# Properties

 Label 1710.2.l.f.1261.1 Level $1710$ Weight $2$ Character 1710.1261 Analytic conductor $13.654$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1710.l (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.6544187456$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 570) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1261.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1710.1261 Dual form 1710.2.l.f.1531.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -2.00000 q^{11} +(1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(4.00000 + 1.73205i) q^{19} +1.00000 q^{20} +(-1.00000 - 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-5.00000 + 8.66025i) q^{29} +1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{34} +(0.500000 + 0.866025i) q^{35} -5.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +(0.500000 + 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(2.50000 + 4.33013i) q^{43} +(1.00000 - 1.73205i) q^{44} -6.00000 q^{46} -6.00000 q^{49} -1.00000 q^{50} +(1.50000 + 2.59808i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(1.00000 + 1.73205i) q^{55} +1.00000 q^{56} -10.0000 q^{58} +(-1.00000 - 1.73205i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(0.500000 + 0.866025i) q^{62} +1.00000 q^{64} -3.00000 q^{65} +(2.50000 - 4.33013i) q^{67} -4.00000 q^{68} +(-0.500000 + 0.866025i) q^{70} +(-5.50000 - 9.52628i) q^{73} +(-2.50000 - 4.33013i) q^{74} +(-3.50000 + 2.59808i) q^{76} +2.00000 q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-1.00000 + 1.73205i) q^{82} -2.00000 q^{83} +(2.00000 - 3.46410i) q^{85} +(-2.50000 + 4.33013i) q^{86} +2.00000 q^{88} +(-1.50000 + 2.59808i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-0.500000 - 4.33013i) q^{95} +(1.00000 + 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{4} - q^{5} - 2q^{7} - 2q^{8} + O(q^{10})$$ $$2q + q^{2} - q^{4} - q^{5} - 2q^{7} - 2q^{8} + q^{10} - 4q^{11} + 3q^{13} - q^{14} - q^{16} + 4q^{17} + 8q^{19} + 2q^{20} - 2q^{22} - 6q^{23} - q^{25} + 6q^{26} + q^{28} - 10q^{29} + 2q^{31} + q^{32} - 4q^{34} + q^{35} - 10q^{37} + q^{38} + q^{40} + 2q^{41} + 5q^{43} + 2q^{44} - 12q^{46} - 12q^{49} - 2q^{50} + 3q^{52} - 12q^{53} + 2q^{55} + 2q^{56} - 20q^{58} - 2q^{59} - 5q^{61} + q^{62} + 2q^{64} - 6q^{65} + 5q^{67} - 8q^{68} - q^{70} - 11q^{73} - 5q^{74} - 7q^{76} + 4q^{77} + 11q^{79} - q^{80} - 2q^{82} - 4q^{83} + 4q^{85} - 5q^{86} + 4q^{88} - 3q^{91} - 6q^{92} - q^{95} + 2q^{97} - 6q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$1027$$ $$1351$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 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
$$3$$ 0 0
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −0.500000 0.866025i −0.223607 0.387298i
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 0.500000 0.866025i 0.158114 0.273861i
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 1.50000 2.59808i 0.416025 0.720577i −0.579510 0.814965i $$-0.696756\pi$$
0.995535 + 0.0943882i $$0.0300895\pi$$
$$14$$ −0.500000 0.866025i −0.133631 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i $$-0.00546033\pi$$
−0.514782 + 0.857321i $$0.672127\pi$$
$$18$$ 0 0
$$19$$ 4.00000 + 1.73205i 0.917663 + 0.397360i
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ −1.00000 1.73205i −0.213201 0.369274i
$$23$$ −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i $$0.381789\pi$$
−0.988436 + 0.151642i $$0.951544\pi$$
$$24$$ 0 0
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 3.00000 0.588348
$$27$$ 0 0
$$28$$ 0.500000 0.866025i 0.0944911 0.163663i
$$29$$ −5.00000 + 8.66025i −0.928477 + 1.60817i −0.142605 + 0.989780i $$0.545548\pi$$
−0.785872 + 0.618389i $$0.787786\pi$$
$$30$$ 0 0
$$31$$ 1.00000 0.179605 0.0898027 0.995960i $$-0.471376\pi$$
0.0898027 + 0.995960i $$0.471376\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ −2.00000 + 3.46410i −0.342997 + 0.594089i
$$35$$ 0.500000 + 0.866025i 0.0845154 + 0.146385i
$$36$$ 0 0
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ 0.500000 + 4.33013i 0.0811107 + 0.702439i
$$39$$ 0 0
$$40$$ 0.500000 + 0.866025i 0.0790569 + 0.136931i
$$41$$ 1.00000 + 1.73205i 0.156174 + 0.270501i 0.933486 0.358614i $$-0.116751\pi$$
−0.777312 + 0.629115i $$0.783417\pi$$
$$42$$ 0 0
$$43$$ 2.50000 + 4.33013i 0.381246 + 0.660338i 0.991241 0.132068i $$-0.0421616\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 1.00000 1.73205i 0.150756 0.261116i
