Properties

Label 338.4.c.d.191.1
Level $338$
Weight $4$
Character 338.191
Analytic conductor $19.943$
Analytic rank $0$
Dimension $2$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [338,4,Mod(191,338)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(338, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("338.191");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 338.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.9426455819\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 191.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 338.191
Dual form 338.4.c.d.315.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} -2.00000 q^{5} +(3.00000 + 5.19615i) q^{6} +(-2.50000 - 4.33013i) q^{7} +8.00000 q^{8} +(9.00000 + 15.5885i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} -2.00000 q^{5} +(3.00000 + 5.19615i) q^{6} +(-2.50000 - 4.33013i) q^{7} +8.00000 q^{8} +(9.00000 + 15.5885i) q^{9} +(2.00000 - 3.46410i) q^{10} +(6.50000 - 11.2583i) q^{11} -12.0000 q^{12} +10.0000 q^{14} +(-3.00000 + 5.19615i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-13.5000 - 23.3827i) q^{17} -36.0000 q^{18} +(37.5000 + 64.9519i) q^{19} +(4.00000 + 6.92820i) q^{20} -15.0000 q^{21} +(13.0000 + 22.5167i) q^{22} +(93.5000 - 161.947i) q^{23} +(12.0000 - 20.7846i) q^{24} -121.000 q^{25} +135.000 q^{27} +(-10.0000 + 17.3205i) q^{28} +(6.50000 - 11.2583i) q^{29} +(-6.00000 - 10.3923i) q^{30} +104.000 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-19.5000 - 33.7750i) q^{33} +54.0000 q^{34} +(5.00000 + 8.66025i) q^{35} +(36.0000 - 62.3538i) q^{36} +(211.500 - 366.329i) q^{37} -150.000 q^{38} -16.0000 q^{40} +(97.5000 - 168.875i) q^{41} +(15.0000 - 25.9808i) q^{42} +(-99.5000 - 172.339i) q^{43} -52.0000 q^{44} +(-18.0000 - 31.1769i) q^{45} +(187.000 + 323.894i) q^{46} -388.000 q^{47} +(24.0000 + 41.5692i) q^{48} +(159.000 - 275.396i) q^{49} +(121.000 - 209.578i) q^{50} -81.0000 q^{51} +618.000 q^{53} +(-135.000 + 233.827i) q^{54} +(-13.0000 + 22.5167i) q^{55} +(-20.0000 - 34.6410i) q^{56} +225.000 q^{57} +(13.0000 + 22.5167i) q^{58} +(245.500 + 425.218i) q^{59} +24.0000 q^{60} +(-87.5000 - 151.554i) q^{61} +(-104.000 + 180.133i) q^{62} +(45.0000 - 77.9423i) q^{63} +64.0000 q^{64} +78.0000 q^{66} +(408.500 - 707.543i) q^{67} +(-54.0000 + 93.5307i) q^{68} +(-280.500 - 485.840i) q^{69} -20.0000 q^{70} +(39.5000 + 68.4160i) q^{71} +(72.0000 + 124.708i) q^{72} -230.000 q^{73} +(423.000 + 732.657i) q^{74} +(-181.500 + 314.367i) q^{75} +(150.000 - 259.808i) q^{76} -65.0000 q^{77} +764.000 q^{79} +(16.0000 - 27.7128i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(195.000 + 337.750i) q^{82} +732.000 q^{83} +(30.0000 + 51.9615i) q^{84} +(27.0000 + 46.7654i) q^{85} +398.000 q^{86} +(-19.5000 - 33.7750i) q^{87} +(52.0000 - 90.0666i) q^{88} +(-520.500 + 901.532i) q^{89} +72.0000 q^{90} -748.000 q^{92} +(156.000 - 270.200i) q^{93} +(388.000 - 672.036i) q^{94} +(-75.0000 - 129.904i) q^{95} -96.0000 q^{96} +(-48.5000 - 84.0045i) q^{97} +(318.000 + 550.792i) q^{98} +234.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} - 4 q^{5} + 6 q^{6} - 5 q^{7} + 16 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} - 4 q^{5} + 6 q^{6} - 5 q^{7} + 16 q^{8} + 18 q^{9} + 4 q^{10} + 13 q^{11} - 24 q^{12} + 20 q^{14} - 6 q^{15} - 16 q^{16} - 27 q^{17} - 72 q^{18} + 75 q^{19} + 8 q^{20} - 30 q^{21} + 26 q^{22} + 187 q^{23} + 24 q^{24} - 242 q^{25} + 270 q^{27} - 20 q^{28} + 13 q^{29} - 12 q^{30} + 208 q^{31} - 32 q^{32} - 39 q^{33} + 108 q^{34} + 10 q^{35} + 72 q^{36} + 423 q^{37} - 300 q^{38} - 32 q^{40} + 195 q^{41} + 30 q^{42} - 199 q^{43} - 104 q^{44} - 36 q^{45} + 374 q^{46} - 776 q^{47} + 48 q^{48} + 318 q^{49} + 242 q^{50} - 162 q^{51} + 1236 q^{53} - 270 q^{54} - 26 q^{55} - 40 q^{56} + 450 q^{57} + 26 q^{58} + 491 q^{59} + 48 q^{60} - 175 q^{61} - 208 q^{62} + 90 q^{63} + 128 q^{64} + 156 q^{66} + 817 q^{67} - 108 q^{68} - 561 q^{69} - 40 q^{70} + 79 q^{71} + 144 q^{72} - 460 q^{73} + 846 q^{74} - 363 q^{75} + 300 q^{76} - 130 q^{77} + 1528 q^{79} + 32 q^{80} - 81 q^{81} + 390 q^{82} + 1464 q^{83} + 60 q^{84} + 54 q^{85} + 796 q^{86} - 39 q^{87} + 104 q^{88} - 1041 q^{89} + 144 q^{90} - 1496 q^{92} + 312 q^{93} + 776 q^{94} - 150 q^{95} - 192 q^{96} - 97 q^{97} + 636 q^{98} + 468 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).

