Properties

Label 750.2.l.b.107.10
Level $750$
Weight $2$
Character 750.107
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
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] = [750,2,Mod(107,750)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(750, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("750.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), 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: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 107.10
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.b.743.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.891007 + 0.453990i) q^{2} +(1.64867 + 0.530925i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(0.152718 + 0.152718i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.43624 + 1.75064i) q^{9} +O(q^{10})\) \(q+(0.891007 + 0.453990i) q^{2} +(1.64867 + 0.530925i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.22794 + 1.22154i) q^{6} +(0.152718 + 0.152718i) q^{7} +(0.156434 + 0.987688i) q^{8} +(2.43624 + 1.75064i) q^{9} +(4.88609 - 1.58759i) q^{11} +(0.539538 + 1.64587i) q^{12} +(-0.674795 - 1.32436i) q^{13} +(0.0667401 + 0.205405i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-4.81543 + 0.762690i) q^{17} +(1.37593 + 2.66586i) q^{18} +(0.283032 - 0.389560i) q^{19} +(0.170700 + 0.332863i) q^{21} +(5.07429 + 0.803689i) q^{22} +(1.21389 - 2.38239i) q^{23} +(-0.266479 + 1.71143i) q^{24} -1.48636i q^{26} +(3.08710 + 4.17969i) q^{27} +(-0.0337860 + 0.213317i) q^{28} +(-7.59423 + 5.51753i) q^{29} +(-1.84019 - 1.33698i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.89846 - 0.0232622i) q^{33} +(-4.63684 - 1.50660i) q^{34} +(0.0156850 + 2.99996i) q^{36} +(-3.83574 + 1.95441i) q^{37} +(0.429039 - 0.218606i) q^{38} +(-0.409380 - 2.54170i) q^{39} +(5.95547 + 1.93505i) q^{41} +(0.000977913 + 0.374079i) q^{42} +(2.72225 - 2.72225i) q^{43} +(4.15636 + 3.01977i) q^{44} +(2.16317 - 1.57163i) q^{46} +(-1.58814 + 10.0271i) q^{47} +(-1.01441 + 1.40392i) q^{48} -6.95335i q^{49} +(-8.34400 - 1.29921i) q^{51} +(0.674795 - 1.32436i) q^{52} +(7.59700 + 1.20325i) q^{53} +(0.853081 + 5.12565i) q^{54} +(-0.126947 + 0.174728i) q^{56} +(0.673453 - 0.491987i) q^{57} +(-9.27141 + 1.46845i) q^{58} +(-1.54130 + 4.74363i) q^{59} +(-4.21680 - 12.9780i) q^{61} +(-1.03265 - 2.02668i) q^{62} +(0.104703 + 0.639411i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(7.93914 + 4.01909i) q^{66} +(-2.35050 - 14.8405i) q^{67} +(-3.44747 - 3.44747i) q^{68} +(3.26618 - 3.28330i) q^{69} +(-7.13100 - 9.81498i) q^{71} +(-1.34798 + 2.68010i) q^{72} +(-8.36209 - 4.26070i) q^{73} -4.30495 q^{74} +0.481522 q^{76} +(0.988647 + 0.503741i) q^{77} +(0.789148 - 2.45053i) q^{78} +(-1.28502 - 1.76867i) q^{79} +(2.87050 + 8.52996i) q^{81} +(4.42787 + 4.42787i) q^{82} +(0.782253 + 4.93895i) q^{83} +(-0.168957 + 0.333751i) q^{84} +(3.66142 - 1.18967i) q^{86} +(-15.4498 + 5.06463i) q^{87} +(2.33240 + 4.57759i) q^{88} +(-3.38311 - 10.4121i) q^{89} +(0.0992002 - 0.305307i) q^{91} +(2.64090 - 0.418278i) q^{92} +(-2.32404 - 3.18124i) q^{93} +(-5.96725 + 8.21321i) q^{94} +(-1.54121 + 0.790366i) q^{96} +(9.96799 + 1.57877i) q^{97} +(3.15676 - 6.19548i) q^{98} +(14.6830 + 4.68606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.891007 + 0.453990i 0.630037 + 0.321020i
\(3\) 1.64867 + 0.530925i 0.951861 + 0.306530i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) 1.22794 + 1.22154i 0.501305 + 0.498691i
\(7\) 0.152718 + 0.152718i 0.0577219 + 0.0577219i 0.735379 0.677657i \(-0.237004\pi\)
−0.677657 + 0.735379i \(0.737004\pi\)
\(8\) 0.156434 + 0.987688i 0.0553079 + 0.349201i
\(9\) 2.43624 + 1.75064i 0.812079 + 0.583547i
\(10\) 0 0
\(11\) 4.88609 1.58759i 1.47321 0.478676i 0.541136 0.840935i \(-0.317995\pi\)
0.932077 + 0.362259i \(0.117995\pi\)
\(12\) 0.539538 + 1.64587i 0.155751 + 0.475123i
\(13\) −0.674795 1.32436i −0.187155 0.367312i 0.778296 0.627897i \(-0.216084\pi\)
−0.965451 + 0.260586i \(0.916084\pi\)
\(14\) 0.0667401 + 0.205405i 0.0178371 + 0.0548968i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −4.81543 + 0.762690i −1.16791 + 0.184979i −0.710121 0.704080i \(-0.751360\pi\)
−0.457793 + 0.889059i \(0.651360\pi\)
\(18\) 1.37593 + 2.66586i 0.324309 + 0.628350i
\(19\) 0.283032 0.389560i 0.0649319 0.0893711i −0.775316 0.631574i \(-0.782409\pi\)
0.840248 + 0.542202i \(0.182409\pi\)
\(20\) 0 0
\(21\) 0.170700 + 0.332863i 0.0372498 + 0.0726367i
\(22\) 5.07429 + 0.803689i 1.08184 + 0.171347i
\(23\) 1.21389 2.38239i 0.253114 0.496763i −0.729130 0.684376i \(-0.760075\pi\)
0.982243 + 0.187612i \(0.0600748\pi\)
\(24\) −0.266479 + 1.71143i −0.0543949 + 0.349344i
\(25\) 0 0
\(26\) 1.48636i 0.291500i
\(27\) 3.08710 + 4.17969i 0.594112 + 0.804382i
\(28\) −0.0337860 + 0.213317i −0.00638496 + 0.0403130i
\(29\) −7.59423 + 5.51753i −1.41021 + 1.02458i −0.416921 + 0.908943i \(0.636891\pi\)
−0.993292 + 0.115637i \(0.963109\pi\)
\(30\) 0 0
\(31\) −1.84019 1.33698i −0.330508 0.240128i 0.410138 0.912023i \(-0.365480\pi\)
−0.740646 + 0.671895i \(0.765480\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 8.89846 0.0232622i 1.54902 0.00404943i
\(34\) −4.63684 1.50660i −0.795211 0.258380i
\(35\) 0 0
\(36\) 0.0156850 + 2.99996i 0.00261417 + 0.499993i
\(37\) −3.83574 + 1.95441i −0.630592 + 0.321303i −0.739912 0.672704i \(-0.765133\pi\)
0.109320 + 0.994007i \(0.465133\pi\)
\(38\) 0.429039 0.218606i 0.0695994 0.0354627i
\(39\) −0.409380 2.54170i −0.0655533 0.406998i
\(40\) 0 0
\(41\) 5.95547 + 1.93505i 0.930087 + 0.302204i 0.734598 0.678502i \(-0.237371\pi\)
0.195489 + 0.980706i \(0.437371\pi\)
\(42\) 0.000977913 0.374079i 0.000150895 0.0577217i
\(43\) 2.72225 2.72225i 0.415139 0.415139i −0.468385 0.883524i \(-0.655164\pi\)
0.883524 + 0.468385i \(0.155164\pi\)
\(44\) 4.15636 + 3.01977i 0.626595 + 0.455248i
\(45\) 0 0
\(46\) 2.16317 1.57163i 0.318942 0.231725i
\(47\) −1.58814 + 10.0271i −0.231654 + 1.46260i 0.548046 + 0.836448i \(0.315372\pi\)
−0.779699 + 0.626154i \(0.784628\pi\)
\(48\) −1.01441 + 1.40392i −0.146417 + 0.202638i
\(49\) 6.95335i 0.993336i
\(50\) 0 0
\(51\) −8.34400 1.29921i −1.16839 0.181926i
\(52\) 0.674795 1.32436i 0.0935773 0.183656i
\(53\) 7.59700 + 1.20325i 1.04353 + 0.165279i 0.654589 0.755985i \(-0.272842\pi\)
0.388939 + 0.921264i \(0.372842\pi\)
\(54\) 0.853081 + 5.12565i 0.116090 + 0.697512i
\(55\) 0 0
\(56\) −0.126947 + 0.174728i −0.0169640 + 0.0233490i
\(57\) 0.673453 0.491987i 0.0892011 0.0651653i
\(58\) −9.27141 + 1.46845i −1.21740 + 0.192817i
\(59\) −1.54130 + 4.74363i −0.200660 + 0.617569i 0.799204 + 0.601061i \(0.205255\pi\)
−0.999864 + 0.0165081i \(0.994745\pi\)
\(60\) 0 0
\(61\) −4.21680 12.9780i −0.539906 1.66166i −0.732803 0.680440i \(-0.761789\pi\)
0.192898 0.981219i \(-0.438211\pi\)
\(62\) −1.03265 2.02668i −0.131146 0.257389i
\(63\) 0.104703 + 0.639411i 0.0131913 + 0.0805582i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) 7.93914 + 4.01909i 0.977241 + 0.494716i
\(67\) −2.35050 14.8405i −0.287159 1.81305i −0.535673 0.844425i \(-0.679942\pi\)
0.248514 0.968628i \(-0.420058\pi\)
