Properties

Label 735.2.q.f.79.5
Level $735$
Weight $2$
Character 735.79
Analytic conductor $5.869$
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] = [735,2,Mod(79,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.q (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: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.89539436150784.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.5
Root \(-0.531325 - 1.98293i\) of defining polynomial
Character \(\chi\) \(=\) 735.79
Dual form 735.2.q.f.214.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.64823 + 0.951606i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.811108 + 1.40488i) q^{4} +(-1.76210 - 1.37659i) q^{5} -1.90321 q^{6} -0.719004i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.64823 + 0.951606i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.811108 + 1.40488i) q^{4} +(-1.76210 - 1.37659i) q^{5} -1.90321 q^{6} -0.719004i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.59438 - 3.94576i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-1.40488 - 0.811108i) q^{12} -6.42864i q^{13} +(2.21432 + 0.311108i) q^{15} +(2.30642 - 3.99484i) q^{16} +(-3.83531 + 2.21432i) q^{17} +(1.64823 - 0.951606i) q^{18} +(1.21432 - 2.10326i) q^{19} +(0.504684 - 3.59210i) q^{20} -3.80642i q^{22} +(1.19320 + 0.688892i) q^{23} +(0.359502 + 0.622675i) q^{24} +(1.21002 + 4.85138i) q^{25} +(6.11753 - 10.5959i) q^{26} +1.00000i q^{27} -0.755569 q^{29} +(3.35366 + 2.61994i) q^{30} +(2.59210 + 4.48966i) q^{31} +(6.35768 - 3.67061i) q^{32} +(1.73205 + 1.00000i) q^{33} -8.42864 q^{34} +1.62222 q^{36} +(-6.59292 - 3.80642i) q^{37} +(4.00296 - 2.31111i) q^{38} +(3.21432 + 5.56737i) q^{39} +(-0.989771 + 1.26696i) q^{40} +8.23506 q^{41} -10.1017i q^{43} +(1.62222 - 2.80976i) q^{44} +(-2.07321 + 0.837733i) q^{45} +(1.31111 + 2.27091i) q^{46} +(2.38639 + 1.37778i) q^{47} +4.61285i q^{48} +(-2.62222 + 9.14764i) q^{50} +(2.21432 - 3.83531i) q^{51} +(9.03147 - 5.21432i) q^{52} +(-7.95376 + 4.59210i) q^{53} +(-0.951606 + 1.64823i) q^{54} +(-0.622216 + 4.42864i) q^{55} +2.42864i q^{57} +(-1.24535 - 0.719004i) q^{58} +(-7.05086 - 12.2124i) q^{59} +(1.35898 + 3.36320i) q^{60} +(3.42864 - 5.93858i) q^{61} +9.86665i q^{62} +4.74620 q^{64} +(-8.84958 + 11.3279i) q^{65} +(1.90321 + 3.29646i) q^{66} +(2.38639 - 1.37778i) q^{67} +(-6.22171 - 3.59210i) q^{68} -1.37778 q^{69} +2.00000 q^{71} +(-0.622675 - 0.359502i) q^{72} +(-1.36084 + 0.785680i) q^{73} +(-7.24443 - 12.5477i) q^{74} +(-3.47359 - 3.59641i) q^{75} +3.93978 q^{76} +12.2351i q^{78} +(-2.42864 + 4.20653i) q^{79} +(-9.56341 + 3.86433i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(13.5733 + 7.83654i) q^{82} +11.6128i q^{83} +(9.80642 + 1.37778i) q^{85} +(9.61285 - 16.6499i) q^{86} +(0.654342 - 0.377784i) q^{87} +(-1.24535 + 0.719004i) q^{88} +(-2.31111 + 4.00296i) q^{89} +(-4.21432 - 0.592104i) q^{90} +2.23506i q^{92} +(-4.48966 - 2.59210i) q^{93} +(2.62222 + 4.54181i) q^{94} +(-5.03508 + 2.03455i) q^{95} +(-3.67061 + 6.35768i) q^{96} +11.9398i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4} + 2 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{4} + 2 q^{5} + 4 q^{6} + 6 q^{9} - 12 q^{10} - 12 q^{11} - 26 q^{16} - 12 q^{19} + 60 q^{20} + 18 q^{24} + 2 q^{25} + 20 q^{26} - 8 q^{29} + 10 q^{30} + 4 q^{31} - 48 q^{34} + 20 q^{36} + 12 q^{39} + 4 q^{40} - 8 q^{41} + 20 q^{44} - 2 q^{45} + 16 q^{46} - 32 q^{50} + 2 q^{54} - 8 q^{55} - 32 q^{59} + 8 q^{60} - 12 q^{61} - 52 q^{64} - 32 q^{65} - 4 q^{66} - 16 q^{69} + 24 q^{71} - 88 q^{74} + 8 q^{75} - 8 q^{76} + 24 q^{79} + 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} - 28 q^{89} - 24 q^{90} + 32 q^{94} - 4 q^{95} - 58 q^{96} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.64823 + 0.951606i 1.16547 + 0.672887i 0.952610 0.304195i \(-0.0983873\pi\)
0.212865 + 0.977082i \(0.431721\pi\)
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.811108 + 1.40488i 0.405554 + 0.702440i
\(5\) −1.76210 1.37659i −0.788037 0.615628i
\(6\) −1.90321 −0.776983
\(7\) 0 0
\(8\) 0.719004i 0.254206i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −1.59438 3.94576i −0.504188 1.24776i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) −1.40488 0.811108i −0.405554 0.234147i
\(13\) 6.42864i 1.78298i −0.453037 0.891492i \(-0.649659\pi\)
0.453037 0.891492i \(-0.350341\pi\)
\(14\) 0 0
\(15\) 2.21432 + 0.311108i 0.571735 + 0.0803277i
\(16\) 2.30642 3.99484i 0.576606 0.998711i
\(17\) −3.83531 + 2.21432i −0.930200 + 0.537051i −0.886875 0.462010i \(-0.847129\pi\)
−0.0433254 + 0.999061i \(0.513795\pi\)
\(18\) 1.64823 0.951606i 0.388492 0.224296i
\(19\) 1.21432 2.10326i 0.278584 0.482522i −0.692449 0.721467i \(-0.743468\pi\)
0.971033 + 0.238945i \(0.0768016\pi\)
\(20\) 0.504684 3.59210i 0.112851 0.803219i
\(21\) 0 0
\(22\) 3.80642i 0.811532i
\(23\) 1.19320 + 0.688892i 0.248799 + 0.143644i 0.619214 0.785222i \(-0.287451\pi\)
−0.370415 + 0.928866i \(0.620785\pi\)
\(24\) 0.359502 + 0.622675i 0.0733830 + 0.127103i
\(25\) 1.21002 + 4.85138i 0.242003 + 0.970275i
\(26\) 6.11753 10.5959i 1.19975 2.07802i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −0.755569 −0.140306 −0.0701528 0.997536i \(-0.522349\pi\)
−0.0701528 + 0.997536i \(0.522349\pi\)
\(30\) 3.35366 + 2.61994i 0.612291 + 0.478333i
\(31\) 2.59210 + 4.48966i 0.465556 + 0.806366i 0.999226 0.0393263i \(-0.0125212\pi\)
−0.533671 + 0.845692i \(0.679188\pi\)
\(32\) 6.35768 3.67061i 1.12389 0.648878i
\(33\) 1.73205 + 1.00000i 0.301511 + 0.174078i
\(34\) −8.42864 −1.44550
\(35\) 0 0
\(36\) 1.62222 0.270369
\(37\) −6.59292 3.80642i −1.08387 0.625772i −0.151932 0.988391i \(-0.548549\pi\)
−0.931938 + 0.362619i \(0.881883\pi\)
\(38\) 4.00296 2.31111i 0.649365 0.374911i
\(39\) 3.21432 + 5.56737i 0.514703 + 0.891492i
\(40\) −0.989771 + 1.26696i −0.156497 + 0.200324i
\(41\) 8.23506 1.28610 0.643050 0.765824i \(-0.277669\pi\)
0.643050 + 0.765824i \(0.277669\pi\)
\(42\) 0 0
\(43\) 10.1017i 1.54050i −0.637744 0.770248i \(-0.720132\pi\)
0.637744 0.770248i \(-0.279868\pi\)
\(44\) 1.62222 2.80976i 0.244558 0.423587i
\(45\) −2.07321 + 0.837733i −0.309056 + 0.124882i
\(46\) 1.31111 + 2.27091i 0.193312 + 0.334827i
\(47\) 2.38639 + 1.37778i 0.348091 + 0.200971i 0.663844 0.747871i \(-0.268924\pi\)
−0.315753 + 0.948841i \(0.602257\pi\)
\(48\) 4.61285i 0.665807i
\(49\) 0 0
\(50\) −2.62222 + 9.14764i −0.370837 + 1.29367i
\(51\) 2.21432 3.83531i 0.310067 0.537051i
\(52\) 9.03147 5.21432i 1.25244 0.723096i
\(53\) −7.95376 + 4.59210i −1.09253 + 0.630774i −0.934250 0.356620i \(-0.883929\pi\)
−0.158283 + 0.987394i \(0.550596\pi\)
\(54\) −0.951606 + 1.64823i −0.129497 + 0.224296i
\(55\) −0.622216 + 4.42864i −0.0838995 + 0.597158i
\(56\) 0 0
\(57\) 2.42864i 0.321681i
\(58\) −1.24535 0.719004i −0.163523 0.0944098i
\(59\) −7.05086 12.2124i −0.917943 1.58992i −0.802534 0.596606i \(-0.796515\pi\)
−0.115409 0.993318i \(-0.536818\pi\)
\(60\) 1.35898 + 3.36320i 0.175444 + 0.434187i
