508980i
\(688\) 22.4657 + 12.9706i 0.0326536 + 0.0188526i
\(689\) 104.802 60.5074i 0.152107 0.0878192i
\(690\) 0 0
\(691\) −846.253 488.584i −1.22468 0.707069i −0.258767 0.965940i \(-0.583316\pi\)
−0.965912 + 0.258871i \(0.916649\pi\)
\(692\) 141.620 0.204654
\(693\) −745.113 + 252.000i −1.07520 + 0.363636i
\(694\) 533.522 0.768763
\(695\) 0 0
\(696\) 209.823 121.142i 0.301470 0.174054i
\(697\) −246.957 + 142.581i −0.354314 + 0.204563i
\(698\) −144.274 + 249.889i −0.206696 + 0.358008i
\(699\) 916.063i 1.31053i
\(700\) 0 0
\(701\) −840.177 −1.19854 −0.599270 0.800547i \(-0.704542\pi\)
−0.599270 + 0.800547i \(0.704542\pi\)
\(702\) −14.4806 8.36039i −0.0206277 0.0119094i
\(703\) −23.2956 40.3492i −0.0331375 0.0573958i
\(704\) −52.9706 91.7477i −0.0752423 0.130323i
\(705\) 0 0
\(706\) 589.835i 0.835460i
\(707\) 131.719 149.857i 0.186306 0.211962i
\(708\) 700.441i 0.989323i
\(709\) 341.279 591.112i 0.481352 0.833727i −0.518419 0.855127i \(-0.673479\pi\)
0.999771 + 0.0214003i \(0.00681244\pi\)
\(710\) 0 0
\(711\) −323.345 560.050i −0.454775 0.787694i
\(712\) −237.456 + 411.286i −0.333506 + 0.577649i
\(713\) −55.9340 −0.0784488
\(714\) 370.555 421.582i 0.518984 0.590451i
\(715\) 0 0
\(716\) −108.816 + 188.475i −0.151978 + 0.263234i
\(717\) −403.733 699.286i −0.563087 0.975295i
\(718\) −219.022 + 126.452i −0.305044 + 0.176117i
\(719\) −119.187 68.8126i −0.165768 0.0957060i 0.414821 0.909903i \(-0.363844\pi\)
−0.580589 + 0.814197i \(0.697178\pi\)
\(720\) 0 0
\(721\) 77.5812 387.754i 0.107602 0.537800i
\(722\) 509.803i 0.706099i
\(723\) 179.375 + 103.562i 0.248099 + 0.143240i
\(724\) 172.617 99.6607i 0.238422 0.137653i
\(725\) 0 0
\(726\) −278.434 160.754i −0.383517 0.221424i
\(727\) 264.137 0.363325 0.181662 0.983361i \(-0.441852\pi\)
0.181662 + 0.983361i \(0.441852\pi\)
\(728\) −34.8450 103.029i −0.0478640 0.141524i
\(729\) −643.368 −0.882534
\(730\) 0 0
\(731\) −76.1543 + 43.9677i −0.104178 + 0.0601474i
\(732\) −479.892 + 277.066i −0.655591 + 0.378505i
\(733\) 289.660 501.705i 0.395170 0.684455i −0.597953 0.801531i \(-0.704019\pi\)
0.993123 + 0.117077i \(0.0373523\pi\)
\(734\) 889.530i 1.21189i
\(735\) 0 0
\(736\) 12.8528 0.0174631
\(737\) 1062.43 + 613.397i 1.44157 + 0.832288i
\(738\) 126.185 + 218.558i 0.170982 + 0.296150i
\(739\) −99.0477 171.556i −0.134029 0.232146i 0.791197 0.611562i \(-0.209458\pi\)
−0.925226 + 0.379416i \(0.876125\pi\)
\(740\) 0 0
\(741\) 16.4800i 0.0222402i
\(742\) −206.585 + 69.8680i −0.278417 + 0.0941617i
\(743\) 976.690i 1.31452i −0.753663 0.657261i \(-0.771715\pi\)
0.753663 0.657261i \(-0.228285\pi\)
\(744\) −145.581 + 252.153i −0.195673 + 0.338916i
\(745\) 0 0
\(746\) −180.707 312.994i −0.242235 0.419563i
\(747\) −458.127 + 793.499i −0.613289 + 1.06225i
