Properties

Label 930.2.bg.g.661.3
Level $930$
Weight $2$
Character 930.661
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 661.3
Character \(\chi\) \(=\) 930.661
Dual form 930.2.bg.g.121.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.66379 + 0.566206i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\) \(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} +(2.66379 + 0.566206i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-2.28838 + 2.54150i) q^{11} +(0.913545 - 0.406737i) q^{12} +(-2.31782 - 1.03196i) q^{13} +(-1.82224 - 2.02381i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.84386 - 4.26904i) q^{17} +(0.913545 + 0.406737i) q^{18} +(-2.59635 + 1.15597i) q^{19} +(0.669131 - 0.743145i) q^{20} +(0.284663 - 2.70838i) q^{21} +(3.34519 - 0.711042i) q^{22} +(1.99369 - 6.13596i) q^{23} +(-0.978148 - 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.26859 + 2.19726i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.284663 + 2.70838i) q^{28} +(-4.42446 - 3.21456i) q^{29} +1.00000 q^{30} +(2.97051 - 4.70915i) q^{31} +1.00000 q^{32} +(2.76678 + 2.01018i) q^{33} +(0.600470 + 5.71309i) q^{34} +(-0.841547 - 2.59001i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.12769 - 3.68526i) q^{37} +(2.77995 + 0.590897i) q^{38} +(-0.784029 + 2.41299i) q^{39} +(-0.978148 + 0.207912i) q^{40} +(0.165860 - 1.57805i) q^{41} +(-1.82224 + 2.02381i) q^{42} +(-3.30706 + 1.47240i) q^{43} +(-3.12426 - 1.39101i) q^{44} +(0.669131 + 0.743145i) q^{45} +(-5.21956 + 3.79223i) q^{46} +(-4.43749 + 3.22403i) q^{47} +(0.669131 + 0.743145i) q^{48} +(0.380376 + 0.169354i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-3.84386 + 4.26904i) q^{51} +(0.265207 - 2.52327i) q^{52} +(-7.85149 + 1.66888i) q^{53} +(0.309017 - 0.951057i) q^{54} +(3.34519 + 0.711042i) q^{55} +(1.36165 - 2.35845i) q^{56} +(1.42103 + 2.46129i) q^{57} +(1.68999 + 5.20126i) q^{58} +(-0.793845 - 7.55293i) q^{59} +(-0.809017 - 0.587785i) q^{60} -6.77906 q^{61} +(-5.17116 + 2.06376i) q^{62} -2.72330 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.265207 + 2.52327i) q^{65} +(-1.05681 - 3.25254i) q^{66} +(6.63617 + 11.4942i) q^{67} +(2.87228 - 4.97493i) q^{68} +(-6.31075 - 1.34139i) q^{69} +(-0.841547 + 2.59001i) q^{70} +(-10.3963 + 2.20980i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(3.96628 - 4.40501i) q^{73} +(-3.88748 + 1.73082i) q^{74} +(0.913545 + 0.406737i) q^{75} +(-1.90171 - 2.11206i) q^{76} +(-7.53477 + 5.47433i) q^{77} +(2.05262 - 1.49131i) q^{78} +(-6.36604 - 7.07020i) q^{79} +(0.913545 + 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-1.06174 + 1.17918i) q^{82} +(1.75292 - 16.6779i) q^{83} +(2.66379 - 0.566206i) q^{84} +(-1.77517 + 5.46340i) q^{85} +(3.54093 + 0.752647i) q^{86} +(-2.73447 + 4.73623i) q^{87} +(1.70996 + 2.96174i) q^{88} +(4.64008 + 14.2807i) q^{89} +(-0.104528 - 0.994522i) q^{90} +(-5.58989 - 4.06129i) q^{91} +6.45173 q^{92} +(-4.99385 - 2.46200i) q^{93} +5.48504 q^{94} +(2.29927 + 1.67052i) q^{95} +(-0.104528 - 0.994522i) q^{96} +(2.60797 + 8.02652i) q^{97} +(-0.208187 - 0.360590i) q^{98} +(1.70996 - 2.96174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{15}\right)\)

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
\(7\) 2.66379 + 0.566206i 1.00682 + 0.214006i 0.681672 0.731658i \(-0.261253\pi\)
0.325146 + 0.945664i \(0.394586\pi\)
\(8\) 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
\(11\) −2.28838 + 2.54150i −0.689971 + 0.766291i −0.981746 0.190196i \(-0.939088\pi\)
0.291775 + 0.956487i \(0.405754\pi\)
\(12\) 0.913545 0.406737i 0.263718 0.117415i
\(13\) −2.31782 1.03196i −0.642848 0.286214i 0.0593055 0.998240i \(-0.481111\pi\)
−0.702154 + 0.712025i \(0.747778\pi\)
\(14\) −1.82224 2.02381i −0.487015 0.540885i
\(15\) −0.809017 + 0.587785i −0.208887 + 0.151765i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −3.84386 4.26904i −0.932272 1.03539i −0.999291 0.0376417i \(-0.988015\pi\)
0.0670189 0.997752i \(-0.478651\pi\)
\(18\) 0.913545 + 0.406737i 0.215325 + 0.0958687i
\(19\) −2.59635 + 1.15597i −0.595643 + 0.265198i −0.682337 0.731037i \(-0.739036\pi\)
0.0866939 + 0.996235i \(0.472370\pi\)
\(20\) 0.669131 0.743145i 0.149622 0.166172i
\(21\) 0.284663 2.70838i 0.0621185 0.591018i
\(22\) 3.34519 0.711042i 0.713197 0.151595i
\(23\) 1.99369 6.13596i 0.415714 1.27944i −0.495897 0.868382i \(-0.665160\pi\)
0.911611 0.411055i \(-0.134840\pi\)
\(24\) −0.978148 0.207912i −0.199664 0.0424398i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.26859 + 2.19726i 0.248790 + 0.430917i
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) 0.284663 + 2.70838i 0.0537962 + 0.511836i
\(29\) −4.42446 3.21456i −0.821601 0.596928i 0.0955694 0.995423i \(-0.469533\pi\)
−0.917171 + 0.398494i \(0.869533\pi\)
\(30\) 1.00000 0.182574
\(31\) 2.97051 4.70915i 0.533520 0.845788i
\(32\) 1.00000 0.176777
\(33\) 2.76678 + 2.01018i 0.481634 + 0.349928i
\(34\) 0.600470 + 5.71309i 0.102980 + 0.979786i
\(35\) −0.841547 2.59001i −0.142247 0.437792i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 2.12769 3.68526i 0.349790 0.605854i −0.636422 0.771341i \(-0.719586\pi\)
0.986212 + 0.165487i \(0.0529197\pi\)
\(38\) 2.77995 + 0.590897i 0.450968 + 0.0958562i
\(39\) −0.784029 + 2.41299i −0.125545 + 0.386388i
\(40\) −0.978148 + 0.207912i −0.154659 + 0.0328737i
\(41\) 0.165860 1.57805i 0.0259030 0.246450i −0.973907 0.226948i \(-0.927125\pi\)
0.999810 0.0195023i \(-0.00620816\pi\)
\(42\) −1.82224 + 2.02381i −0.281178 + 0.312280i
\(43\) −3.30706 + 1.47240i −0.504322 + 0.224539i −0.643096 0.765785i \(-0.722351\pi\)
0.138774 + 0.990324i \(0.455684\pi\)
\(44\) −3.12426 1.39101i −0.470999 0.209702i
\(45\) 0.669131 + 0.743145i 0.0997481 + 0.110781i
\(46\) −5.21956 + 3.79223i −0.769582 + 0.559134i
\(47\) −4.43749 + 3.22403i −0.647275 + 0.470273i −0.862342 0.506327i \(-0.831003\pi\)
0.215067 + 0.976599i \(0.431003\pi\)
\(48\) 0.669131 + 0.743145i 0.0965807 + 0.107264i
\(49\) 0.380376 + 0.169354i 0.0543394 + 0.0241935i
\(50\) 0.913545 0.406737i 0.129195 0.0575212i
\(51\) −3.84386 + 4.26904i −0.538248 + 0.597785i
\(52\) 0.265207 2.52327i 0.0367776 0.349915i
\(53\) −7.85149 + 1.66888i −1.07848 + 0.229239i −0.712706 0.701463i \(-0.752531\pi\)
−0.365779 + 0.930702i \(0.619197\pi\)
\(54\) 0.309017 0.951057i 0.0420519 0.129422i
\(55\) 3.34519 + 0.711042i 0.451065 + 0.0958769i
\(56\) 1.36165 2.35845i 0.181958 0.315161i
\(57\) 1.42103 + 2.46129i 0.188220 + 0.326006i
\(58\) 1.68999 + 5.20126i 0.221907 + 0.682959i
\(59\) −0.793845 7.55293i −0.103350 0.983308i −0.916169 0.400792i \(-0.868735\pi\)
0.812819 0.582516i \(-0.197932\pi\)
\(60\) −0.809017 0.587785i −0.104444 0.0758827i
\(61\) −6.77906 −0.867969 −0.433985 0.900920i \(-0.642893\pi\)
−0.433985 + 0.900920i \(0.642893\pi\)
\(62\) −5.17116 + 2.06376i −0.656738 + 0.262097i
\(63\) −2.72330 −0.343104
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 0.265207 + 2.52327i 0.0328948 + 0.312974i
\(66\) −1.05681 3.25254i −0.130085 0.400360i
\(67\) 6.63617 + 11.4942i 0.810737 + 1.40424i 0.912349 + 0.409413i \(0.134267\pi\)
−0.101612 + 0.994824i \(0.532400\pi\)
\(68\) 2.87228 4.97493i 0.348315 0.603299i
\(69\) −6.31075 1.34139i −0.759725 0.161484i
\(70\) −0.841547 + 2.59001i −0.100584 + 0.309566i
\(71\) −10.3963 + 2.20980i −1.23381 + 0.262255i −0.778254 0.627950i \(-0.783894\pi\)
−0.455560 + 0.890205i \(0.650561\pi\)
\(72\) −0.104528 + 0.994522i −0.0123188 + 0.117206i
\(73\) 3.96628 4.40501i 0.464218 0.515567i −0.464893 0.885367i \(-0.653907\pi\)
0.929111 + 0.369800i \(0.120574\pi\)
\(74\) −3.88748 + 1.73082i −0.451910 + 0.201203i
\(75\) 0.913545 + 0.406737i 0.105487 + 0.0469659i
\(76\) −1.90171 2.11206i −0.218141 0.242270i
\(77\) −7.53477 + 5.47433i −0.858666 + 0.623858i
\(78\) 2.05262 1.49131i 0.232413 0.168858i
