Properties

Label 700.2.c.k.699.13
Level $700$
Weight $2$
Character 700.699
Analytic conductor $5.590$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,2,Mod(699,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.699");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.c (of order \(2\), degree \(1\), not 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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: 16.0.29960650073923649536.7
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7x^{12} + 40x^{8} - 112x^{4} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 699.13
Root \(-0.281691 + 1.38588i\) of defining polynomial
Character \(\chi\) \(=\) 700.699
Dual form 700.2.c.k.699.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.39897 - 0.207107i) q^{2} -1.47363i q^{3} +(1.91421 - 0.579471i) q^{4} +(-0.305198 - 2.06155i) q^{6} +(-0.819496 - 2.51564i) q^{7} +(2.55791 - 1.20711i) q^{8} +0.828427 q^{9} +O(q^{10})\) \(q+(1.39897 - 0.207107i) q^{2} -1.47363i q^{3} +(1.91421 - 0.579471i) q^{4} +(-0.305198 - 2.06155i) q^{6} +(-0.819496 - 2.51564i) q^{7} +(2.55791 - 1.20711i) q^{8} +0.828427 q^{9} +2.79793i q^{11} +(-0.853923 - 2.82083i) q^{12} +5.83095 q^{13} +(-1.66745 - 3.34957i) q^{14} +(3.32843 - 2.21846i) q^{16} -4.12311 q^{17} +(1.15894 - 0.171573i) q^{18} -5.64167 q^{19} +(-3.70711 + 1.20763i) q^{21} +(0.579471 + 3.91421i) q^{22} -3.95687 q^{23} +(-1.77882 - 3.76940i) q^{24} +(8.15731 - 1.20763i) q^{26} -5.64167i q^{27} +(-3.02643 - 4.34059i) q^{28} +0.242641 q^{29} +2.08402 q^{31} +(4.19690 - 3.79289i) q^{32} +4.12311 q^{33} +(-5.76809 + 0.853923i) q^{34} +(1.58579 - 0.480049i) q^{36} -6.24264i q^{37} +(-7.89250 + 1.16843i) q^{38} -8.59264i q^{39} +4.12311i q^{41} +(-4.93601 + 2.45720i) q^{42} +5.59587 q^{43} +(1.62132 + 5.35584i) q^{44} +(-5.53553 + 0.819496i) q^{46} +6.25206i q^{47} +(-3.26918 - 4.90486i) q^{48} +(-5.65685 + 4.12311i) q^{49} +6.07591i q^{51} +(11.1617 - 3.37887i) q^{52} +12.2426i q^{53} +(-1.16843 - 7.89250i) q^{54} +(-5.13284 - 5.44555i) q^{56} +8.31371i q^{57} +(0.339446 - 0.0502525i) q^{58} -2.94725 q^{59} +11.6619i q^{61} +(2.91548 - 0.431615i) q^{62} +(-0.678892 - 2.08402i) q^{63} +(5.08579 - 6.17534i) q^{64} +(5.76809 - 0.853923i) q^{66} +7.43370 q^{67} +(-7.89250 + 2.38922i) q^{68} +5.83095i q^{69} -7.23486i q^{71} +(2.11904 - 1.00000i) q^{72} +12.3693 q^{73} +(-1.29289 - 8.73324i) q^{74} +(-10.7994 + 3.26918i) q^{76} +(7.03858 - 2.29289i) q^{77} +(-1.77959 - 12.0208i) q^{78} +7.91375i q^{79} -5.82843 q^{81} +(0.853923 + 5.76809i) q^{82} -1.47363i q^{83} +(-6.39641 + 4.45982i) q^{84} +(7.82843 - 1.15894i) q^{86} -0.357562i q^{87} +(3.37740 + 7.15685i) q^{88} +12.3693i q^{89} +(-4.77844 - 14.6686i) q^{91} +(-7.57430 + 2.29289i) q^{92} -3.07107i q^{93} +(1.29484 + 8.74643i) q^{94} +(-5.58931 - 6.18466i) q^{96} -8.24621 q^{97} +(-7.05983 + 6.93966i) q^{98} +2.31788i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 32 q^{9} - 24 q^{14} + 8 q^{16} - 48 q^{21} - 64 q^{29} + 48 q^{36} - 8 q^{44} - 32 q^{46} + 40 q^{56} + 104 q^{64} - 32 q^{74} - 48 q^{81} - 40 q^{84} + 80 q^{86}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39897 0.207107i 0.989219 0.146447i
\(3\) 1.47363i 0.850798i −0.905006 0.425399i \(-0.860134\pi\)
0.905006 0.425399i \(-0.139866\pi\)
\(4\) 1.91421 0.579471i 0.957107 0.289735i
\(5\) 0 0
\(6\) −0.305198 2.06155i −0.124597 0.841625i
\(7\) −0.819496 2.51564i −0.309740 0.950821i
\(8\) 2.55791 1.20711i 0.904357 0.426777i
\(9\) 0.828427 0.276142
\(10\) 0 0
\(11\) 2.79793i 0.843608i 0.906687 + 0.421804i \(0.138603\pi\)
−0.906687 + 0.421804i \(0.861397\pi\)
\(12\) −0.853923 2.82083i −0.246506 0.814305i
\(13\) 5.83095 1.61722 0.808608 0.588348i \(-0.200222\pi\)
0.808608 + 0.588348i \(0.200222\pi\)
\(14\) −1.66745 3.34957i −0.445645 0.895210i
\(15\) 0 0
\(16\) 3.32843 2.21846i 0.832107 0.554615i
\(17\) −4.12311 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 1.15894 0.171573i 0.273165 0.0404401i
\(19\) −5.64167 −1.29429 −0.647144 0.762368i \(-0.724037\pi\)
−0.647144 + 0.762368i \(0.724037\pi\)
\(20\) 0 0
\(21\) −3.70711 + 1.20763i −0.808957 + 0.263526i
\(22\) 0.579471 + 3.91421i 0.123544 + 0.834513i
\(23\) −3.95687 −0.825065 −0.412533 0.910943i \(-0.635356\pi\)
−0.412533 + 0.910943i \(0.635356\pi\)
\(24\) −1.77882 3.76940i −0.363101 0.769425i
\(25\) 0 0
\(26\) 8.15731 1.20763i 1.59978 0.236836i
\(27\) 5.64167i 1.08574i
\(28\) −3.02643 4.34059i −0.571941 0.820295i
\(29\) 0.242641 0.0450572 0.0225286 0.999746i \(-0.492828\pi\)
0.0225286 + 0.999746i \(0.492828\pi\)
\(30\) 0 0
\(31\) 2.08402 0.374301 0.187151 0.982331i \(-0.440075\pi\)
0.187151 + 0.982331i \(0.440075\pi\)
\(32\) 4.19690 3.79289i 0.741914 0.670495i
\(33\) 4.12311 0.717741
\(34\) −5.76809 + 0.853923i −0.989219 + 0.146447i
\(35\) 0 0
\(36\) 1.58579 0.480049i 0.264298 0.0800082i
\(37\) 6.24264i 1.02628i −0.858304 0.513142i \(-0.828481\pi\)
0.858304 0.513142i \(-0.171519\pi\)
\(38\) −7.89250 + 1.16843i −1.28033 + 0.189544i
\(39\) 8.59264i 1.37592i
\(40\) 0 0
\(41\) 4.12311i 0.643921i 0.946753 + 0.321960i \(0.104342\pi\)
−0.946753 + 0.321960i \(0.895658\pi\)
\(42\) −4.93601 + 2.45720i −0.761643 + 0.379154i
\(43\) 5.59587 0.853361 0.426681 0.904402i \(-0.359683\pi\)
0.426681 + 0.904402i \(0.359683\pi\)
\(44\) 1.62132 + 5.35584i 0.244423 + 0.807423i
\(45\) 0 0
\(46\) −5.53553 + 0.819496i −0.816170 + 0.120828i
\(47\) 6.25206i 0.911957i 0.889991 + 0.455979i \(0.150711\pi\)
−0.889991 + 0.455979i \(0.849289\pi\)
\(48\) −3.26918 4.90486i −0.471866 0.707955i
\(49\) −5.65685 + 4.12311i −0.808122 + 0.589015i
\(50\) 0 0
\(51\) 6.07591i 0.850798i
\(52\) 11.1617 3.37887i 1.54785 0.468564i
\(53\) 12.2426i 1.68166i 0.541302 + 0.840828i \(0.317931\pi\)
−0.541302 + 0.840828i \(0.682069\pi\)
\(54\) −1.16843 7.89250i −0.159003 1.07403i
\(55\) 0 0
\(56\) −5.13284 5.44555i −0.685904 0.727692i
\(57\) 8.31371i 1.10118i
\(58\) 0.339446 0.0502525i 0.0445715 0.00659848i
\(59\) −2.94725 −0.383699 −0.191850 0.981424i \(-0.561449\pi\)
−0.191850 + 0.981424i \(0.561449\pi\)
\(60\) 0 0
\(61\) 11.6619i 1.49315i 0.665299 + 0.746577i \(0.268304\pi\)
−0.665299 + 0.746577i \(0.731696\pi\)
\(62\) 2.91548 0.431615i 0.370266 0.0548152i
\(63\) −0.678892 2.08402i −0.0855324 0.262562i
