Properties

Label 300.3.c.g.151.7
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [300,3,Mod(151,300)]
 
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, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.151");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), 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: \(8\)
Coefficient field: 8.0.4069419264.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.7
Root \(1.65359 + 0.954702i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.g.151.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.97650 - 0.305673i) q^{2} -1.73205i q^{3} +(3.81313 - 1.20833i) q^{4} +(-0.529441 - 3.42340i) q^{6} +0.329898i q^{7} +(7.16731 - 3.55383i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.97650 - 0.305673i) q^{2} -1.73205i q^{3} +(3.81313 - 1.20833i) q^{4} +(-0.529441 - 3.42340i) q^{6} +0.329898i q^{7} +(7.16731 - 3.55383i) q^{8} -3.00000 q^{9} -20.4920i q^{11} +(-2.09288 - 6.60453i) q^{12} +0.416712 q^{13} +(0.100841 + 0.652044i) q^{14} +(13.0799 - 9.21501i) q^{16} +18.5884 q^{17} +(-5.92951 + 0.917019i) q^{18} +12.4503i q^{19} +0.571400 q^{21} +(-6.26384 - 40.5024i) q^{22} +23.2304i q^{23} +(-6.15542 - 12.4141i) q^{24} +(0.823633 - 0.127378i) q^{26} +5.19615i q^{27} +(0.398624 + 1.25794i) q^{28} -23.9166 q^{29} -42.0148i q^{31} +(23.0357 - 22.2117i) q^{32} -35.4931 q^{33} +(36.7400 - 5.68197i) q^{34} +(-11.4394 + 3.62498i) q^{36} -50.9523 q^{37} +(3.80573 + 24.6081i) q^{38} -0.721767i q^{39} +46.7073 q^{41} +(1.12937 - 0.174661i) q^{42} +55.5866i q^{43} +(-24.7610 - 78.1385i) q^{44} +(7.10090 + 45.9149i) q^{46} +81.7616i q^{47} +(-15.9609 - 22.6550i) q^{48} +48.8912 q^{49} -32.1960i q^{51} +(1.58898 - 0.503524i) q^{52} +29.9744 q^{53} +(1.58832 + 10.2702i) q^{54} +(1.17240 + 2.36448i) q^{56} +21.5646 q^{57} +(-47.2713 + 7.31067i) q^{58} +24.3311i q^{59} -74.8416 q^{61} +(-12.8428 - 83.0424i) q^{62} -0.989693i q^{63} +(38.7406 - 50.9428i) q^{64} +(-70.1523 + 10.8493i) q^{66} +72.8008i q^{67} +(70.8799 - 22.4608i) q^{68} +40.2362 q^{69} +39.2803i q^{71} +(-21.5019 + 10.6615i) q^{72} +46.5814 q^{73} +(-100.707 + 15.5747i) q^{74} +(15.0441 + 47.4747i) q^{76} +6.76026 q^{77} +(-0.220625 - 1.42657i) q^{78} +101.920i q^{79} +9.00000 q^{81} +(92.3170 - 14.2771i) q^{82} +5.88913i q^{83} +(2.17882 - 0.690438i) q^{84} +(16.9913 + 109.867i) q^{86} +41.4248i q^{87} +(-72.8250 - 146.872i) q^{88} -61.0100 q^{89} +0.137472i q^{91} +(28.0699 + 88.5804i) q^{92} -72.7718 q^{93} +(24.9923 + 161.602i) q^{94} +(-38.4717 - 39.8989i) q^{96} -95.5437 q^{97} +(96.6335 - 14.9447i) q^{98} +61.4759i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 8 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 8 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} + 8 q^{13} + 22 q^{14} + 40 q^{16} - 6 q^{18} + 24 q^{21} + 4 q^{22} - 36 q^{24} - 66 q^{26} + 104 q^{28} - 32 q^{29} + 112 q^{32} + 124 q^{34} + 24 q^{36} - 176 q^{37} - 170 q^{38} - 16 q^{41} + 54 q^{42} + 40 q^{44} - 76 q^{46} + 24 q^{48} + 16 q^{49} + 56 q^{52} - 304 q^{53} + 18 q^{54} - 172 q^{56} + 72 q^{57} - 12 q^{58} + 136 q^{61} - 238 q^{62} + 16 q^{64} - 108 q^{66} + 88 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} - 108 q^{74} + 120 q^{76} - 384 q^{77} + 150 q^{78} + 72 q^{81} + 320 q^{82} - 144 q^{84} + 214 q^{86} - 200 q^{88} + 128 q^{89} + 312 q^{92} + 72 q^{93} + 12 q^{94} + 96 q^{96} + 216 q^{97} + 60 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.97650 0.305673i 0.988251 0.152836i
\(3\) 1.73205i 0.577350i
\(4\) 3.81313 1.20833i 0.953282 0.302082i
\(5\) 0 0
\(6\) −0.529441 3.42340i −0.0882402 0.570567i
\(7\) 0.329898i 0.0471283i 0.999722 + 0.0235641i \(0.00750139\pi\)
−0.999722 + 0.0235641i \(0.992499\pi\)
\(8\) 7.16731 3.55383i 0.895913 0.444229i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 20.4920i 1.86291i −0.363861 0.931453i \(-0.618542\pi\)
0.363861 0.931453i \(-0.381458\pi\)
\(12\) −2.09288 6.60453i −0.174407 0.550378i
\(13\) 0.416712 0.0320548 0.0160274 0.999872i \(-0.494898\pi\)
0.0160274 + 0.999872i \(0.494898\pi\)
\(14\) 0.100841 + 0.652044i 0.00720292 + 0.0465746i
\(15\) 0 0
\(16\) 13.0799 9.21501i 0.817493 0.575938i
\(17\) 18.5884 1.09343 0.546717 0.837317i \(-0.315877\pi\)
0.546717 + 0.837317i \(0.315877\pi\)
\(18\) −5.92951 + 0.917019i −0.329417 + 0.0509455i
\(19\) 12.4503i 0.655281i 0.944803 + 0.327640i \(0.106253\pi\)
−0.944803 + 0.327640i \(0.893747\pi\)
\(20\) 0 0
\(21\) 0.571400 0.0272095
\(22\) −6.26384 40.5024i −0.284720 1.84102i
\(23\) 23.2304i 1.01002i 0.863114 + 0.505008i \(0.168511\pi\)
−0.863114 + 0.505008i \(0.831489\pi\)
\(24\) −6.15542 12.4141i −0.256476 0.517256i
\(25\) 0 0
\(26\) 0.823633 0.127378i 0.0316782 0.00489914i
\(27\) 5.19615i 0.192450i
\(28\) 0.398624 + 1.25794i 0.0142366 + 0.0449265i
\(29\) −23.9166 −0.824712 −0.412356 0.911023i \(-0.635294\pi\)
−0.412356 + 0.911023i \(0.635294\pi\)
\(30\) 0 0
\(31\) 42.0148i 1.35532i −0.735377 0.677658i \(-0.762995\pi\)
0.735377 0.677658i \(-0.237005\pi\)
\(32\) 23.0357 22.2117i 0.719865 0.694115i
\(33\) −35.4931 −1.07555
\(34\) 36.7400 5.68197i 1.08059 0.167117i
\(35\) 0 0
\(36\) −11.4394 + 3.62498i −0.317761 + 0.100694i
\(37\) −50.9523 −1.37709 −0.688545 0.725194i \(-0.741750\pi\)
−0.688545 + 0.725194i \(0.741750\pi\)
\(38\) 3.80573 + 24.6081i 0.100151 + 0.647582i
\(39\) 0.721767i 0.0185068i
\(40\) 0 0
\(41\) 46.7073 1.13920 0.569601 0.821921i \(-0.307098\pi\)
0.569601 + 0.821921i \(0.307098\pi\)
\(42\) 1.12937 0.174661i 0.0268898 0.00415861i
\(43\) 55.5866i 1.29271i 0.763036 + 0.646356i \(0.223708\pi\)
−0.763036 + 0.646356i \(0.776292\pi\)
\(44\) −24.7610 78.1385i −0.562750 1.77588i
\(45\) 0 0
\(46\) 7.10090 + 45.9149i 0.154367 + 0.998151i
\(47\) 81.7616i 1.73961i 0.493397 + 0.869804i \(0.335755\pi\)
−0.493397 + 0.869804i \(0.664245\pi\)
\(48\) −15.9609 22.6550i −0.332518 0.471980i
\(49\) 48.8912 0.997779
\(50\) 0 0
\(51\) 32.1960i 0.631295i
\(52\) 1.58898 0.503524i 0.0305572 0.00968316i
\(53\) 29.9744 0.565554 0.282777 0.959186i \(-0.408744\pi\)
0.282777 + 0.959186i \(0.408744\pi\)
\(54\) 1.58832 + 10.2702i 0.0294134 + 0.190189i
\(55\) 0 0
