Properties

Label 129.2.n.b.98.12
Level $129$
Weight $2$
Character 129.98
Analytic conductor $1.030$
Analytic rank $0$
Dimension $144$
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] = [129,2,Mod(5,129)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(129, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 25]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("129.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 129 = 3 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 129.n (of order \(42\), degree \(12\), 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: \(1.03007018607\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(12\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 98.12
Character \(\chi\) \(=\) 129.98
Dual form 129.2.n.b.104.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.40321 - 1.15733i) q^{2} +(-1.69662 - 0.348562i) q^{3} +(3.18904 - 3.99893i) q^{4} +(1.17790 + 1.09293i) q^{5} +(-4.48073 + 1.12587i) q^{6} +(-4.15657 + 2.39980i) q^{7} +(1.84879 - 8.10007i) q^{8} +(2.75701 + 1.18275i) q^{9} +O(q^{10})\) \(q+(2.40321 - 1.15733i) q^{2} +(-1.69662 - 0.348562i) q^{3} +(3.18904 - 3.99893i) q^{4} +(1.17790 + 1.09293i) q^{5} +(-4.48073 + 1.12587i) q^{6} +(-4.15657 + 2.39980i) q^{7} +(1.84879 - 8.10007i) q^{8} +(2.75701 + 1.18275i) q^{9} +(4.09562 + 1.26333i) q^{10} +(0.475385 - 0.379106i) q^{11} +(-6.80446 + 5.67307i) q^{12} +(-1.35661 + 0.418460i) q^{13} +(-7.21177 + 10.5777i) q^{14} +(-1.61749 - 2.26486i) q^{15} +(-2.65508 - 11.6326i) q^{16} +(1.98006 + 2.13399i) q^{17} +(7.99450 - 0.348351i) q^{18} +(-1.04359 + 0.409578i) q^{19} +(8.12694 - 1.22494i) q^{20} +(7.88858 - 2.62271i) q^{21} +(0.703700 - 1.46125i) q^{22} +(0.305206 + 2.02491i) q^{23} +(-5.96006 + 13.0983i) q^{24} +(-0.180701 - 2.41128i) q^{25} +(-2.77593 + 2.57569i) q^{26} +(-4.26532 - 2.96767i) q^{27} +(-3.65885 + 24.2749i) q^{28} +(-1.44195 - 0.983108i) q^{29} +(-6.50835 - 3.57097i) q^{30} +(0.0959321 - 1.28012i) q^{31} +(-9.48309 - 11.8914i) q^{32} +(-0.938687 + 0.477497i) q^{33} +(7.22822 + 2.83687i) q^{34} +(-7.51885 - 1.71613i) q^{35} +(13.5220 - 7.25324i) q^{36} +(-7.41825 - 4.28293i) q^{37} +(-2.03395 + 2.19207i) q^{38} +(2.44751 - 0.237101i) q^{39} +(11.0305 - 7.52048i) q^{40} +(3.15640 + 6.55434i) q^{41} +(15.9226 - 15.4326i) q^{42} +(5.95637 - 2.74257i) q^{43} -3.11002i q^{44} +(1.95481 + 4.40639i) q^{45} +(3.07696 + 4.51306i) q^{46} +(-9.07388 - 7.23617i) q^{47} +(0.449938 + 20.6616i) q^{48} +(8.01805 - 13.8877i) q^{49} +(-3.22490 - 5.58570i) q^{50} +(-2.61557 - 4.31074i) q^{51} +(-2.65290 + 6.75949i) q^{52} +(0.466037 - 1.51085i) q^{53} +(-13.6850 - 2.19557i) q^{54} +(0.974294 + 0.0730132i) q^{55} +(11.7539 + 38.1052i) q^{56} +(1.91333 - 0.331141i) q^{57} +(-4.60310 - 0.693805i) q^{58} +(7.70504 - 1.75862i) q^{59} +(-14.2153 - 0.754496i) q^{60} +(-3.52016 + 0.263799i) q^{61} +(-1.25098 - 3.18743i) q^{62} +(-14.2981 + 1.70006i) q^{63} +(-15.0518 - 7.24854i) q^{64} +(-2.05530 - 0.989783i) q^{65} +(-1.70324 + 2.23389i) q^{66} +(1.96093 + 4.99637i) q^{67} +(14.8482 - 1.11272i) q^{68} +(0.187990 - 3.54188i) q^{69} +(-20.0555 + 4.57754i) q^{70} +(2.68369 + 0.404501i) q^{71} +(14.6775 - 20.1453i) q^{72} +(-1.10298 - 3.57578i) q^{73} +(-22.7844 - 1.70745i) q^{74} +(-0.533904 + 4.15401i) q^{75} +(-1.69017 + 5.47940i) q^{76} +(-1.06619 + 2.71661i) q^{77} +(5.60748 - 3.40237i) q^{78} +(3.63330 + 6.29307i) q^{79} +(9.58628 - 16.6039i) q^{80} +(6.20219 + 6.52172i) q^{81} +(15.1710 + 12.0985i) q^{82} +(8.48661 + 12.4476i) q^{83} +(14.6690 - 39.9098i) q^{84} +4.67770i q^{85} +(11.1404 - 13.4844i) q^{86} +(2.10377 + 2.17057i) q^{87} +(-2.19190 - 4.55153i) q^{88} +(-5.88635 + 4.01325i) q^{89} +(9.79746 + 8.32713i) q^{90} +(4.63464 - 4.99495i) q^{91} +(9.07079 + 5.23703i) q^{92} +(-0.608963 + 2.13844i) q^{93} +(-30.1810 - 6.88863i) q^{94} +(-1.67688 - 0.658129i) q^{95} +(11.9443 + 23.4806i) q^{96} +(-1.59617 - 2.00153i) q^{97} +(3.19651 - 42.6545i) q^{98} +(1.75903 - 0.482937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7} - 26 q^{10} - 4 q^{12} - 48 q^{13} - 19 q^{15} - 8 q^{16} + 16 q^{18} - 10 q^{19} - 15 q^{21} + 14 q^{22} - 11 q^{24} - 16 q^{25} - 14 q^{27} - 42 q^{28} - 6 q^{30} - 36 q^{31} + 7 q^{33} + 80 q^{34} + 48 q^{36} - 6 q^{37} + 7 q^{39} + 118 q^{40} + 46 q^{43} + 78 q^{46} - 41 q^{48} - 54 q^{49} + 7 q^{51} - 4 q^{52} - 52 q^{54} - 22 q^{55} - 110 q^{57} + 18 q^{58} - 9 q^{60} - 58 q^{61} - 82 q^{63} + 72 q^{64} - 127 q^{66} + 10 q^{67} - 15 q^{69} - 196 q^{70} + 179 q^{72} + 42 q^{73} + 119 q^{75} + 4 q^{76} + 62 q^{78} - 30 q^{79} + 200 q^{81} - 28 q^{82} + 111 q^{84} - 18 q^{87} - 14 q^{88} + 131 q^{90} - 38 q^{91} + 156 q^{93} + 28 q^{94} + 304 q^{96} + 72 q^{97} + 121 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/129\mathbb{Z}\right)^\times\).

\(n\) \(44\) \(46\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.40321 1.15733i 1.69933 0.818353i 0.705338 0.708871i \(-0.250795\pi\)
0.993989 0.109482i \(-0.0349191\pi\)
\(3\) −1.69662 0.348562i −0.979541 0.201243i
\(4\) 3.18904 3.99893i 1.59452 1.99947i
\(5\) 1.17790 + 1.09293i 0.526774 + 0.488774i 0.898139 0.439713i \(-0.144920\pi\)
−0.371365 + 0.928487i \(0.621110\pi\)
\(6\) −4.48073 + 1.12587i −1.82925 + 0.459633i
\(7\) −4.15657 + 2.39980i −1.57104 + 0.907038i −0.574993 + 0.818158i \(0.694995\pi\)
−0.996042 + 0.0888799i \(0.971671\pi\)
\(8\) 1.84879 8.10007i 0.653645 2.86381i
\(9\) 2.75701 + 1.18275i 0.919003 + 0.394251i
\(10\) 4.09562 + 1.26333i 1.29515 + 0.399501i
\(11\) 0.475385 0.379106i 0.143334 0.114305i −0.549198 0.835692i \(-0.685067\pi\)
0.692532 + 0.721387i \(0.256495\pi\)
\(12\) −6.80446 + 5.67307i −1.96428 + 1.63767i
\(13\) −1.35661 + 0.418460i −0.376257 + 0.116060i −0.477115 0.878841i \(-0.658317\pi\)
0.100858 + 0.994901i \(0.467841\pi\)
\(14\) −7.21177 + 10.5777i −1.92743 + 2.82702i
\(15\) −1.61749 2.26486i −0.417634 0.584784i
\(16\) −2.65508 11.6326i −0.663769 2.90816i
\(17\) 1.98006 + 2.13399i 0.480234 + 0.517570i 0.925971 0.377595i \(-0.123249\pi\)
−0.445737 + 0.895164i \(0.647058\pi\)
\(18\) 7.99450 0.348351i 1.88432 0.0821071i
\(19\) −1.04359 + 0.409578i −0.239415 + 0.0939637i −0.482015 0.876163i \(-0.660095\pi\)
0.242600 + 0.970126i \(0.422000\pi\)
\(20\) 8.12694 1.22494i 1.81724 0.273905i
\(21\) 7.88858 2.62271i 1.72143 0.572322i
\(22\) 0.703700 1.46125i 0.150029 0.311539i
\(23\) 0.305206 + 2.02491i 0.0636399 + 0.422223i 0.997852 + 0.0655055i \(0.0208660\pi\)
−0.934212 + 0.356717i \(0.883896\pi\)
\(24\) −5.96006 + 13.0983i −1.21659 + 2.67368i
\(25\) −0.180701 2.41128i −0.0361402 0.482257i
\(26\) −2.77593 + 2.57569i −0.544405 + 0.505134i
\(27\) −4.26532 2.96767i −0.820861 0.571128i
\(28\) −3.65885 + 24.2749i −0.691458 + 4.58752i
\(29\) −1.44195 0.983108i −0.267764 0.182559i 0.421993 0.906599i \(-0.361331\pi\)
−0.689758 + 0.724040i \(0.742283\pi\)
\(30\) −6.50835 3.57097i −1.18826 0.651967i
\(31\) 0.0959321 1.28012i 0.0172299 0.229917i −0.981940 0.189190i \(-0.939414\pi\)
0.999170 0.0407267i \(-0.0129673\pi\)
\(32\) −9.48309 11.8914i −1.67639 2.10213i
\(33\) −0.938687 + 0.477497i −0.163404 + 0.0831215i
\(34\) 7.22822 + 2.83687i 1.23963 + 0.486519i
\(35\) −7.51885 1.71613i −1.27092 0.290078i
\(36\) 13.5220 7.25324i 2.25366 1.20887i
\(37\) −7.41825 4.28293i −1.21955 0.704109i −0.254730 0.967012i \(-0.581987\pi\)
−0.964822 + 0.262903i \(0.915320\pi\)
\(38\) −2.03395 + 2.19207i −0.329950 + 0.355601i
\(39\) 2.44751 0.237101i 0.391915 0.0379665i
\(40\) 11.0305 7.52048i 1.74408 1.18909i
\(41\) 3.15640 + 6.55434i 0.492947 + 1.02362i 0.987957 + 0.154728i \(0.0494502\pi\)
−0.495010 + 0.868887i \(0.664836\pi\)
\(42\) 15.9226 15.4326i 2.45691 2.38130i
\(43\) 5.95637 2.74257i 0.908338 0.418238i
\(44\) 3.11002i 0.468853i
\(45\) 1.95481 + 4.40639i 0.291407 + 0.656866i
\(46\) 3.07696 + 4.51306i 0.453672 + 0.665415i
\(47\) −9.07388 7.23617i −1.32356 1.05550i −0.993770 0.111450i \(-0.964450\pi\)
−0.329791 0.944054i \(-0.606978\pi\)
\(48\) 0.449938 + 20.6616i 0.0649430 + 2.98224i
\(49\) 8.01805 13.8877i 1.14544 1.98395i
