Properties

Label 153.4.l.a.127.3
Level $153$
Weight $4$
Character 153.127
Analytic conductor $9.027$
Analytic rank $0$
Dimension $12$
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] = [153,4,Mod(19,153)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(153, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("153.19");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 153.l (of order \(8\), degree \(4\), 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: \(9.02729223088\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 17)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 127.3
Root \(3.68604i\) of defining polynomial
Character \(\chi\) \(=\) 153.127
Dual form 153.4.l.a.100.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.89932 - 1.89932i) q^{2} +0.785167i q^{4} +(-1.92782 - 0.798529i) q^{5} +(23.0956 - 9.56650i) q^{7} +(16.6858 + 16.6858i) q^{8} +O(q^{10})\) \(q+(1.89932 - 1.89932i) q^{2} +0.785167i q^{4} +(-1.92782 - 0.798529i) q^{5} +(23.0956 - 9.56650i) q^{7} +(16.6858 + 16.6858i) q^{8} +(-5.17821 + 2.14488i) q^{10} +(-1.46245 - 3.53068i) q^{11} +17.6726i q^{13} +(25.6960 - 62.0357i) q^{14} +57.1022 q^{16} +(69.7847 - 6.56433i) q^{17} +(113.784 - 113.784i) q^{19} +(0.626979 - 1.51366i) q^{20} +(-9.48355 - 3.92822i) q^{22} +(38.2560 + 92.3581i) q^{23} +(-85.3095 - 85.3095i) q^{25} +(33.5659 + 33.5659i) q^{26} +(7.51131 + 18.1339i) q^{28} +(-185.315 - 76.7600i) q^{29} +(-29.2899 + 70.7121i) q^{31} +(-25.0315 + 25.0315i) q^{32} +(120.076 - 145.011i) q^{34} -52.1632 q^{35} +(-93.6650 + 226.127i) q^{37} -432.224i q^{38} +(-18.8432 - 45.4914i) q^{40} +(49.9941 - 20.7082i) q^{41} +(-100.471 - 100.471i) q^{43} +(2.77217 - 1.14827i) q^{44} +(248.078 + 102.757i) q^{46} +468.451i q^{47} +(199.350 - 199.350i) q^{49} -324.060 q^{50} -13.8759 q^{52} +(-68.2834 + 68.2834i) q^{53} +7.97432i q^{55} +(544.994 + 225.744i) q^{56} +(-497.764 + 206.181i) q^{58} +(-257.729 - 257.729i) q^{59} +(-653.988 + 270.891i) q^{61} +(78.6740 + 189.936i) q^{62} +551.903i q^{64} +(14.1121 - 34.0695i) q^{65} +304.454 q^{67} +(5.15410 + 54.7927i) q^{68} +(-99.0747 + 99.0747i) q^{70} +(179.862 - 434.226i) q^{71} +(-131.243 - 54.3626i) q^{73} +(251.588 + 607.388i) q^{74} +(89.3393 + 89.3393i) q^{76} +(-67.5525 - 67.5525i) q^{77} +(-274.715 - 663.221i) q^{79} +(-110.083 - 45.5977i) q^{80} +(55.6232 - 134.286i) q^{82} +(259.960 - 259.960i) q^{83} +(-139.774 - 43.0703i) q^{85} -381.653 q^{86} +(34.5100 - 83.3146i) q^{88} +1042.28i q^{89} +(169.065 + 408.158i) q^{91} +(-72.5165 + 30.0373i) q^{92} +(889.738 + 889.738i) q^{94} +(-310.214 + 128.495i) q^{95} +(-834.757 - 345.768i) q^{97} -757.260i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8} - 116 q^{10} - 40 q^{11} + 132 q^{14} + 184 q^{16} - 52 q^{17} - 12 q^{19} - 572 q^{20} - 620 q^{22} + 276 q^{23} - 464 q^{25} + 708 q^{26} + 452 q^{28} - 632 q^{29} + 188 q^{31} - 700 q^{32} + 764 q^{34} + 632 q^{35} + 940 q^{37} - 1864 q^{40} - 176 q^{41} - 1360 q^{43} + 1364 q^{44} + 452 q^{46} + 1044 q^{49} - 2856 q^{50} + 792 q^{52} + 360 q^{53} + 1788 q^{56} - 360 q^{58} + 584 q^{59} - 1052 q^{61} + 380 q^{62} - 404 q^{65} + 1080 q^{67} - 2532 q^{68} + 2072 q^{70} - 28 q^{71} + 824 q^{73} + 2292 q^{74} + 1328 q^{76} + 1252 q^{77} - 196 q^{79} + 904 q^{80} - 1528 q^{82} + 1008 q^{83} - 2824 q^{85} + 1200 q^{86} - 56 q^{88} + 2456 q^{91} - 396 q^{92} + 6360 q^{94} - 2172 q^{95} - 904 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/153\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(137\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.89932 1.89932i 0.671511 0.671511i −0.286553 0.958064i \(-0.592510\pi\)
0.958064 + 0.286553i \(0.0925095\pi\)
\(3\) 0 0
\(4\) 0.785167i 0.0981459i
\(5\) −1.92782 0.798529i −0.172429 0.0714226i 0.294799 0.955559i \(-0.404747\pi\)
−0.467228 + 0.884137i \(0.654747\pi\)
\(6\) 0 0
\(7\) 23.0956 9.56650i 1.24704 0.516543i 0.341135 0.940014i \(-0.389189\pi\)
0.905909 + 0.423472i \(0.139189\pi\)
\(8\) 16.6858 + 16.6858i 0.737417 + 0.737417i
\(9\) 0 0
\(10\) −5.17821 + 2.14488i −0.163749 + 0.0678272i
\(11\) −1.46245 3.53068i −0.0400860 0.0967763i 0.902568 0.430546i \(-0.141679\pi\)
−0.942655 + 0.333770i \(0.891679\pi\)
\(12\) 0 0
\(13\) 17.6726i 0.377038i 0.982070 + 0.188519i \(0.0603687\pi\)
−0.982070 + 0.188519i \(0.939631\pi\)
\(14\) 25.6960 62.0357i 0.490540 1.18427i
\(15\) 0 0
\(16\) 57.1022 0.892221
\(17\) 69.7847 6.56433i 0.995605 0.0936520i
\(18\) 0 0
\(19\) 113.784 113.784i 1.37388 1.37388i 0.519279 0.854605i \(-0.326201\pi\)
0.854605 0.519279i \(-0.173799\pi\)
\(20\) 0.626979 1.51366i 0.00700984 0.0169232i
\(21\) 0 0
\(22\) −9.48355 3.92822i −0.0919046 0.0380681i
\(23\) 38.2560 + 92.3581i 0.346823 + 0.837304i 0.996991 + 0.0775138i \(0.0246982\pi\)
−0.650169 + 0.759790i \(0.725302\pi\)
\(24\) 0 0
\(25\) −85.3095 85.3095i −0.682476 0.682476i
\(26\) 33.5659 + 33.5659i 0.253185 + 0.253185i
\(27\) 0 0
\(28\) 7.51131 + 18.1339i 0.0506966 + 0.122392i
\(29\) −185.315 76.7600i −1.18662 0.491516i −0.299970 0.953949i \(-0.596977\pi\)
−0.886655 + 0.462432i \(0.846977\pi\)
\(30\) 0 0
\(31\) −29.2899 + 70.7121i −0.169697 + 0.409686i −0.985733 0.168316i \(-0.946167\pi\)
0.816036 + 0.578001i \(0.196167\pi\)
\(32\) −25.0315 + 25.0315i −0.138281 + 0.138281i
\(33\) 0 0
\(34\) 120.076 145.011i 0.605671 0.731448i
\(35\) −52.1632 −0.251920
\(36\) 0 0
\(37\) −93.6650 + 226.127i −0.416174 + 1.00473i 0.567272 + 0.823531i \(0.307999\pi\)
−0.983446 + 0.181202i \(0.942001\pi\)
\(38\) 432.224i 1.84516i
\(39\) 0 0
\(40\) −18.8432 45.4914i −0.0744841 0.179821i
\(41\) 49.9941 20.7082i 0.190433 0.0788800i −0.285429 0.958400i \(-0.592136\pi\)
0.475862 + 0.879520i \(0.342136\pi\)
\(42\) 0 0
\(43\) −100.471 100.471i −0.356318 0.356318i 0.506136 0.862454i \(-0.331073\pi\)
−0.862454 + 0.506136i \(0.831073\pi\)
\(44\) 2.77217 1.14827i 0.00949820 0.00393428i
\(45\) 0 0
\(46\) 248.078 + 102.757i 0.795154 + 0.329363i
\(47\) 468.451i 1.45384i 0.686721 + 0.726921i \(0.259049\pi\)
−0.686721 + 0.726921i \(0.740951\pi\)
\(48\) 0 0
\(49\) 199.350 199.350i 0.581196 0.581196i
\(50\) −324.060 −0.916580
\(51\) 0 0
\(52\) −13.8759 −0.0370047
