Properties

Label 74.4.f.a.49.2
Level $74$
Weight $4$
Character 74.49
Analytic conductor $4.366$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,4,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), 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: \(4.36614134042\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 49.2
Character \(\chi\) \(=\) 74.49
Dual form 74.4.f.a.71.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.53209 + 1.28558i) q^{2} +(-1.34104 - 1.12526i) q^{3} +(0.694593 - 3.93923i) q^{4} +(6.03617 - 2.19699i) q^{5} +3.50120 q^{6} +(-28.8243 + 10.4912i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-4.15634 - 23.5718i) q^{9} +O(q^{10})\) \(q+(-1.53209 + 1.28558i) q^{2} +(-1.34104 - 1.12526i) q^{3} +(0.694593 - 3.93923i) q^{4} +(6.03617 - 2.19699i) q^{5} +3.50120 q^{6} +(-28.8243 + 10.4912i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-4.15634 - 23.5718i) q^{9} +(-6.42356 + 11.1259i) q^{10} +(-18.0799 - 31.3153i) q^{11} +(-5.36415 + 4.50106i) q^{12} +(10.9484 - 62.0916i) q^{13} +(30.6741 - 53.1292i) q^{14} +(-10.5669 - 3.84605i) q^{15} +(-15.0351 - 5.47232i) q^{16} +(-1.92973 - 10.9441i) q^{17} +(36.6712 + 30.7708i) q^{18} +(-29.3592 - 24.6353i) q^{19} +(-4.46176 - 25.3039i) q^{20} +(50.4598 + 18.3659i) q^{21} +(67.9581 + 24.7347i) q^{22} +(-55.9596 + 96.9249i) q^{23} +(2.43191 - 13.7920i) q^{24} +(-64.1469 + 53.8257i) q^{25} +(63.0494 + 109.205i) q^{26} +(-44.5838 + 77.2214i) q^{27} +(21.3060 + 120.832i) q^{28} +(-135.535 - 234.753i) q^{29} +(21.1339 - 7.69210i) q^{30} +209.997 q^{31} +(30.0702 - 10.9446i) q^{32} +(-10.9922 + 62.3396i) q^{33} +(17.0259 + 14.2865i) q^{34} +(-150.939 + 126.653i) q^{35} -95.7416 q^{36} +(198.086 + 106.840i) q^{37} +76.6514 q^{38} +(-84.5517 + 70.9473i) q^{39} +(39.3659 + 33.0319i) q^{40} +(-77.3955 + 438.932i) q^{41} +(-100.920 + 36.7317i) q^{42} +347.729 q^{43} +(-135.916 + 49.4695i) q^{44} +(-76.8753 - 133.152i) q^{45} +(-38.8691 - 220.438i) q^{46} +(49.0504 - 84.9578i) q^{47} +(14.0048 + 24.2570i) q^{48} +(458.020 - 384.324i) q^{49} +(29.0818 - 164.931i) q^{50} +(-9.72711 + 16.8479i) q^{51} +(-236.988 - 86.2567i) q^{52} +(-201.300 - 73.2671i) q^{53} +(-30.9676 - 175.626i) q^{54} +(-177.933 - 149.303i) q^{55} +(-187.982 - 157.736i) q^{56} +(11.6506 + 66.0737i) q^{57} +(509.443 + 185.422i) q^{58} +(-333.216 - 121.281i) q^{59} +(-22.4902 + 38.9541i) q^{60} +(124.522 - 706.198i) q^{61} +(-321.734 + 269.967i) q^{62} +(367.099 + 635.834i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(-70.3278 - 398.849i) q^{65} +(-63.3013 - 109.641i) q^{66} +(-384.005 + 139.766i) q^{67} -44.4515 q^{68} +(184.110 - 67.0106i) q^{69} +(68.4303 - 388.088i) q^{70} +(-362.994 - 304.588i) q^{71} +(146.685 - 123.083i) q^{72} +269.256 q^{73} +(-440.837 + 90.9669i) q^{74} +146.592 q^{75} +(-117.437 + 98.5412i) q^{76} +(849.673 + 712.961i) q^{77} +(38.3326 - 217.395i) q^{78} +(-366.425 + 133.368i) q^{79} -102.777 q^{80} +(-460.599 + 167.644i) q^{81} +(-445.703 - 771.980i) q^{82} +(-85.2656 - 483.565i) q^{83} +(107.396 - 186.016i) q^{84} +(-35.6922 - 61.8206i) q^{85} +(-532.751 + 447.031i) q^{86} +(-82.4019 + 467.324i) q^{87} +(144.639 - 250.522i) q^{88} +(907.822 + 330.420i) q^{89} +(288.956 + 105.172i) q^{90} +(335.833 + 1904.60i) q^{91} +(342.940 + 287.761i) q^{92} +(-281.614 - 236.302i) q^{93} +(34.0701 + 193.221i) q^{94} +(-231.341 - 84.2011i) q^{95} +(-52.6408 - 19.1597i) q^{96} +(492.404 - 852.869i) q^{97} +(-207.649 + 1177.64i) q^{98} +(-663.010 + 556.332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{3} - 9 q^{5} + 36 q^{6} - 75 q^{7} + 96 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{3} - 9 q^{5} + 36 q^{6} - 75 q^{7} + 96 q^{8} - 48 q^{9} + 6 q^{10} + 87 q^{11} + 24 q^{12} - 45 q^{13} + 6 q^{14} - 141 q^{15} + 120 q^{17} - 192 q^{18} - 177 q^{19} - 36 q^{20} + 159 q^{21} - 42 q^{22} + 45 q^{23} - 48 q^{24} - 321 q^{25} + 150 q^{26} + 435 q^{27} + 96 q^{28} - 153 q^{29} + 282 q^{30} + 1002 q^{31} - 210 q^{33} - 456 q^{34} + 3 q^{35} + 216 q^{36} - 1239 q^{37} + 780 q^{38} - 474 q^{39} - 144 q^{40} - 1437 q^{41} - 318 q^{42} + 504 q^{43} + 84 q^{44} - 171 q^{45} + 714 q^{46} + 396 q^{47} + 144 q^{48} + 399 q^{49} - 1212 q^{50} - 972 q^{51} + 504 q^{52} + 1173 q^{53} + 360 q^{54} + 1755 q^{55} - 408 q^{56} - 3525 q^{57} + 24 q^{58} + 1260 q^{59} - 108 q^{60} + 2946 q^{61} - 1380 q^{62} + 2514 q^{63} - 768 q^{64} + 1599 q^{65} - 252 q^{66} - 645 q^{67} + 1200 q^{68} - 5037 q^{69} - 366 q^{70} - 753 q^{71} - 768 q^{72} - 876 q^{73} - 1338 q^{74} + 6960 q^{75} - 708 q^{76} + 1197 q^{77} - 1590 q^{78} - 3276 q^{79} + 96 q^{80} + 36 q^{81} - 216 q^{82} - 1110 q^{83} + 504 q^{84} + 1992 q^{85} - 192 q^{86} + 1125 q^{87} - 696 q^{88} + 3045 q^{89} + 4590 q^{90} + 5046 q^{91} + 2604 q^{92} - 4917 q^{93} + 78 q^{94} + 2274 q^{95} + 384 q^{96} - 624 q^{97} + 1902 q^{98} - 5904 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.53209 + 1.28558i −0.541675 + 0.454519i
\(3\) −1.34104 1.12526i −0.258083 0.216557i 0.504561 0.863376i \(-0.331654\pi\)
−0.762644 + 0.646819i \(0.776099\pi\)
\(4\) 0.694593 3.93923i 0.0868241 0.492404i
\(5\) 6.03617 2.19699i 0.539892 0.196505i −0.0576579 0.998336i \(-0.518363\pi\)
0.597550 + 0.801832i \(0.296141\pi\)
\(6\) 3.50120 0.238227
\(7\) −28.8243 + 10.4912i −1.55636 + 0.566470i −0.969900 0.243505i \(-0.921703\pi\)
−0.586464 + 0.809975i \(0.699480\pi\)
\(8\) 4.00000 + 6.92820i 0.176777 + 0.306186i
\(9\) −4.15634 23.5718i −0.153938 0.873028i
\(10\) −6.42356 + 11.1259i −0.203131 + 0.351833i
\(11\) −18.0799 31.3153i −0.495572 0.858356i 0.504415 0.863461i \(-0.331708\pi\)
−0.999987 + 0.00510559i \(0.998375\pi\)
\(12\) −5.36415 + 4.50106i −0.129041 + 0.108279i
\(13\) 10.9484 62.0916i 0.233580 1.32470i −0.612003 0.790856i \(-0.709636\pi\)
0.845583 0.533844i \(-0.179253\pi\)
\(14\) 30.6741 53.1292i 0.585572 1.01424i
\(15\) −10.5669 3.84605i −0.181891 0.0662030i
\(16\) −15.0351 5.47232i −0.234923 0.0855050i
\(17\) −1.92973 10.9441i −0.0275311 0.156137i 0.967943 0.251170i \(-0.0808153\pi\)
−0.995474 + 0.0950334i \(0.969704\pi\)
\(18\) 36.6712 + 30.7708i 0.480193 + 0.402930i
\(19\) −29.3592 24.6353i −0.354498 0.297459i 0.448095 0.893986i \(-0.352103\pi\)
−0.802593 + 0.596527i \(0.796547\pi\)
\(20\) −4.46176 25.3039i −0.0498840 0.282906i
\(21\) 50.4598 + 18.3659i 0.524344 + 0.190846i
\(22\) 67.9581 + 24.7347i 0.658578 + 0.239703i
\(23\) −55.9596 + 96.9249i −0.507321 + 0.878706i 0.492643 + 0.870231i \(0.336031\pi\)
−0.999964 + 0.00847437i \(0.997302\pi\)
\(24\) 2.43191 13.7920i 0.0206838 0.117304i
\(25\) −64.1469 + 53.8257i −0.513175 + 0.430605i
\(26\) 63.0494 + 109.205i 0.475577 + 0.823724i
\(27\) −44.5838 + 77.2214i −0.317783 + 0.550417i
\(28\) 21.3060 + 120.832i 0.143802 + 0.815543i
\(29\) −135.535 234.753i −0.867866 1.50319i −0.864173 0.503196i \(-0.832158\pi\)
−0.00369384 0.999993i \(-0.501176\pi\)
\(30\) 21.1339 7.69210i 0.128617 0.0468126i
\(31\) 209.997 1.21666 0.608332 0.793682i \(-0.291839\pi\)
0.608332 + 0.793682i \(0.291839\pi\)
\(32\) 30.0702 10.9446i 0.166116 0.0604612i
\(33\) −10.9922 + 62.3396i −0.0579845 + 0.328847i
\(34\) 17.0259 + 14.2865i 0.0858801 + 0.0720619i
\(35\) −150.939 + 126.653i −0.728954 + 0.611665i
\(36\) −95.7416 −0.443248
\(37\) 198.086 + 106.840i 0.880141 + 0.474712i
\(38\) 76.6514 0.327224
\(39\) −84.5517 + 70.9473i −0.347156 + 0.291299i
\(40\) 39.3659 + 33.0319i 0.155607 + 0.130570i
\(41\) −77.3955 + 438.932i −0.294808 + 1.67194i 0.373172 + 0.927762i \(0.378270\pi\)
−0.667980 + 0.744179i \(0.732841\pi\)
\(42\) −100.920 + 36.7317i −0.370767 + 0.134948i
\(43\) 347.729 1.23321 0.616606 0.787272i \(-0.288507\pi\)
0.616606 + 0.787272i \(0.288507\pi\)
\(44\) −135.916 + 49.4695i −0.465685 + 0.169496i
\(45\) −76.8753 133.152i −0.254664 0.441091i
\(46\) −38.8691 220.438i −0.124586 0.706560i
\(47\) 49.0504 84.9578i 0.152228 0.263667i −0.779818 0.626006i \(-0.784688\pi\)
