Properties

Label 338.4.e.d.23.1
Level $338$
Weight $4$
Character 338.23
Analytic conductor $19.943$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [338,4,Mod(23,338)]
 
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([5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("338.23");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 338.e (of order \(6\), 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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 338.23
Dual form 338.4.e.d.147.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 + 1.00000i) q^{2} +(1.50000 + 2.59808i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.00000i q^{5} +(-5.19615 - 3.00000i) q^{6} +(-4.33013 - 2.50000i) q^{7} +8.00000i q^{8} +(9.00000 - 15.5885i) q^{9} +O(q^{10})\) \(q+(-1.73205 + 1.00000i) q^{2} +(1.50000 + 2.59808i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.00000i q^{5} +(-5.19615 - 3.00000i) q^{6} +(-4.33013 - 2.50000i) q^{7} +8.00000i q^{8} +(9.00000 - 15.5885i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(-11.2583 + 6.50000i) q^{11} +12.0000 q^{12} +10.0000 q^{14} +(-5.19615 + 3.00000i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(13.5000 - 23.3827i) q^{17} +36.0000i q^{18} +(-64.9519 - 37.5000i) q^{19} +(6.92820 + 4.00000i) q^{20} -15.0000i q^{21} +(13.0000 - 22.5167i) q^{22} +(-93.5000 - 161.947i) q^{23} +(-20.7846 + 12.0000i) q^{24} +121.000 q^{25} +135.000 q^{27} +(-17.3205 + 10.0000i) q^{28} +(6.50000 + 11.2583i) q^{29} +(6.00000 - 10.3923i) q^{30} -104.000i q^{31} +(27.7128 + 16.0000i) q^{32} +(-33.7750 - 19.5000i) q^{33} +54.0000i q^{34} +(5.00000 - 8.66025i) q^{35} +(-36.0000 - 62.3538i) q^{36} +(-366.329 + 211.500i) q^{37} +150.000 q^{38} -16.0000 q^{40} +(168.875 - 97.5000i) q^{41} +(15.0000 + 25.9808i) q^{42} +(99.5000 - 172.339i) q^{43} +52.0000i q^{44} +(31.1769 + 18.0000i) q^{45} +(323.894 + 187.000i) q^{46} -388.000i q^{47} +(24.0000 - 41.5692i) q^{48} +(-159.000 - 275.396i) q^{49} +(-209.578 + 121.000i) q^{50} +81.0000 q^{51} +618.000 q^{53} +(-233.827 + 135.000i) q^{54} +(-13.0000 - 22.5167i) q^{55} +(20.0000 - 34.6410i) q^{56} -225.000i q^{57} +(-22.5167 - 13.0000i) q^{58} +(425.218 + 245.500i) q^{59} +24.0000i q^{60} +(-87.5000 + 151.554i) q^{61} +(104.000 + 180.133i) q^{62} +(-77.9423 + 45.0000i) q^{63} -64.0000 q^{64} +78.0000 q^{66} +(707.543 - 408.500i) q^{67} +(-54.0000 - 93.5307i) q^{68} +(280.500 - 485.840i) q^{69} +20.0000i q^{70} +(-68.4160 - 39.5000i) q^{71} +(124.708 + 72.0000i) q^{72} -230.000i q^{73} +(423.000 - 732.657i) q^{74} +(181.500 + 314.367i) q^{75} +(-259.808 + 150.000i) q^{76} +65.0000 q^{77} +764.000 q^{79} +(27.7128 - 16.0000i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-195.000 + 337.750i) q^{82} -732.000i q^{83} +(-51.9615 - 30.0000i) q^{84} +(46.7654 + 27.0000i) q^{85} +398.000i q^{86} +(-19.5000 + 33.7750i) q^{87} +(-52.0000 - 90.0666i) q^{88} +(901.532 - 520.500i) q^{89} -72.0000 q^{90} -748.000 q^{92} +(270.200 - 156.000i) q^{93} +(388.000 + 672.036i) q^{94} +(75.0000 - 129.904i) q^{95} +96.0000i q^{96} +(84.0045 + 48.5000i) q^{97} +(550.792 + 318.000i) q^{98} +234.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} + 8 q^{4} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{3} + 8 q^{4} + 36 q^{9} - 8 q^{10} + 48 q^{12} + 40 q^{14} - 32 q^{16} + 54 q^{17} + 52 q^{22} - 374 q^{23} + 484 q^{25} + 540 q^{27} + 26 q^{29} + 24 q^{30} + 20 q^{35} - 144 q^{36} + 600 q^{38} - 64 q^{40} + 60 q^{42} + 398 q^{43} + 96 q^{48} - 636 q^{49} + 324 q^{51} + 2472 q^{53} - 52 q^{55} + 80 q^{56} - 350 q^{61} + 416 q^{62} - 256 q^{64} + 312 q^{66} - 216 q^{68} + 1122 q^{69} + 1692 q^{74} + 726 q^{75} + 260 q^{77} + 3056 q^{79} - 162 q^{81} - 780 q^{82} - 78 q^{87} - 208 q^{88} - 288 q^{90} - 2992 q^{92} + 1552 q^{94} + 300 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(171\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 + 1.00000i −0.612372 + 0.353553i
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) 2.00000i 0.178885i 0.995992 + 0.0894427i \(0.0285086\pi\)
−0.995992 + 0.0894427i \(0.971491\pi\)
\(6\) −5.19615 3.00000i −0.353553 0.204124i
\(7\) −4.33013 2.50000i −0.233805 0.134987i 0.378521 0.925593i \(-0.376433\pi\)
−0.612326 + 0.790605i \(0.709766\pi\)
\(8\) 8.00000i 0.353553i
\(9\) 9.00000 15.5885i 0.333333 0.577350i
\(10\) −2.00000 3.46410i −0.0632456 0.109545i
\(11\) −11.2583 + 6.50000i −0.308592 + 0.178166i −0.646296 0.763087i \(-0.723683\pi\)
0.337704 + 0.941252i \(0.390350\pi\)
\(12\) 12.0000 0.288675
\(13\) 0 0
\(14\) 10.0000 0.190901
\(15\) −5.19615 + 3.00000i −0.0894427 + 0.0516398i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 13.5000 23.3827i 0.192602 0.333596i −0.753510 0.657437i \(-0.771641\pi\)
0.946112 + 0.323840i \(0.104974\pi\)
\(18\) 36.0000i 0.471405i
\(19\) −64.9519 37.5000i −0.784263 0.452794i 0.0536762 0.998558i \(-0.482906\pi\)
−0.837939 + 0.545764i \(0.816239\pi\)
\(20\) 6.92820 + 4.00000i 0.0774597 + 0.0447214i
\(21\) 15.0000i 0.155870i
\(22\) 13.0000 22.5167i 0.125982 0.218208i
\(23\) −93.5000 161.947i −0.847656 1.46818i −0.883294 0.468819i \(-0.844680\pi\)
0.0356377 0.999365i \(-0.488654\pi\)
\(24\) −20.7846 + 12.0000i −0.176777 + 0.102062i
\(25\) 121.000 0.968000
\(26\) 0 0
\(27\) 135.000 0.962250
\(28\) −17.3205 + 10.0000i −0.116902 + 0.0674937i
\(29\) 6.50000 + 11.2583i 0.0416214 + 0.0720903i 0.886086 0.463522i \(-0.153414\pi\)
−0.844464 + 0.535612i \(0.820081\pi\)
