# Properties

 Label 190.2.b.b.39.4 Level $190$ Weight $2$ Character 190.39 Analytic conductor $1.517$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$190 = 2 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 190.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.51715763840$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.5161984.1 Defining polynomial: $$x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 39.4 Root $$0.432320 + 0.432320i$$ of defining polynomial Character $$\chi$$ $$=$$ 190.39 Dual form 190.2.b.b.39.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -2.76156i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} +2.76156 q^{6} -0.761557i q^{7} -1.00000i q^{8} -4.62620 q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} -2.76156i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} +2.76156 q^{6} -0.761557i q^{7} -1.00000i q^{8} -4.62620 q^{9} +(0.432320 - 2.19388i) q^{10} -0.864641 q^{11} +2.76156i q^{12} -5.62620i q^{13} +0.761557 q^{14} +(-1.19388 + 6.05852i) q^{15} +1.00000 q^{16} -3.62620i q^{17} -4.62620i q^{18} -1.00000 q^{19} +(2.19388 + 0.432320i) q^{20} -2.10308 q^{21} -0.864641i q^{22} +8.01395i q^{23} -2.76156 q^{24} +(4.62620 + 1.89692i) q^{25} +5.62620 q^{26} +4.49084i q^{27} +0.761557i q^{28} +7.35548 q^{29} +(-6.05852 - 1.19388i) q^{30} +8.11704 q^{31} +1.00000i q^{32} +2.38776i q^{33} +3.62620 q^{34} +(-0.329237 + 1.67076i) q^{35} +4.62620 q^{36} +0.476886i q^{37} -1.00000i q^{38} -15.5371 q^{39} +(-0.432320 + 2.19388i) q^{40} -2.65847 q^{41} -2.10308i q^{42} -6.86464i q^{43} +0.864641 q^{44} +(10.1493 + 2.00000i) q^{45} -8.01395 q^{46} +1.25240i q^{47} -2.76156i q^{48} +6.42003 q^{49} +(-1.89692 + 4.62620i) q^{50} -10.0140 q^{51} +5.62620i q^{52} -2.37380i q^{53} -4.49084 q^{54} +(1.89692 + 0.373802i) q^{55} -0.761557 q^{56} +2.76156i q^{57} +7.35548i q^{58} -4.49084 q^{59} +(1.19388 - 6.05852i) q^{60} -10.8646 q^{61} +8.11704i q^{62} +3.52311i q^{63} -1.00000 q^{64} +(-2.43232 + 12.3432i) q^{65} -2.38776 q^{66} +1.03228i q^{67} +3.62620i q^{68} +22.1310 q^{69} +(-1.67076 - 0.329237i) q^{70} -10.1816 q^{71} +4.62620i q^{72} -16.4017i q^{73} -0.476886 q^{74} +(5.23844 - 12.7755i) q^{75} +1.00000 q^{76} +0.658473i q^{77} -15.5371i q^{78} +12.5693 q^{79} +(-2.19388 - 0.432320i) q^{80} -1.47689 q^{81} -2.65847i q^{82} +0.270718i q^{83} +2.10308 q^{84} +(-1.56768 + 7.95543i) q^{85} +6.86464 q^{86} -20.3126i q^{87} +0.864641i q^{88} -0.387755 q^{89} +(-2.00000 + 10.1493i) q^{90} -4.28467 q^{91} -8.01395i q^{92} -22.4157i q^{93} -1.25240 q^{94} +(2.19388 + 0.432320i) q^{95} +2.76156 q^{96} -8.50479i q^{97} +6.42003i q^{98} +4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q - 6q^{4} + 2q^{5} + 4q^{6} - 10q^{9} + O(q^{10})$$ $$6q - 6q^{4} + 2q^{5} + 4q^{6} - 10q^{9} - 8q^{14} + 8q^{15} + 6q^{16} - 6q^{19} - 2q^{20} - 20q^{21} - 4q^{24} + 10q^{25} + 16q^{26} + 16q^{29} - 16q^{30} + 8q^{31} + 4q^{34} + 8q^{35} + 10q^{36} - 20q^{39} + 4q^{41} + 18q^{45} + 6q^{49} - 4q^{50} - 12q^{51} - 4q^{54} + 4q^{55} + 8q^{56} - 4q^{59} - 8q^{60} - 60q^{61} - 6q^{64} - 12q^{65} + 16q^{66} + 44q^{69} - 20q^{70} - 16q^{71} - 28q^{74} + 44q^{75} + 6q^{76} + 2q^{80} - 34q^{81} + 20q^{84} - 12q^{85} + 36q^{86} + 28q^{89} - 12q^{90} + 12q^{91} + 28q^{94} - 2q^{95} + 4q^{96} + 24q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$77$$ $$\chi(n)$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 2.76156i 1.59439i −0.603725 0.797193i $$-0.706317\pi$$
0.603725 0.797193i $$-0.293683\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ −2.19388 0.432320i −0.981132 0.193340i
$$6$$ 2.76156 1.12740
$$7$$ 0.761557i 0.287842i −0.989589 0.143921i $$-0.954029\pi$$
0.989589 0.143921i $$-0.0459710\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −4.62620 −1.54207
$$10$$ 0.432320 2.19388i 0.136712 0.693765i
$$11$$ −0.864641 −0.260699 −0.130350 0.991468i $$-0.541610\pi$$
−0.130350 + 0.991468i $$0.541610\pi$$
$$12$$ 2.76156i 0.797193i
$$13$$ 5.62620i 1.56043i −0.625514 0.780213i $$-0.715111\pi$$
0.625514 0.780213i $$-0.284889\pi$$
$$14$$ 0.761557 0.203535
