Properties

Label 300.3.f.b.199.16
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 199.16
Root \(-1.28061 + 0.600040i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.b.199.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.95141 + 0.438172i) q^{2} -1.73205 q^{3} +(3.61601 + 1.71011i) q^{4} +(-3.37994 - 0.758935i) q^{6} +6.33166 q^{7} +(6.30701 + 4.92155i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(1.95141 + 0.438172i) q^{2} -1.73205 q^{3} +(3.61601 + 1.71011i) q^{4} +(-3.37994 - 0.758935i) q^{6} +6.33166 q^{7} +(6.30701 + 4.92155i) q^{8} +3.00000 q^{9} +9.27963i q^{11} +(-6.26312 - 2.96199i) q^{12} -18.5674i q^{13} +(12.3557 + 2.77436i) q^{14} +(10.1511 + 12.3675i) q^{16} +13.9110i q^{17} +(5.85423 + 1.31451i) q^{18} +17.2468i q^{19} -10.9668 q^{21} +(-4.06607 + 18.1084i) q^{22} +33.7148 q^{23} +(-10.9241 - 8.52438i) q^{24} +(8.13571 - 36.2327i) q^{26} -5.19615 q^{27} +(22.8954 + 10.8278i) q^{28} +28.6177 q^{29} +23.4939i q^{31} +(14.3898 + 28.5820i) q^{32} -16.0728i q^{33} +(-6.09542 + 27.1461i) q^{34} +(10.8480 + 5.13032i) q^{36} -67.3338i q^{37} +(-7.55706 + 33.6556i) q^{38} +32.1597i q^{39} -44.0791 q^{41} +(-21.4007 - 4.80532i) q^{42} -50.2937 q^{43} +(-15.8691 + 33.5552i) q^{44} +(65.7915 + 14.7729i) q^{46} -31.1594 q^{47} +(-17.5822 - 21.4212i) q^{48} -8.91003 q^{49} -24.0946i q^{51} +(31.7522 - 67.1400i) q^{52} -81.6070i q^{53} +(-10.1398 - 2.27681i) q^{54} +(39.9338 + 31.1616i) q^{56} -29.8724i q^{57} +(55.8449 + 12.5395i) q^{58} -19.2751i q^{59} -53.1563 q^{61} +(-10.2943 + 45.8462i) q^{62} +18.9950 q^{63} +(15.5566 + 62.0805i) q^{64} +(7.04264 - 31.3646i) q^{66} -4.49911 q^{67} +(-23.7893 + 50.3025i) q^{68} -58.3958 q^{69} +13.3360i q^{71} +(18.9210 + 14.7647i) q^{72} -40.8904i q^{73} +(29.5037 - 131.396i) q^{74} +(-29.4939 + 62.3647i) q^{76} +58.7555i q^{77} +(-14.0915 + 62.7568i) q^{78} -141.309i q^{79} +9.00000 q^{81} +(-86.0164 - 19.3142i) q^{82} -69.8503 q^{83} +(-39.6559 - 18.7543i) q^{84} +(-98.1438 - 22.0373i) q^{86} -49.5673 q^{87} +(-45.6702 + 58.5266i) q^{88} +46.3079 q^{89} -117.563i q^{91} +(121.913 + 57.6559i) q^{92} -40.6926i q^{93} +(-60.8049 - 13.6532i) q^{94} +(-24.9239 - 49.5055i) q^{96} +68.5543i q^{97} +(-17.3871 - 3.90412i) q^{98} +27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.95141 + 0.438172i 0.975706 + 0.219086i
\(3\) −1.73205 −0.577350
\(4\) 3.61601 + 1.71011i 0.904003 + 0.427526i
\(5\) 0 0
\(6\) −3.37994 0.758935i −0.563324 0.126489i
\(7\) 6.33166 0.904523 0.452262 0.891885i \(-0.350617\pi\)
0.452262 + 0.891885i \(0.350617\pi\)
\(8\) 6.30701 + 4.92155i 0.788376 + 0.615194i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 9.27963i 0.843602i 0.906688 + 0.421801i \(0.138602\pi\)
−0.906688 + 0.421801i \(0.861398\pi\)
\(12\) −6.26312 2.96199i −0.521926 0.246833i
\(13\) 18.5674i 1.42826i −0.700012 0.714131i \(-0.746822\pi\)
0.700012 0.714131i \(-0.253178\pi\)
\(14\) 12.3557 + 2.77436i 0.882549 + 0.198168i
\(15\) 0 0
\(16\) 10.1511 + 12.3675i 0.634442 + 0.772970i
\(17\) 13.9110i 0.818296i 0.912468 + 0.409148i \(0.134174\pi\)
−0.912468 + 0.409148i \(0.865826\pi\)
\(18\) 5.85423 + 1.31451i 0.325235 + 0.0730286i
\(19\) 17.2468i 0.907727i 0.891071 + 0.453864i \(0.149955\pi\)
−0.891071 + 0.453864i \(0.850045\pi\)
\(20\) 0 0
\(21\) −10.9668 −0.522227
\(22\) −4.06607 + 18.1084i −0.184821 + 0.823108i
\(23\) 33.7148 1.46586 0.732931 0.680303i \(-0.238152\pi\)
0.732931 + 0.680303i \(0.238152\pi\)
\(24\) −10.9241 8.52438i −0.455169 0.355183i
\(25\) 0 0
\(26\) 8.13571 36.2327i 0.312912 1.39356i
\(27\) −5.19615 −0.192450
\(28\) 22.8954 + 10.8278i 0.817692 + 0.386708i
\(29\) 28.6177 0.986817 0.493409 0.869798i \(-0.335751\pi\)
0.493409 + 0.869798i \(0.335751\pi\)
\(30\) 0 0
\(31\) 23.4939i 0.757866i 0.925424 + 0.378933i \(0.123709\pi\)
−0.925424 + 0.378933i \(0.876291\pi\)
\(32\) 14.3898 + 28.5820i 0.449682 + 0.893189i
\(33\) 16.0728i 0.487054i
\(34\) −6.09542 + 27.1461i −0.179277 + 0.798416i
\(35\) 0 0
\(36\) 10.8480 + 5.13032i 0.301334 + 0.142509i
\(37\) 67.3338i 1.81983i −0.414793 0.909916i \(-0.636146\pi\)
0.414793 0.909916i \(-0.363854\pi\)
\(38\) −7.55706 + 33.6556i −0.198870 + 0.885674i
\(39\) 32.1597i 0.824608i
\(40\) 0 0
\(41\) −44.0791 −1.07510 −0.537550 0.843232i \(-0.680650\pi\)
−0.537550 + 0.843232i \(0.680650\pi\)
\(42\) −21.4007 4.80532i −0.509540 0.114412i
\(43\) −50.2937 −1.16962 −0.584811 0.811170i \(-0.698831\pi\)
−0.584811 + 0.811170i \(0.698831\pi\)
\(44\) −15.8691 + 33.5552i −0.360662 + 0.762619i
\(45\) 0 0
\(46\) 65.7915 + 14.7729i 1.43025 + 0.321150i
\(47\) −31.1594 −0.662967 −0.331483 0.943461i \(-0.607549\pi\)
−0.331483 + 0.943461i \(0.607549\pi\)
\(48\) −17.5822 21.4212i −0.366295 0.446275i
\(49\) −8.91003 −0.181837
\(50\) 0 0
\(51\) 24.0946i 0.472444i
\(52\) 31.7522 67.1400i 0.610620 1.29115i
\(53\) 81.6070i 1.53975i −0.638192 0.769877i \(-0.720318\pi\)
0.638192 0.769877i \(-0.279682\pi\)
\(54\) −10.1398 2.27681i −0.187775 0.0421631i
\(55\) 0 0
\(56\) 39.9338 + 31.1616i 0.713104 + 0.556457i
\(57\) 29.8724i 0.524077i
\(58\) 55.8449 + 12.5395i 0.962843 + 0.216198i
\(59\) 19.2751i 0.326697i −0.986568 0.163349i \(-0.947770\pi\)
0.986568 0.163349i \(-0.0522296\pi\)
\(60\) 0 0
\(61\) −53.1563 −0.871415 −0.435707 0.900088i \(-0.643502\pi\)
−0.435707 + 0.900088i \(0.643502\pi\)
\(62\) −10.2943 + 45.8462i −0.166038 + 0.739455i
\(63\) 18.9950 0.301508
\(64\) 15.5566 + 62.0805i 0.243072 + 0.970008i
\(65\) 0 0
\(66\) 7.04264 31.3646i 0.106707 0.475221i
\(67\) −4.49911 −0.0671509 −0.0335754 0.999436i \(-0.510689\pi\)
−0.0335754 + 0.999436i \(0.510689\pi\)
\(68\) −23.7893 + 50.3025i −0.349843 + 0.739742i
\(69\) −58.3958 −0.846316
\(70\) 0 0
\(71\) 13.3360i 0.187832i 0.995580 + 0.0939158i \(0.0299385\pi\)
−0.995580 + 0.0939158i \(0.970062\pi\)
\(72\) 18.9210 + 14.7647i 0.262792 + 0.205065i
\(73\) 40.8904i 0.560143i −0.959979 0.280071i \(-0.909642\pi\)
0.959979 0.280071i \(-0.0903581\pi\)
\(74\) 29.5037 131.396i 0.398699 1.77562i
\(75\) 0 0
\(76\) −29.4939 + 62.3647i −0.388077 + 0.820588i