\(68\) −3.44747 3.44747i −0.418067 0.418067i
\(69\) 3.26618 3.28330i 0.393202 0.395263i
\(70\) 0 0
\(71\) −7.13100 9.81498i −0.846294 1.16482i −0.984667 0.174444i \(-0.944187\pi\)
0.138373 0.990380i \(-0.455813\pi\)
\(72\) −1.34798 + 2.68010i −0.158861 + 0.315853i
\(73\) −8.36209 4.26070i −0.978708 0.498677i −0.109963 0.993936i \(-0.535073\pi\)
−0.868745 + 0.495259i \(0.835073\pi\)
\(74\) −4.30495 −0.500441
\(75\) 0 0
\(76\) 0.481522 0.0552344
\(77\) 0.988647 + 0.503741i 0.112667 + 0.0574066i
\(78\) 0.789148 2.45053i 0.0893534 0.277468i
\(79\) −1.28502 1.76867i −0.144576 0.198991i 0.730588 0.682819i \(-0.239246\pi\)
−0.875163 + 0.483828i \(0.839246\pi\)
\(80\) 0 0
\(81\) 2.87050 + 8.52996i 0.318945 + 0.947773i
\(82\) 4.42787 + 4.42787i 0.488976 + 0.488976i
\(83\) 0.782253 + 4.93895i 0.0858634 + 0.542120i 0.992697 + 0.120632i \(0.0384921\pi\)
−0.906834 + 0.421488i \(0.861508\pi\)
\(84\) −0.168957 + 0.333751i −0.0184347 + 0.0364152i
\(85\) 0 0
\(86\) 3.66142 1.18967i 0.394821 0.128285i
\(87\) −15.4498 + 5.06463i −1.65639 + 0.542985i
\(88\) 2.33240 + 4.57759i 0.248634 + 0.487972i
\(89\) −3.38311 10.4121i −0.358609 1.10368i −0.953887 0.300165i \(-0.902958\pi\)
0.595279 0.803519i \(-0.297042\pi\)
\(90\) 0 0
\(91\) 0.0992002 0.305307i 0.0103990 0.0320048i
\(92\) 2.64090 0.418278i 0.275333 0.0436085i
\(93\) −2.32404 3.18124i −0.240991 0.329879i
\(94\) −5.96725 + 8.21321i −0.615475 + 0.847128i
\(95\) 0 0
\(96\) −1.54121 + 0.790366i −0.157299 + 0.0806664i
\(97\) 9.96799 + 1.57877i 1.01210 + 0.160300i 0.640390 0.768050i \(-0.278773\pi\)
0.371706 + 0.928350i \(0.378773\pi\)
\(98\) 3.15676 6.19548i 0.318881 0.625838i
\(99\) 14.6830 + 4.68606i 1.47570 + 0.470967i
\(100\) 0 0
\(101\) 9.53700i 0.948967i 0.880264 + 0.474483i \(0.157365\pi\)
−0.880264 + 0.474483i \(0.842635\pi\)
\(102\) −6.84473 4.94570i −0.677729 0.489697i
\(103\) −1.58215 + 9.98929i −0.155894 + 0.984274i 0.778400 + 0.627769i \(0.216032\pi\)
−0.934293 + 0.356505i \(0.883968\pi\)
\(104\) 1.20249 0.873663i 0.117914 0.0856697i
\(105\) 0 0
\(106\) 6.22271 + 4.52106i 0.604403 + 0.439125i
\(107\) 7.80873 7.80873i 0.754898 0.754898i −0.220491 0.975389i \(-0.570766\pi\)
0.975389 + 0.220491i \(0.0707659\pi\)
\(108\) −1.56689 + 4.95428i −0.150774 + 0.476725i
\(109\) −5.83194 1.89491i −0.558598 0.181500i 0.0160921 0.999871i \(-0.494877\pi\)
−0.574690 + 0.818371i \(0.694877\pi\)
\(110\) 0 0
\(111\) −7.36152 + 1.18569i −0.698725 + 0.112540i
\(112\) −0.192436 + 0.0980509i −0.0181835 + 0.00926494i
\(113\) −9.78864 + 4.98756i −0.920838 + 0.469190i −0.849099 0.528233i \(-0.822855\pi\)
−0.0717385 + 0.997423i \(0.522855\pi\)
\(114\) 0.823409 0.132623i 0.0771193 0.0124212i
\(115\) 0 0
\(116\) −8.92755 2.90074i −0.828902 0.269327i
\(117\) 0.674520 4.40778i 0.0623594 0.407500i
\(118\) −3.52687 + 3.52687i −0.324675 + 0.324675i
\(119\) −0.851879 0.618926i −0.0780916 0.0567369i
\(120\) 0 0
\(121\) 12.4543 9.04858i 1.13221 0.822598i
\(122\) 2.13468 13.4778i 0.193265 1.22023i
\(123\) 8.79124 + 6.35216i 0.792680 + 0.572755i
\(124\) 2.27460i 0.204265i
\(125\) 0 0
\(126\) −0.196996 + 0.617253i −0.0175498 + 0.0549893i
\(127\) 6.82658 13.3979i 0.605761 1.18887i −0.360850 0.932624i \(-0.617513\pi\)
0.966611 0.256249i \(-0.0824868\pi\)
\(128\) −0.987688 0.156434i −0.0873001 0.0138270i
\(129\) 5.93341 3.04279i 0.522407 0.267902i
\(130\) 0 0
\(131\) −5.12870 + 7.05905i −0.448097 + 0.616752i −0.971987 0.235034i \(-0.924480\pi\)
0.523891 + 0.851785i \(0.324480\pi\)
\(132\) 5.24920 + 7.18533i 0.456884 + 0.625403i
\(133\) 0.102717 0.0162687i 0.00890667 0.00141068i
\(134\) 4.64313 14.2901i 0.401105 1.23447i
\(135\) 0 0
\(136\) −1.50660 4.63684i −0.129190 0.397605i
\(137\) −1.28180 2.51567i −0.109511 0.214928i 0.829747 0.558140i \(-0.188485\pi\)
−0.939258 + 0.343212i \(0.888485\pi\)
\(138\) 4.40077 1.44263i 0.374619 0.122805i
\(139\) −6.62014 + 2.15102i −0.561513 + 0.182447i −0.576002 0.817448i \(-0.695388\pi\)
0.0144887 + 0.999895i \(0.495388\pi\)
\(140\) 0 0
\(141\) −7.94195 + 15.6882i −0.668833 + 1.32119i
\(142\) −1.89786 11.9826i −0.159265 1.00556i
\(143\) −5.39965 5.39965i −0.451542 0.451542i
\(144\) −2.41780 + 1.77602i −0.201483 + 0.148002i
\(145\) 0 0
\(146\) −5.51636 7.59261i −0.456537 0.628369i
\(147\) 3.69171 11.4638i 0.304487 0.945518i
\(148\) −3.83574 1.95441i −0.315296 0.160651i
\(149\) 7.72360 0.632742 0.316371 0.948635i \(-0.397535\pi\)
0.316371 + 0.948635i \(0.397535\pi\)
\(150\) 0 0
\(151\) −14.7868 −1.20333 −0.601667 0.798747i \(-0.705497\pi\)
−0.601667 + 0.798747i \(0.705497\pi\)
\(152\) 0.429039 + 0.218606i 0.0347997 + 0.0177313i
\(153\) −13.0667 6.57201i −1.05638 0.531315i
\(154\) 0.652197 + 0.897673i 0.0525556 + 0.0723365i
\(155\) 0 0
\(156\) 1.81565 1.82517i 0.145369 0.146131i
\(157\) 11.5941 + 11.5941i 0.925312 + 0.925312i 0.997398 0.0720863i \(-0.0229657\pi\)
−0.0720863 + 0.997398i \(0.522966\pi\)
\(158\) −0.341997 2.15928i −0.0272078 0.171783i
\(159\) 11.8861 + 6.01719i 0.942630 + 0.477194i
\(160\) 0 0
\(161\) 0.549217 0.178451i 0.0432843 0.0140639i
\(162\) −1.31488 + 8.90343i −0.103307 + 0.699520i
\(163\) 1.84215 + 3.61543i 0.144289 + 0.283182i 0.951829 0.306630i \(-0.0992016\pi\)
−0.807540 + 0.589813i \(0.799202\pi\)
\(164\) 1.93505 + 5.95547i 0.151102 + 0.465044i
\(165\) 0 0
\(166\) −1.54524 + 4.75577i −0.119934 + 0.369119i
\(167\) −13.6706 + 2.16520i −1.05786 + 0.167549i −0.661042 0.750349i \(-0.729886\pi\)
−0.396818 + 0.917897i \(0.629886\pi\)
\(168\) −0.302062 + 0.220670i −0.0233046 + 0.0170250i
\(169\) 6.34263 8.72988i 0.487894 0.671529i
\(170\) 0 0
\(171\) 1.37151 0.453573i 0.104882 0.0346856i
\(172\) 3.80244 + 0.602248i 0.289934 + 0.0459210i
\(173\) 0.412278 0.809140i 0.0313449 0.0615178i −0.874803 0.484479i \(-0.839009\pi\)
0.906148 + 0.422961i \(0.139009\pi\)
\(174\) −16.0652 2.50144i −1.21790 0.189633i
\(175\) 0 0
\(176\) 5.13754i 0.387257i
\(177\) −5.05961 + 7.00238i −0.380304 + 0.526331i
\(178\) 1.71264 10.8132i 0.128368 0.810482i
\(179\) 9.58645 6.96496i 0.716525 0.520586i −0.168747 0.985659i \(-0.553972\pi\)
0.885272 + 0.465074i \(0.153972\pi\)
\(180\) 0 0
\(181\) 13.9076 + 10.1044i 1.03374 + 0.751057i 0.969054 0.246848i \(-0.0793949\pi\)
0.0646876 + 0.997906i \(0.479395\pi\)
\(182\) 0.226994 0.226994i 0.0168259 0.0168259i
\(183\) −0.0617869 23.6352i −0.00456742 1.74717i
\(184\) 2.54296 + 0.826257i 0.187469 + 0.0609125i
\(185\) 0 0
\(186\) −0.626479 3.88960i −0.0459357 0.285199i
\(187\) −22.3178 + 11.3715i −1.63204 + 0.831566i
\(188\) −9.04558 + 4.60895i −0.659716 + 0.336142i
\(189\) −0.166859 + 1.10977i −0.0121372 + 0.0807238i
\(190\) 0 0
\(191\) −4.70151 1.52761i −0.340189 0.110534i 0.133940 0.990989i \(-0.457237\pi\)
−0.474129 + 0.880455i \(0.657237\pi\)
\(192\) −1.73204 + 0.00452789i −0.125000 + 0.000326772i
\(193\) −2.38356 + 2.38356i −0.171572 + 0.171572i −0.787670 0.616098i \(-0.788713\pi\)
0.616098 + 0.787670i \(0.288713\pi\)
\(194\) 8.16479 + 5.93207i 0.586198 + 0.425898i
\(195\) 0 0
\(196\) 5.62538 4.08708i 0.401813 0.291934i
\(197\) 1.14693 7.24145i 0.0817156 0.515932i −0.912548 0.408970i \(-0.865888\pi\)
0.994263 0.106961i \(-0.0341121\pi\)
