Properties

Label 99.2.p.a.2.5
Level $99$
Weight $2$
Character 99.2
Analytic conductor $0.791$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,2,Mod(2,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.p (of order \(30\), degree \(8\), 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: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 2.5
Character \(\chi\) \(=\) 99.2
Dual form 99.2.p.a.50.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.536887 - 0.596273i) q^{2} +(1.73203 + 0.00818115i) q^{3} +(0.141763 - 1.34878i) q^{4} +(-2.14661 - 1.93281i) q^{5} +(-0.925027 - 1.03716i) q^{6} +(0.542079 + 1.21753i) q^{7} +(-2.17861 + 1.58285i) q^{8} +(2.99987 + 0.0283400i) q^{9} +O(q^{10})\) \(q+(-0.536887 - 0.596273i) q^{2} +(1.73203 + 0.00818115i) q^{3} +(0.141763 - 1.34878i) q^{4} +(-2.14661 - 1.93281i) q^{5} +(-0.925027 - 1.03716i) q^{6} +(0.542079 + 1.21753i) q^{7} +(-2.17861 + 1.58285i) q^{8} +(2.99987 + 0.0283400i) q^{9} +2.31767i q^{10} +(2.22482 + 2.45971i) q^{11} +(0.256572 - 2.33497i) q^{12} +(-0.121914 - 0.573561i) q^{13} +(0.434945 - 0.976903i) q^{14} +(-3.70218 - 3.36525i) q^{15} +(-0.539671 - 0.114711i) q^{16} +(-0.407327 - 1.25362i) q^{17} +(-1.59369 - 1.80396i) q^{18} +(4.21041 + 5.79513i) q^{19} +(-2.91125 + 2.62130i) q^{20} +(0.928938 + 2.11323i) q^{21} +(0.272182 - 2.64719i) q^{22} +(-2.62500 + 1.51554i) q^{23} +(-3.78636 + 2.72372i) q^{24} +(0.349510 + 3.32536i) q^{25} +(-0.276545 + 0.380632i) q^{26} +(5.19563 + 0.0736281i) q^{27} +(1.71903 - 0.558546i) q^{28} +(-1.19216 + 0.530783i) q^{29} +(-0.0189612 + 4.01427i) q^{30} +(-7.38644 + 1.57004i) q^{31} +(2.91425 + 5.04763i) q^{32} +(3.83334 + 4.27850i) q^{33} +(-0.528814 + 0.915932i) q^{34} +(1.18963 - 3.66129i) q^{35} +(0.463493 - 4.04214i) q^{36} +(-3.23755 - 2.35222i) q^{37} +(1.19497 - 5.62189i) q^{38} +(-0.206467 - 0.994423i) q^{39} +(7.73596 + 0.813082i) q^{40} +(-2.05694 - 0.915811i) q^{41} +(0.761331 - 1.68847i) q^{42} +(-11.2365 - 6.48742i) q^{43} +(3.63301 - 2.65210i) q^{44} +(-6.38475 - 5.85901i) q^{45} +(2.31301 + 0.751541i) q^{46} +(11.5098 - 1.20973i) q^{47} +(-0.933788 - 0.203097i) q^{48} +(3.49539 - 3.88202i) q^{49} +(1.79518 - 1.99375i) q^{50} +(-0.695247 - 2.17465i) q^{51} +(-0.790891 + 0.0831260i) q^{52} +(-3.40948 - 1.10781i) q^{53} +(-2.74556 - 3.13755i) q^{54} +(-0.0216557 - 9.58019i) q^{55} +(-3.10815 - 1.79449i) q^{56} +(7.24515 + 10.0718i) q^{57} +(0.956546 + 0.425882i) q^{58} +(5.95883 + 0.626298i) q^{59} +(-5.06382 + 4.51636i) q^{60} +(-1.64415 + 7.73512i) q^{61} +(4.90186 + 3.56141i) q^{62} +(1.59166 + 3.66779i) q^{63} +(1.10416 - 3.39825i) q^{64} +(-0.846884 + 1.46685i) q^{65} +(0.493085 - 4.58279i) q^{66} +(-4.35166 - 7.53730i) q^{67} +(-1.74861 + 0.371678i) q^{68} +(-4.55898 + 2.60349i) q^{69} +(-2.82183 + 1.25636i) q^{70} +(4.54327 - 1.47620i) q^{71} +(-6.58039 + 4.68660i) q^{72} +(-5.16130 + 7.10392i) q^{73} +(0.335634 + 3.19334i) q^{74} +(0.578157 + 5.76249i) q^{75} +(8.41325 - 4.85739i) q^{76} +(-1.78874 + 4.04214i) q^{77} +(-0.482099 + 0.657003i) q^{78} +(10.2545 - 9.23323i) q^{79} +(0.936746 + 1.28932i) q^{80} +(8.99839 + 0.170032i) q^{81} +(0.558273 + 1.71819i) q^{82} +(-10.5286 - 2.23793i) q^{83} +(2.98198 - 0.953356i) q^{84} +(-1.54865 + 3.47832i) q^{85} +(2.16448 + 10.1831i) q^{86} +(-2.06920 + 0.909579i) q^{87} +(-8.74036 - 1.83718i) q^{88} +8.87289i q^{89} +(-0.0656827 + 6.95269i) q^{90} +(0.632240 - 0.459350i) q^{91} +(1.67201 + 3.75540i) q^{92} +(-12.8064 + 2.65892i) q^{93} +(-6.90079 - 6.21350i) q^{94} +(2.16281 - 20.5778i) q^{95} +(5.00628 + 8.76649i) q^{96} +(-0.548828 - 0.609535i) q^{97} -4.19137 q^{98} +(6.60446 + 7.44185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27} - 20 q^{28} + 30 q^{29} + 50 q^{30} - 6 q^{31} + 4 q^{33} - 10 q^{34} - 17 q^{36} - 6 q^{37} + 9 q^{38} + 85 q^{39} + 15 q^{40} - 15 q^{41} + 19 q^{42} - 12 q^{45} - 40 q^{46} - 21 q^{47} + 70 q^{48} - q^{49} + 60 q^{50} - 45 q^{51} - 5 q^{52} - 18 q^{55} + 90 q^{56} + 60 q^{57} - 29 q^{58} + 81 q^{59} + 43 q^{60} - 5 q^{61} + 15 q^{63} - 8 q^{64} - 39 q^{66} + 10 q^{67} + 180 q^{68} - 20 q^{69} + 30 q^{70} + 5 q^{72} - 20 q^{73} - 15 q^{74} - 30 q^{75} + 33 q^{77} + 152 q^{78} - 5 q^{79} - 73 q^{81} - 2 q^{82} - 60 q^{83} - 135 q^{84} - 5 q^{85} - 48 q^{86} - 59 q^{88} - 70 q^{90} + 52 q^{91} - 213 q^{92} - 34 q^{93} - 5 q^{94} - 135 q^{95} - 145 q^{96} + 27 q^{97} + 35 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.536887 0.596273i −0.379636 0.421629i 0.522798 0.852457i \(-0.324888\pi\)
−0.902434 + 0.430828i \(0.858222\pi\)
\(3\) 1.73203 + 0.00818115i 0.999989 + 0.00472339i
\(4\) 0.141763 1.34878i 0.0708813 0.674390i
\(5\) −2.14661 1.93281i −0.959991 0.864380i 0.0308346 0.999525i \(-0.490183\pi\)
−0.990826 + 0.135144i \(0.956850\pi\)
\(6\) −0.925027 1.03716i −0.377641 0.423417i
\(7\) 0.542079 + 1.21753i 0.204887 + 0.460183i 0.986538 0.163533i \(-0.0522889\pi\)
−0.781651 + 0.623716i \(0.785622\pi\)
\(8\) −2.17861 + 1.58285i −0.770254 + 0.559622i
\(9\) 2.99987 + 0.0283400i 0.999955 + 0.00944667i
\(10\) 2.31767i 0.732910i
\(11\) 2.22482 + 2.45971i 0.670809 + 0.741630i
\(12\) 0.256572 2.33497i 0.0740659 0.674048i
\(13\) −0.121914 0.573561i −0.0338129 0.159077i 0.958002 0.286762i \(-0.0925788\pi\)
−0.991815 + 0.127685i \(0.959245\pi\)
\(14\) 0.434945 0.976903i 0.116244 0.261088i
\(15\) −3.70218 3.36525i −0.955898 0.868905i
\(16\) −0.539671 0.114711i −0.134918 0.0286776i
\(17\) −0.407327 1.25362i −0.0987913 0.304048i 0.889432 0.457068i \(-0.151100\pi\)
−0.988223 + 0.153019i \(0.951100\pi\)
\(18\) −1.59369 1.80396i −0.375637 0.425196i
\(19\) 4.21041 + 5.79513i 0.965935 + 1.32949i 0.944074 + 0.329734i \(0.106959\pi\)
0.0218608 + 0.999761i \(0.493041\pi\)
\(20\) −2.91125 + 2.62130i −0.650975 + 0.586141i
\(21\) 0.928938 + 2.11323i 0.202711 + 0.461146i
\(22\) 0.272182 2.64719i 0.0580294 0.564382i
\(23\) −2.62500 + 1.51554i −0.547350 + 0.316013i −0.748053 0.663639i \(-0.769011\pi\)
0.200702 + 0.979652i \(0.435678\pi\)
\(24\) −3.78636 + 2.72372i −0.772888 + 0.555978i
\(25\) 0.349510 + 3.32536i 0.0699020 + 0.665073i
\(26\) −0.276545 + 0.380632i −0.0542349 + 0.0746480i
\(27\) 5.19563 + 0.0736281i 0.999900 + 0.0141697i
\(28\) 1.71903 0.558546i 0.324866 0.105555i
\(29\) −1.19216 + 0.530783i −0.221378 + 0.0985639i −0.514429 0.857533i \(-0.671996\pi\)
0.293051 + 0.956097i \(0.405329\pi\)
\(30\) −0.0189612 + 4.01427i −0.00346182 + 0.732902i
\(31\) −7.38644 + 1.57004i −1.32664 + 0.281987i −0.816123 0.577878i \(-0.803881\pi\)
−0.510521 + 0.859865i \(0.670548\pi\)
\(32\) 2.91425 + 5.04763i 0.515171 + 0.892303i
\(33\) 3.83334 + 4.27850i 0.667298 + 0.744791i
\(34\) −0.528814 + 0.915932i −0.0906908 + 0.157081i
\(35\) 1.18963 3.66129i 0.201084 0.618872i
\(36\) 0.463493 4.04214i 0.0772489 0.673691i
\(37\) −3.23755 2.35222i −0.532250 0.386702i 0.288949 0.957345i \(-0.406694\pi\)
−0.821199 + 0.570642i \(0.806694\pi\)
\(38\) 1.19497 5.62189i 0.193850 0.911991i
\(39\) −0.206467 0.994423i −0.0330611 0.159235i
\(40\) 7.73596 + 0.813082i 1.22316 + 0.128560i
\(41\) −2.05694 0.915811i −0.321241 0.143026i 0.239780 0.970827i \(-0.422925\pi\)
−0.561021 + 0.827802i \(0.689591\pi\)
\(42\) 0.761331 1.68847i 0.117476 0.260536i
\(43\) −11.2365 6.48742i −1.71356 0.989322i −0.929652 0.368440i \(-0.879892\pi\)
−0.783904 0.620882i \(-0.786775\pi\)
\(44\) 3.63301 2.65210i 0.547696 0.399819i
\(45\) −6.38475 5.85901i −0.951783 0.873410i
\(46\) 2.31301 + 0.751541i 0.341034 + 0.110809i
\(47\) 11.5098 1.20973i 1.67888 0.176457i 0.783385 0.621537i \(-0.213491\pi\)
0.895491 + 0.445080i \(0.146825\pi\)
\(48\) −0.933788 0.203097i −0.134781 0.0293146i
\(49\) 3.49539 3.88202i 0.499341 0.554574i
\(50\) 1.79518 1.99375i 0.253877 0.281959i
\(51\) −0.695247 2.17465i −0.0973540 0.304512i
\(52\) −0.790891 + 0.0831260i −0.109677 + 0.0115275i
\(53\) −3.40948 1.10781i −0.468328 0.152169i 0.0653400 0.997863i \(-0.479187\pi\)
−0.533668 + 0.845694i \(0.679187\pi\)
\(54\) −2.74556 3.13755i −0.373624 0.426966i
\(55\) −0.0216557 9.58019i −0.00292006 1.29179i
\(56\) −3.10815 1.79449i −0.415343 0.239799i
\(57\) 7.24515 + 10.0718i 0.959644 + 1.33404i
