Properties

Label 930.2.bg.h.121.3
Level $930$
Weight $2$
Character 930.121
Analytic conductor $7.426$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(121,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (of order \(15\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 121.3
Character \(\chi\) \(=\) 930.121
Dual form 930.2.bg.h.661.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.744050 - 0.158153i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.744050 - 0.158153i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(3.69364 + 4.10220i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(2.55391 - 1.13707i) q^{13} +(0.508989 - 0.565290i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.97918 - 5.52994i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(-0.699202 - 0.311305i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.0795119 - 0.756505i) q^{21} +(5.39943 + 1.14768i) q^{22} +(-0.936159 - 2.88120i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.39780 - 2.42106i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.0795119 - 0.756505i) q^{28} +(-2.44952 + 1.77968i) q^{29} +1.00000 q^{30} +(3.60699 - 4.24142i) q^{31} -1.00000 q^{32} +(4.46582 - 3.24461i) q^{33} +(0.777824 - 7.40050i) q^{34} +(-0.235061 + 0.723442i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.95798 - 5.12337i) q^{37} +(-0.748647 + 0.159130i) q^{38} +(-0.863888 - 2.65877i) q^{39} +(0.978148 + 0.207912i) q^{40} +(0.266132 + 2.53207i) q^{41} +(-0.508989 - 0.565290i) q^{42} +(-3.68971 - 1.64277i) q^{43} +(5.04282 - 2.24521i) q^{44} +(0.669131 - 0.743145i) q^{45} +(-2.45090 - 1.78068i) q^{46} +(4.33714 + 3.15112i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(-5.86622 + 2.61181i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(-4.97918 - 5.52994i) q^{51} +(-0.292220 - 2.78029i) q^{52} +(0.893114 + 0.189837i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-5.39943 + 1.14768i) q^{55} +(-0.380336 - 0.658761i) q^{56} +(-0.382686 + 0.662831i) q^{57} +(-0.935635 + 2.87959i) q^{58} +(0.170064 - 1.61805i) q^{59} +(0.809017 - 0.587785i) q^{60} -3.26610 q^{61} +(0.425067 - 5.55151i) q^{62} -0.760672 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.292220 + 2.78029i) q^{65} +(1.70579 - 5.24988i) q^{66} +(-4.83750 + 8.37879i) q^{67} +(-3.72063 - 6.44432i) q^{68} +(-2.96327 + 0.629863i) q^{69} +(0.235061 + 0.723442i) q^{70} +(12.8644 + 2.73440i) q^{71} +(0.104528 + 0.994522i) q^{72} +(8.80644 + 9.78054i) q^{73} +(-5.40450 - 2.40624i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(-0.512134 + 0.568782i) q^{76} +(3.39702 + 2.46808i) q^{77} +(-2.26169 - 1.64321i) q^{78} +(0.935152 - 1.03859i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(1.70362 + 1.89206i) q^{82} +(-0.169591 - 1.61355i) q^{83} +(-0.744050 - 0.158153i) q^{84} +(2.29948 + 7.07706i) q^{85} +(-3.95064 + 0.839734i) q^{86} +(1.51389 + 2.62213i) q^{87} +(2.76003 - 4.78051i) q^{88} +(0.755228 - 2.32435i) q^{89} +(0.104528 - 0.994522i) q^{90} +(1.72040 - 1.24995i) q^{91} -3.02947 q^{92} +(-3.84115 - 4.03057i) q^{93} +5.36100 q^{94} +(0.619199 - 0.449874i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(-3.47976 + 10.7096i) q^{97} +(-3.21069 + 5.56108i) q^{98} +(-2.76003 - 4.78051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{8}{15}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i
\(3\) 0.104528 0.994522i 0.0603495 0.574187i
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 0.744050 0.158153i 0.281224 0.0597761i −0.0651401 0.997876i \(-0.520749\pi\)
0.346364 + 0.938100i \(0.387416\pi\)
\(8\) −0.309017 0.951057i −0.109254 0.336249i
\(9\) −0.978148 0.207912i −0.326049 0.0693039i
\(10\) 0.104528 + 0.994522i 0.0330548 + 0.314495i
\(11\) 3.69364 + 4.10220i 1.11367 + 1.23686i 0.968915 + 0.247393i \(0.0795737\pi\)
0.144758 + 0.989467i \(0.453760\pi\)
\(12\) −0.913545 0.406737i −0.263718 0.117415i
\(13\) 2.55391 1.13707i 0.708327 0.315367i −0.0207641 0.999784i \(-0.506610\pi\)
0.729091 + 0.684417i \(0.239943\pi\)
\(14\) 0.508989 0.565290i 0.136033 0.151080i
\(15\) 0.809017 + 0.587785i 0.208887 + 0.151765i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 4.97918 5.52994i 1.20763 1.34121i 0.283571 0.958951i \(-0.408481\pi\)
0.924057 0.382256i \(-0.124853\pi\)
\(18\) −0.913545 + 0.406737i −0.215325 + 0.0958687i
\(19\) −0.699202 0.311305i −0.160408 0.0714182i 0.324962 0.945727i \(-0.394648\pi\)
−0.485370 + 0.874309i \(0.661315\pi\)
\(20\) 0.669131 + 0.743145i 0.149622 + 0.166172i
\(21\) −0.0795119 0.756505i −0.0173509 0.165083i
\(22\) 5.39943 + 1.14768i 1.15116 + 0.244687i
\(23\) −0.936159 2.88120i −0.195203 0.600772i −0.999974 0.00718727i \(-0.997712\pi\)
0.804772 0.593585i \(-0.202288\pi\)
\(24\) −0.978148 + 0.207912i −0.199664 + 0.0424398i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.39780 2.42106i 0.274131 0.474809i
\(27\) −0.309017 + 0.951057i −0.0594703 + 0.183031i
\(28\) 0.0795119 0.756505i 0.0150263 0.142966i
\(29\) −2.44952 + 1.77968i −0.454865 + 0.330479i −0.791514 0.611152i \(-0.790707\pi\)
0.336649 + 0.941630i \(0.390707\pi\)
\(30\) 1.00000 0.182574
\(31\) 3.60699 4.24142i 0.647834 0.761782i
\(32\) −1.00000 −0.176777
\(33\) 4.46582 3.24461i 0.777399 0.564813i
\(34\) 0.777824 7.40050i 0.133396 1.26918i
\(35\) −0.235061 + 0.723442i −0.0397325 + 0.122284i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −2.95798 5.12337i −0.486289 0.842277i 0.513587 0.858038i \(-0.328316\pi\)
−0.999876 + 0.0157606i \(0.994983\pi\)
\(38\) −0.748647 + 0.159130i −0.121447 + 0.0258143i
\(39\) −0.863888 2.65877i −0.138333 0.425745i
\(40\) 0.978148 + 0.207912i 0.154659 + 0.0328737i
\(41\) 0.266132 + 2.53207i 0.0415628 + 0.395444i 0.995451 + 0.0952800i \(0.0303746\pi\)
−0.953888 + 0.300164i \(0.902959\pi\)
\(42\) −0.508989 0.565290i −0.0785387 0.0872261i
\(43\) −3.68971 1.64277i −0.562676 0.250520i 0.105630 0.994405i \(-0.466314\pi\)
−0.668307 + 0.743886i \(0.732981\pi\)
\(44\) 5.04282 2.24521i 0.760234 0.338478i
\(45\) 0.669131 0.743145i 0.0997481 0.110781i
\(46\) −2.45090 1.78068i −0.361365 0.262547i
\(47\) 4.33714 + 3.15112i 0.632637 + 0.459638i 0.857313 0.514796i \(-0.172132\pi\)
−0.224676 + 0.974434i \(0.572132\pi\)
\(48\) −0.669131 + 0.743145i −0.0965807 + 0.107264i
\(49\) −5.86622 + 2.61181i −0.838032 + 0.373116i
\(50\) −0.913545 0.406737i −0.129195 0.0575212i
\(51\) −4.97918 5.52994i −0.697224 0.774346i
\(52\) −0.292220 2.78029i −0.0405236 0.385556i
\(53\) 0.893114 + 0.189837i 0.122679 + 0.0260762i 0.268842 0.963184i \(-0.413359\pi\)
−0.146163 + 0.989261i \(0.546692\pi\)
\(54\) 0.309017 + 0.951057i 0.0420519 + 0.129422i
\(55\) −5.39943 + 1.14768i −0.728059 + 0.154754i
\(56\) −0.380336 0.658761i −0.0508245 0.0880307i
\(57\) −0.382686 + 0.662831i −0.0506880 + 0.0877942i
\(58\) −0.935635 + 2.87959i −0.122855 + 0.378108i
\(59\) 0.170064 1.61805i 0.0221404 0.210652i −0.977859 0.209267i \(-0.932892\pi\)
0.999999 0.00138549i \(-0.000441016\pi\)
\(60\) 0.809017 0.587785i 0.104444 0.0758827i
\(61\) −3.26610 −0.418181 −0.209091 0.977896i \(-0.567050\pi\)
−0.209091 + 0.977896i \(0.567050\pi\)
\(62\) 0.425067 5.55151i 0.0539836 0.705043i
\(63\) −0.760672 −0.0958357
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −0.292220 + 2.78029i −0.0362454 + 0.344852i
\(66\) 1.70579 5.24988i 0.209968 0.646216i
\(67\) −4.83750 + 8.37879i −0.590995 + 1.02363i 0.403104 + 0.915154i \(0.367931\pi\)
−0.994099 + 0.108478i \(0.965402\pi\)
\(68\) −3.72063 6.44432i −0.451193 0.781489i
\(69\) −2.96327 + 0.629863i −0.356736 + 0.0758266i
\(70\) 0.235061 + 0.723442i 0.0280951 + 0.0864679i
\(71\) 12.8644 + 2.73440i 1.52672 + 0.324514i 0.893359 0.449344i \(-0.148342\pi\)
0.633360 + 0.773858i \(0.281675\pi\)
\(72\) 0.104528 + 0.994522i 0.0123188 + 0.117206i
\(73\) 8.80644 + 9.78054i 1.03072 + 1.14473i 0.989346 + 0.145581i \(0.0465052\pi\)
0.0413690 + 0.999144i \(0.486828\pi\)
