Properties

Label 930.2.z.c.349.3
Level $930$
Weight $2$
Character 930.349
Analytic conductor $7.426$
Analytic rank $0$
Dimension $32$
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] = [930,2,Mod(109,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.z (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 349.3
Character \(\chi\) \(=\) 930.349
Dual form 930.2.z.c.469.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(-1.68258 + 2.31587i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(-1.68258 + 2.31587i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.0762803 - 2.23477i) q^{10} +(-4.86343 - 3.53349i) q^{11} +(0.951057 + 0.309017i) q^{12} +(-0.678685 + 0.220518i) q^{13} +(2.31587 - 1.68258i) q^{14} +(1.25185 + 1.85280i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.19479 + 1.64449i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(-1.57448 + 4.84575i) q^{19} +(-0.763128 + 2.10182i) q^{20} +(-0.884584 + 2.72247i) q^{21} +(3.53349 + 4.86343i) q^{22} +(3.29476 + 4.53484i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(-4.23607 + 2.65626i) q^{25} +0.713612 q^{26} +(0.587785 - 0.809017i) q^{27} +(-2.72247 + 0.884584i) q^{28} +(1.71077 - 5.26520i) q^{29} +(-0.618034 - 2.14896i) q^{30} +(-5.55062 + 0.436608i) q^{31} -1.00000i q^{32} +(-5.71731 - 1.85767i) q^{33} +(-0.628140 - 1.93322i) q^{34} +(-6.01661 - 2.18451i) q^{35} +1.00000 q^{36} +4.26781i q^{37} +(2.99484 - 4.12204i) q^{38} +(-0.577324 + 0.419451i) q^{39} +(1.37527 - 1.76313i) q^{40} +(-0.325157 + 1.00073i) q^{41} +(1.68258 - 2.31587i) q^{42} +(-8.96014 - 2.91133i) q^{43} +(-1.85767 - 5.71731i) q^{44} +(1.76313 + 1.37527i) q^{45} +(-1.73216 - 5.33103i) q^{46} +(-11.0450 + 3.58874i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-0.369067 - 1.13587i) q^{49} +(4.84957 - 1.21724i) q^{50} +(1.64449 + 1.19479i) q^{51} +(-0.678685 - 0.220518i) q^{52} +(-7.79056 - 10.7228i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(4.58757 - 12.6351i) q^{55} +2.86257 q^{56} +5.09513i q^{57} +(-3.25407 + 4.47885i) q^{58} +(1.82481 + 5.61618i) q^{59} +(-0.0762803 + 2.23477i) q^{60} +11.9387 q^{61} +(5.41387 + 1.30000i) q^{62} +2.86257i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.893336 - 1.32218i) q^{65} +(4.86343 + 3.53349i) q^{66} +11.3596i q^{67} +2.03270i q^{68} +(4.53484 + 3.29476i) q^{69} +(5.04708 + 3.93682i) q^{70} +(1.32611 - 0.963477i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-6.11121 + 8.41136i) q^{73} +(1.31883 - 4.05893i) q^{74} +(-3.20791 + 3.83527i) q^{75} +(-4.12204 + 2.99484i) q^{76} +(16.3662 - 5.31771i) q^{77} +(0.678685 - 0.220518i) q^{78} +(-5.63751 + 4.09589i) q^{79} +(-1.85280 + 1.25185i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.618485 - 0.851272i) q^{82} +(10.8103 + 3.51249i) q^{83} +(-2.31587 + 1.68258i) q^{84} +(-2.79553 + 3.58392i) q^{85} +(7.62195 + 5.53767i) q^{86} -5.53616i q^{87} +6.01153i q^{88} +(-11.4566 - 8.32369i) q^{89} +(-1.25185 - 1.85280i) q^{90} +(0.631250 - 1.94279i) q^{91} +5.60537i q^{92} +(-5.14403 + 2.13047i) q^{93} +11.6134 q^{94} +(-11.3864 - 0.388658i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(2.63339 - 3.62455i) q^{97} +1.19432i q^{98} -6.01153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.951057 0.309017i −0.672499 0.218508i
\(3\) 0.951057 0.309017i 0.549093 0.178411i
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) 0.618034 + 2.14896i 0.276393 + 0.961045i
\(6\) −1.00000 −0.408248
\(7\) −1.68258 + 2.31587i −0.635955 + 0.875317i −0.998392 0.0566916i \(-0.981945\pi\)
0.362437 + 0.932008i \(0.381945\pi\)
\(8\) −0.587785 0.809017i −0.207813 0.286031i
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) 0.0762803 2.23477i 0.0241219 0.706695i
\(11\) −4.86343 3.53349i −1.46638 1.06539i −0.981643 0.190728i \(-0.938915\pi\)
−0.484737 0.874660i \(-0.661085\pi\)
\(12\) 0.951057 + 0.309017i 0.274546 + 0.0892055i
\(13\) −0.678685 + 0.220518i −0.188233 + 0.0611608i −0.401617 0.915808i \(-0.631552\pi\)
0.213383 + 0.976969i \(0.431552\pi\)
\(14\) 2.31587 1.68258i 0.618942 0.449688i
\(15\) 1.25185 + 1.85280i 0.323226 + 0.478391i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 1.19479 + 1.64449i 0.289780 + 0.398848i 0.928943 0.370224i \(-0.120719\pi\)
−0.639163 + 0.769072i \(0.720719\pi\)
\(18\) −0.951057 + 0.309017i −0.224166 + 0.0728360i
\(19\) −1.57448 + 4.84575i −0.361211 + 1.11169i 0.591109 + 0.806591i \(0.298690\pi\)
−0.952320 + 0.305101i \(0.901310\pi\)
\(20\) −0.763128 + 2.10182i −0.170641 + 0.469981i
\(21\) −0.884584 + 2.72247i −0.193032 + 0.594091i
\(22\) 3.53349 + 4.86343i 0.753343 + 1.03689i
\(23\) 3.29476 + 4.53484i 0.687004 + 0.945580i 0.999991 0.00417716i \(-0.00132964\pi\)
−0.312987 + 0.949757i \(0.601330\pi\)
\(24\) −0.809017 0.587785i −0.165140 0.119981i
\(25\) −4.23607 + 2.65626i −0.847214 + 0.531252i
\(26\) 0.713612 0.139951
\(27\) 0.587785 0.809017i 0.113119 0.155695i
\(28\) −2.72247 + 0.884584i −0.514498 + 0.167171i
\(29\) 1.71077 5.26520i 0.317682 0.977724i −0.656955 0.753930i \(-0.728156\pi\)
0.974637 0.223794i \(-0.0718442\pi\)
\(30\) −0.618034 2.14896i −0.112837 0.392345i
\(31\) −5.55062 + 0.436608i −0.996921 + 0.0784171i
\(32\) 1.00000i 0.176777i
\(33\) −5.71731 1.85767i −0.995256 0.323378i
\(34\) −0.628140 1.93322i −0.107725 0.331544i
\(35\) −6.01661 2.18451i −1.01699 0.369249i
\(36\) 1.00000 0.166667
\(37\) 4.26781i 0.701624i 0.936446 + 0.350812i \(0.114094\pi\)
−0.936446 + 0.350812i \(0.885906\pi\)
\(38\) 2.99484 4.12204i 0.485827 0.668684i
\(39\) −0.577324 + 0.419451i −0.0924459 + 0.0671659i
\(40\) 1.37527 1.76313i 0.217450 0.278775i
\(41\) −0.325157 + 1.00073i −0.0507810 + 0.156288i −0.973231 0.229828i \(-0.926184\pi\)
0.922450 + 0.386116i \(0.126184\pi\)
\(42\) 1.68258 2.31587i 0.259627 0.357347i
\(43\) −8.96014 2.91133i −1.36641 0.443973i −0.468231 0.883606i \(-0.655109\pi\)
−0.898177 + 0.439633i \(0.855109\pi\)
\(44\) −1.85767 5.71731i −0.280054 0.861917i
\(45\) 1.76313 + 1.37527i 0.262832 + 0.205014i
\(46\) −1.73216 5.33103i −0.255392 0.786017i
\(47\) −11.0450 + 3.58874i −1.61108 + 0.523471i −0.969813 0.243849i \(-0.921590\pi\)
−0.641265 + 0.767320i \(0.721590\pi\)
\(48\) 0.587785 + 0.809017i 0.0848395 + 0.116772i
\(49\) −0.369067 1.13587i −0.0527238 0.162267i
\(50\) 4.84957 1.21724i 0.685833 0.172143i
\(51\) 1.64449 + 1.19479i 0.230275 + 0.167305i
\(52\) −0.678685 0.220518i −0.0941167 0.0305804i
\(53\) −7.79056 10.7228i −1.07012 1.47289i −0.869959 0.493124i \(-0.835855\pi\)
−0.200157 0.979764i \(-0.564145\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) 4.58757 12.6351i 0.618588 1.70372i
\(56\) 2.86257 0.382527
\(57\) 5.09513i 0.674866i
\(58\) −3.25407 + 4.47885i −0.427281 + 0.588102i
\(59\) 1.82481 + 5.61618i 0.237570 + 0.731164i 0.996770 + 0.0803072i \(0.0255901\pi\)
−0.759201 + 0.650857i \(0.774410\pi\)
\(60\) −0.0762803 + 2.23477i −0.00984774 + 0.288507i
\(61\) 11.9387 1.52860 0.764300 0.644861i \(-0.223085\pi\)
0.764300 + 0.644861i \(0.223085\pi\)
\(62\) 5.41387 + 1.30000i 0.687562 + 0.165100i
\(63\) 2.86257i 0.360650i
\(64\) −0.309017 + 0.951057i −0.0386271 + 0.118882i
\(65\) −0.893336 1.32218i −0.110805 0.163996i
\(66\) 4.86343 + 3.53349i 0.598647 + 0.434943i
\(67\) 11.3596i 1.38779i 0.720074 + 0.693897i \(0.244108\pi\)
−0.720074 + 0.693897i \(0.755892\pi\)
\(68\) 2.03270i 0.246502i
\(69\) 4.53484 + 3.29476i 0.545931 + 0.396642i
\(70\) 5.04708 + 3.93682i 0.603242 + 0.470541i
\(71\) 1.32611 0.963477i 0.157381 0.114344i −0.506308 0.862353i \(-0.668990\pi\)
0.663688 + 0.748009i \(0.268990\pi\)
\(72\) −0.951057 0.309017i −0.112083 0.0364180i
