Properties

Label 224.2.be.a.115.4
Level $224$
Weight $2$
Character 224.115
Analytic conductor $1.789$
Analytic rank $0$
Dimension $240$
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] = [224,2,Mod(3,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.be (of order \(24\), 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: \(1.78864900528\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(30\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 115.4
Character \(\chi\) \(=\) 224.115
Dual form 224.2.be.a.187.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25335 + 0.655068i) q^{2} +(-1.36290 - 1.77617i) q^{3} +(1.14177 - 1.64206i) q^{4} +(-1.70413 + 2.22087i) q^{5} +(2.87170 + 1.33337i) q^{6} +(-0.279051 - 2.63099i) q^{7} +(-0.355379 + 2.80601i) q^{8} +(-0.520812 + 1.94370i) q^{9} +O(q^{10})\) \(q+(-1.25335 + 0.655068i) q^{2} +(-1.36290 - 1.77617i) q^{3} +(1.14177 - 1.64206i) q^{4} +(-1.70413 + 2.22087i) q^{5} +(2.87170 + 1.33337i) q^{6} +(-0.279051 - 2.63099i) q^{7} +(-0.355379 + 2.80601i) q^{8} +(-0.520812 + 1.94370i) q^{9} +(0.681054 - 3.89985i) q^{10} +(-0.192495 + 1.46215i) q^{11} +(-4.47269 + 0.209987i) q^{12} +(-0.943125 + 2.27690i) q^{13} +(2.07323 + 3.11476i) q^{14} +6.26720 q^{15} +(-1.39272 - 3.74971i) q^{16} +(-3.38999 + 5.87164i) q^{17} +(-0.620495 - 2.77730i) q^{18} +(1.08500 + 8.24141i) q^{19} +(1.70107 + 5.33401i) q^{20} +(-4.29277 + 4.08142i) q^{21} +(-0.716542 - 1.95868i) q^{22} +(-3.73568 - 1.00097i) q^{23} +(5.46829 - 3.19310i) q^{24} +(-0.734097 - 2.73969i) q^{25} +(-0.309462 - 3.47157i) q^{26} +(-2.04302 + 0.846247i) q^{27} +(-4.63886 - 2.54578i) q^{28} +(1.45199 - 3.50542i) q^{29} +(-7.85499 + 4.10544i) q^{30} +(2.28997 - 3.96634i) q^{31} +(4.20188 + 3.78738i) q^{32} +(2.85937 - 1.65086i) q^{33} +(0.402523 - 9.57990i) q^{34} +(6.31864 + 3.86383i) q^{35} +(2.59702 + 3.07446i) q^{36} +(-1.86727 - 1.43281i) q^{37} +(-6.75857 - 9.61862i) q^{38} +(5.32955 - 1.42805i) q^{39} +(-5.62618 - 5.57107i) q^{40} +(-2.36106 + 2.36106i) q^{41} +(2.70673 - 7.92751i) q^{42} +(-7.51478 + 3.11272i) q^{43} +(2.18115 + 1.98553i) q^{44} +(-3.42917 - 4.46898i) q^{45} +(5.33782 - 1.19256i) q^{46} +(6.98275 - 4.03149i) q^{47} +(-4.76198 + 7.58418i) q^{48} +(-6.84426 + 1.46836i) q^{49} +(2.71476 + 2.95290i) q^{50} +(15.0492 - 1.98127i) q^{51} +(2.66198 + 4.14837i) q^{52} +(0.948037 + 0.124811i) q^{53} +(2.00627 - 2.39896i) q^{54} +(-2.91920 - 2.91920i) q^{55} +(7.48177 + 0.151979i) q^{56} +(13.1594 - 13.1594i) q^{57} +(0.476435 + 5.34467i) q^{58} +(0.136791 - 1.03903i) q^{59} +(7.15571 - 10.2911i) q^{60} +(0.838308 + 6.36758i) q^{61} +(-0.271908 + 6.47130i) q^{62} +(5.25919 + 0.827864i) q^{63} +(-7.74741 - 1.99439i) q^{64} +(-3.44950 - 5.97471i) q^{65} +(-2.50236 + 3.94218i) q^{66} +(1.71169 - 1.31342i) q^{67} +(5.77098 + 12.2706i) q^{68} +(3.31346 + 7.99941i) q^{69} +(-10.4505 - 0.703594i) q^{70} +(-8.54607 - 8.54607i) q^{71} +(-5.26896 - 2.15216i) q^{72} +(-2.13008 - 7.94956i) q^{73} +(3.27894 + 0.572620i) q^{74} +(-3.86564 + 5.03780i) q^{75} +(14.7717 + 7.62817i) q^{76} +(3.90062 + 0.0984410i) q^{77} +(-5.74432 + 5.28106i) q^{78} +(4.04523 + 7.00654i) q^{79} +(10.7010 + 3.29697i) q^{80} +(9.51553 + 5.49379i) q^{81} +(1.41258 - 4.50590i) q^{82} +(-14.6175 - 6.05475i) q^{83} +(1.80058 + 11.7090i) q^{84} +(-7.26315 - 17.5348i) q^{85} +(7.37960 - 8.82402i) q^{86} +(-8.20513 + 2.19856i) q^{87} +(-4.03439 - 1.05976i) q^{88} +(-3.44538 + 12.8583i) q^{89} +(7.22543 + 3.35485i) q^{90} +(6.25370 + 1.84598i) q^{91} +(-5.90894 + 4.99132i) q^{92} +(-10.1659 + 1.33836i) q^{93} +(-6.11093 + 9.62705i) q^{94} +(-20.1521 - 11.6348i) q^{95} +(1.00027 - 12.6251i) q^{96} -1.00276i q^{97} +(7.61638 - 6.32383i) q^{98} +(-2.74172 - 1.13566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25335 + 0.655068i −0.886252 + 0.463203i
\(3\) −1.36290 1.77617i −0.786871 1.02547i −0.998838 0.0481934i \(-0.984654\pi\)
0.211967 0.977277i \(-0.432013\pi\)
\(4\) 1.14177 1.64206i 0.570886 0.821030i
\(5\) −1.70413 + 2.22087i −0.762112 + 0.993203i 0.237650 + 0.971351i \(0.423623\pi\)
−0.999761 + 0.0218522i \(0.993044\pi\)
\(6\) 2.87170 + 1.33337i 1.17237 + 0.544344i
\(7\) −0.279051 2.63099i −0.105471 0.994422i
\(8\) −0.355379 + 2.80601i −0.125645 + 0.992075i
\(9\) −0.520812 + 1.94370i −0.173604 + 0.647900i
\(10\) 0.681054 3.89985i 0.215368 1.23324i
\(11\) −0.192495 + 1.46215i −0.0580395 + 0.440854i 0.937611 + 0.347686i \(0.113033\pi\)
−0.995650 + 0.0931675i \(0.970301\pi\)
\(12\) −4.47269 + 0.209987i −1.29115 + 0.0606180i
\(13\) −0.943125 + 2.27690i −0.261576 + 0.631500i −0.999036 0.0438905i \(-0.986025\pi\)
0.737461 + 0.675390i \(0.236025\pi\)
\(14\) 2.07323 + 3.11476i 0.554094 + 0.832454i
\(15\) 6.26720 1.61818
\(16\) −1.39272 3.74971i −0.348179 0.937428i
\(17\) −3.38999 + 5.87164i −0.822194 + 1.42408i 0.0818504 + 0.996645i \(0.473917\pi\)
−0.904045 + 0.427438i \(0.859416\pi\)
\(18\) −0.620495 2.77730i −0.146252 0.654616i
\(19\) 1.08500 + 8.24141i 0.248917 + 1.89071i 0.423234 + 0.906020i \(0.360895\pi\)
−0.174317 + 0.984690i \(0.555772\pi\)
\(20\) 1.70107 + 5.33401i 0.380370 + 1.19272i
\(21\) −4.29277 + 4.08142i −0.936758 + 0.890640i
\(22\) −0.716542 1.95868i −0.152767 0.417592i
\(23\) −3.73568 1.00097i −0.778943 0.208717i −0.152624 0.988284i \(-0.548772\pi\)
−0.626318 + 0.779567i \(0.715439\pi\)
\(24\) 5.46829 3.19310i 1.11621 0.651790i
\(25\) −0.734097 2.73969i −0.146819 0.547938i
\(26\) −0.309462 3.47157i −0.0606906 0.680831i
\(27\) −2.04302 + 0.846247i −0.393180 + 0.162860i
\(28\) −4.63886 2.54578i −0.876662 0.481107i
\(29\) 1.45199 3.50542i 0.269628 0.650940i −0.729837 0.683621i \(-0.760404\pi\)
0.999466 + 0.0326802i \(0.0104043\pi\)
\(30\) −7.85499 + 4.10544i −1.43412 + 0.749548i
\(31\) 2.28997 3.96634i 0.411291 0.712377i −0.583740 0.811940i \(-0.698411\pi\)
0.995031 + 0.0995638i \(0.0317447\pi\)
\(32\) 4.20188 + 3.78738i 0.742794 + 0.669520i
\(33\) 2.85937 1.65086i 0.497752 0.287377i
\(34\) 0.402523 9.57990i 0.0690321 1.64294i
\(35\) 6.31864 + 3.86383i 1.06804 + 0.653106i
\(36\) 2.59702 + 3.07446i 0.432837 + 0.512411i
\(37\) −1.86727 1.43281i −0.306978 0.235553i 0.443771 0.896140i \(-0.353640\pi\)
−0.750749 + 0.660588i \(0.770307\pi\)
\(38\) −6.75857 9.61862i −1.09639 1.56035i
\(39\) 5.32955 1.42805i 0.853410 0.228671i
\(40\) −5.62618 5.57107i −0.889577 0.880863i
\(41\) −2.36106 + 2.36106i −0.368736 + 0.368736i −0.867016 0.498280i \(-0.833965\pi\)
0.498280 + 0.867016i \(0.333965\pi\)
\(42\) 2.70673 7.92751i 0.417657 1.22324i
\(43\) −7.51478 + 3.11272i −1.14599 + 0.474686i −0.873188 0.487384i \(-0.837951\pi\)
−0.272805 + 0.962069i \(0.587951\pi\)
\(44\) 2.18115 + 1.98553i 0.328820 + 0.299329i
\(45\) −3.42917 4.46898i −0.511190 0.666196i
\(46\) 5.33782 1.19256i 0.787018 0.175833i
\(47\) 6.98275 4.03149i 1.01854 0.588054i 0.104859 0.994487i \(-0.466561\pi\)
0.913680 + 0.406433i \(0.133228\pi\)
\(48\) −4.76198 + 7.58418i −0.687333 + 1.09468i
\(49\) −6.84426 + 1.46836i −0.977752 + 0.209766i
\(50\) 2.71476 + 2.95290i 0.383925 + 0.417604i
\(51\) 15.0492 1.98127i 2.10731 0.277433i
\(52\) 2.66198 + 4.14837i 0.369150 + 0.575276i
\(53\) 0.948037 + 0.124811i 0.130223 + 0.0171442i 0.195356 0.980732i \(-0.437414\pi\)
−0.0651329 + 0.997877i \(0.520747\pi\)
\(54\) 2.00627 2.39896i 0.273019 0.326457i
\(55\) −2.91920 2.91920i −0.393625 0.393625i
\(56\) 7.48177 + 0.151979i 0.999794 + 0.0203091i
\(57\) 13.1594 13.1594i 1.74300 1.74300i
\(58\) 0.476435 + 5.34467i 0.0625589 + 0.701790i
\(59\) 0.136791 1.03903i 0.0178087 0.135270i −0.980231 0.197857i \(-0.936602\pi\)
0.998040 + 0.0625870i \(0.0199351\pi\)
\(60\) 7.15571 10.2911i 0.923798 1.32858i
\(61\) 0.838308 + 6.36758i 0.107334 + 0.815285i 0.957432 + 0.288660i \(0.0932096\pi\)
−0.850097 + 0.526625i \(0.823457\pi\)
\(62\) −0.271908 + 6.47130i −0.0345323 + 0.821856i
\(63\) 5.25919 + 0.827864i 0.662596 + 0.104301i
\(64\) −7.74741 1.99439i −0.968427 0.249299i
\(65\) −3.44950 5.97471i −0.427858 0.741071i
