Properties

Label 35.5.c.d.34.2
Level $35$
Weight $5$
Character 35.34
Analytic conductor $3.618$
Analytic rank $0$
Dimension $2$
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] = [35,5,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, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.34");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(3.61794870793\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-6}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.2
Root \(2.44949i\) of defining polynomial
Character \(\chi\) \(=\) 35.34
Dual form 35.5.c.d.34.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.44949i q^{2} +5.00000 q^{3} +10.0000 q^{4} +(5.00000 - 24.4949i) q^{5} +12.2474i q^{6} +(35.0000 + 34.2929i) q^{7} +63.6867i q^{8} -56.0000 q^{9} +O(q^{10})\) \(q+2.44949i q^{2} +5.00000 q^{3} +10.0000 q^{4} +(5.00000 - 24.4949i) q^{5} +12.2474i q^{6} +(35.0000 + 34.2929i) q^{7} +63.6867i q^{8} -56.0000 q^{9} +(60.0000 + 12.2474i) q^{10} +89.0000 q^{11} +50.0000 q^{12} -5.00000 q^{13} +(-84.0000 + 85.7321i) q^{14} +(25.0000 - 122.474i) q^{15} +4.00000 q^{16} -485.000 q^{17} -137.171i q^{18} -220.454i q^{19} +(50.0000 - 244.949i) q^{20} +(175.000 + 171.464i) q^{21} +218.005i q^{22} -700.554i q^{23} +318.434i q^{24} +(-575.000 - 244.949i) q^{25} -12.2474i q^{26} -685.000 q^{27} +(350.000 + 342.929i) q^{28} +191.000 q^{29} +(300.000 + 61.2372i) q^{30} +1053.28i q^{31} +1028.79i q^{32} +445.000 q^{33} -1188.00i q^{34} +(1015.00 - 685.857i) q^{35} -560.000 q^{36} +1631.36i q^{37} +540.000 q^{38} -25.0000 q^{39} +(1560.00 + 318.434i) q^{40} -2914.89i q^{41} +(-420.000 + 428.661i) q^{42} +377.221i q^{43} +890.000 q^{44} +(-280.000 + 1371.71i) q^{45} +1716.00 q^{46} -2195.00 q^{47} +20.0000 q^{48} +(49.0000 + 2400.50i) q^{49} +(600.000 - 1408.46i) q^{50} -2425.00 q^{51} -50.0000 q^{52} -1587.27i q^{53} -1677.90i q^{54} +(445.000 - 2180.05i) q^{55} +(-2184.00 + 2229.04i) q^{56} -1102.27i q^{57} +467.853i q^{58} +3625.24i q^{59} +(250.000 - 1224.74i) q^{60} -1935.10i q^{61} -2580.00 q^{62} +(-1960.00 - 1920.40i) q^{63} -2456.00 q^{64} +(-25.0000 + 122.474i) q^{65} +1090.02i q^{66} +2047.77i q^{67} -4850.00 q^{68} -3502.77i q^{69} +(1680.00 + 2486.23i) q^{70} +4454.00 q^{71} -3566.46i q^{72} +8650.00 q^{73} -3996.00 q^{74} +(-2875.00 - 1224.74i) q^{75} -2204.54i q^{76} +(3115.00 + 3052.06i) q^{77} -61.2372i q^{78} +5561.00 q^{79} +(20.0000 - 97.9796i) q^{80} +1111.00 q^{81} +7140.00 q^{82} +1990.00 q^{83} +(1750.00 + 1714.64i) q^{84} +(-2425.00 + 11880.0i) q^{85} -924.000 q^{86} +955.000 q^{87} +5668.12i q^{88} +808.332i q^{89} +(-3360.00 - 685.857i) q^{90} +(-175.000 - 171.464i) q^{91} -7005.54i q^{92} +5266.40i q^{93} -5376.63i q^{94} +(-5400.00 - 1102.27i) q^{95} +5143.93i q^{96} +9235.00 q^{97} +(-5880.00 + 120.025i) q^{98} -4984.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 10 q^{3} + 20 q^{4} + 10 q^{5} + 70 q^{7} - 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 10 q^{3} + 20 q^{4} + 10 q^{5} + 70 q^{7} - 112 q^{9} + 120 q^{10} + 178 q^{11} + 100 q^{12} - 10 q^{13} - 168 q^{14} + 50 q^{15} + 8 q^{16} - 970 q^{17} + 100 q^{20} + 350 q^{21} - 1150 q^{25} - 1370 q^{27} + 700 q^{28} + 382 q^{29} + 600 q^{30} + 890 q^{33} + 2030 q^{35} - 1120 q^{36} + 1080 q^{38} - 50 q^{39} + 3120 q^{40} - 840 q^{42} + 1780 q^{44} - 560 q^{45} + 3432 q^{46} - 4390 q^{47} + 40 q^{48} + 98 q^{49} + 1200 q^{50} - 4850 q^{51} - 100 q^{52} + 890 q^{55} - 4368 q^{56} + 500 q^{60} - 5160 q^{62} - 3920 q^{63} - 4912 q^{64} - 50 q^{65} - 9700 q^{68} + 3360 q^{70} + 8908 q^{71} + 17300 q^{73} - 7992 q^{74} - 5750 q^{75} + 6230 q^{77} + 11122 q^{79} + 40 q^{80} + 2222 q^{81} + 14280 q^{82} + 3980 q^{83} + 3500 q^{84} - 4850 q^{85} - 1848 q^{86} + 1910 q^{87} - 6720 q^{90} - 350 q^{91} - 10800 q^{95} + 18470 q^{97} - 11760 q^{98} - 9968 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.44949i 0.612372i 0.951972 + 0.306186i \(0.0990530\pi\)
−0.951972 + 0.306186i \(0.900947\pi\)
\(3\) 5.00000 0.555556 0.277778 0.960645i \(-0.410402\pi\)
0.277778 + 0.960645i \(0.410402\pi\)
\(4\) 10.0000 0.625000
\(5\) 5.00000 24.4949i 0.200000 0.979796i
\(6\) 12.2474i 0.340207i
\(7\) 35.0000 + 34.2929i 0.714286 + 0.699854i
\(8\) 63.6867i 0.995105i
\(9\) −56.0000 −0.691358
\(10\) 60.0000 + 12.2474i 0.600000 + 0.122474i
\(11\) 89.0000 0.735537 0.367769 0.929917i \(-0.380122\pi\)
0.367769 + 0.929917i \(0.380122\pi\)
\(12\) 50.0000 0.347222
\(13\) −5.00000 −0.0295858 −0.0147929 0.999891i \(-0.504709\pi\)
−0.0147929 + 0.999891i \(0.504709\pi\)
\(14\) −84.0000 + 85.7321i −0.428571 + 0.437409i
\(15\) 25.0000 122.474i 0.111111 0.544331i
\(16\) 4.00000 0.0156250
\(17\) −485.000 −1.67820 −0.839100 0.543977i \(-0.816918\pi\)
−0.839100 + 0.543977i \(0.816918\pi\)
\(18\) 137.171i 0.423369i
\(19\) 220.454i 0.610676i −0.952244 0.305338i \(-0.901231\pi\)
0.952244 0.305338i \(-0.0987695\pi\)
\(20\) 50.0000 244.949i 0.125000 0.612372i
