Properties

Label 363.3.b.n.122.9
Level $363$
Weight $3$
Character 363.122
Analytic conductor $9.891$
Analytic rank $0$
Dimension $12$
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] = [363,3,Mod(122,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.122");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 363.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.89103359628\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + 290 x^{8} + 580 x^{7} + 3656 x^{6} + 5424 x^{5} + 6124 x^{4} + 6920 x^{3} - 32528 x^{2} - 23952 x + 48312 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 122.9
Root \(4.48261 + 2.99036i\) of defining polynomial
Character \(\chi\) \(=\) 363.122
Dual form 363.3.b.n.122.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.16906i q^{2} +(0.240294 - 2.99036i) q^{3} -0.704830 q^{4} +5.33026i q^{5} +(6.48628 + 0.521212i) q^{6} +12.4613 q^{7} +7.14743i q^{8} +(-8.88452 - 1.43713i) q^{9} +O(q^{10})\) \(q+2.16906i q^{2} +(0.240294 - 2.99036i) q^{3} -0.704830 q^{4} +5.33026i q^{5} +(6.48628 + 0.521212i) q^{6} +12.4613 q^{7} +7.14743i q^{8} +(-8.88452 - 1.43713i) q^{9} -11.5617 q^{10} +(-0.169366 + 2.10770i) q^{12} -3.85250 q^{13} +27.0293i q^{14} +(15.9394 + 1.28083i) q^{15} -18.3225 q^{16} -10.2747i q^{17} +(3.11723 - 19.2711i) q^{18} +22.0768 q^{19} -3.75693i q^{20} +(2.99438 - 37.2638i) q^{21} +22.3094i q^{23} +(21.3734 + 1.71748i) q^{24} -3.41164 q^{25} -8.35631i q^{26} +(-6.43243 + 26.2226i) q^{27} -8.78310 q^{28} +10.8453i q^{29} +(-2.77820 + 34.5735i) q^{30} -18.9176 q^{31} -11.1530i q^{32} +22.2865 q^{34} +66.4220i q^{35} +(6.26208 + 1.01293i) q^{36} -5.71155 q^{37} +47.8860i q^{38} +(-0.925732 + 11.5204i) q^{39} -38.0976 q^{40} +26.0142i q^{41} +(80.8275 + 6.49499i) q^{42} +62.1199 q^{43} +(7.66028 - 47.3568i) q^{45} -48.3904 q^{46} +57.0848i q^{47} +(-4.40279 + 54.7910i) q^{48} +106.284 q^{49} -7.40007i q^{50} +(-30.7251 - 2.46895i) q^{51} +2.71536 q^{52} -55.7779i q^{53} +(-56.8784 - 13.9523i) q^{54} +89.0663i q^{56} +(5.30492 - 66.0176i) q^{57} -23.5242 q^{58} -67.0487i q^{59} +(-11.2346 - 0.902766i) q^{60} -20.3248 q^{61} -41.0335i q^{62} +(-110.713 - 17.9085i) q^{63} -49.0986 q^{64} -20.5348i q^{65} -88.3646 q^{67} +7.24192i q^{68} +(66.7130 + 5.36080i) q^{69} -144.073 q^{70} -106.717i q^{71} +(10.2718 - 63.5015i) q^{72} +19.6558 q^{73} -12.3887i q^{74} +(-0.819797 + 10.2020i) q^{75} -15.5604 q^{76} +(-24.9884 - 2.00797i) q^{78} +35.7157 q^{79} -97.6638i q^{80} +(76.8693 + 25.5364i) q^{81} -56.4263 q^{82} +81.3571i q^{83} +(-2.11053 + 26.2647i) q^{84} +54.7668 q^{85} +134.742i q^{86} +(32.4314 + 2.60606i) q^{87} -120.618i q^{89} +(102.720 + 16.6156i) q^{90} -48.0072 q^{91} -15.7243i q^{92} +(-4.54579 + 56.5705i) q^{93} -123.820 q^{94} +117.675i q^{95} +(-33.3515 - 2.68000i) q^{96} -85.3365 q^{97} +230.537i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{3} - 44 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{3} - 44 q^{4} - 12 q^{9} - 80 q^{12} + 68 q^{15} + 92 q^{16} - 88 q^{25} - 232 q^{27} - 8 q^{31} + 116 q^{34} + 164 q^{36} - 244 q^{37} + 404 q^{42} - 52 q^{45} + 540 q^{48} + 100 q^{49} - 460 q^{58} + 24 q^{60} - 1276 q^{64} - 128 q^{67} + 128 q^{69} - 784 q^{70} + 684 q^{75} + 528 q^{78} + 348 q^{81} - 380 q^{82} + 120 q^{91} + 196 q^{93} - 156 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.16906i 1.08453i 0.840207 + 0.542266i \(0.182433\pi\)
−0.840207 + 0.542266i \(0.817567\pi\)
\(3\) 0.240294 2.99036i 0.0800979 0.996787i
\(4\) −0.704830 −0.176208
\(5\) 5.33026i 1.06605i 0.846099 + 0.533026i \(0.178945\pi\)
−0.846099 + 0.533026i \(0.821055\pi\)
\(6\) 6.48628 + 0.521212i 1.08105 + 0.0868687i
\(7\) 12.4613 1.78019 0.890093 0.455778i \(-0.150639\pi\)
0.890093 + 0.455778i \(0.150639\pi\)
\(8\) 7.14743i 0.893428i
\(9\) −8.88452 1.43713i −0.987169 0.159681i
\(10\) −11.5617 −1.15617
\(11\) 0 0
\(12\) −0.169366 + 2.10770i −0.0141139 + 0.175641i
\(13\) −3.85250 −0.296346 −0.148173 0.988961i \(-0.547339\pi\)
−0.148173 + 0.988961i \(0.547339\pi\)
\(14\) 27.0293i 1.93067i
\(15\) 15.9394 + 1.28083i 1.06263 + 0.0853885i
\(16\) −18.3225 −1.14516
\(17\) 10.2747i 0.604394i −0.953245 0.302197i \(-0.902280\pi\)
0.953245 0.302197i \(-0.0977201\pi\)
\(18\) 3.11723 19.2711i 0.173179 1.07062i
\(19\) 22.0768 1.16194 0.580969 0.813926i \(-0.302674\pi\)
0.580969 + 0.813926i \(0.302674\pi\)
\(20\) 3.75693i 0.187846i
\(21\) 2.99438 37.2638i 0.142589 1.77447i
\(22\) 0 0
\(23\) 22.3094i 0.969972i 0.874522 + 0.484986i \(0.161175\pi\)
−0.874522 + 0.484986i \(0.838825\pi\)
\(24\) 21.3734 + 1.71748i 0.890558 + 0.0715618i
\(25\) −3.41164 −0.136466
\(26\) 8.35631i 0.321397i
\(27\) −6.43243 + 26.2226i −0.238238 + 0.971207i
\(28\) −8.78310 −0.313682
\(29\) 10.8453i 0.373976i 0.982362 + 0.186988i \(0.0598726\pi\)
−0.982362 + 0.186988i \(0.940127\pi\)
\(30\) −2.77820 + 34.5735i −0.0926065 + 1.15245i
\(31\) −18.9176 −0.610246 −0.305123 0.952313i \(-0.598698\pi\)
−0.305123 + 0.952313i \(0.598698\pi\)
\(32\) 11.1530i 0.348531i
\(33\) 0 0
\(34\) 22.2865 0.655484
\(35\) 66.4220i 1.89777i
\(36\) 6.26208 + 1.01293i 0.173947 + 0.0281370i
\(37\) −5.71155 −0.154366 −0.0771831 0.997017i \(-0.524593\pi\)
−0.0771831 + 0.997017i \(0.524593\pi\)
\(38\) 47.8860i 1.26016i
\(39\) −0.925732 + 11.5204i −0.0237367 + 0.295394i
\(40\) −38.0976 −0.952441
\(41\) 26.0142i 0.634492i 0.948343 + 0.317246i \(0.102758\pi\)
−0.948343 + 0.317246i \(0.897242\pi\)
\(42\) 80.8275 + 6.49499i 1.92446 + 0.154643i
\(43\) 62.1199 1.44465 0.722324 0.691555i \(-0.243074\pi\)
0.722324 + 0.691555i \(0.243074\pi\)
\(44\) 0 0
\(45\) 7.66028 47.3568i 0.170228 1.05237i
\(46\) −48.3904 −1.05196
\(47\) 57.0848i 1.21457i 0.794484 + 0.607285i \(0.207741\pi\)
−0.794484 + 0.607285i \(0.792259\pi\)
\(48\) −4.40279 + 54.7910i −0.0917248 + 1.14148i
\(49\) 106.284 2.16907
\(50\) 7.40007i 0.148001i
\(51\) −30.7251 2.46895i −0.602452 0.0484107i
\(52\) 2.71536 0.0522184
\(53\) 55.7779i 1.05241i −0.850357 0.526207i \(-0.823614\pi\)
0.850357 0.526207i \(-0.176386\pi\)
\(54\) −56.8784 13.9523i −1.05330 0.258377i
\(55\) 0 0
\(56\) 89.0663i 1.59047i
