# Properties

 Label 1078.2.e.q.177.2 Level $1078$ Weight $2$ Character 1078.177 Analytic conductor $8.608$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.60787333789$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{5})$$ Defining polynomial: $$x^{4} - x^{3} + 2 x^{2} + x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 177.2 Root $$0.809017 + 1.40126i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.177 Dual form 1078.2.e.q.67.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(1.61803 + 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.61803 + 2.80252i) q^{5} -3.23607 q^{6} +1.00000 q^{8} +(-3.73607 + 6.47106i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(1.61803 + 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.61803 + 2.80252i) q^{5} -3.23607 q^{6} +1.00000 q^{8} +(-3.73607 + 6.47106i) q^{9} +(-1.61803 - 2.80252i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.61803 - 2.80252i) q^{12} +1.23607 q^{13} -10.4721 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.23607 + 5.60503i) q^{17} +(-3.73607 - 6.47106i) q^{18} +(1.38197 - 2.39364i) q^{19} +3.23607 q^{20} +1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(1.61803 + 2.80252i) q^{24} +(-2.73607 - 4.73901i) q^{25} +(-0.618034 + 1.07047i) q^{26} -14.4721 q^{27} -4.47214 q^{29} +(5.23607 - 9.06914i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.61803 - 2.80252i) q^{33} -6.47214 q^{34} +7.47214 q^{36} +(5.47214 - 9.47802i) q^{37} +(1.38197 + 2.39364i) q^{38} +(2.00000 + 3.46410i) q^{39} +(-1.61803 + 2.80252i) q^{40} +6.47214 q^{41} -1.52786 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-12.0902 - 20.9408i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(1.00000 - 1.73205i) q^{47} -3.23607 q^{48} +5.47214 q^{50} +(-10.4721 + 18.1383i) q^{51} +(-0.618034 - 1.07047i) q^{52} +(0.236068 + 0.408882i) q^{53} +(7.23607 - 12.5332i) q^{54} +3.23607 q^{55} +8.94427 q^{57} +(2.23607 - 3.87298i) q^{58} +(-3.61803 - 6.26662i) q^{59} +(5.23607 + 9.06914i) q^{60} +(2.61803 - 4.53457i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(1.61803 + 2.80252i) q^{66} +(7.70820 + 13.3510i) q^{67} +(3.23607 - 5.60503i) q^{68} -12.9443 q^{69} -2.47214 q^{71} +(-3.73607 + 6.47106i) q^{72} +(2.47214 + 4.28187i) q^{73} +(5.47214 + 9.47802i) q^{74} +(8.85410 - 15.3358i) q^{75} -2.76393 q^{76} -4.00000 q^{78} +(-1.61803 - 2.80252i) q^{80} +(-12.2082 - 21.1452i) q^{81} +(-3.23607 + 5.60503i) q^{82} +10.1803 q^{83} -20.9443 q^{85} +(0.763932 - 1.32317i) q^{86} +(-7.23607 - 12.5332i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} +24.1803 q^{90} +4.00000 q^{92} +(3.23607 - 5.60503i) q^{93} +(1.00000 + 1.73205i) q^{94} +(4.47214 + 7.74597i) q^{95} +(1.61803 - 2.80252i) q^{96} +3.52786 q^{97} +7.47214 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9} + O(q^{10})$$ $$4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 24 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{18} + 10 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 40 q^{27} + 12 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} - 8 q^{34} + 12 q^{36} + 4 q^{37} + 10 q^{38} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 24 q^{43} - 2 q^{44} - 26 q^{45} - 8 q^{46} + 4 q^{47} - 4 q^{48} + 4 q^{50} - 24 q^{51} + 2 q^{52} - 8 q^{53} + 20 q^{54} + 4 q^{55} - 10 q^{59} + 12 q^{60} + 6 q^{61} + 8 q^{62} + 4 q^{64} - 8 q^{65} + 2 q^{66} + 4 q^{67} + 4 q^{68} - 16 q^{69} + 8 q^{71} - 6 q^{72} - 8 q^{73} + 4 q^{74} + 22 q^{75} - 20 q^{76} - 16 q^{78} - 2 q^{80} - 22 q^{81} - 4 q^{82} - 4 q^{83} - 48 q^{85} + 12 q^{86} - 20 q^{87} - 2 q^{88} - 20 q^{89} + 52 q^{90} + 16 q^{92} + 4 q^{93} + 4 q^{94} + 2 q^{96} + 32 q^{97} + 12 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$981$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ 1.61803 + 2.80252i 0.934172 + 1.61803i 0.776103 + 0.630606i $$0.217194\pi$$
0.158069 + 0.987428i $$0.449473\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −1.61803 + 2.80252i −0.723607 + 1.25332i 0.235938 + 0.971768i $$0.424184\pi$$
−0.959545 + 0.281556i $$0.909150\pi$$
$$6$$ −3.23607 −1.32112
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ −3.73607 + 6.47106i −1.24536 + 2.15702i
$$10$$ −1.61803 2.80252i −0.511667 0.886234i
$$11$$ −0.500000 0.866025i −0.150756 0.261116i
$$12$$ 1.61803 2.80252i 0.467086 0.809017i
$$13$$ 1.23607 0.342824 0.171412 0.985199i $$-0.445167\pi$$
0.171412 + 0.985199i $$0.445167\pi$$
$$14$$ 0 0
$$15$$ −10.4721 −2.70389
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 3.23607 + 5.60503i 0.784862 + 1.35942i 0.929082 + 0.369875i $$0.120599\pi$$
−0.144220 + 0.989546i $$0.546067\pi$$
$$18$$ −3.73607 6.47106i −0.880600 1.52524i
$$19$$ 1.38197 2.39364i 0.317045 0.549138i −0.662825 0.748774i $$-0.730643\pi$$
0.979870 + 0.199636i $$0.0639761\pi$$
$$20$$ 3.23607 0.723607
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i $$-0.970262\pi$$
0.578610 + 0.815604i $$0.303595\pi$$
$$24$$ 1.61803 + 2.80252i 0.330280 + 0.572061i
$$25$$ −2.73607 4.73901i −0.547214 0.947802i
$$26$$ −0.618034 + 1.07047i −0.121206 + 0.209936i
$$27$$ −14.4721 −2.78516
$$28$$ 0 0
$$29$$ −4.47214 −0.830455 −0.415227 0.909718i $$-0.636298\pi$$
