Properties

Label 605.2.j.e.444.3
Level $605$
Weight $2$
Character 605.444
Analytic conductor $4.831$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(9,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: 16.0.6879707136000000000000.7
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 444.3
Root \(-0.492303 - 0.159959i\) of defining polynomial
Character \(\chi\) \(=\) 605.444
Dual form 605.2.j.e.124.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.304260 - 0.418778i) q^{2} +(-1.83730 - 0.596975i) q^{3} +(0.535233 + 1.64728i) q^{4} +(-2.23251 - 0.126049i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(3.18230 - 1.03399i) q^{7} +(1.83730 + 0.596975i) q^{8} +(0.592242 + 0.430289i) q^{9} +O(q^{10})\) \(q+(0.304260 - 0.418778i) q^{2} +(-1.83730 - 0.596975i) q^{3} +(0.535233 + 1.64728i) q^{4} +(-2.23251 - 0.126049i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(3.18230 - 1.03399i) q^{7} +(1.83730 + 0.596975i) q^{8} +(0.592242 + 0.430289i) q^{9} +(-0.732051 + 0.896575i) q^{10} -3.34607i q^{12} +(-2.49376 + 3.43237i) q^{13} +(0.535233 - 1.64728i) q^{14} +(4.02655 + 1.56434i) q^{15} +(-1.99350 + 1.44836i) q^{16} +(-2.27103 - 3.12580i) q^{17} +(0.360391 - 0.117098i) q^{18} +(-1.29668 + 3.99078i) q^{19} +(-0.987277 - 3.74503i) q^{20} -6.46410 q^{21} +3.48477i q^{23} +(-3.01929 - 2.19364i) q^{24} +(4.96822 + 0.562811i) q^{25} +(0.678648 + 2.08867i) q^{26} +(2.57529 + 3.54458i) q^{27} +(3.40654 + 4.68870i) q^{28} +(2.14093 + 6.58911i) q^{29} +(1.88023 - 1.21026i) q^{30} +(7.06438 + 5.13257i) q^{31} +5.13922i q^{32} -2.00000 q^{34} +(-7.23485 + 1.90727i) q^{35} +(-0.391818 + 1.20589i) q^{36} +(1.70539 - 0.554114i) q^{37} +(1.27672 + 1.75726i) q^{38} +(6.63083 - 4.81758i) q^{39} +(-4.02655 - 1.56434i) q^{40} +(-0.535233 + 1.64728i) q^{41} +(-1.96677 + 2.70702i) q^{42} +6.45189i q^{43} +(-1.26795 - 1.03528i) q^{45} +(1.45934 + 1.06028i) q^{46} +(-10.8919 - 3.53899i) q^{47} +(4.52729 - 1.47101i) q^{48} +(3.39476 - 2.46644i) q^{49} +(1.74732 - 1.90934i) q^{50} +(2.30653 + 7.09878i) q^{51} +(-6.98881 - 2.27080i) q^{52} +(1.27672 - 1.75726i) q^{53} +2.26795 q^{54} +6.46410 q^{56} +(4.76479 - 6.55817i) q^{57} +(3.41078 + 1.10823i) q^{58} +(0.391818 + 1.20589i) q^{59} +(-0.421768 + 7.47013i) q^{60} +(-9.49143 + 6.89593i) q^{61} +(4.29882 - 1.39677i) q^{62} +(2.32960 + 0.756934i) q^{63} +(-1.83481 - 1.33307i) q^{64} +(6.00000 - 7.34847i) q^{65} -2.20925i q^{67} +(3.93354 - 5.41405i) q^{68} +(2.08032 - 6.40256i) q^{69} +(-1.40255 + 3.61010i) q^{70} +(6.63083 - 4.81758i) q^{71} +(0.831254 + 1.14412i) q^{72} +(-4.65921 + 1.51387i) q^{73} +(0.286831 - 0.882774i) q^{74} +(-8.79213 - 3.99996i) q^{75} -7.26795 q^{76} -4.24264i q^{78} +(-1.18448 - 0.860577i) q^{79} +(4.63308 - 2.98221i) q^{80} +(-3.29420 - 10.1385i) q^{81} +(0.526994 + 0.725345i) q^{82} +(-5.81878 - 8.00886i) q^{83} +(-3.45980 - 10.6482i) q^{84} +(4.67609 + 7.26465i) q^{85} +(2.70191 + 1.96305i) q^{86} -13.3843i q^{87} -0.464102 q^{89} +(-0.819337 + 0.215996i) q^{90} +(-4.38685 + 13.5013i) q^{91} +(-5.74038 + 1.86516i) q^{92} +(-9.91537 - 13.6473i) q^{93} +(-4.79602 + 3.48451i) q^{94} +(3.39789 - 8.74602i) q^{95} +(3.06798 - 9.44228i) q^{96} +(5.37331 - 7.39573i) q^{97} -2.17209i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{6} - 4 q^{9} + 16 q^{10} - 4 q^{15} + 4 q^{16} - 4 q^{19} - 12 q^{20} - 48 q^{21} - 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} - 12 q^{35} + 12 q^{36} + 12 q^{39} + 4 q^{40} - 48 q^{45} + 28 q^{46} - 4 q^{49} + 24 q^{50} - 16 q^{51} + 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} - 40 q^{61} - 16 q^{64} + 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} + 24 q^{74} - 24 q^{75} - 144 q^{76} + 8 q^{79} - 24 q^{80} + 8 q^{81} + 24 q^{84} + 8 q^{85} + 48 q^{86} + 48 q^{89} - 16 q^{90} + 36 q^{91} + 4 q^{94} + 36 q^{95} - 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.304260 0.418778i 0.215144 0.296121i −0.687781 0.725918i \(-0.741415\pi\)
0.902925 + 0.429797i \(0.141415\pi\)
\(3\) −1.83730 0.596975i −1.06077 0.344664i −0.273881 0.961764i \(-0.588307\pi\)
−0.786885 + 0.617100i \(0.788307\pi\)
\(4\) 0.535233 + 1.64728i 0.267617 + 0.823639i
\(5\) −2.23251 0.126049i −0.998410 0.0563708i
\(6\) −0.809017 + 0.587785i −0.330280 + 0.239962i
\(7\) 3.18230 1.03399i 1.20280 0.390812i 0.362007 0.932175i \(-0.382092\pi\)
0.840789 + 0.541364i \(0.182092\pi\)
\(8\) 1.83730 + 0.596975i 0.649584 + 0.211063i
\(9\) 0.592242 + 0.430289i 0.197414 + 0.143430i
\(10\) −0.732051 + 0.896575i −0.231495 + 0.283522i
\(11\) 0 0
\(12\) 3.34607i 0.965926i
\(13\) −2.49376 + 3.43237i −0.691645 + 0.951968i 0.308355 + 0.951271i \(0.400222\pi\)
−1.00000 0.000696272i \(0.999778\pi\)
\(14\) 0.535233 1.64728i 0.143047 0.440254i
\(15\) 4.02655 + 1.56434i 1.03965 + 0.403912i
\(16\) −1.99350 + 1.44836i −0.498375 + 0.362091i
\(17\) −2.27103 3.12580i −0.550805 0.758118i 0.439316 0.898333i \(-0.355221\pi\)
−0.990121 + 0.140214i \(0.955221\pi\)
\(18\) 0.360391 0.117098i 0.0849449 0.0276003i
\(19\) −1.29668 + 3.99078i −0.297479 + 0.915547i 0.684898 + 0.728639i \(0.259847\pi\)
−0.982377 + 0.186908i \(0.940153\pi\)
\(20\) −0.987277 3.74503i −0.220762 0.837415i
\(21\) −6.46410 −1.41058
\(22\) 0 0
\(23\) 3.48477i 0.726624i 0.931668 + 0.363312i \(0.118354\pi\)
−0.931668 + 0.363312i \(0.881646\pi\)
\(24\) −3.01929 2.19364i −0.616311 0.447776i
\(25\) 4.96822 + 0.562811i 0.993645 + 0.112562i
\(26\) 0.678648 + 2.08867i 0.133094 + 0.409621i
\(27\) 2.57529 + 3.54458i 0.495614 + 0.682155i
\(28\) 3.40654 + 4.68870i 0.643776 + 0.886081i
\(29\) 2.14093 + 6.58911i 0.397561 + 1.22357i 0.926949 + 0.375188i \(0.122422\pi\)
−0.529388 + 0.848380i \(0.677578\pi\)
\(30\) 1.88023 1.21026i 0.343281 0.220963i
\(31\) 7.06438 + 5.13257i 1.26880 + 0.921837i 0.999154 0.0411227i \(-0.0130935\pi\)
0.269646 + 0.962960i \(0.413093\pi\)
\(32\) 5.13922i 0.908494i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −7.23485 + 1.90727i −1.22291 + 0.322388i
\(36\) −0.391818 + 1.20589i −0.0653030 + 0.200982i
\(37\) 1.70539 0.554114i 0.280364 0.0910958i −0.165460 0.986217i \(-0.552911\pi\)
0.445824 + 0.895121i \(0.352911\pi\)
\(38\) 1.27672 + 1.75726i 0.207112 + 0.285065i
\(39\) 6.63083 4.81758i 1.06178 0.771430i
\(40\) −4.02655 1.56434i −0.636653 0.247344i
\(41\) −0.535233 + 1.64728i −0.0835894 + 0.257262i −0.984112 0.177547i \(-0.943184\pi\)
0.900523 + 0.434808i \(0.143184\pi\)
\(42\) −1.96677 + 2.70702i −0.303479 + 0.417703i
\(43\) 6.45189i 0.983905i 0.870622 + 0.491952i \(0.163717\pi\)
−0.870622 + 0.491952i \(0.836283\pi\)
\(44\) 0 0
\(45\) −1.26795 1.03528i −0.189015 0.154330i
\(46\) 1.45934 + 1.06028i 0.215168 + 0.156329i
\(47\) −10.8919 3.53899i −1.58875 0.516215i −0.624455 0.781061i \(-0.714679\pi\)
−0.964291 + 0.264846i \(0.914679\pi\)
\(48\) 4.52729 1.47101i 0.653459 0.212322i
\(49\) 3.39476 2.46644i 0.484966 0.352348i
\(50\) 1.74732 1.90934i 0.247109 0.270022i
\(51\) 2.30653 + 7.09878i 0.322979 + 0.994028i
\(52\) −6.98881 2.27080i −0.969174 0.314904i
\(53\) 1.27672 1.75726i 0.175371 0.241378i −0.712279 0.701897i \(-0.752337\pi\)
0.887650 + 0.460519i \(0.152337\pi\)
\(54\) 2.26795 0.308629
\(55\) 0 0
\(56\) 6.46410 0.863802
\(57\) 4.76479 6.55817i 0.631112 0.868651i
\(58\) 3.41078 + 1.10823i 0.447857 + 0.145517i
\(59\) 0.391818 + 1.20589i 0.0510103 + 0.156994i 0.973317 0.229466i \(-0.0736979\pi\)
−0.922306 + 0.386459i \(0.873698\pi\)
\(60\) −0.421768 + 7.47013i −0.0544500 + 0.964390i
