Properties

Label 637.2.g.m.373.5
Level $637$
Weight $2$
Character 637.373
Analytic conductor $5.086$
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] = [637,2,Mod(263,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.5
Root \(-0.141226 + 0.244611i\) of defining polynomial
Character \(\chi\) \(=\) 637.373
Dual form 637.2.g.m.263.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.760387 + 1.31703i) q^{2} -2.12621 q^{3} +(-0.156376 + 0.270851i) q^{4} +(-0.294696 + 0.510428i) q^{5} +(-1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +1.52077 q^{9} +O(q^{10})\) \(q+(0.760387 + 1.31703i) q^{2} -2.12621 q^{3} +(-0.156376 + 0.270851i) q^{4} +(-0.294696 + 0.510428i) q^{5} +(-1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +1.52077 q^{9} -0.896331 q^{10} +1.52077 q^{11} +(0.332488 - 0.575886i) q^{12} +(3.32565 - 1.39285i) q^{13} +(0.626585 - 1.08528i) q^{15} +(2.26384 + 3.92109i) q^{16} +(-2.39740 + 4.15241i) q^{17} +(1.15638 + 2.00290i) q^{18} +1.68391 q^{19} +(-0.0921666 - 0.159637i) q^{20} +(1.15638 + 2.00290i) q^{22} +(-0.886972 - 1.53628i) q^{23} -5.45569 q^{24} +(2.32631 + 4.02929i) q^{25} +(4.36321 + 3.32087i) q^{26} +3.14515 q^{27} +(-3.44625 + 5.96909i) q^{29} +1.90579 q^{30} +(3.04320 + 5.27098i) q^{31} +(-0.876873 + 1.51879i) q^{32} -3.23349 q^{33} -7.29179 q^{34} +(-0.237812 + 0.411903i) q^{36} +(-0.704563 - 1.22034i) q^{37} +(1.28043 + 2.21776i) q^{38} +(-7.07104 + 2.96150i) q^{39} +(-0.756166 + 1.30972i) q^{40} +(-0.677729 + 1.17386i) q^{41} +(5.77978 + 10.0109i) q^{43} +(-0.237812 + 0.411903i) q^{44} +(-0.448165 + 0.776245i) q^{45} +(1.34888 - 2.33633i) q^{46} +(0.232416 - 0.402556i) q^{47} +(-4.81341 - 8.33707i) q^{48} +(-3.53779 + 6.12763i) q^{50} +(5.09737 - 8.82890i) q^{51} +(-0.142796 + 1.11856i) q^{52} +(-4.12340 - 7.14194i) q^{53} +(2.39153 + 4.14225i) q^{54} +(-0.448165 + 0.776245i) q^{55} -3.58035 q^{57} -10.4819 q^{58} +(5.93782 - 10.2846i) q^{59} +(0.195966 + 0.339422i) q^{60} +2.48017 q^{61} +(-4.62802 + 8.01596i) q^{62} +6.38833 q^{64} +(-0.269104 + 2.10797i) q^{65} +(-2.45870 - 4.25859i) q^{66} -7.57284 q^{67} +(-0.749790 - 1.29867i) q^{68} +(1.88589 + 3.26646i) q^{69} +(-3.30235 - 5.71984i) q^{71} +3.90219 q^{72} +(8.18558 + 14.1778i) q^{73} +(1.07148 - 1.85586i) q^{74} +(-4.94622 - 8.56711i) q^{75} +(-0.263323 + 0.456090i) q^{76} +(-9.27710 - 7.06087i) q^{78} +(7.48116 - 12.9577i) q^{79} -2.66858 q^{80} -11.2496 q^{81} -2.06134 q^{82} +10.1222 q^{83} +(-1.41300 - 2.44740i) q^{85} +(-8.78973 + 15.2243i) q^{86} +(7.32746 - 12.6915i) q^{87} +3.90219 q^{88} +(-8.24250 - 14.2764i) q^{89} -1.36312 q^{90} +0.554804 q^{92} +(-6.47049 - 11.2072i) q^{93} +0.706904 q^{94} +(-0.496242 + 0.859516i) q^{95} +(1.86442 - 3.22927i) q^{96} +(0.486935 + 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.760387 + 1.31703i 0.537675 + 0.931280i 0.999029 + 0.0440636i \(0.0140304\pi\)
−0.461354 + 0.887216i \(0.652636\pi\)
\(3\) −2.12621 −1.22757 −0.613784 0.789474i \(-0.710354\pi\)
−0.613784 + 0.789474i \(0.710354\pi\)
\(4\) −0.156376 + 0.270851i −0.0781880 + 0.135426i
\(5\) −0.294696 + 0.510428i −0.131792 + 0.228270i −0.924367 0.381504i \(-0.875406\pi\)
0.792575 + 0.609774i \(0.208740\pi\)
\(6\) −1.61674 2.80028i −0.660032 1.14321i
\(7\) 0 0
\(8\) 2.56592 0.907190
\(9\) 1.52077 0.506924
\(10\) −0.896331 −0.283445
\(11\) 1.52077 0.458530 0.229265 0.973364i \(-0.426368\pi\)
0.229265 + 0.973364i \(0.426368\pi\)
\(12\) 0.332488 0.575886i 0.0959811 0.166244i
\(13\) 3.32565 1.39285i 0.922370 0.386308i
\(14\) 0 0
\(15\) 0.626585 1.08528i 0.161784 0.280217i
\(16\) 2.26384 + 3.92109i 0.565961 + 0.980274i
\(17\) −2.39740 + 4.15241i −0.581454 + 1.00711i 0.413853 + 0.910344i \(0.364183\pi\)
−0.995307 + 0.0967643i \(0.969151\pi\)
\(18\) 1.15638 + 2.00290i 0.272560 + 0.472088i
\(19\) 1.68391 0.386316 0.193158 0.981168i \(-0.438127\pi\)
0.193158 + 0.981168i \(0.438127\pi\)
\(20\) −0.0921666 0.159637i −0.0206091 0.0356960i
\(21\) 0 0
\(22\) 1.15638 + 2.00290i 0.246540 + 0.427020i
\(23\) −0.886972 1.53628i −0.184946 0.320337i 0.758612 0.651543i \(-0.225878\pi\)
−0.943558 + 0.331206i \(0.892544\pi\)
\(24\) −5.45569 −1.11364
\(25\) 2.32631 + 4.02929i 0.465262 + 0.805857i
\(26\) 4.36321 + 3.32087i 0.855696 + 0.651276i
\(27\) 3.14515 0.605284
\(28\) 0 0
\(29\) −3.44625 + 5.96909i −0.639953 + 1.10843i 0.345489 + 0.938423i \(0.387713\pi\)
−0.985443 + 0.170009i \(0.945620\pi\)
\(30\) 1.90579 0.347948
\(31\) 3.04320 + 5.27098i 0.546575 + 0.946695i 0.998506 + 0.0546426i \(0.0174019\pi\)
−0.451931 + 0.892053i \(0.649265\pi\)
\(32\) −0.876873 + 1.51879i −0.155011 + 0.268486i
\(33\) −3.23349 −0.562878
\(34\) −7.29179 −1.25053
\(35\) 0 0
\(36\) −0.237812 + 0.411903i −0.0396354 + 0.0686505i
\(37\) −0.704563 1.22034i −0.115830 0.200623i 0.802282 0.596946i \(-0.203619\pi\)
−0.918111 + 0.396323i \(0.870286\pi\)
\(38\) 1.28043 + 2.21776i 0.207712 + 0.359768i
\(39\) −7.07104 + 2.96150i −1.13227 + 0.474219i
\(40\) −0.756166 + 1.30972i −0.119560 + 0.207085i
\(41\) −0.677729 + 1.17386i −0.105843 + 0.183326i −0.914082 0.405528i \(-0.867088\pi\)
0.808239 + 0.588855i \(0.200421\pi\)
\(42\) 0 0
\(43\) 5.77978 + 10.0109i 0.881408 + 1.52664i 0.849776 + 0.527144i \(0.176737\pi\)
0.0316319 + 0.999500i \(0.489930\pi\)
\(44\) −0.237812 + 0.411903i −0.0358516 + 0.0620967i
\(45\) −0.448165 + 0.776245i −0.0668085 + 0.115716i
\(46\) 1.34888 2.33633i 0.198882 0.344474i
\(47\) 0.232416 0.402556i 0.0339013 0.0587188i −0.848577 0.529072i \(-0.822540\pi\)
0.882478 + 0.470353i \(0.155873\pi\)
\(48\) −4.81341 8.33707i −0.694756 1.20335i
\(49\) 0 0
\(50\) −3.53779 + 6.12763i −0.500319 + 0.866578i
\(51\) 5.09737 8.82890i 0.713775 1.23629i
\(52\) −0.142796 + 1.11856i −0.0198023 + 0.155117i
\(53\) −4.12340 7.14194i −0.566393 0.981021i −0.996919 0.0784430i \(-0.975005\pi\)
0.430526 0.902578i \(-0.358328\pi\)
\(54\) 2.39153 + 4.14225i 0.325446 + 0.563689i
\(55\) −0.448165 + 0.776245i −0.0604306 + 0.104669i
\(56\) 0 0
\(57\) −3.58035 −0.474230
\(58\) −10.4819 −1.37635
\(59\) 5.93782 10.2846i 0.773038 1.33894i −0.162852 0.986651i \(-0.552069\pi\)
0.935890 0.352291i \(-0.114597\pi\)
\(60\) 0.195966 + 0.339422i 0.0252991 + 0.0438193i
\(61\) 2.48017 0.317553 0.158777 0.987315i \(-0.449245\pi\)
0.158777 + 0.987315i \(0.449245\pi\)
\(62\) −4.62802 + 8.01596i −0.587759 + 1.01803i
\(63\) 0 0
\(64\) 6.38833 0.798541
\(65\) −0.269104 + 2.10797i −0.0333783 + 0.261462i
\(66\) −2.45870 4.25859i −0.302645 0.524196i
\(67\) −7.57284 −0.925169 −0.462585 0.886575i \(-0.653078\pi\)
−0.462585 + 0.886575i \(0.653078\pi\)
\(68\) −0.749790 1.29867i −0.0909254 0.157487i
\(69\) 1.88589 + 3.26646i 0.227034 + 0.393235i
\(70\) 0 0
