Properties

Label 731.2.u.a.52.3
Level $731$
Weight $2$
Character 731.52
Analytic conductor $5.837$
Analytic rank $0$
Dimension $348$
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] = [731,2,Mod(52,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.52");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.u (of order \(21\), degree \(12\), 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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(348\)
Relative dimension: \(29\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 52.3
Character \(\chi\) \(=\) 731.52
Dual form 731.2.u.a.239.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.49691 - 1.87707i) q^{2} +(-2.23244 - 0.336487i) q^{3} +(-0.837601 + 3.66977i) q^{4} +(0.525293 + 0.358138i) q^{5} +(2.71016 + 4.69414i) q^{6} +(-0.291720 + 0.505274i) q^{7} +(3.81602 - 1.83770i) q^{8} +(2.00386 + 0.618108i) q^{9} +O(q^{10})\) \(q+(-1.49691 - 1.87707i) q^{2} +(-2.23244 - 0.336487i) q^{3} +(-0.837601 + 3.66977i) q^{4} +(0.525293 + 0.358138i) q^{5} +(2.71016 + 4.69414i) q^{6} +(-0.291720 + 0.505274i) q^{7} +(3.81602 - 1.83770i) q^{8} +(2.00386 + 0.618108i) q^{9} +(-0.114067 - 1.52211i) q^{10} +(-0.934818 - 4.09571i) q^{11} +(3.10472 - 7.91070i) q^{12} +(0.362768 - 4.84080i) q^{13} +(1.38511 - 0.208772i) q^{14} +(-1.05218 - 0.976277i) q^{15} +(-2.37900 - 1.14566i) q^{16} +(0.826239 - 0.563320i) q^{17} +(-1.83937 - 4.68663i) q^{18} +(5.49314 - 1.69441i) q^{19} +(-1.75427 + 1.62773i) q^{20} +(0.821266 - 1.02983i) q^{21} +(-6.28859 + 7.88564i) q^{22} +(-6.72105 + 6.23622i) q^{23} +(-9.13741 + 2.81852i) q^{24} +(-1.67904 - 4.27811i) q^{25} +(-9.62956 + 6.56532i) q^{26} +(1.83673 + 0.884523i) q^{27} +(-1.60989 - 1.49376i) q^{28} +(-6.20812 + 0.935724i) q^{29} +(-0.257524 + 3.43641i) q^{30} +(-0.931018 + 2.37219i) q^{31} +(-0.474300 - 2.07804i) q^{32} +(0.708778 + 9.45798i) q^{33} +(-2.29420 - 0.707667i) q^{34} +(-0.334196 + 0.160940i) q^{35} +(-3.94674 + 6.83596i) q^{36} +(-4.11120 - 7.12081i) q^{37} +(-11.4033 - 7.77463i) q^{38} +(-2.43872 + 10.6847i) q^{39} +(2.66268 + 0.401334i) q^{40} +(0.514100 + 0.644661i) q^{41} -3.16244 q^{42} +(5.80487 - 3.05017i) q^{43} +15.8133 q^{44} +(0.831243 + 1.04235i) q^{45} +(21.7667 + 3.28080i) q^{46} +(-2.04445 + 8.95731i) q^{47} +(4.92547 + 3.35813i) q^{48} +(3.32980 + 5.76738i) q^{49} +(-5.51695 + 9.55563i) q^{50} +(-2.03408 + 0.979561i) q^{51} +(17.4608 + 5.38593i) q^{52} +(-0.438143 - 5.84661i) q^{53} +(-1.08912 - 4.77173i) q^{54} +(0.975777 - 2.48624i) q^{55} +(-0.184669 + 2.46423i) q^{56} +(-12.8333 + 1.93430i) q^{57} +(11.0494 + 10.2524i) q^{58} +(-2.26631 - 1.09140i) q^{59} +(4.46402 - 3.04351i) q^{60} +(2.69324 + 6.86227i) q^{61} +(5.84643 - 1.80338i) q^{62} +(-0.896878 + 0.832182i) q^{63} +(-6.48328 + 8.12978i) q^{64} +(1.92424 - 2.41292i) q^{65} +(16.6923 - 15.4882i) q^{66} +(-7.90923 + 2.43967i) q^{67} +(1.37520 + 3.50394i) q^{68} +(17.1028 - 11.6605i) q^{69} +(0.802360 + 0.386396i) q^{70} +(8.60172 + 7.98123i) q^{71} +(8.78266 - 1.32377i) q^{72} +(0.500250 - 6.67537i) q^{73} +(-7.21215 + 18.3763i) q^{74} +(2.30882 + 10.1156i) q^{75} +(1.61703 + 21.5778i) q^{76} +(2.34216 + 0.722460i) q^{77} +(23.7066 - 11.4165i) q^{78} +(-2.74163 + 4.74864i) q^{79} +(-0.839363 - 1.45382i) q^{80} +(-9.00069 - 6.13656i) q^{81} +(0.440511 - 1.93000i) q^{82} +(-14.2941 - 2.15449i) q^{83} +(3.09136 + 3.87644i) q^{84} +0.635764 q^{85} +(-14.4148 - 6.33030i) q^{86} +14.1741 q^{87} +(-11.0940 - 13.9114i) q^{88} +(-10.9660 - 1.65286i) q^{89} +(0.712257 - 3.12060i) q^{90} +(2.34010 + 1.59546i) q^{91} +(-17.2559 - 29.8882i) q^{92} +(2.87666 - 4.98251i) q^{93} +(19.8739 - 9.57075i) q^{94} +(3.49234 + 1.07724i) q^{95} +(0.359613 + 4.79870i) q^{96} +(-0.854575 - 3.74414i) q^{97} +(5.84136 - 14.8835i) q^{98} +(0.658347 - 8.78502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 348 q - 2 q^{2} + 5 q^{3} - 54 q^{4} + 3 q^{5} + 8 q^{6} - 71 q^{7} - 26 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 348 q - 2 q^{2} + 5 q^{3} - 54 q^{4} + 3 q^{5} + 8 q^{6} - 71 q^{7} - 26 q^{8} + 16 q^{9} - 4 q^{10} + 8 q^{12} - 9 q^{13} - 19 q^{14} - 2 q^{15} - 30 q^{16} + 29 q^{17} + 180 q^{18} + 4 q^{19} - 21 q^{20} + 26 q^{21} - 53 q^{22} + 51 q^{23} + 28 q^{24} + 10 q^{25} - 6 q^{26} - 28 q^{27} + 25 q^{28} - 94 q^{29} - 30 q^{30} - 52 q^{31} - 23 q^{32} - 5 q^{33} + q^{34} + 12 q^{35} - 129 q^{36} - 82 q^{37} - 29 q^{38} - 123 q^{39} + 97 q^{40} - 27 q^{41} + 56 q^{42} - 21 q^{43} - 122 q^{44} - 184 q^{45} + 26 q^{46} + 114 q^{47} + 34 q^{48} - 195 q^{49} - 39 q^{50} - 10 q^{51} - 49 q^{52} + 10 q^{53} + 10 q^{54} - 22 q^{55} + 158 q^{56} - 72 q^{57} - 18 q^{58} + q^{59} - 92 q^{60} + 98 q^{61} - 45 q^{62} - 97 q^{63} - 112 q^{64} - 105 q^{65} + 546 q^{66} - 11 q^{67} + 20 q^{68} - 5 q^{69} - 80 q^{70} + 69 q^{71} - 143 q^{72} + 42 q^{73} + 77 q^{74} + 35 q^{75} - 208 q^{76} + 95 q^{77} - 124 q^{78} + 10 q^{79} + 62 q^{80} - 85 q^{81} - 212 q^{82} + 47 q^{83} + 50 q^{84} + 50 q^{85} + 132 q^{86} - 78 q^{87} - 64 q^{88} + 33 q^{89} + 461 q^{90} + 2 q^{91} - 4 q^{92} - 140 q^{93} + 16 q^{94} + 108 q^{95} - 178 q^{96} + 41 q^{97} - 12 q^{98} + 162 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.49691 1.87707i −1.05848 1.32729i −0.942562 0.334030i \(-0.891591\pi\)
−0.115915 0.993259i \(-0.536980\pi\)
\(3\) −2.23244 0.336487i −1.28890 0.194271i −0.531409 0.847115i \(-0.678337\pi\)
−0.757492 + 0.652845i \(0.773575\pi\)
\(4\) −0.837601 + 3.66977i −0.418800 + 1.83488i
\(5\) 0.525293 + 0.358138i 0.234918 + 0.160164i 0.675058 0.737765i \(-0.264119\pi\)
−0.440140 + 0.897929i \(0.645071\pi\)
\(6\) 2.71016 + 4.69414i 1.10642 + 1.91638i
\(7\) −0.291720 + 0.505274i −0.110260 + 0.190976i −0.915875 0.401464i \(-0.868502\pi\)
0.805615 + 0.592439i \(0.201835\pi\)
\(8\) 3.81602 1.83770i 1.34917 0.649725i
\(9\) 2.00386 + 0.618108i 0.667952 + 0.206036i
\(10\) −0.114067 1.52211i −0.0360710 0.481335i
\(11\) −0.934818 4.09571i −0.281858 1.23490i −0.895408 0.445246i \(-0.853116\pi\)
0.613550 0.789656i \(-0.289741\pi\)
\(12\) 3.10472 7.91070i 0.896256 2.28362i
\(13\) 0.362768 4.84080i 0.100614 1.34260i −0.687103 0.726560i \(-0.741118\pi\)
0.787717 0.616037i \(-0.211263\pi\)
\(14\) 1.38511 0.208772i 0.370187 0.0557967i
\(15\) −1.05218 0.976277i −0.271671 0.252074i
\(16\) −2.37900 1.14566i −0.594749 0.286416i
\(17\) 0.826239 0.563320i 0.200392 0.136625i
\(18\) −1.83937 4.68663i −0.433543 1.10465i
\(19\) 5.49314 1.69441i 1.26021 0.388724i 0.408512 0.912753i \(-0.366048\pi\)
0.851701 + 0.524029i \(0.175572\pi\)
\(20\) −1.75427 + 1.62773i −0.392267 + 0.363970i
\(21\) 0.821266 1.02983i 0.179215 0.224728i
\(22\) −6.28859 + 7.88564i −1.34073 + 1.68122i
\(23\) −6.72105 + 6.23622i −1.40144 + 1.30034i −0.500938 + 0.865483i \(0.667011\pi\)
−0.900498 + 0.434859i \(0.856798\pi\)
\(24\) −9.13741 + 2.81852i −1.86517 + 0.575328i
\(25\) −1.67904 4.27811i −0.335807 0.855623i
\(26\) −9.62956 + 6.56532i −1.88851 + 1.28757i
\(27\) 1.83673 + 0.884523i 0.353479 + 0.170227i
\(28\) −1.60989 1.49376i −0.304241 0.282295i
\(29\) −6.20812 + 0.935724i −1.15282 + 0.173760i −0.697511 0.716574i \(-0.745709\pi\)
−0.455309 + 0.890334i \(0.650471\pi\)
\(30\) −0.257524 + 3.43641i −0.0470171 + 0.627400i
\(31\) −0.931018 + 2.37219i −0.167216 + 0.426059i −0.989778 0.142616i \(-0.954449\pi\)
0.822562 + 0.568675i \(0.192544\pi\)
\(32\) −0.474300 2.07804i −0.0838451 0.367349i
\(33\) 0.708778 + 9.45798i 0.123382 + 1.64642i
\(34\) −2.29420 0.707667i −0.393452 0.121364i
\(35\) −0.334196 + 0.160940i −0.0564895 + 0.0272039i
\(36\) −3.94674 + 6.83596i −0.657791 + 1.13933i
\(37\) −4.11120 7.12081i −0.675878 1.17065i −0.976212 0.216820i \(-0.930431\pi\)
0.300334 0.953834i \(-0.402902\pi\)
\(38\) −11.4033 7.77463i −1.84986 1.26121i
\(39\) −2.43872 + 10.6847i −0.390508 + 1.71093i
\(40\) 2.66268 + 0.401334i 0.421007 + 0.0634566i
\(41\) 0.514100 + 0.644661i 0.0802889 + 0.100679i 0.820354 0.571857i \(-0.193777\pi\)
−0.740065 + 0.672536i \(0.765205\pi\)
\(42\) −3.16244 −0.487974
\(43\) 5.80487 3.05017i 0.885234 0.465147i