\(21\) 175.000 + 171.464i 0.396825 + 0.388808i
\(22\) 218.005i 0.450423i
\(23\) 700.554i 1.32430i −0.749372 0.662149i \(-0.769644\pi\)
0.749372 0.662149i \(-0.230356\pi\)
\(24\) 318.434i 0.552836i
\(25\) −575.000 244.949i −0.920000 0.391918i
\(26\) 12.2474i 0.0181175i
\(27\) −685.000 −0.939643
\(28\) 350.000 + 342.929i 0.446429 + 0.437409i
\(29\) 191.000 0.227111 0.113555 0.993532i \(-0.463776\pi\)
0.113555 + 0.993532i \(0.463776\pi\)
\(30\) 300.000 + 61.2372i 0.333333 + 0.0680414i
\(31\) 1053.28i 1.09603i 0.836470 + 0.548013i \(0.184615\pi\)
−0.836470 + 0.548013i \(0.815385\pi\)
\(32\) 1028.79i 1.00467i
\(33\) 445.000 0.408632
\(34\) 1188.00i 1.02768i
\(35\) 1015.00 685.857i 0.828571 0.559883i
\(36\) −560.000 −0.432099
\(37\) 1631.36i 1.19164i 0.803117 + 0.595822i \(0.203174\pi\)
−0.803117 + 0.595822i \(0.796826\pi\)
\(38\) 540.000 0.373961
\(39\) −25.0000 −0.0164366
\(40\) 1560.00 + 318.434i 0.975000 + 0.199021i
\(41\) 2914.89i 1.73402i −0.498288 0.867012i \(-0.666038\pi\)
0.498288 0.867012i \(-0.333962\pi\)
\(42\) −420.000 + 428.661i −0.238095 + 0.243005i
\(43\) 377.221i 0.204014i 0.994784 + 0.102007i \(0.0325264\pi\)
−0.994784 + 0.102007i \(0.967474\pi\)
\(44\) 890.000 0.459711
\(45\) −280.000 + 1371.71i −0.138272 + 0.677390i
\(46\) 1716.00 0.810964
\(47\) −2195.00 −0.993662 −0.496831 0.867847i \(-0.665503\pi\)
−0.496831 + 0.867847i \(0.665503\pi\)
\(48\) 20.0000 0.00868056
\(49\) 49.0000 + 2400.50i 0.0204082 + 0.999792i
\(50\) 600.000 1408.46i 0.240000 0.563383i
\(51\) −2425.00 −0.932334
\(52\) −50.0000 −0.0184911
\(53\) 1587.27i 0.565066i −0.959258 0.282533i \(-0.908825\pi\)
0.959258 0.282533i \(-0.0911746\pi\)
\(54\) 1677.90i 0.575412i
\(55\) 445.000 2180.05i 0.147107 0.720676i
\(56\) −2184.00 + 2229.04i −0.696429 + 0.710789i
\(57\) 1102.27i 0.339265i
\(58\) 467.853i 0.139076i
\(59\) 3625.24i 1.04144i 0.853728 + 0.520719i \(0.174336\pi\)
−0.853728 + 0.520719i \(0.825664\pi\)
\(60\) 250.000 1224.74i 0.0694444 0.340207i
\(61\) 1935.10i 0.520048i −0.965602 0.260024i \(-0.916270\pi\)
0.965602 0.260024i \(-0.0837304\pi\)
\(62\) −2580.00 −0.671176
\(63\) −1960.00 1920.40i −0.493827 0.483850i
\(64\) −2456.00 −0.599609
\(65\) −25.0000 + 122.474i −0.00591716 + 0.0289880i
\(66\) 1090.02i 0.250235i
\(67\) 2047.77i 0.456176i 0.973641 + 0.228088i \(0.0732474\pi\)
−0.973641 + 0.228088i \(0.926753\pi\)
\(68\) −4850.00 −1.04888
\(69\) 3502.77i 0.735722i
\(70\) 1680.00 + 2486.23i 0.342857 + 0.507394i
\(71\) 4454.00 0.883555 0.441777 0.897125i \(-0.354348\pi\)
0.441777 + 0.897125i \(0.354348\pi\)
\(72\) 3566.46i 0.687974i
\(73\) 8650.00 1.62319 0.811597 0.584218i \(-0.198599\pi\)
0.811597 + 0.584218i \(0.198599\pi\)
\(74\) −3996.00 −0.729730
\(75\) −2875.00 1224.74i −0.511111 0.217732i
\(76\) 2204.54i 0.381673i
\(77\) 3115.00 + 3052.06i 0.525384 + 0.514769i
\(78\) 61.2372i 0.0100653i
\(79\) 5561.00 0.891043 0.445522 0.895271i \(-0.353018\pi\)
0.445522 + 0.895271i \(0.353018\pi\)
\(80\) 20.0000 97.9796i 0.00312500 0.0153093i
\(81\) 1111.00 0.169334
\(82\) 7140.00 1.06187
\(83\) 1990.00 0.288866 0.144433 0.989515i \(-0.453864\pi\)
0.144433 + 0.989515i \(0.453864\pi\)
\(84\) 1750.00 + 1714.64i 0.248016 + 0.243005i
\(85\) −2425.00 + 11880.0i −0.335640 + 1.64429i
\(86\) −924.000 −0.124932
\(87\) 955.000 0.126173
\(88\) 5668.12i 0.731937i
\(89\) 808.332i 0.102049i 0.998697 + 0.0510246i \(0.0162487\pi\)
−0.998697 + 0.0510246i \(0.983751\pi\)
\(90\) −3360.00 685.857i −0.414815 0.0846737i
\(91\) −175.000 171.464i −0.0211327 0.0207057i
\(92\) 7005.54i 0.827687i
\(93\) 5266.40i 0.608903i
\(94\) 5376.63i 0.608491i
\(95\) −5400.00 1102.27i −0.598338 0.122135i
\(96\) 5143.93i 0.558152i
\(97\) 9235.00 0.981507 0.490754 0.871298i \(-0.336722\pi\)
0.490754 + 0.871298i \(0.336722\pi\)
\(98\) −5880.00 + 120.025i −0.612245 + 0.0124974i
\(99\) −4984.00 −0.508520
\(100\) −5750.00 2449.49i −0.575000 0.244949i
\(101\) 4825.49i 0.473041i 0.971626 + 0.236521i \(0.0760071\pi\)
−0.971626 + 0.236521i \(0.923993\pi\)
\(102\) 5940.01i 0.570935i
\(103\) −4715.00 −0.444434 −0.222217 0.974997i \(-0.571329\pi\)
−0.222217 + 0.974997i \(0.571329\pi\)
\(104\) 318.434i 0.0294410i
\(105\) 5075.00 3429.29i 0.460317 0.311046i
\(106\) 3888.00 0.346031
\(107\) 12668.8i 1.10654i −0.833002 0.553269i \(-0.813380\pi\)
0.833002 0.553269i \(-0.186620\pi\)
\(108\) −6850.00 −0.587277
\(109\) 12311.0 1.03619 0.518096 0.855322i \(-0.326641\pi\)
0.518096 + 0.855322i \(0.326641\pi\)
\(110\) 5340.00 + 1090.02i 0.441322 + 0.0900845i
\(111\) 8156.80i 0.662024i
\(112\) 140.000 + 137.171i 0.0111607 + 0.0109352i
\(113\) 3120.65i 0.244393i 0.992506 + 0.122196i \(0.0389938\pi\)
−0.992506 + 0.122196i \(0.961006\pi\)
\(114\) 2700.00 0.207756
\(115\) −17160.0 3502.77i −1.29754 0.264860i
\(116\) 1910.00 0.141944
\(117\) 280.000 0.0204544
\(118\) −8880.00 −0.637748
\(119\) −16975.0 16632.0i −1.19871 1.17450i
\(120\) 7800.00 + 1592.17i 0.541667 + 0.110567i
\(121\) −6720.00 −0.458985
\(122\) 4740.00 0.318463
