Properties

Label 210.4.g.b.169.1
Level $210$
Weight $4$
Character 210.169
Analytic conductor $12.390$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,4,Mod(169,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.169");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 210.g (of order \(2\), degree \(1\), 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: \(12.3904011012\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{21})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 11x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 169.1
Root \(2.79129i\) of defining polynomial
Character \(\chi\) \(=\) 210.169
Dual form 210.4.g.b.169.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(-0.582576 + 11.1652i) q^{5} +6.00000 q^{6} +7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(-0.582576 + 11.1652i) q^{5} +6.00000 q^{6} +7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +(22.3303 + 1.16515i) q^{10} -42.6606 q^{11} -12.0000i q^{12} -73.1652i q^{13} +14.0000 q^{14} +(-33.4955 - 1.74773i) q^{15} +16.0000 q^{16} -48.4864i q^{17} +18.0000i q^{18} -77.6515 q^{19} +(2.33030 - 44.6606i) q^{20} -21.0000 q^{21} +85.3212i q^{22} -12.3485i q^{23} -24.0000 q^{24} +(-124.321 - 13.0091i) q^{25} -146.330 q^{26} -27.0000i q^{27} -28.0000i q^{28} +47.8439 q^{29} +(-3.49545 + 66.9909i) q^{30} -151.808 q^{31} -32.0000i q^{32} -127.982i q^{33} -96.9727 q^{34} +(-78.1561 - 4.07803i) q^{35} +36.0000 q^{36} +212.486i q^{37} +155.303i q^{38} +219.495 q^{39} +(-89.3212 - 4.66061i) q^{40} -227.808 q^{41} +42.0000i q^{42} -299.165i q^{43} +170.642 q^{44} +(5.24318 - 100.486i) q^{45} -24.6970 q^{46} +542.744i q^{47} +48.0000i q^{48} -49.0000 q^{49} +(-26.0182 + 248.642i) q^{50} +145.459 q^{51} +292.661i q^{52} +152.367i q^{53} -54.0000 q^{54} +(24.8530 - 476.312i) q^{55} -56.0000 q^{56} -232.955i q^{57} -95.6879i q^{58} +238.606 q^{59} +(133.982 + 6.99091i) q^{60} -768.744 q^{61} +303.615i q^{62} -63.0000i q^{63} -64.0000 q^{64} +(816.900 + 42.6242i) q^{65} -255.964 q^{66} -313.386i q^{67} +193.945i q^{68} +37.0455 q^{69} +(-8.15606 + 156.312i) q^{70} +122.065 q^{71} -72.0000i q^{72} -31.8076i q^{73} +424.973 q^{74} +(39.0273 - 372.964i) q^{75} +310.606 q^{76} -298.624i q^{77} -438.991i q^{78} -419.579 q^{79} +(-9.32121 + 178.642i) q^{80} +81.0000 q^{81} +455.615i q^{82} +981.633i q^{83} +84.0000 q^{84} +(541.358 + 28.2470i) q^{85} -598.330 q^{86} +143.532i q^{87} -341.285i q^{88} -157.477 q^{89} +(-200.973 - 10.4864i) q^{90} +512.156 q^{91} +49.3939i q^{92} -455.423i q^{93} +1085.49 q^{94} +(45.2379 - 866.991i) q^{95} +96.0000 q^{96} -1752.63i q^{97} +98.0000i q^{98} +383.945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 16 q^{4} + 16 q^{5} + 24 q^{6} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 16 q^{4} + 16 q^{5} + 24 q^{6} - 36 q^{9} + 16 q^{10} - 24 q^{11} + 56 q^{14} - 24 q^{15} + 64 q^{16} + 56 q^{19} - 64 q^{20} - 84 q^{21} - 96 q^{24} - 204 q^{25} - 512 q^{26} + 448 q^{29} + 96 q^{30} + 16 q^{31} + 272 q^{34} - 56 q^{35} + 144 q^{36} + 768 q^{39} - 64 q^{40} - 288 q^{41} + 96 q^{44} - 144 q^{45} - 832 q^{46} - 196 q^{49} - 544 q^{50} - 408 q^{51} - 216 q^{54} + 576 q^{55} - 224 q^{56} - 512 q^{59} + 96 q^{60} - 912 q^{61} - 256 q^{64} + 848 q^{65} - 144 q^{66} + 1248 q^{69} + 224 q^{70} - 1968 q^{71} + 1040 q^{74} + 816 q^{75} - 224 q^{76} + 448 q^{79} + 256 q^{80} + 324 q^{81} + 336 q^{84} + 2752 q^{85} - 2320 q^{86} - 80 q^{89} - 144 q^{90} + 1792 q^{91} + 16 q^{94} + 1904 q^{95} + 384 q^{96} + 216 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 3.00000i 0.577350i
\(4\) −4.00000 −0.500000
\(5\) −0.582576 + 11.1652i −0.0521072 + 0.998641i
\(6\) 6.00000 0.408248
\(7\) 7.00000i 0.377964i
\(8\) 8.00000i 0.353553i
\(9\) −9.00000 −0.333333
\(10\) 22.3303 + 1.16515i 0.706146 + 0.0368453i
\(11\) −42.6606 −1.16933 −0.584666 0.811274i \(-0.698775\pi\)
−0.584666 + 0.811274i \(0.698775\pi\)
\(12\) 12.0000i 0.288675i
\(13\) 73.1652i 1.56095i −0.625186 0.780475i \(-0.714977\pi\)
0.625186 0.780475i \(-0.285023\pi\)
\(14\) 14.0000 0.267261
\(15\) −33.4955 1.74773i −0.576566 0.0300841i
\(16\) 16.0000 0.250000
\(17\) 48.4864i 0.691745i −0.938281 0.345873i \(-0.887583\pi\)
0.938281 0.345873i \(-0.112417\pi\)
\(18\) 18.0000i 0.235702i
\(19\) −77.6515 −0.937604 −0.468802 0.883303i \(-0.655314\pi\)
−0.468802 + 0.883303i \(0.655314\pi\)
\(20\) 2.33030 44.6606i 0.0260536 0.499321i
\(21\) −21.0000 −0.218218
\(22\) 85.3212i 0.826843i
\(23\) 12.3485i 0.111949i −0.998432 0.0559747i \(-0.982173\pi\)
0.998432 0.0559747i \(-0.0178266\pi\)
\(24\) −24.0000 −0.204124
\(25\) −124.321 13.0091i −0.994570 0.104073i
\(26\) −146.330 −1.10376
\(27\) 27.0000i 0.192450i
\(28\) 28.0000i 0.188982i
\(29\) 47.8439 0.306359 0.153179 0.988198i \(-0.451049\pi\)
0.153179 + 0.988198i \(0.451049\pi\)
\(30\) −3.49545 + 66.9909i −0.0212727 + 0.407694i
\(31\) −151.808 −0.879530 −0.439765 0.898113i \(-0.644938\pi\)
−0.439765 + 0.898113i \(0.644938\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 127.982i 0.675114i
\(34\) −96.9727 −0.489138
\(35\) −78.1561 4.07803i −0.377451 0.0196947i
\(36\) 36.0000 0.166667
\(37\) 212.486i 0.944123i 0.881566 + 0.472061i \(0.156490\pi\)
−0.881566 + 0.472061i \(0.843510\pi\)
\(38\) 155.303i 0.662986i
\(39\) 219.495 0.901215
\(40\) −89.3212 4.66061i −0.353073 0.0184227i
\(41\) −227.808 −0.867746 −0.433873 0.900974i \(-0.642853\pi\)
−0.433873 + 0.900974i \(0.642853\pi\)
\(42\) 42.0000i 0.154303i
\(43\) 299.165i 1.06098i −0.847690 0.530491i \(-0.822007\pi\)
0.847690 0.530491i \(-0.177993\pi\)
\(44\) 170.642 0.584666
\(45\) 5.24318 100.486i 0.0173691 0.332880i
\(46\) −24.6970 −0.0791602
\(47\) 542.744i 1.68441i 0.539156 + 0.842206i \(0.318743\pi\)
−0.539156 + 0.842206i \(0.681257\pi\)
\(48\) 48.0000i 0.144338i
\(49\) −49.0000 −0.142857
\(50\) −26.0182 + 248.642i −0.0735905 + 0.703267i
\(51\) 145.459 0.399379
\(52\) 292.661i 0.780475i