\(53\) −68.2834 + 68.2834i −0.176971 + 0.176971i −0.790034 0.613063i \(-0.789937\pi\)
0.613063 + 0.790034i \(0.289937\pi\)
\(54\) 0 0
\(55\) 7.97432i 0.0195501i
\(56\) 544.994 + 225.744i 1.30050 + 0.538684i
\(57\) 0 0
\(58\) −497.764 + 206.181i −1.12689 + 0.466773i
\(59\) −257.729 257.729i −0.568703 0.568703i 0.363062 0.931765i \(-0.381731\pi\)
−0.931765 + 0.363062i \(0.881731\pi\)
\(60\) 0 0
\(61\) −653.988 + 270.891i −1.37270 + 0.568590i −0.942519 0.334153i \(-0.891550\pi\)
−0.430179 + 0.902743i \(0.641550\pi\)
\(62\) 78.6740 + 189.936i 0.161155 + 0.389062i
\(63\) 0 0
\(64\) 551.903i 1.07794i
\(65\) 14.1121 34.0695i 0.0269290 0.0650124i
\(66\) 0 0
\(67\) 304.454 0.555150 0.277575 0.960704i \(-0.410469\pi\)
0.277575 + 0.960704i \(0.410469\pi\)
\(68\) 5.15410 + 54.7927i 0.00919156 + 0.0977146i
\(69\) 0 0
\(70\) −99.0747 + 99.0747i −0.169167 + 0.169167i
\(71\) 179.862 434.226i 0.300644 0.725819i −0.699296 0.714833i \(-0.746503\pi\)
0.999940 0.0109864i \(-0.00349716\pi\)
\(72\) 0 0
\(73\) −131.243 54.3626i −0.210422 0.0871597i 0.274983 0.961449i \(-0.411328\pi\)
−0.485405 + 0.874289i \(0.661328\pi\)
\(74\) 251.588 + 607.388i 0.395224 + 0.954155i
\(75\) 0 0
\(76\) 89.3393 + 89.3393i 0.134841 + 0.134841i
\(77\) −67.5525 67.5525i −0.0999781 0.0999781i
\(78\) 0 0
\(79\) −274.715 663.221i −0.391239 0.944534i −0.989671 0.143360i \(-0.954209\pi\)
0.598432 0.801174i \(-0.295791\pi\)
\(80\) −110.083 45.5977i −0.153845 0.0637248i
\(81\) 0 0
\(82\) 55.6232 134.286i 0.0749092 0.180847i
\(83\) 259.960 259.960i 0.343787 0.343787i −0.514002 0.857789i \(-0.671838\pi\)
0.857789 + 0.514002i \(0.171838\pi\)
\(84\) 0 0
\(85\) −139.774 43.0703i −0.178360 0.0549603i
\(86\) −381.653 −0.478542
\(87\) 0 0
\(88\) 34.5100 83.3146i 0.0418043 0.100925i
\(89\) 1042.28i 1.24137i 0.784061 + 0.620684i \(0.213145\pi\)
−0.784061 + 0.620684i \(0.786855\pi\)
\(90\) 0 0
\(91\) 169.065 + 408.158i 0.194756 + 0.470183i
\(92\) −72.5165 + 30.0373i −0.0821780 + 0.0340392i
\(93\) 0 0
\(94\) 889.738 + 889.738i 0.976271 + 0.976271i
\(95\) −310.214 + 128.495i −0.335024 + 0.138772i
\(96\) 0 0
\(97\) −834.757 345.768i −0.873781 0.361932i −0.0996991 0.995018i \(-0.531788\pi\)
−0.774082 + 0.633086i \(0.781788\pi\)
\(98\) 757.260i 0.780559i
\(99\) 0 0
\(100\) 66.9823 66.9823i 0.0669823 0.0669823i
\(101\) 443.233 0.436667 0.218333 0.975874i \(-0.429938\pi\)
0.218333 + 0.975874i \(0.429938\pi\)
\(102\) 0 0
\(103\) −1396.36 −1.33580 −0.667901 0.744250i \(-0.732807\pi\)
−0.667901 + 0.744250i \(0.732807\pi\)
\(104\) −294.882 + 294.882i −0.278034 + 0.278034i
\(105\) 0 0
\(106\) 259.384i 0.237676i
\(107\) −1703.54 705.628i −1.53913 0.637529i −0.557821 0.829961i \(-0.688363\pi\)
−0.981310 + 0.192432i \(0.938363\pi\)
\(108\) 0 0
\(109\) 344.570 142.726i 0.302788 0.125419i −0.226117 0.974100i \(-0.572603\pi\)
0.528904 + 0.848681i \(0.322603\pi\)
\(110\) 15.1458 + 15.1458i 0.0131281 + 0.0131281i
\(111\) 0 0
\(112\) 1318.81 546.268i 1.11264 0.460870i
\(113\) −680.844 1643.70i −0.566800 1.36838i −0.904238 0.427029i \(-0.859560\pi\)
0.337438 0.941348i \(-0.390440\pi\)
\(114\) 0 0
\(115\) 208.598i 0.169147i
\(116\) 60.2694 145.503i 0.0482403 0.116462i
\(117\) 0 0
\(118\) −979.020 −0.763781
\(119\) 1548.92 819.203i 1.19319 0.631061i
\(120\) 0 0
\(121\) 930.832 930.832i 0.699348 0.699348i
\(122\) −727.624 + 1756.64i −0.539967 + 1.30360i
\(123\) 0 0
\(124\) −55.5208 22.9975i −0.0402090 0.0166551i
\(125\) 196.155 + 473.561i 0.140357 + 0.338852i
\(126\) 0 0
\(127\) 1226.83 + 1226.83i 0.857192 + 0.857192i 0.991006 0.133814i \(-0.0427225\pi\)
−0.133814 + 0.991006i \(0.542723\pi\)
\(128\) 847.988 + 847.988i 0.585565 + 0.585565i
\(129\) 0 0
\(130\) −37.9056 91.5123i −0.0255734 0.0617397i
\(131\) −522.374 216.374i −0.348397 0.144311i 0.201621 0.979464i \(-0.435379\pi\)
−0.550018 + 0.835153i \(0.685379\pi\)
\(132\) 0 0
\(133\) 1539.39 3716.42i 1.00362 2.42296i
\(134\) 578.256 578.256i 0.372789 0.372789i
\(135\) 0 0
\(136\) 1273.95 + 1054.89i 0.803237 + 0.665116i
\(137\) 1150.24 0.717314 0.358657 0.933469i \(-0.383235\pi\)
0.358657 + 0.933469i \(0.383235\pi\)
\(138\) 0 0
\(139\) −376.814 + 909.710i −0.229935 + 0.555112i −0.996169 0.0874493i \(-0.972128\pi\)
0.766234 + 0.642562i \(0.222128\pi\)
\(140\) 40.9569i 0.0247249i
\(141\) 0 0
\(142\) −483.118 1166.35i −0.285510 0.689281i
\(143\) 62.3962 25.8453i 0.0364883 0.0151140i
\(144\) 0 0
\(145\) 295.959 + 295.959i 0.169504 + 0.169504i
\(146\) −352.524 + 146.020i −0.199830 + 0.0827721i
\(147\) 0 0
\(148\) −177.548 73.5428i −0.0986105 0.0408458i
\(149\) 1772.18i 0.974382i −0.873295 0.487191i \(-0.838021\pi\)
0.873295 0.487191i \(-0.161979\pi\)
\(150\) 0 0
\(151\) −1337.91 + 1337.91i −0.721044 + 0.721044i −0.968818 0.247774i \(-0.920301\pi\)
0.247774 + 0.968818i \(0.420301\pi\)
\(152\) 3797.16 2.02625
\(153\) 0 0
\(154\) −256.607 −0.134273
\(155\) 112.931 112.931i 0.0585216 0.0585216i
\(156\) 0 0
\(157\) 289.955i 0.147395i −0.997281 0.0736973i \(-0.976520\pi\)
0.997281 0.0736973i \(-0.0234799\pi\)
\(158\) −1781.44 737.897i −0.896986 0.371544i
\(159\) 0 0
\(160\) 68.2445 28.2678i 0.0337200 0.0139673i
\(161\) 1767.09 + 1767.09i 0.865006 + 0.865006i
\(162\) 0 0
\(163\) 1563.14 647.475i 0.751134 0.311130i 0.0259298 0.999664i \(-0.491745\pi\)
0.725204 + 0.688534i \(0.241745\pi\)
\(164\) 16.2594 + 39.2537i 0.00774175 + 0.0186902i
\(165\) 0 0
\(166\) 987.495i 0.461714i
\(167\) −480.582 + 1160.23i −0.222686 + 0.537612i −0.995253 0.0973216i \(-0.968972\pi\)
0.772567 + 0.634933i \(0.218972\pi\)
\(168\) 0 0
\(169\) 1884.68 0.857842
\(170\) −347.280 + 183.672i −0.156677 + 0.0828645i
\(171\) 0 0
\(172\) 78.8864 78.8864i 0.0349711 0.0349711i
\(173\) −153.530 + 370.654i −0.0674720 + 0.162892i −0.954019 0.299748i \(-0.903098\pi\)
0.886547 + 0.462639i \(0.153098\pi\)
\(174\) 0 0
\(175\) −2786.39 1154.16i −1.20361 0.498550i
\(176\) −83.5093 201.609i −0.0357656 0.0863459i
\(177\) 0 0
\(178\) 1979.63 + 1979.63i 0.833593 + 0.833593i
\(179\) −543.928 543.928i −0.227123 0.227123i 0.584366 0.811490i \(-0.301343\pi\)
−0.811490 + 0.584366i \(0.801343\pi\)
\(180\) 0 0
\(181\) −1005.65 2427.86i −0.412980 0.997022i −0.984333 0.176318i \(-0.943581\pi\)