\(66\) −2.50236 + 3.94218i −0.308020 + 0.485249i
\(67\) 1.71169 1.31342i 0.209116 0.160460i −0.498893 0.866663i \(-0.666260\pi\)
0.708009 + 0.706203i \(0.249593\pi\)
\(68\) 5.77098 + 12.2706i 0.699835 + 1.48803i
\(69\) 3.31346 + 7.99941i 0.398894 + 0.963016i
\(70\) −10.4505 0.703594i −1.24908 0.0840956i
\(71\) −8.54607 8.54607i −1.01423 1.01423i −0.999897 0.0143346i \(-0.995437\pi\)
−0.0143346 0.999897i \(-0.504563\pi\)
\(72\) −5.26896 2.15216i −0.620953 0.253634i
\(73\) −2.13008 7.94956i −0.249307 0.930426i −0.971170 0.238390i \(-0.923380\pi\)
0.721863 0.692036i \(-0.243286\pi\)
\(74\) 3.27894 + 0.572620i 0.381169 + 0.0665658i
\(75\) −3.86564 + 5.03780i −0.446366 + 0.581715i
\(76\) 14.7717 + 7.62817i 1.69443 + 0.875011i
\(77\) 3.90062 + 0.0984410i 0.444516 + 0.0112184i
\(78\) −5.74432 + 5.28106i −0.650416 + 0.597962i
\(79\) 4.04523 + 7.00654i 0.455124 + 0.788297i 0.998695 0.0510654i \(-0.0162617\pi\)
−0.543572 + 0.839363i \(0.682928\pi\)
\(80\) 10.7010 + 3.29697i 1.19641 + 0.368612i
\(81\) 9.51553 + 5.49379i 1.05728 + 0.610421i
\(82\) 1.41258 4.50590i 0.155993 0.497593i
\(83\) −14.6175 6.05475i −1.60447 0.664595i −0.612434 0.790522i \(-0.709810\pi\)
−0.992040 + 0.125927i \(0.959810\pi\)
\(84\) 1.80058 + 11.7090i 0.196460 + 1.27756i
\(85\) −7.26315 17.5348i −0.787799 1.90192i
\(86\) 7.37960 8.82402i 0.795762 0.951518i
\(87\) −8.20513 + 2.19856i −0.879683 + 0.235710i
\(88\) −4.03439 1.05976i −0.430068 0.112971i
\(89\) −3.44538 + 12.8583i −0.365210 + 1.36298i 0.501926 + 0.864910i \(0.332625\pi\)
−0.867136 + 0.498071i \(0.834042\pi\)
\(90\) 7.22543 + 3.35485i 0.761627 + 0.353633i
\(91\) 6.25370 + 1.84598i 0.655566 + 0.193512i
\(92\) −5.90894 + 4.99132i −0.616050 + 0.520381i
\(93\) −10.1659 + 1.33836i −1.05415 + 0.138782i
\(94\) −6.11093 + 9.62705i −0.630294 + 0.992954i
\(95\) −20.1521 11.6348i −2.06756 1.19371i
\(96\) 1.00027 12.6251i 0.102090 1.28854i
\(97\) 1.00276i 0.101814i −0.998703 0.0509072i \(-0.983789\pi\)
0.998703 0.0509072i \(-0.0162113\pi\)
\(98\) 7.61638 6.32383i 0.769370 0.638803i
\(99\) −2.74172 1.13566i −0.275553 0.114138i
\(100\) −5.33690 1.92267i −0.533690 0.192267i
\(101\) −3.55496 0.468020i −0.353732 0.0465697i −0.0484335 0.998826i \(-0.515423\pi\)
−0.305298 + 0.952257i \(0.598756\pi\)
\(102\) −17.5641 + 12.3415i −1.73910 + 1.22199i
\(103\) −8.90936 2.38726i −0.877865 0.235223i −0.208379 0.978048i \(-0.566819\pi\)
−0.669486 + 0.742825i \(0.733486\pi\)
\(104\) −6.05386 3.45558i −0.593629 0.338848i
\(105\) −1.74887 16.4890i −0.170672 1.60916i
\(106\) −1.26998 + 0.464597i −0.123352 + 0.0451256i
\(107\) 2.17418 + 1.66831i 0.210186 + 0.161282i 0.708490 0.705721i \(-0.249377\pi\)
−0.498303 + 0.867003i \(0.666043\pi\)
\(108\) −0.943076 + 4.32098i −0.0907475 + 0.415787i
\(109\) −4.63907 + 3.55968i −0.444342 + 0.340956i −0.806575 0.591132i \(-0.798681\pi\)
0.362233 + 0.932088i \(0.382015\pi\)
\(110\) 5.57105 + 1.74650i 0.531179 + 0.166523i
\(111\) 5.26937i 0.500146i
\(112\) −9.47683 + 4.71059i −0.895477 + 0.445109i
\(113\) 11.7791i 1.10809i 0.832488 + 0.554043i \(0.186916\pi\)
−0.832488 + 0.554043i \(0.813084\pi\)
\(114\) −7.87301 + 25.1136i −0.737375 + 2.35210i
\(115\) 8.58912 6.59066i 0.800940 0.614583i
\(116\) −4.09826 6.38665i −0.380514 0.592985i
\(117\) −3.93442 3.01899i −0.363738 0.279106i
\(118\) 0.509189 + 1.39188i 0.0468747 + 0.128133i
\(119\) 16.3942 + 7.28057i 1.50286 + 0.667409i
\(120\) −2.22723 + 17.5858i −0.203317 + 1.60536i
\(121\) 8.52437 + 2.28410i 0.774942 + 0.207645i
\(122\) −5.22189 7.43166i −0.472768 0.672831i
\(123\) 7.41154 + 0.975747i 0.668276 + 0.0879802i
\(124\) −3.89835 8.28893i −0.350082 0.744367i
\(125\) −5.59580 2.31786i −0.500504 0.207315i
\(126\) −7.13392 + 2.40753i −0.635540 + 0.214479i
\(127\) 12.9896i 1.15264i 0.817223 + 0.576321i \(0.195512\pi\)
−0.817223 + 0.576321i \(0.804488\pi\)
\(128\) 11.0167 2.57541i 0.973746 0.227636i
\(129\) 15.7706 + 9.10516i 1.38852 + 0.801665i
\(130\) 8.23727 + 5.22874i 0.722456 + 0.458591i
\(131\) 3.33354 0.438869i 0.291253 0.0383442i 0.0165160 0.999864i \(-0.494743\pi\)
0.274737 + 0.961519i \(0.411409\pi\)
\(132\) 0.553940 6.58015i 0.0482143 0.572729i
\(133\) 21.3803 5.15441i 1.85391 0.446944i
\(134\) −1.28496 + 2.76745i −0.111004 + 0.239071i
\(135\) 1.60218 5.97940i 0.137893 0.514625i
\(136\) −15.2712 11.5990i −1.30949 0.994608i
\(137\) 21.4128 5.73754i 1.82942 0.490191i 0.831551 0.555449i \(-0.187454\pi\)
0.997868 + 0.0652578i \(0.0207870\pi\)
\(138\) −9.39309 7.85551i −0.799593 0.668706i
\(139\) −6.87092 16.5879i −0.582784 1.40697i −0.890279 0.455416i \(-0.849491\pi\)
0.307495 0.951550i \(-0.400509\pi\)
\(140\) 13.5591 5.96396i 1.14595 0.504047i
\(141\) −16.6774 6.90800i −1.40449 0.581759i
\(142\) 16.3095 + 5.11296i 1.36866 + 0.429070i
\(143\) −3.14762 1.81728i −0.263217 0.151969i
\(144\) 8.01365 0.754123i 0.667805 0.0628436i
\(145\) 5.31070 + 9.19839i 0.441029 + 0.763885i
\(146\) 7.87724 + 8.56824i 0.651925 + 0.709112i
\(147\) 11.9361 + 10.1553i 0.984473 + 0.837596i
\(148\) −4.48476 + 1.43023i −0.368645 + 0.117564i
\(149\) −7.21399 + 9.40146i −0.590993 + 0.770198i −0.989117 0.147134i \(-0.952995\pi\)
0.398123 + 0.917332i \(0.369662\pi\)
\(150\) 1.54490 8.84638i 0.126140 0.722304i
\(151\) 0.697481 + 2.60303i 0.0567602 + 0.211832i 0.988481 0.151342i \(-0.0483596\pi\)
−0.931721 + 0.363174i \(0.881693\pi\)
\(152\) −23.5111 + 0.115710i −1.90700 + 0.00938528i
\(153\) −9.64715 9.64715i −0.779926 0.779926i
\(154\) −4.95332 + 2.43179i −0.399150 + 0.195959i
\(155\) 4.90632 + 11.8449i 0.394085 + 0.951406i
\(156\) 3.74019 10.3819i 0.299455 0.831220i
\(157\) −3.21409 + 2.46626i −0.256513 + 0.196829i −0.729010 0.684503i \(-0.760019\pi\)
0.472497 + 0.881332i \(0.343353\pi\)
\(158\) −9.65985 6.13175i −0.768496 0.487816i
\(159\) −1.07039 1.85398i −0.0848878 0.147030i
\(160\) −15.5718 + 2.87763i −1.23106 + 0.227496i
\(161\) −1.59111 + 10.1079i −0.125397 + 0.796612i
\(162\) −15.5251 0.652325i −1.21977 0.0512515i
\(163\) −0.247177 1.87750i −0.0193604 0.147057i 0.979034 0.203695i \(-0.0652952\pi\)
−0.998395 + 0.0566383i \(0.981962\pi\)
\(164\) 1.18121 + 6.57280i 0.0922371 + 0.513250i
\(165\) −1.20641 + 9.16356i −0.0939186 + 0.713382i
\(166\) 22.2871 1.98671i 1.72981 0.154199i
\(167\) −0.499681 + 0.499681i −0.0386665 + 0.0386665i −0.726176 0.687509i \(-0.758704\pi\)
0.687509 + 0.726176i \(0.258704\pi\)
\(168\) −9.92697 13.4960i −0.765882 1.04124i
\(169\) 4.89758 + 4.89758i 0.376737 + 0.376737i
\(170\) 20.5898 + 17.2194i 1.57916 + 1.32067i
\(171\) −16.5839 2.18331i −1.26820 0.166962i
\(172\) −3.46888 + 15.8937i −0.264500 + 1.21188i
\(173\) −4.72319 + 0.621820i −0.359097 + 0.0472761i −0.307917 0.951413i \(-0.599632\pi\)
−0.0511808 + 0.998689i \(0.516298\pi\)
\(174\) 8.84370 8.13049i 0.670439 0.616371i
\(175\) −7.00325 + 2.69592i −0.529396 + 0.203792i
\(176\) 5.75072 1.31455i 0.433477 0.0990881i
\(177\) −2.03192 + 1.17313i −0.152729 + 0.0881780i
\(178\) −4.10482 18.3730i −0.307669 1.37711i
\(179\) −7.66412 9.98807i −0.572843 0.746544i 0.413634 0.910443i \(-0.364259\pi\)
−0.986477 + 0.163900i \(0.947593\pi\)
\(180\) −11.2537 + 0.528344i −0.838798 + 0.0393804i
\(181\) 20.1372 8.34108i 1.49678 0.619988i 0.524003 0.851717i \(-0.324438\pi\)
0.972780 + 0.231729i \(0.0744381\pi\)
\(182\) −9.04732 + 1.78294i −0.670632 + 0.132160i
\(183\) 10.1674 10.1674i 0.751592 0.751592i
\(184\) 4.13632 10.1266i 0.304933 0.746545i
\(185\) 6.36417 1.70527i 0.467903 0.125374i
\(186\) 11.8647 8.33679i 0.869962 0.611283i
\(187\) −7.93264 6.08693i −0.580092 0.445121i
\(188\) 1.35276 16.0691i 0.0986599 1.17196i
\(189\) 2.79658 + 5.13903i 0.203421 + 0.373809i
\(190\) 32.8792 + 1.38150i 2.38531 + 0.100225i
\(191\) −5.25993 + 3.03682i −0.380595 + 0.219737i −0.678077 0.734991i \(-0.737187\pi\)
0.297482 + 0.954727i \(0.403853\pi\)
\(192\) 7.01658 + 16.4789i 0.506378 + 1.18926i
\(193\) −0.329423 + 0.570577i −0.0237124 + 0.0410710i −0.877638 0.479324i \(-0.840882\pi\)
0.853926 + 0.520395i \(0.174215\pi\)
