Properties

Label 200.4.f.a.149.2
Level $200$
Weight $4$
Character 200.149
Analytic conductor $11.800$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [200,4,Mod(149,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.149");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 200.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.8003820011\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 3x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 8)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.2
Root \(1.32288 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 200.149
Dual form 200.4.f.a.149.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.64575 + 1.00000i) q^{2} -5.29150 q^{3} +(6.00000 - 5.29150i) q^{4} +(14.0000 - 5.29150i) q^{6} +8.00000i q^{7} +(-10.5830 + 20.0000i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-2.64575 + 1.00000i) q^{2} -5.29150 q^{3} +(6.00000 - 5.29150i) q^{4} +(14.0000 - 5.29150i) q^{6} +8.00000i q^{7} +(-10.5830 + 20.0000i) q^{8} +1.00000 q^{9} -15.8745i q^{11} +(-31.7490 + 28.0000i) q^{12} -52.9150 q^{13} +(-8.00000 - 21.1660i) q^{14} +(8.00000 - 63.4980i) q^{16} +14.0000i q^{17} +(-2.64575 + 1.00000i) q^{18} +37.0405i q^{19} -42.3320i q^{21} +(15.8745 + 42.0000i) q^{22} -152.000i q^{23} +(56.0000 - 105.830i) q^{24} +(140.000 - 52.9150i) q^{26} +137.579 q^{27} +(42.3320 + 48.0000i) q^{28} +158.745i q^{29} +224.000 q^{31} +(42.3320 + 176.000i) q^{32} +84.0000i q^{33} +(-14.0000 - 37.0405i) q^{34} +(6.00000 - 5.29150i) q^{36} +243.409 q^{37} +(-37.0405 - 98.0000i) q^{38} +280.000 q^{39} -70.0000 q^{41} +(42.3320 + 112.000i) q^{42} +439.195 q^{43} +(-84.0000 - 95.2470i) q^{44} +(152.000 + 402.154i) q^{46} -336.000i q^{47} +(-42.3320 + 336.000i) q^{48} +279.000 q^{49} -74.0810i q^{51} +(-317.490 + 280.000i) q^{52} -31.7490 q^{53} +(-364.000 + 137.579i) q^{54} +(-160.000 - 84.6640i) q^{56} -196.000i q^{57} +(-158.745 - 420.000i) q^{58} -534.442i q^{59} +95.2470i q^{61} +(-592.648 + 224.000i) q^{62} +8.00000i q^{63} +(-288.000 - 423.320i) q^{64} +(-84.0000 - 222.243i) q^{66} +174.620 q^{67} +(74.0810 + 84.0000i) q^{68} +804.308i q^{69} -72.0000 q^{71} +(-10.5830 + 20.0000i) q^{72} -294.000i q^{73} +(-644.000 + 243.409i) q^{74} +(196.000 + 222.243i) q^{76} +126.996 q^{77} +(-740.810 + 280.000i) q^{78} +464.000 q^{79} -755.000 q^{81} +(185.203 - 70.0000i) q^{82} +545.025 q^{83} +(-224.000 - 253.992i) q^{84} +(-1162.00 + 439.195i) q^{86} -840.000i q^{87} +(317.490 + 168.000i) q^{88} -266.000 q^{89} -423.320i q^{91} +(-804.308 - 912.000i) q^{92} -1185.30 q^{93} +(336.000 + 888.972i) q^{94} +(-224.000 - 931.304i) q^{96} -994.000i q^{97} +(-738.165 + 279.000i) q^{98} -15.8745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 24 q^{4} + 56 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 24 q^{4} + 56 q^{6} + 4 q^{9} - 32 q^{14} + 32 q^{16} + 224 q^{24} + 560 q^{26} + 896 q^{31} - 56 q^{34} + 24 q^{36} + 1120 q^{39} - 280 q^{41} - 336 q^{44} + 608 q^{46} + 1116 q^{49} - 1456 q^{54} - 640 q^{56} - 1152 q^{64} - 336 q^{66} - 288 q^{71} - 2576 q^{74} + 784 q^{76} + 1856 q^{79} - 3020 q^{81} - 896 q^{84} - 4648 q^{86} - 1064 q^{89} + 1344 q^{94} - 896 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(177\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64575 + 1.00000i −0.935414 + 0.353553i
\(3\) −5.29150 −1.01835 −0.509175 0.860663i \(-0.670049\pi\)
−0.509175 + 0.860663i \(0.670049\pi\)
\(4\) 6.00000 5.29150i 0.750000 0.661438i
\(5\) 0 0
\(6\) 14.0000 5.29150i 0.952579 0.360041i
\(7\) 8.00000i 0.431959i 0.976398 + 0.215980i \(0.0692945\pi\)
−0.976398 + 0.215980i \(0.930705\pi\)
\(8\) −10.5830 + 20.0000i −0.467707 + 0.883883i
\(9\) 1.00000 0.0370370
\(10\) 0 0
\(11\) 15.8745i 0.435122i −0.976047 0.217561i \(-0.930190\pi\)
0.976047 0.217561i \(-0.0698101\pi\)
\(12\) −31.7490 + 28.0000i −0.763763 + 0.673575i
\(13\) −52.9150 −1.12892 −0.564461 0.825460i \(-0.690916\pi\)
−0.564461 + 0.825460i \(0.690916\pi\)
\(14\) −8.00000 21.1660i −0.152721 0.404061i
\(15\) 0 0
\(16\) 8.00000 63.4980i 0.125000 0.992157i
\(17\) 14.0000i 0.199735i 0.995001 + 0.0998676i \(0.0318419\pi\)
−0.995001 + 0.0998676i \(0.968158\pi\)
\(18\) −2.64575 + 1.00000i −0.0346450 + 0.0130946i
\(19\) 37.0405i 0.447246i 0.974676 + 0.223623i \(0.0717885\pi\)
−0.974676 + 0.223623i \(0.928212\pi\)
\(20\) 0 0
\(21\) 42.3320i 0.439886i
\(22\) 15.8745 + 42.0000i 0.153839 + 0.407020i
\(23\) 152.000i 1.37801i −0.724757 0.689004i \(-0.758048\pi\)
0.724757 0.689004i \(-0.241952\pi\)
\(24\) 56.0000 105.830i 0.476290 0.900103i
\(25\) 0 0
\(26\) 140.000 52.9150i 1.05601 0.399134i
\(27\) 137.579 0.980633
\(28\) 42.3320 + 48.0000i 0.285714 + 0.323970i
\(29\) 158.745i 1.01649i 0.861212 + 0.508245i \(0.169706\pi\)
−0.861212 + 0.508245i \(0.830294\pi\)
\(30\) 0 0
\(31\) 224.000 1.29779 0.648897 0.760877i \(-0.275231\pi\)
0.648897 + 0.760877i \(0.275231\pi\)
\(32\) 42.3320 + 176.000i 0.233854 + 0.972272i
\(33\) 84.0000i 0.443107i
\(34\) −14.0000 37.0405i −0.0706171 0.186835i
\(35\) 0 0
\(36\) 6.00000 5.29150i 0.0277778 0.0244977i
\(37\) 243.409 1.08152 0.540760 0.841177i \(-0.318137\pi\)
0.540760 + 0.841177i \(0.318137\pi\)
\(38\) −37.0405 98.0000i −0.158125 0.418361i
\(39\) 280.000 1.14964
\(40\) 0 0
\(41\) −70.0000 −0.266638 −0.133319 0.991073i \(-0.542564\pi\)
−0.133319 + 0.991073i \(0.542564\pi\)
\(42\) 42.3320 + 112.000i 0.155523 + 0.411476i
\(43\) 439.195 1.55759 0.778797 0.627276i \(-0.215830\pi\)
0.778797 + 0.627276i \(0.215830\pi\)
\(44\) −84.0000 95.2470i −0.287806 0.326342i
\(45\) 0 0
\(46\) 152.000 + 402.154i 0.487200 + 1.28901i
\(47\) 336.000i 1.04278i −0.853319 0.521390i \(-0.825414\pi\)
0.853319 0.521390i \(-0.174586\pi\)
\(48\) −42.3320 + 336.000i −0.127294 + 1.01036i
\(49\) 279.000 0.813411
\(50\) 0 0
\(51\) 74.0810i 0.203400i
\(52\) −317.490 + 280.000i −0.846692 + 0.746712i
\(53\) −31.7490 −0.0822842 −0.0411421 0.999153i \(-0.513100\pi\)
−0.0411421 + 0.999153i \(0.513100\pi\)
\(54\) −364.000 + 137.579i −0.917299 + 0.346706i
\(55\) 0 0
\(56\) −160.000 84.6640i −0.381802 0.202031i
\(57\) 196.000i 0.455453i
\(58\) −158.745 420.000i −0.359384 0.950840i
\(59\) 534.442i 1.17929i −0.807661 0.589647i \(-0.799267\pi\)
