Properties

Label 950.2.l.d.101.1
Level $950$
Weight $2$
Character 950.101
Analytic conductor $7.586$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(101,950)]
 
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([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), degree \(6\), 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: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) 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: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 101.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 950.101
Dual form 950.2.l.d.301.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766044 + 0.642788i) q^{2} +(1.43969 + 0.524005i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{6} +(1.34730 - 2.33359i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.500000 - 0.419550i) q^{9} +O(q^{10})\) \(q+(-0.766044 + 0.642788i) q^{2} +(1.43969 + 0.524005i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{6} +(1.34730 - 2.33359i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.500000 - 0.419550i) q^{9} +(-1.59240 - 2.75811i) q^{11} +(0.766044 - 1.32683i) q^{12} +(-5.41147 + 1.96962i) q^{13} +(0.467911 + 2.65366i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(4.99273 - 4.18939i) q^{17} +0.652704 q^{18} +(2.82635 - 3.31839i) q^{19} +(3.16250 - 2.65366i) q^{21} +(2.99273 + 1.08926i) q^{22} +(0.120615 - 0.684040i) q^{23} +(0.266044 + 1.50881i) q^{24} +(2.87939 - 4.98724i) q^{26} +(-2.79813 - 4.84651i) q^{27} +(-2.06418 - 1.73205i) q^{28} +(-2.16250 - 1.81456i) q^{29} +(-1.22668 + 2.12467i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.847296 - 4.80526i) q^{33} +(-1.13176 + 6.41852i) q^{34} +(-0.500000 + 0.419550i) q^{36} +4.36959 q^{37} +(-0.0320889 + 4.35878i) q^{38} -8.82295 q^{39} +(0.326352 + 0.118782i) q^{41} +(-0.716881 + 4.06564i) q^{42} +(-1.05303 - 5.97205i) q^{43} +(-2.99273 + 1.08926i) q^{44} +(0.347296 + 0.601535i) q^{46} +(-6.04189 - 5.06975i) q^{47} +(-1.17365 - 0.984808i) q^{48} +(-0.130415 - 0.225885i) q^{49} +(9.38326 - 3.41523i) q^{51} +(1.00000 + 5.67128i) q^{52} +(-1.42602 + 8.08737i) q^{53} +(5.25877 + 1.91404i) q^{54} +2.69459 q^{56} +(5.80793 - 3.29644i) q^{57} +2.82295 q^{58} +(0.439693 - 0.368946i) q^{59} +(0.509800 - 2.89122i) q^{61} +(-0.426022 - 2.41609i) q^{62} +(-1.65270 + 0.601535i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.73783 + 3.13641i) q^{66} +(3.79813 + 3.18701i) q^{67} +(-3.25877 - 5.64436i) q^{68} +(0.532089 - 0.921605i) q^{69} +(-1.46791 - 8.32494i) q^{71} +(0.113341 - 0.642788i) q^{72} +(14.8157 + 5.39246i) q^{73} +(-3.34730 + 2.80872i) q^{74} +(-2.77719 - 3.35965i) q^{76} -8.58172 q^{77} +(6.75877 - 5.67128i) q^{78} +(8.51754 + 3.10013i) q^{79} +(-1.14883 - 6.51536i) q^{81} +(-0.326352 + 0.118782i) q^{82} +(4.23783 - 7.34013i) q^{83} +(-2.06418 - 3.57526i) q^{84} +(4.64543 + 3.89798i) q^{86} +(-2.16250 - 3.74557i) q^{87} +(1.59240 - 2.75811i) q^{88} +(-7.27244 + 2.64695i) q^{89} +(-2.69459 + 15.2818i) q^{91} +(-0.652704 - 0.237565i) q^{92} +(-2.87939 + 2.41609i) q^{93} +7.88713 q^{94} +1.53209 q^{96} +(0.266044 - 0.223238i) q^{97} +(0.245100 + 0.0892091i) q^{98} +(-0.360967 + 2.04715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} - 3 q^{6} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{3} - 3 q^{6} + 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{11} - 12 q^{13} + 12 q^{14} + 12 q^{17} + 6 q^{18} + 18 q^{19} + 24 q^{21} + 12 q^{23} - 3 q^{24} + 6 q^{26} - 3 q^{27} + 6 q^{28} - 18 q^{29} + 6 q^{31} - 3 q^{33} - 12 q^{34} - 3 q^{36} + 12 q^{37} + 9 q^{38} - 12 q^{39} + 3 q^{41} + 12 q^{42} + 6 q^{43} - 30 q^{47} - 6 q^{48} - 15 q^{49} + 21 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 12 q^{56} + 24 q^{57} - 24 q^{58} - 3 q^{59} + 6 q^{61} - 18 q^{62} - 12 q^{63} - 3 q^{64} + 3 q^{66} + 9 q^{67} + 3 q^{68} - 6 q^{69} - 18 q^{71} - 6 q^{72} + 30 q^{73} - 18 q^{74} - 6 q^{76} + 12 q^{77} + 18 q^{78} + 6 q^{79} - 33 q^{81} - 3 q^{82} + 6 q^{83} + 6 q^{84} + 12 q^{86} - 18 q^{87} + 6 q^{88} - 12 q^{91} - 6 q^{92} - 6 q^{93} - 12 q^{94} - 3 q^{97} + 21 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766044 + 0.642788i −0.541675 + 0.454519i
\(3\) 1.43969 + 0.524005i 0.831207 + 0.302535i 0.722354 0.691523i \(-0.243060\pi\)
0.108853 + 0.994058i \(0.465282\pi\)
\(4\) 0.173648 0.984808i 0.0868241 0.492404i
\(5\) 0 0
\(6\) −1.43969 + 0.524005i −0.587752 + 0.213924i
\(7\) 1.34730 2.33359i 0.509230 0.882013i −0.490713 0.871321i \(-0.663264\pi\)
0.999943 0.0106911i \(-0.00340314\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) −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 \(0.992742\pi\)
\(12\) 0.766044 1.32683i 0.221138 0.383022i
\(13\) −5.41147 + 1.96962i −1.50087 + 0.546273i −0.956286 0.292432i \(-0.905536\pi\)
−0.544586 + 0.838705i \(0.683313\pi\)
\(14\) 0.467911 + 2.65366i 0.125055 + 0.709219i
\(15\) 0 0
\(16\) −0.939693 0.342020i −0.234923 0.0855050i
\(17\) 4.99273 4.18939i 1.21091 1.01608i 0.211664 0.977342i \(-0.432112\pi\)
0.999250 0.0387350i \(-0.0123328\pi\)
\(18\) 0.652704 0.153844
\(19\) 2.82635 3.31839i 0.648410 0.761292i
\(20\) 0 0
\(21\) 3.16250 2.65366i 0.690115 0.579075i
\(22\) 2.99273 + 1.08926i 0.638051 + 0.232232i
\(23\) 0.120615 0.684040i 0.0251499 0.142632i −0.969647 0.244508i \(-0.921373\pi\)
0.994797 + 0.101876i \(0.0324845\pi\)
\(24\) 0.266044 + 1.50881i 0.0543061 + 0.307985i
\(25\) 0 0
\(26\) 2.87939 4.98724i 0.564694 0.978079i
\(27\) −2.79813 4.84651i −0.538501 0.932711i
\(28\) −2.06418 1.73205i −0.390093 0.327327i
\(29\) −2.16250 1.81456i −0.401567 0.336955i 0.419532 0.907741i \(-0.362194\pi\)
−0.821099 + 0.570786i \(0.806639\pi\)
\(30\) 0 0
\(31\) −1.22668 + 2.12467i −0.220319 + 0.381603i −0.954905 0.296913i \(-0.904043\pi\)
0.734586 + 0.678515i \(0.237376\pi\)
\(32\) 0.939693 0.342020i 0.166116 0.0604612i
\(33\) −0.847296 4.80526i −0.147495 0.836488i
\(34\) −1.13176 + 6.41852i −0.194095 + 1.10077i
\(35\) 0 0
\(36\) −0.500000 + 0.419550i −0.0833333 + 0.0699250i
\(37\) 4.36959 0.718355 0.359178 0.933269i \(-0.383057\pi\)
0.359178 + 0.933269i \(0.383057\pi\)
\(38\) −0.0320889 + 4.35878i −0.00520550 + 0.707088i
\(39\) −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 \(0.602478\pi\)
\(42\) −0.716881 + 4.06564i −0.110617 + 0.627341i
\(43\) −1.05303 5.97205i −0.160586 0.910729i −0.953499 0.301395i \(-0.902548\pi\)
0.792913 0.609334i \(-0.208563\pi\)
\(44\) −2.99273 + 1.08926i −0.451170 + 0.164213i
\(45\) 0 0
\(46\) 0.347296 + 0.601535i 0.0512061 + 0.0886915i
\(47\) −6.04189 5.06975i −0.881300 0.739499i 0.0851459 0.996368i \(-0.472864\pi\)
−0.966446 + 0.256870i \(0.917309\pi\)
\(48\) −1.17365 0.984808i −0.169402 0.142145i
\(49\) −0.130415 0.225885i −0.0186307 0.0322693i
\(50\) 0 0
\(51\) 9.38326 3.41523i 1.31392 0.478227i
\(52\) 1.00000 + 5.67128i 0.138675 + 0.786465i