\(44\) 15.8133 2.38394
\(45\) 0.831243 + 1.04235i 0.123914 + 0.155384i
\(46\) 21.7667 + 3.28080i 3.20932 + 0.483727i
\(47\) −2.04445 + 8.95731i −0.298213 + 1.30656i 0.574572 + 0.818454i \(0.305169\pi\)
−0.872785 + 0.488104i \(0.837689\pi\)
\(48\) 4.92547 + 3.35813i 0.710931 + 0.484704i
\(49\) 3.32980 + 5.76738i 0.475686 + 0.823912i
\(50\) −5.51695 + 9.55563i −0.780214 + 1.35137i
\(51\) −2.03408 + 0.979561i −0.284828 + 0.137166i
\(52\) 17.4608 + 5.38593i 2.42137 + 0.746895i
\(53\) −0.438143 5.84661i −0.0601836 0.803094i −0.942876 0.333143i \(-0.891891\pi\)
0.882693 0.469951i \(-0.155728\pi\)
\(54\) −1.08912 4.77173i −0.148210 0.649350i
\(55\) 0.975777 2.48624i 0.131574 0.335244i
\(56\) −0.184669 + 2.46423i −0.0246774 + 0.329297i
\(57\) −12.8333 + 1.93430i −1.69981 + 0.256205i
\(58\) 11.0494 + 10.2524i 1.45086 + 1.34620i
\(59\) −2.26631 1.09140i −0.295049 0.142088i 0.280503 0.959853i \(-0.409499\pi\)
−0.575552 + 0.817765i \(0.695213\pi\)
\(60\) 4.46402 3.04351i 0.576302 0.392916i
\(61\) 2.69324 + 6.86227i 0.344834 + 0.878623i 0.993107 + 0.117215i \(0.0373966\pi\)
−0.648272 + 0.761409i \(0.724508\pi\)
\(62\) 5.84643 1.80338i 0.742497 0.229030i
\(63\) −0.896878 + 0.832182i −0.112996 + 0.104845i
\(64\) −6.48328 + 8.12978i −0.810410 + 1.01622i
\(65\) 1.92424 2.41292i 0.238672 0.299285i
\(66\) 16.6923 15.4882i 2.05468 1.90647i
\(67\) −7.90923 + 2.43967i −0.966266 + 0.298054i −0.737439 0.675413i \(-0.763965\pi\)
−0.228827 + 0.973467i \(0.573489\pi\)
\(68\) 1.37520 + 3.50394i 0.166767 + 0.424915i
\(69\) 17.1028 11.6605i 2.05893 1.40376i
\(70\) 0.802360 + 0.386396i 0.0959003 + 0.0461832i
\(71\) 8.60172 + 7.98123i 1.02084 + 0.947198i 0.998618 0.0525552i \(-0.0167365\pi\)
0.0222186 + 0.999753i \(0.492927\pi\)
\(72\) 8.78266 1.32377i 1.03505 0.156008i
\(73\) 0.500250 6.67537i 0.0585498 0.781292i −0.888228 0.459404i \(-0.848063\pi\)
0.946777 0.321889i \(-0.104318\pi\)
\(74\) −7.21215 + 18.3763i −0.838395 + 2.13620i
\(75\) 2.30882 + 10.1156i 0.266600 + 1.16805i
\(76\) 1.61703 + 21.5778i 0.185486 + 2.47514i
\(77\) 2.34216 + 0.722460i 0.266914 + 0.0823320i
\(78\) 23.7066 11.4165i 2.68424 1.29266i
\(79\) −2.74163 + 4.74864i −0.308457 + 0.534263i −0.978025 0.208488i \(-0.933146\pi\)
0.669568 + 0.742751i \(0.266479\pi\)
\(80\) −0.839363 1.45382i −0.0938437 0.162542i
\(81\) −9.00069 6.13656i −1.00008 0.681840i
\(82\) 0.440511 1.93000i 0.0486462 0.213133i
\(83\) −14.2941 2.15449i −1.56899 0.236487i −0.693762 0.720205i \(-0.744048\pi\)
−0.875224 + 0.483718i \(0.839286\pi\)
\(84\) 3.09136 + 3.87644i 0.337295 + 0.422955i
\(85\) 0.635764 0.0689583
\(86\) −14.4148 6.33030i −1.55438 0.682614i
\(87\) 14.1741 1.51963
\(88\) −11.0940 13.9114i −1.18262 1.48296i
\(89\) −10.9660 1.65286i −1.16240 0.175203i −0.460619 0.887598i \(-0.652372\pi\)
−0.701779 + 0.712395i \(0.747611\pi\)
\(90\) 0.712257 3.12060i 0.0750785 0.328940i
\(91\) 2.34010 + 1.59546i 0.245309 + 0.167249i
\(92\) −17.2559 29.8882i −1.79906 3.11606i
\(93\) 2.87666 4.98251i 0.298295 0.516663i
\(94\) 19.8739 9.57075i 2.04983 0.987148i
\(95\) 3.49234 + 1.07724i 0.358306 + 0.110523i
\(96\) 0.359613 + 4.79870i 0.0367029 + 0.489766i
\(97\) −0.854575 3.74414i −0.0867689 0.380159i 0.912834 0.408330i \(-0.133889\pi\)
−0.999603 + 0.0281709i \(0.991032\pi\)
\(98\) 5.84136 14.8835i 0.590066 1.50346i
\(99\) 0.658347 8.78502i 0.0661663 0.882928i
\(100\) 17.1060 2.57832i 1.71060 0.257832i
\(101\) 8.33642 + 7.73507i 0.829505 + 0.769668i 0.975589 0.219604i \(-0.0704766\pi\)
−0.146084 + 0.989272i \(0.546667\pi\)
\(102\) 4.88355 + 2.35179i 0.483543 + 0.232862i
\(103\) −10.1265 + 6.90413i −0.997793 + 0.680284i −0.947932 0.318473i \(-0.896830\pi\)
−0.0498608 + 0.998756i \(0.515878\pi\)
\(104\) −7.51161 19.1393i −0.736574 1.87676i
\(105\) 0.800228 0.246838i 0.0780943 0.0240889i
\(106\) −10.3186 + 9.57430i −1.00224 + 0.929939i
\(107\) −6.65733 + 8.34802i −0.643588 + 0.807034i −0.991447 0.130513i \(-0.958338\pi\)
0.347859 + 0.937547i \(0.386909\pi\)
\(108\) −4.78444 + 5.99950i −0.460383 + 0.577302i
\(109\) −8.25647 + 7.66089i −0.790827 + 0.733780i −0.968150 0.250373i \(-0.919447\pi\)
0.177323 + 0.984153i \(0.443256\pi\)
\(110\) −6.12750 + 1.89008i −0.584234 + 0.180212i
\(111\) 6.78197 + 17.2802i 0.643716 + 1.64016i
\(112\) 1.27288 0.867832i 0.120275 0.0820024i
\(113\) −17.4291 8.39340i −1.63959 0.789585i −0.999778 0.0210521i \(-0.993298\pi\)
−0.639811 0.768532i \(-0.720987\pi\)
\(114\) 22.8411 + 21.1935i 2.13927 + 1.98495i
\(115\) −5.76395 + 0.868776i −0.537491 + 0.0810138i
\(116\) 1.76604 23.5661i 0.163972 2.18806i
\(117\) 3.71907 9.47604i 0.343828 0.876060i
\(118\) 1.34384 + 5.88776i 0.123711 + 0.542012i
\(119\) 0.0436005 + 0.581808i 0.00399685 + 0.0533343i
\(120\) −5.80924 1.79191i −0.530308 0.163578i
\(121\) −5.99027 + 2.88476i −0.544570 + 0.262251i
\(122\) 8.84941 15.3276i 0.801188 1.38770i
\(123\) −0.930778 1.61216i −0.0839255 0.145363i
\(124\) −7.92558 5.40357i −0.711739 0.485255i
\(125\) 1.35753 5.94771i 0.121421 0.531979i
\(126\) 2.90461 + 0.437800i 0.258763 + 0.0390023i
\(127\) 5.19010 + 6.50818i 0.460547 + 0.577508i 0.956828 0.290654i \(-0.0938729\pi\)
−0.496281 + 0.868162i \(0.665301\pi\)
\(128\) 20.7021 1.82982
\(129\) −13.9854 + 4.85607i −1.23134 + 0.427553i
\(130\) −7.40963 −0.649868
\(131\) 8.19556 + 10.2769i 0.716049 + 0.897897i 0.998107 0.0615002i \(-0.0195885\pi\)
−0.282058 + 0.959397i \(0.591017\pi\)
\(132\) −35.3023 5.32096i −3.07267 0.463130i
\(133\) −0.746318 + 3.26983i −0.0647140 + 0.283530i
\(134\) 16.4189 + 11.1942i 1.41837 + 0.967031i
\(135\) 0.648040 + 1.12244i 0.0557744 + 0.0966041i
\(136\) 2.11773 3.66802i 0.181594 0.314530i
\(137\) 12.1935 5.87209i 1.04176 0.501687i 0.166858 0.985981i \(-0.446638\pi\)
0.874905 + 0.484294i \(0.160924\pi\)
\(138\) −47.4889 14.6484i −4.04252 1.24695i
\(139\) −0.404203 5.39371i −0.0342840 0.457489i −0.987756 0.156007i \(-0.950138\pi\)
0.953472 0.301482i \(-0.0974813\pi\)
\(140\) −0.310691 1.36123i −0.0262582 0.115045i
\(141\) 7.57813 19.3088i 0.638194 1.62609i
\(142\) 2.10530 28.0933i 0.176673 2.35753i
\(143\) −20.1656 + 3.03948i −1.68633 + 0.254174i
\(144\) −4.05902 3.76622i −0.338252 0.313852i
\(145\) −3.59620 1.73184i −0.298648 0.143821i
\(146\) −13.2790 + 9.05344i −1.09897 + 0.749268i
\(147\) −5.49294 13.9958i −0.453050 1.15435i
\(148\) 29.5753 9.12276i 2.43107 0.749887i
\(149\) −7.73302 + 7.17520i −0.633514 + 0.587815i −0.930152 0.367175i \(-0.880325\pi\)
0.296638 + 0.954990i \(0.404135\pi\)
\(150\) 15.5316 19.4760i 1.26815 1.59021i
\(151\) 0.875576 1.09794i 0.0712534 0.0893489i −0.744927 0.667146i \(-0.767516\pi\)
0.816181 + 0.577797i \(0.196087\pi\)
\(152\) 17.8481 16.5606i 1.44767 1.34325i
\(153\) 2.00386 0.618108i 0.162002 0.0499711i
\(154\) −2.14990 5.47786i −0.173244 0.441418i
\(155\) −1.33863 + 0.912663i −0.107521 + 0.0733069i
\(156\) −37.1679 17.8991i −2.97581 1.43307i
\(157\) 12.3771 + 11.4843i 0.987802 + 0.916546i 0.996515 0.0834156i \(-0.0265829\pi\)
−0.00871268 + 0.999962i \(0.502773\pi\)
\(158\) 13.0175 1.96207i 1.03562 0.156094i
\(159\) −0.989178 + 13.1997i −0.0784469 + 1.04680i
\(160\) 0.495081 1.26145i 0.0391396 0.0997260i
\(161\) −1.19034 5.21520i −0.0938116 0.411015i
\(162\) 1.95449 + 26.0808i 0.153559 + 2.04910i
\(163\) −15.1308 4.66722i −1.18513 0.365565i −0.361328 0.932439i \(-0.617677\pi\)
−0.823805 + 0.566873i \(0.808153\pi\)
\(164\) −2.79637 + 1.34666i −0.218359 + 0.105156i
\(165\) −3.01495 + 5.22205i −0.234714 + 0.406536i
\(166\) 17.3530 + 30.0562i 1.34685 + 2.33281i
\(167\) −2.35443 1.60522i −0.182191 0.124216i 0.468790 0.883310i \(-0.344690\pi\)
−0.650981 + 0.759094i \(0.725642\pi\)
\(168\) 1.24144 5.43911i 0.0957793 0.419637i
\(169\) −10.4470 1.57463i −0.803612 0.121125i
\(170\) −0.951683 1.19337i −0.0729908 0.0915276i
\(171\) 12.0548 0.921853
\(172\) 6.33126 + 23.8573i 0.482754 + 1.81910i
\(173\) −11.8776 −0.903038 −0.451519 0.892261i \(-0.649118\pi\)
−0.451519 + 0.892261i \(0.649118\pi\)
\(174\) −21.2175 26.6058i −1.60849 2.01698i
\(175\) 2.65143 + 0.399638i 0.200429 + 0.0302098i
\(176\) −2.46838 + 10.8147i −0.186061 + 0.815186i