\(77\) 58.7555i 0.763058i
\(78\) −14.0915 + 62.7568i −0.180660 + 0.804574i
\(79\) 141.309i 1.78872i −0.447352 0.894358i \(-0.647633\pi\)
0.447352 0.894358i \(-0.352367\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −86.0164 19.3142i −1.04898 0.235539i
\(83\) −69.8503 −0.841570 −0.420785 0.907160i \(-0.638245\pi\)
−0.420785 + 0.907160i \(0.638245\pi\)
\(84\) −39.6559 18.7543i −0.472095 0.223266i
\(85\) 0 0
\(86\) −98.1438 22.0373i −1.14121 0.256248i
\(87\) −49.5673 −0.569739
\(88\) −45.6702 + 58.5266i −0.518979 + 0.665076i
\(89\) 46.3079 0.520313 0.260157 0.965566i \(-0.416226\pi\)
0.260157 + 0.965566i \(0.416226\pi\)
\(90\) 0 0
\(91\) 117.563i 1.29190i
\(92\) 121.913 + 57.6559i 1.32514 + 0.626695i
\(93\) 40.6926i 0.437554i
\(94\) −60.8049 13.6532i −0.646860 0.145247i
\(95\) 0 0
\(96\) −24.9239 49.5055i −0.259624 0.515683i
\(97\) 68.5543i 0.706745i 0.935483 + 0.353373i \(0.114965\pi\)
−0.935483 + 0.353373i \(0.885035\pi\)
\(98\) −17.3871 3.90412i −0.177420 0.0398380i
\(99\) 27.8389i 0.281201i
\(100\) 0 0
\(101\) −43.3949 −0.429653 −0.214826 0.976652i \(-0.568919\pi\)
−0.214826 + 0.976652i \(0.568919\pi\)
\(102\) 10.5576 47.0185i 0.103506 0.460966i
\(103\) −85.7919 −0.832931 −0.416465 0.909152i \(-0.636731\pi\)
−0.416465 + 0.909152i \(0.636731\pi\)
\(104\) 91.3805 117.105i 0.878659 1.12601i
\(105\) 0 0
\(106\) 35.7579 159.249i 0.337338 1.50235i
\(107\) 183.075 1.71098 0.855491 0.517818i \(-0.173255\pi\)
0.855491 + 0.517818i \(0.173255\pi\)
\(108\) −18.7893 8.88597i −0.173975 0.0822775i
\(109\) −81.4798 −0.747521 −0.373761 0.927525i \(-0.621932\pi\)
−0.373761 + 0.927525i \(0.621932\pi\)
\(110\) 0 0
\(111\) 116.625i 1.05068i
\(112\) 64.2732 + 78.3070i 0.573868 + 0.699170i
\(113\) 172.814i 1.52933i 0.644429 + 0.764664i \(0.277095\pi\)
−0.644429 + 0.764664i \(0.722905\pi\)
\(114\) 13.0892 58.2933i 0.114818 0.511344i
\(115\) 0 0
\(116\) 103.482 + 48.9393i 0.892086 + 0.421891i
\(117\) 55.7022i 0.476087i
\(118\) 8.44582 37.6137i 0.0715748 0.318760i
\(119\) 88.0800i 0.740168i
\(120\) 0 0
\(121\) 34.8885 0.288335
\(122\) −103.730 23.2916i −0.850244 0.190915i
\(123\) 76.3472 0.620709
\(124\) −40.1770 + 84.9541i −0.324008 + 0.685113i
\(125\) 0 0
\(126\) 37.0670 + 8.32307i 0.294183 + 0.0660561i
\(127\) −22.3785 −0.176208 −0.0881041 0.996111i \(-0.528081\pi\)
−0.0881041 + 0.996111i \(0.528081\pi\)
\(128\) 3.15546 + 127.961i 0.0246520 + 0.999696i
\(129\) 87.1113 0.675282
\(130\) 0 0
\(131\) 1.75315i 0.0133828i −0.999978 0.00669141i \(-0.997870\pi\)
0.999978 0.00669141i \(-0.00212996\pi\)
\(132\) 27.4862 58.1194i 0.208228 0.440298i
\(133\) 109.201i 0.821060i
\(134\) −8.77961 1.97138i −0.0655195 0.0147118i
\(135\) 0 0
\(136\) −68.4639 + 87.7370i −0.503411 + 0.645125i
\(137\) 19.5084i 0.142397i −0.997462 0.0711987i \(-0.977318\pi\)
0.997462 0.0711987i \(-0.0226824\pi\)
\(138\) −113.954 25.5874i −0.825755 0.185416i
\(139\) 257.370i 1.85158i −0.378038 0.925790i \(-0.623401\pi\)
0.378038 0.925790i \(-0.376599\pi\)
\(140\) 0 0
\(141\) 53.9697 0.382764
\(142\) −5.84348 + 26.0241i −0.0411512 + 0.183268i
\(143\) 172.299 1.20489
\(144\) 30.4532 + 37.1026i 0.211481 + 0.257657i
\(145\) 0 0
\(146\) 17.9170 79.7940i 0.122719 0.546534i
\(147\) 15.4326 0.104984
\(148\) 115.148 243.480i 0.778026 1.64513i
\(149\) 111.673 0.749486 0.374743 0.927129i \(-0.377731\pi\)
0.374743 + 0.927129i \(0.377731\pi\)
\(150\) 0 0
\(151\) 6.45275i 0.0427335i 0.999772 + 0.0213667i \(0.00680176\pi\)
−0.999772 + 0.0213667i \(0.993198\pi\)
\(152\) −84.8811 + 108.776i −0.558428 + 0.715630i
\(153\) 41.7331i 0.272765i
\(154\) −25.7450 + 114.656i −0.167175 + 0.744520i
\(155\) 0 0
\(156\) −54.9965 + 116.290i −0.352542 + 0.745448i
\(157\) 75.9075i 0.483488i −0.970340 0.241744i \(-0.922281\pi\)
0.970340 0.241744i \(-0.0777193\pi\)
\(158\) 61.9174 275.751i 0.391882 1.74526i
\(159\) 141.347i 0.888977i
\(160\) 0 0
\(161\) 213.471 1.32591
\(162\) 17.5627 + 3.94354i 0.108412 + 0.0243429i
\(163\) −249.298 −1.52944 −0.764719 0.644364i \(-0.777122\pi\)
−0.764719 + 0.644364i \(0.777122\pi\)
\(164\) −159.391 75.3799i −0.971893 0.459634i
\(165\) 0 0
\(166\) −136.307 30.6064i −0.821124 0.184376i
\(167\) −79.1883 −0.474182 −0.237091 0.971487i \(-0.576194\pi\)
−0.237091 + 0.971487i \(0.576194\pi\)
\(168\) −69.1674 53.9735i −0.411711 0.321271i
\(169\) −175.749 −1.03993
\(170\) 0 0
\(171\) 51.7404i 0.302576i
\(172\) −181.863 86.0076i −1.05734 0.500044i
\(173\) 27.7204i 0.160234i 0.996785 + 0.0801168i \(0.0255293\pi\)
−0.996785 + 0.0801168i \(0.974471\pi\)
\(174\) −96.7262 21.7190i −0.555898 0.124822i
\(175\) 0 0
\(176\) −114.766 + 94.1982i −0.652080 + 0.535217i
\(177\) 33.3855i 0.188619i
\(178\) 90.3657 + 20.2908i 0.507673 + 0.113993i
\(179\) 204.324i 1.14147i 0.821133 + 0.570737i \(0.193342\pi\)
−0.821133 + 0.570737i \(0.806658\pi\)
\(180\) 0 0
\(181\) −49.8262 −0.275283 −0.137641 0.990482i \(-0.543952\pi\)
−0.137641 + 0.990482i \(0.543952\pi\)
\(182\) 51.5126 229.413i 0.283036 1.26051i
\(183\) 92.0694 0.503112
\(184\) 212.640 + 165.929i 1.15565 + 0.901790i
\(185\) 0 0
\(186\) 17.8303 79.4079i 0.0958620 0.426924i
\(187\) −129.089 −0.690317
\(188\) −112.673 53.2859i −0.599324 0.283436i
\(189\) −32.9003 −0.174076
\(190\) 0 0
\(191\) 1.13703i 0.00595301i 0.999996 + 0.00297651i \(0.000947453\pi\)
−0.999996 + 0.00297651i \(0.999053\pi\)
\(192\) −26.9449 107.527i −0.140338 0.560034i
\(193\) 76.6452i 0.397126i 0.980088 + 0.198563i \(0.0636274\pi\)
−0.980088 + 0.198563i \(0.936373\pi\)
\(194\) −30.0385 + 133.778i −0.154838 + 0.689575i
\(195\) 0 0
\(196\) −32.2188 15.2371i −0.164382 0.0777403i
\(197\) 134.496i 0.682719i 0.939933 + 0.341359i \(0.110887\pi\)
−0.939933 + 0.341359i \(0.889113\pi\)
\(198\) −12.1982 + 54.3251i −0.0616071 + 0.274369i
\(199\) 176.014i 0.884491i 0.896894 + 0.442245i \(0.145818\pi\)
−0.896894 + 0.442245i \(0.854182\pi\)
\(200\) 0 0
\(201\) 7.79269 0.0387696
\(202\) −84.6813 19.0144i −0.419214 0.0941308i
\(203\) 181.198 0.892599
\(204\) 41.2044 87.1264i 0.201982 0.427090i
\(205\) 0 0