\(53\) −1.42602 + 8.08737i −0.195879 + 1.11089i 0.715282 + 0.698836i \(0.246298\pi\)
−0.911161 + 0.412050i \(0.864813\pi\)
\(54\) 5.25877 + 1.91404i 0.715628 + 0.260467i
\(55\) 0 0
\(56\) 2.69459 0.360080
\(57\) 5.80793 3.29644i 0.769280 0.436625i
\(58\) 2.82295 0.370671
\(59\) 0.439693 0.368946i 0.0572431 0.0480327i −0.613717 0.789526i \(-0.710327\pi\)
0.670960 + 0.741493i \(0.265882\pi\)
\(60\) 0 0
\(61\) 0.509800 2.89122i 0.0652732 0.370183i −0.934621 0.355645i \(-0.884261\pi\)
0.999894 0.0145378i \(-0.00462769\pi\)
\(62\) −0.426022 2.41609i −0.0541049 0.306844i
\(63\) −1.65270 + 0.601535i −0.208221 + 0.0757863i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0 0
\(66\) 3.73783 + 3.13641i 0.460095 + 0.386065i
\(67\) 3.79813 + 3.18701i 0.464016 + 0.389356i 0.844606 0.535388i \(-0.179835\pi\)
−0.380590 + 0.924744i \(0.624279\pi\)
\(68\) −3.25877 5.64436i −0.395184 0.684479i
\(69\) 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 \(-0.222816\pi\)
\(72\) 0.113341 0.642788i 0.0133573 0.0757532i
\(73\) 14.8157 + 5.39246i 1.73404 + 0.631140i 0.998905 0.0467771i \(-0.0148950\pi\)
0.735138 + 0.677917i \(0.237117\pi\)
\(74\) −3.34730 + 2.80872i −0.389115 + 0.326507i
\(75\) 0 0
\(76\) −2.77719 3.35965i −0.318565 0.385378i
\(77\) −8.58172 −0.977978
\(78\) 6.75877 5.67128i 0.765280 0.642146i
\(79\) 8.51754 + 3.10013i 0.958298 + 0.348792i 0.773366 0.633959i \(-0.218571\pi\)
0.184932 + 0.982751i \(0.440794\pi\)
\(80\) 0 0
\(81\) −1.14883 6.51536i −0.127648 0.723929i
\(82\) −0.326352 + 0.118782i −0.0360395 + 0.0131173i
\(83\) 4.23783 7.34013i 0.465162 0.805684i −0.534047 0.845455i \(-0.679329\pi\)
0.999209 + 0.0397709i \(0.0126628\pi\)
\(84\) −2.06418 3.57526i −0.225220 0.390093i
\(85\) 0 0
\(86\) 4.64543 + 3.89798i 0.500930 + 0.420330i
\(87\) −2.16250 3.74557i −0.231845 0.401567i
\(88\) 1.59240 2.75811i 0.169750 0.294016i
\(89\) −7.27244 + 2.64695i −0.770877 + 0.280576i −0.697363 0.716718i \(-0.745644\pi\)
−0.0735139 + 0.997294i \(0.523421\pi\)
\(90\) 0 0
\(91\) −2.69459 + 15.2818i −0.282470 + 1.60197i
\(92\) −0.652704 0.237565i −0.0680491 0.0247678i
\(93\) −2.87939 + 2.41609i −0.298578 + 0.250537i
\(94\) 7.88713 0.813495
\(95\) 0 0
\(96\) 1.53209 0.156368
\(97\) 0.266044 0.223238i 0.0270127 0.0226664i −0.629181 0.777259i \(-0.716610\pi\)
0.656194 + 0.754592i \(0.272165\pi\)
\(98\) 0.245100 + 0.0892091i 0.0247588 + 0.00901148i
\(99\) −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 \(0.383036\pi\)
\(102\) −4.99273 + 8.64766i −0.494354 + 0.856245i
\(103\) 4.29086 + 7.43199i 0.422791 + 0.732295i 0.996211 0.0869659i \(-0.0277171\pi\)
−0.573420 + 0.819261i \(0.694384\pi\)
\(104\) −4.41147 3.70167i −0.432581 0.362978i
\(105\) 0 0
\(106\) −4.10607 7.11192i −0.398816 0.690770i
\(107\) −5.72668 + 9.91890i −0.553619 + 0.958897i 0.444390 + 0.895833i \(0.353420\pi\)
−0.998010 + 0.0630633i \(0.979913\pi\)
\(108\) −5.25877 + 1.91404i −0.506025 + 0.184178i
\(109\) 1.50980 + 8.56250i 0.144613 + 0.820139i 0.967677 + 0.252191i \(0.0811513\pi\)
−0.823065 + 0.567948i \(0.807738\pi\)
\(110\) 0 0
\(111\) 6.29086 + 2.28969i 0.597102 + 0.217327i
\(112\) −2.06418 + 1.73205i −0.195046 + 0.163663i
\(113\) −2.85978 −0.269026 −0.134513 0.990912i \(-0.542947\pi\)
−0.134513 + 0.990912i \(0.542947\pi\)
\(114\) −2.33022 + 6.25849i −0.218245 + 0.586161i
\(115\) 0 0
\(116\) −2.16250 + 1.81456i −0.200783 + 0.168477i
\(117\) 3.53209 + 1.28558i 0.326542 + 0.118851i
\(118\) −0.0996702 + 0.565258i −0.00917539 + 0.0520362i
\(119\) −3.04963 17.2953i −0.279559 1.58546i
\(120\) 0 0
\(121\) 0.428548 0.742267i 0.0389589 0.0674789i
\(122\) 1.46791 + 2.54250i 0.132898 + 0.230187i
\(123\) 0.407604 + 0.342020i 0.0367524 + 0.0308389i
\(124\) 1.87939 + 1.57699i 0.168774 + 0.141618i
\(125\) 0 0
\(126\) 0.879385 1.52314i 0.0783419 0.135692i
\(127\) 9.14290 3.32774i 0.811301 0.295290i 0.0971401 0.995271i \(-0.469030\pi\)
0.714161 + 0.699981i \(0.246808\pi\)
\(128\) −0.173648 0.984808i −0.0153485 0.0870455i
\(129\) 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 \(0.368959\pi\)
\(132\) −4.87939 −0.424696
\(133\) −3.93582 11.0664i −0.341279 0.959578i
\(134\) −4.95811 −0.428316
\(135\) 0 0
\(136\) 6.12449 + 2.22913i 0.525170 + 0.191146i
\(137\) 2.02481 11.4833i 0.172992 0.981084i −0.767445 0.641115i \(-0.778472\pi\)
0.940437 0.339969i \(-0.110417\pi\)
\(138\) 0.184793 + 1.04801i 0.0157306 + 0.0892126i
\(139\) 7.76517 2.82629i 0.658633 0.239723i 0.00898688 0.999960i \(-0.497139\pi\)
0.649646 + 0.760237i \(0.274917\pi\)
\(140\) 0 0
\(141\) −6.04189 10.4649i −0.508819 0.881300i
\(142\) 6.47565 + 5.43372i 0.543425 + 0.455987i
\(143\) 14.0496 + 11.7890i 1.17489 + 0.985849i
\(144\) 0.326352 + 0.565258i 0.0271960 + 0.0471048i
\(145\) 0 0
\(146\) −14.8157 + 5.39246i −1.22615 + 0.446284i
\(147\) −0.0693923 0.393544i −0.00572338 0.0324589i
\(148\) 0.758770 4.30320i 0.0623705 0.353721i
\(149\) 15.4611 + 5.62738i 1.26662 + 0.461013i 0.885986 0.463712i \(-0.153483\pi\)
0.380637 + 0.924725i \(0.375705\pi\)
\(150\) 0 0
\(151\) 4.65539 0.378850 0.189425 0.981895i \(-0.439338\pi\)
0.189425 + 0.981895i \(0.439338\pi\)
\(152\) 4.28699 + 0.788496i 0.347721 + 0.0639554i
\(153\) −4.25402 −0.343917
\(154\) 6.57398 5.51622i 0.529746 0.444510i
\(155\) 0 0
\(156\) −1.53209 + 8.68891i −0.122665 + 0.695669i
\(157\) −1.46791 8.32494i −0.117152 0.664402i −0.985662 0.168731i \(-0.946033\pi\)
0.868510 0.495671i \(-0.165078\pi\)
\(158\) −8.51754 + 3.10013i −0.677619 + 0.246633i
\(159\) −6.29086 + 10.8961i −0.498898 + 0.864116i
\(160\) 0 0
\(161\) −1.43376 1.20307i −0.112996 0.0948152i
\(162\) 5.06805 + 4.25260i 0.398183 + 0.334116i
\(163\) 8.52481 + 14.7654i 0.667715 + 1.15652i 0.978542 + 0.206050i \(0.0660609\pi\)
−0.310826 + 0.950467i \(0.600606\pi\)
\(164\) 0.173648 0.300767i 0.0135596 0.0234860i
\(165\) 0 0
\(166\) 1.47178 + 8.34689i 0.114232 + 0.647844i
\(167\) 0.554378 3.14403i 0.0428990 0.243292i −0.955816 0.293965i \(-0.905025\pi\)
0.998715 + 0.0506721i \(0.0161363\pi\)
\(168\) 3.87939 + 1.41198i 0.299301 + 0.108937i
\(169\) 15.4461 12.9608i 1.18816 0.996985i
\(170\) 0 0
\(171\) −2.80541 + 0.473401i −0.214535 + 0.0362019i
\(172\) −6.06418 −0.462389
\(173\) −7.37733 + 6.19031i −0.560888 + 0.470641i −0.878608 0.477544i \(-0.841527\pi\)
0.317720 + 0.948185i \(0.397083\pi\)
\(174\) 4.06418 + 1.47924i 0.308105 + 0.112141i
\(175\) 0 0
\(176\) 0.553033 + 3.13641i 0.0416865 + 0.236416i
\(177\) 0.826352 0.300767i 0.0621124 0.0226071i
\(178\) 3.86959 6.70232i 0.290038 0.502360i
\(179\) −9.40807 16.2953i −0.703192 1.21796i −0.967340 0.253482i \(-0.918424\pi\)
0.264148 0.964482i \(-0.414909\pi\)
\(180\) 0 0
\(181\) 2.12836 + 1.78590i 0.158199 + 0.132745i 0.718451 0.695577i \(-0.244851\pi\)
−0.560252 + 0.828322i \(0.689296\pi\)
\(182\) −7.75877 13.4386i −0.575118 0.996134i
\(183\) 2.24897 3.89533i 0.166249 0.287951i
\(184\) 0.652704 0.237565i 0.0481180 0.0175135i
\(185\) 0 0
