Properties

Label 35.2.k.a.33.1
Level $35$
Weight $2$
Character 35.33
Analytic conductor $0.279$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,2,Mod(3,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35.k (of order \(12\), 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: \(0.279476407074\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 35.33
Dual form 35.2.k.a.17.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.133975 - 0.500000i) q^{2} +(-0.500000 - 0.133975i) q^{3} +(1.50000 - 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +0.267949i q^{6} +(-0.866025 + 2.50000i) q^{7} +(-1.36603 - 1.36603i) q^{8} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})\) \(q+(-0.133975 - 0.500000i) q^{2} +(-0.500000 - 0.133975i) q^{3} +(1.50000 - 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +0.267949i q^{6} +(-0.866025 + 2.50000i) q^{7} +(-1.36603 - 1.36603i) q^{8} +(-2.36603 - 1.36603i) q^{9} +(0.866025 + 0.767949i) q^{10} +(1.36603 + 2.36603i) q^{11} +(-0.866025 + 0.232051i) q^{12} +(2.00000 - 2.00000i) q^{13} +(1.36603 + 0.0980762i) q^{14} +(1.09808 - 0.366025i) q^{15} +(1.23205 - 2.13397i) q^{16} +(1.00000 - 3.73205i) q^{17} +(-0.366025 + 1.36603i) q^{18} +(-0.366025 + 0.633975i) q^{19} +(-1.73205 + 3.46410i) q^{20} +(0.767949 - 1.13397i) q^{21} +(1.00000 - 1.00000i) q^{22} +(-0.133975 + 0.0358984i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.96410 - 4.59808i) q^{25} +(-1.26795 - 0.732051i) q^{26} +(2.09808 + 2.09808i) q^{27} +(0.866025 + 4.50000i) q^{28} +3.00000i q^{29} +(-0.330127 - 0.500000i) q^{30} +(-6.46410 + 3.73205i) q^{31} +(-4.96410 - 1.33013i) q^{32} +(-0.366025 - 1.36603i) q^{33} -2.00000 q^{34} +(-1.46410 - 5.73205i) q^{35} -4.73205 q^{36} +(1.26795 + 4.73205i) q^{37} +(0.366025 + 0.0980762i) q^{38} +(-1.26795 + 0.732051i) q^{39} +(4.23205 + 0.866025i) q^{40} -6.46410i q^{41} +(-0.669873 - 0.232051i) q^{42} +(2.83013 + 2.83013i) q^{43} +(4.09808 + 2.36603i) q^{44} +(6.09808 - 0.366025i) q^{45} +(0.0358984 + 0.0621778i) q^{46} +(8.83013 - 2.36603i) q^{47} +(-0.901924 + 0.901924i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(-2.56218 - 0.366025i) q^{50} +(-1.00000 + 1.73205i) q^{51} +(1.26795 - 4.73205i) q^{52} +(-1.83013 + 6.83013i) q^{53} +(0.767949 - 1.33013i) q^{54} +(-5.46410 - 2.73205i) q^{55} +(4.59808 - 2.23205i) q^{56} +(0.267949 - 0.267949i) q^{57} +(1.50000 - 0.401924i) q^{58} +(4.09808 + 7.09808i) q^{59} +(1.33013 - 1.50000i) q^{60} +(1.33013 + 0.767949i) q^{61} +(2.73205 + 2.73205i) q^{62} +(5.46410 - 4.73205i) q^{63} -2.26795i q^{64} +(-1.26795 + 6.19615i) q^{65} +(-0.633975 + 0.366025i) q^{66} +(-10.6962 - 2.86603i) q^{67} +(-1.73205 - 6.46410i) q^{68} +0.0717968 q^{69} +(-2.66987 + 1.50000i) q^{70} +1.26795 q^{71} +(1.36603 + 5.09808i) q^{72} +(-12.9282 - 3.46410i) q^{73} +(2.19615 - 1.26795i) q^{74} +(-1.59808 + 2.03590i) q^{75} +1.26795i q^{76} +(-7.09808 + 1.36603i) q^{77} +(0.535898 + 0.535898i) q^{78} +(-2.83013 - 1.63397i) q^{79} +(0.330127 + 5.50000i) q^{80} +(3.33013 + 5.76795i) q^{81} +(-3.23205 + 0.866025i) q^{82} +(2.09808 - 2.09808i) q^{83} +(0.169873 - 2.36603i) q^{84} +(2.73205 + 8.19615i) q^{85} +(1.03590 - 1.79423i) q^{86} +(0.401924 - 1.50000i) q^{87} +(1.36603 - 5.09808i) q^{88} +(0.330127 - 0.571797i) q^{89} +(-1.00000 - 3.00000i) q^{90} +(3.26795 + 6.73205i) q^{91} +(-0.169873 + 0.169873i) q^{92} +(3.73205 - 1.00000i) q^{93} +(-2.36603 - 4.09808i) q^{94} +(-0.0980762 - 1.63397i) q^{95} +(2.30385 + 1.33013i) q^{96} +(5.92820 + 5.92820i) q^{97} +(-1.42820 + 3.33013i) q^{98} -7.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 2 q^{3} + 6 q^{4} - 4 q^{5} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 2 q^{3} + 6 q^{4} - 4 q^{5} - 2 q^{8} - 6 q^{9} + 2 q^{11} + 8 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{16} + 4 q^{17} + 2 q^{18} + 2 q^{19} + 10 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 6 q^{25} - 12 q^{26} - 2 q^{27} + 16 q^{30} - 12 q^{31} - 6 q^{32} + 2 q^{33} - 8 q^{34} + 8 q^{35} - 12 q^{36} + 12 q^{37} - 2 q^{38} - 12 q^{39} + 10 q^{40} - 20 q^{42} - 6 q^{43} + 6 q^{44} + 14 q^{45} + 14 q^{46} + 18 q^{47} - 14 q^{48} - 22 q^{49} + 14 q^{50} - 4 q^{51} + 12 q^{52} + 10 q^{53} + 10 q^{54} - 8 q^{55} + 8 q^{56} + 8 q^{57} + 6 q^{58} + 6 q^{59} - 12 q^{60} - 12 q^{61} + 4 q^{62} + 8 q^{63} - 12 q^{65} - 6 q^{66} - 22 q^{67} + 28 q^{69} - 28 q^{70} + 12 q^{71} + 2 q^{72} - 24 q^{73} - 12 q^{74} + 4 q^{75} - 18 q^{77} + 16 q^{78} + 6 q^{79} - 16 q^{80} - 4 q^{81} - 6 q^{82} - 2 q^{83} + 18 q^{84} + 4 q^{85} + 18 q^{86} + 12 q^{87} + 2 q^{88} - 16 q^{89} - 4 q^{90} + 20 q^{91} - 18 q^{92} + 8 q^{93} - 6 q^{94} + 10 q^{95} + 30 q^{96} - 4 q^{97} + 22 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.133975 0.500000i −0.0947343 0.353553i 0.902245 0.431224i \(-0.141918\pi\)
−0.996979 + 0.0776710i \(0.975252\pi\)
\(3\) −0.500000 0.133975i −0.288675 0.0773503i 0.111576 0.993756i \(-0.464410\pi\)
−0.400251 + 0.916406i \(0.631077\pi\)
\(4\) 1.50000 0.866025i 0.750000 0.433013i
\(5\) −1.86603 + 1.23205i −0.834512 + 0.550990i
\(6\) 0.267949i 0.109390i
\(7\) −0.866025 + 2.50000i −0.327327 + 0.944911i
\(8\) −1.36603 1.36603i −0.482963 0.482963i
\(9\) −2.36603 1.36603i −0.788675 0.455342i
\(10\) 0.866025 + 0.767949i 0.273861 + 0.242847i
\(11\) 1.36603 + 2.36603i 0.411872 + 0.713384i 0.995094 0.0989291i \(-0.0315417\pi\)
−0.583222 + 0.812313i \(0.698208\pi\)
\(12\) −0.866025 + 0.232051i −0.250000 + 0.0669873i
\(13\) 2.00000 2.00000i 0.554700 0.554700i −0.373094 0.927794i \(-0.621703\pi\)
0.927794 + 0.373094i \(0.121703\pi\)
\(14\) 1.36603 + 0.0980762i 0.365086 + 0.0262120i
\(15\) 1.09808 0.366025i 0.283522 0.0945074i
\(16\) 1.23205 2.13397i 0.308013 0.533494i
\(17\) 1.00000 3.73205i 0.242536 0.905155i −0.732070 0.681229i \(-0.761446\pi\)
0.974606 0.223926i \(-0.0718875\pi\)
\(18\) −0.366025 + 1.36603i −0.0862730 + 0.321975i
\(19\) −0.366025 + 0.633975i −0.0839720 + 0.145444i −0.904953 0.425512i \(-0.860094\pi\)
0.820981 + 0.570956i \(0.193427\pi\)
\(20\) −1.73205 + 3.46410i −0.387298 + 0.774597i
\(21\) 0.767949 1.13397i 0.167580 0.247454i
\(22\) 1.00000 1.00000i 0.213201 0.213201i
\(23\) −0.133975 + 0.0358984i −0.0279356 + 0.00748533i −0.272760 0.962082i \(-0.587936\pi\)
0.244824 + 0.969567i \(0.421270\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 1.96410 4.59808i 0.392820 0.919615i
\(26\) −1.26795 0.732051i −0.248665 0.143567i
\(27\) 2.09808 + 2.09808i 0.403775 + 0.403775i
\(28\) 0.866025 + 4.50000i 0.163663 + 0.850420i
\(29\) 3.00000i 0.557086i 0.960424 + 0.278543i \(0.0898515\pi\)
−0.960424 + 0.278543i \(0.910149\pi\)
\(30\) −0.330127 0.500000i −0.0602727 0.0912871i
\(31\) −6.46410 + 3.73205i −1.16099 + 0.670296i −0.951540 0.307524i \(-0.900500\pi\)
−0.209447 + 0.977820i \(0.567166\pi\)
\(32\) −4.96410 1.33013i −0.877537 0.235135i
\(33\) −0.366025 1.36603i −0.0637168 0.237795i
\(34\) −2.00000 −0.342997
\(35\) −1.46410 5.73205i −0.247478 0.968893i
\(36\) −4.73205 −0.788675
\(37\) 1.26795 + 4.73205i 0.208450 + 0.777944i 0.988370 + 0.152066i \(0.0485927\pi\)
−0.779921 + 0.625878i \(0.784741\pi\)
\(38\) 0.366025 + 0.0980762i 0.0593772 + 0.0159101i
\(39\) −1.26795 + 0.732051i −0.203034 + 0.117222i
\(40\) 4.23205 + 0.866025i 0.669146 + 0.136931i
\(41\) 6.46410i 1.00952i −0.863259 0.504762i \(-0.831580\pi\)
0.863259 0.504762i \(-0.168420\pi\)
\(42\) −0.669873 0.232051i −0.103364 0.0358062i
\(43\) 2.83013 + 2.83013i 0.431590 + 0.431590i 0.889169 0.457579i \(-0.151283\pi\)
−0.457579 + 0.889169i \(0.651283\pi\)
\(44\) 4.09808 + 2.36603i 0.617808 + 0.356692i
\(45\) 6.09808 0.366025i 0.909048 0.0545638i
\(46\) 0.0358984 + 0.0621778i 0.00529293 + 0.00916762i
\(47\) 8.83013 2.36603i 1.28801 0.345120i 0.451103 0.892472i \(-0.351031\pi\)
0.836903 + 0.547351i \(0.184364\pi\)
\(48\) −0.901924 + 0.901924i −0.130181 + 0.130181i
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) −2.56218 0.366025i −0.362347 0.0517638i
\(51\) −1.00000 + 1.73205i −0.140028 + 0.242536i
\(52\) 1.26795 4.73205i 0.175833 0.656217i
