Properties

Label 930.2.bf.a.377.6
Level $930$
Weight $2$
Character 930.377
Analytic conductor $7.426$
Analytic rank $0$
Dimension $256$
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] = [930,2,Mod(377,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.377");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bf (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(64\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 377.6
Character \(\chi\) \(=\) 930.377
Dual form 930.2.bf.a.893.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.45410 - 0.941054i) q^{3} -1.00000i q^{4} +(-1.41418 - 1.73208i) q^{5} +(1.69363 - 0.362781i) q^{6} +(-1.47385 + 0.394917i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.22883 + 2.73678i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.45410 - 0.941054i) q^{3} -1.00000i q^{4} +(-1.41418 - 1.73208i) q^{5} +(1.69363 - 0.362781i) q^{6} +(-1.47385 + 0.394917i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.22883 + 2.73678i) q^{9} +(2.22474 + 0.224784i) q^{10} +(-4.08291 + 2.35727i) q^{11} +(-0.941054 + 1.45410i) q^{12} +(5.36364 + 1.43718i) q^{13} +(0.762922 - 1.32142i) q^{14} +(0.426391 + 3.84944i) q^{15} -1.00000 q^{16} +(0.632802 + 2.36165i) q^{17} +(-2.80411 - 1.06628i) q^{18} +(-4.53715 - 2.61953i) q^{19} +(-1.73208 + 1.41418i) q^{20} +(2.51477 + 0.812723i) q^{21} +(1.22021 - 4.55389i) q^{22} +(0.991741 + 0.991741i) q^{23} +(-0.362781 - 1.69363i) q^{24} +(-1.00017 + 4.89894i) q^{25} +(-4.80891 + 2.77643i) q^{26} +(0.788607 - 5.13596i) q^{27} +(0.394917 + 1.47385i) q^{28} -1.69082 q^{29} +(-3.02347 - 2.42046i) q^{30} +(5.23686 - 1.89086i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.15529 + 0.414526i) q^{33} +(-2.11740 - 1.22248i) q^{34} +(2.76832 + 1.99434i) q^{35} +(2.73678 - 1.22883i) q^{36} +(8.66376 - 2.32145i) q^{37} +(5.06053 - 1.35597i) q^{38} +(-6.44682 - 7.13729i) q^{39} +(0.224784 - 2.22474i) q^{40} +(0.798823 - 0.461201i) q^{41} +(-2.35289 + 1.20353i) q^{42} +(-2.62960 - 9.81381i) q^{43} +(2.35727 + 4.08291i) q^{44} +(3.00252 - 5.99874i) q^{45} -1.40253 q^{46} +(6.84752 - 6.84752i) q^{47} +(1.45410 + 0.941054i) q^{48} +(-4.04590 + 2.33590i) q^{49} +(-2.75685 - 4.17131i) q^{50} +(1.30228 - 4.02958i) q^{51} +(1.43718 - 5.36364i) q^{52} +(0.650026 - 2.42593i) q^{53} +(3.07404 + 4.18930i) q^{54} +(9.85695 + 3.73830i) q^{55} +(-1.32142 - 0.762922i) q^{56} +(4.13237 + 8.07877i) q^{57} +(1.19559 - 1.19559i) q^{58} +(1.38344 - 2.39619i) q^{59} +(3.84944 - 0.426391i) q^{60} -2.66083 q^{61} +(-2.36598 + 5.04006i) q^{62} +(-2.89192 - 3.54832i) q^{63} +1.00000i q^{64} +(-5.09586 - 11.3227i) q^{65} +(-6.05977 + 5.47354i) q^{66} +(-2.88137 + 10.7534i) q^{67} +(2.36165 - 0.632802i) q^{68} +(-0.508812 - 2.37537i) q^{69} +(-3.36771 + 0.547290i) q^{70} +(3.45550 - 1.99503i) q^{71} +(-1.06628 + 2.80411i) q^{72} +(14.9794 + 4.01373i) q^{73} +(-4.48469 + 7.76771i) q^{74} +(6.06453 - 6.18235i) q^{75} +(-2.61953 + 4.53715i) q^{76} +(5.08667 - 5.08667i) q^{77} +(9.60542 + 0.488235i) q^{78} +(2.39505 + 1.38278i) q^{79} +(1.41418 + 1.73208i) q^{80} +(-5.97993 + 6.72610i) q^{81} +(-0.238735 + 0.890972i) q^{82} +(2.50980 - 9.36670i) q^{83} +(0.812723 - 2.51477i) q^{84} +(3.19566 - 4.43586i) q^{85} +(8.79882 + 5.08000i) q^{86} +(2.45863 + 1.59115i) q^{87} +(-4.55389 - 1.22021i) q^{88} +9.06130 q^{89} +(2.11865 + 6.36485i) q^{90} -8.47278 q^{91} +(0.991741 - 0.991741i) q^{92} +(-9.39433 - 2.17866i) q^{93} +9.68386i q^{94} +(1.87914 + 11.5632i) q^{95} +(-1.69363 + 0.362781i) q^{96} +(1.79341 + 1.79341i) q^{97} +(1.20915 - 4.51261i) q^{98} +(-11.4685 - 8.27733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.45410 0.941054i −0.839527 0.543318i
\(4\) 1.00000i 0.500000i
\(5\) −1.41418 1.73208i −0.632442 0.774608i
\(6\) 1.69363 0.362781i 0.691422 0.148105i
\(7\) −1.47385 + 0.394917i −0.557063 + 0.149265i −0.526357 0.850264i \(-0.676442\pi\)
−0.0307066 + 0.999528i \(0.509776\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.22883 + 2.73678i 0.409611 + 0.912260i
\(10\) 2.22474 + 0.224784i 0.703525 + 0.0710831i
\(11\) −4.08291 + 2.35727i −1.23104 + 0.710743i −0.967247 0.253836i \(-0.918308\pi\)
−0.263796 + 0.964579i \(0.584974\pi\)
\(12\) −0.941054 + 1.45410i −0.271659 + 0.419764i
\(13\) 5.36364 + 1.43718i 1.48761 + 0.398603i 0.908928 0.416953i \(-0.136902\pi\)
0.578678 + 0.815556i \(0.303569\pi\)
\(14\) 0.762922 1.32142i 0.203899 0.353164i
\(15\) 0.426391 + 3.84944i 0.110094 + 0.993921i
\(16\) −1.00000 −0.250000
\(17\) 0.632802 + 2.36165i 0.153477 + 0.572784i 0.999231 + 0.0392107i \(0.0124844\pi\)
−0.845754 + 0.533573i \(0.820849\pi\)
\(18\) −2.80411 1.06628i −0.660936 0.251324i
\(19\) −4.53715 2.61953i −1.04089 0.600960i −0.120807 0.992676i \(-0.538548\pi\)
−0.920086 + 0.391716i \(0.871882\pi\)
\(20\) −1.73208 + 1.41418i −0.387304 + 0.316221i
\(21\) 2.51477 + 0.812723i 0.548768 + 0.177351i
\(22\) 1.22021 4.55389i 0.260150 0.970893i
\(23\) 0.991741 + 0.991741i 0.206792 + 0.206792i 0.802903 0.596110i \(-0.203288\pi\)
−0.596110 + 0.802903i \(0.703288\pi\)
\(24\) −0.362781 1.69363i −0.0740523 0.345711i
\(25\) −1.00017 + 4.89894i −0.200035 + 0.979789i
\(26\) −4.80891 + 2.77643i −0.943105 + 0.544502i
\(27\) 0.788607 5.13596i 0.151767 0.988416i
\(28\) 0.394917 + 1.47385i 0.0746323 + 0.278532i
\(29\) −1.69082 −0.313977 −0.156989 0.987600i \(-0.550179\pi\)
−0.156989 + 0.987600i \(0.550179\pi\)
\(30\) −3.02347 2.42046i −0.552007 0.441914i
\(31\) 5.23686 1.89086i 0.940567 0.339608i
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 8.15529 + 0.414526i 1.41965 + 0.0721597i
\(34\) −2.11740 1.22248i −0.363130 0.209653i
\(35\) 2.76832 + 1.99434i 0.467932 + 0.337105i
\(36\) 2.73678 1.22883i 0.456130 0.204806i
\(37\) 8.66376 2.32145i 1.42431 0.381644i 0.537301 0.843390i \(-0.319444\pi\)
0.887012 + 0.461747i \(0.152777\pi\)
\(38\) 5.06053 1.35597i 0.820927 0.219967i
\(39\) −6.44682 7.13729i −1.03232 1.14288i
\(40\) 0.224784 2.22474i 0.0355415 0.351762i
\(41\) 0.798823 0.461201i 0.124755 0.0720275i −0.436324 0.899790i \(-0.643720\pi\)
0.561079 + 0.827762i \(0.310386\pi\)
\(42\) −2.35289 + 1.20353i −0.363059 + 0.185709i
\(43\) −2.62960 9.81381i −0.401010 1.49659i −0.811297 0.584635i \(-0.801238\pi\)
0.410286 0.911957i \(-0.365429\pi\)
\(44\) 2.35727 + 4.08291i 0.355372 + 0.615522i
\(45\) 3.00252 5.99874i 0.447589 0.894240i
\(46\) −1.40253 −0.206792
\(47\) 6.84752 6.84752i 0.998814 0.998814i −0.00118523 0.999999i \(-0.500377\pi\)
0.999999 + 0.00118523i \(0.000377270\pi\)
\(48\) 1.45410 + 0.941054i 0.209882 + 0.135829i
\(49\) −4.04590 + 2.33590i −0.577986 + 0.333700i
\(50\) −2.75685 4.17131i −0.389877 0.589912i
\(51\) 1.30228 4.02958i 0.182356 0.564254i
\(52\) 1.43718 5.36364i 0.199301 0.743803i
\(53\) 0.650026 2.42593i 0.0892879 0.333227i −0.906804 0.421553i \(-0.861485\pi\)
0.996092 + 0.0883260i \(0.0281517\pi\)
\(54\) 3.07404 + 4.18930i 0.418324 + 0.570092i
\(55\) 9.85695 + 3.73830i 1.32911 + 0.504072i
\(56\) −1.32142 0.762922i −0.176582 0.101950i
\(57\) 4.13237 + 8.07877i 0.547346 + 1.07006i
\(58\) 1.19559 1.19559i 0.156989 0.156989i
\(59\) 1.38344 2.39619i 0.180108 0.311957i −0.761809 0.647802i \(-0.775689\pi\)
0.941917 + 0.335845i \(0.109022\pi\)
\(60\) 3.84944 0.426391i 0.496961 0.0550468i
\(61\) −2.66083 −0.340684 −0.170342 0.985385i \(-0.554487\pi\)
−0.170342 + 0.985385i \(0.554487\pi\)
\(62\) −2.36598 + 5.04006i −0.300479 + 0.640088i
\(63\) −2.89192 3.54832i −0.364348 0.447046i
\(64\) 1.00000i 0.125000i
\(65\) −5.09586 11.3227i −0.632064 1.40440i
\(66\) −6.05977 + 5.47354i −0.745907 + 0.673747i
\(67\) −2.88137 + 10.7534i −0.352016 + 1.31374i 0.532183 + 0.846629i \(0.321372\pi\)
−0.884199 + 0.467111i \(0.845295\pi\)
\(68\) 2.36165 0.632802i 0.286392 0.0767385i
\(69\) −0.508812 2.37537i −0.0612537 0.285962i
\(70\) −3.36771 + 0.547290i −0.402518 + 0.0654137i
