Properties

Label 930.2.i.n.211.1
Level $930$
Weight $2$
Character 930.211
Analytic conductor $7.426$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(211,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.211");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.3636603.4
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 4x^{3} + 12x^{2} - 16x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(0.715814 + 1.86751i\) of defining polynomial
Character \(\chi\) \(=\) 930.211
Dual form 930.2.i.n.811.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.25941 - 3.91341i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.25941 - 3.91341i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.93163 - 3.34568i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.51882 + 6.09477i) q^{13} +(2.25941 + 3.91341i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-0.240592 - 0.416717i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.95044 + 6.84237i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.25941 - 3.91341i) q^{21} +(-1.93163 + 3.34568i) q^{22} +5.51882 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.51882 - 6.09477i) q^{26} -1.00000 q^{27} +(-2.25941 - 3.91341i) q^{28} +9.38207 q^{29} +1.00000 q^{30} +(5.12266 - 2.18136i) q^{31} -1.00000 q^{32} +3.86325 q^{33} +(0.240592 + 0.416717i) q^{34} +4.51882 q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.24059 + 2.14877i) q^{37} +(-3.95044 - 6.84237i) q^{38} -7.03763 q^{39} +(0.500000 - 0.866025i) q^{40} +(-4.08719 + 7.07922i) q^{41} +(-2.25941 + 3.91341i) q^{42} +(2.19104 + 3.79498i) q^{43} +(1.93163 - 3.34568i) q^{44} +(-0.500000 - 0.866025i) q^{45} -5.51882 q^{46} +10.5565 q^{47} +(0.500000 + 0.866025i) q^{48} +(-6.70985 + 11.6218i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.240592 - 0.416717i) q^{51} +(-3.51882 + 6.09477i) q^{52} +(0.827781 - 1.43376i) q^{53} +1.00000 q^{54} +(1.93163 + 3.34568i) q^{55} +(2.25941 + 3.91341i) q^{56} +(-3.95044 + 6.84237i) q^{57} -9.38207 q^{58} +(-6.77823 - 11.7402i) q^{59} -1.00000 q^{60} +5.90089 q^{61} +(-5.12266 + 2.18136i) q^{62} +4.51882 q^{63} +1.00000 q^{64} +(-3.51882 - 6.09477i) q^{65} -3.86325 q^{66} +(-1.24059 + 2.14877i) q^{67} +(-0.240592 - 0.416717i) q^{68} +(2.75941 + 4.77944i) q^{69} -4.51882 q^{70} +(-1.51882 + 2.63067i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-1.24059 - 2.14877i) q^{74} +(0.500000 - 0.866025i) q^{75} +(3.95044 + 6.84237i) q^{76} -17.4573 q^{77} +7.03763 q^{78} +(2.19104 + 3.79498i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.08719 - 7.07922i) q^{82} +(0.603846 - 1.04589i) q^{83} +(2.25941 - 3.91341i) q^{84} +0.481183 q^{85} +(-2.19104 - 3.79498i) q^{86} +(4.69104 + 8.12511i) q^{87} +(-1.93163 + 3.34568i) q^{88} -2.96237 q^{89} +(0.500000 + 0.866025i) q^{90} +31.8018 q^{91} +5.51882 q^{92} +(4.45044 + 3.34568i) q^{93} -10.5565 q^{94} -7.90089 q^{95} +(-0.500000 - 0.866025i) q^{96} -11.4573 q^{97} +(6.70985 - 11.6218i) q^{98} +(1.93163 + 3.34568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 6 q^{16} - 11 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 14 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} - 6 q^{27} - 4 q^{28} + 24 q^{29} + 6 q^{30} + 8 q^{31} - 6 q^{32} + 10 q^{33} + 11 q^{34} + 8 q^{35} - 3 q^{36} + 17 q^{37} + 2 q^{38} - 4 q^{39} + 3 q^{40} - 12 q^{41} - 4 q^{42} - 3 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} + 6 q^{47} + 3 q^{48} - 5 q^{49} + 3 q^{50} + 11 q^{51} - 2 q^{52} + 2 q^{53} + 6 q^{54} + 5 q^{55} + 4 q^{56} + 2 q^{57} - 24 q^{58} - 12 q^{59} - 6 q^{60} - 16 q^{61} - 8 q^{62} + 8 q^{63} + 6 q^{64} - 2 q^{65} - 10 q^{66} - 17 q^{67} - 11 q^{68} + 7 q^{69} - 8 q^{70} + 10 q^{71} + 3 q^{72} + 6 q^{73} - 17 q^{74} + 3 q^{75} - 2 q^{76} + 4 q^{77} + 4 q^{78} - 3 q^{79} - 3 q^{80} - 3 q^{81} + 12 q^{82} + 4 q^{84} + 22 q^{85} + 3 q^{86} + 12 q^{87} - 5 q^{88} - 56 q^{89} + 3 q^{90} + 88 q^{91} + 14 q^{92} + q^{93} - 6 q^{94} + 4 q^{95} - 3 q^{96} + 40 q^{97} + 5 q^{98} + 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 1.00000 0.500000
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −2.25941 3.91341i −0.853976 1.47913i −0.877592 0.479409i \(-0.840851\pi\)
0.0236156 0.999721i \(-0.492482\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 1.93163 3.34568i 0.582407 1.00876i −0.412786 0.910828i \(-0.635444\pi\)
0.995193 0.0979312i \(-0.0312225\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −3.51882 + 6.09477i −0.975944 + 1.69038i −0.299161 + 0.954203i \(0.596707\pi\)
−0.676784 + 0.736182i \(0.736627\pi\)
\(14\) 2.25941 + 3.91341i 0.603852 + 1.04590i
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −0.240592 0.416717i −0.0583520 0.101069i 0.835374 0.549682i \(-0.185251\pi\)
−0.893726 + 0.448614i \(0.851918\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 3.95044 + 6.84237i 0.906294 + 1.56975i 0.819171 + 0.573550i \(0.194434\pi\)
0.0871232 + 0.996198i \(0.472233\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) 2.25941 3.91341i 0.493043 0.853976i
\(22\) −1.93163 + 3.34568i −0.411824 + 0.713301i
\(23\) 5.51882 1.15075 0.575376 0.817889i \(-0.304856\pi\)
0.575376 + 0.817889i \(0.304856\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 3.51882 6.09477i 0.690097 1.19528i
\(27\) −1.00000 −0.192450
\(28\) −2.25941 3.91341i −0.426988 0.739565i
\(29\) 9.38207 1.74221 0.871103 0.491100i \(-0.163405\pi\)
0.871103 + 0.491100i \(0.163405\pi\)
\(30\) 1.00000 0.182574
\(31\) 5.12266 2.18136i 0.920057 0.391784i
\(32\) −1.00000 −0.176777
\(33\) 3.86325 0.672506
\(34\) 0.240592 + 0.416717i 0.0412611 + 0.0714664i
\(35\) 4.51882 0.763819
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 1.24059 + 2.14877i 0.203952 + 0.353255i 0.949798 0.312863i \(-0.101288\pi\)
−0.745846 + 0.666118i \(0.767955\pi\)
\(38\) −3.95044 6.84237i −0.640847 1.10998i
\(39\) −7.03763 −1.12692
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −4.08719 + 7.07922i −0.638312 + 1.10559i 0.347491 + 0.937683i \(0.387034\pi\)
−0.985803 + 0.167905i \(0.946300\pi\)
\(42\) −2.25941 + 3.91341i −0.348634 + 0.603852i
\(43\) 2.19104 + 3.79498i 0.334130 + 0.578730i 0.983317 0.181899i \(-0.0582243\pi\)
−0.649188 + 0.760628i \(0.724891\pi\)
\(44\) 1.93163 3.34568i 0.291204 0.504380i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) −5.51882 −0.813705
\(47\) 10.5565 1.53982 0.769908 0.638155i \(-0.220302\pi\)
0.769908 + 0.638155i \(0.220302\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −6.70985 + 11.6218i −0.958550 + 1.66026i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0.240592 0.416717i 0.0336896 0.0583520i
\(52\) −3.51882 + 6.09477i −0.487972 + 0.845192i
\(53\) 0.827781 1.43376i 0.113704 0.196942i −0.803557 0.595228i \(-0.797062\pi\)
0.917261 + 0.398286i \(0.130395\pi\)
\(54\) 1.00000 0.136083
\(55\) 1.93163 + 3.34568i 0.260461 + 0.451131i
\(56\) 2.25941 + 3.91341i 0.301926 + 0.522951i
\(57\) −3.95044 + 6.84237i −0.523249 + 0.906294i
\(58\) −9.38207 −1.23193
\(59\) −6.77823 11.7402i −0.882450 1.52845i −0.848609 0.529021i \(-0.822559\pi\)
−0.0338407 0.999427i \(-0.510774\pi\)
