Properties

Label 224.2.bd.a.37.12
Level $224$
Weight $2$
Character 224.37
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(37,224)]
 
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([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.bd (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 37.12
Character \(\chi\) \(=\) 224.37
Dual form 224.2.bd.a.109.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.460775 + 1.33704i) q^{2} +(1.47397 - 1.92092i) q^{3} +(-1.57537 - 1.23215i) q^{4} +(0.169674 - 0.130196i) q^{5} +(1.88918 + 2.85588i) q^{6} +(-0.114544 - 2.64327i) q^{7} +(2.37333 - 1.53860i) q^{8} +(-0.740878 - 2.76499i) q^{9} +O(q^{10})\) \(q+(-0.460775 + 1.33704i) q^{2} +(1.47397 - 1.92092i) q^{3} +(-1.57537 - 1.23215i) q^{4} +(0.169674 - 0.130196i) q^{5} +(1.88918 + 2.85588i) q^{6} +(-0.114544 - 2.64327i) q^{7} +(2.37333 - 1.53860i) q^{8} +(-0.740878 - 2.76499i) q^{9} +(0.0958956 + 0.286853i) q^{10} +(-5.24840 + 0.690965i) q^{11} +(-4.68892 + 1.21001i) q^{12} +(5.88866 - 2.43916i) q^{13} +(3.58695 + 1.06480i) q^{14} -0.517835i q^{15} +(0.963602 + 3.88220i) q^{16} +(1.68132 - 0.970709i) q^{17} +(4.03829 + 0.283453i) q^{18} +(0.124643 - 0.946756i) q^{19} +(-0.427721 - 0.00395777i) q^{20} +(-5.24635 - 3.67608i) q^{21} +(1.49448 - 7.33573i) q^{22} +(-0.264726 - 0.987973i) q^{23} +(0.542707 - 6.82684i) q^{24} +(-1.28226 + 4.78545i) q^{25} +(0.547922 + 8.99730i) q^{26} +(0.307512 + 0.127376i) q^{27} +(-3.07646 + 4.30527i) q^{28} +(2.48593 + 6.00156i) q^{29} +(0.692369 + 0.238605i) q^{30} +(2.26564 + 3.92421i) q^{31} +(-5.63467 - 0.500441i) q^{32} +(-6.40872 + 11.1002i) q^{33} +(0.523172 + 2.69527i) q^{34} +(-0.363577 - 0.433582i) q^{35} +(-2.23973 + 5.26877i) q^{36} +(6.98279 - 5.35808i) q^{37} +(1.20842 + 0.602894i) q^{38} +(3.99429 - 14.9069i) q^{39} +(0.202375 - 0.570058i) q^{40} +(-8.40410 + 8.40410i) q^{41} +(7.33247 - 5.32075i) q^{42} +(-0.546909 + 1.32035i) q^{43} +(9.11957 + 5.37830i) q^{44} +(-0.485698 - 0.372689i) q^{45} +(1.44294 + 0.101282i) q^{46} +(-1.36538 - 0.788302i) q^{47} +(8.87772 + 3.87126i) q^{48} +(-6.97376 + 0.605540i) q^{49} +(-5.80752 - 3.91945i) q^{50} +(0.613563 - 4.66048i) q^{51} +(-12.2823 - 3.41313i) q^{52} +(1.71102 - 0.225260i) q^{53} +(-0.312000 + 0.352465i) q^{54} +(-0.800558 + 0.800558i) q^{55} +(-4.33878 - 6.09713i) q^{56} +(-1.63492 - 1.63492i) q^{57} +(-9.16981 + 0.558428i) q^{58} +(0.0306545 + 0.232844i) q^{59} +(-0.638052 + 0.815784i) q^{60} +(-5.31438 - 0.699652i) q^{61} +(-6.29079 + 1.22109i) q^{62} +(-7.22376 + 2.27505i) q^{63} +(3.26543 - 7.30322i) q^{64} +(0.681585 - 1.18054i) q^{65} +(-11.8885 - 13.6834i) q^{66} +(-0.0798450 + 0.104056i) q^{67} +(-3.84476 - 0.542410i) q^{68} +(-2.28802 - 0.947727i) q^{69} +(0.747245 - 0.286335i) q^{70} +(2.68008 + 2.68008i) q^{71} +(-6.01256 - 5.42234i) q^{72} +(0.658358 + 0.176406i) q^{73} +(3.94650 + 11.8052i) q^{74} +(7.30245 + 9.51674i) q^{75} +(-1.36291 + 1.33792i) q^{76} +(2.42758 + 13.7938i) q^{77} +(18.0907 + 12.2093i) q^{78} +(-10.7585 - 6.21144i) q^{79} +(0.668943 + 0.533252i) q^{80} +(8.13502 - 4.69675i) q^{81} +(-7.36425 - 15.1090i) q^{82} +(9.53153 - 3.94809i) q^{83} +(3.73546 + 12.2555i) q^{84} +(0.158894 - 0.383604i) q^{85} +(-1.51337 - 1.33963i) q^{86} +(15.1927 + 4.07088i) q^{87} +(-11.3931 + 9.71508i) q^{88} +(5.21525 - 1.39742i) q^{89} +(0.722099 - 0.477673i) q^{90} +(-7.12187 - 15.2859i) q^{91} +(-0.800290 + 1.88261i) q^{92} +(10.8776 + 1.43206i) q^{93} +(1.68313 - 1.46234i) q^{94} +(-0.102115 - 0.176868i) q^{95} +(-9.26667 + 10.0861i) q^{96} -11.9387 q^{97} +(2.40370 - 9.60324i) q^{98} +(5.79894 + 13.9999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.460775 + 1.33704i −0.325817 + 0.945433i
\(3\) 1.47397 1.92092i 0.850999 1.10904i −0.141876 0.989884i \(-0.545313\pi\)
0.992875 0.119159i \(-0.0380199\pi\)
\(4\) −1.57537 1.23215i −0.787687 0.616076i
\(5\) 0.169674 0.130196i 0.0758806 0.0582252i −0.570125 0.821558i \(-0.693105\pi\)
0.646005 + 0.763333i \(0.276438\pi\)
\(6\) 1.88918 + 2.85588i 0.771256 + 1.16591i
\(7\) −0.114544 2.64327i −0.0432935 0.999062i
\(8\) 2.37333 1.53860i 0.839100 0.543977i
\(9\) −0.740878 2.76499i −0.246959 0.921664i
\(10\) 0.0958956 + 0.286853i 0.0303249 + 0.0907108i
\(11\) −5.24840 + 0.690965i −1.58245 + 0.208334i −0.869880 0.493264i \(-0.835804\pi\)
−0.712573 + 0.701598i \(0.752470\pi\)
\(12\) −4.68892 + 1.21001i −1.35358 + 0.349299i
\(13\) 5.88866 2.43916i 1.63322 0.676502i 0.637632 0.770341i \(-0.279914\pi\)
0.995587 + 0.0938394i \(0.0299140\pi\)
\(14\) 3.58695 + 1.06480i 0.958652 + 0.284580i
\(15\) 0.517835i 0.133704i
\(16\) 0.963602 + 3.88220i 0.240901 + 0.970550i
\(17\) 1.68132 0.970709i 0.407779 0.235432i −0.282056 0.959398i \(-0.591016\pi\)
0.689835 + 0.723966i \(0.257683\pi\)
\(18\) 4.03829 + 0.283453i 0.951835 + 0.0668105i
\(19\) 0.124643 0.946756i 0.0285950 0.217201i −0.971181 0.238341i \(-0.923396\pi\)
0.999777 + 0.0211404i \(0.00672969\pi\)
\(20\) −0.427721 0.00395777i −0.0956413 0.000884985i
\(21\) −5.24635 3.67608i −1.14485 0.802187i
\(22\) 1.49448 7.33573i 0.318624 1.56398i
\(23\) −0.264726 0.987973i −0.0551993 0.206007i 0.932819 0.360347i \(-0.117342\pi\)
−0.988018 + 0.154340i \(0.950675\pi\)
\(24\) 0.542707 6.82684i 0.110780 1.39352i
\(25\) −1.28226 + 4.78545i −0.256451 + 0.957089i
\(26\) 0.547922 + 8.99730i 0.107456 + 1.76452i
\(27\) 0.307512 + 0.127376i 0.0591807 + 0.0245134i
\(28\) −3.07646 + 4.30527i −0.581397 + 0.813620i
\(29\) 2.48593 + 6.00156i 0.461625 + 1.11446i 0.967730 + 0.251990i \(0.0810850\pi\)
−0.506104 + 0.862472i \(0.668915\pi\)
\(30\) 0.692369 + 0.238605i 0.126409 + 0.0435632i
\(31\) 2.26564 + 3.92421i 0.406921 + 0.704809i 0.994543 0.104327i \(-0.0332689\pi\)
−0.587622 + 0.809136i \(0.699936\pi\)
\(32\) −5.63467 0.500441i −0.996079 0.0884663i
\(33\) −6.40872 + 11.1002i −1.11561 + 1.93230i
\(34\) 0.523172 + 2.69527i 0.0897233 + 0.462236i
\(35\) −0.363577 0.433582i −0.0614558 0.0732887i
\(36\) −2.23973 + 5.26877i −0.373289 + 0.878128i
\(37\) 6.98279 5.35808i 1.14796 0.880863i 0.153731 0.988113i \(-0.450871\pi\)
0.994232 + 0.107249i \(0.0342043\pi\)
\(38\) 1.20842 + 0.602894i 0.196032 + 0.0978024i
\(39\) 3.99429 14.9069i 0.639598 2.38701i
\(40\) 0.202375 0.570058i 0.0319982 0.0901341i
\(41\) −8.40410 + 8.40410i −1.31250 + 1.31250i −0.392933 + 0.919567i \(0.628539\pi\)
−0.919567 + 0.392933i \(0.871461\pi\)
\(42\) 7.33247 5.32075i 1.13142 0.821009i
\(43\) −0.546909 + 1.32035i −0.0834028 + 0.201352i −0.960079 0.279728i \(-0.909756\pi\)
0.876676 + 0.481081i \(0.159756\pi\)
\(44\) 9.11957 + 5.37830i 1.37483 + 0.810810i
\(45\) −0.485698 0.372689i −0.0724035 0.0555572i
\(46\) 1.44294 + 0.101282i 0.212750 + 0.0149332i
\(47\) −1.36538 0.788302i −0.199161 0.114986i 0.397103 0.917774i \(-0.370016\pi\)
−0.596264 + 0.802788i \(0.703349\pi\)
\(48\) 8.87772 + 3.87126i 1.28139 + 0.558768i
\(49\) −6.97376 + 0.605540i −0.996251 + 0.0865057i
\(50\) −5.80752 3.91945i −0.821308 0.554294i
\(51\) 0.613563 4.66048i 0.0859161 0.652597i
\(52\) −12.2823 3.41313i −1.70324 0.473316i
\(53\) 1.71102 0.225260i 0.235027 0.0309419i −0.0120925 0.999927i \(-0.503849\pi\)
0.247120 + 0.968985i \(0.420516\pi\)
\(54\) −0.312000 + 0.352465i −0.0424579 + 0.0479645i
\(55\) −0.800558 + 0.800558i −0.107947 + 0.107947i
\(56\) −4.33878 6.09713i −0.579794 0.814763i
\(57\) −1.63492 1.63492i −0.216551 0.216551i
\(58\) −9.16981 + 0.558428i −1.20405 + 0.0733251i
\(59\) 0.0306545 + 0.232844i 0.00399088 + 0.0303137i 0.993324 0.115354i \(-0.0368003\pi\)
−0.989334 + 0.145668i \(0.953467\pi\)
\(60\) −0.638052 + 0.815784i −0.0823721 + 0.105317i
\(61\) −5.31438 0.699652i −0.680437 0.0895813i −0.217618 0.976034i \(-0.569829\pi\)
−0.462819 + 0.886453i \(0.653162\pi\)
\(62\) −6.29079 + 1.22109i −0.798931 + 0.155078i
\(63\) −7.22376 + 2.27505i −0.910108 + 0.286630i
\(64\) 3.26543 7.30322i 0.408178 0.912902i
\(65\) 0.681585 1.18054i 0.0845402 0.146428i
\(66\) −11.8885 13.6834i −1.46338 1.68432i
\(67\) −0.0798450 + 0.104056i −0.00975462 + 0.0127125i −0.798205 0.602386i \(-0.794217\pi\)