\(71\) 3.45550 1.99503i 0.410092 0.236767i −0.280737 0.959785i \(-0.590579\pi\)
0.690829 + 0.723018i \(0.257246\pi\)
\(72\) −1.06628 + 2.80411i −0.125662 + 0.330468i
\(73\) 14.9794 + 4.01373i 1.75321 + 0.469771i 0.985307 0.170793i \(-0.0546330\pi\)
0.767904 + 0.640565i \(0.221300\pi\)
\(74\) −4.48469 + 7.76771i −0.521335 + 0.902978i
\(75\) 6.06453 6.18235i 0.700271 0.713877i
\(76\) −2.61953 + 4.53715i −0.300480 + 0.520447i
\(77\) 5.08667 5.08667i 0.579680 0.579680i
\(78\) 9.60542 + 0.488235i 1.08760 + 0.0552817i
\(79\) 2.39505 + 1.38278i 0.269464 + 0.155575i 0.628644 0.777693i \(-0.283610\pi\)
−0.359180 + 0.933268i \(0.616944\pi\)
\(80\) 1.41418 + 1.73208i 0.158110 + 0.193652i
\(81\) −5.97993 + 6.72610i −0.664437 + 0.747344i
\(82\) −0.238735 + 0.890972i −0.0263639 + 0.0983914i
\(83\) 2.50980 9.36670i 0.275486 1.02813i −0.680028 0.733186i \(-0.738033\pi\)
0.955515 0.294943i \(-0.0953008\pi\)
\(84\) 0.812723 2.51477i 0.0886754 0.274384i
\(85\) 3.19566 4.43586i 0.346618 0.481137i
\(86\) 8.79882 + 5.08000i 0.948801 + 0.547791i
\(87\) 2.45863 + 1.59115i 0.263592 + 0.170589i
\(88\) −4.55389 1.22021i −0.485447 0.130075i
\(89\) 9.06130 0.960495 0.480248 0.877133i \(-0.340547\pi\)
0.480248 + 0.877133i \(0.340547\pi\)
\(90\) 2.11865 + 6.36485i 0.223325 + 0.670914i
\(91\) −8.47278 −0.888189
\(92\) 0.991741 0.991741i 0.103396 0.103396i
\(93\) −9.39433 2.17866i −0.974147 0.225916i
\(94\) 9.68386i 0.998814i
\(95\) 1.87914 + 11.5632i 0.192796 + 1.18636i
\(96\) −1.69363 + 0.362781i −0.172856 + 0.0370261i
\(97\) 1.79341 + 1.79341i 0.182093 + 0.182093i 0.792267 0.610174i \(-0.208901\pi\)
−0.610174 + 0.792267i \(0.708901\pi\)
\(98\) 1.20915 4.51261i 0.122143 0.455843i
\(99\) −11.4685 8.27733i −1.15263 0.831903i
\(100\) 4.89894 + 1.00017i 0.489894 + 0.100017i
\(101\) 6.45022i 0.641821i −0.947110 0.320910i \(-0.896011\pi\)
0.947110 0.320910i \(-0.103989\pi\)
\(102\) 1.92849 + 3.77019i 0.190949 + 0.373305i
\(103\) 4.33904 + 1.16264i 0.427538 + 0.114559i 0.466170 0.884695i \(-0.345633\pi\)
−0.0386321 + 0.999254i \(0.512300\pi\)
\(104\) 2.77643 + 4.80891i 0.272251 + 0.471552i
\(105\) −2.14865 5.50511i −0.209686 0.537244i
\(106\) 1.25575 + 2.17503i 0.121970 + 0.211258i
\(107\) 4.39730 + 16.4109i 0.425103 + 1.58651i 0.763698 + 0.645574i \(0.223382\pi\)
−0.338595 + 0.940932i \(0.609952\pi\)
\(108\) −5.13596 0.788607i −0.494208 0.0758837i
\(109\) 7.44218i 0.712831i 0.934328 + 0.356416i \(0.116001\pi\)
−0.934328 + 0.356416i \(0.883999\pi\)
\(110\) −9.61329 + 4.32654i −0.916591 + 0.412519i
\(111\) −14.7826 4.77744i −1.40310 0.453455i
\(112\) 1.47385 0.394917i 0.139266 0.0373162i
\(113\) 0.769632 2.87231i 0.0724009 0.270204i −0.920230 0.391377i \(-0.871999\pi\)
0.992631 + 0.121173i \(0.0386656\pi\)
\(114\) −8.63458 2.79052i −0.808702 0.261356i
\(115\) 0.315267 3.12027i 0.0293988 0.290967i
\(116\) 1.69082i 0.156989i
\(117\) 2.65777 + 16.4452i 0.245711 + 1.52036i
\(118\) 0.716120 + 2.67260i 0.0659242 + 0.246033i
\(119\) −1.86531 3.23081i −0.170993 0.296168i
\(120\) −2.42046 + 3.02347i −0.220957 + 0.276004i
\(121\) 5.61342 9.72274i 0.510311 0.883885i
\(122\) 1.88149 1.88149i 0.170342 0.170342i
\(123\) −1.59559 0.0811023i −0.143869 0.00731275i
\(124\) −1.89086 5.23686i −0.169804 0.470283i
\(125\) 9.89977 5.19563i 0.885462 0.464711i
\(126\) 4.55394 + 0.464144i 0.405697 + 0.0413493i
\(127\) 19.6144 5.25568i 1.74050 0.466366i 0.757943 0.652321i \(-0.226205\pi\)
0.982558 + 0.185955i \(0.0595379\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −5.41161 + 16.7449i −0.476466 + 1.47431i
\(130\) 11.6097 + 4.40302i 1.01823 + 0.386171i
\(131\) 6.66669 + 3.84901i 0.582471 + 0.336290i 0.762115 0.647442i \(-0.224161\pi\)
−0.179644 + 0.983732i \(0.557494\pi\)
\(132\) 0.414526 8.15529i 0.0360799 0.709827i
\(133\) 7.72158 + 2.06899i 0.669546 + 0.179404i
\(134\) −5.56639 9.64126i −0.480862 0.832878i
\(135\) −10.0111 + 5.89726i −0.861619 + 0.507555i
\(136\) −1.22248 + 2.11740i −0.104827 + 0.181565i
\(137\) −18.2982 4.90300i −1.56332 0.418892i −0.629611 0.776911i \(-0.716786\pi\)
−0.933714 + 0.358019i \(0.883452\pi\)
\(138\) 2.03943 + 1.31986i 0.173608 + 0.112354i
\(139\) 7.88991i 0.669213i 0.942358 + 0.334607i \(0.108603\pi\)
−0.942358 + 0.334607i \(0.891397\pi\)
\(140\) 1.99434 2.76832i 0.168552 0.233966i
\(141\) −16.4009 + 3.51312i −1.38120 + 0.295858i
\(142\) −1.03271 + 3.85411i −0.0866627 + 0.323430i
\(143\) −25.2871 + 6.77565i −2.11461 + 0.566609i
\(144\) −1.22883 2.73678i −0.102403 0.228065i
\(145\) 2.39113 + 2.92863i 0.198572 + 0.243209i
\(146\) −13.4302 + 7.75393i −1.11149 + 0.641720i
\(147\) 8.08137 + 0.410769i 0.666540 + 0.0338796i
\(148\) −2.32145 8.66376i −0.190822 0.712157i
\(149\) 6.89382 11.9404i 0.564764 0.978200i −0.432308 0.901726i \(-0.642301\pi\)
0.997072 0.0764736i \(-0.0243661\pi\)
\(150\) 0.0833152 + 8.65985i 0.00680266 + 0.707074i
\(151\) −4.62045 −0.376007 −0.188003 0.982168i \(-0.560202\pi\)
−0.188003 + 0.982168i \(0.560202\pi\)
\(152\) −1.35597 5.06053i −0.109983 0.410463i
\(153\) −5.68570 + 4.63391i −0.459662 + 0.374630i
\(154\) 7.19364i 0.579680i
\(155\) −10.6810 6.39661i −0.857917 0.513788i
\(156\) −7.13729 + 6.44682i −0.571441 + 0.516159i
\(157\) −1.64688 1.64688i −0.131435 0.131435i 0.638329 0.769764i \(-0.279626\pi\)
−0.769764 + 0.638329i \(0.779626\pi\)
\(158\) −2.67133 + 0.715780i −0.212519 + 0.0569444i
\(159\) −3.22814 + 2.91584i −0.256008 + 0.231241i
\(160\) −2.22474 0.224784i −0.175881 0.0177708i
\(161\) −1.85333 1.07002i −0.146063 0.0843296i
\(162\) −0.527617 8.98452i −0.0414535 0.705891i
\(163\) −0.148291 + 0.148291i −0.0116151 + 0.0116151i −0.712890 0.701275i \(-0.752614\pi\)
0.701275 + 0.712890i \(0.252614\pi\)
\(164\) −0.461201 0.798823i −0.0360137 0.0623776i
\(165\) −10.8151 14.7118i −0.841953 1.14531i
\(166\) 4.84856 + 8.39796i 0.376321 + 0.651808i
\(167\) 1.49475 + 5.57847i 0.115667 + 0.431675i 0.999336 0.0364372i \(-0.0116009\pi\)
−0.883669 + 0.468112i \(0.844934\pi\)
\(168\) 1.20353 + 2.35289i 0.0928543 + 0.181530i
\(169\) 15.4448 + 8.91707i 1.18806 + 0.685929i
\(170\) 0.876958 + 5.39630i 0.0672596 + 0.413877i
\(171\) 1.59366 15.6361i 0.121870 1.19573i
\(172\) −9.81381 + 2.62960i −0.748296 + 0.200505i
\(173\) 0.858610 3.20438i 0.0652789 0.243624i −0.925575 0.378565i \(-0.876418\pi\)
0.990854 + 0.134941i \(0.0430844\pi\)
\(174\) −2.86363 + 0.613396i −0.217091 + 0.0465015i
\(175\) −0.460570 7.61530i −0.0348158 0.575663i
\(176\) 4.08291 2.35727i 0.307761 0.177686i
\(177\) −4.26660 + 2.18241i −0.320697 + 0.164040i
\(178\) −6.40730 + 6.40730i −0.480248 + 0.480248i
\(179\) −0.0122486 + 0.0212151i −0.000915500 + 0.00158569i −0.866483 0.499207i \(-0.833625\pi\)
0.865567 + 0.500793i \(0.166958\pi\)
\(180\) −5.99874 3.00252i −0.447120 0.223794i
\(181\) −11.0195 19.0863i −0.819072 1.41867i −0.906367 0.422492i \(-0.861155\pi\)
0.0872946 0.996183i \(-0.472178\pi\)
\(182\) 5.99116 5.99116i 0.444094 0.444094i
\(183\) 3.86912 + 2.50398i 0.286014 + 0.185100i
\(184\) 1.40253i 0.103396i
\(185\) −16.2731 11.7233i −1.19642 0.861917i
\(186\) 8.18334 5.10225i 0.600032 0.374115i
\(187\) −8.15071 8.15071i −0.596039 0.596039i
\(188\) −6.84752 6.84752i −0.499407 0.499407i
\(189\) 0.865990 + 7.88108i 0.0629915 + 0.573264i
\(190\) −9.50516 6.84765i −0.689576 0.496780i
\(191\) 16.8423 9.72389i 1.21866 0.703596i 0.254032 0.967196i \(-0.418243\pi\)
0.964632 + 0.263600i \(0.0849100\pi\)
\(192\) 0.941054 1.45410i 0.0679147 0.104941i
\(193\) 5.52275 + 20.6112i 0.397536 + 1.48362i 0.817417 + 0.576046i \(0.195405\pi\)
−0.419881 + 0.907579i \(0.637928\pi\)
\(194\) −2.53627 −0.182093
\(195\) −3.24534 + 21.2598i −0.232404 + 1.52245i
\(196\) 2.33590 + 4.04590i 0.166850 + 0.288993i
\(197\) 8.00288 + 2.14437i 0.570182 + 0.152780i 0.532380 0.846506i \(-0.321298\pi\)
0.0378018 + 0.999285i \(0.487964\pi\)
\(198\) 13.9624 2.25653i 0.992267 0.160364i
