Properties

Label 144.2.x.e.13.15
Level $144$
Weight $2$
Character 144.13
Analytic conductor $1.150$
Analytic rank $0$
Dimension $72$
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] = [144,2,Mod(13,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 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("144.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.x (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 13.15
Character \(\chi\) \(=\) 144.13
Dual form 144.2.x.e.133.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.24122 - 0.677764i) q^{2} +(-1.37530 + 1.05287i) q^{3} +(1.08127 - 1.68251i) q^{4} +(1.10094 + 4.10876i) q^{5} +(-0.993456 + 2.23898i) q^{6} +(1.63313 - 0.942891i) q^{7} +(0.201751 - 2.82122i) q^{8} +(0.782911 - 2.89604i) q^{9} +O(q^{10})\) \(q+(1.24122 - 0.677764i) q^{2} +(-1.37530 + 1.05287i) q^{3} +(1.08127 - 1.68251i) q^{4} +(1.10094 + 4.10876i) q^{5} +(-0.993456 + 2.23898i) q^{6} +(1.63313 - 0.942891i) q^{7} +(0.201751 - 2.82122i) q^{8} +(0.782911 - 2.89604i) q^{9} +(4.15129 + 4.35372i) q^{10} +(-1.18389 - 0.317223i) q^{11} +(0.284402 + 3.45241i) q^{12} +(-2.31428 + 0.620109i) q^{13} +(1.38803 - 2.27722i) q^{14} +(-5.84014 - 4.49164i) q^{15} +(-1.66171 - 3.63851i) q^{16} +3.44622 q^{17} +(-0.991066 - 4.12526i) q^{18} +(-4.17726 - 4.17726i) q^{19} +(8.10347 + 2.59034i) q^{20} +(-1.25331 + 3.01624i) q^{21} +(-1.68448 + 0.408656i) q^{22} +(-1.34867 - 0.778655i) q^{23} +(2.69292 + 4.09245i) q^{24} +(-11.3397 + 6.54701i) q^{25} +(-2.45225 + 2.33823i) q^{26} +(1.97243 + 4.80724i) q^{27} +(0.179434 - 3.76729i) q^{28} +(-0.343336 + 1.28135i) q^{29} +(-10.2932 - 1.61689i) q^{30} +(1.25840 - 2.17961i) q^{31} +(-4.52860 - 3.38996i) q^{32} +(1.96221 - 0.810213i) q^{33} +(4.27753 - 2.33572i) q^{34} +(5.67210 + 5.67210i) q^{35} +(-4.02609 - 4.44866i) q^{36} +(5.77154 - 5.77154i) q^{37} +(-8.01610 - 2.35371i) q^{38} +(2.52993 - 3.28948i) q^{39} +(11.8139 - 2.27705i) q^{40} +(-3.43245 - 1.98173i) q^{41} +(0.488668 + 4.59328i) q^{42} +(-2.96053 - 0.793272i) q^{43} +(-1.81384 + 1.64891i) q^{44} +(12.7611 + 0.0284289i) q^{45} +(-2.20175 - 0.0524044i) q^{46} +(0.230692 + 0.399570i) q^{47} +(6.11624 + 3.25448i) q^{48} +(-1.72191 + 2.98244i) q^{49} +(-9.63783 + 15.8120i) q^{50} +(-4.73959 + 3.62844i) q^{51} +(-1.45902 + 4.56431i) q^{52} +(5.61507 - 5.61507i) q^{53} +(5.70640 + 4.63001i) q^{54} -5.21358i q^{55} +(-2.33062 - 4.79766i) q^{56} +(10.1431 + 1.34686i) q^{57} +(0.442294 + 1.82314i) q^{58} +(2.92766 + 10.9262i) q^{59} +(-13.8720 + 4.96943i) q^{60} +(1.27078 - 4.74261i) q^{61} +(0.0846915 - 3.55828i) q^{62} +(-1.45205 - 5.46782i) q^{63} +(-7.91859 - 1.13837i) q^{64} +(-5.09576 - 8.82612i) q^{65} +(1.88640 - 2.33557i) q^{66} +(0.286572 - 0.0767867i) q^{67} +(3.72630 - 5.79831i) q^{68} +(2.67465 - 0.349094i) q^{69} +(10.8847 + 3.19600i) q^{70} +13.9935i q^{71} +(-8.01242 - 2.79304i) q^{72} -0.0279090i q^{73} +(3.25203 - 11.0755i) q^{74} +(8.70240 - 20.9434i) q^{75} +(-11.5450 + 2.51154i) q^{76} +(-2.23256 + 0.598214i) q^{77} +(0.910720 - 5.79768i) q^{78} +(2.19067 + 3.79435i) q^{79} +(13.1203 - 10.8333i) q^{80} +(-7.77410 - 4.53468i) q^{81} +(-5.60358 - 0.133372i) q^{82} +(-0.915902 + 3.41819i) q^{83} +(3.71971 + 5.37009i) q^{84} +(3.79408 + 14.1597i) q^{85} +(-4.21233 + 1.02191i) q^{86} +(-0.876906 - 2.12373i) q^{87} +(-1.13381 + 3.27603i) q^{88} +4.74894i q^{89} +(15.8586 - 8.61372i) q^{90} +(-3.19483 + 3.19483i) q^{91} +(-2.76838 + 1.42722i) q^{92} +(0.564177 + 4.32255i) q^{93} +(0.557154 + 0.339601i) q^{94} +(12.5645 - 21.7623i) q^{95} +(9.79739 - 0.105834i) q^{96} +(4.17352 + 7.22875i) q^{97} +(-0.115887 + 4.86893i) q^{98} +(-1.84557 + 3.18025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22} - 40 q^{24} - 4 q^{26} + 8 q^{27} - 16 q^{28} + 4 q^{29} + 18 q^{30} + 28 q^{31} - 46 q^{32} - 32 q^{33} - 14 q^{34} - 16 q^{35} + 14 q^{36} + 16 q^{37} + 2 q^{38} - 10 q^{40} + 26 q^{42} - 10 q^{43} + 60 q^{44} + 40 q^{45} + 20 q^{46} - 56 q^{47} + 2 q^{48} + 4 q^{49} - 36 q^{50} - 54 q^{51} + 6 q^{52} - 8 q^{53} + 92 q^{54} + 52 q^{56} - 14 q^{58} - 14 q^{59} + 18 q^{60} - 32 q^{61} + 16 q^{62} - 108 q^{63} - 44 q^{64} - 64 q^{65} + 26 q^{66} - 18 q^{67} + 16 q^{68} + 32 q^{69} + 14 q^{70} + 114 q^{72} + 38 q^{74} + 86 q^{75} + 10 q^{76} - 36 q^{77} + 16 q^{78} + 44 q^{79} + 144 q^{80} - 44 q^{81} - 88 q^{82} + 20 q^{83} - 58 q^{84} - 8 q^{85} + 76 q^{86} - 42 q^{88} - 80 q^{91} - 68 q^{92} - 4 q^{93} + 20 q^{94} + 48 q^{95} + 94 q^{96} + 40 q^{97} + 88 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24122 0.677764i 0.877677 0.479252i
\(3\) −1.37530 + 1.05287i −0.794031 + 0.607877i
\(4\) 1.08127 1.68251i 0.540636 0.841257i
\(5\) 1.10094 + 4.10876i 0.492355 + 1.83750i 0.544365 + 0.838849i \(0.316771\pi\)
−0.0520092 + 0.998647i \(0.516563\pi\)
\(6\) −0.993456 + 2.23898i −0.405577 + 0.914061i
\(7\) 1.63313 0.942891i 0.617267 0.356379i −0.158537 0.987353i \(-0.550678\pi\)
0.775804 + 0.630974i \(0.217344\pi\)
\(8\) 0.201751 2.82122i 0.0713297 0.997453i
\(9\) 0.782911 2.89604i 0.260970 0.965347i
\(10\) 4.15129 + 4.35372i 1.31275 + 1.37677i
\(11\) −1.18389 0.317223i −0.356957 0.0956464i 0.0758838 0.997117i \(-0.475822\pi\)
−0.432841 + 0.901470i \(0.642489\pi\)
\(12\) 0.284402 + 3.45241i 0.0820997 + 0.996624i
\(13\) −2.31428 + 0.620109i −0.641865 + 0.171987i −0.565048 0.825058i \(-0.691142\pi\)
−0.0768171 + 0.997045i \(0.524476\pi\)
\(14\) 1.38803 2.27722i 0.370966 0.608612i
\(15\) −5.84014 4.49164i −1.50792 1.15974i
\(16\) −1.66171 3.63851i −0.415426 0.909627i
\(17\) 3.44622 0.835831 0.417915 0.908486i \(-0.362761\pi\)
0.417915 + 0.908486i \(0.362761\pi\)
\(18\) −0.991066 4.12526i −0.233596 0.972334i
\(19\) −4.17726 4.17726i −0.958328 0.958328i 0.0408377 0.999166i \(-0.486997\pi\)
−0.999166 + 0.0408377i \(0.986997\pi\)
\(20\) 8.10347 + 2.59034i 1.81199 + 0.579218i
\(21\) −1.25331 + 3.01624i −0.273494 + 0.658199i
\(22\) −1.68448 + 0.408656i −0.359132 + 0.0871257i
\(23\) −1.34867 0.778655i −0.281217 0.162361i 0.352757 0.935715i \(-0.385244\pi\)
−0.633974 + 0.773354i \(0.718578\pi\)
\(24\) 2.69292 + 4.09245i 0.549691 + 0.835368i
\(25\) −11.3397 + 6.54701i −2.26795 + 1.30940i
\(26\) −2.45225 + 2.33823i −0.480925 + 0.458564i
\(27\) 1.97243 + 4.80724i 0.379594 + 0.925153i
\(28\) 0.179434 3.76729i 0.0339099 0.711951i
\(29\) −0.343336 + 1.28135i −0.0637558 + 0.237940i −0.990449 0.137878i \(-0.955972\pi\)
0.926693 + 0.375818i \(0.122638\pi\)
\(30\) −10.2932 1.61689i −1.87927 0.295203i
\(31\) 1.25840 2.17961i 0.226015 0.391469i −0.730609 0.682796i \(-0.760764\pi\)
0.956623 + 0.291327i \(0.0940969\pi\)
\(32\) −4.52860 3.38996i −0.800551 0.599265i
\(33\) 1.96221 0.810213i 0.341576 0.141040i
\(34\) 4.27753 2.33572i 0.733590 0.400573i
\(35\) 5.67210 + 5.67210i 0.958760 + 0.958760i
\(36\) −4.02609 4.44866i −0.671015 0.741444i
\(37\) 5.77154 5.77154i 0.948836 0.948836i −0.0499178 0.998753i \(-0.515896\pi\)
0.998753 + 0.0499178i \(0.0158959\pi\)
\(38\) −8.01610 2.35371i −1.30038 0.381823i
\(39\) 2.52993 3.28948i 0.405114 0.526739i
\(40\) 11.8139 2.27705i 1.86793 0.360033i
\(41\) −3.43245 1.98173i −0.536058 0.309493i 0.207422 0.978252i \(-0.433493\pi\)
−0.743480 + 0.668758i \(0.766826\pi\)
\(42\) 0.488668 + 4.59328i 0.0754032 + 0.708759i
\(43\) −2.96053 0.793272i −0.451477 0.120973i 0.0259136 0.999664i \(-0.491751\pi\)
−0.477390 + 0.878691i \(0.658417\pi\)
\(44\) −1.81384 + 1.64891i −0.273447 + 0.248583i
\(45\) 12.7611 + 0.0284289i 1.90231 + 0.00423794i
\(46\) −2.20175 0.0524044i −0.324630 0.00772660i
\(47\) 0.230692 + 0.399570i 0.0336498 + 0.0582832i 0.882360 0.470575i \(-0.155954\pi\)
−0.848710 + 0.528858i \(0.822620\pi\)
\(48\) 6.11624 + 3.25448i 0.882803 + 0.469743i
\(49\) −1.72191 + 2.98244i −0.245988 + 0.426063i
\(50\) −9.63783 + 15.8120i −1.36300 + 2.23615i
\(51\) −4.73959 + 3.62844i −0.663676 + 0.508083i
\(52\) −1.45902 + 4.56431i −0.202330 + 0.632956i
\(53\) 5.61507 5.61507i 0.771289 0.771289i −0.207043 0.978332i \(-0.566384\pi\)
0.978332 + 0.207043i \(0.0663838\pi\)
\(54\) 5.70640 + 4.63001i 0.776542 + 0.630065i
\(55\) 5.21358i 0.702999i
