Properties

Label 92.2.h.a.11.7
Level $92$
Weight $2$
Character 92.11
Analytic conductor $0.735$
Analytic rank $0$
Dimension $100$
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] = [92,2,Mod(7,92)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(92, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 19]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("92.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 92.h (of order \(22\), degree \(10\), 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: \(0.734623698596\)
Analytic rank: \(0\)
Dimension: \(100\)
Relative dimension: \(10\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 11.7
Character \(\chi\) \(=\) 92.11
Dual form 92.2.h.a.67.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.429294 + 1.34748i) q^{2} +(-1.65123 - 0.237411i) q^{3} +(-1.63141 + 1.15693i) q^{4} +(0.934364 + 3.18215i) q^{5} +(-0.388957 - 2.32692i) q^{6} +(0.148303 + 0.171151i) q^{7} +(-2.25930 - 1.70163i) q^{8} +(-0.208284 - 0.0611576i) q^{9} +O(q^{10})\) \(q+(0.429294 + 1.34748i) q^{2} +(-1.65123 - 0.237411i) q^{3} +(-1.63141 + 1.15693i) q^{4} +(0.934364 + 3.18215i) q^{5} +(-0.388957 - 2.32692i) q^{6} +(0.148303 + 0.171151i) q^{7} +(-2.25930 - 1.70163i) q^{8} +(-0.208284 - 0.0611576i) q^{9} +(-3.88677 + 2.62512i) q^{10} +(3.48603 + 2.24034i) q^{11} +(2.96851 - 1.52305i) q^{12} +(3.81497 - 4.40271i) q^{13} +(-0.166957 + 0.273310i) q^{14} +(-0.787372 - 5.47629i) q^{15} +(1.32301 - 3.77487i) q^{16} +(-0.449525 + 0.205291i) q^{17} +(-0.00700629 - 0.306913i) q^{18} +(-0.608905 + 1.33332i) q^{19} +(-5.20587 - 4.11041i) q^{20} +(-0.204249 - 0.317818i) q^{21} +(-1.52228 + 5.65913i) q^{22} +(4.22490 - 2.26941i) q^{23} +(3.32664 + 3.34617i) q^{24} +(-5.04678 + 3.24337i) q^{25} +(7.57031 + 3.25054i) q^{26} +(4.88178 + 2.22943i) q^{27} +(-0.439953 - 0.107641i) q^{28} +(-0.299010 - 0.654741i) q^{29} +(7.04119 - 3.41191i) q^{30} +(-9.23576 + 1.32790i) q^{31} +(5.65453 + 0.162207i) q^{32} +(-5.22436 - 4.52693i) q^{33} +(-0.469604 - 0.517596i) q^{34} +(-0.406059 + 0.631840i) q^{35} +(0.410552 - 0.141197i) q^{36} +(-1.33496 + 4.54647i) q^{37} +(-2.05802 - 0.248103i) q^{38} +(-7.34464 + 6.36416i) q^{39} +(3.30385 - 8.77938i) q^{40} +(-2.79241 + 0.819926i) q^{41} +(0.340571 - 0.411659i) q^{42} +(0.508752 - 3.53845i) q^{43} +(-8.27907 + 0.378190i) q^{44} -0.719934i q^{45} +(4.87172 + 4.71872i) q^{46} -6.02195i q^{47} +(-3.08080 + 5.91908i) q^{48} +(0.988905 - 6.87799i) q^{49} +(-6.53694 - 5.40809i) q^{50} +(0.791007 - 0.232261i) q^{51} +(-1.13015 + 11.5963i) q^{52} +(4.56115 - 3.95226i) q^{53} +(-0.908399 + 7.53518i) q^{54} +(-3.87187 + 13.1864i) q^{55} +(-0.0438253 - 0.639038i) q^{56} +(1.32199 - 2.05705i) q^{57} +(0.753888 - 0.683987i) q^{58} +(4.34794 + 3.76751i) q^{59} +(7.62023 + 8.02315i) q^{60} +(-9.72972 + 1.39892i) q^{61} +(-5.75419 - 11.8750i) q^{62} +(-0.0204219 - 0.0447178i) q^{63} +(2.20889 + 7.68901i) q^{64} +(17.5746 + 8.02607i) q^{65} +(3.85717 - 8.98311i) q^{66} +(10.2383 - 6.57976i) q^{67} +(0.495852 - 0.854984i) q^{68} +(-7.51506 + 2.74429i) q^{69} +(-1.02571 - 0.275911i) q^{70} +(-2.54626 - 3.96206i) q^{71} +(0.366508 + 0.492596i) q^{72} +(-2.85291 + 6.24699i) q^{73} +(-6.69937 + 0.152935i) q^{74} +(9.10341 - 4.15739i) q^{75} +(-0.549181 - 2.87965i) q^{76} +(0.133554 + 0.928886i) q^{77} +(-11.7286 - 7.16466i) q^{78} +(1.34769 - 1.55532i) q^{79} +(13.2484 + 0.682929i) q^{80} +(-6.98379 - 4.48821i) q^{81} +(-2.30360 - 3.41073i) q^{82} +(-6.97591 - 2.04831i) q^{83} +(0.700909 + 0.282190i) q^{84} +(-1.07329 - 1.23864i) q^{85} +(4.98639 - 0.833502i) q^{86} +(0.338292 + 1.15212i) q^{87} +(-4.06377 - 10.9935i) q^{88} +(14.1914 + 2.04041i) q^{89} +(0.970098 - 0.309064i) q^{90} +1.31930 q^{91} +(-4.26699 + 8.59027i) q^{92} +15.5656 q^{93} +(8.11447 - 2.58519i) q^{94} +(-4.81175 - 0.691826i) q^{95} +(-9.29841 - 1.61029i) q^{96} +(-0.265360 - 0.903735i) q^{97} +(9.69249 - 1.62015i) q^{98} +(-0.589070 - 0.679823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9} - 11 q^{10} - 18 q^{12} - 18 q^{13} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 24 q^{18} - 11 q^{20} - 22 q^{21} - 30 q^{24} - 16 q^{25} + 12 q^{26} - 11 q^{28} - 42 q^{29} - 11 q^{30} - 27 q^{32} - 22 q^{33} + 11 q^{34} + 77 q^{36} - 22 q^{37} + 44 q^{38} + 77 q^{40} - 10 q^{41} + 99 q^{42} + 66 q^{44} + 65 q^{46} + 38 q^{48} - 8 q^{49} + 30 q^{50} + 96 q^{52} - 22 q^{53} + 48 q^{54} + 44 q^{56} - 22 q^{57} + 79 q^{58} + 11 q^{60} - 22 q^{61} - 36 q^{62} + 10 q^{64} - 22 q^{65} - 44 q^{66} - 10 q^{69} + 34 q^{70} - 21 q^{72} - 18 q^{73} - 22 q^{74} - 66 q^{76} + 122 q^{77} - 66 q^{78} - 110 q^{80} + 8 q^{81} - 122 q^{82} - 165 q^{84} + 54 q^{85} - 121 q^{86} - 99 q^{88} + 22 q^{89} - 198 q^{90} - 86 q^{92} + 212 q^{93} - 61 q^{94} - 147 q^{96} + 22 q^{97} - 71 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/92\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(47\)
\(\chi(n)\) \(e\left(\frac{9}{22}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.429294 + 1.34748i 0.303557 + 0.952813i
\(3\) −1.65123 0.237411i −0.953338 0.137069i −0.351943 0.936021i \(-0.614479\pi\)
−0.601395 + 0.798952i \(0.705388\pi\)
\(4\) −1.63141 + 1.15693i −0.815706 + 0.578466i
\(5\) 0.934364 + 3.18215i 0.417860 + 1.42310i 0.852609 + 0.522550i \(0.175019\pi\)
−0.434749 + 0.900552i \(0.643163\pi\)
\(6\) −0.388957 2.32692i −0.158791 0.949961i
\(7\) 0.148303 + 0.171151i 0.0560533 + 0.0646889i 0.783084 0.621916i \(-0.213646\pi\)
−0.727030 + 0.686605i \(0.759100\pi\)
\(8\) −2.25930 1.70163i −0.798784 0.601618i
\(9\) −0.208284 0.0611576i −0.0694279 0.0203859i
\(10\) −3.88677 + 2.62512i −1.22911 + 0.830135i
\(11\) 3.48603 + 2.24034i 1.05108 + 0.675487i 0.947702 0.319156i \(-0.103399\pi\)
0.103376 + 0.994642i \(0.467036\pi\)
\(12\) 2.96851 1.52305i 0.856934 0.439666i
\(13\) 3.81497 4.40271i 1.05808 1.22109i 0.0836287 0.996497i \(-0.473349\pi\)
0.974452 0.224594i \(-0.0721055\pi\)
\(14\) −0.166957 + 0.273310i −0.0446211 + 0.0730451i
\(15\) −0.787372 5.47629i −0.203299 1.41397i
\(16\) 1.32301 3.77487i 0.330753 0.943717i
\(17\) −0.449525 + 0.205291i −0.109026 + 0.0497904i −0.469181 0.883102i \(-0.655451\pi\)
0.360155 + 0.932892i \(0.382724\pi\)
\(18\) −0.00700629 0.306913i −0.00165140 0.0723401i
\(19\) −0.608905 + 1.33332i −0.139692 + 0.305884i −0.966529 0.256559i \(-0.917411\pi\)
0.826836 + 0.562443i \(0.190138\pi\)
\(20\) −5.20587 4.11041i −1.16407 0.919115i
\(21\) −0.204249 0.317818i −0.0445708 0.0693536i
\(22\) −1.52228 + 5.65913i −0.324551 + 1.20653i
\(23\) 4.22490 2.26941i 0.880952 0.473206i
\(24\) 3.32664 + 3.34617i 0.679047 + 0.683034i
\(25\) −5.04678 + 3.24337i −1.00936 + 0.648674i
\(26\) 7.57031 + 3.25054i 1.48466 + 0.637483i
\(27\) 4.88178 + 2.22943i 0.939498 + 0.429054i
\(28\) −0.439953 0.107641i −0.0831433 0.0203422i
\(29\) −0.299010 0.654741i −0.0555248 0.121582i 0.879836 0.475277i \(-0.157652\pi\)
−0.935361 + 0.353695i \(0.884925\pi\)
\(30\) 7.04119 3.41191i 1.28554 0.622927i
\(31\) −9.23576 + 1.32790i −1.65879 + 0.238498i −0.907069 0.420981i \(-0.861686\pi\)
−0.751723 + 0.659479i \(0.770777\pi\)
\(32\) 5.65453 + 0.162207i 0.999589 + 0.0286743i
\(33\) −5.22436 4.52693i −0.909444 0.788038i
\(34\) −0.469604 0.517596i −0.0805365 0.0887670i
\(35\) −0.406059 + 0.631840i −0.0686364 + 0.106800i
\(36\) 0.410552 0.141197i 0.0684253 0.0235328i
\(37\) −1.33496 + 4.54647i −0.219467 + 0.747435i 0.773987 + 0.633201i \(0.218259\pi\)
−0.993454 + 0.114233i \(0.963559\pi\)
\(38\) −2.05802 0.248103i −0.333855 0.0402476i
\(39\) −7.34464 + 6.36416i −1.17608 + 1.01908i
\(40\) 3.30385 8.77938i 0.522384 1.38814i
\(41\) −2.79241 + 0.819926i −0.436101 + 0.128051i −0.492412 0.870362i \(-0.663885\pi\)
0.0563103 + 0.998413i \(0.482066\pi\)
\(42\) 0.340571 0.411659i 0.0525512 0.0635204i
\(43\) 0.508752 3.53845i 0.0775839 0.539608i −0.913548 0.406730i \(-0.866669\pi\)
0.991132 0.132878i \(-0.0424219\pi\)
\(44\) −8.27907 + 0.378190i −1.24812 + 0.0570144i
\(45\) 0.719934i 0.107321i
\(46\) 4.87172 + 4.71872i 0.718296 + 0.695738i
\(47\) 6.02195i 0.878392i −0.898391 0.439196i \(-0.855263\pi\)
0.898391 0.439196i \(-0.144737\pi\)
\(48\) −3.08080 + 5.91908i −0.444674 + 0.854345i