\(74\) −5.40450 2.40624i −0.628260 0.279719i
\(75\) −0.913545 + 0.406737i −0.105487 + 0.0469659i
\(76\) −0.512134 + 0.568782i −0.0587458 + 0.0652438i
\(77\) 3.39702 + 2.46808i 0.387127 + 0.281264i
\(78\) −2.26169 1.64321i −0.256086 0.186057i
\(79\) 0.935152 1.03859i 0.105213 0.116851i −0.688238 0.725485i \(-0.741616\pi\)
0.793451 + 0.608634i \(0.208282\pi\)
\(80\) 0.913545 0.406737i 0.102137 0.0454745i
\(81\) 0.913545 + 0.406737i 0.101505 + 0.0451930i
\(82\) 1.70362 + 1.89206i 0.188134 + 0.208943i
\(83\) −0.169591 1.61355i −0.0186150 0.177110i 0.981264 0.192668i \(-0.0617142\pi\)
−0.999879 + 0.0155581i \(0.995047\pi\)
\(84\) −0.744050 0.158153i −0.0811825 0.0172559i
\(85\) 2.29948 + 7.07706i 0.249413 + 0.767615i
\(86\) −3.95064 + 0.839734i −0.426008 + 0.0905508i
\(87\) 1.51389 + 2.62213i 0.162306 + 0.281122i
\(88\) 2.76003 4.78051i 0.294220 0.509604i
\(89\) 0.755228 2.32435i 0.0800540 0.246381i −0.903017 0.429604i \(-0.858653\pi\)
0.983071 + 0.183223i \(0.0586531\pi\)
\(90\) 0.104528 0.994522i 0.0110183 0.104832i
\(91\) 1.72040 1.24995i 0.180347 0.131030i
\(92\) −3.02947 −0.315845
\(93\) −3.84115 4.03057i −0.398309 0.417951i
\(94\) 5.36100 0.552945
\(95\) 0.619199 0.449874i 0.0635284 0.0461561i
\(96\) −0.104528 + 0.994522i −0.0106684 + 0.101503i
\(97\) −3.47976 + 10.7096i −0.353316 + 1.08740i 0.603663 + 0.797239i \(0.293707\pi\)
−0.956979 + 0.290156i \(0.906293\pi\)
\(98\) −3.21069 + 5.56108i −0.324329 + 0.561754i
\(99\) −2.76003 4.78051i −0.277393 0.480459i
\(100\) −0.978148 + 0.207912i −0.0978148 + 0.0207912i
\(101\) 2.73335 + 8.41237i 0.271978 + 0.837063i 0.990003 + 0.141045i \(0.0450463\pi\)
−0.718025 + 0.696017i \(0.754954\pi\)
\(102\) −7.27865 1.54713i −0.720694 0.153188i
\(103\) −1.02175 9.72126i −0.100676 0.957864i −0.921944 0.387323i \(-0.873400\pi\)
0.821269 0.570542i \(-0.193267\pi\)
\(104\) −1.87062 2.07754i −0.183430 0.203719i
\(105\) 0.694909 + 0.309393i 0.0678161 + 0.0301937i
\(106\) 0.834128 0.371378i 0.0810177 0.0360714i
\(107\) 3.46544 3.84876i 0.335016 0.372073i −0.551974 0.833861i \(-0.686125\pi\)
0.886990 + 0.461788i \(0.152792\pi\)
\(108\) 0.809017 + 0.587785i 0.0778477 + 0.0565597i
\(109\) −7.00225 5.08743i −0.670694 0.487288i 0.199563 0.979885i \(-0.436048\pi\)
−0.870257 + 0.492597i \(0.836048\pi\)
\(110\) −3.69364 + 4.10220i −0.352174 + 0.391129i
\(111\) −5.40450 + 2.40624i −0.512972 + 0.228390i
\(112\) −0.694909 0.309393i −0.0656627 0.0292349i
\(113\) 0.0238232 + 0.0264584i 0.00224110 + 0.00248900i 0.744264 0.667885i \(-0.232800\pi\)
−0.742023 + 0.670374i \(0.766134\pi\)
\(114\) 0.0800031 + 0.761179i 0.00749298 + 0.0712909i
\(115\) 2.96327 + 0.629863i 0.276327 + 0.0587350i
\(116\) 0.935635 + 2.87959i 0.0868715 + 0.267363i
\(117\) −2.73451 + 0.581238i −0.252806 + 0.0537355i
\(118\) −0.813481 1.40899i −0.0748870 0.129708i
\(119\) 2.83018 4.90202i 0.259442 0.449367i
\(120\) 0.309017 0.951057i 0.0282093 0.0868192i
\(121\) −2.03527 + 19.3643i −0.185025 + 1.76039i
\(122\) −2.64233 + 1.91976i −0.239225 + 0.173807i
\(123\) 2.54602 0.229567
\(124\) −2.91921 4.74112i −0.262153 0.425765i
\(125\) 1.00000 0.0894427
\(126\) −0.615397 + 0.447112i −0.0548239 + 0.0398319i
\(127\) 1.04040 9.89879i 0.0923210 0.878375i −0.846133 0.532972i \(-0.821075\pi\)
0.938454 0.345404i \(-0.112258\pi\)
\(128\) −0.309017 + 0.951057i −0.0273135 + 0.0840623i
\(129\) −2.01945 + 3.49779i −0.177802 + 0.307963i
\(130\) 1.39780 + 2.42106i 0.122595 + 0.212341i
\(131\) −5.42433 + 1.15298i −0.473926 + 0.100736i −0.438681 0.898643i \(-0.644554\pi\)
−0.0352445 + 0.999379i \(0.511221\pi\)
\(132\) −1.70579 5.24988i −0.148470 0.456944i
\(133\) −0.569475 0.121046i −0.0493797 0.0104960i
\(134\) 1.01131 + 9.62200i 0.0873641 + 0.831214i
\(135\) −0.669131 0.743145i −0.0575896 0.0639597i
\(136\) −6.79793 3.02663i −0.582918 0.259532i
\(137\) −4.83076 + 2.15080i −0.412720 + 0.183755i −0.602584 0.798056i \(-0.705862\pi\)
0.189864 + 0.981810i \(0.439195\pi\)
\(138\) −2.02711 + 2.25134i −0.172559 + 0.191647i
\(139\) −7.50955 5.45601i −0.636951 0.462772i 0.221850 0.975081i \(-0.428790\pi\)
−0.858802 + 0.512308i \(0.828790\pi\)
\(140\) 0.615397 + 0.447112i 0.0520105 + 0.0377878i
\(141\) 3.58721 3.98400i 0.302098 0.335514i
\(142\) 12.0147 5.34930i 1.00825 0.448903i
\(143\) 14.0977 + 6.27670i 1.17891 + 0.524884i
\(144\) 0.669131 + 0.743145i 0.0557609 + 0.0619287i
\(145\) −0.316489 3.01119i −0.0262830 0.250066i
\(146\) 12.8734 + 2.73633i 1.06541 + 0.226460i
\(147\) 1.98431 + 6.10709i 0.163664 + 0.503705i
\(148\) −5.78668 + 1.23000i −0.475662 + 0.101105i
\(149\) −3.95947 6.85801i −0.324373 0.561830i 0.657012 0.753880i \(-0.271820\pi\)
−0.981385 + 0.192050i \(0.938487\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −4.12911 + 12.7081i −0.336022 + 1.03417i 0.630195 + 0.776437i \(0.282975\pi\)
−0.966217 + 0.257732i \(0.917025\pi\)
\(152\) −0.0800031 + 0.761179i −0.00648911 + 0.0617398i
\(153\) −6.02011 + 4.37387i −0.486697 + 0.353606i
\(154\) 4.19895 0.338361
\(155\) 1.86969 + 5.24445i 0.150177 + 0.421244i
\(156\) −2.79560 −0.223827
\(157\) −0.830694 + 0.603534i −0.0662966 + 0.0481673i −0.620440 0.784254i \(-0.713046\pi\)
0.554143 + 0.832421i \(0.313046\pi\)
\(158\) 0.146085 1.38991i 0.0116219 0.110575i
\(159\) 0.282153 0.868378i 0.0223762 0.0688669i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) −1.15222 1.99570i −0.0908075 0.157283i
\(162\) 0.978148 0.207912i 0.0768505 0.0163351i
\(163\) 0.669481 + 2.06045i 0.0524378 + 0.161387i 0.973846 0.227209i \(-0.0729601\pi\)
−0.921408 + 0.388596i \(0.872960\pi\)
\(164\) 2.49039 + 0.529348i 0.194466 + 0.0413351i
\(165\) 0.577003 + 5.48981i 0.0449196 + 0.427381i
\(166\) −1.08562 1.20571i −0.0842608 0.0935810i
\(167\) 18.5336 + 8.25171i 1.43418 + 0.638536i 0.969085 0.246727i \(-0.0793549\pi\)
0.465091 + 0.885263i \(0.346022\pi\)
\(168\) −0.694909 + 0.309393i −0.0536134 + 0.0238702i
\(169\) −3.46919 + 3.85292i −0.266861 + 0.296379i
\(170\) 6.02011 + 4.37387i 0.461721 + 0.335460i
\(171\) 0.619199 + 0.449874i 0.0473513 + 0.0344027i
\(172\) −2.70255 + 3.00148i −0.206067 + 0.228861i
\(173\) −5.46659 + 2.43388i −0.415617 + 0.185045i −0.603882 0.797074i \(-0.706380\pi\)
0.188265 + 0.982118i \(0.439714\pi\)
\(174\) 2.76601 + 1.23151i 0.209691 + 0.0933604i
\(175\) −0.508989 0.565290i −0.0384760 0.0427319i
\(176\) −0.577003 5.48981i −0.0434932 0.413810i
\(177\) −1.59141 0.338265i −0.119618 0.0254255i
\(178\) −0.755228 2.32435i −0.0566067 0.174218i
\(179\) −5.08327 + 1.08048i −0.379941 + 0.0807591i −0.393924 0.919143i \(-0.628883\pi\)
0.0139821 + 0.999902i \(0.495549\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −13.3456 + 23.1152i −0.991970 + 1.71814i −0.386454 + 0.922309i \(0.626300\pi\)
−0.605516 + 0.795833i \(0.707033\pi\)
\(182\) 0.657136 2.02246i 0.0487101 0.149914i
\(183\) −0.341400 + 3.24821i −0.0252370 + 0.240114i
\(184\) −2.45090 + 1.78068i −0.180682 + 0.131273i
\(185\) 5.91596 0.434950
\(186\) −5.47667 1.00303i −0.401569 0.0735457i
\(187\) 41.0762 3.00379
\(188\) 4.33714 3.15112i 0.316319 0.229819i
\(189\) −0.0795119 + 0.756505i −0.00578364 + 0.0550276i
\(190\) 0.236513 0.727912i 0.0171584 0.0528083i
\(191\) 6.51109 11.2775i 0.471126 0.816014i −0.528329 0.849040i \(-0.677181\pi\)
0.999454 + 0.0330260i \(0.0105144\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −11.1000 + 2.35937i −0.798993 + 0.169831i −0.589277 0.807931i \(-0.700587\pi\)
−0.209716 + 0.977762i \(0.567254\pi\)
\(194\) 3.47976 + 10.7096i 0.249832 + 0.768905i
\(195\) 2.73451 + 0.581238i 0.195822 + 0.0416233i
\(196\) 0.671217 + 6.38620i 0.0479441 + 0.456157i
\(197\) 15.3969 + 17.1000i 1.09699 + 1.21833i 0.974151 + 0.225899i \(0.0725318\pi\)
0.122835 + 0.992427i \(0.460802\pi\)
\(198\) −5.04282 2.24521i −0.358378 0.159560i
\(199\) −4.26288 + 1.89796i −0.302188 + 0.134543i −0.552229 0.833693i \(-0.686223\pi\)
0.250041 + 0.968235i \(0.419556\pi\)
\(200\) −0.669131 + 0.743145i −0.0473147 + 0.0525483i