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ 1.50000 + 2.59808i 0.208013 + 0.360288i
$$53$$ −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i $$0.475021\pi$$
−0.902557 + 0.430570i $$0.858312\pi$$
$$54$$ 0 0
$$55$$ 1.00000 + 1.73205i 0.134840 + 0.233550i
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ −10.0000 −1.31306
$$59$$ −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i $$-0.208225\pi$$
−0.923749 + 0.382998i $$0.874892\pi$$
$$60$$ 0 0
$$61$$ −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i $$-0.937047\pi$$
0.660415 + 0.750901i $$0.270381\pi$$
$$62$$ 0.500000 + 0.866025i 0.0635001 + 0.109985i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −3.00000 −0.372104
$$66$$ 0 0
$$67$$ 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i $$-0.734535\pi$$
0.977356 + 0.211604i $$0.0678686\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 0 0
$$70$$ −0.500000 + 0.866025i −0.0597614 + 0.103510i
$$71$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$72$$ 0 0
$$73$$ −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i $$-0.944054\pi$$
0.340868 0.940111i $$-0.389279\pi$$
$$74$$ −2.50000 4.33013i −0.290619 0.503367i
$$75$$ 0 0
$$76$$ −3.50000 + 2.59808i −0.401478 + 0.298020i
$$77$$ 2.00000 0.227921
$$78$$ 0 0
$$79$$ 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i $$0.0457135\pi$$
−0.370907 + 0.928670i $$0.620953\pi$$
$$80$$ −0.500000 + 0.866025i −0.0559017 + 0.0968246i
$$81$$ 0 0
$$82$$ −1.00000 + 1.73205i −0.110432 + 0.191273i
$$83$$ −2.00000 −0.219529 −0.109764 0.993958i $$-0.535010\pi$$
−0.109764 + 0.993958i $$0.535010\pi$$
$$84$$ 0 0
$$85$$ 2.00000 3.46410i 0.216930 0.375735i
$$86$$ −2.50000 + 4.33013i −0.269582 + 0.466930i
$$87$$ 0 0
$$88$$ 2.00000 0.213201
$$89$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$90$$ 0 0
$$91$$ −1.50000 + 2.59808i −0.157243 + 0.272352i
$$92$$ −3.00000 5.19615i −0.312772 0.541736i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −0.500000 4.33013i −0.0512989 0.444262i
$$96$$ 0 0
$$97$$ 1.00000 + 1.73205i 0.101535 + 0.175863i 0.912317 0.409484i $$-0.134291\pi$$
−0.810782 + 0.585348i $$0.800958\pi$$
$$98$$ −3.00000 5.19615i −0.303046 0.524891i
$$99$$ 0 0
$$100$$ −0.500000 0.866025i −0.0500000 0.0866025i
$$101$$ 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i $$-0.736843\pi$$
0.975796 + 0.218685i $$0.0701767\pi$$
$$102$$ 0 0
$$103$$ 19.0000 1.87213 0.936063 0.351833i $$-0.114441\pi$$
0.936063 + 0.351833i $$0.114441\pi$$
$$104$$ −1.50000 + 2.59808i −0.147087 + 0.254762i
$$105$$ 0 0
$$106$$ −12.0000 −1.16554
$$107$$ 4.00000 0.386695 0.193347 0.981130i $$-0.438066\pi$$
0.193347 + 0.981130i $$0.438066\pi$$
$$108$$ 0 0
$$109$$ 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i $$0.164149\pi$$
−0.00790932 + 0.999969i $$0.502518\pi$$
$$110$$ −1.00000 + 1.73205i −0.0953463 + 0.165145i
$$111$$ 0 0
$$112$$ 0.500000 + 0.866025i 0.0472456 + 0.0818317i
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ 6.00000 0.559503
$$116$$ −5.00000 8.66025i −0.464238 0.804084i
$$117$$ 0 0
$$118$$ 1.00000 1.73205i 0.0920575 0.159448i
$$119$$ −2.00000 3.46410i −0.183340 0.317554i
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ −5.00000 −0.452679
$$123$$ 0 0
$$124$$ −0.500000 + 0.866025i −0.0449013 + 0.0777714i
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −8.00000 + 13.8564i −0.709885 + 1.22956i 0.255014 + 0.966937i $$0.417920\pi$$
−0.964899 + 0.262620i $$0.915413\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ −1.50000 2.59808i −0.131559 0.227866i
$$131$$ −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i $$-0.251085\pi$$
−0.966803 + 0.255524i $$0.917752\pi$$
$$132$$ 0 0
$$133$$ −4.00000 1.73205i −0.346844 0.150188i
$$134$$ 5.00000 0.431934
$$135$$ 0 0
$$136$$ −2.00000 3.46410i −0.171499 0.297044i
$$137$$ −1.00000 + 1.73205i −0.0854358 + 0.147979i −0.905577 0.424182i $$-0.860562\pi$$
0.820141 + 0.572161i $$0.193895\pi$$
$$138$$ 0 0
$$139$$ 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i $$-0.708677\pi$$
0.991303 + 0.131597i $$0.0420106\pi$$
$$140$$ −1.00000 −0.0845154
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −3.00000 + 5.19615i −0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ 10.0000 0.830455
$$146$$ 5.50000 9.52628i 0.455183 0.788400i
$$147$$ 0 0
$$148$$ 2.50000 4.33013i 0.205499 0.355934i
$$149$$ 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i $$0.0972370\pi$$
