Properties

Label 546.2.p.d.281.3
Level $546$
Weight $2$
Character 546.281
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(239,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 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("546.239");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + \cdots + 59049 \) 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 281.3
Root \(-0.962473 + 1.44002i\) of defining polynomial
Character \(\chi\) \(=\) 546.281
Dual form 546.2.p.d.239.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.337674 + 1.69882i) q^{3} -1.00000i q^{4} +(2.19168 - 2.19168i) q^{5} +(-0.962473 - 1.44002i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.77195 - 1.14729i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.337674 + 1.69882i) q^{3} -1.00000i q^{4} +(2.19168 - 2.19168i) q^{5} +(-0.962473 - 1.44002i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.77195 - 1.14729i) q^{9} +3.09950i q^{10} +(1.27674 + 1.27674i) q^{11} +(1.69882 + 0.337674i) q^{12} +(-3.23661 + 1.58883i) q^{13} -1.00000i q^{14} +(2.98318 + 4.46333i) q^{15} -1.00000 q^{16} +3.68191 q^{17} +(2.77132 - 1.14881i) q^{18} +(5.26937 + 5.26937i) q^{19} +(-2.19168 - 2.19168i) q^{20} +(-0.962473 - 1.44002i) q^{21} -1.80559 q^{22} +8.15820 q^{23} +(-1.44002 + 0.962473i) q^{24} -4.60689i q^{25} +(1.16516 - 3.41210i) q^{26} +(2.88505 - 4.32163i) q^{27} +(0.707107 + 0.707107i) q^{28} +9.50505i q^{29} +(-5.26548 - 1.04662i) q^{30} +(-0.125281 - 0.125281i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.60007 + 1.73783i) q^{33} +(-2.60350 + 2.60350i) q^{34} +3.09950i q^{35} +(-1.14729 + 2.77195i) q^{36} +(-0.328266 + 0.328266i) q^{37} -7.45201 q^{38} +(-1.60620 - 6.03491i) q^{39} +3.09950 q^{40} +(-2.21794 + 2.21794i) q^{41} +(1.69882 + 0.337674i) q^{42} +1.43126i q^{43} +(1.27674 - 1.27674i) q^{44} +(-8.58971 + 3.56073i) q^{45} +(-5.76872 + 5.76872i) q^{46} +(-0.805736 - 0.805736i) q^{47} +(0.337674 - 1.69882i) q^{48} -1.00000i q^{49} +(3.25756 + 3.25756i) q^{50} +(-1.24328 + 6.25489i) q^{51} +(1.58883 + 3.23661i) q^{52} -5.59755i q^{53} +(1.01581 + 5.09589i) q^{54} +5.59641 q^{55} -1.00000 q^{56} +(-10.7310 + 7.17236i) q^{57} +(-6.72109 - 6.72109i) q^{58} +(1.49217 + 1.49217i) q^{59} +(4.46333 - 2.98318i) q^{60} -8.14557 q^{61} +0.177174 q^{62} +(2.77132 - 1.14881i) q^{63} +1.00000i q^{64} +(-3.61141 + 10.5758i) q^{65} +(0.609699 - 3.06736i) q^{66} +(-10.6436 - 10.6436i) q^{67} -3.68191i q^{68} +(-2.75481 + 13.8593i) q^{69} +(-2.19168 - 2.19168i) q^{70} +(-0.752235 + 0.752235i) q^{71} +(-1.14881 - 2.77132i) q^{72} +(3.59354 - 3.59354i) q^{73} -0.464238i q^{74} +(7.82626 + 1.55563i) q^{75} +(5.26937 - 5.26937i) q^{76} -1.80559 q^{77} +(5.40308 + 3.13157i) q^{78} +4.38864 q^{79} +(-2.19168 + 2.19168i) q^{80} +(6.36745 + 6.36047i) q^{81} -3.13663i q^{82} +(9.35133 - 9.35133i) q^{83} +(-1.44002 + 0.962473i) q^{84} +(8.06956 - 8.06956i) q^{85} +(-1.01205 - 1.01205i) q^{86} +(-16.1473 - 3.20961i) q^{87} +1.80559i q^{88} +(3.19016 + 3.19016i) q^{89} +(3.55603 - 8.59166i) q^{90} +(1.16516 - 3.41210i) q^{91} -8.15820i q^{92} +(0.255133 - 0.170525i) q^{93} +1.13948 q^{94} +23.0975 q^{95} +(0.962473 + 1.44002i) q^{96} +(1.79334 + 1.79334i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-2.07427 - 5.00386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.337674 + 1.69882i −0.194956 + 0.980812i
\(4\) 1.00000i 0.500000i
\(5\) 2.19168 2.19168i 0.980147 0.980147i −0.0196593 0.999807i \(-0.506258\pi\)
0.999807 + 0.0196593i \(0.00625814\pi\)
\(6\) −0.962473 1.44002i −0.392928 0.587884i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.77195 1.14729i −0.923984 0.382430i
\(10\) 3.09950i 0.980147i
\(11\) 1.27674 + 1.27674i 0.384952 + 0.384952i 0.872883 0.487930i \(-0.162248\pi\)
−0.487930 + 0.872883i \(0.662248\pi\)
\(12\) 1.69882 + 0.337674i 0.490406 + 0.0974780i
\(13\) −3.23661 + 1.58883i −0.897674 + 0.440661i
\(14\) 1.00000i 0.267261i
\(15\) 2.98318 + 4.46333i 0.770255 + 1.15243i
\(16\) −1.00000 −0.250000
\(17\) 3.68191 0.892995 0.446497 0.894785i \(-0.352671\pi\)
0.446497 + 0.894785i \(0.352671\pi\)
\(18\) 2.77132 1.14881i 0.653207 0.270777i
\(19\) 5.26937 + 5.26937i 1.20888 + 1.20888i 0.971391 + 0.237485i \(0.0763232\pi\)
0.237485 + 0.971391i \(0.423677\pi\)
\(20\) −2.19168 2.19168i −0.490074 0.490074i
\(21\) −0.962473 1.44002i −0.210029 0.314237i
\(22\) −1.80559 −0.384952
\(23\) 8.15820 1.70110 0.850551 0.525893i \(-0.176269\pi\)
0.850551 + 0.525893i \(0.176269\pi\)
\(24\) −1.44002 + 0.962473i −0.293942 + 0.196464i
\(25\) 4.60689i 0.921378i
\(26\) 1.16516 3.41210i 0.228506 0.669167i
\(27\) 2.88505 4.32163i 0.555229 0.831698i
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) 9.50505i 1.76504i 0.470272 + 0.882522i \(0.344156\pi\)
−0.470272 + 0.882522i \(0.655844\pi\)
\(30\) −5.26548 1.04662i −0.961340 0.191086i
\(31\) −0.125281 0.125281i −0.0225011 0.0225011i 0.695767 0.718268i \(-0.255065\pi\)
−0.718268 + 0.695767i \(0.755065\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −2.60007 + 1.73783i −0.452614 + 0.302517i
\(34\) −2.60350 + 2.60350i −0.446497 + 0.446497i
\(35\) 3.09950i 0.523911i
\(36\) −1.14729 + 2.77195i −0.191215 + 0.461992i
\(37\) −0.328266 + 0.328266i −0.0539666 + 0.0539666i −0.733575 0.679608i \(-0.762150\pi\)
0.679608 + 0.733575i \(0.262150\pi\)
\(38\) −7.45201 −1.20888
\(39\) −1.60620 6.03491i −0.257199 0.966359i
\(40\) 3.09950 0.490074
\(41\) −2.21794 + 2.21794i −0.346383 + 0.346383i −0.858761 0.512377i \(-0.828765\pi\)
0.512377 + 0.858761i \(0.328765\pi\)
\(42\) 1.69882 + 0.337674i 0.262133 + 0.0521042i
\(43\) 1.43126i 0.218265i 0.994027 + 0.109133i \(0.0348073\pi\)
−0.994027 + 0.109133i \(0.965193\pi\)
\(44\) 1.27674 1.27674i 0.192476 0.192476i
\(45\) −8.58971 + 3.56073i −1.28048 + 0.530803i
\(46\) −5.76872 + 5.76872i −0.850551 + 0.850551i
\(47\) −0.805736 0.805736i −0.117529 0.117529i 0.645896 0.763425i \(-0.276484\pi\)
−0.763425 + 0.645896i \(0.776484\pi\)
\(48\) 0.337674 1.69882i 0.0487390 0.245203i
\(49\) 1.00000i 0.142857i
\(50\) 3.25756 + 3.25756i 0.460689 + 0.460689i
\(51\) −1.24328 + 6.25489i −0.174095 + 0.875860i
\(52\) 1.58883 + 3.23661i 0.220330 + 0.448837i
\(53\) 5.59755i 0.768882i −0.923150 0.384441i \(-0.874394\pi\)
0.923150 0.384441i \(-0.125606\pi\)
\(54\) 1.01581 + 5.09589i 0.138235 + 0.693463i
\(55\) 5.59641 0.754620
\(56\) −1.00000 −0.133631
\(57\) −10.7310 + 7.17236i −1.42136 + 0.950003i
\(58\) −6.72109 6.72109i −0.882522 0.882522i
\(59\) 1.49217 + 1.49217i 0.194264 + 0.194264i 0.797536 0.603272i \(-0.206136\pi\)
−0.603272 + 0.797536i \(0.706136\pi\)
\(60\) 4.46333 2.98318i 0.576213 0.385127i
\(61\) −8.14557 −1.04293 −0.521467 0.853272i \(-0.674615\pi\)
−0.521467 + 0.853272i \(0.674615\pi\)
\(62\) 0.177174 0.0225011
\(63\) 2.77132 1.14881i 0.349154 0.144736i
\(64\) 1.00000i 0.125000i
\(65\) −3.61141 + 10.5758i −0.447940 + 1.31177i
\(66\) 0.609699 3.06736i 0.0750487 0.377566i
\(67\) −10.6436 10.6436i −1.30033 1.30033i −0.928170 0.372157i \(-0.878618\pi\)
−0.372157 0.928170i \(-0.621382\pi\)
\(68\) 3.68191i 0.446497i
\(69\) −2.75481 + 13.8593i −0.331640 + 1.66846i
\(70\) −2.19168 2.19168i −0.261955 0.261955i
