Properties

Label 950.2.u.b.899.1
Level $950$
Weight $2$
Character 950.899
Analytic conductor $7.586$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(99,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 899.1
Root \(-0.342020 - 0.939693i\) of defining polynomial
Character \(\chi\) \(=\) 950.899
Dual form 950.2.u.b.149.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.642788 - 0.766044i) q^{2} +(0.524005 - 1.43969i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{6} +(2.33359 + 1.34730i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.500000 + 0.419550i) q^{9} +O(q^{10})\) \(q+(-0.642788 - 0.766044i) q^{2} +(0.524005 - 1.43969i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{6} +(2.33359 + 1.34730i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.500000 + 0.419550i) q^{9} +(-1.59240 - 2.75811i) q^{11} +(1.32683 + 0.766044i) q^{12} +(1.96962 + 5.41147i) q^{13} +(-0.467911 - 2.65366i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(4.18939 + 4.99273i) q^{17} -0.652704i q^{18} +(-2.82635 + 3.31839i) q^{19} +(3.16250 - 2.65366i) q^{21} +(-1.08926 + 2.99273i) q^{22} +(-0.684040 - 0.120615i) q^{23} +(-0.266044 - 1.50881i) q^{24} +(2.87939 - 4.98724i) q^{26} +(4.84651 - 2.79813i) q^{27} +(-1.73205 + 2.06418i) q^{28} +(2.16250 + 1.81456i) q^{29} +(-1.22668 + 2.12467i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-4.80526 + 0.847296i) q^{33} +(1.13176 - 6.41852i) q^{34} +(-0.500000 + 0.419550i) q^{36} +4.36959i q^{37} +(4.35878 + 0.0320889i) q^{38} +8.82295 q^{39} +(0.326352 + 0.118782i) q^{41} +(-4.06564 - 0.716881i) q^{42} +(-5.97205 + 1.05303i) q^{43} +(2.99273 - 1.08926i) q^{44} +(0.347296 + 0.601535i) q^{46} +(5.06975 - 6.04189i) q^{47} +(-0.984808 + 1.17365i) q^{48} +(0.130415 + 0.225885i) q^{49} +(9.38326 - 3.41523i) q^{51} +(-5.67128 + 1.00000i) q^{52} +(8.08737 + 1.42602i) q^{53} +(-5.25877 - 1.91404i) q^{54} +2.69459 q^{56} +(3.29644 + 5.80793i) q^{57} -2.82295i q^{58} +(-0.439693 + 0.368946i) q^{59} +(0.509800 - 2.89122i) q^{61} +(2.41609 - 0.426022i) q^{62} +(0.601535 + 1.65270i) q^{63} +(0.500000 - 0.866025i) q^{64} +(3.73783 + 3.13641i) q^{66} +(-3.18701 + 3.79813i) q^{67} +(-5.64436 + 3.25877i) q^{68} +(-0.532089 + 0.921605i) q^{69} +(-1.46791 - 8.32494i) q^{71} +(0.642788 + 0.113341i) q^{72} +(5.39246 - 14.8157i) q^{73} +(3.34730 - 2.80872i) q^{74} +(-2.77719 - 3.35965i) q^{76} -8.58172i q^{77} +(-5.67128 - 6.75877i) q^{78} +(-8.51754 - 3.10013i) q^{79} +(-1.14883 - 6.51536i) q^{81} +(-0.118782 - 0.326352i) q^{82} +(-7.34013 - 4.23783i) q^{83} +(2.06418 + 3.57526i) q^{84} +(4.64543 + 3.89798i) q^{86} +(3.74557 - 2.16250i) q^{87} +(-2.75811 - 1.59240i) q^{88} +(7.27244 - 2.64695i) q^{89} +(-2.69459 + 15.2818i) q^{91} +(0.237565 - 0.652704i) q^{92} +(2.41609 + 2.87939i) q^{93} -7.88713 q^{94} +1.53209 q^{96} +(0.223238 + 0.266044i) q^{97} +(0.0892091 - 0.245100i) q^{98} +(0.360967 - 2.04715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{6} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{6} + 6 q^{9} - 12 q^{11} - 24 q^{14} - 36 q^{19} + 48 q^{21} + 6 q^{24} + 12 q^{26} + 36 q^{29} + 12 q^{31} + 24 q^{34} - 6 q^{36} + 24 q^{39} + 6 q^{41} + 30 q^{49} + 42 q^{51} - 18 q^{54} + 24 q^{56} + 6 q^{59} + 12 q^{61} + 6 q^{64} + 6 q^{66} + 12 q^{69} - 36 q^{71} + 36 q^{74} - 12 q^{76} - 12 q^{79} - 66 q^{81} - 12 q^{84} + 24 q^{86} - 24 q^{91} + 24 q^{94} - 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.642788 0.766044i −0.454519 0.541675i
\(3\) 0.524005 1.43969i 0.302535 0.831207i −0.691523 0.722354i \(-0.743060\pi\)
0.994058 0.108853i \(-0.0347177\pi\)
\(4\) −0.173648 + 0.984808i −0.0868241 + 0.492404i
\(5\) 0 0
\(6\) −1.43969 + 0.524005i −0.587752 + 0.213924i
\(7\) 2.33359 + 1.34730i 0.882013 + 0.509230i 0.871321 0.490713i \(-0.163264\pi\)
0.0106911 + 0.999943i \(0.496597\pi\)
\(8\) 0.866025 0.500000i 0.306186 0.176777i
\(9\) 0.500000 + 0.419550i 0.166667 + 0.139850i
\(10\) 0 0
\(11\) −1.59240 2.75811i −0.480126 0.831602i 0.519615 0.854401i \(-0.326076\pi\)
−0.999740 + 0.0227990i \(0.992742\pi\)
\(12\) 1.32683 + 0.766044i 0.383022 + 0.221138i
\(13\) 1.96962 + 5.41147i 0.546273 + 1.50087i 0.838705 + 0.544586i \(0.183313\pi\)
−0.292432 + 0.956286i \(0.594464\pi\)
\(14\) −0.467911 2.65366i −0.125055 0.709219i
\(15\) 0 0
\(16\) −0.939693 0.342020i −0.234923 0.0855050i
\(17\) 4.18939 + 4.99273i 1.01608 + 1.21091i 0.977342 + 0.211664i \(0.0678884\pi\)
0.0387350 + 0.999250i \(0.487667\pi\)
\(18\) 0.652704i 0.153844i
\(19\) −2.82635 + 3.31839i −0.648410 + 0.761292i
\(20\) 0 0
\(21\) 3.16250 2.65366i 0.690115 0.579075i
\(22\) −1.08926 + 2.99273i −0.232232 + 0.638051i
\(23\) −0.684040 0.120615i −0.142632 0.0251499i 0.101876 0.994797i \(-0.467515\pi\)
−0.244508 + 0.969647i \(0.578627\pi\)
\(24\) −0.266044 1.50881i −0.0543061 0.307985i
\(25\) 0 0
\(26\) 2.87939 4.98724i 0.564694 0.978079i
\(27\) 4.84651 2.79813i 0.932711 0.538501i
\(28\) −1.73205 + 2.06418i −0.327327 + 0.390093i
\(29\) 2.16250 + 1.81456i 0.401567 + 0.336955i 0.821099 0.570786i \(-0.193361\pi\)
−0.419532 + 0.907741i \(0.637806\pi\)
\(30\) 0 0
\(31\) −1.22668 + 2.12467i −0.220319 + 0.381603i −0.954905 0.296913i \(-0.904043\pi\)
0.734586 + 0.678515i \(0.237376\pi\)
\(32\) 0.342020 + 0.939693i 0.0604612 + 0.166116i
\(33\) −4.80526 + 0.847296i −0.836488 + 0.147495i
\(34\) 1.13176 6.41852i 0.194095 1.10077i
\(35\) 0 0
\(36\) −0.500000 + 0.419550i −0.0833333 + 0.0699250i
\(37\) 4.36959i 0.718355i 0.933269 + 0.359178i \(0.116943\pi\)
−0.933269 + 0.359178i \(0.883057\pi\)
\(38\) 4.35878 + 0.0320889i 0.707088 + 0.00520550i
\(39\) 8.82295 1.41280
\(40\) 0 0
\(41\) 0.326352 + 0.118782i 0.0509676 + 0.0185507i 0.367378 0.930072i \(-0.380255\pi\)
−0.316411 + 0.948622i \(0.602478\pi\)
\(42\) −4.06564 0.716881i −0.627341 0.110617i
\(43\) −5.97205 + 1.05303i −0.910729 + 0.160586i −0.609334 0.792913i \(-0.708563\pi\)
−0.301395 + 0.953499i \(0.597452\pi\)
\(44\) 2.99273 1.08926i 0.451170 0.164213i
\(45\) 0 0
\(46\) 0.347296 + 0.601535i 0.0512061 + 0.0886915i
\(47\) 5.06975 6.04189i 0.739499 0.881300i −0.256870 0.966446i \(-0.582691\pi\)
0.996368 + 0.0851459i \(0.0271356\pi\)
\(48\) −0.984808 + 1.17365i −0.142145 + 0.169402i
\(49\) 0.130415 + 0.225885i 0.0186307 + 0.0322693i
\(50\) 0 0
\(51\) 9.38326 3.41523i 1.31392 0.478227i
\(52\) −5.67128 + 1.00000i −0.786465 + 0.138675i
\(53\) 8.08737 + 1.42602i 1.11089 + 0.195879i 0.698836 0.715282i \(-0.253702\pi\)
0.412050 + 0.911161i \(0.364813\pi\)
\(54\) −5.25877 1.91404i −0.715628 0.260467i
\(55\) 0 0
\(56\) 2.69459 0.360080
\(57\) 3.29644 + 5.80793i 0.436625 + 0.769280i
\(58\) 2.82295i 0.370671i
\(59\) −0.439693 + 0.368946i −0.0572431 + 0.0480327i −0.670960 0.741493i \(-0.734118\pi\)
0.613717 + 0.789526i \(0.289673\pi\)
\(60\) 0 0
\(61\) 0.509800 2.89122i 0.0652732 0.370183i −0.934621 0.355645i \(-0.884261\pi\)
0.999894 0.0145378i \(-0.00462769\pi\)
\(62\) 2.41609 0.426022i 0.306844 0.0541049i
\(63\) 0.601535 + 1.65270i 0.0757863 + 0.208221i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) 3.73783 + 3.13641i 0.460095 + 0.386065i
\(67\) −3.18701 + 3.79813i −0.389356 + 0.464016i −0.924744 0.380590i \(-0.875721\pi\)
