Properties

Label 28.3.g.a.11.1
Level $28$
Weight $3$
Character 28.11
Analytic conductor $0.763$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [28,3,Mod(11,28)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("28.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 28.g (of order \(6\), degree \(2\), 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: \(0.762944740209\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.1
Root \(-0.407369 + 0.812545i\) of defining polynomial
Character \(\chi\) \(=\) 28.11
Dual form 28.3.g.a.23.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.98615 + 0.234945i) q^{2} +(1.86796 + 1.07847i) q^{3} +(3.88960 - 0.933271i) q^{4} +(3.25304 + 5.63443i) q^{5} +(-3.96343 - 1.70313i) q^{6} +(-2.39669 - 6.57692i) q^{7} +(-7.50608 + 2.76746i) q^{8} +(-2.17382 - 3.76517i) q^{9} +O(q^{10})\) \(q+(-1.98615 + 0.234945i) q^{2} +(1.86796 + 1.07847i) q^{3} +(3.88960 - 0.933271i) q^{4} +(3.25304 + 5.63443i) q^{5} +(-3.96343 - 1.70313i) q^{6} +(-2.39669 - 6.57692i) q^{7} +(-7.50608 + 2.76746i) q^{8} +(-2.17382 - 3.76517i) q^{9} +(-7.78481 - 10.4265i) q^{10} +(0.528732 + 0.305264i) q^{11} +(8.27212 + 2.45149i) q^{12} -10.6645 q^{13} +(6.30540 + 12.4997i) q^{14} +14.0332i q^{15} +(14.2580 - 7.26011i) q^{16} +(5.99069 - 10.3762i) q^{17} +(5.20215 + 6.96747i) q^{18} +(10.5811 - 6.10898i) q^{19} +(17.9115 + 18.8797i) q^{20} +(2.61607 - 14.8702i) q^{21} +(-1.12186 - 0.482077i) q^{22} +(-34.7524 + 20.0643i) q^{23} +(-17.0056 - 2.92555i) q^{24} +(-8.66451 + 15.0074i) q^{25} +(21.1813 - 2.50557i) q^{26} -28.7900i q^{27} +(-15.4602 - 23.3448i) q^{28} -9.04293 q^{29} +(-3.29702 - 27.8720i) q^{30} +(30.2408 + 17.4595i) q^{31} +(-26.6129 + 17.7695i) q^{32} +(0.658433 + 1.14044i) q^{33} +(-9.46059 + 22.0161i) q^{34} +(29.2606 - 34.8989i) q^{35} +(-11.9692 - 12.6162i) q^{36} +(25.4082 + 44.0084i) q^{37} +(-19.5803 + 14.6193i) q^{38} +(-19.9209 - 11.5013i) q^{39} +(-40.0106 - 33.2898i) q^{40} +25.7382 q^{41} +(-1.70225 + 30.1490i) q^{42} +19.8107i q^{43} +(2.34145 + 0.693903i) q^{44} +(14.1430 - 24.4965i) q^{45} +(64.3095 - 48.0156i) q^{46} +(-40.7870 + 23.5484i) q^{47} +(34.4631 + 1.81520i) q^{48} +(-37.5118 + 31.5257i) q^{49} +(13.6831 - 31.8426i) q^{50} +(22.3807 - 12.9215i) q^{51} +(-41.4807 + 9.95288i) q^{52} +(13.4390 - 23.2770i) q^{53} +(6.76404 + 57.1813i) q^{54} +3.97214i q^{55} +(36.1911 + 42.7341i) q^{56} +26.3533 q^{57} +(17.9606 - 2.12459i) q^{58} +(39.8644 + 23.0157i) q^{59} +(13.0967 + 54.5834i) q^{60} +(-21.1035 - 36.5524i) q^{61} +(-64.1648 - 27.5724i) q^{62} +(-19.5532 + 23.3210i) q^{63} +(48.6823 - 41.5455i) q^{64} +(-34.6920 - 60.0884i) q^{65} +(-1.57569 - 2.11039i) q^{66} +(-24.0592 - 13.8906i) q^{67} +(13.6176 - 45.9501i) q^{68} -86.5547 q^{69} +(-49.9168 + 76.1892i) q^{70} -57.1882i q^{71} +(26.7368 + 22.2457i) q^{72} +(-28.1645 + 48.7824i) q^{73} +(-60.8041 - 81.4378i) q^{74} +(-32.3699 + 18.6888i) q^{75} +(35.4548 - 33.6365i) q^{76} +(0.740487 - 4.20905i) q^{77} +(42.2680 + 18.1631i) q^{78} +(-15.9295 + 9.19688i) q^{79} +(87.2884 + 56.7183i) q^{80} +(11.4846 - 19.8919i) q^{81} +(-51.1200 + 6.04705i) q^{82} -37.3775i q^{83} +(-3.70243 - 60.2805i) q^{84} +77.9517 q^{85} +(-4.65441 - 39.3470i) q^{86} +(-16.8918 - 9.75249i) q^{87} +(-4.81351 - 0.828087i) q^{88} +(12.3537 + 21.3973i) q^{89} +(-22.3349 + 51.9766i) q^{90} +(25.5595 + 70.1396i) q^{91} +(-116.448 + 110.476i) q^{92} +(37.6590 + 65.2273i) q^{93} +(75.4767 - 56.3534i) q^{94} +(68.8412 + 39.7455i) q^{95} +(-68.8755 + 4.49166i) q^{96} +109.895 q^{97} +(67.0973 - 71.4280i) q^{98} -2.65435i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 4 q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 4 q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{8} + 4 q^{9} - 2 q^{10} - 24 q^{12} - 24 q^{13} + 2 q^{14} + 16 q^{16} - 2 q^{17} + 56 q^{18} + 152 q^{20} - 78 q^{21} + 44 q^{22} - 44 q^{24} + 56 q^{26} + 8 q^{28} + 72 q^{29} - 74 q^{30} - 112 q^{32} - 14 q^{33} - 316 q^{34} - 160 q^{36} + 86 q^{37} - 2 q^{38} - 148 q^{40} + 8 q^{41} + 68 q^{42} + 64 q^{44} + 156 q^{45} + 162 q^{46} + 512 q^{48} + 108 q^{49} + 208 q^{50} - 64 q^{52} - 74 q^{53} + 182 q^{54} + 16 q^{56} - 220 q^{57} - 176 q^{58} - 232 q^{60} + 86 q^{61} - 532 q^{62} - 160 q^{64} - 140 q^{65} + 102 q^{66} - 68 q^{68} - 300 q^{69} + 90 q^{70} + 152 q^{72} - 234 q^{73} + 290 q^{74} + 576 q^{76} - 262 q^{77} + 64 q^{78} + 146 q^{81} + 272 q^{82} - 28 q^{84} + 268 q^{85} - 16 q^{86} - 188 q^{88} + 6 q^{89} - 640 q^{90} - 448 q^{92} + 162 q^{93} + 102 q^{94} - 320 q^{96} + 744 q^{97} - 190 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98615 + 0.234945i −0.993076 + 0.117472i
\(3\) 1.86796 + 1.07847i 0.622653 + 0.359489i 0.777901 0.628387i \(-0.216284\pi\)
−0.155248 + 0.987875i \(0.549618\pi\)
\(4\) 3.88960 0.933271i 0.972401 0.233318i
\(5\) 3.25304 + 5.63443i 0.650608 + 1.12689i 0.982976 + 0.183736i \(0.0588190\pi\)
−0.332368 + 0.943150i \(0.607848\pi\)
\(6\) −3.96343 1.70313i −0.660572 0.283855i
\(7\) −2.39669 6.57692i −0.342384 0.939560i
\(8\) −7.50608 + 2.76746i −0.938259 + 0.345932i
\(9\) −2.17382 3.76517i −0.241536 0.418352i
\(10\) −7.78481 10.4265i −0.778481 1.04265i
\(11\) 0.528732 + 0.305264i 0.0480665 + 0.0277512i 0.523841 0.851816i \(-0.324499\pi\)
−0.475774 + 0.879567i \(0.657832\pi\)
\(12\) 8.27212 + 2.45149i 0.689343 + 0.204291i
\(13\) −10.6645 −0.820347 −0.410173 0.912008i \(-0.634532\pi\)
−0.410173 + 0.912008i \(0.634532\pi\)
\(14\) 6.30540 + 12.4997i 0.450386 + 0.892834i
\(15\) 14.0332i 0.935544i
\(16\) 14.2580 7.26011i 0.891126 0.453757i
\(17\) 5.99069 10.3762i 0.352393 0.610363i −0.634275 0.773108i \(-0.718701\pi\)
0.986668 + 0.162744i \(0.0520346\pi\)
\(18\) 5.20215 + 6.96747i 0.289008 + 0.387082i
\(19\) 10.5811 6.10898i 0.556898 0.321525i −0.195001 0.980803i \(-0.562471\pi\)
0.751900 + 0.659278i \(0.229138\pi\)
\(20\) 17.9115 + 18.8797i 0.895574 + 0.943986i
\(21\) 2.61607 14.8702i 0.124575 0.708103i
\(22\) −1.12186 0.482077i −0.0509937 0.0219126i
\(23\) −34.7524 + 20.0643i −1.51097 + 0.872361i −0.511055 + 0.859548i \(0.670745\pi\)
−0.999918 + 0.0128131i \(0.995921\pi\)
\(24\) −17.0056 2.92555i −0.708569 0.121898i
\(25\) −8.66451 + 15.0074i −0.346580 + 0.600295i
\(26\) 21.1813 2.50557i 0.814667 0.0963680i
\(27\) 28.7900i 1.06629i
\(28\) −15.4602 23.3448i −0.552151 0.833744i
\(29\) −9.04293 −0.311825 −0.155913 0.987771i \(-0.549832\pi\)
−0.155913 + 0.987771i \(0.549832\pi\)
\(30\) −3.29702 27.8720i −0.109901 0.929067i
\(31\) 30.2408 + 17.4595i 0.975509 + 0.563210i 0.900911 0.434004i \(-0.142899\pi\)
0.0745975 + 0.997214i \(0.476233\pi\)
\(32\) −26.6129 + 17.7695i −0.831652 + 0.555298i
\(33\) 0.658433 + 1.14044i 0.0199525 + 0.0345588i
\(34\) −9.46059 + 22.0161i −0.278253 + 0.647534i
\(35\) 29.2606 34.8989i 0.836019 0.997113i
\(36\) −11.9692 12.6162i −0.332478 0.350451i
\(37\) 25.4082 + 44.0084i 0.686709 + 1.18941i 0.972896 + 0.231241i \(0.0742787\pi\)
−0.286187 + 0.958174i \(0.592388\pi\)
\(38\) −19.5803 + 14.6193i −0.515272 + 0.384719i
\(39\) −19.9209 11.5013i −0.510791 0.294905i
\(40\) −40.0106 33.2898i −1.00026 0.832244i
\(41\) 25.7382 0.627761 0.313881 0.949462i \(-0.398371\pi\)
0.313881 + 0.949462i \(0.398371\pi\)
\(42\) −1.70225 + 30.1490i −0.0405297 + 0.717834i
\(43\) 19.8107i 0.460713i 0.973106 + 0.230357i \(0.0739893\pi\)
−0.973106 + 0.230357i \(0.926011\pi\)
\(44\) 2.34145 + 0.693903i 0.0532148 + 0.0157705i
\(45\) 14.1430 24.4965i 0.314290 0.544366i
\(46\) 64.3095 48.0156i 1.39803 1.04382i
\(47\) −40.7870 + 23.5484i −0.867809 + 0.501030i −0.866620 0.498969i \(-0.833712\pi\)
−0.00118973 + 0.999999i \(0.500379\pi\)
\(48\) 34.4631 + 1.81520i 0.717982 + 0.0378167i
\(49\) −37.5118 + 31.5257i −0.765546 + 0.643381i
\(50\) 13.6831 31.8426i 0.273663 0.636852i
\(51\) 22.3807 12.9215i 0.438837 0.253363i
\(52\) −41.4807 + 9.95288i −0.797706 + 0.191402i
