Properties

Label 405.3.l.h.352.2
Level $405$
Weight $3$
Character 405.352
Analytic conductor $11.035$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,3,Mod(28,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.28");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 405.l (of order \(12\), degree \(4\), 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: \(11.0354507066\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 352.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 405.352
Dual form 405.3.l.h.298.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0822623 - 0.307007i) q^{2} +(3.37662 + 1.94949i) q^{4} +(0.799701 - 4.93563i) q^{5} +(1.26260 - 4.71209i) q^{7} +(1.77526 - 1.77526i) q^{8} +O(q^{10})\) \(q+(0.0822623 - 0.307007i) q^{2} +(3.37662 + 1.94949i) q^{4} +(0.799701 - 4.93563i) q^{5} +(1.26260 - 4.71209i) q^{7} +(1.77526 - 1.77526i) q^{8} +(-1.44949 - 0.651531i) q^{10} +(-5.67423 - 9.82806i) q^{11} +(-2.03163 - 7.58214i) q^{13} +(-1.34278 - 0.775255i) q^{14} +(7.39898 + 12.8154i) q^{16} +(-17.3485 - 17.3485i) q^{17} +8.69694i q^{19} +(12.3223 - 15.1067i) q^{20} +(-3.48406 + 0.933552i) q^{22} +(4.22778 + 15.7783i) q^{23} +(-23.7210 - 7.89406i) q^{25} -2.49490 q^{26} +(13.4495 - 13.4495i) q^{28} +(30.4377 - 17.5732i) q^{29} +(-5.34847 + 9.26382i) q^{31} +(14.2433 - 3.81647i) q^{32} +(-6.75323 + 3.89898i) q^{34} +(-22.2474 - 10.0000i) q^{35} +(-6.04541 - 6.04541i) q^{37} +(2.67002 + 0.715430i) q^{38} +(-7.34233 - 10.1817i) q^{40} +(-0.348469 + 0.603566i) q^{41} +(36.1927 + 9.69781i) q^{43} -44.2474i q^{44} +5.19184 q^{46} +(16.1957 - 60.4431i) q^{47} +(21.8256 + 12.6010i) q^{49} +(-4.37488 + 6.63312i) q^{50} +(7.92127 - 29.5626i) q^{52} +(-0.696938 + 0.696938i) q^{53} +(-53.0454 + 20.1464i) q^{55} +(-6.12372 - 10.6066i) q^{56} +(-2.89123 - 10.7902i) q^{58} +(34.5840 + 19.9671i) q^{59} +(-2.95459 - 5.11750i) q^{61} +(2.40408 + 2.40408i) q^{62} +54.5051i q^{64} +(-39.0473 + 3.96392i) q^{65} +(61.6091 - 16.5081i) q^{67} +(-24.7584 - 92.3998i) q^{68} +(-4.90020 + 6.00750i) q^{70} -68.0000 q^{71} +(77.7878 - 77.7878i) q^{73} +(-2.35329 + 1.35867i) q^{74} +(-16.9546 + 29.3662i) q^{76} +(-53.4750 + 14.3286i) q^{77} +(-21.2132 + 12.2474i) q^{79} +(69.1691 - 26.2702i) q^{80} +(0.156633 + 0.156633i) q^{82} +(-17.9584 - 4.81193i) q^{83} +(-99.4993 + 71.7521i) q^{85} +(5.95459 - 10.3137i) q^{86} +(-27.5205 - 7.37410i) q^{88} +82.1816i q^{89} -38.2929 q^{91} +(-16.4840 + 61.5192i) q^{92} +(-17.2242 - 9.94439i) q^{94} +(42.9249 + 6.95495i) q^{95} +(-9.00273 + 33.5986i) q^{97} +(5.66403 - 5.66403i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + 4 q^{5} - 4 q^{7} + 24 q^{8} + 8 q^{10} - 16 q^{11} + 32 q^{13} + 20 q^{16} - 80 q^{17} + 36 q^{20} - 20 q^{22} - 56 q^{23} - 16 q^{25} + 176 q^{26} + 88 q^{28} + 16 q^{31} + 76 q^{32} - 80 q^{35} + 128 q^{37} + 96 q^{38} - 48 q^{40} + 56 q^{41} + 8 q^{43} - 272 q^{46} - 128 q^{47} - 164 q^{50} + 80 q^{52} + 112 q^{53} - 248 q^{55} + 12 q^{58} - 200 q^{61} + 176 q^{62} + 112 q^{65} + 200 q^{67} + 104 q^{68} + 60 q^{70} - 544 q^{71} + 152 q^{73} - 312 q^{76} - 88 q^{77} + 328 q^{80} + 256 q^{82} + 16 q^{83} - 232 q^{85} + 224 q^{86} - 12 q^{88} - 32 q^{91} - 104 q^{92} - 144 q^{95} + 20 q^{97} - 376 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0822623 0.307007i 0.0411312 0.153504i −0.942306 0.334752i \(-0.891347\pi\)
0.983437 + 0.181249i \(0.0580140\pi\)
\(3\) 0 0
\(4\) 3.37662 + 1.94949i 0.844154 + 0.487372i
\(5\) 0.799701 4.93563i 0.159940 0.987127i
\(6\) 0 0
\(7\) 1.26260 4.71209i 0.180372 0.673156i −0.815203 0.579176i \(-0.803374\pi\)
0.995574 0.0939798i \(-0.0299589\pi\)
\(8\) 1.77526 1.77526i 0.221907 0.221907i
\(9\) 0 0
\(10\) −1.44949 0.651531i −0.144949 0.0651531i
\(11\) −5.67423 9.82806i −0.515840 0.893460i −0.999831 0.0183875i \(-0.994147\pi\)
0.483991 0.875073i \(-0.339187\pi\)
\(12\) 0 0
\(13\) −2.03163 7.58214i −0.156279 0.583241i −0.998992 0.0448789i \(-0.985710\pi\)
0.842713 0.538362i \(-0.180957\pi\)
\(14\) −1.34278 0.775255i −0.0959129 0.0553754i
\(15\) 0 0
\(16\) 7.39898 + 12.8154i 0.462436 + 0.800963i
\(17\) −17.3485 17.3485i −1.02050 1.02050i −0.999785 0.0207127i \(-0.993406\pi\)
−0.0207127 0.999785i \(-0.506594\pi\)
\(18\) 0 0
\(19\) 8.69694i 0.457734i 0.973458 + 0.228867i \(0.0735020\pi\)
−0.973458 + 0.228867i \(0.926498\pi\)
\(20\) 12.3223 15.1067i 0.616113 0.755336i
\(21\) 0 0
\(22\) −3.48406 + 0.933552i −0.158366 + 0.0424342i
\(23\) 4.22778 + 15.7783i 0.183817 + 0.686013i 0.994881 + 0.101056i \(0.0322220\pi\)
−0.811064 + 0.584957i \(0.801111\pi\)
\(24\) 0 0
\(25\) −23.7210 7.89406i −0.948838 0.315763i
\(26\) −2.49490 −0.0959576
\(27\) 0 0
\(28\) 13.4495 13.4495i 0.480339 0.480339i
\(29\) 30.4377 17.5732i 1.04958 0.605973i 0.127045 0.991897i \(-0.459451\pi\)
0.922531 + 0.385924i \(0.126117\pi\)
\(30\) 0 0
\(31\) −5.34847 + 9.26382i −0.172531 + 0.298833i −0.939304 0.343086i \(-0.888528\pi\)
0.766773 + 0.641918i \(0.221861\pi\)
\(32\) 14.2433 3.81647i 0.445102 0.119265i
\(33\) 0 0
\(34\) −6.75323 + 3.89898i −0.198624 + 0.114676i
\(35\) −22.2474 10.0000i −0.635641 0.285714i
\(36\) 0 0
\(37\) −6.04541 6.04541i −0.163389 0.163389i 0.620677 0.784066i \(-0.286858\pi\)
−0.784066 + 0.620677i \(0.786858\pi\)
\(38\) 2.67002 + 0.715430i 0.0702638 + 0.0188271i
\(39\) 0 0
\(40\) −7.34233 10.1817i −0.183558 0.254542i
\(41\) −0.348469 + 0.603566i −0.00849925 + 0.0147211i −0.870244 0.492621i \(-0.836039\pi\)
0.861744 + 0.507343i \(0.169372\pi\)
\(42\) 0 0
\(43\) 36.1927 + 9.69781i 0.841691 + 0.225530i 0.653807 0.756661i \(-0.273171\pi\)
0.187883 + 0.982191i \(0.439837\pi\)
\(44\) 44.2474i 1.00562i
\(45\) 0 0
\(46\) 5.19184 0.112866
\(47\) 16.1957 60.4431i 0.344589 1.28602i −0.548502 0.836149i \(-0.684802\pi\)
0.893091 0.449875i \(-0.148532\pi\)
\(48\) 0 0
\(49\) 21.8256 + 12.6010i 0.445421 + 0.257164i
\(50\) −4.37488 + 6.63312i −0.0874975 + 0.132662i
\(51\) 0 0
\(52\) 7.92127 29.5626i 0.152332 0.568512i
\(53\) −0.696938 + 0.696938i −0.0131498 + 0.0131498i −0.713651 0.700501i \(-0.752960\pi\)
0.700501 + 0.713651i \(0.252960\pi\)
\(54\) 0 0
\(55\) −53.0454 + 20.1464i −0.964462 + 0.366299i
\(56\) −6.12372 10.6066i −0.109352 0.189404i
\(57\) 0 0
\(58\) −2.89123 10.7902i −0.0498487 0.186038i
\(59\) 34.5840 + 19.9671i 0.586170 + 0.338425i 0.763582 0.645711i \(-0.223439\pi\)
−0.177412 + 0.984137i \(0.556772\pi\)
\(60\) 0 0
\(61\) −2.95459 5.11750i −0.0484359 0.0838935i 0.840791 0.541360i \(-0.182090\pi\)