\(194\) 0.656873 + 1.25680i 0.0471608 + 0.0902332i
\(195\) −5.91075 + 14.2698i −0.423278 + 1.02188i
\(196\) −5.40345 + 12.9152i −0.385960 + 0.922515i
\(197\) 7.40087 3.06554i 0.527290 0.218411i −0.103126 0.994668i \(-0.532884\pi\)
0.630416 + 0.776258i \(0.282884\pi\)
\(198\) 4.18027 0.372637i 0.297078 0.0264822i
\(199\) 2.61141 + 9.74591i 0.185118 + 0.690869i 0.994605 + 0.103732i \(0.0330785\pi\)
−0.809487 + 0.587137i \(0.800255\pi\)
\(200\) 7.94848 1.08626i 0.562042 0.0768101i
\(201\) −4.66572 1.25018i −0.329094 0.0881806i
\(202\) 4.76220 1.74215i 0.335067 0.122577i
\(203\) −9.62792 2.84200i −0.675748 0.199469i
\(204\) 13.9294 26.9739i 0.975255 1.88855i
\(205\) −1.22005 9.26718i −0.0852118 0.647248i
\(206\) 12.7304 2.84417i 0.886966 0.198163i
\(207\) 3.89117 6.73971i 0.270455 0.468442i
\(208\) 9.85124 + 0.365366i 0.683061 + 0.0253336i
\(209\) −12.2590 −0.847974
\(210\) 12.9933 + 19.5208i 0.896625 + 1.34706i
\(211\) −1.95523 + 4.72033i −0.134603 + 0.324961i −0.976781 0.214238i \(-0.931273\pi\)
0.842178 + 0.539199i \(0.181273\pi\)
\(212\) 1.28739 1.41423i 0.0884183 0.0971295i
\(213\) −3.53180 + 26.8267i −0.241995 + 1.83813i
\(214\) −3.81787 0.666738i −0.260984 0.0455773i
\(215\) 5.89323 21.9938i 0.401915 1.49997i
\(216\) −1.64853 6.03348i −0.112169 0.410526i
\(217\) −11.0744 4.91809i −0.751783 0.333862i
\(218\) 3.48254 7.50044i 0.235868 0.507994i
\(219\) −11.2167 + 14.6178i −0.757952 + 0.987782i
\(220\) −8.12656 + 1.46044i −0.547892 + 0.0984628i
\(221\) −10.1720 13.2564i −0.684241 0.891721i
\(222\) −3.45180 6.60436i −0.231669 0.443256i
\(223\) 9.50162 0.636275 0.318138 0.948045i \(-0.396943\pi\)
0.318138 + 0.948045i \(0.396943\pi\)
\(224\) 8.79203 12.1120i 0.587442 0.809266i
\(225\) 5.70745 0.380497
\(226\) −7.71613 14.7634i −0.513269 0.982044i
\(227\) 4.45396 + 5.80451i 0.295619 + 0.385259i 0.917422 0.397915i \(-0.130266\pi\)
−0.621803 + 0.783174i \(0.713599\pi\)
\(228\) −6.58347 36.6335i −0.436001 2.42611i
\(229\) 10.8603 14.1534i 0.717669 0.935284i −0.282040 0.959403i \(-0.591011\pi\)
0.999709 + 0.0241182i \(0.00767780\pi\)
\(230\) −6.44784 + 13.8869i −0.425158 + 0.915673i
\(231\) −5.14130 7.06231i −0.338273 0.464666i
\(232\) 9.32025 + 5.32006i 0.611904 + 0.349279i
\(233\) −0.676776 + 2.52576i −0.0443370 + 0.165468i −0.984545 0.175134i \(-0.943964\pi\)
0.940208 + 0.340602i \(0.110631\pi\)
\(234\) 6.90886 + 1.20653i 0.451646 + 0.0788736i
\(235\) −2.94612 + 22.3780i −0.192184 + 1.45978i
\(236\) −1.54997 1.41095i −0.100894 0.0918453i
\(237\) 6.93154 16.7342i 0.450252 1.08700i
\(238\) −25.3170 + 1.61424i −1.64106 + 0.104636i
\(239\) 18.6180 1.20430 0.602148 0.798385i \(-0.294312\pi\)
0.602148 + 0.798385i \(0.294312\pi\)
\(240\) −8.72843 23.5002i −0.563417 1.51693i
\(241\) 8.27688 14.3360i 0.533161 0.923462i −0.466089 0.884738i \(-0.654337\pi\)
0.999250 0.0387240i \(-0.0123293\pi\)
\(242\) −12.1803 + 2.72127i −0.782976 + 0.174930i
\(243\) −2.34491 17.8114i −0.150426 1.14260i
\(244\) 11.4131 + 5.89377i 0.730649 + 0.377310i
\(245\) 8.40250 17.7025i 0.536816 1.13097i
\(246\) −9.92843 + 3.63211i −0.633014 + 0.231575i
\(247\) −19.7882 5.30223i −1.25909 0.337373i
\(248\) 10.3158 + 7.83524i 0.655054 + 0.497538i
\(249\) 9.16789 + 34.2150i 0.580992 + 2.16829i
\(250\) 8.53185 0.760545i 0.539601 0.0481011i
\(251\) −9.70839 + 4.02135i −0.612788 + 0.253825i −0.667420 0.744681i \(-0.732601\pi\)
0.0546319 + 0.998507i \(0.482601\pi\)
\(252\) 7.36420 7.69067i 0.463901 0.484467i
\(253\) 2.18267 5.26943i 0.137223 0.331286i
\(254\) −8.50909 16.2805i −0.533908 1.02153i
\(255\) −21.2458 + 36.7987i −1.33046 + 2.30443i
\(256\) −12.1207 + 10.4446i −0.757543 + 0.652785i
\(257\) 0.457753 0.264284i 0.0285538 0.0164856i −0.485655 0.874150i \(-0.661419\pi\)
0.514209 + 0.857665i \(0.328086\pi\)
\(258\) −25.7306 1.08113i −1.60192 0.0673084i
\(259\) −3.24865 + 5.31262i −0.201861 + 0.330110i
\(260\) −13.7494 1.15747i −0.852699 0.0717832i
\(261\) 6.05727 + 4.64790i 0.374935 + 0.287698i
\(262\) −3.89061 + 2.73375i −0.240362 + 0.168892i
\(263\) −9.77819 + 2.62006i −0.602949 + 0.161560i −0.547365 0.836894i \(-0.684369\pi\)
−0.0555846 + 0.998454i \(0.517702\pi\)
\(264\) 3.61617 + 8.61010i 0.222560 + 0.529915i
\(265\) −1.89277 + 1.89277i −0.116272 + 0.116272i
\(266\) −23.4206 + 20.4659i −1.43601 + 1.25484i
\(267\) 27.5343 11.4051i 1.68507 0.697979i
\(268\) −0.202364 4.31032i −0.0123613 0.263295i
\(269\) −14.7378 19.2067i −0.898582 1.17105i −0.984611 0.174762i \(-0.944084\pi\)
0.0860290 0.996293i \(-0.472582\pi\)
\(270\) 1.90883 + 8.54382i 0.116168 + 0.519960i
\(271\) −14.8899 + 8.59668i −0.904496 + 0.522211i −0.878656 0.477455i \(-0.841559\pi\)
−0.0258397 + 0.999666i \(0.508226\pi\)
\(272\) 26.7383 + 4.53397i 1.62125 + 0.274913i
\(273\) −5.24440 13.6235i −0.317405 0.824532i
\(274\) −23.0792 + 21.2180i −1.39427 + 1.28183i
\(275\) 4.14714 0.545981i 0.250082 0.0329239i
\(276\) 16.9187 + 3.69259i 1.01839 + 0.222268i
\(277\) 28.2293 + 3.71646i 1.69614 + 0.223301i 0.915680 0.401909i \(-0.131653\pi\)
0.780457 + 0.625209i \(0.214986\pi\)
\(278\) 19.4779 + 16.2895i 1.16820 + 0.976979i
\(279\) 6.51673 + 6.51673i 0.390147 + 0.390147i
\(280\) −13.0875 + 16.3570i −0.782125 + 0.977521i
\(281\) −2.85954 + 2.85954i −0.170586 + 0.170586i −0.787237 0.616651i \(-0.788489\pi\)
0.616651 + 0.787237i \(0.288489\pi\)
\(282\) 25.4278 2.26669i 1.51421 0.134979i
\(283\) −1.01044 + 7.67504i −0.0600643 + 0.456234i 0.934813 + 0.355141i \(0.115567\pi\)
−0.994877 + 0.101093i \(0.967766\pi\)
\(284\) −23.7908 + 4.27549i −1.41172 + 0.253704i
\(285\) 6.79993 + 51.6506i 0.402793 + 3.05952i
\(286\) 5.13551 + 0.215781i 0.303669 + 0.0127594i
\(287\) 6.87080 + 5.55309i 0.405571 + 0.327788i
\(288\) −9.54991 + 6.19467i −0.562734 + 0.365024i
\(289\) −14.4841 25.0872i −0.852007 1.47572i
\(290\) −12.6817 8.04994i −0.744697 0.472709i
\(291\) −1.78106 + 1.36666i −0.104408 + 0.0801148i
\(292\) −15.4857 5.57887i −0.906233 0.326479i
\(293\) 8.95439 + 21.6178i 0.523121 + 1.26293i 0.935955 + 0.352120i \(0.114539\pi\)
−0.412834 + 0.910807i \(0.635461\pi\)
\(294\) −21.6125 4.90921i −1.26047 0.286311i
\(295\) 2.07444 + 2.07444i 0.120779 + 0.120779i
\(296\) 4.68407 4.73041i 0.272256 0.274949i
\(297\) −0.844065 3.15009i −0.0489776 0.182787i
\(298\) 2.88306 16.5090i 0.167011 0.956339i
\(299\) 5.80233 7.56174i 0.335557 0.437307i
\(300\) 3.85869 + 12.0996i 0.222781 + 0.698572i
\(301\) 10.2866 + 18.9027i 0.592907 + 1.08953i
\(302\) −2.57935 2.80561i −0.148425 0.161445i
\(303\) 4.01378 + 6.95207i 0.230586 + 0.399386i
\(304\) 29.3918 15.5464i 1.68574 0.891647i
\(305\) −15.5702 8.98943i −0.891544 0.514733i
\(306\) 18.4108 + 5.77171i 1.05248 + 0.329947i
\(307\) −7.88643 3.26667i −0.450102 0.186438i 0.146105 0.989269i \(-0.453326\pi\)
−0.596207 + 0.802831i \(0.703326\pi\)
\(308\) 4.61526 6.29264i 0.262979 0.358557i
\(309\) 7.90241 + 19.0781i 0.449552 + 1.08531i
\(310\) −13.9086 11.6318i −0.789953 0.660644i
\(311\) −27.6552 + 7.41020i −1.56818 + 0.420194i −0.935243 0.354006i \(-0.884819\pi\)
−0.632941 + 0.774200i \(0.718152\pi\)
\(312\) 2.11311 + 15.4623i 0.119631 + 0.875379i
\(313\) 1.31242 4.89803i 0.0741826 0.276853i −0.918864 0.394574i \(-0.870892\pi\)
0.993047 + 0.117721i \(0.0375588\pi\)
\(314\) 2.41281 5.19654i 0.136163 0.293257i
\(315\) −10.8009 + 10.2692i −0.608564 + 0.578603i
\(316\) 16.1239 + 1.35737i 0.907039 + 0.0763577i
\(317\) 14.4031 1.89620i 0.808957 0.106501i 0.285309 0.958436i \(-0.407904\pi\)
0.523648 + 0.851935i \(0.324571\pi\)
\(318\) 2.55606 + 1.62250i 0.143337 + 0.0909853i
\(319\) 4.84594 + 2.79780i 0.271320 + 0.156647i
\(320\) 17.6319 13.8073i 0.985654 0.771851i
\(321\) 6.13546i 0.342448i
\(322\) −4.62713 13.7110i −0.257860 0.764083i
\(323\) −52.0688 21.5676i −2.89718 1.20005i
\(324\) 19.8857 9.35240i 1.10476 0.519578i
\(325\) 6.93035 + 0.912398i 0.384427 + 0.0506107i
\(326\) 1.53969 + 2.19124i 0.0852754 + 0.121362i
\(327\) 12.6452 + 3.38827i 0.699280 + 0.187372i
\(328\) −5.78610 7.46425i −0.319484 0.412144i
