Properties

Label 300.3.f.b.199.5
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $16$
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] = [300,3,Mod(199,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.199");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\), degree \(1\), 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: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.5
Root \(0.422403 - 1.34966i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.b.199.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.696577 - 1.87477i) q^{2} +1.73205 q^{3} +(-3.02956 + 2.61185i) q^{4} +(-1.20651 - 3.24721i) q^{6} +5.46770 q^{7} +(7.00695 + 3.86039i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-0.696577 - 1.87477i) q^{2} +1.73205 q^{3} +(-3.02956 + 2.61185i) q^{4} +(-1.20651 - 3.24721i) q^{6} +5.46770 q^{7} +(7.00695 + 3.86039i) q^{8} +3.00000 q^{9} +11.0403i q^{11} +(-5.24735 + 4.52386i) q^{12} +10.1242i q^{13} +(-3.80867 - 10.2507i) q^{14} +(2.35649 - 15.8255i) q^{16} +24.4146i q^{17} +(-2.08973 - 5.62432i) q^{18} -23.7757i q^{19} +9.47033 q^{21} +(20.6981 - 7.69043i) q^{22} +37.2526 q^{23} +(12.1364 + 6.68640i) q^{24} +(18.9806 - 7.05227i) q^{26} +5.19615 q^{27} +(-16.5647 + 14.2808i) q^{28} +25.7726 q^{29} -4.83647i q^{31} +(-31.3108 + 6.60580i) q^{32} +19.1224i q^{33} +(45.7719 - 17.0066i) q^{34} +(-9.08868 + 7.83555i) q^{36} -35.6493i q^{37} +(-44.5741 + 16.5616i) q^{38} +17.5356i q^{39} -9.30410 q^{41} +(-6.59682 - 17.7547i) q^{42} +70.0287 q^{43} +(-28.8356 - 33.4473i) q^{44} +(-25.9493 - 69.8401i) q^{46} -38.0223 q^{47} +(4.08156 - 27.4106i) q^{48} -19.1043 q^{49} +42.2873i q^{51} +(-26.4428 - 30.6718i) q^{52} +55.7762i q^{53} +(-3.61952 - 9.74162i) q^{54} +(38.3119 + 21.1075i) q^{56} -41.1808i q^{57} +(-17.9526 - 48.3179i) q^{58} -55.5411i q^{59} -82.2412 q^{61} +(-9.06729 + 3.36897i) q^{62} +16.4031 q^{63} +(34.1947 + 54.0992i) q^{64} +(35.8502 - 13.3202i) q^{66} +104.493 q^{67} +(-63.7673 - 73.9656i) q^{68} +64.5233 q^{69} +76.7471i q^{71} +(21.0209 + 11.5812i) q^{72} -93.5215i q^{73} +(-66.8344 + 24.8325i) q^{74} +(62.0986 + 72.0300i) q^{76} +60.3651i q^{77} +(32.8753 - 12.2149i) q^{78} +49.3762i q^{79} +9.00000 q^{81} +(6.48102 + 17.4431i) q^{82} -72.3768 q^{83} +(-28.6910 + 24.7351i) q^{84} +(-48.7804 - 131.288i) q^{86} +44.6395 q^{87} +(-42.6199 + 77.3589i) q^{88} -115.691 q^{89} +55.3560i q^{91} +(-112.859 + 97.2980i) q^{92} -8.37701i q^{93} +(26.4854 + 71.2832i) q^{94} +(-54.2318 + 11.4416i) q^{96} +72.9589i q^{97} +(13.3076 + 35.8162i) q^{98} +33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9} + 40 q^{14} + 68 q^{16} - 96 q^{21} - 36 q^{24} - 72 q^{26} - 128 q^{29} + 184 q^{34} - 60 q^{36} - 32 q^{41} - 344 q^{44} + 304 q^{46} + 112 q^{49} - 36 q^{54} + 232 q^{56} - 352 q^{61} + 220 q^{64} + 216 q^{66} + 192 q^{69} - 264 q^{74} - 48 q^{76} + 144 q^{81} + 72 q^{84} - 400 q^{86} - 160 q^{89} + 192 q^{94} - 348 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.696577 1.87477i −0.348288 0.937387i
\(3\) 1.73205 0.577350
\(4\) −3.02956 + 2.61185i −0.757390 + 0.652962i
\(5\) 0 0
\(6\) −1.20651 3.24721i −0.201084 0.541201i
\(7\) 5.46770 0.781100 0.390550 0.920582i \(-0.372285\pi\)
0.390550 + 0.920582i \(0.372285\pi\)
\(8\) 7.00695 + 3.86039i 0.875869 + 0.482549i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 11.0403i 1.00366i 0.864965 + 0.501832i \(0.167341\pi\)
−0.864965 + 0.501832i \(0.832659\pi\)
\(12\) −5.24735 + 4.52386i −0.437280 + 0.376988i
\(13\) 10.1242i 0.778784i 0.921072 + 0.389392i \(0.127315\pi\)
−0.921072 + 0.389392i \(0.872685\pi\)
\(14\) −3.80867 10.2507i −0.272048 0.732193i
\(15\) 0 0
\(16\) 2.35649 15.8255i 0.147280 0.989095i
\(17\) 24.4146i 1.43615i 0.695964 + 0.718077i \(0.254977\pi\)
−0.695964 + 0.718077i \(0.745023\pi\)
\(18\) −2.08973 5.62432i −0.116096 0.312462i
\(19\) 23.7757i 1.25135i −0.780082 0.625677i \(-0.784823\pi\)
0.780082 0.625677i \(-0.215177\pi\)
\(20\) 0 0
\(21\) 9.47033 0.450968
\(22\) 20.6981 7.69043i 0.940823 0.349565i
\(23\) 37.2526 1.61968 0.809838 0.586653i \(-0.199555\pi\)
0.809838 + 0.586653i \(0.199555\pi\)
\(24\) 12.1364 + 6.68640i 0.505683 + 0.278600i
\(25\) 0 0
\(26\) 18.9806 7.05227i 0.730022 0.271241i
\(27\) 5.19615 0.192450
\(28\) −16.5647 + 14.2808i −0.591598 + 0.510029i
\(29\) 25.7726 0.888712 0.444356 0.895850i \(-0.353433\pi\)
0.444356 + 0.895850i \(0.353433\pi\)
\(30\) 0 0
\(31\) 4.83647i 0.156015i −0.996953 0.0780076i \(-0.975144\pi\)
0.996953 0.0780076i \(-0.0248558\pi\)
\(32\) −31.3108 + 6.60580i −0.978461 + 0.206431i
\(33\) 19.1224i 0.579466i
\(34\) 45.7719 17.0066i 1.34623 0.500196i
\(35\) 0 0
\(36\) −9.08868 + 7.83555i −0.252463 + 0.217654i
\(37\) 35.6493i 0.963495i −0.876310 0.481747i \(-0.840002\pi\)
0.876310 0.481747i \(-0.159998\pi\)
\(38\) −44.5741 + 16.5616i −1.17300 + 0.435832i
\(39\) 17.5356i 0.449631i
\(40\) 0 0
\(41\) −9.30410 −0.226929 −0.113465 0.993542i \(-0.536195\pi\)
−0.113465 + 0.993542i \(0.536195\pi\)
\(42\) −6.59682 17.7547i −0.157067 0.422732i
\(43\) 70.0287 1.62857 0.814287 0.580462i \(-0.197128\pi\)
0.814287 + 0.580462i \(0.197128\pi\)
\(44\) −28.8356 33.4473i −0.655355 0.760166i
\(45\) 0 0
\(46\) −25.9493 69.8401i −0.564114 1.51826i
\(47\) −38.0223 −0.808984 −0.404492 0.914542i \(-0.632552\pi\)
−0.404492 + 0.914542i \(0.632552\pi\)
\(48\) 4.08156 27.4106i 0.0850324 0.571054i
\(49\) −19.1043 −0.389883
\(50\) 0 0
\(51\) 42.2873i 0.829164i
\(52\) −26.4428 30.6718i −0.508516 0.589843i
\(53\) 55.7762i 1.05238i 0.850366 + 0.526191i \(0.176380\pi\)
−0.850366 + 0.526191i \(0.823620\pi\)
\(54\) −3.61952 9.74162i −0.0670281 0.180400i
\(55\) 0 0
\(56\) 38.3119 + 21.1075i 0.684141 + 0.376919i
\(57\) 41.1808i 0.722470i
\(58\) −17.9526 48.3179i −0.309528 0.833067i
\(59\) 55.5411i 0.941374i −0.882300 0.470687i \(-0.844006\pi\)
0.882300 0.470687i \(-0.155994\pi\)
\(60\) 0 0
\(61\) −82.2412 −1.34822 −0.674108 0.738633i \(-0.735472\pi\)
−0.674108 + 0.738633i \(0.735472\pi\)
\(62\) −9.06729 + 3.36897i −0.146247 + 0.0543383i
\(63\) 16.4031 0.260367
\(64\) 34.1947 + 54.0992i 0.534293 + 0.845299i