\(56\) −2.33062 4.79766i −0.311442 0.641115i
\(57\) 10.1431 + 1.34686i 1.34349 + 0.178396i
\(58\) 0.442294 + 1.82314i 0.0580761 + 0.239390i
\(59\) 2.92766 + 10.9262i 0.381148 + 1.42247i 0.844150 + 0.536108i \(0.180106\pi\)
−0.463001 + 0.886358i \(0.653227\pi\)
\(60\) −13.8720 + 4.96943i −1.79087 + 0.641551i
\(61\) 1.27078 4.74261i 0.162707 0.607229i −0.835615 0.549316i \(-0.814888\pi\)
0.998322 0.0579138i \(-0.0184448\pi\)
\(62\) 0.0846915 3.55828i 0.0107558 0.451902i
\(63\) −1.45205 5.46782i −0.182941 0.688881i
\(64\) −7.91859 1.13837i −0.989824 0.142296i
\(65\) −5.09576 8.82612i −0.632052 1.09475i
\(66\) 1.88640 2.33557i 0.232200 0.287489i
\(67\) 0.286572 0.0767867i 0.0350103 0.00938099i −0.241271 0.970458i \(-0.577564\pi\)
0.276282 + 0.961077i \(0.410898\pi\)
\(68\) 3.72630 5.79831i 0.451880 0.703148i
\(69\) 2.67465 0.349094i 0.321991 0.0420260i
\(70\) 10.8847 + 3.19600i 1.30097 + 0.381995i
\(71\) 13.9935i 1.66073i 0.557221 + 0.830364i \(0.311867\pi\)
−0.557221 + 0.830364i \(0.688133\pi\)
\(72\) −8.01242 2.79304i −0.944273 0.329163i
\(73\) 0.0279090i 0.00326650i −0.999999 0.00163325i \(-0.999480\pi\)
0.999999 0.00163325i \(-0.000519880\pi\)
\(74\) 3.25203 11.0755i 0.378040 1.28750i
\(75\) 8.70240 20.9434i 1.00487 2.41834i
\(76\) −11.5450 + 2.51154i −1.32431 + 0.288094i
\(77\) −2.23256 + 0.598214i −0.254424 + 0.0681728i
\(78\) 0.910720 5.79768i 0.103119 0.656458i
\(79\) 2.19067 + 3.79435i 0.246470 + 0.426898i 0.962544 0.271126i \(-0.0873960\pi\)
−0.716074 + 0.698024i \(0.754063\pi\)
\(80\) 13.1203 10.8333i 1.46690 1.21120i
\(81\) −7.77410 4.53468i −0.863789 0.503854i
\(82\) −5.60358 0.133372i −0.618812 0.0147285i
\(83\) −0.915902 + 3.41819i −0.100533 + 0.375195i −0.997800 0.0662931i \(-0.978883\pi\)
0.897267 + 0.441489i \(0.145549\pi\)
\(84\) 3.71971 + 5.37009i 0.405853 + 0.585924i
\(85\) 3.79408 + 14.1597i 0.411526 + 1.53584i
\(86\) −4.21233 + 1.02191i −0.454227 + 0.110196i
\(87\) −0.876906 2.12373i −0.0940142 0.227687i
\(88\) −1.13381 + 3.27603i −0.120864 + 0.349226i
\(89\) 4.74894i 0.503386i 0.967807 + 0.251693i \(0.0809874\pi\)
−0.967807 + 0.251693i \(0.919013\pi\)
\(90\) 15.8586 8.61372i 1.67165 0.907966i
\(91\) −3.19483 + 3.19483i −0.334909 + 0.334909i
\(92\) −2.76838 + 1.42722i −0.288623 + 0.148798i
\(93\) 0.564177 + 4.32255i 0.0585025 + 0.448228i
\(94\) 0.557154 + 0.339601i 0.0574660 + 0.0350271i
\(95\) 12.5645 21.7623i 1.28909 2.23276i
\(96\) 9.79739 0.105834i 0.999942 0.0108016i
\(97\) 4.17352 + 7.22875i 0.423757 + 0.733968i 0.996303 0.0859041i \(-0.0273779\pi\)
−0.572547 + 0.819872i \(0.694045\pi\)
\(98\) −0.115887 + 4.86893i −0.0117063 + 0.491836i
\(99\) −1.84557 + 3.18025i −0.185487 + 0.319627i
\(100\) −1.24591 + 26.1584i −0.124591 + 2.61584i
\(101\) −7.20785 1.93134i −0.717208 0.192175i −0.118282 0.992980i \(-0.537739\pi\)
−0.598926 + 0.800805i \(0.704406\pi\)
\(102\) −3.42367 + 7.71602i −0.338994 + 0.764000i
\(103\) 12.2204 + 7.05547i 1.20411 + 0.695196i 0.961468 0.274919i \(-0.0886509\pi\)
0.242647 + 0.970115i \(0.421984\pi\)
\(104\) 1.28256 + 6.65420i 0.125765 + 0.652498i
\(105\) −13.7729 1.82884i −1.34409 0.178477i
\(106\) 3.16386 10.7753i 0.307302 1.04659i
\(107\) −3.84992 + 3.84992i −0.372186 + 0.372186i −0.868273 0.496087i \(-0.834770\pi\)
0.496087 + 0.868273i \(0.334770\pi\)
\(108\) 10.2210 + 1.87929i 0.983514 + 0.180835i
\(109\) 2.08616 + 2.08616i 0.199818 + 0.199818i 0.799922 0.600104i \(-0.204874\pi\)
−0.600104 + 0.799922i \(0.704874\pi\)
\(110\) −3.53358 6.47122i −0.336914 0.617007i
\(111\) −1.86090 + 14.0143i −0.176629 + 1.33018i
\(112\) −6.14450 4.37536i −0.580601 0.413433i
\(113\) −2.04799 + 3.54722i −0.192658 + 0.333694i −0.946130 0.323786i \(-0.895044\pi\)
0.753472 + 0.657480i \(0.228378\pi\)
\(114\) 13.5027 5.20288i 1.26465 0.487295i
\(115\) 1.71451 6.39862i 0.159878 0.596674i
\(116\) 1.78464 + 1.96315i 0.165700 + 0.182274i
\(117\) −0.0160127 + 7.18773i −0.00148038 + 0.664506i
\(118\) 11.0392 + 11.5775i 1.01624 + 1.06580i
\(119\) 5.62814 3.24941i 0.515931 0.297873i
\(120\) −13.8502 + 15.5701i −1.26434 + 1.42135i
\(121\) −8.22531 4.74888i −0.747755 0.431717i
\(122\) −1.63705 6.74793i −0.148212 0.610929i
\(123\) 6.80716 0.888467i 0.613781 0.0801104i
\(124\) −2.30655 4.47402i −0.207134 0.401779i
\(125\) −24.3454 24.3454i −2.17752 2.17752i
\(126\) −5.50821 5.80264i −0.490711 0.516940i
\(127\) 4.89832 0.434656 0.217328 0.976099i \(-0.430266\pi\)
0.217328 + 0.976099i \(0.430266\pi\)
\(128\) −10.6003 + 3.95397i −0.936942 + 0.349485i
\(129\) 4.90684 2.02608i 0.432023 0.178386i
\(130\) −12.3070 7.50146i −1.07940 0.657922i
\(131\) −17.7751 + 4.76283i −1.55302 + 0.416130i −0.930446 0.366430i \(-0.880580\pi\)
−0.622574 + 0.782561i \(0.713913\pi\)
\(132\) 0.758483 4.17750i 0.0660174 0.363605i
\(133\) −10.7607 2.88332i −0.933072 0.250016i
\(134\) 0.303657 0.289538i 0.0262319 0.0250123i
\(135\) −17.5803 + 13.3967i −1.51307 + 1.15301i
\(136\) 0.695278 9.72255i 0.0596196 0.833702i
\(137\) 13.4198 7.74793i 1.14653 0.661950i 0.198492 0.980103i \(-0.436396\pi\)
0.948040 + 0.318153i \(0.103062\pi\)
\(138\) 3.08324 2.24609i 0.262463 0.191200i
\(139\) −1.90836 7.12209i −0.161865 0.604088i −0.998419 0.0562039i \(-0.982100\pi\)
0.836555 0.547884i \(-0.184566\pi\)
\(140\) 15.6765 3.41031i 1.32490 0.288224i
\(141\) −0.737967 0.306640i −0.0621480 0.0258237i
\(142\) 9.48432 + 17.3691i 0.795907 + 1.45758i
\(143\) 2.93657 0.245568
\(144\) −11.8382 + 1.96374i −0.986519 + 0.163645i
\(145\) −5.64274 −0.468604
\(146\) −0.0189157 0.0346413i −0.00156548 0.00286694i
\(147\) −0.771986 5.91472i −0.0636723 0.487838i
\(148\) −3.47010 15.9513i −0.285240 1.31119i
\(149\) −1.99897 7.46026i −0.163762 0.611168i −0.998195 0.0600585i \(-0.980871\pi\)
0.834433 0.551110i \(-0.185795\pi\)
\(150\) −3.39309 31.8937i −0.277045 2.60411i
\(151\) 3.36540 1.94301i 0.273872 0.158120i −0.356774 0.934191i \(-0.616123\pi\)
0.630646 + 0.776071i \(0.282790\pi\)
\(152\) −12.6277 + 10.9422i −1.02424 + 0.887530i
\(153\) 2.69808 9.98039i 0.218127 0.806867i
\(154\) −2.36566 + 2.25567i −0.190631 + 0.181767i
\(155\) 10.3409 + 2.77084i 0.830602 + 0.222559i
\(156\) −2.79905 7.81347i −0.224104 0.625578i
\(157\) 6.23351 1.67026i 0.497488 0.133302i −0.00134577 0.999999i \(-0.500428\pi\)
0.498834 + 0.866698i \(0.333762\pi\)
\(158\) 5.29079 + 3.22488i 0.420913 + 0.256558i
\(159\) −1.81045 + 13.6344i −0.143578 + 1.08128i
\(160\) 8.94281 22.3391i 0.706991 1.76606i
\(161\) −2.93675 −0.231448
\(162\) −12.7228 0.359546i −0.999601 0.0282486i
\(163\) 10.5783 + 10.5783i 0.828556 + 0.828556i 0.987317 0.158761i \(-0.0507499\pi\)
−0.158761 + 0.987317i \(0.550750\pi\)
\(164\) −7.04569 + 3.63236i −0.550176 + 0.283640i
\(165\) 5.48925 + 7.17025i 0.427337 + 0.558203i
\(166\) 1.17989 + 4.86351i 0.0915773 + 0.377481i
\(167\) −18.7147 10.8050i −1.44819 0.836112i −0.449815 0.893122i \(-0.648510\pi\)
−0.998374 + 0.0570092i \(0.981844\pi\)
\(168\) 8.25664 + 4.14439i 0.637014 + 0.319747i
\(169\) −6.28698 + 3.62979i −0.483614 + 0.279215i
\(170\) 14.3062 + 15.0039i 1.09724 + 1.15074i
\(171\) −15.3679 + 8.82708i −1.17521 + 0.675024i
\(172\) −4.53583 + 4.12339i −0.345854 + 0.314406i
\(173\) −5.00981 + 18.6969i −0.380889 + 1.42150i 0.463657 + 0.886015i \(0.346537\pi\)
−0.844546 + 0.535483i \(0.820130\pi\)
\(174\) −2.52782 2.04168i −0.191634 0.154780i
\(175\) −12.3462 + 21.3843i −0.933287 + 1.61650i
\(176\) 0.813064 + 4.83474i 0.0612870 + 0.364432i
\(177\) −15.5303 11.9443i −1.16733 0.897790i
\(178\) 3.21866 + 5.89449i 0.241249 + 0.441811i
\(179\) −2.88152 2.88152i −0.215375 0.215375i 0.591171 0.806546i \(-0.298666\pi\)
−0.806546 + 0.591171i \(0.798666\pi\)
\(180\) 13.8460 21.4400i 1.03202 1.59804i
\(181\) −9.50186 + 9.50186i −0.706268 + 0.706268i −0.965748 0.259480i \(-0.916449\pi\)
0.259480 + 0.965748i \(0.416449\pi\)
\(182\) −1.80016 + 6.13084i −0.133437 + 0.454448i
\(183\) 3.24567 + 7.86050i 0.239927 + 0.581065i
\(184\) −2.46885 + 3.64780i −0.182006 + 0.268920i
\(185\) 30.0680 + 17.3598i 2.21065 + 1.27632i
\(186\) 3.62994 + 4.98287i 0.266160 + 0.365362i
\(187\) −4.07996 1.09322i −0.298356 0.0799442i