\(199\) −8.04935 + 4.64729i −0.570603 + 0.329438i −0.757390 0.652962i \(-0.773526\pi\)
0.186787 + 0.982400i \(0.440193\pi\)
\(200\) −4.17131 + 2.75685i −0.294956 + 0.194939i
\(201\) 14.3094 12.9251i 1.00931 0.911664i
\(202\) 4.56099 + 4.56099i 0.320910 + 0.320910i
\(203\) 2.49202 0.667734i 0.174905 0.0468657i
\(204\) −4.02958 1.30228i −0.282127 0.0911778i
\(205\) −1.92852 0.731400i −0.134693 0.0510832i
\(206\) −3.89028 + 2.24605i −0.271048 + 0.156490i
\(207\) −1.49549 + 3.93286i −0.103944 + 0.273353i
\(208\) −5.36364 1.43718i −0.371902 0.0996507i
\(209\) 24.6997 1.70851
\(210\) 5.41203 + 2.37338i 0.373465 + 0.163779i
\(211\) 10.0700 17.4418i 0.693248 1.20074i −0.277519 0.960720i \(-0.589512\pi\)
0.970768 0.240021i \(-0.0771544\pi\)
\(212\) −2.42593 0.650026i −0.166614 0.0446440i
\(213\) −6.90209 0.350827i −0.472923 0.0240383i
\(214\) −14.7137 8.49493i −1.00580 0.580702i
\(215\) −13.2795 + 18.4332i −0.905656 + 1.25713i
\(216\) 4.18930 3.07404i 0.285046 0.209162i
\(217\) −6.97161 + 4.85497i −0.473264 + 0.329577i
\(218\) −5.26241 5.26241i −0.356416 0.356416i
\(219\) −18.0045 19.9328i −1.21663 1.34694i
\(220\) 3.73830 9.85695i 0.252036 0.664555i
\(221\) 13.5765i 0.913253i
\(222\) 13.8310 7.07472i 0.928279 0.474824i
\(223\) 6.54747 + 24.4355i 0.438451 + 1.63632i 0.732671 + 0.680583i \(0.238274\pi\)
−0.294220 + 0.955738i \(0.595060\pi\)
\(224\) −0.762922 + 1.32142i −0.0509748 + 0.0882910i
\(225\) −14.6364 + 3.28273i −0.975759 + 0.218849i
\(226\) 1.48682 + 2.57524i 0.0989015 + 0.171302i
\(227\) −7.32934 1.96389i −0.486465 0.130348i 0.00724610 0.999974i \(-0.497693\pi\)
−0.493712 + 0.869626i \(0.664360\pi\)
\(228\) 8.07877 4.13237i 0.535029 0.273673i
\(229\) 9.81089 + 5.66432i 0.648322 + 0.374309i 0.787813 0.615914i \(-0.211213\pi\)
−0.139491 + 0.990223i \(0.544547\pi\)
\(230\) 1.98344 + 2.42929i 0.130784 + 0.160183i
\(231\) −12.1834 + 2.60971i −0.801608 + 0.171707i
\(232\) −1.19559 1.19559i −0.0784943 0.0784943i
\(233\) −7.65930 7.65930i −0.501777 0.501777i 0.410213 0.911990i \(-0.365454\pi\)
−0.911990 + 0.410213i \(0.865454\pi\)
\(234\) −13.5078 9.74916i −0.883034 0.637323i
\(235\) −21.5441 2.17678i −1.40538 0.141998i
\(236\) −2.39619 1.38344i −0.155978 0.0900541i
\(237\) −2.18137 4.26457i −0.141695 0.277014i
\(238\) 3.60350 + 0.965556i 0.233580 + 0.0625877i
\(239\) 5.15341 + 8.92596i 0.333346 + 0.577373i 0.983166 0.182716i \(-0.0584889\pi\)
−0.649820 + 0.760089i \(0.725156\pi\)
\(240\) −0.426391 3.84944i −0.0275234 0.248480i
\(241\) −5.06086 + 8.76567i −0.325999 + 0.564646i −0.981714 0.190362i \(-0.939034\pi\)
0.655715 + 0.755008i \(0.272367\pi\)
\(242\) 2.90572 + 10.8443i 0.186787 + 0.697098i
\(243\) 15.0251 4.15300i 0.963858 0.266415i
\(244\) 2.66083i 0.170342i
\(245\) 9.76760 + 3.70441i 0.624029 + 0.236666i
\(246\) 1.18560 1.07090i 0.0755910 0.0682782i
\(247\) −20.5709 20.5709i −1.30890 1.30890i
\(248\) 5.04006 + 2.36598i 0.320044 + 0.150240i
\(249\) −12.4641 + 11.2583i −0.789879 + 0.713466i
\(250\) −3.32633 + 10.6741i −0.210376 + 0.675087i
\(251\) 1.52211 + 0.878790i 0.0960747 + 0.0554687i 0.547268 0.836958i \(-0.315668\pi\)
−0.451193 + 0.892426i \(0.649001\pi\)
\(252\) −3.54832 + 2.89192i −0.223523 + 0.182174i
\(253\) −6.38698 1.71139i −0.401546 0.107594i
\(254\) −10.1532 + 17.5858i −0.637068 + 1.10343i
\(255\) −8.82120 + 3.44292i −0.552405 + 0.215604i
\(256\) 1.00000 0.0625000
\(257\) 2.67919 + 0.717886i 0.167123 + 0.0447805i 0.341410 0.939914i \(-0.389095\pi\)
−0.174287 + 0.984695i \(0.555762\pi\)
\(258\) −8.01384 15.6670i −0.498920 0.975386i
\(259\) −11.8523 + 6.84294i −0.736467 + 0.425199i
\(260\) −11.3227 + 5.09586i −0.702202 + 0.316032i
\(261\) −2.07774 4.62740i −0.128609 0.286429i
\(262\) −7.43572 + 1.99240i −0.459381 + 0.123091i
\(263\) −20.6656 20.6656i −1.27429 1.27429i −0.943812 0.330482i \(-0.892789\pi\)
−0.330482 0.943812i \(-0.607211\pi\)
\(264\) 5.47354 + 6.05977i 0.336873 + 0.372953i
\(265\) −5.12115 + 2.30481i −0.314590 + 0.141584i
\(266\) −6.92298 + 3.99698i −0.424475 + 0.245071i
\(267\) −13.1761 8.52717i −0.806362 0.521854i
\(268\) 10.7534 + 2.88137i 0.656870 + 0.176008i
\(269\) 11.6913 + 20.2500i 0.712832 + 1.23466i 0.963790 + 0.266663i \(0.0859212\pi\)
−0.250958 + 0.967998i \(0.580745\pi\)
\(270\) 2.90893 11.2489i 0.177032 0.684587i
\(271\) −10.8222 −0.657403 −0.328702 0.944434i \(-0.606611\pi\)
−0.328702 + 0.944434i \(0.606611\pi\)
\(272\) −0.632802 2.36165i −0.0383692 0.143196i
\(273\) 12.3203 + 7.97334i 0.745658 + 0.482569i
\(274\) 16.4058 9.47187i 0.991108 0.572217i
\(275\) −7.46451 22.3596i −0.450127 1.34834i
\(276\) −2.37537 + 0.508812i −0.142981 + 0.0306269i
\(277\) 3.15607 + 3.15607i 0.189630 + 0.189630i 0.795536 0.605906i \(-0.207189\pi\)
−0.605906 + 0.795536i \(0.707189\pi\)
\(278\) −5.57901 5.57901i −0.334607 0.334607i
\(279\) 11.6101 + 12.0086i 0.695078 + 0.718934i
\(280\) 0.547290 + 3.36771i 0.0327068 + 0.201259i
\(281\) 0.479228i 0.0285883i 0.999898 + 0.0142942i \(0.00455013\pi\)
−0.999898 + 0.0142942i \(0.995450\pi\)
\(282\) 9.11304 14.0813i 0.542674 0.838531i
\(283\) 17.8720 17.8720i 1.06238 1.06238i 0.0644616 0.997920i \(-0.479467\pi\)
0.997920 0.0644616i \(-0.0205330\pi\)
\(284\) −1.99503 3.45550i −0.118383 0.205046i
\(285\) 8.14911 18.5824i 0.482711 1.10073i
\(286\) 13.0896 22.6718i 0.774002 1.34061i
\(287\) −0.995211 + 0.995211i −0.0587454 + 0.0587454i
\(288\) 2.80411 + 1.06628i 0.165234 + 0.0628311i
\(289\) 9.54549 5.51109i 0.561499 0.324182i
\(290\) −3.76163 0.380070i −0.220891 0.0223185i
\(291\) −0.920108 4.29550i −0.0539377 0.251807i
\(292\) 4.01373 14.9794i 0.234886 0.876605i
\(293\) 24.4856 6.56090i 1.43047 0.383292i 0.541281 0.840842i \(-0.317939\pi\)
0.889184 + 0.457550i \(0.151273\pi\)
\(294\) −6.00485 + 5.42393i −0.350210 + 0.316330i
\(295\) −6.10681 + 0.992424i −0.355552 + 0.0577812i
\(296\) 7.76771 + 4.48469i 0.451489 + 0.260667i
\(297\) 8.88703 + 22.8286i 0.515678 + 1.32465i
\(298\) 3.56850 + 13.3178i 0.206718 + 0.771482i
\(299\) 3.89403 + 6.74465i 0.225197 + 0.390053i
\(300\) −6.18235 6.06453i −0.356938 0.350136i
\(301\) 7.75128 + 13.4256i 0.446777 + 0.773840i
\(302\) 3.26715 3.26715i 0.188003 0.188003i
\(303\) −6.07000 + 9.37928i −0.348713 + 0.538826i
\(304\) 4.53715 + 2.61953i 0.260223 + 0.150240i
\(305\) 3.76290 + 4.60876i 0.215463 + 0.263897i
\(306\) 0.743729 7.29707i 0.0425161 0.417146i
\(307\) −26.0724 + 6.98609i −1.48803 + 0.398717i −0.909072 0.416638i \(-0.863208\pi\)
−0.578961 + 0.815355i \(0.696542\pi\)
\(308\) −5.08667 5.08667i −0.289840 0.289840i
\(309\) −5.21530 5.77387i −0.296688 0.328464i
\(310\) 12.0757 3.02951i 0.685853 0.172065i
\(311\) 29.3343i 1.66339i 0.555230 + 0.831697i \(0.312630\pi\)
−0.555230 + 0.831697i \(0.687370\pi\)
\(312\) 0.488235 9.60542i 0.0276409 0.543800i
\(313\) −6.62114 24.7104i −0.374249 1.39672i −0.854439 0.519552i \(-0.826099\pi\)
0.480190 0.877165i \(-0.340568\pi\)
\(314\) 2.32904 0.131435
\(315\) −2.05625 + 10.0270i −0.115857 + 0.564957i
\(316\) 1.38278 2.39505i 0.0777875 0.134732i
\(317\) 6.17376 + 23.0408i 0.346753 + 1.29410i 0.890551 + 0.454883i \(0.150319\pi\)
−0.543798 + 0.839216i \(0.683014\pi\)
\(318\) 0.220825 4.34445i 0.0123832 0.243625i
\(319\) 6.90346 3.98571i 0.386520 0.223157i
\(320\) 1.73208 1.41418i 0.0968260 0.0790552i
\(321\) 9.04946 28.0013i 0.505092 1.56288i
\(322\) 2.06712 0.553884i 0.115196 0.0308668i
\(323\) 3.31528 12.3728i 0.184467 0.688440i
\(324\) 6.72610 + 5.97993i 0.373672 + 0.332219i
\(325\) −12.4053 + 24.8387i −0.688120 + 1.37781i
\(326\) 0.209715i 0.0116151i
\(327\) 7.00349 10.8217i 0.387294 0.598441i
\(328\) 0.890972 + 0.238735i 0.0491957 + 0.0131819i
\(329\) −7.38803 + 12.7964i −0.407315 + 0.705490i
\(330\) 18.0502 + 2.75539i 0.993632 + 0.151679i
\(331\) −3.17129 5.49283i −0.174310 0.301913i 0.765612 0.643302i \(-0.222436\pi\)
−0.939922 + 0.341389i \(0.889103\pi\)