\(71\) −0.752235 + 0.752235i −0.0892739 + 0.0892739i −0.750333 0.661060i \(-0.770107\pi\)
0.661060 + 0.750333i \(0.270107\pi\)
\(72\) −1.14881 2.77132i −0.135389 0.326604i
\(73\) 3.59354 3.59354i 0.420592 0.420592i −0.464815 0.885408i \(-0.653879\pi\)
0.885408 + 0.464815i \(0.153879\pi\)
\(74\) 0.464238i 0.0539666i
\(75\) 7.82626 + 1.55563i 0.903699 + 0.179628i
\(76\) 5.26937 5.26937i 0.604438 0.604438i
\(77\) −1.80559 −0.205766
\(78\) 5.40308 + 3.13157i 0.611779 + 0.354580i
\(79\) 4.38864 0.493760 0.246880 0.969046i \(-0.420595\pi\)
0.246880 + 0.969046i \(0.420595\pi\)
\(80\) −2.19168 + 2.19168i −0.245037 + 0.245037i
\(81\) 6.36745 + 6.36047i 0.707494 + 0.706719i
\(82\) 3.13663i 0.346383i
\(83\) 9.35133 9.35133i 1.02644 1.02644i 0.0268014 0.999641i \(-0.491468\pi\)
0.999641 0.0268014i \(-0.00853218\pi\)
\(84\) −1.44002 + 0.962473i −0.157119 + 0.105014i
\(85\) 8.06956 8.06956i 0.875266 0.875266i
\(86\) −1.01205 1.01205i −0.109133 0.109133i
\(87\) −16.1473 3.20961i −1.73118 0.344106i
\(88\) 1.80559i 0.192476i
\(89\) 3.19016 + 3.19016i 0.338156 + 0.338156i 0.855673 0.517517i \(-0.173144\pi\)
−0.517517 + 0.855673i \(0.673144\pi\)
\(90\) 3.55603 8.59166i 0.374838 0.905641i
\(91\) 1.16516 3.41210i 0.122142 0.357685i
\(92\) 8.15820i 0.850551i
\(93\) 0.255133 0.170525i 0.0264560 0.0176826i
\(94\) 1.13948 0.117529
\(95\) 23.0975 2.36975
\(96\) 0.962473 + 1.44002i 0.0982320 + 0.146971i
\(97\) 1.79334 + 1.79334i 0.182086 + 0.182086i 0.792264 0.610178i \(-0.208902\pi\)
−0.610178 + 0.792264i \(0.708902\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) −2.07427 5.00386i −0.208472 0.502907i
\(100\) −4.60689 −0.460689
\(101\) 8.55213 0.850969 0.425484 0.904966i \(-0.360104\pi\)
0.425484 + 0.904966i \(0.360104\pi\)
\(102\) −3.54374 5.30201i −0.350883 0.524977i
\(103\) 6.72083i 0.662223i 0.943592 + 0.331112i \(0.107424\pi\)
−0.943592 + 0.331112i \(0.892576\pi\)
\(104\) −3.41210 1.16516i −0.334584 0.114253i
\(105\) −5.26548 1.04662i −0.513858 0.102140i
\(106\) 3.95806 + 3.95806i 0.384441 + 0.384441i
\(107\) 7.64497i 0.739067i 0.929217 + 0.369534i \(0.120483\pi\)
−0.929217 + 0.369534i \(0.879517\pi\)
\(108\) −4.32163 2.88505i −0.415849 0.277614i
\(109\) −11.0618 11.0618i −1.05953 1.05953i −0.998112 0.0614199i \(-0.980437\pi\)
−0.0614199 0.998112i \(-0.519563\pi\)
\(110\) −3.95726 + 3.95726i −0.377310 + 0.377310i
\(111\) −0.446817 0.668510i −0.0424100 0.0634522i
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) 19.2385i 1.80980i −0.425619 0.904902i \(-0.639944\pi\)
0.425619 0.904902i \(-0.360056\pi\)
\(114\) 2.51635 12.6596i 0.235678 1.18568i
\(115\) 17.8801 17.8801i 1.66733 1.66733i
\(116\) 9.50505 0.882522
\(117\) 10.7946 0.690818i 0.997958 0.0638661i
\(118\) −2.11025 −0.194264
\(119\) −2.60350 + 2.60350i −0.238663 + 0.238663i
\(120\) −1.04662 + 5.26548i −0.0955428 + 0.480670i
\(121\) 7.73986i 0.703624i
\(122\) 5.75979 5.75979i 0.521467 0.521467i
\(123\) −3.01893 4.51680i −0.272207 0.407266i
\(124\) −0.125281 + 0.125281i −0.0112505 + 0.0112505i
\(125\) 0.861568 + 0.861568i 0.0770610 + 0.0770610i
\(126\) −1.14729 + 2.77195i −0.102209 + 0.246945i
\(127\) 12.4807i 1.10749i 0.832688 + 0.553743i \(0.186801\pi\)
−0.832688 + 0.553743i \(0.813199\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −2.43145 0.483299i −0.214077 0.0425521i
\(130\) −4.92456 10.0319i −0.431913 0.879853i
\(131\) 8.33777i 0.728475i 0.931306 + 0.364237i \(0.118670\pi\)
−0.931306 + 0.364237i \(0.881330\pi\)
\(132\) 1.73783 + 2.60007i 0.151258 + 0.226307i
\(133\) −7.45201 −0.646172
\(134\) 15.0524 1.30033
\(135\) −3.14851 15.7947i −0.270981 1.35939i
\(136\) 2.60350 + 2.60350i 0.223249 + 0.223249i
\(137\) −14.2203 14.2203i −1.21492 1.21492i −0.969388 0.245535i \(-0.921036\pi\)
−0.245535 0.969388i \(-0.578964\pi\)
\(138\) −7.85205 11.7479i −0.668411 1.00005i
\(139\) 5.53897 0.469809 0.234905 0.972018i \(-0.424522\pi\)
0.234905 + 0.972018i \(0.424522\pi\)
\(140\) 3.09950 0.261955
\(141\) 1.64087 1.09672i 0.138186 0.0923606i
\(142\) 1.06382i 0.0892739i
\(143\) −6.16083 2.10379i −0.515195 0.175928i
\(144\) 2.77195 + 1.14729i 0.230996 + 0.0956076i
\(145\) 20.8320 + 20.8320i 1.73000 + 1.73000i
\(146\) 5.08204i 0.420592i
\(147\) 1.69882 + 0.337674i 0.140116 + 0.0278509i
\(148\) 0.328266 + 0.328266i 0.0269833 + 0.0269833i
\(149\) −3.72237 + 3.72237i −0.304949 + 0.304949i −0.842946 0.537998i \(-0.819181\pi\)
0.537998 + 0.842946i \(0.319181\pi\)
\(150\) −6.63400 + 4.43401i −0.541663 + 0.362035i
\(151\) −15.2455 + 15.2455i −1.24066 + 1.24066i −0.280929 + 0.959729i \(0.590642\pi\)
−0.959729 + 0.280929i \(0.909358\pi\)
\(152\) 7.45201i 0.604438i
\(153\) −10.2061 4.22422i −0.825113 0.341508i
\(154\) 1.27674 1.27674i 0.102883 0.102883i
\(155\) −0.549149 −0.0441087
\(156\) −6.03491 + 1.60620i −0.483179 + 0.128599i
\(157\) −10.2830 −0.820676 −0.410338 0.911934i \(-0.634589\pi\)
−0.410338 + 0.911934i \(0.634589\pi\)
\(158\) −3.10323 + 3.10323i −0.246880 + 0.246880i
\(159\) 9.50920 + 1.89014i 0.754129 + 0.149898i
\(160\) 3.09950i 0.245037i
\(161\) −5.76872 + 5.76872i −0.454639 + 0.454639i
\(162\) −9.00000 + 0.00493109i −0.707107 + 0.000387423i
\(163\) 16.4136 16.4136i 1.28561 1.28561i 0.348188 0.937425i \(-0.386797\pi\)
0.937425 0.348188i \(-0.113203\pi\)
\(164\) 2.21794 + 2.21794i 0.173192 + 0.173192i
\(165\) −1.88976 + 9.50727i −0.147118 + 0.740140i
\(166\) 13.2248i 1.02644i
\(167\) −10.1688 10.1688i −0.786888 0.786888i 0.194095 0.980983i \(-0.437823\pi\)
−0.980983 + 0.194095i \(0.937823\pi\)
\(168\) 0.337674 1.69882i 0.0260521 0.131067i
\(169\) 7.95127 10.2848i 0.611636 0.791139i
\(170\) 11.4121i 0.875266i
\(171\) −8.56095 20.6519i −0.654672 1.57929i
\(172\) 1.43126 0.109133
\(173\) −8.72942 −0.663686 −0.331843 0.943335i \(-0.607670\pi\)
−0.331843 + 0.943335i \(0.607670\pi\)
\(174\) 13.6874 9.14836i 1.03764 0.693535i
\(175\) 3.25756 + 3.25756i 0.246249 + 0.246249i
\(176\) −1.27674 1.27674i −0.0962380 0.0962380i
\(177\) −3.03879 + 2.03106i −0.228410 + 0.152664i
\(178\) −4.51157 −0.338156
\(179\) −21.4346 −1.60210 −0.801048 0.598600i \(-0.795724\pi\)
−0.801048 + 0.598600i \(0.795724\pi\)
\(180\) 3.56073 + 8.58971i 0.265401 + 0.640240i
\(181\) 7.53227i 0.559869i 0.960019 + 0.279935i \(0.0903128\pi\)
−0.960019 + 0.279935i \(0.909687\pi\)
\(182\) 1.58883 + 3.23661i 0.117772 + 0.239913i
\(183\) 2.75055 13.8378i 0.203326 1.02292i
\(184\) 5.76872 + 5.76872i 0.425275 + 0.425275i
\(185\) 1.43891i 0.105790i
\(186\) −0.0598268 + 0.300985i −0.00438672 + 0.0220693i
\(187\) 4.70085 + 4.70085i 0.343760 + 0.343760i
\(188\) −0.805736 + 0.805736i −0.0587644 + 0.0587644i
\(189\) 1.01581 + 5.09589i 0.0738895 + 0.370672i
\(190\) −16.3324 + 16.3324i −1.18488 + 1.18488i
\(191\) 1.80118i 0.130329i −0.997875 0.0651645i \(-0.979243\pi\)
0.997875 0.0651645i \(-0.0207572\pi\)
\(192\) −1.69882 0.337674i −0.122601 0.0243695i
\(193\) 14.4054 14.4054i 1.03692 1.03692i 0.0376326 0.999292i \(-0.488018\pi\)
0.999292 0.0376326i \(-0.0119817\pi\)
\(194\) −2.53616 −0.182086
\(195\) −16.7468 9.70628i −1.19927 0.695081i
\(196\) −1.00000 −0.0714286
\(197\) 6.93319 6.93319i 0.493970 0.493970i −0.415585 0.909554i \(-0.636423\pi\)
