Properties

Label 392.3.k.o.275.4
Level $392$
Weight $3$
Character 392.275
Analytic conductor $10.681$
Analytic rank $0$
Dimension $16$
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] = [392,3,Mod(67,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 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("392.67");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), not 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: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} - 448 x^{7} - 320 x^{6} + 2816 x^{5} - 5632 x^{4} + 6144 x^{3} + 12288 x^{2} + \cdots + 65536 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 275.4
Root \(0.288997 - 1.97901i\) of defining polynomial
Character \(\chi\) \(=\) 392.275
Dual form 392.3.k.o.67.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.288997 + 1.97901i) q^{2} +(-0.0487183 - 0.0843825i) q^{3} +(-3.83296 - 1.14386i) q^{4} +(-3.00119 - 1.73274i) q^{5} +(0.181073 - 0.0720276i) q^{6} +(3.37142 - 7.25490i) q^{8} +(4.49525 - 7.78601i) q^{9} +O(q^{10})\) \(q+(-0.288997 + 1.97901i) q^{2} +(-0.0487183 - 0.0843825i) q^{3} +(-3.83296 - 1.14386i) q^{4} +(-3.00119 - 1.73274i) q^{5} +(0.181073 - 0.0720276i) q^{6} +(3.37142 - 7.25490i) q^{8} +(4.49525 - 7.78601i) q^{9} +(4.29644 - 5.43862i) q^{10} +(1.46433 + 2.53629i) q^{11} +(0.0902137 + 0.379162i) q^{12} +19.1586i q^{13} +0.337664i q^{15} +(13.3832 + 8.76872i) q^{16} +(7.19487 + 12.4619i) q^{17} +(14.1095 + 11.1463i) q^{18} +(-4.04872 + 7.01259i) q^{19} +(9.52143 + 10.0744i) q^{20} +(-5.44254 + 2.16494i) q^{22} +(14.5144 + 8.37990i) q^{23} +(-0.776436 + 0.0689571i) q^{24} +(-6.49525 - 11.2501i) q^{25} +(-37.9150 - 5.53678i) q^{26} -1.75293 q^{27} +27.1649i q^{29} +(-0.668240 - 0.0975839i) q^{30} +(-38.8779 + 22.4461i) q^{31} +(-21.2211 + 23.9513i) q^{32} +(0.142679 - 0.247128i) q^{33} +(-26.7415 + 10.6373i) q^{34} +(-26.1362 + 24.7015i) q^{36} +(34.2675 + 19.7844i) q^{37} +(-12.7079 - 10.0391i) q^{38} +(1.61665 - 0.933373i) q^{39} +(-22.6891 + 15.9315i) q^{40} +45.8766 q^{41} +61.0334 q^{43} +(-2.71156 - 11.3965i) q^{44} +(-26.9822 + 15.5782i) q^{45} +(-20.7785 + 26.3024i) q^{46} +(-40.0790 - 23.1396i) q^{47} +(0.0879212 - 1.55650i) q^{48} +(24.1412 - 9.60292i) q^{50} +(0.701044 - 1.21424i) q^{51} +(21.9147 - 73.4341i) q^{52} +(-8.39546 + 4.84712i) q^{53} +(0.506593 - 3.46907i) q^{54} -10.1492i q^{55} +0.788986 q^{57} +(-53.7596 - 7.85058i) q^{58} +(57.2770 + 99.2066i) q^{59} +(0.386239 - 1.29425i) q^{60} +(-6.47814 - 3.74016i) q^{61} +(-33.1855 - 83.4265i) q^{62} +(-41.2671 - 48.9186i) q^{64} +(33.1968 - 57.4985i) q^{65} +(0.447834 + 0.353783i) q^{66} +(6.02950 + 10.4434i) q^{67} +(-13.3231 - 55.9958i) q^{68} -1.63302i q^{69} +129.187i q^{71} +(-41.3313 - 58.8625i) q^{72} +(9.14268 + 15.8356i) q^{73} +(-49.0567 + 62.0981i) q^{74} +(-0.632875 + 1.09617i) q^{75} +(23.5400 - 22.2478i) q^{76} +(1.37995 + 3.46911i) q^{78} +(-36.9073 - 21.3084i) q^{79} +(-24.9716 - 49.5061i) q^{80} +(-40.3719 - 69.9261i) q^{81} +(-13.2582 + 90.7903i) q^{82} -109.670 q^{83} -49.8673i q^{85} +(-17.6385 + 120.786i) q^{86} +(2.29224 - 1.32343i) q^{87} +(23.3374 - 2.07265i) q^{88} +(40.4581 - 70.0755i) q^{89} +(-23.0316 - 57.9001i) q^{90} +(-46.0478 - 48.7223i) q^{92} +(3.78812 + 2.18707i) q^{93} +(57.3763 - 72.6295i) q^{94} +(24.3019 - 14.0307i) q^{95} +(3.05493 + 0.623822i) q^{96} +162.086 q^{97} +26.3301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{2} + 8 q^{3} - 5 q^{4} - 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{2} + 8 q^{3} - 5 q^{4} - 44 q^{6} + 26 q^{8} - 48 q^{9} - 16 q^{10} + 32 q^{11} - 30 q^{12} + 71 q^{16} + 80 q^{17} + 29 q^{18} - 56 q^{19} - 216 q^{20} + 132 q^{22} - 22 q^{24} + 16 q^{25} - 24 q^{26} - 64 q^{27} - 96 q^{30} + 19 q^{32} - 32 q^{33} + 148 q^{34} - 66 q^{36} + 14 q^{38} - 84 q^{40} + 256 q^{41} - 50 q^{44} + 152 q^{46} + 268 q^{48} + 66 q^{50} + 368 q^{51} - 132 q^{52} + 228 q^{54} + 112 q^{57} - 24 q^{58} - 104 q^{59} - 192 q^{60} + 240 q^{62} - 110 q^{64} + 72 q^{65} + 276 q^{66} - 304 q^{67} + 190 q^{68} + 209 q^{72} + 112 q^{73} - 8 q^{74} - 72 q^{75} + 140 q^{76} - 608 q^{78} - 124 q^{80} - 48 q^{81} - 450 q^{82} + 144 q^{83} - 210 q^{86} + 486 q^{88} + 512 q^{89} - 368 q^{90} - 944 q^{92} - 472 q^{94} - 558 q^{96} + 128 q^{97} + 512 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.288997 + 1.97901i −0.144499 + 0.989505i
\(3\) −0.0487183 0.0843825i −0.0162394 0.0281275i 0.857791 0.513998i \(-0.171836\pi\)
−0.874031 + 0.485870i \(0.838503\pi\)
\(4\) −3.83296 1.14386i −0.958240 0.285964i
\(5\) −3.00119 1.73274i −0.600237 0.346547i 0.168898 0.985634i \(-0.445979\pi\)
−0.769135 + 0.639086i \(0.779313\pi\)
\(6\) 0.181073 0.0720276i 0.0301789 0.0120046i
\(7\) 0 0
\(8\) 3.37142 7.25490i 0.421428 0.906862i
\(9\) 4.49525 7.78601i 0.499473 0.865112i
\(10\) 4.29644 5.43862i 0.429644 0.543862i
\(11\) 1.46433 + 2.53629i 0.133121 + 0.230572i 0.924878 0.380264i \(-0.124167\pi\)
−0.791757 + 0.610836i \(0.790833\pi\)
\(12\) 0.0902137 + 0.379162i 0.00751781 + 0.0315968i
\(13\) 19.1586i 1.47374i 0.676036 + 0.736869i \(0.263696\pi\)
−0.676036 + 0.736869i \(0.736304\pi\)
\(14\) 0 0
\(15\) 0.337664i 0.0225109i
\(16\) 13.3832 + 8.76872i 0.836449 + 0.548045i
\(17\) 7.19487 + 12.4619i 0.423228 + 0.733052i 0.996253 0.0864856i \(-0.0275637\pi\)
−0.573025 + 0.819538i \(0.694230\pi\)
\(18\) 14.1095 + 11.1463i 0.783859 + 0.619238i
\(19\) −4.04872 + 7.01259i −0.213090 + 0.369083i −0.952680 0.303975i \(-0.901686\pi\)
0.739590 + 0.673058i \(0.235020\pi\)
\(20\) 9.52143 + 10.0744i 0.476071 + 0.503722i
\(21\) 0 0
\(22\) −5.44254 + 2.16494i −0.247388 + 0.0984064i
\(23\) 14.5144 + 8.37990i 0.631062 + 0.364344i 0.781163 0.624327i \(-0.214627\pi\)
−0.150101 + 0.988671i \(0.547960\pi\)
\(24\) −0.776436 + 0.0689571i −0.0323515 + 0.00287321i
\(25\) −6.49525 11.2501i −0.259810 0.450004i
\(26\) −37.9150 5.53678i −1.45827 0.212953i
\(27\) −1.75293 −0.0649234
\(28\) 0 0
\(29\) 27.1649i 0.936720i 0.883538 + 0.468360i \(0.155155\pi\)
−0.883538 + 0.468360i \(0.844845\pi\)
\(30\) −0.668240 0.0975839i −0.0222747 0.00325280i
\(31\) −38.8779 + 22.4461i −1.25412 + 0.724069i −0.971926 0.235287i \(-0.924397\pi\)
−0.282198 + 0.959356i \(0.591064\pi\)
\(32\) −21.2211 + 23.9513i −0.663159 + 0.748479i
\(33\) 0.142679 0.247128i 0.00432362 0.00748872i
\(34\) −26.7415 + 10.6373i −0.786515 + 0.312861i
\(35\) 0 0
\(36\) −26.1362 + 24.7015i −0.726006 + 0.686154i
\(37\) 34.2675 + 19.7844i 0.926149 + 0.534713i 0.885592 0.464465i \(-0.153753\pi\)
0.0405576 + 0.999177i \(0.487087\pi\)
\(38\) −12.7079 10.0391i −0.334419 0.264186i
\(39\) 1.61665 0.933373i 0.0414526 0.0239327i
\(40\) −22.6891 + 15.9315i −0.567227 + 0.398288i
\(41\) 45.8766 1.11894 0.559471 0.828850i \(-0.311004\pi\)
0.559471 + 0.828850i \(0.311004\pi\)
\(42\) 0 0
\(43\) 61.0334 1.41938 0.709690 0.704514i \(-0.248835\pi\)
0.709690 + 0.704514i \(0.248835\pi\)
\(44\) −2.71156 11.3965i −0.0616264 0.259011i
\(45\) −26.9822 + 15.5782i −0.599604 + 0.346182i
\(46\) −20.7785 + 26.3024i −0.451707 + 0.571791i
\(47\) −40.0790 23.1396i −0.852746 0.492333i 0.00883070 0.999961i \(-0.497189\pi\)
−0.861576 + 0.507628i \(0.830522\pi\)
\(48\) 0.0879212 1.55650i 0.00183169 0.0324272i
\(49\) 0 0
\(50\) 24.1412 9.60292i 0.482824 0.192058i
\(51\) 0.701044 1.21424i 0.0137460 0.0238087i