\(65\) 0 0
\(66\) 35.8502 13.3202i 0.543184 0.201821i
\(67\) 104.493 1.55960 0.779802 0.626026i \(-0.215320\pi\)
0.779802 + 0.626026i \(0.215320\pi\)
\(68\) −63.7673 73.9656i −0.937754 1.08773i
\(69\) 64.5233 0.935120
\(70\) 0 0
\(71\) 76.7471i 1.08094i 0.841362 + 0.540472i \(0.181754\pi\)
−0.841362 + 0.540472i \(0.818246\pi\)
\(72\) 21.0209 + 11.5812i 0.291956 + 0.160850i
\(73\) 93.5215i 1.28112i −0.767910 0.640558i \(-0.778703\pi\)
0.767910 0.640558i \(-0.221297\pi\)
\(74\) −66.8344 + 24.8325i −0.903168 + 0.335574i
\(75\) 0 0
\(76\) 62.0986 + 72.0300i 0.817087 + 0.947764i
\(77\) 60.3651i 0.783963i
\(78\) 32.8753 12.2149i 0.421478 0.156601i
\(79\) 49.3762i 0.625016i 0.949915 + 0.312508i \(0.101169\pi\)
−0.949915 + 0.312508i \(0.898831\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 6.48102 + 17.4431i 0.0790368 + 0.212721i
\(83\) −72.3768 −0.872010 −0.436005 0.899944i \(-0.643607\pi\)
−0.436005 + 0.899944i \(0.643607\pi\)
\(84\) −28.6910 + 24.7351i −0.341559 + 0.294465i
\(85\) 0 0
\(86\) −48.7804 131.288i −0.567214 1.52661i
\(87\) 44.6395 0.513098
\(88\) −42.6199 + 77.3589i −0.484318 + 0.879079i
\(89\) −115.691 −1.29990 −0.649950 0.759977i \(-0.725210\pi\)
−0.649950 + 0.759977i \(0.725210\pi\)
\(90\) 0 0
\(91\) 55.3560i 0.608308i
\(92\) −112.859 + 97.2980i −1.22673 + 1.05759i
\(93\) 8.37701i 0.0900754i
\(94\) 26.4854 + 71.2832i 0.281760 + 0.758332i
\(95\) 0 0
\(96\) −54.2318 + 11.4416i −0.564915 + 0.119183i
\(97\) 72.9589i 0.752154i 0.926588 + 0.376077i \(0.122727\pi\)
−0.926588 + 0.376077i \(0.877273\pi\)
\(98\) 13.3076 + 35.8162i 0.135792 + 0.365471i
\(99\) 33.1209i 0.334555i
\(100\) 0 0
\(101\) 29.4092 0.291180 0.145590 0.989345i \(-0.453492\pi\)
0.145590 + 0.989345i \(0.453492\pi\)
\(102\) 79.2792 29.4564i 0.777247 0.288788i
\(103\) 28.1884 0.273673 0.136837 0.990594i \(-0.456306\pi\)
0.136837 + 0.990594i \(0.456306\pi\)
\(104\) −39.0833 + 70.9397i −0.375801 + 0.682112i
\(105\) 0 0
\(106\) 104.568 38.8524i 0.986490 0.366532i
\(107\) −4.50700 −0.0421215 −0.0210607 0.999778i \(-0.506704\pi\)
−0.0210607 + 0.999778i \(0.506704\pi\)
\(108\) −15.7421 + 13.5716i −0.145760 + 0.125663i
\(109\) −193.315 −1.77353 −0.886767 0.462217i \(-0.847054\pi\)
−0.886767 + 0.462217i \(0.847054\pi\)
\(110\) 0 0
\(111\) 61.7464i 0.556274i
\(112\) 12.8846 86.5292i 0.115041 0.772582i
\(113\) 75.5727i 0.668785i 0.942434 + 0.334392i \(0.108531\pi\)
−0.942434 + 0.334392i \(0.891469\pi\)
\(114\) −77.2047 + 28.6856i −0.677234 + 0.251628i
\(115\) 0 0
\(116\) −78.0798 + 67.3142i −0.673102 + 0.580295i
\(117\) 30.3726i 0.259595i
\(118\) −104.127 + 38.6886i −0.882432 + 0.327870i
\(119\) 133.492i 1.12178i
\(120\) 0 0
\(121\) −0.888544 −0.00734334
\(122\) 57.2873 + 154.184i 0.469568 + 1.26380i
\(123\) −16.1152 −0.131018
\(124\) 12.6321 + 14.6524i 0.101872 + 0.118164i
\(125\) 0 0
\(126\) −11.4260 30.7521i −0.0906827 0.244064i
\(127\) −131.306 −1.03390 −0.516951 0.856015i \(-0.672933\pi\)
−0.516951 + 0.856015i \(0.672933\pi\)
\(128\) 77.6045 101.792i 0.606285 0.795247i
\(129\) 121.293 0.940258
\(130\) 0 0
\(131\) 75.7533i 0.578270i −0.957288 0.289135i \(-0.906632\pi\)
0.957288 0.289135i \(-0.0933676\pi\)
\(132\) −49.9448 57.9324i −0.378370 0.438882i
\(133\) 129.999i 0.977433i
\(134\) −72.7877 195.902i −0.543192 1.46195i
\(135\) 0 0
\(136\) −94.2500 + 171.072i −0.693014 + 1.25788i
\(137\) 66.7927i 0.487538i −0.969833 0.243769i \(-0.921616\pi\)
0.969833 0.243769i \(-0.0783839\pi\)
\(138\) −44.9454 120.967i −0.325692 0.876570i
\(139\) 38.1214i 0.274255i −0.990553 0.137127i \(-0.956213\pi\)
0.990553 0.137127i \(-0.0437869\pi\)
\(140\) 0 0
\(141\) −65.8565 −0.467067
\(142\) 143.884 53.4602i 1.01326 0.376481i
\(143\) −111.774 −0.781638
\(144\) 7.06946 47.4765i 0.0490935 0.329698i
\(145\) 0 0
\(146\) −175.332 + 65.1449i −1.20090 + 0.446198i
\(147\) −33.0895 −0.225099
\(148\) 93.1106 + 108.002i 0.629126 + 0.729742i
\(149\) 126.717 0.850449 0.425225 0.905088i \(-0.360195\pi\)
0.425225 + 0.905088i \(0.360195\pi\)
\(150\) 0 0
\(151\) 68.4403i 0.453247i −0.973982 0.226623i \(-0.927231\pi\)
0.973982 0.226623i \(-0.0727687\pi\)
\(152\) 91.7836 166.595i 0.603840 1.09602i
\(153\) 73.2438i 0.478718i
\(154\) 113.171 42.0489i 0.734877 0.273045i
\(155\) 0 0
\(156\) −45.8004 53.1252i −0.293592 0.340546i
\(157\) 25.5777i 0.162915i −0.996677 0.0814577i \(-0.974042\pi\)
0.996677 0.0814577i \(-0.0259575\pi\)
\(158\) 92.5693 34.3943i 0.585882 0.217686i
\(159\) 96.6073i 0.607593i
\(160\) 0 0
\(161\) 203.686 1.26513
\(162\) −6.26919 16.8730i −0.0386987 0.104154i
\(163\) −63.4771 −0.389430 −0.194715 0.980860i \(-0.562378\pi\)
−0.194715 + 0.980860i \(0.562378\pi\)
\(164\) 28.1873 24.3009i 0.171874 0.148176i
\(165\) 0 0
\(166\) 50.4160 + 135.690i 0.303711 + 0.817411i
\(167\) 12.3771 0.0741144 0.0370572 0.999313i \(-0.488202\pi\)
0.0370572 + 0.999313i \(0.488202\pi\)
\(168\) 66.3582 + 36.5592i 0.394989 + 0.217614i
\(169\) 66.5008 0.393496
\(170\) 0 0
\(171\) 71.3272i 0.417118i
\(172\) −212.156 + 182.904i −1.23347 + 1.06340i
\(173\) 59.3729i 0.343196i 0.985167 + 0.171598i \(0.0548930\pi\)
−0.985167 + 0.171598i \(0.945107\pi\)
\(174\) −31.0948 83.6890i −0.178706 0.480971i
\(175\) 0 0
\(176\) 174.719 + 26.0164i 0.992720 + 0.147820i
\(177\) 96.2000i 0.543503i
\(178\) 80.5877 + 216.895i 0.452740 + 1.21851i
\(179\) 252.782i 1.41219i −0.708118 0.706094i \(-0.750455\pi\)
0.708118 0.706094i \(-0.249545\pi\)
\(180\) 0 0
\(181\) 125.373 0.692670 0.346335 0.938111i \(-0.387426\pi\)
0.346335 + 0.938111i \(0.387426\pi\)
\(182\) 103.780 38.5597i 0.570220 0.211867i
\(183\) −142.446 −0.778393
\(184\) 261.027 + 143.809i 1.41862 + 0.781573i
\(185\) 0 0
\(186\) −15.7050 + 5.83523i −0.0844355 + 0.0313722i
\(187\) −269.545 −1.44142
\(188\) 115.191 99.3084i 0.612717 0.528236i
\(189\) 28.4110 0.150323
\(190\) 0 0
\(191\) 97.4640i 0.510283i −0.966904 0.255141i \(-0.917878\pi\)
0.966904 0.255141i \(-0.0821220\pi\)
\(192\) 59.2270 + 93.7025i 0.308474 + 0.488034i
\(193\) 342.376i 1.77397i −0.461798 0.886985i \(-0.652796\pi\)
0.461798 0.886985i \(-0.347204\pi\)
\(194\) 136.782 50.8215i 0.705060 0.261966i
\(195\) 0 0
