Properties

Label 175.2.t.a.109.4
Level $175$
Weight $2$
Character 175.109
Analytic conductor $1.397$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(4,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([3, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.t (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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(18\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 109.4
Character \(\chi\) \(=\) 175.109
Dual form 175.2.t.a.114.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.93770 - 0.203661i) q^{2} +(-0.500958 + 2.35682i) q^{3} +(1.75692 + 0.373445i) q^{4} +(-0.306385 + 2.21498i) q^{5} +(1.45070 - 4.46479i) q^{6} +(-2.52107 + 0.802620i) q^{7} +(0.377701 + 0.122722i) q^{8} +(-2.56301 - 1.14113i) q^{9} +O(q^{10})\) \(q+(-1.93770 - 0.203661i) q^{2} +(-0.500958 + 2.35682i) q^{3} +(1.75692 + 0.373445i) q^{4} +(-0.306385 + 2.21498i) q^{5} +(1.45070 - 4.46479i) q^{6} +(-2.52107 + 0.802620i) q^{7} +(0.377701 + 0.122722i) q^{8} +(-2.56301 - 1.14113i) q^{9} +(1.04479 - 4.22957i) q^{10} +(2.26739 - 1.00951i) q^{11} +(-1.76029 + 3.95367i) q^{12} +(-2.29720 - 3.16183i) q^{13} +(5.04855 - 1.04180i) q^{14} +(-5.06682 - 1.83170i) q^{15} +(-3.98864 - 1.77586i) q^{16} +(-2.30076 + 2.07161i) q^{17} +(4.73395 + 2.73315i) q^{18} +(-5.00961 + 1.06483i) q^{19} +(-1.36546 + 3.77712i) q^{20} +(-0.628681 - 6.34379i) q^{21} +(-4.59912 + 1.49435i) q^{22} +(4.53438 + 0.476582i) q^{23} +(-0.478447 + 0.828694i) q^{24} +(-4.81226 - 1.35727i) q^{25} +(3.80736 + 6.59454i) q^{26} +(-0.275367 + 0.379010i) q^{27} +(-4.72905 + 0.468658i) q^{28} +(-0.797815 - 2.45542i) q^{29} +(9.44495 + 4.58121i) q^{30} +(4.22141 + 4.68835i) q^{31} +(6.67927 + 3.85628i) q^{32} +(1.24336 + 5.84955i) q^{33} +(4.88009 - 3.54559i) q^{34} +(-1.00537 - 5.83003i) q^{35} +(-4.07686 - 2.96201i) q^{36} +(3.31862 - 7.45374i) q^{37} +(9.92401 - 1.04306i) q^{38} +(8.60267 - 3.83016i) q^{39} +(-0.387549 + 0.798998i) q^{40} +(-4.21399 + 3.06164i) q^{41} +(-0.0737844 + 12.4204i) q^{42} +5.80714i q^{43} +(4.36062 - 0.926877i) q^{44} +(3.31284 - 5.32739i) q^{45} +(-8.68922 - 1.84695i) q^{46} +(-1.61989 - 1.45856i) q^{47} +(6.18352 - 8.51089i) q^{48} +(5.71160 - 4.04692i) q^{49} +(9.04830 + 3.61005i) q^{50} +(-3.72984 - 6.46027i) q^{51} +(-2.85523 - 6.41296i) q^{52} +(-1.59789 + 7.51748i) q^{53} +(0.610768 - 0.678327i) q^{54} +(1.54134 + 5.33152i) q^{55} +(-1.05071 - 0.00624181i) q^{56} -12.3402i q^{57} +(1.04586 + 4.92036i) q^{58} +(1.15540 + 10.9929i) q^{59} +(-8.21796 - 5.11033i) q^{60} +(-0.904700 + 8.60765i) q^{61} +(-7.22500 - 9.94436i) q^{62} +(7.37743 + 0.819737i) q^{63} +(-5.09255 - 3.69995i) q^{64} +(7.70721 - 4.11952i) q^{65} +(-1.21794 - 11.5879i) q^{66} +(-6.37162 + 5.73703i) q^{67} +(-4.81588 + 2.78045i) q^{68} +(-3.39475 + 10.4480i) q^{69} +(0.760757 + 11.5016i) q^{70} +(4.36571 + 13.4363i) q^{71} +(-0.828010 - 0.745543i) q^{72} +(-5.00373 - 11.2386i) q^{73} +(-7.94853 + 13.7673i) q^{74} +(5.60958 - 10.6617i) q^{75} -9.19914 q^{76} +(-4.90600 + 4.36489i) q^{77} +(-17.4495 + 5.66968i) q^{78} +(-4.18464 + 4.64751i) q^{79} +(5.15555 - 8.29066i) q^{80} +(-6.38718 - 7.09369i) q^{81} +(8.78899 - 5.07433i) q^{82} +(-4.78601 - 1.55507i) q^{83} +(1.26451 - 11.3803i) q^{84} +(-3.88366 - 5.73084i) q^{85} +(1.18269 - 11.2525i) q^{86} +(6.18666 - 0.650245i) q^{87} +(0.980283 - 0.103032i) q^{88} +(1.45225 - 13.8172i) q^{89} +(-7.50428 + 9.64821i) q^{90} +(8.32916 + 6.12742i) q^{91} +(7.78856 + 2.53066i) q^{92} +(-13.1644 + 7.60044i) q^{93} +(2.84182 + 3.15616i) q^{94} +(-0.823699 - 11.4224i) q^{95} +(-12.4346 + 13.8100i) q^{96} +(4.30851 - 1.39992i) q^{97} +(-11.8916 + 6.67851i) q^{98} -6.96332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93770 0.203661i −1.37016 0.144010i −0.609309 0.792933i \(-0.708553\pi\)
−0.760854 + 0.648923i \(0.775220\pi\)
\(3\) −0.500958 + 2.35682i −0.289228 + 1.36071i 0.558158 + 0.829735i \(0.311508\pi\)
−0.847386 + 0.530977i \(0.821825\pi\)
\(4\) 1.75692 + 0.373445i 0.878460 + 0.186722i
\(5\) −0.306385 + 2.21498i −0.137019 + 0.990568i
\(6\) 1.45070 4.46479i 0.592246 1.82274i
\(7\) −2.52107 + 0.802620i −0.952875 + 0.303362i
\(8\) 0.377701 + 0.122722i 0.133537 + 0.0433889i
\(9\) −2.56301 1.14113i −0.854338 0.380376i
\(10\) 1.04479 4.22957i 0.330390 1.33751i
\(11\) 2.26739 1.00951i 0.683644 0.304378i −0.0353694 0.999374i \(-0.511261\pi\)
0.719013 + 0.694997i \(0.244594\pi\)
\(12\) −1.76029 + 3.95367i −0.508151 + 1.14132i
\(13\) −2.29720 3.16183i −0.637130 0.876934i 0.361329 0.932439i \(-0.382323\pi\)
−0.998458 + 0.0555046i \(0.982323\pi\)
\(14\) 5.04855 1.04180i 1.34928 0.278432i
\(15\) −5.06682 1.83170i −1.30825 0.472944i
\(16\) −3.98864 1.77586i −0.997161 0.443965i
\(17\) −2.30076 + 2.07161i −0.558016 + 0.502440i −0.899189 0.437561i \(-0.855842\pi\)
0.341173 + 0.940001i \(0.389176\pi\)
\(18\) 4.73395 + 2.73315i 1.11580 + 0.644210i
\(19\) −5.00961 + 1.06483i −1.14928 + 0.244288i −0.742892 0.669411i \(-0.766547\pi\)
−0.406392 + 0.913699i \(0.633213\pi\)
\(20\) −1.36546 + 3.77712i −0.305327 + 0.844590i
\(21\) −0.628681 6.34379i −0.137190 1.38433i
\(22\) −4.59912 + 1.49435i −0.980537 + 0.318596i
\(23\) 4.53438 + 0.476582i 0.945483 + 0.0993743i 0.564706 0.825292i \(-0.308990\pi\)
0.380778 + 0.924667i \(0.375656\pi\)
\(24\) −0.478447 + 0.828694i −0.0976625 + 0.169156i
\(25\) −4.81226 1.35727i −0.962451 0.271454i
\(26\) 3.80736 + 6.59454i 0.746684 + 1.29330i
\(27\) −0.275367 + 0.379010i −0.0529943 + 0.0729405i
\(28\) −4.72905 + 0.468658i −0.893707 + 0.0885680i
\(29\) −0.797815 2.45542i −0.148151 0.455960i 0.849252 0.527987i \(-0.177053\pi\)
−0.997403 + 0.0720270i \(0.977053\pi\)
\(30\) 9.44495 + 4.58121i 1.72440 + 0.836411i
\(31\) 4.22141 + 4.68835i 0.758187 + 0.842053i 0.991467 0.130357i \(-0.0416124\pi\)
−0.233280 + 0.972410i \(0.574946\pi\)
\(32\) 6.67927 + 3.85628i 1.18074 + 0.681700i
\(33\) 1.24336 + 5.84955i 0.216441 + 1.01828i
\(34\) 4.88009 3.54559i 0.836929 0.608064i
\(35\) −1.00537 5.83003i −0.169938 0.985455i
\(36\) −4.07686 2.96201i −0.679476 0.493669i
\(37\) 3.31862 7.45374i 0.545578 1.22539i −0.404833 0.914391i \(-0.632670\pi\)
0.950411 0.310997i \(-0.100663\pi\)
\(38\) 9.92401 1.04306i 1.60989 0.169206i
\(39\) 8.60267 3.83016i 1.37753 0.613316i
\(40\) −0.387549 + 0.798998i −0.0612769 + 0.126333i
\(41\) −4.21399 + 3.06164i −0.658114 + 0.478148i −0.866026 0.500000i \(-0.833333\pi\)
0.207911 + 0.978148i \(0.433333\pi\)
\(42\) −0.0737844 + 12.4204i −0.0113852 + 1.91651i
\(43\) 5.80714i 0.885580i 0.896625 + 0.442790i \(0.146011\pi\)
−0.896625 + 0.442790i \(0.853989\pi\)
\(44\) 4.36062 0.926877i 0.657387 0.139732i
\(45\) 3.31284 5.32739i 0.493849 0.794161i
\(46\) −8.68922 1.84695i −1.28116 0.272318i
\(47\) −1.61989 1.45856i −0.236286 0.212753i 0.542478 0.840070i \(-0.317486\pi\)
−0.778764 + 0.627317i \(0.784153\pi\)
\(48\) 6.18352 8.51089i 0.892515 1.22844i
\(49\) 5.71160 4.04692i 0.815943 0.578132i
\(50\) 9.04830 + 3.61005i 1.27962 + 0.510539i
\(51\) −3.72984 6.46027i −0.522282 0.904618i
\(52\) −2.85523 6.41296i −0.395950 0.889317i
\(53\) −1.59789 + 7.51748i −0.219487 + 1.03260i 0.721042 + 0.692891i \(0.243663\pi\)
−0.940529 + 0.339713i \(0.889670\pi\)
\(54\) 0.610768 0.678327i 0.0831150 0.0923086i
\(55\) 1.54134 + 5.33152i 0.207835 + 0.718901i
\(56\) −1.05071 0.00624181i −0.140407 0.000834097i
\(57\) 12.3402i 1.63450i
\(58\) 1.04586 + 4.92036i 0.137328 + 0.646075i
\(59\) 1.15540 + 10.9929i 0.150420 + 1.43115i 0.765880 + 0.642983i \(0.222304\pi\)
−0.615460 + 0.788168i \(0.711030\pi\)
\(60\) −8.21796 5.11033i −1.06093 0.659741i
\(61\) −0.904700 + 8.60765i −0.115835 + 1.10210i 0.769983 + 0.638064i \(0.220264\pi\)
−0.885818 + 0.464032i \(0.846402\pi\)
\(62\) −7.22500 9.94436i −0.917576 1.26294i
\(63\) 7.37743 + 0.819737i 0.929469 + 0.103277i
\(64\) −5.09255 3.69995i −0.636568 0.462494i
\(65\) 7.70721 4.11952i 0.955962 0.510964i
\(66\) −1.21794 11.5879i −0.149918 1.42637i
