Properties

Label 847.2.f.v.729.1
Level $847$
Weight $2$
Character 847.729
Analytic conductor $6.763$
Analytic rank $0$
Dimension $16$
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] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 729.1
Root \(0.751051 - 2.31150i\) of defining polynomial
Character \(\chi\) \(=\) 847.729
Dual form 847.2.f.v.323.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96628 + 1.42858i) q^{2} +(0.443194 + 1.36401i) q^{3} +(1.20736 - 3.71587i) q^{4} +(-1.01825 - 0.739805i) q^{5} +(-2.82005 - 2.04888i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(1.43233 + 4.40826i) q^{8} +(0.762946 - 0.554312i) q^{9} +O(q^{10})\) \(q+(-1.96628 + 1.42858i) q^{2} +(0.443194 + 1.36401i) q^{3} +(1.20736 - 3.71587i) q^{4} +(-1.01825 - 0.739805i) q^{5} +(-2.82005 - 2.04888i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(1.43233 + 4.40826i) q^{8} +(0.762946 - 0.554312i) q^{9} +3.05904 q^{10} +5.60359 q^{12} +(-2.57131 + 1.86816i) q^{13} +(-0.751051 - 2.31150i) q^{14} +(0.557818 - 1.71679i) q^{15} +(-2.79210 - 2.02858i) q^{16} +(4.79276 + 3.48215i) q^{17} +(-0.708281 + 2.17986i) q^{18} +(-0.884474 - 2.72213i) q^{19} +(-3.97842 + 2.89049i) q^{20} -1.43421 q^{21} +6.76343 q^{23} +(-5.37811 + 3.90743i) q^{24} +(-1.05555 - 3.24866i) q^{25} +(2.38707 - 7.34665i) q^{26} +(4.57511 + 3.32401i) q^{27} +(3.16091 + 2.29654i) q^{28} +(-1.38918 + 4.27547i) q^{29} +(1.35575 + 4.17257i) q^{30} +(-7.86972 + 5.71769i) q^{31} -0.882184 q^{32} -14.3984 q^{34} +(1.01825 - 0.739805i) q^{35} +(-1.13860 - 3.50426i) q^{36} +(-1.68567 + 5.18797i) q^{37} +(5.62791 + 4.08892i) q^{38} +(-3.68778 - 2.67933i) q^{39} +(1.80277 - 5.54837i) q^{40} +(0.0971810 + 0.299092i) q^{41} +(2.82005 - 2.04888i) q^{42} +0.132562 q^{43} -1.18696 q^{45} +(-13.2988 + 9.66213i) q^{46} +(2.89705 + 8.91620i) q^{47} +(1.52956 - 4.70751i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(6.71650 + 4.87983i) q^{50} +(-2.62556 + 8.08065i) q^{51} +(3.83736 + 11.8102i) q^{52} +(-3.52078 + 2.55800i) q^{53} -13.7446 q^{54} -4.63512 q^{56} +(3.32102 - 2.41286i) q^{57} +(-3.37635 - 10.3913i) q^{58} +(-2.14670 + 6.60685i) q^{59} +(-5.70587 - 4.14556i) q^{60} +(-1.98383 - 1.44134i) q^{61} +(7.30586 - 22.4851i) q^{62} +(0.291419 + 0.896896i) q^{63} +(7.31882 - 5.31744i) q^{64} +4.00032 q^{65} -9.41987 q^{67} +(18.7258 - 13.6051i) q^{68} +(2.99751 + 9.22539i) q^{69} +(-0.945296 + 2.90932i) q^{70} +(0.0943396 + 0.0685417i) q^{71} +(3.53634 + 2.56930i) q^{72} +(-0.190055 + 0.584930i) q^{73} +(-4.09695 - 12.6091i) q^{74} +(3.96340 - 2.87958i) q^{75} -11.1830 q^{76} +11.0789 q^{78} +(6.90033 - 5.01339i) q^{79} +(1.34232 + 4.13122i) q^{80} +(-1.63207 + 5.02300i) q^{81} +(-0.618364 - 0.449267i) q^{82} +(0.768997 + 0.558709i) q^{83} +(-1.73160 + 5.32933i) q^{84} +(-2.30414 - 7.09142i) q^{85} +(-0.260654 + 0.189376i) q^{86} -6.44746 q^{87} +10.0552 q^{89} +(2.33388 - 1.69567i) q^{90} +(-0.982152 - 3.02275i) q^{91} +(8.16590 - 25.1320i) q^{92} +(-11.2868 - 8.20034i) q^{93} +(-18.4339 - 13.3930i) q^{94} +(-1.11323 + 3.42616i) q^{95} +(-0.390979 - 1.20331i) q^{96} +(-14.2201 + 10.3315i) q^{97} +2.43045 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20} - 8 q^{21} + 32 q^{23} - 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} + 11 q^{28} + 12 q^{29} - 38 q^{30} - 2 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} + 24 q^{39} - 5 q^{40} - 20 q^{41} - 2 q^{42} + 8 q^{43} + 70 q^{45} - 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} + 58 q^{50} - 16 q^{51} - 8 q^{52} - 41 q^{53} - 60 q^{54} - 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} + 12 q^{61} + 61 q^{62} + 12 q^{63} - 3 q^{64} + 8 q^{65} - 38 q^{67} + 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} - 35 q^{72} - 60 q^{73} + 4 q^{74} + 4 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} - 20 q^{83} + 17 q^{84} + 9 q^{85} + 48 q^{86} + 72 q^{87} + 74 q^{89} - 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} - 66 q^{94} + 53 q^{95} - 48 q^{96} - 35 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96628 + 1.42858i −1.39037 + 1.01016i −0.394543 + 0.918877i \(0.629097\pi\)
−0.995825 + 0.0912842i \(0.970903\pi\)
\(3\) 0.443194 + 1.36401i 0.255878 + 0.787512i 0.993655 + 0.112468i \(0.0358755\pi\)
−0.737777 + 0.675044i \(0.764124\pi\)
\(4\) 1.20736 3.71587i 0.603680 1.85794i
\(5\) −1.01825 0.739805i −0.455377 0.330851i 0.336338 0.941741i \(-0.390812\pi\)
−0.791715 + 0.610891i \(0.790812\pi\)
\(6\) −2.82005 2.04888i −1.15128 0.836454i
\(7\) −0.309017 + 0.951057i −0.116797 + 0.359466i
\(8\) 1.43233 + 4.40826i 0.506405 + 1.55855i
\(9\) 0.762946 0.554312i 0.254315 0.184771i
\(10\) 3.05904 0.967354
\(11\) 0 0
\(12\) 5.60359 1.61762
\(13\) −2.57131 + 1.86816i −0.713152 + 0.518135i −0.884189 0.467129i \(-0.845288\pi\)
0.171037 + 0.985265i \(0.445288\pi\)
\(14\) −0.751051 2.31150i −0.200727 0.617774i
\(15\) 0.557818 1.71679i 0.144028 0.443272i
\(16\) −2.79210 2.02858i −0.698026 0.507145i
\(17\) 4.79276 + 3.48215i 1.16242 + 0.844544i 0.990082 0.140494i \(-0.0448691\pi\)
0.172334 + 0.985039i \(0.444869\pi\)
\(18\) −0.708281 + 2.17986i −0.166943 + 0.513799i
\(19\) −0.884474 2.72213i −0.202912 0.624500i −0.999793 0.0203626i \(-0.993518\pi\)
0.796880 0.604137i \(-0.206482\pi\)
\(20\) −3.97842 + 2.89049i −0.889602 + 0.646333i
\(21\) −1.43421 −0.312969
\(22\) 0 0
\(23\) 6.76343 1.41027 0.705136 0.709072i \(-0.250886\pi\)
0.705136 + 0.709072i \(0.250886\pi\)
\(24\) −5.37811 + 3.90743i −1.09780 + 0.797600i
\(25\) −1.05555 3.24866i −0.211111 0.649733i
\(26\) 2.38707 7.34665i 0.468144 1.44080i
\(27\) 4.57511 + 3.32401i 0.880481 + 0.639707i
\(28\) 3.16091 + 2.29654i 0.597356 + 0.434004i
\(29\) −1.38918 + 4.27547i −0.257965 + 0.793934i 0.735266 + 0.677779i \(0.237057\pi\)
−0.993231 + 0.116156i \(0.962943\pi\)
\(30\) 1.35575 + 4.17257i 0.247525 + 0.761803i
\(31\) −7.86972 + 5.71769i −1.41344 + 1.02693i −0.420634 + 0.907231i \(0.638192\pi\)
−0.992811 + 0.119697i \(0.961808\pi\)
\(32\) −0.882184 −0.155950
\(33\) 0 0
\(34\) −14.3984 −2.46931
\(35\) 1.01825 0.739805i 0.172116 0.125050i
\(36\) −1.13860 3.50426i −0.189767 0.584044i
\(37\) −1.68567 + 5.18797i −0.277123 + 0.852897i 0.711527 + 0.702659i \(0.248004\pi\)
−0.988650 + 0.150238i \(0.951996\pi\)
\(38\) 5.62791 + 4.08892i 0.912968 + 0.663310i
\(39\) −3.68778 2.67933i −0.590518 0.429036i
\(40\) 1.80277 5.54837i 0.285044 0.877274i
\(41\) 0.0971810 + 0.299092i 0.0151771 + 0.0467104i 0.958358 0.285569i \(-0.0921824\pi\)
−0.943181 + 0.332279i \(0.892182\pi\)
\(42\) 2.82005 2.04888i 0.435143 0.316150i
\(43\) 0.132562 0.0202155 0.0101078 0.999949i \(-0.496783\pi\)
0.0101078 + 0.999949i \(0.496783\pi\)
\(44\) 0 0
\(45\) −1.18696 −0.176941
\(46\) −13.2988 + 9.66213i −1.96080 + 1.42460i
\(47\) 2.89705 + 8.91620i 0.422578 + 1.30056i 0.905294 + 0.424785i \(0.139650\pi\)
−0.482716 + 0.875777i \(0.660350\pi\)
\(48\) 1.52956 4.70751i 0.220774 0.679471i
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) 6.71650 + 4.87983i 0.949857 + 0.690112i
\(51\) −2.62556 + 8.08065i −0.367652 + 1.13152i
\(52\) 3.83736 + 11.8102i 0.532147 + 1.63778i
\(53\) −3.52078 + 2.55800i −0.483616 + 0.351368i −0.802724 0.596351i \(-0.796617\pi\)
0.319108 + 0.947718i \(0.396617\pi\)
\(54\) −13.7446 −1.87040
\(55\) 0 0
\(56\) −4.63512 −0.619393
\(57\) 3.32102 2.41286i 0.439880 0.319592i