\(53\) −1.83013 + 6.83013i −0.251387 + 0.938190i 0.718677 + 0.695344i \(0.244748\pi\)
−0.970065 + 0.242846i \(0.921919\pi\)
\(54\) 0.767949 1.33013i 0.104505 0.181007i
\(55\) −5.46410 2.73205i −0.736779 0.368390i
\(56\) 4.59808 2.23205i 0.614444 0.298270i
\(57\) 0.267949 0.267949i 0.0354907 0.0354907i
\(58\) 1.50000 0.401924i 0.196960 0.0527752i
\(59\) 4.09808 + 7.09808i 0.533524 + 0.924091i 0.999233 + 0.0391530i \(0.0124660\pi\)
−0.465709 + 0.884938i \(0.654201\pi\)
\(60\) 1.33013 1.50000i 0.171719 0.193649i
\(61\) 1.33013 + 0.767949i 0.170305 + 0.0983258i 0.582730 0.812666i \(-0.301985\pi\)
−0.412424 + 0.910992i \(0.635318\pi\)
\(62\) 2.73205 + 2.73205i 0.346971 + 0.346971i
\(63\) 5.46410 4.73205i 0.688412 0.596182i
\(64\) 2.26795i 0.283494i
\(65\) −1.26795 + 6.19615i −0.157270 + 0.768538i
\(66\) −0.633975 + 0.366025i −0.0780369 + 0.0450546i
\(67\) −10.6962 2.86603i −1.30674 0.350141i −0.462747 0.886490i \(-0.653136\pi\)
−0.843996 + 0.536350i \(0.819803\pi\)
\(68\) −1.73205 6.46410i −0.210042 0.783887i
\(69\) 0.0717968 0.00864332
\(70\) −2.66987 + 1.50000i −0.319111 + 0.179284i
\(71\) 1.26795 0.150478 0.0752389 0.997166i \(-0.476028\pi\)
0.0752389 + 0.997166i \(0.476028\pi\)
\(72\) 1.36603 + 5.09808i 0.160988 + 0.600814i
\(73\) −12.9282 3.46410i −1.51313 0.405442i −0.595658 0.803238i \(-0.703109\pi\)
−0.917474 + 0.397796i \(0.869775\pi\)
\(74\) 2.19615 1.26795i 0.255298 0.147396i
\(75\) −1.59808 + 2.03590i −0.184530 + 0.235085i
\(76\) 1.26795i 0.145444i
\(77\) −7.09808 + 1.36603i −0.808901 + 0.155673i
\(78\) 0.535898 + 0.535898i 0.0606785 + 0.0606785i
\(79\) −2.83013 1.63397i −0.318414 0.183837i 0.332271 0.943184i \(-0.392185\pi\)
−0.650686 + 0.759347i \(0.725518\pi\)
\(80\) 0.330127 + 5.50000i 0.0369093 + 0.614919i
\(81\) 3.33013 + 5.76795i 0.370014 + 0.640883i
\(82\) −3.23205 + 0.866025i −0.356920 + 0.0956365i
\(83\) 2.09808 2.09808i 0.230294 0.230294i −0.582522 0.812815i \(-0.697934\pi\)
0.812815 + 0.582522i \(0.197934\pi\)
\(84\) 0.169873 2.36603i 0.0185347 0.258155i
\(85\) 2.73205 + 8.19615i 0.296333 + 0.888998i
\(86\) 1.03590 1.79423i 0.111704 0.193477i
\(87\) 0.401924 1.50000i 0.0430908 0.160817i
\(88\) 1.36603 5.09808i 0.145619 0.543457i
\(89\) 0.330127 0.571797i 0.0349934 0.0606103i −0.847998 0.529999i \(-0.822192\pi\)
0.882992 + 0.469389i \(0.155526\pi\)
\(90\) −1.00000 3.00000i −0.105409 0.316228i
\(91\) 3.26795 + 6.73205i 0.342574 + 0.705711i
\(92\) −0.169873 + 0.169873i −0.0177105 + 0.0177105i
\(93\) 3.73205 1.00000i 0.386996 0.103695i
\(94\) −2.36603 4.09808i −0.244037 0.422684i
\(95\) −0.0980762 1.63397i −0.0100624 0.167642i
\(96\) 2.30385 + 1.33013i 0.235135 + 0.135756i
\(97\) 5.92820 + 5.92820i 0.601918 + 0.601918i 0.940821 0.338903i \(-0.110056\pi\)
−0.338903 + 0.940821i \(0.610056\pi\)
\(98\) −1.42820 + 3.33013i −0.144270 + 0.336394i
\(99\) 7.46410i 0.750170i
\(100\) −1.03590 8.59808i −0.103590 0.859808i
\(101\) 7.16025 4.13397i 0.712472 0.411346i −0.0995037 0.995037i \(-0.531726\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 1.00000 + 0.267949i 0.0990148 + 0.0265309i
\(103\) 1.23205 + 4.59808i 0.121398 + 0.453062i 0.999686 0.0250698i \(-0.00798081\pi\)
−0.878288 + 0.478132i \(0.841314\pi\)
\(104\) −5.46410 −0.535799
\(105\) −0.0358984 + 3.06218i −0.00350332 + 0.298838i
\(106\) 3.66025 0.355515
\(107\) −3.40192 12.6962i −0.328876 1.22738i −0.910357 0.413823i \(-0.864193\pi\)
0.581481 0.813560i \(-0.302474\pi\)
\(108\) 4.96410 + 1.33013i 0.477671 + 0.127992i
\(109\) 8.76795 5.06218i 0.839817 0.484869i −0.0173849 0.999849i \(-0.505534\pi\)
0.857202 + 0.514980i \(0.172201\pi\)
\(110\) −0.633975 + 3.09808i −0.0604471 + 0.295390i
\(111\) 2.53590i 0.240697i
\(112\) 4.26795 + 4.92820i 0.403283 + 0.465671i
\(113\) −7.73205 7.73205i −0.727370 0.727370i 0.242725 0.970095i \(-0.421959\pi\)
−0.970095 + 0.242725i \(0.921959\pi\)
\(114\) −0.169873 0.0980762i −0.0159101 0.00918568i
\(115\) 0.205771 0.232051i 0.0191883 0.0216388i
\(116\) 2.59808 + 4.50000i 0.241225 + 0.417815i
\(117\) −7.46410 + 2.00000i −0.690056 + 0.184900i
\(118\) 3.00000 3.00000i 0.276172 0.276172i
\(119\) 8.46410 + 5.73205i 0.775903 + 0.525456i
\(120\) −2.00000 1.00000i −0.182574 0.0912871i
\(121\) 1.76795 3.06218i 0.160723 0.278380i
\(122\) 0.205771 0.767949i 0.0186297 0.0695269i
\(123\) −0.866025 + 3.23205i −0.0780869 + 0.291424i
\(124\) −6.46410 + 11.1962i −0.580493 + 1.00544i
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) −3.09808 2.09808i −0.275999 0.186911i
\(127\) 0.464102 0.464102i 0.0411824 0.0411824i −0.686216 0.727398i \(-0.740729\pi\)
0.727398 + 0.686216i \(0.240729\pi\)
\(128\) −11.0622 + 2.96410i −0.977768 + 0.261992i
\(129\) −1.03590 1.79423i −0.0912058 0.157973i
\(130\) 3.26795 0.196152i 0.286618 0.0172037i
\(131\) −13.3923 7.73205i −1.17009 0.675552i −0.216390 0.976307i \(-0.569428\pi\)
−0.953702 + 0.300755i \(0.902761\pi\)
\(132\) −1.73205 1.73205i −0.150756 0.150756i
\(133\) −1.26795 1.46410i −0.109945 0.126954i
\(134\) 5.73205i 0.495174i
\(135\) −6.50000 1.33013i −0.559431 0.114479i
\(136\) −6.46410 + 3.73205i −0.554292 + 0.320021i
\(137\) 13.1962 + 3.53590i 1.12742 + 0.302092i 0.773884 0.633327i \(-0.218311\pi\)
0.353539 + 0.935420i \(0.384978\pi\)
\(138\) −0.00961894 0.0358984i −0.000818819 0.00305587i
\(139\) 5.66025 0.480096 0.240048 0.970761i \(-0.422837\pi\)
0.240048 + 0.970761i \(0.422837\pi\)
\(140\) −7.16025 7.33013i −0.605152 0.619509i
\(141\) −4.73205 −0.398511
\(142\) −0.169873 0.633975i −0.0142554 0.0532020i
\(143\) 7.46410 + 2.00000i 0.624180 + 0.167248i
\(144\) −5.83013 + 3.36603i −0.485844 + 0.280502i
\(145\) −3.69615 5.59808i −0.306949 0.464895i
\(146\) 6.92820i 0.573382i
\(147\) 2.16987 + 2.90192i 0.178968 + 0.239347i
\(148\) 6.00000 + 6.00000i 0.493197 + 0.493197i
\(149\) −0.696152 0.401924i −0.0570310 0.0329269i 0.471213 0.882019i \(-0.343816\pi\)
−0.528244 + 0.849092i \(0.677150\pi\)
\(150\) 1.23205 + 0.526279i 0.100597 + 0.0429705i
\(151\) −6.92820 12.0000i −0.563809 0.976546i −0.997159 0.0753205i \(-0.976002\pi\)
0.433350 0.901226i \(-0.357331\pi\)
\(152\) 1.36603 0.366025i 0.110799 0.0296886i
\(153\) −7.46410 + 7.46410i −0.603437 + 0.603437i
\(154\) 1.63397 + 3.36603i 0.131669 + 0.271242i
\(155\) 7.46410 14.9282i 0.599531 1.19906i
\(156\) −1.26795 + 2.19615i −0.101517 + 0.175833i
\(157\) −1.24167 + 4.63397i −0.0990960 + 0.369831i −0.997609 0.0691164i \(-0.977982\pi\)
0.898513 + 0.438948i \(0.144649\pi\)
\(158\) −0.437822 + 1.63397i −0.0348313 + 0.129992i
\(159\) 1.83013 3.16987i 0.145139 0.251387i
\(160\) 10.9019 3.63397i 0.861873 0.287291i
\(161\) 0.0262794 0.366025i 0.00207111 0.0288468i
\(162\) 2.43782 2.43782i 0.191533 0.191533i
\(163\) 13.5622 3.63397i 1.06227 0.284635i 0.314958 0.949106i \(-0.398010\pi\)
0.747314 + 0.664471i \(0.231343\pi\)
\(164\) −5.59808 9.69615i −0.437136 0.757142i
\(165\) 2.36603 + 2.09808i 0.184195 + 0.163335i
\(166\) −1.33013 0.767949i −0.103238 0.0596044i
\(167\) −11.7583 11.7583i −0.909887 0.909887i 0.0863757 0.996263i \(-0.472471\pi\)
−0.996263 + 0.0863757i \(0.972471\pi\)
\(168\) −2.59808 + 0.500000i −0.200446 + 0.0385758i
\(169\) 5.00000i 0.384615i
\(170\) 3.73205 2.46410i 0.286235 0.188988i
\(171\) 1.73205 1.00000i 0.132453 0.0764719i
\(172\) 6.69615 + 1.79423i 0.510577 + 0.136809i
\(173\) 5.33975 + 19.9282i 0.405973 + 1.51511i 0.802253 + 0.596984i \(0.203634\pi\)
−0.396280 + 0.918130i \(0.629699\pi\)
\(174\) −0.803848 −0.0609395
\(175\) 9.79423 + 8.89230i 0.740374 + 0.672195i
\(176\) 6.73205 0.507447
\(177\) −1.09808 4.09808i −0.0825365 0.308030i
\(178\) −0.330127 0.0884573i −0.0247441 0.00663015i
\(179\) −6.80385 + 3.92820i −0.508543 + 0.293608i −0.732235 0.681052i \(-0.761523\pi\)
0.223691 + 0.974660i \(0.428189\pi\)
\(180\) 8.83013 5.83013i 0.658159 0.434552i
\(181\) 1.19615i 0.0889093i −0.999011 0.0444547i \(-0.985845\pi\)
0.999011 0.0444547i \(-0.0141550\pi\)
\(182\) 2.92820 2.53590i 0.217053 0.187973i
\(183\) −0.562178 0.562178i −0.0415574 0.0415574i
\(184\) 0.232051 + 0.133975i 0.0171070 + 0.00987674i
\(185\) −8.19615 7.26795i −0.602593 0.534350i
\(186\) −1.00000 1.73205i −0.0733236 0.127000i