\(58\) 0.956546 + 0.425882i 0.125601 + 0.0559210i
\(59\) 5.95883 + 0.626298i 0.775773 + 0.0815370i 0.484137 0.874992i \(-0.339134\pi\)
0.291636 + 0.956529i \(0.405800\pi\)
\(60\) −5.06382 + 4.51636i −0.653736 + 0.583059i
\(61\) −1.64415 + 7.73512i −0.210512 + 0.990381i 0.738284 + 0.674490i \(0.235637\pi\)
−0.948796 + 0.315890i \(0.897697\pi\)
\(62\) 4.90186 + 3.56141i 0.622536 + 0.452299i
\(63\) 1.59166 + 3.66779i 0.200530 + 0.462098i
\(64\) 1.10416 3.39825i 0.138020 0.424781i
\(65\) −0.846884 + 1.46685i −0.105043 + 0.181940i
\(66\) 0.493085 4.58279i 0.0606946 0.564102i
\(67\) −4.35166 7.53730i −0.531640 0.920828i −0.999318 0.0369287i \(-0.988243\pi\)
0.467678 0.883899i \(-0.345091\pi\)
\(68\) −1.74861 + 0.371678i −0.212050 + 0.0450726i
\(69\) −4.55898 + 2.60349i −0.548837 + 0.313424i
\(70\) −2.82183 + 1.25636i −0.337273 + 0.150164i
\(71\) 4.54327 1.47620i 0.539187 0.175192i −0.0267483 0.999642i \(-0.508515\pi\)
0.565935 + 0.824450i \(0.308515\pi\)
\(72\) −6.58039 + 4.68660i −0.775506 + 0.552321i
\(73\) −5.16130 + 7.10392i −0.604084 + 0.831451i −0.996075 0.0885185i \(-0.971787\pi\)
0.391990 + 0.919969i \(0.371787\pi\)
\(74\) 0.335634 + 3.19334i 0.0390166 + 0.371218i
\(75\) 0.578157 + 5.76249i 0.0667598 + 0.665396i
\(76\) 8.41325 4.85739i 0.965065 0.557181i
\(77\) −1.78874 + 4.04214i −0.203846 + 0.460645i
\(78\) −0.482099 + 0.657003i −0.0545869 + 0.0743910i
\(79\) 10.2545 9.23323i 1.15373 1.03882i 0.155023 0.987911i \(-0.450455\pi\)
0.998703 0.0509087i \(-0.0162118\pi\)
\(80\) 0.936746 + 1.28932i 0.104731 + 0.144150i
\(81\) 8.99839 + 0.170032i 0.999822 + 0.0188925i
\(82\) 0.558273 + 1.71819i 0.0616510 + 0.189742i
\(83\) −10.5286 2.23793i −1.15567 0.245644i −0.410077 0.912051i \(-0.634498\pi\)
−0.745589 + 0.666407i \(0.767832\pi\)
\(84\) 2.98198 0.953356i 0.325361 0.104020i
\(85\) −1.54865 + 3.47832i −0.167975 + 0.377277i
\(86\) 2.16448 + 10.1831i 0.233401 + 1.09807i
\(87\) −2.06920 + 0.909579i −0.221841 + 0.0975171i
\(88\) −8.74036 1.83718i −0.931726 0.195844i
\(89\) 8.87289i 0.940524i 0.882527 + 0.470262i \(0.155841\pi\)
−0.882527 + 0.470262i \(0.844159\pi\)
\(90\) −0.0656827 + 6.95269i −0.00692356 + 0.732878i
\(91\) 0.632240 0.459350i 0.0662768 0.0481529i
\(92\) 1.67201 + 3.75540i 0.174319 + 0.391527i
\(93\) −12.8064 + 2.65892i −1.32796 + 0.275718i
\(94\) −6.90079 6.21350i −0.711762 0.640873i
\(95\) 2.16281 20.5778i 0.221900 2.11124i
\(96\) 5.00628 + 8.76649i 0.510951 + 0.894726i
\(97\) −0.548828 0.609535i −0.0557250 0.0618889i 0.714638 0.699495i \(-0.246592\pi\)
−0.770363 + 0.637606i \(0.779925\pi\)
\(98\) −4.19137 −0.423392
\(99\) 6.60446 + 7.44185i 0.663773 + 0.747934i
\(100\) 4.53473 0.453473
\(101\) −11.4734 12.7425i −1.14165 1.26793i −0.958579 0.284827i \(-0.908064\pi\)
−0.183068 0.983100i \(-0.558603\pi\)
\(102\) −0.923415 + 1.58210i −0.0914318 + 0.156651i
\(103\) −1.01984 + 9.70315i −0.100488 + 0.956080i 0.821852 + 0.569701i \(0.192941\pi\)
−0.922340 + 0.386379i \(0.873726\pi\)
\(104\) 1.17346 + 1.05659i 0.115068 + 0.103607i
\(105\) 2.09042 6.33174i 0.204005 0.617915i
\(106\) 1.16995 + 2.62775i 0.113636 + 0.255230i
\(107\) 2.38113 1.72999i 0.230193 0.167245i −0.466710 0.884410i \(-0.654561\pi\)
0.696903 + 0.717165i \(0.254561\pi\)
\(108\) 0.835854 6.99733i 0.0804301 0.673318i
\(109\) 1.43952i 0.137881i 0.997621 + 0.0689404i \(0.0219618\pi\)
−0.997621 + 0.0689404i \(0.978038\pi\)
\(110\) −5.70079 + 5.15639i −0.543549 + 0.491643i
\(111\) −5.58830 4.10060i −0.530418 0.389212i
\(112\) −0.152881 0.719247i −0.0144459 0.0679625i
\(113\) 0.769359 1.72801i 0.0723752 0.162557i −0.873735 0.486402i \(-0.838309\pi\)
0.946110 + 0.323845i \(0.104976\pi\)
\(114\) 2.11572 9.72751i 0.198155 0.911065i
\(115\) 8.56410 + 1.82036i 0.798607 + 0.169749i
\(116\) 0.546906 + 1.68320i 0.0507790 + 0.156282i
\(117\) −0.349471 1.72406i −0.0323086 0.159389i
\(118\) −2.82577 3.88934i −0.260133 0.358043i
\(119\) 1.30552 1.17550i 0.119677 0.107758i
\(120\) 13.3923 + 1.47157i 1.22254 + 0.134336i
\(121\) −1.10034 + 10.9448i −0.100031 + 0.994984i
\(122\) 5.49497 3.17252i 0.497491 0.287227i
\(123\) −3.55520 1.60304i −0.320562 0.144541i
\(124\) 1.07051 + 10.1853i 0.0961351 + 0.914664i
\(125\) −2.81217 + 3.87062i −0.251528 + 0.346199i
\(126\) 1.33246 2.91825i 0.118705 0.259979i
\(127\) −4.49091 + 1.45919i −0.398504 + 0.129482i −0.501411 0.865209i \(-0.667186\pi\)
0.102907 + 0.994691i \(0.467186\pi\)
\(128\) 8.03010 3.57523i 0.709768 0.316009i
\(129\) −19.4090 11.3283i −1.70886 0.997405i
\(130\) 1.32932 0.282556i 0.116589 0.0247818i
\(131\) 3.94244 + 6.82851i 0.344453 + 0.596609i 0.985254 0.171097i \(-0.0547312\pi\)
−0.640802 + 0.767707i \(0.721398\pi\)
\(132\) 6.31418 4.56380i 0.549579 0.397228i
\(133\) −4.77337 + 8.26772i −0.413904 + 0.716903i
\(134\) −2.15794 + 6.64146i −0.186418 + 0.573735i
\(135\) −11.0107 10.2002i −0.947647 0.877896i
\(136\) 2.87170 + 2.08641i 0.246247 + 0.178909i
\(137\) −1.40050 + 6.58885i −0.119653 + 0.562923i 0.876951 + 0.480580i \(0.159574\pi\)
−0.996604 + 0.0823435i \(0.973760\pi\)
\(138\) 4.00005 + 1.32062i 0.340507 + 0.112418i
\(139\) −7.37491 0.775135i −0.625532 0.0657461i −0.213541 0.976934i \(-0.568500\pi\)
−0.411991 + 0.911188i \(0.635166\pi\)
\(140\) −4.76964 2.12358i −0.403108 0.179475i
\(141\) 19.9452 2.00112i 1.67969 0.168525i
\(142\) −3.31944 1.91648i −0.278561 0.160827i
\(143\) 1.13956 1.57594i 0.0952945 0.131787i
\(144\) −1.61569 0.359410i −0.134641 0.0299509i
\(145\) 3.58500 + 1.16484i 0.297718 + 0.0967344i
\(146\) 7.00691 0.736456i 0.579896 0.0609496i
\(147\) 6.08588 6.69518i 0.501955 0.552209i
\(148\) −3.63159 + 4.03329i −0.298515 + 0.331534i
\(149\) 4.12377 4.57991i 0.337832 0.375201i −0.550160 0.835059i \(-0.685433\pi\)
0.887992 + 0.459858i \(0.152100\pi\)
\(150\) 3.12562 3.43855i 0.255206 0.280756i
\(151\) 19.6091 2.06100i 1.59577 0.167722i 0.735486 0.677539i \(-0.236954\pi\)
0.860283 + 0.509817i \(0.170287\pi\)
\(152\) −18.3457 5.96087i −1.48803 0.483490i
\(153\) −1.18640 3.77225i −0.0959146 0.304968i
\(154\) 3.37057 1.10360i 0.271609 0.0889303i
\(155\) 18.8904 + 10.9064i 1.51731 + 0.876020i
\(156\) −1.37053 + 0.137506i −0.109730 + 0.0110093i
\(157\) 4.45331 + 1.98274i 0.355413 + 0.158240i 0.576674 0.816975i \(-0.304350\pi\)
−0.221261 + 0.975215i \(0.571017\pi\)
\(158\) −11.0111 1.15731i −0.875993 0.0920706i
\(159\) −5.89626 1.94665i −0.467604 0.154379i
\(160\) 3.50037 16.4680i 0.276729 1.30191i
\(161\) −3.26818 2.37447i −0.257569 0.187134i
\(162\) −4.72973 5.45679i −0.371603 0.428726i
\(163\) 3.43006 10.5566i 0.268663 0.826859i −0.722164 0.691722i \(-0.756852\pi\)
0.990827 0.135137i \(-0.0431476\pi\)
\(164\) −1.52683 + 2.64454i −0.119225 + 0.206504i
\(165\) 0.0408685 16.5934i 0.00318161 1.29179i
\(166\) 4.31826 + 7.47945i 0.335162 + 0.580518i
\(167\) −20.7753 + 4.41592i −1.60764 + 0.341714i −0.922289 0.386501i \(-0.873684\pi\)
−0.685349 + 0.728215i \(0.740350\pi\)
\(168\) −5.36872 3.13354i −0.414206 0.241758i
\(169\) 11.5620 5.14773i 0.889383 0.395979i
\(170\) 2.90548 0.944048i 0.222840 0.0724052i
\(171\) 12.4664 + 17.5040i 0.953332 + 1.33856i
\(172\) −10.3430 + 14.2360i −0.788648 + 1.08548i
\(173\) −1.29542 12.3251i −0.0984892 0.937062i −0.926486 0.376329i \(-0.877186\pi\)
0.827997 0.560733i \(-0.189481\pi\)
\(174\) 1.65328 + 0.745466i 0.125335 + 0.0565136i
\(175\) −3.85927 + 2.22815i −0.291733 + 0.168432i
\(176\) −0.918516 1.58264i −0.0692357 0.119296i
\(177\) 10.3157 + 1.13352i 0.775379 + 0.0852004i
\(178\) 5.29067 4.76374i 0.396552 0.357057i
\(179\) −6.56098 9.03041i −0.490390 0.674964i 0.490070 0.871683i \(-0.336971\pi\)
−0.980460 + 0.196719i \(0.936971\pi\)
\(180\) −8.80764 + 7.78105i −0.656483 + 0.579965i
\(181\) −0.00588405 0.0181092i −0.000437358 0.00134605i 0.950838 0.309690i \(-0.100225\pi\)
−0.951275 + 0.308344i \(0.900225\pi\)
\(182\) −0.613340 0.130369i −0.0454638 0.00966362i
\(183\) −2.91100 + 13.3840i −0.215188 + 0.989375i
\(184\) 3.31996 7.45676i 0.244751 0.549719i
\(185\) 2.40335 + 11.3069i 0.176698 + 0.831297i
\(186\) 8.46103 + 6.20857i 0.620393 + 0.455235i
\(187\) 2.17732 3.79099i 0.159221 0.277225i
\(188\) 15.6957i 1.14473i
