Properties

Label 210.3.k.b.167.10
Level $210$
Weight $3$
Character 210.167
Analytic conductor $5.722$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,3,Mod(83,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.83");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\), degree \(2\), 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: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 167.10
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.b.83.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(0.947561 - 2.84642i) q^{3} -2.00000i q^{4} +(4.64638 - 1.84693i) q^{5} +(-1.89886 - 3.79398i) q^{6} +(-6.25771 - 3.13705i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-7.20426 - 5.39432i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(0.947561 - 2.84642i) q^{3} -2.00000i q^{4} +(4.64638 - 1.84693i) q^{5} +(-1.89886 - 3.79398i) q^{6} +(-6.25771 - 3.13705i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-7.20426 - 5.39432i) q^{9} +(2.79945 - 6.49331i) q^{10} +2.08576i q^{11} +(-5.69285 - 1.89512i) q^{12} +(8.39517 + 8.39517i) q^{13} +(-9.39476 + 3.12066i) q^{14} +(-0.854411 - 14.9756i) q^{15} -4.00000 q^{16} +(4.96522 + 4.96522i) q^{17} +(-12.5986 + 1.80994i) q^{18} +17.3668 q^{19} +(-3.69386 - 9.29276i) q^{20} +(-14.8589 + 14.8395i) q^{21} +(2.08576 + 2.08576i) q^{22} +(-3.08467 - 3.08467i) q^{23} +(-7.58797 + 3.79773i) q^{24} +(18.1777 - 17.1631i) q^{25} +16.7903 q^{26} +(-22.1810 + 15.3949i) q^{27} +(-6.27410 + 12.5154i) q^{28} -39.1891 q^{29} +(-15.8301 - 14.1212i) q^{30} -42.3954i q^{31} +(-4.00000 + 4.00000i) q^{32} +(5.93696 + 1.97638i) q^{33} +9.93045 q^{34} +(-34.8696 - 3.01840i) q^{35} +(-10.7886 + 14.4085i) q^{36} +(36.7464 + 36.7464i) q^{37} +(17.3668 - 17.3668i) q^{38} +(31.8511 - 15.9413i) q^{39} +(-12.9866 - 5.59891i) q^{40} +15.5827 q^{41} +(-0.0193943 + 29.6985i) q^{42} +(22.8274 - 22.8274i) q^{43} +4.17152 q^{44} +(-43.4366 - 11.7583i) q^{45} -6.16934 q^{46} +(33.4161 + 33.4161i) q^{47} +(-3.79024 + 11.3857i) q^{48} +(29.3178 + 39.2615i) q^{49} +(1.01465 - 35.3408i) q^{50} +(18.8380 - 9.42828i) q^{51} +(16.7903 - 16.7903i) q^{52} +(59.7460 + 59.7460i) q^{53} +(-6.78607 + 37.5759i) q^{54} +(3.85225 + 9.69124i) q^{55} +(6.24131 + 18.7895i) q^{56} +(16.4561 - 49.4332i) q^{57} +(-39.1891 + 39.1891i) q^{58} +48.9876i q^{59} +(-29.9513 + 1.70882i) q^{60} -82.9406i q^{61} +(-42.3954 - 42.3954i) q^{62} +(28.1599 + 56.3562i) q^{63} +8.00000i q^{64} +(54.5124 + 23.5019i) q^{65} +(7.91334 - 3.96057i) q^{66} +(-54.8233 - 54.8233i) q^{67} +(9.93045 - 9.93045i) q^{68} +(-11.7032 + 5.85736i) q^{69} +(-37.8880 + 31.8512i) q^{70} -74.9745i q^{71} +(3.61987 + 25.1972i) q^{72} +(75.1938 + 75.1938i) q^{73} +73.4928 q^{74} +(-31.6289 - 68.0045i) q^{75} -34.7336i q^{76} +(6.54314 - 13.0521i) q^{77} +(15.9099 - 47.7924i) q^{78} -3.61068i q^{79} +(-18.5855 + 7.38771i) q^{80} +(22.8026 + 77.7241i) q^{81} +(15.5827 - 15.5827i) q^{82} +(-103.116 + 103.116i) q^{83} +(29.6791 + 29.7179i) q^{84} +(32.2407 + 13.8999i) q^{85} -45.6547i q^{86} +(-37.1340 + 111.549i) q^{87} +(4.17152 - 4.17152i) q^{88} +24.4427i q^{89} +(-55.1950 + 31.6783i) q^{90} +(-26.1984 - 78.8706i) q^{91} +(-6.16934 + 6.16934i) q^{92} +(-120.675 - 40.1722i) q^{93} +66.8321 q^{94} +(80.6927 - 32.0752i) q^{95} +(7.59545 + 15.1759i) q^{96} +(-35.3616 + 35.3616i) q^{97} +(68.5793 + 9.94368i) q^{98} +(11.2513 - 15.0264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9} - 8 q^{14} - 4 q^{15} - 128 q^{16} - 4 q^{18} + 12 q^{21} - 40 q^{22} - 24 q^{23} + 16 q^{25} - 8 q^{28} + 112 q^{29} + 28 q^{30} - 128 q^{32} + 48 q^{35} - 40 q^{36} + 32 q^{37} - 64 q^{39} - 20 q^{42} - 32 q^{43} - 80 q^{44} - 48 q^{46} + 8 q^{50} + 84 q^{51} + 136 q^{53} + 340 q^{57} + 112 q^{58} + 64 q^{60} + 168 q^{63} + 200 q^{65} + 32 q^{67} - 72 q^{72} + 64 q^{74} - 88 q^{77} - 4 q^{78} + 76 q^{81} - 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} - 48 q^{92} - 388 q^{93} - 544 q^{95} - 128 q^{98} - 160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) 0.947561 2.84642i 0.315854 0.948808i
\(4\) 2.00000i 0.500000i
\(5\) 4.64638 1.84693i 0.929276 0.369386i
\(6\) −1.89886 3.79398i −0.316477 0.632331i
\(7\) −6.25771 3.13705i −0.893958 0.448150i
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) −7.20426 5.39432i −0.800473 0.599369i
\(10\) 2.79945 6.49331i 0.279945 0.649331i
\(11\) 2.08576i 0.189615i 0.995496 + 0.0948073i \(0.0302235\pi\)
−0.995496 + 0.0948073i \(0.969777\pi\)
\(12\) −5.69285 1.89512i −0.474404 0.157927i
\(13\) 8.39517 + 8.39517i 0.645782 + 0.645782i 0.951971 0.306189i \(-0.0990538\pi\)
−0.306189 + 0.951971i \(0.599054\pi\)
\(14\) −9.39476 + 3.12066i −0.671054 + 0.222904i
\(15\) −0.854411 14.9756i −0.0569607 0.998376i
\(16\) −4.00000 −0.250000
\(17\) 4.96522 + 4.96522i 0.292072 + 0.292072i 0.837898 0.545826i \(-0.183784\pi\)
−0.545826 + 0.837898i \(0.683784\pi\)
\(18\) −12.5986 + 1.80994i −0.699921 + 0.100552i
\(19\) 17.3668 0.914041 0.457021 0.889456i \(-0.348917\pi\)
0.457021 + 0.889456i \(0.348917\pi\)
\(20\) −3.69386 9.29276i −0.184693 0.464638i
\(21\) −14.8589 + 14.8395i −0.707568 + 0.706645i
\(22\) 2.08576 + 2.08576i 0.0948073 + 0.0948073i
\(23\) −3.08467 3.08467i −0.134116 0.134116i 0.636862 0.770978i \(-0.280232\pi\)
−0.770978 + 0.636862i \(0.780232\pi\)
\(24\) −7.58797 + 3.79773i −0.316165 + 0.158239i
\(25\) 18.1777 17.1631i 0.727109 0.686523i
\(26\) 16.7903 0.645782
\(27\) −22.1810 + 15.3949i −0.821518 + 0.570182i
\(28\) −6.27410 + 12.5154i −0.224075 + 0.446979i
\(29\) −39.1891 −1.35135 −0.675674 0.737201i \(-0.736147\pi\)
−0.675674 + 0.737201i \(0.736147\pi\)
\(30\) −15.8301 14.1212i −0.527669 0.470708i
\(31\) 42.3954i 1.36759i −0.729673 0.683796i \(-0.760328\pi\)
0.729673 0.683796i \(-0.239672\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) 5.93696 + 1.97638i 0.179908 + 0.0598905i
\(34\) 9.93045 0.292072
\(35\) −34.8696 3.01840i −0.996274 0.0862399i
\(36\) −10.7886 + 14.4085i −0.299684 + 0.400236i
\(37\) 36.7464 + 36.7464i 0.993146 + 0.993146i 0.999977 0.00683066i \(-0.00217428\pi\)
−0.00683066 + 0.999977i \(0.502174\pi\)
\(38\) 17.3668 17.3668i 0.457021 0.457021i
\(39\) 31.8511 15.9413i 0.816696 0.408751i
\(40\) −12.9866 5.59891i −0.324665 0.139973i
\(41\) 15.5827 0.380065 0.190032 0.981778i \(-0.439141\pi\)
0.190032 + 0.981778i \(0.439141\pi\)
\(42\) −0.0193943 + 29.6985i −0.000461768 + 0.707107i
\(43\) 22.8274 22.8274i 0.530869 0.530869i −0.389962 0.920831i \(-0.627512\pi\)
0.920831 + 0.389962i \(0.127512\pi\)
\(44\) 4.17152 0.0948073
\(45\) −43.4366 11.7583i −0.965259 0.261296i
\(46\) −6.16934 −0.134116
\(47\) 33.4161 + 33.4161i 0.710980 + 0.710980i 0.966740 0.255760i \(-0.0823257\pi\)
−0.255760 + 0.966740i \(0.582326\pi\)
\(48\) −3.79024 + 11.3857i −0.0789634 + 0.237202i
\(49\) 29.3178 + 39.2615i 0.598323 + 0.801255i
\(50\) 1.01465 35.3408i 0.0202930 0.706816i
\(51\) 18.8380 9.42828i 0.369372 0.184868i
\(52\) 16.7903 16.7903i 0.322891 0.322891i
\(53\) 59.7460 + 59.7460i 1.12728 + 1.12728i 0.990617 + 0.136665i \(0.0436385\pi\)
0.136665 + 0.990617i \(0.456362\pi\)
\(54\) −6.78607 + 37.5759i −0.125668 + 0.695850i
\(55\) 3.85225 + 9.69124i 0.0700409 + 0.176204i
\(56\) 6.24131 + 18.7895i 0.111452 + 0.335527i
\(57\) 16.4561 49.4332i 0.288703 0.867250i
\(58\) −39.1891 + 39.1891i −0.675674 + 0.675674i
\(59\) 48.9876i 0.830298i 0.909754 + 0.415149i \(0.136270\pi\)
−0.909754 + 0.415149i \(0.863730\pi\)
\(60\) −29.9513 + 1.70882i −0.499188 + 0.0284804i
