Properties

Label 418.2.f.c.115.1
Level $418$
Weight $2$
Character 418.115
Analytic conductor $3.338$
Analytic rank $0$
Dimension $4$
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] = [418,2,Mod(115,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.f (of order \(5\), degree \(4\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 115.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 418.115
Dual form 418.2.f.c.229.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 + 2.48990i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.30902 + 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.618034 - 1.90211i) q^{9} +O(q^{10})\) \(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 + 2.48990i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.30902 + 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.618034 - 1.90211i) q^{9} -2.61803 q^{10} +(-3.30902 + 0.224514i) q^{11} -1.00000 q^{12} +(1.50000 + 4.61653i) q^{13} +(-1.30902 - 0.951057i) q^{14} +(-2.11803 + 1.53884i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.0729490 - 0.224514i) q^{17} +(1.61803 - 1.17557i) q^{18} +(0.809017 + 0.587785i) q^{19} +(-0.809017 - 2.48990i) q^{20} -1.61803 q^{21} +(-1.23607 - 3.07768i) q^{22} -1.00000 q^{23} +(-0.309017 - 0.951057i) q^{24} +(-1.50000 - 1.08981i) q^{25} +(-3.92705 + 2.85317i) q^{26} +(1.54508 - 4.75528i) q^{27} +(0.500000 - 1.53884i) q^{28} +(7.23607 - 5.25731i) q^{29} +(-2.11803 - 1.53884i) q^{30} +(2.69098 + 8.28199i) q^{31} +1.00000 q^{32} +(-2.80902 - 1.76336i) q^{33} +0.236068 q^{34} +(-1.30902 - 4.02874i) q^{35} +(1.61803 + 1.17557i) q^{36} +(-7.59017 + 5.51458i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(-1.50000 + 4.61653i) q^{39} +(2.11803 - 1.53884i) q^{40} +(4.92705 + 3.57971i) q^{41} +(-0.500000 - 1.53884i) q^{42} -7.70820 q^{43} +(2.54508 - 2.12663i) q^{44} +5.23607 q^{45} +(-0.309017 - 0.951057i) q^{46} +(7.04508 + 5.11855i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-1.35410 + 4.16750i) q^{49} +(0.572949 - 1.76336i) q^{50} +(0.190983 - 0.138757i) q^{51} +(-3.92705 - 2.85317i) q^{52} +(1.39919 + 4.30625i) q^{53} +5.00000 q^{54} +(2.11803 - 8.42075i) q^{55} +1.61803 q^{56} +(0.309017 + 0.951057i) q^{57} +(7.23607 + 5.25731i) q^{58} +(4.73607 - 3.44095i) q^{59} +(0.809017 - 2.48990i) q^{60} +(4.50000 - 13.8496i) q^{61} +(-7.04508 + 5.11855i) q^{62} +(2.61803 + 1.90211i) q^{63} +(0.309017 + 0.951057i) q^{64} -12.7082 q^{65} +(0.809017 - 3.21644i) q^{66} -5.61803 q^{67} +(0.0729490 + 0.224514i) q^{68} +(-0.809017 - 0.587785i) q^{69} +(3.42705 - 2.48990i) q^{70} +(3.01722 - 9.28605i) q^{71} +(-0.618034 + 1.90211i) q^{72} +(-0.309017 + 0.224514i) q^{73} +(-7.59017 - 5.51458i) q^{74} +(-0.572949 - 1.76336i) q^{75} -1.00000 q^{76} +(4.11803 - 3.44095i) q^{77} -4.85410 q^{78} +(4.63525 + 14.2658i) q^{79} +(2.11803 + 1.53884i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.88197 + 5.79210i) q^{82} +(2.71885 - 8.36775i) q^{83} +(1.30902 - 0.951057i) q^{84} +(0.500000 + 0.363271i) q^{85} +(-2.38197 - 7.33094i) q^{86} +8.94427 q^{87} +(2.80902 + 1.76336i) q^{88} +18.4164 q^{89} +(1.61803 + 4.97980i) q^{90} +(-6.35410 - 4.61653i) q^{91} +(0.809017 - 0.587785i) q^{92} +(-2.69098 + 8.28199i) q^{93} +(-2.69098 + 8.28199i) q^{94} +(-2.11803 + 1.53884i) q^{95} +(0.809017 + 0.587785i) q^{96} +(2.83688 + 8.73102i) q^{97} -4.38197 q^{98} +(2.47214 + 6.15537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - 3 q^{7} - q^{8} + 2 q^{9} - 6 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} - 4 q^{15} - q^{16} + 7 q^{17} + 2 q^{18} + q^{19} - q^{20} - 2 q^{21} + 4 q^{22} - 4 q^{23} + q^{24} - 6 q^{25} - 9 q^{26} - 5 q^{27} + 2 q^{28} + 20 q^{29} - 4 q^{30} + 13 q^{31} + 4 q^{32} - 9 q^{33} - 8 q^{34} - 3 q^{35} + 2 q^{36} - 8 q^{37} + q^{38} - 6 q^{39} + 4 q^{40} + 13 q^{41} - 2 q^{42} - 4 q^{43} - q^{44} + 12 q^{45} + q^{46} + 17 q^{47} + q^{48} + 8 q^{49} + 9 q^{50} + 3 q^{51} - 9 q^{52} - 19 q^{53} + 20 q^{54} + 4 q^{55} + 2 q^{56} - q^{57} + 20 q^{58} + 10 q^{59} + q^{60} + 18 q^{61} - 17 q^{62} + 6 q^{63} - q^{64} - 24 q^{65} + q^{66} - 18 q^{67} + 7 q^{68} - q^{69} + 7 q^{70} - 17 q^{71} + 2 q^{72} + q^{73} - 8 q^{74} - 9 q^{75} - 4 q^{76} + 12 q^{77} - 6 q^{78} - 15 q^{79} + 4 q^{80} - q^{81} - 12 q^{82} + 31 q^{83} + 3 q^{84} + 2 q^{85} - 14 q^{86} + 9 q^{88} + 20 q^{89} + 2 q^{90} - 12 q^{91} + q^{92} - 13 q^{93} - 13 q^{94} - 4 q^{95} + q^{96} + 27 q^{97} - 22 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 + 0.951057i 0.218508 + 0.672499i
\(3\) 0.809017 + 0.587785i 0.467086 + 0.339358i 0.796305 0.604896i \(-0.206785\pi\)
−0.329218 + 0.944254i \(0.606785\pi\)
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) −0.809017 + 2.48990i −0.361803 + 1.11352i 0.590155 + 0.807290i \(0.299067\pi\)
−0.951959 + 0.306227i \(0.900933\pi\)
\(6\) −0.309017 + 0.951057i −0.126156 + 0.388267i
\(7\) −1.30902 + 0.951057i −0.494762 + 0.359466i −0.807013 0.590534i \(-0.798917\pi\)
0.312251 + 0.950000i \(0.398917\pi\)
\(8\) −0.809017 0.587785i −0.286031 0.207813i
\(9\) −0.618034 1.90211i −0.206011 0.634038i
\(10\) −2.61803 −0.827895
\(11\) −3.30902 + 0.224514i −0.997706 + 0.0676935i
\(12\) −1.00000 −0.288675
\(13\) 1.50000 + 4.61653i 0.416025 + 1.28039i 0.911331 + 0.411675i \(0.135056\pi\)
−0.495306 + 0.868719i \(0.664944\pi\)
\(14\) −1.30902 0.951057i −0.349850 0.254181i
\(15\) −2.11803 + 1.53884i −0.546874 + 0.397327i
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 0.0729490 0.224514i 0.0176927 0.0544526i −0.941820 0.336117i \(-0.890886\pi\)
0.959513 + 0.281664i \(0.0908864\pi\)
\(18\) 1.61803 1.17557i 0.381374 0.277085i
\(19\) 0.809017 + 0.587785i 0.185601 + 0.134847i
\(20\) −0.809017 2.48990i −0.180902 0.556758i
\(21\) −1.61803 −0.353084
\(22\) −1.23607 3.07768i −0.263531 0.656164i
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) −0.309017 0.951057i −0.0630778 0.194134i
\(25\) −1.50000 1.08981i −0.300000 0.217963i
\(26\) −3.92705 + 2.85317i −0.770158 + 0.559553i
\(27\) 1.54508 4.75528i 0.297352 0.915155i
\(28\) 0.500000 1.53884i 0.0944911 0.290814i
\(29\) 7.23607 5.25731i 1.34370 0.976258i 0.344405 0.938821i \(-0.388081\pi\)
0.999299 0.0374370i \(-0.0119194\pi\)
\(30\) −2.11803 1.53884i −0.386698 0.280953i
\(31\) 2.69098 + 8.28199i 0.483315 + 1.48749i 0.834407 + 0.551149i \(0.185810\pi\)
−0.351092 + 0.936341i \(0.614190\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.80902 1.76336i −0.488987 0.306961i
\(34\) 0.236068 0.0404853
\(35\) −1.30902 4.02874i −0.221264 0.680981i
\(36\) 1.61803 + 1.17557i 0.269672 + 0.195928i
\(37\) −7.59017 + 5.51458i −1.24782 + 0.906592i −0.998093 0.0617257i \(-0.980340\pi\)
−0.249723 + 0.968317i \(0.580340\pi\)
\(38\) −0.309017 + 0.951057i −0.0501292 + 0.154282i
\(39\) −1.50000 + 4.61653i −0.240192 + 0.739236i
\(40\) 2.11803 1.53884i 0.334891 0.243312i
\(41\) 4.92705 + 3.57971i 0.769476 + 0.559057i 0.901802 0.432149i \(-0.142245\pi\)
−0.132326 + 0.991206i \(0.542245\pi\)
\(42\) −0.500000 1.53884i −0.0771517 0.237448i
\(43\) −7.70820 −1.17549 −0.587745 0.809046i \(-0.699984\pi\)
−0.587745 + 0.809046i \(0.699984\pi\)
\(44\) 2.54508 2.12663i 0.383686 0.320601i
\(45\) 5.23607 0.780547
\(46\) −0.309017 0.951057i −0.0455621 0.140226i
\(47\) 7.04508 + 5.11855i 1.02763 + 0.746618i 0.967833 0.251593i \(-0.0809543\pi\)
0.0597980 + 0.998210i \(0.480954\pi\)
\(48\) 0.809017 0.587785i 0.116772 0.0848395i
\(49\) −1.35410 + 4.16750i −0.193443 + 0.595357i
\(50\) 0.572949 1.76336i 0.0810272 0.249376i
\(51\) 0.190983 0.138757i 0.0267430 0.0194299i
\(52\) −3.92705 2.85317i −0.544584 0.395663i
\(53\) 1.39919 + 4.30625i 0.192193 + 0.591510i 0.999998 + 0.00205944i \(0.000655539\pi\)