\(58\) −3.37635 10.3913i −0.443336 1.36445i
\(59\) −2.14670 + 6.60685i −0.279476 + 0.860139i 0.708524 + 0.705686i \(0.249361\pi\)
−0.988000 + 0.154452i \(0.950639\pi\)
\(60\) −5.70587 4.14556i −0.736625 0.535190i
\(61\) −1.98383 1.44134i −0.254004 0.184545i 0.453495 0.891259i \(-0.350177\pi\)
−0.707499 + 0.706714i \(0.750177\pi\)
\(62\) 7.30586 22.4851i 0.927845 2.85561i
\(63\) 0.291419 + 0.896896i 0.0367154 + 0.112998i
\(64\) 7.31882 5.31744i 0.914853 0.664679i
\(65\) 4.00032 0.496179
\(66\) 0 0
\(67\) −9.41987 −1.15082 −0.575410 0.817865i \(-0.695158\pi\)
−0.575410 + 0.817865i \(0.695158\pi\)
\(68\) 18.7258 13.6051i 2.27084 1.64986i
\(69\) 2.99751 + 9.22539i 0.360858 + 1.11061i
\(70\) −0.945296 + 2.90932i −0.112985 + 0.347731i
\(71\) 0.0943396 + 0.0685417i 0.0111961 + 0.00813441i 0.593369 0.804930i \(-0.297797\pi\)
−0.582173 + 0.813065i \(0.697797\pi\)
\(72\) 3.53634 + 2.56930i 0.416762 + 0.302795i
\(73\) −0.190055 + 0.584930i −0.0222443 + 0.0684608i −0.961562 0.274586i \(-0.911459\pi\)
0.939318 + 0.343047i \(0.111459\pi\)
\(74\) −4.09695 12.6091i −0.476261 1.46578i
\(75\) 3.96340 2.87958i 0.457654 0.332505i
\(76\) −11.1830 −1.28277
\(77\) 0 0
\(78\) 11.0789 1.25443
\(79\) 6.90033 5.01339i 0.776348 0.564050i −0.127533 0.991834i \(-0.540706\pi\)
0.903881 + 0.427784i \(0.140706\pi\)
\(80\) 1.34232 + 4.13122i 0.150075 + 0.461885i
\(81\) −1.63207 + 5.02300i −0.181341 + 0.558111i
\(82\) −0.618364 0.449267i −0.0682868 0.0496133i
\(83\) 0.768997 + 0.558709i 0.0844083 + 0.0613262i 0.629189 0.777252i \(-0.283387\pi\)
−0.544781 + 0.838579i \(0.683387\pi\)
\(84\) −1.73160 + 5.32933i −0.188933 + 0.581477i
\(85\) −2.30414 7.09142i −0.249919 0.769172i
\(86\) −0.260654 + 0.189376i −0.0281070 + 0.0204209i
\(87\) −6.44746 −0.691241
\(88\) 0 0
\(89\) 10.0552 1.06585 0.532923 0.846164i \(-0.321094\pi\)
0.532923 + 0.846164i \(0.321094\pi\)
\(90\) 2.33388 1.69567i 0.246013 0.178739i
\(91\) −0.982152 3.02275i −0.102957 0.316870i
\(92\) 8.16590 25.1320i 0.851353 2.62020i
\(93\) −11.2868 8.20034i −1.17039 0.850336i
\(94\) −18.4339 13.3930i −1.90132 1.38139i
\(95\) −1.11323 + 3.42616i −0.114215 + 0.351516i
\(96\) −0.390979 1.20331i −0.0399041 0.122812i
\(97\) −14.2201 + 10.3315i −1.44383 + 1.04901i −0.456608 + 0.889668i \(0.650936\pi\)
−0.987224 + 0.159337i \(0.949064\pi\)
\(98\) 2.43045 0.245513
\(99\) 0 0
\(100\) −13.3461 −1.33461
\(101\) −10.0934 + 7.33330i −1.00433 + 0.729690i −0.963013 0.269456i \(-0.913156\pi\)
−0.0413196 + 0.999146i \(0.513156\pi\)
\(102\) −6.38130 19.6396i −0.631843 1.94461i
\(103\) 2.53951 7.81581i 0.250225 0.770114i −0.744508 0.667614i \(-0.767316\pi\)
0.994733 0.102500i \(-0.0326843\pi\)
\(104\) −11.9183 8.65915i −1.16869 0.849100i
\(105\) 1.46039 + 1.06103i 0.142519 + 0.103546i
\(106\) 3.26852 10.0595i 0.317466 0.977061i
\(107\) −3.76646 11.5920i −0.364117 1.12064i −0.950532 0.310627i \(-0.899461\pi\)
0.586414 0.810011i \(-0.300539\pi\)
\(108\) 17.8754 12.9873i 1.72006 1.24970i
\(109\) −0.886088 −0.0848718 −0.0424359 0.999099i \(-0.513512\pi\)
−0.0424359 + 0.999099i \(0.513512\pi\)
\(110\) 0 0
\(111\) −7.82353 −0.742577
\(112\) 2.79210 2.02858i 0.263829 0.191683i
\(113\) 1.40449 + 4.32257i 0.132123 + 0.406633i 0.995131 0.0985566i \(-0.0314225\pi\)
−0.863008 + 0.505190i \(0.831423\pi\)
\(114\) −3.08307 + 9.48872i −0.288756 + 0.888700i
\(115\) −6.88689 5.00362i −0.642206 0.466590i
\(116\) 14.2098 + 10.3241i 1.31935 + 0.958565i
\(117\) −0.926221 + 2.85061i −0.0856291 + 0.263539i
\(118\) −5.21744 16.0576i −0.480304 1.47823i
\(119\) −4.79276 + 3.48215i −0.439352 + 0.319208i
\(120\) 8.36702 0.763801
\(121\) 0 0
\(122\) 5.95984 0.539579
\(123\) −0.364895 + 0.265112i −0.0329015 + 0.0239043i
\(124\) 11.7446 + 36.1462i 1.05470 + 3.24602i
\(125\) −3.27325 + 10.0740i −0.292768 + 0.901047i
\(126\) −1.85430 1.34723i −0.165194 0.120021i
\(127\) −6.49462 4.71861i −0.576304 0.418709i 0.261086 0.965316i \(-0.415919\pi\)
−0.837390 + 0.546606i \(0.815919\pi\)
\(128\) −6.24921 + 19.2331i −0.552357 + 1.69998i
\(129\) 0.0587507 + 0.180816i 0.00517271 + 0.0159200i
\(130\) −7.86574 + 5.71479i −0.689871 + 0.501220i
\(131\) −0.101461 −0.00886466 −0.00443233 0.999990i \(-0.501411\pi\)
−0.00443233 + 0.999990i \(0.501411\pi\)
\(132\) 0 0
\(133\) 2.86222 0.248186
\(134\) 18.5221 13.4571i 1.60006 1.16251i
\(135\) −2.19951 6.76938i −0.189303 0.582616i
\(136\) −8.48538 + 26.1153i −0.727615 + 2.23937i
\(137\) 3.69243 + 2.68271i 0.315465 + 0.229199i 0.734238 0.678892i \(-0.237540\pi\)
−0.418773 + 0.908091i \(0.637540\pi\)
\(138\) −19.0732 13.8575i −1.62362 1.17963i
\(139\) 1.18209 3.63810i 0.100264 0.308580i −0.888326 0.459213i \(-0.848131\pi\)
0.988590 + 0.150634i \(0.0481314\pi\)
\(140\) −1.51962 4.67691i −0.128431 0.395271i
\(141\) −10.8778 + 7.90322i −0.916080 + 0.665571i
\(142\) −0.283415 −0.0237837
\(143\) 0 0
\(144\) −3.25469 −0.271224
\(145\) 4.57755 3.32579i 0.380145 0.276192i
\(146\) −0.461920 1.42164i −0.0382288 0.117656i
\(147\) 0.443194 1.36401i 0.0365540 0.112502i
\(148\) 17.2426 + 12.5275i 1.41733 + 1.02975i
\(149\) −3.94172 2.86383i −0.322918 0.234614i 0.414501 0.910049i \(-0.363956\pi\)
−0.737420 + 0.675435i \(0.763956\pi\)
\(150\) −3.67942 + 11.3241i −0.300424 + 0.924609i
\(151\) 5.24521 + 16.1431i 0.426849 + 1.31371i 0.901212 + 0.433378i \(0.142678\pi\)
−0.474363 + 0.880329i \(0.657322\pi\)
\(152\) 10.7330 7.79798i 0.870561 0.632499i
\(153\) 5.58681 0.451667
\(154\) 0 0
\(155\) 12.2434 0.983410
\(156\) −14.4085 + 10.4684i −1.15361 + 0.838144i
\(157\) 0.693691 + 2.13496i 0.0553625 + 0.170388i 0.974914 0.222580i \(-0.0714480\pi\)
−0.919552 + 0.392969i \(0.871448\pi\)
\(158\) −6.40593 + 19.7154i −0.509628 + 1.56847i
\(159\) −5.04952 3.66869i −0.400453 0.290946i
\(160\) 0.898287 + 0.652644i 0.0710158 + 0.0515960i
\(161\) −2.09001 + 6.43240i −0.164716 + 0.506944i
\(162\) −3.96667 12.2082i −0.311651 0.959164i
\(163\) 12.8126 9.30890i 1.00356 0.729129i 0.0407118 0.999171i \(-0.487037\pi\)
0.962849 + 0.270042i \(0.0870374\pi\)
\(164\) 1.22872 0.0959470
\(165\) 0 0
\(166\) −2.31022 −0.179308
\(167\) 16.7803 12.1916i 1.29850 0.943413i 0.298557 0.954392i \(-0.403495\pi\)
0.999940 + 0.0109787i \(0.00349470\pi\)
\(168\) −2.05426 6.32235i −0.158489 0.487780i
\(169\) −0.895639 + 2.75649i −0.0688953 + 0.212038i
\(170\) 14.6613 + 10.6520i 1.12447 + 0.816974i
\(171\) −2.18372 1.58656i −0.166993 0.121327i
\(172\) 0.160050 0.492583i 0.0122037 0.0375591i
\(173\) 6.66099 + 20.5004i 0.506426 + 1.55862i 0.798361 + 0.602180i \(0.205701\pi\)
−0.291935 + 0.956438i \(0.594299\pi\)
\(174\) 12.6775 9.21075i 0.961079 0.698265i
\(175\) 3.41585 0.258214
\(176\) 0 0
\(177\) −9.96322 −0.748881
\(178\) −19.7712 + 14.3647i −1.48192 + 1.07668i
\(179\) 1.47760 + 4.54758i 0.110441 + 0.339902i 0.990969 0.134092i \(-0.0428118\pi\)
−0.880528 + 0.473994i \(0.842812\pi\)
\(180\) −1.43308 + 4.41057i −0.106816 + 0.328745i
\(181\) 6.35309 + 4.61579i 0.472221 + 0.343089i 0.798306 0.602252i \(-0.205730\pi\)
−0.326085 + 0.945340i \(0.605730\pi\)
\(182\) 6.24944 + 4.54048i 0.463239 + 0.336563i
\(183\) 1.08678 3.34477i 0.0803371 0.247252i
\(184\) 9.68746 + 29.8149i 0.714169 + 2.19799i
\(185\) 5.55453 4.03560i 0.408377 0.296703i
\(186\) 33.9079 2.48625
\(187\) 0 0
\(188\) 36.6293 2.67146
\(189\) −4.57511 + 3.32401i −0.332790 + 0.241786i
\(190\) −2.70564 8.32712i −0.196288 0.604112i
