Properties

Label 35.3.c.c.34.4
Level $35$
Weight $3$
Character 35.34
Analytic conductor $0.954$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,3,Mod(34,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.34");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.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: \(0.953680925261\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.4
Root \(1.58114 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 35.34
Dual form 35.3.c.c.34.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000i q^{2} +3.16228 q^{3} -5.00000 q^{4} +(-1.58114 - 4.74342i) q^{5} +9.48683i q^{6} +(-6.32456 - 3.00000i) q^{7} -3.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+3.00000i q^{2} +3.16228 q^{3} -5.00000 q^{4} +(-1.58114 - 4.74342i) q^{5} +9.48683i q^{6} +(-6.32456 - 3.00000i) q^{7} -3.00000i q^{8} +1.00000 q^{9} +(14.2302 - 4.74342i) q^{10} +14.0000 q^{11} -15.8114 q^{12} -3.16228 q^{13} +(9.00000 - 18.9737i) q^{14} +(-5.00000 - 15.0000i) q^{15} -11.0000 q^{16} +6.32456 q^{17} +3.00000i q^{18} +28.4605i q^{19} +(7.90569 + 23.7171i) q^{20} +(-20.0000 - 9.48683i) q^{21} +42.0000i q^{22} -12.0000i q^{23} -9.48683i q^{24} +(-20.0000 + 15.0000i) q^{25} -9.48683i q^{26} -25.2982 q^{27} +(31.6228 + 15.0000i) q^{28} +14.0000 q^{29} +(45.0000 - 15.0000i) q^{30} -37.9473i q^{31} -45.0000i q^{32} +44.2719 q^{33} +18.9737i q^{34} +(-4.23025 + 34.7434i) q^{35} -5.00000 q^{36} +18.0000i q^{37} -85.3815 q^{38} -10.0000 q^{39} +(-14.2302 + 4.74342i) q^{40} +18.9737i q^{41} +(28.4605 - 60.0000i) q^{42} -42.0000i q^{43} -70.0000 q^{44} +(-1.58114 - 4.74342i) q^{45} +36.0000 q^{46} +44.2719 q^{47} -34.7851 q^{48} +(31.0000 + 37.9473i) q^{49} +(-45.0000 - 60.0000i) q^{50} +20.0000 q^{51} +15.8114 q^{52} +54.0000i q^{53} -75.8947i q^{54} +(-22.1359 - 66.4078i) q^{55} +(-9.00000 + 18.9737i) q^{56} +90.0000i q^{57} +42.0000i q^{58} -9.48683i q^{59} +(25.0000 + 75.0000i) q^{60} +66.4078i q^{61} +113.842 q^{62} +(-6.32456 - 3.00000i) q^{63} +91.0000 q^{64} +(5.00000 + 15.0000i) q^{65} +132.816i q^{66} -102.000i q^{67} -31.6228 q^{68} -37.9473i q^{69} +(-104.230 - 12.6907i) q^{70} -16.0000 q^{71} -3.00000i q^{72} +63.2456 q^{73} -54.0000 q^{74} +(-63.2456 + 47.4342i) q^{75} -142.302i q^{76} +(-88.5438 - 42.0000i) q^{77} -30.0000i q^{78} -76.0000 q^{79} +(17.3925 + 52.1776i) q^{80} -89.0000 q^{81} -56.9210 q^{82} +72.7324 q^{83} +(100.000 + 47.4342i) q^{84} +(-10.0000 - 30.0000i) q^{85} +126.000 q^{86} +44.2719 q^{87} -42.0000i q^{88} -56.9210i q^{89} +(14.2302 - 4.74342i) q^{90} +(20.0000 + 9.48683i) q^{91} +60.0000i q^{92} -120.000i q^{93} +132.816i q^{94} +(135.000 - 45.0000i) q^{95} -142.302i q^{96} -69.5701 q^{97} +(-113.842 + 93.0000i) q^{98} +14.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 20 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 20 q^{4} + 4 q^{9} + 56 q^{11} + 36 q^{14} - 20 q^{15} - 44 q^{16} - 80 q^{21} - 80 q^{25} + 56 q^{29} + 180 q^{30} + 40 q^{35} - 20 q^{36} - 40 q^{39} - 280 q^{44} + 144 q^{46} + 124 q^{49} - 180 q^{50} + 80 q^{51} - 36 q^{56} + 100 q^{60} + 364 q^{64} + 20 q^{65} - 360 q^{70} - 64 q^{71} - 216 q^{74} - 304 q^{79} - 356 q^{81} + 400 q^{84} - 40 q^{85} + 504 q^{86} + 80 q^{91} + 540 q^{95} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00000i 1.50000i 0.661438 + 0.750000i \(0.269947\pi\)
−0.661438 + 0.750000i \(0.730053\pi\)
\(3\) 3.16228 1.05409 0.527046 0.849837i \(-0.323299\pi\)
0.527046 + 0.849837i \(0.323299\pi\)
\(4\) −5.00000 −1.25000
\(5\) −1.58114 4.74342i −0.316228 0.948683i
\(6\) 9.48683i 1.58114i
\(7\) −6.32456 3.00000i −0.903508 0.428571i
\(8\) 3.00000i 0.375000i
\(9\) 1.00000 0.111111
\(10\) 14.2302 4.74342i 1.42302 0.474342i
\(11\) 14.0000 1.27273 0.636364 0.771389i \(-0.280438\pi\)
0.636364 + 0.771389i \(0.280438\pi\)
\(12\) −15.8114 −1.31762
\(13\) −3.16228 −0.243252 −0.121626 0.992576i \(-0.538811\pi\)
−0.121626 + 0.992576i \(0.538811\pi\)
\(14\) 9.00000 18.9737i 0.642857 1.35526i
\(15\) −5.00000 15.0000i −0.333333 1.00000i
\(16\) −11.0000 −0.687500
\(17\) 6.32456 0.372033 0.186016 0.982547i \(-0.440442\pi\)
0.186016 + 0.982547i \(0.440442\pi\)
\(18\) 3.00000i 0.166667i
\(19\) 28.4605i 1.49792i 0.662615 + 0.748960i \(0.269447\pi\)
−0.662615 + 0.748960i \(0.730553\pi\)
\(20\) 7.90569 + 23.7171i 0.395285 + 1.18585i
\(21\) −20.0000 9.48683i −0.952381 0.451754i
\(22\) 42.0000i 1.90909i
\(23\) 12.0000i 0.521739i −0.965374 0.260870i \(-0.915991\pi\)
0.965374 0.260870i \(-0.0840093\pi\)
\(24\) 9.48683i 0.395285i
\(25\) −20.0000 + 15.0000i −0.800000 + 0.600000i
\(26\) 9.48683i 0.364878i
\(27\) −25.2982 −0.936971
\(28\) 31.6228 + 15.0000i 1.12938 + 0.535714i
\(29\) 14.0000 0.482759 0.241379 0.970431i \(-0.422400\pi\)
0.241379 + 0.970431i \(0.422400\pi\)
\(30\) 45.0000 15.0000i 1.50000 0.500000i
\(31\) 37.9473i 1.22411i −0.790816 0.612054i \(-0.790344\pi\)
0.790816 0.612054i \(-0.209656\pi\)
\(32\) 45.0000i 1.40625i
\(33\) 44.2719 1.34157
\(34\) 18.9737i 0.558049i
\(35\) −4.23025 + 34.7434i −0.120864 + 0.992669i
\(36\) −5.00000 −0.138889
\(37\) 18.0000i 0.486486i 0.969965 + 0.243243i \(0.0782113\pi\)
−0.969965 + 0.243243i \(0.921789\pi\)
\(38\) −85.3815 −2.24688
\(39\) −10.0000 −0.256410
\(40\) −14.2302 + 4.74342i −0.355756 + 0.118585i
\(41\) 18.9737i 0.462772i 0.972862 + 0.231386i \(0.0743261\pi\)
−0.972862 + 0.231386i \(0.925674\pi\)
\(42\) 28.4605 60.0000i 0.677631 1.42857i
\(43\) 42.0000i 0.976744i −0.872635 0.488372i \(-0.837591\pi\)
0.872635 0.488372i \(-0.162409\pi\)
\(44\) −70.0000 −1.59091
\(45\) −1.58114 4.74342i −0.0351364 0.105409i
\(46\) 36.0000 0.782609
\(47\) 44.2719 0.941955 0.470978 0.882145i \(-0.343901\pi\)
0.470978 + 0.882145i \(0.343901\pi\)
\(48\) −34.7851 −0.724689
\(49\) 31.0000 + 37.9473i 0.632653 + 0.774435i
\(50\) −45.0000 60.0000i −0.900000 1.20000i
\(51\) 20.0000 0.392157
\(52\) 15.8114 0.304065
\(53\) 54.0000i 1.01887i 0.860510 + 0.509434i \(0.170145\pi\)
−0.860510 + 0.509434i \(0.829855\pi\)
\(54\) 75.8947i 1.40546i
\(55\) −22.1359 66.4078i −0.402472 1.20742i
\(56\) −9.00000 + 18.9737i −0.160714 + 0.338815i
\(57\) 90.0000i 1.57895i
\(58\) 42.0000i 0.724138i
\(59\) 9.48683i 0.160794i −0.996763 0.0803969i \(-0.974381\pi\)
0.996763 0.0803969i \(-0.0256188\pi\)