\(61\) 82.9406i 1.35968i −0.733360 0.679841i \(-0.762049\pi\)
0.733360 0.679841i \(-0.237951\pi\)
\(62\) −42.3954 42.3954i −0.683796 0.683796i
\(63\) 28.1599 + 56.3562i 0.446982 + 0.894543i
\(64\) 8.00000i 0.125000i
\(65\) 54.5124 + 23.5019i 0.838653 + 0.361567i
\(66\) 7.91334 3.96057i 0.119899 0.0600087i
\(67\) −54.8233 54.8233i −0.818258 0.818258i 0.167598 0.985855i \(-0.446399\pi\)
−0.985855 + 0.167598i \(0.946399\pi\)
\(68\) 9.93045 9.93045i 0.146036 0.146036i
\(69\) −11.7032 + 5.85736i −0.169611 + 0.0848893i
\(70\) −37.8880 + 31.8512i −0.541257 + 0.455017i
\(71\) 74.9745i 1.05598i −0.849251 0.527990i \(-0.822946\pi\)
0.849251 0.527990i \(-0.177054\pi\)
\(72\) 3.61987 + 25.1972i 0.0502760 + 0.349960i
\(73\) 75.1938 + 75.1938i 1.03005 + 1.03005i 0.999534 + 0.0305180i \(0.00971569\pi\)
0.0305180 + 0.999534i \(0.490284\pi\)
\(74\) 73.4928 0.993146
\(75\) −31.6289 68.0045i −0.421718 0.906727i
\(76\) 34.7336i 0.457021i
\(77\) 6.54314 13.0521i 0.0849758 0.169508i
\(78\) 15.9099 47.7924i 0.203973 0.612723i
\(79\) 3.61068i 0.0457048i −0.999739 0.0228524i \(-0.992725\pi\)
0.999739 0.0228524i \(-0.00727479\pi\)
\(80\) −18.5855 + 7.38771i −0.232319 + 0.0923464i
\(81\) 22.8026 + 77.7241i 0.281514 + 0.959557i
\(82\) 15.5827 15.5827i 0.190032 0.190032i
\(83\) −103.116 + 103.116i −1.24236 + 1.24236i −0.283341 + 0.959019i \(0.591443\pi\)
−0.959019 + 0.283341i \(0.908557\pi\)
\(84\) 29.6791 + 29.7179i 0.353322 + 0.353784i
\(85\) 32.2407 + 13.8999i 0.379303 + 0.163528i
\(86\) 45.6547i 0.530869i
\(87\) −37.1340 + 111.549i −0.426828 + 1.28217i
\(88\) 4.17152 4.17152i 0.0474036 0.0474036i
\(89\) 24.4427i 0.274637i 0.990527 + 0.137319i \(0.0438485\pi\)
−0.990527 + 0.137319i \(0.956152\pi\)
\(90\) −55.1950 + 31.6783i −0.613277 + 0.351981i
\(91\) −26.1984 78.8706i −0.287895 0.866710i
\(92\) −6.16934 + 6.16934i −0.0670580 + 0.0670580i
\(93\) −120.675 40.1722i −1.29758 0.431959i
\(94\) 66.8321 0.710980
\(95\) 80.6927 32.0752i 0.849397 0.337634i
\(96\) 7.59545 + 15.1759i 0.0791193 + 0.158083i
\(97\) −35.3616 + 35.3616i −0.364553 + 0.364553i −0.865486 0.500933i \(-0.832990\pi\)
0.500933 + 0.865486i \(0.332990\pi\)
\(98\) 68.5793 + 9.94368i 0.699789 + 0.101466i
\(99\) 11.2513 15.0264i 0.113649 0.151781i
\(100\) −34.3261 36.3554i −0.343261 0.363554i
\(101\) −12.9923 −0.128637 −0.0643184 0.997929i \(-0.520487\pi\)
−0.0643184 + 0.997929i \(0.520487\pi\)
\(102\) 9.40970 28.2663i 0.0922520 0.277120i
\(103\) 45.5816 + 45.5816i 0.442540 + 0.442540i 0.892865 0.450325i \(-0.148692\pi\)
−0.450325 + 0.892865i \(0.648692\pi\)
\(104\) 33.5807i 0.322891i
\(105\) −41.6327 + 96.3936i −0.396502 + 0.918034i
\(106\) 119.492 1.12728
\(107\) −49.5198 + 49.5198i −0.462802 + 0.462802i −0.899573 0.436771i \(-0.856122\pi\)
0.436771 + 0.899573i \(0.356122\pi\)
\(108\) 30.7898 + 44.3620i 0.285091 + 0.410759i
\(109\) 170.424i 1.56352i 0.623579 + 0.781760i \(0.285678\pi\)
−0.623579 + 0.781760i \(0.714322\pi\)
\(110\) 13.5435 + 5.83899i 0.123123 + 0.0530817i
\(111\) 139.415 69.7764i 1.25599 0.628616i
\(112\) 25.0308 + 12.5482i 0.223490 + 0.112038i
\(113\) −139.393 139.393i −1.23357 1.23357i −0.962583 0.270986i \(-0.912650\pi\)
−0.270986 0.962583i \(-0.587350\pi\)
\(114\) −32.9771 65.8893i −0.289273 0.577976i
\(115\) −20.0297 8.63538i −0.174171 0.0750903i
\(116\) 78.3781i 0.675674i
\(117\) −15.1947 105.767i −0.129869 0.903993i
\(118\) 48.9876 + 48.9876i 0.415149 + 0.415149i
\(119\) −15.4948 46.6471i −0.130208 0.391992i
\(120\) −28.2425 + 31.6601i −0.235354 + 0.263834i
\(121\) 116.650 0.964046
\(122\) −82.9406 82.9406i −0.679841 0.679841i
\(123\) 14.7655 44.3549i 0.120045 0.360609i
\(124\) −84.7907 −0.683796
\(125\) 52.7616 113.319i 0.422093 0.906553i
\(126\) 84.5161 + 28.1963i 0.670763 + 0.223780i
\(127\) −104.552 104.552i −0.823247 0.823247i 0.163325 0.986572i \(-0.447778\pi\)
−0.986572 + 0.163325i \(0.947778\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) −43.3460 86.6067i −0.336016 0.671370i
\(130\) 78.0143 31.0106i 0.600110 0.238543i
\(131\) 1.42804 0.0109011 0.00545054 0.999985i \(-0.498265\pi\)
0.00545054 + 0.999985i \(0.498265\pi\)
\(132\) 3.95277 11.8739i 0.0299452 0.0899539i
\(133\) −108.676 54.4805i −0.817115 0.409628i
\(134\) −109.647 −0.818258
\(135\) −74.6280 + 112.497i −0.552800 + 0.833314i
\(136\) 19.8609i 0.146036i
\(137\) −152.451 + 152.451i −1.11278 + 1.11278i −0.120010 + 0.992773i \(0.538293\pi\)
−0.992773 + 0.120010i \(0.961707\pi\)
\(138\) −5.84582 + 17.5605i −0.0423610 + 0.127250i
\(139\) 75.0255 0.539752 0.269876 0.962895i \(-0.413017\pi\)
0.269876 + 0.962895i \(0.413017\pi\)
\(140\) −6.03679 + 69.7392i −0.0431200 + 0.498137i
\(141\) 126.780 63.4525i 0.899149 0.450018i
\(142\) −74.9745 74.9745i −0.527990 0.527990i
\(143\) −17.5103 + 17.5103i −0.122450 + 0.122450i
\(144\) 28.8170 + 21.5773i 0.200118 + 0.149842i
\(145\) −182.087 + 72.3794i −1.25577 + 0.499168i
\(146\) 150.388 1.03005
\(147\) 139.535 46.2483i 0.949220 0.314614i
\(148\) 73.4928 73.4928i 0.496573 0.496573i
\(149\) −183.297 −1.23018 −0.615091 0.788456i \(-0.710881\pi\)
−0.615091 + 0.788456i \(0.710881\pi\)
\(150\) −99.6334 36.3757i −0.664223 0.242504i
\(151\) −203.889 −1.35026 −0.675130 0.737699i \(-0.735913\pi\)
−0.675130 + 0.737699i \(0.735913\pi\)
\(152\) −34.7336 34.7336i −0.228510 0.228510i
\(153\) −8.98674 62.5547i −0.0587369 0.408855i
\(154\) −6.50894 19.5952i −0.0422659 0.127242i
\(155\) −78.3012 196.985i −0.505169 1.27087i
\(156\) −31.8826 63.7023i −0.204375 0.408348i
\(157\) −3.36424 + 3.36424i −0.0214283 + 0.0214283i −0.717740 0.696311i \(-0.754823\pi\)
0.696311 + 0.717740i \(0.254823\pi\)
\(158\) −3.61068 3.61068i −0.0228524 0.0228524i
\(159\) 226.675 113.449i 1.42563 0.713518i
\(160\) −11.1978 + 25.9732i −0.0699863 + 0.162333i
\(161\) 9.62619 + 28.9797i 0.0597900 + 0.179998i
\(162\) 100.527 + 54.9215i 0.620536 + 0.339022i
\(163\) 105.247 105.247i 0.645690 0.645690i −0.306259 0.951948i \(-0.599077\pi\)
0.951948 + 0.306259i \(0.0990772\pi\)
\(164\) 31.1653i 0.190032i
\(165\) 31.2356 1.78210i 0.189307 0.0108006i
\(166\) 206.232i 1.24236i
\(167\) −34.3084 34.3084i −0.205439 0.205439i 0.596886 0.802326i \(-0.296404\pi\)
−0.802326 + 0.596886i \(0.796404\pi\)
\(168\) 59.3970 + 0.0387885i 0.353553 + 0.000230884i
\(169\) 28.0423i 0.165931i
\(170\) 46.1406 18.3408i 0.271416 0.107887i
\(171\) −125.115 93.6820i −0.731665 0.547848i
\(172\) −45.6547 45.6547i −0.265434 0.265434i
\(173\) −211.509 + 211.509i −1.22260 + 1.22260i −0.255891 + 0.966706i \(0.582369\pi\)
−0.966706 + 0.255891i \(0.917631\pi\)
\(174\) 74.4147 + 148.683i 0.427671 + 0.854499i
\(175\) −167.592 + 50.3770i −0.957670 + 0.287869i
\(176\) 8.34304i 0.0474036i
\(177\) 139.439 + 46.4187i 0.787793 + 0.262253i
\(178\) 24.4427 + 24.4427i 0.137319 + 0.137319i
\(179\) 110.880 0.619440 0.309720 0.950828i \(-0.399765\pi\)
0.309720 + 0.950828i \(0.399765\pi\)
\(180\) −23.5166 + 86.8733i −0.130648 + 0.482629i
\(181\) 24.2997i 0.134253i 0.997744 + 0.0671264i \(0.0213831\pi\)
−0.997744 + 0.0671264i \(0.978617\pi\)
\(182\) −105.069 52.6722i −0.577302 0.289407i
\(183\) −236.084 78.5913i −1.29008 0.429460i
\(184\) 12.3387i 0.0670580i
\(185\) 238.606 + 102.870i 1.28976 + 0.556053i
\(186\) −160.847 + 80.5030i −0.864771 + 0.432812i
\(187\) −10.3563 + 10.3563i −0.0553811 + 0.0553811i
\(188\) 66.8321 66.8321i 0.355490 0.355490i
\(189\) 187.097 26.7540i 0.989930 0.141556i
\(190\) 48.6175 112.768i 0.255882 0.593515i
\(191\) 163.399i 0.855494i −0.903898 0.427747i \(-0.859307\pi\)