\(188\) 0.921721 + 0.0439012i 0.0672234 + 0.00320182i
\(189\) 7.75394 + 5.99108i 0.564016 + 0.435787i
\(190\) 0.845602 35.5276i 0.0613464 2.57744i
\(191\) 2.36417 + 4.09487i 0.171066 + 0.296294i 0.938793 0.344483i \(-0.111946\pi\)
−0.767727 + 0.640777i \(0.778612\pi\)
\(192\) 12.0890 6.77168i 0.872450 0.488704i
\(193\) 9.76542 16.9142i 0.702931 1.21751i −0.264503 0.964385i \(-0.585208\pi\)
0.967433 0.253127i \(-0.0814589\pi\)
\(194\) 10.0797 + 6.14383i 0.723677 + 0.441101i
\(195\) 16.3010 + 6.77338i 1.16734 + 0.485052i
\(196\) 3.15615 + 6.12198i 0.225439 + 0.437284i
\(197\) 6.89966 6.89966i 0.491581 0.491581i −0.417223 0.908804i \(-0.636997\pi\)
0.908804 + 0.417223i \(0.136997\pi\)
\(198\) −0.135313 + 5.19826i −0.00961628 + 0.369424i
\(199\) 24.4752i 1.73500i −0.497438 0.867500i \(-0.665726\pi\)
0.497438 0.867500i \(-0.334274\pi\)
\(200\) 16.1828 + 33.3128i 1.14429 + 2.35557i
\(201\) −0.313276 + 0.407329i −0.0220968 + 0.0287308i
\(202\) −10.2555 + 2.48800i −0.721578 + 0.175055i
\(203\) 0.647456 + 2.41634i 0.0454425 + 0.169594i
\(204\) 0.980111 + 11.8978i 0.0686215 + 0.833009i
\(205\) 4.36352 16.2849i 0.304762 1.13739i
\(206\) 19.9502 + 0.474841i 1.39000 + 0.0330837i
\(207\) −3.31090 + 3.29619i −0.230124 + 0.229101i
\(208\) 6.10192 + 7.39008i 0.423092 + 0.512410i
\(209\) 3.62030 + 6.27055i 0.250422 + 0.433743i
\(210\) −18.3347 + 7.06475i −1.26522 + 0.487514i
\(211\) 21.1840 5.67623i 1.45837 0.390768i 0.559441 0.828870i \(-0.311016\pi\)
0.898925 + 0.438102i \(0.144349\pi\)
\(212\) −3.37602 15.5189i −0.231866 1.06584i
\(213\) −14.7334 19.2453i −1.00952 1.31867i
\(214\) −2.16927 + 7.38795i −0.148288 + 0.505030i
\(215\) 13.0375i 0.889148i
\(216\) 13.9602 4.59479i 0.949873 0.312636i
\(217\) 4.74612i 0.322188i
\(218\) 4.00332 + 1.17547i 0.271139 + 0.0796126i
\(219\) 0.0293847 + 0.0383833i 0.00198563 + 0.00259370i
\(220\) −8.77193 5.63730i −0.591403 0.380066i
\(221\) −7.97551 + 2.13703i −0.536491 + 0.143752i
\(222\) 7.18861 + 18.6562i 0.482468 + 1.25212i
\(223\) −1.56986 2.71908i −0.105126 0.182083i 0.808664 0.588271i \(-0.200191\pi\)
−0.913790 + 0.406188i \(0.866858\pi\)
\(224\) −10.5922 1.26628i −0.707719 0.0846068i
\(225\) 10.0824 + 37.9661i 0.672159 + 2.53107i
\(226\) −0.137832 + 5.79094i −0.00916844 + 0.385208i
\(227\) 3.64479 13.6026i 0.241913 0.902833i −0.732996 0.680233i \(-0.761879\pi\)
0.974910 0.222601i \(-0.0714546\pi\)
\(228\) 13.2336 15.6096i 0.876414 1.03377i
\(229\) −4.91218 18.3325i −0.324606 1.21145i −0.914707 0.404117i \(-0.867579\pi\)
0.590101 0.807330i \(-0.299088\pi\)
\(230\) −2.20867 9.10415i −0.145636 0.600310i
\(231\) 2.44061 3.17333i 0.160580 0.208790i
\(232\) 3.54569 + 1.22714i 0.232786 + 0.0805656i
\(233\) 12.6802i 0.830708i −0.909660 0.415354i \(-0.863658\pi\)
0.909660 0.415354i \(-0.136342\pi\)
\(234\) 4.85171 + 8.93243i 0.317166 + 0.583932i
\(235\) −1.38776 + 1.38776i −0.0905275 + 0.0905275i
\(236\) 21.5490 + 6.88832i 1.40272 + 0.448391i
\(237\) −7.00781 2.91188i −0.455206 0.189147i
\(238\) 4.78344 7.84779i 0.310065 0.508697i
\(239\) −3.69405 + 6.39829i −0.238948 + 0.413871i −0.960413 0.278581i \(-0.910136\pi\)
0.721464 + 0.692451i \(0.243469\pi\)
\(240\) −6.63827 + 28.7132i −0.428499 + 1.85343i
\(241\) 11.1955 + 19.3912i 0.721167 + 1.24910i 0.960533 + 0.278168i \(0.0897271\pi\)
−0.239366 + 0.970929i \(0.576940\pi\)
\(242\) −13.4281 0.319605i −0.863189 0.0205450i
\(243\) 15.4662 1.94859i 0.992156 0.125002i
\(244\) −6.60546 7.26615i −0.422871 0.465168i
\(245\) −14.1499 3.79145i −0.904003 0.242227i
\(246\) 7.84704 5.71644i 0.500309 0.364467i
\(247\) 12.2577 + 7.07698i 0.779938 + 0.450297i
\(248\) −5.89527 3.98996i −0.374350 0.253362i
\(249\) −2.33929 5.66538i −0.148246 0.359029i
\(250\) −46.7185 13.7176i −2.95474 0.867579i
\(251\) −7.52339 + 7.52339i −0.474872 + 0.474872i −0.903487 0.428615i \(-0.859002\pi\)
0.428615 + 0.903487i \(0.359002\pi\)
\(252\) −10.7697 3.46910i −0.678430 0.218533i
\(253\) 1.34967 + 1.34967i 0.0848533 + 0.0848533i
\(254\) 6.07991 3.31991i 0.381487 0.208309i
\(255\) −20.1264 15.4792i −1.26036 0.969343i
\(256\) −10.4775 + 12.0923i −0.654842 + 0.755766i
\(257\) 2.21664 3.83934i 0.138270 0.239491i −0.788572 0.614943i \(-0.789179\pi\)
0.926842 + 0.375452i \(0.122512\pi\)
\(258\) 4.71728 5.84050i 0.293685 0.363613i
\(259\) 3.98377 14.8676i 0.247539 0.923830i
\(260\) −20.3600 0.969736i −1.26267 0.0601405i
\(261\) 3.44203 + 1.99749i 0.213056 + 0.123642i
\(262\) −18.8348 + 17.9591i −1.16362 + 1.10952i
\(263\) 4.61948 2.66706i 0.284850 0.164458i −0.350767 0.936463i \(-0.614079\pi\)
0.635617 + 0.772005i \(0.280746\pi\)
\(264\) −1.88992 5.69928i −0.116316 0.350767i
\(265\) 29.2529 + 16.8891i 1.79699 + 1.03749i
\(266\) −15.3107 + 3.71438i −0.938757 + 0.227743i
\(267\) −5.00004 6.53122i −0.305997 0.399704i
\(268\) 0.180667 0.565189i 0.0110360 0.0345244i
\(269\) 20.6406 + 20.6406i 1.25848 + 1.25848i 0.951818 + 0.306663i \(0.0992124\pi\)
0.306663 + 0.951818i \(0.400788\pi\)
\(270\) −12.7412 + 28.5436i −0.775407 + 1.73711i
\(271\) 23.2339 1.41136 0.705680 0.708530i \(-0.250642\pi\)
0.705680 + 0.708530i \(0.250642\pi\)
\(272\) −5.72660 12.5391i −0.347226 0.760294i
\(273\) 1.03010 7.75762i 0.0623446 0.469512i
\(274\) 11.4057 18.7124i 0.689044 1.13046i
\(275\) 15.5019 4.15373i 0.934801 0.250479i
\(276\) 2.30467 4.87761i 0.138725 0.293598i
\(277\) 19.0092 + 5.09351i 1.14215 + 0.306039i 0.779817 0.626007i \(-0.215312\pi\)
0.362338 + 0.932047i \(0.381979\pi\)
\(278\) −7.19579 7.54668i −0.431575 0.452620i
\(279\) −5.32702 5.35081i −0.318920 0.320344i
\(280\) 17.1466 14.8579i 1.02471 0.887929i
\(281\) −16.3011 + 9.41146i −0.972444 + 0.561441i −0.899980 0.435930i \(-0.856419\pi\)
−0.0724633 + 0.997371i \(0.523086\pi\)
\(282\) −1.12381 + 0.119560i −0.0669220 + 0.00711968i
\(283\) −3.43848 12.8326i −0.204397 0.762819i −0.989633 0.143622i \(-0.954125\pi\)
0.785236 0.619197i \(-0.212542\pi\)
\(284\) 23.5443 + 15.1308i 1.39710 + 0.897848i
\(285\) 5.63302 + 43.1585i 0.333671 + 2.55649i
\(286\) 3.64494 1.99030i 0.215530 0.117689i
\(287\) −7.47420 −0.441188
\(288\) −13.3629 + 10.4610i −0.787419 + 0.616419i
\(289\) −5.12358 −0.301387
\(290\) −7.00390 + 3.82445i −0.411283 + 0.224579i
\(291\) −13.3508 5.54752i −0.782638 0.325201i
\(292\) −0.0469573 0.0301772i −0.00274797 0.00176599i
\(293\) 2.20679 + 8.23584i 0.128922 + 0.481143i 0.999949 0.0100919i \(-0.00321239\pi\)
−0.871027 + 0.491235i \(0.836546\pi\)
\(294\) −4.96699 6.81826i −0.289681 0.397649i
\(295\) −41.6699 + 24.0581i −2.42611 + 1.40072i
\(296\) −15.1184 17.4472i −0.878738 1.01410i
\(297\) −0.810177 6.31696i −0.0470113 0.366547i
\(298\) −7.53746 7.90502i −0.436634 0.457925i
\(299\) 3.60405 + 0.965702i 0.208427 + 0.0558480i
\(300\) −25.8280 37.2875i −1.49118 2.15279i
\(301\) −5.58291 + 1.49594i −0.321794 + 0.0862244i
\(302\) 2.86031 4.69266i 0.164592 0.270032i
\(303\) 11.9464 4.93279i 0.686304 0.283381i
\(304\) −8.25760 + 22.1403i −0.473606 + 1.26984i
\(305\) 20.8853 1.19589
\(306\) −3.41543 14.2166i −0.195247 0.812706i
\(307\) −7.13558 7.13558i −0.407249 0.407249i 0.473529 0.880778i \(-0.342980\pi\)
−0.880778 + 0.473529i \(0.842980\pi\)
\(308\) −1.40750 + 4.40315i −0.0802000 + 0.250893i
\(309\) −24.2353 + 3.16318i −1.37870 + 0.179947i
\(310\) 14.7134 3.56947i 0.835663 0.202732i
\(311\) 10.0741 + 5.81630i 0.571252 + 0.329812i 0.757649 0.652662i \(-0.226348\pi\)
−0.186397 + 0.982474i \(0.559681\pi\)
\(312\) −8.76994 7.80116i −0.496500 0.441654i
\(313\) 5.76956 3.33106i 0.326115 0.188282i −0.328000 0.944678i \(-0.606375\pi\)
0.654115 + 0.756395i \(0.273041\pi\)
\(314\) 6.60513 6.29802i 0.372749 0.355418i
\(315\) 20.8674 11.9859i 1.17574 0.675328i
\(316\) 8.75276 + 0.416890i 0.492381 + 0.0234519i
\(317\) 0.708583 2.64447i 0.0397980 0.148528i −0.943168 0.332317i \(-0.892170\pi\)
0.982966 + 0.183789i \(0.0588363\pi\)
\(318\) 6.99372 + 18.1504i 0.392188 + 1.01782i
\(319\) 0.812945 1.40806i 0.0455162 0.0788364i
\(320\) −4.04061 33.7889i −0.225877 1.88886i
\(321\) 1.24132 9.34829i 0.0692837 0.521770i
\(322\) −3.64516 + 1.99042i −0.203137 + 0.110922i
\(323\) −14.3957 14.3957i −0.801000 0.801000i