\(53\) 13.4390 23.2770i 0.253566 0.439190i −0.710939 0.703254i \(-0.751730\pi\)
0.964505 + 0.264064i \(0.0850631\pi\)
\(54\) 6.76404 + 57.1813i 0.125260 + 1.05891i
\(55\) 3.97214i 0.0722207i
\(56\) 36.1911 + 42.7341i 0.646270 + 0.763109i
\(57\) 26.3533 0.462339
\(58\) 17.9606 2.12459i 0.309666 0.0366308i
\(59\) 39.8644 + 23.0157i 0.675668 + 0.390097i 0.798221 0.602365i \(-0.205775\pi\)
−0.122553 + 0.992462i \(0.539108\pi\)
\(60\) 13.0967 + 54.5834i 0.218279 + 0.909724i
\(61\) −21.1035 36.5524i −0.345959 0.599219i 0.639568 0.768734i \(-0.279113\pi\)
−0.985528 + 0.169515i \(0.945780\pi\)
\(62\) −64.1648 27.5724i −1.03492 0.444715i
\(63\) −19.5532 + 23.3210i −0.310369 + 0.370174i
\(64\) 48.6823 41.5455i 0.760661 0.649149i
\(65\) −34.6920 60.0884i −0.533724 0.924437i
\(66\) −1.57569 2.11039i −0.0238741 0.0319756i
\(67\) −24.0592 13.8906i −0.359092 0.207322i 0.309590 0.950870i \(-0.399808\pi\)
−0.668683 + 0.743548i \(0.733141\pi\)
\(68\) 13.6176 45.9501i 0.200259 0.675737i
\(69\) −86.5547 −1.25442
\(70\) −49.9168 + 76.1892i −0.713097 + 1.08842i
\(71\) 57.1882i 0.805467i −0.915317 0.402734i \(-0.868060\pi\)
0.915317 0.402734i \(-0.131940\pi\)
\(72\) 26.7368 + 22.2457i 0.371345 + 0.308968i
\(73\) −28.1645 + 48.7824i −0.385815 + 0.668251i −0.991882 0.127162i \(-0.959413\pi\)
0.606067 + 0.795414i \(0.292746\pi\)
\(74\) −60.8041 81.4378i −0.821678 1.10051i
\(75\) −32.3699 + 18.6888i −0.431598 + 0.249183i
\(76\) 35.4548 33.6365i 0.466510 0.442586i
\(77\) 0.740487 4.20905i 0.00961672 0.0546630i
\(78\) 42.2680 + 18.1631i 0.541898 + 0.232860i
\(79\) −15.9295 + 9.19688i −0.201639 + 0.116416i −0.597420 0.801929i \(-0.703807\pi\)
0.395781 + 0.918345i \(0.370474\pi\)
\(80\) 87.2884 + 56.7183i 1.09110 + 0.708979i
\(81\) 11.4846 19.8919i 0.141785 0.245579i
\(82\) −51.1200 + 6.04705i −0.623415 + 0.0737445i
\(83\) 37.3775i 0.450332i −0.974320 0.225166i \(-0.927708\pi\)
0.974320 0.225166i \(-0.0722924\pi\)
\(84\) −3.70243 60.2805i −0.0440765 0.717625i
\(85\) 77.9517 0.917079
\(86\) −4.65441 39.3470i −0.0541210 0.457523i
\(87\) −16.8918 9.75249i −0.194159 0.112098i
\(88\) −4.81351 0.828087i −0.0546989 0.00941008i
\(89\) 12.3537 + 21.3973i 0.138806 + 0.240419i 0.927045 0.374950i \(-0.122340\pi\)
−0.788239 + 0.615369i \(0.789007\pi\)
\(90\) −22.3349 + 51.9766i −0.248166 + 0.577517i
\(91\) 25.5595 + 70.1396i 0.280874 + 0.770765i
\(92\) −116.448 + 110.476i −1.26573 + 1.20082i
\(93\) 37.6590 + 65.2273i 0.404935 + 0.701369i
\(94\) 75.4767 56.3534i 0.802944 0.599504i
\(95\) 68.8412 + 39.7455i 0.724644 + 0.418374i
\(96\) −68.8755 + 4.49166i −0.717453 + 0.0467881i
\(97\) 109.895 1.13294 0.566468 0.824084i \(-0.308310\pi\)
0.566468 + 0.824084i \(0.308310\pi\)
\(98\) 67.0973 71.4280i 0.684666 0.728857i
\(99\) 2.65435i 0.0268117i
\(100\) −19.6955 + 66.4590i −0.196955 + 0.664590i
\(101\) −21.5756 + 37.3700i −0.213620 + 0.370000i −0.952845 0.303458i \(-0.901859\pi\)
0.739225 + 0.673458i \(0.235192\pi\)
\(102\) −41.4157 + 30.9223i −0.406036 + 0.303160i
\(103\) 130.437 75.3078i 1.26638 0.731144i 0.292077 0.956395i \(-0.405654\pi\)
0.974301 + 0.225251i \(0.0723202\pi\)
\(104\) 80.0486 29.5136i 0.769698 0.283785i
\(105\) 92.2950 33.6332i 0.879000 0.320316i
\(106\) −21.2231 + 49.3892i −0.200218 + 0.465936i
\(107\) 35.1527 20.2954i 0.328530 0.189677i −0.326658 0.945143i \(-0.605923\pi\)
0.655188 + 0.755466i \(0.272589\pi\)
\(108\) −26.8688 111.982i −0.248786 1.03687i
\(109\) −33.2652 + 57.6170i −0.305185 + 0.528596i −0.977303 0.211848i \(-0.932052\pi\)
0.672117 + 0.740445i \(0.265385\pi\)
\(110\) −0.933232 7.88927i −0.00848392 0.0717206i
\(111\) 109.608i 0.987457i
\(112\) −81.9212 76.3736i −0.731439 0.681907i
\(113\) −143.395 −1.26899 −0.634493 0.772929i \(-0.718791\pi\)
−0.634493 + 0.772929i \(0.718791\pi\)
\(114\) −52.3417 + 6.19157i −0.459138 + 0.0543120i
\(115\) −226.102 130.540i −1.96610 1.13513i
\(116\) −35.1734 + 8.43950i −0.303219 + 0.0727543i
\(117\) 23.1827 + 40.1537i 0.198143 + 0.343194i
\(118\) −84.5842 36.3468i −0.716815 0.308024i
\(119\) −82.6011 14.5318i −0.694127 0.122116i
\(120\) −38.8362 105.334i −0.323635 0.877783i
\(121\) −60.3136 104.466i −0.498460 0.863358i
\(122\) 50.5026 + 67.6404i 0.413956 + 0.554430i
\(123\) 48.0779 + 27.7578i 0.390877 + 0.225673i
\(124\) 133.919 + 39.6877i 1.07999 + 0.320062i
\(125\) 49.9080 0.399264
\(126\) 33.3566 50.9130i 0.264735 0.404071i
\(127\) 83.0059i 0.653590i −0.945095 0.326795i \(-0.894031\pi\)
0.945095 0.326795i \(-0.105969\pi\)
\(128\) −86.9296 + 93.9534i −0.679138 + 0.734011i
\(129\) −21.3651 + 37.0055i −0.165621 + 0.286864i
\(130\) 83.0211 + 111.194i 0.638624 + 0.855338i
\(131\) −25.5368 + 14.7437i −0.194938 + 0.112547i −0.594292 0.804249i \(-0.702568\pi\)
0.399354 + 0.916797i \(0.369234\pi\)
\(132\) 3.62538 + 3.82136i 0.0274650 + 0.0289497i
\(133\) −65.5378 54.9495i −0.492766 0.413154i
\(134\) 51.0487 + 21.9362i 0.380961 + 0.163703i
\(135\) 162.215 93.6548i 1.20159 0.693740i
\(136\) −16.2509 + 94.4633i −0.119492 + 0.694583i
\(137\) 11.7586 20.3664i 0.0858288 0.148660i −0.819915 0.572485i \(-0.805980\pi\)
0.905744 + 0.423825i \(0.139313\pi\)
\(138\) 171.911 20.3355i 1.24573 0.147359i
\(139\) 256.175i 1.84299i 0.388396 + 0.921493i \(0.373029\pi\)
−0.388396 + 0.921493i \(0.626971\pi\)
\(140\) 81.2421 163.051i 0.580301 1.16465i
\(141\) −101.585 −0.720459
\(142\) 13.4361 + 113.584i 0.0946201 + 0.799891i
\(143\) −5.63867 3.25549i −0.0394312 0.0227656i
\(144\) −58.3299 37.9016i −0.405069 0.263206i
\(145\) −29.4170 50.9517i −0.202876 0.351391i
\(146\) 44.4779 103.506i 0.304643 0.708947i
\(147\) −104.070 + 18.4335i −0.707958 + 0.125398i
\(148\) 139.900 + 147.462i 0.945268 + 0.996366i
\(149\) −44.7826 77.5658i −0.300554 0.520576i 0.675707 0.737170i \(-0.263838\pi\)
−0.976262 + 0.216595i \(0.930505\pi\)
\(150\) 59.9007 44.7238i 0.399338 0.298159i
\(151\) −40.8283 23.5722i −0.270386 0.156107i 0.358677 0.933462i \(-0.383228\pi\)
−0.629063 + 0.777354i \(0.716561\pi\)
\(152\) −62.5159 + 75.1371i −0.411289 + 0.494323i
\(153\) −52.0907 −0.340462
\(154\) −0.481827 + 8.53379i −0.00312875 + 0.0554142i
\(155\) 227.186i 1.46572i
\(156\) −88.2181 26.1440i −0.565500 0.167590i
\(157\) 143.897 249.237i 0.916540 1.58749i 0.111910 0.993718i \(-0.464303\pi\)
0.804631 0.593776i \(-0.202363\pi\)
\(158\) 29.4776 22.0089i 0.186567 0.139297i
\(159\) 50.2070 28.9870i 0.315767 0.182308i
\(160\) −186.694 92.1433i −1.16684 0.575895i
\(161\) 215.252 + 180.476i 1.33697 + 1.12097i
\(162\) −18.1367 + 42.2067i −0.111955 + 0.260535i
\(163\) −11.7940 + 6.80925i −0.0723557 + 0.0417746i −0.535741 0.844382i \(-0.679968\pi\)
0.463386 + 0.886157i \(0.346634\pi\)
\(164\) 100.111 24.0207i 0.610435 0.146468i
\(165\) −4.28381 + 7.41978i −0.0259625 + 0.0449684i
\(166\) 8.78164 + 74.2374i 0.0529015 + 0.447214i
\(167\) 241.587i 1.44663i −0.690519 0.723314i \(-0.742618\pi\)
0.690519 0.723314i \(-0.257382\pi\)
\(168\) 21.5162 + 118.856i 0.128072 + 0.707479i
\(169\) −55.2683 −0.327031
\(170\) −154.824 + 18.3143i −0.910729 + 0.107731i
\(171\) −46.0027 26.5597i −0.269022 0.155320i
\(172\) 18.4887 + 77.0556i 0.107493 + 0.447998i
\(173\) 57.3775 + 99.3807i 0.331662 + 0.574455i 0.982838 0.184472i \(-0.0590575\pi\)
−0.651176 + 0.758927i \(0.725724\pi\)
\(174\) 35.8410 + 15.4013i 0.205983 + 0.0885132i
\(175\) 119.468 + 21.0178i 0.682677 + 0.120101i
\(176\) 9.75491 + 0.513800i 0.0554256 + 0.00291932i
\(177\) 49.6434 + 85.9848i 0.280471 + 0.485790i
\(178\) −29.5635 39.5958i −0.166087 0.222448i
\(179\) 23.2381 + 13.4165i 0.129822 + 0.0749526i 0.563504 0.826113i \(-0.309453\pi\)
−0.433683 + 0.901066i \(0.642786\pi\)
\(180\) 32.1490 108.481i 0.178605 0.602671i
\(181\) −46.5388 −0.257120 −0.128560 0.991702i \(-0.541036\pi\)
−0.128560 + 0.991702i \(0.541036\pi\)
\(182\) −67.2440 133.303i −0.369473 0.732433i
\(183\) 91.0377i 0.497474i
\(184\) 205.327 246.780i 1.11591 1.34120i
\(185\) −165.308 + 286.322i −0.893556 + 1.54768i
