Properties

Label 980.2.g.a.391.1
Level $980$
Weight $2$
Character 980.391
Analytic conductor $7.825$
Analytic rank $0$
Dimension $32$
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] = [980,2,Mod(391,980)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(980, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("980.391");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.g (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 391.1
Character \(\chi\) \(=\) 980.391
Dual form 980.2.g.a.391.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40582 - 0.153886i) q^{2} -3.02707 q^{3} +(1.95264 + 0.432671i) q^{4} -1.00000i q^{5} +(4.25550 + 0.465823i) q^{6} +(-2.67847 - 0.908739i) q^{8} +6.16313 q^{9} +O(q^{10})\) \(q+(-1.40582 - 0.153886i) q^{2} -3.02707 q^{3} +(1.95264 + 0.432671i) q^{4} -1.00000i q^{5} +(4.25550 + 0.465823i) q^{6} +(-2.67847 - 0.908739i) q^{8} +6.16313 q^{9} +(-0.153886 + 1.40582i) q^{10} +1.19696i q^{11} +(-5.91077 - 1.30972i) q^{12} -4.83692i q^{13} +3.02707i q^{15} +(3.62559 + 1.68970i) q^{16} +2.54530i q^{17} +(-8.66423 - 0.948419i) q^{18} +1.42226 q^{19} +(0.432671 - 1.95264i) q^{20} +(0.184195 - 1.68270i) q^{22} +5.80651i q^{23} +(8.10790 + 2.75081i) q^{24} -1.00000 q^{25} +(-0.744335 + 6.79982i) q^{26} -9.57500 q^{27} +0.774233 q^{29} +(0.465823 - 4.25550i) q^{30} -6.63865 q^{31} +(-4.83689 - 2.93333i) q^{32} -3.62326i q^{33} +(0.391687 - 3.57823i) q^{34} +(12.0344 + 2.66661i) q^{36} +5.10930 q^{37} +(-1.99944 - 0.218866i) q^{38} +14.6417i q^{39} +(-0.908739 + 2.67847i) q^{40} +7.46685i q^{41} +1.38202i q^{43} +(-0.517888 + 2.33722i) q^{44} -6.16313i q^{45} +(0.893541 - 8.16289i) q^{46} -1.07086 q^{47} +(-10.9749 - 5.11483i) q^{48} +(1.40582 + 0.153886i) q^{50} -7.70480i q^{51} +(2.09280 - 9.44476i) q^{52} +3.36198 q^{53} +(13.4607 + 1.47346i) q^{54} +1.19696 q^{55} -4.30528 q^{57} +(-1.08843 - 0.119144i) q^{58} +9.88412 q^{59} +(-1.30972 + 5.91077i) q^{60} -9.59690i q^{61} +(9.33272 + 1.02160i) q^{62} +(6.34839 + 4.86806i) q^{64} -4.83692 q^{65} +(-0.557570 + 5.09364i) q^{66} -10.5555i q^{67} +(-1.10128 + 4.97006i) q^{68} -17.5767i q^{69} -16.3277i q^{71} +(-16.5077 - 5.60068i) q^{72} +0.107109i q^{73} +(-7.18274 - 0.786250i) q^{74} +3.02707 q^{75} +(2.77716 + 0.615371i) q^{76} +(2.25315 - 20.5835i) q^{78} -10.7688i q^{79} +(1.68970 - 3.62559i) q^{80} +10.4948 q^{81} +(1.14904 - 10.4970i) q^{82} +15.8027 q^{83} +2.54530 q^{85} +(0.212673 - 1.94286i) q^{86} -2.34366 q^{87} +(1.08772 - 3.20601i) q^{88} +3.94128i q^{89} +(-0.948419 + 8.66423i) q^{90} +(-2.51231 + 11.3380i) q^{92} +20.0956 q^{93} +(1.50543 + 0.164790i) q^{94} -1.42226i q^{95} +(14.6416 + 8.87940i) q^{96} -8.71387i q^{97} +7.37699i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40582 0.153886i −0.994062 0.108814i
\(3\) −3.02707 −1.74768 −0.873839 0.486216i \(-0.838377\pi\)
−0.873839 + 0.486216i \(0.838377\pi\)
\(4\) 1.95264 + 0.432671i 0.976319 + 0.216335i
\(5\) 1.00000i 0.447214i
\(6\) 4.25550 + 0.465823i 1.73730 + 0.190171i
\(7\) 0 0
\(8\) −2.67847 0.908739i −0.946982 0.321288i
\(9\) 6.16313 2.05438
\(10\) −0.153886 + 1.40582i −0.0486630 + 0.444558i
\(11\) 1.19696i 0.360896i 0.983585 + 0.180448i \(0.0577547\pi\)
−0.983585 + 0.180448i \(0.942245\pi\)
\(12\) −5.91077 1.30972i −1.70629 0.378085i
\(13\) 4.83692i 1.34152i −0.741674 0.670760i \(-0.765968\pi\)
0.741674 0.670760i \(-0.234032\pi\)
\(14\) 0 0
\(15\) 3.02707i 0.781585i
\(16\) 3.62559 + 1.68970i 0.906398 + 0.422425i
\(17\) 2.54530i 0.617327i 0.951171 + 0.308664i \(0.0998817\pi\)
−0.951171 + 0.308664i \(0.900118\pi\)
\(18\) −8.66423 0.948419i −2.04218 0.223545i
\(19\) 1.42226 0.326289 0.163144 0.986602i \(-0.447836\pi\)
0.163144 + 0.986602i \(0.447836\pi\)
\(20\) 0.432671 1.95264i 0.0967481 0.436623i
\(21\) 0 0
\(22\) 0.184195 1.68270i 0.0392704 0.358753i
\(23\) 5.80651i 1.21074i 0.795943 + 0.605371i \(0.206975\pi\)
−0.795943 + 0.605371i \(0.793025\pi\)
\(24\) 8.10790 + 2.75081i 1.65502 + 0.561508i
\(25\) −1.00000 −0.200000
\(26\) −0.744335 + 6.79982i −0.145976 + 1.33356i
\(27\) −9.57500 −1.84271
\(28\) 0 0
\(29\) 0.774233 0.143772 0.0718858 0.997413i \(-0.477098\pi\)
0.0718858 + 0.997413i \(0.477098\pi\)
\(30\) 0.465823 4.25550i 0.0850473 0.776944i
\(31\) −6.63865 −1.19234 −0.596169 0.802859i \(-0.703311\pi\)
−0.596169 + 0.802859i \(0.703311\pi\)
\(32\) −4.83689 2.93333i −0.855050 0.518545i
\(33\) 3.62326i 0.630729i
\(34\) 0.391687 3.57823i 0.0671737 0.613661i
\(35\) 0 0
\(36\) 12.0344 + 2.66661i 2.00573 + 0.444434i
\(37\) 5.10930 0.839964 0.419982 0.907532i \(-0.362036\pi\)
0.419982 + 0.907532i \(0.362036\pi\)
\(38\) −1.99944 0.218866i −0.324352 0.0355047i
\(39\) 14.6417i 2.34455i
\(40\) −0.908739 + 2.67847i −0.143684 + 0.423503i
\(41\) 7.46685i 1.16613i 0.812427 + 0.583063i \(0.198146\pi\)
−0.812427 + 0.583063i \(0.801854\pi\)
\(42\) 0 0
\(43\) 1.38202i 0.210756i 0.994432 + 0.105378i \(0.0336052\pi\)
−0.994432 + 0.105378i \(0.966395\pi\)
\(44\) −0.517888 + 2.33722i −0.0780745 + 0.352349i
\(45\) 6.16313i 0.918745i
\(46\) 0.893541 8.16289i 0.131745 1.20355i
\(47\) −1.07086 −0.156200 −0.0781002 0.996946i \(-0.524885\pi\)
−0.0781002 + 0.996946i \(0.524885\pi\)
\(48\) −10.9749 5.11483i −1.58409 0.738262i
\(49\) 0 0
\(50\) 1.40582 + 0.153886i 0.198812 + 0.0217628i
\(51\) 7.70480i 1.07889i
\(52\) 2.09280 9.44476i 0.290218 1.30975i
\(53\) 3.36198 0.461804 0.230902 0.972977i \(-0.425832\pi\)
0.230902 + 0.972977i \(0.425832\pi\)
\(54\) 13.4607 + 1.47346i 1.83177 + 0.200512i
\(55\) 1.19696 0.161398
\(56\) 0 0
\(57\) −4.30528 −0.570248
\(58\) −1.08843 0.119144i −0.142918 0.0156443i
\(59\) 9.88412 1.28680 0.643402 0.765529i \(-0.277523\pi\)
0.643402 + 0.765529i \(0.277523\pi\)
\(60\) −1.30972 + 5.91077i −0.169085 + 0.763076i
\(61\) 9.59690i 1.22876i −0.789012 0.614378i \(-0.789407\pi\)
0.789012 0.614378i \(-0.210593\pi\)
\(62\) 9.33272 + 1.02160i 1.18526 + 0.129743i
\(63\) 0 0
\(64\) 6.34839 + 4.86806i 0.793548 + 0.608507i
\(65\) −4.83692 −0.599946
\(66\) −0.557570 + 5.09364i −0.0686321 + 0.626984i
\(67\) 10.5555i 1.28956i −0.764367 0.644781i \(-0.776949\pi\)
0.764367 0.644781i \(-0.223051\pi\)
\(68\) −1.10128 + 4.97006i −0.133550 + 0.602708i
\(69\) 17.5767i 2.11599i
\(70\) 0 0
\(71\) 16.3277i 1.93775i −0.247558 0.968873i \(-0.579628\pi\)
0.247558 0.968873i \(-0.420372\pi\)