−0.889227 + 0.457466i \(0.848757\pi\)
\(62\) 2.40408 + 2.40408i 0.0387755 + 0.0387755i
\(63\) 0 0
\(64\) 54.5051i 0.851642i
\(65\) −39.0473 + 3.96392i −0.600728 + 0.0609835i
\(66\) 0 0
\(67\) 61.6091 16.5081i 0.919539 0.246390i 0.232151 0.972680i \(-0.425424\pi\)
0.687388 + 0.726290i \(0.258757\pi\)
\(68\) −24.7584 92.3998i −0.364095 1.35882i
\(69\) 0 0
\(70\) −4.90020 + 6.00750i −0.0700028 + 0.0858215i
\(71\) −68.0000 −0.957746 −0.478873 0.877884i \(-0.658955\pi\)
−0.478873 + 0.877884i \(0.658955\pi\)
\(72\) 0 0
\(73\) 77.7878 77.7878i 1.06559 1.06559i 0.0678931 0.997693i \(-0.478372\pi\)
0.997693 0.0678931i \(-0.0216277\pi\)
\(74\) −2.35329 + 1.35867i −0.0318013 + 0.0183605i
\(75\) 0 0
\(76\) −16.9546 + 29.3662i −0.223087 + 0.386398i
\(77\) −53.4750 + 14.3286i −0.694481 + 0.186086i
\(78\) 0 0
\(79\) −21.2132 + 12.2474i −0.268522 + 0.155031i −0.628216 0.778039i \(-0.716214\pi\)
0.359694 + 0.933070i \(0.382881\pi\)
\(80\) 69.1691 26.2702i 0.864614 0.328377i
\(81\) 0 0
\(82\) 0.156633 + 0.156633i 0.00191016 + 0.00191016i
\(83\) −17.9584 4.81193i −0.216366 0.0579750i 0.149008 0.988836i \(-0.452392\pi\)
−0.365373 + 0.930861i \(0.619059\pi\)
\(84\) 0 0
\(85\) −99.4993 + 71.7521i −1.17058 + 0.844142i
\(86\) 5.95459 10.3137i 0.0692394 0.119926i
\(87\) 0 0
\(88\) −27.5205 7.37410i −0.312733 0.0837966i
\(89\) 82.1816i 0.923389i 0.887039 + 0.461695i \(0.152758\pi\)
−0.887039 + 0.461695i \(0.847242\pi\)
\(90\) 0 0
\(91\) −38.2929 −0.420801
\(92\) −16.4840 + 61.5192i −0.179174 + 0.668687i
\(93\) 0 0
\(94\) −17.2242 9.94439i −0.183236 0.105791i
\(95\) 42.9249 + 6.95495i 0.451841 + 0.0732100i
\(96\) 0 0
\(97\) −9.00273 + 33.5986i −0.0928117 + 0.346378i −0.996679 0.0814359i \(-0.974049\pi\)
0.903867 + 0.427814i \(0.140716\pi\)
\(98\) 5.66403 5.66403i 0.0577962 0.0577962i
\(99\) 0 0
\(100\) −64.7071 72.8990i −0.647071 0.728990i
\(101\) 52.8105 + 91.4704i 0.522876 + 0.905647i 0.999646 + 0.0266193i \(0.00847419\pi\)
−0.476770 + 0.879028i \(0.658192\pi\)
\(102\) 0 0
\(103\) −32.6668 121.914i −0.317154 1.18363i −0.921968 0.387267i \(-0.873419\pi\)
0.604814 0.796367i \(-0.293247\pi\)
\(104\) −17.0669 9.85357i −0.164105 0.0947459i
\(105\) 0 0
\(106\) 0.156633 + 0.271297i 0.00147767 + 0.00255940i
\(107\) 68.7423 + 68.7423i 0.642452 + 0.642452i 0.951158 0.308706i \(-0.0998958\pi\)
−0.308706 + 0.951158i \(0.599896\pi\)
\(108\) 0 0
\(109\) 68.6969i 0.630247i 0.949051 + 0.315124i \(0.102046\pi\)
−0.949051 + 0.315124i \(0.897954\pi\)
\(110\) 1.82146 + 17.9426i 0.0165587 + 0.163115i
\(111\) 0 0
\(112\) 69.7293 18.6839i 0.622583 0.166821i
\(113\) 35.7392 + 133.381i 0.316276 + 1.18036i 0.922796 + 0.385290i \(0.125899\pi\)
−0.606519 + 0.795069i \(0.707435\pi\)
\(114\) 0 0
\(115\) 81.2568 8.24885i 0.706581 0.0717292i
\(116\) 137.035 1.18134
\(117\) 0 0
\(118\) 8.97500 8.97500i 0.0760593 0.0760593i
\(119\) −103.652 + 59.8434i −0.871023 + 0.502885i
\(120\) 0 0
\(121\) −3.89388 + 6.74439i −0.0321808 + 0.0557388i
\(122\) −1.81416 + 0.486103i −0.0148702 + 0.00398445i
\(123\) 0 0
\(124\) −36.1194 + 20.8536i −0.291286 + 0.168174i
\(125\) −57.9319 + 110.765i −0.463455 + 0.886120i
\(126\) 0 0
\(127\) 164.621 + 164.621i 1.29623 + 1.29623i 0.930865 + 0.365362i \(0.119055\pi\)
0.365362 + 0.930865i \(0.380945\pi\)
\(128\) 73.7065 + 19.7496i 0.575832 + 0.154294i
\(129\) 0 0
\(130\) −1.99517 + 12.3139i −0.0153475 + 0.0947223i
\(131\) −53.0681 + 91.9167i −0.405100 + 0.701654i −0.994333 0.106309i \(-0.966097\pi\)
0.589233 + 0.807963i \(0.299430\pi\)
\(132\) 0 0
\(133\) 40.9808 + 10.9808i 0.308126 + 0.0825621i
\(134\) 20.2724i 0.151287i
\(135\) 0 0
\(136\) −61.5959 −0.452911
\(137\) −60.9912 + 227.622i −0.445191 + 1.66148i 0.270239 + 0.962793i \(0.412897\pi\)
−0.715431 + 0.698684i \(0.753769\pi\)
\(138\) 0 0
\(139\) 165.559 + 95.5857i 1.19107 + 0.687667i 0.958550 0.284924i \(-0.0919683\pi\)
0.232524 + 0.972591i \(0.425302\pi\)
\(140\) −55.6262 77.1373i −0.397330 0.550981i
\(141\) 0 0
\(142\) −5.59384 + 20.8765i −0.0393932 + 0.147018i
\(143\) −62.9898 + 62.9898i −0.440488 + 0.440488i
\(144\) 0 0
\(145\) −62.3939 164.283i −0.430303 1.13298i
\(146\) −17.4824 30.2804i −0.119742 0.207400i
\(147\) 0 0
\(148\) −8.62756 32.1985i −0.0582943 0.217557i
\(149\) −73.4853 42.4268i −0.493190 0.284744i 0.232707 0.972547i \(-0.425242\pi\)
−0.725897 + 0.687803i \(0.758575\pi\)
\(150\) 0 0
\(151\) −74.4847 129.011i −0.493276 0.854379i 0.506694 0.862126i \(-0.330867\pi\)
−0.999970 + 0.00774676i \(0.997534\pi\)
\(152\) 15.4393 + 15.4393i 0.101574 + 0.101574i
\(153\) 0 0
\(154\) 17.5959i 0.114259i
\(155\) 41.4456 + 33.8064i 0.267391 + 0.218106i
\(156\) 0 0
\(157\) −23.0224 + 6.16884i −0.146640 + 0.0392919i −0.331392 0.943493i \(-0.607518\pi\)
0.184753 + 0.982785i \(0.440852\pi\)
\(158\) 2.01501 + 7.52011i 0.0127532 + 0.0475956i
\(159\) 0 0
\(160\) −7.44634 73.3515i −0.0465396 0.458447i
\(161\) 79.6867 0.494949
\(162\) 0 0
\(163\) 130.606 130.606i 0.801265 0.801265i −0.182029 0.983293i \(-0.558266\pi\)
0.983293 + 0.182029i \(0.0582664\pi\)
\(164\) −2.35329 + 1.35867i −0.0143493 + 0.00828460i
\(165\) 0 0
\(166\) −2.95459 + 5.11750i −0.0177987 + 0.0308283i
\(167\) 61.5192 16.4840i 0.368379 0.0987068i −0.0698806 0.997555i \(-0.522262\pi\)
0.438259 + 0.898849i \(0.355595\pi\)
\(168\) 0 0
\(169\) 92.9970 53.6918i 0.550278 0.317703i
\(170\) 13.8434 + 36.4495i 0.0814316 + 0.214409i
\(171\) 0 0
\(172\) 103.303 + 103.303i 0.600599 + 0.600599i
\(173\) −200.302 53.6707i −1.15781 0.310235i −0.371722 0.928344i \(-0.621232\pi\)
−0.786092 + 0.618109i \(0.787899\pi\)
\(174\) 0 0
\(175\) −67.1476 + 101.808i −0.383701 + 0.581761i
\(176\) 83.9671 145.435i 0.477086 0.826337i
\(177\) 0 0
\(178\) 25.2304 + 6.76045i 0.141744 + 0.0379801i
\(179\) 183.712i 1.02632i 0.858292 + 0.513161i \(0.171526\pi\)
−0.858292 + 0.513161i \(0.828474\pi\)
\(180\) 0 0
\(181\) −286.272 −1.58162 −0.790808 0.612064i \(-0.790339\pi\)
−0.790808 + 0.612064i \(0.790339\pi\)
\(182\) −3.15006 + 11.7562i −0.0173080 + 0.0645944i
\(183\) 0 0
\(184\) 35.5159 + 20.5051i 0.193021 + 0.111441i
\(185\) −34.6724 + 25.0034i −0.187419 + 0.135153i
\(186\) 0 0
\(187\) −72.0626 + 268.941i −0.385361 + 1.43819i
\(188\) 172.520 172.520i 0.917659 0.917659i
\(189\) 0 0
\(190\) 5.66632 12.6061i 0.0298228 0.0663480i
\(191\) −24.0454 41.6479i −0.125892 0.218052i 0.796189 0.605048i \(-0.206846\pi\)
−0.922081 + 0.386996i \(0.873513\pi\)
\(192\) 0 0
\(193\) −93.5434 349.109i −0.484681 1.80885i −0.581494 0.813551i \(-0.697532\pi\)
