Properties

 Label 819.2.n.d.100.1 Level $819$ Weight $2$ Character 819.100 Analytic conductor $6.540$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$819 = 3^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 819.n (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$6.53974792554$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 100.1 Root $$-0.181721 + 0.314749i$$ of defining polynomial Character $$\chi$$ $$=$$ 819.100 Dual form 819.2.n.d.172.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.19402 - 2.06810i) q^{2} +(-1.85136 + 3.20665i) q^{4} +(0.491140 - 0.850679i) q^{5} +(2.60682 + 0.452230i) q^{7} +4.06616 q^{8} +O(q^{10})$$ $$q+(-1.19402 - 2.06810i) q^{2} +(-1.85136 + 3.20665i) q^{4} +(0.491140 - 0.850679i) q^{5} +(2.60682 + 0.452230i) q^{7} +4.06616 q^{8} -2.34572 q^{10} +0.587802 q^{11} +(2.39227 + 2.69760i) q^{13} +(-2.17733 - 5.93113i) q^{14} +(-1.15235 - 1.99593i) q^{16} +(-3.22710 + 5.58950i) q^{17} -3.82689 q^{19} +(1.81855 + 3.14983i) q^{20} +(-0.701847 - 1.21563i) q^{22} +(4.13001 + 7.15338i) q^{23} +(2.01756 + 3.49452i) q^{25} +(2.72249 - 8.16844i) q^{26} +(-6.27630 + 7.52191i) q^{28} +(-1.98009 + 3.42962i) q^{29} +(1.49436 + 2.58831i) q^{31} +(1.31430 - 2.27644i) q^{32} +15.4129 q^{34} +(1.66501 - 1.99546i) q^{35} +(-0.877941 - 1.52064i) q^{37} +(4.56938 + 7.91440i) q^{38} +(1.99705 - 3.45900i) q^{40} +(1.83584 - 3.17977i) q^{41} +(-3.19042 - 5.52598i) q^{43} +(-1.08823 + 1.88488i) q^{44} +(9.86261 - 17.0825i) q^{46} +(-2.17030 + 3.75906i) q^{47} +(6.59098 + 2.35776i) q^{49} +(4.81802 - 8.34505i) q^{50} +(-13.0792 + 2.67695i) q^{52} +(0.212770 + 0.368529i) q^{53} +(0.288693 - 0.500031i) q^{55} +(10.5997 + 1.83884i) q^{56} +9.45706 q^{58} +(3.00431 - 5.20362i) q^{59} +2.20674 q^{61} +(3.56859 - 6.18097i) q^{62} -10.8866 q^{64} +(3.46973 - 0.710156i) q^{65} +7.01303 q^{67} +(-11.9491 - 20.6964i) q^{68} +(-6.11486 - 1.06080i) q^{70} +(1.80127 + 3.11988i) q^{71} +(-2.46714 - 4.27321i) q^{73} +(-2.09656 + 3.63134i) q^{74} +(7.08496 - 12.2715i) q^{76} +(1.53229 + 0.265822i) q^{77} +(-1.39270 + 2.41223i) q^{79} -2.26386 q^{80} -8.76812 q^{82} +2.86819 q^{83} +(3.16992 + 5.49045i) q^{85} +(-7.61885 + 13.1962i) q^{86} +2.39010 q^{88} +(-1.04656 - 1.81269i) q^{89} +(5.01627 + 8.11400i) q^{91} -30.5845 q^{92} +10.3655 q^{94} +(-1.87954 + 3.25546i) q^{95} +(-3.84852 - 6.66584i) q^{97} +(-2.99367 - 16.4460i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} + O(q^{10})$$ $$12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} - 8q^{10} + 8q^{11} - 2q^{13} + 2q^{14} + 8q^{16} - 5q^{17} + 2q^{19} + q^{20} - 5q^{22} + q^{23} + 7q^{25} - 5q^{26} - 7q^{28} - 3q^{29} + 16q^{31} - 8q^{32} + 32q^{34} - 8q^{35} - 13q^{37} + 17q^{38} - 5q^{40} + 8q^{41} - 11q^{43} - 21q^{44} + 16q^{46} + q^{47} - 3q^{49} - 6q^{50} - 25q^{52} + 2q^{53} + 9q^{55} + 18q^{56} + 16q^{58} - 13q^{59} + 10q^{61} - 5q^{62} - 30q^{64} - 19q^{65} + 22q^{67} - 29q^{68} - 39q^{70} - 6q^{71} - 30q^{73} + 3q^{74} - 9q^{76} - 11q^{77} + 7q^{79} - 14q^{80} - 2q^{82} + 54q^{83} - q^{85} + 7q^{86} - 4q^{89} - 20q^{91} - 54q^{92} - 90q^{94} + 6q^{95} - 35q^{97} - 62q^{98} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$$.

 $$n$$ $$92$$ $$379$$ $$703$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.19402 2.06810i −0.844299 1.46237i −0.886229 0.463248i $$-0.846684\pi$$
0.0419302 0.999121i $$-0.486649\pi$$
$$3$$ 0 0
$$4$$ −1.85136 + 3.20665i −0.925680 + 1.60333i
$$5$$ 0.491140 0.850679i 0.219644 0.380435i −0.735055 0.678008i $$-0.762844\pi$$
0.954699 + 0.297572i $$0.0961769\pi$$
$$6$$ 0 0
$$7$$ 2.60682 + 0.452230i 0.985284 + 0.170927i
$$8$$ 4.06616 1.43761
$$9$$ 0 0
$$10$$ −2.34572 −0.741782
$$11$$ 0.587802 0.177229 0.0886146 0.996066i $$-0.471756\pi$$
0.0886146 + 0.996066i $$0.471756\pi$$
$$12$$ 0 0
$$13$$ 2.39227 + 2.69760i 0.663496 + 0.748179i
$$14$$ −2.17733 5.93113i −0.581916 1.58516i
$$15$$ 0 0
$$16$$ −1.15235 1.99593i −0.288088 0.498983i
$$17$$ −3.22710 + 5.58950i −0.782687 + 1.35565i 0.147685 + 0.989035i $$0.452818\pi$$
−0.930371 + 0.366619i $$0.880515\pi$$
$$18$$ 0 0
$$19$$ −3.82689 −0.877950 −0.438975 0.898499i $$-0.644658\pi$$
−0.438975 + 0.898499i $$0.644658\pi$$
$$20$$ 1.81855 + 3.14983i 0.406641 + 0.704323i
$$21$$ 0 0
$$22$$ −0.701847 1.21563i −0.149634 0.259174i
$$23$$ 4.13001 + 7.15338i 0.861166 + 1.49158i 0.870805 + 0.491629i $$0.163598\pi$$
−0.00963902 + 0.999954i $$0.503068\pi$$
$$24$$ 0 0
$$25$$ 2.01756 + 3.49452i 0.403513 + 0.698904i
$$26$$ 2.72249 8.16844i 0.533925 1.60196i
$$27$$ 0 0
$$28$$ −6.27630 + 7.52191i −1.18611 + 1.42151i
$$29$$ −1.98009 + 3.42962i −0.367694 + 0.636864i −0.989205 0.146541i $$-0.953186\pi$$
0.621511 + 0.783406i $$0.286519\pi$$
$$30$$ 0 0
$$31$$ 1.49436 + 2.58831i 0.268395 + 0.464874i 0.968448 0.249218i $$-0.0801734\pi$$