\(72\) −16.5077 5.60068i −1.94546 0.660046i
\(73\) 0.107109i 0.0125362i 0.999980 + 0.00626810i \(0.00199521\pi\)
−0.999980 + 0.00626810i \(0.998005\pi\)
\(74\) −7.18274 0.786250i −0.834977 0.0913997i
\(75\) 3.02707 0.349535
\(76\) 2.77716 + 0.615371i 0.318562 + 0.0705879i
\(77\) 0 0
\(78\) 2.25315 20.5835i 0.255119 2.33062i
\(79\) 10.7688i 1.21159i −0.795621 0.605795i \(-0.792855\pi\)
0.795621 0.605795i \(-0.207145\pi\)
\(80\) 1.68970 3.62559i 0.188914 0.405354i
\(81\) 10.4948 1.16609
\(82\) 1.14904 10.4970i 0.126891 1.15920i
\(83\) 15.8027 1.73457 0.867287 0.497808i \(-0.165862\pi\)
0.867287 + 0.497808i \(0.165862\pi\)
\(84\) 0 0
\(85\) 2.54530 0.276077
\(86\) 0.212673 1.94286i 0.0229331 0.209504i
\(87\) −2.34366 −0.251266
\(88\) 1.08772 3.20601i 0.115951 0.341762i
\(89\) 3.94128i 0.417775i 0.977940 + 0.208887i \(0.0669842\pi\)
−0.977940 + 0.208887i \(0.933016\pi\)
\(90\) −0.948419 + 8.66423i −0.0999722 + 0.913290i
\(91\) 0 0
\(92\) −2.51231 + 11.3380i −0.261926 + 1.18207i
\(93\) 20.0956 2.08382
\(94\) 1.50543 + 0.164790i 0.155273 + 0.0169968i
\(95\) 1.42226i 0.145921i
\(96\) 14.6416 + 8.87940i 1.49435 + 0.906250i
\(97\) 8.71387i 0.884760i −0.896828 0.442380i \(-0.854134\pi\)
0.896828 0.442380i \(-0.145866\pi\)
\(98\) 0 0
\(99\) 7.37699i 0.741416i
\(100\) −1.95264 0.432671i −0.195264 0.0432671i
\(101\) 3.00544i 0.299052i −0.988758 0.149526i \(-0.952225\pi\)
0.988758 0.149526i \(-0.0477748\pi\)
\(102\) −1.18566 + 10.8315i −0.117398 + 1.07248i
\(103\) 0.382749 0.0377133 0.0188567 0.999822i \(-0.493997\pi\)
0.0188567 + 0.999822i \(0.493997\pi\)
\(104\) −4.39550 + 12.9555i −0.431014 + 1.27040i
\(105\) 0 0
\(106\) −4.72633 0.517362i −0.459062 0.0502507i
\(107\) 0.842470i 0.0814446i 0.999171 + 0.0407223i \(0.0129659\pi\)
−0.999171 + 0.0407223i \(0.987034\pi\)
\(108\) −18.6965 4.14282i −1.79907 0.398643i
\(109\) 3.95068 0.378407 0.189203 0.981938i \(-0.439409\pi\)
0.189203 + 0.981938i \(0.439409\pi\)
\(110\) −1.68270 0.184195i −0.160439 0.0175623i
\(111\) −15.4662 −1.46799
\(112\) 0 0
\(113\) 2.68201 0.252302 0.126151 0.992011i \(-0.459738\pi\)
0.126151 + 0.992011i \(0.459738\pi\)
\(114\) 6.05243 + 0.662522i 0.566862 + 0.0620508i
\(115\) 5.80651 0.541460
\(116\) 1.51180 + 0.334988i 0.140367 + 0.0311029i
\(117\) 29.8106i 2.75599i
\(118\) −13.8953 1.52103i −1.27916 0.140022i
\(119\) 0 0
\(120\) 2.75081 8.10790i 0.251114 0.740147i
\(121\) 9.56730 0.869754
\(122\) −1.47683 + 13.4915i −0.133706 + 1.22146i
\(123\) 22.6027i 2.03801i
\(124\) −12.9629 2.87235i −1.16410 0.257945i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 2.14034i 0.189925i −0.995481 0.0949624i \(-0.969727\pi\)
0.995481 0.0949624i \(-0.0302731\pi\)
\(128\) −8.17554 7.82052i −0.722622 0.691243i
\(129\) 4.18346i 0.368333i
\(130\) 6.79982 + 0.744335i 0.596384 + 0.0652825i
\(131\) −9.66575 −0.844500 −0.422250 0.906479i \(-0.638760\pi\)
−0.422250 + 0.906479i \(0.638760\pi\)
\(132\) 1.56768 7.07493i 0.136449 0.615793i
\(133\) 0 0
\(134\) −1.62435 + 14.8391i −0.140322 + 1.28190i
\(135\) 9.57500i 0.824085i
\(136\) 2.31302 6.81752i 0.198340 0.584597i
\(137\) 4.27568 0.365296 0.182648 0.983178i \(-0.441533\pi\)
0.182648 + 0.983178i \(0.441533\pi\)
\(138\) −2.70481 + 24.7096i −0.230249 + 2.10342i
\(139\) 7.53742 0.639316 0.319658 0.947533i \(-0.396432\pi\)
0.319658 + 0.947533i \(0.396432\pi\)
\(140\) 0 0
\(141\) 3.24155 0.272988
\(142\) −2.51261 + 22.9538i −0.210854 + 1.92624i
\(143\) 5.78958 0.484149
\(144\) 22.3450 + 10.4138i 1.86208 + 0.867820i
\(145\) 0.774233i 0.0642966i
\(146\) 0.0164826 0.150576i 0.00136411 0.0124618i
\(147\) 0 0
\(148\) 9.97662 + 2.21065i 0.820073 + 0.181714i
\(149\) −2.85765 −0.234108 −0.117054 0.993126i \(-0.537345\pi\)
−0.117054 + 0.993126i \(0.537345\pi\)
\(150\) −4.25550 0.465823i −0.347460 0.0380343i
\(151\) 6.60903i 0.537835i −0.963163 0.268918i \(-0.913334\pi\)
0.963163 0.268918i \(-0.0866659\pi\)
\(152\) −3.80948 1.29246i −0.308990 0.104833i
\(153\) 15.6870i 1.26822i
\(154\) 0 0
\(155\) 6.63865i 0.533229i
\(156\) −6.33503 + 28.5899i −0.507208 + 2.28902i
\(157\) 15.5831i 1.24367i −0.783149 0.621834i \(-0.786388\pi\)
0.783149 0.621834i \(-0.213612\pi\)
\(158\) −1.65717 + 15.1390i −0.131838 + 1.20440i
\(159\) −10.1769 −0.807085
\(160\) −2.93333 + 4.83689i −0.231900 + 0.382390i
\(161\) 0 0
\(162\) −14.7537 1.61500i −1.15916 0.126886i
\(163\) 9.64030i 0.755086i 0.925992 + 0.377543i \(0.123231\pi\)
−0.925992 + 0.377543i \(0.876769\pi\)
\(164\) −3.23069 + 14.5801i −0.252274 + 1.13851i
\(165\) −3.62326 −0.282071
\(166\) −22.2157 2.43182i −1.72427 0.188746i
\(167\) 4.94876 0.382947 0.191473 0.981498i \(-0.438673\pi\)
0.191473 + 0.981498i \(0.438673\pi\)
\(168\) 0 0
\(169\) −10.3958 −0.799678
\(170\) −3.57823 0.391687i −0.274438 0.0300410i
\(171\) 8.76558 0.670320
\(172\) −0.597958 + 2.69858i −0.0455939 + 0.205765i
\(173\) 6.93069i 0.526931i 0.964669 + 0.263465i \(0.0848655\pi\)
−0.964669 + 0.263465i \(0.915135\pi\)
\(174\) 3.29475 + 0.360656i 0.249774 + 0.0273412i
\(175\) 0 0
\(176\) −2.02250 + 4.33967i −0.152451 + 0.327115i
\(177\) −29.9199 −2.24892
\(178\) 0.606507 5.54071i 0.0454596 0.415294i
\(179\) 21.1123i 1.57801i −0.614389 0.789003i \(-0.710597\pi\)
0.614389 0.789003i \(-0.289403\pi\)
\(180\) 2.66661 12.0344i 0.198757 0.896988i
\(181\) 6.10438i 0.453735i 0.973926 + 0.226868i \(0.0728485\pi\)
−0.973926 + 0.226868i \(0.927152\pi\)
\(182\) 0 0
\(183\) 29.0504i 2.14747i
\(184\) 5.27661 15.5526i 0.388997 1.14655i
\(185\) 5.10930i 0.375644i
\(186\) −28.2508 3.09244i −2.07145 0.226748i
\(187\) −3.04662 −0.222791
\(188\) −2.09099 0.463328i −0.152501 0.0337917i
\(189\) 0 0
\(190\) −0.218866 + 1.99944i −0.0158782 + 0.145054i
\(191\) 3.71319i 0.268677i −0.990936 0.134339i \(-0.957109\pi\)
0.990936 0.134339i \(-0.0428909\pi\)
\(192\) −19.2170 14.7359i −1.38687 1.06347i
\(193\) 15.3309 1.10354 0.551771 0.833996i \(-0.313952\pi\)
0.551771 + 0.833996i \(0.313952\pi\)
\(194\) −1.34094 + 12.2501i −0.0962741 + 0.879506i
\(195\) 14.6417 1.04851
\(196\) 0 0
\(197\) −24.4602 −1.74272 −0.871360 0.490644i \(-0.836761\pi\)
−0.871360 + 0.490644i \(0.836761\pi\)
\(198\) 1.13522 10.3707i 0.0806763 0.737013i
\(199\) −12.8662 −0.912062 −0.456031 0.889964i \(-0.650729\pi\)
−0.456031 + 0.889964i \(0.650729\pi\)
\(200\) 2.67847 + 0.908739i 0.189396 + 0.0642576i