\(73\) −6.11121 + 8.41136i −0.715263 + 0.984475i 0.284405 + 0.958704i \(0.408204\pi\)
−0.999668 + 0.0257711i \(0.991796\pi\)
\(74\) 1.31883 4.05893i 0.153311 0.471841i
\(75\) −3.20791 + 3.83527i −0.370418 + 0.442859i
\(76\) −4.12204 + 2.99484i −0.472831 + 0.343532i
\(77\) 16.3662 5.31771i 1.86510 0.606009i
\(78\) 0.678685 0.220518i 0.0768460 0.0249688i
\(79\) −5.63751 + 4.09589i −0.634269 + 0.460824i −0.857877 0.513856i \(-0.828217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(80\) −1.85280 + 1.25185i −0.207149 + 0.139961i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0.618485 0.851272i 0.0683003 0.0940072i
\(83\) 10.8103 + 3.51249i 1.18659 + 0.385545i 0.834810 0.550538i \(-0.185578\pi\)
0.351777 + 0.936084i \(0.385578\pi\)
\(84\) −2.31587 + 1.68258i −0.252682 + 0.183584i
\(85\) −2.79553 + 3.58392i −0.303218 + 0.388730i
\(86\) 7.62195 + 5.53767i 0.821896 + 0.597142i
\(87\) 5.53616i 0.593539i
\(88\) 6.01153i 0.640832i
\(89\) −11.4566 8.32369i −1.21439 0.882309i −0.218772 0.975776i \(-0.570205\pi\)
−0.995622 + 0.0934669i \(0.970205\pi\)
\(90\) −1.25185 1.85280i −0.131957 0.195302i
\(91\) 0.631250 1.94279i 0.0661729 0.203659i
\(92\) 5.60537i 0.584401i
\(93\) −5.14403 + 2.13047i −0.533411 + 0.220920i
\(94\) 11.6134 1.19783
\(95\) −11.3864 0.388658i −1.16822 0.0398754i
\(96\) −0.309017 0.951057i −0.0315389 0.0970668i
\(97\) 2.63339 3.62455i 0.267380 0.368017i −0.654123 0.756388i \(-0.726962\pi\)
0.921503 + 0.388371i \(0.126962\pi\)
\(98\) 1.19432i 0.120645i
\(99\) −6.01153 −0.604182
\(100\) −4.98836 0.340937i −0.498836 0.0340937i
\(101\) 16.0147 11.6354i 1.59353 1.15776i 0.694846 0.719159i \(-0.255473\pi\)
0.898680 0.438605i \(-0.144527\pi\)
\(102\) −1.19479 1.64449i −0.118302 0.162829i
\(103\) −6.32395 2.05478i −0.623117 0.202463i −0.0195935 0.999808i \(-0.506237\pi\)
−0.603524 + 0.797345i \(0.706237\pi\)
\(104\) 0.577324 + 0.419451i 0.0566113 + 0.0411305i
\(105\) −6.39718 0.218358i −0.624301 0.0213095i
\(106\) 4.09574 + 12.6054i 0.397813 + 1.22434i
\(107\) 1.28134 + 1.76361i 0.123872 + 0.170495i 0.866449 0.499266i \(-0.166397\pi\)
−0.742577 + 0.669760i \(0.766397\pi\)
\(108\) 0.951057 0.309017i 0.0915155 0.0297352i
\(109\) 4.34284 + 13.3659i 0.415968 + 1.28022i 0.911382 + 0.411562i \(0.135017\pi\)
−0.495413 + 0.868657i \(0.664983\pi\)
\(110\) −8.26751 + 10.5991i −0.788276 + 1.01058i
\(111\) 1.31883 + 4.05893i 0.125178 + 0.385257i
\(112\) −2.72247 0.884584i −0.257249 0.0835853i
\(113\) 0.549766 0.756688i 0.0517177 0.0711833i −0.782375 0.622808i \(-0.785992\pi\)
0.834093 + 0.551625i \(0.185992\pi\)
\(114\) 1.57448 4.84575i 0.147464 0.453846i
\(115\) −7.70893 + 9.88299i −0.718862 + 0.921594i
\(116\) 4.47885 3.25407i 0.415851 0.302133i
\(117\) −0.419451 + 0.577324i −0.0387782 + 0.0533736i
\(118\) 5.90520i 0.543617i
\(119\) −5.81877 −0.533405
\(120\) 0.763128 2.10182i 0.0696637 0.191869i
\(121\) 7.76824 + 23.9082i 0.706203 + 2.17347i
\(122\) −11.3544 3.68927i −1.02798 0.334011i
\(123\) 1.05223i 0.0948764i
\(124\) −4.74718 2.90935i −0.426309 0.261267i
\(125\) −8.32624 7.46149i −0.744721 0.667376i
\(126\) 0.884584 2.72247i 0.0788050 0.242537i
\(127\) 19.7779 6.42623i 1.75501 0.570236i 0.758342 0.651856i \(-0.226009\pi\)
0.996663 + 0.0816203i \(0.0260095\pi\)
\(128\) 0.587785 0.809017i 0.0519534 0.0715077i
\(129\) −9.42125 −0.829495
\(130\) 0.441036 + 1.53352i 0.0386815 + 0.134499i
\(131\) 8.67192 + 6.30052i 0.757669 + 0.550479i 0.898195 0.439598i \(-0.144879\pi\)
−0.140525 + 0.990077i \(0.544879\pi\)
\(132\) −3.53349 4.86343i −0.307551 0.423308i
\(133\) −8.57295 11.7997i −0.743369 1.02316i
\(134\) 3.51031 10.8036i 0.303244 0.933290i
\(135\) 2.10182 + 0.763128i 0.180896 + 0.0656796i
\(136\) 0.628140 1.93322i 0.0538626 0.165772i
\(137\) −0.556816 + 0.180920i −0.0475720 + 0.0154571i −0.332706 0.943030i \(-0.607962\pi\)
0.285134 + 0.958488i \(0.407962\pi\)
\(138\) −3.29476 4.53484i −0.280468 0.386032i
\(139\) −0.346720 1.06709i −0.0294084 0.0905097i 0.935275 0.353922i \(-0.115152\pi\)
−0.964683 + 0.263412i \(0.915152\pi\)
\(140\) −3.58351 5.30378i −0.302862 0.448251i
\(141\) −9.39543 + 6.82618i −0.791238 + 0.574868i
\(142\) −1.55894 + 0.506530i −0.130823 + 0.0425070i
\(143\) 4.07994 + 1.32565i 0.341182 + 0.110857i
\(144\) 0.809017 + 0.587785i 0.0674181 + 0.0489821i
\(145\) 12.3720 + 0.422300i 1.02744 + 0.0350701i
\(146\) 8.41136 6.11121i 0.696129 0.505768i
\(147\) −0.702007 0.966229i −0.0579005 0.0796932i
\(148\) −2.50856 + 3.45273i −0.206202 + 0.283813i
\(149\) 14.0265 1.14910 0.574548 0.818471i \(-0.305178\pi\)
0.574548 + 0.818471i \(0.305178\pi\)
\(150\) 4.23607 2.65626i 0.345874 0.216883i
\(151\) 3.18555 + 2.31443i 0.259236 + 0.188346i 0.709810 0.704393i \(-0.248781\pi\)
−0.450574 + 0.892739i \(0.648781\pi\)
\(152\) 4.84575 1.57448i 0.393042 0.127707i
\(153\) 1.93322 + 0.628140i 0.156291 + 0.0507821i
\(154\) −17.2085 −1.38670
\(155\) −4.36872 11.6582i −0.350904 0.936411i
\(156\) −0.713612 −0.0571347
\(157\) −2.07073 0.672822i −0.165263 0.0536971i 0.225217 0.974309i \(-0.427691\pi\)
−0.390480 + 0.920612i \(0.627691\pi\)
\(158\) 6.62729 2.15334i 0.527239 0.171310i
\(159\) −10.7228 7.79056i −0.850372 0.617832i
\(160\) 2.14896 0.618034i 0.169890 0.0488599i
\(161\) −16.0458 −1.26459
\(162\) −0.587785 + 0.809017i −0.0461808 + 0.0635624i
\(163\) 2.37292 + 3.26604i 0.185861 + 0.255816i 0.891772 0.452484i \(-0.149462\pi\)
−0.705911 + 0.708301i \(0.749462\pi\)
\(164\) −0.851272 + 0.618485i −0.0664732 + 0.0482956i
\(165\) 0.458561 13.4344i 0.0356990 1.04586i
\(166\) −9.19581 6.68114i −0.713733 0.518557i
\(167\) 10.3363 + 3.35847i 0.799847 + 0.259886i 0.680292 0.732942i \(-0.261853\pi\)
0.119555 + 0.992828i \(0.461853\pi\)
\(168\) 2.72247 0.884584i 0.210043 0.0682471i
\(169\) −10.1052 + 7.34188i −0.777326 + 0.564760i
\(170\) 3.76620 2.54464i 0.288854 0.195165i
\(171\) 1.57448 + 4.84575i 0.120404 + 0.370564i
\(172\) −5.53767 7.62195i −0.422243 0.581168i
\(173\) −22.0747 + 7.17249i −1.67831 + 0.545314i −0.984581 0.174927i \(-0.944031\pi\)
−0.693724 + 0.720241i \(0.744031\pi\)
\(174\) −1.71077 + 5.26520i −0.129693 + 0.399154i
\(175\) 0.975958 14.2796i 0.0737755 1.07943i
\(176\) 1.85767 5.71731i 0.140027 0.430958i
\(177\) 3.47099 + 4.77741i 0.260895 + 0.359092i
\(178\) 8.32369 + 11.4566i 0.623887 + 0.858706i
\(179\) 6.59728 + 4.79320i 0.493104 + 0.358261i 0.806377 0.591402i \(-0.201425\pi\)
−0.313273 + 0.949663i \(0.601425\pi\)
\(180\) 0.618034 + 2.14896i 0.0460655 + 0.160174i
\(181\) 14.7509 1.09643 0.548213 0.836338i \(-0.315308\pi\)
0.548213 + 0.836338i \(0.315308\pi\)
\(182\) −1.20071 + 1.65263i −0.0890024 + 0.122501i
\(183\) 11.3544 3.68927i 0.839343 0.272719i
\(184\) 1.73216 5.33103i 0.127696 0.393009i
\(185\) −9.17137 + 2.63765i −0.674292 + 0.193924i
\(186\) 5.55062 0.436608i 0.406991 0.0320136i
\(187\) 12.2197i 0.893591i
\(188\) −11.0450 3.58874i −0.805539 0.261735i
\(189\) 0.884584 + 2.72247i 0.0643440 + 0.198030i
\(190\) 10.7090 + 3.88823i 0.776914 + 0.282082i
\(191\) −5.39836 −0.390612 −0.195306 0.980742i \(-0.562570\pi\)
−0.195306 + 0.980742i \(0.562570\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 10.1764 14.0066i 0.732514 1.00822i −0.266500 0.963835i \(-0.585867\pi\)
0.999015 0.0443847i \(-0.0141327\pi\)
\(194\) −3.62455 + 2.63339i −0.260228 + 0.189066i
\(195\) −1.25819 0.981413i −0.0901008 0.0702804i
\(196\) 0.369067 1.13587i 0.0263619 0.0811336i
\(197\) 2.60914 3.59118i 0.185894 0.255861i −0.705891 0.708320i \(-0.749453\pi\)
0.891785 + 0.452459i \(0.149453\pi\)
\(198\) 5.71731 + 1.85767i 0.406311 + 0.132019i
\(199\) 1.97477 + 6.07772i 0.139988 + 0.430838i 0.996332 0.0855666i \(-0.0272701\pi\)