0.535388 + 0.844606i \(0.320165\pi\)
\(68\) −5.64436 + 3.25877i −0.684479 + 0.395184i
\(69\) −0.532089 + 0.921605i −0.0640560 + 0.110948i
\(70\) 0 0
\(71\) −1.46791 8.32494i −0.174209 0.987988i −0.939053 0.343773i \(-0.888295\pi\)
0.764844 0.644216i \(-0.222816\pi\)
\(72\) 0.642788 + 0.113341i 0.0757532 + 0.0133573i
\(73\) 5.39246 14.8157i 0.631140 1.73404i −0.0467771 0.998905i \(-0.514895\pi\)
0.677917 0.735138i \(-0.262883\pi\)
\(74\) 3.34730 2.80872i 0.389115 0.326507i
\(75\) 0 0
\(76\) −2.77719 3.35965i −0.318565 0.385378i
\(77\) 8.58172i 0.977978i
\(78\) −5.67128 6.75877i −0.642146 0.765280i
\(79\) −8.51754 3.10013i −0.958298 0.348792i −0.184932 0.982751i \(-0.559206\pi\)
−0.773366 + 0.633959i \(0.781429\pi\)
\(80\) 0 0
\(81\) −1.14883 6.51536i −0.127648 0.723929i
\(82\) −0.118782 0.326352i −0.0131173 0.0360395i
\(83\) −7.34013 4.23783i −0.805684 0.465162i 0.0397709 0.999209i \(-0.487337\pi\)
−0.845455 + 0.534047i \(0.820671\pi\)
\(84\) 2.06418 + 3.57526i 0.225220 + 0.390093i
\(85\) 0 0
\(86\) 4.64543 + 3.89798i 0.500930 + 0.420330i
\(87\) 3.74557 2.16250i 0.401567 0.231845i
\(88\) −2.75811 1.59240i −0.294016 0.169750i
\(89\) 7.27244 2.64695i 0.770877 0.280576i 0.0735139 0.997294i \(-0.476579\pi\)
0.697363 + 0.716718i \(0.254356\pi\)
\(90\) 0 0
\(91\) −2.69459 + 15.2818i −0.282470 + 1.60197i
\(92\) 0.237565 0.652704i 0.0247678 0.0680491i
\(93\) 2.41609 + 2.87939i 0.250537 + 0.298578i
\(94\) −7.88713 −0.813495
\(95\) 0 0
\(96\) 1.53209 0.156368
\(97\) 0.223238 + 0.266044i 0.0226664 + 0.0270127i 0.777259 0.629181i \(-0.216610\pi\)
−0.754592 + 0.656194i \(0.772165\pi\)
\(98\) 0.0892091 0.245100i 0.00901148 0.0247588i
\(99\) 0.360967 2.04715i 0.0362785 0.205746i
\(100\) 0 0
\(101\) 0.347296 0.126406i 0.0345573 0.0125778i −0.324684 0.945823i \(-0.605258\pi\)
0.359241 + 0.933245i \(0.383036\pi\)
\(102\) −8.64766 4.99273i −0.856245 0.494354i
\(103\) 7.43199 4.29086i 0.732295 0.422791i −0.0869659 0.996211i \(-0.527717\pi\)
0.819261 + 0.573420i \(0.194384\pi\)
\(104\) 4.41147 + 3.70167i 0.432581 + 0.362978i
\(105\) 0 0
\(106\) −4.10607 7.11192i −0.398816 0.690770i
\(107\) −9.91890 5.72668i −0.958897 0.553619i −0.0630633 0.998010i \(-0.520087\pi\)
−0.895833 + 0.444390i \(0.853420\pi\)
\(108\) 1.91404 + 5.25877i 0.184178 + 0.506025i
\(109\) −1.50980 8.56250i −0.144613 0.820139i −0.967677 0.252191i \(-0.918849\pi\)
0.823065 0.567948i \(-0.192262\pi\)
\(110\) 0 0
\(111\) 6.29086 + 2.28969i 0.597102 + 0.217327i
\(112\) −1.73205 2.06418i −0.163663 0.195046i
\(113\) 2.85978i 0.269026i 0.990912 + 0.134513i \(0.0429470\pi\)
−0.990912 + 0.134513i \(0.957053\pi\)
\(114\) 2.33022 6.25849i 0.218245 0.586161i
\(115\) 0 0
\(116\) −2.16250 + 1.81456i −0.200783 + 0.168477i
\(117\) −1.28558 + 3.53209i −0.118851 + 0.326542i
\(118\) 0.565258 + 0.0996702i 0.0520362 + 0.00917539i
\(119\) 3.04963 + 17.2953i 0.279559 + 1.58546i
\(120\) 0 0
\(121\) 0.428548 0.742267i 0.0389589 0.0674789i
\(122\) −2.54250 + 1.46791i −0.230187 + 0.132898i
\(123\) 0.342020 0.407604i 0.0308389 0.0367524i
\(124\) −1.87939 1.57699i −0.168774 0.141618i
\(125\) 0 0
\(126\) 0.879385 1.52314i 0.0783419 0.135692i
\(127\) 3.32774 + 9.14290i 0.295290 + 0.811301i 0.995271 + 0.0971401i \(0.0309695\pi\)
−0.699981 + 0.714161i \(0.746808\pi\)
\(128\) −0.984808 + 0.173648i −0.0870455 + 0.0153485i
\(129\) −1.61334 + 9.14971i −0.142047 + 0.805587i
\(130\) 0 0
\(131\) −4.95471 + 4.15749i −0.432895 + 0.363242i −0.833043 0.553209i \(-0.813403\pi\)
0.400148 + 0.916451i \(0.368959\pi\)
\(132\) 4.87939i 0.424696i
\(133\) −11.0664 + 3.93582i −0.959578 + 0.341279i
\(134\) 4.95811 0.428316
\(135\) 0 0
\(136\) 6.12449 + 2.22913i 0.525170 + 0.191146i
\(137\) 11.4833 + 2.02481i 0.981084 + 0.172992i 0.641115 0.767445i \(-0.278472\pi\)
0.339969 + 0.940437i \(0.389583\pi\)
\(138\) 1.04801 0.184793i 0.0892126 0.0157306i
\(139\) −7.76517 + 2.82629i −0.658633 + 0.239723i −0.649646 0.760237i \(-0.725083\pi\)
−0.00898688 + 0.999960i \(0.502861\pi\)
\(140\) 0 0
\(141\) −6.04189 10.4649i −0.508819 0.881300i
\(142\) −5.43372 + 6.47565i −0.455987 + 0.543425i
\(143\) 11.7890 14.0496i 0.985849 1.17489i
\(144\) −0.326352 0.565258i −0.0271960 0.0471048i
\(145\) 0 0
\(146\) −14.8157 + 5.39246i −1.22615 + 0.446284i
\(147\) 0.393544 0.0693923i 0.0324589 0.00572338i
\(148\) −4.30320 0.758770i −0.353721 0.0623705i
\(149\) −15.4611 5.62738i −1.26662 0.461013i −0.380637 0.924725i \(-0.624295\pi\)
−0.885986 + 0.463712i \(0.846517\pi\)
\(150\) 0 0
\(151\) 4.65539 0.378850 0.189425 0.981895i \(-0.439338\pi\)
0.189425 + 0.981895i \(0.439338\pi\)
\(152\) −0.788496 + 4.28699i −0.0639554 + 0.347721i
\(153\) 4.25402i 0.343917i
\(154\) −6.57398 + 5.51622i −0.529746 + 0.444510i
\(155\) 0 0
\(156\) −1.53209 + 8.68891i −0.122665 + 0.695669i
\(157\) 8.32494 1.46791i 0.664402 0.117152i 0.168731 0.985662i \(-0.446033\pi\)
0.495671 + 0.868510i \(0.334922\pi\)
\(158\) 3.10013 + 8.51754i 0.246633 + 0.677619i
\(159\) 6.29086 10.8961i 0.498898 0.864116i
\(160\) 0 0
\(161\) −1.43376 1.20307i −0.112996 0.0948152i
\(162\) −4.25260 + 5.06805i −0.334116 + 0.398183i
\(163\) 14.7654 8.52481i 1.15652 0.667715i 0.206050 0.978542i \(-0.433939\pi\)
0.950467 + 0.310826i \(0.100606\pi\)
\(164\) −0.173648 + 0.300767i −0.0135596 + 0.0234860i
\(165\) 0 0
\(166\) 1.47178 + 8.34689i 0.114232 + 0.647844i
\(167\) 3.14403 + 0.554378i 0.243292 + 0.0428990i 0.293965 0.955816i \(-0.405025\pi\)
−0.0506721 + 0.998715i \(0.516136\pi\)
\(168\) 1.41198 3.87939i 0.108937 0.299301i
\(169\) −15.4461 + 12.9608i −1.18816 + 0.996985i
\(170\) 0 0
\(171\) −2.80541 + 0.473401i −0.214535 + 0.0362019i
\(172\) 6.06418i 0.462389i
\(173\) 6.19031 + 7.37733i 0.470641 + 0.560888i 0.948185 0.317720i \(-0.102917\pi\)
−0.477544 + 0.878608i \(0.658473\pi\)
\(174\) −4.06418 1.47924i −0.308105 0.112141i
\(175\) 0 0
\(176\) 0.553033 + 3.13641i 0.0416865 + 0.236416i
\(177\) 0.300767 + 0.826352i 0.0226071 + 0.0621124i
\(178\) −6.70232 3.86959i −0.502360 0.290038i
\(179\) 9.40807 + 16.2953i 0.703192 + 1.21796i 0.967340 + 0.253482i \(0.0815760\pi\)
−0.264148 + 0.964482i \(0.585091\pi\)
\(180\) 0 0
\(181\) 2.12836 + 1.78590i 0.158199 + 0.132745i 0.718451 0.695577i \(-0.244851\pi\)
−0.560252 + 0.828322i \(0.689296\pi\)
\(182\) 13.4386 7.75877i 0.996134 0.575118i
\(183\) −3.89533 2.24897i −0.287951 0.166249i
\(184\) −0.652704 + 0.237565i −0.0481180 + 0.0175135i
\(185\) 0 0
\(186\) 0.652704 3.70167i 0.0478586 0.271419i
\(187\) 7.09932 19.5052i 0.519154 1.42636i
\(188\) 5.06975 + 6.04189i 0.369749 + 0.440650i
\(189\) 15.0797 1.09688
\(190\) 0 0
\(191\) 9.56212 0.691891 0.345945 0.938255i \(-0.387558\pi\)
0.345945 + 0.938255i \(0.387558\pi\)
\(192\) −0.984808 1.17365i −0.0710724 0.0847008i
\(193\) −8.09937 + 22.2528i −0.583006 + 1.60179i 0.200011 + 0.979794i \(0.435902\pi\)
−0.783017 + 0.622001i \(0.786320\pi\)
\(194\) 0.0603074 0.342020i 0.00432982 0.0245556i
\(195\) 0 0
\(196\) −0.245100 + 0.0892091i −0.0175071 + 0.00637208i
\(197\) −19.8512 11.4611i −1.41434 0.816570i −0.418547 0.908195i \(-0.637460\pi\)
−0.995794 + 0.0916253i \(0.970794\pi\)
\(198\) −1.80023 + 1.03936i −0.127937 + 0.0738643i