\(201\) 31.9523i 2.25374i
\(202\) −0.462495 + 4.22510i −0.0325410 + 0.297277i
\(203\) 0 0
\(204\) 3.33364 15.0447i 0.233402 1.05334i
\(205\) 7.46685 0.521508
\(206\) −0.538074 0.0588997i −0.0374894 0.00410373i
\(207\) 35.7863i 2.48732i
\(208\) 8.17294 17.5367i 0.566692 1.21595i
\(209\) 1.70238i 0.117756i
\(210\) 0 0
\(211\) 16.9384i 1.16609i −0.812441 0.583044i \(-0.801862\pi\)
0.812441 0.583044i \(-0.198138\pi\)
\(212\) 6.56474 + 1.45463i 0.450868 + 0.0999046i
\(213\) 49.4252i 3.38656i
\(214\) 0.129644 1.18436i 0.00886230 0.0809610i
\(215\) 1.38202 0.0942528
\(216\) 25.6463 + 8.70118i 1.74501 + 0.592040i
\(217\) 0 0
\(218\) −5.55393 0.607955i −0.376160 0.0411759i
\(219\) 0.324227i 0.0219092i
\(220\) 2.33722 + 0.517888i 0.157575 + 0.0349160i
\(221\) 12.3114 0.828157
\(222\) 21.7426 + 2.38003i 1.45927 + 0.159737i
\(223\) 18.9687 1.27024 0.635119 0.772414i \(-0.280951\pi\)
0.635119 + 0.772414i \(0.280951\pi\)
\(224\) 0 0
\(225\) −6.16313 −0.410875
\(226\) −3.77042 0.412724i −0.250804 0.0274540i
\(227\) −0.934456 −0.0620220 −0.0310110 0.999519i \(-0.509873\pi\)
−0.0310110 + 0.999519i \(0.509873\pi\)
\(228\) −8.40665 1.86277i −0.556744 0.123365i
\(229\) 13.0808i 0.864401i 0.901777 + 0.432201i \(0.142263\pi\)
−0.901777 + 0.432201i \(0.857737\pi\)
\(230\) −8.16289 0.893541i −0.538245 0.0589184i
\(231\) 0 0
\(232\) −2.07376 0.703576i −0.136149 0.0461920i
\(233\) −15.6016 −1.02209 −0.511047 0.859553i \(-0.670742\pi\)
−0.511047 + 0.859553i \(0.670742\pi\)
\(234\) −4.58743 + 41.9082i −0.299890 + 2.73962i
\(235\) 1.07086i 0.0698550i
\(236\) 19.3001 + 4.27657i 1.25633 + 0.278381i
\(237\) 32.5980i 2.11747i
\(238\) 0 0
\(239\) 14.1327i 0.914167i −0.889424 0.457084i \(-0.848894\pi\)
0.889424 0.457084i \(-0.151106\pi\)
\(240\) −5.11483 + 10.9749i −0.330161 + 0.708427i
\(241\) 21.5832i 1.39029i 0.718868 + 0.695146i \(0.244661\pi\)
−0.718868 + 0.695146i \(0.755339\pi\)
\(242\) −13.4499 1.47227i −0.864590 0.0946413i
\(243\) −3.04338 −0.195233
\(244\) 4.15230 18.7393i 0.265824 1.19966i
\(245\) 0 0
\(246\) −3.47823 + 31.7752i −0.221764 + 2.02591i
\(247\) 6.87936i 0.437723i
\(248\) 17.7814 + 6.03280i 1.12912 + 0.383083i
\(249\) −47.8359 −3.03148
\(250\) 0.153886 1.40582i 0.00973260 0.0889116i
\(251\) −1.04460 −0.0659345 −0.0329673 0.999456i \(-0.510496\pi\)
−0.0329673 + 0.999456i \(0.510496\pi\)
\(252\) 0 0
\(253\) −6.95014 −0.436952
\(254\) −0.329369 + 3.00893i −0.0206665 + 0.188797i
\(255\) −7.70480 −0.482494
\(256\) 10.2898 + 12.2523i 0.643115 + 0.765770i
\(257\) 4.90387i 0.305895i −0.988234 0.152948i \(-0.951123\pi\)
0.988234 0.152948i \(-0.0488766\pi\)
\(258\) −0.643775 + 5.88117i −0.0400797 + 0.366146i
\(259\) 0 0
\(260\) −9.44476 2.09280i −0.585739 0.129790i
\(261\) 4.77170 0.295361
\(262\) 13.5883 + 1.48742i 0.839486 + 0.0918933i
\(263\) 7.79637i 0.480745i 0.970681 + 0.240373i \(0.0772696\pi\)
−0.970681 + 0.240373i \(0.922730\pi\)
\(264\) −3.29260 + 9.70480i −0.202646 + 0.597289i
\(265\) 3.36198i 0.206525i
\(266\) 0 0
\(267\) 11.9305i 0.730135i
\(268\) 4.56707 20.6111i 0.278978 1.25902i
\(269\) 21.1124i 1.28724i −0.765344 0.643622i \(-0.777431\pi\)
0.765344 0.643622i \(-0.222569\pi\)
\(270\) 1.47346 13.4607i 0.0896718 0.819192i
\(271\) 21.5208 1.30729 0.653647 0.756799i \(-0.273238\pi\)
0.653647 + 0.756799i \(0.273238\pi\)
\(272\) −4.30080 + 9.22824i −0.260774 + 0.559544i
\(273\) 0 0
\(274\) −6.01082 0.657967i −0.363127 0.0397492i
\(275\) 1.19696i 0.0721792i
\(276\) 7.60493 34.3209i 0.457763 2.06588i
\(277\) −5.16743 −0.310481 −0.155241 0.987877i \(-0.549615\pi\)
−0.155241 + 0.987877i \(0.549615\pi\)
\(278\) −10.5962 1.15990i −0.635519 0.0695664i
\(279\) −40.9149 −2.44951
\(280\) 0 0
\(281\) 15.6322 0.932539 0.466270 0.884643i \(-0.345598\pi\)
0.466270 + 0.884643i \(0.345598\pi\)
\(282\) −4.55703 0.498830i −0.271367 0.0297049i
\(283\) 28.5700 1.69831 0.849156 0.528142i \(-0.177111\pi\)
0.849156 + 0.528142i \(0.177111\pi\)
\(284\) 7.06454 31.8822i 0.419203 1.89186i
\(285\) 4.30528i 0.255023i
\(286\) −8.13909 0.890936i −0.481274 0.0526821i
\(287\) 0 0
\(288\) −29.8104 18.0785i −1.75660 1.06529i
\(289\) 10.5214 0.618907
\(290\) −0.119144 + 1.08843i −0.00699636 + 0.0639148i
\(291\) 26.3775i 1.54627i
\(292\) −0.0463431 + 0.209146i −0.00271202 + 0.0122393i
\(293\) 0.657174i 0.0383925i −0.999816 0.0191963i \(-0.993889\pi\)
0.999816 0.0191963i \(-0.00611074\pi\)
\(294\) 0 0
\(295\) 9.88412i 0.575476i
\(296\) −13.6851 4.64303i −0.795431 0.269870i
\(297\) 11.4609i 0.665026i
\(298\) 4.01733 + 0.439752i 0.232717 + 0.0254741i
\(299\) 28.0857 1.62424
\(300\) 5.91077 + 1.30972i 0.341258 + 0.0756169i
\(301\) 0 0
\(302\) −1.01704 + 9.29108i −0.0585239 + 0.534642i
\(303\) 9.09766i 0.522647i
\(304\) 5.15654 + 2.40319i 0.295748 + 0.137833i
\(305\) −9.59690 −0.549517
\(306\) 2.41402 22.0531i 0.138000 1.26069i
\(307\) 4.88042 0.278540 0.139270 0.990254i \(-0.455524\pi\)
0.139270 + 0.990254i \(0.455524\pi\)
\(308\) 0 0
\(309\) −1.15861 −0.0659108
\(310\) 1.02160 9.33272i 0.0580227 0.530063i
\(311\) −11.8968 −0.674606 −0.337303 0.941396i \(-0.609515\pi\)
−0.337303 + 0.941396i \(0.609515\pi\)
\(312\) 13.3055 39.2173i 0.753274 2.22024i
\(313\) 26.6074i 1.50394i −0.659197 0.751970i \(-0.729104\pi\)
0.659197 0.751970i \(-0.270896\pi\)
\(314\) −2.39802 + 21.9070i −0.135328 + 1.23628i
\(315\) 0 0
\(316\) 4.65936 21.0277i 0.262110 1.18290i
\(317\) −26.4557 −1.48590 −0.742950 0.669347i \(-0.766574\pi\)
−0.742950 + 0.669347i \(0.766574\pi\)
\(318\) 14.3069 + 1.56609i 0.802292 + 0.0878220i
\(319\) 0.926723i 0.0518865i
\(320\) 4.86806 6.34839i 0.272133 0.354886i
\(321\) 2.55021i 0.142339i
\(322\) 0 0
\(323\) 3.62009i 0.201427i
\(324\) 20.4925 + 4.54078i 1.13847 + 0.252266i
\(325\) 4.83692i 0.268304i
\(326\) 1.48351 13.5525i 0.0821638 0.750603i
\(327\) −11.9590 −0.661333
\(328\) 6.78542 19.9997i 0.374662 1.10430i
\(329\) 0 0
\(330\) 5.09364 + 0.557570i 0.280396 + 0.0306932i
\(331\) 24.2827i 1.33470i −0.744745 0.667349i \(-0.767429\pi\)
0.744745 0.667349i \(-0.232571\pi\)
\(332\) 30.8570 + 6.83738i 1.69350 + 0.375250i
\(333\) 31.4893 1.72560
\(334\) −6.95705 0.761545i −0.380673 0.0416699i
\(335\) −10.5555 −0.576710
\(336\) 0 0
\(337\) 19.7077 1.07355 0.536774 0.843726i \(-0.319643\pi\)
0.536774 + 0.843726i \(0.319643\pi\)
\(338\) 14.6146 + 1.59977i 0.794930 + 0.0870161i
\(339\) −8.11863 −0.440943