\(329\) −12.5554 17.2466i −0.692200 0.950835i
\(330\) −4.49071 12.2754i −0.247205 0.675740i
\(331\) 24.1471 + 18.5287i 1.32725 + 1.01843i 0.997224 + 0.0744587i \(0.0237229\pi\)
0.330022 + 0.943973i \(0.392944\pi\)
\(332\) −26.6320 + 17.0896i −1.46162 + 0.937913i
\(333\) 3.75745 2.88319i 0.205907 0.157998i
\(334\) 0.298950 0.953601i 0.0163578 0.0521787i
\(335\) 6.03968i 0.329983i
\(336\) 21.2828 + 10.4124i 1.16107 + 0.568042i
\(337\) 2.70036i 0.147098i −0.997292 0.0735491i \(-0.976567\pi\)
0.997292 0.0735491i \(-0.0234325\pi\)
\(338\) −9.34663 2.93013i −0.508389 0.159378i
\(339\) 20.9217 16.0538i 1.13631 0.871921i
\(340\) −37.0860 8.09421i −2.01127 0.438970i
\(341\) 5.35857 + 4.11177i 0.290183 + 0.222665i
\(342\) 22.2157 8.12713i 1.20129 0.439465i
\(343\) 5.77315 + 17.5975i 0.311721 + 0.950174i
\(344\) −6.06375 22.1927i −0.326935 1.19655i
\(345\) −23.4122 6.27329i −1.26047 0.337743i
\(346\) 5.51248 3.87337i 0.296353 0.208234i
\(347\) 28.0010 + 3.68640i 1.50317 + 0.197896i 0.836711 0.547645i \(-0.184476\pi\)
0.666459 + 0.745541i \(0.267809\pi\)
\(348\) −5.75822 + 15.9836i −0.308673 + 0.856809i
\(349\) −2.69704 1.11715i −0.144369 0.0597998i 0.309329 0.950955i \(-0.399896\pi\)
−0.453698 + 0.891155i \(0.649896\pi\)
\(350\) 7.01152 7.96653i 0.374781 0.425829i
\(351\) 5.44988i 0.290893i
\(352\) −6.34654 + 5.41471i −0.338272 + 0.288605i
\(353\) 8.47425 + 4.89261i 0.451039 + 0.260407i 0.708269 0.705943i \(-0.249477\pi\)
−0.257230 + 0.966350i \(0.582810\pi\)
\(354\) 1.77823 2.80139i 0.0945119 0.148892i
\(355\) 33.5433 4.41607i 1.78030 0.234380i
\(356\) 17.1803 + 20.3388i 0.910555 + 1.07795i
\(357\) −9.41221 39.0416i −0.498147 2.06630i
\(358\) 16.1487 + 7.49803i 0.853485 + 0.396283i
\(359\) 8.29234 30.9474i 0.437653 1.63334i −0.296983 0.954883i \(-0.595980\pi\)
0.734636 0.678461i \(-0.237353\pi\)
\(360\) 13.7587 8.03411i 0.725145 0.423435i
\(361\) −48.3911 + 12.9663i −2.54690 + 0.682439i
\(362\) −19.7749 + 23.6455i −1.03935 + 1.24278i
\(363\) −7.56093 18.2537i −0.396846 0.958070i
\(364\) 10.1715 8.16126i 0.533132 0.427766i
\(365\) 21.2849 + 8.81649i 1.11410 + 0.461476i
\(366\) −6.08294 + 19.4036i −0.317960 + 1.01424i
\(367\) 19.7133 + 11.3815i 1.02903 + 0.594109i 0.916706 0.399562i \(-0.130838\pi\)
0.112322 + 0.993672i \(0.464171\pi\)
\(368\) 1.44938 + 15.4018i 0.0755542 + 0.802874i
\(369\) −3.35952 5.81887i −0.174890 0.302918i
\(370\) −6.85946 + 6.30627i −0.356606 + 0.327847i
\(371\) 0.0638279 2.52911i 0.00331378 0.131305i
\(372\) −9.40945 + 18.2211i −0.487857 + 0.944720i
\(373\) −22.0739 + 28.7672i −1.14294 + 1.48951i −0.298068 + 0.954545i \(0.596342\pi\)
−0.844874 + 0.534966i \(0.820324\pi\)
\(374\) 13.9297 + 2.43263i 0.720289 + 0.125788i
\(375\) 3.50962 + 13.0981i 0.181236 + 0.676382i
\(376\) 8.83090 + 21.0264i 0.455419 + 1.08435i
\(377\) 6.61210 + 6.61210i 0.340540 + 0.340540i
\(378\) −6.87150 4.60905i −0.353432 0.237064i
\(379\) 3.42524 + 8.26926i 0.175943 + 0.424764i 0.987108 0.160053i \(-0.0511665\pi\)
−0.811166 + 0.584816i \(0.801167\pi\)
\(380\) −42.1141 + 19.8066i −2.16041 + 1.01606i
\(381\) 23.0717 17.7036i 1.18200 0.906981i
\(382\) 4.60321 7.25181i 0.235521 0.371035i
\(383\) 7.24472 + 12.5482i 0.370188 + 0.641185i 0.989594 0.143886i \(-0.0459599\pi\)
−0.619406 + 0.785071i \(0.712627\pi\)
\(384\) −19.5890 16.0574i −0.999647 0.819427i
\(385\) −6.86579 + 8.49500i −0.349913 + 0.432945i
\(386\) 0.0391152 0.930926i 0.00199091 0.0473829i
\(387\) −2.13640 16.2276i −0.108600 0.824895i
\(388\) −1.64658 1.14492i −0.0835926 0.0581244i
\(389\) 2.33024 17.7000i 0.118148 0.897424i −0.825019 0.565105i \(-0.808836\pi\)
0.943167 0.332319i \(-0.107831\pi\)
\(390\) −1.93946 21.7570i −0.0982085 1.10171i
\(391\) 18.5413 18.5413i 0.937672 0.937672i
\(392\) −1.68794 19.7269i −0.0852537 0.996359i
\(393\) −5.32279 5.32279i −0.268499 0.268499i
\(394\) −7.26774 + 8.69027i −0.366143 + 0.437809i
\(395\) −22.4542 2.95615i −1.12979 0.148740i
\(396\) −4.99523 + 3.20540i −0.251020 + 0.161078i
\(397\) −20.7765 + 2.73528i −1.04274 + 0.137280i −0.632393 0.774647i \(-0.717927\pi\)
−0.410352 + 0.911927i \(0.634594\pi\)
\(398\) −9.65725 10.5044i −0.484074 0.526537i
\(399\) −38.2944 30.9501i −1.91712 1.54944i
\(400\) −9.25065 + 6.56826i −0.462533 + 0.328413i
\(401\) −17.8948 + 10.3316i −0.893624 + 0.515934i −0.875126 0.483895i \(-0.839222\pi\)
−0.0184980 + 0.999829i \(0.505888\pi\)
\(402\) 6.66673 1.48946i 0.332506 0.0742873i
\(403\) 6.87126 + 8.95480i 0.342282 + 0.446070i
\(404\) −4.82747 + 5.30309i −0.240176 + 0.263838i
\(405\) −28.4167 + 11.7706i −1.41204 + 0.584885i
\(406\) 13.9289 2.74493i 0.691278 0.136229i
\(407\) 2.45442 2.45442i 0.121661 0.121661i
\(408\) 0.211291 + 42.9325i 0.0104605 + 2.12547i
\(409\) 20.5306 5.50115i 1.01517 0.272014i 0.287383 0.957816i \(-0.407215\pi\)
0.727789 + 0.685801i \(0.240548\pi\)
\(410\) 7.59978 + 10.8158i 0.375326 + 0.534155i
\(411\) −39.3743 30.2130i −1.94219 1.49030i
\(412\) −14.0925 + 11.9040i −0.694286 + 0.586468i
\(413\) −2.77186 0.0699541i −0.136394 0.00344222i
\(414\) −0.462032 + 10.9962i −0.0227077 + 0.540434i
\(415\) 38.3569 22.1454i 1.88287 1.08707i
\(416\) −12.5864 + 5.99530i −0.617099 + 0.293944i
\(417\) −20.0984 + 34.8115i −0.984225 + 1.70473i
\(418\) 15.3648 8.03049i 0.751518 0.392784i
\(419\) −4.07967 + 9.84919i −0.199305 + 0.481164i −0.991658 0.128899i \(-0.958856\pi\)
0.792353 + 0.610063i \(0.208856\pi\)
\(420\) −29.0727 15.9549i −1.41860 0.778519i
\(421\) −25.5754 + 10.5937i −1.24647 + 0.516303i −0.905730 0.423855i \(-0.860677\pi\)
−0.340737 + 0.940159i \(0.610677\pi\)
\(422\) −0.641557 7.19703i −0.0312305 0.350346i
\(423\) 4.19930 + 15.6720i 0.204177 + 0.761999i
\(424\) −0.687135 + 2.61585i −0.0333702 + 0.127037i
\(425\) 18.5751 + 4.97717i 0.901022 + 0.241428i
\(426\) −13.1467 35.9368i −0.636961 1.74114i
\(427\) 16.5191 3.98246i 0.799417 0.192725i
\(428\) 5.22189 1.66531i 0.252409 0.0804958i
\(429\) 1.06210 + 8.06747i 0.0512788 + 0.389501i
\(430\) 7.02118 + 31.4264i 0.338591 + 1.51552i
\(431\) −1.45011 + 2.51166i −0.0698493 + 0.120983i −0.898835 0.438287i \(-0.855585\pi\)
0.828986 + 0.559270i \(0.188919\pi\)
\(432\) 6.01853 + 6.48216i 0.289567 + 0.311873i
\(433\) 27.9227 1.34188 0.670940 0.741511i \(-0.265891\pi\)
0.670940 + 0.741511i \(0.265891\pi\)
\(434\) 17.1018 1.09043i 0.820915 0.0523425i
\(435\) 9.09993 21.9692i 0.436308 1.05334i
\(436\) 0.548453 + 11.6820i 0.0262661 + 0.559465i
\(437\) 4.19620 31.8733i 0.200732 1.52471i
\(438\) 4.48272 25.6689i 0.214193 1.22651i
\(439\) −1.89825 + 7.08435i −0.0905983 + 0.338118i −0.996315 0.0857653i \(-0.972666\pi\)
0.905717 + 0.423883i \(0.139333\pi\)
\(440\) 9.22873 7.15389i 0.439963 0.341048i
\(441\) 0.710525 14.0679i 0.0338345 0.669901i
\(442\) 21.4329 + 9.95155i 1.01946 + 0.473347i
\(443\) 11.7393 15.2990i 0.557751 0.726876i −0.426335 0.904565i \(-0.640196\pi\)
0.984087 + 0.177690i \(0.0568623\pi\)
\(444\) 8.65261 + 6.01641i 0.410635 + 0.285526i
\(445\) −22.6853 29.5641i −1.07539 1.40147i
\(446\) −11.9089 + 6.22421i −0.563900 + 0.294725i
\(447\) 26.5305 1.25485
\(448\) −3.08532 + 20.9399i −0.145768 + 0.989319i
\(449\) −20.8686 −0.984852 −0.492426 0.870354i \(-0.663890\pi\)
−0.492426 + 0.870354i \(0.663890\pi\)
\(450\) −7.15344 + 3.73877i −0.337216 + 0.176247i
\(451\) −2.99773 3.90671i −0.141157 0.183960i
\(452\) 19.3420 + 13.4491i 0.909772 + 0.632591i
\(453\) 3.67282 4.78652i 0.172564 0.224890i
\(454\) −9.38472 4.35744i −0.440447 0.204505i
\(455\) −14.7568 + 10.7429i −0.691811 + 0.503633i
\(456\) 32.2488 + 41.6019i 1.51019 + 1.94819i
\(457\) −4.96796 + 18.5407i −0.232391 + 0.867296i 0.746916 + 0.664918i \(0.231534\pi\)
−0.979308 + 0.202378i \(0.935133\pi\)
\(458\) −4.34030 + 24.8534i −0.202809 + 1.16132i
\(459\) 1.95697 14.8647i 0.0913435 0.693823i
\(460\) −1.01545 21.6289i −0.0473454 1.00845i
\(461\) 7.86022 18.9763i 0.366087 0.883812i −0.628296 0.777974i \(-0.716247\pi\)
0.994383 0.105838i \(-0.0337526\pi\)
\(462\) 11.0701 + 5.48364i 0.515030 + 0.255122i