−0.856345 + 0.516405i \(0.827270\pi\)
\(200\) 4.63886 + 1.86574i 0.328017 + 0.131928i
\(201\) 3.51031 + 10.8036i 0.247598 + 0.762028i
\(202\) −18.8264 + 6.11708i −1.32462 + 0.430397i
\(203\) 9.31503 + 12.8210i 0.653787 + 0.899860i
\(204\) 0.628140 + 1.93322i 0.0439786 + 0.135352i
\(205\) −2.35149 0.0802644i −0.164235 0.00560591i
\(206\) 5.37947 + 3.90842i 0.374806 + 0.272312i
\(207\) 5.33103 + 1.73216i 0.370532 + 0.120393i
\(208\) −0.419451 0.577324i −0.0290837 0.0400302i
\(209\) 24.7798 18.0036i 1.71406 1.24533i
\(210\) 6.01661 + 2.18451i 0.415185 + 0.150745i
\(211\) 1.52468 0.104963 0.0524815 0.998622i \(-0.483287\pi\)
0.0524815 + 0.998622i \(0.483287\pi\)
\(212\) 13.2541i 0.910295i
\(213\) 0.963477 1.32611i 0.0660163 0.0908637i
\(214\) −0.673640 2.07325i −0.0460491 0.141725i
\(215\) 0.718655 21.0543i 0.0490119 1.43589i
\(216\) −1.00000 −0.0680414
\(217\) 8.32822 13.5891i 0.565357 0.922491i
\(218\) 14.0537i 0.951838i
\(219\) −3.21285 + 9.88815i −0.217105 + 0.668179i
\(220\) 11.1382 7.52554i 0.750936 0.507372i
\(221\) −1.17353 0.852619i −0.0789401 0.0573534i
\(222\) 4.26781i 0.286437i
\(223\) 14.6275i 0.979530i −0.871854 0.489765i \(-0.837083\pi\)
0.871854 0.489765i \(-0.162917\pi\)
\(224\) 2.31587 + 1.68258i 0.154736 + 0.112422i
\(225\) −1.86574 + 4.63886i −0.124383 + 0.309257i
\(226\) −0.756688 + 0.549766i −0.0503342 + 0.0365699i
\(227\) 7.32529 + 2.38013i 0.486196 + 0.157975i 0.541850 0.840475i \(-0.317724\pi\)
−0.0556534 + 0.998450i \(0.517724\pi\)
\(228\) −2.99484 + 4.12204i −0.198338 + 0.272989i
\(229\) 2.38911 7.35292i 0.157877 0.485895i −0.840564 0.541712i \(-0.817776\pi\)
0.998441 + 0.0558171i \(0.0177764\pi\)
\(230\) 10.3856 7.01709i 0.684809 0.462693i
\(231\) 13.9219 10.1149i 0.915996 0.665510i
\(232\) −5.26520 + 1.71077i −0.345678 + 0.112317i
\(233\) 4.12333 1.33975i 0.270128 0.0877699i −0.170821 0.985302i \(-0.554642\pi\)
0.440949 + 0.897532i \(0.354642\pi\)
\(234\) 0.577324 0.419451i 0.0377409 0.0274203i
\(235\) −14.5382 21.5173i −0.948370 1.40363i
\(236\) −1.82481 + 5.61618i −0.118785 + 0.365582i
\(237\) −4.09589 + 5.63751i −0.266057 + 0.366195i
\(238\) 5.53398 + 1.79810i 0.358714 + 0.116553i
\(239\) −7.04289 + 5.11696i −0.455567 + 0.330989i −0.791790 0.610794i \(-0.790850\pi\)
0.336223 + 0.941782i \(0.390850\pi\)
\(240\) −1.37527 + 1.76313i −0.0887736 + 0.113809i
\(241\) 4.17836 + 3.03576i 0.269152 + 0.195550i 0.714172 0.699970i \(-0.246803\pi\)
−0.445020 + 0.895521i \(0.646803\pi\)
\(242\) 25.1385i 1.61597i
\(243\) 1.00000i 0.0641500i
\(244\) 9.65864 + 7.01742i 0.618331 + 0.449244i
\(245\) 2.21285 1.49512i 0.141374 0.0955195i
\(246\) 0.325157 1.00073i 0.0207312 0.0638042i
\(247\) 3.63594i 0.231350i
\(248\) 3.61580 + 4.23391i 0.229603 + 0.268854i
\(249\) 11.3666 0.720332
\(250\) 5.61300 + 9.66924i 0.354997 + 0.611537i
\(251\) 0.0275651 + 0.0848368i 0.00173990 + 0.00535485i 0.951923 0.306338i \(-0.0991039\pi\)
−0.950183 + 0.311693i \(0.899104\pi\)
\(252\) −1.68258 + 2.31587i −0.105992 + 0.145886i
\(253\) 33.6969i 2.11851i
\(254\) −20.7957 −1.30484
\(255\) −1.55121 + 4.27237i −0.0971407 + 0.267546i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 6.74059 + 9.27762i 0.420466 + 0.578722i 0.965732 0.259541i \(-0.0835712\pi\)
−0.545266 + 0.838263i \(0.683571\pi\)
\(258\) 8.96014 + 2.91133i 0.557834 + 0.181251i
\(259\) −9.88371 7.18093i −0.614144 0.446201i
\(260\) 0.0544345 1.59476i 0.00337588 0.0989026i
\(261\) −1.71077 5.26520i −0.105894 0.325908i
\(262\) −6.30052 8.67192i −0.389247 0.535753i
\(263\) −17.8687 + 5.80589i −1.10183 + 0.358006i −0.802807 0.596239i \(-0.796661\pi\)
−0.299024 + 0.954246i \(0.596661\pi\)
\(264\) 1.85767 + 5.71731i 0.114331 + 0.351876i
\(265\) 18.2280 23.3687i 1.11974 1.43553i
\(266\) 4.50707 + 13.8713i 0.276346 + 0.850505i
\(267\) −13.4680 4.37602i −0.824229 0.267808i
\(268\) −6.67700 + 9.19010i −0.407863 + 0.561375i
\(269\) 2.05974 6.33923i 0.125585 0.386510i −0.868422 0.495825i \(-0.834866\pi\)
0.994007 + 0.109315i \(0.0348658\pi\)
\(270\) −1.76313 1.37527i −0.107301 0.0836966i
\(271\) 23.0613 16.7550i 1.40087 1.01779i 0.406301 0.913739i \(-0.366818\pi\)
0.994572 0.104054i \(-0.0331816\pi\)
\(272\) −1.19479 + 1.64449i −0.0724450 + 0.0997120i
\(273\) 2.04277i 0.123634i
\(274\) 0.585471 0.0353696
\(275\) 29.9877 + 2.04956i 1.80833 + 0.123593i
\(276\) 1.73216 + 5.33103i 0.104264 + 0.320890i
\(277\) 14.6530 + 4.76104i 0.880412 + 0.286063i 0.714129 0.700015i \(-0.246823\pi\)
0.166284 + 0.986078i \(0.446823\pi\)
\(278\) 1.12201i 0.0672936i
\(279\) −4.23391 + 3.61580i −0.253478 + 0.216472i
\(280\) 1.76917 + 6.15156i 0.105728 + 0.367626i
\(281\) −4.29648 + 13.2232i −0.256306 + 0.788830i 0.737263 + 0.675606i \(0.236118\pi\)
−0.993569 + 0.113224i \(0.963882\pi\)
\(282\) 11.0450 3.58874i 0.657720 0.213706i
\(283\) −4.23413 + 5.82777i −0.251693 + 0.346425i −0.916103 0.400943i \(-0.868683\pi\)
0.664411 + 0.747368i \(0.268683\pi\)
\(284\) 1.63916 0.0972665
\(285\) −10.9492 + 3.14896i −0.648576 + 0.186528i
\(286\) −3.47060 2.52154i −0.205221 0.149102i
\(287\) −1.77046 2.43683i −0.104507 0.143841i
\(288\) −0.587785 0.809017i −0.0346356 0.0476718i
\(289\) 3.97647 12.2383i 0.233910 0.719900i
\(290\) −11.6360 4.22480i −0.683290 0.248089i
\(291\) 1.38446 4.26092i 0.0811582 0.249779i
\(292\) −9.88815 + 3.21285i −0.578660 + 0.188018i
\(293\) 4.33880 + 5.97184i 0.253475 + 0.348879i 0.916725 0.399520i \(-0.130823\pi\)
−0.663249 + 0.748399i \(0.730823\pi\)
\(294\) 0.369067 + 1.13587i 0.0215244 + 0.0662453i
\(295\) −10.9412 + 7.39243i −0.637019 + 0.430404i
\(296\) 3.45273 2.50856i 0.200686 0.145807i
\(297\) −5.71731 + 1.85767i −0.331752 + 0.107793i
\(298\) −13.3400 4.33443i −0.772766 0.251087i
\(299\) −3.23612 2.35118i −0.187150 0.135972i
\(300\) −4.84957 + 1.21724i −0.279990 + 0.0702773i
\(301\) 21.8184 15.8520i 1.25759 0.913693i
\(302\) −2.31443 3.18555i −0.133181 0.183308i
\(303\) 11.6354 16.0147i 0.668435 0.920022i
\(304\) −5.09513 −0.292226
\(305\) 7.37855 + 25.6559i 0.422494 + 1.46905i
\(306\) −1.64449 1.19479i −0.0940094 0.0683018i
\(307\) 0.432024 0.140373i 0.0246569 0.00801152i −0.296663 0.954982i \(-0.595874\pi\)
0.321319 + 0.946971i \(0.395874\pi\)
\(308\) 16.3662 + 5.31771i 0.932552 + 0.303004i
\(309\) −6.64940 −0.378271
\(310\) 0.552314 + 12.4376i 0.0313693 + 0.706411i
\(311\) −29.8677 −1.69364 −0.846821 0.531879i \(-0.821486\pi\)
−0.846821 + 0.531879i \(0.821486\pi\)
\(312\) 0.678685 + 0.220518i 0.0384230 + 0.0124844i
\(313\) −11.1335 + 3.61749i −0.629302 + 0.204473i −0.606266 0.795262i \(-0.707333\pi\)
−0.0230360 + 0.999735i \(0.507333\pi\)
\(314\) 1.76147 + 1.27978i 0.0994056 + 0.0722224i
\(315\) −6.15156 + 1.76917i −0.346601 + 0.0996813i
\(316\) −6.96834 −0.392000
\(317\) −10.5043 + 14.4579i −0.589979 + 0.812037i −0.994745 0.102383i \(-0.967353\pi\)
0.404766 + 0.914420i \(0.367353\pi\)
\(318\) 7.79056 + 10.7228i 0.436873 + 0.601304i
\(319\) −26.9248 + 19.5620i −1.50750 + 1.09526i
\(320\) −2.23477 0.0762803i −0.124927 0.00426420i
\(321\) 1.76361 + 1.28134i 0.0984353 + 0.0715174i
\(322\) 15.2605 + 4.95842i 0.850432 + 0.276322i
\(323\) −9.84998 + 3.20045i −0.548068 + 0.178078i
\(324\) 0.809017 0.587785i 0.0449454 0.0326547i
\(325\) 2.28920 2.73690i 0.126982 0.151816i
\(326\) −1.24752 3.83946i −0.0690936 0.212648i
\(327\) 8.26057 + 11.3697i 0.456811 + 0.628746i
\(328\) 1.00073 0.325157i 0.0552561 0.0179538i
\(329\) 10.2730 31.6171i 0.566370 1.74311i
\(330\) −4.58757 + 12.6351i −0.252537 + 0.695542i
\(331\) −6.50433 + 20.0183i −0.357510 + 1.10030i 0.597029 + 0.802220i \(0.296348\pi\)
−0.954540 + 0.298084i \(0.903652\pi\)