\(340\) 4.97006 + 1.10128i 0.269539 + 0.0597252i
\(341\) 7.94617i 0.430309i
\(342\) −12.3228 1.34890i −0.666340 0.0729401i
\(343\) 0 0
\(344\) 1.25589 3.70169i 0.0677132 0.199582i
\(345\) −17.5767 −0.946298
\(346\) 1.06654 9.74328i 0.0573374 0.523802i
\(347\) 8.43701i 0.452923i −0.974020 0.226461i \(-0.927284\pi\)
0.974020 0.226461i \(-0.0727157\pi\)
\(348\) −4.57631 1.01403i −0.245316 0.0543578i
\(349\) 23.5784i 1.26212i −0.775732 0.631062i \(-0.782619\pi\)
0.775732 0.631062i \(-0.217381\pi\)
\(350\) 0 0
\(351\) 46.3135i 2.47203i
\(352\) 3.51107 5.78955i 0.187141 0.308584i
\(353\) 20.6724i 1.10028i −0.835072 0.550141i \(-0.814574\pi\)
0.835072 0.550141i \(-0.185426\pi\)
\(354\) 42.0619 + 4.60425i 2.23556 + 0.244713i
\(355\) −16.3277 −0.866587
\(356\) −1.70528 + 7.69589i −0.0903794 + 0.407881i
\(357\) 0 0
\(358\) −3.24889 + 29.6800i −0.171709 + 1.56864i
\(359\) 27.4519i 1.44886i 0.689349 + 0.724429i \(0.257896\pi\)
−0.689349 + 0.724429i \(0.742104\pi\)
\(360\) −5.60068 + 16.5077i −0.295182 + 0.870035i
\(361\) −16.9772 −0.893536
\(362\) 0.939379 8.58164i 0.0493727 0.451041i
\(363\) −28.9608 −1.52005
\(364\) 0 0
\(365\) 0.107109 0.00560636
\(366\) 4.47045 40.8396i 0.233674 2.13472i
\(367\) −20.0426 −1.04622 −0.523109 0.852266i \(-0.675228\pi\)
−0.523109 + 0.852266i \(0.675228\pi\)
\(368\) −9.81126 + 21.0521i −0.511447 + 1.09741i
\(369\) 46.0192i 2.39566i
\(370\) −0.786250 + 7.18274i −0.0408752 + 0.373413i
\(371\) 0 0
\(372\) 39.2395 + 8.69480i 2.03447 + 0.450804i
\(373\) 20.5912 1.06617 0.533085 0.846062i \(-0.321033\pi\)
0.533085 + 0.846062i \(0.321033\pi\)
\(374\) 4.28298 + 0.468832i 0.221468 + 0.0242427i
\(375\) 3.02707i 0.156317i
\(376\) 2.86825 + 0.973129i 0.147919 + 0.0501853i
\(377\) 3.74491i 0.192873i
\(378\) 0 0
\(379\) 3.26339i 0.167629i −0.996481 0.0838145i \(-0.973290\pi\)
0.996481 0.0838145i \(-0.0267103\pi\)
\(380\) 0.615371 2.77716i 0.0315678 0.142465i
\(381\) 6.47897i 0.331927i
\(382\) −0.571408 + 5.22006i −0.0292358 + 0.267082i
\(383\) 33.7511 1.72460 0.862300 0.506398i \(-0.169023\pi\)
0.862300 + 0.506398i \(0.169023\pi\)
\(384\) 24.7479 + 23.6732i 1.26291 + 1.20807i
\(385\) 0 0
\(386\) −21.5524 2.35921i −1.09699 0.120081i
\(387\) 8.51755i 0.432971i
\(388\) 3.77024 17.0150i 0.191405 0.863808i
\(389\) −3.61209 −0.183140 −0.0915701 0.995799i \(-0.529189\pi\)
−0.0915701 + 0.995799i \(0.529189\pi\)
\(390\) −20.5835 2.25315i −1.04229 0.114093i
\(391\) −14.7793 −0.747424
\(392\) 0 0
\(393\) 29.2589 1.47591
\(394\) 34.3866 + 3.76409i 1.73237 + 0.189632i
\(395\) −10.7688 −0.541839
\(396\) −3.19181 + 14.4046i −0.160394 + 0.723858i
\(397\) 7.47724i 0.375272i 0.982239 + 0.187636i \(0.0600826\pi\)
−0.982239 + 0.187636i \(0.939917\pi\)
\(398\) 18.0875 + 1.97993i 0.906646 + 0.0992449i
\(399\) 0 0
\(400\) −3.62559 1.68970i −0.181280 0.0844850i
\(401\) −9.54674 −0.476742 −0.238371 0.971174i \(-0.576613\pi\)
−0.238371 + 0.971174i \(0.576613\pi\)
\(402\) 4.91700 44.9190i 0.245238 2.24036i
\(403\) 32.1106i 1.59955i
\(404\) 1.30037 5.86854i 0.0646956 0.291971i
\(405\) 10.4948i 0.521490i
\(406\) 0 0
\(407\) 6.11561i 0.303140i
\(408\) −7.00166 + 20.6371i −0.346634 + 1.02169i
\(409\) 21.6716i 1.07159i 0.844347 + 0.535796i \(0.179988\pi\)
−0.844347 + 0.535796i \(0.820012\pi\)
\(410\) −10.4970 1.14904i −0.518411 0.0567472i
\(411\) −12.9428 −0.638419
\(412\) 0.747370 + 0.165604i 0.0368203 + 0.00815873i
\(413\) 0 0
\(414\) 5.50701 50.3090i 0.270655 2.47255i
\(415\) 15.8027i 0.775725i
\(416\) −14.1883 + 23.3957i −0.695639 + 1.14707i
\(417\) −22.8163 −1.11732
\(418\) 0.261973 2.39324i 0.0128135 0.117057i
\(419\) 13.0327 0.636690 0.318345 0.947975i \(-0.396873\pi\)
0.318345 + 0.947975i \(0.396873\pi\)
\(420\) 0 0
\(421\) −34.2800 −1.67070 −0.835352 0.549715i \(-0.814736\pi\)
−0.835352 + 0.549715i \(0.814736\pi\)
\(422\) −2.60658 + 23.8123i −0.126886 + 1.15916i
\(423\) −6.59983 −0.320895
\(424\) −9.00497 3.05517i −0.437320 0.148372i
\(425\) 2.54530i 0.123465i
\(426\) 7.60584 69.4827i 0.368504 3.36645i
\(427\) 0 0
\(428\) −0.364512 + 1.64504i −0.0176194 + 0.0795159i
\(429\) −17.5255 −0.846137
\(430\) −1.94286 0.212673i −0.0936931 0.0102560i
\(431\) 2.85250i 0.137400i 0.997637 + 0.0687001i \(0.0218852\pi\)
−0.997637 + 0.0687001i \(0.978115\pi\)
\(432\) −34.7151 16.1789i −1.67023 0.778406i
\(433\) 34.6179i 1.66363i 0.555053 + 0.831815i \(0.312698\pi\)
−0.555053 + 0.831815i \(0.687302\pi\)
\(434\) 0 0
\(435\) 2.34366i 0.112370i
\(436\) 7.71426 + 1.70935i 0.369446 + 0.0818628i
\(437\) 8.25838i 0.395052i
\(438\) −0.0498940 + 0.455804i −0.00238403 + 0.0217791i
\(439\) 10.9381 0.522047 0.261023 0.965332i \(-0.415940\pi\)
0.261023 + 0.965332i \(0.415940\pi\)
\(440\) −3.20601 1.08772i −0.152840 0.0518551i
\(441\) 0 0
\(442\) −17.3076 1.89456i −0.823240 0.0901149i
\(443\) 35.3941i 1.68163i −0.541325 0.840813i \(-0.682077\pi\)
0.541325 0.840813i \(-0.317923\pi\)
\(444\) −30.1999 6.69177i −1.43322 0.317578i
\(445\) 3.94128 0.186834
\(446\) −26.6665 2.91902i −1.26270 0.138219i
\(447\) 8.65029 0.409145
\(448\) 0 0
\(449\) 28.0029 1.32154 0.660768 0.750590i \(-0.270231\pi\)
0.660768 + 0.750590i \(0.270231\pi\)
\(450\) 8.66423 + 0.948419i 0.408436 + 0.0447089i
\(451\) −8.93750 −0.420850
\(452\) 5.23700 + 1.16043i 0.246328 + 0.0545820i
\(453\) 20.0060i 0.939962i
\(454\) 1.31367 + 0.143800i 0.0616537 + 0.00674885i
\(455\) 0 0
\(456\) 11.5315 + 3.91237i 0.540014 + 0.183214i
\(457\) 20.1898 0.944439 0.472220 0.881481i \(-0.343453\pi\)
0.472220 + 0.881481i \(0.343453\pi\)
\(458\) 2.01295 18.3892i 0.0940588 0.859269i
\(459\) 24.3713i 1.13755i
\(460\) 11.3380 + 2.51231i 0.528638 + 0.117137i
\(461\) 0.127845i 0.00595433i 0.999996 + 0.00297717i \(0.000947663\pi\)
−0.999996 + 0.00297717i \(0.999052\pi\)
\(462\) 0 0
\(463\) 17.8655i 0.830282i −0.909757 0.415141i \(-0.863732\pi\)
0.909757 0.415141i \(-0.136268\pi\)
\(464\) 2.80705 + 1.30822i 0.130314 + 0.0607327i
\(465\) 20.0956i 0.931913i
\(466\) 21.9330 + 2.40087i 1.01603 + 0.111218i
\(467\) −14.6695 −0.678826 −0.339413 0.940638i \(-0.610228\pi\)
−0.339413 + 0.940638i \(0.610228\pi\)
\(468\) 12.8982 58.2093i 0.596218 2.69072i
\(469\) 0 0
\(470\) 0.164790 1.50543i 0.00760119 0.0694402i
\(471\) 47.1711i 2.17353i
\(472\) −26.4743 8.98209i −1.21858 0.413434i
\(473\) −1.65421 −0.0760608