\(187\) 10.1962 2.73205i 0.745617 0.199787i
\(188\) 11.1962 11.1962i 0.816563 0.816563i
\(189\) −7.06218 + 3.42820i −0.513698 + 0.249365i
\(190\) −0.803848 + 0.267949i −0.0583172 + 0.0194391i
\(191\) −6.63397 + 11.4904i −0.480018 + 0.831415i −0.999737 0.0229220i \(-0.992703\pi\)
0.519720 + 0.854337i \(0.326036\pi\)
\(192\) −0.303848 + 1.13397i −0.0219283 + 0.0818376i
\(193\) 2.09808 7.83013i 0.151023 0.563625i −0.848390 0.529371i \(-0.822428\pi\)
0.999413 0.0342537i \(-0.0109054\pi\)
\(194\) 2.16987 3.75833i 0.155788 0.269832i
\(195\) 1.46410 2.92820i 0.104846 0.209693i
\(196\) −12.0000 1.73205i −0.857143 0.123718i
\(197\) −10.1244 + 10.1244i −0.721330 + 0.721330i −0.968876 0.247546i \(-0.920376\pi\)
0.247546 + 0.968876i \(0.420376\pi\)
\(198\) −3.73205 + 1.00000i −0.265225 + 0.0710669i
\(199\) 5.53590 + 9.58846i 0.392429 + 0.679708i 0.992769 0.120037i \(-0.0383014\pi\)
−0.600340 + 0.799745i \(0.704968\pi\)
\(200\) −8.96410 + 3.59808i −0.633858 + 0.254422i
\(201\) 4.96410 + 2.86603i 0.350141 + 0.202154i
\(202\) −3.02628 3.02628i −0.212928 0.212928i
\(203\) −7.50000 2.59808i −0.526397 0.182349i
\(204\) 3.46410i 0.242536i
\(205\) 7.96410 + 12.0622i 0.556237 + 0.842459i
\(206\) 2.13397 1.23205i 0.148681 0.0858410i
\(207\) 0.366025 + 0.0980762i 0.0254405 + 0.00681677i
\(208\) −1.80385 6.73205i −0.125074 0.466784i
\(209\) −2.00000 −0.138343
\(210\) 1.53590 0.392305i 0.105987 0.0270716i
\(211\) −0.196152 −0.0135037 −0.00675184 0.999977i \(-0.502149\pi\)
−0.00675184 + 0.999977i \(0.502149\pi\)
\(212\) 3.16987 + 11.8301i 0.217708 + 0.812496i
\(213\) −0.633975 0.169873i −0.0434392 0.0116395i
\(214\) −5.89230 + 3.40192i −0.402790 + 0.232551i
\(215\) −8.76795 1.79423i −0.597969 0.122365i
\(216\) 5.73205i 0.390017i
\(217\) −3.73205 19.3923i −0.253348 1.31644i
\(218\) −3.70577 3.70577i −0.250987 0.250987i
\(219\) 6.00000 + 3.46410i 0.405442 + 0.234082i
\(220\) −10.5622 + 0.633975i −0.712102 + 0.0427426i
\(221\) −5.46410 9.46410i −0.367555 0.636624i
\(222\) −1.26795 + 0.339746i −0.0850992 + 0.0228023i
\(223\) −18.1244 + 18.1244i −1.21370 + 1.21370i −0.243895 + 0.969802i \(0.578425\pi\)
−0.969802 + 0.243895i \(0.921575\pi\)
\(224\) 7.62436 11.2583i 0.509424 0.752229i
\(225\) −10.9282 + 8.19615i −0.728547 + 0.546410i
\(226\) −2.83013 + 4.90192i −0.188257 + 0.326071i
\(227\) −5.09808 + 19.0263i −0.338371 + 1.26282i 0.561797 + 0.827275i \(0.310110\pi\)
−0.900168 + 0.435543i \(0.856556\pi\)
\(228\) 0.169873 0.633975i 0.0112501 0.0419860i
\(229\) 9.19615 15.9282i 0.607699 1.05257i −0.383920 0.923366i \(-0.625426\pi\)
0.991619 0.129199i \(-0.0412406\pi\)
\(230\) −0.143594 0.0717968i −0.00946828 0.00473414i
\(231\) 3.73205 + 0.267949i 0.245551 + 0.0176298i
\(232\) 4.09808 4.09808i 0.269052 0.269052i
\(233\) 6.46410 1.73205i 0.423477 0.113470i −0.0407854 0.999168i \(-0.512986\pi\)
0.464263 + 0.885698i \(0.346319\pi\)
\(234\) 2.00000 + 3.46410i 0.130744 + 0.226455i
\(235\) −13.5622 + 15.2942i −0.884699 + 0.997685i
\(236\) 12.2942 + 7.09808i 0.800286 + 0.462045i
\(237\) 1.19615 + 1.19615i 0.0776984 + 0.0776984i
\(238\) 1.73205 5.00000i 0.112272 0.324102i
\(239\) 2.39230i 0.154745i −0.997002 0.0773727i \(-0.975347\pi\)
0.997002 0.0773727i \(-0.0246531\pi\)
\(240\) 0.571797 2.79423i 0.0369093 0.180367i
\(241\) 21.4641 12.3923i 1.38262 0.798259i 0.390155 0.920749i \(-0.372422\pi\)
0.992470 + 0.122491i \(0.0390882\pi\)
\(242\) −1.76795 0.473721i −0.113648 0.0304519i
\(243\) −3.19615 11.9282i −0.205033 0.765195i
\(244\) 2.66025 0.170305
\(245\) 15.5981 + 1.30385i 0.996525 + 0.0832998i
\(246\) 1.73205 0.110432
\(247\) 0.535898 + 2.00000i 0.0340984 + 0.127257i
\(248\) 13.9282 + 3.73205i 0.884442 + 0.236985i
\(249\) −1.33013 + 0.767949i −0.0842934 + 0.0486668i
\(250\) 5.23205 2.47372i 0.330904 0.156452i
\(251\) 21.8564i 1.37956i 0.724017 + 0.689782i \(0.242294\pi\)
−0.724017 + 0.689782i \(0.757706\pi\)
\(252\) 4.09808 11.8301i 0.258155 0.745228i
\(253\) −0.267949 0.267949i −0.0168458 0.0168458i
\(254\) −0.294229 0.169873i −0.0184615 0.0106588i
\(255\) −0.267949 4.46410i −0.0167796 0.279553i
\(256\) 0.696152 + 1.20577i 0.0435095 + 0.0753607i
\(257\) −2.73205 + 0.732051i −0.170421 + 0.0456641i −0.343020 0.939328i \(-0.611450\pi\)
0.172600 + 0.984992i \(0.444783\pi\)
\(258\) −0.758330 + 0.758330i −0.0472116 + 0.0472116i
\(259\) −12.9282 0.928203i −0.803319 0.0576757i
\(260\) 3.46410 + 10.3923i 0.214834 + 0.644503i
\(261\) 4.09808 7.09808i 0.253665 0.439360i
\(262\) −2.07180 + 7.73205i −0.127996 + 0.477688i
\(263\) 4.06218 15.1603i 0.250485 0.934821i −0.720062 0.693909i \(-0.755887\pi\)
0.970547 0.240912i \(-0.0774465\pi\)
\(264\) −1.36603 + 2.36603i −0.0840731 + 0.145619i
\(265\) −5.00000 15.0000i −0.307148 0.921443i
\(266\) −0.562178 + 0.830127i −0.0344693 + 0.0508984i
\(267\) −0.241670 + 0.241670i −0.0147899 + 0.0147899i
\(268\) −18.5263 + 4.96410i −1.13167 + 0.303231i
\(269\) −11.4282 19.7942i −0.696790 1.20688i −0.969574 0.244800i \(-0.921278\pi\)
0.272784 0.962075i \(-0.412056\pi\)
\(270\) 0.205771 + 3.42820i 0.0125228 + 0.208634i
\(271\) 18.4186 + 10.6340i 1.11885 + 0.645968i 0.941107 0.338109i \(-0.109787\pi\)
0.177742 + 0.984077i \(0.443121\pi\)
\(272\) −6.73205 6.73205i −0.408191 0.408191i
\(273\) −0.732051 3.80385i −0.0443057 0.230219i
\(274\) 7.07180i 0.427223i
\(275\) 13.5622 1.63397i 0.817830 0.0985324i
\(276\) 0.107695 0.0621778i 0.00648249 0.00374267i
\(277\) 5.19615 + 1.39230i 0.312207 + 0.0836555i 0.411520 0.911401i \(-0.364998\pi\)
−0.0993135 + 0.995056i \(0.531665\pi\)
\(278\) −0.758330 2.83013i −0.0454816 0.169740i
\(279\) 20.3923 1.22086
\(280\) −5.83013 + 9.83013i −0.348417 + 0.587462i
\(281\) −0.928203 −0.0553720 −0.0276860 0.999617i \(-0.508814\pi\)
−0.0276860 + 0.999617i \(0.508814\pi\)
\(282\) 0.633975 + 2.36603i 0.0377526 + 0.140895i
\(283\) −1.90192 0.509619i −0.113058 0.0302937i 0.201847 0.979417i \(-0.435306\pi\)
−0.314904 + 0.949123i \(0.601972\pi\)
\(284\) 1.90192 1.09808i 0.112858 0.0651588i
\(285\) −0.169873 + 0.830127i −0.0100624 + 0.0491725i
\(286\) 4.00000i 0.236525i
\(287\) 16.1603 + 5.59808i 0.953910 + 0.330444i
\(288\) 9.92820 + 9.92820i 0.585025 + 0.585025i
\(289\) 1.79423 + 1.03590i 0.105543 + 0.0609352i
\(290\) −2.30385 + 2.59808i −0.135287 + 0.152564i
\(291\) −2.16987 3.75833i −0.127200 0.220317i
\(292\) −22.3923 + 6.00000i −1.31041 + 0.351123i
\(293\) 2.39230 2.39230i 0.139760 0.139760i −0.633765 0.773525i \(-0.718492\pi\)
0.773525 + 0.633765i \(0.218492\pi\)
\(294\) 1.16025 1.47372i 0.0676674 0.0859491i
\(295\) −16.3923 8.19615i −0.954397 0.477198i
\(296\) 4.73205 8.19615i 0.275045 0.476392i
\(297\) −2.09808 + 7.83013i −0.121743 + 0.454350i
\(298\) −0.107695 + 0.401924i −0.00623861 + 0.0232828i
\(299\) −0.196152 + 0.339746i −0.0113438 + 0.0196480i
\(300\) −0.633975 + 4.43782i −0.0366025 + 0.256218i
\(301\) −9.52628 + 4.62436i −0.549086 + 0.266543i
\(302\) −5.07180 + 5.07180i −0.291849 + 0.291849i
\(303\) −4.13397 + 1.10770i −0.237491 + 0.0636354i
\(304\) 0.901924 + 1.56218i 0.0517289 + 0.0895970i
\(305\) −3.42820 + 0.205771i −0.196298 + 0.0117824i
\(306\) 4.73205 + 2.73205i 0.270513 + 0.156181i
\(307\) −6.29423 6.29423i −0.359231 0.359231i 0.504299 0.863529i \(-0.331751\pi\)
−0.863529 + 0.504299i \(0.831751\pi\)
\(308\) −9.46410 + 8.19615i −0.539267 + 0.467019i
\(309\) 2.46410i 0.140178i
\(310\) −8.46410 1.73205i −0.480729 0.0983739i
\(311\) −13.2224 + 7.63397i −0.749775 + 0.432883i −0.825613 0.564237i \(-0.809170\pi\)
0.0758374 + 0.997120i \(0.475837\pi\)
\(312\) 2.73205 + 0.732051i 0.154672 + 0.0414442i
\(313\) −1.39230 5.19615i −0.0786977 0.293704i 0.915349 0.402662i \(-0.131915\pi\)
−0.994046 + 0.108958i \(0.965248\pi\)
\(314\) 2.48334 0.140143
\(315\) −4.36603 + 15.5622i −0.245998 + 0.876829i
\(316\) −5.66025 −0.318414
\(317\) −2.46410 9.19615i −0.138398 0.516507i −0.999961 0.00885679i \(-0.997181\pi\)
0.861563 0.507651i \(-0.169486\pi\)
\(318\) −1.83013 0.490381i −0.102628 0.0274992i
\(319\) −7.09808 + 4.09808i −0.397416 + 0.229448i
\(320\) 2.79423 + 4.23205i 0.156202 + 0.236579i
\(321\) 6.80385i 0.379754i
\(322\) −0.186533 + 0.0358984i −0.0103951 + 0.00200054i