\(56\) 1.17240 + 2.36448i 0.0209357 + 0.0422228i
\(57\) 21.5646 0.378326
\(58\) −47.2713 + 7.31067i −0.815023 + 0.126046i
\(59\) 24.3311i 0.412391i 0.978511 + 0.206196i \(0.0661083\pi\)
−0.978511 + 0.206196i \(0.933892\pi\)
\(60\) 0 0
\(61\) −74.8416 −1.22691 −0.613456 0.789729i \(-0.710221\pi\)
−0.613456 + 0.789729i \(0.710221\pi\)
\(62\) −12.8428 83.0424i −0.207142 1.33939i
\(63\) 0.989693i 0.0157094i
\(64\) 38.7406 50.9428i 0.605321 0.795981i
\(65\) 0 0
\(66\) −70.1523 + 10.8493i −1.06291 + 0.164383i
\(67\) 72.8008i 1.08658i 0.839545 + 0.543290i \(0.182822\pi\)
−0.839545 + 0.543290i \(0.817178\pi\)
\(68\) 70.8799 22.4608i 1.04235 0.330307i
\(69\) 40.2362 0.583133
\(70\) 0 0
\(71\) 39.2803i 0.553244i 0.960979 + 0.276622i \(0.0892150\pi\)
−0.960979 + 0.276622i \(0.910785\pi\)
\(72\) −21.5019 + 10.6615i −0.298638 + 0.148076i
\(73\) 46.5814 0.638101 0.319051 0.947738i \(-0.396636\pi\)
0.319051 + 0.947738i \(0.396636\pi\)
\(74\) −100.707 + 15.5747i −1.36091 + 0.210469i
\(75\) 0 0
\(76\) 15.0441 + 47.4747i 0.197948 + 0.624667i
\(77\) 6.76026 0.0877955
\(78\) −0.220625 1.42657i −0.00282852 0.0182894i
\(79\) 101.920i 1.29012i 0.764131 + 0.645062i \(0.223168\pi\)
−0.764131 + 0.645062i \(0.776832\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 92.3170 14.2771i 1.12582 0.174112i
\(83\) 5.88913i 0.0709534i 0.999371 + 0.0354767i \(0.0112950\pi\)
−0.999371 + 0.0354767i \(0.988705\pi\)
\(84\) 2.17882 0.690438i 0.0259383 0.00821950i
\(85\) 0 0
\(86\) 16.9913 + 109.867i 0.197574 + 1.27752i
\(87\) 41.4248i 0.476148i
\(88\) −72.8250 146.872i −0.827557 1.66900i
\(89\) −61.0100 −0.685506 −0.342753 0.939426i \(-0.611359\pi\)
−0.342753 + 0.939426i \(0.611359\pi\)
\(90\) 0 0
\(91\) 0.137472i 0.00151069i
\(92\) 28.0699 + 88.5804i 0.305108 + 0.962831i
\(93\) −72.7718 −0.782492
\(94\) 24.9923 + 161.602i 0.265876 + 1.71917i
\(95\) 0 0
\(96\) −38.4717 39.8989i −0.400747 0.415614i
\(97\) −95.5437 −0.984987 −0.492494 0.870316i \(-0.663914\pi\)
−0.492494 + 0.870316i \(0.663914\pi\)
\(98\) 96.6335 14.9447i 0.986057 0.152497i
\(99\) 61.4759i 0.620969i
\(100\) 0 0
\(101\) 162.675 1.61064 0.805322 0.592838i \(-0.201992\pi\)
0.805322 + 0.592838i \(0.201992\pi\)
\(102\) −9.84145 63.6355i −0.0964848 0.623878i
\(103\) 158.196i 1.53588i −0.640521 0.767941i \(-0.721282\pi\)
0.640521 0.767941i \(-0.278718\pi\)
\(104\) 2.98670 1.48092i 0.0287183 0.0142397i
\(105\) 0 0
\(106\) 59.2445 9.16236i 0.558910 0.0864373i
\(107\) 18.1827i 0.169932i −0.996384 0.0849660i \(-0.972922\pi\)
0.996384 0.0849660i \(-0.0270782\pi\)
\(108\) 6.27865 + 19.8136i 0.0581357 + 0.183459i
\(109\) −156.842 −1.43891 −0.719457 0.694537i \(-0.755609\pi\)
−0.719457 + 0.694537i \(0.755609\pi\)
\(110\) 0 0
\(111\) 88.2520i 0.795063i
\(112\) 3.04001 + 4.31503i 0.0271430 + 0.0385270i
\(113\) 98.7245 0.873668 0.436834 0.899542i \(-0.356100\pi\)
0.436834 + 0.899542i \(0.356100\pi\)
\(114\) 42.6225 6.59172i 0.373882 0.0578221i
\(115\) 0 0
\(116\) −91.1972 + 28.8991i −0.786183 + 0.249130i
\(117\) −1.25014 −0.0106849
\(118\) 7.43735 + 48.0904i 0.0630284 + 0.407546i
\(119\) 6.13227i 0.0515317i
\(120\) 0 0
\(121\) −298.921 −2.47042
\(122\) −147.925 + 22.8770i −1.21250 + 0.187517i
\(123\) 80.8994i 0.657718i
\(124\) −50.7676 160.208i −0.409416 1.29200i
\(125\) 0 0
\(126\) −0.302523 1.95613i −0.00240097 0.0155249i
\(127\) 27.0938i 0.213337i −0.994295 0.106669i \(-0.965982\pi\)
0.994295 0.106669i \(-0.0340184\pi\)
\(128\) 60.9990 112.531i 0.476555 0.879145i
\(129\) 96.2789 0.746348
\(130\) 0 0
\(131\) 4.45811i 0.0340314i −0.999855 0.0170157i \(-0.994583\pi\)
0.999855 0.0170157i \(-0.00541653\pi\)
\(132\) −135.340 + 42.8873i −1.02530 + 0.324904i
\(133\) −4.10734 −0.0308822
\(134\) 22.2533 + 143.891i 0.166069 + 1.07381i
\(135\) 0 0
\(136\) 133.229 66.0600i 0.979622 0.485735i
\(137\) 181.700 1.32628 0.663139 0.748496i \(-0.269224\pi\)
0.663139 + 0.748496i \(0.269224\pi\)
\(138\) 79.5270 12.2991i 0.576282 0.0891241i
\(139\) 223.419i 1.60733i −0.595083 0.803664i \(-0.702881\pi\)
0.595083 0.803664i \(-0.297119\pi\)
\(140\) 0 0
\(141\) 141.615 1.00436
\(142\) 12.0069 + 77.6377i 0.0845559 + 0.546744i
\(143\) 8.53925i 0.0597151i
\(144\) −39.2397 + 27.6450i −0.272498 + 0.191979i
\(145\) 0 0
\(146\) 92.0683 14.2387i 0.630604 0.0975251i
\(147\) 84.6820i 0.576068i
\(148\) −194.288 + 61.5670i −1.31275 + 0.415994i
\(149\) 123.867 0.831324 0.415662 0.909519i \(-0.363550\pi\)
0.415662 + 0.909519i \(0.363550\pi\)
\(150\) 0 0
\(151\) 76.0961i 0.503948i 0.967734 + 0.251974i \(0.0810797\pi\)
−0.967734 + 0.251974i \(0.918920\pi\)
\(152\) 44.2464 + 89.2353i 0.291095 + 0.587075i
\(153\) −55.7651 −0.364478
\(154\) 13.3617 2.06643i 0.0867641 0.0134184i
\(155\) 0 0
\(156\) −0.872130 2.75219i −0.00559058 0.0176422i
\(157\) −34.2940 −0.218433 −0.109217 0.994018i \(-0.534834\pi\)
−0.109217 + 0.994018i \(0.534834\pi\)
\(158\) 31.1541 + 201.445i 0.197178 + 1.27497i
\(159\) 51.9172i 0.326523i
\(160\) 0 0
\(161\) −7.66365 −0.0476003
\(162\) 17.7885 2.75106i 0.109806 0.0169818i
\(163\) 165.538i 1.01557i 0.861483 + 0.507786i \(0.169536\pi\)
−0.861483 + 0.507786i \(0.830464\pi\)
\(164\) 178.101 56.4377i 1.08598 0.344132i
\(165\) 0 0
\(166\) 1.80015 + 11.6399i 0.0108443 + 0.0701198i
\(167\) 83.6064i 0.500637i −0.968164 0.250319i \(-0.919465\pi\)
0.968164 0.250319i \(-0.0805353\pi\)
\(168\) 4.09540 2.03066i 0.0243774 0.0120873i
\(169\) −168.826 −0.998972
\(170\) 0 0
\(171\) 37.3510i 0.218427i
\(172\) 67.1668 + 211.959i 0.390505 + 1.23232i
\(173\) −192.900 −1.11503 −0.557513 0.830168i \(-0.688244\pi\)
−0.557513 + 0.830168i \(0.688244\pi\)
\(174\) 12.6625 + 81.8763i 0.0727727 + 0.470554i
\(175\) 0 0
\(176\) −188.834 268.033i −1.07292 1.52291i
\(177\) 42.1427 0.238094
\(178\) −120.587 + 18.6491i −0.677452 + 0.104770i
\(179\) 120.939i 0.675637i −0.941211 0.337819i \(-0.890311\pi\)
0.941211 0.337819i \(-0.109689\pi\)
\(180\) 0 0
\(181\) −107.583 −0.594381 −0.297191 0.954818i \(-0.596050\pi\)
−0.297191 + 0.954818i \(0.596050\pi\)
\(182\) 0.0420216 + 0.271715i 0.000230888 + 0.00149294i
\(183\) 129.629i 0.708357i
\(184\) 82.5569 + 166.499i 0.448679 + 0.904887i
\(185\) 0 0
\(186\) −143.834 + 22.2444i −0.773299 + 0.119593i
