Properties

Label 44.2.g.a.39.1
Level $44$
Weight $2$
Character 44.39
Analytic conductor $0.351$
Analytic rank $0$
Dimension $16$
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] = [44,2,Mod(7,44)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(44, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("44.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 44.g (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.351341768894\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + 120 x^{7} - 8 x^{6} - 240 x^{5} + 560 x^{4} - 800 x^{3} + 832 x^{2} - 640 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 39.1
Root \(1.40874 - 0.124276i\) of defining polynomial
Character \(\chi\) \(=\) 44.39
Dual form 44.2.g.a.35.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40874 - 0.124276i) q^{2} +(-1.59814 + 2.19965i) q^{3} +(1.96911 + 0.350146i) q^{4} +(-0.720859 + 2.21858i) q^{5} +(2.52473 - 2.90013i) q^{6} +(1.04462 - 0.758960i) q^{7} +(-2.73046 - 0.737979i) q^{8} +(-1.35736 - 4.17752i) q^{9} +O(q^{10})\) \(q+(-1.40874 - 0.124276i) q^{2} +(-1.59814 + 2.19965i) q^{3} +(1.96911 + 0.350146i) q^{4} +(-0.720859 + 2.21858i) q^{5} +(2.52473 - 2.90013i) q^{6} +(1.04462 - 0.758960i) q^{7} +(-2.73046 - 0.737979i) q^{8} +(-1.35736 - 4.17752i) q^{9} +(1.29122 - 3.03582i) q^{10} +(3.29387 - 0.387833i) q^{11} +(-3.91711 + 3.77177i) q^{12} +(-0.279141 + 0.0906984i) q^{13} +(-1.56592 + 0.939359i) q^{14} +(-3.72806 - 5.13123i) q^{15} +(3.75480 + 1.37895i) q^{16} +(2.82281 + 0.917186i) q^{17} +(1.39300 + 6.05373i) q^{18} +(1.38671 + 1.00751i) q^{19} +(-2.19628 + 4.11622i) q^{20} +3.51072i q^{21} +(-4.68841 + 0.137007i) q^{22} -0.525735i q^{23} +(5.98694 - 4.82665i) q^{24} +(-0.357358 - 0.259635i) q^{25} +(0.404509 - 0.0930801i) q^{26} +(3.60079 + 1.16997i) q^{27} +(2.32272 - 1.12871i) q^{28} +(-4.84416 - 6.66742i) q^{29} +(4.61418 + 7.69189i) q^{30} +(-4.22806 + 1.37378i) q^{31} +(-5.11817 - 2.40922i) q^{32} +(-4.41097 + 7.86517i) q^{33} +(-3.86263 - 1.64289i) q^{34} +(0.930788 + 2.86467i) q^{35} +(-1.21005 - 8.70127i) q^{36} +(4.22613 - 3.07046i) q^{37} +(-1.82831 - 1.59165i) q^{38} +(0.246601 - 0.758960i) q^{39} +(3.60554 - 5.52575i) q^{40} +(3.28821 - 4.52583i) q^{41} +(0.436298 - 4.94570i) q^{42} -3.49429 q^{43} +(6.62180 + 0.389649i) q^{44} +10.2466 q^{45} +(-0.0653363 + 0.740626i) q^{46} +(4.50223 - 6.19679i) q^{47} +(-9.03389 + 6.05548i) q^{48} +(-1.64791 + 5.07175i) q^{49} +(0.471158 + 0.410170i) q^{50} +(-6.52872 + 4.74340i) q^{51} +(-0.581417 + 0.0808551i) q^{52} +(0.484791 + 1.49203i) q^{53} +(-4.92719 - 2.09567i) q^{54} +(-1.51398 + 7.58728i) q^{55} +(-3.41238 + 1.30140i) q^{56} +(-4.43232 + 1.44015i) q^{57} +(5.99558 + 9.99468i) q^{58} +(8.27247 + 11.3861i) q^{59} +(-5.54428 - 11.4093i) q^{60} +(-8.98451 - 2.91924i) q^{61} +(6.12698 - 1.40986i) q^{62} +(-4.58849 - 3.33373i) q^{63} +(6.91078 + 4.03004i) q^{64} -0.684676i q^{65} +(7.19137 - 10.5318i) q^{66} -10.4249i q^{67} +(5.23727 + 2.79444i) q^{68} +(1.15643 + 0.840198i) q^{69} +(-0.955231 - 4.15126i) q^{70} +(-3.41904 - 1.11091i) q^{71} +(0.623286 + 12.4082i) q^{72} +(2.51668 + 3.46391i) q^{73} +(-6.33511 + 3.80028i) q^{74} +(1.14221 - 0.371128i) q^{75} +(2.37782 + 2.46944i) q^{76} +(3.14649 - 2.90506i) q^{77} +(-0.441718 + 1.03853i) q^{78} +(-3.04387 - 9.36807i) q^{79} +(-5.76599 + 7.33627i) q^{80} +(2.33275 - 1.69484i) q^{81} +(-5.19469 + 5.96708i) q^{82} +(1.16185 - 3.57581i) q^{83} +(-1.22926 + 6.91300i) q^{84} +(-4.06969 + 5.60145i) q^{85} +(4.92256 + 0.434257i) q^{86} +22.4076 q^{87} +(-9.27998 - 1.37185i) q^{88} +0.598152 q^{89} +(-14.4348 - 1.27341i) q^{90} +(-0.222760 + 0.306602i) q^{91} +(0.184084 - 1.03523i) q^{92} +(3.73519 - 11.4957i) q^{93} +(-7.11260 + 8.17016i) q^{94} +(-3.23485 + 2.35026i) q^{95} +(13.4790 - 7.40791i) q^{96} +(-2.57295 - 7.91872i) q^{97} +(2.95178 - 6.93999i) q^{98} +(-6.09114 - 13.2338i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} - 10 q^{9} - 22 q^{12} - 10 q^{13} + 8 q^{14} + 23 q^{16} - 10 q^{17} + 20 q^{18} + 16 q^{20} + 17 q^{22} + 25 q^{24} + 6 q^{25} - 4 q^{26} + 20 q^{28} - 10 q^{29} - 12 q^{33} - 6 q^{34} - 30 q^{36} + 18 q^{37} - 38 q^{38} - 40 q^{40} + 10 q^{41} - 26 q^{42} - 28 q^{44} + 40 q^{45} - 30 q^{46} - 36 q^{48} + 6 q^{49} - 15 q^{50} - 10 q^{52} + 38 q^{53} - 12 q^{56} + 30 q^{58} + 52 q^{60} - 10 q^{61} + 70 q^{62} + 23 q^{64} + 36 q^{66} + 60 q^{68} - 16 q^{69} + 12 q^{70} + 45 q^{72} - 30 q^{73} + 40 q^{74} + 2 q^{77} + 4 q^{78} - 28 q^{80} - 4 q^{81} - 59 q^{82} - 10 q^{84} - 50 q^{85} - 39 q^{86} - 53 q^{88} - 36 q^{89} - 50 q^{90} + 36 q^{92} - 38 q^{93} - 30 q^{94} - 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/44\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{9}{10}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40874 0.124276i −0.996131 0.0878764i
\(3\) −1.59814 + 2.19965i −0.922686 + 1.26997i 0.0399594 + 0.999201i \(0.487277\pi\)
−0.962645 + 0.270767i \(0.912723\pi\)
\(4\) 1.96911 + 0.350146i 0.984555 + 0.175073i
\(5\) −0.720859 + 2.21858i −0.322378 + 0.992177i 0.650232 + 0.759735i \(0.274672\pi\)
−0.972610 + 0.232442i \(0.925328\pi\)
\(6\) 2.52473 2.90013i 1.03072 1.18397i
\(7\) 1.04462 0.758960i 0.394829 0.286860i −0.372602 0.927991i \(-0.621534\pi\)
0.767431 + 0.641131i \(0.221534\pi\)
\(8\) −2.73046 0.737979i −0.965362 0.260915i
\(9\) −1.35736 4.17752i −0.452453 1.39251i
\(10\) 1.29122 3.03582i 0.408320 0.960010i
\(11\) 3.29387 0.387833i 0.993139 0.116936i
\(12\) −3.91711 + 3.77177i −1.13077 + 1.08882i
\(13\) −0.279141 + 0.0906984i −0.0774198 + 0.0251552i −0.347471 0.937691i \(-0.612959\pi\)
0.270051 + 0.962846i \(0.412959\pi\)
\(14\) −1.56592 + 0.939359i −0.418510 + 0.251054i
\(15\) −3.72806 5.13123i −0.962580 1.32488i
\(16\) 3.75480 + 1.37895i 0.938699 + 0.344738i
\(17\) 2.82281 + 0.917186i 0.684631 + 0.222450i 0.630622 0.776090i \(-0.282800\pi\)
0.0540095 + 0.998540i \(0.482800\pi\)
\(18\) 1.39300 + 6.05373i 0.328334 + 1.42688i
\(19\) 1.38671 + 1.00751i 0.318134 + 0.231138i 0.735379 0.677656i \(-0.237004\pi\)
−0.417245 + 0.908794i \(0.637004\pi\)
\(20\) −2.19628 + 4.11622i −0.491102 + 0.920414i
\(21\) 3.51072i 0.766102i
\(22\) −4.68841 + 0.137007i −0.999573 + 0.0292101i
\(23\) 0.525735i 0.109623i −0.998497 0.0548117i \(-0.982544\pi\)
0.998497 0.0548117i \(-0.0174559\pi\)
\(24\) 5.98694 4.82665i 1.22208 0.985236i
\(25\) −0.357358 0.259635i −0.0714715 0.0519271i
\(26\) 0.404509 0.0930801i 0.0793308 0.0182545i
\(27\) 3.60079 + 1.16997i 0.692972 + 0.225160i
\(28\) 2.32272 1.12871i 0.438953 0.213306i
\(29\) −4.84416 6.66742i −0.899538 1.23811i −0.970615 0.240637i \(-0.922644\pi\)
0.0710771 0.997471i \(-0.477356\pi\)
\(30\) 4.61418 + 7.69189i 0.842431 + 1.40434i
\(31\) −4.22806 + 1.37378i −0.759382 + 0.246738i −0.663013 0.748608i \(-0.730723\pi\)
−0.0963686 + 0.995346i \(0.530723\pi\)
\(32\) −5.11817 2.40922i −0.904773 0.425894i
\(33\) −4.41097 + 7.86517i −0.767851 + 1.36915i
\(34\) −3.86263 1.64289i −0.662435 0.281753i
\(35\) 0.930788 + 2.86467i 0.157332 + 0.484218i
\(36\) −1.21005 8.70127i −0.201675 1.45021i
\(37\) 4.22613 3.07046i 0.694771 0.504781i −0.183454 0.983028i \(-0.558728\pi\)
0.878225 + 0.478248i \(0.158728\pi\)
\(38\) −1.82831 1.59165i −0.296591 0.258200i
\(39\) 0.246601 0.758960i 0.0394878 0.121531i
\(40\) 3.60554 5.52575i 0.570085 0.873697i
\(41\) 3.28821 4.52583i 0.513531 0.706815i −0.470978 0.882145i \(-0.656099\pi\)
0.984510 + 0.175329i \(0.0560990\pi\)
\(42\) 0.436298 4.94570i 0.0673223 0.763138i
\(43\) −3.49429 −0.532874 −0.266437 0.963852i \(-0.585846\pi\)
−0.266437 + 0.963852i \(0.585846\pi\)
\(44\) 6.62180 + 0.389649i 0.998273 + 0.0587419i
\(45\) 10.2466 1.52747
\(46\) −0.0653363 + 0.740626i −0.00963331 + 0.109199i
\(47\) 4.50223 6.19679i 0.656718 0.903895i −0.342649 0.939463i \(-0.611324\pi\)
0.999367 + 0.0355685i \(0.0113242\pi\)
\(48\) −9.03389 + 6.05548i −1.30393 + 0.874033i
\(49\) −1.64791 + 5.07175i −0.235416 + 0.724535i
\(50\) 0.471158 + 0.410170i 0.0666318 + 0.0580069i
\(51\) −6.52872 + 4.74340i −0.914204 + 0.664208i
\(52\) −0.581417 + 0.0808551i −0.0806280 + 0.0112126i