\(186\) −90.1213 120.704i −0.484523 0.648944i
\(187\) 6.33494 3.65748i 0.0338767 0.0195587i
\(188\) −136.668 + 129.659i −0.726959 + 0.689677i
\(189\) −189.349 + 69.0006i −1.00185 + 0.365083i
\(190\) −146.067 62.7667i −0.768774 0.330351i
\(191\) −65.3175 + 37.7111i −0.341976 + 0.197440i −0.661146 0.750258i \(-0.729929\pi\)
0.319169 + 0.947698i \(0.396596\pi\)
\(192\) 135.742 25.1030i 0.706990 0.130745i
\(193\) 83.0347 143.820i 0.430232 0.745183i −0.566661 0.823951i \(-0.691765\pi\)
0.996893 + 0.0787675i \(0.0250985\pi\)
\(194\) −218.268 + 25.8192i −1.12509 + 0.133088i
\(195\) 149.657i 0.767471i
\(196\) −116.484 + 157.631i −0.594305 + 0.804240i
\(197\) 279.737 1.41998 0.709991 0.704210i \(-0.248699\pi\)
0.709991 + 0.704210i \(0.248699\pi\)
\(198\) 0.623626 + 5.27195i 0.00314963 + 0.0266260i
\(199\) 0.238457 + 0.137673i 0.00119828 + 0.000691824i 0.500599 0.865679i \(-0.333113\pi\)
−0.499401 + 0.866371i \(0.666446\pi\)
\(200\) 23.5042 136.625i 0.117521 0.683126i
\(201\) −29.9610 51.8940i −0.149060 0.258179i
\(202\) 34.0725 79.2916i 0.168676 0.392533i
\(203\) 21.6731 + 59.4746i 0.106764 + 0.292978i
\(204\) 74.9928 71.1468i 0.367612 0.348759i
\(205\) 83.7274 + 145.020i 0.408426 + 0.707415i
\(206\) −241.374 + 180.218i −1.17172 + 0.874846i
\(207\) 151.091 + 87.2324i 0.729908 + 0.421413i
\(208\) −152.055 + 77.4255i −0.731032 + 0.372238i
\(209\) 7.45940 0.0356909
\(210\) −175.410 + 88.4848i −0.835286 + 0.421356i
\(211\) 301.264i 1.42779i −0.700252 0.713896i \(-0.746929\pi\)
0.700252 0.713896i \(-0.253071\pi\)
\(212\) 30.5486 103.081i 0.144097 0.486230i
\(213\) 61.6755 106.825i 0.289556 0.501527i
\(214\) −65.0503 + 48.5687i −0.303974 + 0.226957i
\(215\) −111.622 + 64.4449i −0.519171 + 0.299744i
\(216\) 79.6751 + 216.100i 0.368866 + 1.00046i
\(217\) 42.3521 240.736i 0.195171 1.10938i
\(218\) 52.5329 122.252i 0.240977 0.560787i
\(219\) −105.220 + 60.7489i −0.480458 + 0.277392i
\(220\) 3.70708 + 15.4500i 0.0168504 + 0.0702274i
\(221\) −63.8877 + 110.657i −0.289085 + 0.500709i
\(222\) −25.7517 217.698i −0.115999 0.980620i
\(223\) 215.034i 0.964279i 0.876094 + 0.482140i \(0.160140\pi\)
−0.876094 + 0.482140i \(0.839860\pi\)
\(224\) 180.651 + 132.443i 0.806480 + 0.591262i
\(225\) 75.3404 0.334846
\(226\) 284.805 33.6900i 1.26020 0.149071i
\(227\) 364.944 + 210.700i 1.60768 + 0.928195i 0.989887 + 0.141855i \(0.0453067\pi\)
0.617794 + 0.786340i \(0.288027\pi\)
\(228\) 102.504 24.5948i 0.449579 0.107872i
\(229\) −22.7637 39.4278i −0.0994046 0.172174i 0.812034 0.583610i \(-0.198360\pi\)
−0.911438 + 0.411437i \(0.865027\pi\)
\(230\) 479.742 + 206.151i 2.08583 + 0.896307i
\(231\) 5.92252 7.06374i 0.0256386 0.0305790i
\(232\) 67.8769 25.0259i 0.292573 0.107870i
\(233\) −75.7232 131.156i −0.324992 0.562903i 0.656518 0.754310i \(-0.272028\pi\)
−0.981511 + 0.191407i \(0.938695\pi\)
\(234\) −55.4783 74.3047i −0.237087 0.317541i
\(235\) −265.364 153.208i −1.12921 0.651948i
\(236\) 176.537 + 52.3177i 0.748036 + 0.221685i
\(237\) −39.6741 −0.167401
\(238\) 167.473 + 9.45568i 0.703666 + 0.0397297i
\(239\) 200.986i 0.840944i 0.907306 + 0.420472i \(0.138135\pi\)
−0.907306 + 0.420472i \(0.861865\pi\)
\(240\) 101.882 + 200.085i 0.424510 + 0.833688i
\(241\) −124.318 + 215.326i −0.515844 + 0.893468i 0.483987 + 0.875075i \(0.339188\pi\)
−0.999831 + 0.0183927i \(0.994145\pi\)
\(242\) 144.336 + 193.316i 0.596429 + 0.798825i
\(243\) −181.490 + 104.783i −0.746872 + 0.431207i
\(244\) −116.198 122.479i −0.476220 0.501963i
\(245\) −299.656 108.803i −1.22309 0.444094i
\(246\) −102.012 43.8356i −0.414681 0.178193i
\(247\) −112.842 + 65.1493i −0.456850 + 0.263762i
\(248\) −275.308 47.3623i −1.11011 0.190977i
\(249\) 40.3104 69.8196i 0.161889 0.280400i
\(250\) −99.1249 + 11.7256i −0.396500 + 0.0469024i
\(251\) 226.888i 0.903938i −0.892034 0.451969i \(-0.850722\pi\)
0.892034 0.451969i \(-0.149278\pi\)
\(252\) −54.2895 + 108.958i −0.215435 + 0.432372i
\(253\) −24.4996 −0.0968364
\(254\) 19.5018 + 164.862i 0.0767786 + 0.649064i
\(255\) 145.611 + 84.0683i 0.571022 + 0.329680i
\(256\) 150.582 207.029i 0.588210 0.808708i
\(257\) −177.583 307.583i −0.690984 1.19682i −0.971516 0.236975i \(-0.923844\pi\)
0.280532 0.959845i \(-0.409489\pi\)
\(258\) 33.7402 78.5182i 0.130776 0.304334i
\(259\) 228.544 272.582i 0.882408 1.05244i
\(260\) −191.017 201.343i −0.734681 0.774396i
\(261\) 19.6577 + 34.0481i 0.0753169 + 0.130453i
\(262\) 47.2561 35.2830i 0.180367 0.134668i
\(263\) −338.273 195.302i −1.28621 0.742593i −0.308232 0.951311i \(-0.599737\pi\)
−0.977976 + 0.208718i \(0.933071\pi\)
\(264\) −8.09837 6.73804i −0.0306756 0.0255229i
\(265\) 174.870 0.659888
\(266\) 143.078 + 93.7403i 0.537888 + 0.352407i
\(267\) 53.2923i 0.199597i
\(268\) −106.544 31.5751i −0.397553 0.117817i
\(269\) 187.371 324.536i 0.696546 1.20645i −0.273110 0.961983i \(-0.588052\pi\)
0.969657 0.244471i \(-0.0786143\pi\)
\(270\) −300.180 + 224.124i −1.11178 + 0.830090i
\(271\) −132.759 + 76.6485i −0.489886 + 0.282836i −0.724527 0.689246i \(-0.757942\pi\)
0.234641 + 0.972082i \(0.424608\pi\)
\(272\) 10.0831 191.437i 0.0370703 0.703811i
\(273\) −27.8991 + 158.583i −0.102194 + 0.580890i
\(274\) −18.5693 + 43.2134i −0.0677712 + 0.157713i
\(275\) −9.16241 + 5.28992i −0.0333178 + 0.0192361i
\(276\) −336.663 + 80.7790i −1.21979 + 0.292678i
\(277\) −224.888 + 389.517i −0.811869 + 1.40620i 0.0996861 + 0.995019i \(0.468216\pi\)
−0.911555 + 0.411179i \(0.865117\pi\)
\(278\) −60.1869 508.802i −0.216500 1.83022i
\(279\) 151.815i 0.544141i
\(280\) −123.051 + 342.932i −0.439469 + 1.22476i
\(281\) −3.27554 −0.0116567 −0.00582836 0.999983i \(-0.501855\pi\)
−0.00582836 + 0.999983i \(0.501855\pi\)
\(282\) 201.763 23.8668i 0.715470 0.0846339i
\(283\) 296.447 + 171.154i 1.04752 + 0.604783i 0.921953 0.387303i \(-0.126593\pi\)
0.125562 + 0.992086i \(0.459926\pi\)
\(284\) −53.3721 222.439i −0.187930 0.783237i
\(285\) 85.7283 + 148.486i 0.300801 + 0.521003i
\(286\) 11.9641 + 5.14112i 0.0418326 + 0.0179759i
\(287\) −61.6865 169.278i −0.214936 0.589819i
\(288\) 124.757 + 61.5741i 0.433183 + 0.213799i
\(289\) 72.7233 + 125.961i 0.251638 + 0.435850i
\(290\) 70.3974 + 94.2865i 0.242750 + 0.325126i
\(291\) 205.279 + 118.518i 0.705425 + 0.407277i
\(292\) −64.0216 + 216.029i −0.219252 + 0.739826i
\(293\) −243.752 −0.831919 −0.415959 0.909383i \(-0.636554\pi\)
−0.415959 + 0.909383i \(0.636554\pi\)
\(294\) 202.368 61.0624i 0.688325 0.207695i
\(295\) 299.484i 1.01520i
\(296\) −312.507 260.014i −1.05577 0.878425i
\(297\) 8.78853 15.2222i 0.0295910 0.0512531i
\(298\) 107.169 + 143.536i 0.359627 + 0.481664i
\(299\) 370.617 213.976i 1.23952 0.715638i
\(300\) −108.464 + 102.902i −0.361548 + 0.343006i
\(301\) 130.293 47.4801i 0.432868 0.157741i
\(302\) 86.6293 + 37.2256i 0.286852 + 0.123264i
\(303\) −80.6046 + 46.5371i −0.266022 + 0.153588i
\(304\) 106.513 163.922i 0.350372 0.539216i
\(305\) 137.301 237.812i 0.450167 0.779713i
\(306\) 103.460 12.2384i 0.338105 0.0399949i
\(307\) 58.4520i 0.190397i 0.995458 + 0.0951987i \(0.0303487\pi\)
−0.995458 + 0.0951987i \(0.969651\pi\)
\(308\) −1.04799 17.0626i −0.00340255 0.0553981i
\(309\) 324.868 1.05135
\(310\) −53.3761 451.226i −0.172181 1.45557i
\(311\) −107.722 62.1933i −0.346373 0.199978i 0.316714 0.948521i \(-0.397421\pi\)
−0.663086 + 0.748543i \(0.730754\pi\)
\(312\) 181.357 + 31.1995i 0.581272 + 0.0999986i
\(313\) 240.725 + 416.948i 0.769090 + 1.33210i 0.938057 + 0.346481i \(0.112624\pi\)
−0.168967 + 0.985622i \(0.554043\pi\)
\(314\) −227.244 + 528.830i −0.723708 + 1.68417i
\(315\) −195.008 34.3072i −0.619072 0.108912i
\(316\) −53.3761 + 50.6387i −0.168912 + 0.160249i
\(317\) 179.573 + 311.030i 0.566478 + 0.981168i 0.996911 + 0.0785457i \(0.0250276\pi\)
−0.430433 + 0.902623i \(0.641639\pi\)
\(318\) −92.9084 + 69.3685i −0.292165 + 0.218140i
\(319\) −4.78129 2.76048i −0.0149884 0.00865353i
\(320\) 392.451 + 139.148i 1.22641 + 0.434837i