\(60\) 25.0000 + 75.0000i 0.416667 + 1.25000i
\(61\) 66.4078i 1.08865i 0.838873 + 0.544326i \(0.183215\pi\)
−0.838873 + 0.544326i \(0.816785\pi\)
\(62\) 113.842 1.83616
\(63\) −6.32456 3.00000i −0.100390 0.0476190i
\(64\) 91.0000 1.42188
\(65\) 5.00000 + 15.0000i 0.0769231 + 0.230769i
\(66\) 132.816i 2.01236i
\(67\) 102.000i 1.52239i −0.648524 0.761194i \(-0.724613\pi\)
0.648524 0.761194i \(-0.275387\pi\)
\(68\) −31.6228 −0.465041
\(69\) 37.9473i 0.549961i
\(70\) −104.230 12.6907i −1.48900 0.181296i
\(71\) −16.0000 −0.225352 −0.112676 0.993632i \(-0.535942\pi\)
−0.112676 + 0.993632i \(0.535942\pi\)
\(72\) 3.00000i 0.0416667i
\(73\) 63.2456 0.866377 0.433189 0.901303i \(-0.357388\pi\)
0.433189 + 0.901303i \(0.357388\pi\)
\(74\) −54.0000 −0.729730
\(75\) −63.2456 + 47.4342i −0.843274 + 0.632456i
\(76\) 142.302i 1.87240i
\(77\) −88.5438 42.0000i −1.14992 0.545455i
\(78\) 30.0000i 0.384615i
\(79\) −76.0000 −0.962025 −0.481013 0.876714i \(-0.659731\pi\)
−0.481013 + 0.876714i \(0.659731\pi\)
\(80\) 17.3925 + 52.1776i 0.217407 + 0.652220i
\(81\) −89.0000 −1.09877
\(82\) −56.9210 −0.694159
\(83\) 72.7324 0.876294 0.438147 0.898903i \(-0.355635\pi\)
0.438147 + 0.898903i \(0.355635\pi\)
\(84\) 100.000 + 47.4342i 1.19048 + 0.564692i
\(85\) −10.0000 30.0000i −0.117647 0.352941i
\(86\) 126.000 1.46512
\(87\) 44.2719 0.508872
\(88\) 42.0000i 0.477273i
\(89\) 56.9210i 0.639562i −0.947492 0.319781i \(-0.896391\pi\)
0.947492 0.319781i \(-0.103609\pi\)
\(90\) 14.2302 4.74342i 0.158114 0.0527046i
\(91\) 20.0000 + 9.48683i 0.219780 + 0.104251i
\(92\) 60.0000i 0.652174i
\(93\) 120.000i 1.29032i
\(94\) 132.816i 1.41293i
\(95\) 135.000 45.0000i 1.42105 0.473684i
\(96\) 142.302i 1.48232i
\(97\) −69.5701 −0.717218 −0.358609 0.933488i \(-0.616749\pi\)
−0.358609 + 0.933488i \(0.616749\pi\)
\(98\) −113.842 + 93.0000i −1.16165 + 0.948980i
\(99\) 14.0000 0.141414
\(100\) 100.000 75.0000i 1.00000 0.750000i
\(101\) 104.355i 1.03322i −0.856221 0.516610i \(-0.827194\pi\)
0.856221 0.516610i \(-0.172806\pi\)
\(102\) 60.0000i 0.588235i
\(103\) −88.5438 −0.859648 −0.429824 0.902913i \(-0.641424\pi\)
−0.429824 + 0.902913i \(0.641424\pi\)
\(104\) 9.48683i 0.0912195i
\(105\) −13.3772 + 109.868i −0.127402 + 1.04637i
\(106\) −162.000 −1.52830
\(107\) 54.0000i 0.504673i 0.967640 + 0.252336i \(0.0811990\pi\)
−0.967640 + 0.252336i \(0.918801\pi\)
\(108\) 126.491 1.17121
\(109\) 74.0000 0.678899 0.339450 0.940624i \(-0.389759\pi\)
0.339450 + 0.940624i \(0.389759\pi\)
\(110\) 199.223 66.4078i 1.81112 0.603708i
\(111\) 56.9210i 0.512802i
\(112\) 69.5701 + 33.0000i 0.621162 + 0.294643i
\(113\) 78.0000i 0.690265i 0.938554 + 0.345133i \(0.112166\pi\)
−0.938554 + 0.345133i \(0.887834\pi\)
\(114\) −270.000 −2.36842
\(115\) −56.9210 + 18.9737i −0.494965 + 0.164988i
\(116\) −70.0000 −0.603448
\(117\) −3.16228 −0.0270280
\(118\) 28.4605 0.241191
\(119\) −40.0000 18.9737i −0.336134 0.159443i
\(120\) −45.0000 + 15.0000i −0.375000 + 0.125000i
\(121\) 75.0000 0.619835
\(122\) −199.223 −1.63298
\(123\) 60.0000i 0.487805i
\(124\) 189.737i 1.53013i
\(125\) 102.774 + 71.1512i 0.822192 + 0.569210i
\(126\) 9.00000 18.9737i 0.0714286 0.150585i
\(127\) 72.0000i 0.566929i −0.958983 0.283465i \(-0.908516\pi\)
0.958983 0.283465i \(-0.0914838\pi\)
\(128\) 93.0000i 0.726562i
\(129\) 132.816i 1.02958i
\(130\) −45.0000 + 15.0000i −0.346154 + 0.115385i
\(131\) 47.4342i 0.362093i 0.983475 + 0.181046i \(0.0579484\pi\)
−0.983475 + 0.181046i \(0.942052\pi\)
\(132\) −221.359 −1.67697
\(133\) 85.3815 180.000i 0.641966 1.35338i
\(134\) 306.000 2.28358
\(135\) 40.0000 + 120.000i 0.296296 + 0.888889i
\(136\) 18.9737i 0.139512i
\(137\) 84.0000i 0.613139i 0.951848 + 0.306569i \(0.0991811\pi\)
−0.951848 + 0.306569i \(0.900819\pi\)
\(138\) 113.842 0.824942
\(139\) 123.329i 0.887258i −0.896211 0.443629i \(-0.853691\pi\)
0.896211 0.443629i \(-0.146309\pi\)
\(140\) 21.1512 173.717i 0.151080 1.24084i
\(141\) 140.000 0.992908
\(142\) 48.0000i 0.338028i
\(143\) −44.2719 −0.309594
\(144\) −11.0000 −0.0763889
\(145\) −22.1359 66.4078i −0.152662 0.457985i
\(146\) 189.737i 1.29957i
\(147\) 98.0306 + 120.000i 0.666875 + 0.816327i
\(148\) 90.0000i 0.608108i
\(149\) −46.0000 −0.308725 −0.154362 0.988014i \(-0.549332\pi\)
−0.154362 + 0.988014i \(0.549332\pi\)
\(150\) −142.302 189.737i −0.948683 1.26491i
\(151\) 14.0000 0.0927152 0.0463576 0.998925i \(-0.485239\pi\)
0.0463576 + 0.998925i \(0.485239\pi\)
\(152\) 85.3815 0.561720
\(153\) 6.32456 0.0413370
\(154\) 126.000 265.631i 0.818182 1.72488i
\(155\) −180.000 + 60.0000i −1.16129 + 0.387097i
\(156\) 50.0000 0.320513
\(157\) −117.004 −0.745250 −0.372625 0.927982i \(-0.621542\pi\)
−0.372625 + 0.927982i \(0.621542\pi\)
\(158\) 228.000i 1.44304i
\(159\) 170.763i 1.07398i
\(160\) −213.454 + 71.1512i −1.33409 + 0.444695i
\(161\) −36.0000 + 75.8947i −0.223602 + 0.471395i
\(162\) 267.000i 1.64815i
\(163\) 54.0000i 0.331288i 0.986186 + 0.165644i \(0.0529703\pi\)
−0.986186 + 0.165644i \(0.947030\pi\)
\(164\) 94.8683i 0.578465i
\(165\) −70.0000 210.000i −0.424242 1.27273i
\(166\) 218.197i 1.31444i
\(167\) 139.140 0.833175 0.416587 0.909096i \(-0.363226\pi\)
0.416587 + 0.909096i \(0.363226\pi\)
\(168\) −28.4605 + 60.0000i −0.169408 + 0.357143i
\(169\) −159.000 −0.940828
\(170\) 90.0000 30.0000i 0.529412 0.176471i
\(171\) 28.4605i 0.166436i
\(172\) 210.000i 1.22093i
\(173\) −211.873 −1.22470 −0.612349 0.790588i \(-0.709775\pi\)
−0.612349 + 0.790588i \(0.709775\pi\)
\(174\) 132.816i 0.763308i
\(175\) 171.491 34.8683i 0.979949 0.199248i
\(176\) −154.000 −0.875000
\(177\) 30.0000i 0.169492i
\(178\) 170.763 0.959343
\(179\) −178.000 −0.994413 −0.497207 0.867632i \(-0.665641\pi\)
−0.497207 + 0.867632i \(0.665641\pi\)
\(180\) 7.90569 + 23.7171i 0.0439205 + 0.131762i
\(181\) 28.4605i 0.157240i 0.996905 + 0.0786202i \(0.0250514\pi\)
−0.996905 + 0.0786202i \(0.974949\pi\)
\(182\) −28.4605 + 60.0000i −0.156376 + 0.329670i
\(183\) 210.000i 1.14754i
\(184\) −36.0000 −0.195652
\(185\) 85.3815 28.4605i 0.461522 0.153841i
\(186\) 360.000 1.93548
\(187\) 88.5438 0.473496
\(188\) −221.359 −1.17744
\(189\) 160.000 + 75.8947i 0.846561 + 0.401559i
\(190\) 135.000 + 405.000i 0.710526 + 2.13158i
\(191\) −148.000 −0.774869 −0.387435 0.921897i \(-0.626639\pi\)
−0.387435 + 0.921897i \(0.626639\pi\)