\(61\) −9.49143 + 6.89593i −1.21525 + 0.882933i −0.995697 0.0926671i \(-0.970461\pi\)
−0.219556 + 0.975600i \(0.570461\pi\)
\(62\) 4.29882 1.39677i 0.545950 0.177390i
\(63\) 2.32960 + 0.756934i 0.293502 + 0.0953647i
\(64\) −1.83481 1.33307i −0.229351 0.166633i
\(65\) 6.00000 7.34847i 0.744208 0.911465i
\(66\) 0 0
\(67\) 2.20925i 0.269903i −0.990852 0.134952i \(-0.956912\pi\)
0.990852 0.134952i \(-0.0430879\pi\)
\(68\) 3.93354 5.41405i 0.477011 0.656550i
\(69\) 2.08032 6.40256i 0.250441 0.770778i
\(70\) −1.40255 + 3.61010i −0.167637 + 0.431490i
\(71\) 6.63083 4.81758i 0.786934 0.571741i −0.120118 0.992760i \(-0.538327\pi\)
0.907052 + 0.421018i \(0.138327\pi\)
\(72\) 0.831254 + 1.14412i 0.0979642 + 0.134836i
\(73\) −4.65921 + 1.51387i −0.545319 + 0.177185i −0.568705 0.822542i \(-0.692555\pi\)
0.0233860 + 0.999727i \(0.492555\pi\)
\(74\) 0.286831 0.882774i 0.0333434 0.102620i
\(75\) −8.79213 3.99996i −1.01523 0.461875i
\(76\) −7.26795 −0.833691
\(77\) 0 0
\(78\) 4.24264i 0.480384i
\(79\) −1.18448 0.860577i −0.133265 0.0968225i 0.519156 0.854680i \(-0.326246\pi\)
−0.652421 + 0.757857i \(0.726246\pi\)
\(80\) 4.63308 2.98221i 0.517994 0.333421i
\(81\) −3.29420 10.1385i −0.366022 1.12650i
\(82\) 0.526994 + 0.725345i 0.0581967 + 0.0801009i
\(83\) −5.81878 8.00886i −0.638694 0.879087i 0.359851 0.933010i \(-0.382827\pi\)
−0.998545 + 0.0539231i \(0.982827\pi\)
\(84\) −3.45980 10.6482i −0.377495 1.16181i
\(85\) 4.67609 + 7.26465i 0.507194 + 0.787962i
\(86\) 2.70191 + 1.96305i 0.291355 + 0.211681i
\(87\) 13.3843i 1.43494i
\(88\) 0 0
\(89\) −0.464102 −0.0491947 −0.0245973 0.999697i \(-0.507830\pi\)
−0.0245973 + 0.999697i \(0.507830\pi\)
\(90\) −0.819337 + 0.215996i −0.0863657 + 0.0227680i
\(91\) −4.38685 + 13.5013i −0.459867 + 1.41533i
\(92\) −5.74038 + 1.86516i −0.598476 + 0.194457i
\(93\) −9.91537 13.6473i −1.02818 1.41516i
\(94\) −4.79602 + 3.48451i −0.494671 + 0.359400i
\(95\) 3.39789 8.74602i 0.348616 0.897322i
\(96\) 3.06798 9.44228i 0.313125 0.963699i
\(97\) 5.37331 7.39573i 0.545577 0.750922i −0.443827 0.896113i \(-0.646379\pi\)
0.989404 + 0.145190i \(0.0463795\pi\)
\(98\) 2.17209i 0.219414i
\(99\) 0 0
\(100\) 1.73205 + 8.48528i 0.173205 + 0.848528i
\(101\) 15.6887 + 11.3985i 1.56108 + 1.13419i 0.935114 + 0.354348i \(0.115297\pi\)
0.625971 + 0.779847i \(0.284703\pi\)
\(102\) 3.67460 + 1.19395i 0.363840 + 0.118219i
\(103\) −4.03499 + 1.31105i −0.397579 + 0.129181i −0.500981 0.865458i \(-0.667027\pi\)
0.103401 + 0.994640i \(0.467027\pi\)
\(104\) −6.63083 + 4.81758i −0.650206 + 0.472402i
\(105\) 14.4312 + 0.814793i 1.40834 + 0.0795156i
\(106\) −0.347445 1.06933i −0.0337468 0.103862i
\(107\) 2.82191 + 0.916893i 0.272804 + 0.0886394i 0.442224 0.896905i \(-0.354190\pi\)
−0.169420 + 0.985544i \(0.554190\pi\)
\(108\) −4.46053 + 6.13939i −0.429215 + 0.590763i
\(109\) 9.19615 0.880832 0.440416 0.897794i \(-0.354831\pi\)
0.440416 + 0.897794i \(0.354831\pi\)
\(110\) 0 0
\(111\) −3.46410 −0.328798
\(112\) −4.84632 + 6.67038i −0.457934 + 0.630292i
\(113\) 2.68999 + 0.874032i 0.253053 + 0.0822220i 0.432797 0.901492i \(-0.357527\pi\)
−0.179743 + 0.983714i \(0.557527\pi\)
\(114\) −1.29668 3.99078i −0.121445 0.373771i
\(115\) 0.439251 7.77978i 0.0409604 0.725469i
\(116\) −9.70820 + 7.05342i −0.901384 + 0.654894i
\(117\) −2.95382 + 0.959754i −0.273081 + 0.0887293i
\(118\) 0.624215 + 0.202820i 0.0574637 + 0.0186711i
\(119\) −10.4591 7.59901i −0.958787 0.696600i
\(120\) 6.46410 + 5.27792i 0.590089 + 0.481806i
\(121\) 0 0
\(122\) 6.07296i 0.549820i
\(123\) 1.96677 2.70702i 0.177337 0.244084i
\(124\) −4.67368 + 14.3841i −0.419709 + 1.29173i
\(125\) −11.0207 1.88272i −0.985719 0.168396i
\(126\) 1.02579 0.745282i 0.0913849 0.0663950i
\(127\) 0.526994 + 0.725345i 0.0467631 + 0.0643639i 0.831758 0.555138i \(-0.187335\pi\)
−0.784995 + 0.619502i \(0.787335\pi\)
\(128\) −10.8919 + 3.53899i −0.962716 + 0.312805i
\(129\) 3.85162 11.8541i 0.339116 1.04369i
\(130\) −1.25182 4.74851i −0.109792 0.416472i
\(131\) 3.12436 0.272976 0.136488 0.990642i \(-0.456418\pi\)
0.136488 + 0.990642i \(0.456418\pi\)
\(132\) 0 0
\(133\) 14.0406i 1.21747i
\(134\) −0.925187 0.672187i −0.0799239 0.0580681i
\(135\) −5.30257 8.23793i −0.456373 0.709008i
\(136\) −2.30653 7.09878i −0.197784 0.608716i
\(137\) −5.21026 7.17130i −0.445142 0.612686i 0.526203 0.850359i \(-0.323615\pi\)
−0.971345 + 0.237673i \(0.923615\pi\)
\(138\) −2.04829 2.81923i −0.174362 0.239989i
\(139\) −4.50808 13.8744i −0.382370 1.17682i −0.938370 0.345633i \(-0.887664\pi\)
0.555999 0.831183i \(-0.312336\pi\)
\(140\) −7.01414 10.8970i −0.592803 0.920963i
\(141\) 17.8990 + 13.0044i 1.50737 + 1.09517i
\(142\) 4.24264i 0.356034i
\(143\) 0 0
\(144\) −1.80385 −0.150321
\(145\) −3.94911 14.9801i −0.327956 1.24403i
\(146\) −0.783636 + 2.41178i −0.0648542 + 0.199601i
\(147\) −7.70959 + 2.50500i −0.635876 + 0.206609i
\(148\) 1.82556 + 2.51267i 0.150060 + 0.206540i
\(149\) 8.30695 6.03535i 0.680531 0.494435i −0.193002 0.981198i \(-0.561823\pi\)
0.873534 + 0.486763i \(0.161823\pi\)
\(150\) −4.35019 + 2.46492i −0.355191 + 0.201260i
\(151\) −1.29668 + 3.99078i −0.105523 + 0.324765i −0.989853 0.142097i \(-0.954616\pi\)
0.884330 + 0.466862i \(0.154616\pi\)
\(152\) −4.76479 + 6.55817i −0.386475 + 0.531938i
\(153\) 2.82843i 0.228665i
\(154\) 0 0
\(155\) −15.1244 12.3490i −1.21482 0.991894i
\(156\) 11.4849 + 8.34429i 0.919530 + 0.668078i
\(157\) 20.7992 + 6.75806i 1.65995 + 0.539352i 0.980863 0.194701i \(-0.0623737\pi\)
0.679092 + 0.734053i \(0.262374\pi\)
\(158\) −0.720782 + 0.234196i −0.0573423 + 0.0186316i
\(159\) −3.39476 + 2.46644i −0.269222 + 0.195601i
\(160\) 0.647792 11.4734i 0.0512125 0.907049i
\(161\) 3.60322 + 11.0896i 0.283973 + 0.873980i
\(162\) −5.24808 1.70520i −0.412328 0.133973i
\(163\) −3.02076 + 4.15771i −0.236604 + 0.325657i −0.910763 0.412928i \(-0.864506\pi\)
0.674160 + 0.738586i \(0.264506\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) −5.12436 −0.397727
\(167\) 0.304260 0.418778i 0.0235443 0.0324060i −0.797083 0.603870i \(-0.793624\pi\)
0.820627 + 0.571464i \(0.193624\pi\)
\(168\) −11.8765 3.85891i −0.916291 0.297721i
\(169\) −1.54508 4.75528i −0.118853 0.365791i
\(170\) 4.46502 + 0.252098i 0.342452 + 0.0193350i
\(171\) −2.48514 + 1.80556i −0.190043 + 0.138074i
\(172\) −10.6281 + 3.45327i −0.810382 + 0.263309i
\(173\) −20.7026 6.72668i −1.57399 0.511420i −0.613490 0.789702i \(-0.710235\pi\)
−0.960499 + 0.278282i \(0.910235\pi\)
\(174\) −5.60503 4.07230i −0.424917 0.308720i
\(175\) 16.3923 3.34607i 1.23914 0.252939i
\(176\) 0 0
\(177\) 2.44949i 0.184115i
\(178\) −0.141208 + 0.194356i −0.0105840 + 0.0145676i
\(179\) 4.77867 14.7072i 0.357175 1.09927i −0.597563 0.801822i \(-0.703864\pi\)
0.954738 0.297449i \(-0.0961357\pi\)
\(180\) 1.02674 2.64278i 0.0765286 0.196981i
\(181\) 14.0707 10.2229i 1.04586 0.759865i 0.0744429 0.997225i \(-0.476282\pi\)
0.971422 + 0.237360i \(0.0762821\pi\)
\(182\) 4.31932 + 5.94504i 0.320169 + 0.440675i
\(183\) 21.5553 7.00374i 1.59341 0.517731i
\(184\) −2.08032 + 6.40256i −0.153363 + 0.472003i
\(185\) −3.87715 + 1.02210i −0.285053 + 0.0751466i
\(186\) −8.73205 −0.640265
\(187\) 0 0
\(188\) 19.8362i 1.44670i
\(189\) 11.8604 + 8.61708i 0.862717 + 0.626800i
\(190\) −2.62880 4.08403i −0.190713 0.296286i
\(191\) −2.24592 6.91223i −0.162509 0.500151i 0.836335 0.548219i \(-0.184694\pi\)
−0.998844 + 0.0480672i \(0.984694\pi\)
\(192\) 2.57529 + 3.54458i 0.185855 + 0.255808i