\(323\) 2.00000 + 2.00000i 0.111283 + 0.111283i
\(324\) 9.99038 + 5.76795i 0.555021 + 0.320442i
\(325\) −5.26795 13.1244i −0.292213 0.728008i
\(326\) −3.63397 6.29423i −0.201267 0.348605i
\(327\) −5.06218 + 1.35641i −0.279939 + 0.0750094i
\(328\) −8.83013 + 8.83013i −0.487562 + 0.487562i
\(329\) −1.73205 + 24.1244i −0.0954911 + 1.33002i
\(330\) 0.732051 1.46410i 0.0402981 0.0805961i
\(331\) 0.928203 1.60770i 0.0510187 0.0883669i −0.839388 0.543532i \(-0.817087\pi\)
0.890407 + 0.455165i \(0.150420\pi\)
\(332\) 1.33013 4.96410i 0.0730002 0.272440i
\(333\) 3.46410 12.9282i 0.189832 0.708461i
\(334\) −4.30385 + 7.45448i −0.235496 + 0.407891i
\(335\) 23.4904 7.83013i 1.28342 0.427806i
\(336\) −1.47372 3.03590i −0.0803980 0.165622i
\(337\) 9.53590 9.53590i 0.519453 0.519453i −0.397953 0.917406i \(-0.630279\pi\)
0.917406 + 0.397953i \(0.130279\pi\)
\(338\) 2.50000 0.669873i 0.135982 0.0364363i
\(339\) 2.83013 + 4.90192i 0.153711 + 0.266236i
\(340\) 11.1962 + 9.92820i 0.607197 + 0.538432i
\(341\) −17.6603 10.1962i −0.956356 0.552153i
\(342\) −0.732051 0.732051i −0.0395848 0.0395848i
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 7.73205i 0.416884i
\(345\) −0.133975 + 0.0884573i −0.00721295 + 0.00476238i
\(346\) 9.24871 5.33975i 0.497214 0.287067i
\(347\) 29.0885 + 7.79423i 1.56155 + 0.418416i 0.933154 0.359477i \(-0.117045\pi\)
0.628396 + 0.777893i \(0.283712\pi\)
\(348\) −0.696152 2.59808i −0.0373177 0.139272i
\(349\) −6.26795 −0.335516 −0.167758 0.985828i \(-0.553653\pi\)
−0.167758 + 0.985828i \(0.553653\pi\)
\(350\) 3.13397 6.08846i 0.167518 0.325442i
\(351\) 8.39230 0.447948
\(352\) −3.63397 13.5622i −0.193691 0.722867i
\(353\) 13.5622 + 3.63397i 0.721842 + 0.193417i 0.600993 0.799254i \(-0.294772\pi\)
0.120849 + 0.992671i \(0.461438\pi\)
\(354\) −1.90192 + 1.09808i −0.101086 + 0.0583621i
\(355\) −2.36603 + 1.56218i −0.125576 + 0.0829118i
\(356\) 1.14359i 0.0606103i
\(357\) −3.46410 4.00000i −0.183340 0.211702i
\(358\) 2.87564 + 2.87564i 0.151983 + 0.151983i
\(359\) −29.6603 17.1244i −1.56541 0.903789i −0.996693 0.0812542i \(-0.974107\pi\)
−0.568715 0.822535i \(-0.692559\pi\)
\(360\) −8.83013 7.83013i −0.465389 0.412684i
\(361\) 9.23205 + 15.9904i 0.485897 + 0.841599i
\(362\) −0.598076 + 0.160254i −0.0314342 + 0.00842277i
\(363\) −1.29423 + 1.29423i −0.0679294 + 0.0679294i
\(364\) 10.7321 + 7.26795i 0.562512 + 0.380944i
\(365\) 28.3923 9.46410i 1.48612 0.495374i
\(366\) −0.205771 + 0.356406i −0.0107558 + 0.0186297i
\(367\) 0.133975 0.500000i 0.00699342 0.0260998i −0.962341 0.271845i \(-0.912366\pi\)
0.969334 + 0.245746i \(0.0790328\pi\)
\(368\) −0.0884573 + 0.330127i −0.00461115 + 0.0172091i
\(369\) −8.83013 + 15.2942i −0.459678 + 0.796186i
\(370\) −2.53590 + 5.07180i −0.131835 + 0.263670i
\(371\) −15.4904 10.4904i −0.804221 0.544633i
\(372\) 4.73205 4.73205i 0.245345 0.245345i
\(373\) −7.73205 + 2.07180i −0.400350 + 0.107274i −0.453376 0.891320i \(-0.649780\pi\)
0.0530251 + 0.998593i \(0.483114\pi\)
\(374\) −2.73205 4.73205i −0.141271 0.244689i
\(375\) 0.473721 5.76795i 0.0244628 0.297856i
\(376\) −15.2942 8.83013i −0.788740 0.455379i
\(377\) 6.00000 + 6.00000i 0.309016 + 0.309016i
\(378\) 2.66025 + 3.07180i 0.136829 + 0.157996i
\(379\) 2.33975i 0.120185i −0.998193 0.0600923i \(-0.980860\pi\)
0.998193 0.0600923i \(-0.0191395\pi\)
\(380\) −1.56218 2.36603i −0.0801380 0.121375i
\(381\) −0.294229 + 0.169873i −0.0150738 + 0.00870286i
\(382\) 6.63397 + 1.77757i 0.339424 + 0.0909483i
\(383\) 8.18653 + 30.5526i 0.418312 + 1.56116i 0.778107 + 0.628131i \(0.216180\pi\)
−0.359795 + 0.933031i \(0.617153\pi\)
\(384\) 5.92820 0.302522
\(385\) 11.5622 11.2942i 0.589263 0.575607i
\(386\) −4.19615 −0.213579
\(387\) −2.83013 10.5622i −0.143863 0.536906i
\(388\) 14.0263 + 3.75833i 0.712076 + 0.190800i
\(389\) 4.26795 2.46410i 0.216394 0.124935i −0.387886 0.921707i \(-0.626794\pi\)
0.604279 + 0.796773i \(0.293461\pi\)
\(390\) −1.66025 0.339746i −0.0840702 0.0172037i
\(391\) 0.535898i 0.0271015i
\(392\) 1.59808 + 13.4282i 0.0807150 + 0.678227i
\(393\) 5.66025 + 5.66025i 0.285522 + 0.285522i
\(394\) 6.41858 + 3.70577i 0.323364 + 0.186694i
\(395\) 7.29423 0.437822i 0.367012 0.0220292i
\(396\) −6.46410 11.1962i −0.324833 0.562628i
\(397\) −3.63397 + 0.973721i −0.182384 + 0.0488696i −0.348855 0.937177i \(-0.613429\pi\)
0.166471 + 0.986046i \(0.446763\pi\)
\(398\) 4.05256 4.05256i 0.203136 0.203136i
\(399\) 0.437822 + 0.901924i 0.0219185 + 0.0451527i
\(400\) −7.39230 9.85641i −0.369615 0.492820i
\(401\) −5.50000 + 9.52628i −0.274657 + 0.475720i −0.970049 0.242911i \(-0.921898\pi\)
0.695392 + 0.718631i \(0.255231\pi\)
\(402\) 0.767949 2.86603i 0.0383018 0.142944i
\(403\) −5.46410 + 20.3923i −0.272186 + 1.01581i
\(404\) 7.16025 12.4019i 0.356236 0.617019i
\(405\) −13.3205 6.66025i −0.661901 0.330951i
\(406\) −0.294229 + 4.09808i −0.0146023 + 0.203384i
\(407\) −9.46410 + 9.46410i −0.469118 + 0.469118i
\(408\) 3.73205 1.00000i 0.184764 0.0495074i
\(409\) 10.4282 + 18.0622i 0.515641 + 0.893117i 0.999835 + 0.0181564i \(0.00577967\pi\)
−0.484194 + 0.874961i \(0.660887\pi\)
\(410\) 4.96410 5.59808i 0.245160 0.276469i
\(411\) −6.12436 3.53590i −0.302092 0.174413i
\(412\) 5.83013 + 5.83013i 0.287230 + 0.287230i
\(413\) −21.2942 + 4.09808i −1.04782 + 0.201653i
\(414\) 0.196152i 0.00964037i
\(415\) −1.33013 + 6.50000i −0.0652934 + 0.319072i
\(416\) −12.5885 + 7.26795i −0.617200 + 0.356341i
\(417\) −2.83013 0.758330i −0.138592 0.0371356i
\(418\) 0.267949 + 1.00000i 0.0131058 + 0.0489116i
\(419\) −23.8564 −1.16546 −0.582731 0.812665i \(-0.698016\pi\)
−0.582731 + 0.812665i \(0.698016\pi\)
\(420\) 2.59808 + 4.62436i 0.126773 + 0.225645i
\(421\) −17.3397 −0.845088 −0.422544 0.906343i \(-0.638863\pi\)
−0.422544 + 0.906343i \(0.638863\pi\)
\(422\) 0.0262794 + 0.0980762i 0.00127926 + 0.00477428i
\(423\) −24.1244 6.46410i −1.17297 0.314295i
\(424\) 11.8301 6.83013i 0.574522 0.331700i
\(425\) −15.1962 11.9282i −0.737122 0.578603i
\(426\) 0.339746i 0.0164607i
\(427\) −3.07180 + 2.66025i −0.148655 + 0.128739i
\(428\) −16.0981 16.0981i −0.778130 0.778130i
\(429\) −3.46410 2.00000i −0.167248 0.0965609i
\(430\) 0.277568 + 4.62436i 0.0133855 + 0.223006i
\(431\) −3.09808 5.36603i −0.149229 0.258472i 0.781714 0.623637i \(-0.214346\pi\)
−0.930943 + 0.365165i \(0.881013\pi\)
\(432\) 7.06218 1.89230i 0.339779 0.0910436i
\(433\) 17.5359 17.5359i 0.842721 0.842721i −0.146491 0.989212i \(-0.546798\pi\)
0.989212 + 0.146491i \(0.0467978\pi\)
\(434\) −9.19615 + 4.46410i −0.441429 + 0.214284i
\(435\) 1.09808 + 3.29423i 0.0526487 + 0.157946i
\(436\) 8.76795 15.1865i 0.419909 0.727303i
\(437\) 0.0262794 0.0980762i 0.00125712 0.00469162i
\(438\) 0.928203 3.46410i 0.0443513 0.165521i
\(439\) −1.66025 + 2.87564i −0.0792396 + 0.137247i −0.902922 0.429804i \(-0.858583\pi\)
0.823682 + 0.567051i \(0.191916\pi\)
\(440\) 3.73205 + 11.1962i 0.177919 + 0.533756i
\(441\) 7.09808 + 17.7583i 0.338004 + 0.845635i
\(442\) −4.00000 + 4.00000i −0.190261 + 0.190261i
\(443\) 13.0622 3.50000i 0.620603 0.166290i 0.0652010 0.997872i \(-0.479231\pi\)
0.555402 + 0.831582i \(0.312564\pi\)
\(444\) −2.19615 3.80385i −0.104225 0.180523i
\(445\) 0.0884573 + 1.47372i 0.00419328 + 0.0698611i
\(446\) 11.4904 + 6.63397i 0.544085 + 0.314128i
\(447\) 0.294229 + 0.294229i 0.0139165 + 0.0139165i
\(448\) 5.66987 + 1.96410i 0.267876 + 0.0927951i
\(449\) 33.0526i 1.55985i 0.625875 + 0.779923i \(0.284742\pi\)
−0.625875 + 0.779923i \(0.715258\pi\)
\(450\) 5.56218 + 4.36603i 0.262204 + 0.205816i
\(451\) 15.2942 8.83013i 0.720177 0.415794i
\(452\) −18.2942 4.90192i −0.860488 0.230567i
\(453\) 1.85641 + 6.92820i 0.0872216 + 0.325515i
\(454\) 10.1962 0.478529
\(455\) −14.3923 8.53590i −0.674722 0.400169i
\(456\) −0.732051 −0.0342814
\(457\) 3.14359 + 11.7321i 0.147051 + 0.548802i 0.999656 + 0.0262453i \(0.00835510\pi\)
−0.852604 + 0.522557i \(0.824978\pi\)
\(458\) −9.19615 2.46410i −0.429708 0.115140i
\(459\) 9.92820 5.73205i 0.463409 0.267549i
\(460\) 0.107695 0.526279i 0.00502131 0.0245379i
\(461\) 5.60770i 0.261176i −0.991437 0.130588i \(-0.958313\pi\)