\(463\) −22.3488 −1.03864 −0.519318 0.854581i \(-0.673814\pi\)
−0.519318 + 0.854581i \(0.673814\pi\)
\(464\) −15.1665 0.562501i −0.704089 0.0261135i
\(465\) 14.3517 24.8579i 0.665544 1.15276i
\(466\) −0.806309 3.60900i −0.0373515 0.167183i
\(467\) −0.959029 7.28455i −0.0443786 0.337089i −0.999203 0.0399181i \(-0.987290\pi\)
0.954824 0.297171i \(-0.0960430\pi\)
\(468\) −9.44957 + 3.01356i −0.436807 + 0.139302i
\(469\) −3.93326 4.13693i −0.181621 0.191026i
\(470\) −10.9666 29.9773i −0.505851 1.38275i
\(471\) 8.76098 + 2.34750i 0.403684 + 0.108167i
\(472\) 2.86692 + 0.753087i 0.131961 + 0.0346636i
\(473\) −3.10470 11.5869i −0.142754 0.532766i
\(474\) 2.27441 + 25.5145i 0.104467 + 1.17192i
\(475\) 21.7824 9.02257i 0.999445 0.413984i
\(476\) 30.6736 18.6076i 1.40592 0.852876i
\(477\) −0.736346 + 1.77770i −0.0337149 + 0.0813951i
\(478\) −23.3348 + 12.1960i −1.06731 + 0.557834i
\(479\) 14.2061 24.6056i 0.649092 1.12426i −0.334248 0.942485i \(-0.608482\pi\)
0.983340 0.181775i \(-0.0581844\pi\)
\(480\) 26.3340 + 23.7362i 1.20198 + 1.08341i
\(481\) 5.02344 2.90029i 0.229049 0.132242i
\(482\) −0.982785 + 23.3899i −0.0447646 + 1.06538i
\(483\) 20.1218 10.9499i 0.915573 0.498240i
\(484\) 13.4835 11.3896i 0.612886 0.517709i
\(485\) 2.22699 + 1.70883i 0.101122 + 0.0775939i
\(486\) 14.6066 + 20.7878i 0.662571 + 0.942953i
\(487\) −15.5924 + 4.17797i −0.706560 + 0.189322i −0.594167 0.804342i \(-0.702518\pi\)
−0.112393 + 0.993664i \(0.535851\pi\)
\(488\) −18.1654 + 0.0894009i −0.822310 + 0.00404699i
\(489\) −2.99787 + 2.99787i −0.135568 + 0.135568i
\(490\) 1.06508 + 27.6916i 0.0481152 + 1.25098i
\(491\) −3.58723 + 1.48588i −0.161889 + 0.0670567i −0.462156 0.886798i \(-0.652924\pi\)
0.300267 + 0.953855i \(0.402924\pi\)
\(492\) 10.0645 11.0561i 0.453743 0.498447i
\(493\) 15.6603 + 20.4089i 0.705306 + 0.919173i
\(494\) 28.2749 6.31707i 1.27215 0.284218i
\(495\) 7.19440 4.15369i 0.323364 0.186694i
\(496\) −18.0619 3.06274i −0.811005 0.137521i
\(497\) −20.0999 + 24.8694i −0.901603 + 1.11555i
\(498\) −33.9038 36.8778i −1.51926 1.65253i
\(499\) −0.547775 + 0.0721160i −0.0245218 + 0.00322835i −0.142777 0.989755i \(-0.545603\pi\)
0.118255 + 0.992983i \(0.462270\pi\)
\(500\) −10.1952 + 6.54217i −0.455942 + 0.292575i
\(501\) 1.56853 + 0.206501i 0.0700769 + 0.00922579i
\(502\) 9.53376 11.3998i 0.425512 0.508799i
\(503\) 3.75510 + 3.75510i 0.167432 + 0.167432i 0.785850 0.618418i \(-0.212226\pi\)
−0.618418 + 0.785850i \(0.712226\pi\)
\(504\) −4.19200 + 14.4632i −0.186727 + 0.644240i
\(505\) 7.09754 7.09754i 0.315836 0.315836i
\(506\) 0.716187 + 8.03423i 0.0318384 + 0.357165i
\(507\) 2.02400 15.3738i 0.0898891 0.682776i
\(508\) 21.3297 + 14.8312i 0.946354 + 0.658027i
\(509\) 0.365760 + 2.77822i 0.0162120 + 0.123143i 0.997637 0.0687030i \(-0.0218861\pi\)
−0.981425 + 0.191845i \(0.938553\pi\)
\(510\) 2.52269 60.0391i 0.111707 2.65858i
\(511\) −20.3209 + 7.82256i −0.898942 + 0.346050i
\(512\) 8.34956 21.0306i 0.369002 0.929429i
\(513\) −9.19095 15.9192i −0.405791 0.702850i
\(514\) −0.400601 + 0.631099i −0.0176697 + 0.0278366i
\(515\) 20.4845 15.7183i 0.902656 0.692632i
\(516\) 32.9576 15.5002i 1.45088 0.682360i
\(517\) 4.55049 + 10.9858i 0.200130 + 0.483157i
\(518\) 0.591571 8.78665i 0.0259922 0.386063i
\(519\) 7.54169 + 7.54169i 0.331044 + 0.331044i
\(520\) 17.9910 7.55605i 0.788957 0.331355i
\(521\) 11.1466 + 41.5998i 0.488343 + 1.82252i 0.564510 + 0.825426i \(0.309065\pi\)
−0.0761669 + 0.997095i \(0.524268\pi\)
\(522\) −10.6366 1.85753i −0.465550 0.0813018i
\(523\) −11.1050 + 14.4723i −0.485587 + 0.632830i −0.970318 0.241834i \(-0.922251\pi\)
0.484730 + 0.874664i \(0.338918\pi\)
\(524\) 3.08549 5.97496i 0.134790 0.261017i
\(525\) 14.3331 + 8.76468i 0.625549 + 0.382522i
\(526\) 10.5392 9.68923i 0.459530 0.422471i
\(527\) 15.5260 + 26.8918i 0.676322 + 1.17142i
\(528\) −10.1725 8.42263i −0.442702 0.366548i
\(529\) −6.96524 4.02139i −0.302837 0.174843i
\(530\) 1.13241 3.61220i 0.0491888 0.156904i
\(531\) 1.94832 + 0.807021i 0.0845499 + 0.0350217i
\(532\) 15.9476 40.9929i 0.691417 1.77727i
\(533\) −3.14914 7.60269i −0.136404 0.329309i
\(534\) −27.0390 + 32.3314i −1.17009 + 1.39911i
\(535\) −7.41020 + 1.98556i −0.320371 + 0.0858431i
\(536\) 3.07719 + 5.26978i 0.132914 + 0.227620i
\(537\) −7.29505 + 27.2255i −0.314805 + 1.17487i
\(538\) 31.0534 + 14.4185i 1.33881 + 0.621624i
\(539\) −0.829472 10.2900i −0.0357279 0.443220i
\(540\) −7.98921 9.45798i −0.343801 0.407007i
\(541\) −10.9908 + 1.44696i −0.472530 + 0.0622097i −0.363031 0.931777i \(-0.618258\pi\)
−0.109499 + 0.993987i \(0.534925\pi\)
\(542\) 13.0308 20.5285i 0.559722 0.881776i
\(543\) −42.2601 24.3989i −1.81355 1.04706i
\(544\) −36.4825 + 11.8327i −1.56417 + 0.507324i
\(545\) 16.3689i 0.701169i
\(546\) 15.4974 + 13.6396i 0.663227 + 0.583720i
\(547\) 21.9796 + 9.10425i 0.939780 + 0.389270i 0.799380 0.600825i \(-0.205161\pi\)
0.140400 + 0.990095i \(0.455161\pi\)
\(548\) 15.0271 41.7120i 0.641928 1.78185i
\(549\) −12.8133 1.68690i −0.546857 0.0719950i
\(550\) −4.84016 + 3.40096i −0.206385 + 0.145017i
\(551\) 30.4650 + 8.16308i 1.29785 + 0.347759i
\(552\) −23.6240 + 6.45480i −1.00550 + 0.274735i
\(553\) 17.3053 12.5982i 0.735898 0.535728i
\(554\) −37.8158 + 13.8341i −1.60664 + 0.587755i
\(555\) −11.7026 8.97971i −0.496747 0.381167i
\(556\) −35.0833 7.65710i −1.48786 0.324734i
\(557\) 7.41909 5.69287i 0.314357 0.241215i −0.439516 0.898235i \(-0.644850\pi\)
0.753873 + 0.657020i \(0.228183\pi\)
\(558\) −12.4367 3.89884i −0.526485 0.165051i
\(559\) 20.0461i 0.847860i
\(560\) 5.68819 29.0743i 0.240370 1.22861i
\(561\) 22.3856i 0.945120i
\(562\) 1.71081 5.45719i 0.0721661 0.230198i
\(563\) −24.9305 + 19.1299i −1.05070 + 0.806227i −0.981517 0.191377i \(-0.938705\pi\)
−0.0691791 + 0.997604i \(0.522038\pi\)
\(564\) −30.3851 + 19.4979i −1.27944 + 0.821010i
\(565\) −26.1599 20.0732i −1.10055 0.844485i
\(566\) −3.76124 10.2814i −0.158097 0.432160i
\(567\) 11.7988 26.5683i 0.495504 1.11577i
\(568\) 27.0175 20.9433i 1.13363 0.878761i
\(569\) 16.1825 + 4.33608i 0.678405 + 0.181778i 0.581538 0.813519i \(-0.302451\pi\)
0.0968670 + 0.995297i \(0.469118\pi\)
\(570\) −42.3573 60.2818i −1.77415 2.52493i
\(571\) 12.6810 + 1.66949i 0.530684 + 0.0698659i 0.391107 0.920345i \(-0.372092\pi\)
0.139577 + 0.990211i \(0.455426\pi\)
\(572\) −6.57794 + 3.09366i −0.275038 + 0.129352i
\(573\) 12.5627 + 5.20363i 0.524813 + 0.217385i
\(574\) −12.2492 2.45912i −0.511270 0.102642i
\(575\) 10.9694i 0.457456i
\(576\) 7.91145 14.0199i 0.329644 0.584164i
\(577\) −2.13777 1.23424i −0.0889966 0.0513822i 0.454841 0.890573i \(-0.349696\pi\)
−0.543838 + 0.839190i \(0.683029\pi\)
\(578\) 34.5875 + 21.9550i 1.43865 + 0.913207i
\(579\) 1.46241 0.192530i 0.0607757 0.00800127i
\(580\) 21.1679 + 1.78199i 0.878949 + 0.0739931i
\(581\) −11.8510 + 40.1480i −0.491662 + 1.66562i
\(582\) 1.33704 2.87961i 0.0554221 0.119364i
\(583\) −0.364985 + 1.36214i −0.0151161 + 0.0564142i
\(584\) 23.0636 3.15192i 0.954377 0.130428i
\(585\) 13.4096 3.59308i 0.554417 0.148556i
\(586\) −25.3841 21.2290i −1.04861 0.876960i
\(587\) 2.22615 + 5.37441i 0.0918832 + 0.221826i 0.963139 0.269003i \(-0.0866941\pi\)
−0.871256 + 0.490829i \(0.836694\pi\)
\(588\) 30.3039 8.00473i 1.24971 0.330110i
\(589\) 35.1729 + 14.5691i 1.44927 + 0.600309i
\(590\) −3.95890 1.24110i −0.162985 0.0510953i
\(591\) −15.5316 8.96715i −0.638883 0.368859i
\(592\) −2.77204 + 8.99724i −0.113930 + 0.369784i
\(593\) 0.667105 + 1.15546i 0.0273947 + 0.0474490i 0.879398 0.476088i \(-0.157946\pi\)
−0.852003 + 0.523537i \(0.824612\pi\)
\(594\) 3.12144 + 3.39525i 0.128074 + 0.139309i
\(595\) −44.1072 + 24.0024i −1.80822 + 0.984003i
\(596\) 7.20102 + 22.5801i 0.294965 + 0.924918i
\(597\) 13.7513 17.9210i 0.562802 0.733458i
\(598\) −2.31889 + 13.2784i −0.0948265 + 0.542995i
\(599\) 1.82151 + 6.79796i 0.0744248 + 0.277757i 0.993102 0.117251i \(-0.0374083\pi\)
−0.918677 + 0.395009i \(0.870742\pi\)