\(189\) 2.72680 + 6.36575i 0.198345 + 0.463040i
\(190\) −13.4312 + 9.75833i −0.974401 + 0.707943i
\(191\) 1.06374 + 2.38919i 0.0769692 + 0.172876i 0.947932 0.318474i \(-0.103170\pi\)
−0.870962 + 0.491350i \(0.836504\pi\)
\(192\) 1.94024 5.87684i 0.140025 0.424124i
\(193\) 9.54568 + 8.59497i 0.687113 + 0.618680i 0.936890 0.349624i \(-0.113691\pi\)
−0.249777 + 0.968303i \(0.580357\pi\)
\(194\) −0.0687910 + 0.654503i −0.00493891 + 0.0469906i
\(195\) −1.47883 + 2.53370i −0.105901 + 0.181442i
\(196\) −4.74048 5.26483i −0.338606 0.376060i
\(197\) −6.88153 −0.490288 −0.245144 0.969487i \(-0.578835\pi\)
−0.245144 + 0.969487i \(0.578835\pi\)
\(198\) 0.891531 7.93350i 0.0633584 0.563809i
\(199\) 0.0675681 0.00478977 0.00239489 0.999997i \(-0.499238\pi\)
0.00239489 + 0.999997i \(0.499238\pi\)
\(200\) −6.02500 6.69144i −0.426032 0.473156i
\(201\) −7.47555 13.0904i −0.527285 0.923329i
\(202\) −1.43810 + 13.6826i −0.101184 + 0.962703i
\(203\) −1.29249 1.16376i −0.0907149 0.0816800i
\(204\) −3.03168 + 0.629452i −0.212260 + 0.0440705i
\(205\) 2.64536 + 5.94157i 0.184760 + 0.414978i
\(206\) 6.33327 4.60139i 0.441260 0.320594i
\(207\) −7.91760 + 4.47204i −0.550311 + 0.310828i
\(208\) 0.323519i 0.0224320i
\(209\) −4.88694 + 23.2495i −0.338036 + 1.60820i
\(210\) −4.89777 + 2.15297i −0.337978 + 0.148569i
\(211\) 0.253153 + 1.19099i 0.0174278 + 0.0819911i 0.986002 0.166733i \(-0.0533219\pi\)
−0.968574 + 0.248725i \(0.919989\pi\)
\(212\) −1.97753 + 4.44160i −0.135817 + 0.305050i
\(213\) 7.88116 2.51965i 0.540008 0.172644i
\(214\) −2.30995 0.490995i −0.157905 0.0335637i
\(215\) 11.5815 + 35.6440i 0.789848 + 2.43090i
\(216\) −11.4358 + 8.06350i −0.778106 + 0.548652i
\(217\) −5.91561 8.14213i −0.401577 0.552724i
\(218\) 0.858346 0.772858i 0.0581345 0.0523446i
\(219\) −8.99765 + 12.2620i −0.608005 + 0.828588i
\(220\) −12.9246 1.32890i −0.871379 0.0895947i
\(221\) −0.669370 + 0.386461i −0.0450267 + 0.0259962i
\(222\) 0.555203 + 5.53371i 0.0372628 + 0.371399i
\(223\) 1.36427 + 12.9801i 0.0913581 + 0.869214i 0.940213 + 0.340588i \(0.110626\pi\)
−0.848855 + 0.528626i \(0.822707\pi\)
\(224\) −4.56588 + 6.28440i −0.305071 + 0.419894i
\(225\) 0.954242 + 9.98555i 0.0636161 + 0.665703i
\(226\) −1.44342 + 0.468997i −0.0960151 + 0.0311972i
\(227\) 0.722663 0.321750i 0.0479649 0.0213553i −0.382614 0.923908i \(-0.624976\pi\)
0.430579 + 0.902553i \(0.358309\pi\)
\(228\) 14.6117 8.34432i 0.967686 0.552616i
\(229\) 9.55393 2.03075i 0.631342 0.134196i 0.118884 0.992908i \(-0.462068\pi\)
0.512458 + 0.858712i \(0.328735\pi\)
\(230\) −3.51252 6.08387i −0.231609 0.401159i
\(231\) −3.13122 + 6.98649i −0.206019 + 0.459677i
\(232\) 1.75709 3.04337i 0.115359 0.199807i
\(233\) 5.12103 15.7609i 0.335490 1.03253i −0.630991 0.775790i \(-0.717351\pi\)
0.966480 0.256741i \(-0.0826486\pi\)
\(234\) −0.840385 + 1.13401i −0.0549377 + 0.0741323i
\(235\) −27.0452 19.6495i −1.76423 1.28179i
\(236\) 1.68948 7.94836i 0.109976 0.517394i
\(237\) 17.8367 15.9084i 1.15862 1.03336i
\(238\) −1.40183 0.147339i −0.0908674 0.00955055i
\(239\) −1.11131 0.494785i −0.0718844 0.0320050i 0.370480 0.928841i \(-0.379193\pi\)
−0.442364 + 0.896836i \(0.645860\pi\)
\(240\) 1.61193 + 2.24081i 0.104049 + 0.144643i
\(241\) −0.657074 0.379362i −0.0423258 0.0244368i 0.478688 0.877985i \(-0.341113\pi\)
−0.521014 + 0.853548i \(0.674446\pi\)
\(242\) 7.11687 5.22003i 0.457490 0.335556i
\(243\) 15.5841 + 0.368119i 0.999721 + 0.0236148i
\(244\) 10.1999 + 3.31415i 0.652982 + 0.212167i
\(245\) −15.0064 + 1.57724i −0.958725 + 0.100766i
\(246\) 0.952890 + 2.98052i 0.0607541 + 0.190031i
\(247\) 2.81055 3.12144i 0.178831 0.198612i
\(248\) 13.6070 15.1121i 0.864047 0.959621i
\(249\) −18.2176 3.96230i −1.15449 0.251100i
\(250\) 3.81777 0.401263i 0.241457 0.0253781i
\(251\) 9.34419 + 3.03611i 0.589800 + 0.191638i 0.588686 0.808362i \(-0.299645\pi\)
0.00111390 + 0.999999i \(0.499645\pi\)
\(252\) 5.17268 1.62685i 0.325848 0.102482i
\(253\) −9.56795 3.08492i −0.601532 0.193947i
\(254\) 3.28119 + 1.89439i 0.205880 + 0.118865i
\(255\) −2.71076 + 6.01189i −0.169755 + 0.376479i
\(256\) −12.9715 5.77529i −0.810719 0.360955i
\(257\) 22.1626 + 2.32938i 1.38246 + 0.145303i 0.766385 0.642381i \(-0.222053\pi\)
0.616079 + 0.787684i \(0.288720\pi\)
\(258\) 3.66563 + 17.6551i 0.228212 + 1.09916i
\(259\) 1.10889 5.21690i 0.0689029 0.324163i
\(260\) 1.85840 + 1.35020i 0.115253 + 0.0837361i
\(261\) −3.59136 + 1.55849i −0.222299 + 0.0964682i
\(262\) 1.95501 6.01691i 0.120781 0.371726i
\(263\) 7.68495 13.3107i 0.473874 0.820774i −0.525678 0.850683i \(-0.676188\pi\)
0.999553 + 0.0299090i \(0.00952177\pi\)
\(264\) −15.1236 3.25356i −0.930790 0.200243i
\(265\) 5.17763 + 8.96791i 0.318059 + 0.550894i
\(266\) 7.49259 1.59260i 0.459400 0.0976485i
\(267\) −0.0725904 + 15.3681i −0.00444246 + 0.940514i
\(268\) −10.7831 + 4.80093i −0.658681 + 0.293264i
\(269\) 0.906419 0.294513i 0.0552653 0.0179568i −0.281254 0.959633i \(-0.590750\pi\)
0.336519 + 0.941677i \(0.390750\pi\)
\(270\) −0.170645 + 12.0417i −0.0103851 + 0.732837i
\(271\) 13.1444 18.0917i 0.798465 1.09899i −0.194537 0.980895i \(-0.562320\pi\)
0.993002 0.118098i \(-0.0376796\pi\)
\(272\) 0.0760186 + 0.723268i 0.00460930 + 0.0438546i
\(273\) 1.09882 0.790435i 0.0665035 0.0478393i
\(274\) 4.68067 2.70238i 0.282769 0.163257i
\(275\) −7.40183 + 8.25803i −0.446347 + 0.497978i
\(276\) 2.86525 + 6.51814i 0.172468 + 0.392346i
\(277\) 7.70440 6.93707i 0.462912 0.416808i −0.404392 0.914586i \(-0.632517\pi\)
0.867305 + 0.497777i \(0.165850\pi\)
\(278\) 3.49730 + 4.81362i 0.209754 + 0.288702i
\(279\) −22.2028 + 4.50057i −1.32925 + 0.269442i
\(280\) 3.20355 + 9.85952i 0.191449 + 0.589219i
\(281\) −9.29432 1.97557i −0.554453 0.117853i −0.0778399 0.996966i \(-0.524802\pi\)
−0.476613 + 0.879113i \(0.658136\pi\)
\(282\) −11.9015 10.8184i −0.708727 0.644228i
\(283\) −5.04823 + 11.3385i −0.300086 + 0.674004i −0.999157 0.0410477i \(-0.986930\pi\)
0.699071 + 0.715052i \(0.253597\pi\)
\(284\) −1.34700 6.33714i −0.0799298 0.376040i
\(285\) 3.91441 35.6237i 0.231870 2.11017i
\(286\) −1.55151 + 0.166617i −0.0917425 + 0.00985224i
\(287\) 3.00083i 0.177134i
\(288\) 8.59931 + 15.2248i 0.506719 + 0.897130i
\(289\) 12.3476 8.97108i 0.726331 0.527711i
\(290\) −1.23018 2.76302i −0.0722385 0.162250i
\(291\) −0.945600 1.06022i −0.0554321 0.0621514i
\(292\) 8.84995 + 7.96853i 0.517904 + 0.466323i
\(293\) −2.72141 + 25.8925i −0.158987 + 1.51266i 0.566294 + 0.824203i \(0.308377\pi\)
−0.725281 + 0.688453i \(0.758290\pi\)
\(294\) −7.25959 0.0342902i −0.423388 0.00199985i
\(295\) −11.5807 12.8617i −0.674256 0.748838i
\(296\) 10.7766 0.626375
\(297\) 11.3782 + 12.9436i 0.660233 + 0.751061i
\(298\) −4.94488 −0.286449
\(299\) 1.18928 + 1.32083i 0.0687779 + 0.0763856i
\(300\) 7.85430 + 0.0370993i 0.453468 + 0.00214193i
\(301\) 1.80753 17.1975i 0.104184 0.991248i
\(302\) −11.7568 10.5859i −0.676529 0.609149i
\(303\) −19.7681 22.1643i −1.13565 1.27331i
\(304\) −1.60747 3.61044i −0.0921949 0.207073i
\(305\) 18.4799 13.4264i 1.05815 0.768795i
\(306\) −1.61233 + 2.73269i −0.0921707 + 0.156217i
\(307\) 18.0274i 1.02888i −0.857527 0.514440i \(-0.828000\pi\)
0.857527 0.514440i \(-0.172000\pi\)
\(308\) 5.19839 + 2.98564i 0.296206 + 0.170123i
\(309\) −1.84578 + 16.7978i −0.105003 + 0.955595i
\(310\) −3.63882 17.1193i −0.206671 0.972311i
\(311\) 5.11443 11.4872i 0.290013 0.651379i −0.708511 0.705700i \(-0.750633\pi\)
0.998524 + 0.0543209i \(0.0172994\pi\)
\(312\) 2.02383 + 1.83965i 0.114577 + 0.104150i
\(313\) −11.4400 2.43166i −0.646630 0.137445i −0.127089 0.991891i \(-0.540563\pi\)
−0.519540 + 0.854446i \(0.673897\pi\)
\(314\) −1.20867 3.71990i −0.0682091 0.209926i
\(315\) 3.67248 10.9497i 0.206921 0.616945i
\(316\) −10.9999 15.1401i −0.618792 0.851695i
\(317\) 12.2252 11.0076i 0.686636 0.618250i −0.250128 0.968213i \(-0.580473\pi\)
0.936763 + 0.349963i \(0.113806\pi\)
\(318\) 2.00489 + 4.56092i 0.112429 + 0.255763i
\(319\) −3.95791 1.75147i −0.221600 0.0980632i
\(320\) −8.93837 + 5.16057i −0.499670 + 0.288485i
\(321\) 4.13835 2.97692i 0.230980 0.166156i
\(322\) 0.338809 + 3.22355i 0.0188811 + 0.179641i
\(323\) 5.54990 7.63878i 0.308805 0.425033i
