Properties

Label 26.4.c.a.9.1
Level $26$
Weight $4$
Character 26.9
Analytic conductor $1.534$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [26,4,Mod(3,26)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(26, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("26.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 26.c (of order \(3\), degree \(2\), 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: \(1.53404966015\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 26.9
Dual form 26.4.c.a.3.1

$q$-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} +(-13.0000 + 45.0333i) q^{13} +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} +(65.0000 + 67.5500i) q^{26} +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} +(97.5000 + 101.325i) q^{39} -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} +(182.000 - 45.0333i) q^{52} +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} +(-26.0000 + 90.0666i) q^{65} +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} +(273.000 - 67.5500i) q^{78} +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} +(-227.500 + 56.2917i) q^{91} -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 \( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 5 q^{7} - 16 q^{8} + 18 q^{9} + 4 q^{10} - 13 q^{11} - 24 q^{12} - 26 q^{13} + 20 q^{14} + 6 q^{15} - 16 q^{16} - 27 q^{17} + 72 q^{18} - 75 q^{19} - 8 q^{20} + 30 q^{21} + 26 q^{22} + 187 q^{23} - 24 q^{24} - 242 q^{25} + 130 q^{26} + 270 q^{27} + 20 q^{28} + 13 q^{29} - 12 q^{30} - 208 q^{31} + 32 q^{32} + 39 q^{33} - 108 q^{34} + 10 q^{35} + 72 q^{36} - 423 q^{37} - 300 q^{38} + 195 q^{39} - 32 q^{40} - 195 q^{41} + 30 q^{42} - 199 q^{43} + 104 q^{44} + 36 q^{45} - 374 q^{46} + 776 q^{47} + 48 q^{48} + 318 q^{49} - 242 q^{50} - 162 q^{51} + 364 q^{52} + 1236 q^{53} + 270 q^{54} - 26 q^{55} - 40 q^{56} - 450 q^{57} - 26 q^{58} - 491 q^{59} - 48 q^{60} - 175 q^{61} - 208 q^{62} - 90 q^{63} + 128 q^{64} - 52 q^{65} + 156 q^{66} - 817 q^{67} - 108 q^{68} - 561 q^{69} + 40 q^{70} - 79 q^{71} - 144 q^{72} + 460 q^{73} + 846 q^{74} - 363 q^{75} - 300 q^{76} - 130 q^{77} + 546 q^{78} + 1528 q^{79} - 32 q^{80} - 81 q^{81} + 390 q^{82} - 1464 q^{83} - 60 q^{84} - 54 q^{85} - 796 q^{86} - 39 q^{87} + 104 q^{88} + 1041 q^{89} + 144 q^{90} - 455 q^{91} - 1496 q^{92} - 312 q^{93} + 776 q^{94} - 150 q^{95} + 192 q^{96} + 97 q^{97} - 636 q^{98} - 468 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/26\mathbb{Z}\right)^\times\).

