Properties

Label 155.2.u.a.49.2
Level $155$
Weight $2$
Character 155.49
Analytic conductor $1.238$
Analytic rank $0$
Dimension $112$
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] = [155,2,Mod(9,155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(155, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("155.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 155 = 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 155.u (of order \(30\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.23768123133\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 49.2
Character \(\chi\) \(=\) 155.49
Dual form 155.2.u.a.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.48457 - 2.04333i) q^{2} +(0.435922 + 0.979096i) q^{3} +(-1.35323 + 4.16481i) q^{4} +(-1.48566 + 1.67117i) q^{5} +(1.35346 - 2.34427i) q^{6} +(2.47832 - 2.23149i) q^{7} +(5.71488 - 1.85688i) q^{8} +(1.23879 - 1.37582i) q^{9} +O(q^{10})\) \(q+(-1.48457 - 2.04333i) q^{2} +(0.435922 + 0.979096i) q^{3} +(-1.35323 + 4.16481i) q^{4} +(-1.48566 + 1.67117i) q^{5} +(1.35346 - 2.34427i) q^{6} +(2.47832 - 2.23149i) q^{7} +(5.71488 - 1.85688i) q^{8} +(1.23879 - 1.37582i) q^{9} +(5.62032 + 0.554728i) q^{10} +(2.11653 - 0.449882i) q^{11} +(-4.66765 + 0.490590i) q^{12} +(5.65888 + 0.594772i) q^{13} +(-8.23891 - 1.75123i) q^{14} +(-2.28387 - 0.726104i) q^{15} +(-5.19273 - 3.77274i) q^{16} +(-1.26869 + 5.96872i) q^{17} +(-4.65031 - 0.488768i) q^{18} +(-0.0457736 - 0.435507i) q^{19} +(-4.94967 - 8.44896i) q^{20} +(3.26520 + 1.45376i) q^{21} +(-4.06139 - 3.65689i) q^{22} +(-2.68120 + 0.871176i) q^{23} +(4.30930 + 4.78596i) q^{24} +(-0.585630 - 4.96559i) q^{25} +(-7.18566 - 12.4459i) q^{26} +(4.94497 + 1.60672i) q^{27} +(5.93999 + 13.3414i) q^{28} +(0.502231 - 0.364892i) q^{29} +(1.90689 + 5.74465i) q^{30} +(-4.10982 + 3.75625i) q^{31} +4.19340i q^{32} +(1.36312 + 1.87617i) q^{33} +(14.0795 - 6.26861i) q^{34} +(0.0472618 + 7.45694i) q^{35} +(4.05364 + 7.02111i) q^{36} +(-1.47288 - 0.850368i) q^{37} +(-0.821930 + 0.740069i) q^{38} +(1.88449 + 5.79986i) q^{39} +(-5.38720 + 12.3092i) q^{40} +(-5.45189 - 2.42734i) q^{41} +(-1.87689 - 8.83008i) q^{42} +(-3.37019 + 0.354221i) q^{43} +(-0.990474 + 9.42373i) q^{44} +(0.458804 + 4.11423i) q^{45} +(5.76053 + 4.18527i) q^{46} +(7.59692 - 10.4563i) q^{47} +(1.43025 - 6.72880i) q^{48} +(0.430828 - 4.09905i) q^{49} +(-9.27692 + 8.56838i) q^{50} +(-6.39700 + 1.35973i) q^{51} +(-10.1349 + 22.7633i) q^{52} +(-5.36509 - 4.83075i) q^{53} +(-4.05808 - 12.4895i) q^{54} +(-2.39261 + 4.20546i) q^{55} +(10.0197 - 17.3546i) q^{56} +(0.406449 - 0.234664i) q^{57} +(-1.49119 - 0.484517i) q^{58} +(7.68661 - 3.42230i) q^{59} +(6.11468 - 8.52929i) q^{60} -6.39962 q^{61} +(13.7766 + 2.82132i) q^{62} -6.17406i q^{63} +(-1.81697 + 1.32010i) q^{64} +(-9.40113 + 8.57333i) q^{65} +(1.81000 - 5.57061i) q^{66} +(5.07563 - 2.93042i) q^{67} +(-23.1418 - 13.3609i) q^{68} +(-2.02176 - 2.24539i) q^{69} +(15.1668 - 11.1669i) q^{70} +(-2.31253 + 2.56833i) q^{71} +(4.52481 - 10.1629i) q^{72} +(1.55845 + 7.33195i) q^{73} +(0.449006 + 4.27201i) q^{74} +(4.60650 - 2.73799i) q^{75} +(1.87574 + 0.398702i) q^{76} +(4.24154 - 5.83797i) q^{77} +(9.05338 - 12.4609i) q^{78} +(-3.33461 - 0.708794i) q^{79} +(14.0195 - 3.07294i) q^{80} +(0.00193395 + 0.0184003i) q^{81} +(3.13384 + 14.7436i) q^{82} +(0.461036 - 1.03550i) q^{83} +(-10.4732 + 11.6317i) q^{84} +(-8.08992 - 10.9877i) q^{85} +(5.72706 + 6.36054i) q^{86} +(0.576198 + 0.332668i) q^{87} +(11.2603 - 6.50116i) q^{88} +(-5.07259 + 15.6118i) q^{89} +(7.72560 - 7.04533i) q^{90} +(15.3517 - 11.1537i) q^{91} -12.3456i q^{92} +(-5.46929 - 2.38648i) q^{93} -32.6437 q^{94} +(0.795810 + 0.570519i) q^{95} +(-4.10574 + 1.82799i) q^{96} +(-16.5730 - 5.38488i) q^{97} +(-9.01531 + 5.20499i) q^{98} +(2.00298 - 3.46927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q + 16 q^{4} - 5 q^{5} - 26 q^{6} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q + 16 q^{4} - 5 q^{5} - 26 q^{6} - 32 q^{9} - 22 q^{10} - 10 q^{11} - 20 q^{14} - 18 q^{15} - 44 q^{16} - 46 q^{19} + 35 q^{20} + 26 q^{21} + 48 q^{24} + 19 q^{25} - 78 q^{26} + 16 q^{29} + 30 q^{30} - 26 q^{31} - 4 q^{34} - 27 q^{35} - 4 q^{36} - 63 q^{40} - 16 q^{41} - 86 q^{44} - 71 q^{45} + 4 q^{46} + 42 q^{49} - 10 q^{50} + 92 q^{51} + 32 q^{54} - 39 q^{55} - 34 q^{56} + 26 q^{59} - 71 q^{60} + 40 q^{61} + 24 q^{64} - 72 q^{65} + 252 q^{66} - 4 q^{69} - 26 q^{70} + 116 q^{71} - 18 q^{74} - 58 q^{75} + 224 q^{76} - 134 q^{79} + 158 q^{80} - 60 q^{81} - 20 q^{84} - 27 q^{85} - 126 q^{86} + 82 q^{89} + 129 q^{90} + 2 q^{91} - 244 q^{94} + 96 q^{95} + 208 q^{96} + 94 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/155\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(96\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{15}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.48457 2.04333i −1.04975 1.44485i −0.889028 0.457853i \(-0.848619\pi\)
−0.160719 0.987000i \(-0.551381\pi\)
\(3\) 0.435922 + 0.979096i 0.251680 + 0.565281i 0.994563 0.104140i \(-0.0332089\pi\)
−0.742883 + 0.669421i \(0.766542\pi\)
\(4\) −1.35323 + 4.16481i −0.676614 + 2.08240i
\(5\) −1.48566 + 1.67117i −0.664407 + 0.747371i
\(6\) 1.35346 2.34427i 0.552549 0.957042i
\(7\) 2.47832 2.23149i 0.936718 0.843424i −0.0511551 0.998691i \(-0.516290\pi\)
0.987873 + 0.155266i \(0.0496236\pi\)
\(8\) 5.71488 1.85688i 2.02051 0.656505i
\(9\) 1.23879 1.37582i 0.412930 0.458605i
\(10\) 5.62032 + 0.554728i 1.77730 + 0.175420i
\(11\) 2.11653 0.449882i 0.638158 0.135645i 0.122540 0.992464i \(-0.460896\pi\)
0.515618 + 0.856819i \(0.327563\pi\)
\(12\) −4.66765 + 0.490590i −1.34743 + 0.141621i
\(13\) 5.65888 + 0.594772i 1.56949 + 0.164960i 0.848958 0.528461i \(-0.177231\pi\)
0.720533 + 0.693421i \(0.243897\pi\)
\(14\) −8.23891 1.75123i −2.20194 0.468037i
\(15\) −2.28387 0.726104i −0.589693 0.187479i
\(16\) −5.19273 3.77274i −1.29818 0.943185i
\(17\) −1.26869 + 5.96872i −0.307703 + 1.44763i 0.504074 + 0.863660i \(0.331834\pi\)
−0.811777 + 0.583968i \(0.801500\pi\)
\(18\) −4.65031 0.488768i −1.09609 0.115204i
\(19\) −0.0457736 0.435507i −0.0105012 0.0999121i 0.988016 0.154353i \(-0.0493292\pi\)
−0.998517 + 0.0544405i \(0.982662\pi\)
\(20\) −4.94967 8.44896i −1.10678 1.88925i
\(21\) 3.26520 + 1.45376i 0.712525 + 0.317236i
\(22\) −4.06139 3.65689i −0.865891 0.779652i
\(23\) −2.68120 + 0.871176i −0.559070 + 0.181653i −0.574903 0.818222i \(-0.694960\pi\)
0.0158328 + 0.999875i \(0.494960\pi\)
\(24\) 4.30930 + 4.78596i 0.879632 + 0.976930i
\(25\) −0.585630 4.96559i −0.117126 0.993117i
\(26\) −7.18566 12.4459i −1.40922 2.44085i
\(27\) 4.94497 + 1.60672i 0.951660 + 0.309213i
\(28\) 5.93999 + 13.3414i 1.12255 + 2.52130i
\(29\) 0.502231 0.364892i 0.0932619 0.0677587i −0.540177 0.841551i \(-0.681643\pi\)
0.633439 + 0.773793i \(0.281643\pi\)
\(30\) 1.90689 + 5.74465i 0.348148 + 1.04882i
\(31\) −4.10982 + 3.75625i −0.738145 + 0.674642i
\(32\) 4.19340i 0.741295i
\(33\) 1.36312 + 1.87617i 0.237289 + 0.326600i
\(34\) 14.0795 6.26861i 2.41462 1.07506i
\(35\) 0.0472618 + 7.45694i 0.00798870 + 1.26045i
\(36\) 4.05364 + 7.02111i 0.675607 + 1.17019i
\(37\) −1.47288 0.850368i −0.242140 0.139800i 0.374020 0.927421i \(-0.377979\pi\)
−0.616160 + 0.787621i \(0.711313\pi\)
\(38\) −0.821930 + 0.740069i −0.133335 + 0.120055i
\(39\) 1.88449 + 5.79986i 0.301760 + 0.928721i
\(40\) −5.38720 + 12.3092i −0.851791 + 1.94626i
\(41\) −5.45189 2.42734i −0.851443 0.379087i −0.0658491 0.997830i \(-0.520976\pi\)
−0.785594 + 0.618743i \(0.787642\pi\)
\(42\) −1.87689 8.83008i −0.289611 1.36251i
\(43\) −3.37019 + 0.354221i −0.513949 + 0.0540182i −0.357953 0.933740i \(-0.616525\pi\)
−0.155996 + 0.987758i \(0.549859\pi\)
\(44\) −0.990474 + 9.42373i −0.149320 + 1.42068i
\(45\) 0.458804 + 4.11423i 0.0683945 + 0.613312i
\(46\) 5.76053 + 4.18527i 0.849343 + 0.617084i
\(47\) 7.59692 10.4563i 1.10812 1.52520i 0.283974 0.958832i \(-0.408347\pi\)
0.824150 0.566371i \(-0.191653\pi\)
\(48\) 1.43025 6.72880i 0.206439 0.971219i
\(49\) 0.430828 4.09905i 0.0615468 0.585579i