\(199\) −7.72462 6.48173i −0.547584 0.459477i 0.326538 0.945184i \(-0.394118\pi\)
−0.874122 + 0.485707i \(0.838562\pi\)
\(200\) 0 0
\(201\) 3.79813 + 6.57856i 0.267900 + 0.464016i
\(202\) −0.320070 0.184793i −0.0225201 0.0130020i
\(203\) 2.60164 + 7.14796i 0.182600 + 0.501688i
\(204\) 1.73396 + 9.83375i 0.121401 + 0.688500i
\(205\) 0 0
\(206\) −8.06418 2.93512i −0.561858 0.204500i
\(207\) −0.291416 0.347296i −0.0202548 0.0241388i
\(208\) 5.75877i 0.399299i
\(209\) 13.6532 + 2.51120i 0.944410 + 0.173703i
\(210\) 0 0
\(211\) −17.1288 + 14.3728i −1.17920 + 0.989464i −0.179213 + 0.983810i \(0.557355\pi\)
−0.999984 + 0.00565322i \(0.998201\pi\)
\(212\) −2.80872 + 7.71688i −0.192903 + 0.529998i
\(213\) −12.7545 2.24897i −0.873927 0.154097i
\(214\) 1.98886 + 11.2794i 0.135955 + 0.771041i
\(215\) 0 0
\(216\) 2.79813 4.84651i 0.190389 0.329763i
\(217\) −5.72513 + 3.30541i −0.388647 + 0.224386i
\(218\) −5.58878 + 6.66044i −0.378520 + 0.451102i
\(219\) −18.5043 15.5270i −1.25041 1.04922i
\(220\) 0 0
\(221\) −18.7665 + 32.5046i −1.26237 + 2.18649i
\(222\) −2.28969 6.29086i −0.153674 0.422215i
\(223\) 9.13538 1.61081i 0.611751 0.107868i 0.140815 0.990036i \(-0.455028\pi\)
0.470935 + 0.882168i \(0.343917\pi\)
\(224\) −0.467911 + 2.65366i −0.0312636 + 0.177305i
\(225\) 0 0
\(226\) 2.19072 1.83823i 0.145725 0.122278i
\(227\) 7.73648i 0.513488i −0.966479 0.256744i \(-0.917350\pi\)
0.966479 0.256744i \(-0.0826498\pi\)
\(228\) −6.29212 + 2.23783i −0.416706 + 0.148204i
\(229\) 23.0351 1.52220 0.761101 0.648634i \(-0.224659\pi\)
0.761101 + 0.648634i \(0.224659\pi\)
\(230\) 0 0
\(231\) −12.3550 4.49687i −0.812902 0.295872i
\(232\) 2.78006 + 0.490200i 0.182520 + 0.0321832i
\(233\) −8.27201 + 1.45858i −0.541917 + 0.0955546i −0.437905 0.899021i \(-0.644279\pi\)
−0.104012 + 0.994576i \(0.533168\pi\)
\(234\) 3.53209 1.28558i 0.230900 0.0840407i
\(235\) 0 0
\(236\) −0.286989 0.497079i −0.0186814 0.0323571i
\(237\) −8.92647 + 10.6382i −0.579837 + 0.691022i
\(238\) 11.2887 13.4534i 0.731739 0.872052i
\(239\) −7.86484 13.6223i −0.508734 0.881153i −0.999949 0.0101147i \(-0.996780\pi\)
0.491215 0.871038i \(-0.336553\pi\)
\(240\) 0 0
\(241\) −16.4474 + 5.98638i −1.05947 + 0.385616i −0.812230 0.583337i \(-0.801747\pi\)
−0.247242 + 0.968954i \(0.579524\pi\)
\(242\) −0.844075 + 0.148833i −0.0542592 + 0.00956736i
\(243\) 6.55163 + 1.15523i 0.420288 + 0.0741080i
\(244\) 2.75877 + 1.00411i 0.176612 + 0.0642816i
\(245\) 0 0
\(246\) −0.532089 −0.0339247
\(247\) −23.5242 8.75877i −1.49681 0.557307i
\(248\) 2.45336i 0.155789i
\(249\) −9.94743 + 8.34689i −0.630393 + 0.528963i
\(250\) 0 0
\(251\) 1.48767 8.43702i 0.0939011 0.532540i −0.901177 0.433450i \(-0.857296\pi\)
0.995079 0.0990893i \(-0.0315930\pi\)
\(252\) −1.73205 + 0.305407i −0.109109 + 0.0192389i
\(253\) 0.756594 + 2.07873i 0.0475667 + 0.130688i
\(254\) 4.86484 8.42615i 0.305247 0.528703i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) −5.15815 + 6.14724i −0.321756 + 0.383454i −0.902542 0.430602i \(-0.858301\pi\)
0.580785 + 0.814057i \(0.302746\pi\)
\(258\) 8.04612 4.64543i 0.500930 0.289212i
\(259\) −5.88713 + 10.1968i −0.365808 + 0.633598i
\(260\) 0 0
\(261\) 0.319955 + 1.81456i 0.0198047 + 0.112318i
\(262\) 6.36965 + 1.12314i 0.393518 + 0.0693879i
\(263\) −2.03871 + 5.60132i −0.125712 + 0.345392i −0.986544 0.163499i \(-0.947722\pi\)
0.860831 + 0.508891i \(0.169944\pi\)
\(264\) −3.73783 + 3.13641i −0.230047 + 0.193033i
\(265\) 0 0
\(266\) 10.1284 + 5.94745i 0.621009 + 0.364662i
\(267\) 11.8571i 0.725643i
\(268\) −3.18701 3.79813i −0.194678 0.232008i
\(269\) −1.07873 0.392624i −0.0657711 0.0239387i 0.308925 0.951086i \(-0.400031\pi\)
−0.374696 + 0.927148i \(0.622253\pi\)
\(270\) 0 0
\(271\) 3.48246 + 19.7500i 0.211544 + 1.19973i 0.886803 + 0.462147i \(0.152921\pi\)
−0.675259 + 0.737581i \(0.735968\pi\)
\(272\) −2.22913 6.12449i −0.135161 0.371351i
\(273\) 20.5891 + 11.8871i 1.24611 + 0.719442i
\(274\) −5.83022 10.0982i −0.352217 0.610057i
\(275\) 0 0
\(276\) −0.815207 0.684040i −0.0490697 0.0411744i
\(277\) −15.0343 + 8.68004i −0.903322 + 0.521533i −0.878277 0.478153i \(-0.841306\pi\)
−0.0250457 + 0.999686i \(0.507973\pi\)
\(278\) 7.15642 + 4.13176i 0.429213 + 0.247806i
\(279\) −1.50475 + 0.547683i −0.0900869 + 0.0327889i
\(280\) 0 0
\(281\) 0.507274 2.87689i 0.0302614 0.171621i −0.965931 0.258798i \(-0.916674\pi\)
0.996193 + 0.0871772i \(0.0277846\pi\)
\(282\) −4.13290 + 11.3550i −0.246110 + 0.676183i
\(283\) −6.09408 7.26264i −0.362255 0.431719i 0.553875 0.832600i \(-0.313149\pi\)
−0.916130 + 0.400881i \(0.868704\pi\)
\(284\) 8.45336 0.501615
\(285\) 0 0
\(286\) −18.3405 −1.08450
\(287\) 0.601535 + 0.716881i 0.0355075 + 0.0423162i
\(288\) −0.223238 + 0.613341i −0.0131544 + 0.0361415i
\(289\) −4.42427 + 25.0913i −0.260251 + 1.47596i
\(290\) 0 0
\(291\) 0.500000 0.181985i 0.0293105 0.0106682i
\(292\) 13.6542 + 7.88326i 0.799052 + 0.461333i
\(293\) −23.6354 + 13.6459i −1.38079 + 0.797202i −0.992253 0.124230i \(-0.960354\pi\)
−0.388541 + 0.921432i \(0.627021\pi\)
\(294\) −0.306123 0.256867i −0.0178534 0.0149808i
\(295\) 0 0
\(296\) 2.18479 + 3.78417i 0.126988 + 0.219951i
\(297\) −15.4351 8.91147i −0.895637 0.517096i
\(298\) 5.62738 + 15.4611i 0.325985 + 0.895638i
\(299\) −0.694593 3.93923i −0.0401693 0.227812i
\(300\) 0 0
\(301\) −15.3550 5.58878i −0.885050 0.322132i
\(302\) −2.99243 3.56624i −0.172195 0.205214i
\(303\) 0.566237i 0.0325295i
\(304\) 3.79086 2.15160i 0.217421 0.123403i
\(305\) 0 0
\(306\) 3.25877 2.73443i 0.186292 0.156317i
\(307\) −7.29482 + 20.0424i −0.416337 + 1.14388i 0.537424 + 0.843312i \(0.319398\pi\)
−0.953761 + 0.300565i \(0.902825\pi\)
\(308\) 8.45134 + 1.49020i 0.481560 + 0.0849120i
\(309\) −2.28312 12.9482i −0.129882 0.736598i
\(310\) 0 0
\(311\) 14.6459 25.3674i 0.830493 1.43846i −0.0671555 0.997743i \(-0.521392\pi\)
0.897648 0.440713i \(-0.145274\pi\)
\(312\) 7.64090 4.41147i 0.432581 0.249751i
\(313\) −3.57466 + 4.26011i −0.202052 + 0.240796i −0.857550 0.514401i \(-0.828014\pi\)
0.655498 + 0.755197i \(0.272459\pi\)
\(314\) −6.47565 5.43372i −0.365442 0.306642i
\(315\) 0 0
\(316\) 4.53209 7.84981i 0.254950 0.441586i
\(317\) 1.30082 + 3.57398i 0.0730614 + 0.200735i 0.970848 0.239696i \(-0.0770479\pi\)
−0.897786 + 0.440431i \(0.854826\pi\)
\(318\) −12.3906 + 2.18479i −0.694829 + 0.122517i
\(319\) 1.56118 8.85392i 0.0874096 0.495724i
\(320\) 0 0
\(321\) −13.4422 + 11.2794i −0.750271 + 0.629553i
\(322\) 1.87164i 0.104303i
\(323\) −28.4085 0.209141i −1.58069 0.0116369i
\(324\) 6.61587 0.367548
\(325\) 0 0
\(326\) −16.0214 5.83132i −0.887344 0.322967i
\(327\) −13.1185 2.31315i −0.725456 0.127917i
\(328\) 0.342020 0.0603074i 0.0188849 0.00332992i
\(329\) 19.9709 7.26881i 1.10103 0.400743i
\(330\) 0 0
\(331\) −10.2110 17.6859i −0.561245 0.972104i −0.997388 0.0722272i \(-0.976989\pi\)
0.436144 0.899877i \(-0.356344\pi\)
\(332\) 5.44804 6.49273i 0.299000 0.356335i
\(333\) −1.83326 + 2.18479i −0.100462 + 0.119726i
\(334\) −1.59627 2.76481i −0.0873438 0.151284i
\(335\) 0 0
\(336\) −3.87939 + 1.41198i −0.211638 + 0.0770299i
\(337\) 20.0019 3.52687i 1.08957 0.192121i 0.400128 0.916459i \(-0.368966\pi\)