\(57\) 5.30492 66.0176i 0.0930688 1.15820i
\(58\) −23.5242 −0.405589
\(59\) 67.0487i 1.13642i −0.822884 0.568209i \(-0.807636\pi\)
0.822884 0.568209i \(-0.192364\pi\)
\(60\) −11.2346 0.902766i −0.187243 0.0150461i
\(61\) −20.3248 −0.333194 −0.166597 0.986025i \(-0.553278\pi\)
−0.166597 + 0.986025i \(0.553278\pi\)
\(62\) 41.0335i 0.661830i
\(63\) −110.713 17.9085i −1.75734 0.284262i
\(64\) −49.0986 −0.767165
\(65\) 20.5348i 0.315920i
\(66\) 0 0
\(67\) −88.3646 −1.31887 −0.659437 0.751760i \(-0.729205\pi\)
−0.659437 + 0.751760i \(0.729205\pi\)
\(68\) 7.24192i 0.106499i
\(69\) 66.7130 + 5.36080i 0.966855 + 0.0776927i
\(70\) −144.073 −2.05819
\(71\) 106.717i 1.50305i −0.659703 0.751526i \(-0.729318\pi\)
0.659703 0.751526i \(-0.270682\pi\)
\(72\) 10.2718 63.5015i 0.142664 0.881965i
\(73\) 19.6558 0.269257 0.134629 0.990896i \(-0.457016\pi\)
0.134629 + 0.990896i \(0.457016\pi\)
\(74\) 12.3887i 0.167415i
\(75\) −0.819797 + 10.2020i −0.0109306 + 0.136027i
\(76\) −15.5604 −0.204742
\(77\) 0 0
\(78\) −24.9884 2.00797i −0.320364 0.0257432i
\(79\) 35.7157 0.452097 0.226049 0.974116i \(-0.427419\pi\)
0.226049 + 0.974116i \(0.427419\pi\)
\(80\) 97.6638i 1.22080i
\(81\) 76.8693 + 25.5364i 0.949004 + 0.315264i
\(82\) −56.4263 −0.688126
\(83\) 81.3571i 0.980206i 0.871665 + 0.490103i \(0.163041\pi\)
−0.871665 + 0.490103i \(0.836959\pi\)
\(84\) −2.11053 + 26.2647i −0.0251253 + 0.312674i
\(85\) 54.7668 0.644315
\(86\) 134.742i 1.56677i
\(87\) 32.4314 + 2.60606i 0.372775 + 0.0299547i
\(88\) 0 0
\(89\) 120.618i 1.35526i −0.735405 0.677628i \(-0.763008\pi\)
0.735405 0.677628i \(-0.236992\pi\)
\(90\) 102.720 + 16.6156i 1.14133 + 0.184618i
\(91\) −48.0072 −0.527552
\(92\) 15.7243i 0.170916i
\(93\) −4.54579 + 56.5705i −0.0488794 + 0.608285i
\(94\) −123.820 −1.31724
\(95\) 117.675i 1.23869i
\(96\) −33.3515 2.68000i −0.347411 0.0279166i
\(97\) −85.3365 −0.879757 −0.439879 0.898057i \(-0.644979\pi\)
−0.439879 + 0.898057i \(0.644979\pi\)
\(98\) 230.537i 2.35242i
\(99\) 0 0
\(100\) 2.40463 0.0240463
\(101\) 62.9870i 0.623634i −0.950142 0.311817i \(-0.899062\pi\)
0.950142 0.311817i \(-0.100938\pi\)
\(102\) 5.35530 66.6446i 0.0525029 0.653378i
\(103\) 5.92433 0.0575178 0.0287589 0.999586i \(-0.490844\pi\)
0.0287589 + 0.999586i \(0.490844\pi\)
\(104\) 27.5355i 0.264764i
\(105\) 198.626 + 15.9608i 1.89167 + 0.152008i
\(106\) 120.986 1.14137
\(107\) 132.855i 1.24164i −0.783954 0.620819i \(-0.786800\pi\)
0.783954 0.620819i \(-0.213200\pi\)
\(108\) 4.53377 18.4825i 0.0419794 0.171134i
\(109\) −91.4741 −0.839212 −0.419606 0.907706i \(-0.637832\pi\)
−0.419606 + 0.907706i \(0.637832\pi\)
\(110\) 0 0
\(111\) −1.37245 + 17.0796i −0.0123644 + 0.153870i
\(112\) −228.323 −2.03860
\(113\) 84.6038i 0.748706i −0.927286 0.374353i \(-0.877865\pi\)
0.927286 0.374353i \(-0.122135\pi\)
\(114\) 143.196 + 11.5067i 1.25611 + 0.100936i
\(115\) −118.915 −1.03404
\(116\) 7.64410i 0.0658974i
\(117\) 34.2276 + 5.53655i 0.292544 + 0.0473209i
\(118\) 145.433 1.23248
\(119\) 128.036i 1.07593i
\(120\) −9.15462 + 113.926i −0.0762885 + 0.949381i
\(121\) 0 0
\(122\) 44.0858i 0.361359i
\(123\) 77.7917 + 6.25104i 0.632453 + 0.0508215i
\(124\) 13.3337 0.107530
\(125\) 115.071i 0.920572i
\(126\) 38.8447 240.143i 0.308291 1.90589i
\(127\) 35.2600 0.277638 0.138819 0.990318i \(-0.455669\pi\)
0.138819 + 0.990318i \(0.455669\pi\)
\(128\) 151.110i 1.18055i
\(129\) 14.9270 185.761i 0.115713 1.44001i
\(130\) 44.5413 0.342625
\(131\) 119.526i 0.912414i −0.889874 0.456207i \(-0.849208\pi\)
0.889874 0.456207i \(-0.150792\pi\)
\(132\) 0 0
\(133\) 275.106 2.06847
\(134\) 191.668i 1.43036i
\(135\) −139.773 34.2865i −1.03536 0.253974i
\(136\) 73.4377 0.539983
\(137\) 67.5636i 0.493165i −0.969122 0.246582i \(-0.920692\pi\)
0.969122 0.246582i \(-0.0793076\pi\)
\(138\) −11.6279 + 144.705i −0.0842602 + 1.04858i
\(139\) −40.8446 −0.293846 −0.146923 0.989148i \(-0.546937\pi\)
−0.146923 + 0.989148i \(0.546937\pi\)
\(140\) 46.8162i 0.334401i
\(141\) 170.704 + 13.7171i 1.21067 + 0.0972845i
\(142\) 231.475 1.63011
\(143\) 0 0
\(144\) 162.787 + 26.3319i 1.13046 + 0.182860i
\(145\) −57.8083 −0.398678
\(146\) 42.6346i 0.292018i
\(147\) 25.5394 317.828i 0.173738 2.16210i
\(148\) 4.02567 0.0272005
\(149\) 126.283i 0.847535i −0.905771 0.423768i \(-0.860707\pi\)
0.905771 0.423768i \(-0.139293\pi\)
\(150\) −22.1289 1.77819i −0.147526 0.0118546i
\(151\) 144.453 0.956645 0.478322 0.878184i \(-0.341245\pi\)
0.478322 + 0.878184i \(0.341245\pi\)
\(152\) 157.792i 1.03811i
\(153\) −14.7661 + 91.2858i −0.0965104 + 0.596639i
\(154\) 0 0
\(155\) 100.836i 0.650553i
\(156\) 0.652484 8.11990i 0.00418259 0.0520507i
\(157\) −21.7969 −0.138834 −0.0694168 0.997588i \(-0.522114\pi\)
−0.0694168 + 0.997588i \(0.522114\pi\)
\(158\) 77.4695i 0.490313i
\(159\) −166.796 13.4031i −1.04903 0.0842961i
\(160\) 59.4484 0.371552
\(161\) 278.004i 1.72673i
\(162\) −55.3901 + 166.734i −0.341914 + 1.02922i
\(163\) −116.768 −0.716367 −0.358184 0.933651i \(-0.616604\pi\)
−0.358184 + 0.933651i \(0.616604\pi\)
\(164\) 18.3356i 0.111802i
\(165\) 0 0
\(166\) −176.469 −1.06306
\(167\) 7.56849i 0.0453203i −0.999743 0.0226602i \(-0.992786\pi\)
0.999743 0.0226602i \(-0.00721357\pi\)
\(168\) 266.340 + 21.4021i 1.58536 + 0.127393i
\(169\) −154.158 −0.912179
\(170\) 118.793i 0.698780i
\(171\) −196.142 31.7273i −1.14703 0.185540i
\(172\) −43.7840 −0.254558
\(173\) 62.4526i 0.360998i 0.983575 + 0.180499i \(0.0577712\pi\)
−0.983575 + 0.180499i \(0.942229\pi\)
\(174\) −5.65271 + 70.3457i −0.0324868 + 0.404286i
\(175\) −42.5135 −0.242935
\(176\) 0 0
\(177\) −200.500 16.1114i −1.13277 0.0910247i
\(178\) 261.627 1.46982
\(179\) 212.091i 1.18486i −0.805620 0.592432i \(-0.798168\pi\)
0.805620 0.592432i \(-0.201832\pi\)
\(180\) −5.39919 + 33.3785i −0.0299955 + 0.185436i
\(181\) 192.168 1.06170 0.530852 0.847464i \(-0.321872\pi\)
0.530852 + 0.847464i \(0.321872\pi\)
\(182\) 104.131i 0.572146i
\(183\) −4.88393 + 60.7785i −0.0266881 + 0.332123i
\(184\) −159.454 −0.866601
\(185\) 30.4440i 0.164562i
\(186\) −122.705 9.86009i −0.659704 0.0530112i
\(187\) 0 0
\(188\) 40.2351i 0.214016i