−0.216394 + 0.976306i $$0.569430\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ −4.00000 1.73205i −0.324443 0.140488i
$$153$$ 0 0
$$154$$ 1.00000 + 1.73205i 0.0805823 + 0.139573i
$$155$$ −0.500000 0.866025i −0.0401610 0.0695608i
$$156$$ 0 0
$$157$$ 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i $$0.00693820\pi$$
−0.481006 + 0.876717i $$0.659728\pi$$
$$158$$ −5.50000 + 9.52628i −0.437557 + 0.757870i
$$159$$ 0 0
$$160$$ −1.00000 −0.0790569
$$161$$ 3.00000 5.19615i 0.236433 0.409514i
$$162$$ 0 0
$$163$$ −17.0000 −1.33154 −0.665771 0.746156i $$-0.731897\pi$$
−0.665771 + 0.746156i $$0.731897\pi$$
$$164$$ −2.00000 −0.156174
$$165$$ 0 0
$$166$$ −1.00000 1.73205i −0.0776151 0.134433i
$$167$$ 7.00000 12.1244i 0.541676 0.938211i −0.457132 0.889399i $$-0.651123\pi$$
0.998808 0.0488118i $$-0.0155435\pi$$
$$168$$ 0 0
$$169$$ 2.00000 + 3.46410i 0.153846 + 0.266469i
$$170$$ 4.00000 0.306786
$$171$$ 0 0
$$172$$ −5.00000 −0.381246
$$173$$ −13.0000 22.5167i −0.988372 1.71191i −0.625871 0.779926i $$-0.715256\pi$$
−0.362500 0.931984i $$-0.618077\pi$$
$$174$$ 0 0
$$175$$ 0.500000 0.866025i 0.0377964 0.0654654i
$$176$$ 1.00000 + 1.73205i 0.0753778 + 0.130558i
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 10.0000 0.747435 0.373718 0.927543i $$-0.378083\pi$$
0.373718 + 0.927543i $$0.378083\pi$$
$$180$$ 0 0
$$181$$ 3.00000 5.19615i 0.222988 0.386227i −0.732726 0.680524i $$-0.761752\pi$$
0.955714 + 0.294297i $$0.0950855\pi$$
$$182$$ −3.00000 −0.222375
$$183$$ 0 0
$$184$$ 3.00000 5.19615i 0.221163 0.383065i
$$185$$ 2.50000 + 4.33013i 0.183804 + 0.318357i
$$186$$ 0 0
$$187$$ −4.00000 6.92820i −0.292509 0.506640i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 3.50000 2.59808i 0.253917 0.188484i
$$191$$ −16.0000 −1.15772 −0.578860 0.815427i $$-0.696502\pi$$
−0.578860 + 0.815427i $$0.696502\pi$$
$$192$$ 0 0
$$193$$ −12.5000 21.6506i −0.899770 1.55845i −0.827788 0.561041i $$-0.810401\pi$$
−0.0719816 0.997406i $$-0.522932\pi$$
$$194$$ −1.00000 + 1.73205i −0.0717958 + 0.124354i
$$195$$ 0 0
$$196$$ 3.00000 5.19615i 0.214286 0.371154i
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ −2.50000 + 4.33013i −0.177220 + 0.306955i −0.940927 0.338608i $$-0.890044\pi$$
0.763707 + 0.645563i $$0.223377\pi$$
$$200$$ 0.500000 0.866025i 0.0353553 0.0612372i
$$201$$ 0 0
$$202$$ 6.00000 0.422159
$$203$$ 5.00000 8.66025i 0.350931 0.607831i
$$204$$ 0 0
$$205$$ 1.00000 1.73205i 0.0698430 0.120972i
$$206$$ 9.50000 + 16.4545i 0.661896 + 1.14644i
$$207$$ 0 0
$$208$$ −3.00000 −0.208013
$$209$$ −8.00000 3.46410i −0.553372 0.239617i
$$210$$ 0 0
$$211$$ 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i $$-0.111609\pi$$
−0.767049 + 0.641588i $$0.778276\pi$$
$$212$$ −6.00000 10.3923i −0.412082 0.713746i
$$213$$ 0 0
$$214$$ 2.00000 + 3.46410i 0.136717 + 0.236801i
$$215$$ 2.50000 4.33013i 0.170499 0.295312i
$$216$$ 0 0
$$217$$ −1.00000 −0.0678844
$$218$$ −9.00000 + 15.5885i −0.609557 + 1.05578i
$$219$$ 0 0
$$220$$ −2.00000 −0.134840
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i $$-0.156007\pi$$
−0.848799 + 0.528716i $$0.822674\pi$$
$$224$$ −0.500000 + 0.866025i −0.0334077 + 0.0578638i
$$225$$ 0 0
$$226$$ −7.00000 12.1244i −0.465633 0.806500i
$$227$$ 18.0000 1.19470 0.597351 0.801980i $$-0.296220\pi$$
0.597351 + 0.801980i $$0.296220\pi$$
$$228$$ 0 0
$$229$$ −5.00000 −0.330409 −0.165205 0.986259i $$-0.552828\pi$$
−0.165205 + 0.986259i $$0.552828\pi$$
$$230$$ 3.00000 + 5.19615i 0.197814 + 0.342624i
$$231$$ 0 0
$$232$$ 5.00000 8.66025i 0.328266 0.568574i
$$233$$ −2.00000 3.46410i −0.131024 0.226941i 0.793047 0.609160i $$-0.208493\pi$$
−0.924072 + 0.382219i $$0.875160\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 2.00000 0.130189
$$237$$ 0 0
$$238$$ 2.00000 3.46410i 0.129641 0.224544i
$$239$$ 18.0000 1.16432 0.582162 0.813073i $$-0.302207\pi$$
0.582162 + 0.813073i $$0.302207\pi$$
$$240$$ 0 0
$$241$$ −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i $$-0.884818\pi$$
0.774202 + 0.632938i $$0.218151\pi$$
$$242$$ −3.50000 6.06218i −0.224989 0.389692i
$$243$$ 0 0
$$244$$ −2.50000 4.33013i −0.160046 0.277208i
$$245$$ 3.00000 + 5.19615i 0.191663 + 0.331970i
$$246$$ 0 0
$$247$$ 10.5000 7.79423i 0.668099 0.495935i
$$248$$ −1.00000 −0.0635001
$$249$$ 0 0
$$250$$ 0.500000 + 0.866025i 0.0316228 + 0.0547723i
$$251$$ −1.00000 + 1.73205i −0.0631194 + 0.109326i −0.895858 0.444340i $$-0.853438\pi$$
0.832739 + 0.553666i $$0.186772\pi$$
$$252$$ 0 0