\(187\) 380.913i 2.03697i
\(188\) 98.7947 + 311.767i 0.525504 + 1.65834i
\(189\) −1.71420 −0.00906984
\(190\) 0 0
\(191\) 279.706i 1.46443i 0.681075 + 0.732214i \(0.261513\pi\)
−0.681075 + 0.732214i \(0.738487\pi\)
\(192\) −88.2355 67.1006i −0.459560 0.349482i
\(193\) 102.534 0.531263 0.265632 0.964075i \(-0.414420\pi\)
0.265632 + 0.964075i \(0.414420\pi\)
\(194\) −188.842 + 29.2051i −0.973415 + 0.150542i
\(195\) 0 0
\(196\) 186.428 59.0765i 0.951165 0.301411i
\(197\) −38.9632 −0.197783 −0.0988913 0.995098i \(-0.531530\pi\)
−0.0988913 + 0.995098i \(0.531530\pi\)
\(198\) 18.7915 + 121.507i 0.0949067 + 0.613673i
\(199\) 147.646i 0.741940i −0.928645 0.370970i \(-0.879025\pi\)
0.928645 0.370970i \(-0.120975\pi\)
\(200\) 0 0
\(201\) 126.095 0.627337
\(202\) 321.528 49.7254i 1.59172 0.246165i
\(203\) 7.89005i 0.0388672i
\(204\) −38.9033 122.768i −0.190703 0.601802i
\(205\) 0 0
\(206\) −48.3562 312.674i −0.234739 1.51784i
\(207\) 69.6912i 0.336672i
\(208\) 5.45055 3.84001i 0.0262046 0.0184616i
\(209\) 255.132 1.22073
\(210\) 0 0
\(211\) 233.336i 1.10586i −0.833229 0.552928i \(-0.813510\pi\)
0.833229 0.552928i \(-0.186490\pi\)
\(212\) 114.296 36.2189i 0.539133 0.170844i
\(213\) 68.0355 0.319416
\(214\) −5.55797 35.9382i −0.0259718 0.167936i
\(215\) 0 0
\(216\) 18.4663 + 37.2424i 0.0854919 + 0.172419i
\(217\) 13.8606 0.0638737
\(218\) −309.998 + 47.9422i −1.42201 + 0.219918i
\(219\) 80.6813i 0.368408i
\(220\) 0 0
\(221\) 7.74600 0.0350498
\(222\) 26.9762 + 174.430i 0.121515 + 0.785722i
\(223\) 82.7105i 0.370899i −0.982654 0.185450i \(-0.940626\pi\)
0.982654 0.185450i \(-0.0593741\pi\)
\(224\) 7.32758 + 7.59941i 0.0327124 + 0.0339260i
\(225\) 0 0
\(226\) 195.129 30.1774i 0.863403 0.133528i
\(227\) 361.534i 1.59266i −0.604862 0.796330i \(-0.706772\pi\)
0.604862 0.796330i \(-0.293228\pi\)
\(228\) 82.2286 26.0571i 0.360652 0.114286i
\(229\) 121.818 0.531955 0.265977 0.963979i \(-0.414305\pi\)
0.265977 + 0.963979i \(0.414305\pi\)
\(230\) 0 0
\(231\) 11.7091i 0.0506888i
\(232\) −171.418 + 84.9957i −0.738870 + 0.366361i
\(233\) −136.615 −0.586329 −0.293164 0.956062i \(-0.594708\pi\)
−0.293164 + 0.956062i \(0.594708\pi\)
\(234\) −2.47090 + 0.382133i −0.0105594 + 0.00163305i
\(235\) 0 0
\(236\) 29.3999 + 92.7775i 0.124576 + 0.393125i
\(237\) 176.530 0.744853
\(238\) 1.87447 + 12.1204i 0.00787592 + 0.0509262i
\(239\) 56.4632i 0.236248i −0.992999 0.118124i \(-0.962312\pi\)
0.992999 0.118124i \(-0.0376880\pi\)
\(240\) 0 0
\(241\) −2.24158 −0.00930117 −0.00465059 0.999989i \(-0.501480\pi\)
−0.00465059 + 0.999989i \(0.501480\pi\)
\(242\) −590.818 + 91.3720i −2.44140 + 0.377570i
\(243\) 15.5885i 0.0641500i
\(244\) −285.381 + 90.4331i −1.16959 + 0.370627i
\(245\) 0 0
\(246\) −24.7287 159.898i −0.100523 0.649991i
\(247\) 5.18820i 0.0210049i
\(248\) −149.314 301.133i −0.602071 1.21425i
\(249\) 10.2003 0.0409650
\(250\) 0 0
\(251\) 395.809i 1.57693i −0.615081 0.788464i \(-0.710877\pi\)
0.615081 0.788464i \(-0.289123\pi\)
\(252\) −1.19587 3.77383i −0.00474553 0.0149755i
\(253\) 476.036 1.88157
\(254\) −8.28184 53.5510i −0.0326057 0.210831i
\(255\) 0 0
\(256\) 86.1671 241.063i 0.336590 0.941651i
\(257\) −109.778 −0.427151 −0.213576 0.976927i \(-0.568511\pi\)
−0.213576 + 0.976927i \(0.568511\pi\)
\(258\) 190.295 29.4298i 0.737579 0.114069i
\(259\) 16.8091i 0.0648998i
\(260\) 0 0
\(261\) 71.7499 0.274904
\(262\) −1.36272 8.81147i −0.00520124 0.0336316i
\(263\) 327.702i 1.24601i −0.782216 0.623007i \(-0.785911\pi\)
0.782216 0.623007i \(-0.214089\pi\)
\(264\) −254.390 + 126.137i −0.963599 + 0.477790i
\(265\) 0 0
\(266\) −8.11816 + 1.25550i −0.0305194 + 0.00471993i
\(267\) 105.673i 0.395777i
\(268\) 87.9672 + 277.599i 0.328236 + 1.03582i
\(269\) −130.032 −0.483392 −0.241696 0.970352i \(-0.577704\pi\)
−0.241696 + 0.970352i \(0.577704\pi\)
\(270\) 0 0
\(271\) 329.669i 1.21649i 0.793750 + 0.608245i \(0.208126\pi\)
−0.793750 + 0.608245i \(0.791874\pi\)
\(272\) 243.134 171.292i 0.893875 0.629751i
\(273\) 0.238109 0.000872195
\(274\) 359.131 55.5408i 1.31070 0.202704i
\(275\) 0 0
\(276\) 153.426 48.6185i 0.555891 0.176154i
\(277\) −304.124 −1.09792 −0.548960 0.835849i \(-0.684976\pi\)
−0.548960 + 0.835849i \(0.684976\pi\)
\(278\) −68.2930 441.588i −0.245658 1.58844i
\(279\) 126.044i 0.451772i
\(280\) 0 0
\(281\) 240.099 0.854446 0.427223 0.904146i \(-0.359492\pi\)
0.427223 + 0.904146i \(0.359492\pi\)
\(282\) 279.903 43.2879i 0.992563 0.153503i
\(283\) 86.6730i 0.306265i 0.988206 + 0.153133i \(0.0489362\pi\)
−0.988206 + 0.153133i \(0.951064\pi\)
\(284\) 47.4635 + 149.781i 0.167125 + 0.527398i
\(285\) 0 0
\(286\) −2.61022 16.8779i −0.00912664 0.0590135i
\(287\) 15.4086i 0.0536886i
\(288\) −69.1070 + 66.6350i −0.239955 + 0.231372i
\(289\) 56.5280 0.195599
\(290\) 0 0
\(291\) 165.487i 0.568683i
\(292\) 177.621 56.2856i 0.608290 0.192759i
\(293\) −390.339 −1.33222 −0.666108 0.745855i \(-0.732041\pi\)
−0.666108 + 0.745855i \(0.732041\pi\)
\(294\) −25.8850 167.374i −0.0880442 0.569300i
\(295\) 0 0
\(296\) −365.191 + 181.076i −1.23375 + 0.611743i
\(297\) 106.479 0.358517
\(298\) 244.824 37.8629i 0.821557 0.127057i
\(299\) 9.68038i 0.0323759i
\(300\) 0 0
\(301\) −18.3379 −0.0609233
\(302\) 23.2605 + 150.404i 0.0770216 + 0.498027i
\(303\) 281.761i 0.929906i
\(304\) 114.730 + 162.849i 0.377401 + 0.535687i
\(305\) 0 0
\(306\) −110.220 + 17.0459i −0.360196 + 0.0557056i
\(307\) 60.2318i 0.196195i 0.995177 + 0.0980973i \(0.0312757\pi\)
−0.995177 + 0.0980973i \(0.968724\pi\)
\(308\) 25.7777 8.16860i 0.0836939 0.0265214i
\(309\) −274.003 −0.886741
\(310\) 0 0
\(311\) 106.594i 0.342747i 0.985206 + 0.171373i \(0.0548205\pi\)
−0.985206 + 0.171373i \(0.945180\pi\)
\(312\) −2.56504 5.17312i −0.00822127 0.0165805i
\(313\) 46.2243 0.147682 0.0738408 0.997270i \(-0.476474\pi\)
0.0738408 + 0.997270i \(0.476474\pi\)
\(314\) −67.7823 + 10.4828i −0.215867 + 0.0333846i
\(315\) 0 0
\(316\) 123.152 + 388.633i 0.389723 + 1.22985i
\(317\) 8.36780 0.0263969 0.0131984 0.999913i \(-0.495799\pi\)
0.0131984 + 0.999913i \(0.495799\pi\)
\(318\) −15.8697 102.614i −0.0499046 0.322687i
\(319\) 490.099i 1.53636i
\(320\) 0 0
\(321\) −31.4934 −0.0981103