\(30\) 6.00000 10.3923i 0.0365148 0.0632456i
\(31\) 104.000i 0.602547i −0.953538 0.301273i \(-0.902588\pi\)
0.953538 0.301273i \(-0.0974117\pi\)
\(32\) 27.7128 + 16.0000i 0.153093 + 0.0883883i
\(33\) −33.7750 19.5000i −0.178166 0.102864i
\(34\) 54.0000i 0.272380i
\(35\) 5.00000 8.66025i 0.0241473 0.0418243i
\(36\) −36.0000 62.3538i −0.166667 0.288675i
\(37\) −366.329 + 211.500i −1.62768 + 0.939740i −0.642894 + 0.765955i \(0.722266\pi\)
−0.984784 + 0.173785i \(0.944400\pi\)
\(38\) 150.000 0.640348
\(39\) 0 0
\(40\) −16.0000 −0.0632456
\(41\) 168.875 97.5000i 0.643264 0.371389i −0.142607 0.989779i \(-0.545548\pi\)
0.785871 + 0.618391i \(0.212215\pi\)
\(42\) 15.0000 + 25.9808i 0.0551083 + 0.0954504i
\(43\) 99.5000 172.339i 0.352875 0.611197i −0.633877 0.773434i \(-0.718538\pi\)
0.986752 + 0.162237i \(0.0518709\pi\)
\(44\) 52.0000i 0.178166i
\(45\) 31.1769 + 18.0000i 0.103280 + 0.0596285i
\(46\) 323.894 + 187.000i 1.03816 + 0.599384i
\(47\) 388.000i 1.20416i −0.798435 0.602081i \(-0.794338\pi\)
0.798435 0.602081i \(-0.205662\pi\)
\(48\) 24.0000 41.5692i 0.0721688 0.125000i
\(49\) −159.000 275.396i −0.463557 0.802904i
\(50\) −209.578 + 121.000i −0.592777 + 0.342240i
\(51\) 81.0000 0.222397
\(52\) 0 0
\(53\) 618.000 1.60168 0.800838 0.598881i \(-0.204388\pi\)
0.800838 + 0.598881i \(0.204388\pi\)
\(54\) −233.827 + 135.000i −0.589256 + 0.340207i
\(55\) −13.0000 22.5167i −0.0318713 0.0552027i
\(56\) 20.0000 34.6410i 0.0477252 0.0826625i
\(57\) 225.000i 0.522842i
\(58\) −22.5167 13.0000i −0.0509756 0.0294308i
\(59\) 425.218 + 245.500i 0.938284 + 0.541718i 0.889422 0.457087i \(-0.151107\pi\)
0.0488617 + 0.998806i \(0.484441\pi\)
\(60\) 24.0000i 0.0516398i
\(61\) −87.5000 + 151.554i −0.183659 + 0.318108i −0.943124 0.332441i \(-0.892128\pi\)
0.759465 + 0.650549i \(0.225461\pi\)
\(62\) 104.000 + 180.133i 0.213032 + 0.368983i
\(63\) −77.9423 + 45.0000i −0.155870 + 0.0899915i
\(64\) −64.0000 −0.125000
\(65\) 0 0
\(66\) 78.0000 0.145472
\(67\) 707.543 408.500i 1.29015 0.744869i 0.311470 0.950256i \(-0.399179\pi\)
0.978681 + 0.205387i \(0.0658453\pi\)
\(68\) −54.0000 93.5307i −0.0963009 0.166798i
\(69\) 280.500 485.840i 0.489395 0.847656i
\(70\) 20.0000i 0.0341494i
\(71\) −68.4160 39.5000i −0.114359 0.0660252i 0.441729 0.897148i \(-0.354365\pi\)
−0.556088 + 0.831123i \(0.687698\pi\)
\(72\) 124.708 + 72.0000i 0.204124 + 0.117851i
\(73\) 230.000i 0.368760i −0.982855 0.184380i \(-0.940972\pi\)
0.982855 0.184380i \(-0.0590277\pi\)
\(74\) 423.000 732.657i 0.664497 1.15094i
\(75\) 181.500 + 314.367i 0.279438 + 0.484000i
\(76\) −259.808 + 150.000i −0.392131 + 0.226397i
\(77\) 65.0000 0.0962005
\(78\) 0 0
\(79\) 764.000 1.08806 0.544030 0.839066i \(-0.316898\pi\)
0.544030 + 0.839066i \(0.316898\pi\)
\(80\) 27.7128 16.0000i 0.0387298 0.0223607i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −195.000 + 337.750i −0.262612 + 0.454857i
\(83\) 732.000i 0.968041i −0.875057 0.484021i \(-0.839176\pi\)
0.875057 0.484021i \(-0.160824\pi\)
\(84\) −51.9615 30.0000i −0.0674937 0.0389675i
\(85\) 46.7654 + 27.0000i 0.0596755 + 0.0344537i
\(86\) 398.000i 0.499040i
\(87\) −19.5000 + 33.7750i −0.0240301 + 0.0416214i
\(88\) −52.0000 90.0666i −0.0629911 0.109104i
\(89\) 901.532 520.500i 1.07373 0.619920i 0.144534 0.989500i \(-0.453832\pi\)
0.929199 + 0.369580i \(0.120498\pi\)
\(90\) −72.0000 −0.0843274
\(91\) 0 0
\(92\) −748.000 −0.847656
\(93\) 270.200 156.000i 0.301273 0.173940i
\(94\) 388.000 + 672.036i 0.425736 + 0.737396i
\(95\) 75.0000 129.904i 0.0809983 0.140293i
\(96\) 96.0000i 0.102062i
\(97\) 84.0045 + 48.5000i 0.0879316 + 0.0507673i 0.543321 0.839525i \(-0.317167\pi\)
−0.455389 + 0.890292i \(0.650500\pi\)
\(98\) 550.792 + 318.000i 0.567739 + 0.327784i
\(99\) 234.000i 0.237554i
\(100\) 242.000 419.156i 0.242000 0.419156i
\(101\) −404.500 700.615i −0.398507 0.690235i 0.595035 0.803700i \(-0.297138\pi\)
−0.993542 + 0.113465i \(0.963805\pi\)
\(102\) −140.296 + 81.0000i −0.136190 + 0.0786294i
\(103\) −1288.00 −1.23214 −0.616070 0.787691i \(-0.711276\pi\)
−0.616070 + 0.787691i \(0.711276\pi\)
\(104\) 0 0
\(105\) 30.0000 0.0278829
\(106\) −1070.41 + 618.000i −0.980822 + 0.566278i
\(107\) −638.500 1105.91i −0.576880 0.999185i −0.995835 0.0911779i \(-0.970937\pi\)
0.418955 0.908007i \(-0.362397\pi\)
\(108\) 270.000 467.654i 0.240563 0.416667i
\(109\) 826.000i 0.725839i 0.931820 + 0.362920i \(0.118220\pi\)
−0.931820 + 0.362920i \(0.881780\pi\)
\(110\) 45.0333 + 26.0000i 0.0390342 + 0.0225364i
\(111\) −1098.99 634.500i −0.939740 0.542559i
\(112\) 80.0000i 0.0674937i
\(113\) −473.500 + 820.126i −0.394187 + 0.682752i −0.992997 0.118139i \(-0.962307\pi\)
0.598810 + 0.800891i \(0.295640\pi\)
\(114\) 225.000 + 389.711i 0.184852 + 0.320174i
\(115\) 323.894 187.000i 0.262637 0.151633i
\(116\) 52.0000 0.0416214
\(117\) 0 0
\(118\) −982.000 −0.766105
\(119\) −116.913 + 67.5000i −0.0900625 + 0.0519976i
\(120\) −24.0000 41.5692i −0.0182574 0.0316228i
\(121\) −581.000 + 1006.32i −0.436514 + 0.756064i
\(122\) 350.000i 0.259734i
\(123\) 506.625 + 292.500i 0.371389 + 0.214421i
\(124\) −360.267 208.000i −0.260910 0.150637i
\(125\) 492.000i 0.352047i
\(126\) 90.0000 155.885i 0.0636336 0.110217i
\(127\) 588.500 + 1019.31i 0.411188 + 0.712199i 0.995020 0.0996756i \(-0.0317805\pi\)
−0.583832 + 0.811875i \(0.698447\pi\)
\(128\) 110.851 64.0000i 0.0765466 0.0441942i
\(129\) 597.000 0.407464
\(130\) 0 0