\(60\) −1.00000 −0.129099
\(61\) 5.90089 0.755531 0.377766 0.925901i \(-0.376693\pi\)
0.377766 + 0.925901i \(0.376693\pi\)
\(62\) −5.12266 + 2.18136i −0.650579 + 0.277033i
\(63\) 4.51882 0.569317
\(64\) 1.00000 0.125000
\(65\) −3.51882 6.09477i −0.436455 0.755963i
\(66\) −3.86325 −0.475534
\(67\) −1.24059 + 2.14877i −0.151562 + 0.262514i −0.931802 0.362967i \(-0.881764\pi\)
0.780240 + 0.625481i \(0.215097\pi\)
\(68\) −0.240592 0.416717i −0.0291760 0.0505344i
\(69\) 2.75941 + 4.77944i 0.332194 + 0.575376i
\(70\) −4.51882 −0.540102
\(71\) −1.51882 + 2.63067i −0.180250 + 0.312203i −0.941966 0.335709i \(-0.891024\pi\)
0.761715 + 0.647912i \(0.224357\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) −1.24059 2.14877i −0.144216 0.249789i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 3.95044 + 6.84237i 0.453147 + 0.784874i
\(77\) −17.4573 −1.98945
\(78\) 7.03763 0.796855
\(79\) 2.19104 + 3.79498i 0.246511 + 0.426969i 0.962555 0.271085i \(-0.0873826\pi\)
−0.716045 + 0.698055i \(0.754049\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.08719 7.07922i 0.451355 0.781769i
\(83\) 0.603846 1.04589i 0.0662807 0.114802i −0.830981 0.556301i \(-0.812220\pi\)
0.897261 + 0.441500i \(0.145553\pi\)
\(84\) 2.25941 3.91341i 0.246522 0.426988i
\(85\) 0.481183 0.0521917
\(86\) −2.19104 3.79498i −0.236265 0.409224i
\(87\) 4.69104 + 8.12511i 0.502932 + 0.871103i
\(88\) −1.93163 + 3.34568i −0.205912 + 0.356650i
\(89\) −2.96237 −0.314010 −0.157005 0.987598i \(-0.550184\pi\)
−0.157005 + 0.987598i \(0.550184\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) 31.8018 3.33373
\(92\) 5.51882 0.575376
\(93\) 4.45044 + 3.34568i 0.461490 + 0.346930i
\(94\) −10.5565 −1.08881
\(95\) −7.90089 −0.810614
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) −11.4573 −1.16332 −0.581658 0.813433i \(-0.697596\pi\)
−0.581658 + 0.813433i \(0.697596\pi\)
\(98\) 6.70985 11.6218i 0.677797 1.17398i
\(99\) 1.93163 + 3.34568i 0.194136 + 0.336253i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 9.76414 0.971568 0.485784 0.874079i \(-0.338534\pi\)
0.485784 + 0.874079i \(0.338534\pi\)
\(102\) −0.240592 + 0.416717i −0.0238221 + 0.0412611i
\(103\) −7.77823 + 13.4723i −0.766411 + 1.32746i 0.173086 + 0.984907i \(0.444626\pi\)
−0.939497 + 0.342557i \(0.888707\pi\)
\(104\) 3.51882 6.09477i 0.345048 0.597641i
\(105\) 2.25941 + 3.91341i 0.220496 + 0.381910i
\(106\) −0.827781 + 1.43376i −0.0804012 + 0.139259i
\(107\) −2.25941 3.91341i −0.218425 0.378324i 0.735901 0.677089i \(-0.236759\pi\)
−0.954327 + 0.298765i \(0.903425\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 7.90089 0.756768 0.378384 0.925649i \(-0.376480\pi\)
0.378384 + 0.925649i \(0.376480\pi\)
\(110\) −1.93163 3.34568i −0.184173 0.318998i
\(111\) −1.24059 + 2.14877i −0.117752 + 0.203952i
\(112\) −2.25941 3.91341i −0.213494 0.369782i
\(113\) 3.70985 6.42565i 0.348994 0.604475i −0.637077 0.770800i \(-0.719857\pi\)
0.986071 + 0.166325i \(0.0531902\pi\)
\(114\) 3.95044 6.84237i 0.369993 0.640847i
\(115\) −2.75941 + 4.77944i −0.257316 + 0.445685i
\(116\) 9.38207 0.871103
\(117\) −3.51882 6.09477i −0.325315 0.563462i
\(118\) 6.77823 + 11.7402i 0.623986 + 1.08078i
\(119\) −1.08719 + 1.88307i −0.0996625 + 0.172621i
\(120\) 1.00000 0.0912871
\(121\) −1.96237 3.39892i −0.178397 0.308993i
\(122\) −5.90089 −0.534241
\(123\) −8.17438 −0.737059
\(124\) 5.12266 2.18136i 0.460029 0.195892i
\(125\) 1.00000 0.0894427
\(126\) −4.51882 −0.402568
\(127\) 1.60385 + 2.77794i 0.142318 + 0.246503i 0.928369 0.371659i \(-0.121211\pi\)
−0.786051 + 0.618162i \(0.787878\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.19104 + 3.79498i −0.192910 + 0.334130i
\(130\) 3.51882 + 6.09477i 0.308621 + 0.534547i
\(131\) 3.32778 + 5.76389i 0.290750 + 0.503593i 0.973987 0.226603i \(-0.0727620\pi\)
−0.683238 + 0.730196i \(0.739429\pi\)
\(132\) 3.86325 0.336253
\(133\) 17.8513 30.9194i 1.54791 2.68105i
\(134\) 1.24059 2.14877i 0.107171 0.185625i
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 0.240592 + 0.416717i 0.0206306 + 0.0357332i
\(137\) 2.41497 4.18285i 0.206325 0.357365i −0.744229 0.667924i \(-0.767183\pi\)
0.950554 + 0.310559i \(0.100516\pi\)
\(138\) −2.75941 4.77944i −0.234896 0.406853i
\(139\) 8.86325 0.751771 0.375886 0.926666i \(-0.377339\pi\)
0.375886 + 0.926666i \(0.377339\pi\)
\(140\) 4.51882 0.381910
\(141\) 5.27823 + 9.14215i 0.444507 + 0.769908i
\(142\) 1.51882 2.63067i 0.127456 0.220761i
\(143\) 13.5941 + 23.5456i 1.13679 + 1.96899i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −4.69104 + 8.12511i −0.389569 + 0.674754i
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) −13.4197 −1.10684
\(148\) 1.24059 + 2.14877i 0.101976 + 0.176628i
\(149\) 7.82778 + 13.5581i 0.641277 + 1.11072i 0.985148 + 0.171707i \(0.0549283\pi\)
−0.343871 + 0.939017i \(0.611738\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −14.9009 −1.21262 −0.606309 0.795230i \(-0.707350\pi\)
−0.606309 + 0.795230i \(0.707350\pi\)
\(152\) −3.95044 6.84237i −0.320423 0.554989i
\(153\) 0.481183 0.0389014
\(154\) 17.4573 1.40675
\(155\) −0.672219 + 5.52704i −0.0539939 + 0.443942i
\(156\) −7.03763 −0.563462
\(157\) 2.44787 0.195361 0.0976807 0.995218i \(-0.468858\pi\)
0.0976807 + 0.995218i \(0.468858\pi\)
\(158\) −2.19104 3.79498i −0.174309 0.301913i
\(159\) 1.65556 0.131295
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) −12.4693 21.5974i −0.982715 1.70211i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −21.3206 −1.66996 −0.834979 0.550282i \(-0.814520\pi\)
−0.834979 + 0.550282i \(0.814520\pi\)
\(164\) −4.08719 + 7.07922i −0.319156 + 0.552794i
\(165\) −1.93163 + 3.34568i −0.150377 + 0.260461i
\(166\) −0.603846 + 1.04589i −0.0468675 + 0.0811769i
\(167\) 4.29488 + 7.43895i 0.332348 + 0.575643i 0.982972 0.183757i \(-0.0588259\pi\)
−0.650624 + 0.759400i \(0.725493\pi\)
\(168\) −2.25941 + 3.91341i −0.174317 + 0.301926i
\(169\) −18.2641 31.6344i −1.40493 2.43342i
\(170\) −0.481183 −0.0369051
\(171\) −7.90089 −0.604196
\(172\) 2.19104 + 3.79498i 0.167065 + 0.289365i
\(173\) 2.69104 4.66101i 0.204596 0.354370i −0.745408 0.666608i \(-0.767745\pi\)
0.950004 + 0.312238i \(0.101079\pi\)
\(174\) −4.69104 8.12511i −0.355626 0.615963i
\(175\) −2.25941 + 3.91341i −0.170795 + 0.295826i
\(176\) 1.93163 3.34568i 0.145602 0.252190i
\(177\) 6.77823 11.7402i 0.509483 0.882450i
\(178\) 2.96237 0.222039
\(179\) −6.10601 10.5759i −0.456384 0.790481i 0.542382 0.840132i \(-0.317522\pi\)
−0.998767 + 0.0496509i \(0.984189\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 5.38207 9.32202i 0.400046 0.692900i −0.593685 0.804698i \(-0.702327\pi\)
0.993731 + 0.111797i \(0.0356607\pi\)
\(182\) −31.8018 −2.35730
\(183\) 2.95044 + 5.11032i 0.218103 + 0.377766i
\(184\) −5.51882 −0.406853
\(185\) −2.48118 −0.182420
\(186\) −4.45044 3.34568i −0.326322 0.245317i
\(187\) −1.85893 −0.135939
\(188\) 10.5565 0.769908
\(189\) 2.25941 + 3.91341i 0.164348 + 0.284659i
\(190\) 7.90089 0.573191
\(191\) −4.95044 + 8.57442i −0.358202 + 0.620423i −0.987660 0.156611i \(-0.949943\pi\)