\(n\) \(15\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.471491\pi\)
0.0894427 + 0.995992i \(0.471491\pi\)
\(6\) −3.00000 5.19615i −0.204124 0.353553i
\(7\) 2.50000 + 4.33013i 0.134987 + 0.233805i 0.925593 0.378521i \(-0.123567\pi\)
−0.790605 + 0.612326i \(0.790234\pi\)
\(8\) −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 −0.941252 0.337704i \(-0.890350\pi\)
0.763087 + 0.646296i \(0.223683\pi\)
\(12\) −12.0000 −0.288675
\(13\) −13.0000 + 45.0333i −0.277350 + 0.960769i
\(14\) 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 0.545764 0.837939i \(-0.316239\pi\)
−0.998558 + 0.0536762i \(0.982906\pi\)
\(20\) −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
\(26\) 65.0000 + 67.5500i 0.490290 + 0.509525i
\(27\) 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 \(-0.597412\pi\)
−0.301273 + 0.953538i \(0.597412\pi\)
\(32\) 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 \(0.555600\pi\)
−0.765955 + 0.642894i \(0.777734\pi\)
\(38\) −150.000 −0.640348
\(39\) 97.5000 + 101.325i 0.400320 + 0.416025i
\(40\) −16.0000 −0.0632456
\(41\) −97.5000 + 168.875i −0.371389 + 0.643264i −0.989779 0.142607i \(-0.954452\pi\)
0.618391 + 0.785871i \(0.287785\pi\)
\(42\) 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 \(-0.294338\pi\)
0.602081 + 0.798435i \(0.294338\pi\)
\(48\) 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
\(52\) 182.000 45.0333i 0.485363 0.120096i
\(53\) 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 \(-0.984441\pi\)
0.457087 0.889422i \(-0.348893\pi\)
\(60\) −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
\(65\) −26.0000 + 90.0666i −0.0496139 + 0.171868i
\(66\) 78.0000 0.145472
\(67\) −408.500 + 707.543i −0.744869 + 1.29015i 0.205387 + 0.978681i \(0.434155\pi\)
−0.950256 + 0.311470i \(0.899179\pi\)
\(68\) −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 0.831123 0.556088i \(-0.187698\pi\)
−0.897148 + 0.441729i \(0.854365\pi\)
\(72\) −72.0000 124.708i −0.117851 0.204124i
\(73\) 230.000 0.368760 0.184380 0.982855i \(-0.440972\pi\)
0.184380 + 0.982855i \(0.440972\pi\)
\(74\) 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
\(78\) 273.000 67.5500i 0.396297 0.0980581i
\(79\) 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 \(-0.660824\pi\)
−0.484021 + 0.875057i \(0.660824\pi\)
\(84\) −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 \(-0.620498\pi\)
0.989500 0.144534i \(-0.0461683\pi\)
\(90\) 72.0000 0.0843274
\(91\) −227.500 + 56.2917i −0.262071 + 0.0648458i
\(92\) −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 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) −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 \(0.288724\pi\)
\(104\) 104.000 360.267i 0.0980581 0.339683i
\(105\) 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 \(-0.381780\pi\)
0.362920 + 0.931820i \(0.381780\pi\)
\(110\) 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
\(117\) −819.000 + 202.650i −0.647150 + 0.160128i
\(118\) −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
\(130\) 130.000 + 135.100i 0.0877058 + 0.0911465i
\(131\) −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 \(0.103833\pi\)
−0.196118 + 0.980580i \(0.562833\pi\)
\(138\) −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
\(143\) −422.500 439.075i −0.247072 0.256764i
\(144\) −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 0.724239 0.689549i \(-0.242191\pi\)
−0.959287 + 0.282434i \(0.908858\pi\)
\(150\) 363.000 + 628.734i 0.197592 + 0.342240i
\(151\) 2064.00 1.11236 0.556179 0.831063i \(-0.312267\pi\)
0.556179 + 0.831063i \(0.312267\pi\)
\(152\) 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
\(156\) 156.000 540.400i 0.0800641 0.277350i
\(157\) −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 0.959754 0.280843i \(-0.0906139\pi\)
−0.723094 + 0.690750i \(0.757281\pi\)
\(164\) 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 \(-0.649629\pi\)
