Properties

Label 361.2.c.d.292.1
Level $361$
Weight $2$
Character 361.292
Analytic conductor $2.883$
Analytic rank $0$
Dimension $4$
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] = [361,2,Mod(68,361)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(361, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("361.68");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 361.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.88259951297\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 292.1
Root \(0.809017 + 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 361.292
Dual form 361.2.c.d.68.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 - 1.40126i) q^{2} +(-0.190983 - 0.330792i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(-1.61803 - 2.80252i) q^{5} +(-0.309017 + 0.535233i) q^{6} +3.00000 q^{7} -2.23607 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\) \(q+(-0.809017 - 1.40126i) q^{2} +(-0.190983 - 0.330792i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(-1.61803 - 2.80252i) q^{5} +(-0.309017 + 0.535233i) q^{6} +3.00000 q^{7} -2.23607 q^{8} +(1.42705 - 2.47172i) q^{9} +(-2.61803 + 4.53457i) q^{10} -1.61803 q^{11} +0.236068 q^{12} +(0.500000 - 0.866025i) q^{13} +(-2.42705 - 4.20378i) q^{14} +(-0.618034 + 1.07047i) q^{15} +(2.42705 + 4.20378i) q^{16} +(-0.381966 - 0.661585i) q^{17} -4.61803 q^{18} +2.00000 q^{20} +(-0.572949 - 0.992377i) q^{21} +(1.30902 + 2.26728i) q^{22} +(-2.69098 + 4.66092i) q^{23} +(0.427051 + 0.739674i) q^{24} +(-2.73607 + 4.73901i) q^{25} -1.61803 q^{26} -2.23607 q^{27} +(-0.927051 + 1.60570i) q^{28} +(1.80902 - 3.13331i) q^{29} +2.00000 q^{30} -8.85410 q^{31} +(1.69098 - 2.92887i) q^{32} +(0.309017 + 0.535233i) q^{33} +(-0.618034 + 1.07047i) q^{34} +(-4.85410 - 8.40755i) q^{35} +(0.881966 + 1.52761i) q^{36} +8.85410 q^{37} -0.381966 q^{39} +(3.61803 + 6.26662i) q^{40} +(1.50000 + 2.59808i) q^{41} +(-0.927051 + 1.60570i) q^{42} +(0.0729490 + 0.126351i) q^{43} +(0.500000 - 0.866025i) q^{44} -9.23607 q^{45} +8.70820 q^{46} +(-1.50000 + 2.59808i) q^{47} +(0.927051 - 1.60570i) q^{48} +2.00000 q^{49} +8.85410 q^{50} +(-0.145898 + 0.252703i) q^{51} +(0.309017 + 0.535233i) q^{52} +(3.16312 - 5.47868i) q^{53} +(1.80902 + 3.13331i) q^{54} +(2.61803 + 4.53457i) q^{55} -6.70820 q^{56} -5.85410 q^{58} +(-0.163119 - 0.282530i) q^{59} +(-0.381966 - 0.661585i) q^{60} +(5.11803 - 8.86469i) q^{61} +(7.16312 + 12.4069i) q^{62} +(4.28115 - 7.41517i) q^{63} +4.23607 q^{64} -3.23607 q^{65} +(0.500000 - 0.866025i) q^{66} +(3.50000 - 6.06218i) q^{67} +0.472136 q^{68} +2.05573 q^{69} +(-7.85410 + 13.6037i) q^{70} +(3.73607 + 6.47106i) q^{71} +(-3.19098 + 5.52694i) q^{72} +(1.35410 + 2.34537i) q^{73} +(-7.16312 - 12.4069i) q^{74} +2.09017 q^{75} -4.85410 q^{77} +(0.309017 + 0.535233i) q^{78} +(-6.70820 - 11.6190i) q^{79} +(7.85410 - 13.6037i) q^{80} +(-3.85410 - 6.67550i) q^{81} +(2.42705 - 4.20378i) q^{82} +8.47214 q^{83} +0.708204 q^{84} +(-1.23607 + 2.14093i) q^{85} +(0.118034 - 0.204441i) q^{86} -1.38197 q^{87} +3.61803 q^{88} +(3.88197 - 6.72376i) q^{89} +(7.47214 + 12.9421i) q^{90} +(1.50000 - 2.59808i) q^{91} +(-1.66312 - 2.88061i) q^{92} +(1.69098 + 2.92887i) q^{93} +4.85410 q^{94} -1.29180 q^{96} +(-6.92705 - 11.9980i) q^{97} +(-1.61803 - 2.80252i) q^{98} +(-2.30902 + 3.99933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{6} + 12 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{6} + 12 q^{7} - q^{9} - 6 q^{10} - 2 q^{11} - 8 q^{12} + 2 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} - 6 q^{17} - 14 q^{18} + 8 q^{20} - 9 q^{21} + 3 q^{22} - 13 q^{23} - 5 q^{24} - 2 q^{25} - 2 q^{26} + 3 q^{28} + 5 q^{29} + 8 q^{30} - 22 q^{31} + 9 q^{32} - q^{33} + 2 q^{34} - 6 q^{35} + 8 q^{36} + 22 q^{37} - 6 q^{39} + 10 q^{40} + 6 q^{41} + 3 q^{42} + 7 q^{43} + 2 q^{44} - 28 q^{45} + 8 q^{46} - 6 q^{47} - 3 q^{48} + 8 q^{49} + 22 q^{50} - 14 q^{51} - q^{52} - 3 q^{53} + 5 q^{54} + 6 q^{55} - 10 q^{58} + 15 q^{59} - 6 q^{60} + 16 q^{61} + 13 q^{62} - 3 q^{63} + 8 q^{64} - 4 q^{65} + 2 q^{66} + 14 q^{67} - 16 q^{68} + 44 q^{69} - 18 q^{70} + 6 q^{71} - 15 q^{72} - 8 q^{73} - 13 q^{74} - 14 q^{75} - 6 q^{77} - q^{78} + 18 q^{80} - 2 q^{81} + 3 q^{82} + 16 q^{83} - 24 q^{84} + 4 q^{85} - 4 q^{86} - 10 q^{87} + 10 q^{88} + 20 q^{89} + 12 q^{90} + 6 q^{91} + 9 q^{92} + 9 q^{93} + 6 q^{94} - 32 q^{96} - 21 q^{97} - 2 q^{98} - 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 1.40126i −0.572061 0.990839i −0.996354 0.0853143i \(-0.972811\pi\)
0.424293 0.905525i \(-0.360523\pi\)
\(3\) −0.190983 0.330792i −0.110264 0.190983i 0.805613 0.592443i \(-0.201836\pi\)
−0.915877 + 0.401460i \(0.868503\pi\)
\(4\) −0.309017 + 0.535233i −0.154508 + 0.267617i
\(5\) −1.61803 2.80252i −0.723607 1.25332i −0.959545 0.281556i \(-0.909150\pi\)
0.235938 0.971768i \(-0.424184\pi\)
\(6\) −0.309017 + 0.535233i −0.126156 + 0.218508i
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) −2.23607 −0.790569
\(9\) 1.42705 2.47172i 0.475684 0.823908i
\(10\) −2.61803 + 4.53457i −0.827895 + 1.43396i
\(11\) −1.61803 −0.487856 −0.243928 0.969793i \(-0.578436\pi\)
−0.243928 + 0.969793i \(0.578436\pi\)
\(12\) 0.236068 0.0681470
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) −2.42705 4.20378i −0.648657 1.12351i
\(15\) −0.618034 + 1.07047i −0.159576 + 0.276393i
\(16\) 2.42705 + 4.20378i 0.606763 + 1.05094i
\(17\) −0.381966 0.661585i −0.0926404 0.160458i 0.815981 0.578079i \(-0.196197\pi\)
−0.908621 + 0.417621i \(0.862864\pi\)
\(18\) −4.61803 −1.08848
\(19\) 0 0
\(20\) 2.00000 0.447214
\(21\) −0.572949 0.992377i −0.125028 0.216554i
\(22\) 1.30902 + 2.26728i 0.279083 + 0.483387i
\(23\) −2.69098 + 4.66092i −0.561109 + 0.971869i 0.436291 + 0.899805i \(0.356292\pi\)
−0.997400 + 0.0720634i \(0.977042\pi\)
\(24\) 0.427051 + 0.739674i 0.0871714 + 0.150985i
\(25\) −2.73607 + 4.73901i −0.547214 + 0.947802i
\(26\) −1.61803 −0.317323
\(27\) −2.23607 −0.430331
\(28\) −0.927051 + 1.60570i −0.175196 + 0.303449i
\(29\) 1.80902 3.13331i 0.335926 0.581841i −0.647736 0.761865i \(-0.724284\pi\)
0.983662 + 0.180024i \(0.0576175\pi\)
\(30\) 2.00000 0.365148
\(31\) −8.85410 −1.59024 −0.795122 0.606450i \(-0.792593\pi\)
−0.795122 + 0.606450i \(0.792593\pi\)
\(32\) 1.69098 2.92887i 0.298926 0.517756i
\(33\) 0.309017 + 0.535233i 0.0537930 + 0.0931721i
\(34\) −0.618034 + 1.07047i −0.105992 + 0.183583i
\(35\) −4.85410 8.40755i −0.820493 1.42114i
\(36\) 0.881966 + 1.52761i 0.146994 + 0.254602i
\(37\) 8.85410 1.45561 0.727803 0.685787i \(-0.240542\pi\)
0.727803 + 0.685787i \(0.240542\pi\)
\(38\) 0 0
\(39\) −0.381966 −0.0611635
\(40\) 3.61803 + 6.26662i 0.572061 + 0.990839i
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) −0.927051 + 1.60570i −0.143047 + 0.247765i
\(43\) 0.0729490 + 0.126351i 0.0111246 + 0.0192684i 0.871534 0.490335i \(-0.163126\pi\)
−0.860410 + 0.509603i \(0.829792\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) −9.23607 −1.37683
\(46\) 8.70820 1.28395
\(47\) −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) 0.927051 1.60570i 0.133808 0.231763i
\(49\) 2.00000 0.285714
\(50\) 8.85410 1.25216
\(51\) −0.145898 + 0.252703i −0.0204298 + 0.0353855i