\(322\) −15.1472 + 2.34257i −0.0470411 + 0.00727507i
\(323\) 231.432i 0.716506i
\(324\) 34.3182 10.8749i 0.105920 0.0335646i
\(325\) 0 0
\(326\) 50.6006 + 327.187i 0.155217 + 1.00364i
\(327\) 271.658i 0.830757i
\(328\) 334.765 165.990i 1.02063 0.506066i
\(329\) −26.9730 −0.0819847
\(330\) 0 0
\(331\) 111.072i 0.335564i −0.985824 0.167782i \(-0.946339\pi\)
0.985824 0.167782i \(-0.0536605\pi\)
\(332\) 7.11600 + 22.4560i 0.0214337 + 0.0676386i
\(333\) 152.857 0.459030
\(334\) −25.5562 165.248i −0.0765156 0.494755i
\(335\) 0 0
\(336\) 7.47385 5.26546i 0.0222436 0.0156710i
\(337\) 231.853 0.687990 0.343995 0.938972i \(-0.388220\pi\)
0.343995 + 0.938972i \(0.388220\pi\)
\(338\) −333.686 + 51.6057i −0.987236 + 0.152679i
\(339\) 170.996i 0.504412i
\(340\) 0 0
\(341\) −860.966 −2.52483
\(342\) −11.4172 73.8244i −0.0333836 0.215861i
\(343\) 32.2941i 0.0941518i
\(344\) 197.546 + 398.406i 0.574260 + 1.15816i
\(345\) 0 0
\(346\) −381.266 + 58.9642i −1.10193 + 0.170417i
\(347\) 402.088i 1.15875i 0.815059 + 0.579377i \(0.196704\pi\)
−0.815059 + 0.579377i \(0.803296\pi\)
\(348\) 50.0548 + 157.958i 0.143835 + 0.453903i
\(349\) −163.284 −0.467864 −0.233932 0.972253i \(-0.575159\pi\)
−0.233932 + 0.972253i \(0.575159\pi\)
\(350\) 0 0
\(351\) 2.16530i 0.00616894i
\(352\) −455.161 472.046i −1.29307 1.34104i
\(353\) −175.851 −0.498161 −0.249081 0.968483i \(-0.580128\pi\)
−0.249081 + 0.968483i \(0.580128\pi\)
\(354\) 83.2951 12.8819i 0.235297 0.0363895i
\(355\) 0 0
\(356\) −232.639 + 73.7201i −0.653481 + 0.207079i
\(357\) 10.6214 0.0297518
\(358\) −36.9678 239.037i −0.103262 0.667700i
\(359\) 345.628i 0.962753i 0.876514 + 0.481377i \(0.159863\pi\)
−0.876514 + 0.481377i \(0.840137\pi\)
\(360\) 0 0
\(361\) 205.989 0.570607
\(362\) −212.638 + 32.8852i −0.587398 + 0.0908431i
\(363\) 517.746i 1.42630i
\(364\) 0.166112 + 0.524200i 0.000456351 + 0.00144011i
\(365\) 0 0
\(366\) 39.6242 + 256.213i 0.108263 + 0.700035i
\(367\) 728.998i 1.98637i 0.116546 + 0.993185i \(0.462818\pi\)
−0.116546 + 0.993185i \(0.537182\pi\)
\(368\) 214.068 + 303.851i 0.581707 + 0.825682i
\(369\) −140.122 −0.379734
\(370\) 0 0
\(371\) 9.88848i 0.0266536i
\(372\) −277.488 + 87.9321i −0.745936 + 0.236377i
\(373\) 46.6749 0.125134 0.0625668 0.998041i \(-0.480071\pi\)
0.0625668 + 0.998041i \(0.480071\pi\)
\(374\) −116.435 752.875i −0.311323 2.01303i
\(375\) 0 0
\(376\) 290.567 + 586.010i 0.772784 + 1.55854i
\(377\) −9.96635 −0.0264360
\(378\) −3.38812 + 0.523984i −0.00896328 + 0.00138620i
\(379\) 117.629i 0.310368i 0.987886 + 0.155184i \(0.0495970\pi\)
−0.987886 + 0.155184i \(0.950403\pi\)
\(380\) 0 0
\(381\) −46.9278 −0.123170
\(382\) 85.4985 + 552.839i 0.223818 + 1.44722i
\(383\) 251.669i 0.657100i −0.944487 0.328550i \(-0.893440\pi\)
0.944487 0.328550i \(-0.106560\pi\)
\(384\) −194.909 105.653i −0.507575 0.275139i
\(385\) 0 0
\(386\) 202.658 31.3418i 0.525022 0.0811964i
\(387\) 166.760i 0.430904i
\(388\) −364.321 + 115.448i −0.938970 + 0.297547i
\(389\) 356.890 0.917454 0.458727 0.888577i \(-0.348306\pi\)
0.458727 + 0.888577i \(0.348306\pi\)
\(390\) 0 0
\(391\) 431.815i 1.10439i
\(392\) 350.418 173.751i 0.893923 0.443242i
\(393\) −7.72168 −0.0196480
\(394\) −77.0108 + 11.9100i −0.195459 + 0.0302284i
\(395\) 0 0
\(396\) 74.2830 + 234.416i 0.187583 + 0.591958i
\(397\) 103.819 0.261508 0.130754 0.991415i \(-0.458260\pi\)
0.130754 + 0.991415i \(0.458260\pi\)
\(398\) −45.1314 291.823i −0.113396 0.733224i
\(399\) 7.11412i 0.0178299i
\(400\) 0 0
\(401\) −121.598 −0.303237 −0.151618 0.988439i \(-0.548449\pi\)
−0.151618 + 0.988439i \(0.548449\pi\)
\(402\) 249.227 38.5438i 0.619967 0.0958800i
\(403\) 17.5081i 0.0434444i
\(404\) 620.301 196.565i 1.53540 0.486546i
\(405\) 0 0
\(406\) −2.41177 15.5947i −0.00594033 0.0384106i
\(407\) 1044.11i 2.56539i
\(408\) −114.419 230.759i −0.280439 0.565585i
\(409\) 182.788 0.446915 0.223457 0.974714i \(-0.428266\pi\)
0.223457 + 0.974714i \(0.428266\pi\)
\(410\) 0 0
\(411\) 314.714i 0.765727i
\(412\) −191.152 603.221i −0.463962 1.46413i
\(413\) −8.02677 −0.0194353
\(414\) −21.3027 137.745i −0.0514558 0.332717i
\(415\) 0 0
\(416\) 9.59924 9.25587i 0.0230751 0.0222497i
\(417\) −386.972 −0.927991
\(418\) 504.269 77.9869i 1.20638 0.186572i
\(419\) 168.020i 0.401003i 0.979693 + 0.200502i \(0.0642572\pi\)
−0.979693 + 0.200502i \(0.935743\pi\)
\(420\) 0 0
\(421\) 625.291 1.48525 0.742626 0.669706i \(-0.233580\pi\)
0.742626 + 0.669706i \(0.233580\pi\)
\(422\) −71.3244 461.189i −0.169015 1.09286i
\(423\) 245.285i 0.579869i
\(424\) 214.836 106.524i 0.506688 0.251236i
\(425\) 0 0
\(426\) 134.472 20.7966i 0.315663 0.0488184i
\(427\) 24.6901i 0.0578222i
\(428\) −21.9707 69.3331i −0.0513334 0.161993i
\(429\) −14.7904 −0.0344765
\(430\) 0 0
\(431\) 133.413i 0.309544i 0.987950 + 0.154772i \(0.0494643\pi\)
−0.987950 + 0.154772i \(0.950536\pi\)
\(432\) 47.8826 + 67.9651i 0.110839 + 0.157327i
\(433\) −706.716 −1.63214 −0.816069 0.577954i \(-0.803851\pi\)
−0.816069 + 0.577954i \(0.803851\pi\)
\(434\) 27.3955 4.23681i 0.0631233 0.00976223i
\(435\) 0 0
\(436\) −598.057 + 189.516i −1.37169 + 0.434670i
\(437\) −289.226 −0.661844
\(438\) −24.6621 159.467i −0.0563062 0.364080i
\(439\) 507.488i 1.15601i −0.816033 0.578005i \(-0.803831\pi\)
0.816033 0.578005i \(-0.196169\pi\)
\(440\) 0 0
\(441\) −146.674 −0.332593
\(442\) 15.3100 2.36774i 0.0346380 0.00535689i
\(443\) 412.172i 0.930410i 0.885203 + 0.465205i \(0.154019\pi\)
−0.885203 + 0.465205i \(0.845981\pi\)
\(444\) 106.637 + 336.516i 0.240174 + 0.757919i
\(445\) 0 0
\(446\) −25.2824 163.478i −0.0566869 0.366542i
\(447\) 214.544i 0.479965i
\(448\) 16.8059 + 12.7804i 0.0375132 + 0.0285277i
\(449\) −808.617 −1.80093 −0.900465 0.434929i \(-0.856773\pi\)
−0.900465 + 0.434929i \(0.856773\pi\)
\(450\) 0 0
\(451\) 957.124i 2.12223i
\(452\) 376.449 119.291i 0.832852 0.263919i
\(453\) 131.802 0.290955
\(454\) −110.511 714.573i −0.243417 1.57395i
\(455\) 0 0
\(456\) 154.560 76.6370i 0.338948 0.168064i
\(457\) −472.873 −1.03473 −0.517367 0.855764i \(-0.673088\pi\)
−0.517367 + 0.855764i \(0.673088\pi\)
\(458\) 240.773 37.2364i 0.525705 0.0813021i
\(459\) 96.5881i 0.210432i
\(460\) 0 0