0.932046 + 0.362339i \(0.118022\pi\)
\(48\) 14.0048 + 24.2570i 0.0421129 + 0.0729417i
\(49\) 458.020 384.324i 1.33533 1.12048i
\(50\) 29.0818 164.931i 0.0822559 0.466496i
\(51\) −9.72711 + 16.8479i −0.0267072 + 0.0462583i
\(52\) −236.988 86.2567i −0.632007 0.230032i
\(53\) −201.300 73.2671i −0.521710 0.189887i 0.0677229 0.997704i \(-0.478427\pi\)
−0.589433 + 0.807817i \(0.700649\pi\)
\(54\) −30.9676 175.626i −0.0780398 0.442586i
\(55\) −177.933 149.303i −0.436226 0.366037i
\(56\) −187.982 157.736i −0.448574 0.376398i
\(57\) 11.6506 + 66.0737i 0.0270729 + 0.153538i
\(58\) 509.443 + 185.422i 1.15333 + 0.419778i
\(59\) −333.216 121.281i −0.735271 0.267617i −0.0528767 0.998601i \(-0.516839\pi\)
−0.682394 + 0.730984i \(0.739061\pi\)
\(60\) −22.4902 + 38.9541i −0.0483912 + 0.0838160i
\(61\) 124.522 706.198i 0.261367 1.48229i −0.517817 0.855491i \(-0.673255\pi\)
0.779184 0.626795i \(-0.215634\pi\)
\(62\) −321.734 + 269.967i −0.659037 + 0.552998i
\(63\) 367.099 + 635.834i 0.734129 + 1.27155i
\(64\) −32.0000 + 55.4256i −0.0625000 + 0.108253i
\(65\) −70.3278 398.849i −0.134201 0.761094i
\(66\) −63.3013 109.641i −0.118058 0.204483i
\(67\) −384.005 + 139.766i −0.700203 + 0.254853i −0.667498 0.744612i \(-0.732635\pi\)
−0.0327057 + 0.999465i \(0.510412\pi\)
\(68\) −44.4515 −0.0792727
\(69\) 184.110 67.0106i 0.321221 0.116915i
\(70\) 68.4303 388.088i 0.116843 0.662648i
\(71\) −362.994 304.588i −0.606753 0.509126i 0.286855 0.957974i \(-0.407390\pi\)
−0.893608 + 0.448848i \(0.851835\pi\)
\(72\) 146.685 123.083i 0.240097 0.201465i
\(73\) 269.256 0.431700 0.215850 0.976427i \(-0.430748\pi\)
0.215850 + 0.976427i \(0.430748\pi\)
\(74\) −440.837 + 90.9669i −0.692517 + 0.142901i
\(75\) 146.592 0.225692
\(76\) −117.437 + 98.5412i −0.177249 + 0.148730i
\(77\) 849.673 + 712.961i 1.25752 + 1.05519i
\(78\) 38.3326 217.395i 0.0556450 0.315579i
\(79\) −366.425 + 133.368i −0.521849 + 0.189938i −0.589495 0.807772i \(-0.700673\pi\)
0.0676462 + 0.997709i \(0.478451\pi\)
\(80\) −102.777 −0.143635
\(81\) −460.599 + 167.644i −0.631823 + 0.229965i
\(82\) −445.703 771.980i −0.600239 1.03965i
\(83\) −85.2656 483.565i −0.112760 0.639496i −0.987835 0.155508i \(-0.950299\pi\)
0.875074 0.483989i \(-0.160812\pi\)
\(84\) 107.396 186.016i 0.139499 0.241619i
\(85\) −35.6922 61.8206i −0.0455454 0.0788869i
\(86\) −532.751 + 447.031i −0.668000 + 0.560519i
\(87\) −82.4019 + 467.324i −0.101545 + 0.575890i
\(88\) 144.639 250.522i 0.175211 0.303475i
\(89\) 907.822 + 330.420i 1.08122 + 0.393534i 0.820363 0.571843i \(-0.193771\pi\)
0.260861 + 0.965376i \(0.415993\pi\)
\(90\) 288.956 + 105.172i 0.338430 + 0.123178i
\(91\) 335.833 + 1904.60i 0.386867 + 2.19403i
\(92\) 342.940 + 287.761i 0.388630 + 0.326100i
\(93\) −281.614 236.302i −0.314000 0.263478i
\(94\) 34.0701 + 193.221i 0.0373836 + 0.212013i
\(95\) −231.341 84.2011i −0.249843 0.0909353i
\(96\) −52.6408 19.1597i −0.0559649 0.0203696i
\(97\) 492.404 852.869i 0.515423 0.892739i −0.484417 0.874837i \(-0.660968\pi\)
0.999840 0.0179016i \(-0.00569856\pi\)
\(98\) −207.649 + 1177.64i −0.214038 + 1.21387i
\(99\) −663.010 + 556.332i −0.673081 + 0.564782i
\(100\) 167.476 + 290.076i 0.167476 + 0.290076i
\(101\) 467.154 809.135i 0.460234 0.797148i −0.538739 0.842473i \(-0.681099\pi\)
0.998972 + 0.0453250i \(0.0144323\pi\)
\(102\) −6.75638 38.3173i −0.00655864 0.0371959i
\(103\) 18.1071 + 31.3623i 0.0173218 + 0.0300022i 0.874556 0.484924i \(-0.161153\pi\)
−0.857235 + 0.514926i \(0.827819\pi\)
\(104\) 473.977 172.513i 0.446896 0.162657i
\(105\) 344.933 0.320591
\(106\) 402.599 146.534i 0.368905 0.134270i
\(107\) 182.702 1036.15i 0.165069 0.936155i −0.783923 0.620858i \(-0.786784\pi\)
0.948993 0.315298i \(-0.102104\pi\)
\(108\) 273.225 + 229.263i 0.243436 + 0.204267i
\(109\) 506.333 424.864i 0.444935 0.373345i −0.392617 0.919702i \(-0.628430\pi\)
0.837552 + 0.546357i \(0.183986\pi\)
\(110\) 464.549 0.402664
\(111\) −145.418 366.176i −0.124347 0.313116i
\(112\) 490.786 0.414062
\(113\) −762.785 + 640.052i −0.635015 + 0.532841i −0.902483 0.430726i \(-0.858258\pi\)
0.267467 + 0.963567i \(0.413813\pi\)
\(114\) −102.792 86.2531i −0.0844509 0.0708627i
\(115\) −124.839 + 707.998i −0.101229 + 0.574097i
\(116\) −1018.89 + 370.844i −0.815528 + 0.296828i
\(117\) −1509.11 −1.19246
\(118\) 666.431 242.561i 0.519915 0.189234i
\(119\) 170.439 + 295.209i 0.131295 + 0.227410i
\(120\) −15.6215 88.5940i −0.0118837 0.0673958i
\(121\) 11.7354 20.3263i 0.00881697 0.0152714i
\(122\) 717.093 + 1242.04i 0.532152 + 0.921714i
\(123\) 597.704 501.533i 0.438156 0.367657i
\(124\) 145.863 827.227i 0.105636 0.599090i
\(125\) −670.420 + 1161.20i −0.479714 + 0.830888i
\(126\) −1379.84 502.221i −0.975603 0.355090i
\(127\) 554.789 + 201.927i 0.387634 + 0.141087i 0.528483 0.848944i \(-0.322761\pi\)
−0.140849 + 0.990031i \(0.544983\pi\)
\(128\) −22.2270 126.055i −0.0153485 0.0870455i
\(129\) −466.317 391.287i −0.318271 0.267061i
\(130\) 620.499 + 520.660i 0.418626 + 0.351269i
\(131\) 182.342 + 1034.11i 0.121613 + 0.689701i 0.983262 + 0.182197i \(0.0583208\pi\)
−0.861649 + 0.507504i \(0.830568\pi\)
\(132\) 237.935 + 86.6013i 0.156891 + 0.0571036i
\(133\) 1104.71 + 402.082i 0.720230 + 0.262142i
\(134\) 408.649 707.801i 0.263447 0.456304i
\(135\) −99.4610 + 564.072i −0.0634092 + 0.359611i
\(136\) 68.1037 57.1458i 0.0429400 0.0360310i
\(137\) −897.062 1553.76i −0.559424 0.968952i −0.997545 0.0700351i \(-0.977689\pi\)
0.438120 0.898916i \(-0.355644\pi\)
\(138\) −195.926 + 339.354i −0.120857 + 0.209331i
\(139\) −377.176 2139.07i −0.230156 1.30528i −0.852579 0.522598i \(-0.824963\pi\)
0.622424 0.782680i \(-0.286148\pi\)
\(140\) 394.074 + 682.557i 0.237895 + 0.412047i
\(141\) −161.378 + 58.7370i −0.0963867 + 0.0350819i
\(142\) 947.710 0.560071
\(143\) −2142.36 + 779.756i −1.25282 + 0.455989i
\(144\) −66.5014 + 377.148i −0.0384846 + 0.218257i
\(145\) −1333.86 1119.24i −0.763937 0.641020i
\(146\) −412.525 + 346.149i −0.233841 + 0.196216i
\(147\) −1046.69 −0.587275
\(148\) 558.456 706.098i 0.310168 0.392168i
\(149\) 1672.54 0.919596 0.459798 0.888023i \(-0.347922\pi\)
0.459798 + 0.888023i \(0.347922\pi\)
\(150\) −224.591 + 188.454i −0.122252 + 0.102582i
\(151\) −2444.55 2051.22i −1.31745 1.10547i −0.986839 0.161705i \(-0.948301\pi\)
−0.330611 0.943767i \(-0.607255\pi\)
\(152\) 53.2415 301.948i 0.0284109 0.161126i
\(153\) −249.950 + 90.9744i −0.132074 + 0.0480709i
\(154\) −2218.34 −1.16077
\(155\) 1267.58 461.361i 0.656867 0.239080i
\(156\) 220.749 + 382.348i 0.113295 + 0.196233i
\(157\) 464.913 + 2636.65i 0.236332 + 1.34030i 0.839791 + 0.542910i \(0.182678\pi\)
−0.603459 + 0.797394i \(0.706211\pi\)
\(158\) 389.942 675.399i 0.196342 0.340075i
\(159\) 187.506 + 324.769i 0.0935231 + 0.161987i
\(160\) 157.463 132.128i 0.0778036 0.0652850i
\(161\) 596.138 3380.87i 0.291815 1.65497i
\(162\) 490.159 848.980i 0.237719 0.411742i
\(163\) 3812.06 + 1387.48i 1.83180 + 0.666721i 0.992376 + 0.123245i \(0.0393301\pi\)
0.839425 + 0.543476i \(0.182892\pi\)
\(164\) 1675.29 + 609.757i 0.797674 + 0.290330i
\(165\) 70.6088 + 400.443i 0.0333145 + 0.188936i
\(166\) 752.294 + 631.250i 0.351743 + 0.295148i
\(167\) −2426.63 2036.18i −1.12442 0.943500i −0.125600 0.992081i \(-0.540086\pi\)
−0.998819 + 0.0485813i \(0.984530\pi\)
\(168\) 74.5967 + 423.059i 0.0342575 + 0.194284i
\(169\) −1670.99 608.190i −0.760578 0.276828i
\(170\) 134.159 + 48.8297i 0.0605265 + 0.0220298i
\(171\) −458.671 + 794.441i −0.205119 + 0.355277i
\(172\) 241.530 1369.78i 0.107072 0.607238i
\(173\) 319.217 267.855i 0.140287 0.117715i −0.569944 0.821684i \(-0.693035\pi\)
0.710231 + 0.703969i \(0.248591\pi\)
\(174\) −474.534 821.916i −0.206749 0.358100i
\(175\) 1284.29 2224.46i 0.554762 0.960877i
\(176\) 100.465 + 569.767i 0.0430276 + 0.244022i
\(177\) 310.382 + 537.598i 0.131807 + 0.228296i
\(178\) −1815.64 + 660.841i −0.764541 + 0.278270i