\(189\) −80.1565 + 326.768i −0.424109 + 1.72893i
\(190\) −255.245 −1.34339
\(191\) 215.925i 1.13050i 0.824920 + 0.565249i \(0.191220\pi\)
−0.824920 + 0.565249i \(0.808780\pi\)
\(192\) −11.7981 + 146.822i −0.0614484 + 0.764700i
\(193\) −118.484 −0.613909 −0.306954 0.951724i \(-0.599310\pi\)
−0.306954 + 0.951724i \(0.599310\pi\)
\(194\) 185.100i 0.954124i
\(195\) −61.4065 4.93439i −0.314905 0.0253046i
\(196\) −74.9123 −0.382206
\(197\) 78.5365i 0.398662i −0.979932 0.199331i \(-0.936123\pi\)
0.979932 0.199331i \(-0.0638769\pi\)
\(198\) 0 0
\(199\) −223.166 −1.12144 −0.560719 0.828006i \(-0.689475\pi\)
−0.560719 + 0.828006i \(0.689475\pi\)
\(200\) 24.3845i 0.121922i
\(201\) −21.2335 + 264.242i −0.105639 + 1.31464i
\(202\) 136.623 0.676350
\(203\) 135.147i 0.665748i
\(204\) 21.6559 + 1.74019i 0.106157 + 0.00853033i
\(205\) −138.662 −0.676401
\(206\) 12.8502i 0.0623799i
\(207\) 32.0615 198.208i 0.154886 0.957526i
\(208\) 70.5876 0.339363
\(209\) 0 0
\(210\) −34.6199 + 430.831i −0.164857 + 2.05158i
\(211\) −68.8093 −0.326110 −0.163055 0.986617i \(-0.552135\pi\)
−0.163055 + 0.986617i \(0.552135\pi\)
\(212\) 39.3139i 0.185443i
\(213\) −319.122 25.6434i −1.49822 0.120391i
\(214\) 288.171 1.34659
\(215\) 331.115i 1.54007i
\(216\) −187.424 45.9754i −0.867704 0.212849i
\(217\) −235.738 −1.08635
\(218\) 198.413i 0.910151i
\(219\) 4.72316 58.7779i 0.0215670 0.268392i
\(220\) 0 0
\(221\) 39.5833i 0.179110i
\(222\) −37.0467 2.97693i −0.166877 0.0134096i
\(223\) 362.880 1.62726 0.813632 0.581380i \(-0.197487\pi\)
0.813632 + 0.581380i \(0.197487\pi\)
\(224\) 138.981i 0.620451i
\(225\) 30.3108 + 4.90298i 0.134715 + 0.0217910i
\(226\) 183.511 0.811995
\(227\) 385.017i 1.69611i −0.529910 0.848054i \(-0.677774\pi\)
0.529910 0.848054i \(-0.322226\pi\)
\(228\) −3.73907 + 46.5312i −0.0163994 + 0.204084i
\(229\) 114.821 0.501400 0.250700 0.968065i \(-0.419339\pi\)
0.250700 + 0.968065i \(0.419339\pi\)
\(230\) 257.933i 1.12145i
\(231\) 0 0
\(232\) −77.5161 −0.334121
\(233\) 44.4204i 0.190645i −0.995446 0.0953227i \(-0.969612\pi\)
0.995446 0.0953227i \(-0.0303883\pi\)
\(234\) −12.0091 + 74.2418i −0.0513210 + 0.317273i
\(235\) −304.276 −1.29479
\(236\) 47.2579i 0.200245i
\(237\) 8.58226 106.803i 0.0362121 0.450645i
\(238\) 277.718 1.16688
\(239\) 463.337i 1.93865i 0.245789 + 0.969323i \(0.420953\pi\)
−0.245789 + 0.969323i \(0.579047\pi\)
\(240\) −292.050 23.4680i −1.21688 0.0977834i
\(241\) −345.385 −1.43313 −0.716566 0.697520i \(-0.754287\pi\)
−0.716566 + 0.697520i \(0.754287\pi\)
\(242\) 0 0
\(243\) 94.8343 223.731i 0.390265 0.920703i
\(244\) 14.3255 0.0587112
\(245\) 566.522i 2.31234i
\(246\) −13.5589 + 168.735i −0.0551175 + 0.685915i
\(247\) −85.0509 −0.344336
\(248\) 135.212i 0.545211i
\(249\) 243.287 + 19.5496i 0.977056 + 0.0785125i
\(250\) −249.597 −0.998389
\(251\) 215.718i 0.859436i 0.902963 + 0.429718i \(0.141387\pi\)
−0.902963 + 0.429718i \(0.858613\pi\)
\(252\) 78.0336 + 12.6225i 0.309657 + 0.0500892i
\(253\) 0 0
\(254\) 76.4812i 0.301107i
\(255\) 13.1601 163.773i 0.0516083 0.642245i
\(256\) 131.372 0.513173
\(257\) 69.8784i 0.271900i −0.990716 0.135950i \(-0.956591\pi\)
0.990716 0.135950i \(-0.0434087\pi\)
\(258\) 402.927 + 32.3776i 1.56173 + 0.125495i
\(259\) −71.1734 −0.274801
\(260\) 14.4736i 0.0556675i
\(261\) 15.5861 96.3554i 0.0597170 0.369178i
\(262\) 259.260 0.989541
\(263\) 445.231i 1.69290i −0.532472 0.846448i \(-0.678737\pi\)
0.532472 0.846448i \(-0.321263\pi\)
\(264\) 0 0
\(265\) 297.311 1.12193
\(266\) 596.722i 2.24332i
\(267\) −360.691 28.9837i −1.35090 0.108553i
\(268\) 62.2820 0.232396
\(269\) 134.124i 0.498603i 0.968426 + 0.249301i \(0.0802010\pi\)
−0.968426 + 0.249301i \(0.919799\pi\)
\(270\) 74.3696 303.177i 0.275443 1.12288i
\(271\) −204.760 −0.755573 −0.377787 0.925893i \(-0.623315\pi\)
−0.377787 + 0.925893i \(0.623315\pi\)
\(272\) 188.259i 0.692127i
\(273\) −11.5358 + 143.559i −0.0422558 + 0.525857i
\(274\) 146.550 0.534853
\(275\) 0 0
\(276\) −47.0213 3.77845i −0.170367 0.0136900i
\(277\) −58.4995 −0.211190 −0.105595 0.994409i \(-0.533675\pi\)
−0.105595 + 0.994409i \(0.533675\pi\)
\(278\) 88.5944i 0.318685i
\(279\) 168.074 + 27.1871i 0.602415 + 0.0974447i
\(280\) −474.746 −1.69552
\(281\) 1.42405i 0.00506781i −0.999997 0.00253390i \(-0.999193\pi\)
0.999997 0.00253390i \(-0.000806567\pi\)
\(282\) −29.7533 + 370.268i −0.105508 + 1.31301i
\(283\) 293.260 1.03625 0.518127 0.855304i \(-0.326630\pi\)
0.518127 + 0.855304i \(0.326630\pi\)
\(284\) 75.2172i 0.264849i
\(285\) 351.891 + 28.2766i 1.23471 + 0.0992161i
\(286\) 0 0
\(287\) 324.170i 1.12951i
\(288\) −16.0283 + 99.0890i −0.0556539 + 0.344059i
\(289\) 183.431 0.634708
\(290\) 125.390i 0.432379i
\(291\) −20.5058 + 255.187i −0.0704667 + 0.876931i
\(292\) −13.8540 −0.0474452
\(293\) 324.008i 1.10583i 0.833238 + 0.552914i \(0.186484\pi\)
−0.833238 + 0.552914i \(0.813516\pi\)
\(294\) 689.389 + 55.3966i 2.34486 + 0.188424i
\(295\) 357.387 1.21148
\(296\) 40.8229i 0.137915i
\(297\) 0 0
\(298\) 273.915 0.919178
\(299\) 85.9468i 0.287448i
\(300\) 0.577818 7.19071i 0.00192606 0.0239690i
\(301\) 774.095 2.57174
\(302\) 313.328i 1.03751i
\(303\) −188.354 15.1354i −0.621630 0.0499518i
\(304\) −404.503 −1.33060
\(305\) 108.336i 0.355201i
\(306\) −198.004 32.0286i −0.647073 0.104668i
\(307\) −292.921 −0.954140 −0.477070 0.878865i \(-0.658301\pi\)
−0.477070 + 0.878865i \(0.658301\pi\)
\(308\) 0 0
\(309\) 1.42358 17.7159i 0.00460706 0.0573330i
\(310\) 218.719 0.705545
\(311\) 338.912i 1.08975i −0.838517 0.544875i \(-0.816577\pi\)
0.838517 0.544875i \(-0.183423\pi\)
\(312\) −82.3410 6.61660i −0.263913 0.0212071i
\(313\) −356.787 −1.13989 −0.569947 0.821681i \(-0.693036\pi\)
−0.569947 + 0.821681i \(0.693036\pi\)
\(314\) 47.2788i 0.150569i
\(315\) 95.4570 590.127i 0.303038 1.87342i
\(316\) −25.1735 −0.0796629
\(317\) 482.485i 1.52204i −0.648731 0.761018i \(-0.724700\pi\)
0.648731 0.761018i \(-0.275300\pi\)
\(318\) 29.0721 361.791i 0.0914217 1.13771i
\(319\) 0 0
\(320\) 261.708i 0.817838i
\(321\) −397.285 31.9243i −1.23765 0.0994526i
\(322\) −603.007 −1.87269
\(323\) 226.833i 0.702268i
\(324\) −54.1798 17.9988i −0.167222 0.0555520i