\(50\) −9.27692 + 8.56838i −1.31196 + 1.21175i
\(51\) −6.39700 + 1.35973i −0.895760 + 0.190400i
\(52\) −10.1349 + 22.7633i −1.40545 + 3.15670i
\(53\) −5.36509 4.83075i −0.736952 0.663554i 0.212609 0.977137i \(-0.431804\pi\)
−0.949561 + 0.313583i \(0.898471\pi\)
\(54\) −4.05808 12.4895i −0.552235 1.69960i
\(55\) −2.39261 + 4.20546i −0.322620 + 0.567064i
\(56\) 10.0197 17.3546i 1.33894 2.31911i
\(57\) 0.406449 0.234664i 0.0538355 0.0310819i
\(58\) −1.49119 0.484517i −0.195803 0.0636202i
\(59\) 7.68661 3.42230i 1.00071 0.445545i 0.160052 0.987109i \(-0.448834\pi\)
0.840660 + 0.541563i \(0.182167\pi\)
\(60\) 6.11468 8.52929i 0.789401 1.10113i
\(61\) −6.39962 −0.819387 −0.409694 0.912223i \(-0.634364\pi\)
−0.409694 + 0.912223i \(0.634364\pi\)
\(62\) 13.7766 + 2.82132i 1.74962 + 0.358308i
\(63\) 6.17406i 0.777859i
\(64\) −1.81697 + 1.32010i −0.227121 + 0.165013i
\(65\) −9.40113 + 8.57333i −1.16607 + 1.06339i
\(66\) 1.81000 5.57061i 0.222796 0.685695i
\(67\) 5.07563 2.93042i 0.620087 0.358008i −0.156816 0.987628i \(-0.550123\pi\)
0.776903 + 0.629620i \(0.216790\pi\)
\(68\) −23.1418 13.3609i −2.80635 1.62025i
\(69\) −2.02176 2.24539i −0.243391 0.270314i
\(70\) 15.1668 11.1669i 1.81278 1.33470i
\(71\) −2.31253 + 2.56833i −0.274447 + 0.304804i −0.864573 0.502507i \(-0.832411\pi\)
0.590126 + 0.807311i \(0.299078\pi\)
\(72\) 4.52481 10.1629i 0.533254 1.19771i
\(73\) 1.55845 + 7.33195i 0.182403 + 0.858140i 0.970219 + 0.242229i \(0.0778785\pi\)
−0.787816 + 0.615911i \(0.788788\pi\)
\(74\) 0.449006 + 4.27201i 0.0521959 + 0.496611i
\(75\) 4.60650 2.73799i 0.531912 0.316156i
\(76\) 1.87574 + 0.398702i 0.215163 + 0.0457342i
\(77\) 4.24154 5.83797i 0.483368 0.665299i
\(78\) 9.05338 12.4609i 1.02509 1.41092i
\(79\) −3.33461 0.708794i −0.375173 0.0797455i 0.0164659 0.999864i \(-0.494759\pi\)
−0.391639 + 0.920119i \(0.628092\pi\)
\(80\) 14.0195 3.07294i 1.56743 0.343565i
\(81\) 0.00193395 + 0.0184003i 0.000214884 + 0.00204448i
\(82\) 3.13384 + 14.7436i 0.346075 + 1.62815i
\(83\) 0.461036 1.03550i 0.0506052 0.113661i −0.886473 0.462779i \(-0.846852\pi\)
0.937079 + 0.349118i \(0.113519\pi\)
\(84\) −10.4732 + 11.6317i −1.14272 + 1.26912i
\(85\) −8.08992 10.9877i −0.877475 1.19178i
\(86\) 5.72706 + 6.36054i 0.617565 + 0.685875i
\(87\) 0.576198 + 0.332668i 0.0617749 + 0.0356657i
\(88\) 11.2603 6.50116i 1.20036 0.693026i
\(89\) −5.07259 + 15.6118i −0.537694 + 1.65485i 0.200062 + 0.979783i \(0.435886\pi\)
−0.737756 + 0.675068i \(0.764114\pi\)
\(90\) 7.72560 7.04533i 0.814349 0.742643i
\(91\) 15.3517 11.1537i 1.60930 1.16923i
\(92\) 12.3456i 1.28712i
\(93\) −5.46929 2.38648i −0.567139 0.247466i
\(94\) −32.6437 −3.36694
\(95\) 0.795810 + 0.570519i 0.0816484 + 0.0585340i
\(96\) −4.10574 + 1.82799i −0.419040 + 0.186569i
\(97\) −16.5730 5.38488i −1.68273 0.546752i −0.697292 0.716787i \(-0.745612\pi\)
−0.985438 + 0.170035i \(0.945612\pi\)
\(98\) −9.01531 + 5.20499i −0.910684 + 0.525784i
\(99\) 2.00298 3.46927i 0.201307 0.348674i
\(100\) 21.4732 + 4.28053i 2.14732 + 0.428053i
\(101\) −1.45583 4.48057i −0.144860 0.445833i 0.852133 0.523325i \(-0.175309\pi\)
−0.996993 + 0.0774920i \(0.975309\pi\)
\(102\) 12.2751 + 11.0526i 1.21542 + 1.09437i
\(103\) −3.65203 + 8.20260i −0.359845 + 0.808226i 0.639381 + 0.768890i \(0.279191\pi\)
−0.999226 + 0.0393358i \(0.987476\pi\)
\(104\) 33.4442 7.10878i 3.27947 0.697074i
\(105\) −7.28046 + 3.29692i −0.710500 + 0.321746i
\(106\) −1.90598 + 18.1342i −0.185125 + 1.76135i
\(107\) −1.20442 + 5.66637i −0.116436 + 0.547788i 0.880800 + 0.473489i \(0.157006\pi\)
−0.997236 + 0.0742998i \(0.976328\pi\)
\(108\) −13.3833 + 18.4206i −1.28781 + 1.77252i
\(109\) 0.501197 + 0.364141i 0.0480060 + 0.0348784i 0.611529 0.791222i \(-0.290555\pi\)
−0.563523 + 0.826100i \(0.690555\pi\)
\(110\) 12.1451 1.35438i 1.15799 0.129135i
\(111\) 0.190531 1.81279i 0.0180844 0.172062i
\(112\) −21.2881 + 2.23747i −2.01154 + 0.211421i
\(113\) 0.0669159 + 0.314815i 0.00629492 + 0.0296153i 0.981183 0.193080i \(-0.0618478\pi\)
−0.974888 + 0.222695i \(0.928514\pi\)
\(114\) −1.08290 0.482136i −0.101423 0.0451562i
\(115\) 2.52747 5.77502i 0.235688 0.538524i
\(116\) 0.840072 + 2.58548i 0.0779987 + 0.240055i
\(117\) 7.82846 7.04877i 0.723741 0.651659i
\(118\) −18.4042 10.6257i −1.69424 0.978171i
\(119\) 10.1749 + 17.6235i 0.932734 + 1.61554i
\(120\) −14.4003 + 0.0912686i −1.31456 + 0.00833165i
\(121\) −5.77169 + 2.56972i −0.524699 + 0.233611i
\(122\) 9.50066 + 13.0765i 0.860149 + 1.18389i
\(123\) 6.39606i 0.576713i
\(124\) −10.0825 22.1997i −0.905438 1.99359i
\(125\) 9.16839 + 6.39848i 0.820046 + 0.572298i
\(126\) −12.6157 + 9.16581i −1.12389 + 0.816555i
\(127\) −1.28380 2.88345i −0.113918 0.255865i 0.847584 0.530661i \(-0.178056\pi\)
−0.961503 + 0.274796i \(0.911390\pi\)
\(128\) 13.3711 + 4.34454i 1.18185 + 0.384007i
\(129\) −1.81596 3.14533i −0.159886 0.276931i
\(130\) 31.4747 + 6.48195i 2.76052 + 0.568504i
\(131\) 4.38614 + 4.87130i 0.383219 + 0.425608i 0.903634 0.428306i \(-0.140889\pi\)
−0.520415 + 0.853914i \(0.674223\pi\)
\(132\) −9.65851 + 3.13824i −0.840666 + 0.273149i
\(133\) −1.08527 0.977182i −0.0941049 0.0847324i
\(134\) −13.5229 6.02080i −1.16820 0.520118i
\(135\) −10.0316 + 5.87686i −0.863386 + 0.505799i
\(136\) 3.83276 + 36.4663i 0.328657 + 3.12696i
\(137\) −11.0717 1.16368i −0.945920 0.0994202i −0.381008 0.924572i \(-0.624423\pi\)
−0.564911 + 0.825152i \(0.691090\pi\)
\(138\) −1.58664 + 7.46456i −0.135064 + 0.635426i
\(139\) 12.4431 + 9.04041i 1.05541 + 0.766797i 0.973233 0.229821i \(-0.0738140\pi\)
0.0821731 + 0.996618i \(0.473814\pi\)
\(140\) −31.1207 9.89410i −2.63018 0.836204i
\(141\) 13.5494 + 2.88000i 1.14106 + 0.242540i
\(142\) 8.68104 + 0.912415i 0.728497 + 0.0765681i
\(143\) 12.2448 1.28698i 1.02396 0.107622i
\(144\) −11.6233 + 2.47061i −0.968608 + 0.205884i
\(145\) −0.136347 + 1.38142i −0.0113230 + 0.114721i
\(146\) 12.6680 14.0692i 1.04841 1.16438i
\(147\) 4.20117 1.36504i 0.346507 0.112587i
\(148\) 5.53476 4.98352i 0.454955 0.409643i
\(149\) 8.97751 15.5495i 0.735466 1.27386i −0.219053 0.975713i \(-0.570297\pi\)
0.954519 0.298151i \(-0.0963700\pi\)
\(150\) −12.4333 5.34786i −1.01517 0.436651i
\(151\) 2.06027 6.34087i 0.167663 0.516013i −0.831560 0.555435i \(-0.812552\pi\)
0.999223 + 0.0394222i \(0.0125517\pi\)
\(152\) −1.07027 2.40387i −0.0868105 0.194980i
\(153\) 6.64022 + 9.13948i 0.536830 + 0.738883i
\(154\) −18.2257 −1.46867
\(155\) −0.171545 12.4487i −0.0137788 0.999905i
\(156\) −26.7054 −2.13815
\(157\) −6.97662 9.60250i −0.556795 0.766363i 0.434119 0.900855i \(-0.357060\pi\)
−0.990915 + 0.134493i \(0.957060\pi\)
\(158\) 3.50215 + 7.86597i 0.278616 + 0.625783i
\(159\) 2.39101 7.35877i 0.189619 0.583588i
\(160\) −7.00788 6.22996i −0.554022 0.492522i
\(161\) −4.70087 + 8.14214i −0.370480 + 0.641690i
\(162\) 0.0347269 0.0312682i 0.00272840 0.00245666i
\(163\) −3.29477 + 1.07054i −0.258066 + 0.0838508i −0.435193 0.900337i \(-0.643320\pi\)
0.177127 + 0.984188i \(0.443320\pi\)
\(164\) 17.4871 19.4213i 1.36551 1.51655i
\(165\) −5.16054 0.509348i −0.401748 0.0396527i
\(166\) −2.80031 + 0.595225i −0.217346 + 0.0461984i
\(167\) 8.73710 0.918307i 0.676097 0.0710607i 0.239744 0.970836i \(-0.422936\pi\)
0.436353 + 0.899775i \(0.356270\pi\)
\(168\) 21.3597 + 2.24499i 1.64793 + 0.173205i
\(169\) 18.9532 + 4.02863i 1.45794 + 0.309895i
\(170\) −10.4415 + 32.8423i −0.800824 + 2.51889i
\(171\) −0.655881 0.476525i −0.0501565 0.0364408i
\(172\) 3.08537 14.5155i 0.235257 1.10680i
\(173\) −20.1176 2.11444i −1.52951 0.160758i −0.697932 0.716164i \(-0.745896\pi\)
−0.831579 + 0.555406i \(0.812563\pi\)
\(174\) −0.175653 1.67123i −0.0133162 0.126696i
\(175\) −12.5320 10.9995i −0.947333 0.831483i
\(176\) −12.6879 5.64900i −0.956384 0.425809i
\(177\) 6.70152 + 6.03408i 0.503717 + 0.453549i
\(178\) 39.4307 12.8118i 2.95546 0.960287i
\(179\) −6.54508 7.26905i −0.489202 0.543314i 0.447112 0.894478i \(-0.352453\pi\)
−0.936314 + 0.351164i \(0.885786\pi\)
\(180\) −17.7558 3.65665i −1.32344 0.272551i
\(181\) −8.21773 14.2335i −0.610819 1.05797i −0.991103 0.133100i \(-0.957507\pi\)