\(52\) 21.9147 73.4341i 0.421436 1.41219i
\(53\) −8.39546 + 4.84712i −0.158405 + 0.0914551i −0.577107 0.816669i \(-0.695818\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(54\) 0.506593 3.46907i 0.00938135 0.0642421i
\(55\) 10.1492i 0.184531i
\(56\) 0 0
\(57\) 0.788986 0.0138419
\(58\) −53.7596 7.85058i −0.926889 0.135355i
\(59\) 57.2770 + 99.2066i 0.970796 + 1.68147i 0.693164 + 0.720780i \(0.256216\pi\)
0.277632 + 0.960687i \(0.410450\pi\)
\(60\) 0.386239 1.29425i 0.00643732 0.0215709i
\(61\) −6.47814 3.74016i −0.106199 0.0613141i 0.445960 0.895053i \(-0.352862\pi\)
−0.552159 + 0.833739i \(0.686196\pi\)
\(62\) −33.1855 83.4265i −0.535251 1.34559i
\(63\) 0 0
\(64\) −41.2671 48.9186i −0.644798 0.764353i
\(65\) 33.1968 57.4985i 0.510720 0.884592i
\(66\) 0.447834 + 0.353783i 0.00678537 + 0.00536035i
\(67\) 6.02950 + 10.4434i 0.0899925 + 0.155872i 0.907508 0.420035i \(-0.137982\pi\)
−0.817515 + 0.575907i \(0.804649\pi\)
\(68\) −13.3231 55.9958i −0.195927 0.823468i
\(69\) 1.63302i 0.0236669i
\(70\) 0 0
\(71\) 129.187i 1.81953i 0.415124 + 0.909765i \(0.363738\pi\)
−0.415124 + 0.909765i \(0.636262\pi\)
\(72\) −41.3313 58.8625i −0.574046 0.817535i
\(73\) 9.14268 + 15.8356i 0.125242 + 0.216926i 0.921828 0.387600i \(-0.126696\pi\)
−0.796585 + 0.604526i \(0.793363\pi\)
\(74\) −49.0567 + 62.0981i −0.662928 + 0.839164i
\(75\) −0.632875 + 1.09617i −0.00843833 + 0.0146156i
\(76\) 23.5400 22.2478i 0.309737 0.292734i
\(77\) 0 0
\(78\) 1.37995 + 3.46911i 0.0176916 + 0.0444758i
\(79\) −36.9073 21.3084i −0.467180 0.269727i 0.247878 0.968791i \(-0.420267\pi\)
−0.715059 + 0.699064i \(0.753600\pi\)
\(80\) −24.9716 49.5061i −0.312144 0.618826i
\(81\) −40.3719 69.9261i −0.498418 0.863286i
\(82\) −13.2582 + 90.7903i −0.161686 + 1.10720i
\(83\) −109.670 −1.32133 −0.660663 0.750683i \(-0.729725\pi\)
−0.660663 + 0.750683i \(0.729725\pi\)
\(84\) 0 0
\(85\) 49.8673i 0.586674i
\(86\) −17.6385 + 120.786i −0.205099 + 1.40448i
\(87\) 2.29224 1.32343i 0.0263476 0.0152118i
\(88\) 23.3374 2.07265i 0.265198 0.0235529i
\(89\) 40.4581 70.0755i 0.454585 0.787365i −0.544079 0.839034i \(-0.683121\pi\)
0.998664 + 0.0516693i \(0.0164542\pi\)
\(90\) −23.0316 57.9001i −0.255906 0.643334i
\(91\) 0 0
\(92\) −46.0478 48.7223i −0.500519 0.529590i
\(93\) 3.78812 + 2.18707i 0.0407325 + 0.0235169i
\(94\) 57.3763 72.6295i 0.610386 0.772655i
\(95\) 24.3019 14.0307i 0.255810 0.147692i
\(96\) 3.05493 + 0.623822i 0.0318222 + 0.00649815i
\(97\) 162.086 1.67099 0.835495 0.549498i \(-0.185181\pi\)
0.835495 + 0.549498i \(0.185181\pi\)
\(98\) 0 0
\(99\) 26.3301 0.265961
\(100\) 12.0275 + 50.5509i 0.120275 + 0.505509i
\(101\) −92.5150 + 53.4135i −0.915990 + 0.528847i −0.882354 0.470587i \(-0.844042\pi\)
−0.0336364 + 0.999434i \(0.510709\pi\)
\(102\) 2.20040 + 1.73829i 0.0215725 + 0.0170420i
\(103\) 109.662 + 63.3132i 1.06468 + 0.614691i 0.926722 0.375748i \(-0.122614\pi\)
0.137954 + 0.990439i \(0.455947\pi\)
\(104\) 138.994 + 64.5916i 1.33648 + 0.621074i
\(105\) 0 0
\(106\) −7.16623 18.0155i −0.0676060 0.169958i
\(107\) −43.5096 + 75.3608i −0.406632 + 0.704306i −0.994510 0.104643i \(-0.966630\pi\)
0.587878 + 0.808949i \(0.299963\pi\)
\(108\) 6.71892 + 2.00510i 0.0622123 + 0.0185658i
\(109\) 164.477 94.9607i 1.50896 0.871199i 0.509015 0.860758i \(-0.330010\pi\)
0.999945 0.0104412i \(-0.00332359\pi\)
\(110\) 20.0853 + 2.93309i 0.182594 + 0.0266644i
\(111\) 3.85544i 0.0347337i
\(112\) 0 0
\(113\) −40.1848 −0.355617 −0.177809 0.984065i \(-0.556901\pi\)
−0.177809 + 0.984065i \(0.556901\pi\)
\(114\) −0.228015 + 1.56141i −0.00200013 + 0.0136966i
\(115\) −29.0403 50.2993i −0.252524 0.437385i
\(116\) 31.0728 104.122i 0.267869 0.897603i
\(117\) 149.169 + 86.1227i 1.27495 + 0.736091i
\(118\) −212.884 + 84.6812i −1.80410 + 0.717638i
\(119\) 0 0
\(120\) 2.44971 + 1.13841i 0.0204143 + 0.00948672i
\(121\) 56.2115 97.3611i 0.464558 0.804637i
\(122\) 9.27398 11.7394i 0.0760162 0.0962247i
\(123\) −2.23503 3.87119i −0.0181710 0.0314731i
\(124\) 174.692 41.5645i 1.40881 0.335197i
\(125\) 131.655i 1.05324i
\(126\) 0 0
\(127\) 153.657i 1.20989i −0.796266 0.604947i \(-0.793194\pi\)
0.796266 0.604947i \(-0.206806\pi\)
\(128\) 108.736 67.5306i 0.849504 0.527583i
\(129\) −2.97344 5.15015i −0.0230499 0.0399236i
\(130\) 104.196 + 82.3137i 0.801510 + 0.633182i
\(131\) −30.9325 + 53.5766i −0.236126 + 0.408982i −0.959599 0.281371i \(-0.909211\pi\)
0.723474 + 0.690352i \(0.242544\pi\)
\(132\) −0.829563 + 0.784026i −0.00628457 + 0.00593959i
\(133\) 0 0
\(134\) −22.4101 + 8.91433i −0.167240 + 0.0665248i
\(135\) 5.26088 + 3.03737i 0.0389695 + 0.0224990i
\(136\) 114.667 10.1838i 0.843137 0.0748810i
\(137\) −52.9715 91.7494i −0.386653 0.669703i 0.605344 0.795964i \(-0.293036\pi\)
−0.991997 + 0.126261i \(0.959702\pi\)
\(138\) 3.23176 + 0.471938i 0.0234185 + 0.00341984i
\(139\) −185.384 −1.33370 −0.666848 0.745194i \(-0.732357\pi\)
−0.666848 + 0.745194i \(0.732357\pi\)
\(140\) 0 0
\(141\) 4.50930i 0.0319808i
\(142\) −255.662 37.3346i −1.80043 0.262920i
\(143\) −48.5918 + 28.0545i −0.339803 + 0.196185i
\(144\) 128.434 64.7839i 0.891903 0.449888i
\(145\) 47.0696 81.5269i 0.324618 0.562254i
\(146\) −33.9810 + 13.5170i −0.232747 + 0.0925823i
\(147\) 0 0
\(148\) −108.716 115.030i −0.734565 0.777229i
\(149\) 41.0579 + 23.7048i 0.275556 + 0.159093i 0.631410 0.775449i \(-0.282477\pi\)
−0.355854 + 0.934542i \(0.615810\pi\)
\(150\) −1.98644 1.56926i −0.0132429 0.0104617i
\(151\) −99.2255 + 57.2879i −0.657122 + 0.379390i −0.791180 0.611584i \(-0.790533\pi\)
0.134057 + 0.990974i \(0.457199\pi\)
\(152\) 37.2257 + 53.0154i 0.244906 + 0.348786i
\(153\) 129.371 0.845563
\(154\) 0 0
\(155\) 155.573 1.00370
\(156\) −7.26420 + 1.72837i −0.0465654 + 0.0110793i
\(157\) 254.694 147.047i 1.62225 0.936608i 0.635937 0.771741i \(-0.280614\pi\)
0.986316 0.164867i \(-0.0527196\pi\)
\(158\) 52.8357 66.8818i 0.334403 0.423302i
\(159\) 0.818024 + 0.472287i 0.00514481 + 0.00297036i
\(160\) 105.190 35.1118i 0.657436 0.219449i
\(161\) 0 0
\(162\) 150.052 59.6879i 0.926246 0.368444i
\(163\) −85.5104 + 148.108i −0.524603 + 0.908640i 0.474986 + 0.879993i \(0.342453\pi\)
−0.999590 + 0.0286465i \(0.990880\pi\)
\(164\) −175.843 52.4763i −1.07222 0.319977i
\(165\) −0.856414 + 0.494451i −0.00519039 + 0.00299667i
\(166\) 31.6943 217.038i 0.190930 1.30746i
\(167\) 120.657i 0.722499i −0.932469 0.361249i \(-0.882350\pi\)
0.932469 0.361249i \(-0.117650\pi\)
\(168\) 0 0
\(169\) −198.052 −1.17190
\(170\) 98.6878 + 14.4115i 0.580516 + 0.0847735i
\(171\) 36.4000 + 63.0467i 0.212866 + 0.368694i
\(172\) −233.939 69.8134i −1.36011 0.405892i
\(173\) −93.8242 54.1694i −0.542336 0.313118i 0.203689 0.979036i \(-0.434707\pi\)
−0.746025 + 0.665918i \(0.768040\pi\)
\(174\) 1.95662 + 4.91884i 0.0112450 + 0.0282692i
\(175\) 0 0
\(176\) −2.64266 + 46.7840i −0.0150151 + 0.265818i
\(177\) 5.58087 9.66635i 0.0315303 0.0546121i
\(178\) 126.988 + 100.319i 0.713414 + 0.563587i
\(179\) 80.7188 + 139.809i 0.450943 + 0.781056i 0.998445 0.0557481i \(-0.0177544\pi\)
−0.547502 + 0.836805i \(0.684421\pi\)
\(180\) 121.241 28.8468i 0.673560 0.160260i
\(181\) 7.14696i 0.0394860i 0.999805 + 0.0197430i \(0.00628479\pi\)
−0.999805 + 0.0197430i \(0.993715\pi\)
\(182\) 0 0
\(183\) 0.728856i 0.00398282i
\(184\) 109.730 77.0484i 0.596356 0.418741i