\(179\) −549.140 −0.229300 −0.114650 0.993406i \(-0.536575\pi\)
−0.114650 + 0.993406i \(0.536575\pi\)
\(180\) −577.913 + 210.343i −0.239306 + 0.0871003i
\(181\) 42.3254 240.039i 0.0173813 0.0985744i −0.974883 0.222718i \(-0.928507\pi\)
0.992264 + 0.124143i \(0.0396183\pi\)
\(182\) −2963.04 2486.28i −1.20679 1.01261i
\(183\) −961.648 + 806.919i −0.388454 + 0.325952i
\(184\) −895.354 −0.358730
\(185\) 1430.41 + 209.710i 0.568464 + 0.0833416i
\(186\) 735.242 0.289842
\(187\) −307.827 + 258.297i −0.120377 + 0.101008i
\(188\) −300.598 252.232i −0.116614 0.0978506i
\(189\) 474.952 2693.58i 0.182792 1.03666i
\(190\) 462.681 168.402i 0.176665 0.0643010i
\(191\) −390.752 −0.148030 −0.0740152 0.997257i \(-0.523581\pi\)
−0.0740152 + 0.997257i \(0.523581\pi\)
\(192\) 105.282 38.3194i 0.0395732 0.0144035i
\(193\) 718.659 + 1244.75i 0.268032 + 0.464245i 0.968354 0.249582i \(-0.0802933\pi\)
−0.700321 + 0.713828i \(0.746960\pi\)
\(194\) 342.020 + 1939.69i 0.126575 + 0.717844i
\(195\) −354.498 + 614.009i −0.130185 + 0.225488i
\(196\) −1195.80 2071.19i −0.435789 0.754809i
\(197\) 851.520 714.510i 0.307961 0.258410i −0.475688 0.879614i \(-0.657801\pi\)
0.783649 + 0.621204i \(0.213356\pi\)
\(198\) 300.584 1704.70i 0.107887 0.611857i
\(199\) −680.694 + 1179.00i −0.242478 + 0.419984i −0.961419 0.275086i \(-0.911294\pi\)
0.718942 + 0.695070i \(0.244627\pi\)
\(200\) −629.503 229.120i −0.222563 0.0810062i
\(201\) 672.239 + 244.675i 0.235901 + 0.0858609i
\(202\) 324.482 + 1840.23i 0.113022 + 0.640980i
\(203\) 6369.51 + 5344.65i 2.20223 + 1.84789i
\(204\) 59.6112 + 50.0197i 0.0204589 + 0.0171671i
\(205\) 497.155 + 2819.50i 0.169379 + 0.960599i
\(206\) −68.0602 24.7719i −0.0230193 0.00837835i
\(207\) 2517.28 + 916.214i 0.845231 + 0.307639i
\(208\) −504.395 + 873.638i −0.168142 + 0.291230i
\(209\) −240.650 + 1364.80i −0.0796465 + 0.451698i
\(210\) −528.469 + 443.438i −0.173656 + 0.145715i
\(211\) 231.634 + 401.202i 0.0755751 + 0.130900i 0.901336 0.433120i \(-0.142587\pi\)
−0.825761 + 0.564020i \(0.809254\pi\)
\(212\) −428.437 + 742.075i −0.138798 + 0.240405i
\(213\) 144.046 + 816.928i 0.0463376 + 0.262793i
\(214\) 1052.14 + 1822.35i 0.336087 + 0.582119i
\(215\) 2098.95 763.955i 0.665801 0.242332i
\(216\) −713.340 −0.224707
\(217\) −6053.01 + 2203.12i −1.89357 + 0.689204i
\(218\) −229.553 + 1301.86i −0.0713178 + 0.404463i
\(219\) −361.083 302.985i −0.111414 0.0934877i
\(220\) −711.731 + 597.213i −0.218113 + 0.183019i
\(221\) −700.661 −0.213265
\(222\) 693.541 + 374.068i 0.209673 + 0.113089i
\(223\) 4118.87 1.23686 0.618430 0.785840i \(-0.287769\pi\)
0.618430 + 0.785840i \(0.287769\pi\)
\(224\) −751.928 + 630.942i −0.224287 + 0.188199i
\(225\) 1535.38 + 1288.34i 0.454928 + 0.381730i
\(226\) 345.818 1961.23i 0.101785 0.577254i
\(227\) −1495.46 + 544.302i −0.437256 + 0.159148i −0.551262 0.834332i \(-0.685854\pi\)
0.114007 + 0.993480i \(0.463631\pi\)
\(228\) 268.372 0.0779534
\(229\) −4283.45 + 1559.05i −1.23606 + 0.449890i −0.875670 0.482910i \(-0.839580\pi\)
−0.360394 + 0.932800i \(0.617358\pi\)
\(230\) −718.920 1245.21i −0.206105 0.356985i
\(231\) −337.175 1912.21i −0.0960367 0.544651i
\(232\) 1084.28 1878.02i 0.306837 0.531457i
\(233\) 2185.99 + 3786.25i 0.614631 + 1.06457i 0.990449 + 0.137879i \(0.0440285\pi\)
−0.375818 + 0.926694i \(0.622638\pi\)
\(234\) 2312.10 1940.08i 0.645925 0.541995i
\(235\) 109.426 620.583i 0.0303751 0.172265i
\(236\) −709.202 + 1228.37i −0.195615 + 0.338815i
\(237\) 641.465 + 233.474i 0.175813 + 0.0639906i
\(238\) −640.641 233.174i −0.174482 0.0635061i
\(239\) −1182.15 6704.32i −0.319946 1.81450i −0.543041 0.839706i \(-0.682727\pi\)
0.223095 0.974797i \(-0.428384\pi\)
\(240\) 137.828 + 115.651i 0.0370698 + 0.0311052i
\(241\) 1335.61 + 1120.71i 0.356988 + 0.299548i 0.803589 0.595185i \(-0.202921\pi\)
−0.446601 + 0.894733i \(0.647366\pi\)
\(242\) 8.15131 + 46.2284i 0.00216523 + 0.0122796i
\(243\) 3068.66 + 1116.90i 0.810100 + 0.294852i
\(244\) −2695.39 981.041i −0.707190 0.257396i
\(245\) 1920.33 3326.11i 0.500757 0.867337i
\(246\) −270.977 + 1536.79i −0.0702312 + 0.398301i
\(247\) −1851.08 + 1553.24i −0.476848 + 0.400123i
\(248\) 839.989 + 1454.90i 0.215078 + 0.372526i
\(249\) −429.795 + 744.426i −0.109386 + 0.189462i
\(250\) −465.669 2640.94i −0.117806 0.668111i
\(251\) 26.1715 + 45.3304i 0.00658140 + 0.0113993i 0.869297 0.494290i \(-0.164572\pi\)
−0.862716 + 0.505689i \(0.831238\pi\)
\(252\) 2759.68 1004.44i 0.689855 0.251087i
\(253\) 4046.97 1.00566
\(254\) −1109.58 + 403.853i −0.274099 + 0.0997638i
\(255\) −21.7000 + 123.067i −0.00532905 + 0.0302225i
\(256\) 196.107 + 164.554i 0.0478778 + 0.0401742i
\(257\) −3652.03 + 3064.42i −0.886410 + 0.743786i −0.967487 0.252922i \(-0.918608\pi\)
0.0810770 + 0.996708i \(0.474164\pi\)
\(258\) 1217.47 0.293784
\(259\) −6830.57 1001.42i −1.63873 0.240252i
\(260\) −1620.01 −0.386418
\(261\) −4970.21 + 4170.50i −1.17873 + 0.989071i
\(262\) −1608.79 1349.94i −0.379357 0.318319i
\(263\) 592.257 3358.86i 0.138860 0.787513i −0.833234 0.552921i \(-0.813513\pi\)
0.972094 0.234593i \(-0.0753756\pi\)
\(264\) −475.870 + 173.203i −0.110939 + 0.0403784i
\(265\) −1376.05 −0.318981
\(266\) −2209.42 + 804.163i −0.509279 + 0.185362i
\(267\) −845.614 1464.65i −0.193823 0.335711i
\(268\) 283.845 + 1609.76i 0.0646962 + 0.366910i
\(269\) 405.384 702.146i 0.0918837 0.159147i −0.816420 0.577459i \(-0.804045\pi\)
0.908304 + 0.418311i \(0.137378\pi\)
\(270\) −572.773 992.072i −0.129103 0.223613i
\(271\) 5401.77 4532.63i 1.21083 1.01601i 0.211575 0.977362i \(-0.432141\pi\)
0.999253 0.0386435i \(-0.0123037\pi\)
\(272\) −30.8757 + 175.105i −0.00688278 + 0.0390342i
\(273\) 1692.82 2932.05i 0.375290 0.650021i
\(274\) 3371.85 + 1227.25i 0.743434 + 0.270588i
\(275\) 2845.33 + 1035.62i 0.623928 + 0.227091i
\(276\) −136.089 771.797i −0.0296796 0.168321i
\(277\) −2135.70 1792.07i −0.463256 0.388718i 0.381071 0.924546i \(-0.375555\pi\)
−0.844327 + 0.535828i \(0.820000\pi\)
\(278\) 3327.80 + 2792.36i 0.717944 + 0.602427i
\(279\) −872.819 4950.00i −0.187291 1.06218i
\(280\) −1481.24 539.126i −0.316145 0.115068i
\(281\) −886.217 322.557i −0.188140 0.0684773i 0.246232 0.969211i \(-0.420807\pi\)
−0.434372 + 0.900734i \(0.643030\pi\)
\(282\) 171.735 297.454i 0.0362649 0.0628126i
\(283\) 95.6156 542.263i 0.0200840 0.113902i −0.973118 0.230308i \(-0.926026\pi\)
0.993202 + 0.116407i \(0.0371376\pi\)
\(284\) −1451.98 + 1218.35i −0.303376 + 0.254563i
\(285\) 215.488 + 373.236i 0.0447874 + 0.0775741i
\(286\) 2279.85 3948.82i 0.471365 0.816429i
\(287\) −2374.04 13463.8i −0.488276 2.76915i
\(288\) −382.966 663.317i −0.0783559 0.135716i
\(289\) 4500.66 1638.11i 0.916072 0.333423i
\(290\) 3482.46 0.705162
\(291\) −1620.03 + 589.644i −0.326351 + 0.118782i
\(292\) 187.023 1060.66i 0.0374819 0.212571i
\(293\) −5728.32 4806.63i −1.14216 0.958384i −0.142650 0.989773i \(-0.545562\pi\)
−0.999507 + 0.0313893i \(0.990007\pi\)
\(294\) 1603.62 1345.60i 0.318112 0.266928i
\(295\) −2277.80 −0.449555
\(296\) 52.1379 + 1799.74i 0.0102380 + 0.353405i
\(297\) 3224.28 0.629938
\(298\) −2562.48 + 2150.18i −0.498123 + 0.417974i
\(299\) 5405.55 + 4535.79i 1.04552 + 0.877297i
\(300\) 101.821 577.458i 0.0195955 0.111132i
\(301\) −10023.0 + 3648.08i −1.91933 + 0.698577i
\(302\) 6382.28 1.21609
\(303\) −1536.96 + 559.409i −0.291407 + 0.106063i
\(304\) 306.606 + 531.057i 0.0578456 + 0.100191i
\(305\) −799.874 4536.31i −0.150166 0.851634i
\(306\) 265.991 460.711i 0.0496919 0.0860689i
\(307\) 2128.84 + 3687.26i 0.395763 + 0.685482i 0.993198 0.116435i \(-0.0371467\pi\)
−0.597435 + 0.801917i \(0.703813\pi\)
\(308\) 3398.69 2851.84i 0.628761 0.527593i
\(309\) 11.0087 62.4333i 0.00202674 0.0114942i
\(310\) −1348.93 + 2336.42i −0.247142 + 0.428063i
\(311\) −7544.12 2745.83i −1.37552 0.500650i −0.454705 0.890642i \(-0.650255\pi\)
−0.920818 + 0.389993i \(0.872478\pi\)
