Properties

Label 605.2.j.e.124.2
Level $605$
Weight $2$
Character 605.124
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 124.2
Root \(0.492303 - 0.159959i\) of defining polynomial
Character \(\chi\) \(=\) 605.124
Dual form 605.2.j.e.444.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.304260 - 0.418778i) q^{2} +(1.83730 - 0.596975i) q^{3} +(0.535233 - 1.64728i) q^{4} +(-0.570005 - 2.16220i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-3.18230 - 1.03399i) q^{7} +(-1.83730 + 0.596975i) q^{8} +(0.592242 - 0.430289i) q^{9} +O(q^{10})\) \(q+(-0.304260 - 0.418778i) q^{2} +(1.83730 - 0.596975i) q^{3} +(0.535233 - 1.64728i) q^{4} +(-0.570005 - 2.16220i) 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} +(-2.33805 - 3.63233i) 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} +(-3.86682 - 0.218323i) q^{20} -6.46410 q^{21} +3.48477i q^{23} +(-3.01929 + 2.19364i) q^{24} +(-4.35019 + 2.46492i) 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} +(-0.809764 + 2.08429i) q^{30} +(7.06438 - 5.13257i) q^{31} +5.13922i q^{32} -2.00000 q^{34} +(-0.421768 + 7.47013i) 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} +(2.33805 + 3.63233i) 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} +(2.35584 + 1.07179i) 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} +(-7.23485 + 1.90727i) 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} +(3.25665 - 2.09624i) 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} +(-6.52111 + 7.12576i) q^{75} -7.26795 q^{76} -4.24264i q^{78} +(-1.18448 + 0.860577i) q^{79} +(-1.99534 + 5.13591i) 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} +(-8.05309 - 3.12869i) q^{85} +(2.70191 - 1.96305i) q^{86} -13.3843i q^{87} -0.464102 q^{89} +(-0.0477646 + 0.845982i) 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} +(-7.88973 + 5.07844i) 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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.304260 0.418778i −0.215144 0.296121i 0.687781 0.725918i \(-0.258585\pi\)
−0.902925 + 0.429797i \(0.858585\pi\)
\(3\) 1.83730 0.596975i 1.06077 0.344664i 0.273881 0.961764i \(-0.411693\pi\)
0.786885 + 0.617100i \(0.211693\pi\)
\(4\) 0.535233 1.64728i 0.267617 0.823639i
\(5\) −0.570005 2.16220i −0.254914 0.966964i
\(6\) −0.809017 0.587785i −0.330280 0.239962i
\(7\) −3.18230 1.03399i −1.20280 0.390812i −0.362007 0.932175i \(-0.617908\pi\)
−0.840789 + 0.541364i \(0.817908\pi\)
\(8\) −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 1.00000 0.000696272i \(0.000221630\pi\)
−0.308355 + 0.951271i \(0.599778\pi\)
\(14\) 0.535233 + 1.64728i 0.143047 + 0.440254i
\(15\) −2.33805 3.63233i −0.603681 0.937862i
\(16\) −1.99350 1.44836i −0.498375 0.362091i
\(17\) 2.27103 3.12580i 0.550805 0.758118i −0.439316 0.898333i \(-0.644779\pi\)
0.990121 + 0.140214i \(0.0447792\pi\)
\(18\) −0.360391 0.117098i −0.0849449 0.0276003i
\(19\) −1.29668 3.99078i −0.297479 0.915547i −0.982377 0.186908i \(-0.940153\pi\)
0.684898 0.728639i \(-0.259847\pi\)
\(20\) −3.86682 0.218323i −0.864648 0.0488185i
\(21\) −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
\(25\) −4.35019 + 2.46492i −0.870038 + 0.492985i
\(26\) 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 −0.529388 0.848380i \(-0.677578\pi\)
0.926949 0.375188i \(-0.122422\pi\)
\(30\) −0.809764 + 2.08429i −0.147842 + 0.380538i
\(31\) 7.06438 5.13257i 1.26880 0.921837i 0.269646 0.962960i \(-0.413093\pi\)
0.999154 + 0.0411227i \(0.0130935\pi\)
\(32\) 5.13922i 0.908494i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −0.421768 + 7.47013i −0.0712918 + 1.26268i
\(36\) −0.391818 1.20589i −0.0653030 0.200982i
\(37\) −1.70539 0.554114i −0.280364 0.0910958i 0.165460 0.986217i \(-0.447089\pi\)
−0.445824 + 0.895121i \(0.647089\pi\)
\(38\) −1.27672 + 1.75726i −0.207112 + 0.285065i
\(39\) 6.63083 + 4.81758i 1.06178 + 0.771430i
\(40\) 2.33805 + 3.63233i 0.369678 + 0.574321i
\(41\) −0.535233 1.64728i −0.0835894 0.257262i 0.900523 0.434808i \(-0.143184\pi\)
−0.984112 + 0.177547i \(0.943184\pi\)
\(42\) 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 \(-0.285321\pi\)
0.964291 + 0.264846i \(0.0853213\pi\)
\(48\) −4.52729 1.47101i −0.653459 0.212322i
\(49\) 3.39476 + 2.46644i 0.484966 + 0.352348i
\(50\) 2.35584 + 1.07179i 0.333167 + 0.151573i
\(51\) 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 \(-0.247663\pi\)
−0.887650 + 0.460519i \(0.847663\pi\)
\(54\) 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 −0.922306 0.386459i \(-0.873698\pi\)
0.973317 + 0.229466i \(0.0736979\pi\)
\(60\) −7.23485 + 1.90727i −0.934015 + 0.246228i
\(61\) −9.49143 6.89593i −1.21525 0.882933i −0.219556 0.975600i \(-0.570461\pi\)
−0.995697 + 0.0926671i \(0.970461\pi\)
\(62\) −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