0.903898 0.427747i \(-0.140693\pi\)
\(192\) 22.7714 + 7.58049i 0.118601 + 0.0394817i
\(193\) −36.3745 + 36.3745i −0.188469 + 0.188469i −0.795034 0.606565i \(-0.792547\pi\)
0.606565 + 0.795034i \(0.292547\pi\)
\(194\) 70.7233i 0.364553i
\(195\) 118.550 132.896i 0.607950 0.681518i
\(196\) 78.5230 58.6356i 0.400628 0.299161i
\(197\) 19.3286 19.3286i 0.0981145 0.0981145i −0.656346 0.754460i \(-0.727899\pi\)
0.754460 + 0.656346i \(0.227899\pi\)
\(198\) −3.77509 26.2776i −0.0190661 0.132715i
\(199\) 79.6378 0.400190 0.200095 0.979776i \(-0.435875\pi\)
0.200095 + 0.979776i \(0.435875\pi\)
\(200\) −70.6816 2.02930i −0.353408 0.0101465i
\(201\) −207.999 + 104.102i −1.03482 + 0.517920i
\(202\) −12.9923 + 12.9923i −0.0643184 + 0.0643184i
\(203\) 245.234 + 122.938i 1.20805 + 0.605607i
\(204\) −18.8566 37.6760i −0.0924341 0.184686i
\(205\) 72.4030 28.7801i 0.353185 0.140391i
\(206\) 91.1632 0.442540
\(207\) 5.58305 + 38.8624i 0.0269713 + 0.187741i
\(208\) −33.5807 33.5807i −0.161446 0.161446i
\(209\) 36.2230i 0.173316i
\(210\) 54.7608 + 138.026i 0.260766 + 0.657268i
\(211\) −146.466 −0.694152 −0.347076 0.937837i \(-0.612825\pi\)
−0.347076 + 0.937837i \(0.612825\pi\)
\(212\) 119.492 119.492i 0.563641 0.563641i
\(213\) −213.409 71.0429i −1.00192 0.333535i
\(214\) 99.0397i 0.462802i
\(215\) 63.9041 148.225i 0.297229 0.689419i
\(216\) 75.1518 + 13.5721i 0.347925 + 0.0628340i
\(217\) −132.996 + 265.298i −0.612887 + 1.22257i
\(218\) 170.424 + 170.424i 0.781760 + 0.781760i
\(219\) 285.284 142.783i 1.30267 0.651976i
\(220\) 19.3825 7.70450i 0.0881022 0.0350204i
\(221\) 83.3678i 0.377230i
\(222\) 69.6389 209.192i 0.313689 0.942305i
\(223\) −221.408 221.408i −0.992862 0.992862i 0.00711229 0.999975i \(-0.497736\pi\)
−0.999975 + 0.00711229i \(0.997736\pi\)
\(224\) 37.5790 12.4826i 0.167764 0.0557260i
\(225\) −223.540 + 25.5907i −0.993511 + 0.113737i
\(226\) −278.787 −1.23357
\(227\) 70.0030 + 70.0030i 0.308383 + 0.308383i 0.844282 0.535899i \(-0.180027\pi\)
−0.535899 + 0.844282i \(0.680027\pi\)
\(228\) −98.8665 32.9122i −0.433625 0.144352i
\(229\) −287.075 −1.25360 −0.626802 0.779178i \(-0.715637\pi\)
−0.626802 + 0.779178i \(0.715637\pi\)
\(230\) −28.6651 + 11.3943i −0.124631 + 0.0495405i
\(231\) −30.9517 30.9922i −0.133990 0.134165i
\(232\) 78.3781 + 78.3781i 0.337837 + 0.337837i
\(233\) 199.347 + 199.347i 0.855568 + 0.855568i 0.990812 0.135245i \(-0.0431820\pi\)
−0.135245 + 0.990812i \(0.543182\pi\)
\(234\) −120.962 90.5725i −0.516931 0.387062i
\(235\) 216.981 + 93.5467i 0.923323 + 0.398071i
\(236\) 97.9751 0.415149
\(237\) −10.2775 3.42134i −0.0433651 0.0144360i
\(238\) −62.1418 31.1523i −0.261100 0.130892i
\(239\) 46.3651 0.193996 0.0969982 0.995285i \(-0.469076\pi\)
0.0969982 + 0.995285i \(0.469076\pi\)
\(240\) 3.41764 + 59.9026i 0.0142402 + 0.249594i
\(241\) 65.3496i 0.271160i −0.990766 0.135580i \(-0.956710\pi\)
0.990766 0.135580i \(-0.0432898\pi\)
\(242\) 116.650 116.650i 0.482023 0.482023i
\(243\) 242.843 + 8.74241i 0.999353 + 0.0359770i
\(244\) −165.881 −0.679841
\(245\) 208.735 + 128.276i 0.851979 + 0.523575i
\(246\) −29.5893 59.1204i −0.120282 0.240327i
\(247\) 145.797 + 145.797i 0.590272 + 0.590272i
\(248\) −84.7907 + 84.7907i −0.341898 + 0.341898i
\(249\) 195.803 + 391.220i 0.786357 + 1.57116i
\(250\) −60.5574 166.081i −0.242230 0.664323i
\(251\) −139.437 −0.555525 −0.277763 0.960650i \(-0.589593\pi\)
−0.277763 + 0.960650i \(0.589593\pi\)
\(252\) 112.712 56.3198i 0.447271 0.223491i
\(253\) 6.43388 6.43388i 0.0254304 0.0254304i
\(254\) −209.105 −0.823247
\(255\) 70.1151 78.5998i 0.274961 0.308234i
\(256\) 16.0000 0.0625000
\(257\) 323.691 + 323.691i 1.25950 + 1.25950i 0.951332 + 0.308168i \(0.0997158\pi\)
0.308168 + 0.951332i \(0.400284\pi\)
\(258\) −129.953 43.2606i −0.503693 0.167677i
\(259\) −114.673 345.224i −0.442753 1.33291i
\(260\) 47.0038 109.025i 0.180784 0.419326i
\(261\) 282.328 + 211.398i 1.08172 + 0.809956i
\(262\) 1.42804 1.42804i 0.00545054 0.00545054i
\(263\) 137.531 + 137.531i 0.522933 + 0.522933i 0.918456 0.395523i \(-0.129437\pi\)
−0.395523 + 0.918456i \(0.629437\pi\)
\(264\) −7.92115 15.8267i −0.0300043 0.0599496i
\(265\) 387.949 + 167.256i 1.46396 + 0.631155i
\(266\) −163.157 + 54.1958i −0.613371 + 0.203744i
\(267\) 69.5744 + 23.1610i 0.260578 + 0.0867452i
\(268\) −109.647 + 109.647i −0.409129 + 0.409129i
\(269\) 391.957i 1.45709i −0.684998 0.728545i \(-0.740197\pi\)
0.684998 0.728545i \(-0.259803\pi\)
\(270\) 37.8693 + 187.125i 0.140257 + 0.693057i
\(271\) 327.322i 1.20783i 0.797049 + 0.603914i \(0.206393\pi\)
−0.797049 + 0.603914i \(0.793607\pi\)
\(272\) −19.8609 19.8609i −0.0730180 0.0730180i
\(273\) −249.324 0.162818i −0.913274 0.000596403i
\(274\) 304.902i 1.11278i
\(275\) 35.7980 + 37.9144i 0.130175 + 0.137870i
\(276\) 11.7147 + 23.4064i 0.0424447 + 0.0848057i
\(277\) 38.0116 + 38.0116i 0.137226 + 0.137226i 0.772383 0.635157i \(-0.219065\pi\)
−0.635157 + 0.772383i \(0.719065\pi\)
\(278\) 75.0255 75.0255i 0.269876 0.269876i
\(279\) −228.694 + 305.427i −0.819692 + 1.09472i
\(280\) 63.7024 + 75.7760i 0.227509 + 0.270629i
\(281\) 97.5907i 0.347298i 0.984808 + 0.173649i \(0.0555558\pi\)
−0.984808 + 0.173649i \(0.944444\pi\)
\(282\) 63.3275 190.233i 0.224566 0.674584i
\(283\) 394.549 + 394.549i 1.39417 + 1.39417i 0.815720 + 0.578447i \(0.196341\pi\)
0.578447 + 0.815720i \(0.303659\pi\)
\(284\) −149.949 −0.527990
\(285\) −14.8384 260.079i −0.0520645 0.912557i
\(286\) 35.0206i 0.122450i
\(287\) −97.5118 48.8836i −0.339762 0.170326i
\(288\) 50.3943 7.23975i 0.174980 0.0251380i
\(289\) 239.693i 0.829388i
\(290\) −109.708 + 254.467i −0.378303 + 0.877472i
\(291\) 67.1469 + 134.162i 0.230745 + 0.461036i
\(292\) 150.388 150.388i 0.515026 0.515026i
\(293\) −62.2388 + 62.2388i −0.212419 + 0.212419i −0.805294 0.592875i \(-0.797993\pi\)
0.592875 + 0.805294i \(0.297993\pi\)
\(294\) 93.2870 185.784i 0.317303 0.631917i
\(295\) 90.4765 + 227.615i 0.306700 + 0.771576i
\(296\) 146.986i 0.496573i
\(297\) −32.1101 46.2642i −0.108115 0.155772i
\(298\) −183.297 + 183.297i −0.615091 + 0.615091i
\(299\) 51.7926i 0.173220i
\(300\) −136.009 + 63.2577i −0.453363 + 0.210859i
\(301\) −214.458 + 71.2364i −0.712484 + 0.236666i
\(302\) −203.889 + 203.889i −0.675130 + 0.675130i
\(303\) −12.3110 + 36.9817i −0.0406304 + 0.122052i
\(304\) −69.4671 −0.228510
\(305\) −153.185 385.374i −0.502247 1.26352i
\(306\) −71.5415 53.5680i −0.233796 0.175059i
\(307\) −79.7547 + 79.7547i −0.259787 + 0.259787i −0.824967 0.565180i \(-0.808807\pi\)
0.565180 + 0.824967i \(0.308807\pi\)
\(308\) −26.1042 13.0863i −0.0847538 0.0424879i
\(309\) 172.936 86.5532i 0.559663 0.280107i
\(310\) −275.286 118.684i −0.888020 0.382851i
\(311\) −358.994 −1.15432 −0.577160 0.816631i \(-0.695839\pi\)
−0.577160 + 0.816631i \(0.695839\pi\)
\(312\) −95.5848 31.8197i −0.306362 0.101986i
\(313\) −309.220 309.220i −0.987922 0.987922i 0.0120057 0.999928i \(-0.496178\pi\)
−0.999928 + 0.0120057i \(0.996178\pi\)
\(314\) 6.72848i 0.0214283i
\(315\) 234.927 + 209.843i 0.745801 + 0.666169i
\(316\) −7.22137 −0.0228524
\(317\) 46.3542 46.3542i 0.146228 0.146228i −0.630203 0.776431i \(-0.717028\pi\)
0.776431 + 0.630203i \(0.217028\pi\)
\(318\) 113.226 340.125i 0.356056 1.06957i
\(319\) 81.7390i 0.256235i
\(320\) 14.7754 + 37.1710i 0.0461732 + 0.116160i
\(321\) 94.0314 + 187.877i 0.292933 + 0.585288i
\(322\) 38.6059 + 19.3535i 0.119894 + 0.0601041i
\(323\) 86.2300 + 86.2300i 0.266966 + 0.266966i
\(324\) 155.448 45.6053i 0.479779 0.140757i