\(332\) 6.68114 + 9.19581i 0.366675 + 0.504685i
\(333\) 2.50856 + 3.45273i 0.137468 + 0.189209i
\(334\) −8.79258 6.38818i −0.481109 0.349546i
\(335\) −24.4113 + 7.02061i −1.33373 + 0.383577i
\(336\) −2.86257 −0.156166
\(337\) −14.5290 + 19.9975i −0.791447 + 1.08933i 0.202480 + 0.979286i \(0.435100\pi\)
−0.993926 + 0.110046i \(0.964900\pi\)
\(338\) 11.8794 3.85986i 0.646155 0.209949i
\(339\) 0.289029 0.889541i 0.0156979 0.0483132i
\(340\) −4.36820 + 1.25628i −0.236899 + 0.0681314i
\(341\) 28.5378 + 17.4897i 1.54541 + 0.947118i
\(342\) 5.09513i 0.275513i
\(343\) −15.8058 5.13561i −0.853431 0.277297i
\(344\) 2.91133 + 8.96014i 0.156968 + 0.483098i
\(345\) −4.27762 + 11.7815i −0.230299 + 0.634293i
\(346\) 23.2107 1.24781
\(347\) 12.9979i 0.697763i 0.937167 + 0.348882i \(0.113438\pi\)
−0.937167 + 0.348882i \(0.886562\pi\)
\(348\) 3.25407 4.47885i 0.174437 0.240092i
\(349\) 19.5525 14.2057i 1.04662 0.760415i 0.0750546 0.997179i \(-0.476087\pi\)
0.971567 + 0.236764i \(0.0760869\pi\)
\(350\) −5.34082 + 13.2791i −0.285479 + 0.709796i
\(351\) −0.220518 + 0.678685i −0.0117704 + 0.0362255i
\(352\) −3.53349 + 4.86343i −0.188336 + 0.259222i
\(353\) 24.8977 + 8.08976i 1.32517 + 0.430574i 0.884268 0.466980i \(-0.154658\pi\)
0.440904 + 0.897554i \(0.354658\pi\)
\(354\) −1.82481 5.61618i −0.0969874 0.298496i
\(355\) 2.89006 + 2.25430i 0.153388 + 0.119646i
\(356\) −4.37602 13.4680i −0.231929 0.713803i
\(357\) −5.53398 + 1.79810i −0.292889 + 0.0951654i
\(358\) −4.79320 6.59728i −0.253329 0.348677i
\(359\) −1.37220 4.22321i −0.0724222 0.222893i 0.908293 0.418334i \(-0.137386\pi\)
−0.980715 + 0.195442i \(0.937386\pi\)
\(360\) 0.0762803 2.23477i 0.00402032 0.117783i
\(361\) −5.63101 4.09117i −0.296369 0.215325i
\(362\) −14.0290 4.55828i −0.737345 0.239578i
\(363\) 14.7761 + 20.3375i 0.775542 + 1.06744i
\(364\) 1.65263 1.20071i 0.0866215 0.0629342i
\(365\) −21.8526 7.93425i −1.14382 0.415298i
\(366\) −11.9387 −0.624048
\(367\) 28.2549i 1.47490i −0.675404 0.737448i \(-0.736031\pi\)
0.675404 0.737448i \(-0.263969\pi\)
\(368\) −3.29476 + 4.53484i −0.171751 + 0.236395i
\(369\) 0.325157 + 1.00073i 0.0169270 + 0.0520959i
\(370\) 9.53757 + 0.325550i 0.495835 + 0.0169245i
\(371\) 37.9408 1.96979
\(372\) −5.41387 1.30000i −0.280696 0.0674017i
\(373\) 5.03686i 0.260799i −0.991462 0.130399i \(-0.958374\pi\)
0.991462 0.130399i \(-0.0416260\pi\)
\(374\) −3.77609 + 11.6216i −0.195257 + 0.600939i
\(375\) −10.2244 4.52335i −0.527988 0.233585i
\(376\) 9.39543 + 6.82618i 0.484532 + 0.352033i
\(377\) 3.95067i 0.203470i
\(378\) 2.86257i 0.147235i
\(379\) −27.1691 19.7395i −1.39558 1.01395i −0.995226 0.0975926i \(-0.968886\pi\)
−0.400358 0.916359i \(-0.631114\pi\)
\(380\) −8.98336 7.00720i −0.460837 0.359462i
\(381\) 16.8241 12.2234i 0.861925 0.626225i
\(382\) 5.13415 + 1.66818i 0.262686 + 0.0853518i
\(383\) 21.7892 29.9902i 1.11338 1.53243i 0.297027 0.954869i \(-0.404005\pi\)
0.816348 0.577560i \(-0.195995\pi\)
\(384\) 0.309017 0.951057i 0.0157695 0.0485334i
\(385\) 21.5424 + 31.8838i 1.09790 + 1.62495i
\(386\) −14.0066 + 10.1764i −0.712919 + 0.517966i
\(387\) −8.96014 + 2.91133i −0.455470 + 0.147991i
\(388\) 4.26092 1.38446i 0.216315 0.0702851i
\(389\) −11.3252 + 8.22820i −0.574208 + 0.417187i −0.836631 0.547766i \(-0.815478\pi\)
0.262423 + 0.964953i \(0.415478\pi\)
\(390\) 0.893336 + 1.32218i 0.0452358 + 0.0669512i
\(391\) −3.52096 + 10.8364i −0.178063 + 0.548021i
\(392\) −0.702007 + 0.966229i −0.0354567 + 0.0488019i
\(393\) 10.1945 + 3.31238i 0.514242 + 0.167087i
\(394\) −3.59118 + 2.60914i −0.180921 + 0.131447i
\(395\) −12.2861 9.58339i −0.618180 0.482193i
\(396\) −4.86343 3.53349i −0.244397 0.177565i
\(397\) 21.3827i 1.07317i 0.843847 + 0.536584i \(0.180285\pi\)
−0.843847 + 0.536584i \(0.819715\pi\)
\(398\) 6.39049i 0.320326i
\(399\) −11.7997 8.57295i −0.590721 0.429184i
\(400\) −3.83527 3.20791i −0.191764 0.160395i
\(401\) 5.20680 16.0249i 0.260015 0.800245i −0.732785 0.680461i \(-0.761780\pi\)
0.992800 0.119784i \(-0.0382202\pi\)
\(402\) 11.3596i 0.566565i
\(403\) 3.67084 1.52033i 0.182858 0.0757331i
\(404\) 19.7953 0.984853
\(405\) 2.23477 + 0.0762803i 0.111046 + 0.00379040i
\(406\) −4.89720 15.0720i −0.243044 0.748012i
\(407\) 15.0803 20.7562i 0.747502 1.02885i
\(408\) 2.03270i 0.100634i
\(409\) −9.10760 −0.450342 −0.225171 0.974319i \(-0.572294\pi\)
−0.225171 + 0.974319i \(0.572294\pi\)
\(410\) 2.21159 + 0.802986i 0.109223 + 0.0396566i
\(411\) −0.473656 + 0.344131i −0.0233637 + 0.0169747i
\(412\) −3.90842 5.37947i −0.192554 0.265028i
\(413\) −16.0767 5.22364i −0.791083 0.257039i
\(414\) −4.53484 3.29476i −0.222875 0.161928i
\(415\) −0.867050 + 25.4018i −0.0425618 + 1.24692i
\(416\) 0.220518 + 0.678685i 0.0108118 + 0.0332753i
\(417\) −0.659500 0.907724i −0.0322959 0.0444514i
\(418\) −29.1304 + 9.46504i −1.42481 + 0.462950i
\(419\) 4.88354 + 15.0300i 0.238577 + 0.734264i 0.996627 + 0.0820674i \(0.0261523\pi\)
−0.758050 + 0.652196i \(0.773848\pi\)
\(420\) −5.04708 3.93682i −0.246272 0.192097i
\(421\) 6.59168 + 20.2871i 0.321259 + 0.988732i 0.973101 + 0.230378i \(0.0739963\pi\)
−0.651843 + 0.758354i \(0.726004\pi\)
\(422\) −1.45005 0.471151i −0.0705874 0.0229353i
\(423\) −6.82618 + 9.39543i −0.331900 + 0.456822i
\(424\) −4.09574 + 12.6054i −0.198907 + 0.612172i
\(425\) −9.42943 3.79250i −0.457395 0.183963i
\(426\) −1.32611 + 0.963477i −0.0642503 + 0.0466806i
\(427\) −20.0879 + 27.6486i −0.972120 + 1.33801i
\(428\) 2.17995i 0.105372i
\(429\) 4.28990 0.207118
\(430\) −7.18962 + 19.8017i −0.346714 + 0.954925i
\(431\) 2.96352 + 9.12079i 0.142748 + 0.439333i 0.996715 0.0809950i \(-0.0258098\pi\)
−0.853967 + 0.520328i \(0.825810\pi\)
\(432\) 0.951057 + 0.309017i 0.0457577 + 0.0148676i
\(433\) 7.11778i 0.342059i 0.985266 + 0.171029i \(0.0547093\pi\)
−0.985266 + 0.171029i \(0.945291\pi\)
\(434\) −12.1199 + 10.3505i −0.581773 + 0.496839i
\(435\) 11.8970 3.42154i 0.570417 0.164050i
\(436\) −4.34284 + 13.3659i −0.207984 + 0.640110i
\(437\) −27.1623 + 8.82555i −1.29935 + 0.422183i
\(438\) 6.11121 8.41136i 0.292005 0.401910i
\(439\) 39.7425 1.89681 0.948403 0.317068i \(-0.102698\pi\)
0.948403 + 0.317068i \(0.102698\pi\)
\(440\) −12.9186 + 3.71533i −0.615868 + 0.177122i
\(441\) −0.966229 0.702007i −0.0460109 0.0334289i
\(442\) 0.852619 + 1.17353i 0.0405550 + 0.0558191i
\(443\) 1.85205 + 2.54913i 0.0879936 + 0.121113i 0.850744 0.525580i \(-0.176152\pi\)
−0.762751 + 0.646693i \(0.776152\pi\)
\(444\) −1.31883 + 4.05893i −0.0625888 + 0.192628i
\(445\) 10.8067 29.7641i 0.512288 1.41095i
\(446\) −4.52015 + 13.9116i −0.214035 + 0.658733i
\(447\) 13.3400 4.33443i 0.630961 0.205011i
\(448\) −1.68258 2.31587i −0.0794944 0.109415i
\(449\) 10.4270 + 32.0909i 0.492079 + 1.51446i 0.821460 + 0.570266i \(0.193160\pi\)
−0.329382 + 0.944197i \(0.606840\pi\)
\(450\) 3.20791 3.83527i 0.151222 0.180796i
\(451\) 5.11745 3.71804i 0.240971 0.175076i
\(452\) 0.889541 0.289029i 0.0418405 0.0135948i
\(453\) 3.74483 + 1.21677i 0.175948 + 0.0571689i
\(454\) −6.23126 4.52728i −0.292448 0.212476i
\(455\) 4.56511 + 0.155823i 0.214015 + 0.00730508i
\(456\) 4.12204 2.99484i 0.193032 0.140246i
\(457\) −8.40132 11.5634i −0.392997 0.540914i 0.565972 0.824424i \(-0.308501\pi\)
−0.958969 + 0.283510i \(0.908501\pi\)
\(458\) −4.54436 + 6.25477i −0.212344 + 0.292266i
\(459\) 2.03270 0.0948785
\(460\) −12.0457 + 3.46431i −0.561635 + 0.161524i
\(461\) −31.3876 22.8044i −1.46187 1.06211i −0.982872 0.184289i \(-0.941002\pi\)
−0.478994 0.877818i \(-0.658998\pi\)
\(462\) −16.3662 + 5.31771i −0.761425 + 0.247402i
\(463\) −19.6893 6.39744i −0.915039 0.297314i −0.186609 0.982434i \(-0.559750\pi\)