\(461\) 433.776 0.940946 0.470473 0.882414i \(-0.344083\pi\)
0.470473 + 0.882414i \(0.344083\pi\)
\(462\) −3.57916 23.1431i −0.00774709 0.0500933i
\(463\) 530.624i 1.14606i 0.819536 + 0.573028i \(0.194231\pi\)
−0.819536 + 0.573028i \(0.805769\pi\)
\(464\) −312.827 + 220.392i −0.674196 + 0.474983i
\(465\) 0 0
\(466\) −270.019 + 41.7594i −0.579440 + 0.0896124i
\(467\) 355.266i 0.760741i −0.924834 0.380370i \(-0.875797\pi\)
0.924834 0.380370i \(-0.124203\pi\)
\(468\) −4.76693 + 1.51057i −0.0101857 + 0.00322772i
\(469\) −24.0168 −0.0512086
\(470\) 0 0
\(471\) 59.3990i 0.126113i
\(472\) 86.4686 + 174.388i 0.183196 + 0.369467i
\(473\) 1139.08 2.40820
\(474\) 348.912 53.9605i 0.736102 0.113841i
\(475\) 0 0
\(476\) 7.40978 + 23.3831i 0.0155668 + 0.0491242i
\(477\) −89.9232 −0.188518
\(478\) −17.2593 111.600i −0.0361072 0.233472i
\(479\) 548.640i 1.14539i 0.819770 + 0.572693i \(0.194101\pi\)
−0.819770 + 0.572693i \(0.805899\pi\)
\(480\) 0 0
\(481\) −21.2324 −0.0441423
\(482\) −4.43050 + 0.685191i −0.00919190 + 0.00142156i
\(483\) 13.2738i 0.0274821i
\(484\) −1139.82 + 361.194i −2.35501 + 0.746269i
\(485\) 0 0
\(486\) −4.76497 30.8106i −0.00980446 0.0633964i
\(487\) 134.618i 0.276422i 0.990403 + 0.138211i \(0.0441352\pi\)
−0.990403 + 0.138211i \(0.955865\pi\)
\(488\) −536.412 + 265.974i −1.09921 + 0.545029i
\(489\) 286.721 0.586341
\(490\) 0 0
\(491\) 756.810i 1.54136i −0.637220 0.770682i \(-0.719916\pi\)
0.637220 0.770682i \(-0.280084\pi\)
\(492\) −97.7529 308.480i −0.198685 0.626991i
\(493\) −444.572 −0.901768
\(494\) 1.58589 + 10.2545i 0.00321031 + 0.0207581i
\(495\) 0 0
\(496\) −387.167 549.549i −0.780579 1.10796i
\(497\) −12.9585 −0.0260734
\(498\) 20.1609 3.11795i 0.0404837 0.00626094i
\(499\) 706.956i 1.41675i 0.705838 + 0.708373i \(0.250570\pi\)
−0.705838 + 0.708373i \(0.749430\pi\)
\(500\) 0 0
\(501\) −144.811 −0.289043
\(502\) −120.988 782.318i −0.241012 1.55840i
\(503\) 100.567i 0.199935i −0.994991 0.0999673i \(-0.968126\pi\)
0.994991 0.0999673i \(-0.0318738\pi\)
\(504\) −3.51720 7.09344i −0.00697858 0.0140743i
\(505\) 0 0
\(506\) 940.887 145.511i 1.85946 0.287572i
\(507\) 292.416i 0.576757i
\(508\) −32.7382 103.312i −0.0644452 0.203370i
\(509\) 753.185 1.47973 0.739867 0.672753i \(-0.234888\pi\)
0.739867 + 0.672753i \(0.234888\pi\)
\(510\) 0 0
\(511\) 15.3671i 0.0300726i
\(512\) 96.6232 502.800i 0.188717 0.982031i
\(513\) −64.6938 −0.126109
\(514\) −216.976 + 33.5561i −0.422133 + 0.0652843i
\(515\) 0 0
\(516\) 367.124 116.336i 0.711480 0.225458i
\(517\) 1675.46 3.24073
\(518\) −5.13807 33.2231i −0.00991906 0.0641373i
\(519\) 334.112i 0.643761i
\(520\) 0 0
\(521\) 117.708 0.225926 0.112963 0.993599i \(-0.463966\pi\)
0.112963 + 0.993599i \(0.463966\pi\)
\(522\) 141.814 21.9320i 0.271674 0.0420153i
\(523\) 617.411i 1.18052i −0.807214 0.590259i \(-0.799026\pi\)
0.807214 0.590259i \(-0.200974\pi\)
\(524\) −5.38686 16.9994i −0.0102803 0.0324415i
\(525\) 0 0
\(526\) −100.170 647.704i −0.190437 1.23138i
\(527\) 780.988i 1.48195i
\(528\) −464.246 + 327.070i −0.879254 + 0.619450i
\(529\) −10.6508 −0.0201338
\(530\) 0 0
\(531\) 72.9932i 0.137464i
\(532\) −15.6618 + 4.96301i −0.0294395 + 0.00932896i
\(533\) 19.4635 0.0365169
\(534\) 32.3012 + 208.862i 0.0604892 + 0.391127i
\(535\) 0 0
\(536\) 258.722 + 521.786i 0.482690 + 0.973481i
\(537\) −209.473 −0.390079
\(538\) −257.009 + 39.7474i −0.477713 + 0.0738799i
\(539\) 1001.88i 1.85877i
\(540\) 0 0
\(541\) 352.762 0.652056 0.326028 0.945360i \(-0.394290\pi\)
0.326028 + 0.945360i \(0.394290\pi\)
\(542\) 100.771 + 651.591i 0.185924 + 1.20220i
\(543\) 186.339i 0.343166i
\(544\) 428.196 412.879i 0.787125 0.758969i
\(545\) 0 0
\(546\) 0.470623 0.0727835i 0.000861948 0.000133303i
\(547\) 295.110i 0.539507i −0.962929 0.269753i \(-0.913058\pi\)
0.962929 0.269753i \(-0.0869422\pi\)
\(548\) 692.846 219.553i 1.26432 0.400644i
\(549\) 224.525 0.408970
\(550\) 0 0
\(551\) 297.770i 0.540418i
\(552\) 288.385 142.993i 0.522437 0.259045i
\(553\) −33.6231 −0.0608013
\(554\) −601.102 + 92.9624i −1.08502 + 0.167802i
\(555\) 0 0
\(556\) −269.963 851.924i −0.485545 1.53224i
\(557\) −31.8538 −0.0571882 −0.0285941 0.999591i \(-0.509103\pi\)
−0.0285941 + 0.999591i \(0.509103\pi\)
\(558\) 38.5284 + 249.127i 0.0690473 + 0.446465i
\(559\) 23.1636i 0.0414376i
\(560\) 0 0
\(561\) −659.760 −1.17604
\(562\) 474.557 73.3919i 0.844408 0.130591i
\(563\) 906.668i 1.61042i 0.592988 + 0.805211i \(0.297948\pi\)
−0.592988 + 0.805211i \(0.702052\pi\)
\(564\) 539.997 171.117i 0.957441 0.303400i
\(565\) 0 0
\(566\) 26.4936 + 171.310i 0.0468085 + 0.302667i
\(567\) 2.96908i 0.00523647i
\(568\) 139.596 + 281.534i 0.245767 + 0.495659i
\(569\) −465.009 −0.817239 −0.408620 0.912705i \(-0.633990\pi\)
−0.408620 + 0.912705i \(0.633990\pi\)
\(570\) 0 0
\(571\) 265.895i 0.465666i −0.972517 0.232833i \(-0.925200\pi\)
0.972517 0.232833i \(-0.0747995\pi\)
\(572\) −10.3182 32.5613i −0.0180388 0.0569253i
\(573\) 484.464 0.845488
\(574\) 4.71000 + 30.4552i 0.00820557 + 0.0530578i
\(575\) 0 0
\(576\) −116.222 + 152.828i −0.201774 + 0.265327i
\(577\) −138.097 −0.239336 −0.119668 0.992814i \(-0.538183\pi\)
−0.119668 + 0.992814i \(0.538183\pi\)
\(578\) 111.728 17.2791i 0.193301 0.0298946i
\(579\) 177.594i 0.306725i
\(580\) 0 0
\(581\) −1.94281 −0.00334391
\(582\) 50.5848 + 327.085i 0.0869154 + 0.562001i
\(583\) 614.234i 1.05358i
\(584\) 333.863 165.542i 0.571683 0.283463i
\(585\) 0 0
\(586\) −771.507 + 119.316i −1.31656 + 0.203611i
\(587\) 648.473i 1.10472i −0.833604 0.552362i \(-0.813727\pi\)
0.833604 0.552362i \(-0.186273\pi\)
\(588\) −102.324 322.903i −0.174020 0.549155i
\(589\) 523.098 0.888113
\(590\) 0 0
\(591\) 67.4862i 0.114190i
\(592\) −666.451 + 469.526i −1.12576 + 0.793118i
\(593\) 350.392 0.590880 0.295440 0.955361i \(-0.404534\pi\)
0.295440 + 0.955361i \(0.404534\pi\)
\(594\) 210.457 32.5479i 0.354304 0.0547944i
\(595\) 0 0
\(596\) 472.322 149.672i 0.792486 0.251128i
\(597\) −255.731 −0.428359
\(598\) 2.95903 + 19.1333i 0.00494821 + 0.0319955i
\(599\) 276.745i 0.462012i −0.972952 0.231006i \(-0.925798\pi\)
0.972952 0.231006i \(-0.0742017\pi\)
\(600\) 0 0
\(601\) 815.487 1.35688 0.678442 0.734654i \(-0.262656\pi\)