0.629459 + 0.777034i \(0.283277\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −10.6910 18.5174i −0.769558 1.33291i −0.937803 0.347168i \(-0.887143\pi\)
0.168245 0.985745i \(-0.446190\pi\)
\(194\) 11.4573 0.822589
\(195\) 3.51882 6.09477i 0.251988 0.436455i
\(196\) −6.70985 + 11.6218i −0.479275 + 0.830129i
\(197\) −3.65556 + 6.33162i −0.260448 + 0.451109i −0.966361 0.257189i \(-0.917204\pi\)
0.705913 + 0.708299i \(0.250537\pi\)
\(198\) −1.93163 3.34568i −0.137275 0.237767i
\(199\) −1.39615 + 2.41821i −0.0989707 + 0.171422i −0.911259 0.411834i \(-0.864888\pi\)
0.812288 + 0.583256i \(0.198222\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) −2.48118 −0.175009
\(202\) −9.76414 −0.687003
\(203\) −21.1979 36.7159i −1.48780 2.57695i
\(204\) 0.240592 0.416717i 0.0168448 0.0291760i
\(205\) −4.08719 7.07922i −0.285462 0.494434i
\(206\) 7.77823 13.4723i 0.541935 0.938658i
\(207\) −2.75941 + 4.77944i −0.191792 + 0.332194i
\(208\) −3.51882 + 6.09477i −0.243986 + 0.422596i
\(209\) 30.5231 2.11133
\(210\) −2.25941 3.91341i −0.155914 0.270051i
\(211\) 0.0495562 + 0.0858338i 0.00341159 + 0.00590905i 0.867726 0.497043i \(-0.165581\pi\)
−0.864315 + 0.502952i \(0.832247\pi\)
\(212\) 0.827781 1.43376i 0.0568522 0.0984710i
\(213\) −3.03763 −0.208135
\(214\) 2.25941 + 3.91341i 0.154450 + 0.267515i
\(215\) −4.38207 −0.298855
\(216\) 1.00000 0.0680414
\(217\) −20.1107 15.1185i −1.36521 1.02631i
\(218\) −7.90089 −0.535116
\(219\) 2.00000 0.135147
\(220\) 1.93163 + 3.34568i 0.130230 + 0.225565i
\(221\) 3.38639 0.227793
\(222\) 1.24059 2.14877i 0.0832631 0.144216i
\(223\) 8.12266 + 14.0689i 0.543934 + 0.942121i 0.998673 + 0.0514963i \(0.0163990\pi\)
−0.454739 + 0.890625i \(0.650268\pi\)
\(224\) 2.25941 + 3.91341i 0.150963 + 0.261476i
\(225\) 1.00000 0.0666667
\(226\) −3.70985 + 6.42565i −0.246776 + 0.427428i
\(227\) 5.64148 9.77133i 0.374438 0.648546i −0.615805 0.787899i \(-0.711169\pi\)
0.990243 + 0.139353i \(0.0445023\pi\)
\(228\) −3.95044 + 6.84237i −0.261625 + 0.453147i
\(229\) −5.33251 9.23619i −0.352382 0.610344i 0.634284 0.773100i \(-0.281295\pi\)
−0.986666 + 0.162756i \(0.947962\pi\)
\(230\) 2.75941 4.77944i 0.181950 0.315147i
\(231\) −8.72867 15.1185i −0.574304 0.994724i
\(232\) −9.38207 −0.615963
\(233\) 6.48118 0.424596 0.212298 0.977205i \(-0.431905\pi\)
0.212298 + 0.977205i \(0.431905\pi\)
\(234\) 3.51882 + 6.09477i 0.230032 + 0.398428i
\(235\) −5.27823 + 9.14215i −0.344313 + 0.596368i
\(236\) −6.77823 11.7402i −0.441225 0.764224i
\(237\) −2.19104 + 3.79498i −0.142323 + 0.246511i
\(238\) 1.08719 1.88307i 0.0704720 0.122061i
\(239\) 10.3821 17.9823i 0.671560 1.16318i −0.305901 0.952063i \(-0.598958\pi\)
0.977462 0.211113i \(-0.0677089\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 9.82778 + 17.0222i 0.633063 + 1.09650i 0.986922 + 0.161199i \(0.0515360\pi\)
−0.353859 + 0.935299i \(0.615131\pi\)
\(242\) 1.96237 + 3.39892i 0.126146 + 0.218491i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 5.90089 0.377766
\(245\) −6.70985 11.6218i −0.428677 0.742490i
\(246\) 8.17438 0.521179
\(247\) −55.6036 −3.53797
\(248\) −5.12266 + 2.18136i −0.325289 + 0.138516i
\(249\) 1.20769 0.0765344
\(250\) −1.00000 −0.0632456
\(251\) 0.191035 + 0.330883i 0.0120581 + 0.0208852i 0.871991 0.489521i \(-0.162828\pi\)
−0.859933 + 0.510406i \(0.829495\pi\)
\(252\) 4.51882 0.284659
\(253\) 10.6603 18.4642i 0.670207 1.16083i
\(254\) −1.60385 2.77794i −0.100634 0.174304i
\(255\) 0.240592 + 0.416717i 0.0150664 + 0.0260958i
\(256\) 1.00000 0.0625000
\(257\) −10.4859 + 18.1621i −0.654094 + 1.13292i 0.328027 + 0.944668i \(0.393616\pi\)
−0.982120 + 0.188255i \(0.939717\pi\)
\(258\) 2.19104 3.79498i 0.136408 0.236265i
\(259\) 5.60601 9.70989i 0.348340 0.603343i
\(260\) −3.51882 6.09477i −0.218228 0.377982i
\(261\) −4.69104 + 8.12511i −0.290368 + 0.502932i
\(262\) −3.32778 5.76389i −0.205591 0.356094i
\(263\) 2.38207 0.146885 0.0734424 0.997299i \(-0.476601\pi\)
0.0734424 + 0.997299i \(0.476601\pi\)
\(264\) −3.86325 −0.237767
\(265\) 0.827781 + 1.43376i 0.0508502 + 0.0880751i
\(266\) −17.8513 + 30.9194i −1.09454 + 1.89579i
\(267\) −1.48118 2.56548i −0.0906469 0.157005i
\(268\) −1.24059 + 2.14877i −0.0757812 + 0.131257i
\(269\) −9.36541 + 16.2214i −0.571019 + 0.989035i 0.425442 + 0.904986i \(0.360119\pi\)
−0.996462 + 0.0840490i \(0.973215\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −7.82994 −0.475635 −0.237818 0.971310i \(-0.576432\pi\)
−0.237818 + 0.971310i \(0.576432\pi\)
\(272\) −0.240592 0.416717i −0.0145880 0.0252672i
\(273\) 15.9009 + 27.5411i 0.962365 + 1.66687i
\(274\) −2.41497 + 4.18285i −0.145894 + 0.252695i
\(275\) −3.86325 −0.232963
\(276\) 2.75941 + 4.77944i 0.166097 + 0.287688i
\(277\) −14.2077 −0.853657 −0.426829 0.904332i \(-0.640369\pi\)
−0.426829 + 0.904332i \(0.640369\pi\)
\(278\) −8.86325 −0.531583
\(279\) −0.672219 + 5.52704i −0.0402447 + 0.330895i
\(280\) −4.51882 −0.270051
\(281\) 4.62225 0.275740 0.137870 0.990450i \(-0.455974\pi\)
0.137870 + 0.990450i \(0.455974\pi\)
\(282\) −5.27823 9.14215i −0.314314 0.544407i
\(283\) 25.4950 1.51552 0.757759 0.652534i \(-0.226294\pi\)
0.757759 + 0.652534i \(0.226294\pi\)
\(284\) −1.51882 + 2.63067i −0.0901252 + 0.156101i
\(285\) −3.95044 6.84237i −0.234004 0.405307i
\(286\) −13.5941 23.5456i −0.803835 1.39228i
\(287\) 36.9385 2.18041
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 8.38423 14.5219i 0.493190 0.854230i
\(290\) 4.69104 8.12511i 0.275467 0.477123i
\(291\) −5.72867 9.92235i −0.335821 0.581658i
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) 3.86541 + 6.69509i 0.225820 + 0.391132i 0.956565 0.291519i \(-0.0941606\pi\)
−0.730745 + 0.682650i \(0.760827\pi\)
\(294\) 13.4197 0.782653
\(295\) 13.5565 0.789287
\(296\) −1.24059 2.14877i −0.0721079 0.124895i
\(297\) −1.93163 + 3.34568i −0.112084 + 0.194136i
\(298\) −7.82778 13.5581i −0.453451 0.785401i
\(299\) −19.4197 + 33.6359i −1.12307 + 1.94522i
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) 9.90089 17.1488i 0.570678 0.988443i
\(302\) 14.9009 0.857450
\(303\) 4.88207 + 8.45599i 0.280468 + 0.485784i
\(304\) 3.95044 + 6.84237i 0.226573 + 0.392437i
\(305\) −2.95044 + 5.11032i −0.168942 + 0.292616i
\(306\) −0.481183 −0.0275074
\(307\) 0.223935 + 0.387867i 0.0127807 + 0.0221368i 0.872345 0.488891i \(-0.162598\pi\)
−0.859564 + 0.511028i \(0.829265\pi\)
\(308\) −17.4573 −0.994724
\(309\) −15.5565 −0.884976
\(310\) 0.672219 5.52704i 0.0381795 0.313915i
\(311\) 6.68888 0.379291 0.189646 0.981853i \(-0.439266\pi\)
0.189646 + 0.981853i \(0.439266\pi\)
\(312\) 7.03763 0.398428
\(313\) 1.48334 + 2.56923i 0.0838435 + 0.145221i 0.904898 0.425629i \(-0.139947\pi\)
−0.821054 + 0.570850i \(0.806614\pi\)
\(314\) −2.44787 −0.138141
\(315\) −2.25941 + 3.91341i −0.127303 + 0.220496i
\(316\) 2.19104 + 3.79498i 0.123255 + 0.213485i
\(317\) −3.34660 5.79648i −0.187964 0.325563i 0.756608 0.653869i \(-0.226855\pi\)
−0.944571 + 0.328307i \(0.893522\pi\)
\(318\) −1.65556 −0.0928393
\(319\) 18.1227 31.3894i 1.01467 1.75747i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 2.25941 3.91341i 0.126108 0.218425i
\(322\) 12.4693 + 21.5974i 0.694885 + 1.20358i
\(323\) 1.90089 3.29243i 0.105768 0.183196i