\(748\) 359.120 0.480107
\(749\) −326.794 65.3845i −0.436308 0.0872958i
\(750\) 0 0
\(751\) 417.665 723.417i 0.556145 0.963272i −0.441668 0.897178i \(-0.645613\pi\)
0.997813 0.0660933i \(-0.0210535\pi\)
\(752\) −95.5600 165.515i −0.127074 0.220099i
\(753\) −588.553 + 339.801i −0.781611 + 0.451263i
\(754\) 137.823 + 79.5724i 0.182790 + 0.105534i
\(755\) 0 0
\(756\) 22.6325 + 19.8931i 0.0299371 + 0.0263136i
\(757\) 104.221i 0.137677i 0.997628 + 0.0688383i \(0.0219293\pi\)
−0.997628 + 0.0688383i \(0.978071\pi\)
\(758\) −269.138 155.387i −0.355063 0.204996i
\(759\) 108.959 62.9077i 0.143557 0.0828824i
\(760\) 0 0
\(761\) −473.785 273.540i −0.622583 0.359448i 0.155291 0.987869i \(-0.450368\pi\)
−0.777874 + 0.628420i \(0.783702\pi\)
\(762\) 358.730 0.470774
\(763\) 395.950 + 348.025i 0.518939 + 0.456128i
\(764\) −139.809 −0.182996
\(765\) 0 0
\(766\) −20.8644 + 12.0461i −0.0272381 + 0.0157259i
\(767\) −398.447 + 230.044i −0.519488 + 0.299927i
\(768\) 33.4523 57.9411i 0.0435577 0.0754442i
\(769\) 341.205i 0.443700i −0.975081 0.221850i \(-0.928790\pi\)
0.975081 0.221850i \(-0.0712095\pi\)
\(770\) 0 0
\(771\) 414.640 0.537795
\(772\) 56.0112 + 32.3381i 0.0725534 + 0.0418887i
\(773\) 245.497 + 425.213i 0.317590 + 0.550081i 0.979985 0.199074i \(-0.0637933\pi\)
−0.662395 + 0.749155i \(0.730460\pi\)
\(774\) 38.9117 + 67.3970i 0.0502735 + 0.0870763i
\(775\) 0 0
\(776\) 72.3557i 0.0932419i
\(777\) −608.998 1800.68i −0.783781 2.31748i
\(778\) 215.272i 0.276699i
\(779\) 7.54416 13.0669i 0.00968441 0.0167739i
\(780\) 0 0
\(781\) −320.647 555.376i −0.410559 0.711109i
\(782\) −21.7843 + 37.7315i −0.0278571 + 0.0482500i
\(783\) −44.0908 −0.0563101
\(784\) 25.1472 + 194.380i 0.0320755 + 0.247934i
\(785\) 0 0
\(786\) 393.099 680.867i 0.500126 0.866244i
\(787\) 150.228 + 260.202i 0.190887 + 0.330625i 0.945544 0.325493i \(-0.105530\pi\)
−0.754658 + 0.656119i \(0.772197\pi\)
\(788\) −479.956 + 277.103i −0.609081 + 0.351653i
\(789\) −1572.90 908.116i −1.99354 1.15097i
\(790\) 0 0
\(791\) −191.647 566.660i −0.242284 0.716385i
\(792\) 317.823i 0.401292i
\(793\) −315.219 181.992i −0.397502 0.229498i
\(794\) 456.489 263.554i 0.574923 0.331932i
\(795\) 0 0
\(796\) −290.022 167.444i −0.364350 0.210357i
\(797\) −370.072 −0.464331 −0.232165 0.972676i \(-0.574581\pi\)
−0.232165 + 0.972676i \(0.574581\pi\)
\(798\) −5.82655 + 29.1213i −0.00730144 + 0.0364929i
\(799\) 647.860 0.810838
\(800\) 0 0
\(801\) −1233.86 + 712.369i −1.54040 + 0.889349i
\(802\) −798.010 + 460.731i −0.995025 + 0.574478i
\(803\) 867.330 1502.26i 1.08011 1.87081i
\(804\) 774.753i 0.963623i
\(805\) 0 0
\(806\) −191.251 −0.237284
\(807\) 331.019 + 191.114i 0.410184 + 0.236820i
\(808\) 40.3084 + 69.8162i 0.0498867 + 0.0864062i