0.991437 0.130588i \(-0.0416866\pi\)
\(462\) −0.366025 1.90192i −0.0170290 0.0884855i
\(463\) −4.75833 4.75833i −0.221138 0.221138i 0.587839 0.808978i \(-0.299979\pi\)
−0.808978 + 0.587839i \(0.799979\pi\)
\(464\) 6.40192 + 3.69615i 0.297202 + 0.171590i
\(465\) −5.73205 + 6.46410i −0.265817 + 0.299766i
\(466\) −1.73205 3.00000i −0.0802357 0.138972i
\(467\) 13.5981 3.64359i 0.629244 0.168605i 0.0699173 0.997553i \(-0.477726\pi\)
0.559327 + 0.828947i \(0.311060\pi\)
\(468\) −9.46410 + 9.46410i −0.437478 + 0.437478i
\(469\) 16.4282 24.2583i 0.758584 1.12015i
\(470\) 9.46410 + 4.73205i 0.436546 + 0.218273i
\(471\) 1.24167 2.15064i 0.0572131 0.0990960i
\(472\) 4.09808 15.2942i 0.188629 0.703974i
\(473\) −2.83013 + 10.5622i −0.130129 + 0.485649i
\(474\) 0.437822 0.758330i 0.0201098 0.0348313i
\(475\) 2.19615 + 2.92820i 0.100766 + 0.134355i
\(476\) 17.6603 + 1.26795i 0.809456 + 0.0581164i
\(477\) 13.6603 13.6603i 0.625460 0.625460i
\(478\) −1.19615 + 0.320508i −0.0547107 + 0.0146597i
\(479\) −6.53590 11.3205i −0.298633 0.517247i 0.677191 0.735808i \(-0.263197\pi\)
−0.975823 + 0.218560i \(0.929864\pi\)
\(480\) −5.93782 + 0.356406i −0.271023 + 0.0162677i
\(481\) 12.0000 + 6.92820i 0.547153 + 0.315899i
\(482\) −9.07180 9.07180i −0.413209 0.413209i
\(483\) −0.0621778 + 0.179492i −0.00282919 + 0.00816717i
\(484\) 6.12436i 0.278380i
\(485\) −18.3660 3.75833i −0.833958 0.170657i
\(486\) −5.53590 + 3.19615i −0.251113 + 0.144980i
\(487\) −27.2224 7.29423i −1.23357 0.330533i −0.417599 0.908631i \(-0.637128\pi\)
−0.815967 + 0.578098i \(0.803795\pi\)
\(488\) −0.767949 2.86603i −0.0347634 0.129739i
\(489\) −7.26795 −0.328668
\(490\) −1.43782 7.97372i −0.0649542 0.360216i
\(491\) 37.7128 1.70196 0.850978 0.525202i \(-0.176010\pi\)
0.850978 + 0.525202i \(0.176010\pi\)
\(492\) 1.50000 + 5.59808i 0.0676252 + 0.252381i
\(493\) 11.1962 + 3.00000i 0.504249 + 0.135113i
\(494\) 0.928203 0.535898i 0.0417618 0.0241112i
\(495\) 9.19615 + 13.9282i 0.413336 + 0.626026i
\(496\) 18.3923i 0.825839i
\(497\) −1.09808 + 3.16987i −0.0492554 + 0.142188i
\(498\) 0.562178 + 0.562178i 0.0251918 + 0.0251918i
\(499\) 9.97372 + 5.75833i 0.446485 + 0.257778i 0.706345 0.707868i \(-0.250343\pi\)
−0.259860 + 0.965646i \(0.583676\pi\)
\(500\) 12.5263 + 14.7679i 0.560192 + 0.660443i
\(501\) 4.30385 + 7.45448i 0.192282 + 0.333042i
\(502\) 10.9282 2.92820i 0.487750 0.130692i
\(503\) 17.6340 17.6340i 0.786260 0.786260i −0.194619 0.980879i \(-0.562347\pi\)
0.980879 + 0.194619i \(0.0623470\pi\)
\(504\) −13.9282 1.00000i −0.620411 0.0445435i
\(505\) −8.26795 + 16.5359i −0.367919 + 0.735838i
\(506\) −0.0980762 + 0.169873i −0.00436002 + 0.00755178i
\(507\) 0.669873 2.50000i 0.0297501 0.111029i
\(508\) 0.294229 1.09808i 0.0130543 0.0487193i
\(509\) 19.4545 33.6962i 0.862305 1.49356i −0.00739389 0.999973i \(-0.502354\pi\)
0.869699 0.493583i \(-0.164313\pi\)
\(510\) −2.19615 + 0.732051i −0.0972473 + 0.0324158i
\(511\) 19.8564 29.3205i 0.878396 1.29706i
\(512\) −15.6865 + 15.6865i −0.693253 + 0.693253i
\(513\) −2.09808 + 0.562178i −0.0926323 + 0.0248208i
\(514\) 0.732051 + 1.26795i 0.0322894 + 0.0559268i
\(515\) −7.96410 7.06218i −0.350940 0.311197i
\(516\) −3.10770 1.79423i −0.136809 0.0789865i
\(517\) 17.6603 + 17.6603i 0.776697 + 0.776697i
\(518\) 1.26795 + 6.58846i 0.0557105 + 0.289480i
\(519\) 10.6795i 0.468778i
\(520\) 10.1962 6.73205i 0.447131 0.295220i
\(521\) −20.6603 + 11.9282i −0.905142 + 0.522584i −0.878865 0.477071i \(-0.841699\pi\)
−0.0262772 + 0.999655i \(0.508365\pi\)
\(522\) −4.09808 1.09808i −0.179368 0.0480615i
\(523\) −11.4904 42.8827i −0.502439 1.87513i −0.483568 0.875307i \(-0.660659\pi\)
−0.0188717 0.999822i \(-0.506007\pi\)
\(524\) −26.7846 −1.17009
\(525\) −3.70577 5.75833i −0.161733 0.251314i
\(526\) −8.12436 −0.354239
\(527\) 7.46410 + 27.8564i 0.325141 + 1.21344i
\(528\) −3.36603 0.901924i −0.146487 0.0392512i
\(529\) −19.9019 + 11.4904i −0.865301 + 0.499582i
\(530\) −6.83013 + 4.50962i −0.296682 + 0.195885i
\(531\) 22.3923i 0.971743i
\(532\) −3.16987 1.09808i −0.137431 0.0476076i
\(533\) −12.9282 12.9282i −0.559983 0.559983i
\(534\) 0.153212 + 0.0884573i 0.00663015 + 0.00382792i
\(535\) 21.9904 + 19.5000i 0.950727 + 0.843059i
\(536\) 10.6962 + 18.5263i 0.462003 + 0.800213i
\(537\) 3.92820 1.05256i 0.169514 0.0454213i
\(538\) −8.36603 + 8.36603i −0.360685 + 0.360685i
\(539\) 2.73205 18.9282i 0.117678 0.815295i
\(540\) −10.9019 + 3.63397i −0.469144 + 0.156381i
\(541\) −18.3564 + 31.7942i −0.789204 + 1.36694i 0.137252 + 0.990536i \(0.456173\pi\)
−0.926455 + 0.376404i \(0.877160\pi\)
\(542\) 2.84936 10.6340i 0.122391 0.456768i
\(543\) −0.160254 + 0.598076i −0.00687716 + 0.0256659i
\(544\) −9.92820 + 17.1962i −0.425668 + 0.737279i
\(545\) −10.1244 + 20.2487i −0.433680 + 0.867359i
\(546\) −1.80385 + 0.875644i −0.0771975 + 0.0374741i
\(547\) −16.7583 + 16.7583i −0.716534 + 0.716534i −0.967894 0.251359i \(-0.919122\pi\)
0.251359 + 0.967894i \(0.419122\pi\)
\(548\) 22.8564 6.12436i 0.976377 0.261620i
\(549\) −2.09808 3.63397i −0.0895437 0.155094i
\(550\) −2.63397 6.56218i −0.112313 0.279812i
\(551\) −1.90192 1.09808i −0.0810247 0.0467796i
\(552\) −0.0980762 0.0980762i −0.00417440 0.00417440i
\(553\) 6.53590 5.66025i 0.277935 0.240698i
\(554\) 2.78461i 0.118307i
\(555\) 3.12436 + 4.73205i 0.132622 + 0.200864i
\(556\) 8.49038 4.90192i 0.360072 0.207888i
\(557\) −31.2224 8.36603i −1.32294 0.354480i −0.472860 0.881138i \(-0.656778\pi\)
−0.850077 + 0.526658i \(0.823445\pi\)
\(558\) −2.73205 10.1962i −0.115657 0.431638i
\(559\) 11.3205 0.478806
\(560\) −14.0359 3.93782i −0.593125 0.166403i
\(561\) −5.46410 −0.230695
\(562\) 0.124356 + 0.464102i 0.00524563 + 0.0195769i
\(563\) −23.7224 6.35641i −0.999781 0.267891i −0.278427 0.960457i \(-0.589813\pi\)
−0.721354 + 0.692567i \(0.756480\pi\)
\(564\) −7.09808 + 4.09808i −0.298883 + 0.172560i
\(565\) 23.9545 + 4.90192i 1.00777 + 0.206225i
\(566\) 1.01924i 0.0428418i
\(567\) −17.3038 + 3.33013i −0.726693 + 0.139852i
\(568\) −1.73205 1.73205i −0.0726752 0.0726752i
\(569\) 25.0526 + 14.4641i 1.05026 + 0.606367i 0.922722 0.385467i \(-0.125960\pi\)
0.127536 + 0.991834i \(0.459293\pi\)
\(570\) 0.437822 0.0262794i 0.0183384 0.00110072i
\(571\) 9.02628 + 15.6340i 0.377738 + 0.654261i 0.990733 0.135826i \(-0.0433687\pi\)
−0.612995 + 0.790087i \(0.710035\pi\)
\(572\) 12.9282 3.46410i 0.540555 0.144841i
\(573\) 4.85641 4.85641i 0.202879 0.202879i
\(574\) 0.633975 8.83013i 0.0264616 0.368562i
\(575\) −0.0980762 + 0.686533i −0.00409006 + 0.0286304i
\(576\) −3.09808 + 5.36603i −0.129087 + 0.223584i
\(577\) 1.50962 5.63397i 0.0628463 0.234545i −0.927357 0.374177i \(-0.877925\pi\)
0.990204 + 0.139632i \(0.0445919\pi\)
\(578\) 0.277568 1.03590i 0.0115453 0.0430877i
\(579\) −2.09808 + 3.63397i −0.0871931 + 0.151023i
\(580\) −10.3923 5.19615i −0.431517 0.215758i
\(581\) 3.42820 + 7.06218i 0.142226 + 0.292989i
\(582\) −1.58846 + 1.58846i −0.0658437 + 0.0658437i
\(583\) −18.6603 + 5.00000i −0.772829 + 0.207079i
\(584\) 12.9282 + 22.3923i 0.534973 + 0.926600i
\(585\) 11.4641 12.9282i 0.473982 0.534515i
\(586\) −1.51666 0.875644i −0.0626527 0.0361725i
\(587\) −15.7846 15.7846i −0.651501 0.651501i 0.301854 0.953354i \(-0.402395\pi\)
−0.953354 + 0.301854i \(0.902395\pi\)
\(588\) 5.76795 + 2.47372i 0.237866 + 0.102015i
\(589\) 5.46410i 0.225144i
\(590\) −1.90192 + 9.29423i −0.0783010 + 0.382637i
\(591\) 6.41858 3.70577i 0.264025 0.152435i
\(592\) 11.6603 + 3.12436i 0.479233 + 0.128410i
\(593\) 5.56218 + 20.7583i 0.228411 + 0.852442i 0.981009 + 0.193962i \(0.0621338\pi\)
−0.752598 + 0.658481i \(0.771199\pi\)
\(594\) 4.19615 0.172170
\(595\) −22.8564 0.267949i −0.937021 0.0109848i
\(596\) −1.39230 −0.0570310
\(597\) −1.48334 5.53590i −0.0607090 0.226569i
\(598\) 0.196152 + 0.0525589i 0.00802127 + 0.00214929i
\(599\) 15.3397 8.85641i 0.626765 0.361863i −0.152733 0.988267i \(-0.548807\pi\)
0.779498 + 0.626405i \(0.215474\pi\)
\(600\) 4.96410 0.598076i 0.202659 0.0244164i
\(601\) 41.1769i 1.67964i −0.542864 0.839821i \(-0.682660\pi\)
0.542864 0.839821i \(-0.317340\pi\)