\(321\) 87.5517 0.272747
\(322\) −469.925 307.880i −1.45939 0.956149i
\(323\) 146.388i 0.453214i
\(324\) 26.1060 88.0900i 0.0805741 0.271883i
\(325\) 92.4027 160.046i 0.284316 0.492450i
\(326\) 21.8248 16.2951i 0.0669473 0.0499851i
\(327\) −124.276 + 71.7508i −0.380049 + 0.219421i
\(328\) −193.193 + 71.2295i −0.589003 + 0.217163i
\(329\) 252.630 + 211.815i 0.767872 + 0.643814i
\(330\) 6.76507 15.7433i 0.0205002 0.0477069i
\(331\) −109.721 + 63.3476i −0.331484 + 0.191383i −0.656500 0.754326i \(-0.727964\pi\)
0.325016 + 0.945709i \(0.394630\pi\)
\(332\) −34.8834 145.384i −0.105070 0.437903i
\(333\) 110.466 191.333i 0.331729 0.574572i
\(334\) 56.7595 + 479.828i 0.169939 + 1.43661i
\(335\) 180.746i 0.539541i
\(336\) −70.6590 231.012i −0.210295 0.687535i
\(337\) −551.430 −1.63629 −0.818146 0.575011i \(-0.804998\pi\)
−0.818146 + 0.575011i \(0.804998\pi\)
\(338\) 109.771 12.9850i 0.324767 0.0384171i
\(339\) −267.857 154.647i −0.790138 0.456186i
\(340\) 303.201 72.7501i 0.891768 0.213971i
\(341\) 10.6595 + 18.4628i 0.0312596 + 0.0541431i
\(342\) 97.6084 + 41.9435i 0.285405 + 0.122642i
\(343\) 297.246 + 171.154i 0.866606 + 0.498993i
\(344\) −54.8252 148.700i −0.159376 0.432269i
\(345\) −281.566 487.686i −0.816132 1.41358i
\(346\) −137.309 183.905i −0.396848 0.531516i
\(347\) 356.182 + 205.642i 1.02646 + 0.592628i 0.915969 0.401249i \(-0.131424\pi\)
0.110493 + 0.993877i \(0.464757\pi\)
\(348\) −74.8041 22.1687i −0.214954 0.0637031i
\(349\) −402.535 −1.15340 −0.576698 0.816957i \(-0.695659\pi\)
−0.576698 + 0.816957i \(0.695659\pi\)
\(350\) −242.220 13.6760i −0.692058 0.0390744i
\(351\) 307.031i 0.874732i
\(352\) −19.4955 + 1.27138i −0.0553848 + 0.00361187i
\(353\) 29.9594 51.8913i 0.0848709 0.147001i −0.820465 0.571696i \(-0.806286\pi\)
0.905336 + 0.424696i \(0.139619\pi\)
\(354\) −118.801 159.116i −0.335596 0.449479i
\(355\) 322.223 186.035i 0.907669 0.524043i
\(356\) 68.0205 + 71.6975i 0.191069 + 0.201397i
\(357\) −138.623 116.227i −0.388301 0.325567i
\(358\) −49.3065 21.1876i −0.137728 0.0591832i
\(359\) −121.860 + 70.3559i −0.339443 + 0.195977i −0.660026 0.751243i \(-0.729455\pi\)
0.320583 + 0.947221i \(0.396121\pi\)
\(360\) −38.3658 + 223.013i −0.106572 + 0.619480i
\(361\) −105.861 + 183.356i −0.293243 + 0.507912i
\(362\) 92.4331 10.9340i 0.255340 0.0302045i
\(363\) 260.185i 0.716763i
\(364\) 164.876 + 248.961i 0.452955 + 0.683959i
\(365\) −366.481 −1.00406
\(366\) 21.3888 + 180.815i 0.0584394 + 0.494029i
\(367\) −288.714 166.689i −0.786686 0.454193i 0.0521085 0.998641i \(-0.483406\pi\)
−0.838795 + 0.544448i \(0.816739\pi\)
\(368\) −349.831 + 538.383i −0.950627 + 1.46300i
\(369\) −55.9503 96.9087i −0.151627 0.262625i
\(370\) 261.057 607.517i 0.705559 1.64194i
\(371\) −185.300 32.5994i −0.499462 0.0878690i
\(372\) 207.353 + 218.562i 0.557401 + 0.587533i
\(373\) 128.721 + 222.951i 0.345095 + 0.597723i 0.985371 0.170423i \(-0.0545133\pi\)
−0.640276 + 0.768145i \(0.721180\pi\)
\(374\) −11.7228 + 8.75267i −0.0313445 + 0.0234028i
\(375\) 93.2261 + 53.8241i 0.248603 + 0.143531i
\(376\) 240.981 289.633i 0.640908 0.770300i
\(377\) 96.4384 0.255805
\(378\) 359.865 181.532i 0.952024 0.480244i
\(379\) 122.957i 0.324426i −0.986756 0.162213i \(-0.948137\pi\)
0.986756 0.162213i \(-0.0518631\pi\)
\(380\) 304.858 + 90.3466i 0.802259 + 0.237754i
\(381\) 89.5190 155.052i 0.234958 0.406959i
\(382\) 120.870 90.2459i 0.316415 0.236246i
\(383\) −302.009 + 174.365i −0.788535 + 0.455261i −0.839446 0.543442i \(-0.817121\pi\)
0.0509116 + 0.998703i \(0.483787\pi\)
\(384\) −263.706 + 81.7503i −0.686736 + 0.212891i
\(385\) 26.1244 9.51998i 0.0678556 0.0247272i
\(386\) −131.130 + 305.158i −0.339715 + 0.790564i
\(387\) 74.5905 43.0649i 0.192740 0.111279i
\(388\) 427.447 102.562i 1.10167 0.264334i
\(389\) 176.689 306.035i 0.454215 0.786723i −0.544428 0.838808i \(-0.683253\pi\)
0.998643 + 0.0520848i \(0.0165866\pi\)
\(390\) 35.1610 + 297.241i 0.0901565 + 0.762157i
\(391\) 480.796i 1.22966i
\(392\) 194.320 340.446i 0.495714 0.868486i
\(393\) −63.6023 −0.161838
\(394\) −555.600 + 65.7226i −1.41015 + 0.166809i
\(395\) −103.638 59.8356i −0.262375 0.151482i
\(396\) −2.47723 10.3244i −0.00625564 0.0260717i
\(397\) −91.1659 157.904i −0.229637 0.397743i 0.728064 0.685510i \(-0.240421\pi\)
−0.957701 + 0.287767i \(0.907087\pi\)
\(398\) −0.505957 0.217416i −0.00127125 0.000546270i
\(399\) −63.1607 173.324i −0.158298 0.434395i
\(400\) −14.5835 + 276.880i −0.0364588 + 0.692201i
\(401\) −172.934 299.530i −0.431257 0.746959i 0.565725 0.824594i \(-0.308596\pi\)
−0.996982 + 0.0776352i \(0.975263\pi\)
\(402\) 71.6994 + 96.0303i 0.178357 + 0.238881i
\(403\) −322.503 186.197i −0.800255 0.462028i
\(404\) −49.0441 + 165.490i −0.121396 + 0.409629i
\(405\) 149.439 0.368986
\(406\) −57.0193 113.034i −0.140442 0.278408i
\(407\) 31.0248i 0.0762281i
\(408\) −132.232 + 158.928i −0.324097 + 0.389528i
\(409\) −152.896 + 264.823i −0.373828 + 0.647489i −0.990151 0.140005i \(-0.955288\pi\)
0.616323 + 0.787494i \(0.288622\pi\)
\(410\) −200.367 268.361i −0.488700 0.654538i
\(411\) 43.9290 25.3624i 0.106883 0.0617090i
\(412\) 437.065 414.650i 1.06084 1.00643i
\(413\) 55.8300 317.347i 0.135181 0.768394i
\(414\) −320.584 137.759i −0.774358 0.332751i
\(415\) 210.601 121.590i 0.507472 0.292989i
\(416\) 283.813 189.503i 0.682243 0.455537i
\(417\) −276.276 + 478.524i −0.662532 + 1.14754i
\(418\) −14.8155 + 1.75254i −0.0354438 + 0.00419269i
\(419\) 749.709i 1.78928i 0.446786 + 0.894641i \(0.352569\pi\)
−0.446786 + 0.894641i \(0.647431\pi\)
\(420\) 327.602 216.956i 0.780005 0.516562i
\(421\) 356.196 0.846070 0.423035 0.906113i \(-0.360965\pi\)
0.423035 + 0.906113i \(0.360965\pi\)
\(422\) 70.7803 + 598.356i 0.167726 + 1.41791i
\(423\) 177.327 + 102.380i 0.419214 + 0.242033i
\(424\) −36.4559 + 211.911i −0.0859810 + 0.499791i
\(425\) 103.813 + 179.809i 0.244265 + 0.423080i
\(426\) −97.3990 + 226.661i −0.228636 + 0.532069i
\(427\) −189.823 + 226.401i −0.444551 + 0.530213i
\(428\) 117.789 111.748i 0.275208 0.261094i
\(429\) −7.02186 12.1622i −0.0163680 0.0283502i
\(430\) 206.557 154.222i 0.480365 0.358656i
\(431\) 163.925 + 94.6420i 0.380336 + 0.219587i 0.677964 0.735095i \(-0.262862\pi\)
−0.297629 + 0.954682i \(0.596196\pi\)
\(432\) −209.018 410.488i −0.483839 0.950203i
\(433\) 771.353 1.78142 0.890708 0.454575i \(-0.150209\pi\)
0.890708 + 0.454575i \(0.150209\pi\)
\(434\) −27.5580 + 488.089i −0.0634978 + 1.12463i
\(435\) 126.901i 0.291726i
\(436\) −75.6161 + 255.153i −0.173431 + 0.585212i
\(437\) −245.145 + 424.603i −0.560972 + 0.971632i
\(438\) 194.711 145.378i 0.444545 0.331912i
\(439\) 695.621 401.617i 1.58456 0.914845i 0.590377 0.807127i \(-0.298979\pi\)
0.994181 0.107718i \(-0.0343543\pi\)
\(440\) −10.9927 29.8152i −0.0249835 0.0677617i
\(441\) 200.243 + 72.7069i 0.454067 + 0.164868i
\(442\) 100.893 234.791i 0.228264 0.531202i
\(443\) 627.440 362.253i 1.41634 0.817726i 0.420368 0.907354i \(-0.361901\pi\)
0.995975 + 0.0896276i \(0.0285677\pi\)
\(444\) 102.294 + 426.330i 0.230391 + 0.960203i
\(445\) −80.3742 + 139.212i −0.180616 + 0.312836i
\(446\) −50.5211 427.091i −0.113276 0.957603i
\(447\) 193.186i 0.432184i
\(448\) −389.918 220.608i −0.870353 0.492429i
\(449\) 675.025 1.50340 0.751698 0.659507i \(-0.229235\pi\)
0.751698 + 0.659507i \(0.229235\pi\)
\(450\) −149.637 + 17.7008i −0.332528 + 0.0393351i
\(451\) 13.6086 + 7.85694i 0.0301743 + 0.0174212i
\(452\) −557.751 + 133.827i −1.23396 + 0.296077i
\(453\) −50.8437 88.0638i −0.112238 0.194401i
\(454\) −774.337 332.741i −1.70559 0.732911i
\(455\) −312.050 + 372.180i −0.685825 + 0.817978i
\(456\) −197.810 + 72.9317i −0.433794 + 0.159938i
\(457\) −181.945 315.138i −0.398129 0.689579i 0.595366 0.803454i \(-0.297007\pi\)
−0.993495 + 0.113875i \(0.963674\pi\)
\(458\) 54.4755 + 72.9615i 0.118942 + 0.159304i
\(459\) −298.730 172.472i −0.650827 0.375755i