\(123\) 14574.5i 0.963346i
\(124\) 10532.8i 0.685016i
\(125\) −8875.00 + 12859.8i −0.568000 + 0.823029i
\(126\) 4704.00 4801.00i 0.296296 0.302406i
\(127\) 23867.8i 1.47981i −0.672712 0.739904i \(-0.734871\pi\)
0.672712 0.739904i \(-0.265129\pi\)
\(128\) 10444.6i 0.637489i
\(129\) 1886.11i 0.113341i
\(130\) −300.000 61.2372i −0.0177515 0.00362351i
\(131\) 6736.10i 0.392524i −0.980552 0.196262i \(-0.937120\pi\)
0.980552 0.196262i \(-0.0628802\pi\)
\(132\) 4450.00 0.255395
\(133\) 7560.00 7715.89i 0.427384 0.436197i
\(134\) −5016.00 −0.279350
\(135\) −3425.00 + 16779.0i −0.187929 + 0.920659i
\(136\) 30888.1i 1.66999i
\(137\) 23069.3i 1.22912i 0.788871 + 0.614558i \(0.210666\pi\)
−0.788871 + 0.614558i \(0.789334\pi\)
\(138\) 8580.00 0.450536
\(139\) 29491.9i 1.52641i 0.646154 + 0.763207i \(0.276376\pi\)
−0.646154 + 0.763207i \(0.723624\pi\)
\(140\) 10150.0 6858.57i 0.517857 0.349927i
\(141\) −10975.0 −0.552035
\(142\) 10910.0i 0.541065i
\(143\) −445.000 −0.0217615
\(144\) −224.000 −0.0108025
\(145\) 955.000 4678.53i 0.0454221 0.222522i
\(146\) 21188.1i 0.993999i
\(147\) 245.000 + 12002.5i 0.0113379 + 0.555440i
\(148\) 16313.6i 0.744777i
\(149\) 28346.0 1.27679 0.638395 0.769709i \(-0.279599\pi\)
0.638395 + 0.769709i \(0.279599\pi\)
\(150\) 3000.00 7042.28i 0.133333 0.312990i
\(151\) −17551.0 −0.769747 −0.384873 0.922969i \(-0.625755\pi\)
−0.384873 + 0.922969i \(0.625755\pi\)
\(152\) 14040.0 0.607687
\(153\) 27160.0 1.16024
\(154\) −7476.00 + 7630.16i −0.315230 + 0.321731i
\(155\) 25800.0 + 5266.40i 1.07388 + 0.219205i
\(156\) −250.000 −0.0102728
\(157\) −25790.0 −1.04629 −0.523145 0.852244i \(-0.675241\pi\)
−0.523145 + 0.852244i \(0.675241\pi\)
\(158\) 13621.6i 0.545650i
\(159\) 7936.35i 0.313925i
\(160\) 25200.0 + 5143.93i 0.984375 + 0.200935i
\(161\) 24024.0 24519.4i 0.926816 0.945928i
\(162\) 2721.38i 0.103695i
\(163\) 37153.9i 1.39839i −0.714930 0.699196i \(-0.753542\pi\)
0.714930 0.699196i \(-0.246458\pi\)
\(164\) 29148.9i 1.08376i
\(165\) 2225.00 10900.2i 0.0817264 0.400376i
\(166\) 4874.48i 0.176894i
\(167\) −20795.0 −0.745634 −0.372817 0.927905i \(-0.621608\pi\)
−0.372817 + 0.927905i \(0.621608\pi\)
\(168\) −10920.0 + 11145.2i −0.386905 + 0.394883i
\(169\) −28536.0 −0.999125
\(170\) −29100.0 5940.01i −1.00692 0.205537i
\(171\) 12345.4i 0.422196i
\(172\) 3772.21i 0.127509i
\(173\) 115.000 0.00384243 0.00192121 0.999998i \(-0.499388\pi\)
0.00192121 + 0.999998i \(0.499388\pi\)
\(174\) 2339.26i 0.0772646i
\(175\) −11725.0 28291.6i −0.382857 0.923808i
\(176\) 356.000 0.0114928
\(177\) 18126.2i 0.578577i
\(178\) −1980.00 −0.0624921
\(179\) 5318.00 0.165975 0.0829874 0.996551i \(-0.473554\pi\)
0.0829874 + 0.996551i \(0.473554\pi\)
\(180\) −2800.00 + 13717.1i −0.0864198 + 0.423369i
\(181\) 12345.4i 0.376833i 0.982089 + 0.188417i \(0.0603355\pi\)
−0.982089 + 0.188417i \(0.939665\pi\)
\(182\) 420.000 428.661i 0.0126796 0.0129411i
\(183\) 9675.48i 0.288915i
\(184\) 44616.0 1.31782
\(185\) 39960.0 + 8156.80i 1.16757 + 0.238329i
\(186\) −12900.0 −0.372875
\(187\) −43165.0 −1.23438
\(188\) −21950.0 −0.621039
\(189\) −23975.0 23490.6i −0.671174 0.657613i
\(190\) 2700.00 13227.2i 0.0747922 0.366406i
\(191\) −14263.0 −0.390971 −0.195485 0.980707i \(-0.562628\pi\)
−0.195485 + 0.980707i \(0.562628\pi\)
\(192\) −12280.0 −0.333116
\(193\) 32005.0i 0.859219i −0.903015 0.429609i \(-0.858651\pi\)
0.903015 0.429609i \(-0.141349\pi\)
\(194\) 22621.0i 0.601048i
\(195\) −125.000 + 612.372i −0.00328731 + 0.0161045i
\(196\) 490.000 + 24005.0i 0.0127551 + 0.624870i
\(197\) 3394.99i 0.0874795i 0.999043 + 0.0437398i \(0.0139272\pi\)
−0.999043 + 0.0437398i \(0.986073\pi\)
\(198\) 12208.3i 0.311403i
\(199\) 19400.0i 0.489886i 0.969538 + 0.244943i \(0.0787692\pi\)
−0.969538 + 0.244943i \(0.921231\pi\)
\(200\) 15600.0 36619.9i 0.390000 0.915497i
\(201\) 10238.9i 0.253431i
\(202\) −11820.0 −0.289677
\(203\) 6685.00 + 6549.94i 0.162222 + 0.158944i
\(204\) −24250.0 −0.582709
\(205\) −71400.0 14574.5i −1.69899 0.346805i
\(206\) 11549.3i 0.272159i
\(207\) 39231.0i 0.915565i
\(208\) −20.0000 −0.000462278
\(209\) 19620.4i 0.449175i
\(210\) 8400.00 + 12431.2i 0.190476 + 0.281886i
\(211\) 52817.0 1.18634 0.593170 0.805078i \(-0.297876\pi\)
0.593170 + 0.805078i \(0.297876\pi\)
\(212\) 15872.7i 0.353166i
\(213\) 22270.0 0.490864
\(214\) 31032.0 0.677614
\(215\) 9240.00 + 1886.11i 0.199892 + 0.0408027i
\(216\) 43625.4i 0.935044i
\(217\) −36120.0 + 36864.8i −0.767058 + 0.782875i
\(218\) 30155.7i 0.634536i
\(219\) 43250.0 0.901774
\(220\) 4450.00 21800.5i 0.0919421 0.450423i
\(221\) 2425.00 0.0496509
\(222\) −19980.0 −0.405405
\(223\) 13645.0 0.274387 0.137194 0.990544i \(-0.456192\pi\)
0.137194 + 0.990544i \(0.456192\pi\)
\(224\) −35280.0 + 36007.5i −0.703125 + 0.717624i
\(225\) 32200.0 + 13717.1i 0.636049 + 0.270956i
\(226\) −7644.00 −0.149659
\(227\) 74485.0 1.44550 0.722748 0.691111i \(-0.242879\pi\)
0.722748 + 0.691111i \(0.242879\pi\)