−0.415227 + 0.909718i $$0.636298\pi$$
$$30$$ 5.23607 9.06914i 0.955971 1.65579i
$$31$$ −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i $$-0.224149\pi$$
−0.941745 + 0.336327i $$0.890815\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 1.61803 2.80252i 0.281664 0.487856i
$$34$$ −6.47214 −1.10996
$$35$$ 0 0
$$36$$ 7.47214 1.24536
$$37$$ 5.47214 9.47802i 0.899614 1.55818i 0.0716249 0.997432i $$-0.477182\pi$$
0.827989 0.560745i $$-0.189485\pi$$
$$38$$ 1.38197 + 2.39364i 0.224184 + 0.388299i
$$39$$ 2.00000 + 3.46410i 0.320256 + 0.554700i
$$40$$ −1.61803 + 2.80252i −0.255834 + 0.443117i
$$41$$ 6.47214 1.01078 0.505389 0.862892i $$-0.331349\pi$$
0.505389 + 0.862892i $$0.331349\pi$$
$$42$$ 0 0
$$43$$ −1.52786 −0.232997 −0.116499 0.993191i $$-0.537167\pi$$
−0.116499 + 0.993191i $$0.537167\pi$$
$$44$$ −0.500000 + 0.866025i −0.0753778 + 0.130558i
$$45$$ −12.0902 20.9408i −1.80230 3.12167i
$$46$$ −2.00000 3.46410i −0.294884 0.510754i
$$47$$ 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i $$-0.786737\pi$$
0.929695 + 0.368329i $$0.120070\pi$$
$$48$$ −3.23607 −0.467086
$$49$$ 0 0
$$50$$ 5.47214 0.773877
$$51$$ −10.4721 + 18.1383i −1.46639 + 2.53987i
$$52$$ −0.618034 1.07047i −0.0857059 0.148447i
$$53$$ 0.236068 + 0.408882i 0.0324264 + 0.0561642i 0.881783 0.471655i $$-0.156343\pi$$
−0.849357 + 0.527819i $$0.823010\pi$$
$$54$$ 7.23607 12.5332i 0.984704 1.70556i
$$55$$ 3.23607 0.436351
$$56$$ 0 0
$$57$$ 8.94427 1.18470
$$58$$ 2.23607 3.87298i 0.293610 0.508548i
$$59$$ −3.61803 6.26662i −0.471028 0.815844i 0.528423 0.848981i $$-0.322784\pi$$
−0.999451 + 0.0331370i $$0.989450\pi$$
$$60$$ 5.23607 + 9.06914i 0.675973 + 1.17082i
$$61$$ 2.61803 4.53457i 0.335205 0.580592i −0.648319 0.761369i $$-0.724528\pi$$
0.983524 + 0.180777i $$0.0578611\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −2.00000 + 3.46410i −0.248069 + 0.429669i
$$66$$ 1.61803 + 2.80252i 0.199166 + 0.344966i
$$67$$ 7.70820 + 13.3510i 0.941707 + 1.63108i 0.762214 + 0.647325i $$0.224112\pi$$
0.179493 + 0.983759i $$0.442554\pi$$
$$68$$ 3.23607 5.60503i 0.392431 0.679710i
$$69$$ −12.9443 −1.55831
$$70$$ 0 0
$$71$$ −2.47214 −0.293389 −0.146694 0.989182i $$-0.546863\pi$$
−0.146694 + 0.989182i $$0.546863\pi$$
$$72$$ −3.73607 + 6.47106i −0.440300 + 0.762622i
$$73$$ 2.47214 + 4.28187i 0.289342 + 0.501154i 0.973653 0.228036i $$-0.0732303\pi$$
−0.684311 + 0.729190i $$0.739897\pi$$
$$74$$ 5.47214 + 9.47802i 0.636123 + 1.10180i
$$75$$ 8.85410 15.3358i 1.02238 1.77082i
$$76$$ −2.76393 −0.317045
$$77$$ 0 0
$$78$$ −4.00000 −0.452911
$$79$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$80$$ −1.61803 2.80252i −0.180902 0.313331i
$$81$$ −12.2082 21.1452i −1.35647 2.34947i
$$82$$ −3.23607 + 5.60503i −0.357364 + 0.618972i
$$83$$ 10.1803 1.11744 0.558719 0.829357i $$-0.311293\pi$$
0.558719 + 0.829357i $$0.311293\pi$$
$$84$$ 0 0
$$85$$ −20.9443 −2.27173
$$86$$ 0.763932 1.32317i 0.0823769 0.142681i
$$87$$ −7.23607 12.5332i −0.775788 1.34370i
$$88$$ −0.500000 0.866025i −0.0533002 0.0923186i
$$89$$ −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i $$0.344474\pi$$
−0.999388 + 0.0349934i $$0.988859\pi$$
$$90$$ 24.1803 2.54883
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 3.23607 5.60503i 0.335565 0.581215i
$$94$$ 1.00000 + 1.73205i 0.103142 + 0.178647i
$$95$$ 4.47214 + 7.74597i 0.458831 + 0.794719i
$$96$$ 1.61803 2.80252i 0.165140 0.286031i
$$97$$ 3.52786 0.358200 0.179100 0.983831i $$-0.442681\pi$$
0.179100 + 0.983831i $$0.442681\pi$$
$$98$$ 0 0
$$99$$ 7.47214 0.750978
$$100$$ −2.73607 + 4.73901i −0.273607 + 0.473901i
$$101$$ 7.09017 + 12.2805i 0.705498 + 1.22196i 0.966511 + 0.256624i $$0.0826101\pi$$
−0.261013 + 0.965335i $$0.584057\pi$$
$$102$$ −10.4721 18.1383i −1.03690 1.79596i
$$103$$ −1.47214 + 2.54981i −0.145054 + 0.251241i −0.929393 0.369092i $$-0.879669\pi$$
0.784339 + 0.620332i $$0.213002\pi$$
$$104$$ 1.23607 0.121206
$$105$$ 0 0
$$106$$ −0.472136 −0.0458579
$$107$$ 3.23607 5.60503i 0.312842 0.541859i −0.666134 0.745832i $$-0.732052\pi$$
0.978977 + 0.203973i $$0.0653855\pi$$
$$108$$ 7.23607 + 12.5332i 0.696291 + 1.20601i
$$109$$ 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i $$-0.00769755\pi$$
−0.520794 + 0.853682i $$0.674364\pi$$
$$110$$ −1.61803 + 2.80252i −0.154273 + 0.267210i
$$111$$ 35.4164 3.36158
$$112$$ 0 0
$$113$$ 8.47214 0.796992 0.398496 0.917170i $$-0.369532\pi$$
0.398496 + 0.917170i $$0.369532\pi$$
$$114$$ −4.47214 + 7.74597i −0.418854 + 0.725476i
$$115$$ −6.47214 11.2101i −0.603530 1.04534i
$$116$$ 2.23607 + 3.87298i 0.207614 + 0.359597i
$$117$$ −4.61803 + 7.99867i −0.426937 + 0.739477i
$$118$$ 7.23607 0.666134
$$119$$ 0 0
$$120$$ −10.4721 −0.955971
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ 2.61803 + 4.53457i 0.237026 + 0.410540i
$$123$$ 10.4721 + 18.1383i 0.944241 + 1.63547i
$$124$$ −1.00000 + 1.73205i −0.0898027 + 0.155543i
$$125$$ 1.52786 0.136656
$$126$$ 0 0
$$127$$ −12.0000 −1.06483 −0.532414 0.846484i $$-0.678715\pi$$
−0.532414 + 0.846484i $$0.678715\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ −2.47214 4.28187i −0.217659 0.376997i
$$130$$ −2.00000 3.46410i −0.175412 0.303822i
$$131$$ −4.61803 + 7.99867i −0.403480 + 0.698847i −0.994143 0.108071i $$-0.965533\pi$$