\(61\) 3.42864 5.93858i 0.438992 0.760357i −0.558620 0.829424i \(-0.688669\pi\)
0.997612 + 0.0690669i \(0.0220022\pi\)
\(62\) 9.86665i 1.25307i
\(63\) 0 0
\(64\) 4.74620 0.593275
\(65\) −8.84958 + 11.3279i −1.09766 + 1.40506i
\(66\) 1.90321 + 3.29646i 0.234269 + 0.405766i
\(67\) 2.38639 1.37778i 0.291544 0.168323i −0.347094 0.937830i \(-0.612831\pi\)
0.638638 + 0.769507i \(0.279498\pi\)
\(68\) −6.22171 3.59210i −0.754493 0.435607i
\(69\) −1.37778 −0.165866
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −0.622675 0.359502i −0.0733830 0.0423677i
\(73\) −1.36084 + 0.785680i −0.159274 + 0.0919569i −0.577519 0.816378i \(-0.695979\pi\)
0.418244 + 0.908335i \(0.362646\pi\)
\(74\) −7.24443 12.5477i −0.842148 1.45864i
\(75\) −3.47359 3.59641i −0.401096 0.415277i
\(76\) 3.93978 0.451923
\(77\) 0 0
\(78\) 12.2351i 1.38535i
\(79\) −2.42864 + 4.20653i −0.273243 + 0.473271i −0.969690 0.244337i \(-0.921430\pi\)
0.696447 + 0.717608i \(0.254763\pi\)
\(80\) −9.56341 + 3.86433i −1.06922 + 0.432046i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 13.5733 + 7.83654i 1.49892 + 0.865401i
\(83\) 11.6128i 1.27468i 0.770585 + 0.637338i \(0.219964\pi\)
−0.770585 + 0.637338i \(0.780036\pi\)
\(84\) 0 0
\(85\) 9.80642 + 1.37778i 1.06366 + 0.149442i
\(86\) 9.61285 16.6499i 1.03658 1.79541i
\(87\) 0.654342 0.377784i 0.0701528 0.0405027i
\(88\) −1.24535 + 0.719004i −0.132755 + 0.0766461i
\(89\) −2.31111 + 4.00296i −0.244977 + 0.424313i −0.962125 0.272608i \(-0.912114\pi\)
0.717148 + 0.696921i \(0.245447\pi\)
\(90\) −4.21432 0.592104i −0.444228 0.0624133i
\(91\) 0 0
\(92\) 2.23506i 0.233021i
\(93\) −4.48966 2.59210i −0.465556 0.268789i
\(94\) 2.62222 + 4.54181i 0.270461 + 0.468452i
\(95\) −5.03508 + 2.03455i −0.516589 + 0.208740i
\(96\) −3.67061 + 6.35768i −0.374630 + 0.648878i
\(97\) 11.9398i 1.21230i 0.795350 + 0.606150i \(0.207287\pi\)
−0.795350 + 0.606150i \(0.792713\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) −5.83415 + 5.63492i −0.583415 + 0.563492i
\(101\) 0.739747 + 1.28128i 0.0736076 + 0.127492i 0.900480 0.434898i \(-0.143215\pi\)
−0.826872 + 0.562390i \(0.809882\pi\)
\(102\) 7.29942 4.21432i 0.722750 0.417280i
\(103\) 7.67063 + 4.42864i 0.755809 + 0.436367i 0.827789 0.561039i \(-0.189598\pi\)
−0.0719797 + 0.997406i \(0.522932\pi\)
\(104\) −4.62222 −0.453246
\(105\) 0 0
\(106\) −17.4795 −1.69776
\(107\) −1.52848 0.882468i −0.147764 0.0853114i 0.424295 0.905524i \(-0.360522\pi\)
−0.572059 + 0.820212i \(0.693855\pi\)
\(108\) −1.40488 + 0.811108i −0.135185 + 0.0780489i
\(109\) 2.80642 + 4.86087i 0.268807 + 0.465587i 0.968554 0.248804i \(-0.0800374\pi\)
−0.699747 + 0.714390i \(0.746704\pi\)
\(110\) −5.23987 + 6.70731i −0.499602 + 0.639517i
\(111\) 7.61285 0.722580
\(112\) 0 0
\(113\) 11.2859i 1.06169i 0.847469 + 0.530845i \(0.178125\pi\)
−0.847469 + 0.530845i \(0.821875\pi\)
\(114\) −2.31111 + 4.00296i −0.216455 + 0.374911i
\(115\) −1.15421 2.85644i −0.107631 0.266364i
\(116\) −0.612848 1.06148i −0.0569015 0.0985563i
\(117\) −5.56737 3.21432i −0.514703 0.297164i
\(118\) 26.8385i 2.47069i
\(119\) 0 0
\(120\) 0.223688 1.59210i 0.0204198 0.145339i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 11.3024 6.52543i 1.02327 0.590784i
\(123\) −7.13177 + 4.11753i −0.643050 + 0.371265i
\(124\) −4.20495 + 7.28319i −0.377616 + 0.654050i
\(125\) 4.54617 10.2143i 0.406622 0.913597i
\(126\) 0 0
\(127\) 12.8573i 1.14090i −0.821333 0.570450i \(-0.806769\pi\)
0.821333 0.570450i \(-0.193231\pi\)
\(128\) −4.89253 2.82471i −0.432443 0.249671i
\(129\) 5.05086 + 8.74834i 0.444703 + 0.770248i
\(130\) −25.3659 + 10.2497i −2.22473 + 0.898959i
\(131\) −1.05086 + 1.82013i −0.0918136 + 0.159026i −0.908274 0.418375i \(-0.862600\pi\)
0.816461 + 0.577401i \(0.195933\pi\)
\(132\) 3.24443i 0.282391i
\(133\) 0 0
\(134\) 5.24443 0.453050
\(135\) 1.37659 1.76210i 0.118478 0.151658i
\(136\) 1.59210 + 2.75761i 0.136522 + 0.236463i
\(137\) 13.8043 7.96989i 1.17938 0.680914i 0.223506 0.974702i \(-0.428250\pi\)
0.955870 + 0.293789i \(0.0949163\pi\)
\(138\) −2.27091 1.31111i −0.193312 0.111609i
\(139\) 11.6731 0.990097 0.495048 0.868865i \(-0.335150\pi\)
0.495048 + 0.868865i \(0.335150\pi\)
\(140\) 0 0
\(141\) −2.75557 −0.232061
\(142\) 3.29646 + 1.90321i 0.276633 + 0.159714i
\(143\) −11.1347 + 6.42864i −0.931133 + 0.537590i
\(144\) −2.30642 3.99484i −0.192202 0.332904i
\(145\) 1.33139 + 1.04011i 0.110566 + 0.0863761i
\(146\) −2.99063 −0.247506
\(147\) 0 0
\(148\) 12.3497i 1.01514i
\(149\) −10.6128 + 18.3820i −0.869438 + 1.50591i −0.00686675 + 0.999976i \(0.502186\pi\)
−0.862572 + 0.505935i \(0.831148\pi\)
\(150\) −2.30292 9.23320i −0.188032 0.753888i
\(151\) −8.42864 14.5988i −0.685913 1.18804i −0.973149 0.230176i \(-0.926070\pi\)
0.287236 0.957860i \(-0.407264\pi\)
\(152\) −1.51225 0.873100i −0.122660 0.0708178i
\(153\) 4.42864i 0.358034i
\(154\) 0 0
\(155\) 1.61285 11.4795i 0.129547 0.922055i
\(156\) −5.21432 + 9.03147i −0.417480 + 0.723096i
\(157\) 9.03147 5.21432i 0.720790 0.416148i −0.0942537 0.995548i \(-0.530046\pi\)
0.815043 + 0.579400i \(0.196713\pi\)
\(158\) −8.00591 + 4.62222i −0.636916 + 0.367724i
\(159\) 4.59210 7.95376i 0.364178 0.630774i
\(160\) −16.2558 2.28391i −1.28513 0.180559i
\(161\) 0 0
\(162\) 1.90321i 0.149530i
\(163\) 18.0629 + 10.4286i 1.41480 + 0.816834i 0.995835 0.0911693i \(-0.0290605\pi\)
0.418963 + 0.908003i \(0.362394\pi\)
\(164\) 6.67952 + 11.5693i 0.521583 + 0.903409i
\(165\) −1.67547 4.14642i −0.130435 0.322799i
\(166\) −11.0509 + 19.1406i −0.857713 + 1.48560i
\(167\) 15.3461i 1.18752i −0.804642 0.593760i \(-0.797643\pi\)
0.804642 0.593760i \(-0.202357\pi\)
\(168\) 0 0
\(169\) −28.3274 −2.17903
\(170\) 14.8521 + 11.6028i 1.13911 + 0.889891i
\(171\) −1.21432 2.10326i −0.0928614 0.160841i
\(172\) 14.1917 8.19358i 1.08211 0.624754i
\(173\) −1.78421 1.03011i −0.135651 0.0783179i 0.430639 0.902524i \(-0.358288\pi\)
−0.566290 + 0.824206i \(0.691622\pi\)
\(174\) 1.43801 0.109015
\(175\) 0 0
\(176\) −9.22570 −0.695413
\(177\) 12.2124 + 7.05086i 0.917943 + 0.529975i
\(178\) −7.61847 + 4.39853i −0.571029 + 0.329684i
\(179\) 5.00000 + 8.66025i 0.373718 + 0.647298i 0.990134 0.140122i \(-0.0447496\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(180\) −2.85851 2.23312i −0.213061 0.166447i
\(181\) 12.1017 0.899513 0.449757 0.893151i \(-0.351511\pi\)
0.449757 + 0.893151i \(0.351511\pi\)
\(182\) 0 0
\(183\) 6.85728i 0.506905i
\(184\) 0.495316 0.857913i 0.0365152 0.0632462i
\(185\) 6.37753 + 15.7830i 0.468885 + 1.16039i
\(186\) −4.93332 8.54477i −0.361729 0.626533i
\(187\) 7.67063 + 4.42864i 0.560932 + 0.323854i
\(188\) 4.47013i 0.326017i
\(189\) 0 0
\(190\) −10.2351 1.43801i −0.742530 0.104324i
\(191\) −0.244431 + 0.423367i −0.0176864 + 0.0306338i −0.874733 0.484605i \(-0.838963\pi\)
0.857047 + 0.515239i \(0.172297\pi\)
\(192\) −4.11033 + 2.37310i −0.296638 + 0.171264i
\(193\) 19.8831 11.4795i 1.43121 0.826312i 0.434001 0.900912i \(-0.357101\pi\)
0.997214 + 0.0746003i \(0.0237681\pi\)