\(325\) 296.692 + 8.51815i 0.912898 + 0.0262097i
\(326\) 210.495i 0.645690i
\(327\) 485.098 + 161.487i 1.48348 + 0.493844i
\(328\) −31.1653 31.1653i −0.0950162 0.0950162i
\(329\) −104.280 313.936i −0.316961 0.954213i
\(330\) 29.4535 33.0177i 0.0892531 0.100054i
\(331\) 373.528 1.12848 0.564242 0.825609i \(-0.309168\pi\)
0.564242 + 0.825609i \(0.309168\pi\)
\(332\) 206.232 + 206.232i 0.621180 + 0.621180i
\(333\) −66.5087 462.952i −0.199726 1.39025i
\(334\) −68.6168 −0.205439
\(335\) −355.984 153.475i −1.06264 0.458135i
\(336\) 59.4357 59.3582i 0.176892 0.176661i
\(337\) −163.577 163.577i −0.485392 0.485392i 0.421457 0.906848i \(-0.361519\pi\)
−0.906848 + 0.421457i \(0.861519\pi\)
\(338\) −28.0423 28.0423i −0.0829653 0.0829653i
\(339\) −528.856 + 264.689i −1.56005 + 0.780793i
\(340\) 27.7998 64.4815i 0.0817642 0.189651i
\(341\) 88.4266 0.259315
\(342\) −218.797 + 31.4328i −0.639757 + 0.0919087i
\(343\) −60.2970 337.659i −0.175793 0.984427i
\(344\) −91.3095 −0.265434
\(345\) −43.5593 + 48.8305i −0.126259 + 0.141538i
\(346\) 423.018i 1.22260i
\(347\) −231.964 + 231.964i −0.668483 + 0.668483i −0.957365 0.288882i \(-0.906716\pi\)
0.288882 + 0.957365i \(0.406716\pi\)
\(348\) 223.097 + 74.2681i 0.641085 + 0.213414i
\(349\) 143.315 0.410646 0.205323 0.978694i \(-0.434175\pi\)
0.205323 + 0.978694i \(0.434175\pi\)
\(350\) −117.215 + 217.969i −0.334901 + 0.622769i
\(351\) −315.456 56.9702i −0.898735 0.162308i
\(352\) −8.34304 8.34304i −0.0237018 0.0237018i
\(353\) 192.937 192.937i 0.546564 0.546564i −0.378881 0.925445i \(-0.623691\pi\)
0.925445 + 0.378881i \(0.123691\pi\)
\(354\) 185.858 93.0206i 0.525023 0.262770i
\(355\) −138.473 348.360i −0.390064 0.981296i
\(356\) 48.8855 0.137319
\(357\) −147.460 0.0962968i −0.413052 0.000269739i
\(358\) 110.880 110.880i 0.309720 0.309720i
\(359\) −424.811 −1.18332 −0.591659 0.806189i \(-0.701527\pi\)
−0.591659 + 0.806189i \(0.701527\pi\)
\(360\) 63.3566 + 110.390i 0.175991 + 0.306639i
\(361\) −59.3948 −0.164528
\(362\) 24.2997 + 24.2997i 0.0671264 + 0.0671264i
\(363\) 110.533 332.034i 0.304498 0.914695i
\(364\) −157.741 + 52.3969i −0.433355 + 0.143948i
\(365\) 488.257 + 210.502i 1.33769 + 0.576717i
\(366\) −314.675 + 157.493i −0.859769 + 0.430308i
\(367\) 395.856 395.856i 1.07863 1.07863i 0.0819951 0.996633i \(-0.473871\pi\)
0.996633 0.0819951i \(-0.0261292\pi\)
\(368\) 12.3387 + 12.3387i 0.0335290 + 0.0335290i
\(369\) −112.262 84.0579i −0.304232 0.227799i
\(370\) 341.476 135.736i 0.922907 0.366854i
\(371\) −186.447 561.299i −0.502552 1.51294i
\(372\) −80.3444 + 241.350i −0.215980 + 0.648791i
\(373\) 184.517 184.517i 0.494683 0.494683i −0.415095 0.909778i \(-0.636252\pi\)
0.909778 + 0.415095i \(0.136252\pi\)
\(374\) 20.7125i 0.0553811i
\(375\) −272.559 257.559i −0.726825 0.686823i
\(376\) 133.664i 0.355490i
\(377\) −328.999 328.999i −0.872676 0.872676i
\(378\) 160.343 213.851i 0.424187 0.565743i
\(379\) 127.438i 0.336249i −0.985766 0.168124i \(-0.946229\pi\)
0.985766 0.168124i \(-0.0537710\pi\)
\(380\) −64.1504 161.385i −0.168817 0.424698i
\(381\) −396.670 + 198.531i −1.04113 + 0.521078i
\(382\) −163.399 163.399i −0.427747 0.427747i
\(383\) 114.212 114.212i 0.298204 0.298204i −0.542106 0.840310i \(-0.682373\pi\)
0.840310 + 0.542106i \(0.182373\pi\)
\(384\) 30.3519 15.1909i 0.0790413 0.0395596i
\(385\) 6.29565 72.7296i 0.0163523 0.188908i
\(386\) 72.7491i 0.188469i
\(387\) −287.592 + 41.3161i −0.743133 + 0.106760i
\(388\) 70.7233 + 70.7233i 0.182277 + 0.182277i
\(389\) −365.324 −0.939136 −0.469568 0.882896i \(-0.655590\pi\)
−0.469568 + 0.882896i \(0.655590\pi\)
\(390\) −14.3459 251.446i −0.0367842 0.644734i
\(391\) 30.6321i 0.0783431i
\(392\) 19.8874 137.159i 0.0507330 0.349894i
\(393\) 1.35316 4.06481i 0.00344315 0.0103430i
\(394\) 38.6571i 0.0981145i
\(395\) −6.66867 16.7766i −0.0168827 0.0424724i
\(396\) −30.0527 22.5025i −0.0758907 0.0568245i
\(397\) 529.456 529.456i 1.33364 1.33364i 0.431554 0.902087i \(-0.357965\pi\)
0.902087 0.431554i \(-0.142035\pi\)
\(398\) 79.6378 79.6378i 0.200095 0.200095i
\(399\) −258.052 + 257.715i −0.646747 + 0.645903i
\(400\) −72.7109 + 68.6523i −0.181777 + 0.171631i
\(401\) 185.749i 0.463216i 0.972809 + 0.231608i \(0.0743986\pi\)
−0.972809 + 0.231608i \(0.925601\pi\)
\(402\) −103.897 + 312.101i −0.258450 + 0.776369i
\(403\) 355.916 355.916i 0.883167 0.883167i
\(404\) 25.9847i 0.0643184i
\(405\) 249.501 + 319.021i 0.616051 + 0.787706i
\(406\) 368.172 122.296i 0.906827 0.301221i
\(407\) −76.6442 + 76.6442i −0.188315 + 0.188315i
\(408\) −56.5325 18.8194i −0.138560 0.0461260i
\(409\) 615.554 1.50502 0.752511 0.658579i \(-0.228842\pi\)
0.752511 + 0.658579i \(0.228842\pi\)
\(410\) 43.6229 101.183i 0.106397 0.246788i
\(411\) 289.484 + 578.397i 0.704340 + 1.40729i
\(412\) 91.1632 91.1632i 0.221270 0.221270i
\(413\) 153.676 306.550i 0.372098 0.742251i
\(414\) 44.4455 + 33.2794i 0.107356 + 0.0803850i
\(415\) −288.668 + 669.563i −0.695586 + 1.61341i
\(416\) −67.1614 −0.161446
\(417\) 71.0913 213.554i 0.170483 0.512121i
\(418\) 36.2230 + 36.2230i 0.0866578 + 0.0866578i
\(419\) 427.623i 1.02058i 0.860002 + 0.510290i \(0.170462\pi\)
−0.860002 + 0.510290i \(0.829538\pi\)
\(420\) 192.787 + 83.2654i 0.459017 + 0.198251i
\(421\) −294.683 −0.699959 −0.349980 0.936757i \(-0.613811\pi\)
−0.349980 + 0.936757i \(0.613811\pi\)
\(422\) −146.466 + 146.466i −0.347076 + 0.347076i
\(423\) −60.4810 420.995i −0.142981 0.995260i
\(424\) 238.984i 0.563641i
\(425\) 175.475 + 5.03796i 0.412882 + 0.0118540i
\(426\) −284.452 + 142.366i −0.667728 + 0.334193i
\(427\) −260.189 + 519.018i −0.609342 + 1.21550i
\(428\) 99.0397 + 99.0397i 0.231401 + 0.231401i
\(429\) 33.2497 + 66.4339i 0.0775051 + 0.154857i
\(430\) −84.3210 212.129i −0.196095 0.493324i
\(431\) 735.135i 1.70565i −0.522197 0.852825i \(-0.674887\pi\)
0.522197 0.852825i \(-0.325113\pi\)
\(432\) 88.7240 61.5797i 0.205380 0.142546i
\(433\) −6.15401 6.15401i −0.0142125 0.0142125i 0.699965 0.714177i \(-0.253199\pi\)
−0.714177 + 0.699965i \(0.753199\pi\)
\(434\) 132.301 + 398.294i 0.304842 + 0.917729i
\(435\) 33.4836 + 586.882i 0.0769738 + 1.34915i
\(436\) 340.847 0.781760
\(437\) −53.5708 53.5708i −0.122588 0.122588i
\(438\) 142.501 428.067i 0.325346 0.977322i
\(439\) −701.728 −1.59847 −0.799235 0.601019i \(-0.794761\pi\)
−0.799235 + 0.601019i \(0.794761\pi\)
\(440\) 11.6780 27.0870i 0.0265409 0.0615613i
\(441\) 0.575980 441.000i 0.00130608 0.999999i
\(442\) 83.3678 + 83.3678i 0.188615 + 0.188615i
\(443\) 176.482 + 176.482i 0.398379 + 0.398379i 0.877661 0.479282i \(-0.159103\pi\)
−0.479282 + 0.877661i \(0.659103\pi\)
\(444\) −139.553 278.831i −0.314308 0.627997i
\(445\) 45.1440 + 113.570i 0.101447 + 0.255214i
\(446\) −442.817 −0.992862
\(447\) −173.685 + 521.741i −0.388557 + 1.16721i
\(448\) 25.0964 50.0617i 0.0560188 0.111745i
\(449\) 521.716 1.16195 0.580976 0.813921i \(-0.302671\pi\)
0.580976 + 0.813921i \(0.302671\pi\)
\(450\) −197.949 + 249.131i −0.439887 + 0.553624i
\(451\) 32.5017i 0.0720659i
\(452\) −278.787 + 278.787i −0.616785 + 0.616785i
\(453\) −193.198 + 580.355i −0.426485 + 1.28114i
\(454\) 140.006 0.308383
\(455\) −267.396 318.076i −0.587684 0.699069i
\(456\) −131.779 + 65.9543i −0.288988 + 0.144637i
\(457\) 34.8065 + 34.8065i 0.0761631 + 0.0761631i 0.744162 0.667999i \(-0.232849\pi\)
−0.667999 + 0.744162i \(0.732849\pi\)
\(458\) −287.075 + 287.075i −0.626802 + 0.626802i
\(459\) −186.573 33.6944i −0.406477 0.0734082i
\(460\) −17.2708 + 40.0594i −0.0375451 + 0.0870857i