0.807661 0.589647i \(-0.200733\pi\)
\(60\) 0 0
\(61\) 95.2470i 0.199920i 0.994991 + 0.0999601i \(0.0318715\pi\)
−0.994991 + 0.0999601i \(0.968128\pi\)
\(62\) −592.648 + 224.000i −1.21397 + 0.458839i
\(63\) 8.00000i 0.0159985i
\(64\) −288.000 423.320i −0.562500 0.826797i
\(65\) 0 0
\(66\) −84.0000 222.243i −0.156662 0.414488i
\(67\) 174.620 0.318406 0.159203 0.987246i \(-0.449108\pi\)
0.159203 + 0.987246i \(0.449108\pi\)
\(68\) 74.0810 + 84.0000i 0.132112 + 0.149801i
\(69\) 804.308i 1.40329i
\(70\) 0 0
\(71\) −72.0000 −0.120350 −0.0601748 0.998188i \(-0.519166\pi\)
−0.0601748 + 0.998188i \(0.519166\pi\)
\(72\) −10.5830 + 20.0000i −0.0173225 + 0.0327364i
\(73\) 294.000i 0.471371i −0.971829 0.235686i \(-0.924266\pi\)
0.971829 0.235686i \(-0.0757336\pi\)
\(74\) −644.000 + 243.409i −1.01167 + 0.382375i
\(75\) 0 0
\(76\) 196.000 + 222.243i 0.295826 + 0.335435i
\(77\) 126.996 0.187955
\(78\) −740.810 + 280.000i −1.07539 + 0.406458i
\(79\) 464.000 0.660811 0.330406 0.943839i \(-0.392814\pi\)
0.330406 + 0.943839i \(0.392814\pi\)
\(80\) 0 0
\(81\) −755.000 −1.03567
\(82\) 185.203 70.0000i 0.249417 0.0942708i
\(83\) 545.025 0.720774 0.360387 0.932803i \(-0.382645\pi\)
0.360387 + 0.932803i \(0.382645\pi\)
\(84\) −224.000 253.992i −0.290957 0.329914i
\(85\) 0 0
\(86\) −1162.00 + 439.195i −1.45700 + 0.550693i
\(87\) 840.000i 1.03514i
\(88\) 317.490 + 168.000i 0.384597 + 0.203510i
\(89\) −266.000 −0.316808 −0.158404 0.987374i \(-0.550635\pi\)
−0.158404 + 0.987374i \(0.550635\pi\)
\(90\) 0 0
\(91\) 423.320i 0.487649i
\(92\) −804.308 912.000i −0.911467 1.03351i
\(93\) −1185.30 −1.32161
\(94\) 336.000 + 888.972i 0.368678 + 0.975431i
\(95\) 0 0
\(96\) −224.000 931.304i −0.238145 0.990113i
\(97\) 994.000i 1.04047i −0.854024 0.520234i \(-0.825845\pi\)
0.854024 0.520234i \(-0.174155\pi\)
\(98\) −738.165 + 279.000i −0.760876 + 0.287584i
\(99\) 15.8745i 0.0161156i
\(100\) 0 0
\(101\) 751.393i 0.740262i 0.928980 + 0.370131i \(0.120687\pi\)
−0.928980 + 0.370131i \(0.879313\pi\)
\(102\) 74.0810 + 196.000i 0.0719129 + 0.190264i
\(103\) 1176.00i 1.12500i 0.826798 + 0.562499i \(0.190160\pi\)
−0.826798 + 0.562499i \(0.809840\pi\)
\(104\) 560.000 1058.30i 0.528005 0.997836i
\(105\) 0 0
\(106\) 84.0000 31.7490i 0.0769698 0.0290919i
\(107\) −269.867 −0.243822 −0.121911 0.992541i \(-0.538902\pi\)
−0.121911 + 0.992541i \(0.538902\pi\)
\(108\) 825.474 728.000i 0.735475 0.648628i
\(109\) 1894.36i 1.66465i 0.554290 + 0.832324i \(0.312990\pi\)
−0.554290 + 0.832324i \(0.687010\pi\)
\(110\) 0 0
\(111\) −1288.00 −1.10137
\(112\) 507.984 + 64.0000i 0.428571 + 0.0539949i
\(113\) 1710.00i 1.42357i −0.702398 0.711784i \(-0.747887\pi\)
0.702398 0.711784i \(-0.252113\pi\)
\(114\) 196.000 + 518.567i 0.161027 + 0.426037i
\(115\) 0 0
\(116\) 840.000 + 952.470i 0.672345 + 0.762368i
\(117\) −52.9150 −0.0418119
\(118\) 534.442 + 1414.00i 0.416944 + 1.10313i
\(119\) −112.000 −0.0862775
\(120\) 0 0
\(121\) 1079.00 0.810669
\(122\) −95.2470 252.000i −0.0706825 0.187008i
\(123\) 370.405 0.271531
\(124\) 1344.00 1185.30i 0.973345 0.858409i
\(125\) 0 0
\(126\) −8.00000 21.1660i −0.00565632 0.0149652i
\(127\) 1664.00i 1.16265i 0.813673 + 0.581323i \(0.197465\pi\)
−0.813673 + 0.581323i \(0.802535\pi\)
\(128\) 1185.30 + 832.000i 0.818488 + 0.574524i
\(129\) −2324.00 −1.58618
\(130\) 0 0
\(131\) 672.021i 0.448204i −0.974566 0.224102i \(-0.928055\pi\)
0.974566 0.224102i \(-0.0719449\pi\)
\(132\) 444.486 + 504.000i 0.293088 + 0.332330i
\(133\) −296.324 −0.193192
\(134\) −462.000 + 174.620i −0.297841 + 0.112573i
\(135\) 0 0
\(136\) −280.000 148.162i −0.176543 0.0934176i
\(137\) 1062.00i 0.662283i 0.943581 + 0.331142i \(0.107434\pi\)
−0.943581 + 0.331142i \(0.892566\pi\)
\(138\) −804.308 2128.00i −0.496140 1.31266i
\(139\) 2693.37i 1.64352i −0.569835 0.821759i \(-0.692993\pi\)
0.569835 0.821759i \(-0.307007\pi\)
\(140\) 0 0
\(141\) 1777.94i 1.06191i
\(142\) 190.494 72.0000i 0.112577 0.0425500i
\(143\) 840.000i 0.491219i
\(144\) 8.00000 63.4980i 0.00462963 0.0367465i
\(145\) 0 0
\(146\) 294.000 + 777.851i 0.166655 + 0.440927i
\(147\) −1476.33 −0.828337
\(148\) 1460.45 1288.00i 0.811139 0.715358i
\(149\) 793.725i 0.436406i −0.975903 0.218203i \(-0.929980\pi\)
0.975903 0.218203i \(-0.0700195\pi\)
\(150\) 0 0
\(151\) 744.000 0.400966 0.200483 0.979697i \(-0.435749\pi\)
0.200483 + 0.979697i \(0.435749\pi\)
\(152\) −740.810 392.000i −0.395314 0.209180i
\(153\) 14.0000i 0.00739760i
\(154\) −336.000 + 126.996i −0.175816 + 0.0664522i
\(155\) 0 0
\(156\) 1680.00 1481.62i 0.862229 0.760414i
\(157\) 179.911 0.0914552 0.0457276 0.998954i \(-0.485439\pi\)
0.0457276 + 0.998954i \(0.485439\pi\)
\(158\) −1227.63 + 464.000i −0.618132 + 0.233632i
\(159\) 168.000 0.0837941
\(160\) 0 0
\(161\) 1216.00 0.595244
\(162\) 1997.54 755.000i 0.968776 0.366163i
\(163\) 1772.65 0.851809 0.425905 0.904768i \(-0.359956\pi\)
0.425905 + 0.904768i \(0.359956\pi\)
\(164\) −420.000 + 370.405i −0.199979 + 0.176365i
\(165\) 0 0
\(166\) −1442.00 + 545.025i −0.674222 + 0.254832i
\(167\) 1960.00i 0.908200i 0.890951 + 0.454100i \(0.150039\pi\)
−0.890951 + 0.454100i \(0.849961\pi\)
\(168\) 846.640 + 448.000i 0.388808 + 0.205738i
\(169\) 603.000 0.274465
\(170\) 0 0
\(171\) 37.0405i 0.0165647i
\(172\) 2635.17 2324.00i 1.16820 1.03025i
\(173\) −2000.19 −0.879026 −0.439513 0.898236i \(-0.644849\pi\)
−0.439513 + 0.898236i \(0.644849\pi\)
\(174\) 840.000 + 2222.43i 0.365978 + 0.968288i
\(175\) 0 0
\(176\) −1008.00 126.996i −0.431709 0.0543903i
\(177\) 2828.00i 1.20094i
\(178\) 703.770 266.000i 0.296347 0.112009i
\(179\) 3264.86i 1.36328i −0.731688 0.681639i \(-0.761267\pi\)
0.731688 0.681639i \(-0.238733\pi\)
\(180\) 0 0
\(181\) 2338.84i 0.960469i −0.877140 0.480235i \(-0.840552\pi\)
0.877140 0.480235i \(-0.159448\pi\)
\(182\) 423.320 + 1120.00i 0.172410 + 0.456153i
\(183\) 504.000i 0.203589i
\(184\) 3040.00 + 1608.62i 1.21800 + 0.644504i
\(185\) 0 0
\(186\) 3136.00 1185.30i 1.23625 0.467259i
\(187\) 222.243 0.0869092
\(188\) −1777.94 2016.00i −0.689734 0.782085i
\(189\) 1100.63i 0.423594i
\(190\) 0 0
\(191\) 3904.00 1.47897 0.739486 0.673172i \(-0.235069\pi\)
0.739486 + 0.673172i \(0.235069\pi\)
\(192\) 1523.95 + 2240.00i 0.572822 + 0.841969i