\(194\) −11.3620 + 19.6795i −0.815741 + 1.41291i
\(195\) 2.00000 14.2351i 0.143223 1.01939i
\(196\) 0 0
\(197\) 1.18421i 0.0843713i −0.999110 0.0421857i \(-0.986568\pi\)
0.999110 0.0421857i \(-0.0134321\pi\)
\(198\) −3.29646 1.90321i −0.234269 0.135255i
\(199\) −4.39853 7.61847i −0.311803 0.540059i 0.666949 0.745103i \(-0.267600\pi\)
−0.978753 + 0.205044i \(0.934266\pi\)
\(200\) 3.48816 0.870006i 0.246650 0.0615187i
\(201\) −1.37778 + 2.38639i −0.0971814 + 0.168323i
\(202\) 2.81579i 0.198118i
\(203\) 0 0
\(204\) 7.18421 0.502995
\(205\) −14.5110 11.3363i −1.01349 0.791760i
\(206\) 8.42864 + 14.5988i 0.587251 + 1.01715i
\(207\) 1.19320 0.688892i 0.0829329 0.0478813i
\(208\) −25.6814 14.8272i −1.78069 1.02808i
\(209\) −4.85728 −0.335985
\(210\) 0 0
\(211\) 23.2257 1.59892 0.799461 0.600717i \(-0.205118\pi\)
0.799461 + 0.600717i \(0.205118\pi\)
\(212\) −12.9027 7.44938i −0.886162 0.511626i
\(213\) −1.73205 + 1.00000i −0.118678 + 0.0685189i
\(214\) −1.67952 2.90902i −0.114810 0.198857i
\(215\) −13.9059 + 17.8003i −0.948373 + 1.21397i
\(216\) 0.719004 0.0489220
\(217\) 0 0
\(218\) 10.6824i 0.723506i
\(219\) 0.785680 1.36084i 0.0530914 0.0919569i
\(220\) −6.72639 + 2.71797i −0.453493 + 0.183245i
\(221\) 14.2351 + 24.6559i 0.957554 + 1.65853i
\(222\) 12.5477 + 7.24443i 0.842148 + 0.486214i
\(223\) 15.2257i 1.01959i −0.860297 0.509794i \(-0.829722\pi\)
0.860297 0.509794i \(-0.170278\pi\)
\(224\) 0 0
\(225\) 4.80642 + 1.37778i 0.320428 + 0.0918523i
\(226\) −10.7397 + 18.6018i −0.714397 + 1.23737i
\(227\) 12.4434 7.18421i 0.825898 0.476833i −0.0265479 0.999648i \(-0.508451\pi\)
0.852446 + 0.522815i \(0.175118\pi\)
\(228\) −3.41195 + 1.96989i −0.225962 + 0.130459i
\(229\) 2.80642 4.86087i 0.185454 0.321215i −0.758276 0.651934i \(-0.773958\pi\)
0.943729 + 0.330719i \(0.107291\pi\)
\(230\) 0.815792 5.80642i 0.0537917 0.382864i
\(231\) 0 0
\(232\) 0.543257i 0.0356666i
\(233\) 20.1662 + 11.6430i 1.32113 + 0.762756i 0.983909 0.178669i \(-0.0571793\pi\)
0.337222 + 0.941425i \(0.390513\pi\)
\(234\) −6.11753 10.5959i −0.399916 0.692674i
\(235\) −2.30843 5.71288i −0.150585 0.372667i
\(236\) 11.4380 19.8112i 0.744551 1.28960i
\(237\) 4.85728i 0.315514i
\(238\) 0 0
\(239\) 8.48886 0.549099 0.274549 0.961573i \(-0.411471\pi\)
0.274549 + 0.961573i \(0.411471\pi\)
\(240\) 6.34999 8.12831i 0.409890 0.524680i
\(241\) −3.62222 6.27386i −0.233327 0.404135i 0.725458 0.688267i \(-0.241628\pi\)
−0.958785 + 0.284132i \(0.908295\pi\)
\(242\) 11.5376 6.66124i 0.741666 0.428201i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 11.1240 0.712140
\(245\) 0 0
\(246\) −15.6731 −0.999278
\(247\) −13.5211 7.80642i −0.860328 0.496711i
\(248\) 3.22808 1.86373i 0.204983 0.118347i
\(249\) −5.80642 10.0570i −0.367967 0.637338i
\(250\) 17.2131 12.5094i 1.08865 0.791163i
\(251\) −27.6128 −1.74291 −0.871454 0.490478i \(-0.836822\pi\)
−0.871454 + 0.490478i \(0.836822\pi\)
\(252\) 0 0
\(253\) 2.75557i 0.173241i
\(254\) 12.2351 21.1918i 0.767696 1.32969i
\(255\) −9.18150 + 3.71002i −0.574968 + 0.232330i
\(256\) −10.1222 17.5322i −0.632638 1.09576i
\(257\) −0.371213 0.214320i −0.0231556 0.0133689i 0.488378 0.872632i \(-0.337589\pi\)
−0.511533 + 0.859264i \(0.670922\pi\)
\(258\) 19.2257i 1.19694i
\(259\) 0 0
\(260\) −23.0923 3.24443i −1.43213 0.201211i
\(261\) −0.377784 + 0.654342i −0.0233843 + 0.0405027i
\(262\) −3.46410 + 2.00000i −0.214013 + 0.123560i
\(263\) 8.12140 4.68889i 0.500787 0.289129i −0.228252 0.973602i \(-0.573301\pi\)
0.729038 + 0.684473i \(0.239968\pi\)
\(264\) 0.719004 1.24535i 0.0442516 0.0766461i
\(265\) 20.3368 + 2.85728i 1.24928 + 0.175521i
\(266\) 0 0
\(267\) 4.62222i 0.282875i
\(268\) 3.87124 + 2.23506i 0.236474 + 0.136528i
\(269\) −0.873100 1.51225i −0.0532339 0.0922038i 0.838181 0.545393i \(-0.183620\pi\)
−0.891414 + 0.453189i \(0.850286\pi\)
\(270\) 3.94576 1.59438i 0.240131 0.0970310i
\(271\) −1.34767 + 2.33424i −0.0818653 + 0.141795i −0.904051 0.427424i \(-0.859421\pi\)
0.822186 + 0.569219i \(0.192754\pi\)
\(272\) 20.4286i 1.23867i
\(273\) 0 0
\(274\) 30.3368 1.83271
\(275\) 7.19282 6.94719i 0.433743 0.418931i
\(276\) −1.11753 1.93562i −0.0672675 0.116511i
\(277\) −4.43750 + 2.56199i −0.266624 + 0.153935i −0.627352 0.778736i \(-0.715861\pi\)
0.360729 + 0.932671i \(0.382528\pi\)
\(278\) 19.2399 + 11.1082i 1.15393 + 0.666223i
\(279\) 5.18421 0.310370
\(280\) 0 0
\(281\) 23.9813 1.43060 0.715301 0.698816i \(-0.246290\pi\)
0.715301 + 0.698816i \(0.246290\pi\)
\(282\) −4.54181 2.62222i −0.270461 0.156151i
\(283\) 2.05111 1.18421i 0.121926 0.0703939i −0.437797 0.899074i \(-0.644241\pi\)
0.559723 + 0.828680i \(0.310908\pi\)
\(284\) 1.62222 + 2.80976i 0.0962608 + 0.166729i
\(285\) 3.34323 4.27951i 0.198036 0.253497i
\(286\) −24.4701 −1.44695
\(287\) 0 0
\(288\) 7.34122i 0.432585i
\(289\) 1.30642 2.26279i 0.0768485 0.133105i
\(290\) 1.20467 + 2.98129i 0.0707404 + 0.175068i
\(291\) −5.96989 10.3402i −0.349961 0.606150i
\(292\) −2.20757 1.27454i −0.129188 0.0745870i
\(293\) 8.42864i 0.492406i 0.969218 + 0.246203i \(0.0791831\pi\)
−0.969218 + 0.246203i \(0.920817\pi\)
\(294\) 0 0
\(295\) −4.38715 + 31.2257i −0.255430 + 1.81803i
\(296\) −2.73683 + 4.74033i −0.159075 + 0.275526i
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) −34.9848 + 20.1985i −2.02662 + 1.17007i
\(299\) 4.42864 7.67063i 0.256115 0.443604i
\(300\) 2.23506 7.79706i 0.129041 0.450163i
\(301\) 0 0
\(302\) 32.0830i 1.84617i
\(303\) −1.28128 0.739747i −0.0736076 0.0424974i
\(304\) −5.60147 9.70203i −0.321266 0.556450i
\(305\) −14.2166 + 5.74457i −0.814039 + 0.328933i
\(306\) −4.21432 + 7.29942i −0.240917 + 0.417280i
\(307\) 22.5718i 1.28824i 0.764923 + 0.644121i \(0.222777\pi\)
−0.764923 + 0.644121i \(0.777223\pi\)
\(308\) 0 0
\(309\) −8.85728 −0.503873
\(310\) 13.5823 17.3861i 0.771423 0.987461i
\(311\) −12.0415 20.8565i −0.682810 1.18266i −0.974120 0.226033i \(-0.927424\pi\)
0.291310 0.956629i \(-0.405909\pi\)
\(312\) 4.00296 2.31111i 0.226623 0.130841i
\(313\) −8.36090 4.82717i −0.472586 0.272848i 0.244736 0.969590i \(-0.421299\pi\)
−0.717322 + 0.696742i \(0.754632\pi\)
\(314\) 19.8479 1.12008
\(315\) 0 0
\(316\) −7.87955 −0.443260
\(317\) 5.23208 + 3.02074i 0.293863 + 0.169662i 0.639683 0.768639i \(-0.279066\pi\)
−0.345820 + 0.938301i \(0.612399\pi\)
\(318\) 15.1377 8.73975i 0.848879 0.490101i
\(319\) 0.755569 + 1.30868i 0.0423037 + 0.0732722i
\(320\) −8.36330 6.53356i −0.467522 0.365237i
\(321\) 1.76494 0.0985092
\(322\) 0 0
\(323\) 10.7556i 0.598456i
\(324\) 0.811108 1.40488i 0.0450615 0.0780489i
\(325\) 31.1878 7.77875i 1.72999 0.431488i
\(326\) 19.8479 + 34.3776i 1.09927 + 1.90400i
\(327\) −4.86087 2.80642i −0.268807 0.155196i
\(328\) 5.92104i 0.326935i
\(329\) 0 0
\(330\) 1.18421 8.42864i 0.0651885 0.463981i
\(331\) −6.75557 + 11.7010i −0.371320 + 0.643144i −0.989769 0.142680i \(-0.954428\pi\)
0.618449 + 0.785825i \(0.287761\pi\)
\(332\) −16.3147 + 9.41927i −0.895383 + 0.516950i