\(460\) −1001.27 296.734i −2.17668 0.645074i
\(461\) −233.360 −0.506205 −0.253102 0.967439i \(-0.581451\pi\)
−0.253102 + 0.967439i \(0.581451\pi\)
\(462\) −10.1034 + 15.4211i −0.0218689 + 0.0333791i
\(463\) 872.151i 1.88370i −0.336040 0.941848i \(-0.609088\pi\)
0.336040 0.941848i \(-0.390912\pi\)
\(464\) −128.934 + 65.6526i −0.277875 + 0.141493i
\(465\) −245.012 + 424.374i −0.526908 + 0.912632i
\(466\) 181.212 + 242.706i 0.388868 + 0.520828i
\(467\) −664.940 + 383.903i −1.42386 + 0.822063i −0.996626 0.0820802i \(-0.973844\pi\)
−0.427229 + 0.904143i \(0.640510\pi\)
\(468\) 127.646 + 134.546i 0.272748 + 0.287492i
\(469\) −33.6948 + 191.527i −0.0718439 + 0.408373i
\(470\) 563.048 + 241.948i 1.19797 + 0.514783i
\(471\) 537.586 310.376i 1.14137 0.658972i
\(472\) −362.920 62.4346i −0.768899 0.132277i
\(473\) −6.04748 + 10.4745i −0.0127854 + 0.0221449i
\(474\) 78.7988 9.32121i 0.166242 0.0196650i
\(475\) 211.725i 0.445737i
\(476\) −334.847 + 20.5663i −0.703461 + 0.0432066i
\(477\) −116.856 −0.244981
\(478\) −47.2205 399.188i −0.0987876 0.835121i
\(479\) −682.194 393.865i −1.42421 0.822265i −0.427550 0.903992i \(-0.640623\pi\)
−0.996655 + 0.0817264i \(0.973957\pi\)
\(480\) −249.363 373.463i −0.519505 0.778047i
\(481\) −270.966 469.327i −0.563340 0.975733i
\(482\) 196.326 456.878i 0.407315 0.947879i
\(483\) 207.445 + 569.263i 0.429492 + 1.17860i
\(484\) −332.091 350.043i −0.686139 0.723230i
\(485\) 357.492 + 619.194i 0.737096 + 1.27669i
\(486\) 335.849 250.756i 0.691046 0.515958i
\(487\) 31.8410 + 18.3834i 0.0653819 + 0.0377483i 0.532335 0.846534i \(-0.321315\pi\)
−0.466953 + 0.884282i \(0.654648\pi\)
\(488\) 259.562 + 215.962i 0.531889 + 0.442544i
\(489\) −29.3742 −0.0600699
\(490\) 620.726 + 145.697i 1.26679 + 0.297340i
\(491\) 413.002i 0.841145i −0.907259 0.420573i \(-0.861829\pi\)
0.907259 0.420573i \(-0.138171\pi\)
\(492\) 212.909 + 63.0970i 0.432743 + 0.128246i
\(493\) −54.1733 + 93.8310i −0.109885 + 0.190327i
\(494\) 208.815 155.908i 0.422702 0.315603i
\(495\) 14.9558 8.63471i 0.0302137 0.0174439i
\(496\) 557.931 + 29.3867i 1.12486 + 0.0592474i
\(497\) −376.122 + 137.062i −0.756785 + 0.275779i
\(498\) −63.6588 + 148.143i −0.127829 + 0.297476i
\(499\) −585.830 + 338.229i −1.17401 + 0.677814i −0.954621 0.297824i \(-0.903739\pi\)
−0.219388 + 0.975638i \(0.570406\pi\)
\(500\) 194.122 46.5777i 0.388244 0.0931554i
\(501\) 260.543 451.274i 0.520047 0.900747i
\(502\) 53.3062 + 450.635i 0.106188 + 0.897679i
\(503\) 88.3032i 0.175553i −0.996140 0.0877765i \(-0.972024\pi\)
0.996140 0.0877765i \(-0.0279761\pi\)
\(504\) 82.2282 229.162i 0.163151 0.454686i
\(505\) −280.745 −0.555930
\(506\) 48.6599 5.75605i 0.0961659 0.0113756i
\(507\) −103.239 59.6050i −0.203627 0.117564i
\(508\) −77.4670 322.860i −0.152494 0.635551i
\(509\) 130.134 + 225.399i 0.255666 + 0.442827i 0.965076 0.261969i \(-0.0843719\pi\)
−0.709410 + 0.704796i \(0.751039\pi\)
\(510\) −308.956 132.762i −0.605796 0.260318i
\(511\) 388.339 + 68.3195i 0.759959 + 0.133698i
\(512\) −250.438 + 446.570i −0.489136 + 0.872207i
\(513\) −175.877 304.628i −0.342841 0.593818i
\(514\) 424.972 + 569.184i 0.826793 + 1.10736i
\(515\) 848.633 + 489.958i 1.64783 + 0.951375i
\(516\) −48.5657 + 163.876i −0.0941196 + 0.317590i
\(517\) −28.7539 −0.0556168
\(518\) −389.881 + 595.085i −0.752666 + 1.14881i
\(519\) 247.519i 0.476914i
\(520\) 426.693 + 355.019i 0.820564 + 0.682729i
\(521\) 296.145 512.939i 0.568417 0.984528i −0.428305 0.903634i \(-0.640889\pi\)
0.996723 0.0808936i \(-0.0257774\pi\)
\(522\) −47.0426 63.0063i −0.0901200 0.120702i
\(523\) −417.637 + 241.123i −0.798541 + 0.461038i −0.842961 0.537975i \(-0.819189\pi\)
0.0444199 + 0.999013i \(0.485856\pi\)
\(524\) −85.5682 + 81.1799i −0.163298 + 0.154923i
\(525\) 200.495 + 168.103i 0.381895 + 0.320196i
\(526\) 717.746 + 308.424i 1.36454 + 0.586357i
\(527\) 362.326 209.189i 0.687526 0.396943i
\(528\) 17.6677 + 11.4801i 0.0334615 + 0.0217426i
\(529\) 540.652 936.437i 1.02203 1.77020i
\(530\) −347.319 + 41.0848i −0.655319 + 0.0775186i
\(531\) 200.128i 0.376889i
\(532\) −306.199 152.567i −0.575562 0.286780i
\(533\) −274.485 −0.514982
\(534\) −12.5207 105.847i −0.0234471 0.198215i
\(535\) 228.706 + 132.044i 0.427488 + 0.246810i
\(536\) 219.032 + 37.6809i 0.408641 + 0.0703002i
\(537\) 28.9385 + 50.1230i 0.0538892 + 0.0933389i
\(538\) −295.899 + 688.600i −0.549999 + 1.27993i
\(539\) −29.4573 + 5.21767i −0.0546518 + 0.00968027i
\(540\) 543.546 515.671i 1.00657 0.954946i
\(541\) −190.830 330.527i −0.352736 0.610956i 0.633992 0.773340i \(-0.281415\pi\)
−0.986728 + 0.162383i \(0.948082\pi\)
\(542\) 245.672 183.427i 0.453269 0.338426i
\(543\) −86.9325 50.1905i −0.160097 0.0924319i
\(544\) 24.9504 + 382.591i 0.0458646 + 0.703293i
\(545\) −432.852 −0.794223
\(546\) 18.1536 321.525i 0.0332484 0.588873i
\(547\) 826.228i 1.51047i 0.655453 + 0.755236i \(0.272478\pi\)
−0.655453 + 0.755236i \(0.727522\pi\)
\(548\) 26.7287 90.1911i 0.0487750 0.164582i
\(549\) −91.7505 + 158.917i −0.167123 + 0.289466i
\(550\) 16.9551 12.6592i 0.0308274 0.0230168i
\(551\) −95.6838 + 55.2431i −0.173655 + 0.100260i
\(552\) 649.686 239.537i 1.17697 0.433943i
\(553\) 98.6651 + 82.7247i 0.178418 + 0.149593i
\(554\) 355.146 826.476i 0.641058 1.49183i
\(555\) −617.576 + 356.558i −1.11275 + 0.642447i
\(556\) 239.081 + 996.419i 0.430001 + 1.79212i
\(557\) −179.446 + 310.810i −0.322165 + 0.558006i −0.980935 0.194339i \(-0.937744\pi\)
0.658769 + 0.752345i \(0.271077\pi\)
\(558\) 35.6682 + 301.529i 0.0639215 + 0.540374i
\(559\) 211.271i 0.377945i
\(560\) 163.829 710.025i 0.292551 1.26790i
\(561\) 15.7779 0.0281245
\(562\) 6.50572 0.769570i 0.0115760 0.00136934i
\(563\) −80.3362 46.3821i −0.142693 0.0823839i 0.426954 0.904273i \(-0.359587\pi\)
−0.569647 + 0.821890i \(0.692920\pi\)
\(564\) −395.124 + 94.8060i −0.700574 + 0.168096i
\(565\) −466.471 807.951i −0.825612 1.43000i
\(566\) −629.000 270.289i −1.11131 0.477542i
\(567\) −158.353 27.8586i −0.279282 0.0491333i
\(568\) 158.266 + 429.259i 0.278637 + 0.755737i
\(569\) 188.943 + 327.259i 0.332062 + 0.575148i 0.982916 0.184055i \(-0.0589224\pi\)
−0.650854 + 0.759203i \(0.725589\pi\)
\(570\) −205.155 274.774i −0.359922 0.482060i
\(571\) −686.704 396.469i −1.20263 0.694341i −0.241494 0.970402i \(-0.577637\pi\)
−0.961140 + 0.276062i \(0.910971\pi\)
\(572\) −24.9704 7.40014i −0.0436546 0.0129373i
\(573\) −162.680 −0.283910
\(574\) 162.290 + 321.719i 0.282735 + 0.560487i
\(575\) 695.389i 1.20937i
\(576\) −262.253 92.9847i −0.455300 0.161432i
\(577\) −202.147 + 350.129i −0.350342 + 0.606810i −0.986309 0.164906i \(-0.947268\pi\)
0.635967 + 0.771716i \(0.280601\pi\)
\(578\) −174.033 233.091i −0.301096 0.403271i
\(579\) 310.211 179.100i 0.535770 0.309327i
\(580\) −161.972 170.728i −0.279262 0.294358i
\(581\) −245.829 + 89.5823i −0.423113 + 0.154186i
\(582\) −435.560 187.165i −0.748385 0.321590i
\(583\) 14.2113 8.20488i 0.0243761 0.0140736i
\(584\) 76.4017 444.108i 0.130825 0.760459i
\(585\) −150.829 + 261.243i −0.257827 + 0.446569i
\(586\) 484.129 57.2682i 0.826159 0.0977274i
\(587\) 252.412i 0.430003i −0.976614 0.215002i \(-0.931024\pi\)
0.976614 0.215002i \(-0.0689756\pi\)
\(588\) −387.587 + 168.824i −0.659161 + 0.287116i
\(589\) 426.639 0.724345
\(590\) −70.3622 594.821i −0.119258 1.00817i
\(591\) 522.536 + 301.686i 0.884156 + 0.510468i
\(592\) 681.776 + 443.005i 1.15165 + 0.748319i
\(593\) 221.333 + 383.360i 0.373243 + 0.646476i 0.990062 0.140629i \(-0.0449124\pi\)
−0.616819 + 0.787105i \(0.711579\pi\)
\(594\) −13.8790 + 32.2984i −0.0233653 + 0.0543744i
\(595\) −186.826 512.682i −0.313994 0.861651i
\(596\) −246.576 259.906i −0.413719 0.436083i
\(597\) 0.296952 + 0.514335i 0.000497406 + 0.000861533i
\(598\) −685.830 + 512.063i −1.14687 + 0.856293i
\(599\) 201.082 + 116.095i 0.335696 + 0.193814i 0.658367 0.752697i \(-0.271248\pi\)
−0.322671 + 0.946511i \(0.604581\pi\)