\(n\) \(171\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 1.50000 2.59808i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −2.00000 −0.178885 −0.0894427 0.995992i \(-0.528509\pi\)
−0.0894427 + 0.995992i \(0.528509\pi\)
\(6\) 3.00000 + 5.19615i 0.204124 + 0.353553i
\(7\) −2.50000 4.33013i −0.134987 0.233805i 0.790605 0.612326i \(-0.209766\pi\)
−0.925593 + 0.378521i \(0.876433\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 + 15.5885i 0.333333 + 0.577350i
\(10\) 2.00000 3.46410i 0.0632456 0.109545i
\(11\) 6.50000 11.2583i 0.178166 0.308592i −0.763087 0.646296i \(-0.776317\pi\)
0.941252 + 0.337704i \(0.109650\pi\)
\(12\) −12.0000 −0.288675
\(13\) 0 0
\(14\) 10.0000 0.190901
\(15\) −3.00000 + 5.19615i −0.0516398 + 0.0894427i
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −13.5000 23.3827i −0.192602 0.333596i 0.753510 0.657437i \(-0.228359\pi\)
−0.946112 + 0.323840i \(0.895026\pi\)
\(18\) −36.0000 −0.471405
\(19\) 37.5000 + 64.9519i 0.452794 + 0.784263i 0.998558 0.0536762i \(-0.0170939\pi\)
−0.545764 + 0.837939i \(0.683761\pi\)
\(20\) 4.00000 + 6.92820i 0.0447214 + 0.0774597i
\(21\) −15.0000 −0.155870
\(22\) 13.0000 + 22.5167i 0.125982 + 0.218208i
\(23\) 93.5000 161.947i 0.847656 1.46818i −0.0356377 0.999365i \(-0.511346\pi\)
0.883294 0.468819i \(-0.155320\pi\)
\(24\) 12.0000 20.7846i 0.102062 0.176777i
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) 135.000 0.962250
\(28\) −10.0000 + 17.3205i −0.0674937 + 0.116902i
\(29\) 6.50000 11.2583i 0.0416214 0.0720903i −0.844464 0.535612i \(-0.820081\pi\)
0.886086 + 0.463522i \(0.153414\pi\)
\(30\) −6.00000 10.3923i −0.0365148 0.0632456i
\(31\) 104.000 0.602547 0.301273 0.953538i \(-0.402588\pi\)
0.301273 + 0.953538i \(0.402588\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) −19.5000 33.7750i −0.102864 0.178166i
\(34\) 54.0000 0.272380
\(35\) 5.00000 + 8.66025i 0.0241473 + 0.0418243i
\(36\) 36.0000 62.3538i 0.166667 0.288675i
\(37\) 211.500 366.329i 0.939740 1.62768i 0.173785 0.984784i \(-0.444400\pi\)
0.765955 0.642894i \(-0.222266\pi\)
\(38\) −150.000 −0.640348
\(39\) 0 0
\(40\) −16.0000 −0.0632456
\(41\) 97.5000 168.875i 0.371389 0.643264i −0.618391 0.785871i \(-0.712215\pi\)
0.989779 + 0.142607i \(0.0455484\pi\)
\(42\) 15.0000 25.9808i 0.0551083 0.0954504i
\(43\) −99.5000 172.339i −0.352875 0.611197i 0.633877 0.773434i \(-0.281462\pi\)
−0.986752 + 0.162237i \(0.948129\pi\)
\(44\) −52.0000 −0.178166
\(45\) −18.0000 31.1769i −0.0596285 0.103280i
\(46\) 187.000 + 323.894i 0.599384 + 1.03816i
\(47\) −388.000 −1.20416 −0.602081 0.798435i \(-0.705662\pi\)
−0.602081 + 0.798435i \(0.705662\pi\)
\(48\) 24.0000 + 41.5692i 0.0721688 + 0.125000i
\(49\) 159.000 275.396i 0.463557 0.802904i
\(50\) 121.000 209.578i 0.342240 0.592777i
\(51\) −81.0000 −0.222397
\(52\) 0 0
\(53\) 618.000 1.60168 0.800838 0.598881i \(-0.204388\pi\)
0.800838 + 0.598881i \(0.204388\pi\)
\(54\) −135.000 + 233.827i −0.340207 + 0.589256i
\(55\) −13.0000 + 22.5167i −0.0318713 + 0.0552027i
\(56\) −20.0000 34.6410i −0.0477252 0.0826625i
\(57\) 225.000 0.522842
\(58\) 13.0000 + 22.5167i 0.0294308 + 0.0509756i
\(59\) 245.500 + 425.218i 0.541718 + 0.938284i 0.998806 + 0.0488617i \(0.0155594\pi\)
−0.457087 + 0.889422i \(0.651107\pi\)
\(60\) 24.0000 0.0516398
\(61\) −87.5000 151.554i −0.183659 0.318108i 0.759465 0.650549i \(-0.225461\pi\)
−0.943124 + 0.332441i \(0.892128\pi\)
\(62\) −104.000 + 180.133i −0.213032 + 0.368983i
\(63\) 45.0000 77.9423i 0.0899915 0.155870i
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) 78.0000 0.145472
\(67\) 408.500 707.543i 0.744869 1.29015i −0.205387 0.978681i \(-0.565845\pi\)
0.950256 0.311470i \(-0.100821\pi\)
\(68\) −54.0000 + 93.5307i −0.0963009 + 0.166798i
\(69\) −280.500 485.840i −0.489395 0.847656i
\(70\) −20.0000 −0.0341494
\(71\) 39.5000 + 68.4160i 0.0660252 + 0.114359i 0.897148 0.441729i \(-0.145635\pi\)
−0.831123 + 0.556088i \(0.812302\pi\)
\(72\) 72.0000 + 124.708i 0.117851 + 0.204124i
\(73\) −230.000 −0.368760 −0.184380 0.982855i \(-0.559028\pi\)
−0.184380 + 0.982855i \(0.559028\pi\)
\(74\) 423.000 + 732.657i 0.664497 + 1.15094i
\(75\) −181.500 + 314.367i −0.279438 + 0.484000i
\(76\) 150.000 259.808i 0.226397 0.392131i
\(77\) −65.0000 −0.0962005
\(78\) 0 0
\(79\) 764.000 1.08806 0.544030 0.839066i \(-0.316898\pi\)
0.544030 + 0.839066i \(0.316898\pi\)
\(80\) 16.0000 27.7128i 0.0223607 0.0387298i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 195.000 + 337.750i 0.262612 + 0.454857i
\(83\) 732.000 0.968041 0.484021 0.875057i \(-0.339176\pi\)
0.484021 + 0.875057i \(0.339176\pi\)
\(84\) 30.0000 + 51.9615i 0.0389675 + 0.0674937i
\(85\) 27.0000 + 46.7654i 0.0344537 + 0.0596755i
\(86\) 398.000 0.499040
\(87\) −19.5000 33.7750i −0.0240301 0.0416214i
\(88\) 52.0000 90.0666i 0.0629911 0.109104i
\(89\) −520.500 + 901.532i −0.619920 + 1.07373i 0.369580 + 0.929199i \(0.379502\pi\)
−0.989500 + 0.144534i \(0.953832\pi\)
\(90\) 72.0000 0.0843274
\(91\) 0 0
\(92\) −748.000 −0.847656
\(93\) 156.000 270.200i 0.173940 0.301273i
\(94\) 388.000 672.036i 0.425736 0.737396i
\(95\) −75.0000 129.904i −0.0809983 0.140293i
\(96\) −96.0000 −0.102062
\(97\) −48.5000 84.0045i −0.0507673 0.0879316i 0.839525 0.543321i \(-0.182833\pi\)
−0.890292 + 0.455389i \(0.849500\pi\)
\(98\) 318.000 + 550.792i 0.327784 + 0.567739i
\(99\) 234.000 0.237554
\(100\) 242.000 + 419.156i 0.242000 + 0.419156i
\(101\) 404.500 700.615i 0.398507 0.690235i −0.595035 0.803700i \(-0.702862\pi\)
0.993542 + 0.113465i \(0.0361950\pi\)
\(102\) 81.0000 140.296i 0.0786294 0.136190i
\(103\) 1288.00 1.23214 0.616070 0.787691i \(-0.288724\pi\)
0.616070 + 0.787691i \(0.288724\pi\)