−0.728430 + 0.685120i \(0.759750\pi\)
\(464\) 5.53616 0.257010
\(465\) −7.75749 9.73762i −0.359745 0.451571i
\(466\) −4.33552 −0.200839
\(467\) −29.3636 9.54083i −1.35879 0.441497i −0.463149 0.886280i \(-0.653281\pi\)
−0.895638 + 0.444783i \(0.853281\pi\)
\(468\) −0.678685 + 0.220518i −0.0313722 + 0.0101935i
\(469\) −26.3073 19.1134i −1.21476 0.882575i
\(470\) 7.17747 + 24.9567i 0.331072 + 1.15117i
\(471\) −2.17730 −0.100325
\(472\) 3.47099 4.77741i 0.159765 0.219898i
\(473\) 33.2899 + 45.8196i 1.53067 + 2.10679i
\(474\) 5.63751 4.09589i 0.258939 0.188130i
\(475\) −6.20198 24.7092i −0.284566 1.13373i
\(476\) −4.70748 3.42018i −0.215767 0.156764i
\(477\) −12.6054 4.09574i −0.577161 0.187531i
\(478\) 8.27941 2.69014i 0.378692 0.123044i
\(479\) 1.57850 1.14685i 0.0721235 0.0524008i −0.551139 0.834413i \(-0.685807\pi\)
0.623263 + 0.782012i \(0.285807\pi\)
\(480\) 1.85280 1.25185i 0.0845684 0.0571389i
\(481\) −0.941131 2.89650i −0.0429119 0.132069i
\(482\) −3.03576 4.17836i −0.138275 0.190319i
\(483\) −15.2605 + 4.95842i −0.694375 + 0.225616i
\(484\) −7.76824 + 23.9082i −0.353102 + 1.08674i
\(485\) 9.41654 + 3.41896i 0.427583 + 0.155247i
\(486\) −0.309017 + 0.951057i −0.0140173 + 0.0431408i
\(487\) −0.261644 0.360122i −0.0118562 0.0163187i 0.803048 0.595915i \(-0.203210\pi\)
−0.814904 + 0.579596i \(0.803210\pi\)
\(488\) −7.01742 9.65864i −0.317664 0.437226i
\(489\) 3.26604 + 2.37292i 0.147696 + 0.107307i
\(490\) −2.56656 + 0.738133i −0.115945 + 0.0333455i
\(491\) −41.9954 −1.89522 −0.947612 0.319424i \(-0.896511\pi\)
−0.947612 + 0.319424i \(0.896511\pi\)
\(492\) −0.618485 + 0.851272i −0.0278835 + 0.0383783i
\(493\) 10.7026 3.47749i 0.482021 0.156618i
\(494\) −1.12357 + 3.45799i −0.0505517 + 0.155582i
\(495\) −3.71533 12.9186i −0.166992 0.580646i
\(496\) −2.13047 5.14403i −0.0956611 0.230974i
\(497\) 4.69223i 0.210475i
\(498\) −10.8103 3.51249i −0.484422 0.157398i
\(499\) −3.10787 9.56503i −0.139127 0.428190i 0.857082 0.515180i \(-0.172275\pi\)
−0.996209 + 0.0869906i \(0.972275\pi\)
\(500\) −2.35032 10.9305i −0.105109 0.488827i
\(501\) 10.8682 0.485557
\(502\) 0.0892027i 0.00398131i
\(503\) −18.1104 + 24.9268i −0.807502 + 1.11143i 0.184202 + 0.982888i \(0.441030\pi\)
−0.991704 + 0.128543i \(0.958970\pi\)
\(504\) 2.31587 1.68258i 0.103157 0.0749480i
\(505\) 34.9016 + 27.2240i 1.55310 + 1.21145i
\(506\) −10.4129 + 32.0477i −0.462911 + 1.42469i
\(507\) −7.34188 + 10.1052i −0.326064 + 0.448789i
\(508\) 19.7779 + 6.42623i 0.877503 + 0.285118i
\(509\) 7.97317 + 24.5389i 0.353405 + 1.08767i 0.956929 + 0.290323i \(0.0937627\pi\)
−0.603524 + 0.797345i \(0.706237\pi\)
\(510\) 2.79553 3.58392i 0.123788 0.158699i
\(511\) −9.19703 28.3055i −0.406853 1.25216i
\(512\) 0.951057 0.309017i 0.0420312 0.0136568i
\(513\) 2.99484 + 4.12204i 0.132225 + 0.181993i
\(514\) −3.54374 10.9065i −0.156308 0.481065i
\(515\) 0.507218 14.8598i 0.0223507 0.654803i
\(516\) −7.62195 5.53767i −0.335538 0.243782i
\(517\) 66.3974 + 21.5738i 2.92015 + 0.948815i
\(518\) 7.18093 + 9.88371i 0.315512 + 0.434265i
\(519\) −18.7778 + 13.6429i −0.824255 + 0.598856i
\(520\) −0.544577 + 1.49988i −0.0238813 + 0.0657742i
\(521\) 5.31049 0.232657 0.116328 0.993211i \(-0.462887\pi\)
0.116328 + 0.993211i \(0.462887\pi\)
\(522\) 5.53616i 0.242311i
\(523\) −20.5621 + 28.3013i −0.899116 + 1.23753i 0.0716329 + 0.997431i \(0.477179\pi\)
−0.970749 + 0.240096i \(0.922821\pi\)
\(524\) 3.31238 + 10.1945i 0.144702 + 0.445347i
\(525\) −3.48443 13.8822i −0.152073 0.605871i
\(526\) 18.7883 0.819207
\(527\) −7.34984 8.60630i −0.320164 0.374896i
\(528\) 6.01153i 0.261618i
\(529\) −2.60199 + 8.00811i −0.113130 + 0.348179i
\(530\) −24.5572 + 16.5921i −1.06670 + 0.720717i
\(531\) 4.77741 + 3.47099i 0.207322 + 0.150628i
\(532\) 14.5852i 0.632347i
\(533\) 0.750884i 0.0325244i
\(534\) 11.4566 + 8.32369i 0.495774 + 0.360201i
\(535\) −2.99802 + 3.84352i −0.129616 + 0.166170i
\(536\) 9.19010 6.67700i 0.396952 0.288402i
\(537\) 7.75556 + 2.51994i 0.334677 + 0.108743i
\(538\) −3.91786 + 5.39247i −0.168911 + 0.232486i
\(539\) −2.21866 + 6.82832i −0.0955643 + 0.294117i
\(540\) 1.25185 + 1.85280i 0.0538711 + 0.0797318i
\(541\) −26.1788 + 19.0200i −1.12551 + 0.817734i −0.985036 0.172350i \(-0.944864\pi\)
−0.140478 + 0.990084i \(0.544864\pi\)
\(542\) −27.1102 + 8.80862i −1.16448 + 0.378363i
\(543\) 14.0290 4.55828i 0.602040 0.195615i
\(544\) 1.64449 1.19479i 0.0705070 0.0512264i
\(545\) −26.0387 + 17.5932i −1.11538 + 0.753608i
\(546\) −0.631250 + 1.94279i −0.0270150 + 0.0831436i
\(547\) −0.168762 + 0.232281i −0.00721576 + 0.00993164i −0.812610 0.582808i \(-0.801954\pi\)
0.805394 + 0.592740i \(0.201954\pi\)
\(548\) −0.556816 0.180920i −0.0237860 0.00772854i
\(549\) 9.65864 7.01742i 0.412221 0.299496i
\(550\) −27.8867 11.2160i −1.18909 0.478250i
\(551\) 22.8203 + 16.5799i 0.972178 + 0.706328i
\(552\) 5.60537i 0.238581i
\(553\) 19.9474i 0.848249i
\(554\) −12.4646 9.05604i −0.529569 0.384754i
\(555\) −7.90741 + 5.34267i −0.335651 + 0.226784i
\(556\) 0.346720 1.06709i 0.0147042 0.0452549i
\(557\) 6.81147i 0.288611i −0.989533 0.144306i \(-0.953905\pi\)
0.989533 0.144306i \(-0.0460948\pi\)
\(558\) 5.14403 2.13047i 0.217764 0.0901902i
\(559\) 6.72312 0.284358
\(560\) 0.218358 6.39718i 0.00922730 0.270330i
\(561\) −3.77609 11.6216i −0.159427 0.490664i
\(562\) 8.17238 11.2483i 0.344731 0.474482i
\(563\) 19.1459i 0.806902i −0.915001 0.403451i \(-0.867811\pi\)
0.915001 0.403451i \(-0.132189\pi\)
\(564\) −11.6134 −0.489012
\(565\) 1.96587 + 0.713767i 0.0827047 + 0.0300284i
\(566\) 5.82777 4.23413i 0.244960 0.177974i
\(567\) 1.68258 + 2.31587i 0.0706616 + 0.0972574i
\(568\) −1.55894 0.506530i −0.0654116 0.0212535i
\(569\) 15.3122 + 11.1250i 0.641921 + 0.466383i 0.860510 0.509434i \(-0.170145\pi\)
−0.218589 + 0.975817i \(0.570145\pi\)
\(570\) 11.3864 + 0.388658i 0.476925 + 0.0162791i
\(571\) −0.185435 0.570709i −0.00776020 0.0238834i 0.947101 0.320934i \(-0.103997\pi\)
−0.954862 + 0.297051i \(0.903997\pi\)
\(572\) 2.52154 + 3.47060i 0.105431 + 0.145113i
\(573\) −5.13415 + 1.66818i −0.214482 + 0.0696894i
\(574\) 0.930785 + 2.86466i 0.0388502 + 0.119569i
\(575\) −26.0025 10.4582i −1.08438 0.436136i
\(576\) 0.309017 + 0.951057i 0.0128757 + 0.0396274i
\(577\) 14.6695 + 4.76641i 0.610699 + 0.198428i 0.598006 0.801491i \(-0.295960\pi\)
0.0126926 + 0.999919i \(0.495960\pi\)
\(578\) −7.56369 + 10.4105i −0.314608 + 0.433021i
\(579\) 5.35006 16.4658i 0.222341 0.684295i
\(580\) 9.76096 + 7.61375i 0.405302 + 0.316144i
\(581\) −26.3237 + 19.1253i −1.09209 + 0.793450i
\(582\) −2.63339 + 3.62455i −0.109158 + 0.150242i
\(583\) 79.6774i 3.29990i
\(584\) 10.3970 0.430232
\(585\) −1.49988 0.544577i −0.0620125 0.0225155i
\(586\) −2.28104 7.02032i −0.0942289 0.290007i
\(587\) 6.14869 + 1.99783i 0.253784 + 0.0824593i 0.433146 0.901324i \(-0.357403\pi\)
−0.179362 + 0.983783i \(0.557403\pi\)
\(588\) 1.19432i 0.0492531i
\(589\) 6.62365 27.5844i 0.272923 1.13659i
\(590\) 12.6900 3.64961i 0.522441 0.150252i
\(591\) 1.37171 4.22168i 0.0564245 0.173657i
\(592\) −4.05893 + 1.31883i −0.166821 + 0.0542035i
\(593\) 10.3805 14.2875i 0.426274 0.586716i −0.540819 0.841139i \(-0.681886\pi\)
0.967093 + 0.254423i \(0.0818855\pi\)
\(594\) 6.01153 0.246656
\(595\) −3.59620 12.5043i −0.147430 0.512626i
\(596\) 11.3477 + 8.24458i 0.464819 + 0.337711i
\(597\) 3.75624 + 5.17002i 0.153733 + 0.211595i
\(598\) 2.35118 + 3.23612i 0.0961468 + 0.132335i
\(599\) 9.52538 29.3161i 0.389196 1.19782i −0.544194 0.838960i \(-0.683164\pi\)
0.933390 0.358864i \(-0.116836\pi\)
\(600\) 4.98836 + 0.340937i 0.203649 + 0.0139187i