\(198\) 10.9552 + 10.8412i 0.778553 + 0.770454i
\(199\) 8.34182i 0.591336i 0.955291 + 0.295668i \(0.0955422\pi\)
−0.955291 + 0.295668i \(0.904458\pi\)
\(200\) 0 0
\(201\) 4.00398 25.7150i 0.282419 1.81380i
\(202\) −4.32971 + 8.49753i −0.304637 + 0.597884i
\(203\) −2.00240 0.317149i −0.140541 0.0222595i
\(204\) −3.85340 7.51409i −0.269792 0.526092i
\(205\) 0 0
\(206\) −5.94475 + 8.18224i −0.414190 + 0.570084i
\(207\) 7.12804 3.67899i 0.495433 0.255707i
\(208\) 1.46807 0.232519i 0.101792 0.0161223i
\(209\) 0.764459 2.35276i 0.0528787 0.162744i
\(210\) 0 0
\(211\) 1.32487 + 4.07753i 0.0912078 + 0.280709i 0.986247 0.165279i \(-0.0528525\pi\)
−0.895039 + 0.445988i \(0.852852\pi\)
\(212\) 3.49196 + 6.85335i 0.239828 + 0.470690i
\(213\) −6.54566 19.9677i −0.448501 1.36817i
\(214\) 10.5027 3.41254i 0.717951 0.233276i
\(215\) 0 0
\(216\) −3.64531 + 3.70294i −0.248032 + 0.251953i
\(217\) −0.0768498 0.485210i −0.00521690 0.0329382i
\(218\) −4.33602 4.33602i −0.293672 0.293672i
\(219\) −11.5242 11.4641i −0.778735 0.774674i
\(220\) 0 0
\(221\) 4.25951 + 5.86271i 0.286525 + 0.394369i
\(222\) −7.09746 2.28561i −0.476350 0.153400i
\(223\) −0.651256 0.331831i −0.0436113 0.0222211i 0.432049 0.901850i \(-0.357791\pi\)
−0.475660 + 0.879629i \(0.657791\pi\)
\(224\) −0.215976 −0.0144305
\(225\) 0 0
\(226\) −10.9860 −0.730781
\(227\) 2.94981 + 1.50300i 0.195786 + 0.0997579i 0.549135 0.835734i \(-0.314957\pi\)
−0.353349 + 0.935492i \(0.614957\pi\)
\(228\) 0.793872 + 0.255652i 0.0525755 + 0.0169310i
\(229\) −6.20224 8.53665i −0.409855 0.564117i 0.553328 0.832964i \(-0.313358\pi\)
−0.963183 + 0.268846i \(0.913358\pi\)
\(230\) 0 0
\(231\) 1.36251 + 1.35540i 0.0896463 + 0.0891788i
\(232\) −6.63760 6.63760i −0.435780 0.435780i
\(233\) 1.96935 + 12.4340i 0.129016 + 0.814577i 0.964311 + 0.264774i \(0.0852973\pi\)
−0.835294 + 0.549803i \(0.814703\pi\)
\(234\) 2.60209 3.62114i 0.170104 0.236721i
\(235\) 0 0
\(236\) −4.74363 + 1.54130i −0.308784 + 0.100330i
\(237\) −1.17954 3.59821i −0.0766192 0.233729i
\(238\) −0.478043 0.938212i −0.0309869 0.0608152i
\(239\) 3.62951 + 11.1705i 0.234773 + 0.722558i 0.997151 + 0.0754263i \(0.0240318\pi\)
−0.762378 + 0.647132i \(0.775968\pi\)
\(240\) 0 0
\(241\) 0.375849 1.15675i 0.0242106 0.0745125i −0.938221 0.346036i \(-0.887527\pi\)
0.962432 + 0.271524i \(0.0875275\pi\)
\(242\) 15.2048 2.40821i 0.977403 0.154805i
\(243\) 0.203749 + 15.5871i 0.0130705 + 0.999915i
\(244\) 8.02083 11.0397i 0.513481 0.706746i
\(245\) 0 0
\(246\) 4.94923 + 9.65096i 0.315552 + 0.615323i
\(247\) −0.706906 0.111963i −0.0449793 0.00712403i
\(248\) 1.03265 2.02668i 0.0655732 0.128695i
\(249\) −1.33253 + 8.55802i −0.0844459 + 0.542343i
\(250\) 0 0
\(251\) 22.6123i 1.42728i 0.700515 + 0.713638i \(0.252954\pi\)
−0.700515 + 0.713638i \(0.747046\pi\)
\(252\) −0.455752 + 0.460543i −0.0287097 + 0.0290115i
\(253\) 2.14892 13.5678i 0.135102 0.852998i
\(254\) 12.1651 8.83843i 0.763304 0.554573i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −2.98436 + 2.98436i −0.186159 + 0.186159i −0.794033 0.607874i \(-0.792022\pi\)
0.607874 + 0.794033i \(0.292022\pi\)
\(258\) 6.66810 0.0174316i 0.415138 0.00108525i
\(259\) −0.884259 0.287313i −0.0549452 0.0178528i
\(260\) 0 0
\(261\) −28.1606 + 0.147235i −1.74309 + 0.00911361i
\(262\) −7.77445 + 3.96128i −0.480307 + 0.244729i
\(263\) 2.29146 1.16756i 0.141298 0.0719947i −0.381912 0.924199i \(-0.624734\pi\)
0.523210 + 0.852204i \(0.324734\pi\)
\(264\) 1.41500 + 8.78526i 0.0870873 + 0.540696i
\(265\) 0 0
\(266\) 0.0989071 + 0.0321369i 0.00606438 + 0.00197044i
\(267\) −0.0495712 18.9624i −0.00303371 1.16048i
\(268\) 10.6246 10.6246i 0.649002 0.649002i
\(269\) −19.5493 14.2034i −1.19194 0.865996i −0.198473 0.980106i \(-0.563598\pi\)
−0.993468 + 0.114110i \(0.963598\pi\)
\(270\) 0 0
\(271\) −9.36464 + 6.80381i −0.568861 + 0.413302i −0.834691 0.550718i \(-0.814354\pi\)
0.265830 + 0.964020i \(0.414354\pi\)
\(272\) 0.762690 4.81543i 0.0462448 0.291978i
\(273\) 0.325644 0.450683i 0.0197088 0.0272766i
\(274\) 2.82340i 0.170568i
\(275\) 0 0
\(276\) 4.57606 + 0.712519i 0.275446 + 0.0428886i
\(277\) −3.42126 + 6.71461i −0.205564 + 0.403442i −0.970654 0.240482i \(-0.922695\pi\)
0.765090 + 0.643924i \(0.222695\pi\)
\(278\) −6.87513 1.08891i −0.412343 0.0653087i
\(279\) −2.14257 6.47871i −0.128273 0.387870i
\(280\) 0 0
\(281\) 13.8790 19.1028i 0.827952 1.13958i −0.160349 0.987060i \(-0.551262\pi\)
0.988301 0.152517i \(-0.0487380\pi\)
\(282\) −14.1986 + 10.3727i −0.845516 + 0.617687i
\(283\) −9.72347 + 1.54005i −0.578000 + 0.0915463i −0.438588 0.898688i \(-0.644521\pi\)
−0.139412 + 0.990234i \(0.544521\pi\)
\(284\) 3.74899 11.5382i 0.222462 0.684667i
\(285\) 0 0
\(286\) −2.35974 7.26252i −0.139534 0.429442i
\(287\) 0.613989 + 1.20502i 0.0362426 + 0.0711302i
\(288\) −2.96057 + 0.484789i −0.174453 + 0.0285665i
\(289\) 6.43873 2.09207i 0.378749 0.123063i
\(290\) 0 0
\(291\) 15.5957 + 7.89513i 0.914238 + 0.462821i
\(292\) −1.46814 9.26944i −0.0859161 0.542453i
\(293\) 3.33944 + 3.33944i 0.195092 + 0.195092i 0.797892 0.602800i \(-0.205948\pi\)
−0.602800 + 0.797892i \(0.705948\pi\)
\(294\) 8.49379 8.53832i 0.495368 0.497965i
\(295\) 0 0
\(296\) −2.53039 3.48278i −0.147076 0.202433i
\(297\) 21.7195 + 15.5213i 1.26029 + 0.900640i
\(298\) 6.88178 + 3.50644i 0.398651 + 0.203123i
\(299\) −3.97428 −0.229838
\(300\) 0 0
\(301\) 0.831472 0.0479252
\(302\) −13.1751 6.71307i −0.758145 0.386294i
\(303\) −5.06343 + 15.7234i −0.290887 + 0.903285i
\(304\) 0.283032 + 0.389560i 0.0162330 + 0.0223428i
\(305\) 0 0
\(306\) −8.65891 11.7879i −0.494997 0.673868i
\(307\) 11.8133 + 11.8133i 0.674221 + 0.674221i 0.958686 0.284465i \(-0.0918160\pi\)
−0.284465 + 0.958686i \(0.591816\pi\)
\(308\) 0.173577 + 1.09592i 0.00989048 + 0.0624460i
\(309\) −7.91201 + 15.6291i −0.450098 + 0.889106i
\(310\) 0 0
\(311\) 28.7239 9.33296i 1.62878 0.529224i 0.654791 0.755810i \(-0.272756\pi\)
0.973991 + 0.226586i \(0.0727564\pi\)
\(312\) 2.44637 0.801950i 0.138498 0.0454015i
\(313\) 7.57278 + 14.8624i 0.428039 + 0.840073i 0.999807 + 0.0196580i \(0.00625773\pi\)
−0.571768 + 0.820415i \(0.693742\pi\)
\(314\) 5.06682 + 15.5941i 0.285937 + 0.880024i
\(315\) 0 0
\(316\) 0.675573 2.07920i 0.0380040 0.116964i
\(317\) 10.7129 1.69675i 0.601695 0.0952991i 0.151847 0.988404i \(-0.451478\pi\)
0.449848 + 0.893105i \(0.351478\pi\)
\(318\) 7.85886 + 10.7575i 0.440703 + 0.603253i
\(319\) −28.3466 + 39.0157i −1.58710 + 2.18446i
\(320\) 0 0
\(321\) 17.0199 8.72818i 0.949957 0.487160i
\(322\) 0.570371 + 0.0903379i 0.0317855 + 0.00503433i
\(323\) −1.06581 + 2.09176i −0.0593031 + 0.116389i
\(324\) −5.21364 + 7.33607i −0.289647 + 0.407559i
\(325\) 0 0
\(326\) 4.05769i 0.224735i
\(327\) −8.60889 6.22041i −0.476073 0.343989i
\(328\) −0.979584 + 6.18485i −0.0540885 + 0.341501i
\(329\) −1.77385 + 1.28878i −0.0977957 + 0.0710527i
\(330\) 0 0
\(331\) −7.79472 5.66319i −0.428436 0.311277i 0.352587 0.935779i \(-0.385302\pi\)
−0.781023 + 0.624502i \(0.785302\pi\)
\(332\) −3.53590 + 3.53590i −0.194058 + 0.194058i
\(333\) −12.7662 1.95361i −0.699586 0.107057i