\(49\) 0.988905 6.87799i 0.141272 0.982569i
\(50\) −6.53694 5.40809i −0.924463 0.764819i
\(51\) 0.791007 0.232261i 0.110763 0.0325230i
\(52\) −1.13015 + 11.5963i −0.156724 + 1.60812i
\(53\) 4.56115 3.95226i 0.626522 0.542885i −0.282693 0.959210i \(-0.591228\pi\)
0.909216 + 0.416326i \(0.136682\pi\)
\(54\) −0.908399 + 7.53518i −0.123617 + 1.02541i
\(55\) −3.87187 + 13.1864i −0.522083 + 1.77805i
\(56\) −0.0438253 0.639038i −0.00585640 0.0853951i
\(57\) 1.32199 2.05705i 0.175101 0.272463i
\(58\) 0.753888 0.683987i 0.0989903 0.0898119i
\(59\) 4.34794 + 3.76751i 0.566053 + 0.490488i 0.890232 0.455508i \(-0.150542\pi\)
−0.324178 + 0.945996i \(0.605088\pi\)
\(60\) 7.62023 + 8.02315i 0.983767 + 1.03578i
\(61\) −9.72972 + 1.39892i −1.24576 + 0.179114i −0.733485 0.679706i \(-0.762107\pi\)
−0.512278 + 0.858820i \(0.671198\pi\)
\(62\) −5.75419 11.8750i −0.730782 1.50812i
\(63\) −0.0204219 0.0447178i −0.00257292 0.00563391i
\(64\) 2.20889 + 7.68901i 0.276111 + 0.961126i
\(65\) 17.5746 + 8.02607i 2.17987 + 0.995511i
\(66\) 3.85717 8.98311i 0.474785 1.10574i
\(67\) 10.2383 6.57976i 1.25081 0.803846i 0.263810 0.964575i \(-0.415021\pi\)
0.986999 + 0.160729i \(0.0513846\pi\)
\(68\) 0.495852 0.854984i 0.0601309 0.103682i
\(69\) −7.51506 + 2.74429i −0.904707 + 0.330373i
\(70\) −1.02571 0.275911i −0.122596 0.0329777i
\(71\) −2.54626 3.96206i −0.302186 0.470210i 0.656640 0.754204i \(-0.271977\pi\)
−0.958826 + 0.283993i \(0.908341\pi\)
\(72\) 0.366508 + 0.492596i 0.0431934 + 0.0580530i
\(73\) −2.85291 + 6.24699i −0.333907 + 0.731155i −0.999890 0.0148119i \(-0.995285\pi\)
0.665983 + 0.745967i \(0.268012\pi\)
\(74\) −6.69937 + 0.152935i −0.778786 + 0.0177783i
\(75\) 9.10341 4.15739i 1.05117 0.480054i
\(76\) −0.549181 2.87965i −0.0629954 0.330319i
\(77\) 0.133554 + 0.928886i 0.0152198 + 0.105856i
\(78\) −11.7286 7.16466i −1.32800 0.811238i
\(79\) 1.34769 1.55532i 0.151627 0.174987i −0.674854 0.737951i \(-0.735794\pi\)
0.826482 + 0.562964i \(0.190339\pi\)
\(80\) 13.2484 + 0.682929i 1.48121 + 0.0763538i
\(81\) −6.98379 4.48821i −0.775977 0.498690i
\(82\) −2.30360 3.41073i −0.254390 0.376652i
\(83\) −6.97591 2.04831i −0.765706 0.224832i −0.124520 0.992217i \(-0.539739\pi\)
−0.641186 + 0.767386i \(0.721557\pi\)
\(84\) 0.700909 + 0.282190i 0.0764754 + 0.0307894i
\(85\) −1.07329 1.23864i −0.116414 0.134349i
\(86\) 4.98639 0.833502i 0.537697 0.0898788i
\(87\) 0.338292 + 1.15212i 0.0362687 + 0.123520i
\(88\) −4.06377 10.9935i −0.433199 1.17192i
\(89\) 14.1914 + 2.04041i 1.50428 + 0.216283i 0.844655 0.535311i \(-0.179806\pi\)
0.659626 + 0.751594i \(0.270715\pi\)
\(90\) 0.970098 0.309064i 0.102257 0.0325782i
\(91\) 1.31930 0.138300
\(92\) −4.26699 + 8.59027i −0.444865 + 0.895598i
\(93\) 15.5656 1.61408
\(94\) 8.11447 2.58519i 0.836944 0.266642i
\(95\) −4.81175 0.691826i −0.493675 0.0709798i
\(96\) −9.29841 1.61029i −0.949015 0.164349i
\(97\) −0.265360 0.903735i −0.0269433 0.0917604i 0.944924 0.327290i \(-0.106136\pi\)
−0.971867 + 0.235530i \(0.924317\pi\)
\(98\) 9.69249 1.62015i 0.979089 0.163660i
\(99\) −0.589070 0.679823i −0.0592038 0.0683248i
\(100\) 4.48103 11.1301i 0.448103 1.11301i
\(101\) −6.24015 1.83227i −0.620918 0.182318i −0.0438819 0.999037i \(-0.513973\pi\)
−0.577036 + 0.816719i \(0.695791\pi\)
\(102\) 0.652542 + 0.966159i 0.0646113 + 0.0956640i
\(103\) −13.9976 8.99568i −1.37922 0.886371i −0.379966 0.925000i \(-0.624064\pi\)
−0.999254 + 0.0386294i \(0.987701\pi\)
\(104\) −16.1109 + 3.45537i −1.57981 + 0.338826i
\(105\) 0.820502 0.946910i 0.0800728 0.0924089i
\(106\) 7.28367 + 4.44938i 0.707453 + 0.432162i
\(107\) 0.239943 + 1.66884i 0.0231962 + 0.161333i 0.998127 0.0611749i \(-0.0194847\pi\)
−0.974931 + 0.222508i \(0.928576\pi\)
\(108\) −10.5435 + 2.01076i −1.01455 + 0.193486i
\(109\) 9.26235 4.22998i 0.887173 0.405158i 0.0809138 0.996721i \(-0.474216\pi\)
0.806259 + 0.591563i \(0.201489\pi\)
\(110\) −19.4306 + 0.443566i −1.85263 + 0.0422923i
\(111\) 3.28371 7.19033i 0.311676 0.682475i
\(112\) 0.842279 0.333389i 0.0795878 0.0315023i
\(113\) −0.769424 1.19725i −0.0723813 0.112628i 0.803176 0.595742i \(-0.203142\pi\)
−0.875557 + 0.483114i \(0.839506\pi\)
\(114\) 3.33936 + 0.898271i 0.312760 + 0.0841308i
\(115\) 11.1692 + 11.3238i 1.04153 + 1.05595i
\(116\) 1.24530 + 0.722218i 0.115623 + 0.0670562i
\(117\) −1.06385 + 0.683698i −0.0983534 + 0.0632079i
\(118\) −3.21010 + 7.47614i −0.295514 + 0.688234i
\(119\) −0.101802 0.0464912i −0.00933214 0.00426184i
\(120\) −7.53973 + 13.7124i −0.688280 + 1.25177i
\(121\) 2.56374 + 5.61381i 0.233068 + 0.510347i
\(122\) −6.06194 12.5101i −0.548822 1.13261i
\(123\) 4.80557 0.690937i 0.433304 0.0622997i
\(124\) 13.5310 12.8515i 1.21512 1.15410i
\(125\) −2.50424 2.16994i −0.223986 0.194085i
\(126\) 0.0514894 0.0467153i 0.00458704 0.00416173i
\(127\) 5.96025 9.27434i 0.528887 0.822964i −0.469307 0.883035i \(-0.655496\pi\)
0.998194 + 0.0600708i \(0.0191326\pi\)
\(128\) −9.41253 + 6.27728i −0.831958 + 0.554839i
\(129\) −1.68013 + 5.72200i −0.147927 + 0.503794i
\(130\) −3.27028 + 27.1271i −0.286823 + 2.37920i
\(131\) −12.4602 + 10.7968i −1.08865 + 0.943319i −0.998615 0.0526195i \(-0.983243\pi\)
−0.0900338 + 0.995939i \(0.528698\pi\)
\(132\) 13.7604 + 1.34106i 1.19769 + 0.116725i
\(133\) −0.318500 + 0.0935202i −0.0276175 + 0.00810923i
\(134\) 13.2614 + 10.9713i 1.14561 + 0.947774i
\(135\) −2.53304 + 17.6176i −0.218009 + 1.51629i
\(136\) 1.36494 + 0.301112i 0.117043 + 0.0258201i
\(137\) 0.721415i 0.0616346i 0.999525 + 0.0308173i \(0.00981101\pi\)
−0.999525 + 0.0308173i \(0.990189\pi\)
\(138\) −6.92405 8.94830i −0.589414 0.761730i
\(139\) 10.8579i 0.920954i 0.887672 + 0.460477i \(0.152322\pi\)
−0.887672 + 0.460477i \(0.847678\pi\)
\(140\) −0.0685466 1.50057i −0.00579325 0.126822i
\(141\) −1.42968 + 9.94363i −0.120401 + 0.837404i
\(142\) 4.24571 5.13193i 0.356292 0.430662i
\(143\) 23.1626 6.80116i 1.93696 0.568742i
\(144\) −0.506424 + 0.705331i −0.0422020 + 0.0587776i
\(145\) 1.80410 1.56326i 0.149822 0.129822i
\(146\) −9.64244 1.16244i −0.798014 0.0962041i
\(147\) −3.26582 + 11.1224i −0.269360 + 0.917357i
\(148\) −3.08208 8.96163i −0.253345 0.736641i
\(149\) −11.8722 + 18.4735i −0.972611 + 1.51341i −0.118740 + 0.992925i \(0.537886\pi\)
−0.853870 + 0.520486i \(0.825751\pi\)
\(150\) 9.51005 + 10.4819i 0.776492 + 0.855846i
\(151\) −5.04526 4.37174i −0.410577 0.355767i 0.424950 0.905217i \(-0.360292\pi\)
−0.835527 + 0.549450i \(0.814837\pi\)
\(152\) 3.64452 1.97623i 0.295609 0.160293i
\(153\) 0.106184 0.0152669i 0.00858445 0.00123426i
\(154\) −1.19432 + 0.578726i −0.0962412 + 0.0466351i
\(155\) −12.8552 28.1489i −1.03255 2.26097i
\(156\) 4.61922 18.8798i 0.369834 1.51160i
\(157\) −17.8415 8.14792i −1.42390 0.650275i −0.453388 0.891313i \(-0.649785\pi\)
−0.970516 + 0.241039i \(0.922512\pi\)
\(158\) 2.67432 + 1.14830i 0.212758 + 0.0913539i
\(159\) −8.46982 + 5.44322i −0.671700 + 0.431676i
\(160\) 4.76722 + 18.1451i 0.376882 + 1.43450i
\(161\) 1.01498 + 0.386533i 0.0799914 + 0.0304631i
\(162\) 3.04968 11.3373i 0.239605 0.890742i
\(163\) −1.56002 2.42744i −0.122190 0.190132i 0.774770 0.632244i \(-0.217866\pi\)
−0.896960 + 0.442112i \(0.854229\pi\)
\(164\) 3.60698 4.56827i 0.281658 0.356722i
\(165\) 9.52393 20.8545i 0.741437 1.62352i
\(166\) −0.234657 10.2792i −0.0182129 0.797824i
\(167\) −9.48722 + 4.33267i −0.734143 + 0.335272i −0.747161 0.664643i \(-0.768584\pi\)
0.0130176 + 0.999915i \(0.495856\pi\)
\(168\) −0.0793491 + 1.06560i −0.00612192 + 0.0822131i
\(169\) −2.97976 20.7247i −0.229212 1.59420i
\(170\) 1.20829 1.97798i 0.0926714 0.151704i
\(171\) 0.208367 0.240469i 0.0159343 0.0183891i
\(172\) 3.26376 + 6.36126i 0.248859 + 0.485041i
\(173\) −0.735539 0.472702i −0.0559220 0.0359389i 0.512381 0.858758i \(-0.328764\pi\)
−0.568303 + 0.822819i \(0.692400\pi\)
\(174\) −1.40723 + 0.950439i −0.106682 + 0.0720526i
\(175\) −1.30356 0.382759i −0.0985398 0.0289339i
\(176\) 13.0690 10.1953i 0.985116 0.768501i
\(177\) −6.28500 7.25327i −0.472409 0.545189i
\(178\) 3.34286 + 19.9985i 0.250558 + 1.49895i
\(179\) 4.14534 + 14.1177i 0.309838 + 1.05521i 0.956330 + 0.292289i \(0.0944170\pi\)
−0.646492 + 0.762920i \(0.723765\pi\)
\(180\) 0.832915 + 1.17451i 0.0620818 + 0.0875427i
