Properties

Label 980.2.g.a.391.4
Level $980$
Weight $2$
Character 980.391
Analytic conductor $7.825$
Analytic rank $0$
Dimension $32$
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 391.4
Character \(\chi\) \(=\) 980.391
Dual form 980.2.g.a.391.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40582 + 0.153886i) q^{2} +3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} -1.00000i q^{5} +(-4.25550 + 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +O(q^{10})\) \(q+(-1.40582 + 0.153886i) q^{2} +3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} -1.00000i q^{5} +(-4.25550 + 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +(0.153886 + 1.40582i) q^{10} -1.19696i q^{11} +(5.91077 - 1.30972i) q^{12} -4.83692i q^{13} -3.02707i q^{15} +(3.62559 - 1.68970i) q^{16} +2.54530i q^{17} +(-8.66423 + 0.948419i) q^{18} -1.42226 q^{19} +(-0.432671 - 1.95264i) q^{20} +(0.184195 + 1.68270i) q^{22} -5.80651i q^{23} +(-8.10790 + 2.75081i) q^{24} -1.00000 q^{25} +(0.744335 + 6.79982i) q^{26} +9.57500 q^{27} +0.774233 q^{29} +(0.465823 + 4.25550i) q^{30} +6.63865 q^{31} +(-4.83689 + 2.93333i) q^{32} -3.62326i q^{33} +(-0.391687 - 3.57823i) q^{34} +(12.0344 - 2.66661i) q^{36} +5.10930 q^{37} +(1.99944 - 0.218866i) q^{38} -14.6417i q^{39} +(0.908739 + 2.67847i) q^{40} +7.46685i q^{41} -1.38202i q^{43} +(-0.517888 - 2.33722i) q^{44} -6.16313i q^{45} +(0.893541 + 8.16289i) q^{46} +1.07086 q^{47} +(10.9749 - 5.11483i) q^{48} +(1.40582 - 0.153886i) q^{50} +7.70480i q^{51} +(-2.09280 - 9.44476i) q^{52} +3.36198 q^{53} +(-13.4607 + 1.47346i) q^{54} -1.19696 q^{55} -4.30528 q^{57} +(-1.08843 + 0.119144i) q^{58} -9.88412 q^{59} +(-1.30972 - 5.91077i) q^{60} -9.59690i q^{61} +(-9.33272 + 1.02160i) q^{62} +(6.34839 - 4.86806i) q^{64} -4.83692 q^{65} +(0.557570 + 5.09364i) q^{66} +10.5555i q^{67} +(1.10128 + 4.97006i) q^{68} -17.5767i q^{69} +16.3277i q^{71} +(-16.5077 + 5.60068i) q^{72} +0.107109i q^{73} +(-7.18274 + 0.786250i) q^{74} -3.02707 q^{75} +(-2.77716 + 0.615371i) q^{76} +(2.25315 + 20.5835i) q^{78} +10.7688i q^{79} +(-1.68970 - 3.62559i) q^{80} +10.4948 q^{81} +(-1.14904 - 10.4970i) q^{82} -15.8027 q^{83} +2.54530 q^{85} +(0.212673 + 1.94286i) q^{86} +2.34366 q^{87} +(1.08772 + 3.20601i) q^{88} +3.94128i q^{89} +(0.948419 + 8.66423i) q^{90} +(-2.51231 - 11.3380i) q^{92} +20.0956 q^{93} +(-1.50543 + 0.164790i) q^{94} +1.42226i q^{95} +(-14.6416 + 8.87940i) q^{96} -8.71387i q^{97} -7.37699i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 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 \(-0.161623\pi\)
0.873839 + 0.486216i \(0.161623\pi\)
\(4\) 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 \(-0.942245\pi\)
0.983585 0.180448i \(-0.0577547\pi\)
\(12\) 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 \(-0.552164\pi\)
−0.163144 + 0.986602i \(0.552164\pi\)
\(20\) −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 \(-0.793025\pi\)
0.795943 0.605371i \(-0.206975\pi\)
\(24\) −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 \(-0.296689\pi\)
0.596169 + 0.802859i \(0.296689\pi\)
\(32\) −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 \(-0.966395\pi\)
0.994432 0.105378i \(-0.0336052\pi\)
\(44\) −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 \(-0.475115\pi\)
0.0781002 + 0.996946i \(0.475115\pi\)
\(48\) 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 \(-0.722477\pi\)
−0.643402 + 0.765529i \(0.722477\pi\)
\(60\) −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 \(0.223051\pi\)
−0.764367 + 0.644781i \(0.776949\pi\)
\(68\) 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 \(0.420372\pi\)
−0.247558 + 0.968873i \(0.579628\pi\)
\(72\) −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 \(0.207145\pi\)
−0.795621 + 0.605795i \(0.792855\pi\)
\(80\) −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 \(-0.834138\pi\)
−0.867287 + 0.497808i \(0.834138\pi\)
\(84\) 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 \(-0.506003\pi\)
−0.0188567 + 0.999822i \(0.506003\pi\)
\(104\) 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 \(-0.987034\pi\)
0.999171 0.0407223i \(-0.0129659\pi\)
\(108\) 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 \(0.0302731\pi\)
−0.995481 + 0.0949624i \(0.969727\pi\)
\(128\) −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 \(-0.361240\pi\)
0.422250 + 0.906479i \(0.361240\pi\)
\(132\) −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 \(-0.603568\pi\)
−0.319658 + 0.947533i \(0.603568\pi\)
\(140\) 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 \(0.0866659\pi\)
−0.963163 + 0.268918i \(0.913334\pi\)
\(152\) 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 \(-0.876769\pi\)
0.925992 0.377543i \(-0.123231\pi\)
\(164\) 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 \(-0.561327\pi\)
−0.191473 + 0.981498i \(0.561327\pi\)
\(168\) 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 \(0.289403\pi\)
−0.614389 + 0.789003i \(0.710597\pi\)
\(180\) −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 \(0.0428909\pi\)
−0.990936 + 0.134339i \(0.957109\pi\)
\(192\) 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 \(-0.349271\pi\)
0.456031 + 0.889964i \(0.349271\pi\)
\(200\) 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 \(0.198138\pi\)
−0.812441 + 0.583044i \(0.801862\pi\)