\(334\) −13.1635 4.27710i −0.720277 0.234032i
\(335\) 0 0
\(336\) −0.369321 + 0.0594848i −0.0201481 + 0.00324516i
\(337\) 25.0858 12.7818i 1.36651 0.696272i 0.391864 0.920023i \(-0.371830\pi\)
0.974646 + 0.223752i \(0.0718304\pi\)
\(338\) 9.61460 4.89888i 0.522965 0.266464i
\(339\) −18.7863 + 3.02582i −1.02033 + 0.164340i
\(340\) 0 0
\(341\) −11.1139 3.61113i −0.601852 0.195554i
\(342\) 1.42794 + 0.218517i 0.0772143 + 0.0118161i
\(343\) 2.13093 2.13093i 0.115059 0.115059i
\(344\) 3.11459 + 2.26288i 0.167927 + 0.122006i
\(345\) 0 0
\(346\) 0.734684 0.533779i 0.0394969 0.0286962i
\(347\) −3.02097 + 19.0736i −0.162174 + 1.02393i 0.763556 + 0.645742i \(0.223452\pi\)
−0.925730 + 0.378185i \(0.876548\pi\)
\(348\) −13.1785 9.52222i −0.706443 0.510445i
\(349\) 14.4119i 0.771451i −0.922614 0.385725i \(-0.873951\pi\)
0.922614 0.385725i \(-0.126049\pi\)
\(350\) 0 0
\(351\) 3.45226 6.90887i 0.184268 0.368768i
\(352\) −2.33240 + 4.57759i −0.124317 + 0.243986i
\(353\) 34.5802 + 5.47696i 1.84052 + 0.291509i 0.977068 0.212929i \(-0.0683002\pi\)
0.863448 + 0.504438i \(0.168300\pi\)
\(354\) −7.68716 + 3.94215i −0.408568 + 0.209523i
\(355\) 0 0
\(356\) 6.43505 8.85709i 0.341057 0.469425i
\(357\) −1.07586 1.47269i −0.0569408 0.0779430i
\(358\) 11.7036 1.85367i 0.618555 0.0979695i
\(359\) −10.6846 + 32.8840i −0.563914 + 1.73555i 0.107242 + 0.994233i \(0.465798\pi\)
−0.671156 + 0.741316i \(0.734202\pi\)
\(360\) 0 0
\(361\) 5.79967 + 17.8496i 0.305246 + 0.939450i
\(362\) 7.80442 + 15.3170i 0.410191 + 0.805045i
\(363\) 25.3372 8.30583i 1.32986 0.435943i
\(364\) 0.305307 0.0992002i 0.0160024 0.00519950i
\(365\) 0 0
\(366\) 10.6751 21.0872i 0.557997 1.10224i
\(367\) −0.505240 3.18996i −0.0263733 0.166514i 0.970986 0.239135i \(-0.0768638\pi\)
−0.997360 + 0.0726205i \(0.976864\pi\)
\(368\) 1.89068 + 1.89068i 0.0985584 + 0.0985584i
\(369\) 11.1214 + 15.1401i 0.578954 + 0.788163i
\(370\) 0 0
\(371\) 0.976440 + 1.34395i 0.0506942 + 0.0697746i
\(372\) 1.20764 3.75007i 0.0626134 0.194432i
\(373\) −9.65408 4.91900i −0.499869 0.254696i 0.185829 0.982582i \(-0.440503\pi\)
−0.685698 + 0.727886i \(0.740503\pi\)
\(374\) −25.0479 −1.29519
\(375\) 0 0
\(376\) −10.1521 −0.523554
\(377\) 12.4317 + 6.33429i 0.640268 + 0.326233i
\(378\) −0.652497 + 0.913058i −0.0335608 + 0.0469627i
\(379\) 19.6854 + 27.0946i 1.01117 + 1.39176i 0.918213 + 0.396087i \(0.129632\pi\)
0.0929573 + 0.995670i \(0.470368\pi\)
\(380\) 0 0
\(381\) 18.3681 18.4644i 0.941025 0.945958i
\(382\) −3.49555 3.49555i −0.178848 0.178848i
\(383\) 2.54182 + 16.0484i 0.129881 + 0.820034i 0.963503 + 0.267699i \(0.0862632\pi\)
−0.833622 + 0.552335i \(0.813737\pi\)
\(384\) −1.54532 0.782298i −0.0788592 0.0399215i
\(385\) 0 0
\(386\) −3.20588 + 1.04165i −0.163175 + 0.0530187i
\(387\) 11.3977 1.86636i 0.579379 0.0948724i
\(388\) 4.58178 + 8.99225i 0.232605 + 0.456512i
\(389\) −0.804900 2.47723i −0.0408101 0.125600i 0.928576 0.371143i \(-0.121034\pi\)
−0.969386 + 0.245542i \(0.921034\pi\)
\(390\) 0 0
\(391\) −4.02838 + 12.3981i −0.203724 + 0.626998i
\(392\) 6.86775 1.08774i 0.346874 0.0549394i
\(393\) −12.2034 + 8.91510i −0.615578 + 0.449707i
\(394\) 4.30947 5.93148i 0.217108 0.298824i
\(395\) 0 0
\(396\) 4.83934 + 14.6332i 0.243186 + 0.735345i
\(397\) −1.86357 0.295160i −0.0935298 0.0148137i 0.109494 0.993987i \(-0.465077\pi\)
−0.203024 + 0.979174i \(0.565077\pi\)
\(398\) −3.78711 + 7.43262i −0.189831 + 0.372563i
\(399\) 0.177984 + 0.0277131i 0.00891032 + 0.00138739i
\(400\) 0 0
\(401\) 7.16880i 0.357993i 0.983850 + 0.178996i \(0.0572850\pi\)
−0.983850 + 0.178996i \(0.942715\pi\)
\(402\) 15.2419 21.0945i 0.760199 1.05210i
\(403\) −0.528887 + 3.33926i −0.0263458 + 0.166341i
\(404\) −7.71559 + 5.60571i −0.383865 + 0.278894i
\(405\) 0 0
\(406\) −1.64017 1.19165i −0.0814002 0.0591407i
\(407\) −15.6390 + 15.6390i −0.775197 + 0.775197i
\(408\) −0.0220755 8.44451i −0.00109290 0.418066i
\(409\) 15.2838 + 4.96600i 0.755734 + 0.245553i 0.661447 0.749992i \(-0.269943\pi\)
0.0942874 + 0.995545i \(0.469943\pi\)
\(410\) 0 0
\(411\) −0.777631 4.82805i −0.0383577 0.238150i
\(412\) −9.01147 + 4.59157i −0.443963 + 0.226211i
\(413\) −0.959822 + 0.489054i −0.0472297 + 0.0240648i
\(414\) 8.02136 0.0419389i 0.394228 0.00206119i
\(415\) 0 0
\(416\) 1.41362 + 0.459312i 0.0693083 + 0.0225196i
\(417\) −12.0565 + 0.0315179i −0.590408 + 0.00154344i
\(418\) 1.74927 1.74927i 0.0855596 0.0855596i
\(419\) 1.81333 + 1.31746i 0.0885872 + 0.0643624i 0.631197 0.775622i \(-0.282564\pi\)
−0.542610 + 0.839985i \(0.682564\pi\)
\(420\) 0 0
\(421\) 2.09500 1.52210i 0.102104 0.0741828i −0.535562 0.844496i \(-0.679900\pi\)
0.637666 + 0.770313i \(0.279900\pi\)
\(422\) −0.670692 + 4.23458i −0.0326488 + 0.206136i
\(423\) −21.4229 + 21.6481i −1.04162 + 1.05257i
\(424\) 7.69169i 0.373542i
\(425\) 0 0
\(426\) 3.23292 20.7630i 0.156636 1.00597i
\(427\) 1.33799 2.62595i 0.0647498 0.127079i
\(428\) 10.9072 + 1.72754i 0.527222 + 0.0835037i
\(429\) −6.03545 11.7691i −0.291394 0.568216i
\(430\) 0 0
\(431\) −0.661426 + 0.910375i −0.0318598 + 0.0438512i −0.824650 0.565644i \(-0.808628\pi\)
0.792790 + 0.609495i \(0.208628\pi\)
\(432\) −4.92909 + 1.64441i −0.237151 + 0.0791165i
\(433\) −20.2750 + 3.21125i −0.974355 + 0.154323i −0.623258 0.782016i \(-0.714191\pi\)
−0.351097 + 0.936339i \(0.614191\pi\)
\(434\) 0.151807 0.467215i 0.00728698 0.0224270i
\(435\) 0 0
\(436\) −1.89491 5.83194i −0.0907498 0.279299i
\(437\) −0.584515 1.14718i −0.0279611 0.0548768i
\(438\) −5.06355 15.4465i −0.241946 0.738062i
\(439\) 22.3736 7.26963i 1.06783 0.346960i 0.278191 0.960526i \(-0.410265\pi\)
0.789644 + 0.613565i \(0.210265\pi\)
\(440\) 0 0
\(441\) 12.1728 16.9400i 0.579659 0.806668i
\(442\) 1.13363 + 7.15749i 0.0539215 + 0.340447i
\(443\) 13.6168 + 13.6168i 0.646952 + 0.646952i 0.952255 0.305303i \(-0.0987577\pi\)
−0.305303 + 0.952255i \(0.598758\pi\)
\(444\) −5.28624 5.25867i −0.250874 0.249565i
\(445\) 0 0
\(446\) −0.429625 0.591328i −0.0203433 0.0280002i
\(447\) 12.7337 + 4.10066i 0.602283 + 0.193954i
\(448\) −0.192436 0.0980509i −0.00909173 0.00463247i
\(449\) 19.2184 0.906973 0.453487 0.891263i \(-0.350180\pi\)
0.453487 + 0.891263i \(0.350180\pi\)
\(450\) 0 0
\(451\) 32.1710 1.51487
\(452\) −9.78864 4.98756i −0.460419 0.234595i
\(453\) −24.3786 7.85069i −1.14541 0.368858i
\(454\) 1.94595 + 2.67837i 0.0913281 + 0.125702i
\(455\) 0 0
\(456\) 0.591281 + 0.588198i 0.0276893 + 0.0275449i
\(457\) −15.9563 15.9563i −0.746405 0.746405i 0.227397 0.973802i \(-0.426979\pi\)
−0.973802 + 0.227397i \(0.926979\pi\)
\(458\) −1.65068 10.4220i −0.0771311 0.486986i
\(459\) −18.0535 17.7725i −0.842666 0.829551i
\(460\) 0 0
\(461\) 15.2184 4.94475i 0.708790 0.230300i 0.0676337 0.997710i \(-0.478455\pi\)
0.641156 + 0.767410i \(0.278455\pi\)
\(462\) 0.598662 + 1.82624i 0.0278523 + 0.0849642i
\(463\) 2.81092 + 5.51675i 0.130635 + 0.256385i 0.947054 0.321075i \(-0.104044\pi\)
−0.816419 + 0.577460i \(0.804044\pi\)
\(464\) −2.90074 8.92755i −0.134663 0.414451i
\(465\) 0 0
\(466\) −3.89021 + 11.9728i −0.180210 + 0.554630i