\(332\) −9.36670 2.50980i −0.514065 0.137743i
\(333\) 16.9996 + 20.8581i 0.931573 + 1.14302i
\(334\) −5.00152 2.88763i −0.273671 0.158004i
\(335\) 22.7005 10.2166i 1.24026 0.558190i
\(336\) −2.51477 0.812723i −0.137192 0.0443377i
\(337\) 9.67430 + 9.67430i 0.526993 + 0.526993i 0.919674 0.392682i \(-0.128453\pi\)
−0.392682 + 0.919674i \(0.628453\pi\)
\(338\) −17.2265 + 4.61582i −0.936996 + 0.251067i
\(339\) −3.82212 + 3.45237i −0.207589 + 0.187507i
\(340\) −4.43586 3.19566i −0.240568 0.173309i
\(341\) −16.9243 + 20.0649i −0.916504 + 1.08657i
\(342\) 9.92954 + 12.1833i 0.536928 + 0.658798i
\(343\) 12.5931 12.5931i 0.679964 0.679964i
\(344\) 5.08000 8.79882i 0.273895 0.474401i
\(345\) −3.39478 + 4.24051i −0.182769 + 0.228302i
\(346\) 1.65871 + 2.87297i 0.0891727 + 0.154452i
\(347\) −0.253542 0.946230i −0.0136108 0.0507963i 0.958786 0.284128i \(-0.0917040\pi\)
−0.972397 + 0.233331i \(0.925037\pi\)
\(348\) 1.59115 2.45863i 0.0852947 0.131796i
\(349\) 26.4304i 1.41479i 0.706819 + 0.707394i \(0.250129\pi\)
−0.706819 + 0.707394i \(0.749871\pi\)
\(350\) 5.71050 + 5.05916i 0.305239 + 0.270423i
\(351\) 11.6111 26.4141i 0.619756 1.40988i
\(352\) −1.22021 + 4.55389i −0.0650375 + 0.242723i
\(353\) 33.3768 8.94329i 1.77647 0.476003i 0.786536 0.617544i \(-0.211872\pi\)
0.989932 + 0.141540i \(0.0452055\pi\)
\(354\) 1.47375 4.56014i 0.0783287 0.242369i
\(355\) −8.34226 3.16384i −0.442761 0.167919i
\(356\) 9.06130i 0.480248i
\(357\) −0.328015 + 6.45329i −0.0173604 + 0.341545i
\(358\) −0.00634032 0.0236624i −0.000335096 0.00125060i
\(359\) −16.8947 29.2625i −0.891669 1.54442i −0.837874 0.545864i \(-0.816201\pi\)
−0.0537955 0.998552i \(-0.517132\pi\)
\(360\) 6.36485 2.11865i 0.335457 0.111663i
\(361\) 4.22382 + 7.31588i 0.222306 + 0.385046i
\(362\) 21.2880 + 5.70411i 1.11887 + 0.299801i
\(363\) −17.3121 + 8.85533i −0.908651 + 0.464784i
\(364\) 8.47278i 0.444094i
\(365\) −14.2316 31.6217i −0.744915 1.65515i
\(366\) −4.50647 + 0.965297i −0.235557 + 0.0504569i
\(367\) −5.01545 + 18.7179i −0.261804 + 0.977067i 0.702373 + 0.711809i \(0.252124\pi\)
−0.964177 + 0.265258i \(0.914543\pi\)
\(368\) −0.991741 0.991741i −0.0516980 0.0516980i
\(369\) 2.24383 + 1.61947i 0.116809 + 0.0843060i
\(370\) 19.7964 3.21714i 1.02917 0.167251i
\(371\) 3.83217i 0.198956i
\(372\) −2.17866 + 9.39433i −0.112958 + 0.487073i
\(373\) 15.9358 15.9358i 0.825123 0.825123i −0.161714 0.986838i \(-0.551702\pi\)
0.986838 + 0.161714i \(0.0517023\pi\)
\(374\) 11.5268 0.596039
\(375\) −19.2847 1.76124i −0.995855 0.0909503i
\(376\) 9.68386 0.499407
\(377\) −9.06895 2.43002i −0.467075 0.125152i
\(378\) −6.18511 4.96042i −0.318128 0.255136i
\(379\) 7.59600 + 4.38555i 0.390180 + 0.225271i 0.682238 0.731130i \(-0.261007\pi\)
−0.292058 + 0.956401i \(0.594340\pi\)
\(380\) 11.5632 1.87914i 0.593178 0.0963981i
\(381\) −33.4673 10.8160i −1.71458 0.554119i
\(382\) −5.03345 + 18.7851i −0.257534 + 0.961130i
\(383\) −7.11395 + 26.5496i −0.363506 + 1.35662i 0.505930 + 0.862575i \(0.331150\pi\)
−0.869435 + 0.494047i \(0.835517\pi\)
\(384\) 0.362781 + 1.69363i 0.0185131 + 0.0864278i
\(385\) −16.0040 1.61702i −0.815639 0.0824109i
\(386\) −18.4795 10.6691i −0.940581 0.543044i
\(387\) 23.6269 19.2562i 1.20102 0.978847i
\(388\) 1.79341 1.79341i 0.0910466 0.0910466i
\(389\) −5.17308 + 8.96005i −0.262286 + 0.454292i −0.966849 0.255349i \(-0.917810\pi\)
0.704563 + 0.709641i \(0.251143\pi\)
\(390\) −12.7382 17.3278i −0.645022 0.877426i
\(391\) −1.71457 + 2.96972i −0.0867094 + 0.150185i
\(392\) −4.51261 1.20915i −0.227921 0.0610714i
\(393\) −6.07192 11.8706i −0.306288 0.598792i
\(394\) −7.17519 + 4.14260i −0.361481 + 0.208701i
\(395\) −0.991952 6.10391i −0.0499105 0.307121i
\(396\) −8.27733 + 11.4685i −0.415952 + 0.576316i
\(397\) 15.0946 4.04459i 0.757577 0.202992i 0.140701 0.990052i \(-0.455065\pi\)
0.616876 + 0.787060i \(0.288398\pi\)
\(398\) 2.40562 8.97788i 0.120583 0.450021i
\(399\) −9.28094 10.2750i −0.464628 0.514391i
\(400\) 1.00017 4.89894i 0.0500087 0.244947i
\(401\) 8.61518i 0.430221i 0.976590 + 0.215111i \(0.0690112\pi\)
−0.976590 + 0.215111i \(0.930989\pi\)
\(402\) −0.978850 + 19.2577i −0.0488206 + 0.960485i
\(403\) 30.8061 2.61557i 1.53456 0.130291i
\(404\) −6.45022 −0.320910
\(405\) 20.1068 + 0.845769i 0.999116 + 0.0420266i
\(406\) −1.28996 + 2.23428i −0.0640198 + 0.110885i
\(407\) −29.9011 + 29.9011i −1.48214 + 1.48214i
\(408\) 3.77019 1.92849i 0.186652 0.0954746i
\(409\) −15.2529 8.80629i −0.754209 0.435443i 0.0730037 0.997332i \(-0.476742\pi\)
−0.827213 + 0.561889i \(0.810075\pi\)
\(410\) 1.88085 0.846490i 0.0928884 0.0418051i
\(411\) 21.9936 + 24.3491i 1.08486 + 1.20105i
\(412\) 1.16264 4.33904i 0.0572793 0.213769i
\(413\) −1.09269 + 4.07796i −0.0537676 + 0.200663i
\(414\) −1.72348 3.83842i −0.0847044 0.188648i
\(415\) −19.7732 + 8.89906i −0.970626 + 0.436838i
\(416\) 4.80891 2.77643i 0.235776 0.136125i
\(417\) 7.42483 11.4727i 0.363596 0.561823i
\(418\) −17.4653 + 17.4653i −0.854257 + 0.854257i
\(419\) 17.6769 0.863575 0.431787 0.901975i \(-0.357883\pi\)
0.431787 + 0.901975i \(0.357883\pi\)
\(420\) −5.50511 + 2.14865i −0.268622 + 0.104843i
\(421\) −7.58718 13.1414i −0.369777 0.640472i 0.619754 0.784796i \(-0.287232\pi\)
−0.989530 + 0.144325i \(0.953899\pi\)
\(422\) 5.21262 + 19.4538i 0.253746 + 0.946995i
\(423\) 27.1546 + 10.3257i 1.32030 + 0.502053i
\(424\) 2.17503 1.25575i 0.105629 0.0609848i
\(425\) −12.2025 + 0.738001i −0.591908 + 0.0357983i
\(426\) 5.12859 4.63244i 0.248481 0.224442i
\(427\) 3.92167 1.05081i 0.189783 0.0508521i
\(428\) 16.4109 4.39730i 0.793253 0.212552i
\(429\) 43.1463 + 13.9440i 2.08312 + 0.673223i
\(430\) −3.64419 22.4243i −0.175739 1.08139i
\(431\) 13.8277 + 7.98344i 0.666058 + 0.384549i 0.794581 0.607158i \(-0.207690\pi\)
−0.128523 + 0.991706i \(0.541024\pi\)
\(432\) −0.788607 + 5.13596i −0.0379419 + 0.247104i
\(433\) −18.1223 + 18.1223i −0.870904 + 0.870904i −0.992571 0.121667i \(-0.961176\pi\)
0.121667 + 0.992571i \(0.461176\pi\)
\(434\) 1.49669 8.36266i 0.0718436 0.401420i
\(435\) −0.720950 6.50871i −0.0345669 0.312069i
\(436\) 7.44218 0.356416
\(437\) −1.90179 7.09757i −0.0909748 0.339523i
\(438\) 26.8258 + 1.36353i 1.28178 + 0.0651520i
\(439\) 10.5174 6.07222i 0.501967 0.289811i −0.227558 0.973764i \(-0.573074\pi\)
0.729526 + 0.683953i \(0.239741\pi\)
\(440\) 4.32654 + 9.61329i 0.206260 + 0.458296i
\(441\) −11.3646 8.20230i −0.541171 0.390586i
\(442\) −9.60002 9.60002i −0.456627 0.456627i
\(443\) −2.98723 + 11.1485i −0.141927 + 0.529681i 0.857945 + 0.513741i \(0.171741\pi\)
−0.999873 + 0.0159398i \(0.994926\pi\)
\(444\) −4.77744 + 14.7826i −0.226727 + 0.701552i
\(445\) −12.8143 15.6949i −0.607457 0.744007i
\(446\) −21.9083 12.6487i −1.03739 0.598935i
\(447\) −21.2609 + 10.8752i −1.00561 + 0.514379i
\(448\) −0.394917 1.47385i −0.0186581 0.0696329i
\(449\) 38.5895 1.82115 0.910576 0.413343i \(-0.135639\pi\)
0.910576 + 0.413343i \(0.135639\pi\)
\(450\) 8.02824 12.6707i 0.378455 0.597304i
\(451\) −2.17435 + 3.76608i −0.102386 + 0.177338i
\(452\) −2.87231 0.769632i −0.135102 0.0362005i
\(453\) 6.71861 + 4.34809i 0.315668 + 0.204291i
\(454\) 6.57131 3.79395i 0.308407 0.178059i
\(455\) 11.9821 + 14.6755i 0.561728 + 0.687998i
\(456\) −2.79052 + 8.63458i −0.130678 + 0.404351i
\(457\) −13.5998 13.5998i −0.636173 0.636173i 0.313436 0.949609i \(-0.398520\pi\)
−0.949609 + 0.313436i \(0.898520\pi\)
\(458\) −10.9426 + 2.93207i −0.511316 + 0.137007i
\(459\) 12.6284 1.38763i 0.589441 0.0647691i
\(460\) −3.12027 0.315267i −0.145483 0.0146994i
\(461\) 30.7101i 1.43031i −0.698965 0.715156i \(-0.746356\pi\)
0.698965 0.715156i \(-0.253644\pi\)
\(462\) 6.76961 10.4603i 0.314951 0.486657i
\(463\) −9.09465 + 9.09465i −0.422664 + 0.422664i −0.886120 0.463456i \(-0.846609\pi\)
0.463456 + 0.886120i \(0.346609\pi\)
\(464\) 1.69082 0.0784943