0.380283 0.924870i \(-0.375826\pi\)
\(182\) −45.5814 14.8103i −3.37872 1.09781i
\(183\) −2.78973 6.26584i −0.206223 0.463184i
\(184\) −13.7051 + 9.95733i −1.01035 + 0.734064i
\(185\) 3.60931 1.19808i 0.265362 0.0880845i
\(186\) 3.24316 + 14.7184i 0.237800 + 1.07921i
\(187\) 13.2037i 0.965554i
\(188\) 33.2680 + 45.7894i 2.42632 + 3.33954i
\(189\) 15.8406 7.05269i 1.15223 0.513008i
\(190\) −0.0156743 2.47308i −0.00113713 0.179416i
\(191\) −11.6568 20.1901i −0.843453 1.46090i −0.886958 0.461850i \(-0.847186\pi\)
0.0435052 0.999053i \(-0.486147\pi\)
\(192\) −2.08456 1.20352i −0.150440 0.0868569i
\(193\) −0.782799 + 0.704836i −0.0563471 + 0.0507352i −0.696823 0.717243i \(-0.745404\pi\)
0.640476 + 0.767978i \(0.278737\pi\)
\(194\) 13.6006 + 41.8583i 0.976464 + 3.00525i
\(195\) −12.4923 5.46731i −0.894590 0.391522i
\(196\) 16.4888 + 7.34126i 1.17777 + 0.524376i
\(197\) 1.14110 + 5.36843i 0.0812997 + 0.382485i 0.999920 0.0126567i \(-0.00402887\pi\)
−0.918620 + 0.395142i \(0.870696\pi\)
\(198\) −10.0624 + 1.05760i −0.715105 + 0.0751605i
\(199\) 2.06289 19.6271i 0.146235 1.39133i −0.637603 0.770365i \(-0.720074\pi\)
0.783838 0.620966i \(-0.213259\pi\)
\(200\) −12.5673 27.2903i −0.888641 1.92971i
\(201\) 5.08174 + 3.69210i 0.358438 + 0.260421i
\(202\) −6.99402 + 9.62644i −0.492097 + 0.677314i
\(203\) 0.430436 2.02504i 0.0302107 0.142130i
\(204\) 2.99361 28.4823i 0.209595 1.99416i
\(205\) 12.1562 5.50485i 0.849023 0.384475i
\(206\) 22.1823 4.71500i 1.54551 0.328509i
\(207\) −2.12287 + 4.76805i −0.147550 + 0.331402i
\(208\) −27.1411 24.4380i −1.88190 1.69447i
\(209\) −0.292808 0.901170i −0.0202540 0.0623353i
\(210\) 17.5450 + 9.98189i 1.21072 + 0.688816i
\(211\) −6.22352 + 10.7795i −0.428445 + 0.742089i −0.996735 0.0807396i \(-0.974272\pi\)
0.568290 + 0.822828i \(0.307605\pi\)
\(212\) 27.3793 15.8075i 1.88042 1.08566i
\(213\) −3.52272 1.14460i −0.241373 0.0784268i
\(214\) 13.3663 5.95106i 0.913702 0.406806i
\(215\) 4.41499 6.15842i 0.301100 0.420000i
\(216\) 31.2434 2.12584
\(217\) −1.80342 + 18.4802i −0.122424 + 1.25452i
\(218\) 1.56470i 0.105975i
\(219\) −6.49932 + 4.72203i −0.439183 + 0.319085i
\(220\) −14.2772 15.6557i −0.962567 1.05551i
\(221\) −10.7294 + 33.0217i −0.721737 + 2.22128i
\(222\) −3.98698 + 2.30188i −0.267588 + 0.154492i
\(223\) 16.8534 + 9.73030i 1.12859 + 0.651589i 0.943579 0.331148i \(-0.107436\pi\)
0.185006 + 0.982737i \(0.440769\pi\)
\(224\) 9.35752 + 10.3926i 0.625226 + 0.694384i
\(225\) −7.55720 5.34560i −0.503814 0.356373i
\(226\) 0.543929 0.604094i 0.0361816 0.0401838i
\(227\) 1.10777 2.48810i 0.0735254 0.165141i −0.873044 0.487642i \(-0.837857\pi\)
0.946569 + 0.322501i \(0.104524\pi\)
\(228\) 0.427310 + 2.01034i 0.0282993 + 0.133138i
\(229\) 1.55017 + 14.7489i 0.102438 + 0.974636i 0.918165 + 0.396198i \(0.129671\pi\)
−0.815727 + 0.578438i \(0.803663\pi\)
\(230\) −15.5525 + 3.40895i −1.02550 + 0.224779i
\(231\) 7.56491 + 1.60797i 0.497735 + 0.105797i
\(232\) 2.19263 3.01789i 0.143953 0.198134i
\(233\) −7.44703 + 10.2500i −0.487871 + 0.671497i −0.979994 0.199029i \(-0.936221\pi\)
0.492122 + 0.870526i \(0.336221\pi\)
\(234\) −26.0248 5.53175i −1.70130 0.361622i
\(235\) 6.18777 + 28.2302i 0.403646 + 1.84154i
\(236\) 3.85148 + 36.6444i 0.250710 + 2.38535i
\(237\) −0.759653 3.57389i −0.0493448 0.232149i
\(238\) 20.9053 46.9540i 1.35509 3.04357i
\(239\) −15.9261 + 17.6878i −1.03018 + 1.14413i −0.0407374 + 0.999170i \(0.512971\pi\)
−0.989438 + 0.144956i \(0.953696\pi\)
\(240\) 9.12012 + 12.3869i 0.588701 + 0.799571i
\(241\) 0.846449 + 0.940077i 0.0545246 + 0.0605557i 0.769790 0.638297i \(-0.220361\pi\)
−0.715265 + 0.698853i \(0.753694\pi\)
\(242\) 13.8193 + 7.97855i 0.888335 + 0.512881i
\(243\) 13.4914 7.78926i 0.865473 0.499681i
\(244\) 8.66014 26.6532i 0.554409 1.70629i
\(245\) 6.21016 + 6.80978i 0.396752 + 0.435061i
\(246\) −13.0693 + 9.49537i −0.833266 + 0.605403i
\(247\) 2.49170i 0.158543i
\(248\) −16.5122 + 29.0979i −1.04853 + 1.84772i
\(249\) 1.21483 0.0769869
\(250\) −0.536877 28.2330i −0.0339551 1.78561i
\(251\) 10.1070 4.49994i 0.637950 0.284034i −0.0621628 0.998066i \(-0.519800\pi\)
0.700113 + 0.714032i \(0.253133\pi\)
\(252\) 25.7138 + 8.35491i 1.61982 + 0.526310i
\(253\) −5.28292 + 3.05010i −0.332135 + 0.191758i
\(254\) −3.98596 + 6.90389i −0.250102 + 0.433189i
\(255\) 7.23144 12.7106i 0.452850 0.795968i
\(256\) −9.58495 29.4995i −0.599060 1.84372i
\(257\) 4.55811 + 4.10414i 0.284327 + 0.256009i 0.798936 0.601415i \(-0.205396\pi\)
−0.514609 + 0.857425i \(0.672063\pi\)
\(258\) −3.73104 + 8.38004i −0.232284 + 0.521719i
\(259\) −5.54786 + 1.17923i −0.344727 + 0.0732740i
\(260\) −22.9844 50.7556i −1.42543 3.14773i
\(261\) 0.120134 1.14300i 0.00743613 0.0707500i
\(262\) 3.44216 16.1941i 0.212658 1.00048i
\(263\) −0.194569 + 0.267801i −0.0119976 + 0.0165133i −0.814974 0.579498i \(-0.803249\pi\)
0.802976 + 0.596011i \(0.203249\pi\)
\(264\) 11.2739 + 8.19095i 0.693859 + 0.504118i
\(265\) 16.0437 1.78914i 0.985557 0.109906i
\(266\) −0.385550 + 3.66826i −0.0236396 + 0.224915i
\(267\) −17.4967 + 1.83898i −1.07078 + 0.112544i
\(268\) 5.33614 + 25.1046i 0.325957 + 1.53351i
\(269\) −0.969550 0.431672i −0.0591145 0.0263195i 0.376966 0.926227i \(-0.376967\pi\)
−0.436081 + 0.899907i \(0.643634\pi\)
\(270\) 26.9010 + 11.7734i 1.63714 + 0.716505i
\(271\) −6.79718 20.9196i −0.412899 1.27077i −0.914117 0.405452i \(-0.867114\pi\)
0.501217 0.865321i \(-0.332886\pi\)
\(272\) 29.1064 26.2075i 1.76484 1.58906i
\(273\) 17.6127 + 10.1687i 1.06597 + 0.615438i
\(274\) 14.0589 + 24.3507i 0.849329 + 1.47108i
\(275\) −3.47343 10.2463i −0.209456 0.617878i
\(276\) 12.0875 5.38171i 0.727584 0.323941i
\(277\) −11.5640 15.9165i −0.694813 0.956328i −0.999992 0.00403308i \(-0.998716\pi\)
0.305179 0.952295i \(-0.401284\pi\)
\(278\) 38.8464i 2.32985i
\(279\) 0.0767035 + 10.3076i 0.00459212 + 0.617097i
\(280\) 14.1167 + 42.5277i 0.843634 + 2.54152i
\(281\) −18.3198 + 13.3101i −1.09286 + 0.794013i −0.979881 0.199584i \(-0.936041\pi\)
−0.112984 + 0.993597i \(0.536041\pi\)
\(282\) −14.2301 31.9614i −0.847391 1.90327i
\(283\) −17.8036 5.78473i −1.05831 0.343867i −0.272387 0.962188i \(-0.587813\pi\)
−0.785926 + 0.618321i \(0.787813\pi\)
\(284\) −7.56720 13.1068i −0.449031 0.777744i
\(285\) −0.211682 + 1.02788i −0.0125390 + 0.0608862i
\(286\) −20.8079 23.1095i −1.23040 1.36649i
\(287\) −18.9281 + 6.15012i −1.11729 + 0.363030i
\(288\) 5.76934 + 5.19474i 0.339962 + 0.306103i
\(289\) −18.4858 8.23041i −1.08740 0.484142i
\(290\) 3.02511 1.77221i 0.177641 0.104068i
\(291\) −1.95220 18.5739i −0.114440 1.08882i
\(292\) −32.6451 3.43114i −1.91041 0.200792i
\(293\) 3.77002 17.7365i 0.220247 1.03618i −0.719548 0.694442i \(-0.755651\pi\)
0.939795 0.341738i \(-0.111016\pi\)
\(294\) −9.02616 6.55789i −0.526416 0.382464i
\(295\) −5.70044 + 17.9300i −0.331892 + 1.04393i
\(296\) −9.99635 2.12479i −0.581026 0.123501i
\(297\) 11.1890 + 1.17601i 0.649252 + 0.0682392i
\(298\) −45.1005 + 4.74025i −2.61260 + 0.274595i
\(299\) −15.6908 + 3.33517i −0.907420 + 0.192878i
\(300\) 5.16958 + 22.8903i 0.298466 + 1.32157i
\(301\) −7.56197 + 8.39842i −0.435865 + 0.484077i
\(302\) −16.0151 + 5.20362i −0.921566 + 0.299435i
\(303\) 3.75228 3.37857i 0.215563 0.194094i
\(304\) −1.40536 + 2.43416i −0.0806031 + 0.139609i
\(305\) 9.50765 10.6949i 0.544407 0.612386i
\(306\) 8.81713 27.1363i 0.504042 1.55128i
\(307\) 7.19056 + 16.1503i 0.410387 + 0.921744i 0.993966 + 0.109688i \(0.0349850\pi\)
−0.583579 + 0.812056i \(0.698348\pi\)
\(308\) 18.5743 + 25.5653i 1.05837 + 1.45672i
\(309\) −9.62314 −0.547441
\(310\) −25.1822 + 18.8315i −1.43025 + 1.06956i
\(311\) 16.4095 0.930498 0.465249 0.885180i \(-0.345965\pi\)
0.465249 + 0.885180i \(0.345965\pi\)
\(312\) 21.5392 + 29.6462i 1.21942 + 1.67839i
\(313\) 1.88989 + 4.24476i 0.106823 + 0.239928i 0.959046 0.283251i \(-0.0914128\pi\)
−0.852223 + 0.523178i \(0.824746\pi\)
\(314\) −9.26382 + 28.5111i −0.522787 + 1.60897i
\(315\) 10.3179 + 9.17256i 0.581349 + 0.516815i
\(316\) 7.46448 12.9289i 0.419910 0.727305i