\(192\) 287.767 1.49879
\(193\) 258.000i 1.33679i 0.743808 + 0.668394i \(0.233018\pi\)
−0.743808 + 0.668394i \(0.766982\pi\)
\(194\) 208.710i 1.07583i
\(195\) 15.8114 + 47.4342i 0.0810840 + 0.243252i
\(196\) −155.000 189.737i −0.790816 0.968044i
\(197\) 342.000i 1.73604i −0.496529 0.868020i \(-0.665392\pi\)
0.496529 0.868020i \(-0.334608\pi\)
\(198\) 42.0000i 0.212121i
\(199\) 56.9210i 0.286035i 0.989720 + 0.143018i \(0.0456805\pi\)
−0.989720 + 0.143018i \(0.954319\pi\)
\(200\) 45.0000 + 60.0000i 0.225000 + 0.300000i
\(201\) 322.552i 1.60474i
\(202\) 313.065 1.54983
\(203\) −88.5438 42.0000i −0.436176 0.206897i
\(204\) −100.000 −0.490196
\(205\) 90.0000 30.0000i 0.439024 0.146341i
\(206\) 265.631i 1.28947i
\(207\) 12.0000i 0.0579710i
\(208\) 34.7851 0.167236
\(209\) 398.447i 1.90644i
\(210\) −329.605 40.1317i −1.56955 0.191103i
\(211\) 242.000 1.14692 0.573460 0.819234i \(-0.305601\pi\)
0.573460 + 0.819234i \(0.305601\pi\)
\(212\) 270.000i 1.27358i
\(213\) −50.5964 −0.237542
\(214\) −162.000 −0.757009
\(215\) −199.223 + 66.4078i −0.926621 + 0.308874i
\(216\) 75.8947i 0.351364i
\(217\) −113.842 + 240.000i −0.524617 + 1.10599i
\(218\) 222.000i 1.01835i
\(219\) 200.000 0.913242
\(220\) 110.680 + 332.039i 0.503090 + 1.50927i
\(221\) −20.0000 −0.0904977
\(222\) −170.763 −0.769203
\(223\) 44.2719 0.198529 0.0992643 0.995061i \(-0.468351\pi\)
0.0992643 + 0.995061i \(0.468351\pi\)
\(224\) −135.000 + 284.605i −0.602679 + 1.27056i
\(225\) −20.0000 + 15.0000i −0.0888889 + 0.0666667i
\(226\) −234.000 −1.03540
\(227\) 357.337 1.57417 0.787087 0.616842i \(-0.211588\pi\)
0.787087 + 0.616842i \(0.211588\pi\)
\(228\) 450.000i 1.97368i
\(229\) 237.171i 1.03568i −0.855477 0.517840i \(-0.826736\pi\)
0.855477 0.517840i \(-0.173264\pi\)
\(230\) −56.9210 170.763i −0.247483 0.742448i
\(231\) −280.000 132.816i −1.21212 0.574960i
\(232\) 42.0000i 0.181034i
\(233\) 252.000i 1.08155i −0.841169 0.540773i \(-0.818132\pi\)
0.841169 0.540773i \(-0.181868\pi\)
\(234\) 9.48683i 0.0405420i
\(235\) −70.0000 210.000i −0.297872 0.893617i
\(236\) 47.4342i 0.200992i
\(237\) −240.333 −1.01406
\(238\) 56.9210 120.000i 0.239164 0.504202i
\(239\) 242.000 1.01255 0.506276 0.862371i \(-0.331022\pi\)
0.506276 + 0.862371i \(0.331022\pi\)
\(240\) 55.0000 + 165.000i 0.229167 + 0.687500i
\(241\) 265.631i 1.10220i 0.834438 + 0.551102i \(0.185793\pi\)
−0.834438 + 0.551102i \(0.814207\pi\)
\(242\) 225.000i 0.929752i
\(243\) −53.7587 −0.221229
\(244\) 332.039i 1.36082i
\(245\) 130.985 207.046i 0.534631 0.845085i
\(246\) −180.000 −0.731707
\(247\) 90.0000i 0.364372i
\(248\) −113.842 −0.459040
\(249\) 230.000 0.923695
\(250\) −213.454 + 308.322i −0.853815 + 1.23329i
\(251\) 483.828i 1.92760i −0.266620 0.963802i \(-0.585907\pi\)
0.266620 0.963802i \(-0.414093\pi\)
\(252\) 31.6228 + 15.0000i 0.125487 + 0.0595238i
\(253\) 168.000i 0.664032i
\(254\) 216.000 0.850394
\(255\) −31.6228 94.8683i −0.124011 0.372033i
\(256\) 85.0000 0.332031
\(257\) 82.2192 0.319919 0.159960 0.987124i \(-0.448864\pi\)
0.159960 + 0.987124i \(0.448864\pi\)
\(258\) 398.447 1.54437
\(259\) 54.0000 113.842i 0.208494 0.439544i
\(260\) −25.0000 75.0000i −0.0961538 0.288462i
\(261\) 14.0000 0.0536398
\(262\) −142.302 −0.543139
\(263\) 318.000i 1.20913i 0.796558 + 0.604563i \(0.206652\pi\)
−0.796558 + 0.604563i \(0.793348\pi\)
\(264\) 132.816i 0.503090i
\(265\) 256.144 85.3815i 0.966583 0.322194i
\(266\) 540.000 + 256.144i 2.03008 + 0.962949i
\(267\) 180.000i 0.674157i
\(268\) 510.000i 1.90299i
\(269\) 256.144i 0.952210i 0.879388 + 0.476105i \(0.157952\pi\)
−0.879388 + 0.476105i \(0.842048\pi\)
\(270\) −360.000 + 120.000i −1.33333 + 0.444444i
\(271\) 341.526i 1.26024i 0.776496 + 0.630122i \(0.216995\pi\)
−0.776496 + 0.630122i \(0.783005\pi\)
\(272\) −69.5701 −0.255772
\(273\) 63.2456 + 30.0000i 0.231669 + 0.109890i
\(274\) −252.000 −0.919708
\(275\) −280.000 + 210.000i −1.01818 + 0.763636i
\(276\) 189.737i 0.687452i
\(277\) 6.00000i 0.0216606i −0.999941 0.0108303i \(-0.996553\pi\)
0.999941 0.0108303i \(-0.00344747\pi\)
\(278\) 369.986 1.33089
\(279\) 37.9473i 0.136012i
\(280\) 104.230 + 12.6907i 0.372251 + 0.0453241i
\(281\) 14.0000 0.0498221 0.0249110 0.999690i \(-0.492070\pi\)
0.0249110 + 0.999690i \(0.492070\pi\)
\(282\) 420.000i 1.48936i
\(283\) −515.451 −1.82138 −0.910691 0.413088i \(-0.864450\pi\)
−0.910691 + 0.413088i \(0.864450\pi\)
\(284\) 80.0000 0.281690
\(285\) 426.907 142.302i 1.49792 0.499307i
\(286\) 132.816i 0.464390i
\(287\) 56.9210 120.000i 0.198331 0.418118i
\(288\) 45.0000i 0.156250i
\(289\) −249.000 −0.861592
\(290\) 199.223 66.4078i 0.686978 0.228993i
\(291\) −220.000 −0.756014
\(292\) −316.228 −1.08297
\(293\) −458.530 −1.56495 −0.782475 0.622682i \(-0.786043\pi\)
−0.782475 + 0.622682i \(0.786043\pi\)
\(294\) −360.000 + 294.092i −1.22449 + 1.00031i
\(295\) −45.0000 + 15.0000i −0.152542 + 0.0508475i
\(296\) 54.0000 0.182432
\(297\) −354.175 −1.19251
\(298\) 138.000i 0.463087i
\(299\) 37.9473i 0.126914i
\(300\) 316.228 237.171i 1.05409 0.790569i
\(301\) −126.000 + 265.631i −0.418605 + 0.882496i
\(302\) 42.0000i 0.139073i
\(303\) 330.000i 1.08911i
\(304\) 313.065i 1.02982i
\(305\) 315.000 105.000i 1.03279 0.344262i
\(306\) 18.9737i 0.0620054i
\(307\) 91.7061 0.298717 0.149358 0.988783i \(-0.452279\pi\)
0.149358 + 0.988783i \(0.452279\pi\)
\(308\) 442.719 + 210.000i 1.43740 + 0.681818i
\(309\) −280.000 −0.906149
\(310\) −180.000 540.000i −0.580645 1.74194i
\(311\) 360.500i 1.15916i 0.814914 + 0.579581i \(0.196784\pi\)
−0.814914 + 0.579581i \(0.803216\pi\)
\(312\) 30.0000i 0.0961538i
\(313\) 556.561 1.77815 0.889075 0.457762i \(-0.151349\pi\)
0.889075 + 0.457762i \(0.151349\pi\)
\(314\) 351.013i 1.11788i
\(315\) −4.23025 + 34.7434i −0.0134294 + 0.110297i
\(316\) 380.000 1.20253
\(317\) 318.000i 1.00315i 0.865113 + 0.501577i \(0.167247\pi\)
−0.865113 + 0.501577i \(0.832753\pi\)
\(318\) −512.289 −1.61097
\(319\) 196.000 0.614420
\(320\) −143.884 431.651i −0.449636 1.34891i
\(321\) 170.763i 0.531972i
\(322\) −227.684 108.000i −0.707093 0.335404i
\(323\) 180.000i 0.557276i
\(324\) 445.000 1.37346
\(325\) 63.2456 47.4342i 0.194602 0.145951i
\(326\) −162.000 −0.496933
\(327\) 234.009 0.715622
\(328\) 56.9210 0.173540
\(329\) −280.000 132.816i −0.851064 0.403695i