\(324\) 1.50497 12.1128i 0.0836096 0.672931i
\(325\) 1.86469 0.605874i 0.103434 0.0336078i
\(326\) −8.13619 + 3.62247i −0.450622 + 0.200630i
\(327\) −0.0117769 + 2.49329i −0.000651264 + 0.137879i
\(328\) 5.93087 1.26064i 0.327477 0.0696074i
\(329\) 7.71210 + 13.3578i 0.425182 + 0.736437i
\(330\) −9.91613 + 8.88439i −0.545865 + 0.489070i
\(331\) −9.81281 + 16.9963i −0.539361 + 0.934201i 0.459577 + 0.888138i \(0.348001\pi\)
−0.998939 + 0.0460631i \(0.985332\pi\)
\(332\) −4.51104 + 13.8835i −0.247575 + 0.761958i
\(333\) −9.64556 7.14809i −0.528573 0.391713i
\(334\) 13.7871 + 10.0169i 0.754395 + 0.548100i
\(335\) −5.22688 + 24.5906i −0.285575 + 1.34353i
\(336\) −0.258910 1.24701i −0.0141247 0.0680299i
\(337\) 10.6020 + 1.11431i 0.577527 + 0.0607005i 0.388789 0.921327i \(-0.372894\pi\)
0.188738 + 0.982027i \(0.439560\pi\)
\(338\) −9.27693 4.13036i −0.504598 0.224662i
\(339\) 1.34669 2.98667i 0.0731422 0.162214i
\(340\) 4.47195 + 2.58188i 0.242526 + 0.140022i
\(341\) −20.2954 14.6755i −1.09905 0.794721i
\(342\) 3.74407 16.8310i 0.202456 0.910119i
\(343\) 15.4939 + 5.03428i 0.836592 + 0.271825i
\(344\) 34.7486 3.65223i 1.87352 0.196915i
\(345\) 14.8184 + 3.22298i 0.797796 + 0.173519i
\(346\) −6.65365 + 7.38963i −0.357703 + 0.397269i
\(347\) 1.65292 1.83575i 0.0887333 0.0985483i −0.697143 0.716932i \(-0.745546\pi\)
0.785876 + 0.618384i \(0.212212\pi\)
\(348\) 0.933489 + 2.91984i 0.0500402 + 0.156520i
\(349\) −12.7960 + 1.34492i −0.684957 + 0.0719918i −0.440613 0.897697i \(-0.645239\pi\)
−0.244343 + 0.969689i \(0.578572\pi\)
\(350\) 3.40058 + 1.10491i 0.181768 + 0.0590602i
\(351\) −0.591191 2.98899i −0.0315554 0.159540i
\(352\) −5.93202 + 18.3983i −0.316178 + 0.980631i
\(353\) −2.97223 1.71602i −0.158196 0.0913345i 0.418812 0.908073i \(-0.362447\pi\)
−0.577008 + 0.816738i \(0.695780\pi\)
\(354\) −4.86251 6.75958i −0.258439 0.359268i
\(355\) −12.6058 5.61247i −0.669047 0.297879i
\(356\) 11.9676 + 1.25784i 0.634281 + 0.0666656i
\(357\) 2.27082 2.02532i 0.120185 0.107191i
\(358\) −1.86209 + 8.76045i −0.0984145 + 0.463004i
\(359\) 4.07205 + 2.95852i 0.214915 + 0.156145i 0.690035 0.723776i \(-0.257595\pi\)
−0.475120 + 0.879921i \(0.657595\pi\)
\(360\) 23.1838 + 2.65838i 1.22189 + 0.140109i
\(361\) −9.98469 + 30.7297i −0.525510 + 1.61735i
\(362\) −0.00763899 + 0.0132311i −0.000401496 + 0.000695412i
\(363\) −1.99537 + 18.9478i −0.104730 + 0.994501i
\(364\) −0.529934 0.917872i −0.0277761 0.0481096i
\(365\) 24.8098 5.27349i 1.29861 0.276027i
\(366\) 9.54342 5.44995i 0.498842 0.284874i
\(367\) −2.83110 + 1.26049i −0.147782 + 0.0657969i −0.479295 0.877654i \(-0.659108\pi\)
0.331513 + 0.943451i \(0.392441\pi\)
\(368\) 1.59048 0.516779i 0.0829097 0.0269390i
\(369\) −6.14461 2.80560i −0.319875 0.146054i
\(370\) 5.45166 7.50356i 0.283418 0.390092i
\(371\) −0.499420 4.75166i −0.0259286 0.246694i
\(372\) 1.77084 + 17.6500i 0.0918137 + 0.915108i
\(373\) −7.33934 + 4.23737i −0.380016 + 0.219403i −0.677825 0.735223i \(-0.737077\pi\)
0.297809 + 0.954625i \(0.403744\pi\)
\(374\) −3.42944 + 0.737057i −0.177332 + 0.0381123i
\(375\) −4.90243 + 6.68103i −0.253161 + 0.345007i
\(376\) −23.1605 + 20.8538i −1.19441 + 1.07545i
\(377\) 0.449777 + 0.619065i 0.0231647 + 0.0318835i
\(378\) 2.33174 5.04361i 0.119932 0.259415i
\(379\) 6.66353 + 20.5082i 0.342283 + 1.05344i 0.963023 + 0.269421i \(0.0868322\pi\)
−0.620740 + 0.784016i \(0.713168\pi\)
\(380\) −27.4483 5.83433i −1.40807 0.299295i
\(381\) −7.79034 + 2.49062i −0.399111 + 0.127598i
\(382\) 0.853505 1.91700i 0.0436691 0.0980824i
\(383\) 6.68252 + 31.4388i 0.341461 + 1.60645i 0.728947 + 0.684570i \(0.240010\pi\)
−0.387486 + 0.921876i \(0.626656\pi\)
\(384\) 13.9376 6.12672i 0.711252 0.312653i
\(385\) 11.6524 5.21959i 0.593863 0.266015i
\(386\) 10.3064i 0.524580i
\(387\) −33.5243 19.7798i −1.70413 1.00547i
\(388\) −0.899932 + 0.653839i −0.0456871 + 0.0331937i
\(389\) 0.00565467 + 0.0127006i 0.000286703 + 0.000643945i 0.913689 0.406415i \(-0.133221\pi\)
−0.913402 + 0.407059i \(0.866554\pi\)
\(390\) 2.30474 0.478521i 0.116705 0.0242308i
\(391\) 2.96915 + 2.67344i 0.150157 + 0.135202i
\(392\) −1.47041 + 13.9901i −0.0742672 + 0.706605i
\(393\) 6.77256 + 11.8594i 0.341631 + 0.598230i
\(394\) 3.69460 + 4.10327i 0.186131 + 0.206720i
\(395\) −39.8586 −2.00550
\(396\) 10.9737 7.85299i 0.551449 0.394628i
\(397\) −13.9971 −0.702496 −0.351248 0.936283i \(-0.614243\pi\)
−0.351248 + 0.936283i \(0.614243\pi\)
\(398\) −0.0362764 0.0402890i −0.00181837 0.00201951i
\(399\) −8.33527 + 14.2809i −0.417285 + 0.714940i
\(400\) 0.192834 1.83469i 0.00964170 0.0917347i
\(401\) −26.4247 23.7930i −1.31959 1.18816i −0.967695 0.252123i \(-0.918871\pi\)
−0.351894 0.936040i \(-0.614462\pi\)
\(402\) −3.79196 + 11.4856i −0.189126 + 0.572848i
\(403\) 1.80102 + 4.04517i 0.0897154 + 0.201504i
\(404\) −18.8134 + 13.6687i −0.936000 + 0.680044i
\(405\) −18.9874 17.7572i −0.943490 0.882362i
\(406\) 1.39548i 0.0692567i
\(407\) −1.41720 13.1967i −0.0702478 0.654136i
\(408\) 4.95681 + 3.63723i 0.245399 + 0.180070i
\(409\) −2.92170 13.7455i −0.144469 0.679671i −0.989450 0.144875i \(-0.953722\pi\)
0.844981 0.534796i \(-0.179611\pi\)
\(410\) 2.12254 4.76731i 0.104825 0.235441i
\(411\) −2.47962 + 11.4006i −0.122311 + 0.562352i
\(412\) 12.9429 + 2.75109i 0.637649 + 0.135536i
\(413\) 2.46762 + 7.59455i 0.121424 + 0.373703i
\(414\) 6.91741 + 2.32007i 0.339972 + 0.114025i
\(415\) 18.2753 + 25.1538i 0.897099 + 1.23475i
\(416\) 2.53983 2.28688i 0.124526 0.112123i
\(417\) −12.7672 1.40289i −0.625214 0.0687000i
\(418\) 16.4868 9.56842i 0.806396 0.468007i
\(419\) −2.56407 + 1.48037i −0.125263 + 0.0723206i −0.561322 0.827597i \(-0.689707\pi\)
0.436059 + 0.899918i \(0.356374\pi\)
\(420\) −8.24379 3.71713i −0.402256 0.181377i
\(421\) −2.20232 20.9537i −0.107335 1.02122i −0.907102 0.420911i \(-0.861710\pi\)
0.799767 0.600310i \(-0.204956\pi\)
\(422\) 0.574241 0.790375i 0.0279536 0.0384749i
\(423\) 34.5621 3.30284i 1.68047 0.160589i
\(424\) 9.18141 2.98322i 0.445889 0.144878i
\(425\) 4.02639 1.79266i 0.195309 0.0869570i
\(426\) −5.73369 3.34656i −0.277798 0.162141i
\(427\) −10.3090 + 2.19125i −0.498887 + 0.106042i
\(428\) −1.99583 3.45688i −0.0964720 0.167094i
\(429\) 1.98664 2.72026i 0.0959159 0.131335i
\(430\) 15.0357 26.0425i 0.725084 1.25588i
\(431\) −11.7908 + 36.2884i −0.567944 + 1.74795i 0.0910950 + 0.995842i \(0.470963\pi\)
−0.659039 + 0.752109i \(0.729037\pi\)
\(432\) −2.79548 0.635728i −0.134498 0.0305865i
\(433\) 17.1848 + 12.4855i 0.825848 + 0.600014i 0.918382 0.395696i \(-0.129497\pi\)
−0.0925338 + 0.995710i \(0.529497\pi\)
\(434\) −1.67893 + 7.89872i −0.0805910 + 0.379151i
\(435\) 6.19980 + 2.04686i 0.297258 + 0.0981395i
\(436\) 1.94159 + 0.204070i 0.0929855 + 0.00977317i
\(437\) −19.8351 8.83116i −0.948842 0.422452i
\(438\) 12.1422 1.21824i 0.580178 0.0582098i
\(439\) 23.8477 + 13.7685i 1.13819 + 0.657134i 0.945982 0.324220i \(-0.105102\pi\)
0.192208 + 0.981354i \(0.438435\pi\)
\(440\) 15.2112 + 20.8372i 0.725165 + 0.993374i
\(441\) 10.5957 11.5465i 0.504557 0.549832i
\(442\) 0.589813 + 0.191642i 0.0280545 + 0.00911547i
\(443\) −26.6084 + 2.79665i −1.26420 + 0.132873i −0.712801 0.701367i \(-0.752574\pi\)
−0.551402 + 0.834240i \(0.685907\pi\)
\(444\) −6.32303 + 6.95608i −0.300078 + 0.330121i
\(445\) 17.1496 19.0466i 0.812971 0.902895i
\(446\) 7.00725 7.78234i 0.331803 0.368505i
\(447\) 7.17997 7.89881i 0.339601 0.373601i
\(448\) 4.73601 0.497775i 0.223755 0.0235176i
\(449\) −28.1364 9.14206i −1.32784 0.431441i −0.442658 0.896690i \(-0.645964\pi\)
−0.885179 + 0.465250i \(0.845964\pi\)
\(450\) 5.44180 5.93010i 0.256529 0.279548i
\(451\) −2.32371 7.09700i −0.109419 0.334185i
\(452\) −2.22164 1.28266i −0.104497 0.0603314i
\(453\) 33.9805 3.40930i 1.59654 0.160183i
\(454\) −0.579840 0.258161i −0.0272132 0.0121161i
\(455\) −2.24501 0.235960i −0.105248 0.0110620i
\(456\) −31.7265 10.4745i −1.48573 0.490513i
\(457\) 0.0682681 0.321176i 0.00319345 0.0150240i −0.976522 0.215418i \(-0.930889\pi\)
0.979715 + 0.200394i \(0.0642221\pi\)
\(458\) −6.34026 4.60647i −0.296261 0.215246i
\(459\) −2.02402 6.54335i −0.0944731 0.305418i
