Properties

Label 164.2.o.b.11.18
Level $164$
Weight $2$
Character 164.11
Analytic conductor $1.310$
Analytic rank $0$
Dimension $288$
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] = [164,2,Mod(7,164)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(164, base_ring=CyclotomicField(40))
 
chi = DirichletCharacter(H, H._module([20, 39]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("164.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.o (of order \(40\), degree \(16\), 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: \(1.30954659315\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label 11.18
Character \(\chi\) \(=\) 164.11
Dual form 164.2.o.b.15.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40600 + 0.152222i) q^{2} +(0.756584 - 1.82656i) q^{3} +(1.95366 + 0.428048i) q^{4} +(-1.28598 + 2.52388i) q^{5} +(1.34180 - 2.45296i) q^{6} +(-0.634663 - 2.64356i) q^{7} +(2.68168 + 0.899225i) q^{8} +(-0.642564 - 0.642564i) q^{9} +O(q^{10})\) \(q+(1.40600 + 0.152222i) q^{2} +(0.756584 - 1.82656i) q^{3} +(1.95366 + 0.428048i) q^{4} +(-1.28598 + 2.52388i) q^{5} +(1.34180 - 2.45296i) q^{6} +(-0.634663 - 2.64356i) q^{7} +(2.68168 + 0.899225i) q^{8} +(-0.642564 - 0.642564i) q^{9} +(-2.19228 + 3.35282i) q^{10} +(-3.28267 + 3.84351i) q^{11} +(2.25996 - 3.24461i) q^{12} +(-2.94163 - 4.80031i) q^{13} +(-0.489925 - 3.81345i) q^{14} +(3.63706 + 4.25845i) q^{15} +(3.63355 + 1.67252i) q^{16} +(0.0571608 + 0.726296i) q^{17} +(-0.805631 - 1.00126i) q^{18} +(-0.531502 - 0.325705i) q^{19} +(-3.59271 + 4.38034i) q^{20} +(-5.30879 - 0.840829i) q^{21} +(-5.20049 + 4.90427i) q^{22} +(-0.882818 - 0.641405i) q^{23} +(3.67140 - 4.21789i) q^{24} +(-1.77731 - 2.44625i) q^{25} +(-3.40522 - 7.19701i) q^{26} +(3.81983 - 1.58223i) q^{27} +(-0.108342 - 5.43628i) q^{28} +(-0.452928 + 5.75499i) q^{29} +(4.46546 + 6.54101i) q^{30} +(-2.23549 + 6.88014i) q^{31} +(4.85417 + 2.90466i) q^{32} +(4.53677 + 8.90392i) q^{33} +(-0.0301906 + 1.02987i) q^{34} +(7.48820 + 1.79776i) q^{35} +(-0.980301 - 1.53040i) q^{36} +(-1.79487 - 5.52404i) q^{37} +(-0.697710 - 0.538846i) q^{38} +(-10.9936 + 1.74122i) q^{39} +(-5.71813 + 5.61185i) q^{40} +(4.55866 - 4.49651i) q^{41} +(-7.33615 - 1.99032i) q^{42} +(0.642081 + 4.05394i) q^{43} +(-8.05842 + 6.10377i) q^{44} +(2.44808 - 0.795430i) q^{45} +(-1.14360 - 1.03620i) q^{46} +(2.91790 - 12.1539i) q^{47} +(5.80403 - 5.37148i) q^{48} +(-0.348572 + 0.177606i) q^{49} +(-2.12651 - 3.70997i) q^{50} +(1.36987 + 0.445097i) q^{51} +(-3.69218 - 10.6373i) q^{52} +(-7.02659 - 0.553004i) q^{53} +(5.61152 - 1.64314i) q^{54} +(-5.47912 - 13.2278i) q^{55} +(0.675194 - 7.65988i) q^{56} +(-0.997043 + 0.724394i) q^{57} +(-1.51285 + 8.02256i) q^{58} +(2.32978 - 3.20667i) q^{59} +(5.28274 + 9.87638i) q^{60} +(-0.330485 + 2.08660i) q^{61} +(-4.19041 + 9.33317i) q^{62} +(-1.29085 + 2.10647i) q^{63} +(6.38279 + 4.82286i) q^{64} +(15.8983 - 1.25122i) q^{65} +(5.02332 + 13.2095i) q^{66} +(2.50427 - 2.13885i) q^{67} +(-0.199217 + 1.44340i) q^{68} +(-1.83949 + 1.12724i) q^{69} +(10.2547 + 3.66751i) q^{70} +(-9.35782 - 7.99233i) q^{71} +(-1.14534 - 2.30096i) q^{72} +(3.14718 - 3.14718i) q^{73} +(-1.68270 - 8.04001i) q^{74} +(-5.81290 + 1.39555i) q^{75} +(-0.898955 - 0.863823i) q^{76} +(12.2440 + 6.23860i) q^{77} +(-15.7221 + 0.774675i) q^{78} +(14.9861 + 6.20746i) q^{79} +(-8.89392 + 7.01982i) q^{80} -10.9004i q^{81} +(7.09393 - 5.62815i) q^{82} +6.63164i q^{83} +(-10.0116 - 3.91511i) q^{84} +(-1.90659 - 0.789737i) q^{85} +(0.285664 + 5.79756i) q^{86} +(10.1691 + 5.18143i) q^{87} +(-12.2592 + 7.35521i) q^{88} +(7.99728 - 1.91998i) q^{89} +(3.56308 - 0.745720i) q^{90} +(-10.8230 + 10.8230i) q^{91} +(-1.45017 - 1.63097i) q^{92} +(10.8756 + 9.28865i) q^{93} +(5.95266 - 16.6442i) q^{94} +(1.50554 - 0.922597i) q^{95} +(8.97811 - 6.66878i) q^{96} +(-8.34861 + 7.13039i) q^{97} +(-0.517126 + 0.196653i) q^{98} +(4.57903 - 0.360378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/164\mathbb{Z}\right)^\times\).

\(n\) \(83\) \(129\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{40}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40600 + 0.152222i 0.994190 + 0.107637i
\(3\) 0.756584 1.82656i 0.436814 1.05456i −0.540229 0.841518i \(-0.681662\pi\)
0.977043 0.213044i \(-0.0683377\pi\)
\(4\) 1.95366 + 0.428048i 0.976828 + 0.214024i
\(5\) −1.28598 + 2.52388i −0.575109 + 1.12871i 0.401933 + 0.915669i \(0.368338\pi\)
−0.977042 + 0.213046i \(0.931662\pi\)
\(6\) 1.34180 2.45296i 0.547786 1.00142i
\(7\) −0.634663 2.64356i −0.239880 0.999172i −0.954156 0.299308i \(-0.903244\pi\)
0.714276 0.699864i \(-0.246756\pi\)
\(8\) 2.68168 + 0.899225i 0.948116 + 0.317924i
\(9\) −0.642564 0.642564i −0.214188 0.214188i
\(10\) −2.19228 + 3.35282i −0.693260 + 1.06025i
\(11\) −3.28267 + 3.84351i −0.989762 + 1.15886i −0.00246234 + 0.999997i \(0.500784\pi\)
−0.987300 + 0.158866i \(0.949216\pi\)
\(12\) 2.25996 3.24461i 0.652394 0.936637i
\(13\) −2.94163 4.80031i −0.815862 1.33137i −0.940717 0.339191i \(-0.889847\pi\)
0.124855 0.992175i \(-0.460153\pi\)
\(14\) −0.489925 3.81345i −0.130938 1.01919i
\(15\) 3.63706 + 4.25845i 0.939084 + 1.09953i
\(16\) 3.63355 + 1.67252i 0.908387 + 0.418130i
\(17\) 0.0571608 + 0.726296i 0.0138635 + 0.176153i 0.999951 + 0.00992409i \(0.00315899\pi\)
−0.986087 + 0.166229i \(0.946841\pi\)
\(18\) −0.805631 1.00126i −0.189889 0.235998i
\(19\) −0.531502 0.325705i −0.121935 0.0747218i 0.460194 0.887819i \(-0.347780\pi\)
−0.582129 + 0.813097i \(0.697780\pi\)
\(20\) −3.59271 + 4.38034i −0.803355 + 0.979473i
\(21\) −5.30879 0.840829i −1.15847 0.183484i
\(22\) −5.20049 + 4.90427i −1.10875 + 1.04559i
\(23\) −0.882818 0.641405i −0.184080 0.133742i 0.491929 0.870635i \(-0.336292\pi\)
−0.676009 + 0.736893i \(0.736292\pi\)
\(24\) 3.67140 4.21789i 0.749421 0.860974i
\(25\) −1.77731 2.44625i −0.355461 0.489251i
\(26\) −3.40522 7.19701i −0.667818 1.41145i
\(27\) 3.81983 1.58223i 0.735127 0.304500i
\(28\) −0.108342 5.43628i −0.0204747 1.02736i
\(29\) −0.452928 + 5.75499i −0.0841066 + 1.06868i 0.799569 + 0.600575i \(0.205062\pi\)
−0.883675 + 0.468101i \(0.844938\pi\)
\(30\) 4.46546 + 6.54101i 0.815278 + 1.19422i
\(31\) −2.23549 + 6.88014i −0.401506 + 1.23571i 0.522271 + 0.852780i \(0.325085\pi\)
−0.923777 + 0.382930i \(0.874915\pi\)
\(32\) 4.85417 + 2.90466i 0.858103 + 0.513477i
\(33\) 4.53677 + 8.90392i 0.789751 + 1.54997i
\(34\) −0.0301906 + 1.02987i −0.00517765 + 0.176622i
\(35\) 7.48820 + 1.79776i 1.26574 + 0.303877i
\(36\) −0.980301 1.53040i −0.163384 0.255066i
\(37\) −1.79487 5.52404i −0.295075 0.908147i −0.983196 0.182552i \(-0.941564\pi\)
0.688121 0.725596i \(-0.258436\pi\)
\(38\) −0.697710 0.538846i −0.113184 0.0874124i
\(39\) −10.9936 + 1.74122i −1.76039 + 0.278818i
\(40\) −5.71813 + 5.61185i −0.904115 + 0.887312i
\(41\) 4.55866 4.49651i 0.711943 0.702237i
\(42\) −7.33615 1.99032i −1.13199 0.307113i
\(43\) 0.642081 + 4.05394i 0.0979164 + 0.618220i 0.987030 + 0.160534i \(0.0513216\pi\)
−0.889114 + 0.457686i \(0.848678\pi\)
\(44\) −8.05842 + 6.10377i −1.21485 + 0.920177i
\(45\) 2.44808 0.795430i 0.364939 0.118576i
\(46\) −1.14360 1.03620i −0.168615 0.152779i
\(47\) 2.91790 12.1539i 0.425619 1.77283i −0.186903 0.982378i \(-0.559845\pi\)
0.612522 0.790454i \(-0.290155\pi\)
\(48\) 5.80403 5.37148i 0.837740 0.775306i
\(49\) −0.348572 + 0.177606i −0.0497960 + 0.0253723i
\(50\) −2.12651 3.70997i −0.300735 0.524669i
\(51\) 1.36987 + 0.445097i 0.191820 + 0.0623260i
\(52\) −3.69218 10.6373i −0.512013 1.47513i
\(53\) −7.02659 0.553004i −0.965176 0.0759610i −0.413934 0.910307i \(-0.635846\pi\)
−0.551242 + 0.834346i \(0.685846\pi\)
\(54\) 5.61152 1.64314i 0.763632 0.223603i
\(55\) −5.47912 13.2278i −0.738805 1.78363i
\(56\) 0.675194 7.65988i 0.0902266 1.02359i
\(57\) −0.997043 + 0.724394i −0.132062 + 0.0959484i
\(58\) −1.51285 + 8.02256i −0.198647 + 1.05341i
\(59\) 2.32978 3.20667i 0.303312 0.417473i −0.629969 0.776620i \(-0.716932\pi\)
0.933281 + 0.359147i \(0.116932\pi\)
\(60\) 5.28274 + 9.87638i 0.681999 + 1.27504i