$$15$$ −1.19388 + 6.05852i −0.308258 + 1.56430i
$$16$$ 1.00000 0.250000
$$17$$ 3.62620i 0.879482i −0.898125 0.439741i $$-0.855070\pi$$
0.898125 0.439741i $$-0.144930\pi$$
$$18$$ 4.62620i 1.09041i
$$19$$ −1.00000 −0.229416
$$20$$ 2.19388 + 0.432320i 0.490566 + 0.0966698i
$$21$$ −2.10308 −0.458930
$$22$$ 0.864641i 0.184342i
$$23$$ 8.01395i 1.67102i 0.549472 + 0.835512i $$0.314829\pi$$
−0.549472 + 0.835512i $$0.685171\pi$$
$$24$$ −2.76156 −0.563700
$$25$$ 4.62620 + 1.89692i 0.925240 + 0.379383i
$$26$$ 5.62620 1.10339
$$27$$ 4.49084i 0.864262i
$$28$$ 0.761557i 0.143921i
$$29$$ 7.35548 1.36588 0.682939 0.730475i $$-0.260701\pi$$
0.682939 + 0.730475i $$0.260701\pi$$
$$30$$ −6.05852 1.19388i −1.10613 0.217971i
$$31$$ 8.11704 1.45786 0.728931 0.684587i $$-0.240017\pi$$
0.728931 + 0.684587i $$0.240017\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 2.38776i 0.415655i
$$34$$ 3.62620 0.621888
$$35$$ −0.329237 + 1.67076i −0.0556512 + 0.282411i
$$36$$ 4.62620 0.771033
$$37$$ 0.476886i 0.0783995i 0.999231 + 0.0391998i $$0.0124809\pi$$
−0.999231 + 0.0391998i $$0.987519\pi$$
$$38$$ 1.00000i 0.162221i
$$39$$ −15.5371 −2.48792
$$40$$ −0.432320 + 2.19388i −0.0683559 + 0.346883i
$$41$$ −2.65847 −0.415184 −0.207592 0.978216i $$-0.566563\pi$$
−0.207592 + 0.978216i $$0.566563\pi$$
$$42$$ 2.10308i 0.324513i
$$43$$ 6.86464i 1.04685i −0.852072 0.523424i $$-0.824654\pi$$
0.852072 0.523424i $$-0.175346\pi$$
$$44$$ 0.864641 0.130350
$$45$$ 10.1493 + 2.00000i 1.51297 + 0.298142i
$$46$$ −8.01395 −1.18159
$$47$$ 1.25240i 0.182681i 0.995820 + 0.0913404i $$0.0291151\pi$$
−0.995820 + 0.0913404i $$0.970885\pi$$
$$48$$ 2.76156i 0.398596i
$$49$$ 6.42003 0.917147
$$50$$ −1.89692 + 4.62620i −0.268264 + 0.654243i
$$51$$ −10.0140 −1.40223
$$52$$ 5.62620i 0.780213i
$$53$$ 2.37380i 0.326067i −0.986621 0.163033i $$-0.947872\pi$$
0.986621 0.163033i $$-0.0521278\pi$$
$$54$$ −4.49084 −0.611126
$$55$$ 1.89692 + 0.373802i 0.255780 + 0.0504034i
$$56$$ −0.761557 −0.101767
$$57$$ 2.76156i 0.365777i
$$58$$ 7.35548i 0.965822i
$$59$$ −4.49084 −0.584657 −0.292329 0.956318i $$-0.594430\pi$$
−0.292329 + 0.956318i $$0.594430\pi$$
$$60$$ 1.19388 6.05852i 0.154129 0.782151i
$$61$$ −10.8646 −1.39107 −0.695537 0.718490i $$-0.744834\pi$$
−0.695537 + 0.718490i $$0.744834\pi$$
$$62$$ 8.11704i 1.03086i
$$63$$ 3.52311i 0.443871i
$$64$$ −1.00000 −0.125000
$$65$$ −2.43232 + 12.3432i −0.301692 + 1.53098i
$$66$$ −2.38776 −0.293912
$$67$$ 1.03228i 0.126113i 0.998010 + 0.0630563i $$0.0200848\pi$$
−0.998010 + 0.0630563i $$0.979915\pi$$
$$68$$ 3.62620i 0.439741i
$$69$$ 22.1310 2.66426
$$70$$ −1.67076 0.329237i −0.199694 0.0393513i
$$71$$ −10.1816 −1.20833 −0.604166 0.796858i $$-0.706494\pi$$
−0.604166 + 0.796858i $$0.706494\pi$$
$$72$$ 4.62620i 0.545203i
$$73$$ 16.4017i 1.91967i −0.280557 0.959837i $$-0.590519\pi$$
0.280557 0.959837i $$-0.409481\pi$$
$$74$$ −0.476886 −0.0554368
$$75$$ 5.23844 12.7755i 0.604883 1.47519i
$$76$$ 1.00000 0.114708
$$77$$ 0.658473i 0.0750400i
$$78$$ 15.5371i 1.75923i
$$79$$ 12.5693 1.41416 0.707081 0.707133i $$-0.250012\pi$$
0.707081 + 0.707133i $$0.250012\pi$$
$$80$$ −2.19388 0.432320i −0.245283 0.0483349i
$$81$$ −1.47689 −0.164098
$$82$$ 2.65847i 0.293579i
$$83$$ 0.270718i 0.0297152i 0.999890 + 0.0148576i $$0.00472949\pi$$
−0.999890 + 0.0148576i $$0.995271\pi$$
$$84$$ 2.10308 0.229465
$$85$$ −1.56768 + 7.95543i −0.170039 + 0.862888i
$$86$$ 6.86464 0.740233
$$87$$ 20.3126i 2.17774i
$$88$$ 0.864641i 0.0921710i
$$89$$ −0.387755 −0.0411020 −0.0205510 0.999789i $$-0.506542\pi$$
−0.0205510 + 0.999789i $$0.506542\pi$$
$$90$$ −2.00000 + 10.1493i −0.210819 + 1.06983i
$$91$$ −4.28467 −0.449156
$$92$$ 8.01395i 0.835512i
$$93$$ 22.4157i 2.32440i
$$94$$ −1.25240 −0.129175
$$95$$ 2.19388 + 0.432320i 0.225087 + 0.0443551i
$$96$$ 2.76156 0.281850
$$97$$ 8.50479i 0.863531i −0.901986 0.431765i $$-0.857891\pi$$
0.901986 0.431765i $$-0.142109\pi$$
$$98$$ 6.42003i 0.648521i
$$99$$ 4.00000 0.402015
$$100$$ −4.62620 1.89692i −0.462620 0.189692i
$$101$$ 16.4157 1.63342 0.816710 0.577049i $$-0.195796\pi$$
0.816710 + 0.577049i $$0.195796\pi$$