$$253$$ 6.00000 10.3923i 0.377217 0.653359i
$$254$$ −16.0000 −1.00393
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i $$-0.893253\pi$$
0.757159 + 0.653231i $$0.226587\pi$$
$$258$$ 0 0
$$259$$ 5.00000 0.310685
$$260$$ 1.50000 2.59808i 0.0930261 0.161126i
$$261$$ 0 0
$$262$$ 3.00000 5.19615i 0.185341 0.321019i
$$263$$ −5.00000 8.66025i −0.308313 0.534014i 0.669680 0.742650i $$-0.266431\pi$$
−0.977993 + 0.208635i $$0.933098\pi$$
$$264$$ 0 0
$$265$$ 12.0000 0.737154
$$266$$ −0.500000 4.33013i −0.0306570 0.265497i
$$267$$ 0 0
$$268$$ 2.50000 + 4.33013i 0.152712 + 0.264505i
$$269$$ 5.00000 + 8.66025i 0.304855 + 0.528025i 0.977229 0.212187i $$-0.0680585\pi$$
−0.672374 + 0.740212i $$0.734725\pi$$
$$270$$ 0 0
$$271$$ 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i $$-0.0885408\pi$$
−0.718580 + 0.695444i $$0.755208\pi$$
$$272$$ 2.00000 3.46410i 0.121268 0.210042i
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 1.00000 1.73205i 0.0603023 0.104447i
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 9.00000 0.539784
$$279$$ 0 0
$$280$$ −0.500000 0.866025i −0.0298807 0.0517549i
$$281$$ −15.0000 + 25.9808i −0.894825 + 1.54988i −0.0608039 + 0.998150i $$0.519366\pi$$
−0.834021 + 0.551733i $$0.813967\pi$$
$$282$$ 0 0
$$283$$ −4.00000 6.92820i −0.237775 0.411839i 0.722300 0.691580i $$-0.243085\pi$$
−0.960076 + 0.279741i $$0.909752\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −6.00000 −0.354787
$$287$$ −1.00000 1.73205i −0.0590281 0.102240i
$$288$$ 0 0
$$289$$ 0.500000 0.866025i 0.0294118 0.0509427i
$$290$$ 5.00000 + 8.66025i 0.293610 + 0.508548i
$$291$$ 0 0
$$292$$ 11.0000 0.643726
$$293$$ 26.0000 1.51894 0.759468 0.650545i $$-0.225459\pi$$
0.759468 + 0.650545i $$0.225459\pi$$
$$294$$ 0 0
$$295$$ −1.00000 + 1.73205i −0.0582223 + 0.100844i
$$296$$ 5.00000 0.290619
$$297$$ 0 0
$$298$$ −9.00000 + 15.5885i −0.521356 + 0.903015i
$$299$$ 9.00000 + 15.5885i 0.520483 + 0.901504i
$$300$$ 0 0
$$301$$ −2.50000 4.33013i −0.144098 0.249584i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −0.500000 4.33013i −0.0286770 0.248350i
$$305$$ 5.00000 0.286299
$$306$$ 0 0
$$307$$ −2.00000 3.46410i −0.114146 0.197707i 0.803292 0.595585i $$-0.203080\pi$$
−0.917438 + 0.397879i $$0.869747\pi$$
$$308$$ −1.00000 + 1.73205i −0.0569803 + 0.0986928i
$$309$$ 0 0
$$310$$ 0.500000 0.866025i 0.0283981 0.0491869i
$$311$$ 10.0000 0.567048 0.283524 0.958965i $$-0.408496\pi$$
0.283524 + 0.958965i $$0.408496\pi$$
$$312$$ 0 0
$$313$$ −9.00000 + 15.5885i −0.508710 + 0.881112i 0.491239 + 0.871025i $$0.336544\pi$$
−0.999949 + 0.0100869i $$0.996789\pi$$
$$314$$ −6.50000 + 11.2583i −0.366816 + 0.635344i
$$315$$ 0 0
$$316$$ −11.0000 −0.618798
$$317$$ 15.0000 25.9808i 0.842484 1.45922i −0.0453045 0.998973i $$-0.514426\pi$$
0.887788 0.460252i $$-0.152241\pi$$
$$318$$ 0 0
$$319$$ 10.0000 17.3205i 0.559893 0.969762i
$$320$$ −0.500000 0.866025i −0.0279508 0.0484123i
$$321$$ 0 0
$$322$$ 6.00000 0.334367
$$323$$ 2.00000 + 17.3205i 0.111283 + 0.963739i
$$324$$ 0 0
$$325$$ 1.50000 + 2.59808i 0.0832050 + 0.144115i
$$326$$ −8.50000 14.7224i −0.470771 0.815400i
$$327$$ 0 0
$$328$$ −1.00000 1.73205i −0.0552158 0.0956365i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 5.00000 0.274825 0.137412 0.990514i $$-0.456121\pi$$
0.137412 + 0.990514i $$0.456121\pi$$
$$332$$ 1.00000 1.73205i 0.0548821 0.0950586i
$$333$$ 0 0
$$334$$ 14.0000 0.766046
$$335$$ −5.00000 −0.273179
$$336$$ 0 0
$$337$$ −11.5000 19.9186i −0.626445 1.08503i −0.988260 0.152784i $$-0.951176\pi$$
0.361815 0.932250i $$-0.382157\pi$$
$$338$$ −2.00000 + 3.46410i −0.108786 + 0.188422i
$$339$$ 0 0
$$340$$ 2.00000 + 3.46410i 0.108465 + 0.187867i
$$341$$ −2.00000 −0.108306
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ −2.50000 4.33013i −0.134791 0.233465i
$$345$$ 0 0
$$346$$ 13.0000 22.5167i 0.698884 1.21050i
$$347$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$348$$ 0 0
$$349$$ 17.0000 0.909989 0.454995 0.890494i $$-0.349641\pi$$
0.454995 + 0.890494i $$0.349641\pi$$
$$350$$ 1.00000 0.0534522
$$351$$ 0 0
$$352$$ −1.00000 + 1.73205i −0.0533002 + 0.0923186i
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 5.00000 + 8.66025i 0.264258 + 0.457709i
$$359$$ −1.00000 1.73205i −0.0527780 0.0914141i 0.838429 0.545010i $$-0.183474\pi$$
−0.891207 + 0.453596i $$0.850141\pi$$
$$360$$ 0 0
$$361$$ 13.0000 + 13.8564i 0.684211 + 0.729285i
$$362$$ 6.00000 0.315353
$$363$$ 0 0
$$364$$ −1.50000 2.59808i −0.0786214 0.136176i