\(201\) 7.82724 + 5.68682i 0.552091 + 0.401117i
\(202\) 7.15599 + 5.19913i 0.503494 + 0.365810i
\(203\) −1.54111 + 1.71157i −0.108164 + 0.120129i
\(204\) −6.79793 + 3.02663i −0.475951 + 0.211907i
\(205\) −2.32591 1.03556i −0.162448 0.0723267i
\(206\) −6.54062 7.26410i −0.455707 0.506114i
\(207\) 0.316666 + 3.01288i 0.0220098 + 0.209410i
\(208\) −2.73451 0.581238i −0.189604 0.0403016i
\(209\) −1.30556 4.01811i −0.0903077 0.277939i
\(210\) 0.744050 0.158153i 0.0513443 0.0109136i
\(211\) −10.6297 18.4112i −0.731781 1.26748i −0.956121 0.292971i \(-0.905356\pi\)
0.224341 0.974511i \(-0.427977\pi\)
\(212\) 0.456534 0.790739i 0.0313549 0.0543082i
\(213\) 4.06412 12.5081i 0.278469 0.857038i
\(214\) 0.541354 5.15064i 0.0370062 0.352091i
\(215\) 3.26754 2.37400i 0.222844 0.161906i
\(216\) 1.00000 0.0680414
\(217\) 2.01298 3.72628i 0.136650 0.252957i
\(218\) −8.65526 −0.586208
\(219\) 10.6475 7.73585i 0.719490 0.522740i
\(220\) −0.577003 + 5.48981i −0.0389015 + 0.370123i
\(221\) 6.42842 19.7846i 0.432422 1.33086i
\(222\) −2.95798 + 5.12337i −0.198527 + 0.343858i
\(223\) 2.60298 + 4.50850i 0.174309 + 0.301911i 0.939922 0.341390i \(-0.110898\pi\)
−0.765613 + 0.643301i \(0.777564\pi\)
\(224\) −0.744050 + 0.158153i −0.0497139 + 0.0105670i
\(225\) 0.309017 + 0.951057i 0.0206011 + 0.0634038i
\(226\) 0.0348253 + 0.00740234i 0.00231654 + 0.000492396i
\(227\) 3.06955 + 29.2048i 0.203733 + 1.93839i 0.324874 + 0.945757i \(0.394678\pi\)
−0.121140 + 0.992635i \(0.538655\pi\)
\(228\) 0.512134 + 0.568782i 0.0339169 + 0.0376685i
\(229\) −23.2961 10.3721i −1.53945 0.685407i −0.550660 0.834730i \(-0.685624\pi\)
−0.988788 + 0.149323i \(0.952290\pi\)
\(230\) 2.76756 1.23220i 0.182488 0.0812487i
\(231\) 2.80965 3.12043i 0.184861 0.205309i
\(232\) 2.44952 + 1.77968i 0.160819 + 0.116842i
\(233\) −15.0451 10.9309i −0.985635 0.716106i −0.0266745 0.999644i \(-0.508492\pi\)
−0.958961 + 0.283538i \(0.908492\pi\)
\(234\) −1.87062 + 2.07754i −0.122286 + 0.135813i
\(235\) −4.89752 + 2.18052i −0.319479 + 0.142241i
\(236\) −1.48630 0.661745i −0.0967502 0.0430760i
\(237\) −0.935152 1.03859i −0.0607447 0.0674638i
\(238\) −0.591669 5.62935i −0.0383522 0.364897i
\(239\) 1.97912 + 0.420675i 0.128019 + 0.0272112i 0.271475 0.962445i \(-0.412488\pi\)
−0.143457 + 0.989657i \(0.545822\pi\)
\(240\) −0.309017 0.951057i −0.0199470 0.0613904i
\(241\) −27.7905 + 5.90705i −1.79014 + 0.380506i −0.978922 0.204235i \(-0.934529\pi\)
−0.811220 + 0.584741i \(0.801196\pi\)
\(242\) 9.73550 + 16.8624i 0.625821 + 1.08395i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −1.00928 + 3.10624i −0.0646125 + 0.198857i
\(245\) 0.671217 6.38620i 0.0428825 0.407999i
\(246\) 2.05978 1.49651i 0.131326 0.0954143i
\(247\) −2.13967 −0.136144
\(248\) −5.14845 2.11978i −0.326927 0.134606i
\(249\) −1.62244 −0.102818
\(250\) 0.809017 0.587785i 0.0511667 0.0371748i
\(251\) −2.32950 + 22.1637i −0.147037 + 1.39896i 0.633449 + 0.773785i \(0.281639\pi\)
−0.780485 + 0.625174i \(0.785028\pi\)
\(252\) −0.235061 + 0.723442i −0.0148074 + 0.0455726i
\(253\) 8.36143 14.4824i 0.525679 0.910502i
\(254\) −4.97666 8.61982i −0.312263 0.540856i
\(255\) 7.27865 1.54713i 0.455807 0.0968848i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −23.1964 4.93055i −1.44695 0.307559i −0.583550 0.812077i \(-0.698337\pi\)
−0.863401 + 0.504518i \(0.831670\pi\)
\(258\) 0.422180 + 4.01677i 0.0262838 + 0.250073i
\(259\) −3.01116 3.34423i −0.187104 0.207800i
\(260\) 2.55391 + 1.13707i 0.158387 + 0.0705183i
\(261\) 2.76601 1.23151i 0.171212 0.0762284i
\(262\) −3.71067 + 4.12112i −0.229246 + 0.254604i
\(263\) 6.69323 + 4.86292i 0.412722 + 0.299860i 0.774703 0.632325i \(-0.217899\pi\)
−0.361981 + 0.932186i \(0.617899\pi\)
\(264\) −4.46582 3.24461i −0.274852 0.199692i
\(265\) −0.610961 + 0.678541i −0.0375310 + 0.0416824i
\(266\) −0.531863 + 0.236801i −0.0326106 + 0.0145192i
\(267\) −2.23268 0.994052i −0.136638 0.0608350i
\(268\) 6.47384 + 7.18992i 0.395453 + 0.439195i
\(269\) 3.27551 + 31.1644i 0.199712 + 1.90013i 0.393883 + 0.919161i \(0.371132\pi\)
−0.194171 + 0.980968i \(0.562202\pi\)
\(270\) −0.978148 0.207912i −0.0595282 0.0126531i
\(271\) 0.945783 + 2.91082i 0.0574522 + 0.176820i 0.975664 0.219269i \(-0.0703672\pi\)
−0.918212 + 0.396089i \(0.870367\pi\)
\(272\) −7.27865 + 1.54713i −0.441333 + 0.0938083i
\(273\) −1.06327 1.84163i −0.0643519 0.111461i
\(274\) −2.64397 + 4.57948i −0.159728 + 0.276657i
\(275\) 1.70579 5.24988i 0.102863 0.316580i
\(276\) −0.316666 + 3.01288i −0.0190611 + 0.181354i
\(277\) −7.08603 + 5.14830i −0.425758 + 0.309332i −0.779951 0.625841i \(-0.784756\pi\)
0.354192 + 0.935173i \(0.384756\pi\)
\(278\) −9.28231 −0.556716
\(279\) −4.41000 + 3.39880i −0.264020 + 0.203481i
\(280\) 0.760672 0.0454589
\(281\) 11.7868 8.56361i 0.703142 0.510862i −0.177812 0.984064i \(-0.556902\pi\)
0.880954 + 0.473202i \(0.156902\pi\)
\(282\) 0.560378 5.33164i 0.0333700 0.317494i
\(283\) 4.12774 12.7039i 0.245368 0.755167i −0.750207 0.661203i \(-0.770046\pi\)
0.995576 0.0939637i \(-0.0299537\pi\)
\(284\) 6.57588 11.3898i 0.390207 0.675858i
\(285\) −0.382686 0.662831i −0.0226684 0.0392627i
\(286\) 15.0946 3.20846i 0.892565 0.189721i
\(287\) 0.598470 + 1.84190i 0.0353265 + 0.108724i
\(288\) 0.978148 + 0.207912i 0.0576379 + 0.0122513i
\(289\) −4.01101 38.1622i −0.235942 2.24484i
\(290\) −2.02598 2.25008i −0.118970 0.132129i
\(291\) 10.2872 + 4.58016i 0.603046 + 0.268493i
\(292\) 12.0232 5.35307i 0.703603 0.313264i
\(293\) −3.84791 + 4.27353i −0.224797 + 0.249663i −0.844984 0.534792i \(-0.820390\pi\)
0.620187 + 0.784454i \(0.287057\pi\)
\(294\) 5.19500 + 3.77439i 0.302979 + 0.220127i
\(295\) 1.31624 + 0.956305i 0.0766345 + 0.0556782i
\(296\) −3.95855 + 4.39641i −0.230086 + 0.255536i
\(297\) −5.04282 + 2.24521i −0.292614 + 0.130280i
\(298\) −7.23432 3.22093i −0.419073 0.186583i
\(299\) −5.66700 6.29384i −0.327731 0.363982i
\(300\) 0.104528 + 0.994522i 0.00603495 + 0.0574187i
\(301\) −3.00514 0.638762i −0.173213 0.0368176i
\(302\) 4.12911 + 12.7081i 0.237603 + 0.731268i
\(303\) 8.65200 1.83904i 0.497045 0.105650i
\(304\) 0.382686 + 0.662831i 0.0219485 + 0.0380160i
\(305\) 1.63305 2.82852i 0.0935081 0.161961i
\(306\) −2.29948 + 7.07706i −0.131452 + 0.404569i
\(307\) −1.29353 + 12.3071i −0.0738255 + 0.702402i 0.893534 + 0.448995i \(0.148218\pi\)
−0.967360 + 0.253407i \(0.918449\pi\)
\(308\) 3.39702 2.46808i 0.193563 0.140632i
\(309\) −9.77481 −0.556069
\(310\) 4.59522 + 3.14388i 0.260991 + 0.178560i
\(311\) −3.44812 −0.195525 −0.0977625 0.995210i \(-0.531169\pi\)
−0.0977625 + 0.995210i \(0.531169\pi\)
\(312\) −2.26169 + 1.64321i −0.128043 + 0.0930286i
\(313\) −1.09204 + 10.3900i −0.0617256 + 0.587280i 0.919321 + 0.393508i \(0.128739\pi\)
−0.981047 + 0.193771i \(0.937928\pi\)
\(314\) −0.317297 + 0.976539i −0.0179061 + 0.0551093i
\(315\) 0.380336 0.658761i 0.0214295 0.0371170i
\(316\) −0.698781 1.21032i −0.0393095 0.0680861i
\(317\) 0.164567 0.0349798i 0.00924301 0.00196466i −0.203288 0.979119i \(-0.565163\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(318\) −0.282153 0.868378i −0.0158224 0.0486962i
\(319\) −16.3483 3.47493i −0.915327 0.194559i
\(320\) −0.104528 0.994522i −0.00584332 0.0555955i
\(321\) −3.46544 3.84876i −0.193422 0.214817i
\(322\) −2.10521 0.937299i −0.117319 0.0522336i
\(323\) −5.20295 + 2.31650i −0.289500 + 0.128894i
\(324\) 0.669131 0.743145i 0.0371739 0.0412858i
\(325\) −2.26169 1.64321i −0.125456 0.0911490i
\(326\) 1.75272 + 1.27343i 0.0970744 + 0.0705287i
\(327\) −5.79150 + 6.43211i −0.320271 + 0.355697i
\(328\) 2.32591 1.03556i 0.128427 0.0571793i
\(329\) 3.72541 + 1.65866i 0.205388 + 0.0914448i
\(330\) 3.69364 + 4.10220i 0.203328 + 0.225819i
\(331\) 1.47117 + 13.9973i 0.0808630 + 0.769360i 0.957544 + 0.288288i \(0.0930859\pi\)
−0.876681 + 0.481072i \(0.840247\pi\)
\(332\) −1.58699 0.337324i −0.0870971 0.0185131i