\(324\) −16.0356 + 8.17681i −0.890865 + 0.454267i
\(325\) 22.1835 22.1835i 1.23052 1.23052i
\(326\) 20.2996 + 5.96044i 1.12429 + 0.330118i
\(327\) −5.06557 0.672636i −0.280126 0.0371968i
\(328\) −6.28339 + 9.28389i −0.346942 + 0.512617i
\(329\) 0.753501 + 0.435034i 0.0415418 + 0.0239842i
\(330\) 11.6731 + 5.17947i 0.642584 + 0.285120i
\(331\) −19.6789 5.27295i −1.08165 0.289827i −0.326379 0.945239i \(-0.605829\pi\)
−0.755272 + 0.655412i \(0.772495\pi\)
\(332\) 4.76082 + 5.23701i 0.261284 + 0.287418i
\(333\) −12.1960 21.2332i −0.668337 1.16357i
\(334\) −30.5524 0.727186i −1.67175 0.0397898i
\(335\) 0.630997 + 1.09292i 0.0344751 + 0.0597126i
\(336\) 13.0573 0.451944i 0.712332 0.0246555i
\(337\) −0.514533 + 0.891197i −0.0280284 + 0.0485466i −0.879699 0.475530i \(-0.842256\pi\)
0.851671 + 0.524077i \(0.175590\pi\)
\(338\) −5.34341 + 8.76647i −0.290643 + 0.476833i
\(339\) −0.918174 7.03477i −0.0498684 0.382076i
\(340\) 27.9263 + 8.92688i 1.51452 + 0.484128i
\(341\) −2.18123 + 2.18123i −0.118120 + 0.118120i
\(342\) −13.0923 + 21.3722i −0.707953 + 1.15568i
\(343\) 19.6948i 1.06342i
\(344\) −2.83529 + 8.19227i −0.152868 + 0.441698i
\(345\) 4.37898 + 10.6052i 0.235756 + 0.570964i
\(346\) 6.45378 + 26.6025i 0.346957 + 1.43016i
\(347\) −8.08026 30.1559i −0.433771 1.61886i −0.743990 0.668191i \(-0.767069\pi\)
0.310219 0.950665i \(-0.399598\pi\)
\(348\) −4.52137 0.820917i −0.242371 0.0440058i
\(349\) 4.62320 17.2540i 0.247474 0.923587i −0.724649 0.689118i \(-0.757998\pi\)
0.972124 0.234469i \(-0.0753352\pi\)
\(350\) −0.830915 + 34.9105i −0.0444143 + 1.86605i
\(351\) −7.54576 9.90216i −0.402763 0.528538i
\(352\) 4.28601 + 5.44992i 0.228445 + 0.290482i
\(353\) −1.02827 1.78101i −0.0547291 0.0947935i 0.837363 0.546647i \(-0.184096\pi\)
−0.892092 + 0.451854i \(0.850763\pi\)
\(354\) −27.3720 4.29969i −1.45480 0.228526i
\(355\) −57.4962 + 15.4061i −3.05158 + 0.817668i
\(356\) 7.99015 + 5.13489i 0.423477 + 0.272149i
\(357\) −4.31917 + 10.3946i −0.228595 + 0.550143i
\(358\) −5.52961 1.62362i −0.292249 0.0858110i
\(359\) 4.76579i 0.251529i −0.992060 0.125764i \(-0.959862\pi\)
0.992060 0.125764i \(-0.0401383\pi\)
\(360\) 2.65477 35.9961i 0.139918 1.89716i
\(361\) 15.8989i 0.836785i
\(362\) −5.35391 + 18.2340i −0.281395 + 0.958356i
\(363\) 16.3123 2.12907i 0.856171 0.111747i
\(364\) 1.92087 + 8.82983i 0.100681 + 0.462809i
\(365\) 0.114672 0.0307261i 0.00600218 0.00160828i
\(366\) 9.35617 + 7.55683i 0.489055 + 0.395002i
\(367\) 8.61021 + 14.9133i 0.449449 + 0.778469i 0.998350 0.0574187i \(-0.0182870\pi\)
−0.548901 + 0.835887i \(0.684954\pi\)
\(368\) −0.592049 + 6.20104i −0.0308627 + 0.323252i
\(369\) −8.42646 + 8.38900i −0.438664 + 0.436714i
\(370\) 49.0870 + 1.16833i 2.55191 + 0.0607387i
\(371\) 3.87577 14.4646i 0.201220 0.750963i
\(372\) 7.88278 + 3.72461i 0.408703 + 0.193112i
\(373\) 4.29744 + 16.0383i 0.222513 + 0.830430i 0.983386 + 0.181529i \(0.0581046\pi\)
−0.760872 + 0.648901i \(0.775229\pi\)
\(374\) −5.80508 + 1.40832i −0.300174 + 0.0728224i
\(375\) 59.1149 + 7.84962i 3.05268 + 0.405353i
\(376\) 1.17382 0.570219i 0.0605350 0.0294068i
\(377\) 3.17830i 0.163691i
\(378\) 13.6849 + 2.18093i 0.703876 + 0.112175i
\(379\) −22.5741 + 22.5741i −1.15955 + 1.15955i −0.174981 + 0.984572i \(0.555987\pi\)
−0.984572 + 0.174981i \(0.944013\pi\)
\(380\) −23.0297 44.6708i −1.18140 2.29156i
\(381\) −6.73667 + 5.15731i −0.345130 + 0.264217i
\(382\) 5.70983 + 3.48030i 0.292140 + 0.178067i
\(383\) −12.6153 + 21.8504i −0.644614 + 1.11650i 0.339777 + 0.940506i \(0.389648\pi\)
−0.984391 + 0.175997i \(0.943685\pi\)
\(384\) 10.4156 16.5987i 0.531517 0.847048i
\(385\) −4.91584 8.51448i −0.250534 0.433938i
\(386\) 0.657224 27.6130i 0.0334518 1.40546i
\(387\) −4.61518 + 7.95276i −0.234603 + 0.404261i
\(388\) 16.6752 + 0.794231i 0.846554 + 0.0403210i
\(389\) 7.09570 + 1.90129i 0.359766 + 0.0963991i 0.434175 0.900829i \(-0.357040\pi\)
−0.0744082 + 0.997228i \(0.523707\pi\)
\(390\) 24.8239 2.64096i 1.25701 0.133730i
\(391\) −4.64781 2.68342i −0.235050 0.135706i
\(392\) 8.06674 + 5.45962i 0.407432 + 0.275752i
\(393\) 19.4315 25.2653i 0.980190 1.27447i
\(394\) 3.88768 13.2404i 0.195858 0.667040i
\(395\) −13.1783 + 13.1783i −0.663073 + 0.663073i
\(396\) 3.35524 + 6.54391i 0.168607 + 0.328844i
\(397\) −2.23236 2.23236i −0.112039 0.112039i 0.648865 0.760904i \(-0.275244\pi\)
−0.760904 + 0.648865i \(0.775244\pi\)
\(398\) −16.5884 30.3792i −0.831501 1.52277i
\(399\) 17.8350 7.36424i 0.892867 0.368673i
\(400\) 42.6647 + 30.3806i 2.13323 + 1.51903i
\(401\) 9.10949 15.7781i 0.454906 0.787921i −0.543777 0.839230i \(-0.683006\pi\)
0.998683 + 0.0513094i \(0.0163395\pi\)
\(402\) −0.112773 + 0.717914i −0.00562458 + 0.0358063i
\(403\) −1.56069 + 5.82456i −0.0777433 + 0.290142i
\(404\) −11.0431 + 10.0390i −0.549417 + 0.499460i
\(405\) 10.0731 36.9344i 0.500538 1.83528i
\(406\) 2.44134 + 2.56039i 0.121162 + 0.127070i
\(407\) −8.66376 + 5.00202i −0.429447 + 0.247941i
\(408\) 9.28041 + 14.1035i 0.459449 + 0.698226i
\(409\) −22.6986 13.1050i −1.12237 0.648002i −0.180368 0.983599i \(-0.557729\pi\)
−0.942006 + 0.335597i \(0.891062\pi\)
\(410\) −5.62121 23.1706i −0.277612 1.14432i
\(411\) −10.2987 + 24.7851i −0.507997 + 1.22256i
\(412\) 25.0845 12.9322i 1.23583 0.637122i
\(413\) 15.0834 + 15.0834i 0.742207 + 0.742207i
\(414\) −1.87554 + 6.33532i −0.0921775 + 0.311364i
\(415\) −15.0529 −0.738918
\(416\) 12.5826 + 5.03707i 0.616912 + 0.246963i
\(417\) 10.1232 + 7.78576i 0.495737 + 0.381270i
\(418\) 8.74356 + 5.32944i 0.427661 + 0.260671i
\(419\) 11.2202 3.00645i 0.548144 0.146875i 0.0258901 0.999665i \(-0.491758\pi\)
0.522254 + 0.852790i \(0.325091\pi\)
\(420\) −17.9692 + 21.1955i −0.876809 + 1.03424i
\(421\) −9.74548 2.61129i −0.474966 0.127267i 0.0133918 0.999910i \(-0.495737\pi\)
−0.488358 + 0.872644i \(0.662404\pi\)
\(422\) 22.4469 21.4032i 1.09270 1.04189i
\(423\) 1.33778 0.355265i 0.0650451 0.0172736i
\(424\) −14.7085 16.9742i −0.714309 0.824341i
\(425\) −39.0793 + 22.5624i −1.89562 + 1.09444i
\(426\) −31.3313 13.9020i −1.51801 0.673553i
\(427\) −2.39641 8.94353i −0.115970 0.432808i
\(428\) 2.31474 + 10.6404i 0.111887 + 0.514321i
\(429\) −4.03867 + 3.09184i −0.194989 + 0.149276i
\(430\) −8.83633 16.1824i −0.426126 0.780385i
\(431\) −4.07825 −0.196442 −0.0982211 0.995165i \(-0.531315\pi\)
−0.0982211 + 0.995165i \(0.531315\pi\)
\(432\) 14.2136 15.1649i 0.683851 0.729622i
\(433\) −25.1331 −1.20782 −0.603910 0.797052i \(-0.706392\pi\)
−0.603910 + 0.797052i \(0.706392\pi\)
\(434\) −3.21675 5.89100i −0.154409 0.282777i
\(435\) 7.76047 5.94110i 0.372086 0.284854i
\(436\) 5.76570 1.25429i 0.276127 0.0600696i
\(437\) 2.38110 + 8.88638i 0.113903 + 0.425093i
\(438\) 0.0624878 + 0.0277264i 0.00298578 + 0.00132482i
\(439\) 13.5272 7.80991i 0.645616 0.372747i −0.141158 0.989987i \(-0.545083\pi\)
0.786775 + 0.617240i \(0.211749\pi\)
\(440\) −14.7087 1.05185i −0.701209 0.0501448i
\(441\) 7.28917 + 7.32172i 0.347103 + 0.348653i
\(442\) −8.45098 + 8.05805i −0.401972 + 0.383282i
\(443\) 32.6709 + 8.75415i 1.55224 + 0.415922i 0.930197 0.367060i \(-0.119636\pi\)
0.622045 + 0.782982i \(0.286302\pi\)
\(444\) 21.5671 + 18.2843i 1.02353 + 0.867733i
\(445\) −19.5123 + 5.22830i −0.924970 + 0.247845i
\(446\) −3.79144 2.31099i −0.179530 0.109428i
\(447\) 10.6039 + 8.15544i 0.501547 + 0.385739i
\(448\) −14.0055 + 5.60726i −0.661697 + 0.264918i
\(449\) −28.0284 −1.32274 −0.661370 0.750060i \(-0.730025\pi\)
−0.661370 + 0.750060i \(0.730025\pi\)
\(450\) 38.2466 + 40.2909i 1.80296 + 1.89933i
\(451\) 3.43500 + 3.43500i 0.161748 + 0.161748i
\(452\) 3.75381 + 7.28127i 0.176565 + 0.342482i
\(453\) −2.58269 + 6.21557i −0.121345 + 0.292033i
\(454\) −4.69532 19.3541i −0.220362 0.908334i
\(455\) −16.6441 9.60949i −0.780289 0.450500i
\(456\) 5.84618 28.3442i 0.273772 1.32734i
\(457\) 14.8363 8.56574i 0.694012 0.400688i −0.111101 0.993809i \(-0.535438\pi\)
0.805113 + 0.593121i \(0.202104\pi\)
\(458\) −18.5222 19.4254i −0.865488 0.907692i
\(459\) 6.79742 + 16.5668i 0.317276 + 0.773272i
\(460\) −8.91192 9.80332i −0.415521 0.457082i