0.998568 0.0534983i \(-0.0170372\pi\)
\(168\) −120.000 −0.0551083
\(169\) −1859.00 1170.87i −0.846154 0.532939i
\(170\) −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 \(0.568367\pi\)
\(182\) −130.000 + 450.333i −0.0529464 + 0.183412i
\(183\) −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 −0.999932 0.0116407i \(-0.996295\pi\)
0.510047 + 0.860146i \(0.329628\pi\)
\(194\) 194.000 0.0717958
\(195\) 195.000 + 202.650i 0.0716115 + 0.0744208i
\(196\) −1272.00 −0.463557
\(197\) −601.500 + 1041.83i −0.217539 + 0.376788i −0.954055 0.299632i \(-0.903136\pi\)
0.736516 + 0.676420i \(0.236469\pi\)
\(198\) −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
\(208\) −520.000 540.400i −0.173344 0.180144i
\(209\) 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
\(221\) 1228.50 303.975i 0.373927 0.0925229i
\(222\) 2538.00 0.767295
\(223\) 1141.50 1977.14i 0.342782 0.593717i −0.642166 0.766566i \(-0.721964\pi\)
0.984948 + 0.172849i \(0.0552973\pi\)
\(224\) −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 0.629358 0.777116i \(-0.283318\pi\)
−0.987681 + 0.156482i \(0.949985\pi\)
\(228\) 450.000 + 779.423i 0.130710 + 0.226397i
\(229\) −1878.00 −0.541929 −0.270964 0.962589i \(-0.587343\pi\)
−0.270964 + 0.962589i \(0.587343\pi\)
\(230\) −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 \(0.426405\pi\)
\(234\) −468.000 + 1621.20i −0.130744 + 0.452911i
\(235\) 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 \(-0.770059\pi\)
−0.750233 + 0.661173i \(0.770059\pi\)
\(240\) 48.0000 + 83.1384i 0.0129099 + 0.0223607i
\(241\) −2761.50 4783.06i −0.738107 1.27844i −0.953347 0.301878i \(-0.902386\pi\)
0.215239 0.976561i \(-0.430947\pi\)
\(242\) 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
\(247\) 3412.50 844.375i 0.879078 0.217515i
\(248\) 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
\(260\) 364.000 90.0666i 0.0868243 0.0214834i
\(261\) 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 \(0.487703\pi\)
−0.884690 + 0.466180i \(0.845630\pi\)
\(272\) 432.000 0.0963009
\(273\) −195.000 + 675.500i −0.0432305 + 0.149755i
\(274\) 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 \(-0.594713\pi\)
−0.293180 + 0.956057i \(0.594713\pi\)
\(282\) −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
\(286\) −1183.00 + 292.717i −0.244588 + 0.0605199i
\(287\) −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 \(-0.887551\pi\)
0.169507 0.985529i \(-0.445782\pi\)
\(294\) −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
\(299\) 6077.50 + 6315.92i 1.17549 + 1.22160i
\(300\) 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 \(-0.0837409\pi\)
0.965594 + 0.260056i \(0.0837409\pi\)
\(308\) 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 \(0.730697\pi\)
\(312\) −780.000 810.600i −0.141535 0.147087i
\(313\) 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 \(-0.272507\pi\)
0.655383 + 0.755296i \(0.272507\pi\)
\(318\) −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
\(325\) 1573.00 5449.03i 0.268475 0.930024i
\(326\) 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 0.947671 0.319248i \(-0.103430\pi\)
−0.750312 + 0.661084i \(0.770097\pi\)
\(332\) 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 \(0.711125\pi\)
\(338\) −3887.00 + 2049.02i −0.625518 + 0.329739i
\(339\) −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 \(0.434672\pi\)
−0.949749 + 0.313013i \(0.898662\pi\)
\(350\) −1210.00 −0.184792
\(351\) −1755.00 + 6079.50i −0.266880 + 0.924500i
\(352\) −416.000 −0.0629911
\(353\) −1131.50 + 1959.82i −0.170605 + 0.295497i −0.938632 0.344921i \(-0.887906\pi\)
0.768026 + 0.640418i \(0.221239\pi\)
\(354\) −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 \(-0.607015\pi\)
−0.329899 + 0.944016i \(0.607015\pi\)
\(360\) −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
\(364\) 650.000 + 675.500i 0.0935969 + 0.0972687i
\(365\) 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