\(53\) 0.484791 + 1.49203i 0.0665912 + 0.204947i 0.978815 0.204745i \(-0.0656364\pi\)
−0.912224 + 0.409691i \(0.865636\pi\)
\(54\) −4.92719 2.09567i −0.670505 0.285185i
\(55\) −1.51398 + 7.58728i −0.204145 + 1.02307i
\(56\) −3.41238 + 1.30140i −0.455999 + 0.173907i
\(57\) −4.43232 + 1.44015i −0.587075 + 0.190752i
\(58\) 5.99558 + 9.99468i 0.787258 + 1.31237i
\(59\) 8.27247 + 11.3861i 1.07698 + 1.48234i 0.862799 + 0.505548i \(0.168710\pi\)
0.214185 + 0.976793i \(0.431290\pi\)
\(60\) −5.54428 11.4093i −0.715763 1.47294i
\(61\) −8.98451 2.91924i −1.15035 0.373771i −0.329074 0.944304i \(-0.606737\pi\)
−0.821274 + 0.570533i \(0.806737\pi\)
\(62\) 6.12698 1.40986i 0.778127 0.179052i
\(63\) −4.58849 3.33373i −0.578096 0.420011i
\(64\) 6.91078 + 4.03004i 0.863847 + 0.503754i
\(65\) 0.684676i 0.0849236i
\(66\) 7.19137 10.5318i 0.885196 1.29638i
\(67\) 10.4249i 1.27361i −0.771026 0.636803i \(-0.780256\pi\)
0.771026 0.636803i \(-0.219744\pi\)
\(68\) 5.23727 + 2.79444i 0.635113 + 0.338875i
\(69\) 1.15643 + 0.840198i 0.139218 + 0.101148i
\(70\) −0.955231 4.15126i −0.114172 0.496170i
\(71\) −3.41904 1.11091i −0.405765 0.131841i 0.0990215 0.995085i \(-0.468429\pi\)
−0.504786 + 0.863244i \(0.668429\pi\)
\(72\) 0.623286 + 12.4082i 0.0734550 + 1.46232i
\(73\) 2.51668 + 3.46391i 0.294555 + 0.405420i 0.930487 0.366325i \(-0.119384\pi\)
−0.635932 + 0.771745i \(0.719384\pi\)
\(74\) −6.33511 + 3.80028i −0.736441 + 0.441774i
\(75\) 1.14221 0.371128i 0.131891 0.0428541i
\(76\) 2.37782 + 2.46944i 0.272754 + 0.283265i
\(77\) 3.14649 2.90506i 0.358576 0.331062i
\(78\) −0.441718 + 1.03853i −0.0500147 + 0.117591i
\(79\) −3.04387 9.36807i −0.342462 1.05399i −0.962929 0.269757i \(-0.913057\pi\)
0.620467 0.784233i \(-0.286943\pi\)
\(80\) −5.76599 + 7.33627i −0.644657 + 0.820220i
\(81\) 2.33275 1.69484i 0.259194 0.188316i
\(82\) −5.19469 + 5.96708i −0.573657 + 0.658954i
\(83\) 1.16185 3.57581i 0.127530 0.392496i −0.866824 0.498615i \(-0.833842\pi\)
0.994354 + 0.106118i \(0.0338423\pi\)
\(84\) −1.22926 + 6.91300i −0.134124 + 0.754270i
\(85\) −4.06969 + 5.60145i −0.441420 + 0.607563i
\(86\) 4.92256 + 0.434257i 0.530813 + 0.0468271i
\(87\) 22.4076 2.40235
\(88\) −9.27998 1.37185i −0.989249 0.146239i
\(89\) 0.598152 0.0634039 0.0317020 0.999497i \(-0.489907\pi\)
0.0317020 + 0.999497i \(0.489907\pi\)
\(90\) −14.4348 1.27341i −1.52156 0.134229i
\(91\) −0.222760 + 0.306602i −0.0233515 + 0.0321406i
\(92\) 0.184084 1.03523i 0.0191921 0.107930i
\(93\) 3.73519 11.4957i 0.387321 1.19205i
\(94\) −7.11260 + 8.17016i −0.733609 + 0.842688i
\(95\) −3.23485 + 2.35026i −0.331889 + 0.241131i
\(96\) 13.4790 7.40791i 1.37569 0.756067i
\(97\) −2.57295 7.91872i −0.261243 0.804024i −0.992535 0.121960i \(-0.961082\pi\)
0.731292 0.682065i \(-0.238918\pi\)
\(98\) 2.95178 6.93999i 0.298175 0.701045i
\(99\) −6.09114 13.2338i −0.612182 1.33004i
\(100\) −0.612766 0.636378i −0.0612766 0.0636378i
\(101\) −7.30672 + 2.37410i −0.727046 + 0.236232i −0.649075 0.760724i \(-0.724844\pi\)
−0.0779707 + 0.996956i \(0.524844\pi\)
\(102\) 9.78678 5.87086i 0.969036 0.581302i
\(103\) −0.242398 0.333632i −0.0238841 0.0328737i 0.796908 0.604101i \(-0.206468\pi\)
−0.820792 + 0.571227i \(0.806468\pi\)
\(104\) 0.829115 0.0416479i 0.0813014 0.00408391i
\(105\) −7.78880 2.53073i −0.760109 0.246974i
\(106\) −0.497522 2.16214i −0.0483236 0.210006i
\(107\) −4.18738 3.04231i −0.404809 0.294111i 0.366688 0.930344i \(-0.380492\pi\)
−0.771497 + 0.636233i \(0.780492\pi\)
\(108\) 6.68069 + 3.56460i 0.642850 + 0.343003i
\(109\) 12.5948i 1.20636i 0.797604 + 0.603181i \(0.206101\pi\)
−0.797604 + 0.603181i \(0.793899\pi\)
\(110\) 3.07572 10.5004i 0.293259 1.00117i
\(111\) 14.2030i 1.34809i
\(112\) 4.96890 1.40926i 0.469517 0.133163i
\(113\) 2.15258 + 1.56394i 0.202498 + 0.147123i 0.684413 0.729095i \(-0.260059\pi\)
−0.481915 + 0.876218i \(0.660059\pi\)
\(114\) 6.42297 1.47797i 0.601566 0.138424i
\(115\) 1.16638 + 0.378981i 0.108766 + 0.0353402i
\(116\) −7.20412 14.8250i −0.668886 1.37647i
\(117\) 0.757788 + 1.04301i 0.0700575 + 0.0964259i
\(118\) −10.2388 17.0681i −0.942554 1.57125i
\(119\) 3.64487 1.18429i 0.334124 0.108564i
\(120\) 6.39255 + 16.7618i 0.583558 + 1.53014i
\(121\) 10.6992 2.55494i 0.972652 0.232267i
\(122\) 12.2941 + 5.22902i 1.11305 + 0.473413i
\(123\) 4.70022 + 14.4658i 0.423805 + 1.30434i
\(124\) −8.80654 + 1.22469i −0.790851 + 0.109980i
\(125\) −8.60254 + 6.25011i −0.769435 + 0.559027i
\(126\) 6.04970 + 5.26661i 0.538950 + 0.469187i
\(127\) −6.16979 + 18.9887i −0.547481 + 1.68497i 0.167537 + 0.985866i \(0.446419\pi\)
−0.715018 + 0.699107i \(0.753581\pi\)
\(128\) −9.23467 6.53613i −0.816237 0.577717i
\(129\) 5.58436 7.68621i 0.491676 0.676733i
\(130\) −0.0850888 + 0.964532i −0.00746278 + 0.0845951i
\(131\) −20.5136 −1.79228 −0.896139 0.443773i \(-0.853640\pi\)
−0.896139 + 0.443773i \(0.853640\pi\)
\(132\) −11.4396 + 13.9429i −0.995693 + 1.21357i
\(133\) 2.21324 0.191913
\(134\) −1.29557 + 14.6860i −0.111920 + 1.26868i
\(135\) −5.19132 + 7.14524i −0.446798 + 0.614965i
\(136\) −7.03069 4.58751i −0.602876 0.393375i
\(137\) −1.93612 + 5.95875i −0.165414 + 0.509091i −0.999067 0.0431981i \(-0.986245\pi\)
0.833653 + 0.552289i \(0.186245\pi\)
\(138\) −1.52470 1.32734i −0.129791 0.112991i
\(139\) 10.9058 7.92352i 0.925017 0.672064i −0.0197506 0.999805i \(-0.506287\pi\)
0.944768 + 0.327741i \(0.106287\pi\)
\(140\) 0.829772 + 5.96677i 0.0701286 + 0.504284i
\(141\) 6.43557 + 19.8067i 0.541973 + 1.66802i
\(142\) 4.67848 + 1.98989i 0.392609 + 0.166988i
\(143\) −0.884278 + 0.407009i −0.0739471 + 0.0340358i
\(144\) 0.663995 17.5575i 0.0553329 1.46312i
\(145\) 18.2841 5.94087i 1.51841 0.493363i
\(146\) −3.11487 5.19252i −0.257789 0.429736i
\(147\) −8.52247 11.7302i −0.702922 0.967489i
\(148\) 9.39682 4.56632i 0.772414 0.375349i
\(149\) 16.5960 + 5.39238i 1.35960 + 0.441761i 0.895910 0.444237i \(-0.146525\pi\)
0.463690 + 0.885997i \(0.346525\pi\)
\(150\) −1.65521 + 0.380874i −0.135147 + 0.0310982i
\(151\) 7.94818 + 5.77469i 0.646814 + 0.469938i 0.862184 0.506595i \(-0.169096\pi\)
−0.215370 + 0.976532i \(0.569096\pi\)
\(152\) −3.04284 3.77431i −0.246807 0.306137i
\(153\) 13.0373i 1.05400i
\(154\) −4.79363 + 3.70144i −0.386281 + 0.298271i
\(155\) 10.3706i 0.832985i
\(156\) 0.751332 1.40813i 0.0601547 0.112741i
\(157\) −12.4622 9.05431i −0.994591 0.722613i −0.0336696 0.999433i \(-0.510719\pi\)
−0.960922 + 0.276820i \(0.910719\pi\)
\(158\) 3.12380 + 13.5755i 0.248516 + 1.08001i
\(159\) −4.05671 1.31811i −0.321718 0.104533i
\(160\) 9.03452 9.61834i 0.714241 0.760397i
\(161\) −0.399012 0.549193i −0.0314466 0.0432825i
\(162\) −3.49687 + 2.09769i −0.274740 + 0.164810i
\(163\) 10.2403 3.32727i 0.802080 0.260612i 0.120840 0.992672i \(-0.461441\pi\)
0.681240 + 0.732060i \(0.261441\pi\)
\(164\) 8.05954 7.76050i 0.629344 0.605994i
\(165\) −14.2698 15.4557i −1.11090 1.20323i
\(166\) −2.08114 + 4.89301i −0.161528 + 0.379771i
\(167\) 1.98451 + 6.10771i 0.153566 + 0.472629i 0.998013 0.0630114i \(-0.0200704\pi\)
−0.844446 + 0.535640i \(0.820070\pi\)
\(168\) 2.59084 9.58586i 0.199887 0.739566i
\(169\) −10.4475 + 7.59057i −0.803656 + 0.583890i
\(170\) 6.42928 7.38524i 0.493103 0.566422i
\(171\) 2.32661 7.16056i 0.177920 0.547582i
\(172\) −6.88065 1.22351i −0.524644 0.0932919i
\(173\) −2.12650 + 2.92688i −0.161675 + 0.222527i −0.882167 0.470937i \(-0.843916\pi\)
0.720492 + 0.693463i \(0.243916\pi\)
\(174\) −31.5666 2.78473i −2.39305 0.211110i
\(175\) −0.570356 −0.0431148
\(176\) 12.9026 + 3.08586i 0.972571 + 0.232605i
\(177\) −38.2659 −2.87624
\(178\) −0.842641 0.0743359i −0.0631586 0.00557171i
\(179\) −2.94347 + 4.05134i −0.220006 + 0.302812i −0.904726 0.425994i \(-0.859924\pi\)
0.684720 + 0.728806i \(0.259924\pi\)
\(180\) 20.1767 + 3.58781i 1.50388 + 0.267419i
\(181\) 3.02897 9.32220i 0.225141 0.692914i −0.773136 0.634240i \(-0.781313\pi\)
0.998277 0.0586734i \(-0.0186871\pi\)
\(182\) 0.351914 0.404240i 0.0260856 0.0299643i
\(183\) 20.7798 15.0974i 1.53609 1.11603i
\(184\) −0.387982 + 1.43550i −0.0286024 + 0.105826i
\(185\) 3.76561 + 11.5894i 0.276853 + 0.852066i
\(186\) −6.69057 + 15.7303i −0.490576 + 1.15340i