0.571353 0.820704i \(-0.306419\pi\)
\(182\) 1096.33 + 454.115i 0.446514 + 0.184952i
\(183\) 0 0
\(184\) −902.739 + 2179.40i −0.361689 + 0.873195i
\(185\) 361.139 361.139i 0.143521 0.143521i
\(186\) 0 0
\(187\) −125.233 236.787i −0.0489732 0.0925968i
\(188\) −367.812 −0.142689
\(189\) 0 0
\(190\) −345.143 + 833.249i −0.131786 + 0.318159i
\(191\) 207.856i 0.0787430i 0.999225 + 0.0393715i \(0.0125356\pi\)
−0.999225 + 0.0393715i \(0.987464\pi\)
\(192\) 0 0
\(193\) 1751.78 + 4229.18i 0.653348 + 1.57732i 0.807889 + 0.589335i \(0.200610\pi\)
−0.154541 + 0.987986i \(0.549390\pi\)
\(194\) −2242.19 + 928.747i −0.829795 + 0.343712i
\(195\) 0 0
\(196\) 156.523 + 156.523i 0.0570420 + 0.0570420i
\(197\) 2439.95 1010.66i 0.882434 0.365516i 0.104994 0.994473i \(-0.466518\pi\)
0.777440 + 0.628957i \(0.216518\pi\)
\(198\) 0 0
\(199\) −1525.28 631.793i −0.543339 0.225059i 0.0940949 0.995563i \(-0.470004\pi\)
−0.637434 + 0.770505i \(0.720004\pi\)
\(200\) 2846.92i 1.00654i
\(201\) 0 0
\(202\) 841.842 841.842i 0.293227 0.293227i
\(203\) −5014.28 −1.73366
\(204\) 0 0
\(205\) −112.916 −0.0384701
\(206\) −2652.14 + 2652.14i −0.897006 + 0.897006i
\(207\) 0 0
\(208\) 1009.14i 0.336401i
\(209\) −568.137 235.330i −0.188033 0.0778858i
\(210\) 0 0
\(211\) −1020.47 + 422.694i −0.332949 + 0.137912i −0.542894 0.839801i \(-0.682672\pi\)
0.209945 + 0.977713i \(0.432672\pi\)
\(212\) −53.6139 53.6139i −0.0173690 0.0173690i
\(213\) 0 0
\(214\) −4575.77 + 1895.35i −1.46165 + 0.605436i
\(215\) 113.461 + 273.918i 0.0359905 + 0.0868888i
\(216\) 0 0
\(217\) 1913.34i 0.598552i
\(218\) 383.367 925.531i 0.119105 0.287545i
\(219\) 0 0
\(220\) −6.26117 −0.00191876
\(221\) 116.009 + 1233.28i 0.0353103 + 0.375381i
\(222\) 0 0
\(223\) −1530.74 + 1530.74i −0.459667 + 0.459667i −0.898546 0.438879i \(-0.855376\pi\)
0.438879 + 0.898546i \(0.355376\pi\)
\(224\) −338.653 + 817.580i −0.101014 + 0.243870i
\(225\) 0 0
\(226\) −4415.06 1828.78i −1.29949 0.538267i
\(227\) 997.159 + 2407.36i 0.291559 + 0.703885i 0.999998 0.00188682i \(-0.000600593\pi\)
−0.708440 + 0.705771i \(0.750601\pi\)
\(228\) 0 0
\(229\) −798.278 798.278i −0.230357 0.230357i 0.582485 0.812842i \(-0.302081\pi\)
−0.812842 + 0.582485i \(0.802081\pi\)
\(230\) −396.194 396.194i −0.113584 0.113584i
\(231\) 0 0
\(232\) −1811.33 4372.94i −0.512585 1.23749i
\(233\) −3987.43 1651.65i −1.12114 0.464391i −0.256379 0.966576i \(-0.582530\pi\)
−0.864760 + 0.502185i \(0.832530\pi\)
\(234\) 0 0
\(235\) 374.072 903.089i 0.103837 0.250685i
\(236\) 202.361 202.361i 0.0558159 0.0558159i
\(237\) 0 0
\(238\) 1385.97 4497.83i 0.377475 1.22500i
\(239\) −788.197 −0.213323 −0.106662 0.994295i \(-0.534016\pi\)
−0.106662 + 0.994295i \(0.534016\pi\)
\(240\) 0 0
\(241\) −1386.41 + 3347.08i −0.370566 + 0.894625i 0.623089 + 0.782151i \(0.285877\pi\)
−0.993655 + 0.112474i \(0.964123\pi\)
\(242\) 3535.90i 0.939240i
\(243\) 0 0
\(244\) −212.695 513.490i −0.0558048 0.134725i
\(245\) −543.498 + 225.124i −0.141726 + 0.0587047i
\(246\) 0 0
\(247\) 2010.85 + 2010.85i 0.518006 + 0.518006i
\(248\) −1668.62 + 691.164i −0.427247 + 0.176972i
\(249\) 0 0
\(250\) 1272.01 + 526.882i 0.321795 + 0.133292i
\(251\) 5974.99i 1.50254i 0.659994 + 0.751271i \(0.270559\pi\)
−0.659994 + 0.751271i \(0.729441\pi\)
\(252\) 0 0
\(253\) 270.139 270.139i 0.0671284 0.0671284i
\(254\) 4660.28 1.15123
\(255\) 0 0
\(256\) −1194.02 −0.291509
\(257\) −2652.30 + 2652.30i −0.643758 + 0.643758i −0.951477 0.307719i \(-0.900434\pi\)
0.307719 + 0.951477i \(0.400434\pi\)
\(258\) 0 0
\(259\) 6118.59i 1.46792i
\(260\) 26.7503 + 11.0803i 0.00638070 + 0.00264297i
\(261\) 0 0
\(262\) −1403.12 + 581.191i −0.330859 + 0.137046i
\(263\) 5350.27 + 5350.27i 1.25442 + 1.25442i 0.953719 + 0.300699i \(0.0972198\pi\)
0.300699 + 0.953719i \(0.402780\pi\)
\(264\) 0 0
\(265\) 186.164 77.1118i 0.0431547 0.0178752i
\(266\) −4134.87 9982.46i −0.953102 2.30099i
\(267\) 0 0
\(268\) 239.048i 0.0544857i
\(269\) 2675.20 6458.50i 0.606356 1.46387i −0.260579 0.965453i \(-0.583913\pi\)
0.866935 0.498421i \(-0.166087\pi\)
\(270\) 0 0
\(271\) 1356.64 0.304097 0.152049 0.988373i \(-0.451413\pi\)
0.152049 + 0.988373i \(0.451413\pi\)
\(272\) 3984.86 374.837i 0.888300 0.0835583i
\(273\) 0 0
\(274\) 2184.68 2184.68i 0.481684 0.481684i
\(275\) −176.439 + 425.962i −0.0386897 + 0.0934053i
\(276\) 0 0
\(277\) 6628.70 + 2745.70i 1.43783 + 0.595570i 0.959272 0.282484i \(-0.0911583\pi\)
0.478562 + 0.878054i \(0.341158\pi\)
\(278\) 1012.14 + 2443.52i 0.218360 + 0.527168i
\(279\) 0 0
\(280\) −870.387 870.387i −0.185770 0.185770i
\(281\) 4674.98 + 4674.98i 0.992476 + 0.992476i 0.999972 0.00749542i \(-0.00238589\pi\)
−0.00749542 + 0.999972i \(0.502386\pi\)
\(282\) 0 0
\(283\) −884.335 2134.97i −0.185754 0.448449i 0.803380 0.595466i \(-0.203033\pi\)
−0.989134 + 0.147017i \(0.953033\pi\)
\(284\) 340.940 + 141.222i 0.0712362 + 0.0295070i
\(285\) 0 0
\(286\) 69.4217 167.599i 0.0143531 0.0346515i
\(287\) 956.537 956.537i 0.196734 0.196734i
\(288\) 0 0
\(289\) 4826.82 916.180i 0.982459 0.186481i
\(290\) 1124.24 0.227647
\(291\) 0 0
\(292\) 42.6837 103.048i 0.00855437 0.0206521i
\(293\) 6445.85i 1.28522i −0.766192 0.642612i \(-0.777851\pi\)
0.766192 0.642612i \(-0.222149\pi\)
\(294\) 0 0
\(295\) 291.051 + 702.659i 0.0574429 + 0.138679i
\(296\) −5336.01 + 2210.25i −1.04780 + 0.434013i
\(297\) 0 0
\(298\) −3365.94 3365.94i −0.654309 0.654309i
\(299\) −1632.20 + 676.081i −0.315695 + 0.130765i
\(300\) 0 0
\(301\) −3281.59 1359.28i −0.628397 0.260291i
\(302\) 5082.24i 0.968378i
\(303\) 0 0
\(304\) 6497.30 6497.30i 1.22581 1.22581i
\(305\) 1477.08 0.277304
\(306\) 0 0
\(307\) 221.421 0.0411634 0.0205817 0.999788i \(-0.493448\pi\)
0.0205817 + 0.999788i \(0.493448\pi\)
\(308\) 53.0400 53.0400i 0.00981245 0.00981245i
\(309\) 0 0
\(310\) 428.985i 0.0785959i
\(311\) −1195.38 495.142i −0.217954 0.0902795i 0.271035 0.962570i \(-0.412634\pi\)
−0.488989 + 0.872290i \(0.662634\pi\)
\(312\) 0 0
\(313\) −356.107 + 147.504i −0.0643079 + 0.0266372i −0.414606 0.910001i \(-0.636080\pi\)
0.350298 + 0.936638i \(0.386080\pi\)
\(314\) −550.718 550.718i −0.0989772 0.0989772i
\(315\) 0 0