\(185\) −68.5621 118.753i −0.370606 0.641909i
\(186\) −5.42300 + 6.86468i −0.0291559 + 0.0369069i
\(187\) −21.0713 + 36.4966i −0.112681 + 0.195169i
\(188\) 127.153 + 134.538i 0.676346 + 0.715628i
\(189\) 0 0
\(190\) 20.7437 + 52.1486i 0.109178 + 0.274466i
\(191\) −63.4782 36.6491i −0.332347 0.191880i 0.324536 0.945873i \(-0.394792\pi\)
−0.656882 + 0.753993i \(0.728125\pi\)
\(192\) −2.11742 + 5.86545i −0.0110282 + 0.0305492i
\(193\) 42.5353 + 73.6732i 0.220390 + 0.381727i 0.954926 0.296843i \(-0.0959337\pi\)
−0.734536 + 0.678569i \(0.762600\pi\)
\(194\) −46.8424 + 320.770i −0.241456 + 1.65345i
\(195\) −6.46916 −0.0331752
\(196\) 0 0
\(197\) 140.460i 0.712996i −0.934296 0.356498i \(-0.883971\pi\)
0.934296 0.356498i \(-0.116029\pi\)
\(198\) −7.60934 + 52.1076i −0.0384310 + 0.263170i
\(199\) 123.913 71.5411i 0.622677 0.359503i −0.155233 0.987878i \(-0.549613\pi\)
0.777911 + 0.628375i \(0.216280\pi\)
\(200\) −103.517 + 9.19355i −0.517583 + 0.0459677i
\(201\) 0.587494 1.01757i 0.00292285 0.00506253i
\(202\) −78.9694 198.524i −0.390937 0.982794i
\(203\) 0 0
\(204\) −4.07599 + 3.85225i −0.0199804 + 0.0188836i
\(205\) −137.684 79.4921i −0.671631 0.387766i
\(206\) −156.989 + 198.724i −0.762084 + 0.964680i
\(207\) 130.492 75.3396i 0.630396 0.363959i
\(208\) −167.996 + 256.403i −0.807674 + 1.23271i
\(209\) −23.7146 −0.113467
\(210\) 0 0
\(211\) −111.955 −0.530591 −0.265295 0.964167i \(-0.585469\pi\)
−0.265295 + 0.964167i \(0.585469\pi\)
\(212\) 37.7239 8.97562i 0.177943 0.0423378i
\(213\) 10.9011 6.29375i 0.0511788 0.0295481i
\(214\) −136.566 107.885i −0.638157 0.504135i
\(215\) −183.173 105.755i −0.851965 0.491882i
\(216\) −5.90987 + 12.7173i −0.0273605 + 0.0588766i
\(217\) 0 0
\(218\) 140.395 + 352.944i 0.644013 + 1.61901i
\(219\) 0.890831 1.54296i 0.00406772 0.00704550i
\(220\) −11.6092 + 38.9014i −0.0527692 + 0.176825i
\(221\) −238.752 + 137.844i −1.08033 + 0.623727i
\(222\) 7.62996 + 1.11421i 0.0343692 + 0.00501897i
\(223\) 311.438i 1.39658i −0.715814 0.698291i \(-0.753944\pi\)
0.715814 0.698291i \(-0.246056\pi\)
\(224\) 0 0
\(225\) −116.791 −0.519072
\(226\) 11.6133 79.5261i 0.0513862 0.351885i
\(227\) −37.1791 64.3960i −0.163784 0.283683i 0.772439 0.635090i \(-0.219037\pi\)
−0.936223 + 0.351407i \(0.885703\pi\)
\(228\) −3.02415 0.902488i −0.0132638 0.00395828i
\(229\) −67.7847 39.1355i −0.296003 0.170897i 0.344643 0.938734i \(-0.388000\pi\)
−0.640646 + 0.767836i \(0.721333\pi\)
\(230\) 107.935 42.9347i 0.469284 0.186673i
\(231\) 0 0
\(232\) 197.078 + 91.5842i 0.849476 + 0.394760i
\(233\) −46.5287 + 80.5900i −0.199694 + 0.345880i −0.948429 0.316989i \(-0.897328\pi\)
0.748735 + 0.662869i \(0.230661\pi\)
\(234\) −213.547 + 270.318i −0.912594 + 1.15520i
\(235\) 80.1898 + 138.893i 0.341233 + 0.591033i
\(236\) −106.062 445.772i −0.449416 1.88886i
\(237\) 4.15244i 0.0175208i
\(238\) 0 0
\(239\) 291.605i 1.22011i 0.792361 + 0.610053i \(0.208852\pi\)
−0.792361 + 0.610053i \(0.791148\pi\)
\(240\) −2.96088 + 4.51901i −0.0123370 + 0.0188292i
\(241\) −111.874 193.771i −0.464207 0.804029i 0.534959 0.844878i \(-0.320327\pi\)
−0.999165 + 0.0408488i \(0.986994\pi\)
\(242\) 176.434 + 139.380i 0.729065 + 0.575951i
\(243\) −11.8219 + 20.4761i −0.0486498 + 0.0842639i
\(244\) 20.5523 + 21.7459i 0.0842306 + 0.0891227i
\(245\) 0 0
\(246\) 8.30703 3.30438i 0.0337684 0.0134325i
\(247\) −134.351 77.5677i −0.543932 0.314039i
\(248\) 31.7708 + 357.730i 0.128108 + 1.44246i
\(249\) 5.34294 + 9.25424i 0.0214576 + 0.0371656i
\(250\) −260.547 38.0479i −1.04219 0.152192i
\(251\) −310.605 −1.23747 −0.618734 0.785600i \(-0.712354\pi\)
−0.618734 + 0.785600i \(0.712354\pi\)
\(252\) 0 0
\(253\) 49.0838i 0.194007i
\(254\) 304.088 + 44.4063i 1.19720 + 0.174828i
\(255\) −4.20793 + 2.42945i −0.0165017 + 0.00952724i
\(256\) 102.219 + 234.707i 0.399293 + 0.916823i
\(257\) −87.7358 + 151.963i −0.341385 + 0.591295i −0.984690 0.174314i \(-0.944229\pi\)
0.643306 + 0.765610i \(0.277562\pi\)
\(258\) 11.0515 4.39609i 0.0428353 0.0170391i
\(259\) 0 0
\(260\) −193.012 + 182.417i −0.742354 + 0.701604i
\(261\) 211.506 + 122.113i 0.810368 + 0.467866i
\(262\) −97.0892 76.6991i −0.370569 0.292745i
\(263\) −270.310 + 156.064i −1.02779 + 0.593398i −0.916352 0.400373i \(-0.868880\pi\)
−0.111443 + 0.993771i \(0.535547\pi\)
\(264\) −1.31185 1.86830i −0.00496915 0.00707688i
\(265\) 33.5951 0.126774
\(266\) 0 0
\(267\) −7.88419 −0.0295288
\(268\) −11.1651 46.9260i −0.0416607 0.175097i
\(269\) −123.683 + 71.4084i −0.459788 + 0.265459i −0.711955 0.702225i \(-0.752190\pi\)
0.252167 + 0.967684i \(0.418857\pi\)
\(270\) −7.53137 + 9.53354i −0.0278939 + 0.0353094i
\(271\) −230.464 133.059i −0.850421 0.490991i 0.0103718 0.999946i \(-0.496699\pi\)
−0.860793 + 0.508955i \(0.830032\pi\)
\(272\) −12.9845 + 229.870i −0.0477371 + 0.845108i
\(273\) 0 0
\(274\) 196.882 78.3158i 0.718546 0.285824i
\(275\) 19.0224 32.9477i 0.0691723 0.119810i
\(276\) −1.86794 + 6.25929i −0.00676789 + 0.0226786i
\(277\) −317.606 + 183.370i −1.14659 + 0.661986i −0.948055 0.318107i \(-0.896953\pi\)
−0.198539 + 0.980093i \(0.563620\pi\)
\(278\) 53.5754 366.876i 0.192717 1.31970i
\(279\) 403.604i 1.44661i
\(280\) 0 0
\(281\) 147.977 0.526607 0.263303 0.964713i \(-0.415188\pi\)
0.263303 + 0.964713i \(0.415188\pi\)
\(282\) −8.92394 1.30317i −0.0316452 0.00462118i
\(283\) −163.869 283.830i −0.579043 1.00293i −0.995589 0.0938180i \(-0.970093\pi\)
0.416546 0.909115i \(-0.363241\pi\)
\(284\) 147.771 495.167i 0.520320 1.74355i
\(285\) −2.36790 1.36710i −0.00830840 0.00479686i
\(286\) −41.4772 104.271i −0.145025 0.364585i
\(287\) 0 0
\(288\) 91.0909 + 272.895i 0.316288 + 0.947551i
\(289\) 40.9676 70.9580i 0.141756 0.245529i
\(290\) 147.740 + 116.712i 0.509447 + 0.402456i
\(291\) −7.89655 13.6772i −0.0271359 0.0470008i
\(292\) −16.9299 71.1551i −0.0579791 0.243682i
\(293\) 259.881i 0.886966i −0.896283 0.443483i \(-0.853743\pi\)
0.896283 0.443483i \(-0.146257\pi\)
\(294\) 0 0
\(295\) 396.983i 1.34571i
\(296\) 259.064 181.906i 0.875215 0.614547i
\(297\) −2.56687 4.44595i −0.00864267 0.0149695i
\(298\) −58.7776 + 74.4034i −0.197240 + 0.249676i
\(299\) −160.547 + 278.076i −0.536947 + 0.930019i
\(300\) 3.67965 3.47767i 0.0122655 0.0115922i
\(301\) 0 0
\(302\) −84.6974 212.924i −0.280455 0.705047i
\(303\) 9.01434 + 5.20443i 0.0297503 + 0.0171763i
\(304\) −115.676 + 58.3486i −0.380514 + 0.191936i
\(305\) 12.9614 + 22.4498i 0.0424964 + 0.0736060i
\(306\) −37.3879 + 256.027i −0.122183 + 0.836689i
\(307\) 290.462 0.946131 0.473065 0.881027i \(-0.343147\pi\)
0.473065 + 0.881027i \(0.343147\pi\)
\(308\) 0 0
\(309\) 12.3380i 0.0399289i
\(310\) −44.9602 + 307.880i −0.145033 + 0.993162i
\(311\) 64.8723 37.4540i 0.208593 0.120431i −0.392065 0.919938i \(-0.628239\pi\)
0.600657 + 0.799507i \(0.294906\pi\)
\(312\) −1.32112 14.8754i −0.00423436 0.0476776i
\(313\) −142.254 + 246.391i −0.454485 + 0.787190i −0.998658 0.0517821i \(-0.983510\pi\)
0.544174 + 0.838972i \(0.316843\pi\)
\(314\) 217.403 + 546.538i 0.692365 + 1.74057i
\(315\) 0 0
\(316\) 117.090 + 123.891i 0.370539 + 0.392060i
\(317\) 10.6202 + 6.13157i 0.0335022 + 0.0193425i 0.516658 0.856192i \(-0.327176\pi\)
−0.483155 + 0.875535i \(0.660509\pi\)
\(318\) −1.17107 + 1.48239i −0.00368260 + 0.00466160i
\(319\) −68.8982 + 39.7784i −0.215982 + 0.124697i