\(187\) 9.65368 + 1.92631i 0.705947 + 0.140866i
\(188\) 11.0352 10.6257i 0.804823 0.774961i
\(189\) 4.64941 1.51069i 0.338195 0.109886i
\(190\) 4.84916 2.90889i 0.351795 0.211033i
\(191\) −6.87102 9.45715i −0.497170 0.684295i 0.484521 0.874780i \(-0.338994\pi\)
−0.981690 + 0.190485i \(0.938994\pi\)
\(192\) −19.9090 + 8.76072i −1.43681 + 0.632251i
\(193\) −1.09807 0.356784i −0.0790406 0.0256818i 0.269230 0.963076i \(-0.413231\pi\)
−0.348270 + 0.937394i \(0.613231\pi\)
\(194\) 2.64052 + 11.4752i 0.189578 + 0.823871i
\(195\) 1.50605 + 1.09421i 0.107850 + 0.0783578i
\(196\) −5.02077 + 9.40982i −0.358626 + 0.672130i
\(197\) 15.6248i 1.11322i −0.830774 0.556610i \(-0.812102\pi\)
0.830774 0.556610i \(-0.187898\pi\)
\(198\) 6.93621 + 19.4000i 0.492935 + 1.37870i
\(199\) 10.9684i 0.777526i 0.921338 + 0.388763i \(0.127098\pi\)
−0.921338 + 0.388763i \(0.872902\pi\)
\(200\) 0.784143 + 0.972645i 0.0554473 + 0.0687764i
\(201\) 22.9312 + 16.6605i 1.61744 + 1.17514i
\(202\) 10.5883 2.43644i 0.744993 0.171427i
\(203\) −10.1206 3.28839i −0.710328 0.230799i
\(204\) −14.5167 + 7.05427i −1.01637 + 0.493897i
\(205\) 7.67056 + 10.5576i 0.535735 + 0.737376i
\(206\) 0.300013 + 0.500125i 0.0209029 + 0.0348454i
\(207\) −2.19627 + 0.713611i −0.152651 + 0.0495994i
\(208\) −1.17319 0.0443680i −0.0813458 0.00307637i
\(209\) 4.95840 + 2.78078i 0.342980 + 0.192351i
\(210\) 10.6579 + 4.53311i 0.735465 + 0.312815i
\(211\) −5.96517 18.3589i −0.410659 1.26388i −0.916076 0.401004i \(-0.868661\pi\)
0.505417 0.862875i \(-0.331339\pi\)
\(212\) 0.432178 + 3.10773i 0.0296821 + 0.213440i
\(213\) 7.90771 5.74529i 0.541827 0.393661i
\(214\) 5.52086 + 4.80622i 0.377398 + 0.328547i
\(215\) 2.51889 7.75235i 0.171787 0.528706i
\(216\) −8.96838 5.85185i −0.610221 0.398168i
\(217\) −3.37407 + 4.64401i −0.229047 + 0.315256i
\(218\) 1.56523 17.7428i 0.106011 1.20170i
\(219\) −11.6414 −0.786652
\(220\) −5.63785 + 14.4101i −0.380104 + 0.971527i
\(221\) −0.871148 −0.0585998
\(222\) 1.76509 20.0084i 0.118465 1.34288i
\(223\) 6.37102 8.76895i 0.426635 0.587212i −0.540542 0.841317i \(-0.681781\pi\)
0.967177 + 0.254105i \(0.0817808\pi\)
\(224\) −7.17504 + 1.36777i −0.479403 + 0.0913880i
\(225\) −0.599570 + 1.84529i −0.0399713 + 0.123019i
\(226\) −2.83808 2.47071i −0.188786 0.164349i
\(227\) −19.4139 + 14.1050i −1.28854 + 0.936181i −0.999775 0.0212179i \(-0.993246\pi\)
−0.288768 + 0.957399i \(0.593246\pi\)
\(228\) −9.23199 + 1.28385i −0.611403 + 0.0850252i
\(229\) −7.59603 23.3782i −0.501960 1.54487i −0.805822 0.592158i \(-0.798276\pi\)
0.303862 0.952716i \(-0.401724\pi\)
\(230\) −1.59604 0.678840i −0.105240 0.0447614i
\(231\) 1.36157 + 11.5639i 0.0895849 + 0.760846i
\(232\) 8.30636 + 21.7800i 0.545339 + 1.42992i
\(233\) −13.6046 + 4.42039i −0.891264 + 0.289589i −0.718627 0.695396i \(-0.755229\pi\)
−0.172637 + 0.984985i \(0.555229\pi\)
\(234\) −0.937908 1.56350i −0.0613129 0.102209i
\(235\) 10.5026 + 14.4556i 0.685113 + 0.942977i
\(236\) 12.3026 + 25.3170i 0.800832 + 1.64800i
\(237\) 25.4710 + 8.27602i 1.65452 + 0.537585i
\(238\) −5.28186 + 1.21539i −0.342372 + 0.0787820i
\(239\) 15.9893 + 11.6169i 1.03426 + 0.751436i 0.969157 0.246442i \(-0.0792616\pi\)
0.0651055 + 0.997878i \(0.479262\pi\)
\(240\) −6.92237 24.4075i −0.446837 1.57550i
\(241\) 6.53055i 0.420669i −0.977629 0.210335i \(-0.932545\pi\)
0.977629 0.210335i \(-0.0674554\pi\)
\(242\) −15.3899 + 2.26961i −0.989300 + 0.145896i
\(243\) 19.1981i 1.23156i
\(244\) −16.6693 8.89420i −1.06714 0.569393i
\(245\) −10.0641 7.31203i −0.642975 0.467148i
\(246\) −4.82365 20.9627i −0.307545 1.33653i
\(247\) −0.478467 0.155464i −0.0304442 0.00989191i
\(248\) 12.5584 0.630827i 0.797456 0.0400576i
\(249\) 6.00873 + 8.27031i 0.380788 + 0.524109i
\(250\) 12.8955 7.73571i 0.815583 0.489249i
\(251\) 4.53708 1.47419i 0.286378 0.0930498i −0.162306 0.986741i \(-0.551893\pi\)
0.448684 + 0.893691i \(0.351893\pi\)
\(252\) −7.86796 8.17114i −0.495635 0.514733i
\(253\) −0.203897 1.73170i −0.0128189 0.108871i
\(254\) 11.0515 25.9834i 0.693432 1.63034i
\(255\) −5.81729 17.9038i −0.364293 1.12118i
\(256\) 12.1970 + 10.3554i 0.762311 + 0.647210i
\(257\) 2.45693 1.78506i 0.153259 0.111349i −0.508513 0.861054i \(-0.669805\pi\)
0.661772 + 0.749705i \(0.269805\pi\)
\(258\) −8.82214 + 10.1339i −0.549242 + 0.630909i
\(259\) 2.08434 6.41493i 0.129514 0.398604i
\(260\) 0.239736 1.34820i 0.0148678 0.0836120i
\(261\) −21.2780 + 29.2866i −1.31707 + 1.81280i
\(262\) 28.8983 + 2.54934i 1.78534 + 0.157499i
\(263\) −14.1671 −0.873580 −0.436790 0.899564i \(-0.643885\pi\)
−0.436790 + 0.899564i \(0.643885\pi\)
\(264\) 17.8483 18.2203i 1.09849 1.12138i
\(265\) −3.65966 −0.224811
\(266\) −3.11789 0.275053i −0.191170 0.0168646i
\(267\) −0.955929 + 1.31572i −0.0585019 + 0.0805210i
\(268\) 3.65024 20.5278i 0.222974 1.25394i
\(269\) 0.309559 0.952724i 0.0188741 0.0580886i −0.941176 0.337917i \(-0.890278\pi\)
0.960050 + 0.279829i \(0.0902776\pi\)
\(270\) 8.20122 9.42065i 0.499110 0.573322i
\(271\) −14.3933 + 10.4573i −0.874330 + 0.635238i −0.931745 0.363113i \(-0.881714\pi\)
0.0574157 + 0.998350i \(0.481714\pi\)
\(272\) 9.33431 + 7.33636i 0.565976 + 0.444832i
\(273\) −0.318417 0.979986i −0.0192714 0.0593114i
\(274\) 3.46802 8.15373i 0.209511 0.492585i
\(275\) −1.27778 0.716611i −0.0770533 0.0432133i
\(276\) 1.98295 + 2.05936i 0.119360 + 0.123959i
\(277\) 18.4378 5.99082i 1.10782 0.359953i 0.302714 0.953081i \(-0.402107\pi\)
0.805108 + 0.593128i \(0.202107\pi\)
\(278\) −16.3482 + 9.80687i −0.980497 + 0.588177i
\(279\) 11.4780 + 15.7981i 0.687169 + 0.945806i
\(280\) −0.427409 8.50876i −0.0255426 0.508496i
\(281\) −13.9771 4.54142i −0.833802 0.270919i −0.139156 0.990270i \(-0.544439\pi\)
−0.694646 + 0.719352i \(0.744439\pi\)
\(282\) −6.60457 28.7023i −0.393297 1.70920i
\(283\) −2.02002 1.46763i −0.120078 0.0872415i 0.526126 0.850407i \(-0.323644\pi\)
−0.646203 + 0.763165i \(0.723644\pi\)
\(284\) −6.34348 3.38467i −0.376416 0.200843i
\(285\) 10.8716i 0.643977i
\(286\) 1.29630 0.463476i 0.0766519 0.0274059i
\(287\) 7.22339i 0.426383i
\(288\) −3.11737 + 24.6514i −0.183693 + 1.45260i
\(289\) −6.62627 4.81427i −0.389781 0.283192i
\(290\) −26.4959 + 6.09688i −1.55589 + 0.358021i
\(291\) 21.5303 + 6.99563i 1.26213 + 0.410091i
\(292\) 3.74275 + 7.70203i 0.219028 + 0.450727i
\(293\) 4.41949 + 6.08290i 0.258189 + 0.355367i 0.918358 0.395750i \(-0.129515\pi\)
−0.660169 + 0.751117i \(0.729515\pi\)
\(294\) 10.5482 + 17.5839i 0.615183 + 1.02552i
\(295\) −31.2242 + 10.1453i −1.81794 + 0.590685i
\(296\) −13.8052 + 5.26497i −0.802410 + 0.306020i
\(297\) 12.3143 + 2.45722i 0.714547 + 0.142582i
\(298\) −22.7094 9.65896i −1.31552 0.559529i
\(299\) 0.0476833 + 0.146754i 0.00275760 + 0.00848702i
\(300\) 2.37909 0.330850i 0.137357 0.0191016i
\(301\) −3.65020 + 2.65203i −0.210394 + 0.152860i
\(302\) −10.4793 9.12282i −0.603015 0.524960i
\(303\) 6.45497 19.8664i 0.370828 1.14129i
\(304\) 3.81752 + 5.69519i 0.218950 + 0.326642i
\(305\) 12.9531 17.8285i 0.741694 1.02085i
\(306\) −1.62022 + 18.3662i −0.0926219 + 1.04992i
\(307\) 25.7991 1.47243 0.736216 0.676747i \(-0.236611\pi\)
0.736216 + 0.676747i \(0.236611\pi\)
\(308\) 7.21299 4.61865i 0.410998 0.263172i
\(309\) 1.12126 0.0637861
\(310\) −1.28881 + 14.6095i −0.0731997 + 0.829762i
\(311\) 1.74241 2.39822i 0.0988030 0.135991i −0.756753 0.653701i \(-0.773215\pi\)
0.855556 + 0.517710i \(0.173215\pi\)
\(312\) −1.23343 + 1.89032i −0.0698292 + 0.107018i
\(313\) 0.186644 0.574432i 0.0105498 0.0324688i −0.945643 0.325206i \(-0.894566\pi\)
0.956193 + 0.292738i \(0.0945662\pi\)
\(314\) 16.4308 + 14.3039i 0.927243 + 0.807219i
\(315\) 10.7038 7.77677i 0.603091 0.438171i
\(316\) −2.71353 19.5126i −0.152648 1.09767i
\(317\) 7.09054 + 21.8224i 0.398244 + 1.22567i 0.926406 + 0.376526i \(0.122881\pi\)
−0.528162 + 0.849144i \(0.677119\pi\)
\(318\) 5.55106 + 2.36102i 0.311288 + 0.132400i
\(319\) −18.5419 20.0829i −1.03815 1.12443i
\(320\) −13.9226 + 12.4270i −0.778299 + 0.694690i
\(321\) 13.3840 4.34874i 0.747024 0.242723i
\(322\) 0.493854 + 0.823260i 0.0275214 + 0.0458785i
\(323\) 2.99035 + 4.11587i 0.166388 + 0.229013i
\(324\) 5.18688 2.52053i 0.288160 0.140029i