\(333\) 1.82813 + 5.62641i 0.100181 + 0.308325i
\(334\) 19.8443 4.21803i 1.08583 0.230800i
\(335\) −4.83750 8.37879i −0.264301 0.457782i
\(336\) −0.380336 + 0.658761i −0.0207490 + 0.0359384i
\(337\) 5.54721 17.0725i 0.302176 0.930001i −0.678540 0.734563i \(-0.737387\pi\)
0.980716 0.195438i \(-0.0626128\pi\)
\(338\) −0.541940 + 5.15622i −0.0294777 + 0.280461i
\(339\) 0.0288037 0.0209271i 0.00156440 0.00113660i
\(340\) 7.44126 0.403559
\(341\) 30.7221 0.869700i 1.66369 0.0470969i
\(342\) 0.765372 0.0413866
\(343\) −8.25947 + 6.00086i −0.445970 + 0.324016i
\(344\) −0.422180 + 4.01677i −0.0227624 + 0.216570i
\(345\) 0.936159 2.88120i 0.0504011 0.155119i
\(346\) −2.99197 + 5.18224i −0.160849 + 0.278599i
\(347\) −0.0382933 0.0663259i −0.00205569 0.00356056i 0.864996 0.501779i \(-0.167321\pi\)
−0.867051 + 0.498219i \(0.833988\pi\)
\(348\) 2.96161 0.629510i 0.158759 0.0337453i
\(349\) −7.05719 21.7198i −0.377763 1.16263i −0.941596 0.336746i \(-0.890674\pi\)
0.563833 0.825889i \(-0.309326\pi\)
\(350\) −0.744050 0.158153i −0.0397711 0.00845361i
\(351\) 0.292220 + 2.78029i 0.0155975 + 0.148401i
\(352\) −3.69364 4.10220i −0.196872 0.218648i
\(353\) −15.3048 6.81413i −0.814592 0.362680i −0.0432208 0.999066i \(-0.513762\pi\)
−0.771371 + 0.636386i \(0.780429\pi\)
\(354\) −1.48630 + 0.661745i −0.0789962 + 0.0351714i
\(355\) −8.80024 + 9.77366i −0.467068 + 0.518732i
\(356\) −1.97721 1.43653i −0.104792 0.0761359i
\(357\) −4.57933 3.32708i −0.242364 0.176088i
\(358\) −3.47736 + 3.86200i −0.183784 + 0.204113i
\(359\) −25.1921 + 11.2163i −1.32959 + 0.591972i −0.943770 0.330602i \(-0.892748\pi\)
−0.385820 + 0.922574i \(0.626082\pi\)
\(360\) −0.913545 0.406737i −0.0481481 0.0214369i
\(361\) −12.3215 13.6844i −0.648500 0.720233i
\(362\) 2.78999 + 26.5450i 0.146638 + 1.39517i
\(363\) 19.0455 + 4.04825i 0.999630 + 0.212478i
\(364\) −0.657136 2.02246i −0.0344433 0.106005i
\(365\) −12.8734 + 2.73633i −0.673825 + 0.143226i
\(366\) 1.63305 + 2.82852i 0.0853608 + 0.147849i
\(367\) 13.1796 22.8278i 0.687971 1.19160i −0.284522 0.958669i \(-0.591835\pi\)
0.972493 0.232931i \(-0.0748317\pi\)
\(368\) −0.936159 + 2.88120i −0.0488007 + 0.150193i
\(369\) 0.266132 2.53207i 0.0138543 0.131815i
\(370\) 4.78611 3.47731i 0.248818 0.180777i
\(371\) 0.694545 0.0360590
\(372\) −5.02029 + 2.40764i −0.260290 + 0.124830i
\(373\) 26.4502 1.36954 0.684769 0.728760i \(-0.259903\pi\)
0.684769 + 0.728760i \(0.259903\pi\)
\(374\) 33.2313 24.1440i 1.71835 1.24846i
\(375\) 0.104528 0.994522i 0.00539783 0.0513569i
\(376\) 1.65664 5.09862i 0.0854348 0.262941i
\(377\) −4.23223 + 7.33043i −0.217971 + 0.377536i
\(378\) 0.380336 + 0.658761i 0.0195624 + 0.0338830i
\(379\) 33.1679 7.05006i 1.70372 0.362137i 0.749677 0.661804i \(-0.230209\pi\)
0.954044 + 0.299667i \(0.0968754\pi\)
\(380\) −0.236513 0.727912i −0.0121329 0.0373411i
\(381\) −9.73581 2.06941i −0.498781 0.106019i
\(382\) −1.36119 12.9508i −0.0696445 0.662623i
\(383\) 2.18808 + 2.43011i 0.111806 + 0.124173i 0.796450 0.604705i \(-0.206709\pi\)
−0.684644 + 0.728878i \(0.740042\pi\)
\(384\) 0.913545 + 0.406737i 0.0466192 + 0.0207562i
\(385\) −3.83593 + 1.70787i −0.195497 + 0.0870410i
\(386\) −7.59326 + 8.43316i −0.386487 + 0.429237i
\(387\) 3.26754 + 2.37400i 0.166098 + 0.120677i
\(388\) 9.11013 + 6.61890i 0.462497 + 0.336024i
\(389\) −4.29945 + 4.77502i −0.217991 + 0.242103i −0.842215 0.539142i \(-0.818749\pi\)
0.624224 + 0.781245i \(0.285415\pi\)
\(390\) 2.55391 1.13707i 0.129322 0.0575779i
\(391\) −20.5942 9.16911i −1.04149 0.463702i
\(392\) 4.29674 + 4.77201i 0.217018 + 0.241023i
\(393\) 0.579664 + 5.51513i 0.0292402 + 0.278202i
\(394\) 22.5075 + 4.78412i 1.13391 + 0.241020i
\(395\) 0.431871 + 1.32916i 0.0217298 + 0.0668774i
\(396\) −5.39943 + 1.14768i −0.271331 + 0.0576733i
\(397\) −7.01802 12.1556i −0.352224 0.610070i 0.634415 0.772993i \(-0.281241\pi\)
−0.986639 + 0.162923i \(0.947908\pi\)
\(398\) −2.33315 + 4.04114i −0.116950 + 0.202564i
\(399\) −0.179909 + 0.553702i −0.00900670 + 0.0277198i
\(400\) −0.104528 + 0.994522i −0.00522642 + 0.0497261i
\(401\) 32.2517 23.4322i 1.61057 1.17015i 0.748895 0.662688i \(-0.230585\pi\)
0.861675 0.507460i \(-0.169415\pi\)
\(402\) 9.67500 0.482545
\(403\) 4.38910 14.9336i 0.218637 0.743896i
\(404\) 8.84529 0.440070
\(405\) −0.809017 + 0.587785i −0.0402004 + 0.0292073i
\(406\) −0.240744 + 2.29053i −0.0119479 + 0.113677i
\(407\) 10.0914 31.0581i 0.500211 1.53949i
\(408\) −3.72063 + 6.44432i −0.184199 + 0.319042i
\(409\) 12.4786 + 21.6136i 0.617028 + 1.06872i 0.990025 + 0.140891i \(0.0449968\pi\)
−0.372997 + 0.927833i \(0.621670\pi\)
\(410\) −2.49039 + 0.529348i −0.122991 + 0.0261426i
\(411\) 1.63406 + 5.02912i 0.0806023 + 0.248068i
\(412\) −9.56120 2.03230i −0.471047 0.100124i
\(413\) −0.129363 1.23081i −0.00636553 0.0605640i
\(414\) 2.02711 + 2.25134i 0.0996272 + 0.110647i
\(415\) 1.48217 + 0.659906i 0.0727570 + 0.0323935i
\(416\) −2.55391 + 1.13707i −0.125216 + 0.0557496i
\(417\) −6.21108 + 6.89810i −0.304158 + 0.337801i
\(418\) −3.41801 2.48333i −0.167180 0.121464i
\(419\) −18.0697 13.1284i −0.882765 0.641366i 0.0512167 0.998688i \(-0.483690\pi\)
−0.933981 + 0.357321i \(0.883690\pi\)
\(420\) 0.508989 0.565290i 0.0248361 0.0275833i
\(421\) 7.50275 3.34044i 0.365662 0.162803i −0.215677 0.976465i \(-0.569196\pi\)
0.581339 + 0.813662i \(0.302529\pi\)
\(422\) −19.4215 8.64700i −0.945423 0.420929i
\(423\) −3.58721 3.98400i −0.174416 0.193709i
\(424\) −0.0954415 0.908065i −0.00463505 0.0440995i
\(425\) −7.27865 1.54713i −0.353067 0.0750466i
\(426\) −4.06412 12.5081i −0.196907 0.606018i
\(427\) −2.43014 + 0.516542i −0.117603 + 0.0249972i
\(428\) −2.58951 4.48516i −0.125168 0.216798i
\(429\) 7.71593 13.3644i 0.372529 0.645239i
\(430\) 1.24809 3.84122i 0.0601881 0.185240i
\(431\) −0.864508 + 8.22524i −0.0416419 + 0.396196i 0.953772 + 0.300532i \(0.0971642\pi\)
−0.995414 + 0.0956642i \(0.969503\pi\)
\(432\) 0.809017 0.587785i 0.0389238 0.0282798i
\(433\) −15.6819 −0.753624 −0.376812 0.926290i \(-0.622980\pi\)
−0.376812 + 0.926290i \(0.622980\pi\)
\(434\) −0.561716 4.19783i −0.0269632 0.201502i
\(435\) −3.02778 −0.145171
\(436\) −7.00225 + 5.08743i −0.335347 + 0.243644i
\(437\) −0.242367 + 2.30597i −0.0115940 + 0.110310i
\(438\) 4.06698 12.5169i 0.194328 0.598079i
\(439\) 14.3934 24.9301i 0.686959 1.18985i −0.285857 0.958272i \(-0.592278\pi\)
0.972817 0.231576i \(-0.0743883\pi\)
\(440\) 2.76003 + 4.78051i 0.131579 + 0.227902i
\(441\) 6.28106 1.33508i 0.299098 0.0635752i
\(442\) −6.42842 19.7846i −0.305769 0.941059i
\(443\) −23.9497 5.09067i −1.13788 0.241865i −0.399819 0.916594i \(-0.630927\pi\)
−0.738065 + 0.674729i \(0.764260\pi\)
\(444\) 0.618386 + 5.88355i 0.0293473 + 0.279221i
\(445\) 1.63533 + 1.81622i 0.0775223 + 0.0860972i
\(446\) 4.75589 + 2.11746i 0.225198 + 0.100264i
\(447\) −7.23432 + 3.22093i −0.342172 + 0.152345i
\(448\) −0.508989 + 0.565290i −0.0240475 + 0.0267074i
\(449\) −19.9540 14.4975i −0.941689 0.684177i 0.00713729 0.999975i \(-0.497728\pi\)
−0.948827 + 0.315797i \(0.897728\pi\)
\(450\) 0.809017 + 0.587785i 0.0381374 + 0.0277085i
\(451\) −9.40408 + 10.4443i −0.442821 + 0.491802i
\(452\) 0.0325252 0.0144812i 0.00152986 0.000681136i
\(453\) 12.2069 + 5.43484i 0.573528 + 0.255351i
\(454\) 19.6495 + 21.8230i 0.922196 + 1.02420i
\(455\) 0.222283 + 2.11489i 0.0104208 + 0.0991474i
\(456\) 0.748647 + 0.159130i 0.0350586 + 0.00745193i
\(457\) 12.7948 + 39.3783i 0.598514 + 1.84204i 0.536391 + 0.843969i \(0.319787\pi\)
0.0621231 + 0.998068i \(0.480213\pi\)
\(458\) −24.9435 + 5.30190i −1.16553 + 0.247742i
\(459\) 3.72063 + 6.44432i 0.173664 + 0.300795i
\(460\) 1.51474 2.62360i 0.0706250 0.122326i
\(461\) 7.83823 24.1236i 0.365063 1.12355i −0.584879 0.811120i \(-0.698858\pi\)
0.949942 0.312427i \(-0.101142\pi\)
\(462\) 0.438910 4.17595i 0.0204199 0.194283i
\(463\) 24.4288 17.7486i 1.13530 0.824847i 0.148847 0.988860i \(-0.452444\pi\)