\(79\) −6.36604 7.07020i −0.716235 0.795460i 0.269636 0.962962i \(-0.413096\pi\)
−0.985872 + 0.167502i \(0.946430\pi\)
\(80\) 0.913545 + 0.406737i 0.102137 + 0.0454745i
\(81\) 0.913545 0.406737i 0.101505 0.0451930i
\(82\) −1.06174 + 1.17918i −0.117250 + 0.130219i
\(83\) 1.75292 16.6779i 0.192408 1.83064i −0.292726 0.956196i \(-0.594562\pi\)
0.485134 0.874440i \(-0.338771\pi\)
\(84\) 2.66379 0.566206i 0.290643 0.0617782i
\(85\) −1.77517 + 5.46340i −0.192544 + 0.592589i
\(86\) 3.54093 + 0.752647i 0.381828 + 0.0811600i
\(87\) −2.73447 + 4.73623i −0.293165 + 0.507778i
\(88\) 1.70996 + 2.96174i 0.182283 + 0.315723i
\(89\) 4.64008 + 14.2807i 0.491847 + 1.51375i 0.821813 + 0.569757i \(0.192963\pi\)
−0.329966 + 0.943993i \(0.607037\pi\)
\(90\) −0.104528 0.994522i −0.0110183 0.104832i
\(91\) −5.58989 4.06129i −0.585980 0.425739i
\(92\) 6.45173 0.672640
\(93\) −4.99385 2.46200i −0.517838 0.255297i
\(94\) 5.48504 0.565739
\(95\) 2.29927 + 1.67052i 0.235901 + 0.171392i
\(96\) −0.104528 0.994522i −0.0106684 0.101503i
\(97\) 2.60797 + 8.02652i 0.264800 + 0.814969i 0.991740 + 0.128268i \(0.0409418\pi\)
−0.726940 + 0.686701i \(0.759058\pi\)
\(98\) −0.208187 0.360590i −0.0210300 0.0364251i
\(99\) 1.70996 2.96174i 0.171858 0.297666i
\(100\) −0.978148 0.207912i −0.0978148 0.0207912i
\(101\) 1.27484 3.92356i 0.126852 0.390409i −0.867382 0.497642i \(-0.834199\pi\)
0.994234 + 0.107233i \(0.0341992\pi\)
\(102\) 5.61902 1.19436i 0.556366 0.118259i
\(103\) −0.486874 + 4.63230i −0.0479731 + 0.456434i 0.943996 + 0.329956i \(0.107034\pi\)
−0.991969 + 0.126478i \(0.959633\pi\)
\(104\) −1.69770 + 1.88549i −0.166473 + 0.184887i
\(105\) −2.48786 + 1.10767i −0.242790 + 0.108097i
\(106\) 7.33293 + 3.26483i 0.712237 + 0.317108i
\(107\) 10.1672 + 11.2919i 0.982905 + 1.09163i 0.995786 + 0.0917091i \(0.0292330\pi\)
−0.0128812 + 0.999917i \(0.504100\pi\)
\(108\) −0.809017 + 0.587785i −0.0778477 + 0.0565597i
\(109\) −0.179068 + 0.130101i −0.0171516 + 0.0124614i −0.596328 0.802741i \(-0.703374\pi\)
0.579176 + 0.815202i \(0.303374\pi\)
\(110\) −2.28838 2.54150i −0.218188 0.242322i
\(111\) −3.88748 1.73082i −0.368983 0.164282i
\(112\) −2.48786 + 1.10767i −0.235081 + 0.104665i
\(113\) 3.22871 3.58585i 0.303732 0.337328i −0.571886 0.820333i \(-0.693788\pi\)
0.875618 + 0.483005i \(0.160455\pi\)
\(114\) 0.297076 2.82649i 0.0278237 0.264725i
\(115\) −6.31075 + 1.34139i −0.588480 + 0.125085i
\(116\) 1.68999 5.20126i 0.156912 0.482925i
\(117\) 2.48173 + 0.527508i 0.229436 + 0.0487681i
\(118\) −3.79727 + 6.57706i −0.349567 + 0.605468i
\(119\) −7.82208 13.5482i −0.717049 1.24196i
\(120\) 0.309017 + 0.951057i 0.0282093 + 0.0868192i
\(121\) −0.0727390 0.692065i −0.00661263 0.0629150i
\(122\) 5.48437 + 3.98463i 0.496532 + 0.360751i
\(123\) −1.58675 −0.143072
\(124\) 5.39660 + 1.36992i 0.484629 + 0.123022i
\(125\) 1.00000 0.0894427
\(126\) 2.20320 + 1.60072i 0.196276 + 0.142603i
\(127\) −0.527892 5.02255i −0.0468428 0.445680i −0.992656 0.120969i \(-0.961400\pi\)
0.945813 0.324711i \(-0.105267\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) 1.81002 + 3.13504i 0.159363 + 0.276025i
\(130\) 1.26859 2.19726i 0.111262 0.192712i
\(131\) −13.4583 2.86064i −1.17585 0.249935i −0.421763 0.906706i \(-0.638589\pi\)
−0.754090 + 0.656771i \(0.771922\pi\)
\(132\) −1.05681 + 3.25254i −0.0919839 + 0.283097i
\(133\) −7.57065 + 1.60919i −0.656459 + 0.139535i
\(134\) 1.38734 13.1996i 0.119848 1.14027i
\(135\) 0.669131 0.743145i 0.0575896 0.0639597i
\(136\) −5.24791 + 2.33652i −0.450005 + 0.200355i
\(137\) 11.5459 + 5.14055i 0.986430 + 0.439187i 0.835579 0.549370i \(-0.185132\pi\)
0.150850 + 0.988557i \(0.451799\pi\)
\(138\) 4.31705 + 4.79457i 0.367492 + 0.408141i
\(139\) −7.22248 + 5.24744i −0.612603 + 0.445082i −0.850330 0.526250i \(-0.823598\pi\)
0.237727 + 0.971332i \(0.423598\pi\)
\(140\) 2.20320 1.60072i 0.186204 0.135285i
\(141\) 3.67021 + 4.07618i 0.309088 + 0.343276i
\(142\) 9.70968 + 4.32303i 0.814818 + 0.362780i
\(143\) 7.92678 3.52923i 0.662870 0.295129i
\(144\) 0.669131 0.743145i 0.0557609 0.0619287i
\(145\) −0.571659 + 5.43897i −0.0474737 + 0.451682i
\(146\) −5.79799 + 1.23240i −0.479845 + 0.101994i
\(147\) 0.128666 0.395995i 0.0106122 0.0326611i
\(148\) 4.16239 + 0.884742i 0.342146 + 0.0727254i
\(149\) 2.76362 4.78673i 0.226404 0.392144i −0.730335 0.683089i \(-0.760636\pi\)
0.956740 + 0.290945i \(0.0939696\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −4.84612 14.9148i −0.394372 1.21375i −0.929450 0.368949i \(-0.879718\pi\)
0.535078 0.844803i \(-0.320282\pi\)
\(152\) 0.297076 + 2.82649i 0.0240960 + 0.229259i
\(153\) 4.64744 + 3.37656i 0.375723 + 0.272979i
\(154\) 9.31348 0.750502
\(155\) −5.56350 0.217964i −0.446871 0.0175073i
\(156\) −2.53717 −0.203136
\(157\) 12.3878 + 9.00025i 0.988652 + 0.718298i 0.959625 0.281281i \(-0.0907592\pi\)
0.0290266 + 0.999579i \(0.490759\pi\)
\(158\) 0.994473 + 9.46178i 0.0791160 + 0.752739i
\(159\) 2.48045 + 7.63403i 0.196712 + 0.605418i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 8.78501 15.2161i 0.692356 1.19919i
\(162\) −0.978148 0.207912i −0.0768505 0.0163351i
\(163\) 4.08574 12.5746i 0.320020 0.984919i −0.653619 0.756824i \(-0.726750\pi\)
0.973639 0.228095i \(-0.0732498\pi\)
\(164\) 1.55207 0.329903i 0.121196 0.0257611i
\(165\) 0.357479 3.40119i 0.0278297 0.264782i
\(166\) −11.2212 + 12.4624i −0.870931 + 0.967266i
\(167\) 15.8394 7.05214i 1.22569 0.545711i 0.311206 0.950342i \(-0.399267\pi\)
0.914480 + 0.404632i \(0.132600\pi\)
\(168\) −2.48786 1.10767i −0.191943 0.0854583i
\(169\) −4.39134 4.87708i −0.337795 0.375160i
\(170\) 4.64744 3.37656i 0.356443 0.258971i
\(171\) 2.29927 1.67052i 0.175830 0.127748i
\(172\) −2.42227 2.69021i −0.184697 0.205126i
\(173\) 3.10094 + 1.38063i 0.235760 + 0.104967i 0.521216 0.853425i \(-0.325478\pi\)
−0.285456 + 0.958392i \(0.592145\pi\)
\(174\) 4.99612 2.22441i 0.378755 0.168632i
\(175\) −1.82224 + 2.02381i −0.137749 + 0.152985i
\(176\) 0.357479 3.40119i 0.0269460 0.256374i
\(177\) −7.42858 + 1.57899i −0.558366 + 0.118684i
\(178\) 4.64008 14.2807i 0.347788 1.07038i
\(179\) −4.09187 0.869753i −0.305841 0.0650084i 0.0524349 0.998624i \(-0.483302\pi\)
−0.358275 + 0.933616i \(0.616635\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 3.39954 + 5.88818i 0.252686 + 0.437665i 0.964264 0.264942i \(-0.0853527\pi\)
−0.711578 + 0.702607i \(0.752019\pi\)
\(182\) 2.13515 + 6.57131i 0.158268 + 0.487098i
\(183\) 0.708604 + 6.74192i 0.0523815 + 0.498377i
\(184\) −5.21956 3.79223i −0.384791 0.279567i
\(185\) −4.25538 −0.312861
\(186\) 2.59299 + 4.92711i 0.190127 + 0.361273i
\(187\) 19.6459 1.43665
\(188\) −4.43749 3.22403i −0.323638 0.235136i
\(189\) 0.284663 + 2.70838i 0.0207062 + 0.197006i
\(190\) −0.878244 2.70296i −0.0637145 0.196093i
\(191\) −5.64518 9.77774i −0.408471 0.707492i 0.586248 0.810132i \(-0.300605\pi\)
−0.994719 + 0.102639i \(0.967271\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −18.7487 3.98515i −1.34956 0.286858i −0.524262 0.851557i \(-0.675659\pi\)
−0.825297 + 0.564699i \(0.808992\pi\)
\(194\) 2.60797 8.02652i 0.187242 0.576270i
\(195\) 2.48173 0.527508i 0.177720 0.0377756i
\(196\) −0.0435229 + 0.414093i −0.00310878 + 0.0295780i
\(197\) −2.85869 + 3.17490i −0.203674 + 0.226202i −0.836325 0.548235i \(-0.815300\pi\)
0.632651 + 0.774437i \(0.281967\pi\)
\(198\) −3.12426 + 1.39101i −0.222031 + 0.0988547i
\(199\) 15.4171 + 6.86415i 1.09289 + 0.486587i 0.872395 0.488801i \(-0.162566\pi\)
0.220497 + 0.975388i \(0.429232\pi\)
\(200\) 0.669131 + 0.743145i 0.0473147 + 0.0525483i
\(201\) 10.7375 7.80128i 0.757368 0.550260i
\(202\) −3.33758 + 2.42490i −0.234832 + 0.170615i
\(203\) −9.96573 11.0681i −0.699457 0.776826i
\(204\) −5.24791 2.33652i −0.367427 0.163589i
\(205\) −1.44956 + 0.645388i −0.101242 + 0.0450758i