\(333\) −6.59292 + 3.80642i −0.361290 + 0.208591i
\(334\) 14.6035 25.2940i 0.799067 1.38402i
\(335\) −6.10171 0.857279i −0.333372 0.0468382i
\(336\) 0 0
\(337\) 10.4889i 0.571365i 0.958324 + 0.285682i \(0.0922202\pi\)
−0.958324 + 0.285682i \(0.907780\pi\)
\(338\) −46.6901 26.9565i −2.53961 1.46624i
\(339\) −5.64296 9.77389i −0.306483 0.530845i
\(340\) 6.01845 + 14.8944i 0.326396 + 0.807761i
\(341\) 5.18421 8.97931i 0.280741 0.486257i
\(342\) 4.62222i 0.249941i
\(343\) 0 0
\(344\) −7.26317 −0.391604
\(345\) 2.42780 + 1.89664i 0.130708 + 0.102112i
\(346\) −1.96052 3.39572i −0.105398 0.182555i
\(347\) −14.4833 + 8.36196i −0.777507 + 0.448894i −0.835546 0.549421i \(-0.814848\pi\)
0.0580392 + 0.998314i \(0.481515\pi\)
\(348\) 1.06148 + 0.612848i 0.0569015 + 0.0328521i
\(349\) −16.3684 −0.876181 −0.438091 0.898931i \(-0.644345\pi\)
−0.438091 + 0.898931i \(0.644345\pi\)
\(350\) 0 0
\(351\) 6.42864 0.343135
\(352\) −12.7154 7.34122i −0.677731 0.391288i
\(353\) 0.475522 0.274543i 0.0253095 0.0146124i −0.487292 0.873239i \(-0.662015\pi\)
0.512601 + 0.858627i \(0.328682\pi\)
\(354\) 13.4193 + 23.2429i 0.713226 + 1.23534i
\(355\) −3.52421 2.75317i −0.187045 0.146123i
\(356\) −7.49823 −0.397405
\(357\) 0 0
\(358\) 19.0321i 1.00588i
\(359\) −0.142721 + 0.247200i −0.00753253 + 0.0130467i −0.869767 0.493462i \(-0.835731\pi\)
0.862235 + 0.506509i \(0.169064\pi\)
\(360\) 0.602333 + 1.49065i 0.0317457 + 0.0785640i
\(361\) 6.55086 + 11.3464i 0.344782 + 0.597180i
\(362\) 19.9464 + 11.5161i 1.04836 + 0.605271i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 3.47949 + 0.488863i 0.182125 + 0.0255882i
\(366\) −6.52543 + 11.3024i −0.341090 + 0.590784i
\(367\) −1.48485 + 0.857279i −0.0775086 + 0.0447496i −0.538253 0.842783i \(-0.680916\pi\)
0.460745 + 0.887533i \(0.347582\pi\)
\(368\) 5.50403 3.17775i 0.286918 0.165652i
\(369\) 4.11753 7.13177i 0.214350 0.371265i
\(370\) −4.50760 + 32.0830i −0.234339 + 1.66791i
\(371\) 0 0
\(372\) 8.40990i 0.436033i
\(373\) 13.8564 + 8.00000i 0.717458 + 0.414224i 0.813816 0.581122i \(-0.197386\pi\)
−0.0963587 + 0.995347i \(0.530720\pi\)
\(374\) 8.42864 + 14.5988i 0.435835 + 0.754888i
\(375\) 1.17006 + 11.1189i 0.0604216 + 0.574180i
\(376\) 0.990632 1.71583i 0.0510879 0.0884869i
\(377\) 4.85728i 0.250163i
\(378\) 0 0
\(379\) 4.85728 0.249502 0.124751 0.992188i \(-0.460187\pi\)
0.124751 + 0.992188i \(0.460187\pi\)
\(380\) −6.94229 5.42345i −0.356132 0.278217i
\(381\) 6.42864 + 11.1347i 0.329349 + 0.570450i
\(382\) −0.805758 + 0.465205i −0.0412262 + 0.0238019i
\(383\) 7.26349 + 4.19358i 0.371147 + 0.214282i 0.673959 0.738768i \(-0.264592\pi\)
−0.302813 + 0.953050i \(0.597926\pi\)
\(384\) 5.64941 0.288295
\(385\) 0 0
\(386\) 43.6958 2.22406
\(387\) −8.74834 5.05086i −0.444703 0.256749i
\(388\) −16.7740 + 9.68445i −0.851568 + 0.491653i
\(389\) 4.47949 + 7.75871i 0.227119 + 0.393382i 0.956953 0.290242i \(-0.0937359\pi\)
−0.729834 + 0.683625i \(0.760403\pi\)
\(390\) 16.8426 21.5594i 0.852860 1.09170i
\(391\) −6.10171 −0.308577
\(392\) 0 0
\(393\) 2.10171i 0.106017i
\(394\) 1.12690 1.95185i 0.0567724 0.0983326i
\(395\) 10.0702 4.06910i 0.506685 0.204739i
\(396\) −1.62222 2.80976i −0.0815194 0.141196i
\(397\) −2.20757 1.27454i −0.110795 0.0639675i 0.443579 0.896236i \(-0.353709\pi\)
−0.554373 + 0.832268i \(0.687042\pi\)
\(398\) 16.7427i 0.839234i
\(399\) 0 0
\(400\) 22.1713 + 6.35551i 1.10857 + 0.317775i
\(401\) −0.479495 + 0.830509i −0.0239448 + 0.0414736i −0.877750 0.479120i \(-0.840956\pi\)
0.853805 + 0.520593i \(0.174289\pi\)
\(402\) −4.54181 + 2.62222i −0.226525 + 0.130784i
\(403\) 28.8624 16.6637i 1.43774 0.830078i
\(404\) −1.20003 + 2.07851i −0.0597037 + 0.103410i
\(405\) −0.311108 + 2.21432i −0.0154591 + 0.110030i
\(406\) 0 0
\(407\) 15.2257i 0.754710i
\(408\) −2.75761 1.59210i −0.136522 0.0788209i
\(409\) 15.9906 + 27.6966i 0.790686 + 1.36951i 0.925543 + 0.378643i \(0.123609\pi\)
−0.134857 + 0.990865i \(0.543057\pi\)
\(410\) −13.1298 32.4936i −0.648437 1.60474i
\(411\) −7.96989 + 13.8043i −0.393126 + 0.680914i
\(412\) 14.3684i 0.707881i
\(413\) 0 0
\(414\) 2.62222 0.128875
\(415\) 15.9861 20.4630i 0.784727 1.00449i
\(416\) −23.5970 40.8712i −1.15694 2.00388i
\(417\) −10.1092 + 5.83654i −0.495048 + 0.285816i
\(418\) −8.00591 4.62222i −0.391582 0.226080i
\(419\) −0.470127 −0.0229672 −0.0114836 0.999934i \(-0.503655\pi\)
−0.0114836 + 0.999934i \(0.503655\pi\)
\(420\) 0 0
\(421\) −33.6128 −1.63819 −0.819095 0.573658i \(-0.805524\pi\)
−0.819095 + 0.573658i \(0.805524\pi\)
\(422\) 38.2813 + 22.1017i 1.86350 + 1.07589i
\(423\) 2.38639 1.37778i 0.116030 0.0669902i
\(424\) 3.30174 + 5.71878i 0.160347 + 0.277729i
\(425\) −15.3833 15.9272i −0.746199 0.772582i
\(426\) −3.80642 −0.184422
\(427\) 0 0
\(428\) 2.86311i 0.138394i
\(429\) 6.42864 11.1347i 0.310378 0.537590i
\(430\) −39.8589 + 16.1060i −1.92217 + 0.776700i
\(431\) −5.85728 10.1451i −0.282135 0.488673i 0.689775 0.724024i \(-0.257709\pi\)
−0.971910 + 0.235351i \(0.924376\pi\)
\(432\) 3.99484 + 2.30642i 0.192202 + 0.110968i
\(433\) 0.0602231i 0.00289414i −0.999999 0.00144707i \(-0.999539\pi\)
0.999999 0.00144707i \(-0.000460616\pi\)
\(434\) 0 0
\(435\) −1.67307 0.235063i −0.0802176 0.0112704i
\(436\) −4.55262 + 7.88538i −0.218031 + 0.377641i
\(437\) 2.89784 1.67307i 0.138623 0.0800338i
\(438\) 2.58996 1.49532i 0.123753 0.0714490i
\(439\) 11.2143 19.4238i 0.535230 0.927046i −0.463922 0.885876i \(-0.653558\pi\)
0.999152 0.0411699i \(-0.0131085\pi\)
\(440\) 3.18421 + 0.447375i 0.151801 + 0.0213278i
\(441\) 0 0
\(442\) 54.1847i 2.57730i
\(443\) −20.7410 11.9748i −0.985434 0.568940i −0.0815275 0.996671i \(-0.525980\pi\)
−0.903906 + 0.427731i \(0.859313\pi\)
\(444\) 6.17484 + 10.6951i 0.293045 + 0.507569i
\(445\) 9.58283 3.87218i 0.454270 0.183559i
\(446\) 14.4889 25.0954i 0.686068 1.18830i
\(447\) 21.2257i 1.00394i
\(448\) 0 0
\(449\) −29.4291 −1.38885 −0.694423 0.719567i \(-0.744340\pi\)
−0.694423 + 0.719567i \(0.744340\pi\)
\(450\) 6.61098 + 6.84473i 0.311645 + 0.322664i
\(451\) −8.23506 14.2635i −0.387774 0.671644i
\(452\) −15.8554 + 9.15410i −0.745773 + 0.430572i
\(453\) 14.5988 + 8.42864i 0.685913 + 0.396012i
\(454\) 27.3461 1.28342
\(455\) 0 0
\(456\) 1.74620 0.0817733
\(457\) 2.72168 + 1.57136i 0.127315 + 0.0735051i 0.562305 0.826930i \(-0.309915\pi\)
−0.434990 + 0.900435i \(0.643248\pi\)
\(458\) 9.25126 5.34122i 0.432283 0.249579i
\(459\) −2.21432 3.83531i −0.103356 0.179017i
\(460\) 3.07676 3.93841i 0.143455 0.183629i
\(461\) 3.37778 0.157319 0.0786596 0.996902i \(-0.474936\pi\)
0.0786596 + 0.996902i \(0.474936\pi\)
\(462\) 0 0
\(463\) 20.8573i 0.969320i −0.874703 0.484660i \(-0.838943\pi\)
0.874703 0.484660i \(-0.161057\pi\)
\(464\) −1.74266 + 3.01838i −0.0809010 + 0.140125i
\(465\) 4.34298 + 10.7480i 0.201401 + 0.498425i
\(466\) 22.1590 + 38.3805i 1.02650 + 1.77794i
\(467\) −12.4434 7.18421i −0.575813 0.332446i 0.183655 0.982991i \(-0.441207\pi\)
−0.759467 + 0.650545i \(0.774540\pi\)