\(312\) −829.744 302.002i −0.150561 0.0547997i
\(313\) 788.735 + 4473.14i 0.142434 + 0.807785i 0.969392 + 0.245520i \(0.0789587\pi\)
−0.826957 + 0.562265i \(0.809930\pi\)
\(314\) −4101.90 3441.90i −0.737209 0.618592i
\(315\) 3612.79 + 3031.49i 0.646215 + 0.542239i
\(316\) 270.851 + 1536.07i 0.0482169 + 0.273452i
\(317\) 4129.79 + 1503.12i 0.731710 + 0.266321i 0.680888 0.732387i \(-0.261594\pi\)
0.0508215 + 0.998708i \(0.483816\pi\)
\(318\) −704.791 256.523i −0.124285 0.0452361i
\(319\) −4900.90 + 8488.60i −0.860180 + 1.48988i
\(320\) −71.3882 + 404.862i −0.0124710 + 0.0707265i
\(321\) −1410.96 + 1183.93i −0.245333 + 0.205859i
\(322\) 3433.02 + 5946.17i 0.594146 + 1.02909i
\(323\) −212.955 + 368.848i −0.0366846 + 0.0635395i
\(324\) 340.461 + 1930.85i 0.0583781 + 0.331078i
\(325\) 2639.81 + 4572.29i 0.450555 + 0.780384i
\(326\) −7624.12 + 2774.95i −1.29528 + 0.471443i
\(327\) −1157.10 −0.195681
\(328\) −3350.59 + 1219.51i −0.564041 + 0.205294i
\(329\) −522.535 + 2963.44i −0.0875631 + 0.496595i
\(330\) −622.978 522.741i −0.103921 0.0871998i
\(331\) 7999.26 6712.18i 1.32834 1.11461i 0.343873 0.939016i \(-0.388261\pi\)
0.984463 0.175590i \(-0.0561833\pi\)
\(332\) −1964.10 −0.324681
\(333\) 1695.09 5113.31i 0.278950 0.841464i
\(334\) 6335.47 1.03791
\(335\) −2010.85 + 1687.31i −0.327954 + 0.275186i
\(336\) −658.163 552.264i −0.106862 0.0896681i
\(337\) −388.256 + 2201.91i −0.0627586 + 0.355922i 0.937216 + 0.348750i \(0.113394\pi\)
−0.999974 + 0.00717139i \(0.997717\pi\)
\(338\) 3341.98 1216.38i 0.537810 0.195747i
\(339\) 1743.15 0.279277
\(340\) −268.317 + 97.6595i −0.0427987 + 0.0155774i
\(341\) −3796.73 6576.12i −0.602945 1.04433i
\(342\) −318.589 1806.81i −0.0503723 0.285676i
\(343\) −3909.45 + 6771.37i −0.615425 + 1.06595i
\(344\) 1390.91 + 2409.13i 0.218003 + 0.377592i
\(345\) 964.099 808.975i 0.150450 0.126243i
\(346\) −144.721 + 820.756i −0.0224863 + 0.127526i
\(347\) 1890.99 3275.30i 0.292547 0.506706i −0.681864 0.731479i \(-0.738831\pi\)
0.974411 + 0.224772i \(0.0721638\pi\)
\(348\) 1783.66 + 649.200i 0.274754 + 0.100002i
\(349\) −10444.1 3801.33i −1.60189 0.583039i −0.622074 0.782959i \(-0.713710\pi\)
−0.979812 + 0.199920i \(0.935932\pi\)
\(350\) 892.061 + 5059.13i 0.136236 + 0.772633i
\(351\) 4306.67 + 3613.73i 0.654909 + 0.549534i
\(352\) −886.400 743.778i −0.134220 0.112624i
\(353\) 1520.15 + 8621.20i 0.229205 + 1.29989i 0.854481 + 0.519483i \(0.173875\pi\)
−0.625276 + 0.780404i \(0.715014\pi\)
\(354\) −1166.66 424.628i −0.175161 0.0637534i
\(355\) −2860.27 1041.05i −0.427626 0.155643i
\(356\) 1932.17 3346.61i 0.287654 0.498231i
\(357\) 103.623 587.676i 0.0153622 0.0871235i
\(358\) 841.332 705.961i 0.124206 0.104221i
\(359\) 5907.15 + 10231.5i 0.868432 + 1.50417i 0.863598 + 0.504181i \(0.168205\pi\)
0.00483409 + 0.999988i \(0.498461\pi\)
\(360\) 615.002 1065.21i 0.0900374 0.155949i
\(361\) −935.988 5308.25i −0.136461 0.773910i
\(362\) 243.742 + 422.174i 0.0353889 + 0.0612954i
\(363\) −38.6100 + 14.0529i −0.00558265 + 0.00203192i
\(364\) 7735.95 1.11394
\(365\) 1625.28 591.553i 0.233071 0.0848309i
\(366\) 435.976 2472.54i 0.0622646 0.353120i
\(367\) −7991.12 6705.35i −1.13660 0.953723i −0.137280 0.990532i \(-0.543836\pi\)
−0.999322 + 0.0368093i \(0.988281\pi\)
\(368\) 1371.76 1151.04i 0.194315 0.163050i
\(369\) 10668.1 1.50503
\(370\) −2461.11 + 1517.61i −0.345803 + 0.213234i
\(371\) 6570.97 0.919536
\(372\) −1126.46 + 945.209i −0.157000 + 0.131739i
\(373\) −121.179 101.681i −0.0168215 0.0141149i 0.634338 0.773056i \(-0.281273\pi\)
−0.651160 + 0.758941i \(0.725717\pi\)
\(374\) 139.557 791.469i 0.0192950 0.109428i
\(375\) 2205.72 802.816i 0.303741 0.110553i
\(376\) 784.807 0.107642
\(377\) −16060.0 + 5845.38i −2.19399 + 0.798547i
\(378\) 2735.14 + 4737.40i 0.372170 + 0.644617i
\(379\) 1538.07 + 8722.85i 0.208458 + 1.18222i 0.891905 + 0.452223i \(0.149369\pi\)
−0.683447 + 0.730000i \(0.739520\pi\)
\(380\) −492.375 + 852.819i −0.0664693 + 0.115128i
\(381\) −516.772 895.076i −0.0694883 0.120357i
\(382\) 598.666 502.341i 0.0801844 0.0672827i
\(383\) 686.147 3891.33i 0.0915417 0.519159i −0.904211 0.427087i \(-0.859540\pi\)
0.995752 0.0920721i \(-0.0293490\pi\)
\(384\) −112.038 + 194.056i −0.0148892 + 0.0257888i
\(385\) 6695.14 + 2436.83i 0.886275 + 0.322578i
\(386\) −2701.28 983.184i −0.356195 0.129644i
\(387\) −1445.28 8196.58i −0.189839 1.07663i
\(388\) −3017.63 2532.09i −0.394837 0.331308i
\(389\) 7237.73 + 6073.18i 0.943361 + 0.791574i 0.978167 0.207820i \(-0.0666368\pi\)
−0.0348058 + 0.999394i \(0.511081\pi\)
\(390\) −246.232 1396.45i −0.0319704 0.181313i
\(391\) 1168.74 + 425.386i 0.151165 + 0.0550197i
\(392\) 4494.76 + 1635.96i 0.579131 + 0.210787i
\(393\) 919.123 1591.97i 0.117974 0.204336i
\(394\) −386.048 + 2189.39i −0.0493625 + 0.279949i
\(395\) −1918.80 + 1610.06i −0.244418 + 0.205091i
\(396\) 1731.00 + 2998.17i 0.219661 + 0.380465i
\(397\) −5954.74 + 10313.9i −0.752796 + 1.30388i 0.193667 + 0.981067i \(0.437962\pi\)
−0.946463 + 0.322814i \(0.895371\pi\)
\(398\) −472.805 2681.41i −0.0595466 0.337706i
\(399\) −1029.01 1782.30i −0.129110 0.223625i
\(400\) 1259.01 458.240i 0.157376 0.0572801i
\(401\) 12438.1 1.54895 0.774476 0.632603i \(-0.218013\pi\)
0.774476 + 0.632603i \(0.218013\pi\)
\(402\) −1344.48 + 489.350i −0.166807 + 0.0607128i
\(403\) 2299.14 13039.1i 0.284189 1.61172i
\(404\) −2862.89 2402.25i −0.352559 0.295832i
\(405\) −2411.94 + 2023.86i −0.295927 + 0.248312i
\(406\) −16629.6 −2.03279
\(407\) −235.662 8134.79i −0.0287010 0.990728i
\(408\) −155.634 −0.0188849
\(409\) 4086.00 3428.56i 0.493985 0.414502i −0.361467 0.932385i \(-0.617724\pi\)
0.855452 + 0.517883i \(0.173280\pi\)
\(410\) −4386.37 3680.60i −0.528359 0.443346i
\(411\) −545.393 + 3093.08i −0.0654556 + 0.371217i
\(412\) 136.120 49.5438i 0.0162771 0.00592439i
\(413\) 10877.1 1.29595
\(414\) −5034.56 + 1832.43i −0.597669 + 0.217534i
\(415\) −1577.07 2731.56i −0.186542 0.323101i
\(416\) −350.349 1986.93i −0.0412916 0.234176i
\(417\) −1901.21 + 3293.00i −0.223268 + 0.386712i
\(418\) −1385.85 2400.36i −0.162163 0.280874i
\(419\) −1882.73 + 1579.80i −0.219516 + 0.184196i −0.745914 0.666043i \(-0.767987\pi\)
0.526397 + 0.850239i \(0.323542\pi\)
\(420\) 239.588 1358.77i 0.0278350 0.157860i
\(421\) 2578.33 4465.81i 0.298481 0.516984i −0.677308 0.735700i \(-0.736854\pi\)
0.975789 + 0.218716i \(0.0701869\pi\)
\(422\) −870.660 316.894i −0.100434 0.0365549i
\(423\) −2206.48 803.091i −0.253623 0.0923112i
\(424\) −297.589 1687.71i −0.0340854 0.193308i
\(425\) 712.857 + 598.158i 0.0813616 + 0.0682705i
\(426\) −1270.91 1066.42i −0.144545 0.121287i
\(427\) 3819.60 + 21662.0i 0.432888 + 2.45503i
\(428\) −3954.74 1439.41i −0.446635 0.162562i
\(429\) 3750.42 + 1365.04i 0.422079 + 0.153624i
\(430\) −2233.66 + 3868.81i −0.250503 + 0.433885i
\(431\) −810.375 + 4595.86i −0.0905670 + 0.513631i 0.905449 + 0.424455i \(0.139534\pi\)
−0.996016 + 0.0891757i \(0.971577\pi\)
\(432\) 1092.90 917.053i 0.121718 0.102134i
\(433\) −6442.61 11158.9i −0.715040 1.23849i −0.962944 0.269701i \(-0.913075\pi\)
0.247904 0.968785i \(-0.420258\pi\)
\(434\) 6441.48 11157.0i 0.712445 1.23399i
\(435\) 529.314 + 3001.89i 0.0583417 + 0.330872i
\(436\) −1321.94 2289.67i −0.145205 0.251503i
\(437\) 4030.70 1467.06i 0.441224 0.160592i
\(438\) 942.721 0.102842
\(439\) −4320.21 + 1572.43i −0.469687 + 0.170952i −0.566010 0.824398i \(-0.691514\pi\)
0.0963237 + 0.995350i \(0.469292\pi\)
\(440\) 322.672 1829.97i 0.0349609 0.198273i
\(441\) −10962.9 9198.95i −1.18377 0.993300i
\(442\) 1073.48 900.752i 0.115520 0.0969331i
\(443\) −13471.0 −1.44475 −0.722377 0.691499i \(-0.756951\pi\)
−0.722377 + 0.691499i \(0.756951\pi\)
\(444\) −1543.46 + 318.494i −0.164976 + 0.0340429i
\(445\) 6205.70 0.661075
\(446\) −6310.47 + 5295.11i −0.669976 + 0.562177i
\(447\) −2242.94 1882.05i −0.237332 0.199145i
\(448\) 340.896 1933.32i 0.0359505 0.203886i