\(193\) 8.92106 + 12.2788i 0.642152 + 0.883846i 0.998728 0.0504200i \(-0.0160560\pi\)
−0.356576 + 0.934266i \(0.616056\pi\)
\(194\) −1.46228 4.50045i −0.104986 0.323113i
\(195\) −15.4107 + 9.91949i −1.10358 + 0.710350i
\(196\) 5.87989 + 4.27199i 0.419992 + 0.305142i
\(197\) 17.2480i 1.22887i 0.788969 + 0.614433i \(0.210615\pi\)
−0.788969 + 0.614433i \(0.789385\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 8.79213 + 3.99996i 0.621698 + 0.282840i
\(201\) −1.31887 + 4.05906i −0.0930258 + 0.286304i
\(202\) 9.54689 3.10197i 0.671717 0.218254i
\(203\) 13.6262 + 18.7548i 0.956369 + 1.31633i
\(204\) −10.4591 + 7.59901i −0.732286 + 0.532037i
\(205\) 1.40255 3.61010i 0.0979585 0.252141i
\(206\) −0.678648 + 2.08867i −0.0472837 + 0.145524i
\(207\) −1.49946 + 2.06382i −0.104219 + 0.143446i
\(208\) 10.4543i 0.724875i
\(209\) 0 0
\(210\) 4.73205 5.79555i 0.326543 0.399931i
\(211\) −10.6178 7.71430i −0.730961 0.531074i 0.158906 0.987294i \(-0.449203\pi\)
−0.889867 + 0.456219i \(0.849203\pi\)
\(212\) 3.57803 + 1.16257i 0.245740 + 0.0798459i
\(213\) −15.0588 + 4.89290i −1.03181 + 0.335256i
\(214\) 1.24257 0.902778i 0.0849402 0.0617127i
\(215\) 0.813254 14.4039i 0.0554635 0.982340i
\(216\) 2.61555 + 8.04984i 0.177966 + 0.547722i
\(217\) 27.7880 + 9.02886i 1.88637 + 0.612919i
\(218\) 2.79802 3.85115i 0.189506 0.260833i
\(219\) 9.46410 0.639525
\(220\) 0 0
\(221\) 16.3923 1.10267
\(222\) −1.05399 + 1.45069i −0.0707390 + 0.0973639i
\(223\) 1.47691 + 0.479877i 0.0989012 + 0.0321349i 0.358050 0.933703i \(-0.383442\pi\)
−0.259148 + 0.965838i \(0.583442\pi\)
\(224\) 5.31390 + 16.3545i 0.355050 + 1.09273i
\(225\) 2.70022 + 2.47109i 0.180014 + 0.164739i
\(226\) 1.18448 0.860577i 0.0787906 0.0572448i
\(227\) −19.1291 + 6.21543i −1.26964 + 0.412533i −0.864922 0.501907i \(-0.832632\pi\)
−0.404723 + 0.914439i \(0.632632\pi\)
\(228\) 13.3534 + 4.33878i 0.884351 + 0.287343i
\(229\) −3.29415 2.39334i −0.217684 0.158156i 0.473600 0.880740i \(-0.342954\pi\)
−0.691283 + 0.722584i \(0.742954\pi\)
\(230\) −3.12436 2.55103i −0.206014 0.168210i
\(231\) 0 0
\(232\) 13.3843i 0.878720i
\(233\) −0.994306 + 1.36855i −0.0651392 + 0.0896564i −0.840344 0.542054i \(-0.817647\pi\)
0.775204 + 0.631710i \(0.217647\pi\)
\(234\) −0.496805 + 1.52901i −0.0324772 + 0.0999544i
\(235\) 23.8702 + 9.27375i 1.55712 + 0.604953i
\(236\) −1.77672 + 1.29087i −0.115655 + 0.0840282i
\(237\) 1.66251 + 2.28825i 0.107991 + 0.148638i
\(238\) −6.36459 + 2.06798i −0.412555 + 0.134047i
\(239\) 1.74911 5.38322i 0.113141 0.348212i −0.878414 0.477901i \(-0.841398\pi\)
0.991555 + 0.129689i \(0.0413979\pi\)
\(240\) −10.2927 + 2.71338i −0.664388 + 0.175148i
\(241\) −14.1244 −0.909830 −0.454915 0.890535i \(-0.650330\pi\)
−0.454915 + 0.890535i \(0.650330\pi\)
\(242\) 0 0
\(243\) 7.45001i 0.477918i
\(244\) −16.4396 11.9441i −1.05244 0.764642i
\(245\) −7.88973 + 5.07844i −0.504057 + 0.324450i
\(246\) −0.535233 1.64728i −0.0341252 0.105027i
\(247\) −10.4642 14.4027i −0.665821 0.916424i
\(248\) 9.91537 + 13.6473i 0.629626 + 0.866606i
\(249\) 5.90975 + 18.1883i 0.374515 + 1.15264i
\(250\) −4.14159 + 4.04238i −0.261937 + 0.255663i
\(251\) 3.07738 + 2.23585i 0.194242 + 0.141125i 0.680656 0.732604i \(-0.261695\pi\)
−0.486413 + 0.873729i \(0.661695\pi\)
\(252\) 4.24264i 0.267261i
\(253\) 0 0
\(254\) 0.464102 0.0291203
\(255\) −4.25457 16.1389i −0.266432 1.01065i
\(256\) −0.430246 + 1.32416i −0.0268904 + 0.0827600i
\(257\) 14.0742 4.57298i 0.877924 0.285255i 0.164829 0.986322i \(-0.447293\pi\)
0.713095 + 0.701068i \(0.247293\pi\)
\(258\) −3.79233 5.21969i −0.236100 0.324964i
\(259\) 4.85410 3.52671i 0.301619 0.219139i
\(260\) 15.3164 + 5.95053i 0.949881 + 0.369036i
\(261\) −1.56727 + 4.82357i −0.0970117 + 0.298571i
\(262\) 0.950617 1.30841i 0.0587293 0.0808339i
\(263\) 6.79367i 0.418915i 0.977818 + 0.209458i \(0.0671699\pi\)
−0.977818 + 0.209458i \(0.932830\pi\)
\(264\) 0 0
\(265\) −3.07180 + 3.76217i −0.188699 + 0.231108i
\(266\) 5.87989 + 4.27199i 0.360519 + 0.261933i
\(267\) 0.852694 + 0.277057i 0.0521840 + 0.0169556i
\(268\) 3.63925 1.18247i 0.222303 0.0722306i
\(269\) −13.1610 + 9.56206i −0.802443 + 0.583009i −0.911630 0.411012i \(-0.865175\pi\)
0.109187 + 0.994021i \(0.465175\pi\)
\(270\) −5.06322 0.285872i −0.308138 0.0173976i
\(271\) −3.54260 10.9030i −0.215198 0.662311i −0.999139 0.0414762i \(-0.986794\pi\)
0.783942 0.620834i \(-0.213206\pi\)
\(272\) 9.05459 + 2.94201i 0.549015 + 0.178386i
\(273\) 16.1199 22.1872i 0.975622 1.34283i
\(274\) −4.58846 −0.277199
\(275\) 0 0
\(276\) 11.6603 0.701865
\(277\) −18.3313 + 25.2308i −1.10142 + 1.51597i −0.267930 + 0.963438i \(0.586340\pi\)
−0.833489 + 0.552536i \(0.813660\pi\)
\(278\) −7.18194 2.33355i −0.430744 0.139957i
\(279\) 1.97533 + 6.07944i 0.118260 + 0.363967i
\(280\) −14.4312 0.814793i −0.862428 0.0486932i
\(281\) −14.0126 + 10.1807i −0.835921 + 0.607332i −0.921228 0.389023i \(-0.872813\pi\)
0.0853074 + 0.996355i \(0.472813\pi\)
\(282\) 10.8919 3.53899i 0.648603 0.210744i
\(283\) 7.67425 + 2.49351i 0.456187 + 0.148224i 0.528091 0.849187i \(-0.322908\pi\)
−0.0719049 + 0.997411i \(0.522908\pi\)
\(284\) 11.4849 + 8.34429i 0.681505 + 0.495142i
\(285\) −11.4641 + 14.0406i −0.679075 + 0.831693i
\(286\) 0 0
\(287\) 5.79555i 0.342101i
\(288\) −2.21135 + 3.04366i −0.130305 + 0.179349i
\(289\) 0.640220 1.97040i 0.0376600 0.115906i
\(290\) −7.47491 2.90406i −0.438942 0.170532i
\(291\) −14.2874 + 10.3804i −0.837545 + 0.608512i
\(292\) −4.98752 6.86474i −0.291873 0.401728i
\(293\) 14.3380 4.65870i 0.837635 0.272164i 0.141377 0.989956i \(-0.454847\pi\)
0.696258 + 0.717792i \(0.254847\pi\)
\(294\) −1.29668 + 3.99078i −0.0756241 + 0.232747i
\(295\) −0.722737 2.74156i −0.0420794 0.159620i
\(296\) 3.46410 0.201347
\(297\) 0 0
\(298\) 5.31508i 0.307894i
\(299\) −11.9610 8.69018i −0.691723 0.502566i
\(300\) 1.88320 16.6240i 0.108727 0.959787i
\(301\) 6.67120 + 20.5318i 0.384522 + 1.18344i
\(302\) 1.27672 + 1.75726i 0.0734671 + 0.101119i
\(303\) −22.0202 30.3082i −1.26503 1.74116i
\(304\) −3.19516 9.83368i −0.183255 0.564000i
\(305\) 22.0590 14.1989i 1.26309 0.813024i
\(306\) −1.18448 0.860577i −0.0677124 0.0491959i
\(307\) 7.82894i 0.446821i −0.974724 0.223411i \(-0.928281\pi\)
0.974724 0.223411i \(-0.0717191\pi\)
\(308\) 0 0
\(309\) 8.19615 0.466263
\(310\) −9.77322 + 2.57645i −0.555082 + 0.146332i
\(311\) 3.10641 9.56055i 0.176148 0.542129i −0.823536 0.567265i \(-0.808002\pi\)
0.999684 + 0.0251354i \(0.00800169\pi\)
\(312\) 15.0588 4.89290i 0.852536 0.277006i
\(313\) 10.0784 + 13.8718i 0.569666 + 0.784078i 0.992515 0.122122i \(-0.0389700\pi\)
−0.422849 + 0.906200i \(0.638970\pi\)
\(314\) 9.15848 6.65403i 0.516843 0.375509i
\(315\) −5.10546 1.98351i −0.287660 0.111758i
\(316\) 0.783636 2.41178i 0.0440830 0.135673i
\(317\) 7.42160 10.2150i 0.416839 0.573729i −0.548031 0.836458i \(-0.684622\pi\)
0.964870 + 0.262729i \(0.0846224\pi\)
\(318\) 2.17209i 0.121805i
\(319\) 0 0
\(320\) 3.92820 + 3.20736i 0.219593 + 0.179297i
\(321\) −4.63733 3.36921i −0.258830 0.188051i
\(322\) 5.74038 + 1.86516i 0.319899 + 0.103941i
\(323\) 15.4192 5.01000i 0.857946 0.278764i
\(324\) 14.9378 10.8529i 0.829876 0.602940i
\(325\) −14.3213 + 15.6493i −0.794405 + 0.868065i
\(326\) 0.822064 + 2.53005i 0.0455299 + 0.140127i
\(327\) −16.8961 5.48987i −0.934356 0.303591i
\(328\) −1.96677 + 2.70702i −0.108597 + 0.149470i
\(329\) −38.3205 −2.11268
\(330\) 0 0