0.590664 + 0.806918i $$0.298866\pi$$
$$132$$ −3.23607 −0.281664
$$133$$ 0 0
$$134$$ −15.4164 −1.33177
$$135$$ 23.4164 40.5584i 2.01536 3.49071i
$$136$$ 3.23607 + 5.60503i 0.277491 + 0.480628i
$$137$$ −7.94427 13.7599i −0.678725 1.17559i −0.975365 0.220597i $$-0.929200\pi$$
0.296640 0.954989i $$-0.404134\pi$$
$$138$$ 6.47214 11.2101i 0.550945 0.954264i
$$139$$ −8.29180 −0.703301 −0.351650 0.936131i $$-0.614379\pi$$
−0.351650 + 0.936131i $$0.614379\pi$$
$$140$$ 0 0
$$141$$ 6.47214 0.545052
$$142$$ 1.23607 2.14093i 0.103729 0.179663i
$$143$$ −0.618034 1.07047i −0.0516826 0.0895169i
$$144$$ −3.73607 6.47106i −0.311339 0.539255i
$$145$$ 7.23607 12.5332i 0.600923 1.04083i
$$146$$ −4.94427 −0.409191
$$147$$ 0 0
$$148$$ −10.9443 −0.899614
$$149$$ −11.1803 + 19.3649i −0.915929 + 1.58644i −0.110394 + 0.993888i $$0.535211\pi$$
−0.805535 + 0.592548i $$0.798122\pi$$
$$150$$ 8.85410 + 15.3358i 0.722934 + 1.25216i
$$151$$ −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i $$-0.329040\pi$$
−0.999909 + 0.0134886i $$0.995706\pi$$
$$152$$ 1.38197 2.39364i 0.112092 0.194149i
$$153$$ −48.3607 −3.90973
$$154$$ 0 0
$$155$$ 6.47214 0.519854
$$156$$ 2.00000 3.46410i 0.160128 0.277350i
$$157$$ −9.32624 16.1535i −0.744315 1.28919i −0.950514 0.310681i $$-0.899443\pi$$
0.206199 0.978510i $$-0.433890\pi$$
$$158$$ 0 0
$$159$$ −0.763932 + 1.32317i −0.0605838 + 0.104934i
$$160$$ 3.23607 0.255834
$$161$$ 0 0
$$162$$ 24.4164 1.91833
$$163$$ −3.70820 + 6.42280i −0.290449 + 0.503072i −0.973916 0.226909i $$-0.927138\pi$$
0.683467 + 0.729981i $$0.260471\pi$$
$$164$$ −3.23607 5.60503i −0.252694 0.437680i
$$165$$ 5.23607 + 9.06914i 0.407627 + 0.706031i
$$166$$ −5.09017 + 8.81643i −0.395074 + 0.684288i
$$167$$ −15.4164 −1.19296 −0.596479 0.802629i $$-0.703434\pi$$
−0.596479 + 0.802629i $$0.703434\pi$$
$$168$$ 0 0
$$169$$ −11.4721 −0.882472
$$170$$ 10.4721 18.1383i 0.803176 1.39114i
$$171$$ 10.3262 + 17.8856i 0.789667 + 1.36774i
$$172$$ 0.763932 + 1.32317i 0.0582493 + 0.100891i
$$173$$ −0.618034 + 1.07047i −0.0469883 + 0.0813860i −0.888563 0.458755i $$-0.848296\pi$$
0.841575 + 0.540141i $$0.181629\pi$$
$$174$$ 14.4721 1.09713
$$175$$ 0 0
$$176$$ 1.00000 0.0753778
$$177$$ 11.7082 20.2792i 0.880042 1.52428i
$$178$$ −5.00000 8.66025i −0.374766 0.649113i
$$179$$ −4.47214 7.74597i −0.334263 0.578961i 0.649080 0.760720i $$-0.275154\pi$$
−0.983343 + 0.181760i $$0.941821\pi$$
$$180$$ −12.0902 + 20.9408i −0.901148 + 1.56083i
$$181$$ 4.76393 0.354100 0.177050 0.984202i $$-0.443345\pi$$
0.177050 + 0.984202i $$0.443345\pi$$
$$182$$ 0 0
$$183$$ 16.9443 1.25256
$$184$$ −2.00000 + 3.46410i −0.147442 + 0.255377i
$$185$$ 17.7082 + 30.6715i 1.30193 + 2.25501i
$$186$$ 3.23607 + 5.60503i 0.237280 + 0.410981i
$$187$$ 3.23607 5.60503i 0.236645 0.409881i
$$188$$ −2.00000 −0.145865
$$189$$ 0 0
$$190$$ −8.94427 −0.648886
$$191$$ −3.23607 + 5.60503i −0.234154 + 0.405566i −0.959026 0.283317i $$-0.908565\pi$$
0.724873 + 0.688883i $$0.241899\pi$$
$$192$$ 1.61803 + 2.80252i 0.116772 + 0.202254i
$$193$$ −1.47214 2.54981i −0.105967 0.183540i 0.808166 0.588955i $$-0.200460\pi$$
−0.914133 + 0.405415i $$0.867127\pi$$
$$194$$ −1.76393 + 3.05522i −0.126643 + 0.219352i
$$195$$ −12.9443 −0.926959
$$196$$ 0 0
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ −3.73607 + 6.47106i −0.265511 + 0.459878i
$$199$$ −0.527864 0.914287i −0.0374193 0.0648121i 0.846709 0.532056i $$-0.178580\pi$$
−0.884129 + 0.467244i $$0.845247\pi$$
$$200$$ −2.73607 4.73901i −0.193469 0.335099i
$$201$$ −24.9443 + 43.2047i −1.75943 + 3.04743i
$$202$$ −14.1803 −0.997725
$$203$$ 0 0
$$204$$ 20.9443 1.46639
$$205$$ −10.4721 + 18.1383i −0.731406 + 1.26683i
$$206$$ −1.47214 2.54981i −0.102569 0.177654i
$$207$$ −14.9443 25.8842i −1.03870 1.79908i
$$208$$ −0.618034 + 1.07047i −0.0428529 + 0.0742235i
$$209$$ −2.76393 −0.191185
$$210$$ 0 0
$$211$$ −22.4721 −1.54705 −0.773523 0.633768i $$-0.781507\pi$$
−0.773523 + 0.633768i $$0.781507\pi$$
$$212$$ 0.236068 0.408882i 0.0162132 0.0280821i
$$213$$ −4.00000 6.92820i −0.274075 0.474713i
$$214$$ 3.23607 + 5.60503i 0.221213 + 0.383152i
$$215$$ 2.47214 4.28187i 0.168598 0.292021i
$$216$$ −14.4721 −0.984704
$$217$$ 0 0
$$218$$ −10.0000 −0.677285
$$219$$ −8.00000 + 13.8564i −0.540590 + 0.936329i
$$220$$ −1.61803 2.80252i −0.109088 0.188946i
$$221$$ 4.00000 + 6.92820i 0.269069 + 0.466041i
$$222$$ −17.7082 + 30.6715i −1.18850 + 2.05854i
$$223$$ 8.47214 0.567336 0.283668 0.958923i $$-0.408449\pi$$
0.283668 + 0.958923i $$0.408449\pi$$
$$224$$ 0 0
$$225$$ 40.8885 2.72590
$$226$$ −4.23607 + 7.33708i −0.281779 + 0.488056i
$$227$$ 7.38197 + 12.7859i 0.489958 + 0.848633i 0.999933 0.0115566i $$-0.00367866\pi$$
−0.509975 + 0.860189i $$0.670345\pi$$
$$228$$ −4.47214 7.74597i −0.296174 0.512989i
$$229$$ −6.38197 + 11.0539i −0.421732 + 0.730462i −0.996109 0.0881294i $$-0.971911\pi$$
0.574377 + 0.818591i $$0.305244\pi$$
$$230$$ 12.9443 0.853520
$$231$$ 0 0
$$232$$ −4.47214 −0.293610
$$233$$ −1.47214 + 2.54981i −0.0964428 + 0.167044i −0.910210 0.414147i $$-0.864080\pi$$
0.813767 + 0.581191i $$0.197413\pi$$
$$234$$ −4.61803 7.99867i −0.301890 0.522889i
$$235$$ 3.23607 + 5.60503i 0.211098 + 0.365632i