\(461\) 747.746 1.62201 0.811005 0.585040i \(-0.198921\pi\)
0.811005 + 0.585040i \(0.198921\pi\)
\(462\) −61.9439 0.0404518i −0.134078 8.75580e-5i
\(463\) −629.053 + 629.053i −1.35865 + 1.35865i −0.483055 + 0.875590i \(0.660473\pi\)
−0.875590 + 0.483055i \(0.839527\pi\)
\(464\) 156.756 0.337837
\(465\) −634.898 + 36.2231i −1.36537 + 0.0778991i
\(466\) 398.695 0.855568
\(467\) −72.4294 72.4294i −0.155095 0.155095i 0.625294 0.780389i \(-0.284979\pi\)
−0.780389 + 0.625294i \(0.784979\pi\)
\(468\) −211.534 + 30.3894i −0.451997 + 0.0649347i
\(469\) 171.085 + 515.051i 0.364786 + 1.09819i
\(470\) 310.528 123.434i 0.660697 0.262626i
\(471\) 6.38823 + 12.7639i 0.0135631 + 0.0270995i
\(472\) 97.9751 97.9751i 0.207574 0.207574i
\(473\) 47.6124 + 47.6124i 0.100660 + 0.100660i
\(474\) −13.6989 + 6.85619i −0.0289006 + 0.0144645i
\(475\) 315.688 298.067i 0.664607 0.627510i
\(476\) −93.2942 + 30.9895i −0.195996 + 0.0651040i
\(477\) −108.136 752.714i −0.226701 1.57802i
\(478\) 46.3651 46.3651i 0.0969982 0.0969982i
\(479\) 49.3199i 0.102964i −0.998674 0.0514822i \(-0.983605\pi\)
0.998674 0.0514822i \(-0.0163945\pi\)
\(480\) 63.3202 + 56.4849i 0.131917 + 0.117677i
\(481\) 616.985i 1.28271i
\(482\) −65.3496 65.3496i −0.135580 0.135580i
\(483\) 91.6100 + 0.0598249i 0.189669 + 0.000123861i
\(484\) 233.299i 0.482023i
\(485\) −98.9933 + 229.614i −0.204110 + 0.473431i
\(486\) 251.585 234.100i 0.517665 0.481688i
\(487\) 83.8584 + 83.8584i 0.172194 + 0.172194i 0.787943 0.615749i \(-0.211146\pi\)
−0.615749 + 0.787943i \(0.711146\pi\)
\(488\) −165.881 + 165.881i −0.339920 + 0.339920i
\(489\) −199.850 399.307i −0.408692 0.816579i
\(490\) 337.011 80.4590i 0.687777 0.164202i
\(491\) 655.752i 1.33554i 0.744366 + 0.667771i \(0.232752\pi\)
−0.744366 + 0.667771i \(0.767248\pi\)
\(492\) −88.7097 29.5310i −0.180304 0.0600225i
\(493\) −194.583 194.583i −0.394691 0.394691i
\(494\) 291.594 0.590272
\(495\) 24.5250 90.5984i 0.0495455 0.183027i
\(496\) 169.581i 0.341898i
\(497\) −235.199 + 469.169i −0.473237 + 0.944002i
\(498\) 587.023 + 195.417i 1.17876 + 0.392404i
\(499\) 433.348i 0.868433i 0.900809 + 0.434216i \(0.142975\pi\)
−0.900809 + 0.434216i \(0.857025\pi\)
\(500\) −226.638 105.523i −0.453276 0.211047i
\(501\) −130.165 + 65.1469i −0.259811 + 0.130034i
\(502\) −139.437 + 139.437i −0.277763 + 0.277763i
\(503\) −147.463 + 147.463i −0.293167 + 0.293167i −0.838330 0.545163i \(-0.816468\pi\)
0.545163 + 0.838330i \(0.316468\pi\)
\(504\) 56.3926 169.032i 0.111890 0.335381i
\(505\) −60.3673 + 23.9959i −0.119539 + 0.0475166i
\(506\) 12.8678i 0.0254304i
\(507\) −79.8201 26.5717i −0.157436 0.0524098i
\(508\) −209.105 + 209.105i −0.411623 + 0.411623i
\(509\) 554.834i 1.09005i −0.838421 0.545024i \(-0.816521\pi\)
0.838421 0.545024i \(-0.183479\pi\)
\(510\) −8.48468 148.715i −0.0166366 0.291598i
\(511\) −234.654 706.428i −0.459206 1.38244i
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) −385.213 + 267.360i −0.750902 + 0.521170i
\(514\) 647.383 1.25950
\(515\) 295.975 + 127.604i 0.574709 + 0.247774i
\(516\) −173.213 + 86.6921i −0.335685 + 0.168008i
\(517\) −69.6979 + 69.6979i −0.134812 + 0.134812i
\(518\) −459.897 230.551i −0.887831 0.445079i
\(519\) 401.627 + 802.463i 0.773848 + 1.54617i
\(520\) −62.0211 156.029i −0.119271 0.300055i
\(521\) 3.73694 0.00717263 0.00358632 0.999994i \(-0.498858\pi\)
0.00358632 + 0.999994i \(0.498858\pi\)
\(522\) 493.727 70.9297i 0.945836 0.135881i
\(523\) 638.273 + 638.273i 1.22041 + 1.22041i 0.967487 + 0.252921i \(0.0813912\pi\)
0.252921 + 0.967487i \(0.418609\pi\)
\(524\) 2.85608i 0.00545054i
\(525\) −15.4095 + 524.774i −0.0293514 + 0.999569i
\(526\) 275.063 0.522933
\(527\) 210.502 210.502i 0.399435 0.399435i
\(528\) −23.7478 7.90554i −0.0449770 0.0149726i
\(529\) 509.970i 0.964026i
\(530\) 555.205 220.693i 1.04756 0.416402i
\(531\) 264.255 352.919i 0.497655 0.664631i
\(532\) −108.961 + 217.353i −0.204814 + 0.408557i
\(533\) 130.819 + 130.819i 0.245439 + 0.245439i
\(534\) 92.7354 46.4134i 0.173662 0.0869165i
\(535\) −138.628 + 321.548i −0.259119 + 0.601024i
\(536\) 219.293i 0.409129i
\(537\) 105.065 315.611i 0.195652 0.587730i
\(538\) −391.957 391.957i −0.728545 0.728545i
\(539\) −81.8901 + 61.1499i −0.151930 + 0.113451i
\(540\) 224.995 + 149.256i 0.416657 + 0.276400i
\(541\) −967.493 −1.78834 −0.894171 0.447725i \(-0.852234\pi\)
−0.894171 + 0.447725i \(0.852234\pi\)
\(542\) 327.322 + 327.322i 0.603914 + 0.603914i
\(543\) 69.1674 + 23.0255i 0.127380 + 0.0424042i
\(544\) −39.7218 −0.0730180
\(545\) 314.760 + 791.854i 0.577542 + 1.45294i
\(546\) −249.487 + 249.161i −0.456935 + 0.456339i
\(547\) 400.474 + 400.474i 0.732129 + 0.732129i 0.971041 0.238913i \(-0.0767909\pi\)
−0.238913 + 0.971041i \(0.576791\pi\)
\(548\) 304.902 + 304.902i 0.556391 + 0.556391i
\(549\) −447.408 + 597.525i −0.814951 + 1.08839i
\(550\) 73.7124 + 2.11631i 0.134023 + 0.00384784i
\(551\) −680.588 −1.23519
\(552\) 35.1211 + 11.6916i 0.0636252 + 0.0211805i
\(553\) −11.3269 + 22.5946i −0.0204826 + 0.0408582i
\(554\) 76.0232 0.137226
\(555\) 518.905 581.698i 0.934963 1.04810i
\(556\) 150.051i 0.269876i
\(557\) 545.370 545.370i 0.979121 0.979121i −0.0206659 0.999786i \(-0.506579\pi\)
0.999786 + 0.0206659i \(0.00657863\pi\)
\(558\) 76.7329 + 534.121i 0.137514 + 0.957207i
\(559\) 383.279 0.685652
\(560\) 139.478 + 12.0736i 0.249069 + 0.0215600i
\(561\) 19.6651 + 39.2915i 0.0350537 + 0.0700383i
\(562\) 97.5907 + 97.5907i 0.173649 + 0.173649i
\(563\) 575.914 575.914i 1.02294 1.02294i 0.0232074 0.999731i \(-0.492612\pi\)
0.999731 0.0232074i \(-0.00738780\pi\)
\(564\) −126.905 253.560i −0.225009 0.449575i
\(565\) −905.124 390.225i −1.60199 0.690664i
\(566\) 789.098 1.39417
\(567\) 101.132 557.908i 0.178364 0.983965i
\(568\) −149.949 + 149.949i −0.263995 + 0.263995i
\(569\) 524.362 0.921549 0.460775 0.887517i \(-0.347572\pi\)
0.460775 + 0.887517i \(0.347572\pi\)
\(570\) −274.917 245.240i −0.482311 0.430246i
\(571\) 607.181 1.06337 0.531683 0.846944i \(-0.321560\pi\)
0.531683 + 0.846944i \(0.321560\pi\)
\(572\) 35.0206 + 35.0206i 0.0612249 + 0.0612249i
\(573\) −465.104 154.831i −0.811700 0.270211i
\(574\) −146.395 + 48.6281i −0.255044 + 0.0847180i
\(575\) −109.015 3.12986i −0.189591 0.00544323i
\(576\) 43.1546 57.6341i 0.0749211 0.100059i
\(577\) 274.550 274.550i 0.475823 0.475823i −0.427970 0.903793i \(-0.640771\pi\)
0.903793 + 0.427970i \(0.140771\pi\)
\(578\) −239.693 239.693i −0.414694 0.414694i
\(579\) 69.0702 + 138.004i 0.119292 + 0.238350i
\(580\) 144.759 + 364.175i 0.249584 + 0.627887i
\(581\) 968.749 321.789i 1.66738 0.553854i
\(582\) 201.308 + 67.0146i 0.345891 + 0.115145i
\(583\) −124.616 + 124.616i −0.213749 + 0.213749i
\(584\) 300.775i 0.515026i
\(585\) −265.945 463.371i −0.454607 0.792087i
\(586\) 124.478i 0.212419i
\(587\) −504.649 504.649i −0.859709 0.859709i 0.131595 0.991304i \(-0.457990\pi\)
−0.991304 + 0.131595i \(0.957990\pi\)
\(588\) −92.4966 279.071i −0.157307 0.474610i
\(589\) 736.271i 1.25004i
\(590\) 318.091 + 137.138i 0.539138 + 0.232438i
\(591\) −36.7023 73.3322i −0.0621020 0.124082i
\(592\) −146.986 146.986i −0.248287 0.248287i
\(593\) −615.151 + 615.151i −1.03735 + 1.03735i −0.0380802 + 0.999275i \(0.512124\pi\)
−0.999275 + 0.0380802i \(0.987876\pi\)
\(594\) −78.3743 14.1541i −0.131943 0.0238285i
\(595\) −158.148 188.122i −0.265796 0.316172i
\(596\) 366.594i 0.615091i
\(597\) 75.4617 226.683i 0.126401 0.379703i
\(598\) −51.7926 51.7926i −0.0866098 0.0866098i