$$365$$ −5.50000 + 9.52628i −0.287883 + 0.498628i
$$366$$ 0 0
$$367$$ 3.50000 6.06218i 0.182699 0.316443i −0.760100 0.649806i $$-0.774850\pi$$
0.942799 + 0.333363i $$0.108183\pi$$
$$368$$ 6.00000 0.312772
$$369$$ 0 0
$$370$$ −2.50000 + 4.33013i −0.129969 + 0.225113i
$$371$$ 6.00000 10.3923i 0.311504 0.539542i
$$372$$ 0 0
$$373$$ −22.0000 −1.13912 −0.569558 0.821951i $$-0.692886\pi$$
−0.569558 + 0.821951i $$0.692886\pi$$
$$374$$ 4.00000 6.92820i 0.206835 0.358249i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 15.0000 + 25.9808i 0.772539 + 1.33808i
$$378$$ 0 0
$$379$$ −11.0000 −0.565032 −0.282516 0.959263i $$-0.591169\pi$$
−0.282516 + 0.959263i $$0.591169\pi$$
$$380$$ 4.00000 + 1.73205i 0.205196 + 0.0888523i
$$381$$ 0 0
$$382$$ −8.00000 13.8564i −0.409316 0.708955i
$$383$$ −18.0000 31.1769i −0.919757 1.59307i −0.799783 0.600289i $$-0.795052\pi$$
−0.119974 0.992777i $$-0.538281\pi$$
$$384$$ 0 0
$$385$$ −1.00000 1.73205i −0.0509647 0.0882735i
$$386$$ 12.5000 21.6506i 0.636233 1.10199i
$$387$$ 0 0
$$388$$ −2.00000 −0.101535
$$389$$ −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i $$-0.914918\pi$$
0.710980 + 0.703213i $$0.248252\pi$$
$$390$$ 0 0
$$391$$ −24.0000 −1.21373
$$392$$ 6.00000 0.303046
$$393$$ 0 0
$$394$$ 9.00000 + 15.5885i 0.453413 + 0.785335i
$$395$$ 5.50000 9.52628i 0.276735 0.479319i
$$396$$ 0 0
$$397$$ 0.500000 + 0.866025i 0.0250943 + 0.0434646i 0.878300 0.478110i $$-0.158678\pi$$
−0.853206 + 0.521575i $$0.825345\pi$$
$$398$$ −5.00000 −0.250627
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ −19.0000 32.9090i −0.948815 1.64340i −0.747927 0.663781i $$-0.768951\pi$$
−0.200888 0.979614i $$-0.564383\pi$$
$$402$$ 0 0
$$403$$ 1.50000 2.59808i 0.0747203 0.129419i
$$404$$ 3.00000 + 5.19615i 0.149256 + 0.258518i
$$405$$ 0 0
$$406$$ 10.0000 0.496292
$$407$$ 10.0000 0.495682
$$408$$ 0 0
$$409$$ 15.0000 25.9808i 0.741702 1.28467i −0.210017 0.977698i $$-0.567352\pi$$
0.951720 0.306968i $$-0.0993146\pi$$
$$410$$ 2.00000 0.0987730
$$411$$ 0 0
$$412$$ −9.50000 + 16.4545i −0.468031 + 0.810654i
$$413$$ 1.00000 + 1.73205i 0.0492068 + 0.0852286i
$$414$$ 0 0
$$415$$ 1.00000 + 1.73205i 0.0490881 + 0.0850230i
$$416$$ −1.50000 2.59808i −0.0735436 0.127381i
$$417$$ 0 0
$$418$$ −1.00000 8.66025i −0.0489116 0.423587i
$$419$$ 24.0000 1.17248 0.586238 0.810139i $$-0.300608\pi$$
0.586238 + 0.810139i $$0.300608\pi$$
$$420$$ 0 0
$$421$$ 7.00000 + 12.1244i 0.341159 + 0.590905i 0.984648 0.174550i $$-0.0558472\pi$$
−0.643489 + 0.765455i $$0.722514\pi$$
$$422$$ −2.50000 + 4.33013i −0.121698 + 0.210787i
$$423$$ 0 0
$$424$$ 6.00000 10.3923i 0.291386 0.504695i
$$425$$ −4.00000 −0.194029
$$426$$ 0 0
$$427$$ 2.50000 4.33013i 0.120983 0.209550i
$$428$$ −2.00000 + 3.46410i −0.0966736 + 0.167444i
$$429$$ 0 0
$$430$$ 5.00000 0.241121
$$431$$ −10.0000 + 17.3205i −0.481683 + 0.834300i −0.999779 0.0210230i $$-0.993308\pi$$
0.518096 + 0.855323i $$0.326641\pi$$
$$432$$ 0 0
$$433$$ −14.5000 + 25.1147i −0.696826 + 1.20694i 0.272736 + 0.962089i $$0.412071\pi$$
−0.969561 + 0.244848i $$0.921262\pi$$
$$434$$ −0.500000 0.866025i −0.0240008 0.0415705i
$$435$$ 0 0
$$436$$ −18.0000 −0.862044
$$437$$ −21.0000 + 15.5885i −1.00457 + 0.745697i
$$438$$ 0 0
$$439$$ 20.5000 + 35.5070i 0.978412 + 1.69466i 0.668184 + 0.743996i $$0.267072\pi$$
0.310228 + 0.950662i $$0.399595\pi$$
$$440$$ −1.00000 1.73205i −0.0476731 0.0825723i
$$441$$ 0 0
$$442$$ 6.00000 + 10.3923i 0.285391 + 0.494312i
$$443$$ 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i $$-0.741317\pi$$
0.972626 + 0.232377i $$0.0746503\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −0.500000 + 0.866025i −0.0236757 + 0.0410075i
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ −28.0000 −1.32140 −0.660701 0.750649i $$-0.729741\pi$$
−0.660701 + 0.750649i $$0.729741\pi$$
$$450$$ 0 0
$$451$$ −2.00000 3.46410i −0.0941763 0.163118i
$$452$$ 7.00000 12.1244i 0.329252 0.570282i
$$453$$ 0 0
$$454$$ 9.00000 + 15.5885i 0.422391 + 0.731603i
$$455$$ 3.00000 0.140642
$$456$$ 0 0
$$457$$ 23.0000 1.07589 0.537947 0.842978i $$-0.319200\pi$$
0.537947 + 0.842978i $$0.319200\pi$$
$$458$$ −2.50000 4.33013i −0.116817 0.202334i
$$459$$ 0 0
$$460$$ −3.00000 + 5.19615i −0.139876 + 0.242272i
$$461$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$462$$ 0 0
$$463$$ 1.00000 0.0464739 0.0232370 0.999730i $$-0.492603\pi$$
0.0232370 + 0.999730i $$0.492603\pi$$
$$464$$ 10.0000 0.464238
$$465$$ 0 0