$$236$$ −3.61803 + 6.26662i −0.235514 + 0.407922i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 5.23607 9.06914i 0.337987 0.585410i
$$241$$ 5.70820 + 9.88690i 0.367698 + 0.636871i 0.989205 0.146537i $$-0.0468128\pi$$
−0.621507 + 0.783408i $$0.713479\pi$$
$$242$$ −0.500000 0.866025i −0.0321412 0.0556702i
$$243$$ 17.7984 30.8277i 1.14177 1.97760i
$$244$$ −5.23607 −0.335205
$$245$$ 0 0
$$246$$ −20.9443 −1.33536
$$247$$ 1.70820 2.95870i 0.108690 0.188257i
$$248$$ −1.00000 1.73205i −0.0635001 0.109985i
$$249$$ 16.4721 + 28.5306i 1.04388 + 1.80805i
$$250$$ −0.763932 + 1.32317i −0.0483153 + 0.0836846i
$$251$$ 24.7639 1.56309 0.781543 0.623852i $$-0.214433\pi$$
0.781543 + 0.623852i $$0.214433\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ 6.00000 10.3923i 0.376473 0.652071i
$$255$$ −33.8885 58.6967i −2.12218 3.67573i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 5.47214 9.47802i 0.341342 0.591222i −0.643340 0.765581i $$-0.722452\pi$$
0.984682 + 0.174358i $$0.0557851\pi$$
$$258$$ 4.94427 0.307817
$$259$$ 0 0
$$260$$ 4.00000 0.248069
$$261$$ 16.7082 28.9395i 1.03421 1.79131i
$$262$$ −4.61803 7.99867i −0.285303 0.494159i
$$263$$ −6.47214 11.2101i −0.399089 0.691242i 0.594525 0.804077i $$-0.297340\pi$$
−0.993614 + 0.112835i $$0.964007\pi$$
$$264$$ 1.61803 2.80252i 0.0995831 0.172483i
$$265$$ −1.52786 −0.0938559
$$266$$ 0 0
$$267$$ −32.3607 −1.98044
$$268$$ 7.70820 13.3510i 0.470853 0.815542i
$$269$$ 13.6180 + 23.5871i 0.830306 + 1.43813i 0.897796 + 0.440413i $$0.145168\pi$$
−0.0674893 + 0.997720i $$0.521499\pi$$
$$270$$ 23.4164 + 40.5584i 1.42508 + 2.46831i
$$271$$ 8.47214 14.6742i 0.514646 0.891392i −0.485210 0.874398i $$-0.661257\pi$$
0.999856 0.0169947i $$-0.00540983\pi$$
$$272$$ −6.47214 −0.392431
$$273$$ 0 0
$$274$$ 15.8885 0.959862
$$275$$ −2.73607 + 4.73901i −0.164991 + 0.285773i
$$276$$ 6.47214 + 11.2101i 0.389577 + 0.674767i
$$277$$ −6.23607 10.8012i −0.374689 0.648980i 0.615591 0.788065i $$-0.288917\pi$$
−0.990280 + 0.139085i $$0.955584\pi$$
$$278$$ 4.14590 7.18091i 0.248654 0.430682i
$$279$$ 14.9443 0.894690
$$280$$ 0 0
$$281$$ −24.8328 −1.48140 −0.740701 0.671835i $$-0.765506\pi$$
−0.740701 + 0.671835i $$0.765506\pi$$
$$282$$ −3.23607 + 5.60503i −0.192705 + 0.333775i
$$283$$ 8.32624 + 14.4215i 0.494943 + 0.857267i 0.999983 0.00582897i $$-0.00185543\pi$$
−0.505040 + 0.863096i $$0.668522\pi$$
$$284$$ 1.23607 + 2.14093i 0.0733471 + 0.127041i
$$285$$ −14.4721 + 25.0665i −0.857255 + 1.48481i
$$286$$ 1.23607 0.0730902
$$287$$ 0 0
$$288$$ 7.47214 0.440300
$$289$$ −12.4443 + 21.5541i −0.732016 + 1.26789i
$$290$$ 7.23607 + 12.5332i 0.424917 + 0.735977i
$$291$$ 5.70820 + 9.88690i 0.334621 + 0.579580i
$$292$$ 2.47214 4.28187i 0.144671 0.250577i
$$293$$ 4.65248 0.271801 0.135900 0.990723i $$-0.456607\pi$$
0.135900 + 0.990723i $$0.456607\pi$$
$$294$$ 0 0
$$295$$ 23.4164 1.36336
$$296$$ 5.47214 9.47802i 0.318061 0.550899i
$$297$$ 7.23607 + 12.5332i 0.419879 + 0.727252i
$$298$$ −11.1803 19.3649i −0.647660 1.12178i
$$299$$ −2.47214 + 4.28187i −0.142967 + 0.247627i
$$300$$ −17.7082 −1.02238
$$301$$ 0 0
$$302$$ 12.0000 0.690522
$$303$$ −22.9443 + 39.7406i −1.31811 + 2.28304i
$$304$$ 1.38197 + 2.39364i 0.0792612 + 0.137284i
$$305$$ 8.47214 + 14.6742i 0.485113 + 0.840241i
$$306$$ 24.1803 41.8816i 1.38230 2.39421i
$$307$$ 32.0689 1.83027 0.915134 0.403150i $$-0.132085\pi$$
0.915134 + 0.403150i $$0.132085\pi$$
$$308$$ 0 0
$$309$$ −9.52786 −0.542021
$$310$$ −3.23607 + 5.60503i −0.183796 + 0.318345i
$$311$$ −2.70820 4.69075i −0.153568 0.265988i 0.778969 0.627063i $$-0.215743\pi$$
−0.932537 + 0.361075i $$0.882410\pi$$
$$312$$ 2.00000 + 3.46410i 0.113228 + 0.196116i
$$313$$ −14.2361 + 24.6576i −0.804670 + 1.39373i 0.111843 + 0.993726i $$0.464325\pi$$
−0.916514 + 0.400004i $$0.869009\pi$$
$$314$$ 18.6525 1.05262
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 6.52786 11.3066i 0.366641 0.635041i −0.622397 0.782702i $$-0.713841\pi$$
0.989038 + 0.147660i $$0.0471743\pi$$
$$318$$ −0.763932 1.32317i −0.0428392 0.0741996i
$$319$$ 2.23607 + 3.87298i 0.125196 + 0.216845i
$$320$$ −1.61803 + 2.80252i −0.0904508 + 0.156665i
$$321$$ 20.9443 1.16900
$$322$$ 0 0
$$323$$ 17.8885 0.995345
$$324$$ −12.2082 + 21.1452i −0.678234 + 1.17473i
$$325$$ −3.38197 5.85774i −0.187598 0.324929i
$$326$$ −3.70820 6.42280i −0.205378 0.355726i
$$327$$ −16.1803 + 28.0252i −0.894775 + 1.54980i
$$328$$ 6.47214 0.357364
$$329$$ 0 0
$$330$$ −10.4721 −0.576472
$$331$$ −0.472136 + 0.817763i −0.0259509 + 0.0449483i −0.878709 0.477357i $$-0.841595\pi$$
0.852758 + 0.522306i $$0.174928\pi$$
$$332$$ −5.09017 8.81643i −0.279359 0.483865i
$$333$$ 40.8885 + 70.8210i 2.24068 + 3.88097i
$$334$$ 7.70820 13.3510i 0.421774 0.730534i
$$335$$ −49.8885 −2.72570
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 5.73607 9.93516i 0.312001 0.540402i
$$339$$ 13.7082 + 23.7433i 0.744527 + 1.28956i
$$340$$ 10.4721 + 18.1383i 0.567931 + 0.983686i
$$341$$ −1.00000 + 1.73205i −0.0541530 + 0.0937958i
$$342$$ −20.6525 −1.11676
$$343$$ 0 0
$$344$$ −1.52786 −0.0823769
$$345$$ 20.9443 36.2765i 1.12760 1.95306i
$$346$$ −0.618034 1.07047i −0.0332257 0.0575486i
$$347$$ 3.23607 + 5.60503i 0.173721 + 0.300894i 0.939718 0.341950i $$-0.111087\pi$$