\(177\) 4.69217 + 3.19907i 0.352685 + 0.240457i
\(178\) 13.3127 + 23.0582i 0.997827 + 1.72829i
\(179\) 9.86012 17.0782i 0.736980 1.27649i −0.216869 0.976201i \(-0.569585\pi\)
0.953849 0.300286i \(-0.0970821\pi\)
\(180\) −4.52142 + 2.17740i −0.337006 + 0.162294i
\(181\) −3.50206 1.08024i −0.260306 0.0802938i 0.161855 0.986815i \(-0.448252\pi\)
−0.422161 + 0.906521i \(0.638728\pi\)
\(182\) −0.508151 6.78080i −0.0376666 0.502626i
\(183\) −3.70345 16.2259i −0.273767 1.19945i
\(184\) −14.1874 + 36.1489i −1.04591 + 2.66493i
\(185\) 0.390652 5.21289i 0.0287213 0.383259i
\(186\) −13.6586 + 2.05871i −1.00150 + 0.150952i
\(187\) −3.07958 2.85743i −0.225201 0.208956i
\(188\) −31.1588 15.0053i −2.27249 1.09437i
\(189\) −0.982738 + 0.670019i −0.0714836 + 0.0487367i
\(190\) −3.20567 8.16791i −0.232564 0.592562i
\(191\) −16.6044 + 5.12177i −1.20145 + 0.370598i −0.829951 0.557836i \(-0.811632\pi\)
−0.371498 + 0.928434i \(0.621156\pi\)
\(192\) 17.2091 15.9677i 1.24196 1.15237i
\(193\) −8.76411 + 10.9898i −0.630854 + 0.791066i −0.989826 0.142282i \(-0.954556\pi\)
0.358972 + 0.933348i \(0.383127\pi\)
\(194\) −5.74878 + 7.20875i −0.412739 + 0.517558i
\(195\) −5.10766 + 4.73922i −0.365767 + 0.339382i
\(196\) −23.9540 + 7.38883i −1.71100 + 0.527773i
\(197\) −1.20342 3.06626i −0.0857399 0.218462i 0.881573 0.472048i \(-0.156485\pi\)
−0.967313 + 0.253586i \(0.918390\pi\)
\(198\) −17.4756 + 11.9147i −1.24194 + 0.846738i
\(199\) 4.60308 + 2.21673i 0.326304 + 0.157140i 0.589863 0.807504i \(-0.299182\pi\)
−0.263559 + 0.964643i \(0.584896\pi\)
\(200\) −14.2691 13.2398i −1.00898 0.936196i
\(201\) 18.4778 2.78508i 1.30332 0.196445i
\(202\) 2.04036 27.2268i 0.143560 1.91567i
\(203\) 1.33824 3.40977i 0.0939258 0.239319i
\(204\) −1.89102 8.28508i −0.132398 0.580072i
\(205\) 0.0391750 + 0.522754i 0.00273610 + 0.0365108i
\(206\) 28.1180 + 8.67326i 1.95907 + 0.604295i
\(207\) −17.3227 + 8.34216i −1.20401 + 0.579820i
\(208\) −6.40896 + 11.1006i −0.444381 + 0.769691i
\(209\) −12.0749 20.9143i −0.835238 1.44667i
\(210\) −1.66120 1.13259i −0.114634 0.0781561i
\(211\) −4.68877 + 20.5428i −0.322788 + 1.41423i 0.509780 + 0.860305i \(0.329727\pi\)
−0.832568 + 0.553923i \(0.813130\pi\)
\(212\) 21.8227 + 3.28924i 1.49879 + 0.225906i
\(213\) −16.5173 20.7120i −1.13174 1.41916i
\(214\) 25.6353 1.75239
\(215\) 4.14164 + 0.476713i 0.282457 + 0.0325116i
\(216\) 8.63450 0.587503
\(217\) −0.927011 1.16244i −0.0629296 0.0789113i
\(218\) 26.7393 + 4.03029i 1.81101 + 0.272966i
\(219\) −3.36295 + 14.7340i −0.227247 + 0.995634i
\(220\) 8.30661 + 5.66335i 0.560032 + 0.381823i
\(221\) −2.42719 4.20401i −0.163270 0.282792i
\(222\) 22.2841 38.5971i 1.49561 2.59047i
\(223\) −2.77236 + 1.33510i −0.185651 + 0.0894049i −0.524400 0.851472i \(-0.675710\pi\)
0.338749 + 0.940877i \(0.389996\pi\)
\(224\) 1.18834 + 0.366555i 0.0793995 + 0.0244915i
\(225\) −0.720211 9.61055i −0.0480141 0.640703i
\(226\) 10.3348 + 45.2798i 0.687462 + 3.01197i
\(227\) 8.22772 20.9639i 0.546093 1.39142i −0.345430 0.938445i \(-0.612267\pi\)
0.891522 0.452977i \(-0.149638\pi\)
\(228\) 3.65071 48.7153i 0.241774 3.22625i
\(229\) −5.75925 + 0.868068i −0.380582 + 0.0573635i −0.336548 0.941666i \(-0.609259\pi\)
−0.0440346 + 0.999030i \(0.514021\pi\)
\(230\) 10.2589 + 9.51886i 0.676451 + 0.627655i
\(231\) −4.98563 2.40095i −0.328031 0.157971i
\(232\) −21.9708 + 14.9794i −1.44245 + 0.983447i
\(233\) 4.09184 + 10.4258i 0.268065 + 0.683019i 0.999999 + 0.00164304i \(0.000522996\pi\)
−0.731933 + 0.681376i \(0.761382\pi\)
\(234\) −23.3543 + 7.20385i −1.52672 + 0.470931i
\(235\) −4.28189 + 3.97302i −0.279320 + 0.259171i
\(236\) 5.90345 7.40269i 0.384282 0.481874i
\(237\) 7.71837 9.67853i 0.501362 0.628688i
\(238\) 1.02683 0.952758i 0.0665594 0.0617581i
\(239\) −4.64461 + 1.43267i −0.300435 + 0.0926719i −0.441308 0.897356i \(-0.645485\pi\)
0.140873 + 0.990028i \(0.455009\pi\)
\(240\) 1.38464 + 3.52800i 0.0893781 + 0.227732i
\(241\) 13.5440 9.23413i 0.872445 0.594823i −0.0421873 0.999110i \(-0.513433\pi\)
0.914632 + 0.404287i \(0.132480\pi\)
\(242\) 14.3818 + 6.92592i 0.924498 + 0.445215i
\(243\) 13.5454 + 12.5683i 0.868938 + 0.806257i
\(244\) −27.4388 + 4.13573i −1.75659 + 0.264763i
\(245\) −0.316402 + 4.22209i −0.0202142 + 0.269740i
\(246\) −1.63283 + 4.16039i −0.104106 + 0.265257i
\(247\) −6.20956 27.2059i −0.395105 1.73107i
\(248\) 0.806597 + 10.7633i 0.0512189 + 0.683469i
\(249\) 31.1859 + 9.61957i 1.97632 + 0.609615i
\(250\) −13.1964 + 6.35503i −0.834611 + 0.401928i
\(251\) −9.14713 + 15.8433i −0.577362 + 1.00002i 0.418419 + 0.908254i \(0.362584\pi\)
−0.995781 + 0.0917659i \(0.970749\pi\)
\(252\) −2.30269 3.98837i −0.145056 0.251244i
\(253\) 31.8247 + 21.6977i 2.00080 + 1.36412i
\(254\) 4.44718 19.4844i 0.279041 1.22256i
\(255\) −1.41931 0.213926i −0.0888804 0.0133966i
\(256\) −18.0227 22.5998i −1.12642 1.41248i
\(257\) −2.96537 −0.184975 −0.0924875 0.995714i \(-0.529482\pi\)
−0.0924875 + 0.995714i \(0.529482\pi\)
\(258\) 30.0501 + 18.9824i 1.87084 + 1.18179i
\(259\) 4.79728 0.298088
\(260\) 7.24310 + 9.08256i 0.449198 + 0.563277i
\(261\) −13.0186 1.96223i −0.805829 0.121459i
\(262\) 7.02243 30.7673i 0.433847 1.90081i
\(263\) −9.30520 6.34418i −0.573783 0.391199i 0.241379 0.970431i \(-0.422400\pi\)
−0.815163 + 0.579232i \(0.803353\pi\)
\(264\) 20.0856 + 34.7894i 1.23619 + 2.14114i
\(265\) 1.86374 3.22810i 0.114489 0.198301i
\(266\) 7.25488 3.49377i 0.444825 0.214217i
\(267\) 23.9249 + 7.37985i 1.46418 + 0.451639i
\(268\) −2.32826 31.0685i −0.142221 1.89781i
\(269\) −1.03293 4.52556i −0.0629789 0.275928i 0.933627 0.358246i \(-0.116625\pi\)
−0.996606 + 0.0823174i \(0.973768\pi\)
\(270\) 1.13684 2.89661i 0.0691856 0.176282i
\(271\) 1.53685 20.5079i 0.0933573 1.24577i −0.732059 0.681241i \(-0.761440\pi\)
0.825416 0.564525i \(-0.190940\pi\)
\(272\) −2.61100 + 0.393544i −0.158315 + 0.0238621i
\(273\) −4.68730 4.34917i −0.283688 0.263224i
\(274\) −29.2750 14.0981i −1.76857 0.851696i
\(275\) −15.9523 + 10.8761i −0.961960 + 0.655853i
\(276\) 28.4659 + 72.5300i 1.71345 + 4.36579i
\(277\) 5.10712 1.57534i 0.306857 0.0946529i −0.137502 0.990501i \(-0.543907\pi\)
0.444359 + 0.895849i \(0.353431\pi\)
\(278\) −9.51932 + 8.83264i −0.570931 + 0.529747i
\(279\) −3.33190 + 4.17807i −0.199476 + 0.250134i
\(280\) −0.979541 + 1.22831i −0.0585387 + 0.0734053i
\(281\) 22.7627 21.1207i 1.35791 1.25995i 0.422507 0.906360i \(-0.361150\pi\)
0.935399 0.353593i \(-0.115040\pi\)
\(282\) −47.5877 + 14.6789i −2.83381 + 0.874113i
\(283\) 1.91151 + 4.87045i 0.113627 + 0.289518i 0.976363 0.216137i \(-0.0693459\pi\)
−0.862735 + 0.505655i \(0.831251\pi\)
\(284\) −36.4941 + 24.8812i −2.16553 + 1.47643i
\(285\) −7.43397 3.58001i −0.440350 0.212062i
\(286\) 35.8915 + 33.3025i 2.12231 + 1.96922i
\(287\) −0.475703 + 0.0717007i −0.0280799 + 0.00423236i
\(288\) 0.334026 4.45727i 0.0196827 0.262647i
\(289\) 0.365341 0.930874i 0.0214906 0.0547573i
\(290\) 2.13242 + 9.34273i 0.125220 + 0.548624i
\(291\) 0.647937 + 8.64612i 0.0379828 + 0.506845i
\(292\) 24.0780 + 7.42709i 1.40906 + 0.434638i
\(293\) −3.75128 + 1.80652i −0.219152 + 0.105538i −0.540239 0.841512i \(-0.681666\pi\)
0.321087 + 0.947050i \(0.395952\pi\)
\(294\) −18.0486 + 31.2611i −1.05262 + 1.82318i
\(295\) −0.799606 1.38496i −0.0465549 0.0806354i
\(296\) −28.7744 19.6180i −1.67248 1.14027i
\(297\) 1.90574 8.34958i 0.110582 0.484492i
\(298\) 25.0440 + 3.77478i 1.45076 + 0.218667i
\(299\) 27.7501 + 34.7976i 1.60483 + 2.01240i
\(300\) −39.0558 −2.25489
\(301\) −0.152224 + 3.82284i −0.00877403 + 0.220345i
\(302\) −3.37157 −0.194012
\(303\) −16.0078 20.0732i −0.919626 1.15317i
\(304\) −15.0094 2.26230i −0.860848 0.129752i
\(305\) −1.04290 + 4.56925i −0.0597164 + 0.261635i
\(306\) −4.15983 2.83612i −0.237802 0.162130i
\(307\) −12.9487 22.4278i −0.739020 1.28002i −0.952937 0.303168i \(-0.901956\pi\)
0.213917 0.976852i \(-0.431378\pi\)
\(308\) −4.61305 + 7.99004i −0.262853 + 0.455275i
\(309\) 24.9300 12.0056i 1.41822 0.682977i
\(310\) 3.71695 + 1.14653i 0.211108 + 0.0651183i