\(601\) 0.319564 0.983518i 0.0130353 0.0401185i −0.944327 0.329008i \(-0.893286\pi\)
0.957363 + 0.288889i \(0.0932859\pi\)
\(602\) −25.6491 + 8.33388i −1.04538 + 0.339664i
\(603\) 6.67700 + 9.19010i 0.271908 + 0.374250i
\(604\) 1.21677 + 3.74483i 0.0495097 + 0.152375i
\(605\) −46.5767 + 31.4697i −1.89361 + 1.27943i
\(606\) −16.0147 + 11.6354i −0.650554 + 0.472655i
\(607\) 10.9293 3.55114i 0.443607 0.144136i −0.0786924 0.996899i \(-0.525075\pi\)
0.522299 + 0.852762i \(0.325075\pi\)
\(608\) 4.84575 + 1.57448i 0.196521 + 0.0638536i
\(609\) 12.8210 + 9.31503i 0.519535 + 0.377464i
\(610\) 0.910690 26.6803i 0.0368728 1.08025i
\(611\) 6.70469 4.87125i 0.271243 0.197069i
\(612\) 1.19479 + 1.64449i 0.0482967 + 0.0664747i
\(613\) 3.52542 4.85233i 0.142390 0.195984i −0.731865 0.681449i \(-0.761350\pi\)
0.874256 + 0.485466i \(0.161350\pi\)
\(614\) −0.454257 −0.0183323
\(615\) −2.26120 + 0.650314i −0.0911804 + 0.0262232i
\(616\) −13.9219 10.1149i −0.560931 0.407540i
\(617\) −30.6411 + 9.95589i −1.23356 + 0.400809i −0.852004 0.523536i \(-0.824613\pi\)
−0.381559 + 0.924344i \(0.624613\pi\)
\(618\) 6.32395 + 2.05478i 0.254387 + 0.0826552i
\(619\) 28.1606 1.13187 0.565935 0.824450i \(-0.308515\pi\)
0.565935 + 0.824450i \(0.308515\pi\)
\(620\) 3.31816 11.9996i 0.133261 0.481915i
\(621\) 5.60537 0.224936
\(622\) 28.4059 + 9.22962i 1.13897 + 0.370074i
\(623\) 38.5532 12.5267i 1.54460 0.501871i
\(624\) −0.577324 0.419451i −0.0231115 0.0167915i
\(625\) 10.8885 22.5042i 0.435542 0.900169i
\(626\) 11.7064 0.467883
\(627\) 18.0036 24.7798i 0.718994 0.989610i
\(628\) −1.27978 1.76147i −0.0510689 0.0702904i
\(629\) −7.01839 + 5.09916i −0.279842 + 0.203317i
\(630\) 6.39718 + 0.218358i 0.254870 + 0.00869958i
\(631\) −30.8892 22.4423i −1.22968 0.893415i −0.232814 0.972521i \(-0.574793\pi\)
−0.996866 + 0.0791067i \(0.974793\pi\)
\(632\) 6.62729 + 2.15334i 0.263619 + 0.0856551i
\(633\) 1.45005 0.471151i 0.0576344 0.0187266i
\(634\) 14.4579 10.5043i 0.574197 0.417178i
\(635\) 26.0331 + 38.5303i 1.03309 + 1.52903i
\(636\) −4.09574 12.6054i −0.162407 0.499836i
\(637\) 0.500960 + 0.689513i 0.0198488 + 0.0273195i
\(638\) 31.6520 10.2843i 1.25311 0.407161i
\(639\) 0.506530 1.55894i 0.0200380 0.0616706i
\(640\) 2.10182 + 0.763128i 0.0830816 + 0.0301653i
\(641\) 1.23243 3.79302i 0.0486779 0.149815i −0.923763 0.382965i \(-0.874903\pi\)
0.972441 + 0.233149i \(0.0749031\pi\)
\(642\) −1.28134 1.76361i −0.0505704 0.0696042i
\(643\) −9.47668 13.0435i −0.373724 0.514387i 0.580184 0.814485i \(-0.302980\pi\)
−0.953908 + 0.300098i \(0.902980\pi\)
\(644\) −12.9813 9.43148i −0.511536 0.371652i
\(645\) −5.82265 20.2459i −0.229267 0.797181i
\(646\) 10.3569 0.407486
\(647\) −12.8051 + 17.6247i −0.503421 + 0.692899i −0.982793 0.184713i \(-0.940865\pi\)
0.479372 + 0.877612i \(0.340865\pi\)
\(648\) −0.951057 + 0.309017i −0.0373610 + 0.0121393i
\(649\) 10.9699 33.7618i 0.430606 1.32527i
\(650\) −3.02291 + 1.89554i −0.118568 + 0.0743492i
\(651\) 3.72134 15.4976i 0.145851 0.607399i
\(652\) 4.03705i 0.158103i
\(653\) 23.4090 + 7.60606i 0.916066 + 0.297648i 0.728852 0.684671i \(-0.240054\pi\)
0.187214 + 0.982319i \(0.440054\pi\)
\(654\) −4.34284 13.3659i −0.169818 0.522647i
\(655\) −8.18003 + 22.5296i −0.319620 + 0.880303i
\(656\) −1.05223 −0.0410827
\(657\) 10.3970i 0.405626i
\(658\) −19.5404 + 26.8951i −0.761766 + 1.04848i
\(659\) −12.9621 + 9.41752i −0.504932 + 0.366854i −0.810898 0.585188i \(-0.801021\pi\)
0.305966 + 0.952043i \(0.401021\pi\)
\(660\) 8.26751 10.5991i 0.321812 0.412570i
\(661\) −8.76009 + 26.9608i −0.340728 + 1.04865i 0.623103 + 0.782140i \(0.285872\pi\)
−0.963831 + 0.266514i \(0.914128\pi\)
\(662\) 12.3720 17.0286i 0.480850 0.661834i
\(663\) −1.37957 0.448248i −0.0535779 0.0174085i
\(664\) −3.51249 10.8103i −0.136311 0.419522i
\(665\) 20.0586 25.7155i 0.777840 0.997205i
\(666\) −1.31883 4.05893i −0.0511035 0.157280i
\(667\) 29.5134 9.58950i 1.14276 0.371307i
\(668\) 6.38818 + 8.79258i 0.247166 + 0.340195i
\(669\) −4.52015 13.9116i −0.174759 0.537853i
\(670\) 25.3860 + 0.866512i 0.980748 + 0.0334763i
\(671\) −58.0633 42.1854i −2.24151 1.62855i
\(672\) 2.72247 + 0.884584i 0.105022 + 0.0341236i
\(673\) 8.95894 + 12.3309i 0.345342 + 0.475322i 0.945992 0.324190i \(-0.105092\pi\)
−0.600650 + 0.799512i \(0.705092\pi\)
\(674\) 19.9975 14.5290i 0.770275 0.559637i
\(675\) −0.340937 + 4.98836i −0.0131227 + 0.192002i
\(676\) −12.4908 −0.480414
\(677\) 3.13092i 0.120331i 0.998188 + 0.0601655i \(0.0191628\pi\)
−0.998188 + 0.0601655i \(0.980837\pi\)
\(678\) −0.549766 + 0.756688i −0.0211136 + 0.0290604i
\(679\) 3.96310 + 12.1972i 0.152090 + 0.468085i
\(680\) 4.54262 + 0.155055i 0.174202 + 0.00594610i
\(681\) 7.70226 0.295151
\(682\) −21.7365 25.4523i −0.832333 0.974620i
\(683\) 39.1118i 1.49657i −0.663376 0.748286i \(-0.730877\pi\)
0.663376 0.748286i \(-0.269123\pi\)
\(684\) −1.57448 + 4.84575i −0.0602018 + 0.185282i
\(685\) −0.732922 1.08476i −0.0280035 0.0414466i
\(686\) 13.4452 + 9.76850i 0.513340 + 0.372963i
\(687\) 7.73132i 0.294968i
\(688\) 9.42125i 0.359182i
\(689\) 7.65191 + 5.55944i 0.291515 + 0.211798i
\(690\) 7.70893 9.88299i 0.293474 0.376239i
\(691\) 13.1708 9.56912i 0.501040 0.364027i −0.308374 0.951265i \(-0.599785\pi\)
0.809414 + 0.587239i \(0.199785\pi\)
\(692\) −22.0747 7.17249i −0.839153 0.272657i
\(693\) 10.1149 13.9219i 0.384232 0.528851i
\(694\) 4.01657 12.3617i 0.152467 0.469245i
\(695\) 2.07886 1.40459i 0.0788556 0.0532790i
\(696\) −4.47885 + 3.25407i −0.169770 + 0.123345i
\(697\) −2.03419 + 0.660948i −0.0770504 + 0.0250352i
\(698\) −22.9854 + 7.46839i −0.870008 + 0.282683i
\(699\) 3.50751 2.54836i 0.132666 0.0963876i
\(700\) 9.18288 10.9787i 0.347080 0.414958i
\(701\) −5.35979 + 16.4957i −0.202436 + 0.623035i 0.797373 + 0.603487i \(0.206223\pi\)
−0.999809 + 0.0195477i \(0.993777\pi\)
\(702\) 0.419451 0.577324i 0.0158311 0.0217897i
\(703\) −20.6808 6.71959i −0.779990 0.253434i
\(704\) 4.86343 3.53349i 0.183298 0.133173i
\(705\) −20.4759 15.9716i −0.771167 0.601526i
\(706\) −21.1793 15.3876i −0.797092 0.579121i
\(707\) 56.6655i 2.13113i
\(708\) 5.90520i 0.221931i
\(709\) 7.80364 + 5.66968i 0.293072 + 0.212929i 0.724599 0.689171i \(-0.242025\pi\)
−0.431527 + 0.902100i \(0.642025\pi\)
\(710\) −2.05199 3.03704i −0.0770098 0.113978i
\(711\) −2.15334 + 6.62729i −0.0807564 + 0.248543i
\(712\) 14.1611i 0.530710i
\(713\) −20.2679 23.7327i −0.759038 0.888796i
\(714\) 5.81877 0.217762
\(715\) −0.327235 + 9.58693i −0.0122379 + 0.358531i
\(716\) 2.51994 + 7.75556i 0.0941744 + 0.289839i
\(717\) −5.11696 + 7.04289i −0.191096 + 0.263021i
\(718\) 4.44055i 0.165720i
\(719\) 5.04255 0.188055 0.0940277 0.995570i \(-0.470026\pi\)
0.0940277 + 0.995570i \(0.470026\pi\)
\(720\) −0.763128 + 2.10182i −0.0284401 + 0.0783301i
\(721\) 15.3991 11.1881i 0.573494 0.416668i
\(722\) 4.09117 + 5.63101i 0.152258 + 0.209564i
\(723\) 4.91196 + 1.59599i 0.182678 + 0.0593556i
\(724\) 11.9337 + 8.67037i 0.443514 + 0.322232i
\(725\) 6.73883 + 26.8480i 0.250274 + 0.997110i
\(726\) −7.76824 23.9082i −0.288306 0.887316i
\(727\) 14.8874 + 20.4908i 0.552145 + 0.759962i 0.990301 0.138937i \(-0.0443685\pi\)
−0.438157 + 0.898899i \(0.644368\pi\)
\(728\) −1.94279 + 0.631250i −0.0720045 + 0.0233957i
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) 18.3313 + 14.2988i 0.678471 + 0.529221i
\(731\) −5.91787 18.2133i −0.218880 0.673644i
\(732\) 11.3544 + 3.68927i 0.419671 + 0.136359i
\(733\) −4.39548 + 6.04986i −0.162351 + 0.223457i −0.882440 0.470425i \(-0.844101\pi\)
0.720089 + 0.693881i \(0.244101\pi\)
\(734\) −8.73126 + 26.8720i −0.322277 + 0.991865i