\(468\) 10.4286i 0.482064i
\(469\) 0 0
\(470\) 1.63158 11.6128i 0.0752593 0.535661i
\(471\) −5.21432 + 9.03147i −0.240263 + 0.416148i
\(472\) −8.78079 + 5.06959i −0.404169 + 0.233347i
\(473\) −17.4967 + 10.1017i −0.804498 + 0.464477i
\(474\) 4.62222 8.00591i 0.212305 0.367724i
\(475\) 11.6731 + 3.34614i 0.535597 + 0.153532i
\(476\) 0 0
\(477\) 9.18421i 0.420516i
\(478\) 13.9916 + 8.07805i 0.639961 + 0.369482i
\(479\) −3.18421 5.51521i −0.145490 0.251996i 0.784066 0.620678i \(-0.213143\pi\)
−0.929556 + 0.368682i \(0.879809\pi\)
\(480\) 15.2199 6.14998i 0.694690 0.280707i
\(481\) −24.4701 + 42.3835i −1.11574 + 1.93252i
\(482\) 13.7877i 0.628012i
\(483\) 0 0
\(484\) 11.3555 0.516160
\(485\) 16.4361 21.0391i 0.746327 0.955337i
\(486\) 0.951606 + 1.64823i 0.0431657 + 0.0747652i
\(487\) 15.0060 8.66370i 0.679986 0.392590i −0.119864 0.992790i \(-0.538246\pi\)
0.799850 + 0.600200i \(0.204913\pi\)
\(488\) −4.26986 2.46520i −0.193287 0.111595i
\(489\) −20.8573 −0.943199
\(490\) 0 0
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) −11.5693 6.67952i −0.521583 0.301136i
\(493\) 2.89784 1.67307i 0.130512 0.0753513i
\(494\) −14.8573 25.7336i −0.668461 1.15781i
\(495\) 3.52421 + 2.75317i 0.158401 + 0.123746i
\(496\) 23.9140 1.07377
\(497\) 0 0
\(498\) 22.1017i 0.990401i
\(499\) 11.6731 20.2184i 0.522558 0.905098i −0.477097 0.878851i \(-0.658311\pi\)
0.999655 0.0262471i \(-0.00835568\pi\)
\(500\) 18.0373 1.89809i 0.806654 0.0848852i
\(501\) 7.67307 + 13.2901i 0.342808 + 0.593760i
\(502\) −45.5123 26.2766i −2.03131 1.17278i
\(503\) 0.387152i 0.0172623i 0.999963 + 0.00863113i \(0.00274741\pi\)
−0.999963 + 0.00863113i \(0.997253\pi\)
\(504\) 0 0
\(505\) 0.460282 3.27607i 0.0204823 0.145783i
\(506\) 2.62222 4.54181i 0.116572 0.201908i
\(507\) 24.5323 14.1637i 1.08952 0.629032i
\(508\) 18.0629 10.4286i 0.801413 0.462696i
\(509\) 14.9748 25.9371i 0.663747 1.14964i −0.315877 0.948800i \(-0.602299\pi\)
0.979623 0.200843i \(-0.0643681\pi\)
\(510\) −18.6637 2.62222i −0.826443 0.116114i
\(511\) 0 0
\(512\) 27.2306i 1.20343i
\(513\) 2.10326 + 1.21432i 0.0928614 + 0.0536135i
\(514\) −0.407896 0.706496i −0.0179915 0.0311622i
\(515\) −7.42003 18.3630i −0.326966 0.809171i
\(516\) −8.19358 + 14.1917i −0.360702 + 0.624754i
\(517\) 5.51114i 0.242380i
\(518\) 0 0
\(519\) 2.06022 0.0904338
\(520\) 8.14482 + 6.36288i 0.357174 + 0.279031i
\(521\) −9.26025 16.0392i −0.405699 0.702691i 0.588704 0.808349i \(-0.299639\pi\)
−0.994403 + 0.105658i \(0.966305\pi\)
\(522\) −1.24535 + 0.719004i −0.0545075 + 0.0314699i
\(523\) 3.46410 + 2.00000i 0.151475 + 0.0874539i 0.573822 0.818980i \(-0.305460\pi\)
−0.422347 + 0.906434i \(0.638794\pi\)
\(524\) −3.40943 −0.148942
\(525\) 0 0
\(526\) 17.8479 0.778206
\(527\) −19.8831 11.4795i −0.866120 0.500055i
\(528\) 7.98969 4.61285i 0.347706 0.200748i
\(529\) −10.5509 18.2746i −0.458733 0.794549i
\(530\) 30.8007 + 24.0620i 1.33790 + 1.04519i
\(531\) −14.1017 −0.611962
\(532\) 0 0
\(533\) 52.9403i 2.29310i
\(534\) 4.39853 7.61847i 0.190343 0.329684i
\(535\) 1.47854 + 3.65909i 0.0639231 + 0.158196i
\(536\) −0.990632 1.71583i −0.0427888 0.0741124i
\(537\) −8.66025 5.00000i −0.373718 0.215766i
\(538\) 3.32339i 0.143282i
\(539\) 0 0
\(540\) 3.59210 + 0.504684i 0.154580 + 0.0217181i
\(541\) −7.29529 + 12.6358i −0.313649 + 0.543256i −0.979149 0.203142i \(-0.934885\pi\)
0.665501 + 0.746397i \(0.268218\pi\)
\(542\) −4.44255 + 2.56491i −0.190824 + 0.110172i
\(543\) −10.4804 + 6.05086i −0.449757 + 0.259667i
\(544\) −16.2558 + 28.1559i −0.696962 + 1.20717i
\(545\) 1.74620 12.4286i 0.0747990 0.532384i
\(546\) 0 0
\(547\) 18.7556i 0.801930i −0.916093 0.400965i \(-0.868675\pi\)
0.916093 0.400965i \(-0.131325\pi\)
\(548\) 22.3935 + 12.9289i 0.956602 + 0.552294i
\(549\) −3.42864 5.93858i −0.146331 0.253452i
\(550\) 18.4664 4.60583i 0.787410 0.196393i
\(551\) −0.917502 + 1.58916i −0.0390869 + 0.0677005i
\(552\) 0.990632i 0.0421641i
\(553\) 0 0
\(554\) −9.75203 −0.414324
\(555\) −13.4146 10.4797i −0.569419 0.444841i
\(556\) 9.46812 + 16.3993i 0.401538 + 0.695484i
\(557\) 27.6059 15.9382i 1.16970 0.675325i 0.216089 0.976374i \(-0.430670\pi\)
0.953609 + 0.301049i \(0.0973366\pi\)
\(558\) 8.54477 + 4.93332i 0.361729 + 0.208844i
\(559\) −64.9403 −2.74668
\(560\) 0 0
\(561\) −8.85728 −0.373955
\(562\) 39.5266 + 22.8207i 1.66733 + 0.962634i
\(563\) −1.74828 + 1.00937i −0.0736811 + 0.0425398i −0.536388 0.843972i \(-0.680212\pi\)
0.462707 + 0.886511i \(0.346878\pi\)
\(564\) −2.23506 3.87124i −0.0941131 0.163009i
\(565\) 15.5361 19.8870i 0.653607 0.836650i
\(566\) 4.50760 0.189468
\(567\) 0 0
\(568\) 1.43801i 0.0603375i
\(569\) −14.4795 + 25.0792i −0.607012 + 1.05138i 0.384718 + 0.923034i \(0.374299\pi\)
−0.991730 + 0.128341i \(0.959035\pi\)
\(570\) 9.58283 3.87218i 0.401381 0.162188i
\(571\) −4.48886 7.77494i −0.187853 0.325371i 0.756681 0.653784i \(-0.226820\pi\)
−0.944534 + 0.328413i \(0.893486\pi\)
\(572\) −18.0629 10.4286i −0.755249 0.436043i
\(573\) 0.488863i 0.0204225i
\(574\) 0 0
\(575\) −1.89829 + 6.62222i −0.0791642 + 0.276165i
\(576\) 2.37310 4.11033i 0.0988792 0.171264i
\(577\) −24.8347 + 14.3383i −1.03388 + 0.596911i −0.918094 0.396363i \(-0.870272\pi\)
−0.115787 + 0.993274i \(0.536939\pi\)
\(578\) 4.30657 2.48640i 0.179130 0.103421i
\(579\) −11.4795 + 19.8831i −0.477072 + 0.826312i
\(580\) −0.381323 + 2.71408i −0.0158336 + 0.112696i
\(581\) 0 0
\(582\) 22.7239i 0.941937i
\(583\) 15.9075 + 9.18421i 0.658822 + 0.380371i
\(584\) 0.564907 + 0.978448i 0.0233760 + 0.0404885i
\(585\) 5.38548 + 13.3279i 0.222662 + 0.551042i
\(586\) −8.02074 + 13.8923i −0.331334 + 0.573887i
\(587\) 45.2070i 1.86589i −0.360018 0.932945i \(-0.617229\pi\)
0.360018 0.932945i \(-0.382771\pi\)
\(588\) 0 0
\(589\) 12.5906 0.518786
\(590\) −36.9456 + 47.2923i −1.52103 + 1.94699i
\(591\) 0.592104 + 1.02555i 0.0243559 + 0.0421857i
\(592\) −30.4121 + 17.5585i −1.24993 + 0.721648i
\(593\) 15.8168 + 9.13182i 0.649517 + 0.374999i 0.788271 0.615328i \(-0.210976\pi\)
−0.138754 + 0.990327i \(0.544310\pi\)
\(594\) 3.80642 0.156179
\(595\) 0 0
\(596\) −34.4327 −1.41042
\(597\) 7.61847 + 4.39853i 0.311803 + 0.180020i
\(598\) 14.5988 8.42864i 0.596991 0.344673i
\(599\) −11.3684 19.6907i −0.464501 0.804539i 0.534678 0.845056i \(-0.320433\pi\)
−0.999179 + 0.0405167i \(0.987100\pi\)
\(600\) −2.58583 + 2.49753i −0.105566 + 0.101961i
\(601\) −0.488863 −0.0199411 −0.00997056 0.999950i \(-0.503174\pi\)
−0.00997056 + 0.999950i \(0.503174\pi\)
\(602\) 0 0
\(603\) 2.75557i 0.112215i
\(604\) 13.6731 23.6825i 0.556349 0.963625i
\(605\) −14.5125 + 5.86413i −0.590016 + 0.238411i
\(606\) −1.40790 2.43855i −0.0571919 0.0990592i
\(607\) 17.4967 + 10.1017i 0.710168 + 0.410016i 0.811123 0.584875i \(-0.198857\pi\)
−0.100955 + 0.994891i \(0.532190\pi\)
\(608\) 17.8292i 0.723069i
\(609\) 0 0
\(610\) −28.8988 4.06022i −1.17008 0.164394i
\(611\) 8.85728 15.3413i 0.358327 0.620641i
\(612\) −6.22171 + 3.59210i −0.251498 + 0.145202i