−0.765997 + 0.642844i $$0.777754\pi$$
$$348$$ −7.23607 + 12.5332i −0.387894 + 0.671852i
$$349$$ 8.29180 0.443850 0.221925 0.975064i $$-0.428766\pi$$
0.221925 + 0.975064i $$0.428766\pi$$
$$350$$ 0 0
$$351$$ −17.8885 −0.954820
$$352$$ −0.500000 + 0.866025i −0.0266501 + 0.0461593i
$$353$$ 17.4721 + 30.2626i 0.929948 + 1.61072i 0.783404 + 0.621513i $$0.213482\pi$$
0.146544 + 0.989204i $$0.453185\pi$$
$$354$$ 11.7082 + 20.2792i 0.622284 + 1.07783i
$$355$$ 4.00000 6.92820i 0.212298 0.367711i
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ 8.94427 0.472719
$$359$$ 13.4164 23.2379i 0.708091 1.22645i −0.257473 0.966285i $$-0.582890\pi$$
0.965564 0.260164i $$-0.0837767\pi$$
$$360$$ −12.0902 20.9408i −0.637208 1.10368i
$$361$$ 5.68034 + 9.83864i 0.298965 + 0.517823i
$$362$$ −2.38197 + 4.12569i −0.125193 + 0.216841i
$$363$$ −3.23607 −0.169850
$$364$$ 0 0
$$365$$ −16.0000 −0.837478
$$366$$ −8.47214 + 14.6742i −0.442846 + 0.767031i
$$367$$ −10.7082 18.5472i −0.558964 0.968154i −0.997583 0.0694807i $$-0.977866\pi$$
0.438620 0.898673i $$-0.355468\pi$$
$$368$$ −2.00000 3.46410i −0.104257 0.180579i
$$369$$ −24.1803 + 41.8816i −1.25878 + 2.18027i
$$370$$ −35.4164 −1.84121
$$371$$ 0 0
$$372$$ −6.47214 −0.335565
$$373$$ 3.00000 5.19615i 0.155334 0.269047i −0.777847 0.628454i $$-0.783688\pi$$
0.933181 + 0.359408i $$0.117021\pi$$
$$374$$ 3.23607 + 5.60503i 0.167333 + 0.289829i
$$375$$ 2.47214 + 4.28187i 0.127661 + 0.221115i
$$376$$ 1.00000 1.73205i 0.0515711 0.0893237i
$$377$$ −5.52786 −0.284699
$$378$$ 0 0
$$379$$ 5.52786 0.283947 0.141974 0.989870i $$-0.454655\pi$$
0.141974 + 0.989870i $$0.454655\pi$$
$$380$$ 4.47214 7.74597i 0.229416 0.397360i
$$381$$ −19.4164 33.6302i −0.994733 1.72293i
$$382$$ −3.23607 5.60503i −0.165572 0.286778i
$$383$$ −5.94427 + 10.2958i −0.303738 + 0.526090i −0.976980 0.213333i $$-0.931568\pi$$
0.673241 + 0.739423i $$0.264901\pi$$
$$384$$ −3.23607 −0.165140
$$385$$ 0 0
$$386$$ 2.94427 0.149859
$$387$$ 5.70820 9.88690i 0.290164 0.502579i
$$388$$ −1.76393 3.05522i −0.0895501 0.155105i
$$389$$ −3.29180 5.70156i −0.166901 0.289080i 0.770428 0.637527i $$-0.220043\pi$$
−0.937329 + 0.348447i $$0.886709\pi$$
$$390$$ 6.47214 11.2101i 0.327729 0.567644i
$$391$$ −25.8885 −1.30924
$$392$$ 0 0
$$393$$ −29.8885 −1.50768
$$394$$ −9.00000 + 15.5885i −0.453413 + 0.785335i
$$395$$ 0 0
$$396$$ −3.73607 6.47106i −0.187744 0.325183i
$$397$$ 5.14590 8.91296i 0.258265 0.447328i −0.707512 0.706701i $$-0.750182\pi$$
0.965777 + 0.259373i $$0.0835158\pi$$
$$398$$ 1.05573 0.0529189
$$399$$ 0 0
$$400$$ 5.47214 0.273607
$$401$$ 15.1803 26.2931i 0.758070 1.31302i −0.185764 0.982594i $$-0.559476\pi$$
0.943834 0.330421i $$-0.107191\pi$$
$$402$$ −24.9443 43.2047i −1.24411 2.15486i
$$403$$ −1.23607 2.14093i −0.0615729 0.106647i
$$404$$ 7.09017 12.2805i 0.352749 0.610979i
$$405$$ 79.0132 3.92620
$$406$$ 0 0
$$407$$ −10.9443 −0.542487
$$408$$ −10.4721 + 18.1383i −0.518448 + 0.897978i
$$409$$ 11.7082 + 20.2792i 0.578933 + 1.00274i 0.995602 + 0.0936836i $$0.0298642\pi$$
−0.416669 + 0.909058i $$0.636802\pi$$
$$410$$ −10.4721 18.1383i −0.517182 0.895785i
$$411$$ 25.7082 44.5279i 1.26809 2.19640i
$$412$$ 2.94427 0.145054
$$413$$ 0 0
$$414$$ 29.8885 1.46894
$$415$$ −16.4721 + 28.5306i −0.808585 + 1.40051i
$$416$$ −0.618034 1.07047i −0.0303016 0.0524839i
$$417$$ −13.4164 23.2379i −0.657004 1.13796i
$$418$$ 1.38197 2.39364i 0.0675942 0.117077i
$$419$$ 12.7639 0.623559 0.311779 0.950155i $$-0.399075\pi$$
0.311779 + 0.950155i $$0.399075\pi$$
$$420$$ 0 0
$$421$$ 7.52786 0.366886 0.183443 0.983030i $$-0.441276\pi$$
0.183443 + 0.983030i $$0.441276\pi$$
$$422$$ 11.2361 19.4614i 0.546963 0.947368i
$$423$$ 7.47214 + 12.9421i 0.363308 + 0.629267i
$$424$$ 0.236068 + 0.408882i 0.0114645 + 0.0198571i
$$425$$ 17.7082 30.6715i 0.858974 1.48779i
$$426$$ 8.00000 0.387601
$$427$$ 0 0
$$428$$ −6.47214 −0.312842
$$429$$ 2.00000 3.46410i 0.0965609 0.167248i
$$430$$ 2.47214 + 4.28187i 0.119217 + 0.206490i
$$431$$ −20.4721 35.4588i −0.986108 1.70799i −0.636905 0.770942i $$-0.719786\pi$$
−0.349203 0.937047i $$-0.613548\pi$$
$$432$$ 7.23607 12.5332i 0.348145 0.603006i
$$433$$ 19.5279 0.938449 0.469225 0.883079i $$-0.344533\pi$$
0.469225 + 0.883079i $$0.344533\pi$$
$$434$$ 0 0
$$435$$ 46.8328 2.24546
$$436$$ 5.00000 8.66025i 0.239457 0.414751i
$$437$$ 5.52786 + 9.57454i 0.264434 + 0.458012i
$$438$$ −8.00000 13.8564i −0.382255 0.662085i
$$439$$ 4.47214 7.74597i 0.213443 0.369695i −0.739347 0.673325i $$-0.764865\pi$$
0.952790 + 0.303630i $$0.0981988\pi$$
$$440$$ 3.23607 0.154273
$$441$$ 0 0
$$442$$ −8.00000 −0.380521
$$443$$ 3.52786 6.11044i 0.167614 0.290316i −0.769967 0.638084i $$-0.779727\pi$$
0.937580 + 0.347768i $$0.113060\pi$$
$$444$$ −17.7082 30.6715i −0.840394 1.45561i
$$445$$ −16.1803 28.0252i −0.767022 1.32852i
$$446$$ −4.23607 + 7.33708i −0.200584 + 0.347421i
$$447$$ −72.3607 −3.42254
$$448$$ 0 0
$$449$$ 1.05573 0.0498229 0.0249114 0.999690i $$-0.492070\pi$$
0.0249114 + 0.999690i $$0.492070\pi$$
$$450$$ −20.4443 + 35.4105i −0.963752 + 1.66927i
$$451$$ −3.23607 5.60503i −0.152380 0.263931i
$$452$$ −4.23607 7.33708i −0.199248 0.345107i
$$453$$ 19.4164 33.6302i 0.912262 1.58008i
$$454$$ −14.7639 −0.692906