$$466$$ 2.00000 3.46410i 0.0926482 0.160471i
$$467$$ −30.0000 −1.38823 −0.694117 0.719862i $$-0.744205\pi$$
−0.694117 + 0.719862i $$0.744205\pi$$
$$468$$ 0 0
$$469$$ −2.50000 + 4.33013i −0.115439 + 0.199947i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.00000 + 1.73205i 0.0460287 + 0.0797241i
$$473$$ −5.00000 8.66025i −0.229900 0.398199i
$$474$$ 0 0
$$475$$ −3.50000 + 2.59808i −0.160591 + 0.119208i
$$476$$ 4.00000 0.183340
$$477$$ 0 0
$$478$$ 9.00000 + 15.5885i 0.411650 + 0.712999i
$$479$$ 21.0000 36.3731i 0.959514 1.66193i 0.235833 0.971794i $$-0.424218\pi$$
0.723681 0.690134i $$-0.242449\pi$$
$$480$$ 0 0
$$481$$ −7.50000 + 12.9904i −0.341971 + 0.592310i
$$482$$ −5.00000 −0.227744
$$483$$ 0 0
$$484$$ 3.50000 6.06218i 0.159091 0.275554i
$$485$$ 1.00000 1.73205i 0.0454077 0.0786484i
$$486$$ 0 0
$$487$$ 16.0000 0.725029 0.362515 0.931978i $$-0.381918\pi$$
0.362515 + 0.931978i $$0.381918\pi$$
$$488$$ 2.50000 4.33013i 0.113170 0.196016i
$$489$$ 0 0
$$490$$ −3.00000 + 5.19615i −0.135526 + 0.234738i
$$491$$ 14.0000 + 24.2487i 0.631811 + 1.09433i 0.987181 + 0.159603i $$0.0510215\pi$$
−0.355370 + 0.934726i $$0.615645\pi$$
$$492$$ 0 0
$$493$$ −40.0000 −1.80151
$$494$$ 12.0000 + 5.19615i 0.539906 + 0.233786i
$$495$$ 0 0
$$496$$ −0.500000 0.866025i −0.0224507 0.0388857i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i $$0.0223697\pi$$
−0.437955 + 0.898997i $$0.644297\pi$$
$$500$$ −0.500000 + 0.866025i −0.0223607 + 0.0387298i
$$501$$ 0 0
$$502$$ −2.00000 −0.0892644
$$503$$ 22.0000 38.1051i 0.980932 1.69902i 0.322151 0.946688i $$-0.395594\pi$$
0.658781 0.752335i $$-0.271072\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 12.0000 0.533465
$$507$$ 0 0
$$508$$ −8.00000 13.8564i −0.354943 0.614779i
$$509$$ −4.00000 + 6.92820i −0.177297 + 0.307087i −0.940954 0.338535i $$-0.890069\pi$$
0.763657 + 0.645622i $$0.223402\pi$$
$$510$$ 0 0
$$511$$ 5.50000 + 9.52628i 0.243306 + 0.421418i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −6.00000 −0.264649
$$515$$ −9.50000 16.4545i −0.418620 0.725071i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 2.50000 + 4.33013i 0.109844 + 0.190255i
$$519$$ 0 0
$$520$$ 3.00000 0.131559
$$521$$ −8.00000 −0.350486 −0.175243 0.984525i $$-0.556071\pi$$
−0.175243 + 0.984525i $$0.556071\pi$$
$$522$$ 0 0
$$523$$ 5.50000 9.52628i 0.240498 0.416555i −0.720358 0.693602i $$-0.756023\pi$$
0.960856 + 0.277047i $$0.0893559\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ 5.00000 8.66025i 0.218010 0.377605i
$$527$$ 2.00000 + 3.46410i 0.0871214 + 0.150899i
$$528$$ 0 0
$$529$$ −6.50000 11.2583i −0.282609 0.489493i
$$530$$ 6.00000 + 10.3923i 0.260623 + 0.451413i
$$531$$ 0 0
$$532$$ 3.50000 2.59808i 0.151744 0.112641i
$$533$$ 6.00000 0.259889
$$534$$ 0 0
$$535$$ −2.00000 3.46410i −0.0864675 0.149766i
$$536$$ −2.50000 + 4.33013i −0.107984 + 0.187033i
$$537$$ 0 0
$$538$$ −5.00000 + 8.66025i −0.215565 + 0.373370i
$$539$$ 12.0000 0.516877
$$540$$ 0 0
$$541$$ 4.50000 7.79423i 0.193470 0.335100i −0.752928 0.658103i $$-0.771359\pi$$
0.946398 + 0.323003i $$0.104692\pi$$
$$542$$ −4.00000 + 6.92820i −0.171815 + 0.297592i
$$543$$ 0 0
$$544$$ 4.00000 0.171499
$$545$$ 9.00000 15.5885i 0.385518 0.667736i
$$546$$ 0 0
$$547$$ 4.50000 7.79423i 0.192406 0.333257i −0.753641 0.657286i $$-0.771704\pi$$
0.946047 + 0.324029i $$0.105038\pi$$
$$548$$ −1.00000 1.73205i −0.0427179 0.0739895i
$$549$$ 0 0
$$550$$ 2.00000 0.0852803
$$551$$ −35.0000 + 25.9808i −1.49105 + 1.10682i
$$552$$ 0 0
$$553$$ −5.50000 9.52628i −0.233884 0.405099i
$$554$$ −5.00000 8.66025i −0.212430 0.367939i
$$555$$ 0 0
$$556$$ 4.50000 + 7.79423i 0.190843 + 0.330549i
$$557$$ −6.00000 + 10.3923i −0.254228 + 0.440336i −0.964686 0.263404i $$-0.915155\pi$$
0.710457 + 0.703740i $$0.248488\pi$$
$$558$$ 0 0
$$559$$ 15.0000 0.634432
$$560$$ 0.500000 0.866025i 0.0211289 0.0365963i
$$561$$ 0 0
$$562$$ −30.0000 −1.26547
$$563$$ −22.0000 −0.927189 −0.463595 0.886047i $$-0.653441\pi$$
−0.463595 + 0.886047i $$0.653441\pi$$
$$564$$ 0 0
$$565$$ 7.00000 + 12.1244i 0.294492 + 0.510075i
$$566$$ 4.00000 6.92820i 0.168133 0.291214i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 39.0000 1.63210 0.816050 0.577982i $$-0.196160\pi$$
0.816050 + 0.577982i $$0.196160\pi$$
$$572$$ −3.00000 5.19615i −0.125436 0.217262i
$$573$$ 0 0
$$574$$ 1.00000 1.73205i 0.0417392 0.0722944i
$$575$$ −3.00000 5.19615i −0.125109 0.216695i
$$576$$ 0 0
$$577$$ −18.0000 −0.749350 −0.374675 0.927156i $$-0.622246\pi$$