\(317\) 7.57185 6.81772i 0.425277 0.382921i −0.428515 0.903534i \(-0.640963\pi\)
0.853793 + 0.520613i \(0.174297\pi\)
\(318\) −18.5860 + 6.03896i −1.04225 + 0.338648i
\(319\) 0.898828 0.998250i 0.0503247 0.0558913i
\(320\) 0.493275 4.99769i 0.0275749 0.279379i
\(321\) −6.07295 + 1.29085i −0.338959 + 0.0720480i
\(322\) 23.6158 2.48212i 1.31606 0.138323i
\(323\) 2.65749 + 0.279314i 0.147867 + 0.0155414i
\(324\) −0.0792509 0.0168453i −0.00440283 0.000935850i
\(325\) −0.360618 28.4480i −0.0200035 1.57801i
\(326\) 7.07876 + 5.14302i 0.392056 + 0.284846i
\(327\) −0.138046 + 0.649458i −0.00763399 + 0.0359151i
\(328\) −35.6642 3.74845i −1.96922 0.206974i
\(329\) −4.50545 42.8664i −0.248393 2.36330i
\(330\) 6.62040 + 11.3009i 0.364441 + 0.622091i
\(331\) 14.3511 + 6.38953i 0.788809 + 0.351200i 0.761282 0.648421i \(-0.224570\pi\)
0.0275267 + 0.999621i \(0.491237\pi\)
\(332\) 3.68878 + 3.32140i 0.202448 + 0.182285i
\(333\) −2.99454 + 0.972985i −0.164100 + 0.0533192i
\(334\) −14.8472 16.4895i −0.812403 0.902265i
\(335\) −2.64343 + 12.8359i −0.144426 + 0.701298i
\(336\) −11.4706 19.8677i −0.625775 1.08387i
\(337\) −2.39334 0.777642i −0.130373 0.0423609i 0.243104 0.970000i \(-0.421835\pi\)
−0.373477 + 0.927639i \(0.621835\pi\)
\(338\) −19.9055 44.7085i −1.08272 2.43182i
\(339\) −0.279064 + 0.202752i −0.0151567 + 0.0110120i
\(340\) 56.7091 18.8241i 3.07548 1.02088i
\(341\) −7.00868 + 9.79915i −0.379542 + 0.530654i
\(342\) 2.04761i 0.110722i
\(343\) 5.64221 + 7.76584i 0.304651 + 0.419316i
\(344\) −18.6025 + 8.28235i −1.00298 + 0.446554i
\(345\) 6.75609 0.0428198i 0.363735 0.00230534i
\(346\) 25.5454 + 44.2459i 1.37333 + 2.37867i
\(347\) 27.2323 + 15.7225i 1.46190 + 0.844031i 0.999099 0.0424297i \(-0.0135098\pi\)
0.462805 + 0.886460i \(0.346843\pi\)
\(348\) −2.16522 + 1.94958i −0.116068 + 0.104508i
\(349\) 6.82865 + 21.0164i 0.365529 + 1.12498i 0.949649 + 0.313316i \(0.101440\pi\)
−0.584120 + 0.811668i \(0.698560\pi\)
\(350\) −3.87095 + 41.9366i −0.206911 + 2.24160i
\(351\) 27.0273 + 12.0333i 1.44261 + 0.642292i
\(352\) 1.88654 + 8.87545i 0.100553 + 0.473063i
\(353\) 27.5612 2.89680i 1.46694 0.154181i 0.662876 0.748729i \(-0.269335\pi\)
0.804060 + 0.594548i \(0.202669\pi\)
\(354\) 2.38076 22.6514i 0.126536 1.20391i
\(355\) −0.856479 7.68030i −0.0454572 0.407628i
\(356\) −58.1559 42.2527i −3.08226 2.23939i
\(357\) −12.8196 + 17.6447i −0.678486 + 0.933856i
\(358\) −5.13646 + 24.1651i −0.271470 + 1.27717i
\(359\) 0.438079 4.16804i 0.0231209 0.219981i −0.976860 0.213878i \(-0.931391\pi\)
0.999981 0.00610321i \(-0.00194273\pi\)
\(360\) 10.2616 + 22.6603i 0.540834 + 1.19430i
\(361\) 18.3972 3.91045i 0.968275 0.205813i
\(362\) −16.8840 + 37.9222i −0.887405 + 1.99315i
\(363\) −5.03201 4.53084i −0.264112 0.237808i
\(364\) 25.6786 + 79.0306i 1.34592 + 4.14233i
\(365\) −14.5683 8.28834i −0.762539 0.433832i
\(366\) −8.66164 + 15.0024i −0.452751 + 0.784188i
\(367\) −16.3575 + 9.44403i −0.853857 + 0.492974i −0.861950 0.506993i \(-0.830757\pi\)
0.00809346 + 0.999967i \(0.497424\pi\)
\(368\) 17.2095 + 5.59170i 0.897107 + 0.291488i
\(369\) −10.0933 + 4.49384i −0.525437 + 0.233940i
\(370\) −7.80633 5.59639i −0.405832 0.290942i
\(371\) −24.0762 −1.24997
\(372\) 17.3404 19.5491i 0.899058 1.01357i
\(373\) 0.234108i 0.0121216i −0.999982 0.00606082i \(-0.998071\pi\)
0.999982 0.00606082i \(-0.00192923\pi\)
\(374\) 26.9796 19.6018i 1.39508 1.01359i
\(375\) −2.26803 + 11.7660i −0.117120 + 0.607592i
\(376\) 23.9995 73.8628i 1.23768 3.80918i
\(377\) 3.05909 1.76617i 0.157551 0.0909622i
\(378\) −37.9274 21.8974i −1.95077 1.12628i
\(379\) −2.32902 2.58664i −0.119634 0.132867i 0.680353 0.732885i \(-0.261827\pi\)
−0.799986 + 0.600018i \(0.795160\pi\)
\(380\) −3.45301 + 2.54235i −0.177136 + 0.130420i
\(381\) 2.26354 2.51392i 0.115965 0.128792i
\(382\) −23.9498 + 53.7921i −1.22538 + 2.75224i
\(383\) −2.52407 11.8748i −0.128974 0.606776i −0.994395 0.105730i \(-0.966282\pi\)
0.865421 0.501046i \(-0.167051\pi\)
\(384\) 1.57504 + 14.9855i 0.0803759 + 0.764726i
\(385\) 3.45478 + 15.7616i 0.176072 + 0.803284i
\(386\) 2.60233 + 0.553142i 0.132455 + 0.0281542i
\(387\) −3.68761 + 5.07556i −0.187452 + 0.258005i
\(388\) 44.8540 61.7362i 2.27712 3.13418i
\(389\) 33.4352 + 7.10687i 1.69523 + 0.360332i 0.951382 0.308015i \(-0.0996647\pi\)
0.743849 + 0.668347i \(0.232998\pi\)
\(390\) 7.37408 + 33.6424i 0.373401 + 1.70355i
\(391\) −1.79819 17.1086i −0.0909383 0.865220i
\(392\) −5.14930 24.2256i −0.260079 1.22358i
\(393\) −2.85746 + 6.41796i −0.144140 + 0.323743i
\(394\) 9.27545 10.3014i 0.467290 0.518978i
\(395\) 6.13862 4.51968i 0.308867 0.227410i
\(396\) 11.7383 + 13.0367i 0.589873 + 0.655121i
\(397\) −14.7005 8.48731i −0.737795 0.425966i 0.0834722 0.996510i \(-0.473399\pi\)
−0.821267 + 0.570544i \(0.806732\pi\)
\(398\) −43.1672 + 24.9226i −2.16378 + 1.24926i
\(399\) 0.483662 1.48856i 0.0242134 0.0745212i
\(400\) −15.6928 + 27.9944i −0.784642 + 1.39972i
\(401\) 3.54895 2.57846i 0.177226 0.128762i −0.495636 0.868531i \(-0.665065\pi\)
0.672862 + 0.739768i \(0.265065\pi\)
\(402\) 15.8648i 0.791267i
\(403\) −25.4911 + 18.8117i −1.26980 + 0.937080i
\(404\) 20.6308 1.02642
\(405\) −0.0336233 0.0241047i −0.00167076 0.00119777i
\(406\) −4.77684 + 2.12679i −0.237071 + 0.105551i
\(407\) −3.49996 1.13721i −0.173487 0.0563692i
\(408\) −34.0332 + 19.6491i −1.68490 + 0.972776i
\(409\) 5.06723 8.77670i 0.250558 0.433980i −0.713121 0.701041i \(-0.752719\pi\)
0.963680 + 0.267061i \(0.0860525\pi\)
\(410\) −29.2949 16.6667i −1.44677 0.823111i
\(411\) −3.68704 11.3475i −0.181868 0.559733i
\(412\) −29.2202 26.3100i −1.43958 1.29620i
\(413\) 11.4131 25.6342i 0.561600 1.26137i
\(414\) 12.8942 2.74076i 0.633717 0.134701i
\(415\) 1.04556 + 2.30888i 0.0513246 + 0.113338i
\(416\) −2.49411 + 23.7299i −0.122284 + 1.16345i
\(417\) −3.42723 + 16.1239i −0.167832 + 0.789589i
\(418\) −1.40670 + 1.93615i −0.0688037 + 0.0947002i
\(419\) 23.3537 + 16.9674i 1.14090 + 0.828914i 0.987245 0.159211i \(-0.0508949\pi\)
0.153657 + 0.988124i \(0.450895\pi\)
\(420\) −3.87890 34.7832i −0.189271 1.69725i
\(421\) −1.37093 + 13.0435i −0.0668151 + 0.635703i 0.908953 + 0.416898i \(0.136883\pi\)
−0.975769 + 0.218805i \(0.929784\pi\)
\(422\) 31.2652 3.28611i 1.52197 0.159965i
\(423\) −4.97490 23.4051i −0.241888 1.13799i
\(424\) −39.6309 17.6448i −1.92465 0.856908i
\(425\) 30.3812 + 2.80433i 1.47370 + 0.136030i
\(426\) 2.89091 + 8.89732i 0.140065 + 0.431077i
\(427\) −15.8603 + 14.2807i −0.767534 + 0.691091i
\(428\) −21.9695 12.6841i −1.06193 0.613108i
\(429\) 6.59783 + 11.4278i 0.318546 + 0.551738i
\(430\) −19.1380 + 0.121296i −0.922918 + 0.00584941i
\(431\) −10.8310 + 4.82227i −0.521711 + 0.232281i −0.650658 0.759371i \(-0.725507\pi\)
0.128947 + 0.991651i \(0.458840\pi\)
\(432\) −19.6162 26.9993i −0.943783 1.29901i
\(433\) 9.34095i 0.448897i 0.974486 + 0.224449i \(0.0720581\pi\)
−0.974486 + 0.224449i \(0.927942\pi\)
\(434\) 40.4385 23.7501i 1.94111 1.14004i
\(435\) −1.41198 + 0.468694i −0.0676992 + 0.0224722i
\(436\) −2.19481 + 1.59462i −0.105112 + 0.0763687i
\(437\) 0.502131 + 1.12781i 0.0240202 + 0.0539503i
\(438\) 19.2974 + 6.27009i 0.922063 + 0.299596i
\(439\) −6.32026 10.9470i −0.301649 0.522472i 0.674860 0.737946i \(-0.264204\pi\)
−0.976510 + 0.215473i \(0.930871\pi\)
\(440\) −5.86447 + 28.4765i −0.279578 + 1.35756i
\(441\) −5.10584 5.67060i −0.243135 0.270029i
\(442\) 83.4027 27.0992i 3.96706 1.28898i
\(443\) 6.42608 + 5.78606i 0.305312 + 0.274904i 0.807517 0.589845i \(-0.200811\pi\)
−0.502205 + 0.864749i \(0.667478\pi\)
\(444\) 7.29207 + 3.24664i 0.346066 + 0.154079i
\(445\) −18.5539 31.6710i −0.879540 1.50135i
\(446\) −5.13773 48.8823i −0.243279 2.31464i
\(447\) 19.1379 + 2.01148i 0.905194 + 0.0951397i
\(448\) −1.55723 + 7.32619i −0.0735722 + 0.346130i
\(449\) −7.47632 5.43186i −0.352829 0.256346i 0.397226 0.917721i \(-0.369973\pi\)
−0.750055 + 0.661375i \(0.769973\pi\)
\(450\) 0.296347 + 23.3778i 0.0139699 + 1.10204i
\(451\) −12.6311 2.68483i −0.594776 0.126424i
\(452\) −1.40169 0.147324i −0.0659301 0.00692954i