\(67\) −6.37162 + 5.73703i −0.778417 + 0.700890i −0.959230 0.282628i \(-0.908794\pi\)
0.180813 + 0.983518i \(0.442127\pi\)
\(68\) −4.81588 + 2.78045i −0.584011 + 0.337179i
\(69\) −3.39475 + 10.4480i −0.408680 + 1.25779i
\(70\) 0.760757 + 11.5016i 0.0909279 + 1.37471i
\(71\) 4.36571 + 13.4363i 0.518114 + 1.59459i 0.777543 + 0.628830i \(0.216466\pi\)
−0.259428 + 0.965762i \(0.583534\pi\)
\(72\) −0.828010 0.745543i −0.0975819 0.0878631i
\(73\) −5.00373 11.2386i −0.585642 1.31537i −0.926866 0.375392i \(-0.877508\pi\)
0.341224 0.939982i \(-0.389159\pi\)
\(74\) −7.94853 + 13.7673i −0.923998 + 1.60041i
\(75\) 5.60958 10.6617i 0.647739 1.23111i
\(76\) −9.19914 −1.05521
\(77\) −4.90600 + 4.36489i −0.559091 + 0.497426i
\(78\) −17.4495 + 5.66968i −1.97576 + 0.641965i
\(79\) −4.18464 + 4.64751i −0.470809 + 0.522886i −0.931042 0.364912i \(-0.881099\pi\)
0.460233 + 0.887798i \(0.347766\pi\)
\(80\) 5.15555 8.29066i 0.576408 0.926924i
\(81\) −6.38718 7.09369i −0.709687 0.788187i
\(82\) 8.78899 5.07433i 0.970582 0.560366i
\(83\) −4.78601 1.55507i −0.525332 0.170691i 0.0343315 0.999410i \(-0.489070\pi\)
−0.559664 + 0.828720i \(0.689070\pi\)
\(84\) 1.26451 11.3803i 0.137970 1.24169i
\(85\) −3.88366 5.73084i −0.421242 0.621597i
\(86\) 1.18269 11.2525i 0.127532 1.21339i
\(87\) 6.18666 0.650245i 0.663280 0.0697135i
\(88\) 0.980283 0.103032i 0.104499 0.0109832i
\(89\) 1.45225 13.8172i 0.153938 1.46463i −0.595929 0.803037i \(-0.703216\pi\)
0.749867 0.661588i \(-0.230117\pi\)
\(90\) −7.50428 + 9.64821i −0.791020 + 1.01701i
\(91\) 8.32916 + 6.12742i 0.873134 + 0.642328i
\(92\) 7.78856 + 2.53066i 0.812014 + 0.263839i
\(93\) −13.1644 + 7.60044i −1.36508 + 0.788129i
\(94\) 2.84182 + 3.15616i 0.293111 + 0.325533i
\(95\) −0.823699 11.4224i −0.0845097 1.17192i
\(96\) −12.4346 + 13.8100i −1.26910 + 1.40948i
\(97\) 4.30851 1.39992i 0.437463 0.142140i −0.0820021 0.996632i \(-0.526131\pi\)
0.519465 + 0.854492i \(0.326131\pi\)
\(98\) −11.8916 + 6.67851i −1.20123 + 0.674631i
\(99\) −6.96332 −0.699840
\(100\) −7.94788 4.18173i −0.794788 0.418173i
\(101\) −5.70073 + 9.87396i −0.567244 + 0.982495i 0.429593 + 0.903023i \(0.358657\pi\)
−0.996837 + 0.0794728i \(0.974676\pi\)
\(102\) 5.91161 + 13.2777i 0.585337 + 1.31469i
\(103\) 1.13579 + 1.02267i 0.111913 + 0.100767i 0.723188 0.690652i \(-0.242676\pi\)
−0.611274 + 0.791419i \(0.709343\pi\)
\(104\) −0.479628 1.47614i −0.0470314 0.144748i
\(105\) 14.2440 + 0.551125i 1.39007 + 0.0537843i
\(106\) 4.62725 14.2412i 0.449438 1.38323i
\(107\) −7.85780 + 4.53670i −0.759642 + 0.438580i −0.829167 0.559000i \(-0.811185\pi\)
0.0695249 + 0.997580i \(0.477852\pi\)
\(108\) −0.625336 + 0.563055i −0.0601730 + 0.0541800i
\(109\) −0.397371 3.78073i −0.0380612 0.362129i −0.996931 0.0782828i \(-0.975056\pi\)
0.958870 0.283846i \(-0.0916104\pi\)
\(110\) −1.90084 10.6448i −0.181238 1.01494i
\(111\) 15.9046 + 11.5554i 1.50960 + 1.09679i
\(112\) 11.4810 + 1.27570i 1.08485 + 0.120542i
\(113\) 7.52234 + 10.3536i 0.707643 + 0.973986i 0.999845 + 0.0176298i \(0.00561202\pi\)
−0.292202 + 0.956357i \(0.594388\pi\)
\(114\) −2.51321 + 23.9116i −0.235384 + 2.23953i
\(115\) −2.44488 + 9.89753i −0.227987 + 0.922950i
\(116\) −0.484732 4.61192i −0.0450062 0.428206i
\(117\) 2.27971 + 10.7252i 0.210760 + 0.991546i
\(118\) 21.5362i 1.98257i
\(119\) 4.13766 7.06932i 0.379299 0.648043i
\(120\) −1.68895 1.31365i −0.154179 0.119919i
\(121\) −3.23849 + 3.59670i −0.294408 + 0.326973i
\(122\) 3.50608 16.4948i 0.317426 1.49337i
\(123\) −5.10471 11.4654i −0.460276 1.03380i
\(124\) 5.66584 + 9.81351i 0.508807 + 0.881280i
\(125\) 4.48072 10.2432i 0.400768 0.916179i
\(126\) −14.1283 3.09090i −1.25865 0.275359i
\(127\) 5.72589 7.88102i 0.508091 0.699327i −0.475505 0.879713i \(-0.657735\pi\)
0.983596 + 0.180386i \(0.0577346\pi\)
\(128\) −2.34879 2.11486i −0.207605 0.186929i
\(129\) −13.6864 2.90913i −1.20502 0.256135i
\(130\) −15.7733 + 6.41275i −1.38341 + 0.562436i
\(131\) 17.4629 3.71185i 1.52574 0.324306i 0.632740 0.774365i \(-0.281930\pi\)
0.892999 + 0.450059i \(0.148597\pi\)
\(132\) 10.7415i 0.934929i
\(133\) 11.7749 6.70532i 1.02102 0.581425i
\(134\) 13.5147 9.81901i 1.16749 0.848233i
\(135\) −0.755130 0.726054i −0.0649913 0.0624888i
\(136\) −1.12323 + 0.500095i −0.0963163 + 0.0428828i
\(137\) −3.22091 + 0.338532i −0.275181 + 0.0289227i −0.241114 0.970497i \(-0.577513\pi\)
−0.0340673 + 0.999420i \(0.510846\pi\)
\(138\) 8.70586 19.5537i 0.741092 1.66452i
\(139\) 6.18949 + 4.49693i 0.524986 + 0.381424i 0.818479 0.574537i \(-0.194818\pi\)
−0.293493 + 0.955961i \(0.594818\pi\)
\(140\) 0.410842 10.6183i 0.0347225 0.897413i
\(141\) 4.24906 3.08712i 0.357836 0.259983i
\(142\) −5.72301 26.9246i −0.480264 2.25946i
\(143\) −8.40055 4.85006i −0.702489 0.405582i
\(144\) 8.19646 + 9.10310i 0.683039 + 0.758591i
\(145\) 5.68314 1.01484i 0.471959 0.0842778i
\(146\) 7.40689 + 22.7961i 0.612999 + 1.88662i
\(147\) 6.67661 + 15.4886i 0.550677 + 1.27748i
\(148\) 8.61411 11.8563i 0.708075 0.974582i
\(149\) 1.84866 + 3.20197i 0.151448 + 0.262315i 0.931760 0.363075i \(-0.118273\pi\)
−0.780312 + 0.625390i \(0.784940\pi\)
\(150\) −13.0411 + 19.5167i −1.06480 + 1.59354i
\(151\) 1.10361 1.91151i 0.0898105 0.155556i −0.817620 0.575758i \(-0.804707\pi\)
0.907431 + 0.420201i \(0.138041\pi\)
\(152\) −2.02281 0.212606i −0.164072 0.0172446i
\(153\) 8.26085 2.68411i 0.667850 0.216998i
\(154\) 10.3953 7.45870i 0.837679 0.601039i
\(155\) −11.6780 + 7.91389i −0.937997 + 0.635659i
\(156\) 16.5446 3.51665i 1.32462 0.281558i
\(157\) 20.8287 + 12.0255i 1.66231 + 0.959738i 0.971606 + 0.236605i \(0.0760347\pi\)
0.690709 + 0.723133i \(0.257299\pi\)
\(158\) 9.05510 8.15325i 0.720385 0.648638i
\(159\) −16.9169 7.53188i −1.34160 0.597317i
\(160\) −10.5880 + 13.6129i −0.837055 + 1.07620i
\(161\) −11.8140 + 2.43788i −0.931074 + 0.192132i
\(162\) 10.9318 + 15.0463i 0.858880 + 1.18215i
\(163\) 0.394267 0.885537i 0.0308813 0.0693606i −0.897446 0.441124i \(-0.854580\pi\)
0.928328 + 0.371763i \(0.121247\pi\)
\(164\) −8.54699 + 3.80536i −0.667408 + 0.297149i
\(165\) −13.3376 + 0.961805i −1.03833 + 0.0748764i
\(166\) 8.95715 + 3.98798i 0.695210 + 0.309527i
\(167\) 1.74340 + 0.566466i 0.134908 + 0.0438344i 0.375693 0.926744i \(-0.377405\pi\)
−0.240785 + 0.970579i \(0.577405\pi\)
\(168\) 0.541072 2.47321i 0.0417446 0.190812i
\(169\) −0.702803 + 2.16301i −0.0540618 + 0.166385i
\(170\) 6.35823 + 11.8956i 0.487654 + 0.912352i
\(171\) 14.0548 + 2.98744i 1.07480 + 0.228455i
\(172\) −2.16865 + 10.2027i −0.165358 + 0.777947i
\(173\) 7.79368 + 0.819149i 0.592543 + 0.0622788i 0.396054 0.918227i \(-0.370379\pi\)
0.196489 + 0.980506i \(0.437046\pi\)
\(174\) −12.1203 −0.918841
\(175\) 13.2214 0.440639i 0.999445 0.0333092i
\(176\) −10.8365 −0.816836
\(177\) −26.4871 2.78390i −1.99089 0.209251i
\(178\) −5.62806 + 26.4780i −0.421841 + 1.98461i
\(179\) −10.4544 2.22214i −0.781396 0.166091i −0.200092 0.979777i \(-0.564124\pi\)
−0.581304 + 0.813686i \(0.697457\pi\)
\(180\) 7.80988 8.12264i 0.582114 0.605426i
\(181\) −1.89456 + 5.83087i −0.140822 + 0.433405i −0.996450 0.0841859i \(-0.973171\pi\)
0.855628 + 0.517591i \(0.173171\pi\)
\(182\) −14.8915 13.5694i −1.10383 1.00583i
\(183\) −19.8335 6.44429i −1.46613 0.476375i
\(184\) 1.65415 + 0.736475i 0.121946 + 0.0542937i
\(185\) 15.4931 + 9.63438i 1.13908 + 0.708334i
\(186\) 27.0565 12.0463i 1.98388 0.883280i
\(187\) −3.12541 + 7.01978i −0.228553 + 0.513337i
\(188\) −2.30133 3.16751i −0.167842 0.231014i
\(189\) 0.390018 1.17653i 0.0283697 0.0855796i
\(190\) −0.730218 + 22.3010i −0.0529755 + 1.61789i
\(191\) 19.5821 + 8.71852i 1.41691 + 0.630850i 0.965247 0.261338i \(-0.0841637\pi\)
0.451665 + 0.892188i \(0.350830\pi\)
\(192\) 11.2713 10.1487i 0.813434 0.732420i
\(193\) −1.64900 0.952048i −0.118697 0.0685299i 0.439476 0.898254i \(-0.355164\pi\)
−0.558173 + 0.829724i \(0.688498\pi\)
\(194\) −8.63371 + 1.83515i −0.619865 + 0.131756i
\(195\) 5.84799 + 20.2282i 0.418783 + 1.44857i
\(196\) 11.5461 4.97715i 0.824723 0.355511i