\(206\) 3.11669 3.46143i 0.217150 0.241169i
\(207\) −0.674390 + 6.41639i −0.0468733 + 0.445970i
\(208\) 2.48173 0.527508i 0.172077 0.0365761i
\(209\) 3.00353 9.24391i 0.207758 0.639415i
\(210\) 2.66379 + 0.566206i 0.183819 + 0.0390719i
\(211\) 2.63544 4.56472i 0.181431 0.314248i −0.760937 0.648826i \(-0.775260\pi\)
0.942368 + 0.334578i \(0.108594\pi\)
\(212\) −4.01345 6.95149i −0.275645 0.477431i
\(213\) 3.28441 + 10.1084i 0.225044 + 0.692614i
\(214\) −1.58828 15.1115i −0.108573 1.03300i
\(215\) 2.92867 + 2.12780i 0.199733 + 0.145115i
\(216\) 1.00000 0.0680414
\(217\) 10.5792 10.8623i 0.718161 0.737378i
\(218\) 0.221340 0.0149911
\(219\) −4.79546 3.48411i −0.324047 0.235434i
\(220\) 0.357479 + 3.40119i 0.0241013 + 0.229308i
\(221\) 4.50390 + 13.8616i 0.302965 + 0.932431i
\(222\) 2.12769 + 3.68526i 0.142801 + 0.247339i
\(223\) 10.7096 18.5495i 0.717167 1.24217i −0.244951 0.969536i \(-0.578772\pi\)
0.962118 0.272634i \(-0.0878949\pi\)
\(224\) 2.66379 + 0.566206i 0.177982 + 0.0378313i
\(225\) 0.309017 0.951057i 0.0206011 0.0634038i
\(226\) −4.71979 + 1.00322i −0.313956 + 0.0667334i
\(227\) 0.244365 2.32498i 0.0162191 0.154314i −0.983415 0.181370i \(-0.941947\pi\)
0.999634 + 0.0270564i \(0.00861336\pi\)
\(228\) −1.90171 + 2.11206i −0.125944 + 0.139875i
\(229\) 7.02998 3.12995i 0.464554 0.206833i −0.161093 0.986939i \(-0.551502\pi\)
0.625647 + 0.780106i \(0.284835\pi\)
\(230\) 5.89395 + 2.62416i 0.388636 + 0.173032i
\(231\) 6.23194 + 6.92127i 0.410031 + 0.455386i
\(232\) −4.42446 + 3.21456i −0.290480 + 0.211046i
\(233\) −13.6930 + 9.94855i −0.897059 + 0.651751i −0.937709 0.347422i \(-0.887057\pi\)
0.0406500 + 0.999173i \(0.487057\pi\)
\(234\) −1.69770 1.88549i −0.110982 0.123258i
\(235\) 5.01084 + 2.23097i 0.326871 + 0.145532i
\(236\) 6.93795 3.08898i 0.451622 0.201075i
\(237\) −6.36604 + 7.07020i −0.413519 + 0.459259i
\(238\) −1.63526 + 15.5585i −0.105998 + 1.00851i
\(239\) 16.5676 3.52156i 1.07167 0.227791i 0.361896 0.932219i \(-0.382130\pi\)
0.709775 + 0.704428i \(0.248796\pi\)
\(240\) 0.309017 0.951057i 0.0199470 0.0613904i
\(241\) 19.6396 + 4.17452i 1.26510 + 0.268905i 0.791136 0.611641i \(-0.209490\pi\)
0.473962 + 0.880545i \(0.342823\pi\)
\(242\) −0.347939 + 0.602647i −0.0223663 + 0.0387396i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −2.09484 6.44727i −0.134109 0.412744i
\(245\) −0.0435229 0.414093i −0.00278057 0.0264554i
\(246\) 1.28370 + 0.932666i 0.0818460 + 0.0594646i
\(247\) 7.21079 0.458812
\(248\) −3.56073 4.28033i −0.226106 0.271801i
\(249\) −16.7698 −1.06274
\(250\) −0.809017 0.587785i −0.0511667 0.0371748i
\(251\) −0.476324 4.53192i −0.0300653 0.286052i −0.999216 0.0395842i \(-0.987397\pi\)
0.969151 0.246468i \(-0.0792700\pi\)
\(252\) −0.841547 2.59001i −0.0530125 0.163156i
\(253\) 11.0322 + 19.1084i 0.693589 + 1.20133i
\(254\) −2.52511 + 4.37362i −0.158440 + 0.274425i
\(255\) 5.61902 + 1.19436i 0.351877 + 0.0747937i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 1.69590 0.360475i 0.105787 0.0224858i −0.154714 0.987959i \(-0.549446\pi\)
0.260501 + 0.965474i \(0.416112\pi\)
\(258\) 0.378396 3.60020i 0.0235579 0.224139i
\(259\) 7.75434 8.61206i 0.481831 0.535127i
\(260\) −2.31782 + 1.03196i −0.143745 + 0.0639995i
\(261\) 4.99612 + 2.22441i 0.309252 + 0.137688i
\(262\) 9.20651 + 10.2249i 0.568780 + 0.631694i
\(263\) 18.3225 13.3121i 1.12981 0.820856i 0.144144 0.989557i \(-0.453957\pi\)
0.985667 + 0.168700i \(0.0539571\pi\)
\(264\) 2.76678 2.01018i 0.170283 0.123718i
\(265\) 5.37104 + 5.96514i 0.329940 + 0.366436i
\(266\) 7.07064 + 3.14805i 0.433529 + 0.193020i
\(267\) 13.7174 6.10739i 0.839493 0.373766i
\(268\) −8.88093 + 9.86327i −0.542489 + 0.602495i
\(269\) −2.00652 + 19.0908i −0.122340 + 1.16398i 0.745279 + 0.666753i \(0.232316\pi\)
−0.867618 + 0.497231i \(0.834350\pi\)
\(270\) −0.978148 + 0.207912i −0.0595282 + 0.0126531i
\(271\) −0.152099 + 0.468113i −0.00923936 + 0.0284358i −0.955570 0.294765i \(-0.904759\pi\)
0.946331 + 0.323200i \(0.104759\pi\)
\(272\) 5.61902 + 1.19436i 0.340703 + 0.0724187i
\(273\) −3.45474 + 5.98379i −0.209091 + 0.362156i
\(274\) −6.31926 10.9453i −0.381760 0.661228i
\(275\) −1.05681 3.25254i −0.0637283 0.196136i
\(276\) −0.674390 6.41639i −0.0405935 0.386221i
\(277\) 11.1153 + 8.07575i 0.667854 + 0.485225i 0.869306 0.494274i \(-0.164566\pi\)
−0.201452 + 0.979498i \(0.564566\pi\)
\(278\) 8.92748 0.535435
\(279\) −1.92651 + 5.22384i −0.115337 + 0.312743i
\(280\) −2.72330 −0.162748
\(281\) 24.0476 + 17.4716i 1.43456 + 1.04227i 0.989145 + 0.146945i \(0.0469440\pi\)
0.445415 + 0.895324i \(0.353056\pi\)
\(282\) −0.573343 5.45500i −0.0341421 0.324840i
\(283\) −0.894417 2.75273i −0.0531676 0.163633i 0.920947 0.389688i \(-0.127417\pi\)
−0.974115 + 0.226055i \(0.927417\pi\)
\(284\) −5.31428 9.20461i −0.315345 0.546193i
\(285\) 1.42103 2.46129i 0.0841745 0.145795i
\(286\) −8.48732 1.80404i −0.501866 0.106675i
\(287\) 1.33532 4.10969i 0.0788215 0.242588i
\(288\) −0.978148 + 0.207912i −0.0576379 + 0.0122513i
\(289\) −1.67245 + 15.9123i −0.0983792 + 0.936016i
\(290\) 3.65943 4.06421i 0.214889 0.238659i
\(291\) 7.70994 3.43269i 0.451965 0.201228i
\(292\) 5.41506 + 2.41094i 0.316892 + 0.141090i
\(293\) −11.4317 12.6962i −0.667847 0.741719i 0.310070 0.950714i \(-0.399648\pi\)
−0.977917 + 0.208995i \(0.932981\pi\)
\(294\) −0.336853 + 0.244738i −0.0196457 + 0.0142734i
\(295\) −6.14411 + 4.46396i −0.357724 + 0.259902i
\(296\) −2.84740 3.16236i −0.165502 0.183808i
\(297\) −3.12426 1.39101i −0.181288 0.0807145i
\(298\) −5.04938 + 2.24813i −0.292503 + 0.130231i
\(299\) −10.9531 + 12.1647i −0.633434 + 0.703500i
\(300\) −0.104528 + 0.994522i −0.00603495 + 0.0574187i
\(301\) −9.64301 + 2.04968i −0.555814 + 0.118142i
\(302\) −4.84612 + 14.9148i −0.278863 + 0.858252i
\(303\) −4.03533 0.857735i −0.231824 0.0492756i
\(304\) 1.42103 2.46129i 0.0815016 0.141165i
\(305\) 3.38953 + 5.87083i 0.194084 + 0.336163i
\(306\) −1.77517 5.46340i −0.101479 0.312322i
\(307\) −2.08833 19.8691i −0.119187 1.13399i −0.876656 0.481118i \(-0.840231\pi\)
0.757469 0.652871i \(-0.226436\pi\)
\(308\) −7.53477 5.47433i −0.429333 0.311929i
\(309\) 4.65781 0.264974
\(310\) 4.37285 + 3.44648i 0.248361 + 0.195747i
\(311\) 19.1911 1.08823 0.544114 0.839012i \(-0.316866\pi\)
0.544114 + 0.839012i \(0.316866\pi\)
\(312\) 2.05262 + 1.49131i 0.116206 + 0.0844289i
\(313\) −3.56491 33.9179i −0.201501 1.91715i −0.365715 0.930727i \(-0.619175\pi\)
0.164214 0.986425i \(-0.447491\pi\)
\(314\) −4.73171 14.5627i −0.267026 0.821821i
\(315\) 1.36165 + 2.35845i 0.0767203 + 0.132884i
\(316\) 4.75695 8.23927i 0.267599 0.463495i
\(317\) −27.7458 5.89756i −1.55836 0.331240i −0.653494 0.756932i \(-0.726697\pi\)
−0.904868 + 0.425692i \(0.860031\pi\)
\(318\) 2.48045 7.63403i 0.139097 0.428095i
\(319\) 18.2946 3.88864i 1.02430 0.217722i
\(320\) −0.104528 + 0.994522i −0.00584332 + 0.0555955i
\(321\) 10.1672 11.2919i 0.567480 0.630251i
\(322\) −16.0510 + 7.14637i −0.894488 + 0.398252i
\(323\) 14.9149 + 6.64053i 0.829886 + 0.369489i
\(324\) 0.669131 + 0.743145i 0.0371739 + 0.0412858i
\(325\) 2.05262 1.49131i 0.113859 0.0827231i
\(326\) −10.6966 + 7.77153i −0.592430 + 0.430425i
\(327\) 0.148106 + 0.164488i 0.00819026 + 0.00909621i
\(328\) −1.44956 0.645388i −0.0800388 0.0356356i
\(329\) −13.6460 + 6.07560i −0.752330 + 0.334959i
\(330\) −2.28838 + 2.54150i −0.125971 + 0.139905i
\(331\) −1.01163 + 9.62500i −0.0556041 + 0.529038i 0.930897 + 0.365282i \(0.119028\pi\)
−0.986501 + 0.163756i \(0.947639\pi\)
\(332\) 16.4033 3.48663i 0.900248 0.191354i
\(333\) −1.31498 + 4.04710i −0.0720606 + 0.221780i
\(334\) −16.9594 3.60484i −0.927980 0.197248i
\(335\) 6.63617 11.4942i 0.362573 0.627994i
\(336\) 1.36165 + 2.35845i 0.0742842 + 0.128664i
