Properties

Label 930.2.v.a.401.7
Level $930$
Weight $2$
Character 930.401
Analytic conductor $7.426$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(401,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 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("930.401");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.v (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 401.7
Character \(\chi\) \(=\) 930.401
Dual form 930.2.v.a.821.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 + 0.809017i) q^{2} +(1.13234 - 1.31065i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.394770 + 1.68646i) q^{6} +(0.208734 + 0.642416i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.435626 - 2.96820i) q^{9} +O(q^{10})\) \(q+(-0.587785 + 0.809017i) q^{2} +(1.13234 - 1.31065i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.394770 + 1.68646i) q^{6} +(0.208734 + 0.642416i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.435626 - 2.96820i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.449310 - 1.38283i) q^{11} +(-1.59642 - 0.671902i) q^{12} +(-0.843769 - 1.16135i) q^{13} +(-0.642416 - 0.208734i) q^{14} +(-1.31065 - 1.13234i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.380979 - 1.17253i) q^{17} +(2.65738 + 1.39224i) q^{18} +(-0.600732 - 0.436457i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(1.07834 + 0.453854i) q^{21} +(1.38283 + 0.449310i) q^{22} +(1.98014 - 6.09424i) q^{23} +(1.48193 - 0.896594i) q^{24} -1.00000 q^{25} +1.43551 q^{26} +(-4.38356 - 2.79005i) q^{27} +(0.546471 - 0.397035i) q^{28} +(-3.36320 - 2.44350i) q^{29} +(1.68646 - 0.394770i) q^{30} +(0.503674 + 5.54494i) q^{31} -1.00000i q^{32} +(-2.32119 - 0.976945i) q^{33} +(0.724666 + 0.997417i) q^{34} +(0.642416 - 0.208734i) q^{35} +(-2.68831 + 1.33153i) q^{36} +4.89060i q^{37} +(0.706203 - 0.229459i) q^{38} +(-2.47756 - 0.209149i) q^{39} +(0.309017 - 0.951057i) q^{40} +(1.93003 - 2.65646i) q^{41} +(-1.00101 + 0.605628i) q^{42} +(-0.0895077 + 0.123197i) q^{43} +(-1.17631 + 0.854639i) q^{44} +(-2.96820 + 0.435626i) q^{45} +(3.76645 + 5.18407i) q^{46} +(-5.18784 - 7.14046i) q^{47} +(-0.145697 + 1.72591i) q^{48} +(5.29399 - 3.84631i) q^{49} +(0.587785 - 0.809017i) q^{50} +(-1.10539 - 1.82704i) q^{51} +(-0.843769 + 1.16135i) q^{52} +(1.25122 - 3.85086i) q^{53} +(4.83379 - 1.90643i) q^{54} +(-1.38283 + 0.449310i) q^{55} +0.675476i q^{56} +(-1.25228 + 0.293135i) q^{57} +(3.95367 - 1.28463i) q^{58} +(-3.93956 - 5.42234i) q^{59} +(-0.671902 + 1.59642i) q^{60} +0.125726i q^{61} +(-4.78200 - 2.85175i) q^{62} +(1.81589 - 0.899416i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.16135 + 0.843769i) q^{65} +(2.15472 - 1.30365i) q^{66} -6.15728 q^{67} -1.23288 q^{68} +(-5.74526 - 9.49601i) q^{69} +(-0.208734 + 0.642416i) q^{70} +(1.87903 + 0.610533i) q^{71} +(0.502920 - 2.95754i) q^{72} +(-5.80428 + 1.88593i) q^{73} +(-3.95658 - 2.87462i) q^{74} +(-1.13234 + 1.31065i) q^{75} +(-0.229459 + 0.706203i) q^{76} +(0.794569 - 0.577288i) q^{77} +(1.62548 - 1.88145i) q^{78} +(5.83191 + 1.89490i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-8.62046 + 2.58605i) q^{81} +(1.01468 + 3.12286i) q^{82} +(-0.440780 - 0.320246i) q^{83} +(0.0984147 - 1.16581i) q^{84} +(-1.17253 - 0.380979i) q^{85} +(-0.0470570 - 0.144826i) q^{86} +(-7.01086 + 1.64111i) q^{87} -1.45400i q^{88} +(-0.767608 - 2.36245i) q^{89} +(1.39224 - 2.65738i) q^{90} +(0.569945 - 0.784463i) q^{91} -6.40787 q^{92} +(7.83782 + 5.61859i) q^{93} +8.82609 q^{94} +(-0.436457 + 0.600732i) q^{95} +(-1.31065 - 1.13234i) q^{96} +(-1.43029 - 4.40198i) q^{97} +6.54373i q^{98} +(-3.90880 + 1.93604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 + 0.809017i −0.415627 + 0.572061i
\(3\) 1.13234 1.31065i 0.653755 0.756706i
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) 1.00000i 0.447214i
\(6\) 0.394770 + 1.68646i 0.161164 + 0.688496i
\(7\) 0.208734 + 0.642416i 0.0788938 + 0.242810i 0.982723 0.185084i \(-0.0592556\pi\)
−0.903829 + 0.427894i \(0.859256\pi\)
\(8\) 0.951057 + 0.309017i 0.336249 + 0.109254i
\(9\) −0.435626 2.96820i −0.145209 0.989401i
\(10\) 0.809017 + 0.587785i 0.255834 + 0.185874i
\(11\) −0.449310 1.38283i −0.135472 0.416940i 0.860191 0.509972i \(-0.170344\pi\)
−0.995663 + 0.0930316i \(0.970344\pi\)
\(12\) −1.59642 0.671902i −0.460846 0.193961i
\(13\) −0.843769 1.16135i −0.234019 0.322100i 0.675815 0.737071i \(-0.263792\pi\)
−0.909835 + 0.414971i \(0.863792\pi\)
\(14\) −0.642416 0.208734i −0.171693 0.0557864i
\(15\) −1.31065 1.13234i −0.338409 0.292368i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 0.380979 1.17253i 0.0924011 0.284381i −0.894167 0.447734i \(-0.852231\pi\)
0.986568 + 0.163353i \(0.0522310\pi\)
\(18\) 2.65738 + 1.39224i 0.626351 + 0.328153i
\(19\) −0.600732 0.436457i −0.137817 0.100130i 0.516741 0.856142i \(-0.327145\pi\)
−0.654558 + 0.756012i \(0.727145\pi\)
\(20\) −0.951057 + 0.309017i −0.212663 + 0.0690983i
\(21\) 1.07834 + 0.453854i 0.235313 + 0.0990390i
\(22\) 1.38283 + 0.449310i 0.294821 + 0.0957933i
\(23\) 1.98014 6.09424i 0.412888 1.27074i −0.501239 0.865309i \(-0.667122\pi\)
0.914127 0.405429i \(-0.132878\pi\)
\(24\) 1.48193 0.896594i 0.302498 0.183017i
\(25\) −1.00000 −0.200000
\(26\) 1.43551 0.281526
\(27\) −4.38356 2.79005i −0.843617 0.536946i
\(28\) 0.546471 0.397035i 0.103273 0.0750325i
\(29\) −3.36320 2.44350i −0.624530 0.453747i 0.229971 0.973197i \(-0.426137\pi\)
−0.854501 + 0.519450i \(0.826137\pi\)
\(30\) 1.68646 0.394770i 0.307905 0.0720748i
\(31\) 0.503674 + 5.54494i 0.0904626 + 0.995900i
\(32\) 1.00000i 0.176777i
\(33\) −2.32119 0.976945i −0.404067 0.170064i
\(34\) 0.724666 + 0.997417i 0.124279 + 0.171056i
\(35\) 0.642416 0.208734i 0.108588 0.0352824i
\(36\) −2.68831 + 1.33153i −0.448052 + 0.221922i
\(37\) 4.89060i 0.804010i 0.915637 + 0.402005i \(0.131687\pi\)
−0.915637 + 0.402005i \(0.868313\pi\)
\(38\) 0.706203 0.229459i 0.114561 0.0372232i
\(39\) −2.47756 0.209149i −0.396726 0.0334906i
\(40\) 0.309017 0.951057i 0.0488599 0.150375i
\(41\) 1.93003 2.65646i 0.301421 0.414870i −0.631261 0.775570i \(-0.717462\pi\)
0.932682 + 0.360700i \(0.117462\pi\)
\(42\) −1.00101 + 0.605628i −0.154459 + 0.0934504i
\(43\) −0.0895077 + 0.123197i −0.0136498 + 0.0187873i −0.815787 0.578352i \(-0.803696\pi\)
0.802138 + 0.597139i \(0.203696\pi\)
\(44\) −1.17631 + 0.854639i −0.177335 + 0.128842i
\(45\) −2.96820 + 0.435626i −0.442474 + 0.0649393i
\(46\) 3.76645 + 5.18407i 0.555333 + 0.764350i
\(47\) −5.18784 7.14046i −0.756725 1.04154i −0.997479 0.0709564i \(-0.977395\pi\)
0.240755 0.970586i \(-0.422605\pi\)
\(48\) −0.145697 + 1.72591i −0.0210295 + 0.249114i
\(49\) 5.29399 3.84631i 0.756284 0.549473i
\(50\) 0.587785 0.809017i 0.0831254 0.114412i
\(51\) −1.10539 1.82704i −0.154785 0.255836i
\(52\) −0.843769 + 1.16135i −0.117010 + 0.161050i
\(53\) 1.25122 3.85086i 0.171868 0.528957i −0.827608 0.561306i \(-0.810299\pi\)
0.999477 + 0.0323496i \(0.0102990\pi\)
\(54\) 4.83379 1.90643i 0.657796 0.259432i
\(55\) −1.38283 + 0.449310i −0.186461 + 0.0605850i
\(56\) 0.675476i 0.0902643i
\(57\) −1.25228 + 0.293135i −0.165868 + 0.0388267i
\(58\) 3.95367 1.28463i 0.519143 0.168680i
\(59\) −3.93956 5.42234i −0.512887 0.705928i 0.471516 0.881857i \(-0.343707\pi\)
−0.984403 + 0.175929i \(0.943707\pi\)
\(60\) −0.671902 + 1.59642i −0.0867422 + 0.206097i
\(61\) 0.125726i 0.0160976i 0.999968 + 0.00804879i \(0.00256204\pi\)
−0.999968 + 0.00804879i \(0.997438\pi\)
\(62\) −4.78200 2.85175i −0.607315 0.362173i
\(63\) 1.81589 0.899416i 0.228781 0.113316i
\(64\) 0.809017 + 0.587785i 0.101127 + 0.0734732i
\(65\) −1.16135 + 0.843769i −0.144048 + 0.104657i
\(66\) 2.15472 1.30365i 0.265228 0.160468i
\(67\) −6.15728 −0.752232 −0.376116 0.926573i \(-0.622741\pi\)
−0.376116 + 0.926573i \(0.622741\pi\)