\(64\) 5.08579 6.17534i 0.635723 0.771917i
\(65\) 0 0
\(66\) 5.76809 0.853923i 0.710002 0.105111i
\(67\) 7.43370 0.908171 0.454085 0.890958i \(-0.349966\pi\)
0.454085 + 0.890958i \(0.349966\pi\)
\(68\) −7.89250 + 2.38922i −0.957107 + 0.289735i
\(69\) 5.83095i 0.701964i
\(70\) 0 0
\(71\) 7.23486i 0.858619i −0.903157 0.429310i \(-0.858757\pi\)
0.903157 0.429310i \(-0.141243\pi\)
\(72\) 2.11904 1.00000i 0.249731 0.117851i
\(73\) 12.3693 1.44772 0.723860 0.689947i \(-0.242366\pi\)
0.723860 + 0.689947i \(0.242366\pi\)
\(74\) −1.29289 8.73324i −0.150296 1.01522i
\(75\) 0 0
\(76\) −10.7994 + 3.26918i −1.23877 + 0.375001i
\(77\) 7.03858 2.29289i 0.802121 0.261299i
\(78\) −1.77959 12.0208i −0.201499 1.36109i
\(79\) 7.91375i 0.890366i 0.895440 + 0.445183i \(0.146861\pi\)
−0.895440 + 0.445183i \(0.853139\pi\)
\(80\) 0 0
\(81\) −5.82843 −0.647603
\(82\) 0.853923 + 5.76809i 0.0943000 + 0.636979i
\(83\) 1.47363i 0.161751i −0.996724 0.0808757i \(-0.974228\pi\)
0.996724 0.0808757i \(-0.0257717\pi\)
\(84\) −6.39641 + 4.45982i −0.697905 + 0.486606i
\(85\) 0 0
\(86\) 7.82843 1.15894i 0.844161 0.124972i
\(87\) 0.357562i 0.0383346i
\(88\) 3.37740 + 7.15685i 0.360032 + 0.762923i
\(89\) 12.3693i 1.31114i 0.755132 + 0.655572i \(0.227573\pi\)
−0.755132 + 0.655572i \(0.772427\pi\)
\(90\) 0 0
\(91\) −4.77844 14.6686i −0.500916 1.53768i
\(92\) −7.57430 + 2.29289i −0.789676 + 0.239051i
\(93\) 3.07107i 0.318455i
\(94\) 1.29484 + 8.74643i 0.133553 + 0.902125i
\(95\) 0 0
\(96\) −5.58931 6.18466i −0.570456 0.631219i
\(97\) −8.24621 −0.837276 −0.418638 0.908153i \(-0.637492\pi\)
−0.418638 + 0.908153i \(0.637492\pi\)
\(98\) −7.05983 + 6.93966i −0.713150 + 0.701011i
\(99\) 2.31788i 0.232956i
\(100\) 0 0
\(101\) 2.41526i 0.240327i −0.992754 0.120164i \(-0.961658\pi\)
0.992754 0.120164i \(-0.0383419\pi\)
\(102\) 1.25836 + 8.50000i 0.124597 + 0.841625i
\(103\) 7.11529i 0.701091i 0.936546 + 0.350545i \(0.114004\pi\)
−0.936546 + 0.350545i \(0.885996\pi\)
\(104\) 14.9150 7.03858i 1.46254 0.690190i
\(105\) 0 0
\(106\) 2.53553 + 17.1270i 0.246273 + 1.66353i
\(107\) −13.0296 −1.25962 −0.629808 0.776751i \(-0.716866\pi\)
−0.629808 + 0.776751i \(0.716866\pi\)
\(108\) −3.26918 10.7994i −0.314577 1.03917i
\(109\) −2.82843 −0.270914 −0.135457 0.990783i \(-0.543250\pi\)
−0.135457 + 0.990783i \(0.543250\pi\)
\(110\) 0 0
\(111\) −9.19932 −0.873160
\(112\) −8.30847 6.55509i −0.785077 0.619398i
\(113\) 18.3137i 1.72281i −0.507920 0.861404i \(-0.669585\pi\)
0.507920 0.861404i \(-0.330415\pi\)
\(114\) 1.72183 + 11.6306i 0.161264 + 1.08931i
\(115\) 0 0
\(116\) 0.464466 0.140603i 0.0431246 0.0130547i
\(117\) 4.83052 0.446582
\(118\) −4.12311 + 0.610396i −0.379563 + 0.0561915i
\(119\) 3.37887 + 10.3722i 0.309740 + 0.950821i
\(120\) 0 0
\(121\) 3.17157 0.288325
\(122\) 2.41526 + 16.3146i 0.218667 + 1.47706i
\(123\) 6.07591 0.547847
\(124\) 3.98926 1.20763i 0.358246 0.108448i
\(125\) 0 0
\(126\) −1.38136 2.77487i −0.123062 0.247205i
\(127\) 5.59587 0.496553 0.248276 0.968689i \(-0.420136\pi\)
0.248276 + 0.968689i \(0.420136\pi\)
\(128\) 5.83589 9.69239i 0.515825 0.856694i
\(129\) 8.24621i 0.726038i
\(130\) 0 0
\(131\) 13.0098 1.13667 0.568336 0.822797i \(-0.307588\pi\)
0.568336 + 0.822797i \(0.307588\pi\)
\(132\) 7.89250 2.38922i 0.686954 0.207955i
\(133\) 4.62332 + 14.1924i 0.400893 + 1.23064i
\(134\) 10.3995 1.53957i 0.898380 0.132999i
\(135\) 0 0
\(136\) −10.5465 + 4.97703i −0.904357 + 0.426777i
\(137\) 3.48528i 0.297768i −0.988855 0.148884i \(-0.952432\pi\)
0.988855 0.148884i \(-0.0475681\pi\)
\(138\) 1.20763 + 8.15731i 0.102800 + 0.694396i
\(139\) 2.69442 0.228537 0.114269 0.993450i \(-0.463548\pi\)
0.114269 + 0.993450i \(0.463548\pi\)
\(140\) 0 0
\(141\) 9.21320 0.775892
\(142\) −1.49839 10.1213i −0.125742 0.849362i
\(143\) 16.3146i 1.36430i
\(144\) 2.75736 1.83783i 0.229780 0.153153i
\(145\) 0 0
\(146\) 17.3043 2.56177i 1.43211 0.212014i
\(147\) 6.07591 + 8.33609i 0.501133 + 0.687549i
\(148\) −3.61743 11.9497i −0.297351 0.982263i
\(149\) −2.00000 −0.163846 −0.0819232 0.996639i \(-0.526106\pi\)
−0.0819232 + 0.996639i \(0.526106\pi\)
\(150\) 0 0
\(151\) 1.63899i 0.133379i 0.997774 + 0.0666896i \(0.0212437\pi\)
−0.997774 + 0.0666896i \(0.978756\pi\)
\(152\) −14.4309 + 6.81010i −1.17050 + 0.552372i
\(153\) −3.41569 −0.276142
\(154\) 9.37186 4.66542i 0.755206 0.375950i
\(155\) 0 0
\(156\) −4.97918 16.4481i −0.398654 1.31691i
\(157\) −22.3234 −1.78160 −0.890800 0.454396i \(-0.849855\pi\)
−0.890800 + 0.454396i \(0.849855\pi\)
\(158\) 1.63899 + 11.0711i 0.130391 + 0.880767i
\(159\) 18.0411 1.43075
\(160\) 0 0
\(161\) 3.24264 + 9.95406i 0.255556 + 0.784490i
\(162\) −8.15377 + 1.20711i −0.640621 + 0.0948393i
\(163\) −21.9034 −1.71561 −0.857804 0.513977i \(-0.828172\pi\)
−0.857804 + 0.513977i \(0.828172\pi\)
\(164\) 2.38922 + 7.89250i 0.186567 + 0.616301i
\(165\) 0 0
\(166\) −0.305198 2.06155i −0.0236880 0.160008i
\(167\) 17.1778i 1.32926i 0.747172 + 0.664631i \(0.231411\pi\)
−0.747172 + 0.664631i \(0.768589\pi\)
\(168\) −8.02470 + 7.56388i −0.619119 + 0.583566i
\(169\) 21.0000 1.61538
\(170\) 0 0
\(171\) −4.67371 −0.357408
\(172\) 10.7117 3.24264i 0.816758 0.247249i
\(173\) −14.0772 −1.07027 −0.535133 0.844768i \(-0.679739\pi\)
−0.535133 + 0.844768i \(0.679739\pi\)
\(174\) −0.0740534 0.500217i −0.00561398 0.0379213i
\(175\) 0 0
\(176\) 6.20711 + 9.31271i 0.467878 + 0.701972i
\(177\) 4.34315i 0.326451i
\(178\) 2.56177 + 17.3043i 0.192013 + 1.29701i
\(179\) 10.7117i 0.800629i −0.916378 0.400314i \(-0.868901\pi\)
0.916378 0.400314i \(-0.131099\pi\)
\(180\) 0 0
\(181\) 19.9081i 1.47976i −0.672740 0.739879i \(-0.734883\pi\)
0.672740 0.739879i \(-0.265117\pi\)
\(182\) −9.72283 19.5312i −0.720704 1.44775i
\(183\) 17.1853 1.27037
\(184\) −10.1213 + 4.77637i −0.746154 + 0.352119i
\(185\) 0 0
\(186\) −0.636039 4.29632i −0.0466366 0.315021i
\(187\) 11.5362i 0.843608i
\(188\) 3.62289 + 11.9678i 0.264226 + 0.872841i
\(189\) −14.1924 + 4.62332i −1.03234 + 0.336297i
\(190\) 0 0
\(191\) 24.7013i 1.78733i 0.448738 + 0.893663i \(0.351874\pi\)
−0.448738 + 0.893663i \(0.648126\pi\)
\(192\) −9.10013 7.49455i −0.656746 0.540872i
\(193\) 8.31371i 0.598434i 0.954185 + 0.299217i \(0.0967254\pi\)
−0.954185 + 0.299217i \(0.903275\pi\)