\(325\) 0.123302 + 0.0400631i 0.00683954 + 0.00222230i
\(326\) −14.8394 + 3.41464i −0.821879 + 0.189119i
\(327\) −27.7041 20.1282i −1.53204 1.11309i
\(328\) −12.3183 + 9.93094i −0.680162 + 0.548345i
\(329\) 9.89031i 0.545270i
\(330\) 18.1817 + 23.5466i 1.00087 + 1.29620i
\(331\) 4.43442i 0.243738i 0.992546 + 0.121869i \(0.0388887\pi\)
−0.992546 + 0.121869i \(0.961111\pi\)
\(332\) 3.53987 6.63435i 0.194276 0.364107i
\(333\) −18.5633 13.4870i −1.01726 0.739083i
\(334\) −2.03663 8.85081i −0.111439 0.484295i
\(335\) 23.1285 + 7.51490i 1.26364 + 0.410583i
\(336\) −4.84111 + 13.1820i −0.264104 + 0.719139i
\(337\) 10.4401 + 14.3696i 0.568711 + 0.782763i 0.992401 0.123044i \(-0.0392656\pi\)
−0.423691 + 0.905807i \(0.639266\pi\)
\(338\) 15.6612 9.39479i 0.851857 0.511009i
\(339\) −6.88025 + 2.23553i −0.373684 + 0.121417i
\(340\) −9.97500 + 9.60490i −0.540971 + 0.520899i
\(341\) −13.3939 + 6.16483i −0.725320 + 0.333844i
\(342\) −4.16748 + 9.79825i −0.225351 + 0.529829i
\(343\) 4.92088 + 15.1449i 0.265703 + 0.817748i
\(344\) 9.54101 + 2.57871i 0.514417 + 0.139035i
\(345\) −2.69767 + 1.95997i −0.145238 + 0.105521i
\(346\) 3.35944 3.85895i 0.180605 0.207458i
\(347\) 1.19913 3.69054i 0.0643726 0.198119i −0.913697 0.406396i \(-0.866786\pi\)
0.978070 + 0.208277i \(0.0667855\pi\)
\(348\) 44.1231 + 7.84593i 2.36524 + 0.420586i
\(349\) −11.5900 + 15.9522i −0.620396 + 0.853903i −0.997382 0.0723168i \(-0.976961\pi\)
0.376985 + 0.926219i \(0.376961\pi\)
\(350\) 0.803484 + 0.0708815i 0.0429480 + 0.00378878i
\(351\) −1.11124 −0.0593137
\(352\) −17.7930 5.95066i −0.948368 0.317171i
\(353\) −1.59623 −0.0849587 −0.0424794 0.999097i \(-0.513526\pi\)
−0.0424794 + 0.999097i \(0.513526\pi\)
\(354\) 53.9068 + 4.75554i 2.86512 + 0.252754i
\(355\) 4.92929 6.78458i 0.261619 0.360088i
\(356\) 1.17783 + 0.209440i 0.0624247 + 0.0111003i
\(357\) −3.21998 + 9.91009i −0.170420 + 0.524497i
\(358\) 4.65008 5.34150i 0.245764 0.282307i
\(359\) 12.4772 9.06523i 0.658522 0.478445i −0.207641 0.978205i \(-0.566579\pi\)
0.866164 + 0.499760i \(0.166579\pi\)
\(360\) −27.9779 7.56177i −1.47456 0.398541i
\(361\) −4.96342 15.2758i −0.261233 0.803991i
\(362\) −5.42556 + 12.7562i −0.285161 + 0.670449i
\(363\) −11.4788 + 27.6176i −0.602480 + 1.44955i
\(364\) −0.545994 + 0.525735i −0.0286178 + 0.0275560i
\(365\) −9.49912 + 3.08645i −0.497207 + 0.161552i
\(366\) −31.1496 + 18.6859i −1.62822 + 0.976729i
\(367\) −6.20229 8.53673i −0.323757 0.445613i 0.615853 0.787861i \(-0.288812\pi\)
−0.939610 + 0.342248i \(0.888812\pi\)
\(368\) 0.724964 1.97403i 0.0377914 0.102903i
\(369\) −23.3700 7.59337i −1.21659 0.395295i
\(370\) −3.86450 16.7944i −0.200906 0.873099i
\(371\) 1.63882 + 1.19067i 0.0850831 + 0.0618165i
\(372\) 11.3802 21.3285i 0.590035 1.10583i
\(373\) 37.4953i 1.94143i 0.240225 + 0.970717i \(0.422779\pi\)
−0.240225 + 0.970717i \(0.577221\pi\)
\(374\) −13.3602 3.91340i −0.690837 0.202357i
\(375\) 28.9111i 1.49296i
\(376\) −16.8662 + 13.5975i −0.869810 + 0.701238i
\(377\) 1.95693 + 1.42179i 0.100787 + 0.0732259i
\(378\) −6.73757 + 1.55036i −0.346543 + 0.0797417i
\(379\) −20.2850 6.59100i −1.04197 0.338557i −0.262459 0.964943i \(-0.584533\pi\)
−0.779513 + 0.626386i \(0.784533\pi\)
\(380\) −7.19272 + 3.49525i −0.368979 + 0.179303i
\(381\) −31.9082 43.9179i −1.63471 2.24998i
\(382\) 8.50420 + 14.1766i 0.435113 + 0.725338i
\(383\) 27.4201 8.90933i 1.40110 0.455245i 0.491554 0.870847i \(-0.336429\pi\)
0.909547 + 0.415602i \(0.136429\pi\)
\(384\) 29.1355 9.86739i 1.48681 0.503543i
\(385\) 4.17691 + 9.07487i 0.212875 + 0.462498i
\(386\) 1.50255 + 0.639079i 0.0764780 + 0.0325283i
\(387\) 4.74300 + 14.5975i 0.241100 + 0.742031i
\(388\) −2.29371 16.4938i −0.116446 0.837343i
\(389\) 28.2179 20.5015i 1.43070 1.03947i 0.440817 0.897597i \(-0.354689\pi\)
0.989885 0.141869i \(-0.0453112\pi\)
\(390\) −1.98565 1.72862i −0.100547 0.0875322i
\(391\) 0.482197 1.48405i 0.0243858 0.0750516i
\(392\) 8.24239 12.6321i 0.416303 0.638015i
\(393\) 32.7835 45.1226i 1.65371 2.27614i
\(394\) −1.94179 + 22.0113i −0.0978257 + 1.10891i
\(395\) 22.9780 1.15615
\(396\) −7.36038 28.1916i −0.369873 1.41668i
\(397\) 16.9102 0.848698 0.424349 0.905499i \(-0.360503\pi\)
0.424349 + 0.905499i \(0.360503\pi\)
\(398\) 1.36310 15.4516i 0.0683262 0.774518i
\(399\) −3.53707 + 4.86836i −0.177075 + 0.243723i
\(400\) −0.983780 1.46766i −0.0491890 0.0733829i
\(401\) 4.90100 15.0837i 0.244744 0.753246i −0.750934 0.660377i \(-0.770396\pi\)
0.995678 0.0928687i \(-0.0296037\pi\)
\(402\) −30.2336 26.3201i −1.50792 1.31273i
\(403\) 1.05562 0.766956i 0.0525844 0.0382048i
\(404\) −15.2190 + 2.11644i −0.757175 + 0.105297i
\(405\) 2.07855 + 6.39712i 0.103284 + 0.317876i
\(406\) 13.8487 + 5.89024i 0.687298 + 0.292328i
\(407\) 12.7295 11.7527i 0.630977 0.582561i
\(408\) 21.3269 8.13357i 1.05584 0.402672i
\(409\) −26.3195 + 8.55173i −1.30142 + 0.422856i −0.876074 0.482176i \(-0.839846\pi\)
−0.425343 + 0.905032i \(0.639846\pi\)
\(410\) −9.49378 15.8262i −0.468865 0.781602i
\(411\) −10.0130 13.7817i −0.493904 0.679800i
\(412\) −0.360488 0.741832i −0.0177600 0.0365474i
\(413\) 17.2832 + 5.61564i 0.850449 + 0.276328i
\(414\) 3.18266 0.732351i 0.156419 0.0359931i
\(415\) 7.09568 + 5.15531i 0.348313 + 0.253064i
\(416\) 1.64720 + 0.208302i 0.0807608 + 0.0102128i
\(417\) 36.6518i 1.79485i
\(418\) −6.63952 4.53362i −0.324750 0.221746i
\(419\) 22.9710i 1.12221i 0.827746 + 0.561103i \(0.189623\pi\)
−0.827746 + 0.561103i \(0.810377\pi\)
\(420\) −14.4509 7.71051i −0.705131 0.376235i
\(421\) 24.3592 + 17.6980i 1.18719 + 0.862546i 0.992965 0.118410i \(-0.0377796\pi\)
0.194229 + 0.980956i \(0.437780\pi\)
\(422\) 6.12182 + 26.6043i 0.298005 + 1.29508i
\(423\) −31.9983 10.3969i −1.55581 0.505514i
\(424\) −0.222612 4.43170i −0.0108110 0.215222i
\(425\) −0.770618 1.06066i −0.0373804 0.0514498i
\(426\) −11.8539 + 7.11089i −0.574325 + 0.344524i
\(427\) −11.6010 + 3.76939i −0.561411 + 0.182413i
\(428\) −7.18017 7.45684i −0.347066 0.360440i
\(429\) 0.517923 2.59556i 0.0250055 0.125315i
\(430\) −4.51190 + 10.6080i −0.217583 + 0.511565i
\(431\) 3.14369 + 9.67528i 0.151426 + 0.466042i 0.997781 0.0665771i \(-0.0212078\pi\)
−0.846355 + 0.532619i \(0.821208\pi\)
\(432\) 11.9069 + 9.35830i 0.572871 + 0.450252i
\(433\) −22.2763 + 16.1847i −1.07053 + 0.777785i −0.976007 0.217737i \(-0.930132\pi\)
−0.0945224 + 0.995523i \(0.530132\pi\)
\(434\) 5.33033 6.12290i 0.255864 0.293908i
\(435\) −16.1527 + 49.7130i −0.774464 + 2.38356i
\(436\) −4.41002 + 24.8006i −0.211201 + 1.18773i
\(437\) 0.529682 0.729044i 0.0253381 0.0348749i
\(438\) 16.3997 + 1.44675i 0.783609 + 0.0691282i
\(439\) −11.5438 −0.550957 −0.275479 0.961307i \(-0.588836\pi\)
−0.275479 + 0.961307i \(0.588836\pi\)
\(440\) 9.73310 19.5994i 0.464008 0.934366i
\(441\) 23.4241 1.11543
\(442\) 1.22722 + 0.108263i 0.0583731 + 0.00514954i
\(443\) −9.98691 + 13.7458i −0.474492 + 0.653083i −0.977435 0.211237i \(-0.932251\pi\)
0.502942 + 0.864320i \(0.332251\pi\)
\(444\) −4.97313 + 27.9673i −0.236014 + 1.32727i
\(445\) −0.431183 + 1.32704i −0.0204400 + 0.0629080i
\(446\) −10.0649 + 11.5614i −0.476587 + 0.547450i
\(447\) −38.3841 + 27.8877i −1.81551 + 1.31904i
\(448\) 10.2778 1.03515i 0.485579 0.0489063i
\(449\) 1.89015 + 5.81730i 0.0892019 + 0.274535i 0.985699 0.168514i \(-0.0538968\pi\)
−0.896497 + 0.443049i \(0.853897\pi\)
\(450\) 1.07396 2.52502i 0.0506271 0.119031i
\(451\) 9.07566 16.1828i 0.427356 0.762017i
\(452\) 3.69107 + 3.83330i 0.173613 + 0.180303i
\(453\) −25.4046 + 8.25445i −1.19361 + 0.387828i
\(454\) 29.1020 17.4576i 1.36583 0.819327i
\(455\) −0.519642 0.715226i −0.0243612 0.0335303i
\(456\) 13.1650 0.661303i 0.616510 0.0309683i
\(457\) −6.20446 2.01595i −0.290232 0.0943022i 0.160282 0.987071i \(-0.448760\pi\)
−0.450515 + 0.892769i \(0.648760\pi\)
\(458\) 7.79551 + 33.8778i 0.364260 + 1.58301i
\(459\) 9.09126 + 6.60518i 0.424344 + 0.308304i
\(460\) 2.16404 + 1.15466i 0.100899 + 0.0538363i
\(461\) 19.0882i 0.889026i −0.895773 0.444513i \(-0.853377\pi\)
0.895773 0.444513i \(-0.146623\pi\)
\(462\) −0.480994 16.4597i −0.0223779 0.765775i
\(463\) 13.0359i 0.605829i −0.953018 0.302915i \(-0.902040\pi\)