\(52\) 0.309017 + 0.535233i 0.0428529 + 0.0742235i
\(53\) 3.16312 5.47868i 0.434488 0.752555i −0.562766 0.826616i \(-0.690263\pi\)
0.997254 + 0.0740614i \(0.0235961\pi\)
\(54\) 1.80902 + 3.13331i 0.246176 + 0.426389i
\(55\) 2.61803 + 4.53457i 0.353016 + 0.611441i
\(56\) −6.70820 −0.896421
\(57\) 0 0
\(58\) −5.85410 −0.768681
\(59\) −0.163119 0.282530i −0.0212363 0.0367823i 0.855212 0.518278i \(-0.173427\pi\)
−0.876448 + 0.481496i \(0.840094\pi\)
\(60\) −0.381966 0.661585i −0.0493116 0.0854102i
\(61\) 5.11803 8.86469i 0.655297 1.13501i −0.326522 0.945190i \(-0.605877\pi\)
0.981819 0.189818i \(-0.0607899\pi\)
\(62\) 7.16312 + 12.4069i 0.909717 + 1.57568i
\(63\) 4.28115 7.41517i 0.539375 0.934224i
\(64\) 4.23607 0.529508
\(65\) −3.23607 −0.401385
\(66\) 0.500000 0.866025i 0.0615457 0.106600i
\(67\) 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) 0.472136 0.0572549
\(69\) 2.05573 0.247481
\(70\) −7.85410 + 13.6037i −0.938745 + 1.62595i
\(71\) 3.73607 + 6.47106i 0.443390 + 0.767973i 0.997938 0.0641777i \(-0.0204425\pi\)
−0.554549 + 0.832151i \(0.687109\pi\)
\(72\) −3.19098 + 5.52694i −0.376061 + 0.651357i
\(73\) 1.35410 + 2.34537i 0.158486 + 0.274505i 0.934323 0.356428i \(-0.116006\pi\)
−0.775837 + 0.630933i \(0.782672\pi\)
\(74\) −7.16312 12.4069i −0.832696 1.44227i
\(75\) 2.09017 0.241352
\(76\) 0 0
\(77\) −4.85410 −0.553176
\(78\) 0.309017 + 0.535233i 0.0349893 + 0.0606032i
\(79\) −6.70820 11.6190i −0.754732 1.30723i −0.945507 0.325600i \(-0.894434\pi\)
0.190776 0.981634i \(-0.438900\pi\)
\(80\) 7.85410 13.6037i 0.878115 1.52094i
\(81\) −3.85410 6.67550i −0.428234 0.741722i
\(82\) 2.42705 4.20378i 0.268023 0.464229i
\(83\) 8.47214 0.929938 0.464969 0.885327i \(-0.346066\pi\)
0.464969 + 0.885327i \(0.346066\pi\)
\(84\) 0.708204 0.0772714
\(85\) −1.23607 + 2.14093i −0.134070 + 0.232217i
\(86\) 0.118034 0.204441i 0.0127279 0.0220454i
\(87\) −1.38197 −0.148162
\(88\) 3.61803 0.385684
\(89\) 3.88197 6.72376i 0.411488 0.712717i −0.583565 0.812066i \(-0.698343\pi\)
0.995053 + 0.0993490i \(0.0316760\pi\)
\(90\) 7.47214 + 12.9421i 0.787632 + 1.36422i
\(91\) 1.50000 2.59808i 0.157243 0.272352i
\(92\) −1.66312 2.88061i −0.173392 0.300324i
\(93\) 1.69098 + 2.92887i 0.175347 + 0.303710i
\(94\) 4.85410 0.500662
\(95\) 0 0
\(96\) −1.29180 −0.131843
\(97\) −6.92705 11.9980i −0.703335 1.21821i −0.967289 0.253677i \(-0.918360\pi\)
0.263953 0.964535i \(-0.414973\pi\)
\(98\) −1.61803 2.80252i −0.163446 0.283097i
\(99\) −2.30902 + 3.99933i −0.232065 + 0.401948i
\(100\) −1.69098 2.92887i −0.169098 0.292887i
\(101\) 4.59017 7.95041i 0.456739 0.791095i −0.542047 0.840348i \(-0.682351\pi\)
0.998786 + 0.0492528i \(0.0156840\pi\)
\(102\) 0.472136 0.0467484
\(103\) 14.3262 1.41161 0.705803 0.708408i \(-0.250586\pi\)
0.705803 + 0.708408i \(0.250586\pi\)
\(104\) −1.11803 + 1.93649i −0.109632 + 0.189889i
\(105\) −1.85410 + 3.21140i −0.180942 + 0.313400i
\(106\) −10.2361 −0.994215
\(107\) 16.4164 1.58703 0.793517 0.608548i \(-0.208248\pi\)
0.793517 + 0.608548i \(0.208248\pi\)
\(108\) 0.690983 1.19682i 0.0664899 0.115164i
\(109\) 1.64590 + 2.85078i 0.157648 + 0.273055i 0.934020 0.357220i \(-0.116275\pi\)
−0.776372 + 0.630275i \(0.782942\pi\)
\(110\) 4.23607 7.33708i 0.403893 0.699564i
\(111\) −1.69098 2.92887i −0.160501 0.277996i
\(112\) 7.28115 + 12.6113i 0.688004 + 1.19166i
\(113\) 6.76393 0.636297 0.318149 0.948041i \(-0.396939\pi\)
0.318149 + 0.948041i \(0.396939\pi\)
\(114\) 0 0
\(115\) 17.4164 1.62409
\(116\) 1.11803 + 1.93649i 0.103807 + 0.179799i
\(117\) −1.42705 2.47172i −0.131931 0.228511i
\(118\) −0.263932 + 0.457144i −0.0242969 + 0.0420835i
\(119\) −1.14590 1.98475i −0.105044 0.181942i
\(120\) 1.38197 2.39364i 0.126156 0.218508i
\(121\) −8.38197 −0.761997
\(122\) −16.5623 −1.49948
\(123\) 0.572949 0.992377i 0.0516611 0.0894796i
\(124\) 2.73607 4.73901i 0.245706 0.425576i
\(125\) 1.52786 0.136656
\(126\) −13.8541 −1.23422
\(127\) −2.88197 + 4.99171i −0.255733 + 0.442943i −0.965094 0.261902i \(-0.915650\pi\)
0.709361 + 0.704845i \(0.248984\pi\)
\(128\) −6.80902 11.7936i −0.601838 1.04241i
\(129\) 0.0278640 0.0482619i 0.00245329 0.00424923i
\(130\) 2.61803 + 4.53457i 0.229617 + 0.397708i
\(131\) −7.54508 13.0685i −0.659217 1.14180i −0.980819 0.194922i \(-0.937554\pi\)
0.321602 0.946875i \(-0.395779\pi\)
\(132\) −0.381966 −0.0332459
\(133\) 0 0
\(134\) −11.3262 −0.978438
\(135\) 3.61803 + 6.26662i 0.311391 + 0.539345i
\(136\) 0.854102 + 1.47935i 0.0732386 + 0.126853i
\(137\) −3.73607 + 6.47106i −0.319194 + 0.552860i −0.980320 0.197415i \(-0.936745\pi\)
0.661126 + 0.750275i \(0.270079\pi\)
\(138\) −1.66312 2.88061i −0.141574 0.245214i
\(139\) −7.39919 + 12.8158i −0.627591 + 1.08702i 0.360443 + 0.932781i \(0.382626\pi\)
−0.988034 + 0.154238i \(0.950708\pi\)
\(140\) 6.00000 0.507093
\(141\) 1.14590 0.0965020
\(142\) 6.04508 10.4704i 0.507292 0.878656i
\(143\) −0.809017 + 1.40126i −0.0676534 + 0.117179i
\(144\) 13.8541 1.15451
\(145\) −11.7082 −0.972313
\(146\) 2.19098 3.79489i 0.181327 0.314068i
\(147\) −0.381966 0.661585i −0.0315040 0.0545666i
\(148\) −2.73607 + 4.73901i −0.224903 + 0.389544i
\(149\) 0.954915 + 1.65396i 0.0782297 + 0.135498i 0.902486 0.430719i \(-0.141740\pi\)
−0.824257 + 0.566217i \(0.808407\pi\)
\(150\) −1.69098 2.92887i −0.138068 0.239141i
\(151\) −21.0902 −1.71629 −0.858147 0.513404i \(-0.828384\pi\)
−0.858147 + 0.513404i \(0.828384\pi\)
\(152\) 0 0
\(153\) −2.18034 −0.176270
\(154\) 3.92705 + 6.80185i 0.316451 + 0.548109i
\(155\) 14.3262 + 24.8138i 1.15071 + 1.99309i
\(156\) 0.118034 0.204441i 0.00945028 0.0163684i
\(157\) 8.92705 + 15.4621i 0.712456 + 1.23401i 0.963932 + 0.266147i \(0.0857506\pi\)
−0.251476 + 0.967863i \(0.580916\pi\)
\(158\) −10.8541 + 18.7999i −0.863506 + 1.49564i
\(159\) −2.41641 −0.191634
\(160\) −10.9443 −0.865221
\(161\) −8.07295 + 13.9828i −0.636238 + 1.10200i
\(162\) −6.23607 + 10.8012i −0.489952 + 0.848621i
\(163\) 1.76393 0.138162 0.0690809 0.997611i \(-0.477993\pi\)
0.0690809 + 0.997611i \(0.477993\pi\)
\(164\) −1.85410 −0.144781
\(165\) 1.00000 1.73205i 0.0778499 0.134840i
\(166\) −6.85410 11.8717i −0.531981 0.921419i
\(167\) −10.1180 + 17.5249i −0.782957 + 1.35612i 0.147255 + 0.989099i \(0.452956\pi\)
−0.930212 + 0.367023i \(0.880377\pi\)
\(168\) 1.28115 + 2.21902i 0.0988431 + 0.171201i
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) −0.0901699 −0.00687539
\(173\) 0.236068 + 0.408882i 0.0179479 + 0.0310867i 0.874860 0.484376i \(-0.160953\pi\)
−0.856912 + 0.515463i \(0.827620\pi\)
\(174\) 1.11803 + 1.93649i 0.0847579 + 0.146805i
\(175\) −8.20820 + 14.2170i −0.620482 + 1.07471i
\(176\) −3.92705 6.80185i −0.296013 0.512709i
\(177\) −0.0623059 + 0.107917i −0.00468320 + 0.00811154i
\(178\) −12.5623 −0.941585
\(179\) 12.2361 0.914567 0.457283 0.889321i \(-0.348823\pi\)
0.457283 + 0.889321i \(0.348823\pi\)
\(180\) 2.85410 4.94345i 0.212732 0.368463i
\(181\) −6.00000 + 10.3923i −0.445976 + 0.772454i −0.998120 0.0612954i \(-0.980477\pi\)
0.552143 + 0.833749i \(0.313810\pi\)
\(182\) −4.85410 −0.359810
\(183\) −3.90983 −0.289023
\(184\) 6.01722 10.4221i 0.443595 0.768330i