\(194\) −11.5362 + 1.70785i −0.828249 + 0.122616i
\(195\) 0 0
\(196\) −8.43921 + 11.1705i −0.602801 + 0.797892i
\(197\) 2.48528i 0.177069i −0.996073 0.0885345i \(-0.971782\pi\)
0.996073 0.0885345i \(-0.0282183\pi\)
\(198\) 0.480049 + 3.24264i 0.0341156 + 0.230444i
\(199\) 17.5354 1.24305 0.621526 0.783394i \(-0.286513\pi\)
0.621526 + 0.783394i \(0.286513\pi\)
\(200\) 0 0
\(201\) 10.9545i 0.772670i
\(202\) −0.500217 3.37887i −0.0351951 0.237736i
\(203\) −0.198843 0.610396i −0.0139560 0.0428414i
\(204\) 3.52082 + 11.6306i 0.246506 + 0.814305i
\(205\) 0 0
\(206\) 1.47363 + 9.95406i 0.102672 + 0.693532i
\(207\) −3.27798 −0.227835
\(208\) 19.4079 12.9357i 1.34570 0.896932i
\(209\) 15.7850i 1.09187i
\(210\) 0 0
\(211\) 1.44015i 0.0991439i −0.998771 0.0495719i \(-0.984214\pi\)
0.998771 0.0495719i \(-0.0157857\pi\)
\(212\) 7.09425 + 23.4350i 0.487235 + 1.60952i
\(213\) −10.6615 −0.730512
\(214\) −18.2279 + 2.69851i −1.24604 + 0.184466i
\(215\) 0 0
\(216\) −6.81010 14.4309i −0.463368 0.981896i
\(217\) −1.70785 5.24264i −0.115936 0.355894i
\(218\) −3.95687 + 0.585786i −0.267993 + 0.0396745i
\(219\) 18.2277i 1.23172i
\(220\) 0 0
\(221\) −24.0416 −1.61722
\(222\) −12.8695 + 1.90524i −0.863747 + 0.127871i
\(223\) 0.863230i 0.0578062i 0.999582 + 0.0289031i \(0.00920142\pi\)
−0.999582 + 0.0289031i \(0.990799\pi\)
\(224\) −12.9809 7.44961i −0.867322 0.497748i
\(225\) 0 0
\(226\) −3.79289 25.6203i −0.252300 1.70423i
\(227\) 7.11529i 0.472259i −0.971722 0.236129i \(-0.924121\pi\)
0.971722 0.236129i \(-0.0758789\pi\)
\(228\) 4.81755 + 15.9142i 0.319050 + 1.05394i
\(229\) 14.0772i 0.930245i −0.885246 0.465123i \(-0.846010\pi\)
0.885246 0.465123i \(-0.153990\pi\)
\(230\) 0 0
\(231\) −3.37887 10.3722i −0.222313 0.682443i
\(232\) 0.620653 0.292893i 0.0407478 0.0192294i
\(233\) 15.7990i 1.03503i −0.855675 0.517513i \(-0.826858\pi\)
0.855675 0.517513i \(-0.173142\pi\)
\(234\) 6.75773 1.00043i 0.441767 0.0654004i
\(235\) 0 0
\(236\) −5.64167 + 1.70785i −0.367241 + 0.111171i
\(237\) 11.6619 0.757522
\(238\) 6.87508 + 13.8106i 0.445645 + 0.895210i
\(239\) 16.7876i 1.08590i 0.839765 + 0.542950i \(0.182693\pi\)
−0.839765 + 0.542950i \(0.817307\pi\)
\(240\) 0 0
\(241\) 15.7850i 1.01680i −0.861120 0.508401i \(-0.830237\pi\)
0.861120 0.508401i \(-0.169763\pi\)
\(242\) 4.43692 0.656854i 0.285216 0.0422242i
\(243\) 8.33609i 0.534760i
\(244\) 6.75773 + 22.3234i 0.432620 + 1.42911i
\(245\) 0 0
\(246\) 8.50000 1.25836i 0.541940 0.0802303i
\(247\) −32.8963 −2.09314
\(248\) 5.33074 2.51564i 0.338502 0.159743i
\(249\) −2.17157 −0.137618
\(250\) 0 0
\(251\) 13.9778 0.882268 0.441134 0.897441i \(-0.354576\pi\)
0.441134 + 0.897441i \(0.354576\pi\)
\(252\) −2.50717 3.59586i −0.157937 0.226518i
\(253\) 11.0711i 0.696032i
\(254\) 7.82843 1.15894i 0.491199 0.0727185i
\(255\) 0 0
\(256\) 6.15685 14.7680i 0.384803 0.922999i
\(257\) 23.3238 1.45490 0.727450 0.686161i \(-0.240706\pi\)
0.727450 + 0.686161i \(0.240706\pi\)
\(258\) −1.70785 11.5362i −0.106326 0.718211i
\(259\) −15.7042 + 5.11582i −0.975812 + 0.317881i
\(260\) 0 0
\(261\) 0.201010 0.0124422
\(262\) 18.2003 2.69442i 1.12442 0.166462i
\(263\) −27.9793 −1.72528 −0.862640 0.505819i \(-0.831190\pi\)
−0.862640 + 0.505819i \(0.831190\pi\)
\(264\) 10.5465 4.97703i 0.649094 0.306315i
\(265\) 0 0
\(266\) 9.40721 + 18.8972i 0.576793 + 1.15866i
\(267\) 18.2277 1.11552
\(268\) 14.2297 4.30761i 0.869217 0.263129i
\(269\) 2.41526i 0.147261i −0.997286 0.0736305i \(-0.976541\pi\)
0.997286 0.0736305i \(-0.0234585\pi\)
\(270\) 0 0
\(271\) −27.2404 −1.65474 −0.827368 0.561660i \(-0.810163\pi\)
−0.827368 + 0.561660i \(0.810163\pi\)
\(272\) −13.7235 + 9.14695i −0.832107 + 0.554615i
\(273\) −21.6160 + 7.04163i −1.30826 + 0.426179i
\(274\) −0.721825 4.87579i −0.0436071 0.294557i
\(275\) 0 0
\(276\) 3.37887 + 11.1617i 0.203384 + 0.671855i
\(277\) 6.10051i 0.366544i −0.983062 0.183272i \(-0.941331\pi\)
0.983062 0.183272i \(-0.0586689\pi\)
\(278\) 3.76940 0.558032i 0.226074 0.0334685i
\(279\) 1.72646 0.103360
\(280\) 0 0
\(281\) 32.9706 1.96686 0.983429 0.181291i \(-0.0580277\pi\)
0.983429 + 0.181291i \(0.0580277\pi\)
\(282\) 12.8890 1.90812i 0.767526 0.113627i
\(283\) 31.6613i 1.88207i −0.338314 0.941033i \(-0.609856\pi\)
0.338314 0.941033i \(-0.390144\pi\)
\(284\) −4.19239 13.8491i −0.248772 0.821791i
\(285\) 0 0
\(286\) 3.37887 + 22.8236i 0.199797 + 1.34959i
\(287\) 10.3722 3.37887i 0.612254 0.199448i
\(288\) 3.47682 3.14214i 0.204874 0.185152i
\(289\) 0 0
\(290\) 0 0
\(291\) 12.1518i 0.712353i
\(292\) 23.6775 7.16766i 1.38562 0.419455i
\(293\) −16.4924 −0.963498 −0.481749 0.876309i \(-0.659998\pi\)
−0.481749 + 0.876309i \(0.659998\pi\)
\(294\) 10.2265 + 10.4035i 0.596419 + 0.606747i
\(295\) 0 0
\(296\) −7.53553 15.9681i −0.437994 0.928127i
\(297\) 15.7850 0.915939
\(298\) −2.79793 + 0.414214i −0.162080 + 0.0239947i
\(299\) −23.0723 −1.33431
\(300\) 0 0
\(301\) −4.58579 14.0772i −0.264320 0.811394i
\(302\) 0.339446 + 2.29289i 0.0195329 + 0.131941i
\(303\) −3.55919 −0.204470
\(304\) −18.7779 + 12.5158i −1.07699 + 0.717832i
\(305\) 0 0
\(306\) −4.77844 + 0.707413i −0.273165 + 0.0404401i
\(307\) 18.6515i 1.06450i −0.846589 0.532248i \(-0.821348\pi\)
0.846589 0.532248i \(-0.178652\pi\)
\(308\) 12.1447 8.46774i 0.692008 0.482494i
\(309\) 10.4853 0.596487
\(310\) 0 0
\(311\) 11.7890 0.668493 0.334247 0.942486i \(-0.391518\pi\)
0.334247 + 0.942486i \(0.391518\pi\)
\(312\) −10.3722 21.9792i −0.587212 1.24433i
\(313\) −4.83052 −0.273037 −0.136519 0.990638i \(-0.543591\pi\)
−0.136519 + 0.990638i \(0.543591\pi\)
\(314\) −31.2296 + 4.62332i −1.76239 + 0.260909i
\(315\) 0 0
\(316\) 4.58579 + 15.1486i 0.257971 + 0.852176i
\(317\) 25.6569i 1.44103i 0.693438 + 0.720516i \(0.256095\pi\)
−0.693438 + 0.720516i \(0.743905\pi\)
\(318\) 25.2389 3.73643i 1.41532 0.209528i
\(319\) 0.678892i 0.0380107i
\(320\) 0 0
\(321\) 19.2007i 1.07168i
\(322\) 6.59790 + 13.2538i 0.367686 + 0.738606i
\(323\) 23.2612 1.29429
\(324\) −11.1569 + 3.37740i −0.619825 + 0.187634i
\(325\) 0 0
\(326\) −30.6421 + 4.53635i −1.69711 + 0.251245i
\(327\) 4.16804i 0.230493i
\(328\) 4.97703 + 10.5465i 0.274810 + 0.582334i
\(329\) 15.7279 5.12354i 0.867108 0.282470i
\(330\) 0 0