\(453\) 7.10644 0.746917i 0.333890 0.0350932i
\(454\) −6.72856 + 1.43020i −0.315787 + 0.0671226i
\(455\) −4.16773 + 42.2260i −0.195386 + 1.97959i
\(456\) 1.88707 2.09580i 0.0883699 0.0981448i
\(457\) 23.6426 7.68195i 1.10595 0.359346i 0.301563 0.953446i \(-0.402492\pi\)
0.804391 + 0.594100i \(0.202492\pi\)
\(458\) 27.8356 25.0633i 1.30067 1.17113i
\(459\) −15.8637 + 27.4767i −0.740454 + 1.28250i
\(460\) 20.6316 + 18.3414i 0.961954 + 0.855170i
\(461\) −1.61845 + 4.98109i −0.0753789 + 0.231992i −0.981646 0.190714i \(-0.938920\pi\)
0.906267 + 0.422706i \(0.138920\pi\)
\(462\) −7.94500 17.8448i −0.369635 0.830213i
\(463\) 11.5143 + 15.8481i 0.535117 + 0.736526i 0.987899 0.155095i \(-0.0495685\pi\)
−0.452782 + 0.891621i \(0.649569\pi\)
\(464\) −3.98459 −0.184980
\(465\) 12.1137 5.59463i 0.561760 0.259445i
\(466\) 31.9997 1.48236
\(467\) −15.2066 20.9301i −0.703677 0.968528i −0.999910 0.0134123i \(-0.995731\pi\)
0.296233 0.955116i \(-0.404269\pi\)
\(468\) 18.7631 + 42.1426i 0.867325 + 1.94804i
\(469\) 6.03985 18.5888i 0.278894 0.858349i
\(470\) 48.4975 54.5533i 2.23702 2.51636i
\(471\) 6.36051 11.0167i 0.293077 0.507624i
\(472\) 37.5732 33.8311i 1.72945 1.55720i
\(473\) −6.97375 + 2.26591i −0.320653 + 0.104187i
\(474\) −6.17487 + 6.85789i −0.283621 + 0.314993i
\(475\) −2.13574 + 0.482339i −0.0979944 + 0.0221312i
\(476\) −87.1674 + 18.5280i −3.99531 + 0.849230i
\(477\) −13.2924 + 1.39709i −0.608619 + 0.0639684i
\(478\) 59.7853 + 6.28369i 2.73452 + 0.287409i
\(479\) 24.3650 + 5.17893i 1.11326 + 0.236631i 0.727596 0.686006i \(-0.240638\pi\)
0.385668 + 0.922638i \(0.373971\pi\)
\(480\) 3.04484 9.57717i 0.138977 0.437136i
\(481\) −7.82907 5.68815i −0.356975 0.259358i
\(482\) 0.664278 3.12518i 0.0302570 0.142348i
\(483\) −10.0211 1.05326i −0.455978 0.0479252i
\(484\) −2.89199 27.5154i −0.131454 1.25070i
\(485\) 33.6209 19.6962i 1.52664 0.894357i
\(486\) −35.9449 16.0037i −1.63049 0.725942i
\(487\) −29.4963 26.5586i −1.33660 1.20348i −0.960949 0.276724i \(-0.910751\pi\)
−0.375655 0.926760i \(-0.622582\pi\)
\(488\) −36.5730 + 11.8833i −1.65558 + 0.537931i
\(489\) −2.48442 2.75923i −0.112349 0.124777i
\(490\) 4.69525 22.7990i 0.212110 1.02995i
\(491\) 11.4111 + 19.7647i 0.514977 + 0.891967i 0.999849 + 0.0173817i \(0.00553304\pi\)
−0.484871 + 0.874585i \(0.661134\pi\)
\(492\) 26.6383 + 8.65532i 1.20095 + 0.390212i
\(493\) 1.54076 + 3.46061i 0.0693925 + 0.155858i
\(494\) −5.09137 + 3.69910i −0.229072 + 0.166430i
\(495\) 2.82199 + 8.50148i 0.126839 + 0.382113i
\(496\) 35.5125 3.99991i 1.59456 0.179601i
\(497\) 11.5255i 0.516991i
\(498\) −1.80350 2.48230i −0.0808168 0.111235i
\(499\) 1.51833 0.676004i 0.0679698 0.0302621i −0.372470 0.928044i \(-0.621489\pi\)
0.440440 + 0.897782i \(0.354822\pi\)
\(500\) −39.0554 + 29.5260i −1.74661 + 1.32044i
\(501\) 4.70780 + 8.15416i 0.210329 + 0.364301i
\(502\) −24.1994 13.9715i −1.08007 0.623580i
\(503\) 0.571297 0.514398i 0.0254729 0.0229359i −0.656296 0.754504i \(-0.727878\pi\)
0.681769 + 0.731568i \(0.261211\pi\)
\(504\) −11.4645 35.2840i −0.510668 1.57167i
\(505\) 9.65066 + 4.22367i 0.429449 + 0.187951i
\(506\) 14.0752 + 6.26669i 0.625719 + 0.278588i
\(507\) 4.31770 + 20.3132i 0.191756 + 0.902140i
\(508\) 13.7463 1.44479i 0.609893 0.0641023i
\(509\) 0.0171862 0.163516i 0.000761764 0.00724770i −0.994134 0.108152i \(-0.965507\pi\)
0.994896 + 0.100904i \(0.0321735\pi\)
\(510\) −36.7075 + 4.09349i −1.62543 + 0.181263i
\(511\) 20.2235 + 14.6933i 0.894636 + 0.649991i
\(512\) −29.5200 + 40.6308i −1.30461 + 1.79565i
\(513\) 0.473387 2.22711i 0.0209006 0.0983294i
\(514\) 1.61930 15.4066i 0.0714242 0.679556i
\(515\) −8.28228 18.2894i −0.364961 0.805929i
\(516\) 15.5571 3.30676i 0.684862 0.145572i
\(517\) 11.3750 25.5487i 0.500273 1.12363i
\(518\) 10.6457 + 9.58546i 0.467747 + 0.421161i
\(519\) −6.69945 20.6188i −0.294073 0.905064i
\(520\) −37.8067 + 66.4522i −1.65793 + 2.91412i
\(521\) 2.41475 4.18247i 0.105792 0.183238i −0.808269 0.588813i \(-0.799595\pi\)
0.914062 + 0.405575i \(0.132929\pi\)
\(522\) −2.51388 + 1.45139i −0.110029 + 0.0635255i
\(523\) 30.8190 + 10.0137i 1.34762 + 0.437868i 0.891891 0.452251i \(-0.149379\pi\)
0.455728 + 0.890119i \(0.349379\pi\)
\(524\) −26.2235 + 11.6754i −1.14558 + 0.510044i
\(525\) 5.30657 17.0650i 0.231598 0.744777i
\(526\) 0.836056 0.0364538
\(527\) −17.2059 29.2959i −0.749501 1.27615i
\(528\) 14.8852i 0.647793i
\(529\) −12.1775 + 8.84746i −0.529456 + 0.384672i
\(530\) −27.4738 30.1265i −1.19338 1.30861i
\(531\) 4.81364 14.8149i 0.208894 0.642911i
\(532\) 5.53839 3.19759i 0.240120 0.138633i
\(533\) −29.4079 16.9786i −1.27380 0.735427i
\(534\) 29.7327 + 33.0215i 1.28666 + 1.42898i
\(535\) −7.68011 10.4311i −0.332040 0.450976i
\(536\) 23.5652 26.1718i 1.01786 1.13045i
\(537\) 4.26395 9.57700i 0.184003 0.413278i
\(538\) 0.557314 + 2.62196i 0.0240275 + 0.113041i
\(539\) −0.932231 8.86959i −0.0401541 0.382040i
\(540\) −10.9009 49.7326i −0.469099 2.14015i
\(541\) 22.9968 + 4.88812i 0.988709 + 0.210157i 0.673759 0.738951i \(-0.264679\pi\)
0.314951 + 0.949108i \(0.398012\pi\)
\(542\) −32.6547 + 44.9454i −1.40264 + 1.93057i
\(543\) 10.3537 14.2507i 0.444320 0.611554i
\(544\) −25.0292 5.32012i −1.07312 0.228098i
\(545\) −1.35315 + 0.296597i −0.0579626 + 0.0127048i
\(546\) −5.36922 51.0847i −0.229781 2.18622i
\(547\) 2.37990 + 11.1965i 0.101757 + 0.478730i 0.999286 + 0.0377745i \(0.0120268\pi\)
−0.897529 + 0.440955i \(0.854640\pi\)
\(548\) 19.8291 44.5368i 0.847055 1.90252i
\(549\) −7.92778 + 8.80469i −0.338350 + 0.375775i
\(550\) −15.7801 + 22.3088i −0.672867 + 0.951249i
\(551\) −0.181902 0.202022i −0.00774928 0.00860644i
\(552\) −15.7235 9.07798i −0.669238 0.386385i
\(553\) −9.84591 + 5.68454i −0.418691 + 0.241731i
\(554\) −15.3551 + 47.2581i −0.652375 + 2.00781i
\(555\) 2.74641 + 3.01159i 0.116579 + 0.127835i
\(556\) −54.4898 + 39.5892i −2.31088 + 1.67896i
\(557\) 28.8909i 1.22415i 0.790801 + 0.612073i \(0.209664\pi\)
−0.790801 + 0.612073i \(0.790336\pi\)
\(558\) 20.9479 15.4590i 0.886794 0.654431i
\(559\) −19.2822 −0.815549
\(560\) 27.8877 38.9002i 1.17847 1.64383i
\(561\) −12.9277 + 5.75580i −0.545810 + 0.243010i
\(562\) 54.3938 + 17.6736i 2.29446 + 0.745516i
\(563\) −18.8329 + 10.8732i −0.793710 + 0.458249i −0.841267 0.540620i \(-0.818190\pi\)
0.0475568 + 0.998869i \(0.484856\pi\)
\(564\) −30.3300 + 52.5331i −1.27712 + 2.21204i
\(565\) −0.625523 0.355879i −0.0263160 0.0149720i
\(566\) 14.6105 + 44.9664i 0.614124 + 1.89008i
\(567\) 0.0458531 + 0.0412863i 0.00192565 + 0.00173386i
\(568\) −8.44677 + 18.9717i −0.354418 + 0.796037i
\(569\) −41.3408 + 8.78725i −1.73309 + 0.368381i −0.962990 0.269537i \(-0.913129\pi\)
−0.770105 + 0.637918i \(0.779796\pi\)
\(570\) 2.41455 1.09341i 0.101134 0.0457981i
\(571\) 1.34968 12.8414i 0.0564824 0.537394i −0.929295 0.369338i \(-0.879584\pi\)
0.985777 0.168056i \(-0.0537489\pi\)
\(572\) −11.2099 + 52.7386i −0.468711 + 2.20511i
\(573\) 14.6866 20.2144i 0.613542 0.844468i
\(574\) 40.6668 + 29.5462i 1.69740 + 1.23323i
\(575\) 5.89609 + 12.8036i 0.245884 + 0.533945i
\(576\) −0.434621 + 4.13514i −0.0181092 + 0.172298i
\(577\) 2.77593 0.291762i 0.115563 0.0121462i −0.0465702 0.998915i \(-0.514829\pi\)
0.162134 + 0.986769i \(0.448162\pi\)
\(578\) 10.6260 + 49.9912i 0.441982 + 2.07936i
\(579\) −1.03134 0.459183i −0.0428611 0.0190830i
\(580\) −5.56884 2.43723i −0.231233 0.101201i
\(581\) −1.16812 3.59511i −0.0484618 0.149150i
\(582\) −35.0545 + 31.5632i −1.45306 + 1.30834i
\(583\) −13.5286 7.81077i −0.560299 0.323489i
\(584\) 22.5209 + 39.0073i 0.931921 + 1.61413i
\(585\) 0.149289 + 23.5548i 0.00617235 + 0.973870i
\(586\) −41.8385 + 18.6277i −1.72833 + 0.769503i
\(587\) −12.8038 17.6229i −0.528467 0.727373i 0.458428 0.888731i \(-0.348413\pi\)
−0.986896 + 0.161358i \(0.948413\pi\)
\(588\) 19.3443i 0.797745i
\(589\) 1.82399 + 1.61792i 0.0751563 + 0.0666651i
\(590\) 45.0996 14.9704i 1.85672 0.616323i
\(591\) −4.75878 + 3.45746i −0.195750 + 0.142221i
\(592\) 4.44005 + 9.97252i 0.182485 + 0.409868i
\(593\) 5.15035 + 1.67345i 0.211500 + 0.0687204i 0.412851 0.910799i \(-0.364533\pi\)
