Properties

Label 170.2.h.b.21.1
Level $170$
Weight $2$
Character 170.21
Analytic conductor $1.357$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [170,2,Mod(21,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.21");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.h (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: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.23045668864.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 26x^{6} + 237x^{4} + 892x^{2} + 1156 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 21.1
Root \(-3.26843i\) of defining polynomial
Character \(\chi\) \(=\) 170.21
Dual form 170.2.h.b.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-2.31113 + 2.31113i) q^{3} -1.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +(2.31113 + 2.31113i) q^{6} +(-3.26843 - 3.26843i) q^{7} +1.00000i q^{8} -7.68265i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-2.31113 + 2.31113i) q^{3} -1.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +(2.31113 + 2.31113i) q^{6} +(-3.26843 - 3.26843i) q^{7} +1.00000i q^{8} -7.68265i q^{9} +(-0.707107 - 0.707107i) q^{10} +(-1.82843 - 1.82843i) q^{11} +(2.31113 - 2.31113i) q^{12} -0.145782 q^{13} +(-3.26843 + 3.26843i) q^{14} +3.26843i q^{15} +1.00000 q^{16} +(-3.31113 + 2.45691i) q^{17} -7.68265 q^{18} +2.06038i q^{19} +(-0.707107 + 0.707107i) q^{20} +15.1075 q^{21} +(-1.82843 + 1.82843i) q^{22} +(-3.41421 - 3.41421i) q^{23} +(-2.31113 - 2.31113i) q^{24} -1.00000i q^{25} +0.145782i q^{26} +(10.8222 + 10.8222i) q^{27} +(3.26843 + 3.26843i) q^{28} +(2.10308 - 2.10308i) q^{29} +3.26843 q^{30} +(-2.78573 + 2.78573i) q^{31} -1.00000i q^{32} +8.45147 q^{33} +(2.45691 + 3.31113i) q^{34} -4.62226 q^{35} +7.68265i q^{36} +(-2.44000 + 2.44000i) q^{37} +2.06038 q^{38} +(0.336921 - 0.336921i) q^{39} +(0.707107 + 0.707107i) q^{40} +(-5.53686 - 5.53686i) q^{41} -15.1075i q^{42} -0.622260i q^{43} +(1.82843 + 1.82843i) q^{44} +(-5.43245 - 5.43245i) q^{45} +(-3.41421 + 3.41421i) q^{46} +8.47648 q^{47} +(-2.31113 + 2.31113i) q^{48} +14.3653i q^{49} -1.00000 q^{50} +(1.97421 - 13.3307i) q^{51} +0.145782 q^{52} -6.68265i q^{53} +(10.8222 - 10.8222i) q^{54} -2.58579 q^{55} +(3.26843 - 3.26843i) q^{56} +(-4.76182 - 4.76182i) q^{57} +(-2.10308 - 2.10308i) q^{58} -5.71724i q^{59} -3.26843i q^{60} +(2.63995 + 2.63995i) q^{61} +(2.78573 + 2.78573i) q^{62} +(-25.1102 + 25.1102i) q^{63} -1.00000 q^{64} +(-0.103083 + 0.103083i) q^{65} -8.45147i q^{66} +1.58767 q^{67} +(3.31113 - 2.45691i) q^{68} +15.7814 q^{69} +4.62226i q^{70} +(1.83653 - 1.83653i) q^{71} +7.68265 q^{72} +(-5.82220 + 5.82220i) q^{73} +(2.44000 + 2.44000i) q^{74} +(2.31113 + 2.31113i) q^{75} -2.06038i q^{76} +11.9522i q^{77} +(-0.336921 - 0.336921i) q^{78} +(3.29344 + 3.29344i) q^{79} +(0.707107 - 0.707107i) q^{80} -26.9751 q^{81} +(-5.53686 + 5.53686i) q^{82} -8.91382i q^{83} -15.1075 q^{84} +(-0.604023 + 4.07862i) q^{85} -0.622260 q^{86} +9.72100i q^{87} +(1.82843 - 1.82843i) q^{88} -15.9787 q^{89} +(-5.43245 + 5.43245i) q^{90} +(0.476478 + 0.476478i) q^{91} +(3.41421 + 3.41421i) q^{92} -12.8764i q^{93} -8.47648i q^{94} +(1.45691 + 1.45691i) q^{95} +(2.31113 + 2.31113i) q^{96} +(12.5814 - 12.5814i) q^{97} +14.3653 q^{98} +(-14.0472 + 14.0472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} - 4 q^{7} + 8 q^{11} - 12 q^{13} - 4 q^{14} + 8 q^{16} - 8 q^{17} - 28 q^{18} + 16 q^{21} + 8 q^{22} - 16 q^{23} + 12 q^{27} + 4 q^{28} + 24 q^{29} + 4 q^{30} + 4 q^{31} + 16 q^{33} + 12 q^{34} - 20 q^{37} + 20 q^{38} - 4 q^{39} - 8 q^{44} - 8 q^{45} - 16 q^{46} + 20 q^{47} - 8 q^{50} + 4 q^{51} + 12 q^{52} + 12 q^{54} - 32 q^{55} + 4 q^{56} + 40 q^{57} - 24 q^{58} - 16 q^{61} - 4 q^{62} - 64 q^{63} - 8 q^{64} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 8 q^{69} + 4 q^{71} + 28 q^{72} + 28 q^{73} + 20 q^{74} + 4 q^{78} + 8 q^{79} - 8 q^{81} - 16 q^{84} + 8 q^{85} + 32 q^{86} - 8 q^{88} - 44 q^{89} - 8 q^{90} - 44 q^{91} + 16 q^{92} + 4 q^{95} + 20 q^{97} + 48 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −2.31113 + 2.31113i −1.33433 + 1.33433i −0.432880 + 0.901451i \(0.642503\pi\)
−0.901451 + 0.432880i \(0.857497\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) 2.31113 + 2.31113i 0.943515 + 0.943515i
\(7\) −3.26843 3.26843i −1.23535 1.23535i −0.961880 0.273471i \(-0.911828\pi\)
−0.273471 0.961880i \(-0.588172\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 7.68265i 2.56088i
\(10\) −0.707107 0.707107i −0.223607 0.223607i
\(11\) −1.82843 1.82843i −0.551292 0.551292i 0.375522 0.926813i \(-0.377463\pi\)
−0.926813 + 0.375522i \(0.877463\pi\)
\(12\) 2.31113 2.31113i 0.667166 0.667166i
\(13\) −0.145782 −0.0404326 −0.0202163 0.999796i \(-0.506435\pi\)
−0.0202163 + 0.999796i \(0.506435\pi\)
\(14\) −3.26843 + 3.26843i −0.873525 + 0.873525i
\(15\) 3.26843i 0.843905i
\(16\) 1.00000 0.250000
\(17\) −3.31113 + 2.45691i −0.803067 + 0.595889i
\(18\) −7.68265 −1.81082
\(19\) 2.06038i 0.472685i 0.971670 + 0.236342i \(0.0759487\pi\)
−0.971670 + 0.236342i \(0.924051\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) 15.1075 3.29674
\(22\) −1.82843 + 1.82843i −0.389822 + 0.389822i
\(23\) −3.41421 3.41421i −0.711913 0.711913i 0.255022 0.966935i \(-0.417917\pi\)
−0.966935 + 0.255022i \(0.917917\pi\)
\(24\) −2.31113 2.31113i −0.471757 0.471757i
\(25\) 1.00000i 0.200000i
\(26\) 0.145782i 0.0285902i
\(27\) 10.8222 + 10.8222i 2.08273 + 2.08273i
\(28\) 3.26843 + 3.26843i 0.617676 + 0.617676i
\(29\) 2.10308 2.10308i 0.390533 0.390533i −0.484345 0.874877i \(-0.660942\pi\)
0.874877 + 0.484345i \(0.160942\pi\)
\(30\) 3.26843 0.596731
\(31\) −2.78573 + 2.78573i −0.500332 + 0.500332i −0.911541 0.411209i \(-0.865107\pi\)
0.411209 + 0.911541i \(0.365107\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 8.45147 1.47121
\(34\) 2.45691 + 3.31113i 0.421357 + 0.567854i
\(35\) −4.62226 −0.781305
\(36\) 7.68265i 1.28044i
\(37\) −2.44000 + 2.44000i −0.401134 + 0.401134i −0.878633 0.477498i \(-0.841544\pi\)
0.477498 + 0.878633i \(0.341544\pi\)
\(38\) 2.06038 0.334239
\(39\) 0.336921 0.336921i 0.0539505 0.0539505i
\(40\) 0.707107 + 0.707107i 0.111803 + 0.111803i
\(41\) −5.53686 5.53686i −0.864713 0.864713i 0.127168 0.991881i \(-0.459411\pi\)
−0.991881 + 0.127168i \(0.959411\pi\)
\(42\) 15.1075i 2.33114i
\(43\) 0.622260i 0.0948938i −0.998874 0.0474469i \(-0.984892\pi\)
0.998874 0.0474469i \(-0.0151085\pi\)
\(44\) 1.82843 + 1.82843i 0.275646 + 0.275646i
\(45\) −5.43245 5.43245i −0.809822 0.809822i
\(46\) −3.41421 + 3.41421i −0.503398 + 0.503398i
\(47\) 8.47648 1.23642 0.618211 0.786012i \(-0.287858\pi\)
0.618211 + 0.786012i \(0.287858\pi\)
\(48\) −2.31113 + 2.31113i −0.333583 + 0.333583i
\(49\) 14.3653i 2.05218i
\(50\) −1.00000 −0.141421
\(51\) 1.97421 13.3307i 0.276445 1.86667i
\(52\) 0.145782 0.0202163
\(53\) 6.68265i 0.917932i −0.888454 0.458966i \(-0.848220\pi\)
0.888454 0.458966i \(-0.151780\pi\)