\(600\) 191.250 229.862i 0.318751 0.383103i
\(601\) 127.875 0.212770 0.106385 0.994325i \(-0.466072\pi\)
0.106385 + 0.994325i \(0.466072\pi\)
\(602\) −247.627 + 124.914i −0.411341 + 0.207499i
\(603\) 120.783i 0.200303i
\(604\) −180.805 53.5827i −0.299346 0.0887130i
\(605\) 392.405 679.665i 0.648603 1.12341i
\(606\) 149.159 111.367i 0.246137 0.183774i
\(607\) 166.162 95.9334i 0.273742 0.158045i −0.356845 0.934164i \(-0.616148\pi\)
0.630587 + 0.776119i \(0.282814\pi\)
\(608\) −173.039 + 350.598i −0.284603 + 0.576641i
\(609\) −23.6569 + 134.470i −0.0388455 + 0.220804i
\(610\) −216.828 + 504.590i −0.355456 + 0.827197i
\(611\) 434.974 251.132i 0.711905 0.411018i
\(612\) −202.612 + 48.6148i −0.331066 + 0.0794359i
\(613\) −163.435 + 283.077i −0.266615 + 0.461790i −0.967985 0.251006i \(-0.919238\pi\)
0.701371 + 0.712797i \(0.252572\pi\)
\(614\) −13.7330 116.095i −0.0223664 0.189079i
\(615\) 361.189i 0.587299i
\(616\) 6.09022 + 33.6427i 0.00988673 + 0.0546148i
\(617\) −557.014 −0.902778 −0.451389 0.892327i \(-0.649071\pi\)
−0.451389 + 0.892327i \(0.649071\pi\)
\(618\) −645.237 + 76.3259i −1.04407 + 0.123505i
\(619\) −405.320 234.011i −0.654798 0.378048i 0.135494 0.990778i \(-0.456738\pi\)
−0.790292 + 0.612731i \(0.790071\pi\)
\(620\) 212.026 + 883.663i 0.341977 + 1.42526i
\(621\) 577.650 + 1000.52i 0.930194 + 1.61114i
\(622\) 228.564 + 98.2166i 0.367466 + 0.157905i
\(623\) 111.120 132.532i 0.178363 0.212732i
\(624\) −367.533 19.3583i −0.588994 0.0310228i
\(625\) 378.965 + 656.387i 0.606344 + 1.05022i
\(626\) −576.077 771.566i −0.920250 1.23253i
\(627\) 13.9338 + 8.04471i 0.0222230 + 0.0128305i
\(628\) 327.096 1103.73i 0.520853 1.75753i
\(629\) 608.851 0.967967
\(630\) 395.376 + 22.3233i 0.627580 + 0.0354339i
\(631\) 557.865i 0.884096i 0.896991 + 0.442048i \(0.145748\pi\)
−0.896991 + 0.442048i \(0.854252\pi\)
\(632\) 94.1157 113.117i 0.148917 0.178982i
\(633\) 324.903 562.749i 0.513275 0.889018i
\(634\) −429.735 575.564i −0.677816 0.907829i
\(635\) 467.690 270.021i 0.736520 0.425230i
\(636\) 168.233 159.605i 0.264517 0.250951i
\(637\) 400.044 336.206i 0.628013 0.527796i
\(638\) 10.1449 + 4.35939i 0.0159011 + 0.00683290i
\(639\) −215.323 + 124.317i −0.336969 + 0.194549i
\(640\) −812.159 184.165i −1.26900 0.287757i
\(641\) −361.777 + 626.616i −0.564395 + 0.977560i 0.432711 + 0.901533i \(0.357557\pi\)
−0.997106 + 0.0760277i \(0.975776\pi\)
\(642\) −173.891 + 20.5698i −0.270858 + 0.0320402i
\(643\) 145.293i 0.225961i 0.993597 + 0.112980i \(0.0360397\pi\)
−0.993597 + 0.112980i \(0.963960\pi\)
\(644\) 1005.68 + 501.090i 1.56161 + 0.778091i
\(645\) −278.006 −0.431018
\(646\) 34.3931 + 290.749i 0.0532400 + 0.450076i
\(647\) 294.712 + 170.152i 0.455506 + 0.262987i 0.710153 0.704048i \(-0.248626\pi\)
−0.254647 + 0.967034i \(0.581959\pi\)
\(648\) −31.1542 + 181.094i −0.0480775 + 0.279465i
\(649\) 14.0517 + 24.3383i 0.0216514 + 0.0375012i
\(650\) −145.924 + 339.586i −0.224498 + 0.522439i
\(651\) 338.738 404.010i 0.520334 0.620599i
\(652\) −39.5190 + 37.4923i −0.0606119 + 0.0575035i
\(653\) −406.929 704.822i −0.623169 1.07936i −0.988892 0.148637i \(-0.952512\pi\)
0.365723 0.930724i \(-0.380822\pi\)
\(654\) 229.974 171.706i 0.351642 0.262547i
\(655\) −166.145 95.9236i −0.253656 0.146448i
\(656\) 366.976 186.862i 0.559414 0.284851i
\(657\) 244.898 0.372753
\(658\) −551.526 361.343i −0.838186 0.549153i
\(659\) 939.024i 1.42492i 0.701711 + 0.712462i \(0.252420\pi\)
−0.701711 + 0.712462i \(0.747580\pi\)
\(660\) −9.73766 + 32.8580i −0.0147540 + 0.0497848i
\(661\) 104.148 180.389i 0.157561 0.272904i −0.776428 0.630206i \(-0.782970\pi\)
0.933989 + 0.357303i \(0.116304\pi\)
\(662\) 203.040 151.596i 0.306707 0.228998i
\(663\) −238.679 + 137.802i −0.359999 + 0.207845i
\(664\) 103.441 + 280.558i 0.155784 + 0.422528i
\(665\) 96.4118 548.021i 0.144980 0.824091i
\(666\) −174.450 + 405.969i −0.261936 + 0.609563i
\(667\) 314.263 181.440i 0.471159 0.272024i
\(668\) −225.466 939.677i −0.337524 1.40670i
\(669\) −231.907 + 401.675i −0.346648 + 0.600411i
\(670\) 42.4653 + 358.990i 0.0633811 + 0.535805i
\(671\) 25.7685i 0.0384032i
\(672\) 194.615 + 442.224i 0.289605 + 0.658071i
\(673\) 634.671 0.943048 0.471524 0.881853i \(-0.343704\pi\)
0.471524 + 0.881853i \(0.343704\pi\)
\(674\) 1095.22 129.555i 1.62496 0.192219i
\(675\) 432.062 + 249.451i 0.640091 + 0.369557i
\(676\) −214.972 + 51.5803i −0.318005 + 0.0763022i
\(677\) −145.058 251.248i −0.214266 0.371119i 0.738780 0.673947i \(-0.235402\pi\)
−0.953045 + 0.302828i \(0.902069\pi\)
\(678\) 568.338 + 244.221i 0.838256 + 0.360208i
\(679\) −263.384 722.769i −0.387899 1.06446i
\(680\) −585.112 + 215.728i −0.860458 + 0.317247i
\(681\) 454.466 + 787.159i 0.667351 + 1.15589i
\(682\) −25.5091 34.1656i −0.0374034 0.0500961i
\(683\) −617.155 356.315i −0.903595 0.521691i −0.0252299 0.999682i \(-0.508032\pi\)
−0.878365 + 0.477991i \(0.841365\pi\)
\(684\) −203.720 60.3735i −0.297836 0.0882654i
\(685\) 153.004 0.223364
\(686\) −630.588 270.103i −0.919224 0.393736i
\(687\) 98.1994i 0.142939i
\(688\) 143.828 + 282.461i 0.209052 + 0.410553i
\(689\) −143.320 + 248.238i −0.208012 + 0.360288i
\(690\) 673.811 + 902.466i 0.976538 + 1.30792i
\(691\) −350.022 + 202.085i −0.506545 + 0.292454i −0.731412 0.681936i \(-0.761138\pi\)
0.224868 + 0.974389i \(0.427805\pi\)
\(692\) 315.925 + 333.003i 0.456538 + 0.481218i
\(693\) −17.4575 + 6.36166i −0.0251912 + 0.00917989i
\(694\) −755.746 324.753i −1.08897 0.467944i
\(695\) −1443.40 + 833.347i −2.07683 + 1.19906i
\(696\) 153.781 + 26.4555i 0.220949 + 0.0380108i
\(697\) 154.190 267.064i 0.221219 0.383162i
\(698\) 799.496 94.5734i 1.14541 0.135492i
\(699\) 326.660i 0.467324i
\(700\) 484.300 29.7457i 0.691857 0.0424939i
\(701\) −111.341 −0.158831 −0.0794156 0.996842i \(-0.525305\pi\)
−0.0794156 + 0.996842i \(0.525305\pi\)
\(702\) −72.1352 609.810i −0.102757 0.868675i
\(703\) 537.692 + 310.437i 0.764854 + 0.441589i
\(704\) 38.4222 7.10550i 0.0545771 0.0100930i
\(705\) −330.459 572.371i −0.468736 0.811874i
\(706\) −47.3124 + 110.103i −0.0670148 + 0.155953i
\(707\) 297.489 + 52.3365i 0.420777 + 0.0740262i
\(708\) 273.340 + 288.116i 0.386074 + 0.406944i
\(709\) −386.373 669.217i −0.544955 0.943889i −0.998610 0.0527117i \(-0.983214\pi\)
0.453655 0.891177i \(-0.350120\pi\)
\(710\) −596.275 + 445.199i −0.839824 + 0.627041i
\(711\) 69.2556 + 39.9847i 0.0974059 + 0.0562373i
\(712\) −151.944 126.421i −0.213405 0.177558i
\(713\) −1401.25 −1.96529
\(714\) 302.634 + 198.276i 0.423857 + 0.277698i
\(715\) 42.3609i 0.0592460i
\(716\) 102.908 + 30.4975i 0.143726 + 0.0425942i
\(717\) −216.756 + 375.433i −0.302310 + 0.523616i
\(718\) 225.503 168.368i 0.314071 0.234496i
\(719\) 803.582 463.948i 1.11764 0.645269i 0.176841 0.984239i \(-0.443412\pi\)
0.940797 + 0.338971i \(0.110079\pi\)
\(720\) 23.8046 451.951i 0.0330620 0.627710i
\(721\) −807.910 677.384i −1.12054 0.939506i
\(722\) 167.177 389.045i 0.231547 0.538843i
\(723\) −464.443 + 268.146i −0.642383 + 0.370880i
\(724\) −181.017 + 43.4333i −0.250024 + 0.0599907i
\(725\) 78.3525 135.711i 0.108072 0.187187i
\(726\) 61.1290 + 516.767i 0.0841997 + 0.711800i
\(727\) 811.924i 1.11681i −0.829567 0.558407i \(-0.811413\pi\)
0.829567 0.558407i \(-0.188587\pi\)
\(728\) −385.960 455.738i −0.530165 0.626014i
\(729\) −658.744 −0.903627
\(730\) 727.887 86.1027i 0.997105 0.117949i
\(731\) 205.559 + 118.680i 0.281202 + 0.162352i
\(732\) −84.9629 354.101i −0.116070 0.483744i
\(733\) 495.396 + 858.052i 0.675848 + 1.17060i 0.976220 + 0.216781i \(0.0695556\pi\)
−0.300373 + 0.953822i \(0.597111\pi\)
\(734\) 612.592 + 263.238i 0.834594 + 0.358635i
\(735\) −442.405 526.409i −0.601912 0.716202i
\(736\) 568.327 1151.50i 0.772184 1.56454i
\(737\) −8.48057 14.6888i −0.0115069 0.0199305i
\(738\) 133.894 + 179.330i 0.181428 + 0.242995i
\(739\) 989.673 + 571.388i 1.33921 + 0.773191i 0.986690 0.162615i \(-0.0519928\pi\)
0.352516 + 0.935806i \(0.385326\pi\)