0.986458 + 0.164013i \(0.0524439\pi\)
\(464\) 3.02778 0.140561
\(465\) 5.41116 1.31125i 0.250936 0.0608077i
\(466\) −18.5967 −0.861477
\(467\) −19.0216 + 13.8200i −0.880216 + 0.639514i −0.933309 0.359075i \(-0.883092\pi\)
0.0530925 + 0.998590i \(0.483092\pi\)
\(468\) −0.292220 + 2.78029i −0.0135079 + 0.128519i
\(469\) −2.27421 + 6.99930i −0.105013 + 0.323198i
\(470\) −2.68050 + 4.64277i −0.123642 + 0.214155i
\(471\) 0.513397 + 0.889229i 0.0236561 + 0.0409735i
\(472\) −1.59141 + 0.338265i −0.0732506 + 0.0155699i
\(473\) −6.88951 21.2037i −0.316780 0.974949i
\(474\) −1.36702 0.290570i −0.0627894 0.0133463i
\(475\) 0.0800031 + 0.761179i 0.00367080 + 0.0349253i
\(476\) −3.78752 4.20647i −0.173601 0.192803i
\(477\) −0.834128 0.371378i −0.0381921 0.0170042i
\(478\) 1.84841 0.822964i 0.0845442 0.0376415i
\(479\) 18.9400 21.0350i 0.865391 0.961114i −0.134163 0.990959i \(-0.542835\pi\)
0.999555 + 0.0298449i \(0.00950132\pi\)
\(480\) −0.809017 0.587785i −0.0369264 0.0268286i
\(481\) −13.3801 9.72118i −0.610078 0.443248i
\(482\) −19.0109 + 21.1137i −0.865922 + 0.961704i
\(483\) −2.10521 + 0.937299i −0.0957903 + 0.0426486i
\(484\) 17.7876 + 7.91957i 0.808529 + 0.359980i
\(485\) −7.53491 8.36836i −0.342142 0.379988i
\(486\) −0.104528 0.994522i −0.00474151 0.0451124i
\(487\) −3.74250 0.795493i −0.169589 0.0360472i 0.122335 0.992489i \(-0.460962\pi\)
−0.291923 + 0.956442i \(0.594295\pi\)
\(488\) 1.00928 + 3.10624i 0.0456880 + 0.140613i
\(489\) 2.11914 0.450438i 0.0958310 0.0203695i
\(490\) −3.21069 5.56108i −0.145044 0.251224i
\(491\) 3.70274 6.41333i 0.167102 0.289429i −0.770298 0.637684i \(-0.779892\pi\)
0.937400 + 0.348255i \(0.113226\pi\)
\(492\) 0.786764 2.42141i 0.0354701 0.109166i
\(493\) −2.35508 + 22.4071i −0.106067 + 1.00916i
\(494\) −1.73103 + 1.25767i −0.0778828 + 0.0565852i
\(495\) 5.52005 0.248108
\(496\) −5.41116 + 1.31125i −0.242968 + 0.0588768i
\(497\) 10.0042 0.448749
\(498\) −1.31258 + 0.953646i −0.0588182 + 0.0427339i
\(499\) −1.57925 + 15.0256i −0.0706971 + 0.672638i 0.900581 + 0.434689i \(0.143142\pi\)
−0.971278 + 0.237949i \(0.923525\pi\)
\(500\) 0.309017 0.951057i 0.0138197 0.0425325i
\(501\) 10.1438 17.5696i 0.453191 0.784951i
\(502\) 11.1429 + 19.3000i 0.497331 + 0.861403i
\(503\) 31.5697 6.71035i 1.40762 0.299200i 0.559427 0.828880i \(-0.311021\pi\)
0.848197 + 0.529680i \(0.177688\pi\)
\(504\) 0.235061 + 0.723442i 0.0104704 + 0.0322247i
\(505\) −8.65200 1.83904i −0.385009 0.0818362i
\(506\) −1.74801 16.6313i −0.0777087 0.739349i
\(507\) 3.46919 + 3.85292i 0.154072 + 0.171114i
\(508\) −9.09280 4.04838i −0.403428 0.179618i
\(509\) −22.0128 + 9.80074i −0.975701 + 0.434410i −0.831735 0.555173i \(-0.812652\pi\)
−0.143966 + 0.989583i \(0.545986\pi\)
\(510\) 4.97918 5.52994i 0.220482 0.244870i
\(511\) 8.09924 + 5.88444i 0.358289 + 0.260312i
\(512\) 0.809017 + 0.587785i 0.0357538 + 0.0259767i
\(513\) 0.512134 0.568782i 0.0226113 0.0251123i
\(514\) −21.6644 + 9.64560i −0.955575 + 0.425449i
\(515\) 8.92973 + 3.97577i 0.393491 + 0.175193i
\(516\) 2.70255 + 3.00148i 0.118973 + 0.132133i
\(517\) 3.09331 + 29.4309i 0.136044 + 1.29437i
\(518\) −4.40177 0.935624i −0.193403 0.0411090i
\(519\) 1.84914 + 5.69106i 0.0811681 + 0.249810i
\(520\) 2.73451 0.581238i 0.119916 0.0254890i
\(521\) −12.0682 20.9028i −0.528719 0.915769i −0.999439 0.0334859i \(-0.989339\pi\)
0.470720 0.882283i \(-0.343994\pi\)
\(522\) 1.51389 2.62213i 0.0662611 0.114768i
\(523\) −0.966854 + 2.97567i −0.0422776 + 0.130117i −0.969967 0.243235i \(-0.921791\pi\)
0.927690 + 0.373352i \(0.121791\pi\)
\(524\) −0.579664 + 5.51513i −0.0253227 + 0.240930i
\(525\) −0.615397 + 0.447112i −0.0268581 + 0.0195136i
\(526\) 8.27329 0.360733
\(527\) −5.49498 41.0652i −0.239365 1.78883i
\(528\) −5.52005 −0.240230
\(529\) 11.1825 8.12454i 0.486194 0.353241i
\(530\) −0.0954415 + 0.908065i −0.00414571 + 0.0394438i
\(531\) −0.502759 + 1.54733i −0.0218179 + 0.0671486i
\(532\) −0.291098 + 0.504197i −0.0126207 + 0.0218597i
\(533\) 3.55883 + 6.16408i 0.154150 + 0.266996i
\(534\) −2.39056 + 0.508130i −0.103450 + 0.0219889i
\(535\) 1.60040 + 4.92553i 0.0691914 + 0.212949i
\(536\) 9.46358 + 2.01155i 0.408764 + 0.0868855i
\(537\) 0.543217 + 5.16836i 0.0234415 + 0.223031i
\(538\) 20.9679 + 23.2872i 0.903992 + 1.00398i
\(539\) −32.3819 14.4173i −1.39479 0.620998i
\(540\) −0.913545 + 0.406737i −0.0393127 + 0.0175032i
\(541\) 4.83712 5.37217i 0.207964 0.230967i −0.630135 0.776486i \(-0.717000\pi\)
0.838099 + 0.545518i \(0.183667\pi\)
\(542\) 2.47609 + 1.79899i 0.106357 + 0.0772731i
\(543\) 21.5936 + 15.6887i 0.926671 + 0.673266i
\(544\) −4.97918 + 5.52994i −0.213480 + 0.237094i
\(545\) 7.90697 3.52041i 0.338698 0.150798i
\(546\) −1.94269 0.864940i −0.0831393 0.0370160i
\(547\) 7.89365 + 8.76679i 0.337508 + 0.374841i 0.887877 0.460081i \(-0.152180\pi\)
−0.550369 + 0.834922i \(0.685513\pi\)
\(548\) 0.552739 + 5.25896i 0.0236118 + 0.224652i
\(549\) 3.19473 + 0.679060i 0.136348 + 0.0289816i
\(550\) −1.70579 5.24988i −0.0727351 0.223856i
\(551\) 2.26673 0.481809i 0.0965661 0.0205258i
\(552\) 1.51474 + 2.62360i 0.0644715 + 0.111668i
\(553\) 0.531544 0.920660i 0.0226035 0.0391505i
\(554\) −2.70662 + 8.33013i −0.114993 + 0.353913i
\(555\) 0.618386 5.88355i 0.0262490 0.249743i
\(556\) −7.50955 + 5.45601i −0.318476 + 0.231386i
\(557\) 12.3484 0.523219 0.261609 0.965174i \(-0.415747\pi\)
0.261609 + 0.965174i \(0.415747\pi\)
\(558\) −1.57000 + 5.34182i −0.0664635 + 0.226137i
\(559\) −11.2911 −0.477564
\(560\) 0.615397 0.447112i 0.0260053 0.0188939i
\(561\) 4.29363 40.8512i 0.181277 1.72474i
\(562\) 4.50216 13.8562i 0.189912 0.584489i
\(563\) −7.33946 + 12.7123i −0.309321 + 0.535761i −0.978214 0.207598i \(-0.933435\pi\)
0.668893 + 0.743359i \(0.266769\pi\)
\(564\) −2.68050 4.64277i −0.112869 0.195496i
\(565\) −0.0348253 + 0.00740234i −0.00146511 + 0.000311419i
\(566\) −4.12774 12.7039i −0.173502 0.533983i
\(567\) 0.744050 + 0.158153i 0.0312471 + 0.00664179i
\(568\) −1.37473 13.0797i −0.0576825 0.548812i
\(569\) 28.9968 + 32.2042i 1.21561 + 1.35007i 0.918596 + 0.395197i \(0.129324\pi\)
0.297012 + 0.954874i \(0.404010\pi\)
\(570\) −0.699202 0.311305i −0.0292863 0.0130391i
\(571\) −3.76257 + 1.67521i −0.157459 + 0.0701052i −0.483953 0.875094i \(-0.660799\pi\)
0.326494 + 0.945199i \(0.394133\pi\)
\(572\) 10.3259 11.4681i 0.431749 0.479506i
\(573\) −10.5352 7.65424i −0.440113 0.319761i
\(574\) 1.56681 + 1.13836i 0.0653975 + 0.0475141i
\(575\) −2.02711 + 2.25134i −0.0845365 + 0.0938873i
\(576\) 0.913545 0.406737i 0.0380644 0.0169474i
\(577\) −21.7472 9.68247i −0.905347 0.403086i −0.0993816 0.995049i \(-0.531686\pi\)
−0.805965 + 0.591963i \(0.798353\pi\)
\(578\) −25.6762 28.5163i −1.06799 1.18612i
\(579\) 1.18618 + 11.2858i 0.0492961 + 0.469021i
\(580\) −2.96161 0.629510i −0.122974 0.0261390i
\(581\) −0.381372 1.17374i −0.0158220 0.0486950i
\(582\) 11.0147 2.34124i 0.456573 0.0970475i
\(583\) 2.52009 + 4.36492i 0.104371 + 0.180777i
\(584\) 6.58051 11.3978i 0.272303 0.471643i
\(585\) 0.863888 2.65877i 0.0357174 0.109927i
\(586\) −0.601102 + 5.71910i −0.0248313 + 0.236254i
\(587\) 7.59346 5.51697i 0.313416 0.227710i −0.419945 0.907550i \(-0.637951\pi\)
0.733361 + 0.679840i \(0.237951\pi\)
\(588\) 6.42138 0.264813
\(589\) −3.84239 + 1.84274i −0.158323 + 0.0759287i
\(590\) 1.62696 0.0669810
\(591\) 18.6158 13.5251i 0.765750 0.556350i
\(592\) −0.618386 + 5.88355i −0.0254155 + 0.241812i
\(593\) −4.44278 + 13.6735i −0.182443 + 0.561502i −0.999895 0.0144946i \(-0.995386\pi\)
0.817452 + 0.575997i \(0.195386\pi\)
\(594\) −2.76003 + 4.78051i −0.113245 + 0.196147i
\(595\) 2.83018 + 4.90202i 0.116026 + 0.200963i
\(596\) −7.74590 + 1.64644i −0.317284 + 0.0674409i
\(597\) 1.44197 + 4.43792i 0.0590158 + 0.181632i
\(598\) −8.28413 1.76085i −0.338763 0.0720063i
\(599\) −2.17487 20.6925i −0.0888627 0.845472i −0.944636 0.328121i \(-0.893585\pi\)