\(449\) −15847.5 + 5768.02i −1.66568 + 0.606258i −0.991240 0.132072i \(-0.957837\pi\)
−0.674440 + 0.738330i \(0.735615\pi\)
\(450\) −4008.60 −0.419927
\(451\) 15144.6 5512.17i 1.58122 0.575517i
\(452\) 1991.49 + 3449.36i 0.207238 + 0.358948i
\(453\) 970.070 + 5501.54i 0.100613 + 0.570607i
\(454\) 1591.43 2756.44i 0.164515 0.284948i
\(455\) 6211.54 + 10758.7i 0.640003 + 1.10852i
\(456\) −411.170 + 345.013i −0.0422254 + 0.0354313i
\(457\) 1579.32 8956.77i 0.161658 0.916806i −0.790786 0.612092i \(-0.790328\pi\)
0.952444 0.304714i \(-0.0985608\pi\)
\(458\) 4558.36 7895.30i 0.465061 0.805510i
\(459\) 931.150 + 338.911i 0.0946892 + 0.0344641i
\(460\) 2702.26 + 983.541i 0.273898 + 0.0996909i
\(461\) −1963.40 11135.0i −0.198361 1.12496i −0.907550 0.419945i \(-0.862050\pi\)
0.709188 0.705019i \(-0.249062\pi\)
\(462\) 2974.88 + 2496.22i 0.299575 + 0.251374i
\(463\) −437.711 367.283i −0.0439356 0.0368663i 0.620555 0.784163i \(-0.286907\pi\)
−0.664491 + 0.747296i \(0.731352\pi\)
\(464\) 753.130 + 4271.21i 0.0753517 + 0.427341i
\(465\) −2219.03 807.659i −0.221301 0.0805469i
\(466\) −8216.64 2990.61i −0.816799 0.297291i
\(467\) 765.274 1325.49i 0.0758301 0.131342i −0.825617 0.564231i \(-0.809173\pi\)
0.901447 + 0.432890i \(0.142506\pi\)
\(468\) −1048.22 + 5944.74i −0.103534 + 0.587171i
\(469\) 9602.34 8057.32i 0.945404 0.793288i
\(470\) 630.157 + 1091.46i 0.0618446 + 0.107118i
\(471\) 2343.46 4059.00i 0.229259 0.397089i
\(472\) −492.606 2793.71i −0.0480382 0.272438i
\(473\) −6286.89 10889.2i −0.611145 1.05853i
\(474\) −1282.93 + 466.948i −0.124318 + 0.0452482i
\(475\) 3209.31 0.310007
\(476\) 1281.28 466.349i 0.123377 0.0449056i
\(477\) −890.365 + 5049.51i −0.0854655 + 0.484699i
\(478\) 10430.1 + 8751.87i 0.998034 + 0.837450i
\(479\) −2186.16 + 1834.41i −0.208535 + 0.174982i −0.741073 0.671424i \(-0.765683\pi\)
0.532538 + 0.846406i \(0.321238\pi\)
\(480\) −359.843 −0.0342177
\(481\) 8802.58 11129.8i 0.834435 1.05504i
\(482\) −3487.02 −0.329522
\(483\) −4603.82 + 3863.06i −0.433708 + 0.363924i
\(484\) −71.9186 60.3469i −0.00675419 0.00566744i
\(485\) 1098.49 6229.87i 0.102845 0.583265i
\(486\) −6137.31 + 2233.80i −0.572828 + 0.208492i
\(487\) −9600.34 −0.893292 −0.446646 0.894711i \(-0.647382\pi\)
−0.446646 + 0.894711i \(0.647382\pi\)
\(488\) 5390.77 1962.08i 0.500059 0.182007i
\(489\) −3550.84 6150.23i −0.328373 0.568759i
\(490\) 1333.85 + 7564.63i 0.122974 + 0.697419i
\(491\) −4431.50 + 7675.59i −0.407314 + 0.705488i −0.994588 0.103900i \(-0.966868\pi\)
0.587274 + 0.809388i \(0.300201\pi\)
\(492\) −1560.50 2702.86i −0.142993 0.247671i
\(493\) −2307.60 + 1936.31i −0.210810 + 0.176890i
\(494\) 839.212 4759.41i 0.0764331 0.433473i
\(495\) −2779.79 + 4814.74i −0.252409 + 0.437185i
\(496\) −3157.32 1149.17i −0.285823 0.104031i
\(497\) 13658.5 + 4971.29i 1.23273 + 0.448678i
\(498\) −298.532 1693.06i −0.0268625 0.152345i
\(499\) 9865.86 + 8278.44i 0.885083 + 0.742673i 0.967218 0.253948i \(-0.0817293\pi\)
−0.0821346 + 0.996621i \(0.526174\pi\)
\(500\) 4108.57 + 3447.50i 0.367482 + 0.308354i
\(501\) 962.956 + 5461.19i 0.0858716 + 0.487002i
\(502\) −98.3728 35.8048i −0.00874620 0.00318336i
\(503\) −4582.22 1667.79i −0.406185 0.147839i 0.130844 0.991403i \(-0.458231\pi\)
−0.537029 + 0.843564i \(0.680453\pi\)
\(504\) −2936.79 + 5086.67i −0.259554 + 0.449560i
\(505\) 1042.16 5910.41i 0.0918331 0.520812i
\(506\) −6200.32 + 5202.69i −0.544739 + 0.457090i
\(507\) 1556.48 + 2695.91i 0.136343 + 0.236153i
\(508\) 1180.79 2045.19i 0.103128 0.178623i
\(509\) 406.134 + 2303.30i 0.0353666 + 0.200574i 0.997371 0.0724585i \(-0.0230845\pi\)
−0.962005 + 0.273032i \(0.911973\pi\)
\(510\) −124.965 216.446i −0.0108501 0.0187930i
\(511\) −7761.11 + 2824.81i −0.671881 + 0.244545i
\(512\) −512.000 −0.0441942
\(513\) 3211.32 1168.82i 0.276380 0.100594i
\(514\) 1655.70 9389.92i 0.142081 0.805781i
\(515\) 178.200 + 149.528i 0.0152474 + 0.0127941i
\(516\) −1865.27 + 1565.15i −0.159135 + 0.133530i
\(517\) −3547.30 −0.301761
\(518\) 11752.4 7246.95i 0.996858 0.614696i
\(519\) −729.490 −0.0616976
\(520\) 2482.00 2082.64i 0.209313 0.175634i
\(521\) 11502.5 + 9651.76i 0.967244 + 0.811614i 0.982116 0.188275i \(-0.0602896\pi\)
−0.0148720 + 0.999889i \(0.504734\pi\)
\(522\) 2253.31 12779.2i 0.188936 1.07151i
\(523\) −13174.7 + 4795.20i −1.10151 + 0.400917i −0.827873 0.560916i \(-0.810449\pi\)
−0.273637 + 0.961833i \(0.588227\pi\)
\(524\) 4200.26 0.350170
\(525\) −4225.39 + 1537.92i −0.351259 + 0.127848i
\(526\) 3410.67 + 5907.46i 0.282723 + 0.489691i
\(527\) −405.238 2298.22i −0.0334961 0.189966i
\(528\) 506.411 877.129i 0.0417399 0.0722957i
\(529\) −179.455 310.825i −0.0147493 0.0255466i
\(530\) 2108.23 1769.01i 0.172784 0.144983i
\(531\) −1473.84 + 8358.57i −0.120451 + 0.683109i
\(532\) 2351.22 4072.43i 0.191613 0.331884i
\(533\) 26406.6 + 9611.21i 2.14596 + 0.781065i
\(534\) 3178.47 + 1156.87i 0.257576 + 0.0937502i
\(535\) −1173.60 6655.79i −0.0948392 0.537860i
\(536\) −2504.35 2101.40i −0.201812 0.169341i
\(537\) 736.418 + 617.928i 0.0591784 + 0.0496566i
\(538\) 281.577 + 1596.90i 0.0225644 + 0.127969i
\(539\) −20316.2 7394.48i −1.62352 0.590914i
\(540\) 2152.92 + 783.600i 0.171569 + 0.0624459i
\(541\) 1658.35 2872.35i 0.131789 0.228266i −0.792577 0.609772i \(-0.791261\pi\)
0.924366 + 0.381506i \(0.124594\pi\)
\(542\) −2448.97 + 13888.8i −0.194081 + 1.10069i
\(543\) −326.867 + 274.274i −0.0258328 + 0.0216763i
\(544\) −177.806 307.969i −0.0140136 0.0242722i
\(545\) 2122.89 3676.96i 0.166853 0.288997i
\(546\) 1175.82 + 6668.40i 0.0921620 + 0.522676i
\(547\) 5559.62 + 9629.54i 0.434574 + 0.752704i 0.997261 0.0739659i \(-0.0235656\pi\)
−0.562687 + 0.826670i \(0.690232\pi\)
\(548\) −6743.70 + 2454.51i −0.525687 + 0.191334i
\(549\) −17163.9 −1.33431
\(550\) −5690.67 + 2071.23i −0.441184 + 0.160578i
\(551\) −1804.02 + 10231.1i −0.139480 + 0.791032i
\(552\) 1200.70 + 1007.51i 0.0925821 + 0.0776856i
\(553\) 9162.75 7688.46i 0.704593 0.591224i
\(554\) 5575.92 0.427614
\(555\) −1682.25 1890.82i −0.128663 0.144614i
\(556\) −8688.28 −0.662707
\(557\) 2325.64 1951.45i 0.176913 0.148448i −0.550031 0.835144i \(-0.685384\pi\)
0.726944 + 0.686696i \(0.240940\pi\)
\(558\) 7700.84 + 6461.77i 0.584234 + 0.490230i
\(559\) 3807.08 21591.0i 0.288054 1.63364i
\(560\) 2962.47 1078.25i 0.223549 0.0813650i
\(561\) 703.460 0.0529414
\(562\) 1772.43 645.113i 0.133035 0.0484207i
\(563\) 5184.35 + 8979.57i 0.388090 + 0.672191i 0.992193 0.124715i \(-0.0398017\pi\)
−0.604103 + 0.796906i \(0.706468\pi\)
\(564\) 119.286 + 676.505i 0.00890577 + 0.0505071i
\(565\) −3198.11 + 5539.30i −0.238134 + 0.412460i
\(566\) 550.629 + 953.717i 0.0408916 + 0.0708263i
\(567\) 11517.6 9664.44i 0.853078 0.715817i
\(568\) 658.272 3733.25i 0.0486276 0.275781i
\(569\) −7870.69 + 13632.4i −0.579888 + 1.00440i 0.415603 + 0.909546i \(0.363571\pi\)
−0.995492 + 0.0948502i \(0.969763\pi\)
\(570\) −809.970 294.805i −0.0595192 0.0216632i
\(571\) −5552.33 2020.88i −0.406931 0.148111i 0.130441 0.991456i \(-0.458361\pi\)
−0.537372 + 0.843345i \(0.680583\pi\)
\(572\) 1583.57 + 8980.87i 0.115756 + 0.656484i
\(573\) 524.013 + 439.699i 0.0382041 + 0.0320570i
\(574\) 20946.0 + 17575.8i 1.52312 + 1.27805i
\(575\) −1627.41 9229.49i −0.118031 0.669385i
\(576\) 1439.48 + 523.929i 0.104129 + 0.0378999i
\(577\) −10197.3 3711.52i −0.735737 0.267786i −0.0531457 0.998587i \(-0.516925\pi\)
−0.682591 + 0.730800i \(0.739147\pi\)
\(578\) −4789.50 + 8295.66i −0.344666 + 0.596979i
\(579\) 436.928 2477.94i 0.0313612 0.177858i
\(580\) −5335.43 + 4476.96i −0.381969 + 0.320510i
\(581\) 7530.89 + 13043.9i 0.537752 + 0.931413i
\(582\) 1724.01 2986.06i 0.122787 0.212674i
\(583\) 1345.10 + 7628.42i 0.0955543 + 0.541916i
\(584\) 1077.03 + 1865.46i 0.0763144 + 0.132180i
\(585\) −9109.27 + 3315.50i −0.643798 + 0.234323i
\(586\) 14955.6 1.05428
\(587\) −25249.8 + 9190.19i −1.77542 + 0.646201i −0.775532 + 0.631308i \(0.782518\pi\)