\(131\) −1420.00 −0.947069 −0.473534 0.880775i \(-0.657022\pi\)
−0.473534 + 0.880775i \(0.657022\pi\)
\(132\) −135.100 + 78.0000i −0.0890829 + 0.0514320i
\(133\) 187.500 + 324.760i 0.122243 + 0.211731i
\(134\) −817.000 + 1415.09i −0.526702 + 0.912274i
\(135\) 270.000i 0.172133i
\(136\) 187.061 + 108.000i 0.117944 + 0.0680950i
\(137\) −2086.26 1204.50i −1.30103 0.751149i −0.320447 0.947266i \(-0.603833\pi\)
−0.980580 + 0.196118i \(0.937167\pi\)
\(138\) 1122.00i 0.692109i
\(139\) −1413.50 + 2448.25i −0.862529 + 1.49394i 0.00695133 + 0.999976i \(0.497787\pi\)
−0.869480 + 0.493968i \(0.835546\pi\)
\(140\) −20.0000 34.6410i −0.0120736 0.0209121i
\(141\) 1008.05 582.000i 0.602081 0.347612i
\(142\) 158.000 0.0933737
\(143\) 0 0
\(144\) −288.000 −0.166667
\(145\) −22.5167 + 13.0000i −0.0128959 + 0.00744546i
\(146\) 230.000 + 398.372i 0.130376 + 0.225818i
\(147\) 477.000 826.188i 0.267635 0.463557i
\(148\) 1692.00i 0.939740i
\(149\) −740.452 427.500i −0.407115 0.235048i 0.282434 0.959287i \(-0.408858\pi\)
−0.689549 + 0.724239i \(0.742191\pi\)
\(150\) −628.734 363.000i −0.342240 0.197592i
\(151\) 2064.00i 1.11236i −0.831063 0.556179i \(-0.812267\pi\)
0.831063 0.556179i \(-0.187733\pi\)
\(152\) 300.000 519.615i 0.160087 0.277279i
\(153\) −243.000 420.888i −0.128401 0.222397i
\(154\) −112.583 + 65.0000i −0.0589105 + 0.0340120i
\(155\) 208.000 0.107787
\(156\) 0 0
\(157\) −1894.00 −0.962788 −0.481394 0.876504i \(-0.659869\pi\)
−0.481394 + 0.876504i \(0.659869\pi\)
\(158\) −1323.29 + 764.000i −0.666298 + 0.384687i
\(159\) 927.000 + 1605.61i 0.462364 + 0.800838i
\(160\) −32.0000 + 55.4256i −0.0158114 + 0.0273861i
\(161\) 935.000i 0.457691i
\(162\) 140.296 + 81.0000i 0.0680414 + 0.0392837i
\(163\) −853.035 492.500i −0.409907 0.236660i 0.280843 0.959754i \(-0.409386\pi\)
−0.690750 + 0.723094i \(0.742719\pi\)
\(164\) 780.000i 0.371389i
\(165\) 39.0000 67.5500i 0.0184009 0.0318713i
\(166\) 732.000 + 1267.86i 0.342254 + 0.592802i
\(167\) 2039.49 1177.50i 0.945033 0.545615i 0.0534983 0.998568i \(-0.482963\pi\)
0.891534 + 0.452953i \(0.149629\pi\)
\(168\) 120.000 0.0551083
\(169\) 0 0
\(170\) −108.000 −0.0487248
\(171\) −1169.13 + 675.000i −0.522842 + 0.301863i
\(172\) −398.000 689.356i −0.176437 0.305598i
\(173\) −1944.50 + 3367.97i −0.854553 + 1.48013i 0.0225069 + 0.999747i \(0.492835\pi\)
−0.877059 + 0.480382i \(0.840498\pi\)
\(174\) 78.0000i 0.0339837i
\(175\) −523.945 302.500i −0.226323 0.130668i
\(176\) 180.133 + 104.000i 0.0771481 + 0.0445414i
\(177\) 1473.00i 0.625522i
\(178\) −1041.00 + 1803.06i −0.438350 + 0.759244i
\(179\) 1114.50 + 1930.37i 0.465372 + 0.806048i 0.999218 0.0395333i \(-0.0125871\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(180\) 124.708 72.0000i 0.0516398 0.0298142i
\(181\) 1038.00 0.426265 0.213132 0.977023i \(-0.431633\pi\)
0.213132 + 0.977023i \(0.431633\pi\)
\(182\) 0 0
\(183\) −525.000 −0.212072
\(184\) 1295.57 748.000i 0.519081 0.299692i
\(185\) −423.000 732.657i −0.168106 0.291168i
\(186\) −312.000 + 540.400i −0.122994 + 0.213032i
\(187\) 351.000i 0.137260i
\(188\) −1344.07 776.000i −0.521417 0.301041i
\(189\) −584.567 337.500i −0.224979 0.129892i
\(190\) 300.000i 0.114549i
\(191\) 1070.50 1854.16i 0.405543 0.702421i −0.588842 0.808248i \(-0.700416\pi\)
0.994384 + 0.105828i \(0.0337492\pi\)
\(192\) −96.0000 166.277i −0.0360844 0.0625000i
\(193\) −2275.05 + 1313.50i −0.848506 + 0.489885i −0.860146 0.510047i \(-0.829628\pi\)
0.0116407 + 0.999932i \(0.496295\pi\)
\(194\) −194.000 −0.0717958
\(195\) 0 0
\(196\) −1272.00 −0.463557
\(197\) 1041.83 601.500i 0.376788 0.217539i −0.299632 0.954055i \(-0.596864\pi\)
0.676420 + 0.736516i \(0.263531\pi\)
\(198\) −234.000 405.300i −0.0839882 0.145472i
\(199\) 371.500 643.457i 0.132336 0.229213i −0.792240 0.610209i \(-0.791085\pi\)
0.924577 + 0.380996i \(0.124419\pi\)
\(200\) 968.000i 0.342240i
\(201\) 2122.63 + 1225.50i 0.744869 + 0.430050i
\(202\) 1401.23 + 809.000i 0.488070 + 0.281787i
\(203\) 65.0000i 0.0224734i
\(204\) 162.000 280.592i 0.0555994 0.0963009i
\(205\) 195.000 + 337.750i 0.0664361 + 0.115071i
\(206\) 2230.88 1288.00i 0.754529 0.435627i
\(207\) −3366.00 −1.13021
\(208\) 0 0
\(209\) 975.000 0.322690
\(210\) −51.9615 + 30.0000i −0.0170747 + 0.00985808i
\(211\) 177.500 + 307.439i 0.0579128 + 0.100308i 0.893528 0.449007i \(-0.148222\pi\)
−0.835615 + 0.549315i \(0.814889\pi\)
\(212\) 1236.00 2140.81i 0.400419 0.693546i
\(213\) 237.000i 0.0762393i
\(214\) 2211.83 + 1277.00i 0.706530 + 0.407916i
\(215\) 344.678 + 199.000i 0.109334 + 0.0631241i
\(216\) 1080.00i 0.340207i
\(217\) −260.000 + 450.333i −0.0813362 + 0.140878i
\(218\) −826.000 1430.67i −0.256623 0.444484i
\(219\) 597.558 345.000i 0.184380 0.106452i
\(220\) −104.000 −0.0318713
\(221\) 0 0
\(222\) 2538.00 0.767295
\(223\) −1977.14 + 1141.50i −0.593717 + 0.342782i −0.766566 0.642166i \(-0.778036\pi\)
0.172849 + 0.984948i \(0.444703\pi\)
\(224\) −80.0000 138.564i −0.0238626 0.0413313i
\(225\) 1089.00 1886.20i 0.322667 0.558875i
\(226\) 1894.00i 0.557465i
\(227\) −2122.63 1225.50i −0.620633 0.358323i 0.156482 0.987681i \(-0.449985\pi\)
−0.777116 + 0.629358i \(0.783318\pi\)
\(228\) −779.423 450.000i −0.226397 0.130710i
\(229\) 1878.00i 0.541929i 0.962589 + 0.270964i \(0.0873426\pi\)
−0.962589 + 0.270964i \(0.912657\pi\)
\(230\) −374.000 + 647.787i −0.107221 + 0.185712i
\(231\) 97.5000 + 168.875i 0.0277707 + 0.0481002i
\(232\) −90.0666 + 52.0000i −0.0254878 + 0.0147154i