\(71\) −3.30235 5.71984i −0.391917 0.678821i 0.600785 0.799411i \(-0.294855\pi\)
−0.992702 + 0.120590i \(0.961521\pi\)
\(72\) 3.90219 0.459877
\(73\) 8.18558 + 14.1778i 0.958049 + 1.65939i 0.727231 + 0.686393i \(0.240807\pi\)
0.230819 + 0.972997i \(0.425860\pi\)
\(74\) 1.07148 1.85586i 0.124557 0.215739i
\(75\) −4.94622 8.56711i −0.571141 0.989245i
\(76\) −0.263323 + 0.456090i −0.0302053 + 0.0523171i
\(77\) 0 0
\(78\) −9.27710 7.06087i −1.05042 0.799486i
\(79\) 7.48116 12.9577i 0.841696 1.45786i −0.0467635 0.998906i \(-0.514891\pi\)
0.888460 0.458955i \(-0.151776\pi\)
\(80\) −2.66858 −0.298356
\(81\) −11.2496 −1.24995
\(82\) −2.06134 −0.227637
\(83\) 10.1222 1.11105 0.555526 0.831499i \(-0.312517\pi\)
0.555526 + 0.831499i \(0.312517\pi\)
\(84\) 0 0
\(85\) −1.41300 2.44740i −0.153262 0.265457i
\(86\) −8.78973 + 15.2243i −0.947821 + 1.64167i
\(87\) 7.32746 12.6915i 0.785586 1.36068i
\(88\) 3.90219 0.415974
\(89\) −8.24250 14.2764i −0.873703 1.51330i −0.858138 0.513419i \(-0.828379\pi\)
−0.0155650 0.999879i \(-0.504955\pi\)
\(90\) −1.36312 −0.143685
\(91\) 0 0
\(92\) 0.554804 0.0578423
\(93\) −6.47049 11.2072i −0.670958 1.16213i
\(94\) 0.706904 0.0729115
\(95\) −0.496242 + 0.859516i −0.0509133 + 0.0881845i
\(96\) 1.86442 3.22927i 0.190286 0.329586i
\(97\) 0.486935 + 0.843396i 0.0494407 + 0.0856338i 0.889687 0.456572i \(-0.150923\pi\)
−0.840246 + 0.542205i \(0.817589\pi\)
\(98\) 0 0
\(99\) 2.31275 0.232440
\(100\) −1.45511 −0.145511
\(101\) −2.94023 −0.292564 −0.146282 0.989243i \(-0.546731\pi\)
−0.146282 + 0.989243i \(0.546731\pi\)
\(102\) 15.5039 1.53511
\(103\) −0.264341 + 0.457852i −0.0260463 + 0.0451135i −0.878755 0.477274i \(-0.841625\pi\)
0.852708 + 0.522387i \(0.174958\pi\)
\(104\) 8.53336 3.57395i 0.836765 0.350455i
\(105\) 0 0
\(106\) 6.27076 10.8613i 0.609070 1.05494i
\(107\) 9.66119 + 16.7337i 0.933983 + 1.61771i 0.776438 + 0.630194i \(0.217024\pi\)
0.157545 + 0.987512i \(0.449642\pi\)
\(108\) −0.491825 + 0.851866i −0.0473259 + 0.0819709i
\(109\) 2.86620 + 4.96440i 0.274532 + 0.475503i 0.970017 0.243037i \(-0.0781437\pi\)
−0.695485 + 0.718541i \(0.744810\pi\)
\(110\) −1.36312 −0.129968
\(111\) 1.49805 + 2.59470i 0.142189 + 0.246278i
\(112\) 0 0
\(113\) −2.57480 4.45968i −0.242216 0.419531i 0.719129 0.694877i \(-0.244541\pi\)
−0.961345 + 0.275346i \(0.911208\pi\)
\(114\) −2.72245 4.71543i −0.254981 0.441640i
\(115\) 1.04555 0.0974978
\(116\) −1.07782 1.86684i −0.100073 0.173332i
\(117\) 5.05756 2.11821i 0.467572 0.195829i
\(118\) 18.0602 1.66257
\(119\) 0 0
\(120\) 1.60777 2.78474i 0.146769 0.254211i
\(121\) −8.68725 −0.789750
\(122\) 1.88589 + 3.26646i 0.170740 + 0.295731i
\(123\) 1.44099 2.49588i 0.129930 0.225045i
\(124\) −1.90353 −0.170942
\(125\) −5.68917 −0.508855
\(126\) 0 0
\(127\) 4.50166 7.79710i 0.399457 0.691881i −0.594202 0.804316i \(-0.702532\pi\)
0.993659 + 0.112436i \(0.0358652\pi\)
\(128\) 6.61135 + 11.4512i 0.584366 + 1.01215i
\(129\) −12.2890 21.2852i −1.08199 1.87406i
\(130\) −2.98088 + 1.24846i −0.261441 + 0.109497i
\(131\) −3.39920 + 5.88758i −0.296989 + 0.514401i −0.975446 0.220240i \(-0.929316\pi\)
0.678456 + 0.734641i \(0.262649\pi\)
\(132\) 0.505639 0.875793i 0.0440102 0.0762280i
\(133\) 0 0
\(134\) −5.75829 9.97364i −0.497440 0.861592i
\(135\) −0.926861 + 1.60537i −0.0797715 + 0.138168i
\(136\) −6.15153 + 10.6548i −0.527490 + 0.913639i
\(137\) 7.03779 12.1898i 0.601279 1.04145i −0.391349 0.920242i \(-0.627991\pi\)
0.992628 0.121203i \(-0.0386753\pi\)
\(138\) −2.86801 + 4.96754i −0.244141 + 0.422865i
\(139\) −8.64313 14.9703i −0.733101 1.26977i −0.955552 0.294824i \(-0.904739\pi\)
0.222451 0.974944i \(-0.428594\pi\)
\(140\) 0 0
\(141\) −0.494165 + 0.855919i −0.0416162 + 0.0720814i
\(142\) 5.02213 8.69859i 0.421448 0.729969i
\(143\) 5.05756 2.11821i 0.422935 0.177134i
\(144\) 3.44280 + 5.96310i 0.286900 + 0.496925i
\(145\) −2.03119 3.51813i −0.168681 0.292165i
\(146\) −12.4484 + 21.5613i −1.03024 + 1.78442i
\(147\) 0 0
\(148\) 0.440707 0.0362259
\(149\) −17.1252 −1.40295 −0.701475 0.712694i \(-0.747475\pi\)
−0.701475 + 0.712694i \(0.747475\pi\)
\(150\) 7.52209 13.0286i 0.614176 1.06378i
\(151\) −7.89873 13.6810i −0.642789 1.11334i −0.984807 0.173650i \(-0.944444\pi\)
0.342018 0.939693i \(-0.388890\pi\)
\(152\) 4.32079 0.350462
\(153\) −3.64590 + 6.31488i −0.294753 + 0.510528i
\(154\) 0 0
\(155\) −3.58727 −0.288137
\(156\) 0.303615 2.37830i 0.0243086 0.190417i
\(157\) 1.89176 + 3.27662i 0.150979 + 0.261503i 0.931587 0.363517i \(-0.118424\pi\)
−0.780609 + 0.625020i \(0.785091\pi\)
\(158\) 22.7543 1.81023
\(159\) 8.76722 + 15.1853i 0.695286 + 1.20427i
\(160\) −0.516821 0.895161i −0.0408583 0.0707687i
\(161\) 0 0
\(162\) −8.55402 14.8160i −0.672067 1.16406i
\(163\) 1.71551 0.134369 0.0671847 0.997741i \(-0.478598\pi\)
0.0671847 + 0.997741i \(0.478598\pi\)
\(164\) −0.211961 0.367127i −0.0165514 0.0286678i
\(165\) 0.952894 1.65046i 0.0741827 0.128488i
\(166\) 7.69677 + 13.3312i 0.597385 + 1.03470i
\(167\) −6.32605 + 10.9570i −0.489524 + 0.847881i −0.999927 0.0120542i \(-0.996163\pi\)
0.510403 + 0.859935i \(0.329496\pi\)
\(168\) 0 0
\(169\) 9.11992 9.26429i 0.701532 0.712638i
\(170\) 2.14886 3.72193i 0.164810 0.285459i
\(171\) 2.56085 0.195833
\(172\) −3.61527 −0.275662
\(173\) −11.4874 −0.873372 −0.436686 0.899614i \(-0.643848\pi\)
−0.436686 + 0.899614i \(0.643848\pi\)
\(174\) 22.2868 1.68956
\(175\) 0 0
\(176\) 3.44280 + 5.96310i 0.259510 + 0.449485i
\(177\) −12.6251 + 21.8672i −0.948958 + 1.64364i
\(178\) 12.5350 21.7112i 0.939536 1.62732i
\(179\) −2.18451 −0.163278 −0.0816389 0.996662i \(-0.526015\pi\)
−0.0816389 + 0.996662i \(0.526015\pi\)
\(180\) −0.140165 0.242772i −0.0104472 0.0180952i
\(181\) −11.5981 −0.862081 −0.431041 0.902333i \(-0.641853\pi\)
−0.431041 + 0.902333i \(0.641853\pi\)
\(182\) 0 0
\(183\) −5.27337 −0.389819
\(184\) −2.27590 3.94198i −0.167782 0.290606i
\(185\) 0.830527 0.0610616
\(186\) 9.84014 17.0436i 0.721514 1.24970i
\(187\) −3.64590 + 6.31488i −0.266614 + 0.461790i
\(188\) 0.0726885 + 0.125900i 0.00530135 + 0.00918221i
\(189\) 0 0
\(190\) −1.50934 −0.109499
\(191\) 17.7592 1.28501 0.642506 0.766281i \(-0.277895\pi\)
0.642506 + 0.766281i \(0.277895\pi\)
\(192\) −13.5829 −0.980264
\(193\) 22.6379 1.62951 0.814756 0.579804i \(-0.196871\pi\)
0.814756 + 0.579804i \(0.196871\pi\)
\(194\) −0.740517 + 1.28261i −0.0531660 + 0.0920863i
\(195\) 0.572172 4.48200i 0.0409741 0.320962i
\(196\) 0 0
\(197\) −10.0032 + 17.3260i −0.712696 + 1.23442i 0.251146 + 0.967949i \(0.419193\pi\)
−0.963842 + 0.266476i \(0.914141\pi\)
\(198\) 1.75859 + 3.04596i 0.124977 + 0.216467i
\(199\) 0.924426 1.60115i 0.0655309 0.113503i −0.831398 0.555677i \(-0.812459\pi\)
0.896929 + 0.442174i \(0.145793\pi\)