\(206\) −167.415 37.5916i −0.812695 0.182483i
\(207\) 101.144 0.488621
\(208\) 229.633 188.479i 1.10400 0.906150i
\(209\) −160.044 −0.765761
\(210\) 0 0
\(211\) 218.087i 1.03359i −0.856110 0.516793i \(-0.827126\pi\)
0.856110 0.516793i \(-0.172874\pi\)
\(212\) 139.557 295.092i 0.658286 1.39194i
\(213\) 23.0987i 0.108445i
\(214\) 357.255 + 80.2183i 1.66941 + 0.374852i
\(215\) 0 0
\(216\) −32.7722 25.5731i −0.151723 0.118394i
\(217\) 148.755i 0.685508i
\(218\) −159.001 35.7021i −0.729361 0.163771i
\(219\) 70.8243i 0.323399i
\(220\) 0 0
\(221\) 258.292 1.16874
\(222\) −51.1020 + 227.584i −0.230189 + 1.02515i
\(223\) 328.579 1.47345 0.736724 0.676193i \(-0.236372\pi\)
0.736724 + 0.676193i \(0.236372\pi\)
\(224\) 91.1115 + 180.972i 0.406748 + 0.807910i
\(225\) 0 0
\(226\) −75.7222 + 337.231i −0.335054 + 1.49217i
\(227\) −157.649 −0.694491 −0.347245 0.937774i \(-0.612883\pi\)
−0.347245 + 0.937774i \(0.612883\pi\)
\(228\) 51.0849 108.019i 0.224057 0.473767i
\(229\) 273.148 1.19279 0.596393 0.802692i \(-0.296600\pi\)
0.596393 + 0.802692i \(0.296600\pi\)
\(230\) 0 0
\(231\) 101.767i 0.440552i
\(232\) 180.492 + 140.844i 0.777983 + 0.607084i
\(233\) 108.746i 0.466720i −0.972390 0.233360i \(-0.925028\pi\)
0.972390 0.233360i \(-0.0749721\pi\)
\(234\) 24.4071 108.698i 0.104304 0.464521i
\(235\) 0 0
\(236\) 32.9625 69.6992i 0.139672 0.295335i
\(237\) 244.754i 1.03272i
\(238\) −38.5942 + 171.880i −0.162160 + 0.722186i
\(239\) 178.994i 0.748927i 0.927242 + 0.374464i \(0.122173\pi\)
−0.927242 + 0.374464i \(0.877827\pi\)
\(240\) 0 0
\(241\) 358.623 1.48806 0.744032 0.668144i \(-0.232911\pi\)
0.744032 + 0.668144i \(0.232911\pi\)
\(242\) 68.0819 + 15.2872i 0.281330 + 0.0631701i
\(243\) −15.5885 −0.0641500
\(244\) −192.214 90.9029i −0.787762 0.372553i
\(245\) 0 0
\(246\) 148.985 + 33.4532i 0.605629 + 0.135989i
\(247\) 320.229 1.29647
\(248\) −115.626 + 148.176i −0.466235 + 0.597483i
\(249\) 120.984 0.485881
\(250\) 0 0
\(251\) 306.220i 1.22000i 0.792401 + 0.610000i \(0.208831\pi\)
−0.792401 + 0.610000i \(0.791169\pi\)
\(252\) 68.6861 + 32.4834i 0.272564 + 0.128903i
\(253\) 312.861i 1.23660i
\(254\) −43.6696 9.80560i −0.171927 0.0386047i
\(255\) 0 0
\(256\) −49.9113 + 251.087i −0.194966 + 0.980810i
\(257\) 251.062i 0.976895i −0.872593 0.488447i \(-0.837563\pi\)
0.872593 0.488447i \(-0.162437\pi\)
\(258\) 169.990 + 38.1697i 0.658876 + 0.147945i
\(259\) 426.335i 1.64608i
\(260\) 0 0
\(261\) 85.8531 0.328939
\(262\) 0.768181 3.42112i 0.00293199 0.0130577i
\(263\) 48.7645 0.185416 0.0927082 0.995693i \(-0.470448\pi\)
0.0927082 + 0.995693i \(0.470448\pi\)
\(264\) 79.1031 101.371i 0.299633 0.383982i
\(265\) 0 0
\(266\) −47.8488 + 213.096i −0.179883 + 0.801113i
\(267\) −80.2076 −0.300403
\(268\) −16.2688 7.69395i −0.0607046 0.0287088i
\(269\) −148.696 −0.552772 −0.276386 0.961047i \(-0.589137\pi\)
−0.276386 + 0.961047i \(0.589137\pi\)
\(270\) 0 0
\(271\) 83.3415i 0.307533i −0.988107 0.153767i \(-0.950860\pi\)
0.988107 0.153767i \(-0.0491404\pi\)
\(272\) −172.045 + 141.212i −0.632519 + 0.519162i
\(273\) 203.624i 0.745877i
\(274\) 8.54805 38.0690i 0.0311972 0.138938i
\(275\) 0 0
\(276\) −211.160 99.8630i −0.765072 0.361822i
\(277\) 144.080i 0.520146i 0.965589 + 0.260073i \(0.0837466\pi\)
−0.965589 + 0.260073i \(0.916253\pi\)
\(278\) 112.772 502.234i 0.405655 1.80660i
\(279\) 70.4816i 0.252622i
\(280\) 0 0
\(281\) −343.671 −1.22303 −0.611514 0.791233i \(-0.709439\pi\)
−0.611514 + 0.791233i \(0.709439\pi\)
\(282\) 105.317 + 23.6480i 0.373465 + 0.0838581i
\(283\) −314.955 −1.11292 −0.556458 0.830876i \(-0.687840\pi\)
−0.556458 + 0.830876i \(0.687840\pi\)
\(284\) −22.8061 + 48.2233i −0.0803030 + 0.169800i
\(285\) 0 0
\(286\) 336.225 + 75.4964i 1.17561 + 0.263973i
\(287\) −279.094 −0.972453
\(288\) 43.1695 + 85.7461i 0.149894 + 0.297730i
\(289\) 95.4831 0.330391
\(290\) 0 0
\(291\) 118.740i 0.408040i
\(292\) 69.9269 147.860i 0.239476 0.506371i
\(293\) 6.55421i 0.0223693i 0.999937 + 0.0111847i \(0.00356026\pi\)
−0.999937 + 0.0111847i \(0.996440\pi\)
\(294\) 30.1154 + 6.76214i 0.102433 + 0.0230005i
\(295\) 0 0
\(296\) 331.387 424.674i 1.11955 1.43471i
\(297\) 48.2184i 0.162351i
\(298\) 217.921 + 48.9321i 0.731278 + 0.164202i
\(299\) 625.997i 2.09364i
\(300\) 0 0
\(301\) −318.443 −1.05795
\(302\) −2.82741 + 12.5920i −0.00936229 + 0.0416953i
\(303\) 75.1622 0.248060
\(304\) −213.300 + 175.074i −0.701646 + 0.575900i
\(305\) 0 0
\(306\) −18.2863 + 81.4384i −0.0597590 + 0.266139i
\(307\) 354.559 1.15492 0.577458 0.816420i \(-0.304045\pi\)
0.577458 + 0.816420i \(0.304045\pi\)
\(308\) −100.478 + 212.460i −0.326228 + 0.689807i
\(309\) 148.596 0.480893
\(310\) 0 0
\(311\) 193.387i 0.621823i −0.950439 0.310912i \(-0.899366\pi\)
0.950439 0.310912i \(-0.100634\pi\)
\(312\) −158.276 + 202.831i −0.507294 + 0.650101i
\(313\) 23.5224i 0.0751514i 0.999294 + 0.0375757i \(0.0119635\pi\)
−0.999294 + 0.0375757i \(0.988036\pi\)
\(314\) 33.2605 148.127i 0.105925 0.471742i
\(315\) 0 0
\(316\) 241.653 510.973i 0.764724 1.61700i
\(317\) 214.004i 0.675092i −0.941309 0.337546i \(-0.890403\pi\)
0.941309 0.337546i \(-0.109597\pi\)
\(318\) −61.9344 + 275.827i −0.194762 + 0.867380i
\(319\) 265.562i 0.832481i
\(320\) 0 0
\(321\) −317.095 −0.987836
\(322\) 416.570 + 93.5369i 1.29369 + 0.290487i
\(323\) −239.921 −0.742790
\(324\) 32.5441 + 15.3910i 0.100445 + 0.0475029i
\(325\) 0 0
\(326\) −486.483 109.235i −1.49228 0.335078i
\(327\) 141.127 0.431582
\(328\) −278.007 216.938i −0.847583 0.661395i
\(329\) −197.291 −0.599669
\(330\) 0 0
\(331\) 412.454i 1.24609i 0.782188 + 0.623043i \(0.214104\pi\)
−0.782188 + 0.623043i \(0.785896\pi\)
\(332\) −252.579 119.451i −0.760782 0.359793i
\(333\) 202.001i 0.606610i
\(334\) −154.529 34.6981i −0.462662 0.103886i
\(335\) 0 0
\(336\) −111.324 135.632i −0.331323 0.403666i
\(337\) 103.268i 0.306433i 0.988193 + 0.153216i \(0.0489631\pi\)
−0.988193 + 0.153216i \(0.951037\pi\)
\(338\) −342.958 77.0081i −1.01467 0.227835i
\(339\) 299.323i 0.882958i
\(340\) 0 0
\(341\) −218.014 −0.639338