\(197\) 3.23369 1.05069i 0.230391 0.0748586i −0.191546 0.981484i \(-0.561350\pi\)
0.421937 + 0.906625i \(0.361350\pi\)
\(198\) 13.4929 + 1.41816i 0.958895 + 0.100784i
\(199\) 4.13160 7.15614i 0.292881 0.507286i −0.681608 0.731717i \(-0.738719\pi\)
0.974490 + 0.224432i \(0.0720525\pi\)
\(200\) −1.65102 1.10321i −0.116745 0.0780089i
\(201\) −10.3292 17.8908i −0.728569 1.26192i
\(202\) 13.0573 17.9718i 0.918706 1.26449i
\(203\) 3.98212 + 5.54995i 0.279490 + 0.389530i
\(204\) −4.14047 12.7431i −0.289891 0.892192i
\(205\) −5.49037 10.2719i −0.383464 0.717423i
\(206\) −1.99255 2.21296i −0.138828 0.154184i
\(207\) −11.0778 6.39579i −0.769962 0.444538i
\(208\) 3.54777 + 16.6909i 0.245993 + 1.15731i
\(209\) −10.2838 + 7.47162i −0.711345 + 0.516823i
\(210\) −27.4884 3.96886i −1.89688 0.273877i
\(211\) −18.1583 13.1928i −1.25007 0.908228i −0.251842 0.967768i \(-0.581036\pi\)
−0.998226 + 0.0595406i \(0.981036\pi\)
\(212\) −5.61472 + 12.6109i −0.385621 + 0.866118i
\(213\) −33.8539 + 3.55819i −2.31963 + 0.243803i
\(214\) 16.1500 7.19046i 1.10399 0.491530i
\(215\) −12.8627 1.77922i −0.877228 0.121342i
\(216\) −0.150519 + 0.109359i −0.0102415 + 0.00744091i
\(217\) −14.4054 8.43148i −0.977905 0.572366i
\(218\) 7.40687i 0.501656i
\(219\) 28.9940 6.16285i 1.95923 0.416447i
\(220\) 0.716988 + 9.94265i 0.0483393 + 0.670333i
\(221\) 11.8354 + 2.51569i 0.796135 + 0.169224i
\(222\) −28.4651 25.6301i −1.91045 1.72018i
\(223\) 5.23518 7.20560i 0.350573 0.482523i −0.596919 0.802302i \(-0.703609\pi\)
0.947492 + 0.319779i \(0.103609\pi\)
\(224\) −19.9340 4.36104i −1.33190 0.291384i
\(225\) 10.7851 + 8.97010i 0.719004 + 0.598006i
\(226\) −12.4674 21.5942i −0.829322 1.43643i
\(227\) −5.11260 11.4831i −0.339335 0.762159i −0.999935 0.0114208i \(-0.996365\pi\)
0.660600 0.750738i \(-0.270302\pi\)
\(228\) 4.60838 21.6807i 0.305198 1.43584i
\(229\) −11.0658 + 12.2899i −0.731251 + 0.812137i −0.988018 0.154337i \(-0.950676\pi\)
0.256767 + 0.966473i \(0.417343\pi\)
\(230\) 6.75320 18.6806i 0.445293 1.23176i
\(231\) −7.82957 13.7492i −0.515148 0.904631i
\(232\) 1.02532i 0.0673158i
\(233\) 1.21215 + 5.70270i 0.0794104 + 0.373597i 0.999851 0.0172869i \(-0.00550286\pi\)
−0.920440 + 0.390884i \(0.872170\pi\)
\(234\) −2.23310 21.2466i −0.145983 1.38893i
\(235\) 3.72699 3.14115i 0.243122 0.204906i
\(236\) −2.07529 + 19.7451i −0.135090 + 1.28530i
\(237\) −8.85703 12.1907i −0.575326 0.791868i
\(238\) −9.45730 + 12.8556i −0.613025 + 0.833302i
\(239\) −3.29768 2.39590i −0.213309 0.154978i 0.476001 0.879445i \(-0.342086\pi\)
−0.689310 + 0.724467i \(0.742086\pi\)
\(240\) 16.9569 + 16.3040i 1.09456 + 1.05242i
\(241\) −2.37867 22.6315i −0.153224 1.45783i −0.753191 0.657801i \(-0.771487\pi\)
0.599968 0.800024i \(-0.295180\pi\)
\(242\) 7.00773 6.30979i 0.450474 0.405609i
\(243\) 18.7011 10.7971i 1.19968 0.692634i
\(244\) −4.80397 + 14.7851i −0.307542 + 0.946518i
\(245\) 7.21390 + 13.8910i 0.460879 + 0.887463i
\(246\) 7.55637 + 23.2561i 0.481776 + 1.48276i
\(247\) 14.8749 + 13.3934i 0.946468 + 0.852203i
\(248\) 1.01906 + 2.28885i 0.0647106 + 0.145342i
\(249\) 6.06260 10.5007i 0.384202 0.665457i
\(250\) −10.7684 + 18.9357i −0.681057 + 1.19760i
\(251\) 2.64599 0.167014 0.0835068 0.996507i \(-0.473388\pi\)
0.0835068 + 0.996507i \(0.473388\pi\)
\(252\) 12.6554 + 4.19527i 0.797217 + 0.264277i
\(253\) 10.7623 3.49689i 0.676621 0.219848i
\(254\) −12.7001 + 14.1049i −0.796877 + 0.885022i
\(255\) 15.4521 6.28218i 0.967649 0.393406i
\(256\) 12.5445 + 13.9321i 0.784033 + 0.870757i
\(257\) 1.72089 0.993558i 0.107346 0.0619765i −0.445366 0.895349i \(-0.646926\pi\)
0.552712 + 0.833372i \(0.313593\pi\)
\(258\) 25.9277 + 8.42441i 1.61419 + 0.524481i
\(259\) −2.38396 + 21.4550i −0.148132 + 1.33315i
\(260\) 15.0794 4.35945i 0.935182 0.270362i
\(261\) −0.757138 + 7.20369i −0.0468657 + 0.445897i
\(262\) −34.5938 + 3.63596i −2.13721 + 0.224630i
\(263\) 29.2703 3.07643i 1.80488 0.189701i 0.858514 0.512789i \(-0.171388\pi\)
0.946369 + 0.323089i \(0.104721\pi\)
\(264\) −0.248253 + 2.36197i −0.0152789 + 0.145369i
\(265\) −16.1615 5.84253i −0.992792 0.358904i
\(266\) −24.1820 + 10.5948i −1.48269 + 0.649610i
\(267\) 31.8373 + 10.3446i 1.94841 + 0.633077i
\(268\) −13.3369 + 7.70005i −0.814679 + 0.470355i
\(269\) −16.0029 17.7731i −0.975716 1.08364i −0.996478 0.0838581i \(-0.973276\pi\)
0.0207615 0.999784i \(-0.493391\pi\)
\(270\) 1.31535 + 1.56067i 0.0800496 + 0.0949792i
\(271\) 8.07573 8.96901i 0.490566 0.544829i −0.446132 0.894967i \(-0.647199\pi\)
0.936698 + 0.350139i \(0.113865\pi\)
\(272\) 12.8558 4.17710i 0.779497 0.253274i
\(273\) −18.6138 + 16.5608i −1.12656 + 1.00230i
\(274\) 6.31012 0.381208
\(275\) −12.2814 + 1.78055i −0.740598 + 0.107371i
\(276\) −9.86605 + 17.0885i −0.593866 + 1.02861i
\(277\) 7.59132 + 17.0504i 0.456118 + 1.02446i 0.984489 + 0.175444i \(0.0561362\pi\)
−0.528371 + 0.849013i \(0.677197\pi\)
\(278\) −11.0775 9.97426i −0.664387 0.598217i
\(279\) −5.46952 16.8335i −0.327452 1.00779i
\(280\) 0.335747 2.32539i 0.0200647 0.138968i
\(281\) 2.07291 6.37978i 0.123660 0.380585i −0.869995 0.493061i \(-0.835878\pi\)
0.993655 + 0.112475i \(0.0358780\pi\)
\(282\) −8.86214 + 5.11656i −0.527733 + 0.304687i
\(283\) 6.62608 5.96615i 0.393880 0.354651i −0.448267 0.893900i \(-0.647958\pi\)
0.842146 + 0.539249i \(0.181292\pi\)
\(284\) 2.65249 + 25.2368i 0.157397 + 1.49753i
\(285\) 27.3333 + 3.78085i 1.61908 + 0.223958i
\(286\) 15.2900 + 11.1088i 0.904116 + 0.656879i
\(287\) 8.16643 11.1008i 0.482049 0.655262i
\(288\) −12.7186 17.5056i −0.749448 1.03153i
\(289\) −0.775072 + 7.37431i −0.0455924 + 0.433783i
\(290\) −11.2189 + 0.809024i −0.658798 + 0.0475075i
\(291\) 1.14098 + 10.8557i 0.0668853 + 0.636371i
\(292\) −4.59417 21.6139i −0.268853 1.26486i
\(293\) 21.1628i 1.23634i 0.786043 + 0.618171i \(0.212126\pi\)
−0.786043 + 0.618171i \(0.787874\pi\)
\(294\) −9.78287 31.3720i −0.570548 1.82965i
\(295\) −24.7030 0.808866i −1.43826 0.0470940i
\(296\) 2.16819 2.40801i 0.126023 0.139963i
\(297\) −0.241751 + 1.13735i −0.0140278 + 0.0659956i
\(298\) −2.93003 6.58096i −0.169732 0.381225i
\(299\) −8.90952 15.4317i −0.515251 0.892441i
\(300\) 13.8371 16.6369i 0.798887 0.960530i
\(301\) −4.66093 14.6402i −0.268651 0.843848i
\(302\) −2.52777 + 3.47917i −0.145457 + 0.200204i
\(303\) −20.4153 18.3820i −1.17283 1.05602i
\(304\) 21.8725 + 4.64915i 1.25448 + 0.266647i
\(305\) −18.7886 4.64114i −1.07583 0.265751i
\(306\) −16.5537 + 3.51860i −0.946313 + 0.201145i
\(307\) 20.4087i 1.16479i 0.812907 + 0.582393i \(0.197884\pi\)
−0.812907 + 0.582393i \(0.802116\pi\)
\(308\) −10.2495 + 5.83664i −0.584019 + 0.332573i
\(309\) −2.97925 + 2.16455i −0.169483 + 0.123137i
\(310\) 24.2402 12.9564i 1.37675 0.735876i
\(311\) −2.62585 + 1.16910i −0.148898 + 0.0662937i −0.479833 0.877360i \(-0.659303\pi\)
0.330935 + 0.943654i \(0.392636\pi\)
\(312\) 3.71928 0.390912i 0.210563 0.0221310i
\(313\) −1.66346 + 3.73620i −0.0940244 + 0.211182i −0.954435 0.298419i \(-0.903541\pi\)
0.860410 + 0.509602i \(0.170207\pi\)
\(314\) −37.9108 27.5438i −2.13943 1.55439i
\(315\) −4.07603 + 16.0897i −0.229658 + 0.906551i
\(316\) −9.08766 + 6.60257i −0.511221 + 0.371424i
\(317\) −0.712202 3.35065i −0.0400012 0.188191i 0.953611 0.301043i \(-0.0973348\pi\)
−0.993612 + 0.112852i \(0.964001\pi\)
\(318\) 31.2459 + 18.0398i 1.75218 + 1.01162i
\(319\) −4.28772 4.76200i −0.240066 0.266621i
\(320\) 9.75559 10.1463i 0.545354 0.567194i
\(321\) −6.75577 20.7921i −0.377071 1.16050i
\(322\) 23.3885 2.31785i 1.30339 0.129169i
\(323\) 9.32001 12.8279i 0.518579 0.713763i
\(324\) −8.57267 14.8483i −0.476259 0.824905i
\(325\) 6.76328 + 18.3335i 0.375159 + 1.01696i
\(326\) −0.944320 + 1.63561i −0.0523011 + 0.0905881i
\(327\) 9.10958 + 0.957455i 0.503761 + 0.0529474i
\(328\) −1.96736 + 0.639233i −0.108629 + 0.0352957i
\(329\) 5.25454 + 2.37697i 0.289692 + 0.131047i
\(330\) 26.0401 + 0.852650i 1.43346 + 0.0469368i
\(331\) −26.3412 + 5.59900i −1.44784 + 0.307749i −0.863743 0.503932i \(-0.831886\pi\)
−0.584101 + 0.811681i \(0.698553\pi\)