\(200\) 5.96913 + 10.3388i 0.422081 + 0.731066i
\(201\) 16.1015 1.13571
\(202\) −2.23572 3.87237i −0.157304 0.272459i
\(203\) 0 0
\(204\) 1.59421 + 2.76126i 0.111617 + 0.193327i
\(205\) −0.399447 0.691863i −0.0278986 0.0483218i
\(206\) −0.804005 −0.0560177
\(207\) −1.34888 2.33633i −0.0937539 0.162386i
\(208\) 12.9903 + 9.88699i 0.900713 + 0.685540i
\(209\) 2.56085 0.177138
\(210\) 0 0
\(211\) 8.08474 14.0032i 0.556576 0.964019i −0.441203 0.897407i \(-0.645448\pi\)
0.997779 0.0666110i \(-0.0212187\pi\)
\(212\) 2.57920 0.177140
\(213\) 7.02150 + 12.1616i 0.481105 + 0.833299i
\(214\) −14.6925 + 25.4481i −1.00436 + 1.73960i
\(215\) −6.81310 −0.464650
\(216\) 8.07020 0.549108
\(217\) 0 0
\(218\) −4.35884 + 7.54973i −0.295218 + 0.511332i
\(219\) −17.4043 30.1451i −1.17607 2.03701i
\(220\) −0.140165 0.242772i −0.00944989 0.0163677i
\(221\) −2.18921 + 17.1487i −0.147262 + 1.15355i
\(222\) −2.27820 + 3.94595i −0.152902 + 0.264835i
\(223\) 6.21589 10.7662i 0.416247 0.720961i −0.579312 0.815106i \(-0.696679\pi\)
0.995558 + 0.0941455i \(0.0300119\pi\)
\(224\) 0 0
\(225\) 3.53779 + 6.12763i 0.235853 + 0.408509i
\(226\) 3.91568 6.78216i 0.260467 0.451142i
\(227\) −0.617487 + 1.06952i −0.0409841 + 0.0709865i −0.885790 0.464087i \(-0.846383\pi\)
0.844806 + 0.535073i \(0.179716\pi\)
\(228\) 0.559881 0.969743i 0.0370790 0.0642228i
\(229\) −3.27757 + 5.67692i −0.216588 + 0.375141i −0.953763 0.300561i \(-0.902826\pi\)
0.737175 + 0.675702i \(0.236159\pi\)
\(230\) 0.795020 + 1.37702i 0.0524221 + 0.0907977i
\(231\) 0 0
\(232\) −8.84282 + 15.3162i −0.580559 + 1.00556i
\(233\) −3.14944 + 5.45498i −0.206326 + 0.357368i −0.950555 0.310558i \(-0.899484\pi\)
0.744228 + 0.667925i \(0.232818\pi\)
\(234\) 6.63545 + 5.05029i 0.433773 + 0.330148i
\(235\) 0.136984 + 0.237263i 0.00893584 + 0.0154773i
\(236\) 1.85706 + 3.21653i 0.120885 + 0.209378i
\(237\) −15.9065 + 27.5509i −1.03324 + 1.78962i
\(238\) 0 0
\(239\) −18.9193 −1.22379 −0.611895 0.790939i \(-0.709592\pi\)
−0.611895 + 0.790939i \(0.709592\pi\)
\(240\) 5.67397 0.366253
\(241\) −11.1484 + 19.3096i −0.718131 + 1.24384i 0.243609 + 0.969874i \(0.421669\pi\)
−0.961740 + 0.273965i \(0.911665\pi\)
\(242\) −6.60567 11.4414i −0.424628 0.735478i
\(243\) 14.4835 0.929118
\(244\) −0.387839 + 0.671757i −0.0248289 + 0.0430048i
\(245\) 0 0
\(246\) 4.38285 0.279440
\(247\) 5.60011 2.34544i 0.356326 0.149237i
\(248\) 7.80861 + 13.5249i 0.495847 + 0.858833i
\(249\) −21.5219 −1.36389
\(250\) −4.32597 7.49280i −0.273598 0.473886i
\(251\) 3.47657 + 6.02160i 0.219439 + 0.380080i 0.954637 0.297773i \(-0.0962438\pi\)
−0.735197 + 0.677853i \(0.762910\pi\)
\(252\) 0 0
\(253\) −1.34888 2.33633i −0.0848036 0.146884i
\(254\) 13.6920 0.859113
\(255\) 3.00435 + 5.20368i 0.188139 + 0.325867i
\(256\) −3.66603 + 6.34975i −0.229127 + 0.396860i
\(257\) −10.5776 18.3209i −0.659811 1.14283i −0.980664 0.195697i \(-0.937303\pi\)
0.320853 0.947129i \(-0.396030\pi\)
\(258\) 18.6888 32.3700i 1.16352 2.01527i
\(259\) 0 0
\(260\) −0.528865 0.402523i −0.0327988 0.0249634i
\(261\) −5.24097 + 9.07763i −0.324408 + 0.561891i
\(262\) −10.3388 −0.638735
\(263\) −8.42992 −0.519811 −0.259906 0.965634i \(-0.583691\pi\)
−0.259906 + 0.965634i \(0.583691\pi\)
\(264\) −8.29687 −0.510637
\(265\) 4.86060 0.298584
\(266\) 0 0
\(267\) 17.5253 + 30.3547i 1.07253 + 1.85768i
\(268\) 1.18421 2.05111i 0.0723371 0.125292i
\(269\) 2.91519 5.04926i 0.177743 0.307859i −0.763364 0.645968i \(-0.776454\pi\)
0.941107 + 0.338109i \(0.109787\pi\)
\(270\) −2.81909 −0.171565
\(271\) −9.21497 15.9608i −0.559769 0.969549i −0.997515 0.0704502i \(-0.977556\pi\)
0.437746 0.899099i \(-0.355777\pi\)
\(272\) −21.7093 −1.31632
\(273\) 0 0
\(274\) 21.4058 1.29317
\(275\) 3.53779 + 6.12763i 0.213337 + 0.369510i
\(276\) −1.17963 −0.0710054
\(277\) 3.09154 5.35470i 0.185752 0.321733i −0.758077 0.652165i \(-0.773861\pi\)
0.943830 + 0.330432i \(0.107194\pi\)
\(278\) 13.1442 22.7665i 0.788340 1.36544i
\(279\) 4.62802 + 8.01596i 0.277072 + 0.479903i
\(280\) 0 0
\(281\) −5.64049 −0.336483 −0.168242 0.985746i \(-0.553809\pi\)
−0.168242 + 0.985746i \(0.553809\pi\)
\(282\) −1.50303 −0.0895039
\(283\) −16.4554 −0.978173 −0.489086 0.872235i \(-0.662670\pi\)
−0.489086 + 0.872235i \(0.662670\pi\)
\(284\) 2.06563 0.122573
\(285\) 1.05512 1.82751i 0.0624996 0.108253i
\(286\) 6.63545 + 5.05029i 0.392362 + 0.298630i
\(287\) 0 0
\(288\) −1.33353 + 2.30973i −0.0785787 + 0.136102i
\(289\) −2.99502 5.18752i −0.176177 0.305148i
\(290\) 3.08898 5.35028i 0.181391 0.314179i
\(291\) −1.03533 1.79324i −0.0606919 0.105121i
\(292\) −5.12011 −0.299632
\(293\) −15.3086 26.5152i −0.894335 1.54903i −0.834625 0.550819i \(-0.814316\pi\)
−0.0597104 0.998216i \(-0.519018\pi\)
\(294\) 0 0
\(295\) 3.49970 + 6.06166i 0.203760 + 0.352923i
\(296\) −1.80785 3.13130i −0.105079 0.182003i
\(297\) 4.78306 0.277541
\(298\) −13.0218 22.5544i −0.754331 1.30654i
\(299\) −5.08957 3.87371i −0.294338 0.224023i
\(300\) 3.09388 0.178625
\(301\) 0 0
\(302\) 12.0122 20.8057i 0.691223 1.19723i
\(303\) 6.25156 0.359143
\(304\) 3.81212 + 6.60278i 0.218640 + 0.378696i
\(305\) −0.730896 + 1.26595i −0.0418510 + 0.0724880i
\(306\) −11.0892 −0.633925
\(307\) −9.96020 −0.568459 −0.284229 0.958756i \(-0.591738\pi\)
−0.284229 + 0.958756i \(0.591738\pi\)
\(308\) 0 0
\(309\) 0.562044 0.973489i 0.0319736 0.0553799i
\(310\) −2.72771 4.72454i −0.154924 0.268336i
\(311\) −13.8734 24.0294i −0.786687 1.36258i −0.927986 0.372615i \(-0.878461\pi\)
0.141299 0.989967i \(-0.454872\pi\)
\(312\) −18.1437 + 7.59898i −1.02719 + 0.430207i
\(313\) 8.26136 14.3091i 0.466960 0.808798i −0.532328 0.846538i \(-0.678683\pi\)
0.999288 + 0.0377401i \(0.0120159\pi\)
\(314\) −2.87693 + 4.98300i −0.162355 + 0.281207i
\(315\) 0 0
\(316\) 2.33975 + 4.05256i 0.131621 + 0.227974i
\(317\) −11.8396 + 20.5069i −0.664980 + 1.15178i 0.314310 + 0.949320i \(0.398227\pi\)
−0.979291 + 0.202459i \(0.935107\pi\)
\(318\) −13.3330 + 23.0934i −0.747675 + 1.29501i
\(319\) −5.24097 + 9.07763i −0.293438 + 0.508250i
\(320\) −1.88261 + 3.26078i −0.105241 + 0.182283i
\(321\) −20.5417 35.5793i −1.14653 1.98584i
\(322\) 0 0
\(323\) −4.03701 + 6.99230i −0.224625 + 0.389062i
\(324\) 1.75916 3.04696i 0.0977312 0.169275i
\(325\) 13.3487 + 10.1598i 0.740452 + 0.563564i
\(326\) 1.30445 + 2.25938i 0.0722470 + 0.125136i
\(327\) −6.09414 10.5554i −0.337007 0.583713i
\(328\) −1.73900 + 3.01203i −0.0960202 + 0.166312i
\(329\) 0 0
\(330\) 2.89827 0.159545
\(331\) 7.95209 0.437086 0.218543 0.975827i \(-0.429870\pi\)
0.218543 + 0.975827i \(0.429870\pi\)
\(332\) −1.58286 + 2.74160i −0.0868710 + 0.150465i
\(333\) −1.07148 1.85586i −0.0587168 0.101700i
\(334\) −19.2410 −1.05282