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 7.03763 0.390378
\(326\) 21.3206 1.18084
\(327\) 3.95044 + 6.84237i 0.218460 + 0.378384i
\(328\) 4.08719 7.07922i 0.225677 0.390885i
\(329\) −23.8513 41.3117i −1.31497 2.27759i
\(330\) 1.93163 3.34568i 0.106333 0.184173i
\(331\) 3.70512 6.41745i 0.203652 0.352735i −0.746051 0.665889i \(-0.768052\pi\)
0.949702 + 0.313154i \(0.101386\pi\)
\(332\) 0.603846 1.04589i 0.0331403 0.0574008i
\(333\) −2.48118 −0.135968
\(334\) −4.29488 7.43895i −0.235005 0.407041i
\(335\) −1.24059 2.14877i −0.0677808 0.117400i
\(336\) 2.25941 3.91341i 0.123261 0.213494i
\(337\) −15.3821 −0.837915 −0.418957 0.908006i \(-0.637604\pi\)
−0.418957 + 0.908006i \(0.637604\pi\)
\(338\) 18.2641 + 31.6344i 0.993438 + 1.72069i
\(339\) 7.41970 0.402983
\(340\) 0.481183 0.0260958
\(341\) 2.59695 21.3523i 0.140633 1.15629i
\(342\) 7.90089 0.427231
\(343\) 29.0095 1.56636
\(344\) −2.19104 3.79498i −0.118133 0.204612i
\(345\) −5.51882 −0.297123
\(346\) −2.69104 + 4.66101i −0.144671 + 0.250577i
\(347\) 4.64148 + 8.03928i 0.249168 + 0.431571i 0.963295 0.268445i \(-0.0865096\pi\)
−0.714127 + 0.700016i \(0.753176\pi\)
\(348\) 4.69104 + 8.12511i 0.251466 + 0.435552i
\(349\) −18.5898 −0.995087 −0.497544 0.867439i \(-0.665765\pi\)
−0.497544 + 0.867439i \(0.665765\pi\)
\(350\) 2.25941 3.91341i 0.120770 0.209181i
\(351\) 3.51882 6.09477i 0.187821 0.325315i
\(352\) −1.93163 + 3.34568i −0.102956 + 0.178325i
\(353\) −13.2663 22.9779i −0.706094 1.22299i −0.966295 0.257436i \(-0.917122\pi\)
0.260201 0.965554i \(-0.416211\pi\)
\(354\) −6.77823 + 11.7402i −0.360259 + 0.623986i
\(355\) −1.51882 2.63067i −0.0806104 0.139621i
\(356\) −2.96237 −0.157005
\(357\) −2.17438 −0.115080
\(358\) 6.10601 + 10.5759i 0.322712 + 0.558954i
\(359\) −4.56837 + 7.91265i −0.241109 + 0.417614i −0.961031 0.276442i \(-0.910845\pi\)
0.719921 + 0.694056i \(0.244178\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) −21.7120 + 37.6063i −1.14274 + 1.97928i
\(362\) −5.38207 + 9.32202i −0.282875 + 0.489955i
\(363\) 1.96237 3.39892i 0.102998 0.178397i
\(364\) 31.8018 1.66687
\(365\) 1.00000 + 1.73205i 0.0523424 + 0.0906597i
\(366\) −2.95044 5.11032i −0.154222 0.267121i
\(367\) 12.0000 20.7846i 0.626395 1.08495i −0.361874 0.932227i \(-0.617863\pi\)
0.988269 0.152721i \(-0.0488036\pi\)
\(368\) 5.51882 0.287688
\(369\) −4.08719 7.07922i −0.212771 0.368529i
\(370\) 2.48118 0.128991
\(371\) −7.48118 −0.388404
\(372\) 4.45044 + 3.34568i 0.230745 + 0.173465i
\(373\) 25.3959 1.31495 0.657474 0.753477i \(-0.271625\pi\)
0.657474 + 0.753477i \(0.271625\pi\)
\(374\) 1.85893 0.0961232
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) −10.5565 −0.544407
\(377\) −33.0138 + 57.1816i −1.70030 + 2.94500i
\(378\) −2.25941 3.91341i −0.116211 0.201284i
\(379\) 13.9385 + 24.1422i 0.715974 + 1.24010i 0.962583 + 0.270988i \(0.0873503\pi\)
−0.246609 + 0.969115i \(0.579316\pi\)
\(380\) −7.90089 −0.405307
\(381\) −1.60385 + 2.77794i −0.0821675 + 0.142318i
\(382\) 4.95044 8.57442i 0.253287 0.438706i
\(383\) 8.27823 14.3383i 0.422998 0.732653i −0.573234 0.819392i \(-0.694311\pi\)
0.996231 + 0.0867388i \(0.0276446\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 8.72867 15.1185i 0.444854 0.770510i
\(386\) 10.6910 + 18.5174i 0.544159 + 0.942512i
\(387\) −4.38207 −0.222753
\(388\) −11.4573 −0.581658
\(389\) −14.8842 25.7802i −0.754660 1.30711i −0.945543 0.325497i \(-0.894468\pi\)
0.190882 0.981613i \(-0.438865\pi\)
\(390\) −3.51882 + 6.09477i −0.178182 + 0.308621i
\(391\) −1.32778 2.29978i −0.0671488 0.116305i
\(392\) 6.70985 11.6218i 0.338899 0.586990i
\(393\) −3.32778 + 5.76389i −0.167864 + 0.290750i
\(394\) 3.65556 6.33162i 0.184165 0.318982i
\(395\) −4.38207 −0.220486
\(396\) 1.93163 + 3.34568i 0.0970679 + 0.168127i
\(397\) 10.3278 + 17.8882i 0.518336 + 0.897785i 0.999773 + 0.0213042i \(0.00678184\pi\)
−0.481437 + 0.876481i \(0.659885\pi\)
\(398\) 1.39615 2.41821i 0.0699829 0.121214i
\(399\) 35.7027 1.78737
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −18.8394 −0.940795 −0.470398 0.882455i \(-0.655889\pi\)
−0.470398 + 0.882455i \(0.655889\pi\)
\(402\) 2.48118 0.123750
\(403\) −4.73083 + 38.8972i −0.235659 + 1.93761i
\(404\) 9.76414 0.485784
\(405\) 1.00000 0.0496904
\(406\) 21.1979 + 36.7159i 1.05204 + 1.82218i
\(407\) 9.58544 0.475133
\(408\) −0.240592 + 0.416717i −0.0119111 + 0.0206306i
\(409\) −3.67438 6.36421i −0.181686 0.314690i 0.760769 0.649023i \(-0.224822\pi\)
−0.942455 + 0.334333i \(0.891489\pi\)
\(410\) 4.08719 + 7.07922i 0.201852 + 0.349618i
\(411\) 4.82994 0.238243
\(412\) −7.77823 + 13.4723i −0.383206 + 0.663732i
\(413\) −30.6296 + 53.0519i −1.50718 + 2.61052i
\(414\) 2.75941 4.77944i 0.135618 0.234896i
\(415\) 0.603846 + 1.04589i 0.0296416 + 0.0513408i
\(416\) 3.51882 6.09477i 0.172524 0.298821i
\(417\) 4.43163 + 7.67580i 0.217018 + 0.375886i
\(418\) −30.5231 −1.49294
\(419\) −11.8633 −0.579558 −0.289779 0.957094i \(-0.593582\pi\)
−0.289779 + 0.957094i \(0.593582\pi\)
\(420\) 2.25941 + 3.91341i 0.110248 + 0.190955i
\(421\) 9.81370 16.9978i 0.478290 0.828423i −0.521400 0.853312i \(-0.674590\pi\)
0.999690 + 0.0248893i \(0.00792332\pi\)
\(422\) −0.0495562 0.0858338i −0.00241236 0.00417833i
\(423\) −5.27823 + 9.14215i −0.256636 + 0.444507i
\(424\) −0.827781 + 1.43376i −0.0402006 + 0.0696295i
\(425\) −0.240592 + 0.416717i −0.0116704 + 0.0202137i
\(426\) 3.03763 0.147174
\(427\) −13.3325 23.0926i −0.645206 1.11753i
\(428\) −2.25941 3.91341i −0.109213 0.189162i
\(429\) −13.5941 + 23.5456i −0.656329 + 1.13679i
\(430\) 4.38207 0.211322
\(431\) −15.6436 27.0956i −0.753528 1.30515i −0.946103 0.323866i \(-0.895017\pi\)
0.192575 0.981282i \(-0.438316\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 8.68888 0.417561 0.208780 0.977963i \(-0.433051\pi\)
0.208780 + 0.977963i \(0.433051\pi\)
\(434\) 20.1107 + 15.1185i 0.965346 + 0.725711i
\(435\) −9.38207 −0.449836
\(436\) 7.90089 0.378384
\(437\) 21.8018 + 37.7618i 1.04292 + 1.80639i
\(438\) −2.00000 −0.0955637
\(439\) −16.6248 + 28.7950i −0.793460 + 1.37431i 0.130353 + 0.991468i \(0.458389\pi\)
−0.923813 + 0.382845i \(0.874944\pi\)
\(440\) −1.93163 3.34568i −0.0920867 0.159499i
\(441\) −6.70985 11.6218i −0.319517 0.553419i
\(442\) −3.38639 −0.161074
\(443\) −7.41970 + 12.8513i −0.352521 + 0.610584i −0.986690 0.162610i \(-0.948009\pi\)
0.634170 + 0.773194i \(0.281342\pi\)
\(444\) −1.24059 + 2.14877i −0.0588759 + 0.101976i
\(445\) 1.48118 2.56548i 0.0702148 0.121616i
\(446\) −8.12266 14.0689i −0.384619 0.666180i
\(447\) −7.82778 + 13.5581i −0.370241 + 0.641277i
\(448\) −2.25941 3.91341i −0.106747 0.184891i
\(449\) 5.80178 0.273803 0.136901 0.990585i \(-0.456286\pi\)
0.136901 + 0.990585i \(0.456286\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 15.7899 + 27.3488i 0.743515 + 1.28781i
\(452\) 3.70985 6.42565i 0.174497 0.302237i
\(453\) −7.45044 12.9045i −0.350052 0.606309i
\(454\) −5.64148 + 9.77133i −0.264768 + 0.458591i
\(455\) −15.9009 + 27.5411i −0.745445 + 1.29115i
\(456\) 3.95044 6.84237i 0.184996 0.320423i
\(457\) 29.3864 1.37464 0.687319 0.726356i \(-0.258788\pi\)