\(331\) 28.8571i 1.58613i 0.609139 + 0.793064i \(0.291515\pi\)
−0.609139 + 0.793064i \(0.708485\pi\)
\(332\) −0.853923 2.82083i −0.0468651 0.154813i
\(333\) 5.17157i 0.283400i
\(334\) 3.55765 + 24.0312i 0.194666 + 1.31493i
\(335\) 0 0
\(336\) −9.65975 + 12.2436i −0.526983 + 0.667942i
\(337\) 14.7990i 0.806152i 0.915166 + 0.403076i \(0.132059\pi\)
−0.915166 + 0.403076i \(0.867941\pi\)
\(338\) 29.3783 4.34924i 1.59797 0.236568i
\(339\) −26.9876 −1.46576
\(340\) 0 0
\(341\) 5.83095i 0.315764i
\(342\) −6.53836 + 0.967957i −0.353554 + 0.0523411i
\(343\) 15.0080 + 10.8517i 0.810356 + 0.585938i
\(344\) 14.3137 6.75481i 0.771743 0.364195i
\(345\) 0 0
\(346\) −19.6935 + 2.91548i −1.05873 + 0.156737i
\(347\) −19.9832 −1.07276 −0.536378 0.843978i \(-0.680208\pi\)
−0.536378 + 0.843978i \(0.680208\pi\)
\(348\) −0.207196 0.684449i −0.0111069 0.0366903i
\(349\) 14.0772i 0.753533i −0.926308 0.376767i \(-0.877036\pi\)
0.926308 0.376767i \(-0.122964\pi\)
\(350\) 0 0
\(351\) 32.8963i 1.75587i
\(352\) 10.6123 + 11.7426i 0.565635 + 0.625885i
\(353\) −11.6619 −0.620701 −0.310350 0.950622i \(-0.600446\pi\)
−0.310350 + 0.950622i \(0.600446\pi\)
\(354\) 0.899495 + 6.07591i 0.0478076 + 0.322931i
\(355\) 0 0
\(356\) 7.16766 + 23.6775i 0.379885 + 1.25491i
\(357\) 15.2848 4.97918i 0.808957 0.263526i
\(358\) −2.21846 14.9853i −0.117249 0.791997i
\(359\) 20.4633i 1.08001i −0.841662 0.540005i \(-0.818422\pi\)
0.841662 0.540005i \(-0.181578\pi\)
\(360\) 0 0
\(361\) 12.8284 0.675180
\(362\) −4.12311 27.8508i −0.216706 1.46380i
\(363\) 4.67371i 0.245306i
\(364\) −17.6470 25.3098i −0.924952 1.32659i
\(365\) 0 0
\(366\) 24.0416 3.55919i 1.25668 0.186042i
\(367\) 15.9570i 0.832951i 0.909147 + 0.416476i \(0.136735\pi\)
−0.909147 + 0.416476i \(0.863265\pi\)
\(368\) −13.1702 + 8.77817i −0.686542 + 0.457594i
\(369\) 3.41569i 0.177814i
\(370\) 0 0
\(371\) 30.7980 10.0328i 1.59895 0.520876i
\(372\) −1.77959 5.87868i −0.0922677 0.304795i
\(373\) 13.4142i 0.694562i −0.937761 0.347281i \(-0.887105\pi\)
0.937761 0.347281i \(-0.112895\pi\)
\(374\) −2.38922 16.1387i −0.123544 0.834513i
\(375\) 0 0
\(376\) 7.54691 + 15.9922i 0.389202 + 0.824735i
\(377\) 1.41483 0.0728673
\(378\) −18.8972 + 9.40721i −0.971965 + 0.483855i
\(379\) 4.15572i 0.213465i 0.994288 + 0.106732i \(0.0340388\pi\)
−0.994288 + 0.106732i \(0.965961\pi\)
\(380\) 0 0
\(381\) 8.24621i 0.422466i
\(382\) 5.11582 + 34.5563i 0.261748 + 1.76806i
\(383\) 18.3986i 0.940126i −0.882633 0.470063i \(-0.844231\pi\)
0.882633 0.470063i \(-0.155769\pi\)
\(384\) −14.2830 8.59992i −0.728874 0.438863i
\(385\) 0 0
\(386\) 1.72183 + 11.6306i 0.0876386 + 0.591982i
\(387\) 4.63577 0.235649
\(388\) −15.7850 + 4.77844i −0.801362 + 0.242588i
\(389\) −15.5563 −0.788738 −0.394369 0.918952i \(-0.629037\pi\)
−0.394369 + 0.918952i \(0.629037\pi\)
\(390\) 0 0
\(391\) 16.3146 0.825065
\(392\) −9.49268 + 17.3750i −0.479453 + 0.877568i
\(393\) 19.1716i 0.967078i
\(394\) −0.514719 3.47682i −0.0259311 0.175160i
\(395\) 0 0
\(396\) 1.34315 + 4.43692i 0.0674956 + 0.222964i
\(397\) −18.9077 −0.948949 −0.474475 0.880269i \(-0.657362\pi\)
−0.474475 + 0.880269i \(0.657362\pi\)
\(398\) 24.5314 3.63170i 1.22965 0.182041i
\(399\) 20.9143 6.81305i 1.04702 0.341079i
\(400\) 0 0
\(401\) −22.4558 −1.12139 −0.560696 0.828022i \(-0.689466\pi\)
−0.560696 + 0.828022i \(0.689466\pi\)
\(402\) −2.26875 15.3250i −0.113155 0.764340i
\(403\) 12.1518 0.605326
\(404\) −1.39957 4.62332i −0.0696313 0.230019i
\(405\) 0 0
\(406\) −0.404592 0.812741i −0.0200795 0.0403357i
\(407\) 17.4665 0.865782
\(408\) 7.33428 + 15.5416i 0.363101 + 0.769425i
\(409\) 15.7850i 0.780518i −0.920705 0.390259i \(-0.872385\pi\)
0.920705 0.390259i \(-0.127615\pi\)
\(410\) 0 0
\(411\) −5.13600 −0.253340
\(412\) 4.12311 + 13.6202i 0.203131 + 0.671019i
\(413\) 2.41526 + 7.41421i 0.118847 + 0.364830i
\(414\) −4.58579 + 0.678892i −0.225379 + 0.0333657i
\(415\) 0 0
\(416\) 24.4719 22.1162i 1.19983 1.08433i
\(417\) 3.97056i 0.194439i
\(418\) −3.26918 22.0827i −0.159901 1.08010i
\(419\) −24.5460 −1.19915 −0.599575 0.800319i \(-0.704664\pi\)
−0.599575 + 0.800319i \(0.704664\pi\)
\(420\) 0 0
\(421\) −0.686292 −0.0334478 −0.0167239 0.999860i \(-0.505324\pi\)
−0.0167239 + 0.999860i \(0.505324\pi\)
\(422\) −0.298264 2.01472i −0.0145193 0.0980750i
\(423\) 5.17938i 0.251830i
\(424\) 14.7782 + 31.3155i 0.717692 + 1.52082i
\(425\) 0 0
\(426\) −14.9150 + 2.20806i −0.722636 + 0.106981i
\(427\) 29.3371 9.55688i 1.41972 0.462490i
\(428\) −24.9414 + 7.55025i −1.20559 + 0.364955i
\(429\) 24.0416 1.16074
\(430\) 0 0
\(431\) 8.19496i 0.394737i −0.980329 0.197369i \(-0.936760\pi\)
0.980329 0.197369i \(-0.0632396\pi\)
\(432\) −12.5158 18.7779i −0.602168 0.903451i
\(433\) −4.12311 −0.198144 −0.0990719 0.995080i \(-0.531587\pi\)
−0.0990719 + 0.995080i \(0.531587\pi\)
\(434\) −3.47501 6.98057i −0.166806 0.335078i
\(435\) 0 0
\(436\) −5.41421 + 1.63899i −0.259294 + 0.0784934i
\(437\) 22.3234 1.06787
\(438\) −3.77509 25.5000i −0.180381 1.21844i
\(439\) 2.94725 0.140665 0.0703323 0.997524i \(-0.477594\pi\)
0.0703323 + 0.997524i \(0.477594\pi\)
\(440\) 0 0
\(441\) −4.68629 + 3.41569i −0.223157 + 0.162652i
\(442\) −33.6334 + 4.97918i −1.59978 + 0.236836i
\(443\) 1.83783 0.0873181 0.0436591 0.999046i \(-0.486098\pi\)
0.0436591 + 0.999046i \(0.486098\pi\)
\(444\) −17.6095 + 5.33074i −0.835708 + 0.252986i
\(445\) 0 0
\(446\) 0.178781 + 1.20763i 0.00846552 + 0.0571829i
\(447\) 2.94725i 0.139400i
\(448\) −19.7027 7.73333i −0.930864 0.365365i
\(449\) −10.6569 −0.502928 −0.251464 0.967867i \(-0.580912\pi\)
−0.251464 + 0.967867i \(0.580912\pi\)
\(450\) 0 0
\(451\) −11.5362 −0.543217
\(452\) −10.6123 35.0563i −0.499159 1.64891i
\(453\) 2.41526 0.113479
\(454\) −1.47363 9.95406i −0.0691607 0.467167i
\(455\) 0 0
\(456\) 10.0355 + 21.2657i 0.469957 + 0.995858i
\(457\) 29.4853i 1.37926i −0.724160 0.689632i \(-0.757772\pi\)
0.724160 0.689632i \(-0.242228\pi\)
\(458\) −2.91548 19.6935i −0.136231 0.920216i
\(459\) 23.2612i 1.08574i
\(460\) 0 0
\(461\) 2.41526i 0.112490i −0.998417 0.0562449i \(-0.982087\pi\)
0.998417 0.0562449i \(-0.0179128\pi\)
\(462\) −6.87508 13.8106i −0.319858 0.642528i
\(463\) −1.35778 −0.0631016 −0.0315508 0.999502i \(-0.510045\pi\)
−0.0315508 + 0.999502i \(0.510045\pi\)