\(331\) −18.1962 −1.00015 −0.500075 0.865982i \(-0.666694\pi\)
−0.500075 + 0.865982i \(0.666694\pi\)
\(332\) 10.0784 13.8718i 0.553125 0.761311i
\(333\) 1.24843 + 0.405640i 0.0684136 + 0.0222289i
\(334\) −0.0828009 0.254835i −0.00453066 0.0139439i
\(335\) −0.278474 + 4.93218i −0.0152147 + 0.269474i
\(336\) 12.8862 9.36236i 0.702999 0.510759i
\(337\) 16.7642 5.44701i 0.913203 0.296718i 0.185527 0.982639i \(-0.440601\pi\)
0.727676 + 0.685921i \(0.240601\pi\)
\(338\) −2.46152 0.799795i −0.133889 0.0435031i
\(339\) −4.42055 3.21172i −0.240091 0.174437i
\(340\) −9.46410 + 11.5911i −0.513263 + 0.628616i
\(341\) 0 0
\(342\) 1.59008i 0.0859816i
\(343\) −5.51452 + 7.59008i −0.297756 + 0.409826i
\(344\) −3.85162 + 11.8541i −0.207665 + 0.639128i
\(345\) −5.45137 + 14.0316i −0.293492 + 0.755435i
\(346\) −9.11596 + 6.62313i −0.490077 + 0.356062i
\(347\) 2.57529 + 3.54458i 0.138249 + 0.190283i 0.872527 0.488565i \(-0.162479\pi\)
−0.734279 + 0.678848i \(0.762479\pi\)
\(348\) 22.0476 7.16370i 1.18188 0.384015i
\(349\) −2.26216 + 6.96222i −0.121091 + 0.372679i −0.993169 0.116688i \(-0.962772\pi\)
0.872078 + 0.489367i \(0.162772\pi\)
\(350\) 3.58626 7.88281i 0.191694 0.421354i
\(351\) −18.5885 −0.992178
\(352\) 0 0
\(353\) 13.0053i 0.692204i −0.938197 0.346102i \(-0.887505\pi\)
0.938197 0.346102i \(-0.112495\pi\)
\(354\) −1.02579 0.745282i −0.0545203 0.0396113i
\(355\) −15.4107 + 9.91949i −0.817913 + 0.526472i
\(356\) −0.248403 0.764504i −0.0131653 0.0405187i
\(357\) 14.6802 + 20.2055i 0.776956 + 1.06939i
\(358\) −4.70511 6.47603i −0.248673 0.342269i
\(359\) 11.0196 + 33.9149i 0.581594 + 1.78996i 0.612540 + 0.790440i \(0.290148\pi\)
−0.0309462 + 0.999521i \(0.509852\pi\)
\(360\) −1.71157 2.65905i −0.0902076 0.140144i
\(361\) 1.12640 + 0.818376i 0.0592841 + 0.0430724i
\(362\) 9.00292i 0.473183i
\(363\) 0 0
\(364\) −24.5885 −1.28879
\(365\) 10.5926 2.79244i 0.554440 0.146163i
\(366\) 3.62540 11.1578i 0.189503 0.583230i
\(367\) −16.0787 + 5.22430i −0.839304 + 0.272706i −0.696959 0.717111i \(-0.745464\pi\)
−0.142345 + 0.989817i \(0.545464\pi\)
\(368\) −5.04720 6.94688i −0.263104 0.362131i
\(369\) −1.02579 + 0.745282i −0.0534006 + 0.0387978i
\(370\) −0.751625 + 1.93465i −0.0390751 + 0.100578i
\(371\) 2.24592 6.91223i 0.116602 0.358865i
\(372\) 17.1739 23.6379i 0.890426 1.22557i
\(373\) 0.175865i 0.00910597i −0.999990 0.00455298i \(-0.998551\pi\)
0.999990 0.00455298i \(-0.00144926\pi\)
\(374\) 0 0
\(375\) 19.1244 + 10.0382i 0.987577 + 0.518370i
\(376\) −17.8990 13.0044i −0.923069 0.670649i
\(377\) −27.9552 9.08321i −1.43977 0.467809i
\(378\) 7.21729 2.34504i 0.371217 0.120616i
\(379\) 1.18448 0.860577i 0.0608428 0.0442049i −0.556948 0.830547i \(-0.688028\pi\)
0.617791 + 0.786342i \(0.288028\pi\)
\(380\) 16.2258 + 0.916117i 0.832365 + 0.0469958i
\(381\) −0.535233 1.64728i −0.0274208 0.0843926i
\(382\) −3.57803 1.16257i −0.183068 0.0594824i
\(383\) −22.6069 + 31.1157i −1.15516 + 1.58994i −0.427475 + 0.904027i \(0.640597\pi\)
−0.727684 + 0.685913i \(0.759403\pi\)
\(384\) 22.1244 1.12903
\(385\) 0 0
\(386\) 7.85641 0.399881
\(387\) −2.77618 + 3.82108i −0.141121 + 0.194236i
\(388\) 15.0588 + 4.89290i 0.764494 + 0.248399i
\(389\) −1.89253 5.82461i −0.0959551 0.295319i 0.891546 0.452929i \(-0.149621\pi\)
−0.987501 + 0.157610i \(0.949621\pi\)
\(390\) −0.534780 + 9.47175i −0.0270796 + 0.479621i
\(391\) 10.8927 7.91400i 0.550867 0.400228i
\(392\) 7.70959 2.50500i 0.389393 0.126522i
\(393\) −5.74038 1.86516i −0.289564 0.0940850i
\(394\) 7.22307 + 5.24787i 0.363893 + 0.264384i
\(395\) 2.53590 + 2.07055i 0.127595 + 0.104181i
\(396\) 0 0
\(397\) 32.9802i 1.65523i −0.561298 0.827614i \(-0.689698\pi\)
0.561298 0.827614i \(-0.310302\pi\)
\(398\) 0.608520 0.837556i 0.0305024 0.0419829i
\(399\) 8.38189 25.7968i 0.419619 1.29146i
\(400\) −10.7193 + 6.07382i −0.535965 + 0.303691i
\(401\) −1.87733 + 1.36396i −0.0937494 + 0.0681129i −0.633673 0.773601i \(-0.718453\pi\)
0.539923 + 0.841714i \(0.318453\pi\)
\(402\) 1.29857 + 1.78732i 0.0647666 + 0.0891436i
\(403\) −35.2337 + 11.4481i −1.75512 + 0.570272i
\(404\) −10.3794 + 31.9445i −0.516395 + 1.58930i
\(405\) 6.07639 + 23.0496i 0.301938 + 1.14534i
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 14.4195i 0.713873i
\(409\) 21.1350 + 15.3555i 1.04506 + 0.759281i 0.971267 0.237992i \(-0.0764893\pi\)
0.0737938 + 0.997274i \(0.476489\pi\)
\(410\) −1.08509 1.68577i −0.0535888 0.0832542i
\(411\) 5.29172 + 16.2862i 0.261021 + 0.803340i
\(412\) −4.31932 5.94504i −0.212798 0.292891i
\(413\) 2.49376 + 3.43237i 0.122710 + 0.168896i
\(414\) 0.408059 + 1.25588i 0.0200550 + 0.0617230i
\(415\) 11.9810 + 18.6133i 0.588123 + 0.913692i
\(416\) −17.6397 12.8160i −0.864857 0.628355i
\(417\) 28.1827i 1.38011i
\(418\) 0 0
\(419\) 12.3397 0.602836 0.301418 0.953492i \(-0.402540\pi\)
0.301418 + 0.953492i \(0.402540\pi\)
\(420\) 6.38186 + 24.2083i 0.311403 + 1.18124i
\(421\) −5.26953 + 16.2179i −0.256821 + 0.790414i 0.736644 + 0.676281i \(0.236409\pi\)
−0.993465 + 0.114134i \(0.963591\pi\)
\(422\) −6.46116 + 2.09936i −0.314524 + 0.102195i
\(423\) −4.92784 6.78259i −0.239600 0.329781i
\(424\) 3.39476 2.46644i 0.164864 0.119781i
\(425\) −9.52374 16.8078i −0.461969 0.815300i
\(426\) −2.53275 + 7.79500i −0.122712 + 0.377669i
\(427\) −23.0742 + 31.7589i −1.11664 + 1.53692i
\(428\) 5.13922i 0.248413i
\(429\) 0 0
\(430\) −5.78461 4.72311i −0.278959 0.227769i
\(431\) −4.10317 2.98113i −0.197643 0.143596i 0.484562 0.874757i \(-0.338979\pi\)
−0.682205 + 0.731161i \(0.738979\pi\)
\(432\) −10.2677 3.33617i −0.494004 0.160512i
\(433\) 27.3310 8.88039i 1.31345 0.426764i 0.433206 0.901295i \(-0.357382\pi\)
0.880239 + 0.474531i \(0.157382\pi\)
\(434\) 12.2359 8.88987i 0.587340 0.426728i
\(435\) −1.68707 + 29.8805i −0.0808889 + 1.43266i
\(436\) 4.92209 + 15.1486i 0.235725 + 0.725487i
\(437\) −13.9069 4.51863i −0.665259 0.216156i
\(438\) 2.87955 3.96336i 0.137590 0.189377i
\(439\) 28.2487 1.34824 0.674119 0.738623i \(-0.264524\pi\)
0.674119 + 0.738623i \(0.264524\pi\)
\(440\) 0 0
\(441\) 3.07180 0.146276
\(442\) 4.98752 6.86474i 0.237232 0.326522i
\(443\) 26.2145 + 8.51761i 1.24549 + 0.404684i 0.856302 0.516475i \(-0.172756\pi\)
0.389187 + 0.921159i \(0.372756\pi\)
\(444\) −1.85410 5.70634i −0.0879918 0.270811i
\(445\) 1.03611 + 0.0584995i 0.0491164 + 0.00277314i
\(446\) 0.650326 0.472490i 0.0307938 0.0223730i
\(447\) −18.8653 + 6.12971i −0.892298 + 0.289925i
\(448\) −7.21729 2.34504i −0.340985 0.110793i
\(449\) 27.9246 + 20.2884i 1.31784 + 0.957468i 0.999956 + 0.00933886i \(0.00297270\pi\)
0.317885 + 0.948129i \(0.397027\pi\)
\(450\) 1.85641 0.378937i 0.0875118 0.0178633i
\(451\) 0 0
\(452\) 4.89898i 0.230429i
\(453\) 4.76479 6.55817i 0.223869 0.308130i
\(454\) −3.21734 + 9.90197i −0.150997 + 0.464722i
\(455\) 11.4955 29.5890i 0.538919 1.38715i
\(456\) 12.6694 9.20487i 0.593300 0.431057i
\(457\) 12.4688 + 17.1618i 0.583266 + 0.802797i 0.994049 0.108936i \(-0.0347444\pi\)
−0.410782 + 0.911733i \(0.634744\pi\)
\(458\) −2.00456 + 0.651320i −0.0936668 + 0.0304342i
\(459\) 5.23110 16.0997i 0.244167 0.751469i
\(460\) 13.0506 3.44043i 0.608486 0.160411i
\(461\) 33.0000 1.53696 0.768482 0.639872i \(-0.221013\pi\)
0.768482 + 0.639872i \(0.221013\pi\)
\(462\) 0 0
\(463\) 20.3166i 0.944194i −0.881547 0.472097i \(-0.843497\pi\)
0.881547 0.472097i \(-0.156503\pi\)
\(464\) −13.8114 10.0346i −0.641177 0.465842i
\(465\) 20.4159 + 31.7177i 0.946767 + 1.47087i
\(466\) 0.270589 + 0.832787i 0.0125348 + 0.0385781i