\(196\) 57.8775 49.8974i 0.295293 0.254579i
\(197\) 74.4829i 0.378086i −0.981969 0.189043i \(-0.939461\pi\)
0.981969 0.189043i \(-0.0605386\pi\)
\(198\) 62.0943 23.0713i 0.313608 0.116522i
\(199\) 178.027i 0.894606i −0.894382 0.447303i \(-0.852385\pi\)
0.894382 0.447303i \(-0.147615\pi\)
\(200\) 0 0
\(201\) 180.988 0.900438
\(202\) −20.4858 55.1356i −0.101415 0.272949i
\(203\) 140.917 0.694173
\(204\) −110.448 128.112i −0.541413 0.628000i
\(205\) 0 0
\(206\) −19.6354 52.8468i −0.0953172 0.256538i
\(207\) 111.758 0.539892
\(208\) 160.220 + 23.8575i 0.770291 + 0.114700i
\(209\) 262.491 1.25594
\(210\) 0 0
\(211\) 185.893i 0.881008i −0.897751 0.440504i \(-0.854800\pi\)
0.897751 0.440504i \(-0.145200\pi\)
\(212\) −145.679 168.978i −0.687166 0.797064i
\(213\) 132.930i 0.624084i
\(214\) 3.13947 + 8.44961i 0.0146704 + 0.0394842i
\(215\) 0 0
\(216\) 36.4092 + 20.0592i 0.168561 + 0.0928666i
\(217\) 26.4444i 0.121863i
\(218\) 134.659 + 362.422i 0.617701 + 1.66249i
\(219\) 161.984i 0.739653i
\(220\) 0 0
\(221\) −247.178 −1.11845
\(222\) −115.761 + 43.0111i −0.521444 + 0.193744i
\(223\) −202.724 −0.909074 −0.454537 0.890728i \(-0.650195\pi\)
−0.454537 + 0.890728i \(0.650195\pi\)
\(224\) −171.198 + 36.1186i −0.764276 + 0.161244i
\(225\) 0 0
\(226\) 141.682 52.6422i 0.626910 0.232930i
\(227\) 51.2708 0.225863 0.112931 0.993603i \(-0.463976\pi\)
0.112931 + 0.993603i \(0.463976\pi\)
\(228\) 107.558 + 124.760i 0.471745 + 0.547192i
\(229\) −337.056 −1.47186 −0.735930 0.677058i \(-0.763255\pi\)
−0.735930 + 0.677058i \(0.763255\pi\)
\(230\) 0 0
\(231\) 104.555i 0.452621i
\(232\) 180.588 + 99.4925i 0.778395 + 0.428847i
\(233\) 80.2851i 0.344571i −0.985047 0.172286i \(-0.944885\pi\)
0.985047 0.172286i \(-0.0551152\pi\)
\(234\) 56.9417 21.1568i 0.243341 0.0904138i
\(235\) 0 0
\(236\) 145.065 + 168.265i 0.614682 + 0.712988i
\(237\) 85.5221i 0.360853i
\(238\) 250.267 92.9873i 1.05154 0.390703i
\(239\) 330.808i 1.38413i 0.721834 + 0.692066i \(0.243299\pi\)
−0.721834 + 0.692066i \(0.756701\pi\)
\(240\) 0 0
\(241\) −359.914 −1.49342 −0.746710 0.665150i \(-0.768368\pi\)
−0.746710 + 0.665150i \(0.768368\pi\)
\(242\) 0.618939 + 1.66582i 0.00255760 + 0.00688355i
\(243\) 15.5885 0.0641500
\(244\) 249.155 214.802i 1.02113 0.880334i
\(245\) 0 0
\(246\) 11.2255 + 30.2123i 0.0456319 + 0.122814i
\(247\) 240.710 0.974534
\(248\) 18.6707 33.8889i 0.0752850 0.136649i
\(249\) −125.360 −0.503455
\(250\) 0 0
\(251\) 312.213i 1.24388i −0.783067 0.621938i \(-0.786346\pi\)
0.783067 0.621938i \(-0.213654\pi\)
\(252\) −49.6942 + 42.8424i −0.197199 + 0.170010i
\(253\) 411.280i 1.62561i
\(254\) 91.4645 + 246.169i 0.360096 + 0.969167i
\(255\) 0 0
\(256\) −244.894 74.5853i −0.956617 0.291349i
\(257\) 80.2592i 0.312293i −0.987734 0.156146i \(-0.950093\pi\)
0.987734 0.156146i \(-0.0499072\pi\)
\(258\) −84.4901 227.398i −0.327481 0.881386i
\(259\) 194.920i 0.752586i
\(260\) 0 0
\(261\) 77.3179 0.296237
\(262\) −142.020 + 52.7680i −0.542063 + 0.201405i
\(263\) −487.967 −1.85539 −0.927694 0.373342i \(-0.878212\pi\)
−0.927694 + 0.373342i \(0.878212\pi\)
\(264\) −73.8199 + 133.990i −0.279621 + 0.507536i
\(265\) 0 0
\(266\) −243.718 + 90.5540i −0.916233 + 0.340428i
\(267\) −200.383 −0.750498
\(268\) −316.569 + 272.921i −1.18123 + 1.01836i
\(269\) 309.553 1.15076 0.575378 0.817888i \(-0.304855\pi\)
0.575378 + 0.817888i \(0.304855\pi\)
\(270\) 0 0
\(271\) 48.9693i 0.180698i −0.995910 0.0903492i \(-0.971202\pi\)
0.995910 0.0903492i \(-0.0287983\pi\)
\(272\) 386.374 + 57.5327i 1.42049 + 0.211517i
\(273\) 95.8794i 0.351207i
\(274\) −125.221 + 46.5262i −0.457012 + 0.169804i
\(275\) 0 0
\(276\) −195.477 + 168.525i −0.708251 + 0.610598i
\(277\) 199.644i 0.720736i 0.932810 + 0.360368i \(0.117349\pi\)
−0.932810 + 0.360368i \(0.882651\pi\)
\(278\) −71.4690 + 26.5545i −0.257083 + 0.0955197i
\(279\) 14.5094i 0.0520051i
\(280\) 0 0
\(281\) 61.1598 0.217650 0.108825 0.994061i \(-0.465291\pi\)
0.108825 + 0.994061i \(0.465291\pi\)
\(282\) 45.8741 + 123.466i 0.162674 + 0.437823i
\(283\) 432.506 1.52829 0.764145 0.645044i \(-0.223161\pi\)
0.764145 + 0.645044i \(0.223161\pi\)
\(284\) −200.452 232.510i −0.705816 0.818697i
\(285\) 0 0
\(286\) 77.8593 + 209.551i 0.272235 + 0.732697i
\(287\) −50.8720 −0.177254
\(288\) −93.9323 + 19.8174i −0.326154 + 0.0688105i
\(289\) −307.073 −1.06254
\(290\) 0 0
\(291\) 126.369i 0.434256i
\(292\) 244.264 + 283.329i 0.836521 + 0.970305i
\(293\) 283.234i 0.966668i −0.875436 0.483334i \(-0.839426\pi\)
0.875436 0.483334i \(-0.160574\pi\)
\(294\) 23.0494 + 62.0354i 0.0783993 + 0.211005i
\(295\) 0 0
\(296\) 137.620 249.793i 0.464933 0.843895i
\(297\) 57.3672i 0.193155i
\(298\) −88.2681 237.566i −0.296202 0.797200i
\(299\) 377.152i 1.26138i
\(300\) 0 0
\(301\) 382.896 1.27208
\(302\) −128.310 + 47.6739i −0.424868 + 0.157861i
\(303\) 50.9382 0.168113
\(304\) −376.263 56.0272i −1.23771 0.184300i
\(305\) 0 0
\(306\) 137.316 51.0199i 0.448744 0.166732i
\(307\) 100.077 0.325983 0.162992 0.986627i \(-0.447886\pi\)
0.162992 + 0.986627i \(0.447886\pi\)
\(308\) −157.665 182.880i −0.511898 0.593766i
\(309\) 48.8237 0.158005
\(310\) 0 0
\(311\) 404.185i 1.29963i 0.760092 + 0.649815i \(0.225154\pi\)
−0.760092 + 0.649815i \(0.774846\pi\)
\(312\) −67.6943 + 122.871i −0.216969 + 0.393818i
\(313\) 128.579i 0.410795i −0.978679 0.205398i \(-0.934151\pi\)
0.978679 0.205398i \(-0.0658487\pi\)
\(314\) −47.9525 + 17.8168i −0.152715 + 0.0567415i
\(315\) 0 0
\(316\) −128.963 149.588i −0.408112 0.473381i
\(317\) 85.9315i 0.271077i −0.990772 0.135539i \(-0.956724\pi\)
0.990772 0.135539i \(-0.0432765\pi\)
\(318\) 181.117 67.2944i 0.569550 0.211618i
\(319\) 284.538i 0.891969i
\(320\) 0 0
\(321\) −7.80635 −0.0243189
\(322\) −141.883 381.865i −0.440630 1.18592i
\(323\) 580.475 1.79714
\(324\) −27.2661 + 23.5066i −0.0841545 + 0.0725514i
\(325\) 0 0
\(326\) 44.2167 + 119.005i 0.135634 + 0.365047i
\(327\) −334.832 −1.02395
\(328\) −65.1934 35.9175i −0.198760 0.109505i
\(329\) −207.894 −0.631898
\(330\) 0 0
\(331\) 183.391i 0.554052i −0.960862 0.277026i \(-0.910651\pi\)
0.960862 0.277026i \(-0.0893488\pi\)