\(68\) −1.23288 −0.149508
\(69\) −5.74526 9.49601i −0.691648 1.14319i
\(70\) −0.208734 + 0.642416i −0.0249484 + 0.0767834i
\(71\) 1.87903 + 0.610533i 0.222999 + 0.0724569i 0.418386 0.908269i \(-0.362596\pi\)
−0.195386 + 0.980726i \(0.562596\pi\)
\(72\) 0.502920 2.95754i 0.0592697 0.348550i
\(73\) −5.80428 + 1.88593i −0.679340 + 0.220731i −0.628306 0.777966i \(-0.716252\pi\)
−0.0510336 + 0.998697i \(0.516252\pi\)
\(74\) −3.95658 2.87462i −0.459943 0.334168i
\(75\) −1.13234 + 1.31065i −0.130751 + 0.151341i
\(76\) −0.229459 + 0.706203i −0.0263208 + 0.0810070i
\(77\) 0.794569 0.577288i 0.0905495 0.0657881i
\(78\) 1.62548 1.88145i 0.184049 0.213032i
\(79\) 5.83191 + 1.89490i 0.656141 + 0.213193i 0.618120 0.786084i \(-0.287895\pi\)
0.0380212 + 0.999277i \(0.487895\pi\)
\(80\) 0.587785 + 0.809017i 0.0657164 + 0.0904508i
\(81\) −8.62046 + 2.58605i −0.957829 + 0.287339i
\(82\) 1.01468 + 3.12286i 0.112053 + 0.344862i
\(83\) −0.440780 0.320246i −0.0483819 0.0351515i 0.563331 0.826231i \(-0.309519\pi\)
−0.611713 + 0.791079i \(0.709519\pi\)
\(84\) 0.0984147 1.16581i 0.0107379 0.127200i
\(85\) −1.17253 0.380979i −0.127179 0.0413230i
\(86\) −0.0470570 0.144826i −0.00507428 0.0156170i
\(87\) −7.01086 + 1.64111i −0.751643 + 0.175946i
\(88\) 1.45400i 0.154997i
\(89\) −0.767608 2.36245i −0.0813663 0.250420i 0.902095 0.431537i \(-0.142029\pi\)
−0.983461 + 0.181117i \(0.942029\pi\)
\(90\) 1.39224 2.65738i 0.146755 0.280113i
\(91\) 0.569945 0.784463i 0.0597465 0.0822340i
\(92\) −6.40787 −0.668066
\(93\) 7.83782 + 5.61859i 0.812744 + 0.582621i
\(94\) 8.82609 0.910341
\(95\) −0.436457 + 0.600732i −0.0447796 + 0.0616338i
\(96\) −1.31065 1.13234i −0.133768 0.115569i
\(97\) −1.43029 4.40198i −0.145224 0.446954i 0.851816 0.523842i \(-0.175502\pi\)
−0.997040 + 0.0768879i \(0.975502\pi\)
\(98\) 6.54373i 0.661017i
\(99\) −3.90880 + 1.93604i −0.392849 + 0.194580i
\(100\) 0.309017 + 0.951057i 0.0309017 + 0.0951057i
\(101\) 10.5068 + 3.41386i 1.04546 + 0.339691i 0.780886 0.624673i \(-0.214768\pi\)
0.264577 + 0.964365i \(0.414768\pi\)
\(102\) 2.12783 + 0.179626i 0.210687 + 0.0177856i
\(103\) 10.2813 + 7.46983i 1.01305 + 0.736024i 0.964847 0.262814i \(-0.0846504\pi\)
0.0482034 + 0.998838i \(0.484650\pi\)
\(104\) −0.443596 1.36525i −0.0434981 0.133873i
\(105\) 0.453854 1.07834i 0.0442916 0.105235i
\(106\) 2.37996 + 3.27574i 0.231163 + 0.318168i
\(107\) 4.94380 + 1.60634i 0.477935 + 0.155291i 0.538071 0.842900i \(-0.319153\pi\)
−0.0601355 + 0.998190i \(0.519153\pi\)
\(108\) −1.29890 + 5.03119i −0.124987 + 0.484126i
\(109\) 6.06305 4.40507i 0.580735 0.421929i −0.258254 0.966077i \(-0.583147\pi\)
0.838989 + 0.544148i \(0.183147\pi\)
\(110\) 0.449310 1.38283i 0.0428401 0.131848i
\(111\) 6.40989 + 5.53781i 0.608400 + 0.525626i
\(112\) −0.546471 0.397035i −0.0516367 0.0375163i
\(113\) 2.85638 0.928094i 0.268706 0.0873077i −0.171565 0.985173i \(-0.554882\pi\)
0.440271 + 0.897865i \(0.354882\pi\)
\(114\) 0.498918 1.18541i 0.0467280 0.111024i
\(115\) −6.09424 1.98014i −0.568291 0.184649i
\(116\) −1.28463 + 3.95367i −0.119275 + 0.367089i
\(117\) −3.07955 + 3.01039i −0.284704 + 0.278311i
\(118\) 6.70238 0.617004
\(119\) 0.832777 0.0763406
\(120\) −0.896594 1.48193i −0.0818475 0.135281i
\(121\) 7.18883 5.22299i 0.653530 0.474818i
\(122\) −0.101715 0.0739000i −0.00920881 0.00669059i
\(123\) −1.29626 5.53762i −0.116879 0.499310i
\(124\) 5.11790 2.19250i 0.459601 0.196893i
\(125\) 1.00000i 0.0894427i
\(126\) −0.339710 + 1.99775i −0.0302638 + 0.177974i
\(127\) −3.49996 4.81728i −0.310571 0.427465i 0.624988 0.780634i \(-0.285104\pi\)
−0.935559 + 0.353170i \(0.885104\pi\)
\(128\) −0.951057 + 0.309017i −0.0840623 + 0.0273135i
\(129\) 0.0601154 + 0.256814i 0.00529287 + 0.0226112i
\(130\) 1.43551i 0.125902i
\(131\) 17.5812 5.71248i 1.53608 0.499102i 0.585787 0.810465i \(-0.300786\pi\)
0.950291 + 0.311364i \(0.100786\pi\)
\(132\) −0.211843 + 2.50947i −0.0184386 + 0.218422i
\(133\) 0.154994 0.477023i 0.0134397 0.0413631i
\(134\) 3.61916 4.98134i 0.312648 0.430323i
\(135\) −2.79005 + 4.38356i −0.240129 + 0.377277i
\(136\) 0.724666 0.997417i 0.0621396 0.0855278i
\(137\) −0.605625 + 0.440012i −0.0517420 + 0.0375928i −0.613356 0.789807i \(-0.710181\pi\)
0.561614 + 0.827400i \(0.310181\pi\)
\(138\) 11.0594 + 0.933606i 0.941440 + 0.0794739i
\(139\) 6.88593 + 9.47767i 0.584057 + 0.803885i 0.994133 0.108166i \(-0.0344979\pi\)
−0.410076 + 0.912051i \(0.634498\pi\)
\(140\) −0.397035 0.546471i −0.0335556 0.0461853i
\(141\) −15.2331 1.28593i −1.28285 0.108295i
\(142\) −1.59840 + 1.16130i −0.134134 + 0.0974543i
\(143\) −1.22684 + 1.68860i −0.102593 + 0.141208i
\(144\) 2.09709 + 2.14527i 0.174758 + 0.178773i
\(145\) −2.44350 + 3.36320i −0.202922 + 0.279298i
\(146\) 1.88593 5.80428i 0.156080 0.480366i
\(147\) 0.953402 11.2939i 0.0786352 0.931506i
\(148\) 4.65124 1.51128i 0.382330 0.124226i
\(149\) 21.6921i 1.77709i 0.458792 + 0.888544i \(0.348282\pi\)
−0.458792 + 0.888544i \(0.651718\pi\)
\(150\) −0.394770 1.68646i −0.0322328 0.137699i
\(151\) 7.93049 2.57677i 0.645374 0.209695i 0.0320009 0.999488i \(-0.489812\pi\)
0.613374 + 0.789793i \(0.289812\pi\)
\(152\) −0.436457 0.600732i −0.0354014 0.0487258i
\(153\) −3.64628 0.620038i −0.294785 0.0501271i
\(154\) 0.982141i 0.0791432i
\(155\) 5.54494 0.503674i 0.445380 0.0404561i
\(156\) 0.566695 + 2.42093i 0.0453719 + 0.193829i
\(157\) −5.16213 3.75051i −0.411983 0.299323i 0.362421 0.932014i \(-0.381950\pi\)
−0.774404 + 0.632691i \(0.781950\pi\)
\(158\) −4.96092 + 3.60432i −0.394670 + 0.286744i
\(159\) −3.63034 6.00039i −0.287905 0.475862i
\(160\) −1.00000 −0.0790569
\(161\) 4.32836 0.341122
\(162\) 2.97482 8.49414i 0.233724 0.667363i
\(163\) −6.48529 + 19.9597i −0.507967 + 1.56336i 0.287756 + 0.957704i \(0.407091\pi\)
−0.795724 + 0.605659i \(0.792909\pi\)
\(164\) −3.12286 1.01468i −0.243855 0.0792331i
\(165\) −0.976945 + 2.32119i −0.0760550 + 0.180704i
\(166\) 0.518168 0.168363i 0.0402177 0.0130675i
\(167\) 3.00954 + 2.18656i 0.232886 + 0.169201i 0.698108 0.715993i \(-0.254026\pi\)
−0.465222 + 0.885194i \(0.654026\pi\)
\(168\) 0.885315 + 0.764866i 0.0683035 + 0.0590107i
\(169\) 3.38044 10.4039i 0.260034 0.800301i
\(170\) 0.997417 0.724666i 0.0764984 0.0555793i
\(171\) −1.03380 + 1.97323i −0.0790566 + 0.150896i
\(172\) 0.144826 + 0.0470570i 0.0110429 + 0.00358806i
\(173\) 0.815807 + 1.12286i 0.0620246 + 0.0853696i 0.838902 0.544282i \(-0.183198\pi\)
−0.776878 + 0.629651i \(0.783198\pi\)
\(174\) 2.79319 6.63653i 0.211751 0.503114i
\(175\) −0.208734 0.642416i −0.0157788 0.0485621i
\(176\) 1.17631 + 0.854639i 0.0886677 + 0.0644208i
\(177\) −11.5677 0.976516i −0.869482 0.0733994i
\(178\) 2.36245 + 0.767608i 0.177073 + 0.0575346i
\(179\) 7.66133 + 23.5792i 0.572635 + 1.76239i 0.644094 + 0.764946i \(0.277234\pi\)
−0.0714594 + 0.997444i \(0.522766\pi\)
\(180\) 1.33153 + 2.68831i 0.0992464 + 0.200375i
\(181\) 3.46365i 0.257451i 0.991680 + 0.128726i \(0.0410886\pi\)
−0.991680 + 0.128726i \(0.958911\pi\)
\(182\) 0.299638 + 0.922191i 0.0222107 + 0.0683574i
\(183\) 0.164783 + 0.142364i 0.0121811 + 0.0105239i
\(184\) 3.76645 5.18407i 0.277666 0.382175i
\(185\) 4.89060 0.359564
\(186\) −9.15249 + 3.03840i −0.671093 + 0.222787i
\(187\) −1.79260 −0.131088
\(188\) −5.18784 + 7.14046i −0.378362 + 0.520771i
\(189\) 0.877376 3.39845i 0.0638197 0.247201i
\(190\) −0.229459 0.706203i −0.0166467 0.0512333i
\(191\) 5.11410i 0.370043i 0.982734 + 0.185022i \(0.0592355\pi\)
−0.982734 + 0.185022i \(0.940764\pi\)
\(192\) 1.68646 0.394770i 0.121710 0.0284901i
\(193\) −5.44011 16.7430i −0.391588 1.20518i −0.931587 0.363518i \(-0.881575\pi\)
0.539999 0.841666i \(-0.318425\pi\)
\(194\) 4.40198 + 1.43029i 0.316044 + 0.102689i
\(195\) −0.209149 + 2.47756i −0.0149775 + 0.177421i
\(196\) −5.29399 3.84631i −0.378142 0.274736i