0.855773 0.517351i \(-0.173082\pi\)
\(600\) 0.669131 + 0.743145i 0.0273171 + 0.0303388i
\(601\) −29.6390 13.1961i −1.20900 0.538281i −0.299544 0.954082i \(-0.596835\pi\)
−0.909456 + 0.415801i \(0.863501\pi\)
\(602\) −2.80666 + 1.24961i −0.114391 + 0.0509302i
\(603\) 6.47384 7.18992i 0.263635 0.292796i
\(604\) 10.8101 + 7.85403i 0.439858 + 0.319576i
\(605\) −15.7524 11.4448i −0.640425 0.465296i
\(606\) 5.91866 6.57333i 0.240429 0.267023i
\(607\) 36.5751 16.2843i 1.48454 0.660958i 0.505164 0.863023i \(-0.331432\pi\)
0.979372 + 0.202065i \(0.0647652\pi\)
\(608\) 0.699202 + 0.311305i 0.0283564 + 0.0126251i
\(609\) 1.54111 + 1.71157i 0.0624487 + 0.0693563i
\(610\) −0.341400 3.24821i −0.0138229 0.131516i
\(611\) 14.6597 + 3.11602i 0.593069 + 0.126061i
\(612\) 2.29948 + 7.07706i 0.0929509 + 0.286073i
\(613\) 25.9133 5.50804i 1.04663 0.222468i 0.347660 0.937621i \(-0.386976\pi\)
0.698968 + 0.715153i \(0.253643\pi\)
\(614\) 6.18744 + 10.7170i 0.249705 + 0.432501i
\(615\) −1.27301 + 2.20492i −0.0513328 + 0.0889110i
\(616\) 1.29755 3.99344i 0.0522797 0.160900i
\(617\) 4.39667 41.8315i 0.177003 1.68407i −0.440694 0.897657i \(-0.645268\pi\)
0.617697 0.786416i \(-0.288066\pi\)
\(618\) −7.90798 + 5.74549i −0.318106 + 0.231117i
\(619\) −2.96570 −0.119201 −0.0596007 0.998222i \(-0.518983\pi\)
−0.0596007 + 0.998222i \(0.518983\pi\)
\(620\) 5.56553 0.157553i 0.223517 0.00632747i
\(621\) 3.02947 0.121569
\(622\) −2.78959 + 2.02675i −0.111852 + 0.0812654i
\(623\) 0.194325 1.84887i 0.00778545 0.0740736i
\(624\) −0.863888 + 2.65877i −0.0345832 + 0.106436i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 5.22363 + 9.04760i 0.208778 + 0.361615i
\(627\) −4.13257 + 0.878405i −0.165039 + 0.0350801i
\(628\) 0.317297 + 0.976539i 0.0126615 + 0.0389681i
\(629\) −43.0602 9.15273i −1.71692 0.364943i
\(630\) −0.0795119 0.756505i −0.00316783 0.0301399i
\(631\) −13.3118 14.7842i −0.529934 0.588551i 0.417430 0.908709i \(-0.362931\pi\)
−0.947364 + 0.320157i \(0.896264\pi\)
\(632\) −1.27674 0.568440i −0.0507859 0.0226113i
\(633\) −19.4215 + 8.64700i −0.771935 + 0.343687i
\(634\) 0.112577 0.125029i 0.00447100 0.00496555i
\(635\) 8.05240 + 5.85041i 0.319550 + 0.232166i
\(636\) −0.738687 0.536687i −0.0292908 0.0212810i
\(637\) −12.0120 + 13.3406i −0.475932 + 0.528576i
\(638\) −15.2685 + 6.79799i −0.604487 + 0.269135i
\(639\) −12.0147 5.34930i −0.475295 0.211615i
\(640\) −0.669131 0.743145i −0.0264497 0.0293754i
\(641\) −1.27738 12.1534i −0.0504534 0.480032i −0.990352 0.138577i \(-0.955747\pi\)
0.939898 0.341455i \(-0.110920\pi\)
\(642\) −5.06584 1.07678i −0.199933 0.0424970i
\(643\) −9.06275 27.8923i −0.357400 1.09996i −0.954605 0.297875i \(-0.903722\pi\)
0.597205 0.802089i \(-0.296278\pi\)
\(644\) −2.25408 + 0.479119i −0.0888232 + 0.0188799i
\(645\) −2.01945 3.49779i −0.0795157 0.137725i
\(646\) −2.84767 + 4.93230i −0.112040 + 0.194059i
\(647\) 3.51188 10.8085i 0.138066 0.424924i −0.857988 0.513670i \(-0.828286\pi\)
0.996054 + 0.0887452i \(0.0282857\pi\)
\(648\) 0.104528 0.994522i 0.00410627 0.0390685i
\(649\) 7.26572 5.27885i 0.285204 0.207213i
\(650\) −2.79560 −0.109652
\(651\) −3.49546 2.39146i −0.136998 0.0937287i
\(652\) 2.16649 0.0848461
\(653\) −29.4085 + 21.3665i −1.15084 + 0.836137i −0.988593 0.150612i \(-0.951875\pi\)
−0.162251 + 0.986749i \(0.551875\pi\)
\(654\) −0.904721 + 8.60785i −0.0353774 + 0.336593i
\(655\) 1.71366 5.27410i 0.0669582 0.206076i
\(656\) 1.27301 2.20492i 0.0497027 0.0860877i
\(657\) −6.58051 11.3978i −0.256730 0.444669i
\(658\) 3.98885 0.847857i 0.155502 0.0330529i
\(659\) 7.94664 + 24.4572i 0.309557 + 0.952719i 0.977937 + 0.208899i \(0.0669880\pi\)
−0.668380 + 0.743820i \(0.733012\pi\)
\(660\) 5.39943 + 1.14768i 0.210172 + 0.0446735i
\(661\) −2.29450 21.8307i −0.0892459 0.849118i −0.943969 0.330034i \(-0.892940\pi\)
0.854723 0.519084i \(-0.173727\pi\)
\(662\) 9.41760 + 10.4593i 0.366025 + 0.406512i
\(663\) −19.0043 8.46126i −0.738066 0.328608i
\(664\) −1.48217 + 0.659906i −0.0575194 + 0.0256093i
\(665\) 0.389566 0.432657i 0.0151067 0.0167777i
\(666\) 4.78611 + 3.47731i 0.185458 + 0.134743i
\(667\) 7.42077 + 5.39150i 0.287333 + 0.208760i
\(668\) 13.5751 15.0766i 0.525234 0.583332i
\(669\) 4.75589 2.11746i 0.183873 0.0818656i
\(670\) −8.83855 3.93518i −0.341463 0.152029i
\(671\) −12.0638 13.3982i −0.465717 0.517231i
\(672\) 0.0795119 + 0.756505i 0.00306724 + 0.0291828i
\(673\) 5.87020 + 1.24775i 0.226280 + 0.0480972i 0.319656 0.947534i \(-0.396433\pi\)
−0.0933764 + 0.995631i \(0.529766\pi\)
\(674\) −5.54721 17.0725i −0.213670 0.657610i
\(675\) 0.978148 0.207912i 0.0376489 0.00800252i
\(676\) 2.59231 + 4.49001i 0.0997042 + 0.172693i
\(677\) 0.541635 0.938140i 0.0208167 0.0360556i −0.855429 0.517919i \(-0.826707\pi\)
0.876246 + 0.481864i \(0.160040\pi\)
\(678\) 0.0110020 0.0338607i 0.000422530 0.00130041i
\(679\) −0.895363 + 8.51881i −0.0343609 + 0.326922i
\(680\) 6.02011 4.37387i 0.230861 0.167730i
\(681\) 29.3657 1.12530
\(682\) 24.3435 18.7616i 0.932159 0.718418i
\(683\) 34.8992 1.33538 0.667690 0.744440i \(-0.267283\pi\)
0.667690 + 0.744440i \(0.267283\pi\)
\(684\) 0.619199 0.449874i 0.0236757 0.0172014i
\(685\) 0.552739 5.25896i 0.0211191 0.200935i
\(686\) −3.15484 + 9.70959i −0.120452 + 0.370714i
\(687\) −12.7504 + 22.0843i −0.486457 + 0.842568i
\(688\) 2.01945 + 3.49779i 0.0769907 + 0.133352i
\(689\) 2.49679 0.530709i 0.0951202 0.0202184i
\(690\) −0.936159 2.88120i −0.0356390 0.109685i
\(691\) 20.0273 + 4.25693i 0.761874 + 0.161941i 0.572434 0.819951i \(-0.305999\pi\)
0.189440 + 0.981892i \(0.439333\pi\)
\(692\) 0.625491 + 5.95115i 0.0237776 + 0.226229i
\(693\) −2.80965 3.12043i −0.106730 0.118535i
\(694\) −0.0699653 0.0311506i −0.00265585 0.00118246i
\(695\) 8.47981 3.77546i 0.321658 0.143211i
\(696\) 2.02598 2.25008i 0.0767945 0.0852889i
\(697\) 15.3273 + 11.1360i 0.580564 + 0.421805i
\(698\) −18.4760 13.4236i −0.699326 0.508090i
\(699\) −12.4436 + 13.8201i −0.470662 + 0.522723i
\(700\) −0.694909 + 0.309393i −0.0262651 + 0.0116940i
\(701\) 18.9127 + 8.42046i 0.714321 + 0.318036i 0.731524 0.681816i \(-0.238809\pi\)
−0.0172027 + 0.999852i \(0.505476\pi\)
\(702\) 1.87062 + 2.07754i 0.0706021 + 0.0784115i
\(703\) 0.473295 + 4.50310i 0.0178507 + 0.169838i
\(704\) −5.39943 1.14768i −0.203499 0.0432550i
\(705\) 1.65664 + 5.09862i 0.0623927 + 0.192025i
\(706\) −16.3871 + 3.48318i −0.616736 + 0.131091i
\(707\) 3.36418 + 5.82694i 0.126523 + 0.219145i
\(708\) −0.813481 + 1.40899i −0.0305725 + 0.0529531i
\(709\) −3.93700 + 12.1168i −0.147857 + 0.455058i −0.997367 0.0725145i \(-0.976898\pi\)
0.849510 + 0.527572i \(0.176898\pi\)
\(710\) −1.37473 + 13.0797i −0.0515928 + 0.490873i
\(711\) −1.13065 + 0.821467i −0.0424028 + 0.0308074i
\(712\) −2.44397 −0.0915916
\(713\) −15.5971 6.42180i −0.584116 0.240498i
\(714\) −5.66036 −0.211834
\(715\) −12.4846 + 9.07062i −0.466899 + 0.339222i
\(716\) −0.543217 + 5.16836i −0.0203010 + 0.193151i
\(717\) 0.625245 1.92431i 0.0233502 0.0718645i
\(718\) −13.7881 + 23.8817i −0.514568 + 0.891258i
\(719\) 18.9810 + 32.8760i 0.707871 + 1.22607i 0.965645 + 0.259863i \(0.0836775\pi\)
−0.257775 + 0.966205i \(0.582989\pi\)
\(720\) −0.978148 + 0.207912i −0.0364534 + 0.00774841i
\(721\) −2.29767 7.07151i −0.0855698 0.263357i
\(722\) −18.0118 3.82853i −0.670330 0.142483i
\(723\) 2.96979 + 28.2557i 0.110448 + 1.05084i
\(724\) 17.8599 + 19.8354i 0.663757 + 0.737177i
\(725\) 2.76601 + 1.23151i 0.102727 + 0.0457371i
\(726\) 17.7876 7.91957i 0.660161 0.293923i
\(727\) 33.2778 36.9588i 1.23421 1.37073i 0.329801 0.944050i \(-0.393018\pi\)
0.904405 0.426675i \(-0.140315\pi\)
\(728\) −1.72040 1.24995i −0.0637624 0.0463261i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) −8.80644 + 9.78054i −0.325941 + 0.361994i
\(731\) −27.4561 + 12.2243i −1.01550 + 0.452131i
\(732\) 2.98373 + 1.32844i 0.110282 + 0.0491006i
\(733\) 30.7041 + 34.1004i 1.13408 + 1.25953i 0.961582 + 0.274517i \(0.0885180\pi\)