\(191\) −2.72871 + 8.39810i −0.197442 + 0.607665i 0.802497 + 0.596656i \(0.203504\pi\)
−0.999939 + 0.0110091i \(0.996496\pi\)
\(192\) 10.4967 + 7.62630i 0.757534 + 0.550381i
\(193\) 20.7127 + 15.0486i 1.49093 + 1.08322i 0.973824 + 0.227303i \(0.0729908\pi\)
0.517106 + 0.855921i \(0.327009\pi\)
\(194\) 13.2012 40.6292i 0.947793 2.91701i
\(195\) 1.77292 + 5.45648i 0.126961 + 0.390747i
\(196\) −3.16091 + 2.29654i −0.225779 + 0.164038i
\(197\) 11.1977 0.797802 0.398901 0.916994i \(-0.369392\pi\)
0.398901 + 0.916994i \(0.369392\pi\)
\(198\) 0 0
\(199\) −12.2503 −0.868400 −0.434200 0.900817i \(-0.642969\pi\)
−0.434200 + 0.900817i \(0.642969\pi\)
\(200\) 12.8090 9.30631i 0.905736 0.658056i
\(201\) −4.17483 12.8488i −0.294470 0.906285i
\(202\) 9.37022 28.8386i 0.659287 2.02908i
\(203\) −3.63693 2.64238i −0.255262 0.185459i
\(204\) 26.8567 + 19.5125i 1.88034 + 1.36615i
\(205\) 0.122315 0.376447i 0.00854285 0.0262922i
\(206\) 6.17216 + 18.9959i 0.430035 + 1.32351i
\(207\) 5.16013 3.74905i 0.358654 0.260577i
\(208\) 10.9691 0.760568
\(209\) 0 0
\(210\) −4.38730 −0.302752
\(211\) −11.5395 + 8.38393i −0.794411 + 0.577174i −0.909269 0.416208i \(-0.863359\pi\)
0.114858 + 0.993382i \(0.463359\pi\)
\(212\) 5.25434 + 16.1712i 0.360869 + 1.11064i
\(213\) −0.0516809 + 0.159058i −0.00354112 + 0.0108984i
\(214\) 23.9660 + 17.4123i 1.63828 + 1.19028i
\(215\) −0.134982 0.0980700i −0.00920568 0.00668832i
\(216\) −8.10004 + 24.9294i −0.551138 + 1.69623i
\(217\) −3.00597 9.25141i −0.204058 0.628027i
\(218\) 1.74229 1.26585i 0.118003 0.0857343i
\(219\) −0.882082 −0.0596056
\(220\) 0 0
\(221\) −18.8289 −1.26657
\(222\) 15.3832 11.1766i 1.03245 0.750122i
\(223\) −0.915926 2.81893i −0.0613350 0.188770i 0.915694 0.401876i \(-0.131642\pi\)
−0.977029 + 0.213107i \(0.931642\pi\)
\(224\) 0.272610 0.839006i 0.0182145 0.0560585i
\(225\) −2.60611 1.89345i −0.173740 0.126230i
\(226\) −8.93677 6.49294i −0.594465 0.431904i
\(227\) −2.55126 + 7.85197i −0.169333 + 0.521154i −0.999329 0.0366150i \(-0.988342\pi\)
0.829996 + 0.557769i \(0.188342\pi\)
\(228\) −4.95623 15.2537i −0.328234 1.01020i
\(229\) −10.6047 + 7.70475i −0.700777 + 0.509145i −0.880185 0.474630i \(-0.842582\pi\)
0.179408 + 0.983775i \(0.442582\pi\)
\(230\) 20.6896 1.36423
\(231\) 0 0
\(232\) −20.8371 −1.36802
\(233\) −10.3778 + 7.53992i −0.679873 + 0.493957i −0.873316 0.487155i \(-0.838035\pi\)
0.193443 + 0.981112i \(0.438035\pi\)
\(234\) −2.25114 6.92828i −0.147161 0.452916i
\(235\) 3.64632 11.2222i 0.237860 0.732056i
\(236\) 21.9584 + 15.9537i 1.42937 + 1.03850i
\(237\) 9.89650 + 7.19023i 0.642847 + 0.467056i
\(238\) 4.44936 13.6937i 0.288409 0.887633i
\(239\) 1.53924 + 4.73730i 0.0995653 + 0.306430i 0.988417 0.151765i \(-0.0484958\pi\)
−0.888851 + 0.458196i \(0.848496\pi\)
\(240\) −5.04013 + 3.66187i −0.325339 + 0.236372i
\(241\) 2.62686 0.169211 0.0846053 0.996415i \(-0.473037\pi\)
0.0846053 + 0.996415i \(0.473037\pi\)
\(242\) 0 0
\(243\) 9.39070 0.602414
\(244\) −7.75104 + 5.63146i −0.496209 + 0.360517i
\(245\) 0.388938 + 1.19703i 0.0248484 + 0.0764754i
\(246\) 0.338751 1.04257i 0.0215980 0.0664717i
\(247\) 7.35964 + 5.34709i 0.468283 + 0.340227i
\(248\) −36.4771 26.5021i −2.31630 1.68289i
\(249\) −0.421270 + 1.29654i −0.0266969 + 0.0821646i
\(250\) −7.95547 24.4844i −0.503148 1.54853i
\(251\) 21.2148 15.4134i 1.33906 0.972888i 0.339587 0.940575i \(-0.389713\pi\)
0.999478 0.0323129i \(-0.0102873\pi\)
\(252\) 3.68460 0.232108
\(253\) 0 0
\(254\) 19.5112 1.22424
\(255\) 8.65159 6.28575i 0.541784 0.393629i
\(256\) −9.59733 29.5375i −0.599833 1.84610i
\(257\) 9.25561 28.4858i 0.577349 1.77690i −0.0506881 0.998715i \(-0.516141\pi\)
0.628037 0.778183i \(-0.283859\pi\)
\(258\) −0.373831 0.271604i −0.0232737 0.0169093i
\(259\) −4.41315 3.20634i −0.274220 0.199232i
\(260\) 4.82983 14.8647i 0.299533 0.921868i
\(261\) 1.31007 + 4.03199i 0.0810915 + 0.249574i
\(262\) 0.199500 0.144945i 0.0123251 0.00895474i
\(263\) −3.33709 −0.205774 −0.102887 0.994693i \(-0.532808\pi\)
−0.102887 + 0.994693i \(0.532808\pi\)
\(264\) 0 0
\(265\) 5.47747 0.336478
\(266\) −5.62791 + 4.08892i −0.345070 + 0.250708i
\(267\) 4.45639 + 13.7154i 0.272727 + 0.839366i
\(268\) −11.3732 + 35.0030i −0.694727 + 2.13815i
\(269\) 1.40430 + 1.02028i 0.0856218 + 0.0622079i 0.629773 0.776780i \(-0.283148\pi\)
−0.544151 + 0.838987i \(0.683148\pi\)
\(270\) 13.9955 + 10.1683i 0.851737 + 0.618823i
\(271\) 0.765113 2.35478i 0.0464773 0.143042i −0.925125 0.379663i \(-0.876040\pi\)
0.971602 + 0.236621i \(0.0760399\pi\)
\(272\) −6.31807 19.4450i −0.383089 1.17903i
\(273\) 3.68778 2.67933i 0.223195 0.162161i
\(274\) −11.0928 −0.670141
\(275\) 0 0
\(276\) 37.8995 2.28128
\(277\) 4.17105 3.03045i 0.250614 0.182082i −0.455385 0.890295i \(-0.650498\pi\)
0.705999 + 0.708213i \(0.250498\pi\)
\(278\) 2.87302 + 8.84223i 0.172312 + 0.530322i
\(279\) −2.83478 + 8.72457i −0.169714 + 0.522326i
\(280\) 4.71972 + 3.42908i 0.282057 + 0.204927i
\(281\) −18.2599 13.2666i −1.08930 0.791419i −0.110015 0.993930i \(-0.535090\pi\)
−0.979280 + 0.202510i \(0.935090\pi\)
\(282\) 10.0984 31.0798i 0.601354 1.85078i
\(283\) 2.62280 + 8.07216i 0.155909 + 0.479840i 0.998252 0.0591027i \(-0.0188239\pi\)
−0.842342 + 0.538943i \(0.818824\pi\)
\(284\) 0.368594 0.267799i 0.0218720 0.0158910i
\(285\) −5.16669 −0.306049
\(286\) 0 0
\(287\) −0.314484 −0.0185634
\(288\) −0.673058 + 0.489005i −0.0396603 + 0.0288149i
\(289\) 5.59195 + 17.2102i 0.328938 + 1.01237i
\(290\) −4.24957 + 13.0788i −0.249544 + 0.768016i
\(291\) −20.3945 14.8175i −1.19555 0.868618i
\(292\) 1.94406 + 1.41244i 0.113767 + 0.0826569i
\(293\) −7.60988 + 23.4208i −0.444574 + 1.36826i 0.438376 + 0.898792i \(0.355554\pi\)
−0.882950 + 0.469467i \(0.844446\pi\)
\(294\) 1.07716 + 3.31516i 0.0628214 + 0.193344i
\(295\) 7.07366 5.13932i 0.411844 0.299223i
\(296\) −25.2843 −1.46962
\(297\) 0 0
\(298\) 11.8417 0.685973
\(299\) −17.3908 + 12.6352i −1.00574 + 0.730712i
\(300\) −5.91489 18.2042i −0.341497 1.05102i
\(301\) −0.0409639 + 0.126074i −0.00236112 + 0.00726678i
\(302\) −33.3753 24.2486i −1.92053 1.39535i
\(303\) −14.4760 10.5175i −0.831627 0.604212i
\(304\) −3.05252 + 9.39470i −0.175074 + 0.538823i
\(305\) 0.953737 + 2.93530i 0.0546108 + 0.168075i
\(306\) −10.9852 + 7.98123i −0.627984 + 0.456257i
\(307\) −4.59391 −0.262188 −0.131094 0.991370i \(-0.541849\pi\)
−0.131094 + 0.991370i \(0.541849\pi\)
\(308\) 0 0
\(309\) 11.7863 0.670502
\(310\) −24.0738 + 17.4907i −1.36730 + 0.993403i
\(311\) −0.683154 2.10253i −0.0387381 0.119224i 0.929817 0.368021i \(-0.119965\pi\)
−0.968556 + 0.248798i \(0.919965\pi\)
\(312\) 6.52906 20.0944i 0.369635 1.13762i
\(313\) 7.84688 + 5.70110i 0.443532 + 0.322245i 0.787037 0.616906i \(-0.211614\pi\)
−0.343505 + 0.939151i \(0.611614\pi\)
\(314\) −4.41396 3.20693i −0.249094 0.180977i
\(315\) 0.366789 1.12886i 0.0206662 0.0636041i
\(316\) −10.2979 31.6937i −0.579303 1.78291i
\(317\) −5.22252 + 3.79439i −0.293326 + 0.213114i −0.724709 0.689055i \(-0.758026\pi\)
0.431383 + 0.902169i \(0.358026\pi\)
\(318\) 15.1698 0.850680
\(319\) 0 0
\(320\) −11.3863 −0.636513
\(321\) 14.1423 10.2750i 0.789347 0.573494i
\(322\) −5.07968 15.6337i −0.283080 0.871229i
\(323\) 5.23978 16.1264i 0.291549 0.897297i
\(324\) 16.6943 + 12.1291i 0.927463 + 0.673841i
\(325\) 8.78319 + 6.38136i 0.487204 + 0.353974i
\(326\) −11.8946 + 36.6078i −0.658780 + 2.02752i