\(600\) −12.7624 12.6374i −0.521021 0.515918i
\(601\) −26.3534 26.3534i −1.07498 1.07498i −0.996951 0.0780263i \(-0.975138\pi\)
−0.0780263 0.996951i \(-0.524862\pi\)
\(602\) −25.2752 16.9533i −1.03014 0.690966i
\(603\) 1.66143 + 4.01105i 0.0676587 + 0.163343i
\(604\) 5.07070 + 1.82676i 0.206324 + 0.0743300i
\(605\) −19.5993 + 15.0391i −0.796826 + 0.611426i
\(606\) −9.58475 6.08408i −0.389354 0.247149i
\(607\) 3.38930 + 5.87044i 0.137567 + 0.238274i 0.926575 0.376109i \(-0.122738\pi\)
−0.789008 + 0.614383i \(0.789405\pi\)
\(608\) −26.6543 + 38.7387i −1.08097 + 1.57106i
\(609\) 8.07404 + 20.9742i 0.327177 + 0.849916i
\(610\) 25.4035 + 1.06739i 1.02856 + 0.0432174i
\(611\) 2.59372 + 19.7013i 0.104931 + 0.797028i
\(612\) −26.8560 + 4.82635i −1.08559 + 0.195094i
\(613\) 5.87814 44.6489i 0.237416 1.80335i −0.293535 0.955948i \(-0.594832\pi\)
0.530950 0.847403i \(-0.321835\pi\)
\(614\) 12.0243 1.07187i 0.485263 0.0432573i
\(615\) −14.7973 + 14.7973i −0.596683 + 0.596683i
\(616\) −1.66242 + 10.9102i −0.0669809 + 0.439584i
\(617\) −12.0013 12.0013i −0.483154 0.483154i 0.422984 0.906137i \(-0.360983\pi\)
−0.906137 + 0.422984i \(0.860983\pi\)
\(618\) −22.4019 18.7349i −0.901138 0.753629i
\(619\) 38.5027 + 5.06898i 1.54755 + 0.203739i 0.855384 0.517995i \(-0.173321\pi\)
0.692171 + 0.721734i \(0.256655\pi\)
\(620\) 25.0519 + 5.46771i 1.00611 + 0.219588i
\(621\) 8.47914 1.11630i 0.340256 0.0447956i
\(622\) 29.8075 27.4036i 1.19517 1.09879i
\(623\) 34.7917 + 5.47665i 1.39390 + 0.219417i
\(624\) −12.7773 17.9954i −0.511502 0.720393i
\(625\) 26.9653 15.5684i 1.07861 0.622738i
\(626\) 1.56362 + 6.99867i 0.0624948 + 0.279723i
\(627\) 16.7078 + 21.7740i 0.667246 + 0.869572i
\(628\) 0.379985 + 8.09363i 0.0151631 + 0.322971i
\(629\) 14.7430 6.10675i 0.587842 0.243492i
\(630\) 6.81034 19.9462i 0.271331 0.794677i
\(631\) −25.4634 + 25.4634i −1.01368 + 1.01368i −0.0137759 + 0.999905i \(0.504385\pi\)
−0.999905 + 0.0137759i \(0.995615\pi\)
\(632\) −21.0980 + 8.86099i −0.839235 + 0.352471i
\(633\) 11.0489 2.96054i 0.439153 0.117671i
\(634\) −16.8099 + 11.8116i −0.667608 + 0.469098i
\(635\) −28.8483 22.1361i −1.14481 0.878442i
\(636\) −4.26649 0.359168i −0.169177 0.0142419i
\(637\) 3.11167 16.9686i 0.123289 0.672319i
\(638\) −7.90641 0.332207i −0.313018 0.0131522i
\(639\) 21.0619 12.1601i 0.833195 0.481045i
\(640\) −13.0542 + 28.8555i −0.516014 + 1.14061i
\(641\) −12.4095 + 21.4938i −0.490145 + 0.848956i −0.999936 0.0113428i \(-0.996389\pi\)
0.509791 + 0.860298i \(0.329723\pi\)
\(642\) 4.01914 + 7.68987i 0.158623 + 0.303495i
\(643\) −6.27063 + 15.1386i −0.247289 + 0.597009i −0.997972 0.0636536i \(-0.979725\pi\)
0.750683 + 0.660663i \(0.229725\pi\)
\(644\) 14.7810 + 14.1536i 0.582454 + 0.557729i
\(645\) −47.0966 + 19.5080i −1.85443 + 0.768129i
\(646\) 79.3886 7.07686i 3.12350 0.278435i
\(647\) 9.85591 + 36.7828i 0.387476 + 1.44608i 0.834227 + 0.551421i \(0.185914\pi\)
−0.446751 + 0.894658i \(0.647419\pi\)
\(648\) −18.7973 + 24.7483i −0.738426 + 0.972206i
\(649\) 1.49288 + 0.400017i 0.0586008 + 0.0157020i
\(650\) −9.28384 + 3.39630i −0.364142 + 0.133214i
\(651\) 6.35803 + 26.3729i 0.249191 + 1.03364i
\(652\) −3.36518 1.73779i −0.131791 0.0680572i
\(653\) 2.55467 + 19.4046i 0.0999720 + 0.759363i 0.965849 + 0.259106i \(0.0834278\pi\)
−0.865877 + 0.500257i \(0.833239\pi\)
\(654\) −18.0684 + 4.03677i −0.706530 + 0.157850i
\(655\) −4.70613 + 8.15125i −0.183884 + 0.318496i
\(656\) 12.1416 + 5.56502i 0.474050 + 0.217277i
\(657\) 16.5609 0.646103
\(658\) 27.0340 + 13.3914i 1.05389 + 0.522050i
\(659\) −16.3316 + 39.4280i −0.636190 + 1.53590i 0.195528 + 0.980698i \(0.437358\pi\)
−0.831717 + 0.555199i \(0.812642\pi\)
\(660\) 13.6697 + 12.4437i 0.532091 + 0.484370i
\(661\) 1.08911 8.27264i 0.0423616 0.321768i −0.957123 0.289680i \(-0.906451\pi\)
0.999485 0.0320879i \(-0.0102157\pi\)
\(662\) −42.4024 7.40498i −1.64802 0.287803i
\(663\) −9.68215 + 36.1343i −0.376023 + 1.40334i
\(664\) 22.1844 38.8650i 0.860923 1.50826i
\(665\) −24.9877 + 56.2667i −0.968981 + 2.18193i
\(666\) −2.82071 + 6.07504i −0.109300 + 0.235403i
\(667\) −8.93301 + 11.6417i −0.345887 + 0.450769i
\(668\) 0.249984 + 1.39103i 0.00967218 + 0.0538205i
\(669\) −12.9498 16.8765i −0.500667 0.652481i
\(670\) −3.95640 7.56984i −0.152849 0.292448i
\(671\) −9.47171 −0.365651
\(672\) −33.4956 + 0.891317i −1.29212 + 0.0343833i
\(673\) 17.2128 0.663505 0.331753 0.943366i \(-0.392360\pi\)
0.331753 + 0.943366i \(0.392360\pi\)
\(674\) 1.76892 + 3.38450i 0.0681363 + 0.130366i
\(675\) 3.81823 + 4.97601i 0.146964 + 0.191527i
\(676\) 13.6340 2.45020i 0.524386 0.0942384i
\(677\) −6.15110 + 8.01626i −0.236406 + 0.308090i −0.896457 0.443130i \(-0.853868\pi\)
0.660051 + 0.751221i \(0.270535\pi\)
\(678\) −15.7059 + 33.8261i −0.603180 + 1.29908i
\(679\) −2.63824 + 0.279820i −0.101247 + 0.0107385i
\(680\) 51.7840 14.1490i 1.98583 0.542589i
\(681\) 4.23948 15.8219i 0.162457 0.606298i
\(682\) −9.40965 1.64326i −0.360314 0.0629238i
\(683\) 2.50621 19.0366i 0.0958975 0.728414i −0.874177 0.485607i \(-0.838599\pi\)
0.970075 0.242807i \(-0.0780681\pi\)
\(684\) −22.5202 + 24.7389i −0.861080 + 0.945916i
\(685\) −23.7479 + 57.3326i −0.907362 + 2.19057i
\(686\) −18.7633 18.2740i −0.716386 0.697704i
\(687\) −39.9403 −1.52382
\(688\) 22.1378 + 23.8431i 0.843994 + 0.909010i
\(689\) −1.17830 + 2.04088i −0.0448897 + 0.0777512i
\(690\) 33.4531 7.47398i 1.27354 0.284530i
\(691\) −0.0455172 0.345737i −0.00173155 0.0131525i 0.990557 0.137100i \(-0.0437780\pi\)
−0.992289 + 0.123947i \(0.960445\pi\)
\(692\) −4.37174 + 8.46573i −0.166189 + 0.321819i
\(693\) −2.22283 + 7.53035i −0.0844383 + 0.286054i
\(694\) −37.5098 + 13.7222i −1.42385 + 0.520887i
\(695\) 48.5485 + 13.0085i 1.84155 + 0.493442i
\(696\) −3.25326 23.8050i −0.123314 0.902327i
\(697\) −5.85933 21.8673i −0.221938 0.828284i
\(698\) 4.11215 0.366565i 0.155647 0.0138747i
\(699\) 5.40855 2.24029i 0.204570 0.0847357i
\(700\) −3.56926 + 14.5779i −0.134905 + 0.550992i
\(701\) 13.0665 31.5452i 0.493514 1.19145i −0.459406 0.888226i \(-0.651938\pi\)
0.952920 0.303221i \(-0.0980622\pi\)
\(702\) 3.57004 + 6.83061i 0.134743 + 0.257805i
\(703\) 9.78238 16.9436i 0.368950 0.639039i
\(704\) 4.40744 10.9439i 0.166111 0.412465i
\(705\) 43.7623 25.2662i 1.64818 0.951579i
\(706\) −13.8262 0.580941i −0.520355 0.0218640i
\(707\) −0.239343 + 9.48369i −0.00900140 + 0.356671i
\(708\) −0.393641 + 4.67599i −0.0147939 + 0.175734i
\(709\) −41.6574 31.9648i −1.56448 1.20046i −0.883785 0.467893i \(-0.845013\pi\)
−0.680690 0.732571i \(-0.738320\pi\)
\(710\) −39.1487 + 27.5081i −1.46923 + 1.03236i
\(711\) −15.7254 + 4.21361i −0.589749 + 0.158023i
\(712\) −34.8563 14.2374i −1.30629 0.533568i
\(713\) −12.5248 + 12.5248i −0.469057 + 0.469057i
\(714\) 37.3717 + 42.7671i 1.39860 + 1.60052i
\(715\) 9.39991 3.89357i 0.351537 0.145611i
\(716\) −25.1517 + 1.18084i −0.939962 + 0.0441300i
\(717\) −25.3744 33.0686i −0.947625 1.23497i
\(718\) 9.87948 + 44.2200i 0.368699 + 1.65028i
\(719\) 8.24093 4.75790i 0.307335 0.177440i −0.338398 0.941003i \(-0.609885\pi\)
0.645733 + 0.763563i \(0.276552\pi\)
\(720\) −11.9815 + 19.0824i −0.446525 + 0.711159i
\(721\) −3.79469 + 24.1066i −0.141322 + 0.897778i
\(722\) 52.1571 47.9508i 1.94109 1.78454i
\(723\) −36.7437 + 4.83739i −1.36651 + 0.179905i
\(724\) 9.29548 42.5900i 0.345464 1.58285i
\(725\) −10.6697 1.40469i −0.396261 0.0521688i
\(726\) 21.4339 + 17.9253i 0.795486 + 0.665272i
\(727\) −27.1537 27.1537i −1.00707 1.00707i −0.999975 0.00709972i \(-0.997740\pi\)
−0.00709972 0.999975i \(-0.502260\pi\)
\(728\) −7.40229 + 16.8919i −0.274347 + 0.626057i
\(729\) −5.13187 + 5.13187i −0.190069 + 0.190069i
\(730\) −32.4528 + 2.89291i −1.20113 + 0.107071i
\(731\) 7.19826 54.6762i 0.266237 2.02227i
\(732\) −5.08660 28.3042i −0.188006 1.04615i
\(733\) −0.0178942 0.135920i −0.000660939 0.00502033i 0.991111 0.133036i \(-0.0424726\pi\)
−0.991772 + 0.128016i \(0.959139\pi\)
\(734\) −32.1634 1.35142i −1.18717 0.0498819i