\(50\) −3.22490 5.58570i −0.456070 0.789937i
\(51\) −2.61557 4.31074i −0.366252 0.603624i
\(52\) −2.65290 + 6.75949i −0.367892 + 0.937373i
\(53\) 0.466037 1.51085i 0.0640150 0.207532i −0.917915 0.396778i \(-0.870128\pi\)
0.981930 + 0.189246i \(0.0606045\pi\)
\(54\) −13.6850 2.19557i −1.86230 0.298779i
\(55\) 0.974294 + 0.0730132i 0.131374 + 0.00984510i
\(56\) 11.7539 + 38.1052i 1.57068 + 5.09202i
\(57\) 1.91333 0.331141i 0.253427 0.0438607i
\(58\) −4.60310 0.693805i −0.604416 0.0911011i
\(59\) 7.70504 1.75862i 1.00311 0.228953i 0.310739 0.950495i \(-0.399423\pi\)
0.692371 + 0.721542i \(0.256566\pi\)
\(60\) −14.2153 0.754496i −1.83518 0.0974050i
\(61\) −3.52016 + 0.263799i −0.450710 + 0.0337760i −0.298152 0.954518i \(-0.596370\pi\)
−0.152558 + 0.988295i \(0.548751\pi\)
\(62\) −1.25098 3.18743i −0.158874 0.404805i
\(63\) −14.2981 + 1.70006i −1.80139 + 0.214188i
\(64\) −15.0518 7.24854i −1.88147 0.906068i
\(65\) −2.05530 0.989783i −0.254929 0.122767i
\(66\) −1.70324 + 2.23389i −0.209655 + 0.274973i
\(67\) 1.96093 + 4.99637i 0.239566 + 0.610404i 0.999202 0.0399445i \(-0.0127181\pi\)
−0.759636 + 0.650349i \(0.774623\pi\)
\(68\) 14.8482 1.11272i 1.80061 0.134937i
\(69\) 0.187990 3.54188i 0.0226314 0.426392i
\(70\) −20.0555 + 4.57754i −2.39709 + 0.547120i
\(71\) 2.68369 + 0.404501i 0.318495 + 0.0480055i 0.306345 0.951921i \(-0.400894\pi\)
0.0121510 + 0.999926i \(0.496132\pi\)
\(72\) 14.6775 20.1453i 1.72976 2.37415i
\(73\) −1.10298 3.57578i −0.129094 0.418514i 0.867832 0.496858i \(-0.165513\pi\)
−0.996926 + 0.0783439i \(0.975037\pi\)
\(74\) −22.7844 1.70745i −2.64863 0.198487i
\(75\) −0.533904 + 4.15401i −0.0616499 + 0.479664i
\(76\) −1.69017 + 5.47940i −0.193876 + 0.628530i
\(77\) −1.06619 + 2.71661i −0.121504 + 0.309586i
\(78\) 5.60748 3.40237i 0.634922 0.385242i
\(79\) 3.63330 + 6.29307i 0.408779 + 0.708025i 0.994753 0.102304i \(-0.0326215\pi\)
−0.585975 + 0.810329i \(0.699288\pi\)
\(80\) 9.58628 16.6039i 1.07178 1.85638i
\(81\) 6.20219 + 6.52172i 0.689132 + 0.724636i
\(82\) 15.1710 + 12.0985i 1.67536 + 1.33605i
\(83\) 8.48661 + 12.4476i 0.931527 + 1.36630i 0.930497 + 0.366300i \(0.119375\pi\)
0.00103006 + 0.999999i \(0.499672\pi\)
\(84\) 14.6690 39.9098i 1.60052 4.35452i
\(85\) 4.67770i 0.507368i
\(86\) 11.1404 13.4844i 1.20130 1.45406i
\(87\) 2.10377 + 2.17057i 0.225548 + 0.232709i
\(88\) −2.19190 4.55153i −0.233658 0.485195i
\(89\) −5.88635 + 4.01325i −0.623952 + 0.425403i −0.833596 0.552375i \(-0.813722\pi\)
0.209644 + 0.977778i \(0.432769\pi\)
\(90\) 9.79746 + 8.32713i 1.03274 + 0.877757i
\(91\) 4.63464 4.99495i 0.485842 0.523613i
\(92\) 9.07079 + 5.23703i 0.945696 + 0.545998i
\(93\) −0.608963 + 2.13844i −0.0631465 + 0.221746i
\(94\) −30.1810 6.88863i −3.11294 0.710508i
\(95\) −1.67688 0.658129i −0.172045 0.0675226i
\(96\) 11.9443 + 23.4806i 1.21906 + 2.39648i
\(97\) −1.59617 2.00153i −0.162066 0.203225i 0.694167 0.719814i \(-0.255773\pi\)
−0.856233 + 0.516589i \(0.827201\pi\)
\(98\) 3.19651 42.6545i 0.322897 4.30875i
\(99\) 1.75903 0.482937i 0.176789 0.0485370i
\(100\) −10.2188 6.96708i −1.02188 0.696708i
\(101\) 0.355935 2.36147i 0.0354169 0.234976i −0.964118 0.265474i \(-0.914471\pi\)
0.999535 + 0.0304988i \(0.00970956\pi\)
\(102\) −11.2747 7.33256i −1.11636 0.726032i
\(103\) −2.29759 + 2.13185i −0.226389 + 0.210058i −0.785209 0.619231i \(-0.787445\pi\)
0.558821 + 0.829289i \(0.311254\pi\)
\(104\) 0.881462 + 11.7623i 0.0864345 + 1.15339i
\(105\) 12.1584 + 5.53240i 1.18654 + 0.539907i
\(106\) −0.628565 4.17026i −0.0610516 0.405051i
\(107\) 2.72464 5.65777i 0.263401 0.546957i −0.726760 0.686891i \(-0.758975\pi\)
0.990161 + 0.139934i \(0.0446891\pi\)
\(108\) −25.4698 + 7.59271i −2.45083 + 0.730609i
\(109\) 7.07985 1.06712i 0.678127 0.102211i 0.199057 0.979988i \(-0.436212\pi\)
0.479070 + 0.877777i \(0.340974\pi\)
\(110\) 2.42593 0.952109i 0.231304 0.0907800i
\(111\) 11.0930 + 9.85220i 1.05291 + 0.935130i
\(112\) 38.9520 + 41.9803i 3.68062 + 3.96676i
\(113\) 2.75869 + 12.0866i 0.259516 + 1.13701i 0.921771 + 0.387735i \(0.126742\pi\)
−0.662255 + 0.749279i \(0.730400\pi\)
\(114\) 4.21490 3.01015i 0.394762 0.281926i
\(115\) −1.85359 + 2.71871i −0.172848 + 0.253521i
\(116\) −8.52984 + 2.63111i −0.791976 + 0.244292i
\(117\) −4.23513 0.450841i −0.391538 0.0416803i
\(118\) 16.4815 13.1436i 1.51725 1.20996i
\(119\) −13.3514 4.11836i −1.22392 0.377530i
\(120\) −21.3359 + 8.91454i −1.94769 + 0.813782i
\(121\) −2.36546 + 10.3638i −0.215042 + 0.942160i
\(122\) −8.15438 + 4.70793i −0.738262 + 0.426236i
\(123\) −3.07061 12.2204i −0.276867 1.10188i
\(124\) −4.81320 4.46600i −0.432238 0.401058i
\(125\) 7.43178 9.31916i 0.664719 0.833531i
\(126\) −32.3937 + 20.6331i −2.88586 + 1.83815i
\(127\) −14.3316 + 6.90173i −1.27172 + 0.612429i −0.943250 0.332084i \(-0.892248\pi\)
−0.328473 + 0.944514i \(0.606534\pi\)
\(128\) −14.1421 −1.24999
\(129\) −11.0616 + 2.57692i −0.973922 + 0.226885i
\(130\) −6.08483 −0.533675
\(131\) 6.81261 3.28078i 0.595221 0.286643i −0.111919 0.993717i \(-0.535700\pi\)
0.707139 + 0.707074i \(0.249985\pi\)
\(132\) −1.08404 + 5.27650i −0.0943532 + 0.459261i
\(133\) 3.35484 4.20684i 0.290902 0.364779i
\(134\) 10.4950 + 9.73790i 0.906627 + 0.841227i
\(135\) −1.78067 8.15733i −0.153255 0.702071i
\(136\) 20.9462 12.0933i 1.79612 1.03699i
\(137\) −4.15748 + 18.2151i −0.355197 + 1.55622i 0.409793 + 0.912179i \(0.365601\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(138\) −3.64732 8.72945i −0.310481 0.743100i
\(139\) −3.21741 0.992439i −0.272897 0.0841776i 0.155286 0.987870i \(-0.450370\pi\)
−0.428183 + 0.903692i \(0.640846\pi\)
\(140\) −30.8406 + 24.5946i −2.60651 + 2.07862i
\(141\) 12.8726 + 15.4398i 1.08407 + 1.30027i
\(142\) 6.91762 2.13380i 0.580513 0.179065i
\(143\) −0.486272 + 0.713230i −0.0406641 + 0.0596433i
\(144\) 6.43848 35.2116i 0.536540 2.93430i
\(145\) −0.624010 2.73396i −0.0518212 0.227043i
\(146\) −6.78905 7.31685i −0.561866 0.605547i
\(147\) −18.4443 + 20.7672i −1.52126 + 1.71285i
\(148\) −40.7842 + 16.0066i −3.35244 + 1.31574i
\(149\) 13.3886 2.01800i 1.09683 0.165321i 0.424397 0.905476i \(-0.360486\pi\)
0.672436 + 0.740155i \(0.265248\pi\)
\(150\) 3.52446 + 10.6009i 0.287771 + 0.865557i
\(151\) 6.77542 14.0693i 0.551376 1.14494i −0.420029 0.907511i \(-0.637980\pi\)
0.971404 0.237432i \(-0.0763057\pi\)
\(152\) 1.38824 + 9.21035i 0.112601 + 0.747058i
\(153\) 2.93505 + 8.22536i 0.237284 + 0.664981i
\(154\) 0.581720 + 7.76251i 0.0468763 + 0.625521i
\(155\) 1.51209 1.40301i 0.121454 0.112693i
\(156\) 6.85706 10.5436i 0.549004 0.844160i
\(157\) 0.532983 3.53611i 0.0425367 0.282212i −0.957443 0.288623i \(-0.906803\pi\)
0.999979 + 0.00641082i \(0.00204064\pi\)
\(158\) 16.0147 + 10.9187i 1.27406 + 0.868641i
\(159\) −1.31731 + 2.40089i −0.104470 + 0.190403i
\(160\) 1.82638 24.3713i 0.144388 1.92672i
\(161\) −6.12798 7.68425i −0.482953 0.605604i
\(162\) 22.4529 + 8.49512i 1.76407 + 0.667439i
\(163\) −1.63128 0.640231i −0.127772 0.0501467i 0.300594 0.953752i \(-0.402815\pi\)
−0.428366 + 0.903606i \(0.640910\pi\)
\(164\) 36.2763 + 8.27982i 2.83270 + 0.646545i
\(165\) −1.62755 0.463478i −0.126705 0.0360817i
\(166\) 34.8010 + 20.0924i 2.70108 + 1.55947i
\(167\) 6.67157 7.19025i 0.516262 0.556398i −0.420080 0.907487i \(-0.637998\pi\)
0.936342 + 0.351089i \(0.114189\pi\)
\(168\) −6.65980 68.7469i −0.513815 5.30393i
\(169\) −9.07581 + 6.18779i −0.698140 + 0.475983i
\(170\) 5.41363 + 11.2415i 0.415206 + 0.862185i
\(171\) −3.36161 0.105097i −0.257069 0.00803693i
\(172\) 8.02776 32.5653i 0.612111 2.48308i
\(173\) 7.18274i 0.546093i −0.962001 0.273047i \(-0.911969\pi\)
0.962001 0.273047i \(-0.0880314\pi\)
\(174\) 7.56785 + 2.78159i 0.573718 + 0.210872i
\(175\) 6.53769 + 9.58903i 0.494203 + 0.724862i
\(176\) −5.67219 4.52342i −0.427558 0.340966i
\(177\) −13.6855 + 0.298023i −1.02866 + 0.0224008i
\(178\) −9.50151 + 16.4571i −0.712169 + 1.23351i
\(179\) −8.48669 14.6994i −0.634325 1.09868i −0.986658 0.162808i \(-0.947945\pi\)
0.352333 0.935875i \(-0.385389\pi\)
\(180\) 23.8548 + 6.23500i 1.77804 + 0.464729i