0.788451 + 0.615098i \(0.210884\pi\)
\(68\) −3.84476 0.542410i −0.466246 0.0657769i
\(69\) −2.28802 0.947727i −0.275445 0.114093i
\(70\) 0.747245 0.286335i 0.0893128 0.0342236i
\(71\) 2.68008 + 2.68008i 0.318067 + 0.318067i 0.848024 0.529957i \(-0.177792\pi\)
−0.529957 + 0.848024i \(0.677792\pi\)
\(72\) −6.01256 5.42234i −0.708588 0.639029i
\(73\) 0.658358 + 0.176406i 0.0770549 + 0.0206468i 0.297141 0.954834i \(-0.403967\pi\)
−0.220086 + 0.975481i \(0.570634\pi\)
\(74\) 3.94650 + 11.8052i 0.458771 + 1.37232i
\(75\) 7.30245 + 9.51674i 0.843214 + 1.09890i
\(76\) −1.36291 + 1.33792i −0.156336 + 0.153469i
\(77\) 2.42758 + 13.7938i 0.276648 + 1.57195i
\(78\) 18.0907 + 12.2093i 2.04837 + 1.38243i
\(79\) −10.7585 6.21144i −1.21043 0.698842i −0.247576 0.968868i \(-0.579634\pi\)
−0.962853 + 0.270027i \(0.912967\pi\)
\(80\) 0.668943 + 0.533252i 0.0747902 + 0.0596194i
\(81\) 8.13502 4.69675i 0.903891 0.521862i
\(82\) −7.36425 15.1090i −0.813246 1.66852i
\(83\) 9.53153 3.94809i 1.04622 0.433359i 0.207680 0.978197i \(-0.433409\pi\)
0.838541 + 0.544838i \(0.183409\pi\)
\(84\) 3.73546 + 12.2555i 0.407572 + 1.33718i
\(85\) 0.158894 0.383604i 0.0172345 0.0416077i
\(86\) −1.51337 1.33963i −0.163191 0.144456i
\(87\) 15.1927 + 4.07088i 1.62883 + 0.436444i
\(88\) −11.3931 + 9.71508i −1.21451 + 1.03563i
\(89\) 5.21525 1.39742i 0.552816 0.148127i 0.0284121 0.999596i \(-0.490955\pi\)
0.524404 + 0.851470i \(0.324288\pi\)
\(90\) 0.722099 0.477673i 0.0761159 0.0503512i
\(91\) −7.12187 15.2859i −0.746575 1.60240i
\(92\) −0.800290 + 1.88261i −0.0834360 + 0.196276i
\(93\) 10.8776 + 1.43206i 1.12795 + 0.148498i
\(94\) 1.68313 1.46234i 0.173601 0.150829i
\(95\) −0.102115 0.176868i −0.0104768 0.0181463i
\(96\) −9.26667 + 10.0861i −0.945775 + 1.02941i
\(97\) −11.9387 −1.21219 −0.606097 0.795391i \(-0.707266\pi\)
−0.606097 + 0.795391i \(0.707266\pi\)
\(98\) 2.40370 9.60324i 0.242810 0.970074i
\(99\) 5.79894 + 13.9999i 0.582815 + 1.40704i
\(100\) 7.91643 5.95893i 0.791643 0.595893i
\(101\) 1.44894 + 11.0058i 0.144175 + 1.09512i 0.898612 + 0.438744i \(0.144576\pi\)
−0.754438 + 0.656372i \(0.772090\pi\)
\(102\) 5.94855 + 2.96779i 0.588994 + 0.293855i
\(103\) −3.24809 + 0.870324i −0.320044 + 0.0857556i −0.415265 0.909701i \(-0.636311\pi\)
0.0952205 + 0.995456i \(0.469644\pi\)
\(104\) 10.2229 14.8492i 1.00243 1.45609i
\(105\) −1.36878 + 0.0593148i −0.133579 + 0.00578853i
\(106\) −0.487213 + 2.39151i −0.0473223 + 0.232284i
\(107\) 6.75914 + 8.80868i 0.653430 + 0.851567i 0.996131 0.0878774i \(-0.0280084\pi\)
−0.342701 + 0.939445i \(0.611342\pi\)
\(108\) −0.327500 0.579565i −0.0315137 0.0557687i
\(109\) 12.8360 + 9.84940i 1.22946 + 0.943402i 0.999556 0.0298105i \(-0.00949037\pi\)
0.229909 + 0.973212i \(0.426157\pi\)
\(110\) −0.701504 1.43926i −0.0668858 0.137228i
\(111\) 21.3111i 2.02276i
\(112\) 10.1513 2.99174i 0.959210 0.282693i
\(113\) 0.490870i 0.0461772i −0.999733 0.0230886i \(-0.992650\pi\)
0.999733 0.0230886i \(-0.00734998\pi\)
\(114\) 2.93929 1.43263i 0.275290 0.134178i
\(115\) −0.173547 0.133167i −0.0161833 0.0124179i
\(116\) 3.47857 12.5177i 0.322977 1.16224i
\(117\) −11.1070 14.4750i −1.02685 1.33821i
\(118\) −0.325448 0.0663023i −0.0299599 0.00610362i
\(119\) −2.75843 4.33299i −0.252865 0.397204i
\(120\) −0.796741 1.22900i −0.0727321 0.112191i
\(121\) 16.4431 4.40592i 1.49483 0.400538i
\(122\) 3.38420 6.78318i 0.306391 0.614121i
\(123\) 3.75618 + 28.5310i 0.338683 + 2.57256i
\(124\) 1.26599 8.97371i 0.113689 0.805863i
\(125\) 0.814700 + 1.96686i 0.0728690 + 0.175921i
\(126\) 0.286681 10.7068i 0.0255396 0.953835i
\(127\) 7.61855 0.676037 0.338019 0.941139i \(-0.390243\pi\)
0.338019 + 0.941139i \(0.390243\pi\)
\(128\) 8.26010 + 7.73116i 0.730096 + 0.683344i
\(129\) 1.73017 + 2.99674i 0.152333 + 0.263848i
\(130\) 1.26438 + 1.45527i 0.110893 + 0.127636i
\(131\) 13.0595 + 1.71931i 1.14101 + 0.150217i 0.677256 0.735747i \(-0.263169\pi\)
0.463754 + 0.885964i \(0.346502\pi\)
\(132\) 23.7733 9.59048i 2.06920 0.834745i
\(133\) −2.51681 0.221020i −0.218235 0.0191648i
\(134\) −0.102337 0.154703i −0.00884056 0.0133643i
\(135\) 0.0687605 0.0184243i 0.00591796 0.00158571i
\(136\) 2.49680 4.89069i 0.214099 0.419373i
\(137\) −12.7724 3.42236i −1.09122 0.292392i −0.332036 0.943267i \(-0.607735\pi\)
−0.759185 + 0.650875i \(0.774402\pi\)
\(138\) 2.32141 2.62249i 0.197612 0.223241i
\(139\) −3.29303 + 7.95007i −0.279311 + 0.674316i −0.999817 0.0191323i \(-0.993910\pi\)
0.720506 + 0.693449i \(0.243910\pi\)
\(140\) 0.0385313 + 1.13104i 0.00325649 + 0.0955899i
\(141\) −3.52680 + 1.46085i −0.297010 + 0.123026i
\(142\) −4.81830 + 2.34847i −0.404343 + 0.197079i
\(143\) −29.2207 + 16.8706i −2.44356 + 1.41079i
\(144\) 10.0203 5.54059i 0.835029 0.461716i
\(145\) 1.20317 + 0.694653i 0.0999182 + 0.0576878i
\(146\) −0.539218 + 0.798970i −0.0446260 + 0.0661232i
\(147\) −9.11594 + 14.2886i −0.751870 + 1.17850i
\(148\) −17.6025 0.162879i −1.44691 0.0133885i
\(149\) −6.70094 8.73284i −0.548963 0.715422i 0.433652 0.901081i \(-0.357225\pi\)
−0.982614 + 0.185659i \(0.940558\pi\)
\(150\) −16.0891 + 5.37862i −1.31367 + 0.439163i
\(151\) −4.81746 1.29084i −0.392040 0.105047i 0.0574138 0.998350i \(-0.481715\pi\)
−0.449453 + 0.893304i \(0.648381\pi\)
\(152\) −1.16086 2.43874i −0.0941581 0.197808i
\(153\) −3.92965 3.92965i −0.317694 0.317694i
\(154\) −19.5615 3.11006i −1.57631 0.250615i
\(155\) 0.895336 + 0.370860i 0.0719151 + 0.0297882i
\(156\) −24.6601 + 18.5624i −1.97439 + 1.48618i
\(157\) 10.4629 13.6355i 0.835028 1.08823i −0.159849 0.987141i \(-0.551101\pi\)
0.994877 0.101089i \(-0.0322326\pi\)
\(158\) 13.2622 11.5226i 1.05509 0.916685i
\(159\) 2.08930 3.61877i 0.165692 0.286987i
\(160\) −1.02121 + 0.648698i −0.0807340 + 0.0512841i
\(161\) −2.58116 + 0.812910i −0.203424 + 0.0640663i
\(162\) 2.53136 + 13.0410i 0.198882 + 1.02460i
\(163\) −9.93305 1.30771i −0.778016 0.102428i −0.268949 0.963154i \(-0.586676\pi\)
−0.509067 + 0.860727i \(0.670010\pi\)
\(164\) 23.5947 2.88446i 1.84244 0.225239i
\(165\) 0.357806 + 2.71781i 0.0278552 + 0.211581i
\(166\) 0.886881 + 14.5633i 0.0688353 + 1.13033i
\(167\) −3.38255 3.38255i −0.261749 0.261749i 0.564015 0.825765i \(-0.309256\pi\)
−0.825765 + 0.564015i \(0.809256\pi\)
\(168\) −18.1073 0.652549i −1.39701 0.0503452i
\(169\) 19.5344 19.5344i 1.50264 1.50264i
\(170\) 0.439682 + 0.389204i 0.0337220 + 0.0298506i
\(171\) −2.71012 + 0.356794i −0.207248 + 0.0272847i
\(172\) 2.48846 1.40618i 0.189744 0.107220i
\(173\) 2.26199 17.1815i 0.171976 1.30629i −0.659913 0.751342i \(-0.729407\pi\)
0.831888 0.554943i \(-0.187260\pi\)
\(174\) −12.4434 + 18.4376i −0.943329 + 1.39775i
\(175\) 12.7961 + 2.84121i 0.967295 + 0.214775i
\(176\) −7.73984 19.7095i −0.583412 1.48566i
\(177\) 0.492459 + 0.284321i 0.0370155 + 0.0213709i
\(178\) −0.534641 + 7.61692i −0.0400730 + 0.570912i
\(179\) −19.9022 15.2715i −1.48756 1.14144i −0.955598 0.294672i \(-0.904789\pi\)
−0.531959 0.846770i \(-0.678544\pi\)
\(180\) 0.305946 + 1.18558i 0.0228038 + 0.0883677i
\(181\) −3.09294 + 7.46701i −0.229896 + 0.555018i −0.996164 0.0875025i \(-0.972111\pi\)
0.766268 + 0.642521i \(0.222111\pi\)
\(182\) 23.7195 2.47889i 1.75821 0.183748i
\(183\) −9.17724 + 9.17724i −0.678401 + 0.678401i
\(184\) −2.14838 1.93748i −0.158381 0.142833i
\(185\) 0.487200 1.81826i 0.0358197 0.133681i
\(186\) −6.92685 + 13.8840i −0.507901 + 1.01802i
\(187\) −8.15351 + 6.25641i −0.596244 + 0.457514i
\(188\) 1.17967 + 2.92423i 0.0860366 + 0.213271i
\(189\) 0.301464 0.827427i 0.0219283 0.0601864i
\(190\) 0.283532 0.0550357i 0.0205696 0.00399271i
\(191\) −5.87093 + 10.1688i −0.424806 + 0.735785i −0.996402 0.0847496i \(-0.972991\pi\)
0.571596 + 0.820535i \(0.306324\pi\)
\(192\) −9.21574 17.0374i −0.665089 1.22957i
\(193\) −4.86382 8.42438i −0.350105 0.606400i 0.636162 0.771555i \(-0.280521\pi\)
−0.986268 + 0.165155i \(0.947187\pi\)
\(194\) 5.50106 15.9626i 0.394953 1.14605i
\(195\) −1.26308 3.04935i −0.0904513 0.218369i
\(196\) 11.7324 + 7.63878i 0.838028 + 0.545627i