\(61\) −0.330485 + 2.08660i −0.0423142 + 0.267162i −0.999771 0.0214164i \(-0.993182\pi\)
0.957456 + 0.288578i \(0.0931824\pi\)
\(62\) −4.19041 + 9.33317i −0.532182 + 1.18531i
\(63\) −1.29085 + 2.10647i −0.162631 + 0.265390i
\(64\) 6.38279 + 4.82286i 0.797849 + 0.602858i
\(65\) 15.8983 1.25122i 1.97194 0.155195i
\(66\) 5.02332 + 13.2095i 0.618328 + 1.62598i
\(67\) 2.50427 2.13885i 0.305945 0.261302i −0.483198 0.875511i \(-0.660525\pi\)
0.789143 + 0.614209i \(0.210525\pi\)
\(68\) −0.199217 + 1.44340i −0.0241587 + 0.175038i
\(69\) −1.83949 + 1.12724i −0.221448 + 0.135704i
\(70\) 10.2547 + 3.66751i 1.22568 + 0.438352i
\(71\) −9.35782 7.99233i −1.11057 0.948515i −0.111592 0.993754i \(-0.535595\pi\)
−0.998976 + 0.0452390i \(0.985595\pi\)
\(72\) −1.14534 2.30096i −0.134980 0.271171i
\(73\) 3.14718 3.14718i 0.368349 0.368349i −0.498526 0.866875i \(-0.666125\pi\)
0.866875 + 0.498526i \(0.166125\pi\)
\(74\) −1.68270 8.04001i −0.195610 0.934632i
\(75\) −5.81290 + 1.39555i −0.671216 + 0.161145i
\(76\) −0.898955 0.863823i −0.103117 0.0990873i
\(77\) 12.2440 + 6.23860i 1.39533 + 0.710955i
\(78\) −15.7221 + 0.774675i −1.78017 + 0.0877146i
\(79\) 14.9861 + 6.20746i 1.68607 + 0.698394i 0.999587 0.0287504i \(-0.00915279\pi\)
0.686485 + 0.727144i \(0.259153\pi\)
\(80\) −8.89392 + 7.01982i −0.994371 + 0.784840i
\(81\) 10.9004i 1.21115i
\(82\) 7.09393 5.62815i 0.783394 0.621526i
\(83\) 6.63164i 0.727917i 0.931415 + 0.363958i \(0.118575\pi\)
−0.931415 + 0.363958i \(0.881425\pi\)
\(84\) −10.0116 3.91511i −1.09236 0.427173i
\(85\) −1.90659 0.789737i −0.206799 0.0856591i
\(86\) 0.285664 + 5.79756i 0.0308039 + 0.625167i
\(87\) 10.1691 + 5.18143i 1.09025 + 0.555508i
\(88\) −12.2592 + 7.35521i −1.30684 + 0.784068i
\(89\) 7.99728 1.91998i 0.847710 0.203517i 0.213755 0.976887i \(-0.431430\pi\)
0.633955 + 0.773370i \(0.281430\pi\)
\(90\) 3.56308 0.745720i 0.375582 0.0786058i
\(91\) −10.8230 + 10.8230i −1.13456 + 1.13456i
\(92\) −1.45017 1.63097i −0.151191 0.170041i
\(93\) 10.8756 + 9.28865i 1.12775 + 0.963189i
\(94\) 5.95266 16.6442i 0.613970 1.71672i
\(95\) 1.50554 0.922597i 0.154465 0.0946565i
\(96\) 8.97811 6.66878i 0.916325 0.680630i
\(97\) −8.34861 + 7.13039i −0.847673 + 0.723981i −0.963045 0.269341i \(-0.913194\pi\)
0.115372 + 0.993322i \(0.463194\pi\)
\(98\) −0.517126 + 0.196653i −0.0522377 + 0.0198650i
\(99\) 4.57903 0.360378i 0.460210 0.0362193i
\(100\) −2.42513 5.53991i −0.242513 0.553991i
\(101\) −5.80846 + 9.47855i −0.577963 + 0.943151i 0.421379 + 0.906885i \(0.361546\pi\)
−0.999342 + 0.0362659i \(0.988454\pi\)
\(102\) 1.85828 + 0.834329i 0.183997 + 0.0826109i
\(103\) 0.586386 3.70230i 0.0577784 0.364798i −0.941811 0.336143i \(-0.890877\pi\)
0.999589 0.0286553i \(-0.00912251\pi\)
\(104\) −3.57196 15.5181i −0.350259 1.52167i
\(105\) 8.94916 12.3175i 0.873349 1.20206i
\(106\) −9.79518 1.84713i −0.951392 0.179409i
\(107\) 4.95050 3.59675i 0.478583 0.347711i −0.322194 0.946674i \(-0.604420\pi\)
0.800777 + 0.598963i \(0.204420\pi\)
\(108\) 8.13991 1.45606i 0.783263 0.140109i
\(109\) 2.08867 + 5.04249i 0.200058 + 0.482983i 0.991789 0.127888i \(-0.0408196\pi\)
−0.791731 + 0.610870i \(0.790820\pi\)
\(110\) −5.69007 19.4323i −0.542527 1.85279i
\(111\) −11.4479 0.900972i −1.08659 0.0855165i
\(112\) 2.11533 10.6670i 0.199880 1.00794i
\(113\) 3.65621 + 1.18798i 0.343947 + 0.111755i 0.475897 0.879501i \(-0.342124\pi\)
−0.131949 + 0.991256i \(0.542124\pi\)
\(114\) −1.51211 + 0.866724i −0.141622 + 0.0811761i
\(115\) 2.75412 1.40329i 0.256823 0.130858i
\(116\) −3.34828 + 11.0494i −0.310880 + 1.02591i
\(117\) −1.19432 + 4.97470i −0.110415 + 0.459911i
\(118\) 3.76380 4.15393i 0.346486 0.382400i
\(119\) 1.88373 0.612061i 0.172681 0.0561076i
\(120\) 5.92411 + 14.6903i 0.540795 + 1.34104i
\(121\) −2.27589 14.3694i −0.206899 1.30631i
\(122\) −0.782287 + 2.88344i −0.0708250 + 0.261055i
\(123\) −4.76412 11.7286i −0.429566 1.05754i
\(124\) −7.31242 + 12.4845i −0.656674 + 1.12114i
\(125\) −5.52908 + 0.875721i −0.494536 + 0.0783269i
\(126\) −2.13558 + 2.76519i −0.190252 + 0.246343i
\(127\) −2.62707 8.08529i −0.233115 0.717453i −0.997366 0.0725347i \(-0.976891\pi\)
0.764251 0.644919i \(-0.223109\pi\)
\(128\) 8.24004 + 7.75253i 0.728323 + 0.685234i
\(129\) 7.89053 + 1.89435i 0.694722 + 0.166788i
\(130\) 22.5434 + 0.660859i 1.97719 + 0.0579612i
\(131\) 1.26693 + 2.48649i 0.110692 + 0.217246i 0.939707 0.341981i \(-0.111098\pi\)
−0.829015 + 0.559227i \(0.811098\pi\)
\(132\) 5.05199 + 19.3372i 0.439719 + 1.68308i
\(133\) −0.523696 + 1.61177i −0.0454102 + 0.139758i
\(134\) 3.84657 2.62601i 0.332293 0.226852i
\(135\) −0.918884 + 11.6755i −0.0790849 + 1.00487i
\(136\) −0.499817 + 1.99909i −0.0428589 + 0.171421i
\(137\) −19.8790 + 8.23413i −1.69837 + 0.703489i −0.999926 0.0121718i \(-0.996126\pi\)
−0.698448 + 0.715661i \(0.746126\pi\)
\(138\) −2.75791 + 1.30488i −0.234768 + 0.111079i
\(139\) −1.29283 1.77942i −0.109656 0.150929i 0.750662 0.660687i \(-0.229735\pi\)
−0.860318 + 0.509758i \(0.829735\pi\)
\(140\) 13.8599 + 6.71752i 1.17137 + 0.567734i
\(141\) −19.9922 14.5252i −1.68365 1.22324i
\(142\) −11.9405 12.6617i −1.00202 1.06254i
\(143\) 28.1065 + 4.45163i 2.35038 + 0.372264i
\(144\) −1.26009 3.40949i −0.105007 0.284124i
\(145\) −13.9425 8.54396i −1.15786 0.709537i
\(146\) 4.90399 3.94585i 0.405857 0.326561i
\(147\) 0.0606837 + 0.771059i 0.00500511 + 0.0635959i
\(148\) −1.14200 11.5604i −0.0938721 0.950257i
\(149\) 7.79130 + 9.12244i 0.638288 + 0.747339i 0.981404 0.191954i \(-0.0614824\pi\)
−0.343116 + 0.939293i \(0.611482\pi\)
\(150\) −8.38535 + 1.07729i −0.684661 + 0.0879605i
\(151\) 3.89605 + 6.35778i 0.317056 + 0.517388i 0.970977 0.239175i \(-0.0768769\pi\)
−0.653920 + 0.756563i \(0.726877\pi\)
\(152\) −1.13243 1.35137i −0.0918526 0.109611i
\(153\) 0.429963 0.503421i 0.0347604 0.0406992i
\(154\) 16.2653 + 10.6353i 1.31070 + 0.857014i
\(155\) −14.4899 14.4899i −1.16385 1.16385i
\(156\) −22.2231 1.30406i −1.77927 0.104408i
\(157\) −4.46047 18.5792i −0.355984 1.48278i −0.807153 0.590342i \(-0.798993\pi\)
0.451169 0.892439i \(-0.351007\pi\)
\(158\) 20.1255 + 11.0089i 1.60110 + 0.875821i
\(159\) −6.32630 + 12.4161i −0.501708 + 0.984657i
\(160\) −13.5734 + 8.51600i −1.07307 + 0.673249i
\(161\) −1.13530 + 2.74086i −0.0894743 + 0.216010i
\(162\) 1.65928 15.3259i 0.130366 1.20412i
\(163\) −24.4302 −1.91352 −0.956760 0.290880i \(-0.906052\pi\)
−0.956760 + 0.290880i \(0.906052\pi\)
\(164\) 10.8308 6.83331i 0.845742 0.533592i
\(165\) −28.3067 −2.20367
\(166\) −1.00948 + 9.32406i −0.0783510 + 0.723688i
\(167\) −7.00002 + 16.8995i −0.541678 + 1.30773i 0.381861 + 0.924220i \(0.375283\pi\)
−0.923539 + 0.383506i \(0.874717\pi\)
\(168\) −13.4804 7.02862i −1.04003 0.542270i
\(169\) −8.48789 + 16.6584i −0.652915 + 1.28142i
\(170\) −2.56045 1.40059i −0.196378 0.107421i
\(171\) 0.132238 + 0.550810i 0.0101125 + 0.0421215i
\(172\) −0.480876 + 8.19484i −0.0366664 + 0.624851i
\(173\) −2.96217 2.96217i −0.225210 0.225210i 0.585478 0.810688i \(-0.300907\pi\)
−0.810688 + 0.585478i \(0.800907\pi\)
\(174\) 13.5090 + 8.83305i 1.02412 + 0.669632i
\(175\) −5.33883 + 6.25097i −0.403578 + 0.472529i
\(176\) −18.3561 + 8.47527i −1.38364 + 0.638847i
\(177\) −4.09449 6.68159i −0.307760 0.502219i
\(178\) 11.5364 1.48212i 0.864691 0.111089i
\(179\) 7.74208 + 9.06482i 0.578671 + 0.677536i 0.970109 0.242668i \(-0.0780226\pi\)
−0.391439 + 0.920204i \(0.628023\pi\)
\(180\) 5.12320 0.506100i 0.381860 0.0377225i
\(181\) −0.507298 6.44584i −0.0377072 0.479115i −0.986560 0.163397i \(-0.947755\pi\)
0.948853 0.315718i \(-0.102245\pi\)
\(182\) −16.8646 + 13.5696i −1.25008 + 1.00584i
\(183\) 3.56125 + 2.18234i 0.263255 + 0.161323i
\(184\) −1.79067 2.51389i −0.132010 0.185327i
\(185\) 16.2502 + 2.57378i 1.19474 + 0.189228i
\(186\) 13.8771 + 14.7153i 1.01752 + 1.07898i
\(187\) −2.97917 2.16449i −0.217859 0.158283i
\(188\) 10.9030 22.4956i 0.795186 1.64066i
\(189\) −6.60702 9.09378i −0.480590 0.661475i
\(190\) 2.25723 1.06799i 0.163757 0.0774803i