\(325\) 13.1434 0.0404411
\(326\) 253.277i 0.776922i
\(327\) −21.9807 + 273.541i −0.0672191 + 0.836516i
\(328\) −185.934 −0.566873
\(329\) 711.351i 2.16216i
\(330\) 0 0
\(331\) −131.863 −0.398378 −0.199189 0.979961i \(-0.563831\pi\)
−0.199189 + 0.979961i \(0.563831\pi\)
\(332\) 57.3429i 0.172720i
\(333\) 50.7444 + 8.20825i 0.152386 + 0.0246494i
\(334\) 16.4165 0.0491513
\(335\) 471.006i 1.40599i
\(336\) −54.8645 + 682.767i −0.163287 + 2.03205i
\(337\) 550.415 1.63328 0.816639 0.577149i \(-0.195835\pi\)
0.816639 + 0.577149i \(0.195835\pi\)
\(338\) 334.379i 0.989286i
\(339\) −252.996 20.3298i −0.746300 0.0599698i
\(340\) −38.6013 −0.113533
\(341\) 0 0
\(342\) 68.8184 425.444i 0.201223 1.24399i
\(343\) 713.836 2.08115
\(344\) 443.997i 1.29069i
\(345\) −28.5744 + 355.598i −0.0828245 + 1.03072i
\(346\) −135.463 −0.391513
\(347\) 123.006i 0.354484i 0.984167 + 0.177242i \(0.0567175\pi\)
−0.984167 + 0.177242i \(0.943282\pi\)
\(348\) −22.8586 1.83683i −0.0656857 0.00527825i
\(349\) 123.310 0.353323 0.176662 0.984272i \(-0.443470\pi\)
0.176662 + 0.984272i \(0.443470\pi\)
\(350\) 92.2145i 0.263470i
\(351\) 24.7810 101.023i 0.0706010 0.287813i
\(352\) 0 0
\(353\) 473.431i 1.34116i 0.741836 + 0.670582i \(0.233956\pi\)
−0.741836 + 0.670582i \(0.766044\pi\)
\(354\) 34.9466 434.896i 0.0987192 1.22852i
\(355\) 568.828 1.60233
\(356\) 85.0150i 0.238806i
\(357\) −382.874 30.7663i −1.07248 0.0861801i
\(358\) 460.038 1.28502
\(359\) 96.0299i 0.267493i 0.991016 + 0.133746i \(0.0427007\pi\)
−0.991016 + 0.133746i \(0.957299\pi\)
\(360\) 338.479 + 54.7513i 0.940220 + 0.152087i
\(361\) 126.386 0.350099
\(362\) 416.825i 1.15145i
\(363\) 0 0
\(364\) 33.8369 0.0929586
\(365\) 104.770i 0.287042i
\(366\) −131.832 10.5935i −0.360198 0.0289441i
\(367\) 450.970 1.22880 0.614400 0.788995i \(-0.289398\pi\)
0.614400 + 0.788995i \(0.289398\pi\)
\(368\) 408.764i 1.11077i
\(369\) 37.3857 231.123i 0.101316 0.626350i
\(370\) 66.0350 0.178473
\(371\) 695.065i 1.87349i
\(372\) 3.20401 39.8726i 0.00861292 0.107184i
\(373\) 522.030 1.39954 0.699772 0.714366i \(-0.253285\pi\)
0.699772 + 0.714366i \(0.253285\pi\)
\(374\) 0 0
\(375\) 344.105 + 27.6510i 0.917614 + 0.0737359i
\(376\) −408.009 −1.08513
\(377\) 41.7816i 0.110826i
\(378\) −708.779 173.864i −1.87508 0.459959i
\(379\) 667.354 1.76083 0.880414 0.474206i \(-0.157265\pi\)
0.880414 + 0.474206i \(0.157265\pi\)
\(380\) 82.9409i 0.218266i
\(381\) 8.47277 105.440i 0.0222382 0.276746i
\(382\) −468.355 −1.22606
\(383\) 504.576i 1.31743i 0.752392 + 0.658716i \(0.228900\pi\)
−0.752392 + 0.658716i \(0.771100\pi\)
\(384\) −451.873 36.3108i −1.17675 0.0945593i
\(385\) 0 0
\(386\) 257.000i 0.665803i
\(387\) −551.905 89.2744i −1.42611 0.230683i
\(388\) 60.1477 0.155020
\(389\) 92.4975i 0.237783i 0.992907 + 0.118891i \(0.0379340\pi\)
−0.992907 + 0.118891i \(0.962066\pi\)
\(390\) 10.7030 133.195i 0.0274436 0.341525i
\(391\) 229.222 0.586245
\(392\) 759.659i 1.93790i
\(393\) −357.426 28.7214i −0.909482 0.0730825i
\(394\) 170.350 0.432362
\(395\) 190.374i 0.481959i
\(396\) 0 0
\(397\) −97.3003 −0.245089 −0.122544 0.992463i \(-0.539105\pi\)
−0.122544 + 0.992463i \(0.539105\pi\)
\(398\) 484.061i 1.21623i
\(399\) 66.1063 822.666i 0.165680 2.06182i
\(400\) 62.5100 0.156275
\(401\) 239.040i 0.596109i 0.954549 + 0.298054i \(0.0963377\pi\)
−0.954549 + 0.298054i \(0.903662\pi\)
\(402\) −573.157 46.0567i −1.42576 0.114569i
\(403\) 72.8801 0.180844
\(404\) 44.3951i 0.109889i
\(405\) −136.116 + 409.733i −0.336088 + 1.01169i
\(406\) −293.142 −0.722024
\(407\) 0 0
\(408\) 17.6466 219.605i 0.0432515 0.538248i
\(409\) 469.742 1.14851 0.574256 0.818676i \(-0.305291\pi\)
0.574256 + 0.818676i \(0.305291\pi\)
\(410\) 300.767i 0.733578i
\(411\) −202.039 16.2351i −0.491580 0.0395015i
\(412\) −4.17565 −0.0101351
\(413\) 835.514i 2.02304i
\(414\) 429.925 + 69.5433i 1.03847 + 0.167979i
\(415\) −433.654 −1.04495
\(416\) 42.9670i 0.103286i
\(417\) −9.81470 + 122.140i −0.0235365 + 0.292902i
\(418\) 0 0
\(419\) 31.5367i 0.0752667i 0.999292 + 0.0376333i \(0.0119819\pi\)
−0.999292 + 0.0376333i \(0.988018\pi\)
\(420\) −139.997 11.2496i −0.333327 0.0267849i
\(421\) −558.710 −1.32710 −0.663551 0.748131i \(-0.730951\pi\)
−0.663551 + 0.748131i \(0.730951\pi\)
\(422\) 149.252i 0.353677i
\(423\) 82.0382 507.171i 0.193944 1.19898i
\(424\) 398.668 0.940256
\(425\) 35.0536i 0.0824791i
\(426\) 55.6221 692.194i 0.130568 1.62487i
\(427\) −253.274 −0.593147
\(428\) 93.6404i 0.218786i
\(429\) 0 0
\(430\) −718.209 −1.67025
\(431\) 747.635i 1.73465i 0.497740 + 0.867326i \(0.334163\pi\)
−0.497740 + 0.867326i \(0.665837\pi\)
\(432\) 117.858 480.464i 0.272821 1.11219i
\(433\) −568.525 −1.31299 −0.656496 0.754330i \(-0.727962\pi\)
−0.656496 + 0.754330i \(0.727962\pi\)
\(434\) 511.331i 1.17818i
\(435\) −13.8910 + 172.868i −0.0319333 + 0.397397i
\(436\) 64.4737 0.147875
\(437\) 492.519i 1.12705i
\(438\) 127.493 + 10.2448i 0.291080 + 0.0233900i
\(439\) −543.687 −1.23847 −0.619233 0.785207i \(-0.712556\pi\)
−0.619233 + 0.785207i \(0.712556\pi\)
\(440\) 0 0
\(441\) −944.284 152.744i −2.14123 0.346359i
\(442\) −85.8586 −0.194250
\(443\) 15.9346i 0.0359698i −0.999838 0.0179849i \(-0.994275\pi\)
0.999838 0.0179849i \(-0.00572507\pi\)
\(444\) 0.967344 12.0382i 0.00217870 0.0271131i
\(445\) 642.923 1.44477
\(446\) 787.109i 1.76482i
\(447\) −377.631 30.3450i −0.844812 0.0678858i
\(448\) −611.833 −1.36570
\(449\) 369.861i 0.823743i 0.911242 + 0.411872i \(0.135125\pi\)
−0.911242 + 0.411872i \(0.864875\pi\)
\(450\) −10.6349 + 65.7460i −0.0236330 + 0.146102i
\(451\) 0 0
\(452\) 59.6313i 0.131928i
\(453\) 34.7112 431.968i 0.0766253 0.953571i
\(454\) 835.125 1.83948
\(455\) 255.891i 0.562397i
\(456\) 471.856 + 37.9165i 1.03477 + 0.0831503i
\(457\) −47.1793 −0.103237 −0.0516185 0.998667i \(-0.516438\pi\)
−0.0516185 + 0.998667i \(0.516438\pi\)
\(458\) 249.053i 0.543784i
\(459\) 269.429 + 66.0913i 0.586992 + 0.143990i
\(460\) 83.8146 0.182206
\(461\) 731.265i 1.58626i 0.609053 + 0.793129i \(0.291550\pi\)
−0.609053 + 0.793129i \(0.708450\pi\)
\(462\) 0 0
\(463\) 247.761 0.535120 0.267560 0.963541i \(-0.413783\pi\)