\(70\) 3.25665 2.09624i 0.389245 0.250548i
\(71\) 6.63083 + 4.81758i 0.786934 + 0.571741i 0.907052 0.421018i \(-0.138327\pi\)
−0.120118 + 0.992760i \(0.538327\pi\)
\(72\) −0.831254 + 1.14412i −0.0979642 + 0.134836i
\(73\) 4.65921 + 1.51387i 0.545319 + 0.177185i 0.568705 0.822542i \(-0.307445\pi\)
−0.0233860 + 0.999727i \(0.507445\pi\)
\(74\) 0.286831 + 0.882774i 0.0333434 + 0.102620i
\(75\) −6.52111 + 7.12576i −0.752992 + 0.822812i
\(76\) −7.26795 −0.833691
\(77\) 0 0
\(78\) 4.24264i 0.480384i
\(79\) −1.18448 + 0.860577i −0.133265 + 0.0968225i −0.652421 0.757857i \(-0.726246\pi\)
0.519156 + 0.854680i \(0.326246\pi\)
\(80\) −1.99534 + 5.13591i −0.223086 + 0.574213i
\(81\) −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 \(-0.617173\pi\)
0.998545 + 0.0539231i \(0.0171726\pi\)
\(84\) −3.45980 + 10.6482i −0.377495 + 1.16181i
\(85\) −8.05309 3.12869i −0.873481 0.339354i
\(86\) 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 \(0.507830\pi\)
\(90\) −0.0477646 + 0.845982i −0.00503483 + 0.0891744i
\(91\) −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
\(95\) −7.88973 + 5.07844i −0.809469 + 0.521037i
\(96\) 3.06798 + 9.44228i 0.313125 + 0.963699i
\(97\) −5.37331 7.39573i −0.545577 0.750922i 0.443827 0.896113i \(-0.353621\pi\)
−0.989404 + 0.145190i \(0.953621\pi\)
\(98\) 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 0.625971 0.779847i \(-0.284703\pi\)
0.935114 0.354348i \(-0.115297\pi\)
\(102\) −3.67460 + 1.19395i −0.363840 + 0.118219i
\(103\) 4.03499 + 1.31105i 0.397579 + 0.129181i 0.500981 0.865458i \(-0.332973\pi\)
−0.103401 + 0.994640i \(0.532973\pi\)
\(104\) −6.63083 4.81758i −0.650206 0.472402i
\(105\) 3.68457 + 13.9767i 0.359577 + 1.36398i
\(106\) −0.347445 + 1.06933i −0.0337468 + 0.103862i
\(107\) −2.82191 + 0.916893i −0.272804 + 0.0886394i −0.442224 0.896905i \(-0.645810\pi\)
0.169420 + 0.985544i \(0.445810\pi\)
\(108\) 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 \(-0.642473\pi\)
0.179743 + 0.983714i \(0.442473\pi\)
\(114\) −1.29668 + 3.99078i −0.121445 + 0.373771i
\(115\) 7.53475 1.98633i 0.702619 0.185226i
\(116\) −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
\(125\) 7.80928 + 8.00095i 0.698483 + 0.715626i
\(126\) 1.02579 + 0.745282i 0.0913849 + 0.0663950i
\(127\) −0.526994 + 0.725345i −0.0467631 + 0.0643639i −0.831758 0.555138i \(-0.812665\pi\)
0.784995 + 0.619502i \(0.212665\pi\)
\(128\) 10.8919 + 3.53899i 0.962716 + 0.312805i
\(129\) 3.85162 + 11.8541i 0.339116 + 1.04369i
\(130\) −4.90294 0.276823i −0.430016 0.0242789i
\(131\) 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
\(135\) 9.13200 + 3.54785i 0.785958 + 0.305350i
\(136\) −2.30653 + 7.09878i −0.197784 + 0.608716i
\(137\) 5.21026 7.17130i 0.445142 0.612686i −0.526203 0.850359i \(-0.676385\pi\)
0.971345 + 0.237673i \(0.0763847\pi\)
\(138\) 2.04829 2.81923i 0.174362 0.239989i
\(139\) −4.50808 + 13.8744i −0.382370 + 1.17682i 0.555999 + 0.831183i \(0.312336\pi\)
−0.938370 + 0.345633i \(0.887664\pi\)
\(140\) 12.0796 + 4.69303i 1.02092 + 0.396634i
\(141\) 17.8990 13.0044i 1.50737 1.09517i
\(142\) 4.24264i 0.356034i
\(143\) 0 0
\(144\) −1.80385 −0.150321
\(145\) −15.4673 0.873292i −1.28449 0.0725230i
\(146\) −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 0.873534 0.486763i \(-0.161823\pi\)
−0.193002 + 0.981198i \(0.561823\pi\)
\(150\) 4.96822 + 0.562811i 0.405654 + 0.0459534i
\(151\) −1.29668 3.99078i −0.105523 0.324765i 0.884330 0.466862i \(-0.154616\pi\)
−0.989853 + 0.142097i \(0.954616\pi\)
\(152\) 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 \(-0.937626\pi\)
−0.679092 + 0.734053i \(0.737626\pi\)
\(158\) 0.720782 + 0.234196i 0.0573423 + 0.0186316i
\(159\) −3.39476 2.46644i −0.269222 0.195601i
\(160\) 11.1120 2.92938i 0.878480 0.231588i
\(161\) 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 \(-0.135494\pi\)
−0.674160 + 0.738586i \(0.735494\pi\)
\(164\) −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 \(-0.206376\pi\)
−0.820627 + 0.571464i \(0.806376\pi\)
\(168\) 11.8765 3.85891i 0.916291 0.297721i
\(169\) −1.54508 + 4.75528i −0.118853 + 0.365791i
\(170\) 1.14001 + 4.32439i 0.0874347 + 0.331666i
\(171\) −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 \(-0.289765\pi\)
0.960499 + 0.278282i \(0.0897649\pi\)
\(174\) −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 0.954738 + 0.297449i \(0.0961357\pi\)
−0.597563 + 0.801822i \(0.703864\pi\)
\(180\) −2.38404 + 1.53455i −0.177696 + 0.114379i
\(181\) 14.0707 + 10.2229i 1.04586 + 0.759865i 0.971422 0.237360i \(-0.0762821\pi\)
0.0744429 + 0.997225i \(0.476282\pi\)
\(182\) −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
\(185\) −0.226025 + 4.00323i −0.0166177 + 0.294323i
\(186\) −8.73205 −0.640265
\(187\) 0 0
\(188\) 19.8362i 1.44670i