\(467\) −22.9270 + 3.63127i −1.06093 + 0.168035i −0.662424 0.749129i \(-0.730472\pi\)
−0.398509 + 0.917164i \(0.630472\pi\)
\(468\) 3.96244 2.04513i 0.183164 0.0945362i
\(469\) 1.90744 2.62537i 0.0880775 0.121228i
\(470\) 0 0
\(471\) 12.9593 + 25.2705i 0.597133 + 1.16440i
\(472\) −4.92635 0.780256i −0.226753 0.0359142i
\(473\) 8.97936 17.6230i 0.412871 0.810305i
\(474\) 0.582577 3.74153i 0.0267587 0.171854i
\(475\) 0 0
\(476\) 1.05298i 0.0482633i
\(477\) 16.4016 + 16.2310i 0.750979 + 0.743167i
\(478\) −1.83738 + 11.6007i −0.0840396 + 0.530605i
\(479\) −18.1330 + 13.1744i −0.828519 + 0.601954i −0.919140 0.393931i \(-0.871115\pi\)
0.0906212 + 0.995885i \(0.471115\pi\)
\(480\) 0 0
\(481\) 5.17668 + 3.76108i 0.236036 + 0.171491i
\(482\) 0.860035 0.860035i 0.0391735 0.0391735i
\(483\) 1.00022 0.00261477i 0.0455117 0.000118976i
\(484\) 14.6409 + 4.75712i 0.665496 + 0.216233i
\(485\) 0 0
\(486\) −6.89486 + 13.9807i −0.312757 + 0.634179i
\(487\) −18.8976 + 9.62881i −0.856332 + 0.436323i −0.826303 0.563226i \(-0.809560\pi\)
−0.0300294 + 0.999549i \(0.509560\pi\)
\(488\) 12.1585 6.19509i 0.550391 0.280438i
\(489\) 1.11758 + 6.93870i 0.0505389 + 0.313779i
\(490\) 0 0
\(491\) −29.6177 9.62339i −1.33663 0.434297i −0.448456 0.893805i \(-0.648026\pi\)
−0.888174 + 0.459507i \(0.848026\pi\)
\(492\) 0.0283534 + 10.8460i 0.00127827 + 0.488974i
\(493\) 32.3613 32.3613i 1.45748 1.45748i
\(494\) −0.579028 0.420688i −0.0260517 0.0189277i
\(495\) 0 0
\(496\) 1.84019 1.33698i 0.0826270 0.0600320i
\(497\) 0.409892 2.58795i 0.0183862 0.116086i
\(498\) −5.07256 + 7.02030i −0.227307 + 0.314587i
\(499\) 1.25659i 0.0562528i −0.999604 0.0281264i \(-0.991046\pi\)
0.999604 0.0281264i \(-0.00895410\pi\)
\(500\) 0 0
\(501\) −23.6878 3.68833i −1.05829 0.164783i
\(502\) −10.2658 + 20.1477i −0.458184 + 0.899236i
\(503\) −25.9752 4.11407i −1.15818 0.183437i −0.452363 0.891834i \(-0.649419\pi\)
−0.705815 + 0.708397i \(0.749419\pi\)
\(504\) −0.615160 + 0.203439i −0.0274014 + 0.00906191i
\(505\) 0 0
\(506\) 8.07434 11.1134i 0.358948 0.494050i
\(507\) 15.0918 11.0252i 0.670251 0.489648i
\(508\) 14.8517 2.35228i 0.658938 0.104366i
\(509\) −5.31690 + 16.3637i −0.235668 + 0.725310i 0.761365 + 0.648324i \(0.224530\pi\)
−0.997032 + 0.0769863i \(0.975470\pi\)
\(510\) 0 0
\(511\) −0.626355 1.92772i −0.0277083 0.0852775i
\(512\) −0.453990 0.891007i −0.0200637 0.0393773i
\(513\) 2.50199 0.0196223i 0.110465 0.000866347i
\(514\) −4.01395 + 1.30421i −0.177048 + 0.0575263i
\(515\) 0 0
\(516\) 5.94923 + 3.01172i 0.261900 + 0.132584i
\(517\) 8.15912 + 51.5147i 0.358838 + 2.26561i
\(518\) −0.657443 0.657443i −0.0288864 0.0288864i
\(519\) 1.10930 1.11512i 0.0486930 0.0489483i
\(520\) 0 0
\(521\) 7.91212 + 10.8901i 0.346636 + 0.477104i 0.946365 0.323099i \(-0.104725\pi\)
−0.599729 + 0.800203i \(0.704725\pi\)
\(522\) −25.1581 12.6534i −1.10114 0.553826i
\(523\) 22.9585 + 11.6979i 1.00390 + 0.511514i 0.877046 0.480407i \(-0.159511\pi\)
0.126858 + 0.991921i \(0.459511\pi\)
\(524\) −8.72546 −0.381174
\(525\) 0 0
\(526\) 2.57177 0.112134
\(527\) 9.88101 + 5.03463i 0.430424 + 0.219312i
\(528\) −2.72765 + 8.47012i −0.118706 + 0.368615i
\(529\) 9.31679 + 12.8235i 0.405078 + 0.557542i
\(530\) 0 0
\(531\) −12.0594 + 8.85835i −0.523333 + 0.384420i
\(532\) 0.0735370 + 0.0735370i 0.00318823 + 0.00318823i
\(533\) −1.45602 9.19295i −0.0630672 0.398191i
\(534\) 8.56457 16.9181i 0.370625 0.732118i
\(535\) 0 0
\(536\) 14.2901 4.64313i 0.617237 0.200553i
\(537\) 19.5028 6.39325i 0.841607 0.275889i
\(538\) −10.9703 21.5305i −0.472965 0.928246i
\(539\) −11.0391 33.9747i −0.475486 1.46340i
\(540\) 0 0
\(541\) −6.47364 + 19.9238i −0.278323 + 0.856591i 0.709998 + 0.704204i \(0.248696\pi\)
−0.988321 + 0.152387i \(0.951304\pi\)
\(542\) −11.4328 + 1.81078i −0.491082 + 0.0777797i
\(543\) 17.5643 + 24.0428i 0.753757 + 1.03177i
\(544\) 2.86572 3.94433i 0.122867 0.169112i
\(545\) 0 0
\(546\) 0.494756 0.253722i 0.0211736 0.0108583i
\(547\) −43.0967 6.82585i −1.84268 0.291852i −0.864974 0.501817i \(-0.832665\pi\)
−0.977709 + 0.209965i \(0.932665\pi\)
\(548\) 1.28180 2.51567i 0.0547557 0.107464i
\(549\) 12.4467 38.9995i 0.531211 1.66446i
\(550\) 0 0
\(551\) 4.52004i 0.192560i
\(552\) 3.75382 + 2.71235i 0.159773 + 0.115445i
\(553\) 0.0738630 0.466353i 0.00314098 0.0198313i
\(554\) −6.09674 + 4.42954i −0.259025 + 0.188193i
\(555\) 0 0
\(556\) −5.63143 4.09147i −0.238826 0.173517i
\(557\) 20.7979 20.7979i 0.881236 0.881236i −0.112424 0.993660i \(-0.535861\pi\)
0.993660 + 0.112424i \(0.0358615\pi\)
\(558\) 1.03223 6.74528i 0.0436976 0.285551i
\(559\) −5.44220 1.76828i −0.230181 0.0747902i
\(560\) 0 0
\(561\) −42.8322 + 6.89878i −1.80838 + 0.291267i
\(562\) 21.0388 10.7198i 0.887467 0.452187i
\(563\) −14.0139 + 7.14045i −0.590616 + 0.300934i −0.723639 0.690179i \(-0.757532\pi\)
0.133022 + 0.991113i \(0.457532\pi\)
\(564\) −17.3602 + 2.79613i −0.730996 + 0.117738i
\(565\) 0 0
\(566\) −9.36284 3.04217i −0.393550 0.127872i
\(567\) −0.864300 + 1.74105i −0.0362972 + 0.0731174i
\(568\) 8.57861 8.57861i 0.359950 0.359950i
\(569\) −3.20445 2.32817i −0.134338 0.0976021i 0.518587 0.855025i \(-0.326458\pi\)
−0.652925 + 0.757423i \(0.726458\pi\)
\(570\) 0 0
\(571\) −31.7943 + 23.0999i −1.33055 + 0.966702i −0.330815 + 0.943696i \(0.607324\pi\)
−0.999735 + 0.0230060i \(0.992676\pi\)
\(572\) 1.19457 7.54225i 0.0499477 0.315357i
\(573\) −6.94020 5.01468i −0.289931 0.209491i
\(574\) 1.35243i 0.0564492i
\(575\) 0 0
\(576\) −2.85798 0.912121i −0.119082 0.0380050i
\(577\) 8.56788 16.8154i 0.356685 0.700034i −0.641036 0.767511i \(-0.721495\pi\)
0.997721 + 0.0674769i \(0.0214949\pi\)
\(578\) 6.68673 + 1.05907i 0.278131 + 0.0440517i
\(579\) −5.19519 + 2.66421i −0.215905 + 0.110721i
\(580\) 0 0
\(581\) −0.634802 + 0.873729i −0.0263360 + 0.0362484i
\(582\) 10.3116 + 14.1149i 0.427429 + 0.585083i
\(583\) 39.0299 6.18173i 1.61645 0.256021i
\(584\) 2.90012 8.92565i 0.120008 0.369346i
\(585\) 0 0
\(586\) 1.45939 + 4.49153i 0.0602867 + 0.185543i
\(587\) −2.11434 4.14963i −0.0872683 0.171274i 0.843247 0.537526i \(-0.180641\pi\)
−0.930516 + 0.366252i \(0.880641\pi\)
\(588\) 11.4443 3.75160i 0.471957 0.154713i
\(589\) −1.04166 + 0.338457i −0.0429210 + 0.0139459i
\(590\) 0 0
\(591\) 5.73558 11.3298i 0.235930 0.466047i
\(592\) −0.673443 4.25195i −0.0276783 0.174754i
\(593\) −32.4687 32.4687i −1.33333 1.33333i −0.902371 0.430960i \(-0.858175\pi\)
−0.430960 0.902371i \(-0.641825\pi\)
\(594\) 12.3057 + 23.6901i 0.504907 + 0.972015i
\(595\) 0 0
\(596\) 4.53982 + 6.24853i 0.185958 + 0.255950i
\(597\) −4.42888 + 13.7529i −0.181262 + 0.562870i
\(598\) −3.54111 1.80428i −0.144807 0.0737826i
\(599\) 18.2921 0.747393 0.373697 0.927551i \(-0.378090\pi\)
0.373697 + 0.927551i \(0.378090\pi\)
\(600\) 0 0
\(601\) −0.981781 −0.0400477 −0.0200238 0.999800i \(-0.506374\pi\)
−0.0200238 + 0.999800i \(0.506374\pi\)
\(602\) 0.740847 + 0.377480i 0.0301947 + 0.0153850i
\(603\) 20.2540 40.2698i 0.824807 1.63991i
\(604\) −8.69147 11.9628i −0.353651 0.486759i
\(605\) 0 0
\(606\) −11.6498 + 11.7109i −0.473241 + 0.475722i