\(185\) −14.3262 24.8138i −1.05329 1.82434i
\(186\) 2.73607 4.73901i 0.200618 0.347481i
\(187\) 0.618034 + 1.07047i 0.0451951 + 0.0782802i
\(188\) −0.927051 1.60570i −0.0676121 0.117108i
\(189\) −6.70820 −0.487950
\(190\) 0 0
\(191\) 14.2361 1.03009 0.515043 0.857164i \(-0.327776\pi\)
0.515043 + 0.857164i \(0.327776\pi\)
\(192\) −0.809017 1.40126i −0.0583858 0.101127i
\(193\) −2.52786 4.37839i −0.181960 0.315163i 0.760588 0.649235i \(-0.224911\pi\)
−0.942548 + 0.334071i \(0.891577\pi\)
\(194\) −11.2082 + 19.4132i −0.804702 + 1.39379i
\(195\) 0.618034 + 1.07047i 0.0442583 + 0.0766577i
\(196\) −0.618034 + 1.07047i −0.0441453 + 0.0764619i
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 7.47214 0.531022
\(199\) 6.70820 11.6190i 0.475532 0.823646i −0.524075 0.851672i \(-0.675589\pi\)
0.999607 + 0.0280265i \(0.00892227\pi\)
\(200\) 6.11803 10.5967i 0.432610 0.749303i
\(201\) −2.67376 −0.188593
\(202\) −14.8541 −1.04513
\(203\) 5.42705 9.39993i 0.380904 0.659746i
\(204\) −0.0901699 0.156179i −0.00631316 0.0109347i
\(205\) 4.85410 8.40755i 0.339025 0.587209i
\(206\) −11.5902 20.0748i −0.807525 1.39868i
\(207\) 7.68034 + 13.3027i 0.533821 + 0.924604i
\(208\) 4.85410 0.336571
\(209\) 0 0
\(210\) 6.00000 0.414039
\(211\) 1.92705 + 3.33775i 0.132664 + 0.229780i 0.924703 0.380690i \(-0.124314\pi\)
−0.792039 + 0.610471i \(0.790980\pi\)
\(212\) 1.95492 + 3.38601i 0.134264 + 0.232552i
\(213\) 1.42705 2.47172i 0.0977799 0.169360i
\(214\) −13.2812 23.0036i −0.907881 1.57250i
\(215\) 0.236068 0.408882i 0.0160997 0.0278855i
\(216\) 5.00000 0.340207
\(217\) −26.5623 −1.80317
\(218\) 2.66312 4.61266i 0.180369 0.312409i
\(219\) 0.517221 0.895853i 0.0349506 0.0605361i
\(220\) −3.23607 −0.218176
\(221\) −0.763932 −0.0513876
\(222\) −2.73607 + 4.73901i −0.183633 + 0.318061i
\(223\) 5.82624 + 10.0913i 0.390154 + 0.675766i 0.992470 0.122492i \(-0.0390885\pi\)
−0.602316 + 0.798258i \(0.705755\pi\)
\(224\) 5.07295 8.78661i 0.338951 0.587080i
\(225\) 7.80902 + 13.5256i 0.520601 + 0.901708i
\(226\) −5.47214 9.47802i −0.364001 0.630468i
\(227\) 16.4164 1.08960 0.544798 0.838568i \(-0.316606\pi\)
0.544798 + 0.838568i \(0.316606\pi\)
\(228\) 0 0
\(229\) −13.6180 −0.899905 −0.449953 0.893052i \(-0.648559\pi\)
−0.449953 + 0.893052i \(0.648559\pi\)
\(230\) −14.0902 24.4049i −0.929078 1.60921i
\(231\) 0.927051 + 1.60570i 0.0609955 + 0.105647i
\(232\) −4.04508 + 7.00629i −0.265573 + 0.459986i
\(233\) −2.26393 3.92125i −0.148315 0.256889i 0.782290 0.622915i \(-0.214052\pi\)
−0.930605 + 0.366025i \(0.880718\pi\)
\(234\) −2.30902 + 3.99933i −0.150945 + 0.261445i
\(235\) 9.70820 0.633293
\(236\) 0.201626 0.0131247
\(237\) −2.56231 + 4.43804i −0.166440 + 0.288282i
\(238\) −1.85410 + 3.21140i −0.120184 + 0.208164i
\(239\) −0.326238 −0.0211026 −0.0105513 0.999944i \(-0.503359\pi\)
−0.0105513 + 0.999944i \(0.503359\pi\)
\(240\) −6.00000 −0.387298
\(241\) −1.59017 + 2.75426i −0.102432 + 0.177417i −0.912686 0.408661i \(-0.865996\pi\)
0.810254 + 0.586079i \(0.199329\pi\)
\(242\) 6.78115 + 11.7453i 0.435909 + 0.755017i
\(243\) −4.82624 + 8.35929i −0.309603 + 0.536249i
\(244\) 3.16312 + 5.47868i 0.202498 + 0.350737i
\(245\) −3.23607 5.60503i −0.206745 0.358092i
\(246\) −1.85410 −0.118213
\(247\) 0 0
\(248\) 19.7984 1.25720
\(249\) −1.61803 2.80252i −0.102539 0.177602i
\(250\) −1.23607 2.14093i −0.0781758 0.135404i
\(251\) 12.6803 21.9630i 0.800376 1.38629i −0.118993 0.992895i \(-0.537967\pi\)
0.919369 0.393397i \(-0.128700\pi\)
\(252\) 2.64590 + 4.58283i 0.166676 + 0.288691i
\(253\) 4.35410 7.54153i 0.273740 0.474132i
\(254\) 9.32624 0.585180
\(255\) 0.944272 0.0591326
\(256\) −6.78115 + 11.7453i −0.423822 + 0.734081i
\(257\) −10.1803 + 17.6329i −0.635032 + 1.09991i 0.351476 + 0.936197i \(0.385680\pi\)
−0.986508 + 0.163711i \(0.947654\pi\)
\(258\) −0.0901699 −0.00561374
\(259\) 26.5623 1.65050
\(260\) 1.00000 1.73205i 0.0620174 0.107417i
\(261\) −5.16312 8.94278i −0.319589 0.553544i
\(262\) −12.2082 + 21.1452i −0.754225 + 1.30636i
\(263\) 7.47214 + 12.9421i 0.460752 + 0.798045i 0.998999 0.0447419i \(-0.0142466\pi\)
−0.538247 + 0.842787i \(0.680913\pi\)
\(264\) −0.690983 1.19682i −0.0425271 0.0736590i
\(265\) −20.4721 −1.25759
\(266\) 0 0
\(267\) −2.96556 −0.181489
\(268\) 2.16312 + 3.74663i 0.132134 + 0.228862i
\(269\) −15.1631 26.2633i −0.924512 1.60130i −0.792345 0.610074i \(-0.791140\pi\)
−0.132167 0.991227i \(-0.542194\pi\)
\(270\) 5.85410 10.1396i 0.356269 0.617077i
\(271\) −0.572949 0.992377i −0.0348042 0.0602826i 0.848099 0.529838i \(-0.177747\pi\)
−0.882903 + 0.469556i \(0.844414\pi\)
\(272\) 1.85410 3.21140i 0.112421 0.194720i
\(273\) −1.14590 −0.0693529
\(274\) 12.0902 0.730394
\(275\) 4.42705 7.66788i 0.266961 0.462390i
\(276\) −0.635255 + 1.10029i −0.0382379 + 0.0662299i
\(277\) 11.4164 0.685945 0.342973 0.939345i \(-0.388566\pi\)
0.342973 + 0.939345i \(0.388566\pi\)
\(278\) 23.9443 1.43608
\(279\) −12.6353 + 21.8849i −0.756453 + 1.31021i
\(280\) 10.8541 + 18.7999i 0.648657 + 1.12351i
\(281\) 14.7533 25.5534i 0.880107 1.52439i 0.0288869 0.999583i \(-0.490804\pi\)
0.851221 0.524808i \(-0.175863\pi\)
\(282\) −0.927051 1.60570i −0.0552051 0.0956180i
\(283\) −13.0172 22.5465i −0.773793 1.34025i −0.935470 0.353406i \(-0.885023\pi\)
0.161677 0.986844i \(-0.448310\pi\)
\(284\) −4.61803 −0.274030
\(285\) 0 0
\(286\) 2.61803 0.154808
\(287\) 4.50000 + 7.79423i 0.265627 + 0.460079i
\(288\) −4.82624 8.35929i −0.284389 0.492576i
\(289\) 8.20820 14.2170i 0.482836 0.836296i
\(290\) 9.47214 + 16.4062i 0.556223 + 0.963406i
\(291\) −2.64590 + 4.58283i −0.155105 + 0.268650i
\(292\) −1.67376 −0.0979495
\(293\) −10.1459 −0.592730 −0.296365 0.955075i \(-0.595774\pi\)
−0.296365 + 0.955075i \(0.595774\pi\)
\(294\) −0.618034 + 1.07047i −0.0360445 + 0.0624309i
\(295\) −0.527864 + 0.914287i −0.0307334 + 0.0532319i
\(296\) −19.7984 −1.15076
\(297\) 3.61803 0.209940
\(298\) 1.54508 2.67617i 0.0895044 0.155026i
\(299\) 2.69098 + 4.66092i 0.155624 + 0.269548i
\(300\) −0.645898 + 1.11873i −0.0372909 + 0.0645898i
\(301\) 0.218847 + 0.379054i 0.0126141 + 0.0218483i
\(302\) 17.0623 + 29.5528i 0.981825 + 1.70057i
\(303\) −3.50658 −0.201448
\(304\) 0 0
\(305\) −33.1246 −1.89671
\(306\) 1.76393 + 3.05522i 0.100837 + 0.174655i
\(307\) 8.66312 + 15.0050i 0.494430 + 0.856378i 0.999979 0.00641942i \(-0.00204338\pi\)
−0.505549 + 0.862798i \(0.668710\pi\)
\(308\) 1.50000 2.59808i 0.0854704 0.148039i
\(309\) −2.73607 4.73901i −0.155649 0.269593i
\(310\) 23.1803 40.1495i 1.31655 2.28034i
\(311\) 12.6525 0.717456 0.358728 0.933442i \(-0.383211\pi\)
0.358728 + 0.933442i \(0.383211\pi\)
\(312\) 0.854102 0.0483540
\(313\) 5.66312 9.80881i 0.320098 0.554427i −0.660410 0.750906i \(-0.729617\pi\)
0.980508 + 0.196479i \(0.0629507\pi\)
\(314\) 14.4443 25.0182i 0.815137 1.41186i
\(315\) −27.7082 −1.56118
\(316\) 8.29180 0.466450
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 1.95492 + 3.38601i 0.109626 + 0.189878i
\(319\) −2.92705 + 5.06980i −0.163883 + 0.283854i
\(320\) −6.85410 11.8717i −0.383156 0.663646i
\(321\) −3.13525 5.43042i −0.174993 0.303097i
\(322\) 26.1246 1.45587
\(323\) 0 0
\(324\) 4.76393 0.264663
\(325\) 2.73607 + 4.73901i 0.151770 + 0.262873i