\(332\) −7.82789 4.51944i −0.429612 0.248036i
\(333\) −17.0113 + 15.3171i −0.932215 + 0.839370i
\(334\) −3.26283 1.45270i −0.178534 0.0794885i
\(335\) −10.7552 15.8707i −0.587621 0.867111i
\(336\) −8.75809 + 26.4196i −0.477793 + 1.44131i
\(337\) 15.3283 + 21.0976i 0.834986 + 1.14926i 0.986974 + 0.160877i \(0.0514323\pi\)
−0.151988 + 0.988382i \(0.548568\pi\)
\(338\) 1.80234 4.04813i 0.0980345 0.220189i
\(339\) −28.1700 + 12.5421i −1.52998 + 0.681193i
\(340\) −4.68312 11.5190i −0.253978 0.624703i
\(341\) 14.3045 + 6.36877i 0.774632 + 0.344888i
\(342\) −26.6256 8.65119i −1.43975 0.467803i
\(343\) −11.1512 + 14.7868i −0.602109 + 0.798414i
\(344\) −0.712666 + 2.19336i −0.0384244 + 0.118258i
\(345\) −22.1019 10.7204i −1.18993 0.577167i
\(346\) −14.9350 3.17454i −0.802911 0.170664i
\(347\) −5.06067 + 23.8086i −0.271671 + 1.27811i 0.604691 + 0.796460i \(0.293297\pi\)
−0.876362 + 0.481652i \(0.840037\pi\)
\(348\) 11.1123 + 1.16795i 0.595682 + 0.0626087i
\(349\) 28.5904 1.53041 0.765206 0.643786i \(-0.222637\pi\)
0.765206 + 0.643786i \(0.222637\pi\)
\(350\) −25.7089 1.83886i −1.37420 0.0982910i
\(351\) 1.83094 0.0977282
\(352\) 19.0374 + 2.00092i 1.01470 + 0.106649i
\(353\) −0.362725 + 1.70649i −0.0193059 + 0.0908270i −0.986746 0.162274i \(-0.948117\pi\)
0.967440 + 0.253101i \(0.0814505\pi\)
\(354\) 50.7571 + 10.7888i 2.69771 + 0.573416i
\(355\) −31.0986 + 5.55329i −1.65054 + 0.294738i
\(356\) 7.71147 23.7335i 0.408707 1.25787i
\(357\) 14.5883 + 13.2932i 0.772096 + 0.703548i
\(358\) 19.8049 + 6.43500i 1.04672 + 0.340100i
\(359\) 9.94263 + 4.42674i 0.524752 + 0.233635i 0.651976 0.758239i \(-0.273940\pi\)
−0.127224 + 0.991874i \(0.540607\pi\)
\(360\) 1.90505 1.60560i 0.100405 0.0846226i
\(361\) 6.60502 2.94074i 0.347633 0.154776i
\(362\) 4.85862 10.9126i 0.255363 0.573556i
\(363\) −6.85444 9.43433i −0.359765 0.495174i
\(364\) 12.3454 + 13.8759i 0.647076 + 0.727293i
\(365\) 26.4262 7.63983i 1.38321 0.399887i
\(366\) 37.1189 + 16.5264i 1.94024 + 0.863849i
\(367\) 9.26076 8.33843i 0.483408 0.435262i −0.391046 0.920371i \(-0.627887\pi\)
0.874454 + 0.485109i \(0.161220\pi\)
\(368\) −17.2397 9.95333i −0.898680 0.518853i
\(369\) 14.2942 3.03833i 0.744128 0.158169i
\(370\) −28.0589 21.8239i −1.45871 1.13457i
\(371\) −2.00528 20.2346i −0.104109 1.05053i
\(372\) −25.9670 + 8.43721i −1.34633 + 0.437449i
\(373\) 12.9487 + 1.36096i 0.670459 + 0.0704680i 0.433641 0.901086i \(-0.357229\pi\)
0.236818 + 0.971554i \(0.423895\pi\)
\(374\) 7.48577 12.9657i 0.387080 0.670442i
\(375\) 21.8967 + 15.6917i 1.13074 + 0.810315i
\(376\) −0.432837 0.749696i −0.0223219 0.0386626i
\(377\) −5.93088 + 8.16316i −0.305456 + 0.420424i
\(378\) −0.995352 + 2.20033i −0.0511954 + 0.113173i
\(379\) 2.26229 + 6.96260i 0.116206 + 0.357645i 0.992197 0.124683i \(-0.0397914\pi\)
−0.875991 + 0.482328i \(0.839791\pi\)
\(380\) 2.81847 20.3759i 0.144585 1.04526i
\(381\) 15.7057 + 17.4430i 0.804628 + 0.893630i
\(382\) −36.1687 20.8820i −1.85055 1.06842i
\(383\) 1.43254 + 6.73956i 0.0731993 + 0.344375i 0.999472 0.0324772i \(-0.0103396\pi\)
−0.926273 + 0.376853i \(0.877006\pi\)
\(384\) 6.16098 4.47622i 0.314401 0.228426i
\(385\) −8.16502 12.2040i −0.416128 0.621974i
\(386\) 3.00137 + 2.18062i 0.152766 + 0.110991i
\(387\) 6.62668 14.8838i 0.336853 0.756585i
\(388\) 8.09249 0.850555i 0.410834 0.0431804i
\(389\) 9.15883 4.07778i 0.464371 0.206751i −0.161195 0.986923i \(-0.551535\pi\)
0.625566 + 0.780171i \(0.284868\pi\)
\(390\) −7.21197 40.3873i −0.365192 2.04509i
\(391\) −11.4198 + 8.29697i −0.577524 + 0.419596i
\(392\) 2.65392 0.827584i 0.134043 0.0417993i
\(393\) 43.0164i 2.16989i
\(394\) −6.47992 + 1.37735i −0.326454 + 0.0693898i
\(395\) −9.01203 10.6928i −0.453445 0.538014i
\(396\) −12.2340 2.60042i −0.614782 0.130676i
\(397\) −8.25028 7.42859i −0.414070 0.372830i 0.435604 0.900138i \(-0.356535\pi\)
−0.849674 + 0.527308i \(0.823201\pi\)
\(398\) −9.46324 + 13.0250i −0.474349 + 0.652886i
\(399\) 9.90449 + 31.1105i 0.495845 + 1.55747i
\(400\) 16.7841 + 13.9596i 0.839203 + 0.697978i
\(401\) 3.57303 + 6.18867i 0.178429 + 0.309048i 0.941343 0.337453i \(-0.109565\pi\)
−0.762914 + 0.646500i \(0.776232\pi\)
\(402\) 16.3714 + 36.7707i 0.816529 + 1.83395i
\(403\) 5.12633 24.1175i 0.255361 1.20138i
\(404\) −13.7031 + 15.2188i −0.681755 + 0.757165i
\(405\) 17.6693 11.9741i 0.877994 0.594997i
\(406\) −6.58586 11.5652i −0.326851 0.573969i
\(407\) 20.2507i 1.00379i
\(408\) −0.615942 2.89778i −0.0304937 0.143462i
\(409\) 0.409804 + 3.89903i 0.0202635 + 0.192795i 0.999971 0.00763899i \(-0.00243159\pi\)
−0.979707 + 0.200434i \(0.935765\pi\)
\(410\) 8.54671 + 21.0221i 0.422092 + 1.03821i
\(411\) 0.815683 7.76071i 0.0402347 0.382808i
\(412\) 1.61359 + 2.22091i 0.0794957 + 0.109416i
\(413\) −11.7359 26.7865i −0.577488 1.31808i
\(414\) 20.1630 + 14.6493i 0.990956 + 0.719972i
\(415\) 4.91080 10.1245i 0.241062 0.496990i
\(416\) −3.15075 29.9774i −0.154478 1.46976i
\(417\) −13.6991 + 12.3347i −0.670849 + 0.604035i
\(418\) 21.4486 12.3834i 1.04909 0.605690i
\(419\) −7.25128 + 22.3171i −0.354248 + 1.09026i 0.602196 + 0.798348i \(0.294293\pi\)
−0.956444 + 0.291915i \(0.905707\pi\)
\(420\) 24.8197 + 6.28762i 1.21108 + 0.306805i
\(421\) −10.2298 31.4841i −0.498571 1.53444i −0.811317 0.584606i \(-0.801249\pi\)
0.312746 0.949837i \(-0.398751\pi\)
\(422\) 32.4985 + 29.2618i 1.58200 + 1.42444i
\(423\) 2.48741 + 5.58681i 0.120942 + 0.271640i
\(424\) −1.52609 + 2.64326i −0.0741133 + 0.128368i
\(425\) 13.8836 6.84638i 0.673452 0.332098i
\(426\) 66.3235 3.21339
\(427\) −4.62786 22.4266i −0.223958 1.08530i
\(428\) −15.4997 + 5.03617i −0.749208 + 0.243432i
\(429\) 15.6390 17.3689i 0.755060 0.838579i
\(430\) 24.5617 + 6.06722i 1.18447 + 0.292587i
\(431\) −13.8289 15.3585i −0.666113 0.739793i 0.311490 0.950249i \(-0.399172\pi\)
−0.977603 + 0.210456i \(0.932505\pi\)
\(432\) 1.77141 1.02272i 0.0852269 0.0492058i
\(433\) −25.2950 8.21886i −1.21560 0.394973i −0.370124 0.928982i \(-0.620685\pi\)
−0.845479 + 0.534009i \(0.820685\pi\)
\(434\) 26.1963 + 19.2715i 1.25746 + 0.925063i
\(435\) −0.455220 + 13.9026i −0.0218261 + 0.666576i
\(436\) 0.713746 6.79084i 0.0341822 0.325222i
\(437\) −23.2230 + 2.44083i −1.11091 + 0.116761i
\(438\) −57.4368 + 6.03685i −2.74444 + 0.288452i
\(439\) −1.23134 + 11.7154i −0.0587687 + 0.559147i 0.925033 + 0.379887i \(0.124037\pi\)
−0.983802 + 0.179260i \(0.942630\pi\)
\(440\) −0.0721301 + 2.20287i −0.00343867 + 0.105018i
\(441\) −19.2570 + 3.85466i −0.916998 + 0.183555i
\(442\) −22.4211 7.28507i −1.06646 0.346515i
\(443\) −0.871479 + 0.503149i −0.0414052 + 0.0239053i −0.520560 0.853825i \(-0.674277\pi\)
0.479154 + 0.877731i \(0.340943\pi\)
\(444\) 23.6279 + 26.2414i 1.12133 + 1.24536i
\(445\) 30.1600 + 7.45010i 1.42972 + 0.353168i
\(446\) −11.6117 + 12.8961i −0.549831 + 0.610649i
\(447\) −8.47257 + 2.75290i −0.400739 + 0.130208i
\(448\) 15.8083 + 5.24046i 0.746873 + 0.247589i
\(449\) 29.0408 1.37052 0.685261 0.728298i \(-0.259688\pi\)
0.685261 + 0.728298i \(0.259688\pi\)
\(450\) −19.0714 19.5779i −0.899034 0.922910i
\(451\) −6.46400 + 11.1960i −0.304378 + 0.527198i
\(452\) 9.34965 + 20.9996i 0.439770 + 0.987740i
\(453\) 3.95222 + 3.55860i 0.185692 + 0.167198i
\(454\) 7.56804 + 23.2920i 0.355186 + 1.09315i
\(455\) −16.1240 + 16.5716i −0.755906 + 0.776887i
\(456\) 1.51442 4.66090i 0.0709191 0.218267i
\(457\) 11.1386 6.43087i 0.521041 0.300823i −0.216319 0.976323i \(-0.569405\pi\)
0.737361 + 0.675499i \(0.236072\pi\)
\(458\) 23.9453 21.5604i 1.11889 1.00745i
\(459\) −0.151609 1.44246i −0.00707650 0.0673284i
\(460\) −7.99164 + 16.4761i −0.372612 + 0.768204i
\(461\) −9.56290 6.94785i −0.445389 0.323594i 0.342384 0.939560i \(-0.388766\pi\)
−0.787772 + 0.615966i \(0.788766\pi\)
\(462\) 12.3712 + 28.2364i 0.575561 + 1.31368i
\(463\) −20.4731 28.1788i −0.951465 1.30958i −0.950873 0.309580i \(-0.899812\pi\)
−0.000592125 1.00000i \(-0.500188\pi\)
\(464\) −1.17828 + 11.2106i −0.0547004 + 0.520439i
\(465\) −12.8015 31.4874i −0.593654 1.46019i