\(53\) 152.367i 0.394890i 0.980314 + 0.197445i \(0.0632644\pi\)
−0.980314 + 0.197445i \(0.936736\pi\)
\(54\) −54.0000 −0.136083
\(55\) 24.8530 476.312i 0.0609306 1.16774i
\(56\) −56.0000 −0.133631
\(57\) 232.955i 0.541326i
\(58\) 95.6879i 0.216628i
\(59\) 238.606 0.526506 0.263253 0.964727i \(-0.415205\pi\)
0.263253 + 0.964727i \(0.415205\pi\)
\(60\) 133.982 + 6.99091i 0.288283 + 0.0150420i
\(61\) −768.744 −1.61357 −0.806783 0.590847i \(-0.798794\pi\)
−0.806783 + 0.590847i \(0.798794\pi\)
\(62\) 303.615i 0.621922i
\(63\) 63.0000i 0.125988i
\(64\) −64.0000 −0.125000
\(65\) 816.900 + 42.6242i 1.55883 + 0.0813367i
\(66\) −255.964 −0.477378
\(67\) 313.386i 0.571436i −0.958314 0.285718i \(-0.907768\pi\)
0.958314 0.285718i \(-0.0922321\pi\)
\(68\) 193.945i 0.345873i
\(69\) 37.0455 0.0646340
\(70\) −8.15606 + 156.312i −0.0139262 + 0.266898i
\(71\) 122.065 0.204035 0.102017 0.994783i \(-0.467470\pi\)
0.102017 + 0.994783i \(0.467470\pi\)
\(72\) 72.0000i 0.117851i
\(73\) 31.8076i 0.0509972i −0.999675 0.0254986i \(-0.991883\pi\)
0.999675 0.0254986i \(-0.00811733\pi\)
\(74\) 424.973 0.667596
\(75\) 39.0273 372.964i 0.0600864 0.574215i
\(76\) 310.606 0.468802
\(77\) 298.624i 0.441966i
\(78\) 438.991i 0.637256i
\(79\) −419.579 −0.597548 −0.298774 0.954324i \(-0.596578\pi\)
−0.298774 + 0.954324i \(0.596578\pi\)
\(80\) −9.32121 + 178.642i −0.0130268 + 0.249660i
\(81\) 81.0000 0.111111
\(82\) 455.615i 0.613589i
\(83\) 981.633i 1.29817i 0.760715 + 0.649086i \(0.224848\pi\)
−0.760715 + 0.649086i \(0.775152\pi\)
\(84\) 84.0000 0.109109
\(85\) 541.358 + 28.2470i 0.690806 + 0.0360449i
\(86\) −598.330 −0.750228
\(87\) 143.532i 0.176876i
\(88\) 341.285i 0.413421i
\(89\) −157.477 −0.187557 −0.0937784 0.995593i \(-0.529895\pi\)
−0.0937784 + 0.995593i \(0.529895\pi\)
\(90\) −200.973 10.4864i −0.235382 0.0122818i
\(91\) 512.156 0.589984
\(92\) 49.3939i 0.0559747i
\(93\) 455.423i 0.507797i
\(94\) 1085.49 1.19106
\(95\) 45.2379 866.991i 0.0488559 0.936330i
\(96\) 96.0000 0.102062
\(97\) 1752.63i 1.83457i −0.398234 0.917284i \(-0.630377\pi\)
0.398234 0.917284i \(-0.369623\pi\)
\(98\) 98.0000i 0.101015i
\(99\) 383.945 0.389777
\(100\) 497.285 + 52.0364i 0.497285 + 0.0520364i
\(101\) 1081.96 1.06593 0.532964 0.846138i \(-0.321078\pi\)
0.532964 + 0.846138i \(0.321078\pi\)
\(102\) 290.918i 0.282404i
\(103\) 718.330i 0.687177i −0.939120 0.343588i \(-0.888358\pi\)
0.939120 0.343588i \(-0.111642\pi\)
\(104\) 585.321 0.551879
\(105\) 12.2341 234.468i 0.0113707 0.217921i
\(106\) 304.733 0.279229
\(107\) 1950.95i 1.76267i 0.472490 + 0.881336i \(0.343355\pi\)
−0.472490 + 0.881336i \(0.656645\pi\)
\(108\) 108.000i 0.0962250i
\(109\) 1298.24 1.14081 0.570407 0.821362i \(-0.306785\pi\)
0.570407 + 0.821362i \(0.306785\pi\)
\(110\) −952.624 49.7061i −0.825720 0.0430844i
\(111\) −637.459 −0.545090
\(112\) 112.000i 0.0944911i
\(113\) 1010.55i 0.841280i −0.907228 0.420640i \(-0.861805\pi\)
0.907228 0.420640i \(-0.138195\pi\)
\(114\) −465.909 −0.382775
\(115\) 137.873 + 7.19393i 0.111797 + 0.00583337i
\(116\) −191.376 −0.153179
\(117\) 658.486i 0.520317i
\(118\) 477.212i 0.372296i
\(119\) 339.405 0.261455
\(120\) 13.9818 267.964i 0.0106363 0.203847i
\(121\) 488.927 0.367338
\(122\) 1537.49i 1.14096i
\(123\) 683.423i 0.500993i
\(124\) 607.230 0.439765
\(125\) 217.675 1380.49i 0.155756 0.987796i
\(126\) −126.000 −0.0890871
\(127\) 1688.52i 1.17978i 0.807485 + 0.589888i \(0.200828\pi\)
−0.807485 + 0.589888i \(0.799172\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 897.495 0.612559
\(130\) 85.2485 1633.80i 0.0575137 1.10226i
\(131\) −919.194 −0.613056 −0.306528 0.951862i \(-0.599167\pi\)
−0.306528 + 0.951862i \(0.599167\pi\)
\(132\) 511.927i 0.337557i
\(133\) 543.561i 0.354381i
\(134\) −626.773 −0.404067
\(135\) 301.459 + 15.7295i 0.192189 + 0.0100280i
\(136\) 387.891 0.244569
\(137\) 1154.24i 0.719805i 0.932990 + 0.359903i \(0.117190\pi\)
−0.932990 + 0.359903i \(0.882810\pi\)
\(138\) 74.0909i 0.0457032i
\(139\) −3050.52 −1.86145 −0.930724 0.365722i \(-0.880822\pi\)
−0.930724 + 0.365722i \(0.880822\pi\)
\(140\) 312.624 + 16.3121i 0.188726 + 0.00984733i
\(141\) −1628.23 −0.972495
\(142\) 244.130i 0.144274i
\(143\) 3121.27i 1.82527i
\(144\) −144.000 −0.0833333
\(145\) −27.8727 + 534.185i −0.0159635 + 0.305942i
\(146\) −63.6151 −0.0360605
\(147\) 147.000i 0.0824786i
\(148\) 849.945i 0.472061i
\(149\) −1194.36 −0.656681 −0.328340 0.944559i \(-0.606489\pi\)
−0.328340 + 0.944559i \(0.606489\pi\)
\(150\) −745.927 78.0545i −0.406031 0.0424875i
\(151\) 1398.61 0.753755 0.376877 0.926263i \(-0.376998\pi\)
0.376877 + 0.926263i \(0.376998\pi\)
\(152\) 621.212i 0.331493i
\(153\) 436.377i 0.230582i
\(154\) −597.248 −0.312517
\(155\) 88.4394 1694.95i 0.0458298 0.878336i
\(156\) −877.982 −0.450608
\(157\) 3465.39i 1.76158i 0.473506 + 0.880790i \(0.342988\pi\)
−0.473506 + 0.880790i \(0.657012\pi\)
\(158\) 839.158i 0.422530i
\(159\) −457.100 −0.227990
\(160\) 357.285 + 18.6424i 0.176537 + 0.00921133i
\(161\) 86.4394 0.0423129
\(162\) 162.000i 0.0785674i
\(163\) 2697.83i 1.29638i 0.761478 + 0.648191i \(0.224474\pi\)
−0.761478 + 0.648191i \(0.775526\pi\)
\(164\) 911.230 0.433873
\(165\) 1428.94 + 74.5591i 0.674197 + 0.0351783i
\(166\) 1963.27 0.917946
\(167\) 3203.92i 1.48459i 0.670073 + 0.742296i \(0.266263\pi\)
−0.670073 + 0.742296i \(0.733737\pi\)
\(168\) 168.000i 0.0771517i
\(169\) −3156.14 −1.43657
\(170\) 56.4940 1082.72i 0.0254876 0.488473i
\(171\) 698.864 0.312535
\(172\) 1196.66i 0.530491i
\(173\) 231.906i 0.101916i −0.998701 0.0509581i \(-0.983773\pi\)
0.998701 0.0509581i \(-0.0162275\pi\)
\(174\) 287.064 0.125070
\(175\) 91.0636 870.248i 0.0393358 0.375912i
\(176\) −682.570 −0.292333
\(177\) 715.818i 0.303978i
\(178\) 314.955i 0.132623i
\(179\) −2906.13 −1.21349 −0.606744 0.794897i \(-0.707525\pi\)
−0.606744 + 0.794897i \(0.707525\pi\)
\(180\) −20.9727 + 401.945i −0.00868453 + 0.166440i