\(335\) 2.23168 3.86539i 0.121930 0.211189i
\(336\) 0 0
\(337\) −7.91326 −0.431063 −0.215531 0.976497i \(-0.569148\pi\)
−0.215531 + 0.976497i \(0.569148\pi\)
\(338\) 19.1360 + 4.96675i 1.04086 + 0.270156i
\(339\) 5.47456 + 9.48221i 0.297337 + 0.515003i
\(340\) 0.883839 0.0479329
\(341\) 4.62802 + 8.01596i 0.250621 + 0.434089i
\(342\) 1.94724 + 3.37271i 0.105294 + 0.182375i
\(343\) 0 0
\(344\) 14.8305 + 25.6871i 0.799605 + 1.38496i
\(345\) −2.22305 −0.119685
\(346\) −8.73488 15.1292i −0.469590 0.813353i
\(347\) −3.56786 + 6.17971i −0.191533 + 0.331744i −0.945758 0.324871i \(-0.894679\pi\)
0.754226 + 0.656615i \(0.228012\pi\)
\(348\) 2.29168 + 3.96930i 0.122847 + 0.212777i
\(349\) 0.688402 1.19235i 0.0368493 0.0638249i −0.847013 0.531573i \(-0.821601\pi\)
0.883862 + 0.467748i \(0.154935\pi\)
\(350\) 0 0
\(351\) 10.4597 4.38073i 0.558296 0.233826i
\(352\) −1.33353 + 2.30973i −0.0710771 + 0.123109i
\(353\) −0.693215 −0.0368961 −0.0184481 0.999830i \(-0.505873\pi\)
−0.0184481 + 0.999830i \(0.505873\pi\)
\(354\) −38.3997 −2.04092
\(355\) 3.89276 0.206606
\(356\) 5.15571 0.273252
\(357\) 0 0
\(358\) −1.66107 2.87706i −0.0877904 0.152057i
\(359\) 2.90182 5.02611i 0.153152 0.265268i −0.779232 0.626735i \(-0.784391\pi\)
0.932385 + 0.361467i \(0.117724\pi\)
\(360\) −1.14996 + 1.99178i −0.0606081 + 0.104976i
\(361\) −16.1644 −0.850760
\(362\) −8.81905 15.2750i −0.463519 0.802839i
\(363\) 18.4709 0.969472
\(364\) 0 0
\(365\) −9.64902 −0.505053
\(366\) −4.00980 6.94518i −0.209596 0.363030i
\(367\) −7.35157 −0.383749 −0.191874 0.981420i \(-0.561457\pi\)
−0.191874 + 0.981420i \(0.561457\pi\)
\(368\) 4.01593 6.95580i 0.209345 0.362596i
\(369\) −1.03067 + 1.78518i −0.0536546 + 0.0929325i
\(370\) 0.631522 + 1.09383i 0.0328313 + 0.0568654i
\(371\) 0 0
\(372\) 4.04731 0.209843
\(373\) 18.3988 0.952656 0.476328 0.879268i \(-0.341967\pi\)
0.476328 + 0.879268i \(0.341967\pi\)
\(374\) −11.0892 −0.573407
\(375\) 12.0964 0.624654
\(376\) 0.596361 1.03293i 0.0307550 0.0532692i
\(377\) −3.14698 + 24.6512i −0.162078 + 1.26960i
\(378\) 0 0
\(379\) 2.42550 4.20110i 0.124590 0.215796i −0.796983 0.604002i \(-0.793572\pi\)
0.921573 + 0.388206i \(0.126905\pi\)
\(380\) −0.155201 0.268815i −0.00796162 0.0137899i
\(381\) −9.57147 + 16.5783i −0.490361 + 0.849331i
\(382\) 13.5039 + 23.3894i 0.690918 + 1.19671i
\(383\) 22.8205 1.16607 0.583037 0.812446i \(-0.301864\pi\)
0.583037 + 0.812446i \(0.301864\pi\)
\(384\) −14.0571 24.3476i −0.717349 1.24249i
\(385\) 0 0
\(386\) 17.2136 + 29.8148i 0.876147 + 1.51753i
\(387\) 8.78973 + 15.2243i 0.446807 + 0.773893i
\(388\) −0.304579 −0.0154627
\(389\) 10.1561 + 17.5908i 0.514933 + 0.891891i 0.999850 + 0.0173304i \(0.00551672\pi\)
−0.484916 + 0.874561i \(0.661150\pi\)
\(390\) 6.33799 2.65448i 0.320937 0.134415i
\(391\) 8.50569 0.430151
\(392\) 0 0
\(393\) 7.22741 12.5182i 0.364575 0.631462i
\(394\) −30.4251 −1.53279
\(395\) 4.40933 + 7.63719i 0.221858 + 0.384268i
\(396\) −0.361659 + 0.626411i −0.0181740 + 0.0314783i
\(397\) 34.1377 1.71332 0.856662 0.515878i \(-0.172534\pi\)
0.856662 + 0.515878i \(0.172534\pi\)
\(398\) 2.81169 0.140937
\(399\) 0 0
\(400\) −10.5328 + 18.2434i −0.526640 + 0.912168i
\(401\) 1.51298 + 2.62056i 0.0755547 + 0.130865i 0.901327 0.433139i \(-0.142594\pi\)
−0.825773 + 0.564003i \(0.809261\pi\)
\(402\) 12.2433 + 21.2061i 0.610642 + 1.05766i
\(403\) 17.4623 + 13.2907i 0.869860 + 0.662057i
\(404\) 0.459782 0.796365i 0.0228750 0.0396207i
\(405\) 3.31520 5.74209i 0.164734 0.285327i
\(406\) 0 0
\(407\) −1.07148 1.85586i −0.0531114 0.0919916i
\(408\) 13.0795 22.6543i 0.647530 1.12155i
\(409\) 2.69162 4.66203i 0.133092 0.230523i −0.791775 0.610813i \(-0.790843\pi\)
0.924867 + 0.380291i \(0.124176\pi\)
\(410\) 0.607469 1.05217i 0.0300008 0.0519628i
\(411\) −14.9638 + 25.9181i −0.738111 + 1.27845i
\(412\) −0.0826731 0.143194i −0.00407301 0.00705466i
\(413\) 0 0
\(414\) 2.05135 3.55304i 0.100818 0.174622i
\(415\) −2.98296 + 5.16664i −0.146428 + 0.253620i
\(416\) −0.800725 + 6.27232i −0.0392588 + 0.307526i
\(417\) 18.3771 + 31.8301i 0.899932 + 1.55873i
\(418\) 1.94724 + 3.37271i 0.0952425 + 0.164965i
\(419\) 2.94117 5.09426i 0.143686 0.248871i −0.785196 0.619247i \(-0.787438\pi\)
0.928882 + 0.370376i \(0.120771\pi\)
\(420\) 0 0
\(421\) −28.7614 −1.40174 −0.700872 0.713287i \(-0.747206\pi\)
−0.700872 + 0.713287i \(0.747206\pi\)
\(422\) 24.5901 1.19703
\(423\) 0.353452 0.612196i 0.0171854 0.0297660i
\(424\) −10.5803 18.3257i −0.513826 0.889973i
\(425\) −22.3083 −1.08211
\(426\) −10.6781 + 18.4950i −0.517356 + 0.896087i
\(427\) 0 0
\(428\) −6.04311 −0.292105
\(429\) −10.7534 + 4.50377i −0.519181 + 0.217444i
\(430\) −5.18059 8.97305i −0.249830 0.432719i
\(431\) 8.38588 0.403934 0.201967 0.979392i \(-0.435267\pi\)
0.201967 + 0.979392i \(0.435267\pi\)
\(432\) 7.12013 + 12.3324i 0.342567 + 0.593344i
\(433\) −13.7996 23.9017i −0.663168 1.14864i −0.979779 0.200085i \(-0.935878\pi\)
0.316611 0.948556i \(-0.397455\pi\)
\(434\) 0 0
\(435\) 4.31874 + 7.48028i 0.207068 + 0.358652i
\(436\) −1.79282 −0.0858604
\(437\) −1.49358 2.58696i −0.0714478 0.123751i
\(438\) 26.4679 45.8438i 1.26469 2.19050i
\(439\) 15.5869 + 26.9973i 0.743921 + 1.28851i 0.950697 + 0.310121i \(0.100369\pi\)
−0.206776 + 0.978388i \(0.566297\pi\)
\(440\) −1.14996 + 1.99178i −0.0548221 + 0.0949546i
\(441\) 0 0
\(442\) −24.2500 + 10.1564i −1.15345 + 0.483090i
\(443\) 11.7941 20.4281i 0.560357 0.970566i −0.437109 0.899409i \(-0.643997\pi\)
0.997465 0.0711573i \(-0.0226692\pi\)
\(444\) −0.937036 −0.0444698
\(445\) 9.71611 0.460588
\(446\) 18.9059 0.895221
\(447\) 36.4118 1.72222
\(448\) 0 0
\(449\) −1.41328 2.44787i −0.0666968 0.115522i 0.830749 0.556648i \(-0.187913\pi\)
−0.897445 + 0.441125i \(0.854579\pi\)
\(450\) −5.38018 + 9.31874i −0.253624 + 0.439289i
\(451\) −1.03067 + 1.78518i −0.0485324 + 0.0840607i
\(452\) 1.61054 0.0757536
\(453\) 16.7944 + 29.0887i 0.789068 + 1.36671i
\(454\) −1.87812 −0.0881444
\(455\) 0 0
\(456\) −9.18691 −0.430217
\(457\) 18.8716 + 32.6866i 0.882776 + 1.52901i 0.848242 + 0.529609i \(0.177661\pi\)
0.0345338 + 0.999404i \(0.489005\pi\)
\(458\) −9.96888 −0.465815
\(459\) −7.54017 + 13.0599i −0.351945 + 0.609586i
\(460\) −0.163498 + 0.283188i −0.00762315 + 0.0132037i
\(461\) 17.3293 + 30.0152i 0.807106 + 1.39795i 0.914860 + 0.403771i \(0.132301\pi\)
−0.107754 + 0.994178i \(0.534366\pi\)
\(462\) 0 0
\(463\) 18.5114 0.860296 0.430148 0.902758i \(-0.358461\pi\)
0.430148 + 0.902758i \(0.358461\pi\)
\(464\) −31.2071 −1.44875
\(465\) 7.62730 0.353707
\(466\) −9.57916 −0.443746
\(467\) 3.31392 5.73987i 0.153350 0.265610i −0.779107 0.626891i \(-0.784327\pi\)
0.932457 + 0.361281i \(0.117661\pi\)