\(316\) 520.739 215.697i 0.0927021 0.0383985i
\(317\) −248.380 599.641i −0.0440075 0.106244i 0.900347 0.435172i \(-0.143312\pi\)
−0.944355 + 0.328929i \(0.893312\pi\)
\(318\) 0 0
\(319\) 766.545i 0.134540i
\(320\) 440.710 1063.97i 0.0769889 0.185868i
\(321\) 0 0
\(322\) 6712.53 1.16172
\(323\) 7193.46 8687.29i 1.23918 1.49651i
\(324\) 0 0
\(325\) 1507.64 1507.64i 0.257319 0.257319i
\(326\) 1739.15 4198.67i 0.295468 0.713322i
\(327\) 0 0
\(328\) 1179.73 + 488.659i 0.198596 + 0.0822612i
\(329\) 4481.44 + 10819.1i 0.750972 + 1.81301i
\(330\) 0 0
\(331\) 1010.96 + 1010.96i 0.167877 + 0.167877i 0.786046 0.618168i \(-0.212125\pi\)
−0.618168 + 0.786046i \(0.712125\pi\)
\(332\) 204.112 + 204.112i 0.0337413 + 0.0337413i
\(333\) 0 0
\(334\) 1290.87 + 3116.42i 0.211476 + 0.510548i
\(335\) −586.933 243.116i −0.0957241 0.0396502i
\(336\) 0 0
\(337\) 216.355 522.328i 0.0349722 0.0844303i −0.905428 0.424499i \(-0.860450\pi\)
0.940401 + 0.340069i \(0.110450\pi\)
\(338\) 3579.61 3579.61i 0.576051 0.576051i
\(339\) 0 0
\(340\) 33.8174 109.746i 0.00539413 0.0175053i
\(341\) 292.497 0.0464504
\(342\) 0 0
\(343\) −584.286 + 1410.59i −0.0919780 + 0.222055i
\(344\) 3352.88i 0.525509i
\(345\) 0 0
\(346\) 412.388 + 995.592i 0.0640754 + 0.154692i
\(347\) −3500.32 + 1449.88i −0.541518 + 0.224304i −0.636640 0.771161i \(-0.719676\pi\)
0.0951212 + 0.995466i \(0.469676\pi\)
\(348\) 0 0
\(349\) 4516.50 + 4516.50i 0.692730 + 0.692730i 0.962832 0.270102i \(-0.0870573\pi\)
−0.270102 + 0.962832i \(0.587057\pi\)
\(350\) −7484.36 + 3100.12i −1.14302 + 0.473453i
\(351\) 0 0
\(352\) 124.985 + 51.7706i 0.0189254 + 0.00783916i
\(353\) 6291.34i 0.948595i −0.880365 0.474298i \(-0.842702\pi\)
0.880365 0.474298i \(-0.157298\pi\)
\(354\) 0 0
\(355\) −693.484 + 693.484i −0.103680 + 0.103680i
\(356\) −818.367 −0.121835
\(357\) 0 0
\(358\) −2066.19 −0.305032
\(359\) −2382.60 + 2382.60i −0.350275 + 0.350275i −0.860212 0.509937i \(-0.829669\pi\)
0.509937 + 0.860212i \(0.329669\pi\)
\(360\) 0 0
\(361\) 19034.5i 2.77511i
\(362\) −6521.33 2701.22i −0.946832 0.392191i
\(363\) 0 0
\(364\) −320.473 + 132.744i −0.0461465 + 0.0191145i
\(365\) 209.602 + 209.602i 0.0300578 + 0.0300578i
\(366\) 0 0
\(367\) −921.585 + 381.733i −0.131080 + 0.0542951i −0.447259 0.894404i \(-0.647600\pi\)
0.316179 + 0.948699i \(0.397600\pi\)
\(368\) 2184.50 + 5273.85i 0.309443 + 0.747060i
\(369\) 0 0
\(370\) 1371.84i 0.192752i
\(371\) −923.812 + 2230.28i −0.129277 + 0.312103i
\(372\) 0 0
\(373\) −3180.59 −0.441514 −0.220757 0.975329i \(-0.570853\pi\)
−0.220757 + 0.975329i \(0.570853\pi\)
\(374\) −687.593 211.876i −0.0950658 0.0292938i
\(375\) 0 0
\(376\) −7816.50 + 7816.50i −1.07209 + 1.07209i
\(377\) 1356.55 3274.99i 0.185320 0.447402i
\(378\) 0 0
\(379\) −10009.2 4145.96i −1.35657 0.561910i −0.418456 0.908237i \(-0.637429\pi\)
−0.938114 + 0.346327i \(0.887429\pi\)
\(380\) −100.890 243.570i −0.0136199 0.0328813i
\(381\) 0 0
\(382\) 394.785 + 394.785i 0.0528768 + 0.0528768i
\(383\) −5351.33 5351.33i −0.713944 0.713944i 0.253414 0.967358i \(-0.418446\pi\)
−0.967358 + 0.253414i \(0.918446\pi\)
\(384\) 0 0
\(385\) 76.2863 + 184.171i 0.0100985 + 0.0243799i
\(386\) 11359.8 + 4705.37i 1.49792 + 0.620458i
\(387\) 0 0
\(388\) 271.486 655.424i 0.0355221 0.0857580i
\(389\) −6787.77 + 6787.77i −0.884714 + 0.884714i −0.994009 0.109295i \(-0.965141\pi\)
0.109295 + 0.994009i \(0.465141\pi\)
\(390\) 0 0
\(391\) 3275.95 + 6194.06i 0.423713 + 0.801143i
\(392\) 6652.65 0.857168
\(393\) 0 0
\(394\) 2714.68 6553.82i 0.347116 0.838013i
\(395\) 1497.94i 0.190809i
\(396\) 0 0
\(397\) 2017.52 + 4870.72i 0.255054 + 0.615754i 0.998598 0.0529327i \(-0.0168569\pi\)
−0.743545 + 0.668686i \(0.766857\pi\)
\(398\) −4096.98 + 1697.03i −0.515988 + 0.213729i
\(399\) 0 0
\(400\) −4871.36 4871.36i −0.608920 0.608920i
\(401\) −3326.28 + 1377.79i −0.414231 + 0.171580i −0.580059 0.814575i \(-0.696970\pi\)
0.165828 + 0.986155i \(0.446970\pi\)
\(402\) 0 0
\(403\) −1249.66 517.628i −0.154467 0.0639824i
\(404\) 348.012i 0.0428571i
\(405\) 0 0
\(406\) −9523.72 + 9523.72i −1.16417 + 1.16417i
\(407\) 935.364 0.113917
\(408\) 0 0
\(409\) 9516.13 1.15047 0.575235 0.817988i \(-0.304911\pi\)
0.575235 + 0.817988i \(0.304911\pi\)
\(410\) −214.463 + 214.463i −0.0258331 + 0.0258331i
\(411\) 0 0
\(412\) 1096.38i 0.131104i
\(413\) −8417.97 3486.84i −1.00296 0.415439i
\(414\) 0 0
\(415\) −708.742 + 293.570i −0.0838332 + 0.0347248i
\(416\) −442.370 442.370i −0.0521370 0.0521370i
\(417\) 0 0
\(418\) −1526.04 + 632.107i −0.178567 + 0.0739650i
\(419\) −2414.93 5830.16i −0.281568 0.679766i 0.718304 0.695729i \(-0.244919\pi\)
−0.999873 + 0.0159630i \(0.994919\pi\)
\(420\) 0 0
\(421\) 1544.81i 0.178835i −0.995994 0.0894177i \(-0.971499\pi\)
0.995994 0.0894177i \(-0.0285006\pi\)
\(422\) −1135.37 + 2741.04i −0.130970 + 0.316188i
\(423\) 0 0
\(424\) −2278.73 −0.261002
\(425\) −6513.30 5393.30i −0.743392 0.615561i
\(426\) 0 0
\(427\) −12512.8 + 12512.8i −1.41811 + 1.41811i
\(428\) 554.036 1337.56i 0.0625709 0.151060i
\(429\) 0 0
\(430\) 735.757 + 304.761i 0.0825148 + 0.0341787i
\(431\) −343.395 829.029i −0.0383776 0.0926518i 0.903529 0.428528i \(-0.140968\pi\)
−0.941906 + 0.335876i \(0.890968\pi\)
\(432\) 0 0
\(433\) 3462.33 + 3462.33i 0.384270 + 0.384270i 0.872638 0.488368i \(-0.162408\pi\)
−0.488368 + 0.872638i \(0.662408\pi\)
\(434\) 3634.04 + 3634.04i 0.401934 + 0.401934i
\(435\) 0 0
\(436\) 112.064 + 270.545i 0.0123093 + 0.0297174i
\(437\) 14861.8 + 6155.94i 1.62685 + 0.673864i
\(438\) 0 0
\(439\) 537.292 1297.14i 0.0584136 0.141023i −0.891978 0.452079i \(-0.850683\pi\)
0.950392 + 0.311056i \(0.100683\pi\)
\(440\) −133.058 + 133.058i −0.0144166 + 0.0144166i
\(441\) 0 0
\(442\) 2562.72 + 2122.05i 0.275784 + 0.228361i
\(443\) 6453.57 0.692141 0.346070 0.938209i \(-0.387516\pi\)
0.346070 + 0.938209i \(0.387516\pi\)
\(444\) 0 0
\(445\) 832.293 2009.33i 0.0886617 0.214048i
\(446\) 5814.71i 0.617342i
\(447\) 0 0
\(448\) 5279.78 + 12746.5i 0.556799 + 1.34423i
\(449\) 4073.49 1687.29i 0.428151 0.177346i −0.158193 0.987408i \(-0.550567\pi\)
0.586344 + 0.810062i \(0.300567\pi\)
\(450\) 0 0
\(451\) −146.228 146.228i −0.0152674 0.0152674i