\(197\) −13.7727 5.70484i −0.981264 0.406453i −0.166370 0.986063i \(-0.553205\pi\)
−0.814894 + 0.579610i \(0.803205\pi\)
\(198\) −21.3905 + 1.30265i −1.52015 + 0.0925751i
\(199\) −0.748710 + 2.79422i −0.0530746 + 0.198077i −0.987372 0.158416i \(-0.949361\pi\)
0.934298 + 0.356494i \(0.116028\pi\)
\(200\) 4.31966 + 13.3303i 0.305446 + 0.942598i
\(201\) 0.0821938 + 0.306752i 0.00579751 + 0.0216366i
\(202\) −15.3828 3.13389i −1.08233 0.220500i
\(203\) 15.5790 7.25842i 1.09343 0.509442i
\(204\) −6.70901 + 6.58599i −0.469724 + 0.461111i
\(205\) −0.331782 + 2.52013i −0.0231727 + 0.176014i
\(206\) 0.332978 4.74387i 0.0231997 0.330521i
\(207\) −2.53561 + 1.46393i −0.176237 + 0.101750i
\(208\) 15.1436 + 20.5106i 1.05002 + 1.42215i
\(209\) 5.05508i 0.349667i
\(210\) 0.551392 1.85745i 0.0380497 0.128176i
\(211\) 17.5854 7.28413i 1.21063 0.501460i 0.316212 0.948689i \(-0.397589\pi\)
0.894420 + 0.447229i \(0.147589\pi\)
\(212\) −2.97306 1.75337i −0.204190 0.120422i
\(213\) 9.09859 1.19785i 0.623425 0.0820755i
\(214\) −14.8920 + 4.97845i −1.01800 + 0.340320i
\(215\) 0.0791080 + 0.295235i 0.00539512 + 0.0201349i
\(216\) 0.925808 0.170833i 0.0629932 0.0116237i
\(217\) 10.1132 6.43820i 0.686531 0.437054i
\(218\) −19.0836 + 12.6239i −1.29250 + 0.855000i
\(219\) 1.30926 1.00463i 0.0884719 0.0678869i
\(220\) 2.24759 0.274768i 0.151532 0.0185249i
\(221\) 7.53299 9.81718i 0.506723 0.660375i
\(222\) 28.4938 + 9.81959i 1.91238 + 0.659048i
\(223\) −14.2983 −0.957484 −0.478742 0.877956i \(-0.658907\pi\)
−0.478742 + 0.877956i \(0.658907\pi\)
\(224\) −0.677384 + 14.9513i −0.0452596 + 0.998975i
\(225\) 14.1817 0.945448
\(226\) 0.656315 + 0.226180i 0.0436574 + 0.0150453i
\(227\) −1.23134 + 1.60471i −0.0817267 + 0.106508i −0.832427 0.554134i \(-0.813049\pi\)
0.750701 + 0.660643i \(0.229716\pi\)
\(228\) 0.561140 + 4.59009i 0.0371624 + 0.303986i
\(229\) 5.55226 4.26040i 0.366904 0.281535i −0.408811 0.912619i \(-0.634056\pi\)
0.775714 + 0.631084i \(0.217390\pi\)
\(230\) 0.258016 0.170680i 0.0170131 0.0112543i
\(231\) 30.0750 + 15.6685i 1.97879 + 1.03091i
\(232\) 15.1339 + 10.4189i 0.993592 + 0.684032i
\(233\) 2.94294 + 10.9832i 0.192798 + 0.719533i 0.992826 + 0.119570i \(0.0381515\pi\)
−0.800028 + 0.599963i \(0.795182\pi\)
\(234\) 24.4715 8.18090i 1.59975 0.534802i
\(235\) −0.334303 + 0.0440118i −0.0218075 + 0.00287102i
\(236\) 0.238607 0.404588i 0.0155320 0.0263364i
\(237\) −27.7895 + 11.5108i −1.80512 + 0.747705i
\(238\) 7.06441 1.69161i 0.457918 0.109651i
\(239\) 15.4440i 0.998989i −0.866317 0.499494i \(-0.833519\pi\)
0.866317 0.499494i \(-0.166481\pi\)
\(240\) 2.01034 0.498987i 0.129767 0.0322095i
\(241\) −10.9405 + 6.31648i −0.704737 + 0.406880i −0.809109 0.587658i \(-0.800050\pi\)
0.104372 + 0.994538i \(0.466717\pi\)
\(242\) −1.68566 + 24.0153i −0.108359 + 1.54376i
\(243\) 2.83838 21.5596i 0.182082 1.38305i
\(244\) 7.51006 + 7.65034i 0.480782 + 0.489763i
\(245\) −1.10443 + 1.01070i −0.0705593 + 0.0645711i
\(246\) −39.8780 8.12420i −2.54253 0.517980i
\(247\) −1.57531 5.87915i −0.100235 0.374081i
\(248\) 11.4149 + 5.82754i 0.724847 + 0.370049i
\(249\) 6.46526 24.1287i 0.409719 1.52909i
\(250\) −3.00517 + 0.183010i −0.190064 + 0.0115746i
\(251\) 7.71946 + 3.19750i 0.487248 + 0.201825i 0.612763 0.790267i \(-0.290058\pi\)
−0.125515 + 0.992092i \(0.540058\pi\)
\(252\) 14.1833 + 5.31672i 0.893466 + 0.334922i
\(253\) 2.07205 + 5.00236i 0.130268 + 0.314496i
\(254\) −3.51044 + 10.1863i −0.220264 + 0.639148i
\(255\) −0.502667 0.870646i −0.0314783 0.0545219i
\(256\) −14.1429 + 7.48179i −0.883934 + 0.467612i
\(257\) −11.9533 + 20.7037i −0.745625 + 1.29146i 0.204278 + 0.978913i \(0.434515\pi\)
−0.949902 + 0.312547i \(0.898818\pi\)
\(258\) −4.80398 + 0.932488i −0.299083 + 0.0580542i
\(259\) −14.9627 17.8437i −0.929737 1.10875i
\(260\) −2.52835 + 1.01997i −0.156802 + 0.0632561i
\(261\) 14.7525 11.3200i 0.913158 0.700690i
\(262\) −8.31626 + 16.6688i −0.513780 + 1.02980i
\(263\) −5.00798 + 18.6900i −0.308805 + 1.15248i 0.620815 + 0.783957i \(0.286802\pi\)
−0.929620 + 0.368519i \(0.879865\pi\)
\(264\) 1.86877 + 36.2050i 0.115015 + 2.22826i
\(265\) 0.260989 0.260989i 0.0160324 0.0160324i
\(266\) 1.45520 3.26325i 0.0892238 0.200082i
\(267\) 5.00281 12.0779i 0.306167 0.739152i
\(268\) 0.253998 0.0655459i 0.0155154 0.00400385i
\(269\) −15.4012 11.8178i −0.939029 0.720542i 0.0211946 0.999775i \(-0.493253\pi\)
−0.960223 + 0.279233i \(0.909920\pi\)
\(270\) −0.00704898 + 0.100425i −0.000428987 + 0.00611169i
\(271\) 4.47029 + 2.58092i 0.271551 + 0.156780i 0.629592 0.776926i \(-0.283222\pi\)
−0.358041 + 0.933706i \(0.616555\pi\)
\(272\) 5.38861 + 5.59183i 0.326732 + 0.339055i
\(273\) −39.8605 8.85050i −2.41247 0.535657i
\(274\) 10.4610 15.5003i 0.631975 0.936410i
\(275\) 3.42322 26.0020i 0.206428 1.56798i
\(276\) 2.43674 + 4.31221i 0.146674 + 0.259564i
\(277\) 14.8247 1.95171i 0.890732 0.117267i 0.328750 0.944417i \(-0.393373\pi\)
0.561981 + 0.827150i \(0.310039\pi\)
\(278\) −9.11225 8.06612i −0.546517 0.483774i
\(279\) 9.17184 9.17184i 0.549104 0.549104i
\(280\) −1.53000 0.469635i −0.0914349 0.0280660i
\(281\) −15.2312 15.2312i −0.908616 0.908616i 0.0875448 0.996161i \(-0.472098\pi\)
−0.996161 + 0.0875448i \(0.972098\pi\)
\(282\) −0.328158 5.38861i −0.0195415 0.320887i
\(283\) 2.40061 + 18.2344i 0.142701 + 1.08392i 0.901556 + 0.432663i \(0.142426\pi\)
−0.758854 + 0.651260i \(0.774241\pi\)
\(284\) −0.919860 7.52440i −0.0545837 0.446491i
\(285\) −0.490264 0.0645445i −0.0290407 0.00382328i
\(286\) −9.09254 46.8428i −0.537653 2.76988i
\(287\) 23.1769 + 21.2517i 1.36809 + 1.25445i
\(288\) 2.79089 + 15.9506i 0.164455 + 0.939898i
\(289\) −6.61545 + 11.4583i −0.389144 + 0.674017i
\(290\) −1.48317 + 1.28862i −0.0870950 + 0.0756703i
\(291\) −17.5974 + 22.9333i −1.03158 + 1.34438i
\(292\) −0.819800 1.08910i −0.0479751 0.0637349i
\(293\) 2.73138 + 1.13137i 0.159569 + 0.0660955i 0.461038 0.887380i \(-0.347477\pi\)
−0.301469 + 0.953476i \(0.597477\pi\)
\(294\) −14.9041 18.7722i −0.869223 1.09482i
\(295\) 0.0355166 + 0.0355166i 0.00206785 + 0.00206785i
\(296\) 8.32855 23.4602i 0.484087 1.36360i
\(297\) −1.70196 0.456038i −0.0987576 0.0264620i
\(298\) 14.7638 4.93558i 0.855245 0.285911i
\(299\) −3.96871 5.17212i −0.229516 0.299111i
\(300\) 0.221985 23.9901i 0.0128163 1.38507i
\(301\) 3.55270 + 1.29439i 0.204774 + 0.0746074i
\(302\) 3.94567 5.84638i 0.227048 0.336421i
\(303\) 23.2769 + 13.4389i 1.33722 + 0.772046i
\(304\) 3.79560 0.428408i 0.217693 0.0245709i
\(305\) −0.992805 + 0.573196i −0.0568479 + 0.0328211i
\(306\) 7.06481 3.44344i 0.403868 0.196848i
\(307\) −28.6412 + 11.8636i −1.63464 + 0.677090i −0.995740 0.0922013i \(-0.970610\pi\)
−0.638899 + 0.769291i \(0.720610\pi\)
\(308\) 13.1717 24.7215i 0.750529 1.40864i
\(309\) −3.11578 + 7.52216i −0.177251 + 0.427921i
\(310\) −0.908404 + 1.02622i −0.0515939 + 0.0582854i
\(311\) 7.98255 + 2.13892i 0.452649 + 0.121287i 0.477939 0.878393i \(-0.341384\pi\)
−0.0252896 + 0.999680i \(0.508051\pi\)
\(312\) −13.4559 41.5247i −0.761793 2.35087i
\(313\) 0.678304 0.181751i 0.0383400 0.0102732i −0.239598 0.970872i \(-0.577016\pi\)
0.277938 + 0.960599i \(0.410349\pi\)
\(314\) 13.4102 + 20.2722i 0.756782 + 1.14403i
\(315\) −0.929484 + 1.32652i −0.0523705 + 0.0747409i
\(316\) 9.29526 + 23.0415i 0.522899 + 1.29618i
\(317\) −16.6896 2.19723i −0.937382 0.123409i −0.353671 0.935370i \(-0.615067\pi\)
−0.583711 + 0.811961i \(0.698400\pi\)
\(318\) 3.87576 + 4.46092i 0.217342 + 0.250156i
\(319\) −17.1940 29.7809i −0.962681 1.66741i
\(320\) −0.396788 1.66431i −0.0221811 0.0930378i
\(321\) 26.8836 1.50049
\(322\) 0.102435 3.82569i 0.00570850 0.213197i
\(323\) −0.709461 1.71279i −0.0394755 0.0953022i
\(324\) −18.6028 2.62444i −1.03349 0.145802i
\(325\) 4.12171 + 31.3075i 0.228631 + 1.73663i
\(326\) 6.32536 12.6784i 0.350329 0.702189i
\(327\) 37.8398 10.1391i 2.09255 0.560696i
\(328\) −7.01520 + 32.8763i −0.387349 + 1.81529i
\(329\) −1.92730 + 3.69936i −0.106256 + 0.203952i
\(330\) −3.79870 0.773895i −0.209111 0.0426015i