\(197\) 0.111583 + 0.343418i 0.00794998 + 0.0244675i 0.954953 0.296758i \(-0.0959054\pi\)
−0.947003 + 0.321225i \(0.895905\pi\)
\(198\) 0.731245 4.30027i 0.0519673 0.305607i
\(199\) 10.3604 + 14.2598i 0.734427 + 1.01085i 0.998920 + 0.0464642i \(0.0147953\pi\)
−0.264493 + 0.964388i \(0.585205\pi\)
\(200\) −0.951057 0.309017i −0.0672499 0.0218508i
\(201\) −6.97212 + 8.07006i −0.491775 + 0.569218i
\(202\) −8.93759 + 6.49354i −0.628847 + 0.456884i
\(203\) 0.867734 2.67061i 0.0609030 0.187440i
\(204\) −1.39603 + 1.61587i −0.0977417 + 0.113134i
\(205\) −2.65646 1.93003i −0.185536 0.134799i
\(206\) −12.0864 + 3.92712i −0.842102 + 0.273615i
\(207\) −18.9516 3.22265i −1.31722 0.223989i
\(208\) 1.36525 + 0.443596i 0.0946628 + 0.0307578i
\(209\) −0.333633 + 1.02682i −0.0230779 + 0.0710265i
\(210\) 0.605628 + 1.00101i 0.0417923 + 0.0690761i
\(211\) 7.69073 0.529452 0.264726 0.964324i \(-0.414719\pi\)
0.264726 + 0.964324i \(0.414719\pi\)
\(212\) −4.04904 −0.278089
\(213\) 2.92789 1.77142i 0.200616 0.121376i
\(214\) −4.20545 + 3.05544i −0.287479 + 0.208865i
\(215\) 0.123197 + 0.0895077i 0.00840195 + 0.00610437i
\(216\) −3.30684 4.00809i −0.225002 0.272716i
\(217\) −3.45702 + 1.48098i −0.234678 + 0.100536i
\(218\) 7.49434i 0.507581i
\(219\) −4.10061 + 9.74291i −0.277093 + 0.658365i
\(220\) 0.854639 + 1.17631i 0.0576197 + 0.0793068i
\(221\) −1.68318 + 0.546898i −0.113223 + 0.0367883i
\(222\) −8.24782 + 1.93066i −0.553557 + 0.129578i
\(223\) 4.74825i 0.317966i 0.987281 + 0.158983i \(0.0508216\pi\)
−0.987281 + 0.158983i \(0.949178\pi\)
\(224\) 0.642416 0.208734i 0.0429232 0.0139466i
\(225\) 0.435626 + 2.96820i 0.0290417 + 0.197880i
\(226\) −0.928094 + 2.85638i −0.0617359 + 0.190004i
\(227\) −10.2975 + 14.1733i −0.683467 + 0.940712i −0.999969 0.00787995i \(-0.997492\pi\)
0.316502 + 0.948592i \(0.397492\pi\)
\(228\) 0.665762 + 1.10040i 0.0440912 + 0.0728758i
\(229\) 1.79685 2.47315i 0.118739 0.163431i −0.745510 0.666494i \(-0.767794\pi\)
0.864249 + 0.503064i \(0.167794\pi\)
\(230\) 5.18407 3.76645i 0.341828 0.248352i
\(231\) 0.143095 1.69509i 0.00941495 0.111529i
\(232\) −2.44350 3.36320i −0.160424 0.220805i
\(233\) −8.82310 12.1440i −0.578021 0.795577i 0.415456 0.909613i \(-0.363622\pi\)
−0.993477 + 0.114036i \(0.963622\pi\)
\(234\) −0.625344 4.26087i −0.0408800 0.278542i
\(235\) −7.14046 + 5.18784i −0.465792 + 0.338418i
\(236\) −3.93956 + 5.42234i −0.256443 + 0.352964i
\(237\) 9.08725 5.49795i 0.590280 0.357130i
\(238\) −0.489494 + 0.673731i −0.0317292 + 0.0436715i
\(239\) −7.03734 + 21.6587i −0.455208 + 1.40099i 0.415683 + 0.909509i \(0.363542\pi\)
−0.870891 + 0.491476i \(0.836458\pi\)
\(240\) 1.72591 + 0.145697i 0.111407 + 0.00940470i
\(241\) 3.37816 1.09763i 0.217606 0.0707046i −0.198185 0.980165i \(-0.563505\pi\)
0.415791 + 0.909460i \(0.363505\pi\)
\(242\) 8.88589i 0.571207i
\(243\) −6.37184 + 14.2267i −0.408754 + 0.912645i
\(244\) 0.119573 0.0388515i 0.00765486 0.00248721i
\(245\) −3.84631 5.29399i −0.245732 0.338221i
\(246\) 5.24195 + 2.20624i 0.334214 + 0.140665i
\(247\) 1.06593i 0.0678234i
\(248\) −1.23446 + 5.42919i −0.0783881 + 0.344754i
\(249\) −0.918843 + 0.215084i −0.0582293 + 0.0136304i
\(250\) −0.809017 0.587785i −0.0511667 0.0371748i
\(251\) 12.2543 8.90328i 0.773485 0.561970i −0.129531 0.991575i \(-0.541347\pi\)
0.903017 + 0.429605i \(0.141347\pi\)
\(252\) −1.41654 1.44908i −0.0892334 0.0912834i
\(253\) −9.31703 −0.585757
\(254\) 5.95449 0.373618
\(255\) −1.82704 + 1.10539i −0.114413 + 0.0692221i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −15.0377 4.88604i −0.938025 0.304783i −0.200185 0.979758i \(-0.564154\pi\)
−0.737840 + 0.674975i \(0.764154\pi\)
\(258\) −0.243102 0.102317i −0.0151348 0.00636997i
\(259\) −3.14180 + 1.02083i −0.195222 + 0.0634315i
\(260\) 1.16135 + 0.843769i 0.0720238 + 0.0523283i
\(261\) −5.78772 + 11.0471i −0.358251 + 0.683799i
\(262\) −5.71248 + 17.5812i −0.352918 + 1.08617i
\(263\) 0.832004 0.604486i 0.0513036 0.0372742i −0.561838 0.827247i \(-0.689906\pi\)
0.613141 + 0.789973i \(0.289906\pi\)
\(264\) −1.90569 1.64642i −0.117287 0.101330i
\(265\) −3.85086 1.25122i −0.236557 0.0768619i
\(266\) 0.294816 + 0.405780i 0.0180764 + 0.0248800i
\(267\) −3.96555 1.66903i −0.242688 0.102143i
\(268\) 1.90270 + 5.85592i 0.116226 + 0.357707i
\(269\) −0.178030 0.129346i −0.0108547 0.00788637i 0.582345 0.812942i \(-0.302135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(270\) −1.90643 4.83379i −0.116021 0.294175i
\(271\) 18.8372 + 6.12058i 1.14428 + 0.371799i 0.818986 0.573814i \(-0.194537\pi\)
0.325294 + 0.945613i \(0.394537\pi\)
\(272\) 0.380979 + 1.17253i 0.0231003 + 0.0710953i
\(273\) −0.382789 1.63528i −0.0231674 0.0989715i
\(274\) 0.748593i 0.0452242i
\(275\) 0.449310 + 1.38283i 0.0270944 + 0.0833881i
\(276\) −7.25586 + 8.39849i −0.436752 + 0.505530i
\(277\) −0.610742 + 0.840614i −0.0366959 + 0.0505076i −0.826971 0.562245i \(-0.809938\pi\)
0.790275 + 0.612753i \(0.209938\pi\)
\(278\) −11.7150 −0.702621
\(279\) 16.2391 3.91053i 0.972208 0.234117i
\(280\) 0.675476 0.0403674
\(281\) −1.60551 + 2.20979i −0.0957765 + 0.131825i −0.854216 0.519919i \(-0.825962\pi\)
0.758439 + 0.651744i \(0.225962\pi\)
\(282\) 9.99411 11.5679i 0.595140 0.688861i
\(283\) −2.88850 8.88990i −0.171704 0.528450i 0.827764 0.561077i \(-0.189613\pi\)
−0.999468 + 0.0326269i \(0.989613\pi\)
\(284\) 1.97573i 0.117238i
\(285\) 0.293135 + 1.25228i 0.0173638 + 0.0741784i
\(286\) −0.644987 1.98507i −0.0381389 0.117379i
\(287\) 2.10942 + 0.685391i 0.124515 + 0.0404574i
\(288\) −2.96820 + 0.435626i −0.174903 + 0.0256695i
\(289\) 12.5236 + 9.09893i 0.736682 + 0.535231i
\(290\) −1.28463 3.95367i −0.0754359 0.232168i
\(291\) −7.38905 3.10991i −0.433154 0.182306i
\(292\) 3.58724 + 4.93742i 0.209928 + 0.288941i
\(293\) 21.8754 + 7.10774i 1.27797 + 0.415239i 0.867866 0.496799i \(-0.165491\pi\)
0.410107 + 0.912037i \(0.365491\pi\)
\(294\) 8.57657 + 7.40971i 0.500196 + 0.432143i
\(295\) −5.42234 + 3.93956i −0.315701 + 0.229370i
\(296\) −1.51128 + 4.65124i −0.0878413 + 0.270348i
\(297\) −1.88860 + 7.31534i −0.109588 + 0.424479i
\(298\) −17.5493 12.7503i −1.01660 0.738606i
\(299\) −8.74832 + 2.84250i −0.505928 + 0.164386i
\(300\) 1.59642 + 0.671902i 0.0921692 + 0.0387923i
\(301\) −0.0978268 0.0317858i −0.00563864 0.00183211i
\(302\) −2.57677 + 7.93049i −0.148277 + 0.456349i
\(303\) 16.3716 9.90510i 0.940523 0.569033i
\(304\) 0.742546 0.0425879
\(305\) 0.125726 0.00719906
\(306\) 2.64485 2.58546i 0.151196 0.147801i
\(307\) −18.1154 + 13.1616i −1.03390 + 0.751172i −0.969085 0.246726i \(-0.920645\pi\)
−0.0648138 + 0.997897i \(0.520645\pi\)
\(308\) −0.794569 0.577288i −0.0452747 0.0328940i
\(309\) 21.4323 5.01691i 1.21924 0.285402i
\(310\) −2.85175 + 4.78200i −0.161969 + 0.271599i
\(311\) 11.5275i 0.653662i −0.945083 0.326831i \(-0.894019\pi\)
0.945083 0.326831i \(-0.105981\pi\)
\(312\) −2.29167 0.964519i −0.129740 0.0546051i
\(313\) −1.34110 1.84587i −0.0758035 0.104335i 0.769432 0.638729i \(-0.220540\pi\)
−0.845235 + 0.534395i \(0.820540\pi\)
\(314\) 6.06845 1.97176i 0.342462 0.111273i
\(315\) −0.899416 1.81589i −0.0506764 0.102314i
\(316\) 6.13203i 0.344954i
\(317\) 8.64657 2.80944i 0.485639 0.157794i −0.0559557 0.998433i \(-0.517821\pi\)
0.541595 + 0.840639i \(0.317821\pi\)
\(318\) 6.98828 + 0.589932i 0.391883 + 0.0330818i
\(319\) −1.86785 + 5.74864i −0.104579 + 0.321862i
\(320\) 0.587785 0.809017i 0.0328582 0.0452254i
\(321\) 7.70340 4.66070i 0.429962 0.260135i
\(322\) −2.54415 + 3.50172i −0.141780 + 0.195143i
\(323\) −0.740628 + 0.538097i −0.0412096 + 0.0299405i
\(324\) 5.12335 + 7.39941i 0.284631 + 0.411078i
\(325\) 0.843769 + 1.16135i 0.0468039 + 0.0644200i
\(326\) −12.3358 16.9787i −0.683215 0.940364i
\(327\) 1.09190 12.9346i 0.0603824 0.715284i
\(328\) 2.65646 1.93003i 0.146679 0.106568i