\(342\) −22.6712 + 100.967i −0.0662900 + 0.295225i
\(343\) −366.667 −1.06900
\(344\) −317.203 247.523i −0.922102 0.719545i
\(345\) 0 0
\(346\) −12.1463 + 54.0939i −0.0351049 + 0.156341i
\(347\) −153.211 −0.441531 −0.220766 0.975327i \(-0.570856\pi\)
−0.220766 + 0.975327i \(0.570856\pi\)
\(348\) −179.236 84.7654i −0.515046 0.243579i
\(349\) 84.7317 0.242784 0.121392 0.992605i \(-0.461264\pi\)
0.121392 + 0.992605i \(0.461264\pi\)
\(350\) 0 0
\(351\) 96.4791i 0.274869i
\(352\) −265.231 + 133.532i −0.753496 + 0.379353i
\(353\) 256.065i 0.725396i −0.931907 0.362698i \(-0.881856\pi\)
0.931907 0.362698i \(-0.118144\pi\)
\(354\) −14.6286 + 65.1489i −0.0413237 + 0.184036i
\(355\) 0 0
\(356\) 167.450 + 79.1914i 0.470365 + 0.222448i
\(357\) 152.559i 0.427336i
\(358\) −89.5289 + 398.720i −0.250081 + 1.11374i
\(359\) 667.258i 1.85866i 0.369253 + 0.929329i \(0.379614\pi\)
−0.369253 + 0.929329i \(0.620386\pi\)
\(360\) 0 0
\(361\) 63.5473 0.176031
\(362\) −97.2314 21.8324i −0.268595 0.0603106i
\(363\) −60.4287 −0.166470
\(364\) 201.044 425.108i 0.552320 1.16788i
\(365\) 0 0
\(366\) 179.665 + 40.3422i 0.490889 + 0.110225i
\(367\) −245.301 −0.668396 −0.334198 0.942503i \(-0.608465\pi\)
−0.334198 + 0.942503i \(0.608465\pi\)
\(368\) 342.242 + 416.969i 0.930005 + 1.13307i
\(369\) −132.237 −0.358367
\(370\) 0 0
\(371\) 516.708i 1.39274i
\(372\) 69.5886 147.145i 0.187066 0.395550i
\(373\) 698.787i 1.87342i −0.350101 0.936712i \(-0.613853\pi\)
0.350101 0.936712i \(-0.386147\pi\)
\(374\) −251.906 56.5632i −0.673546 0.151239i
\(375\) 0 0
\(376\) −196.523 153.353i −0.522667 0.407853i
\(377\) 531.357i 1.40943i
\(378\) −64.2020 14.4160i −0.169847 0.0381375i
\(379\) 208.691i 0.550636i −0.961353 0.275318i \(-0.911217\pi\)
0.961353 0.275318i \(-0.0887831\pi\)
\(380\) 0 0
\(381\) 38.7606 0.101734
\(382\) −0.498212 + 2.21880i −0.00130422 + 0.00580839i
\(383\) −156.524 −0.408680 −0.204340 0.978900i \(-0.565505\pi\)
−0.204340 + 0.978900i \(0.565505\pi\)
\(384\) −5.46541 221.635i −0.0142328 0.577175i
\(385\) 0 0
\(386\) −33.5838 + 149.566i −0.0870046 + 0.387478i
\(387\) −150.881 −0.389874
\(388\) −117.235 + 247.893i −0.302152 + 0.638900i
\(389\) −386.588 −0.993801 −0.496900 0.867808i \(-0.665529\pi\)
−0.496900 + 0.867808i \(0.665529\pi\)
\(390\) 0 0
\(391\) 469.008i 1.19951i
\(392\) −56.1956 43.8512i −0.143356 0.111865i
\(393\) 3.03655i 0.00772658i
\(394\) −58.9322 + 262.456i −0.149574 + 0.666133i
\(395\) 0 0
\(396\) −47.6074 + 100.666i −0.120221 + 0.254206i
\(397\) 561.155i 1.41349i −0.707470 0.706744i \(-0.750163\pi\)
0.707470 0.706744i \(-0.249837\pi\)
\(398\) −77.1242 + 343.475i −0.193779 + 0.863002i
\(399\) 189.142i 0.474039i
\(400\) 0 0
\(401\) 16.9333 0.0422276 0.0211138 0.999777i \(-0.493279\pi\)
0.0211138 + 0.999777i \(0.493279\pi\)
\(402\) 15.2067 + 3.41453i 0.0378277 + 0.00849387i
\(403\) 436.220 1.08243
\(404\) −156.917 74.2099i −0.388407 0.183688i
\(405\) 0 0
\(406\) 353.591 + 79.3957i 0.870914 + 0.195556i
\(407\) 624.832 1.53521
\(408\) 118.583 151.965i 0.290644 0.372463i
\(409\) −258.490 −0.632006 −0.316003 0.948758i \(-0.602341\pi\)
−0.316003 + 0.948758i \(0.602341\pi\)
\(410\) 0 0
\(411\) 33.7896i 0.0822132i
\(412\) −310.224 146.713i −0.752972 0.356100i
\(413\) 122.044i 0.295505i
\(414\) 197.374 + 44.3186i 0.476750 + 0.107050i
\(415\) 0 0
\(416\) 530.694 267.182i 1.27571 0.642264i
\(417\) 445.777i 1.06901i
\(418\) −312.312 70.1267i −0.747157 0.167767i
\(419\) 258.917i 0.617941i −0.951072 0.308970i \(-0.900016\pi\)
0.951072 0.308970i \(-0.0999844\pi\)
\(420\) 0 0
\(421\) 97.4654 0.231509 0.115755 0.993278i \(-0.463071\pi\)
0.115755 + 0.993278i \(0.463071\pi\)
\(422\) 95.5594 425.577i 0.226444 1.00848i
\(423\) −93.4783 −0.220989
\(424\) 401.633 514.696i 0.947248 1.21390i
\(425\) 0 0
\(426\) 10.1212 45.0751i 0.0237587 0.105810i
\(427\) −336.568 −0.788215
\(428\) 662.002 + 313.078i 1.54673 + 0.731490i
\(429\) −298.430 −0.695641
\(430\) 0 0
\(431\) 389.968i 0.904799i 0.891815 + 0.452399i \(0.149432\pi\)
−0.891815 + 0.452399i \(0.850568\pi\)
\(432\) −52.7465 64.2635i −0.122098 0.148758i
\(433\) 275.893i 0.637166i −0.947895 0.318583i \(-0.896793\pi\)
0.947895 0.318583i \(-0.103207\pi\)
\(434\) −65.1803 + 290.283i −0.150185 + 0.668854i
\(435\) 0 0
\(436\) −294.632 139.339i −0.675761 0.319585i
\(437\) 581.473i 1.33060i
\(438\) −31.0332 + 138.207i −0.0708520 + 0.315542i
\(439\) 446.143i 1.01627i 0.861277 + 0.508136i \(0.169665\pi\)
−0.861277 + 0.508136i \(0.830335\pi\)
\(440\) 0 0
\(441\) −26.7301 −0.0606125
\(442\) 504.034 + 113.176i 1.14035 + 0.256055i
\(443\) −794.679 −1.79386 −0.896929 0.442174i \(-0.854207\pi\)
−0.896929 + 0.442174i \(0.854207\pi\)
\(444\) −199.442 + 421.719i −0.449194 + 0.949818i
\(445\) 0 0
\(446\) 641.193 + 143.974i 1.43765 + 0.322812i
\(447\) −193.424 −0.432716
\(448\) 98.4993 + 393.073i 0.219865 + 0.877395i
\(449\) 750.226 1.67088 0.835441 0.549581i \(-0.185212\pi\)
0.835441 + 0.549581i \(0.185212\pi\)
\(450\) 0 0
\(451\) 409.037i 0.906957i
\(452\) −295.530 + 624.898i −0.653828 + 1.38252i
\(453\) 11.1765i 0.0246722i
\(454\) −307.639 69.0775i −0.677619 0.152153i
\(455\) 0 0
\(456\) 147.018 188.405i 0.322409 0.413169i
\(457\) 101.092i 0.221209i 0.993865 + 0.110604i \(0.0352787\pi\)
−0.993865 + 0.110604i \(0.964721\pi\)
\(458\) 533.024 + 119.686i 1.16381 + 0.261323i
\(459\) 72.2839i 0.157481i
\(460\) 0 0
\(461\) −4.48690 −0.00973297 −0.00486648 0.999988i \(-0.501549\pi\)
−0.00486648 + 0.999988i \(0.501549\pi\)
\(462\) 44.5916 198.590i 0.0965186 0.429849i
\(463\) 515.108 1.11254 0.556272 0.831000i \(-0.312231\pi\)
0.556272 + 0.831000i \(0.312231\pi\)
\(464\) 290.500 + 353.930i 0.626079 + 0.762780i
\(465\) 0 0
\(466\) 47.6493 212.208i 0.102252 0.455382i
\(467\) 295.498 0.632758 0.316379 0.948633i \(-0.397533\pi\)
0.316379 + 0.948633i \(0.397533\pi\)
\(468\) 95.2567 201.420i 0.203540 0.430384i
\(469\) −28.4869 −0.0607396
\(470\) 0 0
\(471\) 131.476i 0.279142i
\(472\) 94.8637 121.568i 0.200982 0.257560i
\(473\) 466.707i 0.986696i