−0.999889 + 0.0148928i \(0.995259\pi\)
\(588\) −727.022 + 4123.15i −0.0509896 + 0.289176i
\(589\) −6165.35 5173.34i −0.431305 0.361908i
\(590\) 3489.79 2928.28i 0.243513 0.204331i
\(591\) −1945.93 −0.135440
\(592\) −2393.58 2690.34i −0.166175 0.186777i
\(593\) −9298.24 −0.643901 −0.321950 0.946757i \(-0.604338\pi\)
−0.321950 + 0.946757i \(0.604338\pi\)
\(594\) −4939.88 + 4145.05i −0.341222 + 0.286319i
\(595\) 1677.37 + 1407.48i 0.115572 + 0.0969766i
\(596\) 1161.73 6588.52i 0.0798431 0.452813i
\(597\) 2239.52 815.118i 0.153530 0.0558803i
\(598\) −14112.9 −0.965081
\(599\) 9123.80 3320.79i 0.622351 0.226517i −0.0115475 0.999933i \(-0.503676\pi\)
0.633899 + 0.773416i \(0.281454\pi\)
\(600\) 586.366 + 1015.62i 0.0398972 + 0.0691039i
\(601\) 4280.93 + 24278.4i 0.290554 + 1.64781i 0.684745 + 0.728783i \(0.259914\pi\)
−0.394191 + 0.919028i \(0.628975\pi\)
\(602\) 10666.3 18474.5i 0.722134 1.25077i
\(603\) 4890.59 + 8470.75i 0.330282 + 0.572066i
\(604\) −9778.22 + 8204.90i −0.658725 + 0.552736i
\(605\) 26.1802 148.475i 0.00175930 0.00997750i
\(606\) 1635.60 2832.94i 0.109640 0.189902i
\(607\) 17930.4 + 6526.13i 1.19897 + 0.436388i 0.862863 0.505438i \(-0.168669\pi\)
0.336102 + 0.941826i \(0.390891\pi\)
\(608\) −1152.46 419.461i −0.0768725 0.0279793i
\(609\) −2527.61 14334.8i −0.168184 0.953816i
\(610\) 7057.24 + 5921.73i 0.468425 + 0.393056i
\(611\) −4738.14 3975.77i −0.313723 0.263245i
\(612\) 184.756 + 1047.80i 0.0122031 + 0.0692073i
\(613\) −12261.9 4462.96i −0.807916 0.294057i −0.0951532 0.995463i \(-0.530334\pi\)
−0.712763 + 0.701405i \(0.752556\pi\)
\(614\) −8001.82 2912.43i −0.525940 0.191427i
\(615\) 2505.98 4340.49i 0.164311 0.284594i
\(616\) −1540.84 + 8738.55i −0.100783 + 0.571569i
\(617\) 6542.28 5489.63i 0.426876 0.358191i −0.403896 0.914805i \(-0.632344\pi\)
0.830771 + 0.556614i \(0.187900\pi\)
\(618\) 63.3964 + 109.806i 0.00412650 + 0.00714731i
\(619\) 10288.3 17819.8i 0.668048 1.15709i −0.310402 0.950605i \(-0.600464\pi\)
0.978449 0.206487i \(-0.0662031\pi\)
\(620\) −936.957 5313.75i −0.0606921 0.344202i
\(621\) −4989.78 8642.55i −0.322436 0.558476i
\(622\) 15088.2 5491.67i 0.972642 0.354013i
\(623\) −29633.8 −1.90570
\(624\) 1659.49 604.004i 0.106463 0.0387492i
\(625\) 321.989 1826.09i 0.0206073 0.116870i
\(626\) −6958.96 5839.26i −0.444307 0.372818i
\(627\) 1858.48 1559.45i 0.118374 0.0993275i
\(628\) 10709.3 0.680490
\(629\) 787.007 2374.04i 0.0498888 0.150492i
\(630\) −9432.33 −0.596497
\(631\) 21657.2 18172.6i 1.36634 1.14650i 0.392374 0.919806i \(-0.371654\pi\)
0.973967 0.226691i \(-0.0727907\pi\)
\(632\) −2389.70 2005.20i −0.150407 0.126206i
\(633\) 140.828 798.677i 0.00884269 0.0501494i
\(634\) −8259.58 + 3006.24i −0.517397 + 0.188317i
\(635\) 3792.43 0.237005
\(636\) 1409.58 513.046i 0.0878829 0.0319868i
\(637\) −18848.7 32646.9i −1.17239 2.03064i
\(638\) −3404.13 19305.8i −0.211239 1.19800i
\(639\) −5670.95 + 9822.38i −0.351079 + 0.608086i
\(640\) −411.108 712.060i −0.0253914 0.0439791i
\(641\) 13333.8 11188.4i 0.821614 0.689416i −0.131735 0.991285i \(-0.542055\pi\)
0.953349 + 0.301869i \(0.0976105\pi\)
\(642\) 639.675 3627.78i 0.0393239 0.223017i
\(643\) 1568.42 2716.58i 0.0961934 0.166612i −0.813913 0.580987i \(-0.802667\pi\)
0.910106 + 0.414375i \(0.136000\pi\)
\(644\) −12904.0 4696.65i −0.789576 0.287382i
\(645\) −3674.42 1337.38i −0.224311 0.0816423i
\(646\) −147.917 838.878i −0.00900884 0.0510916i
\(647\) −6898.89 5788.85i −0.419201 0.351752i 0.408658 0.912688i \(-0.365997\pi\)
−0.827859 + 0.560936i \(0.810441\pi\)
\(648\) −3003.87 2520.54i −0.182104 0.152803i
\(649\) 2226.57 + 12627.5i 0.134669 + 0.763747i
\(650\) −9922.45 3611.47i −0.598754 0.217929i
\(651\) 10596.4 + 3856.78i 0.637951 + 0.232195i
\(652\) 8113.42 14052.9i 0.487340 0.844098i
\(653\) −4934.11 + 27982.7i −0.295692 + 1.67695i 0.368686 + 0.929554i \(0.379808\pi\)
−0.664377 + 0.747397i \(0.731303\pi\)
\(654\) 1772.77 1487.53i 0.105995 0.0889406i
\(655\) 3372.58 + 5841.48i 0.201187 + 0.348466i
\(656\) 3565.62 6175.84i 0.212217 0.367570i
\(657\) −1119.12 6346.85i −0.0664552 0.376886i
\(658\) −3009.16 5212.01i −0.178281 0.308793i
\(659\) −2230.82 + 811.954i −0.131867 + 0.0479958i −0.407111 0.913379i \(-0.633464\pi\)
0.275244 + 0.961375i \(0.411242\pi\)
\(660\) 1626.48 0.0959252
\(661\) 21000.0 7643.38i 1.23571 0.449762i 0.360162 0.932890i \(-0.382721\pi\)
0.875550 + 0.483127i \(0.160499\pi\)
\(662\) −3626.57 + 20567.3i −0.212916 + 1.20751i
\(663\) 939.613 + 788.429i 0.0550400 + 0.0461841i
\(664\) 3009.18 2525.00i 0.175872 0.147574i
\(665\) 7551.59 0.440358
\(666\) 3976.52 + 10013.2i 0.231362 + 0.582589i
\(667\) 30337.8 1.76115
\(668\) −9706.51 + 8144.73i −0.562210 + 0.471750i
\(669\) −5523.56 4634.82i −0.319212 0.267851i
\(670\) 911.647 5170.21i 0.0525672 0.298123i
\(671\) −24366.1 + 8868.55i −1.40185 + 0.510233i
\(672\) 1718.34 0.0986405
\(673\) −8156.02 + 2968.55i −0.467149 + 0.170028i −0.564861 0.825186i \(-0.691070\pi\)
0.0977113 + 0.995215i \(0.468848\pi\)
\(674\) −2235.88 3872.65i −0.127779 0.221319i
\(675\) −1296.58 7353.26i −0.0739338 0.419300i
\(676\) −3556.46 + 6159.97i −0.202347 + 0.350476i
\(677\) −12205.3 21140.3i −0.692894 1.20013i −0.970886 0.239544i \(-0.923002\pi\)
0.277992 0.960583i \(-0.410331\pi\)
\(678\) −2670.66 + 2240.95i −0.151278 + 0.126937i
\(679\) −5245.59 + 29749.2i −0.296476 + 1.68140i
\(680\) 285.537 494.565i 0.0161027 0.0278907i
\(681\) 2617.95 + 952.856i 0.147313 + 0.0536175i
\(682\) 14271.0 + 5194.23i 0.801269 + 0.291638i
\(683\) −3686.65 20908.0i −0.206539 1.17134i −0.895000 0.446066i \(-0.852825\pi\)
0.688462 0.725273i \(-0.258286\pi\)
\(684\) 2810.90 + 2358.62i 0.157131 + 0.131848i
\(685\) −8828.40 7407.91i −0.492432 0.413200i
\(686\) −2715.48 15400.2i −0.151133 0.857120i
\(687\) 7498.62 + 2729.27i 0.416434 + 0.151570i
\(688\) −5228.13 1902.88i −0.289710 0.105446i
\(689\) −6753.18 + 11696.9i −0.373405 + 0.646756i
\(690\) −437.087 + 2478.84i −0.0241154 + 0.136765i
\(691\) 13928.6 11687.5i 0.766815 0.643434i −0.173076 0.984908i \(-0.555371\pi\)
0.939891 + 0.341475i \(0.110926\pi\)
\(692\) −833.417 1443.52i −0.0457829 0.0792983i
\(693\) 13274.2 22991.6i 0.727627 1.26029i
\(694\) 1313.47 + 7449.06i 0.0718424 + 0.407439i
\(695\) −6976.21 12083.2i −0.380752 0.659482i
\(696\) −3567.33 + 1298.40i −0.194280 + 0.0707123i
\(697\) 4953.04 0.269168
\(698\) 20888.1 7602.66i 1.13270 0.412271i
\(699\) 1329.03 7537.32i 0.0719151 0.407851i
\(700\) −7870.60 6604.22i −0.424973 0.356594i
\(701\) −11558.7 + 9698.92i −0.622777 + 0.522572i −0.898675 0.438615i \(-0.855469\pi\)
0.275898 + 0.961187i \(0.411025\pi\)
\(702\) −11243.9 −0.604522
\(703\) −3183.63 8016.65i −0.170801 0.430091i
\(704\) 2314.23 0.123893
\(705\) −845.064 + 709.093i −0.0451446 + 0.0378808i
\(706\) −13412.2 11254.2i −0.714978 0.599938i
\(707\) −4976.60 + 28223.7i −0.264730 + 1.50136i
\(708\) 2333.31 849.256i 0.123858 0.0450805i
\(709\) 20171.3 1.06848 0.534238 0.845334i \(-0.320599\pi\)
0.534238 + 0.845334i \(0.320599\pi\)
\(710\) 5720.54 2082.11i 0.302378 0.110056i
\(711\) 4666.71 + 8082.97i 0.246153 + 0.426350i
\(712\) 1342.07 + 7611.26i 0.0706408 + 0.400624i
\(713\) −11751.4 + 20354.0i −0.617240 + 1.06909i
\(714\) 596.742 + 1033.59i 0.0312780 + 0.0541751i
\(715\) −11218.5 + 9413.48i −0.586783 + 0.492370i
\(716\) −381.429 + 2163.19i −0.0199088 + 0.112908i
\(717\) −5958.82 + 10321.0i −0.310371 + 0.537579i
\(718\) −22203.6 8081.45i −1.15408 0.420052i
\(719\) −19103.5 6953.12i −0.990878 0.360650i −0.204818 0.978800i \(-0.565660\pi\)
−0.786060 + 0.618150i \(0.787882\pi\)
\(720\) 427.176 + 2422.64i 0.0221110 + 0.125398i
\(721\) −850.950 714.032i −0.0439543 0.0368820i
\(722\) 8258.17 + 6929.43i 0.425675 + 0.357184i
\(723\) −530.008 3005.82i −0.0272631 0.154617i
\(724\) −916.170 333.459i −0.0470293 0.0171173i
\(725\) 21329.8 + 7763.43i 1.09265 + 0.397692i