\(809\) 245.618 + 425.422i 0.303607 + 0.525862i 0.976950 0.213468i \(-0.0684758\pi\)
−0.673344 + 0.739330i \(0.735142\pi\)
\(810\) 0 0
\(811\) 156.802i 0.193344i −0.995316 0.0966722i \(-0.969180\pi\)
0.995316 0.0966722i \(-0.0308199\pi\)
\(812\) −215.411 189.338i −0.265284 0.233175i
\(813\) 71.4853i 0.0879278i
\(814\) 608.106 1053.27i 0.747059 1.29394i
\(815\) 0 0
\(816\) 113.397 + 196.409i 0.138967 + 0.240698i
\(817\) 2.32640 4.02944i 0.00284749 0.00493199i
\(818\) −754.575 −0.922463
\(819\) 64.0143 319.946i 0.0781615 0.390654i
\(820\) 0 0
\(821\) 215.316 372.939i 0.262261 0.454249i −0.704581 0.709623i \(-0.748865\pi\)
0.966842 + 0.255374i \(0.0821986\pi\)
\(822\) −347.206 601.378i −0.422392 0.731604i
\(823\) 613.788 354.371i 0.745793 0.430584i −0.0783785 0.996924i \(-0.524974\pi\)
0.824172 + 0.566340i \(0.191641\pi\)
\(824\) 138.375 + 79.8907i 0.167930 + 0.0969547i
\(825\) 0 0
\(826\) 785.418 265.632i 0.950870 0.321588i
\(827\) 1460.10i 1.76554i −0.469805 0.882770i \(-0.655676\pi\)
0.469805 0.882770i \(-0.344324\pi\)
\(828\) 33.3926 + 19.2792i 0.0403292 + 0.0232841i
\(829\) 223.095 128.804i 0.269113 0.155373i −0.359371 0.933195i \(-0.617009\pi\)
0.628485 + 0.777822i \(0.283675\pi\)
\(830\) 0 0
\(831\) −1450.02 837.168i −1.74491 1.00742i
\(832\) 43.9466 0.0528204
\(833\) −613.256 255.632i −0.736202 0.306881i
\(834\) 405.588 0.486316
\(835\) 0 0
\(836\) −16.4558 + 9.50079i −0.0196840 + 0.0113646i
\(837\) 45.8870 26.4929i 0.0548231 0.0316522i
\(838\) 377.774 654.323i 0.450804 0.780815i
\(839\) 213.621i 0.254613i −0.991863 0.127307i \(-0.959367\pi\)
0.991863 0.127307i \(-0.0406332\pi\)
\(840\) 0 0
\(841\) −421.353 −0.501015
\(842\) 192.555 + 111.172i 0.228687 + 0.132033i
\(843\) −1126.28 1950.77i −1.33604 2.31408i
\(844\) −128.073 221.829i −0.151745 0.262831i
\(845\) 0 0
\(846\) 573.360i 0.677730i
\(847\) −74.6646 + 373.177i −0.0881519 + 0.440586i
\(848\) 88.1177i 0.103912i
\(849\) −646.485 + 1119.74i −0.761466 + 1.31890i
\(850\) 0 0
\(851\) 73.7756 + 127.783i 0.0866929 + 0.150156i
\(852\) 202.497 350.735i 0.237673 0.411661i
\(853\) 1127.37 1.32165 0.660826 0.750539i \(-0.270206\pi\)
0.660826 + 0.750539i \(0.270206\pi\)
\(854\) 492.672 + 433.040i 0.576899 + 0.507073i
\(855\) 0 0
\(856\) 67.3310 116.621i 0.0786577 0.136239i
\(857\) 635.212 + 1100.22i 0.741204 + 1.28380i 0.951947 + 0.306261i \(0.0990782\pi\)
−0.210744 + 0.977541i \(0.567588\pi\)
\(858\) 372.556 215.095i 0.434215 0.250694i
\(859\) 221.488 + 127.876i 0.257844 + 0.148867i 0.623351 0.781942i \(-0.285771\pi\)
−0.365506 + 0.930809i \(0.619104\pi\)
\(860\) 0 0
\(861\) 406.404 462.368i 0.472014 0.537013i
\(862\) 323.199i 0.374941i
\(863\) 965.382 + 557.364i 1.11863 + 0.645844i 0.941052 0.338262i \(-0.109839\pi\)