\(474\) −107.244 + 477.615i −0.226253 + 1.00763i
\(475\) 0 0
\(476\) −150.626 + 318.498i −0.316441 + 0.669114i
\(477\) 244.821i 0.513251i
\(478\) −78.4299 + 349.290i −0.164079 + 0.730732i
\(479\) 273.155i 0.570260i −0.958489 0.285130i \(-0.907963\pi\)
0.958489 0.285130i \(-0.0920368\pi\)
\(480\) 0 0
\(481\) −1250.21 −2.59920
\(482\) 699.822 + 157.139i 1.45191 + 0.326014i
\(483\) −369.743 −0.765512
\(484\) 126.157 + 59.6631i 0.260656 + 0.123271i
\(485\) 0 0
\(486\) −30.4195 6.83042i −0.0625915 0.0140544i
\(487\) −357.751 −0.734601 −0.367301 0.930102i \(-0.619718\pi\)
−0.367301 + 0.930102i \(0.619718\pi\)
\(488\) −335.257 261.612i −0.687002 0.536089i
\(489\) 431.797 0.883021
\(490\) 0 0
\(491\) 422.379i 0.860242i −0.902771 0.430121i \(-0.858471\pi\)
0.902771 0.430121i \(-0.141529\pi\)
\(492\) 276.072 + 130.562i 0.561123 + 0.265370i
\(493\) 398.102i 0.807509i
\(494\) 624.898 + 140.315i 1.26498 + 0.284039i
\(495\) 0 0
\(496\) −290.561 + 238.488i −0.585808 + 0.480822i
\(497\) 84.4394i 0.169898i
\(498\) 236.090 + 53.0119i 0.474076 + 0.106450i
\(499\) 207.096i 0.415021i 0.978233 + 0.207511i \(0.0665362\pi\)
−0.978233 + 0.207511i \(0.933464\pi\)
\(500\) 0 0
\(501\) 137.158 0.273769
\(502\) −134.177 + 597.562i −0.267285 + 1.19036i
\(503\) 702.853 1.39732 0.698661 0.715452i \(-0.253779\pi\)
0.698661 + 0.715452i \(0.253779\pi\)
\(504\) 119.802 + 93.4849i 0.237701 + 0.185486i
\(505\) 0 0
\(506\) −137.087 + 610.520i −0.270923 + 1.20656i
\(507\) 304.406 0.600406
\(508\) −80.9207 38.2695i −0.159293 0.0753337i
\(509\) 389.029 0.764300 0.382150 0.924100i \(-0.375184\pi\)
0.382150 + 0.924100i \(0.375184\pi\)
\(510\) 0 0
\(511\) 258.904i 0.506662i
\(512\) −207.417 + 468.105i −0.405111 + 0.914267i
\(513\) 89.6171i 0.174692i
\(514\) 110.008 489.925i 0.214024 0.953162i
\(515\) 0 0
\(516\) 314.996 + 148.970i 0.610457 + 0.288701i
\(517\) 289.148i 0.559280i
\(518\) 186.808 831.954i 0.360633 1.60609i
\(519\) 48.0132i 0.0925109i
\(520\) 0 0
\(521\) −151.753 −0.291273 −0.145637 0.989338i \(-0.546523\pi\)
−0.145637 + 0.989338i \(0.546523\pi\)
\(522\) 167.535 + 37.6184i 0.320948 + 0.0720659i
\(523\) 557.762 1.06647 0.533234 0.845968i \(-0.320977\pi\)
0.533234 + 0.845968i \(0.320977\pi\)
\(524\) 2.99807 6.33941i 0.00572151 0.0120981i
\(525\) 0 0
\(526\) 95.1596 + 21.3672i 0.180912 + 0.0406221i
\(527\) −326.824 −0.620159
\(528\) 198.781 163.156i 0.376478 0.309008i
\(529\) 607.689 1.14875
\(530\) 0 0
\(531\) 57.8254i 0.108899i
\(532\) −186.745 + 394.872i −0.351025 + 0.742241i
\(533\) 818.435i 1.53552i
\(534\) −156.518 35.1447i −0.293105 0.0658141i
\(535\) 0 0
\(536\) −28.3759 22.1426i −0.0529401 0.0413108i
\(537\) 353.899i 0.659030i
\(538\) −290.166 65.1542i −0.539342 0.121104i
\(539\) 82.6818i 0.153398i
\(540\) 0 0
\(541\) 340.979 0.630275 0.315137 0.949046i \(-0.397949\pi\)
0.315137 + 0.949046i \(0.397949\pi\)
\(542\) 36.5179 162.633i 0.0673761 0.300062i
\(543\) 86.3015 0.158935
\(544\) −397.606 + 200.177i −0.730893 + 0.367973i
\(545\) 0 0
\(546\) −89.2224 + 397.355i −0.163411 + 0.727756i
\(547\) 113.651 0.207771 0.103885 0.994589i \(-0.466872\pi\)
0.103885 + 0.994589i \(0.466872\pi\)
\(548\) 33.3615 70.5428i 0.0608787 0.128728i
\(549\) −159.469 −0.290472
\(550\) 0 0
\(551\) 493.564i 0.895761i
\(552\) −368.303 287.398i −0.667215 0.520649i
\(553\) 894.718i 1.61794i
\(554\) −63.1319 + 281.160i −0.113957 + 0.507509i
\(555\) 0 0
\(556\) 440.129 930.651i 0.791599 1.67383i
\(557\) 233.232i 0.418728i 0.977838 + 0.209364i \(0.0671394\pi\)
−0.977838 + 0.209364i \(0.932861\pi\)
\(558\) −30.8830 + 137.539i −0.0553459 + 0.246485i
\(559\) 933.825i 1.67053i
\(560\) 0 0
\(561\) 223.589 0.398554
\(562\) −670.644 150.587i −1.19332 0.267948i
\(563\) −167.786 −0.298021 −0.149011 0.988836i \(-0.547609\pi\)
−0.149011 + 0.988836i \(0.547609\pi\)
\(564\) 195.155 + 92.2939i 0.346020 + 0.163642i
\(565\) 0 0
\(566\) −614.607 138.004i −1.08588 0.243824i
\(567\) 56.9850 0.100503
\(568\) −65.6341 + 84.1105i −0.115553 + 0.148082i
\(569\) −381.089 −0.669752 −0.334876 0.942262i \(-0.608694\pi\)
−0.334876 + 0.942262i \(0.608694\pi\)
\(570\) 0 0
\(571\) 453.871i 0.794870i 0.917630 + 0.397435i \(0.130100\pi\)
−0.917630 + 0.397435i \(0.869900\pi\)
\(572\) 623.034 + 294.649i 1.08922 + 0.515120i
\(573\) 1.96939i 0.00343697i
\(574\) −544.627 122.291i −0.948828 0.213051i
\(575\) 0 0
\(576\) 46.6699 + 186.242i 0.0810241 + 0.323336i
\(577\) 688.294i 1.19288i 0.802656 + 0.596442i \(0.203419\pi\)
−0.802656 + 0.596442i \(0.796581\pi\)
\(578\) 186.327 + 41.8380i 0.322365 + 0.0723841i
\(579\) 132.753i 0.229281i
\(580\) 0 0
\(581\) −442.269 −0.761220
\(582\) 52.0283 231.710i 0.0893957 0.398127i
\(583\) 757.282 1.29894
\(584\) 201.244 257.896i 0.344597 0.441603i
\(585\) 0 0
\(586\) −2.87187 + 12.7900i −0.00490080 + 0.0218259i
\(587\) −249.163 −0.424468 −0.212234 0.977219i \(-0.568074\pi\)
−0.212234 + 0.977219i \(0.568074\pi\)
\(588\) 55.8046 + 26.3914i 0.0949057 + 0.0448834i
\(589\) −405.194 −0.687936
\(590\) 0 0
\(591\) 232.953i 0.394168i
\(592\) 832.752 683.510i 1.40668 1.15458i
\(593\) 163.937i 0.276454i 0.990401 + 0.138227i \(0.0441404\pi\)
−0.990401 + 0.138227i \(0.955860\pi\)
\(594\) 21.1279 94.0938i 0.0355689 0.158407i
\(595\) 0 0
\(596\) 403.812 + 190.973i 0.677538 + 0.320425i
\(597\) 304.865i 0.510661i
\(598\) 274.294 1221.58i 0.458686 2.04277i
\(599\) 170.412i 0.284494i −0.989831 0.142247i \(-0.954567\pi\)
0.989831 0.142247i \(-0.0454327\pi\)
\(600\) 0 0
\(601\) 1119.87 1.86335 0.931674 0.363295i \(-0.118348\pi\)
0.931674 + 0.363295i \(0.118348\pi\)
\(602\) −621.413 139.533i −1.03225 0.231782i
\(603\) −13.4973 −0.0223836
\(604\) −11.0349 + 23.3332i −0.0182697 + 0.0386312i
\(605\) 0 0
\(606\) 146.672 + 32.9339i 0.242034 + 0.0543464i
\(607\) −660.957 −1.08889 −0.544445 0.838796i \(-0.683260\pi\)
−0.544445 + 0.838796i \(0.683260\pi\)
\(608\) −492.949 + 248.179i −0.810772 + 0.408189i
\(609\) −313.844 −0.515342
\(610\) 0 0
\(611\) 578.550i 0.946890i
\(612\) −71.3680 + 150.907i −0.116614 + 0.246581i
\(613\) 179.315i 0.292520i 0.989246 + 0.146260i \(0.0467236\pi\)