\(54\) 10.8222 10.8222i 1.47272 1.47272i
\(55\) −2.58579 −0.348667
\(56\) 3.26843 3.26843i 0.436763 0.436763i
\(57\) −4.76182 4.76182i −0.630718 0.630718i
\(58\) −2.10308 2.10308i −0.276148 0.276148i
\(59\) 5.71724i 0.744321i −0.928168 0.372161i \(-0.878617\pi\)
0.928168 0.372161i \(-0.121383\pi\)
\(60\) 3.26843i 0.421953i
\(61\) 2.63995 + 2.63995i 0.338011 + 0.338011i 0.855618 0.517608i \(-0.173177\pi\)
−0.517608 + 0.855618i \(0.673177\pi\)
\(62\) 2.78573 + 2.78573i 0.353788 + 0.353788i
\(63\) −25.1102 + 25.1102i −3.16359 + 3.16359i
\(64\) −1.00000 −0.125000
\(65\) −0.103083 + 0.103083i −0.0127859 + 0.0127859i
\(66\) 8.45147i 1.04030i
\(67\) 1.58767 0.193964 0.0969822 0.995286i \(-0.469081\pi\)
0.0969822 + 0.995286i \(0.469081\pi\)
\(68\) 3.31113 2.45691i 0.401534 0.297944i
\(69\) 15.7814 1.89986
\(70\) 4.62226i 0.552466i
\(71\) 1.83653 1.83653i 0.217956 0.217956i −0.589680 0.807637i \(-0.700746\pi\)
0.807637 + 0.589680i \(0.200746\pi\)
\(72\) 7.68265 0.905408
\(73\) −5.82220 + 5.82220i −0.681437 + 0.681437i −0.960324 0.278887i \(-0.910035\pi\)
0.278887 + 0.960324i \(0.410035\pi\)
\(74\) 2.44000 + 2.44000i 0.283645 + 0.283645i
\(75\) 2.31113 + 2.31113i 0.266866 + 0.266866i
\(76\) 2.06038i 0.236342i
\(77\) 11.9522i 1.36208i
\(78\) −0.336921 0.336921i −0.0381488 0.0381488i
\(79\) 3.29344 + 3.29344i 0.370541 + 0.370541i 0.867674 0.497133i \(-0.165614\pi\)
−0.497133 + 0.867674i \(0.665614\pi\)
\(80\) 0.707107 0.707107i 0.0790569 0.0790569i
\(81\) −26.9751 −2.99723
\(82\) −5.53686 + 5.53686i −0.611444 + 0.611444i
\(83\) 8.91382i 0.978419i −0.872166 0.489210i \(-0.837285\pi\)
0.872166 0.489210i \(-0.162715\pi\)
\(84\) −15.1075 −1.64837
\(85\) −0.604023 + 4.07862i −0.0655155 + 0.442389i
\(86\) −0.622260 −0.0671001
\(87\) 9.72100i 1.04220i
\(88\) 1.82843 1.82843i 0.194911 0.194911i
\(89\) −15.9787 −1.69374 −0.846872 0.531797i \(-0.821517\pi\)
−0.846872 + 0.531797i \(0.821517\pi\)
\(90\) −5.43245 + 5.43245i −0.572631 + 0.572631i
\(91\) 0.476478 + 0.476478i 0.0499485 + 0.0499485i
\(92\) 3.41421 + 3.41421i 0.355956 + 0.355956i
\(93\) 12.8764i 1.33522i
\(94\) 8.47648i 0.874282i
\(95\) 1.45691 + 1.45691i 0.149476 + 0.149476i
\(96\) 2.31113 + 2.31113i 0.235879 + 0.235879i
\(97\) 12.5814 12.5814i 1.27745 1.27745i 0.335363 0.942089i \(-0.391141\pi\)
0.942089 0.335363i \(-0.108859\pi\)
\(98\) 14.3653 1.45111
\(99\) −14.0472 + 14.0472i −1.41179 + 1.41179i
\(100\) 1.00000i 0.100000i
\(101\) 7.65685 0.761885 0.380943 0.924599i \(-0.375599\pi\)
0.380943 + 0.924599i \(0.375599\pi\)
\(102\) −13.3307 1.97421i −1.31994 0.195476i
\(103\) 8.07295 0.795451 0.397726 0.917504i \(-0.369800\pi\)
0.397726 + 0.917504i \(0.369800\pi\)
\(104\) 0.145782i 0.0142951i
\(105\) 10.6826 10.6826i 1.04252 1.04252i
\(106\) −6.68265 −0.649076
\(107\) 1.68265 1.68265i 0.162667 0.162667i −0.621080 0.783747i \(-0.713306\pi\)
0.783747 + 0.621080i \(0.213306\pi\)
\(108\) −10.8222 10.8222i −1.04137 1.04137i
\(109\) −2.10308 2.10308i −0.201439 0.201439i 0.599177 0.800616i \(-0.295494\pi\)
−0.800616 + 0.599177i \(0.795494\pi\)
\(110\) 2.58579i 0.246545i
\(111\) 11.2783i 1.07049i
\(112\) −3.26843 3.26843i −0.308838 0.308838i
\(113\) −7.19994 7.19994i −0.677314 0.677314i 0.282078 0.959391i \(-0.408976\pi\)
−0.959391 + 0.282078i \(0.908976\pi\)
\(114\) −4.76182 + 4.76182i −0.445985 + 0.445985i
\(115\) −4.82843 −0.450253
\(116\) −2.10308 + 2.10308i −0.195266 + 0.195266i
\(117\) 1.11999i 0.103543i
\(118\) −5.71724 −0.526315
\(119\) 18.8525 + 2.79195i 1.72820 + 0.255938i
\(120\) −3.26843 −0.298366
\(121\) 4.31371i 0.392155i
\(122\) 2.63995 2.63995i 0.239010 0.239010i
\(123\) 25.5928 2.30763
\(124\) 2.78573 2.78573i 0.250166 0.250166i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 25.1102 + 25.1102i 2.23699 + 2.23699i
\(127\) 11.1841i 0.992432i −0.868199 0.496216i \(-0.834722\pi\)
0.868199 0.496216i \(-0.165278\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.43812 + 1.43812i 0.126620 + 0.126620i
\(130\) 0.103083 + 0.103083i 0.00904101 + 0.00904101i
\(131\) 10.5715 10.5715i 0.923633 0.923633i −0.0736515 0.997284i \(-0.523465\pi\)
0.997284 + 0.0736515i \(0.0234653\pi\)
\(132\) −8.45147 −0.735606
\(133\) 6.73423 6.73423i 0.583932 0.583932i
\(134\) 1.58767i 0.137153i
\(135\) 15.3049 1.31724
\(136\) −2.45691 3.31113i −0.210678 0.283927i
\(137\) −14.1583 −1.20963 −0.604815 0.796366i \(-0.706753\pi\)
−0.604815 + 0.796366i \(0.706753\pi\)
\(138\) 15.7814i 1.34340i
\(139\) −15.0729 + 15.0729i −1.27847 + 1.27847i −0.336947 + 0.941524i \(0.609394\pi\)
−0.941524 + 0.336947i \(0.890606\pi\)
\(140\) 4.62226 0.390652
\(141\) −19.5902 + 19.5902i −1.64980 + 1.64980i
\(142\) −1.83653 1.83653i −0.154118 0.154118i
\(143\) 0.266552 + 0.266552i 0.0222902 + 0.0222902i
\(144\) 7.68265i 0.640220i
\(145\) 2.97421i 0.246995i
\(146\) 5.82220 + 5.82220i 0.481849 + 0.481849i
\(147\) −33.2001 33.2001i −2.73829 2.73829i
\(148\) 2.44000 2.44000i 0.200567 0.200567i
\(149\) −10.2791 −0.842098 −0.421049 0.907038i \(-0.638338\pi\)
−0.421049 + 0.907038i \(0.638338\pi\)
\(150\) 2.31113 2.31113i 0.188703 0.188703i
\(151\) 6.53686i 0.531962i 0.963978 + 0.265981i \(0.0856959\pi\)
−0.963978 + 0.265981i \(0.914304\pi\)
\(152\) −2.06038 −0.167119
\(153\) 18.8756 + 25.4382i 1.52600 + 2.05656i
\(154\) 11.9522 0.963134
\(155\) 3.93962i 0.316438i
\(156\) −0.336921 + 0.336921i −0.0269753 + 0.0269753i
\(157\) 12.4337 0.992317 0.496159 0.868232i \(-0.334743\pi\)
0.496159 + 0.868232i \(0.334743\pi\)
\(158\) 3.29344 3.29344i 0.262012 0.262012i
\(159\) 15.4445 + 15.4445i 1.22483 + 1.22483i
\(160\) −0.707107 0.707107i −0.0559017 0.0559017i
\(161\) 22.3182i 1.75892i
\(162\) 26.9751i 2.11936i
\(163\) −0.562654 0.562654i −0.0440705 0.0440705i 0.684728 0.728799i \(-0.259921\pi\)
−0.728799 + 0.684728i \(0.759921\pi\)
\(164\) 5.53686 + 5.53686i 0.432356 + 0.432356i
\(165\) 5.97609 5.97609i 0.465238 0.465238i
\(166\) −8.91382 −0.691847
\(167\) −3.36263 + 3.36263i −0.260208 + 0.260208i −0.825139 0.564930i \(-0.808903\pi\)
0.564930 + 0.825139i \(0.308903\pi\)
\(168\) 15.1075i 1.16557i
\(169\) −12.9787 −0.998365
\(170\) 4.07862 + 0.604023i 0.312816 + 0.0463265i
\(171\) 15.8292 1.21049
\(172\) 0.622260i 0.0474469i
\(173\) 9.00188 9.00188i 0.684400 0.684400i −0.276588 0.960989i \(-0.589204\pi\)
0.960989 + 0.276588i \(0.0892038\pi\)
\(174\) 9.72100 0.736947
\(175\) −3.26843 + 3.26843i −0.247070 + 0.247070i
\(176\) −1.82843 1.82843i −0.137823 0.137823i
\(177\) 13.2133 + 13.2133i 0.993171 + 0.993171i
\(178\) 15.9787i 1.19766i
\(179\) 0.170794i 0.0127658i −0.999980 0.00638288i \(-0.997968\pi\)
0.999980 0.00638288i \(-0.00203175\pi\)
\(180\) 5.43245 + 5.43245i 0.404911 + 0.404911i
\(181\) 3.32882 + 3.32882i 0.247429 + 0.247429i 0.819915 0.572486i \(-0.194021\pi\)
−0.572486 + 0.819915i \(0.694021\pi\)
\(182\) 0.476478 0.476478i 0.0353189 0.0353189i
\(183\) −12.2025 −0.902036
\(184\) 3.41421 3.41421i 0.251699 0.251699i