\(466\) −1.18736 11.2970i −0.0550036 0.523324i
\(467\) 4.91443 + 23.1206i 0.227412 + 1.06989i 0.932611 + 0.360882i \(0.117524\pi\)
−0.705199 + 0.709010i \(0.749142\pi\)
\(468\) 19.6947i 0.910387i
\(469\) 11.4586 19.5774i 0.529111 0.904002i
\(470\) −7.86152 + 5.32757i −0.362625 + 0.245743i
\(471\) −38.7762 + 43.0654i −1.78671 + 1.98435i
\(472\) −0.912678 + 4.29381i −0.0420094 + 0.197639i
\(473\) 5.86235 + 13.1670i 0.269551 + 0.605421i
\(474\) 14.6795 + 25.4257i 0.674253 + 1.16784i
\(475\) 25.5528 + 1.67518i 1.17244 + 0.0768626i
\(476\) 9.90953 10.8750i 0.454203 0.498456i
\(477\) 12.6738 17.4440i 0.580294 0.798706i
\(478\) 5.90197 + 5.31416i 0.269950 + 0.243064i
\(479\) 9.90164 + 2.10466i 0.452418 + 0.0961643i 0.428484 0.903549i \(-0.359048\pi\)
0.0239333 + 0.999714i \(0.492381\pi\)
\(480\) −26.7791 31.7735i −1.22229 1.45026i
\(481\) −31.1910 + 6.62985i −1.42219 + 0.302295i
\(482\) 44.3376i 2.01952i
\(483\) 0.172661 29.0648i 0.00785636 1.32249i
\(484\) −7.03293 + 5.10972i −0.319678 + 0.232260i
\(485\) 1.78073 + 9.97216i 0.0808588 + 0.452813i
\(486\) −38.4361 + 17.1129i −1.74350 + 0.776256i
\(487\) −11.8899 + 1.24968i −0.538783 + 0.0566284i −0.370012 0.929027i \(-0.620646\pi\)
−0.168771 + 0.985655i \(0.553980\pi\)
\(488\) −1.39806 + 3.14009i −0.0632870 + 0.142145i
\(489\) 1.88954 + 1.37283i 0.0854480 + 0.0620816i
\(490\) −11.1494 28.3858i −0.503676 1.28234i
\(491\) 0.443578 0.322278i 0.0200184 0.0145442i −0.577731 0.816227i \(-0.696062\pi\)
0.597749 + 0.801683i \(0.296062\pi\)
\(492\) −4.68688 22.0501i −0.211301 0.994093i
\(493\) 6.92226 + 3.99657i 0.311763 + 0.179996i
\(494\) −26.0954 28.9819i −1.17409 1.30396i
\(495\) 2.13345 15.4236i 0.0958917 0.693240i
\(496\) −8.51185 26.1968i −0.382193 1.17627i
\(497\) −21.7905 30.3698i −0.977437 1.36227i
\(498\) −13.8861 + 19.1126i −0.622252 + 0.856456i
\(499\) −20.0243 34.6832i −0.896412 1.55263i −0.832047 0.554705i \(-0.812831\pi\)
−0.0643647 0.997926i \(-0.520502\pi\)
\(500\) 11.6975 16.3232i 0.523130 0.729994i
\(501\) −2.20843 + 3.82511i −0.0986654 + 0.170893i
\(502\) −5.12715 0.538885i −0.228836 0.0240516i
\(503\) −11.8433 + 3.84812i −0.528066 + 0.171579i −0.560903 0.827882i \(-0.689546\pi\)
0.0328365 + 0.999461i \(0.489546\pi\)
\(504\) 2.68586 + 1.21499i 0.119638 + 0.0541200i
\(505\) −20.1240 15.6522i −0.895505 0.696515i
\(506\) −21.5664 + 4.58407i −0.958741 + 0.203787i
\(507\) −4.74574 2.73996i −0.210766 0.121686i
\(508\) 13.0031 11.7080i 0.576917 0.519459i
\(509\) 11.7881 + 5.24840i 0.522498 + 0.232631i 0.651000 0.759078i \(-0.274350\pi\)
−0.128501 + 0.991709i \(0.541017\pi\)
\(510\) −31.2210 + 9.02601i −1.38249 + 0.399679i
\(511\) 21.6351 + 24.3171i 0.957079 + 1.07573i
\(512\) −17.7546 24.4372i −0.784652 1.07998i
\(513\) 0.975901 2.19191i 0.0430871 0.0967752i
\(514\) −3.53693 + 1.57474i −0.156007 + 0.0694589i
\(515\) −2.61319 + 2.20243i −0.115151 + 0.0970506i
\(516\) −22.9595 10.2222i −1.01073 0.450008i
\(517\) −5.14536 1.67183i −0.226292 0.0735269i
\(518\) 8.98894 41.0879i 0.394951 1.80530i
\(519\) −5.83490 + 17.9580i −0.256124 + 0.788267i
\(520\) 3.41658 0.610098i 0.149827 0.0267546i
\(521\) 38.3716 + 8.15613i 1.68109 + 0.357327i 0.946878 0.321594i \(-0.104219\pi\)
0.734212 + 0.678921i \(0.237552\pi\)
\(522\) 2.93422 13.8044i 0.128427 0.604202i
\(523\) 7.66514 + 0.805639i 0.335173 + 0.0352281i 0.270620 0.962686i \(-0.412771\pi\)
0.0645529 + 0.997914i \(0.479438\pi\)
\(524\) 32.0670 1.40085
\(525\) −5.58487 + 31.3813i −0.243744 + 1.36959i
\(526\) −57.3437 −2.50030
\(527\) −19.4249 2.04164i −0.846161 0.0889351i
\(528\) 5.42866 25.5398i 0.236252 1.11148i
\(529\) −2.16393 0.459958i −0.0940841 0.0199982i
\(530\) 30.1262 + 14.6125i 1.30860 + 0.634728i
\(531\) 9.58297 29.4934i 0.415866 1.27990i
\(532\) 23.1917 7.38341i 1.00549 0.320112i
\(533\) 19.3608 + 6.29070i 0.838608 + 0.272480i
\(534\) −59.5844 26.5287i −2.57847 1.14801i
\(535\) −7.64119 18.7948i −0.330358 0.812572i
\(536\) −3.11062 + 1.38494i −0.134359 + 0.0598203i
\(537\) 10.4744 23.5259i 0.452003 1.01522i
\(538\) 27.3893 + 37.6981i 1.18083 + 1.62528i
\(539\) 8.86503 14.9419i 0.381844 0.643591i
\(540\) −1.05556 1.55762i −0.0454241 0.0670292i
\(541\) 17.4699 + 7.77812i 0.751091 + 0.334407i 0.746325 0.665581i \(-0.231816\pi\)
0.00476580 + 0.999989i \(0.498483\pi\)
\(542\) −17.4750 + 15.7346i −0.750616 + 0.675858i
\(543\) −12.7932 7.38617i −0.549009 0.316971i
\(544\) −23.3561 + 4.96449i −1.00138 + 0.212851i
\(545\) 8.49599 + 0.278190i 0.363928 + 0.0119163i
\(546\) 39.4408 28.2990i 1.68791 1.21108i
\(547\) −17.8957 + 5.81466i −0.765164 + 0.248617i −0.665494 0.746404i \(-0.731779\pi\)
−0.0996705 + 0.995020i \(0.531779\pi\)
\(548\) −5.78531 0.608060i −0.247136 0.0259751i
\(549\) 12.1412 21.0291i 0.518173 0.897501i
\(550\) 24.1604 0.948924i 1.03020 0.0404623i
\(551\) 6.61134 + 11.4512i 0.281653 + 0.487837i
\(552\) −2.56440 + 3.52959i −0.109148 + 0.150229i
\(553\) 6.81959 15.0754i 0.289998 0.641071i
\(554\) −11.2372 34.5846i −0.477424 1.46936i
\(555\) −30.4679 + 31.6881i −1.29329 + 1.34508i
\(556\) 9.19508 + 10.2122i 0.389958 + 0.433092i
\(557\) 2.99630 + 1.72991i 0.126957 + 0.0732988i 0.562134 0.827046i \(-0.309981\pi\)
−0.435176 + 0.900345i \(0.643314\pi\)
\(558\) 7.17000 + 33.7322i 0.303530 + 1.42800i
\(559\) 18.3612 13.3402i 0.776596 0.564230i
\(560\) −6.34325 + 25.0393i −0.268051 + 1.05810i
\(561\) −14.9787 10.8826i −0.632400 0.459466i
\(562\) −5.31600 + 11.9399i −0.224242 + 0.503656i
\(563\) −31.8022 + 3.34255i −1.34030 + 0.140872i −0.747385 0.664391i \(-0.768691\pi\)
−0.592918 + 0.805263i \(0.702024\pi\)
\(564\) 8.61813 3.83704i 0.362889 0.161568i
\(565\) −25.2378 + 13.4896i −1.06176 + 0.567513i
\(566\) −14.0545 + 10.2112i −0.590753 + 0.429207i
\(567\) 21.7961 + 12.7572i 0.915349 + 0.535752i
\(568\) 5.61066i 0.235418i
\(569\) 0.855097 0.181756i 0.0358475 0.00761963i −0.189953 0.981793i \(-0.560834\pi\)
0.225801 + 0.974174i \(0.427500\pi\)
\(570\) −52.1938 12.8929i −2.18616 0.540023i
\(571\) 7.16292 + 1.52253i 0.299759 + 0.0637158i 0.355336 0.934739i \(-0.384366\pi\)
−0.0555769 + 0.998454i \(0.517700\pi\)
\(572\) −12.9479 11.6583i −0.541377 0.487458i
\(573\) −30.3578 + 41.7839i −1.26822 + 1.74555i
\(574\) −18.0849 + 19.8470i −0.754850 + 0.828396i
\(575\) −21.1737 8.44781i −0.883006 0.352298i
\(576\) 8.83015 + 15.2943i 0.367923 + 0.637261i
\(577\) −9.30611 20.9019i −0.387418 0.870156i −0.996998 0.0774306i \(-0.975328\pi\)
0.609580 0.792725i \(-0.291338\pi\)
\(578\) 3.00372 14.1314i 0.124938 0.587788i
\(579\) 3.06988 3.40945i 0.127580 0.141692i
\(580\) 10.3638 + 0.339349i 0.430334 + 0.0140907i
\(581\) 13.3140 + 0.0790927i 0.552357 + 0.00328132i
\(582\) 21.2675i 0.881564i
\(583\) 3.96591 + 18.6581i 0.164251 + 0.772741i
\(584\) −0.510689 4.85888i −0.0211325 0.201062i
\(585\) −24.4546 + 1.76348i −1.01107 + 0.0729109i
\(586\) 4.31003 41.0072i 0.178046 1.69399i
\(587\) 15.5422 + 21.3920i 0.641496 + 0.882943i 0.998694 0.0510854i \(-0.0162681\pi\)
−0.357199 + 0.934028i \(0.616268\pi\)
\(588\) 5.94614 + 29.7055i 0.245214 + 1.22503i
\(589\) −26.1399 18.9918i −1.07708 0.782542i
\(590\) 47.7023 + 6.59837i 1.96387 + 0.271651i
\(591\) 0.856346 + 8.14759i 0.0352254 + 0.335147i
\(592\) −26.4736 + 23.8369i −1.08806 + 0.979691i
\(593\) 7.97900 4.60668i 0.327658 0.189174i −0.327143 0.944975i \(-0.606086\pi\)
0.654801 + 0.755801i \(0.272752\pi\)
\(594\) 0.700074 2.15461i 0.0287244 0.0884045i
\(595\) 14.3907 + 11.3308i 0.589960 + 0.464516i
\(596\) 2.05218 + 6.31597i 0.0840607 + 0.258712i
\(597\) 14.7960 + 13.3224i 0.605560 + 0.545248i
\(598\) 14.1212 + 31.7167i 0.577457 + 1.29699i
\(599\) −6.03999 + 10.4616i −0.246787 + 0.427448i −0.962633 0.270811i \(-0.912708\pi\)
0.715845 + 0.698259i \(0.246042\pi\)
\(600\) 3.42717 3.33851i 0.139914 0.136294i
\(601\) −18.7934 −0.766597 −0.383299 0.923624i \(-0.625212\pi\)
−0.383299 + 0.923624i \(0.625212\pi\)
\(602\) 6.04985 + 29.3176i 0.246574 + 1.19490i
\(603\) 22.8772 7.43326i 0.931632 0.302706i