0.267560 + 0.963541i \(0.413783\pi\)
\(464\) 198.714i 0.428262i
\(465\) −301.535 24.2302i −0.648463 0.0521080i
\(466\) 96.3506 0.206761
\(467\) 222.607i 0.476675i −0.971182 0.238338i \(-0.923398\pi\)
0.971182 0.238338i \(-0.0766024\pi\)
\(468\) −24.1247 3.90232i −0.0515484 0.00833830i
\(469\) −1101.14 −2.34784
\(470\) 659.994i 1.40424i
\(471\) −5.23765 + 65.1805i −0.0111203 + 0.138388i
\(472\) 479.226 1.01531
\(473\) 0 0
\(474\) 231.662 + 18.6154i 0.488738 + 0.0392731i
\(475\) −75.3182 −0.158565
\(476\) 90.2438i 0.189588i
\(477\) −80.1601 + 495.560i −0.168051 + 1.03891i
\(478\) −1005.01 −2.10252
\(479\) 788.075i 1.64525i 0.568583 + 0.822626i \(0.307492\pi\)
−0.568583 + 0.822626i \(0.692508\pi\)
\(480\) 14.2851 177.772i 0.0297606 0.370359i
\(481\) 22.0038 0.0457459
\(482\) 749.161i 1.55428i
\(483\) 831.331 + 66.8026i 1.72118 + 0.138308i
\(484\) 0 0
\(485\) 454.865i 0.937867i
\(486\) 485.286 + 205.702i 0.998531 + 0.423254i
\(487\) −314.723 −0.646248 −0.323124 0.946357i \(-0.604733\pi\)
−0.323124 + 0.946357i \(0.604733\pi\)
\(488\) 145.270i 0.297685i
\(489\) −28.0586 + 349.178i −0.0573795 + 0.714065i
\(490\) −1228.82 −2.50780
\(491\) 706.608i 1.43912i −0.694430 0.719560i \(-0.744343\pi\)
0.694430 0.719560i \(-0.255657\pi\)
\(492\) −54.8300 4.40592i −0.111443 0.00895513i
\(493\) 111.432 0.226029
\(494\) 184.481i 0.373443i
\(495\) 0 0
\(496\) 346.619 0.698828
\(497\) 1329.83i 2.67571i
\(498\) −42.4043 + 527.705i −0.0851492 + 1.05965i
\(499\) −223.148 −0.447190 −0.223595 0.974682i \(-0.571779\pi\)
−0.223595 + 0.974682i \(0.571779\pi\)
\(500\) 81.1058i 0.162212i
\(501\) −22.6325 1.81866i −0.0451747 0.00363006i
\(502\) −467.906 −0.932085
\(503\) 285.889i 0.568368i 0.958770 + 0.284184i \(0.0917226\pi\)
−0.958770 + 0.284184i \(0.908277\pi\)
\(504\) 128.000 791.311i 0.253968 1.57006i
\(505\) 335.737 0.664826
\(506\) 0 0
\(507\) −37.0433 + 460.989i −0.0730636 + 0.909248i
\(508\) −24.8523 −0.0489219
\(509\) 291.204i 0.572110i −0.958213 0.286055i \(-0.907656\pi\)
0.958213 0.286055i \(-0.0923439\pi\)
\(510\) 355.233 + 28.5451i 0.696535 + 0.0559708i
\(511\) 244.937 0.479328
\(512\) 319.485i 0.623994i
\(513\) −142.008 + 578.911i −0.276818 + 1.12848i
\(514\) 151.570 0.294884
\(515\) 31.5782i 0.0613169i
\(516\) −10.5210 + 130.930i −0.0203896 + 0.253740i
\(517\) 0 0
\(518\) 154.380i 0.298030i
\(519\) 186.756 + 15.0070i 0.359838 + 0.0289152i
\(520\) 146.771 0.282252
\(521\) 617.998i 1.18618i 0.805137 + 0.593088i \(0.202092\pi\)
−0.805137 + 0.593088i \(0.797908\pi\)
\(522\) 209.001 + 33.8073i 0.400385 + 0.0647649i
\(523\) 310.931 0.594514 0.297257 0.954798i \(-0.403928\pi\)
0.297257 + 0.954798i \(0.403928\pi\)
\(524\) 84.2457i 0.160774i
\(525\) −10.2157 + 127.131i −0.0194586 + 0.242154i
\(526\) 965.735 1.83600
\(527\) 194.373i 0.368829i
\(528\) 0 0
\(529\) 31.2927 0.0591545
\(530\) 644.885i 1.21676i
\(531\) −96.3577 + 595.695i −0.181465 + 1.12184i
\(532\) −193.903 −0.364479
\(533\) 100.220i 0.188029i
\(534\) 62.8674 782.360i 0.117729 1.46509i
\(535\) 708.153 1.32365
\(536\) 631.580i 1.17832i
\(537\) −634.228 50.9641i −1.18106 0.0949052i
\(538\) −290.924 −0.540750
\(539\) 0 0
\(540\) 98.5163 + 24.1662i 0.182438 + 0.0447522i
\(541\) −119.286 −0.220491 −0.110245 0.993904i \(-0.535164\pi\)
−0.110245 + 0.993904i \(0.535164\pi\)
\(542\) 444.138i 0.819443i
\(543\) 46.1769 574.653i 0.0850403 1.05829i
\(544\) −114.594 −0.210650
\(545\) 487.581i 0.894643i
\(546\) −311.388 25.0219i −0.570308 0.0458277i
\(547\) 736.527 1.34649 0.673243 0.739422i \(-0.264901\pi\)
0.673243 + 0.739422i \(0.264901\pi\)
\(548\) 47.6208i 0.0868993i
\(549\) 180.576 + 29.2094i 0.328918 + 0.0532047i
\(550\) 0 0
\(551\) 239.430i 0.434537i
\(552\) −38.3159 + 476.827i −0.0694129 + 0.863816i
\(553\) 445.064 0.804818
\(554\) 126.889i 0.229042i
\(555\) −91.0387 7.31552i −0.164034 0.0131811i
\(556\) 28.7885 0.0517779
\(557\) 409.020i 0.734326i −0.930157 0.367163i \(-0.880329\pi\)
0.930157 0.367163i \(-0.119671\pi\)
\(558\) −58.9705 + 364.563i −0.105682 + 0.653338i
\(559\) −239.317 −0.428116
\(560\) 1217.02i 2.17325i
\(561\) 0 0
\(562\) 3.08886 0.00549619
\(563\) 468.336i 0.831859i 0.909397 + 0.415929i \(0.136544\pi\)
−0.909397 + 0.415929i \(0.863456\pi\)
\(564\) −120.317 9.66823i −0.213329 0.0171423i
\(565\) 450.960 0.798159
\(566\) 636.098i 1.12385i
\(567\) 957.892 + 318.217i 1.68940 + 0.561230i
\(568\) 762.750 1.34287
\(569\) 208.533i 0.366491i 0.983067 + 0.183245i \(0.0586603\pi\)
−0.983067 + 0.183245i \(0.941340\pi\)
\(570\) −61.3337 + 763.273i −0.107603 + 1.33908i
\(571\) −177.630 −0.311086 −0.155543 0.987829i \(-0.549713\pi\)
−0.155543 + 0.987829i \(0.549713\pi\)
\(572\) 0 0
\(573\) 645.694 + 51.8854i 1.12687 + 0.0905505i
\(574\) −703.146 −1.22499
\(575\) 76.1116i 0.132368i
\(576\) 436.217 + 70.5611i 0.757322 + 0.122502i
\(577\) −194.396 −0.336908 −0.168454 0.985709i \(-0.553878\pi\)
−0.168454 + 0.985709i \(0.553878\pi\)
\(578\) 397.872i 0.688360i
\(579\) −28.4711 + 354.311i −0.0491728 + 0.611936i
\(580\) 40.7450 0.0702500
\(581\) 1013.82i 1.74495i
\(582\) −553.516 44.4784i −0.951058 0.0764234i
\(583\) 0 0
\(584\) 140.488i 0.240562i
\(585\) −29.5112 + 182.442i −0.0504465 + 0.311867i
\(586\) −702.792 −1.19930
\(587\) 439.156i 0.748136i −0.927401 0.374068i \(-0.877963\pi\)
0.927401 0.374068i \(-0.122037\pi\)
\(588\) −18.0010 + 224.015i −0.0306139 + 0.380978i
\(589\) −417.641 −0.709067
\(590\) 775.194i 1.31389i
\(591\) −234.852 18.8718i −0.397381 0.0319320i
\(592\) 104.650 0.176774
\(593\) 987.710i 1.66561i −0.553563 0.832807i \(-0.686732\pi\)
0.553563 0.832807i \(-0.313268\pi\)
\(594\) 0 0
\(595\) 682.466 1.14700
\(596\) 89.0079i 0.149342i
\(597\) −53.6255 + 667.348i −0.0898249 + 1.11784i
\(598\) 186.424 0.311746
\(599\) 317.730i 0.530433i 0.964189 + 0.265217i \(0.0854435\pi\)
−0.964189 + 0.265217i \(0.914557\pi\)
\(600\) −72.9184 5.85944i −0.121531 0.00976573i
\(601\) −176.924 −0.294383 −0.147192 0.989108i \(-0.547023\pi\)
−0.147192 + 0.989108i \(0.547023\pi\)
\(602\) 1679.06i 2.78914i
\(603\) 785.077 + 126.991i 1.30195 + 0.210599i
\(604\) −101.815 −0.168568
\(605\) 0 0