\(228\) 11022.7i 0.212040i
\(229\) 68463.2i 1.30553i −0.757561 0.652764i \(-0.773609\pi\)
0.757561 0.652764i \(-0.226391\pi\)
\(230\) 8580.00 42033.2i 0.162193 0.794579i
\(231\) 15575.0 + 15260.3i 0.291880 + 0.285983i
\(232\) 12164.2i 0.225999i
\(233\) 60169.3i 1.10831i 0.832412 + 0.554157i \(0.186959\pi\)
−0.832412 + 0.554157i \(0.813041\pi\)
\(234\) 685.857i 0.0125257i
\(235\) −10975.0 + 53766.3i −0.198732 + 0.973586i
\(236\) 36252.4i 0.650899i
\(237\) 27805.0 0.495024
\(238\) 40740.0 41580.1i 0.719229 0.734060i
\(239\) −75367.0 −1.31943 −0.659714 0.751517i \(-0.729322\pi\)
−0.659714 + 0.751517i \(0.729322\pi\)
\(240\) 100.000 489.898i 0.00173611 0.00850517i
\(241\) 77869.3i 1.34070i 0.742044 + 0.670351i \(0.233856\pi\)
−0.742044 + 0.670351i \(0.766144\pi\)
\(242\) 16460.6i 0.281070i
\(243\) 61040.0 1.03372
\(244\) 19351.0i 0.325030i
\(245\) 59045.0 + 10802.2i 0.983673 + 0.179963i
\(246\) 35700.0 0.589927
\(247\) 1102.27i 0.0180673i
\(248\) −67080.0 −1.09066
\(249\) 9950.00 0.160481
\(250\) −31500.0 21739.2i −0.504000 0.347828i
\(251\) 50410.5i 0.800154i −0.916482 0.400077i \(-0.868983\pi\)
0.916482 0.400077i \(-0.131017\pi\)
\(252\) −19600.0 19204.0i −0.308642 0.302406i
\(253\) 62349.3i 0.974071i
\(254\) 58464.0 0.906194
\(255\) −12125.0 + 59400.1i −0.186467 + 0.913497i
\(256\) −64880.0 −0.989990
\(257\) 3370.00 0.0510227 0.0255114 0.999675i \(-0.491879\pi\)
0.0255114 + 0.999675i \(0.491879\pi\)
\(258\) −4620.00 −0.0694069
\(259\) −55944.0 + 57097.6i −0.833977 + 0.851174i
\(260\) −250.000 + 1224.74i −0.00369822 + 0.0181175i
\(261\) −10696.0 −0.157015
\(262\) 16500.0 0.240371
\(263\) 59385.4i 0.858556i 0.903173 + 0.429278i \(0.141232\pi\)
−0.903173 + 0.429278i \(0.858768\pi\)
\(264\) 28340.6i 0.406632i
\(265\) −38880.0 7936.35i −0.553649 0.113013i
\(266\) 18900.0 + 18518.1i 0.267115 + 0.261718i
\(267\) 4041.66i 0.0566940i
\(268\) 20477.7i 0.285110i
\(269\) 77012.0i 1.06427i 0.846658 + 0.532137i \(0.178611\pi\)
−0.846658 + 0.532137i \(0.821389\pi\)
\(270\) −41100.0 8389.50i −0.563786 0.115082i
\(271\) 143222.i 1.95016i −0.221855 0.975080i \(-0.571211\pi\)
0.221855 0.975080i \(-0.428789\pi\)
\(272\) −1940.00 −0.0262219
\(273\) −875.000 857.321i −0.0117404 0.0115032i
\(274\) −56508.0 −0.752677
\(275\) −51175.0 21800.5i −0.676694 0.288271i
\(276\) 35027.7i 0.459826i
\(277\) 101928.i 1.32842i −0.747547 0.664209i \(-0.768769\pi\)
0.747547 0.664209i \(-0.231231\pi\)
\(278\) −72240.0 −0.934734
\(279\) 58983.7i 0.757746i
\(280\) 43680.0 + 64642.0i 0.557143 + 0.824516i
\(281\) −47521.0 −0.601829 −0.300914 0.953651i \(-0.597292\pi\)
−0.300914 + 0.953651i \(0.597292\pi\)
\(282\) 26883.1i 0.338051i
\(283\) −43115.0 −0.538339 −0.269169 0.963093i \(-0.586749\pi\)
−0.269169 + 0.963093i \(0.586749\pi\)
\(284\) 44540.0 0.552222
\(285\) −27000.0 5511.35i −0.332410 0.0678529i
\(286\) 1090.02i 0.0133261i
\(287\) 99960.0 102021.i 1.21356 1.23859i
\(288\) 57612.0i 0.694589i
\(289\) 151704. 1.81636
\(290\) 11460.0 + 2339.26i 0.136266 + 0.0278153i
\(291\) 46175.0 0.545282
\(292\) 86500.0 1.01450
\(293\) −162125. −1.88849 −0.944245 0.329243i \(-0.893206\pi\)
−0.944245 + 0.329243i \(0.893206\pi\)
\(294\) −29400.0 + 600.125i −0.340136 + 0.00694300i
\(295\) 88800.0 + 18126.2i 1.02040 + 0.208288i
\(296\) −103896. −1.18581
\(297\) −60965.0 −0.691143
\(298\) 69433.2i 0.781871i
\(299\) 3502.77i 0.0391804i
\(300\) −28750.0 12247.4i −0.319444 0.136083i
\(301\) −12936.0 + 13202.7i −0.142780 + 0.145724i
\(302\) 42991.0i 0.471372i
\(303\) 24127.5i 0.262801i
\(304\) 881.816i 0.00954181i
\(305\) −47400.0 9675.48i −0.509540 0.104010i
\(306\) 66528.1i 0.710497i
\(307\) 33805.0 0.358678 0.179339 0.983787i \(-0.442604\pi\)
0.179339 + 0.983787i \(0.442604\pi\)
\(308\) 31150.0 + 30520.6i 0.328365 + 0.321731i
\(309\) −23575.0 −0.246908
\(310\) −12900.0 + 63196.8i −0.134235 + 0.657615i
\(311\) 50435.0i 0.521448i 0.965413 + 0.260724i \(0.0839613\pi\)
−0.965413 + 0.260724i \(0.916039\pi\)
\(312\) 1592.17i 0.0163561i
\(313\) 68155.0 0.695679 0.347840 0.937554i \(-0.386915\pi\)
0.347840 + 0.937554i \(0.386915\pi\)
\(314\) 63172.3i 0.640719i
\(315\) −56840.0 + 38408.0i −0.572840 + 0.387080i
\(316\) 55610.0 0.556902
\(317\) 42435.0i 0.422285i −0.977455 0.211142i \(-0.932282\pi\)
0.977455 0.211142i \(-0.0677184\pi\)
\(318\) 19440.0 0.192239
\(319\) 16999.0 0.167048
\(320\) −12280.0 + 60159.5i −0.119922 + 0.587495i
\(321\) 63343.8i 0.614744i
\(322\) 60060.0 + 58846.5i 0.579260 + 0.567557i
\(323\) 106920.i 1.02484i
\(324\) 11110.0 0.105834
\(325\) 2875.00 + 1224.74i 0.0272189 + 0.0115952i
\(326\) 91008.0 0.856336
\(327\) 61555.0 0.575662
\(328\) 185640. 1.72554
\(329\) −76825.0 75272.8i −0.709759 0.695419i
\(330\) 26700.0 + 5450.11i 0.245179 + 0.0500470i
\(331\) −114706. −1.04696 −0.523480 0.852038i \(-0.675367\pi\)
−0.523480 + 0.852038i \(0.675367\pi\)
\(332\) 19900.0 0.180541
\(333\) 91356.2i 0.823852i
\(334\) 50937.1i 0.456606i
\(335\) 50160.0 + 10238.9i 0.446959 + 0.0912352i