\(460\) 3.66933 11.2930i 0.171083 0.526541i
\(461\) 1.59304 2.75923i 0.0741955 0.128510i −0.826541 0.562877i \(-0.809694\pi\)
0.900736 + 0.434367i \(0.143028\pi\)
\(462\) 5.84697 1.88389i 0.272026 0.0876464i
\(463\) −13.6457 23.6350i −0.634169 1.09841i −0.986691 0.162609i \(-0.948009\pi\)
0.352521 0.935804i \(-0.385324\pi\)
\(464\) 0.704259 0.149695i 0.0326944 0.00694941i
\(465\) 32.6295 + 19.0447i 1.51316 + 0.883177i
\(466\) −12.1472 + 5.40829i −0.562709 + 0.250534i
\(467\) 17.3622 5.64132i 0.803427 0.261049i 0.121615 0.992577i \(-0.461193\pi\)
0.681811 + 0.731528i \(0.261193\pi\)
\(468\) −2.37492 + 0.226953i −0.109781 + 0.0104909i
\(469\) 6.81794 9.38409i 0.314823 0.433317i
\(470\) 2.80375 + 26.6759i 0.129327 + 1.23047i
\(471\) 7.69705 + 3.47060i 0.354662 + 0.159917i
\(472\) −13.9733 + 8.06747i −0.643172 + 0.371336i
\(473\) −9.04212 42.0720i −0.415757 1.93447i
\(474\) −19.0620 2.09458i −0.875548 0.0962072i
\(475\) −17.7993 + 16.0266i −0.816690 + 0.735351i
\(476\) −1.40041 1.92750i −0.0641878 0.0883469i
\(477\) −10.1966 3.41990i −0.466870 0.156586i
\(478\) 0.301618 + 0.928285i 0.0137957 + 0.0424588i
\(479\) 12.3864 + 2.63282i 0.565951 + 0.120297i 0.481997 0.876173i \(-0.339912\pi\)
0.0839544 + 0.996470i \(0.473245\pi\)
\(480\) 6.19748 28.4944i 0.282875 1.30059i
\(481\) −0.954437 + 2.14370i −0.0435186 + 0.0977444i
\(482\) 0.126571 + 0.595470i 0.00576515 + 0.0271229i
\(483\) −5.64116 4.13939i −0.256682 0.188349i
\(484\) 14.6062 + 3.03569i 0.663918 + 0.137986i
\(485\) 2.36921i 0.107580i
\(486\) −8.14741 9.49003i −0.369574 0.430476i
\(487\) 12.3473 8.97085i 0.559510 0.406508i −0.271769 0.962362i \(-0.587609\pi\)
0.831280 + 0.555854i \(0.187609\pi\)
\(488\) −8.66158 19.4542i −0.392091 0.880652i
\(489\) 6.02733 18.2564i 0.272565 0.825581i
\(490\) 8.99722 + 8.10113i 0.406453 + 0.365972i
\(491\) 2.96920 28.2501i 0.133998 1.27491i −0.696365 0.717687i \(-0.745201\pi\)
0.830364 0.557222i \(-0.188133\pi\)
\(492\) −2.66615 + 4.56794i −0.120199 + 0.205938i
\(493\) 1.15100 + 1.27831i 0.0518384 + 0.0575724i
\(494\) −3.37018 −0.151632
\(495\) 0.206538 28.7399i 0.00928321 1.29176i
\(496\) 4.16635 0.187074
\(497\) 4.26013 + 4.73135i 0.191093 + 0.212230i
\(498\) 7.41817 + 12.9900i 0.332416 + 0.582094i
\(499\) 2.28531 21.7433i 0.102305 0.973363i −0.816151 0.577839i \(-0.803896\pi\)
0.918456 0.395524i \(-0.129437\pi\)
\(500\) 4.82196 + 4.34171i 0.215644 + 0.194167i
\(501\) −36.0195 + 7.47854i −1.60923 + 0.334117i
\(502\) −3.20642 7.20174i −0.143110 0.321429i
\(503\) 16.0796 11.6825i 0.716954 0.520898i −0.168455 0.985709i \(-0.553878\pi\)
0.885410 + 0.464812i \(0.153878\pi\)
\(504\) −9.27316 5.47131i −0.413060 0.243712i
\(505\) 49.5291i 2.20402i
\(506\) 3.29745 + 7.36137i 0.146590 + 0.327253i
\(507\) 20.0678 8.82143i 0.891244 0.391774i
\(508\) 1.33148 + 6.26412i 0.0590748 + 0.277925i
\(509\) −12.5317 + 28.1466i −0.555457 + 1.24758i 0.389694 + 0.920945i \(0.372581\pi\)
−0.945151 + 0.326633i \(0.894086\pi\)
\(510\) 5.04011 1.61135i 0.223180 0.0713518i
\(511\) −11.4471 2.43315i −0.506388 0.107636i
\(512\) −1.91196 5.88441i −0.0844976 0.260057i
\(513\) 21.4491 + 30.4194i 0.946999 + 1.34305i
\(514\) −10.5099 14.4656i −0.463570 0.638049i
\(515\) 20.9436 18.8577i 0.922884 0.830969i
\(516\) −18.0309 + 24.5725i −0.793767 + 1.08174i
\(517\) 28.5828 + 25.6193i 1.25707 + 1.12674i
\(518\) −3.70605 + 2.13969i −0.162834 + 0.0940125i
\(519\) −2.14288 21.3581i −0.0940620 0.937517i
\(520\) −0.476771 4.53617i −0.0209078 0.198924i
\(521\) −16.6718 + 22.9468i −0.730405 + 1.00532i 0.268709 + 0.963221i \(0.413403\pi\)
−0.999114 + 0.0420947i \(0.986597\pi\)
\(522\) 2.85744 + 1.30470i 0.125067 + 0.0571050i
\(523\) −12.9420 + 4.20510i −0.565913 + 0.183876i −0.577980 0.816051i \(-0.696159\pi\)
0.0120671 + 0.999927i \(0.496159\pi\)
\(524\) 9.76905 4.34946i 0.426763 0.190007i
\(525\) −6.70260 + 3.82765i −0.292526 + 0.167052i
\(526\) −12.0628 + 2.56402i −0.525962 + 0.111797i
\(527\) 4.97693 + 8.62030i 0.216799 + 0.375506i
\(528\) −1.57795 2.74870i −0.0686715 0.119622i
\(529\) −6.90625 + 11.9620i −0.300272 + 0.520086i
\(530\) 2.56753 7.90204i 0.111526 0.343242i
\(531\) 17.8579 + 2.04768i 0.774968 + 0.0888619i
\(532\) 10.4747 + 7.61029i 0.454134 + 0.329948i
\(533\) −0.274503 + 1.29143i −0.0118900 + 0.0559382i
\(534\) 9.20258 8.20766i 0.398234 0.355180i
\(535\) −8.45511 0.888668i −0.365546 0.0384205i
\(536\) 21.4110 + 9.53278i 0.924813 + 0.411753i
\(537\) −11.2899 15.6946i −0.487197 0.677273i
\(538\) −0.662255 0.382353i −0.0285518 0.0164844i
\(539\) 17.3252 0.0391632i 0.746251 0.00168688i
\(540\) −15.3188 + 13.4050i −0.659215 + 0.576858i
\(541\) −17.0525 5.54068i −0.733142 0.238212i −0.0814304 0.996679i \(-0.525949\pi\)
−0.651712 + 0.758467i \(0.725949\pi\)
\(542\) −17.8447 + 1.87555i −0.766494 + 0.0805617i
\(543\) −0.0100432 0.0314139i −0.000430995 0.00134810i
\(544\) 5.14077 5.70941i 0.220409 0.244789i
\(545\) 2.78232 3.09008i 0.119181 0.132364i
\(546\) −1.06126 0.230822i −0.0454176 0.00987825i
\(547\) −20.8643 + 2.19293i −0.892095 + 0.0937630i −0.539473 0.842003i \(-0.681376\pi\)
−0.352622 + 0.935766i \(0.614710\pi\)
\(548\) 8.68837 + 2.82302i 0.371149 + 0.120594i
\(549\) −5.15145 + 23.1577i −0.219858 + 0.988348i
\(550\) 8.89799 0.0201137i 0.379412 0.000857649i
\(551\) −8.09543 4.67390i −0.344877 0.199115i
\(552\) 5.81128 12.8882i 0.247345 0.548557i
\(553\) 16.8005 + 7.48007i 0.714430 + 0.318085i
\(554\) −8.27278 0.869505i −0.351477 0.0369417i
\(555\) 4.07017 + 19.6035i 0.172769 + 0.832123i
\(556\) −2.09097 + 9.83726i −0.0886770 + 0.417193i
\(557\) 6.91677 + 5.02533i 0.293073 + 0.212930i 0.724599 0.689170i \(-0.242025\pi\)
−0.431526 + 0.902100i \(0.642025\pi\)
\(558\) 14.6040 + 10.8227i 0.618236 + 0.458160i
\(559\) −2.35104 + 7.23574i −0.0994382 + 0.306039i
\(560\) −1.06200 + 1.83943i −0.0448775 + 0.0777301i
\(561\) 3.80220 6.54831i 0.160529 0.276470i
\(562\) 3.81202 + 6.60262i 0.160800 + 0.278515i
\(563\) 32.7814 6.96790i 1.38157 0.293662i 0.543585 0.839354i \(-0.317067\pi\)
0.837986 + 0.545692i \(0.183733\pi\)
\(564\) 0.128409 27.1854i 0.00540698 1.14471i
\(565\) −4.99143 + 2.22233i −0.209991 + 0.0934939i
\(566\) 9.47118 3.07737i 0.398103 0.129352i
\(567\) 4.67082 + 11.0480i 0.196156 + 0.463972i
\(568\) −7.56140 + 10.4074i −0.317269 + 0.436683i
\(569\) 4.15034 + 39.4878i 0.173991 + 1.65542i 0.638334 + 0.769760i \(0.279624\pi\)
−0.464343 + 0.885656i \(0.653709\pi\)
\(570\) −23.3431 + 16.7918i −0.977734 + 0.703333i
\(571\) −11.7014 + 6.75580i −0.489688 + 0.282721i −0.724445 0.689333i \(-0.757904\pi\)
0.234757 + 0.972054i \(0.424570\pi\)
\(572\) −1.96406 1.76042i −0.0821213 0.0736069i
\(573\) 1.82288 + 4.14686i 0.0761518 + 0.173237i
\(574\) −1.78932 + 1.61111i −0.0746847 + 0.0672464i
\(575\) −5.95720 8.19938i −0.248432 0.341938i
\(576\) 3.40863 10.1630i 0.142026 0.423458i
\(577\) −10.9864 33.8127i −0.457370 1.40764i −0.868330 0.495987i \(-0.834806\pi\)
0.410960 0.911654i \(-0.365194\pi\)
\(578\) −11.9785 2.54611i −0.498240 0.105904i
\(579\) 16.4631 + 14.9649i 0.684183 + 0.621918i
\(580\) 2.07933 4.67024i 0.0863393 0.193921i
\(581\) −2.98260 14.0320i −0.123739 0.582147i
\(582\) −0.124503 + 1.13306i −0.00516081 + 0.0469667i
\(583\) −4.86060 10.8510i −0.201305 0.449403i
\(584\) 23.6462i 0.978487i
\(585\) −2.58211 + 4.37634i −0.106757 + 0.180939i
\(586\) 16.9001 12.2786i 0.698137 0.507226i
\(587\) −10.3483 23.2428i −0.427122 0.959331i −0.991048 0.133506i \(-0.957376\pi\)
0.563926 0.825825i \(-0.309290\pi\)
\(588\) −8.16758 9.15764i −0.336825 0.377655i
\(589\) −40.1985 36.1949i −1.65635 1.49139i
\(590\) −1.45155 + 13.8106i −0.0597593 + 0.568572i
\(591\) −11.9190 0.0562988i −0.490283 0.00231582i
\(592\) 1.47739 + 1.64080i 0.0607202 + 0.0674366i
\(593\) 26.4048 1.08431 0.542157 0.840277i \(-0.317608\pi\)
0.542157 + 0.840277i \(0.317608\pi\)
\(594\) 1.60907 13.7338i 0.0660207 0.563503i
\(595\) −5.07445 −0.208032
\(596\) −5.59270 6.21132i −0.229086 0.254426i
\(597\) 0.117030 0.000552784i 0.00478972 2.26239e-5i
\(598\) 0.149067 1.41827i 0.00609578 0.0579975i
\(599\) 8.53053 + 7.68093i 0.348548 + 0.313834i 0.824745 0.565504i \(-0.191318\pi\)