\(104\) 0 0
\(105\) 30.0000 0.0278829
\(106\) −618.000 + 1070.41i −0.566278 + 0.980822i
\(107\) −638.500 + 1105.91i −0.576880 + 0.999185i 0.418955 + 0.908007i \(0.362397\pi\)
−0.995835 + 0.0911779i \(0.970937\pi\)
\(108\) −270.000 467.654i −0.240563 0.416667i
\(109\) −826.000 −0.725839 −0.362920 0.931820i \(-0.618220\pi\)
−0.362920 + 0.931820i \(0.618220\pi\)
\(110\) −26.0000 45.0333i −0.0225364 0.0390342i
\(111\) −634.500 1098.99i −0.542559 0.939740i
\(112\) 80.0000 0.0674937
\(113\) −473.500 820.126i −0.394187 0.682752i 0.598810 0.800891i \(-0.295640\pi\)
−0.992997 + 0.118139i \(0.962307\pi\)
\(114\) −225.000 + 389.711i −0.184852 + 0.320174i
\(115\) −187.000 + 323.894i −0.151633 + 0.262637i
\(116\) −52.0000 −0.0416214
\(117\) 0 0
\(118\) −982.000 −0.766105
\(119\) −67.5000 + 116.913i −0.0519976 + 0.0900625i
\(120\) −24.0000 + 41.5692i −0.0182574 + 0.0316228i
\(121\) 581.000 + 1006.32i 0.436514 + 0.756064i
\(122\) 350.000 0.259734
\(123\) −292.500 506.625i −0.214421 0.371389i
\(124\) −208.000 360.267i −0.150637 0.260910i
\(125\) 492.000 0.352047
\(126\) 90.0000 + 155.885i 0.0636336 + 0.110217i
\(127\) −588.500 + 1019.31i −0.411188 + 0.712199i −0.995020 0.0996756i \(-0.968220\pi\)
0.583832 + 0.811875i \(0.301553\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) −597.000 −0.407464
\(130\) 0 0
\(131\) −1420.00 −0.947069 −0.473534 0.880775i \(-0.657022\pi\)
−0.473534 + 0.880775i \(0.657022\pi\)
\(132\) −78.0000 + 135.100i −0.0514320 + 0.0890829i
\(133\) 187.500 324.760i 0.122243 0.211731i
\(134\) 817.000 + 1415.09i 0.526702 + 0.912274i
\(135\) −270.000 −0.172133
\(136\) −108.000 187.061i −0.0680950 0.117944i
\(137\) −1204.50 2086.26i −0.751149 1.30103i −0.947266 0.320447i \(-0.896167\pi\)
0.196118 0.980580i \(-0.437167\pi\)
\(138\) 1122.00 0.692109
\(139\) −1413.50 2448.25i −0.862529 1.49394i −0.869480 0.493968i \(-0.835546\pi\)
0.00695133 0.999976i \(-0.497787\pi\)
\(140\) 20.0000 34.6410i 0.0120736 0.0209121i
\(141\) −582.000 + 1008.05i −0.347612 + 0.602081i
\(142\) −158.000 −0.0933737
\(143\) 0 0
\(144\) −288.000 −0.166667
\(145\) −13.0000 + 22.5167i −0.00744546 + 0.0128959i
\(146\) 230.000 398.372i 0.130376 0.225818i
\(147\) −477.000 826.188i −0.267635 0.463557i
\(148\) −1692.00 −0.939740
\(149\) 427.500 + 740.452i 0.235048 + 0.407115i 0.959287 0.282434i \(-0.0911419\pi\)
−0.724239 + 0.689549i \(0.757809\pi\)
\(150\) −363.000 628.734i −0.197592 0.342240i
\(151\) −2064.00 −1.11236 −0.556179 0.831063i \(-0.687733\pi\)
−0.556179 + 0.831063i \(0.687733\pi\)
\(152\) 300.000 + 519.615i 0.160087 + 0.277279i
\(153\) 243.000 420.888i 0.128401 0.222397i
\(154\) 65.0000 112.583i 0.0340120 0.0589105i
\(155\) −208.000 −0.107787
\(156\) 0 0
\(157\) −1894.00 −0.962788 −0.481394 0.876504i \(-0.659869\pi\)
−0.481394 + 0.876504i \(0.659869\pi\)
\(158\) −764.000 + 1323.29i −0.384687 + 0.666298i
\(159\) 927.000 1605.61i 0.462364 0.800838i
\(160\) 32.0000 + 55.4256i 0.0158114 + 0.0273861i
\(161\) −935.000 −0.457691
\(162\) −81.0000 140.296i −0.0392837 0.0680414i
\(163\) −492.500 853.035i −0.236660 0.409907i 0.723094 0.690750i \(-0.242719\pi\)
−0.959754 + 0.280843i \(0.909386\pi\)
\(164\) −780.000 −0.371389
\(165\) 39.0000 + 67.5500i 0.0184009 + 0.0318713i
\(166\) −732.000 + 1267.86i −0.342254 + 0.592802i
\(167\) −1177.50 + 2039.49i −0.545615 + 0.945033i 0.452953 + 0.891534i \(0.350371\pi\)
−0.998568 + 0.0534983i \(0.982963\pi\)
\(168\) −120.000 −0.0551083
\(169\) 0 0
\(170\) −108.000 −0.0487248
\(171\) −675.000 + 1169.13i −0.301863 + 0.522842i
\(172\) −398.000 + 689.356i −0.176437 + 0.305598i
\(173\) 1944.50 + 3367.97i 0.854553 + 1.48013i 0.877059 + 0.480382i \(0.159502\pi\)
−0.0225069 + 0.999747i \(0.507165\pi\)
\(174\) 78.0000 0.0339837
\(175\) 302.500 + 523.945i 0.130668 + 0.226323i
\(176\) 104.000 + 180.133i 0.0445414 + 0.0771481i
\(177\) 1473.00 0.625522
\(178\) −1041.00 1803.06i −0.438350 0.759244i
\(179\) −1114.50 + 1930.37i −0.465372 + 0.806048i −0.999218 0.0395333i \(-0.987413\pi\)
0.533846 + 0.845582i \(0.320746\pi\)
\(180\) −72.0000 + 124.708i −0.0298142 + 0.0516398i
\(181\) −1038.00 −0.426265 −0.213132 0.977023i \(-0.568367\pi\)
−0.213132 + 0.977023i \(0.568367\pi\)
\(182\) 0 0
\(183\) −525.000 −0.212072
\(184\) 748.000 1295.57i 0.299692 0.519081i
\(185\) −423.000 + 732.657i −0.168106 + 0.291168i
\(186\) 312.000 + 540.400i 0.122994 + 0.213032i
\(187\) −351.000 −0.137260
\(188\) 776.000 + 1344.07i 0.301041 + 0.521417i
\(189\) −337.500 584.567i −0.129892 0.224979i
\(190\) 300.000 0.114549
\(191\) 1070.50 + 1854.16i 0.405543 + 0.702421i 0.994384 0.105828i \(-0.0337492\pi\)
−0.588842 + 0.808248i \(0.700416\pi\)
\(192\) 96.0000 166.277i 0.0360844 0.0625000i
\(193\) 1313.50 2275.05i 0.489885 0.848506i −0.510047 0.860146i \(-0.670372\pi\)
0.999932 + 0.0116407i \(0.00370544\pi\)
\(194\) 194.000 0.0717958
\(195\) 0 0
\(196\) −1272.00 −0.463557
\(197\) 601.500 1041.83i 0.217539 0.376788i −0.736516 0.676420i \(-0.763531\pi\)
0.954055 + 0.299632i \(0.0968639\pi\)
\(198\) −234.000 + 405.300i −0.0839882 + 0.145472i
\(199\) −371.500 643.457i −0.132336 0.229213i 0.792240 0.610209i \(-0.208915\pi\)
−0.924577 + 0.380996i \(0.875581\pi\)
\(200\) −968.000 −0.342240
\(201\) −1225.50 2122.63i −0.430050 0.744869i
\(202\) 809.000 + 1401.23i 0.281787 + 0.488070i
\(203\) −65.0000 −0.0224734
\(204\) 162.000 + 280.592i 0.0555994 + 0.0963009i
\(205\) −195.000 + 337.750i −0.0664361 + 0.115071i
\(206\) −1288.00 + 2230.88i −0.435627 + 0.754529i
\(207\) 3366.00 1.13021
\(208\) 0 0
\(209\) 975.000 0.322690
\(210\) −30.0000 + 51.9615i −0.00985808 + 0.0170747i
\(211\) 177.500 307.439i 0.0579128 0.100308i −0.835615 0.549315i \(-0.814889\pi\)