\(193\) 3330.00i 1.24196i 0.783826 + 0.620981i \(0.213266\pi\)
−0.783826 + 0.620981i \(0.786734\pi\)
\(194\) 994.000 + 2629.88i 0.367861 + 0.973269i
\(195\) 0 0
\(196\) 1674.00 1476.33i 0.610058 0.538021i
\(197\) −1195.88 −0.432502 −0.216251 0.976338i \(-0.569383\pi\)
−0.216251 + 0.976338i \(0.569383\pi\)
\(198\) 15.8745 + 42.0000i 0.00569774 + 0.0150748i
\(199\) 1736.00 0.618401 0.309200 0.950997i \(-0.399939\pi\)
0.309200 + 0.950997i \(0.399939\pi\)
\(200\) 0 0
\(201\) −924.000 −0.324248
\(202\) −751.393 1988.00i −0.261722 0.692451i
\(203\) −1269.96 −0.439083
\(204\) −392.000 444.486i −0.134537 0.152550i
\(205\) 0 0
\(206\) −1176.00 3111.40i −0.397747 1.05234i
\(207\) 152.000i 0.0510373i
\(208\) −423.320 + 3360.00i −0.141115 + 1.12007i
\(209\) 588.000 0.194607
\(210\) 0 0
\(211\) 2915.62i 0.951277i −0.879641 0.475638i \(-0.842217\pi\)
0.879641 0.475638i \(-0.157783\pi\)
\(212\) −190.494 + 168.000i −0.0617132 + 0.0544259i
\(213\) 380.988 0.122558
\(214\) 714.000 269.867i 0.228075 0.0862042i
\(215\) 0 0
\(216\) −1456.00 + 2751.58i −0.458649 + 0.866766i
\(217\) 1792.00i 0.560594i
\(218\) −1894.36 5012.00i −0.588542 1.55714i
\(219\) 1555.70i 0.480021i
\(220\) 0 0
\(221\) 740.810i 0.225486i
\(222\) 3407.73 1288.00i 1.03023 0.389391i
\(223\) 1568.00i 0.470857i 0.971892 + 0.235428i \(0.0756493\pi\)
−0.971892 + 0.235428i \(0.924351\pi\)
\(224\) −1408.00 + 338.656i −0.419982 + 0.101015i
\(225\) 0 0
\(226\) 1710.00 + 4524.23i 0.503308 + 1.33163i
\(227\) −1264.67 −0.369775 −0.184888 0.982760i \(-0.559192\pi\)
−0.184888 + 0.982760i \(0.559192\pi\)
\(228\) −1037.13 1176.00i −0.301254 0.341590i
\(229\) 5153.92i 1.48725i −0.668595 0.743626i \(-0.733104\pi\)
0.668595 0.743626i \(-0.266896\pi\)
\(230\) 0 0
\(231\) −672.000 −0.191404
\(232\) −3174.90 1680.00i −0.898459 0.475420i
\(233\) 838.000i 0.235619i −0.993036 0.117809i \(-0.962413\pi\)
0.993036 0.117809i \(-0.0375872\pi\)
\(234\) 140.000 52.9150i 0.0391115 0.0147827i
\(235\) 0 0
\(236\) −2828.00 3206.65i −0.780030 0.884471i
\(237\) −2455.26 −0.672937
\(238\) 296.324 112.000i 0.0807052 0.0305037i
\(239\) −6288.00 −1.70183 −0.850914 0.525305i \(-0.823951\pi\)
−0.850914 + 0.525305i \(0.823951\pi\)
\(240\) 0 0
\(241\) −2926.00 −0.782076 −0.391038 0.920375i \(-0.627884\pi\)
−0.391038 + 0.920375i \(0.627884\pi\)
\(242\) −2854.77 + 1079.00i −0.758311 + 0.286615i
\(243\) 280.450 0.0740364
\(244\) 504.000 + 571.482i 0.132235 + 0.149940i
\(245\) 0 0
\(246\) −980.000 + 370.405i −0.253994 + 0.0960007i
\(247\) 1960.00i 0.504906i
\(248\) −2370.59 + 4480.00i −0.606987 + 1.14710i
\(249\) −2884.00 −0.734000
\(250\) 0 0
\(251\) 5444.96i 1.36925i 0.728894 + 0.684627i \(0.240035\pi\)
−0.728894 + 0.684627i \(0.759965\pi\)
\(252\) 42.3320 + 48.0000i 0.0105820 + 0.0119989i
\(253\) −2412.93 −0.599602
\(254\) −1664.00 4402.53i −0.411058 1.08756i
\(255\) 0 0
\(256\) −3968.00 1015.97i −0.968750 0.248039i
\(257\) 2562.00i 0.621841i −0.950436 0.310921i \(-0.899363\pi\)
0.950436 0.310921i \(-0.100637\pi\)
\(258\) 6148.73 2324.00i 1.48373 0.560798i
\(259\) 1947.27i 0.467172i
\(260\) 0 0
\(261\) 158.745i 0.0376478i
\(262\) 672.021 + 1778.00i 0.158464 + 0.419257i
\(263\) 5896.00i 1.38237i −0.722679 0.691184i \(-0.757089\pi\)
0.722679 0.691184i \(-0.242911\pi\)
\(264\) −1680.00 888.972i −0.391655 0.207244i
\(265\) 0 0
\(266\) 784.000 296.324i 0.180715 0.0683038i
\(267\) 1407.54 0.322622
\(268\) 1047.72 924.000i 0.238804 0.210606i
\(269\) 5365.58i 1.21615i 0.793878 + 0.608077i \(0.208059\pi\)
−0.793878 + 0.608077i \(0.791941\pi\)
\(270\) 0 0
\(271\) −1680.00 −0.376578 −0.188289 0.982114i \(-0.560294\pi\)
−0.188289 + 0.982114i \(0.560294\pi\)
\(272\) 888.972 + 112.000i 0.198169 + 0.0249669i
\(273\) 2240.00i 0.496597i
\(274\) −1062.00 2809.79i −0.234152 0.619509i
\(275\) 0 0
\(276\) 4256.00 + 4825.85i 0.928192 + 1.05247i
\(277\) −1576.87 −0.342039 −0.171019 0.985268i \(-0.554706\pi\)
−0.171019 + 0.985268i \(0.554706\pi\)
\(278\) 2693.37 + 7126.00i 0.581072 + 1.53737i
\(279\) 224.000 0.0480664
\(280\) 0 0
\(281\) −2742.00 −0.582114 −0.291057 0.956706i \(-0.594007\pi\)
−0.291057 + 0.956706i \(0.594007\pi\)
\(282\) −1777.94 4704.00i −0.375444 0.993330i
\(283\) −2989.70 −0.627983 −0.313991 0.949426i \(-0.601666\pi\)
−0.313991 + 0.949426i \(0.601666\pi\)
\(284\) −432.000 + 380.988i −0.0902623 + 0.0796038i
\(285\) 0 0
\(286\) −840.000 2222.43i −0.173672 0.459493i
\(287\) 560.000i 0.115177i
\(288\) 42.3320 + 176.000i 0.00866124 + 0.0360101i
\(289\) 4717.00 0.960106
\(290\) 0 0
\(291\) 5259.75i 1.05956i
\(292\) −1555.70 1764.00i −0.311783 0.353528i
\(293\) 9238.96 1.84214 0.921068 0.389401i \(-0.127318\pi\)
0.921068 + 0.389401i \(0.127318\pi\)
\(294\) 3906.00 1476.33i 0.774839 0.292861i
\(295\) 0 0
\(296\) −2576.00 + 4868.18i −0.505834 + 0.955937i
\(297\) 2184.00i 0.426695i
\(298\) 793.725 + 2100.00i 0.154293 + 0.408221i
\(299\) 8043.08i 1.55566i
\(300\) 0 0
\(301\) 3513.56i 0.672818i
\(302\) −1968.44 + 744.000i −0.375069 + 0.141763i
\(303\) 3976.00i 0.753846i
\(304\) 2352.00 + 296.324i 0.443738 + 0.0559058i
\(305\) 0 0
\(306\) −14.0000 37.0405i −0.00261545 0.00691982i
\(307\) 2587.54 0.481039 0.240520 0.970644i \(-0.422682\pi\)
0.240520 + 0.970644i \(0.422682\pi\)
\(308\) 761.976 672.000i 0.140966 0.124321i
\(309\) 6222.81i 1.14564i
\(310\) 0 0
\(311\) −2744.00 −0.500315 −0.250157 0.968205i \(-0.580482\pi\)
−0.250157 + 0.968205i \(0.580482\pi\)
\(312\) −2963.24 + 5600.00i −0.537694 + 1.01615i
\(313\) 2282.00i 0.412097i 0.978542 + 0.206048i \(0.0660604\pi\)
−0.978542 + 0.206048i \(0.933940\pi\)
\(314\) −476.000 + 179.911i −0.0855485 + 0.0323343i
\(315\) 0 0
\(316\) 2784.00 2455.26i 0.495608 0.437085i
\(317\) 9577.62 1.69695 0.848474 0.529237i \(-0.177522\pi\)
0.848474 + 0.529237i \(0.177522\pi\)
\(318\) −444.486 + 168.000i −0.0783822 + 0.0296257i
\(319\) 2520.00 0.442298
\(320\) 0 0
\(321\) 1428.00 0.248297
\(322\) −3217.23 + 1216.00i −0.556799 + 0.210450i
\(323\) −518.567 −0.0893308
\(324\) −4530.00 + 3995.08i −0.776749 + 0.685028i
\(325\) 0 0
\(326\) −4690.00 + 1772.65i −0.796795 + 0.301160i
\(327\) 10024.0i 1.69519i
\(328\) 740.810 1400.00i 0.124709 0.235677i
\(329\) 2688.00 0.450438
\(330\) 0 0