\(602\) 3.58846 + 4.14359i 0.146255 + 0.168880i
\(603\) 21.3923 + 21.3923i 0.871162 + 0.871162i
\(604\) −20.7846 12.0000i −0.845714 0.488273i
\(605\) 0.473721 + 7.89230i 0.0192595 + 0.320868i
\(606\) 1.10770 + 1.91858i 0.0449970 + 0.0779372i
\(607\) 12.6962 3.40192i 0.515321 0.138080i 0.00821951 0.999966i \(-0.497384\pi\)
0.507101 + 0.861886i \(0.330717\pi\)
\(608\) 2.66025 2.66025i 0.107888 0.107888i
\(609\) 3.40192 + 2.30385i 0.137853 + 0.0933566i
\(610\) 0.562178 + 1.68653i 0.0227619 + 0.0682857i
\(611\) 12.9282 22.3923i 0.523019 0.905896i
\(612\) −4.73205 + 17.6603i −0.191282 + 0.713873i
\(613\) −6.53590 + 24.3923i −0.263982 + 0.985196i 0.698888 + 0.715231i \(0.253679\pi\)
−0.962870 + 0.269965i \(0.912988\pi\)
\(614\) −2.30385 + 3.99038i −0.0929757 + 0.161039i
\(615\) −2.36603 7.09808i −0.0954074 0.286222i
\(616\) 11.5622 + 7.83013i 0.465853 + 0.315485i
\(617\) 33.9090 33.9090i 1.36512 1.36512i 0.497874 0.867249i \(-0.334114\pi\)
0.867249 0.497874i \(-0.165886\pi\)
\(618\) −1.23205 + 0.330127i −0.0495604 + 0.0132797i
\(619\) −5.09808 8.83013i −0.204909 0.354913i 0.745195 0.666847i \(-0.232357\pi\)
−0.950104 + 0.311934i \(0.899023\pi\)
\(620\) −1.73205 28.8564i −0.0695608 1.15890i
\(621\) −0.356406 0.205771i −0.0143021 0.00825732i
\(622\) 5.58846 + 5.58846i 0.224077 + 0.224077i
\(623\) 1.14359 + 1.32051i 0.0458171 + 0.0529050i
\(624\) 3.60770i 0.144423i
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) −2.41154 + 1.39230i −0.0963846 + 0.0556477i
\(627\) 1.00000 + 0.267949i 0.0399362 + 0.0107009i
\(628\) 2.15064 + 8.02628i 0.0858197 + 0.320283i
\(629\) 18.9282 0.754717
\(630\) 8.36603 + 0.0980762i 0.333310 + 0.00390745i
\(631\) −4.58846 −0.182664 −0.0913318 0.995821i \(-0.529112\pi\)
−0.0913318 + 0.995821i \(0.529112\pi\)
\(632\) 1.63397 + 6.09808i 0.0649960 + 0.242568i
\(633\) 0.0980762 + 0.0262794i 0.00389818 + 0.00104451i
\(634\) −4.26795 + 2.46410i −0.169502 + 0.0978620i
\(635\) −0.294229 + 1.43782i −0.0116761 + 0.0570582i
\(636\) 6.33975i 0.251387i
\(637\) −19.6603 + 2.33975i −0.778968 + 0.0927041i
\(638\) 3.00000 + 3.00000i 0.118771 + 0.118771i
\(639\) −3.00000 1.73205i −0.118678 0.0685189i
\(640\) 16.9904 19.1603i 0.671604 0.757376i
\(641\) −5.33013 9.23205i −0.210527 0.364644i 0.741352 0.671116i \(-0.234185\pi\)
−0.951880 + 0.306472i \(0.900851\pi\)
\(642\) 3.40192 0.911543i 0.134263 0.0359757i
\(643\) −17.5359 + 17.5359i −0.691548 + 0.691548i −0.962573 0.271024i \(-0.912638\pi\)
0.271024 + 0.962573i \(0.412638\pi\)
\(644\) −0.277568 0.571797i −0.0109377 0.0225319i
\(645\) 4.14359 + 2.07180i 0.163154 + 0.0815769i
\(646\) 0.732051 1.26795i 0.0288022 0.0498868i
\(647\) 10.5981 39.5526i 0.416653 1.55497i −0.364847 0.931067i \(-0.618879\pi\)
0.781501 0.623904i \(-0.214454\pi\)
\(648\) 3.33013 12.4282i 0.130820 0.488226i
\(649\) −11.1962 + 19.3923i −0.439487 + 0.761215i
\(650\) −5.85641 + 4.39230i −0.229707 + 0.172280i
\(651\) −0.732051 + 10.1962i −0.0286913 + 0.399619i
\(652\) 17.1962 17.1962i 0.673453 0.673453i
\(653\) 19.6603 5.26795i 0.769365 0.206151i 0.147274 0.989096i \(-0.452950\pi\)
0.622091 + 0.782945i \(0.286283\pi\)
\(654\) 1.35641 + 2.34936i 0.0530397 + 0.0918674i
\(655\) 34.5167 2.07180i 1.34868 0.0809518i
\(656\) −13.7942 7.96410i −0.538574 0.310946i
\(657\) 25.8564 + 25.8564i 1.00875 + 1.00875i
\(658\) 12.2942 2.36603i 0.479279 0.0922373i
\(659\) 27.6603i 1.07749i 0.842469 + 0.538745i \(0.181101\pi\)
−0.842469 + 0.538745i \(0.818899\pi\)
\(660\) 5.36603 + 1.09808i 0.208872 + 0.0427426i
\(661\) −41.7224 + 24.0885i −1.62281 + 0.936932i −0.636652 + 0.771151i \(0.719681\pi\)
−0.986163 + 0.165781i \(0.946985\pi\)
\(662\) −0.928203 0.248711i −0.0360756 0.00966644i
\(663\) 1.46410 + 5.46410i 0.0568610 + 0.212208i
\(664\) −5.73205 −0.222447
\(665\) 4.16987 + 1.16987i 0.161701 + 0.0453657i
\(666\) −6.92820 −0.268462
\(667\) −0.107695 0.401924i −0.00416997 0.0155626i
\(668\) −27.8205 7.45448i −1.07641 0.288423i
\(669\) 11.4904 6.63397i 0.444244 0.256484i
\(670\) −7.06218 10.6962i −0.272836 0.413228i
\(671\) 4.19615i 0.161991i
\(672\) −5.32051 + 4.60770i −0.205243 + 0.177746i
\(673\) 4.39230 + 4.39230i 0.169311 + 0.169311i 0.786676 0.617366i \(-0.211800\pi\)
−0.617366 + 0.786676i \(0.711800\pi\)
\(674\) −6.04552 3.49038i −0.232865 0.134444i
\(675\) 13.7679 5.52628i 0.529929 0.212707i
\(676\) 4.33013 + 7.50000i 0.166543 + 0.288462i
\(677\) −25.8564 + 6.92820i −0.993742 + 0.266272i −0.718822 0.695194i \(-0.755318\pi\)
−0.274921 + 0.961467i \(0.588652\pi\)
\(678\) 2.07180 2.07180i 0.0795669 0.0795669i
\(679\) −19.9545 + 9.68653i −0.765783 + 0.371735i
\(680\) 7.46410 14.9282i 0.286235 0.572470i
\(681\) 5.09808 8.83013i 0.195359 0.338371i
\(682\) −2.73205 + 10.1962i −0.104616 + 0.390431i
\(683\) −4.57180 + 17.0622i −0.174935 + 0.652866i 0.821628 + 0.570024i \(0.193066\pi\)
−0.996563 + 0.0828417i \(0.973600\pi\)
\(684\) 1.73205 3.00000i 0.0662266 0.114708i
\(685\) −28.9808 + 9.66025i −1.10730 + 0.369099i
\(686\) −7.08846 6.45448i −0.270639 0.246433i
\(687\) −6.73205 + 6.73205i −0.256844 + 0.256844i
\(688\) 9.52628 2.55256i 0.363186 0.0973154i
\(689\) 10.0000 + 17.3205i 0.380970 + 0.659859i
\(690\) 0.0621778 + 0.0551363i 0.00236707 + 0.00209900i
\(691\) −44.0263 25.4186i −1.67484 0.966969i −0.964867 0.262738i \(-0.915375\pi\)
−0.709971 0.704231i \(-0.751292\pi\)
\(692\) 25.2679 + 25.2679i 0.960543 + 0.960543i
\(693\) 18.6603 + 6.46410i 0.708844 + 0.245551i
\(694\) 15.5885i 0.591730i
\(695\) −10.5622 + 6.97372i −0.400646 + 0.264528i
\(696\) −2.59808 + 1.50000i −0.0984798 + 0.0568574i
\(697\) −24.1244 6.46410i −0.913775 0.244845i
\(698\) 0.839746 + 3.13397i 0.0317849 + 0.118623i
\(699\) −3.46410 −0.131024
\(700\) 22.3923 + 4.85641i 0.846350 + 0.183555i
\(701\) −20.2679 −0.765510 −0.382755 0.923850i \(-0.625025\pi\)
−0.382755 + 0.923850i \(0.625025\pi\)
\(702\) −1.12436 4.19615i −0.0424361 0.158374i
\(703\) −3.46410 0.928203i −0.130651 0.0350078i
\(704\) 5.36603 3.09808i 0.202240 0.116763i
\(705\) 8.83013 5.83013i 0.332562 0.219575i
\(706\) 7.26795i 0.273533i
\(707\) 4.13397 + 21.4808i 0.155474 + 0.807867i
\(708\) −5.19615 5.19615i −0.195283 0.195283i
\(709\) −18.9904 10.9641i −0.713199 0.411765i 0.0990456 0.995083i \(-0.468421\pi\)
−0.812244 + 0.583317i \(0.801754\pi\)
\(710\) 1.09808 + 0.973721i 0.0412101 + 0.0365431i
\(711\) 4.46410 + 7.73205i 0.167417 + 0.289975i
\(712\) −1.23205 + 0.330127i −0.0461731 + 0.0123720i
\(713\) 0.732051 0.732051i 0.0274155 0.0274155i
\(714\) −1.53590 + 2.26795i −0.0574796 + 0.0848759i
\(715\) −16.3923 + 5.46410i −0.613037 + 0.204346i
\(716\) −6.80385 + 11.7846i −0.254272 + 0.440412i
\(717\) −0.320508 + 1.19615i −0.0119696 + 0.0446711i
\(718\) −4.58846 + 17.1244i −0.171240 + 0.639075i
\(719\) −19.2942 + 33.4186i −0.719553 + 1.24630i 0.241624 + 0.970370i \(0.422320\pi\)
−0.961177 + 0.275933i \(0.911013\pi\)
\(720\) 6.73205 13.4641i 0.250889 0.501777i
\(721\) −12.5622 0.901924i −0.467840 0.0335894i
\(722\) 6.75833 6.75833i 0.251519 0.251519i
\(723\) −12.3923 + 3.32051i −0.460875 + 0.123491i
\(724\) −1.03590 1.79423i −0.0384989 0.0666820i
\(725\) 13.7942 + 5.89230i 0.512305 + 0.218835i
\(726\) 0.820508 + 0.473721i 0.0304519 + 0.0175814i
\(727\) 10.0981 + 10.0981i 0.374517 + 0.374517i 0.869119 0.494602i \(-0.164686\pi\)
−0.494602 + 0.869119i \(0.664686\pi\)
\(728\) 4.73205 13.6603i 0.175381 0.506283i
\(729\) 13.5885i 0.503276i
\(730\) −8.53590 12.9282i −0.315928 0.478494i
\(731\) 13.3923 7.73205i 0.495332 0.285980i
\(732\) −1.33013 0.356406i −0.0491629 0.0131732i
\(733\) −1.16987 4.36603i −0.0432102 0.161263i 0.940949 0.338547i \(-0.109935\pi\)
−0.984160 + 0.177284i \(0.943269\pi\)
\(734\) −0.267949 −0.00989019
\(735\) −7.62436 2.74167i −0.281229 0.101128i
\(736\) 0.712813 0.0262746
\(737\) −7.83013 29.2224i −0.288426 1.07642i
\(738\) 8.83013 + 2.36603i 0.325041 + 0.0870946i
\(739\) 19.5622 11.2942i 0.719606 0.415465i −0.0950014 0.995477i \(-0.530286\pi\)
0.814608 + 0.580012i \(0.196952\pi\)
\(740\) −18.5885 3.80385i −0.683325 0.139832i
\(741\) 1.07180i 0.0393734i
\(742\) −3.16987 + 9.15064i −0.116370 + 0.335930i