0.689445 + 0.724338i \(0.257855\pi\)
\(338\) 19.8571 + 3.50134i 1.08008 + 0.190448i
\(339\) 4.11721 + 1.49854i 0.223616 + 0.0813896i
\(340\) 0 0
\(341\) 7.81345 0.423122
\(342\) 2.16593 + 1.84477i 0.117120 + 0.0997537i
\(343\) 18.1593i 0.980511i
\(344\) −4.64543 + 3.89798i −0.250465 + 0.210165i
\(345\) 0 0
\(346\) 1.67230 9.48411i 0.0899036 0.509869i
\(347\) 5.13560 0.905544i 0.275693 0.0486122i −0.0340920 0.999419i \(-0.510854\pi\)
0.309785 + 0.950807i \(0.399743\pi\)
\(348\) 1.47924 + 4.06418i 0.0792956 + 0.217863i
\(349\) 7.17024 12.4192i 0.383814 0.664786i −0.607790 0.794098i \(-0.707944\pi\)
0.991604 + 0.129312i \(0.0412769\pi\)
\(350\) 0 0
\(351\) 24.6878 + 20.7155i 1.31774 + 1.10571i
\(352\) 2.04715 2.43969i 0.109113 0.130036i
\(353\) 22.7331 13.1250i 1.20996 0.698571i 0.247209 0.968962i \(-0.420486\pi\)
0.962750 + 0.270391i \(0.0871531\pi\)
\(354\) 0.439693 0.761570i 0.0233694 0.0404770i
\(355\) 0 0
\(356\) 1.34389 + 7.62159i 0.0712262 + 0.403944i
\(357\) 26.4980 + 4.67230i 1.40242 + 0.247285i
\(358\) 6.43550 17.6814i 0.340127 0.934490i
\(359\) 25.8084 21.6558i 1.36212 1.14295i 0.386792 0.922167i \(-0.373583\pi\)
0.975323 0.220784i \(-0.0708615\pi\)
\(360\) 0 0
\(361\) −3.02347 18.7579i −0.159130 0.987258i
\(362\) 2.77837i 0.146028i
\(363\) −0.844075 1.00593i −0.0443025 0.0527976i
\(364\) −14.5817 5.30731i −0.764290 0.278179i
\(365\) 0 0
\(366\) 0.781059 + 4.42961i 0.0408266 + 0.231539i
\(367\) −3.58056 9.83750i −0.186903 0.513513i 0.810483 0.585762i \(-0.199205\pi\)
−0.997387 + 0.0722488i \(0.976982\pi\)
\(368\) 0.601535 + 0.347296i 0.0313572 + 0.0181041i
\(369\) 0.113341 + 0.196312i 0.00590029 + 0.0102196i
\(370\) 0 0
\(371\) 16.9513 + 14.2238i 0.880068 + 0.738465i
\(372\) −3.25519 + 1.87939i −0.168774 + 0.0974416i
\(373\) −20.7003 11.9513i −1.07182 0.618815i −0.143141 0.989702i \(-0.545720\pi\)
−0.928678 + 0.370887i \(0.879054\pi\)
\(374\) −19.5052 + 7.09932i −1.00859 + 0.367097i
\(375\) 0 0
\(376\) 1.36959 7.76730i 0.0706310 0.400568i
\(377\) −5.56012 + 15.2763i −0.286361 + 0.786770i
\(378\) −9.69302 11.5517i −0.498555 0.594155i
\(379\) −17.8135 −0.915016 −0.457508 0.889206i \(-0.651258\pi\)
−0.457508 + 0.889206i \(0.651258\pi\)
\(380\) 0 0
\(381\) 14.9067 0.763695
\(382\) −6.14641 7.32501i −0.314478 0.374780i
\(383\) 8.57775 23.5672i 0.438302 1.20423i −0.502293 0.864697i \(-0.667510\pi\)
0.940596 0.339529i \(-0.110268\pi\)
\(384\) −0.266044 + 1.50881i −0.0135765 + 0.0769963i
\(385\) 0 0
\(386\) 22.2528 8.09937i 1.13264 0.412247i
\(387\) −3.42782 1.97906i −0.174246 0.100601i
\(388\) −0.300767 + 0.173648i −0.0152692 + 0.00881565i
\(389\) 7.21482 + 6.05395i 0.365806 + 0.306948i 0.807100 0.590415i \(-0.201036\pi\)
−0.441294 + 0.897363i \(0.645480\pi\)
\(390\) 0 0
\(391\) −2.26352 3.92053i −0.114471 0.198270i
\(392\) 0.225885 + 0.130415i 0.0114089 + 0.00658695i
\(393\) 3.38922 + 9.31180i 0.170964 + 0.469718i
\(394\) 3.98040 + 22.5740i 0.200530 + 1.13726i
\(395\) 0 0
\(396\) 1.95336 + 0.710966i 0.0981602 + 0.0357274i
\(397\) −4.40441 5.24897i −0.221051 0.263438i 0.644110 0.764933i \(-0.277228\pi\)
−0.865161 + 0.501495i \(0.832784\pi\)
\(398\) 10.0838i 0.505454i
\(399\) −0.132474 + 17.9946i −0.00663201 + 0.900857i
\(400\) 0 0
\(401\) 3.63634 3.05126i 0.181590 0.152372i −0.547461 0.836831i \(-0.684406\pi\)
0.729052 + 0.684458i \(0.239961\pi\)
\(402\) 2.59808 7.13816i 0.129580 0.356019i
\(403\) −13.9137 2.45336i −0.693091 0.122211i
\(404\) 0.0641778 + 0.363970i 0.00319296 + 0.0181082i
\(405\) 0 0
\(406\) 3.80335 6.58759i 0.188757 0.326937i
\(407\) 12.0518 6.95811i 0.597386 0.344901i
\(408\) 6.41852 7.64930i 0.317764 0.378697i
\(409\) −24.2781 20.3718i −1.20048 1.00732i −0.999616 0.0276988i \(-0.991182\pi\)
−0.200860 0.979620i \(-0.564373\pi\)
\(410\) 0 0
\(411\) 8.93242 15.4714i 0.440604 0.763148i
\(412\) 2.93512 + 8.06418i 0.144603 + 0.397294i
\(413\) −1.52314 + 0.268571i −0.0749488 + 0.0132155i
\(414\) −0.0787257 + 0.446476i −0.00386916 + 0.0219431i
\(415\) 0 0
\(416\) −4.41147 + 3.70167i −0.216290 + 0.181489i
\(417\) 12.6604i 0.619985i
\(418\) −6.85240 12.0731i −0.335162 0.590515i
\(419\) 11.0101 0.537879 0.268939 0.963157i \(-0.413327\pi\)
0.268939 + 0.963157i \(0.413327\pi\)
\(420\) 0 0
\(421\) 8.14290 + 2.96377i 0.396861 + 0.144446i 0.532738 0.846280i \(-0.321163\pi\)
−0.135877 + 0.990726i \(0.543385\pi\)
\(422\) 22.0204 + 3.88279i 1.07194 + 0.189011i
\(423\) 5.06975 0.893933i 0.246500 0.0434645i
\(424\) 7.71688 2.80872i 0.374765 0.136403i
\(425\) 0 0
\(426\) 6.47565 + 11.2162i 0.313746 + 0.543425i
\(427\) 5.08499 6.06006i 0.246080 0.293267i
\(428\) 7.36208 8.77379i 0.355860 0.424097i
\(429\) −14.0496 24.3347i −0.678323 1.17489i
\(430\) 0 0
\(431\) 28.0847 10.2220i 1.35279 0.492376i 0.438975 0.898499i \(-0.355342\pi\)
0.913818 + 0.406123i \(0.133120\pi\)
\(432\) −5.51125 + 0.971782i −0.265160 + 0.0467549i
\(433\) 9.12014 + 1.60813i 0.438286 + 0.0772816i 0.388437 0.921475i \(-0.373015\pi\)
0.0498486 + 0.998757i \(0.484126\pi\)
\(434\) 6.21213 + 2.26103i 0.298192 + 0.108533i
\(435\) 0 0
\(436\) 8.69459 0.416395
\(437\) 2.33359 1.92902i 0.111631 0.0922773i
\(438\) 24.1557i 1.15420i
\(439\) −15.9813 + 13.4099i −0.762747 + 0.640021i −0.938840 0.344352i \(-0.888098\pi\)
0.176093 + 0.984374i \(0.443654\pi\)
\(440\) 0 0
\(441\) −0.0295627 + 0.167658i −0.00140775 + 0.00798372i
\(442\) 36.9628 6.51754i 1.75814 0.310008i
\(443\) −8.14966 22.3910i −0.387202 1.06383i −0.968255 0.249963i \(-0.919582\pi\)
0.581054 0.813865i \(-0.302641\pi\)
\(444\) −3.34730 + 5.79769i −0.158856 + 0.275146i
\(445\) 0 0
\(446\) −7.10607 5.96270i −0.336482 0.282342i
\(447\) −16.2034 + 19.3105i −0.766395 + 0.913353i
\(448\) 2.33359 1.34730i 0.110252 0.0636538i
\(449\) −1.09105 + 1.88976i −0.0514899 + 0.0891832i −0.890622 0.454745i \(-0.849730\pi\)
0.839132 + 0.543928i \(0.183064\pi\)
\(450\) 0 0
\(451\) −0.192066 1.08926i −0.00904406 0.0512914i
\(452\) −2.81634 0.496596i −0.132469 0.0233579i
\(453\) 2.43945 6.70233i 0.114615 0.314903i
\(454\) −5.92649 + 4.97291i −0.278144 + 0.233390i
\(455\) 0 0
\(456\) 5.75877 + 3.38160i 0.269679 + 0.158358i
\(457\) 1.78106i 0.0833144i −0.999132 0.0416572i \(-0.986736\pi\)
0.999132 0.0416572i \(-0.0132637\pi\)
\(458\) −14.8067 17.6459i −0.691870 0.824539i
\(459\) 34.2743 + 12.4748i 1.59979 + 0.582274i
\(460\) 0 0
\(461\) −2.68954 15.2531i −0.125264 0.710410i −0.981150 0.193245i \(-0.938099\pi\)
0.855886 0.517164i \(-0.173012\pi\)
\(462\) 4.49687 + 12.3550i 0.209213 + 0.574808i
\(463\) 2.34699 + 1.35504i 0.109074 + 0.0629739i 0.553545 0.832820i \(-0.313275\pi\)
−0.444471 + 0.895793i \(0.646608\pi\)
\(464\) −1.41147 2.44474i −0.0655260 0.113494i
\(465\) 0 0
\(466\) 6.43448 + 5.39917i 0.298071 + 0.250112i
\(467\) −11.1834 + 6.45677i −0.517508 + 0.298784i −0.735915 0.677074i \(-0.763248\pi\)
0.218406 + 0.975858i \(0.429914\pi\)
\(468\) −3.25519 1.87939i −0.150471 0.0868746i
\(469\) −12.5544 + 4.56942i −0.579707 + 0.210996i
\(470\) 0 0
\(471\) 2.24897 12.7545i 0.103627 0.587698i
\(472\) −0.196312 + 0.539363i −0.00903599 + 0.0248262i
\(473\) 12.4143 + 14.7947i 0.570808 + 0.680262i
\(474\) 13.8871 0.637857