−0.989246 + 0.146260i \(0.953276\pi\)
\(614\) 691.891 + 155.358i 1.12686 + 0.253026i
\(615\) 0 0
\(616\) −289.168 + 370.571i −0.469429 + 0.601576i
\(617\) 63.6752i 0.103201i −0.998668 0.0516007i \(-0.983568\pi\)
0.998668 0.0516007i \(-0.0164323\pi\)
\(618\) 289.972 + 65.1105i 0.469210 + 0.105357i
\(619\) 872.350i 1.40929i 0.709561 + 0.704644i \(0.248893\pi\)
−0.709561 + 0.704644i \(0.751107\pi\)
\(620\) 0 0
\(621\) −175.187 −0.282105
\(622\) 84.7367 377.378i 0.136233 0.606716i
\(623\) 293.206 0.470636
\(624\) −397.736 + 326.456i −0.637397 + 0.523166i
\(625\) 0 0
\(626\) −10.3068 + 45.9019i −0.0164646 + 0.0733257i
\(627\) 277.204 0.442112
\(628\) 129.810 274.483i 0.206704 0.437074i
\(629\) 936.682 1.48916
\(630\) 0 0
\(631\) 340.783i 0.540068i 0.962851 + 0.270034i \(0.0870349\pi\)
−0.962851 + 0.270034i \(0.912965\pi\)
\(632\) 695.458 891.234i 1.10041 1.41018i
\(633\) 377.737i 0.596742i
\(634\) 93.7705 417.610i 0.147903 0.658691i
\(635\) 0 0
\(636\) −241.719 + 511.114i −0.380061 + 0.803638i
\(637\) 165.436i 0.259712i
\(638\) −116.362 + 518.220i −0.182385 + 0.812257i
\(639\) 40.0081i 0.0626105i
\(640\) 0 0
\(641\) 766.210 1.19534 0.597668 0.801744i \(-0.296094\pi\)
0.597668 + 0.801744i \(0.296094\pi\)
\(642\) −618.783 138.942i −0.963837 0.216421i
\(643\) −1163.47 −1.80943 −0.904717 0.426014i \(-0.859917\pi\)
−0.904717 + 0.426014i \(0.859917\pi\)
\(644\) 771.913 + 365.058i 1.19862 + 0.566860i
\(645\) 0 0
\(646\) −468.185 105.127i −0.724744 0.162735i
\(647\) 740.530 1.14456 0.572279 0.820059i \(-0.306059\pi\)
0.572279 + 0.820059i \(0.306059\pi\)
\(648\) 56.7630 + 44.2940i 0.0875973 + 0.0683549i
\(649\) 178.866 0.275603
\(650\) 0 0
\(651\) 257.652i 0.395778i
\(652\) −901.465 426.326i −1.38262 0.653875i
\(653\) 109.569i 0.167793i −0.996474 0.0838967i \(-0.973263\pi\)
0.996474 0.0838967i \(-0.0267366\pi\)
\(654\) 275.397 + 61.8379i 0.421097 + 0.0945534i
\(655\) 0 0
\(656\) −447.450 545.149i −0.682089 0.831020i
\(657\) 122.671i 0.186714i
\(658\) −384.996 86.4473i −0.585100 0.131379i
\(659\) 723.214i 1.09744i −0.836006 0.548721i \(-0.815115\pi\)
0.836006 0.548721i \(-0.184885\pi\)
\(660\) 0 0
\(661\) 700.333 1.05951 0.529753 0.848152i \(-0.322285\pi\)
0.529753 + 0.848152i \(0.322285\pi\)
\(662\) −180.726 + 804.868i −0.273000 + 1.21581i
\(663\) −447.375 −0.674773
\(664\) −440.546 343.772i −0.663473 0.517729i
\(665\) 0 0
\(666\) 88.5112 394.188i 0.132900 0.591873i
\(667\) 964.841 1.44654
\(668\) −286.346 135.420i −0.428662 0.202725i
\(669\) −569.116 −0.850696
\(670\) 0 0
\(671\) 493.271i 0.735128i
\(672\) −157.810 313.452i −0.234836 0.466447i
\(673\) 1221.18i 1.81454i 0.420552 + 0.907269i \(0.361837\pi\)
−0.420552 + 0.907269i \(0.638163\pi\)
\(674\) −45.2490 + 201.518i −0.0671350 + 0.298988i
\(675\) 0 0
\(676\) −635.509 300.549i −0.940103 0.444599i
\(677\) 989.373i 1.46141i 0.682695 + 0.730704i \(0.260808\pi\)
−0.682695 + 0.730704i \(0.739192\pi\)
\(678\) 131.155 584.102i 0.193444 0.861507i
\(679\) 434.063i 0.639268i
\(680\) 0 0
\(681\) 273.057 0.400965
\(682\) −425.435 95.5276i −0.623806 0.140070i
\(683\) −307.312 −0.449945 −0.224972 0.974365i \(-0.572229\pi\)
−0.224972 + 0.974365i \(0.572229\pi\)
\(684\) −88.4816 + 187.094i −0.129359 + 0.273529i
\(685\) 0 0
\(686\) −715.518 160.663i −1.04303 0.234203i
\(687\) −473.107 −0.688656
\(688\) −510.536 622.009i −0.742058 0.904083i
\(689\) −1515.23 −2.19917
\(690\) 0 0
\(691\) 893.378i 1.29288i −0.762966 0.646438i \(-0.776258\pi\)
0.762966 0.646438i \(-0.223742\pi\)
\(692\) −47.4048 + 100.237i −0.0685041 + 0.144852i
\(693\) 176.266i 0.254353i
\(694\) −298.978 67.1329i −0.430805 0.0967332i
\(695\) 0 0
\(696\) −312.621 243.948i −0.449169 0.350500i
\(697\) 613.186i 0.879750i
\(698\) 165.346 + 37.1270i 0.236886 + 0.0531906i
\(699\) 188.353i 0.269461i
\(700\) 0 0
\(701\) 1127.42 1.60830 0.804149 0.594428i \(-0.202622\pi\)
0.804149 + 0.594428i \(0.202622\pi\)
\(702\) −42.2744 + 188.270i −0.0602199 + 0.268191i
\(703\) 1161.29 1.65191
\(704\) −576.084 + 144.360i −0.818301 + 0.205056i
\(705\) 0 0
\(706\) 112.200 499.688i 0.158924 0.707773i
\(707\) −274.762 −0.388631
\(708\) −57.0928 + 120.722i −0.0806395 + 0.170512i
\(709\) −1093.27 −1.54199 −0.770997 0.636839i \(-0.780242\pi\)
−0.770997 + 0.636839i \(0.780242\pi\)
\(710\) 0 0
\(711\) 423.926i 0.596239i
\(712\) 292.064 + 227.907i 0.410202 + 0.320094i
\(713\) 792.091i 1.11093i
\(714\) 66.8470 297.705i 0.0936233 0.416954i
\(715\) 0 0
\(716\) −349.415 + 738.837i −0.488010 + 1.03190i
\(717\) 310.026i 0.432393i
\(718\) −292.374 + 1302.10i −0.407206 + 1.81350i
\(719\) 769.690i 1.07050i −0.844693 0.535251i \(-0.820217\pi\)
0.844693 0.535251i \(-0.179783\pi\)
\(720\) 0 0
\(721\) −543.205 −0.753405
\(722\) 124.007 + 27.8446i 0.171755 + 0.0385660i
\(723\) −621.154 −0.859134
\(724\) −180.172 85.2081i −0.248857 0.117691i
\(725\) 0 0
\(726\) −117.921 26.4782i −0.162426 0.0364713i
\(727\) 295.050 0.405846 0.202923 0.979195i \(-0.434956\pi\)
0.202923 + 0.979195i \(0.434956\pi\)
\(728\) 578.591 741.468i 0.794767 1.01850i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 699.638i 0.957097i
\(732\) 332.924 + 157.448i 0.454814 + 0.215094i
\(733\) 261.200i 0.356344i −0.983999 0.178172i \(-0.942982\pi\)
0.983999 0.178172i \(-0.0570184\pi\)
\(734\) −478.684 107.484i −0.652158 0.146436i
\(735\) 0 0
\(736\) 485.150 + 963.638i 0.659172 + 1.30929i
\(737\) 41.7501i 0.0566487i
\(738\) −258.049 57.9426i −0.349660 0.0785130i
\(739\) 482.679i 0.653151i −0.945171 0.326576i \(-0.894105\pi\)
0.945171 0.326576i \(-0.105895\pi\)
\(740\) 0 0
\(741\) −554.652 −0.748519
\(742\) 226.407 1008.31i 0.305130 1.35891i
\(743\) 23.7067 0.0319067 0.0159534 0.999873i \(-0.494922\pi\)
0.0159534 + 0.999873i \(0.494922\pi\)
\(744\) 200.271 256.648i 0.269181 0.344957i
\(745\) 0 0
\(746\) 306.189 1363.62i 0.410441 1.82791i
\(747\) −209.551 −0.280523
\(748\) −466.788 220.756i −0.624048 0.295129i
\(749\) 1159.17 1.54762
\(750\) 0 0
\(751\) 395.508i 0.526642i 0.964708 + 0.263321i \(0.0848179\pi\)