\(337\) −4.28281 13.1811i −0.233300 0.718022i −0.997342 0.0728567i \(-0.976788\pi\)
0.764043 0.645165i \(-0.223212\pi\)
\(338\) 0.685995 + 6.52680i 0.0373132 + 0.355011i
\(339\) −3.90370 2.83620i −0.212020 0.154041i
\(340\) −5.74456 −0.311542
\(341\) 5.17065 + 18.3258i 0.280006 + 0.992400i
\(342\) −2.84206 −0.153681
\(343\) −14.5050 10.5385i −0.783198 0.569027i
\(344\) 0.378396 + 3.60020i 0.0204018 + 0.194110i
\(345\) 1.99369 + 6.13596i 0.107337 + 0.330349i
\(346\) −1.69720 2.93964i −0.0912421 0.158036i
\(347\) −16.1412 + 27.9574i −0.866505 + 1.50083i −0.000960890 1.00000i \(0.500306\pi\)
−0.865545 + 0.500832i \(0.833027\pi\)
\(348\) −5.34942 1.13705i −0.286759 0.0609525i
\(349\) 1.15321 3.54921i 0.0617298 0.189985i −0.915436 0.402464i \(-0.868154\pi\)
0.977166 + 0.212479i \(0.0681538\pi\)
\(350\) 2.66379 0.566206i 0.142386 0.0302650i
\(351\) 0.265207 2.52327i 0.0141557 0.134682i
\(352\) −2.28838 + 2.54150i −0.121971 + 0.135462i
\(353\) −1.30294 + 0.580107i −0.0693486 + 0.0308760i −0.441118 0.897449i \(-0.645418\pi\)
0.371769 + 0.928325i \(0.378751\pi\)
\(354\) 6.93795 + 3.08898i 0.368748 + 0.164177i
\(355\) 7.11190 + 7.89856i 0.377460 + 0.419212i
\(356\) −12.1479 + 8.82595i −0.643836 + 0.467774i
\(357\) −12.6564 + 9.19541i −0.669847 + 0.486672i
\(358\) 2.79916 + 3.10878i 0.147940 + 0.164304i
\(359\) 22.2846 + 9.92176i 1.17614 + 0.523651i 0.899328 0.437274i \(-0.144056\pi\)
0.276810 + 0.960925i \(0.410723\pi\)
\(360\) 0.913545 0.406737i 0.0481481 0.0214369i
\(361\) −7.30871 + 8.11715i −0.384669 + 0.427218i
\(362\) 0.710698 6.76184i 0.0373535 0.355395i
\(363\) −0.680671 + 0.144681i −0.0357259 + 0.00759378i
\(364\) 2.13515 6.57131i 0.111912 0.344430i
\(365\) −5.79799 1.23240i −0.303481 0.0645068i
\(366\) 3.38953 5.87083i 0.177173 0.306873i
\(367\) −15.9886 27.6930i −0.834597 1.44556i −0.894358 0.447351i \(-0.852367\pi\)
0.0597616 0.998213i \(-0.480966\pi\)
\(368\) 1.99369 + 6.13596i 0.103929 + 0.319859i
\(369\) 0.165860 + 1.57805i 0.00863433 + 0.0821502i
\(370\) 3.44267 + 2.50125i 0.178976 + 0.130034i
\(371\) −21.8597 −1.13490
\(372\) 0.798314 5.51024i 0.0413907 0.285692i
\(373\) 4.43018 0.229386 0.114693 0.993401i \(-0.463412\pi\)
0.114693 + 0.993401i \(0.463412\pi\)
\(374\) −15.8939 11.5476i −0.821854 0.597112i
\(375\) −0.104528 0.994522i −0.00539783 0.0513569i
\(376\) 1.69497 + 5.21659i 0.0874115 + 0.269025i
\(377\) 6.93781 + 12.0166i 0.357315 + 0.618888i
\(378\) 1.36165 2.35845i 0.0700358 0.121306i
\(379\) −25.0801 5.33095i −1.28828 0.273832i −0.487675 0.873025i \(-0.662155\pi\)
−0.800605 + 0.599193i \(0.795488\pi\)
\(380\) −0.878244 + 2.70296i −0.0450530 + 0.138659i
\(381\) −4.93986 + 1.05000i −0.253077 + 0.0537931i
\(382\) −1.18016 + 11.2285i −0.0603824 + 0.574501i
\(383\) −4.69630 + 5.21577i −0.239970 + 0.266513i −0.851085 0.525029i \(-0.824055\pi\)
0.611115 + 0.791542i \(0.290721\pi\)
\(384\) 0.913545 0.406737i 0.0466192 0.0207562i
\(385\) 8.50829 + 3.78814i 0.433623 + 0.193061i
\(386\) 12.8256 + 14.2442i 0.652805 + 0.725013i
\(387\) 2.92867 2.12780i 0.148873 0.108162i
\(388\) −6.82776 + 4.96066i −0.346627 + 0.251839i
\(389\) 5.97230 + 6.63291i 0.302808 + 0.336302i 0.875275 0.483625i \(-0.160680\pi\)
−0.572467 + 0.819928i \(0.694014\pi\)
\(390\) −2.31782 1.03196i −0.117367 0.0522554i
\(391\) −33.8581 + 15.0746i −1.71228 + 0.762356i
\(392\) 0.278608 0.309426i 0.0140718 0.0156284i
\(393\) −1.43820 + 13.6835i −0.0725475 + 0.690244i
\(394\) 4.17889 0.888251i 0.210530 0.0447495i
\(395\) −2.93996 + 9.04825i −0.147925 + 0.455267i
\(396\) 3.34519 + 0.711042i 0.168102 + 0.0357312i
\(397\) −8.07011 + 13.9778i −0.405027 + 0.701528i −0.994325 0.106388i \(-0.966071\pi\)
0.589297 + 0.807916i \(0.299405\pi\)
\(398\) −8.43808 14.6152i −0.422963 0.732593i
\(399\) 2.39172 + 7.36097i 0.119736 + 0.368510i
\(400\) −0.104528 0.994522i −0.00522642 0.0497261i
\(401\) −24.1736 17.5632i −1.20717 0.877063i −0.212202 0.977226i \(-0.568063\pi\)
−0.994971 + 0.100163i \(0.968063\pi\)
\(402\) −13.2723 −0.661964
\(403\) −11.7448 + 7.84951i −0.585049 + 0.391012i
\(404\) 4.12548 0.205250
\(405\) −0.809017 0.587785i −0.0402004 0.0292073i
\(406\) 1.55680 + 14.8120i 0.0772627 + 0.735105i
\(407\) 4.49714 + 13.8408i 0.222915 + 0.686062i
\(408\) 2.87228 + 4.97493i 0.142199 + 0.246296i
\(409\) 14.7124 25.4826i 0.727482 1.26004i −0.230462 0.973081i \(-0.574024\pi\)
0.957944 0.286954i \(-0.0926429\pi\)
\(410\) 1.55207 + 0.329903i 0.0766513 + 0.0162927i
\(411\) 3.90552 12.0199i 0.192645 0.592900i
\(412\) −4.55603 + 0.968414i −0.224459 + 0.0477103i
\(413\) 2.16188 20.5689i 0.106379 1.01213i
\(414\) 4.31705 4.79457i 0.212171 0.235640i
\(415\) −15.3199 + 6.82087i −0.752026 + 0.334824i
\(416\) −2.31782 1.03196i −0.113641 0.0505961i
\(417\) 5.97365 + 6.63441i 0.292531 + 0.324888i
\(418\) −7.86334 + 5.71305i −0.384609 + 0.279434i
\(419\) 13.3864 9.72581i 0.653970 0.475137i −0.210651 0.977561i \(-0.567558\pi\)
0.864621 + 0.502424i \(0.167558\pi\)
\(420\) −1.82224 2.02381i −0.0889164 0.0987517i
\(421\) −13.0295 5.80110i −0.635018 0.282728i 0.0638710 0.997958i \(-0.479655\pi\)
−0.698889 + 0.715230i \(0.746322\pi\)
\(422\) −4.81519 + 2.14386i −0.234400 + 0.104361i
\(423\) 3.67021 4.07618i 0.178452 0.198191i
\(424\) −0.839039 + 7.98292i −0.0407473 + 0.387685i
\(425\) 5.61902 1.19436i 0.272563 0.0579350i
\(426\) 3.28441 10.1084i 0.159130 0.489752i
\(427\) −18.0580 3.83834i −0.873887 0.185751i
\(428\) −7.59735 + 13.1590i −0.367232 + 0.636064i
\(429\) −4.33847 7.51445i −0.209463 0.362801i
\(430\) −1.11865 3.44285i −0.0539462 0.166029i
\(431\) −0.932715 8.87419i −0.0449273 0.427455i −0.993749 0.111641i \(-0.964389\pi\)
0.948821 0.315814i \(-0.102277\pi\)
\(432\) −0.809017 0.587785i −0.0389238 0.0282798i
\(433\) 15.5059 0.745164 0.372582 0.927999i \(-0.378473\pi\)
0.372582 + 0.927999i \(0.378473\pi\)
\(434\) −14.9434 + 2.56947i −0.717306 + 0.123339i
\(435\) 5.46893 0.262215
\(436\) −0.179068 0.130101i −0.00857581 0.00623069i
\(437\) 1.91665 + 18.2358i 0.0916860 + 0.872334i
\(438\) 1.83170 + 5.63741i 0.0875222 + 0.269366i
\(439\) −15.8691 27.4860i −0.757390 1.31184i −0.944178 0.329437i \(-0.893141\pi\)
0.186788 0.982400i \(-0.440192\pi\)
\(440\) 1.70996 2.96174i 0.0815192 0.141195i
\(441\) −0.407275 0.0865689i −0.0193940 0.00412233i
\(442\) 4.50390 13.8616i 0.214229 0.659328i
\(443\) −37.7462 + 8.02320i −1.79338 + 0.381194i −0.979755 0.200201i \(-0.935840\pi\)
−0.813621 + 0.581395i \(0.802507\pi\)
\(444\) 0.444808 4.23206i 0.0211096 0.200845i
\(445\) 10.0474 11.1588i 0.476292 0.528976i
\(446\) −19.5674 + 8.71196i −0.926543 + 0.412523i
\(447\) −5.04938 2.24813i −0.238828 0.106333i
\(448\) −1.82224 2.02381i −0.0860930 0.0956159i
\(449\) −31.6877 + 23.0225i −1.49544 + 1.08650i −0.523279 + 0.852161i \(0.675292\pi\)
−0.972156 + 0.234336i \(0.924708\pi\)
\(450\) −0.809017 + 0.587785i −0.0381374 + 0.0277085i
\(451\) 3.63107 + 4.03271i 0.170980 + 0.189893i
\(452\) 4.40807 + 1.96260i 0.207338 + 0.0923129i
\(453\) −14.3266 + 6.37860i −0.673121 + 0.299693i
\(454\) −1.56428 + 1.73731i −0.0734154 + 0.0815361i
\(455\) −0.722238 + 6.87164i −0.0338590 + 0.322147i
\(456\) 2.77995 0.590897i 0.130183 0.0276713i
\(457\) 2.07952 6.40010i 0.0972757 0.299384i −0.890564 0.454857i \(-0.849690\pi\)
0.987840 + 0.155473i \(0.0496903\pi\)
\(458\) −7.52711 1.59994i −0.351719 0.0747601i
\(459\) 2.87228 4.97493i 0.134066 0.232210i
\(460\) −3.22587 5.58736i −0.150407 0.260512i
\(461\) 11.0899 + 34.1311i 0.516506 + 1.58964i 0.780524 + 0.625125i \(0.214952\pi\)
−0.264018 + 0.964518i \(0.585048\pi\)
\(462\) −0.973524 9.26246i −0.0452924 0.430929i
\(463\) −3.34959 2.43362i −0.155669 0.113100i 0.507224 0.861814i \(-0.330672\pi\)
−0.662893 + 0.748714i \(0.730672\pi\)
\(464\) 5.46893 0.253889
\(465\) 0.364773 + 5.55580i 0.0169160 + 0.257644i
\(466\) 16.9255 0.784058