\(467\) −0.363941 0.500922i −0.0168412 0.0231799i 0.800513 0.599315i \(-0.204560\pi\)
−0.817355 + 0.576135i \(0.804560\pi\)
\(468\) −3.16196 4.35207i −0.146162 0.201174i
\(469\) −2.28435 7.03050i −0.105481 0.324638i
\(470\) 11.1464 7.17468i 0.514144 0.330943i
\(471\) −34.1799 24.8332i −1.57493 1.14425i
\(472\) 2.44949i 0.112747i
\(473\) 0 0
\(474\) 1.46410 0.0672484
\(475\) −8.68826 + 19.0973i −0.398645 + 0.876244i
\(476\) 6.91960 21.2963i 0.317159 0.976116i
\(477\) 1.51226 0.491361i 0.0692414 0.0224979i
\(478\) −1.72219 2.37039i −0.0787711 0.108419i
\(479\) −2.05158 + 1.49056i −0.0937393 + 0.0681056i −0.633668 0.773605i \(-0.718451\pi\)
0.539928 + 0.841711i \(0.318451\pi\)
\(480\) −8.03950 + 20.6933i −0.366951 + 0.944515i
\(481\) −2.35091 + 7.23535i −0.107192 + 0.329903i
\(482\) −4.29748 + 5.91497i −0.195745 + 0.269419i
\(483\) 22.5259i 1.02496i
\(484\) 0 0
\(485\) −12.9282 + 15.8338i −0.587039 + 0.718974i
\(486\) 3.11990 + 2.26674i 0.141521 + 0.102821i
\(487\) −12.1050 3.93314i −0.548529 0.178228i 0.0216245 0.999766i \(-0.493116\pi\)
−0.570153 + 0.821538i \(0.693116\pi\)
\(488\) −21.5553 + 7.00374i −0.975762 + 0.317044i
\(489\) 8.03209 5.83565i 0.363223 0.263897i
\(490\) −0.273789 + 4.84921i −0.0123685 + 0.219065i
\(491\) −12.2719 37.7691i −0.553825 1.70450i −0.699027 0.715095i \(-0.746383\pi\)
0.145203 0.989402i \(-0.453617\pi\)
\(492\) 5.51190 + 1.79092i 0.248496 + 0.0807411i
\(493\) 15.7341 21.6562i 0.708630 0.975346i
\(494\) −9.21539 −0.414620
\(495\) 0 0
\(496\) −21.5167 −0.966127
\(497\) 16.1199 22.1872i 0.723078 0.995231i
\(498\) 9.41498 + 3.05911i 0.421895 + 0.137082i
\(499\) −5.44108 16.7459i −0.243576 0.749650i −0.995867 0.0908194i \(-0.971051\pi\)
0.752291 0.658831i \(-0.228949\pi\)
\(500\) −2.79726 19.1618i −0.125097 0.856943i
\(501\) −0.809017 + 0.587785i −0.0361442 + 0.0262603i
\(502\) 1.87265 0.608460i 0.0835803 0.0271569i
\(503\) 7.02416 + 2.28229i 0.313192 + 0.101762i 0.461395 0.887195i \(-0.347349\pi\)
−0.148204 + 0.988957i \(0.547349\pi\)
\(504\) 3.82831 + 2.78143i 0.170526 + 0.123895i
\(505\) −33.5885 27.4249i −1.49467 1.22039i
\(506\) 0 0
\(507\) 9.65926i 0.428983i
\(508\) −0.912780 + 1.25633i −0.0404981 + 0.0557408i
\(509\) 2.49432 7.67673i 0.110559 0.340265i −0.880436 0.474165i \(-0.842750\pi\)
0.990995 + 0.133900i \(0.0427500\pi\)
\(510\) −8.05309 3.12869i −0.356597 0.138541i
\(511\) −13.2617 + 9.63516i −0.586661 + 0.426234i
\(512\) −13.0395 17.9473i −0.576270 0.793167i
\(513\) −17.4850 + 5.68121i −0.771980 + 0.250831i
\(514\) 2.36715 7.28533i 0.104410 0.321342i
\(515\) 9.17342 2.41832i 0.404229 0.106564i
\(516\) 21.5885 0.950379
\(517\) 0 0
\(518\) 3.10583i 0.136462i
\(519\) 34.0212 + 24.7179i 1.49337 + 1.08499i
\(520\) 15.4107 9.91949i 0.675802 0.434999i
\(521\) −2.85801 8.79605i −0.125212 0.385362i 0.868728 0.495290i \(-0.164938\pi\)
−0.993940 + 0.109928i \(0.964938\pi\)
\(522\) 1.54315 + 2.12396i 0.0675416 + 0.0929631i
\(523\) 15.0659 + 20.7365i 0.658788 + 0.906743i 0.999441 0.0334458i \(-0.0106481\pi\)
−0.340653 + 0.940189i \(0.610648\pi\)
\(524\) 1.67226 + 5.14668i 0.0730530 + 0.224834i
\(525\) −32.1151 3.63807i −1.40162 0.158778i
\(526\) 2.84504 + 2.06704i 0.124050 + 0.0901273i
\(527\) 33.7381i 1.46965i
\(528\) 0 0
\(529\) 10.8564 0.472018
\(530\) 0.640888 + 2.43108i 0.0278384 + 0.105599i
\(531\) −0.286831 + 0.882774i −0.0124474 + 0.0383091i
\(532\) −23.1288 + 7.51499i −1.00276 + 0.325816i
\(533\) −4.31932 5.94504i −0.187091 0.257508i
\(534\) 0.375466 0.272792i 0.0162480 0.0118049i
\(535\) −6.18437 2.40267i −0.267374 0.103877i
\(536\) 1.31887 4.05906i 0.0569665 0.175325i
\(537\) −17.5597 + 24.1689i −0.757757 + 1.04296i
\(538\) 8.42091i 0.363051i
\(539\) 0 0
\(540\) 10.7321 13.1440i 0.461834 0.565629i
\(541\) −2.10967 1.53276i −0.0907018 0.0658987i 0.541510 0.840694i \(-0.317853\pi\)
−0.632212 + 0.774796i \(0.717853\pi\)
\(542\) −5.64381 1.83379i −0.242423 0.0787678i
\(543\) −31.9549 + 10.3828i −1.37132 + 0.445567i
\(544\) 16.0642 11.6713i 0.688746 0.500403i
\(545\) −20.5305 1.15916i −0.879431 0.0496532i
\(546\) −4.38685 13.5013i −0.187740 0.577804i
\(547\) −27.3310 8.88039i −1.16859 0.379698i −0.340474 0.940254i \(-0.610587\pi\)
−0.828116 + 0.560556i \(0.810587\pi\)
\(548\) 9.02443 12.4211i 0.385505 0.530601i
\(549\) −8.58846 −0.366546
\(550\) 0 0
\(551\) −29.0718 −1.23850
\(552\) 7.64434 10.5215i 0.325365 0.447826i
\(553\) −4.65921 1.51387i −0.198130 0.0643762i
\(554\) 4.98864 + 15.3535i 0.211947 + 0.652306i
\(555\) 7.73365 + 0.436646i 0.328275 + 0.0185346i
\(556\) 20.4422 14.8521i 0.866942 0.629871i
\(557\) 35.7614 11.6196i 1.51526 0.492337i 0.570834 0.821065i \(-0.306620\pi\)
0.944425 + 0.328728i \(0.106620\pi\)
\(558\) 3.14695 + 1.02251i 0.133221 + 0.0432862i
\(559\) −22.1453 16.0895i −0.936645 0.680513i
\(560\) 11.6603 14.2808i 0.492736 0.603475i
\(561\) 0 0
\(562\) 8.96575i 0.378198i
\(563\) −9.38837 + 12.9220i −0.395673 + 0.544597i −0.959651 0.281193i \(-0.909270\pi\)
0.563979 + 0.825789i \(0.309270\pi\)
\(564\) −11.8417 + 36.4450i −0.498625 + 1.53461i
\(565\) −5.89527 2.29036i −0.248016 0.0963561i
\(566\) 3.37919 2.45513i 0.142038 0.103197i
\(567\) −20.9662 28.8576i −0.880499 1.21190i
\(568\) 15.0588 4.89290i 0.631853 0.205301i
\(569\) 9.30894 28.6500i 0.390251 1.20107i −0.542348 0.840154i \(-0.682464\pi\)
0.932599 0.360915i \(-0.117536\pi\)
\(570\) 2.39183 + 9.07291i 0.100183 + 0.380022i
\(571\) 19.7128 0.824956 0.412478 0.910968i \(-0.364663\pi\)
0.412478 + 0.910968i \(0.364663\pi\)
\(572\) 0 0
\(573\) 14.0406i 0.586554i
\(574\) 2.42705 + 1.76336i 0.101303 + 0.0736010i
\(575\) −1.96127 + 17.3131i −0.0817904 + 0.722006i
\(576\) −0.513047 1.57900i −0.0213769 0.0657915i
\(577\) −2.21135 3.04366i −0.0920596 0.126709i 0.760503 0.649335i \(-0.224953\pi\)
−0.852562 + 0.522626i \(0.824953\pi\)
\(578\) −0.630365 0.867623i −0.0262197 0.0360884i
\(579\) −9.06054 27.8855i −0.376543 1.15888i
\(580\) 22.5628 14.5231i 0.936868 0.603041i
\(581\) −26.7982 19.4700i −1.11178 0.807752i
\(582\) 9.14162i 0.378932i
\(583\) 0 0
\(584\) −9.46410 −0.391627
\(585\) 6.71541 1.77034i 0.277648 0.0731944i
\(586\) 2.41152 7.42190i 0.0996190 0.306596i
\(587\) −19.3930 + 6.30115i −0.800433 + 0.260076i −0.680540 0.732711i \(-0.738255\pi\)
−0.119892 + 0.992787i \(0.538255\pi\)
\(588\) −8.25286 11.3591i −0.340342 0.468441i
\(589\) −29.6432 + 21.5370i −1.22143 + 0.887419i
\(590\) −1.36800 0.531479i −0.0563198 0.0218807i
\(591\) 10.2966 31.6897i 0.423546 1.30354i
\(592\) −2.59713 + 3.57465i −0.106741 + 0.146917i
\(593\) 0.859411i 0.0352918i −0.999844 0.0176459i \(-0.994383\pi\)
0.999844 0.0176459i \(-0.00561715\pi\)
\(594\) 0 0
\(595\) 22.3923 + 18.2832i 0.917995 + 0.749540i
\(596\) 14.3881 + 10.4535i 0.589358 + 0.428193i
\(597\) −3.67460 1.19395i −0.150391 0.0488651i
\(598\) −7.27851 + 2.36493i −0.297640 + 0.0967092i
\(599\) −31.1025 + 22.5973i −1.27082 + 0.923302i −0.999235 0.0391140i \(-0.987546\pi\)
−0.271581 + 0.962416i \(0.587546\pi\)
\(600\) −13.7659 12.5978i −0.561991 0.514303i
\(601\) −6.18034 19.0211i −0.252101 0.775888i −0.994387 0.105804i \(-0.966258\pi\)
0.742286 0.670084i \(-0.233742\pi\)
\(602\) 10.6281 + 3.45327i 0.433168 + 0.140745i
\(603\) 0.950617 1.30841i 0.0387121 0.0532826i
\(604\) −7.26795 −0.295729
\(605\) 0 0
\(606\) −19.3923 −0.787759
\(607\) 21.3899 29.4406i 0.868188 1.19496i −0.111367 0.993779i \(-0.535523\pi\)
0.979555 0.201179i \(-0.0644772\pi\)