\(191\) 2.82698 1.17097i 0.204553 0.0847287i −0.278055 0.960565i \(-0.589690\pi\)
0.482608 + 0.875837i \(0.339690\pi\)
\(192\) 13.6383 8.00962i 0.984262 0.578044i
\(193\) −0.690746 + 8.77676i −0.0497210 + 0.631765i 0.920688 + 0.390299i \(0.127628\pi\)
−0.970409 + 0.241466i \(0.922372\pi\)
\(194\) −12.8235 + 8.75446i −0.920676 + 0.628534i
\(195\) 9.74298 29.9858i 0.697709 2.14733i
\(196\) −0.757013 + 0.197776i −0.0540724 + 0.0141269i
\(197\) 9.01440 + 17.6918i 0.642249 + 1.26049i 0.950955 + 0.309328i \(0.100104\pi\)
−0.308706 + 0.951158i \(0.599896\pi\)
\(198\) 6.49296 + 0.190341i 0.461435 + 0.0135269i
\(199\) 4.66888 + 1.12090i 0.330968 + 0.0794585i 0.395524 0.918456i \(-0.370563\pi\)
−0.0645557 + 0.997914i \(0.520563\pi\)
\(200\) −2.56643 8.15826i −0.181474 0.576876i
\(201\) −2.01203 6.19240i −0.141918 0.436778i
\(202\) −9.60953 + 12.4426i −0.676124 + 0.875461i
\(203\) 15.5011 2.45514i 1.08797 0.172317i
\(204\) 2.48573 + 1.45594i 0.174036 + 0.101936i
\(205\) 5.48631 + 17.2880i 0.383181 + 1.20744i
\(206\) 1.38803 5.11616i 0.0967086 0.356460i
\(207\) 0.155123 + 0.979411i 0.0107818 + 0.0680738i
\(208\) −2.65996 22.3621i −0.184435 1.55053i
\(209\) 2.99660 0.973653i 0.207279 0.0673490i
\(210\) 14.4575 15.9561i 0.997661 1.10107i
\(211\) −1.07793 + 4.48989i −0.0742076 + 0.309097i −0.997113 0.0759294i \(-0.975808\pi\)
0.922906 + 0.385026i \(0.125808\pi\)
\(212\) −13.4908 4.08810i −0.926554 0.280772i
\(213\) −21.6784 + 11.0457i −1.48538 + 0.756839i
\(214\) 7.50790 4.30344i 0.513229 0.294177i
\(215\) −11.0574 3.59276i −0.754106 0.245024i
\(216\) 11.6663 0.808134i 0.793794 0.0549865i
\(217\) 19.6069 + 1.54309i 1.33100 + 0.104752i
\(218\) 2.16908 + 7.40767i 0.146909 + 0.501711i
\(219\) −3.36739 8.12959i −0.227547 0.549347i
\(220\) −5.04220 28.1878i −0.339945 1.90042i
\(221\) 3.31830 2.41089i 0.223213 0.162174i
\(222\) −15.9586 3.00940i −1.07107 0.201977i
\(223\) 0.321267 0.442186i 0.0215136 0.0296110i −0.798125 0.602492i \(-0.794174\pi\)
0.819638 + 0.572881i \(0.194174\pi\)
\(224\) 4.59790 14.6758i 0.307210 0.980566i
\(225\) −0.429841 + 2.71391i −0.0286561 + 0.180927i
\(226\) 4.95979 + 2.22685i 0.329920 + 0.148128i
\(227\) −6.99372 + 11.4127i −0.464189 + 0.757488i −0.995998 0.0893763i \(-0.971513\pi\)
0.531808 + 0.846865i \(0.321513\pi\)
\(228\) −2.25796 + 0.988435i −0.149537 + 0.0654607i
\(229\) −6.15178 + 0.484155i −0.406521 + 0.0319939i −0.280071 0.959979i \(-0.590358\pi\)
−0.126449 + 0.991973i \(0.540358\pi\)
\(230\) 4.08590 1.55379i 0.269416 0.102454i
\(231\) 20.6587 17.6442i 1.35924 1.16090i
\(232\) −6.38964 + 15.0258i −0.419500 + 0.986489i
\(233\) 13.6270 8.35062i 0.892733 0.547067i 0.00118778 0.999999i \(-0.499622\pi\)
0.891545 + 0.452932i \(0.149622\pi\)
\(234\) −2.43647 + 6.81261i −0.159277 + 0.445354i
\(235\) 26.9227 + 22.9942i 1.75624 + 1.49997i
\(236\) 5.92421 5.26748i 0.385633 0.342884i
\(237\) 22.6765 22.6765i 1.47300 1.47300i
\(238\) 2.74169 0.573811i 0.177717 0.0371946i
\(239\) −10.2595 + 2.46308i −0.663630 + 0.159324i −0.551248 0.834342i \(-0.685848\pi\)
−0.112382 + 0.993665i \(0.535848\pi\)
\(240\) 6.09310 + 21.5563i 0.393308 + 1.39145i
\(241\) −18.0033 9.17316i −1.15970 0.590895i −0.235148 0.971959i \(-0.575558\pi\)
−0.924548 + 0.381064i \(0.875558\pi\)
\(242\) −1.01255 20.5498i −0.0650893 1.32099i
\(243\) −8.45067 3.50038i −0.542111 0.224550i
\(244\) −1.53882 + 3.93503i −0.0985128 + 0.251915i
\(245\) 1.10815i 0.0707973i
\(246\) −4.91298 17.2156i −0.313240 1.09763i
\(247\) 3.50948i 0.223303i
\(248\) −12.1817 + 16.4401i −0.773536 + 1.04395i
\(249\) 12.1130 + 5.01739i 0.767633 + 0.317964i
\(250\) −7.90718 + 0.389612i −0.500094 + 0.0246412i
\(251\) −15.4993 7.89729i −0.978308 0.498473i −0.109696 0.993965i \(-0.534988\pi\)
−0.868612 + 0.495493i \(0.834988\pi\)
\(252\) −3.42354 + 3.56277i −0.215663 + 0.224434i
\(253\) 5.36325 1.28760i 0.337185 0.0809509i
\(254\) −2.46289 11.7678i −0.154536 0.738377i
\(255\) −2.88500 + 2.88500i −0.180666 + 0.180666i
\(256\) 10.4054 + 12.1544i 0.650335 + 0.759647i
\(257\) 4.29097 + 3.66483i 0.267663 + 0.228606i 0.773142 0.634233i \(-0.218684\pi\)
−0.505479 + 0.862839i \(0.668684\pi\)
\(258\) 10.8057 + 3.86456i 0.672733 + 0.240597i
\(259\) −13.4640 + 8.25075i −0.836613 + 0.512677i
\(260\) 31.5954 + 4.36078i 1.95947 + 0.270444i
\(261\) 3.98899 3.40692i 0.246912 0.210883i
\(262\) 1.40280 + 3.68885i 0.0866654 + 0.227898i
\(263\) −11.8015 + 0.928800i −0.727713 + 0.0572723i −0.436903 0.899509i \(-0.643925\pi\)
−0.290810 + 0.956781i \(0.593925\pi\)
\(264\) 4.15954 + 27.9570i 0.256002 + 1.72064i
\(265\) 10.4318 17.0231i 0.640820 1.04572i
\(266\) −0.981662 + 2.18643i −0.0601896 + 0.134058i
\(267\) 2.54367 16.0601i 0.155670 0.982862i
\(268\) 5.80801 3.10662i 0.354780 0.189767i
\(269\) 2.08329 2.86741i 0.127021 0.174829i −0.740770 0.671759i \(-0.765539\pi\)
0.867791 + 0.496930i \(0.165539\pi\)
\(270\) −3.06922 + 16.2759i −0.186787 + 0.990519i
\(271\) 21.9850 15.9731i 1.33550 0.970294i 0.335899 0.941898i \(-0.390960\pi\)
0.999597 0.0283965i \(-0.00904011\pi\)
\(272\) −1.00705 + 2.73464i −0.0610612 + 0.165812i
\(273\) 11.5803 + 27.9572i 0.700869 + 1.69205i
\(274\) −29.2032 + 8.55115i −1.76423 + 0.516594i
\(275\) 15.2365 + 1.19914i 0.918797 + 0.0723109i
\(276\) −4.07624 + 1.41485i −0.245361 + 0.0851639i
\(277\) 8.05122 + 2.61600i 0.483751 + 0.157180i 0.540732 0.841195i \(-0.318147\pi\)
−0.0569809 + 0.998375i \(0.518147\pi\)
\(278\) −1.54684 2.69866i −0.0927735 0.161855i
\(279\) 5.85738 2.98448i 0.350672 0.178676i
\(280\) 18.4644 + 11.5546i 1.10346 + 0.690519i
\(281\) 2.66467 11.0991i 0.158961 0.662119i −0.834797 0.550558i \(-0.814415\pi\)
0.993758 0.111561i \(-0.0355850\pi\)
\(282\) −25.8979 23.4656i −1.54220 1.39736i
\(283\) −5.11521 + 1.66203i −0.304068 + 0.0987976i −0.457077 0.889427i \(-0.651104\pi\)
0.153009 + 0.988225i \(0.451104\pi\)
\(284\) −14.8609 19.6199i −0.881830 1.16422i
\(285\) −0.546106 3.44798i −0.0323485 0.204241i
\(286\) 38.8400 + 10.5374i 2.29666 + 0.623090i
\(287\) −14.7800 9.19733i −0.872437 0.542901i
\(288\) −1.25268 4.98555i −0.0738149 0.293776i
\(289\) 16.2665 2.57635i 0.956851 0.151550i
\(290\) −18.3025 14.1351i −1.07476 0.830044i
\(291\) 6.70762 + 20.6439i 0.393208 + 1.21017i
\(292\) 7.49565 4.80136i 0.438649 0.280978i
\(293\) 5.38474 + 1.29276i 0.314580 + 0.0755240i 0.387661 0.921802i \(-0.373283\pi\)
−0.0730809 + 0.997326i \(0.523283\pi\)
\(294\) −0.0320513 + 1.09334i −0.00186927 + 0.0637652i
\(295\) 5.09720 + 10.0038i 0.296771 + 0.582445i
\(296\) 0.154092 16.4277i 0.00895642 0.954840i
\(297\) −6.45794 + 19.8755i −0.374728 + 1.15329i
\(298\) 9.56591 + 14.0121i 0.554138 + 0.811701i
\(299\) −0.482015 + 6.12458i −0.0278756 + 0.354194i
\(300\) −11.9538 + 0.238232i −0.690151 + 0.0137543i
\(301\) 10.3093 4.27026i 0.594220 0.246134i
\(302\) 4.51004 + 9.53208i 0.259524 + 0.548510i
\(303\) 12.9185 + 17.7808i 0.742148 + 1.02148i
\(304\) −1.38649 2.07241i −0.0795207 0.118861i
\(305\) −4.84133 3.51743i −0.277214 0.201408i
\(306\) 0.681158 0.642359i 0.0389392 0.0367212i
\(307\) −12.5849 1.99325i −0.718259 0.113761i −0.213402 0.976964i \(-0.568455\pi\)
−0.504856 + 0.863203i \(0.668455\pi\)
\(308\) 21.2501 + 17.4291i 1.21083 + 0.993115i
\(309\) −6.31880 3.87217i −0.359464 0.220280i
\(310\) −18.1670 22.5784i −1.03182 1.28237i
\(311\) −1.10426 14.0309i −0.0626166 0.795620i −0.945415 0.325868i \(-0.894343\pi\)
0.882799 0.469752i \(-0.155657\pi\)
\(312\) −31.0471 5.21635i −1.75770 0.295318i
\(313\) 20.7317 + 24.2736i 1.17182 + 1.37203i 0.913939 + 0.405851i \(0.133025\pi\)
0.257883 + 0.966176i \(0.416975\pi\)
\(314\) −3.44324 26.8013i −0.194313 1.51248i
\(315\) −3.65648 5.96683i −0.206019 0.336193i
\(316\) 26.6207 + 18.5420i 1.49753 + 1.04307i
\(317\) −12.3631 + 14.4753i −0.694379 + 0.813013i −0.989817 0.142349i \(-0.954534\pi\)
0.295438 + 0.955362i \(0.404534\pi\)
\(318\) −10.7848 + 16.4939i −0.604779 + 0.924934i
\(319\) −20.6326 20.6326i −1.15520 1.15520i
\(320\) −20.3805 + 9.90730i −1.13930 + 0.553835i
\(321\) −2.82419 11.7636i −0.157631 0.656581i