\(189\) 11.8604 8.61708i 0.862717 0.626800i
\(190\) 4.52727 + 1.75888i 0.328443 + 0.127602i
\(191\) −2.24592 + 6.91223i −0.162509 + 0.500151i −0.998844 0.0480672i \(-0.984694\pi\)
0.836335 + 0.548219i \(0.184694\pi\)
\(192\) −2.57529 + 3.54458i −0.185855 + 0.255808i
\(193\) −8.92106 + 12.2788i −0.642152 + 0.883846i −0.998728 0.0504200i \(-0.983944\pi\)
0.356576 + 0.934266i \(0.383944\pi\)
\(194\) −1.46228 + 4.50045i −0.104986 + 0.323113i
\(195\) 6.63695 17.0832i 0.475282 1.22335i
\(196\) 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 \(0.477417\pi\)
\(200\) 6.52111 7.12576i 0.461112 0.503867i
\(201\) −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
\(205\) −3.25665 + 2.09624i −0.227455 + 0.146407i
\(206\) −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 −0.889867 0.456219i \(-0.849203\pi\)
0.158906 + 0.987294i \(0.449203\pi\)
\(212\) −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
\(215\) 13.9503 3.67761i 0.951400 0.250811i
\(216\) 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 \(-0.616558\pi\)
0.259148 + 0.965838i \(0.416558\pi\)
\(224\) 5.31390 16.3545i 0.355050 1.09273i
\(225\) −1.51573 + 3.33167i −0.101049 + 0.222111i
\(226\) 1.18448 + 0.860577i 0.0787906 + 0.0572448i
\(227\) 19.1291 + 6.21543i 1.26964 + 0.412533i 0.864922 0.501907i \(-0.167368\pi\)
0.404723 + 0.914439i \(0.367368\pi\)
\(228\) −13.3534 + 4.33878i −0.884351 + 0.287343i
\(229\) −3.29415 + 2.39334i −0.217684 + 0.158156i −0.691283 0.722584i \(-0.742954\pi\)
0.473600 + 0.880740i \(0.342954\pi\)
\(230\) −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 \(-0.182353\pi\)
−0.775204 + 0.631710i \(0.782353\pi\)
\(234\) −0.496805 1.52901i −0.0324772 0.0999544i
\(235\) −13.8604 21.5332i −0.904154 1.40467i
\(236\) −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 0.991555 0.129689i \(-0.0413979\pi\)
−0.878414 + 0.477901i \(0.841398\pi\)
\(240\) −0.600028 + 10.6274i −0.0387316 + 0.685995i
\(241\) −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
\(245\) 3.39789 8.74602i 0.217083 0.558762i
\(246\) −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
\(250\) 0.974569 5.70472i 0.0616371 0.360798i
\(251\) 3.07738 2.23585i 0.194242 0.141125i −0.486413 0.873729i \(-0.661695\pi\)
0.680656 + 0.732604i \(0.261695\pi\)
\(252\) 4.24264i 0.267261i
\(253\) 0 0
\(254\) 0.464102 0.0291203
\(255\) −16.6637 0.940842i −1.04352 0.0589178i
\(256\) −0.430246 1.32416i −0.0268904 0.0827600i
\(257\) −14.0742 4.57298i −0.877924 0.285255i −0.164829 0.986322i \(-0.552707\pi\)
−0.713095 + 0.701068i \(0.752707\pi\)
\(258\) 3.79233 5.21969i 0.236100 0.324964i
\(259\) 4.85410 + 3.52671i 0.301619 + 0.219139i
\(260\) −8.89357 13.8168i −0.551556 0.856882i
\(261\) −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 0.109187 0.994021i \(-0.465175\pi\)
−0.911630 + 0.411012i \(0.865175\pi\)
\(270\) −1.29274 4.90375i −0.0786737 0.298433i
\(271\) −3.54260 + 10.9030i −0.215198 + 0.662311i 0.783942 + 0.620834i \(0.213206\pi\)
−0.999139 + 0.0414762i \(0.986794\pi\)
\(272\) −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 0.833489 + 0.552536i \(0.186340\pi\)
0.267930 + 0.963438i \(0.413660\pi\)
\(278\) 7.18194 2.33355i 0.430744 0.139957i
\(279\) 1.97533 6.07944i 0.118260 0.363967i
\(280\) −3.68457 13.9767i −0.220195 0.835265i
\(281\) −14.0126 10.1807i −0.835921 0.607332i 0.0853074 0.996355i \(-0.472813\pi\)
−0.921228 + 0.389023i \(0.872813\pi\)
\(282\) −10.8919 3.53899i −0.648603 0.210744i
\(283\) −7.67425 + 2.49351i −0.456187 + 0.148224i −0.528091 0.849187i \(-0.677092\pi\)
0.0719049 + 0.997411i \(0.477092\pi\)
\(284\) 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
\(290\) 4.34037 + 6.74307i 0.254875 + 0.395967i
\(291\) −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 \(-0.545153\pi\)
−0.696258 + 0.717792i \(0.745153\pi\)
\(294\) −1.29668 3.99078i −0.0756241 0.232747i
\(295\) −2.83071 0.159824i −0.164810 0.00930529i
\(296\) 3.46410 0.201347
\(297\) 0 0
\(298\) 5.31508i 0.307894i
\(299\) −11.9610 + 8.69018i −0.691723 + 0.502566i
\(300\) 8.24780 + 14.5560i 0.476187 + 0.840392i
\(301\) 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
\(305\) −9.50019 + 24.4530i −0.543979 + 1.40018i
\(306\) −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
\(310\) −0.569746 + 10.0911i −0.0323594 + 0.573133i
\(311\) 3.10641 + 9.56055i 0.176148 + 0.542129i 0.999684 0.0251354i \(-0.00800169\pi\)
−0.823536 + 0.567265i \(0.808002\pi\)
\(312\) −15.0588 4.89290i −0.852536 0.277006i
\(313\) −10.0784 + 13.8718i −0.569666 + 0.784078i −0.992515 0.122122i \(-0.961030\pi\)
0.422849 + 0.906200i \(0.361030\pi\)
\(314\) 9.15848 + 6.65403i 0.516843 + 0.375509i
\(315\) 2.96452 + 4.60560i 0.167032 + 0.259496i
\(316\) 0.783636 + 2.41178i 0.0440830 + 0.135673i