−0.964708 + 0.263321i \(0.915182\pi\)
\(752\) −316.302 385.365i −0.420614 0.512453i
\(753\) 530.389i 0.704368i
\(754\) 232.825 1036.90i 0.308787 1.37519i
\(755\) 0 0
\(756\) −118.968 56.2630i −0.157365 0.0744219i
\(757\) 393.940i 0.520396i 0.965555 + 0.260198i \(0.0837879\pi\)
−0.965555 + 0.260198i \(0.916212\pi\)
\(758\) 91.4425 407.242i 0.120637 0.537259i
\(759\) 541.891i 0.713954i
\(760\) 0 0
\(761\) −369.354 −0.485354 −0.242677 0.970107i \(-0.578025\pi\)
−0.242677 + 0.970107i \(0.578025\pi\)
\(762\) 75.6379 + 16.9838i 0.0992623 + 0.0222885i
\(763\) −515.903 −0.676150
\(764\) −1.94443 + 4.11150i −0.00254507 + 0.00538154i
\(765\) 0 0
\(766\) −305.444 68.5846i −0.398751 0.0895360i
\(767\) −357.890 −0.466610
\(768\) 86.4490 434.896i 0.112564 0.566271i
\(769\) 873.491 1.13588 0.567940 0.823070i \(-0.307741\pi\)
0.567940 + 0.823070i \(0.307741\pi\)
\(770\) 0 0
\(771\) 434.852i 0.564010i
\(772\) −131.071 + 277.150i −0.169782 + 0.359003i
\(773\) 1176.93i 1.52254i 0.648432 + 0.761272i \(0.275425\pi\)
−0.648432 + 0.761272i \(0.724575\pi\)
\(774\) −294.431 66.1119i −0.380402 0.0854159i
\(775\) 0 0
\(776\) −337.394 + 432.372i −0.434786 + 0.557181i
\(777\) 738.433i 0.950365i
\(778\) −754.393 169.392i −0.969657 0.217728i
\(779\) 760.224i 0.975897i
\(780\) 0 0
\(781\) −123.754 −0.158455
\(782\) −205.506 + 915.228i −0.262795 + 1.17037i
\(783\) −148.702 −0.189913
\(784\) −90.4464 110.195i −0.115365 0.140555i
\(785\) 0 0
\(786\) −1.33053 + 5.92555i −0.00169278 + 0.00753887i
\(787\) −603.482 −0.766814 −0.383407 0.923580i \(-0.625249\pi\)
−0.383407 + 0.923580i \(0.625249\pi\)
\(788\) −230.002 + 486.338i −0.291880 + 0.617180i
\(789\) −84.4626 −0.107050
\(790\) 0 0
\(791\) 1094.20i 1.38331i
\(792\) −137.011 + 175.580i −0.172993 + 0.221692i
\(793\) 986.975i 1.24461i
\(794\) 245.882 1095.04i 0.309675 1.37915i
\(795\) 0 0
\(796\) −301.002 + 636.467i −0.378143 + 0.799582i
\(797\) 860.121i 1.07920i 0.841922 + 0.539599i \(0.181424\pi\)
−0.841922 + 0.539599i \(0.818576\pi\)
\(798\) 82.8765 369.093i 0.103855 0.462523i
\(799\) 433.460i 0.542503i
\(800\) 0 0
\(801\) 138.924 0.173438
\(802\) 33.0437 + 7.41967i 0.0412017 + 0.00925146i
\(803\) 379.448 0.472538
\(804\) 28.1784 + 13.3263i 0.0350478 + 0.0165750i
\(805\) 0 0
\(806\) 851.245 + 191.139i 1.05614 + 0.237145i
\(807\) 257.548 0.319143
\(808\) −273.692 213.570i −0.338728 0.264320i
\(809\) −941.012 −1.16318 −0.581589 0.813483i \(-0.697569\pi\)
−0.581589 + 0.813483i \(0.697569\pi\)
\(810\) 0 0
\(811\) 1105.29i 1.36287i 0.731878 + 0.681436i \(0.238644\pi\)
−0.731878 + 0.681436i \(0.761356\pi\)
\(812\) 655.213 + 309.867i 0.806912 + 0.381610i
\(813\) 144.352i 0.177554i
\(814\) 1219.30 + 273.784i 1.49792 + 0.336344i
\(815\) 0 0
\(816\) 297.991 244.586i 0.365185 0.299738i
\(817\) 867.407i 1.06170i
\(818\) −504.421 113.263i −0.616652 0.138463i
\(819\) 352.688i 0.430632i
\(820\) 0 0
\(821\) −193.170 −0.235286 −0.117643 0.993056i \(-0.537534\pi\)
−0.117643 + 0.993056i \(0.537534\pi\)
\(822\) −14.8057 + 65.9374i −0.0180117 + 0.0802159i
\(823\) 178.778 0.217227 0.108614 0.994084i \(-0.465359\pi\)
0.108614 + 0.994084i \(0.465359\pi\)
\(824\) −541.090 422.229i −0.656662 0.512414i
\(825\) 0 0
\(826\) 53.4761 238.158i 0.0647410 0.288326i
\(827\) 1558.61 1.88465 0.942326 0.334697i \(-0.108634\pi\)
0.942326 + 0.334697i \(0.108634\pi\)
\(828\) 365.740 + 172.968i 0.441714 + 0.208898i
\(829\) 565.477 0.682119 0.341059 0.940042i \(-0.389214\pi\)
0.341059 + 0.940042i \(0.389214\pi\)
\(830\) 0 0
\(831\) 249.554i 0.300306i
\(832\) 1152.67 288.846i 1.38543 0.347171i
\(833\) 123.948i 0.148797i
\(834\) −195.327 + 869.895i −0.234205 + 1.04304i
\(835\) 0 0
\(836\) −578.721 273.692i −0.692250 0.327383i
\(837\) 122.078i 0.145851i
\(838\) 113.450 505.254i 0.135382 0.602928i
\(839\) 1280.25i 1.52592i 0.646443 + 0.762962i \(0.276256\pi\)
−0.646443 + 0.762962i \(0.723744\pi\)
\(840\) 0 0
\(841\) −22.0271 −0.0261915
\(842\) 190.195 + 42.7066i 0.225885 + 0.0507204i
\(843\) 595.256 0.706116
\(844\) 372.952 788.604i 0.441886 0.934365i
\(845\) 0 0
\(846\) −182.415 40.9595i −0.215620 0.0484155i
\(847\) 220.903 0.260806
\(848\) 1009.28 828.398i 1.19018 0.976885i
\(849\) 545.518 0.642542
\(850\) 0 0
\(851\) 2270.15i 2.66762i
\(852\) 39.5012 83.5252i 0.0463630 0.0980343i
\(853\) 120.366i 0.141109i −0.997508 0.0705546i \(-0.977523\pi\)
0.997508 0.0705546i \(-0.0224769\pi\)
\(854\) −656.782 147.474i −0.769066 0.172687i
\(855\) 0 0
\(856\) 1154.66 + 901.014i 1.34890 + 1.05259i
\(857\) 717.784i 0.837554i −0.908089 0.418777i \(-0.862459\pi\)
0.908089 0.418777i \(-0.137541\pi\)
\(858\) −582.360 130.764i −0.678741 0.152405i
\(859\) 252.894i 0.294405i 0.989106 + 0.147203i \(0.0470269\pi\)
−0.989106 + 0.147203i \(0.952973\pi\)
\(860\) 0 0
\(861\) 483.405 0.561446
\(862\) −170.873 + 760.989i −0.198229 + 0.882817i
\(863\) −1234.73 −1.43075 −0.715373 0.698743i \(-0.753743\pi\)
−0.715373 + 0.698743i \(0.753743\pi\)
\(864\) −74.7717 148.517i −0.0865413 0.171894i
\(865\) 0 0
\(866\) 120.888 538.381i 0.139594 0.621687i
\(867\) −165.382 −0.190752
\(868\) −254.387 + 537.901i −0.293073 + 0.619701i
\(869\) 1311.29 1.50897
\(870\) 0 0
\(871\) 83.5368i 0.0959091i
\(872\) −513.894 401.007i −0.589327 0.459871i
\(873\) 205.663i 0.235582i
\(874\) −254.785 + 1134.69i −0.291516 + 1.29828i
\(875\) 0 0
\(876\) −121.117 + 256.101i −0.138261 + 0.292353i
\(877\) 685.723i 0.781896i −0.920413 0.390948i \(-0.872147\pi\)
0.920413 0.390948i \(-0.127853\pi\)
\(878\) −195.487 + 870.609i −0.222651 + 0.991582i
\(879\) 11.3522i 0.0129149i
\(880\) 0 0
\(881\) −458.454 −0.520379 −0.260189 0.965558i \(-0.583785\pi\)
−0.260189 + 0.965558i \(0.583785\pi\)
\(882\) −52.1614 11.7124i −0.0591399 0.0132793i
\(883\) 771.505 0.873732 0.436866 0.899527i \(-0.356088\pi\)
0.436866 + 0.899527i \(0.356088\pi\)
\(884\) 933.986 + 441.707i 1.05655 + 0.499668i
\(885\) 0 0
\(886\) −1550.75 348.206i −1.75028 0.393009i
\(887\) −1161.05 −1.30896 −0.654480 0.756080i \(-0.727112\pi\)
−0.654480 + 0.756080i \(0.727112\pi\)