\(464\) 0.807612 0.538289i 0.0374924 0.0249894i
\(465\) 0 0
\(466\) −3.27208 22.1023i −0.151576 1.02387i
\(467\) 7.62096i 0.352656i 0.984331 + 0.176328i \(0.0564220\pi\)
−0.984331 + 0.176328i \(0.943578\pi\)
\(468\) 9.24664 2.79914i 0.427426 0.129391i
\(469\) −6.09188 18.7005i −0.281297 0.863508i
\(470\) 0 0
\(471\) 32.8963i 1.51578i
\(472\) −7.53880 + 3.55765i −0.347001 + 0.163754i
\(473\) 15.6569i 0.719903i
\(474\) 16.3146 2.41526i 0.749355 0.110937i
\(475\) 0 0
\(476\) 12.4783 + 17.8967i 0.571941 + 0.820295i
\(477\) 10.1421i 0.464376i
\(478\) 3.47682 + 23.4853i 0.159026 + 1.07419i
\(479\) 8.84175 0.403990 0.201995 0.979387i \(-0.435258\pi\)
0.201995 + 0.979387i \(0.435258\pi\)
\(480\) 0 0
\(481\) 36.4005i 1.65972i
\(482\) −3.26918 22.0827i −0.148907 1.00584i
\(483\) 14.6686 4.77844i 0.667442 0.217426i
\(484\) 6.07107 1.83783i 0.275958 0.0835379i
\(485\) 0 0
\(486\) −1.72646 11.6619i −0.0783138 0.528995i
\(487\) 3.67567 0.166560 0.0832802 0.996526i \(-0.473460\pi\)
0.0832802 + 0.996526i \(0.473460\pi\)
\(488\) 14.0772 + 29.8301i 0.637243 + 1.35034i
\(489\) 32.2774i 1.45964i
\(490\) 0 0
\(491\) 29.3371i 1.32397i −0.749519 0.661983i \(-0.769715\pi\)
0.749519 0.661983i \(-0.230285\pi\)
\(492\) 11.6306 3.52082i 0.524348 0.158731i
\(493\) −1.00043 −0.0450572
\(494\) −46.0208 + 6.81305i −2.07057 + 0.306533i
\(495\) 0 0
\(496\) 6.93651 4.62332i 0.311459 0.207593i
\(497\) −18.2003 + 5.92893i −0.816394 + 0.265949i
\(498\) −3.03796 + 0.449747i −0.136134 + 0.0201537i
\(499\) 16.7876i 0.751516i −0.926718 0.375758i \(-0.877382\pi\)
0.926718 0.375758i \(-0.122618\pi\)
\(500\) 0 0
\(501\) 25.3137 1.13093
\(502\) 19.5544 2.89489i 0.872756 0.129205i
\(503\) 31.0509i 1.38449i 0.721663 + 0.692245i \(0.243378\pi\)
−0.721663 + 0.692245i \(0.756622\pi\)
\(504\) −4.25218 4.51124i −0.189407 0.200947i
\(505\) 0 0
\(506\) −2.29289 15.4881i −0.101932 0.688528i
\(507\) 30.9461i 1.37437i
\(508\) 10.7117 3.24264i 0.475254 0.143869i
\(509\) 8.24621i 0.365507i −0.983159 0.182753i \(-0.941499\pi\)
0.983159 0.182753i \(-0.0585010\pi\)
\(510\) 0 0
\(511\) −10.1366 31.1167i −0.448417 1.37652i
\(512\) 5.55468 21.9350i 0.245485 0.969400i
\(513\) 31.8284i 1.40526i
\(514\) 32.6292 4.83052i 1.43921 0.213065i
\(515\) 0 0
\(516\) −4.77844 15.7850i −0.210359 0.694896i
\(517\) −17.4929 −0.769335
\(518\) −20.9101 + 10.4093i −0.918739 + 0.457359i
\(519\) 20.7445i 0.910581i
\(520\) 0 0
\(521\) 28.8617i 1.26446i 0.774782 + 0.632228i \(0.217859\pi\)
−0.774782 + 0.632228i \(0.782141\pi\)
\(522\) 0.281206 0.0416306i 0.0123081 0.00182212i
\(523\) 4.42088i 0.193311i −0.995318 0.0966557i \(-0.969185\pi\)
0.995318 0.0966557i \(-0.0308146\pi\)
\(524\) 24.9035 7.53880i 1.08792 0.329334i
\(525\) 0 0
\(526\) −39.1421 + 5.79471i −1.70668 + 0.252661i
\(527\) −8.59264 −0.374301
\(528\) 13.7235 9.14695i 0.597237 0.398070i
\(529\) −7.34315 −0.319267
\(530\) 0 0
\(531\) −2.44158 −0.105956
\(532\) 17.0741 + 24.4882i 0.740256 + 1.06170i
\(533\) 24.0416i 1.04136i
\(534\) 25.5000 3.77509i 1.10349 0.163364i
\(535\) 0 0
\(536\) 19.0147 8.97327i 0.821311 0.387586i
\(537\) −15.7850 −0.681173
\(538\) −0.500217 3.37887i −0.0215659 0.145673i
\(539\) −11.5362 15.8275i −0.496898 0.681739i
\(540\) 0 0
\(541\) 10.2426 0.440366 0.220183 0.975459i \(-0.429335\pi\)
0.220183 + 0.975459i \(0.429335\pi\)
\(542\) −38.1084 + 5.64167i −1.63690 + 0.242330i
\(543\) −29.3371 −1.25898
\(544\) −17.3043 + 15.6385i −0.741914 + 0.670495i
\(545\) 0 0
\(546\) −28.7816 + 14.3278i −1.23174 + 0.613174i
\(547\) −13.0296 −0.557104 −0.278552 0.960421i \(-0.589854\pi\)
−0.278552 + 0.960421i \(0.589854\pi\)
\(548\) −2.01962 6.67157i −0.0862738 0.284995i
\(549\) 9.66104i 0.412323i
\(550\) 0 0
\(551\) −1.36890 −0.0583170
\(552\) 7.03858 + 14.9150i 0.299582 + 0.634826i
\(553\) 19.9081 6.48528i 0.846579 0.275782i
\(554\) −1.26346 8.53440i −0.0536791 0.362592i
\(555\) 0 0
\(556\) 5.15769 1.56134i 0.218735 0.0662154i
\(557\) 10.6863i 0.452793i 0.974035 + 0.226396i \(0.0726945\pi\)
−0.974035 + 0.226396i \(0.927306\pi\)
\(558\) 2.41526 0.357562i 0.102246 0.0151368i
\(559\) 32.6292 1.38007
\(560\) 0 0
\(561\) −17.0000 −0.717741
\(562\) 46.1247 6.82843i 1.94565 0.288040i
\(563\) 13.7249i 0.578436i 0.957263 + 0.289218i \(0.0933953\pi\)
−0.957263 + 0.289218i \(0.906605\pi\)
\(564\) 17.6360 5.33878i 0.742611 0.224803i
\(565\) 0 0
\(566\) −6.55726 44.2930i −0.275622 1.86178i
\(567\) 4.77637 + 14.6622i 0.200589 + 0.615755i
\(568\) −8.73324 18.5061i −0.366439 0.776499i
\(569\) −3.68629 −0.154537 −0.0772687 0.997010i \(-0.524620\pi\)
−0.0772687 + 0.997010i \(0.524620\pi\)
\(570\) 0 0
\(571\) 1.35778i 0.0568215i −0.999596 0.0284108i \(-0.990955\pi\)
0.999596 0.0284108i \(-0.00904464\pi\)
\(572\) 9.45384 + 31.2296i 0.395285 + 1.30578i
\(573\) 36.4005 1.52065
\(574\) 13.8106 6.87508i 0.576444 0.286960i
\(575\) 0 0
\(576\) 4.21320 5.11582i 0.175550 0.213159i
\(577\) −7.53880 −0.313844 −0.156922 0.987611i \(-0.550157\pi\)
−0.156922 + 0.987611i \(0.550157\pi\)
\(578\) 0 0
\(579\) 12.2513 0.509146
\(580\) 0 0
\(581\) −3.70711 + 1.20763i −0.153797 + 0.0501009i
\(582\) 2.51673 + 17.0000i 0.104322 + 0.704673i
\(583\) −34.2541 −1.41866
\(584\) 31.6396 14.9311i 1.30925 0.617853i
\(585\) 0 0
\(586\) −23.0723 + 3.41569i −0.953110 + 0.141101i
\(587\) 0.967957i 0.0399519i 0.999800 + 0.0199759i \(0.00635896\pi\)
−0.999800 + 0.0199759i \(0.993641\pi\)
\(588\) 16.4611 + 12.4362i 0.678845 + 0.512862i
\(589\) −11.7574 −0.484454
\(590\) 0 0
\(591\) −3.66237 −0.150650
\(592\) −13.8491 20.7782i −0.569193 0.853978i
\(593\) 24.0312 0.986844 0.493422 0.869790i \(-0.335746\pi\)
0.493422 + 0.869790i \(0.335746\pi\)
\(594\) 22.0827 3.26918i 0.906064 0.134136i
\(595\) 0 0
\(596\) −3.82843 + 1.15894i −0.156818 + 0.0474721i
\(597\) 25.8406i 1.05759i
\(598\) −32.2774 + 4.77844i −1.31992 + 0.195405i
\(599\) 20.7445i 0.847596i 0.905757 + 0.423798i \(0.139303\pi\)
−0.905757 + 0.423798i \(0.860697\pi\)
\(600\) 0 0
\(601\) 15.7850i 0.643884i −0.946759 0.321942i \(-0.895664\pi\)
0.946759 0.321942i \(-0.104336\pi\)
\(602\) −9.33084 18.7437i −0.380297 0.763937i
\(603\) 6.15828 0.250784
\(604\) 0.949747 + 3.13738i 0.0386447 + 0.127658i
\(605\) 0 0
\(606\) −4.97918 + 0.737132i −0.202266 + 0.0299439i