0.893528 + 0.449007i \(0.148222\pi\)
\(212\) −1236.00 2140.81i −0.400419 0.693546i
\(213\) 237.000 0.0762393
\(214\) −1277.00 2211.83i −0.407916 0.706530i
\(215\) 199.000 + 344.678i 0.0631241 + 0.109334i
\(216\) 1080.00 0.340207
\(217\) −260.000 450.333i −0.0813362 0.140878i
\(218\) 826.000 1430.67i 0.256623 0.444484i
\(219\) −345.000 + 597.558i −0.106452 + 0.184380i
\(220\) 104.000 0.0318713
\(221\) 0 0
\(222\) 2538.00 0.767295
\(223\) −1141.50 + 1977.14i −0.342782 + 0.593717i −0.984948 0.172849i \(-0.944703\pi\)
0.642166 + 0.766566i \(0.278036\pi\)
\(224\) −80.0000 + 138.564i −0.0238626 + 0.0413313i
\(225\) −1089.00 1886.20i −0.322667 0.558875i
\(226\) 1894.00 0.557465
\(227\) 1225.50 + 2122.63i 0.358323 + 0.620633i 0.987681 0.156482i \(-0.0500154\pi\)
−0.629358 + 0.777116i \(0.716682\pi\)
\(228\) −450.000 779.423i −0.130710 0.226397i
\(229\) 1878.00 0.541929 0.270964 0.962589i \(-0.412657\pi\)
0.270964 + 0.962589i \(0.412657\pi\)
\(230\) −374.000 647.787i −0.107221 0.185712i
\(231\) −97.5000 + 168.875i −0.0277707 + 0.0481002i
\(232\) 52.0000 90.0666i 0.0147154 0.0254878i
\(233\) 1630.00 0.458304 0.229152 0.973391i \(-0.426405\pi\)
0.229152 + 0.973391i \(0.426405\pi\)
\(234\) 0 0
\(235\) 776.000 0.215407
\(236\) 982.000 1700.87i 0.270859 0.469142i
\(237\) 1146.00 1984.93i 0.314096 0.544030i
\(238\) −135.000 233.827i −0.0367679 0.0636838i
\(239\) 5544.00 1.50047 0.750233 0.661173i \(-0.229941\pi\)
0.750233 + 0.661173i \(0.229941\pi\)
\(240\) −48.0000 83.1384i −0.0129099 0.0223607i
\(241\) 2761.50 + 4783.06i 0.738107 + 1.27844i 0.953347 + 0.301878i \(0.0976135\pi\)
−0.215239 + 0.976561i \(0.569053\pi\)
\(242\) −2324.00 −0.617324
\(243\) 1944.00 + 3367.11i 0.513200 + 0.888889i
\(244\) −350.000 + 606.218i −0.0918297 + 0.159054i
\(245\) −318.000 + 550.792i −0.0829236 + 0.143628i
\(246\) 1170.00 0.303238
\(247\) 0 0
\(248\) 832.000 0.213032
\(249\) 1098.00 1901.79i 0.279449 0.484021i
\(250\) −492.000 + 852.169i −0.124467 + 0.215584i
\(251\) −1087.50 1883.61i −0.273476 0.473674i 0.696274 0.717776i \(-0.254840\pi\)
−0.969749 + 0.244103i \(0.921507\pi\)
\(252\) −360.000 −0.0899915
\(253\) −1215.50 2105.31i −0.302047 0.523160i
\(254\) −1177.00 2038.62i −0.290754 0.503601i
\(255\) 162.000 0.0397837
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2842.50 4923.35i 0.689923 1.19498i −0.281939 0.959432i \(-0.590978\pi\)
0.971862 0.235550i \(-0.0756891\pi\)
\(258\) 597.000 1034.03i 0.144060 0.249520i
\(259\) −2115.00 −0.507412
\(260\) 0 0
\(261\) 234.000 0.0554952
\(262\) 1420.00 2459.51i 0.334839 0.579959i
\(263\) −3058.50 + 5297.48i −0.717092 + 1.24204i 0.245055 + 0.969509i \(0.421194\pi\)
−0.962147 + 0.272531i \(0.912139\pi\)
\(264\) −156.000 270.200i −0.0363679 0.0629911i
\(265\) −1236.00 −0.286517
\(266\) 375.000 + 649.519i 0.0864388 + 0.149716i
\(267\) 1561.50 + 2704.60i 0.357911 + 0.619920i
\(268\) −3268.00 −0.744869
\(269\) 2554.50 + 4424.52i 0.578999 + 1.00285i 0.995595 + 0.0937632i \(0.0298897\pi\)
−0.416596 + 0.909092i \(0.636777\pi\)
\(270\) 270.000 467.654i 0.0608581 0.105409i
\(271\) 3774.50 6537.63i 0.846068 1.46543i −0.0386217 0.999254i \(-0.512297\pi\)
0.884690 0.466180i \(-0.154370\pi\)
\(272\) 432.000 0.0963009
\(273\) 0 0
\(274\) 4818.00 1.06228
\(275\) −786.500 + 1362.26i −0.172464 + 0.298717i
\(276\) −1122.00 + 1943.36i −0.244697 + 0.423828i
\(277\) 490.500 + 849.571i 0.106395 + 0.184281i 0.914307 0.405022i \(-0.132736\pi\)
−0.807913 + 0.589302i \(0.799403\pi\)
\(278\) 5654.00 1.21980
\(279\) 936.000 + 1621.20i 0.200849 + 0.347881i
\(280\) 40.0000 + 69.2820i 0.00853735 + 0.0147871i
\(281\) 2762.00 0.586360 0.293180 0.956057i \(-0.405287\pi\)
0.293180 + 0.956057i \(0.405287\pi\)
\(282\) −1164.00 2016.11i −0.245799 0.425736i
\(283\) −1962.50 + 3399.15i −0.412221 + 0.713988i −0.995132 0.0985482i \(-0.968580\pi\)
0.582911 + 0.812536i \(0.301913\pi\)
\(284\) 158.000 273.664i 0.0330126 0.0571795i
\(285\) −450.000 −0.0935288
\(286\) 0 0
\(287\) −975.000 −0.200531
\(288\) 288.000 498.831i 0.0589256 0.102062i
\(289\) 2092.00 3623.45i 0.425809 0.737523i
\(290\) −26.0000 45.0333i −0.00526473 0.00911879i
\(291\) −291.000 −0.0586210
\(292\) 460.000 + 796.743i 0.0921899 + 0.159678i
\(293\) 3855.50 + 6677.92i 0.768740 + 1.33150i 0.938247 + 0.345967i \(0.112449\pi\)
−0.169507 + 0.985529i \(0.554218\pi\)
\(294\) 1908.00 0.378493
\(295\) −491.000 850.437i −0.0969055 0.167845i
\(296\) 1692.00 2930.63i 0.332248 0.575471i
\(297\) 877.500 1519.87i 0.171440 0.296943i
\(298\) −1710.00 −0.332408
\(299\) 0 0
\(300\) 1452.00 0.279438
\(301\) −497.500 + 861.695i −0.0952672 + 0.165008i
\(302\) 2064.00 3574.95i 0.393278 0.681177i
\(303\) −1213.50 2101.84i −0.230078 0.398507i
\(304\) −1200.00 −0.226397
\(305\) 175.000 + 303.109i 0.0328540 + 0.0569048i
\(306\) 486.000 + 841.777i 0.0907934 + 0.157259i
\(307\) −10388.0 −1.93119 −0.965594 0.260056i \(-0.916259\pi\)
−0.965594 + 0.260056i \(0.916259\pi\)
\(308\) 130.000 + 225.167i 0.0240501 + 0.0416560i
\(309\) 1932.00 3346.32i 0.355688 0.616070i
\(310\) 208.000 360.267i 0.0381084 0.0660057i
\(311\) −7272.00 −1.32591 −0.662954 0.748660i \(-0.730697\pi\)
−0.662954 + 0.748660i \(0.730697\pi\)
\(312\) 0 0
\(313\) 7910.00 1.42843 0.714217 0.699925i \(-0.246783\pi\)
0.714217 + 0.699925i \(0.246783\pi\)
\(314\) 1894.00 3280.50i 0.340397 0.589585i
\(315\) −90.0000 + 155.885i −0.0160982 + 0.0278829i
\(316\) −1528.00 2646.57i −0.272015 0.471144i
\(317\) −7398.00 −1.31077 −0.655383 0.755296i \(-0.727493\pi\)
−0.655383 + 0.755296i \(0.727493\pi\)
\(318\) 1854.00 + 3211.22i 0.326941 + 0.566278i
\(319\) −84.5000 146.358i −0.0148310 0.0256881i
\(320\) −128.000 −0.0223607