\(181\) −999.865 −0.410604 −0.205302 0.978699i \(-0.565818\pi\)
−0.205302 + 0.978699i \(0.565818\pi\)
\(182\) 1024.31i 0.417182i
\(183\) 2306.23i 0.931593i
\(184\) 98.7879 0.0395801
\(185\) −2372.44 123.789i −0.942840 0.0491956i
\(186\) −910.845 −0.359067
\(187\) 2068.46i 0.808880i
\(188\) 2170.98i 0.842206i
\(189\) 189.000 0.0727393
\(190\) −1733.98 90.4758i −0.662086 0.0345463i
\(191\) 2745.04 1.03992 0.519959 0.854191i \(-0.325947\pi\)
0.519959 + 0.854191i \(0.325947\pi\)
\(192\) 192.000i 0.0721688i
\(193\) 3825.38i 1.42672i −0.700798 0.713360i \(-0.747173\pi\)
0.700798 0.713360i \(-0.252827\pi\)
\(194\) −3505.27 −1.29724
\(195\) −127.873 + 2450.70i −0.0469598 + 0.899991i
\(196\) 196.000 0.0714286
\(197\) 4449.00i 1.60902i −0.593936 0.804512i \(-0.702427\pi\)
0.593936 0.804512i \(-0.297573\pi\)
\(198\) 767.891i 0.275614i
\(199\) −4383.22 −1.56140 −0.780699 0.624907i \(-0.785137\pi\)
−0.780699 + 0.624907i \(0.785137\pi\)
\(200\) 104.073 994.570i 0.0367953 0.351633i
\(201\) 940.159 0.329919
\(202\) 2163.91i 0.753724i
\(203\) 334.908i 0.115793i
\(204\) −581.836 −0.199690
\(205\) 132.715 2543.51i 0.0452157 0.866567i
\(206\) −1436.66 −0.485907
\(207\) 111.136i 0.0373165i
\(208\) 1170.64i 0.390238i
\(209\) 3312.66 1.09637
\(210\) −468.936 24.4682i −0.154094 0.00804031i
\(211\) −145.655 −0.0475226 −0.0237613 0.999718i \(-0.507564\pi\)
−0.0237613 + 0.999718i \(0.507564\pi\)
\(212\) 609.467i 0.197445i
\(213\) 366.195i 0.117800i
\(214\) 3901.91 1.24640
\(215\) 3340.22 + 174.286i 1.05954 + 0.0552848i
\(216\) 216.000 0.0680414
\(217\) 1062.65i 0.332431i
\(218\) 2596.48i 0.806678i
\(219\) 95.4227 0.0294432
\(220\) −99.4121 + 1905.25i −0.0304653 + 0.583872i
\(221\) −3547.51 −1.07978
\(222\) 1274.92i 0.385437i
\(223\) 1911.17i 0.573908i −0.957944 0.286954i \(-0.907357\pi\)
0.957944 0.286954i \(-0.0926428\pi\)
\(224\) 224.000 0.0668153
\(225\) 1118.89 + 117.082i 0.331523 + 0.0346909i
\(226\) −2021.10 −0.594875
\(227\) 2083.60i 0.609222i 0.952477 + 0.304611i \(0.0985265\pi\)
−0.952477 + 0.304611i \(0.901474\pi\)
\(228\) 931.818i 0.270663i
\(229\) −2002.03 −0.577720 −0.288860 0.957371i \(-0.593276\pi\)
−0.288860 + 0.957371i \(0.593276\pi\)
\(230\) 14.3879 275.745i 0.00412481 0.0790527i
\(231\) 895.873 0.255169
\(232\) 382.752i 0.108314i
\(233\) 3245.52i 0.912537i 0.889842 + 0.456269i \(0.150814\pi\)
−0.889842 + 0.456269i \(0.849186\pi\)
\(234\) 1316.97 0.367920
\(235\) −6059.82 316.189i −1.68212 0.0877699i
\(236\) −954.424 −0.263253
\(237\) 1258.74i 0.344995i
\(238\) 678.809i 0.184877i
\(239\) 5602.03 1.51617 0.758086 0.652155i \(-0.226135\pi\)
0.758086 + 0.652155i \(0.226135\pi\)
\(240\) −535.927 27.9636i −0.144141 0.00752102i
\(241\) 4789.93 1.28028 0.640138 0.768260i \(-0.278877\pi\)
0.640138 + 0.768260i \(0.278877\pi\)
\(242\) 977.855i 0.259747i
\(243\) 243.000i 0.0641500i
\(244\) 3074.98 0.806783
\(245\) 28.5462 547.092i 0.00744388 0.142663i
\(246\) −1366.85 −0.354256
\(247\) 5681.38i 1.46355i
\(248\) 1214.46i 0.310961i
\(249\) −2944.90 −0.749500
\(250\) −2760.97 435.350i −0.698477 0.110136i
\(251\) −337.467 −0.0848634 −0.0424317 0.999099i \(-0.513510\pi\)
−0.0424317 + 0.999099i \(0.513510\pi\)
\(252\) 252.000i 0.0629941i
\(253\) 526.794i 0.130906i
\(254\) 3377.03 0.834227
\(255\) −84.7409 + 1624.07i −0.0208105 + 0.398837i
\(256\) 256.000 0.0625000
\(257\) 2226.69i 0.540455i 0.962797 + 0.270227i \(0.0870989\pi\)
−0.962797 + 0.270227i \(0.912901\pi\)
\(258\) 1794.99i 0.433144i
\(259\) −1487.40 −0.356845
\(260\) −3267.60 170.497i −0.779415 0.0406684i
\(261\) −430.595 −0.102120
\(262\) 1838.39i 0.433496i
\(263\) 6474.78i 1.51807i −0.651051 0.759034i \(-0.725672\pi\)
0.651051 0.759034i \(-0.274328\pi\)
\(264\) 1023.85 0.238689
\(265\) −1701.20 88.7651i −0.394354 0.0205766i
\(266\) −1087.12 −0.250585
\(267\) 472.432i 0.108286i
\(268\) 1253.55i 0.285718i
\(269\) −4980.38 −1.12884 −0.564422 0.825486i \(-0.690901\pi\)
−0.564422 + 0.825486i \(0.690901\pi\)
\(270\) 31.4591 602.918i 0.00709089 0.135898i
\(271\) 7829.76 1.75507 0.877535 0.479513i \(-0.159186\pi\)
0.877535 + 0.479513i \(0.159186\pi\)
\(272\) 775.782i 0.172936i
\(273\) 1536.47i 0.340627i
\(274\) 2308.48 0.508979
\(275\) 5303.62 + 554.976i 1.16298 + 0.121696i
\(276\) −148.182 −0.0323170
\(277\) 3104.10i 0.673312i 0.941628 + 0.336656i \(0.109296\pi\)
−0.941628 + 0.336656i \(0.890704\pi\)
\(278\) 6101.03i 1.31624i
\(279\) 1366.27 0.293177
\(280\) 32.6242 625.248i 0.00696311 0.133449i
\(281\) 2916.45 0.619148 0.309574 0.950875i \(-0.399814\pi\)
0.309574 + 0.950875i \(0.399814\pi\)
\(282\) 3256.46i 0.687658i
\(283\) 8199.29i 1.72225i 0.508391 + 0.861126i \(0.330240\pi\)
−0.508391 + 0.861126i \(0.669760\pi\)
\(284\) −488.261 −0.102017
\(285\) 2600.97 + 135.714i 0.540591 + 0.0282070i
\(286\) 6242.54 1.29066
\(287\) 1594.65i 0.327977i
\(288\) 288.000i 0.0589256i
\(289\) 2562.07 0.521488
\(290\) 1068.37 + 55.7454i 0.216334 + 0.0112879i
\(291\) 5257.90 1.05919
\(292\) 127.230i 0.0254986i
\(293\) 8448.78i 1.68458i −0.539022 0.842291i \(-0.681206\pi\)
0.539022 0.842291i \(-0.318794\pi\)
\(294\) −294.000 −0.0583212
\(295\) −139.006 + 2664.07i −0.0274347 + 0.525791i
\(296\) −1699.89 −0.333798
\(297\) 1151.84i 0.225038i
\(298\) 2388.71i 0.464344i
\(299\) −903.479 −0.174748
\(300\) −156.109 + 1491.85i −0.0300432 + 0.287108i
\(301\) 2094.16 0.401014
\(302\) 2797.21i 0.532985i
\(303\) 3245.87i 0.615413i
\(304\) −1242.42 −0.234401
\(305\) 447.852 8583.14i 0.0840784 1.61137i
\(306\) 872.755 0.163046
\(307\) 2011.52i 0.373953i −0.982364 0.186977i \(-0.940131\pi\)
0.982364 0.186977i \(-0.0598688\pi\)
\(308\) 1194.50i 0.220983i
\(309\) 2154.99 0.396742
\(310\) −3389.91 176.879i −0.621077 0.0324066i
\(311\) −3741.47 −0.682185 −0.341092 0.940030i \(-0.610797\pi\)
−0.341092 + 0.940030i \(0.610797\pi\)
\(312\) 1755.96i 0.318628i
\(313\) 8474.92i 1.53045i −0.643763 0.765225i \(-0.722628\pi\)
0.643763 0.765225i \(-0.277372\pi\)
\(314\) 6930.78 1.24563