\(327\) −0.392709 1.20863i −0.0217169 0.0668376i
\(328\) −1.17928 + 0.856798i −0.0651149 + 0.0473087i
\(329\) −9.37505 −0.516863
\(330\) 0 0
\(331\) 3.62076 0.199015 0.0995075 0.995037i \(-0.468273\pi\)
0.0995075 + 0.995037i \(0.468273\pi\)
\(332\) 3.00455 2.18293i 0.164896 0.119804i
\(333\) 1.58968 + 4.89253i 0.0871139 + 0.268109i
\(334\) −15.5780 + 47.9441i −0.852389 + 2.62338i
\(335\) 9.59182 + 6.96886i 0.524057 + 0.380750i
\(336\) 4.00445 + 2.90940i 0.218461 + 0.158721i
\(337\) 1.97928 6.09161i 0.107818 0.331831i −0.882563 0.470194i \(-0.844184\pi\)
0.990382 + 0.138363i \(0.0441840\pi\)
\(338\) −2.17681 6.69953i −0.118403 0.364406i
\(339\) −5.27357 + 3.83147i −0.286421 + 0.208097i
\(340\) −29.1327 −1.57994
\(341\) 0 0
\(342\) 6.56033 0.354742
\(343\) 0.809017 0.587785i 0.0436828 0.0317374i
\(344\) 0.189872 + 0.584367i 0.0102372 + 0.0315070i
\(345\) 3.77276 11.6114i 0.203119 0.625135i
\(346\) −42.3839 30.7937i −2.27857 1.65548i
\(347\) −14.1254 10.2627i −0.758293 0.550932i 0.140093 0.990138i \(-0.455260\pi\)
−0.898386 + 0.439206i \(0.855260\pi\)
\(348\) −7.78441 + 23.9580i −0.417288 + 1.28428i
\(349\) 6.68246 + 20.5665i 0.357704 + 1.10090i 0.954425 + 0.298451i \(0.0964699\pi\)
−0.596721 + 0.802449i \(0.703530\pi\)
\(350\) −6.71650 + 4.87983i −0.359012 + 0.260838i
\(351\) −17.9738 −0.959371
\(352\) 0 0
\(353\) 4.40150 0.234268 0.117134 0.993116i \(-0.462629\pi\)
0.117134 + 0.993116i \(0.462629\pi\)
\(354\) 19.5905 14.2333i 1.04122 0.756491i
\(355\) −0.0453542 0.139586i −0.00240715 0.00740844i
\(356\) 12.1402 37.3637i 0.643430 1.98027i
\(357\) −6.87381 4.99412i −0.363801 0.264317i
\(358\) −9.40197 6.83093i −0.496909 0.361026i
\(359\) 3.30084 10.1589i 0.174212 0.536168i −0.825385 0.564570i \(-0.809042\pi\)
0.999597 + 0.0284023i \(0.00904194\pi\)
\(360\) −1.70011 5.23240i −0.0896037 0.275772i
\(361\) 8.74362 6.35261i 0.460191 0.334348i
\(362\) −19.0860 −1.00314
\(363\) 0 0
\(364\) −12.4180 −0.650879
\(365\) 0.626258 0.455003i 0.0327799 0.0238160i
\(366\) 2.64137 + 8.12929i 0.138067 + 0.424925i
\(367\) 3.15715 9.71670i 0.164802 0.507207i −0.834220 0.551432i \(-0.814082\pi\)
0.999022 + 0.0442244i \(0.0140817\pi\)
\(368\) −18.8842 13.7202i −0.984406 0.715213i
\(369\) 0.239934 + 0.174323i 0.0124905 + 0.00907487i
\(370\) −5.15655 + 15.8702i −0.268076 + 0.825054i
\(371\) −1.34482 4.13893i −0.0698195 0.214882i
\(372\) −44.0987 + 32.0396i −2.28641 + 1.66117i
\(373\) 27.8851 1.44383 0.721917 0.691980i \(-0.243261\pi\)
0.721917 + 0.691980i \(0.243261\pi\)
\(374\) 0 0
\(375\) −15.1918 −0.784499
\(376\) −35.1554 + 25.5419i −1.81300 + 1.31722i
\(377\) −4.41526 13.5888i −0.227397 0.699857i
\(378\) 4.24731 13.0719i 0.218458 0.672344i
\(379\) −0.928776 0.674795i −0.0477080 0.0346619i 0.563676 0.825996i \(-0.309387\pi\)
−0.611384 + 0.791334i \(0.709387\pi\)
\(380\) 11.3871 + 8.27322i 0.584146 + 0.424407i
\(381\) 3.55787 10.9500i 0.182275 0.560985i
\(382\) −6.63200 20.4112i −0.339322 1.04433i
\(383\) 16.1412 11.7273i 0.824777 0.599235i −0.0933000 0.995638i \(-0.529742\pi\)
0.918077 + 0.396403i \(0.129742\pi\)
\(384\) −29.0038 −1.48009
\(385\) 0 0
\(386\) −62.2251 −3.16717
\(387\) 0.101138 0.0734808i 0.00514111 0.00373524i
\(388\) 21.2218 + 65.3139i 1.07737 + 3.31581i
\(389\) 0.803445 2.47275i 0.0407363 0.125373i −0.928620 0.371032i \(-0.879004\pi\)
0.969356 + 0.245658i \(0.0790041\pi\)
\(390\) −11.2811 8.19619i −0.571240 0.415030i
\(391\) 32.4155 + 23.5512i 1.63932 + 1.19104i
\(392\) 1.43233 4.40826i 0.0723436 0.222651i
\(393\) −0.0449668 0.138393i −0.00226827 0.00698103i
\(394\) −22.0178 + 15.9968i −1.10924 + 0.805909i
\(395\) −10.7352 −0.540148
\(396\) 0 0
\(397\) 8.77237 0.440272 0.220136 0.975469i \(-0.429350\pi\)
0.220136 + 0.975469i \(0.429350\pi\)
\(398\) 24.0875 17.5006i 1.20740 0.877224i
\(399\) 1.26852 + 3.90410i 0.0635053 + 0.195449i
\(400\) −3.64296 + 11.2119i −0.182148 + 0.560594i
\(401\) −22.9385 16.6658i −1.14549 0.832249i −0.157617 0.987500i \(-0.550381\pi\)
−0.987875 + 0.155252i \(0.950381\pi\)
\(402\) 26.5645 + 19.3002i 1.32492 + 0.962607i
\(403\) 9.55389 29.4039i 0.475913 1.46471i
\(404\) 15.0632 + 46.3598i 0.749422 + 2.30648i
\(405\) 5.37790 3.90727i 0.267230 0.194154i
\(406\) 10.9261 0.542252
\(407\) 0 0
\(408\) −39.3822 −1.94971
\(409\) 16.1039 11.7002i 0.796286 0.578536i −0.113536 0.993534i \(-0.536218\pi\)
0.909822 + 0.414998i \(0.136218\pi\)
\(410\) 0.297281 + 0.914937i 0.0146817 + 0.0451855i
\(411\) −2.02278 + 6.22547i −0.0997763 + 0.307080i
\(412\) −25.9764 18.8730i −1.27977 0.929805i
\(413\) −5.62012 4.08326i −0.276548 0.200924i
\(414\) −4.79041 + 14.7434i −0.235436 + 0.724596i
\(415\) −0.369698 1.13781i −0.0181478 0.0558531i
\(416\) 2.26836 1.64806i 0.111216 0.0808029i
\(417\) 5.48631 0.268666
\(418\) 0 0
\(419\) −30.8957 −1.50935 −0.754676 0.656097i \(-0.772206\pi\)
−0.754676 + 0.656097i \(0.772206\pi\)
\(420\) 5.70587 4.14556i 0.278418 0.202283i
\(421\) −7.47609 23.0090i −0.364362 1.12139i −0.950379 0.311093i \(-0.899305\pi\)
0.586017 0.810299i \(-0.300695\pi\)
\(422\) 10.7127 32.9703i 0.521486 1.60497i
\(423\) 7.15265 + 5.19671i 0.347774 + 0.252673i
\(424\) −16.3192 11.8566i −0.792531 0.575808i
\(425\) 6.25330 19.2457i 0.303330 0.933552i
\(426\) −0.125608 0.386582i −0.00608573 0.0187300i
\(427\) 1.98383 1.44134i 0.0960045 0.0697513i
\(428\) −47.6218 −2.30188
\(429\) 0 0
\(430\) 0.405513 0.0195556
\(431\) 15.6950 11.4031i 0.756000 0.549266i −0.141681 0.989912i \(-0.545251\pi\)
0.897681 + 0.440646i \(0.145251\pi\)
\(432\) −6.03115 18.5620i −0.290174 0.893063i
\(433\) −6.60917 + 20.3409i −0.317616 + 0.977522i 0.657048 + 0.753849i \(0.271805\pi\)
−0.974664 + 0.223674i \(0.928195\pi\)
\(434\) 19.1270 + 13.8966i 0.918125 + 0.667057i
\(435\) 6.56516 + 4.76987i 0.314775 + 0.228698i
\(436\) −1.06983 + 3.29259i −0.0512354 + 0.157686i
\(437\) −5.98208 18.4109i −0.286162 0.880715i
\(438\) 1.73442 1.26013i 0.0828737 0.0602113i
\(439\) 31.7315 1.51446 0.757232 0.653146i \(-0.226551\pi\)
0.757232 + 0.653146i \(0.226551\pi\)
\(440\) 0 0
\(441\) −0.943053 −0.0449073
\(442\) 37.0228 26.8986i 1.76100 1.27944i
\(443\) −0.514855 1.58456i −0.0244615 0.0752847i 0.938081 0.346417i \(-0.112602\pi\)
−0.962542 + 0.271133i \(0.912602\pi\)
\(444\) −9.44582 + 29.0712i −0.448279 + 1.37966i
\(445\) −10.2387 7.43886i −0.485362 0.352636i
\(446\) 5.82805 + 4.23432i 0.275966 + 0.200501i
\(447\) 2.15935 6.64578i 0.102134 0.314335i
\(448\) 2.79554 + 8.60379i 0.132077 + 0.406491i
\(449\) 13.9036 10.1016i 0.656151 0.476722i −0.209210 0.977871i \(-0.567089\pi\)
0.865361 + 0.501149i \(0.167089\pi\)
\(450\) 7.82927 0.369076
\(451\) 0 0
\(452\) 17.7578 0.835258
\(453\) −19.6947 + 14.3091i −0.925339 + 0.672298i
\(454\) −6.20072 19.0839i −0.291014 0.895650i
\(455\) −1.23617 + 3.80453i −0.0579524 + 0.178359i
\(456\) 15.3933 + 11.1839i 0.720858 + 0.523734i
\(457\) 8.26867 + 6.00754i 0.386792 + 0.281021i 0.764140 0.645051i \(-0.223164\pi\)
−0.377348 + 0.926072i \(0.623164\pi\)
\(458\) 9.84486 30.2994i 0.460020 1.41580i
\(459\) 10.3527 + 31.8624i 0.483224 + 1.48721i
\(460\) −26.9078 + 19.5496i −1.25458 + 0.911506i
\(461\) 22.1160 1.03004 0.515022 0.857177i \(-0.327784\pi\)
0.515022 + 0.857177i \(0.327784\pi\)
\(462\) 0 0
\(463\) −30.3717 −1.41149 −0.705747 0.708464i \(-0.749389\pi\)
−0.705747 + 0.708464i \(0.749389\pi\)
\(464\) 12.5519 9.11947i 0.582706 0.423361i
\(465\) 5.42618 + 16.7001i 0.251633 + 0.774447i