\(181\) 4.17709 10.6430i 0.310480 0.791091i −0.687416 0.726264i \(-0.741255\pi\)
0.997896 0.0648274i \(-0.0206497\pi\)
\(182\) 5.35723 17.3677i 0.397104 1.28738i
\(183\) 6.06430 + 0.779428i 0.448286 + 0.0576170i
\(184\) 16.9662 + 1.27144i 1.25076 + 0.0937317i
\(185\) −4.05701 13.1525i −0.298277 0.966992i
\(186\) 1.01140 + 5.84389i 0.0741598 + 0.428495i
\(187\) 1.75030 + 0.263815i 0.127995 + 0.0192921i
\(188\) −57.8739 + 13.2094i −4.22089 + 0.963391i
\(189\) 24.8509 + 2.09941i 1.80764 + 0.152710i
\(190\) −4.79158 + 0.359079i −0.347618 + 0.0260503i
\(191\) −4.49047 11.4415i −0.324919 0.827881i −0.996234 0.0867080i \(-0.972365\pi\)
0.671315 0.741173i \(-0.265730\pi\)
\(192\) 23.0105 + 17.5445i 1.66064 + 1.26616i
\(193\) 18.1248 + 8.72842i 1.30465 + 0.628286i 0.951606 0.307321i \(-0.0994327\pi\)
0.353043 + 0.935607i \(0.385147\pi\)
\(194\) −6.15236 2.96282i −0.441713 0.212718i
\(195\) 3.14206 + 2.39568i 0.225008 + 0.171558i
\(196\) −29.9660 76.3520i −2.14043 5.45371i
\(197\) −19.4215 + 1.45544i −1.38372 + 0.103696i −0.745679 0.666306i \(-0.767875\pi\)
−0.638042 + 0.770001i \(0.720256\pi\)
\(198\) 3.66840 3.19637i 0.260702 0.227156i
\(199\) −24.5221 + 5.59701i −1.73833 + 0.396762i −0.969963 0.243253i \(-0.921786\pi\)
−0.768363 + 0.640014i \(0.778928\pi\)
\(200\) −19.8656 2.99426i −1.40471 0.211726i
\(201\) −1.58540 9.16043i −0.111825 0.646127i
\(202\) −1.87761 6.08706i −0.132108 0.428284i
\(203\) 8.35285 + 0.625959i 0.586255 + 0.0439337i
\(204\) −25.5795 3.28767i −1.79092 0.230183i
\(205\) −3.44552 + 11.1701i −0.240646 + 0.780154i
\(206\) −3.05435 + 7.78236i −0.212807 + 0.542223i
\(207\) −1.55351 + 5.94368i −0.107977 + 0.413114i
\(208\) 8.46970 + 14.6700i 0.587268 + 1.01718i
\(209\) −0.340832 + 0.590338i −0.0235758 + 0.0408345i
\(210\) 35.6220 0.775725i 2.45815 0.0535301i
\(211\) 4.37618 + 3.48989i 0.301268 + 0.240254i 0.762442 0.647056i \(-0.224000\pi\)
−0.461174 + 0.887310i \(0.652572\pi\)
\(212\) −4.55559 6.68182i −0.312879 0.458910i
\(213\) −4.41220 1.62172i −0.302319 0.111118i
\(214\) 16.7501i 1.14501i
\(215\) 10.0135 + 3.27943i 0.682912 + 0.223656i
\(216\) −31.9240 + 29.0628i −2.17215 + 1.97747i
\(217\) 2.67329 + 5.55114i 0.181475 + 0.376836i
\(218\) 15.7794 10.7582i 1.06871 0.728637i
\(219\) 0.624955 + 6.45119i 0.0422305 + 0.435931i
\(220\) 3.39904 3.66329i 0.229163 0.246979i
\(221\) −3.57916 2.06643i −0.240760 0.139003i
\(222\) 38.0611 + 10.8387i 2.55450 + 0.727443i
\(223\) 12.8381 + 2.93020i 0.859700 + 0.196221i 0.629575 0.776940i \(-0.283229\pi\)
0.230125 + 0.973161i \(0.426086\pi\)
\(224\) 67.9541 + 26.6700i 4.54038 + 1.78197i
\(225\) 2.35376 6.86166i 0.156917 0.457444i
\(226\) 20.6179 + 25.8540i 1.37148 + 1.71978i
\(227\) −1.71614 + 22.9002i −0.113904 + 1.51994i 0.588694 + 0.808356i \(0.299642\pi\)
−0.702598 + 0.711587i \(0.747977\pi\)
\(228\) 4.77748 8.70730i 0.316397 0.576655i
\(229\) −14.1045 9.61632i −0.932055 0.635464i −0.000865179 1.00000i \(-0.500275\pi\)
−0.931189 + 0.364536i \(0.881228\pi\)
\(230\) −1.30813 + 8.67885i −0.0862553 + 0.572266i
\(231\) 2.75582 4.23741i 0.181320 0.278801i
\(232\) −10.6291 + 9.86237i −0.697835 + 0.647497i
\(233\) 0.327122 + 4.36514i 0.0214305 + 0.285970i 0.997615 + 0.0690269i \(0.0219894\pi\)
−0.976184 + 0.216943i \(0.930392\pi\)
\(234\) −10.6997 + 3.81795i −0.699460 + 0.249588i
\(235\) −2.77948 18.4406i −0.181313 1.20293i
\(236\) 17.5391 36.4202i 1.14170 2.37076i
\(237\) −3.97079 11.9433i −0.257931 0.775804i
\(238\) −36.8525 + 5.55462i −2.38879 + 0.360053i
\(239\) −8.92097 + 3.50122i −0.577049 + 0.226475i −0.635874 0.771793i \(-0.719360\pi\)
0.0588243 + 0.998268i \(0.481265\pi\)
\(240\) −22.0517 + 24.8291i −1.42343 + 1.60271i
\(241\) −8.12170 8.75311i −0.523165 0.563837i 0.415091 0.909780i \(-0.363750\pi\)
−0.938256 + 0.345942i \(0.887559\pi\)
\(242\) 6.30955 + 27.6439i 0.405593 + 1.77702i
\(243\) −8.24951 13.2267i −0.529206 0.848493i
\(244\) −10.1710 + 14.9181i −0.651132 + 0.955036i
\(245\) 24.6228 7.59511i 1.57309 0.485234i
\(246\) −21.5223 25.8145i −1.37221 1.64587i
\(247\) 1.24435 0.992338i 0.0791763 0.0631410i
\(248\) −10.1917 3.14373i −0.647176 0.199627i
\(249\) −10.0598 24.0769i −0.637512 1.52581i
\(250\) 7.07484 30.9969i 0.447452 1.96042i
\(251\) 10.0497 5.80220i 0.634332 0.366232i −0.148096 0.988973i \(-0.547314\pi\)
0.782428 + 0.622741i \(0.213981\pi\)
\(252\) −38.7987 + 62.5986i −2.44409 + 3.94334i
\(253\) 0.912747 + 0.846905i 0.0573839 + 0.0532445i
\(254\) −26.4543 + 33.1726i −1.65989 + 2.08143i
\(255\) 1.63047 7.93627i 0.102104 0.496988i
\(256\) −3.88288 + 1.86990i −0.242680 + 0.116869i
\(257\) −24.2753 −1.51425 −0.757124 0.653271i \(-0.773396\pi\)
−0.757124 + 0.653271i \(0.773396\pi\)
\(258\) −23.6011 + 18.9948i −1.46934 + 1.18256i
\(259\) 41.1126 2.55461
\(260\) −10.5125 + 5.06257i −0.651959 + 0.313967i
\(261\) −2.81271 4.41591i −0.174102 0.273338i
\(262\) 12.5752 15.7688i 0.776899 0.974201i
\(263\) 8.94557 + 8.30028i 0.551608 + 0.511817i 0.905999 0.423280i \(-0.139121\pi\)
−0.354391 + 0.935097i \(0.615312\pi\)
\(264\) 2.13232 + 8.48622i 0.131235 + 0.522291i
\(265\) 2.20021 1.27029i 0.135158 0.0780333i
\(266\) 3.19371 13.9926i 0.195819 0.857939i
\(267\) 11.3857 4.75717i 0.696796 0.291134i
\(268\) 26.2337 + 8.09201i 1.60248 + 0.494298i
\(269\) 6.66741 5.31709i 0.406519 0.324188i −0.398791 0.917042i \(-0.630570\pi\)
0.805310 + 0.592853i \(0.201999\pi\)
\(270\) −13.7200 17.5430i −0.834973 1.06763i
\(271\) −15.6325 + 4.82199i −0.949607 + 0.292915i −0.730598 0.682808i \(-0.760759\pi\)
−0.219009 + 0.975723i \(0.570282\pi\)
\(272\) 19.5668 28.6992i 1.18641 1.74015i
\(273\) −9.60425 + 6.85905i −0.581276 + 0.415129i
\(274\) 11.0895 + 48.5863i 0.669941 + 2.93521i
\(275\) −1.00004 1.07778i −0.0603044 0.0649927i
\(276\) −13.5642 12.0470i −0.816470 0.725142i
\(277\) −9.62817 + 3.77878i −0.578501 + 0.227045i −0.636506 0.771271i \(-0.719621\pi\)
0.0580057 + 0.998316i \(0.481526\pi\)
\(278\) −8.88069 + 1.33855i −0.532628 + 0.0802808i
\(279\) 1.77856 3.41585i 0.106479 0.204502i
\(280\) −27.8015 + 57.7304i −1.66146 + 3.45005i
\(281\) −3.56553 23.6557i −0.212702 1.41118i −0.799118 0.601174i \(-0.794700\pi\)
0.586417 0.810010i \(-0.300538\pi\)
\(282\) 48.8045 + 22.2073i 2.90627 + 1.32243i
\(283\) −2.30912 30.8130i −0.137263 1.83164i −0.463201 0.886254i \(-0.653299\pi\)
0.325938 0.945391i \(-0.394320\pi\)
\(284\) 10.1760 9.44193i 0.603833 0.560275i
\(285\) 2.61563 + 1.70109i 0.154937 + 0.100764i
\(286\) −0.343175 + 2.27682i −0.0202924 + 0.134631i
\(287\) −28.8489 19.6688i −1.70290 1.16101i
\(288\) −12.0803 44.0009i −0.711841 2.59278i
\(289\) 0.637107 8.50160i 0.0374769 0.500094i
\(290\) −4.66371 5.84811i −0.273863 0.343413i
\(291\) 2.01043 + 3.95220i 0.117853 + 0.231682i
\(292\) −17.8168 6.99257i −1.04265 0.409209i
\(293\) 26.4755 + 6.04286i 1.54671 + 0.353028i 0.908851 0.417121i \(-0.136961\pi\)
0.637864 + 0.770149i \(0.279818\pi\)
\(294\) −20.2910 + 71.2541i −1.18340 + 4.15562i
\(295\) 10.9978 + 6.34960i 0.640318 + 0.369688i
\(296\) −48.4068 + 52.1701i −2.81359 + 3.03232i
\(297\) −3.15273 + 0.206228i −0.182940 + 0.0119665i
\(298\) 29.8400 20.3446i 1.72859 1.17853i
\(299\) −1.26139 2.61930i −0.0729481 0.151478i
\(300\) 14.9090 + 15.3824i 0.860769 + 0.888101i
\(301\) −18.1765 + 25.6938i −1.04767 + 1.48096i
\(302\) 41.6529i 2.39685i
\(303\) −1.42701 + 3.88245i −0.0819794 + 0.223041i
\(304\) 7.53528 + 11.0522i 0.432178 + 0.633889i
\(305\) −4.43471 3.53656i −0.253931 0.202503i
\(306\) 16.5730 + 16.3705i 0.947413 + 0.935837i
\(307\) 3.97263 6.88080i 0.226730 0.392708i −0.730107 0.683333i \(-0.760530\pi\)
0.956837 + 0.290625i \(0.0938631\pi\)
\(308\) 7.46341 + 12.9270i 0.425267 + 0.736584i
\(309\) 4.64122 2.81608i 0.264030 0.160201i
\(310\) 2.01013 5.12172i 0.114167 0.290894i
\(311\) −7.91332 + 25.6543i −0.448723 + 1.45472i 0.395367 + 0.918523i \(0.370617\pi\)
−0.844090 + 0.536201i \(0.819859\pi\)
\(312\) 2.60439 20.2633i 0.147445 1.14719i
\(313\) −16.7782 1.25735i −0.948361 0.0710698i −0.408439 0.912785i \(-0.633927\pi\)
−0.539921 + 0.841716i \(0.681546\pi\)