\(315\) 703.405 + 36.7023i 0.125817 + 0.00656488i
\(316\) 1678.32 0.298774
\(317\) 9371.15i 1.66037i −0.557490 0.830183i \(-0.688236\pi\)
0.557490 0.830183i \(-0.311764\pi\)
\(318\) 914.200i 0.161213i
\(319\) −2041.05 −0.358235
\(320\) 37.2848 714.570i 0.00651339 0.124830i
\(321\) −5852.86 −1.01768
\(322\) 172.879i 0.0299197i
\(323\) 3765.04i 0.648583i
\(324\) −324.000 −0.0555556
\(325\) −951.812 + 9095.98i −0.162452 + 1.55247i
\(326\) 5395.66 0.916680
\(327\) 3894.72i 0.658650i
\(328\) 1822.46i 0.306794i
\(329\) −3799.21 −0.636648
\(330\) 149.118 2857.87i 0.0248748 0.476729i
\(331\) −1757.55 −0.291853 −0.145927 0.989295i \(-0.546616\pi\)
−0.145927 + 0.989295i \(0.546616\pi\)
\(332\) 3926.53i 0.649086i
\(333\) 1912.38i 0.314708i
\(334\) 6407.84 1.04976
\(335\) 3499.01 + 182.571i 0.570660 + 0.0297759i
\(336\) −336.000 −0.0545545
\(337\) 2901.49i 0.469003i −0.972116 0.234502i \(-0.924654\pi\)
0.972116 0.234502i \(-0.0753458\pi\)
\(338\) 6312.28i 1.01581i
\(339\) 3031.65 0.485713
\(340\) −2165.43 112.988i −0.345403 0.0180224i
\(341\) 6476.20 1.02846
\(342\) 1397.73i 0.220995i
\(343\) 343.000i 0.0539949i
\(344\) 2393.32 0.375114
\(345\) −21.5818 + 413.618i −0.00336790 + 0.0645462i
\(346\) −463.812 −0.0720656
\(347\) 261.576i 0.0404672i 0.999795 + 0.0202336i \(0.00644100\pi\)
−0.999795 + 0.0202336i \(0.993559\pi\)
\(348\) 574.127i 0.0884381i
\(349\) −10958.6 −1.68081 −0.840404 0.541961i \(-0.817682\pi\)
−0.840404 + 0.541961i \(0.817682\pi\)
\(350\) −1740.50 182.127i −0.265810 0.0278146i
\(351\) −1975.46 −0.300405
\(352\) 1365.14i 0.206711i
\(353\) 4138.16i 0.623943i 0.950091 + 0.311971i \(0.100989\pi\)
−0.950091 + 0.311971i \(0.899011\pi\)
\(354\) 1431.64 0.214945
\(355\) −71.1122 + 1362.88i −0.0106317 + 0.203758i
\(356\) 629.909 0.0937784
\(357\) 1018.21i 0.150951i
\(358\) 5812.26i 0.858066i
\(359\) 7383.25 1.08544 0.542720 0.839914i \(-0.317395\pi\)
0.542720 + 0.839914i \(0.317395\pi\)
\(360\) 803.891 + 41.9455i 0.117691 + 0.00614089i
\(361\) −829.242 −0.120898
\(362\) 1999.73i 0.290341i
\(363\) 1466.78i 0.212083i
\(364\) −2048.62 −0.294992
\(365\) 355.136 + 18.5303i 0.0509279 + 0.00265732i
\(366\) −4612.46 −0.658736
\(367\) 11585.4i 1.64782i −0.566718 0.823912i \(-0.691787\pi\)
0.566718 0.823912i \(-0.308213\pi\)
\(368\) 197.576i 0.0279874i
\(369\) 2050.27 0.289249
\(370\) −247.579 + 4744.88i −0.0347865 + 0.666689i
\(371\) −1066.57 −0.149254
\(372\) 1821.69i 0.253899i
\(373\) 7712.37i 1.07059i −0.844664 0.535297i \(-0.820200\pi\)
0.844664 0.535297i \(-0.179800\pi\)
\(374\) 4136.92 0.571965
\(375\) 4141.46 + 653.025i 0.570304 + 0.0899255i
\(376\) −4341.95 −0.595529
\(377\) 3500.51i 0.478211i
\(378\) 378.000i 0.0514344i
\(379\) 6663.16 0.903071 0.451535 0.892253i \(-0.350877\pi\)
0.451535 + 0.892253i \(0.350877\pi\)
\(380\) −180.952 + 3467.96i −0.0244279 + 0.468165i
\(381\) −5065.55 −0.681144
\(382\) 5490.08i 0.735333i
\(383\) 8432.12i 1.12496i −0.826810 0.562482i \(-0.809847\pi\)
0.826810 0.562482i \(-0.190153\pi\)
\(384\) −384.000 −0.0510310
\(385\) 3334.18 + 173.971i 0.441366 + 0.0230296i
\(386\) −7650.76 −1.00884
\(387\) 2692.49i 0.353661i
\(388\) 7010.54i 0.917284i
\(389\) −5931.40 −0.773095 −0.386547 0.922270i \(-0.626332\pi\)
−0.386547 + 0.922270i \(0.626332\pi\)
\(390\) 4901.40 + 255.745i 0.636390 + 0.0332056i
\(391\) −598.733 −0.0774405
\(392\) 392.000i 0.0505076i
\(393\) 2757.58i 0.353948i
\(394\) −8897.99 −1.13775
\(395\) 244.436 4684.66i 0.0311365 0.596736i
\(396\) −1535.78 −0.194889
\(397\) 690.377i 0.0872772i −0.999047 0.0436386i \(-0.986105\pi\)
0.999047 0.0436386i \(-0.0138950\pi\)
\(398\) 8766.44i 1.10408i
\(399\) 1630.68 0.204602
\(400\) −1989.14 208.145i −0.248642 0.0260182i
\(401\) −2314.18 −0.288191 −0.144096 0.989564i \(-0.546027\pi\)
−0.144096 + 0.989564i \(0.546027\pi\)
\(402\) 1880.32i 0.233288i
\(403\) 11107.0i 1.37290i
\(404\) −4327.82 −0.532964
\(405\) −47.1886 + 904.377i −0.00578968 + 0.110960i
\(406\) 669.815 0.0818778
\(407\) 9064.80i 1.10399i
\(408\) 1163.67i 0.141202i
\(409\) 11899.3 1.43859 0.719294 0.694706i \(-0.244466\pi\)
0.719294 + 0.694706i \(0.244466\pi\)
\(410\) −5087.01 265.430i −0.612755 0.0319724i
\(411\) −3462.72 −0.415580
\(412\) 2873.32i 0.343588i
\(413\) 1670.24i 0.199001i
\(414\) 222.273 0.0263867
\(415\) −10960.1 571.876i −1.29641 0.0676440i
\(416\) −2341.28 −0.275940
\(417\) 9151.55i 1.07471i
\(418\) 6625.32i 0.775251i
\(419\) −14383.1 −1.67700 −0.838498 0.544904i \(-0.816566\pi\)
−0.838498 + 0.544904i \(0.816566\pi\)
\(420\) −48.9364 + 937.873i −0.00568536 + 0.108961i
\(421\) 4620.71 0.534916 0.267458 0.963569i \(-0.413816\pi\)
0.267458 + 0.963569i \(0.413816\pi\)
\(422\) 291.309i 0.0336036i
\(423\) 4884.70i 0.561470i
\(424\) −1218.93 −0.139615
\(425\) −630.764 + 6027.88i −0.0719918 + 0.687989i
\(426\) 732.391 0.0832968
\(427\) 5381.21i 0.609871i
\(428\) 7803.82i 0.881336i
\(429\) −9363.81 −1.05382
\(430\) 348.573 6680.45i 0.0390923 0.749209i
\(431\) −12339.5 −1.37905 −0.689527 0.724260i \(-0.742181\pi\)
−0.689527 + 0.724260i \(0.742181\pi\)
\(432\) 432.000i 0.0481125i
\(433\) 11280.9i 1.25202i 0.779813 + 0.626012i \(0.215314\pi\)
−0.779813 + 0.626012i \(0.784686\pi\)
\(434\) −2125.31 −0.235064
\(435\) −1602.55 83.6182i −0.176636 0.00921651i
\(436\) −5192.96 −0.570407
\(437\) 958.879i 0.104964i
\(438\) 190.845i 0.0208195i
\(439\) −6585.30 −0.715943 −0.357972 0.933733i \(-0.616532\pi\)
−0.357972 + 0.933733i \(0.616532\pi\)
\(440\) 3810.50 + 198.824i 0.412860 + 0.0215422i
\(441\) 441.000 0.0476190
\(442\) 7095.02i 0.763520i
\(443\) 5521.10i 0.592134i 0.955167 + 0.296067i \(0.0956752\pi\)
−0.955167 + 0.296067i \(0.904325\pi\)
\(444\) 2549.84 0.272545
\(445\) 91.7424 1758.26i 0.00977305 0.187302i
\(446\) −3822.35 −0.405815
\(447\) 3583.07i 0.379135i
\(448\) 448.000i 0.0472456i
\(449\) 10012.7 1.05240 0.526199 0.850361i \(-0.323617\pi\)
0.526199 + 0.850361i \(0.323617\pi\)
\(450\) 234.164 2237.78i 0.0245302 0.234422i