\(185\) 3.45069i 0.253700i
\(186\) −12.8764 −0.944141
\(187\) 10.5464 + 1.56188i 0.771232 + 0.114216i
\(188\) −8.47648 −0.618211
\(189\) 70.7433i 5.14581i
\(190\) 1.45691 1.45691i 0.105696 0.105696i
\(191\) 4.79461 0.346926 0.173463 0.984840i \(-0.444504\pi\)
0.173463 + 0.984840i \(0.444504\pi\)
\(192\) 2.31113 2.31113i 0.166791 0.166791i
\(193\) 10.6819 + 10.6819i 0.768898 + 0.768898i 0.977912 0.209015i \(-0.0670257\pi\)
−0.209015 + 0.977912i \(0.567026\pi\)
\(194\) −12.5814 12.5814i −0.903295 0.903295i
\(195\) 0.476478i 0.0341213i
\(196\) 14.3653i 1.02609i
\(197\) 4.85610 + 4.85610i 0.345983 + 0.345983i 0.858611 0.512628i \(-0.171328\pi\)
−0.512628 + 0.858611i \(0.671328\pi\)
\(198\) 14.0472 + 14.0472i 0.998288 + 0.998288i
\(199\) −2.12810 + 2.12810i −0.150857 + 0.150857i −0.778501 0.627644i \(-0.784019\pi\)
0.627644 + 0.778501i \(0.284019\pi\)
\(200\) 1.00000 0.0707107
\(201\) −3.66930 + 3.66930i −0.258813 + 0.258813i
\(202\) 7.65685i 0.538734i
\(203\) −13.7476 −0.964890
\(204\) −1.97421 + 13.3307i −0.138222 + 0.933335i
\(205\) −7.83031 −0.546892
\(206\) 8.07295i 0.562469i
\(207\) −26.2302 + 26.2302i −1.82312 + 1.82312i
\(208\) −0.145782 −0.0101082
\(209\) 3.76726 3.76726i 0.260587 0.260587i
\(210\) −10.6826 10.6826i −0.737173 0.737173i
\(211\) −1.47648 1.47648i −0.101645 0.101645i 0.654456 0.756100i \(-0.272898\pi\)
−0.756100 + 0.654456i \(0.772898\pi\)
\(212\) 6.68265i 0.458966i
\(213\) 8.48893i 0.581652i
\(214\) −1.68265 1.68265i −0.115023 0.115023i
\(215\) −0.440004 0.440004i −0.0300081 0.0300081i
\(216\) −10.8222 + 10.8222i −0.736358 + 0.736358i
\(217\) 18.2099 1.23617
\(218\) −2.10308 + 2.10308i −0.142439 + 0.142439i
\(219\) 26.9117i 1.81853i
\(220\) 2.58579 0.174334
\(221\) 0.482703 0.358173i 0.0324701 0.0240934i
\(222\) −11.2783 −0.756952
\(223\) 22.6186i 1.51465i −0.653036 0.757327i \(-0.726505\pi\)
0.653036 0.757327i \(-0.273495\pi\)
\(224\) −3.26843 + 3.26843i −0.218381 + 0.218381i
\(225\) −7.68265 −0.512176
\(226\) −7.19994 + 7.19994i −0.478933 + 0.478933i
\(227\) −8.29868 8.29868i −0.550803 0.550803i 0.375870 0.926673i \(-0.377344\pi\)
−0.926673 + 0.375870i \(0.877344\pi\)
\(228\) 4.76182 + 4.76182i 0.315359 + 0.315359i
\(229\) 25.8897i 1.71084i 0.517935 + 0.855420i \(0.326701\pi\)
−0.517935 + 0.855420i \(0.673299\pi\)
\(230\) 4.82843i 0.318377i
\(231\) −27.6230 27.6230i −1.81746 1.81746i
\(232\) 2.10308 + 2.10308i 0.138074 + 0.138074i
\(233\) 9.65141 9.65141i 0.632285 0.632285i −0.316356 0.948641i \(-0.602459\pi\)
0.948641 + 0.316356i \(0.102459\pi\)
\(234\) 1.11999 0.0732161
\(235\) 5.99378 5.99378i 0.390991 0.390991i
\(236\) 5.71724i 0.372161i
\(237\) −15.2232 −0.988850
\(238\) 2.79195 18.8525i 0.180975 1.22202i
\(239\) −25.4736 −1.64775 −0.823875 0.566771i \(-0.808192\pi\)
−0.823875 + 0.566771i \(0.808192\pi\)
\(240\) 3.26843i 0.210976i
\(241\) 5.65763 5.65763i 0.364440 0.364440i −0.501005 0.865445i \(-0.667036\pi\)
0.865445 + 0.501005i \(0.167036\pi\)
\(242\) −4.31371 −0.277296
\(243\) 29.8764 29.8764i 1.91657 1.91657i
\(244\) −2.63995 2.63995i −0.169005 0.169005i
\(245\) 10.1578 + 10.1578i 0.648958 + 0.648958i
\(246\) 25.5928i 1.63174i
\(247\) 0.300367i 0.0191119i
\(248\) −2.78573 2.78573i −0.176894 0.176894i
\(249\) 20.6010 + 20.6010i 1.30554 + 1.30554i
\(250\) −0.707107 + 0.707107i −0.0447214 + 0.0447214i
\(251\) 8.60981 0.543446 0.271723 0.962375i \(-0.412406\pi\)
0.271723 + 0.962375i \(0.412406\pi\)
\(252\) 25.1102 25.1102i 1.58179 1.58179i
\(253\) 12.4853i 0.784943i
\(254\) −11.1841 −0.701755
\(255\) −8.03025 10.8222i −0.502874 0.677713i
\(256\) 1.00000 0.0625000
\(257\) 13.7976i 0.860670i 0.902669 + 0.430335i \(0.141605\pi\)
−0.902669 + 0.430335i \(0.858395\pi\)
\(258\) 1.43812 1.43812i 0.0895337 0.0895337i
\(259\) 15.9500 0.991083
\(260\) 0.103083 0.103083i 0.00639296 0.00639296i
\(261\) −16.1572 16.1572i −1.00011 1.00011i
\(262\) −10.5715 10.5715i −0.653107 0.653107i
\(263\) 22.3271i 1.37674i 0.725357 + 0.688372i \(0.241675\pi\)
−0.725357 + 0.688372i \(0.758325\pi\)
\(264\) 8.45147i 0.520152i
\(265\) −4.72534 4.72534i −0.290276 0.290276i
\(266\) −6.73423 6.73423i −0.412902 0.412902i
\(267\) 36.9290 36.9290i 2.26002 2.26002i
\(268\) −1.58767 −0.0969822
\(269\) 11.2747 11.2747i 0.687428 0.687428i −0.274235 0.961663i \(-0.588425\pi\)
0.961663 + 0.274235i \(0.0884246\pi\)
\(270\) 15.3049i 0.931427i
\(271\) −30.8765 −1.87561 −0.937806 0.347159i \(-0.887146\pi\)
−0.937806 + 0.347159i \(0.887146\pi\)
\(272\) −3.31113 + 2.45691i −0.200767 + 0.148972i
\(273\) −2.20241 −0.133296
\(274\) 14.1583i 0.855337i
\(275\) −1.82843 + 1.82843i −0.110258 + 0.110258i
\(276\) −15.7814 −0.949928
\(277\) −19.7325 + 19.7325i −1.18561 + 1.18561i −0.207340 + 0.978269i \(0.566481\pi\)
−0.978269 + 0.207340i \(0.933519\pi\)
\(278\) 15.0729 + 15.0729i 0.904015 + 0.904015i
\(279\) 21.4018 + 21.4018i 1.28129 + 1.28129i
\(280\) 4.62226i 0.276233i
\(281\) 10.2879i 0.613726i 0.951754 + 0.306863i \(0.0992793\pi\)
−0.951754 + 0.306863i \(0.900721\pi\)
\(282\) 19.5902 + 19.5902i 1.16658 + 1.16658i
\(283\) −8.51730 8.51730i −0.506301 0.506301i 0.407088 0.913389i \(-0.366544\pi\)
−0.913389 + 0.407088i \(0.866544\pi\)
\(284\) −1.83653 + 1.83653i −0.108978 + 0.108978i
\(285\) −6.73423 −0.398901
\(286\) 0.266552 0.266552i 0.0157615 0.0157615i
\(287\) 36.1937i 2.13645i
\(288\) −7.68265 −0.452704
\(289\) 4.92717 16.2703i 0.289833 0.957077i
\(290\) −2.97421 −0.174652
\(291\) 58.1547i 3.40909i
\(292\) 5.82220 5.82220i 0.340719 0.340719i
\(293\) −30.6024 −1.78781 −0.893906 0.448255i \(-0.852046\pi\)
−0.893906 + 0.448255i \(0.852046\pi\)
\(294\) −33.2001 + 33.2001i −1.93627 + 1.93627i
\(295\) −4.04270 4.04270i −0.235375 0.235375i
\(296\) −2.44000 2.44000i −0.141822 0.141822i
\(297\) 39.5752i 2.29639i
\(298\) 10.2791i 0.595453i
\(299\) 0.497731 + 0.497731i 0.0287845 + 0.0287845i
\(300\) −2.31113 2.31113i −0.133433 0.133433i
\(301\) −2.03382 + 2.03382i −0.117227 + 0.117227i
\(302\) 6.53686 0.376154
\(303\) −17.6960 + 17.6960i −1.01661 + 1.01661i
\(304\) 2.06038i 0.118171i
\(305\) 3.73345 0.213777
\(306\) 25.4382 18.8756i 1.45421 1.07905i
\(307\) −13.6268 −0.777722 −0.388861 0.921296i \(-0.627131\pi\)
−0.388861 + 0.921296i \(0.627131\pi\)
\(308\) 11.9522i 0.681039i
\(309\) −18.6576 + 18.6576i −1.06140 + 1.06140i
\(310\) 3.93962 0.223755
\(311\) 8.72792 8.72792i 0.494915 0.494915i −0.414936 0.909851i \(-0.636196\pi\)
0.909851 + 0.414936i \(0.136196\pi\)
\(312\) 0.336921 + 0.336921i 0.0190744 + 0.0190744i
\(313\) −8.73345 8.73345i −0.493644 0.493644i 0.415809 0.909452i \(-0.363499\pi\)
−0.909452 + 0.415809i \(0.863499\pi\)
\(314\) 12.4337i 0.701674i
\(315\) 35.5112i 2.00083i
\(316\) −3.29344 3.29344i −0.185271 0.185271i
\(317\) 11.3288 + 11.3288i 0.636290 + 0.636290i 0.949638 0.313348i \(-0.101451\pi\)
−0.313348 + 0.949638i \(0.601451\pi\)
\(318\) 15.4445 15.4445i 0.866082 0.866082i
\(319\) −7.69067 −0.430595