\(181\) −0.314564 0.0452275i −0.0233814 0.00336173i 0.130614 0.991433i \(-0.458305\pi\)
−0.153996 + 0.988072i \(0.549214\pi\)
\(182\) 0.566367 + 1.77773i 0.0419819 + 0.131774i
\(183\) 16.3981 1.21218
\(184\) −13.4070 2.06193i −0.988379 0.152008i
\(185\) −15.7149 −1.15538
\(186\) 6.68224 + 20.9744i 0.489965 + 1.53792i
\(187\) −2.02698 0.291436i −0.148227 0.0213119i
\(188\) 6.96699 + 9.82429i 0.508120 + 0.716510i
\(189\) 0.342413 + 1.16615i 0.0249069 + 0.0848250i
\(190\) −1.13344 6.78074i −0.0822281 0.491927i
\(191\) 8.85070 + 10.2143i 0.640414 + 0.739077i 0.979448 0.201697i \(-0.0646456\pi\)
−0.339034 + 0.940774i \(0.610100\pi\)
\(192\) −1.82193 13.2207i −0.131486 0.954124i
\(193\) 16.3630 + 4.80462i 1.17784 + 0.345844i 0.811340 0.584575i \(-0.198739\pi\)
0.366498 + 0.930419i \(0.380557\pi\)
\(194\) 1.10385 0.745537i 0.0792517 0.0535264i
\(195\) −27.1143 17.4253i −1.94169 1.24785i
\(196\) 6.34405 + 12.3649i 0.453147 + 0.883209i
\(197\) 3.20560 3.69946i 0.228390 0.263576i −0.629975 0.776615i \(-0.716935\pi\)
0.858365 + 0.513039i \(0.171481\pi\)
\(198\) 0.663164 1.08561i 0.0471290 0.0771506i
\(199\) −1.95487 13.5964i −0.138577 0.963824i −0.933873 0.357604i \(-0.883594\pi\)
0.795296 0.606221i \(-0.207315\pi\)
\(200\) 16.9212 + 1.26002i 1.19651 + 0.0890971i
\(201\) −18.4679 + 8.43401i −1.30263 + 0.594889i
\(202\) −0.209907 9.19507i −0.0147690 0.646963i
\(203\) 0.0677153 0.148276i 0.00475268 0.0104069i
\(204\) −1.02175 + 1.29405i −0.0715367 + 0.0906019i
\(205\) −5.21826 8.11977i −0.364459 0.567109i
\(206\) 6.11244 22.7232i 0.425874 1.58320i
\(207\) −1.01877 + 0.214298i −0.0708094 + 0.0148947i
\(208\) −11.5724 20.2258i −0.802400 1.40241i
\(209\) −5.10974 + 3.28383i −0.353448 + 0.227147i
\(210\) 1.62818 + 0.699108i 0.112355 + 0.0482430i
\(211\) 12.7533 + 5.82424i 0.877974 + 0.400957i 0.802825 0.596215i \(-0.203330\pi\)
0.0751489 + 0.997172i \(0.476057\pi\)
\(212\) −2.86862 + 11.7247i −0.197018 + 0.805257i
\(213\) 3.26383 + 7.14679i 0.223634 + 0.489690i
\(214\) −2.14573 + 1.03974i −0.146679 + 0.0710755i
\(215\) 11.7352 1.68727i 0.800336 0.115071i
\(216\) −7.23573 13.3440i −0.492329 0.907941i
\(217\) −1.59696 1.38378i −0.108409 0.0939368i
\(218\) 9.67609 + 10.6649i 0.655348 + 0.722321i
\(219\) 6.19391 9.63791i 0.418545 0.651269i
\(220\) −8.93913 25.9919i −0.602676 1.75237i
\(221\) −0.811086 + 2.76230i −0.0545595 + 0.185813i
\(222\) 11.0985 + 1.33797i 0.744883 + 0.0897989i
\(223\) 6.13470 5.31575i 0.410810 0.355969i −0.424805 0.905285i \(-0.639657\pi\)
0.835615 + 0.549316i \(0.185112\pi\)
\(224\) 0.810822 + 0.991833i 0.0541753 + 0.0662696i
\(225\) 1.24952 0.366892i 0.0833013 0.0244595i
\(226\) 1.28296 1.55076i 0.0853411 0.103155i
\(227\) −2.87711 + 20.0108i −0.190961 + 1.32816i 0.638511 + 0.769613i \(0.279551\pi\)
−0.829472 + 0.558549i \(0.811358\pi\)
\(228\) 0.223164 + 4.88535i 0.0147794 + 0.323540i
\(229\) 8.45120i 0.558471i 0.960223 + 0.279235i \(0.0900810\pi\)
−0.960223 + 0.279235i \(0.909919\pi\)
\(230\) −10.4637 + 19.9116i −0.689958 + 1.31293i
\(231\) 1.56551i 0.103003i
\(232\) −0.438575 + 1.98806i −0.0287938 + 0.130523i
\(233\) −0.00171763 + 0.0119464i −0.000112525 + 0.000782632i −0.989878 0.141924i \(-0.954671\pi\)
0.989765 + 0.142706i \(0.0455804\pi\)
\(234\) −1.37798 1.14002i −0.0900812 0.0745252i
\(235\) 19.1628 5.62670i 1.25004 0.367045i
\(236\) −11.4520 1.11609i −0.745464 0.0726514i
\(237\) −2.59460 + 2.24823i −0.168537 + 0.146038i
\(238\) 0.0189432 0.157134i 0.00122791 0.0101855i
\(239\) −1.03134 + 3.51242i −0.0667118 + 0.227200i −0.986100 0.166151i \(-0.946866\pi\)
0.919388 + 0.393351i \(0.128684\pi\)
\(240\) −21.7140 4.27298i −1.40163 0.275820i
\(241\) 5.51958 8.58863i 0.355547 0.553242i −0.616700 0.787198i \(-0.711531\pi\)
0.972247 + 0.233956i \(0.0751672\pi\)
\(242\) −6.46391 + 5.86458i −0.415516 + 0.376989i
\(243\) −1.70149 1.47435i −0.109150 0.0945793i
\(244\) 14.2547 13.5388i 0.912565 0.866736i
\(245\) 22.8108 3.27970i 1.45733 0.209532i
\(246\) 2.99403 + 6.17880i 0.190892 + 0.393946i
\(247\) 3.54725 + 7.76738i 0.225706 + 0.494227i
\(248\) 23.1260 + 12.7158i 1.46850 + 0.807451i
\(249\) 11.0325 + 5.03839i 0.699159 + 0.319295i
\(250\) 1.84889 4.30596i 0.116934 0.272333i
\(251\) 8.50515 5.46593i 0.536840 0.345006i −0.243962 0.969785i \(-0.578447\pi\)
0.780802 + 0.624779i \(0.214811\pi\)
\(252\) 0.0850520 + 0.0493264i 0.00535777 + 0.00310727i
\(253\) 19.8124 + 1.55394i 1.24559 + 0.0976954i
\(254\) 15.0557 + 4.04991i 0.944679 + 0.254114i
\(255\) 1.47818 + 2.30009i 0.0925670 + 0.144037i
\(256\) −12.4993 9.98841i −0.781204 0.624275i
\(257\) −5.11757 + 11.2059i −0.319225 + 0.699006i −0.999421 0.0340247i \(-0.989168\pi\)
0.680196 + 0.733031i \(0.261895\pi\)
\(258\) −8.43156 + 0.192478i −0.524926 + 0.0119831i
\(259\) −0.976110 + 0.445775i −0.0606525 + 0.0276991i
\(260\) −37.9571 + 7.23884i −2.35400 + 0.448934i
\(261\) 0.0222365 + 0.154659i 0.00137641 + 0.00957313i
\(262\) −19.8975 12.1548i −1.22927 0.750928i
\(263\) −13.2929 + 15.3408i −0.819675 + 0.945955i −0.999286 0.0377828i \(-0.987970\pi\)
0.179611 + 0.983738i \(0.442516\pi\)
\(264\) 4.10022 + 19.1176i 0.252351 + 1.17661i
\(265\) 16.8385 + 10.8214i 1.03438 + 0.664755i
\(266\) −0.262747 0.389026i −0.0161101 0.0238527i
\(267\) −22.9488 6.73837i −1.40444 0.412381i
\(268\) −9.09056 + 22.5793i −0.555294 + 1.37925i
\(269\) 2.05592 + 2.37266i 0.125352 + 0.144664i 0.814956 0.579523i \(-0.196761\pi\)
−0.689604 + 0.724186i \(0.742216\pi\)
\(270\) −24.8269 + 4.14994i −1.51092 + 0.252557i
\(271\) 0.293217 + 0.998607i 0.0178117 + 0.0606610i 0.967919 0.251261i \(-0.0808453\pi\)
−0.950108 + 0.311922i \(0.899027\pi\)
\(272\) 0.180219 + 1.96850i 0.0109274 + 0.119358i
\(273\) −2.17846 0.313216i −0.131847 0.0189567i
\(274\) −0.972093 + 0.309699i −0.0587263 + 0.0187096i
\(275\) −24.8595 −1.49908
\(276\) 9.08521 13.1715i 0.546865 0.792830i
\(277\) −9.66266 −0.580573 −0.290287 0.956940i \(-0.593751\pi\)
−0.290287 + 0.956940i \(0.593751\pi\)
\(278\) −14.6308 + 4.66123i −0.877498 + 0.279562i
\(279\) 2.00487 + 0.288257i 0.120028 + 0.0172575i
\(280\) 1.99257 0.736553i 0.119079 0.0440175i
\(281\) −6.70438 22.8330i −0.399950 1.36210i −0.875841 0.482600i \(-0.839692\pi\)
0.475891 0.879504i \(-0.342126\pi\)
\(282\) −14.0126 + 2.34228i −0.834439 + 0.139481i
\(283\) −12.0743 13.9345i −0.717741 0.828318i 0.273292 0.961931i \(-0.411887\pi\)
−0.991034 + 0.133614i \(0.957342\pi\)
\(284\) 8.73785 + 3.51790i 0.518496 + 0.208749i
\(285\) 7.78106 + 2.28473i 0.460910 + 0.135335i
\(286\) 19.1080 + 28.2915i 1.12988 + 1.67291i
\(287\) −0.554454 0.356326i −0.0327284 0.0210333i
\(288\) −1.16783 0.379603i −0.0688148 0.0223683i
\(289\) −10.9727 + 12.6632i −0.645453 + 0.744893i
\(290\) 2.88096 + 1.75989i 0.169176 + 0.103344i
\(291\) 0.223614 + 1.55527i 0.0131085 + 0.0911717i
\(292\) −2.57308 13.4920i −0.150578 0.789562i
\(293\) 18.5780 8.48429i 1.08534 0.495658i 0.209277 0.977856i \(-0.432889\pi\)
0.876062 + 0.482199i \(0.160162\pi\)
\(294\) −16.3892 + 0.374136i −0.955836 + 0.0218200i
\(295\) −7.92623 + 17.3560i −0.461483 + 1.01051i
\(296\) 10.7525 8.00022i 0.624977 0.465003i
\(297\) 12.0233 + 18.7087i 0.697665 + 1.08559i
\(298\) −29.9894 8.06701i −1.73724 0.467310i
\(299\) 6.12627 27.2587i 0.354292 1.57641i
\(300\) −10.0416 + 17.3145i −0.579752 + 0.999650i
\(301\) 0.681057 0.437689i 0.0392555 0.0252280i
\(302\) 3.72494 8.67515i 0.214346 0.499199i
\(303\) 9.86891 + 4.50698i 0.566954 + 0.258919i
\(304\) 4.22750 + 4.06253i 0.242464 + 0.233002i
\(305\) −13.5427 29.6543i −0.775452 1.69800i
\(306\) 0.0661560 + 0.136527i 0.00378189 + 0.00780471i
\(307\) −3.69491 + 0.531248i −0.210880 + 0.0303199i −0.246945 0.969030i \(-0.579427\pi\)
0.0360652 + 0.999349i \(0.488518\pi\)
\(308\) −1.29254 1.36088i −0.0736492 0.0775435i
\(309\) 20.9775 + 18.1771i 1.19337 + 1.03406i
\(310\) 32.4114 29.4062i 1.84084 1.67016i
\(311\) 9.86340 15.3477i 0.559302 0.870291i −0.440318 0.897842i \(-0.645134\pi\)
0.999620 + 0.0275508i \(0.00877080\pi\)
\(312\) 27.4232 1.88069i 1.55253 0.106473i
\(313\) −2.31132 + 7.87163i −0.130644 + 0.444931i −0.998668 0.0515898i \(-0.983571\pi\)
0.868025 + 0.496521i \(0.165389\pi\)
\(314\) 3.31993 27.5389i 0.187355 1.55411i