\(233\) −1630.00 −0.458304 −0.229152 0.973391i \(-0.573595\pi\)
−0.229152 + 0.973391i \(0.573595\pi\)
\(234\) 0 0
\(235\) 776.000 0.215407
\(236\) 1700.87 982.000i 0.469142 0.270859i
\(237\) 1146.00 + 1984.93i 0.314096 + 0.544030i
\(238\) 135.000 233.827i 0.0367679 0.0636838i
\(239\) 5544.00i 1.50047i −0.661173 0.750233i \(-0.729941\pi\)
0.661173 0.750233i \(-0.270059\pi\)
\(240\) 83.1384 + 48.0000i 0.0223607 + 0.0129099i
\(241\) 4783.06 + 2761.50i 1.27844 + 0.738107i 0.976561 0.215239i \(-0.0690532\pi\)
0.301878 + 0.953347i \(0.402386\pi\)
\(242\) 2324.00i 0.617324i
\(243\) 1944.00 3367.11i 0.513200 0.888889i
\(244\) 350.000 + 606.218i 0.0918297 + 0.159054i
\(245\) 550.792 318.000i 0.143628 0.0829236i
\(246\) −1170.00 −0.303238
\(247\) 0 0
\(248\) 832.000 0.213032
\(249\) 1901.79 1098.00i 0.484021 0.279449i
\(250\) −492.000 852.169i −0.124467 0.215584i
\(251\) 1087.50 1883.61i 0.273476 0.473674i −0.696274 0.717776i \(-0.745160\pi\)
0.969749 + 0.244103i \(0.0784934\pi\)
\(252\) 360.000i 0.0899915i
\(253\) 2105.31 + 1215.50i 0.523160 + 0.302047i
\(254\) −2038.62 1177.00i −0.503601 0.290754i
\(255\) 162.000i 0.0397837i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2842.50 4923.35i −0.689923 1.19498i −0.971862 0.235550i \(-0.924311\pi\)
0.281939 0.959432i \(-0.409022\pi\)
\(258\) −1034.03 + 597.000i −0.249520 + 0.144060i
\(259\) 2115.00 0.507412
\(260\) 0 0
\(261\) 234.000 0.0554952
\(262\) 2459.51 1420.00i 0.579959 0.334839i
\(263\) −3058.50 5297.48i −0.717092 1.24204i −0.962147 0.272531i \(-0.912139\pi\)
0.245055 0.969509i \(-0.421194\pi\)
\(264\) 156.000 270.200i 0.0363679 0.0629911i
\(265\) 1236.00i 0.286517i
\(266\) −649.519 375.000i −0.149716 0.0864388i
\(267\) 2704.60 + 1561.50i 0.619920 + 0.357911i
\(268\) 3268.00i 0.744869i
\(269\) 2554.50 4424.52i 0.578999 1.00285i −0.416596 0.909092i \(-0.636777\pi\)
0.995595 0.0937632i \(-0.0298897\pi\)
\(270\) −270.000 467.654i −0.0608581 0.105409i
\(271\) −6537.63 + 3774.50i −1.46543 + 0.846068i −0.999254 0.0386217i \(-0.987703\pi\)
−0.466180 + 0.884690i \(0.654370\pi\)
\(272\) −432.000 −0.0963009
\(273\) 0 0
\(274\) 4818.00 1.06228
\(275\) −1362.26 + 786.500i −0.298717 + 0.172464i
\(276\) −1122.00 1943.36i −0.244697 0.423828i
\(277\) −490.500 + 849.571i −0.106395 + 0.184281i −0.914307 0.405022i \(-0.867264\pi\)
0.807913 + 0.589302i \(0.200597\pi\)
\(278\) 5654.00i 1.21980i
\(279\) −1621.20 936.000i −0.347881 0.200849i
\(280\) 69.2820 + 40.0000i 0.0147871 + 0.00853735i
\(281\) 2762.00i 0.586360i 0.956057 + 0.293180i \(0.0947135\pi\)
−0.956057 + 0.293180i \(0.905287\pi\)
\(282\) −1164.00 + 2016.11i −0.245799 + 0.425736i
\(283\) 1962.50 + 3399.15i 0.412221 + 0.713988i 0.995132 0.0985482i \(-0.0314199\pi\)
−0.582911 + 0.812536i \(0.698087\pi\)
\(284\) −273.664 + 158.000i −0.0571795 + 0.0330126i
\(285\) 450.000 0.0935288
\(286\) 0 0
\(287\) −975.000 −0.200531
\(288\) 498.831 288.000i 0.102062 0.0589256i
\(289\) 2092.00 + 3623.45i 0.425809 + 0.737523i
\(290\) 26.0000 45.0333i 0.00526473 0.00911879i
\(291\) 291.000i 0.0586210i
\(292\) −796.743 460.000i −0.159678 0.0921899i
\(293\) 6677.92 + 3855.50i 1.33150 + 0.768740i 0.985529 0.169507i \(-0.0542175\pi\)
0.345967 + 0.938247i \(0.387551\pi\)
\(294\) 1908.00i 0.378493i
\(295\) −491.000 + 850.437i −0.0969055 + 0.167845i
\(296\) −1692.00 2930.63i −0.332248 0.575471i
\(297\) −1519.87 + 877.500i −0.296943 + 0.171440i
\(298\) 1710.00 0.332408
\(299\) 0 0
\(300\) 1452.00 0.279438
\(301\) −861.695 + 497.500i −0.165008 + 0.0952672i
\(302\) 2064.00 + 3574.95i 0.393278 + 0.681177i
\(303\) 1213.50 2101.84i 0.230078 0.398507i
\(304\) 1200.00i 0.226397i
\(305\) −303.109 175.000i −0.0569048 0.0328540i
\(306\) 841.777 + 486.000i 0.157259 + 0.0907934i
\(307\) 10388.0i 1.93119i −0.260056 0.965594i \(-0.583741\pi\)
0.260056 0.965594i \(-0.416259\pi\)
\(308\) 130.000 225.167i 0.0240501 0.0416560i
\(309\) −1932.00 3346.32i −0.355688 0.616070i
\(310\) −360.267 + 208.000i −0.0660057 + 0.0381084i
\(311\) 7272.00 1.32591 0.662954 0.748660i \(-0.269303\pi\)
0.662954 + 0.748660i \(0.269303\pi\)
\(312\) 0 0
\(313\) 7910.00 1.42843 0.714217 0.699925i \(-0.246783\pi\)
0.714217 + 0.699925i \(0.246783\pi\)
\(314\) 3280.50 1894.00i 0.589585 0.340397i
\(315\) −90.0000 155.885i −0.0160982 0.0278829i
\(316\) 1528.00 2646.57i 0.272015 0.471144i
\(317\) 7398.00i 1.31077i 0.755296 + 0.655383i \(0.227493\pi\)
−0.755296 + 0.655383i \(0.772507\pi\)
\(318\) −3211.22 1854.00i −0.566278 0.326941i
\(319\) −146.358 84.5000i −0.0256881 0.0148310i
\(320\) 128.000i 0.0223607i
\(321\) 1915.50 3317.74i 0.333062 0.576880i
\(322\) −935.000 1619.47i −0.161818 0.280278i
\(323\) −1753.70 + 1012.50i −0.302101 + 0.174418i
\(324\) −324.000 −0.0555556
\(325\) 0 0
\(326\) 1970.00 0.334688
\(327\) −2146.01 + 1239.00i −0.362920 + 0.209532i
\(328\) 780.000 + 1351.00i 0.131306 + 0.227428i
\(329\) −970.000 + 1680.09i −0.162547 + 0.281539i
\(330\) 156.000i 0.0260228i
\(331\) 2058.54 + 1188.50i 0.341836 + 0.197359i 0.661084 0.750312i \(-0.270097\pi\)
−0.319248 + 0.947671i \(0.603430\pi\)
\(332\) −2535.72 1464.00i −0.419174 0.242010i
\(333\) 7614.00i 1.25299i
\(334\) −2355.00 + 4078.98i −0.385808 + 0.668239i
\(335\) 817.000 + 1415.09i 0.133246 + 0.230789i
\(336\) −207.846 + 120.000i −0.0337468 + 0.0194837i
\(337\) 7618.00 1.23139 0.615696 0.787984i \(-0.288875\pi\)
0.615696 + 0.787984i \(0.288875\pi\)
\(338\) 0 0
\(339\) −2841.00 −0.455168
\(340\) 187.061 108.000i 0.0298377 0.0172268i