\(452\) 1290.58 534.577i 0.134301 0.0556291i
\(453\) 0 0
\(454\) 6466.26 + 2678.41i 0.668451 + 0.276881i
\(455\) 921.859i 0.0949833i
\(456\) 0 0
\(457\) 8889.44 8889.44i 0.909913 0.909913i −0.0863515 0.996265i \(-0.527521\pi\)
0.996265 + 0.0863515i \(0.0275208\pi\)
\(458\) −3032.37 −0.309374
\(459\) 0 0
\(460\) 163.784 0.0166011
\(461\) −3616.85 + 3616.85i −0.365409 + 0.365409i −0.865800 0.500391i \(-0.833190\pi\)
0.500391 + 0.865800i \(0.333190\pi\)
\(462\) 0 0
\(463\) 5280.96i 0.530080i −0.964237 0.265040i \(-0.914615\pi\)
0.964237 0.265040i \(-0.0853852\pi\)
\(464\) −10581.9 4383.16i −1.05873 0.438541i
\(465\) 0 0
\(466\) −10710.4 + 4436.40i −1.06470 + 0.441014i
\(467\) 3132.80 + 3132.80i 0.310425 + 0.310425i 0.845074 0.534649i \(-0.179556\pi\)
−0.534649 + 0.845074i \(0.679556\pi\)
\(468\) 0 0
\(469\) 7031.55 2912.56i 0.692296 0.286758i
\(470\) −1004.77 2425.74i −0.0986100 0.238066i
\(471\) 0 0
\(472\) 8600.86i 0.838743i
\(473\) −207.796 + 501.664i −0.0201997 + 0.0487665i
\(474\) 0 0
\(475\) −19413.7 −1.87529
\(476\) 643.211 + 1216.16i 0.0619360 + 0.117107i
\(477\) 0 0
\(478\) −1497.04 + 1497.04i −0.143249 + 0.143249i
\(479\) −3328.23 + 8035.07i −0.317476 + 0.766454i 0.681911 + 0.731435i \(0.261149\pi\)
−0.999387 + 0.0350190i \(0.988851\pi\)
\(480\) 0 0
\(481\) −3996.25 1655.30i −0.378822 0.156913i
\(482\) 3723.95 + 8990.41i 0.351911 + 0.849589i
\(483\) 0 0
\(484\) 730.859 + 730.859i 0.0686382 + 0.0686382i
\(485\) 1333.15 + 1333.15i 0.124815 + 0.124815i
\(486\) 0 0
\(487\) 4986.78 + 12039.2i 0.464010 + 1.12022i 0.966737 + 0.255773i \(0.0823301\pi\)
−0.502727 + 0.864445i \(0.667670\pi\)
\(488\) −15432.4 6392.30i −1.43154 0.592963i
\(489\) 0 0
\(490\) −604.694 + 1459.86i −0.0557495 + 0.134591i
\(491\) 8315.81 8315.81i 0.764332 0.764332i −0.212770 0.977102i \(-0.568249\pi\)
0.977102 + 0.212770i \(0.0682486\pi\)
\(492\) 0 0
\(493\) −13436.0 4140.21i −1.22744 0.378226i
\(494\) 7638.51 0.695694
\(495\) 0 0
\(496\) −1672.52 + 4037.81i −0.151408 + 0.365531i
\(497\) 11749.4i 1.06042i
\(498\) 0 0
\(499\) −4104.11 9908.19i −0.368187 0.888881i −0.994048 0.108946i \(-0.965252\pi\)
0.625861 0.779935i \(-0.284748\pi\)
\(500\) −371.825 + 154.015i −0.0332570 + 0.0137755i
\(501\) 0 0
\(502\) 11348.4 + 11348.4i 1.00897 + 1.00897i
\(503\) −3607.71 + 1494.36i −0.319801 + 0.132466i −0.536809 0.843704i \(-0.680370\pi\)
0.217008 + 0.976170i \(0.430370\pi\)
\(504\) 0 0
\(505\) −854.473 353.934i −0.0752942 0.0311879i
\(506\) 1026.16i 0.0901549i
\(507\) 0 0
\(508\) −963.266 + 963.266i −0.0841299 + 0.0841299i
\(509\) 15132.3 1.31774 0.658870 0.752257i \(-0.271035\pi\)
0.658870 + 0.752257i \(0.271035\pi\)
\(510\) 0 0
\(511\) −3551.19 −0.307427
\(512\) −9051.73 + 9051.73i −0.781316 + 0.781316i
\(513\) 0 0
\(514\) 10075.1i 0.864581i
\(515\) 2691.93 + 1115.04i 0.230332 + 0.0954065i
\(516\) 0 0
\(517\) 1653.95 685.088i 0.140697 0.0582788i
\(518\) 11621.2 + 11621.2i 0.985723 + 0.985723i
\(519\) 0 0
\(520\) 803.951 333.007i 0.0677992 0.0280833i
\(521\) −6327.62 15276.2i −0.532088 1.28457i −0.930138 0.367210i \(-0.880313\pi\)
0.398050 0.917364i \(-0.369687\pi\)
\(522\) 0 0
\(523\) 8724.36i 0.729426i −0.931120 0.364713i \(-0.881167\pi\)
0.931120 0.364713i \(-0.118833\pi\)
\(524\) 169.890 410.151i 0.0141635 0.0341938i
\(525\) 0 0
\(526\) 20323.8 1.68471
\(527\) −1579.81 + 5126.89i −0.130584 + 0.423778i
\(528\) 0 0
\(529\) 1536.88 1536.88i 0.126315 0.126315i
\(530\) 207.126 500.046i 0.0169754 0.0409822i
\(531\) 0 0
\(532\) 2918.01 + 1208.68i 0.237804 + 0.0985016i
\(533\) 365.968 + 883.524i 0.0297407 + 0.0718005i
\(534\) 0 0
\(535\) 2720.65 + 2720.65i 0.219858 + 0.219858i
\(536\) 5080.08 + 5080.08i 0.409377 + 0.409377i
\(537\) 0 0
\(538\) −7185.70 17347.8i −0.575832 1.39018i
\(539\) −995.382 412.301i −0.0795438 0.0329481i
\(540\) 0 0
\(541\) −3155.65 + 7618.42i −0.250780 + 0.605437i −0.998267 0.0588391i \(-0.981260\pi\)
0.747487 + 0.664276i \(0.231260\pi\)
\(542\) 2576.70 2576.70i 0.204205 0.204205i
\(543\) 0 0
\(544\) −1582.50 + 1911.13i −0.124723 + 0.150623i
\(545\) −778.240 −0.0611672
\(546\) 0 0
\(547\) 9124.03 22027.4i 0.713191 1.72179i 0.0213210 0.999773i \(-0.493213\pi\)
0.691870 0.722022i \(-0.256787\pi\)
\(548\) 903.134i 0.0704014i
\(549\) 0 0
\(550\) 473.923 + 1144.15i 0.0367421 + 0.0887032i
\(551\) −29819.9 + 12351.8i −2.30557 + 0.954999i
\(552\) 0 0
\(553\) −12689.4 12689.4i −0.975784 0.975784i
\(554\) 17805.0 7375.06i 1.36545 0.565589i
\(555\) 0 0
\(556\) −714.275 295.862i −0.0544820 0.0225672i
\(557\) 19341.5i 1.47132i −0.677350 0.735661i \(-0.736872\pi\)
0.677350 0.735661i \(-0.263128\pi\)
\(558\) 0 0
\(559\) 1775.58 1775.58i 0.134345 0.134345i
\(560\) −2978.63 −0.224768
\(561\) 0 0
\(562\) 17758.6 1.33292
\(563\) −10048.2 + 10048.2i −0.752189 + 0.752189i −0.974887 0.222698i \(-0.928513\pi\)
0.222698 + 0.974887i \(0.428513\pi\)
\(564\) 0 0
\(565\) 3712.44i 0.276431i
\(566\) −5734.63 2375.36i −0.425874 0.176403i
\(567\) 0 0
\(568\) 10246.6 4244.27i 0.756932 0.313531i
\(569\) 6771.36 + 6771.36i 0.498893 + 0.498893i 0.911093 0.412200i \(-0.135239\pi\)
−0.412200 + 0.911093i \(0.635239\pi\)
\(570\) 0 0
\(571\) −13659.5 + 5657.96i −1.00111 + 0.414673i −0.822203 0.569194i \(-0.807255\pi\)
−0.178905 + 0.983866i \(0.557255\pi\)
\(572\) 20.2929 + 48.9914i 0.00148337 + 0.00358118i
\(573\) 0 0
\(574\) 3633.54i 0.264218i
\(575\) 4615.42 11142.6i 0.334742 0.808138i
\(576\) 0 0
\(577\) 11438.5 0.825284 0.412642 0.910893i \(-0.364606\pi\)
0.412642 + 0.910893i \(0.364606\pi\)
\(578\) 7427.56 10907.8i 0.534508 0.784956i
\(579\) 0 0
\(580\) −232.377 + 232.377i −0.0166361 + 0.0166361i
\(581\) 3517.02 8490.84i 0.251137 0.606298i
\(582\) 0 0
\(583\) 340.948 + 141.225i 0.0242206 + 0.0100325i
\(584\) −1282.81 3096.98i −0.0908958 0.219442i
\(585\) 0 0
\(586\) −12242.7 12242.7i −0.863042 0.863042i
\(587\) −5580.55 5580.55i −0.392392 0.392392i 0.483147 0.875539i \(-0.339493\pi\)
−0.875539 + 0.483147i \(0.839493\pi\)
\(588\) 0 0
\(589\) 4713.17 + 11378.6i 0.329716 + 0.796005i
\(590\) 1887.37 + 781.776i 0.131698 + 0.0545512i
\(591\) 0 0
\(592\) −5348.48 + 12912.4i −0.371319 + 0.896444i