\(322\) −2.01345 + 3.68082i −0.112205 + 0.205124i
\(323\) 0.206177 0.404645i 0.0114720 0.0225151i
\(324\) 4.66589 21.2956i 0.259216 1.18309i
\(325\) −6.51459 + 15.7276i −0.361364 + 0.872411i
\(326\) −34.3488 3.71882i −1.90240 0.205966i
\(327\) 10.7906 0.596724
\(328\) 16.2682 7.95893i 0.898263 0.439459i
\(329\) −33.9815 −1.87346
\(330\) −39.7991 4.30890i −2.19087 0.237197i
\(331\) 4.30582 10.3952i 0.236669 0.571371i −0.760265 0.649613i \(-0.774931\pi\)
0.996934 + 0.0782425i \(0.0249309\pi\)
\(332\) −2.83866 + 12.9559i −0.155792 + 0.711050i
\(333\) −2.39623 + 4.70287i −0.131313 + 0.257716i
\(334\) −12.4145 + 22.6951i −0.679291 + 1.24182i
\(335\) 2.17775 + 9.07099i 0.118983 + 0.495601i
\(336\) −17.8834 11.9342i −0.975621 0.651066i
\(337\) 7.28737 + 7.28737i 0.396968 + 0.396968i 0.877162 0.480194i \(-0.159434\pi\)
−0.480194 + 0.877162i \(0.659434\pi\)
\(338\) −14.4697 + 22.1297i −0.787050 + 1.20369i
\(339\) 4.93613 5.77947i 0.268094 0.313898i
\(340\) −3.38679 2.35899i −0.183674 0.127934i
\(341\) −19.1055 31.1774i −1.03462 1.68835i
\(342\) 0.102080 + 0.794567i 0.00551988 + 0.0429653i
\(343\) −11.6687 13.6623i −0.630053 0.737697i
\(344\) −1.92355 + 11.4487i −0.103711 + 0.617274i
\(345\) −0.479471 6.09226i −0.0258139 0.327996i
\(346\) −3.71389 4.61571i −0.199660 0.248142i
\(347\) −12.8925 7.90055i −0.692107 0.424124i 0.131476 0.991319i \(-0.458028\pi\)
−0.823583 + 0.567196i \(0.808028\pi\)
\(348\) 17.6491 + 14.4756i 0.946091 + 0.775975i
\(349\) 18.8446 + 2.98470i 1.00873 + 0.159767i 0.638866 0.769318i \(-0.279404\pi\)
0.369865 + 0.929085i \(0.379404\pi\)
\(350\) −8.45792 + 7.97615i −0.452095 + 0.426343i
\(351\) −18.8317 13.6821i −1.00516 0.730294i
\(352\) −27.0987 + 9.12200i −1.44437 + 0.486204i
\(353\) −11.5751 15.9318i −0.616081 0.847963i 0.380979 0.924584i \(-0.375587\pi\)
−0.997060 + 0.0766208i \(0.975587\pi\)
\(354\) −4.73975 10.0176i −0.251915 0.532428i
\(355\) 32.2057 13.3400i 1.70930 0.708016i
\(356\) 16.4458 0.327755i 0.871625 0.0173710i
\(357\) 0.307237 3.90381i 0.0162607 0.206612i
\(358\) 9.50548 + 13.9236i 0.502380 + 0.735886i
\(359\) −2.00210 + 6.16183i −0.105667 + 0.325209i −0.989886 0.141862i \(-0.954691\pi\)
0.884220 + 0.467071i \(0.154691\pi\)
\(360\) 7.28024 + 0.0682888i 0.383702 + 0.00359914i
\(361\) −8.44941 16.5829i −0.444706 0.872784i
\(362\) 0.267940 9.14005i 0.0140826 0.480390i
\(363\) −27.9684 6.71462i −1.46796 0.352426i
\(364\) −25.7771 + 16.5116i −1.35109 + 0.865444i
\(365\) 3.89589 + 11.9903i 0.203920 + 0.627602i
\(366\) 4.67490 + 3.61046i 0.244361 + 0.188722i
\(367\) 4.12337 0.653077i 0.215238 0.0340903i −0.0478841 0.998853i \(-0.515248\pi\)
0.263122 + 0.964763i \(0.415248\pi\)
\(368\) −2.13500 3.80711i −0.111295 0.198459i
\(369\) −5.81853 0.0399347i −0.302900 0.00207892i
\(370\) 22.4560 + 6.09237i 1.16743 + 0.316727i
\(371\) 2.99761 + 18.9262i 0.155628 + 0.982598i
\(372\) 17.2712 + 22.8021i 0.895472 + 1.18224i
\(373\) 28.3511 9.21184i 1.46797 0.476971i 0.537473 0.843281i \(-0.319379\pi\)
0.930493 + 0.366310i \(0.119379\pi\)
\(374\) −3.85922 3.49677i −0.199556 0.180814i
\(375\) −2.58366 + 10.7617i −0.133420 + 0.555734i
\(376\) 18.7540 29.9691i 0.967162 1.54554i
\(377\) 28.9581 14.7549i 1.49142 0.759916i
\(378\) −7.90517 13.7916i −0.406598 0.709362i
\(379\) 7.77898 + 2.52754i 0.399579 + 0.129831i 0.501911 0.864919i \(-0.332630\pi\)
−0.102332 + 0.994750i \(0.532630\pi\)
\(380\) 3.33623 1.15799i 0.171145 0.0594038i
\(381\) −16.7558 1.31871i −0.858427 0.0675597i
\(382\) 4.15298 1.21606i 0.212485 0.0622189i
\(383\) 10.2389 + 24.7188i 0.523182 + 1.26307i 0.935917 + 0.352222i \(0.114574\pi\)
−0.412735 + 0.910851i \(0.635426\pi\)
\(384\) 20.3947 9.18544i 1.04076 0.468743i
\(385\) −31.4910 + 22.8796i −1.60493 + 1.16605i
\(386\) −2.30720 + 12.2350i −0.117434 + 0.622743i
\(387\) 2.19234 3.01749i 0.111443 0.153388i
\(388\) −19.3625 + 10.3567i −0.982981 + 0.525783i
\(389\) −2.79246 + 17.6309i −0.141583 + 0.893923i 0.809977 + 0.586461i \(0.199479\pi\)
−0.951561 + 0.307461i \(0.900521\pi\)
\(390\) 18.2631 40.6768i 0.924788 2.05975i
\(391\) 0.415388 0.677851i 0.0210071 0.0342804i
\(392\) −1.09446 + 0.162838i −0.0552788 + 0.00822457i
\(393\) 5.50025 0.432879i 0.277451 0.0218359i
\(394\) 9.98114 + 26.2468i 0.502843 + 1.32229i
\(395\) −34.9388 + 29.8406i −1.75796 + 1.50144i
\(396\) 9.10011 + 1.25599i 0.457298 + 0.0631160i
\(397\) 0.556106 0.340782i 0.0279102 0.0171034i −0.508473 0.861078i \(-0.669790\pi\)
0.536384 + 0.843974i \(0.319790\pi\)
\(398\) 6.39381 + 2.28669i 0.320493 + 0.114621i
\(399\) 2.54777 + 2.17600i 0.127548 + 0.108936i
\(400\) −2.36653 11.8612i −0.118326 0.593058i
\(401\) −9.35216 + 9.35216i −0.467024 + 0.467024i −0.900949 0.433925i \(-0.857128\pi\)
0.433925 + 0.900949i \(0.357128\pi\)
\(402\) −1.88629 9.01277i −0.0940796 0.449516i
\(403\) 39.6028 9.50779i 1.97276 0.473617i
\(404\) −15.4050 + 16.0315i −0.766428 + 0.797598i
\(405\) 27.5113 + 14.0177i 1.36705 + 0.696546i
\(406\) 22.1683 1.09230i 1.10019 0.0542099i
\(407\) 27.1237 + 11.2350i 1.34447 + 0.556899i
\(408\) 3.27330 + 2.42542i 0.162053 + 0.120076i
\(409\) 13.3975i 0.662465i −0.943549 0.331233i \(-0.892535\pi\)
0.943549 0.331233i \(-0.107465\pi\)
\(410\) 5.08212 + 25.1420i 0.250988 + 1.24167i
\(411\) 42.5398i 2.09833i
\(412\) 2.73036 6.98202i 0.134515 0.343979i
\(413\) −9.95566 4.12377i −0.489886 0.202917i
\(414\) 0.0690150 + 1.40066i 0.00339190 + 0.0688388i
\(415\) −16.7375 8.52817i −0.821610 0.418631i
\(416\) −0.335893 31.8460i −0.0164685 1.56138i
\(417\) −4.22835 + 1.01514i −0.207063 + 0.0497114i
\(418\) 4.36142 0.912805i 0.213324 0.0446467i
\(419\) 9.87852 9.87852i 0.482597 0.482597i −0.423363 0.905960i \(-0.639150\pi\)
0.905960 + 0.423363i \(0.139150\pi\)
\(420\) 22.7561 20.2334i 1.11038 0.987290i
\(421\) −7.93410 6.77636i −0.386684 0.330260i 0.434762 0.900545i \(-0.356832\pi\)
−0.821446 + 0.570286i \(0.806832\pi\)
\(422\) −2.19903 + 6.14869i −0.107047 + 0.299314i
\(423\) −9.68461 + 5.93474i −0.470882 + 0.288557i
\(424\) −18.3458 7.80146i −0.890949 0.378872i
\(425\) 1.67511 1.43068i 0.0812549 0.0693983i
\(426\) −32.1612 + 12.2303i −1.55821 + 0.592559i
\(427\) 5.72580 0.450630i 0.277091 0.0218075i
\(428\) 11.2112 4.90776i 0.541912 0.237226i
\(429\) 29.3960 47.9700i 1.41925 2.31601i
\(430\) −14.9997 6.73458i −0.723351 0.324770i
\(431\) 1.99028 12.5661i 0.0958684 0.605289i −0.892244 0.451554i \(-0.850870\pi\)
0.988112 0.153735i \(-0.0491302\pi\)
\(432\) 16.5259 + 0.639643i 0.795101 + 0.0307748i
\(433\) −14.8987 + 20.5062i −0.715984 + 0.985467i 0.283664 + 0.958924i \(0.408450\pi\)
−0.999648 + 0.0265431i \(0.991550\pi\)
\(434\) 27.3323 + 5.15418i 1.31199 + 0.247409i
\(435\) −26.1547 + 19.0025i −1.25402 + 0.911099i
\(436\) 1.92211 + 10.7453i 0.0920524 + 0.514609i
\(437\) 0.260311 + 0.628446i 0.0124524 + 0.0300626i
\(438\) −3.49703 11.9428i −0.167095 0.570648i
\(439\) −8.13307 0.640087i −0.388170 0.0305497i −0.117127 0.993117i \(-0.537369\pi\)
−0.271043 + 0.962567i \(0.587369\pi\)
\(440\) −2.79850 40.3996i −0.133413 1.92597i
\(441\) 0.338103 + 0.109856i 0.0161001 + 0.00523125i
\(442\) 5.03251 2.88458i 0.239372 0.137206i
\(443\) 36.7216 18.7106i 1.74470 0.888968i 0.779929 0.625868i \(-0.215255\pi\)
0.964768 0.263100i \(-0.0847450\pi\)
\(444\) −21.9797 6.66046i −1.04311 0.316091i
\(445\) −5.43857 + 22.6533i −0.257813 + 1.07387i
\(446\) 0.519011 0.572808i 0.0245759 0.0271233i
\(447\) 22.5574 7.32935i 1.06693 0.346666i
\(448\) 8.69861 19.9342i 0.410971 0.941802i
\(449\) −0.342383 2.16172i −0.0161580 0.102018i 0.978291 0.207235i \(-0.0664463\pi\)
−0.994449 + 0.105217i \(0.966446\pi\)
\(450\) −1.01747 + 3.75032i −0.0479641 + 0.176792i
\(451\) 2.31782 + 32.2818i 0.109142 + 1.52009i
\(452\) 6.63447 + 3.88593i 0.312059 + 0.182779i
\(453\) 14.5605 2.30616i 0.684113 0.108353i
\(454\) −11.5704 + 14.9816i −0.543027 + 0.703123i
\(455\) −13.3978 41.2340i −0.628096 1.93308i
\(456\) −3.32514 + 1.04603i −0.155714 + 0.0489847i
\(457\) 13.9523 + 3.34965i 0.652662 + 0.156690i 0.546237 0.837631i \(-0.316060\pi\)