\(451\) 9718.41 1.01468
\(452\) 4042.21i 0.420640i
\(453\) 4195.82i 0.435180i
\(454\) 4167.20 0.430785
\(455\) −298.370 + 5718.30i −0.0307424 + 0.589182i
\(456\) 1863.64 0.191388
\(457\) 12128.7i 1.24148i −0.784017 0.620740i \(-0.786832\pi\)
0.784017 0.620740i \(-0.213168\pi\)
\(458\) 4004.06i 0.408509i
\(459\) −1309.13 −0.133126
\(460\) −551.491 28.7757i −0.0558987 0.00291668i
\(461\) −8279.82 −0.836507 −0.418254 0.908330i \(-0.637358\pi\)
−0.418254 + 0.908330i \(0.637358\pi\)
\(462\) 1791.75i 0.180432i
\(463\) 12932.7i 1.29813i −0.760734 0.649064i \(-0.775161\pi\)
0.760734 0.649064i \(-0.224839\pi\)
\(464\) 765.503 0.0765896
\(465\) 5084.86 + 265.318i 0.507107 + 0.0264599i
\(466\) 6491.04 0.645261
\(467\) 7326.71i 0.725995i 0.931790 + 0.362997i \(0.118247\pi\)
−0.931790 + 0.362997i \(0.881753\pi\)
\(468\) 2633.95i 0.260158i
\(469\) 2193.70 0.215983
\(470\) −632.379 + 12119.6i −0.0620627 + 1.18944i
\(471\) −10396.2 −1.01705
\(472\) 1908.85i 0.186148i
\(473\) 12762.6i 1.24064i
\(474\) −2517.47 −0.243948
\(475\) 9653.73 + 1010.18i 0.932513 + 0.0975790i
\(476\) −1357.62 −0.130728
\(477\) 1371.30i 0.131630i
\(478\) 11204.1i 1.07210i
\(479\) −12568.4 −1.19888 −0.599442 0.800418i \(-0.704611\pi\)
−0.599442 + 0.800418i \(0.704611\pi\)
\(480\) −55.9273 + 1071.85i −0.00531816 + 0.101923i
\(481\) 15546.6 1.47373
\(482\) 9579.85i 0.905291i
\(483\) 259.318i 0.0244294i
\(484\) −1955.71 −0.183669
\(485\) 19568.4 + 1021.04i 1.83208 + 0.0955941i
\(486\) 486.000 0.0453609
\(487\) 10464.8i 0.973729i 0.873477 + 0.486865i \(0.161860\pi\)
−0.873477 + 0.486865i \(0.838140\pi\)
\(488\) 6149.95i 0.570482i
\(489\) −8093.49 −0.748466
\(490\) −1094.18 57.0924i −0.100878 0.00526362i
\(491\) −1536.22 −0.141199 −0.0705995 0.997505i \(-0.522491\pi\)
−0.0705995 + 0.997505i \(0.522491\pi\)
\(492\) 2733.69i 0.250497i
\(493\) 2319.78i 0.211922i
\(494\) 11362.8 1.03489
\(495\) −223.677 + 4286.81i −0.0203102 + 0.389248i
\(496\) −2428.92 −0.219883
\(497\) 854.456i 0.0771179i
\(498\) 5889.80i 0.529976i
\(499\) −12736.8 −1.14264 −0.571320 0.820728i \(-0.693568\pi\)
−0.571320 + 0.820728i \(0.693568\pi\)
\(500\) −870.700 + 5521.95i −0.0778778 + 0.493898i
\(501\) −9611.76 −0.857129
\(502\) 674.933i 0.0600075i
\(503\) 6113.67i 0.541938i 0.962588 + 0.270969i \(0.0873441\pi\)
−0.962588 + 0.270969i \(0.912656\pi\)
\(504\) 504.000 0.0445435
\(505\) −630.321 + 12080.2i −0.0555424 + 1.06448i
\(506\) 1053.59 0.0925646
\(507\) 9468.42i 0.829403i
\(508\) 6754.06i 0.589888i
\(509\) −14565.5 −1.26837 −0.634187 0.773179i \(-0.718665\pi\)
−0.634187 + 0.773179i \(0.718665\pi\)
\(510\) 3248.15 + 169.482i 0.282020 + 0.0147153i
\(511\) 222.653 0.0192751
\(512\) 512.000i 0.0441942i
\(513\) 2096.59i 0.180442i
\(514\) 4453.37 0.382159
\(515\) 8020.27 + 418.482i 0.686243 + 0.0358068i
\(516\) −3589.98 −0.306279
\(517\) 23153.8i 1.96964i
\(518\) 2974.81i 0.252327i
\(519\) 695.718 0.0588413
\(520\) −340.994 + 6535.20i −0.0287569 + 0.551130i
\(521\) −18007.0 −1.51420 −0.757102 0.653297i \(-0.773385\pi\)
−0.757102 + 0.653297i \(0.773385\pi\)
\(522\) 861.191i 0.0722094i
\(523\) 8077.14i 0.675313i 0.941269 + 0.337657i \(0.109634\pi\)
−0.941269 + 0.337657i \(0.890366\pi\)
\(524\) 3676.78 0.306528
\(525\) 2610.75 + 273.191i 0.217033 + 0.0227105i
\(526\) −12949.6 −1.07344
\(527\) 7360.60i 0.608411i
\(528\) 2047.71i 0.168779i
\(529\) 12014.5 0.987467
\(530\) −177.530 + 3402.39i −0.0145499 + 0.278850i
\(531\) −2147.45 −0.175502
\(532\) 2174.24i 0.177191i
\(533\) 16667.6i 1.35451i
\(534\) −944.864 −0.0765698
\(535\) −21782.7 1136.58i −1.76028 0.0918478i
\(536\) 2507.09 0.202033
\(537\) 8718.39i 0.700608i
\(538\) 9960.76i 0.798214i
\(539\) 2090.37 0.167047
\(540\) −1205.84 62.9182i −0.0960943 0.00501401i
\(541\) 17455.2 1.38717 0.693585 0.720375i \(-0.256030\pi\)
0.693585 + 0.720375i \(0.256030\pi\)
\(542\) 15659.5i 1.24102i
\(543\) 2999.60i 0.237063i
\(544\) −1551.56 −0.122284
\(545\) −756.323 + 14495.0i −0.0594446 + 1.13926i
\(546\) 3072.94 0.240860
\(547\) 5333.74i 0.416918i 0.978031 + 0.208459i \(0.0668448\pi\)
−0.978031 + 0.208459i \(0.933155\pi\)
\(548\) 4616.96i 0.359903i
\(549\) 6918.70 0.537856
\(550\) 1109.95 10607.2i 0.0860518 0.822353i
\(551\) −3715.15 −0.287243
\(552\) 296.364i 0.0228516i
\(553\) 2937.05i 0.225852i
\(554\) 6208.20 0.476103
\(555\) 371.368 7117.33i 0.0284031 0.544349i
\(556\) 12202.1 0.930724
\(557\) 23117.7i 1.75858i 0.476291 + 0.879288i \(0.341981\pi\)
−0.476291 + 0.879288i \(0.658019\pi\)
\(558\) 2732.54i 0.207307i
\(559\) −21888.5 −1.65614
\(560\) −1250.50 65.2485i −0.0943628 0.00492366i
\(561\) −6205.37 −0.467007
\(562\) 5832.89i 0.437804i
\(563\) 10931.0i 0.818273i −0.912473 0.409137i \(-0.865830\pi\)
0.912473 0.409137i \(-0.134170\pi\)
\(564\) 6512.93 0.486248
\(565\) 11283.0 + 588.723i 0.840138 + 0.0438367i
\(566\) 16398.6 1.21782
\(567\) 567.000i 0.0419961i
\(568\) 976.521i 0.0721372i
\(569\) 14484.1 1.06714 0.533571 0.845755i \(-0.320850\pi\)
0.533571 + 0.845755i \(0.320850\pi\)
\(570\) 271.427 5201.95i 0.0199453 0.382255i
\(571\) 13431.3 0.984381 0.492190 0.870488i \(-0.336196\pi\)
0.492190 + 0.870488i \(0.336196\pi\)
\(572\) 12485.1i 0.912635i
\(573\) 8235.12i 0.600396i
\(574\) −3189.31 −0.231915
\(575\) −160.643 + 1535.18i −0.0116509 + 0.111342i
\(576\) 576.000 0.0416667
\(577\) 19865.0i 1.43326i −0.697452 0.716631i \(-0.745683\pi\)
0.697452 0.716631i \(-0.254317\pi\)
\(578\) 5124.15i 0.368748i
\(579\) 11476.1 0.823717
\(580\) 111.491 2136.74i 0.00798173 0.152971i
\(581\) −6871.43 −0.490663
\(582\) 10515.8i 0.748959i
\(583\) 6500.05i 0.461758i
\(584\) 254.461 0.0180302
\(585\) −7352.10 383.618i −0.519610 0.0271122i
\(586\) −16897.6 −1.19118
\(587\) 12110.3i 0.851526i 0.904835 + 0.425763i \(0.139994\pi\)
−0.904835 + 0.425763i \(0.860006\pi\)
\(588\) 588.000i 0.0412393i
\(589\) 11788.1 0.824651
\(590\) 5328.15 + 278.012i 0.371790 + 0.0193993i
\(591\) 13347.0 0.928971
\(592\) 3399.78i 0.236031i