−0.476197 + 0.879339i \(0.657985\pi\)
\(600\) −10.3807 11.6391i −0.423792 0.475163i
\(601\) −12.2205 27.4476i −0.498483 1.11961i −0.971172 0.238381i \(-0.923383\pi\)
0.472689 0.881229i \(-0.343283\pi\)
\(602\) −11.2249 + 8.15534i −0.457491 + 0.332387i
\(603\) −12.8408 22.7342i −0.522918 0.925809i
\(604\) 26.7406i 1.08806i
\(605\) 23.5163 21.3675i 0.956074 0.868711i
\(606\) −2.60277 + 23.6869i −0.105730 + 0.962214i
\(607\) 8.03806 + 37.8161i 0.326255 + 1.53491i 0.769582 + 0.638549i \(0.220465\pi\)
−0.443327 + 0.896360i \(0.646202\pi\)
\(608\) −16.9815 + 38.1411i −0.688690 + 1.54682i
\(609\) −2.22911 2.02625i −0.0903281 0.0821076i
\(610\) −17.9274 3.81059i −0.725860 0.154286i
\(611\) −2.09706 6.45408i −0.0848379 0.261104i
\(612\) −5.25612 + 1.06543i −0.212466 + 0.0430674i
\(613\) 17.6204 + 24.2524i 0.711681 + 0.979545i 0.999759 + 0.0219380i \(0.00698363\pi\)
−0.288078 + 0.957607i \(0.593016\pi\)
\(614\) −10.7493 + 9.67869i −0.433805 + 0.390600i
\(615\) 4.53324 + 10.3126i 0.182798 + 0.415846i
\(616\) −2.50115 11.6375i −0.100774 0.468890i
\(617\) −3.50285 + 2.02237i −0.141019 + 0.0814176i −0.568850 0.822441i \(-0.692611\pi\)
0.427830 + 0.903859i \(0.359278\pi\)
\(618\) 11.0071 7.91794i 0.442769 0.318506i
\(619\) 2.74139 + 26.0826i 0.110186 + 1.04835i 0.900265 + 0.435343i \(0.143373\pi\)
−0.790079 + 0.613005i \(0.789961\pi\)
\(620\) 17.3882 23.9329i 0.698328 0.961167i
\(621\) −13.7501 + 7.68093i −0.551773 + 0.308225i
\(622\) −9.59538 + 3.11773i −0.384740 + 0.125009i
\(623\) −10.8030 + 4.80981i −0.432813 + 0.192701i
\(624\) −0.00264675 + 0.560345i −0.000105955 + 0.0224317i
\(625\) 29.8709 6.34925i 1.19483 0.253970i
\(626\) 4.69208 + 8.12692i 0.187533 + 0.324817i
\(627\) −8.65454 + 40.2289i −0.345629 + 1.60659i
\(628\) 3.30560 5.72546i 0.131908 0.228471i
\(629\) −1.63005 + 5.01679i −0.0649945 + 0.200033i
\(630\) −8.50071 + 3.68894i −0.338676 + 0.146971i
\(631\) 12.4984 + 9.08065i 0.497555 + 0.361495i 0.808082 0.589070i \(-0.200506\pi\)
−0.310527 + 0.950564i \(0.600506\pi\)
\(632\) −7.72579 + 36.3470i −0.307315 + 1.44581i
\(633\) 0.428725 + 2.06490i 0.0170403 + 0.0820725i
\(634\) −13.1271 1.37971i −0.521344 0.0547955i
\(635\) 12.4606 + 5.54780i 0.494482 + 0.220158i
\(636\) −3.46147 + 7.67680i −0.137256 + 0.304405i
\(637\) −2.65271 1.53154i −0.105104 0.0606819i
\(638\) 1.08060 + 3.30034i 0.0427813 + 0.130662i
\(639\) 13.6710 4.29964i 0.540818 0.170091i
\(640\) −24.1477 7.84607i −0.954522 0.310143i
\(641\) 12.4339 1.30685i 0.491108 0.0516176i 0.144262 0.989540i \(-0.453919\pi\)
0.346846 + 0.937922i \(0.387253\pi\)
\(642\) −3.99689 0.869317i −0.157745 0.0343092i
\(643\) −3.46334 + 3.84642i −0.136581 + 0.151688i −0.807555 0.589793i \(-0.799209\pi\)
0.670974 + 0.741481i \(0.265876\pi\)
\(644\) −3.66595 + 4.07144i −0.144458 + 0.160437i
\(645\) 19.7678 + 61.8314i 0.778358 + 2.43461i
\(646\) −7.53447 + 0.791905i −0.296440 + 0.0311571i
\(647\) 5.07677 + 1.64954i 0.199588 + 0.0648502i 0.407105 0.913381i \(-0.366538\pi\)
−0.207517 + 0.978231i \(0.566538\pi\)
\(648\) −19.8731 + 13.8727i −0.780689 + 0.544970i
\(649\) 11.7168 + 16.0504i 0.459925 + 0.630033i
\(650\) −1.36239 0.786578i −0.0534375 0.0308521i
\(651\) −10.1794 14.1508i −0.398962 0.554615i
\(652\) −13.7523 6.12293i −0.538583 0.239793i
\(653\) −4.72225 0.496328i −0.184796 0.0194228i 0.0116784 0.999932i \(-0.496283\pi\)
−0.196474 + 0.980509i \(0.562949\pi\)
\(654\) 1.49301 1.33159i 0.0583811 0.0520694i
\(655\) 4.73536 22.2781i 0.185026 0.870478i
\(656\) 1.00502 + 0.730189i 0.0392394 + 0.0285091i
\(657\) −15.6845 + 21.1645i −0.611912 + 0.825707i
\(658\) 3.82435 11.7701i 0.149089 0.458847i
\(659\) 19.9356 34.5295i 0.776581 1.34508i −0.157321 0.987547i \(-0.550286\pi\)
0.933902 0.357529i \(-0.116381\pi\)
\(660\) −22.3750 2.40744i −0.870947 0.0937095i
\(661\) −10.4257 18.0579i −0.405515 0.702372i 0.588867 0.808230i \(-0.299574\pi\)
−0.994381 + 0.105858i \(0.966241\pi\)
\(662\) 15.4028 3.27397i 0.598647 0.127246i
\(663\) −1.16253 + 0.663887i −0.0451490 + 0.0257832i
\(664\) 26.4800 11.7897i 1.02762 0.457528i
\(665\) 26.2265 8.52151i 1.01702 0.330450i
\(666\) 0.916357 + 9.58911i 0.0355081 + 0.371570i
\(667\) 2.32499 3.20007i 0.0900239 0.123907i
\(668\) 3.01095 + 28.6473i 0.116497 + 1.10840i
\(669\) 2.25676 + 22.4932i 0.0872514 + 0.869636i
\(670\) 17.4689 10.0857i 0.674884 0.389645i
\(671\) −22.6841 + 13.1651i −0.875710 + 0.508234i
\(672\) −7.95967 + 10.8474i −0.307051 + 0.418448i
\(673\) −15.2185 + 13.7028i −0.586629 + 0.528203i −0.908120 0.418709i \(-0.862483\pi\)
0.321491 + 0.946913i \(0.395816\pi\)
\(674\) −5.02763 6.91994i −0.193657 0.266546i
\(675\) 1.57108 + 17.3031i 0.0604710 + 0.665996i
\(676\) −5.30410 16.3243i −0.204004 0.627859i
\(677\) −6.69542 1.42315i −0.257326 0.0546963i 0.0774423 0.996997i \(-0.475325\pi\)
−0.334768 + 0.942301i \(0.608658\pi\)
\(678\) −2.50389 + 0.800508i −0.0961614 + 0.0307433i
\(679\) 0.444619 0.998630i 0.0170629 0.0383239i
\(680\) −2.13177 10.0292i −0.0817495 0.384601i
\(681\) 1.25431 0.551370i 0.0480652 0.0211285i
\(682\) 2.14573 + 19.9806i 0.0821641 + 0.765098i
\(683\) 4.76117i 0.182181i −0.995843 0.0910905i \(-0.970965\pi\)
0.995843 0.0910905i \(-0.0290353\pi\)
\(684\) 25.3763 14.3331i 0.970286 0.548039i
\(685\) 15.7413 11.4368i 0.601446 0.436976i
\(686\) −5.31667 11.9414i −0.202992 0.455926i
\(687\) 16.5643 3.43916i 0.631968 0.131212i
\(688\) 5.31985 + 4.79002i 0.202817 + 0.182618i
\(689\) −0.219731 + 2.09060i −0.00837109 + 0.0796456i
\(690\) −6.03403 10.5662i −0.229712 0.402248i
\(691\) 33.1686 + 36.8375i 1.26179 + 1.40136i 0.878504 + 0.477735i \(0.158542\pi\)
0.383290 + 0.923628i \(0.374791\pi\)
\(692\) −16.8075 −0.638927
\(693\) −5.48054 + 12.0752i −0.208188 + 0.458699i
\(694\) −1.98204 −0.0752372
\(695\) 14.3328 + 15.9182i 0.543676 + 0.603813i
\(696\) 3.06824 5.25685i 0.116301 0.199260i
\(697\) −0.310233 + 2.95167i −0.0117509 + 0.111802i
\(698\) 7.67197 + 6.90787i 0.290388 + 0.261467i
\(699\) 8.99872 27.2565i 0.340363 1.03093i
\(700\) 2.45819 + 5.52117i 0.0929107 + 0.208681i
\(701\) 18.5663 13.4892i 0.701240 0.509480i −0.179096 0.983832i \(-0.557317\pi\)
0.880336 + 0.474351i \(0.157317\pi\)
\(702\) −1.46485 + 1.95726i −0.0552872 + 0.0738720i
\(703\) 28.6659i 1.08115i
\(704\) 10.8153 4.84459i 0.407615 0.182587i
\(705\) −46.6823 34.2548i −1.75816 1.29011i
\(706\) 0.572536 + 2.69357i 0.0215477 + 0.101374i
\(707\) 9.29489 20.8767i 0.349570 0.785148i
\(708\) 2.99125 13.7530i 0.112418 0.516869i
\(709\) −26.9762 5.73396i −1.01311 0.215343i −0.328696 0.944436i \(-0.606609\pi\)
−0.684415 + 0.729092i \(0.739942\pi\)
\(710\) 3.42133 + 10.5298i 0.128400 + 0.395176i
\(711\) 31.0239 27.4078i 1.16349 1.02787i
\(712\) −14.0445 19.3305i −0.526338 0.724443i
\(713\) 17.0100 15.3158i 0.637028 0.573582i
\(714\) −2.42682 0.266664i −0.0908213 0.00997964i
\(715\) −5.49218 + 1.18038i −0.205396 + 0.0441438i
\(716\) −13.1101 + 7.56915i −0.489949 + 0.282872i
\(717\) −1.92077 0.866075i −0.0717324 0.0323442i
\(718\) −0.422145 4.01644i −0.0157543 0.149892i
\(719\) −21.5090 + 29.6046i −0.802151 + 1.10407i 0.190337 + 0.981719i \(0.439042\pi\)
−0.992487 + 0.122347i \(0.960958\pi\)
\(720\) 2.77357 + 3.89434i 0.103365 + 0.145133i
\(721\) −12.3667 + 4.01819i −0.460561 + 0.149645i
\(722\) 23.6840 10.5448i 0.881426 0.392436i
\(723\) −1.13497 0.662442i −0.0422099 0.0246365i
\(724\) −0.0252595 + 0.00536908i −0.000938763 + 0.000199540i
\(725\) −2.18172 3.77884i −0.0810269 0.140343i
\(726\) 12.3693 8.98303i 0.459070 0.333392i
\(727\) 20.4497 35.4200i 0.758438 1.31365i −0.185208 0.982699i \(-0.559296\pi\)
0.943647 0.330955i \(-0.107371\pi\)
\(728\) −0.650321 + 2.00148i −0.0241025 + 0.0741799i
\(729\) 26.9892 + 0.765089i 0.999598 + 0.0283366i
\(730\) −16.4645 11.9622i −0.609379 0.442740i
\(731\) −3.55583 + 16.7289i −0.131517 + 0.618740i
\(732\) 17.6394 + 5.82366i 0.651972 + 0.215249i
\(733\) −9.27530 0.974873i −0.342591 0.0360078i −0.0683291 0.997663i \(-0.521767\pi\)
−0.274262 + 0.961655i \(0.588433\pi\)
\(734\) 2.27158 + 1.01137i 0.0838454 + 0.0373304i
\(735\) −26.0045 + 2.60906i −0.959191 + 0.0962366i
\(736\) −15.2998 8.83335i −0.563958 0.325601i