\(329\) 3.50426 4.82320i 0.193196 0.265912i
\(330\) −1.30365 2.15472i −0.0717634 0.118614i
\(331\) −15.6231 + 21.5034i −0.858723 + 1.18193i 0.123149 + 0.992388i \(0.460701\pi\)
−0.981872 + 0.189543i \(0.939299\pi\)
\(332\) −0.168363 + 0.518168i −0.00924012 + 0.0284382i
\(333\) 14.5163 2.13047i 0.795489 0.116749i
\(334\) −3.53793 + 1.14954i −0.193587 + 0.0629002i
\(335\) 6.15728i 0.336408i
\(336\) −1.13916 + 0.266658i −0.0621465 + 0.0145474i
\(337\) 20.1667 6.55255i 1.09855 0.356940i 0.297005 0.954876i \(-0.404012\pi\)
0.801544 + 0.597936i \(0.204012\pi\)
\(338\) 6.42997 + 8.85010i 0.349744 + 0.481382i
\(339\) 2.01797 4.79464i 0.109601 0.260409i
\(340\) 1.23288i 0.0668620i
\(341\) 7.44142 3.18789i 0.402976 0.172634i
\(342\) −0.988722 1.99620i −0.0534640 0.107942i
\(343\) 7.40126 + 5.37733i 0.399631 + 0.290349i
\(344\) −0.123197 + 0.0895077i −0.00664232 + 0.00482593i
\(345\) −9.49601 + 5.74526i −0.511248 + 0.309314i
\(346\) −1.38793 −0.0746158
\(347\) −8.19685 −0.440030 −0.220015 0.975496i \(-0.570611\pi\)
−0.220015 + 0.975496i \(0.570611\pi\)
\(348\) 3.72727 + 6.16059i 0.199803 + 0.330242i
\(349\) −4.72574 + 14.5443i −0.252963 + 0.778540i 0.741261 + 0.671217i \(0.234228\pi\)
−0.994224 + 0.107323i \(0.965772\pi\)
\(350\) 0.642416 + 0.208734i 0.0343386 + 0.0111573i
\(351\) 0.458492 + 7.44500i 0.0244725 + 0.397385i
\(352\) −1.38283 + 0.449310i −0.0737053 + 0.0239483i
\(353\) −8.36924 6.08061i −0.445450 0.323638i 0.342347 0.939574i \(-0.388778\pi\)
−0.787797 + 0.615935i \(0.788778\pi\)
\(354\) 7.58935 8.78449i 0.403369 0.466891i
\(355\) 0.610533 1.87903i 0.0324037 0.0997284i
\(356\) −2.00962 + 1.46008i −0.106510 + 0.0773839i
\(357\) 0.942985 1.09148i 0.0499080 0.0577674i
\(358\) −23.5792 7.66133i −1.24620 0.404914i
\(359\) 18.0971 + 24.9085i 0.955128 + 1.31462i 0.949212 + 0.314638i \(0.101883\pi\)
0.00591586 + 0.999983i \(0.498117\pi\)
\(360\) −2.95754 0.502920i −0.155876 0.0265062i
\(361\) −5.70094 17.5457i −0.300049 0.923457i
\(362\) −2.80215 2.03588i −0.147278 0.107004i
\(363\) 1.29465 15.3363i 0.0679513 0.804945i
\(364\) −0.922191 0.299638i −0.0483360 0.0157053i
\(365\) 1.88593 + 5.80428i 0.0987139 + 0.303810i
\(366\) −0.212032 + 0.0496329i −0.0110831 + 0.00259435i
\(367\) 8.26478i 0.431418i 0.976458 + 0.215709i \(0.0692063\pi\)
−0.976458 + 0.215709i \(0.930794\pi\)
\(368\) 1.98014 + 6.09424i 0.103222 + 0.317684i
\(369\) −8.72570 4.57151i −0.454242 0.237983i
\(370\) −2.87462 + 3.95658i −0.149445 + 0.205693i
\(371\) 2.73503 0.141995
\(372\) 2.92158 9.19045i 0.151477 0.476503i
\(373\) 28.4252 1.47180 0.735902 0.677088i \(-0.236758\pi\)
0.735902 + 0.677088i \(0.236758\pi\)
\(374\) 1.05366 1.45024i 0.0544836 0.0749903i
\(375\) 1.31065 + 1.13234i 0.0676819 + 0.0584736i
\(376\) −2.72741 8.39411i −0.140655 0.432893i
\(377\) 5.96760i 0.307347i
\(378\) 2.23369 + 2.70737i 0.114889 + 0.139252i
\(379\) −7.55174 23.2419i −0.387907 1.19385i −0.934350 0.356358i \(-0.884018\pi\)
0.546443 0.837496i \(-0.315982\pi\)
\(380\) 0.706203 + 0.229459i 0.0362274 + 0.0117710i
\(381\) −10.2769 0.867550i −0.526503 0.0444460i
\(382\) −4.13739 3.00599i −0.211687 0.153800i
\(383\) −5.96140 18.3473i −0.304613 0.937503i −0.979821 0.199876i \(-0.935946\pi\)
0.675208 0.737627i \(-0.264054\pi\)
\(384\) −0.671902 + 1.59642i −0.0342879 + 0.0814668i
\(385\) −0.577288 0.794569i −0.0294213 0.0404950i
\(386\) 16.7430 + 5.44011i 0.852194 + 0.276895i
\(387\) 0.404665 + 0.212009i 0.0205703 + 0.0107770i
\(388\) −3.74455 + 2.72058i −0.190101 + 0.138116i
\(389\) −3.27088 + 10.0667i −0.165840 + 0.510404i −0.999097 0.0424821i \(-0.986473\pi\)
0.833257 + 0.552886i \(0.186473\pi\)
\(390\) −1.88145 1.62548i −0.0952709 0.0823092i
\(391\) −6.39131 4.64356i −0.323223 0.234835i
\(392\) 6.22346 2.02212i 0.314332 0.102133i
\(393\) 12.4208 29.5113i 0.626545 1.48865i
\(394\) −0.343418 0.111583i −0.0173012 0.00562149i
\(395\) 1.89490 5.83191i 0.0953429 0.293435i
\(396\) 3.04917 + 3.11922i 0.153227 + 0.156747i
\(397\) 1.24357 0.0624130 0.0312065 0.999513i \(-0.490065\pi\)
0.0312065 + 0.999513i \(0.490065\pi\)
\(398\) −17.6261 −0.883517
\(399\) −0.449706 0.743294i −0.0225135 0.0372113i
\(400\) 0.809017 0.587785i 0.0404508 0.0293893i
\(401\) −22.8298 16.5868i −1.14007 0.828307i −0.152938 0.988236i \(-0.548874\pi\)
−0.987129 + 0.159929i \(0.948874\pi\)
\(402\) −2.43071 10.3840i −0.121233 0.517908i
\(403\) 6.01462 5.26359i 0.299609 0.262198i
\(404\) 11.0475i 0.549632i
\(405\) 2.58605 + 8.62046i 0.128502 + 0.428354i
\(406\) 1.65053 + 2.27176i 0.0819144 + 0.112745i
\(407\) 6.76290 2.19740i 0.335224 0.108921i
\(408\) −0.486702 2.07920i −0.0240954 0.102936i
\(409\) 25.0704i 1.23965i −0.784740 0.619825i \(-0.787204\pi\)
0.784740 0.619825i \(-0.212796\pi\)
\(410\) 3.12286 1.01468i 0.154227 0.0501114i
\(411\) −0.109068 + 1.29201i −0.00537991 + 0.0637300i
\(412\) 3.92712 12.0864i 0.193475 0.595456i
\(413\) 2.66108 3.66266i 0.130943 0.180228i
\(414\) 13.7466 13.4379i 0.675609 0.660437i
\(415\) −0.320246 + 0.440780i −0.0157202 + 0.0216370i
\(416\) −1.16135 + 0.843769i −0.0569398 + 0.0413692i
\(417\) 20.2191 + 1.70685i 0.990135 + 0.0835846i
\(418\) −0.634608 0.873463i −0.0310397 0.0427225i
\(419\) 5.69308 + 7.83585i 0.278125 + 0.382806i 0.925112 0.379695i \(-0.123971\pi\)
−0.646987 + 0.762501i \(0.723971\pi\)
\(420\) −1.16581 0.0984147i −0.0568858 0.00480215i
\(421\) 29.4506 21.3971i 1.43534 1.04283i 0.446345 0.894861i \(-0.352726\pi\)
0.988992 0.147972i \(-0.0472745\pi\)
\(422\) −4.52050 + 6.22193i −0.220054 + 0.302879i
\(423\) −18.9344 + 18.5091i −0.920620 + 0.899945i
\(424\) 2.37996 3.27574i 0.115581 0.159084i
\(425\) −0.380979 + 1.17253i −0.0184802 + 0.0568763i
\(426\) −0.287857 + 3.40993i −0.0139467 + 0.165212i
\(427\) −0.0807684 + 0.0262433i −0.00390866 + 0.00127000i
\(428\) 5.19822i 0.251265i
\(429\) 0.823973 + 3.52002i 0.0397818 + 0.169948i
\(430\) −0.144826 + 0.0470570i −0.00698415 + 0.00226929i
\(431\) −18.8162 25.8982i −0.906342 1.24747i −0.968400 0.249400i \(-0.919766\pi\)
0.0620582 0.998073i \(-0.480234\pi\)
\(432\) 5.18633 0.319394i 0.249527 0.0153669i
\(433\) 8.92346i 0.428834i 0.976742 + 0.214417i \(0.0687851\pi\)
−0.976742 + 0.214417i \(0.931215\pi\)
\(434\) 0.833845 3.66729i 0.0400259 0.176035i
\(435\) 1.64111 + 7.01086i 0.0786854 + 0.336145i
\(436\) −6.06305 4.40507i −0.290368 0.210964i
\(437\) −3.84941 + 2.79676i −0.184142 + 0.133787i
\(438\) −5.47190 9.04420i −0.261458 0.432149i
\(439\) 5.06569 0.241772 0.120886 0.992666i \(-0.461426\pi\)
0.120886 + 0.992666i \(0.461426\pi\)
\(440\) −1.45400 −0.0693167
\(441\) −13.7228 14.0381i −0.653468 0.668480i
\(442\) 0.546898 1.68318i 0.0260133 0.0800607i
\(443\) −17.6492 5.73459i −0.838541 0.272459i −0.141902 0.989881i \(-0.545322\pi\)
−0.696639 + 0.717422i \(0.745322\pi\)
\(444\) 3.28601 7.80744i 0.155947 0.370525i
\(445\) −2.36245 + 0.767608i −0.111991 + 0.0363881i
\(446\) −3.84141 2.79095i −0.181896 0.132155i
\(447\) 28.4309 + 24.5628i 1.34473 + 1.16178i
\(448\) −0.208734 + 0.642416i −0.00986173 + 0.0303513i
\(449\) 4.60627 3.34665i 0.217383 0.157938i −0.473765 0.880651i \(-0.657105\pi\)
0.691148 + 0.722713i \(0.257105\pi\)
\(450\) −2.65738 1.39224i −0.125270 0.0656307i
\(451\) −4.54064 1.47534i −0.213810 0.0694711i
\(452\) −1.76534 2.42978i −0.0830346 0.114287i
\(453\) 5.60273 13.3119i 0.263239 0.625448i
\(454\) −5.41370 16.6617i −0.254078 0.781970i
\(455\) −0.784463 0.569945i −0.0367762 0.0267195i
\(456\) −1.28157 0.108187i −0.0600149 0.00506630i
\(457\) 17.2459 + 5.60353i 0.806729 + 0.262122i 0.683212 0.730220i \(-0.260583\pi\)
0.123517 + 0.992342i \(0.460583\pi\)
\(458\) 0.944660 + 2.90736i 0.0441411 + 0.135852i
\(459\) −4.94148 + 4.07692i −0.230648 + 0.190294i
\(460\) 6.40787i 0.298768i
\(461\) −7.64593 23.5317i −0.356106 1.09598i −0.955365 0.295427i \(-0.904538\pi\)