0.172501 + 0.985009i \(0.444815\pi\)
\(734\) −2.75529 26.2149i −0.101700 0.967608i
\(735\) −6.28106 1.33508i −0.231680 0.0492452i
\(736\) 0.936159 + 2.88120i 0.0345073 + 0.106202i
\(737\) −52.2394 + 11.1038i −1.92426 + 0.409015i
\(738\) −1.27301 2.20492i −0.0468602 0.0811642i
\(739\) 7.98070 13.8230i 0.293575 0.508487i −0.681077 0.732211i \(-0.738488\pi\)
0.974652 + 0.223725i \(0.0718217\pi\)
\(740\) 1.82813 5.62641i 0.0672035 0.206831i
\(741\) −0.223657 + 2.12795i −0.00821624 + 0.0781723i
\(742\) 0.561898 0.408243i 0.0206279 0.0149871i
\(743\) 5.12451 0.188000 0.0940000 0.995572i \(-0.470035\pi\)
0.0940000 + 0.995572i \(0.470035\pi\)
\(744\) −2.64632 + 4.89867i −0.0970189 + 0.179594i
\(745\) 7.91895 0.290128
\(746\) 21.3986 15.5470i 0.783460 0.569217i
\(747\) −0.169591 + 1.61355i −0.00620501 + 0.0590368i
\(748\) 12.6932 39.0658i 0.464111 1.42839i
\(749\) 1.96977 3.41173i 0.0719736 0.124662i
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 47.8157 10.1635i 1.74482 0.370873i 0.778385 0.627787i \(-0.216039\pi\)
0.966434 + 0.256914i \(0.0827057\pi\)
\(752\) −1.65664 5.09862i −0.0604115 0.185927i
\(753\) 21.7988 + 4.63347i 0.794391 + 0.168853i
\(754\) 0.884776 + 8.41808i 0.0322217 + 0.306569i
\(755\) −8.94097 9.92995i −0.325395 0.361388i
\(756\) 0.694909 + 0.309393i 0.0252736 + 0.0112525i
\(757\) 4.78574 2.13075i 0.173941 0.0774434i −0.317919 0.948118i \(-0.602984\pi\)
0.491860 + 0.870675i \(0.336317\pi\)
\(758\) 22.6895 25.1992i 0.824119 0.915277i
\(759\) −13.5291 9.82945i −0.491074 0.356786i
\(760\) −0.619199 0.449874i −0.0224607 0.0163187i
\(761\) −32.0818 + 35.6304i −1.16296 + 1.29160i −0.213778 + 0.976882i \(0.568577\pi\)
−0.949185 + 0.314718i \(0.898090\pi\)
\(762\) −9.09280 + 4.04838i −0.329398 + 0.146657i
\(763\) −6.01461 2.67788i −0.217744 0.0969457i
\(764\) −8.71354 9.67736i −0.315245 0.350115i
\(765\) −0.777824 7.40050i −0.0281223 0.267566i
\(766\) 3.19857 + 0.679878i 0.115569 + 0.0245650i
\(767\) −1.40551 4.32573i −0.0507502 0.156193i
\(768\) 0.978148 0.207912i 0.0352959 0.00750237i
\(769\) 20.8033 + 36.0323i 0.750185 + 1.29936i 0.947733 + 0.319066i \(0.103369\pi\)
−0.197547 + 0.980293i \(0.563298\pi\)
\(770\) −2.09948 + 3.63640i −0.0756598 + 0.131047i
\(771\) −7.32822 + 22.5539i −0.263919 + 0.812260i
\(772\) −1.18618 + 11.2858i −0.0426917 + 0.406184i
\(773\) 44.3459 32.2192i 1.59501 1.15884i 0.698699 0.715415i \(-0.253763\pi\)
0.896311 0.443427i \(-0.146237\pi\)
\(774\) 4.03890 0.145175
\(775\) −5.47667 1.00303i −0.196728 0.0360299i
\(776\) 11.2607 0.404237
\(777\) −3.64066 + 2.64510i −0.130608 + 0.0948923i
\(778\) −0.671640 + 6.39022i −0.0240794 + 0.229101i
\(779\) 0.602167 1.85328i 0.0215749 0.0664006i
\(780\) 1.39780 2.42106i 0.0500493 0.0866879i
\(781\) 36.2992 + 62.8721i 1.29889 + 2.24974i
\(782\) −22.0505 + 4.68698i −0.788524 + 0.167606i
\(783\) −0.935635 2.87959i −0.0334368 0.102908i
\(784\) 6.28106 + 1.33508i 0.224323 + 0.0476814i
\(785\) −0.107329 1.02117i −0.00383074 0.0364471i
\(786\) 3.71067 + 4.12112i 0.132355 + 0.146995i
\(787\) −2.07642 0.924481i −0.0740163 0.0329542i 0.369395 0.929273i \(-0.379565\pi\)
−0.443411 + 0.896318i \(0.646232\pi\)
\(788\) 21.0210 9.35915i 0.748842 0.333406i
\(789\) 5.53591 6.14825i 0.197084 0.218884i
\(790\) 1.13065 + 0.821467i 0.0402268 + 0.0292265i
\(791\) 0.0219101 + 0.0159186i 0.000779035 + 0.000566002i
\(792\) −3.69364 + 4.10220i −0.131248 + 0.145765i
\(793\) −8.34131 + 3.71379i −0.296209 + 0.131881i
\(794\) −12.8226 5.70897i −0.455055 0.202604i
\(795\) 0.610961 + 0.678541i 0.0216686 + 0.0240654i
\(796\) 0.487762 + 4.64074i 0.0172882 + 0.164487i
\(797\) −27.8668 5.92327i −0.987092 0.209813i −0.314041 0.949409i \(-0.601683\pi\)
−0.673051 + 0.739596i \(0.735016\pi\)
\(798\) 0.179909 + 0.553702i 0.00636870 + 0.0196008i
\(799\) 39.0209 8.29415i 1.38046 0.293426i
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) −1.22198 + 2.11654i −0.0431767 + 0.0747842i
\(802\) 12.3190 37.9141i 0.435000 1.33879i
\(803\) −7.59394 + 72.2515i −0.267984 + 2.54970i
\(804\) 7.82724 5.68682i 0.276045 0.200559i
\(805\) 2.30444 0.0812207
\(806\) −5.22690 14.6614i −0.184110 0.516425i
\(807\) 31.3361 1.10308
\(808\) 7.15599 5.19913i 0.251747 0.182905i
\(809\) −3.04186 + 28.9414i −0.106946 + 1.01752i 0.801065 + 0.598578i \(0.204267\pi\)
−0.908011 + 0.418947i \(0.862399\pi\)
\(810\) −0.309017 + 0.951057i −0.0108578 + 0.0334167i
\(811\) −16.0966 + 27.8800i −0.565226 + 0.979001i 0.431802 + 0.901968i \(0.357878\pi\)
−0.997029 + 0.0770325i \(0.975455\pi\)
\(812\) 1.15157 + 1.99458i 0.0404123 + 0.0699961i
\(813\) 2.99374 0.636339i 0.104995 0.0223174i
\(814\) −10.0914 31.0581i −0.353703 1.08859i
\(815\) −2.11914 0.450438i −0.0742303 0.0157781i
\(816\) 0.777824 + 7.40050i 0.0272293 + 0.259069i
\(817\) 2.06845 + 2.29725i 0.0723661 + 0.0803707i
\(818\) 22.7996 + 10.1510i 0.797168 + 0.354922i
\(819\) −1.94269 + 0.864940i −0.0678830 + 0.0302234i
\(820\) −1.70362 + 1.89206i −0.0594930 + 0.0660737i
\(821\) −33.0509 24.0129i −1.15349 0.838056i −0.164545 0.986370i \(-0.552616\pi\)
−0.988940 + 0.148313i \(0.952616\pi\)
\(822\) 4.27803 + 3.10817i 0.149213 + 0.108410i
\(823\) −29.0324 + 32.2437i −1.01200 + 1.12394i −0.0197395 + 0.999805i \(0.506284\pi\)
−0.992265 + 0.124139i \(0.960383\pi\)
\(824\) −8.92973 + 3.97577i −0.311082 + 0.138503i
\(825\) −5.04282 2.24521i −0.175568 0.0781681i
\(826\) −0.828106 0.919705i −0.0288135 0.0320006i
\(827\) −5.47087 52.0519i −0.190241 1.81002i −0.507467 0.861671i \(-0.669418\pi\)
0.317226 0.948350i \(-0.397249\pi\)
\(828\) 2.96327 + 0.629863i 0.102981 + 0.0218893i
\(829\) 14.6557 + 45.1056i 0.509014 + 1.56658i 0.793916 + 0.608027i \(0.208039\pi\)
−0.284902 + 0.958557i \(0.591961\pi\)
\(830\) 1.58699 0.337324i 0.0550851 0.0117087i
\(831\) 4.37941 + 7.58536i 0.151920 + 0.263133i
\(832\) −1.39780 + 2.42106i −0.0484600 + 0.0839352i
\(833\) −14.7658 + 45.4445i −0.511605 + 1.57456i
\(834\) −0.970266 + 9.23146i −0.0335976 + 0.319659i
\(835\) −16.4130 + 11.9247i −0.567996 + 0.412673i
\(836\) −4.22489 −0.146121
\(837\) 2.91921 + 4.74112i 0.100903 + 0.163877i
\(838\) −22.3354 −0.771565
\(839\) −28.3073 + 20.5664i −0.977275 + 0.710032i −0.957098 0.289764i \(-0.906423\pi\)
−0.0201773 + 0.999796i \(0.506423\pi\)
\(840\) 0.0795119 0.756505i 0.00274342 0.0261019i
\(841\) −6.12860 + 18.8619i −0.211331 + 0.650410i
\(842\) 4.10639 7.11248i 0.141516 0.245112i
\(843\) −7.28464 12.6174i −0.250896 0.434565i
\(844\) −20.7949 + 4.42009i −0.715790 + 0.152146i
\(845\) −1.60214 4.93087i −0.0551151 0.169627i
\(846\) −5.24385 1.11462i −0.180287 0.0383213i
\(847\) 1.54818 + 14.7299i 0.0531959 + 0.506126i
\(848\) −0.610961 0.678541i −0.0209805 0.0233012i
\(849\) −12.2028 5.43304i −0.418799 0.186461i
\(850\) −6.79793 + 3.02663i −0.233167 + 0.103813i
\(851\) −11.9923 + 13.3188i −0.411091 + 0.456563i
\(852\) −10.6400 7.73041i −0.364520 0.264839i
\(853\) 30.6279 + 22.2525i 1.04868 + 0.761910i 0.971961 0.235143i \(-0.0755559\pi\)
0.0767181 + 0.997053i \(0.475556\pi\)
\(854\) −1.66241 + 1.84629i −0.0568864 + 0.0631788i
\(855\) −0.699202 + 0.311305i −0.0239122 + 0.0106464i
\(856\) −4.73126 2.10649i −0.161711 0.0719985i
\(857\) 2.79396 + 3.10300i 0.0954397 + 0.105997i 0.788972 0.614429i \(-0.210613\pi\)
−0.693533 + 0.720425i \(0.743947\pi\)
\(858\) −1.61307 15.3473i −0.0550693 0.523949i
\(859\) 20.1512 + 4.28328i 0.687551 + 0.146143i 0.538423 0.842674i \(-0.319020\pi\)
0.149128 + 0.988818i \(0.452353\pi\)
\(860\) −1.24809 3.84122i −0.0425594 0.130984i
\(861\) 1.89437 0.402660i 0.0645599 0.0137226i
\(862\) 4.13527 + 7.16251i 0.140848 + 0.243956i
\(863\) −15.6315 + 27.0746i −0.532103 + 0.921630i 0.467194 + 0.884155i \(0.345265\pi\)
−0.999298 + 0.0374750i \(0.988069\pi\)
\(864\) 0.309017 0.951057i 0.0105130 0.0323556i
\(865\) 0.625491 5.95115i 0.0212673 0.202345i
\(866\) −12.6869 + 9.21758i −0.431119 + 0.313226i