\(593\) −5536.25 + 5536.25i −0.383384 + 0.383384i −0.872320 0.488936i \(-0.837385\pi\)
0.488936 + 0.872320i \(0.337385\pi\)
\(594\) 0 0
\(595\) −3640.20 + 342.416i −0.250813 + 0.0235928i
\(596\) 1391.46 0.0956317
\(597\) 0 0
\(598\) −1815.98 + 4384.17i −0.124182 + 0.299803i
\(599\) 18939.7i 1.29191i −0.763375 0.645956i \(-0.776459\pi\)
0.763375 0.645956i \(-0.223541\pi\)
\(600\) 0 0
\(601\) −6803.11 16424.1i −0.461738 1.11473i −0.967683 0.252168i \(-0.918856\pi\)
0.505945 0.862565i \(-0.331144\pi\)
\(602\) −8814.49 + 3651.08i −0.596764 + 0.247188i
\(603\) 0 0
\(604\) −1050.48 1050.48i −0.0707675 0.0707675i
\(605\) −2537.77 + 1051.18i −0.170537 + 0.0706389i
\(606\) 0 0
\(607\) 16364.9 + 6778.57i 1.09429 + 0.453268i 0.855499 0.517804i \(-0.173250\pi\)
0.238787 + 0.971072i \(0.423250\pi\)
\(608\) 5696.35i 0.379963i
\(609\) 0 0
\(610\) 2805.46 2805.46i 0.186212 0.186212i
\(611\) −8278.74 −0.548154
\(612\) 0 0
\(613\) 25427.3 1.67537 0.837683 0.546156i \(-0.183910\pi\)
0.837683 + 0.546156i \(0.183910\pi\)
\(614\) 420.549 420.549i 0.0276417 0.0276417i
\(615\) 0 0
\(616\) 2254.34i 0.147451i
\(617\) 9265.07 + 3837.72i 0.604534 + 0.250406i 0.663890 0.747831i \(-0.268904\pi\)
−0.0593552 + 0.998237i \(0.518904\pi\)
\(618\) 0 0
\(619\) −4121.37 + 1707.13i −0.267612 + 0.110849i −0.512455 0.858714i \(-0.671264\pi\)
0.244842 + 0.969563i \(0.421264\pi\)
\(620\) 88.6699 + 88.6699i 0.00574366 + 0.00574366i
\(621\) 0 0
\(622\) −3210.84 + 1329.97i −0.206982 + 0.0857348i
\(623\) 9971.00 + 24072.1i 0.641220 + 1.54804i
\(624\) 0 0
\(625\) 14011.2i 0.896714i
\(626\) −396.203 + 956.520i −0.0252963 + 0.0610706i
\(627\) 0 0
\(628\) 227.664 0.0144662
\(629\) −5052.02 + 16395.1i −0.320250 + 1.03929i
\(630\) 0 0
\(631\) 776.752 776.752i 0.0490048 0.0490048i −0.682180 0.731185i \(-0.738968\pi\)
0.731185 + 0.682180i \(0.238968\pi\)
\(632\) 6482.55 15650.3i 0.408009 0.985021i
\(633\) 0 0
\(634\) −1610.66 667.158i −0.100895 0.0417922i
\(635\) −1385.45 3344.76i −0.0865822 0.209028i
\(636\) 0 0
\(637\) 3523.03 + 3523.03i 0.219133 + 0.219133i
\(638\) 1455.91 + 1455.91i 0.0903451 + 0.0903451i
\(639\) 0 0
\(640\) −957.625 2311.91i −0.0591460 0.142791i
\(641\) −982.245 406.859i −0.0605247 0.0250702i 0.352216 0.935919i \(-0.385428\pi\)
−0.412740 + 0.910849i \(0.635428\pi\)
\(642\) 0 0
\(643\) 2514.71 6071.06i 0.154231 0.372347i −0.827811 0.561006i \(-0.810414\pi\)
0.982043 + 0.188660i \(0.0604143\pi\)
\(644\) −1387.46 + 1387.46i −0.0848968 + 0.0848968i
\(645\) 0 0
\(646\) −2837.26 30162.6i −0.172802 1.83705i
\(647\) 14783.1 0.898273 0.449137 0.893463i \(-0.351732\pi\)
0.449137 + 0.893463i \(0.351732\pi\)
\(648\) 0 0
\(649\) −533.041 + 1286.88i −0.0322399 + 0.0778340i
\(650\) 5726.98i 0.345585i
\(651\) 0 0
\(652\) 508.377 + 1227.33i 0.0305361 + 0.0737208i
\(653\) 23939.5 9916.08i 1.43465 0.594251i 0.476155 0.879362i \(-0.342030\pi\)
0.958495 + 0.285110i \(0.0920302\pi\)
\(654\) 0 0
\(655\) 834.261 + 834.261i 0.0497668 + 0.0497668i
\(656\) 2854.77 1182.48i 0.169909 0.0703784i
\(657\) 0 0
\(658\) 29060.7 + 12037.3i 1.72174 + 0.713168i
\(659\) 4302.30i 0.254315i −0.991883 0.127158i \(-0.959415\pi\)
0.991883 0.127158i \(-0.0405854\pi\)
\(660\) 0 0
\(661\) −5280.43 + 5280.43i −0.310719 + 0.310719i −0.845188 0.534469i \(-0.820512\pi\)
0.534469 + 0.845188i \(0.320512\pi\)
\(662\) 3840.28 0.225463
\(663\) 0 0
\(664\) 8675.31 0.507029
\(665\) −5935.33 + 5935.33i −0.346109 + 0.346109i
\(666\) 0 0
\(667\) 20051.9i 1.16403i
\(668\) −910.974 377.338i −0.0527644 0.0218557i
\(669\) 0 0
\(670\) −1576.53 + 653.019i −0.0909054 + 0.0376542i
\(671\) 1912.85 + 1912.85i 0.110052 + 0.110052i
\(672\) 0 0
\(673\) 3914.28 1621.35i 0.224197 0.0928654i −0.267758 0.963486i \(-0.586283\pi\)
0.491955 + 0.870621i \(0.336283\pi\)
\(674\) −581.140 1403.00i −0.0332117 0.0801801i
\(675\) 0 0
\(676\) 1479.79i 0.0841938i
\(677\) −8851.64 + 21369.8i −0.502506 + 1.21316i 0.445609 + 0.895228i \(0.352987\pi\)
−0.948115 + 0.317928i \(0.897013\pi\)
\(678\) 0 0
\(679\) −22587.0 −1.27660
\(680\) −1613.59 3050.91i −0.0909973 0.172055i
\(681\) 0 0
\(682\) 555.545 555.545i 0.0311919 0.0311919i
\(683\) −4391.09 + 10601.0i −0.246004 + 0.593905i −0.997858 0.0654244i \(-0.979160\pi\)
0.751854 + 0.659330i \(0.229160\pi\)
\(684\) 0 0
\(685\) −2217.46 918.503i −0.123686 0.0512324i
\(686\) 1569.42 + 3788.91i 0.0873478 + 0.210876i
\(687\) 0 0
\(688\) −5737.10 5737.10i −0.317914 0.317914i
\(689\) −1206.74 1206.74i −0.0667246 0.0667246i
\(690\) 0 0
\(691\) 5825.05 + 14062.9i 0.320688 + 0.774209i 0.999214 + 0.0396328i \(0.0126188\pi\)
−0.678527 + 0.734576i \(0.737381\pi\)
\(692\) −291.025 120.547i −0.0159872 0.00662210i
\(693\) 0 0
\(694\) −3894.44 + 9402.01i −0.213013 + 0.514258i
\(695\) 1452.86 1452.86i 0.0792951 0.0792951i
\(696\) 0 0
\(697\) 3352.89 1773.29i 0.182209 0.0963678i
\(698\) 17156.6 0.930352
\(699\) 0 0
\(700\) 906.208 2187.78i 0.0489306 0.118129i
\(701\) 23996.1i 1.29289i −0.762959 0.646447i \(-0.776254\pi\)
0.762959 0.646447i \(-0.223746\pi\)
\(702\) 0 0
\(703\) 15072.1 + 36387.2i 0.808612 + 1.95216i
\(704\) 1948.59 807.133i 0.104319 0.0432102i
\(705\) 0 0
\(706\) −11949.3 11949.3i −0.636992 0.636992i
\(707\) 10236.7 4240.19i 0.544543 0.225557i
\(708\) 0 0
\(709\) −20645.7 8551.75i −1.09361 0.452987i −0.238344 0.971181i \(-0.576605\pi\)
−0.855263 + 0.518194i \(0.826605\pi\)
\(710\) 2634.30i 0.139244i
\(711\) 0 0
\(712\) −17391.4 + 17391.4i −0.915406 + 0.915406i
\(713\) −7651.34 −0.401886
\(714\) 0 0
\(715\) −140.927 −0.00737113
\(716\) 427.075 427.075i 0.0222912 0.0222912i
\(717\) 0 0
\(718\) 9050.64i 0.470427i
\(719\) 29996.7 + 12425.0i 1.55590 + 0.644473i 0.984370 0.176111i \(-0.0563519\pi\)
0.571525 + 0.820584i \(0.306352\pi\)
\(720\) 0 0
\(721\) −32249.8 + 13358.3i −1.66581 + 0.689999i
\(722\) −36152.6 36152.6i −1.86352 1.86352i
\(723\) 0 0
\(724\) 1906.27 789.604i 0.0978537 0.0405323i
\(725\) 9260.77 + 22357.5i 0.474395 + 1.14529i
\(726\) 0 0
\(727\) 2899.33i 0.147909i −0.997262 0.0739547i \(-0.976438\pi\)
0.997262 0.0739547i \(-0.0235620\pi\)
\(728\) −3989.48 + 9631.46i −0.203104 + 0.490337i
\(729\) 0 0
\(730\) 796.204 0.0403683
\(731\) −7670.86 6351.81i −0.388122 0.321382i
\(732\) 0 0