\(607\) 16.6722i 0.676703i −0.941020 0.338351i \(-0.890131\pi\)
0.941020 0.338351i \(-0.109869\pi\)
\(608\) −23.6775 + 21.3982i −0.960250 + 0.867814i
\(609\) −0.899495 + 0.293020i −0.0364494 + 0.0118738i
\(610\) 0 0
\(611\) 36.4555i 1.47483i
\(612\) −6.53836 + 1.97929i −0.264298 + 0.0800082i
\(613\) 17.1127i 0.691175i −0.938386 0.345588i \(-0.887680\pi\)
0.938386 0.345588i \(-0.112320\pi\)
\(614\) −3.86285 26.0928i −0.155892 1.05302i
\(615\) 0 0
\(616\) 15.2363 14.3613i 0.613887 0.578634i
\(617\) 22.0000i 0.885687i −0.896599 0.442843i \(-0.853970\pi\)
0.896599 0.442843i \(-0.146030\pi\)
\(618\) 14.6686 2.17157i 0.590056 0.0873535i
\(619\) 18.9043 0.759828 0.379914 0.925022i \(-0.375954\pi\)
0.379914 + 0.925022i \(0.375954\pi\)
\(620\) 0 0
\(621\) 22.3234i 0.895806i
\(622\) 16.4924 2.44158i 0.661286 0.0978986i
\(623\) 31.1167 10.1366i 1.24666 0.406114i
\(624\) −19.0624 28.6000i −0.763109 1.14492i
\(625\) 0 0
\(626\) −6.75773 + 1.00043i −0.270093 + 0.0399854i
\(627\) −23.2612 −0.928963
\(628\) −42.7317 + 12.9357i −1.70518 + 0.516192i
\(629\) 25.7391i 1.02628i
\(630\) 0 0
\(631\) 11.8706i 0.472562i 0.971685 + 0.236281i \(0.0759286\pi\)
−0.971685 + 0.236281i \(0.924071\pi\)
\(632\) 9.55274 + 20.2426i 0.379988 + 0.805209i
\(633\) −2.12224 −0.0843514
\(634\) 5.31371 + 35.8931i 0.211034 + 1.42550i
\(635\) 0 0
\(636\) 34.5345 10.4543i 1.36938 0.414539i
\(637\) −32.9848 + 24.0416i −1.30691 + 0.952564i
\(638\) 0.140603 + 0.949747i 0.00556653 + 0.0376009i
\(639\) 5.99355i 0.237101i
\(640\) 0 0
\(641\) −21.1716 −0.836227 −0.418113 0.908395i \(-0.637309\pi\)
−0.418113 + 0.908395i \(0.637309\pi\)
\(642\) 3.97660 + 26.8611i 0.156944 + 1.06012i
\(643\) 25.5139i 1.00617i −0.864237 0.503086i \(-0.832198\pi\)
0.864237 0.503086i \(-0.167802\pi\)
\(644\) 11.9752 + 17.1752i 0.471889 + 0.676797i
\(645\) 0 0
\(646\) 32.5416 4.81755i 1.28033 0.189544i
\(647\) 46.8598i 1.84225i 0.389268 + 0.921125i \(0.372728\pi\)
−0.389268 + 0.921125i \(0.627272\pi\)
\(648\) −14.9086 + 7.03553i −0.585664 + 0.276382i
\(649\) 8.24621i 0.323692i
\(650\) 0 0
\(651\) −7.72569 + 2.51673i −0.302794 + 0.0986383i
\(652\) −41.9278 + 12.6924i −1.64202 + 0.497072i
\(653\) 29.5563i 1.15663i −0.815814 0.578315i \(-0.803711\pi\)
0.815814 0.578315i \(-0.196289\pi\)
\(654\) 0.863230 + 5.83095i 0.0337550 + 0.228008i
\(655\) 0 0
\(656\) 9.14695 + 13.7235i 0.357128 + 0.535811i
\(657\) 10.2471 0.399777
\(658\) 20.9417 10.4250i 0.816393 0.406409i
\(659\) 6.47360i 0.252176i 0.992019 + 0.126088i \(0.0402421\pi\)
−0.992019 + 0.126088i \(0.959758\pi\)
\(660\) 0 0
\(661\) 27.1539i 1.05616i 0.849193 + 0.528082i \(0.177089\pi\)
−0.849193 + 0.528082i \(0.822911\pi\)
\(662\) 5.97649 + 40.3701i 0.232283 + 1.56903i
\(663\) 35.4284i 1.37592i
\(664\) −1.77882 3.76940i −0.0690317 0.146281i
\(665\) 0 0
\(666\) −1.07107 7.23486i −0.0415030 0.280345i
\(667\) −0.960099 −0.0371752
\(668\) 9.95406 + 32.8821i 0.385134 + 1.27224i
\(669\) 1.27208 0.0491814
\(670\) 0 0
\(671\) −32.6292 −1.25964
\(672\) −10.9779 + 19.1290i −0.423483 + 0.737916i
\(673\) 4.00000i 0.154189i 0.997024 + 0.0770943i \(0.0245643\pi\)
−0.997024 + 0.0770943i \(0.975436\pi\)
\(674\) 3.06497 + 20.7033i 0.118058 + 0.797461i
\(675\) 0 0
\(676\) 40.1985 12.1689i 1.54610 0.468034i
\(677\) −11.6619 −0.448203 −0.224102 0.974566i \(-0.571945\pi\)
−0.224102 + 0.974566i \(0.571945\pi\)
\(678\) −37.7547 + 5.58931i −1.44996 + 0.214656i
\(679\) 6.75773 + 20.7445i 0.259338 + 0.796100i
\(680\) 0 0
\(681\) −10.4853 −0.401797
\(682\) 1.20763 + 8.15731i 0.0462425 + 0.312359i
\(683\) −26.5392 −1.01549 −0.507747 0.861506i \(-0.669521\pi\)
−0.507747 + 0.861506i \(0.669521\pi\)
\(684\) −8.94648 + 2.70828i −0.342077 + 0.103554i
\(685\) 0 0
\(686\) 23.2432 + 12.0729i 0.887428 + 0.460947i
\(687\) −20.7445 −0.791451
\(688\) 18.6254 12.4142i 0.710088 0.473287i
\(689\) 71.3862i 2.71960i
\(690\) 0 0
\(691\) 48.3334 1.83869 0.919345 0.393452i \(-0.128719\pi\)
0.919345 + 0.393452i \(0.128719\pi\)
\(692\) −26.9467 + 8.15731i −1.02436 + 0.310094i
\(693\) 5.83095 1.89949i 0.221500 0.0721558i
\(694\) −27.9558 + 4.13866i −1.06119 + 0.157101i
\(695\) 0 0
\(696\) −0.431615 0.914610i −0.0163603 0.0346682i
\(697\) 17.0000i 0.643921i
\(698\) −2.91548 19.6935i −0.110352 0.745409i
\(699\) −23.2818 −0.880598
\(700\) 0 0
\(701\) −16.8284 −0.635601 −0.317800 0.948158i \(-0.602944\pi\)
−0.317800 + 0.948158i \(0.602944\pi\)
\(702\) −6.81305 46.0208i −0.257142 1.73694i
\(703\) 35.2189i 1.32831i
\(704\) 17.2782 + 14.2297i 0.651196 + 0.536302i
\(705\) 0 0
\(706\) −16.3146 + 2.41526i −0.614008 + 0.0908995i
\(707\) −6.07591 + 1.97929i −0.228508 + 0.0744390i
\(708\) 2.51673 + 8.31371i 0.0945844 + 0.312448i
\(709\) 28.0000 1.05156 0.525781 0.850620i \(-0.323773\pi\)
0.525781 + 0.850620i \(0.323773\pi\)
\(710\) 0 0
\(711\) 6.55596i 0.245868i
\(712\) 14.9311 + 31.6396i 0.559566 + 1.18574i
\(713\) −8.24621 −0.308823
\(714\) 20.3517 10.1313i 0.761643 0.379154i
\(715\) 0 0
\(716\) −6.20711 20.5044i −0.231970 0.766287i
\(717\) 24.7386 0.923881
\(718\) −4.23808 28.6274i −0.158164 1.06837i
\(719\) 36.9454 1.37783 0.688915 0.724842i \(-0.258087\pi\)
0.688915 + 0.724842i \(0.258087\pi\)
\(720\) 0 0
\(721\) 17.8995 5.83095i 0.666612 0.217156i
\(722\) 17.9465 2.65685i 0.667901 0.0988779i
\(723\) −23.2612 −0.865093
\(724\) −11.5362 38.1084i −0.428738 1.41629i
\(725\) 0 0
\(726\) −0.967957 6.53836i −0.0359243 0.242661i
\(727\) 32.2717i 1.19689i 0.801164 + 0.598445i \(0.204214\pi\)
−0.801164 + 0.598445i \(0.795786\pi\)
\(728\) −29.9293 31.7527i −1.10925 1.17683i
\(729\) −29.7696 −1.10258
\(730\) 0 0
\(731\) −23.0723 −0.853361
\(732\) 32.8963 9.95837i 1.21588 0.368072i
\(733\) 24.7386 0.913742 0.456871 0.889533i \(-0.348970\pi\)
0.456871 + 0.889533i \(0.348970\pi\)
\(734\) 3.30481 + 22.3234i 0.121983 + 0.823971i
\(735\) 0 0
\(736\) −16.6066 + 15.0080i −0.612127 + 0.553202i
\(737\) 20.7990i 0.766141i
\(738\) 0.707413 + 4.77844i 0.0260402 + 0.175897i
\(739\) 18.7078i 0.688177i −0.938937 0.344089i \(-0.888188\pi\)
0.938937 0.344089i \(-0.111812\pi\)
\(740\) 0 0
\(741\) 48.4768i 1.78084i
\(742\) 41.0076 20.4140i 1.50543 0.749422i
\(743\) −16.5064 −0.605561 −0.302780 0.953060i \(-0.597915\pi\)
−0.302780 + 0.953060i \(0.597915\pi\)