\(461\) 2.43727 9.09603i 0.113515 0.423644i −0.885656 0.464341i \(-0.846291\pi\)
0.999172 + 0.0406970i \(0.0129578\pi\)
\(462\) 0.878564 5.59297i 0.0408745 0.260209i
\(463\) −0.777204 + 1.34616i −0.0361197 + 0.0625612i −0.883520 0.468393i \(-0.844833\pi\)
0.847400 + 0.530954i \(0.178166\pi\)
\(464\) 5.23271 0.879991i 0.242922 0.0408526i
\(465\) −17.1392 + 7.07694i −0.794812 + 0.328185i
\(466\) −8.59420 15.7390i −0.398118 0.729094i
\(467\) 9.81211 + 9.81211i 0.454050 + 0.454050i 0.896696 0.442646i \(-0.145960\pi\)
−0.442646 + 0.896696i \(0.645960\pi\)
\(468\) 12.0761 + 7.79883i 0.558220 + 0.360501i
\(469\) 0.395609 0.395609i 0.0182675 0.0182675i
\(470\) −0.781946 + 2.66309i −0.0360685 + 0.122839i
\(471\) −6.81438 + 8.86022i −0.313990 + 0.408257i
\(472\) 31.4158 6.05521i 1.44603 0.278713i
\(473\) 3.25331 + 1.87830i 0.149587 + 0.0863643i
\(474\) −10.6718 + 1.13535i −0.490173 + 0.0521484i
\(475\) 74.7175 + 20.0205i 3.42828 + 0.918604i
\(476\) 0.618370 12.9829i 0.0283429 0.595071i
\(477\) −11.8654 20.6576i −0.543278 0.945845i
\(478\) −0.248614 + 10.4454i −0.0113713 + 0.477761i
\(479\) −11.7030 20.2702i −0.534724 0.926169i −0.999177 0.0405710i \(-0.987082\pi\)
0.464453 0.885598i \(-0.346251\pi\)
\(480\) 11.2212 + 40.1386i 0.512175 + 1.83207i
\(481\) −9.77797 + 16.9359i −0.445837 + 0.772212i
\(482\) 27.0388 + 16.4809i 1.23158 + 0.750684i
\(483\) 4.03891 3.09202i 0.183777 0.140692i
\(484\) −16.8838 + 8.70436i −0.767448 + 0.395653i
\(485\) −25.1064 + 25.1064i −1.14002 + 1.14002i
\(486\) 17.8763 12.9011i 0.810886 0.585205i
\(487\) 21.0301i 0.952967i −0.879183 0.476483i \(-0.841911\pi\)
0.879183 0.476483i \(-0.158089\pi\)
\(488\) −13.1236 4.54198i −0.594077 0.205606i
\(489\) −25.6860 3.41073i −1.16156 0.154239i
\(490\) −20.1329 + 4.88425i −0.909511 + 0.220648i
\(491\) −6.82214 25.4606i −0.307879 1.14902i −0.930439 0.366447i \(-0.880574\pi\)
0.622560 0.782572i \(-0.286093\pi\)
\(492\) 5.86553 12.4138i 0.264438 0.559658i
\(493\) −1.18321 + 4.41580i −0.0532891 + 0.198877i
\(494\) 20.0110 + 0.476289i 0.900339 + 0.0214292i
\(495\) −15.0987 4.08177i −0.678638 0.183462i
\(496\) −10.0216 0.956819i −0.449983 0.0429625i
\(497\) 13.1944 + 22.8533i 0.591849 + 1.02511i
\(498\) −6.74337 5.44652i −0.302178 0.244064i
\(499\) 12.8466 3.44223i 0.575092 0.154095i 0.0404610 0.999181i \(-0.487117\pi\)
0.534631 + 0.845086i \(0.320451\pi\)
\(500\) −67.2854 + 14.6375i −3.00909 + 0.654608i
\(501\) 37.1147 4.84419i 1.65816 0.216422i
\(502\) −4.23912 + 14.4373i −0.189201 + 0.644368i
\(503\) 7.97796i 0.355720i 0.984056 + 0.177860i \(0.0569174\pi\)
−0.984056 + 0.177860i \(0.943083\pi\)
\(504\) −15.7189 + 2.99342i −0.700175 + 0.133338i
\(505\) 31.7417i 1.41249i
\(506\) 2.59001 + 0.760486i 0.115140 + 0.0338077i
\(507\) 4.82479 11.6115i 0.214276 0.515683i
\(508\) 5.29641 8.24149i 0.234990 0.365657i
\(509\) 33.3037 8.92371i 1.47616 0.395536i 0.571123 0.820865i \(-0.306508\pi\)
0.905039 + 0.425328i \(0.139841\pi\)
\(510\) −35.4726 5.57216i −1.57075 0.246739i
\(511\) −0.0263151 0.0455792i −0.00116411 0.00201630i
\(512\) −4.80918 + 22.1104i −0.212538 + 0.977153i
\(513\) 11.8417 28.3204i 0.522825 1.25038i
\(514\) 0.149183 6.26784i 0.00658016 0.276463i
\(515\) −15.5353 + 57.9785i −0.684567 + 2.55484i
\(516\) 1.89672 10.4466i 0.0834983 0.459884i
\(517\) −0.146362 0.546229i −0.00643697 0.0240231i
\(518\) −5.13200 21.1541i −0.225487 0.929458i
\(519\) −12.7955 30.9886i −0.561658 1.36025i
\(520\) −25.9285 + 12.5956i −1.13704 + 0.552354i
\(521\) 20.0111i 0.876703i 0.898804 + 0.438352i \(0.144438\pi\)
−0.898804 + 0.438352i \(0.855562\pi\)
\(522\) 5.62615 + 0.146451i 0.246250 + 0.00641000i
\(523\) −11.2432 + 11.2432i −0.491633 + 0.491633i −0.908820 0.417188i \(-0.863016\pi\)
0.417188 + 0.908820i \(0.363016\pi\)
\(524\) −11.2062 + 35.0568i −0.489545 + 1.53146i
\(525\) −5.53518 42.4089i −0.241575 1.85087i
\(526\) 3.92617 6.44134i 0.171189 0.280856i
\(527\) 4.33671 7.51140i 0.188910 0.327202i
\(528\) −6.20858 5.79317i −0.270194 0.252115i
\(529\) −10.2874 17.8183i −0.447278 0.774708i
\(530\) 47.7562 + 1.13666i 2.07440 + 0.0493733i
\(531\) 33.9347 + 0.0755992i 1.47264 + 0.00328072i
\(532\) −16.4865 + 14.9874i −0.714780 + 0.649786i
\(533\) 9.17253 + 2.45777i 0.397306 + 0.106458i
\(534\) −10.6328 4.71786i −0.460126 0.204162i
\(535\) −20.0569 11.5799i −0.867137 0.500642i
\(536\) −0.158816 0.823975i −0.00685982 0.0355903i
\(537\) 6.99685 + 0.929082i 0.301936 + 0.0400929i
\(538\) 39.6091 + 11.6301i 1.70767 + 0.501411i
\(539\) 2.98466 2.98466i 0.128559 0.128559i
\(540\) 3.53113 + 44.0646i 0.151956 + 1.89624i
\(541\) 9.38252 + 9.38252i 0.403386 + 0.403386i 0.879424 0.476038i \(-0.157928\pi\)
−0.476038 + 0.879424i \(0.657928\pi\)
\(542\) 28.8385 15.7471i 1.23872 0.676397i
\(543\) 3.06366 23.0722i 0.131474 0.990123i
\(544\) −15.6065 11.6825i −0.669125 0.500884i
\(545\) −6.27481 + 10.8683i −0.268783 + 0.465546i
\(546\) −3.97925 10.3271i −0.170296 0.441959i
\(547\) −9.70067 + 36.2034i −0.414770 + 1.54794i 0.370524 + 0.928823i \(0.379178\pi\)
−0.785295 + 0.619122i \(0.787489\pi\)
\(548\) 1.47445 30.9566i 0.0629854 1.32240i
\(549\) −12.7399 7.39327i −0.543725 0.315537i
\(550\) 16.4261 15.6624i 0.700411 0.667845i
\(551\) 6.78671 3.91831i 0.289123 0.166926i
\(552\) −0.445259 7.61623i −0.0189515 0.324168i
\(553\) 7.15532 + 4.13113i 0.304275 + 0.175673i
\(554\) 27.0469 6.56160i 1.14911 0.278776i
\(555\) −59.6303 + 7.78291i −2.53116 + 0.330366i
\(556\) −14.0465 4.49007i −0.595703 0.190421i
\(557\) 9.01169 + 9.01169i 0.381838 + 0.381838i 0.871764 0.489926i \(-0.162976\pi\)
−0.489926 + 0.871764i \(0.662976\pi\)
\(558\) −10.2386 3.03108i −0.433435 0.128316i
\(559\) 7.34341 0.310593
\(560\) 11.2126 30.0633i 0.473819 1.27041i
\(561\) 6.76220 2.79217i 0.285500 0.117886i
\(562\) −13.8546 + 22.7300i −0.584420 + 0.958809i
\(563\) −16.4015 + 4.39477i −0.691241 + 0.185218i −0.587304 0.809366i \(-0.699811\pi\)
−0.103937 + 0.994584i \(0.533144\pi\)
\(564\) −1.31387 + 0.910080i −0.0553238 + 0.0383213i
\(565\) −16.8294 4.50942i −0.708018 0.189713i
\(566\) −12.9654 13.5976i −0.544976 0.571551i
\(567\) −16.9719 0.0756196i −0.712751 0.00317573i
\(568\) 39.4789 + 2.82321i 1.65650 + 0.118459i
\(569\) 14.1855 8.19001i 0.594688 0.343343i −0.172261 0.985051i \(-0.555107\pi\)
0.766949 + 0.641708i \(0.221774\pi\)
\(570\) 36.2431 + 49.7514i 1.51806 + 2.08386i
\(571\) −9.58794 35.7827i −0.401243 1.49746i −0.810881 0.585211i \(-0.801012\pi\)
0.409638 0.912248i \(-0.365655\pi\)
\(572\) 3.17523 4.94082i 0.132763 0.206586i
\(573\) −7.56284 3.14250i −0.315942 0.131280i
\(574\) −9.27715 + 5.06575i −0.387221 + 0.211440i
\(575\) 20.3914 0.850382
\(576\) −9.49631 + 22.0413i −0.395680 + 0.918389i
\(577\) −2.14863 −0.0894487 −0.0447243 0.998999i \(-0.514241\pi\)
−0.0447243 + 0.998999i \(0.514241\pi\)
\(578\) −6.35950 + 3.47258i −0.264520 + 0.144440i
\(579\) 4.37813 + 33.5439i 0.181949 + 1.39404i
\(580\) −6.10133 + 9.49399i −0.253344 + 0.394216i
\(581\) 1.72719 + 6.44597i 0.0716560 + 0.267424i
\(582\) −20.3312 + 2.16299i −0.842757 + 0.0896590i
\(583\) −8.42888 + 4.86642i −0.349088 + 0.201546i
\(584\) −0.0787375 0.00563067i −0.00325818 0.000232999i
\(585\) −29.5503 + 7.84747i −1.22176 + 0.324453i
\(586\) 8.32107 + 8.72684i 0.343740 + 0.360502i
\(587\) −21.6014 5.78807i −0.891585 0.238899i −0.216186 0.976352i \(-0.569362\pi\)
−0.675399 + 0.737453i \(0.736028\pi\)
\(588\) −10.7863 5.09654i −0.444821 0.210178i
\(589\) −14.3614 + 3.84813i −0.591752 + 0.158559i
\(590\) −35.4159 + 58.1038i −1.45805 + 2.39210i
\(591\) −2.22464 + 16.7536i −0.0915095 + 0.689151i
\(592\) −30.5904 11.4092i −1.25726 0.468915i
\(593\) 10.7128 0.439921 0.219960 0.975509i \(-0.429407\pi\)
0.219960 + 0.975509i \(0.429407\pi\)
\(594\) −5.28702 7.29165i −0.216929 0.299180i
\(595\) 19.5473 + 19.5473i 0.801361 + 0.801361i
\(596\) −14.7134 4.70327i −0.602685 0.192653i
\(597\) 25.7693 + 33.6608i 1.05467 + 1.37764i
\(598\) 5.12795 1.24404i 0.209697 0.0508727i
\(599\) 23.8944 + 13.7955i 0.976300 + 0.563667i 0.901151 0.433505i \(-0.142723\pi\)
0.0751489 + 0.997172i \(0.476057\pi\)
\(600\) −57.3304 28.7768i −2.34050 1.17481i