−0.700053 + 0.714091i $$0.746840\pi$$
$$32$$ 1.31430 2.27644i 0.232338 0.402421i
$$33$$ 0 0
$$34$$ 15.4129 2.64329
$$35$$ 1.66501 1.99546i 0.281439 0.337294i
$$36$$ 0 0
$$37$$ −0.877941 1.52064i −0.144333 0.249991i 0.784791 0.619760i $$-0.212770\pi$$
−0.929124 + 0.369769i $$0.879437\pi$$
$$38$$ 4.56938 + 7.91440i 0.741252 + 1.28389i
$$39$$ 0 0
$$40$$ 1.99705 3.45900i 0.315762 0.546916i
$$41$$ 1.83584 3.17977i 0.286710 0.496597i −0.686312 0.727307i $$-0.740772\pi$$
0.973023 + 0.230710i $$0.0741049\pi$$
$$42$$ 0 0
$$43$$ −3.19042 5.52598i −0.486535 0.842703i 0.513345 0.858182i $$-0.328406\pi$$
−0.999880 + 0.0154788i $$0.995073\pi$$
$$44$$ −1.08823 + 1.88488i −0.164058 + 0.284156i
$$45$$ 0 0
$$46$$ 9.86261 17.0825i 1.45416 2.51868i
$$47$$ −2.17030 + 3.75906i −0.316570 + 0.548316i −0.979770 0.200127i $$-0.935865\pi$$
0.663200 + 0.748442i $$0.269198\pi$$
$$48$$ 0 0
$$49$$ 6.59098 + 2.35776i 0.941568 + 0.336823i
$$50$$ 4.81802 8.34505i 0.681370 1.18017i
$$51$$ 0 0
$$52$$ −13.0792 + 2.67695i −1.81376 + 0.371226i
$$53$$ 0.212770 + 0.368529i 0.0292263 + 0.0506214i 0.880269 0.474476i $$-0.157362\pi$$
−0.851042 + 0.525097i $$0.824029\pi$$
$$54$$ 0 0
$$55$$ 0.288693 0.500031i 0.0389274 0.0674242i
$$56$$ 10.5997 + 1.83884i 1.41645 + 0.245725i
$$57$$ 0 0
$$58$$ 9.45706 1.24177
$$59$$ 3.00431 5.20362i 0.391128 0.677454i −0.601470 0.798895i $$-0.705418\pi$$
0.992599 + 0.121441i $$0.0387516\pi$$
$$60$$ 0 0
$$61$$ 2.20674 0.282544 0.141272 0.989971i $$-0.454881\pi$$
0.141272 + 0.989971i $$0.454881\pi$$
$$62$$ 3.56859 6.18097i 0.453211 0.784985i
$$63$$ 0 0
$$64$$ −10.8866 −1.36083
$$65$$ 3.46973 0.710156i 0.430367 0.0880841i
$$66$$ 0 0
$$67$$ 7.01303 0.856778 0.428389 0.903594i $$-0.359081\pi$$
0.428389 + 0.903594i $$0.359081\pi$$
$$68$$ −11.9491 20.6964i −1.44904 2.50980i
$$69$$ 0 0
$$70$$ −6.11486 1.06080i −0.730866 0.126790i
$$71$$ 1.80127 + 3.11988i 0.213771 + 0.370262i 0.952892 0.303311i $$-0.0980920\pi$$
−0.739121 + 0.673573i $$0.764759\pi$$
$$72$$ 0 0
$$73$$ −2.46714 4.27321i −0.288756 0.500141i 0.684757 0.728772i $$-0.259908\pi$$
−0.973513 + 0.228631i $$0.926575\pi$$
$$74$$ −2.09656 + 3.63134i −0.243720 + 0.422135i
$$75$$ 0 0
$$76$$ 7.08496 12.2715i 0.812701 1.40764i
$$77$$ 1.53229 + 0.265822i 0.174621 + 0.0302932i
$$78$$ 0 0
$$79$$ −1.39270 + 2.41223i −0.156691 + 0.271397i −0.933674 0.358125i $$-0.883416\pi$$
0.776982 + 0.629522i $$0.216749\pi$$
$$80$$ −2.26386 −0.253108
$$81$$ 0 0
$$82$$ −8.76812 −0.968277
$$83$$ 2.86819 0.314825 0.157412 0.987533i $$-0.449685\pi$$
0.157412 + 0.987533i $$0.449685\pi$$
$$84$$ 0 0
$$85$$ 3.16992 + 5.49045i 0.343826 + 0.595523i
$$86$$ −7.61885 + 13.1962i −0.821562 + 1.42299i
$$87$$ 0 0
$$88$$ 2.39010 0.254786
$$89$$ −1.04656 1.81269i −0.110935 0.192145i 0.805213 0.592986i $$-0.202051\pi$$
−0.916147 + 0.400842i $$0.868718\pi$$
$$90$$ 0 0
$$91$$ 5.01627 + 8.11400i 0.525848 + 0.850578i
$$92$$ −30.5845 −3.18866
$$93$$ 0 0
$$94$$ 10.3655 1.06912
$$95$$ −1.87954 + 3.25546i −0.192837 + 0.334003i
$$96$$ 0 0
$$97$$ −3.84852 6.66584i −0.390758 0.676813i 0.601791 0.798653i $$-0.294454\pi$$
−0.992550 + 0.121840i $$0.961120\pi$$
$$98$$ −2.99367 16.4460i −0.302406 1.66130i
$$99$$ 0 0
$$100$$ −14.9409 −1.49409
$$101$$ 2.63732 0.262423 0.131212 0.991354i $$-0.458113\pi$$
0.131212 + 0.991354i $$0.458113\pi$$
$$102$$ 0 0
$$103$$ 5.43095 9.40669i 0.535128 0.926868i −0.464029 0.885820i $$-0.653597\pi$$
0.999157 0.0410486i $$-0.0130699\pi$$
$$104$$ 9.72736 + 10.9689i 0.953846 + 1.07559i
$$105$$ 0 0
$$106$$ 0.508103 0.880061i 0.0493514 0.0854791i
$$107$$ −7.99024 13.8395i −0.772446 1.33792i −0.936219 0.351418i $$-0.885700\pi$$
0.163773 0.986498i $$-0.447634\pi$$
$$108$$ 0 0
$$109$$ −4.61738 7.99754i −0.442265 0.766026i 0.555592 0.831455i $$-0.312492\pi$$
−0.997857 + 0.0654294i $$0.979158\pi$$
$$110$$ −1.37882 −0.131465
$$111$$ 0 0
$$112$$ −2.10135 5.72416i −0.198559 0.540882i
$$113$$ 5.09012 + 8.81635i 0.478838 + 0.829372i 0.999706 0.0242655i $$-0.00772470\pi$$
−0.520867 + 0.853638i $$0.674391\pi$$
$$114$$ 0 0
$$115$$ 8.11364 0.756601
$$116$$ −7.33173 12.6989i −0.680734 1.17907i
$$117$$ 0 0
$$118$$ −14.3488 −1.32092
$$119$$ −10.9402 + 13.1114i −1.00289 + 1.20192i
$$120$$ 0 0
$$121$$ −10.6545 −0.968590
$$122$$ −2.63489 4.56376i −0.238552 0.413184i
$$123$$ 0 0
$$124$$ −11.0664 −0.993792
$$125$$ 8.87502 0.793806
$$126$$ 0 0
$$127$$ −2.12513 + 3.68083i −0.188575 + 0.326621i −0.944775 0.327719i $$-0.893720\pi$$
0.756201 + 0.654340i $$0.227053\pi$$
$$128$$ 10.3702 + 17.9617i 0.916606 + 1.58761i
$$129$$ 0 0
$$130$$ −5.61160 6.32781i −0.492170 0.554986i
$$131$$ −1.08478 + 1.87890i −0.0947779 + 0.164160i −0.909516 0.415669i $$-0.863547\pi$$
0.814738 + 0.579829i $$0.196881\pi$$
$$132$$ 0 0
$$133$$ −9.97601 1.73063i −0.865030 0.150065i
$$134$$ −8.37369 14.5037i −0.723376 1.25292i
$$135$$ 0 0