\(314\) −2.81156 9.11485i −0.158666 0.514381i
\(315\) −18.6998 13.6243i −1.05361 0.767643i
\(316\) 36.7523 + 5.53952i 2.06748 + 0.311622i
\(317\) 1.94923 0.444900i 0.109480 0.0249881i −0.167430 0.985884i \(-0.553547\pi\)
0.276910 + 0.960896i \(0.410690\pi\)
\(318\) −0.387162 + 7.29442i −0.0217109 + 0.409050i
\(319\) −1.05819 + 0.0793001i −0.0592470 + 0.00443995i
\(320\) −9.80731 24.9886i −0.548245 1.39691i
\(321\) −6.59475 + 8.64935i −0.368083 + 0.482760i
\(322\) −23.6200 11.3748i −1.31629 0.633893i
\(323\) −2.94040 1.41602i −0.163608 0.0787896i
\(324\) 45.8590 4.00410i 2.54772 0.222450i
\(325\) 1.25417 + 3.19556i 0.0695686 + 0.177258i
\(326\) −4.66127 + 0.349314i −0.258164 + 0.0193467i
\(327\) −12.3837 0.657285i −0.684822 0.0363479i
\(328\) 58.9261 13.4495i 3.25365 0.742624i
\(329\) 55.0815 + 8.30221i 3.03674 + 0.457715i
\(330\) −4.44775 + 0.769773i −0.244840 + 0.0423746i
\(331\) 7.08562 + 22.9710i 0.389461 + 1.26260i 0.912072 + 0.410030i \(0.134482\pi\)
−0.522612 + 0.852571i \(0.675042\pi\)
\(332\) 76.8412 + 5.75845i 4.21721 + 0.316036i
\(333\) −15.3865 20.5820i −0.843176 1.12789i
\(334\) 7.71174 25.0009i 0.421968 1.36799i
\(335\) −3.15091 + 8.02840i −0.172153 + 0.438638i
\(336\) −51.4538 84.8016i −2.80704 4.62630i
\(337\) −1.88253 3.26064i −0.102548 0.177618i 0.810186 0.586173i \(-0.199366\pi\)
−0.912734 + 0.408555i \(0.866033\pi\)
\(338\) −14.6498 + 25.3742i −0.796845 + 1.38018i
\(339\) −0.467498 21.4679i −0.0253910 1.16598i
\(340\) 18.7058 + 14.9174i 1.01447 + 0.809009i
\(341\) −0.439699 0.644920i −0.0238110 0.0349244i
\(342\) −8.20029 + 3.63791i −0.443421 + 0.196716i
\(343\) 43.3696i 2.34174i
\(344\) −11.2029 53.3174i −0.604022 2.87468i
\(345\) 4.09247 3.96652i 0.220331 0.213550i
\(346\) −8.31277 17.2616i −0.446897 0.927991i
\(347\) 10.9567 7.47017i 0.588188 0.401020i −0.232333 0.972636i \(-0.574636\pi\)
0.820521 + 0.571616i \(0.193683\pi\)
\(348\) 15.3890 1.49079i 0.824935 0.0799150i
\(349\) −5.66558 + 6.10604i −0.303271 + 0.326849i −0.866239 0.499630i \(-0.833469\pi\)
0.562967 + 0.826479i \(0.309660\pi\)
\(350\) 26.8091 + 15.4782i 1.43301 + 0.827346i
\(351\) 7.02824 + 2.24111i 0.375140 + 0.119622i
\(352\) −9.01623 2.05790i −0.480567 0.109686i
\(353\) −16.8156 6.59965i −0.895006 0.351264i −0.127148 0.991884i \(-0.540582\pi\)
−0.767858 + 0.640620i \(0.778677\pi\)
\(354\) −32.5442 + 16.5548i −1.72970 + 0.879876i
\(355\) 2.71903 + 3.40956i 0.144311 + 0.180960i
\(356\) −2.72312 + 36.3375i −0.144325 + 1.92589i
\(357\) 21.2167 + 11.6411i 1.12291 + 0.616111i
\(358\) −37.4073 25.5039i −1.97704 1.34792i
\(359\) −3.92886 + 26.0663i −0.207357 + 1.37572i 0.606696 + 0.794934i \(0.292495\pi\)
−0.814053 + 0.580790i \(0.802744\pi\)
\(360\) 39.3061 7.68765i 2.07161 0.405175i
\(361\) −13.0067 + 12.0684i −0.684561 + 0.635180i
\(362\) −2.27904 30.4117i −0.119784 1.59841i
\(363\) 7.62570 16.7588i 0.400245 0.879610i
\(364\) −5.19442 34.4627i −0.272262 1.80634i
\(365\) 2.60889 5.41741i 0.136555 0.283560i
\(366\) 15.4758 5.14524i 0.808936 0.268946i
\(367\) 13.7045 2.06562i 0.715370 0.107825i 0.218735 0.975784i \(-0.429807\pi\)
0.496635 + 0.867960i \(0.334569\pi\)
\(368\) 22.7447 8.92664i 1.18565 0.465333i
\(369\) 0.950066 + 21.8036i 0.0494585 + 1.13505i
\(370\) −24.9716 26.9130i −1.29821 1.39914i
\(371\) 1.68863 + 7.39836i 0.0876692 + 0.384104i
\(372\) 6.60947 + 9.25478i 0.342685 + 0.479838i
\(373\) 6.69416 9.81852i 0.346610 0.508384i −0.612861 0.790191i \(-0.709981\pi\)
0.959471 + 0.281807i \(0.0909338\pi\)
\(374\) 4.51166 1.39166i 0.233292 0.0719612i
\(375\) −15.8572 + 13.2206i −0.818862 + 0.682709i
\(376\) −75.3892 + 60.1208i −3.88790 + 3.10050i
\(377\) 2.36757 + 0.730297i 0.121936 + 0.0376122i
\(378\) 62.1517 23.7152i 3.19674 1.21978i
\(379\) 0.474584 2.07929i 0.0243777 0.106806i −0.961275 0.275590i \(-0.911127\pi\)
0.985653 + 0.168784i \(0.0539840\pi\)
\(380\) −7.97947 + 4.60695i −0.409338 + 0.236332i
\(381\) 26.7209 6.71412i 1.36895 0.343975i
\(382\) −24.0331 22.2995i −1.22964 1.14094i
\(383\) −6.12874 + 7.68519i −0.313164 + 0.392695i −0.913357 0.407160i \(-0.866519\pi\)
0.600193 + 0.799855i \(0.295090\pi\)
\(384\) 23.9937 + 4.92940i 1.22442 + 0.251552i
\(385\) −4.22494 + 2.03462i −0.215323 + 0.103694i
\(386\) 53.6593 2.73118
\(387\) 19.6655 0.516373i 0.999655 0.0262487i
\(388\) −13.0942 −0.664760
\(389\) −23.7420 + 11.4336i −1.20377 + 0.579705i −0.924748 0.380580i \(-0.875724\pi\)
−0.279021 + 0.960285i \(0.590010\pi\)
\(390\) 10.3236 + 2.12094i 0.522757 + 0.107398i
\(391\) −3.71682 + 4.66075i −0.187968 + 0.235704i
\(392\) −97.6674 90.6221i −4.93295 4.57711i
\(393\) −12.7019 + 3.19160i −0.640728 + 0.160995i
\(394\) −44.9894 + 25.9747i −2.26654 + 1.30858i
\(395\) −2.59823 + 11.3836i −0.130731 + 0.572769i
\(396\) 3.67838 8.57434i 0.184846 0.430877i
\(397\) −21.1164 6.51355i −1.05980 0.326906i −0.284618 0.958641i \(-0.591867\pi\)
−0.775184 + 0.631735i \(0.782343\pi\)
\(398\) −52.4542 + 41.8309i −2.62929 + 2.09679i
\(399\) −7.15822 + 5.96802i −0.358359 + 0.298775i
\(400\) −27.5698 + 8.50417i −1.37849 + 0.425209i
\(401\) −7.33893 + 10.7642i −0.366489 + 0.537540i −0.964547 0.263913i \(-0.914987\pi\)
0.598058 + 0.801453i \(0.295939\pi\)
\(402\) −14.4116 20.1796i −0.718788 1.00647i
\(403\) 0.405538 + 1.77678i 0.0202013 + 0.0885076i
\(404\) −8.30829 8.95420i −0.413353 0.445488i
\(405\) 0.177768 + 14.4605i 0.00883334 + 0.718549i
\(406\) 20.7981 8.16265i 1.03219 0.405106i
\(407\) −5.15021 + 0.776269i −0.255286 + 0.0384782i
\(408\) −39.7529 + 13.2166i −1.96806 + 0.654320i
\(409\) 4.49472 9.33338i 0.222250 0.461506i −0.759793 0.650165i \(-0.774700\pi\)
0.982043 + 0.188659i \(0.0604141\pi\)
\(410\) 4.64713 + 30.8317i 0.229505 + 1.52267i
\(411\) 13.4027 29.4549i 0.661109 1.45290i
\(412\) 1.19802 + 15.9865i 0.0590223 + 0.787598i
\(413\) −27.8062 + 25.8004i −1.36825 + 1.26955i
\(414\) 3.14535 + 16.0818i 0.154586 + 0.790379i
\(415\) −3.60797 + 23.9373i −0.177108 + 1.17504i
\(416\) 17.8410 + 12.1638i 0.874725 + 0.596378i
\(417\) 5.11278 + 2.80526i 0.250374 + 0.137374i
\(418\) −0.135878 + 1.81316i −0.00664599 + 0.0886846i
\(419\) 13.6549 + 17.1227i 0.667086 + 0.836500i 0.994094 0.108522i \(-0.0346117\pi\)
−0.327008 + 0.945022i \(0.606040\pi\)
\(420\) 60.8974 30.9776i 2.97149 1.51155i
\(421\) 17.2489 + 6.76971i 0.840662 + 0.329935i 0.746306 0.665603i \(-0.231826\pi\)
0.0943557 + 0.995539i \(0.469921\pi\)
\(422\) 14.5558 + 3.32227i 0.708566 + 0.161726i
\(423\) −16.4581 30.6823i −0.800222 1.49183i
\(424\) −11.3764 6.56817i −0.552487 0.318979i
\(425\) 4.78787 5.16010i 0.232246 0.250301i
\(426\) −12.4803 + 1.20902i −0.604672 + 0.0585772i
\(427\) 13.9987 9.54416i 0.677445 0.461874i
\(428\) −13.9361 28.9385i −0.673624 1.39880i
\(429\) 1.07362 1.04058i 0.0518350 0.0502397i
\(430\) 27.8598 3.70766i 1.34352 0.178799i
\(431\) 15.5240i 0.747767i −0.927476 0.373883i \(-0.878026\pi\)
0.927476 0.373883i \(-0.121974\pi\)
\(432\) −23.1971 + 57.4963i −1.11607 + 2.76629i
\(433\) −0.0879925 0.129061i −0.00422865 0.00620229i 0.824119 0.566417i \(-0.191671\pi\)
−0.828347 + 0.560215i \(0.810719\pi\)
\(434\) 12.8490 + 10.2467i 0.616770 + 0.491858i
\(435\) 0.105747 + 4.85599i 0.00507017 + 0.232827i
\(436\) 18.3106 31.7149i 0.876920 1.51887i
\(437\) −1.14787 1.98817i −0.0549100 0.0951069i
\(438\) 8.96802 + 14.7803i 0.428509 + 0.706230i
\(439\) 9.74795 24.8374i 0.465244 1.18542i −0.485166 0.874422i \(-0.661241\pi\)
0.950410 0.311000i \(-0.100664\pi\)
\(440\) 2.39267 7.75686i 0.114066 0.369794i
\(441\) 38.5315 28.8050i 1.83483 1.37167i
\(442\) −10.9930 0.823813i −0.522884 0.0391848i
\(443\) −7.67778 24.8908i −0.364782 1.18260i −0.933049 0.359751i \(-0.882862\pi\)
0.568266 0.822845i \(-0.307614\pi\)
\(444\) 74.7745 12.9412i 3.54864 0.614165i
\(445\) −11.3197 1.70618i −0.536608 0.0808806i
\(446\) 34.2438 7.81592i 1.62149 0.370094i
\(447\) −23.4186 1.24298i −1.10766 0.0587908i
\(448\) 79.9587 5.99208i 3.77769 0.283099i
\(449\) 12.0976 + 30.8242i 0.570921 + 1.45468i 0.866408 + 0.499336i \(0.166423\pi\)
−0.295487 + 0.955347i \(0.595482\pi\)
\(450\) −2.28459 19.2141i −0.107696 0.905760i