\(608\) −20.5095 6.66393i −0.831769 0.270258i
\(609\) −13.8392 42.5927i −0.560793 1.72594i
\(610\) 0.765489 13.5580i 0.0309938 0.548945i
\(611\) 39.3089 28.5596i 1.59027 1.15540i
\(612\) 4.65921 1.51387i 0.188337 0.0611945i
\(613\) −1.70539 0.554114i −0.0688800 0.0223805i 0.274374 0.961623i \(-0.411529\pi\)
−0.343254 + 0.939243i \(0.611529\pi\)
\(614\) −3.27859 2.38203i −0.132313 0.0961311i
\(615\) −4.73205 + 5.79555i −0.190815 + 0.233699i
\(616\) 0 0
\(617\) 13.0053i 0.523575i −0.965126 0.261787i \(-0.915688\pi\)
0.965126 0.261787i \(-0.0843119\pi\)
\(618\) 2.49376 3.43237i 0.100314 0.138070i
\(619\) −3.95066 + 12.1589i −0.158790 + 0.488707i −0.998525 0.0542900i \(-0.982710\pi\)
0.839735 + 0.542997i \(0.182710\pi\)
\(620\) 12.2472 31.5236i 0.491858 1.26602i
\(621\) −12.3520 + 8.97428i −0.495670 + 0.360125i
\(622\) −3.05859 4.20979i −0.122638 0.168797i
\(623\) −1.47691 + 0.479877i −0.0591711 + 0.0192259i
\(624\) −6.24095 + 19.2077i −0.249838 + 0.768923i
\(625\) 24.3665 + 5.59235i 0.974659 + 0.223694i
\(626\) 8.87564 0.354742
\(627\) 0 0
\(628\) 37.8792i 1.51154i
\(629\) −5.60503 4.07230i −0.223487 0.162373i
\(630\) −2.38404 + 1.53455i −0.0949823 + 0.0611380i
\(631\) −4.73430 14.5707i −0.188469 0.580049i 0.811521 0.584323i \(-0.198640\pi\)
−0.999991 + 0.00427343i \(0.998640\pi\)
\(632\) −1.66251 2.28825i −0.0661310 0.0910215i
\(633\) 14.9029 + 20.5121i 0.592337 + 0.815281i
\(634\) −2.01970 6.21601i −0.0802127 0.246869i
\(635\) −1.08509 1.68577i −0.0430605 0.0668977i
\(636\) −5.87989 4.27199i −0.233153 0.169396i
\(637\) 17.8028i 0.705371i
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 24.7624 6.52793i 0.978818 0.258039i
\(641\) −2.42776 + 7.47189i −0.0958909 + 0.295122i −0.987485 0.157714i \(-0.949588\pi\)
0.891594 + 0.452836i \(0.149588\pi\)
\(642\) −2.82191 + 0.916893i −0.111372 + 0.0361869i
\(643\) 6.18272 + 8.50978i 0.243823 + 0.335593i 0.913336 0.407207i \(-0.133497\pi\)
−0.669513 + 0.742800i \(0.733497\pi\)
\(644\) −16.3390 + 11.8710i −0.643848 + 0.467783i
\(645\) −10.0930 + 25.9789i −0.397411 + 1.02292i
\(646\) 2.59336 7.98156i 0.102035 0.314030i
\(647\) 21.9606 30.2261i 0.863358 1.18831i −0.117400 0.993085i \(-0.537456\pi\)
0.980758 0.195226i \(-0.0625441\pi\)
\(648\) 20.5940i 0.809010i
\(649\) 0 0
\(650\) 2.19615 + 10.7589i 0.0861402 + 0.421999i
\(651\) −45.6649 33.1775i −1.78975 1.30033i
\(652\) −8.46572 2.75068i −0.331543 0.107725i
\(653\) −11.5514 + 3.75329i −0.452043 + 0.146878i −0.526185 0.850370i \(-0.676378\pi\)
0.0741421 + 0.997248i \(0.476378\pi\)
\(654\) −7.43984 + 5.40536i −0.290921 + 0.211366i
\(655\) −6.97516 0.393822i −0.272542 0.0153879i
\(656\) −1.31887 4.05906i −0.0514932 0.158480i
\(657\) −3.41078 1.10823i −0.133067 0.0432361i
\(658\) −11.6594 + 16.0478i −0.454531 + 0.625608i
\(659\) −23.3205 −0.908438 −0.454219 0.890890i \(-0.650082\pi\)
−0.454219 + 0.890890i \(0.650082\pi\)
\(660\) 0 0
\(661\) 29.5885 1.15086 0.575429 0.817852i \(-0.304835\pi\)
0.575429 + 0.817852i \(0.304835\pi\)
\(662\) −5.53636 + 7.62015i −0.215177 + 0.296165i
\(663\) −30.1176 9.78580i −1.16967 0.380049i
\(664\) −5.90975 18.1883i −0.229343 0.705845i
\(665\) 1.76980 31.3458i 0.0686300 1.21554i
\(666\) 0.549721 0.399395i 0.0213012 0.0154763i
\(667\) −22.9615 + 7.46065i −0.889073 + 0.288877i
\(668\) 0.852694 + 0.277057i 0.0329917 + 0.0107197i
\(669\) −2.42705 1.76336i −0.0938352 0.0681753i
\(670\) 1.98076 + 1.61729i 0.0765235 + 0.0624812i
\(671\) 0 0
\(672\) 33.2204i 1.28151i
\(673\) 23.9870 33.0153i 0.924631 1.27265i −0.0372864 0.999305i \(-0.511871\pi\)
0.961917 0.273341i \(-0.0881286\pi\)
\(674\) 2.81958 8.67778i 0.108606 0.334256i
\(675\) 10.7997 + 19.0597i 0.415680 + 0.733607i
\(676\) 7.00629 5.09037i 0.269473 0.195783i
\(677\) −11.9637 16.4666i −0.459801 0.632861i 0.514667 0.857390i \(-0.327916\pi\)
−0.974467 + 0.224529i \(0.927916\pi\)
\(678\) −2.68999 + 0.874032i −0.103309 + 0.0335670i
\(679\) 9.45235 29.0914i 0.362748 1.11642i
\(680\) 4.25457 + 16.1389i 0.163155 + 0.618897i
\(681\) 38.8564 1.48898
\(682\) 0 0
\(683\) 29.8372i 1.14169i 0.821058 + 0.570844i \(0.193384\pi\)
−0.821058 + 0.570844i \(0.806616\pi\)
\(684\) −4.30438 3.12732i −0.164582 0.119576i
\(685\) 10.7280 + 16.6668i 0.409897 + 0.636805i
\(686\) 1.50071 + 4.61872i 0.0572975 + 0.176343i
\(687\) 4.62358 + 6.36381i 0.176401 + 0.242795i
\(688\) −9.34468 12.8619i −0.356263 0.490353i
\(689\) 2.84771 + 8.76436i 0.108489 + 0.333895i
\(690\) 4.21748 + 6.55216i 0.160557 + 0.249437i
\(691\) −30.6690 22.2823i −1.16670 0.847660i −0.176093 0.984374i \(-0.556346\pi\)
−0.990611 + 0.136714i \(0.956346\pi\)
\(692\) 37.7033i 1.43326i
\(693\) 0 0
\(694\) 2.26795 0.0860902
\(695\) 8.31549 + 31.5431i 0.315424 + 1.19650i
\(696\) 7.99007 24.5909i 0.302863 0.932116i
\(697\) 6.36459 2.06798i 0.241076 0.0783304i
\(698\) 2.22734 + 3.06567i 0.0843060 + 0.116037i
\(699\) 2.64383 1.92085i 0.0999987 0.0726533i
\(700\) 14.2856 + 25.2118i 0.539945 + 0.952915i
\(701\) −11.6983 + 36.0036i −0.441838 + 1.35984i 0.444077 + 0.895989i \(0.353532\pi\)
−0.885915 + 0.463848i \(0.846468\pi\)
\(702\) −5.65572 + 7.78444i −0.213462 + 0.293805i
\(703\) 7.52433i 0.283786i
\(704\) 0 0
\(705\) −38.3205 31.2886i −1.44323 1.17840i
\(706\) −5.44634 3.95700i −0.204976 0.148924i
\(707\) 61.7121 + 20.0515i 2.32092 + 0.754113i
\(708\) 4.03499 1.31105i 0.151644 0.0492722i
\(709\) 2.10967 1.53276i 0.0792303 0.0575642i −0.547465 0.836829i \(-0.684407\pi\)
0.626695 + 0.779264i \(0.284407\pi\)
\(710\) −0.534780 + 9.47175i −0.0200699 + 0.355468i
\(711\) −0.331203 1.01934i −0.0124211 0.0382282i
\(712\) −0.852694 0.277057i −0.0319561 0.0103832i
\(713\) −17.8858 + 24.6177i −0.669829 + 0.921940i
\(714\) 12.9282 0.483826
\(715\) 0 0
\(716\) 26.7846 1.00099
\(717\) −6.42730 + 8.84642i −0.240032 + 0.330375i
\(718\) 17.5557 + 5.70418i 0.655171 + 0.212878i
\(719\) 15.5115 + 47.7394i 0.578480 + 1.78038i 0.624011 + 0.781415i \(0.285502\pi\)
−0.0455311 + 0.998963i \(0.514498\pi\)
\(720\) 4.02711 + 0.227373i 0.150082 + 0.00847369i
\(721\) −11.4849 + 8.34429i −0.427721 + 0.310758i
\(722\) 0.685436 0.222712i 0.0255093 0.00828847i
\(723\) 25.9507 + 8.43189i 0.965116 + 0.313585i
\(724\) 24.3711 + 17.7067i 0.905745 + 0.658063i
\(725\) 6.92820 + 33.9411i 0.257307 + 1.26054i
\(726\) 0 0
\(727\) 8.24504i 0.305792i 0.988242 + 0.152896i \(0.0488599\pi\)
−0.988242 + 0.152896i \(0.951140\pi\)
\(728\) −16.1199 + 22.1872i −0.597444 + 0.822312i
\(729\) −5.43513 + 16.7276i −0.201301 + 0.619541i
\(730\) 2.05348 5.28556i 0.0760027 0.195627i
\(731\) 20.1673 14.6524i 0.745916 0.541940i
\(732\) 23.0742 + 31.7589i 0.852848 + 1.17384i
\(733\) −8.86146 + 2.87926i −0.327305 + 0.106348i −0.468060 0.883697i \(-0.655047\pi\)
0.140755 + 0.990044i \(0.455047\pi\)
\(734\) −2.70430 + 8.32297i −0.0998174 + 0.307206i
\(735\) 17.5275 4.62065i 0.646512 0.170435i
\(736\) −17.9090 −0.660133
\(737\) 0 0
\(738\) 0.656339i 0.0241602i
\(739\) 31.4936 + 22.8814i 1.15851 + 0.841707i 0.989589 0.143923i \(-0.0459717\pi\)
0.168921 + 0.985630i \(0.445972\pi\)
\(740\) −3.75887 5.83967i −0.138179 0.214671i
\(741\) 10.6278 + 32.7090i 0.390422 + 1.20160i
\(742\) −2.21135 3.04366i −0.0811811 0.111736i
\(743\) 25.5083 + 35.1092i 0.935809 + 1.28803i 0.957550 + 0.288267i \(0.0930789\pi\)
−0.0217414 + 0.999764i \(0.506921\pi\)
\(744\) −10.0704 30.9935i −0.369198 1.13628i
\(745\) −19.3061 + 12.4269i −0.707321 + 0.455287i
\(746\) −0.0736486 0.0535088i −0.00269647 0.00195910i
\(747\) 7.24693i 0.265151i