$$136$$ −13.1219 + 22.7278i −1.12519 + 1.94889i
$$137$$ 4.18158 7.24271i 0.357257 0.618787i −0.630245 0.776396i $$-0.717045\pi$$
0.987501 + 0.157610i $$0.0503788\pi$$
$$138$$ 0 0
$$139$$ 0.288457 + 0.499622i 0.0244666 + 0.0423774i 0.877999 0.478662i $$-0.158878\pi$$
−0.853533 + 0.521039i $$0.825545\pi$$
$$140$$ 3.31619 + 9.03343i 0.280269 + 0.763464i
$$141$$ 0 0
$$142$$ 4.30149 7.45040i 0.360973 0.625224i
$$143$$ 1.40618 + 1.58566i 0.117591 + 0.132599i
$$144$$ 0 0
$$145$$ 1.94500 + 3.36885i 0.161524 + 0.279767i
$$146$$ −5.89161 + 10.2046i −0.487593 + 0.844537i
$$147$$ 0 0
$$148$$ 6.50154 0.534423
$$149$$ −2.80662 −0.229928 −0.114964 0.993370i $$-0.536675\pi$$
−0.114964 + 0.993370i $$0.536675\pi$$
$$150$$ 0 0
$$151$$ 11.5054 + 19.9280i 0.936300 + 1.62172i 0.772300 + 0.635258i $$0.219106\pi$$
0.164000 + 0.986460i $$0.447560\pi$$
$$152$$ −15.5608 −1.26215
$$153$$ 0 0
$$154$$ −1.27984 3.48633i −0.103132 0.280937i
$$155$$ 2.93576 0.235806
$$156$$ 0 0
$$157$$ −11.2880 19.5513i −0.900879 1.56037i −0.826356 0.563148i $$-0.809590\pi$$
−0.0745227 0.997219i $$-0.523743\pi$$
$$158$$ 6.65165 0.529177
$$159$$ 0 0
$$160$$ −1.29101 2.23610i −0.102064 0.176779i
$$161$$ 7.53119 + 20.5153i 0.593541 + 1.61683i
$$162$$ 0 0
$$163$$ 8.17714 0.640483 0.320242 0.947336i $$-0.396236\pi$$
0.320242 + 0.947336i $$0.396236\pi$$
$$164$$ 6.79761 + 11.7738i 0.530804 + 0.919380i
$$165$$ 0 0
$$166$$ −3.42467 5.93170i −0.265806 0.460389i
$$167$$ −1.16386 + 2.01586i −0.0900619 + 0.155992i −0.907537 0.419972i $$-0.862040\pi$$
0.817475 + 0.575964i $$0.195373\pi$$
$$168$$ 0 0
$$169$$ −1.55408 + 12.9068i −0.119545 + 0.992829i
$$170$$ 7.56988 13.1114i 0.580583 1.00560i
$$171$$ 0 0
$$172$$ 23.6265 1.80150
$$173$$ 8.13372 0.618396 0.309198 0.950998i $$-0.399939\pi$$
0.309198 + 0.950998i $$0.399939\pi$$
$$174$$ 0 0
$$175$$ 3.67909 + 10.0220i 0.278113 + 0.757590i
$$176$$ −0.677355 1.17321i −0.0510576 0.0884343i
$$177$$ 0 0
$$178$$ −2.49922 + 4.32877i −0.187324 + 0.324455i
$$179$$ 20.9925 1.56906 0.784528 0.620093i $$-0.212905\pi$$
0.784528 + 0.620093i $$0.212905\pi$$
$$180$$ 0 0
$$181$$ −1.60807 −0.119527 −0.0597635 0.998213i $$-0.519035\pi$$
−0.0597635 + 0.998213i $$0.519035\pi$$
$$182$$ 10.7910 20.0624i 0.799885 1.48713i
$$183$$ 0 0
$$184$$ 16.7933 + 29.0868i 1.23802 + 2.14431i
$$185$$ −1.72477 −0.126807
$$186$$ 0 0
$$187$$ −1.89690 + 3.28552i −0.138715 + 0.240261i
$$188$$ −8.03601 13.9188i −0.586086 1.01513i
$$189$$ 0 0
$$190$$ 8.97683 0.651247
$$191$$ 11.5622 0.836614 0.418307 0.908306i $$-0.362624\pi$$
0.418307 + 0.908306i $$0.362624\pi$$
$$192$$ 0 0
$$193$$ 23.5788 1.69724 0.848621 0.529001i $$-0.177433\pi$$
0.848621 + 0.529001i $$0.177433\pi$$
$$194$$ −9.19041 + 15.9183i −0.659833 + 1.14286i
$$195$$ 0 0
$$196$$ −19.7628 + 16.7699i −1.41163 + 1.19785i
$$197$$ −0.735472 + 1.27387i −0.0524002 + 0.0907598i −0.891036 0.453933i $$-0.850020\pi$$
0.838636 + 0.544693i $$0.183354\pi$$
$$198$$ 0 0
$$199$$ −4.69700 + 8.13543i −0.332961 + 0.576706i −0.983091 0.183117i $$-0.941381\pi$$
0.650130 + 0.759823i $$0.274714\pi$$
$$200$$ 8.20374 + 14.2093i 0.580092 + 1.00475i
$$201$$ 0 0
$$202$$ −3.14901 5.45425i −0.221564 0.383760i
$$203$$ −6.71271 + 8.04493i −0.471140 + 0.564643i
$$204$$ 0 0
$$205$$ −1.80331 3.12343i −0.125949 0.218150i
$$206$$ −25.9386 −1.80723
$$207$$ 0 0
$$208$$ 2.62749 7.88340i 0.182183 0.546615i
$$209$$ −2.24946 −0.155598
$$210$$ 0 0
$$211$$ 4.47109 7.74416i 0.307803 0.533130i −0.670079 0.742290i $$-0.733740\pi$$
0.977881 + 0.209160i $$0.0670730\pi$$
$$212$$ −1.57566 −0.108217
$$213$$ 0 0
$$214$$ −19.0810 + 33.0493i −1.30435 + 2.25920i
$$215$$ −6.26778 −0.427459
$$216$$ 0 0
$$217$$ 2.72501 + 7.42303i 0.184986 + 0.503908i
$$218$$ −11.0265 + 19.0984i −0.746808 + 1.29351i
$$219$$ 0 0
$$220$$ 1.06895 + 1.85148i 0.0720686 + 0.124827i
$$221$$ −22.7983 + 4.66618i −1.53358 + 0.313881i
$$222$$ 0 0
$$223$$ −10.9098 + 18.8963i −0.730574 + 1.26539i 0.226064 + 0.974112i $$0.427414\pi$$
−0.956638 + 0.291279i $$0.905919\pi$$
$$224$$ 4.45562 5.33989i 0.297704 0.356786i
$$225$$ 0 0
$$226$$ 12.1554 21.0538i 0.808565 1.40048i
$$227$$ −9.27627 + 16.0670i −0.615687 + 1.06640i 0.374576 + 0.927196i $$0.377788\pi$$
−0.990263 + 0.139206i $$0.955545\pi$$
$$228$$ 0 0
$$229$$ −9.67525 + 16.7580i −0.639359 + 1.10740i 0.346215 + 0.938155i $$0.387467\pi$$
−0.985574 + 0.169247i $$0.945867\pi$$
$$230$$ −9.68784 16.7798i −0.638797 1.10643i
$$231$$ 0 0
$$232$$ −8.05137 + 13.9454i −0.528599 + 0.915560i
$$233$$ 8.08170 13.9979i 0.529450 0.917034i −0.469960 0.882688i $$-0.655732\pi$$
0.999410 0.0343462i $$-0.0109349\pi$$
$$234$$ 0 0
$$235$$ 2.13184 + 3.69245i 0.139066 + 0.240869i
$$236$$ 11.1241 + 19.2676i 0.724119 + 1.25421i
$$237$$ 0 0
$$238$$ 40.1785 + 6.97016i 2.60439 + 0.451808i
$$239$$ −16.1037 −1.04166 −0.520831 0.853660i $$-0.674378\pi$$