0.953018 0.302915i \(-0.0979597\pi\)
\(464\) −8.99479 31.7146i −0.417573 1.47232i
\(465\) 22.8116 + 16.5736i 1.05786 + 0.768583i
\(466\) 19.7147 4.53647i 0.913264 0.210148i
\(467\) 14.4349 + 4.69019i 0.667969 + 0.217036i 0.623320 0.781967i \(-0.285783\pi\)
0.0446484 + 0.999003i \(0.485783\pi\)
\(468\) 1.12696 + 2.31913i 0.0520940 + 0.107202i
\(469\) −7.91210 10.8901i −0.365347 0.502857i
\(470\) −12.9989 21.6694i −0.599597 0.999534i
\(471\) 39.8326 12.9424i 1.83539 0.596355i
\(472\) −14.1849 37.1941i −0.652914 1.71200i
\(473\) −11.5097 + 1.35520i −0.529219 + 0.0623122i
\(474\) −34.8535 14.8242i −1.60088 0.680899i
\(475\) −0.233968 0.720080i −0.0107352 0.0330395i
\(476\) 7.59182 1.05576i 0.347971 0.0483908i
\(477\) 5.57496 4.05045i 0.255260 0.185457i
\(478\) −21.0811 18.3523i −0.964228 0.839416i
\(479\) −8.09752 + 24.9216i −0.369985 + 1.13870i 0.576815 + 0.816875i \(0.304295\pi\)
−0.946800 + 0.321822i \(0.895705\pi\)
\(480\) 6.71857 + 35.2442i 0.306659 + 1.60867i
\(481\) −0.901199 + 1.24039i −0.0410911 + 0.0565571i
\(482\) −0.811590 + 9.19986i −0.0369669 + 0.419042i
\(483\) 1.84571 0.0839827
\(484\) 21.9625 1.28469i 0.998294 0.0583952i
\(485\) 19.4230 0.881954
\(486\) 2.38586 27.0452i 0.108225 1.22679i
\(487\) −16.0181 + 22.0471i −0.725851 + 0.999048i 0.273458 + 0.961884i \(0.411832\pi\)
−0.999309 + 0.0371640i \(0.988168\pi\)
\(488\) 22.3775 + 14.6012i 1.01298 + 0.660967i
\(489\) −9.04656 + 27.8424i −0.409099 + 1.25908i
\(490\) 13.2691 + 11.5515i 0.599436 + 0.521843i
\(491\) 17.3230 12.5859i 0.781778 0.567995i −0.123734 0.992315i \(-0.539487\pi\)
0.905512 + 0.424320i \(0.139487\pi\)
\(492\) 4.19012 + 30.1305i 0.188905 + 1.35839i
\(493\) −7.55888 23.2638i −0.340435 1.04775i
\(494\) 0.654717 + 0.278470i 0.0294571 + 0.0125290i
\(495\) 33.7510 3.97397i 1.51699 0.178617i
\(496\) −17.7699 0.672029i −0.797891 0.0301750i
\(497\) −4.41473 + 1.43443i −0.198028 + 0.0643431i
\(498\) −7.43695 12.3975i −0.333258 0.555544i
\(499\) −18.1317 24.9561i −0.811685 1.11719i −0.991061 0.133408i \(-0.957408\pi\)
0.179376 0.983781i \(-0.442592\pi\)
\(500\) −19.1278 + 9.29502i −0.855422 + 0.415686i
\(501\) −16.6063 5.39573i −0.741917 0.241063i
\(502\) −6.57478 + 1.51290i −0.293447 + 0.0675240i
\(503\) −25.6773 18.6557i −1.14489 0.831815i −0.157101 0.987583i \(-0.550215\pi\)
−0.987794 + 0.155768i \(0.950215\pi\)
\(504\) 10.0684 + 12.4888i 0.448484 + 0.556296i
\(505\) 17.9219i 0.797515i
\(506\) 0.0720296 + 2.46487i 0.00320211 + 0.109577i
\(507\) 35.1117i 1.55936i
\(508\) −18.7978 + 35.2305i −0.834018 + 1.56310i
\(509\) −5.41179 3.93190i −0.239873 0.174278i 0.461354 0.887216i \(-0.347364\pi\)
−0.701227 + 0.712938i \(0.747364\pi\)
\(510\) 5.97006 + 25.9448i 0.264359 + 1.14885i
\(511\) 5.25794 + 1.70841i 0.232598 + 0.0755756i
\(512\) −15.8955 16.1038i −0.702488 0.711696i
\(513\) 3.81451 + 5.25022i 0.168415 + 0.231803i
\(514\) −3.68302 + 2.20936i −0.162451 + 0.0974505i
\(515\) 0.914922 0.297276i 0.0403163 0.0130995i
\(516\) 13.6875 13.1797i 0.602560 0.580202i
\(517\) 12.4265 22.1575i 0.546515 0.974488i
\(518\) −3.73351 + 8.77795i −0.164041 + 0.385681i
\(519\) −3.03967 9.35513i −0.133426 0.410645i
\(520\) −0.505276 + 1.86948i −0.0221578 + 0.0819820i
\(521\) −10.0067 + 7.27028i −0.438401 + 0.318517i −0.784999 0.619497i \(-0.787337\pi\)
0.346598 + 0.938014i \(0.387337\pi\)
\(522\) 33.6148 38.6130i 1.47128 1.69004i
\(523\) −1.92840 + 5.93501i −0.0843231 + 0.259520i −0.984324 0.176367i \(-0.943565\pi\)
0.900001 + 0.435887i \(0.143565\pi\)
\(524\) −40.3935 7.18274i −1.76460 0.313779i
\(525\) 0.911507 1.25458i 0.0397814 0.0547545i
\(526\) 19.9578 + 1.76063i 0.870200 + 0.0767671i
\(527\) −13.1950 −0.574784
\(528\) −27.4080 + 23.4496i −1.19278 + 1.02051i
\(529\) 22.7236 0.987983
\(530\) 5.15551 + 0.454808i 0.223941 + 0.0197556i
\(531\) 36.3368 50.0134i 1.57688 2.17039i
\(532\) 4.35812 + 0.774958i 0.188949 + 0.0335987i
\(533\) −0.507388 + 1.56158i −0.0219774 + 0.0676395i
\(534\) 1.51017 1.73472i 0.0653515 0.0750685i
\(535\) 9.76811 7.09695i 0.422312 0.306828i
\(536\) −7.69337 + 28.4648i −0.332303 + 1.22949i
\(537\) −4.20746 12.9492i −0.181565 0.558800i
\(538\) −0.554489 + 1.30367i −0.0239057 + 0.0562053i
\(539\) −3.46101 + 17.3448i −0.149076 + 0.747093i
\(540\) −12.7242 + 12.2521i −0.547561 + 0.527245i
\(541\) 24.6331 8.00377i 1.05906 0.344109i 0.272841 0.962059i \(-0.412037\pi\)
0.786217 + 0.617950i \(0.212037\pi\)
\(542\) 21.5760 12.9429i 0.926770 0.555947i
\(543\) 15.6649 + 21.5608i 0.672244 + 0.925264i
\(544\) −12.2379 11.4951i −0.524696 0.492847i
\(545\) −27.9425 9.07907i −1.19693 0.388905i
\(546\) 0.326778 + 1.42012i 0.0139848 + 0.0607755i
\(547\) 13.5035 + 9.81087i 0.577368 + 0.419482i 0.837774 0.546017i \(-0.183857\pi\)
−0.260406 + 0.965499i \(0.583857\pi\)
\(548\) −5.89886 + 11.0555i −0.251987 + 0.472268i
\(549\) 41.4954i 1.77098i
\(550\) 1.71101 + 1.16832i 0.0729578 + 0.0498172i
\(551\) 14.1263i 0.601801i
\(552\) −2.53754 3.14755i −0.108005 0.133968i
\(553\) −10.2897 7.47589i −0.437562 0.317907i
\(554\) −26.7187 + 6.14814i −1.13517 + 0.261209i
\(555\) −31.5105 10.2384i −1.33755 0.434595i
\(556\) 24.2491 11.7837i 1.02839 0.499739i
\(557\) −10.9144 15.0224i −0.462460 0.636522i 0.512557 0.858653i \(-0.328698\pi\)
−0.975017 + 0.222132i \(0.928698\pi\)
\(558\) −14.2062 23.6819i −0.601396 1.00253i
\(559\) 0.975400 0.316927i 0.0412550 0.0134046i
\(560\) −0.455325 + 12.0398i −0.0192410 + 0.508773i
\(561\) −19.6651 + 18.1562i −0.830262 + 0.766555i
\(562\) 19.1257 + 8.13471i 0.806769 + 0.343142i
\(563\) −7.00832 21.5694i −0.295366 0.909042i −0.983098 0.183078i \(-0.941394\pi\)
0.687733 0.725964i \(-0.258606\pi\)
\(564\) 5.73714 + 41.2549i 0.241577 + 1.73714i
\(565\) −5.02144 + 3.64829i −0.211253 + 0.153485i
\(566\) 2.66330 + 2.31855i 0.111947 + 0.0974560i
\(567\) 1.15052 3.54093i 0.0483172 0.148705i
\(568\) 8.51570 + 5.55647i 0.357311 + 0.233144i
\(569\) 0.0874036 0.120301i 0.00366415 0.00504327i −0.807181 0.590304i \(-0.799008\pi\)
0.810845 + 0.585261i \(0.199008\pi\)
\(570\) −1.35108 + 15.3153i −0.0565904 + 0.641486i
\(571\) 22.0331 0.922057 0.461028 0.887385i \(-0.347481\pi\)
0.461028 + 0.887385i \(0.347481\pi\)
\(572\) −1.88375 + 0.491819i −0.0787637 + 0.0205640i
\(573\) 31.7832 1.32776
\(574\) −0.897694 + 10.1759i −0.0374690 + 0.424733i
\(575\) −0.136500 + 0.187876i −0.00569242 + 0.00783495i
\(576\) 7.45515 34.3401i 0.310631 1.43084i
\(577\) 1.21706 3.74573i 0.0506669 0.155937i −0.922522 0.385945i \(-0.873875\pi\)
0.973189 + 0.230008i \(0.0738754\pi\)
\(578\) 8.73642 + 7.60555i 0.363387 + 0.316349i
\(579\) 2.53966 1.84517i 0.105545 0.0766827i
\(580\) 38.0836 5.29613i 1.58134 0.219910i
\(581\) −1.50021 4.61716i −0.0622391 0.191552i
\(582\) −29.4613 12.5307i −1.22121 0.519416i
\(583\) 2.17550 + 4.72655i 0.0901000 + 0.195754i
\(584\) −4.31539 11.3153i −0.178572 0.468231i
\(585\) −2.86025 + 0.929350i −0.118257 + 0.0384239i
\(586\) −5.46996 9.11848i −0.225962 0.376681i
\(587\) −11.1451 15.3399i −0.460006 0.633144i 0.514504 0.857488i \(-0.327976\pi\)
−0.974510 + 0.224344i \(0.927976\pi\)
\(588\) −12.6744 26.0821i −0.522684 1.07561i
\(589\) −7.24720 2.35476i −0.298616 0.0970261i
\(590\) 45.2476 10.4118i 1.86282 0.428646i
\(591\) 34.3690 + 24.9706i 1.41375 + 1.02715i
\(592\) 20.1023 5.70133i 0.826198 0.234323i
\(593\) 31.9983i 1.31401i 0.753885 + 0.657007i \(0.228178\pi\)
−0.753885 + 0.657007i \(0.771822\pi\)
\(594\) −17.0423 4.99196i −0.699253 0.204822i
\(595\) 8.94012i 0.366509i
\(596\) 30.7913 + 16.4292i 1.26126 + 0.672967i
\(597\) −24.1265 17.5290i −0.987433 0.717412i
\(598\) −0.0489355 0.212665i −0.00200112 0.00869651i
\(599\) 8.23336 + 2.67518i 0.336406 + 0.109305i 0.472349 0.881412i \(-0.343406\pi\)
−0.135943 + 0.990717i \(0.543406\pi\)
\(600\) −3.39265 + 0.170418i −0.138504 + 0.00695730i
\(601\) −12.9491 17.8228i −0.528203 0.727009i 0.458652 0.888616i \(-0.348332\pi\)
−0.986855 + 0.161607i \(0.948332\pi\)
\(602\) 5.47178 3.28239i 0.223013 0.133780i
\(603\) −43.5503 + 14.1503i −1.77350 + 0.576246i
\(604\) 13.6289 + 14.1540i 0.554551 + 0.575919i
\(605\) −2.04426 + 25.5787i −0.0831110 + 1.03992i