\(475\) 0 0
\(476\) −17.5621 −0.804958
\(477\) 3.44540 + 4.10607i 0.157754 + 0.188004i
\(478\) −5.37987 + 14.7811i −0.246069 + 0.676070i
\(479\) 3.22163 18.2708i 0.147200 0.834813i −0.818374 0.574685i \(-0.805124\pi\)
0.965574 0.260127i \(-0.0837645\pi\)
\(480\) 0 0
\(481\) −23.6459 + 8.60640i −1.07816 + 0.392418i
\(482\) 15.1580 + 8.75150i 0.690430 + 0.398620i
\(483\) −2.48335 + 1.43376i −0.112996 + 0.0652385i
\(484\) 0.656574 + 0.550931i 0.0298443 + 0.0250423i
\(485\) 0 0
\(486\) −3.32635 5.76141i −0.150886 0.261343i
\(487\) 35.6573 + 20.5868i 1.61579 + 0.932876i 0.987993 + 0.154497i \(0.0493756\pi\)
0.627795 + 0.778379i \(0.283958\pi\)
\(488\) −1.00411 2.75877i −0.0454539 0.124884i
\(489\) −4.53596 25.7247i −0.205123 1.16331i
\(490\) 0 0
\(491\) 21.2160 + 7.72199i 0.957465 + 0.348489i 0.773040 0.634358i \(-0.218735\pi\)
0.184425 + 0.982847i \(0.440958\pi\)
\(492\) 0.342020 + 0.407604i 0.0154195 + 0.0183762i
\(493\) 18.3987i 0.828635i
\(494\) 8.41147 + 23.6506i 0.378450 + 1.06409i
\(495\) 0 0
\(496\) 1.87939 1.57699i 0.0843869 0.0708090i
\(497\) 7.79066 21.4047i 0.349459 0.960131i
\(498\) 12.7882 + 2.25490i 0.573052 + 0.101044i
\(499\) 5.09286 + 28.8831i 0.227988 + 1.29298i 0.856890 + 0.515499i \(0.172393\pi\)
−0.628902 + 0.777484i \(0.716495\pi\)
\(500\) 0 0
\(501\) 2.44562 4.23594i 0.109262 0.189248i
\(502\) −7.41939 + 4.28359i −0.331143 + 0.191186i
\(503\) −21.6085 + 25.7520i −0.963474 + 1.14822i 0.0254316 + 0.999677i \(0.491904\pi\)
−0.988905 + 0.148547i \(0.952540\pi\)
\(504\) 1.34730 + 1.13052i 0.0600133 + 0.0503572i
\(505\) 0 0
\(506\) 1.10607 1.91576i 0.0491707 0.0851661i
\(507\) 10.5657 + 29.0292i 0.469241 + 1.28923i
\(508\) −9.58186 + 1.68954i −0.425126 + 0.0749612i
\(509\) −0.699645 + 3.96788i −0.0310112 + 0.175873i −0.996379 0.0850178i \(-0.972905\pi\)
0.965368 + 0.260891i \(0.0840164\pi\)
\(510\) 0 0
\(511\) 32.5449 27.3084i 1.43970 1.20805i
\(512\) 1.00000i 0.0441942i
\(513\) −4.41263 + 23.9911i −0.194822 + 1.05923i
\(514\) 8.02465 0.353952
\(515\) 0 0
\(516\) −8.73055 3.17766i −0.384341 0.139889i
\(517\) −24.7372 4.36184i −1.08794 0.191834i
\(518\) 11.5954 2.04458i 0.509472 0.0898336i
\(519\) 13.8648 5.04639i 0.608599 0.221512i
\(520\) 0 0
\(521\) −2.49479 4.32110i −0.109299 0.189311i 0.806188 0.591660i \(-0.201527\pi\)
−0.915486 + 0.402349i \(0.868194\pi\)
\(522\) 1.18437 1.41147i 0.0518384 0.0617785i
\(523\) 17.0677 20.3405i 0.746318 0.889427i −0.250583 0.968095i \(-0.580622\pi\)
0.996901 + 0.0786677i \(0.0250666\pi\)
\(524\) −3.23396 5.60138i −0.141276 0.244697i
\(525\) 0 0
\(526\) 5.60132 2.03871i 0.244229 0.0888921i
\(527\) −15.7470 + 2.77662i −0.685949 + 0.120951i
\(528\) 4.80526 + 0.847296i 0.209122 + 0.0368738i
\(529\) −21.1596 7.70145i −0.919981 0.334846i
\(530\) 0 0
\(531\) −0.374638 −0.0162579
\(532\) −1.95437 11.5817i −0.0847326 0.502131i
\(533\) 2.00000i 0.0866296i
\(534\) −9.08306 + 7.62159i −0.393063 + 0.329819i
\(535\) 0 0
\(536\) −0.860967 + 4.88279i −0.0371881 + 0.210904i
\(537\) 28.3900 5.00593i 1.22512 0.216022i
\(538\) 0.392624 + 1.07873i 0.0169272 + 0.0465072i
\(539\) 0.415345 0.719398i 0.0178902 0.0309867i
\(540\) 0 0
\(541\) −9.17024 7.69475i −0.394260 0.330823i 0.424010 0.905657i \(-0.360622\pi\)
−0.818270 + 0.574834i \(0.805067\pi\)
\(542\) 12.8909 15.3628i 0.553712 0.659888i
\(543\) 3.68642 2.12836i 0.158199 0.0913365i
\(544\) −3.25877 + 5.64436i −0.139719 + 0.242000i
\(545\) 0 0
\(546\) −4.12836 23.4131i −0.176677 1.00199i
\(547\) −3.14809 0.555093i −0.134603 0.0237341i 0.105941 0.994372i \(-0.466215\pi\)
−0.240543 + 0.970638i \(0.577326\pi\)
\(548\) −3.98811 + 10.9572i −0.170363 + 0.468070i
\(549\) 1.46791 1.23172i 0.0626489 0.0525687i
\(550\) 0 0
\(551\) −12.1334 + 2.04746i −0.516901 + 0.0872249i
\(552\) 1.06418i 0.0452944i
\(553\) −15.6996 18.7101i −0.667616 0.795633i
\(554\) 16.3131 + 5.93750i 0.693079 + 0.252260i
\(555\) 0 0
\(556\) −1.43494 8.13798i −0.0608552 0.345127i
\(557\) −8.20037 22.5303i −0.347461 0.954641i −0.983167 0.182710i \(-0.941513\pi\)
0.635706 0.771931i \(-0.280709\pi\)
\(558\) 1.38678 + 0.800660i 0.0587072 + 0.0338946i
\(559\) −17.4611 30.2435i −0.738526 1.27916i
\(560\) 0 0
\(561\) −24.3614 20.4417i −1.02854 0.863048i
\(562\) −2.52990 + 1.46064i −0.106717 + 0.0616133i
\(563\) 7.58380 + 4.37851i 0.319619 + 0.184532i 0.651223 0.758887i \(-0.274256\pi\)
−0.331604 + 0.943419i \(0.607590\pi\)
\(564\) 11.3550 4.13290i 0.478133 0.174026i
\(565\) 0 0
\(566\) −1.64631 + 9.33667i −0.0691994 + 0.392450i
\(567\) 6.09722 16.7520i 0.256059 0.703516i
\(568\) −5.43372 6.47565i −0.227994 0.271712i
\(569\) 36.4201 1.52681 0.763406 0.645919i \(-0.223526\pi\)
0.763406 + 0.645919i \(0.223526\pi\)
\(570\) 0 0
\(571\) 34.2131 1.43177 0.715886 0.698217i \(-0.246023\pi\)
0.715886 + 0.698217i \(0.246023\pi\)
\(572\) 11.7890 + 14.0496i 0.492924 + 0.587445i
\(573\) 5.01060 13.7665i 0.209321 0.575104i
\(574\) 0.162504 0.921605i 0.00678278 0.0384670i
\(575\) 0 0
\(576\) 0.613341 0.223238i 0.0255559 0.00930157i
\(577\) 13.4319 + 7.75490i 0.559177 + 0.322841i 0.752815 0.658232i \(-0.228696\pi\)
−0.193638 + 0.981073i \(0.562029\pi\)
\(578\) 22.0649 12.7392i 0.917778 0.529880i
\(579\) 27.7931 + 23.3212i 1.15504 + 0.969196i
\(580\) 0 0
\(581\) −11.4192 19.7787i −0.473749 0.820557i
\(582\) −0.460802 0.266044i −0.0191009 0.0110279i
\(583\) −8.94517 24.5767i −0.370471 1.01786i
\(584\) −2.73783 15.5270i −0.113292 0.642511i
\(585\) 0 0
\(586\) 25.6459 + 9.33434i 1.05942 + 0.385598i
\(587\) 7.44459 + 8.87211i 0.307271 + 0.366191i 0.897477 0.441061i \(-0.145398\pi\)
−0.590206 + 0.807253i \(0.700953\pi\)
\(588\) 0.399615i 0.0164798i
\(589\) −3.58347 10.0757i −0.147654 0.415162i
\(590\) 0 0
\(591\) −26.9026 + 22.5740i −1.10663 + 0.928569i
\(592\) 1.49449 4.10607i 0.0614230 0.168758i
\(593\) −45.6880 8.05603i −1.87618 0.330821i −0.885242 0.465131i \(-0.846007\pi\)
−0.990939 + 0.134310i \(0.957118\pi\)
\(594\) 3.09492 + 17.5522i 0.126986 + 0.720175i
\(595\) 0 0
\(596\) 8.22668 14.2490i 0.336978 0.583663i
\(597\) −13.3794 + 7.72462i −0.547584 + 0.316148i
\(598\) −2.57115 + 3.06418i −0.105142 + 0.125304i
\(599\) −19.6355 16.4761i −0.802283 0.673196i 0.146469 0.989215i \(-0.453209\pi\)
−0.948753 + 0.316019i \(0.897654\pi\)
\(600\) 0 0
\(601\) −3.99613 + 6.92150i −0.163006 + 0.282334i −0.935945 0.352146i \(-0.885452\pi\)
0.772940 + 0.634480i \(0.218786\pi\)
\(602\) 5.58878 + 15.3550i 0.227782 + 0.625825i
\(603\) −3.18701 + 0.561956i −0.129785 + 0.0228846i
\(604\) −0.808400 + 4.58467i −0.0328933 + 0.186547i
\(605\) 0 0
\(606\) −0.433763 + 0.363970i −0.0176204 + 0.0147853i
\(607\) 26.9905i 1.09551i 0.836639 + 0.547755i \(0.184518\pi\)
−0.836639 + 0.547755i \(0.815482\pi\)
\(608\) −4.08494 1.52094i −0.165666 0.0616824i
\(609\) 11.6541 0.472249
\(610\) 0 0
\(611\) 42.6810 + 15.5346i 1.72669 + 0.628463i
\(612\) −4.18939 0.738703i −0.169346 0.0298603i
\(613\) 14.0348 2.47472i 0.566861 0.0999529i 0.117130 0.993117i \(-0.462631\pi\)
0.449732 + 0.893164i \(0.351520\pi\)
\(614\) 20.0424 7.29482i 0.808844 0.294395i
\(615\) 0 0
\(616\) −4.29086 7.43199i −0.172884 0.299443i
\(617\) −19.6438 + 23.4106i −0.790831 + 0.942475i −0.999368 0.0355392i \(-0.988685\pi\)