−0.520831 + 0.853660i $$0.674378\pi$$
$$240$$ 0 0
$$241$$ 2.00300 3.46930i 0.129025 0.223477i −0.794274 0.607559i $$-0.792149\pi$$
0.923299 + 0.384082i $$0.125482\pi$$
$$242$$ 12.7217 + 22.0346i 0.817779 + 1.41643i
$$243$$ 0 0
$$244$$ −4.08548 + 7.07625i −0.261546 + 0.453011i
$$245$$ 5.24279 4.44882i 0.334949 0.284225i
$$246$$ 0 0
$$247$$ −9.15497 10.3234i −0.582517 0.656864i
$$248$$ 6.07631 + 10.5245i 0.385846 + 0.668305i
$$249$$ 0 0
$$250$$ −10.5969 18.3544i −0.670209 1.16084i
$$251$$ 1.62344 + 2.81188i 0.102471 + 0.177484i 0.912702 0.408626i $$-0.133992\pi$$
−0.810231 + 0.586110i $$0.800659\pi$$
$$252$$ 0 0
$$253$$ 2.42763 + 4.20477i 0.152624 + 0.264352i
$$254$$ 10.1498 0.636853
$$255$$ 0 0
$$256$$ 13.8778 24.0371i 0.867365 1.50232i
$$257$$ −13.4462 23.2895i −0.838751 1.45276i −0.890940 0.454122i $$-0.849953\pi$$
0.0521891 0.998637i $$-0.483380\pi$$
$$258$$ 0 0
$$259$$ −1.60095 4.36106i −0.0994784 0.270983i
$$260$$ −4.14650 + 12.4410i −0.257155 + 0.771556i
$$261$$ 0 0
$$262$$ 5.18100 0.320084
$$263$$ 3.80706 0.234753 0.117377 0.993087i $$-0.462552\pi$$
0.117377 + 0.993087i $$0.462552\pi$$
$$264$$ 0 0
$$265$$ 0.418000 0.0256775
$$266$$ 8.33241 + 22.6978i 0.510893 + 1.39169i
$$267$$ 0 0
$$268$$ −12.9836 + 22.4883i −0.793102 + 1.37369i
$$269$$ −11.9190 + 20.6444i −0.726716 + 1.25871i 0.231548 + 0.972824i $$0.425621\pi$$
−0.958264 + 0.285886i $$0.907712\pi$$
$$270$$ 0 0
$$271$$ −4.95068 8.57482i −0.300732 0.520883i 0.675570 0.737296i $$-0.263898\pi$$
−0.976302 + 0.216413i $$0.930564\pi$$
$$272$$ 14.8750 0.901931
$$273$$ 0 0
$$274$$ −19.9715 −1.20653
$$275$$ 1.18593 + 2.05409i 0.0715142 + 0.123866i
$$276$$ 0 0
$$277$$ −5.89289 + 10.2068i −0.354069 + 0.613266i −0.986958 0.160977i $$-0.948536\pi$$
0.632889 + 0.774243i $$0.281869\pi$$
$$278$$ 0.688846 1.19312i 0.0413142 0.0715584i
$$279$$ 0 0
$$280$$ 6.77022 8.11385i 0.404598 0.484895i
$$281$$ −12.9976 −0.775372 −0.387686 0.921791i $$-0.626726\pi$$
−0.387686 + 0.921791i $$0.626726\pi$$
$$282$$ 0 0
$$283$$ −16.8050 −0.998952 −0.499476 0.866328i $$-0.666474\pi$$
−0.499476 + 0.866328i $$0.666474\pi$$
$$284$$ −13.3392 −0.791534
$$285$$ 0 0
$$286$$ 1.60029 4.80143i 0.0946270 0.283914i
$$287$$ 6.22369 7.45886i 0.367373 0.440283i
$$288$$ 0 0
$$289$$ −12.3283 21.3533i −0.725197 1.25608i
$$290$$ 4.64474 8.04493i 0.272749 0.472414i
$$291$$ 0 0
$$292$$ 18.2702 1.06918
$$293$$ −7.04782 12.2072i −0.411738 0.713151i 0.583342 0.812227i $$-0.301745\pi$$
−0.995080 + 0.0990757i $$0.968411\pi$$
$$294$$ 0 0
$$295$$ −2.95108 5.11141i −0.171818 0.297598i
$$296$$ −3.56985 6.18316i −0.207493 0.359389i
$$297$$ 0 0
$$298$$ 3.35116 + 5.80438i 0.194128 + 0.336239i
$$299$$ −9.41686 + 28.2539i −0.544591 + 1.63397i
$$300$$ 0 0
$$301$$ −5.81784 15.8480i −0.335335 0.913464i
$$302$$ 27.4754 47.5888i 1.58103 2.73843i
$$303$$ 0 0
$$304$$ 4.40993 + 7.63822i 0.252927 + 0.438082i
$$305$$ 1.08382 1.87723i 0.0620593 0.107490i
$$306$$ 0 0
$$307$$ 15.8786 0.906240 0.453120 0.891450i $$-0.350311\pi$$
0.453120 + 0.891450i $$0.350311\pi$$
$$308$$ −3.68922 + 4.42140i −0.210213 + 0.251932i
$$309$$ 0 0
$$310$$ −3.50535 6.07145i −0.199091 0.344835i
$$311$$ −14.3017 24.7713i −0.810975 1.40465i −0.912183 0.409784i $$-0.865604\pi$$
0.101208 0.994865i $$-0.467729\pi$$
$$312$$ 0 0
$$313$$ 9.28962 16.0901i 0.525080 0.909465i −0.474493 0.880259i $$-0.657369\pi$$
0.999573 0.0292063i $$-0.00929798\pi$$
$$314$$ −26.9561 + 46.6893i −1.52122 + 2.63483i
$$315$$ 0 0
$$316$$ −5.15679 8.93182i −0.290092 0.502454i
$$317$$ 15.3223 26.5389i 0.860584 1.49057i −0.0107826 0.999942i $$-0.503432\pi$$
0.871366 0.490633i $$-0.163234\pi$$
$$318$$ 0 0
$$319$$ −1.16390 + 2.01594i −0.0651660 + 0.112871i
$$320$$ −5.34685 + 9.26102i −0.298898 + 0.517707i
$$321$$ 0 0
$$322$$ 33.4352 40.0709i 1.86327 2.23306i
$$323$$ 12.3498 21.3904i 0.687160 1.19020i
$$324$$ 0 0
$$325$$ −4.60026 + 13.8024i −0.255177 + 0.765620i
$$326$$ −9.76366 16.9112i −0.540759 0.936622i
$$327$$ 0 0
$$328$$ 7.46483 12.9295i 0.412177 0.713911i
$$329$$ −7.35752 + 8.81772i −0.405633 + 0.486136i
$$330$$ 0 0
$$331$$ 27.2277 1.49657 0.748284 0.663378i $$-0.230878\pi$$
0.748284 + 0.663378i $$0.230878\pi$$
$$332$$ −5.31005 + 9.19728i −0.291427 + 0.504766i
$$333$$ 0 0
$$334$$ 5.55867 0.304157
$$335$$ 3.44438 5.96584i 0.188187 0.325949i
$$336$$ 0 0
$$337$$ −12.3160 −0.670898 −0.335449 0.942058i $$-0.608888\pi$$
−0.335449 + 0.942058i $$0.608888\pi$$
$$338$$ 28.5481 12.1969i 1.55281 0.663426i
$$339$$ 0 0
$$340$$ −23.4746 −1.27309
$$341$$ 0.878389 + 1.52141i 0.0475674 + 0.0823892i
$$342$$ 0 0
$$343$$ 16.1152 + 9.12688i 0.870140 + 0.492805i
$$344$$ −12.9728 22.4695i −0.699445 1.21148i
$$345$$ 0 0
$$346$$ −9.71182 16.8214i −0.522111 0.904322i
$$347$$ 3.07253 5.32177i 0.164942 0.285688i −0.771693 0.635996i $$-0.780590\pi$$
0.936635 + 0.350308i $$0.113923\pi$$