\(474\) 5.01638 45.8268i 0.230410 2.10489i
\(475\) −1.42226 −0.0652578
\(476\) 0 0
\(477\) 20.7203 0.948719
\(478\) −2.17482 + 19.8680i −0.0994740 + 0.908739i
\(479\) −26.1514 −1.19489 −0.597444 0.801911i \(-0.703817\pi\)
−0.597444 + 0.801911i \(0.703817\pi\)
\(480\) 8.87940 14.6416i 0.405287 0.668295i
\(481\) 24.7133i 1.12683i
\(482\) 3.32134 30.3419i 0.151283 1.38204i
\(483\) 0 0
\(484\) 18.6815 + 4.13949i 0.849158 + 0.188159i
\(485\) −8.71387 −0.395677
\(486\) 4.27843 + 0.468333i 0.194073 + 0.0212440i
\(487\) 16.6245i 0.753330i −0.926350 0.376665i \(-0.877071\pi\)
0.926350 0.376665i \(-0.122929\pi\)
\(488\) −8.72108 + 25.7050i −0.394785 + 1.16361i
\(489\) 29.1818i 1.31965i
\(490\) 0 0
\(491\) 21.9094i 0.988758i −0.869246 0.494379i \(-0.835395\pi\)
0.869246 0.494379i \(-0.164605\pi\)
\(492\) 9.77951 44.1348i 0.440894 1.98975i
\(493\) 1.97066i 0.0887540i
\(494\) −1.05864 + 9.67112i −0.0476304 + 0.435124i
\(495\) 7.37699 0.331571
\(496\) −24.0690 11.2173i −1.08073 0.503673i
\(497\) 0 0
\(498\) 67.2485 + 7.36127i 3.01348 + 0.329867i
\(499\) 40.6890i 1.82149i 0.412970 + 0.910745i \(0.364492\pi\)
−0.412970 + 0.910745i \(0.635508\pi\)
\(500\) −0.432671 + 1.95264i −0.0193496 + 0.0873246i
\(501\) −14.9802 −0.669267
\(502\) 1.46851 + 0.160749i 0.0655430 + 0.00717459i
\(503\) 7.19624 0.320864 0.160432 0.987047i \(-0.448711\pi\)
0.160432 + 0.987047i \(0.448711\pi\)
\(504\) 0 0
\(505\) −3.00544 −0.133740
\(506\) 9.77062 + 1.06953i 0.434357 + 0.0475464i
\(507\) 31.4688 1.39758
\(508\) 0.926065 4.17932i 0.0410875 0.185427i
\(509\) 5.14254i 0.227939i −0.993484 0.113970i \(-0.963643\pi\)
0.993484 0.113970i \(-0.0363567\pi\)
\(510\) 10.8315 + 1.18566i 0.479629 + 0.0525020i
\(511\) 0 0
\(512\) −12.5802 18.8080i −0.555970 0.831203i
\(513\) −13.6181 −0.601256
\(514\) −0.754638 + 6.89395i −0.0332856 + 0.304079i
\(515\) 0.382749i 0.0168659i
\(516\) 1.81006 8.16878i 0.0796834 0.359610i
\(517\) 1.28177i 0.0563721i
\(518\) 0 0
\(519\) 20.9797i 0.920905i
\(520\) 12.9555 + 4.39550i 0.568138 + 0.192755i
\(521\) 9.06489i 0.397140i 0.980087 + 0.198570i \(0.0636298\pi\)
−0.980087 + 0.198570i \(0.936370\pi\)
\(522\) −6.70813 0.734298i −0.293607 0.0321393i
\(523\) −17.6074 −0.769918 −0.384959 0.922934i \(-0.625784\pi\)
−0.384959 + 0.922934i \(0.625784\pi\)
\(524\) −18.8737 4.18209i −0.824502 0.182695i
\(525\) 0 0
\(526\) 1.19975 10.9603i 0.0523117 0.477890i
\(527\) 16.8974i 0.736062i
\(528\) 6.12223 13.1365i 0.266436 0.571692i
\(529\) −10.7156 −0.465896
\(530\) −0.517362 + 4.72633i −0.0224728 + 0.205299i
\(531\) 60.9171 2.64358
\(532\) 0 0
\(533\) 36.1166 1.56438
\(534\) −1.83594 + 16.7721i −0.0794488 + 0.725800i
\(535\) 0.842470 0.0364231
\(536\) −9.59222 + 28.2726i −0.414321 + 1.22119i
\(537\) 63.9083i 2.75785i
\(538\) −3.24890 + 29.6801i −0.140070 + 1.27960i
\(539\) 0 0
\(540\) −4.14282 + 18.6965i −0.178279 + 0.804570i
\(541\) −27.9622 −1.20219 −0.601094 0.799178i \(-0.705268\pi\)
−0.601094 + 0.799178i \(0.705268\pi\)
\(542\) −30.2543 3.31175i −1.29953 0.142252i
\(543\) 18.4784i 0.792983i
\(544\) 7.46623 12.3114i 0.320112 0.527846i
\(545\) 3.95068i 0.169229i
\(546\) 0 0
\(547\) 29.6385i 1.26725i 0.773640 + 0.633626i \(0.218434\pi\)
−0.773640 + 0.633626i \(0.781566\pi\)
\(548\) 8.34885 + 1.84996i 0.356645 + 0.0790264i
\(549\) 59.1469i 2.52433i
\(550\) −0.184195 + 1.68270i −0.00785409 + 0.0717506i
\(551\) 1.10116 0.0469111
\(552\) −15.9726 + 47.0786i −0.679841 + 2.00380i
\(553\) 0 0
\(554\) 7.26446 + 0.795196i 0.308637 + 0.0337846i
\(555\) 15.4662i 0.656504i
\(556\) 14.7179 + 3.26122i 0.624176 + 0.138307i
\(557\) 35.7334 1.51407 0.757037 0.653372i \(-0.226646\pi\)
0.757037 + 0.653372i \(0.226646\pi\)
\(558\) 57.5188 + 6.29622i 2.43496 + 0.266540i
\(559\) 6.68471 0.282733
\(560\) 0 0
\(561\) 9.22231 0.389366
\(562\) −21.9760 2.40558i −0.927002 0.101473i
\(563\) −23.0047 −0.969532 −0.484766 0.874644i \(-0.661095\pi\)
−0.484766 + 0.874644i \(0.661095\pi\)
\(564\) 6.32958 + 1.40253i 0.266523 + 0.0590570i
\(565\) 2.68201i 0.112833i
\(566\) −40.1642 4.39653i −1.68823 0.184800i
\(567\) 0 0
\(568\) −14.8377 + 43.7333i −0.622574 + 1.83501i
\(569\) −18.8787 −0.791438 −0.395719 0.918372i \(-0.629505\pi\)
−0.395719 + 0.918372i \(0.629505\pi\)
\(570\) 0.662522 6.05243i 0.0277500 0.253508i
\(571\) 23.9624i 1.00279i −0.865217 0.501397i \(-0.832820\pi\)
0.865217 0.501397i \(-0.167180\pi\)
\(572\) 11.3050 + 2.50498i 0.472684 + 0.104739i
\(573\) 11.2401i 0.469561i
\(574\) 0 0
\(575\) 5.80651i 0.242148i
\(576\) 39.1259 + 30.0025i 1.63025 + 1.25010i
\(577\) 10.6311i 0.442580i 0.975208 + 0.221290i \(0.0710268\pi\)
−0.975208 + 0.221290i \(0.928973\pi\)
\(578\) −14.7912 1.61910i −0.615232 0.0673457i
\(579\) −46.4076 −1.92864
\(580\) 0.334988 1.51180i 0.0139096 0.0627740i
\(581\) 0 0
\(582\) 4.05912 37.0819i 0.168256 1.53709i
\(583\) 4.02415i 0.166663i
\(584\) 0.0973345 0.286889i 0.00402773 0.0118716i
\(585\) −29.8106 −1.23252
\(586\) −0.101130 + 0.923866i −0.00417764 + 0.0381646i
\(587\) 0.240690 0.00993436 0.00496718 0.999988i \(-0.498419\pi\)
0.00496718 + 0.999988i \(0.498419\pi\)
\(588\) 0 0
\(589\) −9.44189 −0.389046
\(590\) −1.52103 + 13.8953i −0.0626197 + 0.572059i
\(591\) 74.0428 3.04571
\(592\) 18.5243 + 8.63319i 0.761342 + 0.354822i
\(593\) 30.9254i 1.26995i 0.772531 + 0.634977i \(0.218990\pi\)
−0.772531 + 0.634977i \(0.781010\pi\)
\(594\) −1.76366 + 16.1119i −0.0723640 + 0.661077i
\(595\) 0 0
\(596\) −5.57995 1.23642i −0.228564 0.0506458i
\(597\) 38.9469 1.59399
\(598\) −39.4833 4.32199i −1.61459 0.176739i
\(599\) 29.9488i 1.22368i 0.790983 + 0.611838i \(0.209570\pi\)
−0.790983 + 0.611838i \(0.790430\pi\)
\(600\) −8.10790 2.75081i −0.331004 0.112302i
\(601\) 23.0748i 0.941241i −0.882336 0.470621i \(-0.844030\pi\)
0.882336 0.470621i \(-0.155970\pi\)
\(602\) 0 0
\(603\) 65.0550i 2.64925i
\(604\) 2.85953 12.9050i 0.116353 0.525099i
\(605\) 9.56730i 0.388966i
\(606\) 1.40000 12.7896i 0.0568712 0.519544i
\(607\) 17.8801 0.725730 0.362865 0.931842i \(-0.381799\pi\)
0.362865 + 0.931842i \(0.381799\pi\)
\(608\) −6.87932 4.17197i −0.278993 0.169196i
\(609\) 0 0
\(610\) 13.4915 + 1.47683i 0.546254 + 0.0597950i
\(611\) 5.17965i 0.209546i
\(612\) −6.78732 + 30.6311i −0.274361 + 1.23819i
\(613\) −8.37011 −0.338065 −0.169033 0.985610i \(-0.554064\pi\)
−0.169033 + 0.985610i \(0.554064\pi\)