\(606\) 32.8296 408.551i 0.0541743 0.674177i
\(607\) −423.517 −0.697722 −0.348861 0.937175i \(-0.613431\pi\)
−0.348861 + 0.937175i \(0.613431\pi\)
\(608\) 246.223i 0.404972i
\(609\) 404.138 + 32.4749i 0.663608 + 0.0533250i
\(610\) 234.988 0.385227
\(611\) 219.919i 0.359933i
\(612\) 10.4076 64.3409i 0.0170059 0.105132i
\(613\) 995.062 1.62327 0.811633 0.584168i \(-0.198579\pi\)
0.811633 + 0.584168i \(0.198579\pi\)
\(614\) 635.364i 1.03479i
\(615\) −33.3197 + 414.650i −0.0541783 + 0.674228i
\(616\) 0 0
\(617\) 82.1697i 0.133176i −0.997781 0.0665881i \(-0.978789\pi\)
0.997781 0.0665881i \(-0.0212113\pi\)
\(618\) 38.4269 + 3.08784i 0.0621794 + 0.00499650i
\(619\) −823.362 −1.33015 −0.665074 0.746777i \(-0.731600\pi\)
−0.665074 + 0.746777i \(0.731600\pi\)
\(620\) 71.0721i 0.114632i
\(621\) −585.009 143.503i −0.942043 0.231084i
\(622\) 735.122 1.18187
\(623\) 1503.05i 2.41261i
\(624\) 16.9618 211.082i 0.0271823 0.338273i
\(625\) −698.652 −1.11784
\(626\) 773.893i 1.23625i
\(627\) 0 0
\(628\) 15.3631 0.0244635
\(629\) 58.6845i 0.0932981i
\(630\) 1280.02 + 207.052i 2.03178 + 0.328654i
\(631\) −238.417 −0.377840 −0.188920 0.981993i \(-0.560499\pi\)
−0.188920 + 0.981993i \(0.560499\pi\)
\(632\) 255.275i 0.403917i
\(633\) −16.5344 + 205.765i −0.0261208 + 0.325062i
\(634\) 1046.54 1.65069
\(635\) 187.945i 0.295976i
\(636\) 117.563 + 9.44690i 0.184847 + 0.0148536i
\(637\) −409.460 −0.642794
\(638\) 0 0
\(639\) −153.366 + 948.127i −0.240009 + 1.48377i
\(640\) 805.455 1.25852
\(641\) 1102.21i 1.71952i 0.510701 + 0.859759i \(0.329386\pi\)
−0.510701 + 0.859759i \(0.670614\pi\)
\(642\) 69.2458 861.736i 0.107859 1.34227i
\(643\) −58.4417 −0.0908892 −0.0454446 0.998967i \(-0.514470\pi\)
−0.0454446 + 0.998967i \(0.514470\pi\)
\(644\) 195.945i 0.304263i
\(645\) 990.153 + 79.5649i 1.53512 + 0.123356i
\(646\) 492.014 0.761632
\(647\) 957.445i 1.47982i −0.672704 0.739911i \(-0.734867\pi\)
0.672704 0.739911i \(-0.265133\pi\)
\(648\) −182.520 + 549.418i −0.281666 + 0.847867i
\(649\) 0 0
\(650\) 28.5088i 0.0438596i
\(651\) −56.6464 + 704.942i −0.0870145 + 1.08286i
\(652\) 82.3015 0.126229
\(653\) 1063.77i 1.62904i 0.580132 + 0.814522i \(0.303001\pi\)
−0.580132 + 0.814522i \(0.696999\pi\)
\(654\) −593.327 47.6774i −0.907227 0.0729012i
\(655\) 637.105 0.972680
\(656\) 476.645i 0.726594i
\(657\) −174.632 28.2479i −0.265802 0.0429953i
\(658\) −1542.96 −2.34493
\(659\) 91.2998i 0.138543i −0.997598 0.0692715i \(-0.977933\pi\)
0.997598 0.0692715i \(-0.0220675\pi\)
\(660\) 0 0
\(661\) −700.759 −1.06015 −0.530075 0.847951i \(-0.677836\pi\)
−0.530075 + 0.847951i \(0.677836\pi\)
\(662\) 286.019i 0.432053i
\(663\) 118.368 + 9.51162i 0.178534 + 0.0143463i
\(664\) −581.494 −0.875744
\(665\) 1466.39i 2.20509i
\(666\) −17.8042 + 110.068i −0.0267330 + 0.165267i
\(667\) −241.952 −0.362746
\(668\) 5.33450i 0.00798578i
\(669\) 87.1978 1085.14i 0.130341 1.62204i
\(670\) 1021.64 1.52484
\(671\) 0 0
\(672\) −415.603 33.3963i −0.618457 0.0496968i
\(673\) 986.110 1.46525 0.732623 0.680635i \(-0.238296\pi\)
0.732623 + 0.680635i \(0.238296\pi\)
\(674\) 1193.88i 1.77134i
\(675\) 21.9452 89.4621i 0.0325114 0.132536i
\(676\) 108.655 0.160733
\(677\) 806.842i 1.19179i −0.803062 0.595895i \(-0.796797\pi\)
0.803062 0.595895i \(-0.203203\pi\)
\(678\) 44.0965 548.764i 0.0650391 0.809386i
\(679\) −1063.40 −1.56613
\(680\) 391.442i 0.575650i
\(681\) −1151.34 92.5171i −1.69066 0.135855i
\(682\) 0 0
\(683\) 189.393i 0.277295i 0.990342 + 0.138648i \(0.0442755\pi\)
−0.990342 + 0.138648i \(0.955724\pi\)
\(684\) 138.247 + 22.3623i 0.202115 + 0.0326935i
\(685\) 360.131 0.525739
\(686\) 1548.35i 2.25708i
\(687\) 27.5907 343.355i 0.0401611 0.499789i
\(688\) −1138.19 −1.65435
\(689\) 214.884i 0.311879i
\(690\) −771.313 61.9797i −1.11785 0.0898257i
\(691\) −1276.88 −1.84787 −0.923936 0.382547i \(-0.875047\pi\)
−0.923936 + 0.382547i \(0.875047\pi\)
\(692\) 44.0184i 0.0636105i
\(693\) 0 0
\(694\) −266.808 −0.384449
\(695\) 217.712i 0.313255i
\(696\) −18.6266 + 231.801i −0.0267624 + 0.333047i
\(697\) 267.288 0.383483
\(698\) 267.466i 0.383190i
\(699\) −132.833 10.6739i −0.190033 0.0152703i
\(700\) 29.9648 0.0428069
\(701\) 754.729i 1.07665i −0.842739 0.538323i \(-0.819058\pi\)
0.842739 0.538323i \(-0.180942\pi\)
\(702\) 219.124 + 53.7514i 0.312143 + 0.0765690i
\(703\) −126.093 −0.179364
\(704\) 0 0
\(705\) −73.1157 + 909.896i −0.103710 + 1.29063i
\(706\) −1026.90 −1.45453
\(707\) 784.901i 1.11018i
\(708\) 141.318 + 11.3558i 0.199602 + 0.0160392i
\(709\) −688.403 −0.970949 −0.485474 0.874251i \(-0.661353\pi\)
−0.485474 + 0.874251i \(0.661353\pi\)
\(710\) 1233.82i 1.73778i
\(711\) −317.317 51.3281i −0.446296 0.0721914i
\(712\) 862.106 1.21082
\(713\) 422.040i 0.591921i
\(714\) 66.7340 830.479i 0.0934650 1.16314i
\(715\) 0 0
\(716\) 149.488i 0.208782i
\(717\) 1385.54 + 111.337i 1.93242 + 0.155282i
\(718\) −208.295 −0.290104
\(719\) 762.189i 1.06007i −0.847976 0.530034i \(-0.822179\pi\)
0.847976 0.530034i \(-0.177821\pi\)
\(720\) −140.356 + 867.696i −0.194938 + 1.20513i
\(721\) 73.8250 0.102392
\(722\) 274.138i 0.379693i
\(723\) −82.9938 + 1032.82i −0.114791 + 1.42853i
\(724\) −135.446 −0.187080
\(725\) 37.0003i 0.0510350i
\(726\) 0 0
\(727\) 64.3444 0.0885067 0.0442534 0.999020i \(-0.485909\pi\)
0.0442534 + 0.999020i \(0.485909\pi\)
\(728\) 343.128i 0.471330i
\(729\) −646.248 337.350i −0.886485 0.462757i
\(730\) −227.253 −0.311306
\(731\) 638.263i 0.873137i
\(732\) 3.44234 42.8385i 0.00470265 0.0585226i
\(733\) −792.311 −1.08092 −0.540458 0.841371i \(-0.681749\pi\)
−0.540458 + 0.841371i \(0.681749\pi\)
\(734\) 978.181i 1.33267i
\(735\) 1694.11 + 136.132i 2.30491 + 0.185213i
\(736\) 248.816 0.338066
\(737\) 0 0
\(738\) 501.321 + 81.0920i 0.679296 + 0.109881i
\(739\) −975.853 −1.32050 −0.660252 0.751044i \(-0.729551\pi\)
−0.660252 + 0.751044i \(0.729551\pi\)
\(740\) 21.4579i 0.0289971i
\(741\) −20.4372 + 254.333i −0.0275806 + 0.343229i
\(742\) 1507.64 2.03186
\(743\) 613.238i 0.825354i −0.910877 0.412677i \(-0.864594\pi\)
0.910877 0.412677i \(-0.135406\pi\)
\(744\) −404.334 32.4907i −0.543459 0.0436703i