−0.201351 + 0.979519i \(0.564533\pi\)
\(594\) −14.2078 24.6087i −0.582955 1.00971i
\(595\) −44.5684 9.17846i −1.82712 0.376280i
\(596\) 52.6120 + 58.4316i 2.15507 + 2.39345i
\(597\) 20.1161 6.53612i 0.823298 0.267506i
\(598\) 30.1088 + 27.1101i 1.23124 + 1.10862i
\(599\) −0.00449614 0.00200181i −0.000183707 8.17917e-5i 0.406645 0.913586i \(-0.366699\pi\)
−0.406828 + 0.913505i \(0.633365\pi\)
\(600\) 21.2414 24.2010i 0.867178 0.988001i
\(601\) 1.81177 + 17.2379i 0.0739037 + 0.703147i 0.967258 + 0.253794i \(0.0816787\pi\)
−0.893354 + 0.449353i \(0.851655\pi\)
\(602\) 28.3870 + 2.98359i 1.15697 + 0.121602i
\(603\) 2.25593 10.6133i 0.0918685 0.432207i
\(604\) 23.6205 + 17.1613i 0.961104 + 0.698283i
\(605\) 4.28032 13.4632i 0.174020 0.547358i
\(606\) −12.4741 2.65144i −0.506724 0.107707i
\(607\) −3.11778 0.327692i −0.126547 0.0133006i 0.0410432 0.999157i \(-0.486932\pi\)
−0.167590 + 0.985857i \(0.553599\pi\)
\(608\) 1.82625 0.191947i 0.0740643 0.00778447i
\(609\) 2.17035 0.461322i 0.0879470 0.0186937i
\(610\) −35.9679 3.55005i −1.45630 0.143737i
\(611\) 49.2091 54.6523i 1.99079 2.21099i
\(612\) −47.0499 + 15.2874i −1.90188 + 0.617958i
\(613\) 27.8368 25.0644i 1.12432 1.01234i 0.124521 0.992217i \(-0.460261\pi\)
0.999798 0.0201236i \(-0.00640597\pi\)
\(614\) 22.3254 38.6688i 0.900982 1.56055i
\(615\) 10.6889 + 9.50237i 0.431019 + 0.383172i
\(616\) 13.3995 41.2393i 0.539879 1.66158i
\(617\) 9.97296 + 22.3996i 0.401496 + 0.901776i 0.995270 + 0.0971438i \(0.0309707\pi\)
−0.593774 + 0.804632i \(0.702363\pi\)
\(618\) 14.2862 + 19.6632i 0.574675 + 0.790972i
\(619\) −20.8505 −0.838051 −0.419025 0.907975i \(-0.637628\pi\)
−0.419025 + 0.907975i \(0.637628\pi\)
\(620\) 52.0786 + 16.1315i 2.09153 + 0.647857i
\(621\) −14.6582 −0.588214
\(622\) −24.3610 33.5301i −0.976788 1.34443i
\(623\) 22.2662 + 50.0106i 0.892074 + 2.00363i
\(624\) 12.0957 37.2268i 0.484216 1.49026i
\(625\) −24.3141 + 5.81599i −0.972563 + 0.232640i
\(626\) 5.86778 10.1633i 0.234524 0.406207i
\(627\) 0.754691 0.679527i 0.0301395 0.0271377i
\(628\) 49.4335 16.0619i 1.97261 0.640940i
\(629\) 6.94424 7.71236i 0.276885 0.307512i
\(630\) 3.42493 34.7002i 0.136452 1.38249i
\(631\) −2.68311 + 0.570313i −0.106813 + 0.0227038i −0.261008 0.965337i \(-0.584055\pi\)
0.154195 + 0.988040i \(0.450722\pi\)
\(632\) −20.3730 + 2.14129i −0.810396 + 0.0851760i
\(633\) −13.2671 1.39443i −0.527320 0.0554235i
\(634\) −25.1718 5.35042i −0.999699 0.212493i
\(635\) 6.72603 + 2.13839i 0.266914 + 0.0848592i
\(636\) 27.4123 + 19.9162i 1.08697 + 0.789728i
\(637\) 4.87600 22.9398i 0.193194 0.908907i
\(638\) −3.37412 0.354635i −0.133583 0.0140401i
\(639\) 0.668803 + 6.36323i 0.0264574 + 0.251726i
\(640\) −27.1254 + 15.8909i −1.07223 + 0.628145i
\(641\) 23.1770 + 10.3191i 0.915436 + 0.407578i 0.809719 0.586818i \(-0.199620\pi\)
0.105717 + 0.994396i \(0.466286\pi\)
\(642\) 11.6533 + 10.4927i 0.459920 + 0.414114i
\(643\) −15.3953 + 5.00225i −0.607133 + 0.197269i −0.596419 0.802673i \(-0.703410\pi\)
−0.0107138 + 0.999943i \(0.503410\pi\)
\(644\) −27.5491 30.5964i −1.08559 1.20567i
\(645\) 7.95427 + 1.63811i 0.313199 + 0.0645006i
\(646\) −3.37449 5.84479i −0.132768 0.229960i
\(647\) 13.9836 + 4.54355i 0.549753 + 0.178626i 0.570705 0.821155i \(-0.306670\pi\)
−0.0209524 + 0.999780i \(0.506670\pi\)
\(648\) 0.0452194 + 0.101564i 0.00177639 + 0.00398983i
\(649\) 14.7293 10.7015i 0.578176 0.420070i
\(650\) −57.5932 + 42.9697i −2.25899 + 1.68541i
\(651\) −18.8801 + 6.29021i −0.739968 + 0.246533i
\(652\) 15.1708i 0.594133i
\(653\) 9.78350 + 13.4658i 0.382858 + 0.526959i 0.956339 0.292260i \(-0.0944073\pi\)
−0.573481 + 0.819219i \(0.694407\pi\)
\(654\) 1.53200 0.682088i 0.0599058 0.0266718i
\(655\) −14.6571 + 0.0928961i −0.572700 + 0.00362975i
\(656\) 19.1525 + 33.1731i 0.747779 + 1.29519i
\(657\) 12.0180 + 6.93860i 0.468867 + 0.270701i
\(658\) −80.9017 + 72.8442i −3.15388 + 2.83976i
\(659\) −8.45643 26.0262i −0.329416 1.01384i −0.969408 0.245456i \(-0.921062\pi\)
0.639992 0.768382i \(-0.278938\pi\)
\(660\) 9.10472 20.8034i 0.354401 0.809771i
\(661\) −3.61957 1.61154i −0.140785 0.0626816i 0.335135 0.942170i \(-0.391218\pi\)
−0.475920 + 0.879489i \(0.657885\pi\)
\(662\) −8.24927 38.8098i −0.320617 1.50838i
\(663\) −37.0086 + 3.88976i −1.43729 + 0.151066i
\(664\) 0.711961 6.77386i 0.0276294 0.262877i
\(665\) 3.24538 0.361914i 0.125851 0.0140344i
\(666\) 6.43372 + 4.67437i 0.249302 + 0.181128i
\(667\) −1.02870 + 1.41588i −0.0398313 + 0.0548231i
\(668\) −7.99872 + 37.6310i −0.309480 + 1.45599i
\(669\) −2.18015 + 20.7427i −0.0842894 + 0.801960i
\(670\) 30.1523 13.6543i 1.16488 0.527511i
\(671\) −13.5450 + 2.87908i −0.522898 + 0.111145i
\(672\) −6.09619 + 13.6923i −0.235166 + 0.528191i
\(673\) −25.6588 23.1033i −0.989074 0.890566i 0.00492173 0.999988i \(-0.498433\pi\)
−0.993995 + 0.109422i \(0.965100\pi\)
\(674\) 1.96409 + 6.04484i 0.0756538 + 0.232839i
\(675\) 5.08237 25.4956i 0.195621 0.981326i
\(676\) −42.4265 + 73.4848i −1.63179 + 2.82634i
\(677\) −10.3699 + 5.98704i −0.398546 + 0.230101i −0.685856 0.727737i \(-0.740572\pi\)
0.287310 + 0.957838i \(0.407239\pi\)
\(678\) 0.828577 + 0.269221i 0.0318213 + 0.0103394i
\(679\) −53.0895 + 23.6370i −2.03739 + 0.907103i
\(680\) −66.6357 47.7713i −2.55536 1.83195i
\(681\) 2.91899 0.111856
\(682\) 30.4278 0.226428i 1.16514 0.00867037i
\(683\) 24.7403i 0.946661i −0.880885 0.473331i \(-0.843052\pi\)
0.880885 0.473331i \(-0.156948\pi\)
\(684\) 2.87219 2.08677i 0.109821 0.0797896i
\(685\) 18.3935 16.7739i 0.702780 0.640897i
\(686\) 7.49194 23.0578i 0.286043 0.880351i
\(687\) −13.7649 + 7.94714i −0.525162 + 0.303202i
\(688\) 18.8369 + 10.8755i 0.718149 + 0.414623i
\(689\) −27.4872 30.5276i −1.04718 1.16301i
\(690\) −10.1174 13.7413i −0.385161 0.523124i
\(691\) −10.1605 + 11.2844i −0.386523 + 0.429277i −0.904735 0.425975i \(-0.859931\pi\)
0.518212 + 0.855252i \(0.326598\pi\)
\(692\) 36.0299 80.9245i 1.36965 3.07629i
\(693\) −2.77760 13.0676i −0.105512 0.496397i
\(694\) −8.30173 78.9857i −0.315129 2.99825i
\(695\) −33.5942 + 7.36351i −1.27430 + 0.279314i
\(696\) 3.91062 + 0.831228i 0.148232 + 0.0315076i
\(697\) 21.4049 29.4613i 0.810768 1.11593i
\(698\) 32.8059 45.1535i 1.24172 1.70908i
\(699\) −13.2820 2.82318i −0.502372 0.106782i
\(700\) 62.7695 37.3087i 2.37246 1.41014i
\(701\) −0.137862 1.31167i −0.00520696 0.0495409i 0.991610 0.129267i \(-0.0412623\pi\)
−0.996817 + 0.0797256i \(0.974596\pi\)
\(702\) −15.5358 73.0901i −0.586360 2.75861i
\(703\) −0.302922 + 0.680374i −0.0114249 + 0.0256608i
\(704\) −3.25178 + 3.61146i −0.122556 + 0.136112i
\(705\) −24.9427 + 18.3646i −0.939397 + 0.691650i
\(706\) −46.8356 52.0162i −1.76268 1.95766i
\(707\) −13.6064 7.85563i −0.511720 0.295441i
\(708\) −34.1995 + 19.7451i −1.28529 + 0.742065i
\(709\) 1.10844 3.41142i 0.0416282 0.128119i −0.928083 0.372374i \(-0.878544\pi\)
0.969711 + 0.244256i \(0.0785437\pi\)
\(710\) −14.4219 + 13.1520i −0.541244 + 0.493585i
\(711\) −5.10605 + 3.70977i −0.191492 + 0.139127i
\(712\) 98.6389i 3.69665i
\(713\) 7.74691 13.6516i 0.290124 0.511258i
\(714\) 55.0855 2.06152
\(715\) −16.0408 + 22.3751i −0.599892 + 0.836782i
\(716\) 39.1312 17.4223i 1.46240 0.651102i
\(717\) −24.2606 7.88273i −0.906027 0.294386i
\(718\) −9.16705 + 5.29260i −0.342111 + 0.197518i
\(719\) 13.8778 24.0371i 0.517556 0.896433i −0.482236 0.876041i \(-0.660175\pi\)
0.999792 0.0203919i \(-0.00649141\pi\)
\(720\) 13.1395 23.0950i 0.489679 0.860700i
\(721\) 9.25312 + 28.4782i 0.344604 + 1.06058i
\(722\) −35.3023 31.7863i −1.31381 1.18296i
\(723\) −0.551440 + 1.23856i −0.0205083 + 0.0460624i
\(724\) 70.4004 14.9641i 2.61641 0.556135i
\(725\) −2.10602 2.28018i −0.0782158 0.0846837i
\(726\) −1.78766 + 17.0084i −0.0663461 + 0.631241i
\(727\) 1.51120 7.10964i 0.0560474 0.263682i −0.941198 0.337855i \(-0.890298\pi\)
0.997245 + 0.0741734i \(0.0236318\pi\)
\(728\) 67.0223 92.2483i 2.48401 3.41895i
\(729\) 13.5525 + 9.84649i 0.501945 + 0.364685i
\(730\) 4.69177 + 42.0724i 0.173650 + 1.55717i
\(731\) 2.16148 20.5651i 0.0799453 0.760628i