$$102$$ 10.0140i 0.991529i
$$103$$ 9.64015i 0.949872i 0.880020 + 0.474936i $$0.157529\pi$$
−0.880020 + 0.474936i $$0.842471\pi$$
$$104$$ −5.62620 −0.551694
$$105$$ 4.61391 + 0.909206i 0.450271 + 0.0887294i
$$106$$ 2.37380 0.230564
$$107$$ 4.28467i 0.414215i 0.978318 + 0.207107i $$0.0664050\pi$$
−0.978318 + 0.207107i $$0.933595\pi$$
$$108$$ 4.49084i 0.432131i
$$109$$ 13.4200 1.28541 0.642703 0.766116i $$-0.277813\pi$$
0.642703 + 0.766116i $$0.277813\pi$$
$$110$$ −0.373802 + 1.89692i −0.0356406 + 0.180864i
$$111$$ 1.31695 0.124999
$$112$$ 0.761557i 0.0719604i
$$113$$ 10.3232i 0.971125i 0.874202 + 0.485563i $$0.161385\pi$$
−0.874202 + 0.485563i $$0.838615\pi$$
$$114$$ −2.76156 −0.258644
$$115$$ 3.46460 17.5816i 0.323075 1.63950i
$$116$$ −7.35548 −0.682939
$$117$$ 26.0279i 2.40628i
$$118$$ 4.49084i 0.413415i
$$119$$ −2.76156 −0.253152
$$120$$ 6.05852 + 1.19388i 0.553065 + 0.108986i
$$121$$ −10.2524 −0.932036
$$122$$ 10.8646i 0.983638i
$$123$$ 7.34153i 0.661963i
$$124$$ −8.11704 −0.728931
$$125$$ −9.32924 6.16160i −0.834432 0.551110i
$$126$$ −3.52311 −0.313864
$$127$$ 16.9817i 1.50688i 0.657517 + 0.753440i $$0.271607\pi$$
−0.657517 + 0.753440i $$0.728393\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −18.9571 −1.66908
$$130$$ −12.3432 2.43232i −1.08257 0.213329i
$$131$$ 0.541436 0.0473055 0.0236528 0.999720i $$-0.492470\pi$$
0.0236528 + 0.999720i $$0.492470\pi$$
$$132$$ 2.38776i 0.207827i
$$133$$ 0.761557i 0.0660354i
$$134$$ −1.03228 −0.0891750
$$135$$ 1.94148 9.85235i 0.167096 0.847955i
$$136$$ −3.62620 −0.310944
$$137$$ 2.87859i 0.245935i 0.992411 + 0.122967i $$0.0392411\pi$$
−0.992411 + 0.122967i $$0.960759\pi$$
$$138$$ 22.1310i 1.88392i
$$139$$ −3.58767 −0.304302 −0.152151 0.988357i $$-0.548620\pi$$
−0.152151 + 0.988357i $$0.548620\pi$$
$$140$$ 0.329237 1.67076i 0.0278256 0.141205i
$$141$$ 3.45856 0.291264
$$142$$ 10.1816i 0.854420i
$$143$$ 4.86464i 0.406802i
$$144$$ −4.62620 −0.385517
$$145$$ −16.1370 3.17992i −1.34011 0.264078i
$$146$$ 16.4017 1.35742
$$147$$ 17.7293i 1.46229i
$$148$$ 0.476886i 0.0391998i
$$149$$ 16.8401 1.37959 0.689796 0.724004i $$-0.257700\pi$$
0.689796 + 0.724004i $$0.257700\pi$$
$$150$$ 12.7755 + 5.23844i 1.04312 + 0.427717i
$$151$$ −16.9817 −1.38195 −0.690975 0.722879i $$-0.742818\pi$$
−0.690975 + 0.722879i $$0.742818\pi$$
$$152$$ 1.00000i 0.0811107i
$$153$$ 16.7755i 1.35622i
$$154$$ −0.658473 −0.0530613
$$155$$ −17.8078 3.50916i −1.43036 0.281863i
$$156$$ 15.5371 1.24396
$$157$$ 14.8401i 1.18437i 0.805804 + 0.592183i $$0.201734\pi$$
−0.805804 + 0.592183i $$0.798266\pi$$
$$158$$ 12.5693i 0.999963i
$$159$$ −6.55539 −0.519876
$$160$$ 0.432320 2.19388i 0.0341779 0.173441i
$$161$$ 6.10308 0.480990
$$162$$ 1.47689i 0.116035i
$$163$$ 13.3694i 1.04717i −0.851972 0.523587i $$-0.824593\pi$$
0.851972 0.523587i $$-0.175407\pi$$
$$164$$ 2.65847 0.207592
$$165$$ 1.03228 5.23844i 0.0803625 0.407812i
$$166$$ −0.270718 −0.0210118
$$167$$ 9.84632i 0.761931i 0.924589 + 0.380966i $$0.124408\pi$$
−0.924589 + 0.380966i $$0.875592\pi$$
$$168$$ 2.10308i 0.162256i
$$169$$ −18.6541 −1.43493
$$170$$ −7.95543 1.56768i −0.610154 0.120236i
$$171$$ 4.62620 0.353774
$$172$$ 6.86464i 0.523424i
$$173$$ 2.98168i 0.226693i −0.993556 0.113346i $$-0.963843\pi$$
0.993556 0.113346i $$-0.0361570\pi$$
$$174$$ 20.3126 1.53989
$$175$$ 1.44461 3.52311i 0.109202 0.266322i
$$176$$ −0.864641 −0.0651748
$$177$$ 12.4017i 0.932169i
$$178$$ 0.387755i 0.0290635i
$$179$$ −11.7938 −0.881512 −0.440756 0.897627i $$-0.645290\pi$$
−0.440756 + 0.897627i $$0.645290\pi$$
$$180$$ −10.1493 2.00000i −0.756485 0.149071i
$$181$$ 14.5693 1.08293 0.541465 0.840723i $$-0.317870\pi$$
0.541465 + 0.840723i $$0.317870\pi$$
$$182$$ 4.28467i 0.317601i
$$183$$ 30.0033i 2.21791i
$$184$$ 8.01395 0.590796
$$185$$ 0.206167 1.04623i 0.0151577 0.0769203i
$$186$$ 22.4157 1.64360
$$187$$ 3.13536i 0.229280i
$$188$$ 1.25240i 0.0913404i
$$189$$ 3.42003 0.248771
$$190$$ −0.432320 + 2.19388i −0.0313638 + 0.159161i
$$191$$ 13.2384 0.957900 0.478950 0.877842i $$-0.341017\pi$$
0.478950 + 0.877842i $$0.341017\pi$$
$$192$$ 2.76156i 0.199298i