\(735\) −42.8943 + 9.20251i −1.58218 + 0.339440i
\(736\) −11.9058 18.3544i −0.438854 0.676551i
\(737\) 1.59093 + 2.75557i 0.0586025 + 0.101503i
\(738\) 8.02241 + 5.09236i 0.295309 + 0.187452i
\(739\) −6.76348 + 5.18980i −0.248799 + 0.190910i −0.725630 0.688085i \(-0.758452\pi\)
0.476832 + 0.878995i \(0.341785\pi\)
\(740\) 4.46627 12.3974i 0.164183 0.455737i
\(741\) 17.5517 + 42.3736i 0.644778 + 1.55663i
\(742\) 1.57674 + 3.21167i 0.0578840 + 0.117904i
\(743\) −13.6464 13.6464i −0.500636 0.500636i 0.410999 0.911636i \(-0.365180\pi\)
−0.911636 + 0.410999i \(0.865180\pi\)
\(744\) −0.142729 29.0012i −0.00523271 1.06324i
\(745\) −8.58581 32.0427i −0.314560 1.17395i
\(746\) 8.82179 50.5153i 0.322989 1.84950i
\(747\) 19.3816 25.2585i 0.709134 0.924161i
\(748\) −19.0524 + 6.07598i −0.696624 + 0.222160i
\(749\) 3.78261 6.18581i 0.138213 0.226025i
\(750\) −12.9789 14.1174i −0.473923 0.515496i
\(751\) −15.0064 25.9918i −0.547590 0.948454i −0.998439 0.0558539i \(-0.982212\pi\)
0.450849 0.892600i \(-0.351121\pi\)
\(752\) −24.8419 20.5686i −0.905892 0.750059i
\(753\) 20.3742 + 11.7630i 0.742476 + 0.428668i
\(754\) −12.6186 3.95590i −0.459544 0.144065i
\(755\) −6.96960 2.88690i −0.253650 0.105065i
\(756\) 11.6316 + 1.27545i 0.423039 + 0.0463878i
\(757\) 9.17142 + 22.1418i 0.333341 + 0.804756i 0.998323 + 0.0578963i \(0.0184393\pi\)
−0.664982 + 0.746860i \(0.731561\pi\)
\(758\) −9.70996 8.12051i −0.352681 0.294950i
\(759\) −12.3341 + 3.30492i −0.447701 + 0.119961i
\(760\) 39.8091 52.4123i 1.44403 1.90119i
\(761\) 6.72409 25.0946i 0.243748 0.909680i −0.730261 0.683169i \(-0.760601\pi\)
0.974009 0.226511i \(-0.0727320\pi\)
\(762\) −17.3199 + 37.3023i −0.627434 + 1.35132i
\(763\) 10.6600 + 11.2120i 0.385919 + 0.405903i
\(764\) −1.01900 + 12.1045i −0.0368660 + 0.437925i
\(765\) 37.8651 4.98504i 1.36902 0.180234i
\(766\) −17.3001 10.9815i −0.625079 0.396779i
\(767\) 2.23676 + 1.29140i 0.0807648 + 0.0466296i
\(768\) 35.0706 + 7.29345i 1.26550 + 0.263180i
\(769\) 42.6140i 1.53670i 0.640029 + 0.768351i \(0.278922\pi\)
−0.640029 + 0.768351i \(0.721078\pi\)
\(770\) 3.04044 15.1448i 0.109570 0.545780i
\(771\) −1.09328 0.452853i −0.0393736 0.0163091i
\(772\) 0.560795 + 1.19240i 0.0201835 + 0.0429154i
\(773\) −2.76257 0.363699i −0.0993628 0.0130814i 0.0806808 0.996740i \(-0.474291\pi\)
−0.180044 + 0.983659i \(0.557624\pi\)
\(774\) 13.3078 + 18.9394i 0.478341 + 0.680762i
\(775\) −12.5476 3.36212i −0.450723 0.120771i
\(776\) 2.81374 + 0.356358i 0.101008 + 0.0127925i
\(777\) 13.8637 1.47042i 0.497357 0.0527510i
\(778\) 8.67407 + 23.7107i 0.310980 + 0.850070i
\(779\) −22.0203 16.8967i −0.788958 0.605389i
\(780\) 16.6831 + 25.9987i 0.597353 + 0.930902i
\(781\) 14.1407 10.8505i 0.505993 0.388262i
\(782\) −11.0929 + 35.3845i −0.396681 + 1.26535i
\(783\) 8.39039i 0.299848i
\(784\) 15.0380 + 23.6190i 0.537073 + 0.843536i
\(785\) 11.3409i 0.404775i
\(786\) 10.1581 + 3.18453i 0.362328 + 0.113588i
\(787\) −12.8264 + 9.84202i −0.457211 + 0.350830i −0.811546 0.584288i \(-0.801374\pi\)
0.354335 + 0.935118i \(0.384707\pi\)
\(788\) 3.41630 15.6528i 0.121701 0.557608i
\(789\) 17.9804 + 13.7968i 0.640118 + 0.491180i
\(790\) 30.0795 11.0040i 1.07018 0.391503i
\(791\) 30.9908 3.28697i 1.10191 0.116871i
\(792\) 4.16102 7.28971i 0.147855 0.259029i
\(793\) −15.2890 4.09667i −0.542928 0.145477i
\(794\) 24.2485 17.0383i 0.860546 0.604667i
\(795\) 5.94154 + 0.782218i 0.210725 + 0.0277424i
\(796\) 18.9850 + 6.83952i 0.672905 + 0.242420i
\(797\) 12.3750 + 5.12587i 0.438343 + 0.181568i 0.590931 0.806722i \(-0.298761\pi\)
−0.152588 + 0.988290i \(0.548761\pi\)
\(798\) 68.2707 + 13.7059i 2.41675 + 0.485183i
\(799\) 54.6670i 1.93398i
\(800\) 7.29165 14.2921i 0.257799 0.505303i
\(801\) −23.1983 13.3936i −0.819673 0.473239i
\(802\) 15.6606 24.6714i 0.552994 0.871177i
\(803\) 12.0335 1.58423i 0.424651 0.0559064i
\(804\) −7.38005 + 6.23397i −0.260274 + 0.219855i
\(805\) −19.7368 20.7588i −0.695631 0.731651i
\(806\) −14.4781 6.72235i −0.509969 0.236785i
\(807\) −14.0281 + 52.3537i −0.493814 + 1.84294i
\(808\) 2.57663 9.80894i 0.0906454 0.345077i
\(809\) 28.9551 7.75850i 1.01801 0.272774i 0.289036 0.957318i \(-0.406665\pi\)
0.728971 + 0.684544i \(0.239999\pi\)
\(810\) 27.9056 33.3676i 0.980501 1.17242i
\(811\) 16.7169 + 40.3581i 0.587008 + 1.41716i 0.886349 + 0.463017i \(0.153233\pi\)
−0.299341 + 0.954146i \(0.596767\pi\)
\(812\) −15.6596 + 12.5647i −0.549545 + 0.440935i
\(813\) 35.5626 + 14.7305i 1.24723 + 0.516621i
\(814\) −1.46843 + 4.68406i −0.0514686 + 0.164176i
\(815\) 4.59090 + 2.65056i 0.160812 + 0.0928450i
\(816\) −28.3885 53.6710i −0.993796 1.87886i
\(817\) −33.8068 58.5551i −1.18275 2.04858i
\(818\) −22.1284 + 20.3438i −0.773700 + 0.711304i
\(819\) −6.84504 + 11.1939i −0.239185 + 0.391147i
\(820\) −16.6103 8.57761i −0.580056 0.299543i
\(821\) 5.98674 7.80207i 0.208939 0.272294i −0.677115 0.735878i \(-0.736770\pi\)
0.886053 + 0.463583i \(0.153437\pi\)
\(822\) 69.1414 + 12.0746i 2.41158 + 0.421149i
\(823\) −8.35156 31.1684i −0.291117 1.08646i −0.944252 0.329222i \(-0.893213\pi\)
0.653135 0.757241i \(-0.273453\pi\)
\(824\) 9.86486 24.1514i 0.343659 0.841354i
\(825\) −6.62188 6.62188i −0.230544 0.230544i
\(826\) 3.51993 1.72808i 0.122474 0.0601275i
\(827\) 10.9485 + 26.4320i 0.380716 + 0.919131i 0.991828 + 0.127586i \(0.0407228\pi\)
−0.611111 + 0.791545i \(0.709277\pi\)
\(828\) −6.62417 14.0848i −0.230206 0.489479i
\(829\) −22.2151 + 17.0462i −0.771561 + 0.592040i −0.917723 0.397221i \(-0.869975\pi\)
0.146162 + 0.989261i \(0.453308\pi\)
\(830\) −33.5679 + 52.8823i −1.16516 + 1.83557i
\(831\) −31.8727 55.2052i −1.10565 1.91505i
\(832\) 11.8478 15.7592i 0.410749 0.546350i
\(833\) 14.5803 45.1648i 0.505178 1.56487i
\(834\) 2.38646 56.7969i 0.0826364 1.96672i
\(835\) −0.258203 1.96125i −0.00893550 0.0678719i
\(836\) −13.9970 + 20.1300i −0.484096 + 0.696211i
\(837\) −1.32195 + 10.0412i −0.0456933 + 0.347075i
\(838\) −1.33864 15.0169i −0.0462425 0.518751i
\(839\) 7.04739 7.04739i 0.243303 0.243303i −0.574912 0.818215i \(-0.694964\pi\)
0.818215 + 0.574912i \(0.194964\pi\)
\(840\) 46.8897 + 0.952485i 1.61785 + 0.0328638i
\(841\) 10.3264 + 10.3264i 0.356083 + 0.356083i
\(842\) 25.1153 30.0312i 0.865530 1.03494i
\(843\) 8.97627 + 1.18175i 0.309159 + 0.0407016i
\(844\) 5.51864 + 8.60014i 0.189960 + 0.296029i
\(845\) −19.2230 + 2.53076i −0.661292 + 0.0870607i
\(846\) −15.5294 16.8917i −0.533913 0.580748i
\(847\) 3.63072 23.0649i 0.124753 0.792521i
\(848\) −0.852339 3.72869i −0.0292694 0.128044i
\(849\) 15.0093 8.66560i 0.515117 0.297403i
\(850\) −26.5414 + 5.92979i −0.910363 + 0.203390i
\(851\) 5.54133 + 7.22161i 0.189954 + 0.247553i
\(852\) 40.0185 + 36.4294i 1.37101 + 1.24805i
\(853\) 17.7877 7.36790i 0.609039 0.252272i −0.0567788 0.998387i \(-0.518083\pi\)
0.665817 + 0.746115i \(0.268083\pi\)
\(854\) −18.0955 + 15.8126i −0.619214 + 0.541095i
\(855\) 33.1100 33.1100i 1.13234 1.13234i
\(856\) −5.45396 + 5.50791i −0.186412 + 0.188256i
\(857\) −8.94759 + 2.39750i −0.305644 + 0.0818970i −0.408381 0.912812i \(-0.633907\pi\)
0.102737 + 0.994709i \(0.467240\pi\)
\(858\) −6.61593 9.41561i −0.225864 0.321444i
\(859\) −40.1430 30.8028i −1.36966 1.05098i −0.992160 0.124971i \(-0.960116\pi\)
−0.377503 0.926008i \(-0.623217\pi\)
\(860\) −29.3864 34.7890i −1.00207 1.18629i
\(861\) 0.498992 19.7720i 0.0170056 0.673828i
\(862\) 0.172184 4.09792i 0.00586461 0.139576i
\(863\) 11.7649 6.79244i 0.400480 0.231217i −0.286211 0.958167i \(-0.592396\pi\)
0.686691 + 0.726949i \(0.259062\pi\)
\(864\) −11.7896 4.18187i −0.401090 0.142270i
\(865\) 6.66797 11.5493i 0.226718 0.392686i
\(866\) −34.9970 + 18.2913i −1.18924 + 0.621563i
\(867\) −24.8187 + 59.9176i −0.842887 + 2.03491i
\(868\) −20.7203 + 12.5696i −0.703292 + 0.426639i
\(869\) −11.0233 + 4.56599i −0.373939 + 0.154891i
\(870\) 2.98591 + 33.4961i 0.101232 + 1.13563i
\(871\) 1.37621 + 5.13607i 0.0466310 + 0.174029i
\(872\) −8.33989 14.2823i −0.282424 0.483661i