0.208538 + 0.978014i \(0.433130\pi\)
\(618\) −8.45134 + 10.0719i −0.339963 + 0.405152i
\(619\) −14.3375 24.8333i −0.576273 0.998133i −0.995902 0.0904380i \(-0.971173\pi\)
0.419629 0.907695i \(-0.362160\pi\)
\(620\) 0 0
\(621\) −3.65270 + 1.32948i −0.146578 + 0.0533500i
\(622\) −28.8468 + 5.08647i −1.15665 + 0.203949i
\(623\) 20.5371 + 3.62124i 0.822801 + 0.145082i
\(624\) −8.29086 3.01763i −0.331900 0.120802i
\(625\) 0 0
\(626\) 5.56118 0.222270
\(627\) 10.7697 18.3405i 0.430100 0.732449i
\(628\) 8.45336i 0.337326i
\(629\) −21.8161 + 18.3059i −0.869867 + 0.729905i
\(630\) 0 0
\(631\) −0.781059 + 4.42961i −0.0310935 + 0.176340i −0.996400 0.0847809i \(-0.972981\pi\)
0.965306 + 0.261121i \(0.0840921\pi\)
\(632\) −8.92647 + 1.57398i −0.355076 + 0.0626095i
\(633\) 11.7168 + 32.1917i 0.465701 + 1.27950i
\(634\) 1.90167 3.29380i 0.0755251 0.130813i
\(635\) 0 0
\(636\) 9.63816 + 8.08737i 0.382178 + 0.320685i
\(637\) −0.965505 + 1.15064i −0.0382547 + 0.0455902i
\(638\) −7.78601 + 4.49525i −0.308251 + 0.177969i
\(639\) 2.75877 4.77833i 0.109135 0.189028i
\(640\) 0 0
\(641\) −2.01573 11.4318i −0.0796165 0.451528i −0.998389 0.0567403i \(-0.981929\pi\)
0.918772 0.394788i \(-0.129182\pi\)
\(642\) 17.2810 + 3.04710i 0.682026 + 0.120260i
\(643\) 8.90809 24.4748i 0.351301 0.965191i −0.630652 0.776066i \(-0.717213\pi\)
0.981953 0.189125i \(-0.0605652\pi\)
\(644\) 1.43376 1.20307i 0.0564982 0.0474076i
\(645\) 0 0
\(646\) 18.1004 + 21.8966i 0.712152 + 0.861511i
\(647\) 2.31490i 0.0910082i 0.998964 + 0.0455041i \(0.0144894\pi\)
−0.998964 + 0.0455041i \(0.985511\pi\)
\(648\) −4.25260 5.06805i −0.167058 0.199092i
\(649\) 1.71776 + 0.625213i 0.0674279 + 0.0245418i
\(650\) 0 0
\(651\) 1.75877 + 9.97448i 0.0689316 + 0.390931i
\(652\) 5.83132 + 16.0214i 0.228372 + 0.627447i
\(653\) −2.86257 1.65270i −0.112021 0.0646753i 0.442943 0.896550i \(-0.353934\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(654\) 6.66044 + 11.5362i 0.260444 + 0.451102i
\(655\) 0 0
\(656\) −0.266044 0.223238i −0.0103873 0.00871597i
\(657\) 8.91215 5.14543i 0.347696 0.200742i
\(658\) −18.4053 10.6263i −0.717513 0.414256i
\(659\) −12.9201 + 4.70253i −0.503295 + 0.183185i −0.581176 0.813778i \(-0.697407\pi\)
0.0778802 + 0.996963i \(0.475185\pi\)
\(660\) 0 0
\(661\) −0.579030 + 3.28384i −0.0225217 + 0.127727i −0.993996 0.109419i \(-0.965101\pi\)
0.971474 + 0.237146i \(0.0762120\pi\)
\(662\) −6.98470 + 19.1903i −0.271468 + 0.745853i
\(663\) 36.9628 + 44.0506i 1.43552 + 1.71078i
\(664\) −8.47565 −0.328919
\(665\) 0 0
\(666\) 2.85204 0.110514
\(667\) −1.26038 1.50206i −0.0488020 0.0581600i
\(668\) −1.09191 + 3.00000i −0.0422473 + 0.116073i
\(669\) 2.46791 13.9962i 0.0954150 0.541125i
\(670\) 0 0
\(671\) −8.78611 + 3.19788i −0.339184 + 0.123453i
\(672\) 3.57526 + 2.06418i 0.137919 + 0.0796274i
\(673\) 33.7585 19.4905i 1.30130 0.751304i 0.320670 0.947191i \(-0.396092\pi\)
0.980626 + 0.195887i \(0.0627587\pi\)
\(674\) −15.5587 13.0553i −0.599299 0.502872i
\(675\) 0 0
\(676\) −10.0817 17.4620i −0.387758 0.671617i
\(677\) −37.7481 21.7939i −1.45078 0.837606i −0.452250 0.891891i \(-0.649379\pi\)
−0.998525 + 0.0542853i \(0.982712\pi\)
\(678\) −1.49854 4.11721i −0.0575512 0.158121i
\(679\) 0.162504 + 0.921605i 0.00623632 + 0.0353680i
\(680\) 0 0
\(681\) −11.1382 4.05396i −0.426815 0.155348i
\(682\) −5.02239 5.98545i −0.192317 0.229195i
\(683\) 32.9317i 1.26010i 0.776556 + 0.630048i \(0.216965\pi\)
−0.776556 + 0.630048i \(0.783035\pi\)
\(684\) 0.0209445 2.84499i 0.000800834 0.108781i
\(685\) 0 0
\(686\) −13.9108 + 11.6726i −0.531119 + 0.445661i
\(687\) 12.0705 33.1634i 0.460518 1.26526i
\(688\) 5.97205 + 1.05303i 0.227682 + 0.0401465i
\(689\) 8.21213 + 46.5733i 0.312857 + 1.77430i
\(690\) 0 0
\(691\) −17.1604 + 29.7228i −0.652814 + 1.13071i 0.329623 + 0.944113i \(0.393078\pi\)
−0.982437 + 0.186594i \(0.940255\pi\)
\(692\) −8.34018 + 4.81521i −0.317046 + 0.183047i
\(693\) 3.60046 4.29086i 0.136770 0.162996i
\(694\) −3.99479 3.35202i −0.151640 0.127241i
\(695\) 0 0
\(696\) 2.16250 3.74557i 0.0819695 0.141975i
\(697\) 0.774169 + 2.12701i 0.0293237 + 0.0805663i
\(698\) −14.1226 + 2.49020i −0.534549 + 0.0942555i
\(699\) −2.23467 + 12.6734i −0.0845230 + 0.479354i
\(700\) 0 0
\(701\) 4.94356 4.14814i 0.186716 0.156673i −0.544638 0.838671i \(-0.683333\pi\)
0.731354 + 0.681998i \(0.238889\pi\)
\(702\) 32.2276i 1.21635i
\(703\) −14.5000 12.3500i −0.546878 0.465788i
\(704\) −3.18479 −0.120031
\(705\) 0 0
\(706\) −24.6668 8.97800i −0.928349 0.337891i
\(707\) 0.980752 + 0.172933i 0.0368850 + 0.00650381i
\(708\) −0.866025 + 0.152704i −0.0325472 + 0.00573895i
\(709\) −3.17530 + 1.15571i −0.119251 + 0.0434037i −0.400956 0.916097i \(-0.631322\pi\)
0.281706 + 0.959501i \(0.409100\pi\)
\(710\) 0 0
\(711\) −2.95811 5.12360i −0.110938 0.192150i
\(712\) 4.97464 5.92855i 0.186433 0.222182i
\(713\) 1.09537 1.30541i 0.0410218 0.0488879i
\(714\) −13.4534 23.3019i −0.503479 0.872052i
\(715\) 0 0
\(716\) −17.6814 + 6.43550i −0.660785 + 0.240506i
\(717\) −23.7331 + 4.18479i −0.886330 + 0.156284i
\(718\) −33.1786 5.85029i −1.23822 0.218331i
\(719\) −29.3209 10.6719i −1.09348 0.397996i −0.268574 0.963259i \(-0.586552\pi\)
−0.824911 + 0.565263i \(0.808775\pi\)
\(720\) 0 0
\(721\) 23.1242 0.861192
\(722\) −12.4259 + 14.3735i −0.462445 + 0.534925i
\(723\) 26.8161i 0.997303i
\(724\) −2.12836 + 1.78590i −0.0790997 + 0.0663725i
\(725\) 0 0
\(726\) −0.228026 + 1.29320i −0.00846283 + 0.0479951i
\(727\) −25.2715 + 4.45605i −0.937269 + 0.165266i −0.621361 0.783524i \(-0.713420\pi\)
−0.315908 + 0.948790i \(0.602309\pi\)
\(728\) 5.30731 + 14.5817i 0.196702 + 0.540434i
\(729\) 15.0201 26.0155i 0.556299 0.963538i
\(730\) 0 0
\(731\) −30.2768 25.4052i −1.11983 0.939647i
\(732\) 2.89122 3.44562i 0.106863 0.127354i
\(733\) −20.6751 + 11.9368i −0.763651 + 0.440894i −0.830605 0.556862i \(-0.812005\pi\)
0.0669540 + 0.997756i \(0.478672\pi\)
\(734\) −5.23442 + 9.06629i −0.193206 + 0.334643i
\(735\) 0 0
\(736\) −0.120615 0.684040i −0.00444592 0.0252141i
\(737\) 15.5507 + 2.74200i 0.572816 + 0.101003i
\(738\) 0.0775297 0.213011i 0.00285391 0.00784104i
\(739\) 35.1924 29.5299i 1.29457 1.08628i 0.303517 0.952826i \(-0.401839\pi\)
0.991056 0.133449i \(-0.0426052\pi\)
\(740\) 0 0
\(741\) −24.9368 + 29.2780i −0.916075 + 1.07555i
\(742\) 22.1284i 0.812357i
\(743\) −32.7895 39.0770i −1.20293 1.43360i −0.871697 0.490046i \(-0.836980\pi\)
−0.331232 0.943549i \(-0.607464\pi\)
\(744\) 3.53209 + 1.28558i 0.129493 + 0.0471315i
\(745\) 0 0
\(746\) 4.15064 + 23.5395i 0.151966 + 0.861841i
\(747\) −1.89209 5.19846i −0.0692278 0.190202i
\(748\) 17.9761 + 10.3785i 0.657271 + 0.379476i
\(749\) −15.4311 26.7274i −0.563839 0.976598i
\(750\) 0 0
\(751\) −27.8607 23.3779i −1.01665 0.853072i −0.0274489 0.999623i \(-0.508738\pi\)
−0.989203 + 0.146551i \(0.953183\pi\)
\(752\) −6.83045 + 3.94356i −0.249081 + 0.143807i
\(753\) −11.3672 6.56283i −0.414242 0.239163i
\(754\) 15.2763 5.56012i 0.556330 0.202488i
\(755\) 0 0
\(756\) −2.61856 + 14.8506i −0.0952359 + 0.540110i
\(757\) 1.98486 5.45336i 0.0721410 0.198206i −0.898382 0.439216i \(-0.855256\pi\)