−0.807805 + 0.589450i \(0.799344\pi\)
\(54\) 5.00000 0.680414
\(55\) 2.11803 8.42075i 0.285596 1.13545i
\(56\) 1.61803 0.216219
\(57\) 0.309017 + 0.951057i 0.0409303 + 0.125971i
\(58\) 7.23607 + 5.25731i 0.950142 + 0.690319i
\(59\) 4.73607 3.44095i 0.616584 0.447974i −0.235143 0.971961i \(-0.575556\pi\)
0.851726 + 0.523987i \(0.175556\pi\)
\(60\) 0.809017 2.48990i 0.104444 0.321444i
\(61\) 4.50000 13.8496i 0.576166 1.77326i −0.0560084 0.998430i \(-0.517837\pi\)
0.632174 0.774826i \(-0.282163\pi\)
\(62\) −7.04508 + 5.11855i −0.894727 + 0.650057i
\(63\) 2.61803 + 1.90211i 0.329841 + 0.239644i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) −12.7082 −1.57626
\(66\) 0.809017 3.21644i 0.0995831 0.395916i
\(67\) −5.61803 −0.686352 −0.343176 0.939271i \(-0.611503\pi\)
−0.343176 + 0.939271i \(0.611503\pi\)
\(68\) 0.0729490 + 0.224514i 0.00884637 + 0.0272263i
\(69\) −0.809017 0.587785i −0.0973942 0.0707610i
\(70\) 3.42705 2.48990i 0.409611 0.297600i
\(71\) 3.01722 9.28605i 0.358078 1.10205i −0.596125 0.802892i \(-0.703294\pi\)
0.954203 0.299160i \(-0.0967063\pi\)
\(72\) −0.618034 + 1.90211i −0.0728360 + 0.224166i
\(73\) −0.309017 + 0.224514i −0.0361677 + 0.0262774i −0.605722 0.795676i \(-0.707116\pi\)
0.569555 + 0.821954i \(0.307116\pi\)
\(74\) −7.59017 5.51458i −0.882339 0.641057i
\(75\) −0.572949 1.76336i −0.0661585 0.203615i
\(76\) −1.00000 −0.114708
\(77\) 4.11803 3.44095i 0.469294 0.392133i
\(78\) −4.85410 −0.549619
\(79\) 4.63525 + 14.2658i 0.521507 + 1.60503i 0.771122 + 0.636688i \(0.219696\pi\)
−0.249615 + 0.968345i \(0.580304\pi\)
\(80\) 2.11803 + 1.53884i 0.236803 + 0.172048i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −1.88197 + 5.79210i −0.207828 + 0.639630i
\(83\) 2.71885 8.36775i 0.298432 0.918480i −0.683615 0.729843i \(-0.739593\pi\)
0.982047 0.188637i \(-0.0604069\pi\)
\(84\) 1.30902 0.951057i 0.142825 0.103769i
\(85\) 0.500000 + 0.363271i 0.0542326 + 0.0394023i
\(86\) −2.38197 7.33094i −0.256854 0.790515i
\(87\) 8.94427 0.958927
\(88\) 2.80902 + 1.76336i 0.299442 + 0.187974i
\(89\) 18.4164 1.95214 0.976068 0.217467i \(-0.0697795\pi\)
0.976068 + 0.217467i \(0.0697795\pi\)
\(90\) 1.61803 + 4.97980i 0.170556 + 0.524917i
\(91\) −6.35410 4.61653i −0.666091 0.483943i
\(92\) 0.809017 0.587785i 0.0843459 0.0612808i
\(93\) −2.69098 + 8.28199i −0.279042 + 0.858803i
\(94\) −2.69098 + 8.28199i −0.277554 + 0.854222i
\(95\) −2.11803 + 1.53884i −0.217306 + 0.157882i
\(96\) 0.809017 + 0.587785i 0.0825700 + 0.0599906i
\(97\) 2.83688 + 8.73102i 0.288042 + 0.886501i 0.985470 + 0.169847i \(0.0543273\pi\)
−0.697429 + 0.716654i \(0.745673\pi\)
\(98\) −4.38197 −0.442645
\(99\) 2.47214 + 6.15537i 0.248459 + 0.618638i
\(100\) 1.85410 0.185410
\(101\) −2.83688 8.73102i −0.282280 0.868769i −0.987201 0.159483i \(-0.949017\pi\)
0.704920 0.709286i \(-0.250983\pi\)
\(102\) 0.190983 + 0.138757i 0.0189101 + 0.0137390i
\(103\) −7.54508 + 5.48183i −0.743439 + 0.540140i −0.893786 0.448493i \(-0.851961\pi\)
0.150347 + 0.988633i \(0.451961\pi\)
\(104\) 1.50000 4.61653i 0.147087 0.452688i
\(105\) 1.30902 4.02874i 0.127747 0.393165i
\(106\) −3.66312 + 2.66141i −0.355794 + 0.258499i
\(107\) −4.66312 3.38795i −0.450801 0.327526i 0.339111 0.940746i \(-0.389874\pi\)
−0.789912 + 0.613220i \(0.789874\pi\)
\(108\) 1.54508 + 4.75528i 0.148676 + 0.457577i
\(109\) 13.0902 1.25381 0.626905 0.779095i \(-0.284321\pi\)
0.626905 + 0.779095i \(0.284321\pi\)
\(110\) 8.66312 0.587785i 0.825996 0.0560431i
\(111\) −9.38197 −0.890497
\(112\) 0.500000 + 1.53884i 0.0472456 + 0.145407i
\(113\) 5.80902 + 4.22050i 0.546466 + 0.397031i 0.826481 0.562965i \(-0.190339\pi\)
−0.280015 + 0.959996i \(0.590339\pi\)
\(114\) −0.809017 + 0.587785i −0.0757714 + 0.0550511i
\(115\) 0.809017 2.48990i 0.0754412 0.232184i
\(116\) −2.76393 + 8.50651i −0.256625 + 0.789809i
\(117\) 7.85410 5.70634i 0.726112 0.527551i
\(118\) 4.73607 + 3.44095i 0.435990 + 0.316766i
\(119\) 0.118034 + 0.363271i 0.0108202 + 0.0333010i
\(120\) 2.61803 0.238993
\(121\) 10.8992 1.48584i 0.990835 0.135076i
\(122\) 14.5623 1.31841
\(123\) 1.88197 + 5.79210i 0.169691 + 0.522256i
\(124\) −7.04508 5.11855i −0.632667 0.459660i
\(125\) −6.66312 + 4.84104i −0.595967 + 0.432996i
\(126\) −1.00000 + 3.07768i −0.0890871 + 0.274182i
\(127\) 4.54508 13.9883i 0.403311 1.24126i −0.518986 0.854783i \(-0.673690\pi\)
0.922297 0.386481i \(-0.126310\pi\)
\(128\) −0.809017 + 0.587785i −0.0715077 + 0.0519534i
\(129\) −6.23607 4.53077i −0.549055 0.398912i
\(130\) −3.92705 12.0862i −0.344425 1.06003i
\(131\) −10.7639 −0.940449 −0.470225 0.882547i \(-0.655827\pi\)
−0.470225 + 0.882547i \(0.655827\pi\)
\(132\) 3.30902 0.224514i 0.288013 0.0195414i
\(133\) −1.61803 −0.140301
\(134\) −1.73607 5.34307i −0.149973 0.461571i
\(135\) 10.5902 + 7.69421i 0.911457 + 0.662212i
\(136\) −0.190983 + 0.138757i −0.0163767 + 0.0118983i
\(137\) −0.781153 + 2.40414i −0.0667384 + 0.205400i −0.978864 0.204510i \(-0.934440\pi\)
0.912126 + 0.409910i \(0.134440\pi\)
\(138\) 0.309017 0.951057i 0.0263053 0.0809593i
\(139\) 2.07295 1.50609i 0.175825 0.127745i −0.496392 0.868099i \(-0.665342\pi\)
0.672217 + 0.740354i \(0.265342\pi\)
\(140\) 3.42705 + 2.48990i 0.289639 + 0.210435i
\(141\) 2.69098 + 8.28199i 0.226622 + 0.697470i
\(142\) 9.76393 0.819371
\(143\) −6.00000 14.9394i −0.501745 1.24929i
\(144\) −2.00000 −0.166667
\(145\) 7.23607 + 22.2703i 0.600923 + 1.84945i
\(146\) −0.309017 0.224514i −0.0255744 0.0185809i
\(147\) −3.54508 + 2.57565i −0.292394 + 0.212436i
\(148\) 2.89919 8.92278i 0.238312 0.733448i
\(149\) 1.21885 3.75123i 0.0998518 0.307312i −0.888636 0.458613i \(-0.848346\pi\)
0.988488 + 0.151301i \(0.0483463\pi\)
\(150\) 1.50000 1.08981i 0.122474 0.0889829i
\(151\) −7.47214 5.42882i −0.608074 0.441791i 0.240662 0.970609i \(-0.422636\pi\)
−0.848736 + 0.528818i \(0.822636\pi\)
\(152\) −0.309017 0.951057i −0.0250646 0.0771409i
\(153\) −0.472136 −0.0381699
\(154\) 4.54508 + 2.85317i 0.366253 + 0.229915i
\(155\) −22.7984 −1.83121
\(156\) −1.50000 4.61653i −0.120096 0.369618i
\(157\) −4.23607 3.07768i −0.338075 0.245626i 0.405774 0.913973i \(-0.367002\pi\)
−0.743849 + 0.668347i \(0.767002\pi\)
\(158\) −12.1353 + 8.81678i −0.965429 + 0.701425i
\(159\) −1.39919 + 4.30625i −0.110963 + 0.341508i
\(160\) −0.809017 + 2.48990i −0.0639584 + 0.196844i
\(161\) 1.30902 0.951057i 0.103165 0.0749538i
\(162\) −0.809017 0.587785i −0.0635624 0.0461808i
\(163\) −3.50000 10.7719i −0.274141 0.843720i −0.989445 0.144907i \(-0.953712\pi\)
0.715304 0.698813i \(-0.246288\pi\)
\(164\) −6.09017 −0.475562
\(165\) 6.66312 5.56758i 0.518723 0.433436i
\(166\) 8.79837 0.682886
\(167\) −0.881966 2.71441i −0.0682486 0.210048i 0.911116 0.412151i \(-0.135222\pi\)
−0.979364 + 0.202103i \(0.935222\pi\)
\(168\) 1.30902 + 0.951057i 0.100993 + 0.0733756i
\(169\) −8.54508 + 6.20837i −0.657314 + 0.477567i
\(170\) −0.190983 + 0.587785i −0.0146477 + 0.0450811i
\(171\) 0.618034 1.90211i 0.0472622 0.145458i
\(172\) 6.23607 4.53077i 0.475496 0.345468i
\(173\) −6.59017 4.78804i −0.501041 0.364028i 0.308373 0.951265i \(-0.400215\pi\)
−0.809415 + 0.587238i \(0.800215\pi\)
\(174\) 2.76393 + 8.50651i 0.209533 + 0.644877i
\(175\) 3.00000 0.226779
\(176\) −0.809017 + 3.21644i −0.0609820 + 0.242448i
\(177\) 5.85410 0.440021
\(178\) 5.69098 + 17.5150i 0.426557 + 1.31281i
\(179\) −9.47214 6.88191i −0.707981 0.514378i 0.174541 0.984650i \(-0.444156\pi\)
−0.882522 + 0.470272i \(0.844156\pi\)
\(180\) −4.23607 + 3.07768i −0.315738 + 0.229397i
\(181\) −3.36475 + 10.3556i −0.250100 + 0.769727i 0.744656 + 0.667448i \(0.232613\pi\)
−0.994756 + 0.102279i \(0.967387\pi\)