\(315\) 0.123217 0.106768i 0.00694250 0.00601571i
\(316\) −0.399242 + 4.09656i −0.0224591 + 0.230449i
\(317\) 7.02989 2.06416i 0.394838 0.115935i −0.0782855 0.996931i \(-0.524945\pi\)
0.473124 + 0.880996i \(0.343126\pi\)
\(318\) −10.9707 9.07618i −0.615206 0.508967i
\(319\) 0.424481 2.95233i 0.0237664 0.165299i
\(320\) −22.4037 + 14.2133i −1.25240 + 0.794550i
\(321\) 2.81261i 0.156985i
\(322\) −0.0851227 + 1.53360i −0.00474370 + 0.0854641i
\(323\) 0.724361i 0.0403045i
\(324\) 16.5860 0.757653i 0.921444 0.0420918i
\(325\) −4.97370 + 34.5929i −0.275891 + 1.91887i
\(326\) 2.60122 3.14419i 0.144068 0.174140i
\(327\) −16.2985 + 4.78568i −0.901310 + 0.264648i
\(328\) 7.70411 + 2.89920i 0.425388 + 0.160082i
\(329\) 1.03066 0.893074i 0.0568222 0.0492367i
\(330\) 32.1896 + 3.88060i 1.77198 + 0.213620i
\(331\) −5.52944 + 18.8316i −0.303926 + 1.03508i 0.655986 + 0.754773i \(0.272253\pi\)
−0.959912 + 0.280303i \(0.909565\pi\)
\(332\) 13.7504 4.72902i 0.754649 0.259539i
\(333\) 0.556102 0.865312i 0.0304742 0.0474188i
\(334\) −9.91100 10.9239i −0.542306 0.597727i
\(335\) 30.5041 + 26.4320i 1.66662 + 1.44413i
\(336\) −1.46995 + 0.350536i −0.0801921 + 0.0191233i
\(337\) −7.17700 + 1.03190i −0.390956 + 0.0562110i −0.334990 0.942222i \(-0.608733\pi\)
−0.0559660 + 0.998433i \(0.517824\pi\)
\(338\) 26.6469 12.9121i 1.44940 0.702328i
\(339\) 0.986256 + 2.15960i 0.0535661 + 0.117293i
\(340\) 3.18400 + 0.779011i 0.172676 + 0.0422478i
\(341\) −35.1711 16.0621i −1.90462 0.869812i
\(342\) 0.413478 + 0.177539i 0.0223583 + 0.00960023i
\(343\) 2.65743 1.70783i 0.143488 0.0922140i
\(344\) −7.17056 + 7.12871i −0.386611 + 0.384354i
\(345\) −15.7545 21.3499i −0.848196 1.14944i
\(346\) 0.321195 1.19405i 0.0172675 0.0641927i
\(347\) −11.1039 17.2780i −0.596089 0.927532i −0.999919 0.0126982i \(-0.995958\pi\)
0.403831 0.914834i \(-0.367678\pi\)
\(348\) −1.88481 1.48820i −0.101037 0.0797756i
\(349\) 7.29006 15.9630i 0.390228 0.854480i −0.607940 0.793983i \(-0.708004\pi\)
0.998168 0.0604973i \(-0.0192687\pi\)
\(350\) −0.0438493 1.92084i −0.00234385 0.102673i
\(351\) 28.4393 12.9878i 1.51798 0.693238i
\(352\) 19.3485 + 13.2335i 1.03128 + 0.705348i
\(353\) 3.14653 + 21.8846i 0.167473 + 1.16480i 0.884084 + 0.467328i \(0.154783\pi\)
−0.716611 + 0.697473i \(0.754308\pi\)
\(354\) 7.07554 11.5827i 0.376061 0.615614i
\(355\) 10.2287 11.8046i 0.542886 0.626523i
\(356\) −25.5126 + 13.0897i −1.35216 + 0.693752i
\(357\) 0.157060 + 0.100937i 0.00831251 + 0.00534213i
\(358\) −17.2438 + 11.6464i −0.911364 + 0.615534i
\(359\) 1.98261 + 0.582148i 0.104638 + 0.0307246i 0.333633 0.942703i \(-0.391726\pi\)
−0.228994 + 0.973428i \(0.573544\pi\)
\(360\) −1.22506 + 1.62655i −0.0645665 + 0.0857266i
\(361\) 11.0354 + 12.7355i 0.580810 + 0.670290i
\(362\) −0.0740975 0.443285i −0.00389448 0.0232986i
\(363\) −2.90055 9.87836i −0.152239 0.518479i
\(364\) −2.15232 + 1.52634i −0.112812 + 0.0800018i
\(365\) −22.5445 3.24141i −1.18003 0.169663i
\(366\) 7.03962 + 22.0962i 0.367967 + 1.15498i
\(367\) 11.7631 0.614031 0.307015 0.951705i \(-0.400670\pi\)
0.307015 + 0.951705i \(0.400670\pi\)
\(368\) −2.97714 18.9509i −0.155194 0.987884i
\(369\) 0.631759 0.0328880
\(370\) −6.74631 21.1755i −0.350724 1.10086i
\(371\) 1.35286 + 0.194513i 0.0702372 + 0.0100986i
\(372\) −25.3940 + 18.0084i −1.31662 + 0.933691i
\(373\) −10.6300 36.2024i −0.550399 1.87449i −0.480626 0.876926i \(-0.659591\pi\)
−0.0697734 0.997563i \(-0.522228\pi\)
\(374\) −0.477467 2.85643i −0.0246892 0.147702i
\(375\) 3.61991 + 4.17760i 0.186931 + 0.215730i
\(376\) −10.2472 + 13.6054i −0.528457 + 0.701645i
\(377\) −4.02334 1.18136i −0.207213 0.0608432i
\(378\) −1.42437 + 0.962017i −0.0732617 + 0.0494808i
\(379\) 12.1796 + 7.82734i 0.625623 + 0.402063i 0.814687 0.579901i \(-0.196909\pi\)
−0.189064 + 0.981965i \(0.560545\pi\)
\(380\) 8.65035 4.43822i 0.443754 0.227676i
\(381\) −12.0436 + 13.8990i −0.617011 + 0.712069i
\(382\) −9.96396 + 16.3111i −0.509801 + 0.834547i
\(383\) −1.64015 11.4075i −0.0838078 0.582896i −0.987845 0.155442i \(-0.950320\pi\)
0.904037 0.427454i \(-0.140589\pi\)
\(384\) 17.0325 8.13060i 0.869188 0.414913i
\(385\) −2.83107 + 1.29290i −0.144285 + 0.0658925i
\(386\) 0.550423 + 24.1115i 0.0280158 + 1.22724i
\(387\) −0.322368 + 0.705887i −0.0163869 + 0.0358822i
\(388\) 1.47847 + 1.16736i 0.0750581 + 0.0592637i
\(389\) −17.1025 26.6120i −0.867131 1.34928i −0.936126 0.351664i \(-0.885616\pi\)
0.0689956 0.997617i \(-0.478021\pi\)
\(390\) 11.8403 44.0166i 0.599554 2.22887i
\(391\) −1.43331 + 1.88749i −0.0724854 + 0.0954546i
\(392\) −13.9380 + 13.8567i −0.703978 + 0.699869i
\(393\) 23.1378 14.8698i 1.16715 0.750082i
\(394\) 6.36110 + 2.73133i 0.320468 + 0.137602i
\(395\) 6.20850 + 2.83533i 0.312383 + 0.142661i
\(396\) 1.74753 + 0.427558i 0.0878165 + 0.0214856i
\(397\) 6.67961 + 14.6263i 0.335240 + 0.734073i 0.999915 0.0130597i \(-0.00415716\pi\)
−0.664675 + 0.747133i \(0.731430\pi\)
\(398\) 17.4817 8.47102i 0.876279 0.424614i
\(399\) 0.548120 0.0788078i 0.0274403 0.00394532i
\(400\) 5.56634 + 23.3420i 0.278317 + 1.16710i
\(401\) −0.720019 0.623900i −0.0359560 0.0311561i 0.636697 0.771114i \(-0.280300\pi\)
−0.672653 + 0.739958i \(0.734845\pi\)
\(402\) −19.2928 21.2645i −0.962239 1.06058i
\(403\) −29.3878 + 45.7282i −1.46391 + 2.27789i
\(404\) 12.3001 4.23024i 0.611951 0.210462i
\(405\) 7.75676 26.4171i 0.385437 1.31268i
\(406\) 0.228869 + 0.0275911i 0.0113586 + 0.00136932i
\(407\) −14.8393 + 12.8584i −0.735559 + 0.637365i
\(408\) −2.18235 0.821257i −0.108042 0.0406583i
\(409\) 4.14518 1.21713i 0.204966 0.0601834i −0.177638 0.984096i \(-0.556846\pi\)
0.382604 + 0.923912i \(0.375027\pi\)
\(410\) 8.70107 10.5173i 0.429715 0.519411i
\(411\) 0.171272 1.19122i 0.00844821 0.0587586i
\(412\) 33.2432 1.51856i 1.63777 0.0748140i
\(413\) 1.30289i 0.0641108i
\(414\) −0.726114 1.28078i −0.0356866 0.0629467i
\(415\) 24.1123i 1.18363i
\(416\) 22.2860 24.2764i 1.09266 1.19025i
\(417\) 2.57778 17.9289i 0.126235 0.877981i
\(418\) −6.61848 5.47555i −0.323721 0.267818i
\(419\) −17.9501 + 5.27063i −0.876920 + 0.257487i −0.689056 0.724708i \(-0.741975\pi\)
−0.187864 + 0.982195i \(0.560156\pi\)
\(420\) −0.243066 + 2.49407i −0.0118604 + 0.121698i
\(421\) −5.24002 + 4.54050i −0.255383 + 0.221290i −0.773137 0.634239i \(-0.781314\pi\)
0.517754 + 0.855529i \(0.326768\pi\)
\(422\) −2.37313 + 19.6852i −0.115522 + 0.958258i
\(423\) −0.368288 + 1.25427i −0.0179068 + 0.0609849i
\(424\) −17.0303 + 1.16794i −0.827065 + 0.0567202i
\(425\) 1.60282 2.49404i 0.0777482 0.120978i
\(426\) −8.22902 + 7.46602i −0.398697 + 0.361730i
\(427\) −1.68237 1.45778i −0.0814157 0.0705471i
\(428\) −2.32219 2.44497i −0.112247 0.118182i
\(429\) −39.8615 + 5.73122i −1.92453 + 0.276706i
\(430\) 7.31144 + 15.0887i 0.352589 + 0.727640i
\(431\) 1.44075 + 3.15481i 0.0693987 + 0.151962i 0.941152 0.337982i \(-0.109744\pi\)
−0.871754 + 0.489944i \(0.837017\pi\)
\(432\) 14.8745 15.4785i 0.715648 0.744709i
\(433\) −1.08463 0.495333i −0.0521239 0.0238042i 0.389183 0.921161i \(-0.372758\pi\)
−0.441306 + 0.897356i \(0.645485\pi\)
\(434\) 1.17905 2.74592i 0.0565960 0.131809i
\(435\) −3.35012 + 2.15299i −0.160626 + 0.103228i
\(436\) −10.2169 + 17.6168i −0.489302 + 0.843690i
\(437\) 0.453286 + 7.01498i 0.0216836 + 0.335572i
\(438\) 15.6459 + 4.20867i 0.747591 + 0.201098i
\(439\) −8.76184 13.6337i −0.418180 0.650701i 0.566703 0.823922i \(-0.308219\pi\)
−0.984883 + 0.173222i \(0.944582\pi\)
\(440\) 31.1861 23.2035i 1.48674 1.10618i
\(441\) −0.626614 + 1.37209i −0.0298388 + 0.0653378i
\(442\) −4.07035 + 0.0929189i −0.193607 + 0.00441970i
\(443\) −24.8880 + 11.3660i −1.18246 + 0.540013i −0.906931 0.421278i \(-0.861582\pi\)
−0.275533 + 0.961292i \(0.588854\pi\)
\(444\) 2.96163 + 15.5294i 0.140553 + 0.736994i
\(445\) 6.76700 + 47.0655i 0.320787 + 2.23112i
\(446\) 9.79646 + 5.98437i 0.463876 + 0.283368i
\(447\) 23.9896 27.6855i 1.13467 1.30948i
\(448\) −0.988395 + 1.51836i −0.0466973 + 0.0717355i
\(449\) −15.7819 10.1424i −0.744793 0.478649i 0.112388 0.993664i \(-0.464150\pi\)
−0.857181 + 0.515015i \(0.827786\pi\)
\(450\) 1.03079 + 1.52620i 0.0485920 + 0.0719458i
\(451\) −11.5713 3.39765i −0.544873 0.159989i
\(452\) 2.64038 + 1.06303i 0.124193 + 0.0500008i