\(186\) 0.652704 3.70167i 0.0478586 0.271419i
\(187\) −19.5052 7.09932i −1.42636 0.519154i
\(188\) −6.04189 + 5.06975i −0.440650 + 0.369749i
\(189\) −15.0797 −1.09688
\(190\) 0 0
\(191\) 9.56212 0.691891 0.345945 0.938255i \(-0.387558\pi\)
0.345945 + 0.938255i \(0.387558\pi\)
\(192\) −1.17365 + 0.984808i −0.0847008 + 0.0710724i
\(193\) −22.2528 8.09937i −1.60179 0.583006i −0.622001 0.783017i \(-0.713680\pi\)
−0.979794 + 0.200011i \(0.935902\pi\)
\(194\) −0.0603074 + 0.342020i −0.00432982 + 0.0245556i
\(195\) 0 0
\(196\) −0.245100 + 0.0892091i −0.0175071 + 0.00637208i
\(197\) −11.4611 + 19.8512i −0.816570 + 1.41434i 0.0916253 + 0.995794i \(0.470794\pi\)
−0.908195 + 0.418547i \(0.862540\pi\)
\(198\) −1.03936 1.80023i −0.0738643 0.127937i
\(199\) 7.72462 + 6.48173i 0.547584 + 0.459477i 0.874122 0.485707i \(-0.161438\pi\)
−0.326538 + 0.945184i \(0.605882\pi\)
\(200\) 0 0
\(201\) 3.79813 + 6.57856i 0.267900 + 0.464016i
\(202\) −0.184793 + 0.320070i −0.0130020 + 0.0225201i
\(203\) −7.14796 + 2.60164i −0.501688 + 0.182600i
\(204\) −1.73396 9.83375i −0.121401 0.688500i
\(205\) 0 0
\(206\) −8.06418 2.93512i −0.561858 0.204500i
\(207\) −0.347296 + 0.291416i −0.0241388 + 0.0202548i
\(208\) 5.75877 0.399299
\(209\) −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 \(0.998201\pi\)
\(212\) 7.71688 + 2.80872i 0.529998 + 0.192903i
\(213\) 2.24897 12.7545i 0.154097 0.873927i
\(214\) −1.98886 11.2794i −0.135955 0.771041i
\(215\) 0 0
\(216\) 2.79813 4.84651i 0.190389 0.329763i
\(217\) 3.30541 + 5.72513i 0.224386 + 0.388647i
\(218\) −6.66044 5.58878i −0.451102 0.378520i
\(219\) 18.5043 + 15.5270i 1.25041 + 1.04922i
\(220\) 0 0
\(221\) −18.7665 + 32.5046i −1.26237 + 2.18649i
\(222\) −6.29086 + 2.28969i −0.422215 + 0.153674i
\(223\) 1.61081 + 9.13538i 0.107868 + 0.611751i 0.990036 + 0.140815i \(0.0449724\pi\)
−0.882168 + 0.470935i \(0.843917\pi\)
\(224\) 0.467911 2.65366i 0.0312636 0.177305i
\(225\) 0 0
\(226\) 2.19072 1.83823i 0.145725 0.122278i
\(227\) −7.73648 −0.513488 −0.256744 0.966479i \(-0.582650\pi\)
−0.256744 + 0.966479i \(0.582650\pi\)
\(228\) −2.23783 6.29212i −0.148204 0.416706i
\(229\) −23.0351 −1.52220 −0.761101 0.648634i \(-0.775341\pi\)
−0.761101 + 0.648634i \(0.775341\pi\)
\(230\) 0 0
\(231\) −12.3550 4.49687i −0.812902 0.295872i
\(232\) 0.490200 2.78006i 0.0321832 0.182520i
\(233\) −1.45858 8.27201i −0.0955546 0.541917i −0.994576 0.104012i \(-0.966832\pi\)
0.899021 0.437905i \(-0.144279\pi\)
\(234\) −3.53209 + 1.28558i −0.230900 + 0.0840407i
\(235\) 0 0
\(236\) −0.286989 0.497079i −0.0186814 0.0323571i
\(237\) 10.6382 + 8.92647i 0.691022 + 0.579837i
\(238\) 13.4534 + 11.2887i 0.872052 + 0.731739i
\(239\) 7.86484 + 13.6223i 0.508734 + 0.881153i 0.999949 + 0.0101147i \(0.00321967\pi\)
−0.491215 + 0.871038i \(0.663447\pi\)
\(240\) 0 0
\(241\) −16.4474 + 5.98638i −1.05947 + 0.385616i −0.812230 0.583337i \(-0.801747\pi\)
−0.247242 + 0.968954i \(0.579524\pi\)
\(242\) 0.148833 + 0.844075i 0.00956736 + 0.0542592i
\(243\) −1.15523 + 6.55163i −0.0741080 + 0.420288i
\(244\) −2.75877 1.00411i −0.176612 0.0642816i
\(245\) 0 0
\(246\) −0.532089 −0.0339247
\(247\) −8.75877 + 23.5242i −0.557307 + 1.49681i
\(248\) −2.45336 −0.155789
\(249\) 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 \(-0.0315930\pi\)
\(252\) 0.305407 + 1.73205i 0.0192389 + 0.109109i
\(253\) −2.07873 + 0.756594i −0.130688 + 0.0475667i
\(254\) −4.86484 + 8.42615i −0.305247 + 0.528703i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) 6.14724 + 5.15815i 0.383454 + 0.321756i 0.814057 0.580785i \(-0.197254\pi\)
−0.430602 + 0.902542i \(0.641699\pi\)
\(258\) 4.64543 + 8.04612i 0.289212 + 0.500930i
\(259\) 5.88713 10.1968i 0.365808 0.633598i
\(260\) 0 0
\(261\) 0.319955 + 1.81456i 0.0198047 + 0.112318i
\(262\) 1.12314 6.36965i 0.0693879 0.393518i
\(263\) −5.60132 2.03871i −0.345392 0.125712i 0.163499 0.986544i \(-0.447722\pi\)
−0.508891 + 0.860831i \(0.669944\pi\)
\(264\) 3.73783 3.13641i 0.230047 0.193033i
\(265\) 0 0
\(266\) 10.1284 + 5.94745i 0.621009 + 0.364662i
\(267\) −11.8571 −0.725643
\(268\) 3.79813 3.18701i 0.232008 0.194678i
\(269\) 1.07873 + 0.392624i 0.0657711 + 0.0239387i 0.374696 0.927148i \(-0.377747\pi\)
−0.308925 + 0.951086i \(0.599969\pi\)
\(270\) 0 0
\(271\) 3.48246 + 19.7500i 0.211544 + 1.19973i 0.886803 + 0.462147i \(0.152921\pi\)
−0.675259 + 0.737581i \(0.735968\pi\)
\(272\) −6.12449 + 2.22913i −0.371351 + 0.135161i
\(273\) −11.8871 + 20.5891i −0.719442 + 1.24611i
\(274\) 5.83022 + 10.0982i 0.352217 + 0.610057i
\(275\) 0 0
\(276\) −0.815207 0.684040i −0.0490697 0.0411744i
\(277\) 8.68004 + 15.0343i 0.521533 + 0.903322i 0.999686 + 0.0250457i \(0.00797312\pi\)
−0.478153 + 0.878277i \(0.658694\pi\)
\(278\) −4.13176 + 7.15642i −0.247806 + 0.429213i
\(279\) 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 \(0.0277846\pi\)
\(282\) 11.3550 + 4.13290i 0.676183 + 0.246110i
\(283\) 7.26264 6.09408i 0.431719 0.362255i −0.400881 0.916130i \(-0.631296\pi\)
0.832600 + 0.553875i \(0.186851\pi\)
\(284\) −8.45336 −0.501615
\(285\) 0 0
\(286\) −18.3405 −1.08450
\(287\) 0.716881 0.601535i 0.0423162 0.0355075i
\(288\) −0.613341 0.223238i −0.0361415 0.0131544i
\(289\) 4.42427 25.0913i 0.260251 1.47596i
\(290\) 0 0
\(291\) 0.500000 0.181985i 0.0293105 0.0106682i
\(292\) 7.88326 13.6542i 0.461333 0.799052i
\(293\) −13.6459 23.6354i −0.797202 1.38079i −0.921432 0.388541i \(-0.872979\pi\)
0.124230 0.992253i \(-0.460354\pi\)
\(294\) 0.306123 + 0.256867i 0.0178534 + 0.0149808i
\(295\) 0 0
\(296\) 2.18479 + 3.78417i 0.126988 + 0.219951i
\(297\) −8.91147 + 15.4351i −0.517096 + 0.895637i
\(298\) −15.4611 + 5.62738i −0.895638 + 0.325985i
\(299\) 0.694593 + 3.93923i 0.0401693 + 0.227812i
\(300\) 0 0
\(301\) −15.3550 5.58878i −0.885050 0.322132i
\(302\) −3.56624 + 2.99243i −0.205214 + 0.172195i
\(303\) 0.566237 0.0325295
\(304\) −3.79086 + 2.15160i −0.217421 + 0.123403i
\(305\) 0 0
\(306\) 3.25877 2.73443i 0.186292 0.156317i
\(307\) 20.0424 + 7.29482i 1.14388 + 0.416337i 0.843312 0.537424i \(-0.180602\pi\)
0.300565 + 0.953761i \(0.402825\pi\)
\(308\) −1.49020 + 8.45134i −0.0849120 + 0.481560i
\(309\) 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 \(-0.145274\pi\)
\(312\) −4.41147 7.64090i −0.249751 0.432581i
\(313\) −4.26011 3.57466i −0.240796 0.202052i 0.514401 0.857550i \(-0.328014\pi\)
−0.755197 + 0.655498i \(0.772459\pi\)
\(314\) 6.47565 + 5.43372i 0.365442 + 0.306642i
\(315\) 0 0
\(316\) 4.53209 7.84981i 0.254950 0.441586i
\(317\) 3.57398 1.30082i 0.200735 0.0730614i −0.239696 0.970848i \(-0.577048\pi\)
0.440431 + 0.897786i \(0.354826\pi\)
\(318\) −2.18479 12.3906i −0.122517 0.694829i
\(319\) −1.56118 + 8.85392i −0.0874096 + 0.495724i
\(320\) 0 0
\(321\) −13.4422 + 11.2794i −0.750271 + 0.629553i
\(322\) 1.87164 0.104303
\(323\) 0.209141 28.4085i 0.0116369 1.58069i
\(324\) −6.61587 −0.367548
\(325\) 0 0