\(331\) 2.42266 + 3.15727i 0.133161 + 0.173539i 0.855175 0.518340i \(-0.173450\pi\)
−0.722013 + 0.691879i \(0.756783\pi\)
\(332\) −19.8804 5.52458i −1.09108 0.303201i
\(333\) −19.9885 15.3377i −1.09536 0.840500i
\(334\) 6.08121 2.96402i 0.332749 0.162184i
\(335\) 0.0280511i 0.00153259i
\(336\) 9.21589 23.9096i 0.502768 1.30438i
\(337\) 5.11004i 0.278362i 0.990267 + 0.139181i \(0.0444469\pi\)
−0.990267 + 0.139181i \(0.955553\pi\)
\(338\) 17.1174 + 35.1193i 0.931062 + 1.91024i
\(339\) −0.942922 0.723529i −0.0512125 0.0392967i
\(340\) −0.722977 + 0.408538i −0.0392089 + 0.0221561i
\(341\) −14.6025 19.0303i −0.790770 1.03055i
\(342\) 0.771705 3.78795i 0.0417290 0.204829i
\(343\) 2.39941 + 18.3642i 0.129556 + 0.991572i
\(344\) 0.733499 + 3.97512i 0.0395476 + 0.214324i
\(345\) −0.511607 + 0.137085i −0.0275440 + 0.00738039i
\(346\) 21.9302 + 10.9412i 1.17897 + 0.588201i
\(347\) −2.01680 15.3191i −0.108268 0.822373i −0.956291 0.292415i \(-0.905541\pi\)
0.848024 0.529958i \(-0.177792\pi\)
\(348\) −18.9183 25.1329i −1.01413 1.34726i
\(349\) 9.24036 + 22.3082i 0.494625 + 1.19413i 0.952342 + 0.305033i \(0.0986673\pi\)
−0.457717 + 0.889098i \(0.651333\pi\)
\(350\) −9.69494 + 15.7998i −0.518217 + 0.844535i
\(351\) 2.12152 0.113238
\(352\) 29.9188 1.26685i 1.59468 0.0675233i
\(353\) −1.72710 2.99143i −0.0919243 0.159218i 0.816396 0.577492i \(-0.195968\pi\)
−0.908321 + 0.418274i \(0.862635\pi\)
\(354\) −0.607063 + 0.527431i −0.0322650 + 0.0280327i
\(355\) 0.803675 + 0.105806i 0.0426546 + 0.00561559i
\(356\) −9.93781 4.22452i −0.526703 0.223899i
\(357\) −12.3892 1.08799i −0.655705 0.0575823i
\(358\) 29.5890 19.5734i 1.56383 1.03448i
\(359\) −21.9189 + 5.87316i −1.15684 + 0.309973i −0.785702 0.618606i \(-0.787698\pi\)
−0.371135 + 0.928579i \(0.621031\pi\)
\(360\) −1.72614 0.137221i −0.0909756 0.00723220i
\(361\) 17.4718 + 4.68155i 0.919567 + 0.246397i
\(362\) −8.55857 7.57600i −0.449829 0.398186i
\(363\) 15.7733 38.0801i 0.827884 1.99869i
\(364\) −7.61497 + 32.8563i −0.399133 + 1.72214i
\(365\) 0.134674 0.0557836i 0.00704914 0.00291985i
\(366\) −8.04173 16.4990i −0.420348 0.862417i
\(367\) −0.698185 + 0.403097i −0.0364450 + 0.0210415i −0.518112 0.855313i \(-0.673365\pi\)
0.481667 + 0.876354i \(0.340032\pi\)
\(368\) 3.58042 1.97973i 0.186642 0.103201i
\(369\) 29.4637 + 17.0109i 1.53382 + 0.885550i
\(370\) 2.20660 + 1.48921i 0.114716 + 0.0774206i
\(371\) −0.791411 4.49690i −0.0410880 0.233467i
\(372\) −15.3717 15.6589i −0.796988 0.811875i
\(373\) 10.6625 + 13.8957i 0.552084 + 0.719490i 0.983144 0.182833i \(-0.0585268\pi\)
−0.431060 + 0.902323i \(0.641860\pi\)
\(374\) −4.60816 13.7844i −0.238282 0.712774i
\(375\) 4.97903 + 1.33413i 0.257116 + 0.0688940i
\(376\) −4.45338 + 0.229867i −0.229666 + 0.0118545i
\(377\) 29.2776 + 29.2776i 1.50787 + 1.50787i
\(378\) 0.967399 + 0.784329i 0.0497576 + 0.0403415i
\(379\) −30.7730 12.7466i −1.58070 0.654748i −0.592177 0.805808i \(-0.701732\pi\)
−0.988525 + 0.151059i \(0.951732\pi\)
\(380\) −0.0570594 + 0.404454i −0.00292709 + 0.0207481i
\(381\) 11.2295 14.6346i 0.575307 0.749755i
\(382\) −10.8909 12.5352i −0.557227 0.641357i
\(383\) 8.82547 15.2862i 0.450961 0.781087i −0.547485 0.836815i \(-0.684415\pi\)
0.998446 + 0.0557287i \(0.0177482\pi\)
\(384\) 27.0261 4.47146i 1.37917 0.228183i
\(385\) 2.20779 + 2.02439i 0.112519 + 0.103173i
\(386\) 13.5049 2.62140i 0.687381 0.133426i
\(387\) 4.05596 + 0.533978i 0.206176 + 0.0271436i
\(388\) 18.8079 + 14.7103i 0.954828 + 0.746803i
\(389\) −0.353065 2.68179i −0.0179011 0.135972i 0.980161 0.198205i \(-0.0635112\pi\)
−0.998062 + 0.0622328i \(0.980178\pi\)
\(390\) 4.65912 0.283733i 0.235924 0.0143674i
\(391\) −1.40412 1.40412i −0.0710096 0.0710096i
\(392\) −15.6194 + 12.1670i −0.788898 + 0.614525i
\(393\) 22.5519 22.5519i 1.13760 1.13760i
\(394\) 13.9737 15.7861i 0.703986 0.795290i
\(395\) −2.63415 + 0.346792i −0.132538 + 0.0174490i
\(396\) 8.11449 29.2002i 0.407768 1.46737i
\(397\) 2.43800 18.5185i 0.122360 0.929415i −0.814611 0.580008i \(-0.803050\pi\)
0.936971 0.349407i \(-0.113617\pi\)
\(398\) −3.39101 2.28857i −0.169976 0.114715i
\(399\) −4.13427 + 4.50881i −0.206973 + 0.225723i
\(400\) −19.8136 0.366709i −0.990682 0.0183355i
\(401\) −1.71854 0.992202i −0.0858200 0.0495482i 0.456476 0.889736i \(-0.349111\pi\)
−0.542296 + 0.840188i \(0.682445\pi\)
\(402\) −0.448013 0.0314466i −0.0223449 0.00156841i
\(403\) 22.9134 + 17.5820i 1.14140 + 0.875824i
\(404\) 11.2782 19.1235i 0.561110 0.951430i
\(405\) 0.768806 1.85606i 0.0382023 0.0922284i
\(406\) 2.52642 + 24.1743i 0.125384 + 1.19975i
\(407\) −32.9462 + 32.9462i −1.63308 + 1.63308i
\(408\) −5.71441 12.0049i −0.282906 0.594331i
\(409\) −9.12508 + 34.0553i −0.451206 + 1.68392i 0.247802 + 0.968811i \(0.420292\pi\)
−0.699008 + 0.715114i \(0.746375\pi\)
\(410\) −3.21665 1.60482i −0.158859 0.0792565i
\(411\) −25.4003 + 19.4903i −1.25290 + 0.961386i
\(412\) 6.18933 + 2.63106i 0.304927 + 0.129623i
\(413\) 0.611959 0.107699i 0.0301125 0.00529952i
\(414\) −0.789000 4.06476i −0.0387772 0.199772i
\(415\) 1.10323 1.91085i 0.0541555 0.0938000i
\(416\) −34.4013 + 10.7970i −1.68666 + 0.529364i
\(417\) 10.4176 + 18.0438i 0.510153 + 0.883611i
\(418\) −6.75887 2.32925i −0.330587 0.113928i
\(419\) −7.44655 17.9776i −0.363788 0.878261i −0.994739 0.102439i \(-0.967335\pi\)
0.630952 0.775822i \(-0.282665\pi\)
\(420\) 2.22942 + 1.59310i 0.108785 + 0.0777354i
\(421\) −18.1563 7.52057i −0.884882 0.366530i −0.106494 0.994313i \(-0.533963\pi\)
−0.778388 + 0.627783i \(0.783963\pi\)
\(422\) 1.63627 + 26.8688i 0.0796525 + 1.30795i
\(423\) −1.16807 + 4.35930i −0.0567936 + 0.211956i
\(424\) 3.71424 3.16720i 0.180380 0.153813i
\(425\) 2.48940 + 9.29056i 0.120753 + 0.450658i
\(426\) −2.59082 + 12.7172i −0.125526 + 0.616148i
\(427\) −1.24064 + 14.1275i −0.0600388 + 0.683677i
\(428\) 0.205469 22.2052i 0.00993171 1.07333i
\(429\) −10.6635 + 80.9973i −0.514839 + 3.91059i
\(430\) −0.431193 0.0302660i −0.0207940 0.00145956i
\(431\) 8.97162 5.17977i 0.432148 0.249501i −0.268113 0.963387i \(-0.586400\pi\)
0.700261 + 0.713887i \(0.253067\pi\)
\(432\) −0.198178 + 1.31656i −0.00953486 + 0.0633431i
\(433\) 27.4963i 1.32139i −0.750656 0.660694i \(-0.770262\pi\)
0.750656 0.660694i \(-0.229738\pi\)
\(434\) 3.94824 + 16.4884i 0.189521 + 0.791468i
\(435\) 3.10782 1.28730i 0.149009 0.0617214i
\(436\) −8.08551 31.3324i −0.387226 1.50055i
\(437\) −0.968366 + 0.127488i −0.0463232 + 0.00609857i
\(438\) 0.739964 + 2.21345i 0.0353568 + 0.105763i
\(439\) 7.99212 + 29.8270i 0.381443 + 1.42357i 0.843698 + 0.536818i \(0.180374\pi\)
−0.462255 + 0.886747i \(0.652959\pi\)
\(440\) −0.668254 + 3.13173i −0.0318577 + 0.149299i
\(441\) 6.84102 + 18.8338i 0.325763 + 0.896846i
\(442\) 9.65499 + 14.5954i 0.459241 + 0.694234i
\(443\) 14.2610 10.9428i 0.677559 0.519909i −0.211688 0.977337i \(-0.567896\pi\)
0.889247 + 0.457428i \(0.151229\pi\)
\(444\) −26.2585 + 33.5729i −1.24617 + 1.59330i
\(445\) 0.702956 0.916110i 0.0333233 0.0434278i
\(446\) 6.58829 19.1174i 0.311964 0.905237i
\(447\) −26.6521 −1.26060
\(448\) −19.6784 7.79487i −0.929718 0.368273i
\(449\) −8.48584 −0.400472 −0.200236 0.979748i \(-0.564171\pi\)
−0.200236 + 0.979748i \(0.564171\pi\)
\(450\) −6.53458 + 18.9616i −0.308043 + 0.893858i
\(451\) 38.3012 49.9150i 1.80353 2.35041i
\(452\) −0.604827 + 0.773303i −0.0284486 + 0.0363731i
\(453\) −9.58041 + 7.35130i −0.450127 + 0.345394i
\(454\) −1.57820 2.38576i −0.0740685 0.111969i
\(455\) −3.19856 1.66639i −0.149951 0.0781216i
\(456\) −6.39571 1.36473i −0.299506 0.0639092i
\(457\) −9.90856 36.9792i −0.463503 1.72982i −0.661806 0.749675i \(-0.730210\pi\)
0.198303 0.980141i \(-0.436457\pi\)
\(458\) 3.13800 + 9.38670i 0.146629 + 0.438612i
\(459\) 0.640670 0.0843457i 0.0299039 0.00393692i
\(460\) 0.109319 + 0.423624i 0.00509702 + 0.0197516i
\(461\) 19.2793 7.98574i 0.897925 0.371933i 0.114503 0.993423i \(-0.463472\pi\)
0.783422 + 0.621490i \(0.213472\pi\)
\(462\) −34.8073 + 32.9919i −1.61938 + 1.53492i
\(463\) 20.4343i 0.949664i 0.880076 + 0.474832i \(0.157491\pi\)