0.687319 + 0.726356i \(0.258788\pi\)
\(458\) 5.33251 + 9.23619i 0.249172 + 0.431579i
\(459\) 0.240592 + 0.416717i 0.0112299 + 0.0194507i
\(460\) −2.75941 + 4.77944i −0.128658 + 0.222842i
\(461\) 25.4907 1.18722 0.593609 0.804754i \(-0.297703\pi\)
0.593609 + 0.804754i \(0.297703\pi\)
\(462\) 8.72867 + 15.1185i 0.406094 + 0.703376i
\(463\) 17.3582 0.806705 0.403353 0.915045i \(-0.367845\pi\)
0.403353 + 0.915045i \(0.367845\pi\)
\(464\) 9.38207 0.435552
\(465\) −5.12266 + 2.18136i −0.237558 + 0.101158i
\(466\) −6.48118 −0.300235
\(467\) 31.9718 1.47948 0.739740 0.672893i \(-0.234948\pi\)
0.739740 + 0.672893i \(0.234948\pi\)
\(468\) −3.51882 6.09477i −0.162657 0.281731i
\(469\) 11.2120 0.517723
\(470\) 5.27823 9.14215i 0.243466 0.421696i
\(471\) 1.22394 + 2.11992i 0.0563960 + 0.0976807i
\(472\) 6.77823 + 11.7402i 0.311993 + 0.540388i
\(473\) 16.9291 0.778399
\(474\) 2.19104 3.79498i 0.100638 0.174309i
\(475\) 3.95044 6.84237i 0.181259 0.313949i
\(476\) −1.08719 + 1.88307i −0.0498313 + 0.0863103i
\(477\) 0.827781 + 1.43376i 0.0379015 + 0.0656473i
\(478\) −10.3821 + 17.9823i −0.474865 + 0.822490i
\(479\) 10.3325 + 17.8964i 0.472105 + 0.817709i 0.999491 0.0319166i \(-0.0101611\pi\)
−0.527386 + 0.849626i \(0.676828\pi\)
\(480\) 1.00000 0.0456435
\(481\) −17.4617 −0.796183
\(482\) −9.82778 17.0222i −0.447643 0.775341i
\(483\) 12.4693 21.5974i 0.567371 0.982715i
\(484\) −1.96237 3.39892i −0.0891985 0.154496i
\(485\) 5.72867 9.92235i 0.260125 0.450551i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 11.6415 20.1636i 0.527526 0.913701i −0.471959 0.881620i \(-0.656453\pi\)
0.999485 0.0320812i \(-0.0102135\pi\)
\(488\) −5.90089 −0.267121
\(489\) −10.6603 18.4642i −0.482075 0.834979i
\(490\) 6.70985 + 11.6218i 0.303120 + 0.525020i
\(491\) 12.8701 22.2918i 0.580822 1.00601i −0.414561 0.910022i \(-0.636065\pi\)
0.995382 0.0959909i \(-0.0306020\pi\)
\(492\) −8.17438 −0.368529
\(493\) −2.25725 3.90967i −0.101661 0.176083i
\(494\) 55.6036 2.50172
\(495\) −3.86325 −0.173640
\(496\) 5.12266 2.18136i 0.230014 0.0979459i
\(497\) 13.7265 0.615718
\(498\) −1.20769 −0.0541180
\(499\) −6.37015 11.0334i −0.285167 0.493924i 0.687483 0.726201i \(-0.258716\pi\)
−0.972650 + 0.232277i \(0.925382\pi\)
\(500\) 1.00000 0.0447214
\(501\) −4.29488 + 7.43895i −0.191881 + 0.332348i
\(502\) −0.191035 0.330883i −0.00852633 0.0147680i
\(503\) 7.15814 + 12.3983i 0.319165 + 0.552811i 0.980314 0.197444i \(-0.0632641\pi\)
−0.661149 + 0.750255i \(0.729931\pi\)
\(504\) −4.51882 −0.201284
\(505\) −4.88207 + 8.45599i −0.217249 + 0.376287i
\(506\) −10.6603 + 18.4642i −0.473908 + 0.820833i
\(507\) 18.2641 31.6344i 0.811139 1.40493i
\(508\) 1.60385 + 2.77794i 0.0711592 + 0.123251i
\(509\) 11.8488 20.5227i 0.525187 0.909651i −0.474383 0.880319i \(-0.657329\pi\)
0.999570 0.0293318i \(-0.00933795\pi\)
\(510\) −0.240592 0.416717i −0.0106536 0.0184525i
\(511\) −9.03763 −0.399801
\(512\) −1.00000 −0.0441942
\(513\) −3.95044 6.84237i −0.174416 0.302098i
\(514\) 10.4859 18.1621i 0.462514 0.801098i
\(515\) −7.77823 13.4723i −0.342750 0.593660i
\(516\) −2.19104 + 3.79498i −0.0964550 + 0.167065i
\(517\) 20.3911 35.3185i 0.896801 1.55330i
\(518\) −5.60601 + 9.70989i −0.246314 + 0.426628i
\(519\) 5.38207 0.236247
\(520\) 3.51882 + 6.09477i 0.154310 + 0.267273i
\(521\) 3.82562 + 6.62617i 0.167603 + 0.290298i 0.937577 0.347778i \(-0.113064\pi\)
−0.769973 + 0.638076i \(0.779730\pi\)
\(522\) 4.69104 8.12511i 0.205321 0.355626i
\(523\) 3.07095 0.134283 0.0671415 0.997743i \(-0.478612\pi\)
0.0671415 + 0.997743i \(0.478612\pi\)
\(524\) 3.32778 + 5.76389i 0.145375 + 0.251797i
\(525\) −4.51882 −0.197217
\(526\) −2.38207 −0.103863
\(527\) −2.14148 1.60988i −0.0932843 0.0701276i
\(528\) 3.86325 0.168127
\(529\) 7.45734 0.324232
\(530\) −0.827781 1.43376i −0.0359565 0.0622785i
\(531\) 13.5565 0.588300
\(532\) 17.8513 30.9194i 0.773953 1.34053i
\(533\) −28.7641 49.8210i −1.24591 2.15799i
\(534\) 1.48118 + 2.56548i 0.0640971 + 0.111019i
\(535\) 4.51882 0.195365
\(536\) 1.24059 2.14877i 0.0535854 0.0928126i
\(537\) 6.10601 10.5759i 0.263494 0.456384i
\(538\) 9.36541 16.2214i 0.403772 0.699353i
\(539\) 25.9219 + 44.8980i 1.11653 + 1.93389i
\(540\) 0.500000 0.866025i 0.0215166 0.0372678i
\(541\) −7.22394 12.5122i −0.310581 0.537942i 0.667907 0.744245i \(-0.267190\pi\)
−0.978488 + 0.206302i \(0.933857\pi\)
\(542\) 7.82994 0.336325
\(543\) 10.7641 0.461934
\(544\) 0.240592 + 0.416717i 0.0103153 + 0.0178666i
\(545\) −3.95044 + 6.84237i −0.169218 + 0.293095i
\(546\) −15.9009 27.5411i −0.680495 1.17865i
\(547\) −8.98334 + 15.5596i −0.384100 + 0.665281i −0.991644 0.129005i \(-0.958822\pi\)
0.607544 + 0.794286i \(0.292155\pi\)
\(548\) 2.41497 4.18285i 0.103162 0.178683i
\(549\) −2.95044 + 5.11032i −0.125922 + 0.218103i
\(550\) 3.86325 0.164730
\(551\) 37.0633 + 64.1956i 1.57895 + 2.73482i
\(552\) −2.75941 4.77944i −0.117448 0.203426i
\(553\) 9.90089 17.1488i 0.421029 0.729243i
\(554\) 14.2077 0.603627
\(555\) −1.24059 2.14877i −0.0526602 0.0912101i
\(556\) 8.86325 0.375886
\(557\) 15.1838 0.643360 0.321680 0.946848i \(-0.395752\pi\)
0.321680 + 0.946848i \(0.395752\pi\)
\(558\) 0.672219 5.52704i 0.0284573 0.233978i
\(559\) −30.8394 −1.30437
\(560\) 4.51882 0.190955
\(561\) −0.929467 1.60988i −0.0392421 0.0679693i
\(562\) −4.62225 −0.194978
\(563\) 15.8535 27.4591i 0.668145 1.15726i −0.310277 0.950646i \(-0.600422\pi\)
0.978422 0.206615i \(-0.0662448\pi\)
\(564\) 5.27823 + 9.14215i 0.222253 + 0.384954i
\(565\) 3.70985 + 6.42565i 0.156075 + 0.270329i
\(566\) −25.4950 −1.07163
\(567\) −2.25941 + 3.91341i −0.0948862 + 0.164348i
\(568\) 1.51882 2.63067i 0.0637281 0.110380i
\(569\) −18.9718 + 32.8602i −0.795341 + 1.37757i 0.127282 + 0.991867i \(0.459375\pi\)
−0.922623 + 0.385704i \(0.873959\pi\)
\(570\) 3.95044 + 6.84237i 0.165466 + 0.286595i
\(571\) −9.38207 + 16.2502i −0.392627 + 0.680051i −0.992795 0.119823i \(-0.961767\pi\)
0.600168 + 0.799874i \(0.295100\pi\)
\(572\) 13.5941 + 23.5456i 0.568397 + 0.984493i
\(573\) −9.90089 −0.413616
\(574\) −36.9385 −1.54178
\(575\) −2.75941 4.77944i −0.115075 0.199316i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −11.6556 20.1880i −0.485227 0.840439i 0.514629 0.857413i \(-0.327930\pi\)
−0.999856 + 0.0169747i \(0.994597\pi\)
\(578\) −8.38423 + 14.5219i −0.348738 + 0.604032i
\(579\) 10.6910 18.5174i 0.444304 0.769558i
\(580\) −4.69104 + 8.12511i −0.194785 + 0.337377i
\(581\) −5.45734 −0.226409
\(582\) 5.72867 + 9.92235i 0.237461 + 0.411294i
\(583\) −3.19793 5.53898i −0.132445 0.229401i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) 7.03763 0.290970
\(586\) −3.86541 6.69509i −0.159679 0.276572i
\(587\) −33.4812 −1.38192 −0.690958 0.722895i \(-0.742811\pi\)
−0.690958 + 0.722895i \(0.742811\pi\)
\(588\) −13.4197 −0.553419
\(589\) 35.1625 + 26.4338i 1.44884 + 1.08919i
\(590\) −13.5565 −0.558110
\(591\) −7.31112 −0.300739
\(592\) 1.24059 + 2.14877i 0.0509880 + 0.0883138i
\(593\) −31.0891 −1.27667 −0.638337 0.769757i \(-0.720377\pi\)
−0.638337 + 0.769757i \(0.720377\pi\)
\(594\) 1.93163 3.34568i 0.0792556 0.137275i