\(607\) 2.39455 + 2.39455i 0.0971917 + 0.0971917i 0.754031 0.656839i \(-0.228107\pi\)
−0.656839 + 0.754031i \(0.728107\pi\)
\(608\) 0.0753267 + 0.475594i 0.00305490 + 0.0192879i
\(609\) −3.13292 1.58600i −0.126952 0.0642679i
\(610\) 0 0
\(611\) 14.3512 4.66298i 0.580586 0.188644i
\(612\) −2.36357 14.4341i −0.0955415 0.583465i
\(613\) −6.24017 12.2470i −0.252038 0.494653i 0.729973 0.683476i \(-0.239533\pi\)
−0.982011 + 0.188823i \(0.939533\pi\)
\(614\) 5.16261 + 15.8889i 0.208346 + 0.641223i
\(615\) 0 0
\(616\) −0.342880 + 1.05528i −0.0138150 + 0.0425183i
\(617\) 10.1292 1.60431i 0.407787 0.0645872i 0.0508287 0.998707i \(-0.483814\pi\)
0.356959 + 0.934120i \(0.383814\pi\)
\(618\) −14.1451 + 10.3336i −0.568999 + 0.415679i
\(619\) 27.3325 37.6199i 1.09859 1.51207i 0.261338 0.965247i \(-0.415836\pi\)
0.837247 0.546825i \(-0.184164\pi\)
\(620\) 0 0
\(621\) 13.7051 2.28099i 0.549966 0.0915329i
\(622\) 29.8303 + 4.72465i 1.19608 + 0.189441i
\(623\) 1.07346 2.10678i 0.0430072 0.0844063i
\(624\) 2.54381 + 0.396086i 0.101834 + 0.0158561i
\(625\) 0 0
\(626\) 16.6805i 0.666686i
\(627\) 2.50948 3.47306i 0.100219 0.138701i
\(628\) −2.56499 + 16.1947i −0.102354 + 0.646239i
\(629\) 16.9802 12.3368i 0.677043 0.491900i
\(630\) 0 0
\(631\) −20.6748 15.0211i −0.823051 0.597981i 0.0945340 0.995522i \(-0.469864\pi\)
−0.917585 + 0.397540i \(0.869864\pi\)
\(632\) 1.54588 1.54588i 0.0614917 0.0614917i
\(633\) 0.0194127 + 7.42591i 0.000771586 + 0.295153i
\(634\) 10.3155 + 3.35172i 0.409683 + 0.133114i
\(635\) 0 0
\(636\) 2.11847 + 13.1529i 0.0840030 + 0.521546i
\(637\) −9.20875 + 4.69209i −0.364864 + 0.185907i
\(638\) −42.9697 + 21.8942i −1.70119 + 0.866798i
\(639\) −0.190290 36.3955i −0.00752777 1.43978i
\(640\) 0 0
\(641\) 0.702023 + 0.228101i 0.0277282 + 0.00900945i 0.322848 0.946451i \(-0.395360\pi\)
−0.295120 + 0.955460i \(0.595360\pi\)
\(642\) 19.1273 0.0500024i 0.754896 0.00197344i
\(643\) −17.1573 + 17.1573i −0.676616 + 0.676616i −0.959233 0.282617i \(-0.908797\pi\)
0.282617 + 0.959233i \(0.408797\pi\)
\(644\) 0.467192 + 0.339435i 0.0184099 + 0.0133756i
\(645\) 0 0
\(646\) −1.89928 + 1.37991i −0.0747262 + 0.0542918i
\(647\) 0.943217 5.95524i 0.0370817 0.234125i −0.962186 0.272394i \(-0.912185\pi\)
0.999267 + 0.0382696i \(0.0121846\pi\)
\(648\) −7.97590 + 4.16954i −0.313323 + 0.163795i
\(649\) 25.6248i 1.00586i
\(650\) 0 0
\(651\) 0.130910 0.840754i 0.00513078 0.0329517i
\(652\) −1.84215 + 3.61543i −0.0721443 + 0.141591i
\(653\) 9.97451 + 1.57981i 0.390333 + 0.0618226i 0.348516 0.937303i \(-0.386686\pi\)
0.0418163 + 0.999125i \(0.486686\pi\)
\(654\) −4.84657 9.45078i −0.189516 0.369555i
\(655\) 0 0
\(656\) −3.68068 + 5.06602i −0.143706 + 0.197795i
\(657\) −12.9131 25.0191i −0.503787 0.976087i
\(658\) −2.16561 + 0.342999i −0.0844242 + 0.0133715i
\(659\) 3.59331 11.0591i 0.139975 0.430800i −0.856355 0.516387i \(-0.827277\pi\)
0.996331 + 0.0855871i \(0.0272766\pi\)
\(660\) 0 0
\(661\) 12.8291 + 39.4838i 0.498993 + 1.53574i 0.810641 + 0.585544i \(0.199119\pi\)
−0.311648 + 0.950197i \(0.600881\pi\)
\(662\) −4.37411 8.58467i −0.170005 0.333653i
\(663\) 3.90987 + 11.9272i 0.151847 + 0.463213i
\(664\) −4.75577 + 1.54524i −0.184560 + 0.0599671i
\(665\) 0 0
\(666\) −10.4879 7.53643i −0.406397 0.292031i
\(667\) 3.92637 + 24.7901i 0.152030 + 0.959877i
\(668\) −9.78704 9.78704i −0.378672 0.378672i
\(669\) −0.897530 0.892849i −0.0347005 0.0345195i
\(670\) 0 0
\(671\) −41.2074 56.7171i −1.59079 2.18954i
\(672\) −0.356073 0.114667i −0.0137358 0.00442337i
\(673\) 23.9046 + 12.1800i 0.921454 + 0.469504i 0.849313 0.527890i \(-0.177017\pi\)
0.0721411 + 0.997394i \(0.477017\pi\)
\(674\) 28.1544 1.08447
\(675\) 0 0
\(676\) 10.7907 0.415028
\(677\) −19.6621 10.0184i −0.755677 0.385037i 0.0333112 0.999445i \(-0.489395\pi\)
−0.788988 + 0.614408i \(0.789395\pi\)
\(678\) −18.1124 5.83277i −0.695602 0.224006i
\(679\) 1.28118 + 1.76340i 0.0491673 + 0.0676729i
\(680\) 0 0
\(681\) 4.06529 + 4.04409i 0.155782 + 0.154970i
\(682\) −8.26315 8.26315i −0.316413 0.316413i
\(683\) −3.06282 19.3379i −0.117196 0.739944i −0.974376 0.224927i \(-0.927786\pi\)
0.857180 0.515017i \(-0.172214\pi\)
\(684\) 1.17310 + 0.842973i 0.0448547 + 0.0322319i
\(685\) 0 0
\(686\) 2.86609 0.931249i 0.109428 0.0355552i
\(687\) −5.69313 17.3670i −0.217207 0.662594i
\(688\) 1.74779 + 3.43023i 0.0666339 + 0.130776i
\(689\) −3.53289 10.8731i −0.134592 0.414232i
\(690\) 0 0
\(691\) 12.6136 38.8206i 0.479843 1.47681i −0.359469 0.933157i \(-0.617042\pi\)
0.839313 0.543649i \(-0.182958\pi\)
\(692\) 0.896939 0.142061i 0.0340965 0.00540036i
\(693\) 1.52671 + 2.95800i 0.0579949 + 0.112365i
\(694\) −11.3510 + 15.6232i −0.430876 + 0.593050i
\(695\) 0 0
\(696\) −7.41915 14.4673i −0.281222 0.548381i
\(697\) −30.1540 4.77592i −1.14216 0.180901i
\(698\) 6.54286 12.8411i 0.247651 0.486042i
\(699\) −3.35470 + 21.5451i −0.126886 + 0.814912i
\(700\) 0 0
\(701\) 1.34594i 0.0508356i 0.999677 + 0.0254178i \(0.00809161\pi\)
−0.999677 + 0.0254178i \(0.991908\pi\)
\(702\) 6.21255 4.58855i 0.234478 0.173184i
\(703\) −0.324278 + 2.04741i −0.0122304 + 0.0772195i
\(704\) −4.15636 + 3.01977i −0.156649 + 0.113812i
\(705\) 0 0
\(706\) 28.3247 + 20.5791i 1.06601 + 0.774503i
\(707\) −1.45647 + 1.45647i −0.0547762 + 0.0547762i
\(708\) −8.63901 + 0.0225840i −0.324674 + 0.000848758i
\(709\) −5.99345 1.94739i −0.225089 0.0731358i 0.194301 0.980942i \(-0.437756\pi\)
−0.419390 + 0.907806i \(0.637756\pi\)
\(710\) 0 0
\(711\) −0.0342906 6.55851i −0.00128600 0.245963i
\(712\) 9.75471 4.97027i 0.365573 0.186269i
\(713\) −5.41900 + 2.76112i −0.202943 + 0.103405i
\(714\) −0.290016 1.80061i −0.0108536 0.0673861i
\(715\) 0 0
\(716\) 11.2695 + 3.66170i 0.421163 + 0.136844i
\(717\) 0.0531816 + 20.3435i 0.00198610 + 0.759740i
\(718\) −24.4491 + 24.4491i −0.912432 + 0.912432i
\(719\) 15.2779 + 11.1001i 0.569770 + 0.413962i 0.835022 0.550217i \(-0.185455\pi\)
−0.265251 + 0.964179i \(0.585455\pi\)
\(720\) 0 0
\(721\) −1.76717 + 1.28392i −0.0658127 + 0.0478157i
\(722\) −2.93598 + 18.5371i −0.109266 + 0.689878i
\(723\) 1.23380 1.70755i 0.0458854 0.0635043i
\(724\) 17.1907i 0.638888i
\(725\) 0 0
\(726\) 26.3463 + 4.10228i 0.977805 + 0.152250i
\(727\) 5.62601 11.0417i 0.208657 0.409513i −0.762832 0.646597i \(-0.776192\pi\)
0.971489 + 0.237084i \(0.0761916\pi\)
\(728\) 0.317066 + 0.0502184i 0.0117513 + 0.00186122i
\(729\) −7.93968 + 25.8062i −0.294062 + 0.955786i
\(730\) 0 0
\(731\) −11.0326 + 15.1850i −0.408055 + 0.561639i
\(732\) 19.0850 13.9424i 0.705401 0.515327i
\(733\) −9.27418 + 1.46889i −0.342550 + 0.0542545i −0.325339 0.945597i \(-0.605478\pi\)
−0.0172103 + 0.999852i \(0.505478\pi\)
\(734\) 0.998039 3.07165i 0.0368383 0.113377i
\(735\) 0 0
\(736\) 0.826257 + 2.54296i 0.0304562 + 0.0937346i
\(737\) −35.0454 68.7804i −1.29091 2.53356i
\(738\) 3.03572 + 18.5389i 0.111746 + 0.682428i
\(739\) −18.0916 + 5.87832i −0.665511 + 0.216238i −0.622241 0.782826i \(-0.713778\pi\)
−0.0432699 + 0.999063i \(0.513778\pi\)
\(740\) 0 0
\(741\) −1.10601 0.559904i −0.0406304 0.0205686i
\(742\) 0.259872 + 1.64077i 0.00954019 + 0.0602344i