0.599259 0.800555i \(-0.295462\pi\)
\(462\) 1.28725 + 1.11211i 0.0598881 + 0.0517402i
\(463\) 12.9279 17.7938i 0.600812 0.826947i −0.394970 0.918694i \(-0.629245\pi\)
0.995782 + 0.0917471i \(0.0292451\pi\)
\(464\) 4.15714 0.192990
\(465\) 5.61859 7.83782i 0.260556 0.363470i
\(466\) 15.0108 0.695360
\(467\) −11.7220 + 16.1339i −0.542429 + 0.746589i −0.988961 0.148179i \(-0.952659\pi\)
0.446532 + 0.894768i \(0.352659\pi\)
\(468\) 3.81469 + 1.99856i 0.176334 + 0.0923836i
\(469\) −1.28523 3.95553i −0.0593464 0.182650i
\(470\) 8.82609i 0.407117i
\(471\) −10.7609 + 2.51893i −0.495835 + 0.116066i
\(472\) −2.07115 6.37434i −0.0953323 0.293403i
\(473\) 0.210577 + 0.0684208i 0.00968236 + 0.00314599i
\(474\) −0.893418 + 10.5834i −0.0410361 + 0.486109i
\(475\) 0.600732 + 0.436457i 0.0275635 + 0.0200260i
\(476\) −0.257342 0.792018i −0.0117953 0.0363021i
\(477\) −11.9752 2.03634i −0.548307 0.0932377i
\(478\) −13.3858 18.4240i −0.612253 0.842694i
\(479\) 1.95285 + 0.634521i 0.0892281 + 0.0289920i 0.353291 0.935514i \(-0.385063\pi\)
−0.264063 + 0.964506i \(0.585063\pi\)
\(480\) −1.13234 + 1.31065i −0.0516839 + 0.0598229i
\(481\) 5.67969 4.12654i 0.258972 0.188154i
\(482\) −1.09763 + 3.37816i −0.0499957 + 0.153871i
\(483\) 4.90116 5.67298i 0.223011 0.258130i
\(484\) −7.18883 5.22299i −0.326765 0.237409i
\(485\) −4.40198 + 1.43029i −0.199884 + 0.0649462i
\(486\) −7.76438 13.5172i −0.352200 0.613152i
\(487\) −29.8884 9.71134i −1.35437 0.440063i −0.460213 0.887808i \(-0.652227\pi\)
−0.894161 + 0.447745i \(0.852227\pi\)
\(488\) −0.0388515 + 0.119573i −0.00175873 + 0.00541280i
\(489\) 18.8167 + 31.1011i 0.850920 + 1.40644i
\(490\) 6.54373 0.295616
\(491\) 38.9313 1.75694 0.878471 0.477795i \(-0.158564\pi\)
0.878471 + 0.477795i \(0.158564\pi\)
\(492\) −4.86602 + 2.94403i −0.219377 + 0.132727i
\(493\) −4.14640 + 3.01254i −0.186745 + 0.135678i
\(494\) −0.862354 0.626537i −0.0387991 0.0281892i
\(495\) 1.93604 + 3.90880i 0.0870187 + 0.175688i
\(496\) −3.66671 4.18989i −0.164640 0.188132i
\(497\) 1.33455i 0.0598630i
\(498\) 0.366075 0.869783i 0.0164042 0.0389759i
\(499\) 13.9783 + 19.2394i 0.625753 + 0.861275i 0.997756 0.0669568i \(-0.0213290\pi\)
−0.372003 + 0.928231i \(0.621329\pi\)
\(500\) 0.951057 0.309017i 0.0425325 0.0138197i
\(501\) 6.27364 1.46855i 0.280286 0.0656098i
\(502\) 15.1472i 0.676051i
\(503\) 19.9882 6.49456i 0.891230 0.289578i 0.172618 0.984989i \(-0.444777\pi\)
0.718613 + 0.695411i \(0.244777\pi\)
\(504\) 2.00495 0.294255i 0.0893075 0.0131072i
\(505\) 3.41386 10.5068i 0.151915 0.467545i
\(506\) 5.47641 7.53763i 0.243456 0.335089i
\(507\) −9.80814 16.2113i −0.435595 0.719970i
\(508\) −3.49996 + 4.81728i −0.155286 + 0.213732i
\(509\) 19.1956 13.9464i 0.850831 0.618165i −0.0745443 0.997218i \(-0.523750\pi\)
0.925375 + 0.379053i \(0.123750\pi\)
\(510\) 0.179626 2.12783i 0.00795398 0.0942221i
\(511\) −2.42310 3.33511i −0.107191 0.147536i
\(512\) 0.587785 + 0.809017i 0.0259767 + 0.0357538i
\(513\) 1.41561 + 3.58931i 0.0625006 + 0.158472i
\(514\) 12.7918 9.29380i 0.564223 0.409932i
\(515\) 7.46983 10.2813i 0.329160 0.453050i
\(516\) 0.225668 0.136533i 0.00993447 0.00601053i
\(517\) −7.54312 + 10.3822i −0.331746 + 0.456609i
\(518\) 1.02083 3.14180i 0.0448528 0.138043i
\(519\) 2.39545 + 0.202218i 0.105149 + 0.00887637i
\(520\) −1.36525 + 0.443596i −0.0598700 + 0.0194530i
\(521\) 33.6388i 1.47374i −0.676033 0.736872i \(-0.736302\pi\)
0.676033 0.736872i \(-0.263698\pi\)
\(522\) −5.53536 11.1757i −0.242276 0.489147i
\(523\) 4.85308 1.57686i 0.212210 0.0689514i −0.200983 0.979595i \(-0.564413\pi\)
0.413193 + 0.910643i \(0.364413\pi\)
\(524\) −10.8658 14.9555i −0.474674 0.653333i
\(525\) −1.07834 0.453854i −0.0470627 0.0198078i
\(526\) 1.02841i 0.0448410i
\(527\) 6.69352 + 1.52193i 0.291574 + 0.0662963i
\(528\) 2.45211 0.573995i 0.106715 0.0249799i
\(529\) −14.6115 10.6158i −0.635281 0.461559i
\(530\) 3.27574 2.37996i 0.142289 0.103379i
\(531\) −14.3784 + 14.0555i −0.623970 + 0.609958i
\(532\) −0.501572 −0.0217459
\(533\) −4.71358 −0.204168
\(534\) 3.68116 2.22717i 0.159299 0.0963790i
\(535\) 1.60634 4.94380i 0.0694481 0.213739i
\(536\) −5.85592 1.90270i −0.252937 0.0821843i
\(537\) 39.5793 + 16.6582i 1.70797 + 0.718854i
\(538\) 0.209286 0.0680012i 0.00902297 0.00293174i
\(539\) −7.69745 5.59253i −0.331553 0.240887i
\(540\) 5.03119 + 1.29890i 0.216508 + 0.0558958i
\(541\) 2.26819 6.98076i 0.0975170 0.300127i −0.890384 0.455209i \(-0.849564\pi\)
0.987901 + 0.155083i \(0.0495644\pi\)
\(542\) −16.0239 + 11.6420i −0.688285 + 0.500069i
\(543\) 4.53965 + 3.92202i 0.194815 + 0.168310i
\(544\) −1.17253 0.380979i −0.0502720 0.0163344i
\(545\) −4.40507 6.06305i −0.188692 0.259713i
\(546\) 1.54796 + 0.651509i 0.0662468 + 0.0278820i
\(547\) −11.5561 35.5661i −0.494105 1.52070i −0.818347 0.574724i \(-0.805109\pi\)
0.324243 0.945974i \(-0.394891\pi\)
\(548\) 0.605625 + 0.440012i 0.0258710 + 0.0187964i
\(549\) 0.373181 0.0547696i 0.0159270 0.00233751i
\(550\) −1.38283 0.449310i −0.0589643 0.0191587i
\(551\) 0.953894 + 2.93578i 0.0406372 + 0.125069i
\(552\) −2.52963 10.8066i −0.107668 0.459961i
\(553\) 4.14204i 0.176137i
\(554\) −0.321086 0.988201i −0.0136416 0.0419846i
\(555\) 5.53781 6.40989i 0.235067 0.272085i
\(556\) 6.88593 9.47767i 0.292028 0.401943i
\(557\) 21.4605 0.909311 0.454656 0.890667i \(-0.349762\pi\)
0.454656 + 0.890667i \(0.349762\pi\)
\(558\) −6.38141 + 15.4362i −0.270147 + 0.653468i
\(559\) 0.218598 0.00924571
\(560\) −0.397035 + 0.546471i −0.0167778 + 0.0230926i
\(561\) −2.02983 + 2.34948i −0.0856993 + 0.0991950i
\(562\) −0.844065 2.59776i −0.0356047 0.109580i
\(563\) 30.1922i 1.27245i 0.771504 + 0.636224i \(0.219505\pi\)
−0.771504 + 0.636224i \(0.780495\pi\)
\(564\) 3.48428 + 14.8849i 0.146714 + 0.626766i
\(565\) −0.928094 2.85638i −0.0390452 0.120169i
\(566\) 8.88990 + 2.88850i 0.373670 + 0.121413i
\(567\) −3.46070 4.99812i −0.145336 0.209901i
\(568\) 1.59840 + 1.16130i 0.0670672 + 0.0487272i
\(569\) −5.52646 17.0087i −0.231681 0.713041i −0.997544 0.0700375i \(-0.977688\pi\)
0.765863 0.643003i \(-0.222312\pi\)
\(570\) −1.18541 0.498918i −0.0496515 0.0208974i
\(571\) 13.6393 + 18.7729i 0.570787 + 0.785621i 0.992648 0.121040i \(-0.0386229\pi\)
−0.421861 + 0.906661i \(0.638623\pi\)
\(572\) 1.98507 + 0.644987i 0.0829998 + 0.0269683i
\(573\) 6.70281 + 5.79088i 0.280014 + 0.241918i
\(574\) −1.79438 + 1.30369i −0.0748959 + 0.0544150i
\(575\) −1.98014 + 6.09424i −0.0825775 + 0.254148i
\(576\) 1.39224 2.65738i 0.0580099 0.110724i
\(577\) −4.93093 3.58253i −0.205277 0.149143i 0.480397 0.877051i \(-0.340493\pi\)
−0.685674 + 0.727909i \(0.740493\pi\)
\(578\) −14.7224 + 4.78359i −0.612370 + 0.198971i
\(579\) −28.1043 11.8286i −1.16797 0.491578i
\(580\) 3.95367 + 1.28463i 0.164167 + 0.0533412i
\(581\) 0.113725 0.350010i 0.00471812 0.0145209i
\(582\) 6.85915 4.14991i 0.284321 0.172019i
\(583\) −5.88729 −0.243827
\(584\) −6.10298 −0.252543
\(585\) 3.01039 + 3.07955i 0.124464 + 0.127324i
\(586\) −18.6083 + 13.5197i −0.768702 + 0.558495i
\(587\) −5.99784 4.35768i −0.247557 0.179861i 0.457086 0.889422i \(-0.348893\pi\)
−0.704644 + 0.709561i \(0.748893\pi\)
\(588\) −11.0358 + 2.58327i −0.455107 + 0.106532i
\(589\) 2.11755 3.55085i 0.0872523 0.146310i
\(590\) 6.70238i 0.275932i
\(591\) 0.576452 + 0.242618i 0.0237121 + 0.00997997i
\(592\) −2.87462 3.95658i −0.118146 0.162614i
\(593\) 29.5074 9.58754i 1.21172 0.393713i 0.367663 0.929959i \(-0.380158\pi\)
0.844062 + 0.536246i \(0.180158\pi\)
\(594\) −4.80814 5.82776i −0.197281 0.239116i
\(595\) 0.832777i 0.0341405i
\(596\) 20.6304 6.70323i 0.845055 0.274575i
\(597\) 30.4211 + 2.56807i 1.24505 + 0.105104i
\(598\) 2.84250 8.74832i 0.116239 0.357745i
\(599\) −9.20229 + 12.6659i −0.375995 + 0.517513i −0.954518 0.298153i \(-0.903629\pi\)