−0.880076 + 0.474832i \(0.842509\pi\)
\(464\) −20.9038 + 15.4340i −0.970435 + 0.716505i
\(465\) 2.03209 1.17323i 0.0942361 0.0544072i
\(466\) −16.0410 1.12594i −0.743087 0.0521582i
\(467\) −5.58239 + 42.4024i −0.258322 + 1.96215i 0.0138579 + 0.999904i \(0.495589\pi\)
−0.272180 + 0.962246i \(0.587745\pi\)
\(468\) −0.337639 + 36.4890i −0.0156074 + 1.68671i
\(469\) 0.284194 + 0.199133i 0.0131229 + 0.00919510i
\(470\) 0.0951927 0.467258i 0.00439091 0.0215530i
\(471\) −10.7707 40.1967i −0.496286 1.85217i
\(472\) 0.431007 + 0.505452i 0.0198387 + 0.0232653i
\(473\) 1.95808 7.30765i 0.0900326 0.336006i
\(474\) −2.58573 42.4596i −0.118766 1.95023i
\(475\) 4.37083 + 1.81046i 0.200547 + 0.0830694i
\(476\) −0.993342 + 10.2249i −0.0455298 + 0.468657i
\(477\) −1.89050 4.56408i −0.0865602 0.208975i
\(478\) 20.6493 + 7.11620i 0.944477 + 0.325488i
\(479\) 6.77441 + 11.7336i 0.309531 + 0.536123i 0.978260 0.207383i \(-0.0664947\pi\)
−0.668729 + 0.743506i \(0.733161\pi\)
\(480\) −0.259146 + 2.91783i −0.0118283 + 0.133180i
\(481\) 28.0500 48.5841i 1.27897 2.21524i
\(482\) −3.40432 17.5384i −0.155063 0.798850i
\(483\) −2.24302 + 6.15640i −0.102061 + 0.280126i
\(484\) −31.3328 13.3195i −1.42422 0.605430i
\(485\) −2.02569 + 1.55437i −0.0919819 + 0.0705802i
\(486\) 27.5183 + 13.7292i 1.24825 + 0.622767i
\(487\) 1.46327 5.46101i 0.0663072 0.247462i −0.924815 0.380418i \(-0.875780\pi\)
0.991122 + 0.132956i \(0.0424469\pi\)
\(488\) −13.6893 + 6.51620i −0.619685 + 0.294974i
\(489\) −17.1531 + 17.1531i −0.775688 + 0.775688i
\(490\) −0.842454 1.94237i −0.0380582 0.0877475i
\(491\) −11.1565 + 26.9342i −0.503487 + 1.21553i 0.444086 + 0.895984i \(0.353529\pi\)
−0.947573 + 0.319541i \(0.896471\pi\)
\(492\) 29.2372 49.5752i 1.31811 2.23502i
\(493\) 10.0054 + 7.67742i 0.450621 + 0.345774i
\(494\) 8.58654 + 0.602700i 0.386327 + 0.0271168i
\(495\) 2.80665 + 1.62042i 0.126150 + 0.0728325i
\(496\) −13.0514 + 12.5771i −0.586024 + 0.564726i
\(497\) 6.77719 7.39117i 0.303999 0.331539i
\(498\) 29.2821 + 19.7622i 1.31216 + 0.885567i
\(499\) −0.828573 + 6.29363i −0.0370920 + 0.281742i 0.962840 + 0.270073i \(0.0870478\pi\)
−0.999932 + 0.0116690i \(0.996286\pi\)
\(500\) 1.14001 4.10237i 0.0509830 0.183464i
\(501\) −11.4834 + 1.51182i −0.513040 + 0.0675430i
\(502\) −7.83214 + 8.84793i −0.349565 + 0.394902i
\(503\) 9.35885 9.35885i 0.417290 0.417290i −0.466978 0.884269i \(-0.654657\pi\)
0.884269 + 0.466978i \(0.154657\pi\)
\(504\) −13.6440 + 16.5139i −0.607752 + 0.735589i
\(505\) 1.67875 + 1.67875i 0.0747034 + 0.0747034i
\(506\) −7.64313 + 0.465455i −0.339778 + 0.0206920i
\(507\) −8.73082 66.3171i −0.387749 2.94525i
\(508\) −12.0021 9.38721i −0.532505 0.416490i
\(509\) −21.9212 2.88598i −0.971640 0.127919i −0.372038 0.928217i \(-0.621341\pi\)
−0.599602 + 0.800299i \(0.704674\pi\)
\(510\) 1.39571 0.270917i 0.0618030 0.0119964i
\(511\) 0.390879 1.76042i 0.0172915 0.0778766i
\(512\) −3.48677 22.3572i −0.154095 0.988056i
\(513\) 0.158923 0.275262i 0.00701661 0.0121531i
\(514\) −22.1740 25.5218i −0.978051 1.12572i
\(515\) −0.437805 + 0.570559i −0.0192920 + 0.0251418i
\(516\) 0.966777 6.85281i 0.0425600 0.301678i
\(517\) 7.71075 + 3.19390i 0.339119 + 0.140467i
\(518\) 30.7522 11.7839i 1.35117 0.517754i
\(519\) −29.6702 29.6702i −1.30238 1.30238i
\(520\) −0.198748 3.85050i −0.00871569 0.168856i
\(521\) −2.06726 0.553920i −0.0905681 0.0242677i 0.213250 0.976998i \(-0.431595\pi\)
−0.303819 + 0.952730i \(0.598262\pi\)
\(522\) 8.33775 + 24.9407i 0.364934 + 1.09163i
\(523\) −0.908538 1.18403i −0.0397276 0.0517740i 0.773067 0.634324i \(-0.218722\pi\)
−0.812795 + 0.582550i \(0.802055\pi\)
\(524\) −18.4551 18.7998i −0.806213 0.821273i
\(525\) 24.3189 20.3924i 1.06136 0.889999i
\(526\) −22.6818 15.3078i −0.988975 0.667451i
\(527\) 7.61853 + 4.39856i 0.331868 + 0.191604i
\(528\) −49.2687 14.1837i −2.14415 0.617267i
\(529\) 19.0126 10.9769i 0.826634 0.477257i
\(530\) 0.228696 + 0.469210i 0.00993393 + 0.0203812i
\(531\) 0.621101 0.257269i 0.0269535 0.0111645i
\(532\) 3.69259 + 3.44928i 0.160094 + 0.149545i
\(533\) −28.9899 + 69.9878i −1.25569 + 3.03151i
\(534\) 13.8434 + 12.2541i 0.599065 + 0.530289i
\(535\) 2.29370 + 0.614596i 0.0991654 + 0.0265713i
\(536\) −0.0293984 + 0.369809i −0.00126982 + 0.0159733i
\(537\) −58.6705 + 15.7207i −2.53182 + 0.678399i
\(538\) 22.8974 15.1468i 0.987176 0.653024i
\(539\) 36.1827 7.99675i 1.55850 0.344444i
\(540\) −0.131025 0.0556982i −0.00563842 0.00239687i
\(541\) −25.4586 3.35169i −1.09455 0.144100i −0.438437 0.898762i \(-0.644468\pi\)
−0.656114 + 0.754662i \(0.727801\pi\)
\(542\) −5.51061 + 4.78775i −0.236701 + 0.205652i
\(543\) 9.78462 + 16.9475i 0.419898 + 0.727285i
\(544\) −9.95946 + 4.62823i −0.427008 + 0.198434i
\(545\) 3.46028 0.148222
\(546\) 30.2002 49.2171i 1.29245 2.10630i
\(547\) 8.86177 + 21.3942i 0.378902 + 0.914750i 0.992172 + 0.124877i \(0.0398537\pi\)
−0.613270 + 0.789873i \(0.710146\pi\)
\(548\) 15.9044 + 21.1290i 0.679404 + 0.902588i
\(549\) 2.00278 + 15.2126i 0.0854764 + 0.649258i
\(550\) 33.1884 + 16.5580i 1.41516 + 0.706037i
\(551\) 5.99187 1.60552i 0.255262 0.0683973i
\(552\) −6.88840 + 1.27107i −0.293190 + 0.0541001i
\(553\) −15.1862 + 29.1492i −0.645783 + 1.23955i
\(554\) −4.22133 + 20.7206i −0.179347 + 0.880334i
\(555\) −2.77460 3.61593i −0.117775 0.153488i
\(556\) 14.9835 8.46682i 0.635440 0.359073i
\(557\) 11.0651 + 8.49058i 0.468845 + 0.359757i 0.816002 0.578050i \(-0.196186\pi\)
−0.347156 + 0.937807i \(0.612853\pi\)
\(558\) 8.03701 + 16.4893i 0.340234 + 0.698048i
\(559\) 9.10911i 0.385274i
\(560\) 1.33291 1.82928i 0.0563256 0.0773012i
\(561\) 24.8840i 1.05060i
\(562\) 27.3829 13.3466i 1.15508 0.562993i
\(563\) 2.44469 + 1.87587i 0.103031 + 0.0790586i 0.658992 0.752150i \(-0.270983\pi\)
−0.555961 + 0.831208i \(0.687650\pi\)
\(564\) 7.35601 + 2.04417i 0.309744 + 0.0860752i
\(565\) −0.0639091 0.0832880i −0.00268868 0.00350395i
\(566\) −25.4864 5.19224i −1.07127 0.218246i
\(567\) −13.3466 20.9651i −0.560505 0.880450i
\(568\) 10.4843 + 2.23716i 0.439911 + 0.0938691i
\(569\) −18.5733 + 4.97670i −0.778633 + 0.208634i −0.626182 0.779677i \(-0.715383\pi\)
−0.152451 + 0.988311i \(0.548717\pi\)
\(570\) 0.312200 0.625764i 0.0130766 0.0262104i
\(571\) 2.75318 + 20.9124i 0.115217 + 0.875159i 0.947264 + 0.320454i \(0.103835\pi\)
−0.832047 + 0.554705i \(0.812831\pi\)
\(572\) 66.8206 + 9.42688i 2.79391 + 0.394158i
\(573\) 10.8798 + 26.2661i 0.454509 + 1.09728i
\(574\) −39.0938 + 21.1964i −1.63174 + 0.884719i
\(575\) 5.06734 0.211323
\(576\) −22.6126 3.61809i −0.942193 0.150754i
\(577\) −12.1593 21.0605i −0.506199 0.876762i −0.999974 0.00717238i \(-0.997717\pi\)
0.493776 0.869589i \(-0.335616\pi\)
\(578\) −12.2720 14.1248i −0.510448 0.587516i
\(579\) −23.3517 3.07431i −0.970463 0.127764i
\(580\) −1.03953 2.57683i −0.0431642 0.106997i
\(581\) −11.5276 24.7422i −0.478247 1.02648i
\(582\) −22.5544 34.0955i −0.934912 1.41331i
\(583\) −8.82449 + 2.36452i −0.365473 + 0.0979282i
\(584\) 1.83392 0.594277i 0.0758882 0.0245914i
\(585\) −3.76915 1.00994i −0.155835 0.0417560i
\(586\) −2.77125 + 3.13066i −0.114479 + 0.129326i
\(587\) 4.10572 9.91207i 0.169461 0.409115i −0.816219 0.577743i \(-0.803934\pi\)
0.985680 + 0.168628i \(0.0539336\pi\)
\(588\) 31.9667 11.2776i 1.31829 0.465081i
\(589\) 3.99767 1.65589i 0.164721 0.0682296i
\(590\) −0.0638523 + 0.0311221i −0.00262876 + 0.00128128i
\(591\) −31.2591 + 18.0475i −1.28583 + 0.742374i
\(592\) 27.5298 + 21.9455i 1.13147 + 0.901955i
\(593\) 18.8079 + 10.8587i 0.772347 + 0.445915i 0.833711 0.552201i \(-0.186212\pi\)
−0.0613642 + 0.998115i \(0.519545\pi\)
\(594\) 1.39396 2.06546i 0.0571950 0.0847469i
\(595\) −1.03217 0.376061i −0.0423149 0.0154170i
\(596\) −0.203700 + 22.0141i −0.00834387 + 0.901731i
\(597\) 4.26390 + 5.55682i 0.174510 + 0.227426i
\(598\) 8.74403 2.92315i 0.357570 0.119537i
\(599\) −3.04141 0.814944i −0.124269 0.0332977i 0.196149 0.980574i \(-0.437156\pi\)
−0.320417 + 0.947276i \(0.603823\pi\)
\(600\) 31.9736 + 11.3509i 1.30532 + 0.463397i