\(321\) 1915.50 + 3317.74i 0.333062 + 0.576880i
\(322\) 935.000 1619.47i 0.161818 0.280278i
\(323\) 1012.50 1753.70i 0.174418 0.302101i
\(324\) 324.000 0.0555556
\(325\) 0 0
\(326\) 1970.00 0.334688
\(327\) −1239.00 + 2146.01i −0.209532 + 0.362920i
\(328\) 780.000 1351.00i 0.131306 0.227428i
\(329\) 970.000 + 1680.09i 0.162547 + 0.281539i
\(330\) −156.000 −0.0260228
\(331\) −1188.50 2058.54i −0.197359 0.341836i 0.750312 0.661084i \(-0.229903\pi\)
−0.947671 + 0.319248i \(0.896570\pi\)
\(332\) −1464.00 2535.72i −0.242010 0.419174i
\(333\) 7614.00 1.25299
\(334\) −2355.00 4078.98i −0.385808 0.668239i
\(335\) −817.000 + 1415.09i −0.133246 + 0.230789i
\(336\) 120.000 207.846i 0.0194837 0.0337468i
\(337\) −7618.00 −1.23139 −0.615696 0.787984i \(-0.711125\pi\)
−0.615696 + 0.787984i \(0.711125\pi\)
\(338\) 0 0
\(339\) −2841.00 −0.455168
\(340\) 108.000 187.061i 0.0172268 0.0298377i
\(341\) 676.000 1170.87i 0.107353 0.185941i
\(342\) −1350.00 2338.27i −0.213449 0.369705i
\(343\) −3305.00 −0.520272
\(344\) −796.000 1378.71i −0.124760 0.216091i
\(345\) 561.000 + 971.681i 0.0875456 + 0.151633i
\(346\) −7778.00 −1.20852
\(347\) −187.500 324.760i −0.0290073 0.0502421i 0.851157 0.524911i \(-0.175901\pi\)
−0.880165 + 0.474669i \(0.842568\pi\)
\(348\) −78.0000 + 135.100i −0.0120151 + 0.0208107i
\(349\) 4863.50 8423.83i 0.745952 1.29203i −0.203797 0.979013i \(-0.565328\pi\)
0.949749 0.313013i \(-0.101338\pi\)
\(350\) −1210.00 −0.184792
\(351\) 0 0
\(352\) −416.000 −0.0629911
\(353\) 1131.50 1959.82i 0.170605 0.295497i −0.768026 0.640418i \(-0.778761\pi\)
0.938632 + 0.344921i \(0.112094\pi\)
\(354\) −1473.00 + 2551.31i −0.221156 + 0.383053i
\(355\) −79.0000 136.832i −0.0118109 0.0204572i
\(356\) 4164.00 0.619920
\(357\) 202.500 + 350.740i 0.0300208 + 0.0519976i
\(358\) −2229.00 3860.74i −0.329068 0.569962i
\(359\) 4488.00 0.659798 0.329899 0.944016i \(-0.392985\pi\)
0.329899 + 0.944016i \(0.392985\pi\)
\(360\) −144.000 249.415i −0.0210819 0.0365148i
\(361\) 617.000 1068.68i 0.0899548 0.155806i
\(362\) 1038.00 1797.87i 0.150707 0.261033i
\(363\) 3486.00 0.504043
\(364\) 0 0
\(365\) 460.000 0.0659658
\(366\) 525.000 909.327i 0.0749787 0.129867i
\(367\) 813.500 1409.02i 0.115707 0.200410i −0.802355 0.596847i \(-0.796420\pi\)
0.918062 + 0.396437i \(0.129753\pi\)
\(368\) 1496.00 + 2591.15i 0.211914 + 0.367046i
\(369\) 3510.00 0.495185
\(370\) −846.000 1465.31i −0.118869 0.205887i
\(371\) −1545.00 2676.02i −0.216206 0.374480i
\(372\) −1248.00 −0.173940
\(373\) −1493.50 2586.82i −0.207320 0.359089i 0.743549 0.668681i \(-0.233141\pi\)
−0.950870 + 0.309592i \(0.899808\pi\)
\(374\) 351.000 607.950i 0.0485288 0.0840544i
\(375\) 738.000 1278.25i 0.101627 0.176023i
\(376\) −3104.00 −0.425736
\(377\) 0 0
\(378\) 1350.00 0.183694
\(379\) −4433.50 + 7679.05i −0.600880 + 1.04076i 0.391808 + 0.920047i \(0.371850\pi\)
−0.992688 + 0.120708i \(0.961484\pi\)
\(380\) −300.000 + 519.615i −0.0404991 + 0.0701466i
\(381\) 1765.50 + 3057.94i 0.237400 + 0.411188i
\(382\) −4282.00 −0.573524
\(383\) 5701.50 + 9875.29i 0.760661 + 1.31750i 0.942510 + 0.334177i \(0.108458\pi\)
−0.181850 + 0.983326i \(0.558208\pi\)
\(384\) 192.000 + 332.554i 0.0255155 + 0.0441942i
\(385\) 130.000 0.0172089
\(386\) 2627.00 + 4550.10i 0.346401 + 0.599984i
\(387\) 1791.00 3102.10i 0.235250 0.407464i
\(388\) −194.000 + 336.018i −0.0253837 + 0.0439658i
\(389\) 2622.00 0.341750 0.170875 0.985293i \(-0.445341\pi\)
0.170875 + 0.985293i \(0.445341\pi\)
\(390\) 0 0
\(391\) −5049.00 −0.653041
\(392\) 1272.00 2203.17i 0.163892 0.283869i
\(393\) −2130.00 + 3689.27i −0.273395 + 0.473534i
\(394\) 1203.00 + 2083.66i 0.153823 + 0.266429i
\(395\) −1528.00 −0.194638
\(396\) −468.000 810.600i −0.0593886 0.102864i
\(397\) 329.500 + 570.711i 0.0416552 + 0.0721490i 0.886101 0.463492i \(-0.153404\pi\)
−0.844446 + 0.535641i \(0.820070\pi\)
\(398\) 1486.00 0.187152
\(399\) −562.500 974.279i −0.0705770 0.122243i
\(400\) 968.000 1676.63i 0.121000 0.209578i
\(401\) −7342.50 + 12717.6i −0.914381 + 1.58376i −0.106577 + 0.994304i \(0.533989\pi\)
−0.807804 + 0.589451i \(0.799344\pi\)
\(402\) 4902.00 0.608183
\(403\) 0 0
\(404\) −3236.00 −0.398507
\(405\) 81.0000 140.296i 0.00993808 0.0172133i
\(406\) 65.0000 112.583i 0.00794556 0.0137621i
\(407\) −2749.50 4762.27i −0.334859 0.579993i
\(408\) −648.000 −0.0786294
\(409\) −3914.50 6780.11i −0.473251 0.819694i 0.526280 0.850311i \(-0.323586\pi\)
−0.999531 + 0.0306167i \(0.990253\pi\)
\(410\) −390.000 675.500i −0.0469774 0.0813672i
\(411\) −7227.00 −0.867352
\(412\) −2576.00 4461.76i −0.308035 0.533532i
\(413\) 1227.50 2126.09i 0.146250 0.253313i
\(414\) −3366.00 + 5830.08i −0.399589 + 0.692109i
\(415\) −1464.00 −0.173169
\(416\) 0 0
\(417\) −8481.00 −0.995962
\(418\) −975.000 + 1688.75i −0.114088 + 0.197606i
\(419\) 1459.50 2527.93i 0.170170 0.294743i −0.768309 0.640079i \(-0.778902\pi\)
0.938479 + 0.345336i \(0.112235\pi\)
\(420\) −60.0000 103.923i −0.00697071 0.0120736i
\(421\) 3110.00 0.360029 0.180014 0.983664i \(-0.442386\pi\)
0.180014 + 0.983664i \(0.442386\pi\)
\(422\) 355.000 + 614.878i 0.0409505 + 0.0709284i
\(423\) −3492.00 6048.32i −0.401387 0.695223i
\(424\) 4944.00 0.566278
\(425\) 1633.50 + 2829.30i 0.186439 + 0.322921i
\(426\) −237.000 + 410.496i −0.0269547 + 0.0466869i
\(427\) −437.500 + 757.772i −0.0495834 + 0.0858810i
\(428\) 5108.00 0.576880
\(429\) 0 0
\(430\) −796.000 −0.0892710
\(431\) −4567.50 + 7911.14i −0.510461 + 0.884145i 0.489465 + 0.872023i \(0.337192\pi\)
−0.999927 + 0.0121219i \(0.996141\pi\)
\(432\) −1080.00 + 1870.61i −0.120281 + 0.208333i
\(433\) 5834.50 + 10105.7i 0.647548 + 1.12159i 0.983707 + 0.179780i \(0.0575387\pi\)