\(744\) −3.70711 7.85551i −0.135909 0.287997i
\(745\) 0 0
\(746\) −2.77817 18.7660i −0.101716 0.687073i
\(747\) 1.22079i 0.0446664i
\(748\) −6.68488 22.0827i −0.244423 0.807423i
\(749\) 10.6777 + 32.7776i 0.390154 + 1.19767i
\(750\) 0 0
\(751\) 21.1422i 0.771488i 0.922606 + 0.385744i \(0.126055\pi\)
−0.922606 + 0.385744i \(0.873945\pi\)
\(752\) 13.8700 + 20.8095i 0.505786 + 0.758846i
\(753\) 20.5980i 0.750632i
\(754\) 1.97929 0.293020i 0.0720816 0.0106712i
\(755\) 0 0
\(756\) −24.4882 + 17.0741i −0.890627 + 0.620979i
\(757\) 12.5858i 0.457438i −0.973492 0.228719i \(-0.926546\pi\)
0.973492 0.228719i \(-0.0734537\pi\)
\(758\) 0.860677 + 5.81371i 0.0312612 + 0.211163i
\(759\) −16.3146 −0.592183
\(760\) 0 0
\(761\) 39.1088i 1.41769i 0.705363 + 0.708847i \(0.250784\pi\)
−0.705363 + 0.708847i \(0.749216\pi\)
\(762\) −1.70785 11.5362i −0.0618687 0.417911i
\(763\) 2.31788 + 7.11529i 0.0839130 + 0.257591i
\(764\) 14.3137 + 47.2836i 0.517852 + 1.71066i
\(765\) 0 0
\(766\) −3.81048 25.7391i −0.137678 0.929990i
\(767\) −17.1853 −0.620525
\(768\) −21.7625 9.07290i −0.785286 0.327390i
\(769\) 40.5236i 1.46132i −0.682742 0.730660i \(-0.739212\pi\)
0.682742 0.730660i \(-0.260788\pi\)
\(770\) 0 0
\(771\) 34.3706i 1.23783i
\(772\) 4.81755 + 15.9142i 0.173387 + 0.572765i
\(773\) 36.4005 1.30924 0.654618 0.755960i \(-0.272829\pi\)
0.654618 + 0.755960i \(0.272829\pi\)
\(774\) 6.48528 0.960099i 0.233109 0.0345100i
\(775\) 0 0
\(776\) −21.0930 + 9.95406i −0.757196 + 0.357330i
\(777\) 7.53880 + 23.1421i 0.270453 + 0.830219i
\(778\) −21.7628 + 3.22183i −0.780234 + 0.115508i
\(779\) 23.2612i 0.833419i
\(780\) 0 0
\(781\) 20.2426 0.724339
\(782\) 22.8236 3.37887i 0.816170 0.120828i
\(783\) 1.36890i 0.0489204i
\(784\) −9.68147 + 26.2730i −0.345767 + 0.938320i
\(785\) 0 0
\(786\) −3.97056 26.8204i −0.141625 0.956651i
\(787\) 20.6308i 0.735407i −0.929943 0.367704i \(-0.880144\pi\)
0.929943 0.367704i \(-0.119856\pi\)
\(788\) −1.44015 4.75736i −0.0513032 0.169474i
\(789\) 41.2311i 1.46786i
\(790\) 0 0
\(791\) −46.0706 + 15.0080i −1.63808 + 0.533623i
\(792\) 2.79793 + 5.92893i 0.0994202 + 0.210675i
\(793\) 68.0000i 2.41475i
\(794\) −26.4512 + 3.91591i −0.938718 + 0.138970i
\(795\) 0 0
\(796\) 33.5665 10.1613i 1.18973 0.360156i
\(797\) 26.7395 0.947162 0.473581 0.880750i \(-0.342961\pi\)
0.473581 + 0.880750i \(0.342961\pi\)
\(798\) 27.8473 13.8627i 0.985785 0.490735i
\(799\) 25.7779i 0.911957i
\(800\) 0 0
\(801\) 10.2471i 0.362063i
\(802\) −31.4150 + 4.65076i −1.10930 + 0.164224i
\(803\) 34.6085i 1.22131i
\(804\) −6.34781 20.9692i −0.223870 0.739528i
\(805\) 0 0
\(806\) 17.0000 2.51673i 0.598799 0.0886479i
\(807\) −3.55919 −0.125289
\(808\) −2.91548 6.17801i −0.102566 0.217342i
\(809\) 1.17157 0.0411903 0.0205952 0.999788i \(-0.493444\pi\)
0.0205952 + 0.999788i \(0.493444\pi\)
\(810\) 0 0
\(811\) −36.0821 −1.26702 −0.633508 0.773736i \(-0.718385\pi\)
−0.633508 + 0.773736i \(0.718385\pi\)
\(812\) −0.734334 1.05320i −0.0257701 0.0369602i
\(813\) 40.1421i 1.40785i
\(814\) 24.4350 3.61743i 0.856447 0.126791i
\(815\) 0 0
\(816\) 13.4792 + 20.2232i 0.471866 + 0.707955i
\(817\) −31.5700 −1.10450
\(818\) −3.26918 22.0827i −0.114304 0.772103i
\(819\) −3.95859 12.1518i −0.138324 0.424619i
\(820\) 0 0
\(821\) 14.5858 0.509047 0.254524 0.967067i \(-0.418081\pi\)
0.254524 + 0.967067i \(0.418081\pi\)
\(822\) −7.18509 + 1.06370i −0.250609 + 0.0371008i
\(823\) 49.1215 1.71227 0.856134 0.516755i \(-0.172860\pi\)
0.856134 + 0.516755i \(0.172860\pi\)
\(824\) 8.58892 + 18.2003i 0.299209 + 0.634036i
\(825\) 0 0
\(826\) 4.91440 + 9.87202i 0.170994 + 0.343491i
\(827\) 47.0024 1.63444 0.817218 0.576329i \(-0.195515\pi\)
0.817218 + 0.576329i \(0.195515\pi\)
\(828\) −6.27476 + 1.89949i −0.218063 + 0.0660120i
\(829\) 26.7395i 0.928701i 0.885651 + 0.464351i \(0.153712\pi\)
−0.885651 + 0.464351i \(0.846288\pi\)
\(830\) 0 0
\(831\) −8.98986 −0.311855
\(832\) 29.6550 36.0081i 1.02810 1.24836i
\(833\) 23.3238 17.0000i 0.808122 0.589015i
\(834\) −0.822330 5.55468i −0.0284750 0.192343i
\(835\) 0 0
\(836\) −9.14695 30.2159i −0.316354 1.04504i
\(837\) 11.7574i 0.406394i
\(838\) −34.3390 + 5.08364i −1.18622 + 0.175611i
\(839\) 37.6605 1.30018 0.650092 0.759855i \(-0.274730\pi\)
0.650092 + 0.759855i \(0.274730\pi\)
\(840\) 0 0
\(841\) −28.9411 −0.997970
\(842\) −0.960099 + 0.142136i −0.0330872 + 0.00489832i
\(843\) 48.5863i 1.67340i
\(844\) −0.834524 2.75675i −0.0287255 0.0948913i
\(845\) 0 0
\(846\) 1.07268 + 7.24578i 0.0368797 + 0.249115i
\(847\) −2.59909 7.97852i −0.0893058 0.274145i
\(848\) 27.1598 + 40.7487i 0.932672 + 1.39932i
\(849\) −46.6569 −1.60126
\(850\) 0 0
\(851\) 24.7013i 0.846751i
\(852\) −20.4083 + 6.17801i −0.699178 + 0.211655i
\(853\) −15.0776 −0.516247 −0.258124 0.966112i \(-0.583104\pi\)
−0.258124 + 0.966112i \(0.583104\pi\)
\(854\) 39.0623 19.4457i 1.33669 0.665417i
\(855\) 0 0
\(856\) −33.3284 + 15.7281i −1.13914 + 0.537575i
\(857\) 5.53793 0.189172 0.0945861 0.995517i \(-0.469847\pi\)
0.0945861 + 0.995517i \(0.469847\pi\)
\(858\) 33.6334 4.97918i 1.14823 0.169987i
\(859\) −36.3350 −1.23973 −0.619867 0.784707i \(-0.712813\pi\)
−0.619867 + 0.784707i \(0.712813\pi\)
\(860\) 0 0
\(861\) −4.97918 15.2848i −0.169690 0.520904i
\(862\) −1.69723 11.4645i −0.0578079 0.390481i
\(863\) 12.1518 0.413653 0.206827 0.978378i \(-0.433686\pi\)
0.206827 + 0.978378i \(0.433686\pi\)
\(864\) −21.3982 23.6775i −0.727983 0.805525i
\(865\) 0 0
\(866\) −5.76809 + 0.853923i −0.196008 + 0.0290175i
\(867\) 0 0
\(868\) −6.30714 9.04589i −0.214078 0.307037i
\(869\) −22.1421 −0.751121
\(870\) 0 0
\(871\) 43.3455 1.46871
\(872\) −7.23486 + 3.41421i −0.245003 + 0.115620i
\(873\) −6.83139 −0.231207
\(874\) 31.2296 4.62332i 1.05636 0.156386i
\(875\) 0 0
\(876\) −10.5624 34.8918i −0.356872 1.17888i
\(877\) 4.97056i 0.167844i −0.996472 0.0839220i \(-0.973255\pi\)
0.996472 0.0839220i \(-0.0267447\pi\)
\(878\) 4.12311 0.610396i 0.139148 0.0205999i
\(879\) 24.3037i 0.819742i
\(880\) 0 0
\(881\) 11.6619i 0.392900i −0.980514 0.196450i \(-0.937059\pi\)
0.980514 0.196450i \(-0.0629413\pi\)
\(882\) −5.84855 + 5.74900i −0.196931 + 0.193579i
\(883\) 7.99611 0.269091 0.134545 0.990907i \(-0.457043\pi\)
0.134545 + 0.990907i \(0.457043\pi\)