\(599\) −103.401 −0.172623 −0.0863115 0.996268i \(-0.527508\pi\)
−0.0863115 + 0.996268i \(0.527508\pi\)
\(600\) −72.7513 + 199.267i −0.121252 + 0.332111i
\(601\) 994.271i 1.65436i −0.561936 0.827180i \(-0.689943\pi\)
0.561936 0.827180i \(-0.310057\pi\)
\(602\) −143.221 + 285.694i −0.237909 + 0.474575i
\(603\) 99.2266 + 690.695i 0.164555 + 1.14543i
\(604\) 407.779i 0.675130i
\(605\) 541.999 215.443i 0.895865 0.356105i
\(606\) 24.6706 + 49.2927i 0.0407106 + 0.0813411i
\(607\) 54.5368 54.5368i 0.0898464 0.0898464i −0.660755 0.750602i \(-0.729764\pi\)
0.750602 + 0.660755i \(0.229764\pi\)
\(608\) −69.4671 + 69.4671i −0.114255 + 0.114255i
\(609\) 582.308 581.548i 0.956171 0.954923i
\(610\) −538.559 232.188i −0.882883 0.380636i
\(611\) 561.067i 0.918277i
\(612\) −125.109 + 17.9735i −0.204427 + 0.0293684i
\(613\) 23.2311 23.2311i 0.0378975 0.0378975i −0.687904 0.725802i \(-0.741469\pi\)
0.725802 + 0.687904i \(0.241469\pi\)
\(614\) 159.509i 0.259787i
\(615\) −13.3140 233.360i −0.0216488 0.379448i
\(616\) −39.1904 + 13.0179i −0.0636208 + 0.0211329i
\(617\) 37.9474 37.9474i 0.0615032 0.0615032i −0.675686 0.737189i \(-0.736153\pi\)
0.737189 + 0.675686i \(0.236153\pi\)
\(618\) 86.3827 259.489i 0.139778 0.419885i
\(619\) −182.389 −0.294651 −0.147326 0.989088i \(-0.547067\pi\)
−0.147326 + 0.989088i \(0.547067\pi\)
\(620\) −393.970 + 156.602i −0.635436 + 0.252585i
\(621\) 115.909 + 20.9328i 0.186649 + 0.0337082i
\(622\) −358.994 + 358.994i −0.577160 + 0.577160i
\(623\) 76.6781 152.955i 0.123079 0.245514i
\(624\) −127.405 + 63.7651i −0.204174 + 0.102188i
\(625\) 35.8585 623.970i 0.0573736 0.998353i
\(626\) −618.439 −0.987922
\(627\) 103.106 + 34.3235i 0.164443 + 0.0547423i
\(628\) 6.72848 + 6.72848i 0.0107141 + 0.0107141i
\(629\) 364.908i 0.580140i
\(630\) 444.770 25.0843i 0.705985 0.0398163i
\(631\) 165.153 0.261732 0.130866 0.991400i \(-0.458224\pi\)
0.130866 + 0.991400i \(0.458224\pi\)
\(632\) −7.22137 + 7.22137i −0.0114262 + 0.0114262i
\(633\) −138.785 + 416.904i −0.219250 + 0.658617i
\(634\) 92.7084i 0.146228i
\(635\) −678.891 292.689i −1.06912 0.460928i
\(636\) −226.899 453.351i −0.356759 0.712815i
\(637\) −83.4789 + 575.735i −0.131050 + 0.903823i
\(638\) −81.7390 81.7390i −0.128118 0.128118i
\(639\) −404.437 + 540.136i −0.632921 + 0.845283i
\(640\) 51.9465 + 22.3956i 0.0811664 + 0.0349932i
\(641\) 168.644i 0.263095i −0.991310 0.131548i \(-0.958005\pi\)
0.991310 0.131548i \(-0.0419946\pi\)
\(642\) 281.909 + 93.8461i 0.439110 + 0.146178i
\(643\) −25.2955 25.2955i −0.0393398 0.0393398i 0.687163 0.726503i \(-0.258856\pi\)
−0.726503 + 0.687163i \(0.758856\pi\)
\(644\) 57.9594 19.2524i 0.0899991 0.0298950i
\(645\) −361.359 322.351i −0.560246 0.499768i
\(646\) 172.460 0.266966
\(647\) 11.1919 + 11.1919i 0.0172981 + 0.0172981i 0.715703 0.698405i \(-0.246106\pi\)
−0.698405 + 0.715703i \(0.746106\pi\)
\(648\) 109.843 201.054i 0.169511 0.310268i
\(649\) −102.176 −0.157437
\(650\) 305.210 288.174i 0.469554 0.443344i
\(651\) 629.128 + 629.950i 0.966402 + 0.967665i
\(652\) −210.495 210.495i −0.322845 0.322845i
\(653\) −319.932 319.932i −0.489941 0.489941i 0.418346 0.908288i \(-0.362610\pi\)
−0.908288 + 0.418346i \(0.862610\pi\)
\(654\) 646.585 323.611i 0.988662 0.494818i
\(655\) 6.63522 2.63749i 0.0101301 0.00402670i
\(656\) −62.3307 −0.0950162
\(657\) −136.096 947.335i −0.207148 1.44191i
\(658\) −418.216 209.656i −0.635587 0.318626i
\(659\) −692.273 −1.05049 −0.525245 0.850951i \(-0.676026\pi\)
−0.525245 + 0.850951i \(0.676026\pi\)
\(660\) −3.56419 62.4712i −0.00540029 0.0946534i
\(661\) 586.898i 0.887894i 0.896053 + 0.443947i \(0.146422\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(662\) 373.528 373.528i 0.564242 0.564242i
\(663\) 237.300 + 78.9961i 0.357919 + 0.119149i
\(664\) 412.464 0.621180
\(665\) −605.573 52.4199i −0.910636 0.0788268i
\(666\) −529.461 396.444i −0.794987 0.595261i
\(667\) 120.885 + 120.885i 0.181237 + 0.181237i
\(668\) −68.6168 + 68.6168i −0.102720 + 0.102720i
\(669\) −840.020 + 420.424i −1.25563 + 0.628437i
\(670\) −509.460 + 202.509i −0.760387 + 0.302253i
\(671\) 172.994 0.257815
\(672\) 0.0775770 118.794i 0.000115442 0.176777i
\(673\) 419.099 419.099i 0.622732 0.622732i −0.323497 0.946229i \(-0.604859\pi\)
0.946229 + 0.323497i \(0.104859\pi\)
\(674\) −327.154 −0.485392
\(675\) −138.976 + 660.538i −0.205890 + 0.978575i
\(676\) −56.0845 −0.0829653
\(677\) −459.724 459.724i −0.679061 0.679061i 0.280727 0.959788i \(-0.409425\pi\)
−0.959788 + 0.280727i \(0.909425\pi\)
\(678\) −264.167 + 793.545i −0.389627 + 1.17042i
\(679\) 332.214 110.352i 0.489270 0.162521i
\(680\) −36.6816 92.2813i −0.0539436 0.135708i
\(681\) 265.590 132.926i 0.390000 0.195192i
\(682\) 88.4266 88.4266i 0.129658 0.129658i
\(683\) 66.6626 + 66.6626i 0.0976027 + 0.0976027i 0.754222 0.656619i \(-0.228014\pi\)
−0.656619 + 0.754222i \(0.728014\pi\)
\(684\) −187.364 + 250.230i −0.273924 + 0.365833i
\(685\) −426.780 + 989.913i −0.623036 + 1.44513i
\(686\) −397.956 277.361i −0.580110 0.404317i
\(687\) −272.021 + 817.138i −0.395956 + 1.18943i
\(688\) −91.3095 + 91.3095i −0.132717 + 0.132717i
\(689\) 1003.16i 1.45596i
\(690\) 5.27115 + 92.3898i 0.00763935 + 0.133898i
\(691\) 11.4526i 0.0165739i 0.999966 + 0.00828695i \(0.00263785\pi\)
−0.999966 + 0.00828695i \(0.997362\pi\)
\(692\) 423.018 + 423.018i 0.611298 + 0.611298i
\(693\) −117.546 + 58.7348i −0.169618 + 0.0847543i
\(694\) 463.927i 0.668483i
\(695\) 348.597 138.567i 0.501579 0.199377i
\(696\) 297.365 148.829i 0.427249 0.213835i
\(697\) 77.3714 + 77.3714i 0.111006 + 0.111006i
\(698\) 143.315 143.315i 0.205323 0.205323i
\(699\) 756.321 378.533i 1.08200 0.541535i
\(700\) 100.754 + 335.184i 0.143934 + 0.478835i
\(701\) 635.231i 0.906178i 0.891465 + 0.453089i \(0.149678\pi\)
−0.891465 + 0.453089i \(0.850322\pi\)
\(702\) −372.426 + 258.486i −0.530522 + 0.368214i
\(703\) 638.167 + 638.167i 0.907777 + 0.907777i
\(704\) −16.6861 −0.0237018
\(705\) 471.876 528.978i 0.669328 0.750324i
\(706\) 385.875i 0.546564i
\(707\) 81.3022 + 40.7576i 0.114996 + 0.0576486i
\(708\) 92.8374 278.879i 0.131126 0.393896i
\(709\) 68.9098i 0.0971930i 0.998818 + 0.0485965i \(0.0154748\pi\)
−0.998818 + 0.0485965i \(0.984525\pi\)
\(710\) −486.833 209.888i −0.685680 0.295616i
\(711\) −19.4772 + 26.0123i −0.0273941 + 0.0365855i
\(712\) 48.8855 48.8855i 0.0686594 0.0686594i
\(713\) −130.776 + 130.776i −0.183416 + 0.183416i
\(714\) −147.556 + 147.363i −0.206661 + 0.206391i
\(715\) −49.0193 + 113.700i −0.0685584 + 0.159021i
\(716\) 221.760i 0.309720i
\(717\) 43.9338 131.975i 0.0612745 0.184065i
\(718\) −424.811 + 424.811i −0.591659 + 0.591659i
\(719\) 457.334i 0.636069i −0.948079 0.318034i \(-0.896977\pi\)
0.948079 0.318034i \(-0.103023\pi\)
\(720\) 173.747 + 47.0333i 0.241315 + 0.0653240i
\(721\) −142.245 428.228i −0.197288 0.593936i
\(722\) −59.3948 + 59.3948i −0.0822642 + 0.0822642i
\(723\) −186.013 61.9228i −0.257279 0.0856470i
\(724\) 48.5995 0.0671264
\(725\) −712.368 + 672.605i −0.982576 + 0.927730i
\(726\) −221.502 442.567i −0.305099 0.609596i
\(727\) −990.753 + 990.753i −1.36280 + 1.36280i −0.492464 + 0.870333i \(0.663904\pi\)
−0.870333 + 0.492464i \(0.836096\pi\)
\(728\) −105.344 + 210.138i −0.144704 + 0.288651i
\(729\) 254.993 682.949i 0.349784 0.936830i
\(730\) 698.758 277.755i 0.957203 0.380486i
\(731\) 226.686 0.310104
\(732\) −157.183 + 472.168i −0.214730 + 0.645038i
\(733\) 443.025 + 443.025i 0.604400 + 0.604400i 0.941477 0.337077i \(-0.109438\pi\)
−0.337077 + 0.941477i \(0.609438\pi\)