\(593\) 12185.9i 0.843868i −0.906627 0.421934i \(-0.861351\pi\)
0.906627 0.421934i \(-0.138649\pi\)
\(594\) 2303.67 0.159126
\(595\) −197.729 + 3789.50i −0.0136237 + 0.261100i
\(596\) 4777.42 0.328340
\(597\) 13149.7i 0.901474i
\(598\) 1806.96i 0.123565i
\(599\) 11323.5 0.772398 0.386199 0.922416i \(-0.373788\pi\)
0.386199 + 0.922416i \(0.373788\pi\)
\(600\) 2983.71 + 312.218i 0.203016 + 0.0212438i
\(601\) 1769.31 0.120086 0.0600429 0.998196i \(-0.480876\pi\)
0.0600429 + 0.998196i \(0.480876\pi\)
\(602\) 4188.31i 0.283560i
\(603\) 2820.48i 0.190479i
\(604\) −5594.42 −0.376877
\(605\) −284.837 + 5458.95i −0.0191410 + 0.366839i
\(606\) 6491.74 0.435163
\(607\) 9715.83i 0.649676i −0.945770 0.324838i \(-0.894690\pi\)
0.945770 0.324838i \(-0.105310\pi\)
\(608\) 2484.85i 0.165747i
\(609\) −1004.72 −0.0668529
\(610\) −17166.3 895.703i −1.13941 0.0594524i
\(611\) 39709.9 2.62928
\(612\) 1745.51i 0.115291i
\(613\) 29107.8i 1.91786i 0.283635 + 0.958932i \(0.408460\pi\)
−0.283635 + 0.958932i \(0.591540\pi\)
\(614\) −4023.04 −0.264425
\(615\) 7630.52 + 398.145i 0.500313 + 0.0261053i
\(616\) 2388.99 0.156259
\(617\) 7034.18i 0.458972i 0.973312 + 0.229486i \(0.0737045\pi\)
−0.973312 + 0.229486i \(0.926296\pi\)
\(618\) 4309.98i 0.280539i
\(619\) 574.633 0.0373125 0.0186563 0.999826i \(-0.494061\pi\)
0.0186563 + 0.999826i \(0.494061\pi\)
\(620\) −353.758 + 6779.82i −0.0229149 + 0.439168i
\(621\) −333.409 −0.0215447
\(622\) 7482.95i 0.482377i
\(623\) 1102.34i 0.0708898i
\(624\) 3511.93 0.225304
\(625\) 15286.5 + 3234.61i 0.978338 + 0.207015i
\(626\) −16949.8 −1.08219
\(627\) 9937.98i 0.632990i
\(628\) 13861.6i 0.880790i
\(629\) 10302.7 0.653093
\(630\) 73.4045 1406.81i 0.00464207 0.0889661i
\(631\) 3009.42 0.189862 0.0949310 0.995484i \(-0.469737\pi\)
0.0949310 + 0.995484i \(0.469737\pi\)
\(632\) 3356.63i 0.211265i
\(633\) 436.964i 0.0274372i
\(634\) −18742.3 −1.17406
\(635\) −18852.5 983.688i −1.17817 0.0614747i
\(636\) 1828.40 0.113995
\(637\) 3585.09i 0.222993i
\(638\) 4082.10i 0.253310i
\(639\) −1098.59 −0.0680116
\(640\) −1429.14 74.5697i −0.0882683 0.00460567i
\(641\) −25041.6 −1.54303 −0.771516 0.636209i \(-0.780501\pi\)
−0.771516 + 0.636209i \(0.780501\pi\)
\(642\) 11705.7i 0.719608i
\(643\) 4245.80i 0.260401i 0.991488 + 0.130201i \(0.0415622\pi\)
−0.991488 + 0.130201i \(0.958438\pi\)
\(644\) −345.758 −0.0211565
\(645\) −522.859 + 10020.7i −0.0319187 + 0.611727i
\(646\) 7530.08 0.458618
\(647\) 6388.02i 0.388159i −0.980986 0.194079i \(-0.937828\pi\)
0.980986 0.194079i \(-0.0621720\pi\)
\(648\) 648.000i 0.0392837i
\(649\) −10179.1 −0.615661
\(650\) 18192.0 + 1903.62i 1.09777 + 0.114871i
\(651\) 3187.96 0.191929
\(652\) 10791.3i 0.648191i
\(653\) 13791.6i 0.826504i −0.910617 0.413252i \(-0.864393\pi\)
0.910617 0.413252i \(-0.135607\pi\)
\(654\) 7789.44 0.465736
\(655\) 535.500 10262.9i 0.0319446 0.612223i
\(656\) −3644.92 −0.216936
\(657\) 286.268i 0.0169991i
\(658\) 7598.42i 0.450178i
\(659\) 28080.4 1.65987 0.829937 0.557856i \(-0.188376\pi\)
0.829937 + 0.557856i \(0.188376\pi\)
\(660\) −5715.75 298.236i −0.337099 0.0175891i
\(661\) 9133.28 0.537433 0.268717 0.963219i \(-0.413400\pi\)
0.268717 + 0.963219i \(0.413400\pi\)
\(662\) 3515.09i 0.206371i
\(663\) 10642.5i 0.623412i
\(664\) −7853.07 −0.458973
\(665\) 6068.94 + 316.665i 0.353900 + 0.0184658i
\(666\) −3824.75 −0.222532
\(667\) 590.800i 0.0342967i
\(668\) 12815.7i 0.742296i
\(669\) 5733.52 0.331346
\(670\) 365.143 6998.01i 0.0210548 0.403518i
\(671\) 32795.1 1.88680
\(672\) 672.000i 0.0385758i
\(673\) 13542.6i 0.775672i 0.921728 + 0.387836i \(0.126777\pi\)
−0.921728 + 0.387836i \(0.873223\pi\)
\(674\) −5802.98 −0.331635
\(675\) −351.245 + 3356.67i −0.0200288 + 0.191405i
\(676\) 12624.6 0.718284
\(677\) 22203.2i 1.26047i 0.776405 + 0.630235i \(0.217041\pi\)
−0.776405 + 0.630235i \(0.782959\pi\)
\(678\) 6063.31i 0.343451i
\(679\) 12268.4 0.693402
\(680\) −225.976 + 4330.86i −0.0127438 + 0.244237i
\(681\) −6250.80 −0.351734
\(682\) 12952.4i 0.727234i
\(683\) 13294.8i 0.744817i −0.928069 0.372409i \(-0.878532\pi\)
0.928069 0.372409i \(-0.121468\pi\)
\(684\) −2795.45 −0.156267
\(685\) −12887.3 672.432i −0.718827 0.0375070i
\(686\) −686.000 −0.0381802
\(687\) 6006.09i 0.333547i
\(688\) 4786.64i 0.265246i
\(689\) 11147.9 0.616404
\(690\) 827.236 + 43.1636i 0.0456411 + 0.00238146i
\(691\) 8047.01 0.443014 0.221507 0.975159i \(-0.428902\pi\)
0.221507 + 0.975159i \(0.428902\pi\)
\(692\) 927.624i 0.0509581i
\(693\) 2687.62i 0.147322i
\(694\) 523.152 0.0286146
\(695\) 1777.16 34059.5i 0.0969948 1.85892i
\(696\) −1148.25 −0.0625352
\(697\) 11045.6i 0.600259i
\(698\) 21917.3i 1.18851i
\(699\) −9736.56 −0.526854
\(700\) −364.255 + 3480.99i −0.0196679 + 0.187956i
\(701\) −29114.5 −1.56867 −0.784336 0.620336i \(-0.786996\pi\)
−0.784336 + 0.620336i \(0.786996\pi\)
\(702\) 3950.92i 0.212419i
\(703\) 16499.9i 0.885213i
\(704\) 2730.28 0.146167
\(705\) 948.568 18179.5i 0.0506740 0.971174i
\(706\) 8276.31 0.441194
\(707\) 7573.69i 0.402883i
\(708\) 2863.27i 0.151989i
\(709\) −18269.1 −0.967717 −0.483858 0.875146i \(-0.660765\pi\)
−0.483858 + 0.875146i \(0.660765\pi\)
\(710\) 2725.75 + 142.224i 0.144078 + 0.00751773i
\(711\) 3776.21 0.199183
\(712\) 1259.82i 0.0663114i
\(713\) 1874.59i 0.0984630i
\(714\) 2036.43 0.106739
\(715\) −34849.4 1818.38i −1.82279 0.0951097i
\(716\) 11624.5 0.606744
\(717\) 16806.1i 0.875362i
\(718\) 14766.5i 0.767522i
\(719\) −19308.5 −1.00151 −0.500755 0.865589i \(-0.666944\pi\)
−0.500755 + 0.865589i \(0.666944\pi\)
\(720\) 83.8909 1607.78i 0.00434226 0.0832201i
\(721\) 5028.31 0.259728
\(722\) 1658.48i 0.0854881i
\(723\) 14369.8i 0.739167i
\(724\) 3999.46 0.205302
\(725\) −5948.02 622.406i −0.304695 0.0318836i
\(726\) 2933.56 0.149965
\(727\) 608.482i 0.0310417i −0.999880 0.0155209i \(-0.995059\pi\)
0.999880 0.0155209i \(-0.00494064\pi\)
\(728\) 4097.25i 0.208591i
\(729\) −729.000 −0.0370370