\(326\) −1.42705 2.47172i −0.0790370 0.136896i
\(327\) 0.628677 1.08890i 0.0347659 0.0602163i
\(328\) −3.35410 5.80948i −0.185199 0.320775i
\(329\) −4.50000 + 7.79423i −0.248093 + 0.429710i
\(330\) −3.23607 −0.178140
\(331\) 10.9443 0.601552 0.300776 0.953695i \(-0.402754\pi\)
0.300776 + 0.953695i \(0.402754\pi\)
\(332\) −2.61803 + 4.53457i −0.143683 + 0.248867i
\(333\) 12.6353 21.8849i 0.692408 1.19929i
\(334\) 32.7426 1.79160
\(335\) −22.6525 −1.23764
\(336\) 2.78115 4.81710i 0.151724 0.262794i
\(337\) 8.56231 + 14.8303i 0.466419 + 0.807861i 0.999264 0.0383518i \(-0.0122107\pi\)
−0.532846 + 0.846212i \(0.678877\pi\)
\(338\) 9.70820 16.8151i 0.528057 0.914621i
\(339\) −1.29180 2.23746i −0.0701607 0.121522i
\(340\) −0.763932 1.32317i −0.0414300 0.0717589i
\(341\) 14.3262 0.775809
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) −0.163119 0.282530i −0.00879478 0.0152330i
\(345\) −3.32624 5.76121i −0.179079 0.310173i
\(346\) 0.381966 0.661585i 0.0205346 0.0355670i
\(347\) 12.7082 + 22.0113i 0.682212 + 1.18163i 0.974304 + 0.225236i \(0.0723153\pi\)
−0.292092 + 0.956390i \(0.594351\pi\)
\(348\) 0.427051 0.739674i 0.0228923 0.0396507i
\(349\) −20.9787 −1.12296 −0.561482 0.827489i \(-0.689769\pi\)
−0.561482 + 0.827489i \(0.689769\pi\)
\(350\) 26.5623 1.41981
\(351\) −1.11803 + 1.93649i −0.0596762 + 0.103362i
\(352\) −2.73607 + 4.73901i −0.145833 + 0.252590i
\(353\) 24.4508 1.30139 0.650694 0.759340i \(-0.274478\pi\)
0.650694 + 0.759340i \(0.274478\pi\)
\(354\) 0.201626 0.0107163
\(355\) 12.0902 20.9408i 0.641680 1.11142i
\(356\) 2.39919 + 4.15551i 0.127157 + 0.220242i
\(357\) −0.437694 + 0.758108i −0.0231652 + 0.0401234i
\(358\) −9.89919 17.1459i −0.523188 0.906189i
\(359\) −3.51722 6.09201i −0.185632 0.321524i 0.758157 0.652072i \(-0.226100\pi\)
−0.943789 + 0.330548i \(0.892767\pi\)
\(360\) 20.6525 1.08848
\(361\) 0 0
\(362\) 19.4164 1.02050
\(363\) 1.60081 + 2.77269i 0.0840209 + 0.145528i
\(364\) 0.927051 + 1.60570i 0.0485907 + 0.0841615i
\(365\) 4.38197 7.58979i 0.229363 0.397268i
\(366\) 3.16312 + 5.47868i 0.165339 + 0.286375i
\(367\) 7.97214 13.8081i 0.416142 0.720779i −0.579405 0.815039i \(-0.696715\pi\)
0.995548 + 0.0942602i \(0.0300485\pi\)
\(368\) −26.1246 −1.36184
\(369\) 8.56231 0.445736
\(370\) −23.1803 + 40.1495i −1.20509 + 2.08727i
\(371\) 9.48936 16.4360i 0.492663 0.853317i
\(372\) −2.09017 −0.108370
\(373\) −5.47214 −0.283336 −0.141668 0.989914i \(-0.545247\pi\)
−0.141668 + 0.989914i \(0.545247\pi\)
\(374\) 1.00000 1.73205i 0.0517088 0.0895622i
\(375\) −0.291796 0.505406i −0.0150683 0.0260990i
\(376\) 3.35410 5.80948i 0.172975 0.299601i
\(377\) −1.80902 3.13331i −0.0931691 0.161374i
\(378\) 5.42705 + 9.39993i 0.279137 + 0.483480i
\(379\) −15.1246 −0.776899 −0.388450 0.921470i \(-0.626989\pi\)
−0.388450 + 0.921470i \(0.626989\pi\)
\(380\) 0 0
\(381\) 2.20163 0.112793
\(382\) −11.5172 19.9484i −0.589272 1.02065i
\(383\) −0.190983 0.330792i −0.00975878 0.0169027i 0.861105 0.508428i \(-0.169773\pi\)
−0.870864 + 0.491525i \(0.836440\pi\)
\(384\) −2.60081 + 4.50474i −0.132722 + 0.229882i
\(385\) 7.85410 + 13.6037i 0.400282 + 0.693309i
\(386\) −4.09017 + 7.08438i −0.208184 + 0.360586i
\(387\) 0.416408 0.0211672
\(388\) 8.56231 0.434685
\(389\) −4.63525 + 8.02850i −0.235017 + 0.407061i −0.959278 0.282465i \(-0.908848\pi\)
0.724261 + 0.689526i \(0.242181\pi\)
\(390\) 1.00000 1.73205i 0.0506370 0.0877058i
\(391\) 4.11146 0.207925
\(392\) −4.47214 −0.225877
\(393\) −2.88197 + 4.99171i −0.145376 + 0.251799i
\(394\) −2.42705 4.20378i −0.122273 0.211783i
\(395\) −21.7082 + 37.5997i −1.09226 + 1.89185i
\(396\) −1.42705 2.47172i −0.0717120 0.124209i
\(397\) 5.73607 + 9.93516i 0.287885 + 0.498631i 0.973305 0.229517i \(-0.0737146\pi\)
−0.685420 + 0.728148i \(0.740381\pi\)
\(398\) −21.7082 −1.08813
\(399\) 0 0
\(400\) −26.5623 −1.32812
\(401\) 17.9443 + 31.0804i 0.896094 + 1.55208i 0.832445 + 0.554108i \(0.186941\pi\)
0.0636496 + 0.997972i \(0.479726\pi\)
\(402\) 2.16312 + 3.74663i 0.107887 + 0.186865i
\(403\) −4.42705 + 7.66788i −0.220527 + 0.381964i
\(404\) 2.83688 + 4.91362i 0.141140 + 0.244462i
\(405\) −12.4721 + 21.6024i −0.619745 + 1.07343i
\(406\) −17.5623 −0.871603
\(407\) −14.3262 −0.710125
\(408\) 0.326238 0.565061i 0.0161512 0.0279747i
\(409\) 4.14590 7.18091i 0.205001 0.355073i −0.745132 0.666917i \(-0.767613\pi\)
0.950133 + 0.311844i \(0.100947\pi\)
\(410\) −15.7082 −0.775773
\(411\) 2.85410 0.140782
\(412\) −4.42705 + 7.66788i −0.218105 + 0.377769i
\(413\) −0.489357 0.847591i −0.0240797 0.0417072i
\(414\) 12.4271 21.5243i 0.610756 1.05786i
\(415\) −13.7082 23.7433i −0.672909 1.16551i
\(416\) −1.69098 2.92887i −0.0829073 0.143600i
\(417\) 5.65248 0.276803
\(418\) 0 0
\(419\) −8.94427 −0.436956 −0.218478 0.975842i \(-0.570109\pi\)
−0.218478 + 0.975842i \(0.570109\pi\)
\(420\) −1.14590 1.98475i −0.0559141 0.0968461i
\(421\) 13.7361 + 23.7916i 0.669455 + 1.15953i 0.978057 + 0.208339i \(0.0668056\pi\)
−0.308602 + 0.951191i \(0.599861\pi\)
\(422\) 3.11803 5.40059i 0.151784 0.262897i
\(423\) 4.28115 + 7.41517i 0.208157 + 0.360538i
\(424\) −7.07295 + 12.2507i −0.343493 + 0.594947i
\(425\) 4.18034 0.202776
\(426\) −4.61803 −0.223744
\(427\) 15.3541 26.5941i 0.743037 1.28698i
\(428\) −5.07295 + 8.78661i −0.245210 + 0.424717i
\(429\) 0.618034 0.0298390
\(430\) −0.763932 −0.0368401
\(431\) −13.8262 + 23.9477i −0.665986 + 1.15352i 0.313030 + 0.949743i \(0.398656\pi\)
−0.979017 + 0.203779i \(0.934678\pi\)
\(432\) −5.42705 9.39993i −0.261109 0.452254i
\(433\) 1.71885 2.97713i 0.0826025 0.143072i −0.821765 0.569827i \(-0.807010\pi\)
0.904367 + 0.426755i \(0.140343\pi\)
\(434\) 21.4894 + 37.2207i 1.03152 + 1.78665i
\(435\) 2.23607 + 3.87298i 0.107211 + 0.185695i
\(436\) −2.03444 −0.0974321
\(437\) 0 0
\(438\) −1.67376 −0.0799754
\(439\) 17.2984 + 29.9617i 0.825606 + 1.42999i 0.901455 + 0.432873i \(0.142500\pi\)
−0.0758487 + 0.997119i \(0.524167\pi\)
\(440\) −5.85410 10.1396i −0.279083 0.483387i
\(441\) 2.85410 4.94345i 0.135910 0.235402i
\(442\) 0.618034 + 1.07047i 0.0293969 + 0.0509169i
\(443\) 3.79180 6.56758i 0.180154 0.312035i −0.761779 0.647837i \(-0.775674\pi\)
0.941933 + 0.335802i \(0.109007\pi\)
\(444\) 2.09017 0.0991951
\(445\) −25.1246 −1.19102
\(446\) 9.42705 16.3281i 0.446384 0.773159i
\(447\) 0.364745 0.631757i 0.0172519 0.0298811i
\(448\) 12.7082 0.600406
\(449\) 2.88854 0.136319 0.0681594 0.997674i \(-0.478287\pi\)
0.0681594 + 0.997674i \(0.478287\pi\)
\(450\) 12.6353 21.8849i 0.595632 1.03166i
\(451\) −2.42705 4.20378i −0.114285 0.197948i
\(452\) −2.09017 + 3.62028i −0.0983133 + 0.170284i
\(453\) 4.02786 + 6.97647i 0.189246 + 0.327783i
\(454\) −13.2812 23.0036i −0.623315 1.07961i
\(455\) −9.70820 −0.455128
\(456\) 0 0
\(457\) 19.7082 0.921911 0.460955 0.887423i \(-0.347507\pi\)
0.460955 + 0.887423i \(0.347507\pi\)
\(458\) 11.0172 + 19.0824i 0.514801 + 0.891661i
\(459\) 0.854102 + 1.47935i 0.0398661 + 0.0690501i
\(460\) −5.38197 + 9.32184i −0.250935 + 0.434633i
\(461\) −10.4721 18.1383i −0.487736 0.844784i 0.512165 0.858887i \(-0.328844\pi\)
−0.999901 + 0.0141038i \(0.995510\pi\)
\(462\) 1.50000 2.59808i 0.0697863 0.120873i