0.0968131 0.995303i \(-0.469135\pi\)
\(194\) 9.57444 + 5.52781i 0.0493528 + 0.0284938i
\(195\) 0 0
\(196\) 49.1311 + 85.0976i 0.250669 + 0.434171i
\(197\) −96.6969 96.6969i −0.490847 0.490847i 0.417726 0.908573i \(-0.362827\pi\)
−0.908573 + 0.417726i \(0.862827\pi\)
\(198\) 0 0
\(199\) 192.606i 0.967870i 0.875104 + 0.483935i \(0.160793\pi\)
−0.875104 + 0.483935i \(0.839207\pi\)
\(200\) −56.1247 + 28.0968i −0.280624 + 0.140484i
\(201\) 0 0
\(202\) 32.4264 8.68862i 0.160527 0.0430130i
\(203\) −44.3759 165.613i −0.218601 0.815828i
\(204\) 0 0
\(205\) 2.70031 + 2.20259i 0.0131723 + 0.0107443i
\(206\) −40.1158 −0.194737
\(207\) 0 0
\(208\) 82.1362 82.1362i 0.394886 0.394886i
\(209\) 85.4741 49.3485i 0.408967 0.236117i
\(210\) 0 0
\(211\) −73.6061 + 127.490i −0.348844 + 0.604216i −0.986044 0.166482i \(-0.946759\pi\)
0.637200 + 0.770698i \(0.280092\pi\)
\(212\) −3.71197 + 0.994619i −0.0175093 + 0.00469160i
\(213\) 0 0
\(214\) 26.7593 15.4495i 0.125043 0.0721939i
\(215\) 76.8082 170.879i 0.357247 0.794784i
\(216\) 0 0
\(217\) 36.8990 + 36.8990i 0.170041 + 0.170041i
\(218\) 21.0905 + 5.65117i 0.0967452 + 0.0259228i
\(219\) 0 0
\(220\) −218.389 35.3847i −0.992678 0.160840i
\(221\) −96.2929 + 166.784i −0.435714 + 0.754679i
\(222\) 0 0
\(223\) −228.712 61.2833i −1.02562 0.274813i −0.293475 0.955967i \(-0.594812\pi\)
−0.732141 + 0.681154i \(0.761479\pi\)
\(224\) 71.9342i 0.321135i
\(225\) 0 0
\(226\) 43.8888 0.194198
\(227\) 92.6672 345.839i 0.408225 1.52352i −0.389803 0.920898i \(-0.627457\pi\)
0.798028 0.602620i \(-0.205876\pi\)
\(228\) 0 0
\(229\) 194.165 + 112.101i 0.847881 + 0.489524i 0.859935 0.510403i \(-0.170504\pi\)
−0.0120546 + 0.999927i \(0.503837\pi\)
\(230\) 4.15192 25.6250i 0.0180518 0.111413i
\(231\) 0 0
\(232\) 22.8377 85.2316i 0.0984386 0.367378i
\(233\) −205.712 + 205.712i −0.882883 + 0.882883i −0.993827 0.110944i \(-0.964613\pi\)
0.110944 + 0.993827i \(0.464613\pi\)
\(234\) 0 0
\(235\) −285.373 128.272i −1.21436 0.545840i
\(236\) 77.8513 + 134.842i 0.329878 + 0.571366i
\(237\) 0 0
\(238\) 9.84571 + 36.7447i 0.0413685 + 0.154389i
\(239\) 299.470 + 172.899i 1.25301 + 0.723427i 0.971706 0.236192i \(-0.0758993\pi\)
0.281305 + 0.959618i \(0.409233\pi\)
\(240\) 0 0
\(241\) −50.7878 87.9670i −0.210738 0.365008i 0.741208 0.671275i \(-0.234253\pi\)
−0.951946 + 0.306267i \(0.900920\pi\)
\(242\) 1.75026 + 1.75026i 0.00723247 + 0.00723247i
\(243\) 0 0
\(244\) 23.0398i 0.0944254i
\(245\) 79.6480 97.6461i 0.325094 0.398556i
\(246\) 0 0
\(247\) 65.9414 17.6689i 0.266969 0.0715342i
\(248\) 6.95075 + 25.9405i 0.0280272 + 0.104599i
\(249\) 0 0
\(250\) 29.2401 + 26.8973i 0.116960 + 0.107589i
\(251\) −331.258 −1.31975 −0.659876 0.751375i \(-0.729391\pi\)
−0.659876 + 0.751375i \(0.729391\pi\)
\(252\) 0 0
\(253\) 131.081 131.081i 0.518105 0.518105i
\(254\) 64.0819 36.9977i 0.252291 0.145660i
\(255\) 0 0
\(256\) −96.8837 + 167.807i −0.378452 + 0.655498i
\(257\) −45.4029 + 12.1657i −0.176665 + 0.0473373i −0.346067 0.938210i \(-0.612483\pi\)
0.169402 + 0.985547i \(0.445816\pi\)
\(258\) 0 0
\(259\) −36.1194 + 20.8536i −0.139457 + 0.0805157i
\(260\) −139.576 62.7378i −0.536829 0.241299i
\(261\) 0 0
\(262\) 23.8536 + 23.8536i 0.0910442 + 0.0910442i
\(263\) 379.969 + 101.812i 1.44475 + 0.387119i 0.894194 0.447679i \(-0.147749\pi\)
0.550555 + 0.834799i \(0.314416\pi\)
\(264\) 0 0
\(265\) 2.88249 + 3.99718i 0.0108773 + 0.0150837i
\(266\) 6.74235 11.6781i 0.0253472 0.0439026i
\(267\) 0 0
\(268\) 240.213 + 64.3648i 0.896316 + 0.240167i
\(269\) 488.499i 1.81598i −0.418988 0.907992i \(-0.637615\pi\)
0.418988 0.907992i \(-0.362385\pi\)
\(270\) 0 0
\(271\) 131.576 0.485518 0.242759 0.970087i \(-0.421947\pi\)
0.242759 + 0.970087i \(0.421947\pi\)
\(272\) 93.9668 350.689i 0.345466 1.28930i
\(273\) 0 0
\(274\) 64.8644 + 37.4495i 0.236731 + 0.136677i
\(275\) 57.0149 + 277.924i 0.207327 + 1.01063i
\(276\) 0 0
\(277\) 37.1551 138.665i 0.134134 0.500595i −0.865866 0.500276i \(-0.833232\pi\)
1.00000 0.000318873i \(-0.000101500\pi\)
\(278\) 42.9648 42.9648i 0.154550 0.154550i
\(279\) 0 0
\(280\) −57.2474 + 21.7423i −0.204455 + 0.0776512i
\(281\) −171.652 297.309i −0.610860 1.05804i −0.991096 0.133150i \(-0.957491\pi\)
0.380236 0.924889i \(-0.375843\pi\)
\(282\) 0 0
\(283\) 0.436242 + 1.62808i 0.00154149 + 0.00575293i 0.966692 0.255941i \(-0.0823854\pi\)
−0.965151 + 0.261694i \(0.915719\pi\)
\(284\) −229.610 132.565i −0.808485 0.466779i
\(285\) 0 0
\(286\) 14.1566 + 24.5200i 0.0494987 + 0.0857343i
\(287\) 2.40408 + 2.40408i 0.00837659 + 0.00837659i
\(288\) 0 0
\(289\) 312.939i 1.08283i
\(290\) −55.5686 + 5.64110i −0.191616 + 0.0194521i
\(291\) 0 0
\(292\) 414.306 111.013i 1.41886 0.380181i
\(293\) 35.3454 + 131.911i 0.120633 + 0.450207i 0.999646 0.0265892i \(-0.00846462\pi\)
−0.879014 + 0.476796i \(0.841798\pi\)
\(294\) 0 0
\(295\) 126.207 154.726i 0.427821 0.524496i
\(296\) −21.4643 −0.0725145
\(297\) 0 0
\(298\) −19.0704 + 19.0704i −0.0639946 + 0.0639946i
\(299\) 111.044 64.1112i 0.371384 0.214419i
\(300\) 0 0
\(301\) 91.3939 158.299i 0.303634 0.525910i
\(302\) −45.7347 + 12.2546i −0.151439 + 0.0405780i
\(303\) 0 0
\(304\) −111.455 + 64.3485i −0.366628 + 0.211673i
\(305\) −27.6209 + 10.4903i −0.0905604 + 0.0343945i
\(306\) 0 0
\(307\) −124.969 124.969i −0.407066 0.407066i 0.473648 0.880714i \(-0.342937\pi\)
−0.880714 + 0.473648i \(0.842937\pi\)
\(308\) −208.498 55.8669i −0.676942 0.181386i
\(309\) 0 0
\(310\) 13.7882 9.94312i 0.0444781 0.0320746i
\(311\) 293.151 507.752i 0.942608 1.63264i 0.182136 0.983273i \(-0.441699\pi\)
0.760472 0.649371i \(-0.224968\pi\)
\(312\) 0 0
\(313\) 139.845 + 37.4713i 0.446788 + 0.119717i 0.475196 0.879880i \(-0.342377\pi\)
−0.0284079 + 0.999596i \(0.509044\pi\)
\(314\) 7.57551i 0.0241258i
\(315\) 0 0
\(316\) −95.5051 −0.302231
\(317\) −39.8174 + 148.601i −0.125607 + 0.468772i −0.999861 0.0166979i \(-0.994685\pi\)
0.874254 + 0.485469i \(0.161351\pi\)
\(318\) 0 0
\(319\) −345.421 199.429i −1.08283 0.625170i
\(320\) 269.017 + 43.5878i 0.840679 + 0.136212i
\(321\) 0 0
\(322\) 6.55522 24.4644i 0.0203578 0.0759764i
\(323\) 150.879 150.879i 0.467116 0.467116i
\(324\) 0 0
\(325\) −11.6617 + 195.893i −0.0358823 + 0.602749i
\(326\) −29.3531 50.8410i −0.0900401 0.155954i
\(327\) 0 0
\(328\) 0.452863 + 1.69011i 0.00138068 + 0.00515276i
\(329\) −264.365 152.631i −0.803541 0.463924i
\(330\) 0 0
\(331\) 122.712 + 212.543i 0.370730 + 0.642124i 0.989678 0.143308i \(-0.0457741\pi\)