$$455$$ 0 0
$$456$$ 8.94427 0.418854
$$457$$ −4.52786 + 7.84249i −0.211805 + 0.366856i −0.952279 0.305228i $$-0.901267\pi$$
0.740475 + 0.672084i $$0.234601\pi$$
$$458$$ −6.38197 11.0539i −0.298210 0.516514i
$$459$$ −46.8328 81.1168i −2.18597 3.78621i
$$460$$ −6.47214 + 11.2101i −0.301765 + 0.522672i
$$461$$ 29.2361 1.36166 0.680830 0.732442i $$-0.261619\pi$$
0.680830 + 0.732442i $$0.261619\pi$$
$$462$$ 0 0
$$463$$ −21.5279 −1.00048 −0.500242 0.865885i $$-0.666756\pi$$
−0.500242 + 0.865885i $$0.666756\pi$$
$$464$$ 2.23607 3.87298i 0.103807 0.179799i
$$465$$ 10.4721 + 18.1383i 0.485634 + 0.841142i
$$466$$ −1.47214 2.54981i −0.0681954 0.118118i
$$467$$ −6.56231 + 11.3662i −0.303667 + 0.525967i −0.976964 0.213405i $$-0.931544\pi$$
0.673296 + 0.739373i $$0.264878\pi$$
$$468$$ 9.23607 0.426937
$$469$$ 0 0
$$470$$ −6.47214 −0.298537
$$471$$ 30.1803 52.2739i 1.39064 2.40865i
$$472$$ −3.61803 6.26662i −0.166534 0.288445i
$$473$$ 0.763932 + 1.32317i 0.0351256 + 0.0608394i
$$474$$ 0 0
$$475$$ −15.1246 −0.693965
$$476$$ 0 0
$$477$$ −3.52786 −0.161530
$$478$$ −10.0000 + 17.3205i −0.457389 + 0.792222i
$$479$$ 16.1803 + 28.0252i 0.739299 + 1.28050i 0.952812 + 0.303562i $$0.0981761\pi$$
−0.213513 + 0.976940i $$0.568491\pi$$
$$480$$ 5.23607 + 9.06914i 0.238993 + 0.413948i
$$481$$ 6.76393 11.7155i 0.308409 0.534180i
$$482$$ −11.4164 −0.520003
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −5.70820 + 9.88690i −0.259196 + 0.448941i
$$486$$ 17.7984 + 30.8277i 0.807351 + 1.39837i
$$487$$ 0.472136 + 0.817763i 0.0213945 + 0.0370564i 0.876524 0.481357i $$-0.159856\pi$$
−0.855130 + 0.518414i $$0.826523\pi$$
$$488$$ 2.61803 4.53457i 0.118513 0.205270i
$$489$$ −24.0000 −1.08532
$$490$$ 0 0
$$491$$ 0.944272 0.0426144 0.0213072 0.999773i $$-0.493217\pi$$
0.0213072 + 0.999773i $$0.493217\pi$$
$$492$$ 10.4721 18.1383i 0.472120 0.817736i
$$493$$ −14.4721 25.0665i −0.651792 1.12894i
$$494$$ 1.70820 + 2.95870i 0.0768557 + 0.133118i
$$495$$ −12.0902 + 20.9408i −0.543413 + 0.941218i
$$496$$ 2.00000 0.0898027
$$497$$ 0 0
$$498$$ −32.9443 −1.47627
$$499$$ −6.18034 + 10.7047i −0.276670 + 0.479207i −0.970555 0.240879i $$-0.922564\pi$$
0.693885 + 0.720086i $$0.255898\pi$$
$$500$$ −0.763932 1.32317i −0.0341641 0.0591739i
$$501$$ −24.9443 43.2047i −1.11443 1.93025i
$$502$$ −12.3820 + 21.4462i −0.552634 + 0.957190i
$$503$$ 4.00000 0.178351 0.0891756 0.996016i $$-0.471577\pi$$
0.0891756 + 0.996016i $$0.471577\pi$$
$$504$$ 0 0
$$505$$ −45.8885 −2.04201
$$506$$ −2.00000 + 3.46410i −0.0889108 + 0.153998i
$$507$$ −18.5623 32.1509i −0.824381 1.42787i
$$508$$ 6.00000 + 10.3923i 0.266207 + 0.461084i
$$509$$ 17.0344 29.5045i 0.755038 1.30776i −0.190317 0.981723i $$-0.560952\pi$$
0.945355 0.326042i $$-0.105715\pi$$
$$510$$ 67.7771 3.00122
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ −20.0000 + 34.6410i −0.883022 + 1.52944i
$$514$$ 5.47214 + 9.47802i 0.241366 + 0.418057i
$$515$$ −4.76393 8.25137i −0.209924 0.363599i
$$516$$ −2.47214 + 4.28187i −0.108830 + 0.188499i
$$517$$ −2.00000 −0.0879599
$$518$$ 0 0
$$519$$ −4.00000 −0.175581
$$520$$ −2.00000 + 3.46410i −0.0877058 + 0.151911i
$$521$$ −17.1803 29.7572i −0.752684 1.30369i −0.946517 0.322653i $$-0.895425\pi$$
0.193833 0.981035i $$-0.437908\pi$$
$$522$$ 16.7082 + 28.9395i 0.731298 + 1.26665i
$$523$$ 13.8541 23.9960i 0.605798 1.04927i −0.386127 0.922446i $$-0.626187\pi$$
0.991925 0.126827i $$-0.0404792\pi$$
$$524$$ 9.23607 0.403480
$$525$$ 0 0
$$526$$ 12.9443 0.564397
$$527$$ 6.47214 11.2101i 0.281931 0.488318i
$$528$$ 1.61803 + 2.80252i 0.0704159 + 0.121964i
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ 0.763932 1.32317i 0.0331831 0.0574748i
$$531$$ 54.0689 2.34639
$$532$$ 0 0
$$533$$ 8.00000 0.346518
$$534$$ 16.1803 28.0252i 0.700192 1.21277i
$$535$$ 10.4721 + 18.1383i 0.452750 + 0.784186i
$$536$$ 7.70820 + 13.3510i 0.332944 + 0.576675i
$$537$$ 14.4721 25.0665i 0.624519 1.08170i
$$538$$ −27.2361 −1.17423
$$539$$ 0 0
$$540$$ −46.8328 −2.01536
$$541$$ 4.52786 7.84249i 0.194668 0.337175i −0.752124 0.659022i $$-0.770970\pi$$
0.946792 + 0.321847i $$0.104304\pi$$
$$542$$ 8.47214 + 14.6742i 0.363909 + 0.630310i
$$543$$ 7.70820 + 13.3510i 0.330791 + 0.572946i
$$544$$ 3.23607 5.60503i 0.138745 0.240314i
$$545$$ −32.3607 −1.38618
$$546$$ 0 0
$$547$$ 16.9443 0.724485 0.362242 0.932084i $$-0.382011\pi$$
0.362242 + 0.932084i $$0.382011\pi$$
$$548$$ −7.94427 + 13.7599i −0.339362 + 0.587793i
$$549$$ 19.5623 + 33.8829i 0.834899 + 1.44609i
$$550$$ −2.73607 4.73901i −0.116666 0.202072i
$$551$$ −6.18034 + 10.7047i −0.263291 + 0.456034i
$$552$$ −12.9443 −0.550945
$$553$$ 0 0
$$554$$ 12.4721 0.529890
$$555$$ −57.3050 + 99.2551i −2.43246 + 4.21314i
$$556$$ 4.14590 + 7.18091i 0.175825 + 0.304538i
$$557$$ 14.4164 + 24.9700i 0.610843 + 1.05801i 0.991099 + 0.133129i $$0.0425026\pi$$
−0.380256 + 0.924881i $$0.624164\pi$$
$$558$$ −7.47214 + 12.9421i −0.316321 + 0.547884i
$$559$$ −1.88854 −0.0798769
$$560$$ 0 0
$$561$$ 20.9443 0.884268
$$562$$ 12.4164 21.5058i 0.523755 0.907169i
$$563$$ −13.3820 23.1782i −0.563983 0.976847i −0.997144 0.0755300i $$-0.975935\pi$$
0.433161 0.901317i $$-0.357398\pi$$
$$564$$ −3.23607 5.60503i −0.136263 0.236015i