\(740\) −375.766 + 1267.95i −0.507792 + 1.71345i
\(741\) −281.045 −0.379278
\(742\) 375.694 + 21.2121i 0.506326 + 0.0285877i
\(743\) 143.488i 0.193120i 0.995327 + 0.0965601i \(0.0307840\pi\)
−0.995327 + 0.0965601i \(0.969216\pi\)
\(744\) −463.185 385.381i −0.622561 0.517986i
\(745\) 291.359 504.649i 0.391086 0.677381i
\(746\) −308.040 412.572i −0.412922 0.553045i
\(747\) −140.733 + 81.2520i −0.188397 + 0.108771i
\(748\) 21.2270 20.1383i 0.0283783 0.0269229i
\(749\) −217.732 182.555i −0.290696 0.243731i
\(750\) −197.807 84.9999i −0.263742 0.113333i
\(751\) −1202.40 + 694.203i −1.60106 + 0.924372i −0.609783 + 0.792568i \(0.708744\pi\)
−0.991276 + 0.131804i \(0.957923\pi\)
\(752\) −410.578 + 631.872i −0.545981 + 0.840255i
\(753\) 244.692 423.818i 0.324956 0.562840i
\(754\) −191.541 + 22.6577i −0.254034 + 0.0300500i
\(755\) 306.725i 0.406258i
\(756\) −672.097 + 445.099i −0.889017 + 0.588756i
\(757\) 206.398 0.272652 0.136326 0.990664i \(-0.456470\pi\)
0.136326 + 0.990664i \(0.456470\pi\)
\(758\) 28.8882 + 244.212i 0.0381110 + 0.322180i
\(759\) −45.7642 26.4220i −0.0602954 0.0348116i
\(760\) −626.721 107.817i −0.824633 0.141865i
\(761\) 284.867 + 493.405i 0.374333 + 0.648363i 0.990227 0.139466i \(-0.0445384\pi\)
−0.615894 + 0.787829i \(0.711205\pi\)
\(762\) −141.370 + 328.988i −0.185525 + 0.431743i
\(763\) 458.669 + 80.6924i 0.601139 + 0.105757i
\(764\) −218.864 + 207.640i −0.286472 + 0.271780i
\(765\) −169.453 293.501i −0.221507 0.383662i
\(766\) 558.870 417.271i 0.729595 0.544740i
\(767\) −425.134 245.451i −0.554282 0.320015i
\(768\) 504.554 224.325i 0.656972 0.292090i
\(769\) −945.548 −1.22958 −0.614791 0.788690i \(-0.710760\pi\)
−0.614791 + 0.788690i \(0.710760\pi\)
\(770\) −49.6504 + 25.0459i −0.0644810 + 0.0325272i
\(771\) 766.069i 0.993604i
\(772\) 188.749 636.898i 0.244493 0.824997i
\(773\) −66.4717 + 115.132i −0.0859918 + 0.148942i −0.905813 0.423677i \(-0.860739\pi\)
0.819822 + 0.572619i \(0.194073\pi\)
\(774\) −138.030 + 103.058i −0.178334 + 0.133150i
\(775\) −524.043 + 302.556i −0.676184 + 0.390395i
\(776\) −824.878 + 304.129i −1.06299 + 0.391919i
\(777\) 720.881 262.696i 0.927775 0.338090i
\(778\) −279.031 + 649.345i −0.358652 + 0.834633i
\(779\) 272.338 157.234i 0.349599 0.201841i
\(780\) −139.670 582.105i −0.179065 0.746289i
\(781\) 17.4575 30.2372i 0.0223527 0.0387160i
\(782\) −112.960 954.934i −0.144451 1.22114i
\(783\) 260.346i 0.332497i
\(784\) −305.963 + 721.833i −0.390259 + 0.920705i
\(785\) 1872.41 2.38523
\(786\) 126.324 14.9430i 0.160717 0.0190115i
\(787\) 202.605 + 116.974i 0.257440 + 0.148633i 0.623166 0.782089i \(-0.285846\pi\)
−0.365726 + 0.930722i \(0.619179\pi\)
\(788\) 1088.06 261.070i 1.38079 0.331307i
\(789\) −421.253 729.631i −0.533907 0.924755i
\(790\) 219.899 + 94.4933i 0.278354 + 0.119612i
\(791\) 343.674 + 943.100i 0.434481 + 1.19229i
\(792\) 7.34582 + 19.9238i 0.00927502 + 0.0251563i
\(793\) 225.059 + 389.813i 0.283807 + 0.491567i
\(794\) 218.168 + 292.202i 0.274771 + 0.368013i
\(795\) 326.651 + 188.592i 0.410881 + 0.237222i
\(796\) 1.05599 + 0.312949i 0.00132662 + 0.000393152i
\(797\) 1208.00 1.51569 0.757843 0.652437i \(-0.226253\pi\)
0.757843 + 0.652437i \(0.226253\pi\)
\(798\) 166.168 + 329.408i 0.208231 + 0.412792i
\(799\) 564.285i 0.706239i
\(800\) −36.0864 553.353i −0.0451080 0.691691i
\(801\) 53.7095 93.0277i 0.0670531 0.116139i
\(802\) 413.846 + 554.283i 0.516018 + 0.691126i
\(803\) −29.7830 + 17.1952i −0.0370896 + 0.0214137i
\(804\) −164.968 173.885i −0.205184 0.216275i
\(805\) −316.654 + 1799.92i −0.393360 + 2.23592i
\(806\) 684.286 + 294.046i 0.848990 + 0.364821i
\(807\) 700.002 404.147i 0.867413 0.500801i
\(808\) 58.5280 340.212i 0.0724356 0.421054i
\(809\) −34.7428 + 60.1763i −0.0429453 + 0.0743835i −0.886699 0.462347i \(-0.847007\pi\)
0.843754 + 0.536730i \(0.180341\pi\)
\(810\) −296.810 + 35.1100i −0.366432 + 0.0433457i
\(811\) 1095.24i 1.35048i −0.737599 0.675239i \(-0.764041\pi\)
0.737599 0.675239i \(-0.235959\pi\)
\(812\) 139.806 + 211.106i 0.172174 + 0.259982i
\(813\) −330.651 −0.406705
\(814\) −7.28911 61.6200i −0.00895469 0.0757003i
\(815\) −76.7325 44.3015i −0.0941503 0.0543577i
\(816\) 225.293 346.721i 0.276094 0.424904i
\(817\) 121.023 + 209.618i 0.148131 + 0.256570i
\(818\) 241.455 561.901i 0.295178 0.686920i
\(819\) 208.526 248.707i 0.254610 0.303671i
\(820\) 461.009 + 485.930i 0.562206 + 0.592598i
\(821\) 378.010 + 654.733i 0.460427 + 0.797483i 0.998982 0.0451075i \(-0.0143630\pi\)
−0.538555 + 0.842590i \(0.681030\pi\)
\(822\) −81.2909 + 60.6945i −0.0988940 + 0.0738375i
\(823\) 277.186 + 160.033i 0.336799 + 0.194451i 0.658856 0.752269i \(-0.271041\pi\)
−0.322057 + 0.946720i \(0.604374\pi\)
\(824\) −770.658 + 926.245i −0.935265 + 1.12408i
\(825\) −22.8200 −0.0276606
\(826\) −36.3279 + 643.416i −0.0439806 + 0.778954i
\(827\) 104.960i 0.126917i −0.997984 0.0634585i \(-0.979787\pi\)
0.997984 0.0634585i \(-0.0202131\pi\)
\(828\) 669.095 + 198.290i 0.808086 + 0.239481i
\(829\) −408.833 + 708.120i −0.493164 + 0.854186i −0.999969 0.00787505i \(-0.997493\pi\)
0.506804 + 0.862061i \(0.330827\pi\)
\(830\) −389.718 + 290.977i −0.469540 + 0.350574i
\(831\) −840.161 + 485.067i −1.01102 + 0.583715i
\(832\) −519.173 + 443.063i −0.624006 + 0.532527i
\(833\) 102.395 + 578.089i 0.122923 + 0.693984i
\(834\) 436.300 1015.33i 0.523141 1.21742i
\(835\) 1361.20 785.891i 1.63018 0.941187i
\(836\) 29.0141 6.96164i 0.0347058 0.00832732i
\(837\) 502.659 870.631i 0.600548 1.04018i
\(838\) −176.140 1489.04i −0.210191 1.77689i
\(839\) 1029.02i 1.22648i 0.789896 + 0.613240i \(0.210134\pi\)
−0.789896 + 0.613240i \(0.789866\pi\)
\(840\) −599.695 + 507.876i −0.713922 + 0.604614i
\(841\) −759.225 −0.902765
\(842\) −707.459 + 83.6862i −0.840212 + 0.0993898i
\(843\) −6.11857 3.53256i −0.00725809 0.00419046i
\(844\) −281.161 1171.80i −0.333129 1.38839i
\(845\) −179.790 311.405i −0.212769 0.368527i
\(846\) −376.253 161.680i −0.444744 0.191111i
\(847\) −542.513 + 647.051i −0.640511 + 0.763933i
\(848\) 22.6197 429.453i 0.0266741 0.506430i
\(849\) 369.167 + 639.416i 0.434825 + 0.753140i
\(850\) −248.433 332.738i −0.292274 0.391456i
\(851\) −1765.99 1019.60i −2.07520 1.19812i
\(852\) 140.196 473.067i 0.164550 0.555243i
\(853\) 583.808 0.684417 0.342209 0.939624i \(-0.388825\pi\)
0.342209 + 0.939624i \(0.388825\pi\)
\(854\) 323.827 494.265i 0.379188 0.578764i
\(855\) 345.598i 0.404209i
\(856\) −207.692 + 249.623i −0.242631 + 0.291615i
\(857\) 549.072 951.020i 0.640691 1.10971i −0.344588 0.938754i \(-0.611981\pi\)
0.985279 0.170955i \(-0.0546852\pi\)
\(858\) 16.8039 + 22.5063i 0.0195850 + 0.0262311i
\(859\) 259.092 149.587i 0.301620 0.174141i −0.341550 0.939864i \(-0.610952\pi\)
0.643171 + 0.765723i \(0.277619\pi\)
\(860\) −374.020 + 354.838i −0.434907 + 0.412603i
\(861\) 67.3329 382.731i 0.0782032 0.444520i
\(862\) −347.815 149.460i −0.403498 0.173388i
\(863\) 815.368 470.753i 0.944807 0.545485i 0.0533431 0.998576i \(-0.483012\pi\)
0.891464 + 0.453092i \(0.149679\pi\)
\(864\) 511.584 + 766.183i 0.592111 + 0.886786i
\(865\) −373.302 + 646.578i −0.431563 + 0.747489i
\(866\) −1532.03 + 181.225i −1.76908 + 0.209267i
\(867\) 313.719i 0.361844i
\(868\) −59.9394 975.894i −0.0690546 1.12430i
\(869\) −11.2299 −0.0129228
\(870\) 29.8147 + 252.045i 0.0342697 + 0.289706i
\(871\) 256.579 + 148.136i 0.294580 + 0.170076i
\(872\) 90.2383 524.538i 0.103484 0.601534i
\(873\) −238.891 413.772i −0.273644 0.473966i
\(874\) 387.137 900.922i 0.442948 1.03080i
\(875\) −119.614 328.241i −0.136702 0.375132i
\(876\) −352.570 + 334.488i −0.402477 + 0.381836i
\(877\) −491.695 851.640i −0.560655 0.971084i −0.997439 0.0715173i \(-0.977216\pi\)
0.436784 0.899566i \(-0.356117\pi\)
\(878\) −1287.25 + 961.105i −1.46612 + 1.09465i
\(879\) −455.319 262.879i −0.517996 0.299065i
\(880\) 28.8381 + 56.6347i 0.0327706 + 0.0643577i