\(182\) 2.42705 7.46969i 0.179905 0.553691i
\(183\) 11.7812 8.55951i 0.870888 0.632737i
\(184\) 0.809017 + 0.587785i 0.0596415 + 0.0433321i
\(185\) −7.59017 23.3601i −0.558040 1.71747i
\(186\) −8.70820 −0.638516
\(187\) −0.190983 + 0.759299i −0.0139661 + 0.0555254i
\(188\) −8.70820 −0.635111
\(189\) 2.50000 + 7.69421i 0.181848 + 0.559671i
\(190\) −2.11803 1.53884i −0.153658 0.111639i
\(191\) −7.04508 + 5.11855i −0.509764 + 0.370366i −0.812734 0.582635i \(-0.802022\pi\)
0.302970 + 0.953000i \(0.402022\pi\)
\(192\) −0.309017 + 0.951057i −0.0223014 + 0.0686366i
\(193\) −0.0450850 + 0.138757i −0.00324529 + 0.00998797i −0.952666 0.304019i \(-0.901671\pi\)
0.949421 + 0.314007i \(0.101671\pi\)
\(194\) −7.42705 + 5.39607i −0.533231 + 0.387415i
\(195\) −10.2812 7.46969i −0.736249 0.534916i
\(196\) −1.35410 4.16750i −0.0967216 0.297678i
\(197\) 23.0000 1.63868 0.819341 0.573306i \(-0.194340\pi\)
0.819341 + 0.573306i \(0.194340\pi\)
\(198\) −5.09017 + 4.25325i −0.361743 + 0.302266i
\(199\) −3.41641 −0.242183 −0.121091 0.992641i \(-0.538639\pi\)
−0.121091 + 0.992641i \(0.538639\pi\)
\(200\) 0.572949 + 1.76336i 0.0405136 + 0.124688i
\(201\) −4.54508 3.30220i −0.320586 0.232919i
\(202\) 7.42705 5.39607i 0.522565 0.379666i
\(203\) −4.47214 + 13.7638i −0.313882 + 0.966031i
\(204\) −0.0729490 + 0.224514i −0.00510745 + 0.0157191i
\(205\) −12.8992 + 9.37181i −0.900918 + 0.654555i
\(206\) −7.54508 5.48183i −0.525691 0.381937i
\(207\) 0.618034 + 1.90211i 0.0429563 + 0.132206i
\(208\) 4.85410 0.336571
\(209\) −2.80902 1.76336i −0.194304 0.121974i
\(210\) 4.23607 0.292316
\(211\) −5.92705 18.2416i −0.408035 1.25580i −0.918334 0.395806i \(-0.870465\pi\)
0.510299 0.859997i \(-0.329535\pi\)
\(212\) −3.66312 2.66141i −0.251584 0.182787i
\(213\) 7.89919 5.73910i 0.541243 0.393236i
\(214\) 1.78115 5.48183i 0.121757 0.374730i
\(215\) 6.23607 19.1926i 0.425296 1.30893i
\(216\) −4.04508 + 2.93893i −0.275233 + 0.199969i
\(217\) −11.3992 8.28199i −0.773827 0.562218i
\(218\) 4.04508 + 12.4495i 0.273968 + 0.843186i
\(219\) −0.381966 −0.0258109
\(220\) 3.23607 + 8.05748i 0.218176 + 0.543235i
\(221\) 1.14590 0.0770814
\(222\) −2.89919 8.92278i −0.194581 0.598858i
\(223\) −10.4721 7.60845i −0.701266 0.509500i 0.179078 0.983835i \(-0.442688\pi\)
−0.880344 + 0.474335i \(0.842688\pi\)
\(224\) −1.30902 + 0.951057i −0.0874624 + 0.0635451i
\(225\) −1.14590 + 3.52671i −0.0763932 + 0.235114i
\(226\) −2.21885 + 6.82891i −0.147596 + 0.454252i
\(227\) −13.8713 + 10.0781i −0.920672 + 0.668907i −0.943691 0.330828i \(-0.892672\pi\)
0.0230192 + 0.999735i \(0.492672\pi\)
\(228\) −0.809017 0.587785i −0.0535785 0.0389270i
\(229\) 5.42705 + 16.7027i 0.358630 + 1.10375i 0.953875 + 0.300204i \(0.0970549\pi\)
−0.595245 + 0.803544i \(0.702945\pi\)
\(230\) 2.61803 0.172628
\(231\) 5.35410 0.363271i 0.352274 0.0239015i
\(232\) −8.94427 −0.587220
\(233\) 0.218847 + 0.673542i 0.0143371 + 0.0441252i 0.957969 0.286871i \(-0.0926152\pi\)
−0.943632 + 0.330996i \(0.892615\pi\)
\(234\) 7.85410 + 5.70634i 0.513439 + 0.373035i
\(235\) −18.4443 + 13.4005i −1.20317 + 0.874155i
\(236\) −1.80902 + 5.56758i −0.117757 + 0.362419i
\(237\) −4.63525 + 14.2658i −0.301092 + 0.926666i
\(238\) −0.309017 + 0.224514i −0.0200306 + 0.0145531i
\(239\) −4.30902 3.13068i −0.278727 0.202507i 0.439635 0.898177i \(-0.355108\pi\)
−0.718362 + 0.695669i \(0.755108\pi\)
\(240\) 0.809017 + 2.48990i 0.0522218 + 0.160722i
\(241\) −6.09017 −0.392302 −0.196151 0.980574i \(-0.562844\pi\)
−0.196151 + 0.980574i \(0.562844\pi\)
\(242\) 4.78115 + 9.90659i 0.307344 + 0.636820i
\(243\) −16.0000 −1.02640
\(244\) 4.50000 + 13.8496i 0.288083 + 0.886628i
\(245\) −9.28115 6.74315i −0.592951 0.430804i
\(246\) −4.92705 + 3.57971i −0.314137 + 0.228234i
\(247\) −1.50000 + 4.61653i −0.0954427 + 0.293742i
\(248\) 2.69098 8.28199i 0.170878 0.525907i
\(249\) 7.11803 5.17155i 0.451087 0.327734i
\(250\) −6.66312 4.84104i −0.421413 0.306174i
\(251\) 4.76393 + 14.6619i 0.300697 + 0.925449i 0.981248 + 0.192749i \(0.0617403\pi\)
−0.680551 + 0.732700i \(0.738260\pi\)
\(252\) −3.23607 −0.203853
\(253\) 3.30902 0.224514i 0.208036 0.0141151i
\(254\) 14.7082 0.922875
\(255\) 0.190983 + 0.587785i 0.0119598 + 0.0368085i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −13.9721 + 10.1514i −0.871558 + 0.633224i −0.931005 0.365008i \(-0.881066\pi\)
0.0594466 + 0.998231i \(0.481066\pi\)
\(258\) 2.38197 7.33094i 0.148295 0.456404i
\(259\) 4.69098 14.4374i 0.291484 0.897094i
\(260\) 10.2812 7.46969i 0.637610 0.463251i
\(261\) −14.4721 10.5146i −0.895803 0.650839i
\(262\) −3.32624 10.2371i −0.205496 0.632451i
\(263\) −12.3820 −0.763505 −0.381752 0.924265i \(-0.624679\pi\)
−0.381752 + 0.924265i \(0.624679\pi\)
\(264\) 1.23607 + 3.07768i 0.0760747 + 0.189418i
\(265\) −11.8541 −0.728192
\(266\) −0.500000 1.53884i −0.0306570 0.0943524i
\(267\) 14.8992 + 10.8249i 0.911815 + 0.662473i
\(268\) 4.54508 3.30220i 0.277635 0.201714i
\(269\) 6.01722 18.5191i 0.366876 1.12913i −0.581921 0.813245i \(-0.697699\pi\)
0.948798 0.315884i \(-0.102301\pi\)
\(270\) −4.04508 + 12.4495i −0.246176 + 0.757652i
\(271\) 11.4721 8.33499i 0.696883 0.506315i −0.182033 0.983292i \(-0.558268\pi\)
0.878915 + 0.476978i \(0.158268\pi\)
\(272\) −0.190983 0.138757i −0.0115800 0.00841340i
\(273\) −2.42705 7.46969i −0.146892 0.452086i
\(274\) −2.52786 −0.152714
\(275\) 5.20820 + 3.26944i 0.314067 + 0.197155i
\(276\) 1.00000 0.0601929
\(277\) 5.29837 + 16.3067i 0.318348 + 0.979776i 0.974354 + 0.225020i \(0.0722447\pi\)
−0.656006 + 0.754756i \(0.727755\pi\)
\(278\) 2.07295 + 1.50609i 0.124327 + 0.0903290i
\(279\) 14.0902 10.2371i 0.843556 0.612880i
\(280\) −1.30902 + 4.02874i −0.0782287 + 0.240763i
\(281\) 6.53444 20.1109i 0.389812 1.19972i −0.543117 0.839657i \(-0.682756\pi\)
0.932929 0.360061i \(-0.117244\pi\)
\(282\) −7.04508 + 5.11855i −0.419529 + 0.304805i
\(283\) 13.8992 + 10.0984i 0.826221 + 0.600285i 0.918488 0.395450i \(-0.129411\pi\)
−0.0922667 + 0.995734i \(0.529411\pi\)
\(284\) 3.01722 + 9.28605i 0.179039 + 0.551026i
\(285\) −2.61803 −0.155079
\(286\) 12.3541 10.3229i 0.730513 0.610404i
\(287\) −9.85410 −0.581669
\(288\) −0.618034 1.90211i −0.0364180 0.112083i
\(289\) 13.7082 + 9.95959i 0.806365 + 0.585858i
\(290\) −18.9443 + 13.7638i −1.11245 + 0.808239i
\(291\) −2.83688 + 8.73102i −0.166301 + 0.511822i
\(292\) 0.118034 0.363271i 0.00690742 0.0212588i
\(293\) 19.7533 14.3516i 1.15400 0.838430i 0.164992 0.986295i \(-0.447240\pi\)
0.989008 + 0.147865i \(0.0472402\pi\)
\(294\) −3.54508 2.57565i −0.206754 0.150215i
\(295\) 4.73607 + 14.5761i 0.275745 + 0.848654i
\(296\) 9.38197 0.545316
\(297\) −4.04508 + 16.0822i −0.234720 + 0.933184i
\(298\) 3.94427 0.228486
\(299\) −1.50000 4.61653i −0.0867472 0.266981i
\(300\) 1.50000 + 1.08981i 0.0866025 + 0.0629204i
\(301\) 10.0902 7.33094i 0.581588 0.422548i
\(302\) 2.85410 8.78402i 0.164235 0.505464i
\(303\) 2.83688 8.73102i 0.162975 0.501584i
\(304\) 0.809017 0.587785i 0.0464003 0.0337118i
\(305\) 30.8435 + 22.4091i 1.76609 + 1.28314i
\(306\) −0.145898 0.449028i −0.00834044 0.0256692i
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) −1.30902 + 5.20431i −0.0745882 + 0.296543i
\(309\) −9.32624 −0.530551
\(310\) −7.04508 21.6825i −0.400134 1.23149i
\(311\) −1.61803 1.17557i −0.0917503 0.0666605i 0.540964 0.841046i \(-0.318059\pi\)
−0.632715 + 0.774385i \(0.718059\pi\)
\(312\) 3.92705 2.85317i 0.222325 0.161529i
\(313\) −6.16312 + 18.9681i −0.348360 + 1.07214i 0.611400 + 0.791322i \(0.290607\pi\)
−0.959760 + 0.280821i \(0.909393\pi\)
\(314\) 1.61803 4.97980i 0.0913109 0.281026i
\(315\) −6.85410 + 4.97980i −0.386185 + 0.280580i
\(316\) −12.1353 8.81678i −0.682661 0.495983i