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) 7.77762i 0.434105i
\(322\) 22.3182 1.24375
\(323\) −5.06218 6.82220i −0.281667 0.379597i
\(324\) 26.9751 1.49862
\(325\) 0.145782i 0.00808653i
\(326\) −0.562654 + 0.562654i −0.0311625 + 0.0311625i
\(327\) 9.72100 0.537572
\(328\) 5.53686 5.53686i 0.305722 0.305722i
\(329\) −27.7048 27.7048i −1.52741 1.52741i
\(330\) −5.97609 5.97609i −0.328973 0.328973i
\(331\) 10.5494i 0.579849i −0.957050 0.289924i \(-0.906370\pi\)
0.957050 0.289924i \(-0.0936302\pi\)
\(332\) 8.91382i 0.489210i
\(333\) 18.7457 + 18.7457i 1.02726 + 1.02726i
\(334\) 3.36263 + 3.36263i 0.183995 + 0.183995i
\(335\) 1.12265 1.12265i 0.0613369 0.0613369i
\(336\) 15.1075 0.824184
\(337\) 8.95840 8.95840i 0.487995 0.487995i −0.419678 0.907673i \(-0.637857\pi\)
0.907673 + 0.419678i \(0.137857\pi\)
\(338\) 12.9787i 0.705951i
\(339\) 33.2800 1.80752
\(340\) 0.604023 4.07862i 0.0327578 0.221194i
\(341\) 10.1870 0.551657
\(342\) 15.8292i 0.855945i
\(343\) 24.0729 24.0729i 1.29982 1.29982i
\(344\) 0.622260 0.0335500
\(345\) 11.1591 11.1591i 0.600787 0.600787i
\(346\) −9.00188 9.00188i −0.483944 0.483944i
\(347\) 2.59024 + 2.59024i 0.139052 + 0.139052i 0.773206 0.634155i \(-0.218652\pi\)
−0.634155 + 0.773206i \(0.718652\pi\)
\(348\) 9.72100i 0.521100i
\(349\) 28.5120i 1.52621i −0.646274 0.763105i \(-0.723674\pi\)
0.646274 0.763105i \(-0.276326\pi\)
\(350\) 3.26843 + 3.26843i 0.174705 + 0.174705i
\(351\) −1.57768 1.57768i −0.0842104 0.0842104i
\(352\) −1.82843 + 1.82843i −0.0974555 + 0.0974555i
\(353\) −9.22691 −0.491099 −0.245550 0.969384i \(-0.578968\pi\)
−0.245550 + 0.969384i \(0.578968\pi\)
\(354\) 13.2133 13.2133i 0.702278 0.702278i
\(355\) 2.59725i 0.137848i
\(356\) 15.9787 0.846872
\(357\) −50.0230 + 37.1179i −2.64750 + 1.96449i
\(358\) −0.170794 −0.00902675
\(359\) 23.1576i 1.22221i −0.791550 0.611105i \(-0.790725\pi\)
0.791550 0.611105i \(-0.209275\pi\)
\(360\) 5.43245 5.43245i 0.286315 0.286315i
\(361\) 14.7548 0.776569
\(362\) 3.32882 3.32882i 0.174959 0.174959i
\(363\) 9.96954 + 9.96954i 0.523265 + 0.523265i
\(364\) −0.476478 0.476478i −0.0249743 0.0249743i
\(365\) 8.23384i 0.430979i
\(366\) 12.2025i 0.637836i
\(367\) −5.65951 5.65951i −0.295424 0.295424i 0.543794 0.839219i \(-0.316987\pi\)
−0.839219 + 0.543794i \(0.816987\pi\)
\(368\) −3.41421 3.41421i −0.177978 0.177978i
\(369\) −42.5378 + 42.5378i −2.21443 + 2.21443i
\(370\) 3.45069 0.179393
\(371\) −21.8418 + 21.8418i −1.13397 + 1.13397i
\(372\) 12.8764i 0.667608i
\(373\) −16.1245 −0.834896 −0.417448 0.908701i \(-0.637075\pi\)
−0.417448 + 0.908701i \(0.637075\pi\)
\(374\) 1.56188 10.5464i 0.0807627 0.545344i
\(375\) 3.26843 0.168781
\(376\) 8.47648i 0.437141i
\(377\) −0.306592 + 0.306592i −0.0157903 + 0.0157903i
\(378\) −70.7433 −3.63864
\(379\) 23.6577 23.6577i 1.21522 1.21522i 0.245929 0.969288i \(-0.420907\pi\)
0.969288 0.245929i \(-0.0790930\pi\)
\(380\) −1.45691 1.45691i −0.0747380 0.0747380i
\(381\) 25.8480 + 25.8480i 1.32423 + 1.32423i
\(382\) 4.79461i 0.245314i
\(383\) 17.5273i 0.895602i −0.894133 0.447801i \(-0.852207\pi\)
0.894133 0.447801i \(-0.147793\pi\)
\(384\) −2.31113 2.31113i −0.117939 0.117939i
\(385\) 8.45147 + 8.45147i 0.430727 + 0.430727i
\(386\) 10.6819 10.6819i 0.543693 0.543693i
\(387\) −4.78061 −0.243012
\(388\) −12.5814 + 12.5814i −0.638726 + 0.638726i
\(389\) 5.39395i 0.273484i −0.990607 0.136742i \(-0.956337\pi\)
0.990607 0.136742i \(-0.0436631\pi\)
\(390\) −0.476478 −0.0241274
\(391\) 19.6933 + 2.91648i 0.995934 + 0.147493i
\(392\) −14.3653 −0.725557
\(393\) 48.8640i 2.46486i
\(394\) 4.85610 4.85610i 0.244647 0.244647i
\(395\) 4.65763 0.234351
\(396\) 14.0472 14.0472i 0.705896 0.705896i
\(397\) 22.1572 + 22.1572i 1.11204 + 1.11204i 0.992874 + 0.119166i \(0.0380220\pi\)
0.119166 + 0.992874i \(0.461978\pi\)
\(398\) 2.12810 + 2.12810i 0.106672 + 0.106672i
\(399\) 31.1274i 1.55832i
\(400\) 1.00000i 0.0500000i
\(401\) −27.5332 27.5332i −1.37494 1.37494i −0.852949 0.521994i \(-0.825188\pi\)
−0.521994 0.852949i \(-0.674812\pi\)
\(402\) 3.66930 + 3.66930i 0.183008 + 0.183008i
\(403\) 0.406109 0.406109i 0.0202297 0.0202297i
\(404\) −7.65685 −0.380943
\(405\) −19.0743 + 19.0743i −0.947808 + 0.947808i
\(406\) 13.7476i 0.682280i
\(407\) 8.92274 0.442284
\(408\) 13.3307 + 1.97421i 0.659968 + 0.0977379i
\(409\) 16.6326 0.822430 0.411215 0.911538i \(-0.365105\pi\)
0.411215 + 0.911538i \(0.365105\pi\)
\(410\) 7.83031i 0.386711i
\(411\) 32.7218 32.7218i 1.61405 1.61405i
\(412\) −8.07295 −0.397726
\(413\) −18.6864 + 18.6864i −0.919498 + 0.919498i
\(414\) 26.2302 + 26.2302i 1.28914 + 1.28914i
\(415\) −6.30303 6.30303i −0.309403 0.309403i
\(416\) 0.145782i 0.00714755i
\(417\) 69.6711i 3.41181i
\(418\) −3.76726 3.76726i −0.184263 0.184263i
\(419\) 20.3049 + 20.3049i 0.991960 + 0.991960i 0.999968 0.00800839i \(-0.00254918\pi\)
−0.00800839 + 0.999968i \(0.502549\pi\)
\(420\) −10.6826 + 10.6826i −0.521260 + 0.521260i
\(421\) 28.5974 1.39375 0.696875 0.717193i \(-0.254573\pi\)
0.696875 + 0.717193i \(0.254573\pi\)
\(422\) −1.47648 + 1.47648i −0.0718738 + 0.0718738i
\(423\) 65.1218i 3.16633i
\(424\) 6.68265 0.324538
\(425\) 2.45691 + 3.31113i 0.119178 + 0.160613i
\(426\) 8.48893 0.411290
\(427\) 17.2570i 0.835123i
\(428\) −1.68265 + 1.68265i −0.0813337 + 0.0813337i
\(429\) −1.23207 −0.0594850
\(430\) −0.440004 + 0.440004i −0.0212189 + 0.0212189i
\(431\) 1.39800 + 1.39800i 0.0673395 + 0.0673395i 0.739974 0.672635i \(-0.234838\pi\)
−0.672635 + 0.739974i \(0.734838\pi\)
\(432\) 10.8222 + 10.8222i 0.520683 + 0.520683i
\(433\) 35.6444i 1.71296i 0.516180 + 0.856480i \(0.327354\pi\)
−0.516180 + 0.856480i \(0.672646\pi\)
\(434\) 18.2099i 0.874104i
\(435\) 6.87378 + 6.87378i 0.329573 + 0.329573i
\(436\) 2.10308 + 2.10308i 0.100719 + 0.100719i
\(437\) 7.03459 7.03459i 0.336510 0.336510i
\(438\) −26.9117 −1.28589
\(439\) −10.9165 + 10.9165i −0.521015 + 0.521015i −0.917878 0.396863i \(-0.870099\pi\)
0.396863 + 0.917878i \(0.370099\pi\)
\(440\) 2.58579i 0.123273i
\(441\) 110.363 5.25540
\(442\) −0.358173 0.482703i −0.0170366 0.0229598i
\(443\) −8.63471 −0.410247 −0.205124 0.978736i \(-0.565760\pi\)
−0.205124 + 0.978736i \(0.565760\pi\)
\(444\) 11.2783i 0.535246i
\(445\) −11.2987 + 11.2987i −0.535609 + 0.535609i
\(446\) −22.6186 −1.07102
\(447\) 23.7564 23.7564i 1.12364 1.12364i
\(448\) 3.26843 + 3.26843i 0.154419 + 0.154419i
\(449\) 5.98677 + 5.98677i 0.282533 + 0.282533i 0.834119 0.551585i \(-0.185977\pi\)
−0.551585 + 0.834119i \(0.685977\pi\)
\(450\) 7.68265i 0.362163i
\(451\) 20.2475i 0.953418i
\(452\) 7.19994 + 7.19994i 0.338657 + 0.338657i
\(453\) −15.1075 15.1075i −0.709814 0.709814i
\(454\) −8.29868 + 8.29868i −0.389476 + 0.389476i
\(455\) 0.673842 0.0315902
\(456\) 4.76182 4.76182i 0.222993 0.222993i
\(457\) 33.1305i 1.54978i −0.632097 0.774889i \(-0.717806\pi\)
0.632097 0.774889i \(-0.282194\pi\)
\(458\) 25.8897 1.20975