\(331\) 4249.08i 0.705590i −0.935701 0.352795i \(-0.885231\pi\)
0.935701 0.352795i \(-0.114769\pi\)
\(332\) 3270.15 2884.00i 0.540580 0.476747i
\(333\) 243.409 0.0400563
\(334\) −1960.00 5185.67i −0.321097 0.849543i
\(335\) 0 0
\(336\) −2688.00 338.656i −0.436436 0.0549857i
\(337\) 6130.00i 0.990868i −0.868646 0.495434i \(-0.835009\pi\)
0.868646 0.495434i \(-0.164991\pi\)
\(338\) −1595.39 + 603.000i −0.256739 + 0.0970381i
\(339\) 9048.47i 1.44969i
\(340\) 0 0
\(341\) 3555.89i 0.564699i
\(342\) −37.0405 98.0000i −0.00585650 0.0154948i
\(343\) 4976.00i 0.783320i
\(344\) −4648.00 + 8783.89i −0.728498 + 1.37673i
\(345\) 0 0
\(346\) 5292.00 2000.19i 0.822253 0.310783i
\(347\) 2481.71 0.383935 0.191967 0.981401i \(-0.438513\pi\)
0.191967 + 0.981401i \(0.438513\pi\)
\(348\) −4444.86 5040.00i −0.684683 0.776357i
\(349\) 328.073i 0.0503191i 0.999683 + 0.0251595i \(0.00800937\pi\)
−0.999683 + 0.0251595i \(0.991991\pi\)
\(350\) 0 0
\(351\) −7280.00 −1.10706
\(352\) 2793.91 672.000i 0.423057 0.101755i
\(353\) 10206.0i 1.53884i −0.638743 0.769420i \(-0.720545\pi\)
0.638743 0.769420i \(-0.279455\pi\)
\(354\) −2828.00 7482.18i −0.424595 1.12337i
\(355\) 0 0
\(356\) −1596.00 + 1407.54i −0.237606 + 0.209549i
\(357\) 592.648 0.0878607
\(358\) 3264.86 + 8638.00i 0.481992 + 1.27523i
\(359\) 3176.00 0.466916 0.233458 0.972367i \(-0.424996\pi\)
0.233458 + 0.972367i \(0.424996\pi\)
\(360\) 0 0
\(361\) 5487.00 0.799971
\(362\) 2338.84 + 6188.00i 0.339577 + 0.898437i
\(363\) −5709.53 −0.825545
\(364\) −2240.00 2539.92i −0.322549 0.365736i
\(365\) 0 0
\(366\) 504.000 + 1333.46i 0.0719795 + 0.190440i
\(367\) 11760.0i 1.67266i 0.548225 + 0.836331i \(0.315304\pi\)
−0.548225 + 0.836331i \(0.684696\pi\)
\(368\) −9651.70 1216.00i −1.36720 0.172251i
\(369\) −70.0000 −0.00987549
\(370\) 0 0
\(371\) 253.992i 0.0355434i
\(372\) −7111.78 + 6272.00i −0.991206 + 0.874161i
\(373\) 10974.6 1.52344 0.761719 0.647908i \(-0.224356\pi\)
0.761719 + 0.647908i \(0.224356\pi\)
\(374\) −588.000 + 222.243i −0.0812961 + 0.0307271i
\(375\) 0 0
\(376\) 6720.00 + 3555.89i 0.921696 + 0.487715i
\(377\) 8400.00i 1.14754i
\(378\) −1100.63 2912.00i −0.149763 0.396236i
\(379\) 3074.36i 0.416674i −0.978057 0.208337i \(-0.933195\pi\)
0.978057 0.208337i \(-0.0668051\pi\)
\(380\) 0 0
\(381\) 8805.06i 1.18398i
\(382\) −10329.0 + 3904.00i −1.38345 + 0.522895i
\(383\) 2688.00i 0.358617i 0.983793 + 0.179309i \(0.0573861\pi\)
−0.983793 + 0.179309i \(0.942614\pi\)
\(384\) −6272.00 4402.53i −0.833507 0.585067i
\(385\) 0 0
\(386\) −3330.00 8810.35i −0.439100 1.16175i
\(387\) 439.195 0.0576887
\(388\) −5259.75 5964.00i −0.688205 0.780351i
\(389\) 10487.8i 1.36697i −0.729966 0.683484i \(-0.760464\pi\)
0.729966 0.683484i \(-0.239536\pi\)
\(390\) 0 0
\(391\) 2128.00 0.275237
\(392\) −2952.66 + 5580.00i −0.380438 + 0.718961i
\(393\) 3556.00i 0.456429i
\(394\) 3164.00 1195.88i 0.404569 0.152913i
\(395\) 0 0
\(396\) −84.0000 95.2470i −0.0106595 0.0120867i
\(397\) −5704.24 −0.721127 −0.360564 0.932735i \(-0.617416\pi\)
−0.360564 + 0.932735i \(0.617416\pi\)
\(398\) −4593.02 + 1736.00i −0.578461 + 0.218638i
\(399\) 1568.00 0.196737
\(400\) 0 0
\(401\) 12402.0 1.54445 0.772227 0.635346i \(-0.219143\pi\)
0.772227 + 0.635346i \(0.219143\pi\)
\(402\) 2444.67 924.000i 0.303307 0.114639i
\(403\) −11853.0 −1.46511
\(404\) 3976.00 + 4508.36i 0.489637 + 0.555196i
\(405\) 0 0
\(406\) 3360.00 1269.96i 0.410724 0.155239i
\(407\) 3864.00i 0.470593i
\(408\) 1481.62 + 784.000i 0.179782 + 0.0951318i
\(409\) 12278.0 1.48437 0.742186 0.670194i \(-0.233789\pi\)
0.742186 + 0.670194i \(0.233789\pi\)
\(410\) 0 0
\(411\) 5619.58i 0.674436i
\(412\) 6222.81 + 7056.00i 0.744116 + 0.843748i
\(413\) 4275.53 0.509407
\(414\) 152.000 + 402.154i 0.0180444 + 0.0477411i
\(415\) 0 0
\(416\) −2240.00 9313.04i −0.264002 1.09762i
\(417\) 14252.0i 1.67368i
\(418\) −1555.70 + 588.000i −0.182038 + 0.0688039i
\(419\) 8207.12i 0.956907i 0.878113 + 0.478454i \(0.158802\pi\)
−0.878113 + 0.478454i \(0.841198\pi\)
\(420\) 0 0
\(421\) 1449.87i 0.167844i −0.996472 0.0839221i \(-0.973255\pi\)
0.996472 0.0839221i \(-0.0267447\pi\)
\(422\) 2915.62 + 7714.00i 0.336327 + 0.889838i
\(423\) 336.000i 0.0386215i
\(424\) 336.000 634.980i 0.0384849 0.0727296i
\(425\) 0 0
\(426\) −1008.00 + 380.988i −0.114643 + 0.0433308i
\(427\) −761.976 −0.0863574
\(428\) −1619.20 + 1428.00i −0.182867 + 0.161273i
\(429\) 4444.86i 0.500233i
\(430\) 0 0
\(431\) 7632.00 0.852948 0.426474 0.904500i \(-0.359756\pi\)
0.426474 + 0.904500i \(0.359756\pi\)
\(432\) 1100.63 8736.00i 0.122579 0.972942i
\(433\) 3794.00i 0.421081i 0.977585 + 0.210540i \(0.0675224\pi\)
−0.977585 + 0.210540i \(0.932478\pi\)
\(434\) −1792.00 4741.19i −0.198200 0.524388i
\(435\) 0 0
\(436\) 10024.0 + 11366.1i 1.10106 + 1.24849i
\(437\) 5630.16 0.616309
\(438\) −1555.70 4116.00i −0.169713 0.449018i
\(439\) 1848.00 0.200912 0.100456 0.994942i \(-0.467970\pi\)
0.100456 + 0.994942i \(0.467970\pi\)
\(440\) 0 0
\(441\) 279.000 0.0301263
\(442\) 740.810 + 1960.00i 0.0797212 + 0.210922i
\(443\) 12334.5 1.32287 0.661433 0.750004i \(-0.269949\pi\)
0.661433 + 0.750004i \(0.269949\pi\)
\(444\) −7728.00 + 6815.46i −0.826024 + 0.728485i
\(445\) 0 0
\(446\) −1568.00 4148.54i −0.166473 0.440446i
\(447\) 4200.00i 0.444414i
\(448\) 3386.56 2304.00i 0.357143 0.242977i
\(449\) 3582.00 0.376492 0.188246 0.982122i \(-0.439720\pi\)
0.188246 + 0.982122i \(0.439720\pi\)
\(450\) 0 0
\(451\) 1111.22i 0.116020i
\(452\) −9048.47 10260.0i −0.941602 1.06768i
\(453\) −3936.88 −0.408324
\(454\) 3346.00 1264.67i 0.345893 0.130735i
\(455\) 0 0
\(456\) 3920.00 + 2074.27i 0.402568 + 0.213019i
\(457\) 2714.00i 0.277802i −0.990306 0.138901i \(-0.955643\pi\)
0.990306 0.138901i \(-0.0443570\pi\)
\(458\) 5153.92 + 13636.0i 0.525823 + 1.39120i
\(459\) 1926.11i 0.195867i
\(460\) 0 0
\(461\) 8349.99i 0.843596i 0.906690 + 0.421798i \(0.138601\pi\)
−0.906690 + 0.421798i \(0.861399\pi\)
\(462\) 1777.94 672.000i 0.179042 0.0676716i
\(463\) 2224.00i 0.223236i 0.993751 + 0.111618i \(0.0356032\pi\)
−0.993751 + 0.111618i \(0.964397\pi\)
\(464\) 10080.0 + 1269.96i 1.00852 + 0.127061i
\(465\) 0 0
\(466\) 838.000 + 2217.14i 0.0833039 + 0.220401i