\(601\) 24.7237 + 24.7237i 1.00850 + 1.00850i 0.999964 + 0.00853894i \(0.00271806\pi\)
0.00853894 + 0.999964i \(0.497282\pi\)
\(602\) −3.36765 + 4.15369i −0.137255 + 0.169292i
\(603\) 0.346869 + 0.143678i 0.0141256 + 0.00585102i
\(604\) 5.99880 + 7.96940i 0.244088 + 0.324270i
\(605\) 2.21634 2.88839i 0.0901071 0.117430i
\(606\) −28.6938 + 24.9299i −1.16561 + 1.01271i
\(607\) 4.24808 7.35790i 0.172424 0.298648i −0.766843 0.641835i \(-0.778173\pi\)
0.939267 + 0.343187i \(0.111507\pi\)
\(608\) −1.17612 + 5.27229i −0.0476979 + 0.213820i
\(609\) 9.02020 40.6248i 0.365517 1.64620i
\(610\) −0.308929 1.59154i −0.0125082 0.0644395i
\(611\) −9.96305 1.31166i −0.403062 0.0530641i
\(612\) 1.34874 + 11.0326i 0.0545196 + 0.445967i
\(613\) −4.34662 33.0158i −0.175558 1.33350i −0.821543 0.570147i \(-0.806886\pi\)
0.645985 0.763350i \(-0.276447\pi\)
\(614\) −2.66498 43.7610i −0.107550 1.76605i
\(615\) 4.35194 + 4.35194i 0.175487 + 0.175487i
\(616\) 26.9846 + 29.0022i 1.08724 + 1.16853i
\(617\) 11.2487 11.2487i 0.452854 0.452854i −0.443446 0.896301i \(-0.646244\pi\)
0.896301 + 0.443446i \(0.146244\pi\)
\(618\) −8.62179 7.63196i −0.346819 0.307003i
\(619\) −44.8907 + 5.90997i −1.80431 + 0.237542i −0.956289 0.292424i \(-0.905538\pi\)
−0.848019 + 0.529965i \(0.822205\pi\)
\(620\) −0.953532 1.68743i −0.0382948 0.0677689i
\(621\) 0.0444370 0.337533i 0.00178320 0.0135447i
\(622\) −6.53799 + 9.68747i −0.262149 + 0.388432i
\(623\) −4.29114 13.6253i −0.171921 0.545885i
\(624\) 61.7204 + 1.14232i 2.47080 + 0.0457293i
\(625\) −21.0583 12.1580i −0.842331 0.486320i
\(626\) −0.0695362 + 0.990668i −0.00277923 + 0.0395951i
\(627\) 9.71041 + 7.45106i 0.387796 + 0.297567i
\(628\) −33.2839 + 8.58912i −1.32817 + 0.342743i
\(629\) 6.53915 15.7869i 0.260733 0.629465i
\(630\) −1.34533 1.85399i −0.0535993 0.0738646i
\(631\) 24.3208 24.3208i 0.968198 0.968198i −0.0313121 0.999510i \(-0.509969\pi\)
0.999510 + 0.0313121i \(0.00996858\pi\)
\(632\) −35.0905 + 1.81124i −1.39583 + 0.0720473i
\(633\) 11.9282 44.5168i 0.474105 1.76938i
\(634\) 10.6279 21.3023i 0.422089 0.846023i
\(635\) 1.29267 0.991901i 0.0512981 0.0393624i
\(636\) −7.75029 + 3.12658i −0.307319 + 0.123977i
\(637\) −39.5891 + 20.5759i −1.56858 + 0.815249i
\(638\) 47.7410 9.26687i 1.89008 0.366879i
\(639\) 5.42479 9.39602i 0.214602 0.371701i
\(640\) 2.40809 + 0.236350i 0.0951880 + 0.00934255i
\(641\) 9.75056 + 16.8885i 0.385124 + 0.667054i 0.991786 0.127905i \(-0.0408254\pi\)
−0.606662 + 0.794960i \(0.707492\pi\)
\(642\) −12.3873 + 35.9445i −0.488886 + 1.41862i
\(643\) −6.18566 14.9335i −0.243939 0.588920i 0.753728 0.657186i \(-0.228253\pi\)
−0.997667 + 0.0682658i \(0.978253\pi\)
\(644\) 5.06791 + 1.89974i 0.199704 + 0.0748603i
\(645\) 0.683726 + 0.283209i 0.0269217 + 0.0111513i
\(646\) 2.61698 0.159370i 0.102964 0.00627033i
\(647\) 11.3391 42.3182i 0.445787 1.66370i −0.268064 0.963401i \(-0.586384\pi\)
0.713851 0.700298i \(-0.246949\pi\)
\(648\) 12.0807 23.6635i 0.474574 0.929590i
\(649\) −0.321775 1.20088i −0.0126308 0.0471386i
\(650\) −43.7587 8.91479i −1.71636 0.349667i
\(651\) 2.53937 28.9164i 0.0995256 1.13332i
\(652\) 14.0370 + 14.2992i 0.549730 + 0.559998i
\(653\) 2.73095 20.7436i 0.106870 0.811760i −0.851122 0.524967i \(-0.824078\pi\)
0.957993 0.286793i \(-0.0925891\pi\)
\(654\) −3.87914 + 55.2654i −0.151687 + 2.16105i
\(655\) 2.43970 1.40856i 0.0953269 0.0550370i
\(656\) −40.7246 24.5282i −1.59003 0.957665i
\(657\) 1.95105i 0.0761177i
\(658\) −4.05816 4.28146i −0.158204 0.166909i
\(659\) 34.3680 14.2357i 1.33879 0.554543i 0.405637 0.914034i \(-0.367050\pi\)
0.933149 + 0.359491i \(0.117050\pi\)
\(660\) 2.78508 4.72243i 0.108409 0.183821i
\(661\) 41.9433 5.52194i 1.63140 0.214778i 0.741509 0.670943i \(-0.234111\pi\)
0.889895 + 0.456165i \(0.150777\pi\)
\(662\) −5.33771 + 1.78441i −0.207456 + 0.0693531i
\(663\) −7.75459 28.9405i −0.301163 1.12396i
\(664\) 16.5470 24.0353i 0.642147 0.932752i
\(665\) −0.455813 + 0.290176i −0.0176757 + 0.0112526i
\(666\) 29.7173 19.6582i 1.15152 0.761741i
\(667\) 5.27129 4.04480i 0.204105 0.156615i
\(668\) 1.16096 + 9.49659i 0.0449190 + 0.367434i
\(669\) −21.0753 + 27.4659i −0.814818 + 1.06189i
\(670\) −0.0375055 0.0129252i −0.00144896 0.000499345i
\(671\) 28.3755 1.09542
\(672\) 27.7218 + 23.3390i 1.06939 + 0.900322i
\(673\) −1.46174 −0.0563458 −0.0281729 0.999603i \(-0.508969\pi\)
−0.0281729 + 0.999603i \(0.508969\pi\)
\(674\) −6.83235 2.35458i −0.263172 0.0906949i
\(675\) −1.00386 + 1.30825i −0.0386385 + 0.0503547i
\(676\) −54.8433 + 6.70461i −2.10936 + 0.257870i
\(677\) −7.95807 + 6.10644i −0.305853 + 0.234690i −0.750271 0.661130i \(-0.770077\pi\)
0.444418 + 0.895820i \(0.353411\pi\)
\(678\) 1.40187 0.927344i 0.0538383 0.0356144i
\(679\) 1.36751 + 31.5573i 0.0524800 + 1.21106i
\(680\) −0.213104 1.15490i −0.00817218 0.0442882i
\(681\) 1.26756 + 4.73060i 0.0485730 + 0.181277i
\(682\) 32.1729 10.7555i 1.23196 0.411849i
\(683\) 4.35097 0.572816i 0.166485 0.0219182i −0.0468227 0.998903i \(-0.514910\pi\)
0.213308 + 0.976985i \(0.431576\pi\)
\(684\) 4.70907 + 2.77720i 0.180056 + 0.106189i
\(685\) −2.61272 + 1.08223i −0.0998270 + 0.0413497i
\(686\) −25.6593 5.25363i −0.979676 0.200585i
\(687\) 16.9452i 0.646498i
\(688\) −5.65288 0.850913i −0.215514 0.0324407i
\(689\) 9.52618 5.49994i 0.362919 0.209531i
\(690\) 0.0524473 0.747206i 0.00199664 0.0284457i
\(691\) −1.44557 + 10.9802i −0.0549922 + 0.417707i 0.941701 + 0.336451i \(0.109227\pi\)
−0.996693 + 0.0812562i \(0.974107\pi\)
\(692\) −24.7337 + 24.2802i −0.940234 + 0.922993i
\(693\) 36.3412 16.9318i 1.38049 0.643185i
\(694\) 21.4116 + 4.36211i 0.812774 + 0.165584i
\(695\) 0.476323 + 1.77766i 0.0180679 + 0.0674305i
\(696\) 42.3208 13.7139i 1.60417 0.519826i
\(697\) −5.97202 + 22.2879i −0.226207 + 0.844214i
\(698\) −34.0848 + 2.07571i −1.29013 + 0.0785668i
\(699\) 25.4356 + 10.5358i 0.962064 + 0.398500i
\(700\) −16.6578 20.2427i −0.629607 0.765103i
\(701\) −10.4345 25.1912i −0.394107 0.951459i −0.989035 0.147680i \(-0.952820\pi\)
0.594928 0.803779i \(-0.297180\pi\)
\(702\) −0.977543 + 2.83657i −0.0368950 + 0.107059i
\(703\) −4.20244 7.27885i −0.158498 0.274527i
\(704\) −12.0920 + 40.5865i −0.455735 + 1.52966i
\(705\) −0.408211 + 0.707042i −0.0153741 + 0.0266287i
\(706\) 4.79548 0.930837i 0.180480 0.0350325i
\(707\) 28.9253 5.09058i 1.08785 0.191451i
\(708\) −0.425480 1.05470i −0.0159905 0.0396379i
\(709\) 17.7646 13.6313i 0.667163 0.511933i −0.218751 0.975781i \(-0.570198\pi\)
0.885915 + 0.463848i \(0.153532\pi\)
\(710\) −0.511780 + 1.02580i −0.0192068 + 0.0384975i
\(711\) −9.20383 + 34.3492i −0.345171 + 1.28819i
\(712\) 10.2275 11.3407i 0.383290 0.425012i
\(713\) 3.27723 3.27723i 0.122733 0.122733i
\(714\) 7.16331 16.0636i 0.268080 0.601164i
\(715\) −2.76152 + 6.66690i −0.103275 + 0.249328i
\(716\) 12.5366 + 48.5807i 0.468513 + 1.81555i
\(717\) −29.6667 22.7640i −1.10792 0.850139i
\(718\) 2.24702 32.0128i 0.0838579 1.19471i
\(719\) 21.2101 + 12.2456i 0.791002 + 0.456685i 0.840315 0.542098i \(-0.182370\pi\)
−0.0493132 + 0.998783i \(0.515703\pi\)
\(720\) 0.978833 2.24470i 0.0364790 0.0836550i
\(721\) 2.67255 + 8.48590i 0.0995310 + 0.316032i
\(722\) −14.3100 + 21.2034i −0.532563 + 0.789109i
\(723\) −3.99251 + 30.3261i −0.148483 + 1.12784i
\(724\) 14.0730 7.95236i 0.523020 0.295547i
\(725\) −31.9078 + 4.20074i −1.18502 + 0.156011i
\(726\) 43.6469 + 38.6360i 1.61989 + 1.43392i
\(727\) −2.73917 + 2.73917i −0.101590 + 0.101590i −0.756075 0.654485i \(-0.772886\pi\)
0.654485 + 0.756075i \(0.272886\pi\)
\(728\) −40.4215 25.3209i −1.49812 0.938455i
\(729\) −17.3039 17.3039i −0.640887 0.640887i
\(730\) 0.0125310 + 0.205768i 0.000463792 + 0.00761583i
\(731\) 0.362153 + 2.75083i 0.0133947 + 0.101743i
\(732\) 25.7653 3.14982i 0.952314 0.116421i
\(733\) 25.4874 + 3.35548i 0.941399 + 0.123938i 0.585578 0.810616i \(-0.300868\pi\)
0.355821 + 0.934554i \(0.384201\pi\)
\(734\) −0.217253 1.11924i −0.00801895 0.0413120i
\(735\) 0.313570 + 3.61126i 0.0115662 + 0.133203i
\(736\) 0.997226 + 5.69938i 0.0367582 + 0.210082i