−0.618948 + 0.785432i \(0.712441\pi\)
\(332\) −51.2577 51.2577i −0.154391 0.154391i
\(333\) 0 0
\(334\) 20.2429i 0.0606074i
\(335\) −32.2091 317.282i −0.0961466 0.947110i
\(336\) 0 0
\(337\) −292.067 + 78.2592i −0.866669 + 0.232223i −0.664647 0.747158i \(-0.731418\pi\)
−0.202022 + 0.979381i \(0.564751\pi\)
\(338\) −8.83363 32.9676i −0.0261350 0.0975372i
\(339\) 0 0
\(340\) −475.851 + 48.3064i −1.39956 + 0.142078i
\(341\) 121.394 0.355994
\(342\) 0 0
\(343\) 255.959 255.959i 0.746237 0.746237i
\(344\) 81.4674 47.0352i 0.236824 0.136730i
\(345\) 0 0
\(346\) −32.9546 + 57.0790i −0.0952445 + 0.164968i
\(347\) 218.632 58.5824i 0.630064 0.168825i 0.0703655 0.997521i \(-0.477583\pi\)
0.559699 + 0.828696i \(0.310917\pi\)
\(348\) 0 0
\(349\) −258.084 + 149.005i −0.739494 + 0.426947i −0.821885 0.569653i \(-0.807078\pi\)
0.0823911 + 0.996600i \(0.473744\pi\)
\(350\) 25.7321 + 28.9898i 0.0735204 + 0.0828280i
\(351\) 0 0
\(352\) −118.328 118.328i −0.336159 0.336159i
\(353\) 30.7627 + 8.24285i 0.0871466 + 0.0233509i 0.302129 0.953267i \(-0.402303\pi\)
−0.214982 + 0.976618i \(0.568969\pi\)
\(354\) 0 0
\(355\) −54.3797 + 335.623i −0.153182 + 0.945417i
\(356\) −160.212 + 277.496i −0.450034 + 0.779482i
\(357\) 0 0
\(358\) 56.4008 + 15.1126i 0.157544 + 0.0422138i
\(359\) 48.2724i 0.134464i 0.997737 + 0.0672318i \(0.0214167\pi\)
−0.997737 + 0.0672318i \(0.978583\pi\)
\(360\) 0 0
\(361\) 285.363 0.790480
\(362\) −23.5494 + 87.8877i −0.0650537 + 0.242784i
\(363\) 0 0
\(364\) −129.300 74.6515i −0.355220 0.205087i
\(365\) −321.725 446.139i −0.881438 1.22230i
\(366\) 0 0
\(367\) 53.6263 200.136i 0.146121 0.545330i −0.853582 0.520958i \(-0.825575\pi\)
0.999703 0.0243716i \(-0.00775850\pi\)
\(368\) −170.924 + 170.924i −0.464467 + 0.464467i
\(369\) 0 0
\(370\) 4.82399 + 12.7015i 0.0130378 + 0.0343284i
\(371\) 2.40408 + 4.16399i 0.00648001 + 0.0112237i
\(372\) 0 0
\(373\) 31.5538 + 117.760i 0.0845947 + 0.315712i 0.995237 0.0974836i \(-0.0310794\pi\)
−0.910642 + 0.413195i \(0.864413\pi\)
\(374\) 76.6388 + 44.2474i 0.204917 + 0.118309i
\(375\) 0 0
\(376\) −78.5505 136.053i −0.208911 0.361844i
\(377\) −195.081 195.081i −0.517455 0.517455i
\(378\) 0 0
\(379\) 210.000i 0.554090i −0.960857 0.277045i \(-0.910645\pi\)
0.960857 0.277045i \(-0.0893551\pi\)
\(380\) 131.382 + 107.166i 0.345743 + 0.282015i
\(381\) 0 0
\(382\) −14.7642 + 3.95606i −0.0386498 + 0.0103562i
\(383\) −3.89126 14.5224i −0.0101599 0.0379174i 0.960660 0.277728i \(-0.0895814\pi\)
−0.970820 + 0.239810i \(0.922915\pi\)
\(384\) 0 0
\(385\) 27.9566 + 275.392i 0.0726146 + 0.715303i
\(386\) −114.874 −0.297601
\(387\) 0 0
\(388\) −95.8990 + 95.8990i −0.247162 + 0.247162i
\(389\) −463.616 + 267.669i −1.19181 + 0.688094i −0.958718 0.284360i \(-0.908219\pi\)
−0.233096 + 0.972454i \(0.574886\pi\)
\(390\) 0 0
\(391\) 200.384 347.075i 0.512490 0.887659i
\(392\) 61.1160 16.3760i 0.155908 0.0417755i
\(393\) 0 0
\(394\) −37.6412 + 21.7321i −0.0955360 + 0.0551577i
\(395\) 43.4847 + 114.495i 0.110088 + 0.289860i
\(396\) 0 0
\(397\) 118.742 + 118.742i 0.299099 + 0.299099i 0.840661 0.541562i \(-0.182167\pi\)
−0.541562 + 0.840661i \(0.682167\pi\)
\(398\) 59.1315 + 15.8442i 0.148572 + 0.0398096i
\(399\) 0 0
\(400\) −74.3452 362.402i −0.185863 0.906004i
\(401\) −210.151 + 363.992i −0.524067 + 0.907711i 0.475540 + 0.879694i \(0.342253\pi\)
−0.999607 + 0.0280172i \(0.991081\pi\)
\(402\) 0 0
\(403\) 81.1057 + 21.7322i 0.201255 + 0.0539260i
\(404\) 411.814i 1.01934i
\(405\) 0 0
\(406\) −54.4949 −0.134224
\(407\) −25.1116 + 93.7177i −0.0616992 + 0.230265i
\(408\) 0 0
\(409\) 446.099 + 257.555i 1.09071 + 0.629719i 0.933764 0.357889i \(-0.116503\pi\)
0.156941 + 0.987608i \(0.449837\pi\)
\(410\) 0.898345 0.647825i 0.00219108 0.00158006i
\(411\) 0 0
\(412\) 127.367 475.341i 0.309144 1.15374i
\(413\) 137.753 137.753i 0.333541 0.333541i
\(414\) 0 0
\(415\) −38.1112 + 84.7878i −0.0918343 + 0.204308i
\(416\) −57.8740 100.241i −0.139120 0.240963i
\(417\) 0 0
\(418\) −8.11904 30.3007i −0.0194235 0.0724896i
\(419\) 76.7312 + 44.3008i 0.183129 + 0.105730i 0.588762 0.808306i \(-0.299615\pi\)
−0.405633 + 0.914036i \(0.632949\pi\)
\(420\) 0 0
\(421\) 128.576 + 222.699i 0.305405 + 0.528977i 0.977351 0.211623i \(-0.0678748\pi\)
−0.671946 + 0.740600i \(0.734541\pi\)
\(422\) 33.0852 + 33.0852i 0.0784009 + 0.0784009i
\(423\) 0 0
\(424\) 2.47449i 0.00583605i
\(425\) 274.572 + 548.472i 0.646053 + 1.29052i
\(426\) 0 0
\(427\) −27.8446 + 7.46094i −0.0652099 + 0.0174729i
\(428\) 98.1040 + 366.129i 0.229215 + 0.855441i
\(429\) 0 0
\(430\) −46.1425 37.6375i −0.107308 0.0875291i
\(431\) 804.636 1.86690 0.933452 0.358702i \(-0.116781\pi\)
0.933452 + 0.358702i \(0.116781\pi\)
\(432\) 0 0
\(433\) −344.848 + 344.848i −0.796416 + 0.796416i −0.982528 0.186113i \(-0.940411\pi\)
0.186113 + 0.982528i \(0.440411\pi\)
\(434\) 14.3636 8.29286i 0.0330960 0.0191080i
\(435\) 0 0
\(436\) −133.924 + 231.963i −0.307165 + 0.532026i
\(437\) −137.223 + 36.7687i −0.314011 + 0.0841390i
\(438\) 0 0
\(439\) 374.927 216.464i 0.854048 0.493085i −0.00796652 0.999968i \(-0.502536\pi\)
0.862015 + 0.506883i \(0.169203\pi\)
\(440\) −58.4041 + 129.934i −0.132737 + 0.295305i
\(441\) 0 0
\(442\) 43.2827 + 43.2827i 0.0979246 + 0.0979246i
\(443\) −334.855 89.7240i −0.755880 0.202537i −0.139755 0.990186i \(-0.544632\pi\)
−0.616124 + 0.787649i \(0.711298\pi\)
\(444\) 0 0
\(445\) 405.618 + 65.7208i 0.911502 + 0.147687i
\(446\) −37.6288 + 65.1750i −0.0843696 + 0.146132i
\(447\) 0 0
\(448\) 256.833 + 68.8182i 0.573288 + 0.153612i
\(449\) 386.091i 0.859890i 0.902855 + 0.429945i \(0.141467\pi\)
−0.902855 + 0.429945i \(0.858533\pi\)
\(450\) 0 0
\(451\) 7.90918 0.0175370
\(452\) −139.346 + 520.048i −0.308289 + 1.15055i
\(453\) 0 0
\(454\) −98.5519 56.8990i −0.217075 0.125328i
\(455\) −30.6228 + 189.000i −0.0673030 + 0.415384i
\(456\) 0 0
\(457\) −81.8971 + 305.644i −0.179206 + 0.668805i 0.816591 + 0.577217i \(0.195861\pi\)
−0.995797 + 0.0915887i \(0.970806\pi\)
\(458\) 50.3883 50.3883i 0.110018 0.110018i
\(459\) 0 0
\(460\) 290.454 + 130.556i 0.631422 + 0.283818i
\(461\) 361.310 + 625.807i 0.783753 + 1.35750i 0.929741 + 0.368213i \(0.120030\pi\)
−0.145989 + 0.989286i \(0.546636\pi\)
\(462\) 0 0
\(463\) −47.4741 177.176i −0.102536 0.382669i 0.895518 0.445025i \(-0.146805\pi\)
−0.998054 + 0.0623562i \(0.980139\pi\)
\(464\) 450.416 + 260.048i 0.970724 + 0.560448i
\(465\) 0 0
\(466\) 46.2327 + 80.0773i 0.0992117 + 0.171840i