−0.336159 + 0.941805i \(0.609128\pi\)
\(434\) 1040.00 0.115027
\(435\) 39.0000 + 67.5500i 0.00429864 + 0.00744546i
\(436\) 1652.00 + 2861.35i 0.181460 + 0.314298i
\(437\) 14025.0 1.53526
\(438\) −690.000 1195.12i −0.0752728 0.130376i
\(439\) −6764.50 + 11716.5i −0.735426 + 1.27380i 0.219110 + 0.975700i \(0.429685\pi\)
−0.954536 + 0.298095i \(0.903649\pi\)
\(440\) −104.000 + 180.133i −0.0112682 + 0.0195171i
\(441\) 5724.00 0.618076
\(442\) 0 0
\(443\) −1932.00 −0.207206 −0.103603 0.994619i \(-0.533037\pi\)
−0.103603 + 0.994619i \(0.533037\pi\)
\(444\) −2538.00 + 4395.94i −0.271280 + 0.469870i
\(445\) 1041.00 1803.06i 0.110895 0.192075i
\(446\) −2283.00 3954.27i −0.242384 0.419821i
\(447\) 2565.00 0.271410
\(448\) −160.000 277.128i −0.0168734 0.0292256i
\(449\) −2678.50 4639.30i −0.281528 0.487621i 0.690233 0.723587i \(-0.257508\pi\)
−0.971761 + 0.235966i \(0.924175\pi\)
\(450\) 4356.00 0.456320
\(451\) −1267.50 2195.37i −0.132338 0.229215i
\(452\) −1894.00 + 3280.50i −0.197094 + 0.341376i
\(453\) −3096.00 + 5362.43i −0.321110 + 0.556179i
\(454\) −4902.00 −0.506745
\(455\) 0 0
\(456\) 1800.00 0.184852
\(457\) 9699.50 16800.0i 0.992830 1.71963i 0.392897 0.919582i \(-0.371473\pi\)
0.599933 0.800050i \(-0.295194\pi\)
\(458\) −1878.00 + 3252.79i −0.191601 + 0.331862i
\(459\) −1822.50 3156.66i −0.185331 0.321003i
\(460\) 1496.00 0.151633
\(461\) −7774.50 13465.8i −0.785455 1.36045i −0.928727 0.370764i \(-0.879096\pi\)
0.143273 0.989683i \(-0.454237\pi\)
\(462\) −195.000 337.750i −0.0196368 0.0340120i
\(463\) −4072.00 −0.408730 −0.204365 0.978895i \(-0.565513\pi\)
−0.204365 + 0.978895i \(0.565513\pi\)
\(464\) 104.000 + 180.133i 0.0104053 + 0.0180226i
\(465\) −312.000 + 540.400i −0.0311154 + 0.0538934i
\(466\) −1630.00 + 2823.24i −0.162035 + 0.280653i
\(467\) 15224.0 1.50853 0.754264 0.656571i \(-0.227994\pi\)
0.754264 + 0.656571i \(0.227994\pi\)
\(468\) 0 0
\(469\) −4085.00 −0.402191
\(470\) −776.000 + 1344.07i −0.0761579 + 0.131909i
\(471\) −2841.00 + 4920.76i −0.277933 + 0.481394i
\(472\) 1964.00 + 3401.75i 0.191526 + 0.331733i
\(473\) −2587.00 −0.251481
\(474\) 2292.00 + 3969.86i 0.222099 + 0.384687i
\(475\) −4537.50 7859.18i −0.438305 0.759166i
\(476\) 540.000 0.0519976
\(477\) 5562.00 + 9633.67i 0.533892 + 0.924728i
\(478\) −5544.00 + 9602.49i −0.530495 + 0.918844i
\(479\) −5167.50 + 8950.37i −0.492921 + 0.853764i −0.999967 0.00815506i \(-0.997404\pi\)
0.507046 + 0.861919i \(0.330737\pi\)
\(480\) 192.000 0.0182574
\(481\) 0 0
\(482\) −11046.0 −1.04384
\(483\) −1402.50 + 2429.20i −0.132124 + 0.228846i
\(484\) 2324.00 4025.29i 0.218257 0.378032i
\(485\) 97.0000 + 168.009i 0.00908153 + 0.0157297i
\(486\) −7776.00 −0.725775
\(487\) 3227.50 + 5590.19i 0.300312 + 0.520156i 0.976207 0.216843i \(-0.0695758\pi\)
−0.675894 + 0.736998i \(0.736243\pi\)
\(488\) −700.000 1212.44i −0.0649334 0.112468i
\(489\) −2955.00 −0.273271
\(490\) −636.000 1101.58i −0.0586358 0.101560i
\(491\) −3888.50 + 6735.08i −0.357404 + 0.619043i −0.987526 0.157454i \(-0.949672\pi\)
0.630122 + 0.776496i \(0.283005\pi\)
\(492\) −1170.00 + 2026.50i −0.107211 + 0.185694i
\(493\) −351.000 −0.0320654
\(494\) 0 0
\(495\) −468.000 −0.0424950
\(496\) −832.000 + 1441.07i −0.0753184 + 0.130455i
\(497\) 197.500 342.080i 0.0178251 0.0308740i
\(498\) 2196.00 + 3803.58i 0.197601 + 0.342254i
\(499\) 3044.00 0.273082 0.136541 0.990634i \(-0.456401\pi\)
0.136541 + 0.990634i \(0.456401\pi\)
\(500\) −984.000 1704.34i −0.0880116 0.152441i
\(501\) 3532.50 + 6118.47i 0.315011 + 0.545615i
\(502\) 4350.00 0.386753
\(503\) −5673.50 9826.79i −0.502920 0.871083i −0.999994 0.00337525i \(-0.998926\pi\)
0.497074 0.867708i \(-0.334408\pi\)
\(504\) 360.000 623.538i 0.0318168 0.0551083i
\(505\) −809.000 + 1401.23i −0.0712872 + 0.123473i
\(506\) 4862.00 0.427159
\(507\) 0 0
\(508\) 4708.00 0.411188
\(509\) 363.500 629.600i 0.0316539 0.0548262i −0.849764 0.527163i \(-0.823256\pi\)
0.881418 + 0.472336i \(0.156589\pi\)
\(510\) −162.000 + 280.592i −0.0140656 + 0.0243624i
\(511\) 575.000 + 995.929i 0.0497779 + 0.0862178i
\(512\) 512.000 0.0441942
\(513\) 5062.50 + 8768.51i 0.435701 + 0.754657i
\(514\) 5685.00 + 9846.71i 0.487849 + 0.844980i
\(515\) −2576.00 −0.220412
\(516\) 1194.00 + 2068.07i 0.101866 + 0.176437i
\(517\) −2522.00 + 4368.23i −0.214540 + 0.371595i
\(518\) 2115.00 3663.29i 0.179397 0.310725i
\(519\) 11667.0 0.986752
\(520\) 0 0
\(521\) 9582.00 0.805749 0.402874 0.915255i \(-0.368011\pi\)
0.402874 + 0.915255i \(0.368011\pi\)
\(522\) −234.000 + 405.300i −0.0196205 + 0.0339837i
\(523\) 5191.50 8991.94i 0.434051 0.751798i −0.563167 0.826343i \(-0.690417\pi\)
0.997218 + 0.0745454i \(0.0237506\pi\)
\(524\) 2840.00 + 4919.02i 0.236767 + 0.410093i
\(525\) 1815.00 0.150882
\(526\) −6117.00 10595.0i −0.507061 0.878255i
\(527\) −1404.00 2431.80i −0.116052 0.201007i
\(528\) 624.000 0.0514320
\(529\) −11401.0 19747.1i −0.937043 1.62301i
\(530\) 1236.00 2140.81i 0.101299 0.175455i
\(531\) −4419.00 + 7653.93i −0.361146 + 0.625522i
\(532\) −1500.00 −0.122243
\(533\) 0 0
\(534\) −6246.00 −0.506163
\(535\) 1277.00 2211.83i 0.103195 0.178740i
\(536\) 3268.00 5660.34i 0.263351 0.456137i
\(537\) 3343.50 + 5791.11i 0.268683 + 0.465372i
\(538\) −10218.0 −0.818828
\(539\) −2067.00 3580.15i −0.165180 0.286100i
\(540\) 540.000 + 935.307i 0.0430331 + 0.0745356i
\(541\) −12230.0 −0.971920 −0.485960 0.873981i \(-0.661530\pi\)
−0.485960 + 0.873981i \(0.661530\pi\)
\(542\) 7549.00 + 13075.3i 0.598261 + 1.03622i
\(543\) −1557.00 + 2696.80i −0.123052 + 0.213132i
\(544\) −432.000 + 748.246i −0.0340475 + 0.0589720i
\(545\) 1652.00 0.129842
\(546\) 0 0
\(547\) −14636.0 −1.14404 −0.572020 0.820239i \(-0.693840\pi\)