$$193$$ 2.54144i 0.182937i −0.995808 0.0914683i $$-0.970844\pi$$
0.995808 0.0914683i $$-0.0291560\pi$$
$$194$$ 8.50479 0.610609
$$195$$ 34.0864 + 6.71699i 2.44098 + 0.481014i
$$196$$ −6.42003 −0.458574
$$197$$ 19.9109i 1.41859i −0.704911 0.709295i $$-0.749013\pi$$
0.704911 0.709295i $$-0.250987\pi$$
$$198$$ 4.00000i 0.284268i
$$199$$ 20.3126 1.43992 0.719960 0.694015i $$-0.244160\pi$$
0.719960 + 0.694015i $$0.244160\pi$$
$$200$$ 1.89692 4.62620i 0.134132 0.327122i
$$201$$ 2.85069 0.201072
$$202$$ 16.4157i 1.15500i
$$203$$ 5.60162i 0.393157i
$$204$$ 10.0140 0.701117
$$205$$ 5.83237 + 1.14931i 0.407350 + 0.0802715i
$$206$$ −9.64015 −0.671661
$$207$$ 37.0741i 2.57683i
$$208$$ 5.62620i 0.390107i
$$209$$ 0.864641 0.0598085
$$210$$ −0.909206 + 4.61391i −0.0627412 + 0.318390i
$$211$$ 18.0419 1.24205 0.621026 0.783790i $$-0.286716\pi$$
0.621026 + 0.783790i $$0.286716\pi$$
$$212$$ 2.37380i 0.163033i
$$213$$ 28.1170i 1.92655i
$$214$$ −4.28467 −0.292894
$$215$$ −2.96772 + 15.0602i −0.202397 + 1.02710i
$$216$$ 4.49084 0.305563
$$217$$ 6.18159i 0.419634i
$$218$$ 13.4200i 0.908919i
$$219$$ −45.2943 −3.06070
$$220$$ −1.89692 0.373802i −0.127890 0.0252017i
$$221$$ −20.4017 −1.37237
$$222$$ 1.31695i 0.0883877i
$$223$$ 13.5231i 0.905575i 0.891619 + 0.452787i $$0.149570\pi$$
−0.891619 + 0.452787i $$0.850430\pi$$
$$224$$ 0.761557 0.0508837
$$225$$ −21.4017 8.77551i −1.42678 0.585034i
$$226$$ −10.3232 −0.686689
$$227$$ 13.6016i 0.902771i 0.892329 + 0.451386i $$0.149070\pi$$
−0.892329 + 0.451386i $$0.850930\pi$$
$$228$$ 2.76156i 0.182889i
$$229$$ −13.5877 −0.897898 −0.448949 0.893557i $$-0.648202\pi$$
−0.448949 + 0.893557i $$0.648202\pi$$
$$230$$ 17.5816 + 3.46460i 1.15930 + 0.228449i
$$231$$ 1.81841 0.119643
$$232$$ 7.35548i 0.482911i
$$233$$ 25.5510i 1.67390i −0.547277 0.836952i $$-0.684336\pi$$
0.547277 0.836952i $$-0.315664\pi$$
$$234$$ −26.0279 −1.70150
$$235$$ 0.541436 2.74760i 0.0353194 0.179234i
$$236$$ 4.49084 0.292329
$$237$$ 34.7110i 2.25472i
$$238$$ 2.76156i 0.179005i
$$239$$ 11.3309 0.732935 0.366468 0.930431i $$-0.380567\pi$$
0.366468 + 0.930431i $$0.380567\pi$$
$$240$$ −1.19388 + 6.05852i −0.0770645 + 0.391076i
$$241$$ −1.25240 −0.0806739 −0.0403370 0.999186i $$-0.512843\pi$$
−0.0403370 + 0.999186i $$0.512843\pi$$
$$242$$ 10.2524i 0.659049i
$$243$$ 17.5510i 1.12590i
$$244$$ 10.8646 0.695537
$$245$$ −14.0848 2.77551i −0.899842 0.177321i
$$246$$ −7.34153 −0.468079
$$247$$ 5.62620i 0.357986i
$$248$$ 8.11704i 0.515432i
$$249$$ 0.747604 0.0473775
$$250$$ 6.16160 9.32924i 0.389694 0.590033i
$$251$$ 10.5939 0.668682 0.334341 0.942452i $$-0.391486\pi$$
0.334341 + 0.942452i $$0.391486\pi$$
$$252$$ 3.52311i 0.221935i
$$253$$ 6.92919i 0.435635i
$$254$$ −16.9817 −1.06553
$$255$$ 21.9694 + 4.32924i 1.37578 + 0.271107i
$$256$$ 1.00000 0.0625000
$$257$$ 0.153681i 0.00958637i −0.999989 0.00479319i $$-0.998474\pi$$
0.999989 0.00479319i $$-0.00152572\pi$$
$$258$$ 18.9571i 1.18022i
$$259$$ 0.363176 0.0225666
$$260$$ 2.43232 12.3432i 0.150846 0.765492i
$$261$$ −34.0279 −2.10627
$$262$$ 0.541436i 0.0334501i
$$263$$ 0.504792i 0.0311268i −0.999879 0.0155634i $$-0.995046\pi$$
0.999879 0.0155634i $$-0.00495419\pi$$
$$264$$ 2.38776 0.146956
$$265$$ −1.02624 + 5.20783i −0.0630416 + 0.319915i
$$266$$ −0.761557 −0.0466941
$$267$$ 1.07081i 0.0655324i
$$268$$ 1.03228i 0.0630563i
$$269$$ 3.49521 0.213107 0.106553 0.994307i $$-0.466019\pi$$
0.106553 + 0.994307i $$0.466019\pi$$
$$270$$ 9.85235 + 1.94148i 0.599595 + 0.118155i
$$271$$ 5.47252 0.332432 0.166216 0.986089i $$-0.446845\pi$$
0.166216 + 0.986089i $$0.446845\pi$$
$$272$$ 3.62620i 0.219871i
$$273$$ 11.8324i 0.716127i
$$274$$ −2.87859 −0.173902
$$275$$ −4.00000 1.64015i −0.241209 0.0989049i
$$276$$ −22.1310 −1.33213
$$277$$ 12.9538i 0.778317i 0.921171 + 0.389158i $$0.127234\pi$$
−0.921171 + 0.389158i $$0.872766\pi$$
$$278$$ 3.58767i 0.215174i
$$279$$ −37.5510 −2.24812
$$280$$ 1.67076 + 0.329237i 0.0998472 + 0.0196757i
$$281$$ 0.153681 0.00916785 0.00458393 0.999989i $$-0.498541\pi$$
0.00458393 + 0.999989i $$0.498541\pi$$
$$282$$ 3.45856i 0.205954i