\(320\) 39.0871 + 218.319i 0.122147 + 0.682246i
\(321\) 8.47885 0.0264139
\(322\) 0 0
\(323\) −116.520 −0.360743
\(324\) 74.7583 + 314.204i 0.230736 + 0.969765i
\(325\) 215.536 124.440i 0.663188 0.382892i
\(326\) −268.395 212.029i −0.823299 0.650395i
\(327\) −16.0260 9.25264i −0.0490093 0.0282955i
\(328\) 154.669 332.830i 0.471553 1.01473i
\(329\) 0 0
\(330\) −0.731022 1.83775i −0.00221522 0.00556893i
\(331\) −97.2329 + 168.412i −0.293755 + 0.508798i −0.974694 0.223541i \(-0.928238\pi\)
0.680940 + 0.732340i \(0.261572\pi\)
\(332\) 420.361 + 125.447i 1.26615 + 0.377852i
\(333\) 308.082 177.871i 0.925172 0.534148i
\(334\) 238.782 + 34.8696i 0.714916 + 0.104400i
\(335\) 41.7901i 0.124747i
\(336\) 0 0
\(337\) 0.596077 0.00176877 0.000884387 1.00000i \(-0.499718\pi\)
0.000884387 1.00000i \(0.499718\pi\)
\(338\) 57.2364 391.946i 0.169338 1.15960i
\(339\) 1.95773 + 3.39089i 0.00577502 + 0.0100026i
\(340\) −57.0410 + 191.139i −0.167768 + 0.562174i
\(341\) −113.860 65.7371i −0.333900 0.192777i
\(342\) −135.290 + 53.8157i −0.395583 + 0.157356i
\(343\) 0 0
\(344\) 205.769 442.791i 0.598166 1.28718i
\(345\) −2.82959 + 4.90099i −0.00820171 + 0.0142058i
\(346\) 134.317 170.024i 0.388199 0.491399i
\(347\) 102.433 + 177.420i 0.295197 + 0.511296i 0.975031 0.222070i \(-0.0712814\pi\)
−0.679834 + 0.733366i \(0.737948\pi\)
\(348\) −10.2999 + 2.45065i −0.0295974 + 0.00704208i
\(349\) 128.396i 0.367898i 0.982936 + 0.183949i \(0.0588882\pi\)
−0.982936 + 0.183949i \(0.941112\pi\)
\(350\) 0 0
\(351\) 33.5837i 0.0956801i
\(352\) −91.8223 18.7503i −0.260859 0.0532679i
\(353\) 95.4207 + 165.274i 0.270314 + 0.468197i 0.968942 0.247288i \(-0.0795393\pi\)
−0.698628 + 0.715485i \(0.746206\pi\)
\(354\) 17.5169 + 13.8381i 0.0494829 + 0.0390908i
\(355\) 223.846 387.713i 0.630553 1.09215i
\(356\) −235.231 + 222.318i −0.660760 + 0.624489i
\(357\) 0 0
\(358\) −300.011 + 119.339i −0.838020 + 0.333349i
\(359\) 186.805 + 107.852i 0.520349 + 0.300424i 0.737077 0.675808i \(-0.236205\pi\)
−0.216728 + 0.976232i \(0.569539\pi\)
\(360\) 22.0497 + 248.274i 0.0612493 + 0.689649i
\(361\) 147.716 + 255.851i 0.409185 + 0.708729i
\(362\) −14.1439 2.06545i −0.0390715 0.00570567i
\(363\) −10.9541 −0.0301766
\(364\) 0 0
\(365\) 63.3674i 0.173609i
\(366\) −1.44241 0.210637i −0.00394102 0.000575512i
\(367\) 393.859 227.395i 1.07319 0.619604i 0.144135 0.989558i \(-0.453960\pi\)
0.929050 + 0.369954i \(0.120627\pi\)
\(368\) 120.768 + 239.423i 0.328174 + 0.650605i
\(369\) 206.227 357.196i 0.558881 0.968010i
\(370\) 254.828 101.366i 0.688724 0.273962i
\(371\) 0 0
\(372\) −12.0180 12.7160i −0.0323065 0.0341829i
\(373\) −312.417 180.374i −0.837579 0.483576i 0.0188617 0.999822i \(-0.493996\pi\)
−0.856441 + 0.516246i \(0.827329\pi\)
\(374\) −66.1376 52.2478i −0.176839 0.139700i
\(375\) 11.1094 6.41401i 0.0296250 0.0171040i
\(376\) −302.999 + 212.756i −0.805848 + 0.565840i
\(377\) −520.441 −1.38048
\(378\) 0 0
\(379\) −268.427 −0.708250 −0.354125 0.935198i \(-0.615221\pi\)
−0.354125 + 0.935198i \(0.615221\pi\)
\(380\) −109.197 + 25.9813i −0.287362 + 0.0683718i
\(381\) −12.9659 + 7.48589i −0.0340313 + 0.0196480i
\(382\) 90.8741 115.032i 0.237890 0.301132i
\(383\) 503.621 + 290.766i 1.31494 + 0.759180i 0.982910 0.184089i \(-0.0589335\pi\)
0.332029 + 0.943269i \(0.392267\pi\)
\(384\) −10.9959 5.88549i −0.0286350 0.0153268i
\(385\) 0 0
\(386\) −158.093 + 62.8863i −0.409566 + 0.162918i
\(387\) 274.360 475.206i 0.708942 1.22792i
\(388\) −621.269 185.403i −1.60121 0.477843i
\(389\) 443.646 256.139i 1.14048 0.658455i 0.193929 0.981016i \(-0.437877\pi\)
0.946549 + 0.322560i \(0.104543\pi\)
\(390\) 1.86957 12.8025i 0.00479377 0.0328270i
\(391\) 241.169i 0.616801i
\(392\) 0 0
\(393\) 6.02790 0.0153382
\(394\) 277.972 + 40.5926i 0.705513 + 0.103027i
\(395\) 73.8437 + 127.901i 0.186946 + 0.323800i
\(396\) −100.922 30.1179i −0.254855 0.0760553i
\(397\) −70.4295 40.6625i −0.177404 0.102424i 0.408668 0.912683i \(-0.365993\pi\)
−0.586073 + 0.810259i \(0.699327\pi\)
\(398\) 105.770 + 265.900i 0.265754 + 0.668090i
\(399\) 0 0
\(400\) 11.7219 207.517i 0.0293047 0.518793i
\(401\) −263.720 + 456.777i −0.657657 + 1.13909i 0.323564 + 0.946206i \(0.395119\pi\)
−0.981221 + 0.192888i \(0.938215\pi\)
\(402\) 1.84399 + 1.45673i 0.00458705 + 0.00362371i
\(403\) −430.036 744.845i −1.06709 1.84825i
\(404\) 415.704 98.9081i 1.02897 0.244822i
\(405\) 279.815i 0.690902i
\(406\) 0 0
\(407\) 115.883i 0.284726i
\(408\) −6.44570 9.17972i −0.0157983 0.0224993i
\(409\) 29.3363 + 50.8120i 0.0717270 + 0.124235i 0.899658 0.436595i \(-0.143816\pi\)
−0.827931 + 0.560830i \(0.810482\pi\)
\(410\) 197.106 249.506i 0.480746 0.608550i
\(411\) −5.16136 + 8.93974i −0.0125581 + 0.0217512i
\(412\) −347.908 368.114i −0.844436 0.893481i
\(413\) 0 0
\(414\) 111.386 + 280.018i 0.269048 + 0.676372i
\(415\) 329.140 + 190.029i 0.793109 + 0.457902i
\(416\) −458.873 406.566i −1.10306 0.977322i
\(417\) 9.03158 + 15.6432i 0.0216585 + 0.0375136i
\(418\) 6.85347 46.9315i 0.0163959 0.112276i
\(419\) 760.704 1.81552 0.907761 0.419487i \(-0.137790\pi\)
0.907761 + 0.419487i \(0.137790\pi\)
\(420\) 0 0
\(421\) 46.2918i 0.109957i 0.998488 + 0.0549784i \(0.0175090\pi\)
−0.998488 + 0.0549784i \(0.982491\pi\)
\(422\) 32.3546 221.559i 0.0766696 0.525022i
\(423\) −360.331 + 208.037i −0.851846 + 0.491814i
\(424\) 6.86074 + 77.2499i 0.0161810 + 0.182193i
\(425\) 93.4650 161.886i 0.219918 0.380909i
\(426\) 9.30501 + 23.3922i 0.0218427 + 0.0549114i
\(427\) 0 0
\(428\) 252.972 239.086i 0.591057 0.558613i
\(429\) 4.73462 + 2.73353i 0.0110364 + 0.00637187i
\(430\) 262.226 331.937i 0.609828 0.771947i
\(431\) 291.137 168.088i 0.675492 0.389996i −0.122662 0.992448i \(-0.539143\pi\)
0.798154 + 0.602453i \(0.205810\pi\)
\(432\) −23.4598 15.3710i −0.0543051 0.0355810i
\(433\) −372.694 −0.860725 −0.430363 0.902656i \(-0.641614\pi\)
−0.430363 + 0.902656i \(0.641614\pi\)
\(434\) 0 0
\(435\) −9.17260 −0.0210864
\(436\) −739.054 + 175.843i −1.69508 + 0.403309i
\(437\) −117.530 + 67.8557i −0.268946 + 0.155276i
\(438\) 2.79610 + 2.20888i 0.00638378 + 0.00504310i
\(439\) 344.226 + 198.739i 0.784115 + 0.452709i 0.837887 0.545844i \(-0.183791\pi\)
−0.0537719 + 0.998553i \(0.517124\pi\)
\(440\) −73.6313 34.2172i −0.167344 0.0777663i
\(441\) 0 0
\(442\) −203.795 512.329i −0.461075 1.15912i
\(443\) −136.765 + 236.884i −0.308725 + 0.534727i −0.978084 0.208212i \(-0.933236\pi\)
0.669359 + 0.742939i \(0.266569\pi\)
\(444\) −4.41007 + 14.7778i −0.00993260 + 0.0332832i
\(445\) −242.844 + 140.206i −0.545718 + 0.315070i
\(446\) 616.339 + 90.0047i 1.38193 + 0.201804i
\(447\) 4.61943i 0.0103343i
\(448\) 0 0
\(449\) 428.702 0.954792 0.477396 0.878688i \(-0.341581\pi\)
0.477396 + 0.878688i \(0.341581\pi\)
\(450\) 33.7523 231.131i 0.0750052 0.513624i
\(451\) 67.1785 + 116.357i 0.148955 + 0.257997i
\(452\) 154.027 + 45.9656i 0.340767 + 0.101694i
\(453\) 9.66819 + 5.58193i 0.0213426 + 0.0123221i
\(454\) 138.185 54.9674i 0.304372 0.121074i
\(455\) 0 0
\(456\) 2.66000 5.72401i 0.00583334 0.0125527i
\(457\) −5.02501 + 8.70357i −0.0109956 + 0.0190450i −0.871471 0.490447i \(-0.836833\pi\)
0.860475 + 0.509492i \(0.170167\pi\)
\(458\) 97.0392 122.837i 0.211876 0.268202i
\(459\) −12.6121 21.8449i −0.0274774 0.0475923i
\(460\) 53.7752 + 226.013i 0.116903 + 0.491333i