\(451\) 3.98530 + 1.91922i 0.187660 + 0.0903725i
\(452\) 57.1312 + 27.5129i 2.68722 + 1.29410i
\(453\) −16.3993 + 21.5085i −0.770507 + 1.01056i
\(454\) 22.3788 + 57.0202i 1.05029 + 2.67609i
\(455\) 10.9183 0.818213i 0.511858 0.0383584i
\(456\) 0.855079 16.1103i 0.0400427 0.754435i
\(457\) 2.16465 0.494067i 0.101258 0.0231115i −0.171592 0.985168i \(-0.554891\pi\)
0.272850 + 0.962057i \(0.412034\pi\)
\(458\) −45.0254 6.78649i −2.10390 0.317112i
\(459\) −2.11259 14.9783i −0.0986074 0.699128i
\(460\) 4.96078 + 16.0825i 0.231298 + 0.749849i
\(461\) 5.50374 + 0.412448i 0.256335 + 0.0192096i 0.202278 0.979328i \(-0.435166\pi\)
0.0540571 + 0.998538i \(0.482785\pi\)
\(462\) 1.71877 13.3728i 0.0799642 0.622157i
\(463\) 3.09704 10.0404i 0.143932 0.466615i −0.854688 0.519142i \(-0.826251\pi\)
0.998619 + 0.0525271i \(0.0167276\pi\)
\(464\) −7.60765 + 19.3840i −0.353176 + 0.899879i
\(465\) −3.05447 + 1.85332i −0.141648 + 0.0859455i
\(466\) 5.83803 + 10.1118i 0.270441 + 0.468418i
\(467\) −4.77930 + 8.27798i −0.221159 + 0.383059i −0.955160 0.296089i \(-0.904317\pi\)
0.734001 + 0.679149i \(0.237651\pi\)
\(468\) −15.3089 + 15.4982i −0.707654 + 0.716406i
\(469\) −20.1410 16.0619i −0.930026 0.741671i
\(470\) −28.0215 41.1000i −1.29254 1.89580i
\(471\) −2.13682 + 5.81364i −0.0984596 + 0.267878i
\(472\) 65.6626i 3.02237i
\(473\) 1.79184 3.56187i 0.0823889 0.163775i
\(474\) −23.3650 24.1069i −1.07319 1.10727i
\(475\) 1.17619 + 2.44238i 0.0539671 + 0.112064i
\(476\) −59.0472 + 40.2577i −2.70642 + 1.84521i
\(477\) 3.07183 3.61423i 0.140650 0.165484i
\(478\) −17.3869 + 18.7386i −0.795259 + 0.857085i
\(479\) −4.51035 2.60405i −0.206083 0.118982i 0.393407 0.919365i \(-0.371297\pi\)
−0.599490 + 0.800382i \(0.704630\pi\)
\(480\) −11.5936 + 40.7121i −0.529172 + 1.85825i
\(481\) 11.8559 + 2.70604i 0.540584 + 0.123385i
\(482\) −29.6484 11.6361i −1.35045 0.530011i
\(483\) 7.71839 + 15.1732i 0.351199 + 0.690404i
\(484\) 33.9004 + 42.5098i 1.54093 + 1.93226i
\(485\) 0.307411 4.10211i 0.0139588 0.186267i
\(486\) −35.1329 22.2392i −1.59366 1.00879i
\(487\) 22.4759 + 15.3238i 1.01848 + 0.694390i 0.952846 0.303454i \(-0.0981399\pi\)
0.0656364 + 0.997844i \(0.479092\pi\)
\(488\) −4.37123 + 29.0012i −0.197876 + 1.31282i
\(489\) 2.54450 + 1.65483i 0.115066 + 0.0748339i
\(490\) 50.3837 46.7492i 2.27610 2.11191i
\(491\) 1.66863 + 22.2663i 0.0753040 + 1.00486i 0.899034 + 0.437879i \(0.144270\pi\)
−0.823730 + 0.566983i \(0.808111\pi\)
\(492\) −58.6608 26.6922i −2.64463 1.20338i
\(493\) −0.757206 5.02373i −0.0341028 0.226258i
\(494\) 1.84198 3.82492i 0.0828748 0.172091i
\(495\) 2.59978 + 1.35365i 0.116851 + 0.0608419i
\(496\) −15.1459 + 2.28288i −0.680073 + 0.102504i
\(497\) −12.1257 + 4.75897i −0.543911 + 0.213469i
\(498\) −52.0405 46.2194i −2.33199 2.07114i
\(499\) 11.4122 + 12.2995i 0.510882 + 0.550600i 0.934834 0.355085i \(-0.115548\pi\)
−0.423952 + 0.905685i \(0.639358\pi\)
\(500\) −13.5664 59.4384i −0.606709 2.65817i
\(501\) −13.8253 + 9.87362i −0.617671 + 0.441121i
\(502\) 17.4365 25.5747i 0.778231 1.14146i
\(503\) 16.3545 5.04469i 0.729210 0.224932i 0.0921494 0.995745i \(-0.470626\pi\)
0.637061 + 0.770814i \(0.280150\pi\)
\(504\) −12.6634 + 118.958i −0.564075 + 5.29883i
\(505\) 3.00019 2.39257i 0.133507 0.106468i
\(506\) 3.17367 + 0.978947i 0.141087 + 0.0435195i
\(507\) 17.5550 7.33480i 0.779645 0.325750i
\(508\) −18.1045 + 79.3209i −0.803257 + 3.51930i
\(509\) −11.3994 + 6.58142i −0.505267 + 0.291716i −0.730886 0.682499i \(-0.760893\pi\)
0.225619 + 0.974216i \(0.427560\pi\)
\(510\) −5.26647 20.9595i −0.233203 0.928103i
\(511\) 13.1658 + 12.2161i 0.582420 + 0.540407i
\(512\) 10.4676 13.1259i 0.462606 0.580089i
\(513\) 5.66673 + 1.35004i 0.250192 + 0.0596057i
\(514\) −58.3386 + 28.0944i −2.57320 + 1.23919i
\(515\) −5.03631 −0.221926
\(516\) −24.9711 + 52.4526i −1.09929 + 2.30910i
\(517\) −7.05686 −0.310360
\(518\) 98.8023 47.5807i 4.34112 2.09058i
\(519\) −2.50363 + 12.1863i −0.109897 + 0.534921i
\(520\) −11.8171 + 14.8182i −0.518215 + 0.649821i
\(521\) −18.7336 17.3822i −0.820733 0.761529i 0.153241 0.988189i \(-0.451029\pi\)
−0.973974 + 0.226660i \(0.927219\pi\)
\(522\) −11.8702 7.35716i −0.519544 0.322014i
\(523\) 24.7141 14.2687i 1.08067 0.623927i 0.149595 0.988747i \(-0.452203\pi\)
0.931078 + 0.364821i \(0.118870\pi\)
\(524\) 8.60609 37.7057i 0.375959 1.64718i
\(525\) −7.74957 18.5477i −0.338219 0.809488i
\(526\) 31.1042 + 9.59438i 1.35621 + 0.418335i
\(527\) 2.92173 2.33000i 0.127273 0.101496i
\(528\) 8.04684 + 9.65162i 0.350194 + 0.420033i
\(529\) 17.9711 5.54334i 0.781351 0.241015i
\(530\) 3.81742 5.59913i 0.165818 0.243211i
\(531\) 23.3229 + 4.26461i 1.01213 + 0.185068i
\(532\) −6.12413 26.8316i −0.265515 1.16330i
\(533\) −7.02474 7.57087i −0.304275 0.327931i
\(534\) 21.8567 24.6095i 0.945834 1.06496i
\(535\) 9.39292 3.68645i 0.406091 0.159379i
\(536\) 44.0963 6.64645i 1.90467 0.287083i
\(537\) 9.27500 + 27.8973i 0.400246 + 1.20386i
\(538\) 9.86961 20.4944i 0.425509 0.883578i
\(539\) −1.45325 9.64168i −0.0625959 0.415296i
\(540\) −38.2992 18.8933i −1.64814 0.813038i
\(541\) 1.98887 + 26.5396i 0.0855080 + 1.14102i 0.860636 + 0.509221i \(0.170066\pi\)
−0.775128 + 0.631804i \(0.782315\pi\)
\(542\) −31.9876 + 29.6802i −1.37399 + 1.27487i
\(543\) −10.7967 + 16.6012i −0.463330 + 0.712425i
\(544\) 6.59916 43.7826i 0.282937 1.87716i
\(545\) 9.50565 + 6.48084i 0.407177 + 0.277609i
\(546\) −15.1429 + 27.5990i −0.648056 + 1.18113i
\(547\) 1.35283 18.0523i 0.0578428 0.771859i −0.890575 0.454836i \(-0.849698\pi\)
0.948418 0.317023i \(-0.102683\pi\)
\(548\) 59.5826 + 74.7142i 2.54524 + 3.19163i
\(549\) −10.0171 3.43618i −0.427520 0.146652i
\(550\) −3.65064 1.43277i −0.155664 0.0610936i
\(551\) 1.90747 + 0.435367i 0.0812608 + 0.0185472i
\(552\) −28.3419 8.07091i −1.20631 0.343521i
\(553\) −30.2042 17.4384i −1.28441 0.741555i
\(554\) −18.7652 + 20.2241i −0.797259 + 0.859241i
\(555\) 2.29872 + 23.7289i 0.0975752 + 1.00723i
\(556\) −14.2292 + 9.70127i −0.603450 + 0.411426i
\(557\) 8.32558 + 17.2883i 0.352766 + 0.732527i 0.999545 0.0301506i \(-0.00959869\pi\)
−0.646779 + 0.762677i \(0.723884\pi\)
\(558\) 0.320997 10.2674i 0.0135889 0.434653i
\(559\) −6.93283 + 6.21310i −0.293228 + 0.262786i
\(560\) 92.0205i 3.88858i
\(561\) −2.87763 1.05768i −0.121494 0.0446554i
\(562\) −35.9461 52.7233i −1.51630 2.22400i
\(563\) 21.3513 + 17.0271i 0.899851 + 0.717607i 0.959827 0.280592i \(-0.0905309\pi\)
−0.0599758 + 0.998200i \(0.519102\pi\)
\(564\) 102.794 2.23850i 4.32841 0.0942580i
\(565\) −9.96040 + 17.2519i −0.419037 + 0.725793i
\(566\) −41.2100 71.3778i −1.73219 3.00023i
\(567\) −41.4306 12.2240i −1.73992 0.513359i
\(568\) 8.23806 20.9902i 0.345661 0.880731i
\(569\) 9.53563 30.9137i 0.399754 1.29597i −0.502429 0.864619i \(-0.667560\pi\)
0.902183 0.431353i \(-0.141964\pi\)
\(570\) 8.25463 + 1.06095i 0.345748 + 0.0444381i
\(571\) −19.7112 1.47715i −0.824889 0.0618169i −0.344406 0.938821i \(-0.611920\pi\)
−0.480483 + 0.877004i \(0.659539\pi\)
\(572\) 1.30142 + 4.21909i 0.0544150 + 0.176409i
\(573\) 3.63051 + 20.9771i 0.151667 + 0.876331i
\(574\) −92.0932 13.8808i −3.84390 0.579374i
\(575\) 4.82748 1.10184i 0.201320 0.0459500i
\(576\) −32.9246 37.7868i −1.37186 1.57445i
\(577\) 23.8118 1.78445i 0.991300 0.0742877i 0.430805 0.902445i \(-0.358230\pi\)
0.560495 + 0.828158i \(0.310611\pi\)
\(578\) −8.30802 21.1685i −0.345568 0.880493i
\(579\) −27.7083 21.1264i −1.15152 0.877983i
\(580\) −12.9229 6.22336i −0.536596 0.258411i
\(581\) −65.1469 31.3731i −2.70275 1.30157i
\(582\) 9.40546 + 7.17124i 0.389869 + 0.297258i
\(583\) −0.351228 0.894914i −0.0145464 0.0370635i
\(584\) −31.0033 + 2.32337i −1.28292 + 0.0961419i
\(585\) −4.49582 5.15976i −0.185879 0.213330i
\(586\) 70.6198 16.1185i 2.91728 0.665849i
\(587\) 13.0905 + 1.97307i 0.540302 + 0.0814374i 0.413523 0.910494i \(-0.364298\pi\)
0.126779 + 0.991931i \(0.459536\pi\)
\(588\) 24.2273 + 139.985i 0.999115 + 5.77288i
\(589\) 0.424197 + 1.37521i 0.0174787 + 0.0566647i
\(590\) 33.7787 + 2.53136i 1.39065 + 0.104214i