$$348$$ 0 0
$$349$$ −6.51563 + 11.2854i −0.348774 + 0.604094i −0.986032 0.166557i $$-0.946735\pi$$
0.637258 + 0.770650i $$0.280068\pi$$
$$350$$ 16.3336 19.5752i 0.873065 1.04634i
$$351$$ 0 0
$$352$$ 0.772550 1.33810i 0.0411771 0.0713208i
$$353$$ −31.6665 −1.68544 −0.842718 0.538356i $$-0.819046\pi$$
−0.842718 + 0.538356i $$0.819046\pi$$
$$354$$ 0 0
$$355$$ 3.53870 0.187814
$$356$$ 7.75021 0.410761
$$357$$ 0 0
$$358$$ −25.0655 43.4147i −1.32475 2.29454i
$$359$$ 9.96610 17.2618i 0.525991 0.911043i −0.473551 0.880767i $$-0.657028\pi$$
0.999542 0.0302764i $$-0.00963874\pi$$
$$360$$ 0 0
$$361$$ −4.35488 −0.229204
$$362$$ 1.92007 + 3.32566i 0.100917 + 0.174793i
$$363$$ 0 0
$$364$$ −35.3057 + 1.06350i −1.85052 + 0.0557426i
$$365$$ −4.84684 −0.253695
$$366$$ 0 0
$$367$$ 19.7190 1.02932 0.514662 0.857393i $$-0.327918\pi$$
0.514662 + 0.857393i $$0.327918\pi$$
$$368$$ 9.51844 16.4864i 0.496183 0.859414i
$$369$$ 0 0
$$370$$ 2.05940 + 3.56699i 0.107063 + 0.185439i
$$371$$ 0.387993 + 1.05691i 0.0201436 + 0.0548719i
$$372$$ 0 0
$$373$$ 17.5469 0.908544 0.454272 0.890863i $$-0.349899\pi$$
0.454272 + 0.890863i $$0.349899\pi$$
$$374$$ 9.05972 0.468467
$$375$$ 0 0
$$376$$ −8.82478 + 15.2850i −0.455103 + 0.788262i
$$377$$ −13.9887 + 2.86308i −0.720452 + 0.147456i
$$378$$ 0 0
$$379$$ 5.85068 10.1337i 0.300529 0.520532i −0.675727 0.737152i $$-0.736170\pi$$
0.976256 + 0.216620i $$0.0695034\pi$$
$$380$$ −6.95942 12.0541i −0.357010 0.618360i
$$381$$ 0 0
$$382$$ −13.8055 23.9119i −0.706352 1.22344i
$$383$$ 21.5288 1.10007 0.550036 0.835141i $$-0.314614\pi$$
0.550036 + 0.835141i $$0.314614\pi$$
$$384$$ 0 0
$$385$$ 0.978699 1.17293i 0.0498791 0.0597783i
$$386$$ −28.1536 48.7634i −1.43298 2.48199i
$$387$$ 0 0
$$388$$ 28.5000 1.44687
$$389$$ 13.2455 + 22.9419i 0.671574 + 1.16320i 0.977458 + 0.211131i $$0.0677147\pi$$
−0.305884 + 0.952069i $$0.598952\pi$$
$$390$$ 0 0
$$391$$ −53.3118 −2.69609
$$392$$ 26.8000 + 9.58703i 1.35360 + 0.484218i
$$393$$ 0 0
$$394$$ 3.51267 0.176966
$$395$$ 1.36802 + 2.36949i 0.0688327 + 0.119222i
$$396$$ 0 0
$$397$$ −33.7989 −1.69632 −0.848160 0.529740i $$-0.822289\pi$$
−0.848160 + 0.529740i $$0.822289\pi$$
$$398$$ 22.4332 1.12447
$$399$$ 0 0
$$400$$ 4.64989 8.05384i 0.232494 0.402692i
$$401$$ 10.8059 + 18.7164i 0.539623 + 0.934655i 0.998924 + 0.0463741i $$0.0147666\pi$$
−0.459301 + 0.888281i $$0.651900\pi$$
$$402$$ 0 0
$$403$$ −3.40730 + 10.2231i −0.169730 + 0.509250i
$$404$$ −4.88264 + 8.45697i −0.242920 + 0.420750i
$$405$$ 0 0
$$406$$ 24.6528 + 4.27676i 1.22350 + 0.212252i
$$407$$ −0.516056 0.893835i −0.0255799 0.0443058i
$$408$$ 0 0
$$409$$ −3.87109 + 6.70492i −0.191413 + 0.331537i −0.945719 0.324986i $$-0.894640\pi$$
0.754306 + 0.656523i $$0.227974\pi$$
$$410$$ −4.30637 + 7.45886i −0.212677 + 0.368367i
$$411$$ 0 0
$$412$$ 20.1093 + 34.8303i 0.990714 + 1.71597i
$$413$$ 10.1849 12.2062i 0.501167 0.600630i
$$414$$ 0 0
$$415$$ 1.40868 2.43991i 0.0691495 0.119770i
$$416$$ 9.28509 1.90040i 0.455239 0.0931746i
$$417$$ 0 0
$$418$$ 2.68589 + 4.65211i 0.131371 + 0.227542i
$$419$$ −4.05097 + 7.01649i −0.197903 + 0.342778i −0.947848 0.318722i $$-0.896746\pi$$
0.749945 + 0.661500i $$0.230080\pi$$
$$420$$ 0 0
$$421$$ −32.1124 −1.56506 −0.782530 0.622612i $$-0.786071\pi$$
−0.782530 + 0.622612i $$0.786071\pi$$
$$422$$ −21.3543 −1.03951
$$423$$ 0 0
$$424$$ 0.865159 + 1.49850i 0.0420158 + 0.0727735i
$$425$$ −26.0435 −1.26330
$$426$$ 0 0
$$427$$ 5.75257 + 0.997954i 0.278386 + 0.0482944i
$$428$$ 59.1713 2.86015
$$429$$ 0 0
$$430$$ 7.48384 + 12.9624i 0.360903 + 0.625102i
$$431$$ 29.5281 1.42232 0.711159 0.703031i $$-0.248171\pi$$
0.711159 + 0.703031i $$0.248171\pi$$
$$432$$ 0 0
$$433$$ −11.0455 19.1314i −0.530813 0.919395i −0.999353 0.0359531i $$-0.988553\pi$$
0.468540 0.883442i $$-0.344780\pi$$
$$434$$ 12.0979 14.4988i 0.580716 0.695967i
$$435$$ 0 0
$$436$$ 34.1938 1.63758
$$437$$ −15.8051 27.3752i −0.756060 1.30953i
$$438$$ 0 0
$$439$$ 3.17790 + 5.50428i 0.151673 + 0.262705i 0.931843 0.362863i $$-0.118201\pi$$
−0.780170 + 0.625568i $$0.784867\pi$$
$$440$$ 1.17387 2.03321i 0.0559622 0.0969294i
$$441$$ 0 0
$$442$$ 36.8718 + 41.5777i 1.75381 + 1.97765i
$$443$$ −6.78135 + 11.7456i −0.322192 + 0.558052i −0.980940 0.194311i $$-0.937753\pi$$
0.658748 + 0.752363i $$0.271086\pi$$
$$444$$ 0 0
$$445$$ −2.05602 −0.0974648
$$446$$ 52.1060 2.46729
$$447$$ 0 0
$$448$$ −28.3794 4.92325i −1.34080 0.232602i
$$449$$ 10.9559 + 18.9762i 0.517041 + 0.895541i 0.999804 + 0.0197900i $$0.00629977\pi$$
−0.482763 + 0.875751i $$0.660367\pi$$
$$450$$ 0 0
$$451$$ 1.07911 1.86908i 0.0508134 0.0880115i
$$452$$ −37.6946 −1.77300
$$453$$ 0 0
$$454$$ 44.3041 2.07930
$$455$$ 9.36610 0.282132i 0.439090 0.0132265i
$$456$$ 0 0
$$457$$ −7.60732 13.1763i −0.355855 0.616359i 0.631409 0.775450i $$-0.282477\pi$$
−0.987264 + 0.159091i $$0.949144\pi$$