\(326\) −16.0214 5.83132i −0.887344 0.322967i
\(327\) −2.31315 + 13.1185i −0.127917 + 0.725456i
\(328\) 0.0603074 + 0.342020i 0.00332992 + 0.0188849i
\(329\) −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 \(-0.356344\pi\)
\(332\) −6.49273 5.44804i −0.356335 0.299000i
\(333\) −2.18479 1.83326i −0.119726 0.100462i
\(334\) 1.59627 + 2.76481i 0.0873438 + 0.151284i
\(335\) 0 0
\(336\) −3.87939 + 1.41198i −0.211638 + 0.0770299i
\(337\) −3.52687 20.0019i −0.192121 1.08957i −0.916459 0.400128i \(-0.868966\pi\)
0.724338 0.689445i \(-0.242145\pi\)
\(338\) −3.50134 + 19.8571i −0.190448 + 1.08008i
\(339\) −4.11721 1.49854i −0.223616 0.0813896i
\(340\) 0 0
\(341\) 7.81345 0.423122
\(342\) 1.84477 2.16593i 0.0997537 0.117120i
\(343\) 18.1593 0.980511
\(344\) 4.64543 3.89798i 0.250465 0.210165i
\(345\) 0 0
\(346\) 1.67230 9.48411i 0.0899036 0.509869i
\(347\) −0.905544 5.13560i −0.0486122 0.275693i 0.950807 0.309785i \(-0.100257\pi\)
−0.999419 + 0.0340920i \(0.989146\pi\)
\(348\) −4.06418 + 1.47924i −0.217863 + 0.0792956i
\(349\) −7.17024 + 12.4192i −0.383814 + 0.664786i −0.991604 0.129312i \(-0.958723\pi\)
0.607790 + 0.794098i \(0.292056\pi\)
\(350\) 0 0
\(351\) 24.6878 + 20.7155i 1.31774 + 1.10571i
\(352\) −2.43969 2.04715i −0.130036 0.109113i
\(353\) 13.1250 + 22.7331i 0.698571 + 1.20996i 0.968962 + 0.247209i \(0.0795136\pi\)
−0.270391 + 0.962750i \(0.587153\pi\)
\(354\) −0.439693 + 0.761570i −0.0233694 + 0.0404770i
\(355\) 0 0
\(356\) 1.34389 + 7.62159i 0.0712262 + 0.403944i
\(357\) 4.67230 26.4980i 0.247285 1.40242i
\(358\) 17.6814 + 6.43550i 0.934490 + 0.340127i
\(359\) −25.8084 + 21.6558i −1.36212 + 1.14295i −0.386792 + 0.922167i \(0.626417\pi\)
−0.975323 + 0.220784i \(0.929139\pi\)
\(360\) 0 0
\(361\) −3.02347 18.7579i −0.159130 0.987258i
\(362\) −2.77837 −0.146028
\(363\) 1.00593 0.844075i 0.0527976 0.0443025i
\(364\) 14.5817 + 5.30731i 0.764290 + 0.278179i
\(365\) 0 0
\(366\) 0.781059 + 4.42961i 0.0408266 + 0.231539i
\(367\) −9.83750 + 3.58056i −0.513513 + 0.186903i −0.585762 0.810483i \(-0.699205\pi\)
0.0722488 + 0.997387i \(0.476982\pi\)
\(368\) −0.347296 + 0.601535i −0.0181041 + 0.0313572i
\(369\) −0.113341 0.196312i −0.00590029 0.0102196i
\(370\) 0 0
\(371\) 16.9513 + 14.2238i 0.880068 + 0.738465i
\(372\) 1.87939 + 3.25519i 0.0974416 + 0.168774i
\(373\) 11.9513 20.7003i 0.618815 1.07182i −0.370887 0.928678i \(-0.620946\pi\)
0.989702 0.143141i \(-0.0457203\pi\)
\(374\) 19.5052 7.09932i 1.00859 0.367097i
\(375\) 0 0
\(376\) 1.36959 7.76730i 0.0706310 0.400568i
\(377\) 15.2763 + 5.56012i 0.786770 + 0.286361i
\(378\) 11.5517 9.69302i 0.594155 0.498555i
\(379\) 17.8135 0.915016 0.457508 0.889206i \(-0.348742\pi\)
0.457508 + 0.889206i \(0.348742\pi\)
\(380\) 0 0
\(381\) 14.9067 0.763695
\(382\) −7.32501 + 6.14641i −0.374780 + 0.314478i
\(383\) 23.5672 + 8.57775i 1.20423 + 0.438302i 0.864697 0.502293i \(-0.167510\pi\)
0.339529 + 0.940596i \(0.389732\pi\)
\(384\) 0.266044 1.50881i 0.0135765 0.0769963i
\(385\) 0 0
\(386\) 22.2528 8.09937i 1.13264 0.412247i
\(387\) −1.97906 + 3.42782i −0.100601 + 0.174246i
\(388\) −0.173648 0.300767i −0.00881565 0.0152692i
\(389\) −7.21482 6.05395i −0.365806 0.306948i 0.441294 0.897363i \(-0.354520\pi\)
−0.807100 + 0.590415i \(0.798964\pi\)
\(390\) 0 0
\(391\) −2.26352 3.92053i −0.114471 0.198270i
\(392\) 0.130415 0.225885i 0.00658695 0.0114089i
\(393\) −9.31180 + 3.38922i −0.469718 + 0.170964i
\(394\) −3.98040 22.5740i −0.200530 1.13726i
\(395\) 0 0
\(396\) 1.95336 + 0.710966i 0.0981602 + 0.0357274i
\(397\) −5.24897 + 4.40441i −0.263438 + 0.221051i −0.764933 0.644110i \(-0.777228\pi\)
0.501495 + 0.865161i \(0.332784\pi\)
\(398\) −10.0838 −0.505454
\(399\) 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 \(0.239961\pi\)
\(402\) −7.13816 2.59808i −0.356019 0.129580i
\(403\) 2.45336 13.9137i 0.122211 0.693091i
\(404\) −0.0641778 0.363970i −0.00319296 0.0181082i
\(405\) 0 0
\(406\) 3.80335 6.58759i 0.188757 0.326937i
\(407\) −6.95811 12.0518i −0.344901 0.597386i
\(408\) 7.64930 + 6.41852i 0.378697 + 0.317764i
\(409\) 24.2781 + 20.3718i 1.20048 + 1.00732i 0.999616 + 0.0276988i \(0.00881794\pi\)
0.200860 + 0.979620i \(0.435627\pi\)
\(410\) 0 0
\(411\) 8.93242 15.4714i 0.440604 0.763148i
\(412\) 8.06418 2.93512i 0.397294 0.144603i
\(413\) −0.268571 1.52314i −0.0132155 0.0749488i
\(414\) 0.0787257 0.446476i 0.00386916 0.0219431i
\(415\) 0 0
\(416\) −4.41147 + 3.70167i −0.216290 + 0.181489i
\(417\) 12.6604 0.619985
\(418\) 12.0731 6.85240i 0.590515 0.335162i
\(419\) −11.0101 −0.537879 −0.268939 0.963157i \(-0.586673\pi\)
−0.268939 + 0.963157i \(0.586673\pi\)
\(420\) 0 0
\(421\) 8.14290 + 2.96377i 0.396861 + 0.144446i 0.532738 0.846280i \(-0.321163\pi\)
−0.135877 + 0.990726i \(0.543385\pi\)
\(422\) 3.88279 22.0204i 0.189011 1.07194i
\(423\) 0.893933 + 5.06975i 0.0434645 + 0.246500i
\(424\) −7.71688 + 2.80872i −0.374765 + 0.136403i
\(425\) 0 0
\(426\) 6.47565 + 11.2162i 0.313746 + 0.543425i
\(427\) −6.06006 5.08499i −0.293267 0.246080i
\(428\) 8.77379 + 7.36208i 0.424097 + 0.355860i
\(429\) 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 \(0.133120\pi\)
\(432\) 0.971782 + 5.51125i 0.0467549 + 0.265160i
\(433\) −1.60813 + 9.12014i −0.0772816 + 0.438286i 0.921475 + 0.388437i \(0.126985\pi\)
−0.998757 + 0.0498486i \(0.984126\pi\)
\(434\) −6.21213 2.26103i −0.298192 0.108533i
\(435\) 0 0
\(436\) 8.69459 0.416395
\(437\) −1.92902 2.33359i −0.0922773 0.111631i
\(438\) −24.1557 −1.15420
\(439\) 15.9813 13.4099i 0.762747 0.640021i −0.176093 0.984374i \(-0.556346\pi\)
0.938840 + 0.344352i \(0.111902\pi\)
\(440\) 0 0
\(441\) −0.0295627 + 0.167658i −0.00140775 + 0.00798372i
\(442\) −6.51754 36.9628i −0.310008 1.75814i
\(443\) 22.3910 8.14966i 1.06383 0.387202i 0.249963 0.968255i \(-0.419582\pi\)
0.813865 + 0.581054i \(0.197359\pi\)
\(444\) 3.34730 5.79769i 0.158856 0.275146i
\(445\) 0 0
\(446\) −7.10607 5.96270i −0.336482 0.282342i
\(447\) 19.3105 + 16.2034i 0.913353 + 0.766395i
\(448\) 1.34730 + 2.33359i 0.0636538 + 0.110252i
\(449\) 1.09105 1.88976i 0.0514899 0.0891832i −0.839132 0.543928i \(-0.816936\pi\)
0.890622 + 0.454745i \(0.150270\pi\)
\(450\) 0 0
\(451\) −0.192066 1.08926i −0.00904406 0.0512914i
\(452\) −0.496596 + 2.81634i −0.0233579 + 0.132469i
\(453\) 6.70233 + 2.43945i 0.314903 + 0.114615i
\(454\) 5.92649 4.97291i 0.278144 0.233390i
\(455\) 0 0
\(456\) 5.75877 + 3.38160i 0.269679 + 0.158358i
\(457\) −1.78106 −0.0833144 −0.0416572 0.999132i \(-0.513264\pi\)
−0.0416572 + 0.999132i \(0.513264\pi\)
\(458\) 17.6459 14.8067i 0.824539 0.691870i
\(459\) −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 \(-0.173012\pi\)
\(462\) 12.3550 4.49687i 0.574808 0.209213i
\(463\) −1.35504 + 2.34699i −0.0629739 + 0.109074i −0.895793 0.444471i \(-0.853392\pi\)
0.832820 + 0.553545i \(0.186725\pi\)
\(464\) 1.41147 + 2.44474i 0.0655260 + 0.113494i
\(465\) 0 0