\(466\) 9.63424 29.6512i 0.446298 1.37356i
\(467\) −20.3799 14.8068i −0.943067 0.685178i 0.00608981 0.999981i \(-0.498062\pi\)
−0.949157 + 0.314803i \(0.898062\pi\)
\(468\) 9.47424 + 6.88344i 0.437947 + 0.318187i
\(469\) 2.91090 8.95883i 0.134413 0.413680i
\(470\) 8.86220 + 27.2751i 0.408783 + 1.25810i
\(471\) −2.60467 + 1.89240i −0.120017 + 0.0871973i
\(472\) −32.1995 −1.48210
\(473\) 0 0
\(474\) −29.7311 −1.36560
\(475\) −7.90968 + 5.74672i −0.362921 + 0.263677i
\(476\) 7.15262 + 22.0135i 0.327840 + 1.00899i
\(477\) −1.26823 + 3.90322i −0.0580685 + 0.178716i
\(478\) −9.79421 7.11591i −0.447977 0.325474i
\(479\) −17.1544 12.4634i −0.783804 0.569467i 0.122314 0.992491i \(-0.460968\pi\)
−0.906118 + 0.423025i \(0.860968\pi\)
\(480\) −0.492098 + 1.51452i −0.0224611 + 0.0691281i
\(481\) −5.35759 16.4890i −0.244285 0.751832i
\(482\) −5.16513 + 3.75268i −0.235265 + 0.170930i
\(483\) −9.70015 −0.441372
\(484\) 0 0
\(485\) 22.1230 1.00455
\(486\) −18.4647 + 13.4154i −0.837577 + 0.608535i
\(487\) −5.19759 15.9965i −0.235525 0.724873i −0.997051 0.0767381i \(-0.975549\pi\)
0.761526 0.648134i \(-0.224451\pi\)
\(488\) 3.51229 10.8097i 0.158994 0.489333i
\(489\) 18.3759 + 13.3509i 0.830988 + 0.603748i
\(490\) −2.47482 1.79806i −0.111801 0.0812281i
\(491\) −1.49504 + 4.60125i −0.0674701 + 0.207652i −0.979107 0.203344i \(-0.934819\pi\)
0.911637 + 0.410996i \(0.134819\pi\)
\(492\) 0.544562 + 1.67599i 0.0245508 + 0.0755595i
\(493\) −21.5458 + 15.6540i −0.970376 + 0.705019i
\(494\) −22.1099 −0.994770
\(495\) 0 0
\(496\) 33.5719 1.50742
\(497\) −0.0943396 + 0.0685417i −0.00423171 + 0.00307452i
\(498\) −1.02388 3.15117i −0.0458810 0.141207i
\(499\) 9.45084 29.0867i 0.423078 1.30210i −0.481745 0.876311i \(-0.659997\pi\)
0.904823 0.425788i \(-0.140003\pi\)
\(500\) 33.4818 + 24.3259i 1.49735 + 1.08789i
\(501\) 24.0664 + 17.4852i 1.07521 + 0.781183i
\(502\) −19.6947 + 60.6142i −0.879019 + 2.70534i
\(503\) 8.72684 + 26.8585i 0.389111 + 1.19756i 0.933454 + 0.358697i \(0.116779\pi\)
−0.544343 + 0.838863i \(0.683221\pi\)
\(504\) −3.53634 + 2.56930i −0.157521 + 0.114446i
\(505\) 15.7029 0.698768
\(506\) 0 0
\(507\) −4.15683 −0.184611
\(508\) −25.3751 + 18.4361i −1.12584 + 0.817970i
\(509\) −1.29807 3.99505i −0.0575360 0.177078i 0.918158 0.396214i \(-0.129676\pi\)
−0.975694 + 0.219136i \(0.929676\pi\)
\(510\) −8.03171 + 24.7191i −0.355650 + 1.09458i
\(511\) −0.497571 0.361506i −0.0220112 0.0159921i
\(512\) 28.3466 + 20.5950i 1.25275 + 0.910179i
\(513\) 5.00183 15.3941i 0.220836 0.679664i
\(514\) 22.4953 + 69.2335i 0.992226 + 3.05376i
\(515\) −8.36804 + 6.07973i −0.368740 + 0.267905i
\(516\) 0.742823 0.0327009
\(517\) 0 0
\(518\) 13.2580 0.582523
\(519\) −25.0107 + 18.1713i −1.09785 + 0.797633i
\(520\) 5.72977 + 17.6344i 0.251267 + 0.773321i
\(521\) −6.38026 + 19.6364i −0.279524 + 0.860287i 0.708462 + 0.705749i \(0.249389\pi\)
−0.987987 + 0.154539i \(0.950611\pi\)
\(522\) −8.33601 6.05646i −0.364857 0.265084i
\(523\) −18.3113 13.3040i −0.800699 0.581742i 0.110420 0.993885i \(-0.464780\pi\)
−0.911119 + 0.412143i \(0.864780\pi\)
\(524\) −0.122500 + 0.377015i −0.00535142 + 0.0164700i
\(525\) 1.51388 + 4.65925i 0.0660713 + 0.203347i
\(526\) 6.56164 4.76731i 0.286101 0.207865i
\(527\) −57.6275 −2.51030
\(528\) 0 0
\(529\) 22.7440 0.988869
\(530\) −10.7702 + 7.82502i −0.467828 + 0.339897i
\(531\) 2.02445 + 6.23061i 0.0878535 + 0.270385i
\(532\) 3.45573 10.6356i 0.149825 0.461113i
\(533\) −0.808636 0.587508i −0.0350259 0.0254478i
\(534\) −28.3560 20.6019i −1.22709 0.891530i
\(535\) −4.74058 + 14.5900i −0.204953 + 0.630781i
\(536\) −13.4924 41.5252i −0.582781 1.79362i
\(537\) −5.54808 + 4.03092i −0.239418 + 0.173947i
\(538\) −4.21881 −0.181886
\(539\) 0 0
\(540\) −27.8098 −1.19674
\(541\) 34.5582 25.1080i 1.48577 1.07948i 0.510134 0.860095i \(-0.329596\pi\)
0.975639 0.219383i \(-0.0704043\pi\)
\(542\) 1.85957 + 5.72317i 0.0798754 + 0.245831i
\(543\) −3.48033 + 10.7114i −0.149355 + 0.459669i
\(544\) −4.22810 3.07189i −0.181278 0.131706i
\(545\) 0.902263 + 0.655532i 0.0386487 + 0.0280799i
\(546\) −3.42355 + 10.5366i −0.146515 + 0.450926i
\(547\) −13.7459 42.3056i −0.587733 1.80886i −0.588007 0.808856i \(-0.700087\pi\)
0.000274240 1.00000i \(-0.499913\pi\)
\(548\) 14.4267 10.4816i 0.616277 0.447752i
\(549\) −2.31251 −0.0986955
\(550\) 0 0
\(551\) 12.8671 0.548156
\(552\) −36.3745 + 26.4276i −1.54820 + 1.12483i
\(553\) 2.63569 + 8.11183i 0.112081 + 0.344950i
\(554\) −3.87220 + 11.9174i −0.164514 + 0.506322i
\(555\) 7.96634 + 5.78788i 0.338152 + 0.245682i
\(556\) −12.0915 8.78500i −0.512794 0.372567i
\(557\) 7.72268 23.7680i 0.327220 1.00708i −0.643208 0.765691i \(-0.722397\pi\)
0.970428 0.241389i \(-0.0776030\pi\)
\(558\) −6.88981 21.2047i −0.291669 0.897665i
\(559\) −0.340857 + 0.247647i −0.0144167 + 0.0104744i
\(560\) −4.34382 −0.183560
\(561\) 0 0
\(562\) 54.8565 2.31398
\(563\) 7.28929 5.29598i 0.307207 0.223199i −0.423490 0.905901i \(-0.639195\pi\)
0.730697 + 0.682702i \(0.239195\pi\)
\(564\) 16.2339 + 49.9627i 0.683569 + 2.10381i
\(565\) 1.76773 5.44052i 0.0743690 0.228884i
\(566\) −16.6889 12.1252i −0.701487 0.509660i
\(567\) −4.27282 3.10438i −0.179442 0.130372i
\(568\) −0.167024 + 0.514048i −0.00700818 + 0.0215690i
\(569\) −9.01521 27.7460i −0.377937 1.16317i −0.941475 0.337082i \(-0.890560\pi\)
0.563538 0.826090i \(-0.309440\pi\)
\(570\) 10.1592 7.38106i 0.425520 0.309158i
\(571\) −1.78994 −0.0749067 −0.0374533 0.999298i \(-0.511925\pi\)
−0.0374533 + 0.999298i \(0.511925\pi\)
\(572\) 0 0
\(573\) −12.6645 −0.529065
\(574\) 0.618364 0.449267i 0.0258100 0.0187521i
\(575\) −7.13917 21.9721i −0.297724 0.916300i
\(576\) 2.63634 8.11383i 0.109848 0.338076i
\(577\) 17.4626 + 12.6873i 0.726978 + 0.528180i 0.888606 0.458671i \(-0.151675\pi\)
−0.161628 + 0.986852i \(0.551675\pi\)
\(578\) −35.5816 25.8515i −1.48000 1.07528i
\(579\) −11.3468 + 34.9218i −0.471556 + 1.45130i
\(580\) −6.83145 21.0250i −0.283660 0.873017i
\(581\) −0.768997 + 0.558709i −0.0319034 + 0.0231791i
\(582\) 61.2694 2.53970
\(583\) 0 0
\(584\) −2.85074 −0.117965
\(585\) 3.05203 2.21743i 0.126186 0.0916793i
\(586\) −18.4955 56.9232i −0.764040 2.35147i
\(587\) 1.70687 5.25321i 0.0704501 0.216823i −0.909632 0.415414i \(-0.863637\pi\)
0.980082 + 0.198591i \(0.0636366\pi\)
\(588\) −4.53340 3.29371i −0.186954 0.135830i
\(589\) 22.5249 + 16.3653i 0.928121 + 0.674319i
\(590\) −6.56684 + 20.2106i −0.270352 + 0.832059i
\(591\) 4.96275 + 15.2738i 0.204140 + 0.628279i
\(592\) 15.2308 11.0658i 0.625982 0.454802i
\(593\) 40.7867 1.67491 0.837454 0.546508i \(-0.184043\pi\)
0.837454 + 0.546508i \(0.184043\pi\)
\(594\) 0 0
\(595\) 7.45636 0.305681
\(596\) −15.4007 + 11.1893i −0.630837 + 0.458330i
\(597\) −5.42925 16.7095i −0.222205 0.683875i
\(598\) 16.1448 49.6886i 0.660210 2.03192i
\(599\) 21.4510 + 15.5851i 0.876465 + 0.636789i 0.932314 0.361650i \(-0.117787\pi\)
−0.0558491 + 0.998439i \(0.517787\pi\)
\(600\) 18.3708 + 13.3472i 0.749985 + 0.544896i
\(601\) 11.6715 35.9213i 0.476092 1.46526i −0.368387 0.929673i \(-0.620090\pi\)
0.844479 0.535589i \(-0.179910\pi\)
\(602\) −0.0995608 0.306417i −0.00405780 0.0124886i
\(603\) −7.18685 + 5.22155i −0.292671 + 0.212638i
\(604\) 66.3186 2.69847
\(605\) 0 0
\(606\) 43.4890 1.76662
\(607\) −22.4295 + 16.2960i −0.910385 + 0.661433i −0.941112 0.338095i \(-0.890218\pi\)