0.970523 + 0.241010i \(0.0774786\pi\)
\(758\) 11.4503 + 13.6459i 0.415892 + 0.495641i
\(759\) 3.38919 0.123020
\(760\) 0 0
\(761\) 22.6355 0.820535 0.410268 0.911965i \(-0.365435\pi\)
0.410268 + 0.911965i \(0.365435\pi\)
\(762\) −9.58186 11.4192i −0.347114 0.413675i
\(763\) 8.01298 22.0155i 0.290089 0.797014i
\(764\) −1.66044 + 9.41685i −0.0600728 + 0.340690i
\(765\) 0 0
\(766\) −23.5672 + 8.57775i −0.851516 + 0.309927i
\(767\) −2.86257 1.65270i −0.103361 0.0596757i
\(768\) 1.32683 0.766044i 0.0478778 0.0276422i
\(769\) −8.35188 7.00806i −0.301177 0.252717i 0.479657 0.877456i \(-0.340761\pi\)
−0.780834 + 0.624739i \(0.785205\pi\)
\(770\) 0 0
\(771\) 6.14724 + 10.6473i 0.221387 + 0.383454i
\(772\) −20.5083 11.8405i −0.738111 0.426149i
\(773\) 1.79585 + 4.93407i 0.0645924 + 0.177466i 0.967790 0.251759i \(-0.0810090\pi\)
−0.903198 + 0.429225i \(0.858787\pi\)
\(774\) 0.687319 + 3.89798i 0.0247052 + 0.140110i
\(775\) 0 0
\(776\) 0.326352 + 0.118782i 0.0117153 + 0.00426404i
\(777\) 11.5954 + 13.8188i 0.415982 + 0.495748i
\(778\) 9.41828i 0.337662i
\(779\) −1.31655 + 0.747243i −0.0471704 + 0.0267728i
\(780\) 0 0
\(781\) −20.6236 + 17.3053i −0.737971 + 0.619231i
\(782\) −1.54834 + 4.25402i −0.0553684 + 0.152124i
\(783\) 15.5580 + 2.74329i 0.555996 + 0.0980371i
\(784\) −0.0452926 0.256867i −0.00161759 0.00917383i
\(785\) 0 0
\(786\) 4.95471 8.58180i 0.176729 0.306103i
\(787\) 2.06758 1.19372i 0.0737011 0.0425514i −0.462697 0.886517i \(-0.653118\pi\)
0.536398 + 0.843965i \(0.319785\pi\)
\(788\) 14.7341 17.5594i 0.524881 0.625529i
\(789\) 6.99588 + 5.87024i 0.249060 + 0.208986i
\(790\) 0 0
\(791\) −3.85298 + 6.67355i −0.136996 + 0.237284i
\(792\) −0.710966 1.95336i −0.0252631 0.0694097i
\(793\) 16.6499 2.93582i 0.591254 0.104254i
\(794\) −1.18984 + 6.74795i −0.0422260 + 0.239476i
\(795\) 0 0
\(796\) 7.72462 6.48173i 0.273792 0.229739i
\(797\) 31.0951i 1.10145i −0.834688 0.550723i \(-0.814352\pi\)
0.834688 0.550723i \(-0.185648\pi\)
\(798\) 13.8698 11.4652i 0.490986 0.405864i
\(799\) 51.4047 1.81857
\(800\) 0 0
\(801\) 4.74675 + 1.72768i 0.167718 + 0.0610444i
\(802\) −4.67479 0.824292i −0.165073 0.0291068i
\(803\) −49.4502 + 8.71941i −1.74506 + 0.307701i
\(804\) −7.13816 + 2.59808i −0.251743 + 0.0916271i
\(805\) 0 0
\(806\) 7.06418 + 12.2355i 0.248825 + 0.430978i
\(807\) −1.13052 + 1.34730i −0.0397960 + 0.0474271i
\(808\) 0.237565 0.283119i 0.00835750 0.00996008i
\(809\) 11.1518 + 19.3155i 0.392077 + 0.679098i 0.992723 0.120417i \(-0.0384232\pi\)
−0.600646 + 0.799515i \(0.705090\pi\)
\(810\) 0 0
\(811\) −3.11886 + 1.13517i −0.109518 + 0.0398613i −0.396198 0.918165i \(-0.629671\pi\)
0.286680 + 0.958026i \(0.407448\pi\)
\(812\) −7.49113 + 1.32089i −0.262887 + 0.0463541i
\(813\) 30.2588 + 5.33544i 1.06122 + 0.187122i
\(814\) −13.0770 4.75963i −0.458348 0.166825i
\(815\) 0 0
\(816\) −9.98545 −0.349561
\(817\) 13.3847 22.7939i 0.468273 0.797456i
\(818\) 31.6928i 1.10811i
\(819\) −7.75877 + 6.51038i −0.271113 + 0.227491i
\(820\) 0 0
\(821\) −0.318201 + 1.80460i −0.0111053 + 0.0629811i −0.989857 0.142069i \(-0.954625\pi\)
0.978752 + 0.205050i \(0.0657357\pi\)
\(822\) −17.5934 + 3.10220i −0.613641 + 0.108202i
\(823\) 11.7100 + 32.1729i 0.408185 + 1.12148i 0.958144 + 0.286287i \(0.0924209\pi\)
−0.549959 + 0.835191i \(0.685357\pi\)
\(824\) 4.29086 7.43199i 0.149479 0.258906i
\(825\) 0 0
\(826\) 1.18479 + 0.994159i 0.0412242 + 0.0345912i
\(827\) −12.7695 + 15.2181i −0.444038 + 0.529184i −0.940918 0.338636i \(-0.890035\pi\)
0.496880 + 0.867820i \(0.334479\pi\)
\(828\) 0.392624 0.226682i 0.0136446 0.00787773i
\(829\) −17.8675 + 30.9475i −0.620565 + 1.07485i 0.368816 + 0.929502i \(0.379763\pi\)
−0.989381 + 0.145347i \(0.953570\pi\)
\(830\) 0 0
\(831\) 4.61856 + 26.1931i 0.160216 + 0.908630i
\(832\) 5.67128 + 1.00000i 0.196616 + 0.0346688i
\(833\) −0.581424 + 1.59745i −0.0201451 + 0.0553483i
\(834\) 9.69846 8.13798i 0.335830 0.281795i
\(835\) 0 0
\(836\) −4.84389 + 13.0097i −0.167530 + 0.449949i
\(837\) 13.7297i 0.474567i
\(838\) −7.07716 8.43423i −0.244476 0.291356i
\(839\) −51.1147 18.6042i −1.76468 0.642290i −0.764679 0.644411i \(-0.777103\pi\)
−0.999998 + 0.00212143i \(0.999325\pi\)
\(840\) 0 0
\(841\) −3.65199 20.7115i −0.125931 0.714188i
\(842\) −2.96377 8.14290i −0.102138 0.280623i
\(843\) −3.87603 2.23783i −0.133498 0.0770748i
\(844\) −11.1800 19.3644i −0.384833 0.666550i
\(845\) 0 0
\(846\) −3.94356 3.30904i −0.135582 0.113767i
\(847\) 2.00011 1.15476i 0.0687245 0.0396781i
\(848\) −7.11192 4.10607i −0.244224 0.141003i
\(849\) −13.6493 + 4.96794i −0.468443 + 0.170499i
\(850\) 0 0
\(851\) 0.527036 2.98897i 0.0180666 0.102461i
\(852\) 4.42961 12.1702i 0.151756 0.416946i
\(853\) 10.2694 + 12.2385i 0.351616 + 0.419040i 0.912643 0.408758i \(-0.134038\pi\)
−0.561027 + 0.827798i \(0.689594\pi\)
\(854\) −7.91085 −0.270704
\(855\) 0 0
\(856\) −11.4534 −0.391468
\(857\) 16.7218 + 19.9283i 0.571207 + 0.680738i 0.971878 0.235484i \(-0.0756675\pi\)
−0.400671 + 0.916222i \(0.631223\pi\)
\(858\) −9.61051 + 26.4047i −0.328097 + 0.901440i
\(859\) −9.25031 + 52.4611i −0.315617 + 1.78995i 0.253124 + 0.967434i \(0.418542\pi\)
−0.568740 + 0.822517i \(0.692569\pi\)
\(860\) 0 0
\(861\) 1.34730 0.490376i 0.0459157 0.0167120i
\(862\) −25.8830 14.9436i −0.881579 0.508980i
\(863\) 2.79876 1.61587i 0.0952710 0.0550048i −0.451608 0.892217i \(-0.649149\pi\)
0.546879 + 0.837212i \(0.315816\pi\)
\(864\) 4.28699 + 3.59721i 0.145846 + 0.122380i
\(865\) 0 0
\(866\) −4.63041 8.02011i −0.157348 0.272535i
\(867\) 33.8054 + 19.5175i 1.14809 + 0.662850i
\(868\) −2.26103 6.21213i −0.0767444 0.210854i
\(869\) 5.01279 + 28.4290i 0.170047 + 0.964387i
\(870\) 0 0
\(871\) −26.8307 9.76557i −0.909123 0.330894i
\(872\) −5.58878 6.66044i −0.189260 0.225551i
\(873\) 0.226682i 0.00767201i
\(874\) −2.97771 0.547683i −0.100723 0.0185257i
\(875\) 0 0
\(876\) 18.5043 15.5270i 0.625204 0.524608i
\(877\) −4.00995 + 11.0172i −0.135406 + 0.372026i −0.988801 0.149239i \(-0.952317\pi\)
0.853395 + 0.521265i \(0.174540\pi\)
\(878\) 20.5452 + 3.62267i 0.693367 + 0.122259i
\(879\) 7.26083 + 41.1782i 0.244902 + 1.38891i
\(880\) 0 0
\(881\) −13.5236 + 23.4236i −0.455623 + 0.789162i −0.998724 0.0505056i \(-0.983917\pi\)
0.543101 + 0.839667i \(0.317250\pi\)
\(882\) 0.147436 0.0851223i 0.00496443 0.00286622i
\(883\) −9.30823 + 11.0931i −0.313247 + 0.373313i −0.899579 0.436758i \(-0.856127\pi\)
0.586333 + 0.810070i \(0.300571\pi\)
\(884\) −28.7520 24.1258i −0.967033 0.811437i
\(885\) 0 0
\(886\) −11.9140 + 20.6357i −0.400259 + 0.693268i
\(887\) −3.96443 10.8922i −0.133112 0.365724i 0.855172 0.518344i \(-0.173451\pi\)
−0.988285 + 0.152620i \(0.951229\pi\)
\(888\) 6.59289 1.16250i 0.221243 0.0390111i
\(889\) −4.55262 + 25.8192i −0.152690 + 0.865948i
\(890\) 0 0
\(891\) −16.1407 + 13.5436i −0.540733 + 0.453729i
\(892\) 9.27631i 0.310594i
\(893\) 5.72048 + 33.8999i 0.191428 + 1.13442i
\(894\) 25.2080 0.843082
\(895\) 0 0
\(896\) −2.53209 0.921605i −0.0845912 0.0307887i
\(897\) −6.03525 1.06418i −0.201511 0.0355319i
\(898\) 2.14895 0.378918i 0.0717115 0.0126447i
\(899\) −6.50805 + 2.36873i −0.217055 + 0.0790017i