\(604\) 2.65280 2.94623i 0.107941 0.119880i
\(605\) −6.97440 8.27515i −0.283549 0.336433i
\(606\) 35.8151 + 39.7767i 1.45489 + 1.61582i
\(607\) −3.61582 + 2.08760i −0.146762 + 0.0847329i −0.571583 0.820544i \(-0.693670\pi\)
0.424821 + 0.905277i \(0.360337\pi\)
\(608\) −37.5668 12.2062i −1.52354 0.495027i
\(609\) −15.0751 + 6.60485i −0.610875 + 0.267642i
\(610\) 35.4614 + 12.8196i 1.43579 + 0.519052i
\(611\) −0.890489 + 8.47244i −0.0360253 + 0.342758i
\(612\) 15.5160 1.63080i 0.627197 0.0659211i
\(613\) 22.1605 2.32916i 0.895054 0.0940740i 0.354180 0.935177i \(-0.384760\pi\)
0.540874 + 0.841103i \(0.318093\pi\)
\(614\) 4.15645 39.5460i 0.167741 1.59595i
\(615\) 26.9595 7.79401i 1.08711 0.314285i
\(616\) −2.38867 + 1.04655i −0.0962422 + 0.0421665i
\(617\) 25.9217 + 8.42248i 1.04357 + 0.339076i 0.780142 0.625603i \(-0.215147\pi\)
0.263428 + 0.964679i \(0.415147\pi\)
\(618\) 6.21373 3.58750i 0.249953 0.144310i
\(619\) −12.7084 14.1141i −0.510792 0.567292i 0.431488 0.902119i \(-0.357989\pi\)
−0.942280 + 0.334827i \(0.891322\pi\)
\(620\) −23.4726 + 9.54299i −0.942684 + 0.383256i
\(621\) −1.42925 + 1.58734i −0.0573537 + 0.0636977i
\(622\) 5.32621 1.73059i 0.213562 0.0693904i
\(623\) 7.42877 + 35.9999i 0.297627 + 1.44230i
\(624\) −41.1148 −1.64591
\(625\) 21.3156 + 13.0631i 0.852625 + 0.522523i
\(626\) 3.98421 6.90086i 0.159241 0.275814i
\(627\) −12.4575 27.9800i −0.497505 1.11742i
\(628\) 32.1036 + 28.9062i 1.28107 + 1.15348i
\(629\) 7.80592 + 24.0242i 0.311242 + 0.957906i
\(630\) 11.1750 30.3469i 0.445222 1.20905i
\(631\) −10.1285 + 31.1724i −0.403210 + 1.24095i 0.519170 + 0.854671i \(0.326241\pi\)
−0.922380 + 0.386283i \(0.873759\pi\)
\(632\) −2.15089 + 1.24182i −0.0855580 + 0.0493969i
\(633\) 40.1895 36.1868i 1.59739 1.43830i
\(634\) 0.697640 + 6.63760i 0.0277068 + 0.263613i
\(635\) 15.7020 + 15.0974i 0.623113 + 0.599120i
\(636\) −26.9088 19.5504i −1.06700 0.775224i
\(637\) −25.9164 8.76251i −1.02685 0.347183i
\(638\) 7.33850 + 10.1006i 0.290534 + 0.399886i
\(639\) 4.14312 39.4192i 0.163899 1.55940i
\(640\) 5.40399 4.55455i 0.213612 0.180034i
\(641\) −4.10837 39.0885i −0.162271 1.54390i −0.708163 0.706049i \(-0.750476\pi\)
0.545892 0.837855i \(-0.316191\pi\)
\(642\) 8.85614 + 41.6649i 0.349524 + 1.64438i
\(643\) 28.8706i 1.13854i −0.822149 0.569272i \(-0.807225\pi\)
0.822149 0.569272i \(-0.192775\pi\)
\(644\) −21.6667 0.128712i −0.853786 0.00507198i
\(645\) 10.6370 29.4237i 0.418830 1.15856i
\(646\) −20.6719 + 22.9585i −0.813327 + 0.903291i
\(647\) −1.08427 + 5.10109i −0.0426271 + 0.200545i −0.994308 0.106544i \(-0.966021\pi\)
0.951681 + 0.307089i \(0.0993548\pi\)
\(648\) −1.54189 3.46314i −0.0605711 0.136045i
\(649\) 13.7171 + 23.7588i 0.538444 + 0.932613i
\(650\) −9.37142 36.9022i −0.367577 1.44742i
\(651\) 27.0880 29.7272i 1.06166 1.16510i
\(652\) 1.02339 1.40858i 0.0400792 0.0551643i
\(653\) 17.1943 + 15.4818i 0.672864 + 0.605849i 0.933066 0.359705i \(-0.117123\pi\)
−0.260202 + 0.965554i \(0.583789\pi\)
\(654\) −17.4567 3.71053i −0.682609 0.145093i
\(655\) 2.87131 + 39.8171i 0.112191 + 1.55578i
\(656\) 22.2451 4.72835i 0.868527 0.184611i
\(657\) 34.5145i 1.34654i
\(658\) −9.69763 5.67601i −0.378053 0.221274i
\(659\) 2.56376 1.86268i 0.0998698 0.0725596i −0.536730 0.843754i \(-0.680340\pi\)
0.636599 + 0.771195i \(0.280340\pi\)
\(660\) −23.7922 3.29103i −0.926111 0.128103i
\(661\) 7.09726 3.15991i 0.276052 0.122906i −0.264042 0.964511i \(-0.585056\pi\)
0.540093 + 0.841605i \(0.318389\pi\)
\(662\) 52.1817 5.48452i 2.02810 0.213162i
\(663\) −11.8581 + 26.6337i −0.460529 + 1.03437i
\(664\) −1.61684 1.17470i −0.0627454 0.0455872i
\(665\) 11.2445 + 28.1357i 0.436042 + 1.09105i
\(666\) 36.0824 26.2154i 1.39816 1.01583i
\(667\) −2.44738 11.5140i −0.0947631 0.445825i
\(668\) 2.85147 + 1.64630i 0.110327 + 0.0636972i
\(669\) 14.3597 + 15.9481i 0.555179 + 0.616588i
\(670\) 17.6082 + 32.9432i 0.680264 + 1.27271i
\(671\) 6.63817 + 20.4302i 0.256264 + 0.788699i
\(672\) 20.2643 44.7963i 0.781712 1.72805i
\(673\) −1.93901 + 2.66881i −0.0747432 + 0.102875i −0.844752 0.535158i \(-0.820252\pi\)
0.770009 + 0.638034i \(0.220252\pi\)
\(674\) −25.4049 44.0027i −0.978562 1.69492i
\(675\) 1.83955 1.45015i 0.0708045 0.0558161i
\(676\) −2.04253 + 3.53777i −0.0785589 + 0.136068i
\(677\) −16.2618 1.70919i −0.624993 0.0656894i −0.213262 0.976995i \(-0.568409\pi\)
−0.411730 + 0.911306i \(0.635075\pi\)
\(678\) 57.1394 18.5657i 2.19443 0.713012i
\(679\) −9.73845 + 6.98739i −0.373727 + 0.268151i
\(680\) −0.763558 2.64115i −0.0292811 0.101284i
\(681\) 29.6248 6.29694i 1.13522 0.241299i
\(682\) −26.4208 15.2541i −1.01170 0.584108i
\(683\) −29.0960 + 26.1981i −1.11333 + 1.00244i −0.113366 + 0.993553i \(0.536163\pi\)
−0.999960 + 0.00889049i \(0.997170\pi\)
\(684\) 23.5775 + 10.4974i 0.901509 + 0.401378i
\(685\) 0.236998 7.23797i 0.00905522 0.276549i
\(686\) 24.6192 26.3814i 0.939967 1.00725i
\(687\) −23.4215 32.2369i −0.893585 1.22991i
\(688\) 10.3127 23.1626i 0.393166 0.883066i
\(689\) 27.4397 12.2169i 1.04537 0.465428i
\(690\) 40.6437 + 25.2742i 1.54728 + 0.962174i
\(691\) 32.7326 + 14.5735i 1.24521 + 0.554402i 0.920252 0.391327i \(-0.127984\pi\)
0.324956 + 0.945729i \(0.394650\pi\)
\(692\) 13.3870 + 4.34969i 0.508896 + 0.165350i
\(693\) 17.5550 5.58890i 0.666861 0.212305i
\(694\) 14.6550 45.1033i 0.556295 1.71210i
\(695\) −11.8570 + 12.3318i −0.449760 + 0.467772i
\(696\) 2.41651 + 0.513644i 0.0915974 + 0.0194696i
\(697\) 3.35283 15.7738i 0.126998 0.597477i
\(698\) −55.3998 5.82275i −2.09691 0.220394i
\(699\) −14.0475 −0.531325
\(700\) 23.3935 + 4.16330i 0.884192 + 0.157358i
\(701\) 4.06365 0.153482 0.0767409 0.997051i \(-0.475549\pi\)
0.0767409 + 0.997051i \(0.475549\pi\)
\(702\) −3.54781 0.372890i −0.133904 0.0140738i
\(703\) −8.68806 + 40.8741i −0.327677 + 1.54160i
\(704\) −15.2819 3.24827i −0.575959 0.122424i
\(705\) 5.53607 + 10.3574i 0.208500 + 0.390083i
\(706\) 1.05040 3.23279i 0.0395322 0.121668i
\(707\) 6.44692 29.4685i 0.242461 1.10828i
\(708\) −45.4960 14.7825i −1.70984 0.555562i
\(709\) 27.1377 + 12.0825i 1.01918 + 0.453767i 0.847166 0.531328i \(-0.178307\pi\)
0.172011 + 0.985095i \(0.444974\pi\)
\(710\) 61.3909 4.42705i 2.30396 0.166144i
\(711\) 16.0287 7.13643i 0.601123 0.267637i
\(712\) 2.24420 5.04056i 0.0841050 0.188903i
\(713\) 16.9071 + 23.2706i 0.633175 + 0.871491i
\(714\) −25.5605 28.7293i −0.956579 1.07517i
\(715\) 13.3166 17.1210i 0.498011 0.640291i
\(716\) −17.5376 7.80825i −0.655412 0.291808i
\(717\) 7.29872 6.57179i 0.272576 0.245428i
\(718\) −18.3643 10.6026i −0.685350 0.395687i
\(719\) −12.2332 + 2.60025i −0.456222 + 0.0969730i −0.430290 0.902691i \(-0.641589\pi\)
−0.0259321 + 0.999664i \(0.508255\pi\)
\(720\) −22.6744 + 15.3659i −0.845026 + 0.572655i
\(721\) −3.68424 1.66662i −0.137208 0.0620683i
\(722\) −13.3975 + 4.35310i −0.498603 + 0.162006i
\(723\) 54.5301 + 5.73135i 2.02800 + 0.213151i
\(724\) −5.50610 + 9.53685i −0.204633 + 0.354434i
\(725\) 0.506620 + 12.8990i 0.0188154 + 0.479056i
\(726\) 11.3605 + 19.6769i 0.421626 + 0.730278i
\(727\) 21.7358 29.9167i 0.806135 1.10955i −0.185773 0.982593i \(-0.559479\pi\)
0.991908 0.126957i \(-0.0405211\pi\)
\(728\) 2.39396 + 3.33650i 0.0887260 + 0.123659i
\(729\) 7.22919 + 22.2491i 0.267748 + 0.824043i
\(730\) −52.7621 + 9.42174i −1.95281 + 0.348714i
\(731\) −12.0301 13.3608i −0.444951 0.494168i
\(732\) −32.4392 18.7288i −1.19899 0.692236i
\(733\) −6.77300 31.8644i −0.250166 1.17694i −0.906413 0.422393i \(-0.861190\pi\)
0.656246 0.754547i \(-0.272143\pi\)
\(734\) −19.6428 + 14.2713i −0.725030 + 0.526765i
\(735\) −36.3524 + 10.0431i −1.34088 + 0.370445i
\(736\) 28.4485 + 20.6690i 1.04863 + 0.761871i
\(737\) −8.65537 + 19.4403i −0.318825 + 0.716092i
\(738\) −28.3167 + 2.97621i −1.04235 + 0.109556i
\(739\) −22.7306 + 10.1203i −0.836157 + 0.372281i −0.779723 0.626125i \(-0.784640\pi\)
−0.0564346 + 0.998406i \(0.517973\pi\)
\(740\) 23.6222 + 22.7126i 0.868370 + 0.834933i
\(741\) −39.0176 + 28.3480i −1.43335 + 1.04139i