\(735\) 1.64253 2.10575i 0.0605854 0.0776717i
\(736\) 4.53484 3.29476i 0.167157 0.121446i
\(737\) 40.1390 55.2466i 1.47854 2.03504i
\(738\) 1.05223i 0.0387331i
\(739\) 17.4441 0.641691 0.320845 0.947132i \(-0.396033\pi\)
0.320845 + 0.947132i \(0.396033\pi\)
\(740\) −8.97017 3.25689i −0.329750 0.119726i
\(741\) −1.12357 3.45799i −0.0412753 0.127032i
\(742\) −36.0839 11.7244i −1.32468 0.430415i
\(743\) 0.843544i 0.0309466i 0.999880 + 0.0154733i \(0.00492550\pi\)
−0.999880 + 0.0154733i \(0.995074\pi\)
\(744\) 4.74718 + 2.90935i 0.174040 + 0.106662i
\(745\) 8.66886 + 30.1424i 0.317602 + 1.10433i
\(746\) −1.55648 + 4.79034i −0.0569867 + 0.175387i
\(747\) 10.8103 3.51249i 0.395529 0.128515i
\(748\) 7.18254 9.88592i 0.262620 0.361465i
\(749\) −6.24025 −0.228014
\(750\) 8.32624 + 7.46149i 0.304031 + 0.272455i
\(751\) −14.3457 10.4228i −0.523482 0.380332i 0.294432 0.955672i \(-0.404870\pi\)
−0.817914 + 0.575341i \(0.804870\pi\)
\(752\) −6.82618 9.39543i −0.248925 0.342616i
\(753\) 0.0524320 + 0.0721665i 0.00191073 + 0.00262989i
\(754\) 1.22082 3.75731i 0.0444598 0.136833i
\(755\) −3.00485 + 8.27601i −0.109358 + 0.301195i
\(756\) −0.884584 + 2.72247i −0.0321720 + 0.0990152i
\(757\) 11.0425 3.58794i 0.401348 0.130406i −0.101386 0.994847i \(-0.532328\pi\)
0.502734 + 0.864441i \(0.332328\pi\)
\(758\) 19.7395 + 27.1691i 0.716972 + 0.986827i
\(759\) −10.4129 32.0477i −0.377965 1.16326i
\(760\) 6.37834 + 9.44025i 0.231367 + 0.342434i
\(761\) 7.47926 5.43400i 0.271123 0.196982i −0.443913 0.896070i \(-0.646410\pi\)
0.715036 + 0.699087i \(0.246410\pi\)
\(762\) −19.7779 + 6.42623i −0.716478 + 0.232798i
\(763\) −38.2608 12.4317i −1.38513 0.450057i
\(764\) −4.36736 3.17308i −0.158006 0.114798i
\(765\) −0.155055 + 4.54262i −0.00560603 + 0.164239i
\(766\) −29.9902 + 21.7892i −1.08359 + 0.787275i
\(767\) −2.47694 3.40921i −0.0894371 0.123100i
\(768\) −0.587785 + 0.809017i −0.0212099 + 0.0291929i
\(769\) −13.1792 −0.475254 −0.237627 0.971357i \(-0.576370\pi\)
−0.237627 + 0.971357i \(0.576370\pi\)
\(770\) −10.6354 36.9803i −0.383274 1.33268i
\(771\) 9.27762 + 6.74059i 0.334125 + 0.242756i
\(772\) 16.4658 5.35006i 0.592617 0.192553i
\(773\) −15.3560 4.98947i −0.552317 0.179459i 0.0195443 0.999809i \(-0.493778\pi\)
−0.571861 + 0.820350i \(0.693778\pi\)
\(774\) 9.42125 0.338640
\(775\) 22.3531 16.5934i 0.802945 0.596053i
\(776\) −4.48019 −0.160829
\(777\) −11.6190 3.77524i −0.416829 0.135436i
\(778\) 13.3135 4.32582i 0.477313 0.155088i
\(779\) −4.33734 3.15126i −0.155401 0.112906i
\(780\) −0.441036 1.53352i −0.0157916 0.0549090i
\(781\) −9.85389 −0.352600
\(782\) 6.69727 9.21800i 0.239494 0.329635i
\(783\) −3.25407 4.47885i −0.116291 0.160061i
\(784\) 0.966229 0.702007i 0.0345082 0.0250717i
\(785\) 0.166085 4.86575i 0.00592783 0.173666i
\(786\) −8.67192 6.30052i −0.309317 0.224732i
\(787\) 3.55143 + 1.15393i 0.126595 + 0.0411331i 0.371629 0.928381i \(-0.378799\pi\)
−0.245034 + 0.969514i \(0.578799\pi\)
\(788\) 4.22168 1.37171i 0.150391 0.0488651i
\(789\) −15.2000 + 11.0435i −0.541135 + 0.393157i
\(790\) 8.72333 + 12.9109i 0.310362 + 0.459351i
\(791\) 0.827367 + 2.54637i 0.0294178 + 0.0905387i
\(792\) 3.53349 + 4.86343i 0.125557 + 0.172815i
\(793\) −8.10265 + 2.63271i −0.287733 + 0.0934903i
\(794\) 6.60762 20.3362i 0.234496 0.721704i
\(795\) 10.1146 27.8577i 0.358727 0.988010i
\(796\) −1.97477 + 6.07772i −0.0699939 + 0.215419i
\(797\) 15.4650 + 21.2857i 0.547797 + 0.753978i 0.989711 0.143079i \(-0.0457004\pi\)
−0.441914 + 0.897057i \(0.645700\pi\)
\(798\) 8.57295 + 11.7997i 0.303479 + 0.417703i
\(799\) −19.0981 13.8756i −0.675644 0.490884i
\(800\) 2.65626 + 4.23607i 0.0939130 + 0.149768i
\(801\) −14.1611 −0.500358
\(802\) −9.90392 + 13.6316i −0.349720 + 0.481348i
\(803\) 59.4429 19.3142i 2.09770 0.681583i
\(804\) −3.51031 + 10.8036i −0.123799 + 0.381014i
\(805\) −9.91685 34.4818i −0.349523 1.21532i
\(806\) −3.96099 + 0.311569i −0.139520 + 0.0109745i
\(807\) 6.66546i 0.234635i
\(808\) −18.8264 6.11708i −0.662312 0.215198i
\(809\) 3.69284 + 11.3654i 0.129833 + 0.399585i 0.994751 0.102329i \(-0.0326293\pi\)
−0.864917 + 0.501914i \(0.832629\pi\)
\(810\) −2.10182 0.763128i −0.0738503 0.0268136i
\(811\) 12.8462 0.451092 0.225546 0.974232i \(-0.427583\pi\)
0.225546 + 0.974232i \(0.427583\pi\)
\(812\) 15.8477i 0.556144i
\(813\) 16.7550 23.0613i 0.587623 0.808794i
\(814\) −20.7562 + 15.0803i −0.727506 + 0.528564i
\(815\) −5.55205 + 7.11783i −0.194480 + 0.249327i
\(816\) −0.628140 + 1.93322i −0.0219893 + 0.0676761i
\(817\) 28.2151 38.8348i 0.987123 1.35866i
\(818\) 8.66184 + 2.81440i 0.302854 + 0.0984033i
\(819\) −0.631250 1.94279i −0.0220576 0.0678865i
\(820\) −1.85522 1.44711i −0.0647869 0.0505351i
\(821\) 3.61764 + 11.1339i 0.126256 + 0.388577i 0.994128 0.108211i \(-0.0345123\pi\)
−0.867871 + 0.496789i \(0.834512\pi\)
\(822\) 0.556816 0.180920i 0.0194212 0.00631032i
\(823\) 4.73665 + 6.51944i 0.165109 + 0.227253i 0.883552 0.468332i \(-0.155145\pi\)
−0.718443 + 0.695586i \(0.755145\pi\)
\(824\) 2.05478 + 6.32395i 0.0715815 + 0.220305i
\(825\) 29.1534 7.31747i 1.01499 0.254762i
\(826\) 13.6757 + 9.93596i 0.475837 + 0.345716i
\(827\) 21.9303 + 7.12560i 0.762592 + 0.247781i 0.664391 0.747385i \(-0.268691\pi\)
0.0982014 + 0.995167i \(0.468691\pi\)
\(828\) 3.29476 + 4.53484i 0.114501 + 0.157597i
\(829\) −28.0264 + 20.3624i −0.973398 + 0.707215i −0.956223 0.292638i \(-0.905467\pi\)
−0.0171742 + 0.999853i \(0.505467\pi\)
\(830\) 8.67420 23.8906i 0.301086 0.829255i
\(831\) 15.4071 0.534465
\(832\) 0.713612i 0.0247400i
\(833\) 1.42697 1.96406i 0.0494417 0.0680506i
\(834\) 0.346720 + 1.06709i 0.0120059 + 0.0369504i
\(835\) −0.829031 + 24.2879i −0.0286898 + 0.840519i
\(836\) 30.6295 1.05934
\(837\) −2.90935 + 4.74718i −0.100562 + 0.164086i
\(838\) 15.8035i 0.545922i
\(839\) −11.7457 + 36.1496i −0.405507 + 1.24802i 0.514964 + 0.857212i \(0.327805\pi\)
−0.920471 + 0.390811i \(0.872195\pi\)
\(840\) 3.58351 + 5.30378i 0.123643 + 0.182998i
\(841\) −1.33415 0.969315i −0.0460051 0.0334246i
\(842\) 21.3311i 0.735119i
\(843\) 13.9037i 0.478869i
\(844\) 1.23349 + 0.896182i 0.0424584 + 0.0308478i
\(845\) −22.0228 17.1782i −0.757607 0.590949i
\(846\) 9.39543 6.82618i 0.323022 0.234689i
\(847\) −68.4389 22.2371i −2.35159 0.764077i
\(848\) 7.79056 10.7228i 0.267529 0.368222i
\(849\) −2.22601 + 6.85096i −0.0763965 + 0.235124i
\(850\) 7.79598 + 6.52073i 0.267400 + 0.223659i
\(851\) −19.3539 + 14.0614i −0.663442 + 0.482019i
\(852\) 1.55894 0.506530i 0.0534083 0.0173534i
\(853\) −3.58823 + 1.16589i −0.122859 + 0.0399192i −0.369801 0.929111i \(-0.620574\pi\)
0.246942 + 0.969030i \(0.420574\pi\)
\(854\) 27.6486 20.0879i 0.946115 0.687393i
\(855\) −9.44025 + 6.37834i −0.322850 + 0.218135i
\(856\) 0.673640 2.07325i 0.0230245 0.0708623i
\(857\) 25.6124 35.2525i 0.874903 1.20420i −0.102904 0.994691i \(-0.532813\pi\)
0.977807 0.209509i \(-0.0671867\pi\)
\(858\) −4.07994 1.32565i −0.139287 0.0452570i
\(859\) 20.5062 14.8986i 0.699661 0.508334i −0.180161 0.983637i \(-0.557662\pi\)
0.879822 + 0.475304i \(0.157662\pi\)
\(860\) 12.9568 16.6109i 0.441823 0.566426i
\(861\) −2.43683 1.77046i −0.0830469 0.0603371i
\(862\) 9.59016i 0.326642i
\(863\) 24.0458i 0.818527i 0.912416 + 0.409263i \(0.134214\pi\)
−0.912416 + 0.409263i \(0.865786\pi\)
\(864\) −0.809017 0.587785i −0.0275233 0.0199969i
\(865\) −29.0563 43.0047i −0.987944 1.46221i
\(866\) 2.19952 6.76941i 0.0747426 0.230034i
\(867\) 12.8681i 0.437024i
\(868\) 14.7252 6.09864i 0.499805 0.207001i
\(869\) 41.8904 1.42104
\(870\) −12.3720 0.422300i −0.419451 0.0143173i