\(737\) 8.85790 27.4730i 0.326285 1.01198i
\(738\) 1.62605 + 5.17016i 0.0598558 + 0.190316i
\(739\) −25.6359 8.32960i −0.943031 0.306409i −0.203150 0.979148i \(-0.565118\pi\)
−0.739881 + 0.672738i \(0.765118\pi\)
\(740\) 15.5912 1.63870i 0.573144 0.0602398i
\(741\) 4.89350 5.38343i 0.179767 0.197765i
\(742\) −2.56516 + 2.84890i −0.0941699 + 0.104586i
\(743\) 14.2469 15.8228i 0.522667 0.580481i −0.422790 0.906228i \(-0.638949\pi\)
0.945457 + 0.325747i \(0.105616\pi\)
\(744\) 23.6914 26.0634i 0.868570 0.955529i
\(745\) −17.7042 + 1.86079i −0.648632 + 0.0681740i
\(746\) 6.46702 + 2.10126i 0.236775 + 0.0769327i
\(747\) −31.5210 7.01186i −1.15329 0.256551i
\(748\) −4.80456 3.47415i −0.175672 0.127027i
\(749\) 3.39708 + 1.96131i 0.124127 + 0.0716646i
\(750\) 6.61577 0.663767i 0.241574 0.0242373i
\(751\) 21.5176 + 9.58027i 0.785190 + 0.349589i 0.759857 0.650090i \(-0.225269\pi\)
0.0253327 + 0.999679i \(0.491935\pi\)
\(752\) −6.35027 0.667440i −0.231570 0.0243390i
\(753\) 16.1596 + 5.33509i 0.588888 + 0.194421i
\(754\) 0.127653 0.600558i 0.00464883 0.0218710i
\(755\) −46.0766 33.4766i −1.67690 1.21834i
\(756\) 8.97256 2.77543i 0.326329 0.100941i
\(757\) −10.5548 + 32.4845i −0.383622 + 1.18067i 0.553853 + 0.832615i \(0.313157\pi\)
−0.937475 + 0.348053i \(0.886843\pi\)
\(758\) 8.65095 14.9839i 0.314217 0.544239i
\(759\) −16.5468 5.42146i −0.600609 0.196787i
\(760\) 27.8597 + 48.2544i 1.01058 + 1.75037i
\(761\) −35.6019 + 7.56741i −1.29057 + 0.274318i −0.801535 0.597948i \(-0.795983\pi\)
−0.489031 + 0.872266i \(0.662650\pi\)
\(762\) 5.66762 + 3.30800i 0.205316 + 0.119836i
\(763\) −1.75266 + 0.780333i −0.0634504 + 0.0282499i
\(764\) 3.37329 1.09605i 0.122041 0.0396537i
\(765\) −4.74431 + 10.3906i −0.171531 + 0.375673i
\(766\) 15.1583 20.8637i 0.547693 0.753835i
\(767\) −0.367245 3.49410i −0.0132605 0.126165i
\(768\) −22.4198 10.1091i −0.809005 0.364781i
\(769\) 13.6195 7.86320i 0.491130 0.283554i −0.233913 0.972258i \(-0.575153\pi\)
0.725043 + 0.688703i \(0.241820\pi\)
\(770\) −9.36834 4.14570i −0.337611 0.149401i
\(771\) 38.3672 + 4.21588i 1.38176 + 0.151831i
\(772\) 12.9460 11.6566i 0.465935 0.419530i
\(773\) 5.16073 + 7.10313i 0.185619 + 0.255482i 0.891678 0.452671i \(-0.149529\pi\)
−0.706059 + 0.708153i \(0.749529\pi\)
\(774\) 6.20455 + 30.6092i 0.223018 + 1.10022i
\(775\) −7.80258 24.0139i −0.280277 0.862604i
\(776\) 2.16048 + 0.459225i 0.0775568 + 0.0164852i
\(777\) 1.96331 9.02677i 0.0704333 0.323834i
\(778\) 0.00453711 0.0101905i 0.000162663 0.000365347i
\(779\) −3.35334 15.7762i −0.120146 0.565241i
\(780\) 3.20776 + 2.35380i 0.114856 + 0.0842796i
\(781\) 13.7390 + 7.89085i 0.491619 + 0.282357i
\(782\) 3.20576i 0.114638i
\(783\) −6.23309 + 2.66998i −0.222753 + 0.0954171i
\(784\) −2.33166 + 1.69405i −0.0832737 + 0.0605019i
\(785\) −5.72724 12.8636i −0.204414 0.459121i
\(786\) 3.43537 10.4055i 0.122536 0.371151i
\(787\) −6.03768 5.43635i −0.215220 0.193785i 0.554468 0.832205i \(-0.312922\pi\)
−0.769688 + 0.638420i \(0.779588\pi\)
\(788\) −0.975543 + 9.28167i −0.0347523 + 0.330646i
\(789\) 13.4195 22.9917i 0.477746 0.818527i
\(790\) 21.3995 + 23.7666i 0.761362 + 0.845578i
\(791\) 2.52095 0.0896348
\(792\) −26.1679 5.75900i −0.929834 0.204637i
\(793\) 4.63701 0.164665
\(794\) 7.51487 + 8.34611i 0.266693 + 0.296192i
\(795\) 8.89444 + 15.5751i 0.315453 + 0.552391i
\(796\) 0.00957862 0.0911345i 0.000339505 0.00323018i
\(797\) −0.960021 0.864407i −0.0340057 0.0306189i 0.651953 0.758260i \(-0.273950\pi\)
−0.685958 + 0.727641i \(0.740617\pi\)
\(798\) 12.9904 2.69713i 0.459856 0.0954775i
\(799\) −6.20479 13.9362i −0.219510 0.493027i
\(800\) −15.7666 + 11.4551i −0.557435 + 0.405000i
\(801\) −0.251458 + 26.6175i −0.00888482 + 0.940483i
\(802\) 28.5305i 1.00745i
\(803\) −28.9565 + 3.10965i −1.02185 + 0.109737i
\(804\) −18.7159 + 8.22715i −0.660059 + 0.290149i
\(805\) 2.42608 + 11.4138i 0.0855082 + 0.402285i
\(806\) 1.44508 3.24570i 0.0509007 0.114325i
\(807\) 1.57236 0.502691i 0.0553495 0.0176956i
\(808\) 45.1655 + 9.60023i 1.58892 + 0.337735i
\(809\) 12.8311 + 39.4900i 0.451117 + 1.38840i 0.875634 + 0.482975i \(0.160444\pi\)
−0.424517 + 0.905420i \(0.639556\pi\)
\(810\) −0.394078 + 20.8553i −0.0138465 + 0.732780i
\(811\) 8.32868 + 11.4634i 0.292459 + 0.402536i 0.929811 0.368037i \(-0.119970\pi\)
−0.637352 + 0.770573i \(0.719970\pi\)
\(812\) −1.75289 + 1.57831i −0.0615142 + 0.0553877i
\(813\) 22.9145 31.2279i 0.803647 1.09521i
\(814\) −7.10797 + 7.93017i −0.249134 + 0.277952i
\(815\) −27.7670 + 16.0313i −0.972635 + 0.561551i
\(816\) 0.125749 + 1.25335i 0.00440211 + 0.0438759i
\(817\) −9.71499 92.4319i −0.339884 3.23378i
\(818\) −6.62746 + 9.12191i −0.231724 + 0.318940i
\(819\) 1.90965 1.36007i 0.0667287 0.0475247i
\(820\) 8.38889 2.72572i 0.292953 0.0951862i
\(821\) −49.5964 + 22.0817i −1.73093 + 0.770658i −0.735247 + 0.677799i \(0.762934\pi\)
−0.995679 + 0.0928594i \(0.970399\pi\)
\(822\) 8.12917 4.64232i 0.283537 0.161920i
\(823\) −25.4218 + 5.40357i −0.886148 + 0.188357i −0.628432 0.777864i \(-0.716303\pi\)
−0.257716 + 0.966221i \(0.582970\pi\)
\(824\) −13.1368 22.7536i −0.457642 0.792660i
\(825\) −12.8878 + 14.2426i −0.448694 + 0.495864i
\(826\) 3.20360 5.54879i 0.111467 0.193067i
\(827\) 6.86114 21.1164i 0.238585 0.734290i −0.758040 0.652208i \(-0.773843\pi\)
0.996626 0.0820821i \(-0.0261570\pi\)
\(828\) 4.90938 + 11.3131i 0.170613 + 0.393156i
\(829\) 6.23980 + 4.53348i 0.216717 + 0.157454i 0.690848 0.723000i \(-0.257238\pi\)
−0.474131 + 0.880455i \(0.657238\pi\)
\(830\) 5.18677 24.4018i 0.180035 0.846999i
\(831\) 13.4010 11.9522i 0.464876 0.414617i
\(832\) −2.08371 0.219007i −0.0722398 0.00759271i
\(833\) −6.29035 2.80065i −0.217948 0.0970366i
\(834\) 6.01806 + 8.36596i 0.208388 + 0.289690i
\(835\) 53.1314 + 30.6755i 1.83869 + 1.06157i
\(836\) 30.6657 + 9.88732i 1.06060 + 0.341960i
\(837\) −38.4928 + 7.61348i −1.33051 + 0.263160i
\(838\) 2.25932 + 0.734097i 0.0780468 + 0.0253589i
\(839\) −46.6084 + 4.89874i −1.60910 + 0.169123i −0.865996 0.500052i \(-0.833314\pi\)
−0.743105 + 0.669175i \(0.766648\pi\)
\(840\) 5.46799 + 17.1032i 0.188664 + 0.590117i
\(841\) −18.2653 + 20.2856i −0.629837 + 0.699505i
\(842\) −11.3117 + 12.5630i −0.389829 + 0.432948i
\(843\) −16.0819 3.49779i −0.553890 0.120470i
\(844\) 1.64227 0.172610i 0.0565293 0.00594147i
\(845\) −34.7686 11.2970i −1.19608 0.388629i
\(846\) −20.5254 18.8352i −0.705676 0.647569i
\(847\) −13.9221 + 4.59326i −0.478370 + 0.157826i
\(848\) 1.71292 + 0.988954i 0.0588219 + 0.0339608i
\(849\) −8.83646 + 19.5974i −0.303266 + 0.672580i
\(850\) −3.23063 1.43837i −0.110810 0.0493357i
\(851\) 12.0635 + 1.26792i 0.413530 + 0.0434638i
\(852\) −2.28120 10.9872i −0.0781528 0.376414i
\(853\) −6.89791 + 32.4521i −0.236180 + 1.11114i 0.686966 + 0.726690i \(0.258942\pi\)
−0.923146 + 0.384450i \(0.874391\pi\)
\(854\) 6.84135 + 4.97053i 0.234106 + 0.170088i
\(855\) 7.07133 61.6694i 0.241834 2.10905i
\(856\) −2.44923 + 7.53796i −0.0837130 + 0.257642i
\(857\) −1.62627 + 2.81679i −0.0555524 + 0.0962196i −0.892464 0.451118i \(-0.851025\pi\)
0.836912 + 0.547338i \(0.184359\pi\)
\(858\) −2.68862 + 0.275892i −0.0917880 + 0.00941880i
\(859\) −3.97946 6.89262i −0.135777 0.235173i 0.790117 0.612956i \(-0.210020\pi\)
−0.925894 + 0.377783i \(0.876686\pi\)
\(860\) 49.7178 10.5678i 1.69536 0.360361i
\(861\) 0.0245503 5.19754i 0.000836671 0.177132i
\(862\) 27.9682 12.4522i 0.952599 0.424124i
\(863\) −38.4621 + 12.4971i −1.30926 + 0.425405i −0.878795 0.477200i \(-0.841652\pi\)
−0.430469 + 0.902605i \(0.641652\pi\)
\(864\) 14.7697 + 26.4402i 0.502476 + 0.899513i
\(865\) −21.0414 + 28.9610i −0.715429 + 0.984704i
\(866\) −1.78153 16.9501i −0.0605388 0.575988i
\(867\) 21.4599 15.4372i 0.728816 0.524274i
\(868\) −11.8206 + 6.82461i −0.401216 + 0.231642i
\(869\) 45.5256 + 4.68091i 1.54435 + 0.158789i
\(870\) −2.10810 4.79571i −0.0714713 0.162590i
\(871\) −3.79257 + 3.41485i −0.128506 + 0.115708i
\(872\) −2.27854 3.13614i −0.0771611 0.106203i
\(873\) −1.62914 1.84408i −0.0551379 0.0624126i
\(874\) 5.38343 + 16.5685i 0.182097 + 0.560437i
\(875\) −6.23701 1.32572i −0.210850 0.0448175i