\(311\) −1.49653 19.9698i −0.0848604 1.13238i −0.863309 0.504675i \(-0.831612\pi\)
0.778449 0.627708i \(-0.216007\pi\)
\(312\) 10.3291 + 45.2549i 0.584772 + 2.56205i
\(313\) −6.56781 + 16.7345i −0.371235 + 0.945890i 0.616161 + 0.787620i \(0.288687\pi\)
−0.987396 + 0.158270i \(0.949408\pi\)
\(314\) 3.02934 40.4237i 0.170956 2.28124i
\(315\) −0.769160 + 0.115932i −0.0433373 + 0.00653204i
\(316\) −15.1300 14.0386i −0.851129 0.789733i
\(317\) −1.15849 0.557898i −0.0650671 0.0313346i 0.401067 0.916049i \(-0.368639\pi\)
−0.466134 + 0.884714i \(0.654354\pi\)
\(318\) 26.2574 17.9020i 1.47244 1.00389i
\(319\) 9.63592 + 24.5519i 0.539508 + 1.37464i
\(320\) −6.31721 + 1.94860i −0.353143 + 0.108930i
\(321\) 17.6711 16.3964i 0.986304 0.915157i
\(322\) −8.00747 + 10.0410i −0.446239 + 0.559566i
\(323\) 3.58415 4.49438i 0.199427 0.250074i
\(324\) 30.0588 27.8904i 1.66993 1.54947i
\(325\) −21.3186 + 6.57592i −1.18254 + 0.364766i
\(326\) 13.8887 + 35.3879i 0.769226 + 1.95996i
\(327\) 21.0099 14.3243i 1.16185 0.792135i
\(328\) 3.14651 + 1.51528i 0.173737 + 0.0836673i
\(329\) −3.92949 3.64603i −0.216640 0.201012i
\(330\) 14.3153 2.15768i 0.788030 0.118776i
\(331\) 2.04486 27.2867i 0.112396 1.49981i −0.601111 0.799165i \(-0.705275\pi\)
0.713507 0.700648i \(-0.247106\pi\)
\(332\) 19.8793 50.6516i 1.09102 2.77987i
\(333\) −3.83683 16.8102i −0.210257 0.921196i
\(334\) 0.511261 + 6.82231i 0.0279750 + 0.373300i
\(335\) −5.02840 1.55106i −0.274731 0.0847433i
\(336\) −3.13363 + 1.50908i −0.170954 + 0.0823270i
\(337\) 4.95049 8.57450i 0.269670 0.467083i −0.699106 0.715018i \(-0.746419\pi\)
0.968777 + 0.247935i \(0.0797519\pi\)
\(338\) 12.6825 + 21.9668i 0.689838 + 1.19483i
\(339\) 36.0851 + 24.6024i 1.95988 + 1.33622i
\(340\) −0.532516 + 2.33311i −0.0288797 + 0.126530i
\(341\) 10.5861 + 1.59560i 0.573272 + 0.0864068i
\(342\) −18.0450 22.6277i −0.975761 1.22357i
\(343\) −7.96955 −0.430315
\(344\) 16.5462 22.3071i 0.892111 1.20272i
\(345\) 13.1600 0.708512
\(346\) 17.7798 + 22.2951i 0.955846 + 1.19859i
\(347\) 27.2592 + 4.10866i 1.46335 + 0.220564i 0.831931 0.554879i \(-0.187235\pi\)
0.631418 + 0.775443i \(0.282473\pi\)
\(348\) −11.8723 + 52.0158i −0.636420 + 2.78834i
\(349\) −9.72755 6.63213i −0.520704 0.355010i 0.274271 0.961652i \(-0.411563\pi\)
−0.794975 + 0.606643i \(0.792516\pi\)
\(350\) −3.21881 5.57514i −0.172052 0.298004i
\(351\) 4.94811 8.57038i 0.264111 0.457453i
\(352\) −8.06767 + 3.88518i −0.430008 + 0.207081i
\(353\) −28.3682 8.75044i −1.50989 0.465739i −0.574244 0.818684i \(-0.694704\pi\)
−0.935644 + 0.352945i \(0.885180\pi\)
\(354\) −1.01890 13.5963i −0.0541539 0.722634i
\(355\) 1.66004 + 7.27309i 0.0881055 + 0.386016i
\(356\) 15.2508 38.8584i 0.808290 2.05949i
\(357\) 0.0984351 1.31352i 0.00520974 0.0695191i
\(358\) −46.8168 + 7.05649i −2.47434 + 0.372947i
\(359\) −3.39707 3.15202i −0.179290 0.166357i 0.585422 0.810728i \(-0.300929\pi\)
−0.764713 + 0.644371i \(0.777119\pi\)
\(360\) 5.08756 + 2.45004i 0.268138 + 0.129128i
\(361\) 11.6050 7.91218i 0.610791 0.416430i
\(362\) 3.21459 + 8.19064i 0.168955 + 0.430490i
\(363\) 14.3436 4.42442i 0.752844 0.232222i
\(364\) −7.81502 + 7.25128i −0.409619 + 0.380070i
\(365\) 2.65348 3.32736i 0.138890 0.174162i
\(366\) −24.9133 + 31.2403i −1.30224 + 1.63296i
\(367\) 4.75159 4.40883i 0.248031 0.230139i −0.546353 0.837555i \(-0.683984\pi\)
0.794384 + 0.607416i \(0.207794\pi\)
\(368\) 23.1340 7.13589i 1.20594 0.371984i
\(369\) 0.631712 + 1.60958i 0.0328856 + 0.0837912i
\(370\) −10.3697 + 7.06997i −0.539097 + 0.367550i
\(371\) 3.08196 + 1.48419i 0.160007 + 0.0770554i
\(372\) 15.8752 + 14.7300i 0.823090 + 0.763716i
\(373\) 32.1139 4.84040i 1.66280 0.250626i 0.750712 0.660630i \(-0.229711\pi\)
0.912084 + 0.410003i \(0.134472\pi\)
\(374\) −0.753736 + 10.0579i −0.0389748 + 0.520082i
\(375\) −5.03192 + 12.8211i −0.259847 + 0.662080i
\(376\) 8.65919 + 37.9384i 0.446564 + 1.95652i
\(377\) 2.27755 + 30.3917i 0.117300 + 1.56525i
\(378\) 2.72875 + 0.841707i 0.140352 + 0.0432927i
\(379\) −6.57226 + 3.16503i −0.337594 + 0.162577i −0.594998 0.803727i \(-0.702847\pi\)
0.257404 + 0.966304i \(0.417133\pi\)
\(380\) −6.87842 + 11.9138i −0.352856 + 0.611164i
\(381\) −9.39669 16.2755i −0.481407 0.833821i
\(382\) 34.4692 + 23.5007i 1.76360 + 1.20240i
\(383\) −1.07614 + 4.71486i −0.0549880 + 0.240918i −0.994952 0.100357i \(-0.968002\pi\)
0.939963 + 0.341275i \(0.110859\pi\)
\(384\) −46.2163 6.96598i −2.35846 0.355481i
\(385\) 0.971578 + 1.21832i 0.0495162 + 0.0620913i
\(386\) 33.7478 1.71772
\(387\) 13.5174 2.52407i 0.687131 0.128306i
\(388\) 14.4559 0.733887
\(389\) −9.24280 11.5901i −0.468628 0.587642i 0.490206 0.871607i \(-0.336921\pi\)
−0.958835 + 0.283965i \(0.908350\pi\)
\(390\) 16.5416 + 2.49324i 0.837615 + 0.126250i
\(391\) −2.04020 + 8.93871i −0.103177 + 0.452050i
\(392\) 23.3053 + 15.8893i 1.17710 + 0.802530i
\(393\) −14.8381 25.7003i −0.748481 1.29641i
\(394\) −3.95417 + 6.84882i −0.199208 + 0.345038i
\(395\) −3.14083 + 1.51254i −0.158032 + 0.0761042i
\(396\) 31.6876 + 9.77432i 1.59236 + 0.491178i
\(397\) 1.53909 + 20.5377i 0.0772445 + 1.03076i 0.892321 + 0.451402i \(0.149076\pi\)
−0.815076 + 0.579354i \(0.803305\pi\)
\(398\) −2.72946 11.9586i −0.136816 0.599429i
\(399\) 2.76637 7.04859i 0.138492 0.352871i
\(400\) −0.906862 + 12.1012i −0.0453431 + 0.605062i
\(401\) 16.4142 2.47404i 0.819685 0.123548i 0.274205 0.961671i \(-0.411585\pi\)
0.545480 + 0.838124i \(0.316347\pi\)
\(402\) −32.8875 30.5151i −1.64028 1.52196i
\(403\) 11.1456 + 5.36743i 0.555201 + 0.267371i
\(404\) −35.3685 + 24.1138i −1.75965 + 1.19971i
\(405\) −2.53026 6.44698i −0.125729 0.320353i
\(406\) −8.40360 + 2.59217i −0.417064 + 0.128647i
\(407\) −25.3215 + 23.4949i −1.25514 + 1.16460i
\(408\) −5.96196 + 7.47606i −0.295161 + 0.370120i
\(409\) −2.35099 + 2.94805i −0.116249 + 0.145771i −0.836551 0.547889i \(-0.815432\pi\)
0.720302 + 0.693660i \(0.244003\pi\)
\(410\) 0.922605 0.856053i 0.0455642 0.0422774i
\(411\) −29.1972 + 9.00615i −1.44019 + 0.444240i
\(412\) −16.8546 42.9448i −0.830366 2.11574i
\(413\) 1.21258 0.826726i 0.0596674 0.0406805i
\(414\) 41.5894 + 20.0284i 2.04401 + 0.984342i
\(415\) −6.73700 6.25102i −0.330706 0.306851i
\(416\) −10.2315 + 1.54214i −0.501638 + 0.0756098i
\(417\) −0.912552 + 12.1772i −0.0446879 + 0.596318i
\(418\) −21.1826 + 53.9724i −1.03607 + 2.63987i
\(419\) −7.25196 31.7729i −0.354282 1.55221i −0.767180 0.641432i \(-0.778341\pi\)
0.412899 0.910777i \(-0.364516\pi\)
\(420\) 0.235566 + 3.14340i 0.0114944 + 0.153382i
\(421\) 6.41251 + 1.97800i 0.312527 + 0.0964017i 0.447051 0.894509i \(-0.352474\pi\)
−0.134524 + 0.990910i \(0.542951\pi\)
\(422\) 45.5791 21.9497i 2.21875 1.06850i
\(423\) −9.63337 + 16.6855i −0.468390 + 0.811276i
\(424\) −12.4163 21.5056i −0.602988 1.04441i
\(425\) −3.79723 2.58891i −0.184193 0.125581i
\(426\) −14.1530 + 62.0082i −0.685713 + 3.00430i
\(427\) −4.25300 0.641036i −0.205817 0.0310219i
\(428\) −25.0591 31.4232i −1.21128 1.51890i
\(429\) 46.0413 2.22290
\(430\) −5.30485 8.48774i −0.255822 0.409315i
\(431\) −18.7558 −0.903437 −0.451719 0.892160i \(-0.649189\pi\)
−0.451719 + 0.892160i \(0.649189\pi\)
\(432\) −3.35621 4.20856i −0.161476 0.202484i
\(433\) 16.8712 + 2.54293i 0.810779 + 0.122205i 0.541331 0.840810i \(-0.317921\pi\)
0.269448 + 0.963015i \(0.413159\pi\)
\(434\) −0.794317 + 3.48013i −0.0381284 + 0.167052i
\(435\) 7.44557 + 5.07630i 0.356988 + 0.243390i
\(436\) −21.1981 36.7161i −1.01520 1.75838i
\(437\) −26.3530 + 45.6447i −1.26063 + 2.18348i
\(438\) 32.6909 15.7431i 1.56203 0.752234i
\(439\) −29.4338 9.07913i −1.40480 0.433323i −0.502554 0.864546i \(-0.667606\pi\)
−0.902246 + 0.431222i \(0.858082\pi\)
\(440\) −0.845374 11.2807i −0.0403016 0.537788i
\(441\) 3.10758 + 13.6152i 0.147980 + 0.648342i
\(442\) −4.25794 + 10.8490i −0.202529 + 0.516036i
\(443\) −2.18362 + 29.1383i −0.103747 + 1.38440i 0.665951 + 0.745996i \(0.268026\pi\)
−0.769697 + 0.638409i \(0.779593\pi\)
\(444\) −69.0948 + 10.4144i −3.27909 + 0.494244i
\(445\) −5.16843 4.79560i −0.245007 0.227333i
\(446\) 6.65606 + 3.20539i 0.315174 + 0.151780i