\(733\) −11596.5 + 11596.5i −0.584346 + 0.584346i −0.936095 0.351749i \(-0.885587\pi\)
0.351749 + 0.936095i \(0.385587\pi\)
\(734\) −1025.35 + 2475.42i −0.0515619 + 0.124481i
\(735\) 0 0
\(736\) −3269.46 1354.25i −0.163742 0.0678240i
\(737\) −445.251 1074.93i −0.0222538 0.0537253i
\(738\) 0 0
\(739\) 4575.44 + 4575.44i 0.227754 + 0.227754i 0.811754 0.584000i \(-0.198513\pi\)
−0.584000 + 0.811754i \(0.698513\pi\)
\(740\) 283.554 + 283.554i 0.0140860 + 0.0140860i
\(741\) 0 0
\(742\) 2481.40 + 5990.63i 0.122770 + 0.296392i
\(743\) −6947.76 2877.86i −0.343053 0.142097i 0.204504 0.978866i \(-0.434442\pi\)
−0.547557 + 0.836769i \(0.684442\pi\)
\(744\) 0 0
\(745\) −1415.14 + 3416.45i −0.0695929 + 0.168012i
\(746\) −6040.96 + 6040.96i −0.296481 + 0.296481i
\(747\) 0 0
\(748\) 185.918 98.3293i 0.00908800 0.00480652i
\(749\) −46094.6 −2.24868
\(750\) 0 0
\(751\) 4179.61 10090.5i 0.203084 0.490289i −0.789220 0.614110i \(-0.789515\pi\)
0.992305 + 0.123821i \(0.0395150\pi\)
\(752\) 26749.6i 1.29715i
\(753\) 0 0
\(754\) −3643.74 8796.78i −0.175991 0.424880i
\(755\) 3647.61 1510.89i 0.175828 0.0728303i
\(756\) 0 0
\(757\) −12100.6 12100.6i −0.580984 0.580984i 0.354189 0.935174i \(-0.384757\pi\)
−0.935174 + 0.354189i \(0.884757\pi\)
\(758\) −26885.3 + 11136.2i −1.28828 + 0.533623i
\(759\) 0 0
\(760\) −7320.23 3032.14i −0.349385 0.144720i
\(761\) 35934.3i 1.71172i 0.517207 + 0.855860i \(0.326972\pi\)
−0.517207 + 0.855860i \(0.673028\pi\)
\(762\) 0 0
\(763\) 6592.67 6592.67i 0.312805 0.312805i
\(764\) −163.202 −0.00772831
\(765\) 0 0
\(766\) −20327.8 −0.958842
\(767\) 4554.74 4554.74i 0.214423 0.214423i
\(768\) 0 0
\(769\) 29085.3i 1.36390i −0.731397 0.681952i \(-0.761131\pi\)
0.731397 0.681952i \(-0.238869\pi\)
\(770\) 494.693 + 204.908i 0.0231526 + 0.00959011i
\(771\) 0 0
\(772\) −3320.61 + 1375.44i −0.154808 + 0.0641234i
\(773\) 11669.3 + 11669.3i 0.542968 + 0.542968i 0.924398 0.381430i \(-0.124568\pi\)
−0.381430 + 0.924398i \(0.624568\pi\)
\(774\) 0 0
\(775\) 8531.12 3533.71i 0.395415 0.163786i
\(776\) −8159.20 19698.0i −0.377446 0.911236i
\(777\) 0 0
\(778\) 25784.3i 1.18819i
\(779\) 3332.25 8044.77i 0.153261 0.370005i
\(780\) 0 0
\(781\) −1796.15 −0.0822937
\(782\) 17986.6 + 5542.42i 0.822505 + 0.253448i
\(783\) 0 0
\(784\) 11383.3 11383.3i 0.518556 0.518556i
\(785\) −231.538 + 558.982i −0.0105273 + 0.0254152i
\(786\) 0 0
\(787\) 25290.4 + 10475.6i 1.14550 + 0.474480i 0.873021 0.487683i \(-0.162158\pi\)
0.272474 + 0.962163i \(0.412158\pi\)
\(788\) 793.539 + 1915.77i 0.0358739 + 0.0866073i
\(789\) 0 0
\(790\) 2845.06 + 2845.06i 0.128130 + 0.128130i
\(791\) −31449.0 31449.0i −1.41365 1.41365i
\(792\) 0 0
\(793\) −4787.34 11557.7i −0.214380 0.517559i
\(794\) 13083.0 + 5419.14i 0.584757 + 0.242214i
\(795\) 0 0
\(796\) 496.064 1197.60i 0.0220886 0.0533266i
\(797\) 22469.1 22469.1i 0.998615 0.998615i −0.00138359 0.999999i \(-0.500440\pi\)
0.999999 + 0.00138359i \(0.000440412\pi\)
\(798\) 0 0
\(799\) 3075.07 + 32690.7i 0.136155 + 1.44745i
\(800\) 4270.84 0.188746
\(801\) 0 0
\(802\) −3700.81 + 8934.54i −0.162943 + 0.393379i
\(803\) 542.879i 0.0238578i
\(804\) 0 0
\(805\) −1995.55 4817.69i −0.0873715 0.210933i
\(806\) −3356.65 + 1390.37i −0.146691 + 0.0607615i
\(807\) 0 0
\(808\) 7395.72 + 7395.72i 0.322006 + 0.322006i
\(809\) −31751.1 + 13151.8i −1.37986 + 0.571559i −0.944445 0.328669i \(-0.893400\pi\)
−0.435420 + 0.900228i \(0.643400\pi\)
\(810\) 0 0
\(811\) 1216.74 + 503.991i 0.0526826 + 0.0218218i 0.408869 0.912593i \(-0.365923\pi\)
−0.356187 + 0.934415i \(0.615923\pi\)
\(812\) 3937.05i 0.170152i
\(813\) 0 0
\(814\) 1776.55 1776.55i 0.0764966 0.0764966i
\(815\) −3530.49 −0.151739
\(816\) 0 0
\(817\) −22863.9 −0.979078
\(818\) 18074.2 18074.2i 0.772553 0.772553i
\(819\) 0 0
\(820\) 88.6577i 0.00377568i
\(821\) −30932.5 12812.7i −1.31492 0.544659i −0.388607 0.921404i \(-0.627044\pi\)
−0.926317 + 0.376744i \(0.877044\pi\)
\(822\) 0 0
\(823\) 10852.6 4495.29i 0.459657 0.190396i −0.140825 0.990035i \(-0.544975\pi\)
0.600482 + 0.799638i \(0.294975\pi\)
\(824\) −23299.5 23299.5i −0.985044 0.985044i
\(825\) 0 0
\(826\) −22611.0 + 9365.80i −0.952468 + 0.394525i
\(827\) −1671.50 4035.36i −0.0702827 0.169678i 0.884835 0.465905i \(-0.154271\pi\)
−0.955117 + 0.296228i \(0.904271\pi\)
\(828\) 0 0
\(829\) 19994.7i 0.837689i 0.908058 + 0.418844i \(0.137565\pi\)
−0.908058 + 0.418844i \(0.862435\pi\)
\(830\) −788.543 + 1903.71i −0.0329768 + 0.0796130i
\(831\) 0 0
\(832\) −9753.55 −0.406422
\(833\) 12603.0 15220.2i 0.524211 0.633072i
\(834\) 0 0
\(835\) 1852.95 1852.95i 0.0767952 0.0767952i
\(836\) 184.774 446.083i 0.00764417 0.0184547i
\(837\) 0 0
\(838\) −15660.1 6486.61i −0.645547 0.267394i
\(839\) 9824.30 + 23718.0i 0.404258 + 0.975965i 0.986620 + 0.163036i \(0.0521286\pi\)
−0.582362 + 0.812929i \(0.697871\pi\)
\(840\) 0 0
\(841\) 11203.9 + 11203.9i 0.459384 + 0.459384i
\(842\) −2934.10 2934.10i −0.120090 0.120090i
\(843\) 0 0
\(844\) −331.885 801.242i −0.0135355 0.0326776i
\(845\) −3633.32 1504.97i −0.147917 0.0612693i
\(846\) 0 0
\(847\) 12593.3 30402.9i 0.510875 1.23336i
\(848\) −3899.13 + 3899.13i −0.157897 + 0.157897i
\(849\) 0 0
\(850\) −22614.4 + 2127.24i −0.912552 + 0.0858395i
\(851\) −24467.9 −0.985605
\(852\) 0 0
\(853\) −5933.37 + 14324.4i −0.238165 + 0.574981i −0.997093 0.0761933i \(-0.975723\pi\)
0.758928 + 0.651174i \(0.225723\pi\)
\(854\) 47531.5i 1.90456i
\(855\) 0 0
\(856\) −16650.9 40198.9i −0.664857 1.60511i
\(857\) 33181.2 13744.1i 1.32258 0.547830i 0.394049 0.919089i \(-0.371074\pi\)
0.928529 + 0.371260i \(0.121074\pi\)
\(858\) 0 0
\(859\) 25862.4 + 25862.4i 1.02726 + 1.02726i 0.999618 + 0.0276409i \(0.00879949\pi\)
0.0276409 + 0.999618i \(0.491201\pi\)
\(860\) −215.072 + 89.0857i −0.00852778 + 0.00353232i
\(861\) 0 0
\(862\) −2226.81 922.374i −0.0879877 0.0364457i
\(863\) 11402.6i 0.449768i −0.974386 0.224884i \(-0.927800\pi\)
0.974386 0.224884i \(-0.0722003\pi\)
\(864\) 0 0
\(865\) 591.955 591.955i 0.0232683 0.0232683i
\(866\) 13152.1 0.516083
\(867\) 0 0
\(868\) −1502.29 −0.0587455
\(869\) −1939.86 + 1939.86i −0.0757252 + 0.0757252i
\(870\) 0 0
\(871\) 5380.50i 0.209312i