\(330\) 630.000 210.000i 1.90909 0.636364i
\(331\) 374.000 1.12991 0.564955 0.825122i \(-0.308894\pi\)
0.564955 + 0.825122i \(0.308894\pi\)
\(332\) −363.662 −1.09537
\(333\) 18.0000i 0.0540541i
\(334\) 417.421i 1.24976i
\(335\) −483.828 + 161.276i −1.44426 + 0.481421i
\(336\) 220.000 + 104.355i 0.654762 + 0.310581i
\(337\) 654.000i 1.94065i 0.241799 + 0.970326i \(0.422263\pi\)
−0.241799 + 0.970326i \(0.577737\pi\)
\(338\) 477.000i 1.41124i
\(339\) 246.658i 0.727604i
\(340\) 50.0000 + 150.000i 0.147059 + 0.441176i
\(341\) 531.263i 1.55795i
\(342\) −85.3815 −0.249653
\(343\) −82.2192 333.000i −0.239706 0.970845i
\(344\) −126.000 −0.366279
\(345\) −180.000 + 60.0000i −0.521739 + 0.173913i
\(346\) 635.618i 1.83705i
\(347\) 282.000i 0.812680i −0.913722 0.406340i \(-0.866805\pi\)
0.913722 0.406340i \(-0.133195\pi\)
\(348\) −221.359 −0.636090
\(349\) 161.276i 0.462109i −0.972941 0.231055i \(-0.925782\pi\)
0.972941 0.231055i \(-0.0742176\pi\)
\(350\) 104.605 + 514.473i 0.298871 + 1.46992i
\(351\) 80.0000 0.227920
\(352\) 630.000i 1.78977i
\(353\) 613.482 1.73791 0.868954 0.494892i \(-0.164792\pi\)
0.868954 + 0.494892i \(0.164792\pi\)
\(354\) 90.0000 0.254237
\(355\) 25.2982 + 75.8947i 0.0712626 + 0.213788i
\(356\) 284.605i 0.799452i
\(357\) −126.491 60.0000i −0.354317 0.168067i
\(358\) 534.000i 1.49162i
\(359\) 254.000 0.707521 0.353760 0.935336i \(-0.384903\pi\)
0.353760 + 0.935336i \(0.384903\pi\)
\(360\) −14.2302 + 4.74342i −0.0395285 + 0.0131762i
\(361\) −449.000 −1.24377
\(362\) −85.3815 −0.235860
\(363\) 237.171 0.653363
\(364\) −100.000 47.4342i −0.274725 0.130314i
\(365\) −100.000 300.000i −0.273973 0.821918i
\(366\) −630.000 −1.72131
\(367\) −69.5701 −0.189564 −0.0947822 0.995498i \(-0.530215\pi\)
−0.0947822 + 0.995498i \(0.530215\pi\)
\(368\) 132.000i 0.358696i
\(369\) 18.9737i 0.0514191i
\(370\) 85.3815 + 256.144i 0.230761 + 0.692282i
\(371\) 162.000 341.526i 0.436658 0.920555i
\(372\) 600.000i 1.61290i
\(373\) 618.000i 1.65684i 0.560110 + 0.828418i \(0.310759\pi\)
−0.560110 + 0.828418i \(0.689241\pi\)
\(374\) 265.631i 0.710244i
\(375\) 325.000 + 225.000i 0.866667 + 0.600000i
\(376\) 132.816i 0.353233i
\(377\) −44.2719 −0.117432
\(378\) −227.684 + 480.000i −0.602339 + 1.26984i
\(379\) −466.000 −1.22955 −0.614776 0.788702i \(-0.710753\pi\)
−0.614776 + 0.788702i \(0.710753\pi\)
\(380\) −675.000 + 225.000i −1.77632 + 0.592105i
\(381\) 227.684i 0.597596i
\(382\) 444.000i 1.16230i
\(383\) −31.6228 −0.0825660 −0.0412830 0.999147i \(-0.513145\pi\)
−0.0412830 + 0.999147i \(0.513145\pi\)
\(384\) 294.092i 0.765864i
\(385\) −59.2235 + 486.408i −0.153827 + 1.26340i
\(386\) −774.000 −2.00518
\(387\) 42.0000i 0.108527i
\(388\) 347.851 0.896522
\(389\) 14.0000 0.0359897 0.0179949 0.999838i \(-0.494272\pi\)
0.0179949 + 0.999838i \(0.494272\pi\)
\(390\) −142.302 + 47.4342i −0.364878 + 0.121626i
\(391\) 75.8947i 0.194104i
\(392\) 113.842 93.0000i 0.290413 0.237245i
\(393\) 150.000i 0.381679i
\(394\) 1026.00 2.60406
\(395\) 120.167 + 360.500i 0.304219 + 0.912657i
\(396\) −70.0000 −0.176768
\(397\) −79.0569 −0.199136 −0.0995679 0.995031i \(-0.531746\pi\)
−0.0995679 + 0.995031i \(0.531746\pi\)
\(398\) −170.763 −0.429053
\(399\) 270.000 569.210i 0.676692 1.42659i
\(400\) 220.000 165.000i 0.550000 0.412500i
\(401\) 404.000 1.00748 0.503741 0.863855i \(-0.331957\pi\)
0.503741 + 0.863855i \(0.331957\pi\)
\(402\) 967.657 2.40711
\(403\) 120.000i 0.297767i
\(404\) 521.776i 1.29152i
\(405\) 140.721 + 422.164i 0.347460 + 1.04238i
\(406\) 126.000 265.631i 0.310345 0.654264i
\(407\) 252.000i 0.619165i
\(408\) 60.0000i 0.147059i
\(409\) 208.710i 0.510294i −0.966902 0.255147i \(-0.917876\pi\)
0.966902 0.255147i \(-0.0821239\pi\)
\(410\) 90.0000 + 270.000i 0.219512 + 0.658537i
\(411\) 265.631i 0.646305i
\(412\) 442.719 1.07456
\(413\) −28.4605 + 60.0000i −0.0689116 + 0.145278i
\(414\) 36.0000 0.0869565
\(415\) −115.000 345.000i −0.277108 0.831325i
\(416\) 142.302i 0.342073i
\(417\) 390.000i 0.935252i
\(418\) −1195.34 −2.85967
\(419\) 237.171i 0.566040i −0.959114 0.283020i \(-0.908664\pi\)
0.959114 0.283020i \(-0.0913363\pi\)
\(420\) 66.8861 549.342i 0.159253 1.30796i
\(421\) 554.000 1.31591 0.657957 0.753055i \(-0.271421\pi\)
0.657957 + 0.753055i \(0.271421\pi\)
\(422\) 726.000i 1.72038i
\(423\) 44.2719 0.104662
\(424\) 162.000 0.382075
\(425\) −126.491 + 94.8683i −0.297626 + 0.223220i
\(426\) 151.789i 0.356313i
\(427\) 199.223 420.000i 0.466566 0.983607i
\(428\) 270.000i 0.630841i
\(429\) −140.000 −0.326340
\(430\) −199.223 597.670i −0.463310 1.38993i
\(431\) −358.000 −0.830626 −0.415313 0.909678i \(-0.636328\pi\)
−0.415313 + 0.909678i \(0.636328\pi\)
\(432\) 278.280 0.644168
\(433\) −107.517 −0.248308 −0.124154 0.992263i \(-0.539622\pi\)
−0.124154 + 0.992263i \(0.539622\pi\)
\(434\) −720.000 341.526i −1.65899 0.786926i
\(435\) −70.0000 210.000i −0.160920 0.482759i
\(436\) −370.000 −0.848624
\(437\) 341.526 0.781524
\(438\) 600.000i 1.36986i
\(439\) 18.9737i 0.0432202i −0.999766 0.0216101i \(-0.993121\pi\)
0.999766 0.0216101i \(-0.00687924\pi\)
\(440\) −199.223 + 66.4078i −0.452781 + 0.150927i
\(441\) 31.0000 + 37.9473i 0.0702948 + 0.0860484i
\(442\) 60.0000i 0.135747i
\(443\) 366.000i 0.826185i −0.910689 0.413093i \(-0.864449\pi\)
0.910689 0.413093i \(-0.135551\pi\)
\(444\) 284.605i 0.641002i
\(445\) −270.000 + 90.0000i −0.606742 + 0.202247i
\(446\) 132.816i 0.297793i
\(447\) −145.465 −0.325425
\(448\) −575.535 273.000i −1.28468 0.609375i
\(449\) 74.0000 0.164811 0.0824053 0.996599i \(-0.473740\pi\)
0.0824053 + 0.996599i \(0.473740\pi\)
\(450\) −45.0000 60.0000i −0.100000 0.133333i
\(451\) 265.631i 0.588983i
\(452\) 390.000i 0.862832i
\(453\) 44.2719 0.0977304
\(454\) 1072.01i 2.36126i
\(455\) 13.3772 109.868i 0.0294005 0.241469i
\(456\) 270.000 0.592105
\(457\) 138.000i 0.301969i 0.988536 + 0.150985i \(0.0482444\pi\)
−0.988536 + 0.150985i \(0.951756\pi\)
\(458\) 711.512 1.55352
\(459\) −160.000 −0.348584
\(460\) 284.605 94.8683i 0.618706 0.206235i
\(461\) 692.539i 1.50225i 0.660158 + 0.751127i \(0.270489\pi\)
−0.660158 + 0.751127i \(0.729511\pi\)
\(462\) 398.447 840.000i 0.862439 1.81818i
\(463\) 606.000i 1.30886i −0.756125 0.654428i \(-0.772910\pi\)
0.756125 0.654428i \(-0.227090\pi\)
\(464\) −154.000 −0.331897