\(734\) 791.713i 1.07863i
\(735\) 562.917 472.599i 0.765873 0.642992i
\(736\) 24.6773 0.0335290
\(737\) 114.348 114.348i 0.155154 0.155154i
\(738\) −196.319 + 28.2036i −0.266015 + 0.0382163i
\(739\) 1424.55i 1.92768i −0.266488 0.963838i \(-0.585863\pi\)
0.266488 0.963838i \(-0.414137\pi\)
\(740\) 205.740 477.212i 0.278027 0.644880i
\(741\) 553.152 276.849i 0.746494 0.373615i
\(742\) −747.746 374.852i −1.00774 0.505192i
\(743\) −823.562 823.562i −1.10843 1.10843i −0.993357 0.115071i \(-0.963291\pi\)
−0.115071 0.993357i \(-0.536709\pi\)
\(744\) 161.006 + 321.695i 0.216406 + 0.432385i
\(745\) −851.668 + 338.536i −1.14318 + 0.454411i
\(746\) 369.034i 0.494683i
\(747\) 1299.11 186.633i 1.73911 0.249844i
\(748\) 20.7125 + 20.7125i 0.0276905 + 0.0276905i
\(749\) 465.227 154.534i 0.621131 0.206321i
\(750\) −530.118 + 15.0005i −0.706824 + 0.0200007i
\(751\) −436.270 −0.580919 −0.290459 0.956887i \(-0.593808\pi\)
−0.290459 + 0.956887i \(0.593808\pi\)
\(752\) −133.664 133.664i −0.177745 0.177745i
\(753\) −132.125 + 396.896i −0.175465 + 0.527087i
\(754\) −657.998 −0.872676
\(755\) −947.348 + 376.569i −1.25476 + 0.498767i
\(756\) −53.5080 374.194i −0.0707778 0.494965i
\(757\) 39.6428 + 39.6428i 0.0523684 + 0.0523684i 0.732806 0.680438i \(-0.238210\pi\)
−0.680438 + 0.732806i \(0.738210\pi\)
\(758\) −127.438 127.438i −0.168124 0.168124i
\(759\) −12.2171 24.4100i −0.0160962 0.0321608i
\(760\) −225.536 97.2350i −0.296758 0.127941i
\(761\) 1032.38 1.35661 0.678307 0.734778i \(-0.262714\pi\)
0.678307 + 0.734778i \(0.262714\pi\)
\(762\) −198.139 + 595.201i −0.260026 + 0.781103i
\(763\) 534.628 1066.46i 0.700692 1.39772i
\(764\) −326.799 −0.427747
\(765\) −157.290 274.055i −0.205608 0.358242i
\(766\) 228.424i 0.298204i
\(767\) −411.259 + 411.259i −0.536191 + 0.536191i
\(768\) 15.1610 45.5428i 0.0197409 0.0593005i
\(769\) 119.034 0.154791 0.0773956 0.997000i \(-0.475340\pi\)
0.0773956 + 0.997000i \(0.475340\pi\)
\(770\) −66.4340 79.0253i −0.0862779 0.102630i
\(771\) 1228.08 614.646i 1.59284 0.797206i
\(772\) 72.7491 + 72.7491i 0.0942345 + 0.0942345i
\(773\) −386.934 + 386.934i −0.500562 + 0.500562i −0.911612 0.411051i \(-0.865162\pi\)
0.411051 + 0.911612i \(0.365162\pi\)
\(774\) −246.276 + 328.908i −0.318186 + 0.424946i
\(775\) −727.634 770.651i −0.938883 0.994388i
\(776\) 141.447 0.182277
\(777\) −1091.31 0.712669i −1.40452 0.000917206i
\(778\) −365.324 + 365.324i −0.469568 + 0.469568i
\(779\) 270.621 0.347395
\(780\) −265.792 237.100i −0.340759 0.303975i
\(781\) 156.379 0.200229
\(782\) −30.6321 30.6321i −0.0391715 0.0391715i
\(783\) 869.253 603.313i 1.11016 0.770514i
\(784\) −117.271 157.046i −0.149581 0.200314i
\(785\) −9.41804 + 21.8451i −0.0119975 + 0.0278281i
\(786\) −2.71165 5.41797i −0.00344994 0.00689309i
\(787\) −111.605 + 111.605i −0.141810 + 0.141810i −0.774448 0.632638i \(-0.781972\pi\)
0.632638 + 0.774448i \(0.281972\pi\)
\(788\) −38.6571 38.6571i −0.0490572 0.0490572i
\(789\) 521.792 261.153i 0.661333 0.330993i
\(790\) −23.4453 10.1079i −0.0296776 0.0127949i
\(791\) 434.999 + 1309.57i 0.549935 + 1.65558i
\(792\) −52.5552 + 7.55019i −0.0663576 + 0.00953307i
\(793\) 696.300 696.300i 0.878058 0.878058i
\(794\) 1058.91i 1.33364i
\(795\) 843.687 945.782i 1.06124 1.18966i
\(796\) 159.276i 0.200095i
\(797\) −80.8641 80.8641i −0.101461 0.101461i 0.654554 0.756015i \(-0.272856\pi\)
−0.756015 + 0.654554i \(0.772856\pi\)
\(798\) −0.336816 + 515.767i −0.000422075 + 0.646325i
\(799\) 331.837i 0.415315i
\(800\) −4.05860 + 141.363i −0.00507324 + 0.176704i
\(801\) 131.852 176.092i 0.164609 0.219840i
\(802\) 185.749 + 185.749i 0.231608 + 0.231608i
\(803\) −156.836 + 156.836i −0.195313 + 0.195313i
\(804\) 208.204 + 415.997i 0.258960 + 0.517410i
\(805\) 98.2504 + 116.872i 0.122050 + 0.145183i
\(806\) 711.833i 0.883167i
\(807\) −1115.68 371.403i −1.38250 0.460227i
\(808\) 25.9847 + 25.9847i 0.0321592 + 0.0321592i
\(809\) −115.327 −0.142555 −0.0712776 0.997457i \(-0.522708\pi\)
−0.0712776 + 0.997457i \(0.522708\pi\)
\(810\) 568.522 + 69.5205i 0.701879 + 0.0858278i
\(811\) 285.468i 0.351996i 0.984391 + 0.175998i \(0.0563152\pi\)
−0.984391 + 0.175998i \(0.943685\pi\)
\(812\) 245.876 490.468i 0.302803 0.604024i
\(813\) 931.696 + 310.157i 1.14600 + 0.381497i
\(814\) 153.288i 0.188315i
\(815\) 294.635 683.404i 0.361516 0.838533i
\(816\) −75.3519 + 37.7131i −0.0923430 + 0.0462170i
\(817\) 396.438 396.438i 0.485236 0.485236i
\(818\) 615.554 615.554i 0.752511 0.752511i
\(819\) −236.713 + 709.527i −0.289027 + 0.866333i
\(820\) −57.5601 144.806i −0.0701953 0.176593i
\(821\) 607.687i 0.740179i −0.928996 0.370089i \(-0.879327\pi\)
0.928996 0.370089i \(-0.120673\pi\)
\(822\) 867.881 + 288.914i 1.05582 + 0.351476i
\(823\) −1073.10 + 1073.10i −1.30388 + 1.30388i −0.378132 + 0.925752i \(0.623433\pi\)
−0.925752 + 0.378132i \(0.876567\pi\)
\(824\) 182.326i 0.221270i
\(825\) 141.841 65.9702i 0.171929 0.0799639i
\(826\) −152.873 460.226i −0.185077 0.557175i
\(827\) 874.440 874.440i 1.05736 1.05736i 0.0591122 0.998251i \(-0.481173\pi\)
0.998251 0.0591122i \(-0.0188270\pi\)
\(828\) 77.7249 11.1661i 0.0938706 0.0134856i
\(829\) −369.045 −0.445169 −0.222585 0.974913i \(-0.571449\pi\)
−0.222585 + 0.974913i \(0.571449\pi\)
\(830\) 380.895 + 958.231i 0.458910 + 1.15450i
\(831\) 144.215 72.1788i 0.173544 0.0868578i
\(832\) −67.1614 + 67.1614i −0.0807228 + 0.0807228i
\(833\) −49.3726 + 340.512i −0.0592708 + 0.408777i
\(834\) −142.463 284.646i −0.170819 0.341302i
\(835\) −222.775 96.0447i −0.266796 0.115024i
\(836\) 72.4459 0.0866578
\(837\) 652.673 + 940.371i 0.779777 + 1.12350i
\(838\) 427.623 + 427.623i 0.510290 + 0.510290i
\(839\) 1424.80i 1.69821i 0.528223 + 0.849106i \(0.322858\pi\)
−0.528223 + 0.849106i \(0.677142\pi\)
\(840\) 276.053 109.522i 0.328634 0.130383i
\(841\) 694.784 0.826140
\(842\) −294.683 + 294.683i −0.349980 + 0.349980i
\(843\) 277.784 + 92.4731i 0.329519 + 0.109695i
\(844\) 292.932i 0.347076i
\(845\) −51.7920 130.295i −0.0612923 0.154195i
\(846\) −481.476 360.514i −0.569121 0.426139i
\(847\) −729.959 365.936i −0.861817 0.432037i
\(848\) −238.984 238.984i −0.281821 0.281821i
\(849\) 1496.91 749.195i 1.76315 0.882444i
\(850\) 180.513 170.437i 0.212368 0.200514i
\(851\) 226.701i 0.266394i
\(852\) −142.086 + 426.819i −0.166767 + 0.500961i
\(853\) 459.198 + 459.198i 0.538332 + 0.538332i 0.923039 0.384707i \(-0.125697\pi\)
−0.384707 + 0.923039i \(0.625697\pi\)
\(854\) 258.829 + 779.207i 0.303079 + 0.912420i
\(855\) −754.355 204.204i −0.882286 0.238835i
\(856\) 198.079 0.231401
\(857\) −733.866 733.866i −0.856319 0.856319i 0.134583 0.990902i \(-0.457030\pi\)
−0.990902 + 0.134583i \(0.957030\pi\)
\(858\) 99.6835 + 33.1842i 0.116181 + 0.0386762i
\(859\) 223.858 0.260603 0.130301 0.991474i \(-0.458405\pi\)
0.130301 + 0.991474i \(0.458405\pi\)
\(860\) −296.450 127.808i −0.344710 0.148614i
\(861\) −231.542 + 231.240i −0.268922 + 0.268571i
\(862\) −735.135 735.135i −0.852825 0.852825i
\(863\) −500.157 500.157i −0.579556 0.579556i 0.355225 0.934781i \(-0.384404\pi\)
−0.934781 + 0.355225i \(0.884404\pi\)
\(864\) 27.1443 150.304i 0.0314170 0.173963i
\(865\) −592.110 + 1373.39i −0.684520 + 1.58774i
\(866\) −12.3080 −0.0142125
\(867\) −682.268 227.124i −0.786930 0.261965i
\(868\) 530.596 + 265.993i 0.611285 + 0.306443i
\(869\) 7.53102 0.00866630
\(870\) 620.365 + 553.398i 0.713064 + 0.636090i
\(871\) 920.501i 1.05683i
\(872\) 340.847 340.847i 0.390880 0.390880i
\(873\) 445.506 64.0023i 0.510317 0.0733131i