\(467\) 21.2911 + 15.4689i 0.985234 + 0.715815i 0.958872 0.283838i \(-0.0916078\pi\)
0.0263619 + 0.999652i \(0.491608\pi\)
\(468\) 0.265207 + 2.52327i 0.0122592 + 0.116638i
\(469\) 11.1693 + 34.3755i 0.515750 + 1.58731i
\(470\) −2.74252 4.75019i −0.126503 0.219110i
\(471\) 7.65607 13.2607i 0.352773 0.611021i
\(472\) −7.42858 1.57899i −0.341928 0.0726790i
\(473\) 3.82570 11.7743i 0.175906 0.541383i
\(474\) 9.30599 1.97805i 0.427438 0.0908548i
\(475\) 0.297076 2.82649i 0.0136308 0.129688i
\(476\) 10.4680 11.6259i 0.479799 0.532871i
\(477\) 7.33293 3.26483i 0.335752 0.149486i
\(478\) −15.4734 6.88921i −0.707738 0.315105i
\(479\) 10.7563 + 11.9460i 0.491466 + 0.545828i 0.936951 0.349461i \(-0.113635\pi\)
−0.445485 + 0.895289i \(0.646969\pi\)
\(480\) −0.809017 + 0.587785i −0.0369264 + 0.0268286i
\(481\) −8.73465 + 6.34609i −0.398266 + 0.289357i
\(482\) −13.4350 14.9211i −0.611949 0.679639i
\(483\) −16.0510 7.14637i −0.730346 0.325171i
\(484\) 0.635715 0.283039i 0.0288962 0.0128654i
\(485\) 5.64718 6.27183i 0.256425 0.284789i
\(486\) −0.104528 + 0.994522i −0.00474151 + 0.0451124i
\(487\) 29.0165 6.16764i 1.31486 0.279483i 0.503484 0.864004i \(-0.332051\pi\)
0.811378 + 0.584522i \(0.198718\pi\)
\(488\) −2.09484 + 6.44727i −0.0948291 + 0.291854i
\(489\) −12.9328 2.74895i −0.584841 0.124312i
\(490\) −0.208187 + 0.360590i −0.00940492 + 0.0162898i
\(491\) 13.9852 + 24.2230i 0.631141 + 1.09317i 0.987319 + 0.158751i \(0.0507465\pi\)
−0.356177 + 0.934418i \(0.615920\pi\)
\(492\) −0.490331 1.50908i −0.0221058 0.0680348i
\(493\) 3.28393 + 31.2445i 0.147901 + 1.40718i
\(494\) −5.83365 4.23840i −0.262468 0.190695i
\(495\) −3.41992 −0.153714
\(496\) 0.364773 + 5.55580i 0.0163788 + 0.249463i
\(497\) −28.9448 −1.29835
\(498\) 13.5670 + 9.85701i 0.607953 + 0.441703i
\(499\) −0.476683 4.53534i −0.0213393 0.203029i 0.978658 0.205497i \(-0.0658812\pi\)
−0.999997 + 0.00246775i \(0.999214\pi\)
\(500\) 0.309017 + 0.951057i 0.0138197 + 0.0425325i
\(501\) −8.66917 15.0154i −0.387310 0.670840i
\(502\) −2.27844 + 3.94638i −0.101692 + 0.176135i
\(503\) 35.3006 + 7.50338i 1.57398 + 0.334559i 0.910459 0.413600i \(-0.135729\pi\)
0.663519 + 0.748159i \(0.269062\pi\)
\(504\) −0.841547 + 2.59001i −0.0374855 + 0.115368i
\(505\) −4.03533 + 0.857735i −0.179570 + 0.0381687i
\(506\) 2.30636 21.9436i 0.102530 0.975510i
\(507\) −4.39134 + 4.87708i −0.195026 + 0.216599i
\(508\) 4.61361 2.05411i 0.204696 0.0911364i
\(509\) −6.79989 3.02750i −0.301400 0.134192i 0.250465 0.968126i \(-0.419417\pi\)
−0.551864 + 0.833934i \(0.686083\pi\)
\(510\) −3.84386 4.26904i −0.170209 0.189036i
\(511\) 13.0595 9.48828i 0.577718 0.419737i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) −1.90171 2.11206i −0.0839625 0.0932498i
\(514\) −1.58389 0.705195i −0.0698626 0.0311048i
\(515\) 4.25512 1.89450i 0.187503 0.0834818i
\(516\) −2.42227 + 2.69021i −0.106635 + 0.118430i
\(517\) 1.96079 18.6557i 0.0862354 0.820475i
\(518\) −11.3354 + 2.40942i −0.498050 + 0.105864i
\(519\) 1.04893 3.22827i 0.0460428 0.141705i
\(520\) 2.48173 + 0.527508i 0.108831 + 0.0231327i
\(521\) 9.63107 16.6815i 0.421945 0.730830i −0.574185 0.818726i \(-0.694681\pi\)
0.996130 + 0.0878958i \(0.0280143\pi\)
\(522\) −2.73447 4.73623i −0.119684 0.207299i
\(523\) 4.28806 + 13.1973i 0.187504 + 0.577077i 0.999983 0.00591377i \(-0.00188242\pi\)
−0.812479 + 0.582991i \(0.801882\pi\)
\(524\) −1.43820 13.6835i −0.0628280 0.597768i
\(525\) 2.20320 + 1.60072i 0.0961554 + 0.0698610i
\(526\) −22.6478 −0.987492
\(527\) −31.5217 + 5.42007i −1.37311 + 0.236102i
\(528\) −3.41992 −0.148833
\(529\) −15.0678 10.9474i −0.655122 0.475974i
\(530\) −0.839039 7.98292i −0.0364455 0.346756i
\(531\) 2.34684 + 7.22283i 0.101844 + 0.313444i
\(532\) −3.86989 6.70285i −0.167781 0.290605i
\(533\) −2.01292 + 3.48649i −0.0871894 + 0.151016i
\(534\) −14.6875 3.12192i −0.635589 0.135099i
\(535\) 4.69542 14.4510i 0.203001 0.624772i
\(536\) 12.9823 2.75947i 0.560750 0.119191i
\(537\) −0.437272 + 4.16037i −0.0188697 + 0.179533i
\(538\) 12.8446 14.2653i 0.553769 0.615022i
\(539\) −1.30086 + 0.579179i −0.0560319 + 0.0249470i
\(540\) 0.913545 + 0.406737i 0.0393127 + 0.0175032i
\(541\) 5.76039 + 6.39756i 0.247659 + 0.275053i 0.854138 0.520047i \(-0.174085\pi\)
−0.606479 + 0.795099i \(0.707419\pi\)
\(542\) 0.398200 0.289310i 0.0171042 0.0124269i
\(543\) 5.50058 3.99640i 0.236052 0.171502i
\(544\) −3.84386 4.26904i −0.164804 0.183033i
\(545\) 0.202205 + 0.0900273i 0.00866149 + 0.00385635i
\(546\) 6.31213 2.81034i 0.270134 0.120272i
\(547\) 18.2332 20.2500i 0.779596 0.865829i −0.214230 0.976783i \(-0.568724\pi\)
0.993825 + 0.110954i \(0.0353908\pi\)
\(548\) −1.32109 + 12.5693i −0.0564340 + 0.536933i
\(549\) 6.63092 1.40945i 0.283001 0.0601536i
\(550\) −1.05681 + 3.25254i −0.0450627 + 0.138689i
\(551\) 15.2034 + 3.23158i 0.647685 + 0.137670i
\(552\) −3.22587 + 5.58736i −0.137302 + 0.237814i
\(553\) −12.9546 22.4380i −0.550886 0.954162i
\(554\) −4.24567 13.0668i −0.180381 0.555157i
\(555\) 0.444808 + 4.23206i 0.0188810 + 0.179641i
\(556\) −7.22248 5.24744i −0.306301 0.222541i
\(557\) −20.9917 −0.889447 −0.444723 0.895668i \(-0.646698\pi\)
−0.444723 + 0.895668i \(0.646698\pi\)
\(558\) 4.62908 3.09380i 0.195965 0.130971i
\(559\) 9.18464 0.388469
\(560\) 2.20320 + 1.60072i 0.0931021 + 0.0676426i
\(561\) −2.05356 19.5383i −0.0867014 0.824908i
\(562\) −9.18537 28.2697i −0.387461 1.19248i
\(563\) −5.20172 9.00964i −0.219226 0.379711i 0.735345 0.677693i \(-0.237020\pi\)
−0.954572 + 0.297981i \(0.903687\pi\)
\(564\) −2.74252 + 4.75019i −0.115481 + 0.200019i
\(565\) −4.71979 1.00322i −0.198563 0.0422059i
\(566\) −0.894417 + 2.75273i −0.0375952 + 0.115706i
\(567\) 2.66379 0.566206i 0.111869 0.0237784i
\(568\) −1.11099 + 10.5703i −0.0466160 + 0.443522i
\(569\) −10.6236 + 11.7987i −0.445366 + 0.494629i −0.923468 0.383675i \(-0.874658\pi\)
0.478102 + 0.878304i \(0.341325\pi\)
\(570\) −2.59635 + 1.15597i −0.108749 + 0.0484182i
\(571\) −10.5275 4.68714i −0.440561 0.196151i 0.174455 0.984665i \(-0.444184\pi\)
−0.615016 + 0.788515i \(0.710850\pi\)
\(572\) 5.80600 + 6.44822i 0.242761 + 0.269614i
\(573\) −9.13409 + 6.63631i −0.381582 + 0.277236i
\(574\) −3.49591 + 2.53993i −0.145917 + 0.106015i
\(575\) 4.31705 + 4.79457i 0.180033 + 0.199947i
\(576\) 0.913545 + 0.406737i 0.0380644 + 0.0169474i
\(577\) 29.9664 13.3419i 1.24752 0.555431i 0.326591 0.945166i \(-0.394100\pi\)
0.920927 + 0.389735i \(0.127433\pi\)
\(578\) 10.7060 11.8903i 0.445312 0.494569i
\(579\) −2.00355 + 19.0625i −0.0832648 + 0.792211i
\(580\) −5.34942 + 1.13705i −0.222123 + 0.0472136i
\(581\) 14.1125 43.4339i 0.585486 1.80194i
\(582\) −8.25515 1.75469i −0.342187 0.0727341i
\(583\) 13.7257 23.7736i 0.568460 0.984601i
\(584\) −2.96376 5.13338i −0.122641 0.212421i
\(585\) −0.784029 2.41299i −0.0324156 0.0997650i
\(586\) 1.78581 + 16.9908i 0.0737710 + 0.701884i
\(587\) −10.6644 7.74815i −0.440167 0.319800i 0.345534 0.938406i \(-0.387698\pi\)
−0.785701 + 0.618606i \(0.787698\pi\)
\(588\) 0.416373 0.0171710
\(589\) −2.26886 + 15.6604i −0.0934866 + 0.645276i
\(590\) 7.59454 0.312662
\(591\) 3.45632 + 2.51117i 0.142174 + 0.103296i
\(592\) 0.444808 + 4.23206i 0.0182815 + 0.173937i
\(593\) −0.0777306 0.239230i −0.00319201 0.00982401i 0.949448 0.313925i \(-0.101644\pi\)
−0.952640 + 0.304101i \(0.901644\pi\)
\(594\) 1.70996 + 2.96174i 0.0701606 + 0.121522i
\(595\) −7.82208 + 13.5482i −0.320674 + 0.555424i
\(596\) 5.40645 + 1.14918i 0.221457 + 0.0470721i
\(597\) 5.21502 16.0502i 0.213437 0.656890i
\(598\) 16.0115 3.40334i 0.654757 0.139173i
\(599\) 1.51892 14.4516i 0.0620614 0.590475i −0.918658 0.395054i \(-0.870726\pi\)
0.980719 0.195421i \(-0.0626073\pi\)
\(600\) 0.669131 0.743145i 0.0273171 0.0303388i