\(212\) 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 \(-0.719049\pi\)
−0.635119 + 0.772414i \(0.719049\pi\)
\(224\) 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 \(-0.490127\pi\)
0.0310110 + 0.999519i \(0.490127\pi\)
\(228\) −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 \(0.151106\pi\)
−0.889424 + 0.457084i \(0.848894\pi\)
\(240\) −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 \(-0.489504\pi\)
0.0329673 + 0.999456i \(0.489504\pi\)
\(252\) 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 \(-0.922730\pi\)
0.970681 0.240373i \(-0.0772696\pi\)
\(264\) 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 \(-0.726762\pi\)
−0.653647 + 0.756799i \(0.726762\pi\)
\(272\) 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 \(-0.822889\pi\)
−0.849156 + 0.528142i \(0.822889\pi\)
\(284\) 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 \(-0.544476\pi\)
−0.139270 + 0.990254i \(0.544476\pi\)
\(308\) 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 \(-0.390485\pi\)
0.337303 + 0.941396i \(0.390485\pi\)
\(312\) 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 \(0.232571\pi\)
−0.744745 + 0.667349i \(0.767429\pi\)
\(332\) −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 \(0.0727157\pi\)
−0.974020 + 0.226461i \(0.927284\pi\)
\(348\) 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 \(-0.742104\pi\)
0.689349 0.724429i \(-0.257896\pi\)
\(360\) 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 \(-0.324772\pi\)
0.523109 + 0.852266i \(0.324772\pi\)
\(368\) −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 \(0.0267103\pi\)
−0.996481 + 0.0838145i \(0.973290\pi\)
\(380\) 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 \(-0.830977\pi\)
−0.862300 + 0.506398i \(0.830977\pi\)
\(384\) −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 \(-0.603127\pi\)
−0.318345 + 0.947975i \(0.603127\pi\)
\(420\) 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 \(-0.978115\pi\)
0.997637 0.0687001i \(-0.0218852\pi\)
\(432\) 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 \(-0.584060\pi\)
−0.261023 + 0.965332i \(0.584060\pi\)
\(440\) 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 \(0.317923\pi\)
−0.541325 + 0.840813i \(0.682077\pi\)
\(444\) 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 \(0.136268\pi\)
−0.909757 + 0.415141i \(0.863732\pi\)
\(464\) 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 \(-0.389772\pi\)
0.339413 + 0.940638i \(0.389772\pi\)
\(468\) −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 \(-0.296183\pi\)
0.597444 + 0.801911i \(0.296183\pi\)
\(480\) 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 \(0.122929\pi\)
−0.926350 + 0.376665i \(0.877071\pi\)
\(488\) 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 \(0.164605\pi\)
−0.869246 + 0.494379i \(0.835395\pi\)
\(492\) 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 \(-0.635508\pi\)
0.412970 0.910745i \(-0.364492\pi\)
\(500\) 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 \(-0.551289\pi\)
−0.160432 + 0.987047i \(0.551289\pi\)
\(504\) 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 \(-0.374216\pi\)
0.384959 + 0.922934i \(0.374216\pi\)
\(524\) 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 \(-0.781566\pi\)
0.773640 0.633626i \(-0.218434\pi\)
\(548\) 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 \(-0.338905\pi\)
0.484766 + 0.874644i \(0.338905\pi\)
\(564\) 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 \(0.167180\pi\)
−0.865217 + 0.501397i \(0.832820\pi\)
\(572\) −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 \(-0.501581\pi\)
−0.00496718 + 0.999988i \(0.501581\pi\)
\(588\) 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 \(-0.790430\pi\)
0.790983 0.611838i \(-0.209570\pi\)
\(600\) 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 \(-0.618201\pi\)
−0.362865 + 0.931842i \(0.618201\pi\)
\(608\) 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 \(-0.733271\pi\)
−0.668986 + 0.743275i \(0.733271\pi\)
\(620\) −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 \(-0.670921\pi\)
0.511528 0.859266i \(-0.329079\pi\)
\(632\) −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 \(-0.230856\pi\)
0.748331 + 0.663326i \(0.230856\pi\)
\(644\) 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 \(-0.556533\pi\)
−0.176672 + 0.984270i \(0.556533\pi\)
\(648\) −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 \(-0.744159\pi\)
0.694014 0.719962i \(-0.255841\pi\)
\(660\) −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 \(-0.880290\pi\)
0.930111 0.367278i \(-0.119710\pi\)
\(684\) −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 \(-0.414167\pi\)
0.266397 + 0.963863i \(0.414167\pi\)
\(692\) 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 \(-0.489445\pi\)
0.0331523 + 0.999450i \(0.489445\pi\)
\(720\) −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 \(-0.668024\pi\)
−0.503689 + 0.863885i \(0.668024\pi\)
\(728\) 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 \(-0.795926\pi\)
0.801429 0.598091i \(-0.204074\pi\)
\(740\) −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 \(-0.946060\pi\)
0.985676 0.168648i \(-0.0539401\pi\)
\(744\) −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 \(-0.879193\pi\)
0.928840 0.370481i \(-0.120807\pi\)
\(752\) 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