\(332\) 219.270 189.037i 0.660452 0.569390i
\(333\) 106.948i 0.321165i
\(334\) −8.62160 23.2043i −0.0258132 0.0694739i
\(335\) 0 0
\(336\) 22.3167 149.873i 0.0664188 0.446050i
\(337\) 168.130i 0.498901i −0.968388 0.249451i \(-0.919750\pi\)
0.968388 0.249451i \(-0.0802500\pi\)
\(338\) −46.3229 124.674i −0.137050 0.368858i
\(339\) 130.896i 0.386123i
\(340\) 0 0
\(341\) 53.3962 0.156587
\(342\) −133.722 + 49.6849i −0.391001 + 0.145277i
\(343\) −372.374 −1.08564
\(344\) 490.688 + 270.338i 1.42642 + 0.785867i
\(345\) 0 0
\(346\) 111.311 41.3578i 0.321708 0.119531i
\(347\) 137.414 0.396006 0.198003 0.980201i \(-0.436554\pi\)
0.198003 + 0.980201i \(0.436554\pi\)
\(348\) −135.238 + 116.592i −0.388615 + 0.335034i
\(349\) 13.4893 0.0386513 0.0193256 0.999813i \(-0.493848\pi\)
0.0193256 + 0.999813i \(0.493848\pi\)
\(350\) 0 0
\(351\) 52.6068i 0.149877i
\(352\) −72.9301 345.681i −0.207188 0.982047i
\(353\) 243.547i 0.689935i 0.938615 + 0.344968i \(0.112110\pi\)
−0.938615 + 0.344968i \(0.887890\pi\)
\(354\) −180.353 + 67.0107i −0.509473 + 0.189296i
\(355\) 0 0
\(356\) 350.493 302.168i 0.984532 0.848786i
\(357\) 231.215i 0.647660i
\(358\) −473.909 + 176.082i −1.32377 + 0.491849i
\(359\) 17.9166i 0.0499068i 0.999689 + 0.0249534i \(0.00794374\pi\)
−0.999689 + 0.0249534i \(0.992056\pi\)
\(360\) 0 0
\(361\) −204.285 −0.565887
\(362\) −87.3321 235.047i −0.241249 0.649300i
\(363\) −1.53900 −0.00423968
\(364\) −144.582 167.704i −0.397202 0.460727i
\(365\) 0 0
\(366\) 99.2245 + 267.054i 0.271105 + 0.729656i
\(367\) 238.417 0.649637 0.324818 0.945776i \(-0.394697\pi\)
0.324818 + 0.945776i \(0.394697\pi\)
\(368\) 87.7852 589.541i 0.238547 1.60201i
\(369\) −27.9123 −0.0756431
\(370\) 0 0
\(371\) 304.968i 0.822016i
\(372\) 21.8795 + 25.3787i 0.0588158 + 0.0682222i
\(373\) 181.271i 0.485981i −0.970029 0.242990i \(-0.921872\pi\)
0.970029 0.242990i \(-0.0781283\pi\)
\(374\) 187.759 + 505.336i 0.502029 + 1.35117i
\(375\) 0 0
\(376\) −266.420 146.781i −0.708564 0.390375i
\(377\) 260.927i 0.692114i
\(378\) −19.7904 53.2642i −0.0523557 0.140911i
\(379\) 306.206i 0.807931i −0.914774 0.403965i \(-0.867632\pi\)
0.914774 0.403965i \(-0.132368\pi\)
\(380\) 0 0
\(381\) −227.428 −0.596924
\(382\) −182.723 + 67.8912i −0.478333 + 0.177726i
\(383\) 144.027 0.376050 0.188025 0.982164i \(-0.439791\pi\)
0.188025 + 0.982164i \(0.439791\pi\)
\(384\) 134.415 176.308i 0.350039 0.459136i
\(385\) 0 0
\(386\) −641.878 + 238.491i −1.66290 + 0.617853i
\(387\) 210.086 0.542858
\(388\) −190.558 221.034i −0.491128 0.569674i
\(389\) −14.0099 −0.0360152 −0.0180076 0.999838i \(-0.505732\pi\)
−0.0180076 + 0.999838i \(0.505732\pi\)
\(390\) 0 0
\(391\) 909.506i 2.32610i
\(392\) −133.863 73.7499i −0.341486 0.188138i
\(393\) 131.209i 0.333864i
\(394\) −139.639 + 51.8831i −0.354413 + 0.131683i
\(395\) 0 0
\(396\) −86.5069 100.342i −0.218452 0.253389i
\(397\) 39.1084i 0.0985098i −0.998786 0.0492549i \(-0.984315\pi\)
0.998786 0.0492549i \(-0.0156847\pi\)
\(398\) −333.760 + 124.009i −0.838592 + 0.311581i
\(399\) 225.164i 0.564321i
\(400\) 0 0
\(401\) −121.067 −0.301913 −0.150957 0.988540i \(-0.548235\pi\)
−0.150957 + 0.988540i \(0.548235\pi\)
\(402\) −126.072 339.312i −0.313612 0.844059i
\(403\) 48.9653 0.121502
\(404\) −89.0970 + 76.8124i −0.220537 + 0.190130i
\(405\) 0 0
\(406\) −98.1595 264.188i −0.241772 0.650709i
\(407\) 393.579 0.967026
\(408\) −163.246 + 296.305i −0.400112 + 0.726239i
\(409\) 541.795 1.32468 0.662342 0.749202i \(-0.269563\pi\)
0.662342 + 0.749202i \(0.269563\pi\)
\(410\) 0 0
\(411\) 115.688i 0.281480i
\(412\) −85.3983 + 73.6237i −0.207278 + 0.178698i
\(413\) 303.682i 0.735307i
\(414\) −77.8478 209.520i −0.188038 0.506088i
\(415\) 0 0
\(416\) −66.8784 316.996i −0.160765 0.762009i
\(417\) 66.0282i 0.158341i
\(418\) −182.845 492.112i −0.437429 1.17730i
\(419\) 687.825i 1.64159i −0.571224 0.820794i \(-0.693531\pi\)
0.571224 0.820794i \(-0.306469\pi\)
\(420\) 0 0
\(421\) −454.396 −1.07932 −0.539662 0.841882i \(-0.681448\pi\)
−0.539662 + 0.841882i \(0.681448\pi\)
\(422\) −348.507 + 129.489i −0.825846 + 0.306845i
\(423\) −114.067 −0.269661
\(424\) −215.318 + 390.821i −0.507826 + 0.921749i
\(425\) 0 0
\(426\) 249.214 92.5959i 0.585008 0.217361i
\(427\) −449.670 −1.05309
\(428\) 13.6542 11.7716i 0.0319024 0.0275037i
\(429\) −193.599 −0.451279
\(430\) 0 0
\(431\) 466.145i 1.08154i 0.841169 + 0.540772i \(0.181868\pi\)
−0.841169 + 0.540772i \(0.818132\pi\)
\(432\) 12.2447 82.2318i 0.0283441 0.190351i
\(433\) 457.094i 1.05565i 0.849355 + 0.527823i \(0.176991\pi\)
−0.849355 + 0.527823i \(0.823009\pi\)
\(434\) −49.5772 + 18.4205i −0.114233 + 0.0424436i
\(435\) 0 0
\(436\) 585.660 504.910i 1.34326 1.15805i
\(437\) 885.706i 2.02679i
\(438\) −303.684 + 112.834i −0.693341 + 0.257613i
\(439\) 777.467i 1.77100i 0.464644 + 0.885498i \(0.346182\pi\)
−0.464644 + 0.885498i \(0.653818\pi\)
\(440\) 0 0
\(441\) −57.3128 −0.129961
\(442\) 172.178 + 463.403i 0.389544 + 1.04842i
\(443\) 247.484 0.558654 0.279327 0.960196i \(-0.409889\pi\)
0.279327 + 0.960196i \(0.409889\pi\)
\(444\) 161.272 + 187.065i 0.363226 + 0.421316i
\(445\) 0 0
\(446\) 141.213 + 380.061i 0.316620 + 0.852155i
\(447\) 219.480 0.491007
\(448\) 186.967 + 295.798i 0.417336 + 0.660263i
\(449\) −412.508 −0.918726 −0.459363 0.888249i \(-0.651922\pi\)
−0.459363 + 0.888249i \(0.651922\pi\)
\(450\) 0 0
\(451\) 102.720i 0.227761i
\(452\) −197.384 228.952i −0.436691 0.506531i
\(453\) 118.542i 0.261682i
\(454\) −35.7141 96.1213i −0.0786654 0.211721i
\(455\) 0 0
\(456\) 158.974 288.552i 0.348627 0.632789i
\(457\) 745.400i 1.63107i 0.578706 + 0.815537i \(0.303558\pi\)
−0.578706 + 0.815537i \(0.696442\pi\)
\(458\) 234.785 + 631.904i 0.512631 + 1.37970i
\(459\) 126.862i 0.276388i
\(460\) 0 0
\(461\) 81.6151 0.177039 0.0885196 0.996074i \(-0.471786\pi\)
0.0885196 + 0.996074i \(0.471786\pi\)
\(462\) 196.018 72.8309i 0.424281 0.157643i
\(463\) 292.248 0.631205 0.315603 0.948891i \(-0.397793\pi\)
0.315603 + 0.948891i \(0.397793\pi\)
\(464\) 60.7329 407.865i 0.130890 0.879020i
\(465\) 0 0
\(466\) −150.517 + 55.9248i −0.322997 + 0.120010i