\(465\) −569.210 + 189.737i −1.22411 + 0.408036i
\(466\) 756.000 1.62232
\(467\) −534.425 −1.14438 −0.572189 0.820121i \(-0.693906\pi\)
−0.572189 + 0.820121i \(0.693906\pi\)
\(468\) 15.8114 0.0337850
\(469\) −306.000 + 645.105i −0.652452 + 1.37549i
\(470\) 630.000 210.000i 1.34043 0.446809i
\(471\) −370.000 −0.785563
\(472\) −28.4605 −0.0602977
\(473\) 588.000i 1.24313i
\(474\) 720.999i 1.52110i
\(475\) −426.907 569.210i −0.898753 1.19834i
\(476\) 200.000 + 94.8683i 0.420168 + 0.199303i
\(477\) 54.0000i 0.113208i
\(478\) 726.000i 1.51883i
\(479\) 531.263i 1.10911i −0.832148 0.554554i \(-0.812889\pi\)
0.832148 0.554554i \(-0.187111\pi\)
\(480\) −675.000 + 225.000i −1.40625 + 0.468750i
\(481\) 56.9210i 0.118339i
\(482\) −796.894 −1.65331
\(483\) −113.842 + 240.000i −0.235698 + 0.496894i
\(484\) −375.000 −0.774793
\(485\) 110.000 + 330.000i 0.226804 + 0.680412i
\(486\) 161.276i 0.331844i
\(487\) 108.000i 0.221766i 0.993833 + 0.110883i \(0.0353679\pi\)
−0.993833 + 0.110883i \(0.964632\pi\)
\(488\) 199.223 0.408245
\(489\) 170.763i 0.349209i
\(490\) 621.138 + 392.954i 1.26763 + 0.801947i
\(491\) 674.000 1.37271 0.686354 0.727267i \(-0.259210\pi\)
0.686354 + 0.727267i \(0.259210\pi\)
\(492\) 300.000i 0.609756i
\(493\) 88.5438 0.179602
\(494\) 270.000 0.546559
\(495\) −22.1359 66.4078i −0.0447191 0.134157i
\(496\) 417.421i 0.841574i
\(497\) 101.193 + 48.0000i 0.203607 + 0.0965795i
\(498\) 690.000i 1.38554i
\(499\) 62.0000 0.124248 0.0621242 0.998068i \(-0.480212\pi\)
0.0621242 + 0.998068i \(0.480212\pi\)
\(500\) −513.870 355.756i −1.02774 0.711512i
\(501\) 440.000 0.878244
\(502\) 1451.49 2.89141
\(503\) 632.456 1.25737 0.628683 0.777661i \(-0.283594\pi\)
0.628683 + 0.777661i \(0.283594\pi\)
\(504\) −9.00000 + 18.9737i −0.0178571 + 0.0376462i
\(505\) −495.000 + 165.000i −0.980198 + 0.326733i
\(506\) 504.000 0.996047
\(507\) −502.802 −0.991720
\(508\) 360.000i 0.708661i
\(509\) 635.618i 1.24876i −0.781122 0.624379i \(-0.785352\pi\)
0.781122 0.624379i \(-0.214648\pi\)
\(510\) 284.605 94.8683i 0.558049 0.186016i
\(511\) −400.000 189.737i −0.782779 0.371305i
\(512\) 627.000i 1.22461i
\(513\) 720.000i 1.40351i
\(514\) 246.658i 0.479879i
\(515\) 140.000 + 420.000i 0.271845 + 0.815534i
\(516\) 664.078i 1.28697i
\(517\) 619.806 1.19885
\(518\) 341.526 + 162.000i 0.659317 + 0.312741i
\(519\) −670.000 −1.29094
\(520\) 45.0000 15.0000i 0.0865385 0.0288462i
\(521\) 398.447i 0.764773i −0.924002 0.382387i \(-0.875102\pi\)
0.924002 0.382387i \(-0.124898\pi\)
\(522\) 42.0000i 0.0804598i
\(523\) 262.469 0.501853 0.250926 0.968006i \(-0.419265\pi\)
0.250926 + 0.968006i \(0.419265\pi\)
\(524\) 237.171i 0.452616i
\(525\) 542.302 110.263i 1.03296 0.210025i
\(526\) −954.000 −1.81369
\(527\) 240.000i 0.455408i
\(528\) −486.991 −0.922331
\(529\) 385.000 0.727788
\(530\) 256.144 + 768.433i 0.483291 + 1.44987i
\(531\) 9.48683i 0.0178660i
\(532\) −426.907 + 900.000i −0.802458 + 1.69173i
\(533\) 60.0000i 0.112570i
\(534\) 540.000 1.01124
\(535\) 256.144 85.3815i 0.478775 0.159592i
\(536\) −306.000 −0.570896
\(537\) −562.885 −1.04820
\(538\) −768.433 −1.42832
\(539\) 434.000 + 531.263i 0.805195 + 0.985645i
\(540\) −200.000 600.000i −0.370370 1.11111i
\(541\) −1006.00 −1.85952 −0.929760 0.368167i \(-0.879985\pi\)
−0.929760 + 0.368167i \(0.879985\pi\)
\(542\) −1024.58 −1.89037
\(543\) 90.0000i 0.165746i
\(544\) 284.605i 0.523171i
\(545\) −117.004 351.013i −0.214687 0.644060i
\(546\) −90.0000 + 189.737i −0.164835 + 0.347503i
\(547\) 318.000i 0.581353i 0.956821 + 0.290676i \(0.0938803\pi\)
−0.956821 + 0.290676i \(0.906120\pi\)
\(548\) 420.000i 0.766423i
\(549\) 66.4078i 0.120961i
\(550\) −630.000 840.000i −1.14545 1.52727i
\(551\) 398.447i 0.723134i
\(552\) −113.842 −0.206235
\(553\) 480.666 + 228.000i 0.869197 + 0.412297i
\(554\) 18.0000 0.0324910
\(555\) 270.000 90.0000i 0.486486 0.162162i
\(556\) 616.644i 1.10907i
\(557\) 18.0000i 0.0323160i 0.999869 + 0.0161580i \(0.00514347\pi\)
−0.999869 + 0.0161580i \(0.994857\pi\)
\(558\) 113.842 0.204018
\(559\) 132.816i 0.237595i
\(560\) 46.5327 382.178i 0.0830942 0.682460i
\(561\) 280.000 0.499109
\(562\) 42.0000i 0.0747331i
\(563\) −60.0833 −0.106720 −0.0533599 0.998575i \(-0.516993\pi\)
−0.0533599 + 0.998575i \(0.516993\pi\)
\(564\) −700.000 −1.24113
\(565\) 369.986 123.329i 0.654843 0.218281i
\(566\) 1546.35i 2.73207i
\(567\) 562.885 + 267.000i 0.992743 + 0.470899i
\(568\) 48.0000i 0.0845070i
\(569\) 464.000 0.815466 0.407733 0.913101i \(-0.366319\pi\)
0.407733 + 0.913101i \(0.366319\pi\)
\(570\) 426.907 + 1280.72i 0.748960 + 2.24688i
\(571\) 314.000 0.549912 0.274956 0.961457i \(-0.411337\pi\)
0.274956 + 0.961457i \(0.411337\pi\)
\(572\) 221.359 0.386992
\(573\) −468.017 −0.816784
\(574\) 360.000 + 170.763i 0.627178 + 0.297497i
\(575\) 180.000 + 240.000i 0.313043 + 0.417391i
\(576\) 91.0000 0.157986
\(577\) −676.727 −1.17284 −0.586419 0.810008i \(-0.699463\pi\)
−0.586419 + 0.810008i \(0.699463\pi\)
\(578\) 747.000i 1.29239i
\(579\) 815.868i 1.40910i
\(580\) 110.680 + 332.039i 0.190827 + 0.572481i
\(581\) −460.000 218.197i −0.791738 0.375554i
\(582\) 660.000i 1.13402i
\(583\) 756.000i 1.29674i
\(584\) 189.737i 0.324892i
\(585\) 5.00000 + 15.0000i 0.00854701 + 0.0256410i
\(586\) 1375.59i 2.34742i
\(587\) 585.021 0.996629 0.498315 0.866996i \(-0.333952\pi\)
0.498315 + 0.866996i \(0.333952\pi\)
\(588\) −490.153 600.000i −0.833594 1.02041i
\(589\) 1080.00 1.83362
\(590\) −45.0000 135.000i −0.0762712 0.228814i
\(591\) 1081.50i 1.82995i
\(592\) 198.000i 0.334459i
\(593\) −449.043 −0.757240 −0.378620 0.925552i \(-0.623601\pi\)
−0.378620 + 0.925552i \(0.623601\pi\)
\(594\) 1062.53i 1.78876i
\(595\) −26.7544 + 219.737i −0.0449655 + 0.369305i
\(596\) 230.000 0.385906
\(597\) 180.000i 0.301508i
\(598\) −113.842 −0.190371
\(599\) −136.000 −0.227045 −0.113523 0.993535i \(-0.536213\pi\)
−0.113523 + 0.993535i \(0.536213\pi\)
\(600\) 142.302 + 189.737i 0.237171 + 0.316228i
\(601\) 360.500i 0.599833i −0.953965 0.299917i \(-0.903041\pi\)
0.953965 0.299917i \(-0.0969588\pi\)
\(602\) −796.894 378.000i −1.32374 0.627907i
\(603\) 102.000i 0.169154i
\(604\) −70.0000 −0.115894
\(605\) −118.585 355.756i −0.196009 0.588027i
\(606\) 990.000 1.63366
\(607\) −828.517 −1.36494 −0.682468 0.730915i \(-0.739094\pi\)