\(748\) 0 0
\(749\) 9.92820 0.362769
\(750\) 10.0226 4.95464i 0.365972 0.180918i
\(751\) 15.0309 46.2604i 0.548485 1.68806i −0.164070 0.986449i \(-0.552462\pi\)
0.712556 0.701616i \(-0.247538\pi\)
\(752\) 26.8387 8.72043i 0.978707 0.318001i
\(753\) −4.31932 5.94504i −0.157405 0.216649i
\(754\) −12.3095 + 8.94338i −0.448286 + 0.325699i
\(755\) 3.39789 8.74602i 0.123662 0.318300i
\(756\) −7.84665 + 24.1495i −0.285380 + 0.878309i
\(757\) 29.2569 40.2687i 1.06336 1.46359i 0.186741 0.982409i \(-0.440207\pi\)
0.876621 0.481182i \(-0.159793\pi\)
\(758\) 0.757875i 0.0275273i
\(759\) 0 0
\(760\) 11.4641 14.0406i 0.415847 0.509306i
\(761\) −16.0642 11.6713i −0.582326 0.423084i 0.257236 0.966349i \(-0.417188\pi\)
−0.839562 + 0.543264i \(0.817188\pi\)
\(762\) −0.852694 0.277057i −0.0308898 0.0100367i
\(763\) 29.2649 9.50874i 1.05946 0.344239i
\(764\) 10.1843 7.39931i 0.368454 0.267698i
\(765\) −0.356520 + 6.31450i −0.0128900 + 0.228301i
\(766\) 6.15221 + 18.9346i 0.222288 + 0.684133i
\(767\) −5.11616 1.66234i −0.184734 0.0600237i
\(768\) 1.58098 2.17603i 0.0570488 0.0785209i
\(769\) −9.85641 −0.355431 −0.177716 0.984082i \(-0.556871\pi\)
−0.177716 + 0.984082i \(0.556871\pi\)
\(770\) 0 0
\(771\) −28.5885 −1.02959
\(772\) −15.4517 + 21.2675i −0.556120 + 0.765433i
\(773\) −11.4549 3.72192i −0.412004 0.133868i 0.0956791 0.995412i \(-0.469498\pi\)
−0.507683 + 0.861544i \(0.669498\pi\)
\(774\) 0.755504 + 2.32520i 0.0271560 + 0.0835777i
\(775\) 32.2087 + 29.4757i 1.15697 + 1.05880i
\(776\) 14.2874 10.3804i 0.512889 0.372636i
\(777\) −11.0238 + 3.58185i −0.395477 + 0.128498i
\(778\) −3.01504 0.979646i −0.108094 0.0351220i
\(779\) −5.87989 4.27199i −0.210669 0.153060i
\(780\) −24.5885 20.0764i −0.880408 0.718850i
\(781\) 0 0
\(782\) 6.96953i 0.249230i
\(783\) −17.8421 + 24.5576i −0.637625 + 0.877616i
\(784\) −3.19516 + 9.83368i −0.114113 + 0.351203i
\(785\) −45.5826 17.7092i −1.62691 0.632067i
\(786\) −2.52766 + 1.83645i −0.0901585 + 0.0655040i
\(787\) 10.2196 + 14.0661i 0.364290 + 0.501403i 0.951338 0.308150i \(-0.0997098\pi\)
−0.587048 + 0.809552i \(0.699710\pi\)
\(788\) −28.4122 + 9.23168i −1.01214 + 0.328865i
\(789\) 4.05565 12.4820i 0.144385 0.444371i
\(790\) 1.63867 0.431992i 0.0583014 0.0153696i
\(791\) 9.46410 0.336505
\(792\) 0 0
\(793\) 49.7749i 1.76756i
\(794\) −13.8114 10.0346i −0.490147 0.356113i
\(795\) 7.88973 5.07844i 0.279820 0.180114i
\(796\) 1.07047 + 3.29456i 0.0379417 + 0.116772i
\(797\) 21.2705 + 29.2763i 0.753440 + 1.03702i 0.997731 + 0.0673193i \(0.0214446\pi\)
−0.244292 + 0.969702i \(0.578555\pi\)
\(798\) −8.25286 11.3591i −0.292148 0.402107i
\(799\) 13.6736 + 42.0830i 0.483737 + 1.48879i
\(800\) −2.89241 + 25.5328i −0.102262 + 0.902720i
\(801\) −0.274860 0.199698i −0.00971171 0.00705597i
\(802\) 1.20118i 0.0424153i
\(803\) 0 0
\(804\) −7.39230 −0.260706
\(805\) −6.64640 25.2118i −0.234255 0.888598i
\(806\) −5.92599 + 18.2383i −0.208734 + 0.642418i
\(807\) 29.8891 9.71156i 1.05215 0.341863i
\(808\) 22.0202 + 30.3082i 0.774669 + 1.06624i
\(809\) 11.7598 8.54399i 0.413452 0.300391i −0.361546 0.932354i \(-0.617751\pi\)
0.774998 + 0.631964i \(0.217751\pi\)
\(810\) 11.5015 + 4.46840i 0.404120 + 0.157004i
\(811\) −5.86538 + 18.0518i −0.205961 + 0.633884i 0.793711 + 0.608295i \(0.208146\pi\)
−0.999673 + 0.0255890i \(0.991854\pi\)
\(812\) −23.6012 + 32.4843i −0.828240 + 1.13997i
\(813\) 22.1469i 0.776727i
\(814\) 0 0
\(815\) 7.26795 8.90138i 0.254585 0.311802i
\(816\) −14.8797 10.8107i −0.520893 0.378451i
\(817\) −25.7481 8.36606i −0.900811 0.292691i
\(818\) 12.8611 4.17882i 0.449678 0.146109i
\(819\) −8.40755 + 6.10844i −0.293784 + 0.213446i
\(820\) 6.69754 + 0.378147i 0.233888 + 0.0132055i
\(821\) −9.02211 27.7672i −0.314874 0.969082i −0.975806 0.218636i \(-0.929839\pi\)
0.660933 0.750445i \(-0.270161\pi\)
\(822\) 8.43037 + 2.73919i 0.294043 + 0.0955404i
\(823\) −3.97137 + 5.46612i −0.138433 + 0.190537i −0.872605 0.488427i \(-0.837571\pi\)
0.734171 + 0.678964i \(0.237571\pi\)
\(824\) −8.19615 −0.285526
\(825\) 0 0
\(826\) 2.19615 0.0764139
\(827\) −20.0316 + 27.5712i −0.696568 + 0.958743i 0.303415 + 0.952858i \(0.401873\pi\)
−0.999983 + 0.00588462i \(0.998127\pi\)
\(828\) −4.20225 1.36539i −0.146038 0.0474507i
\(829\) 3.08423 + 9.49227i 0.107120 + 0.329680i 0.990222 0.139500i \(-0.0445495\pi\)
−0.883103 + 0.469180i \(0.844550\pi\)
\(830\) 11.4402 + 0.645919i 0.397095 + 0.0224202i
\(831\) 48.7422 35.4133i 1.69085 1.22847i
\(832\) 9.15115 2.97339i 0.317259 0.103084i
\(833\) −15.4192 5.01000i −0.534243 0.173586i
\(834\) 11.8023 + 8.57488i 0.408681 + 0.296924i
\(835\) −0.732051 + 0.896575i −0.0253337 + 0.0310273i
\(836\) 0 0
\(837\) 38.2581i 1.32239i
\(838\) 3.75449 5.16761i 0.129697 0.178512i
\(839\) 11.9851 36.8864i 0.413772 1.27346i −0.499573 0.866272i \(-0.666510\pi\)
0.913345 0.407187i \(-0.133490\pi\)
\(840\) 26.0280 + 10.1121i 0.898052 + 0.348900i
\(841\) −15.3713 + 11.1679i −0.530046 + 0.385101i
\(842\) 5.18841 + 7.14124i 0.178804 + 0.246103i
\(843\) 31.8230 10.3399i 1.09604 0.356125i
\(844\) 7.02459 21.6195i 0.241796 0.744173i
\(845\) 2.85002 + 10.8110i 0.0980438 + 0.371909i
\(846\) −4.33975 −0.149204
\(847\) 0 0
\(848\) 5.35225i 0.183797i
\(849\) −12.6113 9.16267i −0.432820 0.314462i
\(850\) −9.93645 1.12562i −0.340817 0.0386085i
\(851\) 1.93096 + 5.94288i 0.0661924 + 0.203719i
\(852\) −16.1199 22.1872i −0.552260 0.760120i
\(853\) −27.2523 37.5096i −0.933102 1.28430i −0.958637 0.284631i \(-0.908129\pi\)
0.0255350 0.999674i \(-0.491871\pi\)
\(854\) 6.27938 + 19.3260i 0.214876 + 0.661320i
\(855\) 5.77568 3.71768i 0.197524 0.127142i
\(856\) 4.63733 + 3.36921i 0.158501 + 0.115157i
\(857\) 29.3195i 1.00154i 0.865581 + 0.500768i \(0.166949\pi\)
−0.865581 + 0.500768i \(0.833051\pi\)
\(858\) 0 0
\(859\) 22.1962 0.757323 0.378661 0.925535i \(-0.376384\pi\)
0.378661 + 0.925535i \(0.376384\pi\)
\(860\) 24.1626 6.36981i 0.823937 0.217209i
\(861\) 3.45980 10.6482i 0.117910 0.362889i
\(862\) −2.49686 + 0.811279i −0.0850434 + 0.0276323i
\(863\) −10.0566 13.8417i −0.342330 0.471176i 0.602790 0.797900i \(-0.294056\pi\)
−0.945120 + 0.326723i \(0.894056\pi\)
\(864\) −18.2164 + 13.2350i −0.619733 + 0.450263i
\(865\) 45.3709 + 17.6269i 1.54266 + 0.599334i
\(866\) 4.59683 14.1476i 0.156207 0.480754i
\(867\) −2.35255 + 3.23801i −0.0798969 + 0.109969i
\(868\) 50.6071i 1.71772i
\(869\) 0 0
\(870\) 12.0000 + 9.79796i 0.406838 + 0.332182i
\(871\) 7.58297 + 5.50935i 0.256939 + 0.186677i
\(872\) 16.8961 + 5.48987i 0.572174 + 0.185911i
\(873\) 6.36459 2.06798i 0.215409 0.0699906i
\(874\) −6.12363 + 4.44908i −0.207135 + 0.150492i
\(875\) −37.0178 + 5.40390i −1.25143 + 0.182685i
\(876\) 5.06550 + 15.5900i 0.171147 + 0.526738i
\(877\) 11.3135 + 3.67598i 0.382030 + 0.124129i 0.493735 0.869612i \(-0.335631\pi\)
−0.111705 + 0.993741i \(0.535631\pi\)
\(878\) 8.59495 11.8299i 0.290066 0.399241i
\(879\) −29.1244 −0.982340
\(880\) 0 0
\(881\) −26.9090 −0.906586 −0.453293 0.891362i \(-0.649751\pi\)
−0.453293 + 0.891362i \(0.649751\pi\)
\(882\) 0.934625 1.28640i 0.0314705 0.0433154i
\(883\) −20.5095 6.66393i −0.690199 0.224259i −0.0571437 0.998366i \(-0.518199\pi\)
−0.633055 + 0.774107i \(0.718199\pi\)
\(884\) 8.77370 + 27.0027i 0.295092 + 0.908199i
\(885\) −0.308755 + 5.46852i −0.0103787 + 0.183822i
\(886\) 11.5430 8.38649i 0.387795 0.281750i
\(887\) −14.9269 + 4.85004i −0.501196 + 0.162848i −0.548694 0.836023i \(-0.684875\pi\)