\(613\) 8.97931 5.18421i 0.362671 0.209388i −0.307581 0.951522i \(-0.599519\pi\)
0.670252 + 0.742134i \(0.266186\pi\)
\(614\) −21.4795 + 37.2036i −0.866842 + 1.50141i
\(615\) 18.2351 + 2.56199i 0.735309 + 0.103310i
\(616\) 0 0
\(617\) 39.2859i 1.58159i 0.612080 + 0.790796i \(0.290333\pi\)
−0.612080 + 0.790796i \(0.709667\pi\)
\(618\) −14.5988 8.42864i −0.587251 0.339050i
\(619\) −21.4494 37.1514i −0.862123 1.49324i −0.869875 0.493272i \(-0.835801\pi\)
0.00775178 0.999970i \(-0.497533\pi\)
\(620\) 17.4355 7.04525i 0.700227 0.282944i
\(621\) −0.688892 + 1.19320i −0.0276443 + 0.0478813i
\(622\) 45.8350i 1.83782i
\(623\) 0 0
\(624\) 29.6543 1.18712
\(625\) −22.0717 + 11.7405i −0.882869 + 0.469619i
\(626\) −9.18712 15.9126i −0.367191 0.635994i
\(627\) 4.20653 2.42864i 0.167993 0.0969905i
\(628\) 14.6510 + 8.45875i 0.584638 + 0.337541i
\(629\) 33.7146 1.34429
\(630\) 0 0
\(631\) 15.3461 0.610920 0.305460 0.952205i \(-0.401190\pi\)
0.305460 + 0.952205i \(0.401190\pi\)
\(632\) 3.02451 + 1.74620i 0.120308 + 0.0694601i
\(633\) −20.1140 + 11.6128i −0.799461 + 0.461569i
\(634\) 5.74912 + 9.95776i 0.228327 + 0.395473i
\(635\) −17.6992 + 22.6559i −0.702370 + 0.899070i
\(636\) 14.8988 0.590775
\(637\) 0 0
\(638\) 2.87601i 0.113863i
\(639\) 1.00000 1.73205i 0.0395594 0.0685189i
\(640\) 4.73270 + 11.7124i 0.187076 + 0.462974i
\(641\) −15.3368 26.5641i −0.605766 1.04922i −0.991930 0.126787i \(-0.959533\pi\)
0.386164 0.922430i \(-0.373800\pi\)
\(642\) 2.90902 + 1.67952i 0.114810 + 0.0662855i
\(643\) 49.0607i 1.93477i 0.253320 + 0.967383i \(0.418477\pi\)
−0.253320 + 0.967383i \(0.581523\pi\)
\(644\) 0 0
\(645\) 3.14272 22.3684i 0.123745 0.880756i
\(646\) −10.2351 + 17.7276i −0.402693 + 0.697485i
\(647\) −13.2901 + 7.67307i −0.522490 + 0.301660i −0.737953 0.674852i \(-0.764207\pi\)
0.215463 + 0.976512i \(0.430874\pi\)
\(648\) −0.622675 + 0.359502i −0.0244610 + 0.0141226i
\(649\) −14.1017 + 24.4249i −0.553541 + 0.958760i
\(650\) 58.8069 + 16.8573i 2.30660 + 0.661197i
\(651\) 0 0
\(652\) 33.8350i 1.32508i
\(653\) 16.8612 + 9.73483i 0.659830 + 0.380953i 0.792212 0.610246i \(-0.208929\pi\)
−0.132382 + 0.991199i \(0.542263\pi\)
\(654\) −5.34122 9.25126i −0.208858 0.361753i
\(655\) 4.35729 1.76067i 0.170253 0.0687951i
\(656\) 18.9935 32.8978i 0.741573 1.28444i
\(657\) 1.57136i 0.0613046i
\(658\) 0 0
\(659\) −30.9403 −1.20526 −0.602631 0.798020i \(-0.705881\pi\)
−0.602631 + 0.798020i \(0.705881\pi\)
\(660\) 4.46624 5.71702i 0.173848 0.222535i
\(661\) 23.8988 + 41.3939i 0.929554 + 1.61004i 0.784068 + 0.620675i \(0.213141\pi\)
0.145486 + 0.989360i \(0.453525\pi\)
\(662\) −22.2695 + 12.8573i −0.865527 + 0.499712i
\(663\) −24.6559 14.2351i −0.957554 0.552844i
\(664\) 8.34968 0.324030
\(665\) 0 0
\(666\) −14.4889 −0.561432
\(667\) −0.901542 0.520505i −0.0349078 0.0201540i
\(668\) 21.5595 12.4474i 0.834162 0.481603i
\(669\) 7.61285 + 13.1858i 0.294330 + 0.509794i
\(670\) −9.24123 7.21942i −0.357020 0.278910i
\(671\) −13.7146 −0.529445
\(672\) 0 0
\(673\) 27.8163i 1.07224i 0.844142 + 0.536119i \(0.180110\pi\)
−0.844142 + 0.536119i \(0.819890\pi\)
\(674\) −9.98126 + 17.2881i −0.384464 + 0.665911i
\(675\) −4.85138 + 1.21002i −0.186730 + 0.0465735i
\(676\) −22.9766 39.7966i −0.883715 1.53064i
\(677\) 16.4549 + 9.50024i 0.632413 + 0.365124i 0.781686 0.623672i \(-0.214360\pi\)
−0.149273 + 0.988796i \(0.547693\pi\)
\(678\) 21.4795i 0.824915i
\(679\) 0 0
\(680\) 0.990632 7.05086i 0.0379890 0.270388i
\(681\) −7.18421 + 12.4434i −0.275299 + 0.476833i
\(682\) 17.0895 9.86665i 0.654392 0.377813i
\(683\) 3.91487 2.26025i 0.149798 0.0864862i −0.423227 0.906024i \(-0.639103\pi\)
0.573026 + 0.819537i \(0.305769\pi\)
\(684\) 1.96989 3.41195i 0.0753206 0.130459i
\(685\) −35.2958 4.95899i −1.34858 0.189473i
\(686\) 0 0
\(687\) 5.61285i 0.214143i
\(688\) −40.3547 23.2988i −1.53851 0.888259i
\(689\) 29.5210 + 51.1318i 1.12466 + 1.94797i
\(690\) 2.19672 + 5.43641i 0.0836275 + 0.206960i
\(691\) −0.592104 + 1.02555i −0.0225247 + 0.0390139i −0.877068 0.480366i \(-0.840504\pi\)
0.854543 + 0.519380i \(0.173837\pi\)
\(692\) 3.34213i 0.127049i
\(693\) 0 0
\(694\) −31.8292 −1.20822
\(695\) −20.5692 16.0690i −0.780233 0.609532i
\(696\) −0.271628 0.470474i −0.0102960 0.0178333i
\(697\) −31.5841 + 18.2351i −1.19633 + 0.690702i
\(698\) −26.9789 15.5763i −1.02117 0.589571i
\(699\) −23.2859 −0.880754
\(700\) 0 0
\(701\) −26.6735 −1.00745 −0.503723 0.863865i \(-0.668037\pi\)
−0.503723 + 0.863865i \(0.668037\pi\)
\(702\) 10.5959 + 6.11753i 0.399916 + 0.230891i
\(703\) −16.0118 + 9.24443i −0.603897 + 0.348660i
\(704\) −4.74620 8.22066i −0.178879 0.309828i
\(705\) 4.85560 + 3.79328i 0.182872 + 0.142863i
\(706\) 1.04503 0.0393301
\(707\) 0 0
\(708\) 22.8760i 0.859733i
\(709\) −9.10171 + 15.7646i −0.341822 + 0.592053i −0.984771 0.173856i \(-0.944377\pi\)
0.642949 + 0.765909i \(0.277711\pi\)
\(710\) −3.18877 7.89152i −0.119672 0.296163i
\(711\) 2.42864 + 4.20653i 0.0910811 + 0.157757i
\(712\) 2.87814 + 1.66170i 0.107863 + 0.0622747i
\(713\) 7.14272i 0.267497i
\(714\) 0 0
\(715\) 28.4701 + 4.00000i 1.06472 + 0.149592i
\(716\) −8.11108 + 14.0488i −0.303125 + 0.525028i
\(717\) −7.35157 + 4.24443i −0.274549 + 0.158511i
\(718\) −0.470474 + 0.271628i −0.0175579 + 0.0101371i
\(719\) −2.42864 + 4.20653i −0.0905730 + 0.156877i −0.907752 0.419506i \(-0.862203\pi\)
0.817179 + 0.576383i \(0.195537\pi\)
\(720\) −1.43509 + 10.2143i −0.0534828 + 0.380665i
\(721\) 0 0
\(722\) 24.9353i 0.927997i
\(723\) 6.27386 + 3.62222i 0.233327 + 0.134712i
\(724\) 9.81579 + 17.0015i 0.364801 + 0.631854i
\(725\) −0.914250 3.66555i −0.0339544 0.136135i
\(726\) −6.66124 + 11.5376i −0.247222 + 0.428201i
\(727\) 21.0607i 0.781098i 0.920582 + 0.390549i \(0.127715\pi\)
−0.920582 + 0.390549i \(0.872285\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 5.26980 + 4.11687i 0.195044 + 0.152372i
\(731\) 22.3684 + 38.7432i 0.827326 + 1.43297i
\(732\) −9.63365 + 5.56199i −0.356070 + 0.205577i
\(733\) 8.18473 + 4.72546i 0.302310 + 0.174539i 0.643480 0.765463i \(-0.277490\pi\)
−0.341170 + 0.940002i \(0.610823\pi\)
\(734\) −3.26317 −0.120446
\(735\) 0 0
\(736\) 10.1146 0.372830
\(737\) −4.77279 2.75557i −0.175808 0.101503i
\(738\) 13.5733 7.83654i 0.499639 0.288467i
\(739\) −4.10171 7.10437i −0.150884 0.261338i 0.780669 0.624945i \(-0.214879\pi\)
−0.931553 + 0.363607i \(0.881545\pi\)
\(740\) −17.0004 + 21.7614i −0.624948 + 0.799965i
\(741\) 15.6128 0.573552
\(742\) 0 0
\(743\) 8.33677i 0.305847i 0.988238 + 0.152923i \(0.0488687\pi\)
−0.988238 + 0.152923i \(0.951131\pi\)
\(744\) −1.86373 + 3.22808i −0.0683277 + 0.118347i
\(745\) 44.0053 17.7815i 1.61223 0.651462i
\(746\) 15.2257 + 26.3717i 0.557452 + 0.965536i
\(747\) 10.0570 + 5.80642i 0.367967 + 0.212446i
\(748\) 14.3684i 0.525361i
\(749\) 0 0
\(750\) −8.65233 + 19.4400i −0.315938 + 0.709849i
\(751\) 12.9590 22.4456i 0.472880 0.819053i −0.526638 0.850090i \(-0.676548\pi\)
0.999518 + 0.0310371i \(0.00988099\pi\)