\(467\) 415.258 + 415.258i 0.889203 + 0.889203i 0.994446 0.105244i \(-0.0335623\pi\)
−0.105244 + 0.994446i \(0.533562\pi\)
\(468\) 0 0
\(469\) 311.151i 0.663435i
\(470\) −62.8561 + 77.0597i −0.133736 + 0.163957i
\(471\) 0 0
\(472\) 96.8421 25.9488i 0.205174 0.0549762i
\(473\) −110.055 410.732i −0.232675 0.868355i
\(474\) 0 0
\(475\) 68.6542 206.300i 0.144535 0.434315i
\(476\) −466.656 −0.980370
\(477\) 0 0
\(478\) 77.7163 77.7163i 0.162586 0.162586i
\(479\) 264.094 152.474i 0.551344 0.318318i −0.198320 0.980137i \(-0.563549\pi\)
0.749664 + 0.661819i \(0.230215\pi\)
\(480\) 0 0
\(481\) −33.5551 + 58.1191i −0.0697611 + 0.120830i
\(482\) −31.1844 + 8.35584i −0.0646980 + 0.0173358i
\(483\) 0 0
\(484\) −26.2962 + 15.1821i −0.0543311 + 0.0313681i
\(485\) 158.631 + 71.3031i 0.327074 + 0.147017i
\(486\) 0 0
\(487\) −429.318 429.318i −0.881556 0.881556i 0.112137 0.993693i \(-0.464231\pi\)
−0.993693 + 0.112137i \(0.964231\pi\)
\(488\) −14.3300 3.83972i −0.0293648 0.00786828i
\(489\) 0 0
\(490\) −23.4260 32.4851i −0.0478082 0.0662961i
\(491\) 207.159 358.810i 0.421912 0.730773i −0.574214 0.818705i \(-0.694692\pi\)
0.996127 + 0.0879316i \(0.0280257\pi\)
\(492\) 0 0
\(493\) −832.916 223.179i −1.68948 0.452696i
\(494\) 21.6980i 0.0439230i
\(495\) 0 0
\(496\) −158.293 −0.319139
\(497\) −85.8569 + 320.422i −0.172750 + 0.644713i
\(498\) 0 0
\(499\) −318.338 183.792i −0.637951 0.368321i 0.145874 0.989303i \(-0.453401\pi\)
−0.783825 + 0.620982i \(0.786734\pi\)
\(500\) −411.549 + 261.073i −0.823098 + 0.522147i
\(501\) 0 0
\(502\) −27.2500 + 101.698i −0.0542829 + 0.202587i
\(503\) −9.59133 + 9.59133i −0.0190683 + 0.0190683i −0.716577 0.697508i \(-0.754292\pi\)
0.697508 + 0.716577i \(0.254292\pi\)
\(504\) 0 0
\(505\) 493.697 187.504i 0.977618 0.371295i
\(506\) −29.4597 51.0257i −0.0582207 0.100841i
\(507\) 0 0
\(508\) 234.935 + 876.788i 0.462470 + 1.72596i
\(509\) −673.325 388.745i −1.32284 0.763742i −0.338659 0.940909i \(-0.609973\pi\)
−0.984181 + 0.177167i \(0.943307\pi\)
\(510\) 0 0
\(511\) −268.328 464.758i −0.525104 0.909507i
\(512\) 259.376 + 259.376i 0.506593 + 0.506593i
\(513\) 0 0
\(514\) 14.9398i 0.0290658i
\(515\) −627.848 + 63.7365i −1.21912 + 0.123760i
\(516\) 0 0
\(517\) −685.937 + 183.796i −1.32676 + 0.355505i
\(518\) 3.43093 + 12.8044i 0.00662341 + 0.0247189i
\(519\) 0 0
\(520\) −62.2820 + 76.3560i −0.119773 + 0.146838i
\(521\) 321.605 0.617284 0.308642 0.951178i \(-0.400125\pi\)
0.308642 + 0.951178i \(0.400125\pi\)
\(522\) 0 0
\(523\) −582.454 + 582.454i −1.11368 + 1.11368i −0.121030 + 0.992649i \(0.538620\pi\)
−0.992649 + 0.121030i \(0.961380\pi\)
\(524\) −358.381 + 206.911i −0.683934 + 0.394869i
\(525\) 0 0
\(526\) 62.5143 108.278i 0.118848 0.205852i
\(527\) 253.501 67.9254i 0.481026 0.128891i
\(528\) 0 0
\(529\) 227.047 131.086i 0.429201 0.247799i
\(530\) 1.46428 0.556128i 0.00276280 0.00104930i
\(531\) 0 0
\(532\) 116.969 + 116.969i 0.219867 + 0.219867i
\(533\) 5.28428 + 1.41592i 0.00991423 + 0.00265651i
\(534\) 0 0
\(535\) 394.260 284.314i 0.736935 0.531427i
\(536\) 80.0658 138.678i 0.149377 0.258728i
\(537\) 0 0
\(538\) −149.973 40.1851i −0.278760 0.0746935i
\(539\) 286.005i 0.530621i
\(540\) 0 0
\(541\) 460.697 0.851566 0.425783 0.904825i \(-0.359999\pi\)
0.425783 + 0.904825i \(0.359999\pi\)
\(542\) 10.8237 40.3946i 0.0199699 0.0745288i
\(543\) 0 0
\(544\) −313.309 180.889i −0.575935 0.332516i
\(545\) 339.063 + 54.9370i 0.622134 + 0.100802i
\(546\) 0 0
\(547\) −242.227 + 904.005i −0.442829 + 1.65266i 0.278777 + 0.960356i \(0.410071\pi\)
−0.721606 + 0.692304i \(0.756596\pi\)
\(548\) −649.691 + 649.691i −1.18557 + 1.18557i
\(549\) 0 0
\(550\) 90.0148 + 5.35867i 0.163663 + 0.00974304i
\(551\) 152.833 + 264.715i 0.277374 + 0.480426i
\(552\) 0 0
\(553\) 30.9273 + 115.422i 0.0559264 + 0.208720i
\(554\) −39.5146 22.8138i −0.0713260 0.0411801i
\(555\) 0 0
\(556\) 372.687 + 645.512i 0.670300 + 1.16099i
\(557\) 125.909 + 125.909i 0.226049 + 0.226049i 0.811040 0.584991i \(-0.198902\pi\)
−0.584991 + 0.811040i \(0.698902\pi\)
\(558\) 0 0
\(559\) 294.120i 0.526155i
\(560\) −36.4543 359.100i −0.0650970 0.641250i
\(561\) 0 0
\(562\) −105.397 + 28.2409i −0.187538 + 0.0502507i
\(563\) −73.2084 273.218i −0.130033 0.485289i 0.869936 0.493164i \(-0.164160\pi\)
−0.999969 + 0.00787538i \(0.997493\pi\)
\(564\) 0 0
\(565\) 686.898 69.7310i 1.21575 0.123418i
\(566\) 0.535718 0.000946498
\(567\) 0 0
\(568\) −120.717 + 120.717i −0.212531 + 0.212531i
\(569\) −519.476 + 299.919i −0.912962 + 0.527099i −0.881383 0.472402i \(-0.843387\pi\)
−0.0315793 + 0.999501i \(0.510054\pi\)
\(570\) 0 0
\(571\) 123.985 214.749i 0.217137 0.376092i −0.736795 0.676117i \(-0.763662\pi\)
0.953932 + 0.300024i \(0.0969948\pi\)
\(572\) −335.490 + 89.8943i −0.586521 + 0.157158i
\(573\) 0 0
\(574\) 0.935836 0.540305i 0.00163038 0.000941298i
\(575\) 24.2679 407.650i 0.0422050 0.708957i
\(576\) 0 0
\(577\) −292.121 292.121i −0.506276 0.506276i 0.407105 0.913381i \(-0.366538\pi\)
−0.913381 + 0.407105i \(0.866538\pi\)
\(578\) 96.0745 + 25.7431i 0.166219 + 0.0445382i
\(579\) 0 0
\(580\) 109.587 676.356i 0.188943 1.16613i
\(581\) −45.3485 + 78.5459i −0.0780524 + 0.135191i
\(582\) 0 0
\(583\) 10.8041 + 2.89496i 0.0185320 + 0.00496563i
\(584\) 276.186i 0.472922i
\(585\) 0 0
\(586\) 43.4051 0.0740702
\(587\) 223.721 834.938i 0.381126 1.42238i −0.463058 0.886328i \(-0.653248\pi\)
0.844184 0.536053i \(-0.180085\pi\)
\(588\) 0 0
\(589\) −80.5669 46.5153i −0.136786 0.0789734i
\(590\) −37.1200 51.4746i −0.0629153 0.0872452i
\(591\) 0 0
\(592\) 32.7445 122.204i 0.0553117 0.206426i
\(593\) 524.742 524.742i 0.884894 0.884894i −0.109133 0.994027i \(-0.534807\pi\)
0.994027 + 0.109133i \(0.0348074\pi\)
\(594\) 0 0
\(595\) 212.474 + 559.444i 0.357100 + 0.940242i
\(596\) −165.421 286.518i −0.277552 0.480735i
\(597\) 0 0
\(598\) −10.5479 39.3652i −0.0176386 0.0658281i
\(599\) 319.441 + 184.429i 0.533290 + 0.307895i 0.742355 0.670007i \(-0.233709\pi\)
−0.209065 + 0.977902i \(0.567042\pi\)
\(600\) 0 0
\(601\) −466.242 807.555i −0.775777 1.34368i −0.934357 0.356339i \(-0.884025\pi\)
0.158580 0.987346i \(-0.449308\pi\)
\(602\) −41.0806 41.0806i −0.0682402 0.0682402i
\(603\) 0 0
\(604\) 580.829i 0.961637i
\(605\) 30.1739 + 24.6122i 0.0498742 + 0.0406814i
\(606\) 0 0
\(607\) −701.605 + 187.995i −1.15586 + 0.309711i −0.785310 0.619103i \(-0.787496\pi\)
−0.370547 + 0.928814i \(0.620830\pi\)
\(608\) 33.1916 + 123.873i 0.0545914 + 0.203738i
\(609\) 0 0