\(341\) 676.000 + 1170.87i 0.107353 + 0.185941i
\(342\) 1350.00 2338.27i 0.213449 0.369705i
\(343\) 3305.00i 0.520272i
\(344\) 1378.71 + 796.000i 0.216091 + 0.124760i
\(345\) 971.681 + 561.000i 0.151633 + 0.0875456i
\(346\) 7778.00i 1.20852i
\(347\) −187.500 + 324.760i −0.0290073 + 0.0502421i −0.880165 0.474669i \(-0.842568\pi\)
0.851157 + 0.524911i \(0.175901\pi\)
\(348\) 78.0000 + 135.100i 0.0120151 + 0.0208107i
\(349\) −8423.83 + 4863.50i −1.29203 + 0.745952i −0.979013 0.203797i \(-0.934672\pi\)
−0.313013 + 0.949749i \(0.601338\pi\)
\(350\) 1210.00 0.184792
\(351\) 0 0
\(352\) −416.000 −0.0629911
\(353\) 1959.82 1131.50i 0.295497 0.170605i −0.344921 0.938632i \(-0.612094\pi\)
0.640418 + 0.768026i \(0.278761\pi\)
\(354\) −1473.00 2551.31i −0.221156 0.383053i
\(355\) 79.0000 136.832i 0.0118109 0.0204572i
\(356\) 4164.00i 0.619920i
\(357\) −350.740 202.500i −0.0519976 0.0300208i
\(358\) −3860.74 2229.00i −0.569962 0.329068i
\(359\) 4488.00i 0.659798i 0.944016 + 0.329899i \(0.107015\pi\)
−0.944016 + 0.329899i \(0.892985\pi\)
\(360\) −144.000 + 249.415i −0.0210819 + 0.0365148i
\(361\) −617.000 1068.68i −0.0899548 0.155806i
\(362\) −1797.87 + 1038.00i −0.261033 + 0.150707i
\(363\) −3486.00 −0.504043
\(364\) 0 0
\(365\) 460.000 0.0659658
\(366\) 909.327 525.000i 0.129867 0.0749787i
\(367\) 813.500 + 1409.02i 0.115707 + 0.200410i 0.918062 0.396437i \(-0.129753\pi\)
−0.802355 + 0.596847i \(0.796420\pi\)
\(368\) −1496.00 + 2591.15i −0.211914 + 0.367046i
\(369\) 3510.00i 0.495185i
\(370\) 1465.31 + 846.000i 0.205887 + 0.118869i
\(371\) −2676.02 1545.00i −0.374480 0.216206i
\(372\) 1248.00i 0.173940i
\(373\) −1493.50 + 2586.82i −0.207320 + 0.359089i −0.950870 0.309592i \(-0.899808\pi\)
0.743549 + 0.668681i \(0.233141\pi\)
\(374\) −351.000 607.950i −0.0485288 0.0840544i
\(375\) −1278.25 + 738.000i −0.176023 + 0.101627i
\(376\) 3104.00 0.425736
\(377\) 0 0
\(378\) 1350.00 0.183694
\(379\) −7679.05 + 4433.50i −1.04076 + 0.600880i −0.920047 0.391808i \(-0.871850\pi\)
−0.120708 + 0.992688i \(0.538516\pi\)
\(380\) −300.000 519.615i −0.0404991 0.0701466i
\(381\) −1765.50 + 3057.94i −0.237400 + 0.411188i
\(382\) 4282.00i 0.573524i
\(383\) −9875.29 5701.50i −1.31750 0.760661i −0.334177 0.942510i \(-0.608458\pi\)
−0.983326 + 0.181850i \(0.941792\pi\)
\(384\) 332.554 + 192.000i 0.0441942 + 0.0255155i
\(385\) 130.000i 0.0172089i
\(386\) 2627.00 4550.10i 0.346401 0.599984i
\(387\) −1791.00 3102.10i −0.235250 0.407464i
\(388\) 336.018 194.000i 0.0439658 0.0253837i
\(389\) −2622.00 −0.341750 −0.170875 0.985293i \(-0.554659\pi\)
−0.170875 + 0.985293i \(0.554659\pi\)
\(390\) 0 0
\(391\) −5049.00 −0.653041
\(392\) 2203.17 1272.00i 0.283869 0.163892i
\(393\) −2130.00 3689.27i −0.273395 0.473534i
\(394\) −1203.00 + 2083.66i −0.153823 + 0.266429i
\(395\) 1528.00i 0.194638i
\(396\) 810.600 + 468.000i 0.102864 + 0.0593886i
\(397\) 570.711 + 329.500i 0.0721490 + 0.0416552i 0.535641 0.844446i \(-0.320070\pi\)
−0.463492 + 0.886101i \(0.653404\pi\)
\(398\) 1486.00i 0.187152i
\(399\) −562.500 + 974.279i −0.0705770 + 0.122243i
\(400\) −968.000 1676.63i −0.121000 0.209578i
\(401\) 12717.6 7342.50i 1.58376 0.914381i 0.589451 0.807804i \(-0.299344\pi\)
0.994304 0.106577i \(-0.0339891\pi\)
\(402\) −4902.00 −0.608183
\(403\) 0 0
\(404\) −3236.00 −0.398507
\(405\) 140.296 81.0000i 0.0172133 0.00993808i
\(406\) 65.0000 + 112.583i 0.00794556 + 0.0137621i
\(407\) 2749.50 4762.27i 0.334859 0.579993i
\(408\) 648.000i 0.0786294i
\(409\) 6780.11 + 3914.50i 0.819694 + 0.473251i 0.850311 0.526280i \(-0.176414\pi\)
−0.0306167 + 0.999531i \(0.509747\pi\)
\(410\) −675.500 390.000i −0.0813672 0.0469774i
\(411\) 7227.00i 0.867352i
\(412\) −2576.00 + 4461.76i −0.308035 + 0.533532i
\(413\) −1227.50 2126.09i −0.146250 0.253313i
\(414\) 5830.08 3366.00i 0.692109 0.399589i
\(415\) 1464.00 0.173169
\(416\) 0 0
\(417\) −8481.00 −0.995962
\(418\) −1688.75 + 975.000i −0.197606 + 0.114088i
\(419\) 1459.50 + 2527.93i 0.170170 + 0.294743i 0.938479 0.345336i \(-0.112235\pi\)
−0.768309 + 0.640079i \(0.778902\pi\)
\(420\) 60.0000 103.923i 0.00697071 0.0120736i
\(421\) 3110.00i 0.360029i −0.983664 0.180014i \(-0.942386\pi\)
0.983664 0.180014i \(-0.0576144\pi\)
\(422\) −614.878 355.000i −0.0709284 0.0409505i
\(423\) −6048.32 3492.00i −0.695223 0.401387i
\(424\) 4944.00i 0.566278i
\(425\) 1633.50 2829.30i 0.186439 0.322921i
\(426\) 237.000 + 410.496i 0.0269547 + 0.0466869i
\(427\) 757.772 437.500i 0.0858810 0.0495834i
\(428\) −5108.00 −0.576880
\(429\) 0 0
\(430\) −796.000 −0.0892710
\(431\) −7911.14 + 4567.50i −0.884145 + 0.510461i −0.872023 0.489465i \(-0.837192\pi\)
−0.0121219 + 0.999927i \(0.503859\pi\)
\(432\) −1080.00 1870.61i −0.120281 0.208333i
\(433\) −5834.50 + 10105.7i −0.647548 + 1.12159i 0.336159 + 0.941805i \(0.390872\pi\)
−0.983707 + 0.179780i \(0.942461\pi\)
\(434\) 1040.00i 0.115027i
\(435\) −67.5500 39.0000i −0.00744546 0.00429864i
\(436\) 2861.35 + 1652.00i 0.314298 + 0.181460i
\(437\) 14025.0i 1.53526i
\(438\) −690.000 + 1195.12i −0.0752728 + 0.130376i
\(439\) 6764.50 + 11716.5i 0.735426 + 1.27380i 0.954536 + 0.298095i \(0.0963512\pi\)
−0.219110 + 0.975700i \(0.570315\pi\)
\(440\) 180.133 104.000i 0.0195171 0.0112682i
\(441\) −5724.00 −0.618076
\(442\) 0 0
\(443\) −1932.00 −0.207206 −0.103603 0.994619i \(-0.533037\pi\)
−0.103603 + 0.994619i \(0.533037\pi\)
\(444\) −4395.94 + 2538.00i −0.469870 + 0.271280i
\(445\) 1041.00 + 1803.06i 0.110895 + 0.192075i