\(871\) −2.50500 7.70959i −0.0848786 0.261229i
\(872\) 8.26057 11.3697i 0.279738 0.385027i
\(873\) 4.48019i 0.151631i
\(874\) 28.5601 0.966060
\(875\) 31.2894 6.72795i 1.05777 0.227446i
\(876\) −8.41136 + 6.11121i −0.284194 + 0.206479i
\(877\) 3.02912 + 4.16922i 0.102286 + 0.140785i 0.857092 0.515164i \(-0.172269\pi\)
−0.754806 + 0.655948i \(0.772269\pi\)
\(878\) −37.7974 12.2811i −1.27560 0.414467i
\(879\) 5.97184 + 4.33880i 0.201425 + 0.146344i
\(880\) 13.4344 + 0.458561i 0.452873 + 0.0154581i
\(881\) −6.26151 19.2710i −0.210956 0.649255i −0.999416 0.0341694i \(-0.989121\pi\)
0.788460 0.615086i \(-0.210879\pi\)
\(882\) 0.702007 + 0.966229i 0.0236378 + 0.0325346i
\(883\) −32.9893 + 10.7189i −1.11018 + 0.360719i −0.806012 0.591899i \(-0.798378\pi\)
−0.304168 + 0.952618i \(0.598378\pi\)
\(884\) −0.448248 1.37957i −0.0150762 0.0463999i
\(885\) −8.12127 + 10.4116i −0.272993 + 0.349983i
\(886\) −0.973681 2.99668i −0.0327115 0.100676i
\(887\) −10.9385 3.55413i −0.367279 0.119336i 0.119562 0.992827i \(-0.461851\pi\)
−0.486841 + 0.873491i \(0.661851\pi\)
\(888\) 2.50856 3.45273i 0.0841817 0.115866i
\(889\) −18.3956 + 56.6157i −0.616967 + 1.89883i
\(890\) −19.4754 + 24.9678i −0.652817 + 0.836924i
\(891\) −4.86343 + 3.53349i −0.162931 + 0.118376i
\(892\) 8.59783 11.8339i 0.287877 0.396228i
\(893\) 59.1717i 1.98011i
\(894\) −14.0265 −0.469117
\(895\) −6.22306 + 17.1397i −0.208014 + 0.572915i
\(896\) 0.884584 + 2.72247i 0.0295519 + 0.0909513i
\(897\) −3.80429 1.23609i −0.127021 0.0412718i
\(898\) 33.7424i 1.12600i
\(899\) −7.19699 + 29.9721i −0.240033 + 0.999625i
\(900\) −4.23607 + 2.65626i −0.141202 + 0.0885421i
\(901\) 8.32543 25.6230i 0.277360 0.853627i
\(902\) −6.01592 + 1.95469i −0.200308 + 0.0650841i
\(903\) 15.8520 21.8184i 0.527521 0.726071i
\(904\) −0.935318 −0.0311082
\(905\) 9.11657 + 31.6991i 0.303045 + 1.05372i
\(906\) −3.18555 2.31443i −0.105833 0.0768919i
\(907\) 31.2388 + 42.9965i 1.03727 + 1.42767i 0.899349 + 0.437231i \(0.144041\pi\)
0.137917 + 0.990444i \(0.455959\pi\)
\(908\) 4.52728 + 6.23126i 0.150243 + 0.206792i
\(909\) 6.11708 18.8264i 0.202891 0.624434i
\(910\) −4.29352 1.55889i −0.142329 0.0516768i
\(911\) −4.57003 + 14.0651i −0.151412 + 0.465998i −0.997780 0.0666009i \(-0.978785\pi\)
0.846368 + 0.532599i \(0.178785\pi\)
\(912\) −4.84575 + 1.57448i −0.160459 + 0.0521363i
\(913\) −40.1639 55.2809i −1.32923 1.82953i
\(914\) 4.41683 + 13.5936i 0.146096 + 0.449637i
\(915\) 14.9455 + 22.1201i 0.494084 + 0.731268i
\(916\) 6.25477 4.54436i 0.206663 0.150150i
\(917\) −29.1824 + 9.48193i −0.963687 + 0.313121i
\(918\) −1.93322 0.628140i −0.0638057 0.0207317i
\(919\) −15.9296 11.5735i −0.525468 0.381775i 0.293192 0.956054i \(-0.405282\pi\)
−0.818660 + 0.574279i \(0.805282\pi\)
\(920\) 12.5267 + 0.427579i 0.412993 + 0.0140969i
\(921\) 0.367502 0.267006i 0.0121096 0.00879814i
\(922\) 22.8044 + 31.3876i 0.751023 + 1.03370i
\(923\) −0.687548 + 0.946329i −0.0226309 + 0.0311488i
\(924\) 17.2085 0.566117
\(925\) −11.3364 18.0788i −0.372740 0.594426i
\(926\) 16.7487 + 12.1687i 0.550397 + 0.399887i
\(927\) −6.32395 + 2.05478i −0.207706 + 0.0674877i
\(928\) −5.26520 1.71077i −0.172839 0.0561587i
\(929\) −27.3040 −0.895816 −0.447908 0.894080i \(-0.647831\pi\)
−0.447908 + 0.894080i \(0.647831\pi\)
\(930\) 4.36872 + 11.6582i 0.143256 + 0.382288i
\(931\) 6.08524 0.199436
\(932\) 4.12333 + 1.33975i 0.135064 + 0.0438850i
\(933\) −28.4059 + 9.22962i −0.929966 + 0.302164i
\(934\) 24.9782 + 18.1477i 0.817312 + 0.593812i
\(935\) 26.2596 7.55217i 0.858781 0.246982i
\(936\) 0.713612 0.0233251
\(937\) −8.91173 + 12.2659i −0.291134 + 0.400711i −0.929382 0.369120i \(-0.879659\pi\)
0.638248 + 0.769831i \(0.279659\pi\)
\(938\) 19.1134 + 26.3073i 0.624075 + 0.858965i
\(939\) −9.47071 + 6.88087i −0.309065 + 0.224549i
\(940\) 0.885873 25.9532i 0.0288940 0.846501i
\(941\) 23.9696 + 17.4149i 0.781386 + 0.567710i 0.905395 0.424571i \(-0.139575\pi\)
−0.124009 + 0.992281i \(0.539575\pi\)
\(942\) 2.07073 + 0.672822i 0.0674682 + 0.0219217i
\(943\) −5.60947 + 1.82263i −0.182669 + 0.0593529i
\(944\) −4.77741 + 3.47099i −0.155491 + 0.112971i
\(945\) −5.30378 + 3.58351i −0.172532 + 0.116572i
\(946\) −17.5015 53.8642i −0.569024 1.75128i
\(947\) 3.84425 + 5.29115i 0.124921 + 0.171939i 0.866897 0.498487i \(-0.166111\pi\)
−0.741976 + 0.670427i \(0.766111\pi\)
\(948\) −6.62729 + 2.15334i −0.215244 + 0.0699371i
\(949\) 2.29273 7.05630i 0.0744252 0.229057i
\(950\) −1.73712 + 25.4163i −0.0563595 + 0.824615i
\(951\) −5.52243 + 16.9963i −0.179077 + 0.551142i
\(952\) 3.42018 + 4.70748i 0.110849 + 0.152570i
\(953\) −21.4612 29.5389i −0.695198 0.956857i −0.999990 0.00443861i \(-0.998587\pi\)
0.304793 0.952419i \(-0.401413\pi\)
\(954\) 10.7228 + 7.79056i 0.347163 + 0.252229i
\(955\) −3.33637 11.6009i −0.107962 0.375395i
\(956\) −8.70549 −0.281556
\(957\) −19.5620 + 26.9248i −0.632349 + 0.870354i
\(958\) −1.85564 + 0.602933i −0.0599529 + 0.0194799i
\(959\) 0.517898 1.59393i 0.0167238 0.0514706i
\(960\) −2.14896 + 0.618034i −0.0693574 + 0.0199470i
\(961\) 30.6187 4.84689i 0.987702 0.156351i
\(962\) 3.04556i 0.0981929i
\(963\) 2.07325 + 0.673640i 0.0668096 + 0.0217078i
\(964\) 1.59599 + 4.91196i 0.0514035 + 0.158204i
\(965\) 36.3891 + 13.2121i 1.17141 + 0.425314i
\(966\) 16.0458 0.516265
\(967\) 14.9024i 0.479227i 0.970868 + 0.239614i \(0.0770208\pi\)
−0.970868 + 0.239614i \(0.922979\pi\)
\(968\) 14.7761 20.3375i 0.474921 0.653672i
\(969\) −8.37890 + 6.08763i −0.269169 + 0.195563i
\(970\) −7.89915 6.16149i −0.253626 0.197834i
\(971\) −0.150456 + 0.463057i −0.00482838 + 0.0148602i −0.953442 0.301577i \(-0.902487\pi\)
0.948613 + 0.316438i \(0.102487\pi\)
\(972\) 0.587785 0.809017i 0.0188532 0.0259492i
\(973\) 3.05463 + 0.992511i 0.0979271 + 0.0318184i
\(974\) 0.137554 + 0.423348i 0.00440752 + 0.0135650i
\(975\) 1.33141 3.31035i 0.0426394 0.106016i
\(976\) 3.68927 + 11.3544i 0.118091 + 0.363446i
\(977\) 0.117922 0.0383152i 0.00377266 0.00122581i −0.307130 0.951668i \(-0.599369\pi\)
0.310903 + 0.950442i \(0.399369\pi\)
\(978\) −2.37292 3.26604i −0.0758776 0.104437i
\(979\) 26.3066 + 80.9634i 0.840763 + 2.58760i
\(980\) 2.66904 + 0.0911034i 0.0852593 + 0.00291019i
\(981\) 11.3697 + 8.26057i 0.363007 + 0.263740i
\(982\) 39.9400 + 12.9773i 1.27454 + 0.414122i
\(983\) −21.8338 30.0517i −0.696390 0.958499i −0.999984 0.00569740i \(-0.998186\pi\)
0.303593 0.952802i \(-0.401814\pi\)
\(984\) 0.851272 0.618485i 0.0271376 0.0197166i
\(985\) 9.32984 + 3.38748i 0.297273 + 0.107934i
\(986\) −11.2534 −0.358381
\(987\) 33.2442i 1.05817i
\(988\) 2.13715 2.94154i 0.0679919 0.0935828i
\(989\) −16.3191 50.2249i −0.518916 1.59706i
\(990\) −0.458561 + 13.4344i −0.0145740 + 0.426972i
\(991\) −11.4777 −0.364600 −0.182300 0.983243i \(-0.558354\pi\)
−0.182300 + 0.983243i \(0.558354\pi\)
\(992\) 0.436608 + 5.55062i 0.0138623 + 0.176232i
\(993\) 21.0485i 0.667953i
\(994\) 1.44998 4.46257i 0.0459905 0.141544i
\(995\) −11.8403 + 7.99994i −0.375363 + 0.253615i
\(996\) 9.19581 + 6.68114i 0.291380 + 0.211700i
\(997\) 4.29619i 0.136062i −0.997683 0.0680309i \(-0.978328\pi\)
0.997683 0.0680309i \(-0.0216716\pi\)
\(998\) 10.0573i 0.318357i
\(999\) 3.45273 + 2.50856i 0.109240 + 0.0793673i
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.z.c.349.3 32
5.4 even 2 inner 930.2.z.c.349.6 yes 32
31.4 even 5 inner 930.2.z.c.469.8 yes 32
155.4 even 10 inner 930.2.z.c.469.1 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.z.c.349.3 32 1.1 even 1 trivial
930.2.z.c.349.6 yes 32 5.4 even 2 inner
930.2.z.c.469.1 yes 32 155.4 even 10 inner
930.2.z.c.469.8 yes 32 31.4 even 5 inner