−0.682468 + 0.730915i \(0.739094\pi\)
\(608\) 1280.72 2.10645
\(609\) −280.000 132.816i −0.459770 0.218088i
\(610\) 315.000 + 945.000i 0.516393 + 1.54918i
\(611\) −140.000 −0.229133
\(612\) −31.6228 −0.0516712
\(613\) 198.000i 0.323002i 0.986873 + 0.161501i \(0.0516334\pi\)
−0.986873 + 0.161501i \(0.948367\pi\)
\(614\) 275.118i 0.448075i
\(615\) 284.605 94.8683i 0.462772 0.154257i
\(616\) −126.000 + 265.631i −0.204545 + 0.431220i
\(617\) 822.000i 1.33225i −0.745839 0.666126i \(-0.767951\pi\)
0.745839 0.666126i \(-0.232049\pi\)
\(618\) 840.000i 1.35922i
\(619\) 863.302i 1.39467i 0.716745 + 0.697336i \(0.245631\pi\)
−0.716745 + 0.697336i \(0.754369\pi\)
\(620\) 900.000 300.000i 1.45161 0.483871i
\(621\) 303.579i 0.488855i
\(622\) −1081.50 −1.73874
\(623\) −170.763 + 360.000i −0.274098 + 0.577849i
\(624\) 110.000 0.176282
\(625\) 175.000 600.000i 0.280000 0.960000i
\(626\) 1669.68i 2.66722i
\(627\) 1260.00i 2.00957i
\(628\) 585.021 0.931563
\(629\) 113.842i 0.180989i
\(630\) −104.230 12.6907i −0.165445 0.0201440i
\(631\) −16.0000 −0.0253566 −0.0126783 0.999920i \(-0.504036\pi\)
−0.0126783 + 0.999920i \(0.504036\pi\)
\(632\) 228.000i 0.360759i
\(633\) 765.271 1.20896
\(634\) −954.000 −1.50473
\(635\) −341.526 + 113.842i −0.537836 + 0.179279i
\(636\) 853.815i 1.34248i
\(637\) −98.0306 120.000i −0.153894 0.188383i
\(638\) 588.000i 0.921630i
\(639\) −16.0000 −0.0250391
\(640\) 441.138 147.046i 0.689278 0.229759i
\(641\) −1156.00 −1.80343 −0.901716 0.432329i \(-0.857692\pi\)
−0.901716 + 0.432329i \(0.857692\pi\)
\(642\) −512.289 −0.797958
\(643\) 736.811 1.14590 0.572948 0.819592i \(-0.305800\pi\)
0.572948 + 0.819592i \(0.305800\pi\)
\(644\) 180.000 379.473i 0.279503 0.589244i
\(645\) −630.000 + 210.000i −0.976744 + 0.325581i
\(646\) −540.000 −0.835913
\(647\) 746.298 1.15347 0.576737 0.816930i \(-0.304326\pi\)
0.576737 + 0.816930i \(0.304326\pi\)
\(648\) 267.000i 0.412037i
\(649\) 132.816i 0.204647i
\(650\) 142.302 + 189.737i 0.218927 + 0.291903i
\(651\) −360.000 + 758.947i −0.552995 + 1.16582i
\(652\) 270.000i 0.414110i
\(653\) 834.000i 1.27718i 0.769546 + 0.638591i \(0.220482\pi\)
−0.769546 + 0.638591i \(0.779518\pi\)
\(654\) 702.026i 1.07343i
\(655\) 225.000 75.0000i 0.343511 0.114504i
\(656\) 208.710i 0.318156i
\(657\) 63.2456 0.0962642
\(658\) 398.447 840.000i 0.605543 1.27660i
\(659\) −958.000 −1.45372 −0.726859 0.686787i \(-0.759021\pi\)
−0.726859 + 0.686787i \(0.759021\pi\)
\(660\) 350.000 + 1050.00i 0.530303 + 1.59091i
\(661\) 104.355i 0.157875i 0.996880 + 0.0789373i \(0.0251527\pi\)
−0.996880 + 0.0789373i \(0.974847\pi\)
\(662\) 1122.00i 1.69486i
\(663\) −63.2456 −0.0953930
\(664\) 218.197i 0.328610i
\(665\) −988.815 120.395i −1.48694 0.181045i
\(666\) −54.0000 −0.0810811
\(667\) 168.000i 0.251874i
\(668\) −695.701 −1.04147
\(669\) 140.000 0.209268
\(670\) −483.828 1451.49i −0.722132 2.16640i
\(671\) 929.710i 1.38556i
\(672\) −426.907 + 900.000i −0.635279 + 1.33929i
\(673\) 456.000i 0.677563i −0.940865 0.338782i \(-0.889985\pi\)
0.940865 0.338782i \(-0.110015\pi\)
\(674\) −1962.00 −2.91098
\(675\) 505.964 379.473i 0.749577 0.562183i
\(676\) 795.000 1.17604
\(677\) 243.495 0.359668 0.179834 0.983697i \(-0.442444\pi\)
0.179834 + 0.983697i \(0.442444\pi\)
\(678\) −739.973 −1.09141
\(679\) 440.000 + 208.710i 0.648012 + 0.307379i
\(680\) −90.0000 + 30.0000i −0.132353 + 0.0441176i
\(681\) 1130.00 1.65932
\(682\) 1593.79 2.33693
\(683\) 882.000i 1.29136i −0.763607 0.645681i \(-0.776574\pi\)
0.763607 0.645681i \(-0.223426\pi\)
\(684\) 142.302i 0.208045i
\(685\) 398.447 132.816i 0.581674 0.193891i
\(686\) 999.000 246.658i 1.45627 0.359559i
\(687\) 750.000i 1.09170i
\(688\) 462.000i 0.671512i
\(689\) 170.763i 0.247842i
\(690\) −180.000 540.000i −0.260870 0.782609i
\(691\) 901.249i 1.30427i −0.758104 0.652134i \(-0.773874\pi\)
0.758104 0.652134i \(-0.226126\pi\)
\(692\) 1059.36 1.53087
\(693\) −88.5438 42.0000i −0.127769 0.0606061i
\(694\) 846.000 1.21902
\(695\) −585.000 + 195.000i −0.841727 + 0.280576i
\(696\) 132.816i 0.190827i
\(697\) 120.000i 0.172166i
\(698\) 483.828 0.693164
\(699\) 796.894i 1.14005i
\(700\) −857.456 + 174.342i −1.22494 + 0.249059i
\(701\) −358.000 −0.510699 −0.255350 0.966849i \(-0.582191\pi\)
−0.255350 + 0.966849i \(0.582191\pi\)
\(702\) 240.000i 0.341880i
\(703\) −512.289 −0.728718
\(704\) 1274.00 1.80966
\(705\) −221.359 664.078i −0.313985 0.941955i
\(706\) 1840.45i 2.60686i
\(707\) −313.065 + 660.000i −0.442808 + 0.933522i
\(708\) 150.000i 0.211864i
\(709\) −238.000 −0.335684 −0.167842 0.985814i \(-0.553680\pi\)
−0.167842 + 0.985814i \(0.553680\pi\)
\(710\) −227.684 + 75.8947i −0.320682 + 0.106894i
\(711\) −76.0000 −0.106892
\(712\) −170.763 −0.239836
\(713\) −455.368 −0.638665
\(714\) 180.000 379.473i 0.252101 0.531475i
\(715\) 70.0000 + 210.000i 0.0979021 + 0.293706i
\(716\) 890.000 1.24302
\(717\) 765.271 1.06732
\(718\) 762.000i 1.06128i
\(719\) 569.210i 0.791669i 0.918322 + 0.395834i \(0.129545\pi\)
−0.918322 + 0.395834i \(0.870455\pi\)
\(720\) 17.3925 + 52.1776i 0.0241563 + 0.0724689i
\(721\) 560.000 + 265.631i 0.776699 + 0.368421i
\(722\) 1347.00i 1.86565i
\(723\) 840.000i 1.16183i
\(724\) 142.302i 0.196550i
\(725\) −280.000 + 210.000i −0.386207 + 0.289655i
\(726\) 711.512i 0.980045i
\(727\) −1037.23 −1.42672 −0.713361 0.700797i \(-0.752828\pi\)
−0.713361 + 0.700797i \(0.752828\pi\)
\(728\) 28.4605 60.0000i 0.0390941 0.0824176i
\(729\) 631.000 0.865569
\(730\) 900.000 300.000i 1.23288 0.410959i
\(731\) 265.631i 0.363381i
\(732\) 1050.00i 1.43443i
\(733\) −629.293 −0.858517 −0.429259 0.903182i \(-0.641225\pi\)
−0.429259 + 0.903182i \(0.641225\pi\)
\(734\) 208.710i 0.284346i
\(735\) 414.210 654.737i 0.563551 0.890798i
\(736\) −540.000 −0.733696
\(737\) 1428.00i 1.93758i
\(738\) −56.9210 −0.0771287
\(739\) −466.000 −0.630582 −0.315291 0.948995i \(-0.602102\pi\)
−0.315291 + 0.948995i \(0.602102\pi\)
\(740\) −426.907 + 142.302i −0.576902 + 0.192301i
\(741\) 284.605i 0.384082i
\(742\) 1024.58 + 486.000i 1.38083 + 0.654987i
\(743\) 924.000i 1.24361i 0.783173 + 0.621803i \(0.213600\pi\)
−0.783173 + 0.621803i \(0.786400\pi\)
\(744\) −360.000 −0.483871
\(745\) 72.7324 + 218.197i 0.0976274 + 0.292882i
\(746\) −1854.00 −2.48525
\(747\) 72.7324 0.0973660
\(748\) −442.719 −0.591870