\(595\) −1.08719 1.88307i −0.0445704 0.0771982i
\(596\) 7.82778 + 13.5581i 0.320638 + 0.555362i
\(597\) −2.79231 −0.114282
\(598\) 19.4197 33.6359i 0.794131 1.37547i
\(599\) 2.65556 4.59957i 0.108503 0.187933i −0.806661 0.591015i \(-0.798728\pi\)
0.915164 + 0.403081i \(0.132061\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) 16.2287 + 28.1089i 0.661981 + 1.14659i 0.980094 + 0.198532i \(0.0636175\pi\)
−0.318113 + 0.948053i \(0.603049\pi\)
\(602\) −9.90089 + 17.1488i −0.403530 + 0.698935i
\(603\) −1.24059 2.14877i −0.0505208 0.0875046i
\(604\) −14.9009 −0.606309
\(605\) 3.92473 0.159563
\(606\) −4.88207 8.45599i −0.198321 0.343501i
\(607\) 12.7641 22.1081i 0.518081 0.897342i −0.481699 0.876337i \(-0.659980\pi\)
0.999779 0.0210050i \(-0.00668659\pi\)
\(608\) −3.95044 6.84237i −0.160212 0.277495i
\(609\) 21.1979 36.7159i 0.858983 1.48780i
\(610\) 2.95044 5.11032i 0.119460 0.206911i
\(611\) −37.1462 + 64.3391i −1.50277 + 2.60288i
\(612\) 0.481183 0.0194507
\(613\) 4.82994 + 8.36570i 0.195080 + 0.337888i 0.946927 0.321450i \(-0.104170\pi\)
−0.751847 + 0.659338i \(0.770837\pi\)
\(614\) −0.223935 0.387867i −0.00903730 0.0156531i
\(615\) 4.08719 7.07922i 0.164811 0.285462i
\(616\) 17.4573 0.703376
\(617\) −2.20296 3.81564i −0.0886878 0.153612i 0.818269 0.574836i \(-0.194934\pi\)
−0.906957 + 0.421224i \(0.861601\pi\)
\(618\) 15.5565 0.625772
\(619\) −48.4907 −1.94900 −0.974502 0.224379i \(-0.927965\pi\)
−0.974502 + 0.224379i \(0.927965\pi\)
\(620\) −0.672219 + 5.52704i −0.0269970 + 0.221971i
\(621\) −5.51882 −0.221462
\(622\) −6.68888 −0.268199
\(623\) 6.69320 + 11.5930i 0.268157 + 0.464462i
\(624\) −7.03763 −0.281731
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −1.48334 2.56923i −0.0592863 0.102687i
\(627\) 15.2616 + 26.4338i 0.609488 + 1.05566i
\(628\) 2.44787 0.0976807
\(629\) 0.596952 1.03395i 0.0238020 0.0412263i
\(630\) 2.25941 3.91341i 0.0900170 0.155914i
\(631\) −6.35133 + 11.0008i −0.252843 + 0.437936i −0.964307 0.264786i \(-0.914699\pi\)
0.711465 + 0.702722i \(0.248032\pi\)
\(632\) −2.19104 3.79498i −0.0871547 0.150956i
\(633\) −0.0495562 + 0.0858338i −0.00196968 + 0.00341159i
\(634\) 3.34660 + 5.79648i 0.132910 + 0.230208i
\(635\) −3.20769 −0.127293
\(636\) 1.65556 0.0656473
\(637\) −47.2215 81.7900i −1.87098 3.24064i
\(638\) −18.1227 + 31.3894i −0.717483 + 1.24272i
\(639\) −1.51882 2.63067i −0.0600835 0.104068i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −18.4693 + 31.9897i −0.729492 + 1.26352i 0.227606 + 0.973753i \(0.426910\pi\)
−0.957098 + 0.289764i \(0.906423\pi\)
\(642\) −2.25941 + 3.91341i −0.0891717 + 0.154450i
\(643\) −13.2873 −0.523999 −0.262000 0.965068i \(-0.584382\pi\)
−0.262000 + 0.965068i \(0.584382\pi\)
\(644\) −12.4693 21.5974i −0.491358 0.851056i
\(645\) −2.19104 3.79498i −0.0862719 0.149427i
\(646\) −1.90089 + 3.29243i −0.0747894 + 0.129539i
\(647\) 5.27864 0.207525 0.103762 0.994602i \(-0.466912\pi\)
0.103762 + 0.994602i \(0.466912\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −52.3720 −2.05578
\(650\) −7.03763 −0.276039
\(651\) 3.03763 24.9757i 0.119054 0.978873i
\(652\) −21.3206 −0.834979
\(653\) −32.4197 −1.26868 −0.634341 0.773054i \(-0.718728\pi\)
−0.634341 + 0.773054i \(0.718728\pi\)
\(654\) −3.95044 6.84237i −0.154475 0.267558i
\(655\) −6.65556 −0.260054
\(656\) −4.08719 + 7.07922i −0.159578 + 0.276397i
\(657\) 1.00000 + 1.73205i 0.0390137 + 0.0675737i
\(658\) 23.8513 + 41.3117i 0.929822 + 1.61050i
\(659\) −13.2496 −0.516133 −0.258066 0.966127i \(-0.583085\pi\)
−0.258066 + 0.966127i \(0.583085\pi\)
\(660\) −1.93163 + 3.34568i −0.0751885 + 0.130230i
\(661\) −17.9881 + 31.1563i −0.699655 + 1.21184i 0.268931 + 0.963159i \(0.413330\pi\)
−0.968586 + 0.248679i \(0.920004\pi\)
\(662\) −3.70512 + 6.41745i −0.144004 + 0.249421i
\(663\) 1.69320 + 2.93270i 0.0657583 + 0.113897i
\(664\) −0.603846 + 1.04589i −0.0234338 + 0.0405885i
\(665\) 17.8513 + 30.9194i 0.692245 + 1.19900i
\(666\) 2.48118 0.0961439
\(667\) 51.7779 2.00485
\(668\) 4.29488 + 7.43895i 0.166174 + 0.287822i
\(669\) −8.12266 + 14.0689i −0.314040 + 0.543934i
\(670\) 1.24059 + 2.14877i 0.0479282 + 0.0830141i
\(671\) 11.3983 19.7425i 0.440027 0.762149i
\(672\) −2.25941 + 3.91341i −0.0871586 + 0.150963i
\(673\) −6.69104 + 11.5892i −0.257920 + 0.446731i −0.965685 0.259717i \(-0.916371\pi\)
0.707764 + 0.706449i \(0.249704\pi\)
\(674\) 15.3821 0.592495
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −18.2641 31.6344i −0.702467 1.21671i
\(677\) 2.10127 3.63951i 0.0807585 0.139878i −0.822817 0.568306i \(-0.807599\pi\)
0.903576 + 0.428428i \(0.140932\pi\)
\(678\) −7.41970 −0.284952
\(679\) 25.8868 + 44.8373i 0.993444 + 1.72070i
\(680\) −0.481183 −0.0184525
\(681\) 11.2830 0.432364
\(682\) −2.59695 + 21.3523i −0.0994424 + 0.817623i
\(683\) 35.8299 1.37099 0.685497 0.728075i \(-0.259585\pi\)
0.685497 + 0.728075i \(0.259585\pi\)
\(684\) −7.90089 −0.302098
\(685\) 2.41497 + 4.18285i 0.0922713 + 0.159819i
\(686\) −29.0095 −1.10759
\(687\) 5.33251 9.23619i 0.203448 0.352382i
\(688\) 2.19104 + 3.79498i 0.0835324 + 0.144682i
\(689\) 5.82562 + 10.0903i 0.221938 + 0.384409i
\(690\) 5.51882 0.210098
\(691\) 17.4693 30.2576i 0.664562 1.15106i −0.314842 0.949144i \(-0.601951\pi\)
0.979404 0.201911i \(-0.0647152\pi\)
\(692\) 2.69104 4.66101i 0.102298 0.177185i
\(693\) 8.72867 15.1185i 0.331575 0.574304i
\(694\) −4.64148 8.03928i −0.176188 0.305167i
\(695\) −4.43163 + 7.67580i −0.168101 + 0.291160i
\(696\) −4.69104 8.12511i −0.177813 0.307982i
\(697\) 3.93337 0.148987
\(698\) 18.5898 0.703633
\(699\) 3.24059 + 5.61287i 0.122570 + 0.212298i
\(700\) −2.25941 + 3.91341i −0.0853976 + 0.147913i
\(701\) −19.5376 33.8402i −0.737926 1.27813i −0.953428 0.301622i \(-0.902472\pi\)
0.215501 0.976504i \(-0.430861\pi\)
\(702\) −3.51882 + 6.09477i −0.132809 + 0.230032i
\(703\) −9.80178 + 16.9772i −0.369681 + 0.640306i
\(704\) 1.93163 3.34568i 0.0728009 0.126095i
\(705\) −10.5565 −0.397579
\(706\) 13.2663 + 22.9779i 0.499284 + 0.864785i
\(707\) −22.0612 38.2111i −0.829696 1.43708i
\(708\) 6.77823 11.7402i 0.254741 0.441225i
\(709\) −45.1557 −1.69586 −0.847929 0.530110i \(-0.822150\pi\)
−0.847929 + 0.530110i \(0.822150\pi\)
\(710\) 1.51882 + 2.63067i 0.0570002 + 0.0987272i
\(711\) −4.38207 −0.164340
\(712\) 2.96237 0.111019
\(713\) 28.2710 12.0385i 1.05876 0.450846i
\(714\) 2.17438 0.0813741
\(715\) −27.1882 −1.01678
\(716\) −6.10601 10.5759i −0.228192 0.395240i
\(717\) 20.7641 0.775451
\(718\) 4.56837 7.91265i 0.170490 0.295298i
\(719\) −3.18630 5.51884i −0.118829 0.205818i 0.800475 0.599366i \(-0.204581\pi\)
−0.919304 + 0.393548i \(0.871247\pi\)
\(720\) −0.500000 0.866025i −0.0186339 0.0322749i
\(721\) 70.2967 2.61799
\(722\) 21.7120 37.6063i 0.808037 1.39956i
\(723\) −9.82778 + 17.0222i −0.365499 + 0.633063i
\(724\) 5.38207 9.32202i 0.200023 0.346450i
\(725\) −4.69104 8.12511i −0.174221 0.301759i
\(726\) −1.96237 + 3.39892i −0.0728303 + 0.126146i
\(727\) −25.9902 45.0164i −0.963925 1.66957i −0.712477 0.701695i \(-0.752427\pi\)
−0.251447 0.967871i \(-0.580907\pi\)
\(728\) −31.8018 −1.17865
\(729\) 1.00000 0.0370370