\(447\) 19.6779 13.4162i 0.930732 0.634562i
\(448\) −2.21646 5.64745i −0.104718 0.266817i
\(449\) −8.25276 + 2.54564i −0.389472 + 0.120136i −0.483305 0.875452i \(-0.660564\pi\)
0.0938339 + 0.995588i \(0.470088\pi\)
\(450\) −16.9616 + 15.7380i −0.799577 + 0.741899i
\(451\) 2.15975 2.70824i 0.101699 0.127526i
\(452\) 45.4004 56.9303i 2.13546 2.67778i
\(453\) −2.32411 + 2.15646i −0.109196 + 0.101319i
\(454\) −51.6669 + 15.9371i −2.42485 + 0.747966i
\(455\) 0.657845 + 1.67616i 0.0308403 + 0.0785797i
\(456\) −45.4174 + 30.9650i −2.12686 + 1.45007i
\(457\) −9.78754 4.71343i −0.457842 0.220485i 0.190724 0.981644i \(-0.438916\pi\)
−0.648566 + 0.761159i \(0.724631\pi\)
\(458\) 10.2505 + 9.51110i 0.478976 + 0.444425i
\(459\) 2.01585 0.303840i 0.0940918 0.0141820i
\(460\) 1.63968 21.8801i 0.0764506 1.02016i
\(461\) −1.95610 + 4.98407i −0.0911047 + 0.232131i −0.969162 0.246425i \(-0.920744\pi\)
0.878057 + 0.478556i \(0.158839\pi\)
\(462\) 2.95630 + 12.9524i 0.137540 + 0.602601i
\(463\) 1.11509 + 14.8798i 0.0518226 + 0.691525i 0.961253 + 0.275668i \(0.0888992\pi\)
−0.909430 + 0.415857i \(0.863482\pi\)
\(464\) 15.8411 + 4.88634i 0.735406 + 0.226843i
\(465\) 3.29552 1.58704i 0.152826 0.0735971i
\(466\) 13.4449 23.2872i 0.622823 1.07876i
\(467\) 20.1373 + 34.8788i 0.931842 + 1.61400i 0.780171 + 0.625566i \(0.215132\pi\)
0.151670 + 0.988431i \(0.451535\pi\)
\(468\) 31.6598 + 21.5853i 1.46347 + 0.997779i
\(469\) 1.07458 4.70803i 0.0496193 0.217397i
\(470\) 13.8673 + 2.09015i 0.639649 + 0.0964115i
\(471\) −23.7669 29.8028i −1.09512 1.37324i
\(472\) −10.6540 −0.490389
\(473\) −17.9191 20.9237i −0.823921 0.962071i
\(474\) −29.7210 −1.36513
\(475\) −16.4721 20.6553i −0.755790 0.947730i
\(476\) −2.17162 0.327319i −0.0995361 0.0150027i
\(477\) 2.73586 11.9866i 0.125267 0.548828i
\(478\) 9.64181 + 6.57368i 0.441006 + 0.300673i
\(479\) 5.21812 + 9.03804i 0.238422 + 0.412959i 0.960262 0.279101i \(-0.0900366\pi\)
−0.721840 + 0.692060i \(0.756703\pi\)
\(480\) −1.52970 + 2.64952i −0.0698209 + 0.120933i
\(481\) −35.9619 + 17.3183i −1.63972 + 0.789647i
\(482\) −37.6073 11.6003i −1.71297 0.528380i
\(483\) 0.902511 + 12.0432i 0.0410657 + 0.547983i
\(484\) −5.56895 24.3992i −0.253134 1.10905i
\(485\) 0.892018 2.27282i 0.0405044 0.103204i
\(486\) 3.31528 44.2393i 0.150384 2.00674i
\(487\) 22.3880 3.37444i 1.01450 0.152911i 0.379309 0.925270i \(-0.376162\pi\)
0.635186 + 0.772359i \(0.280924\pi\)
\(488\) 22.8883 + 21.2372i 1.03610 + 0.961363i
\(489\) 32.2081 + 15.5106i 1.45650 + 0.701414i
\(490\) 8.39879 5.72620i 0.379419 0.258683i
\(491\) 11.8539 + 30.2033i 0.534960 + 1.36305i 0.901551 + 0.432673i \(0.142429\pi\)
−0.366591 + 0.930382i \(0.619475\pi\)
\(492\) 6.69586 2.06540i 0.301873 0.0931153i
\(493\) −4.60228 + 4.27029i −0.207276 + 0.192324i
\(494\) −41.7722 + 52.3806i −1.87942 + 2.35672i
\(495\) 3.49208 4.37893i 0.156957 0.196818i
\(496\) 4.93263 4.57681i 0.221482 0.205505i
\(497\) −6.54200 + 2.01794i −0.293449 + 0.0905170i
\(498\) −28.6260 72.9378i −1.28276 3.26842i
\(499\) −13.1485 + 8.96446i −0.588606 + 0.401304i −0.820675 0.571395i \(-0.806403\pi\)
0.232070 + 0.972699i \(0.425450\pi\)
\(500\) 20.6896 + 9.96361i 0.925269 + 0.445586i
\(501\) 4.71599 + 4.37580i 0.210695 + 0.195496i
\(502\) 43.4315 6.54624i 1.93844 0.292173i
\(503\) −0.586669 + 7.82855i −0.0261583 + 0.349058i 0.968733 + 0.248106i \(0.0798080\pi\)
−0.994891 + 0.100952i \(0.967811\pi\)
\(504\) −1.89321 + 4.82382i −0.0843302 + 0.214870i
\(505\) 1.60884 + 7.04877i 0.0715922 + 0.313666i
\(506\) −6.91069 92.2168i −0.307218 4.09954i
\(507\) 22.7924 + 7.03052i 1.01225 + 0.312236i
\(508\) −28.2308 + 13.5952i −1.25254 + 0.603190i
\(509\) 10.0517 17.4101i 0.445535 0.771689i −0.552554 0.833477i \(-0.686347\pi\)
0.998089 + 0.0617877i \(0.0196802\pi\)
\(510\) 1.72302 + 2.98437i 0.0762968 + 0.132150i
\(511\) 3.22695 + 2.20010i 0.142752 + 0.0973267i
\(512\) −6.22960 + 27.2936i −0.275312 + 1.20622i
\(513\) 11.5882 + 1.74664i 0.511630 + 0.0771158i
\(514\) 4.43891 + 5.56622i 0.195792 + 0.245515i
\(515\) −7.79201 −0.343357
\(516\) −6.10650 55.3905i −0.268824 2.43843i
\(517\) 38.5977 1.69753
\(518\) −7.18111 9.00483i −0.315520 0.395650i
\(519\) 26.5161 + 3.99666i 1.16393 + 0.175434i
\(520\) 2.90872 12.7439i 0.127556 0.558858i
\(521\) 8.29140 + 5.65298i 0.363253 + 0.247662i 0.731168 0.682198i \(-0.238976\pi\)
−0.367915 + 0.929860i \(0.619928\pi\)
\(522\) 15.8044 + 27.3741i 0.691741 + 1.19813i
\(523\) 12.0756 20.9155i 0.528029 0.914573i −0.471437 0.881900i \(-0.656265\pi\)
0.999466 0.0326733i \(-0.0104021\pi\)
\(524\) −44.5785 + 21.4679i −1.94742 + 0.937827i
\(525\) −5.78468 1.78434i −0.252464 0.0778749i
\(526\) 2.02061 + 26.9632i 0.0881029 + 1.17565i
\(527\) 0.567062 + 2.48446i 0.0247016 + 0.108225i
\(528\) 9.14950 23.3125i 0.398181 1.01455i
\(529\) 4.56325 60.8923i 0.198402 2.64749i
\(530\) −8.84924 + 1.33381i −0.384386 + 0.0579369i
\(531\) −3.86677 3.58783i −0.167803 0.155699i
\(532\) −11.3744 5.47763i −0.493143 0.237485i
\(533\) 3.30717 2.25479i 0.143250 0.0976659i
\(534\) −21.9610 55.9557i −0.950345 2.42144i
\(535\) −6.48679 + 2.00091i −0.280449 + 0.0865069i
\(536\) −25.6984 + 23.8446i −1.11000 + 1.02993i
\(537\) −27.7587 + 34.8084i −1.19788 + 1.50209i
\(538\) −6.94859 + 8.71326i −0.299575 + 0.375655i
\(539\) 20.5087 19.0293i 0.883374 0.819651i
\(540\) −4.66189 + 1.43800i −0.200616 + 0.0618817i
\(541\) −13.9711 35.5979i −0.600666 1.53047i −0.830371 0.557212i \(-0.811871\pi\)
0.229705 0.973260i \(-0.426224\pi\)
\(542\) −40.7953 + 27.8138i −1.75231 + 1.19470i
\(543\) 7.45466 + 3.58997i 0.319910 + 0.154060i
\(544\) −1.56249 1.44978i −0.0669911 0.0621587i
\(545\) −7.08072 + 1.06725i −0.303305 + 0.0457159i
\(546\) −1.14723 + 15.3087i −0.0490969 + 0.655153i
\(547\) −8.15511 + 20.7789i −0.348687 + 0.888441i 0.643699 + 0.765279i \(0.277399\pi\)
−0.992387 + 0.123162i \(0.960696\pi\)
\(548\) 11.3359 + 49.6659i 0.484246 + 2.12162i
\(549\) 1.15525 + 15.4157i 0.0493048 + 0.657927i
\(550\) 44.2944 + 13.6630i 1.88872 + 0.582593i
\(551\) −32.5166 + 15.6592i −1.38525 + 0.667103i
\(552\) 43.8361 75.9264i 1.86579 3.23164i
\(553\) −1.59957 2.77054i −0.0680208 0.117815i
\(554\) −10.6019 7.22828i −0.450433 0.307100i
\(555\) −2.62618 + 11.5060i −0.111475 + 0.488404i
\(556\) 20.1322 + 3.03445i 0.853797 + 0.128689i
\(557\) 14.7640 + 18.5135i 0.625571 + 0.784441i 0.989116 0.147135i \(-0.0470053\pi\)
−0.363545 + 0.931576i \(0.618434\pi\)
\(558\) 12.8301 0.543141
\(559\) −12.6595 29.2067i −0.535438 1.23531i
\(560\) 0.979436 0.0413887
\(561\) 5.91349 + 7.41528i 0.249668 + 0.313073i
\(562\) −73.7187 11.1113i −3.10964 0.468702i
\(563\) 5.48768 24.0431i 0.231278 1.01330i −0.717303 0.696762i \(-0.754623\pi\)
0.948581 0.316535i \(-0.102519\pi\)
\(564\) 64.5112 + 43.9830i 2.71641 + 1.85202i
\(565\) −6.14937 10.6510i −0.258706 0.448091i
\(566\) 6.28081 10.8787i 0.264002 0.457265i
\(567\) 5.72632 2.75765i 0.240483 0.115811i
\(568\) 47.4915 + 14.6492i 1.99270 + 0.614666i
\(569\) −1.89017 25.2226i −0.0792401 1.05739i −0.885137 0.465330i \(-0.845936\pi\)
0.805897 0.592056i \(-0.201684\pi\)
\(570\) 4.40808 + 19.3130i 0.184634 + 0.808935i
\(571\) 0.0379569 0.0967127i 0.00158845 0.00404730i −0.930077 0.367364i \(-0.880260\pi\)
0.931666 + 0.363317i \(0.118356\pi\)
\(572\) 5.73656 76.5490i 0.239858 3.20068i
\(573\) 38.7917 5.84691i 1.62055 0.244258i
\(574\) 0.846674 + 0.785599i 0.0353395 + 0.0327903i
\(575\) 37.9642 + 18.2826i 1.58321 + 0.762436i
\(576\) −18.0166 + 12.2835i −0.750693 + 0.511814i
\(577\) −9.47613 24.1448i −0.394497 1.00516i −0.980791 0.195063i \(-0.937509\pi\)
0.586294 0.810098i \(-0.300586\pi\)
\(578\) −2.29420 + 0.707667i −0.0954261 + 0.0294351i
\(579\) 23.2633 21.5852i 0.966790 0.897050i
\(580\) 9.36763 11.7466i 0.388970 0.487752i
\(581\) 5.25849 6.59394i 0.218159 0.273563i
\(582\) 15.2595 14.1587i 0.632525 0.586898i
\(583\) −23.5364 + 7.26003i −0.974779 + 0.300680i
\(584\) −10.3584 26.3927i −0.428632 1.09214i
\(585\) 5.34734 3.64575i 0.221085 0.150733i
\(586\) 9.00631 + 4.33721i 0.372047 + 0.179168i