\(336\) 700.000 + 685.857i 0.00620040 + 0.00607512i
\(337\) 117007.i 1.03027i 0.857108 + 0.515137i \(0.172259\pi\)
−0.857108 + 0.515137i \(0.827741\pi\)
\(338\) 69898.6i 0.611836i
\(339\) 15603.2i 0.135774i
\(340\) −24250.0 + 118800.i −0.209775 + 1.02768i
\(341\) 93742.0i 0.806168i
\(342\) −30240.0 −0.258541
\(343\) −80605.0 + 85697.8i −0.685131 + 0.728420i
\(344\) −24024.0 −0.203015
\(345\) −85800.0 17513.9i −0.720857 0.147144i
\(346\) 281.691i 0.00235300i
\(347\) 70481.6i 0.585352i −0.956212 0.292676i \(-0.905454\pi\)
0.956212 0.292676i \(-0.0945457\pi\)
\(348\) 9550.00 0.0788578
\(349\) 91390.5i 0.750326i 0.926959 + 0.375163i \(0.122413\pi\)
−0.926959 + 0.375163i \(0.877587\pi\)
\(350\) 69300.0 28720.3i 0.565714 0.234451i
\(351\) 3425.00 0.0278001
\(352\) 91561.9i 0.738975i
\(353\) −11405.0 −0.0915263 −0.0457631 0.998952i \(-0.514572\pi\)
−0.0457631 + 0.998952i \(0.514572\pi\)
\(354\) −44400.0 −0.354304
\(355\) 22270.0 109100.i 0.176711 0.865703i
\(356\) 8083.32i 0.0637807i
\(357\) −84875.0 83160.2i −0.665953 0.652498i
\(358\) 13026.4i 0.101638i
\(359\) 230366. 1.78743 0.893716 0.448633i \(-0.148089\pi\)
0.893716 + 0.448633i \(0.148089\pi\)
\(360\) −87360.0 17832.3i −0.674074 0.137595i
\(361\) 81721.0 0.627075
\(362\) −30240.0 −0.230762
\(363\) −33600.0 −0.254992
\(364\) −1750.00 1714.64i −0.0132079 0.0129411i
\(365\) 43250.0 211881.i 0.324639 1.59040i
\(366\) 23700.0 0.176924
\(367\) 74485.0 0.553015 0.276507 0.961012i \(-0.410823\pi\)
0.276507 + 0.961012i \(0.410823\pi\)
\(368\) 2802.22i 0.0206922i
\(369\) 163234.i 1.19883i
\(370\) −19980.0 + 97881.6i −0.145946 + 0.714986i
\(371\) 54432.0 55554.4i 0.395464 0.403618i
\(372\) 52664.0i 0.380564i
\(373\) 102550.i 0.737088i −0.929610 0.368544i \(-0.879856\pi\)
0.929610 0.368544i \(-0.120144\pi\)
\(374\) 105732.i 0.755900i
\(375\) −44375.0 + 64299.1i −0.315556 + 0.457238i
\(376\) 139792.i 0.988799i
\(377\) −955.000 −0.00671925
\(378\) 57540.0 58726.5i 0.402704 0.411008i
\(379\) −172954. −1.20407 −0.602036 0.798469i \(-0.705643\pi\)
−0.602036 + 0.798469i \(0.705643\pi\)
\(380\) −54000.0 11022.7i −0.373961 0.0763345i
\(381\) 119339.i 0.822116i
\(382\) 34937.1i 0.239420i
\(383\) −144050. −0.982010 −0.491005 0.871157i \(-0.663370\pi\)
−0.491005 + 0.871157i \(0.663370\pi\)
\(384\) 52223.1i 0.354161i
\(385\) 90335.0 61041.3i 0.609445 0.411815i
\(386\) 78396.0 0.526162
\(387\) 21124.4i 0.141047i
\(388\) 92350.0 0.613442
\(389\) −148969. −0.984457 −0.492228 0.870466i \(-0.663818\pi\)
−0.492228 + 0.870466i \(0.663818\pi\)
\(390\) −1500.00 306.186i −0.00986193 0.00201306i
\(391\) 339769.i 2.22244i
\(392\) −152880. + 3120.65i −0.994898 + 0.0203083i
\(393\) 33680.5i 0.218069i
\(394\) −8316.00 −0.0535700
\(395\) 27805.0 136216.i 0.178209 0.873040i
\(396\) −49840.0 −0.317825
\(397\) −256925. −1.63014 −0.815071 0.579361i \(-0.803302\pi\)
−0.815071 + 0.579361i \(0.803302\pi\)
\(398\) −47520.0 −0.299992
\(399\) 37800.0 38579.5i 0.237436 0.242332i
\(400\) −2300.00 979.796i −0.0143750 0.00612372i
\(401\) −35641.0 −0.221647 −0.110823 0.993840i \(-0.535349\pi\)
−0.110823 + 0.993840i \(0.535349\pi\)
\(402\) −25080.0 −0.155194
\(403\) 5266.40i 0.0324268i
\(404\) 48254.9i 0.295651i
\(405\) 5555.00 27213.8i 0.0338668 0.165913i
\(406\) −16044.0 + 16374.8i −0.0973331 + 0.0993402i
\(407\) 145191.i 0.876498i
\(408\) 154440.i 0.927770i
\(409\) 151721.i 0.906985i −0.891260 0.453493i \(-0.850178\pi\)
0.891260 0.453493i \(-0.149822\pi\)
\(410\) 35700.0 174894.i 0.212374 1.04041i
\(411\) 115346.i 0.682843i
\(412\) −47150.0 −0.277771
\(413\) −124320. + 126884.i −0.728855 + 0.743884i
\(414\) −96096.0 −0.560667
\(415\) 9950.00 48744.8i 0.0577733 0.283030i
\(416\) 5143.93i 0.0297241i
\(417\) 147459.i 0.848008i
\(418\) 48060.0 0.275062
\(419\) 150889.i 0.859465i 0.902956 + 0.429733i \(0.141392\pi\)
−0.902956 + 0.429733i \(0.858608\pi\)
\(420\) 50750.0 34292.9i 0.287698 0.194404i
\(421\) −4681.00 −0.0264104 −0.0132052 0.999913i \(-0.504203\pi\)
−0.0132052 + 0.999913i \(0.504203\pi\)
\(422\) 129375.i 0.726481i
\(423\) 122920. 0.686976
\(424\) 101088. 0.562300
\(425\) 278875. + 118800.i 1.54394 + 0.657718i
\(426\) 54550.1i 0.300591i
\(427\) 66360.0 67728.4i 0.363957 0.371463i
\(428\) 126688.i 0.691587i
\(429\) −2225.00 −0.0120897
\(430\) −4620.00 + 22633.3i −0.0249865 + 0.122408i
\(431\) −87103.0 −0.468898 −0.234449 0.972128i \(-0.575329\pi\)
−0.234449 + 0.972128i \(0.575329\pi\)
\(432\) −2740.00 −0.0146819
\(433\) 231730. 1.23597 0.617983 0.786192i \(-0.287950\pi\)
0.617983 + 0.786192i \(0.287950\pi\)
\(434\) −90300.0 88475.6i −0.479411 0.469725i
\(435\) 4775.00 23392.6i 0.0252345 0.123623i
\(436\) 123110. 0.647620
\(437\) −154440. −0.808718
\(438\) 105940.i 0.552222i
\(439\) 246272.i 1.27787i −0.769262 0.638933i \(-0.779376\pi\)
0.769262 0.638933i \(-0.220624\pi\)
\(440\) 138840. + 28340.6i 0.717149 + 0.146387i
\(441\) −2744.00 134428.i −0.0141093 0.691214i
\(442\) 5940.01i 0.0304048i