\(606\) −11.5623 + 27.1844i −0.469687 + 1.10429i
\(607\) 13.2005 + 40.6268i 0.535790 + 1.64899i 0.741936 + 0.670471i \(0.233908\pi\)
−0.206146 + 0.978521i \(0.566092\pi\)
\(608\) −4.67013 8.49748i −0.189399 0.344618i
\(609\) 23.4074 17.0065i 0.948517 0.689138i
\(610\) −20.4633 + 23.5059i −0.828534 + 0.951728i
\(611\) −0.694718 + 2.13812i −0.0281053 + 0.0864992i
\(612\) 4.56495 25.6718i 0.184527 1.03772i
\(613\) −5.74748 + 7.91073i −0.232139 + 0.319511i −0.909156 0.416456i \(-0.863272\pi\)
0.677018 + 0.735967i \(0.263272\pi\)
\(614\) −36.3443 3.20621i −1.46673 0.129392i
\(615\) −35.4817 −1.43076
\(616\) −10.7352 + 5.61008i −0.432535 + 0.226037i
\(617\) −22.4213 −0.902649 −0.451324 0.892360i \(-0.649048\pi\)
−0.451324 + 0.892360i \(0.649048\pi\)
\(618\) −1.57956 0.139345i −0.0635393 0.00560529i
\(619\) −11.3322 + 15.5975i −0.455481 + 0.626916i −0.973564 0.228414i \(-0.926646\pi\)
0.518083 + 0.855331i \(0.326646\pi\)
\(620\) 3.63121 20.4208i 0.145833 0.820120i
\(621\) 0.615093 1.89306i 0.0246828 0.0759660i
\(622\) −2.75265 + 3.16194i −0.110371 + 0.126782i
\(623\) 0.624841 0.453973i 0.0250337 0.0181881i
\(624\) 1.97251 2.50969i 0.0789635 0.100468i
\(625\) −8.34762 25.6913i −0.333905 1.02765i
\(626\) −0.334322 + 0.786031i −0.0133622 + 0.0314161i
\(627\) −14.0409 + 6.46266i −0.560741 + 0.258094i
\(628\) −21.3691 22.1925i −0.852720 0.885579i
\(629\) 14.7457 4.79118i 0.587951 0.191037i
\(630\) −16.0454 + 9.62524i −0.639263 + 0.383479i
\(631\) 22.5021 + 30.9715i 0.895794 + 1.23296i 0.971790 + 0.235847i \(0.0757864\pi\)
−0.0759958 + 0.997108i \(0.524214\pi\)
\(632\) 1.39772 + 27.8254i 0.0555982 + 1.10683i
\(633\) 49.9163 + 16.2188i 1.98400 + 0.644639i
\(634\) −7.27674 31.6234i −0.288996 1.25592i
\(635\) −37.6803 27.3763i −1.49530 1.08640i
\(636\) −7.52659 4.01594i −0.298449 0.159242i
\(637\) 1.56519i 0.0620153i
\(638\) 23.6249 + 30.5959i 0.935319 + 1.21130i
\(639\) 15.7910i 0.624682i
\(640\) 21.1578 15.7762i 0.836335 0.623608i
\(641\) 25.5946 + 18.5955i 1.01092 + 0.734480i 0.964403 0.264438i \(-0.0851864\pi\)
0.0465216 + 0.998917i \(0.485186\pi\)
\(642\) −19.3951 + 4.46293i −0.765463 + 0.176138i
\(643\) 14.1716 + 4.60464i 0.558874 + 0.181589i 0.574814 0.818284i \(-0.305074\pi\)
−0.0159405 + 0.999873i \(0.505074\pi\)
\(644\) −0.593402 1.22114i −0.0233833 0.0481195i
\(645\) 13.0269 + 17.9300i 0.512934 + 0.705993i
\(646\) −3.70114 6.16983i −0.145619 0.242749i
\(647\) −39.0933 + 12.7022i −1.53692 + 0.499374i −0.950523 0.310653i \(-0.899452\pi\)
−0.586393 + 0.810027i \(0.699452\pi\)
\(648\) −7.62022 + 2.90617i −0.299351 + 0.114165i
\(649\) 31.6643 + 34.2959i 1.24293 + 1.34623i
\(650\) −0.168721 0.0717621i −0.00661780 0.00281474i
\(651\) −4.82296 14.8435i −0.189027 0.581764i
\(652\) 21.3293 2.96617i 0.835318 0.116164i
\(653\) −3.70761 + 2.69374i −0.145090 + 0.105414i −0.657962 0.753051i \(-0.728581\pi\)
0.512872 + 0.858465i \(0.328581\pi\)
\(654\) 36.5265 + 31.7985i 1.42830 + 1.24342i
\(655\) 14.7874 45.5109i 0.577791 1.77826i
\(656\) 18.5874 12.4593i 0.725718 0.486453i
\(657\) 11.0545 15.2152i 0.431278 0.593603i
\(658\) −1.22913 + 13.9329i −0.0479164 + 0.543161i
\(659\) 38.0732 1.48312 0.741560 0.670886i \(-0.234086\pi\)
0.741560 + 0.670886i \(0.234086\pi\)
\(660\) −22.6870 35.4306i −0.883092 1.37913i
\(661\) −9.34038 −0.363299 −0.181649 0.983363i \(-0.558144\pi\)
−0.181649 + 0.983363i \(0.558144\pi\)
\(662\) 0.551092 6.24696i 0.0214188 0.242795i
\(663\) 1.39222 1.91622i 0.0540692 0.0744198i
\(664\) −5.81126 + 8.90617i −0.225521 + 0.345627i
\(665\) −1.59544 + 4.91025i −0.0618684 + 0.190411i
\(666\) 24.4748 + 21.3067i 0.948377 + 0.825617i
\(667\) −3.50530 + 2.54675i −0.135726 + 0.0986104i
\(668\) 1.76914 + 12.7216i 0.0684501 + 0.492214i
\(669\) 9.10685 + 28.0280i 0.352091 + 1.08363i
\(670\) −31.6481 13.4609i −1.22267 0.520039i
\(671\) −30.7260 6.13113i −1.18616 0.236689i
\(672\) 8.45810 17.9685i 0.326278 0.693148i
\(673\) 13.4864 4.38199i 0.519862 0.168913i −0.0373208 0.999303i \(-0.511882\pi\)
0.557183 + 0.830390i \(0.311882\pi\)
\(674\) −12.9217 21.5406i −0.497724 0.829711i
\(675\) −0.983004 1.35299i −0.0378358 0.0520766i
\(676\) −23.2301 + 11.2885i −0.893467 + 0.434174i
\(677\) −4.48196 1.45628i −0.172256 0.0559692i 0.221619 0.975133i \(-0.428866\pi\)
−0.393875 + 0.919164i \(0.628866\pi\)
\(678\) 9.97033 2.29424i 0.382908 0.0881096i
\(679\) −8.69775 6.31929i −0.333789 0.242512i
\(680\) 15.2459 12.2912i 0.584652 0.471345i
\(681\) 65.2454i 2.50021i
\(682\) 19.6347 7.02012i 0.751851 0.268814i
\(683\) 18.0462i 0.690519i 0.938507 + 0.345260i \(0.112209\pi\)
−0.938507 + 0.345260i \(0.887791\pi\)
\(684\) 7.08859 13.2853i 0.271039 0.507976i
\(685\) −11.8243 8.59084i −0.451782 0.328239i
\(686\) −5.05010 21.9468i −0.192814 0.837934i
\(687\) 63.5633 + 20.6530i 2.42509 + 0.787960i
\(688\) −13.1203 4.81846i −0.500209 0.183702i
\(689\) −0.270650 0.372518i −0.0103109 0.0141918i
\(690\) 4.04390 2.42584i 0.153949 0.0923501i
\(691\) −1.27888 + 0.415533i −0.0486509 + 0.0158076i −0.333241 0.942842i \(-0.608142\pi\)
0.284590 + 0.958649i \(0.408142\pi\)
\(692\) −5.21216 + 5.01877i −0.198137 + 0.190785i
\(693\) −16.4068 9.20132i −0.623244 0.349529i
\(694\) −2.14791 + 5.05000i −0.0815336 + 0.191695i
\(695\) 9.71740 + 29.9071i 0.368602 + 1.13444i
\(696\) −61.1830 16.5363i −2.31914 0.626808i
\(697\) 13.4330 9.75964i 0.508811 0.369673i
\(698\) 18.3098 21.0322i 0.693034 0.796081i
\(699\) 12.0187 36.9896i 0.454587 1.39908i
\(700\) −1.12309 0.199708i −0.0424490 0.00754824i
\(701\) −9.79382 + 13.4800i −0.369907 + 0.509134i −0.952876 0.303361i \(-0.901891\pi\)
0.582968 + 0.812495i \(0.301891\pi\)
\(702\) 1.56545 + 0.138101i 0.0590842 + 0.00521227i
\(703\) 8.95393 0.337704
\(704\) 24.3262 + 10.5942i 0.916827 + 0.399284i
\(705\) −48.5817 −1.82969
\(706\) 2.24868 + 0.198373i 0.0846300 + 0.00746587i
\(707\) −5.83090 + 8.02554i −0.219293 + 0.301832i
\(708\) −75.3498 13.3987i −2.83182 0.503552i
\(709\) 7.43557 22.8843i 0.279249 0.859440i −0.708815 0.705394i \(-0.750770\pi\)
0.988064 0.154045i \(-0.0492301\pi\)
\(710\) −7.78726 + 8.94514i −0.292251 + 0.335705i
\(711\) −35.0036 + 25.4316i −1.31274 + 0.953761i
\(712\) −1.63323 0.441423i −0.0612077 0.0165430i
\(713\) 0.722245 + 2.22284i 0.0270483 + 0.0832460i
\(714\) 5.76771 13.5606i 0.215851 0.507493i
\(715\) −0.265540 2.25523i −0.00993063 0.0843410i
\(716\) −7.21459 + 6.94690i −0.269622 + 0.259618i
\(717\) −51.1063 + 16.6054i −1.90860 + 0.620141i
\(718\) −18.7038 + 11.2200i −0.698019 + 0.418725i
\(719\) −6.65923 9.16564i −0.248347 0.341821i 0.666584 0.745430i \(-0.267756\pi\)
−0.914932 + 0.403609i \(0.867756\pi\)
\(720\) 38.4739 + 14.1296i 1.43384 + 0.526578i
\(721\) −0.506426 0.164548i −0.0188603 0.00612808i
\(722\) 5.09376 + 22.1365i 0.189570 + 0.823837i
\(723\) 14.3649 + 10.4367i 0.534237 + 0.388146i
\(724\) 9.22850 17.2959i 0.342975 0.642796i
\(725\) 3.64037i 0.135200i
\(726\) 19.6028 37.4795i 0.727530 1.39100i
\(727\) 0.700673i 0.0259865i −0.999916 0.0129933i \(-0.995864\pi\)
0.999916 0.0129933i \(-0.00413600\pi\)
\(728\) 0.834501 0.672772i 0.0309287 0.0249346i
\(729\) −35.2308 25.5967i −1.30485 0.948026i
\(730\) 13.7654 3.16750i 0.509480 0.117235i
\(731\) −9.86371 3.20491i −0.364823 0.118538i
\(732\) 46.2040 22.4525i 1.70775 0.829869i
\(733\) 17.6206 + 24.2526i 0.650830 + 0.895790i 0.999135 0.0415908i \(-0.0132426\pi\)
−0.348305 + 0.937381i \(0.613243\pi\)
\(734\) 7.67653 + 12.7968i 0.283346 + 0.472340i
\(735\) 32.1678 10.4519i 1.18653 0.385526i
\(736\) −1.26661 + 2.69080i −0.0466879 + 0.0991843i
\(737\) −4.04313 34.3383i −0.148930 1.26487i
\(738\) 31.9786 + 13.6014i 1.17715 + 0.500676i
\(739\) −13.4812 41.4910i −0.495915 1.52627i −0.815526 0.578721i \(-0.803552\pi\)
0.319611 0.947549i \(-0.396448\pi\)
\(740\) 3.35694 + 24.1392i 0.123404 + 0.887376i
\(741\) 1.10662 0.804008i 0.0406528 0.0295360i
\(742\) −2.16070 1.88101i −0.0793218 0.0690542i
\(743\) 10.5703 32.5321i 0.387788 1.19349i −0.546650 0.837361i \(-0.684097\pi\)
0.934438 0.356127i \(-0.115903\pi\)
\(744\) −18.6824 + 28.6321i −0.684929 + 1.04970i
\(745\) −23.9268 + 32.9324i −0.876610 + 1.20655i
\(746\) 4.65977 52.8213i 0.170606 1.93392i