\(752\) 11.0081 6.35551i 0.401423 0.231762i
\(753\) 23.9134 13.8064i 0.871454 0.503134i
\(754\) −4.62222 + 8.00591i −0.168331 + 0.291558i
\(755\) −5.24443 + 37.3274i −0.190864 + 1.35848i
\(756\) 0 0
\(757\) 8.94025i 0.324939i −0.986714 0.162470i \(-0.948054\pi\)
0.986714 0.162470i \(-0.0519459\pi\)
\(758\) 8.00591 + 4.62222i 0.290788 + 0.167886i
\(759\) 1.37778 + 2.38639i 0.0500104 + 0.0866206i
\(760\) 1.46285 + 3.62024i 0.0530631 + 0.131320i
\(761\) −0.412818 + 0.715022i −0.0149646 + 0.0259195i −0.873411 0.486984i \(-0.838097\pi\)
0.858446 + 0.512904i \(0.171430\pi\)
\(762\) 24.4701i 0.886459i
\(763\) 0 0
\(764\) −0.793040 −0.0286912
\(765\) 6.09641 7.80372i 0.220416 0.282144i
\(766\) 7.98126 + 13.8240i 0.288375 + 0.499480i
\(767\) −78.5094 + 45.3274i −2.83481 + 1.63668i
\(768\) 17.5322 + 10.1222i 0.632638 + 0.365254i
\(769\) 21.2257 0.765418 0.382709 0.923869i \(-0.374991\pi\)
0.382709 + 0.923869i \(0.374991\pi\)
\(770\) 0 0
\(771\) 0.428639 0.0154371
\(772\) 32.2546 + 18.6222i 1.16087 + 0.670228i
\(773\) −25.5385 + 14.7447i −0.918557 + 0.530329i −0.883174 0.469045i \(-0.844598\pi\)
−0.0353823 + 0.999374i \(0.511265\pi\)
\(774\) −9.61285 16.6499i −0.345527 0.598470i
\(775\) −18.6445 + 18.0078i −0.669731 + 0.646860i
\(776\) 8.58474 0.308174
\(777\) 0 0
\(778\) 17.0509i 0.611303i
\(779\) 10.0000 17.3205i 0.358287 0.620572i
\(780\) 21.6208 8.73641i 0.774148 0.312814i
\(781\) −2.00000 3.46410i −0.0715656 0.123955i
\(782\) −10.0570 5.80642i −0.359638 0.207637i
\(783\) 0.755569i 0.0270018i
\(784\) 0 0
\(785\) −23.0923 3.24443i −0.824201 0.115799i
\(786\) 2.00000 3.46410i 0.0713376 0.123560i
\(787\) −29.8358 + 17.2257i −1.06353 + 0.614030i −0.926407 0.376524i \(-0.877119\pi\)
−0.137124 + 0.990554i \(0.543786\pi\)
\(788\) 1.66367 0.960521i 0.0592658 0.0342171i
\(789\) −4.68889 + 8.12140i −0.166929 + 0.289129i
\(790\) 20.4701 + 2.87601i 0.728294 + 0.102324i
\(791\) 0 0
\(792\) 1.43801i 0.0510974i
\(793\) −38.1770 22.0415i −1.35570 0.782716i
\(794\) −2.42573 4.20148i −0.0860858 0.149105i
\(795\) −19.0408 + 7.69391i −0.675308 + 0.272875i
\(796\) 7.13536 12.3588i 0.252906 0.438046i
\(797\) 18.9175i 0.670092i 0.942202 + 0.335046i \(0.108752\pi\)
−0.942202 + 0.335046i \(0.891248\pi\)
\(798\) 0 0
\(799\) −12.2034 −0.431726
\(800\) 25.5004 + 26.4020i 0.901576 + 0.933452i
\(801\) 2.31111 + 4.00296i 0.0816590 + 0.141438i
\(802\) −1.58063 + 0.912580i −0.0558142 + 0.0322243i
\(803\) 2.72168 + 1.57136i 0.0960459 + 0.0554521i
\(804\) −4.47013 −0.157649
\(805\) 0 0
\(806\) 63.4291 2.23420
\(807\) 1.51225 + 0.873100i 0.0532339 + 0.0307346i
\(808\) 0.921245 0.531881i 0.0324093 0.0187115i
\(809\) 10.6128 + 18.3820i 0.373128 + 0.646276i 0.990045 0.140752i \(-0.0449519\pi\)
−0.616917 + 0.787028i \(0.711619\pi\)
\(810\) −2.61994 + 3.35366i −0.0920552 + 0.117835i
\(811\) 21.5081 0.755251 0.377625 0.925958i \(-0.376741\pi\)
0.377625 + 0.925958i \(0.376741\pi\)
\(812\) 0 0
\(813\) 2.69535i 0.0945299i
\(814\) −14.4889 + 25.0954i −0.507834 + 0.879595i
\(815\) −17.4728 43.2415i −0.612046 1.51469i
\(816\) −10.2143 17.6917i −0.357573 0.619334i
\(817\) −21.2466 12.2667i −0.743323 0.429158i
\(818\) 60.8671i 2.12817i
\(819\) 0 0
\(820\) 4.15610 29.5812i 0.145137 1.03302i
\(821\) 23.1017 40.0133i 0.806255 1.39648i −0.109185 0.994021i \(-0.534824\pi\)
0.915440 0.402454i \(-0.131843\pi\)
\(822\) −26.2724 + 15.1684i −0.916356 + 0.529058i
\(823\) −15.4456 + 8.91750i −0.538399 + 0.310845i −0.744430 0.667701i \(-0.767279\pi\)
0.206031 + 0.978545i \(0.433945\pi\)
\(824\) 3.18421 5.51521i 0.110927 0.192131i
\(825\) −2.75557 + 9.61285i −0.0959366 + 0.334676i
\(826\) 0 0
\(827\) 35.2128i 1.22447i −0.790676 0.612234i \(-0.790271\pi\)
0.790676 0.612234i \(-0.209729\pi\)
\(828\) 1.93562 + 1.11753i 0.0672675 + 0.0388369i
\(829\) −7.19358 12.4596i −0.249843 0.432741i 0.713639 0.700514i \(-0.247046\pi\)
−0.963482 + 0.267773i \(0.913712\pi\)
\(830\) 45.8215 18.5153i 1.59049 0.642676i
\(831\) 2.56199 4.43750i 0.0888745 0.153935i
\(832\) 30.5116i 1.05780i
\(833\) 0 0
\(834\) −22.2163 −0.769289
\(835\) −21.1253 + 27.0415i −0.731071 + 0.935809i
\(836\) −3.93978 6.82389i −0.136260 0.236009i
\(837\) −4.48966 + 2.59210i −0.155185 + 0.0895962i
\(838\) −0.774877 0.447375i −0.0267677 0.0154543i
\(839\) 1.51114 0.0521703 0.0260851 0.999660i \(-0.491696\pi\)
0.0260851 + 0.999660i \(0.491696\pi\)
\(840\) 0 0
\(841\) −28.4291 −0.980314
\(842\) −55.4017 31.9862i −1.90927 1.10232i
\(843\) −20.7684 + 11.9906i −0.715301 + 0.412979i
\(844\) 18.8385 + 32.6293i 0.648449 + 1.12315i
\(845\) 49.9158 + 38.9951i 1.71716 + 1.34147i
\(846\) 5.24443 0.180307
\(847\) 0 0
\(848\) 42.3654i 1.45483i
\(849\) −1.18421 + 2.05111i −0.0406419 + 0.0703939i
\(850\) −10.1988 40.8905i −0.349815 1.40253i
\(851\) −5.24443 9.08362i −0.179777 0.311383i
\(852\) −2.80976 1.62222i −0.0962608 0.0555762i
\(853\) 15.4064i 0.527504i 0.964591 + 0.263752i \(0.0849600\pi\)
−0.964591 + 0.263752i \(0.915040\pi\)
\(854\) 0 0
\(855\) −0.755569 + 5.37778i −0.0258399 + 0.183916i
\(856\) −0.634498 + 1.09898i −0.0216867 + 0.0375625i
\(857\) 17.1973 9.92888i 0.587449 0.339164i −0.176639 0.984276i \(-0.556523\pi\)
0.764088 + 0.645112i \(0.223189\pi\)
\(858\) 21.1918 12.2351i 0.723474 0.417698i
\(859\) −1.21432 + 2.10326i −0.0414321 + 0.0717624i −0.885998 0.463689i \(-0.846525\pi\)
0.844566 + 0.535452i \(0.179859\pi\)
\(860\) −36.2864 5.09817i −1.23736 0.173846i
\(861\) 0 0
\(862\) 22.2953i 0.759380i
\(863\) 34.0311 + 19.6479i 1.15843 + 0.668822i 0.950928 0.309412i \(-0.100132\pi\)
0.207505 + 0.978234i \(0.433466\pi\)
\(864\) 3.67061 + 6.35768i 0.124877 + 0.216293i
\(865\) 1.72592 + 4.27128i 0.0586829 + 0.145228i
\(866\) 0.0573086 0.0992614i 0.00194743 0.00337304i
\(867\) 2.61285i 0.0887370i
\(868\) 0 0
\(869\) 9.71456 0.329544
\(870\) −2.53392 1.97954i −0.0859078 0.0671128i
\(871\) −8.85728 15.3413i −0.300117 0.519819i
\(872\) 3.49498 2.01783i 0.118355 0.0683323i
\(873\) 10.3402 + 5.96989i 0.349961 + 0.202050i
\(874\) 6.36842 0.215415
\(875\) 0 0
\(876\) 2.54909 0.0861256
\(877\) −48.7454 28.1432i −1.64602 0.950328i −0.978633 0.205614i \(-0.934081\pi\)
−0.667384 0.744714i \(-0.732586\pi\)
\(878\) 36.9676 21.3432i 1.24759 0.720299i
\(879\) −4.21432 7.29942i −0.142145 0.246203i
\(880\) 16.2566 + 12.7000i 0.548011 + 0.428116i
\(881\) 2.33677 0.0787279 0.0393640 0.999225i \(-0.487467\pi\)
0.0393640 + 0.999225i \(0.487467\pi\)
\(882\) 0 0
\(883\) 33.7146i 1.13459i 0.823516 + 0.567293i \(0.192009\pi\)
−0.823516 + 0.567293i \(0.807991\pi\)
\(884\) −23.0923 + 39.9971i −0.776680 + 1.34525i
\(885\) −11.8135 29.2358i −0.397105 0.982751i
\(886\) −22.7906 39.4745i −0.765665 1.32617i
\(887\) −41.4820 23.9496i −1.39283 0.804150i −0.399200 0.916864i \(-0.630712\pi\)
−0.993627 + 0.112714i \(0.964046\pi\)
\(888\) 5.47367i 0.183684i
\(889\) 0 0
\(890\) 19.4795 + 2.73683i 0.652954 + 0.0917388i
\(891\) −1.00000 + 1.73205i −0.0335013 + 0.0580259i
\(892\) 21.3903 12.3497i 0.716199 0.413498i