−0.374675 + 0.927156i $$0.622246\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ 0 0
$$580$$ −5.00000 + 8.66025i −0.207614 + 0.359597i
$$581$$ 2.00000 0.0829740
$$582$$ 0 0
$$583$$ 12.0000 20.7846i 0.496989 0.860811i
$$584$$ 5.50000 + 9.52628i 0.227592 + 0.394200i
$$585$$ 0 0
$$586$$ 13.0000 + 22.5167i 0.537025 + 0.930155i
$$587$$ 9.00000 + 15.5885i 0.371470 + 0.643404i 0.989792 0.142520i $$-0.0455206\pi$$
−0.618322 + 0.785925i $$0.712187\pi$$
$$588$$ 0 0
$$589$$ 4.00000 + 1.73205i 0.164817 + 0.0713679i
$$590$$ −2.00000 −0.0823387
$$591$$ 0 0
$$592$$ 2.50000 + 4.33013i 0.102749 + 0.177967i
$$593$$ 14.0000 24.2487i 0.574911 0.995775i −0.421140 0.906996i $$-0.638370\pi$$
0.996051 0.0887797i $$-0.0282967\pi$$
$$594$$ 0 0
$$595$$ −2.00000 + 3.46410i −0.0819920 + 0.142014i
$$596$$ −18.0000 −0.737309
$$597$$ 0 0
$$598$$ −9.00000 + 15.5885i −0.368037 + 0.637459i
$$599$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$600$$ 0 0
$$601$$ 7.00000 0.285536 0.142768 0.989756i $$-0.454400\pi$$
0.142768 + 0.989756i $$0.454400\pi$$
$$602$$ 2.50000 4.33013i 0.101892 0.176483i
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 3.50000 + 6.06218i 0.142295 + 0.246463i
$$606$$ 0 0
$$607$$ −9.00000 −0.365299 −0.182649 0.983178i $$-0.558467\pi$$
−0.182649 + 0.983178i $$0.558467\pi$$
$$608$$ 3.50000 2.59808i 0.141944 0.105366i
$$609$$ 0 0
$$610$$ 2.50000 + 4.33013i 0.101222 + 0.175322i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 11.0000 + 19.0526i 0.444286 + 0.769526i 0.998002 0.0631797i $$-0.0201241\pi$$
−0.553716 + 0.832705i $$0.686791\pi$$
$$614$$ 2.00000 3.46410i 0.0807134 0.139800i
$$615$$ 0 0
$$616$$ −2.00000 −0.0805823
$$617$$ 12.0000 20.7846i 0.483102 0.836757i −0.516710 0.856161i $$-0.672843\pi$$
0.999812 + 0.0194037i $$0.00617676\pi$$
$$618$$ 0 0
$$619$$ −29.0000 −1.16561 −0.582804 0.812613i $$-0.698045\pi$$
−0.582804 + 0.812613i $$0.698045\pi$$
$$620$$ 1.00000 0.0401610
$$621$$ 0 0
$$622$$ 5.00000 + 8.66025i 0.200482 + 0.347245i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ −18.0000 −0.719425
$$627$$ 0 0
$$628$$ −13.0000 −0.518756
$$629$$ −10.0000 17.3205i −0.398726 0.690614i
$$630$$ 0 0
$$631$$ 21.5000 37.2391i 0.855901 1.48246i −0.0199047 0.999802i $$-0.506336\pi$$
0.875806 0.482663i $$-0.160330\pi$$
$$632$$ −5.50000 9.52628i −0.218778 0.378935i
$$633$$ 0 0
$$634$$ 30.0000 1.19145
$$635$$ 16.0000 0.634941
$$636$$ 0 0
$$637$$ −9.00000 + 15.5885i −0.356593 + 0.617637i
$$638$$ 20.0000 0.791808
$$639$$ 0 0
$$640$$ 0.500000 0.866025i 0.0197642 0.0342327i
$$641$$ 12.0000 + 20.7846i 0.473972 + 0.820943i 0.999556 0.0297987i $$-0.00948663\pi$$
−0.525584 + 0.850741i $$0.676153\pi$$
$$642$$ 0 0
$$643$$ −20.5000 35.5070i −0.808441 1.40026i −0.913943 0.405842i $$-0.866978\pi$$
0.105502 0.994419i $$-0.466355\pi$$
$$644$$ 3.00000 + 5.19615i 0.118217 + 0.204757i
$$645$$ 0 0
$$646$$ −14.0000 + 10.3923i −0.550823 + 0.408880i
$$647$$ −46.0000 −1.80845 −0.904223 0.427060i $$-0.859549\pi$$
−0.904223 + 0.427060i $$0.859549\pi$$
$$648$$ 0 0
$$649$$ 2.00000 + 3.46410i 0.0785069 + 0.135978i
$$650$$ −1.50000 + 2.59808i −0.0588348 + 0.101905i
$$651$$ 0 0
$$652$$ 8.50000 14.7224i 0.332886 0.576575i
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ −3.00000 + 5.19615i −0.117220 + 0.203030i
$$656$$ 1.00000 1.73205i 0.0390434 0.0676252i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 9.00000 15.5885i 0.350590 0.607240i −0.635763 0.771885i $$-0.719314\pi$$
0.986353 + 0.164644i $$0.0526477\pi$$
$$660$$ 0 0
$$661$$ −23.0000 + 39.8372i −0.894596 + 1.54949i −0.0602929 + 0.998181i $$0.519203\pi$$
−0.834303 + 0.551306i $$0.814130\pi$$
$$662$$ 2.50000 + 4.33013i 0.0971653 + 0.168295i
$$663$$ 0 0
$$664$$ 2.00000 0.0776151
$$665$$ 0.500000 + 4.33013i 0.0193892 + 0.167915i
$$666$$ 0 0
$$667$$ −30.0000 51.9615i −1.16160 2.01196i
$$668$$ 7.00000 + 12.1244i 0.270838 + 0.469105i
$$669$$ 0 0
$$670$$ −2.50000 4.33013i −0.0965834 0.167287i
$$671$$ 5.00000 8.66025i 0.193023 0.334325i
$$672$$ 0 0
$$673$$ −23.0000 −0.886585 −0.443292 0.896377i $$-0.646190\pi$$
−0.443292 + 0.896377i $$0.646190\pi$$
$$674$$ 11.5000 19.9186i 0.442963 0.767235i
$$675$$ 0 0
$$676$$ −4.00000 −0.153846
$$677$$ −48.0000 −1.84479 −0.922395 0.386248i $$-0.873771\pi$$
−0.922395 + 0.386248i $$0.873771\pi$$
$$678$$ 0 0
$$679$$ −1.00000 1.73205i −0.0383765 0.0664700i
$$680$$ −2.00000 + 3.46410i −0.0766965 + 0.132842i
$$681$$ 0 0