\(467\) 10292.0 1.01982 0.509910 0.860228i \(-0.329679\pi\)
0.509910 + 0.860228i \(0.329679\pi\)
\(468\) −317.490 + 280.000i −0.0313589 + 0.0276560i
\(469\) 1396.96i 0.137538i
\(470\) 0 0
\(471\) −952.000 −0.0931334
\(472\) 10688.8 + 5656.00i 1.04236 + 0.551565i
\(473\) 6972.00i 0.677744i
\(474\) 6496.00 2455.26i 0.629475 0.237919i
\(475\) 0 0
\(476\) −672.000 + 592.648i −0.0647081 + 0.0570672i
\(477\) −31.7490 −0.00304756
\(478\) 16636.5 6288.00i 1.59191 0.601687i
\(479\) −17696.0 −1.68800 −0.843999 0.536345i \(-0.819805\pi\)
−0.843999 + 0.536345i \(0.819805\pi\)
\(480\) 0 0
\(481\) −12880.0 −1.22095
\(482\) 7741.47 2926.00i 0.731565 0.276505i
\(483\) −6434.47 −0.606166
\(484\) 6474.00 5709.53i 0.608002 0.536207i
\(485\) 0 0
\(486\) −742.000 + 280.450i −0.0692547 + 0.0261758i
\(487\) 1304.00i 0.121334i −0.998158 0.0606672i \(-0.980677\pi\)
0.998158 0.0606672i \(-0.0193228\pi\)
\(488\) −1904.94 1008.00i −0.176706 0.0935041i
\(489\) −9380.00 −0.867440
\(490\) 0 0
\(491\) 16662.9i 1.53154i 0.643112 + 0.765772i \(0.277643\pi\)
−0.643112 + 0.765772i \(0.722357\pi\)
\(492\) 2222.43 1960.00i 0.203648 0.179601i
\(493\) −2222.43 −0.203029
\(494\) 1960.00 + 5185.67i 0.178511 + 0.472296i
\(495\) 0 0
\(496\) 1792.00 14223.6i 0.162224 1.28761i
\(497\) 576.000i 0.0519862i
\(498\) 7630.35 2884.00i 0.686594 0.259508i
\(499\) 3095.53i 0.277705i −0.990313 0.138853i \(-0.955659\pi\)
0.990313 0.138853i \(-0.0443414\pi\)
\(500\) 0 0
\(501\) 10371.3i 0.924865i
\(502\) −5444.96 14406.0i −0.484104 1.28082i
\(503\) 19320.0i 1.71260i −0.516481 0.856298i \(-0.672758\pi\)
0.516481 0.856298i \(-0.327242\pi\)
\(504\) −160.000 84.6640i −0.0141408 0.00748261i
\(505\) 0 0
\(506\) 6384.00 2412.93i 0.560876 0.211991i
\(507\) −3190.78 −0.279502
\(508\) 8805.06 + 9984.00i 0.769018 + 0.871985i
\(509\) 4476.61i 0.389828i 0.980820 + 0.194914i \(0.0624427\pi\)
−0.980820 + 0.194914i \(0.937557\pi\)
\(510\) 0 0
\(511\) 2352.00 0.203613
\(512\) 11514.3 1280.00i 0.993878 0.110485i
\(513\) 5096.00i 0.438585i
\(514\) 2562.00 + 6778.41i 0.219854 + 0.581679i
\(515\) 0 0
\(516\) −13944.0 + 12297.5i −1.18963 + 1.04916i
\(517\) −5333.83 −0.453737
\(518\) −1947.27 5152.00i −0.165170 0.437000i
\(519\) 10584.0 0.895156
\(520\) 0 0
\(521\) −2982.00 −0.250756 −0.125378 0.992109i \(-0.540014\pi\)
−0.125378 + 0.992109i \(0.540014\pi\)
\(522\) −158.745 420.000i −0.0133105 0.0352163i
\(523\) −2016.06 −0.168559 −0.0842794 0.996442i \(-0.526859\pi\)
−0.0842794 + 0.996442i \(0.526859\pi\)
\(524\) −3556.00 4032.12i −0.296459 0.336153i
\(525\) 0 0
\(526\) 5896.00 + 15599.3i 0.488741 + 1.29309i
\(527\) 3136.00i 0.259215i
\(528\) 5333.83 + 672.000i 0.439631 + 0.0553883i
\(529\) −10937.0 −0.898907
\(530\) 0 0
\(531\) 534.442i 0.0436776i
\(532\) −1777.94 + 1568.00i −0.144894 + 0.127785i
\(533\) 3704.05 0.301014
\(534\) −3724.00 + 1407.54i −0.301785 + 0.114064i
\(535\) 0 0
\(536\) −1848.00 + 3492.39i −0.148921 + 0.281433i
\(537\) 17276.0i 1.38830i
\(538\) −5365.58 14196.0i −0.429975 1.13761i
\(539\) 4428.99i 0.353933i
\(540\) 0 0
\(541\) 15419.4i 1.22539i 0.790321 + 0.612693i \(0.209914\pi\)
−0.790321 + 0.612693i \(0.790086\pi\)
\(542\) 4444.86 1680.00i 0.352257 0.133141i
\(543\) 12376.0i 0.978094i
\(544\) −2464.00 + 592.648i −0.194197 + 0.0467088i
\(545\) 0 0
\(546\) −2240.00 5926.48i −0.175574 0.464524i
\(547\) −12609.7 −0.985649 −0.492824 0.870129i \(-0.664035\pi\)
−0.492824 + 0.870129i \(0.664035\pi\)
\(548\) 5619.58 + 6372.00i 0.438059 + 0.496712i
\(549\) 95.2470i 0.00740445i
\(550\) 0 0
\(551\) −5880.00 −0.454621
\(552\) −16086.2 8512.00i −1.24035 0.656331i
\(553\) 3712.00i 0.285444i
\(554\) 4172.00 1576.87i 0.319948 0.120929i
\(555\) 0 0
\(556\) −14252.0 16160.2i −1.08709 1.23264i
\(557\) −7143.53 −0.543413 −0.271706 0.962380i \(-0.587588\pi\)
−0.271706 + 0.962380i \(0.587588\pi\)
\(558\) −592.648 + 224.000i −0.0449620 + 0.0169940i
\(559\) −23240.0 −1.75840
\(560\) 0 0
\(561\) −1176.00 −0.0885040
\(562\) 7254.65 2742.00i 0.544518 0.205808i
\(563\) 7572.14 0.566834 0.283417 0.958997i \(-0.408532\pi\)
0.283417 + 0.958997i \(0.408532\pi\)
\(564\) 9408.00 + 10667.7i 0.702391 + 0.796436i
\(565\) 0 0
\(566\) 7910.00 2989.70i 0.587424 0.222025i
\(567\) 6040.00i 0.447365i
\(568\) 761.976 1440.00i 0.0562884 0.106375i
\(569\) −15594.0 −1.14892 −0.574459 0.818533i \(-0.694788\pi\)
−0.574459 + 0.818533i \(0.694788\pi\)
\(570\) 0 0
\(571\) 16737.0i 1.22666i −0.789827 0.613330i \(-0.789830\pi\)
0.789827 0.613330i \(-0.210170\pi\)
\(572\) 4444.86 + 5040.00i 0.324911 + 0.368414i
\(573\) −20658.0 −1.50611
\(574\) 560.000 + 1481.62i 0.0407212 + 0.107738i
\(575\) 0 0
\(576\) −288.000 423.320i −0.0208333 0.0306221i
\(577\) 6594.00i 0.475757i −0.971295 0.237879i \(-0.923548\pi\)
0.971295 0.237879i \(-0.0764520\pi\)
\(578\) −12480.0 + 4717.00i −0.898097 + 0.339449i
\(579\) 17620.7i 1.26475i
\(580\) 0 0
\(581\) 4360.20i 0.311345i
\(582\) −5259.75 13916.0i −0.374611 0.991128i
\(583\) 504.000i 0.0358037i
\(584\) 5880.00 + 3111.40i 0.416637 + 0.220464i
\(585\) 0 0
\(586\) −24444.0 + 9238.96i −1.72316 + 0.651294i
\(587\) −23213.8 −1.63226 −0.816130 0.577868i \(-0.803885\pi\)
−0.816130 + 0.577868i \(0.803885\pi\)
\(588\) −8857.98 + 7812.00i −0.621253 + 0.547894i
\(589\) 8297.08i 0.580433i
\(590\) 0 0
\(591\) 6328.00 0.440438
\(592\) 1947.27 15456.0i 0.135190 1.07304i
\(593\) 14322.0i 0.991794i 0.868381 + 0.495897i \(0.165161\pi\)
−0.868381 + 0.495897i \(0.834839\pi\)
\(594\) 2184.00 + 5778.32i 0.150860 + 0.399137i
\(595\) 0 0
\(596\) −4200.00 4762.35i −0.288656 0.327305i
\(597\) −9186.05 −0.629749
\(598\) −8043.08 21280.0i −0.550010 1.45519i
\(599\) 16088.0 1.09739 0.548696 0.836022i \(-0.315124\pi\)
0.548696 + 0.836022i \(0.315124\pi\)
\(600\) 0 0
\(601\) −21238.0 −1.44146 −0.720729 0.693217i \(-0.756193\pi\)
−0.720729 + 0.693217i \(0.756193\pi\)
\(602\) −3513.56 9296.00i −0.237877 0.629363i
\(603\) 174.620 0.0117928
\(604\) 4464.00 3936.88i 0.300724 0.265214i
\(605\) 0 0
\(606\) 3976.00 + 10519.5i 0.266525 + 0.705158i
\(607\) 13664.0i 0.913681i 0.889549 + 0.456841i \(0.151019\pi\)
−0.889549 + 0.456841i \(0.848981\pi\)
\(608\) −6519.13 + 1568.00i −0.434845 + 0.104590i
\(609\) 6720.00 0.447140
\(610\) 0 0
\(611\) 17779.4i 1.17722i