\(601\) −9.37490 + 5.41260i −0.382410 + 0.220785i −0.678866 0.734262i \(-0.737528\pi\)
0.296456 + 0.955046i \(0.404195\pi\)
\(602\) −5.91575 + 5.64069i −0.241108 + 0.229897i
\(603\) 0.00198282 0.890041i 8.07466e−5 0.0362453i
\(604\) 0.369760 7.76325i 0.0150453 0.315882i
\(605\) 10.4565 39.0241i 0.425116 1.58655i
\(606\) 11.4849 14.2196i 0.466543 0.577630i
\(607\) 19.0270 32.9557i 0.772282 1.33763i −0.164028 0.986456i \(-0.552449\pi\)
0.936310 0.351175i \(-0.114218\pi\)
\(608\) 4.75640 + 33.0778i 0.192898 + 1.34148i
\(609\) −3.43455 2.64150i −0.139175 0.107039i
\(610\) 25.9234 14.1553i 1.04961 0.573133i
\(611\) −0.781661 0.781661i −0.0316226 0.0316226i
\(612\) −13.8748 15.3311i −0.560855 0.619722i
\(613\) −34.9758 + 34.9758i −1.41266 + 1.41266i −0.673168 + 0.739489i \(0.735067\pi\)
−0.739489 + 0.673168i \(0.764933\pi\)
\(614\) −13.6931 4.02061i −0.552608 0.162259i
\(615\) 11.1448 + 26.9909i 0.449401 + 1.08838i
\(616\) 1.23727 + 6.41925i 0.0498511 + 0.258639i
\(617\) −11.9478 6.89807i −0.481001 0.277706i 0.239833 0.970814i \(-0.422907\pi\)
−0.720834 + 0.693108i \(0.756241\pi\)
\(618\) −27.9375 + 20.3520i −1.12381 + 0.818679i
\(619\) 32.9231 + 8.82171i 1.32329 + 0.354574i 0.850209 0.526445i \(-0.176475\pi\)
0.473080 + 0.881019i \(0.343142\pi\)
\(620\) 15.8433 14.4027i 0.636282 0.578426i
\(621\) 1.08302 8.01922i 0.0434603 0.321800i
\(622\) 16.4463 + 0.391444i 0.659438 + 0.0156955i
\(623\) 4.47773 + 7.75565i 0.179396 + 0.310724i
\(624\) −16.1728 3.73903i −0.647430 0.149681i
\(625\) 40.4916 70.1335i 1.61966 2.80534i
\(626\) 4.90364 8.04499i 0.195989 0.321542i
\(627\) −11.5811 4.81217i −0.462505 0.192180i
\(628\) 3.92987 12.2940i 0.156819 0.490583i
\(629\) 19.8900 19.8900i 0.793066 0.793066i
\(630\) 17.7775 29.0203i 0.708271 1.15620i
\(631\) 7.97657i 0.317542i 0.987315 + 0.158771i \(0.0507532\pi\)
−0.987315 + 0.158771i \(0.949247\pi\)
\(632\) 11.1467 5.41486i 0.443392 0.215391i
\(633\) −23.1580 + 30.1106i −0.920449 + 1.19679i
\(634\) −0.912816 3.76263i −0.0362526 0.149433i
\(635\) 5.39276 + 20.1260i 0.214005 + 0.798677i
\(636\) 20.9825 + 17.7886i 0.832008 + 0.705363i
\(637\) 2.13555 7.96998i 0.0846135 0.315782i
\(638\) 0.0547121 2.29871i 0.00216607 0.0910066i
\(639\) 40.5259 + 10.9557i 1.60318 + 0.433401i
\(640\) −27.9162 39.2010i −1.10349 1.54956i
\(641\) −18.6956 32.3818i −0.738434 1.27900i −0.953200 0.302339i \(-0.902232\pi\)
0.214767 0.976665i \(-0.431101\pi\)
\(642\) −4.79518 12.4446i −0.189251 0.491150i
\(643\) 12.4765 3.34308i 0.492026 0.131838i −0.00427070 0.999991i \(-0.501359\pi\)
0.496297 + 0.868153i \(0.334693\pi\)
\(644\) −3.17542 + 4.94112i −0.125129 + 0.194707i
\(645\) 13.7268 + 17.9305i 0.540493 + 0.706011i
\(646\) −27.6252 8.11141i −1.08690 0.319139i
\(647\) 4.85394i 0.190828i 0.995438 + 0.0954140i \(0.0304175\pi\)
−0.995438 + 0.0954140i \(0.969582\pi\)
\(648\) −14.3618 + 21.0176i −0.564184 + 0.825649i
\(649\) 13.8641i 0.544215i
\(650\) 12.4995 42.5698i 0.490270 1.66973i
\(651\) 4.99707 + 6.52735i 0.195851 + 0.255827i
\(652\) 29.2361 6.36013i 1.14498 0.249082i
\(653\) −37.4249 + 10.0280i −1.46455 + 0.392425i −0.901059 0.433696i \(-0.857209\pi\)
−0.563492 + 0.826121i \(0.690542\pi\)
\(654\) −6.74339 + 2.59837i −0.263687 + 0.101604i
\(655\) −39.1387 67.7902i −1.52928 2.64878i
\(656\) −1.50680 + 15.7820i −0.0588307 + 0.616185i
\(657\) −0.0808256 0.0218503i −0.00315331 0.000852460i
\(658\) 1.23011 + 0.0292783i 0.0479548 + 0.00114139i
\(659\) 9.85502 36.7794i 0.383897 1.43272i −0.456001 0.889979i \(-0.650719\pi\)
0.839898 0.542744i \(-0.182615\pi\)
\(660\) 17.9994 1.48275i 0.700626 0.0577161i
\(661\) 3.10339 + 11.5820i 0.120708 + 0.450488i 0.999650 0.0264400i \(-0.00841709\pi\)
−0.878943 + 0.476927i \(0.841750\pi\)
\(662\) −27.9997 + 6.79276i −1.08824 + 0.264008i
\(663\) 8.71871 11.3363i 0.338606 0.440264i
\(664\) 9.45870 + 3.27359i 0.367069 + 0.127040i
\(665\) 47.3876i 1.83761i
\(666\) −29.5291 18.0891i −1.14423 0.700940i
\(667\) 1.46077 1.46077i 0.0565613 0.0565613i
\(668\) −38.4152 + 19.8047i −1.48633 + 0.766267i
\(669\) 5.02188 + 2.08669i 0.194157 + 0.0806760i
\(670\) 1.52395 + 0.928890i 0.0588753 + 0.0358861i
\(671\) −3.00893 + 5.21163i −0.116159 + 0.201193i
\(672\) 15.9007 9.41071i 0.613381 0.363026i
\(673\) 14.9076 + 25.8207i 0.574645 + 0.995314i 0.996080 + 0.0884554i \(0.0281931\pi\)
−0.421435 + 0.906858i \(0.638474\pi\)
\(674\) −0.0346286 + 1.45491i −0.00133385 + 0.0560409i
\(675\) −53.8399 41.5994i −2.07230 1.60116i
\(676\) −0.690758 + 14.5027i −0.0265676 + 0.557797i
\(677\) 27.4303 + 7.34993i 1.05423 + 0.282481i 0.744000 0.668180i \(-0.232926\pi\)
0.310233 + 0.950661i \(0.399593\pi\)
\(678\) −5.90757 8.10941i −0.226879 0.311440i
\(679\) 13.6318 + 7.87034i 0.523142 + 0.302036i
\(680\) 40.7131 7.84721i 1.56128 0.300927i
\(681\) 9.30909 + 22.5451i 0.356725 + 0.863931i
\(682\) −1.22903 + 4.18575i −0.0470621 + 0.160281i
\(683\) 34.9639 34.9639i 1.33786 1.33786i 0.439721 0.898134i \(-0.355077\pi\)
0.898134 0.439721i \(-0.144923\pi\)
\(684\) −1.76520 + 35.4012i −0.0674940 + 1.35360i
\(685\) 46.6088 + 46.6088i 1.78083 + 1.78083i
\(686\) 13.3484 + 24.4456i 0.509645 + 0.933338i
\(687\) 26.0576 + 20.0408i 0.994159 + 0.764606i
\(688\) 2.03321 + 12.0901i 0.0775153 + 0.460931i
\(689\) −9.51288 + 16.4768i −0.362412 + 0.627716i
\(690\) 12.6231 + 10.1955i 0.480554 + 0.388136i
\(691\) −3.37585 + 12.5989i −0.128424 + 0.479283i −0.999939 0.0110856i \(-0.996471\pi\)
0.871515 + 0.490369i \(0.163138\pi\)
\(692\) 26.0408 + 28.6455i 0.989922 + 1.08894i
\(693\) −0.0154473 + 6.93394i −0.000586795 + 0.263399i
\(694\) −30.4680 31.9538i −1.15655 1.21295i
\(695\) 27.1620 15.6820i 1.03031 0.594851i
\(696\) −6.16842 + 2.04548i −0.233813 + 0.0775338i
\(697\) −11.8290 6.82946i −0.448054 0.258684i
\(698\) −5.95574 24.5495i −0.225428 0.929214i
\(699\) 13.3507 + 17.4391i 0.504969 + 0.659608i
\(700\) 22.6297 + 43.8949i 0.855324 + 1.65907i
\(701\) −1.18582 1.18582i −0.0447879 0.0447879i 0.684358 0.729146i \(-0.260083\pi\)
−0.729146 + 0.684358i \(0.760083\pi\)
\(702\) −16.0773 7.17655i −0.606799 0.270861i
\(703\) −48.2184 −1.81859
\(704\) 9.01365 + 3.85967i 0.339715 + 0.145467i
\(705\) 0.447452 3.36973i 0.0168520 0.126911i
\(706\) −2.48341 1.51371i −0.0934644 0.0569691i
\(707\) −13.5924 + 3.64208i −0.511196 + 0.136975i
\(708\) −36.8889 + 13.2149i −1.38637 + 0.496646i
\(709\) 13.3909 + 3.58808i 0.502906 + 0.134753i 0.501349 0.865245i \(-0.332837\pi\)
0.00155784 + 0.999999i \(0.499504\pi\)
\(710\) −60.9239 + 58.0912i −2.28643 + 2.18012i
\(711\) 12.7037 3.37363i 0.476426 0.126521i
\(712\) 13.3978 + 0.958103i 0.502104 + 0.0359064i
\(713\) −3.39432 + 1.95971i −0.127118 + 0.0733919i
\(714\) 1.68406 + 15.8294i 0.0630243 + 0.592402i
\(715\) 3.23299 + 12.0657i 0.120907 + 0.451231i
\(716\) −7.96391 + 1.73250i −0.297625 + 0.0647464i
\(717\) −1.65615 12.6889i −0.0618502 0.473877i
\(718\) −3.23008 5.91541i −0.120546 0.220761i
\(719\) 22.9314 0.855198 0.427599 0.903968i \(-0.359359\pi\)
0.427599 + 0.903968i \(0.359359\pi\)
\(720\) −21.1017 46.4785i −0.786415 1.73215i
\(721\) 26.6101 0.991013
\(722\) 10.7757 + 19.7341i 0.401031 + 0.734428i
\(723\) −35.8137 14.8813i −1.33193 0.553441i
\(724\) 5.71293 + 26.2611i 0.212319 + 0.975986i
\(725\) −4.49564 16.7780i −0.166964 0.623118i
\(726\) 18.8041 13.6985i 0.697887 0.508400i
\(727\) 14.6244 8.44338i 0.542387 0.313147i −0.203659 0.979042i \(-0.565283\pi\)
0.746046 + 0.665894i \(0.231950\pi\)
\(728\) 8.36877 + 9.65789i 0.310167 + 0.357945i
\(729\) −19.2191 + 18.9639i −0.711817 + 0.702365i
\(730\) 0.121508 0.115858i 0.00449721 0.00428811i
\(731\) −10.2026 2.73379i −0.377358 0.101113i
\(732\) 16.7348 + 3.03844i 0.618538 + 0.112304i
\(733\) −39.1181 + 10.4817i −1.44486 + 0.387149i −0.894232 0.447603i \(-0.852278\pi\)
−0.550626 + 0.834752i \(0.685611\pi\)
\(734\) 20.7949 + 12.6751i 0.767554 + 0.467845i
\(735\) 23.4523 9.68366i 0.865051 0.357187i
\(736\) 3.46798 + 8.09815i 0.127831 + 0.298502i
\(737\) −0.363629 −0.0133945
\(738\) −4.77335 + 16.1238i −0.175710 + 0.593524i
\(739\) 20.2719 + 20.2719i 0.745713 + 0.745713i 0.973671 0.227958i \(-0.0732050\pi\)