\(881\) −155.250 −0.176220 −0.0881102 0.996111i \(-0.528083\pi\)
−0.0881102 + 0.996111i \(0.528083\pi\)
\(882\) −414.796 97.3609i −0.470290 0.110386i
\(883\) 612.809i 0.694008i −0.937864 0.347004i \(-0.887199\pi\)
0.937864 0.347004i \(-0.112801\pi\)
\(884\) −145.225 + 490.036i −0.164282 + 0.554339i
\(885\) −322.984 + 559.424i −0.364953 + 0.632117i
\(886\) −1161.08 + 866.903i −1.31048 + 0.978445i
\(887\) −123.796 + 71.4737i −0.139567 + 0.0805791i −0.568158 0.822920i \(-0.692344\pi\)
0.428591 + 0.903499i \(0.359010\pi\)
\(888\) −303.335 822.724i −0.341593 0.926490i
\(889\) −545.923 + 198.939i −0.614087 + 0.223779i
\(890\) 126.928 295.380i 0.142616 0.331888i
\(891\) 12.1446 7.01167i 0.0136303 0.00786944i
\(892\) 200.685 + 836.398i 0.224984 + 0.937666i
\(893\) −287.714 + 498.335i −0.322188 + 0.558045i
\(894\) 45.3880 + 383.697i 0.0507696 + 0.429191i
\(895\) 174.578i 0.195059i
\(896\) 826.267 + 346.552i 0.922173 + 0.386777i
\(897\) 923.063 1.02906
\(898\) −1340.70 + 158.593i −1.49299 + 0.176607i
\(899\) −273.465 157.885i −0.304188 0.175623i
\(900\) 293.044 70.3130i 0.325605 0.0781256i
\(901\) −161.018 278.891i −0.178710 0.309535i
\(902\) −28.8747 12.4078i −0.0320119 0.0137559i
\(903\) 294.588 + 51.8261i 0.326232 + 0.0573932i
\(904\) 1076.34 396.841i 1.19064 0.438984i
\(905\) −151.392 262.219i −0.167284 0.289745i
\(906\) 121.673 + 162.963i 0.134297 + 0.179870i
\(907\) 1169.79 + 675.381i 1.28974 + 0.744632i 0.978608 0.205735i \(-0.0659584\pi\)
0.311132 + 0.950367i \(0.399292\pi\)
\(908\) 1616.13 + 478.949i 1.77987 + 0.527477i
\(909\) 187.606 0.206387
\(910\) 532.338 812.521i 0.584987 0.892880i
\(911\) 215.218i 0.236244i −0.992999 0.118122i \(-0.962313\pi\)
0.992999 0.118122i \(-0.0376874\pi\)
\(912\) 375.746 191.328i 0.412002 0.209789i
\(913\) 11.4100 19.7627i 0.0124973 0.0216459i
\(914\) 435.410 + 583.165i 0.476379 + 0.638036i
\(915\) 512.945 296.149i 0.560596 0.323660i
\(916\) −125.338 132.114i −0.136832 0.144229i
\(917\) 158.172 + 132.618i 0.172489 + 0.144621i
\(918\) 633.844 + 272.370i 0.690462 + 0.296699i
\(919\) 7.65593 4.42016i 0.00833072 0.00480975i −0.495829 0.868420i \(-0.665136\pi\)
0.504160 + 0.863611i \(0.331802\pi\)
\(920\) 2058.40 + 354.115i 2.23739 + 0.384907i
\(921\) −63.0385 + 109.186i −0.0684457 + 0.118551i
\(922\) 463.489 54.8268i 0.502700 0.0594650i
\(923\) 609.884i 0.660763i
\(924\) 16.4439 33.0025i 0.0177964 0.0357169i
\(925\) −880.599 −0.951999
\(926\) 204.907 + 1732.22i 0.221282 + 1.87065i
\(927\) −567.093 327.411i −0.611751 0.353195i
\(928\) 240.658 160.688i 0.259330 0.173156i
\(929\) −712.274 1233.69i −0.766710 1.32798i −0.939338 0.342994i \(-0.888559\pi\)
0.172627 0.984987i \(-0.444774\pi\)
\(930\) 386.927 900.435i 0.416051 0.968210i
\(931\) −204.325 + 562.734i −0.219468 + 0.604440i
\(932\) −416.938 439.476i −0.447358 0.471541i
\(933\) −134.147 232.349i −0.143780 0.249034i
\(934\) 1230.48 918.715i 1.31743 0.983635i
\(935\) 41.2156 + 23.7958i 0.0440808 + 0.0254501i
\(936\) −285.135 237.239i −0.304631 0.253461i
\(937\) 616.709 0.658174 0.329087 0.944300i \(-0.393259\pi\)
0.329087 + 0.944300i \(0.393259\pi\)
\(938\) 21.9248 388.318i 0.0233740 0.413985i
\(939\) 1038.46i 1.10592i
\(940\) −1175.14 348.261i −1.25015 0.370490i
\(941\) −467.668 + 810.025i −0.496991 + 0.860813i −0.999994 0.00347133i \(-0.998895\pi\)
0.503003 + 0.864285i \(0.332228\pi\)
\(942\) −994.808 + 742.756i −1.05606 + 0.788489i
\(943\) −894.464 + 516.419i −0.948531 + 0.547634i
\(944\) 735.484 + 38.7386i 0.779114 + 0.0410366i
\(945\) −1004.74 842.413i −1.06322 0.891442i
\(946\) 9.55028 22.2248i 0.0100954 0.0234935i
\(947\) −988.080 + 570.468i −1.04338 + 0.602395i −0.920788 0.390062i \(-0.872453\pi\)
−0.122590 + 0.992457i \(0.539120\pi\)
\(948\) −154.316 + 37.0267i −0.162781 + 0.0390577i
\(949\) 300.361 520.240i 0.316502 0.548198i
\(950\) −49.7437 420.519i −0.0523618 0.442651i
\(951\) 774.656i 0.814570i
\(952\) 660.226 119.518i 0.693515 0.125545i
\(953\) −1265.64 −1.32806 −0.664030 0.747706i \(-0.731155\pi\)
−0.664030 + 0.747706i \(0.731155\pi\)
\(954\) 232.094 27.4547i 0.243285 0.0287785i
\(955\) −424.960 245.351i −0.444985 0.256912i
\(956\) 187.574 + 781.754i 0.196207 + 0.817734i
\(957\) −5.95416 10.3129i −0.00622169 0.0107763i
\(958\) 1447.48 + 621.998i 1.51094 + 0.649267i
\(959\) −162.130 28.5231i −0.169061 0.0297425i
\(960\) 583.015 + 683.167i 0.607307 + 0.711633i
\(961\) 129.169 + 223.728i 0.134411 + 0.232807i
\(962\) 648.446 + 868.494i 0.674061 + 0.902800i
\(963\) −152.831 88.2373i −0.158703 0.0916275i
\(964\) −282.592 + 953.554i −0.293145 + 0.989164i
\(965\) 1080.46 1.11965
\(966\) −545.762 1081.91i −0.564971 1.11998i
\(967\) 1527.55i 1.57968i −0.613313 0.789840i \(-0.710164\pi\)
0.613313 0.789840i \(-0.289836\pi\)
\(968\) 741.825 + 617.216i 0.766348 + 0.637620i
\(969\) 157.874 273.447i 0.162925 0.282195i
\(970\) −855.509 1145.82i −0.881968 1.18126i
\(971\) −156.301 + 90.2405i −0.160969 + 0.0929356i −0.578321 0.815810i \(-0.696292\pi\)
0.417351 + 0.908745i \(0.362958\pi\)
\(972\) −608.133 + 576.945i −0.625651 + 0.593565i
\(973\) 1684.84 613.972i 1.73160 0.631009i
\(974\) −67.5601 29.0314i −0.0693636 0.0298063i
\(975\) 345.209 199.306i 0.354060 0.204417i
\(976\) −566.268 367.950i −0.580193 0.376998i
\(977\) 446.888 774.033i 0.457408 0.792255i −0.541415 0.840756i \(-0.682111\pi\)
0.998823 + 0.0485011i \(0.0154444\pi\)
\(978\) 58.3416 6.90131i 0.0596540 0.00705655i
\(979\) 15.0846i 0.0154081i
\(980\) −1267.09 143.540i −1.29295 0.146469i
\(981\) 289.250 0.294852
\(982\) 97.0326 + 820.285i 0.0988112 + 0.835321i
\(983\) −561.180 323.997i −0.570885 0.329600i 0.186618 0.982433i \(-0.440247\pi\)
−0.757503 + 0.652832i \(0.773581\pi\)
\(984\) −437.695 75.2984i −0.444812 0.0765228i
\(985\) 909.994 + 1576.16i 0.923852 + 1.60016i
\(986\) 85.5514 199.090i 0.0867662 0.201917i
\(987\) 243.467 + 668.114i 0.246674 + 0.676914i
\(988\) −378.108 + 358.717i −0.382700 + 0.363074i
\(989\) −397.487 688.468i −0.401908 0.696126i
\(990\) −27.6757 + 20.6636i −0.0279553 + 0.0208724i
\(991\) 1167.47 + 674.041i 1.17808 + 0.680162i 0.955569 0.294769i \(-0.0952427\pi\)
0.222507 + 0.974931i \(0.428576\pi\)
\(992\) −1115.04 + 72.7164i −1.12403 + 0.0733028i
\(993\) −273.273 −0.275199
\(994\) 714.834 360.595i 0.719149 0.362771i
\(995\) 1.79142i 0.00180042i
\(996\) 91.6307 309.191i 0.0919987 0.310433i
\(997\) −256.786 + 444.766i −0.257559 + 0.446105i −0.965587 0.260079i \(-0.916251\pi\)
0.708029 + 0.706184i \(0.249585\pi\)
\(998\) 1084.08 809.412i 1.08626 0.811034i
\(999\) 1267.00 731.502i 1.26827 0.732234i
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 28.3.g.a.11.1 12
3.2 odd 2 252.3.y.c.235.6 12
4.3 odd 2 inner 28.3.g.a.11.5 yes 12
7.2 even 3 inner 28.3.g.a.23.5 yes 12
7.3 odd 6 196.3.c.h.99.3 6
7.4 even 3 196.3.c.i.99.3 6
7.5 odd 6 196.3.g.i.79.5 12
7.6 odd 2 196.3.g.i.67.1 12
8.3 odd 2 448.3.r.h.319.5 12
8.5 even 2 448.3.r.h.319.2 12
12.11 even 2 252.3.y.c.235.2 12
21.2 odd 6 252.3.y.c.163.2 12
28.3 even 6 196.3.c.h.99.4 6
28.11 odd 6 196.3.c.i.99.4 6
28.19 even 6 196.3.g.i.79.1 12
28.23 odd 6 inner 28.3.g.a.23.1 yes 12
28.27 even 2 196.3.g.i.67.5 12
56.37 even 6 448.3.r.h.191.5 12
56.51 odd 6 448.3.r.h.191.2 12
84.23 even 6 252.3.y.c.163.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.3.g.a.11.1 12 1.1 even 1 trivial
28.3.g.a.11.5 yes 12 4.3 odd 2 inner
28.3.g.a.23.1 yes 12 28.23 odd 6 inner
28.3.g.a.23.5 yes 12 7.2 even 3 inner
196.3.c.h.99.3 6 7.3 odd 6
196.3.c.h.99.4 6 28.3 even 6
196.3.c.i.99.3 6 7.4 even 3
196.3.c.i.99.4 6 28.11 odd 6
196.3.g.i.67.1 12 7.6 odd 2
196.3.g.i.67.5 12 28.27 even 2
196.3.g.i.79.1 12 28.19 even 6
196.3.g.i.79.5 12 7.5 odd 6
252.3.y.c.163.2 12 21.2 odd 6
252.3.y.c.163.6 12 84.23 even 6
252.3.y.c.235.2 12 12.11 even 2
252.3.y.c.235.6 12 3.2 odd 2
448.3.r.h.191.2 12 56.51 odd 6
448.3.r.h.191.5 12 56.37 even 6
448.3.r.h.319.2 12 8.5 even 2
448.3.r.h.319.5 12 8.3 odd 2