0.0307275 + 0.999528i \(0.490218\pi\)
\(608\) 0.780268 + 2.40142i 0.0316441 + 0.0973904i
\(609\) 1.99238 6.13190i 0.0807351 0.248477i
\(610\) −6.06864 4.40912i −0.245712 0.178520i
\(611\) −24.1061 17.5141i −0.975229 0.708546i
\(612\) 6.74530 20.7599i 0.272662 0.839169i
\(613\) −11.1946 34.4534i −0.452145 1.39156i −0.874454 0.485108i \(-0.838780\pi\)
0.422309 0.906452i \(-0.361220\pi\)
\(614\) 9.03289 6.56278i 0.364538 0.264852i
\(615\) 0.567687 0.0228914
\(616\) 0 0
\(617\) 41.1920 1.65833 0.829163 0.559007i \(-0.188817\pi\)
0.829163 + 0.559007i \(0.188817\pi\)
\(618\) −23.1752 + 16.8378i −0.932244 + 0.677315i
\(619\) −11.0441 33.9903i −0.443901 1.36619i −0.883685 0.468082i \(-0.844945\pi\)
0.439784 0.898104i \(-0.355055\pi\)
\(620\) 14.7821 45.4947i 0.593665 1.82711i
\(621\) 30.9435 + 22.4817i 1.24172 + 0.902161i
\(622\) 4.34691 + 3.15822i 0.174295 + 0.126633i
\(623\) −3.10722 + 9.56303i −0.124488 + 0.383135i
\(624\) 4.86143 + 14.9619i 0.194613 + 0.598957i
\(625\) −3.03159 + 2.20258i −0.121264 + 0.0881032i
\(626\) −23.5736 −0.942192
\(627\) 0 0
\(628\) 8.77077 0.349992
\(629\) −26.1443 + 18.9949i −1.04244 + 0.757378i
\(630\) 0.891464 + 2.74364i 0.0355168 + 0.109309i
\(631\) 0.854456 2.62975i 0.0340154 0.104689i −0.932607 0.360893i \(-0.882472\pi\)
0.966623 + 0.256204i \(0.0824720\pi\)
\(632\) 31.9838 + 23.2376i 1.27225 + 0.924343i
\(633\) −16.5500 12.0243i −0.657804 0.477922i
\(634\) 4.84833 14.9216i 0.192552 0.592614i
\(635\) 3.12231 + 9.60950i 0.123905 + 0.381341i
\(636\) −19.7290 + 14.3340i −0.782306 + 0.568378i
\(637\) 3.17831 0.125929
\(638\) 0 0
\(639\) 0.109970 0.00435033
\(640\) 20.5920 14.9610i 0.813971 0.591385i
\(641\) 11.8930 + 36.6028i 0.469744 + 1.44572i 0.852917 + 0.522046i \(0.174831\pi\)
−0.383173 + 0.923676i \(0.625169\pi\)
\(642\) −13.1290 + 40.4070i −0.518161 + 1.59474i
\(643\) 21.3404 + 15.5047i 0.841582 + 0.611445i 0.922812 0.385250i \(-0.125885\pi\)
−0.0812301 + 0.996695i \(0.525885\pi\)
\(644\) 21.3786 + 15.5325i 0.842435 + 0.612065i
\(645\) 0.0739455 0.227581i 0.00291160 0.00896098i
\(646\) 12.7350 + 39.1944i 0.501054 + 1.54208i
\(647\) 22.1032 16.0589i 0.868968 0.631342i −0.0613422 0.998117i \(-0.519538\pi\)
0.930310 + 0.366775i \(0.119538\pi\)
\(648\) −24.4803 −0.961678
\(649\) 0 0
\(650\) −26.3865 −1.03496
\(651\) 11.2868 8.20034i 0.442365 0.321397i
\(652\) −19.1213 58.8492i −0.748846 2.30471i
\(653\) −2.61479 + 8.04751i −0.102325 + 0.314923i −0.989093 0.147290i \(-0.952945\pi\)
0.886768 + 0.462214i \(0.152945\pi\)
\(654\) 2.49881 + 1.81549i 0.0977112 + 0.0709913i
\(655\) 0.103313 + 0.0750611i 0.00403676 + 0.00293288i
\(656\) 0.335394 1.03224i 0.0130949 0.0403021i
\(657\) 0.179232 + 0.551619i 0.00699251 + 0.0215207i
\(658\) 18.4339 13.3930i 0.718630 0.522115i
\(659\) 5.29247 0.206165 0.103083 0.994673i \(-0.467129\pi\)
0.103083 + 0.994673i \(0.467129\pi\)
\(660\) 0 0
\(661\) −19.2700 −0.749517 −0.374759 0.927122i \(-0.622274\pi\)
−0.374759 + 0.927122i \(0.622274\pi\)
\(662\) −7.11942 + 5.17256i −0.276704 + 0.201037i
\(663\) −8.34485 25.6828i −0.324087 0.997437i
\(664\) −1.36147 + 4.19019i −0.0528355 + 0.162611i
\(665\) −2.91446 2.11748i −0.113018 0.0821124i
\(666\) −10.1151 7.34908i −0.391954 0.284771i
\(667\) −9.39565 + 28.9168i −0.363801 + 1.11966i
\(668\) −25.0425 77.0730i −0.968925 2.98204i
\(669\) 3.43912 2.49867i 0.132964 0.0966041i
\(670\) −28.8158 −1.11325
\(671\) 0 0
\(672\) 1.26523 0.0488074
\(673\) −15.3650 + 11.1633i −0.592278 + 0.430315i −0.843130 0.537710i \(-0.819289\pi\)
0.250851 + 0.968026i \(0.419289\pi\)
\(674\) 4.81055 + 14.8054i 0.185296 + 0.570281i
\(675\) 5.96932 18.3717i 0.229759 0.707126i
\(676\) 9.16142 + 6.65616i 0.352362 + 0.256006i
\(677\) 26.2299 + 19.0571i 1.00810 + 0.732424i 0.963809 0.266595i \(-0.0858986\pi\)
0.0442864 + 0.999019i \(0.485899\pi\)
\(678\) 4.89572 15.0675i 0.188019 0.578663i
\(679\) −5.43159 16.7167i −0.208445 0.641529i
\(680\) 27.9605 20.3145i 1.07224 0.779025i
\(681\) −11.8409 −0.453744
\(682\) 0 0
\(683\) 15.1260 0.578779 0.289389 0.957211i \(-0.406548\pi\)
0.289389 + 0.957211i \(0.406548\pi\)
\(684\) −8.53200 + 6.19886i −0.326229 + 0.237019i
\(685\) −1.77515 5.46335i −0.0678250 0.208744i
\(686\) −0.751051 + 2.31150i −0.0286753 + 0.0882534i
\(687\) −15.2093 11.0502i −0.580271 0.421592i
\(688\) −0.370127 0.268913i −0.0141109 0.0102522i
\(689\) 4.27425 13.1548i 0.162836 0.501157i
\(690\) 9.16952 + 28.2209i 0.349078 + 1.07435i
\(691\) 25.4119 18.4628i 0.966712 0.702358i 0.0120125 0.999928i \(-0.496176\pi\)
0.954700 + 0.297570i \(0.0961762\pi\)
\(692\) 84.2192 3.20153
\(693\) 0 0
\(694\) 42.4357 1.61084
\(695\) −3.89515 + 2.83000i −0.147752 + 0.107348i
\(696\) −9.23489 28.4221i −0.350048 1.07734i
\(697\) −0.575718 + 1.77188i −0.0218069 + 0.0671146i
\(698\) −42.5205 30.8930i −1.60943 1.16932i
\(699\) −14.8839 10.8138i −0.562962 0.409016i
\(700\) 4.12416 12.6929i 0.155879 0.479745i
\(701\) 4.96426 + 15.2784i 0.187498 + 0.577058i 0.999982 0.00592402i \(-0.00188568\pi\)
−0.812485 + 0.582982i \(0.801886\pi\)
\(702\) 35.3415 25.6771i 1.33388 0.969120i
\(703\) 15.6133 0.588865
\(704\) 0 0
\(705\) 16.9232 0.637366
\(706\) −8.65457 + 6.28791i −0.325719 + 0.236649i
\(707\) −3.85534 11.8655i −0.144995 0.446249i
\(708\) −12.0292 + 37.0221i −0.452085 + 1.39137i
\(709\) −32.1162 23.3338i −1.20615 0.876318i −0.211273 0.977427i \(-0.567761\pi\)
−0.994875 + 0.101109i \(0.967761\pi\)
\(710\) 0.288589 + 0.209672i 0.0108306 + 0.00786886i
\(711\) 2.48560 7.64988i 0.0932172 0.286893i
\(712\) 14.4023 + 44.3258i 0.539749 + 1.66118i
\(713\) −53.2263 + 38.6712i −1.99334 + 1.44825i
\(714\) 20.6503 0.772819
\(715\) 0 0
\(716\) 18.6822 0.698187
\(717\) −5.77954 + 4.19909i −0.215841 + 0.156818i
\(718\) 8.02253 + 24.6908i 0.299398 + 0.921453i
\(719\) −3.04765 + 9.37971i −0.113658 + 0.349804i −0.991665 0.128845i \(-0.958873\pi\)
0.878007 + 0.478649i \(0.158873\pi\)
\(720\) 3.31410 + 2.40784i 0.123509 + 0.0897347i
\(721\) 6.64852 + 4.83043i 0.247604 + 0.179895i
\(722\) −8.11714 + 24.9820i −0.302089 + 0.929734i
\(723\) 1.16421 + 3.58306i 0.0432973 + 0.133255i
\(724\) 24.8221 18.0343i 0.922507 0.670241i
\(725\) 15.3559 0.570305
\(726\) 0 0
\(727\) −31.5764 −1.17111 −0.585553 0.810634i \(-0.699122\pi\)
−0.585553 + 0.810634i \(0.699122\pi\)
\(728\) 11.9183 8.65915i 0.441722 0.320930i
\(729\) 9.05812 + 27.8780i 0.335486 + 1.03252i
\(730\) −0.581387 + 1.78933i −0.0215181 + 0.0662259i
\(731\) 0.635338 + 0.461600i 0.0234988 + 0.0170729i
\(732\) −11.1166 8.07667i −0.410881 0.298522i
\(733\) −12.7601 + 39.2716i −0.471305 + 1.45053i 0.379571 + 0.925163i \(0.376072\pi\)
−0.850876 + 0.525366i \(0.823928\pi\)
\(734\) 7.67329 + 23.6160i 0.283226 + 0.871681i
\(735\) −1.46039 + 1.06103i −0.0538672 + 0.0391368i
\(736\) −5.96659 −0.219931
\(737\) 0 0
\(738\) −0.720812 −0.0265335
\(739\) 28.6469 20.8132i 1.05379 0.765626i 0.0808639 0.996725i \(-0.474232\pi\)
0.972930 + 0.231099i \(0.0742321\pi\)
\(740\) −8.28946 25.5123i −0.304727 0.937853i
\(741\) −4.03174 + 12.4084i −0.148110 + 0.455835i
\(742\) 8.55709 + 6.21709i 0.314141 + 0.228237i
\(743\) −3.25555 2.36530i −0.119435 0.0867743i 0.526464 0.850197i \(-0.323517\pi\)
−0.645899 + 0.763423i \(0.723517\pi\)
\(744\) 19.9828 61.5007i 0.732605 2.25473i
\(745\) 1.89500 + 5.83221i 0.0694274 + 0.213676i
\(746\) −54.8298 + 39.8361i −2.00746 + 1.45850i
\(747\) 0.896402 0.0327976
\(748\) 0 0