\(876\) 15.2632 + 13.8742i 0.515696 + 0.468764i
\(877\) −11.4141 + 25.6365i −0.385427 + 0.865684i 0.611782 + 0.791027i \(0.290453\pi\)
−0.997209 + 0.0746577i \(0.976214\pi\)
\(878\) −4.59375 21.6119i −0.155032 0.729366i
\(879\) −4.92540 + 44.8244i −0.166130 + 1.51189i
\(880\) −1.08726 + 5.17263i −0.0366516 + 0.174369i
\(881\) 23.2639i 0.783780i 0.920012 + 0.391890i \(0.128179\pi\)
−0.920012 + 0.391890i \(0.871821\pi\)
\(882\) −12.5736 0.118783i −0.423374 0.00399965i
\(883\) −23.6812 + 17.2054i −0.796937 + 0.579008i −0.910014 0.414578i \(-0.863929\pi\)
0.113077 + 0.993586i \(0.463929\pi\)
\(884\) 0.426360 + 0.957620i 0.0143400 + 0.0322082i
\(885\) −19.9530 22.3716i −0.670712 0.752014i
\(886\) 15.9533 + 14.3644i 0.535960 + 0.482581i
\(887\) −0.509963 + 4.85197i −0.0171229 + 0.162913i −0.999742 0.0227207i \(-0.992767\pi\)
0.982619 + 0.185634i \(0.0594338\pi\)
\(888\) 18.6653 + 0.0881646i 0.626368 + 0.00295861i
\(889\) −4.21104 4.67683i −0.141234 0.156856i
\(890\) −20.5644 −0.689320
\(891\) 19.6016 + 22.5117i 0.656678 + 0.754171i
\(892\) 17.7008 0.592665
\(893\) 55.4715 + 61.6074i 1.85628 + 2.06161i
\(894\) −8.56468 0.0404548i −0.286446 0.00135301i
\(895\) −3.37026 + 32.0659i −0.112655 + 1.07184i
\(896\) 8.70590 + 7.83883i 0.290844 + 0.261877i
\(897\) 2.04907 + 2.29745i 0.0684163 + 0.0767096i
\(898\) 9.65488 + 21.6852i 0.322188 + 0.723645i
\(899\) 7.97246 5.79233i 0.265896 0.193185i
\(900\) 13.6036 + 0.128514i 0.453453 + 0.00428381i
\(901\) 4.72544i 0.157427i
\(902\) −2.98419 + 5.19585i −0.0993626 + 0.173003i
\(903\) 3.27140 29.7718i 0.108865 0.990745i
\(904\) 1.05905 + 4.98243i 0.0352234 + 0.165713i
\(905\) −0.0223710 + 0.0502462i −0.000743638 + 0.00167024i
\(906\) −20.2766 18.4313i −0.673644 0.612338i
\(907\) 10.0126 + 2.12823i 0.332461 + 0.0706669i 0.371118 0.928586i \(-0.378975\pi\)
−0.0386566 + 0.999253i \(0.512308\pi\)
\(908\) −0.331524 1.02033i −0.0110020 0.0338607i
\(909\) −34.0576 38.5510i −1.12962 1.27866i
\(910\) 1.06462 + 1.46532i 0.0352918 + 0.0485749i
\(911\) −4.84142 + 4.35923i −0.160403 + 0.144428i −0.745424 0.666590i \(-0.767753\pi\)
0.585021 + 0.811018i \(0.301086\pi\)
\(912\) −2.75465 6.26655i −0.0912157 0.207506i
\(913\) −17.9196 30.8763i −0.593053 1.02186i
\(914\) −0.228161 + 0.131729i −0.00754689 + 0.00435720i
\(915\) 32.1176 23.1038i 1.06177 0.763788i
\(916\) −1.38465 13.1740i −0.0457501 0.435283i
\(917\) −6.17680 + 8.50163i −0.203976 + 0.280749i
\(918\) −2.81496 + 4.71991i −0.0929075 + 0.155780i
\(919\) 22.0654 7.16949i 0.727871 0.236500i 0.0784385 0.996919i \(-0.475007\pi\)
0.649432 + 0.760419i \(0.275007\pi\)
\(920\) −21.5392 + 9.58985i −0.710125 + 0.316168i
\(921\) 0.147485 31.2241i 0.00485979 1.02887i
\(922\) −2.50054 + 0.531507i −0.0823510 + 0.0175042i
\(923\) −1.40058 2.42587i −0.0461006 0.0798485i
\(924\) 8.97935 + 5.21376i 0.295399 + 0.171520i
\(925\) 6.69043 11.5882i 0.219980 0.381016i
\(926\) −6.76675 + 20.8259i −0.222369 + 0.684382i
\(927\) −3.33438 + 29.0793i −0.109515 + 0.955088i
\(928\) −6.15344 4.47074i −0.201997 0.146759i
\(929\) −1.54441 + 7.26589i −0.0506705 + 0.238386i −0.996194 0.0871692i \(-0.972218\pi\)
0.945523 + 0.325555i \(0.105551\pi\)
\(930\) −6.16250 29.6810i −0.202076 0.973277i
\(931\) 37.2138 + 3.91133i 1.21963 + 0.128189i
\(932\) −20.5320 9.14145i −0.672549 0.299438i
\(933\) 8.95233 19.8543i 0.293086 0.650002i
\(934\) −12.6853 7.32387i −0.415076 0.239644i
\(935\) −12.0011 + 3.92942i −0.392479 + 0.128506i
\(936\) 3.49029 + 3.20289i 0.114084 + 0.104690i
\(937\) −44.2612 14.3813i −1.44595 0.469817i −0.522203 0.852821i \(-0.674890\pi\)
−0.923747 + 0.383004i \(0.874890\pi\)
\(938\) −9.25595 + 0.972839i −0.302217 + 0.0317643i
\(939\) −19.7946 4.30530i −0.645973 0.140498i
\(940\) −30.3368 + 33.6924i −0.989478 + 1.09893i
\(941\) 11.8484 13.1590i 0.386247 0.428971i −0.518396 0.855141i \(-0.673471\pi\)
0.904643 + 0.426170i \(0.140137\pi\)
\(942\) −2.06302 6.45287i −0.0672168 0.210246i
\(943\) 6.78743 0.713388i 0.221029 0.0232311i
\(944\) −3.14396 1.02153i −0.102327 0.0332481i
\(945\) 6.45044 18.9351i 0.209833 0.615960i
\(946\) −20.2318 + 27.9795i −0.657792 + 0.909691i
\(947\) 24.8531 + 14.3490i 0.807618 + 0.466278i 0.846128 0.532980i \(-0.178928\pi\)
−0.0385102 + 0.999258i \(0.512261\pi\)
\(948\) −18.9283 26.3130i −0.614763 0.854608i
\(949\) 4.70377 + 2.09425i 0.152691 + 0.0679823i
\(950\) 19.1125 + 2.00880i 0.620091 + 0.0651742i
\(951\) 21.2645 18.9655i 0.689549 0.615000i
\(952\) −0.983581 + 4.62739i −0.0318781 + 0.149974i
\(953\) 30.0074 + 21.8016i 0.972033 + 0.706224i 0.955914 0.293646i \(-0.0948688\pi\)
0.0161193 + 0.999870i \(0.494869\pi\)
\(954\) 3.43522 + 7.91605i 0.111219 + 0.256292i
\(955\) 2.33443 7.18465i 0.0755405 0.232490i
\(956\) −0.824898 + 1.42877i −0.0266791 + 0.0462096i
\(957\) −6.84089 3.06597i −0.221135 0.0991088i
\(958\) −5.08024 8.79924i −0.164135 0.284290i
\(959\) −8.78130 + 1.86652i −0.283563 + 0.0602732i
\(960\) −15.5238 + 8.86514i −0.501027 + 0.286121i
\(961\) 23.7746 10.5851i 0.766923 0.341456i
\(962\) 1.79066 0.581820i 0.0577331 0.0187586i
\(963\) 7.19211 5.12227i 0.231762 0.165063i
\(964\) −0.604824 + 0.832469i −0.0194801 + 0.0268120i
\(965\) −3.87835 36.9000i −0.124848 1.18785i
\(966\) 0.560455 + 5.58606i 0.0180323 + 0.179729i
\(967\) 47.1454 27.2194i 1.51609 0.875317i 0.516272 0.856425i \(-0.327319\pi\)
0.999822 0.0188923i \(-0.00601398\pi\)
\(968\) −14.9268 25.5862i −0.479766 0.822370i
\(969\) 9.67510 13.1852i 0.310809 0.423570i
\(970\) 1.41270 1.27200i 0.0453590 0.0408414i
\(971\) −4.73162 6.51252i −0.151845 0.208997i 0.726317 0.687360i \(-0.241230\pi\)
−0.878162 + 0.478363i \(0.841230\pi\)
\(972\) 2.70576 20.9674i 0.0867871 0.672529i
\(973\) −3.05404 9.39936i −0.0979080 0.301330i
\(974\) −11.9782 2.54604i −0.383806 0.0815805i
\(975\) 3.23466 1.03414i 0.103592 0.0331189i
\(976\) 1.77460 3.98582i 0.0568035 0.127583i
\(977\) 2.64186 + 12.4290i 0.0845205 + 0.397638i 0.999989 0.00475272i \(-0.00151284\pi\)
−0.915468 + 0.402390i \(0.868180\pi\)
\(978\) −14.1218 + 6.20766i −0.451565 + 0.198499i
\(979\) −21.8247 + 19.7406i −0.697522 + 0.630912i
\(980\) 20.4640i 0.653698i
\(981\) −0.0407959 + 4.31836i −0.00130251 + 0.137875i
\(982\) −18.4389 + 13.3967i −0.588409 + 0.427504i
\(983\) 2.14903 + 4.82680i 0.0685434 + 0.153951i 0.944568 0.328315i \(-0.106481\pi\)
−0.876025 + 0.482266i \(0.839814\pi\)
\(984\) 10.2828 2.13495i 0.327802 0.0680599i
\(985\) 14.7719 + 13.3007i 0.470673 + 0.423796i
\(986\) 0.144268 1.37262i 0.00459444 0.0437132i
\(987\) 13.2483 + 23.1991i 0.421699 + 0.738437i
\(988\) −3.81170 4.23332i −0.121266 0.134680i
\(989\) 39.3279 1.25055
\(990\) −17.2477 + 15.3069i −0.548169 + 0.486486i
\(991\) 54.4977 1.73118 0.865589 0.500756i \(-0.166945\pi\)
0.865589 + 0.500756i \(0.166945\pi\)
\(992\) −29.4509 32.7085i −0.935067 1.03850i
\(993\) −17.1352 + 29.3578i −0.543768 + 0.931643i
\(994\) 0.533972 5.08040i 0.0169365 0.161141i
\(995\) −0.145042 0.130596i −0.00459814 0.00414018i
\(996\) −7.92684 + 24.0098i −0.251172 + 0.760780i
\(997\) 3.11130 + 6.98810i 0.0985360 + 0.221315i 0.956087 0.293084i \(-0.0946816\pi\)
−0.857551 + 0.514399i \(0.828015\pi\)
\(998\) −14.1919 + 10.3110i −0.449236 + 0.326389i
\(999\) −16.6479 12.4596i −0.526717 0.394205i
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 99.2.p.a.2.5 80
3.2 odd 2 297.2.t.a.35.6 80
9.2 odd 6 891.2.k.a.728.13 80
9.4 even 3 297.2.t.a.233.6 80
9.5 odd 6 inner 99.2.p.a.68.5 yes 80
9.7 even 3 891.2.k.a.728.8 80
11.6 odd 10 inner 99.2.p.a.83.5 yes 80
33.17 even 10 297.2.t.a.116.6 80
99.50 even 30 inner 99.2.p.a.50.5 yes 80
99.61 odd 30 891.2.k.a.809.13 80
99.83 even 30 891.2.k.a.809.8 80
99.94 odd 30 297.2.t.a.17.6 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.2.5 80 1.1 even 1 trivial
99.2.p.a.50.5 yes 80 99.50 even 30 inner
99.2.p.a.68.5 yes 80 9.5 odd 6 inner
99.2.p.a.83.5 yes 80 11.6 odd 10 inner
297.2.t.a.17.6 80 99.94 odd 30
297.2.t.a.35.6 80 3.2 odd 2
297.2.t.a.116.6 80 33.17 even 10
297.2.t.a.233.6 80 9.4 even 3
891.2.k.a.728.8 80 9.7 even 3
891.2.k.a.728.13 80 9.2 odd 6
891.2.k.a.809.8 80 99.83 even 30
891.2.k.a.809.13 80 99.61 odd 30