\(587\) −19.7975 18.3694i −0.817132 0.758187i 0.156167 0.987731i \(-0.450086\pi\)
−0.973298 + 0.229543i \(0.926277\pi\)
\(588\) 55.9621 8.43494i 2.30784 0.347851i
\(589\) −1.09474 + 14.6083i −0.0451081 + 0.601926i
\(590\) −1.40272 + 3.57408i −0.0577492 + 0.147143i
\(591\) 1.65480 + 7.25017i 0.0680695 + 0.298232i
\(592\) 1.62248 + 21.6505i 0.0666834 + 0.889828i
\(593\) −20.3583 6.27970i −0.836015 0.257877i −0.152950 0.988234i \(-0.548877\pi\)
−0.683065 + 0.730357i \(0.739354\pi\)
\(594\) −18.5255 + 8.92140i −0.760109 + 0.366049i
\(595\) −0.185465 + 0.321235i −0.00760332 + 0.0131693i
\(596\) −19.8541 34.3884i −0.813257 1.40860i
\(597\) −9.53022 6.49759i −0.390046 0.265929i
\(598\) 23.7779 104.178i 0.972352 4.26015i
\(599\) 0.200873 + 0.0302767i 0.00820743 + 0.00123707i 0.153145 0.988204i \(-0.451060\pi\)
−0.144937 + 0.989441i \(0.546298\pi\)
\(600\) 27.4000 + 34.3585i 1.11860 + 1.40268i
\(601\) −21.3498 −0.870877 −0.435439 0.900218i \(-0.643407\pi\)
−0.435439 + 0.900218i \(0.643407\pi\)
\(602\) 7.40361 5.43673i 0.301749 0.221585i
\(603\) −17.3569 −0.706829
\(604\) 3.29579 + 4.13279i 0.134104 + 0.168161i
\(605\) −4.17979 0.630002i −0.169933 0.0256132i
\(606\) −13.7164 + 60.0956i −0.557192 + 2.44122i
\(607\) 20.3221 + 13.8554i 0.824849 + 0.562372i 0.900547 0.434758i \(-0.143166\pi\)
−0.0756984 + 0.997131i \(0.524119\pi\)
\(608\) −6.12645 10.6113i −0.248460 0.430346i
\(609\) −4.13488 + 7.16182i −0.167554 + 0.290211i
\(610\) 10.1379 4.88218i 0.410473 0.197674i
\(611\) 42.6189 + 13.1462i 1.72418 + 0.531838i
\(612\) 0.589881 + 7.87142i 0.0238445 + 0.318183i
\(613\) 4.36971 + 19.1449i 0.176491 + 0.773257i 0.983233 + 0.182354i \(0.0583715\pi\)
−0.806742 + 0.590904i \(0.798771\pi\)
\(614\) −22.7154 + 57.8780i −0.916721 + 2.33577i
\(615\) 0.0884438 1.18020i 0.00356640 0.0475903i
\(616\) 10.2654 1.54726i 0.413605 0.0623408i
\(617\) 13.9359 + 12.9306i 0.561039 + 0.520568i 0.908920 0.416971i \(-0.136908\pi\)
−0.347881 + 0.937539i \(0.613099\pi\)
\(618\) −59.8534 28.8239i −2.40766 1.15947i
\(619\) −7.79410 + 5.31393i −0.313272 + 0.213585i −0.709740 0.704463i \(-0.751188\pi\)
0.396469 + 0.918048i \(0.370235\pi\)
\(620\) −2.22802 5.67691i −0.0894796 0.227990i
\(621\) −17.8609 + 5.50934i −0.716731 + 0.221082i
\(622\) −35.2446 + 32.7022i −1.41318 + 1.31124i
\(623\) 4.03416 5.05868i 0.161625 0.202672i
\(624\) 18.0428 22.6250i 0.722292 0.905726i
\(625\) −14.0016 + 12.9916i −0.560065 + 0.519664i
\(626\) 41.2433 12.7219i 1.64841 0.508468i
\(627\) 19.9191 + 50.7531i 0.795493 + 2.02688i
\(628\) −52.5118 + 35.8019i −2.09545 + 1.42865i
\(629\) −7.40813 3.56757i −0.295382 0.142248i
\(630\) 1.36898 + 1.27023i 0.0545414 + 0.0506070i
\(631\) −11.1595 + 1.68203i −0.444254 + 0.0669606i −0.367360 0.930079i \(-0.619738\pi\)
−0.0768941 + 0.997039i \(0.524500\pi\)
\(632\) −1.73554 + 23.1592i −0.0690361 + 0.921223i
\(633\) 17.3798 44.2830i 0.690785 1.76009i
\(634\) 0.686941 + 3.00968i 0.0272819 + 0.119530i
\(635\) 0.395492 + 5.27748i 0.0156946 + 0.209430i
\(636\) −47.6112 14.6861i −1.88791 0.582342i
\(637\) 29.1267 14.0267i 1.15404 0.555757i
\(638\) 31.6615 54.8394i 1.25349 2.17111i
\(639\) 12.3034 + 21.3100i 0.486713 + 0.843012i
\(640\) 10.8747 + 7.41422i 0.429859 + 0.293073i
\(641\) −6.97095 + 30.5417i −0.275336 + 1.20632i 0.628282 + 0.777986i \(0.283758\pi\)
−0.903618 + 0.428339i \(0.859099\pi\)
\(642\) −57.2293 8.62592i −2.25866 0.340438i
\(643\) 5.28508 + 6.62728i 0.208423 + 0.261355i 0.875045 0.484042i \(-0.160832\pi\)
−0.666622 + 0.745396i \(0.732260\pi\)
\(644\) 20.1356 0.793454
\(645\) −9.08556 2.45784i −0.357743 0.0967774i
\(646\) −13.8014 −0.543010
\(647\) −13.7286 17.2151i −0.539728 0.676797i 0.434939 0.900460i \(-0.356770\pi\)
−0.974667 + 0.223663i \(0.928199\pi\)
\(648\) −45.6240 6.87671i −1.79228 0.270143i
\(649\) −2.35146 + 10.3024i −0.0923029 + 0.404405i
\(650\) 44.2556 + 30.1729i 1.73585 + 1.18348i
\(651\) 1.67836 + 2.90700i 0.0657799 + 0.113934i
\(652\) 29.8012 51.6171i 1.16710 2.02148i
\(653\) 9.15615 4.40937i 0.358308 0.172552i −0.246066 0.969253i \(-0.579138\pi\)
0.604373 + 0.796701i \(0.293424\pi\)
\(654\) −58.3377 17.9948i −2.28118 0.703652i
\(655\) 0.624511 + 8.33353i 0.0244017 + 0.325618i
\(656\) −0.484477 2.12263i −0.0189156 0.0828749i
\(657\) 5.12852 13.0673i 0.200083 0.509803i
\(658\) −0.961755 + 12.8337i −0.0374931 + 0.500311i
\(659\) 41.6793 6.28215i 1.62360 0.244718i 0.726699 0.686956i \(-0.241053\pi\)
0.896898 + 0.442238i \(0.145815\pi\)
\(660\) −16.6384 15.4382i −0.647648 0.600930i
\(661\) −9.77248 4.70618i −0.380105 0.183049i 0.234068 0.972220i \(-0.424796\pi\)
−0.614173 + 0.789171i \(0.710510\pi\)
\(662\) −54.2801 + 37.0075i −2.10965 + 1.43834i
\(663\) 4.00396 + 10.2019i 0.155501 + 0.396210i
\(664\) −58.5061 + 18.0467i −2.27048 + 0.700349i
\(665\) −1.56309 + 1.45033i −0.0606140 + 0.0562415i
\(666\) −25.8106 + 32.3655i −1.00014 + 1.25414i
\(667\) 35.8897 45.0043i 1.38966 1.74257i
\(668\) 7.86287 7.29567i 0.304223 0.282278i
\(669\) 6.63838 2.04767i 0.256655 0.0791675i
\(670\) 4.61564 + 11.7605i 0.178318 + 0.454346i
\(671\) 25.5881 17.4457i 0.987819 0.673484i
\(672\) −2.52957 1.21817i −0.0975801 0.0469921i
\(673\) −2.14823 1.99327i −0.0828082 0.0768348i 0.637683 0.770299i \(-0.279893\pi\)
−0.720491 + 0.693464i \(0.756084\pi\)
\(674\) −23.5054 + 3.54287i −0.905394 + 0.136466i
\(675\) 0.700153 9.34289i 0.0269489 0.359608i
\(676\) 14.5289 37.0190i 0.558804 1.42381i
\(677\) 3.50238 + 15.3449i 0.134607 + 0.589753i 0.996568 + 0.0827780i \(0.0263792\pi\)
−0.861961 + 0.506975i \(0.830764\pi\)
\(678\) −7.83584 104.562i −0.300934 4.01568i
\(679\) 2.14111 + 0.660445i 0.0821683 + 0.0253456i
\(680\) 2.42609 1.16834i 0.0930363 0.0448039i
\(681\) −25.4220 + 44.0321i −0.974172 + 1.68731i
\(682\) −12.8515 22.2594i −0.492109 0.852357i
\(683\) −0.793210 0.540802i −0.0303514 0.0206932i 0.548049 0.836446i \(-0.315371\pi\)
−0.578401 + 0.815753i \(0.696323\pi\)
\(684\) −10.0971 + 44.2383i −0.386072 + 1.69149i
\(685\) 8.50819 + 1.28240i 0.325081 + 0.0489981i
\(686\) 11.9297 + 14.9594i 0.455479 + 0.571153i
\(687\) 13.1493 0.501677
\(688\) −17.3042 + 0.605918i −0.659718 + 0.0231004i
\(689\) −28.4612 −1.08429
\(690\) −19.6994 24.7023i −0.749944 0.940400i
\(691\) −1.71829 0.258991i −0.0653669 0.00985247i 0.116277 0.993217i \(-0.462904\pi\)
−0.181644 + 0.983364i \(0.558142\pi\)
\(692\) 9.94870 43.5881i 0.378193 1.65697i
\(693\) 4.24679 + 2.89541i 0.161322 + 0.109988i
\(694\) −33.0924 57.3177i −1.25617 2.17575i
\(695\) 1.71937 2.97804i 0.0652195 0.112963i
\(696\) 54.0888 26.0478i 2.05023 0.987339i
\(697\) 0.787919 + 0.243041i 0.0298446 + 0.00920583i
\(698\) 2.11232 + 28.1870i 0.0799527 + 1.06689i
\(699\) −5.62664 24.6519i −0.212819 0.932421i
\(700\) −3.68742 + 9.39538i −0.139371 + 0.355112i
\(701\) −1.63881 + 21.8683i −0.0618968 + 0.825956i 0.876721 + 0.480998i \(0.159726\pi\)
−0.938618 + 0.344958i \(0.887893\pi\)
\(702\) −23.4941 + 3.54116i −0.886727 + 0.133653i
\(703\) −34.6490 32.1496i −1.30681 1.21254i
\(704\) 39.3579 + 18.9537i 1.48336 + 0.714346i
\(705\) 10.8959 7.42873i 0.410365 0.279782i
\(706\) 26.0396 + 66.3478i 0.980013 + 2.49703i
\(707\) −6.34023 + 1.95570i −0.238449 + 0.0735517i
\(708\) −15.6700 + 14.5396i −0.588915 + 0.546433i
\(709\) 18.9919 23.8151i 0.713256 0.894395i −0.284679 0.958623i \(-0.591887\pi\)
0.997935 + 0.0642280i \(0.0204585\pi\)
\(710\) 11.1672 14.0032i 0.419097 0.525530i
\(711\) −8.42899 + 7.82096i −0.316112 + 0.293309i
\(712\) −44.8841 + 13.8449i −1.68210 + 0.518860i
\(713\) −8.53612 21.7497i −0.319680 0.814532i
\(714\) −2.61293 + 1.78146i −0.0977863 + 0.0666696i
\(715\) −11.6814 5.62547i −0.436860 0.210381i
\(716\) 54.4143 + 50.4891i 2.03356 + 1.88687i
\(717\) 10.8509 1.63551i 0.405234 0.0610793i
\(718\) −0.831443 + 11.0948i −0.0310292 + 0.414056i
\(719\) −18.1784 + 46.3177i −0.677938 + 1.72736i 0.00828308 + 0.999966i \(0.497363\pi\)
−0.686221 + 0.727393i \(0.740732\pi\)
\(720\) −0.783346 3.43206i −0.0291936 0.127905i
\(721\) −0.534374 7.13072i −0.0199011 0.265562i
\(722\) −32.2234 9.93961i −1.19923 0.369914i