\(730\) −1.00000 1.73205i −0.0370117 0.0641061i
\(731\) 1.05429 1.82608i 0.0389943 0.0675401i
\(732\) 2.95044 + 5.11032i 0.109052 + 0.188883i
\(733\) 15.0586 26.0823i 0.556202 0.963371i −0.441606 0.897209i \(-0.645591\pi\)
0.997809 0.0661621i \(-0.0210754\pi\)
\(734\) −12.0000 + 20.7846i −0.442928 + 0.767174i
\(735\) 6.70985 11.6218i 0.247497 0.428677i
\(736\) −5.51882 −0.203426
\(737\) 4.79272 + 8.30124i 0.176542 + 0.305780i
\(738\) 4.08719 + 7.07922i 0.150452 + 0.260590i
\(739\) 16.6060 28.7624i 0.610862 1.05804i −0.380234 0.924890i \(-0.624156\pi\)
0.991095 0.133153i \(-0.0425102\pi\)
\(740\) −2.48118 −0.0912101
\(741\) −27.8018 48.1541i −1.02132 1.76898i
\(742\) 7.48118 0.274643
\(743\) −19.3444 −0.709679 −0.354839 0.934927i \(-0.615464\pi\)
−0.354839 + 0.934927i \(0.615464\pi\)
\(744\) −4.45044 3.34568i −0.163161 0.122658i
\(745\) −15.6556 −0.573575
\(746\) −25.3959 −0.929808
\(747\) 0.603846 + 1.04589i 0.0220936 + 0.0382672i
\(748\) −1.85893 −0.0679693
\(749\) −10.2099 + 17.6840i −0.373060 + 0.646159i
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 11.8325 + 20.4945i 0.431775 + 0.747856i 0.997026 0.0770630i \(-0.0245543\pi\)
−0.565252 + 0.824919i \(0.691221\pi\)
\(752\) 10.5565 0.384954
\(753\) −0.191035 + 0.330883i −0.00696172 + 0.0120581i
\(754\) 33.0138 57.1816i 1.20229 2.08243i
\(755\) 7.45044 12.9045i 0.271149 0.469645i
\(756\) 2.25941 + 3.91341i 0.0821739 + 0.142329i
\(757\) −17.6107 + 30.5027i −0.640073 + 1.10864i 0.345343 + 0.938477i \(0.387763\pi\)
−0.985416 + 0.170163i \(0.945571\pi\)
\(758\) −13.9385 24.1422i −0.506270 0.876885i
\(759\) 21.3206 0.773888
\(760\) 7.90089 0.286595
\(761\) −1.77606 3.07623i −0.0643823 0.111513i 0.832038 0.554719i \(-0.187174\pi\)
−0.896420 + 0.443206i \(0.853841\pi\)
\(762\) 1.60385 2.77794i 0.0581012 0.100634i
\(763\) −17.8513 30.9194i −0.646262 1.11936i
\(764\) −4.95044 + 8.57442i −0.179101 + 0.310212i
\(765\) −0.240592 + 0.416717i −0.00869861 + 0.0150664i
\(766\) −8.27823 + 14.3383i −0.299104 + 0.518064i
\(767\) 95.4053 3.44489
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −8.69104 15.0533i −0.313407 0.542836i 0.665691 0.746228i \(-0.268137\pi\)
−0.979098 + 0.203391i \(0.934804\pi\)
\(770\) −8.72867 + 15.1185i −0.314559 + 0.544833i
\(771\) −20.9718 −0.755282
\(772\) −10.6910 18.5174i −0.384779 0.666456i
\(773\) −28.0753 −1.00980 −0.504899 0.863179i \(-0.668470\pi\)
−0.504899 + 0.863179i \(0.668470\pi\)
\(774\) 4.38207 0.157510
\(775\) −4.45044 3.34568i −0.159865 0.120180i
\(776\) 11.4573 0.411294
\(777\) 11.2120 0.402229
\(778\) 14.8842 + 25.7802i 0.533626 + 0.924267i
\(779\) −64.5849 −2.31399
\(780\) 3.51882 6.09477i 0.125994 0.218228i
\(781\) 5.86758 + 10.1629i 0.209958 + 0.363659i
\(782\) 1.32778 + 2.29978i 0.0474814 + 0.0822401i
\(783\) −9.38207 −0.335288
\(784\) −6.70985 + 11.6218i −0.239638 + 0.415064i
\(785\) −1.22394 + 2.11992i −0.0436841 + 0.0756631i
\(786\) 3.32778 5.76389i 0.118698 0.205591i
\(787\) 24.1791 + 41.8795i 0.861892 + 1.49284i 0.870100 + 0.492875i \(0.164054\pi\)
−0.00820790 + 0.999966i \(0.502613\pi\)
\(788\) −3.65556 + 6.33162i −0.130224 + 0.225555i
\(789\) 1.19104 + 2.06293i 0.0424020 + 0.0734424i
\(790\) 4.38207 0.155907
\(791\) −33.5283 −1.19213
\(792\) −1.93163 3.34568i −0.0686374 0.118883i
\(793\) −20.7641 + 35.9645i −0.737356 + 1.27714i
\(794\) −10.3278 17.8882i −0.366519 0.634830i
\(795\) −0.827781 + 1.43376i −0.0293584 + 0.0508502i
\(796\) −1.39615 + 2.41821i −0.0494854 + 0.0857112i
\(797\) −10.7287 + 18.5826i −0.380029 + 0.658229i −0.991066 0.133373i \(-0.957419\pi\)
0.611037 + 0.791602i \(0.290753\pi\)
\(798\) −35.7027 −1.26386
\(799\) −2.53979 4.39905i −0.0898514 0.155627i
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) 1.48118 2.56548i 0.0523350 0.0906469i
\(802\) 18.8394 0.665243
\(803\) −3.86325 6.69135i −0.136331 0.236133i
\(804\) −2.48118 −0.0875046
\(805\) 24.9385 0.878967
\(806\) 4.73083 38.8972i 0.166636 1.37010i
\(807\) −18.7308 −0.659356
\(808\) −9.76414 −0.343501
\(809\) −17.7522 30.7477i −0.624135 1.08103i −0.988707 0.149858i \(-0.952118\pi\)
0.364573 0.931175i \(-0.381215\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −10.3444 + 17.9171i −0.363242 + 0.629154i −0.988492 0.151270i \(-0.951664\pi\)
0.625250 + 0.780424i \(0.284997\pi\)
\(812\) −21.1979 36.7159i −0.743901 1.28848i
\(813\) −3.91497 6.78093i −0.137304 0.237818i
\(814\) −9.58544 −0.335970
\(815\) 10.6603 18.4642i 0.373414 0.646772i
\(816\) 0.240592 0.416717i 0.00842239 0.0145880i
\(817\) −17.3111 + 29.9837i −0.605640 + 1.04900i
\(818\) 3.67438 + 6.36421i 0.128472 + 0.222519i
\(819\) −15.9009 + 27.5411i −0.555622 + 0.962365i
\(820\) −4.08719 7.07922i −0.142731 0.247217i
\(821\) 1.34876 0.0470720 0.0235360 0.999723i \(-0.492508\pi\)
0.0235360 + 0.999723i \(0.492508\pi\)
\(822\) −4.82994 −0.168464
\(823\) −9.33468 16.1681i −0.325386 0.563586i 0.656204 0.754583i \(-0.272161\pi\)
−0.981590 + 0.190998i \(0.938828\pi\)
\(824\) 7.77823 13.4723i 0.270967 0.469329i
\(825\) −1.93163 3.34568i −0.0672506 0.116481i
\(826\) 30.6296 53.0519i 1.06574 1.84591i
\(827\) 13.0376 22.5818i 0.453363 0.785248i −0.545229 0.838287i \(-0.683557\pi\)
0.998592 + 0.0530392i \(0.0168908\pi\)
\(828\) −2.75941 + 4.77944i −0.0958961 + 0.166097i
\(829\) −21.5608 −0.748837 −0.374418 0.927260i \(-0.622158\pi\)
−0.374418 + 0.927260i \(0.622158\pi\)
\(830\) −0.603846 1.04589i −0.0209598 0.0363034i
\(831\) −7.10385 12.3042i −0.246430 0.426829i
\(832\) −3.51882 + 6.09477i −0.121993 + 0.211298i
\(833\) 6.45734 0.223733
\(834\) −4.43163 7.67580i −0.153455 0.265791i
\(835\) −8.58976 −0.297261
\(836\) 30.5231 1.05566
\(837\) −5.12266 + 2.18136i −0.177065 + 0.0753988i
\(838\) 11.8633 0.409809
\(839\) −9.56077 −0.330074 −0.165037 0.986287i \(-0.552774\pi\)
−0.165037 + 0.986287i \(0.552774\pi\)
\(840\) −2.25941 3.91341i −0.0779570 0.135025i
\(841\) 59.0233 2.03528
\(842\) −9.81370 + 16.9978i −0.338202 + 0.585784i
\(843\) 2.31112 + 4.00299i 0.0795994 + 0.137870i
\(844\) 0.0495562 + 0.0858338i 0.00170579 + 0.00295452i
\(845\) 36.5283 1.25661
\(846\) 5.27823 9.14215i 0.181469 0.314314i
\(847\) −8.86758 + 15.3591i −0.304693 + 0.527745i
\(848\) 0.827781 1.43376i 0.0284261 0.0492355i
\(849\) 12.7475 + 22.0793i 0.437493 + 0.757759i
\(850\) 0.240592 0.416717i 0.00825223 0.0142933i
\(851\) 6.84660 + 11.8587i 0.234698 + 0.406509i
\(852\) −3.03763 −0.104068
\(853\) −42.6412 −1.46001 −0.730003 0.683444i \(-0.760481\pi\)
−0.730003 + 0.683444i \(0.760481\pi\)
\(854\) 13.3325 + 23.0926i 0.456229 + 0.790212i
\(855\) 3.95044 6.84237i 0.135102 0.234004i
\(856\) 2.25941 + 3.91341i 0.0772250 + 0.133758i
\(857\) −11.6765 + 20.2244i −0.398863 + 0.690851i −0.993586 0.113080i \(-0.963928\pi\)
0.594723 + 0.803931i \(0.297262\pi\)
\(858\) 13.5941 23.5456i 0.464094 0.803835i
\(859\) 2.56837 4.44855i 0.0876318 0.151783i −0.818878 0.573968i \(-0.805403\pi\)
0.906510 + 0.422185i \(0.138737\pi\)
\(860\) −4.38207 −0.149427
\(861\) 18.4693 + 31.9897i 0.629431 + 1.09021i
\(862\) 15.6436 + 27.0956i 0.532824 + 0.922879i
\(863\) 22.1672 38.3947i 0.754580 1.30697i −0.191003 0.981589i \(-0.561174\pi\)
0.945583 0.325381i \(-0.105493\pi\)