\(610\) 0.948440 + 9.34278i 0.00155482 + 0.0153160i
\(611\) −491.192 −0.803915
\(612\) 0 0
\(613\) −615.287 + 615.287i −1.00373 + 1.00373i −0.00373821 + 0.999993i \(0.501190\pi\)
−0.999993 + 0.00373821i \(0.998810\pi\)
\(614\) −48.6468 + 28.0862i −0.0792293 + 0.0457430i
\(615\) 0 0
\(616\) −69.4949 + 120.369i −0.112816 + 0.195404i
\(617\) −746.876 + 200.125i −1.21050 + 0.324352i −0.806957 0.590610i \(-0.798887\pi\)
−0.403540 + 0.914962i \(0.632220\pi\)
\(618\) 0 0
\(619\) 132.389 76.4347i 0.213875 0.123481i −0.389236 0.921138i \(-0.627261\pi\)
0.603111 + 0.797657i \(0.293928\pi\)
\(620\) 74.0408 + 194.949i 0.119421 + 0.314434i
\(621\) 0 0
\(622\) −131.768 131.768i −0.211846 0.211846i
\(623\) 387.247 + 103.763i 0.621585 + 0.166553i
\(624\) 0 0
\(625\) 500.367 + 374.510i 0.800588 + 0.599215i
\(626\) 23.0079 39.8509i 0.0367539 0.0636595i
\(627\) 0 0
\(628\) −89.7639 24.0522i −0.142936 0.0382996i
\(629\) 209.757i 0.333477i
\(630\) 0 0
\(631\) −41.4847 −0.0657444 −0.0328722 0.999460i \(-0.510465\pi\)
−0.0328722 + 0.999460i \(0.510465\pi\)
\(632\) −15.9165 + 59.4012i −0.0251843 + 0.0939892i
\(633\) 0 0
\(634\) 42.3460 + 24.4485i 0.0667918 + 0.0385622i
\(635\) 944.156 680.861i 1.48686 1.07222i
\(636\) 0 0
\(637\) 51.2012 191.085i 0.0803786 0.299977i
\(638\) −89.6413 + 89.6413i −0.140504 + 0.140504i
\(639\) 0 0
\(640\) 156.420 347.994i 0.244406 0.543741i
\(641\) −23.6061 40.8870i −0.0368270 0.0637863i 0.847024 0.531554i \(-0.178392\pi\)
−0.883851 + 0.467768i \(0.845058\pi\)
\(642\) 0 0
\(643\) 168.508 + 628.880i 0.262065 + 0.978041i 0.964022 + 0.265822i \(0.0856432\pi\)
−0.701957 + 0.712219i \(0.747690\pi\)
\(644\) 269.071 + 155.348i 0.417813 + 0.241224i
\(645\) 0 0
\(646\) −33.9092 58.7324i −0.0524910 0.0909171i
\(647\) −281.287 281.287i −0.434756 0.434756i 0.455487 0.890243i \(-0.349465\pi\)
−0.890243 + 0.455487i \(0.849465\pi\)
\(648\) 0 0
\(649\) 453.192i 0.698293i
\(650\) 59.1814 + 19.6949i 0.0910482 + 0.0302998i
\(651\) 0 0
\(652\) 695.622 186.391i 1.06690 0.285876i
\(653\) 32.8775 + 122.700i 0.0503484 + 0.187903i 0.986520 0.163641i \(-0.0523237\pi\)
−0.936172 + 0.351543i \(0.885657\pi\)
\(654\) 0 0
\(655\) 411.228 + 335.431i 0.627830 + 0.512108i
\(656\) −10.3133 −0.0157214
\(657\) 0 0
\(658\) −68.6061 + 68.6061i −0.104265 + 0.104265i
\(659\) 936.379 540.619i 1.42091 0.820362i 0.424532 0.905413i \(-0.360439\pi\)
0.996377 + 0.0850507i \(0.0271052\pi\)
\(660\) 0 0
\(661\) 316.196 547.668i 0.478361 0.828545i −0.521332 0.853354i \(-0.674564\pi\)
0.999692 + 0.0248092i \(0.00789783\pi\)
\(662\) 75.3468 20.1891i 0.113817 0.0304971i
\(663\) 0 0
\(664\) −40.4231 + 23.3383i −0.0608781 + 0.0351480i
\(665\) 86.9694 193.485i 0.130781 0.290954i
\(666\) 0 0
\(667\) 405.959 + 405.959i 0.608634 + 0.608634i
\(668\) 239.862 + 64.2709i 0.359075 + 0.0962139i
\(669\) 0 0
\(670\) −100.057 16.2119i −0.149339 0.0241969i
\(671\) −33.5301 + 58.0758i −0.0499703 + 0.0865512i
\(672\) 0 0
\(673\) −318.684 85.3911i −0.473527 0.126881i 0.0141597 0.999900i \(-0.495493\pi\)
−0.487687 + 0.873018i \(0.662159\pi\)
\(674\) 96.1046i 0.142588i
\(675\) 0 0
\(676\) 418.687 0.619359
\(677\) −17.7113 + 66.0996i −0.0261615 + 0.0976360i −0.977772 0.209670i \(-0.932761\pi\)
0.951611 + 0.307306i \(0.0994276\pi\)
\(678\) 0 0
\(679\) 146.953 + 84.8434i 0.216426 + 0.124953i
\(680\) −49.2583 + 304.015i −0.0724387 + 0.447081i
\(681\) 0 0
\(682\) 9.98614 37.2688i 0.0146424 0.0546463i
\(683\) 213.410 213.410i 0.312459 0.312459i −0.533402 0.845862i \(-0.679087\pi\)
0.845862 + 0.533402i \(0.179087\pi\)
\(684\) 0 0
\(685\) 1074.69 + 483.060i 1.56888 + 0.705197i
\(686\) −57.5255 99.6371i −0.0838564 0.145244i
\(687\) 0 0
\(688\) 143.508 + 535.578i 0.208587 + 0.778457i
\(689\) 6.70020 + 3.86836i 0.00972453 + 0.00561446i
\(690\) 0 0
\(691\) −75.5607 130.875i −0.109350 0.189399i 0.806157 0.591701i \(-0.201544\pi\)
−0.915507 + 0.402302i \(0.868210\pi\)
\(692\) −571.712 571.712i −0.826173 0.826173i
\(693\) 0 0
\(694\) 71.9408i 0.103661i
\(695\) 604.174 740.700i 0.869315 1.06576i
\(696\) 0 0
\(697\) 16.5164 4.42555i 0.0236964 0.00634942i
\(698\) 24.5149 + 91.4910i 0.0351217 + 0.131076i
\(699\) 0 0
\(700\) −425.206 + 212.864i −0.607437 + 0.304091i
\(701\) −745.680 −1.06374 −0.531869 0.846827i \(-0.678510\pi\)
−0.531869 + 0.846827i \(0.678510\pi\)
\(702\) 0 0
\(703\) 52.5765 52.5765i 0.0747888 0.0747888i
\(704\) 535.680 309.275i 0.760908 0.439311i
\(705\) 0 0
\(706\) 5.06123 8.76631i 0.00716888 0.0124169i
\(707\) 497.695 133.357i 0.703954 0.188624i
\(708\) 0 0
\(709\) 622.715 359.524i 0.878300 0.507087i 0.00820246 0.999966i \(-0.497389\pi\)
0.870097 + 0.492880i \(0.164056\pi\)
\(710\) 98.5653 + 44.3041i 0.138824 + 0.0624001i
\(711\) 0 0
\(712\) 145.893 + 145.893i 0.204906 + 0.204906i
\(713\) −168.779 45.2243i −0.236717 0.0634282i
\(714\) 0 0
\(715\) 260.522 + 361.268i 0.364366 + 0.505269i
\(716\) −358.144 + 620.324i −0.500201 + 0.866374i
\(717\) 0 0
\(718\) 14.8200 + 3.97100i 0.0206407 + 0.00553065i
\(719\) 605.271i 0.841824i −0.907101 0.420912i \(-0.861710\pi\)
0.907101 0.420912i \(-0.138290\pi\)
\(720\) 0 0
\(721\) −615.716 −0.853975
\(722\) 23.4746 87.6086i 0.0325134 0.121342i
\(723\) 0 0
\(724\) −966.632 558.085i −1.33513 0.770836i
\(725\) −860.735 + 176.576i −1.18722 + 0.243553i
\(726\) 0 0
\(727\) −90.0884 + 336.214i −0.123918 + 0.462468i −0.999799 0.0200593i \(-0.993614\pi\)
0.875881 + 0.482528i \(0.160281\pi\)
\(728\) −67.9796 + 67.9796i −0.0933786 + 0.0933786i
\(729\) 0 0
\(730\) −163.434 + 62.0714i −0.223882 + 0.0850294i
\(731\) −459.646 796.130i −0.628791 1.08910i
\(732\) 0 0
\(733\) −99.1060 369.869i −0.135206 0.504596i −0.999997 0.00246376i \(-0.999216\pi\)
0.864791 0.502132i \(-0.167451\pi\)
\(734\) −57.0318 32.9273i −0.0776999 0.0448601i
\(735\) 0 0
\(736\) 120.435 + 208.599i 0.163634 + 0.283423i
\(737\) −511.828 511.828i −0.694474 0.694474i
\(738\) 0 0
\(739\) 515.666i 0.697789i −0.937162 0.348895i \(-0.886557\pi\)
0.937162 0.348895i \(-0.113443\pi\)
\(740\) −165.819 + 16.8333i −0.224080 + 0.0227477i
\(741\) 0 0
\(742\) 1.47614 0.395531i 0.00198941 0.000533060i
\(743\) 153.987 + 574.689i 0.207251 + 0.773471i 0.988752 + 0.149567i \(0.0477879\pi\)
−0.781501 + 0.623904i \(0.785545\pi\)
\(744\) 0 0
\(745\) −268.169 + 328.768i −0.359959 + 0.441299i
\(746\) 38.7490 0.0519424
\(747\) 0 0
\(748\) −767.626 + 767.626i −1.02624 + 1.02624i
\(749\) 410.714 237.126i 0.548350 0.316590i
\(750\) 0 0
\(751\) 429.893 744.597i 0.572428 0.991474i −0.423888 0.905715i \(-0.639335\pi\)