\(317\) −5.25329 16.1680i −0.295054 0.908083i −0.983203 0.182514i \(-0.941577\pi\)
0.688149 0.725569i \(-0.258423\pi\)
\(318\) −4.52786 −0.253910
\(319\) −22.7639 + 19.0211i −1.27454 + 1.06498i
\(320\) −2.61803 −0.146353
\(321\) −1.78115 5.48183i −0.0994143 0.305966i
\(322\) 1.30902 + 0.951057i 0.0729487 + 0.0530003i
\(323\) 0.190983 0.138757i 0.0106266 0.00772066i
\(324\) 0.309017 0.951057i 0.0171676 0.0528365i
\(325\) 2.78115 8.55951i 0.154271 0.474796i
\(326\) 9.16312 6.65740i 0.507498 0.368719i
\(327\) 10.5902 + 7.69421i 0.585638 + 0.425491i
\(328\) −1.88197 5.79210i −0.103914 0.319815i
\(329\) −14.0902 −0.776816
\(330\) 7.35410 + 4.61653i 0.404830 + 0.254131i
\(331\) −24.1803 −1.32907 −0.664536 0.747256i \(-0.731371\pi\)
−0.664536 + 0.747256i \(0.731371\pi\)
\(332\) 2.71885 + 8.36775i 0.149216 + 0.459240i
\(333\) 15.1803 + 11.0292i 0.831878 + 0.604394i
\(334\) 2.30902 1.67760i 0.126344 0.0917941i
\(335\) 4.54508 13.9883i 0.248325 0.764264i
\(336\) −0.500000 + 1.53884i −0.0272772 + 0.0839507i
\(337\) 5.66312 4.11450i 0.308490 0.224131i −0.422758 0.906242i \(-0.638938\pi\)
0.731248 + 0.682111i \(0.238938\pi\)
\(338\) −8.54508 6.20837i −0.464791 0.337691i
\(339\) 2.21885 + 6.82891i 0.120511 + 0.370895i
\(340\) −0.618034 −0.0335176
\(341\) −10.7639 26.8011i −0.582900 1.45136i
\(342\) 2.00000 0.108148
\(343\) −5.69098 17.5150i −0.307284 0.945724i
\(344\) 6.23607 + 4.53077i 0.336226 + 0.244283i
\(345\) 2.11803 1.53884i 0.114031 0.0828485i
\(346\) 2.51722 7.74721i 0.135327 0.416493i
\(347\) −3.90983 + 12.0332i −0.209891 + 0.645977i 0.789586 + 0.613639i \(0.210295\pi\)
−0.999477 + 0.0323376i \(0.989705\pi\)
\(348\) −7.23607 + 5.25731i −0.387894 + 0.281821i
\(349\) 12.9271 + 9.39205i 0.691969 + 0.502745i 0.877307 0.479930i \(-0.159338\pi\)
−0.185338 + 0.982675i \(0.559338\pi\)
\(350\) 0.927051 + 2.85317i 0.0495530 + 0.152508i
\(351\) 24.2705 1.29546
\(352\) −3.30902 + 0.224514i −0.176371 + 0.0119666i
\(353\) −26.0000 −1.38384 −0.691920 0.721974i \(-0.743235\pi\)
−0.691920 + 0.721974i \(0.743235\pi\)
\(354\) 1.80902 + 5.56758i 0.0961482 + 0.295914i
\(355\) 20.6803 + 15.0251i 1.09760 + 0.797452i
\(356\) −14.8992 + 10.8249i −0.789655 + 0.573718i
\(357\) −0.118034 + 0.363271i −0.00624702 + 0.0192264i
\(358\) 3.61803 11.1352i 0.191219 0.588512i
\(359\) −21.4443 + 15.5802i −1.13179 + 0.822290i −0.985954 0.167019i \(-0.946586\pi\)
−0.145832 + 0.989309i \(0.546586\pi\)
\(360\) −4.23607 3.07768i −0.223260 0.162208i
\(361\) 0.309017 + 0.951057i 0.0162641 + 0.0500556i
\(362\) −10.8885 −0.572289
\(363\) 9.69098 + 5.20431i 0.508645 + 0.273155i
\(364\) 7.85410 0.411667
\(365\) −0.309017 0.951057i −0.0161747 0.0497806i
\(366\) 11.7812 + 8.55951i 0.615811 + 0.447413i
\(367\) 11.2533 8.17599i 0.587417 0.426783i −0.253973 0.967211i \(-0.581738\pi\)
0.841390 + 0.540428i \(0.181738\pi\)
\(368\) −0.309017 + 0.951057i −0.0161086 + 0.0495772i
\(369\) 3.76393 11.5842i 0.195942 0.603049i
\(370\) 19.8713 14.4374i 1.03306 0.750563i
\(371\) −5.92705 4.30625i −0.307717 0.223570i
\(372\) −2.69098 8.28199i −0.139521 0.429401i
\(373\) 21.2361 1.09956 0.549781 0.835309i \(-0.314711\pi\)
0.549781 + 0.835309i \(0.314711\pi\)
\(374\) −0.781153 + 0.0530006i −0.0403925 + 0.00274059i
\(375\) −8.23607 −0.425309
\(376\) −2.69098 8.28199i −0.138777 0.427111i
\(377\) 35.1246 + 25.5195i 1.80901 + 1.31432i
\(378\) −6.54508 + 4.75528i −0.336643 + 0.244585i
\(379\) 7.86475 24.2052i 0.403985 1.24334i −0.517755 0.855529i \(-0.673232\pi\)
0.921740 0.387809i \(-0.126768\pi\)
\(380\) 0.809017 2.48990i 0.0415017 0.127729i
\(381\) 11.8992 8.64527i 0.609614 0.442910i
\(382\) −7.04508 5.11855i −0.360458 0.261888i
\(383\) 4.42705 + 13.6251i 0.226212 + 0.696208i 0.998166 + 0.0605305i \(0.0192792\pi\)
−0.771955 + 0.635678i \(0.780721\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 5.23607 + 13.0373i 0.266855 + 0.664441i
\(386\) −0.145898 −0.00742601
\(387\) 4.76393 + 14.6619i 0.242164 + 0.745305i
\(388\) −7.42705 5.39607i −0.377051 0.273944i
\(389\) 21.1803 15.3884i 1.07389 0.780224i 0.0972792 0.995257i \(-0.468986\pi\)
0.976607 + 0.215033i \(0.0689860\pi\)
\(390\) 3.92705 12.0862i 0.198854 0.612010i
\(391\) −0.0729490 + 0.224514i −0.00368919 + 0.0113542i
\(392\) 3.54508 2.57565i 0.179054 0.130090i
\(393\) −8.70820 6.32688i −0.439271 0.319149i
\(394\) 7.10739 + 21.8743i 0.358065 + 1.10201i
\(395\) −39.2705 −1.97591
\(396\) −5.61803 3.52671i −0.282317 0.177224i
\(397\) −10.8197 −0.543023 −0.271512 0.962435i \(-0.587524\pi\)
−0.271512 + 0.962435i \(0.587524\pi\)
\(398\) −1.05573 3.24920i −0.0529189 0.162868i
\(399\) −1.30902 0.951057i −0.0655328 0.0476124i
\(400\) −1.50000 + 1.08981i −0.0750000 + 0.0544907i
\(401\) 5.12868 15.7844i 0.256114 0.788238i −0.737494 0.675353i \(-0.763991\pi\)
0.993608 0.112884i \(-0.0360089\pi\)
\(402\) 1.73607 5.34307i 0.0865872 0.266488i
\(403\) −34.1976 + 24.8460i −1.70350 + 1.23767i
\(404\) 7.42705 + 5.39607i 0.369510 + 0.268464i
\(405\) −0.809017 2.48990i −0.0402004 0.123724i
\(406\) −14.4721 −0.718240
\(407\) 23.8779 19.9519i 1.18358 0.988981i
\(408\) −0.236068 −0.0116871
\(409\) 1.01722 + 3.13068i 0.0502983 + 0.154802i 0.973051 0.230591i \(-0.0740659\pi\)
−0.922752 + 0.385393i \(0.874066\pi\)
\(410\) −12.8992 9.37181i −0.637045 0.462841i
\(411\) −2.04508 + 1.48584i −0.100877 + 0.0732911i
\(412\) 2.88197 8.86978i 0.141984 0.436983i
\(413\) −2.92705 + 9.00854i −0.144031 + 0.443281i
\(414\) −1.61803 + 1.17557i −0.0795220 + 0.0577761i
\(415\) 18.6353 + 13.5393i 0.914769 + 0.664618i
\(416\) 1.50000 + 4.61653i 0.0735436 + 0.226344i
\(417\) 2.56231 0.125477
\(418\) 0.809017 3.21644i 0.0395703 0.157321i
\(419\) 25.5279 1.24712 0.623559 0.781776i \(-0.285686\pi\)
0.623559 + 0.781776i \(0.285686\pi\)
\(420\) 1.30902 + 4.02874i 0.0638735 + 0.196582i
\(421\) −20.1353 14.6291i −0.981332 0.712980i −0.0233263 0.999728i \(-0.507426\pi\)
−0.958006 + 0.286748i \(0.907426\pi\)
\(422\) 15.5172 11.2739i 0.755366 0.548806i
\(423\) 5.38197 16.5640i 0.261680 0.805369i
\(424\) 1.39919 4.30625i 0.0679505 0.209130i
\(425\) −0.354102 + 0.257270i −0.0171765 + 0.0124794i
\(426\) 7.89919 + 5.73910i 0.382717 + 0.278060i
\(427\) 7.28115 + 22.4091i 0.352360 + 1.08445i
\(428\) 5.76393 0.278610
\(429\) 3.92705 15.6129i 0.189600 0.753799i
\(430\) 20.1803 0.973182
\(431\) 11.5344 + 35.4994i 0.555595 + 1.70994i 0.694368 + 0.719620i \(0.255684\pi\)
−0.138774 + 0.990324i \(0.544316\pi\)
\(432\) −4.04508 2.93893i −0.194619 0.141399i
\(433\) 19.3262 14.0413i 0.928760 0.674783i −0.0169291 0.999857i \(-0.505389\pi\)
0.945689 + 0.325073i \(0.105389\pi\)
\(434\) 4.35410 13.4005i 0.209004 0.643247i
\(435\) −7.23607 + 22.2703i −0.346943 + 1.06778i
\(436\) −10.5902 + 7.69421i −0.507177 + 0.368486i
\(437\) −0.809017 0.587785i −0.0387005 0.0281176i
\(438\) −0.118034 0.363271i −0.00563988 0.0173578i
\(439\) 10.8541 0.518038 0.259019 0.965872i \(-0.416601\pi\)
0.259019 + 0.965872i \(0.416601\pi\)
\(440\) −6.66312 + 5.56758i −0.317652 + 0.265424i
\(441\) 8.76393 0.417330
\(442\) 0.354102 + 1.08981i 0.0168429 + 0.0518372i
\(443\) 8.73607 + 6.34712i 0.415063 + 0.301561i 0.775648 0.631165i \(-0.217423\pi\)
−0.360585 + 0.932726i \(0.617423\pi\)
\(444\) 7.59017 5.51458i 0.360214 0.261710i
\(445\) −14.8992 + 45.8550i −0.706289 + 2.17373i
\(446\) 4.00000 12.3107i 0.189405 0.582930i
\(447\) 3.19098 2.31838i 0.150928 0.109656i
\(448\) −1.30902 0.951057i −0.0618452 0.0449332i
\(449\) 3.98278 + 12.2577i 0.187959 + 0.578478i 0.999987 0.00514051i \(-0.00163628\pi\)
−0.812028 + 0.583619i \(0.801636\pi\)
\(450\) −3.70820 −0.174806
\(451\) −17.1074 10.7391i −0.805556 0.505686i
\(452\) −7.18034 −0.337735