\(732\) 29.8712 3.13959i 1.10407 0.116042i
\(733\) 10.9048 + 51.3028i 0.402776 + 1.89491i 0.444489 + 0.895784i \(0.353385\pi\)
−0.0417127 + 0.999130i \(0.513281\pi\)
\(734\) 43.5811 + 19.4036i 1.60861 + 0.716199i
\(735\) −3.96029 + 9.04887i −0.146078 + 0.333773i
\(736\) −3.65319 11.2434i −0.134658 0.414435i
\(737\) 9.42439 8.48576i 0.347152 0.312577i
\(738\) 24.1666 + 13.9526i 0.889585 + 0.513602i
\(739\) −4.31139 7.46754i −0.158597 0.274698i 0.775766 0.631021i \(-0.217364\pi\)
−0.934363 + 0.356323i \(0.884030\pi\)
\(740\) 0.105548 + 16.6534i 0.00388003 + 0.612189i
\(741\) 2.43962 1.08619i 0.0896216 0.0399021i
\(742\) 35.7427 + 49.1956i 1.31216 + 1.80603i
\(743\) 9.82282i 0.360364i −0.983633 0.180182i \(-0.942331\pi\)
0.983633 0.180182i \(-0.0576687\pi\)
\(744\) −35.6877 3.48263i −1.30837 0.127680i
\(745\) 12.6484 + 38.1042i 0.463400 + 1.39603i
\(746\) −0.478359 + 0.347548i −0.0175140 + 0.0127247i
\(747\) −0.853535 1.91707i −0.0312292 0.0701420i
\(748\) −54.9911 17.8677i −2.01067 0.653307i
\(749\) 9.65950 + 16.7307i 0.352950 + 0.611328i
\(750\) 27.4088 12.8330i 1.00083 0.468597i
\(751\) −18.1870 20.1987i −0.663654 0.737062i 0.313502 0.949588i \(-0.398498\pi\)
−0.977156 + 0.212525i \(0.931831\pi\)
\(752\) −78.8975 + 25.6354i −2.87710 + 0.934825i
\(753\) 8.81174 + 7.93413i 0.321118 + 0.289136i
\(754\) −8.15028 3.62874i −0.296816 0.132151i
\(755\) 7.53582 + 12.8635i 0.274257 + 0.468149i
\(756\) 7.93715 + 75.5169i 0.288671 + 2.74652i
\(757\) 53.6533 + 5.63919i 1.95006 + 0.204960i 0.995624 0.0934516i \(-0.0297900\pi\)
0.954437 + 0.298411i \(0.0964567\pi\)
\(758\) −1.82777 + 8.59900i −0.0663877 + 0.312330i
\(759\) −5.28928 3.84289i −0.191989 0.139488i
\(760\) 5.60734 + 1.78273i 0.203400 + 0.0646662i
\(761\) −15.1031 3.21027i −0.547487 0.116372i −0.0741399 0.997248i \(-0.523621\pi\)
−0.473347 + 0.880876i \(0.656954\pi\)
\(762\) −8.49714 0.893086i −0.307819 0.0323531i
\(763\) 2.05471 0.215958i 0.0743854 0.00781822i
\(764\) 99.8620 21.2263i 3.61288 0.767942i
\(765\) −25.1388 2.48121i −0.908893 0.0897083i
\(766\) −20.5171 + 22.7865i −0.741311 + 0.823310i
\(767\) 45.5331 14.7946i 1.64410 0.534202i
\(768\) 24.7045 22.2440i 0.891447 0.802663i
\(769\) −7.71652 + 13.3654i −0.278265 + 0.481969i −0.970954 0.239268i \(-0.923093\pi\)
0.692689 + 0.721237i \(0.256426\pi\)
\(770\) 27.0773 30.4584i 0.975797 1.09764i
\(771\) −2.03137 + 6.25192i −0.0731580 + 0.225157i
\(772\) −1.87620 4.21401i −0.0675259 0.151666i
\(773\) −5.84542 8.04553i −0.210245 0.289378i 0.690851 0.722997i \(-0.257236\pi\)
−0.901096 + 0.433620i \(0.857236\pi\)
\(774\) 15.8456 0.569557
\(775\) 21.0588 + 18.2079i 0.756455 + 0.654046i
\(776\) −104.712 −3.75892
\(777\) −3.57302 4.91783i −0.128181 0.176426i
\(778\) −35.1151 78.8697i −1.25894 2.82762i
\(779\) −0.807570 + 2.48544i −0.0289342 + 0.0890503i
\(780\) 39.6752 44.6294i 1.42060 1.59799i
\(781\) −3.73910 + 6.47631i −0.133795 + 0.231741i
\(782\) −32.2890 + 29.0732i −1.15465 + 1.03965i
\(783\) 3.06979 0.997436i 0.109705 0.0356455i
\(784\) −17.7018 + 19.6599i −0.632208 + 0.702138i
\(785\) 26.4123 + 2.60691i 0.942696 + 0.0930446i
\(786\) 17.3561 3.68915i 0.619072 0.131588i
\(787\) 37.2354 3.91360i 1.32730 0.139505i 0.585799 0.810456i \(-0.300781\pi\)
0.741501 + 0.670952i \(0.234114\pi\)
\(788\) −23.9026 2.51227i −0.851496 0.0894959i
\(789\) −0.347020 0.0737613i −0.0123542 0.00262597i
\(790\) −18.3484 5.83345i −0.652806 0.207545i
\(791\) 0.868345 + 0.630889i 0.0308748 + 0.0224318i
\(792\) 5.00480 23.5457i 0.177838 0.836660i
\(793\) −36.2146 3.80631i −1.28602 0.135166i
\(794\) 4.48142 + 42.6379i 0.159040 + 1.51316i
\(795\) 8.74554 + 14.9284i 0.310172 + 0.529456i
\(796\) 78.9516 + 35.1515i 2.79837 + 1.24591i
\(797\) −9.19134 8.27592i −0.325574 0.293148i 0.490093 0.871670i \(-0.336963\pi\)
−0.815667 + 0.578522i \(0.803630\pi\)
\(798\) −3.75965 + 1.22158i −0.133090 + 0.0432436i
\(799\) 52.7724 + 58.6097i 1.86695 + 2.07346i
\(800\) 20.8227 2.45578i 0.736192 0.0868249i
\(801\) 15.1951 + 26.3187i 0.536894 + 0.929927i
\(802\) −10.5373 3.42378i −0.372085 0.120898i
\(803\) 6.59703 + 14.8172i 0.232804 + 0.522887i
\(804\) −22.2536 + 16.1682i −0.784825 + 0.570209i
\(805\) −6.62302 19.9524i −0.233431 0.703230i
\(806\) 76.2818 + 24.1594i 2.68691 + 0.850978i
\(807\) 1.13746i 0.0400404i
\(808\) −16.6397 22.9026i −0.585383 0.805711i
\(809\) −16.4737 + 7.33456i −0.579184 + 0.257869i −0.675352 0.737496i \(-0.736008\pi\)
0.0961677 + 0.995365i \(0.469341\pi\)
\(810\) 0.000662244 0.104488i 2.32689e−5 0.00367135i
\(811\) 6.82127 + 11.8148i 0.239527 + 0.414873i 0.960579 0.278008i \(-0.0896743\pi\)
−0.721052 + 0.692881i \(0.756341\pi\)
\(812\) 7.85144 + 4.53303i 0.275531 + 0.159078i
\(813\) 17.5192 15.7744i 0.614426 0.553232i
\(814\) 2.87224 + 8.83984i 0.100672 + 0.309836i
\(815\) 3.10586 7.09658i 0.108793 0.248582i
\(816\) 38.3478 + 17.0735i 1.34244 + 0.597694i
\(817\) 0.308531 + 1.45153i 0.0107941 + 0.0507825i
\(818\) −25.4563 + 2.67557i −0.890060 + 0.0935490i
\(819\) 3.67216 34.9383i 0.128316 1.22084i
\(820\) 6.47658 + 58.0774i 0.226172 + 2.02815i
\(821\) −21.1470 15.3642i −0.738034 0.536213i 0.154061 0.988061i \(-0.450765\pi\)
−0.892095 + 0.451848i \(0.850765\pi\)
\(822\) −17.7131 + 24.3800i −0.617816 + 0.850351i
\(823\) −6.71803 + 31.6058i −0.234176 + 1.10171i 0.691201 + 0.722662i \(0.257082\pi\)
−0.925377 + 0.379048i \(0.876252\pi\)
\(824\) −5.63971 + 53.6582i −0.196468 + 1.86927i
\(825\) 8.51802 7.86743i 0.296559 0.273909i
\(826\) −69.3225 + 14.7350i −2.41204 + 0.512695i
\(827\) 6.44208 14.4691i 0.224013 0.503141i −0.766218 0.642581i \(-0.777864\pi\)
0.990231 + 0.139440i \(0.0445302\pi\)
\(828\) −16.9853 15.2936i −0.590279 0.531490i
\(829\) −15.9341 49.0401i −0.553414 1.70323i −0.700094 0.714050i \(-0.746859\pi\)
0.146680 0.989184i \(-0.453141\pi\)
\(830\) 3.16559 5.56411i 0.109879 0.193133i
\(831\) 10.5428 18.2606i 0.365724 0.633453i
\(832\) −11.0672 + 6.38963i −0.383685 + 0.221520i
\(833\) 23.9195 + 7.77192i 0.828762 + 0.269281i
\(834\) 38.0343 16.9340i 1.31702 0.586376i
\(835\) −11.4457 + 15.9655i −0.396095 + 0.552509i
\(836\) 4.14944 0.143511
\(837\) −26.3581 + 11.9712i −0.911071 + 0.413786i
\(838\) 72.9086i 2.51858i
\(839\) −1.61755 + 1.17522i −0.0558439 + 0.0405730i −0.615357 0.788249i \(-0.710988\pi\)
0.559513 + 0.828822i \(0.310988\pi\)
\(840\) −35.4849 + 32.3604i −1.22435 + 1.11654i
\(841\) −8.84240 + 27.2141i −0.304910 + 0.938418i
\(842\) 28.6875 16.5627i 0.988636 0.570790i
\(843\) −21.0178 12.1346i −0.723893 0.417940i
\(844\) −36.4725 40.5068i −1.25544 1.39430i
\(845\) −34.8906 + 25.6889i −1.20027 + 0.883725i
\(846\) −40.4387 + 44.9118i −1.39031 + 1.54410i
\(847\) −8.56980 + 19.2481i −0.294462 + 0.661372i
\(848\) 9.63431 + 45.3259i 0.330844 + 1.55650i
\(849\) −2.09716 19.9531i −0.0719742 0.684789i
\(850\) −39.3727 66.2420i −1.35047 2.27208i
\(851\) 4.68991 + 0.996872i 0.160768 + 0.0341723i
\(852\) 9.53409 13.1225i 0.326632 0.449571i
\(853\) −7.89044 + 10.8603i −0.270163 + 0.371848i −0.922445 0.386129i \(-0.873812\pi\)
0.652281 + 0.757977i \(0.273812\pi\)
\(854\) 52.7259 + 11.2072i 1.80424 + 0.383503i
\(855\) 1.77077 0.388135i 0.0605591 0.0132739i
\(856\) 3.63861 + 34.6191i 0.124365 + 1.18325i
\(857\) 9.09352 + 42.7816i 0.310629 + 1.46139i 0.805587 + 0.592477i \(0.201850\pi\)
−0.494959 + 0.868916i \(0.664817\pi\)
\(858\) 13.5558 30.4469i 0.462788 1.03944i
\(859\) 19.7873 21.9761i 0.675136 0.749814i −0.304078 0.952647i \(-0.598348\pi\)
0.979213 + 0.202833i \(0.0650149\pi\)
\(860\) 19.6741 + 26.7213i 0.670882 + 0.911189i
\(861\) −14.2727 15.8515i −0.486414 0.540217i
\(862\) 25.9328 + 14.9723i 0.883276 + 0.509960i
\(863\) 17.7236 10.2327i 0.603317 0.348325i −0.167028 0.985952i \(-0.553417\pi\)
0.770345 + 0.637627i \(0.220084\pi\)
\(864\) −6.73760 + 20.7362i −0.229218 + 0.705460i
\(865\) 33.4215 30.4786i 1.13636 1.03630i
\(866\) 19.0866 13.8673i 0.648590 0.471229i
\(867\) 21.6872i 0.736536i
\(868\) −74.5261 32.5188i −2.52958 1.10376i
\(869\) −7.37668 −0.250237
\(870\) 3.05387 + 2.18933i 0.103536 + 0.0742253i