\(468\) −0.217161 + 1.70108i −0.0100383 + 0.0786326i
\(469\) 0 0
\(470\) −0.208321 + 0.360823i −0.00960915 + 0.0166435i
\(471\) −4.02227 6.96678i −0.185337 0.321012i
\(472\) 15.2360 26.3895i 0.701293 1.21468i
\(473\) 8.78973 + 15.2243i 0.404152 + 0.700012i
\(474\) −48.3804 −2.22219
\(475\) 3.91730 + 6.78497i 0.179738 + 0.311316i
\(476\) 0 0
\(477\) −6.27076 10.8613i −0.287118 0.497304i
\(478\) −14.3860 24.9173i −0.658001 1.13969i
\(479\) 17.4526 0.797430 0.398715 0.917075i \(-0.369456\pi\)
0.398715 + 0.917075i \(0.369456\pi\)
\(480\) 1.09887 + 1.90330i 0.0501564 + 0.0868734i
\(481\) −4.04289 3.07707i −0.184340 0.140302i
\(482\) −33.9083 −1.54448
\(483\) 0 0
\(484\) 1.35848 2.35295i 0.0617489 0.106952i
\(485\) −0.573990 −0.0260635
\(486\) 11.0131 + 19.0752i 0.499563 + 0.865269i
\(487\) 17.7569 30.7558i 0.804641 1.39368i −0.111892 0.993720i \(-0.535691\pi\)
0.916533 0.399959i \(-0.130976\pi\)
\(488\) 6.36393 0.288081
\(489\) −3.64754 −0.164948
\(490\) 0 0
\(491\) 14.9059 25.8178i 0.672695 1.16514i −0.304442 0.952531i \(-0.598470\pi\)
0.977137 0.212611i \(-0.0681966\pi\)
\(492\) 0.450674 + 0.780590i 0.0203179 + 0.0351917i
\(493\) −16.5241 28.6205i −0.744207 1.28900i
\(494\) 7.34726 + 5.59206i 0.330569 + 0.251599i
\(495\) −0.681558 + 1.18049i −0.0306338 + 0.0530592i
\(496\) −13.7787 + 23.8653i −0.618680 + 1.07159i
\(497\) 0 0
\(498\) −16.3649 28.3449i −0.733331 1.27017i
\(499\) 3.75483 6.50355i 0.168089 0.291139i −0.769659 0.638455i \(-0.779574\pi\)
0.937748 + 0.347316i \(0.112907\pi\)
\(500\) 0.889649 1.54092i 0.0397863 0.0689119i
\(501\) 13.4505 23.2970i 0.600925 1.04083i
\(502\) −5.28708 + 9.15750i −0.235974 + 0.408719i
\(503\) 0.492171 + 0.852466i 0.0219448 + 0.0380096i 0.876789 0.480875i \(-0.159681\pi\)
−0.854844 + 0.518884i \(0.826348\pi\)
\(504\) 0 0
\(505\) 0.866474 1.50078i 0.0385576 0.0667837i
\(506\) 2.05135 3.55304i 0.0911934 0.157952i
\(507\) −19.3909 + 19.6978i −0.861179 + 0.874811i
\(508\) 1.40790 + 2.43856i 0.0624655 + 0.108193i
\(509\) 6.48958 + 11.2403i 0.287646 + 0.498217i 0.973247 0.229760i \(-0.0737941\pi\)
−0.685602 + 0.727977i \(0.740461\pi\)
\(510\) −4.56893 + 7.91362i −0.202316 + 0.350421i
\(511\) 0 0
\(512\) 15.2950 0.675949
\(513\) 5.29616 0.233831
\(514\) 16.0861 27.8619i 0.709527 1.22894i
\(515\) −0.155800 0.269854i −0.00686538 0.0118912i
\(516\) 7.68683 0.338394
\(517\) 0.353452 0.612196i 0.0155448 0.0269244i
\(518\) 0 0
\(519\) 24.4247 1.07212
\(520\) −0.690500 + 5.40890i −0.0302804 + 0.237196i
\(521\) −9.70730 16.8135i −0.425285 0.736614i 0.571162 0.820837i \(-0.306493\pi\)
−0.996447 + 0.0842226i \(0.973159\pi\)
\(522\) −15.9407 −0.697704
\(523\) 13.6360 + 23.6182i 0.596259 + 1.03275i 0.993368 + 0.114979i \(0.0366801\pi\)
−0.397109 + 0.917771i \(0.629987\pi\)
\(524\) −1.06311 1.84135i −0.0464420 0.0804399i
\(525\) 0 0
\(526\) −6.41000 11.1024i −0.279489 0.484090i
\(527\) −29.1830 −1.27123
\(528\) −7.32011 12.6788i −0.318567 0.551774i
\(529\) 9.92656 17.1933i 0.431590 0.747535i
\(530\) 3.69593 + 6.40154i 0.160541 + 0.278065i
\(531\) 9.03008 15.6406i 0.391872 0.678742i
\(532\) 0 0
\(533\) −0.618874 + 4.84783i −0.0268064 + 0.209983i
\(534\) −26.6520 + 46.1626i −1.15334 + 1.99765i
\(535\) −11.3884 −0.492365
\(536\) −19.4313 −0.839305
\(537\) 4.64473 0.200435
\(538\) 8.86670 0.382271
\(539\) 0 0
\(540\) −0.289878 0.502083i −0.0124743 0.0216062i
\(541\) 15.0495 26.0665i 0.647029 1.12069i −0.336799 0.941576i \(-0.609344\pi\)
0.983829 0.179111i \(-0.0573223\pi\)
\(542\) 14.0139 24.2727i 0.601947 1.04260i
\(543\) 24.6600 1.05826
\(544\) −4.20442 7.28228i −0.180263 0.312225i
\(545\) −3.37863 −0.144724
\(546\) 0 0
\(547\) −26.1451 −1.11788 −0.558942 0.829207i \(-0.688793\pi\)
−0.558942 + 0.829207i \(0.688793\pi\)
\(548\) 2.20108 + 3.81238i 0.0940255 + 0.162857i
\(549\) 3.77178 0.160976
\(550\) −5.38018 + 9.31874i −0.229411 + 0.397352i
\(551\) −5.80319 + 10.0514i −0.247224 + 0.428205i
\(552\) 4.83905 + 8.38147i 0.205963 + 0.356739i
\(553\) 0 0
\(554\) 9.40305 0.399497
\(555\) −1.76588 −0.0749573
\(556\) 5.40631 0.229279
\(557\) 17.9063 0.758716 0.379358 0.925250i \(-0.376145\pi\)
0.379358 + 0.925250i \(0.376145\pi\)
\(558\) −7.03817 + 12.1905i −0.297949 + 0.516063i
\(559\) 33.1652 + 25.2423i 1.40274 + 1.06764i
\(560\) 0 0
\(561\) 7.75195 13.4268i 0.327287 0.566878i
\(562\) −4.28895 7.42868i −0.180919 0.313360i
\(563\) −15.8275 + 27.4140i −0.667048 + 1.15536i 0.311678 + 0.950188i \(0.399109\pi\)
−0.978726 + 0.205173i \(0.934224\pi\)
\(564\) −0.154551 0.267690i −0.00650777 0.0112718i
\(565\) 3.03512 0.127689
\(566\) −12.5125 21.6722i −0.525939 0.910953i
\(567\) 0 0
\(568\) −8.47358 14.6767i −0.355544 0.615820i
\(569\) 13.0555 + 22.6129i 0.547317 + 0.947981i 0.998457 + 0.0555278i \(0.0176841\pi\)
−0.451140 + 0.892453i \(0.648983\pi\)
\(570\) 3.20918 0.134418
\(571\) −6.65205 11.5217i −0.278380 0.482168i 0.692602 0.721320i \(-0.256464\pi\)
−0.970982 + 0.239152i \(0.923131\pi\)
\(572\) −0.217161 + 1.70108i −0.00907994 + 0.0711259i
\(573\) −37.7599 −1.57744
\(574\) 0 0
\(575\) 4.12674 7.14773i 0.172097 0.298081i
\(576\) 9.71520 0.404800
\(577\) −8.38564 14.5244i −0.349099 0.604657i 0.636991 0.770871i \(-0.280179\pi\)
−0.986090 + 0.166214i \(0.946846\pi\)
\(578\) 4.55474 7.88904i 0.189452 0.328141i
\(579\) −48.1329 −2.00034
\(580\) 1.27052 0.0527554
\(581\) 0 0
\(582\) 1.57450 2.72711i 0.0652650 0.113042i
\(583\) −6.27076 10.8613i −0.259708 0.449828i
\(584\) 21.0036 + 36.3792i 0.869133 + 1.50538i
\(585\) −0.409246 + 3.20575i −0.0169203 + 0.132541i
\(586\) 23.2808 40.3236i 0.961723 1.66575i
\(587\) −5.03261 + 8.71673i −0.207718 + 0.359778i −0.950995 0.309205i \(-0.899937\pi\)
0.743277 + 0.668983i \(0.233270\pi\)
\(588\) 0 0
\(589\) 5.12448 + 8.87587i 0.211151 + 0.365724i
\(590\) −5.32225 + 9.21841i −0.219114 + 0.379516i
\(591\) 21.2688 36.8387i 0.874883 1.51534i
\(592\) 3.19004 5.52532i 0.131110 0.227089i
\(593\) 19.7161 34.1493i 0.809643 1.40234i −0.103468 0.994633i \(-0.532994\pi\)
0.913111 0.407710i \(-0.133673\pi\)
\(594\) 3.63697 + 6.29942i 0.149227 + 0.258468i
\(595\) 0 0
\(596\) 2.67797 4.63838i 0.109694 0.189995i
\(597\) −1.96553 + 3.40439i −0.0804436 + 0.139332i
\(598\) 1.23175 9.64863i 0.0503698 0.394562i
\(599\) −6.88601 11.9269i −0.281355 0.487321i 0.690364 0.723462i \(-0.257450\pi\)
−0.971719 + 0.236142i \(0.924117\pi\)
\(600\) −12.6916 21.9825i −0.518133 0.897433i
\(601\) 16.6312 28.8060i 0.678399 1.17502i −0.297064 0.954858i \(-0.596007\pi\)
0.975463 0.220164i \(-0.0706592\pi\)
\(602\) 0 0
\(603\) −11.5166 −0.468991
\(604\) 4.94068 0.201034
\(605\) 2.56009 4.43421i 0.104083 0.180276i
\(606\) 4.75360 + 8.23348i 0.193102 + 0.334462i
\(607\) −43.9649 −1.78448 −0.892240 0.451562i \(-0.850867\pi\)