\(872\) 8130.94 + 3367.95i 0.315767 + 0.130795i
\(873\) 0 0
\(874\) 39919.3 16535.1i 1.54496 0.639942i
\(875\) 9060.64 + 9060.64i 0.350063 + 0.350063i
\(876\) 0 0
\(877\) 21641.6 8964.22i 0.833276 0.345154i 0.0750774 0.997178i \(-0.476080\pi\)
0.758199 + 0.652023i \(0.226080\pi\)
\(878\) −1443.19 3484.17i −0.0554731 0.133924i
\(879\) 0 0
\(880\) 455.351i 0.0174430i
\(881\) 938.538 2265.83i 0.0358912 0.0866490i −0.904918 0.425587i \(-0.860068\pi\)
0.940809 + 0.338938i \(0.110068\pi\)
\(882\) 0 0
\(883\) −3832.99 −0.146082 −0.0730409 0.997329i \(-0.523270\pi\)
−0.0730409 + 0.997329i \(0.523270\pi\)
\(884\) −968.328 + 91.0862i −0.0368421 + 0.00346557i
\(885\) 0 0
\(886\) 12257.4 12257.4i 0.464780 0.464780i
\(887\) −5102.84 + 12319.3i −0.193164 + 0.466340i −0.990554 0.137125i \(-0.956214\pi\)
0.797390 + 0.603465i \(0.206214\pi\)
\(888\) 0 0
\(889\) 40070.8 + 16597.9i 1.51173 + 0.626180i
\(890\) −2235.58 5397.16i −0.0841985 0.203273i
\(891\) 0 0
\(892\) −1201.88 1201.88i −0.0451144 0.0451144i
\(893\) 53302.1 + 53302.1i 1.99741 + 1.99741i
\(894\) 0 0
\(895\) 614.253 + 1482.94i 0.0229410 + 0.0553845i
\(896\) 27697.1 + 11472.5i 1.03269 + 0.427756i
\(897\) 0 0
\(898\) 4532.15 10941.6i 0.168418 0.406598i
\(899\) 10855.7 10855.7i 0.402734 0.402734i
\(900\) 0 0
\(901\) −4316.90 + 5213.37i −0.159619 + 0.192767i
\(902\) −555.468 −0.0205045
\(903\) 0 0
\(904\) 16066.1 38787.0i 0.591096 1.42703i
\(905\) 5483.51i 0.201412i
\(906\) 0 0
\(907\) −5523.15 13334.1i −0.202198 0.488148i 0.789957 0.613162i \(-0.210103\pi\)
−0.992155 + 0.125013i \(0.960103\pi\)
\(908\) −1890.18 + 782.937i −0.0690834 + 0.0286153i
\(909\) 0 0
\(910\) −1750.90 1750.90i −0.0637823 0.0637823i
\(911\) 46624.0 19312.3i 1.69563 0.702354i 0.695760 0.718274i \(-0.255068\pi\)
0.999873 + 0.0159195i \(0.00506754\pi\)
\(912\) 0 0
\(913\) −1298.01 537.655i −0.0470515 0.0194894i
\(914\) 33767.8i 1.22203i
\(915\) 0 0
\(916\) 626.782 626.782i 0.0226086 0.0226086i
\(917\) −14134.5 −0.509009
\(918\) 0 0
\(919\) −33955.2 −1.21880 −0.609401 0.792862i \(-0.708590\pi\)
−0.609401 + 0.792862i \(0.708590\pi\)
\(920\) 3480.63 3480.63i 0.124732 0.124732i
\(921\) 0 0
\(922\) 13739.1i 0.490753i
\(923\) 7673.90 + 3178.63i 0.273661 + 0.113354i
\(924\) 0 0
\(925\) 27281.3 11300.3i 0.969735 0.401677i
\(926\) −10030.2 10030.2i −0.355955 0.355955i
\(927\) 0 0
\(928\) 6560.12 2717.29i 0.232054 0.0961200i
\(929\) 5666.65 + 13680.5i 0.200126 + 0.483146i 0.991800 0.127797i \(-0.0407905\pi\)
−0.791675 + 0.610943i \(0.790790\pi\)
\(930\) 0 0
\(931\) 45365.6i 1.59699i
\(932\) 1296.82 3130.80i 0.0455781 0.110035i
\(933\) 0 0
\(934\) 11900.4 0.416908
\(935\) 52.3460 + 556.486i 0.00183091 + 0.0194642i
\(936\) 0 0
\(937\) 3635.47 3635.47i 0.126751 0.126751i −0.640885 0.767637i \(-0.721433\pi\)
0.767637 + 0.640885i \(0.221433\pi\)
\(938\) 7823.28 18887.1i 0.272323 0.657446i
\(939\) 0 0
\(940\) 709.076 + 293.709i 0.0246037 + 0.0101912i
\(941\) −14908.7 35992.9i −0.516484 1.24690i −0.940050 0.341037i \(-0.889222\pi\)
0.423566 0.905865i \(-0.360778\pi\)
\(942\) 0 0
\(943\) 3825.14 + 3825.14i 0.132093 + 0.132093i
\(944\) −14716.9 14716.9i −0.507409 0.507409i
\(945\) 0 0
\(946\) 558.149 + 1347.49i 0.0191829 + 0.0463116i
\(947\) −13111.3 5430.89i −0.449906 0.186357i 0.146213 0.989253i \(-0.453291\pi\)
−0.596119 + 0.802896i \(0.703291\pi\)
\(948\) 0 0
\(949\) 960.727 2319.40i 0.0328625 0.0793371i
\(950\) −36872.8 + 36872.8i −1.25927 + 1.25927i
\(951\) 0 0
\(952\) 39514.2 + 12176.0i 1.34523 + 0.414523i
\(953\) 32646.8 1.10969 0.554844 0.831955i \(-0.312778\pi\)
0.554844 + 0.831955i \(0.312778\pi\)
\(954\) 0 0
\(955\) 165.979 400.708i 0.00562403 0.0135776i
\(956\) 618.867i 0.0209368i
\(957\) 0 0
\(958\) 8939.78 + 21582.5i 0.301494 + 0.727871i
\(959\) 26565.5 11003.8i 0.894522 0.370523i
\(960\) 0 0
\(961\) 16923.1 + 16923.1i 0.568061 + 0.568061i
\(962\) −10734.1 + 4446.22i −0.359752 + 0.149014i
\(963\) 0 0
\(964\) −2628.02 1088.56i −0.0878038 0.0363695i
\(965\) 9551.94i 0.318640i
\(966\) 0 0
\(967\) −11443.7 + 11443.7i −0.380562 + 0.380562i −0.871305 0.490743i \(-0.836726\pi\)
0.490743 + 0.871305i \(0.336726\pi\)
\(968\) 31063.4 1.03142
\(969\) 0 0
\(970\) 5064.18 0.167630
\(971\) 20370.1 20370.1i 0.673233 0.673233i −0.285227 0.958460i \(-0.592069\pi\)
0.958460 + 0.285227i \(0.0920690\pi\)
\(972\) 0 0
\(973\) 24615.1i 0.811021i
\(974\) 32337.7 + 13394.7i 1.06383 + 0.440651i
\(975\) 0 0
\(976\) −37344.1 + 15468.4i −1.22475 + 0.507308i
\(977\) −2231.39 2231.39i −0.0730689 0.0730689i 0.669628 0.742697i \(-0.266454\pi\)
−0.742697 + 0.669628i \(0.766454\pi\)
\(978\) 0 0
\(979\) 3679.96 1524.29i 0.120135 0.0497615i
\(980\) −176.760 426.737i −0.00576163 0.0139098i
\(981\) 0 0
\(982\) 31588.8i 1.02651i
\(983\) −5670.86 + 13690.7i −0.184000 + 0.444216i −0.988784 0.149352i \(-0.952281\pi\)
0.804784 + 0.593568i \(0.202281\pi\)
\(984\) 0 0
\(985\) −5510.83 −0.178264
\(986\) −33382.9 + 17655.7i −1.07822 + 0.570257i
\(987\) 0 0
\(988\) −1578.86 + 1578.86i −0.0508402 + 0.0508402i
\(989\) 5435.68 13122.9i 0.174767 0.421925i
\(990\) 0 0
\(991\) 820.788 + 339.981i 0.0263100 + 0.0108979i 0.395800 0.918337i \(-0.370467\pi\)
−0.369490 + 0.929235i \(0.620467\pi\)
\(992\) −1036.86 2503.19i −0.0331857 0.0801175i
\(993\) 0 0
\(994\) −22315.8 22315.8i −0.712086 0.712086i
\(995\) 2435.97 + 2435.97i 0.0776134 + 0.0776134i
\(996\) 0 0
\(997\) 1958.18 + 4727.46i 0.0622027 + 0.150171i 0.951925 0.306332i \(-0.0991018\pi\)
−0.889722 + 0.456503i \(0.849102\pi\)
\(998\) −26613.8 11023.8i −0.844135 0.349652i
\(999\) 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 153.4.l.a.127.3 12
3.2 odd 2 17.4.d.a.8.1 12
17.15 even 8 inner 153.4.l.a.100.3 12
51.11 even 16 289.4.b.e.288.3 12
51.23 even 16 289.4.b.e.288.4 12
51.32 odd 8 17.4.d.a.15.1 yes 12
51.41 even 16 289.4.a.g.1.10 12
51.44 even 16 289.4.a.g.1.9 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.d.a.8.1 12 3.2 odd 2
17.4.d.a.15.1 yes 12 51.32 odd 8
153.4.l.a.100.3 12 17.15 even 8 inner
153.4.l.a.127.3 12 1.1 even 1 trivial
289.4.a.g.1.9 12 51.44 even 16
289.4.a.g.1.10 12 51.41 even 16
289.4.b.e.288.3 12 51.11 even 16
289.4.b.e.288.4 12 51.23 even 16