\(446\) 2283.00 3954.27i 0.242384 0.419821i
\(447\) 2565.00i 0.271410i
\(448\) 277.128 + 160.000i 0.0292256 + 0.0168734i
\(449\) −4639.30 2678.50i −0.487621 0.281528i 0.235966 0.971761i \(-0.424175\pi\)
−0.723587 + 0.690233i \(0.757508\pi\)
\(450\) 4356.00i 0.456320i
\(451\) −1267.50 + 2195.37i −0.132338 + 0.229215i
\(452\) 1894.00 + 3280.50i 0.197094 + 0.341376i
\(453\) 5362.43 3096.00i 0.556179 0.321110i
\(454\) 4902.00 0.506745
\(455\) 0 0
\(456\) 1800.00 0.184852
\(457\) 16800.0 9699.50i 1.71963 0.992830i 0.800050 0.599933i \(-0.204806\pi\)
0.919582 0.392897i \(-0.128527\pi\)
\(458\) −1878.00 3252.79i −0.191601 0.331862i
\(459\) 1822.50 3156.66i 0.185331 0.321003i
\(460\) 1496.00i 0.151633i
\(461\) 13465.8 + 7774.50i 1.36045 + 0.785455i 0.989683 0.143273i \(-0.0457625\pi\)
0.370764 + 0.928727i \(0.379096\pi\)
\(462\) −337.750 195.000i −0.0340120 0.0196368i
\(463\) 4072.00i 0.408730i −0.978895 0.204365i \(-0.934487\pi\)
0.978895 0.204365i \(-0.0655129\pi\)
\(464\) 104.000 180.133i 0.0104053 0.0180226i
\(465\) 312.000 + 540.400i 0.0311154 + 0.0538934i
\(466\) 2823.24 1630.00i 0.280653 0.162035i
\(467\) −15224.0 −1.50853 −0.754264 0.656571i \(-0.772006\pi\)
−0.754264 + 0.656571i \(0.772006\pi\)
\(468\) 0 0
\(469\) −4085.00 −0.402191
\(470\) −1344.07 + 776.000i −0.131909 + 0.0761579i
\(471\) −2841.00 4920.76i −0.277933 0.481394i
\(472\) −1964.00 + 3401.75i −0.191526 + 0.331733i
\(473\) 2587.00i 0.251481i
\(474\) −3969.86 2292.00i −0.384687 0.222099i
\(475\) −7859.18 4537.50i −0.759166 0.438305i
\(476\) 540.000i 0.0519976i
\(477\) 5562.00 9633.67i 0.533892 0.924728i
\(478\) 5544.00 + 9602.49i 0.530495 + 0.918844i
\(479\) 8950.37 5167.50i 0.853764 0.492921i −0.00815506 0.999967i \(-0.502596\pi\)
0.861919 + 0.507046i \(0.169263\pi\)
\(480\) −192.000 −0.0182574
\(481\) 0 0
\(482\) −11046.0 −1.04384
\(483\) −2429.20 + 1402.50i −0.228846 + 0.132124i
\(484\) 2324.00 + 4025.29i 0.218257 + 0.378032i
\(485\) −97.0000 + 168.009i −0.00908153 + 0.0157297i
\(486\) 7776.00i 0.725775i
\(487\) −5590.19 3227.50i −0.520156 0.300312i 0.216843 0.976207i \(-0.430424\pi\)
−0.736998 + 0.675894i \(0.763757\pi\)
\(488\) −1212.44 700.000i −0.112468 0.0649334i
\(489\) 2955.00i 0.273271i
\(490\) −636.000 + 1101.58i −0.0586358 + 0.101560i
\(491\) 3888.50 + 6735.08i 0.357404 + 0.619043i 0.987526 0.157454i \(-0.0503285\pi\)
−0.630122 + 0.776496i \(0.716995\pi\)
\(492\) 2026.50 1170.00i 0.185694 0.107211i
\(493\) 351.000 0.0320654
\(494\) 0 0
\(495\) −468.000 −0.0424950
\(496\) −1441.07 + 832.000i −0.130455 + 0.0753184i
\(497\) 197.500 + 342.080i 0.0178251 + 0.0308740i
\(498\) −2196.00 + 3803.58i −0.197601 + 0.342254i
\(499\) 3044.00i 0.273082i −0.990634 0.136541i \(-0.956401\pi\)
0.990634 0.136541i \(-0.0435986\pi\)
\(500\) 1704.34 + 984.000i 0.152441 + 0.0880116i
\(501\) 6118.47 + 3532.50i 0.545615 + 0.315011i
\(502\) 4350.00i 0.386753i
\(503\) −5673.50 + 9826.79i −0.502920 + 0.871083i 0.497074 + 0.867708i \(0.334408\pi\)
−0.999994 + 0.00337525i \(0.998926\pi\)
\(504\) −360.000 623.538i −0.0318168 0.0551083i
\(505\) 1401.23 809.000i 0.123473 0.0712872i
\(506\) −4862.00 −0.427159
\(507\) 0 0
\(508\) 4708.00 0.411188
\(509\) 629.600 363.500i 0.0548262 0.0316539i −0.472336 0.881418i \(-0.656589\pi\)
0.527163 + 0.849764i \(0.323256\pi\)
\(510\) −162.000 280.592i −0.0140656 0.0243624i
\(511\) −575.000 + 995.929i −0.0497779 + 0.0862178i
\(512\) 512.000i 0.0441942i
\(513\) −8768.51 5062.50i −0.754657 0.435701i
\(514\) 9846.71 + 5685.00i 0.844980 + 0.487849i
\(515\) 2576.00i 0.220412i
\(516\) 1194.00 2068.07i 0.101866 0.176437i
\(517\) 2522.00 + 4368.23i 0.214540 + 0.371595i
\(518\) −3663.29 + 2115.00i −0.310725 + 0.179397i
\(519\) −11667.0 −0.986752
\(520\) 0 0
\(521\) 9582.00 0.805749 0.402874 0.915255i \(-0.368011\pi\)
0.402874 + 0.915255i \(0.368011\pi\)
\(522\) −405.300 + 234.000i −0.0339837 + 0.0196205i
\(523\) 5191.50 + 8991.94i 0.434051 + 0.751798i 0.997218 0.0745454i \(-0.0237506\pi\)
−0.563167 + 0.826343i \(0.690417\pi\)
\(524\) −2840.00 + 4919.02i −0.236767 + 0.410093i
\(525\) 1815.00i 0.150882i
\(526\) 10595.0 + 6117.00i 0.878255 + 0.507061i
\(527\) −2431.80 1404.00i −0.201007 0.116052i
\(528\) 624.000i 0.0514320i
\(529\) −11401.0 + 19747.1i −0.937043 + 1.62301i
\(530\) −1236.00 2140.81i −0.101299 0.175455i
\(531\) 7653.93 4419.00i 0.625522 0.361146i
\(532\) 1500.00 0.122243
\(533\) 0 0
\(534\) −6246.00 −0.506163
\(535\) 2211.83 1277.00i 0.178740 0.103195i
\(536\) 3268.00 + 5660.34i 0.263351 + 0.456137i
\(537\) −3343.50 + 5791.11i −0.268683 + 0.465372i
\(538\) 10218.0i 0.818828i
\(539\) 3580.15 + 2067.00i 0.286100 + 0.165180i
\(540\) 935.307 + 540.000i 0.0745356 + 0.0430331i
\(541\) 12230.0i 0.971920i −0.873981 0.485960i \(-0.838470\pi\)
0.873981 0.485960i \(-0.161530\pi\)
\(542\) 7549.00 13075.3i 0.598261 1.03622i
\(543\) 1557.00 + 2696.80i 0.123052 + 0.213132i
\(544\) 748.246 432.000i 0.0589720 0.0340475i
\(545\) −1652.00 −0.129842
\(546\) 0 0
\(547\) −14636.0 −1.14404 −0.572020 0.820239i \(-0.693840\pi\)
−0.572020 + 0.820239i \(0.693840\pi\)
\(548\) −8345.02 + 4818.00i −0.650514 + 0.375574i
\(549\) 1575.00 + 2727.98i 0.122440 + 0.212072i
\(550\) 1573.00 2724.52i 0.121951 0.211225i
\(551\) 975.000i 0.0753837i
\(552\) 3886.72 + 2244.00i 0.299692 + 0.173027i
\(553\) −3308.22 1910.00i −0.254394 0.146874i
\(554\) 1962.00i 0.150465i
\(555\) 1269.00 2197.97i 0.0970559 0.168106i