$$283$$ 18.2341i 1.08390i 0.840410 + 0.541952i $$0.182314\pi$$
−0.840410 + 0.541952i $$0.817686\pi$$
$$284$$ 10.1816 0.604166
$$285$$ 1.19388 6.05852i 0.0707192 0.358876i
$$286$$ −4.86464 −0.287652
$$287$$ 2.02458i 0.119507i
$$288$$ 4.62620i 0.272601i
$$289$$ 3.85069 0.226511
$$290$$ 3.17992 16.1370i 0.186732 0.947599i
$$291$$ −23.4865 −1.37680
$$292$$ 16.4017i 0.959837i
$$293$$ 2.03853i 0.119092i −0.998226 0.0595462i $$-0.981035\pi$$
0.998226 0.0595462i $$-0.0189654\pi$$
$$294$$ 17.7293 1.03399
$$295$$ 9.85235 + 1.94148i 0.573626 + 0.113037i
$$296$$ 0.476886 0.0277184
$$297$$ 3.88296i 0.225312i
$$298$$ 16.8401i 0.975519i
$$299$$ 45.0881 2.60751
$$300$$ −5.23844 + 12.7755i −0.302442 + 0.737594i
$$301$$ −5.22782 −0.301326
$$302$$ 16.9817i 0.977186i
$$303$$ 45.3328i 2.60430i
$$304$$ −1.00000 −0.0573539
$$305$$ 23.8357 + 4.69701i 1.36483 + 0.268950i
$$306$$ −16.7755 −0.958992
$$307$$ 16.5414i 0.944070i 0.881580 + 0.472035i $$0.156480\pi$$
−0.881580 + 0.472035i $$0.843520\pi$$
$$308$$ 0.658473i 0.0375200i
$$309$$ 26.6218 1.51446
$$310$$ 3.50916 17.8078i 0.199307 1.01141i
$$311$$ −21.4725 −1.21759 −0.608797 0.793326i $$-0.708348\pi$$
−0.608797 + 0.793326i $$0.708348\pi$$
$$312$$ 15.5371i 0.879613i
$$313$$ 1.12141i 0.0633856i 0.999498 + 0.0316928i $$0.0100898\pi$$
−0.999498 + 0.0316928i $$0.989910\pi$$
$$314$$ −14.8401 −0.837473
$$315$$ 1.52311 7.72928i 0.0858178 0.435496i
$$316$$ −12.5693 −0.707081
$$317$$ 29.8882i 1.67869i −0.543601 0.839344i $$-0.682940\pi$$
0.543601 0.839344i $$-0.317060\pi$$
$$318$$ 6.55539i 0.367608i
$$319$$ −6.35985 −0.356083
$$320$$ 2.19388 + 0.432320i 0.122641 + 0.0241674i
$$321$$ 11.8324 0.660418
$$322$$ 6.10308i 0.340112i
$$323$$ 3.62620i 0.201767i
$$324$$ 1.47689 0.0820492
$$325$$ 10.6724 26.0279i 0.592000 1.44377i
$$326$$ 13.3694 0.740464
$$327$$ 37.0602i 2.04943i
$$328$$ 2.65847i 0.146790i
$$329$$ 0.953771 0.0525831
$$330$$ 5.23844 + 1.03228i 0.288367 + 0.0568249i
$$331$$ 32.3126 1.77606 0.888030 0.459786i $$-0.152074\pi$$
0.888030 + 0.459786i $$0.152074\pi$$
$$332$$ 0.270718i 0.0148576i
$$333$$ 2.20617i 0.120897i
$$334$$ −9.84632 −0.538767
$$335$$ 0.446274 2.26469i 0.0243825 0.123733i
$$336$$ −2.10308 −0.114733
$$337$$ 26.3511i 1.43544i 0.696334 + 0.717718i $$0.254813\pi$$
−0.696334 + 0.717718i $$0.745187\pi$$
$$338$$ 18.6541i 1.01465i
$$339$$ 28.5081 1.54835
$$340$$ 1.56768 7.95543i 0.0850194 0.431444i
$$341$$ −7.01832 −0.380063
$$342$$ 4.62620i 0.250156i
$$343$$ 10.2201i 0.551835i
$$344$$ −6.86464 −0.370117
$$345$$ −48.5527 9.56768i −2.61399 0.515107i
$$346$$ 2.98168 0.160296
$$347$$ 2.77551i 0.148997i −0.997221 0.0744986i $$-0.976264\pi$$
0.997221 0.0744986i $$-0.0237356\pi$$
$$348$$ 20.3126i 1.08887i
$$349$$ −11.5510 −0.618312 −0.309156 0.951011i $$-0.600047\pi$$
−0.309156 + 0.951011i $$0.600047\pi$$
$$350$$ 3.52311 + 1.44461i 0.188318 + 0.0772177i
$$351$$ 25.2663 1.34862
$$352$$ 0.864641i 0.0460855i
$$353$$ 8.40171i 0.447178i 0.974684 + 0.223589i $$0.0717773\pi$$
−0.974684 + 0.223589i $$0.928223\pi$$
$$354$$ −12.4017 −0.659143
$$355$$ 22.3372 + 4.40171i 1.18553 + 0.233618i
$$356$$ 0.387755 0.0205510
$$357$$ 7.62620i 0.403621i
$$358$$ 11.7938i 0.623323i
$$359$$ −22.7895 −1.20278 −0.601391 0.798955i $$-0.705387\pi$$
−0.601391 + 0.798955i $$0.705387\pi$$
$$360$$ 2.00000 10.1493i 0.105409 0.534916i
$$361$$ 1.00000 0.0526316
$$362$$ 14.5693i 0.765748i
$$363$$ 28.3126i 1.48602i
$$364$$ 4.28467 0.224578
$$365$$ −7.09079 + 35.9833i −0.371149 + 1.88345i
$$366$$ −30.0033 −1.56830
$$367$$ 4.06455i 0.212168i 0.994357 + 0.106084i $$0.0338312\pi$$
−0.994357 + 0.106084i $$0.966169\pi$$
$$368$$ 8.01395i 0.417756i
$$369$$ 12.2986 0.640241
$$370$$ 1.04623 + 0.206167i 0.0543908 + 0.0107181i
$$371$$ −1.80779 −0.0938556
$$372$$ 22.4157i 1.16220i
$$373$$ 18.4017i 0.952804i 0.879227 + 0.476402i $$0.158059\pi$$
−0.879227 + 0.476402i $$0.841941\pi$$
$$374$$ −3.13536 −0.162126
$$375$$ −17.0156 + 25.7632i −0.878683 + 1.33041i
$$376$$ 1.25240 0.0645874
$$377$$ 41.3834i 2.13135i
$$378$$ 3.42003i 0.175907i
$$379$$ −1.23844 −0.0636145 −0.0318073 0.999494i $$-0.510126\pi$$