\(453\) −2.85410 8.78402i −0.134097 0.412709i
\(454\) −13.8713 10.0781i −0.651013 0.472989i
\(455\) 16.6353 12.0862i 0.779873 0.566611i
\(456\) 0.309017 0.951057i 0.0144710 0.0445373i
\(457\) 0.600813 1.84911i 0.0281048 0.0864978i −0.936020 0.351946i \(-0.885520\pi\)
0.964125 + 0.265448i \(0.0855200\pi\)
\(458\) −14.2082 + 10.3229i −0.663906 + 0.482356i
\(459\) −0.954915 0.693786i −0.0445716 0.0323832i
\(460\) 0.809017 + 2.48990i 0.0377206 + 0.116092i
\(461\) −20.2361 −0.942488 −0.471244 0.882003i \(-0.656195\pi\)
−0.471244 + 0.882003i \(0.656195\pi\)
\(462\) 2.00000 + 4.97980i 0.0930484 + 0.231681i
\(463\) 29.8541 1.38744 0.693719 0.720246i \(-0.255971\pi\)
0.693719 + 0.720246i \(0.255971\pi\)
\(464\) −2.76393 8.50651i −0.128312 0.394905i
\(465\) −18.4443 13.4005i −0.855333 0.621436i
\(466\) −0.572949 + 0.416272i −0.0265414 + 0.0192834i
\(467\) −0.718847 + 2.21238i −0.0332643 + 0.102377i −0.966310 0.257381i \(-0.917141\pi\)
0.933046 + 0.359758i \(0.117141\pi\)
\(468\) −3.00000 + 9.23305i −0.138675 + 0.426798i
\(469\) 7.35410 5.34307i 0.339581 0.246720i
\(470\) −18.4443 13.4005i −0.850771 0.618121i
\(471\) −1.61803 4.97980i −0.0745551 0.229457i
\(472\) −5.85410 −0.269457
\(473\) 25.5066 1.73060i 1.17279 0.0795731i
\(474\) −15.0000 −0.688973
\(475\) −0.572949 1.76336i −0.0262887 0.0809083i
\(476\) −0.309017 0.224514i −0.0141638 0.0102906i
\(477\) 7.32624 5.32282i 0.335445 0.243715i
\(478\) 1.64590 5.06555i 0.0752816 0.231693i
\(479\) 5.69098 17.5150i 0.260028 0.800283i −0.732770 0.680477i \(-0.761773\pi\)
0.992797 0.119806i \(-0.0382273\pi\)
\(480\) −2.11803 + 1.53884i −0.0966746 + 0.0702382i
\(481\) −36.8435 26.7683i −1.67992 1.22053i
\(482\) −1.88197 5.79210i −0.0857212 0.263823i
\(483\) 1.61803 0.0736231
\(484\) −7.94427 + 7.60845i −0.361103 + 0.345839i
\(485\) −24.0344 −1.09135
\(486\) −4.94427 15.2169i −0.224277 0.690253i
\(487\) 30.9894 + 22.5151i 1.40426 + 1.02026i 0.994126 + 0.108232i \(0.0345188\pi\)
0.410136 + 0.912024i \(0.365481\pi\)
\(488\) −11.7812 + 8.55951i −0.533308 + 0.387471i
\(489\) 3.50000 10.7719i 0.158275 0.487122i
\(490\) 3.54508 10.9106i 0.160151 0.492893i
\(491\) 5.78115 4.20025i 0.260900 0.189555i −0.449644 0.893208i \(-0.648449\pi\)
0.710544 + 0.703653i \(0.248449\pi\)
\(492\) −4.92705 3.57971i −0.222129 0.161386i
\(493\) −0.652476 2.00811i −0.0293860 0.0904409i
\(494\) −4.85410 −0.218396
\(495\) −17.3262 + 1.17557i −0.778756 + 0.0528380i
\(496\) 8.70820 0.391010
\(497\) 4.88197 + 15.0251i 0.218986 + 0.673970i
\(498\) 7.11803 + 5.17155i 0.318967 + 0.231743i
\(499\) 26.6074 19.3314i 1.19111 0.865392i 0.197729 0.980257i \(-0.436643\pi\)
0.993381 + 0.114864i \(0.0366433\pi\)
\(500\) 2.54508 7.83297i 0.113820 0.350301i
\(501\) 0.881966 2.71441i 0.0394033 0.121271i
\(502\) −12.4721 + 9.06154i −0.556659 + 0.404436i
\(503\) 21.8262 + 15.8577i 0.973184 + 0.707059i 0.956175 0.292796i \(-0.0945856\pi\)
0.0170089 + 0.999855i \(0.494586\pi\)
\(504\) −1.00000 3.07768i −0.0445435 0.137091i
\(505\) 24.0344 1.06952
\(506\) 1.23607 + 3.07768i 0.0549499 + 0.136820i
\(507\) −10.5623 −0.469088
\(508\) 4.54508 + 13.9883i 0.201656 + 0.620632i
\(509\) 3.51722 + 2.55541i 0.155898 + 0.113267i 0.663000 0.748620i \(-0.269283\pi\)
−0.507102 + 0.861886i \(0.669283\pi\)
\(510\) −0.500000 + 0.363271i −0.0221404 + 0.0160859i
\(511\) 0.190983 0.587785i 0.00844859 0.0260021i
\(512\) 0.309017 0.951057i 0.0136568 0.0420312i
\(513\) 4.04508 2.93893i 0.178595 0.129757i
\(514\) −13.9721 10.1514i −0.616284 0.447757i
\(515\) −7.54508 23.2214i −0.332476 1.02326i
\(516\) 7.70820 0.339335
\(517\) −24.4615 15.3557i −1.07582 0.675341i
\(518\) 15.1803 0.666986
\(519\) −2.51722 7.74721i −0.110494 0.340065i
\(520\) 10.2812 + 7.46969i 0.450858 + 0.327568i
\(521\) −5.13525 + 3.73098i −0.224980 + 0.163457i −0.694565 0.719430i \(-0.744403\pi\)
0.469586 + 0.882887i \(0.344403\pi\)
\(522\) 5.52786 17.0130i 0.241948 0.744639i
\(523\) −0.774575 + 2.38390i −0.0338698 + 0.104241i −0.966562 0.256432i \(-0.917453\pi\)
0.932692 + 0.360673i \(0.117453\pi\)
\(524\) 8.70820 6.32688i 0.380420 0.276391i
\(525\) 2.42705 + 1.76336i 0.105925 + 0.0769592i
\(526\) −3.82624 11.7759i −0.166832 0.513456i
\(527\) 2.05573 0.0895489
\(528\) −2.54508 + 2.12663i −0.110761 + 0.0925496i
\(529\) −22.0000 −0.956522
\(530\) −3.66312 11.2739i −0.159116 0.489708i
\(531\) −9.47214 6.88191i −0.411056 0.298649i
\(532\) 1.30902 0.951057i 0.0567531 0.0412335i
\(533\) −9.13525 + 28.1154i −0.395692 + 1.21781i
\(534\) −5.69098 + 17.5150i −0.246273 + 0.757950i
\(535\) 12.2082 8.86978i 0.527807 0.383474i
\(536\) 4.54508 + 3.30220i 0.196318 + 0.142633i
\(537\) −3.61803 11.1352i −0.156130 0.480518i
\(538\) 19.4721 0.839503
\(539\) 3.54508 14.0943i 0.152698 0.607086i
\(540\) −13.0902 −0.563311
\(541\) 12.2254 + 37.6260i 0.525612 + 1.61767i 0.763102 + 0.646278i \(0.223675\pi\)
−0.237490 + 0.971390i \(0.576325\pi\)
\(542\) 11.4721 + 8.33499i 0.492770 + 0.358019i
\(543\) −8.80902 + 6.40013i −0.378031 + 0.274656i
\(544\) 0.0729490 0.224514i 0.00312766 0.00962596i
\(545\) −10.5902 + 32.5932i −0.453633 + 1.39614i
\(546\) 6.35410 4.61653i 0.271930 0.197569i
\(547\) 1.88197 + 1.36733i 0.0804671 + 0.0584627i 0.627291 0.778785i \(-0.284163\pi\)
−0.546824 + 0.837247i \(0.684163\pi\)
\(548\) −0.781153 2.40414i −0.0333692 0.102700i
\(549\) −29.1246 −1.24301
\(550\) −1.50000 + 5.96361i −0.0639602 + 0.254289i
\(551\) 8.94427 0.381039
\(552\) 0.309017 + 0.951057i 0.0131526 + 0.0404797i
\(553\) −19.6353 14.2658i −0.834976 0.606646i
\(554\) −13.8713 + 10.0781i −0.589336 + 0.428178i
\(555\) 7.59017 23.3601i 0.322185 0.991583i
\(556\) −0.791796 + 2.43690i −0.0335796 + 0.103347i
\(557\) −12.8541 + 9.33905i −0.544646 + 0.395708i −0.825808 0.563952i \(-0.809280\pi\)
0.281162 + 0.959660i \(0.409280\pi\)
\(558\) 14.0902 + 10.2371i 0.596484 + 0.433371i
\(559\) −11.5623 35.5851i −0.489033 1.50509i
\(560\) −4.23607 −0.179007
\(561\) −0.600813 + 0.502029i −0.0253663 + 0.0211957i
\(562\) 21.1459 0.891986
\(563\) −7.54508 23.2214i −0.317987 0.978665i −0.974507 0.224356i \(-0.927972\pi\)
0.656520 0.754309i \(-0.272028\pi\)
\(564\) −7.04508 5.11855i −0.296652 0.215530i
\(565\) −15.2082 + 11.0494i −0.639814 + 0.464852i
\(566\) −5.30902 + 16.3395i −0.223155 + 0.686799i
\(567\) 0.500000 1.53884i 0.0209980 0.0646253i
\(568\) −7.89919 + 5.73910i −0.331443 + 0.240807i
\(569\) 16.1803 + 11.7557i 0.678315 + 0.492825i 0.872798 0.488081i \(-0.162303\pi\)
−0.194483 + 0.980906i \(0.562303\pi\)
\(570\) −0.809017 2.48990i −0.0338860 0.104290i
\(571\) 19.3607 0.810219 0.405110 0.914268i \(-0.367233\pi\)
0.405110 + 0.914268i \(0.367233\pi\)
\(572\) 13.6353 + 8.55951i 0.570119 + 0.357891i
\(573\) −8.70820 −0.363790
\(574\) −3.04508 9.37181i −0.127099 0.391172i
\(575\) 1.50000 + 1.08981i 0.0625543 + 0.0454484i
\(576\) 1.61803 1.17557i 0.0674181 0.0489821i
\(577\) 1.19098 3.66547i 0.0495813 0.152595i −0.923200 0.384319i \(-0.874436\pi\)
0.972782 + 0.231723i \(0.0744364\pi\)
\(578\) −5.23607 + 16.1150i −0.217792 + 0.670294i
\(579\) −0.118034 + 0.0857567i −0.00490533 + 0.00356393i
\(580\) −18.9443 13.7638i −0.786618 0.571511i
\(581\) 4.39919 + 13.5393i 0.182509 + 0.561705i
\(582\) −9.18034 −0.380537
\(583\) −5.59675 13.9353i −0.231794 0.577143i
\(584\) 0.381966 0.0158059
\(585\) 7.85410 + 24.1724i 0.324727 + 0.999407i
\(586\) 19.7533 + 14.3516i 0.816001 + 0.592859i
\(587\) −4.13525 + 3.00444i −0.170680 + 0.124006i −0.669846 0.742500i \(-0.733640\pi\)
0.499166 + 0.866507i \(0.333640\pi\)
\(588\) 1.35410 4.16750i 0.0558422 0.171865i
\(589\) −2.69098 + 8.28199i −0.110880 + 0.341254i
\(590\) −12.3992 + 9.00854i −0.510466 + 0.370876i
\(591\) 18.6074 + 13.5191i 0.765406 + 0.556100i