\(726\) 41.0879 71.1664i 0.00210044 0.00363806i
\(727\) 2228.29 12637.3i 0.113676 0.644691i −0.873721 0.486428i \(-0.838300\pi\)
0.987397 0.158263i \(-0.0505893\pi\)
\(728\) −11852.2 + 9945.14i −0.603393 + 0.506307i
\(729\) 3758.77 + 6510.38i 0.190965 + 0.330761i
\(730\) −1729.58 + 2995.73i −0.0876915 + 0.151886i
\(731\) −671.023 3805.56i −0.0339517 0.192550i
\(732\) 2510.69 + 4348.64i 0.126773 + 0.219577i
\(733\) 17803.4 6479.92i 0.897114 0.326523i 0.148018 0.988985i \(-0.452711\pi\)
0.749096 + 0.662462i \(0.230488\pi\)
\(734\) 20863.3 1.04916
\(735\) −6317.99 + 2299.56i −0.317065 + 0.115402i
\(736\) −621.906 + 3527.01i −0.0311464 + 0.176640i
\(737\) 11319.6 + 9498.25i 0.565756 + 0.474726i
\(738\) −16344.4 + 13714.6i −0.815240 + 0.684067i
\(739\) 23856.0 1.18749 0.593747 0.804652i \(-0.297648\pi\)
0.593747 + 0.804652i \(0.297648\pi\)
\(740\) 1819.65 5489.05i 0.0903941 0.272678i
\(741\) 4230.18 0.209716
\(742\) −10067.3 + 8447.48i −0.498090 + 0.417947i
\(743\) 22875.8 + 19195.1i 1.12952 + 0.947779i 0.999046 0.0436727i \(-0.0139059\pi\)
0.130473 + 0.991452i \(0.458350\pi\)
\(744\) 510.694 2896.29i 0.0251653 0.142719i
\(745\) 10095.7 3674.55i 0.496483 0.180705i
\(746\) 316.376 0.0155273
\(747\) −11044.1 + 4019.72i −0.540940 + 0.196886i
\(748\) 803.679 + 1392.01i 0.0392853 + 0.0680442i
\(749\) 5604.21 + 31783.1i 0.273396 + 1.55051i
\(750\) −2347.28 + 4065.60i −0.114281 + 0.197940i
\(751\) 13684.5 + 23702.3i 0.664919 + 1.15167i 0.979307 + 0.202380i \(0.0648675\pi\)
−0.314388 + 0.949295i \(0.601799\pi\)
\(752\) −1202.39 + 1008.93i −0.0583069 + 0.0489253i
\(753\) 15.9117 90.2397i 0.000770059 0.00436722i
\(754\) 17090.7 29602.0i 0.825475 1.42976i
\(755\) −19262.3 7010.89i −0.928511 0.337950i
\(756\) −10280.8 3741.89i −0.494586 0.180015i
\(757\) 5211.38 + 29555.2i 0.250212 + 1.41902i 0.808069 + 0.589088i \(0.200513\pi\)
−0.557857 + 0.829937i \(0.688376\pi\)
\(758\) −13570.3 11386.9i −0.650260 0.545633i
\(759\) −5427.14 4553.92i −0.259543 0.217782i
\(760\) −342.000 1939.58i −0.0163232 0.0925736i
\(761\) 13026.2 + 4741.15i 0.620499 + 0.225843i 0.633091 0.774078i \(-0.281786\pi\)
−0.0125919 + 0.999921i \(0.504008\pi\)
\(762\) 1942.43 + 706.986i 0.0923448 + 0.0336108i
\(763\) −10137.4 + 17558.4i −0.480992 + 0.833102i
\(764\) −271.413 + 1539.26i −0.0128526 + 0.0728907i
\(765\) −1308.87 + 1098.27i −0.0618593 + 0.0519061i
\(766\) 3951.36 + 6843.96i 0.186382 + 0.322823i
\(767\) −11178.7 + 19362.1i −0.526257 + 0.911504i
\(768\) −77.8211 441.345i −0.00365641 0.0207366i
\(769\) 4097.19 + 7096.54i 0.192130 + 0.332780i 0.945956 0.324295i \(-0.105127\pi\)
−0.753826 + 0.657075i \(0.771794\pi\)
\(770\) −13390.3 + 4873.66i −0.626691 + 0.228097i
\(771\) 8345.79 0.389839
\(772\) 5402.55 1966.37i 0.251868 0.0916724i
\(773\) 4027.62 22841.8i 0.187404 1.06282i −0.735423 0.677609i \(-0.763016\pi\)
0.922827 0.385214i \(-0.125873\pi\)
\(774\) 12751.6 + 10699.9i 0.592180 + 0.496898i
\(775\) −13470.7 + 11303.2i −0.624362 + 0.523902i
\(776\) 7878.46 0.364459
\(777\) 8033.19 + 9029.14i 0.370900 + 0.416884i
\(778\) −18896.4 −0.870781
\(779\) 13085.5 10980.0i 0.601843 0.505007i
\(780\) 2172.49 + 1822.94i 0.0997278 + 0.0836815i
\(781\) −2975.37 + 16874.2i −0.136322 + 0.773118i
\(782\) −2337.48 + 850.772i −0.106890 + 0.0389048i
\(783\) 24170.6 1.10317
\(784\) −8989.51 + 3271.91i −0.409508 + 0.149049i
\(785\) 8598.99 + 14893.9i 0.390969 + 0.677179i
\(786\) 638.416 + 3620.64i 0.0289714 + 0.164305i
\(787\) −318.630 + 551.883i −0.0144319 + 0.0249968i −0.873151 0.487450i \(-0.837927\pi\)
0.858719 + 0.512446i \(0.171261\pi\)
\(788\) −2223.16 3850.63i −0.100504 0.174077i
\(789\) −4573.84 + 3837.91i −0.206379 + 0.173173i
\(790\) 869.913 4933.52i 0.0391774 0.222186i
\(791\) 15271.8 26451.5i 0.686476 1.18901i
\(792\) −6506.42 2368.14i −0.291914 0.106248i
\(793\) −42485.6 15463.5i −1.90253 0.692466i
\(794\) −4136.12 23457.1i −0.184868 1.04844i
\(795\) 1845.33 + 1548.42i 0.0823235 + 0.0690776i
\(796\) 4171.53 + 3500.33i 0.185749 + 0.155862i
\(797\) −1426.64 8090.86i −0.0634054 0.359590i −0.999959 0.00906517i \(-0.997114\pi\)
0.936554 0.350525i \(-0.113997\pi\)
\(798\) 3867.81 + 1407.77i 0.171578 + 0.0624492i
\(799\) −1024.44 372.865i −0.0453592 0.0165094i
\(800\) −1339.81 + 2320.61i −0.0592116 + 0.102558i
\(801\) 4015.37 22772.3i 0.177124 1.00452i
\(802\) −19056.3 + 15990.1i −0.839029 + 0.704029i
\(803\) −4868.12 8431.84i −0.213938 0.370552i
\(804\) 1430.76 2478.15i 0.0627601 0.108704i
\(805\) −3829.33 21717.2i −0.167660 0.950847i
\(806\) 13240.2 + 22932.7i 0.578618 + 1.00220i
\(807\) −1333.74 + 485.440i −0.0581781 + 0.0211751i
\(808\) 7474.47 0.325434
\(809\) −12939.2 + 4709.50i −0.562324 + 0.204669i −0.607513 0.794309i \(-0.707833\pi\)
0.0451899 + 0.998978i \(0.485611\pi\)
\(810\) 1093.49 6201.47i 0.0474335 0.269009i
\(811\) −5051.79 4238.95i −0.218733 0.183539i 0.526837 0.849967i \(-0.323378\pi\)
−0.745569 + 0.666428i \(0.767822\pi\)
\(812\) 25478.0 21378.6i 1.10111 0.923944i
\(813\) −12344.4 −0.532517
\(814\) 10818.9 + 12160.3i 0.465852 + 0.523608i
\(815\) 26058.5 1.11999
\(816\) 238.445 200.079i 0.0102295 0.00858354i
\(817\) −10209.0 8566.40i −0.437171 0.366830i
\(818\) −1852.44 + 10505.7i −0.0791799 + 0.449051i
\(819\) 43499.1 15832.4i 1.85590 0.675491i
\(820\) 11452.0 0.487709
\(821\) 18310.0 6664.29i 0.778348 0.283295i 0.0778641 0.996964i \(-0.475190\pi\)
0.700483 + 0.713669i \(0.252968\pi\)
\(822\) −3140.79 5440.01i −0.133270 0.230830i
\(823\) −5815.88 32983.5i −0.246329 1.39700i −0.817386 0.576091i \(-0.804577\pi\)
0.571057 0.820911i \(-0.306534\pi\)
\(824\) −144.856 + 250.899i −0.00612416 + 0.0106074i
\(825\) −2650.36 4590.56i −0.111847 0.193724i
\(826\) −16664.6 + 13983.3i −0.701982 + 0.589033i
\(827\) 855.001 4848.95i 0.0359508 0.203887i −0.961542 0.274659i \(-0.911435\pi\)
0.997493 + 0.0707718i \(0.0225462\pi\)
\(828\) 5357.66 9279.74i 0.224869 0.389485i
\(829\) −22263.8 8103.35i −0.932754 0.339495i −0.169453 0.985538i \(-0.554200\pi\)
−0.763301 + 0.646043i \(0.776422\pi\)
\(830\) 5927.83 + 2157.55i 0.247901 + 0.0902286i
\(831\) 847.509 + 4806.46i 0.0353788 + 0.200643i
\(832\) 3091.11 + 2593.75i 0.128804 + 0.108080i
\(833\) −5089.92 4270.95i −0.211711 0.177647i
\(834\) −1320.57 7489.32i −0.0548292 0.310952i
\(835\) −19121.0 6959.48i −0.792467 0.288434i
\(836\) 5209.09 + 1895.95i 0.215503 + 0.0784365i
\(837\) −9362.47 + 16216.3i −0.386636 + 0.669673i
\(838\) 853.560 4840.78i 0.0351858 0.199549i
\(839\) 10438.8 8759.23i 0.429546 0.360432i −0.402235 0.915537i \(-0.631766\pi\)
0.831780 + 0.555105i \(0.187322\pi\)
\(840\) 1379.73 + 2389.77i 0.0566730 + 0.0981606i
\(841\) −24544.7 + 42512.7i −1.00638 + 1.74311i
\(842\) 1790.89 + 10156.7i 0.0732995 + 0.415702i
\(843\) 825.489 + 1429.79i 0.0337264 + 0.0584158i
\(844\) 1741.32 633.788i 0.0710174 0.0258482i
\(845\) −11422.6 −0.465028
\(846\) 4412.95 1606.18i 0.179339 0.0652739i
\(847\) −125.017 + 709.008i −0.00507160 + 0.0287625i
\(848\) 2625.62 + 2203.15i 0.106326 + 0.0892177i
\(849\) −738.414 + 619.603i −0.0298496 + 0.0250468i
\(850\) −1861.14 −0.0751018
\(851\) −21440.3 + 13220.8i −0.863647 + 0.532553i
\(852\) 3318.12 0.133424
\(853\) −6219.41 + 5218.70i −0.249646 + 0.209478i −0.759020 0.651067i \(-0.774322\pi\)
0.509374 + 0.860545i \(0.329877\pi\)
\(854\) −33700.1 28277.8i −1.35035 1.13307i
\(855\) −1023.24 + 5803.08i −0.0409287 + 0.232118i
\(856\) 7909.48 2878.82i 0.315818 0.114948i
\(857\) −13247.3 −0.528027 −0.264014 0.964519i \(-0.585046\pi\)
−0.264014 + 0.964519i \(0.585046\pi\)
\(858\) −7500.84 + 2730.08i −0.298455 + 0.108629i
\(859\) −18765.5 32502.9i −0.745369 1.29102i −0.950022 0.312183i \(-0.898940\pi\)
0.204653 0.978835i \(-0.434393\pi\)
\(860\) −1551.48 8798.89i −0.0615175 0.348883i
\(861\) −11966.7 + 20726.9i −0.473664 + 0.820409i
\(862\) −4666.76 8083.07i −0.184397 0.319386i
\(863\) 25235.8 21175.3i 0.995406 0.835245i 0.00906480 0.999959i \(-0.497115\pi\)