$$458$$ 46.2097 2.15924
$$459$$ 0 0
$$460$$ −15.0213 + 26.0176i −0.700371 + 1.21308i
$$461$$ −8.10813 14.0437i −0.377633 0.654080i 0.613084 0.790018i $$-0.289929\pi$$
−0.990717 + 0.135937i $$0.956595\pi$$
$$462$$ 0 0
$$463$$ −1.44769 −0.0672799 −0.0336400 0.999434i $$-0.510710\pi$$
−0.0336400 + 0.999434i $$0.510710\pi$$
$$464$$ 9.12705 0.423713
$$465$$ 0 0
$$466$$ −38.5988 −1.78805
$$467$$ 7.00337 12.1302i 0.324078 0.561319i −0.657248 0.753675i $$-0.728279\pi$$
0.981325 + 0.192356i $$0.0616128\pi$$
$$468$$ 0 0
$$469$$ 18.2817 + 3.17150i 0.844169 + 0.146446i
$$470$$ 5.09091 8.81772i 0.234826 0.406731i
$$471$$ 0 0
$$472$$ 12.2160 21.1588i 0.562288 0.973912i
$$473$$ −1.87534 3.24818i −0.0862282 0.149352i
$$474$$ 0 0
$$475$$ −7.72100 13.3732i −0.354264 0.613603i
$$476$$ −21.7895 59.3553i −0.998719 2.72055i
$$477$$ 0 0
$$478$$ 19.2281 + 33.3041i 0.879474 + 1.52329i
$$479$$ 30.0243 1.37185 0.685923 0.727674i $$-0.259399\pi$$
0.685923 + 0.727674i $$0.259399\pi$$
$$480$$ 0 0
$$481$$ 2.00180 6.00611i 0.0912742 0.273855i
$$482$$ −9.56649 −0.435742
$$483$$ 0 0
$$484$$ 19.7253 34.1652i 0.896605 1.55296i
$$485$$ −7.56065 −0.343312
$$486$$ 0 0
$$487$$ 14.2452 24.6733i 0.645510 1.11806i −0.338674 0.940904i $$-0.609978\pi$$
0.984184 0.177152i $$-0.0566884\pi$$
$$488$$ 8.97297 0.406187
$$489$$ 0 0
$$490$$ −15.4606 5.53064i −0.698438 0.249849i
$$491$$ −14.2339 + 24.6538i −0.642365 + 1.11261i 0.342539 + 0.939504i $$0.388713\pi$$
−0.984903 + 0.173105i $$0.944620\pi$$
$$492$$ 0 0
$$493$$ −12.7799 22.1354i −0.575578 0.996930i
$$494$$ −10.4187 + 31.2598i −0.468759 + 1.40644i
$$495$$ 0 0
$$496$$ 3.44406 5.96528i 0.154643 0.267849i
$$497$$ 3.28467 + 8.94755i 0.147337 + 0.401353i
$$498$$ 0 0
$$499$$ 13.1164 22.7183i 0.587172 1.01701i −0.407429 0.913237i $$-0.633575\pi$$
0.994601 0.103775i $$-0.0330921\pi$$
$$500$$ −16.4309 + 28.4591i −0.734811 + 1.27273i
$$501$$ 0 0
$$502$$ 3.87684 6.71488i 0.173032 0.299700i
$$503$$ 4.26588 + 7.38872i 0.190206 + 0.329447i 0.945318 0.326149i $$-0.105751\pi$$
−0.755112 + 0.655595i $$0.772418\pi$$
$$504$$ 0 0
$$505$$ 1.29529 2.24352i 0.0576398 0.0998351i
$$506$$ 5.79726 10.0412i 0.257720 0.446384i
$$507$$ 0 0
$$508$$ −7.86876 13.6291i −0.349120 0.604693i
$$509$$ −6.51298 11.2808i −0.288683 0.500014i 0.684813 0.728719i $$-0.259884\pi$$
−0.973496 + 0.228706i $$0.926551\pi$$
$$510$$ 0 0
$$511$$ −4.49890 12.2552i −0.199020 0.542137i
$$512$$ −24.8008 −1.09605
$$513$$ 0 0
$$514$$ −32.1100 + 55.6162i −1.41631 + 2.45312i
$$515$$ −5.33472 9.24000i −0.235076 0.407163i
$$516$$ 0 0
$$517$$ −1.27571 + 2.20959i −0.0561055 + 0.0971775i
$$518$$ −7.10753 + 8.51811i −0.312287 + 0.374264i
$$519$$ 0 0
$$520$$ 14.1085 2.88761i 0.618698 0.126630i
$$521$$ 2.23285 + 3.86741i 0.0978230 + 0.169434i 0.910783 0.412885i $$-0.135479\pi$$
−0.812960 + 0.582319i $$0.802145\pi$$
$$522$$ 0 0
$$523$$ 1.45406 + 2.51850i 0.0635815 + 0.110126i 0.896064 0.443925i $$-0.146414\pi$$
−0.832482 + 0.554051i $$0.813081\pi$$
$$524$$ −4.01665 6.95704i −0.175468 0.303920i
$$525$$ 0 0
$$526$$ −4.54570 7.87339i −0.198202 0.343296i
$$527$$ −19.2898 −0.840277
$$528$$ 0 0
$$529$$ −22.6139 + 39.1684i −0.983213 + 1.70297i
$$530$$ −0.499100 0.864466i −0.0216795 0.0375500i
$$531$$ 0 0
$$532$$ 24.0187 28.7855i 1.04134 1.24801i
$$533$$ 12.9696 2.65451i 0.561775 0.114980i
$$534$$ 0 0
$$535$$ −15.6973 −0.678654
$$536$$ 28.5161 1.23171
$$537$$ 0 0
$$538$$ 56.9262 2.45426
$$539$$ 3.87419 + 1.38590i 0.166873 + 0.0596948i
$$540$$ 0 0
$$541$$ 9.23193 15.9902i 0.396912 0.687471i −0.596431 0.802664i $$-0.703415\pi$$
0.993343 + 0.115193i $$0.0367486\pi$$
$$542$$ −11.8224 + 20.4770i −0.507815 + 0.879562i
$$543$$ 0 0
$$544$$ 8.48277 + 14.6926i 0.363696 + 0.629940i
$$545$$ −9.07112 −0.388564
$$546$$ 0 0
$$547$$ 34.9817 1.49571 0.747856 0.663861i $$-0.231083\pi$$
0.747856 + 0.663861i $$0.231083\pi$$
$$548$$ 15.4832 + 26.8177i 0.661411 + 1.14560i
$$549$$ 0 0
$$550$$ 2.83204 4.90524i 0.120759 0.209160i
$$551$$ 7.57760 13.1248i 0.322817 0.559135i
$$552$$ 0 0
$$553$$ −4.72140 + 5.65842i −0.200774 + 0.240621i
$$554$$ 28.1449 1.19576
$$555$$ 0 0
$$556$$ −2.13615 −0.0905930
$$557$$ −0.0531413 −0.00225167 −0.00112583 0.999999i $$-0.500358\pi$$
−0.00112583 + 0.999999i $$0.500358\pi$$
$$558$$ 0 0
$$559$$ 7.27451 21.8261i 0.307679 0.923146i
$$560$$ −5.90148 1.02379i −0.249383 0.0432629i
$$561$$ 0 0
$$562$$ 15.5194 + 26.8804i 0.654646 + 1.13388i
$$563$$ 3.99253 6.91527i 0.168265 0.291444i −0.769545 0.638593i $$-0.779517\pi$$
0.937810 + 0.347149i $$0.112850\pi$$
$$564$$ 0 0
$$565$$ 9.99985 0.420697
$$566$$ 20.0655 + 34.7544i 0.843414 + 1.46084i
$$567$$ 0 0
$$568$$ 7.32424 + 12.6860i 0.307318 + 0.532291i
$$569$$ −13.3621 23.1438i −0.560167 0.970237i −0.997481 0.0709285i $$-0.977404\pi$$
0.437315 0.899308i $$-0.355930\pi$$
$$570$$ 0 0