−0.227958 + 0.973671i \(0.573205\pi\)
\(740\) 61.7198 31.8192i 2.26886 1.16970i
\(741\) −24.3092 + 3.17282i −0.893020 + 0.116557i
\(742\) −4.99287 20.5806i −0.183294 0.755538i
\(743\) 33.3722 + 19.2674i 1.22431 + 0.706853i 0.965833 0.259165i \(-0.0834474\pi\)
0.258473 + 0.966019i \(0.416781\pi\)
\(744\) 12.3087 0.719590i 0.451259 0.0263815i
\(745\) 28.4517 16.4266i 1.04239 0.601824i
\(746\) 16.2043 + 16.9944i 0.593280 + 0.622210i
\(747\) 9.18216 + 5.32863i 0.335958 + 0.194964i
\(748\) −6.25090 + 5.68251i −0.228555 + 0.207773i
\(749\) −2.65738 + 9.91749i −0.0970987 + 0.362377i
\(750\) 78.6949 30.3228i 2.87353 1.10723i
\(751\) −2.59701 + 4.49815i −0.0947663 + 0.164140i −0.909511 0.415680i \(-0.863544\pi\)
0.814745 + 0.579820i \(0.196877\pi\)
\(752\) 1.07050 1.50334i 0.0390369 0.0548212i
\(753\) 2.42575 18.2681i 0.0883991 0.665727i
\(754\) −2.15414 3.94497i −0.0784490 0.143667i
\(755\) 11.6885 + 11.6885i 0.425388 + 0.425388i
\(756\) 18.4642 6.56813i 0.671536 0.238881i
\(757\) 16.3310 16.3310i 0.593562 0.593562i −0.345030 0.938592i \(-0.612131\pi\)
0.938592 + 0.345030i \(0.112131\pi\)
\(758\) −12.7196 + 43.3194i −0.461996 + 1.57343i
\(759\) −3.27725 0.435172i −0.118957 0.0157957i
\(760\) −58.8613 39.8377i −2.13512 1.44506i
\(761\) −30.2706 17.4767i −1.09731 0.633530i −0.161794 0.986824i \(-0.551728\pi\)
−0.935512 + 0.353294i \(0.885061\pi\)
\(762\) −4.86627 + 10.9673i −0.176286 + 0.397302i
\(763\) 5.37400 + 1.43996i 0.194552 + 0.0521300i
\(764\) 9.44599 + 0.449908i 0.341744 + 0.0162771i
\(765\) 43.9775 + 0.0979723i 1.59001 + 0.00354220i
\(766\) −0.849026 + 35.6715i −0.0306766 + 1.28886i
\(767\) −13.5508 23.4707i −0.489292 0.847478i
\(768\) 1.67805 27.6620i 0.0605515 0.998165i
\(769\) −11.5439 + 19.9946i −0.416284 + 0.721024i −0.995562 0.0941052i \(-0.970001\pi\)
0.579279 + 0.815130i \(0.303334\pi\)
\(770\) −11.8725 7.23659i −0.427854 0.260789i
\(771\) 0.993788 + 7.61410i 0.0357904 + 0.274215i
\(772\) −17.8993 34.7193i −0.644211 1.24958i
\(773\) 14.4736 14.4736i 0.520581 0.520581i −0.397166 0.917747i \(-0.630006\pi\)
0.917747 + 0.397166i \(0.130006\pi\)
\(774\) −0.338374 + 12.9991i −0.0121626 + 0.467245i
\(775\) 32.9549i 1.18378i
\(776\) 21.2359 10.3160i 0.762325 0.370323i
\(777\) 10.1749 + 24.6419i 0.365021 + 0.884023i
\(778\) 10.0960 2.44929i 0.361958 0.0878113i
\(779\) 6.06004 + 22.6164i 0.217124 + 0.810316i
\(780\) 29.0221 20.1028i 1.03916 0.719796i
\(781\) 4.43908 16.5669i 0.158843 0.592809i
\(782\) −7.58770 0.180597i −0.271335 0.00645813i
\(783\) −6.83694 + 0.876867i −0.244332 + 0.0313367i
\(784\) 13.7130 + 1.30925i 0.489749 + 0.0467591i
\(785\) 13.7254 + 23.7732i 0.489882 + 0.848501i
\(786\) 6.99491 44.5299i 0.249500 1.58833i
\(787\) −33.2907 + 8.92022i −1.18669 + 0.317971i −0.797575 0.603220i \(-0.793884\pi\)
−0.389110 + 0.921191i \(0.627218\pi\)
\(788\) −4.14837 19.0692i −0.147780 0.679312i
\(789\) −3.54511 + 8.53175i −0.126209 + 0.303738i
\(790\) −7.42544 + 25.2890i −0.264185 + 0.899743i
\(791\) 7.72411i 0.274638i
\(792\) 8.59984 + 5.84839i 0.305582 + 0.207814i
\(793\) 11.7637i 0.417743i
\(794\) −4.28387 1.25784i −0.152029 0.0446392i
\(795\) −58.0137 + 7.57191i −2.05753 + 0.268548i
\(796\) −41.1798 26.4643i −1.45958 0.938002i
\(797\) 19.0745 5.11099i 0.675652 0.181040i 0.0953525 0.995444i \(-0.469602\pi\)
0.580299 + 0.814403i \(0.302936\pi\)
\(798\) 17.1460 21.2286i 0.606962 0.751484i
\(799\) 0.795014 + 1.37700i 0.0281256 + 0.0487149i
\(800\) 73.5472 + 8.79247i 2.60029 + 0.310861i
\(801\) 13.7531 + 3.71800i 0.485943 + 0.131369i
\(802\) 0.613079 25.7582i 0.0216486 0.909555i
\(803\) −0.00885339 + 0.0330413i −0.000312429 + 0.00116600i
\(804\) 0.346601 + 0.967525i 0.0122237 + 0.0341220i
\(805\) −3.23318 12.0664i −0.113955 0.425285i
\(806\) 2.01052 + 8.28736i 0.0708175 + 0.291910i
\(807\) −50.1191 6.65511i −1.76428 0.234271i
\(808\) −6.90293 + 19.9453i −0.242844 + 0.701673i
\(809\) 2.32596i 0.0817763i 0.999164 + 0.0408882i \(0.0130187\pi\)
−0.999164 + 0.0408882i \(0.986981\pi\)
\(810\) −12.5298 52.6710i −0.440252 1.85067i
\(811\) 34.5092 34.5092i 1.21178 1.21178i 0.241343 0.970440i \(-0.422412\pi\)
0.970440 0.241343i \(-0.0775878\pi\)
\(812\) 4.76560 + 1.52336i 0.167240 + 0.0534595i
\(813\) −31.9537 + 24.4624i −1.12066 + 0.857934i
\(814\) −7.36347 + 12.0806i −0.258089 + 0.423425i
\(815\) −31.8177 + 55.1098i −1.11452 + 1.93041i
\(816\) 21.0779 + 11.2156i 0.737874 + 0.392626i
\(817\) 9.05319 + 15.6806i 0.316731 + 0.548594i
\(818\) −37.0562 0.881984i −1.29564 0.0308378i
\(819\) 6.75109 + 11.7536i 0.235902 + 0.410705i
\(820\) −22.6814 24.9501i −0.792069 0.871294i
\(821\) −51.3558 13.7607i −1.79233 0.480253i −0.799590 0.600547i \(-0.794950\pi\)
−0.992738 + 0.120294i \(0.961616\pi\)
\(822\) 4.01549 + 37.7439i 0.140056 + 1.31647i
\(823\) 8.35343 + 4.82286i 0.291182 + 0.168114i 0.638475 0.769643i \(-0.279566\pi\)
−0.347293 + 0.937757i \(0.612899\pi\)
\(824\) 22.3705 33.0531i 0.779314 1.15146i
\(825\) −16.9465 + 22.0342i −0.590000 + 0.767132i
\(826\) 28.9449 + 8.49890i 1.00712 + 0.295714i
\(827\) −18.2747 + 18.2747i −0.635475 + 0.635475i −0.949436 0.313961i \(-0.898344\pi\)
0.313961 + 0.949436i \(0.398344\pi\)
\(828\) 1.96589 + 9.13471i 0.0683195 + 0.317453i
\(829\) 6.63529 + 6.63529i 0.230453 + 0.230453i 0.812882 0.582429i \(-0.197897\pi\)
−0.582429 + 0.812882i \(0.697897\pi\)
\(830\) −18.6840 + 10.2023i −0.648532 + 0.354128i
\(831\) −31.5063 + 13.0092i −1.09294 + 0.451285i
\(832\) 19.0317 2.27589i 0.659807 0.0789022i
\(833\) −5.93409 + 10.2782i −0.205604 + 0.356117i
\(834\) 17.8421 + 2.80270i 0.617821 + 0.0970496i
\(835\) 23.7912 88.7900i 0.823329 3.07271i
\(836\) 14.4648 + 0.688953i 0.500276 + 0.0238279i
\(837\) 12.9600 + 1.75029i 0.447963 + 0.0604990i
\(838\) 11.8891 11.3363i 0.410704 0.391608i
\(839\) −34.7829 + 20.0819i −1.20084 + 0.693306i −0.960742 0.277443i \(-0.910513\pi\)
−0.240099 + 0.970749i \(0.577180\pi\)
\(840\) −7.93825 + 38.4873i −0.273896 + 1.32794i
\(841\) 23.5908 + 13.6201i 0.813475 + 0.469660i
\(842\) −13.8662 + 3.36394i −0.477860 + 0.115929i
\(843\) 12.5099 30.1066i 0.430863 1.03693i
\(844\) 13.3553 41.7799i 0.459708 1.43812i
\(845\) −21.8355 21.8355i −0.751166 0.751166i
\(846\) 1.41970 1.34766i 0.0488102 0.0463336i
\(847\) −17.9107 −0.615419
\(848\) −29.7611 11.0999i −1.02200 0.381171i
\(849\) 18.2401 + 14.0284i 0.625997 + 0.481453i
\(850\) −33.2141 + 54.4915i −1.13923 + 1.86904i
\(851\) −12.2779 + 3.28987i −0.420883 + 0.112775i
\(852\) −48.3114 + 3.97979i −1.65512 + 0.136345i
\(853\) −2.70204 0.724010i −0.0925162 0.0247896i 0.212264 0.977212i \(-0.431916\pi\)
−0.304780 + 0.952423i \(0.598583\pi\)
\(854\) −9.03609 9.47672i −0.309209 0.324287i
\(855\) −53.1876 53.4251i −1.81898 1.82710i
\(856\) 10.0848 + 11.6382i 0.344690 + 0.397786i
\(857\) 32.4678 18.7453i 1.10908 0.640326i 0.170488 0.985360i \(-0.445466\pi\)
0.938590 + 0.345033i \(0.112132\pi\)
\(858\) −2.91736 + 6.57493i −0.0995969 + 0.224465i
\(859\) 12.4963 + 46.6369i 0.426369 + 1.59123i 0.760916 + 0.648850i \(0.224750\pi\)
−0.334547 + 0.942379i \(0.608583\pi\)
\(860\) −21.9357 14.0970i −0.748002 0.480705i
\(861\) 10.2793 7.86939i 0.350317 0.268188i
\(862\) −5.06202 + 2.76409i −0.172413 + 0.0941453i
\(863\) −40.4745 −1.37777 −0.688883 0.724872i \(-0.741899\pi\)
−0.688883 + 0.724872i \(0.741899\pi\)
\(864\) 7.36398 28.4565i 0.250528 0.968109i
\(865\) −82.3366 −2.79953
\(866\) −31.1958 + 17.0343i −1.06008 + 0.578850i
\(867\) 7.04647 5.39448i 0.239311 0.183206i
\(868\) −7.98542 5.13184i −0.271043 0.174186i
\(869\) −1.38986 5.18704i −0.0471479 0.175958i
\(870\) 5.60581 12.6340i 0.190055 0.428333i
\(871\) −0.615591 + 0.355412i −0.0208585 + 0.0120427i
\(872\) 6.30641 5.46464i 0.213562 0.185056i
\(873\) 24.2022 6.42722i 0.819122 0.217528i
\(874\) 8.97835 + 9.41616i 0.303697 + 0.318506i
\(875\) −62.7143 16.8042i −2.12013 0.568087i
\(876\) 0.0963532 0.00793737i 0.00325547 0.000268179i
\(877\) 31.1530 8.34743i 1.05196 0.281873i 0.308901 0.951094i \(-0.400039\pi\)
0.743063 + 0.669222i \(0.233372\pi\)
\(878\) 11.4970 18.8621i 0.388003 0.636564i
\(879\) −11.7063 9.00330i −0.394844 0.303674i