\(463\) 28.2705 1.31384 0.656921 0.753959i \(-0.271858\pi\)
0.656921 + 0.753959i \(0.271858\pi\)
\(464\) 17.5623 0.815310
\(465\) 5.47214 9.47802i 0.253764 0.439533i
\(466\) −3.66312 + 6.34471i −0.169691 + 0.293913i
\(467\) −15.9443 −0.737813 −0.368906 0.929467i \(-0.620268\pi\)
−0.368906 + 0.929467i \(0.620268\pi\)
\(468\) 1.76393 0.0815378
\(469\) 10.5000 18.1865i 0.484845 0.839776i
\(470\) −7.85410 13.6037i −0.362283 0.627492i
\(471\) 3.40983 5.90600i 0.157117 0.272134i
\(472\) 0.364745 + 0.631757i 0.0167888 + 0.0290790i
\(473\) −0.118034 0.204441i −0.00542721 0.00940020i
\(474\) 8.29180 0.380855
\(475\) 0 0
\(476\) 1.41641 0.0649209
\(477\) −9.02786 15.6367i −0.413357 0.715956i
\(478\) 0.263932 + 0.457144i 0.0120720 + 0.0209093i
\(479\) −11.5451 + 19.9967i −0.527508 + 0.913671i 0.471978 + 0.881611i \(0.343540\pi\)
−0.999486 + 0.0320608i \(0.989793\pi\)
\(480\) 2.09017 + 3.62028i 0.0954028 + 0.165242i
\(481\) 4.42705 7.66788i 0.201856 0.349625i
\(482\) 5.14590 0.234389
\(483\) 6.16718 0.280617
\(484\) 2.59017 4.48631i 0.117735 0.203923i
\(485\) −22.4164 + 38.8264i −1.01788 + 1.76301i
\(486\) 15.6180 0.708448
\(487\) 4.18034 0.189429 0.0947146 0.995504i \(-0.469806\pi\)
0.0947146 + 0.995504i \(0.469806\pi\)
\(488\) −11.4443 + 19.8221i −0.518058 + 0.897303i
\(489\) −0.336881 0.583495i −0.0152343 0.0263866i
\(490\) −5.23607 + 9.06914i −0.236541 + 0.409702i
\(491\) 10.6074 + 18.3725i 0.478705 + 0.829141i 0.999702 0.0244174i \(-0.00777307\pi\)
−0.520997 + 0.853559i \(0.674440\pi\)
\(492\) 0.354102 + 0.613323i 0.0159641 + 0.0276507i
\(493\) −2.76393 −0.124481
\(494\) 0 0
\(495\) 14.9443 0.671695
\(496\) −21.4894 37.2207i −0.964901 1.67126i
\(497\) 11.2082 + 19.4132i 0.502757 + 0.870800i
\(498\) −2.61803 + 4.53457i −0.117317 + 0.203199i
\(499\) −12.5623 21.7586i −0.562366 0.974047i −0.997289 0.0735791i \(-0.976558\pi\)
0.434923 0.900467i \(-0.356775\pi\)
\(500\) −0.472136 + 0.817763i −0.0211146 + 0.0365715i
\(501\) 7.72949 0.345328
\(502\) −41.0344 −1.83146
\(503\) −17.9164 + 31.0321i −0.798853 + 1.38365i 0.121510 + 0.992590i \(0.461226\pi\)
−0.920363 + 0.391064i \(0.872107\pi\)
\(504\) −9.57295 + 16.5808i −0.426413 + 0.738569i
\(505\) −29.7082 −1.32200
\(506\) −14.0902 −0.626384
\(507\) 2.29180 3.96951i 0.101782 0.176292i
\(508\) −1.78115 3.08505i −0.0790259 0.136877i
\(509\) −1.01722 + 1.76188i −0.0450875 + 0.0780939i −0.887688 0.460445i \(-0.847690\pi\)
0.842601 + 0.538538i \(0.181023\pi\)
\(510\) −0.763932 1.32317i −0.0338275 0.0585909i
\(511\) 4.06231 + 7.03612i 0.179706 + 0.311260i
\(512\) −5.29180 −0.233867
\(513\) 0 0
\(514\) 32.9443 1.45311
\(515\) −23.1803 40.1495i −1.02145 1.76920i
\(516\) 0.0172209 + 0.0298275i 0.000758109 + 0.00131308i
\(517\) 2.42705 4.20378i 0.106742 0.184882i
\(518\) −21.4894 37.2207i −0.944188 1.63538i
\(519\) 0.0901699 0.156179i 0.00395802 0.00685549i
\(520\) 7.23607 0.317323
\(521\) 6.27051 0.274716 0.137358 0.990521i \(-0.456139\pi\)
0.137358 + 0.990521i \(0.456139\pi\)
\(522\) −8.35410 + 14.4697i −0.365649 + 0.633323i
\(523\) 2.20820 3.82472i 0.0965580 0.167243i −0.813700 0.581285i \(-0.802550\pi\)
0.910258 + 0.414042i \(0.135883\pi\)
\(524\) 9.32624 0.407419
\(525\) 6.27051 0.273667
\(526\) 12.0902 20.9408i 0.527156 0.913062i
\(527\) 3.38197 + 5.85774i 0.147321 + 0.255167i
\(528\) −1.50000 + 2.59808i −0.0652791 + 0.113067i
\(529\) −2.98278 5.16632i −0.129686 0.224623i
\(530\) 16.5623 + 28.6868i 0.719421 + 1.24607i
\(531\) −0.931116 −0.0404070
\(532\) 0 0
\(533\) 3.00000 0.129944
\(534\) 2.39919 + 4.15551i 0.103823 + 0.179827i
\(535\) −26.5623 46.0073i −1.14839 1.98907i
\(536\) −7.82624 + 13.5554i −0.338042 + 0.585506i
\(537\) −2.33688 4.04760i −0.100844 0.174667i
\(538\) −24.5344 + 42.4949i −1.05775 + 1.83209i
\(539\) −3.23607 −0.139387
\(540\) −4.47214 −0.192450
\(541\) 14.9164 25.8360i 0.641306 1.11078i −0.343835 0.939030i \(-0.611726\pi\)
0.985141 0.171745i \(-0.0549406\pi\)
\(542\) −0.927051 + 1.60570i −0.0398202 + 0.0689707i
\(543\) 4.58359 0.196701
\(544\) −2.58359 −0.110771
\(545\) 5.32624 9.22531i 0.228151 0.395169i
\(546\) 0.927051 + 1.60570i 0.0396741 + 0.0687176i
\(547\) 13.4615 23.3160i 0.575572 0.996920i −0.420407 0.907335i \(-0.638113\pi\)
0.995979 0.0895843i \(-0.0285538\pi\)
\(548\) −2.30902 3.99933i −0.0986363 0.170843i
\(549\) −14.6074 25.3007i −0.623428 1.07981i
\(550\) −14.3262 −0.610873
\(551\) 0 0
\(552\) −4.59675 −0.195651
\(553\) −20.1246 34.8569i −0.855786 1.48226i
\(554\) −9.23607 15.9973i −0.392403 0.679662i
\(555\) −5.47214 + 9.47802i −0.232279 + 0.402319i
\(556\) −4.57295 7.92058i −0.193936 0.335907i
\(557\) 0.409830 0.709846i 0.0173651 0.0300772i −0.857212 0.514963i \(-0.827806\pi\)
0.874577 + 0.484886i \(0.161139\pi\)
\(558\) 40.8885 1.73095
\(559\) 0.145898 0.00617083
\(560\) 23.5623 40.8111i 0.995689 1.72458i
\(561\) 0.236068 0.408882i 0.00996680 0.0172630i
\(562\) −47.7426 −2.01390
\(563\) −32.8328 −1.38374 −0.691869 0.722023i \(-0.743212\pi\)
−0.691869 + 0.722023i \(0.743212\pi\)
\(564\) −0.354102 + 0.613323i −0.0149104 + 0.0258255i
\(565\) −10.9443 18.9560i −0.460429 0.797486i
\(566\) −21.0623 + 36.4810i −0.885315 + 1.53341i
\(567\) −11.5623 20.0265i −0.485571 0.841034i
\(568\) −8.35410 14.4697i −0.350530 0.607136i
\(569\) 16.9098 0.708897 0.354448 0.935076i \(-0.384669\pi\)
0.354448 + 0.935076i \(0.384669\pi\)
\(570\) 0 0
\(571\) 6.67376 0.279288 0.139644 0.990202i \(-0.455404\pi\)
0.139644 + 0.990202i \(0.455404\pi\)
\(572\) −0.500000 0.866025i −0.0209061 0.0362103i
\(573\) −2.71885 4.70918i −0.113581 0.196729i
\(574\) 7.28115 12.6113i 0.303909 0.526387i
\(575\) −14.7254 25.5052i −0.614093 1.06364i
\(576\) 6.04508 10.4704i 0.251879 0.436266i
\(577\) −12.1246 −0.504754 −0.252377 0.967629i \(-0.581212\pi\)
−0.252377 + 0.967629i \(0.581212\pi\)
\(578\) −26.5623 −1.10485
\(579\) −0.965558 + 1.67240i −0.0401272 + 0.0695024i
\(580\) 3.61803 6.26662i 0.150231 0.260207i
\(581\) 25.4164 1.05445
\(582\) 8.56231 0.354919
\(583\) −5.11803 + 8.86469i −0.211967 + 0.367138i
\(584\) −3.02786 5.24441i −0.125294 0.217015i
\(585\) −4.61803 + 7.99867i −0.190932 + 0.330704i
\(586\) 8.20820 + 14.2170i 0.339078 + 0.587300i
\(587\) 1.06231 + 1.83997i 0.0438461 + 0.0759436i 0.887116 0.461547i \(-0.152706\pi\)
−0.843270 + 0.537491i \(0.819372\pi\)
\(588\) 0.472136 0.0194706
\(589\) 0 0
\(590\) 1.70820 0.0703256
\(591\) −0.572949 0.992377i −0.0235680 0.0408209i
\(592\) 21.4894 + 37.2207i 0.883207 + 1.52976i
\(593\) −0.354102 + 0.613323i −0.0145412 + 0.0251861i −0.873204 0.487354i \(-0.837962\pi\)
0.858663 + 0.512540i \(0.171295\pi\)
\(594\) −2.92705 5.06980i −0.120098 0.208016i
\(595\) −3.70820 + 6.42280i −0.152022 + 0.263309i
\(596\) −1.18034 −0.0483486
\(597\) −5.12461 −0.209736
\(598\) 4.35410 7.54153i 0.178052 0.308396i
\(599\) −14.2082 + 24.6093i −0.580531 + 1.00551i 0.414885 + 0.909874i \(0.363822\pi\)
−0.995416 + 0.0956361i \(0.969511\pi\)
\(600\) −4.67376 −0.190806
\(601\) 20.2918 0.827720 0.413860 0.910341i \(-0.364180\pi\)
0.413860 + 0.910341i \(0.364180\pi\)
\(602\) 0.354102 0.613323i 0.0144321 0.0249972i
\(603\) −9.98936 17.3021i −0.406798 0.704595i
\(604\) 6.51722 11.2882i 0.265182 0.459309i