−0.572020 + 0.820239i \(0.693840\pi\)
\(548\) −4818.00 + 8345.02i −0.375574 + 0.650514i
\(549\) 1575.00 2727.98i 0.122440 0.212072i
\(550\) −1573.00 2724.52i −0.121951 0.211225i
\(551\) 975.000 0.0753837
\(552\) −2244.00 3886.72i −0.173027 0.299692i
\(553\) −1910.00 3308.22i −0.146874 0.254394i
\(554\) −1962.00 −0.150465
\(555\) 1269.00 + 2197.97i 0.0970559 + 0.168106i
\(556\) −5654.00 + 9793.02i −0.431264 + 0.746972i
\(557\) −382.500 + 662.509i −0.0290970 + 0.0503975i −0.880207 0.474590i \(-0.842597\pi\)
0.851110 + 0.524987i \(0.175930\pi\)
\(558\) −3744.00 −0.284043
\(559\) 0 0
\(560\) −160.000 −0.0120736
\(561\) −526.500 + 911.925i −0.0396236 + 0.0686301i
\(562\) −2762.00 + 4783.92i −0.207309 + 0.359071i
\(563\) −2957.50 5122.54i −0.221392 0.383462i 0.733839 0.679324i \(-0.237727\pi\)
−0.955231 + 0.295861i \(0.904393\pi\)
\(564\) 4656.00 0.347612
\(565\) 947.000 + 1640.25i 0.0705143 + 0.122134i
\(566\) −3925.00 6798.30i −0.291484 0.504865i
\(567\) 405.000 0.0299972
\(568\) 316.000 + 547.328i 0.0233434 + 0.0404320i
\(569\) 608.500 1053.95i 0.0448324 0.0776520i −0.842738 0.538323i \(-0.819058\pi\)
0.887571 + 0.460671i \(0.152391\pi\)
\(570\) 450.000 779.423i 0.0330674 0.0572744i
\(571\) −23436.0 −1.71763 −0.858814 0.512287i \(-0.828798\pi\)
−0.858814 + 0.512287i \(0.828798\pi\)
\(572\) 0 0
\(573\) 6423.00 0.468280
\(574\) 975.000 1688.75i 0.0708985 0.122800i
\(575\) −11313.5 + 19595.6i −0.820531 + 1.42120i
\(576\) 576.000 + 997.661i 0.0416667 + 0.0721688i
\(577\) −7854.00 −0.566666 −0.283333 0.959022i \(-0.591440\pi\)
−0.283333 + 0.959022i \(0.591440\pi\)
\(578\) 4184.00 + 7246.90i 0.301092 + 0.521507i
\(579\) −3940.50 6825.15i −0.282835 0.489885i
\(580\) 104.000 0.00744546
\(581\) −1830.00 3169.65i −0.130673 0.226333i
\(582\) 291.000 504.027i 0.0207257 0.0358979i
\(583\) 4017.00 6957.65i 0.285364 0.494265i
\(584\) −1840.00 −0.130376
\(585\) 0 0
\(586\) −15422.0 −1.08716
\(587\) 8516.50 14751.0i 0.598831 1.03721i −0.394163 0.919040i \(-0.628966\pi\)
0.992994 0.118165i \(-0.0377011\pi\)
\(588\) −1908.00 + 3304.75i −0.133817 + 0.231778i
\(589\) 3900.00 + 6755.00i 0.272830 + 0.472555i
\(590\) 1964.00 0.137045
\(591\) −1804.50 3125.49i −0.125596 0.217539i
\(592\) 3384.00 + 5861.26i 0.234935 + 0.406919i
\(593\) 14506.0 1.00454 0.502268 0.864712i \(-0.332499\pi\)
0.502268 + 0.864712i \(0.332499\pi\)
\(594\) 1755.00 + 3039.75i 0.121226 + 0.209970i
\(595\) 135.000 233.827i 0.00930161 0.0161109i
\(596\) 1710.00 2961.81i 0.117524 0.203558i
\(597\) −2229.00 −0.152809
\(598\) 0 0
\(599\) 15388.0 1.04964 0.524822 0.851212i \(-0.324132\pi\)
0.524822 + 0.851212i \(0.324132\pi\)
\(600\) −1452.00 + 2514.94i −0.0987961 + 0.171120i
\(601\) 3038.50 5262.84i 0.206228 0.357197i −0.744295 0.667851i \(-0.767214\pi\)
0.950523 + 0.310653i \(0.100548\pi\)
\(602\) −995.000 1723.39i −0.0673641 0.116678i
\(603\) 14706.0 0.993159
\(604\) 4128.00 + 7149.91i 0.278089 + 0.481665i
\(605\) −1162.00 2012.64i −0.0780860 0.135249i
\(606\) 4854.00 0.325380
\(607\) −5107.50 8846.45i −0.341527 0.591543i 0.643189 0.765707i \(-0.277611\pi\)
−0.984717 + 0.174165i \(0.944277\pi\)
\(608\) 1200.00 2078.46i 0.0800435 0.138639i
\(609\) −97.5000 + 168.875i −0.00648752 + 0.0112367i
\(610\) −700.000 −0.0464626
\(611\) 0 0
\(612\) −1944.00 −0.128401
\(613\) −1728.50 + 2993.85i −0.113888 + 0.197260i −0.917335 0.398117i \(-0.869664\pi\)
0.803447 + 0.595377i \(0.202997\pi\)
\(614\) 10388.0 17992.5i 0.682778 1.18261i
\(615\) 585.000 + 1013.25i 0.0383569 + 0.0664361i
\(616\) −520.000 −0.0340120
\(617\) −3584.50 6208.54i −0.233884 0.405099i 0.725064 0.688682i \(-0.241810\pi\)
−0.958948 + 0.283583i \(0.908477\pi\)
\(618\) 3864.00 + 6692.64i 0.251510 + 0.435627i
\(619\) −20212.0 −1.31242 −0.656211 0.754578i \(-0.727842\pi\)
−0.656211 + 0.754578i \(0.727842\pi\)
\(620\) 416.000 + 720.533i 0.0269467 + 0.0466731i
\(621\) 12622.5 21862.8i 0.815658 1.41276i
\(622\) 7272.00 12595.5i 0.468779 0.811949i
\(623\) 5205.00 0.334725
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) −7910.00 + 13700.5i −0.505027 + 0.874733i
\(627\) 1462.50 2533.12i 0.0931525 0.161345i
\(628\) 3788.00 + 6561.01i 0.240697 + 0.416899i
\(629\) −11421.0 −0.723983
\(630\) −180.000 311.769i −0.0113831 0.0197162i
\(631\) −4472.50 7746.60i −0.282167 0.488728i 0.689751 0.724046i \(-0.257720\pi\)
−0.971918 + 0.235319i \(0.924387\pi\)
\(632\) 6112.00 0.384687
\(633\) −532.500 922.317i −0.0334360 0.0579128i
\(634\) 7398.00 12813.7i 0.463426 0.802677i
\(635\) 1177.00 2038.62i 0.0735556 0.127402i
\(636\) −7416.00 −0.462364
\(637\) 0 0
\(638\) 338.000 0.0209742
\(639\) −711.000 + 1231.49i −0.0440168 + 0.0762393i
\(640\) 128.000 221.703i 0.00790569 0.0136931i
\(641\) −14121.5 24459.2i −0.870149 1.50714i −0.861842 0.507177i \(-0.830689\pi\)
−0.00830761 0.999965i \(-0.502644\pi\)
\(642\) −7662.00 −0.471020
\(643\) 2615.50 + 4530.18i 0.160413 + 0.277843i 0.935017 0.354604i \(-0.115384\pi\)
−0.774604 + 0.632446i \(0.782051\pi\)
\(644\) 1870.00 + 3238.94i 0.114423 + 0.198186i
\(645\) 1194.00 0.0728895
\(646\) 2025.00 + 3507.40i 0.123332 + 0.213618i
\(647\) 2435.50 4218.41i 0.147990 0.256326i −0.782495 0.622657i \(-0.786053\pi\)
0.930484 + 0.366332i \(0.119386\pi\)
\(648\) −324.000 + 561.184i −0.0196419 + 0.0340207i
\(649\) 6383.00 0.386063
\(650\) 0 0
\(651\) −1560.00 −0.0939189
\(652\) −1970.00 + 3412.14i −0.118330 + 0.204954i
\(653\) −6127.50 + 10613.1i −0.367209 + 0.636025i −0.989128 0.147057i \(-0.953020\pi\)
0.621919 + 0.783082i \(0.286353\pi\)
\(654\) −2478.00 4292.02i −0.148161 0.256623i
\(655\) 2840.00 0.169417
\(656\) 1560.00 + 2702.00i 0.0928472 + 0.160816i