\(317\) −7.42160 10.2150i −0.416839 0.573729i 0.548031 0.836458i \(-0.315378\pi\)
−0.964870 + 0.262729i \(0.915378\pi\)
\(318\) 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
\(325\) −19.3089 8.78452i −1.07106 0.487277i
\(326\) 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
\(335\) −4.77684 + 1.25928i −0.260987 + 0.0688021i
\(336\) 12.8862 + 9.36236i 0.702999 + 0.510759i
\(337\) −16.7642 5.44701i −0.913203 0.296718i −0.185527 0.982639i \(-0.559399\pi\)
−0.727676 + 0.685921i \(0.759399\pi\)
\(338\) 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
\(345\) 12.6578 8.14755i 0.681473 0.438649i
\(346\) −9.11596 6.62313i −0.490077 0.356062i
\(347\) −2.57529 + 3.54458i −0.138249 + 0.190283i −0.872527 0.488565i \(-0.837521\pi\)
0.734279 + 0.678848i \(0.237521\pi\)
\(348\) −22.0476 7.16370i −1.18188 0.384015i
\(349\) −2.26216 6.96222i −0.121091 0.372679i 0.872078 0.489367i \(-0.162772\pi\)
−0.993169 + 0.116688i \(0.962772\pi\)
\(350\) −6.38878 5.84666i −0.341495 0.312517i
\(351\) −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
\(355\) 6.63695 17.0832i 0.352253 0.906682i
\(356\) −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 −0.0309462 0.999521i \(-0.509852\pi\)
0.612540 0.790440i \(-0.290148\pi\)
\(360\) 2.94764 + 1.14518i 0.155354 + 0.0603562i
\(361\) 1.12640 0.818376i 0.0592841 0.0430724i
\(362\) 9.00292i 0.473183i
\(363\) 0 0
\(364\) −24.5885 −1.28879
\(365\) 0.617511 10.9370i 0.0323220 0.572470i
\(366\) 3.62540 + 11.1578i 0.189503 + 0.583230i
\(367\) 16.0787 + 5.22430i 0.839304 + 0.272706i 0.696959 0.717111i \(-0.254536\pi\)
0.142345 + 0.989817i \(0.454536\pi\)
\(368\) 5.04720 6.94688i 0.263104 0.362131i
\(369\) −1.02579 0.745282i −0.0534006 0.0387978i
\(370\) 1.74524 1.12337i 0.0907305 0.0584012i
\(371\) 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 0.617791 0.786342i \(-0.288028\pi\)
−0.556948 + 0.830547i \(0.688028\pi\)
\(380\) 4.14276 + 15.7147i 0.212519 + 0.806149i
\(381\) −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 0.727684 + 0.685913i \(0.240597\pi\)
0.427475 + 0.904027i \(0.359403\pi\)
\(384\) 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 −0.987501 0.157610i \(-0.949621\pi\)
0.891546 + 0.452929i \(0.149621\pi\)
\(390\) −9.17342 + 2.41832i −0.464514 + 0.122457i
\(391\) 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
\(400\) 12.2422 + 1.38682i 0.612110 + 0.0693412i
\(401\) −1.87733 1.36396i −0.0937494 0.0681129i 0.539923 0.841714i \(-0.318453\pi\)
−0.633673 + 0.773601i \(0.718453\pi\)
\(402\) −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
\(405\) 23.7991 + 1.34371i 1.18259 + 0.0667696i
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 14.4195i 0.713873i
\(409\) 21.1350 15.3555i 1.04506 0.759281i 0.0737938 0.997274i \(-0.476489\pi\)
0.971267 + 0.237992i \(0.0764893\pi\)
\(410\) 1.86873 + 0.726014i 0.0922899 + 0.0358553i
\(411\) 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
\(415\) −20.6335 8.01625i −1.01286 0.393502i
\(416\) −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 \(0.402540\pi\)
\(420\) 24.9955 + 1.41126i 1.21966 + 0.0688626i
\(421\) −5.26953 16.2179i −0.256821 0.790414i −0.993465 0.114134i \(-0.963591\pi\)
0.736644 0.676281i \(-0.236409\pi\)
\(422\) 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
\(425\) −2.17454 + 19.1957i −0.105481 + 0.931130i
\(426\) −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 −0.682205 0.731161i \(-0.738979\pi\)
0.484562 + 0.874757i \(0.338979\pi\)
\(432\) 10.2677 3.33617i 0.494004 0.160512i
\(433\) −27.3310 8.88039i −1.31345 0.426764i −0.433206 0.901295i \(-0.642618\pi\)
−0.880239 + 0.474531i \(0.842618\pi\)
\(434\) 12.2359 + 8.88987i 0.587340 + 0.426728i
\(435\) −28.9394 + 7.62909i −1.38754 + 0.365787i
\(436\) 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 \(-0.827244\pi\)
−0.389187 + 0.921159i \(0.627244\pi\)
\(444\) −1.85410 + 5.70634i −0.0879918 + 0.270811i
\(445\) 0.264540 + 1.00348i 0.0125404 + 0.0475695i
\(446\) 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 0.317885 0.948129i \(-0.397027\pi\)
0.999956 0.00933886i \(-0.00297270\pi\)
\(450\) 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
\(455\) −26.6920 + 17.1811i −1.25134 + 0.805461i
\(456\) 12.6694 + 9.20487i 0.593300 + 0.431057i
\(457\) −12.4688 + 17.1618i −0.583266 + 0.802797i −0.994049 0.108936i \(-0.965256\pi\)
0.410782 + 0.911733i \(0.365256\pi\)
\(458\) 2.00456 + 0.651320i 0.0936668 + 0.0304342i
\(459\) 5.23110 + 16.0997i 0.244167 + 0.751469i
\(460\) 0.760805 13.4750i 0.0354727 0.628274i
\(461\) 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
\(465\) −35.1600 13.6599i −1.63051 0.633464i
\(466\) 0.270589 0.832787i 0.0125348 0.0385781i
\(467\) 0.363941 0.500922i 0.0168412 0.0231799i −0.800513 0.599315i \(-0.795440\pi\)