\(612\) 74.0810 + 84.0000i 0.00489305 + 0.00554820i
\(613\) −20393.5 −1.34369 −0.671846 0.740690i \(-0.734499\pi\)
−0.671846 + 0.740690i \(0.734499\pi\)
\(614\) −6846.00 + 2587.54i −0.449971 + 0.170073i
\(615\) 0 0
\(616\) −1344.00 + 2539.92i −0.0879080 + 0.166130i
\(617\) 3782.00i 0.246771i 0.992359 + 0.123385i \(0.0393751\pi\)
−0.992359 + 0.123385i \(0.960625\pi\)
\(618\) 6222.81 + 16464.0i 0.405045 + 1.07165i
\(619\) 5825.94i 0.378295i −0.981949 0.189147i \(-0.939428\pi\)
0.981949 0.189147i \(-0.0605724\pi\)
\(620\) 0 0
\(621\) 20912.0i 1.35132i
\(622\) 7259.94 2744.00i 0.468002 0.176888i
\(623\) 2128.00i 0.136848i
\(624\) 2240.00 17779.4i 0.143705 1.14062i
\(625\) 0 0
\(626\) −2282.00 6037.60i −0.145698 0.385481i
\(627\) −3111.40 −0.198178
\(628\) 1079.47 952.000i 0.0685914 0.0604919i
\(629\) 3407.73i 0.216017i
\(630\) 0 0
\(631\) 2056.00 0.129712 0.0648558 0.997895i \(-0.479341\pi\)
0.0648558 + 0.997895i \(0.479341\pi\)
\(632\) −4910.51 + 9280.00i −0.309066 + 0.584080i
\(633\) 15428.0i 0.968733i
\(634\) −25340.0 + 9577.62i −1.58735 + 0.599962i
\(635\) 0 0
\(636\) 1008.00 888.972i 0.0628456 0.0554246i
\(637\) −14763.3 −0.918278
\(638\) −6667.29 + 2520.00i −0.413731 + 0.156376i
\(639\) −72.0000 −0.00445740
\(640\) 0 0
\(641\) 11842.0 0.729689 0.364845 0.931068i \(-0.381122\pi\)
0.364845 + 0.931068i \(0.381122\pi\)
\(642\) −3778.13 + 1428.00i −0.232260 + 0.0877861i
\(643\) 16250.2 0.996649 0.498325 0.866991i \(-0.333949\pi\)
0.498325 + 0.866991i \(0.333949\pi\)
\(644\) 7296.00 6434.47i 0.446433 0.393717i
\(645\) 0 0
\(646\) 1372.00 518.567i 0.0835613 0.0315832i
\(647\) 19320.0i 1.17395i −0.809604 0.586976i \(-0.800318\pi\)
0.809604 0.586976i \(-0.199682\pi\)
\(648\) 7990.17 15100.0i 0.484388 0.915407i
\(649\) −8484.00 −0.513137
\(650\) 0 0
\(651\) 9482.37i 0.570881i
\(652\) 10635.9 9380.00i 0.638857 0.563419i
\(653\) 2317.68 0.138894 0.0694470 0.997586i \(-0.477877\pi\)
0.0694470 + 0.997586i \(0.477877\pi\)
\(654\) 10024.0 + 26521.0i 0.599342 + 1.58571i
\(655\) 0 0
\(656\) −560.000 + 4444.86i −0.0333298 + 0.264547i
\(657\) 294.000i 0.0174582i
\(658\) −7111.78 + 2688.00i −0.421347 + 0.159254i
\(659\) 27732.8i 1.63932i −0.572847 0.819662i \(-0.694161\pi\)
0.572847 0.819662i \(-0.305839\pi\)
\(660\) 0 0
\(661\) 22467.7i 1.32208i 0.750352 + 0.661039i \(0.229884\pi\)
−0.750352 + 0.661039i \(0.770116\pi\)
\(662\) 4249.08 + 11242.0i 0.249464 + 0.660019i
\(663\) 3920.00i 0.229623i
\(664\) −5768.00 + 10900.5i −0.337111 + 0.637080i
\(665\) 0 0
\(666\) −644.000 + 243.409i −0.0374692 + 0.0141620i
\(667\) 24129.3 1.40073
\(668\) 10371.3 + 11760.0i 0.600718 + 0.681150i
\(669\) 8297.08i 0.479497i
\(670\) 0 0
\(671\) 1512.00 0.0869897
\(672\) 7450.44 1792.00i 0.427689 0.102869i
\(673\) 10078.0i 0.577234i −0.957445 0.288617i \(-0.906805\pi\)
0.957445 0.288617i \(-0.0931954\pi\)
\(674\) 6130.00 + 16218.5i 0.350325 + 0.926872i
\(675\) 0 0
\(676\) 3618.00 3190.78i 0.205849 0.181542i
\(677\) 16160.2 0.917413 0.458707 0.888588i \(-0.348313\pi\)
0.458707 + 0.888588i \(0.348313\pi\)
\(678\) −9048.47 23940.0i −0.512543 1.35606i
\(679\) 7952.00 0.449440
\(680\) 0 0
\(681\) 6692.00 0.376561
\(682\) 3555.89 + 9408.00i 0.199651 + 0.528227i
\(683\) 16356.0 0.916320 0.458160 0.888870i \(-0.348509\pi\)
0.458160 + 0.888870i \(0.348509\pi\)
\(684\) 196.000 + 222.243i 0.0109565 + 0.0124235i
\(685\) 0 0
\(686\) −4976.00 13165.3i −0.276945 0.732729i
\(687\) 27272.0i 1.51454i
\(688\) 3513.56 27888.0i 0.194699 1.54538i
\(689\) 1680.00 0.0928925
\(690\) 0 0
\(691\) 29246.1i 1.61009i −0.593211 0.805047i \(-0.702140\pi\)
0.593211 0.805047i \(-0.297860\pi\)
\(692\) −12001.1 + 10584.0i −0.659269 + 0.581421i
\(693\) 126.996 0.00696130
\(694\) −6566.00 + 2481.71i −0.359138 + 0.135742i
\(695\) 0 0
\(696\) 16800.0 + 8889.72i 0.914946 + 0.484144i
\(697\) 980.000i 0.0532570i
\(698\) −328.073 868.000i −0.0177905 0.0470692i
\(699\) 4434.28i 0.239943i
\(700\) 0 0
\(701\) 2465.84i 0.132858i 0.997791 + 0.0664290i \(0.0211606\pi\)
−0.997791 + 0.0664290i \(0.978839\pi\)
\(702\) 19261.1 7280.00i 1.03556 0.391404i
\(703\) 9016.00i 0.483705i
\(704\) −6720.00 + 4571.86i −0.359758 + 0.244756i
\(705\) 0 0
\(706\) 10206.0 + 27002.5i 0.544062 + 1.43945i
\(707\) −6011.15 −0.319763
\(708\) 14964.4 + 16968.0i 0.794344 + 0.900701i
\(709\) 31674.9i 1.67782i 0.544267 + 0.838912i \(0.316808\pi\)
−0.544267 + 0.838912i \(0.683192\pi\)
\(710\) 0 0
\(711\) 464.000 0.0244745
\(712\) 2815.08 5320.00i 0.148174 0.280022i
\(713\) 34048.0i 1.78837i
\(714\) −1568.00 + 592.648i −0.0821862 + 0.0310635i
\(715\) 0 0
\(716\) −17276.0 19589.1i −0.901724 1.02246i
\(717\) 33273.0 1.73306
\(718\) −8402.91 + 3176.00i −0.436760 + 0.165080i
\(719\) 9296.00 0.482173 0.241086 0.970504i \(-0.422496\pi\)
0.241086 + 0.970504i \(0.422496\pi\)
\(720\) 0 0
\(721\) −9408.00 −0.485953
\(722\) −14517.2 + 5487.00i −0.748304 + 0.282832i
\(723\) 15482.9 0.796427
\(724\) −12376.0 14033.1i −0.635291 0.720352i
\(725\) 0 0
\(726\) 15106.0 5709.53i 0.772226 0.291874i
\(727\) 21672.0i 1.10560i −0.833315 0.552799i \(-0.813560\pi\)
0.833315 0.552799i \(-0.186440\pi\)
\(728\) 8466.40 + 4480.00i 0.431024 + 0.228077i
\(729\) 18901.0 0.960270
\(730\) 0 0
\(731\) 6148.73i 0.311106i
\(732\) −2666.92 3024.00i −0.134661 0.152692i
\(733\) 9471.79 0.477283 0.238642 0.971108i \(-0.423298\pi\)
0.238642 + 0.971108i \(0.423298\pi\)
\(734\) −11760.0 31114.0i −0.591375 1.56463i
\(735\) 0 0
\(736\) 26752.0 6434.47i 1.33980 0.322252i
\(737\) 2772.00i 0.138545i
\(738\) 185.203 70.0000i 0.00923767 0.00349151i
\(739\) 6863.08i 0.341627i −0.985303 0.170814i \(-0.945360\pi\)
0.985303 0.170814i \(-0.0546396\pi\)
\(740\) 0 0
\(741\) 10371.3i 0.514171i
\(742\) 253.992 + 672.000i 0.0125665 + 0.0332478i
\(743\) 17432.0i 0.860724i 0.902656 + 0.430362i \(0.141614\pi\)
−0.902656 + 0.430362i \(0.858386\pi\)
\(744\) 12544.0 23705.9i 0.618125 1.16815i
\(745\) 0 0
\(746\) −29036.0 + 10974.6i −1.42504 + 0.538616i
\(747\) 545.025 0.0266953
\(748\) 1333.46 1176.00i 0.0651819 0.0574851i
\(749\) 2158.93i 0.105321i
\(750\) 0 0
\(751\) −11632.0 −0.565190 −0.282595 0.959239i \(-0.591195\pi\)
−0.282595 + 0.959239i \(0.591195\pi\)
\(752\) −21335.3 2688.00i −1.03460 0.130347i