\(874\) −107.142 −0.122588
\(875\) −685.655 + 543.602i −0.783605 + 0.621259i
\(876\) −285.565 570.568i −0.325988 0.651334i
\(877\) −845.141 845.141i −0.963673 0.963673i 0.0356898 0.999363i \(-0.488637\pi\)
−0.999363 + 0.0356898i \(0.988637\pi\)
\(878\) −701.728 + 701.728i −0.799235 + 0.799235i
\(879\) 118.183 + 236.133i 0.134452 + 0.268638i
\(880\) −15.4090 38.7649i −0.0175102 0.0440511i
\(881\) −1655.83 −1.87949 −0.939747 0.341870i \(-0.888940\pi\)
−0.939747 + 0.341870i \(0.888940\pi\)
\(882\) −440.424 441.576i −0.499347 0.500653i
\(883\) −128.174 + 128.174i −0.145158 + 0.145158i −0.775951 0.630793i \(-0.782730\pi\)
0.630793 + 0.775951i \(0.282730\pi\)
\(884\) 166.736 0.188615
\(885\) 733.620 41.8555i 0.828949 0.0472944i
\(886\) 352.964 0.398379
\(887\) 1006.62 + 1006.62i 1.13486 + 1.13486i 0.989359 + 0.145497i \(0.0464781\pi\)
0.145497 + 0.989359i \(0.453522\pi\)
\(888\) −418.383 139.278i −0.471152 0.156844i
\(889\) 326.272 + 982.244i 0.367010 + 1.10489i
\(890\) 158.714 + 68.4263i 0.178331 + 0.0768835i
\(891\) −162.114 + 47.5608i −0.181946 + 0.0533791i
\(892\) −442.817 + 442.817i −0.496431 + 0.496431i
\(893\) 580.330 + 580.330i 0.649865 + 0.649865i
\(894\) 348.056 + 695.426i 0.389324 + 0.777881i
\(895\) 515.190 204.787i 0.575631 0.228812i
\(896\) −24.9653 75.1581i −0.0278630 0.0838818i
\(897\) −147.424 49.0767i −0.164352 0.0547120i
\(898\) 521.716 521.716i 0.580976 0.580976i
\(899\) 1661.44i 1.84809i
\(900\) 51.1814 + 447.080i 0.0568683 + 0.496755i
\(901\) 593.304i 0.658495i
\(902\) 32.5017 + 32.5017i 0.0360329 + 0.0360329i
\(903\) −0.442720 + 677.938i −0.000490277 + 0.750762i
\(904\) 557.573i 0.616785i
\(905\) 44.8799 + 112.906i 0.0495910 + 0.124758i
\(906\) 387.158 + 773.553i 0.427327 + 0.853811i
\(907\) 9.93474 + 9.93474i 0.0109534 + 0.0109534i 0.712562 0.701609i \(-0.247535\pi\)
−0.701609 + 0.712562i \(0.747535\pi\)
\(908\) 140.006 140.006i 0.154192 0.154192i
\(909\) 93.6001 + 70.0848i 0.102970 + 0.0771010i
\(910\) −585.472 50.6799i −0.643376 0.0556922i
\(911\) 297.086i 0.326110i 0.986617 + 0.163055i \(0.0521348\pi\)
−0.986617 + 0.163055i \(0.947865\pi\)
\(912\) −65.8244 + 197.733i −0.0721758 + 0.216812i
\(913\) −215.075 215.075i −0.235570 0.235570i
\(914\) 69.6131 0.0761631
\(915\) −1242.09 + 70.8654i −1.35747 + 0.0774485i
\(916\) 574.151i 0.626802i
\(917\) −8.93627 4.47984i −0.00974511 0.00488532i
\(918\) −220.267 + 152.878i −0.239942 + 0.166534i
\(919\) 67.9916i 0.0739843i −0.999316 0.0369922i \(-0.988222\pi\)
0.999316 0.0369922i \(-0.0117777\pi\)
\(920\) 22.7886 + 57.3302i 0.0247703 + 0.0623154i
\(921\) 151.443 + 302.588i 0.164433 + 0.328543i
\(922\) 747.746 747.746i 0.811005 0.811005i
\(923\) 629.424 629.424i 0.681933 0.681933i
\(924\) −61.9844 + 61.9035i −0.0670826 + 0.0669951i
\(925\) 1298.65 + 37.2847i 1.40394 + 0.0403078i
\(926\) 1258.11i 1.35865i
\(927\) −82.4998 574.263i −0.0889965 0.619486i
\(928\) 156.756 156.756i 0.168918 0.168918i
\(929\) 81.2126i 0.0874194i 0.999044 + 0.0437097i \(0.0139177\pi\)
−0.999044 + 0.0437097i \(0.986082\pi\)
\(930\) −598.675 + 671.121i −0.643737 + 0.721636i
\(931\) 509.156 + 681.846i 0.546892 + 0.732380i
\(932\) 398.695 398.695i 0.427784 0.427784i
\(933\) −340.168 + 1021.85i −0.364596 + 1.09523i
\(934\) −144.859 −0.155095
\(935\) −28.9919 + 67.2464i −0.0310074 + 0.0719213i
\(936\) −181.145 + 241.924i −0.193531 + 0.258466i
\(937\) −411.914 + 411.914i −0.439609 + 0.439609i −0.891881 0.452271i \(-0.850614\pi\)
0.452271 + 0.891881i \(0.350614\pi\)
\(938\) 686.136 + 343.967i 0.731488 + 0.366702i
\(939\) −1173.17 + 587.166i −1.24939 + 0.625310i
\(940\) 187.093 433.962i 0.199036 0.461661i
\(941\) 379.719 0.403528 0.201764 0.979434i \(-0.435333\pi\)
0.201764 + 0.979434i \(0.435333\pi\)
\(942\) 19.1521 + 6.37565i 0.0203313 + 0.00676821i
\(943\) −48.0674 48.0674i −0.0509728 0.0509728i
\(944\) 195.950i 0.207574i
\(945\) 819.910 469.864i 0.867630 0.497210i
\(946\) 95.2248 0.100660
\(947\) 54.3340 54.3340i 0.0573749 0.0573749i −0.677837 0.735212i \(-0.737083\pi\)
0.735212 + 0.677837i \(0.237083\pi\)
\(948\) −6.84268 + 20.5551i −0.00721802 + 0.0216826i
\(949\) 1262.53i 1.33038i
\(950\) 17.6212 613.756i 0.0185486 0.646059i
\(951\) −88.0202 175.867i −0.0925554 0.184929i
\(952\) −62.3046 + 124.284i −0.0654460 + 0.130550i
\(953\) −749.903 749.903i −0.786887 0.786887i 0.194096 0.980983i \(-0.437823\pi\)
−0.980983 + 0.194096i \(0.937823\pi\)
\(954\) −860.851 644.578i −0.902359 0.675658i
\(955\) −301.787 759.216i −0.316007 0.794990i
\(956\) 92.7303i 0.0969982i
\(957\) −232.664 77.4527i −0.243118 0.0809328i
\(958\) −49.3199 49.3199i −0.0514822 0.0514822i
\(959\) 1432.24 475.748i 1.49347 0.496087i
\(960\) 119.805 6.83529i 0.124797 0.00712009i
\(961\) −836.367 −0.870309
\(962\) 616.985 + 616.985i 0.641356 + 0.641356i
\(963\) 623.879 89.6278i 0.647850 0.0930714i
\(964\) −130.699 −0.135580
\(965\) −101.829 + 236.191i −0.105522 + 0.244758i
\(966\) 91.6698 91.5501i 0.0948963 0.0947724i
\(967\) 401.607 + 401.607i 0.415313 + 0.415313i 0.883584 0.468272i \(-0.155123\pi\)
−0.468272 + 0.883584i \(0.655123\pi\)
\(968\) −233.299 233.299i −0.241012 0.241012i
\(969\) 327.155 163.739i 0.337621 0.168977i
\(970\) 130.621 + 328.607i 0.134661 + 0.338770i
\(971\) −1146.42 −1.18065 −0.590327 0.807164i \(-0.701001\pi\)
−0.590327 + 0.807164i \(0.701001\pi\)
\(972\) 17.4848 485.685i 0.0179885 0.499676i
\(973\) −469.488 235.359i −0.482516 0.241890i
\(974\) 167.717 0.172194
\(975\) 305.380 836.439i 0.313210 0.857886i
\(976\) 331.762i 0.339920i
\(977\) 11.8173 11.8173i 0.0120955 0.0120955i −0.701033 0.713129i \(-0.747278\pi\)
0.713129 + 0.701033i \(0.247278\pi\)
\(978\) −599.158 199.457i −0.612636 0.203943i
\(979\) −50.9817 −0.0520753
\(980\) 256.552 417.470i 0.261788 0.425990i
\(981\) 919.320 1227.78i 0.937126 1.25156i
\(982\) 655.752 + 655.752i 0.667771 + 0.667771i
\(983\) 884.682 884.682i 0.899982 0.899982i −0.0954519 0.995434i \(-0.530430\pi\)
0.995434 + 0.0954519i \(0.0304296\pi\)
\(984\) −118.241 + 59.1787i −0.120163 + 0.0601409i
\(985\) 54.1094 125.506i 0.0549334 0.127418i
\(986\) −389.165 −0.394691
\(987\) −992.407 0.648080i −1.00548 0.000656616i
\(988\) 291.594 291.594i 0.295136 0.295136i
\(989\) −140.830 −0.142396
\(990\) −66.0734 115.123i −0.0667408 0.116286i
\(991\) −227.430 −0.229496 −0.114748 0.993395i \(-0.536606\pi\)
−0.114748 + 0.993395i \(0.536606\pi\)
\(992\) 169.581 + 169.581i 0.170949 + 0.170949i
\(993\) 353.941 1063.22i 0.356436 1.07072i
\(994\) 233.970 + 704.368i 0.235382 + 0.708619i
\(995\) 370.028 147.085i 0.371887 0.147824i
\(996\) 782.440 391.606i 0.785582 0.393179i
\(997\) 720.354 720.354i 0.722521 0.722521i −0.246597 0.969118i \(-0.579312\pi\)
0.969118 + 0.246597i \(0.0793123\pi\)
\(998\) 433.348 + 433.348i 0.434216 + 0.434216i
\(999\) −1380.78 249.364i −1.38216 0.249613i
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 210.3.k.b.167.10 yes 32
3.2 odd 2 210.3.k.a.167.2 yes 32
5.3 odd 4 210.3.k.a.83.15 yes 32
7.6 odd 2 inner 210.3.k.b.167.7 yes 32
15.8 even 4 inner 210.3.k.b.83.7 yes 32
21.20 even 2 210.3.k.a.167.15 yes 32
35.13 even 4 210.3.k.a.83.2 32
105.83 odd 4 inner 210.3.k.b.83.10 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.k.a.83.2 32 35.13 even 4
210.3.k.a.83.15 yes 32 5.3 odd 4
210.3.k.a.167.2 yes 32 3.2 odd 2
210.3.k.a.167.15 yes 32 21.20 even 2
210.3.k.b.83.7 yes 32 15.8 even 4 inner
210.3.k.b.83.10 yes 32 105.83 odd 4 inner
210.3.k.b.167.7 yes 32 7.6 odd 2 inner
210.3.k.b.167.10 yes 32 1.1 even 1 trivial