0.678442 + 0.734654i \(0.262656\pi\)
\(602\) −36.2449 + 5.60540i −0.0602075 + 0.00931130i
\(603\) 218.403i 0.362193i
\(604\) 91.9490 + 290.164i 0.152233 + 0.480405i
\(605\) 0 0
\(606\) −86.1269 556.902i −0.142124 0.918981i
\(607\) 247.049i 0.407001i 0.979075 + 0.203500i \(0.0652318\pi\)
−0.979075 + 0.203500i \(0.934768\pi\)
\(608\) 276.543 + 286.802i 0.454840 + 0.471713i
\(609\) −13.6660 −0.0224400
\(610\) 0 0
\(611\) 34.0710i 0.0557627i
\(612\) −212.640 + 67.3825i −0.347450 + 0.110102i
\(613\) −1005.15 −1.63972 −0.819862 0.572561i \(-0.805950\pi\)
−0.819862 + 0.572561i \(0.805950\pi\)
\(614\) 18.4112 + 119.048i 0.0299857 + 0.193890i
\(615\) 0 0
\(616\) 48.4528 24.0248i 0.0786572 0.0390013i
\(617\) −533.282 −0.864314 −0.432157 0.901798i \(-0.642247\pi\)
−0.432157 + 0.901798i \(0.642247\pi\)
\(618\) −541.568 + 83.7553i −0.876324 + 0.135526i
\(619\) 1136.85i 1.83659i −0.395900 0.918294i \(-0.629567\pi\)
0.395900 0.918294i \(-0.370433\pi\)
\(620\) 0 0
\(621\) −120.709 −0.194378
\(622\) 32.5830 + 210.684i 0.0523842 + 0.338720i
\(623\) 20.1271i 0.0323067i
\(624\) −6.65109 9.44063i −0.0106588 0.0151292i
\(625\) 0 0
\(626\) 91.3625 14.1295i 0.145946 0.0225711i
\(627\) 441.901i 0.704787i
\(628\) −130.768 + 41.4384i −0.208229 + 0.0659847i
\(629\) −947.121 −1.50576
\(630\) 0 0
\(631\) 936.738i 1.48453i 0.670107 + 0.742265i \(0.266248\pi\)
−0.670107 + 0.742265i \(0.733752\pi\)
\(632\) 362.206 + 730.490i 0.573110 + 1.15584i
\(633\) −404.149 −0.638466
\(634\) 16.5390 2.55781i 0.0260867 0.00403440i
\(635\) 0 0
\(636\) −62.7329 197.967i −0.0986366 0.311269i
\(637\) 20.3735 0.0319836
\(638\) 149.810 + 968.682i 0.234812 + 1.51831i
\(639\) 117.841i 0.184415i
\(640\) 0 0
\(641\) 214.558 0.334723 0.167362 0.985896i \(-0.446475\pi\)
0.167362 + 0.985896i \(0.446475\pi\)
\(642\) −62.2468 + 9.62669i −0.0969577 + 0.0149948i
\(643\) 786.394i 1.22301i 0.791241 + 0.611504i \(0.209435\pi\)
−0.791241 + 0.611504i \(0.790565\pi\)
\(644\) −29.2225 + 9.26020i −0.0453765 + 0.0143792i
\(645\) 0 0
\(646\) 70.7424 + 457.425i 0.109508 + 0.708088i
\(647\) 316.550i 0.489258i 0.969617 + 0.244629i \(0.0786661\pi\)
−0.969617 + 0.244629i \(0.921334\pi\)
\(648\) 64.5058 31.9845i 0.0995459 0.0493588i
\(649\) 498.592 0.768246
\(650\) 0 0
\(651\) 24.0073i 0.0368775i
\(652\) 200.024 + 631.219i 0.306786 + 0.968127i
\(653\) 516.391 0.790797 0.395399 0.918510i \(-0.370606\pi\)
0.395399 + 0.918510i \(0.370606\pi\)
\(654\) 83.0384 + 536.932i 0.126970 + 0.820997i
\(655\) 0 0
\(656\) 610.926 430.408i 0.931290 0.656110i
\(657\) −139.744 −0.212700
\(658\) −53.3121 + 8.24491i −0.0810215 + 0.0125303i
\(659\) 285.118i 0.432653i −0.976321 0.216326i \(-0.930592\pi\)
0.976321 0.216326i \(-0.0694076\pi\)
\(660\) 0 0
\(661\) −391.847 −0.592809 −0.296405 0.955062i \(-0.595788\pi\)
−0.296405 + 0.955062i \(0.595788\pi\)
\(662\) −33.9516 219.534i −0.0512865 0.331622i
\(663\) 13.4165i 0.0202360i
\(664\) 20.9290 + 42.2092i 0.0315196 + 0.0635681i
\(665\) 0 0
\(666\) 302.122 46.7242i 0.453637 0.0701565i
\(667\) 555.593i 0.832973i
\(668\) −101.024 318.802i −0.151233 0.477248i
\(669\) −143.259 −0.214139
\(670\) 0 0
\(671\) 1533.65i 2.28562i
\(672\) 13.1626 12.6917i 0.0195872 0.0188865i
\(673\) −1213.59 −1.80325 −0.901626 0.432517i \(-0.857625\pi\)
−0.901626 + 0.432517i \(0.857625\pi\)
\(674\) 458.257 70.8711i 0.679907 0.105150i
\(675\) 0 0
\(676\) −643.756 + 203.997i −0.952303 + 0.301771i
\(677\) 251.863 0.372028 0.186014 0.982547i \(-0.440443\pi\)
0.186014 + 0.982547i \(0.440443\pi\)
\(678\) −52.2688 337.974i −0.0770926 0.498486i
\(679\) 31.5197i 0.0464207i
\(680\) 0 0
\(681\) −626.195 −0.919523
\(682\) −1701.70 + 263.174i −2.49517 + 0.385886i
\(683\) 664.793i 0.973342i −0.873585 0.486671i \(-0.838211\pi\)
0.873585 0.486671i \(-0.161789\pi\)
\(684\) −45.1322 142.424i −0.0659828 0.208222i
\(685\) 0 0
\(686\) 9.87143 + 63.8293i 0.0143898 + 0.0930457i
\(687\) 210.994i 0.307124i
\(688\) 512.231 + 727.067i 0.744522 + 1.05678i
\(689\) 12.4907 0.0181287
\(690\) 0 0
\(691\) 654.347i 0.946957i 0.880805 + 0.473479i \(0.157002\pi\)
−0.880805 + 0.473479i \(0.842998\pi\)
\(692\) −735.551 + 233.086i −1.06293 + 0.336829i
\(693\) −20.2808 −0.0292652
\(694\) 122.907 + 794.728i 0.177100 + 1.14514i
\(695\) 0 0
\(696\) 147.217 + 296.904i 0.211519 + 0.426587i
\(697\) 868.213 1.24564
\(698\) −322.732 + 49.9117i −0.462367 + 0.0715067i
\(699\) 236.623i 0.338517i
\(700\) 0 0
\(701\) −1266.25 −1.80635 −0.903174 0.429275i \(-0.858769\pi\)
−0.903174 + 0.429275i \(0.858769\pi\)
\(702\) 0.661874 + 4.27972i 0.000942840 + 0.00609647i
\(703\) 634.373i 0.902380i
\(704\) −1043.92 793.870i −1.48284 1.12766i
\(705\) 0 0
\(706\) −347.570 + 53.7529i −0.492309 + 0.0761372i
\(707\) 53.6661i 0.0759068i
\(708\) 160.695 50.9221i 0.226971 0.0719239i
\(709\) −493.220 −0.695656 −0.347828 0.937558i \(-0.613081\pi\)
−0.347828 + 0.937558i \(0.613081\pi\)
\(710\) 0 0
\(711\) 305.759i 0.430041i
\(712\) −437.278 + 216.819i −0.614154 + 0.304522i
\(713\) 976.020 1.36889
\(714\) 20.9932 3.24667i 0.0294023 0.00454716i
\(715\) 0 0
\(716\) −146.134 461.156i −0.204098 0.644073i
\(717\) −97.7971 −0.136398
\(718\) 105.649 + 683.135i 0.147144 + 0.951442i
\(719\) 60.3910i 0.0839930i −0.999118 0.0419965i \(-0.986628\pi\)
0.999118 0.0419965i \(-0.0133718\pi\)
\(720\) 0 0
\(721\) 52.1884 0.0723834
\(722\) 407.138 62.9653i 0.563904 0.0872096i
\(723\) 3.88254i 0.00537003i
\(724\) −410.228 + 129.995i −0.566613 + 0.179552i
\(725\) 0 0
\(726\) 158.261 + 1023.33i 0.217990 + 1.40954i
\(727\) 994.690i 1.36821i −0.729383 0.684106i \(-0.760193\pi\)
0.729383 0.684106i \(-0.239807\pi\)
\(728\) 0.488554 + 0.985307i 0.000671090 + 0.00135344i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 1033.27i 1.41350i
\(732\) 156.635 + 494.294i 0.213982 + 0.675264i
\(733\) 1167.65 1.59298 0.796488 0.604654i \(-0.206689\pi\)
0.796488 + 0.604654i \(0.206689\pi\)
\(734\) 222.835 + 1440.87i 0.303590 + 1.96303i
\(735\) 0 0
\(736\) 515.986 + 535.127i 0.701067 + 0.727075i
\(737\) 1491.83 2.02420
\(738\) −276.951 + 42.8314i −0.375273 + 0.0580372i
\(739\) 79.9863i 0.108236i 0.998535 + 0.0541179i \(0.0172347\pi\)
−0.998535 + 0.0541179i \(0.982765\pi\)