\(884\) −46.0208 + 13.9314i −1.54785 + 0.468564i
\(885\) 0 0
\(886\) 2.57107 0.380628i 0.0863767 0.0127874i
\(887\) 10.9258i 0.366852i −0.983034 0.183426i \(-0.941281\pi\)
0.983034 0.183426i \(-0.0587187\pi\)
\(888\) −23.5310 + 11.1046i −0.789649 + 0.372645i
\(889\) −4.58579 14.0772i −0.153802 0.472133i
\(890\) 0 0
\(891\) 16.3075i 0.546323i
\(892\) 0.500217 + 1.65241i 0.0167485 + 0.0553267i
\(893\) 35.2721i 1.18034i
\(894\) 0.610396 + 4.12311i 0.0204147 + 0.137897i
\(895\) 0 0
\(896\) −29.1650 6.73811i −0.974335 0.225104i
\(897\) 34.0000i 1.13523i
\(898\) −14.9086 + 2.20711i −0.497506 + 0.0736521i
\(899\) 0.505668 0.0168650
\(900\) 0 0
\(901\) 50.4777i 1.68166i
\(902\) −16.1387 + 2.38922i −0.537360 + 0.0795523i
\(903\) −20.7445 + 6.75773i −0.690333 + 0.224883i
\(904\) −22.1066 46.8448i −0.735255 1.55803i
\(905\) 0 0
\(906\) 3.37887 0.500217i 0.112255 0.0166186i
\(907\) 39.5687 1.31386 0.656929 0.753952i \(-0.271855\pi\)
0.656929 + 0.753952i \(0.271855\pi\)
\(908\) −4.12311 13.6202i −0.136830 0.452002i
\(909\) 2.00087i 0.0663645i
\(910\) 0 0
\(911\) 30.2972i 1.00379i −0.864928 0.501896i \(-0.832636\pi\)
0.864928 0.501896i \(-0.167364\pi\)
\(912\) 18.4436 + 27.6716i 0.610730 + 0.916297i
\(913\) 4.12311 0.136455
\(914\) −6.10660 41.2489i −0.201988 1.36439i
\(915\) 0 0
\(916\) −8.15731 26.9467i −0.269525 0.890344i
\(917\) −10.6615 32.7279i −0.352073 1.08077i
\(918\) 4.81755 + 32.5416i 0.159003 + 1.07403i
\(919\) 22.7811i 0.751481i 0.926725 + 0.375740i \(0.122612\pi\)
−0.926725 + 0.375740i \(0.877388\pi\)
\(920\) 0 0
\(921\) −27.4853 −0.905671
\(922\) −0.500217 3.37887i −0.0164738 0.111277i
\(923\) 42.1861i 1.38857i
\(924\) −12.4783 17.8967i −0.410505 0.588759i
\(925\) 0 0
\(926\) −1.89949 + 0.281206i −0.0624213 + 0.00924102i
\(927\) 5.89450i 0.193601i
\(928\) 1.01834 0.920310i 0.0334286 0.0302107i
\(929\) 39.8162i 1.30633i −0.757216 0.653164i \(-0.773441\pi\)
0.757216 0.653164i \(-0.226559\pi\)
\(930\) 0 0
\(931\) 31.9141 23.2612i 1.04594 0.762355i
\(932\) −9.15505 30.2426i −0.299884 0.990631i
\(933\) 17.3726i 0.568753i
\(934\) 1.57835 + 10.6615i 0.0516453 + 0.348854i
\(935\) 0 0
\(936\) 12.3560 5.83095i 0.403869 0.190591i
\(937\) −10.9545 −0.357868 −0.178934 0.983861i \(-0.557265\pi\)
−0.178934 + 0.983861i \(0.557265\pi\)
\(938\) −12.3953 24.8997i −0.404722 0.813003i
\(939\) 7.11838i 0.232299i
\(940\) 0 0
\(941\) 24.7386i 0.806456i 0.915099 + 0.403228i \(0.132112\pi\)
−0.915099 + 0.403228i \(0.867888\pi\)
\(942\) 6.81305 + 46.0208i 0.221981 + 1.49944i
\(943\) 16.3146i 0.531277i
\(944\) −9.80971 + 6.53836i −0.319279 + 0.212806i
\(945\) 0 0
\(946\) 3.24264 + 21.9034i 0.105427 + 0.712141i
\(947\) −19.5032 −0.633768 −0.316884 0.948464i \(-0.602637\pi\)
−0.316884 + 0.948464i \(0.602637\pi\)
\(948\) 22.3234 6.75773i 0.725029 0.219481i
\(949\) 72.1249 2.34127
\(950\) 0 0
\(951\) 37.8086 1.22603
\(952\) 21.1632 + 22.4526i 0.685904 + 0.727692i
\(953\) 53.7696i 1.74177i 0.491490 + 0.870883i \(0.336453\pi\)
−0.491490 + 0.870883i \(0.663547\pi\)
\(954\) 2.10051 + 14.1885i 0.0680064 + 0.459370i
\(955\) 0 0
\(956\) 9.72792 + 32.1350i 0.314623 + 1.03932i
\(957\) 1.00043 0.0323394
\(958\) 12.3693 1.83119i 0.399634 0.0591630i
\(959\) −8.76770 + 2.85617i −0.283124 + 0.0922306i
\(960\) 0 0
\(961\) −26.6569 −0.859899
\(962\) −7.53880 50.9231i −0.243061 1.64183i
\(963\) −10.7940 −0.347833
\(964\) −9.14695 30.2159i −0.294604 0.973188i
\(965\) 0 0
\(966\) 19.5312 9.72283i 0.628405 0.312827i
\(967\) 9.55274 0.307195 0.153598 0.988133i \(-0.450914\pi\)
0.153598 + 0.988133i \(0.450914\pi\)
\(968\) 8.11259 3.82843i 0.260749 0.123050i
\(969\) 34.2783i 1.10118i
\(970\) 0 0
\(971\) 4.92655 0.158100 0.0790502 0.996871i \(-0.474811\pi\)
0.0790502 + 0.996871i \(0.474811\pi\)
\(972\) −4.83052 15.9570i −0.154939 0.511823i
\(973\) −2.20806 6.77817i −0.0707872 0.217298i
\(974\) 5.14214 0.761256i 0.164765 0.0243922i
\(975\) 0 0
\(976\) 25.8715 + 38.8158i 0.828126 + 1.24246i
\(977\) 7.28427i 0.233044i 0.993188 + 0.116522i \(0.0371746\pi\)
−0.993188 + 0.116522i \(0.962825\pi\)
\(978\) 6.68488 + 45.1550i 0.213759 + 1.44390i
\(979\) −34.6085 −1.10609
\(980\) 0 0
\(981\) −2.34315 −0.0748109
\(982\) −6.07591 41.0416i −0.193890 1.30969i
\(983\) 11.6409i 0.371287i −0.982617 0.185644i \(-0.940563\pi\)
0.982617 0.185644i \(-0.0594370\pi\)
\(984\) 15.5416 7.33428i 0.495449 0.233808i
\(985\) 0 0
\(986\) −1.39957 + 0.207196i −0.0445715 + 0.00659848i
\(987\) −7.55018 23.1771i −0.240325 0.737734i
\(988\) −62.9705 + 19.0624i −2.00336 + 0.606457i
\(989\) −22.1421 −0.704079
\(990\) 0 0
\(991\) 6.27476i 0.199324i −0.995021 0.0996621i \(-0.968224\pi\)
0.995021 0.0996621i \(-0.0317762\pi\)
\(992\) 8.74643 7.90447i 0.277699 0.250967i
\(993\) 42.5245 1.34947
\(994\) −24.2336 + 12.0638i −0.768644 + 0.382640i
\(995\) 0 0
\(996\) −4.15685 + 1.25836i −0.131715 + 0.0398728i
\(997\) 2.41526 0.0764920 0.0382460 0.999268i \(-0.487823\pi\)
0.0382460 + 0.999268i \(0.487823\pi\)
\(998\) −3.47682 23.4853i −0.110057 0.743414i
\(999\) −35.2189 −1.11428
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 700.2.c.k.699.13 16
4.3 odd 2 inner 700.2.c.k.699.2 16
5.2 odd 4 700.2.g.i.251.7 yes 8
5.3 odd 4 700.2.g.k.251.2 yes 8
5.4 even 2 inner 700.2.c.k.699.4 16
7.6 odd 2 inner 700.2.c.k.699.14 16
20.3 even 4 700.2.g.k.251.3 yes 8
20.7 even 4 700.2.g.i.251.6 yes 8
20.19 odd 2 inner 700.2.c.k.699.15 16
28.27 even 2 inner 700.2.c.k.699.1 16
35.13 even 4 700.2.g.k.251.1 yes 8
35.27 even 4 700.2.g.i.251.8 yes 8
35.34 odd 2 inner 700.2.c.k.699.3 16
140.27 odd 4 700.2.g.i.251.5 8
140.83 odd 4 700.2.g.k.251.4 yes 8
140.139 even 2 inner 700.2.c.k.699.16 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.2.c.k.699.1 16 28.27 even 2 inner
700.2.c.k.699.2 16 4.3 odd 2 inner
700.2.c.k.699.3 16 35.34 odd 2 inner
700.2.c.k.699.4 16 5.4 even 2 inner
700.2.c.k.699.13 16 1.1 even 1 trivial
700.2.c.k.699.14 16 7.6 odd 2 inner
700.2.c.k.699.15 16 20.19 odd 2 inner
700.2.c.k.699.16 16 140.139 even 2 inner
700.2.g.i.251.5 8 140.27 odd 4
700.2.g.i.251.6 yes 8 20.7 even 4
700.2.g.i.251.7 yes 8 5.2 odd 4
700.2.g.i.251.8 yes 8 35.27 even 4
700.2.g.k.251.1 yes 8 35.13 even 4
700.2.g.k.251.2 yes 8 5.3 odd 4
700.2.g.k.251.3 yes 8 20.3 even 4
700.2.g.k.251.4 yes 8 140.83 odd 4