\(467\) 51.4163 0.110099 0.0550495 0.998484i \(-0.482468\pi\)
0.0550495 + 0.998484i \(0.482468\pi\)
\(468\) −79.3285 92.0155i −0.169505 0.196614i
\(469\) 571.339 1.21821
\(470\) 0 0
\(471\) 44.3019i 0.0940592i
\(472\) 214.410 389.174i 0.454259 0.824520i
\(473\) 773.139i 1.63454i
\(474\) 160.335 59.5727i 0.338259 0.125681i
\(475\) 0 0
\(476\) −348.660 404.422i −0.732480 0.849625i
\(477\) 167.329i 0.350794i
\(478\) 620.190 230.433i 1.29747 0.482077i
\(479\) 122.593i 0.255935i 0.991778 + 0.127967i \(0.0408453\pi\)
−0.991778 + 0.127967i \(0.959155\pi\)
\(480\) 0 0
\(481\) 360.920 0.750354
\(482\) 250.708 + 674.758i 0.520141 + 1.39991i
\(483\) 352.794 0.730423
\(484\) 2.69190 2.32074i 0.00556177 0.00479492i
\(485\) 0 0
\(486\) −10.8586 29.2248i −0.0223427 0.0601334i
\(487\) −65.9859 −0.135495 −0.0677474 0.997703i \(-0.521581\pi\)
−0.0677474 + 0.997703i \(0.521581\pi\)
\(488\) −576.260 317.483i −1.18086 0.650580i
\(489\) −109.946 −0.224837
\(490\) 0 0
\(491\) 361.163i 0.735567i −0.929911 0.367783i \(-0.880117\pi\)
0.929911 0.367783i \(-0.119883\pi\)
\(492\) 48.8219 42.0904i 0.0992315 0.0855496i
\(493\) 629.229i 1.27633i
\(494\) −167.673 451.277i −0.339419 0.913516i
\(495\) 0 0
\(496\) −76.5396 11.3971i −0.154314 0.0229780i
\(497\) 419.630i 0.844326i
\(498\) 87.3231 + 235.022i 0.175348 + 0.471933i
\(499\) 711.138i 1.42513i −0.701608 0.712564i \(-0.747534\pi\)
0.701608 0.712564i \(-0.252466\pi\)
\(500\) 0 0
\(501\) 21.4378 0.0427900
\(502\) −585.328 + 217.480i −1.16599 + 0.433227i
\(503\) 353.756 0.703292 0.351646 0.936133i \(-0.385622\pi\)
0.351646 + 0.936133i \(0.385622\pi\)
\(504\) 114.936 + 63.3224i 0.228047 + 0.125640i
\(505\) 0 0
\(506\) 771.057 286.488i 1.52383 0.566182i
\(507\) 115.183 0.227185
\(508\) 397.799 342.951i 0.783068 0.675100i
\(509\) −478.049 −0.939192 −0.469596 0.882881i \(-0.655600\pi\)
−0.469596 + 0.882881i \(0.655600\pi\)
\(510\) 0 0
\(511\) 511.348i 1.00068i
\(512\) 30.7568 + 511.075i 0.0600720 + 0.998194i
\(513\) 123.542i 0.240823i
\(514\) −150.468 + 55.9067i −0.292739 + 0.108768i
\(515\) 0 0
\(516\) −367.466 + 316.800i −0.712142 + 0.613953i
\(517\) 419.778i 0.811949i
\(518\) −365.431 + 135.777i −0.705464 + 0.262117i
\(519\) 102.837i 0.198144i
\(520\) 0 0
\(521\) −35.7365 −0.0685921 −0.0342960 0.999412i \(-0.510919\pi\)
−0.0342960 + 0.999412i \(0.510919\pi\)
\(522\) −53.8579 144.954i −0.103176 0.277689i
\(523\) 733.562 1.40260 0.701302 0.712864i \(-0.252602\pi\)
0.701302 + 0.712864i \(0.252602\pi\)
\(524\) 197.856 + 229.499i 0.377588 + 0.437976i
\(525\) 0 0
\(526\) 339.906 + 914.828i 0.646210 + 1.73922i
\(527\) 118.081 0.224062
\(528\) 302.622 + 45.0617i 0.573147 + 0.0853441i
\(529\) 858.753 1.62335
\(530\) 0 0
\(531\) 166.623i 0.313791i
\(532\) 339.537 + 393.839i 0.638227 + 0.740298i
\(533\) 94.1965i 0.176729i
\(534\) 139.582 + 375.673i 0.261390 + 0.703507i
\(535\) 0 0
\(536\) 732.181 + 403.386i 1.36601 + 0.752585i
\(537\) 437.831i 0.815327i
\(538\) −215.628 580.342i −0.400795 1.07870i
\(539\) 210.917i 0.391312i
\(540\) 0 0
\(541\) 608.939 1.12558 0.562790 0.826600i \(-0.309728\pi\)
0.562790 + 0.826600i \(0.309728\pi\)
\(542\) −91.8064 + 34.1109i −0.169384 + 0.0629352i
\(543\) 217.153 0.399913
\(544\) −161.278 764.440i −0.296467 1.40522i
\(545\) 0 0
\(546\) 179.752 66.7874i 0.329217 0.122321i
\(547\) 78.5868 0.143669 0.0718344 0.997417i \(-0.477115\pi\)
0.0718344 + 0.997417i \(0.477115\pi\)
\(548\) 174.452 + 202.353i 0.318344 + 0.369257i
\(549\) −246.724 −0.449405
\(550\) 0 0
\(551\) 612.763i 1.11209i
\(552\) 452.112 + 249.085i 0.819043 + 0.451242i
\(553\) 269.974i 0.488200i
\(554\) 374.287 139.067i 0.675609 0.251024i
\(555\) 0 0
\(556\) 99.5673 + 115.491i 0.179078 + 0.207718i
\(557\) 928.488i 1.66694i 0.552561 + 0.833472i \(0.313651\pi\)
−0.552561 + 0.833472i \(0.686349\pi\)
\(558\) −27.2019 + 10.1069i −0.0487489 + 0.0181128i
\(559\) 708.984i 1.26831i
\(560\) 0 0
\(561\) −466.866 −0.832202
\(562\) −42.6025 114.661i −0.0758051 0.204023i
\(563\) −447.978 −0.795697 −0.397849 0.917451i \(-0.630243\pi\)
−0.397849 + 0.917451i \(0.630243\pi\)
\(564\) 199.516 172.007i 0.353752 0.304977i
\(565\) 0 0
\(566\) −301.274 810.852i −0.532286 1.43260i
\(567\) 49.2093 0.0867889
\(568\) −296.274 + 537.763i −0.521609 + 0.946766i
\(569\) −571.441 −1.00429 −0.502145 0.864783i \(-0.667456\pi\)
−0.502145 + 0.864783i \(0.667456\pi\)
\(570\) 0 0
\(571\) 990.801i 1.73520i 0.497260 + 0.867602i \(0.334340\pi\)
−0.497260 + 0.867602i \(0.665660\pi\)
\(572\) 338.627 291.937i 0.592005 0.510380i
\(573\) 168.813i 0.294612i
\(574\) 35.4363 + 95.3736i 0.0617357 + 0.166156i
\(575\) 0 0
\(576\) 102.584 + 162.298i 0.178098 + 0.281766i
\(577\) 826.638i 1.43265i −0.697768 0.716324i \(-0.745823\pi\)
0.697768 0.716324i \(-0.254177\pi\)
\(578\) 213.900 + 575.693i 0.370069 + 0.996008i
\(579\) 593.013i 1.02420i
\(580\) 0 0
\(581\) −395.735 −0.681127
\(582\) 236.913 88.0254i 0.407066 0.151246i
\(583\) −615.787 −1.05624
\(584\) 361.030 655.301i 0.618202 1.12209i
\(585\) 0 0
\(586\) −530.999 + 197.294i −0.906142 + 0.336679i
\(587\) −900.009 −1.53323 −0.766617 0.642104i \(-0.778062\pi\)
−0.766617 + 0.642104i \(0.778062\pi\)
\(588\) 100.247 86.4249i 0.170488 0.146981i
\(589\) −114.991 −0.195230
\(590\) 0 0
\(591\) 129.008i 0.218288i
\(592\) −564.169 84.0071i −0.952987 0.141904i
\(593\) 704.088i 1.18733i −0.804711 0.593666i \(-0.797680\pi\)
0.804711 0.593666i \(-0.202320\pi\)
\(594\) 107.551 39.9606i 0.181061 0.0672738i
\(595\) 0 0
\(596\) −383.897 + 330.965i −0.644122 + 0.555311i
\(597\) 308.351i 0.516501i
\(598\) 707.075 262.715i 1.18240 0.439323i
\(599\) 376.098i 0.627876i −0.949444 0.313938i \(-0.898352\pi\)
0.949444 0.313938i \(-0.101648\pi\)
\(600\) 0 0
\(601\) 430.191 0.715791 0.357896 0.933762i \(-0.383494\pi\)
0.357896 + 0.933762i \(0.383494\pi\)
\(602\) −266.716 717.844i −0.443051 1.19243i
\(603\) 313.480 0.519868
\(604\) 178.756 + 207.344i 0.295953 + 0.343285i
\(605\) 0 0
\(606\) −35.4824 95.4977i −0.0585518 0.157587i
\(607\) 93.4019 0.153875 0.0769373 0.997036i \(-0.475486\pi\)
0.0769373 + 0.997036i \(0.475486\pi\)
\(608\) 157.058 + 744.436i 0.258319 + 1.22440i