0.106424 + 0.994321i \(0.466060\pi\)
\(458\) −8.72308 0.255716i −0.407603 0.0119488i
\(459\) 1.36751 + 2.68389i 0.0638299 + 0.125273i
\(460\) 5.98128 1.56266i 0.278879 0.0728593i
\(461\) 11.1103 34.1941i 0.517460 1.59258i −0.261300 0.965258i \(-0.584151\pi\)
0.778760 0.627321i \(-0.215849\pi\)
\(462\) 31.7320 21.6630i 1.47630 1.00785i
\(463\) 0.631098 8.01886i 0.0293296 0.372668i −0.964684 0.263411i \(-0.915153\pi\)
0.994013 0.109258i \(-0.0348474\pi\)
\(464\) −11.2711 + 20.1535i −0.523246 + 0.935604i
\(465\) −37.4293 + 15.5037i −1.73574 + 0.718968i
\(466\) 20.4306 9.66662i 0.946431 0.447798i
\(467\) −15.2064 20.9298i −0.703667 0.968514i −0.999910 0.0134017i \(-0.995734\pi\)
0.296244 0.955112i \(-0.404266\pi\)
\(468\) −4.46270 + 9.20762i −0.206288 + 0.425622i
\(469\) −7.24353 5.26273i −0.334475 0.243011i
\(470\) 34.3530 + 36.4280i 1.58459 + 1.68030i
\(471\) −37.3106 5.90942i −1.71918 0.272292i
\(472\) 9.13125 6.50426i 0.420300 0.299383i
\(473\) −17.6891 10.8399i −0.813346 0.498419i
\(474\) 35.3350 28.4313i 1.62299 1.30589i
\(475\) 0.147886 + 1.87907i 0.00678546 + 0.0862174i
\(476\) 3.94216 0.389430i 0.180688 0.0178495i
\(477\) 4.15969 + 4.87037i 0.190459 + 0.222999i
\(478\) −14.7997 + 1.90137i −0.676924 + 0.0869665i
\(479\) 1.60696 + 2.62232i 0.0734238 + 0.119817i 0.887245 0.461299i \(-0.152616\pi\)
−0.813821 + 0.581116i \(0.802616\pi\)
\(480\) 5.28552 + 31.2356i 0.241250 + 1.42571i
\(481\) −21.2373 + 24.8656i −0.968336 + 1.13378i
\(482\) −23.9163 15.6379i −1.08936 0.712289i
\(483\) 4.14738 + 4.14738i 0.188712 + 0.188712i
\(484\) 1.70449 29.0471i 0.0774768 1.32032i
\(485\) −7.26010 30.2405i −0.329664 1.37315i
\(486\) −11.3488 6.20791i −0.514791 0.281596i
\(487\) −5.28944 + 10.3811i −0.239687 + 0.470413i −0.979245 0.202681i \(-0.935035\pi\)
0.739558 + 0.673093i \(0.235035\pi\)
\(488\) −2.76257 + 5.29840i −0.125056 + 0.239847i
\(489\) −18.4835 + 44.6231i −0.835852 + 2.01792i
\(490\) 0.168685 1.55806i 0.00762043 0.0703859i
\(491\) 20.0584 0.905222 0.452611 0.891708i \(-0.350493\pi\)
0.452611 + 0.891708i \(0.350493\pi\)
\(492\) −4.28703 24.9530i −0.193274 1.12497i
\(493\) −4.20572 −0.189416
\(494\) −0.534220 + 4.93431i −0.0240357 + 0.222005i
\(495\) −4.97900 + 12.0204i −0.223790 + 0.540276i
\(496\) −19.6299 + 21.2604i −0.881410 + 0.954621i
\(497\) −15.1892 + 29.8104i −0.681327 + 1.33718i
\(498\) 16.2672 + 8.89831i 0.728949 + 0.398743i
\(499\) −10.3645 43.1711i −0.463977 1.93260i −0.340447 0.940264i \(-0.610578\pi\)
−0.123531 0.992341i \(-0.539422\pi\)
\(500\) −11.1768 0.655857i −0.499841 0.0293308i
\(501\) 25.5718 + 25.5718i 1.14247 + 1.14247i
\(502\) −20.5898 13.4629i −0.918970 0.600879i
\(503\) 4.45713 5.21863i 0.198734 0.232687i −0.652086 0.758145i \(-0.726106\pi\)
0.850820 + 0.525458i \(0.176106\pi\)
\(504\) −5.35582 + 4.48811i −0.238567 + 0.199916i
\(505\) −16.4532 26.8491i −0.732156 1.19477i
\(506\) 7.73672 0.993959i 0.343939 0.0441869i
\(507\) 24.0057 + 28.1071i 1.06613 + 1.24828i
\(508\) −1.67150 16.9204i −0.0741608 0.750721i
\(509\) −0.905115 11.5006i −0.0401185 0.509754i −0.983844 0.179025i \(-0.942706\pi\)
0.943726 0.330729i \(-0.107294\pi\)
\(510\) −4.49546 + 3.61714i −0.199062 + 0.160170i
\(511\) −10.3171 6.32236i −0.456404 0.279685i
\(512\) 12.7797 + 18.6729i 0.564790 + 0.825234i
\(513\) −2.54559 0.403181i −0.112390 0.0178009i
\(514\) 5.47522 + 5.80592i 0.241501 + 0.256088i
\(515\) 8.59008 + 6.24106i 0.378524 + 0.275014i
\(516\) 14.6045 + 7.07843i 0.642928 + 0.311611i
\(517\) 37.1353 + 51.1123i 1.63321 + 2.24792i
\(518\) −20.1863 + 9.55102i −0.886935 + 0.419648i
\(519\) −7.65170 + 3.16944i −0.335872 + 0.139123i
\(520\) 43.7593 + 10.9408i 1.91897 + 0.479785i
\(521\) 1.86742 23.7279i 0.0818133 1.03954i −0.809790 0.586720i \(-0.800419\pi\)
0.891603 0.452817i \(-0.149581\pi\)
\(522\) 6.12711 4.18290i 0.268177 0.183081i
\(523\) −0.794080 + 2.44393i −0.0347227 + 0.106865i −0.966916 0.255096i \(-0.917893\pi\)
0.932193 + 0.361962i \(0.117893\pi\)
\(524\) 1.41081 + 5.40006i 0.0616315 + 0.235903i
\(525\) 7.37846 + 14.4810i 0.322022 + 0.632005i
\(526\) −16.7343 0.490564i −0.729650 0.0213896i
\(527\) −5.12480 1.23036i −0.223240 0.0535952i
\(528\) 1.59262 + 39.9407i 0.0693099 + 1.73819i
\(529\) −6.73942 20.7418i −0.293018 0.901818i
\(530\) 17.2584 22.3465i 0.749655 0.970671i
\(531\) −3.55753 + 0.563457i −0.154384 + 0.0244520i
\(532\) −1.71304 + 2.92468i −0.0742696 + 0.126801i
\(533\) −34.9946 8.65589i −1.51578 0.374928i
\(534\) 6.02110 22.1933i 0.260558 0.960396i
\(535\) 2.71152 + 17.1198i 0.117229 + 0.740156i
\(536\) 8.63894 3.48380i 0.373145 0.150477i
\(537\) 22.4149 7.28305i 0.967275 0.314287i
\(538\) 3.36559 3.71445i 0.145101 0.160141i
\(539\) 0.461614 1.92276i 0.0198831 0.0828192i
\(540\) −6.79287 + 22.4166i −0.292319 + 0.964659i
\(541\) 3.81669 1.94470i 0.164092 0.0836093i −0.370015 0.929026i \(-0.620648\pi\)
0.534108 + 0.845416i \(0.320648\pi\)
\(542\) 33.3424 19.1115i 1.43218 0.820908i
\(543\) −12.1575 3.95021i −0.521728 0.169520i
\(544\) −1.83218 + 3.69160i −0.0785540 + 0.158276i
\(545\) −15.4126 1.21300i −0.660205 0.0519593i
\(546\) 12.0261 + 41.0706i 0.514670 + 1.75766i
\(547\) 7.69475 + 18.5768i 0.329004 + 0.794285i 0.998667 + 0.0516203i \(0.0164385\pi\)
−0.669663 + 0.742665i \(0.733561\pi\)
\(548\) −42.3613 + 7.57752i −1.80958 + 0.323695i
\(549\) 1.55313 1.12842i 0.0662860 0.0481596i
\(550\) 21.2400 + 4.00533i 0.905676 + 0.170788i
\(551\) 2.11516 2.91127i 0.0901088 0.124024i
\(552\) −5.94655 + 1.36878i −0.253102 + 0.0582591i
\(553\) 6.89866 43.5564i 0.293361 1.85221i
\(554\) 10.9218 + 4.90366i 0.464022 + 0.208337i
\(555\) 16.9958 27.7346i 0.721431 1.17727i
\(556\) −1.76406 4.02978i −0.0748128 0.170901i
\(557\) −13.2413 + 1.04212i −0.561053 + 0.0441559i −0.355815 0.934556i \(-0.615797\pi\)
−0.205238 + 0.978712i \(0.565797\pi\)
\(558\) 8.68976 3.30455i 0.367867 0.139893i
\(559\) 17.5714 15.0074i 0.743191 0.634745i
\(560\) 24.2020 + 19.0564i 1.02272 + 0.805280i
\(561\) −6.20756 + 3.80400i −0.262083 + 0.160605i
\(562\) 5.43605 15.1997i 0.229306 0.641162i
\(563\) −16.3853 13.9944i −0.690558 0.589792i 0.233356 0.972391i \(-0.425029\pi\)
−0.923915 + 0.382599i \(0.875029\pi\)
\(564\) −32.8404 36.9348i −1.38283 1.55524i
\(565\) −7.70013 + 7.70013i −0.323947 + 0.323947i
\(566\) −7.44497 + 1.55816i −0.312936 + 0.0654945i
\(567\) −28.8158 + 6.91807i −1.21015 + 0.290532i
\(568\) −17.9077 29.8476i −0.751392 1.25238i
\(569\) 9.76143 + 4.97370i 0.409220 + 0.208508i 0.646468 0.762941i \(-0.276245\pi\)
−0.237248 + 0.971449i \(0.576245\pi\)
\(570\) −0.242965 4.93098i −0.0101767 0.206536i
\(571\) −21.0442 8.71679i −0.880672 0.364786i −0.103915 0.994586i \(-0.533137\pi\)
−0.776757 + 0.629800i \(0.783137\pi\)
\(572\) 53.0049 + 20.7279i 2.21625 + 0.866676i
\(573\) 6.04958i 0.252725i
\(574\) −19.3806 15.1813i −0.808932 0.633654i
\(575\) 3.29957i 0.137602i
\(576\) −1.00235 7.20035i −0.0417647 0.300015i
\(577\) −37.8164 15.6641i −1.57432 0.652104i −0.586818 0.809719i \(-0.699620\pi\)
−0.987501 + 0.157615i \(0.949620\pi\)
\(578\) 23.2628 1.14623i 0.967604 0.0476769i
\(579\) 15.5086 + 7.90204i 0.644516 + 0.328398i
\(580\) −23.5816 22.6600i −0.979172 0.940906i
\(581\) 17.5311 4.20885i 0.727314 0.174613i
\(582\) 6.28843 + 30.0464i 0.260664 + 1.24546i
\(583\) 25.1915 25.1915i 1.04332 1.04332i
\(584\) 11.2697 5.60969i 0.466345 0.232131i
\(585\) −11.0197 9.41169i −0.455607 0.389126i
\(586\) 7.37415 + 2.63730i 0.304623 + 0.108946i
\(587\) −7.99125 + 4.89704i −0.329834 + 0.202123i −0.677549 0.735478i \(-0.736958\pi\)
0.347715 + 0.937600i \(0.386958\pi\)
\(588\) −0.211495 + 1.53236i −0.00872193 + 0.0631935i
\(589\) 3.42906 2.92870i 0.141292 0.120675i
\(590\) 5.64385 + 14.8413i 0.232354 + 0.611005i
\(591\) 39.1351 3.08000i 1.60980 0.126694i
\(592\) 2.71731 23.0738i 0.111681 0.948329i
\(593\) −6.44326 + 10.5145i −0.264593 + 0.431777i −0.957153 0.289584i \(-0.906483\pi\)
0.692559 + 0.721361i \(0.256483\pi\)
\(594\) −12.1053 + 26.9619i −0.496688 + 1.10626i
\(595\) −0.877674 + 5.54142i −0.0359811 + 0.227176i