\(864\) 1.00000 0.0340207
\(865\) 2.69104 + 4.66101i 0.0914980 + 0.158479i
\(866\) −8.68888 −0.295260
\(867\) 16.7685 0.569487
\(868\) −20.1107 15.1185i −0.682603 0.513155i
\(869\) 16.9291 0.574279
\(870\) 9.38207 0.318082
\(871\) −8.73083 15.1222i −0.295833 0.512398i
\(872\) −7.90089 −0.267558
\(873\) 5.72867 9.92235i 0.193886 0.335821i
\(874\) −21.8018 37.7618i −0.737456 1.27731i
\(875\) −2.25941 3.91341i −0.0763819 0.132297i
\(876\) 2.00000 0.0675737
\(877\) −4.17911 + 7.23844i −0.141119 + 0.244425i −0.927918 0.372784i \(-0.878403\pi\)
0.786800 + 0.617209i \(0.211737\pi\)
\(878\) 16.6248 28.7950i 0.561061 0.971785i
\(879\) −3.86541 + 6.69509i −0.130377 + 0.225820i
\(880\) 1.93163 + 3.34568i 0.0651151 + 0.112783i
\(881\) −2.49311 + 4.31819i −0.0839949 + 0.145483i −0.904962 0.425491i \(-0.860101\pi\)
0.820968 + 0.570975i \(0.193435\pi\)
\(882\) 6.70985 + 11.6218i 0.225932 + 0.391327i
\(883\) 16.1600 0.543827 0.271914 0.962322i \(-0.412343\pi\)
0.271914 + 0.962322i \(0.412343\pi\)
\(884\) 3.38639 0.113897
\(885\) 6.77823 + 11.7402i 0.227848 + 0.394644i
\(886\) 7.41970 12.8513i 0.249270 0.431748i
\(887\) 23.0586 + 39.9387i 0.774232 + 1.34101i 0.935225 + 0.354054i \(0.115197\pi\)
−0.160993 + 0.986956i \(0.551470\pi\)
\(888\) 1.24059 2.14877i 0.0416315 0.0721079i
\(889\) 7.24749 12.5530i 0.243073 0.421015i
\(890\) −1.48118 + 2.56548i −0.0496494 + 0.0859952i
\(891\) −3.86325 −0.129424
\(892\) 8.12266 + 14.0689i 0.271967 + 0.471060i
\(893\) 41.7027 + 72.2311i 1.39553 + 2.41712i
\(894\) 7.82778 13.5581i 0.261800 0.453451i
\(895\) 12.2120 0.408203
\(896\) 2.25941 + 3.91341i 0.0754815 + 0.130738i
\(897\) −38.8394 −1.29681
\(898\) −5.80178 −0.193608
\(899\) 48.0612 20.4657i 1.60293 0.682568i
\(900\) 1.00000 0.0333333
\(901\) −0.796629 −0.0265396
\(902\) −15.7899 27.3488i −0.525745 0.910616i
\(903\) 19.8018 0.658962
\(904\) −3.70985 + 6.42565i −0.123388 + 0.213714i
\(905\) 5.38207 + 9.32202i 0.178906 + 0.309874i
\(906\) 7.45044 + 12.9045i 0.247524 + 0.428725i
\(907\) 50.0753 1.66272 0.831361 0.555733i \(-0.187562\pi\)
0.831361 + 0.555733i \(0.187562\pi\)
\(908\) 5.64148 9.77133i 0.187219 0.324273i
\(909\) −4.88207 + 8.45599i −0.161928 + 0.280468i
\(910\) 15.9009 27.5411i 0.527109 0.912980i
\(911\) −24.7146 42.8069i −0.818831 1.41826i −0.906544 0.422111i \(-0.861289\pi\)
0.0877135 0.996146i \(-0.472044\pi\)
\(912\) −3.95044 + 6.84237i −0.130812 + 0.226573i
\(913\) −2.33281 4.04055i −0.0772047 0.133723i
\(914\) −29.3864 −0.972015
\(915\) −5.90089 −0.195077
\(916\) −5.33251 9.23619i −0.176191 0.305172i
\(917\) 15.0376 26.0459i 0.496586 0.860113i
\(918\) −0.240592 0.416717i −0.00794071 0.0137537i
\(919\) −10.6958 + 18.5256i −0.352821 + 0.611104i −0.986743 0.162294i \(-0.948111\pi\)
0.633922 + 0.773397i \(0.281444\pi\)
\(920\) 2.75941 4.77944i 0.0909750 0.157573i
\(921\) −0.223935 + 0.387867i −0.00737892 + 0.0127807i
\(922\) −25.4907 −0.839490
\(923\) −10.6889 18.5137i −0.351829 0.609385i
\(924\) −8.72867 15.1185i −0.287152 0.497362i
\(925\) 1.24059 2.14877i 0.0407904 0.0706510i
\(926\) −17.3582 −0.570427
\(927\) −7.77823 13.4723i −0.255470 0.442488i
\(928\) −9.38207 −0.307982
\(929\) −50.1744 −1.64617 −0.823084 0.567920i \(-0.807748\pi\)
−0.823084 + 0.567920i \(0.807748\pi\)
\(930\) 5.12266 2.18136i 0.167979 0.0715296i
\(931\) −106.028 −3.47491
\(932\) 6.48118 0.212298
\(933\) 3.34444 + 5.79274i 0.109492 + 0.189646i
\(934\) −31.9718 −1.04615
\(935\) 0.929467 1.60988i 0.0303968 0.0526488i
\(936\) 3.51882 + 6.09477i 0.115016 + 0.199214i
\(937\) −8.80178 15.2451i −0.287541 0.498036i 0.685681 0.727902i \(-0.259505\pi\)
−0.973222 + 0.229866i \(0.926171\pi\)
\(938\) −11.2120 −0.366085
\(939\) −1.48334 + 2.56923i −0.0484071 + 0.0838435i
\(940\) −5.27823 + 9.14215i −0.172157 + 0.298184i
\(941\) −13.0188 + 22.5493i −0.424401 + 0.735085i −0.996364 0.0851948i \(-0.972849\pi\)
0.571963 + 0.820279i \(0.306182\pi\)
\(942\) −1.22394 2.11992i −0.0398780 0.0690707i
\(943\) −22.5565 + 39.0689i −0.734539 + 1.27226i
\(944\) −6.77823 11.7402i −0.220612 0.382112i
\(945\) −4.51882 −0.146997
\(946\) −16.9291 −0.550411
\(947\) −5.44355 9.42851i −0.176892 0.306385i 0.763923 0.645308i \(-0.223271\pi\)
−0.940814 + 0.338923i \(0.889938\pi\)
\(948\) −2.19104 + 3.79498i −0.0711615 + 0.123255i
\(949\) 7.03763 + 12.1895i 0.228451 + 0.395689i
\(950\) −3.95044 + 6.84237i −0.128169 + 0.221996i
\(951\) 3.34660 5.79648i 0.108521 0.187964i
\(952\) 1.08719 1.88307i 0.0352360 0.0610306i
\(953\) 26.0991 0.845433 0.422717 0.906262i \(-0.361077\pi\)
0.422717 + 0.906262i \(0.361077\pi\)
\(954\) −0.827781 1.43376i −0.0268004 0.0464197i
\(955\) −4.95044 8.57442i −0.160193 0.277462i
\(956\) 10.3821 17.9823i 0.335780 0.581588i
\(957\) 36.2453 1.17164
\(958\) −10.3325 17.8964i −0.333828 0.578208i
\(959\) −21.8256 −0.704786
\(960\) −1.00000 −0.0322749
\(961\) 21.4833 22.3487i 0.693011 0.720927i
\(962\) 17.4617 0.562986
\(963\) 4.51882 0.145617
\(964\) 9.82778 + 17.0222i 0.316532 + 0.548249i
\(965\) 21.3821 0.688313
\(966\) −12.4693 + 21.5974i −0.401192 + 0.694885i
\(967\) 22.1505 + 38.3658i 0.712313 + 1.23376i 0.963987 + 0.265950i \(0.0856857\pi\)
−0.251674 + 0.967812i \(0.580981\pi\)
\(968\) 1.96237 + 3.39892i 0.0630729 + 0.109245i
\(969\) 3.80178 0.122131
\(970\) −5.72867 + 9.92235i −0.183936 + 0.318587i
\(971\) 9.41281 16.3035i 0.302071 0.523203i −0.674534 0.738244i \(-0.735655\pi\)
0.976605 + 0.215041i \(0.0689885\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) −20.0257 34.6855i −0.641995 1.11197i
\(974\) −11.6415 + 20.1636i −0.373017 + 0.646084i
\(975\) 3.51882 + 6.09477i 0.112692 + 0.195189i
\(976\) 5.90089 0.188883
\(977\) −35.0376 −1.12095 −0.560477 0.828170i \(-0.689382\pi\)
−0.560477 + 0.828170i \(0.689382\pi\)
\(978\) 10.6603 + 18.4642i 0.340879 + 0.590419i
\(979\) −5.72219 + 9.91112i −0.182882 + 0.316761i
\(980\) −6.70985 11.6218i −0.214338 0.371245i
\(981\) −3.95044 + 6.84237i −0.126128 + 0.218460i
\(982\) −12.8701 + 22.2918i −0.410703 + 0.711358i
\(983\) 0.617929 1.07028i 0.0197089 0.0341368i −0.856003 0.516971i \(-0.827059\pi\)
0.875712 + 0.482834i \(0.160393\pi\)
\(984\) 8.17438 0.260590
\(985\) −3.65556 6.33162i −0.116476 0.201742i
\(986\) 2.25725 + 3.90967i 0.0718854 + 0.124509i
\(987\) 23.8513 41.3117i 0.759196 1.31497i
\(988\) −55.6036 −1.76898
\(989\) 12.0919 + 20.9438i 0.384501 + 0.665975i
\(990\) 3.86325 0.122782
\(991\) 3.65124 0.115986 0.0579928 0.998317i \(-0.481530\pi\)
0.0579928 + 0.998317i \(0.481530\pi\)
\(992\) −5.12266 + 2.18136i −0.162645 + 0.0692582i
\(993\) 7.41024 0.235157
\(994\) −13.7265 −0.435378
\(995\) −1.39615 2.41821i −0.0442611 0.0766624i
\(996\) 1.20769 0.0382672
\(997\) 21.7899 37.7411i 0.690092 1.19527i −0.281716 0.959498i \(-0.590904\pi\)
0.971807 0.235776i \(-0.0757631\pi\)
\(998\) 6.37015 + 11.0334i 0.201644 + 0.349257i
\(999\) −1.24059 2.14877i −0.0392506 0.0679840i
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.i.n.211.1 6
31.5 even 3 inner 930.2.i.n.811.1 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.i.n.211.1 6 1.1 even 1 trivial
930.2.i.n.811.1 yes 6 31.5 even 3 inner