0.909554 + 0.415585i \(0.136423\pi\)
\(198\) 5.00500 + 2.07153i 0.355690 + 0.147217i
\(199\) 10.2593i 0.727262i 0.931543 + 0.363631i \(0.118463\pi\)
−0.931543 + 0.363631i \(0.881537\pi\)
\(200\) 3.25756 3.25756i 0.230345 0.230345i
\(201\) 21.6756 14.4875i 1.52888 1.02187i
\(202\) −6.04727 + 6.04727i −0.425484 + 0.425484i
\(203\) −6.72109 6.72109i −0.471728 0.471728i
\(204\) 6.25489 + 1.24328i 0.437930 + 0.0870473i
\(205\) 9.72199i 0.679013i
\(206\) −4.75235 4.75235i −0.331112 0.331112i
\(207\) −22.6141 9.35983i −1.57179 0.650553i
\(208\) 3.23661 1.58883i 0.224418 0.110165i
\(209\) 13.4552i 0.930719i
\(210\) 4.46333 2.98318i 0.307999 0.205859i
\(211\) −19.4541 −1.33928 −0.669638 0.742687i \(-0.733551\pi\)
−0.669638 + 0.742687i \(0.733551\pi\)
\(212\) −5.59755 −0.384441
\(213\) −1.02390 1.53192i −0.0701564 0.104965i
\(214\) −5.40581 5.40581i −0.369534 0.369534i
\(215\) 3.13686 + 3.13686i 0.213932 + 0.213932i
\(216\) 5.09589 1.01581i 0.346732 0.0691173i
\(217\) 0.177174 0.0120273
\(218\) 15.6438 1.05953
\(219\) 4.89132 + 7.31821i 0.330525 + 0.494519i
\(220\) 5.59641i 0.377310i
\(221\) −11.9169 + 5.84991i −0.801618 + 0.393508i
\(222\) 0.788656 + 0.156761i 0.0529311 + 0.0105211i
\(223\) 11.9464 + 11.9464i 0.799992 + 0.799992i 0.983094 0.183102i \(-0.0586140\pi\)
−0.183102 + 0.983094i \(0.558614\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) −5.28544 + 12.7701i −0.352363 + 0.851339i
\(226\) 13.6037 + 13.6037i 0.904902 + 0.904902i
\(227\) 18.6457 18.6457i 1.23756 1.23756i 0.276560 0.960997i \(-0.410805\pi\)
0.960997 0.276560i \(-0.0891946\pi\)
\(228\) 7.17236 + 10.7310i 0.475001 + 0.710679i
\(229\) −1.93830 + 1.93830i −0.128087 + 0.128087i −0.768244 0.640157i \(-0.778869\pi\)
0.640157 + 0.768244i \(0.278869\pi\)
\(230\) 25.2863i 1.66733i
\(231\) 0.609699 3.06736i 0.0401152 0.201817i
\(232\) −6.72109 + 6.72109i −0.441261 + 0.441261i
\(233\) −3.76840 −0.246876 −0.123438 0.992352i \(-0.539392\pi\)
−0.123438 + 0.992352i \(0.539392\pi\)
\(234\) −7.14443 + 8.12140i −0.467046 + 0.530912i
\(235\) −3.53183 −0.230391
\(236\) 1.49217 1.49217i 0.0971321 0.0971321i
\(237\) −1.48193 + 7.45549i −0.0962615 + 0.484286i
\(238\) 3.68191i 0.238663i
\(239\) −2.94952 + 2.94952i −0.190789 + 0.190789i −0.796037 0.605248i \(-0.793074\pi\)
0.605248 + 0.796037i \(0.293074\pi\)
\(240\) −2.98318 4.46333i −0.192564 0.288107i
\(241\) 14.8333 14.8333i 0.955499 0.955499i −0.0435517 0.999051i \(-0.513867\pi\)
0.999051 + 0.0435517i \(0.0138673\pi\)
\(242\) 5.47291 + 5.47291i 0.351812 + 0.351812i
\(243\) −12.9554 + 8.66936i −0.831089 + 0.556140i
\(244\) 8.14557i 0.521467i
\(245\) −2.19168 2.19168i −0.140021 0.140021i
\(246\) 5.32857 + 1.05916i 0.339737 + 0.0675295i
\(247\) −25.4270 8.68278i −1.61788 0.552472i
\(248\) 0.177174i 0.0112505i
\(249\) 12.7285 + 19.0439i 0.806636 + 1.20686i
\(250\) −1.21844 −0.0770610
\(251\) 26.0328 1.64318 0.821589 0.570080i \(-0.193088\pi\)
0.821589 + 0.570080i \(0.193088\pi\)
\(252\) −1.14881 2.77132i −0.0723682 0.174577i
\(253\) 10.4159 + 10.4159i 0.654843 + 0.654843i
\(254\) −8.82521 8.82521i −0.553743 0.553743i
\(255\) 10.9838 + 16.4336i 0.687833 + 1.02911i
\(256\) 1.00000 0.0625000
\(257\) 1.24091 0.0774055 0.0387028 0.999251i \(-0.487677\pi\)
0.0387028 + 0.999251i \(0.487677\pi\)
\(258\) 2.06104 1.37755i 0.128315 0.0857624i
\(259\) 0.464238i 0.0288464i
\(260\) 10.5758 + 3.61141i 0.655883 + 0.223970i
\(261\) 10.9051 26.3476i 0.675006 1.63087i
\(262\) −5.89570 5.89570i −0.364237 0.364237i
\(263\) 11.9752i 0.738425i −0.929345 0.369213i \(-0.879627\pi\)
0.929345 0.369213i \(-0.120373\pi\)
\(264\) −3.06736 0.609699i −0.188783 0.0375244i
\(265\) −12.2680 12.2680i −0.753618 0.753618i
\(266\) 5.26937 5.26937i 0.323086 0.323086i
\(267\) −6.49672 + 4.34226i −0.397593 + 0.265742i
\(268\) −10.6436 + 10.6436i −0.650163 + 0.650163i
\(269\) 7.12840i 0.434626i −0.976102 0.217313i \(-0.930271\pi\)
0.976102 0.217313i \(-0.0697293\pi\)
\(270\) 13.3949 + 8.94221i 0.815187 + 0.544206i
\(271\) 9.80032 9.80032i 0.595327 0.595327i −0.343738 0.939065i \(-0.611693\pi\)
0.939065 + 0.343738i \(0.111693\pi\)
\(272\) −3.68191 −0.223249
\(273\) 5.40308 + 3.13157i 0.327009 + 0.189531i
\(274\) 20.1105 1.21492
\(275\) 5.88181 5.88181i 0.354686 0.354686i
\(276\) 13.8593 + 2.75481i 0.834231 + 0.165820i
\(277\) 1.47925i 0.0888795i 0.999012 + 0.0444397i \(0.0141503\pi\)
−0.999012 + 0.0444397i \(0.985850\pi\)
\(278\) −3.91664 + 3.91664i −0.234905 + 0.234905i
\(279\) 0.203539 + 0.491005i 0.0121855 + 0.0293957i
\(280\) −2.19168 + 2.19168i −0.130978 + 0.130978i
\(281\) −11.3699 11.3699i −0.678270 0.678270i 0.281339 0.959609i \(-0.409222\pi\)
−0.959609 + 0.281339i \(0.909222\pi\)
\(282\) −0.384773 + 1.93577i −0.0229129 + 0.115274i
\(283\) 19.9300i 1.18471i 0.805676 + 0.592357i \(0.201802\pi\)
−0.805676 + 0.592357i \(0.798198\pi\)
\(284\) 0.752235 + 0.752235i 0.0446369 + 0.0446369i
\(285\) −7.79942 + 39.2384i −0.461998 + 2.32428i
\(286\) 5.84397 2.86876i 0.345561 0.169633i
\(287\) 3.13663i 0.185150i
\(288\) −2.77132 + 1.14881i −0.163302 + 0.0676943i
\(289\) −3.44353 −0.202561
\(290\) −29.4609 −1.73000
\(291\) −3.65211 + 2.44099i −0.214090 + 0.143093i
\(292\) −3.59354 3.59354i −0.210296 0.210296i
\(293\) 10.3404 + 10.3404i 0.604092 + 0.604092i 0.941396 0.337304i \(-0.109515\pi\)
−0.337304 + 0.941396i \(0.609515\pi\)
\(294\) −1.44002 + 0.962473i −0.0839834 + 0.0561326i
\(295\) 6.54072 0.380815
\(296\) −0.464238 −0.0269833
\(297\) 9.20107 1.83414i 0.533900 0.106427i
\(298\) 5.26423i 0.304949i
\(299\) −26.4049 + 12.9620i −1.52703 + 0.749609i
\(300\) 1.55563 7.82626i 0.0898141 0.451849i
\(301\) −1.01205 1.01205i −0.0583338 0.0583338i
\(302\) 21.5603i 1.24066i
\(303\) −2.88783 + 14.5285i −0.165901 + 0.834640i
\(304\) −5.26937 5.26937i −0.302219 0.302219i
\(305\) −17.8525 + 17.8525i −1.02223 + 1.02223i
\(306\) 10.2038 4.22981i 0.583311 0.241802i
\(307\) −6.10278 + 6.10278i −0.348304 + 0.348304i −0.859478 0.511174i \(-0.829211\pi\)
0.511174 + 0.859478i \(0.329211\pi\)
\(308\) 1.80559i 0.102883i
\(309\) −11.4175 2.26945i −0.649517 0.129104i
\(310\) 0.388307 0.388307i 0.0220544 0.0220544i
\(311\) 21.9647 1.24550 0.622752 0.782420i \(-0.286015\pi\)
0.622752 + 0.782420i \(0.286015\pi\)
\(312\) 3.13157 5.40308i 0.177290 0.305889i
\(313\) −4.26972 −0.241339 −0.120669 0.992693i \(-0.538504\pi\)
−0.120669 + 0.992693i \(0.538504\pi\)
\(314\) 7.27121 7.27121i 0.410338 0.410338i
\(315\) 3.55603 8.59166i 0.200359 0.484085i
\(316\) 4.38864i 0.246880i
\(317\) −17.6141 + 17.6141i −0.989307 + 0.989307i −0.999943 0.0106369i \(-0.996614\pi\)
0.0106369 + 0.999943i \(0.496614\pi\)
\(318\) −8.06055 + 5.38749i −0.452013 + 0.302115i
\(319\) −12.1355 + 12.1355i −0.679457 + 0.679457i
\(320\) 2.19168 + 2.19168i 0.122518 + 0.122518i
\(321\) −12.9874 2.58150i −0.724886 0.144086i
\(322\) 8.15820i 0.454639i
\(323\) 19.4014 + 19.4014i 1.07952 + 1.07952i
\(324\) 6.36047 6.36745i 0.353360 0.353747i
\(325\) 7.31954 + 14.9107i 0.406015 + 0.827097i
\(326\) 23.2123i 1.28561i
\(327\) 22.5273 15.0567i 1.24576 0.832639i
\(328\) −3.13663 −0.173192
\(329\) 1.13948 0.0628217
\(330\) −5.38639 8.05892i −0.296511 0.443629i