\(749\) 12.1885 0.445359
\(750\) 29.8712 21.7027i 1.09074 0.792471i
\(751\) 7.54588 + 23.2238i 0.275353 + 0.847450i 0.989126 + 0.147072i \(0.0469850\pi\)
−0.713773 + 0.700378i \(0.753015\pi\)
\(752\) 9.99838 30.7719i 0.364603 1.12213i
\(753\) 30.4264 + 22.1060i 1.10880 + 0.805589i
\(754\) 28.0943 + 20.4117i 1.02313 + 0.743351i
\(755\) 6.60179 20.3182i 0.240264 0.739456i
\(756\) 6.82780 + 21.0138i 0.248325 + 0.764265i
\(757\) 1.06566 0.774247i 0.0387321 0.0281405i −0.568251 0.822855i \(-0.692380\pi\)
0.606983 + 0.794715i \(0.292380\pi\)
\(758\) 2.79023 0.101346
\(759\) 0 0
\(760\) −16.6979 −0.605696
\(761\) −5.86055 + 4.25794i −0.212445 + 0.154350i −0.688919 0.724838i \(-0.741915\pi\)
0.476474 + 0.879188i \(0.341915\pi\)
\(762\) 8.64723 + 26.6134i 0.313256 + 0.964103i
\(763\) 0.273816 0.842720i 0.00991281 0.0305085i
\(764\) 27.9117 + 20.2791i 1.00981 + 0.733671i
\(765\) −5.68880 4.13315i −0.205679 0.149434i
\(766\) −14.9847 + 46.1181i −0.541419 + 1.66632i
\(767\) −6.82286 20.9986i −0.246359 0.758216i
\(768\) 36.0361 26.1817i 1.30034 0.944752i
\(769\) −44.3139 −1.59800 −0.798999 0.601332i \(-0.794637\pi\)
−0.798999 + 0.601332i \(0.794637\pi\)
\(770\) 0 0
\(771\) 42.9570 1.54706
\(772\) 80.9265 58.7965i 2.91261 2.11613i
\(773\) 5.88861 + 18.1233i 0.211799 + 0.651849i 0.999365 + 0.0356198i \(0.0113405\pi\)
−0.787567 + 0.616229i \(0.788659\pi\)
\(774\) −0.0938911 + 0.288967i −0.00337485 + 0.0103867i
\(775\) 26.8818 + 19.5308i 0.965622 + 0.701565i
\(776\) −65.9118 47.8877i −2.36610 1.71907i
\(777\) 2.41760 7.44062i 0.0867310 0.266931i
\(778\) 1.95273 + 6.00990i 0.0700089 + 0.215465i
\(779\) 0.728215 0.529079i 0.0260910 0.0189562i
\(780\) 22.4161 0.802626
\(781\) 0 0
\(782\) −97.3828 −3.48240
\(783\) −20.5674 + 14.9431i −0.735018 + 0.534022i
\(784\) 1.06649 + 3.28231i 0.0380889 + 0.117225i
\(785\) 0.873101 2.68713i 0.0311623 0.0959077i
\(786\) 0.286124 + 0.207881i 0.0102057 + 0.00741488i
\(787\) 25.4517 + 18.4917i 0.907255 + 0.659159i 0.940319 0.340294i \(-0.110527\pi\)
−0.0330644 + 0.999453i \(0.510527\pi\)
\(788\) 13.5196 41.6092i 0.481617 1.48227i
\(789\) −1.47898 4.55182i −0.0526530 0.162049i
\(790\) 21.1084 15.3362i 0.751004 0.545636i
\(791\) −4.54502 −0.161602
\(792\) 0 0
\(793\) 7.79370 0.276763
\(794\) −17.2489 + 12.5321i −0.612141 + 0.444746i
\(795\) 2.42758 + 7.47133i 0.0860974 + 0.264981i
\(796\) −14.7905 + 45.5205i −0.524236 + 1.61343i
\(797\) 10.1493 + 7.37392i 0.359508 + 0.261198i 0.752847 0.658196i \(-0.228680\pi\)
−0.393339 + 0.919394i \(0.628680\pi\)
\(798\) −8.07159 5.86435i −0.285731 0.207596i
\(799\) −17.1626 + 52.8212i −0.607171 + 1.86868i
\(800\) 0.931193 + 2.86592i 0.0329227 + 0.101326i
\(801\) 7.67154 5.57370i 0.271061 0.196937i
\(802\) 68.9118 2.43336
\(803\) 0 0
\(804\) −52.7850 −1.86159
\(805\) 6.88689 5.00362i 0.242731 0.176354i
\(806\) 23.2203 + 71.4647i 0.817900 + 2.51724i
\(807\) −0.769302 + 2.36767i −0.0270807 + 0.0833458i
\(808\) −46.7841 33.9907i −1.64586 1.19579i
\(809\) −4.35271 3.16243i −0.153033 0.111185i 0.508634 0.860983i \(-0.330151\pi\)
−0.661667 + 0.749798i \(0.730151\pi\)
\(810\) −4.99258 + 15.3656i −0.175421 + 0.539891i
\(811\) −4.23351 13.0294i −0.148659 0.457524i 0.848805 0.528707i \(-0.177323\pi\)
−0.997463 + 0.0711822i \(0.977323\pi\)
\(812\) −14.2098 + 10.3241i −0.498668 + 0.362303i
\(813\) 3.55103 0.124540
\(814\) 0 0
\(815\) −19.9333 −0.698231
\(816\) 23.7231 17.2358i 0.830474 0.603375i
\(817\) −0.117248 0.360851i −0.00410198 0.0126246i
\(818\) −14.9501 + 46.0115i −0.522716 + 1.60876i
\(819\) −2.42488 1.76178i −0.0847321 0.0615614i
\(820\) −1.25115 0.909014i −0.0436921 0.0317442i
\(821\) 2.85258 8.77935i 0.0995559 0.306401i −0.888858 0.458182i \(-0.848501\pi\)
0.988414 + 0.151781i \(0.0485007\pi\)
\(822\) −4.91627 15.1307i −0.171474 0.527744i
\(823\) 10.0663 7.31362i 0.350890 0.254937i −0.398352 0.917233i \(-0.630418\pi\)
0.749242 + 0.662296i \(0.230418\pi\)
\(824\) 38.0915 1.32698
\(825\) 0 0
\(826\) 16.8840 0.587469
\(827\) −3.62752 + 2.63555i −0.126141 + 0.0916471i −0.649067 0.760731i \(-0.724841\pi\)
0.522926 + 0.852378i \(0.324841\pi\)
\(828\) −7.70087 23.7008i −0.267624 0.823661i
\(829\) −11.3958 + 35.0726i −0.395792 + 1.21812i 0.532551 + 0.846398i \(0.321234\pi\)
−0.928343 + 0.371725i \(0.878766\pi\)
\(830\) 2.35239 + 1.70911i 0.0816528 + 0.0593242i
\(831\) 5.98215 + 4.34629i 0.207519 + 0.150771i
\(832\) −8.88510 + 27.3455i −0.308035 + 0.948035i
\(833\) −1.83067 5.63423i −0.0634290 0.195215i
\(834\) −10.7876 + 7.83765i −0.373544 + 0.271396i
\(835\) −26.1060 −0.903435
\(836\) 0 0
\(837\) −55.0105 −1.90144
\(838\) 60.7495 44.1371i 2.09856 1.52469i
\(839\) 2.83185 + 8.71555i 0.0977665 + 0.300894i 0.987965 0.154679i \(-0.0494343\pi\)
−0.890198 + 0.455573i \(0.849434\pi\)
\(840\) −2.58555 + 7.95751i −0.0892100 + 0.274560i
\(841\) 7.11170 + 5.16695i 0.245231 + 0.178171i
\(842\) 47.5704 + 34.5619i 1.63938 + 1.19108i
\(843\) 10.0031 30.7864i 0.344526 1.06034i
\(844\) 17.2213 + 53.0017i 0.592782 + 1.82439i
\(845\) 2.95126 2.14421i 0.101526 0.0737632i
\(846\) −21.4880 −0.738774
\(847\) 0 0
\(848\) 15.0195 0.515771
\(849\) −9.84810 + 7.15507i −0.337986 + 0.245561i
\(850\) 15.1983 + 46.7757i 0.521299 + 1.60439i
\(851\) −11.4009 + 35.0885i −0.390819 + 1.20282i
\(852\) 0.528640 + 0.384080i 0.0181109 + 0.0131583i
\(853\) 5.27519 + 3.83265i 0.180619 + 0.131227i 0.674421 0.738347i \(-0.264393\pi\)
−0.493802 + 0.869574i \(0.664393\pi\)
\(854\) −1.84169 + 5.66815i −0.0630214 + 0.193960i
\(855\) 1.04983 + 3.23105i 0.0359035 + 0.110500i
\(856\) 45.7056 33.2070i 1.56218 1.13499i
\(857\) −48.0736 −1.64216 −0.821082 0.570810i \(-0.806629\pi\)
−0.821082 + 0.570810i \(0.806629\pi\)
\(858\) 0 0
\(859\) −0.316298 −0.0107920 −0.00539598 0.999985i \(-0.501718\pi\)
−0.00539598 + 0.999985i \(0.501718\pi\)
\(860\) −0.527387 + 0.383169i −0.0179838 + 0.0130660i
\(861\) −0.139378 0.428960i −0.00474998 0.0146189i
\(862\) −14.5704 + 44.8432i −0.496271 + 1.52736i
\(863\) −2.93425 2.13186i −0.0998830 0.0725692i 0.536723 0.843759i \(-0.319662\pi\)
−0.636606 + 0.771189i \(0.719662\pi\)
\(864\) −4.03609 2.93239i −0.137311 0.0997620i
\(865\) 8.38373 25.8025i 0.285055 0.877310i
\(866\) −16.0633 49.4377i −0.545852 1.67996i
\(867\) −20.9966 + 15.2550i −0.713083 + 0.518085i
\(868\) −38.0064 −1.29002
\(869\) 0 0
\(870\) −19.7231 −0.668675
\(871\) 24.2214 17.5979i 0.820710 0.596280i
\(872\) −1.26917 3.90610i −0.0429795 0.132277i
\(873\) −5.12228 + 15.7648i −0.173363 + 0.533556i
\(874\) 38.0640 + 27.6551i 1.28753 + 0.935448i
\(875\) −8.56947 6.22608i −0.289701 0.210480i
\(876\) −1.06499 + 3.27770i −0.0359827 + 0.110743i
\(877\) −8.25311 25.4004i −0.278688 0.857712i −0.988220 0.153039i \(-0.951094\pi\)
0.709533 0.704673i \(-0.248906\pi\)
\(878\) −62.3930 + 45.3312i −2.10566 + 1.52985i
\(879\) −35.3189 −1.19128
\(880\) 0 0
\(881\) 2.91937 0.0983560 0.0491780 0.998790i \(-0.484340\pi\)
0.0491780 + 0.998790i \(0.484340\pi\)
\(882\) 1.85430 1.34723i 0.0624376 0.0453636i
\(883\) −13.9544 42.9472i −0.469603 1.44529i −0.853100 0.521748i \(-0.825280\pi\)
0.383497 0.923542i \(-0.374720\pi\)
\(884\) −22.7332 + 69.9657i −0.764602 + 2.35320i
\(885\) 10.1451 + 7.37084i 0.341023 + 0.247768i
\(886\) 3.27602 + 2.38017i 0.110060 + 0.0799634i
\(887\) 7.42409 22.8490i 0.249277 0.767194i −0.745627 0.666363i \(-0.767850\pi\)
0.994904 0.100831i \(-0.0321501\pi\)