\(465\) 9.51170 + 19.3527i 0.441094 + 0.897461i
\(466\) 10.8319 0.501777
\(467\) 14.0216 14.0216i 0.648843 0.648843i −0.303870 0.952713i \(-0.598279\pi\)
0.952713 + 0.303870i \(0.0982789\pi\)
\(468\) 16.4452 2.65777i 0.760178 0.122855i
\(469\) 16.9869i 0.784380i
\(470\) 16.7732 13.6948i 0.773689 0.631692i
\(471\) 0.844930 + 3.94453i 0.0389323 + 0.181754i
\(472\) 2.67260 0.716120i 0.123016 0.0329621i
\(473\) 33.8702 + 33.8702i 1.55735 + 1.55735i
\(474\) 4.55797 + 1.47305i 0.209355 + 0.0676592i
\(475\) 17.3708 19.6073i 0.797029 0.899643i
\(476\) −3.23081 + 1.86531i −0.148084 + 0.0854964i
\(477\) 7.43801 1.20209i 0.340563 0.0550398i
\(478\) −9.95562 2.66760i −0.455359 0.122013i
\(479\) −16.7906 + 29.0822i −0.767184 + 1.32880i 0.171901 + 0.985114i \(0.445009\pi\)
−0.939084 + 0.343687i \(0.888324\pi\)
\(480\) 3.02347 + 2.42046i 0.138002 + 0.110478i
\(481\) 49.8056 2.27094
\(482\) −2.61969 9.77683i −0.119324 0.445323i
\(483\) 1.68799 + 3.30001i 0.0768062 + 0.150156i
\(484\) −9.72274 5.61342i −0.441943 0.255156i
\(485\) 0.570113 5.64253i 0.0258875 0.256214i
\(486\) −7.68771 + 13.5609i −0.348722 + 0.615137i
\(487\) −4.74717 + 17.7167i −0.215115 + 0.802819i 0.771011 + 0.636821i \(0.219751\pi\)
−0.986126 + 0.165998i \(0.946916\pi\)
\(488\) −1.88149 1.88149i −0.0851711 0.0851711i
\(489\) 0.355181 0.0760807i 0.0160618 0.00344049i
\(490\) −9.52615 + 4.28732i −0.430348 + 0.193681i
\(491\) −35.2739 + 20.3654i −1.59189 + 0.919077i −0.598905 + 0.800820i \(0.704397\pi\)
−0.992983 + 0.118256i \(0.962270\pi\)
\(492\) −0.0811023 + 1.59559i −0.00365637 + 0.0719346i
\(493\) −1.06995 3.99312i −0.0481883 0.179841i
\(494\) 29.0917 1.30890
\(495\) 1.88165 + 31.5700i 0.0845737 + 1.41897i
\(496\) −5.23686 + 1.89086i −0.235142 + 0.0849021i
\(497\) −4.30502 + 4.30502i −0.193106 + 0.193106i
\(498\) 0.852621 16.7743i 0.0382068 0.751672i
\(499\) −5.28721 3.05257i −0.236688 0.136652i 0.376966 0.926227i \(-0.376968\pi\)
−0.613654 + 0.789575i \(0.710301\pi\)
\(500\) −5.19563 9.89977i −0.232355 0.442731i
\(501\) 3.07613 9.51832i 0.137431 0.425247i
\(502\) −1.69769 + 0.454895i −0.0757717 + 0.0203030i
\(503\) 30.8022 8.25344i 1.37340 0.368003i 0.504683 0.863305i \(-0.331609\pi\)
0.868721 + 0.495302i \(0.164943\pi\)
\(504\) 0.464144 4.55394i 0.0206746 0.202848i
\(505\) −11.1723 + 9.12179i −0.497159 + 0.405914i
\(506\) 5.72641 3.30615i 0.254570 0.146976i
\(507\) −14.0669 27.5008i −0.624734 1.22135i
\(508\) −5.25568 19.6144i −0.233183 0.870250i
\(509\) 6.32359 + 10.9528i 0.280288 + 0.485473i 0.971456 0.237221i \(-0.0762367\pi\)
−0.691168 + 0.722695i \(0.742903\pi\)
\(510\) 3.80302 8.67204i 0.168401 0.384004i
\(511\) −23.6626 −1.04677
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −17.0318 + 21.2369i −0.751973 + 0.937630i
\(514\) −2.40209 + 1.38685i −0.105952 + 0.0611713i
\(515\) −4.12241 9.15973i −0.181655 0.403626i
\(516\) 16.7449 + 5.41161i 0.737153 + 0.238233i
\(517\) −11.8164 + 44.0993i −0.519683 + 1.93948i
\(518\) 3.54216 13.2195i 0.155634 0.580833i
\(519\) −4.26400 + 3.85150i −0.187169 + 0.169062i
\(520\) 4.40302 11.6097i 0.193085 0.509117i
\(521\) 10.5286 + 6.07869i 0.461266 + 0.266312i 0.712577 0.701594i \(-0.247528\pi\)
−0.251310 + 0.967907i \(0.580861\pi\)
\(522\) 4.74125 + 1.80289i 0.207519 + 0.0789101i
\(523\) −1.41079 + 1.41079i −0.0616896 + 0.0616896i −0.737279 0.675589i \(-0.763889\pi\)
0.675589 + 0.737279i \(0.263889\pi\)
\(524\) 3.84901 6.66669i 0.168145 0.291236i
\(525\) −6.49669 + 11.5069i −0.283539 + 0.502200i
\(526\) 29.2255 1.27429
\(527\) 7.77943 + 11.1711i 0.338877 + 0.486619i
\(528\) −8.15529 0.414526i −0.354913 0.0180399i
\(529\) 21.0329i 0.914474i
\(530\) 1.99145 5.25095i 0.0865031 0.228087i
\(531\) 8.25785 + 0.841653i 0.358360 + 0.0365246i
\(532\) 2.06899 7.72158i 0.0897022 0.334773i
\(533\) 4.94743 1.32566i 0.214297 0.0574207i
\(534\) 15.3465 3.28726i 0.664108 0.142254i
\(535\) 22.2064 30.8245i 0.960067 1.33266i
\(536\) −9.64126 + 5.56639i −0.416439 + 0.240431i
\(537\) 0.0377753 0.0193224i 0.00163012 0.000833824i
\(538\) −22.5859 6.05187i −0.973747 0.260915i
\(539\) 11.0127 19.0745i 0.474350 0.821599i
\(540\) 5.89726 + 10.0111i 0.253778 + 0.430810i
\(541\) −18.0686 + 31.2957i −0.776829 + 1.34551i 0.156932 + 0.987609i \(0.449840\pi\)
−0.933761 + 0.357898i \(0.883494\pi\)
\(542\) 7.65247 7.65247i 0.328702 0.328702i
\(543\) −1.93778 + 38.1234i −0.0831581 + 1.63603i
\(544\) 2.11740 + 1.22248i 0.0907826 + 0.0524133i
\(545\) 12.8904 10.5246i 0.552165 0.450824i
\(546\) −14.3498 + 3.07376i −0.614114 + 0.131545i
\(547\) 10.0767 37.6068i 0.430849 1.60795i −0.319961 0.947431i \(-0.603670\pi\)
0.750810 0.660519i \(-0.229664\pi\)
\(548\) −4.90300 + 18.2982i −0.209446 + 0.781662i
\(549\) −3.26972 7.28210i −0.139548 0.310793i
\(550\) 21.0888 + 10.5324i 0.899231 + 0.449104i
\(551\) 7.67150 + 4.42914i 0.326817 + 0.188688i
\(552\) 1.31986 2.03943i 0.0561769 0.0868038i
\(553\) −4.07603 1.09217i −0.173330 0.0464437i
\(554\) −4.46336 −0.189630
\(555\) 12.6304 + 32.3608i 0.536131 + 1.37364i
\(556\) 7.88991 0.334607
\(557\) 18.2629 18.2629i 0.773823 0.773823i −0.204950 0.978773i \(-0.565703\pi\)
0.978773 + 0.204950i \(0.0657031\pi\)
\(558\) −16.7009 0.281768i −0.707006 0.0119282i
\(559\) 56.4170i 2.38618i
\(560\) −2.76832 1.99434i −0.116983 0.0842761i
\(561\) 4.18171 + 19.5222i 0.176552 + 0.824229i
\(562\) −0.338865 0.338865i −0.0142942 0.0142942i
\(563\) 2.51351 9.38054i 0.105932 0.395343i −0.892517 0.451013i \(-0.851063\pi\)
0.998449 + 0.0556701i \(0.0177295\pi\)
\(564\) 3.51312 + 16.4009i 0.147929 + 0.690602i
\(565\) −6.06345 + 2.72891i −0.255091 + 0.114806i
\(566\) 25.2749i 1.06238i
\(567\) 6.15728 12.2748i 0.258582 0.515495i
\(568\) 3.85411 + 1.03271i 0.161715 + 0.0433313i
\(569\) 7.57016 + 13.1119i 0.317358 + 0.549680i 0.979936 0.199313i \(-0.0638711\pi\)
−0.662578 + 0.748993i \(0.730538\pi\)
\(570\) 7.37748 + 18.9021i 0.309008 + 0.791720i
\(571\) −9.39411 16.2711i −0.393131 0.680923i 0.599730 0.800203i \(-0.295275\pi\)
−0.992861 + 0.119280i \(0.961941\pi\)
\(572\) 6.77565 + 25.2871i 0.283304 + 1.05731i
\(573\) −33.6411 1.70995i −1.40538 0.0714341i
\(574\) 1.40744i 0.0587454i
\(575\) −5.85039 + 3.86657i −0.243978 + 0.161247i
\(576\) −2.73678 + 1.22883i −0.114033 + 0.0512014i
\(577\) 6.17161 1.65368i 0.256928 0.0688435i −0.128056 0.991767i \(-0.540874\pi\)
0.384984 + 0.922923i \(0.374207\pi\)
\(578\) −2.85275 + 10.6466i −0.118659 + 0.442841i
\(579\) 11.3656 35.1680i 0.472338 1.46153i
\(580\) 2.92863 2.39113i 0.121605 0.0992862i
\(581\) 14.7963i 0.613854i
\(582\) 3.68799 + 2.38676i 0.152872 + 0.0989345i
\(583\) 3.06457 + 11.4371i 0.126922 + 0.473678i
\(584\) 7.75393 + 13.4302i 0.320860 + 0.555746i
\(585\) 24.7257 27.8599i 1.02228 1.15187i
\(586\) −12.6747 + 21.9532i −0.523587 + 0.906879i
\(587\) −9.83018 + 9.83018i −0.405735 + 0.405735i −0.880248 0.474513i \(-0.842624\pi\)
0.474513 + 0.880248i \(0.342624\pi\)
\(588\) 0.410769 8.08137i 0.0169398 0.333270i
\(589\) −28.7136 5.13896i −1.18312 0.211747i
\(590\) 3.61642 5.01992i 0.148885 0.206667i
\(591\) −9.61905 10.6493i −0.395675 0.438053i
\(592\) −8.66376 + 2.32145i −0.356078 + 0.0954109i
\(593\) −18.5120 18.5120i −0.760197 0.760197i 0.216161 0.976358i \(-0.430646\pi\)
−0.976358 + 0.216161i \(0.930646\pi\)
\(594\) −22.4263 9.85819i −0.920164 0.404486i
\(595\) −2.95812 + 7.79982i −0.121271 + 0.319761i
\(596\) −11.9404 6.89382i −0.489100 0.282382i
\(597\) 16.0779 + 0.817228i 0.658026 + 0.0334469i
\(598\) −7.52268 2.01570i −0.307625 0.0824280i
\(599\) −2.42298 4.19673i −0.0990004 0.171474i 0.812271 0.583281i \(-0.198231\pi\)
−0.911271 + 0.411807i \(0.864898\pi\)
\(600\) 8.65985 0.0833152i 0.353537 0.00340133i
\(601\) 9.26392 16.0456i 0.377883 0.654513i −0.612871 0.790183i \(-0.709985\pi\)
0.990754 + 0.135670i \(0.0433188\pi\)
\(602\) −14.9743 4.01236i −0.610308 0.163532i