\(614\) −6.86097 0.751028i −0.276886 0.0303090i
\(615\) −22.6027 −0.911427
\(616\) 0 0
\(617\) 33.7886 1.36028 0.680139 0.733084i \(-0.261920\pi\)
0.680139 + 0.733084i \(0.261920\pi\)
\(618\) 1.62879 + 0.178293i 0.0655194 + 0.00717200i
\(619\) 33.2883 1.33797 0.668986 0.743275i \(-0.266729\pi\)
0.668986 + 0.743275i \(0.266729\pi\)
\(620\) −2.87235 + 12.9629i −0.115356 + 0.520602i
\(621\) 55.5974i 2.23105i
\(622\) 16.7247 + 1.83075i 0.670600 + 0.0734065i
\(623\) 0 0
\(624\) −24.7400 + 53.0848i −0.990394 + 2.12509i
\(625\) 1.00000 0.0400000
\(626\) −4.09451 + 37.4051i −0.163649 + 1.49501i
\(627\) 5.15323i 0.205800i
\(628\) 6.74236 30.4282i 0.269049 1.21422i
\(629\) 13.0047i 0.518533i
\(630\) 0 0
\(631\) 43.1690i 1.71853i 0.511528 + 0.859266i \(0.329079\pi\)
−0.511528 + 0.859266i \(0.670921\pi\)
\(632\) −9.78607 + 28.8440i −0.389269 + 1.14735i
\(633\) 51.2737i 2.03794i
\(634\) 37.1918 + 4.07116i 1.47708 + 0.161686i
\(635\) −2.14034 −0.0849370
\(636\) −19.8719 4.40327i −0.787972 0.174601i
\(637\) 0 0
\(638\) 0.142610 1.30280i 0.00564597 0.0515784i
\(639\) 100.630i 3.98086i
\(640\) −7.82052 + 8.17554i −0.309133 + 0.323166i
\(641\) 32.0262 1.26496 0.632479 0.774578i \(-0.282038\pi\)
0.632479 + 0.774578i \(0.282038\pi\)
\(642\) −0.392442 + 3.58513i −0.0154884 + 0.141494i
\(643\) −37.9515 −1.49666 −0.748331 0.663326i \(-0.769144\pi\)
−0.748331 + 0.663326i \(0.769144\pi\)
\(644\) 0 0
\(645\) −4.18346 −0.164723
\(646\) 0.557081 5.08918i 0.0219180 0.200231i
\(647\) 8.98771 0.353344 0.176672 0.984270i \(-0.443467\pi\)
0.176672 + 0.984270i \(0.443467\pi\)
\(648\) −28.1099 9.53702i −1.10426 0.374649i
\(649\) 11.8309i 0.464402i
\(650\) 0.744335 6.79982i 0.0291952 0.266711i
\(651\) 0 0
\(652\) −4.17108 + 18.8240i −0.163352 + 0.737205i
\(653\) 18.2791 0.715317 0.357658 0.933852i \(-0.383575\pi\)
0.357658 + 0.933852i \(0.383575\pi\)
\(654\) 16.8121 + 1.84032i 0.657406 + 0.0719622i
\(655\) 9.66575i 0.377672i
\(656\) −12.6167 + 27.0718i −0.492601 + 1.05697i
\(657\) 0.660129i 0.0257541i
\(658\) 0 0
\(659\) 36.9643i 1.43992i 0.694014 + 0.719962i \(0.255841\pi\)
−0.694014 + 0.719962i \(0.744159\pi\)
\(660\) −7.07493 1.56768i −0.275391 0.0610219i
\(661\) 23.0087i 0.894933i −0.894301 0.447466i \(-0.852326\pi\)
0.894301 0.447466i \(-0.147674\pi\)
\(662\) −3.73677 + 34.1370i −0.145234 + 1.32677i
\(663\) −37.2675 −1.44735
\(664\) −42.3271 14.3606i −1.64261 0.557298i
\(665\) 0 0
\(666\) −44.2682 4.84576i −1.71536 0.187769i
\(667\) 4.49560i 0.174070i
\(668\) 9.66314 + 2.14118i 0.373878 + 0.0828449i
\(669\) −57.4195 −2.21997
\(670\) 14.8391 + 1.62435i 0.573285 + 0.0627540i
\(671\) 11.4871 0.443453
\(672\) 0 0
\(673\) −42.0925 −1.62255 −0.811273 0.584668i \(-0.801225\pi\)
−0.811273 + 0.584668i \(0.801225\pi\)
\(674\) −27.7054 3.03274i −1.06717 0.116817i
\(675\) 9.57500 0.368542
\(676\) −20.2993 4.49797i −0.780741 0.172999i
\(677\) 24.3252i 0.934894i −0.884021 0.467447i \(-0.845174\pi\)
0.884021 0.467447i \(-0.154826\pi\)
\(678\) 11.4133 + 1.24934i 0.438325 + 0.0479807i
\(679\) 0 0
\(680\) −6.81752 2.31302i −0.261440 0.0887002i
\(681\) 2.82866 0.108394
\(682\) −1.22280 + 11.1709i −0.0468236 + 0.427754i
\(683\) 19.1971i 0.734555i 0.930111 + 0.367278i \(0.119710\pi\)
−0.930111 + 0.367278i \(0.880290\pi\)
\(684\) 17.1160 + 3.79261i 0.654447 + 0.145014i
\(685\) 4.27568i 0.163365i
\(686\) 0 0
\(687\) 39.5963i 1.51069i
\(688\) −2.33519 + 5.01063i −0.0890284 + 0.191028i
\(689\) 16.2617i 0.619520i
\(690\) 24.7096 + 2.70481i 0.940679 + 0.102970i
\(691\) −14.0055 −0.532794 −0.266397 0.963863i \(-0.585833\pi\)
−0.266397 + 0.963863i \(0.585833\pi\)
\(692\) −2.99871 + 13.5331i −0.113994 + 0.514453i
\(693\) 0 0
\(694\) −1.29834 + 11.8609i −0.0492842 + 0.450233i
\(695\) 7.53742i 0.285911i
\(696\) 6.27741 + 2.12977i 0.237945 + 0.0807288i
\(697\) −19.0054 −0.719882
\(698\) −3.62839 + 33.1469i −0.137337 + 1.25463i
\(699\) 47.2271 1.78629
\(700\) 0 0
\(701\) 11.9124 0.449923 0.224962 0.974368i \(-0.427774\pi\)
0.224962 + 0.974368i \(0.427774\pi\)
\(702\) 7.12700 65.1083i 0.268991 2.45736i
\(703\) 7.26676 0.274071
\(704\) −5.82685 + 7.59874i −0.219608 + 0.286388i
\(705\) 3.24155i 0.122084i
\(706\) −3.18120 + 29.0616i −0.119726 + 1.09375i
\(707\) 0 0
\(708\) −58.4227 12.9455i −2.19566 0.486520i
\(709\) 47.2981 1.77632 0.888158 0.459538i \(-0.151985\pi\)
0.888158 + 0.459538i \(0.151985\pi\)
\(710\) 22.9538 + 2.51261i 0.861441 + 0.0942966i
\(711\) 66.3698i 2.48906i
\(712\) 3.58159 10.5566i 0.134226 0.395625i
\(713\) 38.5474i 1.44361i
\(714\) 0 0
\(715\) 5.78958i 0.216518i
\(716\) 9.13467 41.2247i 0.341379 1.54064i
\(717\) 42.7806i 1.59767i
\(718\) 4.22447 38.5924i 0.157656 1.44025i
\(719\) −1.77790 −0.0663045 −0.0331523 0.999450i \(-0.510555\pi\)
−0.0331523 + 0.999450i \(0.510555\pi\)
\(720\) 10.4138 22.3450i 0.388101 0.832749i
\(721\) 0 0
\(722\) 23.8668 + 2.61255i 0.888230 + 0.0972290i
\(723\) 65.3336i 2.42978i
\(724\) −2.64119 + 11.9196i −0.0981590 + 0.442990i
\(725\) −0.774233 −0.0287543
\(726\) 40.7136 + 4.45667i 1.51102 + 0.165402i
\(727\) 27.1619 1.00738 0.503689 0.863885i \(-0.331976\pi\)
0.503689 + 0.863885i \(0.331976\pi\)
\(728\) 0 0
\(729\) −22.2718 −0.824883
\(730\) −0.150576 0.0164826i −0.00557307 0.000610050i
\(731\) −3.51765 −0.130105
\(732\) −12.5693 + 56.7250i −0.464574 + 2.09662i
\(733\) 22.7760i 0.841249i −0.907235 0.420625i \(-0.861811\pi\)
0.907235 0.420625i \(-0.138189\pi\)
\(734\) 28.1763 + 3.08428i 1.04001 + 0.113843i
\(735\) 0 0
\(736\) 17.0324 28.0855i 0.627824 1.03525i
\(737\) 12.6345 0.465398
\(738\) 7.08171 64.6945i 0.260681 2.38144i
\(739\) 32.5176i 1.19618i 0.801429 + 0.598091i \(0.204074\pi\)
−0.801429 + 0.598091i \(0.795926\pi\)
\(740\) 2.21065 9.97662i 0.0812650 0.366748i
\(741\) 20.8243i 0.764999i
\(742\) 0 0
\(743\) 9.19402i 0.337296i 0.985676 + 0.168648i \(0.0539401\pi\)
−0.985676 + 0.168648i \(0.946060\pi\)
\(744\) −53.8255 18.2617i −1.97334 0.669506i
\(745\) 2.85765i 0.104696i
\(746\) −28.9474 3.16869i −1.05984 0.116014i
\(747\) 97.3942 3.56347
\(748\) −5.94894 1.31818i −0.217515 0.0481975i
\(749\) 0 0
\(750\) −0.465823 + 4.25550i −0.0170095 + 0.155389i
\(751\) 20.3056i 0.740962i 0.928840 + 0.370481i \(0.120807\pi\)
−0.928840 + 0.370481i \(0.879193\pi\)
\(752\) −3.88249 1.80942i −0.141580 0.0659829i
\(753\) 3.16207 0.115232
\(754\) −0.576289 + 5.26465i −0.0209872 + 0.191727i