0.578523 + 0.815666i \(0.303629\pi\)
\(600\) −1.48193 + 0.896594i −0.0604996 + 0.0366033i
\(601\) −9.12607 + 12.5610i −0.372260 + 0.512372i −0.953513 0.301350i \(-0.902563\pi\)
0.581253 + 0.813723i \(0.302563\pi\)
\(602\) 0.0832164 0.0604603i 0.00339165 0.00246418i
\(603\) 2.68227 + 18.2761i 0.109231 + 0.744259i
\(604\) −4.90131 6.74608i −0.199432 0.274494i
\(605\) −5.22299 7.18883i −0.212345 0.292268i
\(606\) −1.60958 + 19.0670i −0.0653848 + 0.774543i
\(607\) 29.8867 21.7140i 1.21306 0.881343i 0.217559 0.976047i \(-0.430191\pi\)
0.995505 + 0.0947046i \(0.0301907\pi\)
\(608\) −0.436457 + 0.600732i −0.0177007 + 0.0243629i
\(609\) −2.51768 4.16133i −0.102021 0.168626i
\(610\) −0.0739000 + 0.101715i −0.00299212 + 0.00411830i
\(611\) −3.91521 + 12.0498i −0.158393 + 0.487482i
\(612\) 0.537073 + 3.65942i 0.0217099 + 0.147923i
\(613\) −9.14581 + 2.97165i −0.369396 + 0.120024i −0.487832 0.872938i \(-0.662212\pi\)
0.118436 + 0.992962i \(0.462212\pi\)
\(614\) 22.3918i 0.903661i
\(615\) −5.53762 + 1.29626i −0.223298 + 0.0522701i
\(616\) 0.934071 0.303498i 0.0376348 0.0122283i
\(617\) 4.03198 + 5.54955i 0.162322 + 0.223416i 0.882428 0.470447i \(-0.155907\pi\)
−0.720107 + 0.693863i \(0.755907\pi\)
\(618\) −8.53882 + 20.2880i −0.343482 + 0.816101i
\(619\) 47.6373i 1.91470i 0.288925 + 0.957352i \(0.406702\pi\)
−0.288925 + 0.957352i \(0.593298\pi\)
\(620\) −2.19250 5.11790i −0.0880530 0.205540i
\(621\) −25.6833 + 21.1898i −1.03064 + 0.850317i
\(622\) 9.32591 + 6.77567i 0.373935 + 0.271680i
\(623\) 1.35745 0.986247i 0.0543852 0.0395131i
\(624\) 2.12732 1.28707i 0.0851609 0.0515239i
\(625\) 1.00000 0.0400000
\(626\) 2.28162 0.0911918
\(627\) 0.968017 + 1.59998i 0.0386589 + 0.0638971i
\(628\) −1.97176 + 6.06845i −0.0786817 + 0.242157i
\(629\) 5.73440 + 1.86322i 0.228645 + 0.0742914i
\(630\) 1.99775 + 0.339710i 0.0795923 + 0.0135344i
\(631\) −12.4918 + 4.05882i −0.497289 + 0.161579i −0.546914 0.837189i \(-0.684197\pi\)
0.0496247 + 0.998768i \(0.484197\pi\)
\(632\) 4.96092 + 3.60432i 0.197335 + 0.143372i
\(633\) 8.70850 10.0799i 0.346132 0.400639i
\(634\) −2.80944 + 8.64657i −0.111577 + 0.343399i
\(635\) −4.81728 + 3.49996i −0.191168 + 0.138892i
\(636\) −4.58487 + 5.30688i −0.181802 + 0.210432i
\(637\) −8.93381 2.90277i −0.353970 0.115012i
\(638\) −3.55285 4.89008i −0.140659 0.193600i
\(639\) 0.993632 5.84330i 0.0393075 0.231157i
\(640\) 0.309017 + 0.951057i 0.0122150 + 0.0375938i
\(641\) −26.2693 19.0858i −1.03758 0.753843i −0.0677645 0.997701i \(-0.521587\pi\)
−0.969811 + 0.243859i \(0.921587\pi\)
\(642\) −0.757365 + 8.97167i −0.0298908 + 0.354084i
\(643\) −19.3064 6.27304i −0.761371 0.247385i −0.0975043 0.995235i \(-0.531086\pi\)
−0.663867 + 0.747851i \(0.731086\pi\)
\(644\) −1.33754 4.11651i −0.0527063 0.162213i
\(645\) 0.256814 0.0601154i 0.0101120 0.00236704i
\(646\) 0.915466i 0.0360185i
\(647\) 3.46555 + 10.6659i 0.136245 + 0.419318i 0.995782 0.0917558i \(-0.0292479\pi\)
−0.859537 + 0.511074i \(0.829248\pi\)
\(648\) −8.99768 0.204385i −0.353462 0.00802902i
\(649\) −5.72811 + 7.88407i −0.224848 + 0.309477i
\(650\) −1.43551 −0.0563052
\(651\) −1.97346 + 6.20793i −0.0773459 + 0.243308i
\(652\) 20.9869 0.821909
\(653\) −9.09720 + 12.5212i −0.356001 + 0.489993i −0.949029 0.315189i \(-0.897932\pi\)
0.593028 + 0.805182i \(0.297932\pi\)
\(654\) 9.82249 + 8.48612i 0.384090 + 0.331834i
\(655\) −5.71248 17.5812i −0.223205 0.686955i
\(656\) 3.28357i 0.128202i
\(657\) 8.12631 + 16.4067i 0.317037 + 0.640088i
\(658\) 1.84230 + 5.67002i 0.0718203 + 0.221040i
\(659\) −37.9456 12.3293i −1.47815 0.480280i −0.544591 0.838702i \(-0.683315\pi\)
−0.933560 + 0.358421i \(0.883315\pi\)
\(660\) 2.50947 + 0.211843i 0.0976811 + 0.00824598i
\(661\) −1.00974 0.733622i −0.0392745 0.0285346i 0.567975 0.823046i \(-0.307727\pi\)
−0.607249 + 0.794511i \(0.707727\pi\)
\(662\) −8.21355 25.2787i −0.319229 0.982485i
\(663\) −1.18913 + 2.82534i −0.0461821 + 0.109727i
\(664\) −0.320246 0.440780i −0.0124279 0.0171056i
\(665\) −0.477023 0.154994i −0.0184982 0.00601042i
\(666\) −6.80888 + 12.9962i −0.263839 + 0.503592i
\(667\) −21.5509 + 15.6577i −0.834455 + 0.606267i
\(668\) 1.14954 3.53793i 0.0444772 0.136887i
\(669\) 6.22331 + 5.37662i 0.240607 + 0.207872i
\(670\) −4.98134 3.61916i −0.192446 0.139820i
\(671\) 0.173858 0.0564900i 0.00671173 0.00218077i
\(672\) 0.453854 1.07834i 0.0175078 0.0415979i
\(673\) −26.0905 8.47732i −1.00572 0.326777i −0.240568 0.970632i \(-0.577334\pi\)
−0.765147 + 0.643855i \(0.777334\pi\)
\(674\) −6.55255 + 20.1667i −0.252395 + 0.776791i
\(675\) 4.38356 + 2.79005i 0.168723 + 0.107389i
\(676\) −10.9393 −0.420743
\(677\) −11.9878 −0.460728 −0.230364 0.973105i \(-0.573992\pi\)
−0.230364 + 0.973105i \(0.573992\pi\)
\(678\) 2.69281 + 4.45079i 0.103417 + 0.170932i
\(679\) 2.52935 1.83768i 0.0970677 0.0705238i
\(680\) −0.997417 0.724666i −0.0382492 0.0277897i
\(681\) 6.91602 + 29.5453i 0.265022 + 1.13218i
\(682\) −1.79490 + 7.89404i −0.0687302 + 0.302278i
\(683\) 19.2763i 0.737589i 0.929511 + 0.368794i \(0.120229\pi\)
−0.929511 + 0.368794i \(0.879771\pi\)
\(684\) 2.19611 + 0.373441i 0.0839704 + 0.0142789i
\(685\) 0.440012 + 0.605625i 0.0168120 + 0.0231397i
\(686\) −8.70071 + 2.82703i −0.332194 + 0.107937i
\(687\) −1.20681 5.15549i −0.0460425 0.196694i
\(688\) 0.152280i 0.00580560i
\(689\) −5.52793 + 1.79613i −0.210598 + 0.0684273i
\(690\) 0.933606 11.0594i 0.0355418 0.421025i
\(691\) −9.71725 + 29.9066i −0.369662 + 1.13770i 0.577348 + 0.816498i \(0.304087\pi\)
−0.947010 + 0.321204i \(0.895913\pi\)
\(692\) 0.815807 1.12286i 0.0310123 0.0426848i
\(693\) −2.05964 2.10696i −0.0782393 0.0800368i
\(694\) 4.81799 6.63139i 0.182888 0.251724i
\(695\) 9.47767 6.88593i 0.359508 0.261198i
\(696\) −7.17486 0.605682i −0.271962 0.0229583i
\(697\) −2.37949 3.27509i −0.0901297 0.124053i
\(698\) −8.98889 12.3721i −0.340234 0.468293i
\(699\) −25.9073 2.18702i −0.979902 0.0827208i
\(700\) −0.546471 + 0.397035i −0.0206547 + 0.0150065i
\(701\) 27.8064 38.2723i 1.05023 1.44552i 0.161630 0.986851i \(-0.448325\pi\)
0.888605 0.458673i \(-0.151675\pi\)
\(702\) −6.29263 4.00513i −0.237500 0.151164i
\(703\) 2.13454 2.93794i 0.0805057 0.110807i
\(704\) 0.449310 1.38283i 0.0169340 0.0521175i
\(705\) −1.28593 + 15.2331i −0.0484311 + 0.573710i
\(706\) 9.83864 3.19677i 0.370282 0.120312i
\(707\) 7.46230i 0.280649i
\(708\) 2.64590 + 11.3033i 0.0994389 + 0.424804i
\(709\) −36.9322 + 12.0000i −1.38702 + 0.450670i −0.904970 0.425475i \(-0.860107\pi\)
−0.482048 + 0.876145i \(0.660107\pi\)
\(710\) 1.16130 + 1.59840i 0.0435829 + 0.0599867i
\(711\) 3.08392 18.1358i 0.115656 0.680144i
\(712\) 2.48403i 0.0930930i
\(713\) 34.7895 + 7.91023i 1.30288 + 0.296241i
\(714\) 0.328756 + 1.40445i 0.0123034 + 0.0525601i
\(715\) 1.68860 + 1.22684i 0.0631500 + 0.0458812i
\(716\) 20.0576 14.5727i 0.749589 0.544608i
\(717\) 20.4184 + 33.7485i 0.762540 + 1.26036i
\(718\) −30.7886 −1.14902
\(719\) −34.4064 −1.28314 −0.641572 0.767063i \(-0.721717\pi\)
−0.641572 + 0.767063i \(0.721717\pi\)
\(720\) 2.14527 2.09709i 0.0799496 0.0781541i
\(721\) −2.65267 + 8.16409i −0.0987908 + 0.304047i
\(722\) 17.5457 + 5.70094i 0.652983 + 0.212167i
\(723\) 2.38660 5.67048i 0.0887587 0.210888i
\(724\) 3.29413 1.07033i 0.122425 0.0397784i
\(725\) 3.36320 + 2.44350i 0.124906 + 0.0907495i
\(726\) 11.6463 + 10.0618i 0.432236 + 0.373429i
\(727\) 3.78771 11.6574i 0.140478 0.432348i −0.855924 0.517102i \(-0.827011\pi\)
0.996402 + 0.0847545i \(0.0270106\pi\)
\(728\) 0.784463 0.569945i 0.0290741 0.0211236i
\(729\) 11.4312 + 24.4607i 0.423379 + 0.905953i
\(730\) −5.80428 1.88593i −0.214826 0.0698012i
\(731\) 0.110352 + 0.151886i 0.00408151 + 0.00561771i
\(732\) 0.0844757 0.200711i 0.00312231 0.00741851i
\(733\) 0.391126 + 1.20376i 0.0144466 + 0.0444620i 0.958020 0.286702i \(-0.0925588\pi\)