\(745\) 673.120 0.903516
\(746\) 1132.32i 1.51785i
\(747\) 116.921 722.818i 0.156520 0.967628i
\(748\) 0 0
\(749\) 1655.55i 2.21035i
\(750\) −59.9767 + 746.386i −0.0799689 + 0.995181i
\(751\) 986.977 1.31422 0.657108 0.753796i \(-0.271779\pi\)
0.657108 + 0.753796i \(0.271779\pi\)
\(752\) 1045.94i 1.39087i
\(753\) 645.076 + 51.8358i 0.856674 + 0.0688390i
\(754\) 90.6268 0.120195
\(755\) 769.974i 1.01983i
\(756\) 56.4967 230.316i 0.0747311 0.304650i
\(757\) 1307.29 1.72694 0.863471 0.504399i \(-0.168286\pi\)
0.863471 + 0.504399i \(0.168286\pi\)
\(758\) 1447.53i 1.90967i
\(759\) 0 0
\(760\) −841.074 −1.10668
\(761\) 487.251i 0.640278i 0.947371 + 0.320139i \(0.103730\pi\)
−0.947371 + 0.320139i \(0.896270\pi\)
\(762\) 228.706 + 18.3780i 0.300140 + 0.0241181i
\(763\) −1139.89 −1.49395
\(764\) 152.190i 0.199202i
\(765\) −486.577 78.7070i −0.636048 0.102885i
\(766\) −1094.46 −1.42879
\(767\) 258.305i 0.336773i
\(768\) 31.5680 392.851i 0.0411041 0.511525i
\(769\) 887.598 1.15422 0.577112 0.816665i \(-0.304180\pi\)
0.577112 + 0.816665i \(0.304180\pi\)
\(770\) 0 0
\(771\) −208.962 16.7913i −0.271027 0.0217786i
\(772\) 83.5113 0.108175
\(773\) 299.226i 0.387097i −0.981091 0.193548i \(-0.938000\pi\)
0.981091 0.193548i \(-0.0619996\pi\)
\(774\) 193.642 1197.12i 0.250183 1.54666i
\(775\) 64.5402 0.0832776
\(776\) 609.936i 0.786000i
\(777\) −17.1025 + 212.834i −0.0220110 + 0.273918i
\(778\) −200.633 −0.257883
\(779\) 574.310i 0.737240i
\(780\) 43.2812 + 3.47791i 0.0554887 + 0.00445885i
\(781\) 0 0
\(782\) 497.197i 0.635801i
\(783\) −284.392 69.7617i −0.363208 0.0890954i
\(784\) −1947.40 −2.48392
\(785\) 116.183i 0.148004i
\(786\) 62.2985 775.280i 0.0792602 0.986362i
\(787\) −1451.63 −1.84451 −0.922253 0.386587i \(-0.873654\pi\)
−0.922253 + 0.386587i \(0.873654\pi\)
\(788\) 55.3549i 0.0702473i
\(789\) −1331.40 106.986i −1.68746 0.135597i
\(790\) −412.933 −0.522699
\(791\) 1054.27i 1.33284i
\(792\) 0 0
\(793\) 78.3013 0.0987407
\(794\) 211.050i 0.265807i
\(795\) 71.4419 889.066i 0.0898640 1.11832i
\(796\) 157.294 0.197606
\(797\) 375.053i 0.470581i −0.971925 0.235290i \(-0.924396\pi\)
0.971925 0.235290i \(-0.0756041\pi\)
\(798\) 1784.41 + 143.389i 2.23611 + 0.179685i
\(799\) 586.529 0.734079
\(800\) 38.0501i 0.0475626i
\(801\) −173.343 + 1071.63i −0.216409 + 1.33787i
\(802\) −518.492 −0.646499
\(803\) 0 0
\(804\) 14.9660 186.246i 0.0186144 0.231649i
\(805\) −1481.83 −1.84078
\(806\) 158.081i 0.196131i
\(807\) 401.080 + 32.2292i 0.497001 + 0.0399371i
\(808\) 450.195 0.557172
\(809\) 795.417i 0.983210i 0.870818 + 0.491605i \(0.163590\pi\)
−0.870818 + 0.491605i \(0.836410\pi\)
\(810\) −888.737 295.243i −1.09721 0.364498i
\(811\) −941.339 −1.16071 −0.580357 0.814362i \(-0.697087\pi\)
−0.580357 + 0.814362i \(0.697087\pi\)
\(812\) 95.2555i 0.117310i
\(813\) −49.2027 + 612.308i −0.0605199 + 0.753146i
\(814\) 0 0
\(815\) 622.403i 0.763684i
\(816\) 562.961 + 45.2374i 0.689903 + 0.0554380i
\(817\) 1371.41 1.67859
\(818\) 1018.90i 1.24560i
\(819\) 426.521 + 68.9926i 0.520782 + 0.0842401i
\(820\) 97.7333 0.119187
\(821\) 881.769i 1.07402i 0.843576 + 0.537009i \(0.180446\pi\)
−0.843576 + 0.537009i \(0.819554\pi\)
\(822\) 35.2150 438.236i 0.0428406 0.533134i
\(823\) 784.531 0.953257 0.476629 0.879105i \(-0.341859\pi\)
0.476629 + 0.879105i \(0.341859\pi\)
\(824\) 42.3438i 0.0513881i
\(825\) 0 0
\(826\) 1812.28 2.19405
\(827\) 631.410i 0.763495i −0.924267 0.381747i \(-0.875322\pi\)
0.924267 0.381747i \(-0.124678\pi\)
\(828\) −22.5979 + 139.703i −0.0272921 + 0.168723i
\(829\) −873.984 −1.05426 −0.527132 0.849784i \(-0.676733\pi\)
−0.527132 + 0.849784i \(0.676733\pi\)
\(830\) 940.623i 1.13328i
\(831\) −14.0571 + 174.935i −0.0169159 + 0.210511i
\(832\) 189.152 0.227347
\(833\) 1092.04i 1.31097i
\(834\) −264.929 21.2887i −0.317661 0.0255260i
\(835\) 40.3420 0.0483138
\(836\) 0 0
\(837\) 121.686 496.069i 0.145384 0.592675i
\(838\) −68.4051 −0.0816290
\(839\) 130.049i 0.155005i 0.996992 + 0.0775025i \(0.0246946\pi\)
−0.996992 + 0.0775025i \(0.975305\pi\)
\(840\) −114.079 + 1419.66i −0.135808 + 1.69007i
\(841\) 723.379 0.860142
\(842\) 1211.88i 1.43928i
\(843\) −4.25843 0.342191i −0.00505152 0.000405921i
\(844\) 48.4988 0.0574631
\(845\) 821.703i 0.972430i
\(846\) 1100.08 + 177.946i 1.30034 + 0.210338i
\(847\) 0 0
\(848\) 1021.99i 1.20518i
\(849\) 70.4685 876.952i 0.0830018 1.03292i
\(850\) −76.0335 −0.0894512
\(851\) 127.421i 0.149731i
\(852\) 224.926 + 18.0742i 0.263998 + 0.0212139i
\(853\) −955.546 −1.12022 −0.560109 0.828419i \(-0.689241\pi\)
−0.560109 + 0.828419i \(0.689241\pi\)
\(854\) 549.366i 0.643286i
\(855\) 169.114 1045.49i 0.197795 1.22279i
\(856\) 949.573 1.10931
\(857\) 884.890i 1.03254i 0.856425 + 0.516272i \(0.172681\pi\)
−0.856425 + 0.516272i \(0.827319\pi\)
\(858\) 0 0
\(859\) −248.741 −0.289570 −0.144785 0.989463i \(-0.546249\pi\)
−0.144785 + 0.989463i \(0.546249\pi\)
\(860\) 233.380i 0.271372i
\(861\) 969.387 + 77.8962i 1.12588 + 0.0904717i
\(862\) −1621.67 −1.88128
\(863\) 990.278i 1.14748i 0.819036 + 0.573742i \(0.194509\pi\)
−0.819036 + 0.573742i \(0.805491\pi\)
\(864\) 292.461 + 71.7409i 0.338496 + 0.0830335i
\(865\) −332.888 −0.384842
\(866\) 1233.17i 1.42398i
\(867\) 44.0772 548.523i 0.0508388 0.632668i
\(868\) 166.155 0.191423
\(869\) 0 0
\(870\) −374.961 30.1304i −0.430989 0.0346326i
\(871\) 340.425 0.390843
\(872\) 653.805i 0.749776i
\(873\) 758.173 + 122.640i 0.868469 + 0.140481i
\(874\) −1068.31 −1.22232
\(875\) 1433.94i 1.63879i
\(876\) −3.32903 + 41.4284i −0.00380026 + 0.0472927i
\(877\) 1073.75 1.22435 0.612173 0.790724i \(-0.290296\pi\)
0.612173 + 0.790724i \(0.290296\pi\)
\(878\) 1179.29i 1.34316i
\(879\) 968.899 + 77.8570i 1.10227 + 0.0885745i
\(880\) 0 0
\(881\) 1093.03i 1.24067i 0.784337 + 0.620335i \(0.213003\pi\)
−0.784337 + 0.620335i \(0.786997\pi\)
\(882\) 331.312 2048.21i 0.375637 2.32223i
\(883\) −1362.62 −1.54317 −0.771586 0.636125i \(-0.780536\pi\)
−0.771586 + 0.636125i \(0.780536\pi\)
\(884\) 27.8995i 0.0315605i
\(885\) 85.8778 1068.72i 0.0970371 1.20759i
\(886\) 34.5631 0.0390103
\(887\) 207.746i 0.234212i −0.993119 0.117106i \(-0.962638\pi\)