\(753\) 28812.0i 1.39438i
\(754\) 8400.00 + 22224.3i 0.405716 + 1.07342i
\(755\) 0 0
\(756\) 5824.00 + 6603.80i 0.280181 + 0.317695i
\(757\) −16731.7 −0.803336 −0.401668 0.915785i \(-0.631569\pi\)
−0.401668 + 0.915785i \(0.631569\pi\)
\(758\) 3074.36 + 8134.00i 0.147316 + 0.389763i
\(759\) 12768.0 0.610605
\(760\) 0 0
\(761\) 39466.0 1.87995 0.939975 0.341244i \(-0.110848\pi\)
0.939975 + 0.341244i \(0.110848\pi\)
\(762\) 8805.06 + 23296.0i 0.418601 + 1.10751i
\(763\) −15154.9 −0.719060
\(764\) 23424.0 20658.0i 1.10923 0.978248i
\(765\) 0 0
\(766\) −2688.00 7111.78i −0.126790 0.335456i
\(767\) 28280.0i 1.33133i
\(768\) 20996.7 + 5376.00i 0.986527 + 0.252591i
\(769\) −35266.0 −1.65374 −0.826869 0.562395i \(-0.809880\pi\)
−0.826869 + 0.562395i \(0.809880\pi\)
\(770\) 0 0
\(771\) 13556.8i 0.633252i
\(772\) 17620.7 + 19980.0i 0.821481 + 0.931471i
\(773\) −16244.9 −0.755872 −0.377936 0.925832i \(-0.623366\pi\)
−0.377936 + 0.925832i \(0.623366\pi\)
\(774\) −1162.00 + 439.195i −0.0539628 + 0.0203960i
\(775\) 0 0
\(776\) 19880.0 + 10519.5i 0.919653 + 0.486634i
\(777\) 10304.0i 0.475745i
\(778\) 10487.8 + 27748.0i 0.483296 + 1.27868i
\(779\) 2592.84i 0.119253i
\(780\) 0 0
\(781\) 1142.96i 0.0523668i
\(782\) −5630.16 + 2128.00i −0.257460 + 0.0973109i
\(783\) 21840.0i 0.996805i
\(784\) 2232.00 17716.0i 0.101676 0.807031i
\(785\) 0 0
\(786\) −3556.00 9408.29i −0.161372 0.426950i
\(787\) 34844.5 1.57824 0.789119 0.614240i \(-0.210537\pi\)
0.789119 + 0.614240i \(0.210537\pi\)
\(788\) −7175.28 + 6328.00i −0.324376 + 0.286073i
\(789\) 31198.7i 1.40774i
\(790\) 0 0
\(791\) 13680.0 0.614924
\(792\) 317.490 + 168.000i 0.0142443 + 0.00753740i
\(793\) 5040.00i 0.225694i
\(794\) 15092.0 5704.24i 0.674553 0.254957i
\(795\) 0 0
\(796\) 10416.0 9186.05i 0.463801 0.409034i
\(797\) 2550.50 0.113354 0.0566772 0.998393i \(-0.481949\pi\)
0.0566772 + 0.998393i \(0.481949\pi\)
\(798\) −4148.54 + 1568.00i −0.184031 + 0.0695571i
\(799\) 4704.00 0.208280
\(800\) 0 0
\(801\) −266.000 −0.0117336
\(802\) −32812.6 + 12402.0i −1.44471 + 0.546047i
\(803\) −4667.11 −0.205104
\(804\) −5544.00 + 4889.35i −0.243186 + 0.214470i
\(805\) 0 0
\(806\) 31360.0 11853.0i 1.37048 0.517994i
\(807\) 28392.0i 1.23847i
\(808\) −15027.9 7952.00i −0.654305 0.346226i
\(809\) 24390.0 1.05996 0.529979 0.848010i \(-0.322200\pi\)
0.529979 + 0.848010i \(0.322200\pi\)
\(810\) 0 0
\(811\) 9582.91i 0.414922i −0.978243 0.207461i \(-0.933480\pi\)
0.978243 0.207461i \(-0.0665200\pi\)
\(812\) −7619.76 + 6720.00i −0.329312 + 0.290426i
\(813\) 8889.72 0.383489
\(814\) 3864.00 + 10223.2i 0.166380 + 0.440199i
\(815\) 0 0
\(816\) −4704.00 592.648i −0.201805 0.0254250i
\(817\) 16268.0i 0.696628i
\(818\) −32484.5 + 12278.0i −1.38850 + 0.524805i
\(819\) 423.320i 0.0180611i
\(820\) 0 0
\(821\) 8773.31i 0.372948i −0.982460 0.186474i \(-0.940294\pi\)
0.982460 0.186474i \(-0.0597061\pi\)
\(822\) 5619.58 + 14868.0i 0.238449 + 0.630877i
\(823\) 21688.0i 0.918586i −0.888285 0.459293i \(-0.848103\pi\)
0.888285 0.459293i \(-0.151897\pi\)
\(824\) −23520.0 12445.6i −0.994367 0.526169i
\(825\) 0 0
\(826\) −11312.0 + 4275.53i −0.476507 + 0.180103i
\(827\) −19446.3 −0.817670 −0.408835 0.912608i \(-0.634065\pi\)
−0.408835 + 0.912608i \(0.634065\pi\)
\(828\) −804.308 912.000i −0.0337580 0.0382780i
\(829\) 19546.8i 0.818925i 0.912327 + 0.409462i \(0.134284\pi\)
−0.912327 + 0.409462i \(0.865716\pi\)
\(830\) 0 0
\(831\) 8344.00 0.348315
\(832\) 15239.5 + 22400.0i 0.635019 + 0.933390i
\(833\) 3906.00i 0.162467i
\(834\) −14252.0 37707.2i −0.591734 1.56558i
\(835\) 0 0
\(836\) 3528.00 3111.40i 0.145955 0.128720i
\(837\) 30817.7 1.27266
\(838\) −8207.12 21714.0i −0.338318 0.895105i
\(839\) 18760.0 0.771951 0.385976 0.922509i \(-0.373865\pi\)
0.385976 + 0.922509i \(0.373865\pi\)
\(840\) 0 0
\(841\) −811.000 −0.0332527
\(842\) 1449.87 + 3836.00i 0.0593419 + 0.157004i
\(843\) 14509.3 0.592796
\(844\) −15428.0 17493.7i −0.629210 0.713458i
\(845\) 0 0
\(846\) 336.000 + 888.972i 0.0136547 + 0.0361271i
\(847\) 8632.00i 0.350176i
\(848\) −253.992 + 2016.00i −0.0102855 + 0.0816388i
\(849\) 15820.0 0.639506
\(850\) 0 0
\(851\) 36998.2i 1.49034i
\(852\) 2285.93 2016.00i 0.0919186 0.0810646i
\(853\) −28732.9 −1.15333 −0.576667 0.816979i \(-0.695647\pi\)
−0.576667 + 0.816979i \(0.695647\pi\)
\(854\) 2016.00 761.976i 0.0807800 0.0305320i
\(855\) 0 0
\(856\) 2856.00 5397.33i 0.114037 0.215511i
\(857\) 8778.00i 0.349884i −0.984579 0.174942i \(-0.944026\pi\)
0.984579 0.174942i \(-0.0559738\pi\)
\(858\) 4444.86 + 11760.0i 0.176859 + 0.467925i
\(859\) 5646.03i 0.224261i 0.993693 + 0.112130i \(0.0357675\pi\)
−0.993693 + 0.112130i \(0.964233\pi\)
\(860\) 0 0
\(861\) 2963.24i 0.117290i
\(862\) −20192.4 + 7632.00i −0.797860 + 0.301563i
\(863\) 9312.00i 0.367305i −0.982991 0.183652i \(-0.941208\pi\)
0.982991 0.183652i \(-0.0587921\pi\)
\(864\) 5824.00 + 24213.9i 0.229325 + 0.953442i
\(865\) 0 0
\(866\) −3794.00 10038.0i −0.148875 0.393885i
\(867\) −24960.0 −0.977724
\(868\) 9482.37 + 10752.0i 0.370798 + 0.420445i
\(869\) 7365.77i 0.287534i
\(870\) 0 0
\(871\) −9240.00 −0.359455
\(872\) −37887.2 20048.0i −1.47135 0.778568i
\(873\) 994.000i 0.0385359i
\(874\) −14896.0 + 5630.16i −0.576504 + 0.217898i
\(875\) 0 0
\(876\) 8232.00 + 9334.21i 0.317504 + 0.360016i
\(877\) 137.579 0.00529728 0.00264864 0.999996i \(-0.499157\pi\)
0.00264864 + 0.999996i \(0.499157\pi\)
\(878\) −4889.35 + 1848.00i −0.187936 + 0.0710330i
\(879\) −48888.0 −1.87594
\(880\) 0 0
\(881\) −31150.0 −1.19123 −0.595613 0.803272i \(-0.703091\pi\)
−0.595613 + 0.803272i \(0.703091\pi\)
\(882\) −738.165 + 279.000i −0.0281806 + 0.0106513i
\(883\) −12577.9 −0.479366 −0.239683 0.970851i \(-0.577043\pi\)
−0.239683 + 0.970851i \(0.577043\pi\)
\(884\) −3920.00 4444.86i −0.149145 0.169114i
\(885\) 0 0
\(886\) −32634.0 + 12334.5i −1.23743 + 0.467704i
\(887\) 37128.0i 1.40545i −0.711460 0.702726i \(-0.751966\pi\)
0.711460 0.702726i \(-0.248034\pi\)
\(888\) 13630.9 25760.0i 0.515116 0.973479i
\(889\) −13312.0 −0.502216
\(890\) 0 0
\(891\) 11985.3i 0.450641i
\(892\) 8297.08 + 9408.00i 0.311442 + 0.353143i
\(893\) 12445.6 0.466379
\(894\) −4200.00 11112.2i −0.157124 0.415711i
\(895\) 0 0