\(747\) −16.5151 −0.604255
\(748\) 18.3347 + 7.17332i 0.670382 + 0.262283i
\(749\) −6.68321 −0.244199
\(750\) −3.59296 + 40.7283i −0.131196 + 1.48719i
\(751\) 0.851372 1.17181i 0.0310670 0.0427600i −0.793201 0.608960i \(-0.791587\pi\)
0.824268 + 0.566200i \(0.191587\pi\)
\(752\) 25.4500 17.0593i 0.928068 0.622090i
\(753\) −4.00819 + 12.3359i −0.146067 + 0.449546i
\(754\) −2.58011 2.24614i −0.0939621 0.0817995i
\(755\) −18.5411 + 13.4709i −0.674780 + 0.490257i
\(756\) 9.68417 1.34674i 0.352210 0.0489803i
\(757\) 9.41100 + 28.9641i 0.342049 + 1.05272i 0.963145 + 0.268983i \(0.0866875\pi\)
−0.621096 + 0.783734i \(0.713312\pi\)
\(758\) 27.7573 + 11.8060i 1.00819 + 0.428812i
\(759\) 4.13500 + 2.31900i 0.150091 + 0.0841744i
\(760\) 10.5671 4.03002i 0.383308 0.146184i
\(761\) 22.8716 7.43142i 0.829094 0.269389i 0.136430 0.990650i \(-0.456437\pi\)
0.692664 + 0.721261i \(0.256437\pi\)
\(762\) 39.4925 + 65.8345i 1.43066 + 2.38493i
\(763\) 9.55895 + 13.1568i 0.346057 + 0.476307i
\(764\) −10.2184 21.0280i −0.369690 0.760768i
\(765\) 28.9242 + 9.39804i 1.04576 + 0.339787i
\(766\) −39.7351 + 9.14329i −1.43569 + 0.330360i
\(767\) −3.34188 2.42802i −0.120668 0.0876707i
\(768\) −42.2706 + 10.2798i −1.52531 + 0.370939i
\(769\) 14.6461i 0.528151i −0.964502 0.264076i \(-0.914933\pi\)
0.964502 0.264076i \(-0.0850669\pi\)
\(770\) −4.75640 13.3032i −0.171409 0.479416i
\(771\) 8.25715i 0.297374i
\(772\) −2.03729 1.08703i −0.0733236 0.0391231i
\(773\) 21.4727 + 15.6009i 0.772320 + 0.561124i 0.902664 0.430345i \(-0.141608\pi\)
−0.130344 + 0.991469i \(0.541608\pi\)
\(774\) −4.86755 21.1535i −0.174961 0.760347i
\(775\) 1.86761 + 0.606824i 0.0670866 + 0.0217977i
\(776\) 1.18147 + 23.5205i 0.0424125 + 0.844337i
\(777\) 10.7795 + 14.8367i 0.386713 + 0.532265i
\(778\) −42.2995 + 25.3745i −1.51651 + 0.909720i
\(779\) 9.11960 2.96314i 0.326743 0.106165i
\(780\) 2.58244 + 2.68195i 0.0924662 + 0.0960293i
\(781\) −11.6927 2.33319i −0.418398 0.0834880i
\(782\) −0.863723 + 2.03072i −0.0308867 + 0.0726184i
\(783\) −9.64214 29.6755i −0.344582 1.06051i
\(784\) −13.1813 + 16.7710i −0.470759 + 0.598964i
\(785\) 29.0712 21.1214i 1.03759 0.753857i
\(786\) −51.7912 + 59.4920i −1.84733 + 2.12201i
\(787\) 6.33834 19.5074i 0.225937 0.695364i −0.772258 0.635309i \(-0.780873\pi\)
0.998195 0.0600544i \(-0.0191274\pi\)
\(788\) 5.47095 30.7669i 0.194895 1.09603i
\(789\) 22.6410 31.1626i 0.806040 1.10942i
\(790\) −32.3700 2.85561i −1.15167 0.101598i
\(791\) 3.43560 0.122156
\(792\) 6.86534 + 40.6294i 0.243949 + 1.44370i
\(793\) 2.77271 0.0984620
\(794\) −23.8221 2.10153i −0.845414 0.0745805i
\(795\) 5.84864 8.04996i 0.207430 0.285503i
\(796\) −3.84052 + 21.5979i −0.136124 + 0.765518i
\(797\) −10.1514 + 31.2427i −0.359580 + 1.10667i 0.593726 + 0.804667i \(0.297656\pi\)
−0.953306 + 0.302006i \(0.902344\pi\)
\(798\) 5.58784 6.41869i 0.197808 0.227219i
\(799\) 18.3925 13.3630i 0.650682 0.472748i
\(800\) 1.20350 + 2.18981i 0.0425501 + 0.0774215i
\(801\) −0.811905 2.49879i −0.0286873 0.0882903i
\(802\) −8.77880 + 20.6400i −0.309990 + 0.728825i
\(803\) 9.63304 + 10.4336i 0.339942 + 0.368195i
\(804\) 39.3204 + 40.8356i 1.38672 + 1.44016i
\(805\) 1.50606 0.489348i 0.0530816 0.0172473i
\(806\) −1.58242 + 0.949255i −0.0557383 + 0.0334361i
\(807\) 1.60094 + 2.20350i 0.0563557 + 0.0775670i
\(808\) 21.7027 1.09016i 0.763499 0.0383518i
\(809\) 17.7783 + 5.77654i 0.625053 + 0.203092i 0.604383 0.796694i \(-0.293420\pi\)
0.0206708 + 0.999786i \(0.493420\pi\)
\(810\) −2.13313 9.27021i −0.0749507 0.325722i
\(811\) −22.1490 16.0922i −0.777758 0.565074i 0.126547 0.991961i \(-0.459610\pi\)
−0.904305 + 0.426886i \(0.859610\pi\)
\(812\) −18.7772 10.0189i −0.658950 0.351594i
\(813\) 48.3724i 1.69650i
\(814\) −19.3932 + 14.9746i −0.679730 + 0.524860i
\(815\) 25.1173i 0.879821i
\(816\) −31.0549 + 8.80768i −1.08714 + 0.308331i
\(817\) −4.84558 3.52052i −0.169525 0.123167i
\(818\) 38.1402 8.77630i 1.33354 0.306856i
\(819\) 1.58320 + 0.514413i 0.0553215 + 0.0179750i
\(820\) 11.4075 + 23.4749i 0.398366 + 0.819780i
\(821\) 5.06427 + 6.97036i 0.176744 + 0.243267i 0.888193 0.459470i \(-0.151961\pi\)
−0.711449 + 0.702738i \(0.751961\pi\)
\(822\) 12.3930 + 20.6592i 0.432255 + 0.720573i
\(823\) −3.63990 + 1.18267i −0.126879 + 0.0412254i −0.371768 0.928326i \(-0.621248\pi\)
0.244889 + 0.969551i \(0.421248\pi\)
\(824\) 0.415643 + 1.08985i 0.0144796 + 0.0379667i
\(825\) 3.61837 1.66543i 0.125975 0.0579830i
\(826\) −23.6496 10.0589i −0.822876 0.349993i
\(827\) −8.45284 26.0152i −0.293934 0.904636i −0.983577 0.180487i \(-0.942233\pi\)
0.689643 0.724149i \(-0.257767\pi\)
\(828\) −4.57456 + 0.636165i −0.158977 + 0.0221083i
\(829\) −14.2443 + 10.3491i −0.494723 + 0.359438i −0.806998 0.590554i \(-0.798909\pi\)
0.312274 + 0.949992i \(0.398909\pi\)
\(830\) −9.35530 8.14433i −0.324727 0.282694i
\(831\) −16.2885 + 50.1309i −0.565043 + 1.73902i
\(832\) −2.29460 0.498152i −0.0795509 0.0172703i
\(833\) −9.30347 + 12.8051i −0.322346 + 0.443671i
\(834\) 4.55494 51.6329i 0.157725 1.78790i
\(835\) −14.9810 −0.518438
\(836\) 8.78996 + 7.21183i 0.304007 + 0.249426i
\(837\) −16.8316 −0.581786
\(838\) 2.85474 32.3602i 0.0986154 1.11786i
\(839\) −0.148971 + 0.205041i −0.00514306 + 0.00707881i −0.811581 0.584240i \(-0.801393\pi\)
0.806438 + 0.591319i \(0.201393\pi\)
\(840\) 19.3993 + 12.6580i 0.669341 + 0.436743i
\(841\) −12.0270 + 37.0154i −0.414726 + 1.27639i
\(842\) −32.1164 27.9592i −1.10680 0.963536i
\(843\) 32.3268 23.4868i 1.11340 0.808929i
\(844\) −5.31779 38.2394i −0.183046 1.31625i
\(845\) −9.30907 28.6504i −0.320242 0.985603i
\(846\) 43.7853 + 18.6232i 1.50537 + 0.640278i
\(847\) 9.23746 10.7892i 0.317403 0.370721i
\(848\) −0.237151 + 6.27079i −0.00814381 + 0.215340i
\(849\) 6.45654 2.09786i 0.221588 0.0719983i
\(850\) 0.953787 + 1.58997i 0.0327146 + 0.0545356i
\(851\) −1.61425 2.22182i −0.0553358 0.0761632i
\(852\) 17.5828 8.54426i 0.602378 0.292721i
\(853\) −35.2985 11.4692i −1.20860 0.392697i −0.365680 0.930741i \(-0.619163\pi\)
−0.842917 + 0.538044i \(0.819163\pi\)
\(854\) 16.8112 3.86837i 0.575269 0.132373i
\(855\) 14.2091 + 10.3235i 0.485941 + 0.353057i
\(856\) 9.18830 + 11.3971i 0.314050 + 0.389545i
\(857\) 20.9360i 0.715161i 0.933882 + 0.357580i \(0.116398\pi\)
−0.933882 + 0.357580i \(0.883602\pi\)
\(858\) −1.05219 + 3.59211i −0.0359210 + 0.122633i
\(859\) 20.6926i 0.706022i 0.935619 + 0.353011i \(0.114842\pi\)
−0.935619 + 0.353011i \(0.885158\pi\)
\(860\) 7.67443 14.3833i 0.261696 0.490465i
\(861\) 15.8889 + 11.5440i 0.541493 + 0.393417i
\(862\) −3.22624 14.0207i −0.109886 0.477546i
\(863\) −35.9307 11.6746i −1.22309 0.397408i −0.374887 0.927071i \(-0.622318\pi\)
−0.848208 + 0.529663i \(0.822318\pi\)
\(864\) −15.6107 14.6632i −0.531088 0.498852i
\(865\) −4.96060 6.82768i −0.168666 0.232148i
\(866\) 33.3929 20.0316i 1.13474 0.680702i
\(867\) 21.1794 6.88161i 0.719290 0.233712i
\(868\) −8.27000 + 7.96315i −0.280702 + 0.270287i
\(869\) −13.6594 29.6767i −0.463362 1.00671i
\(870\) 28.9332 68.0254i 0.980926 2.30628i
\(871\) 0.945523 + 2.91002i 0.0320378 + 0.0986023i
\(872\) 9.29469 34.3895i 0.314758 1.16458i
\(873\) −29.5882 + 21.4971i −1.00141 + 0.727566i
\(874\) −0.836788 + 0.961209i −0.0283048 + 0.0325134i
\(875\) −4.24279 + 13.0580i −0.143433 + 0.441440i
\(876\) −22.9232 4.07619i −0.774503 0.137722i
\(877\) 6.81007 9.37325i 0.229960 0.316512i −0.678408 0.734686i \(-0.737330\pi\)
0.908367 + 0.418173i \(0.137330\pi\)
\(878\) 16.2623 + 1.43462i 0.548826 + 0.0484161i
\(879\) −20.4432 −0.689532
\(880\) −16.1472 + 26.4010i −0.544321 + 0.889976i
\(881\) −24.6157 −0.829325 −0.414662 0.909975i \(-0.636100\pi\)
−0.414662 + 0.909975i \(0.636100\pi\)
\(882\) −32.9985 2.91106i −1.11112 0.0980203i
\(883\) −23.0095 + 31.6699i −0.774333 + 1.06578i 0.221552 + 0.975149i \(0.428888\pi\)
−0.995885 + 0.0906289i \(0.971112\pi\)
\(884\) −1.71539 0.305029i −0.0576947 0.0102592i
\(885\) 27.5843 84.8959i 0.927237 2.85374i
\(886\) 15.7773 18.1232i 0.530047 0.608860i
\(887\) 38.4919 27.9660i 1.29243 0.939006i 0.292580 0.956241i \(-0.405486\pi\)
0.999851 + 0.0172350i \(0.00548633\pi\)