\(749\) 162.000 341.526i 0.216288 0.455976i
\(750\) −675.000 + 975.000i −0.900000 + 1.30000i
\(751\) 1142.00 1.52064 0.760320 0.649549i \(-0.225042\pi\)
0.760320 + 0.649549i \(0.225042\pi\)
\(752\) −486.991 −0.647594
\(753\) 1530.00i 2.03187i
\(754\) 132.816i 0.176148i
\(755\) −22.1359 66.4078i −0.0293191 0.0879574i
\(756\) −800.000 379.473i −1.05820 0.501949i
\(757\) 162.000i 0.214003i −0.994259 0.107001i \(-0.965875\pi\)
0.994259 0.107001i \(-0.0341249\pi\)
\(758\) 1398.00i 1.84433i
\(759\) 531.263i 0.699951i
\(760\) −135.000 405.000i −0.177632 0.532895i
\(761\) 929.710i 1.22169i 0.791748 + 0.610847i \(0.209171\pi\)
−0.791748 + 0.610847i \(0.790829\pi\)
\(762\) 683.052 0.896394
\(763\) −468.017 222.000i −0.613391 0.290957i
\(764\) 740.000 0.968586
\(765\) −10.0000 30.0000i −0.0130719 0.0392157i
\(766\) 94.8683i 0.123849i
\(767\) 30.0000i 0.0391134i
\(768\) 268.794 0.349992
\(769\) 151.789i 0.197385i −0.995118 0.0986927i \(-0.968534\pi\)
0.995118 0.0986927i \(-0.0314661\pi\)
\(770\) −1459.22 177.670i −1.89510 0.230741i
\(771\) 260.000 0.337224
\(772\) 1290.00i 1.67098i
\(773\) −1274.40 −1.64864 −0.824319 0.566125i \(-0.808442\pi\)
−0.824319 + 0.566125i \(0.808442\pi\)
\(774\) 126.000 0.162791
\(775\) 569.210 + 758.947i 0.734464 + 0.979286i
\(776\) 208.710i 0.268957i
\(777\) 170.763 360.000i 0.219772 0.463320i
\(778\) 42.0000i 0.0539846i
\(779\) −540.000 −0.693196
\(780\) −79.0569 237.171i −0.101355 0.304065i
\(781\) −224.000 −0.286812
\(782\) 227.684 0.291156
\(783\) −354.175 −0.452331
\(784\) −341.000 417.421i −0.434949 0.532424i
\(785\) 185.000 + 555.000i 0.235669 + 0.707006i
\(786\) −450.000 −0.572519
\(787\) −230.846 −0.293324 −0.146662 0.989187i \(-0.546853\pi\)
−0.146662 + 0.989187i \(0.546853\pi\)
\(788\) 1710.00i 2.17005i
\(789\) 1005.60i 1.27453i
\(790\) −1081.50 + 360.500i −1.36899 + 0.456329i
\(791\) 234.000 493.315i 0.295828 0.623660i
\(792\) 42.0000i 0.0530303i
\(793\) 210.000i 0.264817i
\(794\) 237.171i 0.298704i
\(795\) 810.000 270.000i 1.01887 0.339623i
\(796\) 284.605i 0.357544i
\(797\) 1192.18 1.49583 0.747916 0.663793i \(-0.231054\pi\)
0.747916 + 0.663793i \(0.231054\pi\)
\(798\) 1707.63 + 810.000i 2.13989 + 1.01504i
\(799\) 280.000 0.350438
\(800\) 675.000 + 900.000i 0.843750 + 1.12500i
\(801\) 56.9210i 0.0710624i
\(802\) 1212.00i 1.51122i
\(803\) 885.438 1.10266
\(804\) 1612.76i 2.00592i
\(805\) 416.921 + 50.7630i 0.517914 + 0.0630596i
\(806\) −360.000 −0.446650
\(807\) 810.000i 1.00372i
\(808\) −313.065 −0.387457
\(809\) 1424.00 1.76020 0.880099 0.474790i \(-0.157476\pi\)
0.880099 + 0.474790i \(0.157476\pi\)
\(810\) −1266.49 + 422.164i −1.56357 + 0.521190i
\(811\) 1109.96i 1.36863i −0.729186 0.684315i \(-0.760101\pi\)
0.729186 0.684315i \(-0.239899\pi\)
\(812\) 442.719 + 210.000i 0.545220 + 0.258621i
\(813\) 1080.00i 1.32841i
\(814\) −756.000 −0.928747
\(815\) 256.144 85.3815i 0.314288 0.104763i
\(816\) −220.000 −0.269608
\(817\) 1195.34 1.46309
\(818\) 626.131 0.765441
\(819\) 20.0000 + 9.48683i 0.0244200 + 0.0115834i
\(820\) −450.000 + 150.000i −0.548780 + 0.182927i
\(821\) 662.000 0.806334 0.403167 0.915126i \(-0.367909\pi\)
0.403167 + 0.915126i \(0.367909\pi\)
\(822\) −796.894 −0.969457
\(823\) 1182.00i 1.43621i −0.695935 0.718104i \(-0.745010\pi\)
0.695935 0.718104i \(-0.254990\pi\)
\(824\) 265.631i 0.322368i
\(825\) −885.438 + 664.078i −1.07326 + 0.804943i
\(826\) −180.000 85.3815i −0.217918 0.103367i
\(827\) 18.0000i 0.0217654i 0.999941 + 0.0108827i \(0.00346414\pi\)
−0.999941 + 0.0108827i \(0.996536\pi\)
\(828\) 60.0000i 0.0724638i
\(829\) 1166.88i 1.40758i −0.710410 0.703788i \(-0.751491\pi\)
0.710410 0.703788i \(-0.248509\pi\)
\(830\) 1035.00 345.000i 1.24699 0.415663i
\(831\) 18.9737i 0.0228323i
\(832\) −287.767 −0.345874
\(833\) 196.061 + 240.000i 0.235368 + 0.288115i
\(834\) 1170.00 1.40288
\(835\) −220.000 660.000i −0.263473 0.790419i
\(836\) 1992.23i 2.38306i
\(837\) 960.000i 1.14695i
\(838\) 711.512 0.849060
\(839\) 1119.45i 1.33426i 0.744940 + 0.667131i \(0.232478\pi\)
−0.744940 + 0.667131i \(0.767522\pi\)
\(840\) 329.605 + 40.1317i 0.392387 + 0.0477758i
\(841\) −645.000 −0.766944
\(842\) 1662.00i 1.97387i
\(843\) 44.2719 0.0525171
\(844\) −1210.00 −1.43365
\(845\) 251.401 + 754.203i 0.297516 + 0.892548i
\(846\) 132.816i 0.156993i
\(847\) −474.342 225.000i −0.560026 0.265643i
\(848\) 594.000i 0.700472i
\(849\) −1630.00 −1.91991
\(850\) −284.605 379.473i −0.334829 0.446439i
\(851\) 216.000 0.253819
\(852\) 252.982 0.296927
\(853\) −1407.21 −1.64972 −0.824861 0.565335i \(-0.808747\pi\)
−0.824861 + 0.565335i \(0.808747\pi\)
\(854\) 1260.00 + 597.670i 1.47541 + 0.699848i
\(855\) 135.000 45.0000i 0.157895 0.0526316i
\(856\) 162.000 0.189252
\(857\) −126.491 −0.147598 −0.0737988 0.997273i \(-0.523512\pi\)
−0.0737988 + 0.997273i \(0.523512\pi\)
\(858\) 420.000i 0.489510i
\(859\) 1546.35i 1.80018i −0.435705 0.900090i \(-0.643501\pi\)
0.435705 0.900090i \(-0.356499\pi\)
\(860\) 996.117 332.039i 1.15828 0.386092i
\(861\) 180.000 379.473i 0.209059 0.440736i
\(862\) 1074.00i 1.24594i
\(863\) 162.000i 0.187717i −0.995586 0.0938586i \(-0.970080\pi\)
0.995586 0.0938586i \(-0.0299202\pi\)
\(864\) 1138.42i 1.31762i
\(865\) 335.000 + 1005.00i 0.387283 + 1.16185i
\(866\) 322.552i 0.372462i
\(867\) −787.407 −0.908197
\(868\) 569.210 1200.00i 0.655772 1.38249i
\(869\) −1064.00 −1.22440
\(870\) 630.000 210.000i 0.724138 0.241379i
\(871\) 322.552i 0.370324i
\(872\) 222.000i 0.254587i
\(873\) −69.5701 −0.0796908
\(874\) 1024.58i 1.17229i
\(875\) −436.546 758.322i −0.498910 0.866654i
\(876\) −1000.00 −1.14155
\(877\) 426.000i 0.485747i −0.970058 0.242873i \(-0.921910\pi\)
0.970058 0.242873i \(-0.0780900\pi\)
\(878\) 56.9210 0.0648303
\(879\) −1450.00 −1.64960
\(880\) 243.495 + 730.486i 0.276699 + 0.830098i
\(881\) 455.368i 0.516876i −0.966028 0.258438i \(-0.916792\pi\)
0.966028 0.258438i \(-0.0832078\pi\)
\(882\) −113.842 + 93.0000i −0.129073 + 0.105442i
\(883\) 342.000i 0.387316i −0.981069 0.193658i \(-0.937965\pi\)
0.981069 0.193658i \(-0.0620352\pi\)
\(884\) 100.000 0.113122
\(885\) −142.302 + 47.4342i −0.160794 + 0.0535979i
\(886\) 1098.00 1.23928
\(887\) 139.140 0.156866 0.0784330 0.996919i \(-0.475008\pi\)
0.0784330 + 0.996919i \(0.475008\pi\)
\(888\) 170.763 0.192301