\(723\) −33.3433 + 16.0573i −1.24005 + 0.597177i
\(724\) 6.89756 11.9469i 0.256346 0.444004i
\(725\) 14.4268 + 24.9879i 0.535798 + 0.928029i
\(726\) −29.7761 20.3010i −1.10509 0.753441i
\(727\) 6.27178 27.4785i 0.232607 1.01912i −0.714860 0.699268i \(-0.753510\pi\)
0.947467 0.319852i \(-0.103633\pi\)
\(728\) 11.8619 + 1.78789i 0.439630 + 0.0662635i
\(729\) −5.63418 7.06504i −0.208673 0.261668i
\(730\) −10.2177 −0.378175
\(731\) 3.07798 5.79017i 0.113843 0.214157i
\(732\) 62.6471 2.31551
\(733\) 2.26906 + 2.84531i 0.0838097 + 0.105094i 0.821968 0.569533i \(-0.192876\pi\)
−0.738159 + 0.674627i \(0.764304\pi\)
\(734\) −15.3884 2.31943i −0.567997 0.0856117i
\(735\) 2.12703 9.31911i 0.0784566 0.343741i
\(736\) 16.1469 + 11.0088i 0.595184 + 0.405789i
\(737\) 17.3859 + 30.1132i 0.640417 + 1.10924i
\(738\) 2.07567 3.59516i 0.0764064 0.132340i
\(739\) −13.7342 + 6.61404i −0.505221 + 0.243301i −0.669091 0.743180i \(-0.733316\pi\)
0.163870 + 0.986482i \(0.447602\pi\)
\(740\) 18.8029 + 5.79992i 0.691208 + 0.213209i
\(741\) 4.70808 + 62.8250i 0.172956 + 2.30793i
\(742\) −1.82749 8.00675i −0.0670893 0.293937i
\(743\) 3.32021 8.45975i 0.121807 0.310358i −0.856945 0.515408i \(-0.827640\pi\)
0.978752 + 0.205050i \(0.0657356\pi\)
\(744\) 1.82102 24.2998i 0.0667618 0.890874i
\(745\) −6.63182 + 0.999585i −0.242971 + 0.0366220i
\(746\) −57.1575 53.0344i −2.09269 1.94173i
\(747\) −27.3117 13.1526i −0.999282 0.481229i
\(748\) 13.0656 8.90795i 0.477724 0.325707i
\(749\) −2.27596 5.79906i −0.0831618 0.211893i
\(750\) 31.5985 9.74685i 1.15381 0.355905i
\(751\) −28.8518 + 26.7706i −1.05282 + 0.976873i −0.999764 0.0217188i \(-0.993086\pi\)
−0.0530544 + 0.998592i \(0.516896\pi\)
\(752\) 15.1258 18.9672i 0.551582 0.691662i
\(753\) 25.7515 32.2914i 0.938437 1.17676i
\(754\) 53.6381 49.7689i 1.95339 1.81248i
\(755\) 0.853147 0.263161i 0.0310492 0.00957741i
\(756\) −1.63567 4.16763i −0.0594889 0.151575i
\(757\) −8.38406 + 5.71616i −0.304724 + 0.207757i −0.706021 0.708191i \(-0.749512\pi\)
0.401297 + 0.915948i \(0.368559\pi\)
\(758\) 15.7791 + 7.59881i 0.573123 + 0.276001i
\(759\) −63.7458 59.1475i −2.31383 2.14692i
\(760\) 15.3065 2.30708i 0.555225 0.0836867i
\(761\) 1.49487 19.9477i 0.0541890 0.723102i −0.902258 0.431197i \(-0.858092\pi\)
0.956447 0.291906i \(-0.0942894\pi\)
\(762\) −16.4843 + 42.0013i −0.597163 + 1.52155i
\(763\) −1.46227 6.40661i −0.0529376 0.231935i
\(764\) −4.88788 65.2242i −0.176837 2.35973i
\(765\) 1.27398 + 0.392971i 0.0460608 + 0.0142079i
\(766\) 10.4610 5.03776i 0.377972 0.182022i
\(767\) −6.10539 + 10.5749i −0.220453 + 0.381836i
\(768\) 32.6301 + 56.5170i 1.17744 + 2.03938i
\(769\) −4.98496 3.39869i −0.179762 0.122560i 0.470096 0.882615i \(-0.344219\pi\)
−0.649858 + 0.760055i \(0.725172\pi\)
\(770\) 0.832504 3.64744i 0.0300014 0.131445i
\(771\) 6.62003 + 0.997808i 0.238414 + 0.0359352i
\(772\) −32.9894 41.3674i −1.18731 1.48884i
\(773\) −19.8164 −0.712745 −0.356373 0.934344i \(-0.615987\pi\)
−0.356373 + 0.934344i \(0.615987\pi\)
\(774\) −24.9723 21.5949i −0.897611 0.776212i
\(775\) 11.7117 0.420698
\(776\) −10.1417 12.7173i −0.364065 0.456523i
\(777\) −10.7096 1.61422i −0.384206 0.0579098i
\(778\) −7.91977 + 34.6988i −0.283937 + 1.24401i
\(779\) 3.91634 + 2.67012i 0.140317 + 0.0956668i
\(780\) −13.1136 22.7135i −0.469544 0.813274i
\(781\) 24.6477 42.6911i 0.881965 1.52761i
\(782\) 19.8326 9.55088i 0.709212 0.341539i
\(783\) −12.2303 3.77256i −0.437076 0.134820i
\(784\) −1.31410 17.5354i −0.0469321 0.626265i
\(785\) 2.38865 + 10.4653i 0.0852544 + 0.373524i
\(786\) −26.0299 + 66.3232i −0.928457 + 2.36567i
\(787\) −3.48306 + 46.4783i −0.124158 + 1.65677i 0.493072 + 0.869988i \(0.335874\pi\)
−0.617230 + 0.786783i \(0.711745\pi\)
\(788\) 12.2604 1.84796i 0.436760 0.0658309i
\(789\) 18.6386 + 17.2941i 0.663552 + 0.615686i
\(790\) 7.54069 + 3.63141i 0.268286 + 0.129200i
\(791\) 9.32537 6.35793i 0.331572 0.226062i
\(792\) −13.6320 34.7337i −0.484391 1.23421i
\(793\) 34.1959 10.5480i 1.21433 0.374572i
\(794\) 36.2468 33.6321i 1.28635 1.19356i
\(795\) −5.24691 + 6.57942i −0.186089 + 0.233348i
\(796\) −11.9904 + 15.0355i −0.424989 + 0.532920i
\(797\) −17.6832 + 16.4076i −0.626371 + 0.581188i −0.928157 0.372188i \(-0.878608\pi\)
0.301786 + 0.953376i \(0.402417\pi\)
\(798\) −17.3717 + 5.35846i −0.614952 + 0.189687i
\(799\) 3.35663 + 8.55256i 0.118749 + 0.302568i
\(800\) −8.09373 + 5.51821i −0.286157 + 0.195098i
\(801\) −20.9527 10.0903i −0.740328 0.356523i
\(802\) −29.2146 27.1071i −1.03160 0.957187i
\(803\) −27.8080 + 4.19138i −0.981322 + 0.147911i
\(804\) −5.25642 + 70.1421i −0.185380 + 2.47372i
\(805\) 1.24249 3.16581i 0.0437920 0.111580i
\(806\) −6.60893 28.9556i −0.232790 1.01992i
\(807\) 0.783166 + 10.4506i 0.0275687 + 0.367879i
\(808\) 46.0267 + 14.1974i 1.61921 + 0.499461i
\(809\) 16.3546 7.87594i 0.574996 0.276903i −0.123703 0.992319i \(-0.539477\pi\)
0.698699 + 0.715416i \(0.253763\pi\)
\(810\) −8.31387 + 14.4000i −0.292120 + 0.505966i
\(811\) −9.21729 15.9648i −0.323663 0.560601i 0.657578 0.753387i \(-0.271581\pi\)
−0.981241 + 0.192786i \(0.938248\pi\)
\(812\) 11.3922 + 7.76704i 0.399786 + 0.272570i
\(813\) −10.3316 + 45.2656i −0.362344 + 1.58753i
\(814\) 82.0058 + 12.3604i 2.87430 + 0.433231i
\(815\) −6.27657 7.87057i −0.219859 0.275694i
\(816\) 5.96132 0.208688
\(817\) 26.7187 26.5908i 0.934769 0.930295i
\(818\) 9.05291 0.316528
\(819\) 3.70307 + 4.64350i 0.129396 + 0.162257i
\(820\) −1.95120 0.294096i −0.0681389 0.0102703i
\(821\) 8.66945 37.9833i 0.302566 1.32563i −0.563674 0.825998i \(-0.690612\pi\)
0.866239 0.499629i \(-0.166530\pi\)
\(822\) 60.6109 + 41.3238i 2.11405 + 1.44133i
\(823\) −1.86423 3.22893i −0.0649828 0.112554i 0.831704 0.555220i \(-0.187366\pi\)
−0.896686 + 0.442666i \(0.854033\pi\)
\(824\) −25.9552 + 44.9558i −0.904193 + 1.56611i
\(825\) 39.2723 18.9125i 1.36728 0.658449i
\(826\) −3.36696 1.03857i −0.117151 0.0361364i
\(827\) 0.359064 + 4.79138i 0.0124859 + 0.166612i 0.999961 + 0.00883737i \(0.00281306\pi\)
−0.987475 + 0.157775i \(0.949568\pi\)
\(828\) −16.1043 70.5576i −0.559664 2.45205i
\(829\) −0.847329 + 2.15896i −0.0294289 + 0.0749837i −0.944833 0.327553i \(-0.893776\pi\)
0.915404 + 0.402536i \(0.131871\pi\)
\(830\) −1.64890 + 22.0031i −0.0572342 + 0.763737i
\(831\) −11.9314 + 1.79837i −0.413897 + 0.0623849i
\(832\) 37.0027 + 34.3335i 1.28284 + 1.19030i
\(833\) 6.00009 + 2.88949i 0.207891 + 0.100115i
\(834\) 24.2234 16.5152i 0.838788 0.571876i
\(835\) −0.661872 1.68642i −0.0229050 0.0583611i
\(836\) 86.8647 26.7942i 3.00428 0.926697i
\(837\) −3.80829 + 3.53358i −0.131634 + 0.122138i
\(838\) −48.7844 + 61.1738i −1.68523 + 2.11321i
\(839\) −25.8929 + 32.4686i −0.893921 + 1.12094i 0.0981381 + 0.995173i \(0.468711\pi\)
−0.992060 + 0.125769i \(0.959860\pi\)
\(840\) 2.60008 2.41252i 0.0897111 0.0832398i
\(841\) 9.95360 3.07028i 0.343228 0.105872i
\(842\) −5.88614 14.9976i −0.202850 0.516852i
\(843\) −57.9231 + 39.4913i −1.99498 + 1.36015i
\(844\) −71.4602 34.4134i −2.45976 1.18456i
\(845\) −4.92378 4.56860i −0.169383 0.157165i
\(846\) 45.7401 6.89422i 1.57258 0.237028i
\(847\) 0.289887 3.86827i 0.00996062 0.132915i
\(848\) −5.65592 + 14.4110i −0.194225 + 0.494877i
\(849\) −2.62850 11.5162i −0.0902097 0.395235i
\(850\) 0.824564 + 11.0030i 0.0282823 + 0.377401i
\(851\) 72.0386 + 22.2210i 2.46945 + 0.761725i
\(852\) 89.8431 43.2662i 3.07797 1.48227i
\(853\) −2.29099 + 3.96812i −0.0784422 + 0.135866i −0.902578 0.430526i \(-0.858328\pi\)
0.824136 + 0.566392i \(0.191661\pi\)
\(854\) 5.16310 + 8.94275i 0.176678 + 0.306015i
\(855\) 6.33229 + 4.31728i 0.216560 + 0.147648i
\(856\) −10.0634 + 44.0904i −0.343958 + 1.50698i
\(857\) −50.3182 7.58425i −1.71884 0.259073i −0.785704 0.618602i \(-0.787699\pi\)
−0.933134 + 0.359529i \(0.882937\pi\)
\(858\) −68.9199 86.4228i −2.35289 2.95043i
\(859\) 35.4743 1.21037 0.605185 0.796085i \(-0.293099\pi\)
0.605185 + 0.796085i \(0.293099\pi\)
\(860\) −5.21847 + 14.7996i −0.177948 + 0.504661i
\(861\) 1.08611 0.0370144
\(862\) 28.0759 + 35.2060i 0.956268 + 1.19912i