\(453\) 7.29298 + 8.41654i 0.342654 + 0.395444i
\(454\) −28.1993 + 4.71365i −1.32346 + 0.221223i
\(455\) 1.23270 + 4.19820i 0.0577900 + 0.196815i
\(456\) −6.48711 + 2.39796i −0.303787 + 0.112295i
\(457\) −10.9084 1.56839i −0.510275 0.0733664i −0.117631 0.993057i \(-0.537530\pi\)
−0.392643 + 0.919691i \(0.628439\pi\)
\(458\) −11.3878 + 3.62805i −0.532118 + 0.169528i
\(459\) −2.65216 −0.123792
\(460\) −31.3225 5.55177i −1.46042 0.258853i
\(461\) −8.45702 −0.393882 −0.196941 0.980415i \(-0.563101\pi\)
−0.196941 + 0.980415i \(0.563101\pi\)
\(462\) 2.10950 0.672065i 0.0981426 0.0312673i
\(463\) −34.9943 5.03142i −1.62632 0.233830i −0.732018 0.681285i \(-0.761421\pi\)
−0.894306 + 0.447455i \(0.852330\pi\)
\(464\) −2.86715 + 0.262493i −0.133104 + 0.0121859i
\(465\) 14.5440 + 49.5322i 0.674460 + 2.29700i
\(466\) −0.0168349 + 0.00281403i −0.000779860 + 0.000130358i
\(467\) 21.4802 + 24.7895i 0.993985 + 1.14712i 0.989117 + 0.147131i \(0.0470040\pi\)
0.00486789 + 0.999988i \(0.498450\pi\)
\(468\) 0.944593 2.34620i 0.0436638 0.108453i
\(469\) 2.64450 + 0.776496i 0.122112 + 0.0358552i
\(470\) 15.8083 + 23.4060i 0.729184 + 1.07964i
\(471\) 27.5259 + 17.6898i 1.26833 + 0.815105i
\(472\) −3.41238 15.9105i −0.157068 0.732342i
\(473\) 9.70083 11.1954i 0.446045 0.514763i
\(474\) −4.14330 2.53102i −0.190308 0.116254i
\(475\) −1.25143 8.70386i −0.0574194 0.399361i
\(476\) 0.219868 0.0419312i 0.0100776 0.00192191i
\(477\) −1.19172 + 0.544242i −0.0545653 + 0.0249191i
\(478\) −5.17567 + 0.118151i −0.236730 + 0.00540412i
\(479\) −4.39145 + 9.61594i −0.200651 + 0.439364i −0.983032 0.183437i \(-0.941278\pi\)
0.782381 + 0.622800i \(0.214005\pi\)
\(480\) −3.56393 31.0936i −0.162670 1.41922i
\(481\) 14.9239 + 23.2221i 0.680472 + 1.05883i
\(482\) 13.9425 + 3.75048i 0.635065 + 0.170829i
\(483\) −1.58419 0.879222i −0.0720833 0.0400060i
\(484\) −10.6773 6.19237i −0.485333 0.281471i
\(485\) 2.62788 1.68883i 0.119326 0.0766860i
\(486\) 1.25622 2.92565i 0.0569831 0.132710i
\(487\) 0.361362 + 0.165028i 0.0163749 + 0.00747815i 0.423586 0.905856i \(-0.360771\pi\)
−0.407211 + 0.913334i \(0.633499\pi\)
\(488\) 24.3628 + 13.3958i 1.10285 + 0.606401i
\(489\) 1.99965 + 4.37863i 0.0904274 + 0.198008i
\(490\) 14.2119 + 29.3292i 0.642027 + 1.32496i
\(491\) −24.0344 + 3.45563i −1.08466 + 0.155950i −0.661382 0.750049i \(-0.730030\pi\)
−0.423278 + 0.906000i \(0.639121\pi\)
\(492\) −7.04050 + 6.68693i −0.317410 + 0.301470i
\(493\) 0.268825 + 0.232938i 0.0121073 + 0.0104910i
\(494\) −8.94359 + 8.11434i −0.402391 + 0.365082i
\(495\) 1.61289 2.50971i 0.0724942 0.112803i
\(496\) −7.20639 + 36.6206i −0.323576 + 1.64431i
\(497\) 0.300492 1.02338i 0.0134789 0.0459049i
\(498\) −2.05293 + 17.0291i −0.0919941 + 0.763092i
\(499\) 17.2176 14.9191i 0.770766 0.667873i −0.177937 0.984042i \(-0.556942\pi\)
0.948703 + 0.316169i \(0.102397\pi\)
\(500\) 6.59593 + 0.642825i 0.294979 + 0.0287480i
\(501\) 16.6942 4.90186i 0.745842 0.218999i
\(502\) 11.0164 + 9.11404i 0.491688 + 0.406779i
\(503\) 1.84791 12.8525i 0.0823944 0.573066i −0.906244 0.422754i \(-0.861063\pi\)
0.988639 0.150311i \(-0.0480276\pi\)
\(504\) −0.0299540 + 0.135782i −0.00133426 + 0.00604819i
\(505\) 21.5691i 0.959812i
\(506\) 6.41144 + 27.3639i 0.285023 + 1.21647i
\(507\) 34.9286i 1.55123i
\(508\) 1.00615 + 22.0259i 0.0446406 + 0.977240i
\(509\) 3.61245 25.1252i 0.160119 1.11365i −0.738287 0.674487i \(-0.764365\pi\)
0.898406 0.439166i \(-0.144726\pi\)
\(510\) −2.46475 + 2.97923i −0.109141 + 0.131923i
\(511\) −1.49227 + 0.438171i −0.0660142 + 0.0193835i
\(512\) 8.09333 21.1305i 0.357678 0.933845i
\(513\) −5.94507 + 5.15144i −0.262481 + 0.227441i
\(514\) −17.2967 2.08519i −0.762925 0.0919740i
\(515\) 15.5468 52.9476i 0.685074 2.33315i
\(516\) −3.87898 11.2787i −0.170763 0.496519i
\(517\) 13.4912 20.9927i 0.593342 0.923259i
\(518\) −1.01971 1.12392i −0.0448036 0.0493823i
\(519\) 1.10232 + 0.955165i 0.0483865 + 0.0419271i
\(520\) −26.0490 48.0389i −1.14232 2.10665i
\(521\) 29.0404 4.17538i 1.27228 0.182927i 0.527110 0.849797i \(-0.323275\pi\)
0.745174 + 0.666870i \(0.232366\pi\)
\(522\) −0.198854 + 0.0963574i −0.00870358 + 0.00421745i
\(523\) 14.2767 + 31.2616i 0.624277 + 1.36698i 0.912367 + 0.409372i \(0.134252\pi\)
−0.288091 + 0.957603i \(0.593020\pi\)
\(524\) 7.83650 32.0296i 0.342339 1.39922i
\(525\) 2.06160 + 0.941503i 0.0899757 + 0.0410905i
\(526\) −26.3780 11.3262i −1.15014 0.493846i
\(527\) 3.87910 2.49294i 0.168976 0.108594i
\(528\) −24.0005 + 13.7321i −1.04449 + 0.597612i
\(529\) 12.6995 19.1761i 0.552153 0.833743i
\(530\) −7.35301 + 27.3351i −0.319394 + 1.18736i
\(531\) −0.675193 1.05062i −0.0293009 0.0455931i
\(532\) 0.411409 0.521054i 0.0178368 0.0225905i
\(533\) −7.04306 + 15.4222i −0.305069 + 0.668008i
\(534\) −0.771955 33.8158i −0.0334058 1.46335i
\(535\) −5.08632 + 2.32284i −0.219901 + 0.100425i
\(536\) −34.3278 2.55618i −1.48273 0.110410i
\(537\) −3.49321 24.2958i −0.150743 1.04844i
\(538\) −2.31452 + 3.78889i −0.0997861 + 0.163351i
\(539\) 18.8564 21.7614i 0.812201 0.937330i
\(540\) −16.2500 31.6722i −0.699289 1.36295i
\(541\) 12.2280 + 7.85844i 0.525721 + 0.337861i 0.776432 0.630202i \(-0.217028\pi\)
−0.250710 + 0.968062i \(0.580664\pi\)
\(542\) −1.21973 + 0.823801i −0.0523918 + 0.0353853i
\(543\) 0.508680 + 0.149362i 0.0218296 + 0.00640974i
\(544\) −2.57515 + 1.08791i −0.110409 + 0.0466437i
\(545\) 22.1148 + 25.5219i 0.947295 + 1.09324i
\(546\) −0.513150 3.06990i −0.0219608 0.131380i
\(547\) −8.99528 30.6351i −0.384611 1.30986i −0.893512 0.449039i \(-0.851767\pi\)
0.508902 0.860825i \(-0.330052\pi\)
\(548\) −0.834628 1.17693i −0.0356536 0.0502758i
\(549\) 2.11210 + 0.303674i 0.0901421 + 0.0129605i
\(550\) −10.6720 33.4977i −0.455057 1.42835i
\(551\) 1.05505 0.0449464
\(552\) 21.6486 + 6.58770i 0.921424 + 0.280391i
\(553\) 0.466061 0.0198189
\(554\) −4.14813 13.0203i −0.176237 0.553178i
\(555\) 25.9489 + 3.73089i 1.10147 + 0.158367i
\(556\) −12.5618 17.7137i −0.532741 0.751228i
\(557\) 4.57086 + 15.5669i 0.193674 + 0.659592i 0.997870 + 0.0652286i \(0.0207777\pi\)
−0.804197 + 0.594363i \(0.797404\pi\)
\(558\) 0.472259 + 2.82527i 0.0199923 + 0.119603i
\(559\) −13.6379 15.7389i −0.576820 0.665686i
\(560\) 1.84789 + 2.36875i 0.0780876 + 0.100098i
\(561\) 3.27782 + 0.962454i 0.138390 + 0.0406348i
\(562\) 27.8889 18.8361i 1.17642 0.794554i
\(563\) 29.5452 + 18.9876i 1.24518 + 0.800230i 0.986185 0.165648i \(-0.0529716\pi\)
0.258997 + 0.965878i \(0.416608\pi\)
\(564\) −9.17171 17.8762i −0.386199 0.752724i
\(565\) 3.09090 3.56709i 0.130035 0.150068i
\(566\) 13.5930 22.2518i 0.571357 0.935315i
\(567\) −0.267556 1.86090i −0.0112363 0.0781503i
\(568\) −0.989202 + 13.2843i −0.0415060 + 0.557397i
\(569\) −31.5524 + 14.4095i −1.32274 + 0.604077i −0.946578 0.322475i \(-0.895485\pi\)
−0.376166 + 0.926552i \(0.622758\pi\)
\(570\) 0.261741 + 11.4657i 0.0109631 + 0.480243i
\(571\) 1.13150 2.47764i 0.0473518 0.103686i −0.884478 0.466583i \(-0.845485\pi\)
0.931829 + 0.362897i \(0.118212\pi\)
\(572\) −29.9193 + 37.8931i −1.25099 + 1.58439i
\(573\) −12.1896 18.9673i −0.509226 0.792372i
\(574\) 0.242119 0.900085i 0.0101058 0.0375688i
\(575\) −13.9616 + 25.1562i −0.582239 + 1.04908i
\(576\) 0.0101661 1.73659i 0.000423587 0.0723577i
\(577\) 0.656067 0.421629i 0.0273124 0.0175526i −0.526913 0.849919i \(-0.676651\pi\)
0.554226 + 0.832366i \(0.313014\pi\)
\(578\) −21.7739 9.34928i −0.905675 0.388879i
\(579\) −25.8785 11.8183i −1.07547 0.491152i
\(580\) −1.13464 + 4.63755i −0.0471135 + 0.192564i
\(581\) −0.683978 1.49770i −0.0283762 0.0621352i
\(582\) −1.99970 + 0.968986i −0.0828904 + 0.0401658i
\(583\) 24.7547 3.55919i 1.02524 0.147407i
\(584\) 17.0757 9.25924i 0.706596 0.383150i
\(585\) −3.16966 2.74652i −0.131049 0.113555i
\(586\) 19.4079 + 21.3913i 0.801731 + 0.883665i
\(587\) 10.9250 16.9996i 0.450922 0.701648i −0.539150 0.842210i \(-0.681255\pi\)
0.990072 + 0.140562i \(0.0448909\pi\)
\(588\) −7.53992 21.9235i −0.310941 0.904109i
\(589\) 3.85319 13.1228i 0.158768 0.540714i
\(590\) −26.7896 3.22960i −1.10291 0.132961i
\(591\) −6.17147 + 5.34761i −0.253861 + 0.219971i
\(592\) 15.3961 + 11.0543i 0.632777 + 0.454331i