\(596\) 11.3167 + 21.1572i 0.463549 + 0.866631i
\(597\) 5.57979 7.67992i 0.228365 0.314318i
\(598\) −1.61001 + 8.53777i −0.0658382 + 0.349135i
\(599\) −25.6621 + 18.6446i −1.04852 + 0.761797i −0.971931 0.235266i \(-0.924404\pi\)
−0.0765920 + 0.997063i \(0.524404\pi\)
\(600\) −16.8432 1.48468i −0.687622 0.0606117i
\(601\) 16.2201 + 39.1587i 0.661631 + 1.59732i 0.795248 + 0.606285i \(0.207341\pi\)
−0.133617 + 0.991033i \(0.542659\pi\)
\(602\) 15.1449 4.43467i 0.617261 0.180744i
\(603\) −2.98350 0.234806i −0.121497 0.00956205i
\(604\) 4.89011 + 14.0886i 0.198976 + 0.573257i
\(605\) 39.1935 + 12.7347i 1.59344 + 0.517740i
\(606\) 15.4567 + 26.9662i 0.627887 + 1.09543i
\(607\) −34.0026 + 17.3252i −1.38012 + 0.703207i −0.977258 0.212053i \(-0.931985\pi\)
−0.402864 + 0.915260i \(0.631985\pi\)
\(608\) −1.63393 3.12486i −0.0662648 0.126730i
\(609\) 7.24346 30.1712i 0.293520 1.22260i
\(610\) −6.27147 5.68246i −0.253924 0.230076i
\(611\) −66.9260 + 21.7456i −2.70754 + 0.879732i
\(612\) 1.05549 0.799468i 0.0426656 0.0323166i
\(613\) 0.878651 + 5.54758i 0.0354884 + 0.224065i 0.999058 0.0433924i \(-0.0138166\pi\)
−0.963570 + 0.267457i \(0.913817\pi\)
\(614\) −17.3909 4.71821i −0.701841 0.190412i
\(615\) 35.7283 + 3.05874i 1.44070 + 0.123340i
\(616\) 27.2244 + 27.7400i 1.09690 + 1.11768i
\(617\) −21.1341 + 3.34731i −0.850827 + 0.134758i −0.566593 0.823998i \(-0.691739\pi\)
−0.284233 + 0.958755i \(0.591739\pi\)
\(618\) −8.29478 6.40612i −0.333665 0.257692i
\(619\) 1.59079 + 4.89595i 0.0639393 + 0.196785i 0.977923 0.208966i \(-0.0670099\pi\)
−0.913984 + 0.405751i \(0.867010\pi\)
\(620\) −22.1059 34.5106i −0.887793 1.38598i
\(621\) −4.38707 1.05324i −0.176047 0.0422651i
\(622\) 0.583235 19.8955i 0.0233856 0.797737i
\(623\) −10.1512 19.9228i −0.406697 0.798189i
\(624\) −42.8581 12.0602i −1.71570 0.482796i
\(625\) 9.57202 29.4596i 0.382881 1.17839i
\(626\) 25.4537 + 37.2845i 1.01733 + 1.49019i
\(627\) 0.488745 6.21010i 0.0195186 0.248007i
\(628\) −0.761436 38.2067i −0.0303846 1.52461i
\(629\) 3.90950 1.61937i 0.155882 0.0645684i
\(630\) −4.23271 8.94594i −0.168635 0.356415i
\(631\) 11.5974 + 15.9625i 0.461687 + 0.635457i 0.974857 0.222829i \(-0.0715292\pi\)
−0.513171 + 0.858287i \(0.671529\pi\)
\(632\) 34.6061 + 30.1223i 1.37656 + 1.19820i
\(633\) 7.38549 + 5.36588i 0.293547 + 0.213274i
\(634\) −19.5859 + 18.4703i −0.777855 + 0.733548i
\(635\) 23.7847 + 3.76712i 0.943867 + 0.149494i
\(636\) −17.6741 + 21.5487i −0.700823 + 0.854463i
\(637\) 1.87793 + 1.15080i 0.0744065 + 0.0455964i
\(638\) −25.8686 32.1501i −1.02415 1.27283i
\(639\) 0.877412 + 11.1486i 0.0347099 + 0.441031i
\(640\) −30.1630 + 10.8273i −1.19230 + 0.427985i
\(641\) −1.63876 1.91874i −0.0647271 0.0757857i 0.727098 0.686534i \(-0.240869\pi\)
−0.791825 + 0.610748i \(0.790869\pi\)
\(642\) −2.18012 16.9695i −0.0860426 0.669733i
\(643\) 4.45384 + 7.26801i 0.175642 + 0.286622i 0.928331 0.371754i \(-0.121244\pi\)
−0.752689 + 0.658376i \(0.771244\pi\)
\(644\) −3.39121 + 4.86873i −0.133632 + 0.191855i
\(645\) −14.9282 + 17.4787i −0.587797 + 0.688222i
\(646\) 0.351480 0.537545i 0.0138288 0.0211494i
\(647\) 33.1653 + 33.1653i 1.30386 + 1.30386i 0.925765 + 0.378099i \(0.123422\pi\)
0.378099 + 0.925765i \(0.376578\pi\)
\(648\) 9.80190 29.2313i 0.385055 1.14832i
\(649\) 4.67698 + 19.4810i 0.183587 + 0.764696i
\(650\) −11.5536 + 21.1213i −0.453169 + 0.828446i
\(651\) 17.6528 34.6455i 0.691867 1.35786i
\(652\) −47.7282 10.4573i −1.86918 0.409539i
\(653\) 7.49515 18.0949i 0.293308 0.708108i −0.706692 0.707521i \(-0.749813\pi\)
1.00000 0.000586444i \(-0.000186671\pi\)
\(654\) 15.1716 + 1.64258i 0.593257 + 0.0642298i
\(655\) −7.90486 −0.308868
\(656\) 24.0846 8.71385i 0.940346 0.340219i
\(657\) −4.04453 −0.157792
\(658\) −47.7779 5.17274i −1.86258 0.201655i
\(659\) 14.3361 34.6103i 0.558454 1.34823i −0.352536 0.935798i \(-0.614680\pi\)
0.910990 0.412429i \(-0.135320\pi\)
\(660\) −55.3015 12.1166i −2.15261 0.471639i
\(661\) −17.8575 + 35.0473i −0.694575 + 1.36318i 0.226582 + 0.973992i \(0.427245\pi\)
−0.921158 + 0.389189i \(0.872755\pi\)
\(662\) 7.63635 13.9602i 0.296795 0.542577i
\(663\) −1.89305 7.88510i −0.0735198 0.306232i
\(664\) −5.96333 + 17.7839i −0.231422 + 0.690149i
\(665\) −3.39445 3.39445i −0.131631 0.131631i
\(666\) −4.08498 + 6.24746i −0.158290 + 0.242084i
\(667\) 4.09113 4.79010i 0.158409 0.185474i
\(668\) −20.9094 + 30.0195i −0.809011 + 1.16149i
\(669\) −0.564612 0.921362i −0.0218291 0.0356219i
\(670\) 1.68111 + 13.0853i 0.0649468 + 0.505529i
\(671\) −6.93500 8.11984i −0.267723 0.313463i
\(672\) −23.3274 19.5018i −0.899874 0.752297i
\(673\) 2.07791 + 26.4024i 0.0800977 + 1.01774i 0.897310 + 0.441401i \(0.145518\pi\)
−0.817212 + 0.576337i \(0.804482\pi\)
\(674\) 9.13672 + 11.3553i 0.351933 + 0.437391i
\(675\) −10.6595 6.53218i −0.410286 0.251424i
\(676\) −23.7130 + 28.9116i −0.912040 + 1.11199i
\(677\) −26.6632 4.22303i −1.02475 0.162304i −0.378635 0.925546i \(-0.623607\pi\)
−0.646113 + 0.763242i \(0.723607\pi\)
\(678\) 7.81995 7.37453i 0.300324 0.283217i
\(679\) 24.1482 + 17.5447i 0.926722 + 0.673303i
\(680\) −4.40272 3.83228i −0.168837 0.146961i
\(681\) 15.5546 + 21.4091i 0.596054 + 0.820398i
\(682\) −22.1164 46.7436i −0.846882 1.78990i
\(683\) 8.77240 3.63365i 0.335666 0.139038i −0.208483 0.978026i \(-0.566853\pi\)
0.544149 + 0.838988i \(0.316853\pi\)
\(684\) 0.0225740 + 1.13270i 0.000863138 + 0.0433098i
\(685\) 4.78200 60.7611i 0.182711 2.32156i
\(686\) −14.3265 20.9855i −0.546989 0.801229i
\(687\) −3.77000 + 11.6029i −0.143834 + 0.442677i
\(688\) −4.44725 + 15.8041i −0.169550 + 0.602525i
\(689\) 18.0151 + 35.3565i 0.686319 + 1.34698i
\(690\) 0.253242 8.63869i 0.00964077 0.328869i
\(691\) −4.80124 1.15268i −0.182648 0.0438499i 0.141090 0.989997i \(-0.454939\pi\)
−0.323737 + 0.946147i \(0.604939\pi\)
\(692\) −4.51911 7.05501i −0.171791 0.268191i
\(693\) −3.85882 11.8762i −0.146584 0.451141i
\(694\) −16.9242 13.0707i −0.642434 0.496156i
\(695\) 6.15361 0.974636i 0.233420 0.0369700i
\(696\) 22.6111 + 23.0393i 0.857070 + 0.873301i
\(697\) 3.52638 + 3.05391i 0.133571 + 0.115675i
\(698\) 26.0412 + 7.06505i 0.985673 + 0.267416i
\(699\) −4.94292 31.2084i −0.186958 1.18041i
\(700\) −13.1060 + 9.92697i −0.495359 + 0.375204i
\(701\) 17.9627 5.83644i 0.678442 0.220439i 0.0505289 0.998723i \(-0.483909\pi\)
0.627913 + 0.778283i \(0.283909\pi\)
\(702\) −24.3946 22.1035i −0.920717 0.834244i
\(703\) −0.845230 + 3.52064i −0.0318784 + 0.132783i
\(704\) −39.4893 + 8.70047i −1.48831 + 0.327911i
\(705\) 62.3694 31.7788i 2.34897 1.19686i
\(706\) −13.8494 24.1620i −0.521229 0.909350i
\(707\) 28.7435 + 9.33934i 1.08101 + 0.351242i
\(708\) −5.13918 14.8062i −0.193142 0.556450i
\(709\) 22.0561 + 1.73585i 0.828335 + 0.0651914i 0.485535 0.874217i \(-0.338625\pi\)
0.342800 + 0.939408i \(0.388625\pi\)
\(710\) 47.3118 13.8536i 1.77558 0.519917i
\(711\) −5.64086 13.6182i −0.211549 0.510724i
\(712\) 23.1726 + 2.04259i 0.868431 + 0.0765494i
\(713\) 6.38649 4.64006i 0.239176 0.173771i
\(714\) 1.02622 5.44198i 0.0384054 0.203661i
\(715\) −47.3798 + 65.2127i −1.77190 + 2.43882i
\(716\) 11.2452 + 21.0235i 0.420253 + 0.785686i
\(717\) −3.26320 + 20.6030i −0.121866 + 0.769434i
\(718\) −3.75291 + 8.35875i −0.140058 + 0.311946i
\(719\) −18.6415 + 30.4201i −0.695210 + 1.13448i 0.288975 + 0.957337i \(0.406686\pi\)
−0.984185 + 0.177143i \(0.943314\pi\)
\(720\) 10.2256 + 1.20423i 0.381086 + 0.0448789i
\(721\) −10.1594 + 0.799563i −0.378356 + 0.0297773i
\(722\) −9.35556 24.6017i −0.348178 0.915580i
\(723\) −30.3763 + 25.9438i −1.12971 + 0.964861i
\(724\) 1.76804 12.8101i 0.0657088 0.476084i
\(725\) 14.8832 9.12042i 0.552747 0.338724i
\(726\) −38.3014 13.6982i −1.42150 0.508386i
\(727\) −8.78570 7.50370i −0.325844 0.278297i 0.471444 0.881896i \(-0.343733\pi\)
−0.797288 + 0.603599i \(0.793733\pi\)
\(728\) −38.7560 + 19.2914i −1.43639 + 0.714988i
\(729\) 10.3359 10.3359i 0.382813 0.382813i
\(730\) 3.65242 + 17.4514i 0.135182 + 0.645905i
\(731\) −2.90766 + 0.698067i −0.107544 + 0.0258189i