\(863\) 34.3823 + 5.18229i 1.17039 + 0.176407i 0.705333 0.708876i \(-0.250797\pi\)
0.465052 + 0.885283i \(0.346035\pi\)
\(864\) 0.966916 4.23633i 0.0328951 0.144123i
\(865\) −6.23923 4.25383i −0.212140 0.144635i
\(866\) −20.4815 35.4750i −0.695989 1.20549i
\(867\) −1.12883 + 1.95519i −0.0383370 + 0.0664017i
\(868\) 5.04233 2.42826i 0.171148 0.0824205i
\(869\) 22.0119 + 6.78978i 0.746704 + 0.230328i
\(870\) −1.61680 21.5746i −0.0548145 0.731449i
\(871\) 8.94076 + 39.1720i 0.302946 + 1.32729i
\(872\) −17.4285 + 44.4071i −0.590203 + 1.50381i
\(873\) 0.601835 8.03093i 0.0203690 0.271806i
\(874\) 125.126 18.8598i 4.23246 0.637941i
\(875\) 2.60920 + 2.42099i 0.0882072 + 0.0818443i
\(876\) −51.2537 24.6825i −1.73170 0.833944i
\(877\) 15.8816 10.8279i 0.536282 0.365631i −0.264689 0.964334i \(-0.585269\pi\)
0.800971 + 0.598703i \(0.204317\pi\)
\(878\) 27.0177 + 68.8400i 0.911804 + 2.32324i
\(879\) 8.98238 2.77070i 0.302968 0.0934533i
\(880\) −5.16977 + 4.79684i −0.174273 + 0.161702i
\(881\) −16.7953 + 21.0606i −0.565847 + 0.709549i −0.979627 0.200828i \(-0.935637\pi\)
0.413780 + 0.910377i \(0.364208\pi\)
\(882\) 20.9049 26.2139i 0.703904 0.882667i
\(883\) −24.3319 + 22.5767i −0.818834 + 0.759767i −0.973619 0.228182i \(-0.926722\pi\)
0.154785 + 0.987948i \(0.450532\pi\)
\(884\) 17.4608 5.38593i 0.587269 0.181149i
\(885\) 1.31905 + 3.36090i 0.0443395 + 0.112975i
\(886\) 57.9634 39.5188i 1.94732 1.32766i
\(887\) −28.2245 13.5922i −0.947686 0.456382i −0.104812 0.994492i \(-0.533424\pi\)
−0.842874 + 0.538110i \(0.819138\pi\)
\(888\) 57.6359 + 53.4783i 1.93413 + 1.79461i
\(889\) −4.80247 + 0.723856i −0.161070 + 0.0242773i
\(890\) −1.26499 + 16.8801i −0.0424025 + 0.565822i
\(891\) −16.7196 + 42.6007i −0.560126 + 1.42718i
\(892\) −2.57737 11.2922i −0.0862968 0.378091i
\(893\) 3.94692 + 52.6679i 0.132078 + 1.76246i
\(894\) −54.6392 16.8539i −1.82741 0.563680i
\(895\) 11.2958 5.43978i 0.377578 0.181832i
\(896\) −6.03922 + 10.4602i −0.201756 + 0.349452i
\(897\) −50.2417 87.0211i −1.67752 2.90555i
\(898\) 17.1320 + 11.6804i 0.571702 + 0.389780i
\(899\) 3.56015 15.5981i 0.118738 0.520224i
\(900\) 35.8717 + 5.40679i 1.19572 + 0.180226i
\(901\) −3.65553 4.58389i −0.121783 0.152711i
\(902\) −8.31652 −0.276910
\(903\) 1.62617 8.48305i 0.0541154 0.282298i
\(904\) −81.9343 −2.72509
\(905\) −1.45273 1.82167i −0.0482904 0.0605542i
\(906\) 7.52683 + 1.13449i 0.250062 + 0.0376908i
\(907\) 8.90457 39.0135i 0.295671 1.29542i −0.580831 0.814024i \(-0.697272\pi\)
0.876503 0.481397i \(-0.159870\pi\)
\(908\) 70.0410 + 47.7532i 2.32439 + 1.58474i
\(909\) 11.9239 + 20.6528i 0.395490 + 0.685009i
\(910\) 2.16154 3.74389i 0.0716542 0.124109i
\(911\) 16.2837 7.84183i 0.539504 0.259811i −0.144228 0.989544i \(-0.546070\pi\)
0.683732 + 0.729733i \(0.260356\pi\)
\(912\) 32.7464 + 10.1009i 1.08434 + 0.334475i
\(913\) 4.53824 + 60.5587i 0.150194 + 2.00420i
\(914\) 5.80366 + 25.4275i 0.191968 + 0.841067i
\(915\) 3.86571 9.84967i 0.127796 0.325620i
\(916\) 1.63835 21.8622i 0.0541325 0.722348i
\(917\) −7.58346 + 1.14302i −0.250428 + 0.0377459i
\(918\) −3.58788 3.32907i −0.118418 0.109876i
\(919\) 3.19097 + 1.53669i 0.105260 + 0.0506907i 0.485773 0.874085i \(-0.338538\pi\)
−0.380513 + 0.924776i \(0.624252\pi\)
\(920\) −20.3988 + 13.9077i −0.672529 + 0.458523i
\(921\) 21.3605 + 54.4257i 0.703853 + 1.79339i
\(922\) 12.2836 3.78898i 0.404537 0.124783i
\(923\) 41.7560 38.7439i 1.37442 1.27527i
\(924\) 12.9869 16.2851i 0.427238 0.535740i
\(925\) −23.5608 + 29.5443i −0.774674 + 0.971410i
\(926\) 26.2613 24.3669i 0.863001 0.800748i
\(927\) −24.5595 + 7.57561i −0.806641 + 0.248816i
\(928\) 4.88898 + 12.4569i 0.160489 + 0.408919i
\(929\) 41.7913 28.4928i 1.37113 0.934820i 0.371148 0.928574i \(-0.378964\pi\)
0.999980 0.00624599i \(-0.00198817\pi\)
\(930\) −7.91208 3.81026i −0.259447 0.124943i
\(931\) 28.0634 + 26.0390i 0.919739 + 0.853393i
\(932\) −41.6877 + 6.28341i −1.36553 + 0.205820i
\(933\) −3.37865 + 45.0850i −0.110612 + 1.47602i
\(934\) 35.3262 90.0096i 1.15591 2.94520i
\(935\) −0.594324 2.60390i −0.0194365 0.0851567i
\(936\) −3.22205 42.9953i −0.105316 1.40535i
\(937\) 48.9157 + 15.0885i 1.59801 + 0.492919i 0.960676 0.277672i \(-0.0895630\pi\)
0.637329 + 0.770592i \(0.280039\pi\)
\(938\) −10.4458 + 5.03045i −0.341069 + 0.164250i
\(939\) 20.2932 35.1488i 0.662243 1.14704i
\(940\) −10.9935 19.0414i −0.358570 0.621061i
\(941\) −17.4020 11.8645i −0.567290 0.386772i 0.245440 0.969412i \(-0.421068\pi\)
−0.812731 + 0.582640i \(0.802020\pi\)
\(942\) −20.3649 + 89.2243i −0.663523 + 2.90709i
\(943\) −7.47554 1.12676i −0.243437 0.0366922i
\(944\) 4.14118 + 5.19287i 0.134784 + 0.169014i
\(945\) −0.756185 −0.0245987
\(946\) −12.4519 + 64.9563i −0.404845 + 2.11191i
\(947\) −43.4346 −1.41144 −0.705718 0.708493i \(-0.749375\pi\)
−0.705718 + 0.708493i \(0.749375\pi\)
\(948\) 29.0531 + 36.4314i 0.943600 + 1.18324i
\(949\) −32.1326 4.84322i −1.04307 0.157217i
\(950\) −14.1142 + 61.8384i −0.457926 + 2.00630i
\(951\) 2.39853 + 1.63529i 0.0777776 + 0.0530279i
\(952\) 1.23557 + 2.14007i 0.0400451 + 0.0693601i
\(953\) −7.13284 + 12.3544i −0.231055 + 0.400200i −0.958119 0.286370i \(-0.907551\pi\)
0.727064 + 0.686570i \(0.240885\pi\)
\(954\) −26.5950 + 12.8075i −0.861046 + 0.414658i
\(955\) −10.5565 3.25623i −0.341599 0.105369i
\(956\) −1.36725 18.2447i −0.0442200 0.590074i
\(957\) −13.2502 58.0531i −0.428319 1.87659i
\(958\) 9.15397 23.3239i 0.295751 0.753562i
\(959\) −0.590080 + 7.87407i −0.0190547 + 0.254267i
\(960\) 14.7585 2.22448i 0.476328 0.0717948i
\(961\) 17.9641 + 16.6682i 0.579487 + 0.537685i
\(962\) 86.3395 + 41.5789i 2.78370 + 1.34056i
\(963\) −18.5003 + 12.6133i −0.596164 + 0.406458i
\(964\) 22.5427 + 57.4378i 0.726051 + 1.84995i
\(965\) −8.53961 + 2.63412i −0.274900 + 0.0847953i
\(966\) 21.2549 19.7217i 0.683865 0.634534i
\(967\) 26.9494 33.7934i 0.866633 1.08672i −0.128839 0.991666i \(-0.541125\pi\)
0.995472 0.0950579i \(-0.0303036\pi\)
\(968\) −17.5577 + 22.0166i −0.564325 + 0.707641i
\(969\) −9.51371 + 8.82743i −0.305624 + 0.283578i
\(970\) −5.60152 + 1.72784i −0.179854 + 0.0554776i
\(971\) −17.1349 43.6591i −0.549887 1.40109i −0.887939 0.459961i \(-0.847863\pi\)
0.338053 0.941127i \(-0.390232\pi\)
\(972\) −57.4684 + 39.1813i −1.84330 + 1.25674i
\(973\) 2.84322 + 1.36922i 0.0911493 + 0.0438952i
\(974\) −39.8469 36.9725i −1.27678 1.18468i
\(975\) 49.8052 7.50693i 1.59504 0.240414i
\(976\) 1.45464 19.4109i 0.0465620 0.621327i
\(977\) −14.4590 + 36.8409i −0.462584 + 1.17865i 0.489280 + 0.872127i \(0.337259\pi\)
−0.951865 + 0.306519i \(0.900836\pi\)
\(978\) −19.0983 83.6749i −0.610695 2.67563i
\(979\) 3.48161 + 46.4588i 0.111273 + 1.48483i
\(980\) −15.2291 4.69755i −0.486475 0.150058i
\(981\) −21.2800 + 10.2479i −0.679419 + 0.327191i
\(982\) 38.9494 67.4623i 1.24292 2.15281i
\(983\) −14.6670 25.4039i −0.467804 0.810260i 0.531519 0.847046i \(-0.321621\pi\)
−0.999323 + 0.0367861i \(0.988288\pi\)
\(984\) −6.51453 4.44153i −0.207676 0.141591i
\(985\) 0.465998 2.04167i 0.0148479 0.0650531i
\(986\) 14.9049 + 2.24655i 0.474667 + 0.0715446i
\(987\) 7.54552 + 9.46178i 0.240176 + 0.301172i
\(988\) 105.040 3.34178
\(989\) −19.9932 + 56.7008i −0.635748 + 1.80298i
\(990\) −13.4469 −0.427371
\(991\) −13.3731 16.7694i −0.424811 0.532697i 0.522658 0.852542i \(-0.324940\pi\)
−0.947470 + 0.319846i \(0.896369\pi\)
\(992\) 5.37110 + 0.809563i 0.170533 + 0.0257037i
\(993\) −13.7466 + 60.2280i −0.436236 + 1.91128i
\(994\) 13.5806 + 9.25911i 0.430751 + 0.293681i
\(995\) 1.62407 + 2.81297i 0.0514865 + 0.0891772i
\(996\) −61.4229 + 106.388i −1.94626 + 3.37102i
\(997\) −16.7014 + 8.04295i −0.528937 + 0.254723i −0.679239 0.733917i \(-0.737690\pi\)
0.150301 + 0.988640i \(0.451976\pi\)
\(998\) 36.5090 + 11.2615i 1.15567 + 0.356478i
\(999\) −1.25265 16.7155i −0.0396321 0.528854i
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 731.2.u.a.52.3 348
43.24 even 21 inner 731.2.u.a.239.3 yes 348
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.u.a.52.3 348 1.1 even 1 trivial
731.2.u.a.239.3 yes 348 43.24 even 21 inner