\(730\) 37.0606 710.273i 0.00187901 0.0360115i
\(731\) −14505.4 −0.733930
\(732\) 9224.93i 0.465797i
\(733\) 3210.00i 0.161752i 0.996724 + 0.0808759i \(0.0257718\pi\)
−0.996724 + 0.0808759i \(0.974228\pi\)
\(734\) −23170.7 −1.16519
\(735\) 1641.28 + 85.6386i 0.0823666 + 0.00429773i
\(736\) −395.152 −0.0197901
\(737\) 13369.3i 0.668199i
\(738\) 4100.54i 0.204530i
\(739\) −11630.3 −0.578930 −0.289465 0.957189i \(-0.593477\pi\)
−0.289465 + 0.957189i \(0.593477\pi\)
\(740\) 9489.77 + 495.158i 0.471420 + 0.0245978i
\(741\) −17044.2 −0.844983
\(742\) 2133.13i 0.105539i
\(743\) 3312.11i 0.163539i 0.996651 + 0.0817695i \(0.0260571\pi\)
−0.996651 + 0.0817695i \(0.973943\pi\)
\(744\) 3643.38 0.179533
\(745\) 695.803 13335.2i 0.0342178 0.655789i
\(746\) −15424.7 −0.757024
\(747\) 8834.70i 0.432724i
\(748\) 8273.83i 0.404440i
\(749\) −13656.7 −0.666227
\(750\) 1306.05 8282.92i 0.0635869 0.403266i
\(751\) −1536.93 −0.0746783 −0.0373391 0.999303i \(-0.511888\pi\)
−0.0373391 + 0.999303i \(0.511888\pi\)
\(752\) 8683.90i 0.421103i
\(753\) 1012.40i 0.0489959i
\(754\) −7001.02 −0.338146
\(755\) −814.794 + 15615.6i −0.0392760 + 0.752731i
\(756\) −756.000 −0.0363696
\(757\) 19998.4i 0.960179i 0.877220 + 0.480089i \(0.159396\pi\)
−0.877220 + 0.480089i \(0.840604\pi\)
\(758\) 13326.3i 0.638567i
\(759\) −1580.38 −0.0755787
\(760\) 6935.93 + 361.903i 0.331043 + 0.0172732i
\(761\) −19227.9 −0.915915 −0.457957 0.888974i \(-0.651419\pi\)
−0.457957 + 0.888974i \(0.651419\pi\)
\(762\) 10131.1i 0.481641i
\(763\) 9087.68i 0.431187i
\(764\) −10980.2 −0.519959
\(765\) −4872.22 254.223i −0.230269 0.0120150i
\(766\) −16864.2 −0.795469
\(767\) 17457.6i 0.821850i
\(768\) 768.000i 0.0360844i
\(769\) 5846.72 0.274172 0.137086 0.990559i \(-0.456226\pi\)
0.137086 + 0.990559i \(0.456226\pi\)
\(770\) 347.942 6668.37i 0.0162844 0.312093i
\(771\) −6680.06 −0.312032
\(772\) 15301.5i 0.713360i
\(773\) 26893.4i 1.25134i −0.780086 0.625672i \(-0.784825\pi\)
0.780086 0.625672i \(-0.215175\pi\)
\(774\) 5384.97 0.250076
\(775\) 18872.9 + 1974.88i 0.874754 + 0.0915351i
\(776\) 14021.1 0.648618
\(777\) 4462.21i 0.206024i
\(778\) 11862.8i 0.546660i
\(779\) 17689.6 0.813602
\(780\) 511.491 9802.80i 0.0234799 0.449996i
\(781\) −5207.37 −0.238584
\(782\) 1197.47i 0.0547587i
\(783\) 1291.79i 0.0589587i
\(784\) −784.000 −0.0357143
\(785\) −38691.6 2018.85i −1.75919 0.0917910i
\(786\) −5515.16 −0.250279
\(787\) 38318.9i 1.73560i −0.496910 0.867802i \(-0.665532\pi\)
0.496910 0.867802i \(-0.334468\pi\)
\(788\) 17796.0i 0.804512i
\(789\) 19424.3 0.876457
\(790\) −9369.32 488.873i −0.421956 0.0220169i
\(791\) 7073.86 0.317974
\(792\) 3071.56i 0.137807i
\(793\) 56245.3i 2.51870i
\(794\) −1380.75 −0.0617143
\(795\) 266.295 5103.59i 0.0118799 0.227680i
\(796\) 17532.9 0.780699
\(797\) 4597.04i 0.204311i −0.994768 0.102155i \(-0.967426\pi\)
0.994768 0.102155i \(-0.0325739\pi\)
\(798\) 3261.36i 0.144675i
\(799\) 26315.7 1.16518
\(800\) −416.291 + 3978.28i −0.0183976 + 0.175817i
\(801\) 1417.30 0.0625189
\(802\) 4628.36i 0.203782i
\(803\) 1356.93i 0.0596327i
\(804\) −3760.64 −0.164959
\(805\) −50.3575 + 965.109i −0.00220481 + 0.0422554i
\(806\) 22214.0 0.970790
\(807\) 14941.1i 0.651739i
\(808\) 8655.65i 0.376862i
\(809\) 22083.1 0.959706 0.479853 0.877349i \(-0.340690\pi\)
0.479853 + 0.877349i \(0.340690\pi\)
\(810\) 1808.75 + 94.3773i 0.0784607 + 0.00409392i
\(811\) 1458.44 0.0631478 0.0315739 0.999501i \(-0.489948\pi\)
0.0315739 + 0.999501i \(0.489948\pi\)
\(812\) 1339.63i 0.0578963i
\(813\) 23489.3i 1.01329i
\(814\) −18129.6 −0.780641
\(815\) −30121.7 1571.69i −1.29462 0.0675508i
\(816\) 2327.35 0.0998448
\(817\) 23230.6i 0.994782i
\(818\) 23798.6i 1.01724i
\(819\) −4609.40 −0.196661
\(820\) −530.861 + 10174.0i −0.0226079 + 0.433283i
\(821\) 10466.2 0.444911 0.222456 0.974943i \(-0.428593\pi\)
0.222456 + 0.974943i \(0.428593\pi\)
\(822\) 6925.44i 0.293859i
\(823\) 33033.9i 1.39914i −0.714566 0.699568i \(-0.753376\pi\)
0.714566 0.699568i \(-0.246624\pi\)
\(824\) 5746.64 0.242954
\(825\) −1664.93 + 15910.9i −0.0702610 + 0.671448i
\(826\) 3340.48 0.140715
\(827\) 26197.7i 1.10155i 0.834653 + 0.550777i \(0.185668\pi\)
−0.834653 + 0.550777i \(0.814332\pi\)
\(828\) 444.545i 0.0186582i
\(829\) 46489.0 1.94768 0.973841 0.227229i \(-0.0729664\pi\)
0.973841 + 0.227229i \(0.0729664\pi\)
\(830\) −1143.75 + 21920.2i −0.0478316 + 0.916699i
\(831\) −9312.30 −0.388737
\(832\) 4682.57i 0.195119i
\(833\) 2375.83i 0.0988208i
\(834\) −18303.1 −0.759933
\(835\) −35772.2 1866.53i −1.48257 0.0773578i
\(836\) −13250.6 −0.548185
\(837\) 4098.80i 0.169266i
\(838\) 28766.2i 1.18582i
\(839\) −29036.9 −1.19484 −0.597418 0.801930i \(-0.703806\pi\)
−0.597418 + 0.801930i \(0.703806\pi\)
\(840\) 1875.75 + 97.8727i 0.0770469 + 0.00402015i
\(841\) −22100.0 −0.906144
\(842\) 9241.42i 0.378243i
\(843\) 8749.34i 0.357465i
\(844\) 582.618 0.0237613
\(845\) 1838.69 35238.8i 0.0748555 1.43462i
\(846\) −9769.39 −0.397020
\(847\) 3422.49i 0.138841i
\(848\) 2437.87i 0.0987225i
\(849\) −24597.9 −0.994343
\(850\) 12055.8 + 1261.53i 0.486482 + 0.0509059i
\(851\) 2623.88 0.105694
\(852\) 1464.78i 0.0588998i
\(853\) 6062.80i 0.243360i −0.992569 0.121680i \(-0.961172\pi\)
0.992569 0.121680i \(-0.0388282\pi\)
\(854\) −10762.4 −0.431244
\(855\) −407.141 + 7802.92i −0.0162853 + 0.312110i
\(856\) −15607.6 −0.623199
\(857\) 2836.79i 0.113072i −0.998401 0.0565362i \(-0.981994\pi\)
0.998401 0.0565362i \(-0.0180056\pi\)
\(858\) 18727.6i 0.745164i
\(859\) −25527.2 −1.01394 −0.506972 0.861962i \(-0.669235\pi\)
−0.506972 + 0.861962i \(0.669235\pi\)
\(860\) −13360.9 697.145i −0.529771 0.0276424i
\(861\) 4783.96 0.189358
\(862\) 24679.0i 0.975138i
\(863\) 24340.9i 0.960109i −0.877239 0.480055i \(-0.840617\pi\)
0.877239 0.480055i \(-0.159383\pi\)
\(864\) −864.000 −0.0340207
\(865\) 2589.27 + 135.103i 0.101778 + 0.00531056i
\(866\) 22561.9 0.885315
\(867\) 7686.22i 0.301081i