\(888\) 10.4815 38.7807i 0.351737 1.30140i
\(889\) 7.96657 + 24.5186i 0.267190 + 0.822326i
\(890\) 0.772346 1.81588i 0.0258891 0.0608684i
\(891\) 7.02646 6.48731i 0.235395 0.217333i
\(892\) 15.6157 15.0363i 0.522851 0.503451i
\(893\) 12.4866 4.05715i 0.417848 0.135767i
\(894\) 57.5391 34.5163i 1.92439 1.15440i
\(895\) −6.86639 9.45077i −0.229518 0.315904i
\(896\) −14.6074 + 0.180981i −0.487998 + 0.00604616i
\(897\) −0.399012 0.129647i −0.0133226 0.00432879i
\(898\) −1.93979 8.42997i −0.0647316 0.281312i
\(899\) 29.6410 + 21.5354i 0.988581 + 0.718246i
\(900\) −1.82674 + 3.42363i −0.0608913 + 0.114121i
\(901\) 4.65637i 0.155126i
\(902\) −14.7964 + 21.6695i −0.492666 + 0.721514i
\(903\) 12.2675i 0.408236i
\(904\) −4.72338 5.85884i −0.157097 0.194862i
\(905\) 18.4986 + 13.4400i 0.614913 + 0.446760i
\(906\) 36.8144 8.47122i 1.22308 0.281437i
\(907\) −3.43208 1.11515i −0.113960 0.0370279i 0.251482 0.967862i \(-0.419082\pi\)
−0.365442 + 0.930834i \(0.619082\pi\)
\(908\) −43.1668 + 20.9766i −1.43254 + 0.696133i
\(909\) 19.8357 + 27.3015i 0.657908 + 0.905532i
\(910\) 0.643156 + 1.07215i 0.0213204 + 0.0355414i
\(911\) −29.8894 + 9.71164i −0.990278 + 0.321761i −0.758974 0.651121i \(-0.774299\pi\)
−0.231304 + 0.972881i \(0.574299\pi\)
\(912\) −18.6283 0.704495i −0.616846 0.0233282i
\(913\) 2.44017 12.2289i 0.0807579 0.404716i
\(914\) 8.48995 + 3.61102i 0.280823 + 0.119442i
\(915\) 18.5154 + 56.9847i 0.612102 + 1.88386i
\(916\) −6.77166 48.6940i −0.223742 1.60889i
\(917\) −21.4289 + 15.5690i −0.707643 + 0.514133i
\(918\) −11.9864 10.4348i −0.395609 0.344401i
\(919\) −8.08812 + 24.8927i −0.266802 + 0.821133i 0.724470 + 0.689306i \(0.242084\pi\)
−0.991273 + 0.131827i \(0.957916\pi\)
\(920\) −2.90508 1.89556i −0.0957776 0.0624947i
\(921\) −41.2305 + 56.7489i −1.35859 + 1.86994i
\(922\) −2.37220 + 26.8903i −0.0781244 + 0.885586i
\(923\) 1.05515 0.0347307
\(924\) −1.36795 + 23.2473i −0.0450023 + 0.764779i
\(925\) −2.30744 −0.0758681
\(926\) −1.62005 + 18.3642i −0.0532381 + 0.603486i
\(927\) −1.06473 + 1.46548i −0.0349704 + 0.0481326i
\(928\) 8.72997 + 45.7956i 0.286575 + 1.50331i
\(929\) 8.71671 26.8273i 0.285986 0.880175i −0.700115 0.714030i \(-0.746868\pi\)
0.986101 0.166145i \(-0.0531320\pi\)
\(930\) −30.0760 26.1829i −0.986231 0.858571i
\(931\) −7.39499 + 5.37278i −0.242361 + 0.176086i
\(932\) −28.3367 + 3.94066i −0.928198 + 0.129080i
\(933\) 2.49063 + 7.66538i 0.0815397 + 0.250953i
\(934\) −19.7522 8.40119i −0.646312 0.274895i
\(935\) −11.2326 + 20.0288i −0.367346 + 0.655013i
\(936\) −1.29939 3.40711i −0.0424719 0.111365i
\(937\) 20.4298 6.63805i 0.667413 0.216856i 0.0443365 0.999017i \(-0.485883\pi\)
0.623076 + 0.782161i \(0.285883\pi\)
\(938\) 9.79274 + 16.3246i 0.319744 + 0.533017i
\(939\) 0.965265 + 1.32857i 0.0315002 + 0.0433563i
\(940\) 15.6192 + 32.1420i 0.509442 + 1.04836i
\(941\) 27.2146 + 8.84257i 0.887172 + 0.288260i 0.716932 0.697143i \(-0.245546\pi\)
0.170240 + 0.985403i \(0.445546\pi\)
\(942\) −57.7223 + 13.2823i −1.88070 + 0.432760i
\(943\) −2.37939 1.72873i −0.0774835 0.0562951i
\(944\) 15.3606 + 54.1597i 0.499944 + 1.76275i
\(945\) 11.4041i 0.370974i
\(946\) 16.3827 0.478743i 0.532647 0.0155653i
\(947\) 0.894236i 0.0290588i 0.999894 + 0.0145294i \(0.00462501\pi\)
−0.999894 + 0.0145294i \(0.995375\pi\)
\(948\) 47.2574 + 25.2150i 1.53485 + 0.818944i
\(949\) −1.01668 0.738661i −0.0330028 0.0239779i
\(950\) 0.240112 + 1.04348i 0.00779027 + 0.0338551i
\(951\) −59.3333 19.2786i −1.92402 0.625150i
\(952\) −10.8261 + 0.543815i −0.350877 + 0.0176251i
\(953\) −5.07423 6.98407i −0.164370 0.226236i 0.718885 0.695129i \(-0.244653\pi\)
−0.883255 + 0.468893i \(0.844653\pi\)
\(954\) −8.35706 + 5.01320i −0.270570 + 0.162308i
\(955\) 25.9344 8.42661i 0.839219 0.272679i
\(956\) 27.4171 + 28.4736i 0.886733 + 0.920902i
\(957\) 73.8078 8.69041i 2.38587 0.280921i
\(958\) 14.5045 34.1018i 0.468618 1.10178i
\(959\) 2.49995 + 7.69406i 0.0807277 + 0.248454i
\(960\) −5.08472 50.4850i −0.164109 1.62940i
\(961\) −9.09031 + 6.60449i −0.293236 + 0.213048i
\(962\) 1.42371 1.63540i 0.0459022 0.0527274i
\(963\) −7.02553 + 21.6224i −0.226395 + 0.696771i
\(964\) 2.28664 12.8594i 0.0736478 0.414172i
\(965\) 1.58310 2.17895i 0.0509619 0.0701430i
\(966\) −2.60013 0.229377i −0.0836578 0.00738010i
\(967\) −23.2776 −0.748557 −0.374278 0.927316i \(-0.622110\pi\)
−0.374278 + 0.927316i \(0.622110\pi\)
\(968\) −31.0991 0.919604i −0.999563 0.0295572i
\(969\) −13.8325 −0.444363
\(970\) −27.3620 2.41382i −0.878542 0.0775030i
\(971\) 18.9657 26.1040i 0.608638 0.837718i −0.387827 0.921732i \(-0.626774\pi\)
0.996465 + 0.0840143i \(0.0267742\pi\)
\(972\) −6.72214 + 37.8032i −0.215613 + 1.21254i
\(973\) 5.37876 16.5541i 0.172435 0.530701i
\(974\) 25.3053 29.0680i 0.810835 0.931398i
\(975\) −0.285178 + 0.207194i −0.00913300 + 0.00663551i
\(976\) −29.7095 23.3504i −0.950978 0.747427i
\(977\) 2.86676 + 8.82297i 0.0917157 + 0.282272i 0.986384 0.164459i \(-0.0525880\pi\)
−0.894668 + 0.446731i \(0.852588\pi\)
\(978\) 16.2044 38.0986i 0.518160 1.21826i
\(979\) 1.97023 0.231983i 0.0629689 0.00741420i
\(980\) −17.2571 17.9221i −0.551259 0.572501i
\(981\) 52.6150 17.0956i 1.67987 0.545822i
\(982\) −25.9678 + 15.5775i −0.828667 + 0.497098i
\(983\) −13.6886 18.8408i −0.436599 0.600927i 0.532853 0.846208i \(-0.321120\pi\)
−0.969452 + 0.245281i \(0.921120\pi\)
\(984\) −2.15830 42.9669i −0.0688040 1.36973i
\(985\) 34.6648 + 11.2633i 1.10451 + 0.358877i
\(986\) 7.75737 + 33.7121i 0.247045 + 1.07361i
\(987\) 21.7552 + 15.8061i 0.692476 + 0.503113i
\(988\) −0.887721 0.473658i −0.0282422 0.0150691i
\(989\) 1.83707i 0.0584155i
\(990\) −48.0403 + 1.40386i −1.52682 + 0.0446176i
\(991\) 42.4003i 1.34689i −0.739237 0.673446i \(-0.764814\pi\)
0.739237 0.673446i \(-0.235186\pi\)
\(992\) 24.9497 + 3.15509i 0.792153 + 0.100174i
\(993\) −9.75417 7.08682i −0.309539 0.224893i
\(994\) 6.39748 1.47210i 0.202916 0.0466922i
\(995\) −24.3341 7.90664i −0.771444 0.250657i
\(996\) 8.93604 + 18.3891i 0.283149 + 0.582680i
\(997\) −2.61173 3.59473i −0.0827142 0.113846i 0.765655 0.643252i \(-0.222415\pi\)
−0.848369 + 0.529405i \(0.822415\pi\)
\(998\) 22.4414 + 37.4100i 0.710370 + 1.18419i
\(999\) 18.8097 6.11165i 0.595113 0.193364i
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 44.2.g.a.39.1 yes 16
3.2 odd 2 396.2.r.a.127.4 16
4.3 odd 2 inner 44.2.g.a.39.2 yes 16
8.3 odd 2 704.2.u.c.127.1 16
8.5 even 2 704.2.u.c.127.4 16
11.2 odd 10 inner 44.2.g.a.35.2 yes 16
11.3 even 5 484.2.c.d.483.8 16
11.4 even 5 484.2.g.f.239.3 16
11.5 even 5 484.2.g.j.403.3 16
11.6 odd 10 484.2.g.f.403.2 16
11.7 odd 10 484.2.g.j.239.2 16
11.8 odd 10 484.2.c.d.483.9 16
11.9 even 5 484.2.g.i.475.3 16
11.10 odd 2 484.2.g.i.215.4 16
12.11 even 2 396.2.r.a.127.3 16
33.2 even 10 396.2.r.a.343.3 16
44.3 odd 10 484.2.c.d.483.10 16
44.7 even 10 484.2.g.j.239.3 16
44.15 odd 10 484.2.g.f.239.2 16
44.19 even 10 484.2.c.d.483.7 16
44.27 odd 10 484.2.g.j.403.2 16
44.31 odd 10 484.2.g.i.475.4 16
44.35 even 10 inner 44.2.g.a.35.1 16
44.39 even 10 484.2.g.f.403.3 16
44.43 even 2 484.2.g.i.215.3 16
88.13 odd 10 704.2.u.c.255.1 16
88.35 even 10 704.2.u.c.255.4 16
132.35 odd 10 396.2.r.a.343.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
44.2.g.a.35.1 16 44.35 even 10 inner
44.2.g.a.35.2 yes 16 11.2 odd 10 inner
44.2.g.a.39.1 yes 16 1.1 even 1 trivial
44.2.g.a.39.2 yes 16 4.3 odd 2 inner
396.2.r.a.127.3 16 12.11 even 2
396.2.r.a.127.4 16 3.2 odd 2
396.2.r.a.343.3 16 33.2 even 10
396.2.r.a.343.4 16 132.35 odd 10
484.2.c.d.483.7 16 44.19 even 10
484.2.c.d.483.8 16 11.3 even 5
484.2.c.d.483.9 16 11.8 odd 10
484.2.c.d.483.10 16 44.3 odd 10
484.2.g.f.239.2 16 44.15 odd 10
484.2.g.f.239.3 16 11.4 even 5
484.2.g.f.403.2 16 11.6 odd 10
484.2.g.f.403.3 16 44.39 even 10
484.2.g.i.215.3 16 44.43 even 2
484.2.g.i.215.4 16 11.10 odd 2
484.2.g.i.475.3 16 11.9 even 5
484.2.g.i.475.4 16 44.31 odd 10
484.2.g.j.239.2 16 11.7 odd 10
484.2.g.j.239.3 16 44.7 even 10
484.2.g.j.403.2 16 44.27 odd 10
484.2.g.j.403.3 16 11.5 even 5
704.2.u.c.127.1 16 8.3 odd 2
704.2.u.c.127.4 16 8.5 even 2
704.2.u.c.255.1 16 88.13 odd 10
704.2.u.c.255.4 16 88.35 even 10