\(331\) −16.3963 16.3963i −0.901220 0.901220i 0.0943216 0.995542i \(-0.469932\pi\)
−0.995542 + 0.0943216i \(0.969932\pi\)
\(332\) −9.35133 9.35133i −0.513221 0.513221i
\(333\) 1.28655 0.533321i 0.0705028 0.0292258i
\(334\) 14.3809 0.786888
\(335\) −46.6548 −2.54902
\(336\) 0.962473 + 1.44002i 0.0525072 + 0.0785593i
\(337\) 8.77212i 0.477848i 0.971038 + 0.238924i \(0.0767947\pi\)
−0.971038 + 0.238924i \(0.923205\pi\)
\(338\) 1.65006 + 12.8949i 0.0897516 + 0.701388i
\(339\) 32.6827 + 6.49633i 1.77508 + 0.352832i
\(340\) −8.06956 8.06956i −0.437633 0.437633i
\(341\) 0.319902i 0.0173237i
\(342\) 20.6566 + 8.54963i 1.11698 + 0.462311i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −1.01205 + 1.01205i −0.0545663 + 0.0545663i
\(345\) 24.3374 + 36.4127i 1.31028 + 1.96039i
\(346\) 6.17263 6.17263i 0.331843 0.331843i
\(347\) 8.56153i 0.459607i 0.973237 + 0.229803i \(0.0738083\pi\)
−0.973237 + 0.229803i \(0.926192\pi\)
\(348\) −3.20961 + 16.1473i −0.172053 + 0.865588i
\(349\) −0.0314225 + 0.0314225i −0.00168201 + 0.00168201i −0.707947 0.706265i \(-0.750379\pi\)
0.706265 + 0.707947i \(0.250379\pi\)
\(350\) −4.60689 −0.246249
\(351\) −2.47147 + 18.5713i −0.131917 + 0.991261i
\(352\) 1.80559 0.0962380
\(353\) 1.70236 1.70236i 0.0906076 0.0906076i −0.660350 0.750958i \(-0.729592\pi\)
0.750958 + 0.660350i \(0.229592\pi\)
\(354\) 0.712576 3.58493i 0.0378730 0.190537i
\(355\) 3.29731i 0.175003i
\(356\) 3.19016 3.19016i 0.169078 0.169078i
\(357\) −3.54374 5.30201i −0.187555 0.280612i
\(358\) 15.1565 15.1565i 0.801048 0.801048i
\(359\) −19.7911 19.7911i −1.04453 1.04453i −0.998961 0.0455713i \(-0.985489\pi\)
−0.0455713 0.998961i \(-0.514511\pi\)
\(360\) −8.59166 3.55603i −0.452820 0.187419i
\(361\) 36.5325i 1.92276i
\(362\) −5.32612 5.32612i −0.279935 0.279935i
\(363\) 13.1486 + 2.61355i 0.690123 + 0.137176i
\(364\) −3.41210 1.16516i −0.178842 0.0610709i
\(365\) 15.7518i 0.824485i
\(366\) 7.83989 + 11.7298i 0.409798 + 0.613124i
\(367\) −18.1422 −0.947016 −0.473508 0.880790i \(-0.657012\pi\)
−0.473508 + 0.880790i \(0.657012\pi\)
\(368\) −8.15820 −0.425275
\(369\) 8.69263 3.60340i 0.452520 0.187585i
\(370\) −1.01746 1.01746i −0.0528952 0.0528952i
\(371\) 3.95806 + 3.95806i 0.205492 + 0.205492i
\(372\) −0.170525 0.255133i −0.00884130 0.0132280i
\(373\) −27.3139 −1.41426 −0.707130 0.707083i \(-0.750011\pi\)
−0.707130 + 0.707083i \(0.750011\pi\)
\(374\) −6.64800 −0.343760
\(375\) −1.75457 + 1.17272i −0.0906058 + 0.0605588i
\(376\) 1.13948i 0.0587644i
\(377\) −15.1019 30.7641i −0.777786 1.58443i
\(378\) −4.32163 2.88505i −0.222281 0.148391i
\(379\) 11.0481 + 11.0481i 0.567502 + 0.567502i 0.931428 0.363926i \(-0.118564\pi\)
−0.363926 + 0.931428i \(0.618564\pi\)
\(380\) 23.0975i 1.18488i
\(381\) −21.2025 4.21441i −1.08624 0.215911i
\(382\) 1.27363 + 1.27363i 0.0651645 + 0.0651645i
\(383\) 18.4315 18.4315i 0.941808 0.941808i −0.0565899 0.998398i \(-0.518023\pi\)
0.998398 + 0.0565899i \(0.0180227\pi\)
\(384\) 1.44002 0.962473i 0.0734855 0.0491160i
\(385\) −3.95726 + 3.95726i −0.201681 + 0.201681i
\(386\) 20.3723i 1.03692i
\(387\) 1.64207 3.96738i 0.0834712 0.201673i
\(388\) 1.79334 1.79334i 0.0910428 0.0910428i
\(389\) 13.3245 0.675579 0.337790 0.941222i \(-0.390321\pi\)
0.337790 + 0.941222i \(0.390321\pi\)
\(390\) 18.7052 4.97843i 0.947174 0.252093i
\(391\) 30.0378 1.51907
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) −14.1643 2.81545i −0.714497 0.142020i
\(394\) 9.80502i 0.493970i
\(395\) 9.61847 9.61847i 0.483958 0.483958i
\(396\) −5.00386 + 2.07427i −0.251454 + 0.104236i
\(397\) −16.7117 + 16.7117i −0.838738 + 0.838738i −0.988693 0.149955i \(-0.952087\pi\)
0.149955 + 0.988693i \(0.452087\pi\)
\(398\) −7.25442 7.25442i −0.363631 0.363631i
\(399\) 2.51635 12.6596i 0.125975 0.633773i
\(400\) 4.60689i 0.230345i
\(401\) −0.352145 0.352145i −0.0175853 0.0175853i 0.698259 0.715845i \(-0.253958\pi\)
−0.715845 + 0.698259i \(0.753958\pi\)
\(402\) −5.08279 + 25.5712i −0.253506 + 1.27538i
\(403\) 0.604533 + 0.206435i 0.0301140 + 0.0102833i
\(404\) 8.55213i 0.425484i
\(405\) 27.8955 0.0152839i 1.38614 0.000759463i
\(406\) 9.50505 0.471728
\(407\) −0.838222 −0.0415491
\(408\) −5.30201 + 3.54374i −0.262489 + 0.175441i
\(409\) −23.1842 23.1842i −1.14638 1.14638i −0.987258 0.159126i \(-0.949132\pi\)
−0.159126 0.987258i \(-0.550868\pi\)
\(410\) −6.87449 6.87449i −0.339507 0.339507i
\(411\) 28.9595 19.3559i 1.42847 0.954754i
\(412\) 6.72083 0.331112
\(413\) −2.11025 −0.103839
\(414\) 22.6090 9.37222i 1.11117 0.460619i
\(415\) 40.9902i 2.01213i
\(416\) −1.16516 + 3.41210i −0.0571266 + 0.167292i
\(417\) −1.87036 + 9.40969i −0.0915921 + 0.460795i
\(418\) −9.51430 9.51430i −0.465360 0.465360i
\(419\) 9.60922i 0.469441i 0.972063 + 0.234721i \(0.0754175\pi\)
−0.972063 + 0.234721i \(0.924582\pi\)
\(420\) −1.04662 + 5.26548i −0.0510698 + 0.256929i
\(421\) −10.1653 10.1653i −0.495425 0.495425i 0.414586 0.910010i \(-0.363927\pi\)
−0.910010 + 0.414586i \(0.863927\pi\)
\(422\) 13.7561 13.7561i 0.669638 0.669638i
\(423\) 1.30905 + 3.15788i 0.0636481 + 0.153541i
\(424\) 3.95806 3.95806i 0.192220 0.192220i
\(425\) 16.9622i 0.822786i
\(426\) 1.80724 + 0.359224i 0.0875609 + 0.0174045i
\(427\) 5.75979 5.75979i 0.278736 0.278736i
\(428\) 7.64497 0.369534
\(429\) 5.65431 9.75573i 0.272993 0.471011i
\(430\) −4.43619 −0.213932
\(431\) 6.40858 6.40858i 0.308690 0.308690i −0.535711 0.844401i \(-0.679956\pi\)
0.844401 + 0.535711i \(0.179956\pi\)
\(432\) −2.88505 + 4.32163i −0.138807 + 0.207924i
\(433\) 33.5644i 1.61300i −0.591232 0.806502i \(-0.701358\pi\)
0.591232 0.806502i \(-0.298642\pi\)
\(434\) −0.125281 + 0.125281i −0.00601366 + 0.00601366i
\(435\) −42.4241 + 28.3553i −2.03408 + 1.35953i
\(436\) −11.0618 + 11.0618i −0.529766 + 0.529766i
\(437\) 42.9886 + 42.9886i 2.05642 + 2.05642i
\(438\) −8.63345 1.71607i −0.412522 0.0819970i
\(439\) 7.08017i 0.337918i −0.985623 0.168959i \(-0.945959\pi\)
0.985623 0.168959i \(-0.0540405\pi\)
\(440\) 3.95726 + 3.95726i 0.188655 + 0.188655i
\(441\) −1.14729 + 2.77195i −0.0546329 + 0.131998i
\(442\) 4.29001 12.5630i 0.204055 0.597563i
\(443\) 6.61082i 0.314089i −0.987591 0.157045i \(-0.949803\pi\)
0.987591 0.157045i \(-0.0501967\pi\)
\(444\) −0.668510 + 0.446817i −0.0317261 + 0.0212050i
\(445\) 13.9836 0.662886
\(446\) −16.8948 −0.799992
\(447\) −5.06668 7.58057i −0.239646 0.358549i
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) −15.0860 15.0860i −0.711951 0.711951i 0.254992 0.966943i \(-0.417927\pi\)
−0.966943 + 0.254992i \(0.917927\pi\)
\(450\) −5.29244 12.7672i −0.249488 0.601851i
\(451\) −5.66346 −0.266682
\(452\) −19.2385 −0.904902
\(453\) −20.7512 31.0472i −0.974978 1.45873i
\(454\) 26.3690i 1.23756i
\(455\) −4.92456 10.0319i −0.230867 0.470301i
\(456\) −12.6596 2.51635i −0.592840 0.117839i
\(457\) −18.4880 18.4880i −0.864831 0.864831i 0.127063 0.991895i \(-0.459445\pi\)
−0.991895 + 0.127063i \(0.959445\pi\)
\(458\) 2.74117i 0.128087i
\(459\) 10.6225 15.9119i 0.495816 0.742702i
\(460\) −17.8801 17.8801i −0.833665 0.833665i
\(461\) −11.9307 + 11.9307i −0.555668 + 0.555668i −0.928071 0.372403i \(-0.878534\pi\)
0.372403 + 0.928071i \(0.378534\pi\)