$$565$$ −13.7082 + 23.7433i −0.576708 + 0.998888i
$$566$$ −16.6525 −0.699956
$$567$$ 0 0
$$568$$ −2.47214 −0.103729
$$569$$ −8.41641 + 14.5776i −0.352834 + 0.611127i −0.986745 0.162280i $$-0.948115\pi$$
0.633911 + 0.773406i $$0.281449\pi$$
$$570$$ −14.4721 25.0665i −0.606171 1.04992i
$$571$$ 22.9443 + 39.7406i 0.960188 + 1.66309i 0.722022 + 0.691870i $$0.243213\pi$$
0.238165 + 0.971225i $$0.423454\pi$$
$$572$$ −0.618034 + 1.07047i −0.0258413 + 0.0447584i
$$573$$ −20.9443 −0.874960
$$574$$ 0 0
$$575$$ 21.8885 0.912815
$$576$$ −3.73607 + 6.47106i −0.155669 + 0.269627i
$$577$$ −4.52786 7.84249i −0.188497 0.326487i 0.756252 0.654280i $$-0.227028\pi$$
−0.944749 + 0.327793i $$0.893695\pi$$
$$578$$ −12.4443 21.5541i −0.517613 0.896533i
$$579$$ 4.76393 8.25137i 0.197982 0.342915i
$$580$$ −14.4721 −0.600923
$$581$$ 0 0
$$582$$ −11.4164 −0.473225
$$583$$ 0.236068 0.408882i 0.00977694 0.0169342i
$$584$$ 2.47214 + 4.28187i 0.102298 + 0.177185i
$$585$$ −14.9443 25.8842i −0.617870 1.07018i
$$586$$ −2.32624 + 4.02916i −0.0960960 + 0.166443i
$$587$$ −28.1803 −1.16313 −0.581564 0.813501i $$-0.697559\pi$$
−0.581564 + 0.813501i $$0.697559\pi$$
$$588$$ 0 0
$$589$$ −5.52786 −0.227772
$$590$$ −11.7082 + 20.2792i −0.482019 + 0.834882i
$$591$$ 29.1246 + 50.4453i 1.19803 + 2.07504i
$$592$$ 5.47214 + 9.47802i 0.224903 + 0.389544i
$$593$$ −12.0000 + 20.7846i −0.492781 + 0.853522i −0.999965 0.00831589i $$-0.997353\pi$$
0.507184 + 0.861838i $$0.330686\pi$$
$$594$$ −14.4721 −0.593799
$$595$$ 0 0
$$596$$ 22.3607 0.915929
$$597$$ 1.70820 2.95870i 0.0699121 0.121091i
$$598$$ −2.47214 4.28187i −0.101093 0.175098i
$$599$$ −6.18034 10.7047i −0.252522 0.437381i 0.711698 0.702486i $$-0.247927\pi$$
−0.964219 + 0.265105i $$0.914593\pi$$
$$600$$ 8.85410 15.3358i 0.361467 0.626080i
$$601$$ 18.8328 0.768207 0.384103 0.923290i $$-0.374511\pi$$
0.384103 + 0.923290i $$0.374511\pi$$
$$602$$ 0 0
$$603$$ −115.193 −4.69104
$$604$$ −6.00000 + 10.3923i −0.244137 + 0.422857i
$$605$$ −1.61803 2.80252i −0.0657824 0.113939i
$$606$$ −22.9443 39.7406i −0.932047 1.61435i
$$607$$ 16.0000 27.7128i 0.649420 1.12483i −0.333842 0.942629i $$-0.608345\pi$$
0.983262 0.182199i $$-0.0583216\pi$$
$$608$$ −2.76393 −0.112092
$$609$$ 0 0
$$610$$ −16.9443 −0.686054
$$611$$ 1.23607 2.14093i 0.0500060 0.0866129i
$$612$$ 24.1803 + 41.8816i 0.977432 + 1.69296i
$$613$$ −9.76393 16.9116i −0.394362 0.683054i 0.598658 0.801005i $$-0.295701\pi$$
−0.993019 + 0.117951i $$0.962368\pi$$
$$614$$ −16.0344 + 27.7725i −0.647097 + 1.12081i
$$615$$ −67.7771 −2.73304
$$616$$ 0 0
$$617$$ −5.41641 −0.218056 −0.109028 0.994039i $$-0.534774\pi$$
−0.109028 + 0.994039i $$0.534774\pi$$
$$618$$ 4.76393 8.25137i 0.191633 0.331919i
$$619$$ 24.2705 + 42.0378i 0.975514 + 1.68964i 0.678228 + 0.734852i $$0.262748\pi$$
0.297286 + 0.954788i $$0.403918\pi$$
$$620$$ −3.23607 5.60503i −0.129964 0.225104i
$$621$$ 28.9443 50.1329i 1.16149 2.01177i
$$622$$ 5.41641 0.217178
$$623$$ 0 0
$$624$$ −4.00000 −0.160128
$$625$$ 11.2082 19.4132i 0.448328 0.776527i
$$626$$ −14.2361 24.6576i −0.568988 0.985516i
$$627$$ −4.47214 7.74597i −0.178600 0.309344i
$$628$$ −9.32624 + 16.1535i −0.372157 + 0.644596i
$$629$$ 70.8328 2.82429
$$630$$ 0 0
$$631$$ −4.58359 −0.182470 −0.0912350 0.995829i $$-0.529081\pi$$
−0.0912350 + 0.995829i $$0.529081\pi$$
$$632$$ 0 0
$$633$$ −36.3607 62.9785i −1.44521 2.50317i
$$634$$ 6.52786 + 11.3066i 0.259255 + 0.449042i
$$635$$ 19.4164 33.6302i 0.770517 1.33457i
$$636$$ 1.52786 0.0605838
$$637$$ 0 0
$$638$$ −4.47214 −0.177054
$$639$$ 9.23607 15.9973i 0.365373 0.632845i
$$640$$ −1.61803 2.80252i −0.0639584 0.110779i
$$641$$ −18.2361 31.5858i −0.720281 1.24756i −0.960887 0.276941i $$-0.910679\pi$$
0.240606 0.970623i $$-0.422654\pi$$
$$642$$ −10.4721 + 18.1383i −0.413302 + 0.715860i
$$643$$ −23.2361 −0.916341 −0.458171 0.888864i $$-0.651495\pi$$
−0.458171 + 0.888864i $$0.651495\pi$$
$$644$$ 0 0
$$645$$ 16.0000 0.629999
$$646$$ −8.94427 + 15.4919i −0.351908 + 0.609522i
$$647$$ −12.4164 21.5058i −0.488139 0.845482i 0.511768 0.859124i $$-0.328991\pi$$
−0.999907 + 0.0136418i $$0.995658\pi$$
$$648$$ −12.2082 21.1452i −0.479584 0.830663i
$$649$$ −3.61803 + 6.26662i −0.142020 + 0.245986i
$$650$$ 6.76393 0.265303
$$651$$ 0 0
$$652$$ 7.41641 0.290449
$$653$$ −0.819660 + 1.41969i −0.0320758 + 0.0555569i −0.881618 0.471964i $$-0.843545\pi$$
0.849542 + 0.527521i $$0.176878\pi$$
$$654$$ −16.1803 28.0252i −0.632701 1.09587i
$$655$$ −14.9443 25.8842i −0.583921 1.01138i
$$656$$ −3.23607 + 5.60503i −0.126347 + 0.218840i
$$657$$ −36.9443 −1.44133
$$658$$ 0 0
$$659$$ 43.4164 1.69126 0.845632 0.533767i $$-0.179224\pi$$
0.845632 + 0.533767i $$0.179224\pi$$
$$660$$ 5.23607 9.06914i 0.203814 0.353016i
$$661$$ −18.5623 32.1509i −0.721990 1.25052i −0.960201 0.279310i $$-0.909894\pi$$
0.238211 0.971213i $$-0.423439\pi$$
$$662$$ −0.472136 0.817763i −0.0183501 0.0317833i
$$663$$ −12.9443 + 22.4201i −0.502714 + 0.870726i
$$664$$ 10.1803 0.395074
$$665$$ 0 0
$$666$$ −81.7771 −3.16880
$$667$$ 8.94427 15.4919i 0.346324 0.599850i
$$668$$ 7.70820 + 13.3510i 0.298239 + 0.516566i
$$669$$ 13.7082 + 23.7433i 0.529990 + 0.917969i
$$670$$ 24.9443 43.2047i 0.963681 1.66914i
$$671$$ −5.23607 −0.202136
$$672$$ 0 0