\(605\) 13.5623 + 23.4906i 0.551386 + 0.955029i
\(606\) 2.83688 + 4.91362i 0.115240 + 0.199602i
\(607\) −6.27051 −0.254512 −0.127256 0.991870i \(-0.540617\pi\)
−0.127256 + 0.991870i \(0.540617\pi\)
\(608\) 0 0
\(609\) −4.14590 −0.168000
\(610\) 26.7984 + 46.4161i 1.08503 + 1.87933i
\(611\) 1.50000 + 2.59808i 0.0606835 + 0.105107i
\(612\) 0.673762 1.16699i 0.0272352 0.0471728i
\(613\) 9.97214 + 17.2722i 0.402771 + 0.697619i 0.994059 0.108841i \(-0.0347138\pi\)
−0.591288 + 0.806460i \(0.701381\pi\)
\(614\) 14.0172 24.2785i 0.565689 0.979802i
\(615\) −3.70820 −0.149529
\(616\) 10.8541 0.437324
\(617\) −3.83688 + 6.64567i −0.154467 + 0.267545i −0.932865 0.360227i \(-0.882699\pi\)
0.778398 + 0.627771i \(0.216033\pi\)
\(618\) −4.42705 + 7.66788i −0.178082 + 0.308447i
\(619\) 10.1246 0.406943 0.203471 0.979081i \(-0.434778\pi\)
0.203471 + 0.979081i \(0.434778\pi\)
\(620\) −17.7082 −0.711179
\(621\) 6.01722 10.4221i 0.241463 0.418226i
\(622\) −10.2361 17.7294i −0.410429 0.710884i
\(623\) 11.6459 20.1713i 0.466583 0.808146i
\(624\) −0.927051 1.60570i −0.0371117 0.0642794i
\(625\) 11.2082 + 19.4132i 0.448328 + 0.776527i
\(626\) −18.3262 −0.732464
\(627\) 0 0
\(628\) −11.0344 −0.440322
\(629\) −3.38197 5.85774i −0.134848 0.233563i
\(630\) 22.4164 + 38.8264i 0.893091 + 1.54688i
\(631\) −14.6803 + 25.4271i −0.584415 + 1.01224i 0.410533 + 0.911846i \(0.365343\pi\)
−0.994948 + 0.100391i \(0.967991\pi\)
\(632\) 15.0000 + 25.9808i 0.596668 + 1.03346i
\(633\) 0.736068 1.27491i 0.0292561 0.0506730i
\(634\) 29.1246 1.15669
\(635\) 18.6525 0.740201
\(636\) 0.746711 1.29334i 0.0296090 0.0512843i
\(637\) 1.00000 1.73205i 0.0396214 0.0686264i
\(638\) 9.47214 0.375005
\(639\) 21.3262 0.843653
\(640\) −22.0344 + 38.1648i −0.870988 + 1.50860i
\(641\) 19.7533 + 34.2137i 0.780208 + 1.35136i 0.931820 + 0.362920i \(0.118220\pi\)
−0.151612 + 0.988440i \(0.548447\pi\)
\(642\) −5.07295 + 8.78661i −0.200213 + 0.346780i
\(643\) 12.1459 + 21.0373i 0.478987 + 0.829631i 0.999710 0.0240956i \(-0.00767060\pi\)
−0.520722 + 0.853726i \(0.674337\pi\)
\(644\) −4.98936 8.64182i −0.196608 0.340535i
\(645\) −0.180340 −0.00710088
\(646\) 0 0
\(647\) 7.47214 0.293760 0.146880 0.989154i \(-0.453077\pi\)
0.146880 + 0.989154i \(0.453077\pi\)
\(648\) 8.61803 + 14.9269i 0.338548 + 0.586383i
\(649\) 0.263932 + 0.457144i 0.0103602 + 0.0179445i
\(650\) 4.42705 7.66788i 0.173643 0.300759i
\(651\) 5.07295 + 8.78661i 0.198825 + 0.344374i
\(652\) −0.545085 + 0.944115i −0.0213472 + 0.0369744i
\(653\) −23.5623 −0.922064 −0.461032 0.887383i \(-0.652521\pi\)
−0.461032 + 0.887383i \(0.652521\pi\)
\(654\) −2.03444 −0.0795530
\(655\) −24.4164 + 42.2905i −0.954028 + 1.65242i
\(656\) −7.28115 + 12.6113i −0.284281 + 0.492390i
\(657\) 7.72949 0.301556
\(658\) 14.5623 0.567698
\(659\) 12.8885 22.3236i 0.502066 0.869604i −0.497931 0.867217i \(-0.665907\pi\)
0.999997 0.00238770i \(-0.000760030\pi\)
\(660\) 0.618034 + 1.07047i 0.0240569 + 0.0416678i
\(661\) −2.70820 + 4.69075i −0.105337 + 0.182449i −0.913876 0.405994i \(-0.866925\pi\)
0.808539 + 0.588443i \(0.200259\pi\)
\(662\) −8.85410 15.3358i −0.344124 0.596041i
\(663\) 0.145898 + 0.252703i 0.00566621 + 0.00981416i
\(664\) −18.9443 −0.735180
\(665\) 0 0
\(666\) −40.8885 −1.58440
\(667\) 9.73607 + 16.8634i 0.376982 + 0.652952i
\(668\) −6.25329 10.8310i −0.241947 0.419065i
\(669\) 2.22542 3.85455i 0.0860399 0.149025i
\(670\) 18.3262 + 31.7420i 0.708004 + 1.22630i
\(671\) −8.28115 + 14.3434i −0.319690 + 0.553720i
\(672\) −3.87539 −0.149496
\(673\) 34.1246 1.31541 0.657704 0.753277i \(-0.271528\pi\)
0.657704 + 0.753277i \(0.271528\pi\)
\(674\) 13.8541 23.9960i 0.533640 0.924292i
\(675\) 6.11803 10.5967i 0.235483 0.407869i
\(676\) −7.41641 −0.285246
\(677\) −30.7426 −1.18154 −0.590768 0.806842i \(-0.701175\pi\)
−0.590768 + 0.806842i \(0.701175\pi\)
\(678\) −2.09017 + 3.62028i −0.0802725 + 0.139036i
\(679\) −20.7812 35.9940i −0.797507 1.38132i
\(680\) 2.76393 4.78727i 0.105992 0.183583i
\(681\) −3.13525 5.43042i −0.120143 0.208094i
\(682\) −11.5902 20.0748i −0.443811 0.768702i
\(683\) 9.65248 0.369342 0.184671 0.982800i \(-0.440878\pi\)
0.184671 + 0.982800i \(0.440878\pi\)
\(684\) 0 0
\(685\) 24.1803 0.923883
\(686\) 12.1353 + 21.0189i 0.463326 + 0.802504i
\(687\) 2.60081 + 4.50474i 0.0992272 + 0.171867i
\(688\) −0.354102 + 0.613323i −0.0135000 + 0.0233827i
\(689\) −3.16312 5.47868i −0.120505 0.208721i
\(690\) −5.38197 + 9.32184i −0.204888 + 0.354876i
\(691\) −39.1803 −1.49049 −0.745245 0.666791i \(-0.767668\pi\)
−0.745245 + 0.666791i \(0.767668\pi\)
\(692\) −0.291796 −0.0110924
\(693\) −6.92705 + 11.9980i −0.263137 + 0.455766i
\(694\) 20.5623 35.6150i 0.780534 1.35193i
\(695\) 47.8885 1.81652
\(696\) 3.09017 0.117133
\(697\) 1.14590 1.98475i 0.0434040 0.0751779i
\(698\) 16.9721 + 29.3966i 0.642405 + 1.11268i
\(699\) −0.864745 + 1.49778i −0.0327077 + 0.0566513i
\(700\) −5.07295 8.78661i −0.191739 0.332102i
\(701\) 19.8156 + 34.3216i 0.748425 + 1.29631i 0.948578 + 0.316545i \(0.102523\pi\)
−0.200153 + 0.979765i \(0.564144\pi\)
\(702\) 3.61803 0.136554
\(703\) 0 0
\(704\) −6.85410 −0.258324
\(705\) −1.85410 3.21140i −0.0698295 0.120948i
\(706\) −19.7812 34.2620i −0.744474 1.28947i
\(707\) 13.7705 23.8512i 0.517893 0.897018i
\(708\) −0.0385072 0.0666964i −0.00144719 0.00250660i
\(709\) −8.29180 + 14.3618i −0.311405 + 0.539369i −0.978667 0.205454i \(-0.934133\pi\)
0.667262 + 0.744823i \(0.267466\pi\)
\(710\) −39.1246 −1.46832
\(711\) −38.2918 −1.43605
\(712\) −8.68034 + 15.0348i −0.325309 + 0.563453i
\(713\) 23.8262 41.2683i 0.892300 1.54551i
\(714\) 1.41641 0.0530077
\(715\) 5.23607 0.195818
\(716\) −3.78115 + 6.54915i −0.141308 + 0.244753i
\(717\) 0.0623059 + 0.107917i 0.00232686 + 0.00403023i
\(718\) −5.69098 + 9.85707i −0.212386 + 0.367863i
\(719\) −23.5172 40.7330i −0.877044 1.51909i −0.854569 0.519338i \(-0.826179\pi\)
−0.0224754 0.999747i \(-0.507155\pi\)
\(720\) −22.4164 38.8264i −0.835410 1.44697i
\(721\) 42.9787 1.60061
\(722\) 0 0
\(723\) 1.21478 0.0451782
\(724\) −3.70820 6.42280i −0.137814 0.238701i
\(725\) 9.89919 + 17.1459i 0.367647 + 0.636783i
\(726\) 2.59017 4.48631i 0.0961302 0.166502i
\(727\) 8.03444 + 13.9161i 0.297981 + 0.516118i 0.975674 0.219227i \(-0.0703535\pi\)
−0.677693 + 0.735345i \(0.737020\pi\)
\(728\) −3.35410 + 5.80948i −0.124311 + 0.215313i
\(729\) −19.4377 −0.719915
\(730\) −14.1803 −0.524838
\(731\) 0.0557281 0.0965239i 0.00206118 0.00357006i
\(732\) 1.20820 2.09267i 0.0446565 0.0773473i
\(733\) −52.9574 −1.95603 −0.978014 0.208541i \(-0.933129\pi\)
−0.978014 + 0.208541i \(0.933129\pi\)
\(734\) −25.7984 −0.952235
\(735\) −1.23607 + 2.14093i −0.0455931 + 0.0789695i
\(736\) 9.10081 + 15.7631i 0.335460 + 0.581034i
\(737\) −5.66312 + 9.80881i −0.208604 + 0.361312i
\(738\) −6.92705 11.9980i −0.254988 0.441653i
\(739\) 12.5000 + 21.6506i 0.459820 + 0.796431i 0.998951 0.0457903i \(-0.0145806\pi\)
−0.539131 + 0.842222i \(0.681247\pi\)
\(740\) 17.7082 0.650967
\(741\) 0 0
\(742\) −30.7082 −1.12733
\(743\) 1.68034 + 2.91043i 0.0616457 + 0.106773i 0.895201 0.445662i \(-0.147032\pi\)
−0.833555 + 0.552436i \(0.813698\pi\)