\(609\) 244.075 0.400781
\(610\) 0 0
\(611\) 384.944i 0.630024i
\(612\) −191.302 221.897i −0.312585 0.362576i
\(613\) 156.506i 0.255312i −0.991818 0.127656i \(-0.959255\pi\)
0.991818 0.127656i \(-0.0407454\pi\)
\(614\) −69.7113 187.622i −0.113536 0.305573i
\(615\) 0 0
\(616\) −233.033 + 422.976i −0.378301 + 0.686649i
\(617\) 553.493i 0.897072i 0.893765 + 0.448536i \(0.148054\pi\)
−0.893765 + 0.448536i \(0.851946\pi\)
\(618\) −34.0094 91.5334i −0.0550314 0.148112i
\(619\) 14.4398i 0.0233276i −0.999932 0.0116638i \(-0.996287\pi\)
0.999932 0.0116638i \(-0.00371278\pi\)
\(620\) 0 0
\(621\) 193.570 0.311707
\(622\) 757.756 281.546i 1.21826 0.452646i
\(623\) −632.564 −1.01535
\(624\) 277.510 + 41.3224i 0.444728 + 0.0662219i
\(625\) 0 0
\(626\) −241.056 + 89.5651i −0.385074 + 0.143075i
\(627\) 454.649 0.725117
\(628\) 66.8051 + 77.4893i 0.106378 + 0.123391i
\(629\) 870.364 1.38373
\(630\) 0 0
\(631\) 352.389i 0.558460i 0.960224 + 0.279230i \(0.0900793\pi\)
−0.960224 + 0.279230i \(0.909921\pi\)
\(632\) −190.612 + 345.977i −0.301601 + 0.547432i
\(633\) 321.976i 0.508650i
\(634\) −161.102 + 59.8579i −0.254104 + 0.0944130i
\(635\) 0 0
\(636\) −252.324 292.678i −0.396735 0.460185i
\(637\) 193.415i 0.303634i
\(638\) 533.445 198.203i 0.836120 0.310662i
\(639\) 230.241i 0.360315i
\(640\) 0 0
\(641\) −545.742 −0.851391 −0.425696 0.904866i \(-0.639971\pi\)
−0.425696 + 0.904866i \(0.639971\pi\)
\(642\) 5.43772 + 14.6352i 0.00846997 + 0.0227962i
\(643\) −757.447 −1.17799 −0.588995 0.808137i \(-0.700476\pi\)
−0.588995 + 0.808137i \(0.700476\pi\)
\(644\) −617.079 + 531.997i −0.958197 + 0.826082i
\(645\) 0 0
\(646\) −404.345 1088.26i −0.625922 1.68461i
\(647\) −1161.36 −1.79500 −0.897499 0.441016i \(-0.854618\pi\)
−0.897499 + 0.441016i \(0.854618\pi\)
\(648\) 63.0626 + 34.7435i 0.0973188 + 0.0536166i
\(649\) 613.191 0.944824
\(650\) 0 0
\(651\) 45.8030i 0.0703579i
\(652\) 192.308 165.793i 0.294950 0.254283i
\(653\) 621.231i 0.951348i −0.879622 0.475674i \(-0.842204\pi\)
0.879622 0.475674i \(-0.157796\pi\)
\(654\) 233.236 + 627.734i 0.356630 + 0.959838i
\(655\) 0 0
\(656\) −21.9250 + 147.242i −0.0334223 + 0.224455i
\(657\) 280.565i 0.427039i
\(658\) 144.814 + 389.755i 0.220083 + 0.592333i
\(659\) 736.047i 1.11692i −0.829533 0.558458i \(-0.811393\pi\)
0.829533 0.558458i \(-0.188607\pi\)
\(660\) 0 0
\(661\) 383.845 0.580704 0.290352 0.956920i \(-0.406228\pi\)
0.290352 + 0.956920i \(0.406228\pi\)
\(662\) −343.817 + 127.746i −0.519362 + 0.192970i
\(663\) −428.125 −0.645739
\(664\) −507.141 279.403i −0.763766 0.420788i
\(665\) 0 0
\(666\) −200.503 + 74.4974i −0.301056 + 0.111858i
\(667\) 960.096 1.43942
\(668\) −37.4972 + 32.3271i −0.0561335 + 0.0483939i
\(669\) −351.128 −0.524854
\(670\) 0 0
\(671\) 907.968i 1.35316i
\(672\) −296.523 + 62.5592i −0.441255 + 0.0930940i
\(673\) 984.464i 1.46280i 0.681949 + 0.731400i \(0.261133\pi\)
−0.681949 + 0.731400i \(0.738867\pi\)
\(674\) −315.205 + 117.115i −0.467664 + 0.173761i
\(675\) 0 0
\(676\) −201.468 + 173.690i −0.298030 + 0.256938i
\(677\) 673.154i 0.994319i −0.867659 0.497160i \(-0.834376\pi\)
0.867659 0.497160i \(-0.165624\pi\)
\(678\) 245.400 91.1789i 0.361947 0.134482i
\(679\) 398.918i 0.587507i
\(680\) 0 0
\(681\) 88.8037 0.130402
\(682\) −37.1945 100.106i −0.0545374 0.146783i
\(683\) −291.192 −0.426343 −0.213171 0.977015i \(-0.568379\pi\)
−0.213171 + 0.977015i \(0.568379\pi\)
\(684\) 186.296 + 216.090i 0.272362 + 0.315921i
\(685\) 0 0
\(686\) 259.387 + 698.117i 0.378115 + 1.01766i
\(687\) −583.798 −0.849778
\(688\) 165.022 1108.24i 0.239857 1.61081i
\(689\) −564.689 −0.819578
\(690\) 0 0
\(691\) 943.693i 1.36569i −0.730563 0.682846i \(-0.760742\pi\)
0.730563 0.682846i \(-0.239258\pi\)
\(692\) −155.073 179.874i −0.224094 0.259933i
\(693\) 181.095i 0.261321i
\(694\) −95.7193 257.620i −0.137924 0.371211i
\(695\) 0 0
\(696\) 312.787 + 172.326i 0.449406 + 0.247595i
\(697\) 227.156i 0.325905i
\(698\) −9.39633 25.2894i −0.0134618 0.0362312i
\(699\) 139.058i 0.198938i
\(700\) 0 0
\(701\) 885.681 1.26345 0.631727 0.775191i \(-0.282346\pi\)
0.631727 + 0.775191i \(0.282346\pi\)
\(702\) 98.6259 36.6447i 0.140493 0.0522004i
\(703\) −847.588 −1.20567
\(704\) −597.272 + 377.521i −0.848397 + 0.536251i
\(705\) 0 0
\(706\) 456.596 169.649i 0.646737 0.240296i
\(707\) 160.801 0.227441
\(708\) 251.260 + 291.444i 0.354887 + 0.411644i
\(709\) 286.183 0.403644 0.201822 0.979422i \(-0.435314\pi\)
0.201822 + 0.979422i \(0.435314\pi\)
\(710\) 0 0
\(711\) 148.129i 0.208339i
\(712\) −810.642 446.613i −1.13854 0.627266i
\(713\) 180.171i 0.252694i
\(714\) 433.475 161.059i 0.607108 0.225572i
\(715\) 0 0
\(716\) 660.228 + 765.818i 0.922106 + 1.06958i
\(717\) 572.976i 0.799129i
\(718\) 33.5895 12.4803i 0.0467820 0.0173820i
\(719\) 666.163i 0.926513i 0.886224 + 0.463257i \(0.153319\pi\)
−0.886224 + 0.463257i \(0.846681\pi\)
\(720\) 0 0
\(721\) 154.125 0.213766
\(722\) 142.300 + 382.989i 0.197092 + 0.530455i
\(723\) −623.389 −0.862226
\(724\) −379.826 + 327.456i −0.524622 + 0.452287i
\(725\) 0 0
\(726\) 1.07203 + 2.88528i 0.00147663 + 0.00397422i
\(727\) −856.270 −1.17781 −0.588907 0.808201i \(-0.700441\pi\)
−0.588907 + 0.808201i \(0.700441\pi\)
\(728\) −213.696 + 387.877i −0.293538 + 0.532798i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 1709.72i 2.33888i
\(732\) 431.549 372.047i 0.589547 0.508261i
\(733\) 769.487i 1.04978i −0.851171 0.524889i \(-0.824107\pi\)
0.851171 0.524889i \(-0.175893\pi\)
\(734\) −166.076 446.978i −0.226261 0.608961i
\(735\) 0 0
\(736\) −1166.41 + 246.083i −1.58479 + 0.334352i
\(737\) 1153.64i 1.56532i
\(738\) 19.4431 + 52.3293i 0.0263456 + 0.0709069i
\(739\) 1156.70i 1.56522i 0.622511 + 0.782611i \(0.286113\pi\)
−0.622511 + 0.782611i \(0.713887\pi\)
\(740\) 0 0
\(741\) 416.922 0.562647
\(742\) 571.746 212.433i 0.770547 0.286298i
\(743\) −426.794 −0.574421 −0.287210 0.957868i \(-0.592728\pi\)
−0.287210 + 0.957868i \(0.592728\pi\)
\(744\) 32.3386 58.6973i 0.0434658 0.0788942i
\(745\) 0 0
\(746\) −339.842 + 126.269i −0.455552 + 0.169261i
\(747\) −217.130 −0.290670
\(748\) 816.603 704.011i 1.09172 0.941191i