\(755\) −6.60903 −0.240527
\(756\) 0 0
\(757\) 10.9555 0.398184 0.199092 0.979981i \(-0.436201\pi\)
0.199092 + 0.979981i \(0.436201\pi\)
\(758\) −0.502190 + 4.58772i −0.0182404 + 0.166634i
\(759\) 21.0385 0.763651
\(760\) −1.29246 + 3.80948i −0.0468826 + 0.138184i
\(761\) 31.4198i 1.13897i 0.822003 + 0.569484i \(0.192857\pi\)
−0.822003 + 0.569484i \(0.807143\pi\)
\(762\) 0.997022 9.10823i 0.0361183 0.329957i
\(763\) 0 0
\(764\) 1.60659 7.25052i 0.0581243 0.262314i
\(765\) 15.6870 0.567166
\(766\) −47.4478 5.19382i −1.71436 0.187660i
\(767\) 47.8087i 1.72627i
\(768\) −31.1480 37.0886i −1.12396 1.33832i
\(769\) 23.9511i 0.863700i 0.901945 + 0.431850i \(0.142139\pi\)
−0.901945 + 0.431850i \(0.857861\pi\)
\(770\) 0 0
\(771\) 14.8444i 0.534606i
\(772\) 29.9357 + 6.63323i 1.07741 + 0.238735i
\(773\) 15.1850i 0.546165i −0.961991 0.273083i \(-0.911957\pi\)
0.961991 0.273083i \(-0.0880433\pi\)
\(774\) 1.31073 11.9741i 0.0471133 0.430401i
\(775\) 6.63865 0.238467
\(776\) −7.91864 + 23.3398i −0.284263 + 0.837851i
\(777\) 0 0
\(778\) 5.07793 + 0.555850i 0.182053 + 0.0199282i
\(779\) 10.6198i 0.380494i
\(780\) 28.5899 + 6.33503i 1.02368 + 0.226830i
\(781\) 19.5436 0.699324
\(782\) 20.7770 + 2.27433i 0.742986 + 0.0813300i
\(783\) −7.41329 −0.264929
\(784\) 0 0
\(785\) −15.5831 −0.556185
\(786\) −41.1326 4.50253i −1.46715 0.160600i
\(787\) −18.2996 −0.652312 −0.326156 0.945316i \(-0.605753\pi\)
−0.326156 + 0.945316i \(0.605753\pi\)
\(788\) −47.7620 10.5832i −1.70145 0.377012i
\(789\) 23.6001i 0.840187i
\(790\) 15.1390 + 1.65717i 0.538622 + 0.0589596i
\(791\) 0 0
\(792\) 6.70376 19.7590i 0.238208 0.702107i
\(793\) −46.4194 −1.64840
\(794\) 1.15064 10.5116i 0.0408348 0.373044i
\(795\) 10.1769i 0.360939i
\(796\) −25.1231 5.56683i −0.890463 0.197311i
\(797\) 15.0960i 0.534728i −0.963596 0.267364i \(-0.913847\pi\)
0.963596 0.267364i \(-0.0861526\pi\)
\(798\) 0 0
\(799\) 2.72566i 0.0964268i
\(800\) 4.83689 + 2.93333i 0.171010 + 0.103709i
\(801\) 24.2906i 0.858266i
\(802\) 13.4210 + 1.46911i 0.473911 + 0.0518761i
\(803\) −0.128205 −0.00452426
\(804\) −13.8248 + 62.3912i −0.487563 + 2.20037i
\(805\) 0 0
\(806\) 4.94138 45.1417i 0.174053 1.59005i
\(807\) 63.9085i 2.24969i
\(808\) −2.73116 + 8.04998i −0.0960819 + 0.283197i
\(809\) 44.4480 1.56271 0.781355 0.624087i \(-0.214529\pi\)
0.781355 + 0.624087i \(0.214529\pi\)
\(810\) −1.61500 + 14.7537i −0.0567453 + 0.518393i
\(811\) −34.6449 −1.21655 −0.608274 0.793727i \(-0.708138\pi\)
−0.608274 + 0.793727i \(0.708138\pi\)
\(812\) 0 0
\(813\) −65.1449 −2.28473
\(814\) 0.941107 8.59743i 0.0329858 0.301340i
\(815\) 9.64030 0.337685
\(816\) 13.0188 27.9345i 0.455749 0.977902i
\(817\) 1.96559i 0.0687672i
\(818\) 3.33496 30.4663i 0.116604 1.06523i
\(819\) 0 0
\(820\) 14.5801 + 3.23069i 0.509158 + 0.112821i
\(821\) 23.7100 0.827484 0.413742 0.910394i \(-0.364222\pi\)
0.413742 + 0.910394i \(0.364222\pi\)
\(822\) 18.1951 + 1.99171i 0.634629 + 0.0694688i
\(823\) 6.49176i 0.226289i −0.993579 0.113144i \(-0.963908\pi\)
0.993579 0.113144i \(-0.0360922\pi\)
\(824\) −1.02518 0.347819i −0.0357138 0.0121168i
\(825\) 3.62326i 0.126146i
\(826\) 0 0
\(827\) 39.4872i 1.37310i 0.727081 + 0.686552i \(0.240877\pi\)
−0.727081 + 0.686552i \(0.759123\pi\)
\(828\) −15.4837 + 69.8777i −0.538095 + 2.42842i
\(829\) 3.26274i 0.113320i −0.998394 0.0566598i \(-0.981955\pi\)
0.998394 0.0566598i \(-0.0180451\pi\)
\(830\) −2.43182 + 22.2157i −0.0844096 + 0.771119i
\(831\) 15.6422 0.542621
\(832\) 23.5464 30.7067i 0.816325 1.06456i
\(833\) 0 0
\(834\) 32.0755 + 3.51110i 1.11068 + 0.121580i
\(835\) 4.94876i 0.171259i
\(836\) −0.736572 + 3.32414i −0.0254749 + 0.114968i
\(837\) 63.5651 2.19713
\(838\) −18.3216 2.00555i −0.632909 0.0692807i
\(839\) 5.39522 0.186264 0.0931318 0.995654i \(-0.470312\pi\)
0.0931318 + 0.995654i \(0.470312\pi\)
\(840\) 0 0
\(841\) −28.4006 −0.979330
\(842\) 48.1914 + 5.27521i 1.66078 + 0.181796i
\(843\) −47.3197 −1.62978
\(844\) 7.32875 33.0746i 0.252266 1.13847i
\(845\) 10.3958i 0.357627i
\(846\) 9.27814 + 1.01562i 0.318989 + 0.0349178i
\(847\) 0 0
\(848\) 12.1892 + 5.68074i 0.418578 + 0.195077i
\(849\) −86.4834 −2.96810
\(850\) −0.391687 + 3.57823i −0.0134347 + 0.122732i
\(851\) 29.6672i 1.01698i
\(852\) −21.3848 + 96.5094i −0.732632 + 3.30636i
\(853\) 10.7675i 0.368672i 0.982863 + 0.184336i \(0.0590134\pi\)
−0.982863 + 0.184336i \(0.940987\pi\)
\(854\) 0 0
\(855\) 8.76558i 0.299776i
\(856\) 0.765585 2.25653i 0.0261672 0.0771265i
\(857\) 35.1897i 1.20206i −0.799227 0.601029i \(-0.794758\pi\)
0.799227 0.601029i \(-0.205242\pi\)
\(858\) 24.6376 + 2.69692i 0.841112 + 0.0920714i
\(859\) 41.2385 1.40704 0.703520 0.710675i \(-0.251610\pi\)
0.703520 + 0.710675i \(0.251610\pi\)
\(860\) 2.69858 + 0.597958i 0.0920208 + 0.0203902i
\(861\) 0 0
\(862\) 0.438960 4.01010i 0.0149510 0.136584i
\(863\) 23.0295i 0.783933i 0.919980 + 0.391966i \(0.128205\pi\)
−0.919980 + 0.391966i \(0.871795\pi\)
\(864\) 46.3133 + 28.0867i 1.57561 + 0.955528i
\(865\) 6.93069 0.235651
\(866\) 5.32721 48.6664i 0.181026 1.65375i
\(867\) −31.8491 −1.08165
\(868\) 0 0
\(869\) 12.8898 0.437258
\(870\) 0.360656 3.29475i 0.0122274 0.111702i
\(871\) −51.0562 −1.72997
\(872\) −10.5818 3.59014i −0.358344 0.121578i
\(873\) 53.7047i 1.81763i
\(874\) 1.27085 11.6098i 0.0429871 0.392706i
\(875\) 0 0
\(876\) 0.140284 0.633098i 0.00473974 0.0213904i
\(877\) 4.06272 0.137188 0.0685941 0.997645i \(-0.478149\pi\)
0.0685941 + 0.997645i \(0.478149\pi\)
\(878\) −15.3770 1.68322i −0.518947 0.0568059i
\(879\) 1.98931i 0.0670978i
\(880\) 4.33967 + 2.02250i 0.146290 + 0.0681783i
\(881\) 42.0606i 1.41706i 0.705682 + 0.708529i \(0.250641\pi\)
−0.705682 + 0.708529i \(0.749359\pi\)
\(882\) 0 0
\(883\) 54.8918i 1.84725i −0.383291 0.923627i \(-0.625210\pi\)
0.383291 0.923627i \(-0.374790\pi\)
\(884\) 24.0398 + 5.32680i 0.808546 + 0.179160i
\(885\) 29.9199i 1.00575i
\(886\) −5.44666 + 49.7577i −0.182984 + 1.67164i
\(887\) −38.1245 −1.28009 −0.640047 0.768336i \(-0.721085\pi\)
−0.640047 + 0.768336i \(0.721085\pi\)
\(888\) 41.4257 + 14.0547i 1.39016 + 0.471646i
\(889\) 0 0
\(890\) −5.54071 0.606507i −0.185725 0.0203302i
\(891\) 12.5618i 0.420836i
\(892\) 37.0390 + 8.20720i 1.24016 + 0.274798i
\(893\) −1.52304 −0.0509665
\(894\) −12.1607 1.33116i −0.406715 0.0445206i