\(601\) −17.3832 + 7.73952i −0.709078 + 0.315702i −0.729396 0.684092i \(-0.760199\pi\)
0.0203183 + 0.999794i \(0.493532\pi\)
\(602\) 9.00613 + 4.00979i 0.367063 + 0.163427i
\(603\) −8.88093 9.86327i −0.361659 0.401663i
\(604\) 12.6873 9.21787i 0.516239 0.375070i
\(605\) −0.562976 + 0.409026i −0.0228882 + 0.0166293i
\(606\) 2.76048 + 3.06583i 0.112137 + 0.124541i
\(607\) −12.3697 5.50733i −0.502069 0.223535i 0.140044 0.990145i \(-0.455275\pi\)
−0.642113 + 0.766610i \(0.721942\pi\)
\(608\) −2.59635 + 1.15597i −0.105296 + 0.0468807i
\(609\) −9.96573 + 11.0681i −0.403832 + 0.448501i
\(610\) 0.708604 6.74192i 0.0286906 0.272972i
\(611\) 13.6124 2.89340i 0.550699 0.117055i
\(612\) −1.77517 + 5.46340i −0.0717568 + 0.220845i
\(613\) 26.7256 + 5.68070i 1.07944 + 0.229441i 0.713115 0.701047i \(-0.247284\pi\)
0.366321 + 0.930489i \(0.380617\pi\)
\(614\) −9.98927 + 17.3019i −0.403134 + 0.698249i
\(615\) 0.793373 + 1.37416i 0.0319919 + 0.0554116i
\(616\) 2.87802 + 8.85765i 0.115959 + 0.356885i
\(617\) 3.08536 + 29.3552i 0.124212 + 1.18180i 0.862052 + 0.506821i \(0.169179\pi\)
−0.737840 + 0.674976i \(0.764154\pi\)
\(618\) −3.76825 2.73779i −0.151581 0.110130i
\(619\) −30.9615 −1.24445 −0.622223 0.782840i \(-0.713770\pi\)
−0.622223 + 0.782840i \(0.713770\pi\)
\(620\) −1.51192 5.35855i −0.0607201 0.215205i
\(621\) 6.45173 0.258899
\(622\) −15.5259 11.2802i −0.622533 0.452297i
\(623\) 4.27438 + 40.6680i 0.171249 + 1.62933i
\(624\) −0.784029 2.41299i −0.0313863 0.0965971i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −17.0524 + 29.5355i −0.681549 + 1.18048i
\(627\) −9.50723 2.02082i −0.379682 0.0807039i
\(628\) −4.73171 + 14.5627i −0.188816 + 0.581115i
\(629\) −23.9111 + 5.08245i −0.953396 + 0.202651i
\(630\) 0.284663 2.70838i 0.0113412 0.107905i
\(631\) −23.6028 + 26.2136i −0.939614 + 1.04355i 0.0593587 + 0.998237i \(0.481094\pi\)
−0.998973 + 0.0453106i \(0.985572\pi\)
\(632\) −8.69138 + 3.86965i −0.345724 + 0.153926i
\(633\) −4.81519 2.14386i −0.191387 0.0852108i
\(634\) 18.9804 + 21.0798i 0.753806 + 0.837187i
\(635\) −4.08571 + 2.96845i −0.162137 + 0.117799i
\(636\) −6.49389 + 4.71809i −0.257500 + 0.187084i
\(637\) −0.706877 0.785067i −0.0280075 0.0311055i
\(638\) −17.0863 7.60733i −0.676455 0.301177i
\(639\) 9.70968 4.32303i 0.384109 0.171016i
\(640\) 0.669131 0.743145i 0.0264497 0.0293754i
\(641\) −4.61463 + 43.9053i −0.182267 + 1.73415i 0.395951 + 0.918272i \(0.370415\pi\)
−0.578218 + 0.815882i \(0.696252\pi\)
\(642\) −14.8627 + 3.15916i −0.586583 + 0.124682i
\(643\) −0.848458 + 2.61128i −0.0334599 + 0.102979i −0.966392 0.257074i \(-0.917241\pi\)
0.932932 + 0.360053i \(0.117241\pi\)
\(644\) 17.1861 + 3.65301i 0.677226 + 0.143949i
\(645\) 1.81002 3.13504i 0.0712693 0.123442i
\(646\) −8.16318 14.1390i −0.321176 0.556293i
\(647\) 1.76825 + 5.44210i 0.0695169 + 0.213951i 0.979779 0.200080i \(-0.0641203\pi\)
−0.910263 + 0.414032i \(0.864120\pi\)
\(648\) −0.104528 0.994522i −0.00410627 0.0390685i
\(649\) 21.0124 + 15.2664i 0.824808 + 0.599258i
\(650\) −2.53717 −0.0995161
\(651\) −11.9086 9.38580i −0.466734 0.367859i
\(652\) 13.2217 0.517803
\(653\) 5.89725 + 4.28461i 0.230777 + 0.167670i 0.697165 0.716911i \(-0.254445\pi\)
−0.466387 + 0.884581i \(0.654445\pi\)
\(654\) −0.0231364 0.220128i −0.000904704 0.00860768i
\(655\) 4.25174 + 13.0855i 0.166129 + 0.511293i
\(656\) 0.793373 + 1.37416i 0.0309760 + 0.0536520i
\(657\) −2.96376 + 5.13338i −0.115627 + 0.200272i
\(658\) 14.6110 + 3.10567i 0.569597 + 0.121071i
\(659\) 3.11208 9.57799i 0.121229 0.373106i −0.871966 0.489567i \(-0.837155\pi\)
0.993195 + 0.116461i \(0.0371550\pi\)
\(660\) 3.34519 0.711042i 0.130211 0.0276773i
\(661\) 0.770472 7.33055i 0.0299679 0.285125i −0.969267 0.246012i \(-0.920880\pi\)
0.999235 0.0391138i \(-0.0124535\pi\)
\(662\) 6.47586 7.19217i 0.251691 0.279532i
\(663\) 13.3149 5.92816i 0.517106 0.230231i
\(664\) −15.3199 6.82087i −0.594529 0.264701i
\(665\) 5.17893 + 5.75178i 0.200830 + 0.223044i
\(666\) 3.44267 2.50125i 0.133401 0.0969214i
\(667\) −28.5454 + 20.7395i −1.10528 + 0.803035i
\(668\) 11.6016 + 12.8849i 0.448880 + 0.498531i
\(669\) −19.5674 8.71196i −0.756519 0.336824i
\(670\) −12.1249 + 5.39834i −0.468425 + 0.208556i
\(671\) 15.5130 17.2290i 0.598874 0.665117i
\(672\) 0.284663 2.70838i 0.0109811 0.104478i
\(673\) 36.1456 7.68298i 1.39331 0.296157i 0.550710 0.834697i \(-0.314357\pi\)
0.842600 + 0.538539i \(0.181024\pi\)
\(674\) −4.28281 + 13.1811i −0.164968 + 0.507718i
\(675\) −0.978148 0.207912i −0.0376489 0.00800252i
\(676\) 3.28138 5.68351i 0.126207 0.218597i
\(677\) −21.3936 37.0548i −0.822224 1.42413i −0.904023 0.427484i \(-0.859400\pi\)
0.0817992 0.996649i \(-0.473933\pi\)
\(678\) 1.49108 + 4.58907i 0.0572645 + 0.176242i
\(679\) 2.40243 + 22.8576i 0.0921969 + 0.877195i
\(680\) 4.64744 + 3.37656i 0.178221 + 0.129485i
\(681\) −2.33778 −0.0895840
\(682\) 6.58852 17.8651i 0.252288 0.684092i
\(683\) 49.7881 1.90509 0.952544 0.304402i \(-0.0984565\pi\)
0.952544 + 0.304402i \(0.0984565\pi\)
\(684\) 2.29927 + 1.67052i 0.0879149 + 0.0638739i
\(685\) −1.32109 12.5693i −0.0504761 0.480248i
\(686\) 5.54043 + 17.0517i 0.211535 + 0.651036i
\(687\) −3.84764 6.66430i −0.146796 0.254259i
\(688\) 1.81002 3.13504i 0.0690062 0.119522i
\(689\) 19.9206 + 4.23425i 0.758913 + 0.161312i
\(690\) 1.99369 6.13596i 0.0758987 0.233592i
\(691\) −42.3245 + 8.99634i −1.61010 + 0.342237i −0.923141 0.384461i \(-0.874387\pi\)
−0.686957 + 0.726698i \(0.741054\pi\)
\(692\) −0.354812 + 3.37581i −0.0134879 + 0.128329i
\(693\) 6.23194 6.92127i 0.236732 0.262917i
\(694\) 29.4915 13.1304i 1.11948 0.498425i
\(695\) 8.15566 + 3.63113i 0.309362 + 0.137737i
\(696\) 3.65943 + 4.06421i 0.138710 + 0.154053i
\(697\) −7.37431 + 5.35775i −0.279322 + 0.202939i
\(698\) −3.01914 + 2.19353i −0.114276 + 0.0830264i
\(699\) 11.3254 + 12.5781i 0.428365 + 0.475747i
\(700\) −2.48786 1.10767i −0.0940323 0.0418659i
\(701\) 25.4521 11.3320i 0.961314 0.428004i 0.134770 0.990877i \(-0.456970\pi\)
0.826544 + 0.562873i \(0.190304\pi\)
\(702\) −1.69770 + 1.88549i −0.0640755 + 0.0711631i
\(703\) −1.26417 + 12.0278i −0.0476791 + 0.453636i
\(704\) 3.34519 0.711042i 0.126077 0.0267984i
\(705\) 1.69497 5.21659i 0.0638363 0.196468i
\(706\) 1.39508 + 0.296533i 0.0525045 + 0.0111602i
\(707\) 5.61746 9.72973i 0.211266 0.365924i
\(708\) −3.79727 6.57706i −0.142710 0.247181i
\(709\) 10.8800 + 33.4853i 0.408608 + 1.25757i 0.917845 + 0.396940i \(0.129928\pi\)
−0.509237 + 0.860626i \(0.670072\pi\)
\(710\) −1.11099 10.5703i −0.0416946 0.396698i
\(711\) 7.69690 + 5.59213i 0.288656 + 0.209721i
\(712\) 15.0156 0.562733
\(713\) −22.9729 27.6155i −0.860340 1.03421i
\(714\) 15.6442 0.585468
\(715\) −7.01979 5.10017i −0.262525 0.190736i
\(716\) −0.437272 4.16037i −0.0163416 0.155480i
\(717\) −5.23406 16.1088i −0.195469 0.601593i
\(718\) −12.1968 21.1255i −0.455180 0.788395i
\(719\) 3.40469 5.89709i 0.126973 0.219925i −0.795529 0.605915i \(-0.792807\pi\)
0.922503 + 0.385991i \(0.126140\pi\)
\(720\) −0.978148 0.207912i −0.0364534 0.00774841i
\(721\) −3.91977 + 12.0638i −0.145980 + 0.449280i
\(722\) 10.6840 2.27096i 0.397618 0.0845163i
\(723\) 2.09876 19.9684i 0.0780537 0.742631i
\(724\) −4.54948 + 5.05271i −0.169080 + 0.187782i
\(725\) 4.99612 2.22441i 0.185551 0.0826127i
\(726\) 0.635715 + 0.283039i 0.0235936 + 0.0105046i
\(727\) 28.2295 + 31.3520i 1.04697 + 1.16278i 0.986357 + 0.164622i \(0.0526404\pi\)
0.0606178 + 0.998161i \(0.480693\pi\)
\(728\) −5.58989 + 4.06129i −0.207175 + 0.150522i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 3.96628 + 4.40501i 0.146799 + 0.163037i
\(731\) 18.9976 + 8.45828i 0.702652 + 0.312841i
\(732\) −6.19298 + 2.75729i −0.228899 + 0.101912i
\(733\) 8.75247 9.72060i 0.323280 0.359039i −0.559496 0.828833i \(-0.689005\pi\)
0.882776 + 0.469794i \(0.155672\pi\)