0.993119 0.117106i \(-0.0373617\pi\)
\(888\) −122.075 9.80949i −0.137472 0.0110467i
\(889\) 439.386 0.494248
\(890\) 1394.54i 1.56690i
\(891\) 0 0
\(892\) −255.769 −0.286736
\(893\) 1260.25i 1.41125i
\(894\) 65.8201 819.105i 0.0736243 0.916225i
\(895\) 1130.50 1.26313
\(896\) 1883.03i 2.10159i
\(897\) −257.012 20.6525i −0.286524 0.0230240i
\(898\) −802.251 −0.893375
\(899\) 205.167i 0.228217i
\(900\) −21.3640 3.45577i −0.0237377 0.00383974i
\(901\) −573.101 −0.636072
\(902\) 0 0
\(903\) 186.010 2314.82i 0.205991 2.56348i
\(904\) 604.699 0.668915
\(905\) 1024.31i 1.13183i
\(906\) 936.965 + 75.2908i 1.03418 + 0.0831025i
\(907\) −966.468 −1.06557 −0.532783 0.846252i \(-0.678854\pi\)
−0.532783 + 0.846252i \(0.678854\pi\)
\(908\) 271.371i 0.298867i
\(909\) −90.5206 + 559.609i −0.0995826 + 0.615632i
\(910\) 555.043 0.609937
\(911\) 107.416i 0.117910i 0.998261 + 0.0589548i \(0.0187768\pi\)
−0.998261 + 0.0589548i \(0.981223\pi\)
\(912\) −97.1996 + 1209.61i −0.106579 + 1.32633i
\(913\) 0 0
\(914\) 102.335i 0.111964i
\(915\) −323.965 26.0326i −0.354060 0.0284509i
\(916\) −80.9290 −0.0883504
\(917\) 1489.45i 1.62427i
\(918\) −143.356 + 584.409i −0.156161 + 0.636611i
\(919\) 41.7982 0.0454823 0.0227411 0.999741i \(-0.492761\pi\)
0.0227411 + 0.999741i \(0.492761\pi\)
\(920\) 849.934i 0.923841i
\(921\) −70.3871 + 875.940i −0.0764247 + 0.951075i
\(922\) −1586.16 −1.72035
\(923\) 411.126i 0.445424i
\(924\) 0 0
\(925\) 19.4858 0.0210657
\(926\) 537.408i 0.580354i
\(927\) −52.6349 8.51404i −0.0567798 0.00918451i
\(928\) 120.958 0.130342
\(929\) 96.9891i 0.104402i −0.998637 0.0522008i \(-0.983376\pi\)
0.998637 0.0522008i \(-0.0166236\pi\)
\(930\) 52.5568 654.049i 0.0565127 0.703278i
\(931\) 2346.42 2.52032
\(932\) 31.3088i 0.0335932i
\(933\) −1013.47 81.4385i −1.08625 0.0872868i
\(934\) 482.849 0.516969
\(935\) 0 0
\(936\) −39.5721 + 244.639i −0.0422778 + 0.261367i
\(937\) −438.349 −0.467821 −0.233911 0.972258i \(-0.575152\pi\)
−0.233911 + 0.972258i \(0.575152\pi\)
\(938\) 2388.44i 2.54631i
\(939\) −85.7337 + 1066.92i −0.0913032 + 1.13623i
\(940\) 214.463 0.228152
\(941\) 1152.48i 1.22474i 0.790571 + 0.612370i \(0.209784\pi\)
−0.790571 + 0.612370i \(0.790216\pi\)
\(942\) −141.381 11.3608i −0.150086 0.0120603i
\(943\) −580.359 −0.615439
\(944\) 1228.50i 1.30138i
\(945\) −1741.76 427.255i −1.84313 0.452122i
\(946\) 0 0
\(947\) 654.797i 0.691443i −0.938337 0.345722i \(-0.887634\pi\)
0.938337 0.345722i \(-0.112366\pi\)
\(948\) −6.04903 + 75.2778i −0.00638084 + 0.0794070i
\(949\) −75.7239 −0.0797934
\(950\) 163.370i 0.171968i
\(951\) −1442.81 115.938i −1.51715 0.121912i
\(952\) 915.130 0.961271
\(953\) 1074.05i 1.12702i 0.826111 + 0.563508i \(0.190548\pi\)
−0.826111 + 0.563508i \(0.809452\pi\)
\(954\) −1074.90 173.872i −1.12673 0.182256i
\(955\) −1150.94 −1.20517
\(956\) 326.573i 0.341604i
\(957\) 0 0
\(958\) −1709.38 −1.78433
\(959\) 841.931i 0.877925i
\(960\) −782.602 62.8868i −0.815210 0.0655071i
\(961\) −603.124 −0.627600
\(962\) 47.7275i 0.0496128i
\(963\) −190.930 + 1180.35i −0.198266 + 1.22571i
\(964\) 243.437 0.252529
\(965\) 631.552i 0.654458i
\(966\) −144.899 + 1803.21i −0.149999 + 1.86668i
\(967\) −981.769 −1.01527 −0.507636 0.861571i \(-0.669481\pi\)
−0.507636 + 0.861571i \(0.669481\pi\)
\(968\) 0 0
\(969\) −678.312 54.5065i −0.700012 0.0562502i
\(970\) 986.631 1.01715
\(971\) 1094.95i 1.12765i −0.825893 0.563827i \(-0.809328\pi\)
0.825893 0.563827i \(-0.190672\pi\)
\(972\) −66.8421 + 157.692i −0.0687676 + 0.162235i
\(973\) −508.977 −0.523101
\(974\) 682.653i 0.700876i
\(975\) 3.15827 39.3034i 0.00323925 0.0403112i
\(976\) 372.402 0.381559
\(977\) 710.323i 0.727045i 0.931585 + 0.363523i \(0.118426\pi\)
−0.931585 + 0.363523i \(0.881574\pi\)
\(978\) −757.389 60.8608i −0.774426 0.0622299i
\(979\) 0 0
\(980\) 399.302i 0.407451i
\(981\) 812.703 + 131.460i 0.828444 + 0.134006i
\(982\) 1532.68 1.56077
\(983\) 1520.74i 1.54703i −0.633775 0.773517i \(-0.718495\pi\)
0.633775 0.773517i \(-0.281505\pi\)
\(984\) −44.6789 + 556.011i −0.0454054 + 0.565052i
\(985\) 418.620 0.424994
\(986\) 241.704i 0.245136i
\(987\) 2127.20 + 170.933i 2.15521 + 0.173185i
\(988\) 59.9465 0.0606746
\(989\) 1385.85i 1.40127i
\(990\) 0 0
\(991\) −339.543 −0.342627 −0.171313 0.985217i \(-0.554801\pi\)
−0.171313 + 0.985217i \(0.554801\pi\)
\(992\) 210.988i 0.212690i
\(993\) −31.6859 + 394.318i −0.0319092 + 0.397098i
\(994\) 2884.48 2.90190
\(995\) 1189.53i 1.19551i
\(996\) −171.476 13.7791i −0.172165 0.0138345i
\(997\) 903.470 0.906189 0.453094 0.891463i \(-0.350320\pi\)
0.453094 + 0.891463i \(0.350320\pi\)
\(998\) 484.022i 0.484992i
\(999\) 36.7392 149.772i 0.0367760 0.149922i
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 363.3.b.n.122.9 yes 12
3.2 odd 2 inner 363.3.b.n.122.4 yes 12
11.2 odd 10 363.3.h.r.323.3 48
11.3 even 5 363.3.h.r.251.10 48
11.4 even 5 363.3.h.r.269.3 48
11.5 even 5 363.3.h.r.245.4 48
11.6 odd 10 363.3.h.r.245.10 48
11.7 odd 10 363.3.h.r.269.9 48
11.8 odd 10 363.3.h.r.251.4 48
11.9 even 5 363.3.h.r.323.9 48
11.10 odd 2 inner 363.3.b.n.122.3 12
33.2 even 10 363.3.h.r.323.10 48
33.5 odd 10 363.3.h.r.245.9 48
33.8 even 10 363.3.h.r.251.9 48
33.14 odd 10 363.3.h.r.251.3 48
33.17 even 10 363.3.h.r.245.3 48
33.20 odd 10 363.3.h.r.323.4 48
33.26 odd 10 363.3.h.r.269.10 48
33.29 even 10 363.3.h.r.269.4 48
33.32 even 2 inner 363.3.b.n.122.10 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.3.b.n.122.3 12 11.10 odd 2 inner
363.3.b.n.122.4 yes 12 3.2 odd 2 inner
363.3.b.n.122.9 yes 12 1.1 even 1 trivial
363.3.b.n.122.10 yes 12 33.32 even 2 inner
363.3.h.r.245.3 48 33.17 even 10
363.3.h.r.245.4 48 11.5 even 5
363.3.h.r.245.9 48 33.5 odd 10
363.3.h.r.245.10 48 11.6 odd 10
363.3.h.r.251.3 48 33.14 odd 10
363.3.h.r.251.4 48 11.8 odd 10
363.3.h.r.251.9 48 33.8 even 10
363.3.h.r.251.10 48 11.3 even 5
363.3.h.r.269.3 48 11.4 even 5
363.3.h.r.269.4 48 33.29 even 10
363.3.h.r.269.9 48 11.7 odd 10
363.3.h.r.269.10 48 33.26 odd 10
363.3.h.r.323.3 48 11.2 odd 10
363.3.h.r.323.4 48 33.20 odd 10
363.3.h.r.323.9 48 11.9 even 5
363.3.h.r.323.10 48 33.2 even 10