\(461\) 825.802i 1.79133i −0.444732 0.895664i \(-0.646701\pi\)
0.444732 0.895664i \(-0.353299\pi\)
\(462\) 0 0
\(463\) 114.707i 0.247748i −0.992298 0.123874i \(-0.960468\pi\)
0.992298 0.123874i \(-0.0395318\pi\)
\(464\) −238.201 + 363.553i −0.513365 + 0.783519i
\(465\) −7.57924 13.1276i −0.0162995 0.0282315i
\(466\) −146.042 115.371i −0.313394 0.247577i
\(467\) 100.864 174.701i 0.215982 0.374092i −0.737594 0.675245i \(-0.764038\pi\)
0.953576 + 0.301153i \(0.0973714\pi\)
\(468\) −473.247 500.733i −1.01121 1.06994i
\(469\) 0 0
\(470\) −298.045 + 118.557i −0.634138 + 0.252248i
\(471\) −24.8165 14.3278i −0.0526889 0.0304200i
\(472\) 912.838 81.0713i 1.93398 0.171761i
\(473\) 89.3730 + 154.799i 0.188949 + 0.327270i
\(474\) −8.21772 1.20004i −0.0173370 0.00253174i
\(475\) 105.190 0.221452
\(476\) 0 0
\(477\) 87.1561i 0.182717i
\(478\) −577.090 84.2732i −1.20730 0.176304i
\(479\) −517.483 + 298.769i −1.08034 + 0.623735i −0.930988 0.365050i \(-0.881052\pi\)
−0.149352 + 0.988784i \(0.547719\pi\)
\(480\) −8.08749 7.16559i −0.0168489 0.0149283i
\(481\) −379.040 + 656.517i −0.788026 + 1.36490i
\(482\) 415.806 165.400i 0.862668 0.343154i
\(483\) 0 0
\(484\) −326.824 + 308.884i −0.675255 + 0.638189i
\(485\) −486.450 280.852i −1.00299 0.579077i
\(486\) −37.1060 29.3132i −0.0763497 0.0603152i
\(487\) 298.887 172.562i 0.613730 0.354337i −0.160694 0.987004i \(-0.551373\pi\)
0.774424 + 0.632667i \(0.218040\pi\)
\(488\) −48.9750 + 34.3886i −0.100359 + 0.0704685i
\(489\) 16.6637 0.0340770
\(490\) 0 0
\(491\) 373.498 0.760689 0.380344 0.924845i \(-0.375805\pi\)
0.380344 + 0.924845i \(0.375805\pi\)
\(492\) 4.13870 + 17.3947i 0.00841199 + 0.0353550i
\(493\) −338.526 + 195.448i −0.686665 + 0.396446i
\(494\) 192.334 243.466i 0.389341 0.492845i
\(495\) −79.0217 45.6232i −0.159640 0.0921680i
\(496\) −717.133 40.5082i −1.44583 0.0816698i
\(497\) 0 0
\(498\) −19.8583 + 7.89927i −0.0398761 + 0.0158620i
\(499\) 425.158 736.396i 0.852021 1.47574i −0.0273604 0.999626i \(-0.508710\pi\)
0.879381 0.476118i \(-0.157956\pi\)
\(500\) 150.595 504.629i 0.301189 1.00926i
\(501\) −10.1814 + 5.87822i −0.0203221 + 0.0117330i
\(502\) 89.7639 614.689i 0.178812 1.22448i
\(503\) 459.256i 0.913033i −0.889715 0.456517i \(-0.849097\pi\)
0.889715 0.456517i \(-0.150903\pi\)
\(504\) 0 0
\(505\) 370.206 0.733082
\(506\) −97.1373 14.1851i −0.191971 0.0280338i
\(507\) 9.64873 + 16.7121i 0.0190310 + 0.0329627i
\(508\) −175.761 + 588.960i −0.345987 + 1.15937i
\(509\) 583.623 + 336.955i 1.14661 + 0.661994i 0.948058 0.318097i \(-0.103044\pi\)
0.198549 + 0.980091i \(0.436377\pi\)
\(510\) −3.59182 9.02963i −0.00704279 0.0177052i
\(511\) 0 0
\(512\) −494.028 + 134.463i −0.964898 + 0.262623i
\(513\) 7.09713 12.2926i 0.0138346 0.0239622i
\(514\) −275.381 217.547i −0.535760 0.423243i
\(515\) −219.410 380.029i −0.426039 0.737921i
\(516\) 5.50605 + 23.1415i 0.0106706 + 0.0448479i
\(517\) 135.536i 0.262159i
\(518\) 0 0
\(519\) 10.5562i 0.0203394i
\(520\) −305.225 434.691i −0.586972 0.835944i
\(521\) 243.236 + 421.298i 0.466864 + 0.808633i 0.999284 0.0378482i \(-0.0120503\pi\)
−0.532419 + 0.846481i \(0.678717\pi\)
\(522\) −302.788 + 383.282i −0.580053 + 0.734257i
\(523\) 340.043 588.973i 0.650179 1.12614i −0.332900 0.942962i \(-0.608027\pi\)
0.983079 0.183181i \(-0.0586393\pi\)
\(524\) 179.847 169.975i 0.343219 0.324379i
\(525\) 0 0
\(526\) −230.732 580.048i −0.438655 1.10275i
\(527\) −559.442 322.994i −1.06156 0.612892i
\(528\) 4.07650 2.05624i 0.00772064 0.00389440i
\(529\) −124.054 214.869i −0.234507 0.406179i
\(530\) −9.70890 + 66.4851i −0.0183187 + 0.125444i
\(531\) 1029.90 1.93954
\(532\) 0 0
\(533\) 878.931i 1.64903i
\(534\) 2.27851 15.6029i 0.00426687 0.0292189i
\(535\) 261.161 150.781i 0.488151 0.281834i
\(536\) 96.0938 8.53431i 0.179279 0.0159222i
\(537\) 7.86496 13.6225i 0.0146461 0.0253678i
\(538\) −105.574 265.407i −0.196234 0.493321i
\(539\) 0 0
\(540\) −16.6904 17.6598i −0.0309082 0.0327034i
\(541\) 688.489 + 397.499i 1.27262 + 0.734749i 0.975481 0.220084i \(-0.0706331\pi\)
0.297142 + 0.954833i \(0.403966\pi\)
\(542\) 329.928 417.637i 0.608723 0.770548i
\(543\) 0.603078 0.348187i 0.00111064 0.000641229i
\(544\) −451.162 92.1281i −0.829341 0.169353i
\(545\) −658.167 −1.20765
\(546\) 0 0
\(547\) −736.752 −1.34690 −0.673448 0.739235i \(-0.735187\pi\)
−0.673448 + 0.739235i \(0.735187\pi\)
\(548\) 98.0896 + 412.264i 0.178996 + 0.752306i
\(549\) −58.2418 + 33.6259i −0.106087 + 0.0612494i
\(550\) 59.7065 + 47.1673i 0.108557 + 0.0857587i
\(551\) −190.496 109.983i −0.345728 0.199606i
\(552\) −11.8474 5.50559i −0.0214626 0.00997389i
\(553\) 0 0
\(554\) −271.104 681.540i −0.489357 1.23022i
\(555\) −6.68046 + 11.5709i −0.0120369 + 0.0208485i
\(556\) 710.569 + 212.053i 1.27800 + 0.381389i
\(557\) −360.057 + 207.879i −0.646421 + 0.373212i −0.787084 0.616846i \(-0.788410\pi\)
0.140662 + 0.990058i \(0.455077\pi\)
\(558\) −798.737 116.641i −1.43143 0.209033i
\(559\) 1169.31i 2.09179i
\(560\) 0 0
\(561\) 4.10624 0.00731950
\(562\) −42.7648 + 292.847i −0.0760940 + 0.521080i
\(563\) 48.2498 + 83.5711i 0.0857012 + 0.148439i 0.905690 0.423941i \(-0.139354\pi\)
−0.819989 + 0.572380i \(0.806020\pi\)
\(564\) 5.15799 17.2840i 0.00914537 0.0306453i
\(565\) 120.602 + 69.6296i 0.213455 + 0.123238i
\(566\) 609.060 242.273i 1.07608 0.428044i
\(567\) 0 0
\(568\) 937.235 + 435.542i 1.65006 + 0.766800i
\(569\) −173.977 + 301.336i −0.305759 + 0.529589i −0.977430 0.211260i \(-0.932243\pi\)
0.671671 + 0.740849i \(0.265577\pi\)
\(570\) 3.38983 4.29100i 0.00594707 0.00752807i
\(571\) 6.86255 + 11.8863i 0.0120185 + 0.0208166i 0.871972 0.489556i \(-0.162841\pi\)
−0.859954 + 0.510372i \(0.829508\pi\)
\(572\) 218.341 51.9497i 0.381715 0.0908212i
\(573\) 7.14193i 0.0124641i
\(574\) 0 0
\(575\) 217.718i 0.378641i
\(576\) −566.386 + 101.404i −0.983310 + 0.176049i
\(577\) 413.660 + 716.480i 0.716915 + 1.24173i 0.962216 + 0.272286i \(0.0877797\pi\)
−0.245302 + 0.969447i \(0.578887\pi\)
\(578\) 128.587 + 101.582i 0.222469 + 0.175747i
\(579\) 4.14449 7.17846i 0.00715801 0.0123980i
\(580\) −273.671 + 258.649i −0.471847 + 0.445946i
\(581\) 0 0
\(582\) 29.3495 11.6747i 0.0504286 0.0200596i
\(583\) −24.5874 14.1956i −0.0421740 0.0243492i
\(584\) 145.709 12.9408i 0.249502 0.0221589i
\(585\) −298.456 516.941i −0.510181 0.883659i
\(586\) 514.307 + 75.1049i 0.877657 + 0.128165i
\(587\) −675.987 −1.15160 −0.575798 0.817592i \(-0.695308\pi\)
−0.575798 + 0.817592i \(0.695308\pi\)
\(588\) 0 0
\(589\) 363.512i 0.617169i
\(590\) 785.634 + 114.727i 1.33158 + 0.194453i
\(591\) −11.8524 + 6.84298i −0.0200548 + 0.0115786i
\(592\) 285.125 + 565.260i 0.481630 + 0.954831i
\(593\) 207.058 358.635i 0.349171 0.604781i −0.636932 0.770920i \(-0.719797\pi\)
0.986102 + 0.166139i \(0.0531301\pi\)
\(594\) 9.54041 3.79500i 0.0160613 0.00638889i
\(595\) 0 0
\(596\) −130.258 137.824i −0.218554 0.231248i
\(597\) −12.0736 6.97072i −0.0202238 0.0116762i
\(598\) −503.917 398.087i −0.842671 0.665698i
\(599\) 626.399 361.652i 1.04574 0.603759i 0.124287 0.992246i \(-0.460336\pi\)
0.921454 + 0.388487i \(0.127002\pi\)
\(600\) 5.81893 + 8.28710i 0.00969821 + 0.0138118i
\(601\) 68.7503 0.114393 0.0571966 0.998363i \(-0.481784\pi\)
0.0571966 + 0.998363i \(0.481784\pi\)
\(602\) 0 0
\(603\) 108.416 0.179795
\(604\) 445.857 106.082i 0.738173 0.175633i