0.986341 + 0.164714i \(0.0526701\pi\)
\(864\) −495.481 + 2810.01i −0.0195100 + 0.110646i
\(865\) 1338.38 2318.14i 0.0526083 0.0911202i
\(866\) 24216.3 + 8814.02i 0.950235 + 0.345857i
\(867\) −7878.86 2867.67i −0.308628 0.112331i
\(868\) 4474.21 + 25374.5i 0.174959 + 0.992242i
\(869\) 10801.4 + 9063.44i 0.421648 + 0.353804i
\(870\) −4670.11 3918.69i −0.181990 0.152708i
\(871\) 4474.06 + 25373.7i 0.174050 + 0.987088i
\(872\) 4968.87 + 1808.52i 0.192967 + 0.0702343i
\(873\) −22150.2 8062.02i −0.858730 0.312552i
\(874\) −4289.38 + 7429.43i −0.166008 + 0.287534i
\(875\) 7142.00 40504.3i 0.275935 1.56491i
\(876\) −1444.33 + 1211.94i −0.0557071 + 0.0467438i
\(877\) −5510.12 9543.80i −0.212159 0.367470i 0.740231 0.672353i \(-0.234716\pi\)
−0.952390 + 0.304882i \(0.901383\pi\)
\(878\) 4597.47 7963.06i 0.176717 0.306082i
\(879\) 2273.16 + 12891.8i 0.0872263 + 0.494685i
\(880\) 1858.20 + 3218.49i 0.0711816 + 0.123290i
\(881\) 24680.7 8983.02i 0.943828 0.343525i 0.176152 0.984363i \(-0.443635\pi\)
0.767676 + 0.640838i \(0.221413\pi\)
\(882\) 28622.1 1.09269
\(883\) 12921.6 4703.07i 0.492464 0.179242i −0.0838376 0.996479i \(-0.526718\pi\)
0.576301 + 0.817237i \(0.304495\pi\)
\(884\) −486.674 + 2760.07i −0.0185165 + 0.105013i
\(885\) 3054.62 + 2563.13i 0.116022 + 0.0973543i
\(886\) 20638.8 17318.0i 0.782588 0.656669i
\(887\) 12605.9 0.477187 0.238593 0.971120i \(-0.423314\pi\)
0.238593 + 0.971120i \(0.423314\pi\)
\(888\) 1955.27 2472.19i 0.0738902 0.0934249i
\(889\) −18109.8 −0.683222
\(890\) −9507.69 + 7977.90i −0.358088 + 0.300472i
\(891\) 13577.4 + 11392.8i 0.510505 + 0.428365i
\(892\) 2860.94 16225.2i 0.107389 0.609035i
\(893\) −3533.04 + 1285.92i −0.132395 + 0.0481878i
\(894\) 5855.90 0.219072
\(895\) −3314.71 + 1206.45i −0.123797 + 0.0450585i
\(896\) 1963.14 + 3400.27i 0.0731965 + 0.126780i
\(897\) −2145.08 12165.3i −0.0798462 0.452830i
\(898\) 16864.6 29210.3i 0.626701 1.08548i
\(899\) −28461.9 49297.4i −1.05590 1.82888i
\(900\) 6141.53 5153.35i 0.227464 0.190865i
\(901\) −413.385 + 2344.42i −0.0152851 + 0.0866859i
\(902\) −16116.5 + 27914.6i −0.594924 + 1.03044i
\(903\) 17546.3 + 6386.33i 0.646627 + 0.235353i
\(904\) −7485.55 2724.52i −0.275405 0.100239i
\(905\) −271.880 1541.91i −0.00998628 0.0566350i
\(906\) −8558.88 7181.75i −0.313852 0.263353i
\(907\) 462.475 + 388.062i 0.0169308 + 0.0142066i 0.651214 0.758894i \(-0.274260\pi\)
−0.634283 + 0.773101i \(0.718705\pi\)
\(908\) 1105.40 + 6269.02i 0.0404008 + 0.229124i
\(909\) −21014.4 7648.61i −0.766780 0.279085i
\(910\) −23347.8 8497.89i −0.850517 0.309563i
\(911\) 23967.0 41512.0i 0.871637 1.50972i 0.0113336 0.999936i \(-0.496392\pi\)
0.860303 0.509783i \(-0.170274\pi\)
\(912\) 186.409 1057.18i 0.00676823 0.0383846i
\(913\) −13601.4 + 11412.9i −0.493034 + 0.413705i
\(914\) 9094.95 + 15752.9i 0.329140 + 0.570088i
\(915\) −4031.89 + 6983.43i −0.145672 + 0.252312i
\(916\) 3166.20 + 17956.4i 0.114208 + 0.647704i
\(917\) −16104.9 27894.5i −0.579969 1.00454i
\(918\) −1862.30 + 677.822i −0.0669554 + 0.0243698i
\(919\) −11605.1 −0.416558 −0.208279 0.978069i \(-0.566786\pi\)
−0.208279 + 0.978069i \(0.566786\pi\)
\(920\) −5404.51 + 1967.08i −0.193675 + 0.0704921i
\(921\) 1294.29 7340.26i 0.0463064 0.262617i
\(922\) 17323.0 + 14535.7i 0.618765 + 0.519206i
\(923\) −22886.6 + 19204.1i −0.816165 + 0.684844i
\(924\) −7766.85 −0.276527
\(925\) −18457.4 + 3808.69i −0.656080 + 0.135383i
\(926\) 1142.78 0.0405553
\(927\) 664.006 557.168i 0.0235263 0.0197409i
\(928\) −6644.83 5575.67i −0.235051 0.197231i
\(929\) −6966.69 + 39510.1i −0.246039 + 1.39535i 0.572030 + 0.820233i \(0.306156\pi\)
−0.818068 + 0.575121i \(0.804955\pi\)
\(930\) 4438.05 1615.32i 0.156483 0.0569552i
\(931\) −22915.0 −0.806670
\(932\) 16433.3 5981.23i 0.577564 0.210216i
\(933\) 7027.16 + 12171.4i 0.246580 + 0.427089i
\(934\) 531.554 + 3014.59i 0.0186220 + 0.105611i
\(935\) −1290.62 + 2235.42i −0.0451420 + 0.0781883i
\(936\) −6036.45 10455.4i −0.210799 0.365114i
\(937\) −21711.0 + 18217.7i −0.756957 + 0.635162i −0.937333 0.348436i \(-0.886713\pi\)
0.180376 + 0.983598i \(0.442269\pi\)
\(938\) −4353.35 + 24689.0i −0.151537 + 0.859409i
\(939\) 3975.74 6886.18i 0.138172 0.239321i
\(940\) −2368.61 862.105i −0.0821869 0.0299136i
\(941\) 38546.4 + 14029.8i 1.33536 + 0.486033i 0.908350 0.418212i \(-0.137343\pi\)
0.427015 + 0.904245i \(0.359565\pi\)
\(942\) 1627.75 + 9231.45i 0.0563005 + 0.319296i
\(943\) −38212.4 32064.0i −1.31958 1.10726i
\(944\) 4346.24 + 3646.93i 0.149850 + 0.125739i
\(945\) −3050.88 17302.4i −0.105021 0.595606i
\(946\) 23631.0 + 8600.98i 0.812167 + 0.295604i
\(947\) 16096.6 + 5858.67i 0.552342 + 0.201036i 0.603087 0.797676i \(-0.293937\pi\)
−0.0507446 + 0.998712i \(0.516159\pi\)
\(948\) 1365.26 2364.71i 0.0467740 0.0810149i
\(949\) 2947.93 16718.5i 0.100837 0.571872i
\(950\) −4916.95 + 4125.81i −0.167923 + 0.140904i
\(951\) −3846.80 6662.85i −0.131168 0.227190i
\(952\) −1363.51 + 2361.67i −0.0464199 + 0.0804015i
\(953\) −2134.80 12107.1i −0.0725635 0.411528i −0.999354 0.0359484i \(-0.988555\pi\)
0.926790 0.375579i \(-0.122556\pi\)
\(954\) −5127.41 8880.93i −0.174010 0.301395i
\(955\) −2358.64 + 858.476i −0.0799204 + 0.0290886i
\(956\) −27231.0 −0.921247
\(957\) 16124.2 5868.73i 0.544641 0.198233i
\(958\) 991.125 5620.95i 0.0334257 0.189566i
\(959\) 42157.9 + 35374.6i 1.41955 + 1.19114i
\(960\) 551.311 462.605i 0.0185349 0.0155526i
\(961\) 14307.8 0.480273
\(962\) 821.815 + 28368.2i 0.0275430 + 0.950756i
\(963\) −25183.3 −0.842701
\(964\) 5342.43 4482.83i 0.178494 0.149774i
\(965\) 7072.66 + 5934.67i 0.235935 + 0.197973i
\(966\) 2087.20 11837.1i 0.0695182 0.394257i
\(967\) −12659.7 + 4607.75i −0.421001 + 0.153232i −0.543829 0.839196i \(-0.683026\pi\)
0.122828 + 0.992428i \(0.460804\pi\)
\(968\) 187.766 0.00623454
\(969\) 700.632 255.009i 0.0232276 0.00845416i
\(970\) 6325.97 + 10956.9i 0.209397 + 0.362686i
\(971\) 106.782 + 605.594i 0.00352916 + 0.0200149i 0.986521 0.163632i \(-0.0523209\pi\)
−0.982992 + 0.183647i \(0.941210\pi\)
\(972\) 6531.19 11312.4i 0.215523 0.373296i
\(973\) 33313.2 + 57700.1i 1.09761 + 1.90111i
\(974\) 14708.6 12342.0i 0.483874 0.406018i
\(975\) 1604.95 9102.10i 0.0527173 0.298975i
\(976\) −5736.74 + 9936.33i −0.188144 + 0.325875i
\(977\) 1158.79 + 421.766i 0.0379458 + 0.0138112i 0.360923 0.932595i \(-0.382462\pi\)
−0.322978 + 0.946407i \(0.604684\pi\)
\(978\) 13346.8 + 4857.83i 0.436384 + 0.158831i
\(979\) −6066.12 34402.7i −0.198033 1.12310i
\(980\) −11768.5 9874.92i −0.383602 0.321880i
\(981\) −12119.3 10169.3i −0.394433 0.330969i
\(982\) −3078.09 17456.7i −0.100026 0.567277i
\(983\) −16870.4 6140.32i −0.547388 0.199233i 0.0534977 0.998568i \(-0.482963\pi\)
−0.600886 + 0.799335i \(0.705185\pi\)
\(984\) 5865.54 + 2134.88i 0.190027 + 0.0691642i
\(985\) 3570.15 6183.69i 0.115487 0.200029i
\(986\) 1046.18 5933.19i 0.0337903 0.191634i
\(987\) 4035.39 3386.10i 0.130140 0.109200i
\(988\) 4832.83 + 8370.71i 0.155620 + 0.269542i
\(989\) −19458.8 + 33703.5i −0.625634 + 1.08363i
\(990\) −1930.82 10950.2i −0.0619854 0.351537i
\(991\) 26772.4 + 46371.1i 0.858175 + 1.48640i 0.873667 + 0.486524i \(0.161735\pi\)
−0.0154920 + 0.999880i \(0.504931\pi\)
\(992\) 6314.65 2298.34i 0.202107 0.0735610i
\(993\) −18280.3 −0.584197
\(994\) −27317.0 + 9942.59i −0.871674 + 0.317263i
\(995\) −1518.55 + 8612.10i −0.0483830 + 0.274394i
\(996\) 2633.93 + 2210.13i 0.0837946 + 0.0703120i
\(997\) −6319.19 + 5302.43i −0.200733 + 0.168435i −0.737613 0.675223i \(-0.764047\pi\)
0.536880 + 0.843659i \(0.319603\pi\)
\(998\) −25757.9 −0.816987
\(999\) −17081.8 + 10533.2i −0.540984 + 0.333589i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 74.4.f.a.49.2 24
37.34 even 9 inner 74.4.f.a.71.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.4.f.a.49.2 24 1.1 even 1 trivial
74.4.f.a.71.2 yes 24 37.34 even 9 inner