\(592\) 2.89919 + 8.92278i 0.119156 + 0.366724i
\(593\) −19.9443 −0.819013 −0.409507 0.912307i \(-0.634299\pi\)
−0.409507 + 0.912307i \(0.634299\pi\)
\(594\) −16.5451 + 1.12257i −0.678853 + 0.0460596i
\(595\) −1.00000 −0.0409960
\(596\) 1.21885 + 3.75123i 0.0499259 + 0.153656i
\(597\) −2.76393 2.00811i −0.113120 0.0821866i
\(598\) 3.92705 2.85317i 0.160589 0.116675i
\(599\) 4.40983 13.5721i 0.180181 0.554539i −0.819651 0.572863i \(-0.805833\pi\)
0.999832 + 0.0183233i \(0.00583282\pi\)
\(600\) −0.572949 + 1.76336i −0.0233905 + 0.0719887i
\(601\) −23.5902 + 17.1393i −0.962263 + 0.699125i −0.953675 0.300838i \(-0.902734\pi\)
−0.00858786 + 0.999963i \(0.502734\pi\)
\(602\) 10.0902 + 7.33094i 0.411245 + 0.298787i
\(603\) 3.47214 + 10.6861i 0.141396 + 0.435173i
\(604\) 9.23607 0.375810
\(605\) −5.11803 + 28.3399i −0.208078 + 1.15218i
\(606\) 9.18034 0.372926
\(607\) −10.1287 31.1729i −0.411110 1.26527i −0.915684 0.401899i \(-0.868350\pi\)
0.504574 0.863369i \(-0.331650\pi\)
\(608\) 0.809017 + 0.587785i 0.0328100 + 0.0238378i
\(609\) −11.7082 + 8.50651i −0.474440 + 0.344701i
\(610\) −11.7812 + 36.2587i −0.477005 + 1.46807i
\(611\) −13.0623 + 40.2016i −0.528444 + 1.62638i
\(612\) 0.381966 0.277515i 0.0154401 0.0112179i
\(613\) −4.61803 3.35520i −0.186521 0.135515i 0.490606 0.871381i \(-0.336775\pi\)
−0.677127 + 0.735866i \(0.736775\pi\)
\(614\) 7.10739 + 21.8743i 0.286831 + 0.882775i
\(615\) −15.9443 −0.642935
\(616\) −5.35410 + 0.363271i −0.215723 + 0.0146366i
\(617\) 22.2705 0.896577 0.448288 0.893889i \(-0.352034\pi\)
0.448288 + 0.893889i \(0.352034\pi\)
\(618\) −2.88197 8.86978i −0.115930 0.356795i
\(619\) 14.2082 + 10.3229i 0.571076 + 0.414911i 0.835496 0.549497i \(-0.185181\pi\)
−0.264420 + 0.964408i \(0.585181\pi\)
\(620\) 18.4443 13.4005i 0.740740 0.538179i
\(621\) −1.54508 + 4.75528i −0.0620021 + 0.190823i
\(622\) 0.618034 1.90211i 0.0247809 0.0762678i
\(623\) −24.1074 + 17.5150i −0.965842 + 0.701725i
\(624\) 3.92705 + 2.85317i 0.157208 + 0.114218i
\(625\) −9.52786 29.3238i −0.381115 1.17295i
\(626\) −19.9443 −0.797133
\(627\) −1.23607 3.07768i −0.0493638 0.122911i
\(628\) 5.23607 0.208942
\(629\) 0.684405 + 2.10638i 0.0272890 + 0.0839870i
\(630\) −6.85410 4.97980i −0.273074 0.198400i
\(631\) −15.2984 + 11.1149i −0.609019 + 0.442478i −0.849069 0.528283i \(-0.822836\pi\)
0.240050 + 0.970761i \(0.422836\pi\)
\(632\) 4.63525 14.2658i 0.184381 0.567465i
\(633\) 5.92705 18.2416i 0.235579 0.725038i
\(634\) 13.7533 9.99235i 0.546213 0.396847i
\(635\) 31.1525 + 22.6336i 1.23625 + 0.898187i
\(636\) −1.39919 4.30625i −0.0554814 0.170754i
\(637\) −21.2705 −0.842768
\(638\) −25.1246 15.7719i −0.994693 0.624417i
\(639\) −19.5279 −0.772510
\(640\) −0.809017 2.48990i −0.0319792 0.0984219i
\(641\) −18.3262 13.3148i −0.723843 0.525903i 0.163767 0.986499i \(-0.447636\pi\)
−0.887610 + 0.460596i \(0.847636\pi\)
\(642\) 4.66312 3.38795i 0.184039 0.133712i
\(643\) −5.27051 + 16.2210i −0.207849 + 0.639692i 0.791736 + 0.610864i \(0.209178\pi\)
−0.999584 + 0.0288285i \(0.990822\pi\)
\(644\) −0.500000 + 1.53884i −0.0197028 + 0.0606389i
\(645\) 16.3262 11.8617i 0.642845 0.467054i
\(646\) 0.190983 + 0.138757i 0.00751413 + 0.00545933i
\(647\) 7.37132 + 22.6866i 0.289797 + 0.891902i 0.984920 + 0.173012i \(0.0553498\pi\)
−0.695123 + 0.718891i \(0.744650\pi\)
\(648\) 1.00000 0.0392837
\(649\) −14.8992 + 12.4495i −0.584844 + 0.488685i
\(650\) 9.00000 0.353009
\(651\) −4.35410 13.4005i −0.170651 0.525209i
\(652\) 9.16312 + 6.65740i 0.358855 + 0.260724i
\(653\) 31.2984 22.7396i 1.22480 0.889869i 0.228311 0.973588i \(-0.426680\pi\)
0.996489 + 0.0837190i \(0.0266798\pi\)
\(654\) −4.04508 + 12.4495i −0.158175 + 0.486814i
\(655\) 8.70820 26.8011i 0.340258 1.04721i
\(656\) 4.92705 3.57971i 0.192369 0.139764i
\(657\) 0.618034 + 0.449028i 0.0241118 + 0.0175182i
\(658\) −4.35410 13.4005i −0.169741 0.522408i
\(659\) −15.6525 −0.609734 −0.304867 0.952395i \(-0.598612\pi\)
−0.304867 + 0.952395i \(0.598612\pi\)
\(660\) −2.11803 + 8.42075i −0.0824444 + 0.327777i
\(661\) −23.8541 −0.927817 −0.463909 0.885883i \(-0.653553\pi\)
−0.463909 + 0.885883i \(0.653553\pi\)
\(662\) −7.47214 22.9969i −0.290413 0.893799i
\(663\) 0.927051 + 0.673542i 0.0360037 + 0.0261582i
\(664\) −7.11803 + 5.17155i −0.276233 + 0.200695i
\(665\) 1.30902 4.02874i 0.0507615 0.156228i
\(666\) −5.79837 + 17.8456i −0.224682 + 0.691501i
\(667\) −7.23607 + 5.25731i −0.280182 + 0.203564i
\(668\) 2.30902 + 1.67760i 0.0893385 + 0.0649083i
\(669\) −4.00000 12.3107i −0.154649 0.475960i
\(670\) 14.7082 0.568227
\(671\) −11.7812 + 46.8388i −0.454806 + 1.80819i
\(672\) −1.61803 −0.0624170
\(673\) 4.42705 + 13.6251i 0.170650 + 0.525208i 0.999408 0.0343998i \(-0.0109520\pi\)
−0.828758 + 0.559607i \(0.810952\pi\)
\(674\) 5.66312 + 4.11450i 0.218135 + 0.158484i
\(675\) −7.50000 + 5.44907i −0.288675 + 0.209735i
\(676\) 3.26393 10.0453i 0.125536 0.386360i
\(677\) −1.83688 + 5.65334i −0.0705971 + 0.217275i −0.980130 0.198357i \(-0.936440\pi\)
0.909533 + 0.415632i \(0.136440\pi\)
\(678\) −5.80902 + 4.22050i −0.223094 + 0.162087i
\(679\) −12.0172 8.73102i −0.461179 0.335066i
\(680\) −0.190983 0.587785i −0.00732386 0.0225405i
\(681\) −17.1459 −0.657032
\(682\) 22.1631 18.5191i 0.848670 0.709133i
\(683\) −1.97871 −0.0757134 −0.0378567 0.999283i \(-0.512053\pi\)
−0.0378567 + 0.999283i \(0.512053\pi\)
\(684\) 0.618034 + 1.90211i 0.0236311 + 0.0727291i
\(685\) −5.35410 3.88998i −0.204570 0.148629i
\(686\) 14.8992 10.8249i 0.568854 0.413296i
\(687\) −5.42705 + 16.7027i −0.207055 + 0.637249i
\(688\) −2.38197 + 7.33094i −0.0908116 + 0.279489i
\(689\) −17.7812 + 12.9188i −0.677408 + 0.492166i
\(690\) 2.11803 + 1.53884i 0.0806322 + 0.0585827i
\(691\) 3.58359 + 11.0292i 0.136326 + 0.419569i 0.995794 0.0916210i \(-0.0292048\pi\)
−0.859468 + 0.511190i \(0.829205\pi\)
\(692\) 8.14590 0.309661
\(693\) −9.09017 5.70634i −0.345307 0.216766i
\(694\) −12.6525 −0.480281
\(695\) 2.07295 + 6.37988i 0.0786314 + 0.242003i
\(696\) −7.23607 5.25731i −0.274282 0.199278i
\(697\) 1.16312 0.845055i 0.0440563 0.0320088i
\(698\) −4.93769 + 15.1967i −0.186894 + 0.575202i
\(699\) −0.218847 + 0.673542i −0.00827756 + 0.0254757i
\(700\) −2.42705 + 1.76336i −0.0917339 + 0.0666486i
\(701\) −21.2533 15.4414i −0.802726 0.583214i 0.108987 0.994043i \(-0.465239\pi\)
−0.911712 + 0.410829i \(0.865239\pi\)
\(702\) 7.50000 + 23.0826i 0.283069 + 0.871198i
\(703\) −9.38197 −0.353848
\(704\) −1.23607 3.07768i −0.0465861 0.115995i
\(705\) −22.7984 −0.858636
\(706\) −8.03444 24.7275i −0.302380 0.930631i
\(707\) 12.0172 + 8.73102i 0.451954 + 0.328364i
\(708\) −4.73607 + 3.44095i −0.177992 + 0.129319i
\(709\) −14.9615 + 46.0467i −0.561891 + 1.72932i 0.115123 + 0.993351i \(0.463274\pi\)
−0.677014 + 0.735970i \(0.736726\pi\)
\(710\) −7.89919 + 24.3112i −0.296451 + 0.912383i
\(711\) 24.2705 17.6336i 0.910215 0.661310i
\(712\) −14.8992 10.8249i −0.558371 0.405680i
\(713\) −2.69098 8.28199i −0.100778 0.310163i
\(714\) −0.381966 −0.0142947
\(715\) 42.0517 2.85317i 1.57264 0.106702i
\(716\) 11.7082 0.437556
\(717\) −1.64590 5.06555i −0.0614672 0.189177i
\(718\) −21.4443 15.5802i −0.800293 0.581447i
\(719\) 11.0172 8.00448i 0.410873 0.298517i −0.363082 0.931757i \(-0.618276\pi\)
0.773955 + 0.633240i \(0.218276\pi\)
\(720\) 1.61803 4.97980i 0.0603006 0.185586i
\(721\) 4.66312 14.3516i 0.173664 0.534482i
\(722\) −0.809017 + 0.587785i −0.0301085 + 0.0218751i
\(723\) −4.92705 3.57971i −0.183239 0.133131i
\(724\) −3.36475 10.3556i −0.125050 0.384864i
\(725\) −16.5836 −0.615899
\(726\) −1.95492 + 10.8249i −0.0725537 + 0.401749i
\(727\) 31.2918 1.16055 0.580274 0.814421i \(-0.302945\pi\)