\(732\) 6.02331 + 5.78792i 0.222628 + 0.213928i
\(733\) 4.65376 + 2.37121i 0.171891 + 0.0875827i 0.537819 0.843060i \(-0.319248\pi\)
−0.365928 + 0.930643i \(0.619248\pi\)
\(734\) 5.89685 0.290556i 0.217657 0.0107246i
\(735\) −2.02410 0.838410i −0.0746601 0.0309252i
\(736\) −2.42228 5.67778i −0.0892864 0.209286i
\(737\) 16.6463i 0.613175i
\(738\) −8.17476 0.941858i −0.300917 0.0346703i
\(739\) 29.2677i 1.07663i −0.842744 0.538315i \(-0.819061\pi\)
0.842744 0.538315i \(-0.180939\pi\)
\(740\) 30.6456 + 11.9842i 1.12656 + 0.440546i
\(741\) 6.41025 + 2.65521i 0.235487 + 0.0975417i
\(742\) 1.33365 + 27.0665i 0.0489598 + 0.993641i
\(743\) 38.7076 + 19.7225i 1.42004 + 0.723549i 0.984297 0.176520i \(-0.0564842\pi\)
0.435747 + 0.900069i \(0.356484\pi\)
\(744\) 20.8123 + 34.6888i 0.763016 + 1.27175i
\(745\) −33.0434 + 7.93303i −1.21062 + 0.290644i
\(746\) 41.2639 8.63615i 1.51078 0.316192i
\(747\) 4.26125 4.26125i 0.155911 0.155911i
\(748\) −4.89377 5.50391i −0.178934 0.201243i
\(749\) −12.6501 10.8042i −0.462226 0.394778i
\(750\) −5.27080 + 14.7377i −0.192462 + 0.538144i
\(751\) 7.37569 4.51983i 0.269143 0.164931i −0.381378 0.924419i \(-0.624550\pi\)
0.650521 + 0.759488i \(0.274550\pi\)
\(752\) 30.9300 39.2816i 1.12790 1.43245i
\(753\) −26.1514 + 22.3354i −0.953009 + 0.813946i
\(754\) 42.9610 16.3373i 1.56455 0.594968i
\(755\) −21.0565 + 1.65719i −0.766326 + 0.0603111i
\(756\) −9.01527 20.5942i −0.327882 0.749006i
\(757\) 27.2402 44.4520i 0.990062 1.61564i 0.222220 0.974997i \(-0.428670\pi\)
0.767843 0.640638i \(-0.221330\pi\)
\(758\) 10.5525 + 4.73785i 0.383283 + 0.172086i
\(759\) 1.70587 10.7705i 0.0619192 0.390943i
\(760\) 4.86700 1.12029i 0.176545 0.0406371i
\(761\) −13.1818 + 18.1431i −0.477839 + 0.657688i −0.978088 0.208193i \(-0.933242\pi\)
0.500249 + 0.865881i \(0.333242\pi\)
\(762\) −23.3579 4.40472i −0.846168 0.159566i
\(763\) 12.0045 8.72180i 0.434593 0.315750i
\(764\) 6.02419 1.07760i 0.217947 0.0389861i
\(765\) 0.717652 + 1.73257i 0.0259468 + 0.0626411i
\(766\) 10.6331 + 36.3132i 0.384189 + 1.31205i
\(767\) −22.2464 1.75083i −0.803271 0.0632188i
\(768\) 30.0731 9.81018i 1.08517 0.353994i
\(769\) −34.1687 11.1021i −1.23215 0.400351i −0.380660 0.924715i \(-0.624303\pi\)
−0.851494 + 0.524364i \(0.824303\pi\)
\(770\) −47.7591 + 27.3750i −1.72112 + 0.986525i
\(771\) 9.94049 5.06493i 0.357998 0.182409i
\(772\) −5.10636 + 16.8511i −0.183782 + 0.606484i
\(773\) 4.89576 20.3923i 0.176088 0.733460i −0.812518 0.582936i \(-0.801904\pi\)
0.988606 0.150524i \(-0.0480961\pi\)
\(774\) 3.54175 3.90886i 0.127306 0.140501i
\(775\) 20.8037 6.75954i 0.747292 0.242810i
\(776\) −28.8001 + 11.6141i −1.03386 + 0.416923i
\(777\) 4.88381 + 30.8351i 0.175206 + 1.10620i
\(778\) −6.61001 + 24.3639i −0.236980 + 0.873490i
\(779\) −3.88747 + 0.905126i −0.139283 + 0.0324295i
\(780\) 31.8698 54.4115i 1.14112 1.94824i
\(781\) 61.4373 9.73071i 2.19840 0.348192i
\(782\) 0.687218 0.889825i 0.0245749 0.0318201i
\(783\) 7.37560 + 22.6997i 0.263582 + 0.811223i
\(784\) −1.56360 + 0.0623481i −0.0558429 + 0.00222672i
\(785\) 52.6278 + 12.6348i 1.87837 + 0.450956i
\(786\) 7.79923 + 0.228634i 0.278189 + 0.00815510i
\(787\) −21.7189 42.6257i −0.774194 1.51944i −0.852626 0.522522i \(-0.824991\pi\)
0.0784319 0.996919i \(-0.475009\pi\)
\(788\) 10.0381 + 38.4222i 0.357593 + 1.36873i
\(789\) −7.23234 + 22.2589i −0.257478 + 0.792436i
\(790\) −53.6663 + 36.6373i −1.90936 + 1.30350i
\(791\) 0.820023 10.4194i 0.0291567 0.370471i
\(792\) 12.6035 + 3.15116i 0.447847 + 0.111972i
\(793\) 10.9885 4.55158i 0.390213 0.161631i
\(794\) 0.833759 0.394487i 0.0295890 0.0139998i
\(795\) −23.2012 31.9337i −0.822860 1.13257i
\(796\) 8.64159 + 4.18836i 0.306293 + 0.148452i
\(797\) 15.1228 + 10.9873i 0.535676 + 0.389191i 0.822477 0.568799i \(-0.192592\pi\)
−0.286801 + 0.957990i \(0.592592\pi\)
\(798\) 3.25092 + 3.44727i 0.115081 + 0.122032i
\(799\) 8.99414 + 1.42453i 0.318190 + 0.0503963i
\(800\) −1.52180 17.0370i −0.0538038 0.602349i
\(801\) −6.37247 3.90506i −0.225160 0.137978i
\(802\) −14.5727 + 11.7255i −0.514580 + 0.414042i
\(803\) 1.76507 + 22.4274i 0.0622880 + 0.791444i
\(804\) −1.28017 12.9591i −0.0451483 0.457031i
\(805\) −5.45763 6.39006i −0.192356 0.225220i
\(806\) 57.1287 7.33950i 2.01227 0.258523i
\(807\) −3.66129 5.97469i −0.128884 0.210319i
\(808\) −24.0998 + 20.1953i −0.847827 + 0.710468i
\(809\) 7.20366 8.43441i 0.253267 0.296538i −0.619177 0.785251i \(-0.712534\pi\)
0.872444 + 0.488714i \(0.162534\pi\)
\(810\) 36.5470 + 23.8967i 1.28413 + 0.839644i
\(811\) 15.4961 + 15.4961i 0.544143 + 0.544143i 0.924741 0.380598i \(-0.124282\pi\)
−0.380598 + 0.924741i \(0.624282\pi\)
\(812\) 31.3348 + 1.83873i 1.09964 + 0.0645269i
\(813\) −12.5422 52.2418i −0.439873 1.83220i
\(814\) 36.4256 + 19.9252i 1.27672 + 0.698379i
\(815\) 31.4168 61.6589i 1.10048 2.15982i
\(816\) 4.23305 + 3.90841i 0.148186 + 0.136822i
\(817\) 0.979119 2.36380i 0.0342550 0.0826990i
\(818\) 2.03940 18.8369i 0.0713061 0.658617i
\(819\) 13.9089 0.486016
\(820\) 3.31829 + 36.1231i 0.115880 + 1.26147i
\(821\) −20.7056 −0.722631 −0.361316 0.932444i \(-0.617672\pi\)
−0.361316 + 0.932444i \(0.617672\pi\)
\(822\) −6.47551 + 59.8109i −0.225859 + 2.08614i
\(823\) 2.47391 5.97256i 0.0862352 0.208190i −0.874879 0.484342i \(-0.839059\pi\)
0.961114 + 0.276151i \(0.0890591\pi\)
\(824\) 4.90170 9.40107i 0.170759 0.327502i
\(825\) 13.7180 26.9231i 0.477600 0.937342i
\(826\) −13.3699 7.31348i −0.465198 0.254469i
\(827\) 2.44994 + 10.2048i 0.0851929 + 0.354854i 0.998642 0.0520992i \(-0.0165912\pi\)
−0.913449 + 0.406953i \(0.866591\pi\)
\(828\) −0.116177 + 1.97983i −0.00403743 + 0.0688040i
\(829\) 15.3889 + 15.3889i 0.534478 + 0.534478i 0.921902 0.387424i \(-0.126635\pi\)
−0.387424 + 0.921902i \(0.626635\pi\)
\(830\) −22.2347 14.5384i −0.771776 0.504635i
\(831\) 10.8697 12.7268i 0.377065 0.441487i
\(832\) 4.37540 44.8265i 0.151690 1.55408i
\(833\) −0.148919 0.243014i −0.00515975 0.00841995i
\(834\) −6.09957 + 0.783630i −0.211211 + 0.0271349i
\(835\) −33.6505 39.3997i −1.16453 1.36348i
\(836\) 6.27109 0.619496i 0.216890 0.0214257i
\(837\) 2.34673 + 29.8180i 0.0811149 + 1.03066i
\(838\) 15.3929 12.3854i 0.531739 0.427848i
\(839\) 9.05214 + 5.54716i 0.312514 + 0.191509i 0.669907 0.742445i \(-0.266334\pi\)
−0.357392 + 0.933954i \(0.616334\pi\)
\(840\) 35.0749 24.9842i 1.21020 0.862035i
\(841\) −4.27185 0.676594i −0.147305 0.0233308i
\(842\) −10.1238 10.7353i −0.348890 0.369963i
\(843\) −18.2571 13.2646i −0.628809 0.456857i
\(844\) −4.02779 + 8.31030i −0.138642 + 0.286052i
\(845\) −31.1286 42.8449i −1.07086 1.47391i
\(846\) −14.5199 + 6.87001i −0.499206 + 0.236196i
\(847\) −36.5420 + 15.1362i −1.25560 + 0.520085i
\(848\) −24.6065 13.7615i −0.844992 0.472571i
\(849\) −0.834292 + 10.6007i −0.0286328 + 0.363814i
\(850\) 2.57299 1.75655i 0.0882527 0.0602490i
\(851\) −1.95860 + 6.02796i −0.0671401 + 0.206636i
\(852\) −47.0803 + 12.3001i −1.61294 + 0.421395i
\(853\) 8.84839 + 17.3659i 0.302963 + 0.594599i 0.991425 0.130673i \(-0.0417139\pi\)
−0.688462 + 0.725272i \(0.741714\pi\)
\(854\) 8.11905 + 0.238009i 0.277828 + 0.00814451i
\(855\) −1.56024 0.374579i −0.0533589 0.0128103i
\(856\) 16.5099 5.19371i 0.564298 0.177517i
\(857\) 6.41597 + 19.7463i 0.219165 + 0.674522i 0.998832 + 0.0483265i \(0.0153888\pi\)
−0.779666 + 0.626195i \(0.784611\pi\)
\(858\) 48.6329 62.9709i 1.66030 2.14979i
\(859\) 19.1389 3.03130i 0.653009 0.103426i 0.178865 0.983874i \(-0.442758\pi\)
0.474144 + 0.880447i \(0.342758\pi\)
\(860\) −20.0644 11.7521i −0.684191 0.400743i
\(861\) −27.9817 + 20.0380i −0.953615 + 0.682892i
\(862\) 4.71117 17.3650i 0.160463 0.591453i
\(863\) −5.66701 35.7801i −0.192907 1.21797i −0.874057 0.485824i \(-0.838520\pi\)
0.681150 0.732144i \(-0.261480\pi\)
\(864\) 23.1379 + 3.41494i 0.787169 + 0.116179i
\(865\) 11.2855 3.66687i 0.383717 0.124677i
\(866\) −24.0690 + 26.5638i −0.817897 + 0.902675i
\(867\) 7.60109 31.6608i 0.258147 1.07526i
\(868\) 37.6445 + 11.4074i 1.27774 + 0.387191i