\(734\) −3.34252 + 31.8020i −0.123375 + 1.17383i
\(735\) −0.407275 + 0.0865689i −0.0150226 + 0.00319314i
\(736\) 1.99369 6.13596i 0.0734886 0.226175i
\(737\) −44.3985 9.43719i −1.63544 0.347623i
\(738\) 0.793373 1.37416i 0.0292045 0.0505836i
\(739\) −17.2682 29.9093i −0.635220 1.10023i −0.986469 0.163951i \(-0.947576\pi\)
0.351249 0.936282i \(-0.385757\pi\)
\(740\) −1.31498 4.04710i −0.0483397 0.148774i
\(741\) −0.753733 7.17129i −0.0276891 0.263444i
\(742\) 17.6848 + 12.8488i 0.649231 + 0.471694i
\(743\) 5.49552 0.201611 0.100805 0.994906i \(-0.467858\pi\)
0.100805 + 0.994906i \(0.467858\pi\)
\(744\) −3.88468 + 3.98864i −0.142419 + 0.146231i
\(745\) −5.52724 −0.202502
\(746\) −3.58409 2.60399i −0.131223 0.0953390i
\(747\) 1.75292 + 16.6779i 0.0641359 + 0.610212i
\(748\) 6.07093 + 18.6844i 0.221975 + 0.683169i
\(749\) 20.6899 + 35.8359i 0.755992 + 1.30942i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) −13.3088 2.82886i −0.485643 0.103227i −0.0414183 0.999142i \(-0.513188\pi\)
−0.444225 + 0.895915i \(0.646521\pi\)
\(752\) 1.69497 5.21659i 0.0618093 0.190229i
\(753\) −4.45730 + 0.947429i −0.162433 + 0.0345262i
\(754\) 1.45040 13.7996i 0.0528204 0.502552i
\(755\) −10.4936 + 11.6543i −0.381900 + 0.424143i
\(756\) −2.48786 + 1.10767i −0.0904826 + 0.0402854i
\(757\) 5.82174 + 2.59201i 0.211595 + 0.0942080i 0.509797 0.860295i \(-0.329720\pi\)
−0.298203 + 0.954503i \(0.596387\pi\)
\(758\) 17.1568 + 19.0546i 0.623163 + 0.692093i
\(759\) 17.8505 12.9691i 0.647932 0.470750i
\(760\) 2.29927 1.67052i 0.0834034 0.0605961i
\(761\) −23.9983 26.6528i −0.869939 0.966165i 0.129739 0.991548i \(-0.458586\pi\)
−0.999678 + 0.0253832i \(0.991919\pi\)
\(762\) 4.61361 + 2.05411i 0.167133 + 0.0744125i
\(763\) −0.550664 + 0.245171i −0.0199354 + 0.00887580i
\(764\) 7.55473 8.39037i 0.273320 0.303553i
\(765\) 0.600470 5.71309i 0.0217100 0.206557i
\(766\) 6.86513 1.45923i 0.248047 0.0527241i
\(767\) −5.95434 + 18.3256i −0.214999 + 0.661698i
\(768\) −0.978148 0.207912i −0.0352959 0.00750237i
\(769\) −4.79620 + 8.30727i −0.172955 + 0.299568i −0.939452 0.342681i \(-0.888665\pi\)
0.766496 + 0.642249i \(0.221998\pi\)
\(770\) −4.65674 8.06571i −0.167817 0.290668i
\(771\) −0.535770 1.64893i −0.0192953 0.0593848i
\(772\) −2.00355 19.0625i −0.0721094 0.686075i
\(773\) 17.5041 + 12.7175i 0.629579 + 0.457416i 0.856254 0.516554i \(-0.172786\pi\)
−0.226675 + 0.973970i \(0.572786\pi\)
\(774\) −3.62003 −0.130119
\(775\) 2.59299 + 4.92711i 0.0931428 + 0.176987i
\(776\) 8.43958 0.302963
\(777\) −9.37543 6.81165i −0.336342 0.244367i
\(778\) −0.932965 8.87657i −0.0334484 0.318241i
\(779\) 1.39355 + 4.28891i 0.0499291 + 0.153666i
\(780\) 1.26859 + 2.19726i 0.0454227 + 0.0786744i
\(781\) 18.1744 31.4790i 0.650332 1.12641i
\(782\) 36.2524 + 7.70569i 1.29638 + 0.275555i
\(783\) 1.68999 5.20126i 0.0603954 0.185878i
\(784\) −0.407275 + 0.0865689i −0.0145455 + 0.00309175i
\(785\) 1.60055 15.2283i 0.0571262 0.543520i
\(786\) 9.20651 10.2249i 0.328385 0.364709i
\(787\) 9.65488 4.29863i 0.344159 0.153230i −0.227376 0.973807i \(-0.573015\pi\)
0.571535 + 0.820577i \(0.306348\pi\)
\(788\) −3.90290 1.73768i −0.139035 0.0619023i
\(789\) −15.1543 16.8306i −0.539509 0.599185i
\(790\) 7.69690 5.59213i 0.273843 0.198959i
\(791\) 10.6309 7.72383i 0.377993 0.274628i
\(792\) −2.28838 2.54150i −0.0813139 0.0903082i
\(793\) 15.7126 + 6.99572i 0.557972 + 0.248425i
\(794\) 14.7448 6.56482i 0.523275 0.232977i
\(795\) 5.37104 5.96514i 0.190491 0.211562i
\(796\) −1.76404 + 16.7837i −0.0625247 + 0.594883i
\(797\) −23.1647 + 4.92380i −0.820535 + 0.174410i −0.599007 0.800744i \(-0.704438\pi\)
−0.221528 + 0.975154i \(0.571104\pi\)
\(798\) 2.39172 7.36097i 0.0846661 0.260576i
\(799\) 30.8206 + 6.55112i 1.09035 + 0.231762i
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) −7.50780 13.0039i −0.265275 0.459470i
\(802\) 9.23350 + 28.4178i 0.326046 + 1.00347i
\(803\) 2.11897 + 20.1606i 0.0747767 + 0.711453i
\(804\) 10.7375 + 7.80128i 0.378684 + 0.275130i
\(805\) −17.5700 −0.619262
\(806\) 14.1155 + 0.553013i 0.497199 + 0.0194791i
\(807\) 19.1959 0.675728
\(808\) −3.33758 2.42490i −0.117416 0.0853075i
\(809\) 3.37637 + 32.1240i 0.118707 + 1.12942i 0.877997 + 0.478667i \(0.158880\pi\)
−0.759290 + 0.650752i \(0.774454\pi\)
\(810\) 0.309017 + 0.951057i 0.0108578 + 0.0334167i
\(811\) 21.1115 + 36.5663i 0.741326 + 1.28401i 0.951892 + 0.306435i \(0.0991363\pi\)
−0.210565 + 0.977580i \(0.567530\pi\)
\(812\) 7.44678 12.8982i 0.261331 0.452638i
\(813\) 0.481447 + 0.102335i 0.0168851 + 0.00358904i
\(814\) 4.49714 13.8408i 0.157625 0.485119i
\(815\) −12.9328 + 2.74895i −0.453016 + 0.0962915i
\(816\) 0.600470 5.71309i 0.0210206 0.199998i
\(817\) 6.88424 7.64573i 0.240849 0.267490i
\(818\) −26.8809 + 11.9682i −0.939869 + 0.418457i
\(819\) 6.31213 + 2.81034i 0.220564 + 0.0982013i
\(820\) −1.06174 1.17918i −0.0370776 0.0411788i
\(821\) 4.54563 3.30260i 0.158644 0.115261i −0.505631 0.862750i \(-0.668740\pi\)
0.664275 + 0.747488i \(0.268740\pi\)
\(822\) −10.2248 + 7.42874i −0.356630 + 0.259107i
\(823\) −15.1885 16.8686i −0.529439 0.588001i 0.417797 0.908541i \(-0.362802\pi\)
−0.947235 + 0.320539i \(0.896136\pi\)
\(824\) 4.25512 + 1.89450i 0.148234 + 0.0659982i
\(825\) −3.12426 + 1.39101i −0.108773 + 0.0484287i
\(826\) −13.8391 + 15.3699i −0.481524 + 0.534787i
\(827\) 3.29773 31.3758i 0.114673 1.09104i −0.774216 0.632921i \(-0.781856\pi\)
0.888890 0.458121i \(-0.151477\pi\)
\(828\) −6.31075 + 1.34139i −0.219314 + 0.0466165i
\(829\) 4.86179 14.9631i 0.168857 0.519689i −0.830443 0.557104i \(-0.811912\pi\)
0.999300 + 0.0374154i \(0.0119125\pi\)
\(830\) 16.4033 + 3.48663i 0.569367 + 0.121023i
\(831\) 6.86964 11.8986i 0.238305 0.412757i
\(832\) 1.26859 + 2.19726i 0.0439803 + 0.0761761i
\(833\) −0.739132 2.27481i −0.0256094 0.0788176i
\(834\) −0.933176 8.87857i −0.0323132 0.307440i
\(835\) −14.0270 10.1912i −0.485425 0.352682i
\(836\) 9.71962 0.336160
\(837\) 5.39660 + 1.36992i 0.186534 + 0.0473513i
\(838\) −16.5465 −0.571591
\(839\) −3.41799 2.48331i −0.118002 0.0857335i 0.527219 0.849729i \(-0.323235\pi\)
−0.645221 + 0.763996i \(0.723235\pi\)
\(840\) 0.284663 + 2.70838i 0.00982179 + 0.0934481i
\(841\) 0.280961 + 0.864710i 0.00968832 + 0.0298176i
\(842\) 7.13128 + 12.3517i 0.245760 + 0.425669i
\(843\) 14.8622 25.7422i 0.511883 0.886607i
\(844\) 5.15570 + 1.09588i 0.177466 + 0.0377217i
\(845\) −2.02800 + 6.24155i −0.0697654 + 0.214716i
\(846\) −5.36518 + 1.14040i −0.184459 + 0.0392079i
\(847\) 0.198090 1.88470i 0.00680646 0.0647591i
\(848\) 5.37104 5.96514i 0.184442 0.204844i
\(849\) −2.64416 + 1.17726i −0.0907474 + 0.0404033i
\(850\) −5.24791 2.33652i −0.180002 0.0801420i
\(851\) −18.3707 20.4027i −0.629739 0.699396i
\(852\) −8.59869 + 6.24731i −0.294586 + 0.214029i
\(853\) −17.6095 + 12.7941i −0.602938 + 0.438060i −0.846920 0.531720i \(-0.821546\pi\)
0.243983 + 0.969780i \(0.421546\pi\)
\(854\) 12.3531 + 13.7195i 0.422714 + 0.469472i
\(855\) −2.59635 1.15597i −0.0887933 0.0395333i
\(856\) 13.8811 6.18024i 0.474445 0.211236i
\(857\) 33.6890 37.4154i 1.15079 1.27809i 0.196071 0.980590i \(-0.437182\pi\)
0.954723 0.297497i \(-0.0961518\pi\)
\(858\) −0.906987 + 8.62940i −0.0309640 + 0.294603i
\(859\) 34.6826 7.37201i 1.18336 0.251530i 0.426117 0.904668i \(-0.359881\pi\)
0.757239 + 0.653138i \(0.226548\pi\)
\(860\) −1.11865 + 3.44285i −0.0381457 + 0.117400i
\(861\) −4.22676 0.898425i −0.144048 0.0306183i
\(862\) −4.46154 + 7.72761i −0.151961 + 0.263203i
\(863\) −11.2487 19.4834i −0.382911 0.663222i 0.608566 0.793503i \(-0.291745\pi\)
−0.991477 + 0.130282i \(0.958412\pi\)
\(864\) 0.309017 + 0.951057i 0.0105130 + 0.0323556i
\(865\) −0.354812 3.37581i −0.0120640 0.114781i
\(866\) −12.5445 9.11412i −0.426280 0.309710i
\(867\) 15.9999 0.543386