−0.892240 + 0.451562i \(0.850867\pi\)
\(608\) −1.47658 + 2.55751i −0.0598831 + 0.103721i
\(609\) 0 0
\(610\) −2.22305 −0.0900088
\(611\) 0.212233 1.66248i 0.00858602 0.0672568i
\(612\) −1.14026 1.97499i −0.0460923 0.0798342i
\(613\) 2.70091 0.109089 0.0545443 0.998511i \(-0.482629\pi\)
0.0545443 + 0.998511i \(0.482629\pi\)
\(614\) −7.57361 13.1179i −0.305646 0.529394i
\(615\) 0.849310 + 1.47105i 0.0342475 + 0.0593184i
\(616\) 0 0
\(617\) −3.00208 5.19975i −0.120859 0.209334i 0.799248 0.601002i \(-0.205232\pi\)
−0.920107 + 0.391668i \(0.871898\pi\)
\(618\) 1.70948 0.0687655
\(619\) −6.68204 11.5736i −0.268574 0.465184i 0.699920 0.714221i \(-0.253219\pi\)
−0.968494 + 0.249038i \(0.919886\pi\)
\(620\) 0.560963 0.971616i 0.0225288 0.0390210i
\(621\) −2.78966 4.83183i −0.111945 0.193895i
\(622\) 21.0983 36.5433i 0.845963 1.46525i
\(623\) 0 0
\(624\) −27.6201 21.0218i −1.10569 0.841547i
\(625\) −9.95497 + 17.2425i −0.398199 + 0.689701i
\(626\) 25.1273 1.00429
\(627\) −5.44491 −0.217449
\(628\) −1.18330 −0.0472188
\(629\) 6.75647 0.269398
\(630\) 0 0
\(631\) −20.2228 35.0270i −0.805059 1.39440i −0.916251 0.400604i \(-0.868800\pi\)
0.111192 0.993799i \(-0.464533\pi\)
\(632\) 19.1961 33.2486i 0.763579 1.32256i
\(633\) −17.1899 + 29.7737i −0.683236 + 1.18340i
\(634\) −36.0108 −1.43017
\(635\) 2.65324 + 4.59554i 0.105291 + 0.182369i
\(636\) −5.48393 −0.217452
\(637\) 0 0
\(638\) −15.9407 −0.631097
\(639\) −5.02213 8.69859i −0.198672 0.344111i
\(640\) −7.79334 −0.308059
\(641\) −5.10991 + 8.85062i −0.201829 + 0.349578i −0.949118 0.314921i \(-0.898022\pi\)
0.747289 + 0.664500i \(0.231355\pi\)
\(642\) 31.2393 54.1081i 1.23292 2.13548i
\(643\) 15.9014 + 27.5420i 0.627088 + 1.08615i 0.988133 + 0.153600i \(0.0490868\pi\)
−0.361045 + 0.932548i \(0.617580\pi\)
\(644\) 0 0
\(645\) 14.4861 0.570389
\(646\) −12.2787 −0.483101
\(647\) 34.5233 1.35725 0.678626 0.734484i \(-0.262576\pi\)
0.678626 + 0.734484i \(0.262576\pi\)
\(648\) −28.8655 −1.13394
\(649\) 9.03008 15.6406i 0.354462 0.613946i
\(650\) −3.23057 + 25.3060i −0.126713 + 0.992582i
\(651\) 0 0
\(652\) −0.268265 + 0.464649i −0.0105061 + 0.0181970i
\(653\) −5.05899 8.76244i −0.197974 0.342901i 0.749898 0.661554i \(-0.230103\pi\)
−0.947871 + 0.318653i \(0.896769\pi\)
\(654\) 9.26781 16.0523i 0.362400 0.627695i
\(655\) −2.00346 3.47009i −0.0782816 0.135588i
\(656\) −6.13709 −0.239613
\(657\) 12.4484 + 21.5613i 0.485659 + 0.841185i
\(658\) 0 0
\(659\) 17.3841 + 30.1101i 0.677187 + 1.17292i 0.975824 + 0.218556i \(0.0701345\pi\)
−0.298637 + 0.954367i \(0.596532\pi\)
\(660\) 0.298019 + 0.516185i 0.0116004 + 0.0200925i
\(661\) 16.5615 0.644168 0.322084 0.946711i \(-0.395617\pi\)
0.322084 + 0.946711i \(0.395617\pi\)
\(662\) 6.04666 + 10.4731i 0.235010 + 0.407050i
\(663\) 4.65471 36.4617i 0.180774 1.41606i
\(664\) 25.9727 1.00794
\(665\) 0 0
\(666\) 1.62948 2.82234i 0.0631411 0.109364i
\(667\) 12.2269 0.473428
\(668\) −1.97848 3.42683i −0.0765498 0.132588i
\(669\) −13.2163 + 22.8913i −0.510972 + 0.885029i
\(670\) 6.78777 0.262234
\(671\) 3.77178 0.145608
\(672\) 0 0
\(673\) 20.9437 36.2756i 0.807321 1.39832i −0.107393 0.994217i \(-0.534250\pi\)
0.914713 0.404104i \(-0.132417\pi\)
\(674\) −6.01714 10.4220i −0.231771 0.401440i
\(675\) 7.31659 + 12.6727i 0.281616 + 0.487772i
\(676\) 1.08311 + 3.91885i 0.0416579 + 0.150725i
\(677\) −15.7858 + 27.3417i −0.606696 + 1.05083i 0.385085 + 0.922881i \(0.374172\pi\)
−0.991781 + 0.127947i \(0.959161\pi\)
\(678\) −8.32556 + 14.4203i −0.319741 + 0.553808i
\(679\) 0 0
\(680\) −3.62566 6.27983i −0.139038 0.240820i
\(681\) 1.31291 2.27402i 0.0503107 0.0871408i
\(682\) −7.03817 + 12.1905i −0.269505 + 0.466797i
\(683\) 13.1338 22.7484i 0.502551 0.870444i −0.497445 0.867496i \(-0.665728\pi\)
0.999996 0.00294809i \(-0.000938408\pi\)
\(684\) −0.400455 + 0.693609i −0.0153118 + 0.0265208i
\(685\) 4.14801 + 7.18457i 0.158487 + 0.274508i
\(686\) 0 0
\(687\) 6.96880 12.0703i 0.265876 0.460512i
\(688\) −26.1690 + 45.3261i −0.997686 + 1.72804i
\(689\) −23.6607 18.0083i −0.901400 0.686062i
\(690\) −1.69038 2.92783i −0.0643517 0.111460i
\(691\) 3.05047 + 5.28358i 0.116046 + 0.200997i 0.918197 0.396124i \(-0.129645\pi\)
−0.802152 + 0.597120i \(0.796311\pi\)
\(692\) 1.79635 3.11138i 0.0682872 0.118277i
\(693\) 0 0
\(694\) −10.8518 −0.411929
\(695\) 10.1884 0.386467
\(696\) 18.8017 32.5655i 0.712677 1.23439i
\(697\) −3.24957 5.62842i −0.123086 0.213192i
\(698\) 2.09381 0.0792518
\(699\) 6.69636 11.5984i 0.253280 0.438693i
\(700\) 0 0
\(701\) −20.5701 −0.776921 −0.388461 0.921465i \(-0.626993\pi\)
−0.388461 + 0.921465i \(0.626993\pi\)
\(702\) 13.7229 + 10.4446i 0.517939 + 0.394207i
\(703\) −1.18642 2.05495i −0.0447468 0.0775038i
\(704\) 9.71520 0.366155
\(705\) −0.291257 0.504471i −0.0109694 0.0189995i
\(706\) −0.527111 0.912984i −0.0198381 0.0343606i
\(707\) 0 0
\(708\) −3.94851 6.83902i −0.148394 0.257026i
\(709\) −43.1529 −1.62064 −0.810320 0.585988i \(-0.800707\pi\)
−0.810320 + 0.585988i \(0.800707\pi\)
\(710\) 2.96000 + 5.12687i 0.111087 + 0.192408i
\(711\) 11.3771 19.7058i 0.426676 0.739025i
\(712\) −21.1496 36.6322i −0.792615 1.37285i
\(713\) 5.39847 9.35042i 0.202174 0.350176i
\(714\) 0 0
\(715\) −0.409246 + 3.20575i −0.0153050 + 0.119888i
\(716\) 0.341605 0.591677i 0.0127664 0.0221120i
\(717\) 40.2265 1.50229
\(718\) 8.82603 0.329385
\(719\) −28.2084 −1.05200 −0.525999 0.850485i \(-0.676308\pi\)
−0.525999 + 0.850485i \(0.676308\pi\)
\(720\) −4.05831 −0.151244
\(721\) 0 0
\(722\) −12.2912 21.2890i −0.457432 0.792295i
\(723\) 23.7038 41.0562i 0.881555 1.52690i
\(724\) 1.81367 3.14136i 0.0674044 0.116748i
\(725\) −32.0682 −1.19098
\(726\) 14.0450 + 24.3267i 0.521260 + 0.902850i
\(727\) −19.5116 −0.723646 −0.361823 0.932247i \(-0.617845\pi\)
−0.361823 + 0.932247i \(0.617845\pi\)
\(728\) 0 0
\(729\) 2.95370 0.109396
\(730\) −7.33698 12.7080i −0.271554 0.470345i
\(731\) −55.4257 −2.04999
\(732\) 0.824628 1.42830i 0.0304791 0.0527914i
\(733\) −10.1833 + 17.6380i −0.376129 + 0.651475i −0.990495 0.137546i \(-0.956078\pi\)
0.614366 + 0.789021i \(0.289412\pi\)
\(734\) −5.59003 9.68222i −0.206332 0.357377i
\(735\) 0 0
\(736\) 3.11105 0.114675
\(737\) −11.5166 −0.424218
\(738\) −3.13484 −0.115395
\(739\) −10.4199 −0.383303 −0.191651 0.981463i \(-0.561384\pi\)
−0.191651 + 0.981463i \(0.561384\pi\)
\(740\) −0.129874 + 0.224949i −0.00477428 + 0.00826929i
\(741\) −11.9070 + 4.98691i −0.437415 + 0.183199i
\(742\) 0 0
\(743\) 8.70470 15.0770i 0.319344 0.553121i −0.661007 0.750380i \(-0.729871\pi\)
0.980351 + 0.197259i \(0.0632040\pi\)
\(744\) −16.6028 28.7568i −0.608687 1.05428i
\(745\) 5.04672 8.74118i 0.184898 0.320252i