\(556\) 5654.00 + 9793.02i 0.431264 + 0.746972i
\(557\) 662.509 382.500i 0.0503975 0.0290970i −0.474590 0.880207i \(-0.657403\pi\)
0.524987 + 0.851110i \(0.324070\pi\)
\(558\) 3744.00 0.284043
\(559\) 0 0
\(560\) −160.000 −0.0120736
\(561\) −911.925 + 526.500i −0.0686301 + 0.0396236i
\(562\) −2762.00 4783.92i −0.207309 0.359071i
\(563\) 2957.50 5122.54i 0.221392 0.383462i −0.733839 0.679324i \(-0.762273\pi\)
0.955231 + 0.295861i \(0.0956066\pi\)
\(564\) 4656.00i 0.347612i
\(565\) −1640.25 947.000i −0.122134 0.0705143i
\(566\) −6798.30 3925.00i −0.504865 0.291484i
\(567\) 405.000i 0.0299972i
\(568\) 316.000 547.328i 0.0233434 0.0404320i
\(569\) −608.500 1053.95i −0.0448324 0.0776520i 0.842738 0.538323i \(-0.180942\pi\)
−0.887571 + 0.460671i \(0.847609\pi\)
\(570\) −779.423 + 450.000i −0.0572744 + 0.0330674i
\(571\) 23436.0 1.71763 0.858814 0.512287i \(-0.171202\pi\)
0.858814 + 0.512287i \(0.171202\pi\)
\(572\) 0 0
\(573\) 6423.00 0.468280
\(574\) 1688.75 975.000i 0.122800 0.0708985i
\(575\) −11313.5 19595.6i −0.820531 1.42120i
\(576\) −576.000 + 997.661i −0.0416667 + 0.0721688i
\(577\) 7854.00i 0.566666i 0.959022 + 0.283333i \(0.0914402\pi\)
−0.959022 + 0.283333i \(0.908560\pi\)
\(578\) −7246.90 4184.00i −0.521507 0.301092i
\(579\) −6825.15 3940.50i −0.489885 0.282835i
\(580\) 104.000i 0.00744546i
\(581\) −1830.00 + 3169.65i −0.130673 + 0.226333i
\(582\) −291.000 504.027i −0.0207257 0.0358979i
\(583\) −6957.65 + 4017.00i −0.494265 + 0.285364i
\(584\) 1840.00 0.130376
\(585\) 0 0
\(586\) −15422.0 −1.08716
\(587\) 14751.0 8516.50i 1.03721 0.598831i 0.118165 0.992994i \(-0.462299\pi\)
0.919040 + 0.394163i \(0.128966\pi\)
\(588\) −1908.00 3304.75i −0.133817 0.231778i
\(589\) −3900.00 + 6755.00i −0.272830 + 0.472555i
\(590\) 1964.00i 0.137045i
\(591\) 3125.49 + 1804.50i 0.217539 + 0.125596i
\(592\) 5861.26 + 3384.00i 0.406919 + 0.234935i
\(593\) 14506.0i 1.00454i 0.864712 + 0.502268i \(0.167501\pi\)
−0.864712 + 0.502268i \(0.832499\pi\)
\(594\) 1755.00 3039.75i 0.121226 0.209970i
\(595\) −135.000 233.827i −0.00930161 0.0161109i
\(596\) −2961.81 + 1710.00i −0.203558 + 0.117524i
\(597\) 2229.00 0.152809
\(598\) 0 0
\(599\) 15388.0 1.04964 0.524822 0.851212i \(-0.324132\pi\)
0.524822 + 0.851212i \(0.324132\pi\)
\(600\) −2514.94 + 1452.00i −0.171120 + 0.0987961i
\(601\) 3038.50 + 5262.84i 0.206228 + 0.357197i 0.950523 0.310653i \(-0.100548\pi\)
−0.744295 + 0.667851i \(0.767214\pi\)
\(602\) 995.000 1723.39i 0.0673641 0.116678i
\(603\) 14706.0i 0.993159i
\(604\) −7149.91 4128.00i −0.481665 0.278089i
\(605\) −2012.64 1162.00i −0.135249 0.0780860i
\(606\) 4854.00i 0.325380i
\(607\) −5107.50 + 8846.45i −0.341527 + 0.591543i −0.984717 0.174165i \(-0.944277\pi\)
0.643189 + 0.765707i \(0.277611\pi\)
\(608\) −1200.00 2078.46i −0.0800435 0.138639i
\(609\) 168.875 97.5000i 0.0112367 0.00648752i
\(610\) 700.000 0.0464626
\(611\) 0 0
\(612\) −1944.00 −0.128401
\(613\) −2993.85 + 1728.50i −0.197260 + 0.113888i −0.595377 0.803447i \(-0.702997\pi\)
0.398117 + 0.917335i \(0.369664\pi\)
\(614\) 10388.0 + 17992.5i 0.682778 + 1.18261i
\(615\) −585.000 + 1013.25i −0.0383569 + 0.0664361i
\(616\) 520.000i 0.0340120i
\(617\) 6208.54 + 3584.50i 0.405099 + 0.233884i 0.688682 0.725064i \(-0.258190\pi\)
−0.283583 + 0.958948i \(0.591523\pi\)
\(618\) 6692.64 + 3864.00i 0.435627 + 0.251510i
\(619\) 20212.0i 1.31242i −0.754578 0.656211i \(-0.772158\pi\)
0.754578 0.656211i \(-0.227842\pi\)
\(620\) 416.000 720.533i 0.0269467 0.0466731i
\(621\) −12622.5 21862.8i −0.815658 1.41276i
\(622\) −12595.5 + 7272.00i −0.811949 + 0.468779i
\(623\) −5205.00 −0.334725
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) −13700.5 + 7910.00i −0.874733 + 0.505027i
\(627\) 1462.50 + 2533.12i 0.0931525 + 0.161345i
\(628\) −3788.00 + 6561.01i −0.240697 + 0.416899i
\(629\) 11421.0i 0.723983i
\(630\) 311.769 + 180.000i 0.0197162 + 0.0113831i
\(631\) −7746.60 4472.50i −0.488728 0.282167i 0.235319 0.971918i \(-0.424387\pi\)
−0.724046 + 0.689751i \(0.757720\pi\)
\(632\) 6112.00i 0.384687i
\(633\) −532.500 + 922.317i −0.0334360 + 0.0579128i
\(634\) −7398.00 12813.7i −0.463426 0.802677i
\(635\) −2038.62 + 1177.00i −0.127402 + 0.0735556i
\(636\) 7416.00 0.462364
\(637\) 0 0
\(638\) 338.000 0.0209742
\(639\) −1231.49 + 711.000i −0.0762393 + 0.0440168i
\(640\) 128.000 + 221.703i 0.00790569 + 0.0136931i
\(641\) 14121.5 24459.2i 0.870149 1.50714i 0.00830761 0.999965i \(-0.497356\pi\)
0.861842 0.507177i \(-0.169311\pi\)
\(642\) 7662.00i 0.471020i
\(643\) −4530.18 2615.50i −0.277843 0.160413i 0.354604 0.935017i \(-0.384616\pi\)
−0.632446 + 0.774604i \(0.717949\pi\)
\(644\) 3238.94 + 1870.00i 0.198186 + 0.114423i
\(645\) 1194.00i 0.0728895i
\(646\) 2025.00 3507.40i 0.123332 0.213618i
\(647\) −2435.50 4218.41i −0.147990 0.256326i 0.782495 0.622657i \(-0.213947\pi\)
−0.930484 + 0.366332i \(0.880614\pi\)
\(648\) 561.184 324.000i 0.0340207 0.0196419i
\(649\) −6383.00 −0.386063
\(650\) 0 0
\(651\) −1560.00 −0.0939189
\(652\) −3412.14 + 1970.00i −0.204954 + 0.118330i
\(653\) −6127.50 10613.1i −0.367209 0.636025i 0.621919 0.783082i \(-0.286353\pi\)
−0.989128 + 0.147057i \(0.953020\pi\)
\(654\) 2478.00 4292.02i 0.148161 0.256623i
\(655\) 2840.00i 0.169417i
\(656\) −2702.00 1560.00i −0.160816 0.0928472i
\(657\) −3585.35 2070.00i −0.212904 0.122920i
\(658\) 3880.00i 0.229876i
\(659\) 1072.50 1857.62i 0.0633971 0.109807i −0.832585 0.553898i \(-0.813140\pi\)
0.895982 + 0.444091i \(0.146473\pi\)