\(377\) 422.500 + 439.075i 0.0577185 + 0.0599828i
\(378\) 1350.00 0.183694
\(379\) 4433.50 7679.05i 0.600880 1.04076i −0.391808 0.920047i \(-0.628150\pi\)
0.992688 0.120708i \(-0.0385165\pi\)
\(380\) −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 \(-0.891542\pi\)
0.181850 0.983326i \(-0.441792\pi\)
\(384\) −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 \(0.445341\pi\)
\(390\) 546.000 135.100i 0.0708918 0.0175412i
\(391\) −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 0.844446 0.535641i \(-0.179930\pi\)
−0.886101 + 0.463492i \(0.846596\pi\)
\(398\) −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 \(-0.466011\pi\)
0.807804 0.589451i \(-0.200656\pi\)
\(402\) 4902.00 0.608183
\(403\) 1352.00 4683.47i 0.167116 0.578908i
\(404\) −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 0.999531 0.0306167i \(-0.00974712\pi\)
−0.526280 + 0.850311i \(0.676414\pi\)
\(410\) 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
\(416\) −1456.00 + 360.267i −0.171602 + 0.0424604i
\(417\) −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 \(-0.557614\pi\)
−0.180014 + 0.983664i \(0.557614\pi\)
\(422\) −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
\(429\) −1774.50 + 439.075i −0.199706 + 0.0494143i
\(430\) −796.000 −0.0892710
\(431\) 4567.50 7911.14i 0.510461 0.884145i −0.489465 0.872023i \(-0.662808\pi\)
0.999927 0.0121219i \(-0.00385860\pi\)
\(432\) −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
\(442\) 702.000 2431.80i 0.0755446 0.261694i
\(443\) −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 0.971761 0.235966i \(-0.0758253\pi\)
−0.690233 + 0.723587i \(0.742492\pi\)
\(450\) −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
\(455\) −455.000 + 112.583i −0.0468807 + 0.0116000i
\(456\) 1800.00 0.184852
\(457\) −9699.50 + 16800.0i −0.992830 + 1.71963i −0.392897 + 0.919582i \(0.628527\pi\)
−0.599933 + 0.800050i \(0.704806\pi\)
\(458\) −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 \(0.120904\pi\)
−0.143273 + 0.989683i \(0.545763\pi\)
\(462\) 195.000 + 337.750i 0.0196368 + 0.0340120i
\(463\) 4072.00 0.408730 0.204365 0.978895i \(-0.434487\pi\)
0.204365 + 0.978895i \(0.434487\pi\)
\(464\) 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 \(0.227994\pi\)
\(468\) 2340.00 + 2431.80i 0.231125 + 0.240192i
\(469\) −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 −0.507046 0.861919i \(-0.669263\pi\)
0.999967 + 0.00815506i \(0.00259587\pi\)
\(480\) 192.000 0.0182574
\(481\) −13747.5 14286.8i −1.30319 1.35431i
\(482\) −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 0.675894 0.736998i \(-0.263757\pi\)
−0.976207 + 0.216843i \(0.930424\pi\)
\(488\) 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
\(494\) 1950.00 6755.00i 0.177601 0.615226i
\(495\) −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 \(-0.543599\pi\)
−0.136541 + 0.990634i \(0.543599\pi\)
\(500\) 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
\(507\) −5830.50 + 3073.52i −0.510733 + 0.269231i
\(508\) 4708.00 0.411188
\(509\) −363.500 + 629.600i −0.0316539 + 0.0548262i −0.881418 0.472336i \(-0.843411\pi\)
0.849764 + 0.527163i \(0.176744\pi\)
\(510\) −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
\(520\) 208.000 720.533i 0.0175412 0.0607644i
\(521\) 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
\(533\) −6337.50 6586.12i −0.515024 0.535228i
\(534\) −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 \(-0.338470\pi\)
0.485960 + 0.873981i \(0.338470\pi\)
\(542\) 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
\(546\) 975.000 + 1013.25i 0.0764215 + 0.0794196i
\(547\) −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 −0.851110 0.524987i \(-0.824070\pi\)
0.880207 + 0.474590i \(0.157403\pi\)
\(558\) −3744.00 −0.284043
\(559\) 9054.50 2240.41i 0.685089 0.169515i
\(560\) −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 \(0.828798\pi\)