\(889\) −216.000 + 455.368i −0.242970 + 0.512225i
\(890\) −270.000 810.000i −0.303371 0.910112i
\(891\) −1246.00 −1.39843
\(892\) −221.359 −0.248161
\(893\) 1260.00i 1.41097i
\(894\) 436.394i 0.488137i
\(895\) 281.443 + 844.328i 0.314461 + 0.943383i
\(896\) 279.000 588.184i 0.311384 0.656455i
\(897\) 120.000i 0.133779i
\(898\) 222.000i 0.247216i
\(899\) 531.263i 0.590948i
\(900\) 100.000 75.0000i 0.111111 0.0833333i
\(901\) 341.526i 0.379052i
\(902\) −796.894 −0.883474
\(903\) −398.447 + 840.000i −0.441248 + 0.930233i
\(904\) 234.000 0.258850
\(905\) 135.000 45.0000i 0.149171 0.0497238i
\(906\) 132.816i 0.146596i
\(907\) 1446.00i 1.59427i −0.603803 0.797133i \(-0.706349\pi\)
0.603803 0.797133i \(-0.293651\pi\)
\(908\) −1786.69 −1.96772
\(909\) 104.355i 0.114802i
\(910\) 329.605 + 40.1317i 0.362203 + 0.0441007i
\(911\) 374.000 0.410538 0.205269 0.978706i \(-0.434193\pi\)
0.205269 + 0.978706i \(0.434193\pi\)
\(912\) 990.000i 1.08553i
\(913\) 1018.25 1.11528
\(914\) −414.000 −0.452954
\(915\) 996.117 332.039i 1.08865 0.362884i
\(916\) 1185.85i 1.29460i
\(917\) 142.302 300.000i 0.155183 0.327154i
\(918\) 480.000i 0.522876i
\(919\) 704.000 0.766050 0.383025 0.923738i \(-0.374882\pi\)
0.383025 + 0.923738i \(0.374882\pi\)
\(920\) 56.9210 + 170.763i 0.0618706 + 0.185612i
\(921\) 290.000 0.314875
\(922\) −2077.62 −2.25338
\(923\) 50.5964 0.0548174
\(924\) 1400.00 + 664.078i 1.51515 + 0.718699i
\(925\) −270.000 360.000i −0.291892 0.389189i
\(926\) 1818.00 1.96328
\(927\) −88.5438 −0.0955165
\(928\) 630.000i 0.678879i
\(929\) 303.579i 0.326780i −0.986562 0.163390i \(-0.947757\pi\)
0.986562 0.163390i \(-0.0522429\pi\)
\(930\) −569.210 1707.63i −0.612054 1.83616i
\(931\) −1080.00 + 882.275i −1.16004 + 0.947664i
\(932\) 1260.00i 1.35193i
\(933\) 1140.00i 1.22186i
\(934\) 1603.27i 1.71657i
\(935\) −140.000 420.000i −0.149733 0.449198i
\(936\) 9.48683i 0.0101355i
\(937\) −278.280 −0.296991 −0.148495 0.988913i \(-0.547443\pi\)
−0.148495 + 0.988913i \(0.547443\pi\)
\(938\) −1935.31 918.000i −2.06323 0.978678i
\(939\) 1760.00 1.87433
\(940\) 350.000 + 1050.00i 0.372340 + 1.11702i
\(941\) 1072.01i 1.13923i 0.821913 + 0.569613i \(0.192907\pi\)
−0.821913 + 0.569613i \(0.807093\pi\)
\(942\) 1110.00i 1.17834i
\(943\) 227.684 0.241446
\(944\) 104.355i 0.110546i
\(945\) 107.018 878.947i 0.113246 0.930102i
\(946\) 1764.00 1.86469
\(947\) 354.000i 0.373812i 0.982378 + 0.186906i \(0.0598460\pi\)
−0.982378 + 0.186906i \(0.940154\pi\)
\(948\) 1201.67 1.26758
\(949\) −200.000 −0.210748
\(950\) 1707.63 1280.72i 1.79751 1.34813i
\(951\) 1005.60i 1.05742i
\(952\) −56.9210 + 120.000i −0.0597910 + 0.126050i
\(953\) 612.000i 0.642183i −0.947048 0.321091i \(-0.895950\pi\)
0.947048 0.321091i \(-0.104050\pi\)
\(954\) −162.000 −0.169811
\(955\) 234.009 + 702.026i 0.245035 + 0.735105i
\(956\) −1210.00 −1.26569
\(957\) 619.806 0.647656
\(958\) 1593.79 1.66366
\(959\) 252.000 531.263i 0.262774 0.553976i
\(960\) −455.000 1365.00i −0.473958 1.42188i
\(961\) −479.000 −0.498439
\(962\) 170.763 0.177508
\(963\) 54.0000i 0.0560748i
\(964\) 1328.16i 1.37776i
\(965\) 1223.80 407.934i 1.26819 0.422729i
\(966\) −720.000 341.526i −0.745342 0.353547i
\(967\) 1644.00i 1.70010i 0.526699 + 0.850052i \(0.323429\pi\)
−0.526699 + 0.850052i \(0.676571\pi\)
\(968\) 225.000i 0.232438i
\(969\) 569.210i 0.587420i
\(970\) −990.000 + 330.000i −1.02062 + 0.340206i
\(971\) 85.3815i 0.0879315i 0.999033 + 0.0439658i \(0.0139992\pi\)
−0.999033 + 0.0439658i \(0.986001\pi\)
\(972\) 268.794 0.276537
\(973\) −369.986 + 780.000i −0.380253 + 0.801644i
\(974\) −324.000 −0.332649
\(975\) 200.000 150.000i 0.205128 0.153846i
\(976\) 730.486i 0.748449i
\(977\) 888.000i 0.908905i 0.890771 + 0.454452i \(0.150165\pi\)
−0.890771 + 0.454452i \(0.849835\pi\)
\(978\) −512.289 −0.523813
\(979\) 796.894i 0.813988i
\(980\) −654.923 + 1035.23i −0.668289 + 1.05636i
\(981\) 74.0000 0.0754332
\(982\) 2022.00i 2.05906i
\(983\) 101.193 0.102943 0.0514715 0.998674i \(-0.483609\pi\)
0.0514715 + 0.998674i \(0.483609\pi\)
\(984\) 180.000 0.182927
\(985\) −1622.25 + 540.749i −1.64695 + 0.548984i
\(986\) 265.631i 0.269403i
\(987\) −885.438 420.000i −0.897100 0.425532i
\(988\) 450.000i 0.455466i
\(989\) −504.000 −0.509606
\(990\) 199.223 66.4078i 0.201236 0.0670786i
\(991\) 1244.00 1.25530 0.627649 0.778497i \(-0.284017\pi\)
0.627649 + 0.778497i \(0.284017\pi\)
\(992\) −1707.63 −1.72140
\(993\) 1182.69 1.19103
\(994\) −144.000 + 303.579i −0.144869 + 0.305411i
\(995\) 270.000 90.0000i 0.271357 0.0904523i
\(996\) −1150.00 −1.15462
\(997\) 1211.15 1.21480 0.607398 0.794397i \(-0.292213\pi\)
0.607398 + 0.794397i \(0.292213\pi\)
\(998\) 186.000i 0.186373i
\(999\) 455.368i 0.455824i
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 35.3.c.c.34.4 yes 4
3.2 odd 2 315.3.e.c.244.2 4
4.3 odd 2 560.3.p.f.209.1 4
5.2 odd 4 175.3.d.b.76.1 2
5.3 odd 4 175.3.d.h.76.2 2
5.4 even 2 inner 35.3.c.c.34.1 4
7.2 even 3 245.3.i.c.129.3 8
7.3 odd 6 245.3.i.c.19.2 8
7.4 even 3 245.3.i.c.19.1 8
7.5 odd 6 245.3.i.c.129.4 8
7.6 odd 2 inner 35.3.c.c.34.3 yes 4
15.14 odd 2 315.3.e.c.244.3 4
20.19 odd 2 560.3.p.f.209.3 4
21.20 even 2 315.3.e.c.244.1 4
28.27 even 2 560.3.p.f.209.4 4
35.4 even 6 245.3.i.c.19.4 8
35.9 even 6 245.3.i.c.129.2 8
35.13 even 4 175.3.d.h.76.1 2
35.19 odd 6 245.3.i.c.129.1 8
35.24 odd 6 245.3.i.c.19.3 8
35.27 even 4 175.3.d.b.76.2 2
35.34 odd 2 inner 35.3.c.c.34.2 yes 4
105.104 even 2 315.3.e.c.244.4 4
140.139 even 2 560.3.p.f.209.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.3.c.c.34.1 4 5.4 even 2 inner
35.3.c.c.34.2 yes 4 35.34 odd 2 inner
35.3.c.c.34.3 yes 4 7.6 odd 2 inner
35.3.c.c.34.4 yes 4 1.1 even 1 trivial
175.3.d.b.76.1 2 5.2 odd 4
175.3.d.b.76.2 2 35.27 even 4
175.3.d.h.76.1 2 35.13 even 4
175.3.d.h.76.2 2 5.3 odd 4
245.3.i.c.19.1 8 7.4 even 3
245.3.i.c.19.2 8 7.3 odd 6
245.3.i.c.19.3 8 35.24 odd 6
245.3.i.c.19.4 8 35.4 even 6
245.3.i.c.129.1 8 35.19 odd 6
245.3.i.c.129.2 8 35.9 even 6
245.3.i.c.129.3 8 7.2 even 3
245.3.i.c.129.4 8 7.5 odd 6
315.3.e.c.244.1 4 21.20 even 2
315.3.e.c.244.2 4 3.2 odd 2
315.3.e.c.244.3 4 15.14 odd 2
315.3.e.c.244.4 4 105.104 even 2
560.3.p.f.209.1 4 4.3 odd 2
560.3.p.f.209.2 4 140.139 even 2
560.3.p.f.209.3 4 20.19 odd 2
560.3.p.f.209.4 4 28.27 even 2