\(462\) 1.73783 + 2.60007i 0.0808511 + 0.120966i
\(463\) 2.01800 2.01800i 0.0937846 0.0937846i −0.658658 0.752443i \(-0.728876\pi\)
0.752443 + 0.658658i \(0.228876\pi\)
\(464\) 9.50505i 0.441261i
\(465\) 0.185433 0.932903i 0.00859926 0.0432624i
\(466\) 2.66466 2.66466i 0.123438 0.123438i
\(467\) −11.3847 −0.526823 −0.263411 0.964684i \(-0.584848\pi\)
−0.263411 + 0.964684i \(0.584848\pi\)
\(468\) −0.690818 10.7946i −0.0319331 0.498979i
\(469\) 15.0524 0.695054
\(470\) 2.49738 2.49738i 0.115195 0.115195i
\(471\) 3.47231 17.4690i 0.159996 0.804929i
\(472\) 2.11025i 0.0971321i
\(473\) −1.82735 + 1.82735i −0.0840216 + 0.0840216i
\(474\) −4.22394 6.31970i −0.194012 0.290274i
\(475\) 24.2754 24.2754i 1.11383 1.11383i
\(476\) 2.60350 + 2.60350i 0.119331 + 0.119331i
\(477\) −6.42201 + 15.5161i −0.294044 + 0.710435i
\(478\) 4.17126i 0.190789i
\(479\) −21.9770 21.9770i −1.00415 1.00415i −0.999991 0.00416246i \(-0.998675\pi\)
−0.00416246 0.999991i \(-0.501325\pi\)
\(480\) 5.26548 + 1.04662i 0.240335 + 0.0477714i
\(481\) 0.540911 1.58403i 0.0246634 0.0722254i
\(482\) 20.9775i 0.955499i
\(483\) −7.85205 11.7479i −0.357281 0.534550i
\(484\) −7.73986 −0.351812
\(485\) 7.86082 0.356942
\(486\) 3.03069 15.2910i 0.137475 0.693614i
\(487\) −21.7649 21.7649i −0.986263 0.986263i 0.0136436 0.999907i \(-0.495657\pi\)
−0.999907 + 0.0136436i \(0.995657\pi\)
\(488\) −5.75979 5.75979i −0.260733 0.260733i
\(489\) 22.3413 + 33.4261i 1.01031 + 1.51158i
\(490\) 3.09950 0.140021
\(491\) 24.6630 1.11303 0.556513 0.830839i \(-0.312139\pi\)
0.556513 + 0.830839i \(0.312139\pi\)
\(492\) −4.51680 + 3.01893i −0.203633 + 0.136104i
\(493\) 34.9968i 1.57617i
\(494\) 24.1193 11.8400i 1.08518 0.532705i
\(495\) −15.5130 6.42071i −0.697257 0.288589i
\(496\) 0.125281 + 0.125281i 0.00562527 + 0.00562527i
\(497\) 1.06382i 0.0477189i
\(498\) −22.4665 4.46566i −1.00675 0.200111i
\(499\) 30.6363 + 30.6363i 1.37147 + 1.37147i 0.858268 + 0.513202i \(0.171541\pi\)
0.513202 + 0.858268i \(0.328459\pi\)
\(500\) 0.861568 0.861568i 0.0385305 0.0385305i
\(501\) 20.7087 13.8412i 0.925197 0.618380i
\(502\) −18.4080 + 18.4080i −0.821589 + 0.821589i
\(503\) 34.2723i 1.52813i 0.645141 + 0.764064i \(0.276799\pi\)
−0.645141 + 0.764064i \(0.723201\pi\)
\(504\) 2.77195 + 1.14729i 0.123473 + 0.0511044i
\(505\) 18.7435 18.7435i 0.834075 0.834075i
\(506\) −14.7303 −0.654843
\(507\) 14.7871 + 16.9807i 0.656717 + 0.754137i
\(508\) 12.4807 0.553743
\(509\) 3.24519 3.24519i 0.143840 0.143840i −0.631520 0.775360i \(-0.717568\pi\)
0.775360 + 0.631520i \(0.217568\pi\)
\(510\) −19.3870 3.85356i −0.858472 0.170638i
\(511\) 5.08204i 0.224816i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 37.9747 7.56985i 1.67662 0.334217i
\(514\) −0.877452 + 0.877452i −0.0387028 + 0.0387028i
\(515\) 14.7299 + 14.7299i 0.649077 + 0.649077i
\(516\) −0.483299 + 2.43145i −0.0212760 + 0.107038i
\(517\) 2.05743i 0.0904858i
\(518\) 0.328266 + 0.328266i 0.0144232 + 0.0144232i
\(519\) 2.94770 14.8297i 0.129389 0.650951i
\(520\) −10.0319 + 4.92456i −0.439926 + 0.215956i
\(521\) 44.5505i 1.95179i 0.218238 + 0.975896i \(0.429969\pi\)
−0.218238 + 0.975896i \(0.570031\pi\)
\(522\) 10.9195 + 26.3416i 0.477933 + 1.15294i
\(523\) 16.3414 0.714560 0.357280 0.933997i \(-0.383704\pi\)
0.357280 + 0.933997i \(0.383704\pi\)
\(524\) 8.33777 0.364237
\(525\) −6.63400 + 4.43401i −0.289531 + 0.193516i
\(526\) 8.46778 + 8.46778i 0.369213 + 0.369213i
\(527\) −0.461272 0.461272i −0.0200933 0.0200933i
\(528\) 2.60007 1.73783i 0.113154 0.0756292i
\(529\) 43.5562 1.89375
\(530\) 17.3496 0.753618
\(531\) −2.42428 5.84819i −0.105205 0.253790i
\(532\) 7.45201i 0.323086i
\(533\) 3.65468 10.7025i 0.158302 0.463577i
\(534\) 1.52344 7.66432i 0.0659256 0.331668i
\(535\) 16.7553 + 16.7553i 0.724395 + 0.724395i
\(536\) 15.0524i 0.650163i
\(537\) 7.23789 36.4134i 0.312338 1.57135i
\(538\) 5.04054 + 5.04054i 0.217313 + 0.217313i
\(539\) 1.27674 1.27674i 0.0549932 0.0549932i
\(540\) −15.7947 + 3.14851i −0.679696 + 0.135490i
\(541\) 14.6761 14.6761i 0.630977 0.630977i −0.317336 0.948313i \(-0.602788\pi\)
0.948313 + 0.317336i \(0.102788\pi\)
\(542\) 13.8597i 0.595327i
\(543\) −12.7959 2.54345i −0.549127 0.109150i
\(544\) 2.60350 2.60350i 0.111624 0.111624i
\(545\) −48.4879 −2.07699
\(546\) −6.03491 + 1.60620i −0.258270 + 0.0687392i
\(547\) 3.25656 0.139240 0.0696202 0.997574i \(-0.477821\pi\)
0.0696202 + 0.997574i \(0.477821\pi\)
\(548\) −14.2203 + 14.2203i −0.607461 + 0.607461i
\(549\) 22.5791 + 9.34534i 0.963654 + 0.398849i
\(550\) 8.31814i 0.354686i
\(551\) −50.0856 + 50.0856i −2.13372 + 2.13372i
\(552\) −11.7479 + 7.85205i −0.500025 + 0.334205i
\(553\) −3.10323 + 3.10323i −0.131963 + 0.131963i
\(554\) −1.04599 1.04599i −0.0444397 0.0444397i
\(555\) −2.44444 0.485881i −0.103761 0.0206245i
\(556\) 5.53897i 0.234905i
\(557\) 3.70450 + 3.70450i 0.156965 + 0.156965i 0.781220 0.624255i \(-0.214598\pi\)
−0.624255 + 0.781220i \(0.714598\pi\)
\(558\) −0.491117 0.203270i −0.0207906 0.00860509i
\(559\) −2.27402 4.63243i −0.0961809 0.195931i
\(560\) 3.09950i 0.130978i
\(561\) −9.57323 + 6.39853i −0.404182 + 0.270146i
\(562\) 16.0794 0.678270
\(563\) 15.3860 0.648443 0.324221 0.945981i \(-0.394898\pi\)
0.324221 + 0.945981i \(0.394898\pi\)
\(564\) −1.09672 1.64087i −0.0461803 0.0690932i
\(565\) −42.1645 42.1645i −1.77388 1.77388i
\(566\) −14.0926 14.0926i −0.592357 0.592357i
\(567\) −9.00000 + 0.00493109i −0.377964 + 0.000207086i
\(568\) −1.06382 −0.0446369
\(569\) 33.4793 1.40353 0.701763 0.712410i \(-0.252397\pi\)
0.701763 + 0.712410i \(0.252397\pi\)
\(570\) −22.2307 33.2608i −0.931143 1.39314i
\(571\) 1.76074i 0.0736845i 0.999321 + 0.0368423i \(0.0117299\pi\)
−0.999321 + 0.0368423i \(0.988270\pi\)
\(572\) −2.10379 + 6.16083i −0.0879640 + 0.257597i
\(573\) 3.05988 + 0.608212i 0.127828 + 0.0254084i
\(574\) 2.21794 + 2.21794i 0.0925748 + 0.0925748i
\(575\) 37.5839i 1.56736i
\(576\) 1.14729 2.77195i 0.0478038 0.115498i
\(577\) −25.8072 25.8072i −1.07437 1.07437i −0.997003 0.0773650i \(-0.975349\pi\)
−0.0773650 0.997003i \(-0.524651\pi\)
\(578\) 2.43494 2.43494i 0.101280 0.101280i
\(579\) 19.6078 + 29.3365i 0.814873 + 1.21918i
\(580\) 20.8320 20.8320i 0.865002 0.865002i
\(581\) 13.2248i 0.548656i
\(582\) 0.856394 4.30847i 0.0354987 0.178592i
\(583\) 7.14662 7.14662i 0.295983 0.295983i
\(584\) 5.08204 0.210296
\(585\) 22.1442 25.1723i 0.915548 1.04074i
\(586\) −14.6235 −0.604092
\(587\) −4.03302 + 4.03302i −0.166460 + 0.166460i −0.785422 0.618961i \(-0.787554\pi\)
0.618961 + 0.785422i \(0.287554\pi\)
\(588\) 0.337674 1.69882i 0.0139254 0.0700580i
\(589\) 1.32030i 0.0544020i
\(590\) −4.62499 + 4.62499i −0.190408 + 0.190408i
\(591\) 9.43707 + 14.1194i 0.388189 + 0.580794i
\(592\) 0.328266 0.328266i 0.0134917 0.0134917i
\(593\) 1.35646 + 1.35646i 0.0557030 + 0.0557030i 0.734410 0.678707i \(-0.237459\pi\)
−0.678707 + 0.734410i \(0.737459\pi\)
\(594\) −5.20921 + 7.80307i −0.213736 + 0.320164i
\(595\) 11.4121i 0.467850i
\(596\) 3.72237 + 3.72237i 0.152474 + 0.152474i
\(597\) −17.4287 3.46429i −0.713307 0.141784i
\(598\) 9.50560 27.8366i 0.388713 1.13832i
\(599\) 19.3845i 0.792029i −0.918244 0.396014i \(-0.870393\pi\)