\(896\) −6656.00 + 9482.37i −0.248171 + 0.353553i
\(897\) 42560.0i 1.58421i
\(898\) −9477.08 + 3582.00i −0.352176 + 0.133110i
\(899\) 35558.9i 1.31919i
\(900\) 0 0
\(901\) 444.486i 0.0164351i
\(902\) −1111.22 2940.00i −0.0410193 0.108527i
\(903\) 18592.0i 0.685164i
\(904\) 34200.0 + 18096.9i 1.25827 + 0.665813i
\(905\) 0 0
\(906\) 10416.0 3936.88i 0.381952 0.144364i
\(907\) 35204.4 1.28880 0.644400 0.764688i \(-0.277107\pi\)
0.644400 + 0.764688i \(0.277107\pi\)
\(908\) −7588.01 + 6692.00i −0.277332 + 0.244584i
\(909\) 751.393i 0.0274171i
\(910\) 0 0
\(911\) −10512.0 −0.382303 −0.191152 0.981561i \(-0.561222\pi\)
−0.191152 + 0.981561i \(0.561222\pi\)
\(912\) −12445.6 1568.00i −0.451881 0.0569317i
\(913\) 8652.00i 0.313625i
\(914\) 2714.00 + 7180.57i 0.0982179 + 0.259860i
\(915\) 0 0
\(916\) −27272.0 30923.5i −0.983725 1.11544i
\(917\) 5376.17 0.193606
\(918\) −1926.11 5096.00i −0.0692495 0.183217i
\(919\) 46104.0 1.65488 0.827438 0.561557i \(-0.189798\pi\)
0.827438 + 0.561557i \(0.189798\pi\)
\(920\) 0 0
\(921\) −13692.0 −0.489866
\(922\) −8349.99 22092.0i −0.298256 0.789112i
\(923\) 3809.88 0.135865
\(924\) −4032.00 + 3555.89i −0.143553 + 0.126602i
\(925\) 0 0
\(926\) −2224.00 5884.15i −0.0789257 0.208818i
\(927\) 1176.00i 0.0416666i
\(928\) −27939.1 + 6720.00i −0.988305 + 0.237710i
\(929\) 5726.00 0.202222 0.101111 0.994875i \(-0.467760\pi\)
0.101111 + 0.994875i \(0.467760\pi\)
\(930\) 0 0
\(931\) 10334.3i 0.363795i
\(932\) −4434.28 5028.00i −0.155847 0.176714i
\(933\) 14519.9 0.509496
\(934\) −27230.0 + 10292.0i −0.953954 + 0.360561i
\(935\) 0 0
\(936\) 560.000 1058.30i 0.0195557 0.0369569i
\(937\) 1274.00i 0.0444181i −0.999753 0.0222091i \(-0.992930\pi\)
0.999753 0.0222091i \(-0.00706994\pi\)
\(938\) −1396.96 3696.00i −0.0486271 0.128655i
\(939\) 12075.2i 0.419659i
\(940\) 0 0
\(941\) 26446.9i 0.916201i −0.888900 0.458101i \(-0.848530\pi\)
0.888900 0.458101i \(-0.151470\pi\)
\(942\) 2518.76 952.000i 0.0871183 0.0329276i
\(943\) 10640.0i 0.367430i
\(944\) −33936.0 4275.53i −1.17005 0.147412i
\(945\) 0 0
\(946\) 6972.00 + 18446.2i 0.239619 + 0.633971i
\(947\) 23922.9 0.820897 0.410448 0.911884i \(-0.365372\pi\)
0.410448 + 0.911884i \(0.365372\pi\)
\(948\) −14731.5 + 12992.0i −0.504703 + 0.445106i
\(949\) 15557.0i 0.532141i
\(950\) 0 0
\(951\) −50680.0 −1.72809
\(952\) 1185.30 2240.00i 0.0403526 0.0762593i
\(953\) 38250.0i 1.30015i 0.759872 + 0.650073i \(0.225262\pi\)
−0.759872 + 0.650073i \(0.774738\pi\)
\(954\) 84.0000 31.7490i 0.00285073 0.00107748i
\(955\) 0 0
\(956\) −37728.0 + 33273.0i −1.27637 + 1.12565i
\(957\) −13334.6 −0.450414
\(958\) 46819.2 17696.0i 1.57898 0.596797i
\(959\) −8496.00 −0.286079
\(960\) 0 0
\(961\) 20385.0 0.684267
\(962\) 34077.3 12880.0i 1.14210 0.431671i
\(963\) −269.867 −0.00903046
\(964\) −17556.0 + 15482.9i −0.586557 + 0.517294i
\(965\) 0 0
\(966\) 17024.0 6434.47i 0.567017 0.214312i
\(967\) 4664.00i 0.155103i −0.996988 0.0775513i \(-0.975290\pi\)
0.996988 0.0775513i \(-0.0247101\pi\)
\(968\) −11419.1 + 21580.0i −0.379156 + 0.716537i
\(969\) 2744.00 0.0909701
\(970\) 0 0
\(971\) 30971.2i 1.02360i 0.859106 + 0.511798i \(0.171020\pi\)
−0.859106 + 0.511798i \(0.828980\pi\)
\(972\) 1682.70 1484.00i 0.0555273 0.0489705i
\(973\) 21547.0 0.709933
\(974\) 1304.00 + 3450.06i 0.0428982 + 0.113498i
\(975\) 0 0
\(976\) 6048.00 + 761.976i 0.198352 + 0.0249900i
\(977\) 4814.00i 0.157639i 0.996889 + 0.0788196i \(0.0251151\pi\)
−0.996889 + 0.0788196i \(0.974885\pi\)
\(978\) 24817.1 9380.00i 0.811416 0.306686i
\(979\) 4222.62i 0.137850i
\(980\) 0 0
\(981\) 1894.36i 0.0616536i
\(982\) −16662.9 44086.0i −0.541483 1.43263i
\(983\) 12376.0i 0.401560i −0.979636 0.200780i \(-0.935652\pi\)
0.979636 0.200780i \(-0.0643476\pi\)
\(984\) −3920.00 + 7408.10i −0.126997 + 0.240002i
\(985\) 0 0
\(986\) 5880.00 2222.43i 0.189916 0.0717816i
\(987\) −14223.6 −0.458704
\(988\) −10371.3 11760.0i −0.333964 0.378680i
\(989\) 66757.6i 2.14638i
\(990\) 0 0
\(991\) 45344.0 1.45348 0.726740 0.686912i \(-0.241034\pi\)
0.726740 + 0.686912i \(0.241034\pi\)
\(992\) 9482.37 + 39424.0i 0.303494 + 1.26181i
\(993\) 22484.0i 0.718538i
\(994\) 576.000 + 1523.95i 0.0183799 + 0.0486286i
\(995\) 0 0
\(996\) −17304.0 + 15260.7i −0.550500 + 0.485496i
\(997\) −26002.4 −0.825984 −0.412992 0.910735i \(-0.635516\pi\)
−0.412992 + 0.910735i \(0.635516\pi\)
\(998\) 3095.53 + 8190.00i 0.0981836 + 0.259769i
\(999\) 33488.0 1.06057
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 200.4.f.a.149.2 4
4.3 odd 2 800.4.f.a.49.3 4
5.2 odd 4 8.4.b.a.5.1 2
5.3 odd 4 200.4.d.a.101.2 2
5.4 even 2 inner 200.4.f.a.149.3 4
8.3 odd 2 800.4.f.a.49.1 4
8.5 even 2 inner 200.4.f.a.149.4 4
15.2 even 4 72.4.d.b.37.2 2
20.3 even 4 800.4.d.a.401.2 2
20.7 even 4 32.4.b.a.17.1 2
20.19 odd 2 800.4.f.a.49.2 4
40.3 even 4 800.4.d.a.401.1 2
40.13 odd 4 200.4.d.a.101.1 2
40.19 odd 2 800.4.f.a.49.4 4
40.27 even 4 32.4.b.a.17.2 2
40.29 even 2 inner 200.4.f.a.149.1 4
40.37 odd 4 8.4.b.a.5.2 yes 2
60.47 odd 4 288.4.d.a.145.2 2
80.27 even 4 256.4.a.j.1.1 2
80.37 odd 4 256.4.a.l.1.2 2
80.67 even 4 256.4.a.j.1.2 2
80.77 odd 4 256.4.a.l.1.1 2
120.77 even 4 72.4.d.b.37.1 2
120.107 odd 4 288.4.d.a.145.1 2
240.77 even 4 2304.4.a.bn.1.2 2
240.107 odd 4 2304.4.a.v.1.1 2
240.197 even 4 2304.4.a.bn.1.1 2
240.227 odd 4 2304.4.a.v.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.4.b.a.5.1 2 5.2 odd 4
8.4.b.a.5.2 yes 2 40.37 odd 4
32.4.b.a.17.1 2 20.7 even 4
32.4.b.a.17.2 2 40.27 even 4
72.4.d.b.37.1 2 120.77 even 4
72.4.d.b.37.2 2 15.2 even 4
200.4.d.a.101.1 2 40.13 odd 4
200.4.d.a.101.2 2 5.3 odd 4
200.4.f.a.149.1 4 40.29 even 2 inner
200.4.f.a.149.2 4 1.1 even 1 trivial
200.4.f.a.149.3 4 5.4 even 2 inner
200.4.f.a.149.4 4 8.5 even 2 inner
256.4.a.j.1.1 2 80.27 even 4
256.4.a.j.1.2 2 80.67 even 4
256.4.a.l.1.1 2 80.77 odd 4
256.4.a.l.1.2 2 80.37 odd 4
288.4.d.a.145.1 2 120.107 odd 4
288.4.d.a.145.2 2 60.47 odd 4
800.4.d.a.401.1 2 40.3 even 4
800.4.d.a.401.2 2 20.3 even 4
800.4.f.a.49.1 4 8.3 odd 2
800.4.f.a.49.2 4 20.19 odd 2
800.4.f.a.49.3 4 4.3 odd 2
800.4.f.a.49.4 4 40.19 odd 2
2304.4.a.v.1.1 2 240.107 odd 4
2304.4.a.v.1.2 2 240.227 odd 4
2304.4.a.bn.1.1 2 240.197 even 4
2304.4.a.bn.1.2 2 240.77 even 4