\(572\) −676.000 + 2341.73i −0.0494143 + 0.171176i
\(573\) 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 \(-0.408560\pi\)
0.283333 + 0.959022i \(0.408560\pi\)
\(578\) −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
\(585\) −1638.00 + 405.300i −0.115766 + 0.0286446i
\(586\) −15422.0 −1.08716
\(587\) −8516.50 + 14751.0i −0.598831 + 1.03721i 0.394163 + 0.919040i \(0.371034\pi\)
−0.992994 + 0.118165i \(0.962299\pi\)
\(588\) −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 \(-0.667501\pi\)
−0.502268 + 0.864712i \(0.667501\pi\)
\(594\) 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
\(598\) 17017.0 4210.62i 1.16367 0.287935i
\(599\) 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
\(611\) −5044.00 + 17472.9i −0.333974 + 1.15692i
\(612\) −1944.00 −0.128401
\(613\) 1728.50 2993.85i 0.113888 0.197260i −0.803447 0.595377i \(-0.797003\pi\)
0.917335 + 0.398117i \(0.130336\pi\)
\(614\) 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 0.958948 0.283583i \(-0.0915230\pi\)
−0.725064 + 0.688682i \(0.758190\pi\)
\(618\) −3864.00 6692.64i −0.251510 0.435627i
\(619\) 20212.0 1.31242 0.656211 0.754578i \(-0.272158\pi\)
0.656211 + 0.754578i \(0.272158\pi\)
\(620\) 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
\(624\) −2184.00 + 540.400i −0.140112 + 0.0346688i
\(625\) 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 0.971918 0.235319i \(-0.0756134\pi\)
−0.689751 + 0.724046i \(0.742280\pi\)
\(632\) −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
\(637\) 10335.0 + 10740.4i 0.642838 + 0.668057i
\(638\) 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 0.774604 0.632446i \(-0.217949\pi\)
−0.935017 + 0.354604i \(0.884616\pi\)
\(644\) −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
\(650\) −7865.00 8173.55i −0.474601 0.493220i
\(651\) −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 −0.895408 0.445247i \(-0.853116\pi\)
0.833299 + 0.552823i \(0.186449\pi\)
\(662\) 4754.00 0.279108
\(663\) 1053.00 3647.70i 0.0616819 0.213673i
\(664\) 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
\(676\) −338.000 + 8781.50i −0.0192308 + 0.499630i
\(677\) −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 0.530265 0.847832i \(-0.322092\pi\)
−0.999377 + 0.0353071i \(0.988759\pi\)
\(684\) −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
\(689\) −8034.00 + 27830.6i −0.444225 + 1.53884i
\(690\) −2244.00 −0.123808
\(691\) −5154.50 + 8927.86i −0.283772 + 0.491507i −0.972311 0.233692i \(-0.924919\pi\)
0.688539 + 0.725200i \(0.258253\pi\)
\(692\) 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 \(0.727110\pi\)
\(702\) 8775.00 + 9119.25i 0.471782 + 0.490290i
\(703\) 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 0.648263 0.761416i \(-0.275496\pi\)
−0.983537 + 0.180704i \(0.942162\pi\)
\(710\) −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
\(715\) −845.000 878.150i −0.0441975 0.0459314i
\(716\) 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 \(0.411230\pi\)
\(728\) 1820.00 450.333i 0.0926562 0.0229265i
\(729\) 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 \(-0.521654\pi\)
−0.0679761 + 0.997687i \(0.521654\pi\)
\(734\) −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 −0.899212 0.437513i \(-0.855859\pi\)
0.828503 + 0.559984i \(0.189193\pi\)
\(740\) 3384.00 0.168106
\(741\) 2925.00 10132.5i 0.145010 0.502330i
\(742\) 6180.00 0.305761
\(743\) 4595.50 7959.64i 0.226908 0.393016i −0.729982 0.683466i \(-0.760472\pi\)
0.956890 + 0.290450i \(0.0938050\pi\)
\(744\) 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
\(754\) 1183.00 292.717i 0.0571384 0.0141381i
\(755\) 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 0.806217 0.591620i \(-0.201512\pi\)
−0.915467 + 0.402394i \(0.868178\pi\)
\(762\) 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
\(767\) 22340.5 5527.84i 1.05172 0.260233i
\(768\) −768.000 −0.0360844