$$673$$ 31.8885 1.22921 0.614607 0.788834i $$-0.289315\pi$$
0.614607 + 0.788834i $$0.289315\pi$$
$$674$$ −9.00000 + 15.5885i −0.346667 + 0.600445i
$$675$$ 39.5967 + 68.5836i 1.52408 + 2.63978i
$$676$$ 5.73607 + 9.93516i 0.220618 + 0.382122i
$$677$$ −16.0344 + 27.7725i −0.616254 + 1.06738i 0.373910 + 0.927465i $$0.378017\pi$$
−0.990163 + 0.139917i $$0.955316\pi$$
$$678$$ −27.4164 −1.05292
$$679$$ 0 0
$$680$$ −20.9443 −0.803176
$$681$$ −23.8885 + 41.3762i −0.915411 + 1.58554i
$$682$$ −1.00000 1.73205i −0.0382920 0.0663237i
$$683$$ −7.52786 13.0386i −0.288046 0.498910i 0.685297 0.728263i $$-0.259672\pi$$
−0.973343 + 0.229353i $$0.926339\pi$$
$$684$$ 10.3262 17.8856i 0.394834 0.683872i
$$685$$ 51.4164 1.96452
$$686$$ 0 0
$$687$$ −41.3050 −1.57588
$$688$$ 0.763932 1.32317i 0.0291246 0.0504453i
$$689$$ 0.291796 + 0.505406i 0.0111165 + 0.0192544i
$$690$$ 20.9443 + 36.2765i 0.797335 + 1.38102i
$$691$$ 9.32624 16.1535i 0.354787 0.614509i −0.632295 0.774728i $$-0.717887\pi$$
0.987081 + 0.160219i $$0.0512201\pi$$
$$692$$ 1.23607 0.0469883
$$693$$ 0 0
$$694$$ −6.47214 −0.245679
$$695$$ 13.4164 23.2379i 0.508913 0.881464i
$$696$$ −7.23607 12.5332i −0.274282 0.475071i
$$697$$ 20.9443 + 36.2765i 0.793321 + 1.37407i
$$698$$ −4.14590 + 7.18091i −0.156925 + 0.271801i
$$699$$ −9.52786 −0.360377
$$700$$ 0 0
$$701$$ 46.7214 1.76464 0.882321 0.470649i $$-0.155980\pi$$
0.882321 + 0.470649i $$0.155980\pi$$
$$702$$ 8.94427 15.4919i 0.337580 0.584705i
$$703$$ −15.1246 26.1966i −0.570436 0.988023i
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ −10.4721 + 18.1383i −0.394403 + 0.683127i
$$706$$ −34.9443 −1.31515
$$707$$ 0 0
$$708$$ −23.4164 −0.880042
$$709$$ 2.23607 3.87298i 0.0839773 0.145453i −0.820978 0.570960i $$-0.806571\pi$$
0.904955 + 0.425507i $$0.139904\pi$$
$$710$$ 4.00000 + 6.92820i 0.150117 + 0.260011i
$$711$$ 0 0
$$712$$ −5.00000 + 8.66025i −0.187383 + 0.324557i
$$713$$ 8.00000 0.299602
$$714$$ 0 0
$$715$$ 4.00000 0.149592
$$716$$ −4.47214 + 7.74597i −0.167132 + 0.289480i
$$717$$ 32.3607 + 56.0503i 1.20853 + 2.09324i
$$718$$ 13.4164 + 23.2379i 0.500696 + 0.867231i
$$719$$ 18.4164 31.8982i 0.686816 1.18960i −0.286046 0.958216i $$-0.592341\pi$$
0.972862 0.231385i $$-0.0743256\pi$$
$$720$$ 24.1803 0.901148
$$721$$ 0 0
$$722$$ −11.3607 −0.422801
$$723$$ −18.4721 + 31.9947i −0.686986 + 1.18989i
$$724$$ −2.38197 4.12569i −0.0885251 0.153330i
$$725$$ 12.2361 + 21.1935i 0.454436 + 0.787107i
$$726$$ 1.61803 2.80252i 0.0600509 0.104011i
$$727$$ 18.0000 0.667583 0.333792 0.942647i $$-0.391672\pi$$
0.333792 + 0.942647i $$0.391672\pi$$
$$728$$ 0 0
$$729$$ 41.9443 1.55349
$$730$$ 8.00000 13.8564i 0.296093 0.512849i
$$731$$ −4.94427 8.56373i −0.182871 0.316741i
$$732$$ −8.47214 14.6742i −0.313139 0.542373i
$$733$$ −4.43769 + 7.68631i −0.163910 + 0.283900i −0.936268 0.351287i $$-0.885744\pi$$
0.772358 + 0.635188i $$0.219077\pi$$
$$734$$ 21.4164 0.790494
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 7.70820 13.3510i 0.283935 0.491790i
$$738$$ −24.1803 41.8816i −0.890091 1.54168i
$$739$$ −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i $$-0.286575\pi$$
−0.989230 + 0.146369i $$0.953241\pi$$
$$740$$ 17.7082 30.6715i 0.650967 1.12751i
$$741$$ 11.0557 0.406142
$$742$$ 0 0
$$743$$ −13.8885 −0.509521 −0.254761 0.967004i $$-0.581997\pi$$
−0.254761 + 0.967004i $$0.581997\pi$$
$$744$$ 3.23607 5.60503i 0.118640 0.205491i
$$745$$ −36.1803 62.6662i −1.32555 2.29591i
$$746$$ 3.00000 + 5.19615i 0.109838 + 0.190245i
$$747$$ −38.0344 + 65.8776i −1.39161 + 2.41033i
$$748$$ −6.47214 −0.236645
$$749$$ 0 0
$$750$$ −4.94427 −0.180539
$$751$$ −0.472136 + 0.817763i −0.0172285 + 0.0298406i −0.874511 0.485005i $$-0.838818\pi$$
0.857283 + 0.514846i $$0.172151\pi$$
$$752$$ 1.00000 + 1.73205i 0.0364662 + 0.0631614i
$$753$$ 40.0689 + 69.4013i 1.46019 + 2.52913i
$$754$$ 2.76393 4.78727i 0.100656 0.174342i
$$755$$ 38.8328 1.41327
$$756$$ 0 0
$$757$$ 39.3050 1.42856 0.714281 0.699859i $$-0.246754\pi$$
0.714281 + 0.699859i $$0.246754\pi$$
$$758$$ −2.76393 + 4.78727i −0.100391 + 0.173882i
$$759$$ 6.47214 + 11.2101i 0.234924 + 0.406900i
$$760$$ 4.47214 + 7.74597i 0.162221 + 0.280976i
$$761$$ −7.70820 + 13.3510i −0.279422 + 0.483973i −0.971241 0.238097i $$-0.923476\pi$$
0.691819 + 0.722071i $$0.256810\pi$$
$$762$$ 38.8328 1.40676
$$763$$ 0 0
$$764$$ 6.47214 0.234154
$$765$$ 78.2492 135.532i 2.82911 4.90016i
$$766$$ −5.94427 10.2958i −0.214775 0.372002i
$$767$$ −4.47214 7.74597i −0.161479 0.279691i
$$768$$ 1.61803 2.80252i 0.0583858 0.101127i
$$769$$ −16.5836 −0.598020 −0.299010 0.954250i $$-0.596656\pi$$
−0.299010 + 0.954250i $$0.596656\pi$$
$$770$$ 0 0
$$771$$ 35.4164 1.27549
$$772$$ −1.47214 + 2.54981i −0.0529833 + 0.0917698i
$$773$$ −1.14590 1.98475i −0.0412151 0.0713866i 0.844682 0.535268i $$-0.179790\pi$$
−0.885897 + 0.463882i $$0.846456\pi$$
$$774$$ 5.70820 + 9.88690i 0.205177 + 0.355377i
$$775$$ −5.47214 + 9.47802i −0.196565 + 0.340460i
$$776$$ 3.52786 0.126643
$$777$$ 0 0
$$778$$ 6.58359 0.236033
$$779$$ 8.94427 15.4919i 0.320462 0.555056i
$$780$$ 6.47214 + 11.2101i 0.231740 + 0.401385i
$$781$$ 1.23607 + 2.14093i 0.0442300 + 0.0766086i
$$782$$ 12.9443 22.4201i 0.462886 0.801742i
$$783$$ 64.7214 2.31295