\(888\) −573.979 + 735.558i −0.646372 + 0.828331i
\(889\) −141.693 −0.159385
\(890\) 0 0
\(891\) 83.5166i 0.0937336i
\(892\) 1188.15 + 561.905i 1.33200 + 0.629938i
\(893\) 537.401i 0.601793i
\(894\) −377.450 84.7529i −0.422203 0.0948019i
\(895\) 0 0
\(896\) 19.9793 + 810.207i 0.0222983 + 0.904248i
\(897\) 1084.26i 1.20876i
\(898\) 1464.00 + 328.728i 1.63029 + 0.366066i
\(899\) 672.340i 0.747876i
\(900\) 0 0
\(901\) 1135.24 1.25997
\(902\) 179.229 798.200i 0.198701 0.884923i
\(903\) 551.560 0.610808
\(904\) −850.514 + 1089.94i −0.940834 + 1.20569i
\(905\) 0 0
\(906\) 4.89722 21.8099i 0.00540532 0.0240728i
\(907\) 392.544 0.432793 0.216397 0.976306i \(-0.430570\pi\)
0.216397 + 0.976306i \(0.430570\pi\)
\(908\) −570.062 269.597i −0.627822 0.296913i
\(909\) −130.185 −0.143218
\(910\) 0 0
\(911\) 1013.40i 1.11240i −0.831048 0.556201i \(-0.812259\pi\)
0.831048 0.556201i \(-0.187741\pi\)
\(912\) 369.447 303.237i 0.405096 0.332496i
\(913\) 648.185i 0.709950i
\(914\) −44.2958 + 197.273i −0.0484637 + 0.215835i
\(915\) 0 0
\(916\) 987.707 + 467.112i 1.07828 + 0.509948i
\(917\) 11.1004i 0.0121051i
\(918\) 31.6727 141.056i 0.0345019 0.153655i
\(919\) 970.018i 1.05551i −0.849395 0.527757i \(-0.823033\pi\)
0.849395 0.527757i \(-0.176967\pi\)
\(920\) 0 0
\(921\) −614.115 −0.666791
\(922\) −8.75578 1.96603i −0.00949651 0.00213236i
\(923\) 247.616 0.268273
\(924\) 174.033 367.992i 0.188348 0.398260i
\(925\) 0 0
\(926\) 1005.19 + 225.706i 1.08552 + 0.243743i
\(927\) −257.376 −0.277644
\(928\) 411.804 + 817.952i 0.443754 + 0.881414i
\(929\) −980.857 −1.05582 −0.527910 0.849300i \(-0.677024\pi\)
−0.527910 + 0.849300i \(0.677024\pi\)
\(930\) 0 0
\(931\) 153.670i 0.165059i
\(932\) 185.967 393.226i 0.199535 0.421917i
\(933\) 334.956i 0.359010i
\(934\) 576.638 + 129.479i 0.617386 + 0.138628i
\(935\) 0 0
\(936\) 274.141 351.314i 0.292886 0.375336i
\(937\) 964.666i 1.02953i 0.857333 + 0.514763i \(0.172120\pi\)
−0.857333 + 0.514763i \(0.827880\pi\)
\(938\) −55.5896 12.4821i −0.0592639 0.0133072i
\(939\) 40.7420i 0.0433887i
\(940\) 0 0
\(941\) −1581.10 −1.68023 −0.840117 0.542405i \(-0.817514\pi\)
−0.840117 + 0.542405i \(0.817514\pi\)
\(942\) −57.6089 + 256.563i −0.0611560 + 0.272360i
\(943\) −1486.12 −1.57595
\(944\) 238.386 195.663i 0.252527 0.207271i
\(945\) 0 0
\(946\) 204.498 910.738i 0.216171 0.962725i
\(947\) −1245.27 −1.31497 −0.657483 0.753469i \(-0.728379\pi\)
−0.657483 + 0.753469i \(0.728379\pi\)
\(948\) −418.555 + 885.032i −0.441513 + 0.933578i
\(949\) −759.229 −0.800031
\(950\) 0 0
\(951\) 370.666i 0.389765i
\(952\) −433.490 + 555.521i −0.455347 + 0.583530i
\(953\) 1106.52i 1.16109i −0.814228 0.580546i \(-0.802839\pi\)
0.814228 0.580546i \(-0.197161\pi\)
\(954\) 107.274 477.746i 0.112446 0.500782i
\(955\) 0 0
\(956\) −306.098 + 647.243i −0.320186 + 0.677032i
\(957\) 459.966i 0.480633i
\(958\) 119.689 533.037i 0.124936 0.556406i
\(959\) 123.521i 0.128802i
\(960\) 0 0
\(961\) 409.039 0.425638
\(962\) −2439.68 547.808i −2.53605 0.569447i
\(963\) 549.225 0.570327
\(964\) 1296.79 + 613.284i 1.34521 + 0.636187i
\(965\) 0 0
\(966\) −721.520 162.011i −0.746915 0.167713i
\(967\) 406.453 0.420324 0.210162 0.977667i \(-0.432601\pi\)
0.210162 + 0.977667i \(0.432601\pi\)
\(968\) 220.042 + 171.706i 0.227316 + 0.177382i
\(969\) 415.555 0.428850
\(970\) 0 0
\(971\) 1815.22i 1.86943i 0.355393 + 0.934717i \(0.384347\pi\)
−0.355393 + 0.934717i \(0.615653\pi\)
\(972\) −56.3680 26.6579i −0.0579918 0.0274258i
\(973\) 1629.58i 1.67480i
\(974\) −698.119 156.756i −0.716754 0.160941i
\(975\) 0 0
\(976\) −539.594 657.412i −0.552862 0.673578i
\(977\) 1457.74i 1.49205i −0.665916 0.746027i \(-0.731959\pi\)
0.665916 0.746027i \(-0.268041\pi\)
\(978\) 842.614 + 189.201i 0.861568 + 0.193457i
\(979\) 429.720i 0.438938i
\(980\) 0 0
\(981\) −244.439 −0.249174
\(982\) 185.074 824.235i 0.188467 0.839343i
\(983\) −19.9496 −0.0202946 −0.0101473 0.999949i \(-0.503230\pi\)
−0.0101473 + 0.999949i \(0.503230\pi\)
\(984\) 481.522 + 375.747i 0.489352 + 0.381857i
\(985\) 0 0
\(986\) −174.437 + 776.860i −0.176914 + 0.787891i
\(987\) 341.718 0.346219
\(988\) 1157.95 + 547.625i 1.17201 + 0.554276i
\(989\) −1695.65 −1.71450
\(990\) 0 0
\(991\) 605.720i 0.611221i −0.952157 0.305611i \(-0.901139\pi\)
0.952157 0.305611i \(-0.0988605\pi\)
\(992\) −671.502 + 338.073i −0.676918 + 0.340799i
\(993\) 714.392i 0.719428i
\(994\) −36.9989 + 164.776i −0.0372223 + 0.165771i
\(995\) 0 0
\(996\) 437.481 + 206.896i 0.439237 + 0.207727i
\(997\) 1238.47i 1.24220i 0.783732 + 0.621099i \(0.213314\pi\)
−0.783732 + 0.621099i \(0.786686\pi\)
\(998\) −90.7434 + 404.129i −0.0909253 + 0.404939i
\(999\) 349.876i 0.350227i
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.199.16 16
3.2 odd 2 900.3.f.f.199.1 16
4.3 odd 2 inner 300.3.f.b.199.2 16
5.2 odd 4 300.3.c.d.151.6 8
5.3 odd 4 60.3.c.a.31.3 8
5.4 even 2 inner 300.3.f.b.199.1 16
12.11 even 2 900.3.f.f.199.15 16
15.2 even 4 900.3.c.u.451.3 8
15.8 even 4 180.3.c.b.91.6 8
15.14 odd 2 900.3.f.f.199.16 16
20.3 even 4 60.3.c.a.31.4 yes 8
20.7 even 4 300.3.c.d.151.5 8
20.19 odd 2 inner 300.3.f.b.199.15 16
40.3 even 4 960.3.e.c.511.2 8
40.13 odd 4 960.3.e.c.511.5 8
60.23 odd 4 180.3.c.b.91.5 8
60.47 odd 4 900.3.c.u.451.4 8
60.59 even 2 900.3.f.f.199.2 16
120.53 even 4 2880.3.e.j.2431.5 8
120.83 odd 4 2880.3.e.j.2431.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.c.a.31.3 8 5.3 odd 4
60.3.c.a.31.4 yes 8 20.3 even 4
180.3.c.b.91.5 8 60.23 odd 4
180.3.c.b.91.6 8 15.8 even 4
300.3.c.d.151.5 8 20.7 even 4
300.3.c.d.151.6 8 5.2 odd 4
300.3.f.b.199.1 16 5.4 even 2 inner
300.3.f.b.199.2 16 4.3 odd 2 inner
300.3.f.b.199.15 16 20.19 odd 2 inner
300.3.f.b.199.16 16 1.1 even 1 trivial
900.3.c.u.451.3 8 15.2 even 4
900.3.c.u.451.4 8 60.47 odd 4
900.3.f.f.199.1 16 3.2 odd 2
900.3.f.f.199.2 16 60.59 even 2
900.3.f.f.199.15 16 12.11 even 2
900.3.f.f.199.16 16 15.14 odd 2
960.3.e.c.511.2 8 40.3 even 4
960.3.e.c.511.5 8 40.13 odd 4
2880.3.e.j.2431.5 8 120.53 even 4
2880.3.e.j.2431.8 8 120.83 odd 4