\(466\) 6.43448 + 5.39917i 0.298071 + 0.250112i
\(467\) 6.45677 + 11.1834i 0.298784 + 0.517508i 0.975858 0.218406i \(-0.0700858\pi\)
−0.677074 + 0.735915i \(0.736752\pi\)
\(468\) 1.87939 3.25519i 0.0868746 0.150471i
\(469\) 12.5544 4.56942i 0.579707 0.210996i
\(470\) 0 0
\(471\) 2.24897 12.7545i 0.103627 0.587698i
\(472\) 0.539363 + 0.196312i 0.0248262 + 0.00903599i
\(473\) −14.7947 + 12.4143i −0.680262 + 0.570808i
\(474\) −13.8871 −0.637857
\(475\) 0 0
\(476\) −17.5621 −0.804958
\(477\) 4.10607 3.44540i 0.188004 0.157754i
\(478\) −14.7811 5.37987i −0.676070 0.246069i
\(479\) −3.22163 + 18.2708i −0.147200 + 0.834813i 0.818374 + 0.574685i \(0.194876\pi\)
−0.965574 + 0.260127i \(0.916236\pi\)
\(480\) 0 0
\(481\) −23.6459 + 8.60640i −1.07816 + 0.392418i
\(482\) 8.75150 15.1580i 0.398620 0.690430i
\(483\) −1.43376 2.48335i −0.0652385 0.112996i
\(484\) −0.656574 0.550931i −0.0298443 0.0250423i
\(485\) 0 0
\(486\) −3.32635 5.76141i −0.150886 0.261343i
\(487\) 20.5868 35.6573i 0.932876 1.61579i 0.154497 0.987993i \(-0.450624\pi\)
0.778379 0.627795i \(-0.216042\pi\)
\(488\) 2.75877 1.00411i 0.124884 0.0454539i
\(489\) 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 \(0.440958\pi\)
\(492\) 0.407604 0.342020i 0.0183762 0.0154195i
\(493\) −18.3987 −0.828635
\(494\) −8.41147 23.6506i −0.378450 1.06409i
\(495\) 0 0
\(496\) 1.87939 1.57699i 0.0843869 0.0708090i
\(497\) −21.4047 7.79066i −0.960131 0.349459i
\(498\) −2.25490 + 12.7882i −0.101044 + 0.573052i
\(499\) −5.09286 28.8831i −0.227988 1.29298i −0.856890 0.515499i \(-0.827607\pi\)
0.628902 0.777484i \(-0.283505\pi\)
\(500\) 0 0
\(501\) 2.44562 4.23594i 0.109262 0.189248i
\(502\) 4.28359 + 7.41939i 0.191186 + 0.331143i
\(503\) −25.7520 21.6085i −1.14822 0.963474i −0.148547 0.988905i \(-0.547460\pi\)
−0.999677 + 0.0254316i \(0.991904\pi\)
\(504\) −1.34730 1.13052i −0.0600133 0.0503572i
\(505\) 0 0
\(506\) 1.10607 1.91576i 0.0491707 0.0851661i
\(507\) 29.0292 10.5657i 1.28923 0.469241i
\(508\) −1.68954 9.58186i −0.0749612 0.425126i
\(509\) 0.699645 3.96788i 0.0310112 0.175873i −0.965368 0.260891i \(-0.915984\pi\)
0.996379 + 0.0850178i \(0.0270947\pi\)
\(510\) 0 0
\(511\) 32.5449 27.3084i 1.43970 1.20805i
\(512\) −1.00000 −0.0441942
\(513\) −23.9911 4.41263i −1.05923 0.194822i
\(514\) −8.02465 −0.353952
\(515\) 0 0
\(516\) −8.73055 3.17766i −0.384341 0.139889i
\(517\) −4.36184 + 24.7372i −0.191834 + 1.08794i
\(518\) 2.04458 + 11.5954i 0.0898336 + 0.509472i
\(519\) −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 \(0.868194\pi\)
\(522\) −1.41147 1.18437i −0.0617785 0.0518384i
\(523\) 20.3405 + 17.0677i 0.889427 + 0.746318i 0.968095 0.250583i \(-0.0806222\pi\)
−0.0786677 + 0.996901i \(0.525067\pi\)
\(524\) 3.23396 + 5.60138i 0.141276 + 0.244697i
\(525\) 0 0
\(526\) 5.60132 2.03871i 0.244229 0.0888921i
\(527\) 2.77662 + 15.7470i 0.120951 + 0.685949i
\(528\) −0.847296 + 4.80526i −0.0368738 + 0.209122i
\(529\) 21.1596 + 7.70145i 0.919981 + 0.334846i
\(530\) 0 0
\(531\) −0.374638 −0.0162579
\(532\) −11.5817 + 1.95437i −0.502131 + 0.0847326i
\(533\) −2.00000 −0.0866296
\(534\) 9.08306 7.62159i 0.393063 0.329819i
\(535\) 0 0
\(536\) −0.860967 + 4.88279i −0.0371881 + 0.210904i
\(537\) −5.00593 28.3900i −0.216022 1.22512i
\(538\) −1.07873 + 0.392624i −0.0465072 + 0.0169272i
\(539\) −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 \(0.805067\pi\)
\(542\) −15.3628 12.8909i −0.659888 0.553712i
\(543\) 2.12836 + 3.68642i 0.0913365 + 0.158199i
\(544\) 3.25877 5.64436i 0.139719 0.242000i
\(545\) 0 0
\(546\) −4.12836 23.4131i −0.176677 1.00199i
\(547\) −0.555093 + 3.14809i −0.0237341 + 0.134603i −0.994372 0.105941i \(-0.966215\pi\)
0.970638 + 0.240543i \(0.0773257\pi\)
\(548\) −10.9572 3.98811i −0.468070 0.170363i
\(549\) −1.46791 + 1.23172i −0.0626489 + 0.0525687i
\(550\) 0 0
\(551\) −12.1334 + 2.04746i −0.516901 + 0.0872249i
\(552\) 1.06418 0.0452944
\(553\) 18.7101 15.6996i 0.795633 0.667616i
\(554\) −16.3131 5.93750i −0.693079 0.252260i
\(555\) 0 0
\(556\) −1.43494 8.13798i −0.0608552 0.345127i
\(557\) −22.5303 + 8.20037i −0.954641 + 0.347461i −0.771931 0.635706i \(-0.780709\pi\)
−0.182710 + 0.983167i \(0.558487\pi\)
\(558\) −0.800660 + 1.38678i −0.0338946 + 0.0587072i
\(559\) 17.4611 + 30.2435i 0.738526 + 1.27916i
\(560\) 0 0
\(561\) −24.3614 20.4417i −1.02854 0.863048i
\(562\) 1.46064 + 2.52990i 0.0616133 + 0.106717i
\(563\) −4.37851 + 7.58380i −0.184532 + 0.319619i −0.943419 0.331604i \(-0.892410\pi\)
0.758887 + 0.651223i \(0.225744\pi\)
\(564\) −11.3550 + 4.13290i −0.478133 + 0.174026i
\(565\) 0 0
\(566\) −1.64631 + 9.33667i −0.0691994 + 0.392450i
\(567\) −16.7520 6.09722i −0.703516 0.256059i
\(568\) 6.47565 5.43372i 0.271712 0.227994i
\(569\) −36.4201 −1.52681 −0.763406 0.645919i \(-0.776474\pi\)
−0.763406 + 0.645919i \(0.776474\pi\)
\(570\) 0 0
\(571\) 34.2131 1.43177 0.715886 0.698217i \(-0.246023\pi\)
0.715886 + 0.698217i \(0.246023\pi\)
\(572\) 14.0496 11.7890i 0.587445 0.492924i
\(573\) 13.7665 + 5.01060i 0.575104 + 0.209321i
\(574\) −0.162504 + 0.921605i −0.00678278 + 0.0384670i
\(575\) 0 0
\(576\) 0.613341 0.223238i 0.0255559 0.00930157i
\(577\) 7.75490 13.4319i 0.322841 0.559177i −0.658232 0.752815i \(-0.728696\pi\)
0.981073 + 0.193638i \(0.0620289\pi\)
\(578\) 12.7392 + 22.0649i 0.529880 + 0.917778i
\(579\) −27.7931 23.3212i −1.15504 0.969196i
\(580\) 0 0
\(581\) −11.4192 19.7787i −0.473749 0.820557i
\(582\) −0.266044 + 0.460802i −0.0110279 + 0.0191009i
\(583\) 24.5767 8.94517i 1.01786 0.370471i
\(584\) 2.73783 + 15.5270i 0.113292 + 0.642511i
\(585\) 0 0
\(586\) 25.6459 + 9.33434i 1.05942 + 0.385598i
\(587\) 8.87211 7.44459i 0.366191 0.307271i −0.441061 0.897477i \(-0.645398\pi\)
0.807253 + 0.590206i \(0.200953\pi\)
\(588\) −0.399615 −0.0164798
\(589\) 3.58347 + 10.0757i 0.147654 + 0.415162i
\(590\) 0 0
\(591\) −26.9026 + 22.5740i −1.10663 + 0.928569i
\(592\) −4.10607 1.49449i −0.168758 0.0614230i
\(593\) 8.05603 45.6880i 0.330821 1.87618i −0.134310 0.990939i \(-0.542882\pi\)
0.465131 0.885242i \(-0.346007\pi\)
\(594\) −3.09492 17.5522i −0.126986 0.720175i
\(595\) 0 0
\(596\) 8.22668 14.2490i 0.336978 0.583663i
\(597\) 7.72462 + 13.3794i 0.316148 + 0.547584i
\(598\) −3.06418 2.57115i −0.125304 0.105142i
\(599\) 19.6355 + 16.4761i 0.802283 + 0.673196i 0.948753 0.316019i \(-0.102346\pi\)
−0.146469 + 0.989215i \(0.546791\pi\)
\(600\) 0 0
\(601\) −3.99613 + 6.92150i −0.163006 + 0.282334i −0.935945 0.352146i \(-0.885452\pi\)
0.772940 + 0.634480i \(0.218786\pi\)
\(602\) 15.3550 5.58878i 0.625825 0.227782i
\(603\) −0.561956 3.18701i −0.0228846 0.129785i
\(604\) 0.808400 4.58467i 0.0328933 0.186547i
\(605\) 0 0
\(606\) −0.433763 + 0.363970i −0.0176204 + 0.0147853i
\(607\) 26.9905 1.09551 0.547755 0.836639i \(-0.315482\pi\)
0.547755 + 0.836639i \(0.315482\pi\)
\(608\) 1.52094 4.08494i 0.0616824 0.165666i
\(609\) −11.6541 −0.472249