\(869\) −73.0530 + 37.2224i −2.47815 + 1.26268i
\(870\) −39.6660 + 22.7361i −1.34480 + 0.770826i
\(871\) −17.6338 5.72955i −0.597497 0.194139i
\(872\) 1.06680 + 15.4005i 0.0361265 + 0.521527i
\(873\) 9.94625 + 0.782787i 0.336630 + 0.0264933i
\(874\) 0.270333 + 0.923218i 0.00914414 + 0.0312283i
\(875\) 5.82413 + 14.0607i 0.196891 + 0.475338i
\(876\) −3.09886 17.3238i −0.104701 0.585318i
\(877\) 24.2703 17.6334i 0.819551 0.595439i −0.0970325 0.995281i \(-0.530935\pi\)
0.916584 + 0.399842i \(0.130935\pi\)
\(878\) −11.3376 2.13799i −0.382627 0.0721538i
\(879\) 6.43531 8.85745i 0.217058 0.298754i
\(880\) 2.21503 57.2277i 0.0746687 1.92914i
\(881\) −0.466405 + 2.94477i −0.0157136 + 0.0992117i −0.994299 0.106631i \(-0.965994\pi\)
0.978585 + 0.205843i \(0.0659936\pi\)
\(882\) 0.458649 + 0.205924i 0.0154435 + 0.00693384i
\(883\) −12.3771 + 20.1977i −0.416524 + 0.679705i −0.990244 0.139346i \(-0.955500\pi\)
0.573720 + 0.819052i \(0.305500\pi\)
\(884\) 7.51480 3.28965i 0.252750 0.110643i
\(885\) 22.1290 1.74159i 0.743858 0.0585429i
\(886\) 54.4787 20.7172i 1.83025 0.696008i
\(887\) 14.0083 11.9642i 0.470354 0.401720i −0.382430 0.923985i \(-0.624913\pi\)
0.852784 + 0.522265i \(0.174913\pi\)
\(888\) −29.8895 12.7104i −1.00303 0.426533i
\(889\) −19.7067 + 12.0763i −0.660940 + 0.405025i
\(890\) −11.0949 + 31.0226i −0.371903 + 1.03988i
\(891\) 41.8958 + 35.7824i 1.40356 + 1.19876i
\(892\) 0.816922 0.726362i 0.0273526 0.0243204i
\(893\) −5.50946 + 5.50946i −0.184367 + 0.184367i
\(894\) 32.8313 6.87130i 1.09804 0.229811i
\(895\) −32.8347 + 7.88292i −1.09754 + 0.263497i
\(896\) 15.2646 26.7033i 0.509956 0.892094i
\(897\) 10.8222 + 5.51418i 0.361343 + 0.184113i
\(898\) −0.152327 3.09149i −0.00508323 0.103164i
\(899\) −38.5826 15.9815i −1.28680 0.533011i
\(900\) −2.00145 + 5.11805i −0.0667148 + 0.170602i
\(901\) 5.13500i 0.171071i
\(902\) −1.65516 + 45.7410i −0.0551109 + 1.52301i
\(903\) 22.0614i 0.734156i
\(904\) 8.73652 + 6.47352i 0.290572 + 0.215306i
\(905\) 16.9209 + 7.00887i 0.562470 + 0.232983i
\(906\) 20.8231 1.02602i 0.691801 0.0340872i
\(907\) 36.7094 + 18.7044i 1.21891 + 0.621068i 0.940631 0.339431i \(-0.110234\pi\)
0.278284 + 0.960499i \(0.410234\pi\)
\(908\) −18.5485 + 19.3029i −0.615554 + 0.640588i
\(909\) 9.82288 2.35827i 0.325804 0.0782187i
\(910\) −12.5605 60.0144i −0.416375 1.98946i
\(911\) 0.623160 0.623160i 0.0206462 0.0206462i −0.696708 0.717355i \(-0.745353\pi\)
0.717355 + 0.696708i \(0.245353\pi\)
\(912\) −4.83437 + 0.964549i −0.160082 + 0.0319394i
\(913\) −25.4888 21.7695i −0.843556 0.720464i
\(914\) 19.1070 + 6.83346i 0.632004 + 0.226031i
\(915\) −10.0877 + 6.18173i −0.333488 + 0.204362i
\(916\) −12.2257 1.68738i −0.403949 0.0557527i
\(917\) 5.76912 4.92729i 0.190513 0.162713i
\(918\) 1.51417 + 3.98171i 0.0499750 + 0.131416i
\(919\) −3.04641 + 0.239758i −0.100492 + 0.00790888i −0.128605 0.991696i \(-0.541050\pi\)
0.0281135 + 0.999605i \(0.491050\pi\)
\(920\) 8.64754 1.28661i 0.285101 0.0424183i
\(921\) −13.1623 + 21.4790i −0.433714 + 0.707756i
\(922\) 20.8262 46.3856i 0.685875 1.52763i
\(923\) −10.8384 + 68.4309i −0.356750 + 2.25243i
\(924\) 47.9127 25.6278i 1.57621 0.843094i
\(925\) −10.3232 + 14.2086i −0.339424 + 0.467177i
\(926\) 2.10797 11.1784i 0.0692723 0.367346i
\(927\) −2.75575 + 2.00217i −0.0905108 + 0.0657600i
\(928\) −18.9149 + 26.6201i −0.620912 + 0.873847i
\(929\) 15.7525 + 38.0299i 0.516822 + 1.24772i 0.939845 + 0.341601i \(0.110969\pi\)
−0.423023 + 0.906119i \(0.639031\pi\)
\(930\) −54.9855 + 16.1006i −1.80305 + 0.527961i
\(931\) 0.243114 + 0.0191335i 0.00796773 + 0.000627074i
\(932\) 30.1969 10.4812i 0.989132 0.343325i
\(933\) −26.4637 8.59857i −0.866382 0.281505i
\(934\) −18.1941 31.7419i −0.595330 1.03863i
\(935\) 9.29409 4.73558i 0.303949 0.154870i
\(936\) −7.67615 + 12.2666i −0.250903 + 0.400945i
\(937\) 11.4057 47.5082i 0.372608 1.55203i −0.399620 0.916681i \(-0.630858\pi\)
0.772229 0.635345i \(-0.219142\pi\)
\(938\) −9.38328 8.50202i −0.306375 0.277601i
\(939\) 60.0224 19.5025i 1.95876 0.636439i
\(940\) 42.7551 + 56.4469i 1.39452 + 1.84110i
\(941\) 2.87736 + 18.1670i 0.0937994 + 0.592226i 0.989155 + 0.146874i \(0.0469213\pi\)
−0.895356 + 0.445352i \(0.853079\pi\)
\(942\) −51.5591 13.9881i −1.67989 0.455758i
\(943\) −6.90855 + 1.04565i −0.224973 + 0.0340512i
\(944\) 13.8286 7.75499i 0.450083 0.252404i
\(945\) 31.4481 4.98090i 1.02301 0.162029i
\(946\) −23.2208 17.9335i −0.754972 0.583070i
\(947\) 3.53461 + 10.8784i 0.114859 + 0.353501i 0.991918 0.126883i \(-0.0404974\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(948\) 54.0088 34.5955i 1.75412 1.12361i
\(949\) −24.3653 5.84958i −0.790930 0.189885i
\(950\) −0.0781088 + 2.66447i −0.00253418 + 0.0864469i
\(951\) 17.0862 + 33.5336i 0.554058 + 1.08740i
\(952\) 5.60194 + 0.0525463i 0.181560 + 0.00170304i
\(953\) −3.25321 + 10.0123i −0.105382 + 0.324332i −0.989820 0.142326i \(-0.954542\pi\)
0.884438 + 0.466658i \(0.154542\pi\)
\(954\) 5.10714 + 7.48093i 0.165350 + 0.242204i
\(955\) −0.680047 + 8.64082i −0.0220058 + 0.279610i
\(956\) −21.0978 + 0.420467i −0.682352 + 0.0135989i
\(957\) −53.2968 + 22.0763i −1.72284 + 0.713625i
\(958\) 1.86020 + 3.93158i 0.0601004 + 0.127024i
\(959\) 34.3839 + 47.3253i 1.11031 + 1.52821i
\(960\) 2.67667 + 44.7218i 0.0863892 + 1.44339i
\(961\) −17.2594 12.5397i −0.556754 0.404505i
\(962\) −33.6446 + 31.7282i −1.08475 + 1.02296i
\(963\) −5.49216 0.869872i −0.176982 0.0280312i
\(964\) −31.2458 25.6275i −1.00636 0.825406i
\(965\) −21.2632 13.0301i −0.684487 0.419454i
\(966\) 5.19988 + 6.46253i 0.167303 + 0.207928i
\(967\) 2.25579 + 28.6626i 0.0725414 + 0.921726i 0.920267 + 0.391291i \(0.127971\pi\)
−0.847726 + 0.530435i \(0.822029\pi\)
\(968\) 6.81812 40.5807i 0.219143 1.30431i
\(969\) −0.583117 0.682742i −0.0187324 0.0219328i
\(970\) −5.60440 43.6232i −0.179946 1.40066i
\(971\) −7.73945 12.6296i −0.248371 0.405304i 0.704022 0.710178i \(-0.251386\pi\)
−0.952393 + 0.304874i \(0.901386\pi\)
\(972\) −15.0114 10.4558i −0.481490 0.335371i
\(973\) −3.88351 + 4.54700i −0.124499 + 0.145770i
\(974\) −9.01717 + 13.7906i −0.288929 + 0.441880i
\(975\) 23.7985 + 23.7985i 0.762162 + 0.762162i
\(976\) −4.69071 + 7.02902i −0.150146 + 0.224993i
\(977\) −2.35266 9.79953i −0.0752682 0.313515i 0.922017 0.387149i \(-0.126540\pi\)
−0.997285 + 0.0736345i \(0.976540\pi\)
\(978\) −32.7803 + 59.9263i −1.04820 + 1.91623i
\(979\) −18.8730 + 37.0403i −0.603183 + 1.18381i
\(980\) 0.474343 2.16495i 0.0151523 0.0691568i
\(981\) 1.89802 4.58223i 0.0605991 0.146299i
\(982\) 28.2020 + 3.05333i 0.899963 + 0.0974357i
\(983\) −43.4797 −1.38679 −0.693394 0.720559i \(-0.743885\pi\)
−0.693394 + 0.720559i \(0.743885\pi\)
\(984\) −2.22915 35.7364i −0.0710627 1.13924i
\(985\) −56.2443 −1.79209
\(986\) −5.91323 0.640204i −0.188316 0.0203883i
\(987\) −25.7099 + 62.0691i −0.818354 + 1.97568i
\(988\) −1.50223 + 6.85631i −0.0477921 + 0.218128i
\(989\) 2.03338 3.99072i 0.0646576 0.126898i
\(990\) −8.83023 + 16.1427i −0.280643 + 0.513049i
\(991\) 6.96145 + 28.9965i 0.221138 + 0.921105i 0.966953 + 0.254953i \(0.0820600\pi\)
−0.745816 + 0.666152i \(0.767940\pi\)
\(992\) −30.8359 + 26.9040i −0.979042 + 0.854202i
\(993\) −15.7296 15.7296i −0.499165 0.499165i
\(994\) −25.8937 + 39.6012i −0.821299 + 1.25607i
\(995\) −8.83312 + 10.3423i −0.280029 + 0.327872i
\(996\) 21.5171 + 14.9872i 0.681794 + 0.474888i
\(997\) 1.80751 + 2.94958i 0.0572443 + 0.0934142i 0.879982 0.475007i \(-0.157554\pi\)
−0.822738 + 0.568421i \(0.807554\pi\)
\(998\) −8.00081 62.2762i −0.253261 1.97132i
\(999\) −15.5964 18.2610i −0.493448 0.577753i
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 164.2.o.b.11.18 yes 288
4.3 odd 2 inner 164.2.o.b.11.17 288
41.15 odd 40 inner 164.2.o.b.15.17 yes 288
164.15 even 40 inner 164.2.o.b.15.18 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
164.2.o.b.11.17 288 4.3 odd 2 inner
164.2.o.b.11.18 yes 288 1.1 even 1 trivial
164.2.o.b.15.17 yes 288 41.15 odd 40 inner
164.2.o.b.15.18 yes 288 164.15 even 40 inner