$$571$$ −6.74647 11.6852i −0.282331 0.489012i 0.689627 0.724164i $$-0.257774\pi$$
−0.971958 + 0.235153i $$0.924441\pi$$
$$572$$ −7.68799 + 1.57352i −0.321451 + 0.0657920i
$$573$$ 0 0
$$574$$ −22.8569 3.96520i −0.954028 0.165504i
$$575$$ −16.6651 + 28.8648i −0.694982 + 1.20374i
$$576$$ 0 0
$$577$$ −6.00662 10.4038i −0.250059 0.433115i 0.713483 0.700673i $$-0.247117\pi$$
−0.963542 + 0.267558i $$0.913783\pi$$
$$578$$ −29.4406 + 50.9925i −1.22457 + 2.12101i
$$579$$ 0 0
$$580$$ −14.4036 −0.598078
$$581$$ 7.47684 + 1.29708i 0.310192 + 0.0538119i
$$582$$ 0 0
$$583$$ 0.125067 + 0.216622i 0.00517974 + 0.00897158i
$$584$$ −10.0318 17.3756i −0.415118 0.719005i
$$585$$ 0 0
$$586$$ −16.8305 + 29.1512i −0.695260 + 1.20422i
$$587$$ 5.21177 9.02705i 0.215113 0.372586i −0.738195 0.674588i $$-0.764321\pi$$
0.953307 + 0.302002i $$0.0976548\pi$$
$$588$$ 0 0
$$589$$ −5.71876 9.90518i −0.235637 0.408136i
$$590$$ −7.04728 + 12.2062i −0.290132 + 0.502523i
$$591$$ 0 0
$$592$$ −2.02339 + 3.50462i −0.0831610 + 0.144039i
$$593$$ −11.1751 + 19.3558i −0.458905 + 0.794847i −0.998903 0.0468194i $$-0.985091\pi$$
0.539998 + 0.841666i $$0.318425\pi$$
$$594$$ 0 0
$$595$$ 5.78044 + 15.7461i 0.236975 + 0.645528i
$$596$$ 5.19607 8.99986i 0.212839 0.368649i
$$597$$ 0 0
$$598$$ 69.6759 14.2607i 2.84926 0.583163i
$$599$$ 0.579463 + 1.00366i 0.0236762 + 0.0410084i 0.877621 0.479356i $$-0.159130\pi$$
−0.853945 + 0.520364i $$0.825796\pi$$
$$600$$ 0 0
$$601$$ −21.0907 + 36.5301i −0.860306 + 1.49009i 0.0113271 + 0.999936i $$0.496394\pi$$
−0.871633 + 0.490158i $$0.836939\pi$$
$$602$$ −25.8287 + 30.9547i −1.05270 + 1.26162i
$$603$$ 0 0
$$604$$ −85.2029 −3.46686
$$605$$ −5.23284 + 9.06355i −0.212745 + 0.368486i
$$606$$ 0 0
$$607$$ −18.1569 −0.736965 −0.368482 0.929635i $$-0.620123\pi$$
−0.368482 + 0.929635i $$0.620123\pi$$
$$608$$ −5.02970 + 8.71169i −0.203981 + 0.353306i
$$609$$ 0 0
$$610$$ −5.17640 −0.209586
$$611$$ −15.3324 + 3.13811i −0.620282 + 0.126954i
$$612$$ 0 0
$$613$$ −0.902645 −0.0364575 −0.0182288 0.999834i $$-0.505803\pi$$
−0.0182288 + 0.999834i $$0.505803\pi$$
$$614$$ −18.9594 32.8386i −0.765137 1.32526i
$$615$$ 0 0
$$616$$ 6.23055 + 1.08087i 0.251036 + 0.0435497i
$$617$$ −13.0218 22.5544i −0.524238 0.908008i −0.999602 0.0282180i $$-0.991017\pi$$
0.475363 0.879790i $$-0.342317\pi$$
$$618$$ 0 0
$$619$$ −13.4171 23.2390i −0.539277 0.934056i −0.998943 0.0459638i $$-0.985364\pi$$
0.459666 0.888092i $$-0.347969\pi$$
$$620$$ −5.43515 + 9.41396i −0.218281 + 0.378074i
$$621$$ 0 0
$$622$$ −34.1530 + 59.1547i −1.36941 + 2.37189i
$$623$$ −1.90843 5.19863i −0.0764596 0.208279i
$$624$$ 0 0
$$625$$ −5.72894 + 9.92281i −0.229158 + 0.396912i
$$626$$ −44.3679 −1.77330
$$627$$ 0 0
$$628$$ 83.5925 3.33570
$$629$$ 11.3328 0.451869
$$630$$ 0 0
$$631$$ 16.8061 + 29.1089i 0.669039 + 1.15881i 0.978173 + 0.207791i $$0.0666273\pi$$
−0.309135 + 0.951018i $$0.600039\pi$$
$$632$$ −5.66296 + 9.80853i −0.225260 + 0.390162i
$$633$$ 0 0
$$634$$ −73.1802 −2.90636
$$635$$ 2.08747 + 3.61561i 0.0828388 + 0.143481i
$$636$$ 0 0
$$637$$ 9.40711 + 23.4202i 0.372723 + 0.927942i
$$638$$ 5.55889 0.220078
$$639$$ 0 0
$$640$$ 20.3729 0.805310
$$641$$ 10.5921 18.3460i 0.418361 0.724622i −0.577414 0.816452i $$-0.695938\pi$$
0.995775 + 0.0918294i $$0.0292714\pi$$
$$642$$ 0 0
$$643$$ −0.330770 0.572910i −0.0130443 0.0225933i 0.859430 0.511254i $$-0.170819\pi$$
−0.872474 + 0.488661i $$0.837486\pi$$
$$644$$ −79.7282 13.8312i −3.14173 0.545027i
$$645$$ 0 0
$$646$$ −58.9834 −2.32067
$$647$$ 40.0323 1.57383 0.786916 0.617060i $$-0.211676\pi$$
0.786916 + 0.617060i $$0.211676\pi$$
$$648$$ 0 0
$$649$$ 1.76594 3.05870i 0.0693193 0.120065i
$$650$$ 34.0376 6.96654i 1.33506 0.273250i
$$651$$ 0 0
$$652$$ −15.1388 + 26.2212i −0.592883 + 1.02690i
$$653$$ 6.35602 + 11.0089i 0.248730 + 0.430813i 0.963174 0.268880i $$-0.0866534\pi$$
−0.714444 + 0.699693i $$0.753320\pi$$
$$654$$ 0 0
$$655$$ 1.06556 + 1.84560i 0.0416349 + 0.0721138i
$$656$$ −8.46215 −0.330391
$$657$$ 0 0
$$658$$ 27.0209 + 4.68759i 1.05339 + 0.182741i
$$659$$ −7.09522 12.2893i −0.276391 0.478723i 0.694094 0.719884i $$-0.255805\pi$$
−0.970485 + 0.241161i $$0.922472\pi$$
$$660$$ 0 0
$$661$$ 50.1780 1.95170 0.975848 0.218449i $$-0.0700996\pi$$
0.975848 + 0.218449i $$0.0700996\pi$$
$$662$$ −32.5104 56.3096i −1.26355 2.18853i
$$663$$ 0 0
$$664$$ 11.6625 0.452594
$$665$$ −6.37183 + 7.63640i −0.247089 + 0.296127i
$$666$$ 0 0
$$667$$ −32.7112 −1.26658
$$668$$ −4.30944 7.46417i −0.166737 0.288797i
$$669$$ 0 0
$$670$$ −16.4506 −0.635542
$$671$$ 1.29713 0.0500751
$$672$$ 0 0
$$673$$ 0.937137 1.62317i 0.0361240 0.0625685i −0.847398 0.530958i $$-0.821832\pi$$
0.883522 + 0.468389i $$0.155166\pi$$
$$674$$ 14.7056 + 25.4708i 0.566438 + 0.981100i
$$675$$ 0 0
$$676$$ −38.5104 28.8785i −1.48117 1.11071i