\(459\) −62.4229 9.24452i −2.91365 0.431497i
\(460\) 4.82843 0.225127
\(461\) 12.8035i 0.596320i −0.954516 0.298160i \(-0.903627\pi\)
0.954516 0.298160i \(-0.0963729\pi\)
\(462\) −27.6230 + 27.6230i −1.28514 + 1.28514i
\(463\) 25.9877 1.20775 0.603875 0.797079i \(-0.293623\pi\)
0.603875 + 0.797079i \(0.293623\pi\)
\(464\) 2.10308 2.10308i 0.0976332 0.0976332i
\(465\) −9.10496 9.10496i −0.422233 0.422233i
\(466\) −9.65141 9.65141i −0.447093 0.447093i
\(467\) 11.1805i 0.517371i 0.965962 + 0.258686i \(0.0832894\pi\)
−0.965962 + 0.258686i \(0.916711\pi\)
\(468\) 1.11999i 0.0517716i
\(469\) −5.18918 5.18918i −0.239614 0.239614i
\(470\) −5.99378 5.99378i −0.276472 0.276472i
\(471\) −28.7359 + 28.7359i −1.32408 + 1.32408i
\(472\) 5.71724 0.263157
\(473\) −1.13776 + 1.13776i −0.0523142 + 0.0523142i
\(474\) 15.2232i 0.699223i
\(475\) 2.06038 0.0945369
\(476\) −18.8525 2.79195i −0.864101 0.127969i
\(477\) −51.3404 −2.35072
\(478\) 25.4736i 1.16514i
\(479\) −7.57878 + 7.57878i −0.346283 + 0.346283i −0.858723 0.512440i \(-0.828742\pi\)
0.512440 + 0.858723i \(0.328742\pi\)
\(480\) 3.26843 0.149183
\(481\) 0.355709 0.355709i 0.0162189 0.0162189i
\(482\) −5.65763 5.65763i −0.257698 0.257698i
\(483\) −51.5804 51.5804i −2.34699 2.34699i
\(484\) 4.31371i 0.196078i
\(485\) 17.7928i 0.807931i
\(486\) −29.8764 29.8764i −1.35522 1.35522i
\(487\) −19.9761 19.9761i −0.905203 0.905203i 0.0906773 0.995880i \(-0.471097\pi\)
−0.995880 + 0.0906773i \(0.971097\pi\)
\(488\) −2.63995 + 2.63995i −0.119505 + 0.119505i
\(489\) 2.60073 0.117609
\(490\) 10.1578 10.1578i 0.458882 0.458882i
\(491\) 9.08253i 0.409889i −0.978774 0.204944i \(-0.934299\pi\)
0.978774 0.204944i \(-0.0657014\pi\)
\(492\) −25.5928 −1.15381
\(493\) −1.79649 + 12.1307i −0.0809099 + 0.546338i
\(494\) −0.300367 −0.0135141
\(495\) 19.8657i 0.892896i
\(496\) −2.78573 + 2.78573i −0.125083 + 0.125083i
\(497\) −12.0052 −0.538505
\(498\) 20.6010 20.6010i 0.923153 0.923153i
\(499\) −2.62304 2.62304i −0.117423 0.117423i 0.645953 0.763377i \(-0.276460\pi\)
−0.763377 + 0.645953i \(0.776460\pi\)
\(500\) 0.707107 + 0.707107i 0.0316228 + 0.0316228i
\(501\) 15.5430i 0.694408i
\(502\) 8.60981i 0.384275i
\(503\) 2.84354 + 2.84354i 0.126787 + 0.126787i 0.767653 0.640866i \(-0.221425\pi\)
−0.640866 + 0.767653i \(0.721425\pi\)
\(504\) −25.1102 25.1102i −1.11850 1.11850i
\(505\) 5.41421 5.41421i 0.240929 0.240929i
\(506\) 12.4853 0.555038
\(507\) 29.9956 29.9956i 1.33215 1.33215i
\(508\) 11.1841i 0.496216i
\(509\) 21.0221 0.931790 0.465895 0.884840i \(-0.345732\pi\)
0.465895 + 0.884840i \(0.345732\pi\)
\(510\) −10.8222 + 8.03025i −0.479215 + 0.355585i
\(511\) 38.0589 1.68363
\(512\) 1.00000i 0.0441942i
\(513\) −22.2979 + 22.2979i −0.984476 + 0.984476i
\(514\) 13.7976 0.608586
\(515\) 5.70844 5.70844i 0.251544 0.251544i
\(516\) −1.43812 1.43812i −0.0633099 0.0633099i
\(517\) −15.4986 15.4986i −0.681629 0.681629i
\(518\) 15.9500i 0.700802i
\(519\) 41.6090i 1.82643i
\(520\) −0.103083 0.103083i −0.00452051 0.00452051i
\(521\) −3.14578 3.14578i −0.137819 0.137819i 0.634831 0.772651i \(-0.281070\pi\)
−0.772651 + 0.634831i \(0.781070\pi\)
\(522\) −16.1572 + 16.1572i −0.707183 + 0.707183i
\(523\) −2.55823 −0.111864 −0.0559318 0.998435i \(-0.517813\pi\)
−0.0559318 + 0.998435i \(0.517813\pi\)
\(524\) −10.5715 + 10.5715i −0.461816 + 0.461816i
\(525\) 15.1075i 0.659347i
\(526\) 22.3271 0.973506
\(527\) 2.37962 16.0682i 0.103658 0.699942i
\(528\) 8.45147 0.367803
\(529\) 0.313708i 0.0136395i
\(530\) −4.72534 + 4.72534i −0.205256 + 0.205256i
\(531\) −43.9235 −1.90612
\(532\) −6.73423 + 6.73423i −0.291966 + 0.291966i
\(533\) 0.807175 + 0.807175i 0.0349626 + 0.0349626i
\(534\) −36.9290 36.9290i −1.59807 1.59807i
\(535\) 2.37962i 0.102880i
\(536\) 1.58767i 0.0685767i
\(537\) 0.394728 + 0.394728i 0.0170338 + 0.0170338i
\(538\) −11.2747 11.2747i −0.486085 0.486085i
\(539\) 26.2659 26.2659i 1.13135 1.13135i
\(540\) −15.3049 −0.658618
\(541\) −20.3318 + 20.3318i −0.874132 + 0.874132i −0.992920 0.118787i \(-0.962099\pi\)
0.118787 + 0.992920i \(0.462099\pi\)
\(542\) 30.8765i 1.32626i
\(543\) −15.3867 −0.660305
\(544\) 2.45691 + 3.31113i 0.105339 + 0.141964i
\(545\) −2.97421 −0.127401
\(546\) 2.20241i 0.0942543i
\(547\) −7.93417 + 7.93417i −0.339241 + 0.339241i −0.856081 0.516841i \(-0.827108\pi\)
0.516841 + 0.856081i \(0.327108\pi\)
\(548\) 14.1583 0.604815
\(549\) 20.2818 20.2818i 0.865605 0.865605i
\(550\) 1.82843 + 1.82843i 0.0779644 + 0.0779644i
\(551\) 4.33316 + 4.33316i 0.184599 + 0.184599i
\(552\) 15.7814i 0.671700i
\(553\) 21.5288i 0.915497i
\(554\) 19.7325 + 19.7325i 0.838352 + 0.838352i
\(555\) −7.97499 7.97499i −0.338519 0.338519i
\(556\) 15.0729 15.0729i 0.639235 0.639235i
\(557\) 37.4862 1.58834 0.794170 0.607696i \(-0.207906\pi\)
0.794170 + 0.607696i \(0.207906\pi\)
\(558\) 21.4018 21.4018i 0.906009 0.906009i
\(559\) 0.0907143i 0.00383681i
\(560\) −4.62226 −0.195326
\(561\) −27.9839 + 20.7645i −1.18148 + 0.876678i
\(562\) 10.2879 0.433970
\(563\) 21.9751i 0.926140i 0.886322 + 0.463070i \(0.153252\pi\)
−0.886322 + 0.463070i \(0.846748\pi\)
\(564\) 19.5902 19.5902i 0.824898 0.824898i
\(565\) −10.1823 −0.428371
\(566\) −8.51730 + 8.51730i −0.358009 + 0.358009i
\(567\) 88.1663 + 88.1663i 3.70264 + 3.70264i
\(568\) 1.83653 + 1.83653i 0.0770592 + 0.0770592i
\(569\) 15.3425i 0.643190i −0.946877 0.321595i \(-0.895781\pi\)
0.946877 0.321595i \(-0.104219\pi\)
\(570\) 6.73423i 0.282066i
\(571\) 1.57068 + 1.57068i 0.0657308 + 0.0657308i 0.739208 0.673477i \(-0.235200\pi\)
−0.673477 + 0.739208i \(0.735200\pi\)
\(572\) −0.266552 0.266552i −0.0111451 0.0111451i
\(573\) −11.0810 + 11.0810i −0.462914 + 0.462914i
\(574\) 36.1937 1.51070
\(575\) −3.41421 + 3.41421i −0.142383 + 0.142383i
\(576\) 7.68265i 0.320110i
\(577\) 1.36685 0.0569026 0.0284513 0.999595i \(-0.490942\pi\)
0.0284513 + 0.999595i \(0.490942\pi\)
\(578\) −16.2703 4.92717i −0.676756 0.204943i
\(579\) −49.3744 −2.05193
\(580\) 2.97421i 0.123497i
\(581\) −29.1342 + 29.1342i −1.20869 + 1.20869i
\(582\) 58.1547 2.41059
\(583\) −12.2187 + 12.2187i −0.506048 + 0.506048i
\(584\) −5.82220 5.82220i −0.240924 0.240924i
\(585\) 0.791953 + 0.791953i 0.0327432 + 0.0327432i
\(586\) 30.6024i 1.26417i
\(587\) 36.4050i 1.50260i 0.659963 + 0.751298i \(0.270572\pi\)
−0.659963 + 0.751298i \(0.729428\pi\)
\(588\) 33.2001 + 33.2001i 1.36915 + 1.36915i
\(589\) −5.73967 5.73967i −0.236499 0.236499i
\(590\) −4.04270 + 4.04270i −0.166435 + 0.166435i
\(591\) −22.4461 −0.923311
\(592\) −2.44000 + 2.44000i −0.100284 + 0.100284i
\(593\) 20.7822i 0.853421i −0.904388 0.426711i \(-0.859672\pi\)
0.904388 0.426711i \(-0.140328\pi\)
\(594\) −39.5752 −1.62379
\(595\) 15.3049 11.3565i 0.627440 0.465571i
\(596\) 10.2791 0.421049
\(597\) 9.83661i 0.402586i
\(598\) 0.497731 0.497731i 0.0203537 0.0203537i
\(599\) 11.2961 0.461546 0.230773 0.973008i \(-0.425874\pi\)
0.230773 + 0.973008i \(0.425874\pi\)