\(873\) 1.94905 + 0.522248i 0.0659655 + 0.0176754i
\(874\) 15.6199 + 42.6972i 0.528351 + 1.44425i
\(875\) −4.53675 + 15.3693i −0.153370 + 0.519578i
\(876\) 11.1965 + 35.1087i 0.378294 + 1.18621i
\(877\) 0.799830 + 6.07532i 0.0270084 + 0.205149i 0.999629 0.0272513i \(-0.00867544\pi\)
−0.972620 + 0.232400i \(0.925342\pi\)
\(878\) −2.26157 10.1226i −0.0763241 0.341623i
\(879\) 26.1929 45.3674i 0.883465 1.53021i
\(880\) −6.88054 + 15.0118i −0.231943 + 0.506047i
\(881\) 51.9129 1.74899 0.874495 0.485035i \(-0.161193\pi\)
0.874495 + 0.485035i \(0.161193\pi\)
\(882\) 8.32491 + 18.0975i 0.280314 + 0.609374i
\(883\) 18.1106 43.7229i 0.609471 1.47139i −0.254106 0.967176i \(-0.581781\pi\)
0.863577 0.504217i \(-0.168219\pi\)
\(884\) −33.3818 + 1.56723i −1.12275 + 0.0527117i
\(885\) 0.857296 6.51181i 0.0288177 0.218892i
\(886\) −4.69159 + 26.8650i −0.157617 + 0.902547i
\(887\) 1.46757 5.47703i 0.0492761 0.183901i −0.936901 0.349594i \(-0.886320\pi\)
0.986177 + 0.165693i \(0.0529862\pi\)
\(888\) −14.7859 1.87262i −0.496183 0.0628410i
\(889\) 34.1756 3.62476i 1.14621 0.121571i
\(890\) 47.7991 + 22.1937i 1.60223 + 0.743935i
\(891\) −9.86442 + 12.8556i −0.330471 + 0.430678i
\(892\) 10.8487 15.6022i 0.363241 0.522401i
\(893\) 40.8015 + 53.1736i 1.36537 + 1.77939i
\(894\) −33.2520 + 17.3793i −1.11211 + 0.581251i
\(895\) 35.2429 1.17804
\(896\) −9.85010 28.2662i −0.329069 0.944306i
\(897\) −21.3389 −0.712485
\(898\) 26.1557 13.6704i 0.872827 0.456186i
\(899\) −10.5787 13.7864i −0.352819 0.459803i
\(900\) 6.51661 9.37198i 0.217220 0.312399i
\(901\) −3.94669 + 5.14343i −0.131483 + 0.171352i
\(902\) 6.31637 + 2.93276i 0.210312 + 0.0976504i
\(903\) 19.5548 44.0332i 0.650744 1.46533i
\(904\) −33.0524 4.18605i −1.09930 0.139226i
\(905\) −15.7919 + 58.9363i −0.524942 + 1.95911i
\(906\) −1.46784 + 8.40513i −0.0487657 + 0.279242i
\(907\) −2.17458 + 16.5176i −0.0722059 + 0.548458i 0.916662 + 0.399663i \(0.130873\pi\)
−0.988868 + 0.148795i \(0.952460\pi\)
\(908\) 14.6167 0.686237i 0.485074 0.0227736i
\(909\) 2.76116 6.66603i 0.0915818 0.221098i
\(910\) 11.4582 23.1313i 0.379835 0.766795i
\(911\) −11.0861 −0.367299 −0.183649 0.982992i \(-0.558791\pi\)
−0.183649 + 0.982992i \(0.558791\pi\)
\(912\) −67.6711 31.0166i −2.24081 1.02706i
\(913\) 11.6667 20.2073i 0.386112 0.668766i
\(914\) −5.91881 26.4923i −0.195777 0.876287i
\(915\) 5.25384 + 39.9069i 0.173687 + 1.31928i
\(916\) −10.8408 33.9932i −0.358189 1.12317i
\(917\) −2.08489 8.64806i −0.0688491 0.285584i
\(918\) 7.28460 + 19.9126i 0.240428 + 0.657213i
\(919\) −42.6700 11.4334i −1.40755 0.377153i −0.526502 0.850174i \(-0.676497\pi\)
−0.881051 + 0.473022i \(0.843163\pi\)
\(920\) 15.4411 + 26.4434i 0.509078 + 0.871812i
\(921\) 4.94627 + 18.4597i 0.162985 + 0.608269i
\(922\) 2.57913 + 28.9329i 0.0849392 + 0.952853i
\(923\) 27.5186 11.3986i 0.905785 0.375189i
\(924\) −17.4669 + 0.378782i −0.574619 + 0.0124610i
\(925\) −2.55469 + 6.16757i −0.0839977 + 0.202788i
\(926\) 28.0108 14.6400i 0.920493 0.481099i
\(927\) 9.28021 16.0738i 0.304802 0.527933i
\(928\) 19.3775 9.23010i 0.636096 0.302993i
\(929\) 13.3160 7.68797i 0.436882 0.252234i −0.265392 0.964141i \(-0.585501\pi\)
0.702274 + 0.711906i \(0.252168\pi\)
\(930\) −1.70410 + 40.5569i −0.0558796 + 1.32991i
\(931\) −19.5274 54.8132i −0.639985 1.79643i
\(932\) 3.37472 + 3.99515i 0.110543 + 0.130865i
\(933\) 50.8531 + 39.0209i 1.66485 + 1.27749i
\(934\) 5.97387 + 8.50186i 0.195471 + 0.278189i
\(935\) 27.0366 7.24443i 0.884190 0.236918i
\(936\) 9.86954 9.96716i 0.322596 0.325787i
\(937\) 21.3919 21.3919i 0.698844 0.698844i −0.265318 0.964161i \(-0.585477\pi\)
0.964161 + 0.265318i \(0.0854768\pi\)
\(938\) 7.63972 + 2.60847i 0.249446 + 0.0851694i
\(939\) −10.4884 + 4.34445i −0.342277 + 0.141776i
\(940\) 33.3822 + 30.3882i 1.08881 + 0.991155i
\(941\) −4.72958 6.16370i −0.154180 0.200931i 0.709877 0.704326i \(-0.248751\pi\)
−0.864056 + 0.503395i \(0.832084\pi\)
\(942\) −12.5183 + 2.79680i −0.407870 + 0.0911247i
\(943\) 11.1835 6.45681i 0.364186 0.210263i
\(944\) −4.08658 + 0.934148i −0.133007 + 0.0304039i
\(945\) −16.1789 2.54676i −0.526298 0.0828461i
\(946\) 11.4815 + 12.4886i 0.373295 + 0.406041i
\(947\) 10.5674 1.39122i 0.343394 0.0452087i 0.0431431 0.999069i \(-0.486263\pi\)
0.300251 + 0.953860i \(0.402930\pi\)
\(948\) −19.5643 30.4886i −0.635420 0.990225i
\(949\) 20.1093 + 2.64744i 0.652776 + 0.0859396i
\(950\) −21.3906 + 25.5774i −0.694002 + 0.829840i
\(951\) −22.9979 22.9979i −0.745758 0.745758i
\(952\) −26.2555 + 43.4151i −0.850947 + 1.40709i
\(953\) 19.6134 19.6134i 0.635340 0.635340i −0.314062 0.949402i \(-0.601690\pi\)
0.949402 + 0.314062i \(0.101690\pi\)
\(954\) −0.241613 2.71043i −0.00782251 0.0877534i
\(955\) 2.21924 16.8568i 0.0718128 0.545472i
\(956\) 21.2575 30.5718i 0.687515 0.988762i
\(957\) −1.63517 12.4203i −0.0528574 0.401492i
\(958\) −1.68681 + 40.1454i −0.0544983 + 1.29704i
\(959\) −21.0707 54.7359i −0.680408 1.76751i
\(960\) −48.5546 12.4993i −1.56709 0.403412i
\(961\) 5.01207 + 8.68117i 0.161680 + 0.280038i
\(962\) −4.39625 + 6.92577i −0.141741 + 0.223296i
\(963\) −4.37504 + 3.35708i −0.140984 + 0.108180i
\(964\) −14.0902 29.9595i −0.453815 0.964932i
\(965\) −0.705797 1.70394i −0.0227204 0.0548519i
\(966\) −18.0467 + 26.9052i −0.580642 + 0.865662i
\(967\) 15.5423 + 15.5423i 0.499807 + 0.499807i 0.911378 0.411571i \(-0.135020\pi\)
−0.411571 + 0.911378i \(0.635020\pi\)
\(968\) −9.43858 + 23.1078i −0.303367 + 0.742711i
\(969\) 32.6569 + 121.877i 1.04909 + 3.91526i
\(970\) −3.91060 0.682931i −0.125562 0.0219276i
\(971\) −14.9017 + 19.4202i −0.478217 + 0.623225i −0.968703 0.248224i \(-0.920153\pi\)
0.490485 + 0.871450i \(0.336820\pi\)
\(972\) −31.9247 16.4860i −1.02398 0.528789i
\(973\) −41.7253 + 22.7062i −1.33765 + 0.727928i
\(974\) 16.8059 15.4506i 0.538495 0.495068i
\(975\) −7.82481 13.5530i −0.250594 0.434042i
\(976\) 22.7091 12.0116i 0.726900 0.384483i
\(977\) −2.33924 1.35056i −0.0748389 0.0432083i 0.462114 0.886821i \(-0.347091\pi\)
−0.536953 + 0.843612i \(0.680425\pi\)
\(978\) 1.79357 5.72119i 0.0573521 0.182943i
\(979\) −18.1376 7.51282i −0.579679 0.240111i
\(980\) −19.4748 34.0096i −0.622100 1.08640i
\(981\) −4.50287 10.8709i −0.143765 0.347081i
\(982\) 3.52270 4.21220i 0.112414 0.134417i
\(983\) 10.4637 2.80375i 0.333741 0.0894256i −0.0880571 0.996115i \(-0.528066\pi\)
0.421798 + 0.906690i \(0.361399\pi\)
\(984\) −5.37186 + 20.4501i −0.171249 + 0.651926i
\(985\) −5.80390 + 21.6605i −0.184928 + 0.690160i
\(986\) −32.9971 15.3210i −1.05084 0.487919i
\(987\) −13.5211 + 45.8058i −0.430381 + 1.45802i
\(988\) −31.3002 + 26.4395i −0.995792 + 0.841151i
\(989\) 31.1885 4.10605i 0.991737 0.130565i
\(990\) −6.29615 + 9.91885i −0.200105 + 0.315242i
\(991\) −16.3281 9.42704i −0.518680 0.299460i 0.217715 0.976012i \(-0.430140\pi\)
−0.736394 + 0.676553i \(0.763473\pi\)
\(992\) 24.6442 7.99311i 0.782455 0.253782i
\(993\) 68.1422i 2.16243i
\(994\) 8.90099 44.3369i 0.282322 1.40628i
\(995\) −26.0946 10.8087i −0.827254 0.342660i
\(996\) 66.6508 + 24.0115i 2.11191 + 0.760835i
\(997\) −31.8631 4.19486i −1.00912 0.132853i −0.392198 0.919881i \(-0.628285\pi\)
−0.616917 + 0.787028i \(0.711619\pi\)
\(998\) 0.639313 0.449217i 0.0202371 0.0142197i
\(999\) 5.02739 + 1.34709i 0.159060 + 0.0426199i
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 224.2.be.a.115.4 yes 240
4.3 odd 2 896.2.bi.a.367.24 240
7.5 odd 6 inner 224.2.be.a.19.25 240
28.19 even 6 896.2.bi.a.495.24 240
32.5 even 8 896.2.bi.a.143.24 240
32.27 odd 8 inner 224.2.be.a.59.25 yes 240
224.5 odd 24 896.2.bi.a.271.24 240
224.187 even 24 inner 224.2.be.a.187.4 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.be.a.19.25 240 7.5 odd 6 inner
224.2.be.a.59.25 yes 240 32.27 odd 8 inner
224.2.be.a.115.4 yes 240 1.1 even 1 trivial
224.2.be.a.187.4 yes 240 224.187 even 24 inner
896.2.bi.a.143.24 240 32.5 even 8
896.2.bi.a.271.24 240 224.5 odd 24
896.2.bi.a.367.24 240 4.3 odd 2
896.2.bi.a.495.24 240 28.19 even 6