\(880\) −18.9697 + 8.66344i −0.639467 + 0.292045i
\(881\) −44.0930 −1.48553 −0.742765 0.669552i \(-0.766486\pi\)
−0.742765 + 0.669552i \(0.766486\pi\)
\(882\) 14.0099 + 4.14755i 0.471738 + 0.139655i
\(883\) −28.6867 28.6867i −0.965385 0.965385i 0.0340356 0.999421i \(-0.489164\pi\)
−0.999421 + 0.0340356i \(0.989164\pi\)
\(884\) −5.02810 + 15.7296i −0.169113 + 0.529044i
\(885\) 31.9785 76.9603i 1.07494 2.58699i
\(886\) 46.4852 11.2773i 1.56170 0.378869i
\(887\) −6.66474 3.84789i −0.223780 0.129199i 0.383919 0.923367i \(-0.374574\pi\)
−0.607699 + 0.794167i \(0.707907\pi\)
\(888\) 39.1621 + 8.07743i 1.31419 + 0.271061i
\(889\) 7.99961 4.61858i 0.268298 0.154902i
\(890\) −20.6755 + 19.7142i −0.693045 + 0.660822i
\(891\) 7.76520 + 7.83471i 0.260144 + 0.262473i
\(892\) −6.27233 0.298748i −0.210013 0.0100028i
\(893\) 0.705446 2.63276i 0.0236069 0.0881020i
\(894\) 18.6893 + 2.93578i 0.625063 + 0.0981871i
\(895\) 8.66712 15.0119i 0.289710 0.501792i
\(896\) −13.5835 + 16.4523i −0.453794 + 0.549632i
\(897\) −5.97342 + 2.46648i −0.199447 + 0.0823533i
\(898\) −34.7895 + 18.9966i −1.16094 + 0.633926i
\(899\) 2.36078 + 2.36078i 0.0787364 + 0.0787364i
\(900\) 74.7803 + 24.0879i 2.49268 + 0.802930i
\(901\) 19.3508 19.3508i 0.644667 0.644667i
\(902\) 6.59173 + 1.93548i 0.219481 + 0.0644446i
\(903\) 6.10316 7.93547i 0.203100 0.264076i
\(904\) 9.59430 + 6.49348i 0.319102 + 0.215970i
\(905\) −49.5019 28.5799i −1.64550 0.950029i
\(906\) 1.00700 + 9.46537i 0.0334553 + 0.314466i
\(907\) −30.2432 8.10365i −1.00421 0.269077i −0.281002 0.959707i \(-0.590667\pi\)
−0.723208 + 0.690630i \(0.757333\pi\)
\(908\) −18.9455 20.8405i −0.628728 0.691615i
\(909\) −11.2363 + 19.3622i −0.372686 + 0.642203i
\(910\) −27.1721 0.646730i −0.900745 0.0214389i
\(911\) 11.1615 + 19.3322i 0.369796 + 0.640506i 0.989533 0.144304i \(-0.0460942\pi\)
−0.619737 + 0.784809i \(0.712761\pi\)
\(912\) −11.9543 39.1439i −0.395847 1.29618i
\(913\) 2.16866 3.75623i 0.0717722 0.124313i
\(914\) 12.6096 20.6875i 0.417089 0.684282i
\(915\) −28.7236 + 21.9896i −0.949574 + 0.726955i
\(916\) −36.1561 11.5576i −1.19463 0.381874i
\(917\) −24.5383 + 24.5383i −0.810327 + 0.810327i
\(918\) 19.6655 + 15.9560i 0.649058 + 0.526628i
\(919\) 51.8070i 1.70895i −0.519489 0.854477i \(-0.673877\pi\)
0.519489 0.854477i \(-0.326123\pi\)
\(920\) −17.7060 6.12793i −0.583750 0.202032i
\(921\) 17.3264 + 2.30071i 0.570926 + 0.0758109i
\(922\) −3.13976 12.9421i −0.103403 0.426225i
\(923\) −8.67752 32.3849i −0.285624 1.06596i
\(924\) −2.70022 7.53759i −0.0888308 0.247968i
\(925\) −27.6615 + 103.234i −0.909505 + 3.39432i
\(926\) −0.0523067 + 2.19764i −0.00171890 + 0.0722190i
\(927\) 30.0004 29.8671i 0.985344 0.980963i
\(928\) 5.89853 4.63881i 0.193629 0.152276i
\(929\) −13.9260 24.1206i −0.456899 0.791372i 0.541897 0.840445i \(-0.317706\pi\)
−0.998795 + 0.0490736i \(0.984373\pi\)
\(930\) −16.4771 + 20.4004i −0.540306 + 0.668956i
\(931\) 19.6513 5.26555i 0.644046 0.172571i
\(932\) −21.3346 13.7107i −0.698839 0.449110i
\(933\) −19.9788 + 2.60762i −0.654077 + 0.0853698i
\(934\) 18.8293 + 5.52872i 0.616114 + 0.180905i
\(935\) 17.9671i 0.587589i
\(936\) 20.2750 + 1.49531i 0.662708 + 0.0488757i
\(937\) 35.0104i 1.14374i 0.820344 + 0.571870i \(0.193782\pi\)
−0.820344 + 0.571870i \(0.806218\pi\)
\(938\) 0.222910 0.759169i 0.00727825 0.0247877i
\(939\) −4.42770 + 10.6558i −0.144493 + 0.347740i
\(940\) 0.834381 + 3.83547i 0.0272145 + 0.125099i
\(941\) 25.0151 6.70277i 0.815468 0.218504i 0.173104 0.984904i \(-0.444620\pi\)
0.642364 + 0.766400i \(0.277954\pi\)
\(942\) −2.45303 + 15.6161i −0.0799239 + 0.508799i
\(943\) 3.08616 + 5.34539i 0.100499 + 0.174070i
\(944\) 34.8900 28.8084i 1.13557 0.937633i
\(945\) −16.0793 + 38.4549i −0.523060 + 1.25094i
\(946\) 5.31113 + 0.126412i 0.172680 + 0.00411000i
\(947\) 5.18039 19.3335i 0.168340 0.628254i −0.829250 0.558877i \(-0.811232\pi\)
0.997591 0.0693768i \(-0.0221011\pi\)
\(948\) −12.4766 + 8.64221i −0.405222 + 0.280686i
\(949\) 0.0173066 + 0.0645892i 0.000561797 + 0.00209665i
\(950\) 106.310 25.7910i 3.44916 0.836770i
\(951\) 1.80978 + 4.38299i 0.0586861 + 0.142128i
\(952\) −8.03182 16.5338i −0.260313 0.535864i
\(953\) 6.37793i 0.206601i 0.994650 + 0.103301i \(0.0329404\pi\)
−0.994650 + 0.103301i \(0.967060\pi\)
\(954\) −28.7285 17.5987i −0.930121 0.569780i
\(955\) −14.2220 + 14.2220i −0.460215 + 0.460215i
\(956\) 6.77093 + 13.1336i 0.218988 + 0.424770i
\(957\) 0.364468 + 2.79244i 0.0117816 + 0.0902668i
\(958\) −28.2645 17.2280i −0.913183 0.556610i
\(959\) 14.6109 25.3068i 0.471810 0.817199i
\(960\) 41.1325 + 42.2157i 1.32755 + 1.36251i
\(961\) 12.3329 + 21.3612i 0.397835 + 0.689070i
\(962\) −0.658068 + 27.6484i −0.0212170 + 0.891421i
\(963\) 8.13538 + 14.1637i 0.262159 + 0.456418i
\(964\) 44.7314 + 2.13053i 1.44070 + 0.0686199i
\(965\) 80.2477 + 21.5023i 2.58326 + 0.692183i
\(966\) 2.91753 6.57532i 0.0938699 0.211558i
\(967\) 32.7206 + 18.8912i 1.05222 + 0.607501i 0.923271 0.384149i \(-0.125505\pi\)
0.128952 + 0.991651i \(0.458839\pi\)
\(968\) −15.0571 + 22.2473i −0.483954 + 0.715056i
\(969\) 34.9554 + 4.64158i 1.12293 + 0.149109i
\(970\) −14.1464 + 48.1789i −0.454215 + 1.54693i
\(971\) 39.2528 39.2528i 1.25968 1.25968i 0.308436 0.951245i \(-0.400194\pi\)
0.951245 0.308436i \(-0.0998057\pi\)
\(972\) 13.4446 28.1290i 0.431236 0.902239i
\(973\) −9.83195 9.83195i −0.315198 0.315198i
\(974\) −14.2535 26.1031i −0.456711 0.836398i
\(975\) −7.15256 + 53.8654i −0.229065 + 1.72507i
\(976\) −19.3677 + 3.25709i −0.619945 + 0.104257i
\(977\) −13.9657 + 24.1893i −0.446803 + 0.773885i −0.998176 0.0603737i \(-0.980771\pi\)
0.551373 + 0.834259i \(0.314104\pi\)
\(978\) −34.1937 + 13.1756i −1.09339 + 0.421308i
\(979\) 1.50647 5.62224i 0.0481471 0.179687i
\(980\) −21.6790 + 19.7078i −0.692511 + 0.629542i
\(981\) 7.67488 4.40833i 0.245040 0.140747i
\(982\) −25.7240 26.9784i −0.820887 0.860916i
\(983\) −31.3818 + 18.1183i −1.00092 + 0.577883i −0.908521 0.417839i \(-0.862788\pi\)
−0.0924017 + 0.995722i \(0.529454\pi\)
\(984\) −1.13321 19.3838i −0.0361255 0.617932i
\(985\) 35.9452 + 20.7530i 1.14531 + 0.661245i
\(986\) 1.52424 + 6.28293i 0.0485418 + 0.200089i
\(987\) −1.49433 + 0.195039i −0.0475650 + 0.00620815i
\(988\) 25.1610 12.9716i 0.800478 0.412681i
\(989\) 3.37509 + 3.37509i 0.107322 + 0.107322i
\(990\) −21.5074 + 5.16700i −0.683550 + 0.164218i
\(991\) 52.0673 1.65397 0.826985 0.562223i \(-0.190054\pi\)
0.826985 + 0.562223i \(0.190054\pi\)
\(992\) −13.0875 + 5.60466i −0.415530 + 0.177948i
\(993\) 32.6162 13.4675i 1.03504 0.427379i
\(994\) 31.8663 + 19.4234i 1.01074 + 0.616073i
\(995\) 100.563 26.9457i 3.18805 0.854236i
\(996\) −12.0615 2.18993i −0.382183 0.0693905i
\(997\) −52.9980 14.2008i −1.67846 0.449743i −0.711091 0.703100i \(-0.751798\pi\)
−0.967373 + 0.253357i \(0.918465\pi\)
\(998\) 13.6125 12.9795i 0.430895 0.410860i
\(999\) 39.1291 + 16.3612i 1.23799 + 0.517646i
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 144.2.x.e.13.15 72
3.2 odd 2 432.2.y.e.253.4 72
4.3 odd 2 576.2.bb.e.337.16 72
9.2 odd 6 432.2.y.e.397.15 72
9.7 even 3 inner 144.2.x.e.61.4 yes 72
12.11 even 2 1728.2.bc.e.145.1 72
16.5 even 4 inner 144.2.x.e.85.4 yes 72
16.11 odd 4 576.2.bb.e.49.6 72
36.7 odd 6 576.2.bb.e.529.6 72
36.11 even 6 1728.2.bc.e.721.18 72
48.5 odd 4 432.2.y.e.37.15 72
48.11 even 4 1728.2.bc.e.1009.18 72
144.11 even 12 1728.2.bc.e.1585.1 72
144.43 odd 12 576.2.bb.e.241.16 72
144.101 odd 12 432.2.y.e.181.4 72
144.133 even 12 inner 144.2.x.e.133.15 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.15 72 1.1 even 1 trivial
144.2.x.e.61.4 yes 72 9.7 even 3 inner
144.2.x.e.85.4 yes 72 16.5 even 4 inner
144.2.x.e.133.15 yes 72 144.133 even 12 inner
432.2.y.e.37.15 72 48.5 odd 4
432.2.y.e.181.4 72 144.101 odd 12
432.2.y.e.253.4 72 3.2 odd 2
432.2.y.e.397.15 72 9.2 odd 6
576.2.bb.e.49.6 72 16.11 odd 4
576.2.bb.e.241.16 72 144.43 odd 12
576.2.bb.e.337.16 72 4.3 odd 2
576.2.bb.e.529.6 72 36.7 odd 6
1728.2.bc.e.145.1 72 12.11 even 2
1728.2.bc.e.721.18 72 36.11 even 6
1728.2.bc.e.1009.18 72 48.11 even 4
1728.2.bc.e.1585.1 72 144.11 even 12