\(610\) 0 0
\(611\) 42.6810 + 15.5346i 1.72669 + 0.628463i
\(612\) −0.738703 + 4.18939i −0.0298603 + 0.169346i
\(613\) 2.47472 + 14.0348i 0.0999529 + 0.566861i 0.993117 + 0.117130i \(0.0373693\pi\)
−0.893164 + 0.449732i \(0.851520\pi\)
\(614\) −20.0424 + 7.29482i −0.808844 + 0.294395i
\(615\) 0 0
\(616\) −4.29086 7.43199i −0.172884 0.299443i
\(617\) 23.4106 + 19.6438i 0.942475 + 0.790831i 0.978014 0.208538i \(-0.0668704\pi\)
−0.0355392 + 0.999368i \(0.511315\pi\)
\(618\) −10.0719 8.45134i −0.405152 0.339963i
\(619\) 14.3375 + 24.8333i 0.576273 + 0.998133i 0.995902 + 0.0904380i \(0.0288267\pi\)
−0.419629 + 0.907695i \(0.637840\pi\)
\(620\) 0 0
\(621\) −3.65270 + 1.32948i −0.146578 + 0.0533500i
\(622\) 5.08647 + 28.8468i 0.203949 + 1.15665i
\(623\) −3.62124 + 20.5371i −0.145082 + 0.822801i
\(624\) 8.29086 + 3.01763i 0.331900 + 0.120802i
\(625\) 0 0
\(626\) 5.56118 0.222270
\(627\) −18.3405 10.7697i −0.732449 0.430100i
\(628\) −8.45336 −0.337326
\(629\) 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 \(0.0840921\pi\)
\(632\) 1.57398 + 8.92647i 0.0626095 + 0.355076i
\(633\) −32.1917 + 11.7168i −1.27950 + 0.465701i
\(634\) −1.90167 + 3.29380i −0.0755251 + 0.130813i
\(635\) 0 0
\(636\) 9.63816 + 8.08737i 0.382178 + 0.320685i
\(637\) 1.15064 + 0.965505i 0.0455902 + 0.0382547i
\(638\) −4.49525 7.78601i −0.177969 0.308251i
\(639\) −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 \(-0.129182\pi\)
\(642\) 3.04710 17.2810i 0.120260 0.682026i
\(643\) 24.4748 + 8.90809i 0.965191 + 0.351301i 0.776066 0.630652i \(-0.217213\pi\)
0.189125 + 0.981953i \(0.439435\pi\)
\(644\) −1.43376 + 1.20307i −0.0564982 + 0.0474076i
\(645\) 0 0
\(646\) 18.1004 + 21.8966i 0.712152 + 0.861511i
\(647\) 2.31490 0.0910082 0.0455041 0.998964i \(-0.485511\pi\)
0.0455041 + 0.998964i \(0.485511\pi\)
\(648\) 5.06805 4.25260i 0.199092 0.167058i
\(649\) −1.71776 0.625213i −0.0674279 0.0245418i
\(650\) 0 0
\(651\) 1.75877 + 9.97448i 0.0689316 + 0.390931i
\(652\) 16.0214 5.83132i 0.627447 0.228372i
\(653\) 1.65270 2.86257i 0.0646753 0.112021i −0.831875 0.554964i \(-0.812732\pi\)
0.896550 + 0.442943i \(0.146066\pi\)
\(654\) −6.66044 11.5362i −0.260444 0.451102i
\(655\) 0 0
\(656\) −0.266044 0.223238i −0.0103873 0.00871597i
\(657\) −5.14543 8.91215i −0.200742 0.347696i
\(658\) 10.6263 18.4053i 0.414256 0.717513i
\(659\) 12.9201 4.70253i 0.503295 0.183185i −0.0778802 0.996963i \(-0.524815\pi\)
0.581176 + 0.813778i \(0.302593\pi\)
\(660\) 0 0
\(661\) −0.579030 + 3.28384i −0.0225217 + 0.127727i −0.993996 0.109419i \(-0.965101\pi\)
0.971474 + 0.237146i \(0.0762120\pi\)
\(662\) 19.1903 + 6.98470i 0.745853 + 0.271468i
\(663\) −44.0506 + 36.9628i −1.71078 + 1.43552i
\(664\) 8.47565 0.328919
\(665\) 0 0
\(666\) 2.85204 0.110514
\(667\) −1.50206 + 1.26038i −0.0581600 + 0.0488020i
\(668\) −3.00000 1.09191i −0.116073 0.0422473i
\(669\) −2.46791 + 13.9962i −0.0954150 + 0.541125i
\(670\) 0 0
\(671\) −8.78611 + 3.19788i −0.339184 + 0.123453i
\(672\) 2.06418 3.57526i 0.0796274 0.137919i
\(673\) 19.4905 + 33.7585i 0.751304 + 1.30130i 0.947191 + 0.320670i \(0.103908\pi\)
−0.195887 + 0.980626i \(0.562759\pi\)
\(674\) 15.5587 + 13.0553i 0.599299 + 0.502872i
\(675\) 0 0
\(676\) −10.0817 17.4620i −0.387758 0.671617i
\(677\) −21.7939 + 37.7481i −0.837606 + 1.45078i 0.0542853 + 0.998525i \(0.482712\pi\)
−0.891891 + 0.452250i \(0.850621\pi\)
\(678\) 4.11721 1.49854i 0.158121 0.0575512i
\(679\) −0.162504 0.921605i −0.00623632 0.0353680i
\(680\) 0 0
\(681\) −11.1382 4.05396i −0.426815 0.155348i
\(682\) −5.98545 + 5.02239i −0.229195 + 0.192317i
\(683\) −32.9317 −1.26010 −0.630048 0.776556i \(-0.716965\pi\)
−0.630048 + 0.776556i \(0.716965\pi\)
\(684\) −0.0209445 + 2.84499i −0.000800834 + 0.108781i
\(685\) 0 0
\(686\) −13.9108 + 11.6726i −0.531119 + 0.445661i
\(687\) −33.1634 12.0705i −1.26526 0.460518i
\(688\) −1.05303 + 5.97205i −0.0401465 + 0.227682i
\(689\) −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 \(0.940255\pi\)
\(692\) 4.81521 + 8.34018i 0.183047 + 0.317046i
\(693\) 4.29086 + 3.60046i 0.162996 + 0.136770i
\(694\) 3.99479 + 3.35202i 0.151640 + 0.127241i
\(695\) 0 0
\(696\) 2.16250 3.74557i 0.0819695 0.141975i
\(697\) 2.12701 0.774169i 0.0805663 0.0293237i
\(698\) −2.49020 14.1226i −0.0942555 0.534549i
\(699\) 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 \(0.238889\pi\)
\(702\) −32.2276 −1.21635
\(703\) 12.3500 14.5000i 0.465788 0.546878i
\(704\) 3.18479 0.120031
\(705\) 0 0
\(706\) −24.6668 8.97800i −0.928349 0.337891i
\(707\) 0.172933 0.980752i 0.00650381 0.0368850i
\(708\) −0.152704 0.866025i −0.00573895 0.0325472i
\(709\) 3.17530 1.15571i 0.119251 0.0434037i −0.281706 0.959501i \(-0.590900\pi\)
0.400956 + 0.916097i \(0.368678\pi\)
\(710\) 0 0
\(711\) −2.95811 5.12360i −0.110938 0.192150i
\(712\) −5.92855 4.97464i −0.222182 0.186433i
\(713\) 1.30541 + 1.09537i 0.0488879 + 0.0410218i
\(714\) 13.4534 + 23.3019i 0.503479 + 0.872052i
\(715\) 0 0
\(716\) −17.6814 + 6.43550i −0.660785 + 0.240506i
\(717\) 4.18479 + 23.7331i 0.156284 + 0.886330i
\(718\) 5.85029 33.1786i 0.218331 1.23822i
\(719\) 29.3209 + 10.6719i 1.09348 + 0.397996i 0.824911 0.565263i \(-0.191225\pi\)
0.268574 + 0.963259i \(0.413448\pi\)
\(720\) 0 0
\(721\) 23.1242 0.861192
\(722\) 14.3735 + 12.4259i 0.534925 + 0.462445i
\(723\) −26.8161 −0.997303
\(724\) 2.12836 1.78590i 0.0790997 0.0663725i
\(725\) 0 0
\(726\) −0.228026 + 1.29320i −0.00846283 + 0.0479951i
\(727\) 4.45605 + 25.2715i 0.165266 + 0.937269i 0.948790 + 0.315908i \(0.102309\pi\)
−0.783524 + 0.621361i \(0.786580\pi\)
\(728\) −14.5817 + 5.30731i −0.540434 + 0.196702i
\(729\) −15.0201 + 26.0155i −0.556299 + 0.963538i
\(730\) 0 0
\(731\) −30.2768 25.4052i −1.11983 0.939647i
\(732\) −3.44562 2.89122i −0.127354 0.106863i
\(733\) −11.9368 20.6751i −0.440894 0.763651i 0.556862 0.830605i \(-0.312005\pi\)
−0.997756 + 0.0669540i \(0.978672\pi\)
\(734\) 5.23442 9.06629i 0.193206 0.334643i
\(735\) 0 0
\(736\) −0.120615 0.684040i −0.00444592 0.0252141i
\(737\) 2.74200 15.5507i 0.101003 0.572816i
\(738\) 0.213011 + 0.0775297i 0.00784104 + 0.00285391i
\(739\) −35.1924 + 29.5299i −1.29457 + 1.08628i −0.303517 + 0.952826i \(0.598161\pi\)
−0.991056 + 0.133449i \(0.957395\pi\)
\(740\) 0 0
\(741\) −24.9368 + 29.2780i −0.916075 + 1.07555i
\(742\) −22.1284 −0.812357
\(743\) 39.0770 32.7895i 1.43360 1.20293i 0.490046 0.871697i \(-0.336980\pi\)
0.943549 0.331232i \(-0.107464\pi\)
\(744\) −3.53209 1.28558i −0.129493 0.0471315i
\(745\) 0 0
\(746\) 4.15064 + 23.5395i 0.151966 + 0.861841i
\(747\) −5.19846 + 1.89209i −0.190202 + 0.0692278i
\(748\) −10.3785 + 17.9761i −0.379476 + 0.657271i
\(749\) 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 \(0.953183\pi\)
\(752\) 3.94356 + 6.83045i 0.143807 + 0.249081i
\(753\) 6.56283 11.3672i 0.239163 0.414242i
\(754\) −15.2763 + 5.56012i −0.556330 + 0.202488i