0.996316 0.0857596i \(-0.0273317\pi\)
\(752\) 894.435 239.663i 1.18941 0.318701i
\(753\) 0 0
\(754\) −75.9389 + 43.8434i −0.100715 + 0.0581477i
\(755\) −696.318 + 264.459i −0.922275 + 0.350276i
\(756\) 0 0
\(757\) −956.075 956.075i −1.26298 1.26298i −0.949642 0.313337i \(-0.898553\pi\)
−0.313337 0.949642i \(-0.601447\pi\)
\(758\) −64.4715 17.2751i −0.0850548 0.0227904i
\(759\) 0 0
\(760\) 88.5495 63.8558i 0.116512 0.0840208i
\(761\) 161.379 279.517i 0.212062 0.367302i −0.740298 0.672279i \(-0.765315\pi\)
0.952360 + 0.304977i \(0.0986488\pi\)
\(762\) 0 0
\(763\) 323.706 + 86.7368i 0.424255 + 0.113679i
\(764\) 187.505i 0.245426i
\(765\) 0 0
\(766\) −4.77858 −0.00623835
\(767\) 81.1314 302.786i 0.105778 0.394767i
\(768\) 0 0
\(769\) −599.638 346.201i −0.779763 0.450196i 0.0565833 0.998398i \(-0.481979\pi\)
−0.836346 + 0.548202i \(0.815313\pi\)
\(770\) 86.8470 + 14.0715i 0.112788 + 0.0182746i
\(771\) 0 0
\(772\) 364.724 1361.17i 0.472440 1.76317i
\(773\) 375.226 375.226i 0.485415 0.485415i −0.421441 0.906856i \(-0.638475\pi\)
0.906856 + 0.421441i \(0.138475\pi\)
\(774\) 0 0
\(775\) 200.000 177.526i 0.258065 0.229065i
\(776\) 43.6640 + 75.6283i 0.0562681 + 0.0974592i
\(777\) 0 0
\(778\) 44.0381 + 164.352i 0.0566042 + 0.211250i
\(779\) −5.24918 3.03062i −0.00673836 0.00389039i
\(780\) 0 0
\(781\) 385.848 + 668.308i 0.494043 + 0.855708i
\(782\) −90.0704 90.0704i −0.115180 0.115180i
\(783\) 0 0
\(784\) 372.939i 0.475687i
\(785\) 12.0361 + 118.563i 0.0153326 + 0.151036i
\(786\) 0 0
\(787\) −1244.44 + 333.445i −1.58124 + 0.423692i −0.939309 0.343072i \(-0.888533\pi\)
−0.641930 + 0.766763i \(0.721866\pi\)
\(788\) −137.999 515.018i −0.175125 0.653576i
\(789\) 0 0
\(790\) 38.7279 3.93150i 0.0490227 0.00497658i
\(791\) 673.626 0.851613
\(792\) 0 0
\(793\) −32.7990 + 32.7990i −0.0413606 + 0.0413606i
\(794\) 46.2228 26.6867i 0.0582151 0.0336105i
\(795\) 0 0
\(796\) −375.484 + 650.357i −0.471713 + 0.817031i
\(797\) 9.85838 2.64154i 0.0123694 0.00331436i −0.252629 0.967563i \(-0.581295\pi\)
0.264998 + 0.964249i \(0.414629\pi\)
\(798\) 0 0
\(799\) −1329.57 + 767.626i −1.66404 + 0.960733i
\(800\) −367.991 21.9069i −0.459989 0.0273836i
\(801\) 0 0
\(802\) 94.4607 + 94.4607i 0.117781 + 0.117781i
\(803\) −1205.89 323.117i −1.50173 0.402387i
\(804\) 0 0
\(805\) 63.7256 393.305i 0.0791622 0.488577i
\(806\) 13.3439 23.1123i 0.0165557 0.0286753i
\(807\) 0 0
\(808\) 256.135 + 68.6313i 0.316999 + 0.0849397i
\(809\) 150.000i 0.185414i −0.995693 0.0927070i \(-0.970448\pi\)
0.995693 0.0927070i \(-0.0295520\pi\)
\(810\) 0 0
\(811\) 1336.85 1.64839 0.824197 0.566304i \(-0.191627\pi\)
0.824197 + 0.566304i \(0.191627\pi\)
\(812\) 173.021 645.722i 0.213080 0.795224i
\(813\) 0 0
\(814\) 26.7063 + 15.4189i 0.0328087 + 0.0189421i
\(815\) −540.178 749.070i −0.662795 0.919104i
\(816\) 0 0
\(817\) −84.3412 + 314.766i −0.103233 + 0.385270i
\(818\) 115.768 115.768i 0.141526 0.141526i
\(819\) 0 0
\(820\) 4.82399 + 12.7015i 0.00588291 + 0.0154897i
\(821\) 16.9467 + 29.3525i 0.0206415 + 0.0357521i 0.876162 0.482017i \(-0.160096\pi\)
−0.855520 + 0.517770i \(0.826762\pi\)
\(822\) 0 0
\(823\) 176.289 + 657.920i 0.214203 + 0.799417i 0.986446 + 0.164089i \(0.0524685\pi\)
−0.772242 + 0.635328i \(0.780865\pi\)
\(824\) −274.421 158.437i −0.333035 0.192278i
\(825\) 0 0
\(826\) −30.9592 53.6229i −0.0374808 0.0649187i
\(827\) 350.756 + 350.756i 0.424131 + 0.424131i 0.886623 0.462492i \(-0.153045\pi\)
−0.462492 + 0.886623i \(0.653045\pi\)
\(828\) 0 0
\(829\) 697.423i 0.841283i −0.907227 0.420641i \(-0.861805\pi\)
0.907227 0.420641i \(-0.138195\pi\)
\(830\) 22.8953 + 18.6753i 0.0275847 + 0.0225003i
\(831\) 0 0
\(832\) 413.265 110.734i 0.496713 0.133094i
\(833\) −160.032 597.249i −0.192116 0.716986i
\(834\) 0 0
\(835\) −32.1621 316.819i −0.0385175 0.379424i
\(836\) 384.817 0.460308
\(837\) 0 0
\(838\) 19.9127 19.9127i 0.0237622 0.0237622i
\(839\) 62.6764 36.1862i 0.0747037 0.0431302i −0.462183 0.886785i \(-0.652934\pi\)
0.536887 + 0.843654i \(0.319600\pi\)
\(840\) 0 0
\(841\) 197.136 341.449i 0.234406 0.406004i
\(842\) 78.9472 21.1538i 0.0937615 0.0251233i
\(843\) 0 0
\(844\) −497.079 + 286.989i −0.588956 + 0.340034i
\(845\) −190.633 501.936i −0.225602 0.594008i
\(846\) 0 0
\(847\) 26.8638 + 26.8638i 0.0317164 + 0.0317164i
\(848\) −14.0882 3.77492i −0.0166134 0.00445155i
\(849\) 0 0
\(850\) 190.972 39.1771i 0.224673 0.0460907i
\(851\) 69.8275 120.945i 0.0820535 0.142121i
\(852\) 0 0
\(853\) 101.864 + 27.2945i 0.119419 + 0.0319982i 0.318034 0.948079i \(-0.396978\pi\)
−0.198615 + 0.980078i \(0.563644\pi\)
\(854\) 9.16225i 0.0107286i
\(855\) 0 0
\(856\) 244.070 0.285129
\(857\) −107.310 + 400.486i −0.125216 + 0.467311i −0.999847 0.0174768i \(-0.994437\pi\)
0.874632 + 0.484788i \(0.161103\pi\)
\(858\) 0 0
\(859\) 681.447 + 393.434i 0.793303 + 0.458014i 0.841124 0.540842i \(-0.181894\pi\)
−0.0478212 + 0.998856i \(0.515228\pi\)
\(860\) 592.478 427.254i 0.688927 0.496808i
\(861\) 0 0
\(862\) 66.1912 247.029i 0.0767879 0.286577i
\(863\) −1072.68 + 1072.68i −1.24297 + 1.24297i −0.284204 + 0.958764i \(0.591729\pi\)
−0.958764 + 0.284204i \(0.908271\pi\)
\(864\) 0 0
\(865\) −425.081 + 945.696i −0.491423 + 1.09329i
\(866\) 77.5028 + 134.239i 0.0894952 + 0.155010i
\(867\) 0 0
\(868\) 52.6595 + 196.528i 0.0606676 + 0.226415i
\(869\) 240.737 + 138.990i 0.277028 + 0.159942i
\(870\) 0 0
\(871\) −250.334 433.591i −0.287410 0.497808i
\(872\) 121.955 + 121.955i 0.139856 + 0.139856i
\(873\) 0 0
\(874\) 45.1531i 0.0516626i
\(875\) 448.790 + 412.832i 0.512903 + 0.471808i
\(876\) 0 0
\(877\) −327.108 + 87.6483i −0.372985 + 0.0999411i −0.440442 0.897781i \(-0.645178\pi\)
0.0674567 + 0.997722i \(0.478512\pi\)
\(878\) −35.6137 132.912i −0.0405623 0.151381i
\(879\) 0 0
\(880\) −650.667 530.736i −0.739394 0.603109i
\(881\) 62.8490 0.0713382 0.0356691 0.999364i \(-0.488644\pi\)
0.0356691 + 0.999364i \(0.488644\pi\)
\(882\) 0 0
\(883\) −158.061 + 158.061i −0.179005 + 0.179005i −0.790922 0.611917i \(-0.790399\pi\)
0.611917 + 0.790922i \(0.290399\pi\)
\(884\) −650.288 + 375.444i −0.735620 + 0.424710i
\(885\) 0 0
\(886\) −55.0918 + 95.4219i −0.0621804 + 0.107700i
\(887\) −41.2630 + 11.0564i −0.0465198 + 0.0124649i −0.282004 0.959413i \(-0.590999\pi\)
0.235484 + 0.971878i \(0.424332\pi\)
\(888\) 0 0
\(889\) 983.559 567.858i 1.10637 0.638761i
\(890\) 53.5439 119.121i 0.0601616 0.133844i
\(891\) 0 0
\(892\) −652.803 652.803i −0.731841 0.731841i