−0.943573 + 0.331164i \(0.892559\pi\)
\(734\) −6.68635 4.85792i −0.246798 0.179309i
\(735\) −11.2939 0.953402i −0.416582 0.0351668i
\(736\) −6.09424 1.98014i −0.224637 0.0729889i
\(737\) 2.76653 + 8.51450i 0.101906 + 0.313636i
\(738\) 8.82727 4.37217i 0.324936 0.160942i
\(739\) 1.05733i 0.0388946i 0.999811 + 0.0194473i \(0.00619066\pi\)
−0.999811 + 0.0194473i \(0.993809\pi\)
\(740\) −1.51128 4.65124i −0.0555557 0.170983i
\(741\) 1.39706 + 1.20699i 0.0513224 + 0.0443399i
\(742\) −1.60761 + 2.21268i −0.0590171 + 0.0812301i
\(743\) 16.9609 0.622234 0.311117 0.950372i \(-0.399297\pi\)
0.311117 + 0.950372i \(0.399297\pi\)
\(744\) 5.71797 + 7.76562i 0.209631 + 0.284701i
\(745\) 21.6921 0.794738
\(746\) −16.7079 + 22.9965i −0.611721 + 0.841962i
\(747\) −0.758539 + 1.44783i −0.0277535 + 0.0529734i
\(748\) 0.553943 + 1.70486i 0.0202542 + 0.0623360i
\(749\) 3.51127i 0.128299i
\(750\) −1.68646 + 0.394770i −0.0615809 + 0.0144150i
\(751\) −2.28887 7.04441i −0.0835219 0.257054i 0.900571 0.434709i \(-0.143149\pi\)
−0.984093 + 0.177655i \(0.943149\pi\)
\(752\) 8.39411 + 2.72741i 0.306102 + 0.0994585i
\(753\) 2.20689 26.1427i 0.0804237 0.952692i
\(754\) −4.82789 3.50766i −0.175821 0.127742i
\(755\) −2.57677 7.93049i −0.0937784 0.288620i
\(756\) −3.50324 + 0.215743i −0.127412 + 0.00784650i
\(757\) 16.5507 + 22.7801i 0.601547 + 0.827958i 0.995849 0.0910230i \(-0.0290137\pi\)
−0.394302 + 0.918981i \(0.629014\pi\)
\(758\) 23.2419 + 7.55174i 0.844183 + 0.274292i
\(759\) −10.5500 + 12.2114i −0.382941 + 0.443246i
\(760\) −0.600732 + 0.436457i −0.0217908 + 0.0158320i
\(761\) −1.09866 + 3.38134i −0.0398265 + 0.122574i −0.968993 0.247088i \(-0.920526\pi\)
0.929167 + 0.369661i \(0.120526\pi\)
\(762\) 6.74249 7.80427i 0.244254 0.282719i
\(763\) 4.09545 + 2.97552i 0.148265 + 0.107721i
\(764\) 4.86380 1.58034i 0.175966 0.0571748i
\(765\) −0.620038 + 3.64628i −0.0224175 + 0.131832i
\(766\) 18.3473 + 5.96140i 0.662915 + 0.215394i
\(767\) −2.97314 + 9.15040i −0.107354 + 0.330402i
\(768\) −0.896594 1.48193i −0.0323531 0.0534746i
\(769\) −31.2687 −1.12758 −0.563789 0.825919i \(-0.690657\pi\)
−0.563789 + 0.825919i \(0.690657\pi\)
\(770\) 0.982141 0.0353939
\(771\) −23.4316 + 14.1765i −0.843869 + 0.510556i
\(772\) −14.2424 + 10.3477i −0.512595 + 0.372422i
\(773\) −39.7021 28.8453i −1.42798 1.03749i −0.990388 0.138320i \(-0.955830\pi\)
−0.437597 0.899171i \(-0.644170\pi\)
\(774\) −0.409375 + 0.202765i −0.0147147 + 0.00728823i
\(775\) −0.503674 5.54494i −0.0180925 0.199180i
\(776\) 4.62852i 0.166154i
\(777\) −2.21962 + 5.27374i −0.0796284 + 0.189194i
\(778\) −6.22158 8.56328i −0.223055 0.307008i
\(779\) −2.31887 + 0.753446i −0.0830820 + 0.0269950i
\(780\) 2.42093 0.566695i 0.0866831 0.0202909i
\(781\) 2.87270i 0.102793i
\(782\) 7.51344 2.44127i 0.268680 0.0872995i
\(783\) 7.92527 + 20.0947i 0.283226 + 0.718128i
\(784\) −2.02212 + 6.22346i −0.0722187 + 0.222266i
\(785\) −3.75051 + 5.16213i −0.133861 + 0.184244i
\(786\) 16.5744 + 27.3949i 0.591190 + 0.977145i
\(787\) 5.66316 7.79466i 0.201870 0.277850i −0.696065 0.717979i \(-0.745067\pi\)
0.897934 + 0.440129i \(0.145067\pi\)
\(788\) 0.292129 0.212244i 0.0104067 0.00756088i
\(789\) 0.149837 1.77495i 0.00533433 0.0631899i
\(790\) 3.60432 + 4.96092i 0.128236 + 0.176502i
\(791\) 1.19244 + 1.64126i 0.0423984 + 0.0583564i
\(792\) −4.31576 + 0.633400i −0.153354 + 0.0225069i
\(793\) 0.146012 0.106084i 0.00518503 0.00376715i
\(794\) −0.730952 + 1.00607i −0.0259405 + 0.0357041i
\(795\) −6.00039 + 3.63034i −0.212812 + 0.128755i
\(796\) 10.3604 14.2598i 0.367213 0.505426i
\(797\) −14.9203 + 45.9199i −0.528503 + 1.62657i 0.228779 + 0.973478i \(0.426527\pi\)
−0.757282 + 0.653088i \(0.773473\pi\)
\(798\) 0.865668 + 0.0730774i 0.0306443 + 0.00258691i
\(799\) −10.3489 + 3.36256i −0.366117 + 0.118959i
\(800\) 1.00000i 0.0353553i
\(801\) −6.67785 + 3.30756i −0.235950 + 0.116867i
\(802\) 26.8381 8.72022i 0.947685 0.307922i
\(803\) 5.21585 + 7.17900i 0.184063 + 0.253341i
\(804\) 9.82959 + 4.13709i 0.346663 + 0.145904i
\(805\) 4.32836i 0.152555i
\(806\) 0.723027 + 7.95979i 0.0254676 + 0.280371i
\(807\) −0.371117 + 0.0868718i −0.0130639 + 0.00305803i
\(808\) 8.93759 + 6.49354i 0.314423 + 0.228442i
\(809\) −1.73957 + 1.26387i −0.0611600 + 0.0444354i −0.617945 0.786221i \(-0.712035\pi\)
0.556785 + 0.830657i \(0.312035\pi\)
\(810\) −8.49414 2.97482i −0.298454 0.104524i
\(811\) −35.3789 −1.24232 −0.621160 0.783683i \(-0.713338\pi\)
−0.621160 + 0.783683i \(0.713338\pi\)
\(812\) −2.80805 −0.0985431
\(813\) 29.3520 17.7585i 1.02942 0.622818i
\(814\) −2.19740 + 6.76290i −0.0770188 + 0.237039i
\(815\) 19.9597 + 6.48529i 0.699157 + 0.227170i
\(816\) 1.96818 + 0.828372i 0.0689002 + 0.0289988i
\(817\) 0.107540 0.0349419i 0.00376236 0.00122246i
\(818\) 20.2823 + 14.7360i 0.709155 + 0.515232i
\(819\) −2.57673 1.34998i −0.0900382 0.0471722i
\(820\) −1.01468 + 3.12286i −0.0354341 + 0.109055i
\(821\) −16.9372 + 12.3056i −0.591112 + 0.429468i −0.842713 0.538363i \(-0.819043\pi\)
0.251601 + 0.967831i \(0.419043\pi\)
\(822\) −0.981146 0.847660i −0.0342214 0.0295655i
\(823\) 10.3124 + 3.35070i 0.359468 + 0.116798i 0.483182 0.875520i \(-0.339481\pi\)
−0.123715 + 0.992318i \(0.539481\pi\)
\(824\) 7.46983 + 10.2813i 0.260224 + 0.358167i
\(825\) 2.32119 + 0.976945i 0.0808134 + 0.0340128i
\(826\) 1.39901 + 4.30571i 0.0486778 + 0.149815i
\(827\) −32.4643 23.5867i −1.12889 0.820190i −0.143361 0.989670i \(-0.545791\pi\)
−0.985533 + 0.169481i \(0.945791\pi\)
\(828\) 2.79143 + 19.0199i 0.0970090 + 0.660985i
\(829\) −25.7783 8.37588i −0.895318 0.290906i −0.175015 0.984566i \(-0.555997\pi\)
−0.720303 + 0.693659i \(0.755997\pi\)
\(830\) −0.168363 0.518168i −0.00584397 0.0179859i
\(831\) 0.410188 + 1.75233i 0.0142293 + 0.0607876i
\(832\) 1.43551i 0.0497672i
\(833\) −2.49303 7.67275i −0.0863783 0.265845i
\(834\) −13.2654 + 15.3544i −0.459342 + 0.531678i
\(835\) 2.18656 3.00954i 0.0756691 0.104150i
\(836\) 1.07966 0.0373408
\(837\) 13.2628 25.7118i 0.458428 0.888731i
\(838\) −9.68564 −0.334585
\(839\) −23.8321 + 32.8020i −0.822774 + 1.13245i 0.166451 + 0.986050i \(0.446769\pi\)
−0.989225 + 0.146402i \(0.953231\pi\)
\(840\) 0.764866 0.885315i 0.0263904 0.0305463i
\(841\) −3.62112 11.1447i −0.124866 0.384299i
\(842\) 36.4030i 1.25453i
\(843\) 1.07830 + 4.60649i 0.0371385 + 0.158656i
\(844\) −2.37657 7.31432i −0.0818048 0.251769i
\(845\) −10.4039 3.38044i −0.357906 0.116291i
\(846\) −3.84487 26.1976i −0.132190 0.900693i
\(847\) 4.85588 + 3.52801i 0.166850 + 0.121224i
\(848\) 1.25122 + 3.85086i 0.0429671 + 0.132239i
\(849\) −14.9223 6.28053i −0.512133 0.215547i
\(850\) −0.724666 0.997417i −0.0248558 0.0342111i
\(851\) 29.8045 + 9.68408i 1.02169 + 0.331966i
\(852\) −2.58949 2.23719i −0.0887145 0.0766448i
\(853\) −10.3520 + 7.52118i −0.354446 + 0.257520i −0.750732 0.660607i \(-0.770299\pi\)
0.396286 + 0.918127i \(0.370299\pi\)
\(854\) 0.0262433 0.0807684i 0.000898026 0.00276384i
\(855\) 1.97323 + 1.03380i 0.0674829 + 0.0353552i
\(856\) 4.20545 + 3.05544i 0.143739 + 0.104433i
\(857\) 9.42017 3.06080i 0.321787 0.104555i −0.143670 0.989626i \(-0.545890\pi\)
0.465456 + 0.885071i \(0.345890\pi\)
\(858\) −3.33208 1.40241i −0.113755 0.0478775i
\(859\) −14.7538 4.79379i −0.503392 0.163562i 0.0463032 0.998927i \(-0.485256\pi\)
−0.549695 + 0.835366i \(0.685256\pi\)
\(860\) 0.0470570 0.144826i 0.00160463 0.00493854i
\(861\) 3.28688 1.98862i 0.112017 0.0677720i
\(862\) 32.0120 1.09033
\(863\) 26.9284 0.916653 0.458326 0.888784i \(-0.348449\pi\)
0.458326 + 0.888784i \(0.348449\pi\)
\(864\) −2.79005 + 4.38356i −0.0949195 + 0.149132i
\(865\) 1.12286 0.815807i 0.0381784 0.0277383i
\(866\) −7.21923 5.24508i −0.245319 0.178235i
\(867\) 26.1065 6.11105i 0.886622 0.207542i