\(742\) −0.235348 + 39.6170i −0.00863988 + 1.45439i
\(743\) 37.2111i 1.36514i −0.730819 0.682572i \(-0.760862\pi\)
0.730819 0.682572i \(-0.239138\pi\)
\(744\) −5.90493 + 1.25513i −0.216485 + 0.0460153i
\(745\) −7.65869 + 3.11370i −0.280593 + 0.114077i
\(746\) −24.8136 5.27429i −0.908489 0.193105i
\(747\) 10.4921 + 9.44710i 0.383885 + 0.345651i
\(748\) −8.11259 + 11.1660i −0.296626 + 0.408270i
\(749\) 16.1688 17.7442i 0.590796 0.648358i
\(750\) −39.2336 34.8653i −1.43261 1.27310i
\(751\) −2.82557 4.89402i −0.103106 0.178585i 0.809857 0.586628i \(-0.199545\pi\)
−0.912963 + 0.408042i \(0.866212\pi\)
\(752\) 3.87098 + 8.69437i 0.141160 + 0.317051i
\(753\) −1.32553 + 6.23613i −0.0483050 + 0.227257i
\(754\) 13.1548 14.6099i 0.479070 0.532061i
\(755\) 3.89582 + 3.03013i 0.141783 + 0.110278i
\(756\) 1.12460 1.92141i 0.0409012 0.0698810i
\(757\) 38.6504i 1.40477i 0.711796 + 0.702386i \(0.247882\pi\)
−0.711796 + 0.702386i \(0.752118\pi\)
\(758\) −2.96563 13.9522i −0.107716 0.506766i
\(759\) 2.85008 + 27.1167i 0.103451 + 0.984272i
\(760\) 1.09068 4.41535i 0.0395630 0.160161i
\(761\) 0.140549 1.33724i 0.00509490 0.0484748i −0.991679 0.128735i \(-0.958908\pi\)
0.996774 + 0.0802600i \(0.0255751\pi\)
\(762\) −26.8806 36.9979i −0.973780 1.34029i
\(763\) 4.03629 + 9.21256i 0.146124 + 0.333517i
\(764\) 31.1483 + 22.6306i 1.12691 + 0.818745i
\(765\) 3.41425 + 19.1200i 0.123443 + 0.691284i
\(766\) −1.40325 13.3510i −0.0507014 0.482392i
\(767\) 32.1034 28.9061i 1.15919 1.04374i
\(768\) −39.1198 + 22.5858i −1.41161 + 0.814996i
\(769\) −6.22029 + 19.1441i −0.224309 + 0.690353i 0.774052 + 0.633122i \(0.218227\pi\)
−0.998361 + 0.0572306i \(0.981773\pi\)
\(770\) 13.3359 + 25.3107i 0.480592 + 0.912133i
\(771\) 1.47954 + 4.55357i 0.0532845 + 0.163993i
\(772\) −2.54161 2.28848i −0.0914747 0.0823642i
\(773\) −16.7727 37.6722i −0.603274 1.35497i −0.914480 0.404632i \(-0.867400\pi\)
0.311206 0.950343i \(-0.399267\pi\)
\(774\) −15.8718 + 27.4907i −0.570499 + 0.988134i
\(775\) −13.9511 28.2911i −0.501140 1.01625i
\(776\) 1.79913 0.0645849
\(777\) −49.3714 16.3666i −1.77119 0.587149i
\(778\) −18.5776 + 6.03622i −0.666039 + 0.216409i
\(779\) 17.8503 19.8248i 0.639555 0.710297i
\(780\) 2.72032 + 37.7233i 0.0974029 + 1.35071i
\(781\) 23.4628 + 26.0581i 0.839564 + 0.932430i
\(782\) 23.8180 13.7513i 0.851728 0.491746i
\(783\) 1.15032 + 0.373762i 0.0411091 + 0.0133572i
\(784\) −29.9683 + 5.99874i −1.07030 + 0.214241i
\(785\) −33.0178 + 42.4508i −1.17846 + 1.51513i
\(786\) 8.76075 83.3529i 0.312485 2.97310i
\(787\) 44.5159 4.67881i 1.58682 0.166781i 0.730384 0.683036i \(-0.239341\pi\)
0.856435 + 0.516255i \(0.172674\pi\)
\(788\) 6.07371 0.638373i 0.216367 0.0227411i
\(789\) −7.41258 + 70.5260i −0.263895 + 2.51079i
\(790\) 15.2849 + 22.5549i 0.543813 + 0.802467i
\(791\) −27.2744 20.0646i −0.969765 0.713416i
\(792\) −2.63005 0.854556i −0.0934548 0.0303653i
\(793\) 29.2942 16.9130i 1.04027 0.600599i
\(794\) 14.4737 + 16.0747i 0.513652 + 0.570468i
\(795\) 21.8660 35.1629i 0.775508 1.24710i
\(796\) 9.93131 11.0298i 0.352006 0.390942i
\(797\) −36.7627 + 11.9449i −1.30220 + 0.423111i −0.876347 0.481680i \(-0.840027\pi\)
−0.425855 + 0.904791i \(0.640027\pi\)
\(798\) −12.8560 62.3001i −0.455096 2.20540i
\(799\) 6.74855 0.238747
\(800\) −26.9084 27.6230i −0.951354 0.976620i
\(801\) −19.4894 + 33.7566i −0.688623 + 1.19273i
\(802\) −5.66309 12.7195i −0.199970 0.449141i
\(803\) −22.6908 20.4309i −0.800742 0.720991i
\(804\) −11.4664 35.2900i −0.404390 1.24458i
\(805\) −1.78023 26.9147i −0.0627449 0.948619i
\(806\) −14.8451 + 45.6885i −0.522896 + 1.60931i
\(807\) 49.9047 28.8125i 1.75673 1.01425i
\(808\) −3.36492 + 3.02979i −0.118378 + 0.106588i
\(809\) 0.555120 + 5.28161i 0.0195170 + 0.185692i 0.999937 0.0112262i \(-0.00357349\pi\)
−0.980420 + 0.196918i \(0.936907\pi\)
\(810\) −36.6765 + 19.6037i −1.28868 + 0.688802i
\(811\) −11.3010 8.21065i −0.396831 0.288315i 0.371418 0.928466i \(-0.378872\pi\)
−0.768249 + 0.640151i \(0.778872\pi\)
\(812\) 4.92366 + 11.2379i 0.172787 + 0.394374i
\(813\) 17.0928 + 23.5262i 0.599469 + 0.825098i
\(814\) −4.12427 + 39.2398i −0.144556 + 1.37536i
\(815\) 1.84065 + 1.14461i 0.0644751 + 0.0400938i
\(816\) 3.40447 + 32.3914i 0.119180 + 1.13392i
\(817\) −6.18360 29.0915i −0.216337 1.01778i
\(818\) 7.63862i 0.267078i
\(819\) −14.3556 25.2093i −0.501625 0.880884i
\(820\) −5.81013 20.0973i −0.202899 0.701828i
\(821\) −5.60839 + 6.22875i −0.195734 + 0.217385i −0.833020 0.553242i \(-0.813390\pi\)
0.637286 + 0.770627i \(0.280057\pi\)
\(822\) −3.16110 + 14.8718i −0.110256 + 0.518714i
\(823\) −12.3634 27.7686i −0.430960 0.967951i −0.990291 0.139007i \(-0.955609\pi\)
0.559332 0.828944i \(-0.311058\pi\)
\(824\) 0.303485 + 0.525652i 0.0105724 + 0.0183120i
\(825\) 1.95605 29.8371i 0.0681009 1.03880i
\(826\) 17.2854 + 54.2944i 0.601437 + 1.88914i
\(827\) −27.3277 + 37.6133i −0.950277 + 1.30794i 0.00112745 + 0.999999i \(0.499641\pi\)
−0.951404 + 0.307945i \(0.900359\pi\)
\(828\) −17.0744 15.3738i −0.593376 0.534278i
\(829\) −7.32566 1.55712i −0.254431 0.0540809i 0.0789304 0.996880i \(-0.474850\pi\)
−0.333361 + 0.942799i \(0.608183\pi\)
\(830\) −11.5776 + 18.6180i −0.401865 + 0.646242i
\(831\) −43.9876 + 9.34986i −1.52591 + 0.324343i
\(832\) 24.6013i 0.852897i
\(833\) −4.75736 + 21.1432i −0.164833 + 0.732569i
\(834\) 29.0569 21.1111i 1.00616 0.731018i
\(835\) −1.78886 + 3.68804i −0.0619061 + 0.127630i
\(836\) −20.8580 + 9.28660i −0.721390 + 0.321184i
\(837\) −2.93937 + 0.308940i −0.101599 + 0.0106785i
\(838\) 18.5959 41.7672i 0.642386 1.44282i
\(839\) 1.12707 + 0.818863i 0.0389107 + 0.0282703i 0.607071 0.794648i \(-0.292345\pi\)
−0.568160 + 0.822918i \(0.692345\pi\)
\(840\) 5.31233 + 1.95622i 0.183293 + 0.0674958i
\(841\) 18.0689 13.1278i 0.623066 0.452684i
\(842\) 13.4103 + 63.0903i 0.462148 + 2.17424i
\(843\) 13.9975 + 8.08149i 0.482101 + 0.278341i
\(844\) −26.9759 29.9597i −0.928548 1.03126i
\(845\) −4.57568 2.21941i −0.157408 0.0763499i
\(846\) −3.68204 11.3322i −0.126591 0.389608i
\(847\) 5.27767 11.6668i 0.181343 0.400877i
\(848\) 19.7234 27.1469i 0.677304 0.932229i
\(849\) 10.7418 + 18.6053i 0.368657 + 0.638532i
\(850\) −28.2966 + 10.4387i −0.970565 + 0.358045i
\(851\) 18.6002 32.2165i 0.637607 1.10437i
\(852\) −60.8074 6.39112i −2.08323 0.218956i
\(853\) 13.5727 4.41002i 0.464719 0.150996i −0.0672930 0.997733i \(-0.521436\pi\)
0.532012 + 0.846737i \(0.321436\pi\)
\(854\) 4.39999 + 44.3986i 0.150564 + 1.51929i
\(855\) −10.9233 + 30.2158i −0.373569 + 1.03336i
\(856\) −3.52465 + 0.749188i −0.120470 + 0.0256067i
\(857\) 40.7351 + 23.5184i 1.39148 + 0.803374i 0.993480 0.114009i \(-0.0363693\pi\)
0.398005 + 0.917383i \(0.369703\pi\)
\(858\) −33.8412 + 30.4707i −1.15532 + 1.04025i
\(859\) −34.9266 15.5503i −1.19168 0.530571i −0.287525 0.957773i \(-0.592833\pi\)
−0.904156 + 0.427202i \(0.859499\pi\)
\(860\) −21.9343 7.92944i −0.747952 0.270392i
\(861\) 22.0717 + 24.8079i 0.752201 + 0.845450i
\(862\) 23.6683 + 32.5766i 0.806146 + 1.10956i
\(863\) 17.0870 38.3781i 0.581649 1.30640i −0.347840 0.937554i \(-0.613085\pi\)
0.929489 0.368850i \(-0.120249\pi\)
\(864\) −3.30082 + 1.46962i −0.112296 + 0.0499974i
\(865\) −4.20226 + 17.0119i −0.142881 + 0.578421i
\(866\) 47.3404 + 21.0773i 1.60869 + 0.716236i
\(867\) −16.9917 5.52093i −0.577067 0.187500i
\(868\) −22.1605 20.1931i −0.752176 0.685397i
\(869\) −4.79651 + 14.7621i −0.162711 + 0.500771i
\(870\) 3.71349 26.8463i 0.125899 0.910175i
\(871\) 32.7764 + 6.96684i 1.11059 + 0.236062i
\(872\) 0.313893 1.47675i 0.0106298 0.0500091i
\(873\) −12.6402 1.32854i −0.427807 0.0449644i
\(874\) 45.4963 1.53894
\(875\) −3.07483 + 29.4202i −0.103948 + 0.994583i
\(876\) 53.2415 1.79886
\(877\) 23.9901 + 2.52146i 0.810089 + 0.0851438i 0.500511 0.865730i \(-0.333145\pi\)
0.309578 + 0.950874i \(0.399812\pi\)
\(878\) 4.77195 22.4502i 0.161045 0.757659i
\(879\) −49.8769 10.6017i −1.68231 0.357585i
\(880\) 3.32015 24.0027i 0.111922 0.809132i