0.177583 + 0.984106i \(0.443172\pi\)
\(864\) −10.5442 + 6.08767i −0.0122039 + 0.00704592i
\(865\) 0 0
\(866\) −58.2426 33.6264i −0.0672548 0.0388296i
\(867\) 439.677 0.507125
\(868\) 337.954 + 67.6173i 0.389348 + 0.0779001i
\(869\) −1009.26 −1.16141
\(870\) 0 0
\(871\) −440.720 + 254.450i −0.505993 + 0.292135i
\(872\) −184.468 + 106.503i −0.211546 + 0.122136i
\(873\) 108.534 187.986i 0.124323 0.215333i
\(874\) 2.30528i 0.00263762i
\(875\) 0 0
\(876\) 1095.48 1.25055
\(877\) 954.194 + 550.904i 1.08802 + 0.628169i 0.933049 0.359750i \(-0.117138\pi\)
0.154972 + 0.987919i \(0.450471\pi\)
\(878\) 52.2226 + 90.4523i 0.0594791 + 0.103021i
\(879\) 684.500 + 1185.59i 0.778725 + 1.34879i
\(880\) 0 0
\(881\) 217.067i 0.246387i −0.992383 0.123194i \(-0.960686\pi\)
0.992383 0.123194i \(-0.0393136\pi\)
\(882\) −226.236 + 542.735i −0.256503 + 0.615346i
\(883\) 516.544i 0.584988i 0.956267 + 0.292494i \(0.0944851\pi\)
−0.956267 + 0.292494i \(0.905515\pi\)
\(884\) −74.4853 + 129.012i −0.0842594 + 0.145942i
\(885\) 0 0
\(886\) 165.915 + 287.374i 0.187263 + 0.324350i
\(887\) 564.905 978.445i 0.636872 1.10309i −0.349243 0.937032i \(-0.613561\pi\)
0.986115 0.166062i \(-0.0531053\pi\)
\(888\) 768.071 0.864944
\(889\) −136.043 402.251i −0.153029 0.452476i
\(890\) 0 0
\(891\) −565.246 + 979.034i −0.634395 + 1.09880i
\(892\) −417.169 722.558i −0.467679 0.810043i
\(893\) −29.6867 + 17.1396i −0.0332438 + 0.0191933i
\(894\) −135.187 78.0504i −0.151216 0.0873047i
\(895\) 0 0
\(896\) −77.6569 15.5375i −0.0866706 0.0173409i
\(897\) 52.1909i 0.0581838i
\(898\) 312.508 + 180.426i 0.348004 + 0.200920i
\(899\) −436.742 + 252.153i −0.485809 + 0.280482i
\(900\) 0 0
\(901\) 258.684 + 149.351i 0.287107 + 0.165762i
\(902\) 393.863 0.436655
\(903\) 125.323 142.581i 0.138785 0.157897i
\(904\) 241.706 0.267373
\(905\) 0 0
\(906\) −687.349 + 396.841i −0.758663 + 0.438014i
\(907\) 51.9808 30.0111i 0.0573107 0.0330884i −0.471071 0.882095i \(-0.656132\pi\)
0.528382 + 0.849007i \(0.322799\pi\)
\(908\) −232.260 + 402.286i −0.255793 + 0.443047i
\(909\) 241.851i 0.266062i
\(910\) 0 0
\(911\) 1422.25 1.56120 0.780598 0.625033i \(-0.214915\pi\)
0.780598 + 0.625033i \(0.214915\pi\)
\(912\) −10.3923 6.00000i −0.0113951 0.00657895i
\(913\) 714.980 + 1238.38i 0.783111 + 1.35639i
\(914\) 103.050 + 178.488i 0.112746 + 0.195283i
\(915\) 0 0
\(916\) 167.244i 0.182581i
\(917\) −912.547 182.581i −0.995144 0.199107i
\(918\) 41.2721i 0.0449587i
\(919\) 834.849 1446.00i 0.908432 1.57345i 0.0921886 0.995742i \(-0.470614\pi\)
0.816243 0.577708i \(-0.196053\pi\)
\(920\) 0 0
\(921\) −535.529 927.563i −0.581465 1.00713i
\(922\) 628.144 1087.98i 0.681284 1.18002i
\(923\) 266.022 0.288215
\(924\) −734.382 + 248.371i −0.794786 + 0.268800i
\(925\) 0 0