\(603\) −32.9705 + 5.32850i −1.34266 + 0.216993i
\(604\) 4.62045i 0.188003i
\(605\) −24.7789 + 4.02685i −1.00741 + 0.163715i
\(606\) −2.34001 10.9243i −0.0950566 0.443769i
\(607\) −5.57659 + 20.8121i −0.226347 + 0.844738i 0.755514 + 0.655133i \(0.227387\pi\)
−0.981860 + 0.189605i \(0.939279\pi\)
\(608\) −5.06053 + 1.35597i −0.205232 + 0.0549917i
\(609\) −4.25202 1.37417i −0.172301 0.0556841i
\(610\) −5.91965 0.598113i −0.239680 0.0242169i
\(611\) 46.5688 26.8865i 1.88397 1.08771i
\(612\) 4.63391 + 5.68570i 0.187315 + 0.229831i
\(613\) −7.25360 27.0708i −0.292970 1.09338i −0.942816 0.333313i \(-0.891833\pi\)
0.649846 0.760066i \(-0.274833\pi\)
\(614\) 13.4961 23.3759i 0.544658 0.943375i
\(615\) 2.11598 + 2.87837i 0.0853244 + 0.116067i
\(616\) 7.19364 0.289840
\(617\) −0.592619 2.21169i −0.0238580 0.0890391i 0.952970 0.303064i \(-0.0980094\pi\)
−0.976828 + 0.214024i \(0.931343\pi\)
\(618\) 7.77052 + 0.394969i 0.312576 + 0.0158880i
\(619\) 42.4235i 1.70514i 0.522610 + 0.852572i \(0.324958\pi\)
−0.522610 + 0.852572i \(0.675042\pi\)
\(620\) −6.39661 + 10.6810i −0.256894 + 0.428959i
\(621\) 5.87563 4.31145i 0.235781 0.173012i
\(622\) −20.7425 20.7425i −0.831697 0.831697i
\(623\) −13.3550 + 3.57846i −0.535057 + 0.143368i
\(624\) 6.44682 + 7.13729i 0.258079 + 0.285720i
\(625\) −22.9993 9.79959i −0.919972 0.391984i
\(626\) 22.1548 + 12.7911i 0.885483 + 0.511234i
\(627\) −35.9159 23.2437i −1.43434 0.928266i
\(628\) −1.64688 + 1.64688i −0.0657176 + 0.0657176i
\(629\) 10.9649 + 18.9917i 0.437198 + 0.757250i
\(630\) −5.63617 8.54415i −0.224550 0.340407i
\(631\) −7.83936 13.5782i −0.312080 0.540539i 0.666732 0.745297i \(-0.267692\pi\)
−0.978813 + 0.204759i \(0.934359\pi\)
\(632\) 0.715780 + 2.67133i 0.0284722 + 0.106260i
\(633\) −31.0565 + 15.8857i −1.23438 + 0.631401i
\(634\) −20.6578 11.9268i −0.820426 0.473673i
\(635\) −36.8416 26.5412i −1.46202 1.05326i
\(636\) 2.91584 + 3.22814i 0.115621 + 0.128004i
\(637\) −25.0579 + 6.71424i −0.992829 + 0.266028i
\(638\) −2.06316 + 7.69981i −0.0816812 + 0.304838i
\(639\) 9.70620 + 7.00538i 0.383971 + 0.277128i
\(640\) −0.224784 + 2.22474i −0.00888538 + 0.0879406i
\(641\) −1.60034 + 0.923957i −0.0632097 + 0.0364941i −0.531272 0.847201i \(-0.678286\pi\)
0.468062 + 0.883696i \(0.344952\pi\)
\(642\) 13.4010 + 26.1989i 0.528895 + 1.03399i
\(643\) 33.8564 33.8564i 1.33517 1.33517i 0.434488 0.900678i \(-0.356929\pi\)
0.900678 0.434488i \(-0.143071\pi\)
\(644\) −1.07002 + 1.85333i −0.0421648 + 0.0730316i
\(645\) 36.6564 14.3070i 1.44335 0.563338i
\(646\) 6.40463 + 11.0931i 0.251987 + 0.436454i
\(647\) −24.1002 + 24.1002i −0.947475 + 0.947475i −0.998688 0.0512124i \(-0.983691\pi\)
0.0512124 + 0.998688i \(0.483691\pi\)
\(648\) −8.98452 + 0.527617i −0.352945 + 0.0207268i
\(649\) 13.0445i 0.512043i
\(650\) −8.79181 26.3355i −0.344843 1.03296i
\(651\) 14.7062 0.498963i 0.576383 0.0195559i
\(652\) 0.148291 + 0.148291i 0.00580753 + 0.00580753i
\(653\) −9.05246 9.05246i −0.354250 0.354250i 0.507438 0.861688i \(-0.330593\pi\)
−0.861688 + 0.507438i \(0.830593\pi\)
\(654\) 2.69988 + 12.6043i 0.105574 + 0.492868i
\(655\) −2.76113 16.9904i −0.107886 0.663871i
\(656\) −0.798823 + 0.461201i −0.0311888 + 0.0180069i
\(657\) 7.42255 + 45.9276i 0.289581 + 1.79181i
\(658\) −3.82432 14.2726i −0.149088 0.556403i
\(659\) 19.7762 0.770370 0.385185 0.922839i \(-0.374138\pi\)
0.385185 + 0.922839i \(0.374138\pi\)
\(660\) −14.7118 + 10.8151i −0.572656 + 0.420976i
\(661\) −9.46536 16.3945i −0.368160 0.637672i 0.621118 0.783717i \(-0.286679\pi\)
−0.989278 + 0.146045i \(0.953345\pi\)
\(662\) 6.12646 + 1.64158i 0.238112 + 0.0638018i
\(663\) 12.7762 19.7416i 0.496187 0.766701i
\(664\) 8.39796 4.84856i 0.325904 0.188161i
\(665\) −7.33608 16.3003i −0.284481 0.632098i
\(666\) −26.7695 2.72839i −1.03730 0.105723i
\(667\) −1.67685 1.67685i −0.0649280 0.0649280i
\(668\) 5.57847 1.49475i 0.215838 0.0578335i
\(669\) 13.4744 41.6933i 0.520951 1.61195i
\(670\) −8.82751 + 23.2759i −0.341037 + 0.899227i
\(671\) 10.8639 6.27229i 0.419397 0.242139i
\(672\) 2.35289 1.20353i 0.0907648 0.0464272i
\(673\) −15.7429 4.21828i −0.606842 0.162603i −0.0577031 0.998334i \(-0.518378\pi\)
−0.549139 + 0.835731i \(0.685044\pi\)
\(674\) −13.6815 −0.526993
\(675\) 24.3720 + 9.00020i 0.938080 + 0.346418i
\(676\) 8.91707 15.4448i 0.342964 0.594032i
\(677\) −19.9621 5.34883i −0.767206 0.205572i −0.146069 0.989274i \(-0.546662\pi\)
−0.621137 + 0.783702i \(0.713329\pi\)
\(678\) 0.261457 5.14384i 0.0100412 0.197548i
\(679\) −3.35147 1.93497i −0.128618 0.0742574i
\(680\) 5.39630 0.876958i 0.206939 0.0336298i
\(681\) 8.80949 + 9.75301i 0.337581 + 0.373736i
\(682\) −2.22070 26.1553i −0.0850348 1.00154i
\(683\) 3.95466 + 3.95466i 0.151321 + 0.151321i 0.778708 0.627387i \(-0.215876\pi\)
−0.627387 + 0.778708i \(0.715876\pi\)
\(684\) −15.6361 1.59366i −0.597863 0.0609351i
\(685\) 17.3847 + 38.6277i 0.664235 + 1.47589i
\(686\) 17.8093i 0.679964i
\(687\) −8.93562 17.4691i −0.340915 0.666488i
\(688\) 2.62960 + 9.81381i 0.100253 + 0.374148i
\(689\) 6.97301 12.0776i 0.265651 0.460120i
\(690\) −0.598027 5.39897i −0.0227665 0.205535i
\(691\) 20.5420 + 35.5798i 0.781454 + 1.35352i 0.931095 + 0.364778i \(0.118855\pi\)
−0.149640 + 0.988740i \(0.547812\pi\)
\(692\) −3.20438 0.858610i −0.121812 0.0326395i
\(693\) 20.1718 + 7.67043i 0.766263 + 0.291376i
\(694\) 0.848367 + 0.489805i 0.0322036 + 0.0185927i
\(695\) 13.6659 11.1578i 0.518378 0.423238i
\(696\) 0.613396 + 2.86363i 0.0232507 + 0.108545i
\(697\) 1.59469 + 1.59469i 0.0604032 + 0.0604032i
\(698\) −18.6891 18.6891i −0.707394 0.707394i
\(699\) 3.92960 + 18.3452i 0.148631 + 0.693880i
\(700\) −7.61530 + 0.460570i −0.287831 + 0.0174079i
\(701\) −39.6219 22.8757i −1.49650 0.864005i −0.496508 0.868032i \(-0.665385\pi\)
−0.999992 + 0.00402704i \(0.998718\pi\)
\(702\) 10.4673 + 26.8879i 0.395062 + 1.01482i
\(703\) −45.3899 12.1622i −1.71191 0.458705i
\(704\) −2.35727 4.08291i −0.0888429 0.153880i
\(705\) 29.2789 + 23.4394i 1.10271 + 0.882779i
\(706\) −17.2771 + 29.9248i −0.650233 + 1.12624i
\(707\) 2.54730 + 9.50666i 0.0958012 + 0.357535i
\(708\) 2.18241 + 4.26660i 0.0820200 + 0.160349i
\(709\) 29.0248i 1.09005i −0.838421 0.545024i \(-0.816521\pi\)
0.838421 0.545024i \(-0.183479\pi\)
\(710\) 8.13604 3.66169i 0.305340 0.137421i
\(711\) −0.841253 + 8.25392i −0.0315494 + 0.309546i
\(712\) 6.40730 + 6.40730i 0.240124 + 0.240124i
\(713\) 7.06884 + 3.31836i 0.264730 + 0.124274i
\(714\) −4.33123 4.79511i −0.162092 0.179452i
\(715\) 47.4965 + 34.2171i 1.77627 + 1.27965i
\(716\) 0.0212151 + 0.0122486i 0.000792847 + 0.000457750i
\(717\) 0.906228 17.8289i 0.0338437 0.665833i
\(718\) 32.6381 + 8.74535i 1.21804 + 0.326374i
\(719\) 1.02315 1.77215i 0.0381570 0.0660899i −0.846316 0.532681i \(-0.821185\pi\)
0.884473 + 0.466591i \(0.154518\pi\)
\(720\) −3.00252 + 5.99874i −0.111897 + 0.223560i
\(721\) −6.85425 −0.255265
\(722\) −8.15980 2.18641i −0.303676 0.0813698i
\(723\) 15.6080 7.98364i 0.580467 0.296915i
\(724\) −19.0863 + 11.0195i −0.709337 + 0.409536i
\(725\) 1.69111 8.28323i 0.0628064 0.307631i
\(726\) 5.97986 18.5032i 0.221933 0.686717i
\(727\) 31.3318 8.39534i 1.16203 0.311366i 0.374256 0.927326i \(-0.377898\pi\)
0.787778 + 0.615960i \(0.211232\pi\)
\(728\) −5.99116 5.99116i −0.222047 0.222047i
\(729\) −25.7562 8.10051i −0.953933 0.300019i
\(730\) 32.4232 + 12.2967i 1.20003 + 0.455119i
\(731\) 21.5127 12.4204i 0.795677 0.459385i
\(732\) 2.50398 3.86912i 0.0925499 0.143007i
\(733\) −13.5343 3.62651i −0.499902 0.133948i 5.25650e−5 1.00000i \(-0.499983\pi\)
−0.499954 + 0.866052i \(0.666650\pi\)
\(734\) −9.68910 16.7820i −0.357631 0.619436i
\(735\) −10.7170 14.5784i −0.395304 0.537734i
\(736\) 1.40253 0.0516980
\(737\) −13.5843 50.6974i −0.500386 1.86746i
\(738\) −2.73176 + 0.441491i −0.100557 + 0.0162515i