\(740\) 0 0
\(741\) 8.98623 0.0121272
\(742\) 3.02264 + 19.5446i 0.00407364 + 0.0263405i
\(743\) 402.122i 0.541214i −0.962690 0.270607i \(-0.912776\pi\)
0.962690 0.270607i \(-0.0872244\pi\)
\(744\) −521.578 + 258.619i −0.701045 + 0.347606i
\(745\) 0 0
\(746\) 92.2530 14.2672i 0.123664 0.0191250i
\(747\) 17.6674i 0.0236511i
\(748\) −460.267 1452.47i −0.615330 1.94180i
\(749\) 5.99844 0.00800860
\(750\) 0 0
\(751\) 58.7486i 0.0782271i 0.999235 + 0.0391136i \(0.0124534\pi\)
−0.999235 + 0.0391136i \(0.987547\pi\)
\(752\) 753.434 + 1069.43i 1.00191 + 1.42212i
\(753\) −685.561 −0.910440
\(754\) −19.6985 + 3.04644i −0.0261254 + 0.00404038i
\(755\) 0 0
\(756\) −6.53646 + 2.07131i −0.00864611 + 0.00273983i
\(757\) −1040.91 −1.37504 −0.687522 0.726164i \(-0.741301\pi\)
−0.687522 + 0.726164i \(0.741301\pi\)
\(758\) 35.9561 + 232.495i 0.0474355 + 0.306721i
\(759\) 824.519i 1.08632i
\(760\) 0 0
\(761\) 750.095 0.985670 0.492835 0.870123i \(-0.335961\pi\)
0.492835 + 0.870123i \(0.335961\pi\)
\(762\) −92.7530 + 14.3446i −0.121723 + 0.0188249i
\(763\) 51.7417i 0.0678135i
\(764\) 337.976 + 1066.55i 0.442377 + 1.39601i
\(765\) 0 0
\(766\) −76.9285 497.425i −0.100429 0.649380i
\(767\) 10.1391i 0.0132191i
\(768\) −417.533 149.246i −0.543663 0.194331i
\(769\) 1065.98 1.38619 0.693094 0.720847i \(-0.256247\pi\)
0.693094 + 0.720847i \(0.256247\pi\)
\(770\) 0 0
\(771\) 190.141i 0.246616i
\(772\) 390.975 123.894i 0.506444 0.160485i
\(773\) −947.271 −1.22545 −0.612724 0.790297i \(-0.709926\pi\)
−0.612724 + 0.790297i \(0.709926\pi\)
\(774\) −50.9740 329.601i −0.0658579 0.425842i
\(775\) 0 0
\(776\) −684.791 + 339.546i −0.882463 + 0.437560i
\(777\) −29.1141 −0.0374699
\(778\) 705.393 109.092i 0.906675 0.140220i
\(779\) 581.521i 0.746497i
\(780\) 0 0
\(781\) 804.931 1.03064
\(782\) 131.994 + 853.484i 0.168791 + 1.09141i
\(783\) 124.275i 0.158716i
\(784\) 639.491 450.533i 0.815678 0.574659i
\(785\) 0 0
\(786\) −15.2619 + 2.36031i −0.0194172 + 0.00300294i
\(787\) 11.5874i 0.0147236i 0.999973 + 0.00736178i \(0.00234335\pi\)
−0.999973 + 0.00736178i \(0.997657\pi\)
\(788\) −148.572 + 47.0803i −0.188543 + 0.0597465i
\(789\) −567.596 −0.719387
\(790\) 0 0
\(791\) 32.5690i 0.0411744i
\(792\) 218.475 + 440.617i 0.275852 + 0.556334i
\(793\) −31.1874 −0.0393284
\(794\) 205.198 31.7345i 0.258436 0.0399679i
\(795\) 0 0
\(796\) −178.405 562.994i −0.224127 0.707278i
\(797\) −780.220 −0.978946 −0.489473 0.872018i \(-0.662811\pi\)
−0.489473 + 0.872018i \(0.662811\pi\)
\(798\) 2.17459 + 14.0611i 0.00272505 + 0.0176204i
\(799\) 1519.82i 1.90215i
\(800\) 0 0
\(801\) 183.030 0.228502
\(802\) −240.339 + 37.1692i −0.299674 + 0.0463457i
\(803\) 954.545i 1.18872i
\(804\) 480.815 152.364i 0.598029 0.189507i
\(805\) 0 0
\(806\) −5.35175 34.6048i −0.00663989 0.0429340i
\(807\) 225.223i 0.279086i
\(808\) 1165.94 578.120i 1.44300 0.715495i
\(809\) −1061.80 −1.31249 −0.656243 0.754549i \(-0.727855\pi\)
−0.656243 + 0.754549i \(0.727855\pi\)
\(810\) 0 0
\(811\) 309.236i 0.381302i 0.981658 + 0.190651i \(0.0610599\pi\)
−0.981658 + 0.190651i \(0.938940\pi\)
\(812\) −9.53376 30.0858i −0.0117411 0.0370514i
\(813\) 571.003 0.702341
\(814\) 319.157 + 2063.69i 0.392085 + 2.53525i
\(815\) 0 0
\(816\) −296.687 421.121i −0.363587 0.516079i
\(817\) −692.072 −0.847089
\(818\) 361.281 55.8734i 0.441664 0.0683049i
\(819\) 0.412417i 0.000503562i
\(820\) 0 0
\(821\) −1156.76 −1.40897 −0.704483 0.709721i \(-0.748821\pi\)
−0.704483 + 0.709721i \(0.748821\pi\)
\(822\) −96.1995 622.033i −0.117031 0.756731i
\(823\) 1441.89i 1.75200i −0.482314 0.875998i \(-0.660204\pi\)
0.482314 0.875998i \(-0.339796\pi\)
\(824\) −562.201 1133.84i −0.682283 1.37602i
\(825\) 0 0
\(826\) −15.8649 + 2.45357i −0.0192069 + 0.00297042i
\(827\) 367.599i 0.444497i 0.974990 + 0.222249i \(0.0713397\pi\)
−0.974990 + 0.222249i \(0.928660\pi\)
\(828\) −84.2097 265.741i −0.101703 0.320944i
\(829\) 172.743 0.208375 0.104188 0.994558i \(-0.466776\pi\)
0.104188 + 0.994558i \(0.466776\pi\)
\(830\) 0 0
\(831\) 526.758i 0.633884i
\(832\) 16.1437 21.2285i 0.0194034 0.0255150i
\(833\) 908.808 1.09101
\(834\) −764.852 + 118.287i −0.917089 + 0.141831i
\(835\) 0 0
\(836\) 972.850 308.283i 1.16370 0.368759i
\(837\) 218.315 0.260831
\(838\) 51.3593 + 332.093i 0.0612879 + 0.396292i
\(839\) 1083.17i 1.29103i −0.763748 0.645514i \(-0.776643\pi\)
0.763748 0.645514i \(-0.223357\pi\)
\(840\) 0 0
\(841\) −268.994 −0.319850
\(842\) 1235.89 191.135i 1.46780 0.227001i
\(843\) 415.864i 0.493315i
\(844\) −281.946 889.739i −0.334059 1.05419i
\(845\) 0 0
\(846\) −74.9769 484.806i −0.0886252 0.573057i
\(847\) 98.6133i 0.116427i
\(848\) 392.062 276.214i 0.462337 0.325724i
\(849\) 150.122 0.176822
\(850\) 0 0
\(851\) 1183.64i 1.39088i
\(852\) 259.428 82.2092i 0.304493 0.0964896i
\(853\) 1218.00 1.42790 0.713951 0.700196i \(-0.246904\pi\)
0.713951 + 0.700196i \(0.246904\pi\)
\(854\) −7.54709 48.8000i −0.00883734 0.0571429i
\(855\) 0 0
\(856\) −64.6184 130.321i −0.0754888 0.152244i
\(857\) −207.055 −0.241604 −0.120802 0.992677i \(-0.538547\pi\)
−0.120802 + 0.992677i \(0.538547\pi\)
\(858\) −29.2333 + 4.52103i −0.0340715 + 0.00526927i
\(859\) 1186.36i 1.38109i −0.723290 0.690544i \(-0.757371\pi\)
0.723290 0.690544i \(-0.242629\pi\)
\(860\) 0 0
\(861\) 26.6885 0.0309971
\(862\) 40.7809 + 263.692i 0.0473096 + 0.305907i
\(863\) 885.953i 1.02660i 0.858210 + 0.513298i \(0.171577\pi\)
−0.858210 + 0.513298i \(0.828423\pi\)
\(864\) 115.415 + 119.697i 0.133582 + 0.138538i
\(865\) 0 0
\(866\) −1396.83 + 216.024i −1.61296 + 0.249450i
\(867\) 97.9093i 0.112929i
\(868\) 52.8522 16.7481i 0.0608897 0.0192951i
\(869\) 2088.54 2.40338
\(870\) 0 0
\(871\) 30.3370i 0.0348301i
\(872\) −1124.13 + 557.389i −1.28914 + 0.639207i
\(873\) 286.631 0.328329
\(874\) −571.656 + 88.4086i −0.654069 + 0.101154i
\(875\) 0 0
\(876\) −97.4894 307.648i −0.111289 0.351197i
\(877\) 643.339 0.733567 0.366784 0.930306i \(-0.380459\pi\)
0.366784 + 0.930306i \(0.380459\pi\)
\(878\) −155.125 1003.05i −0.176680 1.14243i
\(879\) 676.088i 0.769155i
\(880\) 0 0
\(881\) 353.918 0.401723 0.200861 0.979620i \(-0.435626\pi\)
0.200861 + 0.979620i \(0.435626\pi\)