\(443\) 349841.i 1.78264i 0.453376 + 0.891319i \(0.350219\pi\)
−0.453376 + 0.891319i \(0.649781\pi\)
\(444\) 81568.0i 0.413765i
\(445\) 19800.0 + 4041.66i 0.0999874 + 0.0204098i
\(446\) 33423.3i 0.168027i
\(447\) 141730. 0.709327
\(448\) −85960.0 84223.3i −0.428292 0.419639i
\(449\) 254711. 1.26344 0.631721 0.775196i \(-0.282349\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(450\) −33600.0 + 78873.6i −0.165926 + 0.389499i
\(451\) 259425.i 1.27544i
\(452\) 31206.5i 0.152745i
\(453\) −87755.0 −0.427637
\(454\) 182450.i 0.885182i
\(455\) −5075.00 + 3429.29i −0.0245139 + 0.0165646i
\(456\) 70200.0 0.337604
\(457\) 263629.i 1.26229i 0.775663 + 0.631147i \(0.217415\pi\)
−0.775663 + 0.631147i \(0.782585\pi\)
\(458\) 167700. 0.799470
\(459\) 332225. 1.57691
\(460\) −171600. 35027.7i −0.810964 0.165537i
\(461\) 128255.i 0.603495i −0.953388 0.301747i \(-0.902430\pi\)
0.953388 0.301747i \(-0.0975699\pi\)
\(462\) −37380.0 + 38150.8i −0.175128 + 0.178739i
\(463\) 81857.0i 0.381851i −0.981605 0.190926i \(-0.938851\pi\)
0.981605 0.190926i \(-0.0611489\pi\)
\(464\) 764.000 0.00354860
\(465\) 129000. + 26332.0i 0.596601 + 0.121781i
\(466\) −147384. −0.678701
\(467\) 204445. 0.937438 0.468719 0.883347i \(-0.344716\pi\)
0.468719 + 0.883347i \(0.344716\pi\)
\(468\) 2800.00 0.0127840
\(469\) −70224.0 + 71672.1i −0.319257 + 0.325840i
\(470\) −131700. 26883.1i −0.596197 0.121698i
\(471\) −128950. −0.581272
\(472\) −230880. −1.03634
\(473\) 33572.7i 0.150060i
\(474\) 68108.1i 0.303139i
\(475\) −54000.0 + 126761.i −0.239335 + 0.561822i
\(476\) −169750. 166320.i −0.749197 0.734060i
\(477\) 88887.1i 0.390663i
\(478\) 184611.i 0.807981i
\(479\) 79534.9i 0.346647i −0.984865 0.173323i \(-0.944549\pi\)
0.984865 0.173323i \(-0.0554505\pi\)
\(480\) 126000. + 25719.6i 0.546875 + 0.111630i
\(481\) 8156.80i 0.0352557i
\(482\) −190740. −0.821009
\(483\) 120120. 122597.i 0.514898 0.525515i
\(484\) −67200.0 −0.286866
\(485\) 46175.0 226210.i 0.196301 0.961677i
\(486\) 149517.i 0.633020i
\(487\) 164958.i 0.695531i −0.937582 0.347766i \(-0.886941\pi\)
0.937582 0.347766i \(-0.113059\pi\)
\(488\) 123240. 0.517502
\(489\) 185769.i 0.776884i
\(490\) −26460.0 + 144630.i −0.110204 + 0.602375i
\(491\) −74191.0 −0.307743 −0.153872 0.988091i \(-0.549174\pi\)
−0.153872 + 0.988091i \(0.549174\pi\)
\(492\) 145745.i 0.602091i
\(493\) −92635.0 −0.381137
\(494\) −2700.00 −0.0110639
\(495\) −24920.0 + 122083.i −0.101704 + 0.498245i
\(496\) 4213.12i 0.0171254i
\(497\) 155890. + 152740.i 0.631111 + 0.618360i
\(498\) 24372.4i 0.0982743i
\(499\) −278527. −1.11858 −0.559289 0.828973i \(-0.688926\pi\)
−0.559289 + 0.828973i \(0.688926\pi\)
\(500\) −88750.0 + 128598.i −0.355000 + 0.514393i
\(501\) −103975. −0.414241
\(502\) 123480. 0.489992
\(503\) −60275.0 −0.238233 −0.119116 0.992880i \(-0.538006\pi\)
−0.119116 + 0.992880i \(0.538006\pi\)
\(504\) 122304. 124826.i 0.481481 0.491410i
\(505\) 118200. + 24127.5i 0.463484 + 0.0946083i
\(506\) 152724. 0.596494
\(507\) −142680. −0.555069
\(508\) 238678.i 0.924880i
\(509\) 348709.i 1.34595i 0.739666 + 0.672974i \(0.234983\pi\)
−0.739666 + 0.672974i \(0.765017\pi\)
\(510\) −145500. 29700.1i −0.559400 0.114187i
\(511\) 302750. + 296633.i 1.15942 + 1.13600i
\(512\) 8191.09i 0.0312465i
\(513\) 151011.i 0.573818i
\(514\) 8254.78i 0.0312449i
\(515\) −23575.0 + 115493.i −0.0888868 + 0.435455i
\(516\) 18861.1i 0.0708381i
\(517\) −195355. −0.730876
\(518\) −139860. 137034.i −0.521236 0.510704i
\(519\) 575.000 0.00213468
\(520\) −7800.00 1592.17i −0.0288462 0.00588820i
\(521\) 84727.9i 0.312141i 0.987746 + 0.156070i \(0.0498827\pi\)
−0.987746 + 0.156070i \(0.950117\pi\)
\(522\) 26199.7i 0.0961515i
\(523\) −235610. −0.861371 −0.430686 0.902502i \(-0.641728\pi\)
−0.430686 + 0.902502i \(0.641728\pi\)
\(524\) 67361.0i 0.245327i
\(525\) −58625.0 141458.i −0.212698 0.513226i
\(526\) −145464. −0.525756
\(527\) 510841.i 1.83935i
\(528\) 1780.00 0.00638487
\(529\) −210935. −0.753767
\(530\) 19440.0 95236.2i 0.0692061 0.339039i
\(531\) 203014.i 0.720006i
\(532\) 75600.0 77158.9i 0.267115 0.272623i
\(533\) 14574.5i 0.0513025i
\(534\) −9900.00 −0.0347178
\(535\) −310320. 63343.8i −1.08418 0.221308i
\(536\) −130416. −0.453943
\(537\) 26590.0 0.0922082
\(538\) −188640. −0.651732
\(539\) 4361.00 + 213644.i 0.0150110 + 0.735384i
\(540\) −34250.0 + 167790.i −0.117455 + 0.575412i
\(541\) 259199. 0.885602 0.442801 0.896620i \(-0.353985\pi\)
0.442801 + 0.896620i \(0.353985\pi\)
\(542\) 350820. 1.19422
\(543\) 61727.1i 0.209352i
\(544\) 498961.i 1.68604i
\(545\) 61555.0 301557.i 0.207238 1.01526i
\(546\) 2100.00 2143.30i 0.00704424 0.00718950i
\(547\) 423894.i 1.41672i −0.705854 0.708358i \(-0.749436\pi\)
0.705854 0.708358i \(-0.250564\pi\)
\(548\) 230693.i 0.768198i
\(549\) 108365.i 0.359539i
\(550\) 53400.0 125353.i 0.176529 0.414389i
\(551\) 42106.7i 0.138691i
\(552\) 223080. 0.732120
\(553\) 194635. + 190703.i 0.636459 + 0.623600i
\(554\) 249672. 0.813486