0.0474989 + 0.998871i \(0.484875\pi\)
\(888\) −6.36459 2.06798i −0.213582 0.0693969i
\(889\) 2.42705 + 1.76336i 0.0814007 + 0.0591411i
\(890\) 0.339746 0.416102i 0.0113883 0.0139478i
\(891\) 0 0
\(892\) 2.68973i 0.0900587i
\(893\) 28.2466 38.8782i 0.945238 1.30101i
\(894\) −3.17297 + 9.76540i −0.106120 + 0.326604i
\(895\) −12.5223 + 32.2317i −0.418573 + 1.07739i
\(896\) −31.0019 + 22.5242i −1.03570 + 0.752482i
\(897\) 16.7881 + 23.1069i 0.560539 + 0.771516i
\(898\) 16.9927 5.52125i 0.567052 0.184246i
\(899\) −18.6947 + 57.5365i −0.623504 + 1.91895i
\(900\) −2.62533 + 5.77062i −0.0875109 + 0.192354i
\(901\) −8.39230 −0.279588
\(902\) 0 0
\(903\) 41.7057i 1.38788i
\(904\) 4.42055 + 3.21172i 0.147025 + 0.106820i
\(905\) −32.7015 + 21.0492i −1.08704 + 0.699701i
\(906\) −1.29668 3.99078i −0.0430794 0.132585i
\(907\) −17.7009 24.3632i −0.587749 0.808967i 0.406769 0.913531i \(-0.366655\pi\)
−0.994518 + 0.104564i \(0.966655\pi\)
\(908\) −20.4771 28.1843i −0.679556 0.935329i
\(909\) 4.38685 + 13.5013i 0.145503 + 0.447811i
\(910\) −8.89357 13.8168i −0.294819 0.458023i
\(911\) 24.4717 + 17.7797i 0.810784 + 0.589069i 0.914058 0.405584i \(-0.132932\pi\)
−0.103274 + 0.994653i \(0.532932\pi\)
\(912\) 19.9749i 0.661434i
\(913\) 0 0
\(914\) 10.9808 0.363211
\(915\) −49.0053 + 12.9189i −1.62006 + 0.427086i
\(916\) 2.17936 6.70738i 0.0720081 0.221618i
\(917\) 9.94263 3.23056i 0.328335 0.106682i
\(918\) −5.15058 7.08916i −0.169994 0.233977i
\(919\) 15.3558 11.1566i 0.506540 0.368023i −0.304970 0.952362i \(-0.598646\pi\)
0.811509 + 0.584339i \(0.198646\pi\)
\(920\) 5.45137 14.0316i 0.179726 0.462607i
\(921\) −4.67368 + 14.3841i −0.154003 + 0.473973i
\(922\) 10.0406 13.8197i 0.330669 0.455127i
\(923\) 34.7733i 1.14458i
\(924\) 0 0
\(925\) 8.78461 1.79315i 0.288836 0.0589584i
\(926\) −8.50816 6.18154i −0.279595 0.203138i
\(927\) −2.95382 0.959754i −0.0970161 0.0315225i
\(928\) −33.8629 + 11.0027i −1.11160 + 0.361182i
\(929\) −35.4806 + 25.7781i −1.16408 + 0.845754i −0.990288 0.139029i \(-0.955602\pi\)
−0.173792 + 0.984782i \(0.555602\pi\)
\(930\) 19.4944 + 1.10067i 0.639247 + 0.0360922i
\(931\) 5.44108 + 16.7459i 0.178324 + 0.548825i
\(932\) −2.78656 0.905408i −0.0912768 0.0296576i
\(933\) −11.4148 + 15.7112i −0.373704 + 0.514360i
\(934\) −0.320508 −0.0104873
\(935\) 0 0
\(936\) −6.00000 −0.196116
\(937\) −18.3313 + 25.2308i −0.598857 + 0.824255i −0.995603 0.0936728i \(-0.970139\pi\)
0.396746 + 0.917928i \(0.370139\pi\)
\(938\) −3.63925 1.18247i −0.118826 0.0386089i
\(939\) −10.2360 31.5031i −0.334039 1.02807i
\(940\) −2.50033 + 44.2845i −0.0815516 + 1.44440i
\(941\) −21.8435 + 15.8702i −0.712076 + 0.517354i −0.883843 0.467784i \(-0.845053\pi\)
0.171766 + 0.985138i \(0.445053\pi\)
\(942\) −20.7992 + 6.75806i −0.677674 + 0.220190i
\(943\) −5.74038 1.86516i −0.186932 0.0607380i
\(944\) −2.52766 1.83645i −0.0822682 0.0597714i
\(945\) −25.3923 20.7327i −0.826012 0.674436i
\(946\) 0 0
\(947\) 19.9749i 0.649096i 0.945869 + 0.324548i \(0.105212\pi\)
−0.945869 + 0.324548i \(0.894788\pi\)
\(948\) −2.87955 + 3.96336i −0.0935234 + 0.128724i
\(949\) 6.42280 19.7673i 0.208493 0.641675i
\(950\) 5.35403 + 9.44900i 0.173708 + 0.306566i
\(951\) −19.7338 + 14.3374i −0.639912 + 0.464923i
\(952\) −14.6802 20.2055i −0.475787 0.654864i
\(953\) 15.8761 5.15847i 0.514279 0.167099i −0.0403686 0.999185i \(-0.512853\pi\)
0.554647 + 0.832086i \(0.312853\pi\)
\(954\) 0.254347 0.782801i 0.00823480 0.0253441i
\(955\) 4.14276 + 15.7147i 0.134057 + 0.508517i
\(956\) 9.80385 0.317079
\(957\) 0 0
\(958\) 1.31268i 0.0424107i
\(959\) −23.9956 17.4339i −0.774860 0.562969i
\(960\) −5.30257 8.23793i −0.171140 0.265878i
\(961\) 13.9826 + 43.0341i 0.451052 + 1.38820i
\(962\) 2.31472 + 3.18594i 0.0746295 + 0.102719i
\(963\) 1.27672 + 1.75726i 0.0411418 + 0.0566268i
\(964\) −7.55982 23.2667i −0.243486 0.749371i
\(965\) −18.3686 28.5370i −0.591308 0.918639i
\(966\) −9.43334 6.85373i −0.303513 0.220515i
\(967\) 4.24264i 0.136434i 0.997671 + 0.0682171i \(0.0217310\pi\)
−0.997671 + 0.0682171i \(0.978269\pi\)
\(968\) 0 0
\(969\) −31.3205 −1.00616
\(970\) 2.69729 + 10.2316i 0.0866048 + 0.328518i
\(971\) −7.70324 + 23.7081i −0.247209 + 0.760830i 0.748057 + 0.663635i \(0.230987\pi\)
−0.995265 + 0.0971952i \(0.969013\pi\)
\(972\) −12.2722 + 3.98749i −0.393632 + 0.127899i
\(973\) −28.6921 39.4913i −0.919827 1.26603i
\(974\) −5.33017 + 3.87260i −0.170790 + 0.124086i
\(975\) 35.6548 20.2029i 1.14187 0.647010i
\(976\) 8.93336 27.4941i 0.285950 0.880063i
\(977\) 17.1142 23.5557i 0.547533 0.753614i −0.442142 0.896945i \(-0.645781\pi\)
0.989675 + 0.143331i \(0.0457813\pi\)
\(978\) 5.13922i 0.164334i
\(979\) 0 0
\(980\) −12.5885 10.2784i −0.402124 0.328332i
\(981\) 5.44634 + 3.95700i 0.173888 + 0.126337i
\(982\) −19.5507 6.35242i −0.623889 0.202714i
\(983\) 53.2817 17.3123i 1.69942 0.552176i 0.710906 0.703287i \(-0.248285\pi\)
0.988517 + 0.151112i \(0.0482853\pi\)
\(984\) 5.22957 3.79950i 0.166713 0.121124i
\(985\) 2.17409 38.5063i 0.0692722 1.22691i
\(986\) −4.28187 13.1782i −0.136362 0.419680i
\(987\) 70.4063 + 22.8764i 2.24106 + 0.728163i
\(988\) 18.1245 24.9463i 0.576618 0.793647i
\(989\) −22.4833 −0.714929
\(990\) 0 0
\(991\) 19.9090 0.632429 0.316215 0.948688i \(-0.397588\pi\)
0.316215 + 0.948688i \(0.397588\pi\)
\(992\) −26.3774 + 36.3054i −0.837483 + 1.15270i
\(993\) 33.4318 + 10.8626i 1.06093 + 0.344716i
\(994\) −4.38685 13.5013i −0.139143 0.428237i
\(995\) −4.46502 0.252098i −0.141551 0.00799204i
\(996\) −26.7982 + 19.4700i −0.849132 + 0.616931i
\(997\) 32.4472 10.5427i 1.02761 0.333892i 0.253767 0.967265i \(-0.418330\pi\)
0.773846 + 0.633374i \(0.218330\pi\)
\(998\) −8.66832 2.81651i −0.274391 0.0891550i
\(999\) 6.35597 + 4.61788i 0.201094 + 0.146103i
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 605.2.j.e.444.3 16
5.4 even 2 inner 605.2.j.e.444.2 16
11.2 odd 10 605.2.j.f.269.3 16
11.3 even 5 inner 605.2.j.e.124.2 16
11.4 even 5 inner 605.2.j.e.9.3 16
11.5 even 5 605.2.b.e.364.3 yes 4
11.6 odd 10 605.2.b.d.364.2 4
11.7 odd 10 605.2.j.f.9.2 16
11.8 odd 10 605.2.j.f.124.3 16
11.9 even 5 inner 605.2.j.e.269.2 16
11.10 odd 2 605.2.j.f.444.2 16
55.4 even 10 inner 605.2.j.e.9.2 16
55.9 even 10 inner 605.2.j.e.269.3 16
55.14 even 10 inner 605.2.j.e.124.3 16
55.17 even 20 3025.2.a.y.1.3 4
55.19 odd 10 605.2.j.f.124.2 16
55.24 odd 10 605.2.j.f.269.2 16
55.27 odd 20 3025.2.a.z.1.2 4
55.28 even 20 3025.2.a.y.1.2 4
55.29 odd 10 605.2.j.f.9.3 16
55.38 odd 20 3025.2.a.z.1.3 4
55.39 odd 10 605.2.b.d.364.3 yes 4
55.49 even 10 605.2.b.e.364.2 yes 4
55.54 odd 2 605.2.j.f.444.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.b.d.364.2 4 11.6 odd 10
605.2.b.d.364.3 yes 4 55.39 odd 10
605.2.b.e.364.2 yes 4 55.49 even 10
605.2.b.e.364.3 yes 4 11.5 even 5
605.2.j.e.9.2 16 55.4 even 10 inner
605.2.j.e.9.3 16 11.4 even 5 inner
605.2.j.e.124.2 16 11.3 even 5 inner
605.2.j.e.124.3 16 55.14 even 10 inner
605.2.j.e.269.2 16 11.9 even 5 inner
605.2.j.e.269.3 16 55.9 even 10 inner
605.2.j.e.444.2 16 5.4 even 2 inner
605.2.j.e.444.3 16 1.1 even 1 trivial
605.2.j.f.9.2 16 11.7 odd 10
605.2.j.f.9.3 16 55.29 odd 10
605.2.j.f.124.2 16 55.19 odd 10
605.2.j.f.124.3 16 11.8 odd 10
605.2.j.f.269.2 16 55.24 odd 10
605.2.j.f.269.3 16 11.2 odd 10
605.2.j.f.444.2 16 11.10 odd 2
605.2.j.f.444.3 16 55.54 odd 2
3025.2.a.y.1.2 4 55.28 even 20
3025.2.a.y.1.3 4 55.17 even 20
3025.2.a.z.1.2 4 55.27 odd 20
3025.2.a.z.1.3 4 55.38 odd 20