\(926\) 165.473 286.608i 0.178697 0.309512i
\(927\) 239.672 + 415.124i 0.258546 + 0.447814i
\(928\) 100.357 57.9411i 0.108143 0.0624366i
\(929\) −839.058 484.430i −0.903184 0.521453i −0.0249519 0.999689i \(-0.507943\pi\)
−0.878232 + 0.478235i \(0.841277\pi\)
\(930\) 0 0
\(931\) 34.8640 4.51039i 0.0374479 0.00484468i
\(932\) 438.146i 0.470114i
\(933\) 783.408 + 452.301i 0.839666 + 0.484781i
\(934\) −963.407 + 556.223i −1.03148 + 0.595528i
\(935\) 0 0
\(936\) 114.177 + 65.9199i 0.121984 + 0.0704272i
\(937\) 1212.57 1.29410 0.647049 0.762449i \(-0.276003\pi\)
0.647049 + 0.762449i \(0.276003\pi\)
\(938\) 868.746 293.813i 0.926168 0.313234i
\(939\) 655.742 0.698341
\(940\) 0 0
\(941\) −1293.90 + 747.032i −1.37502 + 0.793870i −0.991555 0.129684i \(-0.958604\pi\)
−0.383468 + 0.923554i \(0.625270\pi\)
\(942\) 1160.98 670.290i 1.23246 0.711560i
\(943\) −23.8918 + 41.3818i −0.0253360 + 0.0438832i
\(944\) 335.016i 0.354889i
\(945\) 0 0
\(946\) 121.456 0.128389
\(947\) −671.570 387.731i −0.709155 0.409431i 0.101593 0.994826i \(-0.467606\pi\)
−0.810748 + 0.585395i \(0.800939\pi\)
\(948\) −318.689 551.985i −0.336169 0.582262i
\(949\) 359.787 + 623.169i 0.379122 + 0.656659i
\(950\) 0 0
\(951\) 1873.45i 1.96998i
\(952\) 177.234 201.640i 0.186170 0.211806i
\(953\) 1055.40i 1.10745i −0.832701 0.553723i \(-0.813206\pi\)
0.832701 0.553723i \(-0.186794\pi\)
\(954\) 132.177 228.937i 0.138550 0.239976i
\(955\) 0 0
\(956\) −193.103 334.464i −0.201990 0.349857i
\(957\) 567.183 982.389i 0.592667 1.02653i
\(958\) −1042.18 −1.08787
\(959\) −542.665 + 617.393i −0.565866 + 0.643788i
\(960\) 0 0
\(961\) −177.477 + 307.400i −0.184680 + 0.319875i
\(962\) 252.255 + 436.919i 0.262220 + 0.454178i
\(963\) 349.862 201.993i 0.363304 0.209754i
\(964\) 85.7939 + 49.5332i 0.0889979 + 0.0513829i
\(965\) 0 0
\(966\) 18.4523 92.2251i 0.0191017 0.0954712i
\(967\) 1221.63i 1.26332i 0.775245 + 0.631661i \(0.217627\pi\)
−0.775245 + 0.631661i \(0.782373\pi\)
\(968\) −133.173 76.8873i −0.137575 0.0794290i
\(969\) 35.2279 20.3389i 0.0363549 0.0209895i
\(970\) 0 0
\(971\) −455.753 263.129i −0.469365 0.270988i 0.246609 0.969115i \(-0.420684\pi\)
−0.715974 + 0.698127i \(0.754017\pi\)
\(972\) −675.194 −0.694644
\(973\) −153.813 454.794i −0.158081 0.467414i
\(974\) 382.825 0.393045
\(975\) 0 0
\(976\) −229.529 + 132.519i −0.235173 + 0.135777i
\(977\) −866.114 + 500.051i −0.886504 + 0.511823i −0.872797 0.488083i \(-0.837696\pi\)
−0.0137065 + 0.999906i \(0.504363\pi\)
\(978\) 271.959 471.047i 0.278077 0.481643i
\(979\) 2223.53i 2.27123i
\(980\) 0 0
\(981\) −639.015 −0.651392
\(982\) 931.003 + 537.515i 0.948068 + 0.547367i
\(983\) −537.850 931.584i −0.547152 0.947695i −0.998468 0.0553306i \(-0.982379\pi\)
0.451316 0.892364i \(-0.350955\pi\)