\(749\) −24.6429 −0.0329011
\(750\) 0 0
\(751\) 1222.03i 1.62721i −0.581420 0.813604i \(-0.697503\pi\)
0.581420 0.813604i \(-0.302497\pi\)
\(752\) −89.5990 + 601.722i −0.119148 + 0.800162i
\(753\) 540.768i 0.718152i
\(754\) 489.179 181.756i 0.648779 0.241055i
\(755\) 0 0
\(756\) −86.0729 + 74.2053i −0.113853 + 0.0981551i
\(757\) 1312.95i 1.73442i 0.497945 + 0.867209i \(0.334088\pi\)
−0.497945 + 0.867209i \(0.665912\pi\)
\(758\) −574.067 + 213.296i −0.757344 + 0.281393i
\(759\) 712.358i 0.938548i
\(760\) 0 0
\(761\) −189.584 −0.249124 −0.124562 0.992212i \(-0.539753\pi\)
−0.124562 + 0.992212i \(0.539753\pi\)
\(762\) 158.421 + 426.376i 0.207902 + 0.559549i
\(763\) −1056.99 −1.38531
\(764\) 254.561 + 295.273i 0.333195 + 0.386483i
\(765\) 0 0
\(766\) −100.326 270.019i −0.130974 0.352505i
\(767\) 562.308 0.733127
\(768\) −424.169 129.185i −0.552303 0.168210i
\(769\) −254.995 −0.331594 −0.165797 0.986160i \(-0.553020\pi\)
−0.165797 + 0.986160i \(0.553020\pi\)
\(770\) 0 0
\(771\) 139.013i 0.180302i
\(772\) 894.235 + 1037.25i 1.15834 + 1.34359i
\(773\) 23.2536i 0.0300823i 0.999887 + 0.0150411i \(0.00478793\pi\)
−0.999887 + 0.0150411i \(0.995212\pi\)
\(774\) −146.341 393.864i −0.189071 0.508869i
\(775\) 0 0
\(776\) −281.650 + 511.220i −0.362951 + 0.658788i
\(777\) 337.611i 0.434506i
\(778\) 9.75897 + 26.2654i 0.0125437 + 0.0337602i
\(779\) 221.212i 0.283969i
\(780\) 0 0
\(781\) −847.312 −1.08491
\(782\) 1705.12 633.541i 2.18046 0.810155i
\(783\) 133.919 0.171033
\(784\) −45.0189 + 302.335i −0.0574221 + 0.385631i
\(785\) 0 0
\(786\) −245.987 + 91.3969i −0.312960 + 0.116281i
\(787\) 220.593 0.280296 0.140148 0.990131i \(-0.455242\pi\)
0.140148 + 0.990131i \(0.455242\pi\)
\(788\) 194.538 + 225.651i 0.246876 + 0.286359i
\(789\) −845.183 −1.07121
\(790\) 0 0
\(791\) 413.209i 0.522388i
\(792\) −127.860 + 232.077i −0.161439 + 0.293026i
\(793\) 832.625i 1.04997i
\(794\) −73.3194 + 27.2420i −0.0923418 + 0.0343098i
\(795\) 0 0
\(796\) 464.979 + 539.343i 0.584144 + 0.677566i
\(797\) 1010.38i 1.26773i −0.773442 0.633867i \(-0.781467\pi\)
0.773442 0.633867i \(-0.218533\pi\)
\(798\) −422.132 + 156.844i −0.528987 + 0.196546i
\(799\) 928.298i 1.16183i
\(800\) 0 0
\(801\) −347.073 −0.433300
\(802\) 84.3327 + 226.974i 0.105153 + 0.283010i
\(803\) 1032.51 1.28581
\(804\) −548.314 + 472.713i −0.681983 + 0.587952i
\(805\) 0 0
\(806\) −34.1081 91.7990i −0.0423178 0.113894i
\(807\) 536.162 0.664389
\(808\) 206.069 + 113.531i 0.255036 + 0.140509i
\(809\) −1410.37 −1.74335 −0.871674 0.490086i \(-0.836965\pi\)
−0.871674 + 0.490086i \(0.836965\pi\)
\(810\) 0 0
\(811\) 950.157i 1.17159i −0.810460 0.585793i \(-0.800783\pi\)
0.810460 0.585793i \(-0.199217\pi\)
\(812\) −426.917 + 368.054i −0.525760 + 0.453269i
\(813\) 84.8173i 0.104326i
\(814\) −274.158 737.873i −0.336804 0.906478i
\(815\) 0 0
\(816\) 669.219 + 99.6496i 0.820121 + 0.122120i
\(817\) 1664.98i 2.03792i
\(818\) −377.402 1015.74i −0.461372 1.24174i
\(819\) 166.068i 0.202769i
\(820\) 0 0
\(821\) 77.3347 0.0941957 0.0470979 0.998890i \(-0.485003\pi\)
0.0470979 + 0.998890i \(0.485003\pi\)
\(822\) −216.890 + 80.5858i −0.263856 + 0.0980363i
\(823\) 1260.16 1.53118 0.765591 0.643328i \(-0.222447\pi\)
0.765591 + 0.643328i \(0.222447\pi\)
\(824\) 197.514 + 108.818i 0.239702 + 0.132061i
\(825\) 0 0
\(826\) −569.335 + 211.538i −0.689268 + 0.256099i
\(827\) −438.047 −0.529681 −0.264841 0.964292i \(-0.585319\pi\)
−0.264841 + 0.964292i \(0.585319\pi\)
\(828\) −338.577 + 291.894i −0.408909 + 0.352529i
\(829\) −361.388 −0.435933 −0.217966 0.975956i \(-0.569942\pi\)
−0.217966 + 0.975956i \(0.569942\pi\)
\(830\) 0 0
\(831\) 345.793i 0.416117i
\(832\) −547.710 + 346.194i −0.658305 + 0.416098i
\(833\) 466.423i 0.559931i
\(834\) −123.788 + 45.9937i −0.148427 + 0.0551483i
\(835\) 0 0
\(836\) −795.234 + 685.588i −0.951237 + 0.820082i
\(837\) 25.1310i 0.0300251i
\(838\) −1289.52 + 479.123i −1.53880 + 0.571746i
\(839\) 785.017i 0.935658i 0.883819 + 0.467829i \(0.154964\pi\)
−0.883819 + 0.467829i \(0.845036\pi\)
\(840\) 0 0
\(841\) −176.771 −0.210192
\(842\) 316.521 + 851.890i 0.375916 + 1.01175i
\(843\) 105.932 0.125661
\(844\) 485.524 + 563.173i 0.575265 + 0.667267i
\(845\) 0 0
\(846\) 79.4563 + 213.849i 0.0939199 + 0.252777i
\(847\) −4.85829 −0.00573588
\(848\) 882.688 + 131.436i 1.04091 + 0.154995i
\(849\) 749.123 0.882359
\(850\) 0 0
\(851\) 1328.03i 1.56055i
\(852\) −347.193 402.719i −0.407503 0.472675i
\(853\) 1113.79i 1.30573i 0.757474 + 0.652865i \(0.226433\pi\)
−0.757474 + 0.652865i \(0.773567\pi\)
\(854\) 313.230 + 843.030i 0.366780 + 0.987155i
\(855\) 0 0
\(856\) −31.5803 17.3988i −0.0368929 0.0203257i
\(857\) 306.591i 0.357749i 0.983872 + 0.178875i \(0.0572456\pi\)
−0.983872 + 0.178875i \(0.942754\pi\)
\(858\) 134.856 + 362.954i 0.157175 + 0.423023i
\(859\) 204.542i 0.238116i 0.992887 + 0.119058i \(0.0379875\pi\)
−0.992887 + 0.119058i \(0.962013\pi\)
\(860\) 0 0
\(861\) −88.1130 −0.102338
\(862\) 873.918 324.706i 1.01383 0.376689i
\(863\) −654.384 −0.758266 −0.379133 0.925342i \(-0.623778\pi\)
−0.379133 + 0.925342i \(0.623778\pi\)
\(864\) −162.695 + 34.3248i −0.188305 + 0.0397277i
\(865\) 0 0
\(866\) 856.949 318.401i 0.989549 0.367669i
\(867\) −531.866 −0.613456
\(868\) 69.0687 + 80.1149i 0.0795722 + 0.0922982i
\(869\) −545.129 −0.627306
\(870\) 0 0
\(871\) 1057.91i 1.21459i
\(872\) −1354.55 746.272i −1.55338 0.855817i
\(873\) 218.877i 0.250718i
\(874\) −1660.50 + 616.963i −1.89989 + 0.705907i
\(875\) 0 0
\(876\) 423.078 + 490.741i 0.482966 + 0.560206i
\(877\) 604.453i 0.689228i 0.938744 + 0.344614i \(0.111990\pi\)
−0.938744 + 0.344614i \(0.888010\pi\)
\(878\) 1457.58 541.565i 1.66011 0.616817i
\(879\) 490.575i 0.558106i
\(880\) 0 0
\(881\) 1436.81 1.63089 0.815445 0.578834i \(-0.196492\pi\)
0.815445 + 0.578834i \(0.196492\pi\)
\(882\) 39.9227 + 107.449i 0.0452639 + 0.121824i
\(883\) 120.993 0.137025 0.0685123 0.997650i \(-0.478175\pi\)
0.0685123 + 0.997650i \(0.478175\pi\)
\(884\) 748.841 645.592i 0.847105 0.730307i
\(885\) 0 0
\(886\) −172.392 463.977i −0.194573 0.523676i