$$677$$ −1.00439 + 1.73966i −0.0386020 + 0.0668607i −0.884681 0.466197i $$-0.845624\pi$$
0.846079 + 0.533058i $$0.178957\pi$$
$$678$$ 0 0
$$679$$ −7.01790 19.1170i −0.269322 0.733644i
$$680$$ 12.8894 + 22.3251i 0.494286 + 0.856128i
$$681$$ 0 0
$$682$$ 2.09762 3.63319i 0.0803222 0.139122i
$$683$$ −7.05061 + 12.2120i −0.269784 + 0.467280i −0.968806 0.247820i $$-0.920286\pi$$
0.699022 + 0.715100i $$0.253619\pi$$
$$684$$ 0 0
$$685$$ −4.10748 7.11437i −0.156939 0.271826i
$$686$$ −0.366563 44.2255i −0.0139955 1.68854i
$$687$$ 0 0
$$688$$ −7.35298 + 12.7357i −0.280330 + 0.485546i
$$689$$ −0.485139 + 1.45559i −0.0184823 + 0.0554536i
$$690$$ 0 0
$$691$$ 17.8460 + 30.9102i 0.678895 + 1.17588i 0.975314 + 0.220822i $$0.0708741\pi$$
−0.296419 + 0.955058i $$0.595793\pi$$
$$692$$ −15.0585 + 26.0820i −0.572437 + 0.991489i
$$693$$ 0 0
$$694$$ −14.6746 −0.557041
$$695$$ 0.566691 0.0214958
$$696$$ 0 0
$$697$$ 11.8489 + 20.5229i 0.448809 + 0.777360i
$$698$$ 31.1191 1.17788
$$699$$ 0 0
$$700$$ −38.9483 6.75674i −1.47211 0.255381i
$$701$$ 6.15865 0.232609 0.116305 0.993214i $$-0.462895\pi$$
0.116305 + 0.993214i $$0.462895\pi$$
$$702$$ 0 0
$$703$$ 3.35979 + 5.81932i 0.126717 + 0.219480i
$$704$$ −6.39918 −0.241178
$$705$$ 0 0
$$706$$ 37.8103 + 65.4894i 1.42301 + 2.46473i
$$707$$ 6.87501 + 1.19268i 0.258561 + 0.0448552i
$$708$$ 0 0
$$709$$ 34.0371 1.27829 0.639144 0.769087i $$-0.279289\pi$$
0.639144 + 0.769087i $$0.279289\pi$$
$$710$$ −4.22527 7.31838i −0.158571 0.274654i
$$711$$ 0 0
$$712$$ −4.25547 7.37069i −0.159480 0.276228i
$$713$$ −12.3434 + 21.3794i −0.462265 + 0.800667i
$$714$$ 0 0
$$715$$ 2.03952 0.417432i 0.0762736 0.0156111i
$$716$$ −38.8648 + 67.3158i −1.45244 + 2.51571i
$$717$$ 0 0
$$718$$ −47.5989 −1.77637
$$719$$ 22.9648 0.856444 0.428222 0.903674i $$-0.359140\pi$$
0.428222 + 0.903674i $$0.359140\pi$$
$$720$$ 0 0
$$721$$ 18.4115 22.0655i 0.685679 0.821761i
$$722$$ 5.19981 + 9.00633i 0.193517 + 0.335181i
$$723$$ 0 0
$$724$$ 2.97712 5.15653i 0.110644 0.191641i
$$725$$ −15.9798 −0.593476
$$726$$ 0 0
$$727$$ 1.06558 0.0395203 0.0197601 0.999805i $$-0.493710\pi$$
0.0197601 + 0.999805i $$0.493710\pi$$
$$728$$ 20.3970 + 32.9928i 0.755963 + 1.22280i
$$729$$ 0 0
$$730$$ 5.78721 + 10.0237i 0.214194 + 0.370996i
$$731$$ 41.1833 1.52322
$$732$$ 0 0
$$733$$ 13.1689 22.8092i 0.486404 0.842476i −0.513474 0.858105i $$-0.671642\pi$$
0.999878 + 0.0156289i $$0.00497504\pi$$
$$734$$ −23.5448 40.7809i −0.869056 1.50525i
$$735$$ 0 0
$$736$$ 21.7123 0.800326
$$737$$ 4.12228 0.151846
$$738$$ 0 0
$$739$$ 34.2149 1.25862 0.629308 0.777156i $$-0.283338\pi$$
0.629308 + 0.777156i $$0.283338\pi$$
$$740$$ 3.19317 5.53073i 0.117383 0.203314i
$$741$$ 0 0
$$742$$ 1.72252 2.06438i 0.0632358 0.0757857i
$$743$$ 11.2391 19.4667i 0.412322 0.714163i −0.582821 0.812600i $$-0.698051\pi$$
0.995143 + 0.0984379i $$0.0313846\pi$$
$$744$$ 0 0
$$745$$ −1.37845 + 2.38754i −0.0505023 + 0.0874726i
$$746$$ −20.9513 36.2888i −0.767083 1.32863i
$$747$$ 0 0
$$748$$ −7.02368 12.1654i −0.256811 0.444810i
$$749$$ −14.5705 39.6905i −0.532393 1.45026i
$$750$$ 0 0
$$751$$ 21.2712 + 36.8428i 0.776197 + 1.34441i 0.934119 + 0.356961i $$0.116187\pi$$
−0.157923 + 0.987451i $$0.550480\pi$$
$$752$$ 10.0038 0.364801
$$753$$ 0 0
$$754$$ 22.6239 + 25.5114i 0.823912 + 0.929069i
$$755$$ 22.6031 0.822612
$$756$$ 0 0
$$757$$ 5.61902 9.73243i 0.204227 0.353731i −0.745659 0.666327i $$-0.767865\pi$$
0.949886 + 0.312596i $$0.101199\pi$$
$$758$$ −27.9433 −1.01495
$$759$$ 0 0
$$760$$ −7.64252 + 13.2372i −0.277223 + 0.480165i
$$761$$ −12.8084 −0.464306 −0.232153 0.972679i $$-0.574577\pi$$
−0.232153 + 0.972679i $$0.574577\pi$$
$$762$$ 0 0
$$763$$ −8.41994 22.9362i −0.304822 0.830347i
$$764$$ −21.4059 + 37.0760i −0.774437 + 1.34136i
$$765$$ 0 0
$$766$$ −25.7058 44.5238i −0.928789 1.60871i
$$767$$ 21.2244 4.34404i 0.766369 0.156854i
$$768$$ 0 0
$$769$$ 25.6759 44.4719i 0.925895 1.60370i 0.135780 0.990739i $$-0.456646\pi$$
0.790115 0.612958i $$-0.210021\pi$$
$$770$$ −3.59433 0.623543i −0.129531 0.0224709i
$$771$$ 0 0
$$772$$ −43.6529 + 75.6091i −1.57110 + 2.72123i
$$773$$ 10.0023 17.3245i 0.359759 0.623120i −0.628162 0.778083i $$-0.716192\pi$$
0.987920 + 0.154963i $$0.0495257\pi$$
$$774$$ 0 0
$$775$$ −6.02993 + 10.4441i −0.216602 + 0.375165i
$$776$$ −15.6487 27.1044i −0.561756 0.972990i
$$777$$ 0 0
$$778$$ 31.6308 54.7861i 1.13402 1.96418i
$$779$$ −7.02558 + 12.1687i −0.251717 + 0.435987i
$$780$$ 0 0
$$781$$ 1.05879 + 1.83388i 0.0378864 + 0.0656212i
$$782$$ 63.6552 + 110.254i 2.27631 + 3.94268i
$$783$$ 0 0
$$784$$ −2.88920 15.8721i −0.103186 0.566861i
$$785$$ −22.1759 −0.791492
$$786$$ 0 0
$$787$$ −14.6596 + 25.3911i −0.522558 + 0.905096i 0.477098 + 0.878850i $$0.341689\pi$$
−0.999656 + 0.0262462i $$0.991645\pi$$
$$788$$ −2.72325 4.71680i −0.0970117 0.168029i
$$789$$ 0 0
$$790$$ 3.26689 5.65842i 0.116231