0.918244 0.396014i \(-0.129607\pi\)
\(600\) 4.43401 + 6.63400i 0.181018 + 0.270832i
\(601\) −37.2292 −1.51861 −0.759306 0.650734i \(-0.774461\pi\)
−0.759306 + 0.650734i \(0.774461\pi\)
\(602\) 1.43126 0.0583338
\(603\) 17.2923 + 41.7150i 0.704197 + 1.69877i
\(604\) 15.2455 + 15.2455i 0.620329 + 0.620329i
\(605\) −16.9633 16.9633i −0.689655 0.689655i
\(606\) −8.23120 12.3152i −0.334370 0.500271i
\(607\) −15.3314 −0.622284 −0.311142 0.950363i \(-0.600711\pi\)
−0.311142 + 0.950363i \(0.600711\pi\)
\(608\) 7.45201 0.302219
\(609\) 13.6874 9.14836i 0.554642 0.370710i
\(610\) 25.2472i 1.02223i
\(611\) 3.88803 + 1.32768i 0.157293 + 0.0537121i
\(612\) −4.22422 + 10.2061i −0.170754 + 0.412557i
\(613\) −12.6416 12.6416i −0.510591 0.510591i 0.404116 0.914708i \(-0.367579\pi\)
−0.914708 + 0.404116i \(0.867579\pi\)
\(614\) 8.63063i 0.348304i
\(615\) −16.5159 3.28286i −0.665985 0.132378i
\(616\) −1.27674 1.27674i −0.0514414 0.0514414i
\(617\) −0.724231 + 0.724231i −0.0291564 + 0.0291564i −0.721535 0.692378i \(-0.756563\pi\)
0.692378 + 0.721535i \(0.256563\pi\)
\(618\) 9.67811 6.46862i 0.389311 0.260206i
\(619\) −4.40767 + 4.40767i −0.177159 + 0.177159i −0.790116 0.612957i \(-0.789980\pi\)
0.612957 + 0.790116i \(0.289980\pi\)
\(620\) 0.549149i 0.0220544i
\(621\) 23.5368 35.2567i 0.944500 1.41480i
\(622\) −15.5314 + 15.5314i −0.622752 + 0.622752i
\(623\) −4.51157 −0.180752
\(624\) 1.60620 + 6.03491i 0.0642997 + 0.241590i
\(625\) 26.8110 1.07244
\(626\) 3.01915 3.01915i 0.120669 0.120669i
\(627\) −22.8580 4.54348i −0.912860 0.181449i
\(628\) 10.2830i 0.410338i
\(629\) −1.20865 + 1.20865i −0.0481919 + 0.0481919i
\(630\) 3.56073 + 8.58971i 0.141863 + 0.342222i
\(631\) −9.93188 + 9.93188i −0.395382 + 0.395382i −0.876601 0.481219i \(-0.840194\pi\)
0.481219 + 0.876601i \(0.340194\pi\)
\(632\) 3.10323 + 3.10323i 0.123440 + 0.123440i
\(633\) 6.56914 33.0490i 0.261100 1.31358i
\(634\) 24.9101i 0.989307i
\(635\) 27.3537 + 27.3537i 1.08550 + 1.08550i
\(636\) 1.89014 9.50920i 0.0749491 0.377064i
\(637\) 1.58883 + 3.23661i 0.0629516 + 0.128239i
\(638\) 17.1622i 0.679457i
\(639\) 2.94819 1.22213i 0.116629 0.0483466i
\(640\) −3.09950 −0.122518
\(641\) 12.1939 0.481630 0.240815 0.970571i \(-0.422585\pi\)
0.240815 + 0.970571i \(0.422585\pi\)
\(642\) 11.0089 7.35808i 0.434486 0.290400i
\(643\) 28.6315 + 28.6315i 1.12912 + 1.12912i 0.990321 + 0.138797i \(0.0443234\pi\)
0.138797 + 0.990321i \(0.455677\pi\)
\(644\) 5.76872 + 5.76872i 0.227319 + 0.227319i
\(645\) −6.38818 + 4.26971i −0.251534 + 0.168120i
\(646\) −27.4377 −1.07952
\(647\) −18.5157 −0.727925 −0.363963 0.931414i \(-0.618576\pi\)
−0.363963 + 0.931414i \(0.618576\pi\)
\(648\) 0.00493109 + 9.00000i 0.000193711 + 0.353553i
\(649\) 3.81024i 0.149565i
\(650\) −15.7192 5.36776i −0.616556 0.210541i
\(651\) −0.0598268 + 0.300985i −0.00234480 + 0.0117965i
\(652\) −16.4136 16.4136i −0.642806 0.642806i
\(653\) 42.5130i 1.66366i 0.555028 + 0.831831i \(0.312707\pi\)
−0.555028 + 0.831831i \(0.687293\pi\)
\(654\) −5.28250 + 26.5759i −0.206562 + 1.03920i
\(655\) 18.2737 + 18.2737i 0.714012 + 0.714012i
\(656\) 2.21794 2.21794i 0.0865958 0.0865958i
\(657\) −14.0840 + 5.83829i −0.549468 + 0.227774i
\(658\) −0.805736 + 0.805736i −0.0314109 + 0.0314109i
\(659\) 26.7078i 1.04039i −0.854049 0.520193i \(-0.825860\pi\)
0.854049 0.520193i \(-0.174140\pi\)
\(660\) 9.50727 + 1.88976i 0.370070 + 0.0735588i
\(661\) −17.9757 + 17.9757i −0.699175 + 0.699175i −0.964233 0.265057i \(-0.914609\pi\)
0.265057 + 0.964233i \(0.414609\pi\)
\(662\) 23.1878 0.901220
\(663\) −5.91390 22.2200i −0.229677 0.862953i
\(664\) 13.2248 0.513221
\(665\) −16.3324 + 16.3324i −0.633344 + 0.633344i
\(666\) −0.532616 + 1.28685i −0.0206385 + 0.0498643i
\(667\) 77.5441i 3.00252i
\(668\) −10.1688 + 10.1688i −0.393444 + 0.393444i
\(669\) −24.3288 + 16.2608i −0.940604 + 0.628678i
\(670\) 32.9899 32.9899i 1.27451 1.27451i
\(671\) −10.3998 10.3998i −0.401480 0.401480i
\(672\) −1.69882 0.337674i −0.0655333 0.0130260i
\(673\) 17.8573i 0.688350i 0.938906 + 0.344175i \(0.111841\pi\)
−0.938906 + 0.344175i \(0.888159\pi\)
\(674\) −6.20283 6.20283i −0.238924 0.238924i
\(675\) −19.9093 13.2911i −0.766308 0.511575i
\(676\) −10.2848 7.95127i −0.395570 0.305818i
\(677\) 7.00399i 0.269185i −0.990901 0.134593i \(-0.957027\pi\)
0.990901 0.134593i \(-0.0429726\pi\)
\(678\) −27.7037 + 18.5165i −1.06396 + 0.711123i
\(679\) −2.53616 −0.0973289
\(680\) 11.4121 0.437633
\(681\) 25.3794 + 37.9717i 0.972542 + 1.45508i
\(682\) 0.226205 + 0.226205i 0.00866183 + 0.00866183i
\(683\) −2.50202 2.50202i −0.0957372 0.0957372i 0.657616 0.753353i \(-0.271565\pi\)
−0.753353 + 0.657616i \(0.771565\pi\)
\(684\) −20.6519 + 8.56095i −0.789647 + 0.327336i
\(685\) −62.3326 −2.38161
\(686\) −1.00000 −0.0381802
\(687\) −2.63830 3.94733i −0.100658 0.150600i
\(688\) 1.43126i 0.0545663i
\(689\) 8.89352 + 18.1171i 0.338816 + 0.690205i
\(690\) −42.9568 8.53853i −1.63534 0.325056i
\(691\) −16.1198 16.1198i −0.613227 0.613227i 0.330558 0.943786i \(-0.392763\pi\)
−0.943786 + 0.330558i \(0.892763\pi\)
\(692\) 8.72942i 0.331843i
\(693\) 5.00500 + 2.07153i 0.190124 + 0.0786910i
\(694\) −6.05391 6.05391i −0.229803 0.229803i
\(695\) 12.1396 12.1396i 0.460482 0.460482i
\(696\) −9.14836 13.6874i −0.346768 0.518820i
\(697\) −8.16624 + 8.16624i −0.309318 + 0.309318i
\(698\) 0.0444381i 0.00168201i
\(699\) 1.27249 6.40182i 0.0481300 0.242139i
\(700\) 3.25756 3.25756i 0.123124 0.123124i
\(701\) 44.4648 1.67941 0.839706 0.543041i \(-0.182727\pi\)
0.839706 + 0.543041i \(0.182727\pi\)
\(702\) −11.3843 14.8795i −0.429672 0.561589i
\(703\) −3.45951 −0.130478
\(704\) −1.27674 + 1.27674i −0.0481190 + 0.0481190i
\(705\) 1.19260 5.99992i 0.0449161 0.225970i
\(706\) 2.40751i 0.0906076i
\(707\) −6.04727 + 6.04727i −0.227431 + 0.227431i
\(708\) 2.03106 + 3.03879i 0.0763319 + 0.114205i
\(709\) 17.0295 17.0295i 0.639557 0.639557i −0.310890 0.950446i \(-0.600627\pi\)
0.950446 + 0.310890i \(0.100627\pi\)
\(710\) −2.33155 2.33155i −0.0875016 0.0875016i
\(711\) −12.1651 5.03504i −0.456227 0.188829i
\(712\) 4.51157i 0.169078i
\(713\) −1.02206 1.02206i −0.0382766 0.0382766i
\(714\) 6.25489 + 1.24328i 0.234083 + 0.0465287i
\(715\) −18.1134 + 8.89172i −0.677402 + 0.332531i
\(716\) 21.4346i 0.801048i
\(717\) −4.01472 6.00667i −0.149933 0.224323i
\(718\) 27.9888 1.04453
\(719\) 6.18328 0.230598 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(720\) 8.58971 3.56073i 0.320120 0.132701i
\(721\) −4.75235 4.75235i −0.176987 0.176987i
\(722\) −25.8324 25.8324i −0.961382 0.961382i
\(723\) 20.1903 + 30.2079i 0.750885 + 1.12345i
\(724\) 7.53227 0.279935
\(725\) 43.7887 1.62627
\(726\) −11.1455 + 7.44941i −0.413649 + 0.276473i
\(727\) 38.6481i 1.43338i −0.697392 0.716690i \(-0.745656\pi\)
0.697392 0.716690i \(-0.254344\pi\)
\(728\) 3.23661 1.58883i 0.119957 0.0588858i
\(729\) −10.3529 24.9362i −0.383443 0.923565i
\(730\) 11.1382 + 11.1382i 0.412243 + 0.412243i
\(731\) 5.26977i 0.194909i
\(732\) −13.8378 2.75055i −0.511461 0.101663i
\(733\) −11.6899 11.6899i −0.431776 0.431776i 0.457456 0.889232i \(-0.348761\pi\)
−0.889232 + 0.457456i \(0.848761\pi\)