\(868\) 13.5998 + 6.70476i 0.461606 + 0.227575i
\(869\) 32.5368 1.10374
\(870\) −4.42446 3.21456i −0.150003 0.108984i
\(871\) −3.51991 33.4897i −0.119268 1.13476i
\(872\) 0.0683980 + 0.210507i 0.00231625 + 0.00712868i
\(873\) −4.21979 7.30889i −0.142818 0.247368i
\(874\) 9.16810 15.8796i 0.310116 0.537136i
\(875\) 2.66379 + 0.566206i 0.0900526 + 0.0191413i
\(876\) 1.83170 5.63741i 0.0618875 0.190470i
\(877\) 11.7149 2.49008i 0.395585 0.0840842i −0.00582415 0.999983i \(-0.501854\pi\)
0.401409 + 0.915899i \(0.368521\pi\)
\(878\) −3.31754 + 31.5643i −0.111962 + 1.06524i
\(879\) −11.4317 + 12.6962i −0.385582 + 0.428232i
\(880\) −3.12426 + 1.39101i −0.105319 + 0.0468909i
\(881\) −3.05357 1.35954i −0.102877 0.0458040i 0.354653 0.934998i \(-0.384599\pi\)
−0.457530 + 0.889194i \(0.651266\pi\)
\(882\) 0.278608 + 0.309426i 0.00938123 + 0.0104189i
\(883\) 11.1536 8.10357i 0.375349 0.272707i −0.384077 0.923301i \(-0.625480\pi\)
0.759425 + 0.650594i \(0.225480\pi\)
\(884\) −11.7914 + 8.56693i −0.396586 + 0.288137i
\(885\) 5.08174 + 5.64384i 0.170821 + 0.189716i
\(886\) 35.2532 + 15.6958i 1.18436 + 0.527309i
\(887\) −24.4687 + 10.8942i −0.821578 + 0.365790i −0.774085 0.633082i \(-0.781790\pi\)
−0.0474927 + 0.998872i \(0.515123\pi\)
\(888\) −2.84740 + 3.16236i −0.0955526 + 0.106122i
\(889\) 1.43761 13.6779i 0.0482158 0.458743i
\(890\) −14.6875 + 3.12192i −0.492325 + 0.104647i
\(891\) −1.05681 + 3.25254i −0.0354046 + 0.108964i
\(892\) 20.9511 + 4.45330i 0.701495 + 0.149107i
\(893\) 7.79441 13.5003i 0.260830 0.451771i
\(894\) 2.76362 + 4.78673i 0.0924292 + 0.160092i
\(895\) 1.29271 + 3.97854i 0.0432104 + 0.132988i
\(896\) 0.284663 + 2.70838i 0.00950991 + 0.0904807i
\(897\) 13.2429 + 9.62155i 0.442168 + 0.321254i
\(898\) 39.1682 1.30706
\(899\) −28.2807 + 11.2865i −0.943215 + 0.376427i
\(900\) 1.00000 0.0333333
\(901\) 37.3045 + 27.1033i 1.24279 + 0.902943i
\(902\) −0.567229 5.39682i −0.0188867 0.179694i
\(903\) 3.04643 + 9.37593i 0.101379 + 0.312012i
\(904\) −2.41262 4.17877i −0.0802424 0.138984i
\(905\) 3.39954 5.88818i 0.113005 0.195730i
\(906\) 15.3397 + 3.26055i 0.509627 + 0.108325i
\(907\) 13.1330 40.4192i 0.436074 1.34210i −0.455909 0.890027i \(-0.650686\pi\)
0.891982 0.452070i \(-0.149314\pi\)
\(908\) 2.28670 0.486052i 0.0758867 0.0161302i
\(909\) −0.431230 + 4.10288i −0.0143030 + 0.136084i
\(910\) 4.62335 5.13475i 0.153263 0.170215i
\(911\) −22.3867 + 9.96720i −0.741705 + 0.330228i −0.742567 0.669771i \(-0.766392\pi\)
0.000862607 1.00000i \(0.499725\pi\)
\(912\) −2.59635 1.15597i −0.0859737 0.0382780i
\(913\) 38.3755 + 42.6203i 1.27004 + 1.41053i
\(914\) −5.44425 + 3.95548i −0.180080 + 0.130836i
\(915\) 5.48437 3.98463i 0.181308 0.131728i
\(916\) 5.14914 + 5.71870i 0.170132 + 0.188951i
\(917\) −34.2303 15.2403i −1.13038 0.503279i
\(918\) −5.24791 + 2.33652i −0.173207 + 0.0771167i
\(919\) −18.3797 + 20.4127i −0.606291 + 0.673354i −0.965650 0.259845i \(-0.916328\pi\)
0.359360 + 0.933199i \(0.382995\pi\)
\(920\) −0.674390 + 6.41639i −0.0222340 + 0.211542i
\(921\) −19.5420 + 4.15377i −0.643930 + 0.136871i
\(922\) 11.0899 34.1311i 0.365225 1.12405i
\(923\) 26.3772 + 5.60665i 0.868217 + 0.184545i
\(924\) −4.65674 + 8.06571i −0.153196 + 0.265343i
\(925\) 2.12769 + 3.68526i 0.0699579 + 0.121171i
\(926\) 1.27943 + 3.93768i 0.0420447 + 0.129400i
\(927\) −0.486874 4.63230i −0.0159910 0.152145i
\(928\) −4.42446 3.21456i −0.145240 0.105523i
\(929\) 12.1960 0.400139 0.200070 0.979782i \(-0.435883\pi\)
0.200070 + 0.979782i \(0.435883\pi\)
\(930\) 2.97051 4.70915i 0.0974069 0.154419i
\(931\) −1.18336 −0.0387830
\(932\) −13.6930 9.94855i −0.448529 0.325876i
\(933\) −2.00602 19.0860i −0.0656740 0.624846i
\(934\) −8.13247 25.0292i −0.266103 0.818980i
\(935\) −9.82297 17.0139i −0.321245 0.556413i
\(936\) 1.26859 2.19726i 0.0414650 0.0718196i
\(937\) −8.75346 1.86061i −0.285963 0.0607833i 0.0626969 0.998033i \(-0.480030\pi\)
−0.348660 + 0.937249i \(0.613363\pi\)
\(938\) 11.1693 34.3755i 0.364690 1.12240i
\(939\) −33.3594 + 7.09077i −1.08864 + 0.231398i
\(940\) −0.573343 + 5.45500i −0.0187004 + 0.177922i
\(941\) −3.66562 + 4.07108i −0.119496 + 0.132714i −0.799924 0.600101i \(-0.795127\pi\)
0.680428 + 0.732815i \(0.261794\pi\)
\(942\) −13.9883 + 6.22801i −0.455764 + 0.202919i
\(943\) −9.35220 4.16387i −0.304549 0.135594i
\(944\) 5.08174 + 5.64384i 0.165396 + 0.183691i
\(945\) 2.20320 1.60072i 0.0716700 0.0520713i
\(946\) −10.0158 + 7.27692i −0.325642 + 0.236593i
\(947\) −35.5232 39.4525i −1.15435 1.28203i −0.953155 0.302481i \(-0.902185\pi\)
−0.201192 0.979552i \(-0.564482\pi\)
\(948\) −8.69138 3.86965i −0.282283 0.125680i
\(949\) −13.7389 + 6.11697i −0.445985 + 0.198565i
\(950\) −1.90171 + 2.11206i −0.0616996 + 0.0685243i
\(951\) −2.96502 + 28.2103i −0.0961475 + 0.914782i
\(952\) −15.3023 + 3.25260i −0.495950 + 0.105417i
\(953\) 7.74828 23.8467i 0.250991 0.772472i −0.743602 0.668623i \(-0.766884\pi\)
0.994593 0.103849i \(-0.0331159\pi\)
\(954\) −7.85149 1.66888i −0.254201 0.0540321i
\(955\) −5.64518 + 9.77774i −0.182674 + 0.316400i
\(956\) 8.46888 + 14.6685i 0.273903 + 0.474414i
\(957\) −5.77965 17.7879i −0.186829 0.575002i
\(958\) −1.68029 15.9869i −0.0542878 0.516514i
\(959\) 27.8452 + 20.2307i 0.899167 + 0.653283i
\(960\) 1.00000 0.0322749
\(961\) −13.3521 27.9771i −0.430714 0.902489i
\(962\) 10.7966 0.348097
\(963\) −12.2928 8.93123i −0.396129 0.287805i
\(964\) 2.09876 + 19.9684i 0.0675965 + 0.643138i
\(965\) 5.92309 + 18.2294i 0.190671 + 0.586825i
\(966\) 8.78501 + 15.2161i 0.282653 + 0.489569i
\(967\) 20.8269 36.0733i 0.669748 1.16004i −0.308226 0.951313i \(-0.599735\pi\)
0.977974 0.208725i \(-0.0669314\pi\)
\(968\) −0.680671 0.144681i −0.0218776 0.00465022i
\(969\) 5.04512 15.5273i 0.162073 0.498809i
\(970\) −8.25515 + 1.75469i −0.265057 + 0.0563396i
\(971\) 1.93673 18.4268i 0.0621527 0.591343i −0.918477 0.395474i \(-0.870580\pi\)
0.980630 0.195869i \(-0.0627529\pi\)
\(972\) 0.669131 0.743145i 0.0214624 0.0238364i
\(973\) −22.2103 + 9.88867i −0.712030 + 0.317016i
\(974\) −27.1001 12.0657i −0.868342 0.386611i
\(975\) −1.69770 1.88549i −0.0543699 0.0603839i
\(976\) 5.48437 3.98463i 0.175550 0.127545i
\(977\) −28.9474 + 21.0315i −0.926109 + 0.672858i −0.945037 0.326963i \(-0.893975\pi\)
0.0189277 + 0.999821i \(0.493975\pi\)
\(978\) 8.84706 + 9.82565i 0.282898 + 0.314190i
\(979\) −46.9126 20.8868i −1.49933 0.667546i
\(980\) 0.380376 0.169354i 0.0121507 0.00540983i
\(981\) 0.148106 0.164488i 0.00472865 0.00525170i
\(982\) 2.92369 27.8171i 0.0932988 0.887679i
\(983\) 41.1667 8.75024i 1.31301 0.279089i 0.502381 0.864646i \(-0.332457\pi\)
0.810631 + 0.585557i \(0.199124\pi\)
\(984\) −0.490331 + 1.50908i −0.0156312 + 0.0481079i
\(985\) 4.17889 + 0.888251i 0.133151 + 0.0283020i
\(986\) 15.7083 27.2076i 0.500254 0.866465i
\(987\) 7.46872 + 12.9362i 0.237732 + 0.411764i
\(988\) 2.22826 + 6.85787i 0.0708903 + 0.218178i
\(989\) 2.44131 + 23.2275i 0.0776292 + 0.738592i
\(990\) 2.76678 + 2.01018i 0.0879339 + 0.0638877i
\(991\) −11.1764 −0.355031 −0.177515 0.984118i \(-0.556806\pi\)
−0.177515 + 0.984118i \(0.556806\pi\)
\(992\) 2.97051 4.70915i 0.0943138 0.149516i
\(993\) 9.67802 0.307123
\(994\) 23.4168 + 17.0133i 0.742737 + 0.539630i
\(995\) −1.76404 16.7837i −0.0559238 0.532079i
\(996\) −5.18214 15.9490i −0.164202 0.505363i
\(997\) −14.7047 25.4693i −0.465702 0.806620i 0.533530 0.845781i \(-0.320865\pi\)
−0.999233 + 0.0391605i \(0.987532\pi\)
\(998\) −2.28016 + 3.94935i −0.0721772 + 0.125015i
\(999\) 4.16239 + 0.884742i 0.131692 + 0.0279920i
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.g.661.3 yes 24
31.28 even 15 inner 930.2.bg.g.121.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.g.121.3 24 31.28 even 15 inner
930.2.bg.g.661.3 yes 24 1.1 even 1 trivial