\(593\) −32.9444 + 9.67334i −1.35286 + 0.397237i −0.876242 0.481872i \(-0.839957\pi\)
−0.476622 + 0.879108i \(0.658139\pi\)
\(594\) −20.0481 + 24.2328i −0.822582 + 0.994283i
\(595\) 0.0528224 0.367388i 0.00216551 0.0150614i
\(596\) −2.00415 43.8733i −0.0820930 1.79712i
\(597\) 22.9149i 0.937845i
\(598\) 39.3606 3.44697i 1.60957 0.140957i
\(599\) 0.463611i 0.0189426i 0.999955 + 0.00947132i \(0.00301486\pi\)
−0.999955 + 0.00947132i \(0.996985\pi\)
\(600\) −27.6417 6.09787i −1.12847 0.248945i
\(601\) 0.181420 1.26180i 0.00740027 0.0514700i −0.985787 0.168002i \(-0.946269\pi\)
0.993187 + 0.116532i \(0.0371777\pi\)
\(602\) 0.882152 + 0.729814i 0.0359538 + 0.0297450i
\(603\) −2.53488 + 0.744307i −0.103228 + 0.0303105i
\(604\) 13.2887 + 1.29509i 0.540710 + 0.0526964i
\(605\) −15.4685 + 13.4036i −0.628886 + 0.544932i
\(606\) −1.83640 + 15.2330i −0.0745988 + 0.618798i
\(607\) −2.29758 + 7.82486i −0.0932561 + 0.317601i −0.992889 0.119047i \(-0.962016\pi\)
0.899633 + 0.436648i \(0.143834\pi\)
\(608\) −3.65934 + 7.44050i −0.148406 + 0.301752i
\(609\) −0.147016 + 0.228761i −0.00595738 + 0.00926987i
\(610\) 34.1449 30.9790i 1.38249 1.25430i
\(611\) −26.5129 22.9735i −1.07260 0.929410i
\(612\) −0.155567 + 0.147754i −0.00628842 + 0.00597261i
\(613\) 31.4275 4.51859i 1.26934 0.182504i 0.525463 0.850816i \(-0.323892\pi\)
0.743881 + 0.668312i \(0.232983\pi\)
\(614\) −2.30205 4.75076i −0.0929033 0.191725i
\(615\) 6.68882 + 14.6465i 0.269719 + 0.590603i
\(616\) 1.27888 2.32589i 0.0515277 0.0937128i
\(617\) 30.6896 + 14.0155i 1.23552 + 0.564242i 0.922680 0.385565i \(-0.125994\pi\)
0.312836 + 0.949807i \(0.398721\pi\)
\(618\) −15.4878 + 36.0701i −0.623010 + 1.45095i
\(619\) 11.9212 7.66127i 0.479152 0.307932i −0.278678 0.960385i \(-0.589896\pi\)
0.757830 + 0.652452i \(0.226260\pi\)
\(620\) 53.5384 + 31.0498i 2.15015 + 1.24699i
\(621\) 25.6845 1.65965i 1.03068 0.0665995i
\(622\) 24.9151 + 6.70204i 0.999005 + 0.268727i
\(623\) 1.75540 + 2.73146i 0.0703287 + 0.109434i
\(624\) 14.3068 + 36.1449i 0.572731 + 1.44695i
\(625\) −7.89543 + 17.2886i −0.315817 + 0.691543i
\(626\) −11.5991 + 0.264787i −0.463594 + 0.0105830i
\(627\) 9.21697 4.20925i 0.368090 0.168101i
\(628\) 38.5334 7.34874i 1.53765 0.293247i
\(629\) −0.333250 2.31781i −0.0132876 0.0924170i
\(630\) 0.196765 + 0.120198i 0.00783930 + 0.00478880i
\(631\) −31.1382 + 35.9354i −1.23959 + 1.43056i −0.375810 + 0.926697i \(0.622635\pi\)
−0.863781 + 0.503867i \(0.831910\pi\)
\(632\) −5.69143 + 1.22066i −0.226393 + 0.0485552i
\(633\) −19.6759 12.6449i −0.782046 0.502591i
\(634\) 5.79931 + 8.58652i 0.230320 + 0.341014i
\(635\) 35.0814 + 10.3008i 1.39216 + 0.408776i
\(636\) 7.52033 18.6791i 0.298200 0.740676i
\(637\) −26.5091 30.5931i −1.05033 1.21214i
\(638\) 4.16044 0.695439i 0.164713 0.0275327i
\(639\) 0.288035 + 0.980957i 0.0113945 + 0.0388060i
\(640\) −28.7700 24.0868i −1.13723 0.952116i
\(641\) 13.2032 + 1.89834i 0.521496 + 0.0749798i 0.398036 0.917370i \(-0.369692\pi\)
0.123460 + 0.992350i \(0.460601\pi\)
\(642\) 3.78994 1.20744i 0.149577 0.0476538i
\(643\) 11.2686 0.444389 0.222194 0.975002i \(-0.428678\pi\)
0.222194 + 0.975002i \(0.428678\pi\)
\(644\) −2.10304 + 0.543664i −0.0828714 + 0.0214234i
\(645\) −19.7781 −0.778763
\(646\) 0.976063 0.310964i 0.0384027 0.0122347i
\(647\) −6.89859 0.991868i −0.271212 0.0389944i 0.00536711 0.999986i \(-0.498292\pi\)
−0.276579 + 0.960991i \(0.589201\pi\)
\(648\) 8.14120 + 22.0241i 0.319817 + 0.865187i
\(649\) 6.71656 + 22.8745i 0.263648 + 0.897903i
\(650\) −48.7484 + 8.14855i −1.91207 + 0.319612i
\(651\) 2.30843 + 2.66407i 0.0904744 + 0.104413i
\(652\) 5.35342 + 2.15532i 0.209656 + 0.0844087i
\(653\) 33.8759 + 9.94686i 1.32567 + 0.389251i 0.866534 0.499117i \(-0.166342\pi\)
0.459132 + 0.888368i \(0.348161\pi\)
\(654\) −13.4455 19.9075i −0.525760 0.778444i
\(655\) −45.9993 29.5620i −1.79734 1.15508i
\(656\) −0.599286 + 11.6258i −0.0233982 + 0.453910i
\(657\) 0.976265 1.12667i 0.0380877 0.0439556i
\(658\) 1.64586 + 1.00541i 0.0641622 + 0.0391948i
\(659\) 4.18500 + 29.1073i 0.163024 + 1.13386i 0.892892 + 0.450271i \(0.148673\pi\)
−0.729867 + 0.683589i \(0.760418\pi\)
\(660\) 8.58979 + 45.0408i 0.334357 + 1.75321i
\(661\) −21.9073 + 10.0047i −0.852096 + 0.389139i −0.793080 0.609118i \(-0.791524\pi\)
−0.0590160 + 0.998257i \(0.518796\pi\)
\(662\) −27.7489 + 0.633459i −1.07849 + 0.0246201i
\(663\) 1.99509 4.36864i 0.0774829 0.169664i
\(664\) 12.2752 + 16.4982i 0.476371 + 0.640254i
\(665\) −0.595191 0.926135i −0.0230805 0.0359140i
\(666\) 1.40472 + 0.377864i 0.0544319 + 0.0146419i
\(667\) −2.74917 2.08763i −0.106448 0.0808335i
\(668\) 10.4650 18.0444i 0.404902 0.698161i
\(669\) −11.3918 + 7.32107i −0.440433 + 0.283049i
\(670\) −22.5213 + 52.4508i −0.870075 + 2.02635i
\(671\) −37.0522 16.9212i −1.43038 0.653234i
\(672\) −1.10338 1.83024i −0.0425638 0.0706031i
\(673\) −13.1225 28.7344i −0.505837 1.10763i −0.974528 0.224266i \(-0.928002\pi\)
0.468691 0.883362i \(-0.344726\pi\)
\(674\) −4.47151 9.22788i −0.172236 0.355445i
\(675\) −31.8681 + 4.58195i −1.22661 + 0.176359i
\(676\) 28.8382 + 30.3631i 1.10916 + 1.16781i
\(677\) 9.38954 + 8.13608i 0.360869 + 0.312695i 0.816358 0.577547i \(-0.195990\pi\)
−0.455488 + 0.890242i \(0.650535\pi\)
\(678\) −2.48663 + 2.25607i −0.0954983 + 0.0866437i
\(679\) 0.115321 0.179443i 0.00442562 0.00688640i
\(680\) 0.317169 + 4.62480i 0.0121629 + 0.177353i
\(681\) 9.50155 32.3593i 0.364100 1.24001i
\(682\) 6.54463 54.2878i 0.250607 2.07879i
\(683\) 17.9654 15.5671i 0.687428 0.595659i −0.239502 0.970896i \(-0.576984\pi\)
0.926929 + 0.375237i \(0.122439\pi\)
\(684\) −0.0617270 + 0.633371i −0.00236019 + 0.0242175i
\(685\) −2.29565 + 0.674064i −0.0877123 + 0.0257547i
\(686\) 3.44209 + 2.84768i 0.131419 + 0.108725i
\(687\) 2.00641 13.9549i 0.0765492 0.532411i
\(688\) −12.6841 6.60188i −0.483576 0.251694i
\(689\) 35.1591i 1.33946i
\(690\) 22.0052 30.3943i 0.837726 1.15709i
\(691\) 5.58196i 0.212348i 0.994348 + 0.106174i \(0.0338600\pi\)
−0.994348 + 0.106174i \(0.966140\pi\)
\(692\) 1.74685 0.0797967i 0.0664054 0.00303342i
\(693\) 0.0289914 0.201640i 0.00110129 0.00765965i
\(694\) 18.5149 22.3796i 0.702818 0.849520i
\(695\) −34.5515 + 10.1452i −1.31061 + 0.384830i
\(696\) 1.19618 3.17862i 0.0453409 0.120485i
\(697\) 1.08693 0.941834i 0.0411706 0.0356745i
\(698\) 24.6394 + 2.97039i 0.932616 + 0.112431i
\(699\) 0.00567239 0.0193184i 0.000214550 0.000730689i
\(700\) 2.56947 0.883691i 0.0971168 0.0334004i
\(701\) −3.08890 + 4.80642i −0.116666 + 0.181536i −0.894676 0.446717i \(-0.852593\pi\)
0.778009 + 0.628253i \(0.216230\pi\)
\(702\) 29.7097 + 32.7459i 1.12132 + 1.23591i
\(703\) −5.24901 4.54829i −0.197970 0.171542i
\(704\) −9.52571 + 31.7528i −0.359014 + 1.19673i
\(705\) −32.9780 + 4.74152i −1.24202 + 0.178576i
\(706\) −28.1383 + 13.6348i −1.05900 + 0.513154i
\(707\) −0.611838 1.33974i −0.0230105 0.0503860i
\(708\) 18.6450 + 4.56176i 0.700721 + 0.171442i
\(709\) −3.66776 1.67501i −0.137746 0.0629063i 0.345350 0.938474i \(-0.387760\pi\)
−0.483095 + 0.875568i \(0.660488\pi\)
\(710\) 20.2976 + 8.71540i 0.761757 + 0.327083i
\(711\) −0.375822 + 0.241526i −0.0140944 + 0.00905794i
\(712\) −28.5905 28.7584i −1.07148 1.07777i
\(713\) −36.0066 + 26.5700i −1.34846 + 0.995055i
\(714\) −0.0685850 + 0.254967i −0.00256673 + 0.00954191i
\(715\) 43.2847 + 67.3522i 1.61875 + 2.51883i
\(716\) −23.0960 18.2360i −0.863140 0.681511i
\(717\) 2.53687 5.55496i 0.0947410 0.207454i
\(718\) 0.0666916 + 2.92145i 0.00248891 + 0.109028i
\(719\) −14.2275 + 6.49749i −0.530597 + 0.242316i −0.662653 0.748927i \(-0.730569\pi\)
0.132056 + 0.991242i \(0.457842\pi\)
\(720\) −2.71766 0.952483i −0.101281 0.0354969i
\(721\) −0.536261 3.72978i −0.0199714 0.138904i
\(722\) −12.4234 + 20.3373i −0.462353 + 0.756875i
\(723\) −11.1531 + 12.8714i −0.414789 + 0.478692i
\(724\) 0.565509 0.290145i 0.0210170 0.0107832i
\(725\) 3.63261 + 2.33453i 0.134912 + 0.0867024i
\(726\) 12.0657 8.14916i 0.447801 0.302444i
\(727\) 19.3621 + 5.68523i 0.718101 + 0.210853i 0.620314 0.784354i \(-0.287005\pi\)
0.0977873 + 0.995207i \(0.468824\pi\)
\(728\) −2.98069 2.24496i −0.110472 0.0832038i
\(729\) 18.7688 + 21.6603i 0.695140 + 0.802235i
\(730\) −5.31050 31.7699i −0.196550 1.17585i