\(755\) 0 0
\(756\) −2.61856 + 14.8506i −0.0952359 + 0.540110i
\(757\) −5.45336 1.98486i −0.198206 0.0721410i 0.241010 0.970523i \(-0.422521\pi\)
−0.439216 + 0.898382i \(0.644744\pi\)
\(758\) −13.6459 + 11.4503i −0.495641 + 0.415892i
\(759\) −3.38919 −0.123020
\(760\) 0 0
\(761\) 22.6355 0.820535 0.410268 0.911965i \(-0.365435\pi\)
0.410268 + 0.911965i \(0.365435\pi\)
\(762\) −11.4192 + 9.58186i −0.413675 + 0.347114i
\(763\) 22.0155 + 8.01298i 0.797014 + 0.290089i
\(764\) 1.66044 9.41685i 0.0600728 0.340690i
\(765\) 0 0
\(766\) −23.5672 + 8.57775i −0.851516 + 0.309927i
\(767\) −1.65270 + 2.86257i −0.0596757 + 0.103361i
\(768\) 0.766044 + 1.32683i 0.0276422 + 0.0478778i
\(769\) 8.35188 + 7.00806i 0.301177 + 0.252717i 0.780834 0.624739i \(-0.214795\pi\)
−0.479657 + 0.877456i \(0.659239\pi\)
\(770\) 0 0
\(771\) 6.14724 + 10.6473i 0.221387 + 0.383454i
\(772\) −11.8405 + 20.5083i −0.426149 + 0.738111i
\(773\) −4.93407 + 1.79585i −0.177466 + 0.0645924i −0.429225 0.903198i \(-0.641213\pi\)
0.251759 + 0.967790i \(0.418991\pi\)
\(774\) −0.687319 3.89798i −0.0247052 0.140110i
\(775\) 0 0
\(776\) 0.326352 + 0.118782i 0.0117153 + 0.00426404i
\(777\) 13.8188 11.5954i 0.495748 0.415982i
\(778\) 9.41828 0.337662
\(779\) 1.31655 0.747243i 0.0471704 0.0267728i
\(780\) 0 0
\(781\) −20.6236 + 17.3053i −0.737971 + 0.619231i
\(782\) 4.25402 + 1.54834i 0.152124 + 0.0553684i
\(783\) −2.74329 + 15.5580i −0.0980371 + 0.555996i
\(784\) 0.0452926 + 0.256867i 0.00161759 + 0.00917383i
\(785\) 0 0
\(786\) 4.95471 8.58180i 0.176729 0.306103i
\(787\) −1.19372 2.06758i −0.0425514 0.0737011i 0.843965 0.536398i \(-0.180215\pi\)
−0.886517 + 0.462697i \(0.846882\pi\)
\(788\) 17.5594 + 14.7341i 0.625529 + 0.524881i
\(789\) −6.99588 5.87024i −0.249060 0.208986i
\(790\) 0 0
\(791\) −3.85298 + 6.67355i −0.136996 + 0.237284i
\(792\) −1.95336 + 0.710966i −0.0694097 + 0.0252631i
\(793\) 2.93582 + 16.6499i 0.104254 + 0.591254i
\(794\) 1.18984 6.74795i 0.0422260 0.239476i
\(795\) 0 0
\(796\) 7.72462 6.48173i 0.273792 0.229739i
\(797\) −31.0951 −1.10145 −0.550723 0.834688i \(-0.685648\pi\)
−0.550723 + 0.834688i \(0.685648\pi\)
\(798\) 11.4652 + 13.8698i 0.405864 + 0.490986i
\(799\) −51.4047 −1.81857
\(800\) 0 0
\(801\) 4.74675 + 1.72768i 0.167718 + 0.0610444i
\(802\) −0.824292 + 4.67479i −0.0291068 + 0.165073i
\(803\) −8.71941 49.4502i −0.307701 1.74506i
\(804\) 7.13816 2.59808i 0.251743 0.0916271i
\(805\) 0 0
\(806\) 7.06418 + 12.2355i 0.248825 + 0.430978i
\(807\) 1.34730 + 1.13052i 0.0474271 + 0.0397960i
\(808\) 0.283119 + 0.237565i 0.00996008 + 0.00835750i
\(809\) −11.1518 19.3155i −0.392077 0.679098i 0.600646 0.799515i \(-0.294910\pi\)
−0.992723 + 0.120417i \(0.961577\pi\)
\(810\) 0 0
\(811\) −3.11886 + 1.13517i −0.109518 + 0.0398613i −0.396198 0.918165i \(-0.629671\pi\)
0.286680 + 0.958026i \(0.407448\pi\)
\(812\) 1.32089 + 7.49113i 0.0463541 + 0.262887i
\(813\) −5.33544 + 30.2588i −0.187122 + 1.06122i
\(814\) 13.0770 + 4.75963i 0.458348 + 0.166825i
\(815\) 0 0
\(816\) −9.98545 −0.349561
\(817\) −22.7939 13.3847i −0.797456 0.468273i
\(818\) −31.6928 −1.10811
\(819\) 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 \(0.0657357\pi\)
\(822\) 3.10220 + 17.5934i 0.108202 + 0.613641i
\(823\) −32.1729 + 11.7100i −1.12148 + 0.408185i −0.835191 0.549959i \(-0.814643\pi\)
−0.286287 + 0.958144i \(0.592421\pi\)
\(824\) −4.29086 + 7.43199i −0.149479 + 0.258906i
\(825\) 0 0
\(826\) 1.18479 + 0.994159i 0.0412242 + 0.0345912i
\(827\) 15.2181 + 12.7695i 0.529184 + 0.444038i 0.867820 0.496880i \(-0.165521\pi\)
−0.338636 + 0.940918i \(0.609965\pi\)
\(828\) 0.226682 + 0.392624i 0.00787773 + 0.0136446i
\(829\) 17.8675 30.9475i 0.620565 1.07485i −0.368816 0.929502i \(-0.620237\pi\)
0.989381 0.145347i \(-0.0464300\pi\)
\(830\) 0 0
\(831\) 4.61856 + 26.1931i 0.160216 + 0.908630i
\(832\) 1.00000 5.67128i 0.0346688 0.196616i
\(833\) −1.59745 0.581424i −0.0553483 0.0201451i
\(834\) −9.69846 + 8.13798i −0.335830 + 0.281795i
\(835\) 0 0
\(836\) −4.84389 + 13.0097i −0.167530 + 0.449949i
\(837\) 13.7297 0.474567
\(838\) 8.43423 7.07716i 0.291356 0.244476i
\(839\) 51.1147 + 18.6042i 1.76468 + 0.642290i 0.999998 0.00212143i \(-0.000675272\pi\)
0.764679 + 0.644411i \(0.222897\pi\)
\(840\) 0 0
\(841\) −3.65199 20.7115i −0.125931 0.714188i
\(842\) −8.14290 + 2.96377i −0.280623 + 0.102138i
\(843\) 2.23783 3.87603i 0.0770748 0.133498i
\(844\) 11.1800 + 19.3644i 0.384833 + 0.666550i
\(845\) 0 0
\(846\) −3.94356 3.30904i −0.135582 0.113767i
\(847\) −1.15476 2.00011i −0.0396781 0.0687245i
\(848\) 4.10607 7.11192i 0.141003 0.244224i
\(849\) 13.6493 4.96794i 0.468443 0.170499i
\(850\) 0 0
\(851\) 0.527036 2.98897i 0.0180666 0.102461i
\(852\) −12.1702 4.42961i −0.416946 0.151756i
\(853\) −12.2385 + 10.2694i −0.419040 + 0.351616i −0.827798 0.561027i \(-0.810406\pi\)
0.408758 + 0.912643i \(0.365962\pi\)
\(854\) 7.91085 0.270704
\(855\) 0 0
\(856\) −11.4534 −0.391468
\(857\) 19.9283 16.7218i 0.680738 0.571207i −0.235484 0.971878i \(-0.575668\pi\)
0.916222 + 0.400671i \(0.131223\pi\)
\(858\) −26.4047 9.61051i −0.901440 0.328097i
\(859\) 9.25031 52.4611i 0.315617 1.78995i −0.253124 0.967434i \(-0.581458\pi\)
0.568740 0.822517i \(-0.307431\pi\)
\(860\) 0 0
\(861\) 1.34730 0.490376i 0.0459157 0.0167120i
\(862\) −14.9436 + 25.8830i −0.508980 + 0.881579i
\(863\) 1.61587 + 2.79876i 0.0550048 + 0.0952710i 0.892217 0.451608i \(-0.149149\pi\)
−0.837212 + 0.546879i \(0.815816\pi\)
\(864\) −4.28699 3.59721i −0.145846 0.122380i
\(865\) 0 0
\(866\) −4.63041 8.02011i −0.157348 0.272535i
\(867\) 19.5175 33.8054i 0.662850 1.14809i
\(868\) 6.21213 2.26103i 0.210854 0.0767444i
\(869\) −5.01279 28.4290i −0.170047 0.964387i
\(870\) 0 0
\(871\) −26.8307 9.76557i −0.909123 0.330894i
\(872\) −6.66044 + 5.58878i −0.225551 + 0.189260i
\(873\) −0.226682 −0.00767201
\(874\) 2.97771 + 0.547683i 0.100723 + 0.0185257i
\(875\) 0 0
\(876\) 18.5043 15.5270i 0.625204 0.524608i
\(877\) 11.0172 + 4.00995i 0.372026 + 0.135406i 0.521265 0.853395i \(-0.325460\pi\)
−0.149239 + 0.988801i \(0.547683\pi\)
\(878\) −3.62267 + 20.5452i −0.122259 + 0.693367i
\(879\) −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 \(0.317250\pi\)
\(882\) −0.0851223 0.147436i −0.00286622 0.00496443i
\(883\) −11.0931 9.30823i −0.373313 0.313247i 0.436758 0.899579i \(-0.356127\pi\)
−0.810070 + 0.586333i \(0.800571\pi\)
\(884\) 28.7520 + 24.1258i 0.967033 + 0.811437i
\(885\) 0 0
\(886\) −11.9140 + 20.6357i −0.400259 + 0.693268i
\(887\) −10.8922 + 3.96443i −0.365724 + 0.133112i −0.518344 0.855172i \(-0.673451\pi\)
0.152620 + 0.988285i \(0.451229\pi\)
\(888\) 1.16250 + 6.59289i 0.0390111 + 0.221243i
\(889\) 4.55262 25.8192i 0.152690 0.865948i
\(890\) 0 0
\(891\) −16.1407 + 13.5436i −0.540733 + 0.453729i
\(892\) 9.27631 0.310594
\(893\) −33.8999 + 5.72048i −1.13442 + 0.191428i
\(894\) −25.2080 −0.843082
\(895\) 0 0