−0.0318073 + 0.999494i $$0.510126\pi$$
$$380$$ −2.19388 0.432320i −0.112544 0.0221776i
$$381$$ 46.8959 2.40255
$$382$$ 13.2384i 0.677338i
$$383$$ 16.8646i 0.861743i −0.902413 0.430871i $$-0.858206\pi$$
0.902413 0.430871i $$-0.141794\pi$$
$$384$$ −2.76156 −0.140925
$$385$$ 0.284672 1.44461i 0.0145082 0.0736242i
$$386$$ 2.54144 0.129356
$$387$$ 31.7572i 1.61431i
$$388$$ 8.50479i 0.431765i
$$389$$ −8.59392 −0.435729 −0.217865 0.975979i $$-0.569909\pi$$
−0.217865 + 0.975979i $$0.569909\pi$$
$$390$$ −6.71699 + 34.0864i −0.340128 + 1.72603i
$$391$$ 29.0602 1.46964
$$392$$ 6.42003i 0.324261i
$$393$$ 1.49521i 0.0754233i
$$394$$ 19.9109 1.00310
$$395$$ −27.5756 5.43398i −1.38748 0.273413i
$$396$$ −4.00000 −0.201008
$$397$$ 16.0558i 0.805818i 0.915240 + 0.402909i $$0.132001\pi$$
−0.915240 + 0.402909i $$0.867999\pi$$
$$398$$ 20.3126i 1.01818i
$$399$$ 2.10308 0.105286
$$400$$ 4.62620 + 1.89692i 0.231310 + 0.0948458i
$$401$$ −14.8925 −0.743698 −0.371849 0.928293i $$-0.621276\pi$$
−0.371849 + 0.928293i $$0.621276\pi$$
$$402$$ 2.85069i 0.142179i
$$403$$ 45.6681i 2.27489i
$$404$$ −16.4157 −0.816710
$$405$$ 3.24011 + 0.638488i 0.161002 + 0.0317267i
$$406$$ 5.60162 0.278004
$$407$$ 0.412335i 0.0204387i
$$408$$ 10.0140i 0.495765i
$$409$$ 18.3511 0.907404 0.453702 0.891153i $$-0.350103\pi$$
0.453702 + 0.891153i $$0.350103\pi$$
$$410$$ −1.14931 + 5.83237i −0.0567605 + 0.288040i
$$411$$ 7.94940 0.392115
$$412$$ 9.64015i 0.474936i
$$413$$ 3.42003i 0.168289i
$$414$$ 37.0741 1.82209
$$415$$ 0.117037 0.593923i 0.00574512 0.0291545i
$$416$$ 5.62620 0.275847
$$417$$ 9.90754i 0.485174i
$$418$$ 0.864641i 0.0422910i
$$419$$ −34.7509 −1.69769 −0.848847 0.528639i $$-0.822703\pi$$
−0.848847 + 0.528639i $$0.822703\pi$$
$$420$$ −4.61391 0.909206i −0.225136 0.0443647i
$$421$$ −40.1589 −1.95722 −0.978612 0.205713i $$-0.934049\pi$$
−0.978612 + 0.205713i $$0.934049\pi$$
$$422$$ 18.0419i 0.878264i
$$423$$ 5.79383i 0.281706i
$$424$$ −2.37380 −0.115282
$$425$$ 6.87859 16.7755i 0.333661 0.813732i
$$426$$ −28.1170 −1.36227
$$427$$ 8.27405i 0.400409i
$$428$$ 4.28467i 0.207107i
$$429$$ 13.4340 0.648599
$$430$$ −15.0602 2.96772i −0.726266 0.143116i
$$431$$ 34.9571 1.68382 0.841912 0.539615i $$-0.181430\pi$$
0.841912 + 0.539615i $$0.181430\pi$$
$$432$$ 4.49084i 0.216066i
$$433$$ 1.13536i 0.0545619i −0.999628 0.0272809i $$-0.991315\pi$$
0.999628 0.0272809i $$-0.00868487\pi$$
$$434$$ 6.18159 0.296726
$$435$$ −8.78154 + 44.5633i −0.421043 + 2.13665i
$$436$$ −13.4200 −0.642703
$$437$$ 8.01395i 0.383359i
$$438$$ 45.2943i 2.16424i
$$439$$ 6.80009 0.324551 0.162275 0.986746i $$-0.448117\pi$$
0.162275 + 0.986746i $$0.448117\pi$$
$$440$$ 0.373802 1.89692i 0.0178203 0.0904319i
$$441$$ −29.7003 −1.41430
$$442$$ 20.4017i 0.970410i
$$443$$ 38.0679i 1.80866i −0.426835 0.904330i $$-0.640371\pi$$
0.426835 0.904330i $$-0.359629\pi$$
$$444$$ −1.31695 −0.0624995
$$445$$ 0.850688 + 0.167635i 0.0403265 + 0.00794664i
$$446$$ −13.5231 −0.640338
$$447$$ 46.5048i 2.19960i
$$448$$ 0.761557i 0.0359802i
$$449$$ 18.5414 0.875024 0.437512 0.899212i $$-0.355860\pi$$
0.437512 + 0.899212i $$0.355860\pi$$
$$450$$ 8.77551 21.4017i 0.413682 1.00889i
$$451$$ 2.29862 0.108238
$$452$$ 10.3232i 0.485563i
$$453$$ 46.8959i 2.20336i
$$454$$ −13.6016 −0.638356
$$455$$ 9.40005 + 1.85235i 0.440681 + 0.0868396i
$$456$$ 2.76156 0.129322
$$457$$ 16.3738i 0.765934i 0.923762 + 0.382967i $$0.125098\pi$$
−0.923762 + 0.382967i $$0.874902\pi$$
$$458$$ 13.5877i 0.634910i
$$459$$ 16.2847 0.760103
$$460$$ −3.46460 + 17.5816i −0.161538 + 0.819748i
$$461$$ 1.70470 0.0793959 0.0396979 0.999212i $$-0.487360\pi$$
0.0396979 + 0.999212i $$0.487360\pi$$
$$462$$ 1.81841i 0.0846002i
$$463$$ 10.0279i 0.466036i 0.972472 + 0.233018i $$0.0748602\pi$$
−0.972472 + 0.233018i $$0.925140\pi$$
$$464$$ 7.35548 0.341470
$$465$$ −9.69075 + 49.1772i −0.449398 + 2.28054i
$$466$$ 25.5510 1.18363
$$467$$ 32.7509i 1.51553i 0.652526 + 0.757766i $$0.273709\pi$$
−0.652526 + 0.757766i $$0.726291\pi$$
$$468$$ 26.0279i 1.20314i
$$469$$ 0.786137 0.0363004
$$470$$ 2.74760 + 0.541436i 0.126738 + 0.0249746i
$$471$$ 40.9817 1.88834