\(731\) 0.497715 + 1.69506i 0.0184086 + 0.0626941i
\(732\) −26.7521 + 18.9715i −0.988786 + 0.701208i
\(733\) −21.9322 3.15338i −0.810085 0.116473i −0.275189 0.961390i \(-0.588740\pi\)
−0.534896 + 0.844918i \(0.679649\pi\)
\(734\) 5.04985 + 15.8506i 0.186393 + 0.585057i
\(735\) −38.4445 −1.41805
\(736\) 24.2579 12.1472i 0.894159 0.447750i
\(737\) 50.4319 1.85768
\(738\) 0.271210 + 0.851283i 0.00998340 + 0.0313362i
\(739\) 50.8417 + 7.30993i 1.87024 + 0.268900i 0.981776 0.190042i \(-0.0608624\pi\)
0.888466 + 0.458942i \(0.151771\pi\)
\(740\) 25.6375 18.1811i 0.942452 0.668349i
\(741\) −4.01325 13.6679i −0.147431 0.502102i
\(742\) 0.318675 + 1.90646i 0.0116989 + 0.0699885i
\(743\) 12.4738 + 14.3955i 0.457620 + 0.528121i 0.936927 0.349526i \(-0.113657\pi\)
−0.479307 + 0.877647i \(0.659112\pi\)
\(744\) −35.1674 26.4870i −1.28930 0.971060i
\(745\) −69.8786 20.5182i −2.56015 0.751729i
\(746\) 44.2187 29.8652i 1.61896 1.09344i
\(747\) 1.32770 + 0.853260i 0.0485780 + 0.0312192i
\(748\) 3.64401 1.86963i 0.133238 0.0683603i
\(749\) −0.250040 + 0.288561i −0.00913625 + 0.0105438i
\(750\) −4.07523 + 6.67119i −0.148806 + 0.243597i
\(751\) 2.94158 + 20.4591i 0.107340 + 0.746564i 0.970407 + 0.241475i \(0.0776312\pi\)
−0.863067 + 0.505089i \(0.831460\pi\)
\(752\) −22.7321 7.96713i −0.828954 0.290531i
\(753\) −15.3416 + 7.00628i −0.559080 + 0.255323i
\(754\) −0.135338 5.92853i −0.00492872 0.215904i
\(755\) 9.19743 20.1396i 0.334729 0.732954i
\(756\) −1.90777 1.50632i −0.0693851 0.0547845i
\(757\) 7.54433 + 11.7392i 0.274203 + 0.426669i 0.950856 0.309634i \(-0.100206\pi\)
−0.676653 + 0.736302i \(0.736570\pi\)
\(758\) −5.31857 + 19.7720i −0.193179 + 0.718151i
\(759\) −32.3459 7.26959i −1.17408 0.263869i
\(760\) 9.69397 + 9.75088i 0.351637 + 0.353702i
\(761\) 7.36982 4.73630i 0.267156 0.171691i −0.400204 0.916426i \(-0.631061\pi\)
0.667360 + 0.744735i \(0.267424\pi\)
\(762\) −23.8989 10.2617i −0.865767 0.371743i
\(763\) 2.09760 + 0.957941i 0.0759382 + 0.0346798i
\(764\) −26.2563 6.42400i −0.949921 0.232412i
\(765\) 0.147796 + 0.323628i 0.00534358 + 0.0117008i
\(766\) 14.6673 7.10725i 0.529951 0.256795i
\(767\) 33.1745 4.76977i 1.19786 0.172226i
\(768\) 18.2678 + 19.4606i 0.659183 + 0.702225i
\(769\) −30.6072 26.5213i −1.10372 0.956382i −0.104452 0.994530i \(-0.533309\pi\)
−0.999272 + 0.0381479i \(0.987854\pi\)
\(770\) −2.95753 3.25977i −0.106582 0.117474i
\(771\) 11.1107 17.2886i 0.400142 0.622633i
\(772\) −32.2535 + 11.0926i −1.16083 + 0.399232i
\(773\) −10.1397 + 34.5325i −0.364698 + 1.24205i 0.549058 + 0.835785i \(0.314987\pi\)
−0.913756 + 0.406264i \(0.866831\pi\)
\(774\) −1.08956 0.131351i −0.0391634 0.00472132i
\(775\) 42.3040 36.6566i 1.51961 1.31675i
\(776\) −0.938296 + 2.49336i −0.0336829 + 0.0895062i
\(777\) 1.71761 0.504337i 0.0616191 0.0180930i
\(778\) 28.5172 34.4697i 1.02239 1.23580i
\(779\) 0.607093 4.22242i 0.0217514 0.151284i
\(780\) 64.3945 2.94156i 2.30569 0.105325i
\(781\) 19.5164i 0.698350i
\(782\) −3.15867 1.12106i −0.112954 0.0400891i
\(783\) 3.86292i 0.138049i
\(784\) −24.6552 12.8327i −0.880541 0.458309i
\(785\) 9.25750 64.3873i 0.330414 2.29808i
\(786\) 29.9697 + 24.7943i 1.06898 + 0.884383i
\(787\) 28.5686 8.38848i 1.01836 0.299017i 0.270390 0.962751i \(-0.412847\pi\)
0.747969 + 0.663734i \(0.231029\pi\)
\(788\) −0.949631 + 9.74401i −0.0338292 + 0.347116i
\(789\) 25.5917 22.1753i 0.911088 0.789462i
\(790\) −1.15528 + 9.58303i −0.0411029 + 0.340949i
\(791\) 0.0908019 0.309243i 0.00322854 0.0109954i
\(792\) 0.174077 + 2.53831i 0.00618556 + 0.0901948i
\(793\) −30.9595 + 48.1739i −1.09940 + 1.71071i
\(794\) −16.8412 + 15.2796i −0.597670 + 0.542254i
\(795\) −25.2350 21.8663i −0.894995 0.775518i
\(796\) 18.9193 + 19.9197i 0.670578 + 0.706035i
\(797\) 12.5901 1.81019i 0.445966 0.0641202i 0.0843264 0.996438i \(-0.473126\pi\)
0.361640 + 0.932318i \(0.382217\pi\)
\(798\) 0.341497 + 0.704750i 0.0120889 + 0.0249479i
\(799\) 1.23625 + 2.70702i 0.0437355 + 0.0957674i
\(800\) −29.0633 + 17.5211i −1.02754 + 0.619465i
\(801\) −2.83104 1.29289i −0.100030 0.0456821i
\(802\) 0.531593 1.23805i 0.0187712 0.0437170i
\(803\) −23.9407 + 15.3857i −0.844848 + 0.542951i
\(804\) 20.3712 35.1255i 0.718436 1.23878i
\(805\) −0.281650 + 3.59097i −0.00992686 + 0.126565i
\(806\) −74.2340 19.9686i −2.61478 0.703363i
\(807\) −2.83151 4.40591i −0.0996737 0.155095i
\(808\) 10.9805 + 14.7581i 0.386293 + 0.519188i
\(809\) −13.6199 + 29.8234i −0.478850 + 1.04853i 0.503929 + 0.863745i \(0.331887\pi\)
−0.982778 + 0.184789i \(0.940840\pi\)
\(810\) 38.9265 0.888623i 1.36774 0.0312230i
\(811\) −33.4165 + 15.2608i −1.17341 + 0.535880i −0.904162 0.427190i \(-0.859504\pi\)
−0.269251 + 0.963070i \(0.586776\pi\)
\(812\) 0.0610735 + 0.320241i 0.00214326 + 0.0112383i
\(813\) −0.247089 1.71854i −0.00866579 0.0602719i
\(814\) −23.6968 14.4757i −0.830574 0.507373i
\(815\) 6.26685 7.23233i 0.219518 0.253338i
\(816\) 0.169760 3.29323i 0.00594279 0.115286i
\(817\) 4.40808 + 2.83290i 0.154219 + 0.0991108i
\(818\) 3.41957 + 5.06304i 0.119562 + 0.177025i
\(819\) −0.274788 0.0806851i −0.00960187 0.00281936i
\(820\) 17.9072 + 7.20952i 0.625345 + 0.251767i
\(821\) 7.29501 + 8.41889i 0.254597 + 0.293821i 0.868632 0.495458i \(-0.165000\pi\)
−0.614034 + 0.789279i \(0.710454\pi\)
\(822\) 1.67867 0.280599i 0.0585505 0.00978702i
\(823\) −5.42382 18.4718i −0.189062 0.643887i −0.998400 0.0565438i \(-0.981992\pi\)
0.809338 0.587344i \(-0.199826\pi\)
\(824\) 16.3173 + 44.1427i 0.568442 + 1.53778i
\(825\) 41.0487 + 5.90192i 1.42913 + 0.205478i
\(826\) −1.75561 + 0.559322i −0.0610857 + 0.0194613i
\(827\) −10.8862 −0.378552 −0.189276 0.981924i \(-0.560614\pi\)
−0.189276 + 0.981924i \(0.560614\pi\)
\(828\) 1.41411 1.52826i 0.0491436 0.0531105i
\(829\) 27.3003 0.948177 0.474089 0.880477i \(-0.342778\pi\)
0.474089 + 0.880477i \(0.342778\pi\)
\(830\) 32.4909 10.3513i 1.12777 0.359298i
\(831\) 15.9553 + 2.29402i 0.553482 + 0.0795787i
\(832\) 42.2793 + 19.6082i 1.46577 + 0.679793i
\(833\) 0.967452 + 3.29484i 0.0335202 + 0.114159i
\(834\) 25.2654 4.22325i 0.874871 0.146239i
\(835\) −22.6517 26.1415i −0.783895 0.904663i
\(836\) 4.53692 11.2689i 0.156913 0.389743i
\(837\) −48.0474 14.1080i −1.66076 0.487643i
\(838\) −14.8080 21.9248i −0.511532 0.757379i
\(839\) 10.9536 + 7.03945i 0.378160 + 0.243029i 0.715888 0.698215i \(-0.246022\pi\)
−0.337728 + 0.941244i \(0.609658\pi\)
\(840\) −3.46505 + 0.743161i −0.119556 + 0.0256415i
\(841\) 18.6517 21.5252i 0.643161 0.742248i
\(842\) −8.36775 5.11161i −0.288372 0.176158i
\(843\) 5.64966 + 39.2943i 0.194585 + 1.35337i
\(844\) −27.5441 + 5.25298i −0.948109 + 0.180815i
\(845\) 63.1648 28.8464i 2.17294 0.992347i
\(846\) −1.84822 + 0.0421915i −0.0635430 + 0.00145057i
\(847\) −0.580598 + 1.27133i −0.0199496 + 0.0436835i
\(848\) −8.88480 22.4466i −0.305105 0.770821i
\(849\) 16.6292 + 25.8756i 0.570713 + 0.888047i
\(850\) 4.04875 + 1.08909i 0.138871 + 0.0373556i
\(851\) 4.67774 + 22.2379i 0.160351 + 0.762307i
\(852\) −13.5930 7.88333i −0.465689 0.270078i
\(853\) −3.55643 + 2.28558i −0.121770 + 0.0782567i −0.600108 0.799919i \(-0.704876\pi\)
0.478338 + 0.878176i \(0.341239\pi\)
\(854\) 1.24210 2.89279i 0.0425039 0.0989891i
\(855\) 0.959899 + 0.438371i 0.0328279 + 0.0149920i
\(856\) 2.29766 4.17872i 0.0785322 0.142826i
\(857\) 5.27755 + 11.5562i 0.180278 + 0.394753i 0.978099 0.208141i \(-0.0667414\pi\)
−0.797821 + 0.602894i \(0.794014\pi\)
\(858\) −24.8350 51.2522i −0.847854 1.74972i
\(859\) 50.8716 7.31424i 1.73572 0.249559i 0.799422 0.600770i \(-0.205139\pi\)
0.936296 + 0.351212i \(0.114230\pi\)
\(860\) −17.1929 + 16.3295i −0.586274 + 0.556831i
\(861\) 0.830935 + 0.720009i 0.0283182 + 0.0245379i
\(862\) −3.63254 + 3.29573i −0.123725 + 0.112253i
\(863\) −6.32054 + 9.83496i −0.215154 + 0.334786i −0.932008 0.362437i \(-0.881945\pi\)
0.716854 + 0.697223i \(0.245581\pi\)
\(864\) 27.2425 + 13.3982i 0.926809 + 0.455817i
\(865\) 0.816949 2.78227i 0.0277771 0.0946001i
\(866\) 0.201827 1.67416i 0.00685837 0.0568903i
\(867\) 21.1248 18.3048i 0.717437 0.621663i
\(868\) 4.20624 + 0.409931i 0.142769 + 0.0139140i
\(869\) 8.18254 2.40261i 0.277574 0.0815030i
\(870\) −4.33930 3.58996i −0.147116 0.121711i