\(868\) 2.47678 + 2.83017i 0.0840672 + 0.0960623i
\(869\) 8.91597i 0.302453i
\(870\) −6.63653 2.79319i −0.224999 0.0946980i
\(871\) 5.19532 + 7.15075i 0.176037 + 0.242294i
\(872\) 7.12755 2.31588i 0.241369 0.0784256i
\(873\) −12.4429 + 6.16302i −0.421129 + 0.208586i
\(874\) 4.75813i 0.160946i
\(875\) −0.642416 + 0.208734i −0.0217176 + 0.00705648i
\(876\) 10.5332 + 0.889186i 0.355884 + 0.0300428i
\(877\) 16.5931 51.0683i 0.560309 1.72445i −0.121186 0.992630i \(-0.538670\pi\)
0.681495 0.731823i \(-0.261330\pi\)
\(878\) −2.97754 + 4.09823i −0.100487 + 0.138308i
\(879\) 34.0861 20.6227i 1.14969 0.695586i
\(880\) 0.854639 1.17631i 0.0288099 0.0396534i
\(881\) −8.07539 + 5.86711i −0.272067 + 0.197668i −0.715450 0.698664i \(-0.753778\pi\)
0.443383 + 0.896332i \(0.353778\pi\)
\(882\) 19.4231 2.85062i 0.654011 0.0959854i
\(883\) −2.73934 3.77038i −0.0921862 0.126883i 0.760433 0.649417i \(-0.224987\pi\)
−0.852619 + 0.522534i \(0.824987\pi\)
\(884\) 1.04026 + 1.43180i 0.0349878 + 0.0481566i
\(885\) −0.976516 + 11.5677i −0.0328252 + 0.388844i
\(886\) 15.0133 10.9078i 0.504383 0.366456i
\(887\) −10.1362 + 13.9513i −0.340341 + 0.468439i −0.944541 0.328394i \(-0.893493\pi\)
0.604200 + 0.796833i \(0.293493\pi\)
\(888\) 4.38489 + 7.24753i 0.147147 + 0.243211i
\(889\) 2.36414 3.25396i 0.0792906 0.109134i
\(890\) 0.767608 2.36245i 0.0257303 0.0791896i
\(891\) 7.44935 + 10.7587i 0.249562 + 0.360431i
\(892\) 4.51585 1.46729i 0.151202 0.0491285i
\(893\) 6.55377i 0.219314i
\(894\) −36.5830 + 8.56340i −1.22352 + 0.286403i
\(895\) 23.5792 7.66133i 0.788165 0.256090i
\(896\) −0.397035 0.546471i −0.0132640 0.0182563i
\(897\) −6.18051 + 14.6847i −0.206361 + 0.490307i
\(898\) 5.69366i 0.190000i
\(899\) 11.8551 19.8794i 0.395390 0.663016i
\(900\) 2.68831 1.33153i 0.0896104 0.0443843i
\(901\) −4.03858 2.93420i −0.134545 0.0977523i
\(902\) 3.86250 2.80627i 0.128607 0.0934385i
\(903\) −0.152433 + 0.0922247i −0.00507266 + 0.00306905i
\(904\) 3.00338 0.0998908
\(905\) 3.46365 0.115136
\(906\) 7.47636 + 12.3572i 0.248385 + 0.410542i
\(907\) 12.4787 38.4055i 0.414348 1.27523i −0.498484 0.866899i \(-0.666110\pi\)
0.912833 0.408334i \(-0.133890\pi\)
\(908\) 16.6617 + 5.41370i 0.552937 + 0.179660i
\(909\) 5.55600 32.6734i 0.184281 1.08371i
\(910\) 0.922191 0.299638i 0.0305703 0.00993291i
\(911\) 46.3134 + 33.6486i 1.53443 + 1.11483i 0.953710 + 0.300727i \(0.0972292\pi\)
0.580721 + 0.814103i \(0.302771\pi\)
\(912\) 0.840812 0.973220i 0.0278421 0.0322265i
\(913\) −0.244800 + 0.753416i −0.00810169 + 0.0249344i
\(914\) −14.6702 + 10.6586i −0.485248 + 0.352554i
\(915\) 0.142364 0.164783i 0.00470642 0.00544757i
\(916\) −2.90736 0.944660i −0.0960620 0.0312124i
\(917\) 7.33957 + 10.1021i 0.242374 + 0.333599i
\(918\) −0.393773 6.39409i −0.0129965 0.211037i
\(919\) −2.66559 8.20384i −0.0879297 0.270620i 0.897417 0.441183i \(-0.145441\pi\)
−0.985347 + 0.170564i \(0.945441\pi\)
\(920\) −5.18407 3.76645i −0.170914 0.124176i
\(921\) −3.26242 + 38.6463i −0.107500 + 1.27344i
\(922\) 23.5317 + 7.64593i 0.774977 + 0.251805i
\(923\) −0.876423 2.69735i −0.0288478 0.0887844i
\(924\) −1.65634 + 0.387720i −0.0544897 + 0.0127550i
\(925\) 4.89060i 0.160802i
\(926\) 6.79662 + 20.9178i 0.223351 + 0.687403i
\(927\) 17.6931 33.7711i 0.581119 1.10919i
\(928\) −2.44350 + 3.36320i −0.0802120 + 0.110402i
\(929\) −29.4226 −0.965324 −0.482662 0.875807i \(-0.660330\pi\)
−0.482662 + 0.875807i \(0.660330\pi\)
\(930\) 3.03840 + 9.15249i 0.0996332 + 0.300122i
\(931\) −4.85902 −0.159248
\(932\) −8.82310 + 12.1440i −0.289010 + 0.397789i
\(933\) −15.1085 13.0530i −0.494630 0.427335i
\(934\) −6.16261 18.9666i −0.201647 0.620605i
\(935\) 1.79260i 0.0586242i
\(936\) −3.85909 + 1.91142i −0.126138 + 0.0624767i
\(937\) 2.31253 + 7.11725i 0.0755472 + 0.232510i 0.981698 0.190444i \(-0.0609929\pi\)
−0.906151 + 0.422955i \(0.860993\pi\)
\(938\) 3.95553 + 1.28523i 0.129153 + 0.0419643i
\(939\) −3.93787 0.332425i −0.128508 0.0108483i
\(940\) 7.14046 + 5.18784i 0.232896 + 0.169209i
\(941\) −1.72558 5.31080i −0.0562524 0.173127i 0.918983 0.394298i \(-0.129012\pi\)
−0.975235 + 0.221171i \(0.929012\pi\)
\(942\) 4.28723 10.1863i 0.139686 0.331888i
\(943\) −12.3674 17.0223i −0.402738 0.554321i
\(944\) 6.37434 + 2.07115i 0.207467 + 0.0674101i
\(945\) −3.39845 0.877376i −0.110551 0.0285411i
\(946\) −0.179128 + 0.130144i −0.00582395 + 0.00423135i
\(947\) −4.42399 + 13.6156i −0.143760 + 0.442449i −0.996849 0.0793164i \(-0.974726\pi\)
0.853089 + 0.521765i \(0.174726\pi\)
\(948\) −8.03697 6.94353i −0.261029 0.225515i
\(949\) 7.08769 + 5.14951i 0.230076 + 0.167160i
\(950\) −0.706203 + 0.229459i −0.0229122 + 0.00744464i
\(951\) 6.10862 14.5139i 0.198086 0.470645i
\(952\) 0.792018 + 0.257342i 0.0256695 + 0.00834051i
\(953\) 3.07800 9.47311i 0.0997062 0.306864i −0.888745 0.458401i \(-0.848422\pi\)
0.988452 + 0.151537i \(0.0484223\pi\)
\(954\) 8.68629 8.49121i 0.281229 0.274913i
\(955\) 5.11410 0.165488
\(956\) 22.7733 0.736542
\(957\) 5.41944 + 8.95749i 0.175186 + 0.289555i
\(958\) −1.66120 + 1.20693i −0.0536708 + 0.0389941i
\(959\) −0.409085 0.297217i −0.0132100 0.00959765i
\(960\) −0.394770 1.68646i −0.0127412 0.0544304i
\(961\) −30.4926 + 5.58569i −0.983633 + 0.180183i
\(962\) 7.02049i 0.226350i
\(963\) 2.61429 15.3740i 0.0842443 0.495419i
\(964\) −2.08782 2.87363i −0.0672441 0.0925535i
\(965\) −16.7430 + 5.44011i −0.538975 + 0.175123i
\(966\) 1.70871 + 7.29962i 0.0549767 + 0.234861i
\(967\) 48.4499i 1.55804i −0.626996 0.779022i \(-0.715716\pi\)
0.626996 0.779022i \(-0.284284\pi\)
\(968\) 8.45098 2.74589i 0.271625 0.0882563i
\(969\) −0.133381 + 1.58001i −0.00428480 + 0.0507574i
\(970\) 1.43029 4.40198i 0.0459239 0.141339i
\(971\) 9.49673 13.0711i 0.304765 0.419473i −0.628975 0.777426i \(-0.716525\pi\)
0.933740 + 0.357953i \(0.116525\pi\)
\(972\) 15.4994 + 1.66369i 0.497144 + 0.0533627i
\(973\) −4.65128 + 6.40193i −0.149113 + 0.205237i
\(974\) 25.4246 18.4721i 0.814658 0.591883i
\(975\) 2.47756 + 0.209149i 0.0793453 + 0.00669812i
\(976\) −0.0739000 0.101715i −0.00236548 0.00325580i
\(977\) −13.1094 18.0435i −0.419406 0.577263i 0.546075 0.837736i \(-0.316121\pi\)
−0.965481 + 0.260474i \(0.916121\pi\)
\(978\) −36.2215 3.05772i −1.15823 0.0977751i
\(979\) −2.92199 + 2.12295i −0.0933872 + 0.0678498i
\(980\) −3.84631 + 5.29399i −0.122866 + 0.169110i
\(981\) −15.7164 16.0774i −0.501785 0.513312i
\(982\) −22.8832 + 31.4960i −0.730233 + 1.00508i
\(983\) −18.0009 + 55.4010i −0.574139 + 1.76702i 0.0649529 + 0.997888i \(0.479310\pi\)
−0.639092 + 0.769130i \(0.720690\pi\)
\(984\) 0.478406 5.66715i 0.0152510 0.180662i
\(985\) 0.343418 0.111583i 0.0109422 0.00355534i
\(986\) 5.12523i 0.163221i
\(987\) −2.35354 10.0544i −0.0749141 0.320034i
\(988\) 1.01376 0.329390i 0.0322519 0.0104793i
\(989\) 0.573553 + 0.789428i 0.0182379 + 0.0251024i
\(990\) −4.30027 0.731245i −0.136671 0.0232405i
\(991\) 12.0194i 0.381808i 0.981609 + 0.190904i \(0.0611419\pi\)
−0.981609 + 0.190904i \(0.938858\pi\)
\(992\) 5.54494 0.503674i 0.176052 0.0159917i
\(993\) 10.4928 + 44.8255i 0.332980 + 1.42249i
\(994\) −1.07968 0.784432i −0.0342453 0.0248807i
\(995\) 14.2598 10.3604i 0.452067 0.328446i
\(996\) 0.488495 + 0.807407i 0.0154786 + 0.0255837i
\(997\) 27.5953 0.873951 0.436976 0.899473i \(-0.356050\pi\)
0.436976 + 0.899473i \(0.356050\pi\)
\(998\) −23.7812 −0.752782
\(999\) 13.6450 21.4383i 0.431710 0.678277i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 930.2.v.a.401.7 80
3.2 odd 2 inner 930.2.v.a.401.11 yes 80
31.15 odd 10 inner 930.2.v.a.821.11 yes 80
93.77 even 10 inner 930.2.v.a.821.7 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.v.a.401.7 80 1.1 even 1 trivial
930.2.v.a.401.11 yes 80 3.2 odd 2 inner
930.2.v.a.821.7 yes 80 93.77 even 10 inner
930.2.v.a.821.11 yes 80 31.15 odd 10 inner