\(600\) −2.31113 + 2.31113i −0.0943515 + 0.0943515i
\(601\) −30.6356 30.6356i −1.24965 1.24965i −0.955873 0.293779i \(-0.905087\pi\)
−0.293779 0.955873i \(-0.594913\pi\)
\(602\) 2.03382 + 2.03382i 0.0828921 + 0.0828921i
\(603\) 12.1975i 0.496720i
\(604\) 6.53686i 0.265981i
\(605\) −3.05025 3.05025i −0.124010 0.124010i
\(606\) 17.6960 + 17.6960i 0.718850 + 0.718850i
\(607\) −28.6035 + 28.6035i −1.16098 + 1.16098i −0.176719 + 0.984261i \(0.556548\pi\)
−0.984261 + 0.176719i \(0.943452\pi\)
\(608\) 2.06038 0.0835596
\(609\) 31.7724 31.7724i 1.28748 1.28748i
\(610\) 3.73345i 0.151163i
\(611\) −1.23572 −0.0499918
\(612\) −18.8756 25.4382i −0.763000 1.02828i
\(613\) −6.73799 −0.272145 −0.136072 0.990699i \(-0.543448\pi\)
−0.136072 + 0.990699i \(0.543448\pi\)
\(614\) 13.6268i 0.549933i
\(615\) 18.0969 18.0969i 0.729736 0.729736i
\(616\) −11.9522 −0.481567
\(617\) 17.4915 17.4915i 0.704182 0.704182i −0.261124 0.965305i \(-0.584093\pi\)
0.965305 + 0.261124i \(0.0840931\pi\)
\(618\) 18.6576 + 18.6576i 0.750520 + 0.750520i
\(619\) 15.9442 + 15.9442i 0.640850 + 0.640850i 0.950764 0.309915i \(-0.100301\pi\)
−0.309915 + 0.950764i \(0.600301\pi\)
\(620\) 3.93962i 0.158219i
\(621\) 73.8986i 2.96545i
\(622\) −8.72792 8.72792i −0.349958 0.349958i
\(623\) 52.2254 + 52.2254i 2.09237 + 2.09237i
\(624\) 0.336921 0.336921i 0.0134876 0.0134876i
\(625\) −1.00000 −0.0400000
\(626\) −8.73345 + 8.73345i −0.349059 + 0.349059i
\(627\) 17.4133i 0.695419i
\(628\) −12.4337 −0.496159
\(629\) 2.08430 14.0740i 0.0831063 0.561169i
\(630\) 35.5112 1.41480
\(631\) 5.83297i 0.232207i −0.993237 0.116103i \(-0.962960\pi\)
0.993237 0.116103i \(-0.0370404\pi\)
\(632\) −3.29344 + 3.29344i −0.131006 + 0.131006i
\(633\) 6.82467 0.271256
\(634\) 11.3288 11.3288i 0.449925 0.449925i
\(635\) −7.90838 7.90838i −0.313834 0.313834i
\(636\) −15.4445 15.4445i −0.612413 0.612413i
\(637\) 2.09420i 0.0829752i
\(638\) 7.69067i 0.304477i
\(639\) −14.1094 14.1094i −0.558160 0.558160i
\(640\) 0.707107 + 0.707107i 0.0279508 + 0.0279508i
\(641\) 8.08629 8.08629i 0.319389 0.319389i −0.529143 0.848532i \(-0.677487\pi\)
0.848532 + 0.529143i \(0.177487\pi\)
\(642\) 7.77762 0.306958
\(643\) −2.42192 + 2.42192i −0.0955110 + 0.0955110i −0.753248 0.657737i \(-0.771514\pi\)
0.657737 + 0.753248i \(0.271514\pi\)
\(644\) 22.3182i 0.879462i
\(645\) 2.03382 0.0800814
\(646\) −6.82220 + 5.06218i −0.268416 + 0.199169i
\(647\) 32.9671 1.29607 0.648035 0.761611i \(-0.275591\pi\)
0.648035 + 0.761611i \(0.275591\pi\)
\(648\) 26.9751i 1.05968i
\(649\) −10.4536 + 10.4536i −0.410338 + 0.410338i
\(650\) 0.145782 0.00571804
\(651\) −42.0855 + 42.0855i −1.64946 + 1.64946i
\(652\) 0.562654 + 0.562654i 0.0220352 + 0.0220352i
\(653\) 2.47382 + 2.47382i 0.0968080 + 0.0968080i 0.753852 0.657044i \(-0.228193\pi\)
−0.657044 + 0.753852i \(0.728193\pi\)
\(654\) 9.72100i 0.380121i
\(655\) 14.9503i 0.584156i
\(656\) −5.53686 5.53686i −0.216178 0.216178i
\(657\) 44.7299 + 44.7299i 1.74508 + 1.74508i
\(658\) −27.7048 + 27.7048i −1.08005 + 1.08005i
\(659\) 38.0355 1.48165 0.740826 0.671697i \(-0.234434\pi\)
0.740826 + 0.671697i \(0.234434\pi\)
\(660\) −5.97609 + 5.97609i −0.232619 + 0.232619i
\(661\) 16.7077i 0.649853i −0.945739 0.324926i \(-0.894661\pi\)
0.945739 0.324926i \(-0.105339\pi\)
\(662\) −10.5494 −0.410015
\(663\) −0.287804 + 1.94337i −0.0111774 + 0.0754744i
\(664\) 8.91382 0.345923
\(665\) 9.52364i 0.369311i
\(666\) 18.7457 18.7457i 0.726381 0.726381i
\(667\) −14.3608 −0.556051
\(668\) 3.36263 3.36263i 0.130104 0.130104i
\(669\) 52.2746 + 52.2746i 2.02105 + 2.02105i
\(670\) −1.12265 1.12265i −0.0433717 0.0433717i
\(671\) 9.65390i 0.372685i
\(672\) 15.1075i 0.582786i
\(673\) 21.0829 + 21.0829i 0.812687 + 0.812687i 0.985036 0.172349i \(-0.0551356\pi\)
−0.172349 + 0.985036i \(0.555136\pi\)
\(674\) −8.95840 8.95840i −0.345065 0.345065i
\(675\) 10.8222 10.8222i 0.416547 0.416547i
\(676\) 12.9787 0.499183
\(677\) 7.32517 7.32517i 0.281529 0.281529i −0.552189 0.833719i \(-0.686208\pi\)
0.833719 + 0.552189i \(0.186208\pi\)
\(678\) 33.2800i 1.27811i
\(679\) −82.2432 −3.15620
\(680\) −4.07862 0.604023i −0.156408 0.0231632i
\(681\) 38.3587 1.46991
\(682\) 10.1870i 0.390081i
\(683\) −20.1403 + 20.1403i −0.770649 + 0.770649i −0.978220 0.207571i \(-0.933444\pi\)
0.207571 + 0.978220i \(0.433444\pi\)
\(684\) −15.8292 −0.605245
\(685\) −10.0115 + 10.0115i −0.382518 + 0.382518i
\(686\) −24.0729 24.0729i −0.919109 0.919109i
\(687\) −59.8345 59.8345i −2.28283 2.28283i
\(688\) 0.622260i 0.0237235i
\(689\) 0.974209i 0.0371144i
\(690\) −11.1591 11.1591i −0.424821 0.424821i
\(691\) 34.6090 + 34.6090i 1.31659 + 1.31659i 0.916457 + 0.400132i \(0.131036\pi\)
0.400132 + 0.916457i \(0.368964\pi\)
\(692\) −9.00188 + 9.00188i −0.342200 + 0.342200i
\(693\) 91.8243 3.48812
\(694\) 2.59024 2.59024i 0.0983243 0.0983243i
\(695\) 21.3164i 0.808576i
\(696\) −9.72100 −0.368474
\(697\) 31.9369 + 4.72969i 1.20969 + 0.179150i
\(698\) −28.5120 −1.07919
\(699\) 44.6113i 1.68736i
\(700\) 3.26843 3.26843i 0.123535 0.123535i
\(701\) −8.53155 −0.322232 −0.161116 0.986935i \(-0.551509\pi\)
−0.161116 + 0.986935i \(0.551509\pi\)
\(702\) −1.57768 + 1.57768i −0.0595458 + 0.0595458i
\(703\) −5.02735 5.02735i −0.189610 0.189610i
\(704\) 1.82843 + 1.82843i 0.0689114 + 0.0689114i
\(705\) 27.7048i 1.04342i
\(706\) 9.22691i 0.347260i
\(707\) −25.0259 25.0259i −0.941196 0.941196i
\(708\) −13.2133 13.2133i −0.496586 0.496586i
\(709\) 9.95226 9.95226i 0.373765 0.373765i −0.495082 0.868846i \(-0.664862\pi\)
0.868846 + 0.495082i \(0.164862\pi\)
\(710\) −2.59725 −0.0974730
\(711\) 25.3024 25.3024i 0.948913 0.948913i
\(712\) 15.9787i 0.598829i
\(713\) 19.0221 0.712385
\(714\) 37.1179 + 50.0230i 1.38910 + 1.87207i
\(715\) 0.376961 0.0140975
\(716\) 0.170794i 0.00638288i
\(717\) 58.8728 58.8728i 2.19865 2.19865i
\(718\) −23.1576 −0.864233
\(719\) 2.74660 2.74660i 0.102431 0.102431i −0.654034 0.756465i \(-0.726925\pi\)
0.756465 + 0.654034i \(0.226925\pi\)
\(720\) −5.43245 5.43245i −0.202455 0.202455i
\(721\) −26.3859 26.3859i −0.982661 0.982661i
\(722\) 14.7548i 0.549117i
\(723\) 26.1511i 0.972568i
\(724\) −3.32882 3.32882i −0.123714 0.123714i
\(725\) −2.10308 2.10308i −0.0781066 0.0781066i
\(726\) 9.96954 9.96954i 0.370004 0.370004i
\(727\) −43.7477 −1.62251 −0.811256 0.584691i \(-0.801216\pi\)
−0.811256 + 0.584691i \(0.801216\pi\)
\(728\) −0.476478 + 0.476478i −0.0176595 + 0.0176595i
\(729\) 57.1710i 2.11745i
\(730\) 8.23384 0.304748
\(731\) 1.52884 + 2.06038i 0.0565461 + 0.0762061i
\(732\) 12.2025 0.451018
\(733\) 27.1945i 1.00445i −0.864737 0.502226i \(-0.832515\pi\)
0.864737 0.502226i \(-0.167485\pi\)
\(734\) −5.65951 + 5.65951i −0.208896 + 0.208896i
\(735\) −46.9520 −1.73185
\(736\) −3.41421 + 3.41421i −0.125850 + 0.125850i
\(737\) −2.90293 2.90293i −0.106931 0.106931i
\(738\) 42.5378 + 42.5378i 1.56584 + 1.56584i