\(882\) −289.901 + 44.8341i −0.328686 + 0.0508323i
\(883\) 1093.51i 1.23840i 0.785233 + 0.619200i \(0.212543\pi\)
−0.785233 + 0.619200i \(0.787457\pi\)
\(884\) 29.5365 9.35971i 0.0334123 0.0105879i
\(885\) 0 0
\(886\) 125.990 + 814.659i 0.142201 + 0.919479i
\(887\) 520.234i 0.586510i −0.956034 0.293255i \(-0.905262\pi\)
0.956034 0.293255i \(-0.0947384\pi\)
\(888\) 313.633 + 632.529i 0.353190 + 0.712307i
\(889\) 8.93819 0.0100542
\(890\) 0 0
\(891\) 184.428i 0.206990i
\(892\) −99.9413 315.386i −0.112042 0.353571i
\(893\) −1017.96 −1.13993
\(894\) −65.5804 424.048i −0.0733562 0.474326i
\(895\) 0 0
\(896\) 37.1236 + 20.1234i 0.0414326 + 0.0224592i
\(897\) 16.7669 0.0186922
\(898\) −1598.23 + 247.172i −1.77977 + 0.275248i
\(899\) 1004.85i 1.11775i
\(900\) 0 0
\(901\) 557.175 0.618397
\(902\) −292.567 1891.76i −0.324354 2.09729i
\(903\) 31.7622i 0.0351741i
\(904\) 707.588 350.850i 0.782730 0.388109i
\(905\) 0 0
\(906\) 260.508 40.2884i 0.287536 0.0444685i
\(907\) 567.834i 0.626057i 0.949744 + 0.313029i \(0.101344\pi\)
−0.949744 + 0.313029i \(0.898656\pi\)
\(908\) −436.851 1378.58i −0.481114 1.51825i
\(909\) −488.025 −0.536881
\(910\) 0 0
\(911\) 1180.19i 1.29549i −0.761858 0.647744i \(-0.775713\pi\)
0.761858 0.647744i \(-0.224287\pi\)
\(912\) 282.063 198.718i 0.309279 0.217893i
\(913\) 120.680 0.132180
\(914\) −934.635 + 144.545i −1.02258 + 0.158145i
\(915\) 0 0
\(916\) 464.506 147.196i 0.507103 0.160694i
\(917\) 1.47072 0.00160384
\(918\) 29.5244 + 190.907i 0.0321616 + 0.207959i
\(919\) 54.5449i 0.0593524i −0.999560 0.0296762i \(-0.990552\pi\)
0.999560 0.0296762i \(-0.00944761\pi\)
\(920\) 0 0
\(921\) 104.324 0.113273
\(922\) 857.360 132.594i 0.929892 0.143811i
\(923\) 16.3686i 0.0177341i
\(924\) −14.1484 44.6483i −0.0153122 0.0483207i
\(925\) 0 0
\(926\) 162.197 + 1048.78i 0.175159 + 1.13259i
\(927\) 474.587i 0.511960i
\(928\) −550.936 + 531.228i −0.593681 + 0.572444i
\(929\) 175.428 0.188835 0.0944175 0.995533i \(-0.469901\pi\)
0.0944175 + 0.995533i \(0.469901\pi\)
\(930\) 0 0
\(931\) 608.711i 0.653825i
\(932\) −520.929 + 165.075i −0.558937 + 0.177119i
\(933\) 184.627 0.197885
\(934\) −108.595 702.184i −0.116269 0.751803i
\(935\) 0 0
\(936\) −8.96011 + 4.44277i −0.00957277 + 0.00474655i
\(937\) 335.374 0.357923 0.178962 0.983856i \(-0.442726\pi\)
0.178962 + 0.983856i \(0.442726\pi\)
\(938\) −47.4694 + 7.34130i −0.0506070 + 0.00782654i
\(939\) 80.0629i 0.0852640i
\(940\) 0 0
\(941\) 709.182 0.753647 0.376823 0.926285i \(-0.377016\pi\)
0.376823 + 0.926285i \(0.377016\pi\)
\(942\) 18.1567 + 117.402i 0.0192746 + 0.124631i
\(943\) 1085.03i 1.15061i
\(944\) 224.211 + 318.248i 0.237512 + 0.337127i
\(945\) 0 0
\(946\) 2251.39 348.186i 2.37991 0.368061i
\(947\) 992.486i 1.04803i −0.851708 0.524016i \(-0.824433\pi\)
0.851708 0.524016i \(-0.175567\pi\)
\(948\) 673.132 213.306i 0.710055 0.225007i
\(949\) 19.4110 0.0204542
\(950\) 0 0
\(951\) 14.4935i 0.0152402i
\(952\) 21.7930 + 43.9518i 0.0228919 + 0.0461679i
\(953\) −1438.16 −1.50908 −0.754542 0.656251i \(-0.772141\pi\)
−0.754542 + 0.656251i \(0.772141\pi\)
\(954\) −177.733 + 27.4871i −0.186303 + 0.0288124i
\(955\) 0 0
\(956\) −68.2260 215.301i −0.0713661 0.225211i
\(957\) 848.877 0.887018
\(958\) 167.704 + 1084.39i 0.175057 + 1.13193i
\(959\) 59.9425i 0.0625052i
\(960\) 0 0
\(961\) −804.245 −0.836883
\(962\) −41.9660 + 6.49018i −0.0436237 + 0.00674655i
\(963\) 54.5482i 0.0566440i
\(964\) −8.54744 + 2.70857i −0.00886664 + 0.00280971i
\(965\) 0 0
\(966\) 4.05745 + 26.2358i 0.00420026 + 0.0271592i
\(967\) 1376.32i 1.42329i 0.702539 + 0.711646i \(0.252050\pi\)
−0.702539 + 0.711646i \(0.747950\pi\)
\(968\) −2142.46 + 1062.31i −2.21328 + 1.09743i
\(969\) 400.851 0.413675
\(970\) 0 0
\(971\) 652.667i 0.672159i −0.941834 0.336080i \(-0.890899\pi\)
0.941834 0.336080i \(-0.109101\pi\)
\(972\) −18.8360 59.4408i −0.0193786 0.0611531i
\(973\) 73.7053 0.0757506
\(974\) 41.1490 + 266.072i 0.0422474 + 0.273175i
\(975\) 0 0
\(976\) −978.920 + 689.666i −1.00299 + 0.706625i
\(977\) −467.260 −0.478260 −0.239130 0.970988i \(-0.576862\pi\)
−0.239130 + 0.970988i \(0.576862\pi\)
\(978\) 566.705 87.6428i 0.579453 0.0896143i
\(979\) 1250.22i 1.27703i
\(980\) 0 0
\(981\) 470.525 0.479638
\(982\) −231.336 1495.84i −0.235577 1.52326i
\(983\) 1044.27i 1.06233i 0.847268 + 0.531165i \(0.178246\pi\)
−0.847268 + 0.531165i \(0.821754\pi\)
\(984\) −287.503 579.830i −0.292178 0.589259i
\(985\) 0 0
\(986\) −878.697 + 135.894i −0.891174 + 0.137823i
\(987\) 46.7185i 0.0473339i
\(988\) 6.26905 + 19.7833i 0.00634519 + 0.0200236i
\(989\) −1291.30 −1.30566
\(990\) 0 0
\(991\) 1705.99i 1.72148i −0.509044 0.860740i \(-0.670001\pi\)
0.509044 0.860740i \(-0.329999\pi\)
\(992\) −933.219 967.839i −0.940745 0.975644i
\(993\) −192.382 −0.193738
\(994\) −25.6125 + 3.96106i −0.0257671 + 0.00398497i
\(995\) 0 0
\(996\) 38.8950 12.3253i 0.0390512 0.0123748i
\(997\) −1262.24 −1.26604 −0.633020 0.774136i \(-0.718185\pi\)
−0.633020 + 0.774136i \(0.718185\pi\)
\(998\) 216.097 + 1397.30i 0.216530 + 1.40010i
\(999\) 264.756i 0.265021i
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.c.g.151.7 yes 8
3.2 odd 2 900.3.c.n.451.2 8
4.3 odd 2 inner 300.3.c.g.151.8 yes 8
5.2 odd 4 300.3.f.c.199.10 16
5.3 odd 4 300.3.f.c.199.7 16
5.4 even 2 300.3.c.e.151.2 yes 8
12.11 even 2 900.3.c.n.451.1 8
15.2 even 4 900.3.f.h.199.7 16
15.8 even 4 900.3.f.h.199.10 16
15.14 odd 2 900.3.c.t.451.7 8
20.3 even 4 300.3.f.c.199.9 16
20.7 even 4 300.3.f.c.199.8 16
20.19 odd 2 300.3.c.e.151.1 8
60.23 odd 4 900.3.f.h.199.8 16
60.47 odd 4 900.3.f.h.199.9 16
60.59 even 2 900.3.c.t.451.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.3.c.e.151.1 8 20.19 odd 2
300.3.c.e.151.2 yes 8 5.4 even 2
300.3.c.g.151.7 yes 8 1.1 even 1 trivial
300.3.c.g.151.8 yes 8 4.3 odd 2 inner
300.3.f.c.199.7 16 5.3 odd 4
300.3.f.c.199.8 16 20.7 even 4
300.3.f.c.199.9 16 20.3 even 4
300.3.f.c.199.10 16 5.2 odd 4
900.3.c.n.451.1 8 12.11 even 2
900.3.c.n.451.2 8 3.2 odd 2
900.3.c.t.451.7 8 15.14 odd 2
900.3.c.t.451.8 8 60.59 even 2
900.3.f.h.199.7 16 15.2 even 4
900.3.f.h.199.8 16 60.23 odd 4
900.3.f.h.199.9 16 60.47 odd 4
900.3.f.h.199.10 16 15.8 even 4