\(605\) −337.402 + 194.799i −0.557690 + 0.321982i
\(606\) −12.9047 + 16.3354i −0.0212950 + 0.0269561i
\(607\) −122.338 70.6317i −0.201545 0.116362i 0.395831 0.918323i \(-0.370457\pi\)
−0.597376 + 0.801961i \(0.703790\pi\)
\(608\) −82.0424 245.787i −0.134938 0.404255i
\(609\) 0 0
\(610\) −48.1742 + 19.1628i −0.0789742 + 0.0314145i
\(611\) 443.323 767.858i 0.725569 1.25672i
\(612\) −495.874 147.982i −0.810252 0.241801i
\(613\) 83.7767 48.3685i 0.136667 0.0789046i −0.430108 0.902778i \(-0.641524\pi\)
0.566774 + 0.823873i \(0.308191\pi\)
\(614\) −83.9428 + 574.828i −0.136715 + 0.936201i
\(615\) 15.4909i 0.0251884i
\(616\) 0 0
\(617\) 580.418 0.940709 0.470355 0.882478i \(-0.344126\pi\)
0.470355 + 0.882478i \(0.344126\pi\)
\(618\) 24.4171 + 3.56566i 0.0395099 + 0.00576967i
\(619\) −78.9725 136.784i −0.127581 0.220976i 0.795158 0.606402i \(-0.207388\pi\)
−0.922739 + 0.385426i \(0.874055\pi\)
\(620\) −596.305 177.953i −0.961782 0.287021i
\(621\) −25.4428 14.6894i −0.0409707 0.0236544i
\(622\) 55.3740 + 139.207i 0.0890257 + 0.223806i
\(623\) 0 0
\(624\) 29.8204 + 1.68445i 0.0477891 + 0.00269943i
\(625\) 65.7420 113.869i 0.105187 0.182190i
\(626\) −446.498 352.728i −0.713256 0.563463i
\(627\) 1.15534 + 2.00110i 0.00184264 + 0.00319155i
\(628\) −1144.43 + 272.294i −1.82234 + 0.433589i
\(629\) 569.384i 0.905221i
\(630\) 0 0
\(631\) 771.793i 1.22313i 0.791195 + 0.611564i \(0.209459\pi\)
−0.791195 + 0.611564i \(0.790541\pi\)
\(632\) −279.020 + 195.919i −0.441488 + 0.309998i
\(633\) 5.45424 + 9.44701i 0.00861649 + 0.0149242i
\(634\) −15.2036 + 19.2455i −0.0239805 + 0.0303556i
\(635\) −266.246 + 461.152i −0.419286 + 0.726224i
\(636\) −2.59523 2.74596i −0.00408055 0.00431755i
\(637\) 0 0
\(638\) −58.8104 147.846i −0.0921793 0.231733i
\(639\) 1005.85 + 580.726i 1.57410 + 0.908805i
\(640\) −443.351 + 14.2602i −0.692736 + 0.0222816i
\(641\) 293.451 + 508.273i 0.457802 + 0.792937i 0.998845 0.0480584i \(-0.0153034\pi\)
−0.541042 + 0.840996i \(0.681970\pi\)
\(642\) −2.45036 + 16.7797i −0.00381677 + 0.0261366i
\(643\) 865.328 1.34577 0.672883 0.739749i \(-0.265056\pi\)
0.672883 + 0.739749i \(0.265056\pi\)
\(644\) 0 0
\(645\) 20.6087i 0.0319515i
\(646\) 33.6740 230.594i 0.0521269 0.356957i
\(647\) −115.080 + 66.4414i −0.177867 + 0.102691i −0.586290 0.810101i \(-0.699412\pi\)
0.408423 + 0.912793i \(0.366079\pi\)
\(648\) −643.418 + 57.1434i −0.992928 + 0.0881843i
\(649\) −167.745 + 290.542i −0.258466 + 0.447677i
\(650\) 183.978 + 462.511i 0.283044 + 0.711555i
\(651\) 0 0
\(652\) 497.173 469.882i 0.762535 0.720677i
\(653\) −315.501 182.155i −0.483156 0.278950i 0.238575 0.971124i \(-0.423320\pi\)
−0.721731 + 0.692174i \(0.756653\pi\)
\(654\) 22.9426 29.0417i 0.0350804 0.0444063i
\(655\) 185.668 107.196i 0.283463 0.163657i
\(656\) 613.975 + 402.279i 0.935938 + 0.613231i
\(657\) 164.395 0.250220
\(658\) 0 0
\(659\) −18.8972 −0.0286756 −0.0143378 0.999897i \(-0.504564\pi\)
−0.0143378 + 0.999897i \(0.504564\pi\)
\(660\) 3.84818 0.915596i 0.00583058 0.00138727i
\(661\) −293.674 + 169.553i −0.444288 + 0.256510i −0.705415 0.708795i \(-0.749239\pi\)
0.261127 + 0.965304i \(0.415906\pi\)
\(662\) −305.190 241.096i −0.461011 0.364193i
\(663\) 23.2632 + 13.4310i 0.0350878 + 0.0202579i
\(664\) −369.744 + 795.645i −0.556843 + 1.19826i
\(665\) 0 0
\(666\) 262.974 + 661.102i 0.394856 + 0.992646i
\(667\) −227.639 + 394.283i −0.341288 + 0.591128i
\(668\) −138.015 + 462.475i −0.206609 + 0.692328i
\(669\) −26.2799 + 15.1727i −0.0392824 + 0.0226797i
\(670\) 82.7031 + 12.0772i 0.123437 + 0.0180257i
\(671\) 21.9073i 0.0326487i
\(672\) 0 0
\(673\) 674.869 1.00278 0.501389 0.865222i \(-0.332823\pi\)
0.501389 + 0.865222i \(0.332823\pi\)
\(674\) −0.172265 + 1.17964i −0.000255585 + 0.00175021i
\(675\) 11.3857 + 19.7207i 0.0168678 + 0.0292158i
\(676\) 759.124 + 226.543i 1.12296 + 0.335122i
\(677\) −856.280 494.374i −1.26482 0.730242i −0.290813 0.956780i \(-0.593926\pi\)
−0.974002 + 0.226538i \(0.927259\pi\)
\(678\) −7.27639 + 2.89441i −0.0107321 + 0.00426905i
\(679\) 0 0
\(680\) −361.782 168.123i −0.532032 0.247240i
\(681\) −3.62260 + 6.27453i −0.00531953 + 0.00921369i
\(682\) 163.000 206.332i 0.239002 0.302540i
\(683\) 259.062 + 448.709i 0.379301 + 0.656968i 0.990961 0.134153i \(-0.0428312\pi\)
−0.611660 + 0.791121i \(0.709498\pi\)
\(684\) −67.4035 283.292i −0.0985431 0.414170i
\(685\) 367.143i 0.535975i
\(686\) 0 0
\(687\) 7.62646i 0.0111011i
\(688\) 816.821 + 535.184i 1.18724 + 0.777884i
\(689\) −92.8640 160.845i −0.134781 0.233447i
\(690\) −8.88137 7.01616i −0.0128715 0.0101683i
\(691\) 308.511 534.356i 0.446470 0.773309i −0.551683 0.834054i \(-0.686014\pi\)
0.998153 + 0.0607450i \(0.0193476\pi\)
\(692\) 297.662 + 314.951i 0.430148 + 0.455131i
\(693\) 0 0
\(694\) −380.718 + 151.443i −0.548585 + 0.218217i
\(695\) 556.371 + 321.221i 0.800534 + 0.462189i
\(696\) −1.87321 21.0918i −0.00269140 0.0303043i
\(697\) 330.076 + 571.709i 0.473567 + 0.820243i
\(698\) −254.098 37.1062i −0.364037 0.0531608i
\(699\) 9.06718 0.0129717
\(700\) 0 0
\(701\) 97.6954i 0.139366i 0.997569 + 0.0696829i \(0.0221987\pi\)
−0.997569 + 0.0696829i \(0.977801\pi\)
\(702\) 66.4625 + 9.70561i 0.0946760 + 0.0138256i
\(703\) −277.479 + 160.203i −0.394707 + 0.227884i
\(704\) 63.6434 176.298i 0.0904025 0.250424i
\(705\) 7.81342 13.5332i 0.0110829 0.0191961i
\(706\) −354.654 + 141.075i −0.502343 + 0.199823i
\(707\) 0 0
\(708\) −32.4482 + 30.6670i −0.0458308 + 0.0433150i
\(709\) 1082.31 + 624.872i 1.52653 + 0.881343i 0.999504 + 0.0314953i \(0.0100269\pi\)
0.527028 + 0.849848i \(0.323306\pi\)
\(710\) 702.597 + 555.042i 0.989573 + 0.781749i
\(711\) −331.815 + 191.573i −0.466688 + 0.269442i
\(712\) −371.989 529.773i −0.522456 0.744063i
\(713\) −752.386 −1.05524
\(714\) 0 0
\(715\) 194.444 0.271950
\(716\) −149.470 628.214i −0.208758 0.877393i
\(717\) 24.6064 14.2065i 0.0343186 0.0198138i
\(718\) −267.427 + 338.521i −0.372460 + 0.471477i
\(719\) −367.839 212.372i −0.511599 0.295372i 0.221892 0.975071i \(-0.428777\pi\)
−0.733491 + 0.679700i \(0.762110\pi\)
\(720\) −497.708 28.1137i −0.691261 0.0390468i
\(721\) 0 0
\(722\) −549.022 + 218.391i −0.760418 + 0.302480i
\(723\) −10.9006 + 18.8804i −0.0150769 + 0.0261140i
\(724\) 8.17510 27.3940i 0.0112916 0.0378370i
\(725\) 305.608 176.443i 0.421528 0.243369i
\(726\) 3.16571 21.6783i 0.00436048 0.0298599i
\(727\) 79.1445i 0.108865i 0.998517 + 0.0544323i \(0.0173349\pi\)
−0.998517 + 0.0544323i \(0.982665\pi\)
\(728\) 0 0
\(729\) −724.390 −0.993676
\(730\) 125.405 + 18.3130i 0.171787 + 0.0250863i
\(731\) 439.127 + 760.591i 0.600721 + 1.04048i
\(732\) 0.833707 2.79368i 0.00113894 0.00381650i
\(733\) −574.839 331.883i −0.784227 0.452774i 0.0536990 0.998557i \(-0.482899\pi\)
−0.837926 + 0.545783i \(0.816232\pi\)
\(734\) 336.192 + 845.167i 0.458027 + 1.15145i
\(735\) 0 0
\(736\) −508.721 + 169.809i −0.691198 + 0.230718i
\(737\) −17.6584 + 30.5852i −0.0239598 + 0.0414996i
\(738\) 647.295 + 511.354i 0.877093 + 0.692892i
\(739\) −416.056 720.630i −0.562998 0.975142i −0.997233 0.0743418i \(-0.976314\pi\)
0.434235 0.900800i \(-0.357019\pi\)
\(740\) 126.959 + 533.601i 0.171567 + 0.721083i
\(741\) 15.1159i 0.0203993i
\(742\) 0 0
\(743\) 283.217i 0.381180i −0.981670 0.190590i \(-0.938960\pi\)
0.981670 0.190590i \(-0.0610401\pi\)