\(868\) 4250.61i 0.166216i
\(869\) 17899.5 0.698732
\(870\) −167.236 + 3205.11i −0.00651706 + 0.124900i
\(871\) −22929.0 −0.891984
\(872\) 10385.9i 0.403339i
\(873\) 15773.7i 0.611523i
\(874\) 1917.76 0.0742209
\(875\) 9663.40 + 1523.72i 0.373352 + 0.0588701i
\(876\) −381.691 −0.0147216
\(877\) 144.805i 0.00557550i 0.999996 + 0.00278775i \(0.000887369\pi\)
−0.999996 + 0.00278775i \(0.999113\pi\)
\(878\) 13170.6i 0.506248i
\(879\) 25346.3 0.972594
\(880\) 397.649 7620.99i 0.0152326 0.291936i
\(881\) −10781.9 −0.412319 −0.206159 0.978518i \(-0.566097\pi\)
−0.206159 + 0.978518i \(0.566097\pi\)
\(882\) 882.000i 0.0336718i
\(883\) 20688.7i 0.788483i −0.919007 0.394241i \(-0.871007\pi\)
0.919007 0.394241i \(-0.128993\pi\)
\(884\) 14190.0 0.539890
\(885\) −7992.22 417.018i −0.303566 0.0158395i
\(886\) 11042.2 0.418702
\(887\) 35310.9i 1.33667i −0.743862 0.668334i \(-0.767008\pi\)
0.743862 0.668334i \(-0.232992\pi\)
\(888\) 5099.67i 0.192718i
\(889\) −11819.6 −0.445913
\(890\) −3516.52 183.485i −0.132443 0.00691059i
\(891\) −3455.51 −0.129926
\(892\) 7644.69i 0.286954i
\(893\) 42144.9i 1.57931i
\(894\) −7166.14 −0.268089
\(895\) 1693.04 32447.4i 0.0632314 1.21184i
\(896\) −896.000 −0.0334077
\(897\) 2710.44i 0.100891i
\(898\) 20025.3i 0.744158i
\(899\) −7263.07 −0.269452
\(900\) −4475.56 468.327i −0.165762 0.0173455i
\(901\) 7387.71 0.273163
\(902\) 19436.8i 0.717489i
\(903\) 6282.47i 0.231525i
\(904\) 8084.41 0.297438
\(905\) 582.497 11163.6i 0.0213954 0.410047i
\(906\) 8391.64 0.307719
\(907\) 46702.8i 1.70975i 0.518835 + 0.854875i \(0.326366\pi\)
−0.518835 + 0.854875i \(0.673634\pi\)
\(908\) 8334.40i 0.304611i
\(909\) −9737.60 −0.355309
\(910\) 11436.6 + 596.739i 0.416615 + 0.0217382i
\(911\) 31094.5 1.13085 0.565426 0.824799i \(-0.308712\pi\)
0.565426 + 0.824799i \(0.308712\pi\)
\(912\) 3727.27i 0.135332i
\(913\) 41877.1i 1.51799i
\(914\) −24257.4 −0.877859
\(915\) 25749.4 + 1343.55i 0.930328 + 0.0485427i
\(916\) 8008.12 0.288860
\(917\) 6434.36i 0.231713i
\(918\) 2618.26i 0.0941346i
\(919\) −12244.5 −0.439509 −0.219755 0.975555i \(-0.570526\pi\)
−0.219755 + 0.975555i \(0.570526\pi\)
\(920\) −57.5514 + 1102.98i −0.00206241 + 0.0395263i
\(921\) 6034.56 0.215902
\(922\) 16559.6i 0.591500i
\(923\) 8930.91i 0.318488i
\(924\) −3583.49 −0.127585
\(925\) 2764.25 26416.6i 0.0982574 0.938996i
\(926\) −25865.4 −0.917915
\(927\) 6464.97i 0.229059i
\(928\) 1531.01i 0.0541570i
\(929\) −40170.0 −1.41866 −0.709331 0.704876i \(-0.751003\pi\)
−0.709331 + 0.704876i \(0.751003\pi\)
\(930\) 530.636 10169.7i 0.0187100 0.358579i
\(931\) 3804.92 0.133943
\(932\) 12982.1i 0.456269i
\(933\) 11224.4i 0.393860i
\(934\) 14653.4 0.513356
\(935\) −23094.6 1205.03i −0.807781 0.0421484i
\(936\) −5267.89 −0.183960
\(937\) 30532.4i 1.06452i 0.846582 + 0.532258i \(0.178656\pi\)
−0.846582 + 0.532258i \(0.821344\pi\)
\(938\) 4387.41i 0.152723i
\(939\) 25424.8 0.883606
\(940\) 24239.3 + 1264.76i 0.841062 + 0.0438849i
\(941\) 22126.9 0.766544 0.383272 0.923636i \(-0.374797\pi\)
0.383272 + 0.923636i \(0.374797\pi\)
\(942\) 20792.3i 0.719162i
\(943\) 2813.08i 0.0971436i
\(944\) 3817.70 0.131627
\(945\) −110.107 + 2110.21i −0.00379024 + 0.0726405i
\(946\) 25525.1 0.877266
\(947\) 14922.2i 0.512046i 0.966671 + 0.256023i \(0.0824123\pi\)
−0.966671 + 0.256023i \(0.917588\pi\)
\(948\) 5034.95i 0.172497i
\(949\) −2327.21 −0.0796041
\(950\) 2020.35 19307.5i 0.0689988 0.659386i
\(951\) 28113.5 0.958613
\(952\) 2715.24i 0.0924384i
\(953\) 20720.7i 0.704313i −0.935941 0.352156i \(-0.885448\pi\)
0.935941 0.352156i \(-0.114552\pi\)
\(954\) −2742.60 −0.0930765
\(955\) −1599.19 + 30648.8i −0.0541871 + 1.03850i
\(956\) −22408.1 −0.758086
\(957\) 6123.15i 0.206827i
\(958\) 25136.8i 0.847739i
\(959\) −8079.68 −0.272061
\(960\) 2143.71 + 111.855i 0.0720707 + 0.00376051i
\(961\) −6745.46 −0.226426
\(962\) 31093.2i 1.04208i
\(963\) 17558.6i 0.587557i
\(964\) −19159.7 −0.640138
\(965\) 42710.9 + 2228.57i 1.42478 + 0.0743423i
\(966\) 518.636 0.0172742
\(967\) 34075.1i 1.13318i −0.824001 0.566589i \(-0.808263\pi\)
0.824001 0.566589i \(-0.191737\pi\)
\(968\) 3911.42i 0.129874i
\(969\) −11295.1 −0.374460
\(970\) 2042.08 39136.9i 0.0675953 1.29547i
\(971\) 36786.0 1.21578 0.607889 0.794022i \(-0.292017\pi\)
0.607889 + 0.794022i \(0.292017\pi\)
\(972\) 972.000i 0.0320750i
\(973\) 21353.6i 0.703561i
\(974\) 20929.6 0.688531
\(975\) −27287.9 2855.44i −0.896322 0.0937920i
\(976\) −12299.9 −0.403392
\(977\) 29429.9i 0.963711i 0.876251 + 0.481855i \(0.160037\pi\)
−0.876251 + 0.481855i \(0.839963\pi\)
\(978\) 16187.0i 0.529246i
\(979\) 6718.08 0.219316
\(980\) −114.185 + 2188.37i −0.00372194 + 0.0713315i
\(981\) −11684.2 −0.380272
\(982\) 3072.44i 0.0998427i
\(983\) 209.332i 0.00679212i −0.999994 0.00339606i \(-0.998919\pi\)
0.999994 0.00339606i \(-0.00108100\pi\)
\(984\) 5467.38 0.177128
\(985\) 49673.7 + 2591.88i 1.60684 + 0.0838417i
\(986\) −4639.56 −0.149852
\(987\) 11397.6i 0.367569i
\(988\) 22725.5i 0.731777i
\(989\) −3694.24 −0.118776
\(990\) 8573.62 + 447.355i 0.275240 + 0.0143615i
\(991\) 221.264 0.00709250 0.00354625 0.999994i \(-0.498871\pi\)
0.00354625 + 0.999994i \(0.498871\pi\)
\(992\) 4857.84i 0.155480i
\(993\) 5272.64i 0.168502i
\(994\) 1708.91 0.0545306
\(995\) 2553.56 48939.3i 0.0813600 1.55928i
\(996\) 11779.6 0.374750
\(997\) 25509.1i 0.810313i 0.914247 + 0.405157i \(0.132783\pi\)
−0.914247 + 0.405157i \(0.867217\pi\)
\(998\) 25473.6i 0.807968i
\(999\) 5737.13 0.181697
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 210.4.g.b.169.1 4
3.2 odd 2 630.4.g.d.379.4 4
5.2 odd 4 1050.4.a.bh.1.1 2
5.3 odd 4 1050.4.a.ba.1.1 2
5.4 even 2 inner 210.4.g.b.169.3 yes 4
15.14 odd 2 630.4.g.d.379.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.4.g.b.169.1 4 1.1 even 1 trivial
210.4.g.b.169.3 yes 4 5.4 even 2 inner
630.4.g.d.379.2 4 15.14 odd 2
630.4.g.d.379.4 4 3.2 odd 2
1050.4.a.ba.1.1 2 5.3 odd 4
1050.4.a.bh.1.1 2 5.2 odd 4