\(887\) 286.448 0.322941 0.161470 0.986878i \(-0.448376\pi\)
0.161470 + 0.986878i \(0.448376\pi\)
\(888\) 238.365 432.654i 0.268429 0.487223i
\(889\) −717.940 −0.807582
\(890\) 0 0
\(891\) 99.3628i 0.111518i
\(892\) 614.164 529.483i 0.688524 0.593591i
\(893\) 904.007i 1.01233i
\(894\) −152.885 411.476i −0.171012 0.460264i
\(895\) 0 0
\(896\) 424.318 556.566i 0.473569 0.621168i
\(897\) 653.246i 0.728256i
\(898\) 287.344 + 773.360i 0.319982 + 0.861203i
\(899\) 124.649i 0.138652i
\(900\) 0 0
\(901\) −1361.75 −1.51138
\(902\) −192.577 + 71.5525i −0.213500 + 0.0793265i
\(903\) 663.195 0.734436
\(904\) −291.740 + 529.534i −0.322721 + 0.585768i
\(905\) 0 0
\(906\) −222.240 + 82.5736i −0.245298 + 0.0911409i
\(907\) −234.706 −0.258772 −0.129386 0.991594i \(-0.541301\pi\)
−0.129386 + 0.991594i \(0.541301\pi\)
\(908\) −155.328 + 133.912i −0.171066 + 0.147480i
\(909\) 88.2276 0.0970601
\(910\) 0 0
\(911\) 491.244i 0.539236i −0.962967 0.269618i \(-0.913103\pi\)
0.962967 0.269618i \(-0.0868974\pi\)
\(912\) −651.707 97.0420i −0.714591 0.106406i
\(913\) 799.063i 0.875206i
\(914\) 1397.46 519.229i 1.52895 0.568084i
\(915\) 0 0
\(916\) 1021.13 880.339i 1.11477 0.961069i
\(917\) 414.197i 0.451687i
\(918\) 237.838 88.3691i 0.259082 0.0962627i
\(919\) 356.091i 0.387477i −0.981053 0.193738i \(-0.937939\pi\)
0.981053 0.193738i \(-0.0620613\pi\)
\(920\) 0 0
\(921\) 173.338 0.188207
\(922\) −56.8511 153.010i −0.0616607 0.165954i
\(923\) −777.002 −0.841822
\(924\) −273.083 316.757i −0.295545 0.342811i
\(925\) 0 0
\(926\) −203.573 547.899i −0.219841 0.591684i
\(927\) 84.5651 0.0912244
\(928\) −806.961 + 170.249i −0.869570 + 0.183458i
\(929\) 916.019 0.986027 0.493014 0.870022i \(-0.335895\pi\)
0.493014 + 0.870022i \(0.335895\pi\)
\(930\) 0 0
\(931\) 454.217i 0.487881i
\(932\) 209.693 + 243.229i 0.224992 + 0.260975i
\(933\) 700.069i 0.750342i
\(934\) −35.8154 96.3939i −0.0383462 0.103205i
\(935\) 0 0
\(936\) −117.250 + 212.819i −0.125267 + 0.227371i
\(937\) 143.818i 0.153488i −0.997051 0.0767440i \(-0.975548\pi\)
0.997051 0.0767440i \(-0.0244524\pi\)
\(938\) −397.981 1071.13i −0.424287 1.14193i
\(939\) 222.705i 0.237173i
\(940\) 0 0
\(941\) −1488.04 −1.58133 −0.790667 0.612246i \(-0.790266\pi\)
−0.790667 + 0.612246i \(0.790266\pi\)
\(942\) −83.0561 + 30.8597i −0.0881699 + 0.0327597i
\(943\) −346.602 −0.367552
\(944\) −878.966 130.882i −0.931108 0.138646i
\(945\) 0 0
\(946\) 1449.46 538.551i 1.53220 0.569292i
\(947\) 1095.51 1.15682 0.578411 0.815745i \(-0.303673\pi\)
0.578411 + 0.815745i \(0.303673\pi\)
\(948\) −223.371 259.095i −0.235623 0.273307i
\(949\) 946.829 0.997713
\(950\) 0 0
\(951\) 148.838i 0.156506i
\(952\) −515.331 + 935.370i −0.541314 + 0.982532i
\(953\) 1277.86i 1.34089i 0.741961 + 0.670443i \(0.233896\pi\)
−0.741961 + 0.670443i \(0.766104\pi\)
\(954\) 313.704 116.557i 0.328830 0.122177i
\(955\) 0 0
\(956\) −864.020 1002.20i −0.903786 1.04833i
\(957\) 492.834i 0.514978i
\(958\) 229.834 85.3953i 0.239910 0.0891392i
\(959\) 365.202i 0.380816i
\(960\) 0 0
\(961\) 937.609 0.975659
\(962\) −251.409 676.644i −0.261339 0.703372i
\(963\) −13.5210 −0.0140405
\(964\) 1090.38 940.041i 1.13110 0.975146i
\(965\) 0 0
\(966\) −245.748 661.410i −0.254398 0.684689i
\(967\) 237.958 0.246079 0.123039 0.992402i \(-0.460736\pi\)
0.123039 + 0.992402i \(0.460736\pi\)
\(968\) −6.22598 3.43013i −0.00643180 0.00354352i
\(969\) 1005.41 1.03758
\(970\) 0 0
\(971\) 1602.10i 1.64995i 0.565169 + 0.824975i \(0.308811\pi\)
−0.565169 + 0.824975i \(0.691189\pi\)
\(972\) −47.2262 + 40.7147i −0.0485866 + 0.0418876i
\(973\) 208.436i 0.214220i
\(974\) 45.9643 + 123.709i 0.0471912 + 0.127011i
\(975\) 0 0
\(976\) −193.800 + 1301.51i −0.198566 + 1.33351i
\(977\) 918.977i 0.940611i −0.882504 0.470305i \(-0.844144\pi\)
0.882504 0.470305i \(-0.155856\pi\)
\(978\) 76.5855 + 206.123i 0.0783083 + 0.210760i
\(979\) 1277.27i 1.30466i
\(980\) 0 0
\(981\) −579.945 −0.591178
\(982\) −677.100 + 251.578i −0.689511 + 0.256189i
\(983\) 1162.30 1.18240 0.591200 0.806525i \(-0.298654\pi\)
0.591200 + 0.806525i \(0.298654\pi\)
\(984\) −112.918 62.2109i −0.114754 0.0632225i
\(985\) 0 0
\(986\) 1179.66 438.306i 1.19641 0.444530i
\(987\) −360.083 −0.364826
\(988\) −729.245 + 628.698i −0.738103 + 0.636334i
\(989\) 2608.75 2.63776
\(990\) 0 0
\(991\) 491.614i 0.496079i 0.968750 + 0.248040i \(0.0797863\pi\)
−0.968750 + 0.248040i \(0.920214\pi\)
\(992\) 31.9488 + 151.434i 0.0322064 + 0.152655i
\(993\) 317.643i 0.319882i
\(994\) 786.712 292.305i 0.791461 0.294069i
\(995\) 0 0
\(996\) 379.787 327.422i 0.381312 0.328737i
\(997\) 1262.51i 1.26630i 0.774027 + 0.633152i \(0.218239\pi\)
−0.774027 + 0.633152i \(0.781761\pi\)
\(998\) −1333.22 + 495.363i −1.33590 + 0.496355i
\(999\) 185.239i 0.185425i
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 300.3.f.b.199.5 16
3.2 odd 2 900.3.f.f.199.12 16
4.3 odd 2 inner 300.3.f.b.199.11 16
5.2 odd 4 60.3.c.a.31.7 8
5.3 odd 4 300.3.c.d.151.2 8
5.4 even 2 inner 300.3.f.b.199.12 16
12.11 even 2 900.3.f.f.199.6 16
15.2 even 4 180.3.c.b.91.2 8
15.8 even 4 900.3.c.u.451.7 8
15.14 odd 2 900.3.f.f.199.5 16
20.3 even 4 300.3.c.d.151.1 8
20.7 even 4 60.3.c.a.31.8 yes 8
20.19 odd 2 inner 300.3.f.b.199.6 16
40.27 even 4 960.3.e.c.511.3 8
40.37 odd 4 960.3.e.c.511.8 8
60.23 odd 4 900.3.c.u.451.8 8
60.47 odd 4 180.3.c.b.91.1 8
60.59 even 2 900.3.f.f.199.11 16
120.77 even 4 2880.3.e.j.2431.3 8
120.107 odd 4 2880.3.e.j.2431.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.c.a.31.7 8 5.2 odd 4
60.3.c.a.31.8 yes 8 20.7 even 4
180.3.c.b.91.1 8 60.47 odd 4
180.3.c.b.91.2 8 15.2 even 4
300.3.c.d.151.1 8 20.3 even 4
300.3.c.d.151.2 8 5.3 odd 4
300.3.f.b.199.5 16 1.1 even 1 trivial
300.3.f.b.199.6 16 20.19 odd 2 inner
300.3.f.b.199.11 16 4.3 odd 2 inner
300.3.f.b.199.12 16 5.4 even 2 inner
900.3.c.u.451.7 8 15.8 even 4
900.3.c.u.451.8 8 60.23 odd 4
900.3.f.f.199.5 16 15.14 odd 2
900.3.f.f.199.6 16 12.11 even 2
900.3.f.f.199.11 16 60.59 even 2
900.3.f.f.199.12 16 3.2 odd 2
960.3.e.c.511.3 8 40.27 even 4
960.3.e.c.511.8 8 40.37 odd 4
2880.3.e.j.2431.2 8 120.107 odd 4
2880.3.e.j.2431.3 8 120.77 even 4