\(743\) −23.1938 23.1938i −0.850899 0.850899i 0.139345 0.990244i \(-0.455500\pi\)
−0.990244 + 0.139345i \(0.955500\pi\)
\(744\) 2.77851 2.79308i 0.101865 0.102399i
\(745\) 0 0
\(746\) −6.36867 8.76572i −0.233174 0.320936i
\(747\) −6.74058 + 13.4019i −0.246625 + 0.490350i
\(748\) −22.3178 11.3715i −0.816020 0.415783i
\(749\) 2.38506 0.0871483
\(750\) 0 0
\(751\) 35.1267 1.28179 0.640895 0.767628i \(-0.278563\pi\)
0.640895 + 0.767628i \(0.278563\pi\)
\(752\) −9.04558 4.60895i −0.329858 0.168071i
\(753\) −12.0054 + 37.2803i −0.437502 + 1.35857i
\(754\) 8.20106 + 11.2878i 0.298665 + 0.411077i
\(755\) 0 0
\(756\) −0.995899 + 0.517314i −0.0362205 + 0.0188145i
\(757\) −20.0652 20.0652i −0.729283 0.729283i 0.241194 0.970477i \(-0.422461\pi\)
−0.970477 + 0.241194i \(0.922461\pi\)
\(758\) 5.23911 + 33.0785i 0.190293 + 1.20146i
\(759\) 10.7463 21.2279i 0.390067 0.770523i
\(760\) 0 0
\(761\) −30.4666 + 9.89919i −1.10441 + 0.358845i −0.803799 0.594901i \(-0.797191\pi\)
−0.300613 + 0.953746i \(0.597191\pi\)
\(762\) 24.7487 8.11294i 0.896552 0.293901i
\(763\) −0.601254 1.18003i −0.0217669 0.0427199i
\(764\) −1.52761 4.70151i −0.0552671 0.170095i
\(765\) 0 0
\(766\) −5.02104 + 15.4532i −0.181418 + 0.558346i
\(767\) 7.32235 1.15975i 0.264395 0.0418760i
\(768\) −1.02173 1.39859i −0.0368686 0.0504674i
\(769\) −8.74366 + 12.0346i −0.315305 + 0.433980i −0.937026 0.349259i \(-0.886433\pi\)
0.621722 + 0.783238i \(0.286433\pi\)
\(770\) 0 0
\(771\) −6.50470 + 3.33576i −0.234261 + 0.120134i
\(772\) −3.32936 0.527318i −0.119826 0.0189786i
\(773\) 10.0990 19.8204i 0.363235 0.712889i −0.634985 0.772524i \(-0.718994\pi\)
0.998220 + 0.0596354i \(0.0189938\pi\)
\(774\) 11.0028 + 3.51152i 0.395486 + 0.126219i
\(775\) 0 0
\(776\) 10.0922i 0.362290i
\(777\) −1.30531 0.943161i −0.0468278 0.0338357i
\(778\) 0.407467 2.57264i 0.0146084 0.0922337i
\(779\) 2.43940 1.77233i 0.0874006 0.0635003i
\(780\) 0 0
\(781\) −50.4249 36.6358i −1.80435 1.31093i
\(782\) −9.21792 + 9.21792i −0.329632 + 0.329632i
\(783\) −46.5057 14.7084i −1.66198 0.525635i
\(784\) 6.61303 + 2.14870i 0.236180 + 0.0767395i
\(785\) 0 0
\(786\) −14.9207 + 2.40320i −0.532202 + 0.0857193i
\(787\) 45.7145 23.2927i 1.62955 0.830295i 0.631035 0.775755i \(-0.282631\pi\)
0.998512 0.0545406i \(-0.0173694\pi\)
\(788\) 6.53260 3.32853i 0.232714 0.118574i
\(789\) 4.39775 0.708326i 0.156564 0.0252171i
\(790\) 0 0
\(791\) −2.25659 0.733210i −0.0802351 0.0260700i
\(792\) −2.33144 + 15.2353i −0.0828442 + 0.541362i
\(793\) −14.3420 + 14.3420i −0.509301 + 0.509301i
\(794\) −1.52645 1.10903i −0.0541717 0.0393580i
\(795\) 0 0
\(796\) −6.74867 + 4.90320i −0.239200 + 0.173789i
\(797\) −0.485494 + 3.06529i −0.0171971 + 0.108578i −0.994794 0.101909i \(-0.967505\pi\)
0.977597 + 0.210487i \(0.0675050\pi\)
\(798\) 0.146003 + 0.105495i 0.00516845 + 0.00373450i
\(799\) 49.4961i 1.75105i
\(800\) 0 0
\(801\) 9.98587 31.2890i 0.352833 1.10554i
\(802\) −3.25457 + 6.38745i −0.114923 + 0.225549i
\(803\) −47.6222 7.54261i −1.68055 0.266173i
\(804\) 23.1574 11.8756i 0.816698 0.418821i
\(805\) 0 0
\(806\) −1.98724 + 2.73520i −0.0699974 + 0.0963431i
\(807\) −24.6894 33.7959i −0.869109 1.18967i
\(808\) −9.41958 + 1.49192i −0.331380 + 0.0524854i
\(809\) 4.71934 14.5246i 0.165923 0.510659i −0.833180 0.553002i \(-0.813482\pi\)
0.999103 + 0.0423432i \(0.0134823\pi\)
\(810\) 0 0
\(811\) 1.02202 + 3.14544i 0.0358879 + 0.110451i 0.967396 0.253270i \(-0.0815060\pi\)
−0.931508 + 0.363721i \(0.881506\pi\)
\(812\) −0.920402 1.80639i −0.0322998 0.0633919i
\(813\) −19.0515 + 6.24533i −0.668166 + 0.219033i
\(814\) −21.0344 + 6.83450i −0.737256 + 0.239549i
\(815\) 0 0
\(816\) 3.81406 7.53414i 0.133519 0.263748i
\(817\) −0.289996 1.83096i −0.0101457 0.0640572i
\(818\) 11.3634 + 11.3634i 0.397313 + 0.397313i
\(819\) 0.776158 0.570136i 0.0271212 0.0199222i
\(820\) 0 0
\(821\) 18.3359 + 25.2372i 0.639927 + 0.880784i 0.998612 0.0526750i \(-0.0167748\pi\)
−0.358685 + 0.933459i \(0.616775\pi\)
\(822\) 1.49901 4.65486i 0.0522841 0.162357i
\(823\) −13.9035 7.08420i −0.484647 0.246940i 0.194555 0.980892i \(-0.437674\pi\)
−0.679202 + 0.733952i \(0.737674\pi\)
\(824\) −10.1138 −0.352331
\(825\) 0 0
\(826\) −1.07723 −0.0374817
\(827\) −3.23908 1.65039i −0.112634 0.0573898i 0.396766 0.917920i \(-0.370132\pi\)
−0.509400 + 0.860530i \(0.670132\pi\)
\(828\) 7.16612 + 3.60425i 0.249040 + 0.125256i
\(829\) −14.6691 20.1903i −0.509480 0.701239i 0.474351 0.880336i \(-0.342683\pi\)
−0.983832 + 0.179096i \(0.942683\pi\)
\(830\) 0 0
\(831\) −9.20549 + 9.25375i −0.319335 + 0.321009i
\(832\) 1.05102 + 1.05102i 0.0364375 + 0.0364375i
\(833\) 5.30325 + 33.4834i 0.183747 + 1.16013i
\(834\) −10.7567 5.44544i −0.372474 0.188560i
\(835\) 0 0
\(836\) 2.35276 0.764459i 0.0813720 0.0264394i
\(837\) −0.0926914 11.8188i −0.00320388 0.408518i
\(838\) 1.01758 + 1.99711i 0.0351516 + 0.0689889i
\(839\) 5.55073 + 17.0834i 0.191632 + 0.589784i 0.999999 + 0.00110507i \(0.000351754\pi\)
−0.808367 + 0.588679i \(0.799648\pi\)
\(840\) 0 0
\(841\) 18.2677 56.2221i 0.629920 1.93869i
\(842\) 2.55767 0.405096i 0.0881433 0.0139605i
\(843\) 33.0241 24.1255i 1.13741 0.830928i
\(844\) −2.52005 + 3.46855i −0.0867437 + 0.119392i
\(845\) 0 0
\(846\) −28.9160 + 9.56282i −0.994153 + 0.328776i
\(847\) 3.28387 + 0.520114i 0.112835 + 0.0178713i
\(848\) −3.49196 + 6.85335i −0.119914 + 0.235345i
\(849\) −16.8485 2.62340i −0.578238 0.0900350i
\(850\) 0 0
\(851\) 11.5107i 0.394581i
\(852\) 12.3068 17.0323i 0.421623 0.583516i
\(853\) 4.94081 31.1950i 0.169170 1.06810i −0.746270 0.665643i \(-0.768157\pi\)
0.915440 0.402454i \(-0.131843\pi\)
\(854\) 2.38431 1.73230i 0.0815894 0.0592782i
\(855\) 0 0
\(856\) 8.93414 + 6.49104i 0.305363 + 0.221859i
\(857\) 8.57240 8.57240i 0.292828 0.292828i −0.545369 0.838196i \(-0.683610\pi\)
0.838196 + 0.545369i \(0.183610\pi\)
\(858\) −0.0345761 13.2264i −0.00118041 0.451540i
\(859\) 1.99366 + 0.647780i 0.0680228 + 0.0221020i 0.342831 0.939397i \(-0.388614\pi\)
−0.274808 + 0.961499i \(0.588614\pi\)
\(860\) 0 0
\(861\) 0.372491 + 2.31267i 0.0126944 + 0.0788155i
\(862\) −1.00264 + 0.510869i −0.0341500 + 0.0174003i
\(863\) 25.5918 13.0397i 0.871155 0.443876i 0.0395333 0.999218i \(-0.487413\pi\)
0.831622 + 0.555343i \(0.187413\pi\)
\(864\) −5.13840 0.772583i −0.174812 0.0262838i
\(865\) 0 0
\(866\) −19.5231 6.34342i −0.663420 0.215558i
\(867\) 11.7261 0.0306542i 0.398239 0.00104107i
\(868\) 0.347372 0.347372i 0.0117906 0.0117906i
\(869\) −9.08664 6.60183i −0.308243 0.223952i
\(870\) 0 0
\(871\) −18.0680 + 13.1272i −0.612212 + 0.444798i
\(872\) 0.959266 6.05656i 0.0324848 0.205101i
\(873\) 21.5205 + 21.2966i 0.728359 + 0.720782i
\(874\) 1.28751i 0.0435505i
\(875\) 0 0
\(876\) 2.50091 16.0617i 0.0844978 0.542676i
\(877\) −7.83550 + 15.3780i −0.264586 + 0.519279i −0.984631 0.174648i \(-0.944121\pi\)
0.720045 + 0.693927i \(0.244121\pi\)
\(878\) 23.2354 + 3.68012i 0.784156 + 0.124198i
\(879\) 3.73264 + 7.27862i 0.125899 + 0.245502i
\(880\) 0 0
\(881\) −11.5046 + 15.8347i −0.387600 + 0.533485i −0.957578 0.288175i \(-0.906952\pi\)
0.569978 + 0.821660i \(0.306952\pi\)