\(555\) 199800. + 40784.0i 0.648649 + 0.132405i
\(556\) 294919.i 0.954009i
\(557\) 133389.i 0.429943i 0.976620 + 0.214972i \(0.0689659\pi\)
−0.976620 + 0.214972i \(0.931034\pi\)
\(558\) 144480. 0.464023
\(559\) 1886.11i 0.00603591i
\(560\) 4060.00 2743.43i 0.0129464 0.00874818i
\(561\) −215825. −0.685766
\(562\) 116402.i 0.368543i
\(563\) −369770. −1.16658 −0.583290 0.812264i \(-0.698235\pi\)
−0.583290 + 0.812264i \(0.698235\pi\)
\(564\) −109750. −0.345022
\(565\) 76440.0 + 15603.2i 0.239455 + 0.0488785i
\(566\) 105610.i 0.329664i
\(567\) 38885.0 + 38099.4i 0.120953 + 0.118509i
\(568\) 283661.i 0.879230i
\(569\) −326134. −1.00733 −0.503665 0.863899i \(-0.668015\pi\)
−0.503665 + 0.863899i \(0.668015\pi\)
\(570\) 13500.0 66136.2i 0.0415512 0.203559i
\(571\) 306374. 0.939679 0.469840 0.882752i \(-0.344312\pi\)
0.469840 + 0.882752i \(0.344312\pi\)
\(572\) −4450.00 −0.0136009
\(573\) −71315.0 −0.217206
\(574\) 249900. + 244851.i 0.758477 + 0.743153i
\(575\) −171600. + 402819.i −0.519017 + 1.21835i
\(576\) 137536. 0.414545
\(577\) 387595. 1.16420 0.582099 0.813118i \(-0.302232\pi\)
0.582099 + 0.813118i \(0.302232\pi\)
\(578\) 371597.i 1.11229i
\(579\) 160025.i 0.477344i
\(580\) 9550.00 46785.3i 0.0283888 0.139076i
\(581\) 69650.0 + 68242.8i 0.206333 + 0.202164i
\(582\) 113105.i 0.333915i
\(583\) 141267.i 0.415627i
\(584\) 550890.i 1.61525i
\(585\) 1400.00 6858.57i 0.00409088 0.0200411i
\(586\) 397124.i 1.15646i
\(587\) 467350. 1.35633 0.678166 0.734909i \(-0.262775\pi\)
0.678166 + 0.734909i \(0.262775\pi\)
\(588\) 2450.00 + 120025.i 0.00708617 + 0.347150i
\(589\) 232200. 0.669317
\(590\) −44400.0 + 217515.i −0.127550 + 0.624863i
\(591\) 16975.0i 0.0485997i
\(592\) 6525.44i 0.0186194i
\(593\) 214315. 0.609457 0.304729 0.952439i \(-0.401434\pi\)
0.304729 + 0.952439i \(0.401434\pi\)
\(594\) 149333.i 0.423237i
\(595\) −492275. + 332641.i −1.39051 + 0.939597i
\(596\) 283460. 0.797993
\(597\) 96999.8i 0.272159i
\(598\) −8580.00 −0.0239930
\(599\) −283999. −0.791522 −0.395761 0.918353i \(-0.629519\pi\)
−0.395761 + 0.918353i \(0.629519\pi\)
\(600\) 78000.0 183099.i 0.216667 0.508609i
\(601\) 91219.0i 0.252544i −0.991996 0.126272i \(-0.959699\pi\)
0.991996 0.126272i \(-0.0403011\pi\)
\(602\) −32340.0 31686.6i −0.0892374 0.0874345i
\(603\) 114675.i 0.315381i
\(604\) −175510. −0.481092
\(605\) −33600.0 + 164606.i −0.0917970 + 0.449712i
\(606\) −59100.0 −0.160932
\(607\) −193715. −0.525758 −0.262879 0.964829i \(-0.584672\pi\)
−0.262879 + 0.964829i \(0.584672\pi\)
\(608\) 226800. 0.613530
\(609\) 33425.0 + 32749.7i 0.0901232 + 0.0883024i
\(610\) 23700.0 116106.i 0.0636926 0.312029i
\(611\) 10975.0 0.0293983
\(612\) 271600. 0.725148
\(613\) 296231.i 0.788334i −0.919039 0.394167i \(-0.871033\pi\)
0.919039 0.394167i \(-0.128967\pi\)
\(614\) 82805.0i 0.219644i
\(615\) −357000. 72872.3i −0.943883 0.192669i
\(616\) −194376. + 198384.i −0.512249 + 0.522812i
\(617\) 424751.i 1.11574i −0.829927 0.557872i \(-0.811618\pi\)
0.829927 0.557872i \(-0.188382\pi\)
\(618\) 57746.7i 0.151200i
\(619\) 375825.i 0.980855i −0.871482 0.490427i \(-0.836841\pi\)
0.871482 0.490427i \(-0.163159\pi\)
\(620\) 258000. + 52664.0i 0.671176 + 0.137003i
\(621\) 479880.i 1.24437i
\(622\) −123540. −0.319321
\(623\) −27720.0 + 28291.6i −0.0714196 + 0.0728923i
\(624\) −100.000 −0.000256821
\(625\) 270625. + 281691.i 0.692800 + 0.721130i
\(626\) 166945.i 0.426015i
\(627\) 98102.1i 0.249542i
\(628\) −257900. −0.653931
\(629\) 791210.i 1.99982i
\(630\) −94080.0 139229.i −0.237037 0.350791i
\(631\) −471511. −1.18422 −0.592111 0.805856i \(-0.701705\pi\)
−0.592111 + 0.805856i \(0.701705\pi\)
\(632\) 354162.i 0.886682i
\(633\) 264085. 0.659077
\(634\) 103944. 0.258595
\(635\) −584640. 119339.i −1.44991 0.295962i
\(636\) 79363.5i 0.196203i
\(637\) −245.000 12002.5i −0.000603792 0.0295796i
\(638\) 41638.9i 0.102296i
\(639\) −249424. −0.610853
\(640\) 255840. + 52223.1i 0.624609 + 0.127498i
\(641\) 558794. 1.35999 0.679995 0.733217i \(-0.261982\pi\)
0.679995 + 0.733217i \(0.261982\pi\)
\(642\) 155160. 0.376452
\(643\) −454235. −1.09865 −0.549324 0.835609i \(-0.685115\pi\)
−0.549324 + 0.835609i \(0.685115\pi\)
\(644\) 240240. 245194.i 0.579260 0.591205i
\(645\) 46200.0 + 9430.54i 0.111051 + 0.0226682i
\(646\) −261900. −0.627582
\(647\) −129530. −0.309430 −0.154715 0.987959i \(-0.549446\pi\)
−0.154715 + 0.987959i \(0.549446\pi\)
\(648\) 70756.0i 0.168505i
\(649\) 322647.i 0.766016i
\(650\) −3000.00 + 7042.28i −0.00710059 + 0.0166681i
\(651\) −180600. + 184324.i −0.426143 + 0.434931i
\(652\) 371539.i 0.873995i
\(653\) 343903.i 0.806511i −0.915087 0.403255i \(-0.867879\pi\)
0.915087 0.403255i \(-0.132121\pi\)
\(654\) 150778.i 0.352520i
\(655\) −165000. 33680.5i −0.384593 0.0785047i
\(656\) 11659.6i 0.0270941i
\(657\) −484400. −1.12221
\(658\) 184380. 188182.i 0.425855 0.434637i
\(659\) 526913. 1.21330 0.606650 0.794969i \(-0.292513\pi\)
0.606650 + 0.794969i \(0.292513\pi\)