\(657\) −2070.00 3585.35i −0.122920 0.212904i
\(658\) −3880.00 −0.229876
\(659\) 1072.50 + 1857.62i 0.0633971 + 0.109807i 0.895982 0.444091i \(-0.146473\pi\)
−0.832585 + 0.553898i \(0.813140\pi\)
\(660\) 156.000 270.200i 0.00920044 0.0159356i
\(661\) 1055.50 1828.18i 0.0621092 0.107576i −0.833299 0.552823i \(-0.813551\pi\)
0.895408 + 0.445247i \(0.146884\pi\)
\(662\) 4754.00 0.279108
\(663\) 0 0
\(664\) 5856.00 0.342254
\(665\) −375.000 + 649.519i −0.0218675 + 0.0378756i
\(666\) −7614.00 + 13187.8i −0.442998 + 0.767295i
\(667\) −1215.50 2105.31i −0.0705612 0.122216i
\(668\) 9420.00 0.545615
\(669\) 3424.50 + 5931.41i 0.197906 + 0.342782i
\(670\) −1634.00 2830.17i −0.0942193 0.163193i
\(671\) −2275.00 −0.130887
\(672\) 240.000 + 415.692i 0.0137771 + 0.0238626i
\(673\) 11636.5 20155.0i 0.666499 1.15441i −0.312377 0.949958i \(-0.601125\pi\)
0.978876 0.204453i \(-0.0655414\pi\)
\(674\) 7618.00 13194.8i 0.435363 0.754070i
\(675\) −16335.0 −0.931458
\(676\) 0 0
\(677\) −5910.00 −0.335509 −0.167755 0.985829i \(-0.553652\pi\)
−0.167755 + 0.985829i \(0.553652\pi\)
\(678\) 2841.00 4920.76i 0.160926 0.278732i
\(679\) −242.500 + 420.022i −0.0137059 + 0.0237393i
\(680\) 216.000 + 374.123i 0.0121812 + 0.0210985i
\(681\) 7353.00 0.413756
\(682\) 1352.00 + 2341.73i 0.0759102 + 0.131480i
\(683\) 8373.50 + 14503.3i 0.469111 + 0.812525i 0.999377 0.0353071i \(-0.0112409\pi\)
−0.530265 + 0.847832i \(0.677908\pi\)
\(684\) 5400.00 0.301863
\(685\) 2409.00 + 4172.51i 0.134370 + 0.232735i
\(686\) 3305.00 5724.43i 0.183944 0.318600i
\(687\) 2817.00 4879.19i 0.156441 0.270964i
\(688\) 3184.00 0.176437
\(689\) 0 0
\(690\) −2244.00 −0.123808
\(691\) 5154.50 8927.86i 0.283772 0.491507i −0.688539 0.725200i \(-0.741747\pi\)
0.972311 + 0.233692i \(0.0750808\pi\)
\(692\) 7778.00 13471.9i 0.427276 0.740064i
\(693\) −585.000 1013.25i −0.0320668 0.0555414i
\(694\) 750.000 0.0410225
\(695\) 2827.00 + 4896.51i 0.154294 + 0.267245i
\(696\) −156.000 270.200i −0.00849593 0.0147154i
\(697\) −5265.00 −0.286121
\(698\) 9727.00 + 16847.7i 0.527468 + 0.913601i
\(699\) 2445.00 4234.86i 0.132301 0.229152i
\(700\) 1210.00 2095.78i 0.0653339 0.113162i
\(701\) −24294.0 −1.30895 −0.654473 0.756085i \(-0.727110\pi\)
−0.654473 + 0.756085i \(0.727110\pi\)
\(702\) 0 0
\(703\) 31725.0 1.70204
\(704\) 416.000 720.533i 0.0222707 0.0385740i
\(705\) 1164.00 2016.11i 0.0621827 0.107704i
\(706\) 2263.00 + 3919.63i 0.120636 + 0.208948i
\(707\) −4045.00 −0.215174
\(708\) −2946.00 5102.62i −0.156381 0.270859i
\(709\) 6329.50 + 10963.0i 0.335274 + 0.580712i 0.983537 0.180704i \(-0.0578377\pi\)
−0.648263 + 0.761416i \(0.724504\pi\)
\(710\) 316.000 0.0167032
\(711\) 6876.00 + 11909.6i 0.362687 + 0.628192i
\(712\) −4164.00 + 7212.26i −0.219175 + 0.379622i
\(713\) 9724.00 16842.5i 0.510753 0.884650i
\(714\) −810.000 −0.0424559
\(715\) 0 0
\(716\) 8916.00 0.465372
\(717\) 8316.00 14403.7i 0.433147 0.750233i
\(718\) −4488.00 + 7773.44i −0.233274 + 0.404042i
\(719\) −6545.50 11337.1i −0.339508 0.588044i 0.644833 0.764324i \(-0.276927\pi\)
−0.984340 + 0.176279i \(0.943594\pi\)
\(720\) 576.000 0.0298142
\(721\) −3220.00 5577.20i −0.166323 0.288080i
\(722\) 1234.00 + 2137.35i 0.0636077 + 0.110172i
\(723\) 16569.0 0.852293
\(724\) 2076.00 + 3595.74i 0.106566 + 0.184578i
\(725\) −786.500 + 1362.26i −0.0402895 + 0.0697834i
\(726\) −3486.00 + 6037.93i −0.178206 + 0.308662i
\(727\) 10792.0 0.550555 0.275277 0.961365i \(-0.411230\pi\)
0.275277 + 0.961365i \(0.411230\pi\)
\(728\) 0 0
\(729\) 9477.00 0.481481
\(730\) −460.000 + 796.743i −0.0233224 + 0.0403956i
\(731\) −2686.50 + 4653.15i −0.135929 + 0.235435i
\(732\) 1050.00 + 1818.65i 0.0530179 + 0.0918297i
\(733\) 2698.00 0.135952 0.0679761 0.997687i \(-0.478346\pi\)
0.0679761 + 0.997687i \(0.478346\pi\)
\(734\) 1627.00 + 2818.05i 0.0818170 + 0.141711i
\(735\) 954.000 + 1652.38i 0.0478759 + 0.0829236i
\(736\) −5984.00 −0.299692
\(737\) −5310.50 9198.06i −0.265420 0.459721i
\(738\) −3510.00 + 6079.50i −0.175074 + 0.303238i
\(739\) 1420.50 2460.38i 0.0707090 0.122472i −0.828503 0.559984i \(-0.810807\pi\)
0.899212 + 0.437513i \(0.144141\pi\)
\(740\) 3384.00 0.168106
\(741\) 0 0
\(742\) 6180.00 0.305761
\(743\) −4595.50 + 7959.64i −0.226908 + 0.393016i −0.956890 0.290450i \(-0.906195\pi\)
0.729982 + 0.683466i \(0.239528\pi\)
\(744\) 1248.00 2161.60i 0.0614972 0.106516i
\(745\) −855.000 1480.90i −0.0420467 0.0728270i
\(746\) 5974.00 0.293195
\(747\) 6588.00 + 11410.8i 0.322680 + 0.558899i
\(748\) 702.000 + 1215.90i 0.0343151 + 0.0594354i
\(749\) 6385.00 0.311486
\(750\) 1476.00 + 2556.51i 0.0718612 + 0.124467i
\(751\) 829.500 1436.74i 0.0403048 0.0698099i −0.845169 0.534499i \(-0.820500\pi\)
0.885474 + 0.464689i \(0.153834\pi\)
\(752\) 3104.00 5376.29i 0.150520 0.260709i
\(753\) −6525.00 −0.315782
\(754\) 0 0
\(755\) 4128.00 0.198985
\(756\) −1350.00 + 2338.27i −0.0649458 + 0.112489i
\(757\) 6964.50 12062.9i 0.334384 0.579171i −0.648982 0.760804i \(-0.724805\pi\)
0.983366 + 0.181633i \(0.0581383\pi\)
\(758\) −8867.00 15358.1i −0.424886 0.735925i
\(759\) −7293.00 −0.348774
\(760\) −600.000 1039.23i −0.0286372 0.0496011i
\(761\) 2293.50 + 3972.46i 0.109250 + 0.189227i 0.915467 0.402394i \(-0.131822\pi\)
−0.806217 + 0.591620i \(0.798488\pi\)
\(762\) −7062.00 −0.335734
\(763\) 2065.00 + 3576.68i 0.0979791 + 0.169705i
\(764\) 4282.00 7416.64i 0.202771 0.351210i
\(765\) −486.000 + 841.777i −0.0229691 + 0.0397837i
\(766\) −22806.0 −1.07574
\(767\) 0 0
\(768\) −768.000 −0.0360844
\(769\) 7249.50 12556.5i 0.339953 0.588815i −0.644471 0.764629i \(-0.722922\pi\)
0.984423 + 0.175814i \(0.0562556\pi\)
\(770\) −130.000 + 225.167i −0.00608425 + 0.0105382i
\(771\) −8527.50