\(895\) −21.1123 −0.705706
\(896\) 0 0
\(897\) −85.0171 −2.83864
\(898\) −39.3669 4.30925i −1.31369 0.143801i
\(899\) −5.13987 −0.171424
\(900\) −12.0344 2.66661i −0.401145 0.0888869i
\(901\) 8.55727i 0.285084i
\(902\) 12.5645 + 1.37536i 0.418351 + 0.0457943i
\(903\) 0 0
\(904\) −7.18369 2.43725i −0.238926 0.0810617i
\(905\) 6.10438 0.202917
\(906\) 3.07864 28.1247i 0.102281 0.934381i
\(907\) 0.354708i 0.0117779i 0.999983 + 0.00588894i \(0.00187452\pi\)
−0.999983 + 0.00588894i \(0.998125\pi\)
\(908\) −1.82465 0.404312i −0.0605533 0.0134176i
\(909\) 18.5229i 0.614366i
\(910\) 0 0
\(911\) 12.2958i 0.407379i −0.979036 0.203690i \(-0.934707\pi\)
0.979036 0.203690i \(-0.0652934\pi\)
\(912\) −15.6092 7.27462i −0.516872 0.240887i
\(913\) 18.9152i 0.626001i
\(914\) −28.3832 3.10693i −0.938831 0.102768i
\(915\) 29.0504 0.960378
\(916\) −5.65967 + 25.5420i −0.187001 + 0.843932i
\(917\) 0 0
\(918\) −3.75040 + 34.2616i −0.123782 + 1.13080i
\(919\) 0.280729i 0.00926038i −0.999989 0.00463019i \(-0.998526\pi\)
0.999989 0.00463019i \(-0.00147384\pi\)
\(920\) −15.5526 5.27661i −0.512753 0.173965i
\(921\) −14.7734 −0.486799
\(922\) 0.0196735 0.179727i 0.000647914 0.00591898i
\(923\) −78.9760 −2.59953
\(924\) 0 0
\(925\) −5.10930 −0.167993
\(926\) −2.74926 + 25.1157i −0.0903462 + 0.825352i
\(927\) 2.35893 0.0774774
\(928\) −3.74489 2.27109i −0.122932 0.0745520i
\(929\) 32.4836i 1.06575i −0.846194 0.532875i \(-0.821111\pi\)
0.846194 0.532875i \(-0.178889\pi\)
\(930\) −3.09244 + 28.2508i −0.101405 + 0.926379i
\(931\) 0 0
\(932\) −30.4643 6.75036i −0.997891 0.221115i
\(933\) 36.0124 1.17899
\(934\) 20.6227 + 2.25744i 0.674795 + 0.0738656i
\(935\) 3.04662i 0.0996350i
\(936\) −27.0900 + 79.8467i −0.885466 + 2.60987i
\(937\) 59.7020i 1.95038i 0.221368 + 0.975190i \(0.428948\pi\)
−0.221368 + 0.975190i \(0.571052\pi\)
\(938\) 0 0
\(939\) 80.5424i 2.62840i
\(940\) −0.463328 + 2.09099i −0.0151121 + 0.0682007i
\(941\) 14.2458i 0.464401i 0.972668 + 0.232201i \(0.0745926\pi\)
−0.972668 + 0.232201i \(0.925407\pi\)
\(942\) 7.25897 66.3139i 0.236510 2.16062i
\(943\) −43.3564 −1.41188
\(944\) 35.8358 + 16.7012i 1.16636 + 0.543578i
\(945\) 0 0
\(946\) 2.32552 + 0.254560i 0.0756092 + 0.00827647i
\(947\) 30.1026i 0.978202i 0.872227 + 0.489101i \(0.162675\pi\)
−0.872227 + 0.489101i \(0.837325\pi\)
\(948\) −14.1042 + 63.6521i −0.458083 + 2.06732i
\(949\) 0.518080 0.0168176
\(950\) 1.99944 + 0.218866i 0.0648703 + 0.00710095i
\(951\) 80.0831 2.59687
\(952\) 0 0
\(953\) 3.58515 0.116134 0.0580672 0.998313i \(-0.481506\pi\)
0.0580672 + 0.998313i \(0.481506\pi\)
\(954\) −29.1290 3.18857i −0.943086 0.103234i
\(955\) −3.71319 −0.120156
\(956\) 6.11480 27.5960i 0.197767 0.892519i
\(957\) 2.80525i 0.0906809i
\(958\) 36.7640 + 4.02433i 1.18779 + 0.130020i
\(959\) 0 0
\(960\) −14.7359 + 19.2170i −0.475600 + 0.620225i
\(961\) 13.0717 0.421668
\(962\) −3.80303 + 34.7424i −0.122615 + 1.12014i
\(963\) 5.19225i 0.167318i
\(964\) −9.33840 + 42.1441i −0.300770 + 1.35737i
\(965\) 15.3309i 0.493519i
\(966\) 0 0
\(967\) 46.1614i 1.48445i 0.670150 + 0.742226i \(0.266230\pi\)
−0.670150 + 0.742226i \(0.733770\pi\)
\(968\) −25.6257 8.69418i −0.823641 0.279441i
\(969\) 10.9582i 0.352029i
\(970\) 12.2501 + 1.34094i 0.393327 + 0.0430551i
\(971\) −11.6623 −0.374260 −0.187130 0.982335i \(-0.559919\pi\)
−0.187130 + 0.982335i \(0.559919\pi\)
\(972\) −5.94261 1.31678i −0.190609 0.0422357i
\(973\) 0 0
\(974\) −2.55828 + 23.3710i −0.0819727 + 0.748856i
\(975\) 14.6417i 0.468909i
\(976\) 16.2159 34.7944i 0.519057 1.11374i
\(977\) −42.4830 −1.35915 −0.679575 0.733606i \(-0.737836\pi\)
−0.679575 + 0.733606i \(0.737836\pi\)
\(978\) −4.49067 + 41.0243i −0.143596 + 1.31181i
\(979\) −4.71754 −0.150773
\(980\) 0 0
\(981\) 24.3486 0.777390
\(982\) −3.37155 + 30.8006i −0.107591 + 0.982887i
\(983\) −31.7431 −1.01245 −0.506223 0.862402i \(-0.668959\pi\)
−0.506223 + 0.862402i \(0.668959\pi\)
\(984\) −20.5399 + 60.5405i −0.654789 + 1.92996i
\(985\) 24.4602i 0.779368i
\(986\) 0.303257 2.77039i 0.00965767 0.0882270i
\(987\) 0 0
\(988\) 2.97650 13.4329i 0.0946951 0.427358i
\(989\) −8.02470 −0.255171
\(990\) −10.3707 1.13522i −0.329602 0.0360795i
\(991\) 29.3504i 0.932347i 0.884693 + 0.466173i \(0.154368\pi\)
−0.884693 + 0.466173i \(0.845632\pi\)
\(992\) 32.1105 + 19.4734i 1.01951 + 0.618281i
\(993\) 73.5053i 2.33262i
\(994\) 0 0
\(995\) 12.8662i 0.407886i
\(996\) −93.4062 20.6972i −2.95969 0.655816i
\(997\) 10.8068i 0.342256i 0.985249 + 0.171128i \(0.0547411\pi\)
−0.985249 + 0.171128i \(0.945259\pi\)
\(998\) 6.26147 57.2012i 0.198203 1.81067i
\(999\) −48.9216 −1.54781
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 980.2.g.a.391.1 32
4.3 odd 2 inner 980.2.g.a.391.4 32
7.2 even 3 980.2.o.f.31.10 32
7.3 odd 6 980.2.o.f.411.11 32
7.4 even 3 140.2.o.a.131.11 yes 32
7.5 odd 6 140.2.o.a.31.10 32
7.6 odd 2 inner 980.2.g.a.391.2 32
28.3 even 6 980.2.o.f.411.10 32
28.11 odd 6 140.2.o.a.131.10 yes 32
28.19 even 6 140.2.o.a.31.11 yes 32
28.23 odd 6 980.2.o.f.31.11 32
28.27 even 2 inner 980.2.g.a.391.3 32
35.4 even 6 700.2.p.c.551.6 32
35.12 even 12 700.2.t.d.199.3 32
35.18 odd 12 700.2.t.d.299.4 32
35.19 odd 6 700.2.p.c.451.7 32
35.32 odd 12 700.2.t.c.299.13 32
35.33 even 12 700.2.t.c.199.14 32
140.19 even 6 700.2.p.c.451.6 32
140.39 odd 6 700.2.p.c.551.7 32
140.47 odd 12 700.2.t.d.199.4 32
140.67 even 12 700.2.t.c.299.14 32
140.103 odd 12 700.2.t.c.199.13 32
140.123 even 12 700.2.t.d.299.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.10 32 7.5 odd 6
140.2.o.a.31.11 yes 32 28.19 even 6
140.2.o.a.131.10 yes 32 28.11 odd 6
140.2.o.a.131.11 yes 32 7.4 even 3
700.2.p.c.451.6 32 140.19 even 6
700.2.p.c.451.7 32 35.19 odd 6
700.2.p.c.551.6 32 35.4 even 6
700.2.p.c.551.7 32 140.39 odd 6
700.2.t.c.199.13 32 140.103 odd 12
700.2.t.c.199.14 32 35.33 even 12
700.2.t.c.299.13 32 35.32 odd 12
700.2.t.c.299.14 32 140.67 even 12
700.2.t.d.199.3 32 35.12 even 12
700.2.t.d.199.4 32 140.47 odd 12
700.2.t.d.299.3 32 140.123 even 12
700.2.t.d.299.4 32 35.18 odd 12
980.2.g.a.391.1 32 1.1 even 1 trivial
980.2.g.a.391.2 32 7.6 odd 2 inner
980.2.g.a.391.3 32 28.27 even 2 inner
980.2.g.a.391.4 32 4.3 odd 2 inner
980.2.o.f.31.10 32 7.2 even 3
980.2.o.f.31.11 32 28.23 odd 6
980.2.o.f.411.10 32 28.3 even 6
980.2.o.f.411.11 32 7.3 odd 6