\(746\) 13.9902 + 24.2318i 0.512219 + 0.887189i
\(747\) 15.3935 0.563220
\(748\) −1.14026 1.97499i −0.0416921 0.0722128i
\(749\) 0 0
\(750\) 9.19792 + 15.9313i 0.335861 + 0.581728i
\(751\) 0.907626 + 1.57205i 0.0331197 + 0.0573651i 0.882110 0.471043i \(-0.156122\pi\)
−0.848990 + 0.528408i \(0.822789\pi\)
\(752\) 2.10461 0.0767474
\(753\) −7.39193 12.8032i −0.269377 0.466575i
\(754\) −34.8593 + 14.5998i −1.26950 + 0.531694i
\(755\) 9.31088 0.338858
\(756\) 0 0
\(757\) −26.7814 + 46.3867i −0.973385 + 1.68595i −0.288220 + 0.957564i \(0.593063\pi\)
−0.685165 + 0.728388i \(0.740270\pi\)
\(758\) 7.37728 0.267955
\(759\) 2.86801 + 4.96754i 0.104102 + 0.180310i
\(760\) −1.27332 + 2.20545i −0.0461881 + 0.0800001i
\(761\) 3.68166 0.133460 0.0667300 0.997771i \(-0.478743\pi\)
0.0667300 + 0.997771i \(0.478743\pi\)
\(762\) −29.1121 −1.05462
\(763\) 0 0
\(764\) −2.77711 + 4.81010i −0.100472 + 0.174023i
\(765\) −2.14886 3.72193i −0.0776922 0.134567i
\(766\) 17.3524 + 30.0553i 0.626968 + 1.08594i
\(767\) 5.42218 42.4735i 0.195783 1.53363i
\(768\) 7.79476 13.5009i 0.281269 0.487172i
\(769\) −2.61897 + 4.53619i −0.0944424 + 0.163579i −0.909376 0.415976i \(-0.863440\pi\)
0.814933 + 0.579555i \(0.196773\pi\)
\(770\) 0 0
\(771\) 22.4902 + 38.9541i 0.809963 + 1.40290i
\(772\) −3.54002 + 6.13150i −0.127408 + 0.220677i
\(773\) 20.3069 35.1726i 0.730388 1.26507i −0.226329 0.974051i \(-0.572672\pi\)
0.956717 0.291019i \(-0.0939942\pi\)
\(774\) −13.3672 + 23.1527i −0.480474 + 0.832205i
\(775\) −14.1588 + 24.5238i −0.508601 + 0.880922i
\(776\) 1.24944 + 2.16409i 0.0448522 + 0.0776862i
\(777\) 0 0
\(778\) −15.4451 + 26.7517i −0.553733 + 0.959094i
\(779\) −1.14124 + 1.97668i −0.0408890 + 0.0708219i
\(780\) 1.12448 + 0.855850i 0.0402628 + 0.0306443i
\(781\) −5.02213 8.69859i −0.179706 0.311260i
\(782\) 6.46762 + 11.2022i 0.231281 + 0.400591i
\(783\) −10.8390 + 18.7737i −0.387353 + 0.670916i
\(784\) 0 0
\(785\) −2.22997 −0.0795911
\(786\) 21.9825 0.784090
\(787\) −17.1000 + 29.6181i −0.609550 + 1.05577i 0.381765 + 0.924259i \(0.375316\pi\)
−0.991315 + 0.131512i \(0.958017\pi\)
\(788\) −3.12851 5.41873i −0.111448 0.193034i
\(789\) 17.9238 0.638104
\(790\) −6.70559 + 11.6144i −0.238574 + 0.413223i
\(791\) 0 0
\(792\) 5.93434 0.210868
\(793\) 8.24819 3.45451i 0.292902 0.122673i
\(794\) 25.9579 + 44.9604i 0.921211 + 1.59558i
\(795\) −10.3347 −0.366532
\(796\) 0.289116 + 0.500764i 0.0102474 + 0.0177491i
\(797\) −15.6903 27.1763i −0.555778 0.962635i −0.997843 0.0656522i \(-0.979087\pi\)
0.442065 0.896983i \(-0.354246\pi\)
\(798\) 0 0
\(799\) 1.11439 + 1.93017i 0.0394241 + 0.0682846i
\(800\) −8.15951 −0.288482
\(801\) −12.5350 21.7112i −0.442901 0.767128i
\(802\) −2.30090 + 3.98528i −0.0812477 + 0.140725i
\(803\) 12.4484 + 21.5613i 0.439295 + 0.760881i
\(804\) −2.51788 + 4.36109i −0.0887988 + 0.153804i
\(805\) 0 0
\(806\) −4.22612 + 33.1044i −0.148859 + 1.16605i
\(807\) −6.19832 + 10.7358i −0.218191 + 0.377918i
\(808\) −7.54441 −0.265412
\(809\) −37.9418 −1.33396 −0.666981 0.745075i \(-0.732414\pi\)
−0.666981 + 0.745075i \(0.732414\pi\)
\(810\) 10.0833 0.354292
\(811\) −32.1023 −1.12726 −0.563632 0.826026i \(-0.690597\pi\)
−0.563632 + 0.826026i \(0.690597\pi\)
\(812\) 0 0
\(813\) 19.5930 + 33.9360i 0.687155 + 1.19019i
\(814\) 1.62948 2.82234i 0.0571133 0.0989231i
\(815\) −0.505555 + 0.875646i −0.0177088 + 0.0306725i
\(816\) 46.1586 1.61588
\(817\) 9.73265 + 16.8574i 0.340502 + 0.589767i
\(818\) 8.18670 0.286241
\(819\) 0 0
\(820\) 0.249856 0.00872534
\(821\) 8.46117 + 14.6552i 0.295297 + 0.511469i 0.975054 0.221968i \(-0.0712481\pi\)
−0.679757 + 0.733437i \(0.737915\pi\)
\(822\) −45.5132 −1.58745
\(823\) 7.23666 12.5343i 0.252254 0.436917i −0.711892 0.702289i \(-0.752161\pi\)
0.964146 + 0.265372i \(0.0854948\pi\)
\(824\) −0.678278 + 1.17481i −0.0236289 + 0.0409265i
\(825\) −7.52209 13.0286i −0.261885 0.453599i
\(826\) 0 0
\(827\) 27.5792 0.959021 0.479511 0.877536i \(-0.340814\pi\)
0.479511 + 0.877536i \(0.340814\pi\)
\(828\) 0.843731 0.0293217
\(829\) 21.0930 0.732592 0.366296 0.930498i \(-0.380626\pi\)
0.366296 + 0.930498i \(0.380626\pi\)
\(830\) −9.07281 −0.314922
\(831\) −6.57326 + 11.3852i −0.228024 + 0.394949i
\(832\) 21.2454 8.89800i 0.736550 0.308483i
\(833\) 0 0
\(834\) −27.9474 + 48.4064i −0.967741 + 1.67618i
\(835\) −3.72852 6.45798i −0.129031 0.223488i
\(836\) −0.400455 + 0.693609i −0.0138500 + 0.0239890i
\(837\) 9.57131 + 16.5780i 0.330833 + 0.573020i
\(838\) 8.94572 0.309025
\(839\) 6.35488 + 11.0070i 0.219395 + 0.380003i 0.954623 0.297817i \(-0.0962584\pi\)
−0.735228 + 0.677819i \(0.762925\pi\)
\(840\) 0 0
\(841\) −9.25333 16.0272i −0.319080 0.552663i
\(842\) −21.8698 37.8796i −0.753682 1.30542i
\(843\) 11.9929 0.413056
\(844\) 2.52852 + 4.37952i 0.0870351 + 0.150749i
\(845\) 2.04115 + 7.38521i 0.0702177 + 0.254059i
\(846\) 1.07504 0.0369606
\(847\) 0 0
\(848\) 18.6695 32.3365i 0.641113 1.11044i
\(849\) 34.9877 1.20077
\(850\) −16.9630 29.3807i −0.581825 1.00775i
\(851\) −1.24986 + 2.16481i −0.0428445 + 0.0742089i
\(852\) −4.39197 −0.150467
\(853\) −35.0471 −1.19999 −0.599996 0.800003i \(-0.704831\pi\)
−0.599996 + 0.800003i \(0.704831\pi\)
\(854\) 0 0
\(855\) −0.754672 + 1.30713i −0.0258092 + 0.0447029i
\(856\) 24.7899 + 42.9373i 0.847300 + 1.46757i
\(857\) 12.7970 + 22.1651i 0.437138 + 0.757145i 0.997467 0.0711250i \(-0.0226589\pi\)
−0.560330 + 0.828270i \(0.689326\pi\)
\(858\) −14.1084 10.7380i −0.481652 0.366589i
\(859\) −0.372743 + 0.645610i −0.0127178 + 0.0220279i −0.872314 0.488946i \(-0.837382\pi\)
0.859596 + 0.510974i \(0.170715\pi\)
\(860\) 1.06541 1.84534i 0.0363300 0.0629254i
\(861\) 0 0
\(862\) 6.37651 + 11.0444i 0.217185 + 0.376175i
\(863\) 10.9908 19.0367i 0.374132 0.648015i −0.616065 0.787695i \(-0.711274\pi\)
0.990197 + 0.139680i \(0.0446075\pi\)
\(864\) −2.75790 + 4.77682i −0.0938255 + 0.162511i
\(865\) 3.38529 5.86350i 0.115103 0.199365i
\(866\) 20.9861 36.3490i 0.713137 1.23519i
\(867\) 6.36804 + 11.0298i 0.216270 + 0.374590i
\(868\) 0 0
\(869\) 11.3771 19.7058i 0.385943 0.668473i
\(870\) −6.56783 + 11.3758i −0.222670 + 0.385676i
\(871\) −25.1846 + 10.5479i −0.853348 + 0.357400i
\(872\) 7.35444 + 12.7383i 0.249053 + 0.431372i
\(873\) 0.740517 + 1.28261i 0.0250627 + 0.0434099i
\(874\) 2.27140 3.93418i 0.0768313 0.133076i
\(875\) 0 0
\(876\) 10.8864 0.367818
\(877\) 29.4190 0.993411 0.496705 0.867919i \(-0.334543\pi\)
0.496705 + 0.867919i \(0.334543\pi\)
\(878\) −23.7041 + 41.0567i −0.799975 + 1.38560i
\(879\) 32.5492 + 56.3769i 1.09786 + 1.90155i
\(880\) −4.05831 −0.136806
\(881\) 24.1414 41.8142i 0.813345 1.40876i −0.0971649 0.995268i \(-0.530977\pi\)
0.910510 0.413487i \(-0.135689\pi\)
\(882\) 0 0