\(900\) 0 0
\(901\) 26.7615 + 46.3522i 0.891553 + 1.54422i
\(902\) −0.710966 + 0.847296i −0.0236726 + 0.0282119i
\(903\) −16.0922 + 19.1780i −0.535516 + 0.638203i
\(904\) 1.42989 + 2.47665i 0.0475575 + 0.0823720i
\(905\) 0 0
\(906\) −6.70233 + 2.43945i −0.222670 + 0.0810453i
\(907\) 41.3409 7.28952i 1.37270 0.242044i 0.561823 0.827258i \(-0.310100\pi\)
0.810879 + 0.585213i \(0.198989\pi\)
\(908\) 7.61895 + 1.34343i 0.252844 + 0.0445832i
\(909\) 0.226682 + 0.0825054i 0.00751855 + 0.00273653i
\(910\) 0 0
\(911\) −44.8675 −1.48653 −0.743264 0.668999i \(-0.766723\pi\)
−0.743264 + 0.668999i \(0.766723\pi\)
\(912\) −1.11121 6.58512i −0.0367959 0.218055i
\(913\) 26.9932i 0.893344i
\(914\) −1.36437 + 1.14484i −0.0451294 + 0.0378680i
\(915\) 0 0
\(916\) −4.00000 + 22.6851i −0.132164 + 0.749538i
\(917\) −17.1636 + 3.02641i −0.566792 + 0.0999408i
\(918\) −12.4748 34.2743i −0.411730 1.13122i
\(919\) −16.2635 + 28.1692i −0.536484 + 0.929217i 0.462606 + 0.886564i \(0.346914\pi\)
−0.999090 + 0.0426535i \(0.986419\pi\)
\(920\) 0 0
\(921\) 25.0323 + 21.0046i 0.824843 + 0.692125i
\(922\) −9.95578 + 11.8648i −0.327876 + 0.390748i
\(923\) 42.1590 24.3405i 1.38768 0.801177i
\(924\) 6.57398 11.3865i 0.216268 0.374587i
\(925\) 0 0
\(926\) −0.470599 2.66890i −0.0154649 0.0877056i
\(927\) 5.51622 + 0.972659i 0.181177 + 0.0319463i
\(928\) −0.965505 + 2.65270i −0.0316943 + 0.0870793i
\(929\) −9.07011 + 7.61072i −0.297581 + 0.249700i −0.779336 0.626606i \(-0.784444\pi\)
0.481756 + 0.876305i \(0.339999\pi\)
\(930\) 0 0
\(931\) −1.11817 0.205663i −0.0366467 0.00674034i
\(932\) 8.39961i 0.275139i
\(933\) −28.8468 34.3783i −0.944401 1.12549i
\(934\) 12.1348 + 4.41669i 0.397061 + 0.144518i
\(935\) 0 0
\(936\) 0.652704 + 3.70167i 0.0213343 + 0.120993i
\(937\) −0.261243 0.717759i −0.00853443 0.0234482i 0.935352 0.353718i \(-0.115083\pi\)
−0.943887 + 0.330269i \(0.892860\pi\)
\(938\) 11.5702 + 6.68004i 0.377780 + 0.218111i
\(939\) 4.26011 + 7.37874i 0.139024 + 0.240796i
\(940\) 0 0
\(941\) −16.4652 13.8160i −0.536751 0.450388i 0.333674 0.942688i \(-0.391711\pi\)
−0.870425 + 0.492301i \(0.836156\pi\)
\(942\) −11.2162 + 6.47565i −0.365442 + 0.210988i
\(943\) −0.208911 0.120615i −0.00680307 0.00392776i
\(944\) 0.539363 0.196312i 0.0175548 0.00638941i
\(945\) 0 0
\(946\) 3.35369 19.0197i 0.109038 0.618385i
\(947\) −10.8369 + 29.7743i −0.352153 + 0.967533i 0.629524 + 0.776981i \(0.283250\pi\)
−0.981677 + 0.190552i \(0.938972\pi\)
\(948\) −8.92647 10.6382i −0.289918 0.345511i
\(949\) 90.7957 2.94735
\(950\) 0 0
\(951\) 5.82707 0.188956
\(952\) 11.2887 + 13.4534i 0.365869 + 0.436026i
\(953\) 19.1091 52.5017i 0.619003 1.70070i −0.0904104 0.995905i \(-0.528818\pi\)
0.709414 0.704792i \(-0.248960\pi\)
\(954\) 0.930770 5.27866i 0.0301348 0.170903i
\(955\) 0 0
\(956\) 14.7811 5.37987i 0.478054 0.173997i
\(957\) −11.9289 6.88713i −0.385605 0.222629i
\(958\) −16.0670 + 9.27631i −0.519103 + 0.299704i
\(959\) 24.0692 + 20.1965i 0.777236 + 0.652178i
\(960\) 0 0
\(961\) 12.4905 + 21.6342i 0.402920 + 0.697877i
\(962\) 21.7922 + 12.5817i 0.702608 + 0.405651i
\(963\) −2.55682 7.02481i −0.0823925 0.226371i
\(964\) −3.03936 17.2371i −0.0978913 0.555169i
\(965\) 0 0
\(966\) 2.69459 + 0.980752i 0.0866971 + 0.0315552i
\(967\) −13.8564 16.5134i −0.445592 0.531036i 0.495761 0.868459i \(-0.334889\pi\)
−0.941353 + 0.337423i \(0.890445\pi\)
\(968\) 0.857097i 0.0275481i
\(969\) −15.1873 + 40.7900i −0.487887 + 1.31036i
\(970\) 0 0
\(971\) 37.2729 31.2757i 1.19614 1.00368i 0.196413 0.980521i \(-0.437071\pi\)
0.999732 0.0231632i \(-0.00737372\pi\)
\(972\) −2.27536 + 6.25150i −0.0729822 + 0.200517i
\(973\) −21.9285 3.86659i −0.702996 0.123957i
\(974\) −7.14971 40.5480i −0.229092 1.29924i
\(975\) 0 0
\(976\) −1.46791 + 2.54250i −0.0469867 + 0.0813833i
\(977\) 43.7760 25.2741i 1.40052 0.808590i 0.406073 0.913841i \(-0.366898\pi\)
0.994446 + 0.105251i \(0.0335646\pi\)
\(978\) −16.7906 + 20.0103i −0.536904 + 0.639858i
\(979\) −18.8812 15.8432i −0.603446 0.506351i
\(980\) 0 0
\(981\) 2.83750 4.91469i 0.0905943 0.156914i
\(982\) −7.72199 21.2160i −0.246419 0.677030i
\(983\) 29.6034 5.21987i 0.944201 0.166488i 0.319706 0.947517i \(-0.396416\pi\)
0.624495 + 0.781029i \(0.285305\pi\)
\(984\) 0.0923963 0.524005i 0.00294549 0.0167047i
\(985\) 0 0
\(986\) 14.0942 11.8264i 0.448851 0.376631i
\(987\) 32.5609i 1.03642i
\(988\) 12.7106 21.6459i 0.404379 0.688648i
\(989\) 4.21213 0.133938
\(990\) 0 0
\(991\) −2.58677 0.941508i −0.0821715 0.0299080i 0.300607 0.953748i \(-0.402811\pi\)
−0.382779 + 0.923840i \(0.625033\pi\)
\(992\) −2.41609 0.426022i −0.0767110 0.0135262i
\(993\) −30.8128 + 5.43313i −0.977816 + 0.172415i
\(994\) −21.4047 + 7.79066i −0.678915 + 0.247105i
\(995\) 0 0
\(996\) −6.49273 11.2457i −0.205730 0.356335i
\(997\) 5.59527 6.66819i 0.177204 0.211184i −0.670130 0.742244i \(-0.733762\pi\)
0.847334 + 0.531060i \(0.178206\pi\)
\(998\) 18.8521 22.4670i 0.596752 0.711182i
\(999\) 12.2267 + 21.1772i 0.386835 + 0.670018i
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 950.2.u.b.899.1 12
5.2 odd 4 38.2.e.a.25.1 6
5.3 odd 4 950.2.l.d.101.1 6
5.4 even 2 inner 950.2.u.b.899.2 12
15.2 even 4 342.2.u.c.253.1 6
19.16 even 9 inner 950.2.u.b.149.2 12
20.7 even 4 304.2.u.c.177.1 6
95.2 even 36 722.2.e.l.423.1 6
95.7 odd 12 722.2.e.m.389.1 6
95.12 even 12 722.2.e.a.389.1 6
95.17 odd 36 722.2.e.b.423.1 6
95.22 even 36 722.2.e.k.415.1 6
95.27 even 12 722.2.e.l.99.1 6
95.32 even 36 722.2.c.l.653.3 6
95.37 even 4 722.2.e.k.595.1 6
95.42 odd 36 722.2.a.l.1.3 3
95.47 odd 36 722.2.c.k.429.1 6
95.52 even 36 722.2.e.a.245.1 6
95.54 even 18 inner 950.2.u.b.149.1 12
95.62 odd 36 722.2.e.m.245.1 6
95.67 even 36 722.2.c.l.429.3 6
95.72 even 36 722.2.a.k.1.1 3
95.73 odd 36 950.2.l.d.301.1 6
95.82 odd 36 722.2.c.k.653.1 6
95.87 odd 12 722.2.e.b.99.1 6
95.92 odd 36 38.2.e.a.35.1 yes 6
285.92 even 36 342.2.u.c.73.1 6
285.137 even 36 6498.2.a.bl.1.2 3
285.167 odd 36 6498.2.a.bq.1.2 3
380.167 odd 36 5776.2.a.bo.1.3 3
380.187 even 36 304.2.u.c.225.1 6
380.327 even 36 5776.2.a.bn.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.e.a.25.1 6 5.2 odd 4
38.2.e.a.35.1 yes 6 95.92 odd 36
304.2.u.c.177.1 6 20.7 even 4
304.2.u.c.225.1 6 380.187 even 36
342.2.u.c.73.1 6 285.92 even 36
342.2.u.c.253.1 6 15.2 even 4
722.2.a.k.1.1 3 95.72 even 36
722.2.a.l.1.3 3 95.42 odd 36
722.2.c.k.429.1 6 95.47 odd 36
722.2.c.k.653.1 6 95.82 odd 36
722.2.c.l.429.3 6 95.67 even 36
722.2.c.l.653.3 6 95.32 even 36
722.2.e.a.245.1 6 95.52 even 36
722.2.e.a.389.1 6 95.12 even 12
722.2.e.b.99.1 6 95.87 odd 12
722.2.e.b.423.1 6 95.17 odd 36
722.2.e.k.415.1 6 95.22 even 36
722.2.e.k.595.1 6 95.37 even 4
722.2.e.l.99.1 6 95.27 even 12
722.2.e.l.423.1 6 95.2 even 36
722.2.e.m.245.1 6 95.62 odd 36
722.2.e.m.389.1 6 95.7 odd 12
950.2.l.d.101.1 6 5.3 odd 4
950.2.l.d.301.1 6 95.73 odd 36
950.2.u.b.149.1 12 95.54 even 18 inner
950.2.u.b.149.2 12 19.16 even 9 inner
950.2.u.b.899.1 12 1.1 even 1 trivial
950.2.u.b.899.2 12 5.4 even 2 inner
5776.2.a.bn.1.1 3 380.327 even 36
5776.2.a.bo.1.3 3 380.167 odd 36
6498.2.a.bl.1.2 3 285.137 even 36
6498.2.a.bq.1.2 3 285.167 odd 36