\(896\) −2.53209 0.921605i −0.0845912 0.0307887i
\(897\) −1.06418 + 6.03525i −0.0355319 + 0.201511i
\(898\) 0.378918 + 2.14895i 0.0126447 + 0.0717115i
\(899\) 6.50805 2.36873i 0.217055 0.0790017i
\(900\) 0 0
\(901\) 26.7615 + 46.3522i 0.891553 + 1.54422i
\(902\) 0.847296 + 0.710966i 0.0282119 + 0.0236726i
\(903\) −19.1780 16.0922i −0.638203 0.535516i
\(904\) −1.42989 2.47665i −0.0475575 0.0823720i
\(905\) 0 0
\(906\) −6.70233 + 2.43945i −0.222670 + 0.0810453i
\(907\) −7.28952 41.3409i −0.242044 1.37270i −0.827258 0.561823i \(-0.810100\pi\)
0.585213 0.810879i \(-0.301011\pi\)
\(908\) −1.34343 + 7.61895i −0.0445832 + 0.252844i
\(909\) −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 \(0.766723\pi\)
\(912\) −6.58512 + 1.11121i −0.218055 + 0.0367959i
\(913\) −26.9932 −0.893344
\(914\) 1.36437 1.14484i 0.0451294 0.0378680i
\(915\) 0 0
\(916\) −4.00000 + 22.6851i −0.132164 + 0.749538i
\(917\) 3.02641 + 17.1636i 0.0999408 + 0.566792i
\(918\) 34.2743 12.4748i 1.13122 0.411730i
\(919\) 16.2635 28.1692i 0.536484 0.929217i −0.462606 0.886564i \(-0.653086\pi\)
0.999090 0.0426535i \(-0.0135811\pi\)
\(920\) 0 0
\(921\) 25.0323 + 21.0046i 0.824843 + 0.692125i
\(922\) 11.8648 + 9.95578i 0.390748 + 0.327876i
\(923\) 24.3405 + 42.1590i 0.801177 + 1.38768i
\(924\) −6.57398 + 11.3865i −0.216268 + 0.374587i
\(925\) 0 0
\(926\) −0.470599 2.66890i −0.0154649 0.0877056i
\(927\) 0.972659 5.51622i 0.0319463 0.181177i
\(928\) −2.65270 0.965505i −0.0870793 0.0316943i
\(929\) 9.07011 7.61072i 0.297581 0.249700i −0.481756 0.876305i \(-0.660001\pi\)
0.779336 + 0.626606i \(0.215556\pi\)
\(930\) 0 0
\(931\) −1.11817 0.205663i −0.0366467 0.00674034i
\(932\) −8.39961 −0.275139
\(933\) 34.3783 28.8468i 1.12549 0.944401i
\(934\) −12.1348 4.41669i −0.397061 0.144518i
\(935\) 0 0
\(936\) 0.652704 + 3.70167i 0.0213343 + 0.120993i
\(937\) −0.717759 + 0.261243i −0.0234482 + 0.00853443i −0.353718 0.935352i \(-0.615083\pi\)
0.330269 + 0.943887i \(0.392860\pi\)
\(938\) −6.68004 + 11.5702i −0.218111 + 0.377780i
\(939\) −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 \(0.836156\pi\)
\(942\) 6.47565 + 11.2162i 0.210988 + 0.365442i
\(943\) 0.120615 0.208911i 0.00392776 0.00680307i
\(944\) −0.539363 + 0.196312i −0.0175548 + 0.00638941i
\(945\) 0 0
\(946\) 3.35369 19.0197i 0.109038 0.618385i
\(947\) 29.7743 + 10.8369i 0.967533 + 0.352153i 0.776981 0.629524i \(-0.216750\pi\)
0.190552 + 0.981677i \(0.438972\pi\)
\(948\) 10.6382 8.92647i 0.345511 0.289918i
\(949\) −90.7957 −2.94735
\(950\) 0 0
\(951\) 5.82707 0.188956
\(952\) 13.4534 11.2887i 0.436026 0.365869i
\(953\) 52.5017 + 19.1091i 1.70070 + 0.619003i 0.995905 0.0904104i \(-0.0288179\pi\)
0.704792 + 0.709414i \(0.251040\pi\)
\(954\) −0.930770 + 5.27866i −0.0301348 + 0.170903i
\(955\) 0 0
\(956\) 14.7811 5.37987i 0.478054 0.173997i
\(957\) −6.88713 + 11.9289i −0.222629 + 0.385605i
\(958\) −9.27631 16.0670i −0.299704 0.519103i
\(959\) −24.0692 20.1965i −0.777236 0.652178i
\(960\) 0 0
\(961\) 12.4905 + 21.6342i 0.402920 + 0.697877i
\(962\) 12.5817 21.7922i 0.405651 0.702608i
\(963\) 7.02481 2.55682i 0.226371 0.0823925i
\(964\) 3.03936 + 17.2371i 0.0978913 + 0.555169i
\(965\) 0 0
\(966\) 2.69459 + 0.980752i 0.0866971 + 0.0315552i
\(967\) −16.5134 + 13.8564i −0.531036 + 0.445592i −0.868459 0.495761i \(-0.834889\pi\)
0.337423 + 0.941353i \(0.390445\pi\)
\(968\) 0.857097 0.0275481
\(969\) 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 \(-0.00737372\pi\)
\(972\) 6.25150 + 2.27536i 0.200517 + 0.0729822i
\(973\) 3.86659 21.9285i 0.123957 0.702996i
\(974\) 7.14971 + 40.5480i 0.229092 + 1.29924i
\(975\) 0 0
\(976\) −1.46791 + 2.54250i −0.0469867 + 0.0813833i
\(977\) −25.2741 43.7760i −0.808590 1.40052i −0.913841 0.406073i \(-0.866898\pi\)
0.105251 0.994446i \(-0.466435\pi\)
\(978\) −20.0103 16.7906i −0.639858 0.536904i
\(979\) 18.8812 + 15.8432i 0.603446 + 0.506351i
\(980\) 0 0
\(981\) 2.83750 4.91469i 0.0905943 0.156914i
\(982\) −21.2160 + 7.72199i −0.677030 + 0.246419i
\(983\) 5.21987 + 29.6034i 0.166488 + 0.944201i 0.947517 + 0.319706i \(0.103584\pi\)
−0.781029 + 0.624495i \(0.785305\pi\)
\(984\) −0.0923963 + 0.524005i −0.00294549 + 0.0167047i
\(985\) 0 0
\(986\) 14.0942 11.8264i 0.448851 0.376631i
\(987\) −32.5609 −1.03642
\(988\) 21.6459 + 12.7106i 0.688648 + 0.404379i
\(989\) −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 \(0.625033\pi\)
\(992\) −0.426022 + 2.41609i −0.0135262 + 0.0767110i
\(993\) −5.43313 30.8128i −0.172415 0.977816i
\(994\) 21.4047 7.79066i 0.678915 0.247105i
\(995\) 0 0
\(996\) −6.49273 11.2457i −0.205730 0.356335i
\(997\) −6.66819 5.59527i −0.211184 0.177204i 0.531060 0.847334i \(-0.321794\pi\)
−0.742244 + 0.670130i \(0.766238\pi\)
\(998\) 22.4670 + 18.8521i 0.711182 + 0.596752i
\(999\) −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.l.d.101.1 6
5.2 odd 4 950.2.u.b.899.1 12
5.3 odd 4 950.2.u.b.899.2 12
5.4 even 2 38.2.e.a.25.1 6
15.14 odd 2 342.2.u.c.253.1 6
19.16 even 9 inner 950.2.l.d.301.1 6
20.19 odd 2 304.2.u.c.177.1 6
95.4 even 18 722.2.a.l.1.3 3
95.9 even 18 722.2.c.k.429.1 6
95.14 odd 18 722.2.e.a.245.1 6
95.24 even 18 722.2.e.m.245.1 6
95.29 odd 18 722.2.c.l.429.3 6
95.34 odd 18 722.2.a.k.1.1 3
95.44 even 18 722.2.c.k.653.1 6
95.49 even 6 722.2.e.b.99.1 6
95.54 even 18 38.2.e.a.35.1 yes 6
95.59 odd 18 722.2.e.l.423.1 6
95.64 even 6 722.2.e.m.389.1 6
95.69 odd 6 722.2.e.a.389.1 6
95.73 odd 36 950.2.u.b.149.1 12
95.74 even 18 722.2.e.b.423.1 6
95.79 odd 18 722.2.e.k.415.1 6
95.84 odd 6 722.2.e.l.99.1 6
95.89 odd 18 722.2.c.l.653.3 6
95.92 odd 36 950.2.u.b.149.2 12
95.94 odd 2 722.2.e.k.595.1 6
285.149 odd 18 342.2.u.c.73.1 6
285.194 odd 18 6498.2.a.bl.1.2 3
285.224 even 18 6498.2.a.bq.1.2 3
380.99 odd 18 5776.2.a.bn.1.1 3
380.319 even 18 5776.2.a.bo.1.3 3
380.339 odd 18 304.2.u.c.225.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.e.a.25.1 6 5.4 even 2
38.2.e.a.35.1 yes 6 95.54 even 18
304.2.u.c.177.1 6 20.19 odd 2
304.2.u.c.225.1 6 380.339 odd 18
342.2.u.c.73.1 6 285.149 odd 18
342.2.u.c.253.1 6 15.14 odd 2
722.2.a.k.1.1 3 95.34 odd 18
722.2.a.l.1.3 3 95.4 even 18
722.2.c.k.429.1 6 95.9 even 18
722.2.c.k.653.1 6 95.44 even 18
722.2.c.l.429.3 6 95.29 odd 18
722.2.c.l.653.3 6 95.89 odd 18
722.2.e.a.245.1 6 95.14 odd 18
722.2.e.a.389.1 6 95.69 odd 6
722.2.e.b.99.1 6 95.49 even 6
722.2.e.b.423.1 6 95.74 even 18
722.2.e.k.415.1 6 95.79 odd 18
722.2.e.k.595.1 6 95.94 odd 2
722.2.e.l.99.1 6 95.84 odd 6
722.2.e.l.423.1 6 95.59 odd 18
722.2.e.m.245.1 6 95.24 even 18
722.2.e.m.389.1 6 95.64 even 6
950.2.l.d.101.1 6 1.1 even 1 trivial
950.2.l.d.301.1 6 19.16 even 9 inner
950.2.u.b.149.1 12 95.73 odd 36
950.2.u.b.149.2 12 95.92 odd 36
950.2.u.b.899.1 12 5.2 odd 4
950.2.u.b.899.2 12 5.3 odd 4
5776.2.a.bn.1.1 3 380.99 odd 18
5776.2.a.bo.1.3 3 380.319 even 18
6498.2.a.bl.1.2 3 285.194 odd 18
6498.2.a.bq.1.2 3 285.224 even 18