\(882\) 18.5367 9.56732i 0.624163 0.322148i
\(883\) −13.3245 + 2.11040i −0.448406 + 0.0710206i −0.376554 0.926395i \(-0.622891\pi\)
−0.0718524 + 0.997415i \(0.522891\pi\)
\(884\) −2.23936 + 6.89203i −0.0753177 + 0.231804i
\(885\) 0 0
\(886\) 5.95075 + 18.3145i 0.199919 + 0.615288i
\(887\) 23.7996 + 46.7094i 0.799114 + 1.56835i 0.822597 + 0.568624i \(0.192524\pi\)
−0.0234837 + 0.999724i \(0.507476\pi\)
\(888\) −2.32268 7.08541i −0.0779442 0.237771i
\(889\) 3.08864 1.00356i 0.103590 0.0336583i
\(890\) 0 0
\(891\) 27.5676 + 37.1210i 0.923550 + 1.24360i
\(892\) −0.114341 0.721923i −0.00382843 0.0241718i
\(893\) 3.45666 + 3.45666i 0.115673 + 0.115673i
\(894\) 9.48414 + 9.43468i 0.317197 + 0.315543i
\(895\) 0 0
\(896\) −0.126947 0.174728i −0.00424101 0.00583725i
\(897\) −6.55228 2.11004i −0.218774 0.0704523i
\(898\) 17.1237 + 8.72498i 0.571426 + 0.291156i
\(899\) 21.3516 0.712117
\(900\) 0 0
\(901\) −37.5005 −1.24932
\(902\) 28.6646 + 14.6053i 0.954427 + 0.486305i
\(903\) 1.37082 + 0.441449i 0.0456182 + 0.0146905i
\(904\) −6.45744 8.88790i −0.214771 0.295607i
\(905\) 0 0
\(906\) −18.1574 18.0627i −0.603238 0.600092i
\(907\) −7.30011 7.30011i −0.242396 0.242396i 0.575445 0.817841i \(-0.304829\pi\)
−0.817841 + 0.575445i \(0.804829\pi\)
\(908\) 0.517900 + 3.26989i 0.0171871 + 0.108515i
\(909\) −16.6959 + 23.2344i −0.553767 + 0.770636i
\(910\) 0 0
\(911\) 26.9954 8.77133i 0.894397 0.290607i 0.174474 0.984662i \(-0.444177\pi\)
0.719922 + 0.694055i \(0.244177\pi\)
\(912\) 0.259799 + 0.792525i 0.00860281 + 0.0262431i
\(913\) 11.6632 + 22.8903i 0.385995 + 0.757557i
\(914\) −6.97317 21.4612i −0.230652 0.709874i
\(915\) 0 0
\(916\) 3.26071 10.0354i 0.107737 0.331580i
\(917\) −1.86129 + 0.294799i −0.0614651 + 0.00973511i
\(918\) −8.01723 24.0316i −0.264608 0.793160i
\(919\) 4.27526 5.88440i 0.141028 0.194108i −0.732660 0.680594i \(-0.761722\pi\)
0.873688 + 0.486486i \(0.161722\pi\)
\(920\) 0 0
\(921\) 13.2043 + 25.7483i 0.435096 + 0.848434i
\(922\) 15.8045 + 2.50319i 0.520494 + 0.0824382i
\(923\) −8.18661 + 16.0671i −0.269466 + 0.528856i
\(924\) −0.295681 + 1.89897i −0.00972720 + 0.0624717i
\(925\) 0 0
\(926\) 6.19159i 0.203468i
\(927\) −21.3422 + 21.5665i −0.700969 + 0.708337i
\(928\) 1.46845 9.27141i 0.0482041 0.304349i
\(929\) 5.66314 4.11451i 0.185802 0.134993i −0.490996 0.871162i \(-0.663367\pi\)
0.676798 + 0.736169i \(0.263367\pi\)
\(930\) 0 0
\(931\) −2.70875 1.96802i −0.0887756 0.0644992i
\(932\) −8.90175 + 8.90175i −0.291586 + 0.291586i
\(933\) 52.3114 0.136752i 1.71260 0.00447705i
\(934\) −22.0766 7.17313i −0.722369 0.234712i
\(935\) 0 0
\(936\) 4.45903 0.0233136i 0.145748 0.000762030i
\(937\) 35.4943 18.0852i 1.15955 0.590819i 0.235040 0.971986i \(-0.424478\pi\)
0.924506 + 0.381167i \(0.124478\pi\)
\(938\) 2.89144 1.47326i 0.0944088 0.0481037i
\(939\) 4.59420 + 28.5238i 0.149926 + 0.930840i
\(940\) 0 0
\(941\) 0.912873 + 0.296610i 0.0297588 + 0.00966922i 0.323859 0.946106i \(-0.395020\pi\)
−0.294100 + 0.955775i \(0.595020\pi\)
\(942\) 0.0742418 + 28.3996i 0.00241893 + 0.925309i
\(943\) 11.8393 11.8393i 0.385542 0.385542i
\(944\) −4.03518 2.93173i −0.131334 0.0954196i
\(945\) 0 0
\(946\) 16.0013 11.6256i 0.520248 0.377982i
\(947\) 5.95470 37.5965i 0.193502 1.22172i −0.679378 0.733788i \(-0.737750\pi\)
0.872880 0.487935i \(-0.162250\pi\)
\(948\) 2.21770 3.06924i 0.0720275 0.0996843i
\(949\) 13.9495i 0.452820i
\(950\) 0 0
\(951\) 18.5629 + 2.89034i 0.601942 + 0.0937258i
\(952\) 0.478043 0.938212i 0.0154935 0.0304076i
\(953\) 56.6214 + 8.96795i 1.83415 + 0.290500i 0.975161 0.221499i \(-0.0710949\pi\)
0.858986 + 0.511999i \(0.171095\pi\)
\(954\) 7.24523 + 21.9081i 0.234573 + 0.709302i
\(955\) 0 0
\(956\) −6.90374 + 9.50218i −0.223283 + 0.307322i
\(957\) −67.4486 + 49.2742i −2.18030 + 1.59281i
\(958\) −22.1377 + 3.50627i −0.715236 + 0.113282i
\(959\) 0.188434 0.579941i 0.00608486 0.0187273i
\(960\) 0 0
\(961\) −7.98073 24.5622i −0.257443 0.792328i
\(962\) 2.90496 + 5.70131i 0.0936598 + 0.183818i
\(963\) 32.6942 5.35363i 1.05356 0.172518i
\(964\) 1.15675 0.375849i 0.0372563 0.0121053i
\(965\) 0 0
\(966\) 0.892392 + 0.451762i 0.0287122 + 0.0145352i
\(967\) 6.91329 + 43.6488i 0.222316 + 1.40365i 0.806118 + 0.591755i \(0.201565\pi\)
−0.583802 + 0.811896i \(0.698435\pi\)
\(968\) 10.8855 + 10.8855i 0.349872 + 0.349872i
\(969\) −2.86773 + 2.88277i −0.0921249 + 0.0926078i
\(970\) 0 0
\(971\) −32.4405 44.6505i −1.04107 1.43290i −0.896306 0.443437i \(-0.853759\pi\)
−0.144760 0.989467i \(-0.546241\pi\)
\(972\) −12.4905 + 9.32672i −0.400633 + 0.299155i
\(973\) −1.33951 0.682516i −0.0429428 0.0218804i
\(974\) −21.2093 −0.679589
\(975\) 0 0
\(976\) 13.6458 0.436793
\(977\) 29.4915 + 15.0267i 0.943516 + 0.480746i 0.856892 0.515496i \(-0.172392\pi\)
0.0866240 + 0.996241i \(0.472392\pi\)
\(978\) −2.15433 + 6.68980i −0.0688878 + 0.213916i
\(979\) −33.0604 45.5037i −1.05661 1.45430i
\(980\) 0 0
\(981\) −10.8907 14.8261i −0.347712 0.473360i
\(982\) −22.0207 22.0207i −0.702708 0.702708i
\(983\) −3.05030 19.2588i −0.0972894 0.614261i −0.987367 0.158451i \(-0.949350\pi\)
0.890077 0.455809i \(-0.150650\pi\)
\(984\) −4.89871 + 9.67671i −0.156165 + 0.308482i
\(985\) 0 0
\(986\) 43.5259 14.1424i 1.38615 0.450386i
\(987\) −3.60875 + 1.18299i −0.114868 + 0.0376550i
\(988\) −0.324929 0.637709i −0.0103374 0.0202882i
\(989\) −3.18096 9.78998i −0.101149 0.311303i
\(990\) 0 0
\(991\) 10.9360 33.6576i 0.347394 1.06917i −0.612896 0.790164i \(-0.709995\pi\)
0.960290 0.279005i \(-0.0900046\pi\)
\(992\) 2.24660 0.355826i 0.0713295 0.0112975i
\(993\) −9.84420 13.4752i −0.312396 0.427621i
\(994\) 1.54012 2.11980i 0.0488497 0.0672359i
\(995\) 0 0
\(996\) −7.70683 + 3.95224i −0.244200 + 0.125231i
\(997\) −45.5136 7.20864i −1.44143 0.228300i −0.613750 0.789501i \(-0.710340\pi\)
−0.827680 + 0.561201i \(0.810340\pi\)
\(998\) 0.570481 1.11963i 0.0180583 0.0354414i
\(999\) −20.0101 9.99878i −0.633093 0.316347i
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 750.2.l.b.107.10 80
3.2 odd 2 inner 750.2.l.b.107.1 80
5.2 odd 4 750.2.l.c.143.4 80
5.3 odd 4 750.2.l.a.143.7 80
5.4 even 2 150.2.l.a.17.1 80
15.2 even 4 750.2.l.c.143.8 80
15.8 even 4 750.2.l.a.143.3 80
15.14 odd 2 150.2.l.a.17.10 yes 80
25.3 odd 20 inner 750.2.l.b.743.1 80
25.4 even 10 750.2.l.c.257.8 80
25.21 even 5 750.2.l.a.257.3 80
25.22 odd 20 150.2.l.a.53.10 yes 80
75.29 odd 10 750.2.l.c.257.4 80
75.47 even 20 150.2.l.a.53.1 yes 80
75.53 even 20 inner 750.2.l.b.743.10 80
75.71 odd 10 750.2.l.a.257.7 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.l.a.17.1 80 5.4 even 2
150.2.l.a.17.10 yes 80 15.14 odd 2
150.2.l.a.53.1 yes 80 75.47 even 20
150.2.l.a.53.10 yes 80 25.22 odd 20
750.2.l.a.143.3 80 15.8 even 4
750.2.l.a.143.7 80 5.3 odd 4
750.2.l.a.257.3 80 25.21 even 5
750.2.l.a.257.7 80 75.71 odd 10
750.2.l.b.107.1 80 3.2 odd 2 inner
750.2.l.b.107.10 80 1.1 even 1 trivial
750.2.l.b.743.1 80 25.3 odd 20 inner
750.2.l.b.743.10 80 75.53 even 20 inner
750.2.l.c.143.4 80 5.2 odd 4
750.2.l.c.143.8 80 15.2 even 4
750.2.l.c.257.4 80 75.29 odd 10
750.2.l.c.257.8 80 25.4 even 10