\(734\) 12.8285 12.8285i 0.473508 0.473508i
\(735\) 4.46333 2.98318i 0.164632 0.110036i
\(736\) 5.76872 5.76872i 0.212638 0.212638i
\(737\) 27.1783i 1.00113i
\(738\) −3.59863 + 8.69460i −0.132467 + 0.320053i
\(739\) −3.88750 + 3.88750i −0.143004 + 0.143004i −0.774984 0.631980i \(-0.782242\pi\)
0.631980 + 0.774984i \(0.282242\pi\)
\(740\) 1.43891 0.0528952
\(741\) 23.3365 40.2638i 0.857287 1.47913i
\(742\) −5.59755 −0.205492
\(743\) −1.32188 + 1.32188i −0.0484952 + 0.0484952i −0.730939 0.682443i \(-0.760917\pi\)
0.682443 + 0.730939i \(0.260917\pi\)
\(744\) 0.300985 + 0.0598268i 0.0110347 + 0.00219336i
\(745\) 16.3165i 0.597789i
\(746\) 19.3138 19.3138i 0.707130 0.707130i
\(747\) −36.6502 + 15.1928i −1.34096 + 0.555874i
\(748\) 4.70085 4.70085i 0.171880 0.171880i
\(749\) −5.40581 5.40581i −0.197524 0.197524i
\(750\) 0.411436 2.06991i 0.0150235 0.0755823i
\(751\) 14.9686i 0.546210i 0.961984 + 0.273105i \(0.0880507\pi\)
−0.961984 + 0.273105i \(0.911949\pi\)
\(752\) 0.805736 + 0.805736i 0.0293822 + 0.0293822i
\(753\) −8.79060 + 44.2250i −0.320347 + 1.61165i
\(754\) 32.4322 + 11.0749i 1.18111 + 0.403324i
\(755\) 66.8262i 2.43205i
\(756\) 5.09589 1.01581i 0.185336 0.0369448i
\(757\) 16.6501 0.605159 0.302579 0.953124i \(-0.402152\pi\)
0.302579 + 0.953124i \(0.402152\pi\)
\(758\) −15.6243 −0.567502
\(759\) −21.2119 + 14.1775i −0.769943 + 0.514612i
\(760\) 16.3324 + 16.3324i 0.592439 + 0.592439i
\(761\) −0.381043 0.381043i −0.0138128 0.0138128i 0.700167 0.713979i \(-0.253109\pi\)
−0.713979 + 0.700167i \(0.753109\pi\)
\(762\) 17.9725 12.0124i 0.651073 0.435162i
\(763\) 15.6438 0.566344
\(764\) −1.80118 −0.0651645
\(765\) −31.6266 + 13.1103i −1.14346 + 0.474004i
\(766\) 26.0661i 0.941808i
\(767\) −7.20038 2.45878i −0.259991 0.0887813i
\(768\) −0.337674 + 1.69882i −0.0121847 + 0.0613007i
\(769\) 29.7844 + 29.7844i 1.07405 + 1.07405i 0.997029 + 0.0770249i \(0.0245421\pi\)
0.0770249 + 0.997029i \(0.475458\pi\)
\(770\) 5.59641i 0.201681i
\(771\) −0.419021 + 2.10807i −0.0150907 + 0.0759203i
\(772\) −14.4054 14.4054i −0.518462 0.518462i
\(773\) 22.5034 22.5034i 0.809390 0.809390i −0.175151 0.984541i \(-0.556042\pi\)
0.984541 + 0.175151i \(0.0560415\pi\)
\(774\) 1.64424 + 3.96648i 0.0591011 + 0.142572i
\(775\) −0.577154 + 0.577154i −0.0207320 + 0.0207320i
\(776\) 2.53616i 0.0910428i
\(777\) 0.788656 + 0.156761i 0.0282929 + 0.00562377i
\(778\) −9.42185 + 9.42185i −0.337790 + 0.337790i
\(779\) −23.3742 −0.837469
\(780\) −9.70628 + 16.7468i −0.347541 + 0.599633i
\(781\) −1.92082 −0.0687323
\(782\) −21.2399 + 21.2399i −0.759537 + 0.759537i
\(783\) 41.0773 + 27.4226i 1.46798 + 0.980003i
\(784\) 1.00000i 0.0357143i
\(785\) −22.5371 + 22.5371i −0.804383 + 0.804383i
\(786\) 12.0065 8.02488i 0.428259 0.286238i
\(787\) −21.9665 + 21.9665i −0.783021 + 0.783021i −0.980340 0.197318i \(-0.936777\pi\)
0.197318 + 0.980340i \(0.436777\pi\)
\(788\) −6.93319 6.93319i −0.246985 0.246985i
\(789\) 20.3437 + 4.04373i 0.724256 + 0.143960i
\(790\) 13.6026i 0.483958i
\(791\) 13.6037 + 13.6037i 0.483691 + 0.483691i
\(792\) 2.07153 5.00500i 0.0736087 0.177845i
\(793\) 26.3640 12.9419i 0.936214 0.459580i
\(794\) 23.6340i 0.838738i
\(795\) 24.9837 16.6985i 0.886080 0.592235i
\(796\) 10.2593 0.363631
\(797\) 38.7028 1.37092 0.685461 0.728109i \(-0.259601\pi\)
0.685461 + 0.728109i \(0.259601\pi\)
\(798\) 7.17236 + 10.7310i 0.253899 + 0.379874i
\(799\) −2.96665 2.96665i −0.104952 0.104952i
\(800\) −3.25756 3.25756i −0.115172 0.115172i
\(801\) −5.18293 12.5030i −0.183130 0.441772i
\(802\) 0.498008 0.0175853
\(803\) 9.17605 0.323816
\(804\) −14.4875 21.6756i −0.510935 0.764441i
\(805\) 25.2863i 0.891226i
\(806\) −0.573441 + 0.281498i −0.0201986 + 0.00991534i
\(807\) 12.1098 + 2.40707i 0.426287 + 0.0847330i
\(808\) 6.04727 + 6.04727i 0.212742 + 0.212742i
\(809\) 29.2625i 1.02881i −0.857546 0.514407i \(-0.828012\pi\)
0.857546 0.514407i \(-0.171988\pi\)
\(810\) −19.7143 + 19.7359i −0.692689 + 0.693449i
\(811\) 6.61904 + 6.61904i 0.232426 + 0.232426i 0.813705 0.581279i \(-0.197447\pi\)
−0.581279 + 0.813705i \(0.697447\pi\)
\(812\) −6.72109 + 6.72109i −0.235864 + 0.235864i
\(813\) 13.3396 + 19.9583i 0.467841 + 0.699967i
\(814\) 0.592712 0.592712i 0.0207746 0.0207746i
\(815\) 71.9466i 2.52018i
\(816\) 1.24328 6.25489i 0.0435237 0.218965i
\(817\) −7.54184 + 7.54184i −0.263855 + 0.263855i
\(818\) 32.7874 1.14638
\(819\) −7.14443 + 8.12140i −0.249647 + 0.283785i
\(820\) 9.72199 0.339507
\(821\) −5.05583 + 5.05583i −0.176450 + 0.176450i −0.789806 0.613357i \(-0.789819\pi\)
0.613357 + 0.789806i \(0.289819\pi\)
\(822\) −6.79080 + 34.1641i −0.236856 + 1.19161i
\(823\) 18.8908i 0.658493i 0.944244 + 0.329246i \(0.106795\pi\)
−0.944244 + 0.329246i \(0.893205\pi\)
\(824\) −4.75235 + 4.75235i −0.165556 + 0.165556i
\(825\) 8.00598 + 11.9782i 0.278733 + 0.417029i
\(826\) 1.49217 1.49217i 0.0519193 0.0519193i
\(827\) 11.3749 + 11.3749i 0.395543 + 0.395543i 0.876658 0.481115i \(-0.159768\pi\)
−0.481115 + 0.876658i \(0.659768\pi\)
\(828\) −9.35983 + 22.6141i −0.325276 + 0.785896i
\(829\) 13.7831i 0.478708i −0.970932 0.239354i \(-0.923064\pi\)
0.970932 0.239354i \(-0.0769357\pi\)
\(830\) 28.9844 + 28.9844i 1.00606 + 1.00606i
\(831\) −2.51297 0.499503i −0.0871740 0.0173276i
\(832\) −1.58883 3.23661i −0.0550826 0.112209i
\(833\) 3.68191i 0.127571i
\(834\) −5.33111 7.97621i −0.184601 0.276193i
\(835\) −44.5736 −1.54253
\(836\) 13.4552 0.465360
\(837\) −0.902857 + 0.179975i −0.0312073 + 0.00622085i
\(838\) −6.79475 6.79475i −0.234721 0.234721i
\(839\) −2.49384 2.49384i −0.0860970 0.0860970i 0.662747 0.748844i \(-0.269391\pi\)
−0.748844 + 0.662747i \(0.769391\pi\)
\(840\) −2.98318 4.46333i −0.102930 0.153999i
\(841\) −61.3460 −2.11538
\(842\) 14.3759 0.495425
\(843\) 23.1546 15.4760i 0.797488 0.533023i
\(844\) 19.4541i 0.669638i
\(845\) −5.11437 39.9676i −0.175940 1.37493i
\(846\) −3.15859 1.30732i −0.108595 0.0449465i
\(847\) 5.47291 + 5.47291i 0.188051 + 0.188051i
\(848\) 5.59755i 0.192220i
\(849\) −33.8573 6.72982i −1.16198 0.230967i
\(850\) 11.9941 + 11.9941i 0.411393 + 0.411393i
\(851\) −2.67806 + 2.67806i −0.0918027 + 0.0918027i
\(852\) −1.53192 + 1.02390i −0.0524827 + 0.0350782i
\(853\) 25.6064 25.6064i 0.876745 0.876745i −0.116451 0.993196i \(-0.537152\pi\)
0.993196 + 0.116451i \(0.0371519\pi\)
\(854\) 8.14557i 0.278736i
\(855\) −64.0252 26.4996i −2.18962 0.906266i
\(856\) −5.40581 + 5.40581i −0.184767 + 0.184767i
\(857\) 42.3721 1.44740 0.723701 0.690113i \(-0.242439\pi\)
0.723701 + 0.690113i \(0.242439\pi\)
\(858\) 2.90014 + 10.8965i 0.0990092 + 0.372002i
\(859\) −6.25574 −0.213443 −0.106722 0.994289i \(-0.534035\pi\)
−0.106722 + 0.994289i \(0.534035\pi\)
\(860\) 3.13686 3.13686i 0.106966 0.106966i
\(861\) 5.32857 + 1.05916i 0.181597 + 0.0360960i
\(862\) 9.06310i 0.308690i
\(863\) 20.0524 20.0524i 0.682591 0.682591i −0.277992 0.960583i \(-0.589669\pi\)
0.960583 + 0.277992i \(0.0896689\pi\)
\(864\) −1.01581 5.09589i −0.0345587 0.173366i
\(865\) −19.1321 + 19.1321i −0.650510 + 0.650510i
\(866\) 23.7336 + 23.7336i 0.806502 + 0.806502i
\(867\) 1.16279 5.84993i 0.0394904 0.198674i
\(868\) 0.177174i 0.00601366i