\(744\) 28.6384 20.1089i 0.0384924 0.0270281i
\(745\) −82.1483 142.285i −0.110266 0.190987i
\(746\) 447.250 566.149i 0.599530 0.758912i
\(747\) −492.995 + 853.892i −0.659966 + 1.14309i
\(748\) 122.513 115.788i 0.163787 0.154796i
\(749\) 0 0
\(750\) 9.48280 + 23.8392i 0.0126437 + 0.0317856i
\(751\) −324.743 187.490i −0.432414 0.249654i 0.267960 0.963430i \(-0.413650\pi\)
−0.700375 + 0.713776i \(0.746984\pi\)
\(752\) −333.480 661.124i −0.443458 0.879154i
\(753\) 15.1321 + 26.2096i 0.0200958 + 0.0348069i
\(754\) 150.406 1029.96i 0.199477 1.36599i
\(755\) 397.059 0.525906
\(756\) 0 0
\(757\) 63.0951i 0.0833488i 0.999131 + 0.0416744i \(0.0132692\pi\)
−0.999131 + 0.0416744i \(0.986731\pi\)
\(758\) 77.5746 531.220i 0.102341 0.700817i
\(759\) 4.14181 2.39128i 0.00545694 0.00315056i
\(760\) −19.8594 223.611i −0.0261308 0.294225i
\(761\) −233.753 + 404.871i −0.307165 + 0.532025i −0.977741 0.209815i \(-0.932714\pi\)
0.670576 + 0.741841i \(0.266047\pi\)
\(762\) −11.0675 27.8231i −0.0145243 0.0365133i
\(763\) 0 0
\(764\) 201.388 + 213.085i 0.263597 + 0.278907i
\(765\) −388.267 224.166i −0.507538 0.293027i
\(766\) −720.974 + 912.641i −0.941219 + 1.19144i
\(767\) −1900.66 + 1097.35i −2.47804 + 1.43070i
\(768\) 14.8252 20.0600i 0.0193037 0.0261198i
\(769\) 900.573 1.17110 0.585548 0.810638i \(-0.300879\pi\)
0.585548 + 0.810638i \(0.300879\pi\)
\(770\) 0 0
\(771\) 17.0974 0.0221756
\(772\) −78.7643 331.041i −0.102026 0.428809i
\(773\) 1058.94 611.381i 1.36991 0.790919i 0.378996 0.925398i \(-0.376269\pi\)
0.990916 + 0.134479i \(0.0429360\pi\)
\(774\) 861.148 + 680.295i 1.11259 + 0.878935i
\(775\) 505.043 + 291.587i 0.651668 + 0.376241i
\(776\) 546.460 1175.92i 0.704201 1.51536i
\(777\) 0 0
\(778\) 378.689 + 952.003i 0.486747 + 1.22365i
\(779\) −185.742 + 321.714i −0.238436 + 0.412983i
\(780\) 24.7960 + 7.39979i 0.0317898 + 0.00948691i
\(781\) −327.655 + 189.172i −0.419533 + 0.242217i
\(782\) −477.277 69.6973i −0.610328 0.0891270i
\(783\) 47.6182i 0.0608151i
\(784\) 0 0
\(785\) −1019.18 −1.29832
\(786\) −1.74205 + 11.9293i −0.00221635 + 0.0151772i
\(787\) −431.471 747.330i −0.548248 0.949593i −0.998395 0.0566385i \(-0.981962\pi\)
0.450147 0.892954i \(-0.351372\pi\)
\(788\) −160.666 + 538.378i −0.203891 + 0.683221i
\(789\) 26.3381 + 15.2063i 0.0333816 + 0.0192729i
\(790\) −274.458 + 109.174i −0.347415 + 0.138195i
\(791\) 0 0
\(792\) 88.7700 191.022i 0.112083 0.241190i
\(793\) 71.6561 124.112i 0.0903608 0.156510i
\(794\) 100.825 127.629i 0.126984 0.160742i
\(795\) −1.63670 2.83484i −0.00205874 0.00356584i
\(796\) −556.786 + 132.476i −0.699479 + 0.166427i
\(797\) 1078.34i 1.35300i −0.736442 0.676500i \(-0.763496\pi\)
0.736442 0.676500i \(-0.236504\pi\)
\(798\) 0 0
\(799\) 665.947i 0.833476i
\(800\) 407.291 + 83.1697i 0.509114 + 0.103962i
\(801\) −363.739 630.014i −0.454106 0.786534i
\(802\) −827.752 653.912i −1.03211 0.815352i
\(803\) −26.7758 + 46.3771i −0.0333447 + 0.0577547i
\(804\) −3.41579 + 3.22829i −0.00424850 + 0.00401529i
\(805\) 0 0
\(806\) 1598.33 635.788i 1.98305 0.788819i
\(807\) 12.0512 + 6.95779i 0.0149334 + 0.00862180i
\(808\) 75.6029 + 851.266i 0.0935680 + 1.05355i
\(809\) −166.694 288.723i −0.206050 0.356888i 0.744417 0.667715i \(-0.232727\pi\)
−0.950467 + 0.310827i \(0.899394\pi\)
\(810\) −553.757 80.8658i −0.683651 0.0998344i
\(811\) −1246.04 −1.53642 −0.768211 0.640197i \(-0.778853\pi\)
−0.768211 + 0.640197i \(0.778853\pi\)
\(812\) 0 0
\(813\) 25.9295i 0.0318936i
\(814\) −229.334 33.4900i −0.281737 0.0411425i
\(815\) 513.265 296.334i 0.629773 0.363600i
\(816\) 20.0296 10.1032i 0.0245460 0.0123814i
\(817\) −247.107 + 428.002i −0.302456 + 0.523870i
\(818\) −109.036 + 43.3724i −0.133295 + 0.0530224i
\(819\) 0 0
\(820\) 436.811 + 462.181i 0.532696 + 0.563636i
\(821\) −1263.25 729.338i −1.53867 0.888353i −0.998917 0.0465306i \(-0.985184\pi\)
−0.539755 0.841822i \(-0.681483\pi\)
\(822\) −16.2002 12.7979i −0.0197083 0.0155693i
\(823\) 401.876 232.023i 0.488306 0.281924i −0.235565 0.971859i \(-0.575694\pi\)
0.723872 + 0.689935i \(0.242361\pi\)
\(824\) 829.046 582.129i 1.00612 0.706467i
\(825\) −3.70695 −0.00449328
\(826\) 0 0
\(827\) 1077.41 1.30279 0.651394 0.758739i \(-0.274184\pi\)
0.651394 + 0.758739i \(0.274184\pi\)
\(828\) −586.348 + 139.509i −0.708150 + 0.168490i
\(829\) −31.1210 + 17.9677i −0.0375404 + 0.0216740i −0.518653 0.854985i \(-0.673566\pi\)
0.481112 + 0.876659i \(0.340233\pi\)
\(830\) −471.190 + 596.454i −0.567699 + 0.718619i
\(831\) 30.9465 + 17.8670i 0.0372400 + 0.0215006i
\(832\) 937.211 790.619i 1.12646 0.950263i
\(833\) 0 0
\(834\) −33.5681 + 13.3528i −0.0402495 + 0.0160105i
\(835\) −209.067 + 362.115i −0.250380 + 0.433671i
\(836\) 90.8973 + 27.1262i 0.108729 + 0.0324476i
\(837\) 68.1503 39.3466i 0.0814221 0.0470091i
\(838\) −219.841 + 1505.44i −0.262341 + 1.79647i
\(839\) 734.676i 0.875656i −0.899059 0.437828i \(-0.855748\pi\)
0.899059 0.437828i \(-0.144252\pi\)
\(840\) 0 0
\(841\) 103.069 0.122555
\(842\) −91.6119 13.3782i −0.108803 0.0158886i
\(843\) −7.20916 12.4866i −0.00855179 0.0148121i
\(844\) 429.118 + 128.060i 0.508433 + 0.151730i
\(845\) 594.390 + 343.171i 0.703420 + 0.406119i
\(846\) −307.573 773.221i −0.363561 0.913972i
\(847\) 0 0
\(848\) −154.861 8.74753i −0.182619 0.0103155i
\(849\) −15.9669 + 27.6554i −0.0188067 + 0.0325741i
\(850\) 293.363 + 231.753i 0.345133 + 0.272651i
\(851\) 331.582 + 574.317i 0.389638 + 0.674873i
\(852\) −48.9826 + 11.6544i −0.0574913 + 0.0136789i
\(853\) 402.566i 0.471942i −0.971760 0.235971i \(-0.924173\pi\)
0.971760 0.235971i \(-0.0758270\pi\)
\(854\) 0 0
\(855\) 252.287i 0.295072i
\(856\) 400.046 + 569.730i 0.467343 + 0.665573i
\(857\) −276.001 478.048i −0.322055 0.557816i 0.658857 0.752268i \(-0.271040\pi\)
−0.980912 + 0.194453i \(0.937707\pi\)
\(858\) −6.77798 + 8.57988i −0.00789975 + 0.00999986i
\(859\) 165.058 285.889i 0.192152 0.332817i −0.753811 0.657091i \(-0.771787\pi\)
0.945963 + 0.324274i \(0.105120\pi\)
\(860\) 581.125 + 614.877i 0.675727 + 0.714973i
\(861\) 0 0
\(862\) 248.510 + 624.740i 0.288295 + 0.724757i
\(863\) −967.063 558.334i −1.12058 0.646969i −0.179033 0.983843i \(-0.557297\pi\)
−0.941550 + 0.336874i \(0.890630\pi\)
\(864\) 37.1991 41.9851i 0.0430546 0.0485938i
\(865\) 187.723 + 325.145i 0.217020 + 0.375890i
\(866\) 107.708 737.565i 0.124374 0.851692i
\(867\) −7.98348 −0.00920817
\(868\) 0 0
\(869\) 124.810i 0.143625i
\(870\) 2.65086 18.1527i 0.00304696 0.0208651i
\(871\) −200.081 + 115.517i −0.229714 + 0.132625i
\(872\) −134.410 1513.41i −0.154140 1.73557i
\(873\) 728.618 1262.00i 0.834614 1.44559i
\(874\) −100.321 252.202i −0.114784 0.288561i
\(875\) 0 0
\(876\) −5.17945 + 4.89514i −0.00591262 + 0.00558806i
\(877\) 0.647303 + 0.373720i 0.000738087 + 0.000426135i 0.500369 0.865812i \(-0.333198\pi\)
−0.499631 + 0.866238i \(0.666531\pi\)
\(878\) −492.787 + 623.792i −0.561261 + 0.710469i
\(879\) −21.9294 + 12.6610i −0.0249481 + 0.0144038i
\(880\) 88.9954 135.828i 0.101131 0.154351i
\(881\) −247.826 −0.281301 −0.140650 0.990059i \(-0.544919\pi\)
−0.140650 + 0.990059i \(0.544919\pi\)
\(882\) 0 0
\(883\) −1613.74 −1.82757 −0.913784 0.406200i \(-0.866854\pi\)
−0.913784 + 0.406200i \(0.866854\pi\)
\(884\) 1072.80 255.251i 1.21358 0.288745i
\(885\) −33.4985 + 19.3403i −0.0378514 + 0.0218535i
\(886\) −429.271 339.118i −0.484505 0.382752i