\(871\) 30.4653 13.5640i 1.03228 0.459600i
\(872\) 3.54045 + 1.15036i 0.119895 + 0.0389561i
\(873\) −27.9390 + 16.1306i −0.945593 + 0.545938i
\(874\) 1.55903 2.70032i 0.0527350 0.0913398i
\(875\) 37.0004 4.60169i 1.25084 0.155566i
\(876\) −10.8713 33.4584i −0.367307 1.13045i
\(877\) −12.2600 11.0390i −0.413991 0.372759i 0.435654 0.900114i \(-0.356517\pi\)
−0.849645 + 0.527355i \(0.823184\pi\)
\(878\) −12.9855 + 29.1659i −0.438240 + 0.984303i
\(879\) 19.0092 4.04053i 0.641165 0.136284i
\(880\) 28.2903 12.8111i 0.953666 0.431862i
\(881\) −4.24351 + 40.3743i −0.142968 + 1.36025i 0.654124 + 0.756387i \(0.273037\pi\)
−0.797092 + 0.603858i \(0.793629\pi\)
\(882\) −4.00697 + 18.8513i −0.134922 + 0.634756i
\(883\) −15.8592 + 21.8283i −0.533704 + 0.734581i −0.987689 0.156428i \(-0.950002\pi\)
0.453985 + 0.891009i \(0.350002\pi\)
\(884\) −123.010 89.3717i −4.13726 3.00590i
\(885\) −20.0402 + 2.23481i −0.673643 + 0.0751223i
\(886\) 2.28291 21.7204i 0.0766957 0.729711i
\(887\) −29.0332 + 3.05151i −0.974839 + 0.102460i −0.578533 0.815659i \(-0.696375\pi\)
−0.396306 + 0.918119i \(0.629708\pi\)
\(888\) −2.27725 10.7136i −0.0764196 0.359526i
\(889\) −9.61605 4.28134i −0.322512 0.143592i
\(890\) −37.1699 + 84.9295i −1.24594 + 2.84684i
\(891\) 0.0123713 + 0.0380748i 0.000414453 + 0.00127555i
\(892\) −63.3313 + 57.0237i −2.12049 + 1.90930i
\(893\) −4.90151 2.82989i −0.164023 0.0946986i
\(894\) −24.3014 42.0913i −0.812762 1.40774i
\(895\) 21.8716 0.138621i 0.731086 0.00463360i
\(896\) 42.8328 19.0704i 1.43094 0.637097i
\(897\) −10.1054 13.9089i −0.337409 0.464404i
\(898\) 23.3406i 0.778884i
\(899\) −0.693452 + 3.38614i −0.0231279 + 0.112934i
\(900\) 32.4900 24.2405i 1.08300 0.808016i
\(901\) 35.6400 25.8940i 1.18734 0.862655i
\(902\) 13.2657 + 29.7953i 0.441701 + 0.992077i
\(903\) −11.5193 3.74284i −0.383338 0.124554i
\(904\) 0.966987 + 1.67487i 0.0321615 + 0.0557054i
\(905\) 35.9954 + 7.41294i 1.19653 + 0.246415i
\(906\) −12.0762 13.4120i −0.401204 0.445583i
\(907\) 15.8036 5.13489i 0.524748 0.170501i −0.0346508 0.999399i \(-0.511032\pi\)
0.559399 + 0.828898i \(0.311032\pi\)
\(908\) 8.86337 + 7.98062i 0.294141 + 0.264846i
\(909\) −7.96790 3.54754i −0.264279 0.117664i
\(910\) 92.4689 54.1713i 3.06532 1.79576i
\(911\) −0.143837 1.36852i −0.00476554 0.0453411i 0.991881 0.127172i \(-0.0405900\pi\)
−0.996646 + 0.0818307i \(0.973923\pi\)
\(912\) −2.99591 0.314882i −0.0992044 0.0104268i
\(913\) 0.509941 2.39909i 0.0168766 0.0793982i
\(914\) −50.7958 36.9053i −1.68018 1.22072i
\(915\) 14.6159 + 4.64679i 0.483186 + 0.153618i
\(916\) −63.5241 13.5025i −2.09890 0.446134i
\(917\) 21.7405 + 2.28502i 0.717936 + 0.0754581i
\(918\) 79.6947 8.37625i 2.63032 0.276458i
\(919\) −10.5953 + 2.25210i −0.349507 + 0.0742900i −0.379320 0.925265i \(-0.623842\pi\)
0.0298131 + 0.999555i \(0.490509\pi\)
\(920\) 3.72069 37.6967i 0.122667 1.24282i
\(921\) −12.6781 + 14.0805i −0.417759 + 0.463968i
\(922\) 12.5807 4.08772i 0.414324 0.134622i
\(923\) −14.6139 + 13.1584i −0.481022 + 0.433114i
\(924\) −16.9339 + 29.3305i −0.557086 + 0.964901i
\(925\) −3.36001 + 7.81171i −0.110476 + 0.256848i
\(926\) 15.2892 47.0552i 0.502433 1.54633i
\(927\) 6.76116 + 15.1858i 0.222066 + 0.498768i
\(928\) 1.53014 + 2.10605i 0.0502292 + 0.0691346i
\(929\) 32.1627 1.05522 0.527611 0.849486i \(-0.323088\pi\)
0.527611 + 0.849486i \(0.323088\pi\)
\(930\) −29.4153 16.4467i −0.964565 0.539309i
\(931\) −1.80488 −0.0591527
\(932\) −32.6116 44.8860i −1.06823 1.47029i
\(933\) 7.15327 + 16.0665i 0.234187 + 0.525994i
\(934\) −20.1919 + 62.1441i −0.660698 + 2.03342i
\(935\) −22.0657 19.6163i −0.721626 0.641521i
\(936\) 31.6500 54.8193i 1.03451 1.79183i
\(937\) 36.6149 32.9682i 1.19616 1.07702i 0.200914 0.979609i \(-0.435609\pi\)
0.995244 0.0974159i \(-0.0310577\pi\)
\(938\) −46.9495 + 15.2548i −1.53296 + 0.498088i
\(939\) −3.33218 + 3.70076i −0.108742 + 0.120770i
\(940\) −125.947 12.4310i −4.10793 0.405455i
\(941\) −31.3754 + 6.66904i −1.02281 + 0.217404i −0.688635 0.725108i \(-0.741790\pi\)
−0.334172 + 0.942512i \(0.608457\pi\)
\(942\) −31.9534 + 3.35844i −1.04110 + 0.109424i
\(943\) 16.7323 + 1.75863i 0.544878 + 0.0572690i
\(944\) −52.8259 11.2285i −1.71934 0.365457i
\(945\) −11.7475 + 36.9503i −0.382146 + 1.20199i
\(946\) 14.9830 + 10.8858i 0.487139 + 0.353927i
\(947\) 5.41787 25.4891i 0.176057 0.828283i −0.798120 0.602498i \(-0.794172\pi\)
0.974177 0.225785i \(-0.0724946\pi\)
\(948\) 15.9125 + 1.67247i 0.516815 + 0.0543194i
\(949\) 4.45826 + 42.4175i 0.144721 + 1.37693i
\(950\) 4.15622 + 3.64796i 0.134846 + 0.118355i
\(951\) 9.97594 + 4.44157i 0.323492 + 0.144028i
\(952\) 90.8731 + 81.8225i 2.94521 + 2.65188i
\(953\) 1.14177 0.370982i 0.0369854 0.0120173i −0.290466 0.956885i \(-0.593810\pi\)
0.327451 + 0.944868i \(0.393810\pi\)
\(954\) 22.5882 + 25.0868i 0.731321 + 0.812214i
\(955\) 51.0591 + 10.5152i 1.65223 + 0.340263i
\(956\) −52.1144 90.2648i −1.68550 2.91937i
\(957\) 1.36920 + 0.444881i 0.0442600 + 0.0143809i
\(958\) −25.5891 57.4741i −0.826747 1.85690i
\(959\) −30.0360 + 21.8224i −0.969913 + 0.704683i
\(960\) 5.10825 1.69564i 0.164868 0.0547265i
\(961\) 2.78120 30.8750i 0.0897163 0.995967i
\(962\) 24.4418i 0.788036i
\(963\) 6.30385 + 8.67651i 0.203139 + 0.279596i
\(964\) −5.06068 + 2.25316i −0.162993 + 0.0725694i
\(965\) −0.0149280 2.35534i −0.000480550 0.0758210i
\(966\) 12.7249 + 22.0402i 0.409417 + 0.709130i
\(967\) 38.4970 + 22.2263i 1.23798 + 0.714748i 0.968681 0.248308i \(-0.0798745\pi\)
0.269299 + 0.963057i \(0.413208\pi\)
\(968\) −28.2128 + 25.4030i −0.906795 + 0.816482i
\(969\) 0.884983 + 2.72370i 0.0284298 + 0.0874978i
\(970\) −90.1582 39.4582i −2.89480 1.26693i
\(971\) −36.3099 16.1662i −1.16524 0.518798i −0.269336 0.963046i \(-0.586804\pi\)
−0.895904 + 0.444248i \(0.853471\pi\)
\(972\) 14.1838 + 66.7297i 0.454946 + 2.14035i
\(973\) 51.0115 5.36152i 1.63535 0.171883i
\(974\) −10.4787 + 99.6986i −0.335761 + 3.19455i
\(975\) 27.6961 12.7542i 0.886985 0.408460i
\(976\) 33.2315 + 24.1441i 1.06371 + 0.772833i
\(977\) −16.3146 + 22.4552i −0.521951 + 0.718404i −0.985877 0.167470i \(-0.946440\pi\)
0.463926 + 0.885874i \(0.346440\pi\)
\(978\) −1.94973 + 9.17275i −0.0623454 + 0.293312i
\(979\) −3.71281 + 35.3250i −0.118662 + 1.12899i
\(980\) −36.7652 + 16.6489i −1.17442 + 0.531830i
\(981\) 1.12187 0.238461i 0.0358185 0.00761347i
\(982\) 23.4452 52.6587i 0.748165 1.68041i
\(983\) −4.06617 3.66119i −0.129691 0.116774i 0.601733 0.798697i \(-0.294477\pi\)
−0.731424 + 0.681923i \(0.761144\pi\)
\(984\) −11.8767 36.5527i −0.378615 1.16526i
\(985\) −10.6668 6.06870i −0.339874 0.193365i
\(986\) 4.78381 8.28580i 0.152347 0.263874i
\(987\) 40.0064 23.0977i 1.27342 0.735207i
\(988\) 10.3775 + 3.37184i 0.330151 + 0.107273i
\(989\) 8.72758 3.88577i 0.277521 0.123560i
\(990\) 13.1819 18.3873i 0.418948 0.584386i
\(991\) 6.88861 0.218824 0.109412 0.993996i \(-0.465103\pi\)
0.109412 + 0.993996i \(0.465103\pi\)
\(992\) −15.7514 17.2341i −0.500109 0.547183i
\(993\) 16.8365i 0.534289i
\(994\) 23.5505 17.1104i 0.746975 0.542709i
\(995\) 29.7355 + 32.6067i 0.942680 + 1.03370i
\(996\) −1.64395 + 5.05954i −0.0520904 + 0.160318i
\(997\) 11.4097 6.58742i 0.361350 0.208626i −0.308323 0.951282i \(-0.599768\pi\)
0.669673 + 0.742656i \(0.266434\pi\)
\(998\) −3.63536 2.09888i −0.115075 0.0664388i
\(999\) −5.91705 6.57154i −0.187207 0.207914i
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 155.2.u.a.49.2 yes 112
5.2 odd 4 775.2.bl.f.576.13 112
5.3 odd 4 775.2.bl.f.576.2 112
5.4 even 2 inner 155.2.u.a.49.13 yes 112
31.19 even 15 inner 155.2.u.a.19.13 yes 112
155.19 even 30 inner 155.2.u.a.19.2 112
155.112 odd 60 775.2.bl.f.701.13 112
155.143 odd 60 775.2.bl.f.701.2 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
155.2.u.a.19.2 112 155.19 even 30 inner
155.2.u.a.19.13 yes 112 31.19 even 15 inner
155.2.u.a.49.2 yes 112 1.1 even 1 trivial
155.2.u.a.49.13 yes 112 5.4 even 2 inner
775.2.bl.f.576.2 112 5.3 odd 4
775.2.bl.f.576.13 112 5.2 odd 4
775.2.bl.f.701.2 112 155.143 odd 60
775.2.bl.f.701.13 112 155.112 odd 60