\(739\) 14.5227i 0.534228i −0.963665 0.267114i \(-0.913930\pi\)
0.963665 0.267114i \(-0.0860700\pi\)
\(740\) 3.45069i 0.126850i
\(741\) 0.694187 + 0.694187i 0.0255016 + 0.0255016i
\(742\) 21.8418 + 21.8418i 0.801837 + 0.801837i
\(743\) 36.1912 36.1912i 1.32773 1.32773i 0.420375 0.907351i \(-0.361899\pi\)
0.907351 0.420375i \(-0.138101\pi\)
\(744\) 12.8764 0.472070
\(745\) −7.26843 + 7.26843i −0.266295 + 0.266295i
\(746\) 16.1245i 0.590361i
\(747\) −68.4817 −2.50562
\(748\) −10.5464 1.56188i −0.385616 0.0571078i
\(749\) −10.9992 −0.401903
\(750\) 3.26843i 0.119346i
\(751\) 12.4234 12.4234i 0.453337 0.453337i −0.443124 0.896461i \(-0.646130\pi\)
0.896461 + 0.443124i \(0.146130\pi\)
\(752\) 8.47648 0.309105
\(753\) −19.8984 + 19.8984i −0.725138 + 0.725138i
\(754\) 0.306592 + 0.306592i 0.0111654 + 0.0111654i
\(755\) 4.62226 + 4.62226i 0.168221 + 0.168221i
\(756\) 70.7433i 2.57291i
\(757\) 37.5091i 1.36329i 0.731682 + 0.681646i \(0.238735\pi\)
−0.731682 + 0.681646i \(0.761265\pi\)
\(758\) −23.6577 23.6577i −0.859288 0.859288i
\(759\) −28.8551 28.8551i −1.04737 1.04737i
\(760\) −1.45691 + 1.45691i −0.0528478 + 0.0528478i
\(761\) −31.7851 −1.15221 −0.576105 0.817375i \(-0.695428\pi\)
−0.576105 + 0.817375i \(0.695428\pi\)
\(762\) 25.8480 25.8480i 0.936374 0.936374i
\(763\) 13.7476i 0.497695i
\(764\) −4.79461 −0.173463
\(765\) 31.3346 + 4.64050i 1.13291 + 0.167778i
\(766\) −17.5273 −0.633286
\(767\) 0.833470i 0.0300949i
\(768\) −2.31113 + 2.31113i −0.0833957 + 0.0833957i
\(769\) −31.9023 −1.15043 −0.575213 0.818004i \(-0.695081\pi\)
−0.575213 + 0.818004i \(0.695081\pi\)
\(770\) 8.45147 8.45147i 0.304570 0.304570i
\(771\) −31.8880 31.8880i −1.14842 1.14842i
\(772\) −10.6819 10.6819i −0.384449 0.384449i
\(773\) 27.0913i 0.974408i 0.873288 + 0.487204i \(0.161983\pi\)
−0.873288 + 0.487204i \(0.838017\pi\)
\(774\) 4.78061i 0.171835i
\(775\) 2.78573 + 2.78573i 0.100066 + 0.100066i
\(776\) 12.5814 + 12.5814i 0.451647 + 0.451647i
\(777\) −36.8625 + 36.8625i −1.32243 + 1.32243i
\(778\) −5.39395 −0.193382
\(779\) 11.4081 11.4081i 0.408736 0.408736i
\(780\) 0.476478i 0.0170607i
\(781\) −6.71593 −0.240315
\(782\) 2.91648 19.6933i 0.104293 0.704232i
\(783\) 45.5200 1.62675
\(784\) 14.3653i 0.513046i
\(785\) 8.79195 8.79195i 0.313798 0.313798i
\(786\) 48.8640 1.74292
\(787\) −37.0771 + 37.0771i −1.32166 + 1.32166i −0.409219 + 0.912436i \(0.634199\pi\)
−0.912436 + 0.409219i \(0.865801\pi\)
\(788\) −4.85610 4.85610i −0.172991 0.172991i
\(789\) −51.6007 51.6007i −1.83703 1.83703i
\(790\) 4.65763i 0.165711i
\(791\) 47.0650i 1.67344i
\(792\) −14.0472 14.0472i −0.499144 0.499144i
\(793\) −0.384857 0.384857i −0.0136667 0.0136667i
\(794\) 22.1572 22.1572i 0.786331 0.786331i
\(795\) 21.8418 0.774648
\(796\) 2.12810 2.12810i 0.0754284 0.0754284i
\(797\) 34.4375i 1.21984i 0.792464 + 0.609919i \(0.208798\pi\)
−0.792464 + 0.609919i \(0.791202\pi\)
\(798\) 31.1274 1.10190
\(799\) −28.0667 + 20.8260i −0.992929 + 0.736770i
\(800\) −1.00000 −0.0353553
\(801\) 122.759i 4.33748i
\(802\) −27.5332 + 27.5332i −0.972232 + 0.972232i
\(803\) 21.2909 0.751341
\(804\) 3.66930 3.66930i 0.129406 0.129406i
\(805\) 15.7814 + 15.7814i 0.556221 + 0.556221i
\(806\) −0.406109 0.406109i −0.0143046 0.0143046i
\(807\) 52.1144i 1.83451i
\(808\) 7.65685i 0.269367i
\(809\) −4.90215 4.90215i −0.172351 0.172351i 0.615661 0.788011i \(-0.288889\pi\)
−0.788011 + 0.615661i \(0.788889\pi\)
\(810\) 19.0743 + 19.0743i 0.670202 + 0.670202i
\(811\) −16.9360 + 16.9360i −0.594702 + 0.594702i −0.938898 0.344196i \(-0.888152\pi\)
0.344196 + 0.938898i \(0.388152\pi\)
\(812\) 13.7476 0.482445
\(813\) 71.3596 71.3596i 2.50269 2.50269i
\(814\) 8.92274i 0.312742i
\(815\) −0.795713 −0.0278726
\(816\) 1.97421 13.3307i 0.0691111 0.466668i
\(817\) 1.28210 0.0448549
\(818\) 16.6326i 0.581546i
\(819\) 3.66061 3.66061i 0.127912 0.127912i
\(820\) 7.83031 0.273446
\(821\) 14.1244 14.1244i 0.492947 0.492947i −0.416287 0.909233i \(-0.636669\pi\)
0.909233 + 0.416287i \(0.136669\pi\)
\(822\) −32.7218 32.7218i −1.14130 1.14130i
\(823\) 4.17345 + 4.17345i 0.145477 + 0.145477i 0.776094 0.630617i \(-0.217198\pi\)
−0.630617 + 0.776094i \(0.717198\pi\)
\(824\) 8.07295i 0.281234i
\(825\) 8.45147i 0.294242i
\(826\) 18.6864 + 18.6864i 0.650183 + 0.650183i
\(827\) −18.0258 18.0258i −0.626818 0.626818i 0.320448 0.947266i \(-0.396167\pi\)
−0.947266 + 0.320448i \(0.896167\pi\)
\(828\) 26.2302 26.2302i 0.911562 0.911562i
\(829\) 18.4375 0.640359 0.320180 0.947357i \(-0.396257\pi\)
0.320180 + 0.947357i \(0.396257\pi\)
\(830\) −6.30303 + 6.30303i −0.218781 + 0.218781i
\(831\) 91.2086i 3.16399i
\(832\) 0.145782 0.00505408
\(833\) −35.2943 47.5653i −1.22287 1.64804i
\(834\) −69.6711 −2.41251
\(835\) 4.75548i 0.164570i
\(836\) −3.76726 + 3.76726i −0.130294 + 0.130294i
\(837\) −60.2954 −2.08412
\(838\) 20.3049 20.3049i 0.701421 0.701421i
\(839\) 8.28424 + 8.28424i 0.286004 + 0.286004i 0.835498 0.549494i \(-0.185179\pi\)
−0.549494 + 0.835498i \(0.685179\pi\)
\(840\) 10.6826 + 10.6826i 0.368586 + 0.368586i
\(841\) 20.1541i 0.694968i
\(842\) 28.5974i 0.985530i
\(843\) −23.7767 23.7767i −0.818914 0.818914i
\(844\) 1.47648 + 1.47648i 0.0508225 + 0.0508225i
\(845\) −9.17736 + 9.17736i −0.315711 + 0.315711i
\(846\) −65.1218 −2.23893
\(847\) −14.0991 + 14.0991i −0.484449 + 0.484449i
\(848\) 6.68265i 0.229483i
\(849\) 39.3692 1.35115
\(850\) 3.31113 2.45691i 0.113571 0.0842714i
\(851\) 16.6614 0.571145
\(852\) 8.48893i 0.290826i
\(853\) 9.64915 9.64915i 0.330381 0.330381i −0.522350 0.852731i \(-0.674945\pi\)
0.852731 + 0.522350i \(0.174945\pi\)
\(854\) −17.2570 −0.590521
\(855\) 11.1929 11.1929i 0.382790 0.382790i
\(856\) 1.68265 + 1.68265i 0.0575116 + 0.0575116i
\(857\) 22.9313 + 22.9313i 0.783318 + 0.783318i 0.980389 0.197071i \(-0.0631429\pi\)
−0.197071 + 0.980389i \(0.563143\pi\)
\(858\) 1.23207i 0.0420622i
\(859\) 14.1902i 0.484164i 0.970256 + 0.242082i \(0.0778304\pi\)
−0.970256 + 0.242082i \(0.922170\pi\)
\(860\) 0.440004 + 0.440004i 0.0150040 + 0.0150040i
\(861\) −83.6484 83.6484i −2.85073 2.85073i
\(862\) 1.39800 1.39800i 0.0476162 0.0476162i
\(863\) −52.0480 −1.77174 −0.885868 0.463937i \(-0.846436\pi\)
−0.885868 + 0.463937i \(0.846436\pi\)
\(864\) 10.8222 10.8222i 0.368179 0.368179i
\(865\) 12.7306i 0.432853i
\(866\) 35.6444 1.21125
\(867\) 26.2155 + 48.9901i 0.890325 + 1.66379i
\(868\) −18.2099 −0.618085
\(869\) 12.0436i 0.408553i
\(870\) 6.87378 6.87378i 0.233043 0.233043i
\(871\) −0.231453 −0.00784249
\(872\) 2.10308 2.10308i 0.0712194 0.0712194i
\(873\) −96.6588 96.6588i −3.27140 3.27140i
\(874\) −7.03459 7.03459i −0.237949 0.237949i
\(875\) 4.62226i 0.156261i
\(876\) 26.9117i 0.909263i
\(877\) 3.85156 + 3.85156i 0.130058 + 0.130058i 0.769139 0.639081i \(-0.220685\pi\)
−0.639081 + 0.769139i \(0.720685\pi\)
\(878\) 10.9165 + 10.9165i 0.368413 + 0.368413i
\(879\) 70.7261 70.7261i 2.38553 2.38553i
\(880\) −2.58579 −0.0871668