\(591\) 33.4580 + 4.30027i 1.37628 + 0.176890i
\(592\) −30.1258 + 97.6653i −1.23816 + 4.01402i
\(593\) 4.36051 11.1104i 0.179065 0.456250i −0.812956 0.582325i \(-0.802143\pi\)
0.992021 + 0.126076i \(0.0402382\pi\)
\(594\) −7.33800 + 4.14434i −0.301082 + 0.170044i
\(595\) −11.2255 19.4432i −0.460202 0.797094i
\(596\) 34.6268 59.9754i 1.41837 2.45669i
\(597\) 43.5555 0.948489i 1.78261 0.0388191i
\(598\) −6.06277 4.83490i −0.247925 0.197714i
\(599\) 22.5917 + 33.1360i 0.923072 + 1.35390i 0.935256 + 0.353973i \(0.115169\pi\)
−0.0121835 + 0.999926i \(0.503878\pi\)
\(600\) 32.6607 + 12.0045i 1.33337 + 0.490083i
\(601\) 5.41526i 0.220893i −0.993882 0.110446i \(-0.964772\pi\)
0.993882 0.110446i \(-0.0352281\pi\)
\(602\) −13.9458 + 82.7836i −0.568389 + 3.37401i
\(603\) −0.503169 + 16.0943i −0.0204906 + 0.655412i
\(604\) −34.6551 71.9620i −1.41010 2.92809i
\(605\) −14.1132 + 9.62220i −0.573782 + 0.391198i
\(606\) 1.06386 + 10.9819i 0.0432163 + 0.446107i
\(607\) 11.0591 11.9189i 0.448877 0.483774i −0.467555 0.883964i \(-0.654865\pi\)
0.916432 + 0.400189i \(0.131056\pi\)
\(608\) 14.7669 + 8.52568i 0.598877 + 0.345762i
\(609\) −13.9534 3.97350i −0.565420 0.161014i
\(610\) −14.7505 3.36671i −0.597230 0.136314i
\(611\) 15.3378 + 6.01964i 0.620500 + 0.243528i
\(612\) 42.2526 + 14.4940i 1.70796 + 0.585884i
\(613\) −23.4657 29.4251i −0.947771 1.18847i −0.981967 0.189052i \(-0.939458\pi\)
0.0341958 0.999415i \(-0.489113\pi\)
\(614\) 1.58375 21.1337i 0.0639149 0.852885i
\(615\) 9.73920 17.7504i 0.392722 0.715765i
\(616\) 20.0336 + 13.6586i 0.807175 + 0.550322i
\(617\) 0.607729 4.03202i 0.0244663 0.162323i −0.973261 0.229701i \(-0.926225\pi\)
0.997728 + 0.0673779i \(0.0214633\pi\)
\(618\) 7.89470 12.1390i 0.317571 0.488304i
\(619\) −21.0482 + 19.5299i −0.845998 + 0.784971i −0.978508 0.206211i \(-0.933887\pi\)
0.132510 + 0.991182i \(0.457696\pi\)
\(620\) −0.788441 10.5210i −0.0316645 0.422534i
\(621\) 4.70746 9.54264i 0.188904 0.382933i
\(622\) 10.6731 + 70.8111i 0.427951 + 2.83927i
\(623\) 14.8361 30.8074i 0.594394 1.23427i
\(624\) −9.25643 27.8415i −0.370554 1.11455i
\(625\) 6.98393 1.05266i 0.279357 0.0421064i
\(626\) −41.7768 + 16.3962i −1.66973 + 0.655323i
\(627\) 0.784030 0.882775i 0.0313112 0.0352547i
\(628\) −12.4410 13.4082i −0.496448 0.535044i
\(629\) −5.54881 24.3109i −0.221246 0.969340i
\(630\) −60.7073 11.1004i −2.41864 0.442250i
\(631\) −1.06455 + 1.56140i −0.0423789 + 0.0621585i −0.846843 0.531842i \(-0.821500\pi\)
0.804465 + 0.594001i \(0.202452\pi\)
\(632\) 57.6915 17.7955i 2.29484 0.707865i
\(633\) −6.20825 7.44636i −0.246756 0.295966i
\(634\) 4.16952 3.32508i 0.165593 0.132056i
\(635\) −24.4243 7.53390i −0.969249 0.298974i
\(636\) 5.40005 + 12.9244i 0.214126 + 0.512486i
\(637\) −5.06596 + 22.1954i −0.200721 + 0.879415i
\(638\) −2.45127 + 1.41524i −0.0970466 + 0.0560299i
\(639\) 6.92053 + 4.28936i 0.273772 + 0.169684i
\(640\) −16.6580 15.4563i −0.658464 0.610965i
\(641\) 16.9681 21.2773i 0.670198 0.840402i −0.324213 0.945984i \(-0.605099\pi\)
0.994411 + 0.105583i \(0.0336708\pi\)
\(642\) −5.83846 + 28.4185i −0.230426 + 1.12159i
\(643\) −3.06825 + 1.47759i −0.121000 + 0.0582706i −0.493404 0.869800i \(-0.664248\pi\)
0.372404 + 0.928071i \(0.378533\pi\)
\(644\) −50.2712 −1.98096
\(645\) −15.8459 9.05425i −0.623932 0.356511i
\(646\) −8.70520 −0.342502
\(647\) −36.0417 + 17.3568i −1.41695 + 0.682365i −0.976521 0.215424i \(-0.930887\pi\)
−0.440426 + 0.897789i \(0.645173\pi\)
\(648\) 64.2929 38.1809i 2.52566 1.49989i
\(649\) 2.99615 3.75705i 0.117609 0.147477i
\(650\) 6.71234 + 6.22814i 0.263279 + 0.244288i
\(651\) −2.60062 10.3500i −0.101927 0.405647i
\(652\) −7.76246 + 4.48166i −0.304002 + 0.175515i
\(653\) 4.11898 18.0464i 0.161188 0.706212i −0.828142 0.560519i \(-0.810602\pi\)
0.989330 0.145693i \(-0.0465411\pi\)
\(654\) −30.5214 + 12.7524i −1.19348 + 0.498659i
\(655\) 11.6103 + 3.58129i 0.453650 + 0.139933i
\(656\) 67.8638 54.1196i 2.64964 2.11301i
\(657\) 1.18834 11.1630i 0.0463614 0.435511i
\(658\) 141.981 43.7953i 5.53499 1.70732i
\(659\) 15.9668 23.4190i 0.621979 0.912276i −0.377929 0.925835i \(-0.623364\pi\)
0.999908 + 0.0135585i \(0.00431595\pi\)
\(660\) −7.04375 + 5.03042i −0.274178 + 0.195809i
\(661\) −0.527074 2.30926i −0.0205008 0.0898198i 0.963643 0.267195i \(-0.0860967\pi\)
−0.984143 + 0.177375i \(0.943240\pi\)
\(662\) 43.6132 + 47.0038i 1.69507 + 1.82685i
\(663\) 5.35218 + 4.75350i 0.207861 + 0.184611i
\(664\) 116.516 45.7292i 4.52170 1.77464i
\(665\) 8.54947 1.28862i 0.331534 0.0499707i
\(666\) −60.7972 31.6557i −2.35584 1.22663i
\(667\) 1.55061 3.21988i 0.0600400 0.124674i
\(668\) −7.47738 49.6092i −0.289308 1.91944i
\(669\) −20.7599 9.44629i −0.802624 0.365215i
\(670\) 1.71916 + 22.9406i 0.0664169 + 0.886272i
\(671\) −1.57342 + 1.45992i −0.0607412 + 0.0563596i
\(672\) −105.996 68.9350i −4.08888 2.65923i
\(673\) 3.95997 26.2727i 0.152646 1.01274i −0.773016 0.634386i \(-0.781253\pi\)
0.925662 0.378352i \(-0.123509\pi\)
\(674\) −8.29773 5.65730i −0.319617 0.217911i
\(675\) −6.38514 + 10.8212i −0.245764 + 0.416507i
\(676\) −4.19862 + 56.0267i −0.161485 + 2.15487i
\(677\) −15.2345 19.1035i −0.585510 0.734206i 0.397532 0.917588i \(-0.369867\pi\)
−0.983042 + 0.183382i \(0.941295\pi\)
\(678\) −25.9689 51.0509i −0.997328 1.96060i
\(679\) 11.4379 + 4.48903i 0.438945 + 0.172273i
\(680\) 37.8897 + 8.64808i 1.45300 + 0.331639i
\(681\) 10.8938 38.2547i 0.417451 1.46592i
\(682\) −1.80307 1.04100i −0.0690432 0.0398621i
\(683\) 7.03713 7.58422i 0.269268 0.290202i −0.583914 0.811816i \(-0.698479\pi\)
0.853182 + 0.521614i \(0.174670\pi\)
\(684\) −11.1406 + 13.1077i −0.425971 + 0.501185i
\(685\) −24.8050 + 16.9117i −0.947750 + 0.646165i
\(686\) 50.1927 + 104.226i 1.91637 + 3.97938i
\(687\) 20.5781 + 21.2315i 0.785104 + 0.810033i
\(688\) −47.7179 62.0066i −1.81923 2.36398i
\(689\) 2.24466i 0.0855148i
\(690\) 5.24451 14.2687i 0.199655 0.543200i
\(691\) −21.7028 31.8322i −0.825614 1.21095i −0.975007 0.222175i \(-0.928684\pi\)
0.149393 0.988778i \(-0.452268\pi\)
\(692\) −28.7233 22.9061i −1.09190 0.870757i
\(693\) −6.15257 + 6.22867i −0.233717 + 0.236608i
\(694\) 17.6859 30.6329i 0.671348 1.16281i
\(695\) −2.70512 4.68541i −0.102611 0.177728i
\(696\) 21.4712 13.0277i 0.813862 0.493815i
\(697\) −7.73706 + 19.7137i −0.293062 + 0.746710i
\(698\) −6.54890 + 21.2310i −0.247880 + 0.803606i
\(699\) 0.966523 7.51998i 0.0365573 0.284432i
\(700\) 59.1949 + 4.43604i 2.23736 + 0.167667i
\(701\) 8.26097 + 26.7814i 0.312012 + 1.01152i 0.966763 + 0.255674i \(0.0822975\pi\)
−0.654751 + 0.755845i \(0.727226\pi\)
\(702\) 19.4840 2.74810i 0.735377 0.103720i
\(703\) 9.49579 + 1.43126i 0.358140 + 0.0539810i
\(704\) −9.90334 + 2.26037i −0.373246 + 0.0851910i
\(705\) −1.71201 + 32.2555i −0.0644779 + 1.21481i
\(706\) −48.0495 + 3.60081i −1.80837 + 0.135518i
\(707\) 4.18759 + 10.6698i 0.157491 + 0.401279i
\(708\) −42.4518 + 55.6777i −1.59544 + 2.09250i
\(709\) −0.382413 0.184161i −0.0143618 0.00691629i 0.426689 0.904398i \(-0.359680\pi\)
−0.441051 + 0.897482i \(0.645394\pi\)
\(710\) 10.4804 + 5.04708i 0.393321 + 0.189414i
\(711\) 2.57391 + 21.6473i 0.0965290 + 0.811839i
\(712\) 21.6250 + 55.0995i 0.810429 + 2.06494i
\(713\) 2.62142 0.196448i 0.0981728 0.00735703i
\(714\) 64.4607 + 3.42134i 2.41238 + 0.128041i
\(715\) −1.35229 + 0.308652i −0.0505729 + 0.0115429i
\(716\) −85.8463 12.9392i −3.20822 0.483562i
\(717\) 16.3558 2.83071i 0.610820 0.105715i
\(718\) 20.7253 + 67.1897i 0.773460 + 2.50750i
\(719\) −1.89919 0.142325i −0.0708278 0.00530781i 0.0392690 0.999229i \(-0.487497\pi\)
−0.110097 + 0.993921i \(0.535116\pi\)
\(720\) 46.0678 34.4390i 1.71685 1.28346i
\(721\) 4.43409 14.3750i 0.165134 0.535351i
\(722\) −17.2907 + 44.0559i −0.643492 + 1.63959i
\(723\) 10.7284 + 17.6816i 0.398993 + 0.657585i
\(724\) −29.2399 50.6450i −1.08669 1.88221i
\(725\) −2.10999 + 3.65461i −0.0783631 + 0.135729i
\(726\) −1.06924 49.1004i −0.0396831 1.82229i
\(727\) −5.67824 4.52825i −0.210594 0.167943i 0.512512 0.858680i \(-0.328715\pi\)
−0.723106 + 0.690737i \(0.757286\pi\)