0.580274 + 0.814421i \(0.302945\pi\)
\(728\) 2.42705 + 7.46969i 0.0899525 + 0.276845i
\(729\) −10.5172 7.64121i −0.389527 0.283008i
\(730\) 0.809017 0.587785i 0.0299431 0.0217549i
\(731\) −0.562306 + 1.73060i −0.0207976 + 0.0640085i
\(732\) −4.50000 + 13.8496i −0.166325 + 0.511895i
\(733\) −17.8713 + 12.9843i −0.660092 + 0.479585i −0.866694 0.498840i \(-0.833760\pi\)
0.206602 + 0.978425i \(0.433760\pi\)
\(734\) 11.2533 + 8.17599i 0.415366 + 0.301781i
\(735\) −3.54508 10.9106i −0.130762 0.402445i
\(736\) −1.00000 −0.0368605
\(737\) 18.5902 1.26133i 0.684778 0.0464616i
\(738\) 12.1803 0.448365
\(739\) −9.79837 30.1563i −0.360439 1.10932i −0.952788 0.303636i \(-0.901799\pi\)
0.592349 0.805681i \(-0.298201\pi\)
\(740\) 19.8713 + 14.4374i 0.730484 + 0.530728i
\(741\) −3.92705 + 2.85317i −0.144264 + 0.104814i
\(742\) 2.26393 6.96767i 0.0831116 0.255791i
\(743\) 4.52786 13.9353i 0.166111 0.511238i −0.833005 0.553265i \(-0.813382\pi\)
0.999116 + 0.0420273i \(0.0133817\pi\)
\(744\) 7.04508 5.11855i 0.258285 0.187655i
\(745\) 8.35410 + 6.06961i 0.306071 + 0.222373i
\(746\) 6.56231 + 20.1967i 0.240263 + 0.739454i
\(747\) −17.5967 −0.643831
\(748\) −0.291796 0.726543i −0.0106691 0.0265650i
\(749\) 9.32624 0.340773
\(750\) −2.54508 7.83297i −0.0929334 0.286019i
\(751\) −9.28115 6.74315i −0.338674 0.246061i 0.405428 0.914127i \(-0.367122\pi\)
−0.744102 + 0.668066i \(0.767122\pi\)
\(752\) 7.04508 5.11855i 0.256908 0.186654i
\(753\) −4.76393 + 14.6619i −0.173607 + 0.534308i
\(754\) −13.4164 + 41.2915i −0.488597 + 1.50375i
\(755\) 19.5623 14.2128i 0.711945 0.517258i
\(756\) −6.54508 4.75528i −0.238042 0.172948i
\(757\) −14.9894 46.1325i −0.544797 1.67671i −0.721471 0.692445i \(-0.756534\pi\)
0.176674 0.984269i \(-0.443466\pi\)
\(758\) 25.4508 0.924416
\(759\) 2.80902 + 1.76336i 0.101961 + 0.0640058i
\(760\) 2.61803 0.0949661
\(761\) −15.7254 48.3979i −0.570046 1.75442i −0.652460 0.757824i \(-0.726263\pi\)
0.0824133 0.996598i \(-0.473737\pi\)
\(762\) 11.8992 + 8.64527i 0.431062 + 0.313185i
\(763\) −17.1353 + 12.4495i −0.620338 + 0.450702i
\(764\) 2.69098 8.28199i 0.0973563 0.299632i
\(765\) 0.381966 1.17557i 0.0138100 0.0425028i
\(766\) −11.5902 + 8.42075i −0.418770 + 0.304254i
\(767\) 22.9894 + 16.7027i 0.830098 + 0.603101i
\(768\) −0.309017 0.951057i −0.0111507 0.0343183i
\(769\) 3.29180 0.118705 0.0593526 0.998237i \(-0.481096\pi\)
0.0593526 + 0.998237i \(0.481096\pi\)
\(770\) −10.7812 + 9.00854i −0.388526 + 0.324645i
\(771\) −17.2705 −0.621982
\(772\) −0.0450850 0.138757i −0.00162264 0.00499398i
\(773\) 14.9164 + 10.8374i 0.536506 + 0.389794i 0.822786 0.568352i \(-0.192419\pi\)
−0.286280 + 0.958146i \(0.592419\pi\)
\(774\) −12.4721 + 9.06154i −0.448302 + 0.325710i
\(775\) 4.98936 15.3557i 0.179223 0.551592i
\(776\) 2.83688 8.73102i 0.101838 0.313425i
\(777\) 12.2812 8.92278i 0.440584 0.320103i
\(778\) 21.1803 + 15.3884i 0.759352 + 0.551702i
\(779\) 1.88197 + 5.79210i 0.0674284 + 0.207523i
\(780\) 12.7082 0.455027
\(781\) −7.89919 + 31.4051i −0.282655 + 1.12376i
\(782\) −0.236068 −0.00844177
\(783\) −13.8197 42.5325i −0.493874 1.51999i
\(784\) 3.54508 + 2.57565i 0.126610 + 0.0919877i
\(785\) 11.0902 8.05748i 0.395825 0.287584i
\(786\) 3.32624 10.2371i 0.118643 0.365146i
\(787\) 10.9656 33.7485i 0.390880 1.20300i −0.541244 0.840866i \(-0.682046\pi\)
0.932124 0.362139i \(-0.117954\pi\)
\(788\) −18.6074 + 13.5191i −0.662861 + 0.481597i
\(789\) −10.0172 7.27794i −0.356623 0.259101i
\(790\) −12.1353 37.3485i −0.431753 1.32880i
\(791\) −11.6180 −0.413090
\(792\) 1.61803 6.43288i 0.0574943 0.228582i
\(793\) 70.6869 2.51017
\(794\) −3.34346 10.2901i −0.118655 0.365182i
\(795\) −9.59017 6.96767i −0.340128 0.247118i
\(796\) 2.76393 2.00811i 0.0979650 0.0711757i
\(797\) −4.50000 + 13.8496i −0.159398 + 0.490577i −0.998580 0.0532739i \(-0.983034\pi\)
0.839182 + 0.543851i \(0.183034\pi\)
\(798\) 0.500000 1.53884i 0.0176998 0.0544744i
\(799\) 1.66312 1.20833i 0.0588369 0.0427475i
\(800\) −1.50000 1.08981i −0.0530330 0.0385307i
\(801\) −11.3820 35.0301i −0.402162 1.23773i
\(802\) 16.5967 0.586052
\(803\) 0.972136 0.812299i 0.0343059 0.0286654i
\(804\) 5.61803 0.198133
\(805\) 1.30902 + 4.02874i 0.0461368 + 0.141994i
\(806\) −34.1976 24.8460i −1.20456 0.875162i
\(807\) 15.7533 11.4454i 0.554542 0.402898i
\(808\) −2.83688 + 8.73102i −0.0998011 + 0.307156i
\(809\) −5.52786 + 17.0130i −0.194349 + 0.598146i 0.805634 + 0.592413i \(0.201825\pi\)
−0.999984 + 0.00573251i \(0.998175\pi\)
\(810\) 2.11803 1.53884i 0.0744201 0.0540694i
\(811\) −21.4164 15.5599i −0.752032 0.546383i 0.144424 0.989516i \(-0.453867\pi\)
−0.896456 + 0.443133i \(0.853867\pi\)
\(812\) −4.47214 13.7638i −0.156941 0.483015i
\(813\) 14.1803 0.497326
\(814\) 26.3541 + 16.5437i 0.923711 + 0.579858i
\(815\) 29.6525 1.03868
\(816\) −0.0729490 0.224514i −0.00255373 0.00785956i
\(817\) −6.23607 4.53077i −0.218172 0.158512i
\(818\) −2.66312 + 1.93487i −0.0931138 + 0.0676511i
\(819\) −4.85410 + 14.9394i −0.169616 + 0.522025i
\(820\) 4.92705 15.1639i 0.172060 0.529546i
\(821\) 11.2082 8.14324i 0.391169 0.284201i −0.374765 0.927120i \(-0.622277\pi\)
0.765934 + 0.642919i \(0.222277\pi\)
\(822\) −2.04508 1.48584i −0.0713305 0.0518247i
\(823\) 1.76393 + 5.42882i 0.0614868 + 0.189237i 0.977082 0.212865i \(-0.0682796\pi\)
−0.915595 + 0.402102i \(0.868280\pi\)
\(824\) 9.32624 0.324895
\(825\) 2.29180 + 5.70634i 0.0797901 + 0.198669i
\(826\) −9.47214 −0.329578
\(827\) 6.68034 + 20.5600i 0.232298 + 0.714940i 0.997468 + 0.0711122i \(0.0226548\pi\)
−0.765170 + 0.643828i \(0.777345\pi\)
\(828\) −1.61803 1.17557i −0.0562306 0.0408539i
\(829\) 35.1246 25.5195i 1.21993 0.886330i 0.223834 0.974627i \(-0.428143\pi\)
0.996094 + 0.0882976i \(0.0281426\pi\)
\(830\) −7.11803 + 21.9071i −0.247071 + 0.760405i
\(831\) −5.29837 + 16.3067i −0.183799 + 0.565674i
\(832\) −3.92705 + 2.85317i −0.136146 + 0.0989159i
\(833\) 0.836881 + 0.608030i 0.0289962 + 0.0210670i
\(834\) 0.791796 + 2.43690i 0.0274177 + 0.0843829i
\(835\) 7.47214 0.258584
\(836\) 3.30902 0.224514i 0.114445 0.00776498i
\(837\) 43.5410 1.50500
\(838\) 7.88854 + 24.2784i 0.272505 + 0.838685i
\(839\) −4.73607 3.44095i −0.163507 0.118795i 0.503023 0.864273i \(-0.332221\pi\)
−0.666530 + 0.745478i \(0.732221\pi\)
\(840\) −3.42705 + 2.48990i −0.118244 + 0.0859097i
\(841\) 15.7599 48.5039i 0.543444 1.67255i
\(842\) 7.69098 23.6704i 0.265049 0.815736i
\(843\) 17.1074 12.4292i 0.589210 0.428086i
\(844\) 15.5172 + 11.2739i 0.534125 + 0.388064i
\(845\) −8.54508 26.2991i −0.293960 0.904715i
\(846\) 17.4164 0.598788
\(847\) −12.8541 + 12.3107i −0.441672 + 0.423002i
\(848\) 4.52786 0.155487
\(849\) 5.30902 + 16.3395i 0.182205 + 0.560769i
\(850\) −0.354102 0.257270i −0.0121456 0.00882429i
\(851\) 7.59017 5.51458i 0.260188 0.189037i
\(852\) −3.01722 + 9.28605i −0.103368 + 0.318135i
\(853\) 7.15248 22.0131i 0.244896 0.753713i −0.750757 0.660578i \(-0.770311\pi\)
0.995654 0.0931347i \(-0.0296887\pi\)
\(854\) −19.0623 + 13.8496i −0.652299 + 0.473923i
\(855\) 4.23607 + 3.07768i 0.144870 + 0.105255i
\(856\) 1.78115 + 5.48183i 0.0608786 + 0.187365i
\(857\) 33.8541 1.15643 0.578217 0.815883i \(-0.303749\pi\)
0.578217 + 0.815883i \(0.303749\pi\)
\(858\) 16.0623 1.08981i 0.548358 0.0372056i
\(859\) −16.3050 −0.556318 −0.278159 0.960535i \(-0.589724\pi\)
−0.278159 + 0.960535i \(0.589724\pi\)
\(860\) 6.23607 + 19.1926i 0.212648 + 0.654464i
\(861\) −7.97214 5.79210i −0.271690 0.197394i
\(862\) −30.1976 + 21.9398i −1.02853 + 0.747273i
\(863\) 0.381966 1.17557i 0.0130023 0.0400169i −0.944345 0.328957i \(-0.893303\pi\)
0.957347 + 0.288940i \(0.0933029\pi\)