\(887\) −961.795 555.293i −1.08432 0.626034i −0.152264 0.988340i \(-0.548656\pi\)
−0.932059 + 0.362305i \(0.881990\pi\)
\(888\) −27.9708 12.9983i −0.0314987 0.0146377i
\(889\) 0 0
\(890\) −207.288 521.111i −0.232908 0.585518i
\(891\) 118.236 204.790i 0.132700 0.229843i
\(892\) −356.240 + 1193.73i −0.399373 + 1.33826i
\(893\) 324.538 187.372i 0.363424 0.209823i
\(894\) 9.14189 + 1.33500i 0.0102258 + 0.00149329i
\(895\) 559.458i 0.625092i
\(896\) 0 0
\(897\) 31.2863 0.0348788
\(898\) −123.894 + 848.405i −0.137966 + 0.944771i
\(899\) −609.747 1056.11i −0.678250 1.17476i
\(900\) 447.656 + 133.592i 0.497396 + 0.148436i
\(901\) −120.808 69.7488i −0.134083 0.0774127i
\(902\) −249.685 + 99.3202i −0.276813 + 0.110111i
\(903\) 0 0
\(904\) −135.480 + 291.536i −0.149867 + 0.322496i
\(905\) 12.3838 21.4494i 0.0136837 0.0237009i
\(906\) −13.8408 + 17.5203i −0.0152768 + 0.0193381i
\(907\) 259.004 + 448.609i 0.285562 + 0.494607i 0.972745 0.231876i \(-0.0744865\pi\)
−0.687184 + 0.726484i \(0.741153\pi\)
\(908\) 68.8460 + 289.355i 0.0758216 + 0.318673i
\(909\) 960.430i 1.05658i
\(910\) 0 0
\(911\) 1065.61i 1.16972i 0.811135 + 0.584860i \(0.198850\pi\)
−0.811135 + 0.584860i \(0.801150\pi\)
\(912\) 10.5591 + 6.91840i 0.0115780 + 0.00758597i
\(913\) −160.593 278.155i −0.175896 0.304661i
\(914\) −15.7722 12.4598i −0.0172563 0.0136322i
\(915\) 1.26292 2.18743i 0.00138024 0.00239064i
\(916\) 215.051 + 227.541i 0.234772 + 0.248407i
\(917\) 0 0
\(918\) 46.8761 18.6464i 0.0510632 0.0203120i
\(919\) −1025.08 591.831i −1.11543 0.643994i −0.175200 0.984533i \(-0.556057\pi\)
−0.940231 + 0.340538i \(0.889391\pi\)
\(920\) −462.823 + 41.1044i −0.503069 + 0.0446787i
\(921\) −14.1508 24.5099i −0.0153646 0.0266123i
\(922\) 1634.27 + 238.654i 1.77253 + 0.258844i
\(923\) −2475.03 −2.68151
\(924\) 0 0
\(925\) 514.018i 0.555695i
\(926\) 227.007 + 33.1501i 0.245148 + 0.0357992i
\(927\) 985.914 569.217i 1.06355 0.614043i
\(928\) −650.635 576.468i −0.701115 0.621194i
\(929\) 189.509 328.240i 0.203993 0.353326i −0.745818 0.666149i \(-0.767941\pi\)
0.949811 + 0.312823i \(0.101275\pi\)
\(930\) 28.1701 11.2055i 0.0302904 0.0120490i
\(931\) 0 0
\(932\) 270.526 255.676i 0.290264 0.274331i
\(933\) −6.32093 3.64939i −0.00677485 0.00391146i
\(934\) 316.585 + 250.098i 0.338957 + 0.267771i
\(935\) 126.478 73.0221i 0.135271 0.0780985i
\(936\) 1127.72 791.849i 1.20483 0.845993i
\(937\) 1316.09 1.40458 0.702289 0.711892i \(-0.252161\pi\)
0.702289 + 0.711892i \(0.252161\pi\)
\(938\) 0 0
\(939\) 27.7214 0.0295223
\(940\) −148.491 624.096i −0.157969 0.663932i
\(941\) 430.441 248.515i 0.457430 0.264097i −0.253533 0.967327i \(-0.581593\pi\)
0.710963 + 0.703230i \(0.248259\pi\)
\(942\) 35.5268 44.9714i 0.0377142 0.0477403i
\(943\) 665.872 + 384.442i 0.706121 + 0.407679i
\(944\) −103.367 + 1829.95i −0.109499 + 1.93850i
\(945\) 0 0
\(946\) −332.176 + 132.134i −0.351138 + 0.139676i
\(947\) −404.243 + 700.170i −0.426867 + 0.739356i −0.996593 0.0824792i \(-0.973716\pi\)
0.569726 + 0.821835i \(0.307050\pi\)
\(948\) 4.74980 15.9161i 0.00501033 0.0167892i
\(949\) −303.387 + 175.161i −0.319692 + 0.184574i
\(950\) −30.3996 + 208.172i −0.0319995 + 0.219128i
\(951\) 1.19488i 0.00125644i
\(952\) 0 0
\(953\) −1345.58 −1.41194 −0.705969 0.708243i \(-0.749488\pi\)
−0.705969 + 0.708243i \(0.749488\pi\)
\(954\) −172.483 25.1879i −0.180800 0.0264024i
\(955\) 127.007 + 219.982i 0.132991 + 0.230347i
\(956\) 333.555 1117.71i 0.348907 1.16915i
\(957\) 6.71320 + 3.87587i 0.00701484 + 0.00405002i
\(958\) −441.715 1110.45i −0.461081 1.15913i
\(959\) 0 0
\(960\) 16.5180 13.9344i 0.0172063 0.0145150i
\(961\) 527.158 913.065i 0.548552 0.950119i
\(962\) −1189.71 939.857i −1.23671 0.976982i
\(963\) 391.173 + 677.532i 0.406203 + 0.703564i
\(964\) 207.161 + 870.685i 0.214898 + 0.903200i
\(965\) 294.809i 0.305502i
\(966\) 0 0
\(967\) 140.279i 0.145066i 0.997366 + 0.0725330i \(0.0231083\pi\)
−0.997366 + 0.0725330i \(0.976892\pi\)
\(968\) −516.832 736.054i −0.533918 0.760386i
\(969\) 5.67666 + 9.83226i 0.00585826 + 0.0101468i
\(970\) 696.392 881.525i 0.717930 0.908788i
\(971\) −719.336 + 1245.93i −0.740820 + 1.28314i 0.211303 + 0.977421i \(0.432229\pi\)
−0.952122 + 0.305717i \(0.901104\pi\)
\(972\) 68.7346 64.9616i 0.0707146 0.0668330i
\(973\) 0 0
\(974\) 255.125 + 641.370i 0.261935 + 0.658491i
\(975\) −21.0011 12.1250i −0.0215396 0.0124359i
\(976\) −53.9018 106.860i −0.0552272 0.109488i
\(977\) −451.095 781.319i −0.461714 0.799712i 0.537332 0.843371i \(-0.319432\pi\)
−0.999047 + 0.0436581i \(0.986099\pi\)
\(978\) −4.81576 + 32.9776i −0.00492409 + 0.0337194i
\(979\) 236.976 0.242059
\(980\) 0 0
\(981\) 1707.49i 1.74056i
\(982\) −107.940 + 739.157i −0.109918 + 0.752705i
\(983\) 435.778 251.597i 0.443315 0.255948i −0.261688 0.965153i \(-0.584279\pi\)
0.705003 + 0.709205i \(0.250946\pi\)
\(984\) −35.6203 + 3.16352i −0.0361995 + 0.00321496i
\(985\) −243.380 + 421.547i −0.247087 + 0.427967i
\(986\) −288.960 726.430i −0.293063 0.736744i
\(987\) 0 0
\(988\) 426.237 + 450.993i 0.431414 + 0.456470i
\(989\) 885.864 + 511.454i 0.895717 + 0.517142i
\(990\) 113.126 143.200i 0.114268 0.144646i
\(991\) 784.898 453.161i 0.792026 0.457277i −0.0486491 0.998816i \(-0.515492\pi\)
0.840675 + 0.541539i \(0.182158\pi\)
\(992\) 287.416 1407.51i 0.289734 1.41886i
\(993\) 18.9481 0.0190816
\(994\) 0 0
\(995\) −495.847 −0.498339
\(996\) −9.89374 41.5827i −0.00993347 0.0417497i
\(997\) −527.085 + 304.313i −0.528671 + 0.305228i −0.740475 0.672084i \(-0.765399\pi\)
0.211804 + 0.977312i \(0.432066\pi\)
\(998\) 1334.47 + 1054.21i 1.33714 + 1.05632i
\(999\) −60.0687 34.6807i −0.0601288 0.0347154i
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 392.3.k.o.275.4 16
7.2 even 3 56.3.g.b.43.7 8
7.3 odd 6 392.3.k.n.67.2 16
7.4 even 3 inner 392.3.k.o.67.2 16
7.5 odd 6 392.3.g.m.99.7 8
7.6 odd 2 392.3.k.n.275.4 16
8.3 odd 2 inner 392.3.k.o.275.2 16
21.2 odd 6 504.3.g.b.379.2 8
28.19 even 6 1568.3.g.m.687.5 8
28.23 odd 6 224.3.g.b.15.4 8
56.3 even 6 392.3.k.n.67.4 16
56.5 odd 6 1568.3.g.m.687.6 8
56.11 odd 6 inner 392.3.k.o.67.4 16
56.19 even 6 392.3.g.m.99.8 8
56.27 even 2 392.3.k.n.275.2 16
56.37 even 6 224.3.g.b.15.3 8
56.51 odd 6 56.3.g.b.43.8 yes 8
84.23 even 6 2016.3.g.b.1135.4 8
112.37 even 12 1792.3.d.j.1023.7 16
112.51 odd 12 1792.3.d.j.1023.8 16
112.93 even 12 1792.3.d.j.1023.10 16
112.107 odd 12 1792.3.d.j.1023.9 16
168.107 even 6 504.3.g.b.379.1 8
168.149 odd 6 2016.3.g.b.1135.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.3.g.b.43.7 8 7.2 even 3
56.3.g.b.43.8 yes 8 56.51 odd 6
224.3.g.b.15.3 8 56.37 even 6
224.3.g.b.15.4 8 28.23 odd 6
392.3.g.m.99.7 8 7.5 odd 6
392.3.g.m.99.8 8 56.19 even 6
392.3.k.n.67.2 16 7.3 odd 6
392.3.k.n.67.4 16 56.3 even 6
392.3.k.n.275.2 16 56.27 even 2
392.3.k.n.275.4 16 7.6 odd 2
392.3.k.o.67.2 16 7.4 even 3 inner
392.3.k.o.67.4 16 56.11 odd 6 inner
392.3.k.o.275.2 16 8.3 odd 2 inner
392.3.k.o.275.4 16 1.1 even 1 trivial
504.3.g.b.379.1 8 168.107 even 6
504.3.g.b.379.2 8 21.2 odd 6
1568.3.g.m.687.5 8 28.19 even 6
1568.3.g.m.687.6 8 56.5 odd 6
1792.3.d.j.1023.7 16 112.37 even 12
1792.3.d.j.1023.8 16 112.51 odd 12
1792.3.d.j.1023.9 16 112.107 odd 12
1792.3.d.j.1023.10 16 112.93 even 12
2016.3.g.b.1135.4 8 84.23 even 6
2016.3.g.b.1135.5 8 168.149 odd 6