\(744\) −3.78115 6.54915i −0.138624 0.240103i
\(745\) 3.09017 5.35233i 0.113215 0.196094i
\(746\) 4.42705 + 7.66788i 0.162086 + 0.280741i
\(747\) 12.0902 20.9408i 0.442356 0.766183i
\(748\) −0.763932 −0.0279321
\(749\) 49.2492 1.79953
\(750\) −0.472136 + 0.817763i −0.0172400 + 0.0298605i
\(751\) 8.57295 14.8488i 0.312831 0.541840i −0.666143 0.745824i \(-0.732056\pi\)
0.978974 + 0.203984i \(0.0653892\pi\)
\(752\) −14.5623 −0.531033
\(753\) −9.68692 −0.353011
\(754\) −2.92705 + 5.06980i −0.106597 + 0.184631i
\(755\) 34.1246 + 59.1056i 1.24192 + 2.15107i
\(756\) 2.07295 3.59045i 0.0753924 0.130584i
\(757\) −13.3713 23.1598i −0.485989 0.841758i 0.513881 0.857861i \(-0.328207\pi\)
−0.999870 + 0.0161036i \(0.994874\pi\)
\(758\) 12.2361 + 21.1935i 0.444434 + 0.769782i
\(759\) −3.32624 −0.120735
\(760\) 0 0
\(761\) 4.88854 0.177210 0.0886048 0.996067i \(-0.471759\pi\)
0.0886048 + 0.996067i \(0.471759\pi\)
\(762\) −1.78115 3.08505i −0.0645244 0.111759i
\(763\) 4.93769 + 8.55234i 0.178757 + 0.309615i
\(764\) −4.39919 + 7.61962i −0.159157 + 0.275668i
\(765\) 3.52786 + 6.11044i 0.127550 + 0.220923i
\(766\) −0.309017 + 0.535233i −0.0111652 + 0.0193388i
\(767\) −0.326238 −0.0117798
\(768\) 5.18034 0.186929
\(769\) −18.3156 + 31.7235i −0.660477 + 1.14398i 0.320013 + 0.947413i \(0.396313\pi\)
−0.980490 + 0.196567i \(0.937021\pi\)
\(770\) 12.7082 22.0113i 0.457972 0.793231i
\(771\) 7.77709 0.280085
\(772\) 3.12461 0.112457
\(773\) 17.9615 31.1102i 0.646030 1.11896i −0.338033 0.941134i \(-0.609761\pi\)
0.984063 0.177822i \(-0.0569052\pi\)
\(774\) −0.336881 0.583495i −0.0121089 0.0209733i
\(775\) 24.2254 41.9597i 0.870203 1.50724i
\(776\) 15.4894 + 26.8284i 0.556036 + 0.963082i
\(777\) −5.07295 8.78661i −0.181991 0.315218i
\(778\) 15.0000 0.537776
\(779\) 0 0
\(780\) −0.763932 −0.0273532
\(781\) −6.04508 10.4704i −0.216310 0.374660i
\(782\) −3.32624 5.76121i −0.118946 0.206021i
\(783\) −4.04508 + 7.00629i −0.144560 + 0.250384i
\(784\) 4.85410 + 8.40755i 0.173361 + 0.300270i
\(785\) 28.8885 50.0364i 1.03108 1.78588i
\(786\) 9.32624 0.332656
\(787\) 38.0000 1.35455 0.677277 0.735728i \(-0.263160\pi\)
0.677277 + 0.735728i \(0.263160\pi\)
\(788\) −0.927051 + 1.60570i −0.0330248 + 0.0572007i
\(789\) 2.85410 4.94345i 0.101609 0.175991i
\(790\) 70.2492 2.49936
\(791\) 20.2918 0.721493
\(792\) 5.16312 8.94278i 0.183463 0.317768i
\(793\) −5.11803 8.86469i −0.181747 0.314795i
\(794\) 9.28115 16.0754i 0.329376 0.570496i
\(795\) 3.90983 + 6.77202i 0.138667 + 0.240179i
\(796\) 4.14590 + 7.18091i 0.146947 + 0.254520i
\(797\) −20.2918 −0.718772 −0.359386 0.933189i \(-0.617014\pi\)
−0.359386 + 0.933189i \(0.617014\pi\)
\(798\) 0 0
\(799\) 2.29180 0.0810779
\(800\) 9.25329 + 16.0272i 0.327153 + 0.566646i
\(801\) −11.0795 19.1903i −0.391476 0.678056i
\(802\) 29.0344 50.2891i 1.02524 1.77577i
\(803\) −2.19098 3.79489i −0.0773181 0.133919i
\(804\) 0.826238 1.43109i 0.0291392 0.0504705i
\(805\) 52.2492 1.84154
\(806\) 14.3262 0.504620
\(807\) −5.79180 + 10.0317i −0.203881 + 0.353132i
\(808\) −10.2639 + 17.7777i −0.361084 + 0.625416i
\(809\) −24.7984 −0.871864 −0.435932 0.899980i \(-0.643581\pi\)
−0.435932 + 0.899980i \(0.643581\pi\)
\(810\) 40.3607 1.41813
\(811\) −11.4894 + 19.9001i −0.403446 + 0.698789i −0.994139 0.108107i \(-0.965521\pi\)
0.590693 + 0.806896i \(0.298854\pi\)
\(812\) 3.35410 + 5.80948i 0.117706 + 0.203873i
\(813\) −0.218847 + 0.379054i −0.00767530 + 0.0132940i
\(814\) 11.5902 + 20.0748i 0.406235 + 0.703620i
\(815\) −2.85410 4.94345i −0.0999748 0.173161i
\(816\) −1.41641 −0.0495842
\(817\) 0 0
\(818\) −13.4164 −0.469094
\(819\) −4.28115 7.41517i −0.149596 0.259107i
\(820\) 3.00000 + 5.19615i 0.104765 + 0.181458i
\(821\) −26.0238 + 45.0745i −0.908237 + 1.57311i −0.0917245 + 0.995784i \(0.529238\pi\)
−0.816512 + 0.577328i \(0.804095\pi\)
\(822\) −2.30902 3.99933i −0.0805362 0.139493i
\(823\) 12.7984 22.1674i 0.446123 0.772708i −0.552006 0.833840i \(-0.686138\pi\)
0.998130 + 0.0611317i \(0.0194710\pi\)
\(824\) −32.0344 −1.11597
\(825\) −3.38197 −0.117745
\(826\) −0.791796 + 1.37143i −0.0275501 + 0.0477182i
\(827\) −16.2984 + 28.2296i −0.566750 + 0.981640i 0.430135 + 0.902765i \(0.358466\pi\)
−0.996885 + 0.0788750i \(0.974867\pi\)
\(828\) −9.49342 −0.329919
\(829\) 4.67376 0.162326 0.0811632 0.996701i \(-0.474136\pi\)
0.0811632 + 0.996701i \(0.474136\pi\)
\(830\) −22.1803 + 38.4175i −0.769891 + 1.33349i
\(831\) −2.18034 3.77646i −0.0756352 0.131004i
\(832\) 2.11803 3.66854i 0.0734296 0.127184i
\(833\) −0.763932 1.32317i −0.0264687 0.0458451i
\(834\) −4.57295 7.92058i −0.158348 0.274267i
\(835\) 65.4853 2.26621
\(836\) 0 0
\(837\) 19.7984 0.684332
\(838\) 7.23607 + 12.5332i 0.249966 + 0.432954i
\(839\) −7.60081 13.1650i −0.262409 0.454506i 0.704472 0.709731i \(-0.251184\pi\)
−0.966882 + 0.255225i \(0.917850\pi\)
\(840\) 4.14590 7.18091i 0.143047 0.247765i
\(841\) 7.95492 + 13.7783i 0.274307 + 0.475114i
\(842\) 22.2254 38.4956i 0.765939 1.32664i
\(843\) −11.2705 −0.388177
\(844\) −2.38197 −0.0819907
\(845\) 19.4164 33.6302i 0.667945 1.15691i
\(846\) 6.92705 11.9980i 0.238157 0.412500i
\(847\) −25.1459 −0.864023
\(848\) 30.7082 1.05452
\(849\) −4.97214 + 8.61199i −0.170643 + 0.295563i
\(850\) −3.38197 5.85774i −0.116000 0.200919i
\(851\) −23.8262 + 41.2683i −0.816753 + 1.41466i
\(852\) 0.881966 + 1.52761i 0.0302157 + 0.0523351i
\(853\) −15.3541 26.5941i −0.525714 0.910564i −0.999551 0.0299515i \(-0.990465\pi\)
0.473837 0.880613i \(-0.342869\pi\)
\(854\) −49.6869 −1.70025
\(855\) 0 0
\(856\) −36.7082 −1.25466
\(857\) 5.30902 + 9.19549i 0.181353 + 0.314112i 0.942341 0.334653i \(-0.108619\pi\)
−0.760989 + 0.648765i \(0.775286\pi\)
\(858\) −0.500000 0.866025i −0.0170697 0.0295656i
\(859\) 24.2705 42.0378i 0.828099 1.43431i −0.0714285 0.997446i \(-0.522756\pi\)
0.899528 0.436864i \(-0.143911\pi\)
\(860\) 0.145898 + 0.252703i 0.00497508 + 0.00861709i
\(861\) 1.71885 2.97713i 0.0585782 0.101460i
\(862\) 44.7426 1.52394
\(863\) −27.0557 −0.920988 −0.460494 0.887663i \(-0.652328\pi\)
−0.460494 + 0.887663i \(0.652328\pi\)
\(864\) −3.78115 + 6.54915i −0.128637 + 0.222807i
\(865\) 0.763932 1.32317i 0.0259745 0.0449891i
\(866\) −5.56231 −0.189015
\(867\) −6.27051 −0.212958
\(868\) 8.20820 14.2170i 0.278605 0.482557i
\(869\) 10.8541 + 18.7999i 0.368200 + 0.637741i
\(870\) 3.61803 6.26662i 0.122663 0.212458i
\(871\) −3.50000 6.06218i −0.118593 0.205409i
\(872\) −3.68034 6.37454i −0.124632 0.215869i
\(873\) −39.5410 −1.33826
\(874\) 0 0
\(875\) 4.58359 0.154954
\(876\) 0.319660 + 0.553668i 0.0108003 + 0.0187067i
\(877\) −5.90983 10.2361i −0.199561 0.345649i 0.748825 0.662767i \(-0.230618\pi\)
−0.948386 + 0.317118i \(0.897285\pi\)
\(878\) 27.9894 48.4790i 0.944595 1.63609i
\(879\) 1.93769 + 3.35618i 0.0653568 + 0.113201i
\(880\) −12.7082 + 22.0113i −0.428393 + 0.741999i
\(881\) 32.4508 1.09330 0.546648 0.837362i \(-0.315903\pi\)
0.546648 + 0.837362i \(0.315903\pi\)
\(882\) −9.23607 −0.310995
\(883\) 25.4615 44.1006i 0.856847 1.48410i −0.0180730 0.999837i \(-0.505753\pi\)
0.874920 0.484267i \(-0.160914\pi\)
\(884\) 0.236068 0.408882i 0.00793983 0.0137522i
\(885\) 0.403252 0.0135552
\(886\) −12.2705 −0.412236