\(864\) 1.54508 4.75528i 0.0525649 0.161778i
\(865\) 17.2533 12.5352i 0.586629 0.426211i
\(866\) 19.3262 + 14.0413i 0.656732 + 0.477144i
\(867\) 5.23607 + 16.1150i 0.177826 + 0.547293i
\(868\) 14.0902 0.478252
\(869\) −18.5410 46.1653i −0.628961 1.56605i
\(870\) −23.4164 −0.793891
\(871\) −8.42705 25.9358i −0.285540 0.878801i
\(872\) −10.5902 7.69421i −0.358628 0.260559i
\(873\) 14.8541 10.7921i 0.502735 0.365258i
\(874\) 0.309017 0.951057i 0.0104527 0.0321700i
\(875\) 4.11803 12.6740i 0.139215 0.428460i
\(876\) 0.309017 0.224514i 0.0104407 0.00758562i
\(877\) 12.7361 + 9.25330i 0.430066 + 0.312462i 0.781675 0.623685i \(-0.214365\pi\)
−0.351609 + 0.936147i \(0.614365\pi\)
\(878\) 3.35410 + 10.3229i 0.113195 + 0.348380i
\(879\) 24.4164 0.823545
\(880\) −7.35410 4.61653i −0.247907 0.155623i
\(881\) −31.4164 −1.05845 −0.529223 0.848483i \(-0.677516\pi\)
−0.529223 + 0.848483i \(0.677516\pi\)
\(882\) 2.70820 + 8.33499i 0.0911900 + 0.280654i
\(883\) −42.5066 30.8828i −1.43046 1.03929i −0.989931 0.141552i \(-0.954791\pi\)
−0.440529 0.897738i \(-0.645209\pi\)
\(884\) −0.927051 + 0.673542i −0.0311801 + 0.0226537i
\(885\) −4.73607 + 14.5761i −0.159201 + 0.489971i
\(886\) −3.33688 + 10.2699i −0.112105 + 0.345023i
\(887\) −25.5172 + 18.5393i −0.856784 + 0.622490i −0.927008 0.375041i \(-0.877629\pi\)
0.0702238 + 0.997531i \(0.477629\pi\)
\(888\) 7.59017 + 5.51458i 0.254709 + 0.185057i
\(889\) 7.35410 + 22.6336i 0.246649 + 0.759107i
\(890\) −48.2148 −1.61616
\(891\) 2.54508 2.12663i 0.0852636 0.0712447i
\(892\) 12.9443 0.433406
\(893\) 2.69098 + 8.28199i 0.0900503 + 0.277146i
\(894\) 3.19098 + 2.31838i 0.106722 + 0.0775384i
\(895\) 24.7984 18.0171i 0.828918 0.602244i
\(896\) 0.500000 1.53884i 0.0167038 0.0514091i
\(897\) 1.50000 4.61653i 0.0500835 0.154141i
\(898\) −10.4271 + 7.57570i −0.347955 + 0.252804i
\(899\) 63.0132 + 45.7817i 2.10161 + 1.52691i
\(900\) −1.14590 3.52671i −0.0381966 0.117557i
\(901\) 1.06888 0.0356097
\(902\) 4.92705 19.5887i 0.164053 0.652231i
\(903\) 12.4721 0.415047
\(904\) −2.21885 6.82891i −0.0737978 0.227126i
\(905\) −23.0623 16.7557i −0.766617 0.556980i
\(906\) 7.47214 5.42882i 0.248245 0.180361i
\(907\) −14.8262 + 45.6305i −0.492297 + 1.51513i 0.328830 + 0.944389i \(0.393346\pi\)
−0.821127 + 0.570746i \(0.806654\pi\)
\(908\) 5.29837 16.3067i 0.175833 0.541157i
\(909\) −14.8541 + 10.7921i −0.492679 + 0.357953i
\(910\) 16.6353 + 12.0862i 0.551453 + 0.400654i
\(911\) 9.88854 + 30.4338i 0.327622 + 1.00832i 0.970243 + 0.242133i \(0.0778470\pi\)
−0.642621 + 0.766184i \(0.722153\pi\)
\(912\) 1.00000 0.0331133
\(913\) −7.11803 + 28.2994i −0.235573 + 0.936575i
\(914\) 1.94427 0.0643108
\(915\) 11.7812 + 36.2587i 0.389473 + 1.19867i
\(916\) −14.2082 10.3229i −0.469452 0.341077i
\(917\) 14.0902 10.2371i 0.465298 0.338059i
\(918\) 0.364745 1.12257i 0.0120384 0.0370503i
\(919\) 8.90576 27.4091i 0.293774 0.904144i −0.689856 0.723946i \(-0.742326\pi\)
0.983630 0.180197i \(-0.0576737\pi\)
\(920\) −2.11803 + 1.53884i −0.0698295 + 0.0507341i
\(921\) 18.6074 + 13.5191i 0.613134 + 0.445468i
\(922\) −6.25329 19.2456i −0.205941 0.633822i
\(923\) 47.3951 1.56003
\(924\) −4.11803 + 3.44095i −0.135473 + 0.113199i
\(925\) 17.3951 0.571948
\(926\) 9.22542 + 28.3929i 0.303166 + 0.933050i
\(927\) 15.0902 + 10.9637i 0.495626 + 0.360094i
\(928\) 7.23607 5.25731i 0.237536 0.172580i
\(929\) 12.6008 38.7813i 0.413419 1.27237i −0.500238 0.865888i \(-0.666754\pi\)
0.913657 0.406486i \(-0.133246\pi\)
\(930\) 7.04508 21.6825i 0.231017 0.710999i
\(931\) −3.54508 + 2.57565i −0.116185 + 0.0844137i
\(932\) −0.572949 0.416272i −0.0187676 0.0136354i
\(933\) −0.618034 1.90211i −0.0202335 0.0622724i
\(934\) −2.32624 −0.0761168
\(935\) −1.73607 1.08981i −0.0567755 0.0356407i
\(936\) −9.70820 −0.317323
\(937\) −16.6738 51.3166i −0.544708 1.67644i −0.721683 0.692224i \(-0.756631\pi\)
0.176975 0.984215i \(-0.443369\pi\)
\(938\) 7.35410 + 5.34307i 0.240120 + 0.174457i
\(939\) −16.1353 + 11.7229i −0.526554 + 0.382564i
\(940\) 7.04508 21.6825i 0.229785 0.707207i
\(941\) −3.28773 + 10.1186i −0.107177 + 0.329857i −0.990235 0.139407i \(-0.955481\pi\)
0.883058 + 0.469263i \(0.155481\pi\)
\(942\) 4.23607 3.07768i 0.138019 0.100276i
\(943\) −4.92705 3.57971i −0.160447 0.116571i
\(944\) −1.80902 5.56758i −0.0588785 0.181209i
\(945\) −21.1803 −0.688997
\(946\) 9.52786 + 23.7234i 0.309778 + 0.771315i
\(947\) 20.8885 0.678786 0.339393 0.940645i \(-0.389778\pi\)
0.339393 + 0.940645i \(0.389778\pi\)
\(948\) −4.63525 14.2658i −0.150546 0.463333i
\(949\) −1.50000 1.08981i −0.0486921 0.0353769i
\(950\) 1.50000 1.08981i 0.0486664 0.0353582i
\(951\) 5.25329 16.1680i 0.170350 0.524282i
\(952\) 0.118034 0.363271i 0.00382550 0.0117737i
\(953\) −0.145898 + 0.106001i −0.00472610 + 0.00343371i −0.590146 0.807297i \(-0.700930\pi\)
0.585420 + 0.810730i \(0.300930\pi\)
\(954\) 7.32624 + 5.32282i 0.237196 + 0.172333i
\(955\) −7.04508 21.6825i −0.227974 0.701631i
\(956\) 5.32624 0.172263
\(957\) −29.5967 + 2.00811i −0.956727 + 0.0649131i
\(958\) 18.4164 0.595007
\(959\) −1.26393 3.88998i −0.0408145 0.125614i
\(960\) −2.11803 1.53884i −0.0683593 0.0496659i
\(961\) −36.2705 + 26.3521i −1.17002 + 0.850067i
\(962\) 14.0729 43.3121i 0.453730 1.39644i
\(963\) −3.56231 + 10.9637i −0.114794 + 0.353299i
\(964\) 4.92705 3.57971i 0.158690 0.115295i
\(965\) −0.309017 0.224514i −0.00994761 0.00722736i
\(966\) 0.500000 + 1.53884i 0.0160872 + 0.0495114i
\(967\) 11.7426 0.377618 0.188809 0.982014i \(-0.439537\pi\)
0.188809 + 0.982014i \(0.439537\pi\)
\(968\) −9.69098 5.20431i −0.311480 0.167273i
\(969\) 0.236068 0.00758360
\(970\) −7.42705 22.8581i −0.238468 0.733930i
\(971\) −13.2639 9.63681i −0.425660 0.309260i 0.354251 0.935150i \(-0.384736\pi\)
−0.779911 + 0.625890i \(0.784736\pi\)
\(972\) 12.9443 9.40456i 0.415188 0.301652i
\(973\) −1.28115 + 3.94298i −0.0410719 + 0.126406i
\(974\) −11.8369 + 36.4302i −0.379278 + 1.16730i
\(975\) 7.28115 5.29007i 0.233184 0.169418i
\(976\) −11.7812 8.55951i −0.377106 0.273983i
\(977\) 1.61803 + 4.97980i 0.0517655 + 0.159318i 0.973597 0.228272i \(-0.0733076\pi\)
−0.921832 + 0.387590i \(0.873308\pi\)
\(978\) 11.3262 0.362173
\(979\) −60.9402 + 4.13474i −1.94766 + 0.132147i
\(980\) 11.4721 0.366464
\(981\) −8.09017 24.8990i −0.258299 0.794963i
\(982\) 5.78115 + 4.20025i 0.184484 + 0.134035i
\(983\) −9.94427 + 7.22494i −0.317173 + 0.230440i −0.734968 0.678102i \(-0.762803\pi\)
0.417795 + 0.908541i \(0.362803\pi\)
\(984\) 1.88197 5.79210i 0.0599949 0.184645i
\(985\) −18.6074 + 57.2677i −0.592881 + 1.82470i
\(986\) 1.70820 1.24108i 0.0544003 0.0395241i
\(987\) −11.3992 8.28199i −0.362840 0.263619i
\(988\) −1.50000 4.61653i −0.0477214 0.146871i
\(989\) 7.70820 0.245107
\(990\) −6.47214 16.1150i −0.205698 0.512167i
\(991\) 47.0000 1.49300 0.746502 0.665383i \(-0.231732\pi\)
0.746502 + 0.665383i \(0.231732\pi\)
\(992\) 2.69098 + 8.28199i 0.0854388 + 0.262954i
\(993\) −19.5623 14.2128i −0.620791 0.451031i
\(994\) −12.7812 + 9.28605i −0.405394 + 0.294536i
\(995\) 2.76393 8.50651i 0.0876225 0.269674i
\(996\) −2.71885 + 8.36775i −0.0861500 + 0.265142i
\(997\) 15.1353 10.9964i 0.479338 0.348260i −0.321731 0.946831i \(-0.604265\pi\)
0.801069 + 0.598571i \(0.204265\pi\)
\(998\) 26.6074 + 19.3314i 0.842242 + 0.611925i
\(999\) 14.4959 + 44.6139i 0.458631 + 1.41152i
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 418.2.f.c.115.1 4
11.3 even 5 4598.2.a.bd.1.1 2
11.8 odd 10 4598.2.a.u.1.1 2
11.9 even 5 inner 418.2.f.c.229.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.c.115.1 4 1.1 even 1 trivial
418.2.f.c.229.1 yes 4 11.9 even 5 inner
4598.2.a.u.1.1 2 11.8 odd 10
4598.2.a.bd.1.1 2 11.3 even 5