\(888\) −11.2059 34.4881i −0.376044 1.15735i
\(889\) 6.49462 4.71861i 0.217822 0.158257i
\(890\) 30.7592 1.03105
\(891\) 0 0
\(892\) −11.5806 −0.387749
\(893\) 21.7087 15.7723i 0.726454 0.527800i
\(894\) 5.24819 + 16.1523i 0.175526 + 0.540212i
\(895\) 1.85975 5.72372i 0.0621646 0.191323i
\(896\) −16.3606 11.8867i −0.546571 0.397107i
\(897\) −24.9421 18.1215i −0.832791 0.605058i
\(898\) −12.9074 + 39.7249i −0.430726 + 1.32564i
\(899\) −13.5133 41.5897i −0.450694 1.38709i
\(900\) −10.1823 + 7.39788i −0.339411 + 0.246596i
\(901\) −25.7816 −0.858909
\(902\) 0 0
\(903\) −0.190121 −0.00632684
\(904\) −17.0433 + 12.3827i −0.566852 + 0.411842i
\(905\) −3.05427 9.40009i −0.101527 0.312469i
\(906\) 18.2836 56.2712i 0.607432 1.86948i
\(907\) 12.9661 + 9.42041i 0.430532 + 0.312800i 0.781861 0.623452i \(-0.214270\pi\)
−0.351330 + 0.936252i \(0.614270\pi\)
\(908\) 26.0966 + 18.9603i 0.866048 + 0.629220i
\(909\) −3.63579 + 11.1898i −0.120592 + 0.371143i
\(910\) −3.00444 9.24673i −0.0995964 0.306526i
\(911\) 13.2714 9.64223i 0.439701 0.319461i −0.345815 0.938303i \(-0.612398\pi\)
0.785516 + 0.618841i \(0.212398\pi\)
\(912\) −14.1673 −0.469127
\(913\) 0 0
\(914\) −24.8408 −0.821660
\(915\) −3.58109 + 2.60182i −0.118387 + 0.0860134i
\(916\) 15.8262 + 48.7081i 0.522913 + 1.60936i
\(917\) 0.0313531 0.0964948i 0.00103537 0.00318654i
\(918\) −65.8745 47.8606i −2.17418 1.57964i
\(919\) 26.1475 + 18.9973i 0.862527 + 0.626663i 0.928571 0.371154i \(-0.121038\pi\)
−0.0660439 + 0.997817i \(0.521038\pi\)
\(920\) 12.1929 37.5260i 0.401989 1.23720i
\(921\) −2.03599 6.26614i −0.0670882 0.206476i
\(922\) −43.4861 + 31.5945i −1.43214 + 1.04051i
\(923\) −0.370623 −0.0121992
\(924\) 0 0
\(925\) 18.6333 0.612659
\(926\) 59.7193 43.3886i 1.96250 1.42584i
\(927\) −2.39489 7.37072i −0.0786585 0.242086i
\(928\) 1.22552 3.77175i 0.0402295 0.123814i
\(929\) 6.63015 + 4.81708i 0.217528 + 0.158043i 0.691213 0.722651i \(-0.257077\pi\)
−0.473685 + 0.880694i \(0.657077\pi\)
\(930\) −34.5268 25.0852i −1.13218 0.822576i
\(931\) −0.884474 + 2.72213i −0.0289875 + 0.0892142i
\(932\) 15.4876 + 47.6660i 0.507314 + 1.56135i
\(933\) 2.56511 1.86366i 0.0839778 0.0610135i
\(934\) 61.2253 2.00335
\(935\) 0 0
\(936\) −13.8929 −0.454103
\(937\) 27.6178 20.0655i 0.902233 0.655510i −0.0368058 0.999322i \(-0.511718\pi\)
0.939038 + 0.343812i \(0.111718\pi\)
\(938\) 7.07480 + 21.7740i 0.231000 + 0.710946i
\(939\) −4.29866 + 13.2299i −0.140282 + 0.431742i
\(940\) −37.2979 27.0985i −1.21652 0.883856i
\(941\) 0.792327 + 0.575660i 0.0258291 + 0.0187660i 0.600625 0.799531i \(-0.294919\pi\)
−0.574796 + 0.818297i \(0.694919\pi\)
\(942\) 2.41805 7.44198i 0.0787842 0.242473i
\(943\) 0.657277 + 2.02289i 0.0214039 + 0.0658744i
\(944\) 19.3963 14.0923i 0.631297 0.458664i
\(945\) 7.11775 0.231540
\(946\) 0 0
\(947\) 0.935599 0.0304029 0.0152014 0.999884i \(-0.495161\pi\)
0.0152014 + 0.999884i \(0.495161\pi\)
\(948\) 38.6666 28.0929i 1.25583 0.912416i
\(949\) −0.604054 1.85909i −0.0196084 0.0603485i
\(950\) 7.34295 22.5993i 0.238237 0.733217i
\(951\) −7.49017 5.44193i −0.242886 0.176467i
\(952\) −22.2150 16.1401i −0.719993 0.523105i
\(953\) −5.17049 + 15.9131i −0.167489 + 0.515477i −0.999211 0.0397147i \(-0.987355\pi\)
0.831722 + 0.555192i \(0.187355\pi\)
\(954\) −3.08238 9.48660i −0.0997958 0.307140i
\(955\) 8.99147 6.53269i 0.290957 0.211393i
\(956\) 19.4616 0.629434
\(957\) 0 0
\(958\) 51.5353 1.66503
\(959\) −3.69243 + 2.68271i −0.119235 + 0.0866291i
\(960\) −5.04633 15.5310i −0.162870 0.501262i
\(961\) 19.6611 60.5105i 0.634228 1.95195i
\(962\) 34.0904 + 24.7681i 1.09912 + 0.798556i
\(963\) −9.29918 6.75625i −0.299662 0.217717i
\(964\) 3.17156 9.76106i 0.102149 0.314383i
\(965\) −9.95770 30.6467i −0.320550 0.986551i
\(966\) 19.0732 13.8575i 0.613670 0.445857i
\(967\) −36.4439 −1.17196 −0.585978 0.810327i \(-0.699290\pi\)
−0.585978 + 0.810327i \(0.699290\pi\)
\(968\) 0 0
\(969\) 24.3188 0.781233
\(970\) −43.4999 + 31.6045i −1.39670 + 1.01476i
\(971\) −10.2723 31.6148i −0.329653 1.01457i −0.969296 0.245895i \(-0.920918\pi\)
0.639644 0.768671i \(-0.279082\pi\)
\(972\) 11.3380 34.8946i 0.363665 1.11925i
\(973\) 3.09475 + 2.24847i 0.0992133 + 0.0720827i
\(974\) 33.0723 + 24.0284i 1.05971 + 0.769921i
\(975\) −4.81159 + 14.8086i −0.154094 + 0.474253i
\(976\) 2.61519 + 8.04874i 0.0837103 + 0.257634i
\(977\) −18.2568 + 13.2643i −0.584086 + 0.424363i −0.840195 0.542285i \(-0.817559\pi\)
0.256109 + 0.966648i \(0.417559\pi\)
\(978\) −55.2050 −1.76526
\(979\) 0 0
\(980\) 4.91760 0.157087
\(981\) −0.676037 + 0.491170i −0.0215842 + 0.0156818i
\(982\) −3.63362 11.1831i −0.115953 0.356868i
\(983\) −4.66763 + 14.3655i −0.148874 + 0.458188i −0.997489 0.0708236i \(-0.977437\pi\)
0.848615 + 0.529012i \(0.177437\pi\)
\(984\) −1.69133 1.22882i −0.0539177 0.0391735i
\(985\) −11.4021 8.28410i −0.363301 0.263953i
\(986\) 20.0021 61.5601i 0.636996 1.96047i
\(987\) −4.15497 12.7877i −0.132254 0.407036i
\(988\) 28.7548 20.8916i 0.914813 0.664651i
\(989\) 0.896574 0.0285094
\(990\) 0 0
\(991\) −55.1534 −1.75201 −0.876003 0.482305i \(-0.839800\pi\)
−0.876003 + 0.482305i \(0.839800\pi\)
\(992\) 6.94254 5.04405i 0.220426 0.160149i
\(993\) 1.60470 + 4.93876i 0.0509236 + 0.156727i
\(994\) 0.0875802 0.269544i 0.00277788 0.00854942i
\(995\) 12.4739 + 9.06282i 0.395449 + 0.287311i
\(996\) 4.30914 + 3.13077i 0.136540 + 0.0992023i
\(997\) −15.3596 + 47.2721i −0.486444 + 1.49712i 0.343434 + 0.939177i \(0.388410\pi\)
−0.829878 + 0.557944i \(0.811590\pi\)
\(998\) 22.9698 + 70.6938i 0.727097 + 2.23777i
\(999\) −24.9570 + 18.1323i −0.789606 + 0.573682i
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 847.2.f.v.729.1 16
11.2 odd 10 847.2.a.p.1.1 8
11.3 even 5 847.2.f.x.148.4 16
11.4 even 5 inner 847.2.f.v.323.1 16
11.5 even 5 847.2.f.x.372.4 16
11.6 odd 10 77.2.f.b.64.1 16
11.7 odd 10 847.2.f.w.323.4 16
11.8 odd 10 77.2.f.b.71.1 yes 16
11.9 even 5 847.2.a.o.1.8 8
11.10 odd 2 847.2.f.w.729.4 16
33.2 even 10 7623.2.a.ct.1.8 8
33.8 even 10 693.2.m.i.379.4 16
33.17 even 10 693.2.m.i.64.4 16
33.20 odd 10 7623.2.a.cw.1.1 8
77.6 even 10 539.2.f.e.295.1 16
77.13 even 10 5929.2.a.bt.1.1 8
77.17 even 30 539.2.q.f.471.1 32
77.19 even 30 539.2.q.f.214.1 32
77.20 odd 10 5929.2.a.bs.1.8 8
77.30 odd 30 539.2.q.g.214.1 32
77.39 odd 30 539.2.q.g.471.1 32
77.41 even 10 539.2.f.e.148.1 16
77.52 even 30 539.2.q.f.324.4 32
77.61 even 30 539.2.q.f.361.4 32
77.72 odd 30 539.2.q.g.361.4 32
77.74 odd 30 539.2.q.g.324.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.64.1 16 11.6 odd 10
77.2.f.b.71.1 yes 16 11.8 odd 10
539.2.f.e.148.1 16 77.41 even 10
539.2.f.e.295.1 16 77.6 even 10
539.2.q.f.214.1 32 77.19 even 30
539.2.q.f.324.4 32 77.52 even 30
539.2.q.f.361.4 32 77.61 even 30
539.2.q.f.471.1 32 77.17 even 30
539.2.q.g.214.1 32 77.30 odd 30
539.2.q.g.324.4 32 77.74 odd 30
539.2.q.g.361.4 32 77.72 odd 30
539.2.q.g.471.1 32 77.39 odd 30
693.2.m.i.64.4 16 33.17 even 10
693.2.m.i.379.4 16 33.8 even 10
847.2.a.o.1.8 8 11.9 even 5
847.2.a.p.1.1 8 11.2 odd 10
847.2.f.v.323.1 16 11.4 even 5 inner
847.2.f.v.729.1 16 1.1 even 1 trivial
847.2.f.w.323.4 16 11.7 odd 10
847.2.f.w.729.4 16 11.10 odd 2
847.2.f.x.148.4 16 11.3 even 5
847.2.f.x.372.4 16 11.5 even 5
5929.2.a.bs.1.8 8 77.20 odd 10
5929.2.a.bt.1.1 8 77.13 even 10
7623.2.a.ct.1.8 8 33.2 even 10
7623.2.a.cw.1.1 8 33.20 odd 10