\(867\) −38.3724 −1.30320
\(868\) −2.92186 3.06595i −0.0991744 0.104065i
\(869\) 7.71462 0.261701
\(870\) −2.44952 + 1.77968i −0.0830466 + 0.0603369i
\(871\) −2.82723 + 26.8993i −0.0957969 + 0.911447i
\(872\) −2.67462 + 8.23164i −0.0905742 + 0.278759i
\(873\) 5.63037 9.75209i 0.190559 0.330058i
\(874\) 1.15934 + 2.00803i 0.0392152 + 0.0679226i
\(875\) 0.744050 0.158153i 0.0251535 0.00534653i
\(876\) −4.06698 12.5169i −0.137410 0.422906i
\(877\) −29.5511 6.28128i −0.997869 0.212104i −0.320104 0.947382i \(-0.603718\pi\)
−0.677765 + 0.735279i \(0.737051\pi\)
\(878\) −3.00904 28.6291i −0.101550 0.966185i
\(879\) 3.84791 + 4.27353i 0.129787 + 0.144143i
\(880\) 5.04282 + 2.24521i 0.169993 + 0.0756859i
\(881\) −3.42159 + 1.52339i −0.115276 + 0.0513243i −0.463564 0.886063i \(-0.653430\pi\)
0.348288 + 0.937388i \(0.386763\pi\)
\(882\) 4.29674 4.77201i 0.144679 0.160682i
\(883\) −35.9250 26.1011i −1.20897 0.878371i −0.213837 0.976869i \(-0.568596\pi\)
−0.995137 + 0.0984983i \(0.968596\pi\)
\(884\) −16.8298 12.2276i −0.566048 0.411258i
\(885\) 1.08865 1.20907i 0.0365946 0.0406424i
\(886\) −22.3679 + 9.95885i −0.751465 + 0.334574i
\(887\) −46.6121 20.7531i −1.56508 0.696819i −0.572671 0.819785i \(-0.694093\pi\)
−0.992411 + 0.122966i \(0.960759\pi\)
\(888\) 3.95855 + 4.39641i 0.132840 + 0.147534i
\(889\) −0.791407 7.52973i −0.0265429 0.252539i
\(890\) 2.39056 + 0.508130i 0.0801318 + 0.0170325i
\(891\) 1.70579 + 5.24988i 0.0571461 + 0.175878i
\(892\) 5.09220 1.08238i 0.170500 0.0362408i
\(893\) −2.05158 3.55344i −0.0686535 0.118911i
\(894\) −3.95947 + 6.85801i −0.132425 + 0.229366i
\(895\) 1.60591 4.94248i 0.0536796 0.165209i
\(896\) −0.0795119 + 0.756505i −0.00265631 + 0.0252731i
\(897\) −6.85173 + 4.97807i −0.228772 + 0.166213i
\(898\) −24.6646 −0.823067
\(899\) −1.28701 + 16.8087i −0.0429241 + 0.560603i
\(900\) 1.00000 0.0333333
\(901\) 5.49676 3.99363i 0.183124 0.133047i
\(902\) −1.46906 + 13.9772i −0.0489144 + 0.465390i
\(903\) −0.949385 + 2.92191i −0.0315936 + 0.0972350i
\(904\) 0.0178016 0.0308333i 0.000592074 0.00102550i
\(905\) −13.3456 23.1152i −0.443622 0.768376i
\(906\) 13.0701 2.77813i 0.434224 0.0922972i
\(907\) 1.87666 + 5.77577i 0.0623135 + 0.191781i 0.977367 0.211552i \(-0.0678516\pi\)
−0.915053 + 0.403333i \(0.867852\pi\)
\(908\) 28.7240 + 6.10547i 0.953239 + 0.202617i
\(909\) −0.924585 8.79684i −0.0306665 0.291773i
\(910\) 1.42293 + 1.58032i 0.0471697 + 0.0523872i
\(911\) 10.5458 + 4.69528i 0.349397 + 0.155561i 0.573929 0.818905i \(-0.305419\pi\)
−0.224532 + 0.974467i \(0.572085\pi\)
\(912\) 0.699202 0.311305i 0.0231529 0.0103083i
\(913\) 5.99270 6.65557i 0.198329 0.220267i
\(914\) 33.4972 + 24.3371i 1.10799 + 0.805000i
\(915\) −2.64233 1.91976i −0.0873527 0.0634655i
\(916\) −17.0633 + 18.9507i −0.563788 + 0.626150i
\(917\) −3.85362 + 1.71574i −0.127258 + 0.0566589i
\(918\) 6.79793 + 3.02663i 0.224365 + 0.0998938i
\(919\) −25.3009 28.0995i −0.834599 0.926916i 0.163623 0.986523i \(-0.447682\pi\)
−0.998222 + 0.0596068i \(0.981015\pi\)
\(920\) −0.316666 3.01288i −0.0104402 0.0993317i
\(921\) 12.1045 + 2.57288i 0.398855 + 0.0847793i
\(922\) −7.83823 24.1236i −0.258138 0.794468i
\(923\) 35.9636 7.64430i 1.18376 0.251615i
\(924\) −2.09948 3.63640i −0.0690677 0.119629i
\(925\) −2.95798 + 5.12337i −0.0972578 + 0.168455i
\(926\) 9.33099 28.7178i 0.306635 0.943726i
\(927\) −1.02175 + 9.72126i −0.0335585 + 0.319288i
\(928\) 2.44952 1.77968i 0.0804095 0.0584209i
\(929\) 44.6319 1.46432 0.732162 0.681130i \(-0.238511\pi\)
0.732162 + 0.681130i \(0.238511\pi\)
\(930\) 3.60699 4.24142i 0.118278 0.139082i
\(931\) 4.91474 0.161074
\(932\) −15.0451 + 10.9309i −0.492818 + 0.358053i
\(933\) −0.360427 + 3.42923i −0.0117998 + 0.112268i
\(934\) −7.26562 + 22.3613i −0.237738 + 0.731683i
\(935\) −20.5381 + 35.5730i −0.671667 + 1.16336i
\(936\) 1.39780 + 2.42106i 0.0456885 + 0.0791349i
\(937\) −30.2728 + 6.43469i −0.988971 + 0.210212i −0.673873 0.738847i \(-0.735371\pi\)
−0.315098 + 0.949059i \(0.602037\pi\)
\(938\) 2.27421 + 6.99930i 0.0742556 + 0.228535i
\(939\) 10.2190 + 2.17211i 0.333484 + 0.0708841i
\(940\) 0.560378 + 5.33164i 0.0182775 + 0.173899i
\(941\) 15.7855 + 17.5316i 0.514593 + 0.571514i 0.943305 0.331928i \(-0.107699\pi\)
−0.428711 + 0.903441i \(0.641032\pi\)
\(942\) 0.938023 + 0.417635i 0.0305624 + 0.0136073i
\(943\) 7.04628 3.13720i 0.229458 0.102161i
\(944\) −1.08865 + 1.20907i −0.0354326 + 0.0393518i
\(945\) −0.615397 0.447112i −0.0200189 0.0145445i
\(946\) −18.0370 13.1046i −0.586433 0.426068i
\(947\) 27.7035 30.7679i 0.900244 0.999822i −0.0997449 0.995013i \(-0.531803\pi\)
0.999988 0.00480874i \(-0.00153067\pi\)
\(948\) −1.27674 + 0.568440i −0.0414665 + 0.0184621i
\(949\) 33.6120 + 14.9650i 1.09109 + 0.485785i
\(950\) 0.512134 + 0.568782i 0.0166158 + 0.0184537i
\(951\) −0.0175863 0.167322i −0.000570273 0.00542579i
\(952\) −5.53667 1.17686i −0.179444 0.0381421i
\(953\) −6.87455 21.1577i −0.222688 0.685365i −0.998518 0.0544221i \(-0.982668\pi\)
0.775830 0.630943i \(-0.217332\pi\)
\(954\) −0.893114 + 0.189837i −0.0289156 + 0.00614621i
\(955\) 6.51109 + 11.2775i 0.210694 + 0.364933i
\(956\) 1.01167 1.75226i 0.0327197 0.0566721i
\(957\) −5.16475 + 15.8955i −0.166953 + 0.513828i
\(958\) 2.95872 28.1503i 0.0955919 0.909496i
\(959\) −3.25417 + 2.36430i −0.105083 + 0.0763471i
\(960\) −1.00000 −0.0322749
\(961\) −4.97932 30.5975i −0.160623 0.987016i
\(962\) −16.5387 −0.533228
\(963\) −4.18991 + 3.04415i −0.135018 + 0.0980963i
\(964\) −2.96979 + 28.2557i −0.0956506 + 0.910054i
\(965\) 3.50671 10.7925i 0.112885 0.347424i
\(966\) −1.15222 + 1.99570i −0.0370720 + 0.0642106i
\(967\) −27.4155 47.4850i −0.881623 1.52702i −0.849536 0.527530i \(-0.823118\pi\)
−0.0320863 0.999485i \(-0.510215\pi\)
\(968\) 19.0455 4.04825i 0.612146 0.130116i
\(969\) 1.75995 + 5.41658i 0.0565379 + 0.174006i
\(970\) −11.0147 2.34124i −0.353660 0.0751727i
\(971\) 5.97841 + 56.8807i 0.191856 + 1.82539i 0.490974 + 0.871174i \(0.336641\pi\)
−0.299118 + 0.954216i \(0.596692\pi\)
\(972\) −0.669131 0.743145i −0.0214624 0.0238364i
\(973\) −6.45036 2.87188i −0.206789 0.0920684i
\(974\) −3.49533 + 1.55622i −0.111997 + 0.0498645i
\(975\) −1.87062 + 2.07754i −0.0599078 + 0.0665344i
\(976\) 2.64233 + 1.91976i 0.0845789 + 0.0614502i
\(977\) −20.6480 15.0016i −0.660587 0.479945i 0.206274 0.978494i \(-0.433866\pi\)
−0.866861 + 0.498549i \(0.833866\pi\)
\(978\) 1.44966 1.61001i 0.0463551 0.0514825i
\(979\) 12.3245 5.48722i 0.393893 0.175372i
\(980\) −5.86622 2.61181i −0.187390 0.0834312i
\(981\) 5.79150 + 6.43211i 0.184908 + 0.205362i
\(982\) −0.774083 7.36490i −0.0247020 0.235024i
\(983\) 38.7333 + 8.23302i 1.23540 + 0.262592i 0.778910 0.627136i \(-0.215773\pi\)
0.456491 + 0.889728i \(0.349106\pi\)
\(984\) −0.786764 2.42141i −0.0250811 0.0771918i
\(985\) −22.5075 + 4.78412i −0.717149 + 0.152435i
\(986\) 11.2652 + 19.5120i 0.358758 + 0.621388i
\(987\) 2.03898 3.53162i 0.0649016 0.112413i
\(988\) −0.661195 + 2.03495i −0.0210354 + 0.0647404i
\(989\) −1.27898 + 12.1687i −0.0406693 + 0.386942i
\(990\) 4.46582 3.24461i 0.141933 0.103120i
\(991\) −2.99463 −0.0951277 −0.0475638 0.998868i \(-0.515146\pi\)
−0.0475638 + 0.998868i \(0.515146\pi\)
\(992\) −3.60699 + 4.24142i −0.114522 + 0.134665i
\(993\) 14.0744 0.446637
\(994\) 8.09355 5.88031i 0.256712 0.186512i
\(995\) 0.487762 4.64074i 0.0154631 0.147121i
\(996\) −0.501361 + 1.54303i −0.0158862 + 0.0488928i
\(997\) −1.68806 + 2.92381i −0.0534615 + 0.0925981i −0.891518 0.452986i \(-0.850359\pi\)
0.838056 + 0.545584i \(0.183692\pi\)
\(998\) 7.55418 + 13.0842i 0.239123 + 0.414174i
\(999\) 5.78668 1.23000i 0.183082 0.0389154i
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 930.2.bg.h.121.3 24
31.10 even 15 inner 930.2.bg.h.661.3 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.h.121.3 24 1.1 even 1 trivial
930.2.bg.h.661.3 yes 24 31.10 even 15 inner