$$472$$ 4.49084i 0.206708i
$$473$$ 5.93545i 0.272912i
$$474$$ 34.7110 1.59433
$$475$$ −4.62620 1.89692i −0.212265 0.0870365i
$$476$$ 2.76156 0.126576
$$477$$ 10.9817i 0.502816i
$$478$$ 11.3309i 0.518263i
$$479$$ −27.2803 −1.24647 −0.623234 0.782035i $$-0.714182\pi$$
−0.623234 + 0.782035i $$0.714182\pi$$
$$480$$ −6.05852 1.19388i −0.276532 0.0544928i
$$481$$ 2.68305 0.122337
$$482$$ 1.25240i 0.0570451i
$$483$$ 16.8540i 0.766884i
$$484$$ 10.2524 0.466018
$$485$$ −3.67680 + 18.6585i −0.166955 + 0.847238i
$$486$$ −17.5510 −0.796130
$$487$$ 11.0741i 0.501817i −0.968011 0.250908i $$-0.919271\pi$$
0.968011 0.250908i $$-0.0807293\pi$$
$$488$$ 10.8646i 0.491819i
$$489$$ −36.9205 −1.66960
$$490$$ 2.77551 14.0848i 0.125385 0.636285i
$$491$$ 8.11704 0.366317 0.183158 0.983083i $$-0.441368\pi$$
0.183158 + 0.983083i $$0.441368\pi$$
$$492$$ 7.34153i 0.330982i
$$493$$ 26.6724i 1.20127i
$$494$$ −5.62620 −0.253135
$$495$$ −8.77551 1.72928i −0.394430 0.0777254i
$$496$$ 8.11704 0.364466
$$497$$ 7.75386i 0.347808i
$$498$$ 0.747604i 0.0335009i
$$499$$ −0.295298 −0.0132193 −0.00660967 0.999978i $$-0.502104\pi$$
−0.00660967 + 0.999978i $$0.502104\pi$$
$$500$$ 9.32924 + 6.16160i 0.417216 + 0.275555i
$$501$$ 27.1912 1.21481
$$502$$ 10.5939i 0.472830i
$$503$$ 19.6016i 0.873993i −0.899463 0.436996i $$-0.856042\pi$$
0.899463 0.436996i $$-0.143958\pi$$
$$504$$ 3.52311 0.156932
$$505$$ −36.0140 7.09683i −1.60260 0.315805i
$$506$$ 6.92919 0.308040
$$507$$ 51.5144i 2.28783i
$$508$$ 16.9817i 0.753440i
$$509$$ 1.79383 0.0795102 0.0397551 0.999209i $$-0.487342\pi$$
0.0397551 + 0.999209i $$0.487342\pi$$
$$510$$ −4.32924 + 21.9694i −0.191702 + 0.972821i
$$511$$ −12.4908 −0.552562
$$512$$ 1.00000i 0.0441942i
$$513$$ 4.49084i 0.198275i
$$514$$ 0.153681 0.00677859
$$515$$ 4.16763 21.1493i 0.183648 0.931950i
$$516$$ 18.9571 0.834540
$$517$$ 1.08287i 0.0476247i
$$518$$ 0.363176i 0.0159570i
$$519$$ −8.23407 −0.361436
$$520$$ 12.3432 + 2.43232i 0.541285 + 0.106664i
$$521$$ −2.61850 −0.114719 −0.0573593 0.998354i $$-0.518268\pi$$
−0.0573593 + 0.998354i $$0.518268\pi$$
$$522$$ 34.0279i 1.48936i
$$523$$ 14.9956i 0.655713i −0.944728 0.327857i $$-0.893674\pi$$
0.944728 0.327857i $$-0.106326\pi$$
$$524$$ −0.541436 −0.0236528
$$525$$ −9.72928 3.98937i −0.424621 0.174111i
$$526$$ 0.504792 0.0220100
$$527$$ 29.4340i 1.28216i
$$528$$ 2.38776i 0.103914i
$$529$$ −41.2234 −1.79232
$$530$$ −5.20783 1.02624i −0.226214 0.0445772i
$$531$$ 20.7755 0.901580
$$532$$ 0.761557i 0.0330177i
$$533$$ 14.9571i 0.647864i
$$534$$ −1.07081 −0.0463384
$$535$$ 1.85235 9.40005i 0.0800841 0.406399i
$$536$$ 1.03228 0.0445875
$$537$$ 32.5693i 1.40547i
$$538$$ 3.49521i 0.150689i
$$539$$ −5.55102 −0.239099
$$540$$ −1.94148 + 9.85235i −0.0835481 + 0.423978i
$$541$$ 3.40608 0.146439 0.0732194 0.997316i $$-0.476673\pi$$
0.0732194 + 0.997316i $$0.476673\pi$$
$$542$$ 5.47252i 0.235065i
$$543$$ 40.2341i 1.72661i
$$544$$ 3.62620 0.155472
$$545$$ −29.4419 5.80175i −1.26115 0.248520i
$$546$$ −11.8324 −0.506378
$$547$$ 4.74760i 0.202993i 0.994836 + 0.101496i $$0.0323630\pi$$
−0.994836 + 0.101496i $$0.967637\pi$$
$$548$$ 2.87859i 0.122967i
$$549$$ 50.2620 2.14513
$$550$$ 1.64015 4.00000i 0.0699363 0.170561i
$$551$$ −7.35548 −0.313354
$$552$$ 22.1310i 0.941958i
$$553$$ 9.57227i 0.407054i
$$554$$ −12.9538 −0.550353
$$555$$ −2.88922 0.569343i −0.122641 0.0241673i
$$556$$ 3.58767 0.152151
$$557$$ 43.0462i 1.82393i 0.410271 + 0.911964i $$0.365434\pi$$
−0.410271 + 0.911964i $$0.634566\pi$$
$$558$$ 37.5510i 1.58966i
$$559$$ −38.6218 −1.63353
$$560$$ −0.329237 + 1.67076i −0.0139128 + 0.0706026i
$$561$$ 8.65847 0.365561
$$562$$ 0.153681i 0.00648265i
$$563$$ 17.0096i 0.716869i −0.933555 0.358434i $$-0.883311\pi$$
0.933555 0.358434i $$-0.116689\pi$$
$$564$$ −3.45856 −0.145632
$$565$$ 4.46293 22.6478i 0.187757 0.952802i
$$566$$ −18.2341 −0.766435
$$567$$ 1.12473i 0.0472343i
$$568$$ 10.1816i 0.427210i
$$569$$ 19.7572 0.828264 0.414132 0.910217i $$-0.364085\pi$$
0.414132 + 0.910217i $$0.364085\pi$$
$$570$$ 6.05852 + 1.19388i 0.253763 + 0.0500060i
$$571$$ −11.3973 −0.476964 −0.238482 0.971147i $$-0.576650\pi$$