\(743\) −6.16987 6.16987i −0.226351 0.226351i 0.584816 0.811166i \(-0.301167\pi\)
−0.811166 + 0.584816i \(0.801167\pi\)
\(744\) −6.46410 3.73205i −0.236985 0.136824i
\(745\) 1.79423 0.107695i 0.0657355 0.00394565i
\(746\) 2.07180 + 3.58846i 0.0758539 + 0.131383i
\(747\) −7.83013 + 2.09808i −0.286489 + 0.0767646i
\(748\) 12.9282 12.9282i 0.472702 0.472702i
\(749\) 34.6865 + 2.49038i 1.26742 + 0.0909965i
\(750\) −2.94744 + 0.535898i −0.107625 + 0.0195682i
\(751\) 3.19615 5.53590i 0.116629 0.202008i −0.801801 0.597592i \(-0.796124\pi\)
0.918430 + 0.395584i \(0.129458\pi\)
\(752\) 5.83013 21.7583i 0.212603 0.793445i
\(753\) 2.92820 10.9282i 0.106710 0.398246i
\(754\) 2.19615 3.80385i 0.0799792 0.138528i
\(755\) 27.7128 + 13.8564i 1.00857 + 0.504286i
\(756\) −7.62436 + 11.2583i −0.277295 + 0.409462i
\(757\) 12.7321 12.7321i 0.462754 0.462754i −0.436803 0.899557i \(-0.643889\pi\)
0.899557 + 0.436803i \(0.143889\pi\)
\(758\) −1.16987 + 0.313467i −0.0424917 + 0.0113856i
\(759\) 0.0980762 + 0.169873i 0.00355994 + 0.00616600i
\(760\) −2.09808 + 2.36603i −0.0761052 + 0.0858248i
\(761\) 24.9282 + 14.3923i 0.903647 + 0.521721i 0.878382 0.477960i \(-0.158624\pi\)
0.0252651 + 0.999681i \(0.491957\pi\)
\(762\) 0.124356 + 0.124356i 0.00450493 + 0.00450493i
\(763\) 5.06218 + 26.3038i 0.183263 + 0.952263i
\(764\) 22.9808i 0.831415i
\(765\) 4.73205 23.1244i 0.171088 0.836063i
\(766\) 14.1795 8.18653i 0.512326 0.295791i
\(767\) 22.3923 + 6.00000i 0.808539 + 0.216647i
\(768\) −0.186533 0.696152i −0.00673095 0.0251202i
\(769\) −15.1769 −0.547294 −0.273647 0.961830i \(-0.588230\pi\)
−0.273647 + 0.961830i \(0.588230\pi\)
\(770\) −7.19615 4.26795i −0.259331 0.153806i
\(771\) 1.46410 0.0527283
\(772\) −3.63397 13.5622i −0.130790 0.488113i
\(773\) 15.1962 + 4.07180i 0.546568 + 0.146452i 0.521528 0.853234i \(-0.325362\pi\)
0.0250395 + 0.999686i \(0.492029\pi\)
\(774\) −4.90192 + 2.83013i −0.176196 + 0.101727i
\(775\) 4.46410 + 37.0526i 0.160355 + 1.33097i
\(776\) 16.1962i 0.581408i
\(777\) 6.33975 + 2.19615i 0.227437 + 0.0787865i
\(778\) −1.80385 1.80385i −0.0646711 0.0646711i
\(779\) 4.09808 + 2.36603i 0.146829 + 0.0847717i
\(780\) −0.339746 5.66025i −0.0121649 0.202670i
\(781\) 1.73205 + 3.00000i 0.0619777 + 0.107348i
\(782\) 0.267949 0.0717968i 0.00958184 0.00256745i
\(783\) −6.29423 + 6.29423i −0.224937 + 0.224937i
\(784\) −16.0167 + 6.40192i −0.572024 + 0.228640i
\(785\) −3.39230 10.1769i −0.121077 0.363230i
\(786\) 2.07180 3.58846i 0.0738985 0.127996i
\(787\) 8.35641 31.1865i 0.297874 1.11168i −0.641034 0.767512i \(-0.721494\pi\)
0.938908 0.344168i \(-0.111839\pi\)
\(788\) −6.41858 + 23.9545i −0.228653 + 0.853343i
\(789\) −4.06218 + 7.03590i −0.144617 + 0.250485i
\(790\) −1.19615 3.58846i −0.0425572 0.127672i
\(791\) 26.0263 12.6340i 0.925388 0.449212i
\(792\) −10.1962 + 10.1962i −0.362305 + 0.362305i
\(793\) 4.19615 1.12436i 0.149010 0.0399270i
\(794\) 0.973721 + 1.68653i 0.0345560 + 0.0598528i
\(795\) 0.490381 + 8.16987i 0.0173920 + 0.289756i
\(796\) 16.6077 + 9.58846i 0.588644 + 0.339854i
\(797\) −22.5359 22.5359i −0.798262 0.798262i 0.184559 0.982821i \(-0.440914\pi\)
−0.982821 + 0.184559i \(0.940914\pi\)
\(798\) 0.392305 0.339746i 0.0138874 0.0120269i
\(799\) 35.3205i 1.24955i
\(800\) −15.8660 + 20.2128i −0.560949 + 0.714631i
\(801\) −1.56218 + 0.901924i −0.0551968 + 0.0318679i
\(802\) 5.50000 + 1.47372i 0.194212 + 0.0520389i
\(803\) −9.46410 35.3205i −0.333981 1.24643i
\(804\) 9.92820 0.350141
\(805\) 0.401924 + 0.715390i 0.0141660 + 0.0252142i
\(806\) 10.9282 0.384930
\(807\) 3.06218 + 11.4282i 0.107794 + 0.402292i
\(808\) −15.4282 4.13397i −0.542762 0.145433i
\(809\) 3.99038 2.30385i 0.140294 0.0809990i −0.428210 0.903679i \(-0.640856\pi\)
0.568504 + 0.822680i \(0.307522\pi\)
\(810\) −1.54552 + 7.55256i −0.0543039 + 0.265370i
\(811\) 42.9282i 1.50741i 0.657211 + 0.753707i \(0.271736\pi\)
−0.657211 + 0.753707i \(0.728264\pi\)
\(812\) −13.5000 + 2.59808i −0.473757 + 0.0911746i
\(813\) −7.78461 7.78461i −0.273018 0.273018i
\(814\) 6.00000 + 3.46410i 0.210300 + 0.121417i
\(815\) −20.8301 + 23.4904i −0.729648 + 0.822832i
\(816\) 2.46410 + 4.26795i 0.0862608 + 0.149408i
\(817\) −2.83013 + 0.758330i −0.0990136 + 0.0265306i
\(818\) 7.63397 7.63397i 0.266916 0.266916i
\(819\) 1.46410 20.3923i 0.0511599 0.712565i
\(820\) 22.3923 + 11.1962i 0.781973 + 0.390987i
\(821\) 24.6603 42.7128i 0.860649 1.49069i −0.0106549 0.999943i \(-0.503392\pi\)
0.871304 0.490744i \(-0.163275\pi\)
\(822\) −0.947441 + 3.53590i −0.0330458 + 0.123329i
\(823\) 14.3038 53.3827i 0.498601 1.86080i −0.0102479 0.999947i \(-0.503262\pi\)
0.508849 0.860856i \(-0.330071\pi\)
\(824\) 4.59808 7.96410i 0.160182 0.277443i
\(825\) −7.00000 1.00000i −0.243709 0.0348155i
\(826\) 4.90192 + 10.0981i 0.170560 + 0.351357i
\(827\) −33.2224 + 33.2224i −1.15526 + 1.15526i −0.169774 + 0.985483i \(0.554304\pi\)
−0.985483 + 0.169774i \(0.945696\pi\)
\(828\) 0.633975 0.169873i 0.0220321 0.00590349i
\(829\) 7.26795 + 12.5885i 0.252426 + 0.437215i 0.964193 0.265200i \(-0.0854381\pi\)
−0.711767 + 0.702416i \(0.752105\pi\)
\(830\) 3.42820 0.205771i 0.118995 0.00714243i
\(831\) −2.41154 1.39230i −0.0836555 0.0482985i
\(832\) −4.53590 4.53590i −0.157254 0.157254i
\(833\) −21.6603 + 16.1962i −0.750483 + 0.561163i
\(834\) 1.51666i 0.0525177i
\(835\) 36.4282 + 7.45448i 1.26065 + 0.257973i
\(836\) −3.00000 + 1.73205i −0.103757 + 0.0599042i
\(837\) −21.3923 5.73205i −0.739426 0.198129i
\(838\) 3.19615 + 11.9282i 0.110409 + 0.412053i
\(839\) −6.87564 −0.237374 −0.118687 0.992932i \(-0.537868\pi\)
−0.118687 + 0.992932i \(0.537868\pi\)
\(840\) 4.23205 4.13397i 0.146020 0.142636i
\(841\) 20.0000 0.689655
\(842\) 2.32309 + 8.66987i 0.0800588 + 0.298784i
\(843\) 0.464102 + 0.124356i 0.0159845 + 0.00428304i
\(844\) −0.294229 + 0.169873i −0.0101278 + 0.00584727i
\(845\) −6.16025 9.33013i −0.211919 0.320966i
\(846\) 12.9282i 0.444481i
\(847\) 6.12436 + 7.07180i 0.210435 + 0.242990i
\(848\) 12.3205 + 12.3205i 0.423088 + 0.423088i
\(849\) 0.882686 + 0.509619i 0.0302937 + 0.0174901i
\(850\) −3.92820 + 9.19615i −0.134736 + 0.315425i
\(851\) −0.339746 0.588457i −0.0116463 0.0201721i
\(852\) −1.09808 + 0.294229i −0.0376195 + 0.0100801i
\(853\) 18.1244 18.1244i 0.620566 0.620566i −0.325110 0.945676i \(-0.605401\pi\)
0.945676 + 0.325110i \(0.105401\pi\)
\(854\) 1.74167 + 1.17949i 0.0595987 + 0.0403614i
\(855\) −2.00000 + 4.00000i −0.0683986 + 0.136797i
\(856\) −12.6962 + 21.9904i −0.433946 + 0.751616i
\(857\) −2.97372 + 11.0981i −0.101580 + 0.379103i −0.997935 0.0642351i \(-0.979539\pi\)
0.896354 + 0.443338i \(0.146206\pi\)
\(858\) −0.535898 + 2.00000i −0.0182953 + 0.0682789i
\(859\) 17.4641 30.2487i 0.595867 1.03207i −0.397556 0.917578i \(-0.630142\pi\)
0.993424 0.114495i \(-0.0365250\pi\)
\(860\) −14.7058 + 4.90192i −0.501463 + 0.167154i
\(861\) −7.33013 4.96410i −0.249810 0.169176i
\(862\) −2.26795 + 2.26795i −0.0772467 + 0.0772467i
\(863\) −49.9449 + 13.3827i −1.70014 + 0.455552i −0.972976 0.230908i \(-0.925830\pi\)
−0.727167 + 0.686460i \(0.759164\pi\)
\(864\) −7.62436 13.2058i −0.259386 0.449269i
\(865\) −34.5167 30.6077i −1.17360 1.04069i
\(866\) −11.1173 6.41858i −0.377782 0.218112i
\(867\) −0.758330 0.758330i −0.0257542 0.0257542i
\(868\) −22.3923 25.8564i −0.760044 0.877624i
\(869\) 8.92820i 0.302869i
\(870\) 1.50000 0.990381i 0.0508548 0.0335771i
\(871\) −27.1244 + 15.6603i −0.919074 + 0.530627i
\(872\) −18.8923 5.06218i −0.639774 0.171427i
\(873\) −5.92820 22.1244i −0.200639 0.748796i
\(874\) −0.0525589 −0.00177783
\(875\) −29.2321 4.52628i −0.988224 0.153016i
\(876\) 12.0000 0.405442
\(877\) 10.4904 + 39.1506i 0.354235 + 1.32202i 0.881444 + 0.472288i \(0.156572\pi\)
−0.527209 + 0.849735i \(0.676762\pi\)
\(878\) 1.66025 + 0.444864i 0.0560309 + 0.0150134i
\(879\) −1.51666 + 0.875644i −0.0511557 + 0.0295348i
\(880\) −12.5622 + 8.29423i −0.423471 + 0.279598i
\(881\) 25.1436i 0.847109i 0.905871 + 0.423555i \(0.139218\pi\)
−0.905871 + 0.423555i \(0.860782\pi\)
\(882\) 7.92820 5.92820i 0.266956 0.199613i
\(883\) 8.07180 + 8.07180i 0.271638 + 0.271638i 0.829759 0.558122i \(-0.188478\pi\)