\(869\) 5.60315 + 5.60315i 0.190074 + 0.190074i
\(870\) 9.94817 50.0486i 0.337274 1.69681i
\(871\) 51.3601 + 17.5384i 1.74027 + 0.594266i
\(872\) 15.6438i 0.529766i
\(873\) −2.91356 7.02852i −0.0986092 0.237879i
\(874\) −60.7950 −2.05642
\(875\) −1.21844 −0.0411908
\(876\) 7.31821 4.89132i 0.247260 0.165263i
\(877\) 2.73719 + 2.73719i 0.0924283 + 0.0924283i 0.751809 0.659381i \(-0.229181\pi\)
−0.659381 + 0.751809i \(0.729181\pi\)
\(878\) 5.00643 + 5.00643i 0.168959 + 0.168959i
\(879\) −21.0581 + 14.0747i −0.710272 + 0.474729i
\(880\) −5.59641 −0.188655
\(881\) 1.97857 0.0666596 0.0333298 0.999444i \(-0.489389\pi\)
0.0333298 + 0.999444i \(0.489389\pi\)
\(882\) −1.14881 2.77132i −0.0386824 0.0933153i
\(883\) 13.2612i 0.446275i −0.974787 0.223137i \(-0.928370\pi\)
0.974787 0.223137i \(-0.0716298\pi\)
\(884\) 5.84991 + 11.9169i 0.196754 + 0.400809i
\(885\) −2.20863 + 11.1115i −0.0742422 + 0.373508i
\(886\) 4.67455 + 4.67455i 0.157045 + 0.157045i
\(887\) 19.8583i 0.666778i 0.942789 + 0.333389i \(0.108192\pi\)
−0.942789 + 0.333389i \(0.891808\pi\)
\(888\) 0.156761 0.788656i 0.00526056 0.0264655i
\(889\) −8.82521 8.82521i −0.295988 0.295988i
\(890\) −9.88789 + 9.88789i −0.331443 + 0.331443i
\(891\) 0.00890350 + 16.2503i 0.000298279 + 0.544404i
\(892\) 11.9464 11.9464i 0.399996 0.399996i
\(893\) 8.49144i 0.284155i
\(894\) 8.94296 + 1.77759i 0.299097 + 0.0594515i
\(895\) −46.9777 + 46.9777i −1.57029 + 1.57029i
\(896\) 1.00000 0.0334077
\(897\) −13.1037 49.2340i −0.437521 1.64387i
\(898\) 21.3348 0.711951
\(899\) 1.19080 1.19080i 0.0397154 0.0397154i
\(900\) 12.7701 + 5.28544i 0.425669 + 0.176181i
\(901\) 20.6097i 0.686607i
\(902\) 4.00467 4.00467i 0.133341 0.133341i
\(903\) 2.06104 1.37755i 0.0685870 0.0458420i
\(904\) 13.6037 13.6037i 0.452451 0.452451i
\(905\) 16.5083 + 16.5083i 0.548755 + 0.548755i
\(906\) 36.6270 + 7.28035i 1.21685 + 0.241874i
\(907\) 45.3220i 1.50489i 0.658654 + 0.752446i \(0.271126\pi\)
−0.658654 + 0.752446i \(0.728874\pi\)
\(908\) −18.6457 18.6457i −0.618778 0.618778i
\(909\) −23.7061 9.81178i −0.786282 0.325436i
\(910\) 10.5758 + 3.61141i 0.350584 + 0.119717i
\(911\) 6.89031i 0.228286i 0.993464 + 0.114143i \(0.0364122\pi\)
−0.993464 + 0.114143i \(0.963588\pi\)
\(912\) 10.7310 7.17236i 0.355340 0.237501i
\(913\) 23.8785 0.790262
\(914\) 26.1460 0.864831
\(915\) −24.2997 36.3564i −0.803325 1.20190i
\(916\) 1.93830 + 1.93830i 0.0640433 + 0.0640433i
\(917\) −5.89570 5.89570i −0.194693 0.194693i
\(918\) 3.74013 + 18.7626i 0.123443 + 0.619259i
\(919\) 25.9569 0.856239 0.428119 0.903722i \(-0.359176\pi\)
0.428119 + 0.903722i \(0.359176\pi\)
\(920\) 25.2863 0.833665
\(921\) −8.30675 12.4282i −0.273717 0.409525i
\(922\) 16.8726i 0.555668i
\(923\) 1.23952 3.62986i 0.0407993 0.119478i
\(924\) −3.06736 0.609699i −0.100909 0.0200576i
\(925\) 1.51229 + 1.51229i 0.0497237 + 0.0497237i
\(926\) 2.85389i 0.0937846i
\(927\) 7.71075 18.6298i 0.253254 0.611884i
\(928\) 6.72109 + 6.72109i 0.220630 + 0.220630i
\(929\) 0.188091 0.188091i 0.00617106 0.00617106i −0.704015 0.710186i \(-0.748611\pi\)
0.710186 + 0.704015i \(0.248611\pi\)
\(930\) 0.528541 + 0.790783i 0.0173316 + 0.0259308i
\(931\) 5.26937 5.26937i 0.172697 0.172697i
\(932\) 3.76840i 0.123438i
\(933\) −7.41690 + 37.3140i −0.242818 + 1.22160i
\(934\) 8.05022 8.05022i 0.263411 0.263411i
\(935\) 20.6055 0.673871
\(936\) 8.12140 + 7.14443i 0.265456 + 0.233523i
\(937\) −31.1002 −1.01600 −0.508000 0.861357i \(-0.669615\pi\)
−0.508000 + 0.861357i \(0.669615\pi\)
\(938\) −10.6436 + 10.6436i −0.347527 + 0.347527i
\(939\) 1.44177 7.25347i 0.0470504 0.236708i
\(940\) 3.53183i 0.115195i
\(941\) −8.58050 + 8.58050i −0.279716 + 0.279716i −0.832996 0.553279i \(-0.813376\pi\)
0.553279 + 0.832996i \(0.313376\pi\)
\(942\) 9.89715 + 14.8077i 0.322466 + 0.482462i
\(943\) −18.0944 + 18.0944i −0.589233 + 0.589233i
\(944\) −1.49217 1.49217i −0.0485661 0.0485661i
\(945\) 13.3949 + 8.94221i 0.435736 + 0.290890i
\(946\) 2.58426i 0.0840216i
\(947\) −14.0525 14.0525i −0.456644 0.456644i 0.440908 0.897552i \(-0.354656\pi\)
−0.897552 + 0.440908i \(0.854656\pi\)
\(948\) 7.45549 + 1.48193i 0.242143 + 0.0481307i
\(949\) −5.92138 + 17.3404i −0.192216 + 0.562893i
\(950\) 34.3306i 1.11383i
\(951\) −23.9753 35.8709i −0.777453 1.16319i
\(952\) −3.68191 −0.119331
\(953\) 55.9530 1.81250 0.906248 0.422747i \(-0.138934\pi\)
0.906248 + 0.422747i \(0.138934\pi\)
\(954\) −6.43051 15.5126i −0.208196 0.502239i
\(955\) −3.94761 3.94761i −0.127742 0.127742i
\(956\) 2.94952 + 2.94952i 0.0953944 + 0.0953944i
\(957\) −16.5181 24.7138i −0.533956 0.798884i
\(958\) 31.0801 1.00415
\(959\) 20.1105 0.649404
\(960\) −4.46333 + 2.98318i −0.144053 + 0.0962818i
\(961\) 30.9686i 0.998987i
\(962\) 0.737594 + 1.50256i 0.0237810 + 0.0484444i
\(963\) 8.77100 21.1915i 0.282642 0.682886i
\(964\) −14.8333 14.8333i −0.477750 0.477750i
\(965\) 63.1440i 2.03268i
\(966\) 13.8593 + 2.75481i 0.445915 + 0.0886345i
\(967\) 2.62952 + 2.62952i 0.0845598 + 0.0845598i 0.748122 0.663562i \(-0.230956\pi\)
−0.663562 + 0.748122i \(0.730956\pi\)
\(968\) 5.47291 5.47291i 0.175906 0.175906i
\(969\) −39.5107 + 26.4080i −1.26927 + 0.848347i
\(970\) −5.55844 + 5.55844i −0.178471 + 0.178471i
\(971\) 17.7506i 0.569645i 0.958580 + 0.284823i \(0.0919347\pi\)
−0.958580 + 0.284823i \(0.908065\pi\)
\(972\) 8.66936 + 12.9554i 0.278070 + 0.415544i
\(973\) −3.91664 + 3.91664i −0.125562 + 0.125562i
\(974\) 30.7803 0.986263
\(975\) −27.8022 + 7.39961i −0.890382 + 0.236977i
\(976\) 8.14557 0.260733
\(977\) −8.56492 + 8.56492i −0.274016 + 0.274016i −0.830715 0.556699i \(-0.812068\pi\)
0.556699 + 0.830715i \(0.312068\pi\)
\(978\) −39.4335 7.83820i −1.26094 0.250638i
\(979\) 8.14602i 0.260348i
\(980\) −2.19168 + 2.19168i −0.0700105 + 0.0700105i
\(981\) 17.9717 + 43.3540i 0.573794 + 1.38419i
\(982\) −17.4394 + 17.4394i −0.556513 + 0.556513i
\(983\) −4.10551 4.10551i −0.130945 0.130945i 0.638596 0.769542i \(-0.279515\pi\)
−0.769542 + 0.638596i \(0.779515\pi\)
\(984\) 1.05916 5.32857i 0.0337647 0.169868i
\(985\) 30.3906i 0.968326i
\(986\) −24.7464 24.7464i −0.788087 0.788087i
\(987\) −0.384773 + 1.93577i −0.0122475 + 0.0616163i
\(988\) −8.68278 + 25.4270i −0.276236 + 0.808941i
\(989\) 11.6765i 0.371291i
\(990\) 15.5095 6.42921i 0.492923 0.204334i
\(991\) 60.0976 1.90906 0.954532 0.298108i \(-0.0963555\pi\)
0.954532 + 0.298108i \(0.0963555\pi\)
\(992\) −0.177174 −0.00562527
\(993\) 33.3908 22.3177i 1.05963 0.708229i
\(994\) 0.752235 + 0.752235i 0.0238594 + 0.0238594i
\(995\) 22.4851 + 22.4851i 0.712824 + 0.712824i
\(996\) 19.0439 12.7285i 0.603429 0.403318i
\(997\) 55.3278 1.75225 0.876124 0.482086i \(-0.160121\pi\)
0.876124 + 0.482086i \(0.160121\pi\)
\(998\) −43.3263 −1.37147
\(999\) 0.471579 + 2.36571i 0.0149201 + 0.0748477i
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 546.2.p.d.281.3 yes 20
3.2 odd 2 546.2.p.c.281.8 yes 20
13.5 odd 4 546.2.p.c.239.8 20
39.5 even 4 inner 546.2.p.d.239.3 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.p.c.239.8 20 13.5 odd 4
546.2.p.c.281.8 yes 20 3.2 odd 2
546.2.p.d.239.3 yes 20 39.5 even 4 inner
546.2.p.d.281.3 yes 20 1.1 even 1 trivial