\(871\) 10.0900 70.1778i 0.341888 2.37788i
\(872\) −28.1243 6.20434i −0.952410 0.210106i
\(873\) 0.204462i 0.00691999i
\(874\) −9.25796 + 3.62229i −0.313155 + 0.122526i
\(875\) 0.750411i 0.0253685i
\(876\) 1.04559 + 22.8893i 0.0353273 + 0.773359i
\(877\) −5.09080 + 35.4073i −0.171904 + 1.19562i 0.702952 + 0.711237i \(0.251865\pi\)
−0.874856 + 0.484382i \(0.839044\pi\)
\(878\) 14.6097 17.6593i 0.493055 0.595972i
\(879\) −32.6908 + 9.59889i −1.10263 + 0.323763i
\(880\) 44.6543 + 32.0615i 1.50530 + 1.08079i
\(881\) −18.0081 + 15.6041i −0.606708 + 0.525716i −0.903144 0.429337i \(-0.858747\pi\)
0.296436 + 0.955053i \(0.404202\pi\)
\(882\) −2.11787 0.255319i −0.0713125 0.00859703i
\(883\) 10.7479 36.6040i 0.361695 1.23182i −0.554870 0.831937i \(-0.687232\pi\)
0.916566 0.399884i \(-0.130950\pi\)
\(884\) −1.87258 5.44483i −0.0629818 0.183129i
\(885\) 17.2085 26.7770i 0.578459 0.900099i
\(886\) −25.9997 28.6568i −0.873477 0.962743i
\(887\) −22.8778 19.8237i −0.768160 0.665614i 0.179908 0.983683i \(-0.442420\pi\)
−0.948067 + 0.318069i \(0.896966\pi\)
\(888\) −19.6542 + 10.6574i −0.659552 + 0.357640i
\(889\) 2.47123 0.355310i 0.0828825 0.0119167i
\(890\) −60.5149 + 29.3234i −2.02846 + 0.982922i
\(891\) −14.2906 31.2921i −0.478754 1.04832i
\(892\) −3.85826 + 15.7696i −0.129184 + 0.528006i
\(893\) 8.02917 + 3.66680i 0.268686 + 0.122705i
\(894\) 47.6042 + 20.4403i 1.59212 + 0.683626i
\(895\) −41.0515 + 26.3822i −1.37220 + 0.881860i
\(896\) −2.47027 0.680022i −0.0825259 0.0227179i
\(897\) −16.5874 + 43.5560i −0.553837 + 1.45429i
\(898\) 6.89162 25.6199i 0.229976 0.854946i
\(899\) 3.63102 + 5.64997i 0.121101 + 0.188437i
\(900\) −1.61401 + 2.04416i −0.0538004 + 0.0681388i
\(901\) −1.23899 + 2.71300i −0.0412766 + 0.0903832i
\(902\) −0.389239 17.0508i −0.0129602 0.567728i
\(903\) −1.22849 + 0.561034i −0.0408817 + 0.0186701i
\(904\) −0.298915 + 4.01422i −0.00994176 + 0.133511i
\(905\) −0.149997 1.04325i −0.00498606 0.0346788i
\(906\) −8.21030 + 13.4403i −0.272769 + 0.446525i
\(907\) −35.7471 + 41.2544i −1.18696 + 1.36983i −0.274031 + 0.961721i \(0.588357\pi\)
−0.912933 + 0.408109i \(0.866188\pi\)
\(908\) −18.4574 35.9745i −0.612529 1.19385i
\(909\) 1.18766 + 0.763265i 0.0393923 + 0.0253159i
\(910\) −5.12781 + 3.46331i −0.169985 + 0.114808i
\(911\) 46.1314 + 13.5454i 1.52840 + 0.448779i 0.934561 0.355804i \(-0.115793\pi\)
0.593840 + 0.804583i \(0.297611\pi\)
\(912\) −6.01609 7.71183i −0.199213 0.255364i
\(913\) −19.7293 22.7689i −0.652946 0.753540i
\(914\) −2.56954 15.3722i −0.0849929 0.508467i
\(915\) 15.3218 + 52.1813i 0.506524 + 1.72506i
\(916\) −9.77747 13.7874i −0.323057 0.455548i
\(917\) −3.69576 0.531369i −0.122045 0.0175474i
\(918\) −1.13856 3.57374i −0.0375780 0.117951i
\(919\) 5.18549 0.171053 0.0855267 0.996336i \(-0.472743\pi\)
0.0855267 + 0.996336i \(0.472743\pi\)
\(920\) −5.96566 44.5898i −0.196682 1.47008i
\(921\) 6.22727 0.205196
\(922\) −3.63055 11.3957i −0.119566 0.375296i
\(923\) −27.1577 3.90469i −0.893907 0.128524i
\(924\) 1.81119 + 2.55399i 0.0595838 + 0.0840202i
\(925\) −8.00861 27.2748i −0.263321 0.896790i
\(926\) −8.24312 49.3142i −0.270886 1.62056i
\(927\) 2.36531 + 2.72971i 0.0776869 + 0.0896555i
\(928\) −1.58456 3.75075i −0.0520157 0.123124i
\(929\) −5.81700 1.70802i −0.190849 0.0560384i 0.184911 0.982755i \(-0.440800\pi\)
−0.375761 + 0.926717i \(0.622618\pi\)
\(930\) −60.5000 + 40.8616i −1.98387 + 1.33990i
\(931\) 8.56838 + 5.50656i 0.280817 + 0.180470i
\(932\) −0.0110190 0.0214766i −0.000360939 0.000703490i
\(933\) −19.9305 + 23.0010i −0.652494 + 0.753018i
\(934\) −24.1820 + 39.5861i −0.791260 + 1.29530i
\(935\) −0.966544 6.72246i −0.0316094 0.219848i
\(936\) 3.56697 + 0.265611i 0.116590 + 0.00868176i
\(937\) 23.3197 10.6498i 0.761822 0.347912i 0.00367246 0.999993i \(-0.498831\pi\)
0.758149 + 0.652081i \(0.226104\pi\)
\(938\) 0.0889563 + 3.89676i 0.00290452 + 0.127234i
\(939\) 5.68533 12.4491i 0.185534 0.406262i
\(940\) −24.7527 + 31.3495i −0.807343 + 1.02251i
\(941\) 17.8794 + 27.8210i 0.582853 + 0.906937i 0.999998 0.00190261i \(-0.000605621\pi\)
−0.417145 + 0.908840i \(0.636969\pi\)
\(942\) −12.0200 + 44.6848i −0.391633 + 1.45591i
\(943\) −9.93690 + 9.80124i −0.323590 + 0.319172i
\(944\) 19.9742 11.4284i 0.650106 0.371964i
\(945\) −3.39093 + 2.17922i −0.110307 + 0.0708900i
\(946\) 19.2501 + 8.26559i 0.625873 + 0.268737i
\(947\) 7.00174 + 3.19759i 0.227526 + 0.103908i 0.525916 0.850536i \(-0.323722\pi\)
−0.298390 + 0.954444i \(0.596450\pi\)
\(948\) 1.63181 6.66957i 0.0529987 0.216618i
\(949\) 16.6199 + 36.3926i 0.539506 + 1.18135i
\(950\) 11.1911 5.42279i 0.363086 0.175939i
\(951\) −12.0980 + 1.73943i −0.392305 + 0.0564050i
\(952\) 0.150889 + 0.278267i 0.00489036 + 0.00901868i
\(953\) 31.2472 + 27.0759i 1.01220 + 0.877073i 0.992440 0.122732i \(-0.0391654\pi\)
0.0197566 + 0.999805i \(0.493711\pi\)
\(954\) −1.24496 1.37219i −0.0403070 0.0444262i
\(955\) −24.2335 + 37.7081i −0.784178 + 1.22021i
\(956\) −2.38109 6.92340i −0.0770101 0.223919i
\(957\) −1.40183 + 4.77420i −0.0453148 + 0.154328i
\(958\) −14.8425 1.78933i −0.479540 0.0578107i
\(959\) −0.123471 + 0.106988i −0.00398708 + 0.00345482i
\(960\) 40.3680 18.1506i 1.30287 0.585809i
\(961\) 53.7917 15.7947i 1.73522 0.509506i
\(962\) −24.8845 + 30.0788i −0.802310 + 0.969779i
\(963\) 0.0520862 0.362267i 0.00167845 0.0116739i
\(964\) 0.931758 + 20.3974i 0.0300099 + 0.656955i
\(965\) 56.5589i 1.82070i
\(966\) 0.504650 2.51212i 0.0162369 0.0808260i
\(967\) 4.17765i 0.134344i 0.997741 + 0.0671721i \(0.0213976\pi\)
−0.997741 + 0.0671721i \(0.978602\pi\)
\(968\) 3.76039 17.0459i 0.120863 0.547874i
\(969\) −0.171971 + 1.19609i −0.00552452 + 0.0384238i
\(970\) 3.40381 + 2.81601i 0.109290 + 0.0904166i
\(971\) −22.7195 + 6.67106i −0.729104 + 0.214084i −0.625158 0.780498i \(-0.714965\pi\)
−0.103947 + 0.994583i \(0.533147\pi\)
\(972\) 4.48154 + 0.436762i 0.143746 + 0.0140091i
\(973\) −1.85834 + 1.61026i −0.0595755 + 0.0516225i
\(974\) −0.0672421 + 0.557774i −0.00215458 + 0.0178722i
\(975\) 16.4254 55.9399i 0.526035 1.79151i
\(976\) −7.59181 + 38.5792i −0.243008 + 1.23489i
\(977\) 15.4331 24.0144i 0.493749 0.768289i −0.501551 0.865128i \(-0.667237\pi\)
0.995300 + 0.0968393i \(0.0308733\pi\)
\(978\) −5.04168 + 4.57421i −0.161215 + 0.146267i
\(979\) 44.9003 + 38.9063i 1.43502 + 1.24345i
\(980\) −33.4194 + 31.7411i −1.06754 + 1.01393i
\(981\) −2.18789 + 0.314572i −0.0698540 + 0.0100435i
\(982\) −14.9743 30.9025i −0.477848 0.986138i
\(983\) −18.0583 39.5422i −0.575971 1.26120i −0.943557 0.331210i \(-0.892543\pi\)
0.367586 0.929989i \(-0.380184\pi\)
\(984\) −12.0330 6.61629i −0.383597 0.210920i
\(985\) 14.7674 + 6.74406i 0.470530 + 0.214884i
\(986\) −0.198475 + 0.462236i −0.00632072 + 0.0147206i
\(987\) −1.91388 + 1.22998i −0.0609196 + 0.0391507i
\(988\) −14.7734 8.56788i −0.470003 0.272581i
\(989\) −5.88078 16.1041i −0.186998 0.512082i
\(990\) 4.07420 + 1.09594i 0.129486 + 0.0348312i
\(991\) 5.81282 + 9.04493i 0.184650 + 0.287322i 0.921222 0.389038i \(-0.127193\pi\)
−0.736571 + 0.676360i \(0.763556\pi\)
\(992\) −52.4393 + 6.01056i −1.66495 + 0.190835i
\(993\) 13.6012 29.7825i 0.431621 0.945118i
\(994\) 1.50799 0.0344247i 0.0478304 0.00109188i
\(995\) 41.4393 18.9247i 1.31371 0.599953i
\(996\) −23.8277 + 4.54421i −0.755010 + 0.143989i
\(997\) −8.06259 56.0766i −0.255345 1.77596i −0.564978 0.825106i \(-0.691115\pi\)
0.309633 0.950856i \(-0.399794\pi\)
\(998\) 27.4947 + 16.7957i 0.870329 + 0.531659i
\(999\) −16.6530 + 19.2186i −0.526878 + 0.608050i
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 92.2.h.a.11.7 yes 100
3.2 odd 2 828.2.u.a.379.4 100
4.3 odd 2 inner 92.2.h.a.11.3 100
12.11 even 2 828.2.u.a.379.8 100
23.21 odd 22 inner 92.2.h.a.67.3 yes 100
69.44 even 22 828.2.u.a.343.8 100
92.67 even 22 inner 92.2.h.a.67.7 yes 100
276.251 odd 22 828.2.u.a.343.4 100
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
92.2.h.a.11.3 100 4.3 odd 2 inner
92.2.h.a.11.7 yes 100 1.1 even 1 trivial
92.2.h.a.67.3 yes 100 23.21 odd 22 inner
92.2.h.a.67.7 yes 100 92.67 even 22 inner
828.2.u.a.343.4 100 276.251 odd 22
828.2.u.a.343.8 100 69.44 even 22
828.2.u.a.379.4 100 3.2 odd 2
828.2.u.a.379.8 100 12.11 even 2