\(739\) 10.9719 6.33462i 0.403607 0.233023i −0.284432 0.958696i \(-0.591805\pi\)
0.688039 + 0.725674i \(0.258472\pi\)
\(740\) −11.7233 + 16.2731i −0.430958 + 0.598210i
\(741\) 10.5539 + 49.2706i 0.387707 + 1.81000i
\(742\) −2.70975 2.70975i −0.0994781 0.0994781i
\(743\) 7.89277 + 7.89277i 0.289558 + 0.289558i 0.836905 0.547348i \(-0.184362\pi\)
−0.547348 + 0.836905i \(0.684362\pi\)
\(744\) −5.10225 8.18334i −0.187058 0.300016i
\(745\) −30.4309 + 4.94536i −1.11490 + 0.181184i
\(746\) 22.5366i 0.825123i
\(747\) 28.7187 4.64135i 1.05076 0.169818i
\(748\) −8.15071 + 8.15071i −0.298019 + 0.298019i
\(749\) −12.9619 22.4507i −0.473619 0.820332i
\(750\) 14.8817 12.3909i 0.543403 0.452453i
\(751\) 12.4585 21.5787i 0.454616 0.787417i −0.544050 0.839053i \(-0.683110\pi\)
0.998666 + 0.0516353i \(0.0164433\pi\)
\(752\) −6.84752 + 6.84752i −0.249704 + 0.249704i
\(753\) −1.38631 2.71024i −0.0505201 0.0987666i
\(754\) 8.13100 4.69443i 0.296113 0.170961i
\(755\) 6.53416 + 8.00297i 0.237802 + 0.291258i
\(756\) 7.88108 0.865990i 0.286632 0.0314958i
\(757\) 7.87564 29.3923i 0.286245 1.06828i −0.661680 0.749786i \(-0.730156\pi\)
0.947925 0.318494i \(-0.103177\pi\)
\(758\) −8.47224 + 2.27013i −0.307725 + 0.0824548i
\(759\) 7.67683 + 8.49903i 0.278651 + 0.308495i
\(760\) −6.84765 + 9.50516i −0.248390 + 0.344788i
\(761\) −6.33239 3.65601i −0.229549 0.132530i 0.380815 0.924651i \(-0.375643\pi\)
−0.610364 + 0.792121i \(0.708977\pi\)
\(762\) 31.3130 16.0169i 1.13435 0.580232i
\(763\) −2.93904 10.9687i −0.106401 0.397092i
\(764\) −9.72389 16.8423i −0.351798 0.609332i
\(765\) 16.0669 + 3.29487i 0.580900 + 0.119126i
\(766\) −13.7431 23.8037i −0.496558 0.860064i
\(767\) 10.8640 10.8640i 0.392277 0.392277i
\(768\) −1.45410 0.941054i −0.0524704 0.0339574i
\(769\) −8.88607 5.13037i −0.320440 0.185006i 0.331149 0.943579i \(-0.392564\pi\)
−0.651589 + 0.758573i \(0.725897\pi\)
\(770\) 12.4599 10.1731i 0.449025 0.366614i
\(771\) −3.22025 3.56514i −0.115974 0.128395i
\(772\) 20.6112 5.52275i 0.741812 0.198768i
\(773\) −16.1198 16.1198i −0.579789 0.579789i 0.355056 0.934845i \(-0.384462\pi\)
−0.934845 + 0.355056i \(0.884462\pi\)
\(774\) −3.09056 + 30.3229i −0.111088 + 1.08993i
\(775\) 4.02545 + 27.5462i 0.144598 + 0.989490i
\(776\) 2.53627i 0.0910466i
\(777\) 23.6741 + 1.20333i 0.849302 + 0.0431693i
\(778\) −2.67779 9.99363i −0.0960033 0.358289i
\(779\) −4.83251 −0.173143
\(780\) 21.2598 + 3.24534i 0.761224 + 0.116202i
\(781\) −9.40566 + 16.2911i −0.336561 + 0.582940i
\(782\) −0.887525 3.31229i −0.0317378 0.118447i
\(783\) −1.33339 + 8.68398i −0.0476515 + 0.310340i
\(784\) 4.04590 2.33590i 0.144496 0.0834250i
\(785\) −0.523531 + 5.18150i −0.0186856 + 0.184936i
\(786\) 12.6873 + 4.10027i 0.452540 + 0.146252i
\(787\) 20.2839 5.43504i 0.723042 0.193738i 0.121513 0.992590i \(-0.461225\pi\)
0.601528 + 0.798851i \(0.294559\pi\)
\(788\) 2.14437 8.00288i 0.0763899 0.285091i
\(789\) 10.6025 + 49.4973i 0.377458 + 1.76215i
\(790\) 5.01753 + 3.61470i 0.178516 + 0.128605i
\(791\) 4.53729i 0.161328i
\(792\) −2.25653 13.9624i −0.0801821 0.496134i
\(793\) −14.2717 3.82410i −0.506804 0.135798i
\(794\) −7.81355 + 13.5335i −0.277292 + 0.480285i
\(795\) 9.61564 + 1.46784i 0.341032 + 0.0520590i
\(796\) 4.64729 + 8.04935i 0.164719 + 0.285302i
\(797\) −51.8174 13.8844i −1.83547 0.491812i −0.837001 0.547201i \(-0.815693\pi\)
−0.998465 + 0.0553899i \(0.982360\pi\)
\(798\) 13.8281 + 0.702871i 0.489510 + 0.0248813i
\(799\) 20.5046 + 11.8383i 0.725399 + 0.418809i
\(800\) 2.75685 + 4.17131i 0.0974693 + 0.147478i
\(801\) 11.1348 + 24.7988i 0.393430 + 0.876222i
\(802\) −6.09185 6.09185i −0.215111 0.215111i
\(803\) −70.6211 + 18.9229i −2.49216 + 0.667774i
\(804\) −12.9251 14.3094i −0.455832 0.504653i
\(805\) 0.767592 + 4.72332i 0.0270541 + 0.166475i
\(806\) −19.9337 + 23.6327i −0.702136 + 0.832427i
\(807\) 2.05592 40.4477i 0.0723718 1.42383i
\(808\) 4.56099 4.56099i 0.160455 0.160455i
\(809\) 11.2518 19.4887i 0.395593 0.685187i −0.597584 0.801807i \(-0.703872\pi\)
0.993177 + 0.116619i \(0.0372057\pi\)
\(810\) −14.8157 + 13.6196i −0.520572 + 0.478545i
\(811\) −6.85535 11.8738i −0.240724 0.416946i 0.720197 0.693770i \(-0.244051\pi\)
−0.960921 + 0.276824i \(0.910718\pi\)
\(812\) −0.667734 2.49202i −0.0234329 0.0874526i
\(813\) 15.7366 + 10.1843i 0.551908 + 0.357179i
\(814\) 42.2865i 1.48214i
\(815\) 0.466562 + 0.0471407i 0.0163430 + 0.00165127i
\(816\) −1.30228 + 4.02958i −0.0455889 + 0.141064i
\(817\) −13.7766 + 51.4150i −0.481983 + 1.79878i
\(818\) 17.0124 4.55847i 0.594826 0.159383i
\(819\) −10.4116 23.1881i −0.363812 0.810259i
\(820\) −0.731400 + 1.92852i −0.0255416 + 0.0673467i
\(821\) 5.92651i 0.206837i −0.994638 0.103418i \(-0.967022\pi\)
0.994638 0.103418i \(-0.0329781\pi\)
\(822\) −32.7692 1.66563i −1.14296 0.0580955i
\(823\) −9.01999 33.6631i −0.314417 1.17342i −0.924531 0.381107i \(-0.875543\pi\)
0.610114 0.792314i \(-0.291124\pi\)
\(824\) 2.24605 + 3.89028i 0.0782449 + 0.135524i
\(825\) −10.1874 + 39.5377i −0.354681 + 1.37653i
\(826\) −2.11091 3.65620i −0.0734479 0.127216i
\(827\) −1.51228 0.405214i −0.0525871 0.0140907i 0.232430 0.972613i \(-0.425332\pi\)
−0.285017 + 0.958523i \(0.591999\pi\)
\(828\) 3.93286 + 1.49549i 0.136676 + 0.0519719i
\(829\) 40.5084i 1.40692i −0.710737 0.703458i \(-0.751638\pi\)
0.710737 0.703458i \(-0.248362\pi\)
\(830\) 7.68914 20.2743i 0.266894 0.703732i
\(831\) −1.61922 7.55930i −0.0561702 0.262229i
\(832\) −1.43718 + 5.36364i −0.0498254 + 0.185951i
\(833\) −8.07683 8.07683i −0.279845 0.279845i
\(834\) 2.86231 + 13.3626i 0.0991135 + 0.462709i
\(835\) 7.54849 10.4780i 0.261226 0.362606i
\(836\) 24.6997i 0.854257i
\(837\) −5.58156 28.3874i −0.192927 0.981213i
\(838\) −12.4995 + 12.4995i −0.431787 + 0.431787i
\(839\) 3.27832 0.113180 0.0565902 0.998397i \(-0.481977\pi\)
0.0565902 + 0.998397i \(0.481977\pi\)
\(840\) 2.37338 5.41203i 0.0818894 0.186733i
\(841\) −26.1411 −0.901418
\(842\) 14.6573 + 3.92741i 0.505124 + 0.135348i
\(843\) 0.450979 0.696847i 0.0155325 0.0240007i
\(844\) −17.4418 10.0700i −0.600371 0.346624i
\(845\) −6.39676 39.3620i −0.220055 1.35409i
\(846\) −26.5026 + 11.8999i −0.911178 + 0.409126i
\(847\) −4.43368 + 16.5467i −0.152343 + 0.568552i
\(848\) −0.650026 + 2.42593i −0.0223220 + 0.0833068i
\(849\) −42.8063 + 9.16923i −1.46911 + 0.314687i
\(850\) 8.10662 9.15031i 0.278055 0.313853i
\(851\) 10.8945 + 6.28993i 0.373458 + 0.215616i
\(852\) −0.350827 + 6.90209i −0.0120191 + 0.236462i
\(853\) −2.78602 + 2.78602i −0.0953914 + 0.0953914i −0.753192 0.657801i \(-0.771487\pi\)
0.657801 + 0.753192i \(0.271487\pi\)
\(854\) −2.03000 + 3.51607i −0.0694653 + 0.120317i
\(855\) −29.3367 + 19.3520i −1.00329 + 0.661825i
\(856\) −8.49493 + 14.7137i −0.290351 + 0.502902i
\(857\) −20.5729 5.51249i −0.702757 0.188303i −0.110292 0.993899i \(-0.535179\pi\)
−0.592465 + 0.805596i \(0.701845\pi\)
\(858\) −40.3689 + 20.6491i −1.37817 + 0.704950i
\(859\) −36.1520 + 20.8724i −1.23349 + 0.712156i −0.967756 0.251890i \(-0.918948\pi\)
−0.265735 + 0.964046i \(0.585615\pi\)
\(860\) 18.4332 + 13.2795i 0.628566 + 0.452828i
\(861\) 2.38369 0.510592i 0.0812358 0.0174009i
\(862\) −15.4228 + 4.13253i −0.525303 + 0.140755i
\(863\) −13.0000 + 48.5168i −0.442526 + 1.65153i 0.279859 + 0.960041i \(0.409712\pi\)
−0.722386 + 0.691490i \(0.756954\pi\)
\(864\) −3.07404 4.18930i −0.104581 0.142523i
\(865\) −6.76446 + 3.04440i −0.229998 + 0.103513i
\(866\) 25.6288i 0.870904i
\(867\) −19.0664 0.969127i −0.647528 0.0329133i
\(868\) 4.85497 + 6.97161i 0.164788 + 0.236632i
\(869\) −13.0383 −0.442295
\(870\) 5.11214 + 4.09256i 0.173318 + 0.138751i
\(871\) −30.9093 + 53.5365i −1.04732 + 1.81401i
\(872\) −5.26241 + 5.26241i −0.178208 + 0.178208i
\(873\) −2.70437 + 7.11198i −0.0915290 + 0.240704i
\(874\) 6.36350 + 3.67397i 0.215249 + 0.124274i
\(875\) −12.5389 + 11.5672i −0.423894 + 0.391042i