\(984\) 124.368 + 215.411i 0.126390 + 0.218914i
\(985\) 0 0
\(986\) 392.819i 0.398396i
\(987\) −1324.84 + 448.066i −1.34229 + 0.453968i
\(988\) 7.88225i 0.00797799i
\(989\) −7.36753 + 12.7609i −0.00744948 + 0.0129029i
\(990\) 0 0
\(991\) 938.017 + 1624.69i 0.946536 + 1.63945i 0.752646 + 0.658426i \(0.228777\pi\)
0.193891 + 0.981023i \(0.437889\pi\)
\(992\) −69.6302 + 120.603i −0.0701917 + 0.121576i
\(993\) 230.015 0.231636
\(994\) −470.080 94.0530i −0.472918 0.0946207i
\(995\) 0 0
\(996\) −451.529 + 782.071i −0.453342 + 0.785212i
\(997\) 291.112 + 504.221i 0.291988 + 0.505738i 0.974280 0.225342i \(-0.0723499\pi\)
−0.682292 + 0.731080i \(0.739017\pi\)
\(998\) 153.696 88.7365i 0.154004 0.0889144i
\(999\) −121.048 69.8869i −0.121169 0.0699569i
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 350.3.i.a.299.4 8
5.2 odd 4 350.3.k.a.201.1 4
5.3 odd 4 14.3.d.a.5.2 yes 4
5.4 even 2 inner 350.3.i.a.299.1 8
7.3 odd 6 inner 350.3.i.a.199.1 8
15.8 even 4 126.3.n.c.19.1 4
20.3 even 4 112.3.s.b.33.2 4
35.3 even 12 14.3.d.a.3.2 4
35.13 even 4 98.3.d.a.19.2 4
35.17 even 12 350.3.k.a.101.1 4
35.18 odd 12 98.3.d.a.31.2 4
35.23 odd 12 98.3.b.b.97.1 4
35.24 odd 6 inner 350.3.i.a.199.4 8
35.33 even 12 98.3.b.b.97.2 4
40.3 even 4 448.3.s.c.257.1 4
40.13 odd 4 448.3.s.d.257.2 4
60.23 odd 4 1008.3.cg.l.145.1 4
105.23 even 12 882.3.c.f.685.4 4
105.38 odd 12 126.3.n.c.73.1 4
105.53 even 12 882.3.n.b.325.1 4
105.68 odd 12 882.3.c.f.685.3 4
105.83 odd 4 882.3.n.b.19.1 4
140.3 odd 12 112.3.s.b.17.2 4
140.23 even 12 784.3.c.e.97.4 4
140.83 odd 4 784.3.s.c.705.1 4
140.103 odd 12 784.3.c.e.97.1 4
140.123 even 12 784.3.s.c.129.1 4
280.3 odd 12 448.3.s.c.129.1 4
280.213 even 12 448.3.s.d.129.2 4
420.143 even 12 1008.3.cg.l.577.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.3.d.a.3.2 4 35.3 even 12
14.3.d.a.5.2 yes 4 5.3 odd 4
98.3.b.b.97.1 4 35.23 odd 12
98.3.b.b.97.2 4 35.33 even 12
98.3.d.a.19.2 4 35.13 even 4
98.3.d.a.31.2 4 35.18 odd 12
112.3.s.b.17.2 4 140.3 odd 12
112.3.s.b.33.2 4 20.3 even 4
126.3.n.c.19.1 4 15.8 even 4
126.3.n.c.73.1 4 105.38 odd 12
350.3.i.a.199.1 8 7.3 odd 6 inner
350.3.i.a.199.4 8 35.24 odd 6 inner
350.3.i.a.299.1 8 5.4 even 2 inner
350.3.i.a.299.4 8 1.1 even 1 trivial
350.3.k.a.101.1 4 35.17 even 12
350.3.k.a.201.1 4 5.2 odd 4
448.3.s.c.129.1 4 280.3 odd 12
448.3.s.c.257.1 4 40.3 even 4
448.3.s.d.129.2 4 280.213 even 12
448.3.s.d.257.2 4 40.13 odd 4
784.3.c.e.97.1 4 140.103 odd 12
784.3.c.e.97.4 4 140.23 even 12
784.3.s.c.129.1 4 140.123 even 12
784.3.s.c.705.1 4 140.83 odd 4
882.3.c.f.685.3 4 105.68 odd 12
882.3.c.f.685.4 4 105.23 even 12
882.3.n.b.19.1 4 105.83 odd 4
882.3.n.b.325.1 4 105.53 even 12
1008.3.cg.l.145.1 4 60.23 odd 4
1008.3.cg.l.577.1 4 420.143 even 12