0.817355 + 0.576135i \(0.195440\pi\)
\(468\) 3.16196 4.35207i 0.146162 0.201174i
\(469\) −2.28435 + 7.03050i −0.105481 + 0.324638i
\(470\) −4.80044 + 12.3561i −0.221428 + 0.569945i
\(471\) −34.1799 + 24.8332i −1.57493 + 1.14425i
\(472\) 2.44949i 0.112747i
\(473\) 0 0
\(474\) 1.46410 0.0672484
\(475\) 15.4778 + 14.1644i 0.710169 + 0.649908i
\(476\) 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 0.539928 0.841711i \(-0.318451\pi\)
−0.633668 + 0.773605i \(0.718451\pi\)
\(480\) 18.6673 12.0157i 0.852042 0.548440i
\(481\) −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 \(-0.506884\pi\)
0.570153 + 0.821538i \(0.306884\pi\)
\(488\) 21.5553 + 7.00374i 0.975762 + 0.317044i
\(489\) 8.03209 + 5.83565i 0.363223 + 0.263897i
\(490\) −4.69648 + 1.23810i −0.212165 + 0.0559317i
\(491\) −12.2719 + 37.7691i −0.553825 + 1.70450i 0.145203 + 0.989402i \(0.453617\pi\)
−0.699027 + 0.715095i \(0.746383\pi\)
\(492\) −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 0.752291 + 0.658831i \(0.228949\pi\)
−0.995867 + 0.0908194i \(0.971051\pi\)
\(500\) 17.3596 8.58168i 0.776344 0.383785i
\(501\) −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 \(-0.652651\pi\)
0.148204 + 0.988957i \(0.452651\pi\)
\(504\) 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 0.990995 0.133900i \(-0.0427500\pi\)
−0.880436 + 0.474165i \(0.842750\pi\)
\(510\) 4.67609 + 7.26465i 0.207061 + 0.321684i
\(511\) −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
\(515\) 0.534780 9.47175i 0.0235652 0.417375i
\(516\) 21.5885 0.950379
\(517\) 0 0
\(518\) 3.10583i 0.136462i
\(519\) 34.0212 24.7179i 1.49337 1.08499i
\(520\) −6.63695 + 17.0832i −0.291049 + 0.749148i
\(521\) −2.85801 + 8.79605i −0.125212 + 0.385362i −0.993940 0.109928i \(-0.964938\pi\)
0.868728 + 0.495290i \(0.164938\pi\)
\(522\) −1.54315 + 2.12396i −0.0675416 + 0.0929631i
\(523\) −15.0659 + 20.7365i −0.658788 + 0.906743i −0.999441 0.0334458i \(-0.989352\pi\)
0.340653 + 0.940189i \(0.389352\pi\)
\(524\) 1.67226 5.14668i 0.0730530 0.224834i
\(525\) 28.1201 15.9335i 1.22726 0.695396i
\(526\) 2.84504 2.06704i 0.124050 0.0901273i
\(527\) 33.7381i 1.46965i
\(528\) 0 0
\(529\) 10.8564 0.472018
\(530\) 2.51014 + 0.141724i 0.109033 + 0.00615609i
\(531\) −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
\(535\) 3.59100 + 5.57888i 0.155253 + 0.241196i
\(536\) 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 −0.632212 0.774796i \(-0.717853\pi\)
0.541510 + 0.840694i \(0.317853\pi\)
\(542\) 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
\(545\) −5.24185 19.8839i −0.224536 0.851732i
\(546\) −4.38685 + 13.5013i −0.187740 + 0.577804i
\(547\) 27.3310 8.88039i 1.16859 0.379698i 0.340474 0.940254i \(-0.389413\pi\)
0.828116 + 0.560556i \(0.189413\pi\)
\(548\) −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
\(555\) 1.97455 + 7.49007i 0.0838152 + 0.317936i
\(556\) 20.4422 + 14.8521i 0.866942 + 0.629871i
\(557\) −35.7614 11.6196i −1.51526 0.492337i −0.570834 0.821065i \(-0.693380\pi\)
−0.944425 + 0.328728i \(0.893380\pi\)
\(558\) −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 \(-0.0907300\pi\)
−0.563979 + 0.825789i \(0.690730\pi\)
\(564\) −11.8417 36.4450i −0.498625 1.53461i
\(565\) 3.42314 + 5.31809i 0.144013 + 0.223734i
\(566\) 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 0.932599 + 0.360915i \(0.117536\pi\)
−0.542348 + 0.840154i \(0.682464\pi\)
\(570\) 9.36796 + 0.528920i 0.392381 + 0.0221540i
\(571\) 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
\(575\) −8.58968 15.1594i −0.358215 0.632190i
\(576\) −0.513047 + 1.57900i −0.0213769 + 0.0657915i
\(577\) 2.21135 3.04366i 0.0920596 0.126709i −0.760503 0.649335i \(-0.775047\pi\)
0.852562 + 0.522626i \(0.175047\pi\)
\(578\) 0.630365 0.867623i 0.0262197 0.0360884i
\(579\) −9.06054 + 27.8855i −0.376543 + 1.15888i
\(580\) −9.71717 + 25.0115i −0.403483 + 1.03855i
\(581\) −26.7982 + 19.4700i −1.11178 + 0.807752i
\(582\) 9.14162i 0.378932i
\(583\) 0 0
\(584\) −9.46410 −0.391627
\(585\) 0.391486 6.93380i 0.0161860 0.286677i
\(586\) 2.41152 + 7.42190i 0.0996190 + 0.306596i
\(587\) 19.3930 + 6.30115i 0.800433 + 0.260076i 0.680540 0.732711i \(-0.261745\pi\)
0.119892 + 0.992787i \(0.461745\pi\)
\(588\) 8.25286 11.3591i 0.340342 0.468441i
\(589\) −29.6432 21.5370i −1.22143 0.887419i
\(590\) 0.794342 + 1.23407i 0.0327025 + 0.0508058i
\(591\) 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 −0.271581 0.962416i \(-0.587546\pi\)
−0.999235 + 0.0391140i \(0.987546\pi\)
\(600\) 7.72733 16.9851i 0.315467 0.693414i
\(601\) −6.18034 + 19.0211i −0.252101 + 0.775888i 0.742286 + 0.670084i \(0.233742\pi\)
−0.994387 + 0.105804i \(0.966258\pi\)
\(602\) −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 −0.979555 0.201179i \(-0.935523\pi\)
0.111367 0.993779i \(-0.464477\pi\)