−0.558122 + 0.829759i \(0.688478\pi\)
\(884\) −16.3923 9.46410i −0.551333 0.318312i
\(885\) 7.09808 + 6.29423i 0.238599 + 0.211578i
\(886\) −3.50000 6.06218i −0.117585 0.203663i
\(887\) 10.8923 2.91858i 0.365728 0.0979965i −0.0712748 0.997457i \(-0.522707\pi\)
0.437003 + 0.899460i \(0.356040\pi\)
\(888\) −3.46410 + 3.46410i −0.116248 + 0.116248i
\(889\) 0.758330 + 1.56218i 0.0254336 + 0.0523938i
\(890\) 0.725009 0.241670i 0.0243024 0.00810079i
\(891\) −9.09808 + 15.7583i −0.304797 + 0.527924i
\(892\) −11.4904 + 42.8827i −0.384726 + 1.43582i
\(893\) −1.73205 + 6.46410i −0.0579609 + 0.216313i
\(894\) 0.107695 0.186533i 0.00360186 0.00623861i
\(895\) 7.85641 15.7128i 0.262611 0.525221i
\(896\) 2.16987 30.2224i 0.0724904 1.00966i
\(897\) 0.143594 0.143594i 0.00479445 0.00479445i
\(898\) 16.5263 4.42820i 0.551489 0.147771i
\(899\) −11.1962 19.3923i −0.373413 0.646770i
\(900\) −9.29423 + 21.7583i −0.309808 + 0.725278i
\(901\) 23.6603 + 13.6603i 0.788237 + 0.455089i
\(902\) −6.46410 6.46410i −0.215231 0.215231i
\(903\) 5.38269 1.03590i 0.179125 0.0344725i
\(904\) 21.1244i 0.702586i
\(905\) 1.47372 + 2.23205i 0.0489881 + 0.0741959i
\(906\) 3.21539 1.85641i 0.106824 0.0616750i
\(907\) 32.4545 + 8.69615i 1.07763 + 0.288751i 0.753626 0.657304i \(-0.228303\pi\)
0.324007 + 0.946055i \(0.394970\pi\)
\(908\) 8.83013 + 32.9545i 0.293038 + 1.09363i
\(909\) −22.5885 −0.749212
\(910\) −2.33975 + 8.33975i −0.0775618 + 0.276460i
\(911\) −7.51666 −0.249038 −0.124519 0.992217i \(-0.539739\pi\)
−0.124519 + 0.992217i \(0.539739\pi\)
\(912\) −0.241670 0.901924i −0.00800249 0.0298657i
\(913\) 7.83013 + 2.09808i 0.259139 + 0.0694362i
\(914\) 5.44486 3.14359i 0.180100 0.103981i
\(915\) 1.74167 + 0.356406i 0.0575778 + 0.0117824i
\(916\) 31.8564i 1.05257i
\(917\) 30.9282 26.7846i 1.02134 0.884506i
\(918\) −4.19615 4.19615i −0.138494 0.138494i
\(919\) 48.6673 + 28.0981i 1.60539 + 0.926870i 0.990384 + 0.138344i \(0.0441780\pi\)
0.615002 + 0.788526i \(0.289155\pi\)
\(920\) −0.598076 + 0.0358984i −0.0197180 + 0.00118353i
\(921\) 2.30385 + 3.99038i 0.0759144 + 0.131488i
\(922\) −2.80385 + 0.751289i −0.0923398 + 0.0247424i
\(923\) 2.53590 2.53590i 0.0834701 0.0834701i
\(924\) 5.83013 2.83013i 0.191797 0.0931043i
\(925\) 24.2487 + 3.46410i 0.797293 + 0.113899i
\(926\) −1.74167 + 3.01666i −0.0572348 + 0.0991336i
\(927\) 3.36603 12.5622i 0.110555 0.412596i
\(928\) 3.99038 14.8923i 0.130991 0.488864i
\(929\) 18.1603 31.4545i 0.595819 1.03199i −0.397612 0.917554i \(-0.630161\pi\)
0.993431 0.114435i \(-0.0365056\pi\)
\(930\) 4.00000 + 2.00000i 0.131165 + 0.0655826i
\(931\) 4.75833 1.90192i 0.155948 0.0623330i
\(932\) 8.19615 8.19615i 0.268474 0.268474i
\(933\) 7.63397 2.04552i 0.249925 0.0669672i
\(934\) −3.64359 6.31089i −0.119222 0.206499i
\(935\) −15.6603 + 17.6603i −0.512145 + 0.577552i
\(936\) 12.9282 + 7.46410i 0.422572 + 0.243972i
\(937\) −17.0718 17.0718i −0.557711 0.557711i 0.370944 0.928655i \(-0.379034\pi\)
−0.928655 + 0.370944i \(0.879034\pi\)
\(938\) −14.3301 4.96410i −0.467895 0.162084i
\(939\) 2.78461i 0.0908723i
\(940\) −7.09808 + 34.6865i −0.231514 + 1.13135i
\(941\) 35.1962 20.3205i 1.14736 0.662430i 0.199119 0.979975i \(-0.436192\pi\)
0.948243 + 0.317546i \(0.102859\pi\)
\(942\) −1.24167 0.332704i −0.0404558 0.0108401i
\(943\) 0.232051 + 0.866025i 0.00755661 + 0.0282017i
\(944\) 20.1962 0.657329
\(945\) 8.95448 15.0981i 0.291289 0.491140i
\(946\) 5.66025 0.184031
\(947\) 0.349365 + 1.30385i 0.0113528 + 0.0423694i 0.971370 0.237572i \(-0.0763516\pi\)
−0.960017 + 0.279941i \(0.909685\pi\)
\(948\) 2.83013 + 0.758330i 0.0919183 + 0.0246294i
\(949\) −32.7846 + 18.9282i −1.06423 + 0.614435i
\(950\) 1.16987 1.49038i 0.0379557 0.0483543i
\(951\) 4.92820i 0.159808i
\(952\) −3.73205 19.3923i −0.120956 0.628508i
\(953\) −37.8564 37.8564i −1.22629 1.22629i −0.965357 0.260932i \(-0.915970\pi\)
−0.260932 0.965357i \(-0.584030\pi\)
\(954\) −8.66025 5.00000i −0.280386 0.161881i
\(955\) −1.77757 29.6147i −0.0575208 0.958310i
\(956\) −2.07180 3.58846i −0.0670067 0.116059i
\(957\) 4.09808 1.09808i 0.132472 0.0354958i
\(958\) −4.78461 + 4.78461i −0.154584 + 0.154584i
\(959\) −20.2679 + 29.9282i −0.654486 + 0.966432i
\(960\) −0.830127 2.49038i −0.0267922 0.0803767i
\(961\) 12.3564 21.4019i 0.398594 0.690385i
\(962\) 1.85641 6.92820i 0.0598529 0.223374i
\(963\) −9.29423 + 34.6865i −0.299502 + 1.11776i
\(964\) 21.4641 37.1769i 0.691312 1.19739i
\(965\) 5.73205 + 17.1962i 0.184521 + 0.553564i
\(966\) 0.0980762 + 0.00704156i 0.00315555 + 0.000226558i
\(967\) −13.5622 + 13.5622i −0.436130 + 0.436130i −0.890707 0.454577i \(-0.849790\pi\)
0.454577 + 0.890707i \(0.349790\pi\)
\(968\) −6.59808 + 1.76795i −0.212070 + 0.0568240i
\(969\) −0.732051 1.26795i −0.0235169 0.0407324i
\(970\) 0.581416 + 9.68653i 0.0186681 + 0.311016i
\(971\) 29.0718 + 16.7846i 0.932958 + 0.538644i 0.887746 0.460334i \(-0.152270\pi\)
0.0452124 + 0.998977i \(0.485604\pi\)
\(972\) −15.1244 15.1244i −0.485114 0.485114i
\(973\) −4.90192 + 14.1506i −0.157148 + 0.453649i
\(974\) 14.5885i 0.467444i
\(975\) 0.875644 + 7.26795i 0.0280431 + 0.232761i
\(976\) 3.27757 1.89230i 0.104912 0.0605712i
\(977\) 0.562178 + 0.150635i 0.0179857 + 0.00481924i 0.267801 0.963474i \(-0.413703\pi\)
−0.249815 + 0.968294i \(0.580370\pi\)
\(978\) 0.973721 + 3.63397i 0.0311362 + 0.116202i
\(979\) 1.80385 0.0576512
\(980\) 24.5263 11.5526i 0.783463 0.369033i
\(981\) −27.6603 −0.883124
\(982\) −5.05256 18.8564i −0.161234 0.601732i
\(983\) 54.1147 + 14.5000i 1.72599 + 0.462478i 0.979253 0.202639i \(-0.0649519\pi\)
0.746739 + 0.665118i \(0.231619\pi\)
\(984\) 5.59808 3.23205i 0.178460 0.103034i
\(985\) 6.41858 31.3660i 0.204513 0.999405i
\(986\) 6.00000i 0.191079i
\(987\) 4.09808 11.8301i 0.130443 0.376557i
\(988\) 2.53590 + 2.53590i 0.0806777 + 0.0806777i
\(989\) −0.480762 0.277568i −0.0152873 0.00882615i
\(990\) 5.73205 6.46410i 0.182177 0.205443i
\(991\) −15.8564 27.4641i −0.503695 0.872426i −0.999991 0.00427229i \(-0.998640\pi\)
0.496296 0.868154i \(-0.334693\pi\)
\(992\) 37.0526 9.92820i 1.17642 0.315221i
\(993\) −0.679492 + 0.679492i −0.0215630 + 0.0215630i
\(994\) 1.73205 + 0.124356i 0.0549373 + 0.00394432i
\(995\) −22.1436 11.0718i −0.701999 0.351000i
\(996\) −1.33013 + 2.30385i −0.0421467 + 0.0730002i
\(997\) −10.6865 + 39.8827i −0.338446 + 1.26310i 0.561639 + 0.827382i \(0.310171\pi\)
−0.900085 + 0.435715i \(0.856496\pi\)
\(998\) 1.54294 5.75833i 0.0488409 0.182277i
\(999\) −7.26795 + 12.5885i −0.229948 + 0.398281i
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 35.2.k.a.33.1 yes 4
3.2 odd 2 315.2.bz.b.208.1 4
4.3 odd 2 560.2.ci.a.33.1 4
5.2 odd 4 35.2.k.b.12.1 yes 4
5.3 odd 4 175.2.o.a.82.1 4
5.4 even 2 175.2.o.b.68.1 4
7.2 even 3 245.2.f.a.48.1 4
7.3 odd 6 35.2.k.b.3.1 yes 4
7.4 even 3 245.2.l.b.178.1 4
7.5 odd 6 245.2.f.b.48.1 4
7.6 odd 2 245.2.l.a.68.1 4
15.2 even 4 315.2.bz.a.82.1 4
20.7 even 4 560.2.ci.b.257.1 4
21.17 even 6 315.2.bz.a.73.1 4
28.3 even 6 560.2.ci.b.353.1 4
35.2 odd 12 245.2.f.b.97.1 4
35.3 even 12 175.2.o.b.157.1 4
35.12 even 12 245.2.f.a.97.1 4
35.17 even 12 inner 35.2.k.a.17.1 4
35.24 odd 6 175.2.o.a.143.1 4
35.27 even 4 245.2.l.b.117.1 4
35.32 odd 12 245.2.l.a.227.1 4
105.17 odd 12 315.2.bz.b.262.1 4
140.87 odd 12 560.2.ci.a.17.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.k.a.17.1 4 35.17 even 12 inner
35.2.k.a.33.1 yes 4 1.1 even 1 trivial
35.2.k.b.3.1 yes 4 7.3 odd 6
35.2.k.b.12.1 yes 4 5.2 odd 4
175.2.o.a.82.1 4 5.3 odd 4
175.2.o.a.143.1 4 35.24 odd 6
175.2.o.b.68.1 4 5.4 even 2
175.2.o.b.157.1 4 35.3 even 12
245.2.f.a.48.1 4 7.2 even 3
245.2.f.a.97.1 4 35.12 even 12
245.2.f.b.48.1 4 7.5 odd 6
245.2.f.b.97.1 4 35.2 odd 12
245.2.l.a.68.1 4 7.6 odd 2
245.2.l.a.227.1 4 35.32 odd 12
245.2.l.b.117.1 4 35.27 even 4
245.2.l.b.178.1 4 7.4 even 3
315.2.bz.a.73.1 4 21.17 even 6
315.2.bz.a.82.1 4 15.2 even 4
315.2.bz.b.208.1 4 3.2 odd 2
315.2.bz.b.262.1 4 105.17 odd 12
560.2.ci.a.17.1 4 140.87 odd 12
560.2.ci.a.33.1 4 4.3 odd 2
560.2.ci.b.257.1 4 20.7 even 4
560.2.ci.b.353.1 4 28.3 even 6