\(660\) 22250.0 109002.i 0.0510790 0.250235i
\(661\) 191844.i 0.439082i −0.975603 0.219541i \(-0.929544\pi\)
0.975603 0.219541i \(-0.0704559\pi\)
\(662\) 280971.i 0.641130i
\(663\) 12125.0 0.0275838
\(664\) 126737.i 0.287452i
\(665\) −151200. 223761.i −0.341907 0.505989i
\(666\) 223776. 0.504505
\(667\) 133806.i 0.300762i
\(668\) −207950. −0.466022
\(669\) 68225.0 0.152437
\(670\) −25080.0 + 122866.i −0.0558699 + 0.273706i
\(671\) 172224.i 0.382514i
\(672\) −176400. + 180037.i −0.390625 + 0.398680i
\(673\) 429792.i 0.948918i 0.880278 + 0.474459i \(0.157356\pi\)
−0.880278 + 0.474459i \(0.842644\pi\)
\(674\) −286608. −0.630912
\(675\) 393875. + 167790.i 0.864472 + 0.368263i
\(676\) −285360. −0.624453
\(677\) −79685.0 −0.173860 −0.0869299 0.996214i \(-0.527706\pi\)
−0.0869299 + 0.996214i \(0.527706\pi\)
\(678\) −38220.0 −0.0831441
\(679\) 323225. + 316695.i 0.701076 + 0.686912i
\(680\) −756600. 154440.i −1.63625 0.333997i
\(681\) 372425. 0.803054
\(682\) −229620. −0.493675
\(683\) 719577.i 1.54254i −0.636510 0.771269i \(-0.719622\pi\)
0.636510 0.771269i \(-0.280378\pi\)
\(684\) 123454.i 0.263872i
\(685\) 565080. + 115346.i 1.20428 + 0.245823i
\(686\) −209916. 197441.i −0.446064 0.419555i
\(687\) 342316.i 0.725294i
\(688\) 1508.89i 0.00318771i
\(689\) 7936.35i 0.0167179i
\(690\) 42900.0 210166.i 0.0901071 0.441433i
\(691\) 398532.i 0.834655i −0.908756 0.417328i \(-0.862967\pi\)
0.908756 0.417328i \(-0.137033\pi\)
\(692\) 1150.00 0.00240152
\(693\) −174440. 170916.i −0.363228 0.355890i
\(694\) 172644. 0.358453
\(695\) 722400. + 147459.i 1.49557 + 0.305283i
\(696\) 60820.8i 0.125555i
\(697\) 1.41372e6i 2.91004i
\(698\) −223860. −0.459479
\(699\) 300846.i 0.615730i
\(700\) −117250. 282916.i −0.239286 0.577380i
\(701\) −658873. −1.34081 −0.670403 0.741998i \(-0.733879\pi\)
−0.670403 + 0.741998i \(0.733879\pi\)
\(702\) 8389.50i 0.0170240i
\(703\) 359640. 0.727708
\(704\) −218584. −0.441035
\(705\) −54875.0 + 268831.i −0.110407 + 0.540881i
\(706\) 27936.4i 0.0560482i
\(707\) −165480. + 168892.i −0.331060 + 0.337887i
\(708\) 181262.i 0.361610i
\(709\) −593737. −1.18114 −0.590570 0.806986i \(-0.701097\pi\)
−0.590570 + 0.806986i \(0.701097\pi\)
\(710\) 267240. + 54550.1i 0.530133 + 0.108213i
\(711\) −311416. −0.616030
\(712\) −51480.0 −0.101550
\(713\) 737880. 1.45147
\(714\) 203700. 207900.i 0.399572 0.407811i
\(715\) −2225.00 + 10900.2i −0.00435229 + 0.0213218i
\(716\) 53180.0 0.103734
\(717\) −376835. −0.733015
\(718\) 564279.i 1.09457i
\(719\) 75321.8i 0.145701i −0.997343 0.0728506i \(-0.976790\pi\)
0.997343 0.0728506i \(-0.0232096\pi\)
\(720\) −1120.00 + 5486.86i −0.00216049 + 0.0105842i
\(721\) −165025. 161691.i −0.317453 0.311039i
\(722\) 200175.i 0.384003i
\(723\) 389346.i 0.744834i
\(724\) 123454.i 0.235521i
\(725\) −109825. 46785.3i −0.208942 0.0890088i
\(726\) 82302.9i 0.156150i
\(727\) 342190. 0.647438 0.323719 0.946153i \(-0.395067\pi\)
0.323719 + 0.946153i \(0.395067\pi\)
\(728\) 10920.0 11145.2i 0.0206044 0.0210293i
\(729\) 215209. 0.404954
\(730\) 519000. + 105940.i 0.973916 + 0.198800i
\(731\) 182952.i 0.342376i
\(732\) 96754.8i 0.180572i
\(733\) 958555. 1.78406 0.892029 0.451978i \(-0.149281\pi\)
0.892029 + 0.451978i \(0.149281\pi\)
\(734\) 182450.i 0.338651i
\(735\) 295225. + 54011.2i 0.546485 + 0.0999792i
\(736\) 720720. 1.33049
\(737\) 182252.i 0.335534i
\(738\) −399840. −0.734131
\(739\) −229399. −0.420052 −0.210026 0.977696i \(-0.567355\pi\)
−0.210026 + 0.977696i \(0.567355\pi\)
\(740\) 399600. + 81568.0i 0.729730 + 0.148955i
\(741\) 5511.35i 0.0100374i
\(742\) 136080. + 133331.i 0.247165 + 0.242171i
\(743\) 97803.2i 0.177164i −0.996069 0.0885820i \(-0.971766\pi\)
0.996069 0.0885820i \(-0.0282335\pi\)
\(744\) −335400. −0.605923
\(745\) 141730. 694332.i 0.255358 1.25099i
\(746\) 251196. 0.451372
\(747\) −111440. −0.199710
\(748\) −431650. −0.771487
\(749\) 434448. 443407.i 0.774416 0.790385i
\(750\) −157500. 108696.i −0.280000 0.193238i
\(751\) 246977. 0.437902 0.218951 0.975736i \(-0.429737\pi\)
0.218951 + 0.975736i \(0.429737\pi\)
\(752\) −8780.00 −0.0155260
\(753\) 252052.i 0.444530i
\(754\) 2339.26i 0.00411468i
\(755\) −87755.0 + 429910.i −0.153949 + 0.754195i
\(756\) −239750. 234906.i −0.419484 0.411008i
\(757\) 1.05636e6i 1.84340i 0.387906 + 0.921699i \(0.373198\pi\)
−0.387906 + 0.921699i \(0.626802\pi\)
\(758\) 423649.i 0.737340i
\(759\) 311747.i 0.541151i
\(760\) 70200.0 343908.i 0.121537 0.595409i
\(761\) 406836.i 0.702506i 0.936281 + 0.351253i \(0.114244\pi\)
−0.936281 + 0.351253i \(0.885756\pi\)
\(762\) 292320. 0.503441
\(763\) 430885. + 422179.i 0.740137 + 0.725184i
\(764\) −142630. −0.244357
\(765\) 135800. 665281.i 0.232048 1.13680i
\(766\) 352849.i 0.601356i
\(767\) 18126.2i 0.0308118i
\(768\) −324400. −0.549995
\(769\) 592238.i 1.00148i 0.865597 + 0.500741i \(0.166939\pi\)
−0.865597 + 0.500741i \(0.833061\pi\)
\(770\) 149520. + 221275.i 0.252184 + 0.373207i
\(771\) 16850.0 0.0283460
\(772\) 320050.i