\(883\) 16.4465 0.553469 0.276735 0.960946i \(-0.410748\pi\)
0.276735 + 0.960946i \(0.410748\pi\)
\(884\) −4.30240 3.27459i −0.144705 0.110136i
\(885\) −7.44110 12.8884i −0.250130 0.433238i
\(886\) 35.8724 1.20516
\(887\) 14.5827 + 25.2579i 0.489638 + 0.848078i 0.999929 0.0119239i \(-0.00379559\pi\)
−0.510291 + 0.860002i \(0.670462\pi\)
\(888\) 3.84388 + 6.65780i 0.128992 + 0.223421i
\(889\) 0 0
\(890\) 7.38800 + 12.7964i 0.247646 + 0.428936i
\(891\) −17.1080 −0.573141
\(892\) 1.94403 + 3.36716i 0.0650910 + 0.112741i
\(893\) 0.391368 0.677869i 0.0130966 0.0226840i
\(894\) 27.6870 + 47.9553i 0.925993 + 1.60387i
\(895\) 0.643765 1.11503i 0.0215187 0.0372715i
\(896\) 0 0
\(897\) 10.8215 + 8.23633i 0.361320 + 0.275003i
\(898\) 2.14928 3.72266i 0.0717224 0.124227i
\(899\) −41.9506 −1.39913
\(900\) −2.21290 −0.0737633
\(901\) 39.5417 1.31733
\(902\) −3.13484 −0.104379
\(903\) 0 0
\(904\) −6.60673 11.4432i −0.219736 0.380595i
\(905\) 3.41791 5.92000i 0.113615 0.196787i
\(906\) −25.5404 + 44.2373i −0.848524 + 1.46969i
\(907\) −35.3215 −1.17283 −0.586416 0.810010i \(-0.699461\pi\)
−0.586416 + 0.810010i \(0.699461\pi\)
\(908\) −0.193120 0.334494i −0.00640892 0.0111006i
\(909\) −4.47143 −0.148308
\(910\) 0 0
\(911\) −43.6496 −1.44617 −0.723087 0.690757i \(-0.757278\pi\)
−0.723087 + 0.690757i \(0.757278\pi\)
\(912\) −8.10537 14.0389i −0.268396 0.464875i
\(913\) 15.3935 0.509452
\(914\) −28.6994 + 49.7088i −0.949292 + 1.64422i
\(915\) 1.55404 2.69167i 0.0513749 0.0889840i
\(916\) −1.02507 1.77547i −0.0338691 0.0586630i
\(917\) 0 0
\(918\) −22.9338 −0.756927
\(919\) −17.7878 −0.586765 −0.293382 0.955995i \(-0.594781\pi\)
−0.293382 + 0.955995i \(0.594781\pi\)
\(920\) 2.68279 0.0884491
\(921\) 21.1775 0.697822
\(922\) −26.3539 + 45.6463i −0.867921 + 1.50328i
\(923\) −18.9494 14.4225i −0.623726 0.474723i
\(924\) 0 0
\(925\) 3.27806 5.67777i 0.107782 0.186684i
\(926\) 14.0758 + 24.3800i 0.462559 + 0.801176i
\(927\) −0.402003 + 0.696289i −0.0132035 + 0.0228691i
\(928\) −6.04385 10.4683i −0.198399 0.343638i
\(929\) −3.91420 −0.128421 −0.0642103 0.997936i \(-0.520453\pi\)
−0.0642103 + 0.997936i \(0.520453\pi\)
\(930\) 5.79969 + 10.0454i 0.190179 + 0.329401i
\(931\) 0 0
\(932\) −0.984992 1.70606i −0.0322645 0.0558837i
\(933\) 29.4977 + 51.0916i 0.965712 + 1.67266i
\(934\) 10.0794 0.329809
\(935\) −2.14886 3.72193i −0.0702752 0.121720i
\(936\) 12.9773 5.43517i 0.424177 0.177654i
\(937\) 0.207362 0.00677421 0.00338710 0.999994i \(-0.498922\pi\)
0.00338710 + 0.999994i \(0.498922\pi\)
\(938\) 0 0
\(939\) −17.5654 + 30.4242i −0.573225 + 0.992855i
\(940\) −0.0856839 −0.00279470
\(941\) 13.7328 + 23.7859i 0.447677 + 0.775400i 0.998234 0.0593977i \(-0.0189180\pi\)
−0.550557 + 0.834797i \(0.685585\pi\)
\(942\) 6.11697 10.5949i 0.199302 0.345200i
\(943\) 2.40451 0.0783015
\(944\) 53.7692 1.75004
\(945\) 0 0
\(946\) −13.3672 + 23.1527i −0.434605 + 0.752758i
\(947\) 11.5182 + 19.9501i 0.374290 + 0.648290i 0.990221 0.139511i \(-0.0445531\pi\)
−0.615930 + 0.787801i \(0.711220\pi\)
\(948\) −4.97479 8.61660i −0.161574 0.279854i
\(949\) 46.9700 + 35.7492i 1.52471 + 1.16047i
\(950\) −5.95733 + 10.3184i −0.193281 + 0.334773i
\(951\) 25.1736 43.6019i 0.816309 1.41389i
\(952\) 0 0
\(953\) −7.22808 12.5194i −0.234140 0.405543i 0.724882 0.688873i \(-0.241894\pi\)
−0.959022 + 0.283330i \(0.908561\pi\)
\(954\) 9.53641 16.5175i 0.308753 0.534775i
\(955\) −5.23357 + 9.06480i −0.169354 + 0.293330i
\(956\) 2.95853 5.12432i 0.0956856 0.165732i
\(957\) 11.1434 19.3010i 0.360215 0.623911i
\(958\) 13.2707 + 22.9856i 0.428758 + 0.742630i
\(959\) 0 0
\(960\) 4.00283 6.93311i 0.129191 0.223765i
\(961\) −3.02213 + 5.23448i −0.0974881 + 0.168854i
\(962\) 0.978433 7.66436i 0.0315460 0.247109i
\(963\) 14.6925 + 25.4481i 0.473459 + 0.820054i
\(964\) −3.48668 6.03910i −0.112298 0.194506i
\(965\) −6.67129 + 11.5550i −0.214756 + 0.371969i
\(966\) 0 0
\(967\) 32.3357 1.03984 0.519922 0.854213i \(-0.325961\pi\)
0.519922 + 0.854213i \(0.325961\pi\)
\(968\) −22.2908 −0.716454
\(969\) 8.58353 14.8671i 0.275743 0.477600i
\(970\) −0.436454 0.755961i −0.0140137 0.0242725i
\(971\) −24.6235 −0.790206 −0.395103 0.918637i \(-0.629291\pi\)
−0.395103 + 0.918637i \(0.629291\pi\)
\(972\) −2.26487 + 3.92287i −0.0726458 + 0.125826i
\(973\) 0 0
\(974\) 54.0084 1.73054
\(975\) −28.3821 21.6019i −0.908956 0.691813i
\(976\) 5.61472 + 9.72499i 0.179723 + 0.311289i
\(977\) 6.00992 0.192274 0.0961372 0.995368i \(-0.469351\pi\)
0.0961372 + 0.995368i \(0.469351\pi\)
\(978\) −2.77354 4.80392i −0.0886882 0.153612i
\(979\) −12.5350 21.7112i −0.400619 0.693893i
\(980\) 0 0
\(981\) 4.35884 + 7.54973i 0.139167 + 0.241044i
\(982\) 45.3371 1.44676
\(983\) −17.9546 31.0984i −0.572664 0.991884i −0.996291 0.0860467i \(-0.972577\pi\)
0.423627 0.905837i \(-0.360757\pi\)
\(984\) 3.69748 6.40422i 0.117871 0.204159i
\(985\) −5.89578 10.2118i −0.187855 0.325374i
\(986\) 25.1294 43.5253i 0.800282 1.38613i
\(987\) 0 0
\(988\) −0.240456 + 1.88357i −0.00764994 + 0.0599242i
\(989\) 10.2530 17.7587i 0.326027 0.564694i
\(990\) −2.07299 −0.0658840
\(991\) 28.0000 0.889449 0.444724 0.895668i \(-0.353302\pi\)
0.444724 + 0.895668i \(0.353302\pi\)
\(992\) −10.6740 −0.338900
\(993\) −16.9078 −0.536553
\(994\) 0 0
\(995\) 0.544849 + 0.943706i 0.0172729 + 0.0299175i
\(996\) 3.36550 5.82922i 0.106640 0.184706i
\(997\) −16.5040 + 28.5858i −0.522688 + 0.905323i 0.476963 + 0.878923i \(0.341737\pi\)
−0.999651 + 0.0263994i \(0.991596\pi\)
\(998\) 11.4205 0.361509
\(999\) −2.21596 3.83815i −0.0701097 0.121434i
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 637.2.g.m.373.5 16
7.2 even 3 637.2.f.l.295.6 yes 16
7.3 odd 6 637.2.h.m.165.3 16
7.4 even 3 637.2.h.m.165.4 16
7.5 odd 6 637.2.f.l.295.5 16
7.6 odd 2 inner 637.2.g.m.373.6 16
13.3 even 3 637.2.h.m.471.4 16
91.3 odd 6 inner 637.2.g.m.263.6 16
91.9 even 3 8281.2.a.ci.1.3 8
91.16 even 3 637.2.f.l.393.6 yes 16
91.30 even 6 8281.2.a.cl.1.5 8
91.55 odd 6 637.2.h.m.471.3 16
91.61 odd 6 8281.2.a.ci.1.4 8
91.68 odd 6 637.2.f.l.393.5 yes 16
91.81 even 3 inner 637.2.g.m.263.5 16
91.82 odd 6 8281.2.a.cl.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.l.295.5 16 7.5 odd 6
637.2.f.l.295.6 yes 16 7.2 even 3
637.2.f.l.393.5 yes 16 91.68 odd 6
637.2.f.l.393.6 yes 16 91.16 even 3
637.2.g.m.263.5 16 91.81 even 3 inner
637.2.g.m.263.6 16 91.3 odd 6 inner
637.2.g.m.373.5 16 1.1 even 1 trivial
637.2.g.m.373.6 16 7.6 odd 2 inner
637.2.h.m.165.3 16 7.3 odd 6
637.2.h.m.165.4 16 7.4 even 3
637.2.h.m.471.3 16 91.55 odd 6
637.2.h.m.471.4 16 13.3 even 3
8281.2.a.ci.1.3 8 91.9 even 3
8281.2.a.ci.1.4 8 91.61 odd 6
8281.2.a.cl.1.5 8 91.30 even 6
8281.2.a.cl.1.6 8 91.82 odd 6