\(728\) −31.8910 46.7755i −1.18196 1.73361i
\(729\) 9.38591 + 25.3161i 0.347626 + 0.937633i
\(730\) 16.0385i 0.593612i
\(731\) 17.6466 + 7.28041i 0.652682 + 0.269276i
\(732\) 22.4562 21.7651i 0.830005 0.804461i
\(733\) 19.8910 + 41.3041i 0.734690 + 1.52560i 0.846804 + 0.531905i \(0.178524\pi\)
−0.112114 + 0.993695i \(0.535762\pi\)
\(734\) 30.5442 20.8247i 1.12741 0.768654i
\(735\) −44.4227 + 4.30342i −1.63856 + 0.158734i
\(736\) 21.1848 22.8317i 0.780881 0.841589i
\(737\) 2.82635 + 1.63180i 0.104110 + 0.0601080i
\(738\) 27.5171 + 51.2991i 1.01292 + 1.88835i
\(739\) −47.4534 10.8309i −1.74560 0.398422i −0.773652 0.633611i \(-0.781572\pi\)
−0.971950 + 0.235189i \(0.924429\pi\)
\(740\) −65.5340 25.7202i −2.40908 0.945493i
\(741\) −2.45708 + 1.24988i −0.0902631 + 0.0459156i
\(742\) 12.6204 + 15.8255i 0.463311 + 0.580974i
\(743\) 0.136955 1.82754i 0.00502441 0.0670461i −0.994128 0.108211i \(-0.965488\pi\)
0.999152 + 0.0411648i \(0.0131069\pi\)
\(744\) 16.1957 + 8.88616i 0.593762 + 0.325783i
\(745\) 17.9759 + 12.2558i 0.658587 + 0.449017i
\(746\) 4.72424 31.3433i 0.172967 1.14756i
\(747\) 8.67526 + 44.3556i 0.317411 + 1.62289i
\(748\) 6.63676 6.15801i 0.242664 0.225159i
\(749\) 2.25235 + 30.0555i 0.0822990 + 1.09820i
\(750\) −22.8076 + 50.1238i −0.832818 + 1.83026i
\(751\) −2.25285 14.9467i −0.0822075 0.545411i −0.991587 0.129443i \(-0.958681\pi\)
0.909379 0.415968i \(-0.136557\pi\)
\(752\) −60.0840 + 124.766i −2.19104 + 4.54974i
\(753\) −19.0729 + 6.34116i −0.695056 + 0.231085i
\(754\) 6.53495 0.984986i 0.237989 0.0358711i
\(755\) 23.3576 9.16717i 0.850069 0.333627i
\(756\) 87.6460 92.6819i 3.18765 3.37081i
\(757\) −4.04415 4.35855i −0.146987 0.158414i 0.655267 0.755398i \(-0.272556\pi\)
−0.802254 + 0.596983i \(0.796366\pi\)
\(758\) −1.26589 5.54621i −0.0459791 0.201448i
\(759\) −1.25338 1.75502i −0.0454948 0.0637033i
\(760\) −8.43109 + 12.3661i −0.305828 + 0.448567i
\(761\) −5.09559 + 1.57178i −0.184715 + 0.0569770i −0.385733 0.922611i \(-0.626051\pi\)
0.201018 + 0.979588i \(0.435575\pi\)
\(762\) 56.4455 47.0602i 2.04480 1.70481i
\(763\) −26.8670 + 21.4257i −0.972652 + 0.775664i
\(764\) −60.0742 18.5305i −2.17341 0.670408i
\(765\) −5.53257 + 12.8965i −0.200030 + 0.466273i
\(766\) −5.83438 + 25.5621i −0.210805 + 0.923595i
\(767\) −9.71684 + 5.61002i −0.350855 + 0.202566i
\(768\) 7.23953 1.81907i 0.261234 0.0656400i
\(769\) 31.1460 + 28.8993i 1.12315 + 1.04214i 0.998754 + 0.0499030i \(0.0158912\pi\)
0.124400 + 0.992232i \(0.460299\pi\)
\(770\) −7.79870 + 9.77926i −0.281046 + 0.352420i
\(771\) 41.1858 + 8.46144i 1.48327 + 0.304731i
\(772\) 92.7050 44.6444i 3.33653 1.60679i
\(773\) 40.9009 1.47110 0.735551 0.677469i \(-0.236923\pi\)
0.735551 + 0.677469i \(0.236923\pi\)
\(774\) 46.6628 24.0004i 1.67726 0.862676i
\(775\) −3.10408 −0.111502
\(776\) −19.1635 + 9.22867i −0.687930 + 0.331290i
\(777\) −69.7523 14.3303i −2.50235 0.514097i
\(778\) −43.8248 + 54.9546i −1.57119 + 1.97022i
\(779\) −5.97850 5.54724i −0.214202 0.198750i
\(780\) 19.6003 4.92496i 0.701805 0.176342i
\(781\) 1.42913 0.825111i 0.0511384 0.0295248i
\(782\) −3.53831 + 15.5023i −0.126530 + 0.554362i
\(783\) 3.23286 + 8.47251i 0.115533 + 0.302783i
\(784\) −182.839 56.3983i −6.52996 2.01423i
\(785\) 4.49253 3.58267i 0.160345 0.127871i
\(786\) −26.8317 + 22.3704i −0.957056 + 0.797925i
\(787\) −9.61457 + 2.96570i −0.342722 + 0.105716i −0.461338 0.887224i \(-0.652631\pi\)
0.118616 + 0.992940i \(0.462154\pi\)
\(788\) −56.1156 + 82.3065i −1.99904 + 2.93205i
\(789\) −12.2840 17.2005i −0.437323 0.612353i
\(790\) 6.93041 + 30.3641i 0.246573 + 1.08031i
\(791\) −40.4721 43.6186i −1.43902 1.55090i
\(792\) −0.659755 15.1411i −0.0234434 0.538015i
\(793\) 4.66510 1.83092i 0.165663 0.0650178i
\(794\) −58.2855 + 8.78513i −2.06848 + 0.311773i
\(795\) −4.17568 + 1.38828i −0.148096 + 0.0492374i
\(796\) −55.8200 + 115.911i −1.97849 + 4.10837i
\(797\) −0.350504 2.32544i −0.0124155 0.0823713i 0.981765 0.190099i \(-0.0608808\pi\)
−0.994180 + 0.107727i \(0.965643\pi\)
\(798\) −10.2958 + 22.6268i −0.364467 + 0.800980i
\(799\) −2.52484 33.6916i −0.0893224 1.19192i
\(800\) −26.9600 + 25.0152i −0.953180 + 0.884422i
\(801\) −20.9754 + 4.10245i −0.741129 + 0.144953i
\(802\) −5.17928 + 34.3623i −0.182887 + 1.21337i
\(803\) −1.87994 1.28172i −0.0663418 0.0452311i
\(804\) −41.6878 22.8731i −1.47022 0.806672i
\(805\) 1.18021 15.7488i 0.0415968 0.555071i
\(806\) 3.03090 + 3.80063i 0.106759 + 0.133872i
\(807\) −13.1654 + 6.69704i −0.463443 + 0.235747i
\(808\) −18.4701 7.24896i −0.649774 0.255018i
\(809\) −36.8747 8.41642i −1.29645 0.295906i −0.482014 0.876163i \(-0.660095\pi\)
−0.814433 + 0.580258i \(0.802952\pi\)
\(810\) 17.1627 + 34.5460i 0.603037 + 1.21382i
\(811\) −14.7944 8.54157i −0.519503 0.299935i 0.217228 0.976121i \(-0.430298\pi\)
−0.736731 + 0.676186i \(0.763632\pi\)
\(812\) 29.1408 31.4063i 1.02264 1.10214i
\(813\) 28.2031 2.73216i 0.989127 0.0958209i
\(814\) −11.4786 + 7.82600i −0.402326 + 0.274301i
\(815\) −1.22176 2.53701i −0.0427964 0.0888675i
\(816\) −43.2008 + 41.8713i −1.51233 + 1.46579i
\(817\) −5.09270 + 5.30171i −0.178171 + 0.185483i
\(818\) 27.6319i 0.966128i
\(819\) 18.6855 8.28949i 0.652925 0.289658i
\(820\) 33.6806 + 49.4003i 1.17618 + 1.72513i
\(821\) 18.2619 + 14.5634i 0.637345 + 0.508265i 0.888019 0.459806i \(-0.152081\pi\)
−0.250675 + 0.968071i \(0.580652\pi\)
\(822\) −1.87927 86.2976i −0.0655469 3.00998i
\(823\) −20.3035 + 35.1667i −0.707736 + 1.22583i 0.257959 + 0.966156i \(0.416950\pi\)
−0.965695 + 0.259679i \(0.916383\pi\)
\(824\) 13.0204 + 22.5520i 0.453587 + 0.785636i
\(825\) 1.32100 + 2.17716i 0.0459914 + 0.0757989i
\(826\) −36.9647 + 94.1845i −1.28617 + 3.27710i
\(827\) 14.0784 45.6410i 0.489554 1.58709i −0.287579 0.957757i \(-0.592850\pi\)
0.777132 0.629337i \(-0.216673\pi\)
\(828\) 18.8141 + 25.1670i 0.653837 + 0.874615i
\(829\) 10.0702 + 0.754657i 0.349752 + 0.0262103i 0.248448 0.968645i \(-0.420079\pi\)
0.101304 + 0.994856i \(0.467698\pi\)
\(830\) 19.0326 + 61.7020i 0.660630 + 2.14171i
\(831\) 17.6524 3.05511i 0.612356 0.105981i
\(832\) 23.4526 + 3.53491i 0.813074 + 0.122551i
\(833\) 45.5124 10.3879i 1.57691 0.359920i
\(834\) 15.5337 + 0.824473i 0.537887 + 0.0285492i
\(835\) 15.7169 1.17782i 0.543906 0.0407601i
\(836\) 1.27379 + 3.24558i 0.0440551 + 0.112251i
\(837\) −4.20816 + 5.17545i −0.145455 + 0.178890i
\(838\) 52.6322 + 25.3463i 1.81815 + 0.875575i
\(839\) 29.7889 + 14.3456i 1.02843 + 0.495264i 0.870491 0.492185i \(-0.163802\pi\)
0.157936 + 0.987449i \(0.449516\pi\)
\(840\) 67.2911 88.2557i 2.32176 3.04511i
\(841\) −9.48216 24.1601i −0.326971 0.833108i
\(842\) 49.2876 3.69359i 1.69856 0.127290i
\(843\) −2.19617 + 41.3775i −0.0756402 + 1.42512i
\(844\) 27.9116 6.37065i 0.960758 0.219287i
\(845\) −17.4532 2.63065i −0.600410 0.0904972i
\(846\) −75.0619 54.6887i −2.58068 1.88024i
\(847\) −15.0387 48.7543i −0.516737 1.67522i
\(848\) −18.8126 1.40981i −0.646027 0.0484130i
\(849\) −6.82258 + 53.0827i −0.234150 + 1.82180i
\(850\) 5.53435 17.9419i 0.189827 0.615403i
\(851\) 6.40845 16.3285i 0.219679 0.559732i
\(852\) −20.5558 + 12.4724i −0.704231 + 0.427296i
\(853\) −19.1151 33.1082i −0.654487 1.13360i −0.982022 0.188766i \(-0.939551\pi\)
0.327535 0.944839i \(-0.393782\pi\)
\(854\) 22.5962 39.1377i 0.773225 1.33926i
\(855\) −3.84478 3.79781i −0.131489 0.129882i
\(856\) −40.7910 32.5298i −1.39421 1.11184i
\(857\) 11.3420 + 16.6356i 0.387435 + 0.568262i 0.969565 0.244833i \(-0.0787331\pi\)
−0.582131 + 0.813095i \(0.697781\pi\)
\(858\) 1.37585 3.74327i 0.0469707 0.127793i
\(859\) 6.58153i 0.224559i −0.993677 0.112280i \(-0.964185\pi\)
0.993677 0.112280i \(-0.0358152\pi\)
\(860\) 45.0476 29.5849i 1.53611 1.00884i
\(861\) 42.0897 + 43.4261i 1.43441 + 1.47996i
\(862\) −17.9664 37.3075i −0.611937 1.27070i
\(863\) 26.6479 18.1682i 0.907104 0.618453i −0.0173072 0.999850i \(-0.505509\pi\)
0.924411 + 0.381397i \(0.124557\pi\)
\(864\) 5.15864 + 78.8634i 0.175501 + 2.68299i
\(865\) 7.85025 8.46056i 0.266916 0.287668i
\(866\) −0.360830 0.208326i −0.0122615 0.00707919i