\(893\) 525.670 + 140.853i 0.588657 + 0.157730i
\(894\) 0 0
\(895\) 906.734 + 146.915i 1.01311 + 0.164150i
\(896\) 186.124 322.376i 0.207727 0.359794i
\(897\) 0 0
\(898\) 118.533 + 31.7607i 0.131996 + 0.0353683i
\(899\) 375.959i 0.418197i
\(900\) 0 0
\(901\) 24.1816 0.0268387
\(902\) 0.650628 2.42818i 0.000721317 0.00269199i
\(903\) 0 0
\(904\) 300.231 + 173.338i 0.332114 + 0.191746i
\(905\) −228.932 + 1412.94i −0.252964 + 1.56126i
\(906\) 0 0
\(907\) 209.126 780.467i 0.230568 0.860493i −0.749528 0.661972i \(-0.769720\pi\)
0.980097 0.198521i \(-0.0636138\pi\)
\(908\) 987.110 987.110i 1.08713 1.08713i
\(909\) 0 0
\(910\) 55.5051 + 24.9490i 0.0609946 + 0.0274165i
\(911\) −86.6811 150.136i −0.0951494 0.164804i 0.814522 0.580133i \(-0.197000\pi\)
−0.909671 + 0.415330i \(0.863666\pi\)
\(912\) 0 0
\(913\) 54.6080 + 203.800i 0.0598116 + 0.223220i
\(914\) 87.0979 + 50.2860i 0.0952931 + 0.0550175i
\(915\) 0 0
\(916\) 437.080 + 757.044i 0.477161 + 0.826467i
\(917\) 366.116 + 366.116i 0.399254 + 0.399254i
\(918\) 0 0
\(919\) 1147.42i 1.24856i 0.781202 + 0.624278i \(0.214607\pi\)
−0.781202 + 0.624278i \(0.785393\pi\)
\(920\) 129.608 158.895i 0.140878 0.172712i
\(921\) 0 0
\(922\) 221.850 59.4444i 0.240618 0.0644733i
\(923\) 138.151 + 515.585i 0.149676 + 0.558597i
\(924\) 0 0
\(925\) 95.6800 + 191.126i 0.103438 + 0.206622i
\(926\) −58.2995 −0.0629584
\(927\) 0 0
\(928\) 366.464 366.464i 0.394897 0.394897i
\(929\) −190.779 + 110.146i −0.205360 + 0.118565i −0.599153 0.800635i \(-0.704496\pi\)
0.393793 + 0.919199i \(0.371163\pi\)
\(930\) 0 0
\(931\) −109.590 + 189.816i −0.117712 + 0.203884i
\(932\) −1095.64 + 293.576i −1.17558 + 0.314996i
\(933\) 0 0
\(934\) 161.647 93.3270i 0.173070 0.0999219i
\(935\) 1269.77 + 570.747i 1.35804 + 0.610425i
\(936\) 0 0
\(937\) −396.090 396.090i −0.422721 0.422721i 0.463418 0.886140i \(-0.346623\pi\)
−0.886140 + 0.463418i \(0.846623\pi\)
\(938\) −95.5256 25.5960i −0.101840 0.0272879i
\(939\) 0 0
\(940\) −713.531 989.459i −0.759075 1.05262i
\(941\) −92.8854 + 160.882i −0.0987093 + 0.170970i −0.911151 0.412073i \(-0.864805\pi\)
0.812441 + 0.583043i \(0.198138\pi\)
\(942\) 0 0
\(943\) −10.9965 2.94650i −0.0116612 0.00312461i
\(944\) 590.944i 0.626000i
\(945\) 0 0
\(946\) −135.151 −0.142866
\(947\) −309.361 + 1154.55i −0.326675 + 1.21917i 0.585943 + 0.810352i \(0.300724\pi\)
−0.912618 + 0.408814i \(0.865942\pi\)
\(948\) 0 0
\(949\) −747.833 431.762i −0.788022 0.454965i
\(950\) −57.6878 38.0480i −0.0607240 0.0400506i
\(951\) 0 0
\(952\) −77.7711 + 290.246i −0.0816923 + 0.304880i
\(953\) −630.499 + 630.499i −0.661594 + 0.661594i −0.955756 0.294161i \(-0.904960\pi\)
0.294161 + 0.955756i \(0.404960\pi\)
\(954\) 0 0
\(955\) −224.788 + 85.3735i −0.235380 + 0.0893963i
\(956\) 674.130 + 1167.63i 0.705156 + 1.22137i
\(957\) 0 0
\(958\) −25.0858 93.6215i −0.0261856 0.0977260i
\(959\) 995.570 + 574.792i 1.03813 + 0.599366i
\(960\) 0 0
\(961\) 423.288 + 733.156i 0.440466 + 0.762909i
\(962\) 15.0827 + 15.0827i 0.0156785 + 0.0156785i
\(963\) 0 0
\(964\) 396.041i 0.410831i
\(965\) −1797.88 + 182.513i −1.86309 + 0.189133i
\(966\) 0 0
\(967\) 521.399 139.708i 0.539192 0.144476i 0.0210624 0.999778i \(-0.493295\pi\)
0.518130 + 0.855302i \(0.326628\pi\)
\(968\) 5.06039 + 18.8856i 0.00522768 + 0.0195100i
\(969\) 0 0
\(970\) 34.9399 42.8353i 0.0360205 0.0441601i
\(971\) −1000.44 −1.03032 −0.515159 0.857095i \(-0.672267\pi\)
−0.515159 + 0.857095i \(0.672267\pi\)
\(972\) 0 0
\(973\) 659.444 659.444i 0.677743 0.677743i
\(974\) −167.120 + 96.4870i −0.171581 + 0.0990626i
\(975\) 0 0
\(976\) 43.7219 75.7286i 0.0447971 0.0775908i
\(977\) −810.957 + 217.295i −0.830048 + 0.222411i −0.648735 0.761015i \(-0.724702\pi\)
−0.181313 + 0.983425i \(0.558035\pi\)
\(978\) 0 0
\(979\) 807.686 466.318i 0.825011 0.476321i
\(980\) 459.301 174.441i 0.468674 0.178001i
\(981\) 0 0
\(982\) −93.1158 93.1158i −0.0948226 0.0948226i
\(983\) 1662.91 + 445.576i 1.69167 + 0.453282i 0.970820 0.239807i \(-0.0770843\pi\)
0.720852 + 0.693090i \(0.243751\pi\)
\(984\) 0 0
\(985\) −554.589 + 399.932i −0.563035 + 0.406022i
\(986\) −137.035 + 237.352i −0.138981 + 0.240722i
\(987\) 0 0
\(988\) 257.104 + 68.8908i 0.260227 + 0.0697276i
\(989\) 612.059i 0.618867i
\(990\) 0 0
\(991\) −544.061 −0.549002 −0.274501 0.961587i \(-0.588513\pi\)
−0.274501 + 0.961587i \(0.588513\pi\)
\(992\) −40.8245 + 152.359i −0.0411538 + 0.153588i
\(993\) 0 0
\(994\) 91.3091 + 52.7173i 0.0918603 + 0.0530356i
\(995\) 950.633 + 154.027i 0.955410 + 0.154801i
\(996\) 0 0
\(997\) −115.932 + 432.666i −0.116281 + 0.433967i −0.999380 0.0352205i \(-0.988787\pi\)
0.883098 + 0.469188i \(0.155453\pi\)
\(998\) −82.6128 + 82.6128i −0.0827783 + 0.0827783i
\(999\) 0 0
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 405.3.l.h.352.2 8
3.2 odd 2 405.3.l.f.352.1 8
5.3 odd 4 inner 405.3.l.h.28.1 8
9.2 odd 6 405.3.l.f.217.2 8
9.4 even 3 15.3.f.a.7.2 4
9.5 odd 6 45.3.g.b.37.1 4
9.7 even 3 inner 405.3.l.h.217.1 8
15.8 even 4 405.3.l.f.28.2 8
36.23 even 6 720.3.bh.k.577.2 4
36.31 odd 6 240.3.bg.a.97.2 4
45.4 even 6 75.3.f.c.7.1 4
45.13 odd 12 15.3.f.a.13.2 yes 4
45.14 odd 6 225.3.g.a.82.2 4
45.22 odd 12 75.3.f.c.43.1 4
45.23 even 12 45.3.g.b.28.1 4
45.32 even 12 225.3.g.a.118.2 4
45.38 even 12 405.3.l.f.298.1 8
45.43 odd 12 inner 405.3.l.h.298.2 8
72.13 even 6 960.3.bg.i.577.2 4
72.67 odd 6 960.3.bg.h.577.1 4
180.23 odd 12 720.3.bh.k.433.2 4
180.67 even 12 1200.3.bg.k.193.1 4
180.103 even 12 240.3.bg.a.193.2 4
180.139 odd 6 1200.3.bg.k.1057.1 4
360.13 odd 12 960.3.bg.i.193.2 4
360.283 even 12 960.3.bg.h.193.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.3.f.a.7.2 4 9.4 even 3
15.3.f.a.13.2 yes 4 45.13 odd 12
45.3.g.b.28.1 4 45.23 even 12
45.3.g.b.37.1 4 9.5 odd 6
75.3.f.c.7.1 4 45.4 even 6
75.3.f.c.43.1 4 45.22 odd 12
225.3.g.a.82.2 4 45.14 odd 6
225.3.g.a.118.2 4 45.32 even 12
240.3.bg.a.97.2 4 36.31 odd 6
240.3.bg.a.193.2 4 180.103 even 12
405.3.l.f.28.2 8 15.8 even 4
405.3.l.f.217.2 8 9.2 odd 6
405.3.l.f.298.1 8 45.38 even 12
405.3.l.f.352.1 8 3.2 odd 2
405.3.l.h.28.1 8 5.3 odd 4 inner
405.3.l.h.217.1 8 9.7 even 3 inner
405.3.l.h.298.2 8 45.43 odd 12 inner
405.3.l.h.352.2 8 1.1 even 1 trivial
720.3.bh.k.433.2 4 180.23 odd 12
720.3.bh.k.577.2 4 36.23 even 6
960.3.bg.h.193.1 4 360.283 even 12
960.3.bg.h.577.1 4 72.67 odd 6
960.3.bg.i.193.2 4 360.13 odd 12
960.3.bg.i.577.2 4 72.13 even 6
1200.3.bg.k.193.1 4 180.67 even 12
1200.3.bg.k.1057.1 4 180.139 odd 6