\(881\) 12.6672 12.6672i 0.426769 0.426769i −0.460757 0.887526i \(-0.652422\pi\)
0.887526 + 0.460757i \(0.152422\pi\)
\(882\) 110.363i 3.71613i
\(883\) 15.1362 0.509374 0.254687 0.967024i \(-0.418028\pi\)
0.254687 + 0.967024i \(0.418028\pi\)
\(884\) −0.482703 + 0.358173i −0.0162351 + 0.0120467i
\(885\) 18.6864 0.628137
\(886\) 8.63471i 0.290089i
\(887\) −29.5122 + 29.5122i −0.990922 + 0.990922i −0.999959 0.00903736i \(-0.997123\pi\)
0.00903736 + 0.999959i \(0.497123\pi\)
\(888\) 11.2783 0.378476
\(889\) −36.5546 + 36.5546i −1.22600 + 1.22600i
\(890\) 11.2987 + 11.2987i 0.378733 + 0.378733i
\(891\) 49.3220 + 49.3220i 1.65235 + 1.65235i
\(892\) 22.6186i 0.757327i
\(893\) 17.4648i 0.584438i
\(894\) −23.7564 23.7564i −0.794532 0.794532i
\(895\) −0.120770 0.120770i −0.00403689 0.00403689i
\(896\) 3.26843 3.26843i 0.109191 0.109191i
\(897\) −2.30064 −0.0768162
\(898\) 5.98677 5.98677i 0.199781 0.199781i
\(899\) 11.7172i 0.390792i
\(900\) 7.68265 0.256088
\(901\) 16.4187 + 22.1271i 0.546985 + 0.737161i
\(902\) 20.2475 0.674168
\(903\) 9.40082i 0.312840i
\(904\) 7.19994 7.19994i 0.239467 0.239467i
\(905\) 4.70766 0.156488
\(906\) −15.1075 + 15.1075i −0.501914 + 0.501914i
\(907\) −9.65865 9.65865i −0.320710 0.320710i 0.528329 0.849040i \(-0.322819\pi\)
−0.849040 + 0.528329i \(0.822819\pi\)
\(908\) 8.29868 + 8.29868i 0.275401 + 0.275401i
\(909\) 58.8249i 1.95110i
\(910\) 0.673842i 0.0223376i
\(911\) 0.866458 + 0.866458i 0.0287070 + 0.0287070i 0.721315 0.692608i \(-0.243538\pi\)
−0.692608 + 0.721315i \(0.743538\pi\)
\(912\) −4.76182 4.76182i −0.157680 0.157680i
\(913\) −16.2983 + 16.2983i −0.539394 + 0.539394i
\(914\) −33.1305 −1.09586
\(915\) −8.62848 + 8.62848i −0.285249 + 0.285249i
\(916\) 25.8897i 0.855420i
\(917\) −69.1042 −2.28202
\(918\) −9.24452 + 62.4229i −0.305115 + 2.06026i
\(919\) 21.7152 0.716317 0.358158 0.933661i \(-0.383405\pi\)
0.358158 + 0.933661i \(0.383405\pi\)
\(920\) 4.82843i 0.159189i
\(921\) 31.4933 31.4933i 1.03774 1.03774i
\(922\) −12.8035 −0.421662
\(923\) −0.267733 + 0.267733i −0.00881255 + 0.00881255i
\(924\) 27.6230 + 27.6230i 0.908731 + 0.908731i
\(925\) 2.44000 + 2.44000i 0.0802269 + 0.0802269i
\(926\) 25.9877i 0.854008i
\(927\) 62.0216i 2.03706i
\(928\) −2.10308 2.10308i −0.0690371 0.0690371i
\(929\) −14.9022 14.9022i −0.488924 0.488924i 0.419043 0.907967i \(-0.362366\pi\)
−0.907967 + 0.419043i \(0.862366\pi\)
\(930\) −9.10496 + 9.10496i −0.298564 + 0.298564i
\(931\) −29.5980 −0.970036
\(932\) −9.65141 + 9.65141i −0.316142 + 0.316142i
\(933\) 40.3427i 1.32076i
\(934\) 11.1805 0.365837
\(935\) 8.56188 6.35305i 0.280003 0.207767i
\(936\) −1.11999 −0.0366081
\(937\) 48.3234i 1.57866i −0.613971 0.789328i \(-0.710429\pi\)
0.613971 0.789328i \(-0.289571\pi\)
\(938\) −5.18918 + 5.18918i −0.169433 + 0.169433i
\(939\) 40.3683 1.31737
\(940\) −5.99378 + 5.99378i −0.195495 + 0.195495i
\(941\) 11.0045 + 11.0045i 0.358735 + 0.358735i 0.863347 0.504611i \(-0.168364\pi\)
−0.504611 + 0.863347i \(0.668364\pi\)
\(942\) 28.7359 + 28.7359i 0.936266 + 0.936266i
\(943\) 37.8081i 1.23120i
\(944\) 5.71724i 0.186080i
\(945\) −50.0230 50.0230i −1.62725 1.62725i
\(946\) 1.13776 + 1.13776i 0.0369917 + 0.0369917i
\(947\) 21.4879 21.4879i 0.698262 0.698262i −0.265774 0.964035i \(-0.585627\pi\)
0.964035 + 0.265774i \(0.0856274\pi\)
\(948\) 15.2232 0.494425
\(949\) 0.848772 0.848772i 0.0275523 0.0275523i
\(950\) 2.06038i 0.0668477i
\(951\) −52.3647 −1.69804
\(952\) −2.79195 + 18.8525i −0.0904877 + 0.611011i
\(953\) −18.6150 −0.602998 −0.301499 0.953467i \(-0.597487\pi\)
−0.301499 + 0.953467i \(0.597487\pi\)
\(954\) 51.3404i 1.66221i
\(955\) 3.39030 3.39030i 0.109708 0.109708i
\(956\) 25.4736 0.823875
\(957\) 17.7741 17.7741i 0.574556 0.574556i
\(958\) 7.57878 + 7.57878i 0.244859 + 0.244859i
\(959\) 46.2756 + 46.2756i 1.49432 + 1.49432i
\(960\) 3.26843i 0.105488i
\(961\) 15.4794i 0.499337i
\(962\) −0.355709 0.355709i −0.0114685 0.0114685i
\(963\) −12.9272 12.9272i −0.416572 0.416572i
\(964\) −5.65763 + 5.65763i −0.182220 + 0.182220i
\(965\) 15.1064 0.486294
\(966\) −51.5804 + 51.5804i −1.65957 + 1.65957i
\(967\) 24.1990i 0.778188i −0.921198 0.389094i \(-0.872788\pi\)
0.921198 0.389094i \(-0.127212\pi\)
\(968\) 4.31371 0.138648
\(969\) 27.4664 + 4.06763i 0.882347 + 0.130671i
\(970\) −17.7928 −0.571294
\(971\) 23.8896i 0.766653i −0.923613 0.383327i \(-0.874778\pi\)
0.923613 0.383327i \(-0.125222\pi\)
\(972\) −29.8764 + 29.8764i −0.958285 + 0.958285i
\(973\) 98.5298 3.15872
\(974\) −19.9761 + 19.9761i −0.640075 + 0.640075i
\(975\) −0.336921 0.336921i −0.0107901 0.0107901i
\(976\) 2.63995 + 2.63995i 0.0845026 + 0.0845026i
\(977\) 23.3337i 0.746510i −0.927729 0.373255i \(-0.878242\pi\)
0.927729 0.373255i \(-0.121758\pi\)
\(978\) 2.60073i 0.0831623i
\(979\) 29.2160 + 29.2160i 0.933747 + 0.933747i
\(980\) −10.1578 10.1578i −0.324479 0.324479i
\(981\) −16.1572 + 16.1572i −0.515861 + 0.515861i
\(982\) −9.08253 −0.289835
\(983\) 37.4373 37.4373i 1.19406 1.19406i 0.218147 0.975916i \(-0.429999\pi\)
0.975916 0.218147i \(-0.0700012\pi\)
\(984\) 25.5928i 0.815869i
\(985\) 6.86756 0.218819
\(986\) 12.1307 + 1.79649i 0.386319 + 0.0572120i
\(987\) 128.059 4.07615
\(988\) 0.300367i 0.00955595i
\(989\) −2.12453 + 2.12453i −0.0675561 + 0.0675561i
\(990\) 19.8657 0.631373
\(991\) 39.1164 39.1164i 1.24257 1.24257i 0.283645 0.958929i \(-0.408456\pi\)
0.958929 0.283645i \(-0.0915436\pi\)
\(992\) 2.78573 + 2.78573i 0.0884470 + 0.0884470i
\(993\) 24.3811 + 24.3811i 0.773711 + 0.773711i
\(994\) 12.0052i 0.380780i
\(995\) 3.00958i 0.0954102i
\(996\) −20.6010 20.6010i −0.652768 0.652768i
\(997\) 36.7958 + 36.7958i 1.16534 + 1.16534i 0.983290 + 0.182045i \(0.0582718\pi\)
0.182045 + 0.983290i \(0.441728\pi\)
\(998\) −2.62304 + 2.62304i −0.0830308 + 0.0830308i
\(999\) −52.8124 −1.67091
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 170.2.h.b.21.1 8
3.2 odd 2 1530.2.q.g.361.1 8
4.3 odd 2 1360.2.bt.b.1041.4 8
5.2 odd 4 850.2.g.l.599.4 8
5.3 odd 4 850.2.g.i.599.1 8
5.4 even 2 850.2.h.n.701.4 8
17.2 even 8 2890.2.b.o.2311.8 8
17.8 even 8 2890.2.a.be.1.4 4
17.9 even 8 2890.2.a.bd.1.1 4
17.13 even 4 inner 170.2.h.b.81.1 yes 8
17.15 even 8 2890.2.b.o.2311.1 8
51.47 odd 4 1530.2.q.g.1441.1 8
68.47 odd 4 1360.2.bt.b.81.4 8
85.13 odd 4 850.2.g.l.149.4 8
85.47 odd 4 850.2.g.i.149.1 8
85.64 even 4 850.2.h.n.251.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.h.b.21.1 8 1.1 even 1 trivial
170.2.h.b.81.1 yes 8 17.13 even 4 inner
850.2.g.i.149.1 8 85.47 odd 4
850.2.g.i.599.1 8 5.3 odd 4
850.2.g.l.149.4 8 85.13 odd 4
850.2.g.l.599.4 8 5.2 odd 4
850.2.h.n.251.4 8 85.64 even 4
850.2.h.n.701.4 8 5.4 even 2
1360.2.bt.b.81.4 8 68.47 odd 4
1360.2.bt.b.1041.4 8 4.3 odd 2
1530.2.q.g.361.1 8 3.2 odd 2
1530.2.q.g.1441.1 8 51.47 odd 4
2890.2.a.bd.1.1 4 17.9 even 8
2890.2.a.be.1.4 4 17.8 even 8
2890.2.b.o.2311.1 8 17.15 even 8
2890.2.b.o.2311.8 8 17.2 even 8