\(893\) 5.79569 3.34614i 0.193945 0.111974i
\(894\) 20.1985 34.9848i 0.675539 1.17007i
\(895\) 3.11108 22.1432i 0.103992 0.740165i
\(896\) 0 0
\(897\) 8.85728i 0.295736i
\(898\) −48.5059 28.0049i −1.61866 0.934536i
\(899\) −1.95851 3.39224i −0.0653201 0.113138i
\(900\) 1.96291 + 7.86998i 0.0654302 + 0.262333i
\(901\) 20.3368 35.2243i 0.677516 1.17349i
\(902\) 31.3461i 1.04371i
\(903\) 0 0
\(904\) 8.11462 0.269888
\(905\) −21.3245 16.6591i −0.708849 0.553766i
\(906\) 16.0415 + 27.7847i 0.532943 + 0.923084i
\(907\) −20.5760 + 11.8796i −0.683215 + 0.394454i −0.801065 0.598577i \(-0.795733\pi\)
0.117851 + 0.993031i \(0.462400\pi\)
\(908\) 20.1859 + 11.6543i 0.669893 + 0.386763i
\(909\) 1.47949 0.0490717
\(910\) 0 0
\(911\) 22.9403 0.760045 0.380022 0.924977i \(-0.375916\pi\)
0.380022 + 0.924977i \(0.375916\pi\)
\(912\) 9.70203 + 5.60147i 0.321266 + 0.185483i
\(913\) 20.1140 11.6128i 0.665678 0.384329i
\(914\) 2.99063 + 5.17993i 0.0989213 + 0.171337i
\(915\) 9.43964 12.0832i 0.312065 0.399459i
\(916\) 9.10525 0.300846
\(917\) 0 0
\(918\) 8.42864i 0.278187i
\(919\) 8.48886 14.7031i 0.280022 0.485012i −0.691368 0.722503i \(-0.742992\pi\)
0.971390 + 0.237491i \(0.0763250\pi\)
\(920\) −2.05379 + 0.829885i −0.0677114 + 0.0273605i
\(921\) −11.2859 19.5478i −0.371884 0.644121i
\(922\) 5.56737 + 3.21432i 0.183351 + 0.105858i
\(923\) 12.8573i 0.423202i
\(924\) 0 0
\(925\) 10.4889 36.5906i 0.344872 1.20309i
\(926\) 19.8479 34.3776i 0.652243 1.12972i
\(927\) 7.67063 4.42864i 0.251936 0.145456i
\(928\) −4.80367 + 2.77340i −0.157688 + 0.0910412i
\(929\) −19.6702 + 34.0697i −0.645357 + 1.11779i 0.338862 + 0.940836i \(0.389958\pi\)
−0.984219 + 0.176955i \(0.943375\pi\)
\(930\) −3.06959 + 21.8479i −0.100656 + 0.716421i
\(931\) 0 0
\(932\) 37.7748i 1.23735i
\(933\) 20.8565 + 12.0415i 0.682810 + 0.394221i
\(934\) −13.6731 23.6825i −0.447397 0.774914i
\(935\) −7.42003 18.3630i −0.242661 0.600535i
\(936\) −2.31111 + 4.00296i −0.0755409 + 0.130841i
\(937\) 17.7748i 0.580677i −0.956924 0.290338i \(-0.906232\pi\)
0.956924 0.290338i \(-0.0937679\pi\)
\(938\) 0 0
\(939\) 9.65433 0.315057
\(940\) 6.15352 7.87682i 0.200706 0.256914i
\(941\) 17.7906 + 30.8142i 0.579957 + 1.00452i 0.995484 + 0.0949340i \(0.0302640\pi\)
−0.415527 + 0.909581i \(0.636403\pi\)
\(942\) −17.1888 + 9.92396i −0.560041 + 0.323340i
\(943\) 9.82605 + 5.67307i 0.319980 + 0.184741i
\(944\) −65.0490 −2.11717
\(945\) 0 0
\(946\) −38.4514 −1.25016
\(947\) 26.4153 + 15.2509i 0.858382 + 0.495587i 0.863470 0.504400i \(-0.168286\pi\)
−0.00508803 + 0.999987i \(0.501620\pi\)
\(948\) 6.82389 3.93978i 0.221630 0.127958i
\(949\) 5.05086 + 8.74834i 0.163958 + 0.283983i
\(950\) 16.0557 + 16.6234i 0.520916 + 0.539333i
\(951\) −6.04149 −0.195909
\(952\) 0 0
\(953\) 51.1655i 1.65741i −0.559684 0.828706i \(-0.689077\pi\)
0.559684 0.828706i \(-0.310923\pi\)
\(954\) −8.73975 + 15.1377i −0.282960 + 0.490101i
\(955\) 1.01352 0.409536i 0.0327966 0.0132523i
\(956\) 6.88538 + 11.9258i 0.222689 + 0.385709i
\(957\) −1.30868 0.755569i −0.0423037 0.0244241i
\(958\) 12.1204i 0.391594i
\(959\) 0 0
\(960\) 10.5096 + 1.47658i 0.339196 + 0.0476564i
\(961\) 2.06199 3.57148i 0.0665159 0.115209i
\(962\) −80.6648 + 46.5718i −2.60074 + 1.50154i
\(963\) −1.52848 + 0.882468i −0.0492546 + 0.0284371i
\(964\) 5.87601 10.1776i 0.189254 0.327797i
\(965\) −50.8385 7.14272i −1.63655 0.229932i
\(966\) 0 0
\(967\) 47.8992i 1.54034i −0.637841 0.770168i \(-0.720172\pi\)
0.637841 0.770168i \(-0.279828\pi\)
\(968\) −4.35873 2.51651i −0.140095 0.0808838i
\(969\) −5.37778 9.31460i −0.172759 0.299228i
\(970\) 47.1115 19.0366i 1.51266 0.611228i
\(971\) 20.3368 35.2243i 0.652638 1.13040i −0.329842 0.944036i \(-0.606996\pi\)
0.982480 0.186366i \(-0.0596711\pi\)
\(972\) 1.62222i 0.0520326i
\(973\) 0 0
\(974\) 32.9777 1.05667
\(975\) −23.1200 + 22.3305i −0.740433 + 0.715148i
\(976\) −15.8158 27.3938i −0.506251 0.876853i
\(977\) 23.8065 13.7447i 0.761636 0.439731i −0.0682466 0.997668i \(-0.521740\pi\)
0.829883 + 0.557938i \(0.188407\pi\)
\(978\) −34.3776 19.8479i −1.09927 0.634666i
\(979\) 9.24443 0.295453
\(980\) 0 0
\(981\) 5.61285 0.179204
\(982\) 3.29646 + 1.90321i 0.105194 + 0.0607339i
\(983\) −20.7846 + 12.0000i −0.662926 + 0.382741i −0.793391 0.608712i \(-0.791686\pi\)
0.130465 + 0.991453i \(0.458353\pi\)
\(984\) 2.96052 + 5.12777i 0.0943779 + 0.163467i
\(985\) −1.63017 + 2.08670i −0.0519414 + 0.0664877i
\(986\) 6.36842 0.202812
\(987\) 0 0
\(988\) 25.3274i 0.805772i
\(989\) 6.95899 12.0533i 0.221283 0.383273i
\(990\) 3.18877 + 7.89152i 0.101346 + 0.250809i
\(991\) 17.3461 + 30.0444i 0.551018 + 0.954392i 0.998201 + 0.0599493i \(0.0190939\pi\)
−0.447183 + 0.894442i \(0.647573\pi\)
\(992\) 32.9595 + 19.0292i 1.04647 + 0.604178i
\(993\) 13.5111i 0.428763i
\(994\) 0 0
\(995\) −2.73683 + 19.4795i −0.0867634 + 0.617541i
\(996\) 9.41927 16.3147i 0.298461 0.516950i
\(997\) −24.8347 + 14.3383i −0.786522 + 0.454099i −0.838737 0.544537i \(-0.816705\pi\)
0.0522147 + 0.998636i \(0.483372\pi\)
\(998\) 38.4798 22.2163i 1.21806 0.703246i
\(999\) 3.80642 6.59292i 0.120430 0.208591i
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 735.2.q.f.79.5 12
5.4 even 2 inner 735.2.q.f.79.2 12
7.2 even 3 735.2.d.b.589.2 6
7.3 odd 6 735.2.q.e.214.2 12
7.4 even 3 inner 735.2.q.f.214.2 12
7.5 odd 6 105.2.d.b.64.2 6
7.6 odd 2 735.2.q.e.79.5 12
21.2 odd 6 2205.2.d.l.1324.5 6
21.5 even 6 315.2.d.e.64.5 6
28.19 even 6 1680.2.t.k.1009.2 6
35.2 odd 12 3675.2.a.bi.1.3 3
35.4 even 6 inner 735.2.q.f.214.5 12
35.9 even 6 735.2.d.b.589.5 6
35.12 even 12 525.2.a.j.1.3 3
35.19 odd 6 105.2.d.b.64.5 yes 6
35.23 odd 12 3675.2.a.bj.1.1 3
35.24 odd 6 735.2.q.e.214.5 12
35.33 even 12 525.2.a.k.1.1 3
35.34 odd 2 735.2.q.e.79.2 12
84.47 odd 6 5040.2.t.v.1009.4 6
105.44 odd 6 2205.2.d.l.1324.2 6
105.47 odd 12 1575.2.a.x.1.1 3
105.68 odd 12 1575.2.a.w.1.3 3
105.89 even 6 315.2.d.e.64.2 6
140.19 even 6 1680.2.t.k.1009.5 6
140.47 odd 12 8400.2.a.dg.1.3 3
140.103 odd 12 8400.2.a.dj.1.1 3
420.299 odd 6 5040.2.t.v.1009.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.d.b.64.2 6 7.5 odd 6
105.2.d.b.64.5 yes 6 35.19 odd 6
315.2.d.e.64.2 6 105.89 even 6
315.2.d.e.64.5 6 21.5 even 6
525.2.a.j.1.3 3 35.12 even 12
525.2.a.k.1.1 3 35.33 even 12
735.2.d.b.589.2 6 7.2 even 3
735.2.d.b.589.5 6 35.9 even 6
735.2.q.e.79.2 12 35.34 odd 2
735.2.q.e.79.5 12 7.6 odd 2
735.2.q.e.214.2 12 7.3 odd 6
735.2.q.e.214.5 12 35.24 odd 6
735.2.q.f.79.2 12 5.4 even 2 inner
735.2.q.f.79.5 12 1.1 even 1 trivial
735.2.q.f.214.2 12 7.4 even 3 inner
735.2.q.f.214.5 12 35.4 even 6 inner
1575.2.a.w.1.3 3 105.68 odd 12
1575.2.a.x.1.1 3 105.47 odd 12
1680.2.t.k.1009.2 6 28.19 even 6
1680.2.t.k.1009.5 6 140.19 even 6
2205.2.d.l.1324.2 6 105.44 odd 6
2205.2.d.l.1324.5 6 21.2 odd 6
3675.2.a.bi.1.3 3 35.2 odd 12
3675.2.a.bj.1.1 3 35.23 odd 12
5040.2.t.v.1009.3 6 420.299 odd 6
5040.2.t.v.1009.4 6 84.47 odd 6
8400.2.a.dg.1.3 3 140.47 odd 12
8400.2.a.dj.1.1 3 140.103 odd 12