\(881\) −0.227231 + 0.699346i −0.00765562 + 0.0235616i −0.954811 0.297213i \(-0.903943\pi\)
0.947156 + 0.320774i \(0.103943\pi\)
\(882\) 38.0993 3.54729i 1.28287 0.119443i
\(883\) 33.2858 + 10.8152i 1.12016 + 0.363961i 0.809827 0.586668i \(-0.199561\pi\)
0.310329 + 0.950629i \(0.399561\pi\)
\(884\) 19.8544 + 8.83973i 0.667775 + 0.297312i
\(885\) 14.2815 57.8153i 0.480068 1.94344i
\(886\) 1.79114 0.797467i 0.0601745 0.0267914i
\(887\) 2.65764 5.96915i 0.0892347 0.200424i −0.863415 0.504494i \(-0.831679\pi\)
0.952650 + 0.304070i \(0.0983456\pi\)
\(888\) 4.58909 + 6.31634i 0.154000 + 0.211962i
\(889\) −8.10993 + 24.4643i −0.271998 + 0.820507i
\(890\) −56.9237 20.5785i −1.90809 0.689792i
\(891\) −21.6434 9.63624i −0.725080 0.322826i
\(892\) 11.8887 10.7046i 0.398062 0.358417i
\(893\) 9.66815 + 5.58191i 0.323532 + 0.186792i
\(894\) 16.9780 3.60878i 0.567828 0.120696i
\(895\) 8.12506 22.4754i 0.271591 0.751268i
\(896\) 7.61888 + 3.44652i 0.254529 + 0.115140i
\(897\) 40.8332 13.2675i 1.36338 0.442989i
\(898\) −56.2725 5.91448i −1.87784 0.197369i
\(899\) 8.14397 14.1058i 0.271617 0.470454i
\(900\) 15.5986 + 19.7874i 0.519955 + 0.659579i
\(901\) −11.8969 20.6061i −0.396344 0.686489i
\(902\) 14.8055 20.3780i 0.492969 0.678514i
\(903\) 36.8393 3.65084i 1.22594 0.121492i
\(904\) 1.57057 + 4.83373i 0.0522365 + 0.160767i
\(905\) −12.3348 5.98290i −0.410022 0.198878i
\(906\) −6.93349 7.70042i −0.230350 0.255829i
\(907\) 8.99454 + 5.19300i 0.298659 + 0.172431i 0.641840 0.766838i \(-0.278171\pi\)
−0.343181 + 0.939269i \(0.611505\pi\)
\(908\) −4.69413 22.0841i −0.155780 0.732887i
\(909\) 25.8785 18.8018i 0.858335 0.623617i
\(910\) 34.6185 28.8269i 1.14759 0.955604i
\(911\) −8.33705 6.05722i −0.276219 0.200685i 0.441048 0.897484i \(-0.354607\pi\)
−0.717267 + 0.696799i \(0.754607\pi\)
\(912\) −21.9144 + 49.2207i −0.725660 + 1.62986i
\(913\) −12.4216 + 1.30556i −0.411095 + 0.0432078i
\(914\) −22.8930 + 10.1926i −0.757233 + 0.337142i
\(915\) 20.3506 41.9563i 0.672771 1.38703i
\(916\) −24.0314 + 17.4598i −0.794019 + 0.576888i
\(917\) −41.0460 + 23.3739i −1.35546 + 0.771874i
\(918\) 2.82594i 0.0932700i
\(919\) 18.5903 3.95149i 0.613237 0.130348i 0.109186 0.994021i \(-0.465176\pi\)
0.504051 + 0.863674i \(0.331842\pi\)
\(920\) −2.13808 + 3.43826i −0.0704905 + 0.113356i
\(921\) −48.0997 10.2239i −1.58494 0.336889i
\(922\) 17.1151 + 15.4105i 0.563654 + 0.507516i
\(923\) 32.4543 44.6695i 1.06825 1.47031i
\(924\) −8.62136 27.0801i −0.283622 0.890871i
\(925\) −26.0868 + 31.3651i −0.857728 + 1.03128i
\(926\) 33.9319 + 58.7717i 1.11507 + 1.93136i
\(927\) −1.74406 3.91721i −0.0572823 0.128658i
\(928\) 4.13997 19.4770i 0.135901 0.639365i
\(929\) 5.04067 5.59823i 0.165379 0.183672i −0.654759 0.755838i \(-0.727230\pi\)
0.820138 + 0.572166i \(0.193897\pi\)
\(930\) 18.3927 + 63.6204i 0.603120 + 2.08620i
\(931\) −24.3037 + 26.3554i −0.796520 + 0.863763i
\(932\) 10.4719i 0.343017i
\(933\) −1.43993 6.77432i −0.0471411 0.221781i
\(934\) −4.81395 45.8016i −0.157517 1.49868i
\(935\) −14.5911 9.07347i −0.477180 0.296734i
\(936\) −0.455174 + 4.33069i −0.0148778 + 0.141553i
\(937\) −25.6070 35.2449i −0.836543 1.15140i −0.986670 0.162735i \(-0.947968\pi\)
0.150127 0.988667i \(-0.452032\pi\)
\(938\) −26.1906 + 35.6016i −0.855154 + 1.16243i
\(939\) −7.97222 5.79216i −0.260164 0.189020i
\(940\) 7.72106 4.12692i 0.251833 0.134605i
\(941\) −3.75201 35.6979i −0.122312 1.16372i −0.867700 0.497089i \(-0.834402\pi\)
0.745388 0.666631i \(-0.232264\pi\)
\(942\) 83.9075 75.5507i 2.73386 2.46157i
\(943\) −20.5669 + 11.8743i −0.669752 + 0.386681i
\(944\) 14.9133 45.8985i 0.485388 1.49387i
\(945\) 2.48648 + 1.22435i 0.0808853 + 0.0398281i
\(946\) −8.67788 26.7078i −0.282142 0.868344i
\(947\) −39.6257 35.6791i −1.28766 1.15942i −0.978008 0.208566i \(-0.933120\pi\)
−0.309653 0.950850i \(-0.600213\pi\)
\(948\) −11.0086 24.7256i −0.357541 0.803050i
\(949\) −24.0398 + 41.6382i −0.780366 + 1.35163i
\(950\) −49.1726 8.45011i −1.59537 0.274158i
\(951\) 8.25366 0.267643
\(952\) 2.43036 2.16230i 0.0787684 0.0700806i
\(953\) −15.3638 + 4.99201i −0.497683 + 0.161707i −0.547094 0.837071i \(-0.684266\pi\)
0.0494103 + 0.998779i \(0.484266\pi\)
\(954\) −28.1107 + 31.2201i −0.910118 + 1.01079i
\(955\) −25.3110 + 40.7027i −0.819044 + 1.31711i
\(956\) −4.89902 5.44091i −0.158446 0.175972i
\(957\) 13.3712 7.71984i 0.432228 0.249547i
\(958\) −18.7578 6.09478i −0.606037 0.196913i
\(959\) 7.84844 3.43863i 0.253439 0.111039i
\(960\) 19.0258 + 28.0750i 0.614055 + 0.906118i
\(961\) −0.919947 + 8.75271i −0.0296757 + 0.282345i
\(962\) 61.7892 6.49430i 1.99216 0.209385i
\(963\) 25.3166 2.66088i 0.815816 0.0857457i
\(964\) 4.27250 40.6501i 0.137608 1.30925i
\(965\) 2.61399 3.36080i 0.0841474 0.108188i
\(966\) −6.25392 + 56.2838i −0.201217 + 1.81090i
\(967\) −20.2807 6.58960i −0.652183 0.211907i −0.0358066 0.999359i \(-0.511400\pi\)
−0.616376 + 0.787452i \(0.711400\pi\)
\(968\) −1.66457 + 0.961042i −0.0535014 + 0.0308891i
\(969\) 25.5641 + 28.3918i 0.821238 + 0.912077i
\(970\) −1.41959 19.6857i −0.0455802 0.632071i
\(971\) 7.28813 8.09429i 0.233887 0.259758i −0.614764 0.788711i \(-0.710749\pi\)
0.848651 + 0.528953i \(0.177415\pi\)
\(972\) 36.8885 11.9858i 1.18320 0.384444i
\(973\) −19.2135 6.36927i −0.615955 0.204189i
\(974\) 23.2936 0.746376
\(975\) −46.5968 + 6.75555i −1.49229 + 0.216351i
\(976\) 18.8945 32.7262i 0.604798 1.04754i
\(977\) 4.88427 + 10.9703i 0.156262 + 0.350969i 0.974663 0.223677i \(-0.0718062\pi\)
−0.818402 + 0.574647i \(0.805139\pi\)
\(978\) −3.38178 3.04497i −0.108137 0.0973673i
\(979\) −10.6558 32.7951i −0.340560 1.04814i
\(980\) 7.48673 + 27.0993i 0.239155 + 0.865657i
\(981\) −3.29583 + 10.1435i −0.105228 + 0.323858i
\(982\) −0.925158 + 0.534140i −0.0295230 + 0.0170451i
\(983\) −18.2465 + 16.4292i −0.581973 + 0.524011i −0.906689 0.421801i \(-0.861398\pi\)
0.324715 + 0.945812i \(0.394732\pi\)
\(984\) −0.520995 4.95694i −0.0166087 0.158021i
\(985\) 1.33650 + 7.48447i 0.0425845 + 0.238475i
\(986\) −12.5993 9.15396i −0.401245 0.291521i
\(987\) −8.23440 + 11.1932i −0.262104 + 0.356285i
\(988\) 21.1323 + 29.0861i 0.672308 + 0.925353i
\(989\) −2.76758 + 26.3318i −0.0880039 + 0.837302i
\(990\) −7.27519 + 29.4519i −0.231221 + 0.936042i
\(991\) 4.22654 + 40.2128i 0.134260 + 1.27740i 0.829452 + 0.558578i \(0.188653\pi\)
−0.695192 + 0.718824i \(0.744680\pi\)
\(992\) 10.1163 + 47.5937i 0.321194 + 1.51110i
\(993\) 64.8864i 2.05911i
\(994\) 36.0384 + 63.2855i 1.14307 + 2.00729i
\(995\) 14.5848 + 11.3439i 0.462371 + 0.359627i
\(996\) 14.5730 16.1849i 0.461762 0.512838i
\(997\) −8.76722 + 41.2465i −0.277661 + 1.30629i 0.589300 + 0.807914i \(0.299404\pi\)
−0.866961 + 0.498377i \(0.833930\pi\)
\(998\) 31.7376 + 71.2838i 1.00464 + 2.25645i
\(999\) 1.91120 + 3.31030i 0.0604678 + 0.104733i
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 175.2.t.a.109.4 yes 144
5.2 odd 4 875.2.q.b.326.31 288
5.3 odd 4 875.2.q.b.326.6 288
5.4 even 2 875.2.u.a.424.15 144
7.2 even 3 inner 175.2.t.a.9.15 144
25.2 odd 20 875.2.q.b.676.6 288
25.11 even 5 875.2.u.a.74.4 144
25.14 even 10 inner 175.2.t.a.39.15 yes 144
25.23 odd 20 875.2.q.b.676.31 288
35.2 odd 12 875.2.q.b.576.6 288
35.9 even 6 875.2.u.a.674.4 144
35.23 odd 12 875.2.q.b.576.31 288
175.2 odd 60 875.2.q.b.51.31 288
175.23 odd 60 875.2.q.b.51.6 288
175.86 even 15 875.2.u.a.324.15 144
175.114 even 30 inner 175.2.t.a.114.4 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.t.a.9.15 144 7.2 even 3 inner
175.2.t.a.39.15 yes 144 25.14 even 10 inner
175.2.t.a.109.4 yes 144 1.1 even 1 trivial
175.2.t.a.114.4 yes 144 175.114 even 30 inner
875.2.q.b.51.6 288 175.23 odd 60
875.2.q.b.51.31 288 175.2 odd 60
875.2.q.b.326.6 288 5.3 odd 4
875.2.q.b.326.31 288 5.2 odd 4
875.2.q.b.576.6 288 35.2 odd 12
875.2.q.b.576.31 288 35.23 odd 12
875.2.q.b.676.6 288 25.2 odd 20
875.2.q.b.676.31 288 25.23 odd 20
875.2.u.a.74.4 144 25.11 even 5
875.2.u.a.324.15 144 175.86 even 15
875.2.u.a.424.15 144 5.4 even 2
875.2.u.a.674.4 144 35.9 even 6