\(887\) −13.6738 + 23.6837i −0.459120 + 0.795219i −0.998915 0.0465775i \(-0.985169\pi\)
0.539795 + 0.841797i \(0.318502\pi\)
\(888\) 3.78115 + 6.54915i 0.126887 + 0.219775i
\(889\) −8.64590 + 14.9751i −0.289974 + 0.502250i
\(890\) 20.3262 + 35.2061i 0.681337 + 1.18011i
\(891\) 6.23607 + 10.8012i 0.208916 + 0.361853i
\(892\) −7.20163 −0.241128
\(893\) 0 0
\(894\) −1.18034 −0.0394765
\(895\) −19.7984 34.2918i −0.661787 1.14625i
\(896\) −20.4271 35.3807i −0.682420 1.18199i
\(897\) 1.02786 1.78031i 0.0343194 0.0594429i
\(898\) −2.33688 4.04760i −0.0779827 0.135070i
\(899\) −16.0172 + 27.7426i −0.534204 + 0.925269i
\(900\) −9.65248 −0.321749
\(901\) −4.83282 −0.161004
\(902\) −3.92705 + 6.80185i −0.130756 + 0.226477i
\(903\) 0.0835921 0.144786i 0.00278177 0.00481817i
\(904\) −15.1246 −0.503037
\(905\) 38.8328 1.29085
\(906\) 6.51722 11.2882i 0.216520 0.375024i
\(907\) 13.2361 + 22.9255i 0.439496 + 0.761230i 0.997651 0.0685071i \(-0.0218236\pi\)
−0.558154 + 0.829737i \(0.688490\pi\)
\(908\) −5.07295 + 8.78661i −0.168352 + 0.291594i
\(909\) −13.1008 22.6913i −0.434527 0.752622i
\(910\) 7.85410 + 13.6037i 0.260361 + 0.450958i
\(911\) 3.38197 0.112050 0.0560248 0.998429i \(-0.482157\pi\)
0.0560248 + 0.998429i \(0.482157\pi\)
\(912\) 0 0
\(913\) −13.7082 −0.453675
\(914\) −15.9443 27.6163i −0.527390 0.913466i
\(915\) 6.32624 + 10.9574i 0.209139 + 0.362239i
\(916\) 4.20820 7.28882i 0.139043 0.240829i
\(917\) −22.6353 39.2054i −0.747482 1.29468i
\(918\) 1.38197 2.39364i 0.0456117 0.0790017i
\(919\) 23.2918 0.768325 0.384163 0.923265i \(-0.374490\pi\)
0.384163 + 0.923265i \(0.374490\pi\)
\(920\) −38.9443 −1.28395
\(921\) 3.30902 5.73139i 0.109036 0.188856i
\(922\) −16.9443 + 29.3483i −0.558030 + 0.966536i
\(923\) 7.47214 0.245948
\(924\) −1.14590 −0.0376973
\(925\) −24.2254 + 41.9597i −0.796527 + 1.37963i
\(926\) −22.8713 39.6143i −0.751598 1.30181i
\(927\) 20.4443 35.4105i 0.671478 1.16303i
\(928\) −6.11803 10.5967i −0.200834 0.347855i
\(929\) −8.19098 14.1872i −0.268737 0.465467i 0.699799 0.714340i \(-0.253273\pi\)
−0.968536 + 0.248873i \(0.919940\pi\)
\(930\) −17.7082 −0.580675
\(931\) 0 0
\(932\) 2.79837 0.0916638
\(933\) −2.41641 4.18534i −0.0791096 0.137022i
\(934\) 12.8992 + 22.3420i 0.422074 + 0.731054i
\(935\) 2.00000 3.46410i 0.0654070 0.113288i
\(936\) 3.19098 + 5.52694i 0.104301 + 0.180654i
\(937\) −20.2812 + 35.1280i −0.662556 + 1.14758i 0.317385 + 0.948297i \(0.397195\pi\)
−0.979942 + 0.199285i \(0.936138\pi\)
\(938\) −33.9787 −1.10944
\(939\) −4.32624 −0.141181
\(940\) −3.00000 + 5.19615i −0.0978492 + 0.169480i
\(941\) 5.34346 9.25514i 0.174192 0.301709i −0.765689 0.643210i \(-0.777602\pi\)
0.939881 + 0.341501i \(0.110935\pi\)
\(942\) −11.0344 −0.359522
\(943\) −16.1459 −0.525783
\(944\) 0.791796 1.37143i 0.0257708 0.0446363i
\(945\) 10.8541 + 18.7999i 0.353084 + 0.611559i
\(946\) −0.190983 + 0.330792i −0.00620939 + 0.0107550i
\(947\) 16.3262 + 28.2779i 0.530531 + 0.918907i 0.999365 + 0.0356211i \(0.0113409\pi\)
−0.468834 + 0.883286i \(0.655326\pi\)
\(948\) −1.58359 2.74286i −0.0514327 0.0890840i
\(949\) 2.70820 0.0879120
\(950\) 0 0
\(951\) 6.87539 0.222950
\(952\) 2.56231 + 4.43804i 0.0830448 + 0.143838i
\(953\) −8.64590 14.9751i −0.280068 0.485092i 0.691333 0.722536i \(-0.257024\pi\)
−0.971401 + 0.237444i \(0.923690\pi\)
\(954\) −14.6074 + 25.3007i −0.472932 + 0.819142i
\(955\) −23.0344 39.8968i −0.745377 1.29103i
\(956\) 0.100813 0.174613i 0.00326053 0.00564740i
\(957\) 2.23607 0.0722818
\(958\) 37.3607 1.20707
\(959\) −11.2082 + 19.4132i −0.361932 + 0.626884i
\(960\) −2.61803 + 4.53457i −0.0844967 + 0.146353i
\(961\) 47.3951 1.52887
\(962\) −14.3262 −0.461896
\(963\) 23.4271 40.5768i 0.754926 1.30757i
\(964\) −0.982779 1.70222i −0.0316532 0.0548249i
\(965\) −8.18034 + 14.1688i −0.263334 + 0.456109i
\(966\) −4.98936 8.64182i −0.160530 0.278046i
\(967\) −3.27051 5.66469i −0.105173 0.182164i 0.808636 0.588309i \(-0.200206\pi\)
−0.913809 + 0.406145i \(0.866873\pi\)
\(968\) 18.7426 0.602411
\(969\) 0 0
\(970\) 72.5410 2.32915
\(971\) −11.7533 20.3573i −0.377181 0.653297i 0.613470 0.789718i \(-0.289773\pi\)
−0.990651 + 0.136421i \(0.956440\pi\)
\(972\) −2.98278 5.16632i −0.0956727 0.165710i
\(973\) −22.1976 + 38.4473i −0.711621 + 1.23256i
\(974\) −3.38197 5.85774i −0.108365 0.187694i
\(975\) 1.04508 1.81014i 0.0334695 0.0579709i
\(976\) 49.6869 1.59044
\(977\) 10.6393 0.340382 0.170191 0.985411i \(-0.445562\pi\)
0.170191 + 0.985411i \(0.445562\pi\)
\(978\) −0.545085 + 0.944115i −0.0174299 + 0.0301895i
\(979\) −6.28115 + 10.8793i −0.200747 + 0.347703i
\(980\) 4.00000 0.127775
\(981\) 9.39512 0.299963
\(982\) 17.1631 29.7274i 0.547697 0.948639i
\(983\) −16.3090 28.2480i −0.520177 0.900973i −0.999725 0.0234571i \(-0.992533\pi\)
0.479548 0.877516i \(-0.340801\pi\)
\(984\) −1.28115 + 2.21902i −0.0408417 + 0.0707398i
\(985\) −4.85410 8.40755i −0.154665 0.267887i
\(986\) 2.23607 + 3.87298i 0.0712109 + 0.123341i
\(987\) 3.43769 0.109423
\(988\) 0 0
\(989\) −0.785218 −0.0249685
\(990\) −12.0902 20.9408i −0.384251 0.665542i
\(991\) −3.72542 6.45263i −0.118342 0.204974i 0.800769 0.598974i \(-0.204425\pi\)
−0.919111 + 0.393999i \(0.871091\pi\)
\(992\) −14.9721 + 25.9325i −0.475366 + 0.823358i
\(993\) −2.09017 3.62028i −0.0663295 0.114886i
\(994\) 18.1353 31.4112i 0.575215 0.996302i
\(995\) −43.4164 −1.37639
\(996\) 2.00000 0.0633724
\(997\) −19.8541 + 34.3883i −0.628786 + 1.08909i 0.359010 + 0.933334i \(0.383114\pi\)
−0.987796 + 0.155755i \(0.950219\pi\)
\(998\) −20.3262 + 35.2061i −0.643416 + 1.11443i
\(999\) −19.7984 −0.626393
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 361.2.c.d.292.1 4
19.2 odd 18 361.2.e.i.28.1 12
19.3 odd 18 361.2.e.i.234.1 12
19.4 even 9 361.2.e.j.245.2 12
19.5 even 9 361.2.e.j.99.1 12
19.6 even 9 361.2.e.j.62.1 12
19.7 even 3 361.2.a.f.1.2 yes 2
19.8 odd 6 361.2.c.g.68.2 4
19.9 even 9 361.2.e.j.54.2 12
19.10 odd 18 361.2.e.i.54.1 12
19.11 even 3 inner 361.2.c.d.68.1 4
19.12 odd 6 361.2.a.c.1.1 2
19.13 odd 18 361.2.e.i.62.2 12
19.14 odd 18 361.2.e.i.99.2 12
19.15 odd 18 361.2.e.i.245.1 12
19.16 even 9 361.2.e.j.234.2 12
19.17 even 9 361.2.e.j.28.2 12
19.18 odd 2 361.2.c.g.292.2 4
57.26 odd 6 3249.2.a.i.1.1 2
57.50 even 6 3249.2.a.o.1.2 2
76.7 odd 6 5776.2.a.s.1.2 2
76.31 even 6 5776.2.a.bg.1.1 2
95.64 even 6 9025.2.a.n.1.1 2
95.69 odd 6 9025.2.a.s.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
361.2.a.c.1.1 2 19.12 odd 6
361.2.a.f.1.2 yes 2 19.7 even 3
361.2.c.d.68.1 4 19.11 even 3 inner
361.2.c.d.292.1 4 1.1 even 1 trivial
361.2.c.g.68.2 4 19.8 odd 6
361.2.c.g.292.2 4 19.18 odd 2
361.2.e.i.28.1 12 19.2 odd 18
361.2.e.i.54.1 12 19.10 odd 18
361.2.e.i.62.2 12 19.13 odd 18
361.2.e.i.99.2 12 19.14 odd 18
361.2.e.i.234.1 12 19.3 odd 18
361.2.e.i.245.1 12 19.15 odd 18
361.2.e.j.28.2 12 19.17 even 9
361.2.e.j.54.2 12 19.9 even 9
361.2.e.j.62.1 12 19.6 even 9
361.2.e.j.99.1 12 19.5 even 9
361.2.e.j.234.2 12 19.16 even 9
361.2.e.j.245.2 12 19.4 even 9
3249.2.a.i.1.1 2 57.26 odd 6
3249.2.a.o.1.2 2 57.50 even 6
5776.2.a.s.1.2 2 76.7 odd 6
5776.2.a.bg.1.1 2 76.31 even 6
9025.2.a.n.1.1 2 95.64 even 6
9025.2.a.s.1.2 2 95.69 odd 6