\(737\) 0.347160 0.601298i 0.0127878 0.0221491i
\(738\) −36.3204 + 31.5561i −1.33697 + 1.16159i
\(739\) 1.78652 2.32824i 0.0657183 0.0856457i −0.759338 0.650697i \(-0.774477\pi\)
0.825056 + 0.565051i \(0.191144\pi\)
\(740\) −3.00789 + 2.26413i −0.110572 + 0.0832310i
\(741\) −13.6153 5.63966i −0.500172 0.207178i
\(742\) 6.37721 + 1.01390i 0.234115 + 0.0372216i
\(743\) −26.4536 26.4536i −0.970487 0.970487i 0.0290893 0.999577i \(-0.490739\pi\)
−0.999577 + 0.0290893i \(0.990739\pi\)
\(744\) 28.0195 13.3375i 1.02725 0.488976i
\(745\) −2.27395 0.609304i −0.0833112 0.0223232i
\(746\) −23.4921 + 7.85349i −0.860108 + 0.287537i
\(747\) −17.9781 23.4296i −0.657786 0.857243i
\(748\) 20.5537 + 0.190187i 0.751516 + 0.00695391i
\(749\) 22.5095 18.8752i 0.822480 0.689685i
\(750\) −4.07799 + 6.04245i −0.148907 + 0.220639i
\(751\) 24.9518 + 14.4059i 0.910505 + 0.525680i 0.880594 0.473872i \(-0.157144\pi\)
0.0299115 + 0.999553i \(0.490477\pi\)
\(752\) 1.74466 6.06029i 0.0636214 0.220996i
\(753\) 17.5204 10.1154i 0.638480 0.368627i
\(754\) −52.6358 + 25.6550i −1.91688 + 0.934301i
\(755\) −0.985460 + 0.408191i −0.0358646 + 0.0148556i
\(756\) −1.49443 + 0.932056i −0.0543521 + 0.0338986i
\(757\) 13.3623 32.2596i 0.485663 1.17249i −0.471219 0.882016i \(-0.656186\pi\)
0.956882 0.290477i \(-0.0938141\pi\)
\(758\) 31.2222 35.2715i 1.13404 1.28112i
\(759\) 12.6633 + 3.39312i 0.459648 + 0.123162i
\(760\) −0.514481 0.262653i −0.0186622 0.00952743i
\(761\) 29.4093 7.88021i 1.06609 0.285657i 0.317203 0.948358i \(-0.397256\pi\)
0.748885 + 0.662700i \(0.230590\pi\)
\(762\) 14.3928 + 21.7577i 0.521398 + 0.788197i
\(763\) 24.5644 35.0572i 0.889289 1.26916i
\(764\) 21.7784 8.78570i 0.787914 0.317856i
\(765\) −1.17838 0.155137i −0.0426046 0.00560900i
\(766\) 16.3717 + 18.8435i 0.591534 + 0.680844i
\(767\) 0.748459 + 1.29637i 0.0270253 + 0.0468091i
\(768\) −6.47440 + 38.1954i −0.233625 + 1.37826i
\(769\) −7.33213 −0.264403 −0.132202 0.991223i \(-0.542205\pi\)
−0.132202 + 0.991223i \(0.542205\pi\)
\(770\) −3.72400 + 2.01912i −0.134203 + 0.0727642i
\(771\) 22.1513 + 53.4780i 0.797759 + 1.92596i
\(772\) −2.71779 + 19.2645i −0.0978153 + 0.693345i
\(773\) −0.739761 5.61904i −0.0266073 0.202103i 0.972978 0.230898i \(-0.0741663\pi\)
−0.999585 + 0.0287950i \(0.990833\pi\)
\(774\) −2.58284 + 5.17696i −0.0928382 + 0.186082i
\(775\) −21.6842 + 5.81027i −0.778921 + 0.208711i
\(776\) −28.3346 + 18.3689i −1.01715 + 0.659405i
\(777\) −56.3309 + 2.44105i −2.02086 + 0.0875721i
\(778\) 3.74836 + 0.763640i 0.134385 + 0.0273778i
\(779\) 6.90912 + 9.00415i 0.247545 + 0.322607i
\(780\) −1.76744 + 6.36018i −0.0632845 + 0.227731i
\(781\) −15.9180 12.2143i −0.569590 0.437062i
\(782\) 2.52436 1.23039i 0.0902709 0.0439987i
\(783\) 2.16220i 0.0772706i
\(784\) −9.07076 26.4900i −0.323956 0.946072i
\(785\) 3.67581i 0.131195i
\(786\) 19.7616 + 40.5443i 0.704872 + 1.44617i
\(787\) 29.4853 + 22.6248i 1.05104 + 0.806488i 0.981571 0.191096i \(-0.0612042\pi\)
0.0694648 + 0.997584i \(0.477871\pi\)
\(788\) 14.6679 + 25.9573i 0.522523 + 0.924691i
\(789\) 28.5204 + 37.1685i 1.01535 + 1.32323i
\(790\) 0.750072 3.68176i 0.0266864 0.130991i
\(791\) −1.29750 + 0.0562261i −0.0461339 + 0.00199917i
\(792\) 35.3030 + 24.3041i 1.25444 + 0.863610i
\(793\) −33.0011 + 8.84263i −1.17191 + 0.314011i
\(794\) 23.6366 + 11.7926i 0.838833 + 0.418502i
\(795\) −0.116648 0.886028i −0.00413707 0.0314242i
\(796\) 4.62241 3.47942i 0.163837 0.123325i
\(797\) −18.3903 44.3982i −0.651419 1.57267i −0.810719 0.585435i \(-0.800924\pi\)
0.159300 0.987230i \(-0.449076\pi\)
\(798\) −4.12351 7.60525i −0.145971 0.269223i
\(799\) −3.06085 −0.108285
\(800\) 9.61993 26.3227i 0.340116 0.930650i
\(801\) −7.72773 13.3848i −0.273046 0.472929i
\(802\) 2.11848 1.84059i 0.0748061 0.0649934i
\(803\) −3.57722 0.470950i −0.126237 0.0166195i
\(804\) 0.248479 0.584524i 0.00876317 0.0206146i
\(805\) −0.332118 + 0.473985i −0.0117056 + 0.0167058i
\(806\) −34.0659 + 22.5348i −1.19992 + 0.793755i
\(807\) −45.4020 + 12.1654i −1.59823 + 0.428243i
\(808\) 20.3723 + 23.8910i 0.716694 + 0.840484i
\(809\) 11.2549 + 3.01573i 0.395700 + 0.106027i 0.451181 0.892432i \(-0.351003\pi\)
−0.0554817 + 0.998460i \(0.517669\pi\)
\(810\) 2.12739 + 1.88315i 0.0747488 + 0.0661672i
\(811\) −8.55829 + 20.6616i −0.300522 + 0.725525i 0.699419 + 0.714712i \(0.253442\pi\)
−0.999942 + 0.0108135i \(0.996558\pi\)
\(812\) −33.4862 7.76098i −1.17514 0.272357i
\(813\) 11.5468 4.78286i 0.404965 0.167742i
\(814\) −28.8698 59.2314i −1.01189 2.07606i
\(815\) −1.85564 + 1.07135i −0.0650002 + 0.0375279i
\(816\) 18.6841 2.10887i 0.654075 0.0738252i
\(817\) 1.18189 + 0.682362i 0.0413490 + 0.0238728i
\(818\) −41.3288 27.8924i −1.44503 0.975236i
\(819\) −36.9890 + 31.0169i −1.29250 + 1.08382i
\(820\) 3.62787 3.56135i 0.126691 0.124368i
\(821\) 9.63341 + 12.5545i 0.336208 + 0.438155i 0.930610 0.366013i \(-0.119278\pi\)
−0.594401 + 0.804169i \(0.702611\pi\)
\(822\) −14.3556 42.9419i −0.500709 1.49777i
\(823\) −32.2480 8.64083i −1.12409 0.301200i −0.351555 0.936167i \(-0.614347\pi\)
−0.772539 + 0.634967i \(0.781014\pi\)
\(824\) −6.36973 + 7.06308i −0.221900 + 0.246054i
\(825\) −44.9019 44.9019i −1.56328 1.56328i
\(826\) −0.137977 + 0.867841i −0.00480083 + 0.0301961i
\(827\) 9.63237 + 3.98986i 0.334950 + 0.138741i 0.543819 0.839203i \(-0.316978\pi\)
−0.208868 + 0.977944i \(0.566978\pi\)
\(828\) 5.79832 + 0.818012i 0.201505 + 0.0284279i
\(829\) 0.651336 0.848838i 0.0226218 0.0294813i −0.781905 0.623397i \(-0.785752\pi\)
0.804527 + 0.593916i \(0.202419\pi\)
\(830\) 2.04655 + 2.35554i 0.0710369 + 0.0817620i
\(831\) 18.1022 31.3539i 0.627957 1.08765i
\(832\) 1.41525 50.9710i 0.0490651 1.76710i
\(833\) −11.1373 + 7.78760i −0.385885 + 0.269824i
\(834\) −28.9256 + 5.61467i −1.00161 + 0.194420i
\(835\) −1.01432 0.133538i −0.0351021 0.00462128i
\(836\) 6.22863 7.96364i 0.215422 0.275428i
\(837\) 0.196864 + 1.49533i 0.00680460 + 0.0516861i
\(838\) 27.4680 1.67276i 0.948865 0.0577845i
\(839\) 3.97257 + 3.97257i 0.137148 + 0.137148i 0.772348 0.635200i \(-0.219082\pi\)
−0.635200 + 0.772348i \(0.719082\pi\)
\(840\) −3.15731 + 2.24678i −0.108937 + 0.0775211i
\(841\) −9.33282 + 9.33282i −0.321822 + 0.321822i
\(842\) 18.4213 20.8104i 0.634839 0.717175i
\(843\) −51.7082 + 6.80752i −1.78093 + 0.234463i
\(844\) −36.6788 10.1927i −1.26254 0.350848i
\(845\) 0.771190 5.85777i 0.0265297 0.201513i
\(846\) −5.29036 3.57042i −0.181886 0.122754i
\(847\) −13.5295 42.9590i −0.464879 1.47609i
\(848\) 2.52325 + 6.42547i 0.0866488 + 0.220652i
\(849\) 38.5653 + 22.2657i 1.32356 + 0.764156i
\(850\) −13.5689 0.952420i −0.465411 0.0326677i
\(851\) −7.14217 5.48038i −0.244830 0.187865i
\(852\) −15.8096 9.32378i −0.541628 0.319428i
\(853\) −9.70512 + 23.4302i −0.332297 + 0.802236i 0.666112 + 0.745852i \(0.267957\pi\)
−0.998409 + 0.0563845i \(0.982043\pi\)
\(854\) −18.3174 8.16838i −0.626810 0.279516i
\(855\) −0.413384 + 0.413384i −0.0141374 + 0.0141374i
\(856\) 29.5947 + 10.5063i 1.01153 + 0.359099i
\(857\) 0.666614 2.48784i 0.0227711 0.0849829i −0.953605 0.301060i \(-0.902660\pi\)
0.976376 + 0.216077i \(0.0693262\pi\)
\(858\) −103.384 51.5791i −3.52946 1.76088i
\(859\) −32.2686 + 24.7606i −1.10099 + 0.844820i −0.988856 0.148873i \(-0.952435\pi\)
−0.112135 + 0.993693i \(0.535769\pi\)
\(860\) 0.239150 0.562579i 0.00815495 0.0191838i
\(861\) 74.9850 13.1967i 2.55548 0.449741i
\(862\) 2.79168 + 14.3822i 0.0950850 + 0.489858i
\(863\) −18.3711 + 31.8197i −0.625360 + 1.08316i 0.363111 + 0.931746i \(0.381715\pi\)
−0.988471 + 0.151410i \(0.951619\pi\)
\(864\) −1.66898 0.871611i −0.0567800 0.0296528i
\(865\) −1.85315 3.20976i −0.0630091 0.109135i
\(866\) 36.7637 + 12.6696i 1.24928 + 0.430530i
\(867\) 12.2595 + 29.5970i 0.416353 + 1.00517i
\(868\) −23.8650 2.31847i −0.810029 0.0786940i
\(869\) 60.7570 + 25.1664i 2.06104 + 0.853711i
\(870\) 0.289174 + 4.74845i 0.00980390 + 0.160988i
\(871\) −0.216370 + 0.807505i −0.00733143 + 0.0273613i
\(872\) 45.6184 + 3.62648i 1.54483 + 0.122808i
\(873\) 8.84513 + 33.0105i 0.299362 + 1.11724i