\(660\) −156.000 270.200i −0.00920044 0.0159356i
\(661\) −1828.18 + 1055.50i −0.107576 + 0.0621092i −0.552823 0.833299i \(-0.686449\pi\)
0.445247 + 0.895408i \(0.353116\pi\)
\(662\) −4754.00 −0.279108
\(663\) 0 0
\(664\) 5856.00 0.342254
\(665\) −649.519 + 375.000i −0.0378756 + 0.0218675i
\(666\) −7614.00 13187.8i −0.442998 0.767295i
\(667\) 1215.50 2105.31i 0.0705612 0.122216i
\(668\) 9420.00i 0.545615i
\(669\) −5931.41 3424.50i −0.342782 0.197906i
\(670\) −2830.17 1634.00i −0.163193 0.0942193i
\(671\) 2275.00i 0.130887i
\(672\) 240.000 415.692i 0.0137771 0.0238626i
\(673\) −11636.5 20155.0i −0.666499 1.15441i −0.978876 0.204453i \(-0.934459\pi\)
0.312377 0.949958i \(-0.398875\pi\)
\(674\) −13194.8 + 7618.00i −0.754070 + 0.435363i
\(675\) 16335.0 0.931458
\(676\) 0 0
\(677\) −5910.00 −0.335509 −0.167755 0.985829i \(-0.553652\pi\)
−0.167755 + 0.985829i \(0.553652\pi\)
\(678\) 4920.76 2841.00i 0.278732 0.160926i
\(679\) −242.500 420.022i −0.0137059 0.0237393i
\(680\) −216.000 + 374.123i −0.0121812 + 0.0210985i
\(681\) 7353.00i 0.413756i
\(682\) −2341.73 1352.00i −0.131480 0.0759102i
\(683\) 14503.3 + 8373.50i 0.812525 + 0.469111i 0.847832 0.530265i \(-0.177908\pi\)
−0.0353071 + 0.999377i \(0.511241\pi\)
\(684\) 5400.00i 0.301863i
\(685\) 2409.00 4172.51i 0.134370 0.232735i
\(686\) −3305.00 5724.43i −0.183944 0.318600i
\(687\) −4879.19 + 2817.00i −0.270964 + 0.156441i
\(688\) −3184.00 −0.176437
\(689\) 0 0
\(690\) −2244.00 −0.123808
\(691\) 8927.86 5154.50i 0.491507 0.283772i −0.233692 0.972311i \(-0.575081\pi\)
0.725200 + 0.688539i \(0.241747\pi\)
\(692\) 7778.00 + 13471.9i 0.427276 + 0.740064i
\(693\) 585.000 1013.25i 0.0320668 0.0555414i
\(694\) 750.000i 0.0410225i
\(695\) −4896.51 2827.00i −0.267245 0.154294i
\(696\) −270.200 156.000i −0.0147154 0.00849593i
\(697\) 5265.00i 0.286121i
\(698\) 9727.00 16847.7i 0.527468 0.913601i
\(699\) −2445.00 4234.86i −0.132301 0.229152i
\(700\) −2095.78 + 1210.00i −0.113162 + 0.0653339i
\(701\) 24294.0 1.30895 0.654473 0.756085i \(-0.272890\pi\)
0.654473 + 0.756085i \(0.272890\pi\)
\(702\) 0 0
\(703\) 31725.0 1.70204
\(704\) 720.533 416.000i 0.0385740 0.0222707i
\(705\) 1164.00 + 2016.11i 0.0621827 + 0.107704i
\(706\) −2263.00 + 3919.63i −0.120636 + 0.208948i
\(707\) 4045.00i 0.215174i
\(708\) 5102.62 + 2946.00i 0.270859 + 0.156381i
\(709\) 10963.0 + 6329.50i 0.580712 + 0.335274i 0.761416 0.648263i \(-0.224504\pi\)
−0.180704 + 0.983537i \(0.557838\pi\)
\(710\) 316.000i 0.0167032i
\(711\) 6876.00 11909.6i 0.362687 0.628192i
\(712\) 4164.00 + 7212.26i 0.219175 + 0.379622i
\(713\) −16842.5 + 9724.00i −0.884650 + 0.510753i
\(714\) 810.000 0.0424559
\(715\) 0 0
\(716\) 8916.00 0.465372
\(717\) 14403.7 8316.00i 0.750233 0.433147i
\(718\) −4488.00 7773.44i −0.233274 0.404042i
\(719\) 6545.50 11337.1i 0.339508 0.588044i −0.644833 0.764324i \(-0.723073\pi\)
0.984340 + 0.176279i \(0.0564062\pi\)
\(720\) 576.000i 0.0298142i
\(721\) 5577.20 + 3220.00i 0.288080 + 0.166323i
\(722\) 2137.35 + 1234.00i 0.110172 + 0.0636077i
\(723\) 16569.0i 0.852293i
\(724\) 2076.00 3595.74i 0.106566 0.184578i
\(725\) 786.500 + 1362.26i 0.0402895 + 0.0697834i
\(726\) 6037.93 3486.00i 0.308662 0.178206i
\(727\) −10792.0 −0.550555 −0.275277 0.961365i \(-0.588770\pi\)
−0.275277 + 0.961365i \(0.588770\pi\)
\(728\) 0 0
\(729\) 9477.00 0.481481
\(730\) −796.743 + 460.000i −0.0403956 + 0.0233224i
\(731\) −2686.50 4653.15i −0.135929 0.235435i
\(732\) −1050.00 + 1818.65i −0.0530179 + 0.0918297i
\(733\) 2698.00i 0.135952i −0.997687 0.0679761i \(-0.978346\pi\)
0.997687 0.0679761i \(-0.0216542\pi\)
\(734\) −2818.05 1627.00i −0.141711 0.0818170i
\(735\) 1652.38 + 954.000i 0.0829236 + 0.0478759i
\(736\) 5984.00i 0.299692i
\(737\) −5310.50 + 9198.06i −0.265420 + 0.459721i
\(738\) 3510.00 + 6079.50i 0.175074 + 0.303238i
\(739\) −2460.38 + 1420.50i −0.122472 + 0.0707090i −0.559984 0.828503i \(-0.689193\pi\)
0.437513 + 0.899212i \(0.355859\pi\)
\(740\) −3384.00 −0.168106
\(741\) 0 0
\(742\) 6180.00 0.305761
\(743\) −7959.64 + 4595.50i −0.393016 + 0.226908i −0.683466 0.729982i \(-0.739528\pi\)
0.290450 + 0.956890i \(0.406195\pi\)
\(744\) 1248.00 + 2161.60i 0.0614972 + 0.106516i
\(745\) 855.000 1480.90i 0.0420467 0.0728270i
\(746\) 5974.00i 0.293195i
\(747\) −11410.8 6588.00i −0.558899 0.322680i
\(748\) 1215.90 + 702.000i 0.0594354 + 0.0343151i
\(749\) 6385.00i 0.311486i
\(750\) 1476.00 2556.51i 0.0718612 0.124467i
\(751\) −829.500 1436.74i −0.0403048 0.0698099i 0.845169 0.534499i \(-0.179500\pi\)
−0.885474 + 0.464689i \(0.846166\pi\)
\(752\) −5376.29 + 3104.00i −0.260709 + 0.150520i
\(753\) 6525.00 0.315782
\(754\) 0 0
\(755\) 4128.00 0.198985
\(756\) −2338.27 + 1350.00i −0.112489 + 0.0649458i
\(757\) 6964.50 + 12062.9i 0.334384 + 0.579171i 0.983366 0.181633i \(-0.0581383\pi\)
−0.648982 + 0.760804i \(0.724805\pi\)
\(758\) 8867.00 15358.1i 0.424886 0.735925i
\(759\) 7293.00i 0.348774i
\(760\) 1039.23 + 600.000i 0.0496011 + 0.0286372i
\(761\) 3972.46 + 2293.50i 0.189227 + 0.109250i 0.591620 0.806217i \(-0.298488\pi\)
−0.402394 + 0.915467i \(0.631822\pi\)
\(762\) 7062.00i 0.335734i
\(763\) 2065.00 3576.68i 0.0979791 0.169705i
\(764\) −4282.00 7416.64i −0.202771 0.351210i
\(765\) 841.777 486.000i 0.0397837 0.0229691i
\(766\) 22806.0 1.07574
\(767\) 0 0
\(768\) −768.000 −0.0360844
\(769\) 12556.5 7249.50i 0.588815 0.339953i −0.175814 0.984423i \(-0.556256\pi\)
0.764629 + 0.644471i \(0.222922\pi\)
\(770\)