\(867\) −4.04427 + 14.2019i −0.137350 + 0.482321i
\(868\) 30.7239 + 7.01253i 1.04284 + 0.238021i
\(869\) 4.11296 + 1.61422i 0.139523 + 0.0547586i
\(870\) 5.87410 + 11.5476i 0.199151 + 0.391500i
\(871\) −4.75101 5.95757i −0.160982 0.201865i
\(872\) 4.44543 59.3201i 0.150541 2.00883i
\(873\) −2.03333 7.40612i −0.0688179 0.250659i
\(874\) −5.05953 3.44953i −0.171141 0.116682i
\(875\) −8.52663 + 56.5705i −0.288253 + 1.91243i
\(876\) 27.7909 + 18.0740i 0.938967 + 0.610663i
\(877\) −15.1103 + 14.0203i −0.510238 + 0.473432i −0.892772 0.450510i \(-0.851242\pi\)
0.382533 + 0.923942i \(0.375052\pi\)
\(878\) −5.31854 70.9710i −0.179492 2.39515i
\(879\) −42.8124 19.4808i −1.44403 0.657070i
\(880\) −1.73749 11.5275i −0.0585707 0.388591i
\(881\) 9.82189 20.3954i 0.330908 0.687137i −0.667436 0.744667i \(-0.732608\pi\)
0.998344 + 0.0575299i \(0.0183224\pi\)
\(882\) 59.2625 113.818i 1.99547 3.83246i
\(883\) −38.4469 + 5.79493i −1.29384 + 0.195015i −0.759641 0.650343i \(-0.774625\pi\)
−0.534200 + 0.845358i \(0.679387\pi\)
\(884\) −19.6776 + 7.72289i −0.661830 + 0.259749i
\(885\) −16.4459 14.6063i −0.552821 0.490984i
\(886\) −47.2580 50.9320i −1.58766 1.71110i
\(887\) −9.29882 40.7408i −0.312224 1.36794i −0.850855 0.525401i \(-0.823915\pi\)
0.538631 0.842542i \(-0.318942\pi\)
\(888\) 100.312 71.6398i 3.36626 2.40407i
\(889\) 43.0075 63.0804i 1.44242 2.11565i
\(890\) −29.1784 + 9.00033i −0.978061 + 0.301692i
\(891\) 5.42085 + 0.749034i 0.181605 + 0.0250936i
\(892\) 52.6588 41.9940i 1.76315 1.40606i
\(893\) 12.4332 + 3.83512i 0.416060 + 0.128338i
\(894\) −57.7184 + 24.1158i −1.93039 + 0.806554i
\(895\) 6.06895 26.5898i 0.202863 0.888799i
\(896\) 58.7825 33.9381i 1.96379 1.13379i
\(897\) 1.22710 + 4.88362i 0.0409718 + 0.163059i
\(898\) 64.7467 + 60.0762i 2.16063 + 2.00477i
\(899\) −1.39683 + 1.75157i −0.0465869 + 0.0584181i
\(900\) −19.9331 31.2946i −0.664435 1.04315i
\(901\) 4.14693 1.99706i 0.138154 0.0665316i
\(902\) 11.7987 0.392853
\(903\) 39.7943 37.2568i 1.32427 1.23983i
\(904\) 103.003 3.42582
\(905\) 16.5523 7.97118i 0.550218 0.264971i
\(906\) −14.5186 + 70.6689i −0.482349 + 2.34782i
\(907\) 0.158684 0.198984i 0.00526903 0.00660715i −0.779190 0.626788i \(-0.784369\pi\)
0.784459 + 0.620181i \(0.212941\pi\)
\(908\) 86.1037 + 79.8926i 2.85745 + 2.65133i
\(909\) 3.77436 6.08962i 0.125188 0.201980i
\(910\) 25.2920 14.6024i 0.838423 0.484064i
\(911\) −8.53251 + 37.3834i −0.282695 + 1.23857i 0.611628 + 0.791145i \(0.290515\pi\)
−0.894323 + 0.447422i \(0.852342\pi\)
\(912\) −8.93208 21.3779i −0.295771 0.707893i
\(913\) 8.75336 + 2.70005i 0.289694 + 0.0893588i
\(914\) 4.63031 3.69255i 0.153157 0.122139i
\(915\) 6.29129 + 7.54596i 0.207983 + 0.249462i
\(916\) −83.4350 + 25.7363i −2.75677 + 0.850351i
\(917\) −20.4439 + 29.9857i −0.675117 + 0.990214i
\(918\) −22.4118 33.5511i −0.739700 1.10735i
\(919\) 4.01757 + 17.6021i 0.132527 + 0.580640i 0.996962 + 0.0778943i \(0.0248197\pi\)
−0.864434 + 0.502746i \(0.832323\pi\)
\(920\) 18.5949 + 20.0405i 0.613055 + 0.660716i
\(921\) −9.13842 + 10.2894i −0.301121 + 0.339046i
\(922\) 13.7040 5.37842i 0.451317 0.177129i
\(923\) −3.81000 + 0.574265i −0.125408 + 0.0189022i
\(924\) −8.15667 24.5336i −0.268335 0.807097i
\(925\) −8.98687 + 18.6614i −0.295487 + 0.613584i
\(926\) −4.17712 27.7134i −0.137269 0.910719i
\(927\) −8.85594 + 3.16006i −0.290867 + 0.103790i
\(928\) 1.98364 + 26.4698i 0.0651161 + 0.868914i
\(929\) −16.3074 + 15.1310i −0.535027 + 0.496433i −0.900778 0.434280i \(-0.857003\pi\)
0.365751 + 0.930713i \(0.380812\pi\)
\(930\) −5.19565 + 7.98893i −0.170372 + 0.261967i
\(931\) −2.67945 + 17.7770i −0.0878156 + 0.582618i
\(932\) 18.4991 + 12.6125i 0.605958 + 0.413135i
\(933\) 22.3680 40.7673i 0.732295 1.33466i
\(934\) −1.90534 + 25.4249i −0.0623445 + 0.831930i
\(935\) 1.77335 + 2.22371i 0.0579947 + 0.0727230i
\(936\) −11.4817 + 33.4713i −0.375291 + 1.09404i
\(937\) 31.9909 + 12.5555i 1.04510 + 0.410171i 0.824897 0.565284i \(-0.191233\pi\)
0.220201 + 0.975454i \(0.429329\pi\)
\(938\) −66.9920 15.2905i −2.18737 0.499252i
\(939\) 28.0279 + 7.98150i 0.914656 + 0.260466i
\(940\) −82.6067 47.6930i −2.69433 1.55557i
\(941\) −32.0458 + 34.5372i −1.04466 + 1.12588i −0.0527969 + 0.998605i \(0.516814\pi\)
−0.991867 + 0.127275i \(0.959377\pi\)
\(942\) 1.59304 + 16.4444i 0.0519041 + 0.535788i
\(943\) −12.3086 + 8.39186i −0.400823 + 0.273276i
\(944\) −40.9149 84.9607i −1.33167 2.76523i
\(945\) 26.9774 + 29.6333i 0.877575 + 0.963970i
\(946\) 0.183923 10.6337i 0.00597984 0.345731i
\(947\) 34.9639i 1.13617i −0.822969 0.568086i \(-0.807684\pi\)
0.822969 0.568086i \(-0.192316\pi\)
\(948\) −60.4237 22.2089i −1.96247 0.721312i
\(949\) 2.99264 + 4.38940i 0.0971453 + 0.142486i
\(950\) 5.65325 + 4.50832i 0.183416 + 0.146269i
\(951\) −3.46217 + 0.0753943i −0.112269 + 0.00244483i
\(952\) −58.0429 + 100.533i −1.88118 + 3.25830i
\(953\) −2.46970 4.27765i −0.0800016 0.138567i 0.823249 0.567681i \(-0.192159\pi\)
−0.903250 + 0.429114i \(0.858826\pi\)
\(954\) 3.19942 12.2409i 0.103585 0.396313i
\(955\) 7.21550 18.3848i 0.233488 0.594918i
\(956\) −14.4482 + 46.8399i −0.467288 + 1.51491i
\(957\) 1.82298 + 0.234302i 0.0589284 + 0.00757391i
\(958\) −13.8531 1.03814i −0.447572 0.0335409i
\(959\) −26.4317 85.6894i −0.853524 2.76706i
\(960\) 7.92914 + 45.8145i 0.255912 + 1.47866i
\(961\) 29.0242 + 4.37470i 0.936266 + 0.141119i
\(962\) 31.6241 7.21798i 1.01960 0.232717i
\(963\) 14.2036 12.3759i 0.457704 0.398809i
\(964\) −60.9035 + 4.56409i −1.96157 + 0.146999i
\(965\) 11.8096 + 30.0904i 0.380164 + 0.968643i
\(966\) 36.1093 + 27.5317i 1.16180 + 0.885818i
\(967\) 12.8270 + 6.17716i 0.412489 + 0.198644i 0.628607 0.777723i \(-0.283625\pi\)
−0.216118 + 0.976367i \(0.569340\pi\)
\(968\) 79.5739 + 38.3208i 2.55760 + 1.23168i
\(969\) 4.49516 + 3.42736i 0.144405 + 0.110103i
\(970\) −4.00871 10.2140i −0.128712 0.327952i
\(971\) 4.49339 0.336733i 0.144200 0.0108063i −0.00243456 0.999997i \(-0.500775\pi\)
0.146634 + 0.989191i \(0.453156\pi\)
\(972\) −79.2007 9.19129i −2.54036 0.294811i
\(973\) 15.7550 3.59598i 0.505083 0.115282i
\(974\) 71.7491 + 10.8144i 2.29899 + 0.346517i
\(975\) −1.01398 5.85880i −0.0324735 0.187632i
\(976\) 12.4150 + 40.2483i 0.397393 + 1.28832i
\(977\) −57.0477 4.27513i −1.82512 0.136774i −0.882429 0.470446i \(-0.844093\pi\)
−0.942689 + 0.333673i \(0.891712\pi\)
\(978\) 8.03014 + 1.03209i 0.256775 + 0.0330027i
\(979\) −1.27683 + 4.13939i −0.0408077 + 0.132295i
\(980\) 48.1507 122.686i 1.53812 3.91906i
\(981\) 20.7813 + 5.43167i 0.663497 + 0.173420i
\(982\) 29.7794 + 51.5794i 0.950298 + 1.64596i
\(983\) −15.0992 + 26.1527i −0.481591 + 0.834140i −0.999777 0.0211280i \(-0.993274\pi\)
0.518186 + 0.855268i \(0.326608\pi\)
\(984\) −104.663 + 2.27920i −3.33653 + 0.0726582i
\(985\) −24.4672 19.5120i −0.779591 0.621703i
\(986\) −7.63382 11.1968i −0.243110 0.356577i
\(987\) −90.5584 33.2850i −2.88250 1.05947i
\(988\) 8.14069i 0.258990i
\(989\) 7.37138 + 11.2241i 0.234396 + 0.356904i
\(990\) 7.81443 + 0.244308i 0.248359 + 0.00776463i
\(991\) −7.72566 16.0425i −0.245414 0.509607i 0.741481 0.670974i \(-0.234124\pi\)
−0.986894 + 0.161367i \(0.948410\pi\)
\(992\) −16.1322 + 10.9988i −0.512199 + 0.349211i
\(993\) −4.01474 41.4427i −0.127404 1.31515i
\(994\) −23.6329 + 25.4702i −0.749589 + 0.807865i
\(995\) −35.0018 20.2083i −1.10963 0.640646i
\(996\) −128.363 36.5538i −4.06733 1.15825i
\(997\) 9.22610 + 2.10580i 0.292194 + 0.0666913i 0.366105 0.930574i \(-0.380691\pi\)
−0.0739114 + 0.997265i \(0.523548\pi\)
\(998\) 41.6605 + 16.3505i 1.31874 + 0.517567i
\(999\) 18.9309 + 40.2829i 0.598947 + 1.27450i
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 129.2.n.b.98.12 yes 144
3.2 odd 2 inner 129.2.n.b.98.1 144
43.18 odd 42 inner 129.2.n.b.104.1 yes 144
129.104 even 42 inner 129.2.n.b.104.12 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
129.2.n.b.98.1 144 3.2 odd 2 inner
129.2.n.b.98.12 yes 144 1.1 even 1 trivial
129.2.n.b.104.1 yes 144 43.18 odd 42 inner
129.2.n.b.104.12 yes 144 129.104 even 42 inner