\(874\) 0.275742 1.35349i 0.00932710 0.0457825i
\(875\) 5.10562 2.37876i 0.172602 0.0804169i
\(876\) −3.30044 0.0305396i −0.111512 0.00103184i
\(877\) 3.69795 28.0887i 0.124871 0.948488i −0.808228 0.588869i \(-0.799573\pi\)
0.933099 0.359619i \(-0.117093\pi\)
\(878\) −43.5626 3.05771i −1.47017 0.103193i
\(879\) 6.19925 3.57914i 0.209096 0.120721i
\(880\) −3.87934 2.33651i −0.130773 0.0787636i
\(881\) 33.0378i 1.11307i −0.830824 0.556535i \(-0.812130\pi\)
0.830824 0.556535i \(-0.187870\pi\)
\(882\) −28.3337 + 0.468618i −0.954047 + 0.0157792i
\(883\) 0.990869 0.410432i 0.0333454 0.0138121i −0.365948 0.930635i \(-0.619255\pi\)
0.399294 + 0.916823i \(0.369255\pi\)
\(884\) −23.9635 + 6.18394i −0.805980 + 0.207988i
\(885\) 0.120575 0.0158740i 0.00405308 0.000533598i
\(886\) 8.05994 + 24.1097i 0.270779 + 0.809982i
\(887\) 6.99046 + 26.0887i 0.234717 + 0.875974i 0.978276 + 0.207305i \(0.0664692\pi\)
−0.743560 + 0.668670i \(0.766864\pi\)
\(888\) −32.7892 50.5782i −1.10033 1.69729i
\(889\) −0.872657 20.1379i −0.0292680 0.675403i
\(890\) 0.900975 + 1.36200i 0.0302007 + 0.0456544i
\(891\) −39.4506 + 30.2715i −1.32164 + 1.01413i
\(892\) 22.5251 + 17.6177i 0.754197 + 0.589883i
\(893\) −0.916515 + 1.19443i −0.0306700 + 0.0399699i
\(894\) 12.2806 35.6350i 0.410725 1.19181i
\(895\) −5.36516 −0.179337
\(896\) 19.4894 22.7192i 0.651095 0.758996i
\(897\) −15.7850 −0.527046
\(898\) 3.91006 11.3459i 0.130480 0.378619i
\(899\) −17.9192 + 23.3527i −0.597637 + 0.778856i
\(900\) −22.3415 17.4740i −0.744717 0.582468i
\(901\) 2.65811 2.03964i 0.0885545 0.0679503i
\(902\) 49.0904 + 74.2099i 1.63453 + 2.47092i
\(903\) 7.72300 4.91656i 0.257005 0.163613i
\(904\) −0.755252 1.16500i −0.0251193 0.0387473i
\(905\) 0.447380 + 1.66965i 0.0148714 + 0.0555009i
\(906\) −5.41461 16.1967i −0.179888 0.538100i
\(907\) −39.0013 + 5.13462i −1.29502 + 0.170492i −0.746353 0.665551i \(-0.768197\pi\)
−0.548664 + 0.836043i \(0.684863\pi\)
\(908\) 3.91706 1.01082i 0.129992 0.0335453i
\(909\) 29.3574 12.1602i 0.973723 0.403329i
\(910\) 3.70185 3.50878i 0.122715 0.116315i
\(911\) 11.6967i 0.387528i −0.981048 0.193764i \(-0.937930\pi\)
0.981048 0.193764i \(-0.0620695\pi\)
\(912\) 4.77168 7.92251i 0.158006 0.262341i
\(913\) −47.2973 + 27.3071i −1.56531 + 0.903734i
\(914\) 54.0085 + 3.79092i 1.78644 + 0.125393i
\(915\) −0.362304 + 2.75198i −0.0119774 + 0.0909775i
\(916\) −13.9963 0.129511i −0.462452 0.00427915i
\(917\) 3.04872 34.7166i 0.100678 1.14644i
\(918\) −0.182430 + 0.895468i −0.00602110 + 0.0295548i
\(919\) 7.37588 + 27.5271i 0.243308 + 0.908037i 0.974226 + 0.225572i \(0.0724251\pi\)
−0.730919 + 0.682464i \(0.760908\pi\)
\(920\) −0.616776 0.0490312i −0.0203345 0.00161651i
\(921\) −19.4274 + 72.5040i −0.640154 + 2.38909i
\(922\) 1.79388 + 29.4569i 0.0590783 + 0.970110i
\(923\) 22.3192 + 9.24493i 0.734646 + 0.304300i
\(924\) −28.0733 61.7407i −0.923545 2.03112i
\(925\) 16.6871 + 40.2862i 0.548668 + 1.32460i
\(926\) −27.3216 9.41563i −0.897844 0.309417i
\(927\) 4.81288 + 8.33615i 0.158076 + 0.273795i
\(928\) −11.0040 35.0609i −0.361223 1.15093i
\(929\) −27.9344 + 48.3838i −0.916498 + 1.58742i −0.111804 + 0.993730i \(0.535663\pi\)
−0.804693 + 0.593691i \(0.797670\pi\)
\(930\) 0.632322 + 3.25759i 0.0207347 + 0.106821i
\(931\) −0.295930 + 6.67793i −0.00969872 + 0.218860i
\(932\) 8.89674 20.9288i 0.291422 0.685545i
\(933\) 15.8748 12.1811i 0.519717 0.398793i
\(934\) −54.1217 27.0019i −1.77092 0.883528i
\(935\) −0.568883 + 2.12310i −0.0186045 + 0.0694328i
\(936\) −48.6319 17.2647i −1.58958 0.564313i
\(937\) 2.71725 2.71725i 0.0887688 0.0887688i −0.661328 0.750097i \(-0.730007\pi\)
0.750097 + 0.661328i \(0.230007\pi\)
\(938\) −0.397199 + 0.288224i −0.0129690 + 0.00941086i
\(939\) 0.650673 1.57086i 0.0212339 0.0512632i
\(940\) 0.580881 + 0.342577i 0.0189463 + 0.0111736i
\(941\) −27.8415 21.3636i −0.907608 0.696432i 0.0455315 0.998963i \(-0.485502\pi\)
−0.953140 + 0.302531i \(0.902169\pi\)
\(942\) 58.7076 + 4.12076i 1.91280 + 0.134262i
\(943\) 10.5278 + 6.07823i 0.342833 + 0.197934i
\(944\) −0.874409 + 0.343376i −0.0284596 + 0.0111759i
\(945\) −0.0565766 0.179642i −0.00184044 0.00584376i
\(946\) 8.86842 + 5.98522i 0.288337 + 0.194596i
\(947\) 4.76127 36.1654i 0.154720 1.17522i −0.721187 0.692740i \(-0.756403\pi\)
0.875908 0.482478i \(-0.160263\pi\)
\(948\) 57.9618 + 16.1071i 1.88251 + 0.523134i
\(949\) 4.30713 0.567044i 0.139815 0.0184070i
\(950\) −4.43463 + 5.00978i −0.143878 + 0.162539i
\(951\) −28.8207 + 28.8207i −0.934577 + 0.934577i
\(952\) −13.2134 6.03951i −0.428249 0.195742i
\(953\) 3.07164 + 3.07164i 0.0995002 + 0.0995002i 0.755105 0.655604i \(-0.227586\pi\)
−0.655604 + 0.755105i \(0.727586\pi\)
\(954\) 6.97347 0.424674i 0.225774 0.0137493i
\(955\) 0.327781 + 2.48974i 0.0106067 + 0.0805662i
\(956\) −19.0294 + 24.3301i −0.615453 + 0.786890i
\(957\) −82.5503 10.8680i −2.66847 0.351311i
\(958\) −18.8098 + 3.65113i −0.607719 + 0.117963i
\(959\) −7.58322 + 34.1529i −0.244875 + 1.10286i
\(960\) −3.78186 1.69095i −0.122059 0.0545753i
\(961\) 5.23373 9.06508i 0.168830 0.292422i
\(962\) 52.0343 + 59.8904i 1.67765 + 1.93094i
\(963\) 19.3482 25.2151i 0.623488 0.812546i
\(964\) 25.0182 + 3.52950i 0.805782 + 0.113678i
\(965\) −1.92208 0.796152i −0.0618740 0.0256290i
\(966\) −7.19785 5.83573i −0.231587 0.187762i
\(967\) 5.66948 + 5.66948i 0.182318 + 0.182318i 0.792365 0.610047i \(-0.208849\pi\)
−0.610047 + 0.792365i \(0.708849\pi\)
\(968\) 32.2461 35.7561i 1.03643 1.14924i
\(969\) −4.33586 1.16179i −0.139288 0.0373221i
\(970\) −1.14487 3.42465i −0.0367596 0.109959i
\(971\) 10.5473 + 13.7455i 0.338479 + 0.441115i 0.931318 0.364206i \(-0.118660\pi\)
−0.592839 + 0.805321i \(0.701993\pi\)
\(972\) −31.0362 + 30.4671i −0.995487 + 0.977233i
\(973\) 21.3914 + 7.79373i 0.685777 + 0.249856i
\(974\) 6.62737 + 4.47275i 0.212355 + 0.143316i
\(975\) 66.2145 + 38.2289i 2.12056 + 1.22431i
\(976\) −2.40476 21.3057i −0.0769746 0.681978i
\(977\) 31.4028 18.1304i 1.00466 0.580043i 0.0950390 0.995474i \(-0.469702\pi\)
0.909625 + 0.415431i \(0.136369\pi\)
\(978\) −15.0307 30.8381i −0.480629 0.986093i
\(979\) −26.4062 + 10.9378i −0.843945 + 0.349574i
\(980\) 2.98522 0.231402i 0.0953593 0.00739185i
\(981\) 17.7236 42.7886i 0.565872 1.36614i
\(982\) −30.8716 27.3274i −0.985153 0.872052i
\(983\) −3.68639 0.987766i −0.117578 0.0315048i 0.199550 0.979888i \(-0.436052\pi\)
−0.317128 + 0.948383i \(0.602719\pi\)
\(984\) 52.8125 + 61.9344i 1.68360 + 1.97440i
\(985\) −3.07962 + 0.825181i −0.0981247 + 0.0262924i
\(986\) −14.8753 + 9.84011i −0.473726 + 0.313373i
\(987\) 4.26539 + 9.15495i 0.135769 + 0.291405i
\(988\) −4.76230 + 11.2029i −0.151509 + 0.356411i
\(989\) 1.44926 + 0.190798i 0.0460836 + 0.00606703i
\(990\) −3.45981 + 3.00597i −0.109960 + 0.0955359i
\(991\) 3.35414 + 5.80955i 0.106548 + 0.184546i 0.914370 0.404881i \(-0.132687\pi\)
−0.807822 + 0.589427i \(0.799354\pi\)
\(992\) −10.8023 23.2455i −0.342974 0.738044i
\(993\) 9.63580 0.305783
\(994\) 6.75956 + 12.4671i 0.214400 + 0.395431i
\(995\) 0.236759 + 0.571586i 0.00750576 + 0.0181205i
\(996\) −39.9154 + 30.0455i −1.26477 + 0.952028i
\(997\) −1.92660 14.6340i −0.0610161 0.463463i −0.994491 0.104821i \(-0.966573\pi\)
0.933475 0.358642i \(-0.116760\pi\)
\(998\) −8.03308 4.00779i −0.254283 0.126864i
\(999\) 2.82978 0.758237i 0.0895302 0.0239896i
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.bd.a.37.12 240
4.3 odd 2 896.2.bh.a.625.6 240
7.4 even 3 inner 224.2.bd.a.165.10 yes 240
28.11 odd 6 896.2.bh.a.753.25 240
32.13 even 8 inner 224.2.bd.a.205.10 yes 240
32.19 odd 8 896.2.bh.a.401.25 240
224.109 even 24 inner 224.2.bd.a.109.12 yes 240
224.179 odd 24 896.2.bh.a.529.6 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.bd.a.37.12 240 1.1 even 1 trivial
224.2.bd.a.109.12 yes 240 224.109 even 24 inner
224.2.bd.a.165.10 yes 240 7.4 even 3 inner
224.2.bd.a.205.10 yes 240 32.13 even 8 inner
896.2.bh.a.401.25 240 32.19 odd 8
896.2.bh.a.529.6 240 224.179 odd 24
896.2.bh.a.625.6 240 4.3 odd 2
896.2.bh.a.753.25 240 28.11 odd 6