\(876\) −19.9328 + 18.0045i −0.673468 + 0.608316i
\(877\) −0.804379 + 3.00198i −0.0271619 + 0.101370i −0.978176 0.207778i \(-0.933377\pi\)
0.951014 + 0.309147i \(0.100044\pi\)
\(878\) −3.14321 + 11.7306i −0.106078 + 0.395889i
\(879\) −41.7788 13.5021i −1.40916 0.455413i
\(880\) −9.85695 3.73830i −0.332278 0.126018i
\(881\) 13.5152 7.80303i 0.455340 0.262891i −0.254743 0.967009i \(-0.581991\pi\)
0.710083 + 0.704118i \(0.248657\pi\)
\(882\) 13.8359 2.23607i 0.465878 0.0752925i
\(883\) −4.35149 + 4.35149i −0.146439 + 0.146439i −0.776525 0.630086i \(-0.783020\pi\)
0.630086 + 0.776525i \(0.283020\pi\)
\(884\) 13.5765 0.456627
\(885\) 9.81386 + 4.30375i 0.329889 + 0.144669i
\(886\) −5.77088 9.99546i −0.193877 0.335804i
\(887\) −4.18317 15.6118i −0.140457 0.524192i −0.999916 0.0129873i \(-0.995866\pi\)
0.859459 0.511205i \(-0.170801\pi\)
\(888\) −7.07472 13.8310i −0.237412 0.464139i
\(889\) −26.8332 + 15.4922i −0.899958 + 0.519591i
\(890\) 20.1590 + 2.03684i 0.675732 + 0.0682750i
\(891\) 8.56031 41.5583i 0.286781 1.39226i
\(892\) 24.4355 6.54747i 0.818161 0.219225i
\(893\) −49.0055 + 13.1310i −1.63991 + 0.439412i
\(894\) 7.34383 22.7237i 0.245615 0.759993i
\(895\) 0.0540679 0.00878663i 0.00180729 0.000293705i
\(896\) 1.32142 + 0.762922i 0.0441455 + 0.0254874i
\(897\) 0.684766 13.4719i 0.0228637 0.449814i
\(898\) −27.2869 + 27.2869i −0.910576 + 0.910576i
\(899\) −8.85458 + 3.19710i −0.295317 + 0.106629i
\(900\) 3.28273 + 14.6364i 0.109424 + 0.487879i
\(901\) 6.14053 0.204571
\(902\) −1.12553 4.20052i −0.0374759 0.139862i
\(903\) 1.36306 26.8166i 0.0453600 0.892401i
\(904\) 2.57524 1.48682i 0.0856512 0.0494507i
\(905\) −17.4754 + 46.0781i −0.580901 + 1.53169i
\(906\) −7.82534 + 1.67621i −0.259980 + 0.0556883i
\(907\) −1.58130 1.58130i −0.0525064 0.0525064i 0.680366 0.732872i \(-0.261821\pi\)
−0.732872 + 0.680366i \(0.761821\pi\)
\(908\) −1.96389 + 7.32934i −0.0651740 + 0.243233i
\(909\) 17.6528 7.92625i 0.585507 0.262897i
\(910\) −18.8497 1.90455i −0.624863 0.0631352i
\(911\) 3.74204 + 2.16047i 0.123979 + 0.0715795i 0.560707 0.828014i \(-0.310529\pi\)
−0.436728 + 0.899594i \(0.643863\pi\)
\(912\) −4.13237 8.07877i −0.136836 0.267515i
\(913\) 11.8325 + 44.1597i 0.391600 + 1.46147i
\(914\) 19.2331 0.636173
\(915\) −1.13455 10.2427i −0.0375072 0.338613i
\(916\) 5.66432 9.81089i 0.187154 0.324161i
\(917\) −11.3457 3.04008i −0.374670 0.100392i
\(918\) −7.94840 + 9.91080i −0.262336 + 0.327105i
\(919\) −9.27998 + 5.35780i −0.306118 + 0.176737i −0.645188 0.764024i \(-0.723221\pi\)
0.339070 + 0.940761i \(0.389888\pi\)
\(920\) 2.42929 1.98344i 0.0800914 0.0653920i
\(921\) 44.4863 + 14.3771i 1.46587 + 0.473741i
\(922\) 21.7153 + 21.7153i 0.715156 + 0.715156i
\(923\) 21.4013 5.73446i 0.704432 0.188752i
\(924\) 2.60971 + 12.1834i 0.0858533 + 0.400804i
\(925\) 2.70737 + 44.7651i 0.0890179 + 1.47187i
\(926\) 12.8618i 0.422664i
\(927\) 2.15006 + 13.3037i 0.0706173 + 0.436951i
\(928\) −1.19559 + 1.19559i −0.0392472 + 0.0392472i
\(929\) −32.2807 −1.05910 −0.529548 0.848280i \(-0.677638\pi\)
−0.529548 + 0.848280i \(0.677638\pi\)
\(930\) −20.4102 6.95865i −0.669278 0.228183i
\(931\) 24.4758 0.802162
\(932\) −7.65930 + 7.65930i −0.250889 + 0.250889i
\(933\) 27.6051 42.6551i 0.903752 1.39646i
\(934\) 19.8296i 0.648843i
\(935\) −2.59105 + 25.6442i −0.0847365 + 0.838656i
\(936\) −9.74916 + 13.5078i −0.318661 + 0.441517i
\(937\) 13.7568 3.68613i 0.449416 0.120421i −0.0270102 0.999635i \(-0.508599\pi\)
0.476426 + 0.879215i \(0.341932\pi\)
\(938\) 12.0115 + 12.0115i 0.392190 + 0.392190i
\(939\) −13.6260 + 42.1624i −0.444669 + 1.37592i
\(940\) −2.17678 + 21.5441i −0.0709988 + 0.702691i
\(941\) −45.9141 + 26.5085i −1.49676 + 0.864153i −0.999993 0.00373322i \(-0.998812\pi\)
−0.496763 + 0.867886i \(0.665478\pi\)
\(942\) −3.38666 2.19175i −0.110343 0.0714111i
\(943\) 1.24962 + 0.334834i 0.0406931 + 0.0109037i
\(944\) −1.38344 + 2.39619i −0.0450271 + 0.0779892i
\(945\) 12.4260 12.6452i 0.404216 0.411350i
\(946\) −47.8997 −1.55735
\(947\) 11.6952 + 43.6470i 0.380042 + 1.41834i 0.845836 + 0.533443i \(0.179102\pi\)
−0.465794 + 0.884893i \(0.654231\pi\)
\(948\) −4.26457 + 2.18137i −0.138507 + 0.0708477i
\(949\) 74.5759 + 43.0564i 2.42084 + 1.39767i
\(950\) 1.58139 + 26.1475i 0.0513070 + 0.848336i
\(951\) 12.7053 39.3135i 0.411999 1.27483i
\(952\) 0.965556 3.60350i 0.0312938 0.116790i
\(953\) 34.7890 + 34.7890i 1.12693 + 1.12693i 0.990674 + 0.136252i \(0.0435057\pi\)
0.136252 + 0.990674i \(0.456494\pi\)
\(954\) −4.40947 + 6.10947i −0.142762 + 0.197801i
\(955\) −40.6606 15.4207i −1.31574 0.499003i
\(956\) 8.92596 5.15341i 0.288686 0.166673i
\(957\) −13.7891 0.700889i −0.445739 0.0226565i
\(958\) −8.69147 32.4370i −0.280809 1.04799i
\(959\) 28.9052 0.933397
\(960\) −3.84944 + 0.426391i −0.124240 + 0.0137617i
\(961\) 23.8493 19.8043i 0.769332 0.638849i
\(962\) −35.2179 + 35.2179i −1.13547 + 1.13547i
\(963\) −39.5096 + 32.2008i −1.27318 + 1.03766i
\(964\) 8.76567 + 5.06086i 0.282323 + 0.162999i
\(965\) 27.8899 38.7138i 0.897809 1.24624i
\(966\) −3.52705 1.13987i −0.113481 0.0366748i
\(967\) 3.90972 1.04761i 0.125728 0.0336888i −0.195406 0.980722i \(-0.562603\pi\)
0.321134 + 0.947034i \(0.395936\pi\)
\(968\) 10.8443 2.90572i 0.348549 0.0933934i
\(969\) −16.4642 + 14.8715i −0.528907 + 0.477740i
\(970\) 3.58674 + 4.39301i 0.115163 + 0.141051i
\(971\) 24.6046 14.2055i 0.789598 0.455875i −0.0502230 0.998738i \(-0.515993\pi\)
0.839821 + 0.542863i \(0.182660\pi\)
\(972\) −4.15300 15.0251i −0.133208 0.481929i
\(973\) −3.11586 11.6286i −0.0998899 0.372794i
\(974\) −9.17083 15.8843i −0.293852 0.508967i
\(975\) 41.4131 24.4441i 1.32628 0.782837i
\(976\) 2.66083 0.0851711
\(977\) −2.15467 + 2.15467i −0.0689340 + 0.0689340i −0.740733 0.671799i \(-0.765522\pi\)
0.671799 + 0.740733i \(0.265522\pi\)
\(978\) −0.197353 + 0.304948i −0.00631067 + 0.00975116i
\(979\) −36.9964 + 21.3599i −1.18241 + 0.682665i
\(980\) 3.70441 9.76760i 0.118333 0.312015i
\(981\) −20.3676 + 9.14520i −0.650288 + 0.291984i
\(982\) 10.5419 39.3429i 0.336405 1.25548i
\(983\) −11.5380 + 43.0603i −0.368004 + 1.37341i 0.495298 + 0.868723i \(0.335059\pi\)
−0.863302 + 0.504687i \(0.831608\pi\)
\(984\) −1.07090 1.18560i −0.0341391 0.0377955i
\(985\) −7.60333 16.8941i −0.242262 0.538292i
\(986\) 3.58013 + 2.06699i 0.114015 + 0.0658264i
\(987\) 22.7851 11.6548i 0.725258 0.370977i
\(988\) −20.5709 + 20.5709i −0.654448 + 0.654448i
\(989\) 7.12487 12.3406i 0.226558 0.392409i
\(990\) −23.6539 20.9929i −0.751771 0.667197i
\(991\) −32.9770 −1.04755 −0.523774 0.851857i \(-0.675477\pi\)
−0.523774 + 0.851857i \(0.675477\pi\)
\(992\) 2.36598 5.04006i 0.0751198 0.160022i
\(993\) −0.557672 + 10.9715i −0.0176972 + 0.348170i
\(994\) 6.08822i 0.193106i
\(995\) 19.4327 + 7.36996i 0.616059 + 0.233643i
\(996\) 11.2583 + 12.4641i 0.356733 + 0.394940i
\(997\) 7.44463 27.7837i 0.235774 0.879920i −0.742025 0.670373i \(-0.766134\pi\)
0.977798 0.209547i \(-0.0671990\pi\)
\(998\) 5.89712 1.58013i 0.186670 0.0500181i
\(999\) −5.09056 46.3274i −0.161058 1.46574i
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 930.2.bf.a.377.6 256
3.2 odd 2 inner 930.2.bf.a.377.53 yes 256
5.3 odd 4 inner 930.2.bf.a.563.54 yes 256
15.8 even 4 inner 930.2.bf.a.563.27 yes 256
31.25 even 3 inner 930.2.bf.a.707.27 yes 256
93.56 odd 6 inner 930.2.bf.a.707.54 yes 256
155.118 odd 12 inner 930.2.bf.a.893.53 yes 256
465.428 even 12 inner 930.2.bf.a.893.6 yes 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bf.a.377.6 256 1.1 even 1 trivial
930.2.bf.a.377.53 yes 256 3.2 odd 2 inner
930.2.bf.a.563.27 yes 256 15.8 even 4 inner
930.2.bf.a.563.54 yes 256 5.3 odd 4 inner
930.2.bf.a.707.27 yes 256 31.25 even 3 inner
930.2.bf.a.707.54 yes 256 93.56 odd 6 inner
930.2.bf.a.893.6 yes 256 465.428 even 12 inner
930.2.bf.a.893.53 yes 256 155.118 odd 12 inner