$$682$$ −1.00000 1.73205i −0.0382920 0.0663237i
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 2.00000 0.0764161
$$686$$ 6.50000 + 11.2583i 0.248171 + 0.429845i
$$687$$ 0 0
$$688$$ 2.50000 4.33013i 0.0953116 0.165085i
$$689$$ 18.0000 + 31.1769i 0.685745 + 1.18775i
$$690$$ 0 0
$$691$$ 4.00000 0.152167 0.0760836 0.997101i $$-0.475758\pi$$
0.0760836 + 0.997101i $$0.475758\pi$$
$$692$$ 26.0000 0.988372
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −9.00000 −0.341389
$$696$$ 0 0
$$697$$ −4.00000 + 6.92820i −0.151511 + 0.262424i
$$698$$ 8.50000 + 14.7224i 0.321730 + 0.557252i
$$699$$ 0 0
$$700$$ 0.500000 + 0.866025i 0.0188982 + 0.0327327i
$$701$$ 14.0000 + 24.2487i 0.528773 + 0.915861i 0.999437 + 0.0335489i $$0.0106809\pi$$
−0.470664 + 0.882312i $$0.655986\pi$$
$$702$$ 0 0
$$703$$ −20.0000 8.66025i −0.754314 0.326628i
$$704$$ −2.00000 −0.0753778
$$705$$ 0 0
$$706$$ 3.00000 + 5.19615i 0.112906 + 0.195560i
$$707$$ −3.00000 + 5.19615i −0.112827 + 0.195421i
$$708$$ 0 0
$$709$$ −9.50000 + 16.4545i −0.356780 + 0.617961i −0.987421 0.158114i $$-0.949459\pi$$
0.630641 + 0.776075i $$0.282792\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −3.00000 + 5.19615i −0.112351 + 0.194597i
$$714$$ 0 0
$$715$$ 6.00000 0.224387
$$716$$ −5.00000 + 8.66025i −0.186859 + 0.323649i
$$717$$ 0 0
$$718$$ 1.00000 1.73205i 0.0373197 0.0646396i
$$719$$ 13.0000 + 22.5167i 0.484818 + 0.839730i 0.999848 0.0174426i $$-0.00555244\pi$$
−0.515030 + 0.857172i $$0.672219\pi$$
$$720$$ 0 0
$$721$$ −19.0000 −0.707597
$$722$$ −5.50000 + 18.1865i −0.204689 + 0.676833i
$$723$$ 0 0
$$724$$ 3.00000 + 5.19615i 0.111494 + 0.193113i
$$725$$ −5.00000 8.66025i −0.185695 0.321634i
$$726$$ 0 0
$$727$$ 22.5000 + 38.9711i 0.834479 + 1.44536i 0.894454 + 0.447160i $$0.147564\pi$$
−0.0599753 + 0.998200i $$0.519102\pi$$
$$728$$ 1.50000 2.59808i 0.0555937 0.0962911i
$$729$$ 0 0
$$730$$ −11.0000 −0.407128
$$731$$ −10.0000 + 17.3205i −0.369863 + 0.640622i
$$732$$ 0 0
$$733$$ −34.0000 −1.25582 −0.627909 0.778287i $$-0.716089\pi$$
−0.627909 + 0.778287i $$0.716089\pi$$
$$734$$ 7.00000 0.258375
$$735$$ 0 0
$$736$$ 3.00000 + 5.19615i 0.110581 + 0.191533i
$$737$$ −5.00000 + 8.66025i −0.184177 + 0.319005i
$$738$$ 0 0
$$739$$ −0.500000 0.866025i −0.0183928 0.0318573i 0.856683 0.515844i $$-0.172522\pi$$
−0.875075 + 0.483987i $$0.839188\pi$$
$$740$$ −5.00000 −0.183804
$$741$$ 0 0
$$742$$ 12.0000 0.440534
$$743$$ 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i $$-0.131563\pi$$
−0.805735 + 0.592277i $$0.798229\pi$$
$$744$$ 0 0
$$745$$ 9.00000 15.5885i 0.329734 0.571117i
$$746$$ −11.0000 19.0526i −0.402739 0.697564i
$$747$$ 0 0
$$748$$ 8.00000 0.292509
$$749$$ −4.00000 −0.146157
$$750$$ 0 0
$$751$$ 23.5000 40.7032i 0.857527 1.48528i −0.0167534 0.999860i $$-0.505333\pi$$
0.874281 0.485421i $$-0.161334\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −15.0000 + 25.9808i −0.546268 + 0.946164i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 3.50000 + 6.06218i 0.127210 + 0.220334i 0.922595 0.385771i $$-0.126065\pi$$
−0.795385 + 0.606105i $$0.792731\pi$$
$$758$$ −5.50000 9.52628i −0.199769 0.346010i
$$759$$ 0 0
$$760$$ 0.500000 + 4.33013i 0.0181369 + 0.157070i
$$761$$ −10.0000 −0.362500 −0.181250 0.983437i $$-0.558014\pi$$
−0.181250 + 0.983437i $$0.558014\pi$$
$$762$$ 0 0
$$763$$ −9.00000 15.5885i −0.325822 0.564340i
$$764$$ 8.00000 13.8564i 0.289430 0.501307i
$$765$$ 0 0
$$766$$ 18.0000 31.1769i 0.650366 1.12647i
$$767$$ −6.00000 −0.216647
$$768$$ 0 0
$$769$$ 16.5000 28.5788i 0.595005 1.03058i −0.398541 0.917151i $$-0.630483\pi$$
0.993546 0.113429i $$-0.0361834\pi$$
$$770$$ 1.00000 1.73205i 0.0360375 0.0624188i
$$771$$ 0 0
$$772$$ 25.0000 0.899770
$$773$$ −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i $$-0.867747\pi$$
0.807018 + 0.590527i $$0.201080\pi$$
$$774$$ 0 0
$$775$$ −0.500000 + 0.866025i −0.0179605 + 0.0311086i
$$776$$ −1.00000 1.73205i −0.0358979 0.0621770i
$$777$$ 0 0
$$778$$ −10.0000 −0.358517
$$779$$ 1.00000 + 8.66025i 0.0358287 + 0.310286i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −12.0000 20.7846i −0.429119 0.743256i
$$783$$ 0 0
$$784$$ 3.00000 + 5.19615i 0.107143 + 0.185577i
$$785$$ 6.50000 11.2583i 0.231995 0.401827i
$$786$$ 0 0
$$787$$ −23.0000 −0.819861 −0.409931 0.912117i $$-0.634447\pi$$
−0.409931 + 0.912117i $$0.634447\pi$$
$$788$$ −9.00000 + 15.5885i −0.320612 + 0.555316i
$$789$$ 0 0
$$790$$ 11.0000 0.391362
$$791$$ 14.0000 0.497783
$$792$$ 0