\(608\) 20.5095 6.66393i 0.831769 0.270258i
\(609\) −13.8392 + 42.5927i −0.560793 + 1.72594i
\(610\) 13.1309 3.46161i 0.531656 0.140157i
\(611\) 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 \(-0.588471\pi\)
0.343254 + 0.939243i \(0.388471\pi\)
\(614\) −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 0.839735 0.542997i \(-0.182710\pi\)
−0.998525 + 0.0542900i \(0.982710\pi\)
\(620\) −28.4373 + 18.3044i −1.14207 + 0.735124i
\(621\) −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
\(625\) 12.8483 21.4458i 0.513932 0.857831i
\(626\) 8.87564 0.354742
\(627\) 0 0
\(628\) 37.8792i 1.51154i
\(629\) −5.60503 + 4.07230i −0.223487 + 0.162373i
\(630\) 1.02674 2.64278i 0.0409063 0.105291i
\(631\) −4.73430 + 14.5707i −0.188469 + 0.580049i −0.999991 0.00427343i \(-0.998640\pi\)
0.811521 + 0.584323i \(0.198640\pi\)
\(632\) 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
\(635\) 1.86873 + 0.726014i 0.0741582 + 0.0288110i
\(636\) −5.87989 + 4.27199i −0.233153 + 0.169396i
\(637\) 17.8028i 0.705371i
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 1.44356 25.5676i 0.0570619 1.01065i
\(641\) −2.42776 7.47189i −0.0958909 0.295122i 0.891594 0.452836i \(-0.149588\pi\)
−0.987485 + 0.157714i \(0.949588\pi\)
\(642\) 2.82191 + 0.916893i 0.111372 + 0.0361869i
\(643\) −6.18272 + 8.50978i −0.243823 + 0.335593i −0.913336 0.407207i \(-0.866503\pi\)
0.669513 + 0.742800i \(0.266503\pi\)
\(644\) −16.3390 11.8710i −0.643848 0.467783i
\(645\) 23.4354 15.0848i 0.922767 0.593965i
\(646\) 2.59336 + 7.98156i 0.102035 + 0.314030i
\(647\) −21.9606 30.2261i −0.863358 1.18831i −0.980758 0.195226i \(-0.937456\pi\)
0.117400 0.993085i \(-0.462544\pi\)
\(648\) 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 \(-0.323622\pi\)
−0.0741421 + 0.997248i \(0.523622\pi\)
\(654\) −7.43984 5.40536i −0.290921 0.211366i
\(655\) −1.78090 6.75547i −0.0695854 0.263958i
\(656\) −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
\(665\) 30.3585 8.00321i 1.17725 0.310351i
\(666\) 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 −0.961917 0.273341i \(-0.911871\pi\)
0.0372864 0.999305i \(-0.488129\pi\)
\(674\) 2.81958 + 8.67778i 0.108606 + 0.334256i
\(675\) 2.46587 21.7675i 0.0949113 0.837831i
\(676\) 7.00629 + 5.09037i 0.269473 + 0.195783i
\(677\) 11.9637 16.4666i 0.459801 0.632861i −0.514667 0.857390i \(-0.672084\pi\)
0.974467 + 0.224529i \(0.0720843\pi\)
\(678\) 2.68999 + 0.874032i 0.103309 + 0.0335670i
\(679\) 9.45235 + 29.0914i 0.362748 + 1.11642i
\(680\) 16.6637 + 0.940842i 0.639024 + 0.0360796i
\(681\) 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
\(685\) −18.4756 7.17792i −0.705918 0.274254i
\(686\) 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
\(690\) −7.26328 2.82184i −0.276508 0.107426i
\(691\) −30.6690 + 22.2823i −1.16670 + 0.847660i −0.990611 0.136714i \(-0.956346\pi\)
−0.176093 + 0.984374i \(0.556346\pi\)
\(692\) 37.7033i 1.43326i
\(693\) 0 0
\(694\) 2.26795 0.0860902
\(695\) 32.5689 + 1.83886i 1.23541 + 0.0697519i
\(696\) 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
\(700\) 3.26180 28.7936i 0.123285 1.08830i
\(701\) −11.6983 36.0036i −0.441838 1.35984i −0.885915 0.463848i \(-0.846468\pi\)
0.444077 0.895989i \(-0.353532\pi\)
\(702\) 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 0.626695 0.779264i \(-0.284407\pi\)
−0.547465 + 0.836829i \(0.684407\pi\)
\(710\) −9.17342 + 2.41832i −0.344272 + 0.0907581i
\(711\) −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 −0.0455311 0.998963i \(-0.514498\pi\)
0.624011 0.781415i \(-0.285502\pi\)
\(720\) 1.02820 + 3.90027i 0.0383188 + 0.145355i
\(721\) −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
\(730\) −4.76807 + 3.06910i −0.176474 + 0.113593i
\(731\) 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 \(-0.344953\pi\)
−0.140755 + 0.990044i \(0.544953\pi\)
\(734\) −2.70430 8.32297i −0.0998174 0.307206i
\(735\) 1.02180 18.0975i 0.0376895 0.667537i
\(736\) −17.9090 −0.660133
\(737\) 0 0
\(738\) 0.656339i 0.0241602i
\(739\) 31.4936 22.8814i 1.15851 0.841707i 0.168921 0.985630i \(-0.445972\pi\)
0.989589 + 0.143923i \(0.0459717\pi\)
\(740\) 6.47346 + 2.51499i 0.237969 + 0.0924528i
\(741\) 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 0.0217414 + 0.999764i \(0.493079\pi\)
−0.957550 + 0.288267i \(0.906921\pi\)
\(744\) −10.0704 + 30.9935i −0.369198 + 1.13628i
\(745\) 8.31461 21.4014i 0.304624 0.784088i
\(746\) −0.0736486 + 0.0535088i −0.00269647 + 0.00195910i
\(747\) 7.24693i 0.265151i
\(748\) 0 0
\(749\) 9.92820 0.362769
\(750\) −1.61500 11.0631i −0.0589715 0.403967i
\(751\) 15.0309 + 46.2604i 0.548485 + 1.68806i 0.712556 + 0.701616i \(0.247538\pi\)
−0.164070 + 0.986449i \(0.552462\pi\)
\(752\) −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
\(755\) −7.88973 + 5.07844i −0.287137 + 0.184824i
\(756\) −7.84665 24.1495i −0.285380 0.878309i
\(757\) −29.2569 40.2687i −1.06336 1.46359i −0.876621 0.481182i \(-0.840207\pi\)
−0.186741 0.982409i \(-0.559793\pi\)
\(758\) 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 −0.839562 0.543264i \(-0.817188\pi\)
0.257236 + 0.966349i \(0.417188\pi\)
\(762\) 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
\(765\) −6.11562 + 1.61222i −0.221111 + 0.0582898i
\(766\) 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 \(-0.530502\pi\)
0.507683 + 0.861544i \(0.330502\pi\)
\(774\) 0.755504 2.32520i 0.0271560 0.0835777i
\(775\) −18.0800 + 39.7408i −0.649452 + 1.42753i
\(776\) 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
\(785\) 26.4679 + 41.1198i 0.944679 + 1.46763i
\(786\) −2.52766 1.83645i −0.0901585 0.0655040i
\(787\) −10.2196 + 14.0661i −0.364290 + 0.501403i −0.951338 0.308150i \(-0.900290\pi\)
0.587048 + 0.809552i \(0.300290\pi\)
\(788\) 28.4122 + 9.23168i 1.01214 + 0.328865i
\(789\) 4.05565 + 12.4820i 0.144385 + 0.444371i
\(790\) 0.0955293 1.69196i 0.00339878 0.0601974i
\(791\) 9.46410 0.336505
\(792\) 0 0
\(793\) 49.7749i 1.76756i
\(794\) −13.8114 + 10.0346i −0.490147 + 0.356113i
\(795\) −3.39789 + 8.74602i −0.120511 + 0.310189i
\(796\) 1.07047 3.29456i 0.0379417 0.116772i
\(797\) −21.2705 + 29.2763i −0.753440 + 1.03702i 0.244292 + 0.969702i \(0.421445\pi\)
−0.997731 + 0.0673193i \(0.978555\pi\)
\(798\) 8.25286 11.3591i 0.292148 0.402107i
\(799\) 13.6736 42.0830i 0.483737 1.48879i
\(800\) −12.6678 22.3566i −0.447874 0.790424i
\(801\) −0.274860 + 0.199698i −0.00971171 + 0.00705597i
\(802\) 1.20118i 0.0424153i
\(803\) 0 0
\(804\) −7.39230 −0.260706
\(805\) −26.0317 1.46976i −0.917496 0.0518023i
\(806\) −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 0.774998 0.631964i \(-0.217751\pi\)
−0.361546 + 0.932354i \(0.617751\pi\)
\(810\) −6.67841 10.3754i −0.234655 0.364554i
\(811\) −5.86538 18.0518i −0.205961 0.633884i −0.999673 0.0255890i \(-0.991854\pi\)
0.793711 0.608295i \(-0.208146\pi\)
\(812\) 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
\(820\) 1.71001 + 6.48659i 0.0597163 + 0.226522i
\(821\) −9.02211 + 27.7672i −0.314874 + 0.969082i 0.660933 + 0.750445i \(0.270161\pi\)
−0.975806 + 0.218636i \(0.929839\pi\)
\(822\) −8.43037 + 2.73919i −0.294043 + 0.0955404i
\(823\) 3.97137 + 5.46612i 0.138433 + 0.190537i 0.872605 0.488427i \(-0.162429\pi\)
−0.734171 + 0.678964i \(0.762429\pi\)
\(824\) −8.19615 −0.285526
\(825\) 0 0
\(826\) 2.19615 0.0764139
\(827\) 20.0316 + 27.5712i 0.696568 + 0.958743i 0.999983 + 0.00588462i \(0.00187314\pi\)
−0.303415 + 0.952858i \(0.598127\pi\)
\(828\) 4.20225 1.36539i 0.146038 0.0474507i
\(829\) 3.08423 9.49227i 0.107120 0.329680i −0.883103 0.469180i \(-0.844550\pi\)
0.990222 + 0.139500i \(0.0445495\pi\)
\(830\) 2.92091 + 11.0799i 0.101386 + 0.384588i
\(831\) 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 0.913345 + 0.407187i \(0.133490\pi\)
−0.499573 + 0.866272i \(0.666510\pi\)
\(840\) −15.1134 23.4797i −0.521461 0.810127i
\(841\) −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
\(845\) 11.1626 + 0.630244i 0.384004 + 0.0216811i
\(846\) −4.33975 −0.149204
\(847\) 0 0
\(848\) 5.35225i 0.183797i
\(849\) −12.6113 + 9.16267i −0.432820 + 0.314462i
\(850\) 8.70038 4.92985i 0.298421 0.169092i
\(851\) 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 −0.0255350 0.999674i \(-0.508129\pi\)
0.958637 0.284631i \(-0.0918711\pi\)
\(854\) 6.27938 19.3260i 0.214876 0.661320i
\(855\) −2.48743 + 6.40253i −0.0850683 + 0.218962i
\(856\) 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 \(0.376384\pi\)
\(860\) 1.40860 24.9483i 0.0480328 0.850731i
\(861\) 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 \(-0.705944\pi\)
0.945120 + 0.326723i \(0.105944\pi\)
\(864\) −18.2164 13.2350i −0.619733 0.450263i
\(865\) −26.3450 40.9289i −0.895757 1.39162i
\(866\) 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
\(875\) −16.5785 33.5361i −0.560457 1.13373i
\(876\) 5.06550 15.5900i 0.171147 0.526738i
\(877\) −11.3135 + 3.67598i −0.382030 + 0.124129i −0.493735 0.869612i \(-0.664369\pi\)
0.111705 + 0.993741i \(0.464369\pi\)
\(878\) −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 \(-0.481801\pi\)
0.633055 + 0.774107i \(0.281801\pi\)
\(884\) 8.77370 27.0027i 0.295092 0.908199i
\(885\) −5.29628 + 1.39622i −0.178032 + 0.0469334i
\(886\) 11.5430 + 8.38649i 0.387795 + 0.281750i
\(887\) 14.9269 + 4.85004i 0.501196 + 0.162848i 0.548694 0.836023i \(-0.315125\pi\)
−0.0474989 + 0.998871i \(0.515125\pi\)
\(888\) 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
\(895\) 29.0761 18.7156i 0.971906 0.625594i
\(896\) −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
\(900\) 4.67691 + 4.28005i 0.155897 + 0.142668i
\(901\) −8.39230 −0.279588
\(902\) 0 0
\(903\) 41.7057i 1.38788i
\(904\) 4.42055 3.21172i 0.147025 0.106820i
\(905\) 14.0837 36.2507i 0.468157 1.20501i
\(906\) −1.29668 + 3.99078i −0.0430794 + 0.132585i
\(907\) 17.7009 24.3632i 0.587749 0.808967i −0.406769 0.913531i \(-0.633345\pi\)
0.994518 + 0.104564i \(0.0333446\pi\)
\(908\) 20.4771 28.1843i 0.679556 0.935329i
\(909\) 4.38685 13.5013i 0.145503 0.447811i
\(910\) 15.3164 + 5.95053i 0.507733 + 0.197258i
\(911\) 24.4717 17.7797i 0.810784 0.589069i −0.103274 0.994653i \(-0.532932\pi\)
0.914058 + 0.405584i \(0.132932\pi\)
\(912\) 19.9749i 0.661434i
\(913\) 0 0
\(914\) 10.9808 0.363211
\(915\) −2.85685 + 50.5990i −0.0944444 + 1.67275i
\(916\) 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 0.811509 0.584339i \(-0.198646\pi\)
−0.304970 + 0.952362i \(0.598646\pi\)
\(920\) −12.6578 + 8.14755i −0.417315 + 0.268617i
\(921\) −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 −0.173792 0.984782i \(-0.555602\pi\)
−0.990288 + 0.139029i \(0.955602\pi\)
\(930\) 4.97731 + 18.8804i 0.163212 + 0.619113i
\(931\) 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 \(-0.0298608\pi\)
−0.396746 + 0.917928i \(0.629861\pi\)
\(938\) 3.63925 1.18247i 0.118826 0.0386089i
\(939\) −10.2360 + 31.5031i −0.334039 + 1.02807i
\(940\) −42.8897 + 11.3067i −1.39891 + 0.368784i
\(941\) −21.8435 15.8702i −0.712076 0.517354i 0.171766 0.985138i \(-0.445053\pi\)
−0.883843 + 0.467784i \(0.845053\pi\)
\(942\) 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
\(950\) 1.22248 10.7914i 0.0396624 0.350120i
\(951\) −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 \(-0.487147\pi\)
−0.554647 + 0.832086i \(0.687147\pi\)
\(954\) 0.254347 + 0.782801i 0.00823480 + 0.0253441i
\(955\) 16.2258 + 0.916117i 0.525054 + 0.0296448i
\(956\) 9.80385 0.317079
\(957\) 0 0
\(958\) 1.31268i 0.0424107i
\(959\) −23.9956 + 17.4339i −0.774860 + 0.562969i
\(960\) 9.13200 + 3.54785i 0.294734 + 0.114506i
\(961\) 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
\(965\) 31.6342 + 12.2901i 1.01834 + 0.395633i
\(966\) −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
\(970\) 10.5644 + 0.596470i 0.339201 + 0.0191515i
\(971\) −7.70324 23.7081i −0.247209 0.760830i −0.995265 0.0971952i \(-0.969013\pi\)
0.748057 0.663635i \(-0.230987\pi\)
\(972\) 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
\(975\) −40.7203 4.61289i −1.30409 0.147731i
\(976\) 8.93336 + 27.4941i 0.285950 + 0.880063i
\(977\) −17.1142 23.5557i −0.547533 0.753614i 0.442142 0.896945i \(-0.354219\pi\)
−0.989675 + 0.143331i \(0.954219\pi\)
\(978\) 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 \(-0.751715\pi\)
−0.988517 + 0.151112i \(0.951715\pi\)
\(984\) 5.22957 + 3.79950i 0.166713 + 0.121124i
\(985\) 37.2935 9.83142i 1.18827 0.313255i
\(986\) −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
\(995\) −1.14001 4.32439i −0.0361407 0.137092i
\(996\) −26.7982 19.4700i −0.849132 0.616931i
\(997\) −32.4472 10.5427i −1.02761 0.333892i −0.253767 0.967265i \(-0.581670\pi\)
−0.773846 + 0.633374i \(0.781670\pi\)
\(998\) 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.124.2 16
5.4 even 2 inner 605.2.j.e.124.3 16
11.2 odd 10 605.2.b.d.364.2 4
11.3 even 5 inner 605.2.j.e.269.2 16
11.4 even 5 inner 605.2.j.e.444.3 16
11.5 even 5 inner 605.2.j.e.9.3 16
11.6 odd 10 605.2.j.f.9.2 16
11.7 odd 10 605.2.j.f.444.2 16
11.8 odd 10 605.2.j.f.269.3 16
11.9 even 5 605.2.b.e.364.3 yes 4
11.10 odd 2 605.2.j.f.124.3 16
55.2 even 20 3025.2.a.y.1.3 4
55.4 even 10 inner 605.2.j.e.444.2 16
55.9 even 10 605.2.b.e.364.2 yes 4
55.13 even 20 3025.2.a.y.1.2 4
55.14 even 10 inner 605.2.j.e.269.3 16
55.19 odd 10 605.2.j.f.269.2 16
55.24 odd 10 605.2.b.d.364.3 yes 4
55.29 odd 10 605.2.j.f.444.3 16
55.39 odd 10 605.2.j.f.9.3 16
55.42 odd 20 3025.2.a.z.1.2 4
55.49 even 10 inner 605.2.j.e.9.2 16
55.53 odd 20 3025.2.a.z.1.3 4
55.54 odd 2 605.2.j.f.124.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.b.d.364.2 4 11.2 odd 10
605.2.b.d.364.3 yes 4 55.24 odd 10
605.2.b.e.364.2 yes 4 55.9 even 10
605.2.b.e.364.3 yes 4 11.9 even 5
605.2.j.e.9.2 16 55.49 even 10 inner
605.2.j.e.9.3 16 11.5 even 5 inner
605.2.j.e.124.2 16 1.1 even 1 trivial
605.2.j.e.124.3 16 5.4 even 2 inner
605.2.j.e.269.2 16 11.3 even 5 inner
605.2.j.e.269.3 16 55.14 even 10 inner
605.2.j.e.444.2 16 55.4 even 10 inner
605.2.j.e.444.3 16 11.4 even 5 inner
605.2.j.f.9.2 16 11.6 odd 10
605.2.j.f.9.3 16 55.39 odd 10
605.2.j.f.124.2 16 55.54 odd 2
605.2.j.f.124.3 16 11.10 odd 2
605.2.j.f.269.2 16 55.19 odd 10
605.2.j.f.269.3 16 11.8 odd 10
605.2.j.f.444.2 16 11.7 odd 10
605.2.j.f.444.3 16 55.29 odd 10
3025.2.a.y.1.2 4 55.13 even 20
3025.2.a.y.1.3 4 55.2 even 20
3025.2.a.z.1.2 4 55.42 odd 20
3025.2.a.z.1.3 4 55.53 odd 20