−0.238482 + 0.971147i $$0.576650\pi$$
$$572$$ 4.86464i 0.203401i
$$573$$ 36.5587i 1.52726i
$$574$$ −2.02458 −0.0845043
$$575$$ −15.2018 + 37.0741i −0.633959 + 1.54610i
$$576$$ 4.62620 0.192758
$$577$$ 18.3372i 0.763386i −0.924289 0.381693i $$-0.875341\pi$$
0.924289 0.381693i $$-0.124659\pi$$
$$578$$ 3.85069i 0.160167i
$$579$$ −7.01832 −0.291672
$$580$$ 16.1370 + 3.17992i 0.670053 + 0.132039i
$$581$$ 0.206167 0.00855327
$$582$$ 23.4865i 0.973546i
$$583$$ 2.05249i 0.0850053i
$$584$$ −16.4017 −0.678708
$$585$$ 11.2524 57.1020i 0.465229 2.36088i
$$586$$ 2.03853 0.0842110
$$587$$ 11.9475i 0.493127i −0.969127 0.246563i $$-0.920699\pi$$
0.969127 0.246563i $$-0.0793013\pi$$
$$588$$ 17.7293i 0.731143i
$$589$$ −8.11704 −0.334457
$$590$$ −1.94148 + 9.85235i −0.0799295 + 0.405615i
$$591$$ −54.9850 −2.26178
$$592$$ 0.476886i 0.0195999i
$$593$$ 24.3911i 1.00162i 0.865557 + 0.500811i $$0.166965\pi$$
−0.865557 + 0.500811i $$0.833035\pi$$
$$594$$ 3.88296 0.159320
$$595$$ 6.05852 + 1.19388i 0.248375 + 0.0489442i
$$596$$ −16.8401 −0.689796
$$597$$ 56.0943i 2.29579i
$$598$$ 45.0881i 1.84379i
$$599$$ 21.0708 0.860930 0.430465 0.902607i $$-0.358350\pi$$
0.430465 + 0.902607i $$0.358350\pi$$
$$600$$ −12.7755 5.23844i −0.521558 0.213859i
$$601$$ 32.3878 1.32112 0.660562 0.750771i $$-0.270318\pi$$
0.660562 + 0.750771i $$0.270318\pi$$
$$602$$ 5.22782i 0.213070i
$$603$$ 4.77551i 0.194474i
$$604$$ 16.9817 0.690975
$$605$$ 22.4925 + 4.43232i 0.914450 + 0.180199i
$$606$$ 45.3328 1.84152
$$607$$ 19.0183i 0.771930i 0.922513 + 0.385965i $$0.126131\pi$$
−0.922513 + 0.385965i $$0.873869\pi$$
$$608$$ 1.00000i 0.0405554i
$$609$$ −15.4692 −0.626843
$$610$$ −4.69701 + 23.8357i −0.190176 + 0.965079i
$$611$$ 7.04623 0.285060
$$612$$ 16.7755i 0.678110i
$$613$$ 23.5756i 0.952210i 0.879389 + 0.476105i $$0.157952\pi$$
−0.879389 + 0.476105i $$0.842048\pi$$
$$614$$ −16.5414 −0.667558
$$615$$ 3.17389 16.1064i 0.127984 0.649473i
$$616$$ 0.658473 0.0265307
$$617$$ 26.2707i 1.05762i −0.848740 0.528810i $$-0.822639\pi$$
0.848740 0.528810i $$-0.177361\pi$$
$$618$$ 26.6218i 1.07089i
$$619$$ −11.4985 −0.462165 −0.231083 0.972934i $$-0.574227\pi$$
−0.231083 + 0.972934i $$0.574227\pi$$
$$620$$ 17.8078 + 3.50916i 0.715178 + 0.140931i
$$621$$ −35.9894 −1.44420
$$622$$ 21.4725i 0.860969i
$$623$$ 0.295298i 0.0118309i
$$624$$ −15.5371 −0.621980
$$625$$ 17.8034 + 17.5510i 0.712137 + 0.702041i
$$626$$ −1.12141 −0.0448204
$$627$$ 2.38776i 0.0953578i
$$628$$ 14.8401i 0.592183i
$$629$$ 1.72928 0.0689510
$$630$$ 7.72928 + 1.52311i 0.307942 + 0.0606823i
$$631$$ −45.8130 −1.82379 −0.911893 0.410427i $$-0.865380\pi$$
−0.911893 + 0.410427i $$0.865380\pi$$
$$632$$ 12.5693i 0.499982i
$$633$$ 49.8236i 1.98031i
$$634$$ 29.8882 1.18701
$$635$$ 7.34153 37.2557i 0.291340 1.47845i
$$636$$ 6.55539 0.259938
$$637$$ 36.1204i 1.43114i
$$638$$ 6.35985i 0.251789i
$$639$$ 47.1020 1.86333
$$640$$ −0.432320 + 2.19388i −0.0170890 + 0.0867206i
$$641$$ 1.36943 0.0540894 0.0270447 0.999634i $$-0.491390\pi$$
0.0270447 + 0.999634i $$0.491390\pi$$
$$642$$ 11.8324i 0.466986i
$$643$$ 24.7389i 0.975606i 0.872954 + 0.487803i $$0.162201\pi$$
−0.872954 + 0.487803i $$0.837799\pi$$
$$644$$ −6.10308 −0.240495
$$645$$ 41.5896 + 8.19554i 1.63759 + 0.322699i
$$646$$ −3.62620 −0.142671
$$647$$ 6.82611i 0.268362i −0.990957 0.134181i $$-0.957160\pi$$
0.990957 0.134181i $$-0.0428404\pi$$
$$648$$ 1.47689i 0.0580175i
$$649$$ 3.88296 0.152420
$$650$$ 26.0279 + 10.6724i 1.02090 + 0.418607i
$$651$$ −17.0708 −0.669058
$$652$$ 13.3694i 0.523587i
$$653$$ 6.91713i 0.270688i −0.990799 0.135344i $$-0.956786\pi$$
0.990799 0.135344i $$-0.0432140\pi$$
$$654$$ 37.0602 1.44917
$$655$$ −1.18785 0.234074i −0.0464130 0.00914603i
$$656$$ −2.65847 −0.103796
$$657$$ 75.8776i 2.96027i
$$658$$ 0.953771i 0.0371819i
$$659$$ −9.44461 −0.367910 −0.183955 0.982935i $$-0.558890\pi$$
−0.183955 + 0.982935i $$0.558890\pi$$
$$660$$ −1.03228 + 5.23844i −0.0401813 + 0.203906i
$$661$$ −22.1955 −0.863306 −0.431653 0.902040i $$-0.642070\pi$$
−0.431653 + 0.902040i $$0.642070\pi$$
$$662$$ 32.3126i 1.25586i
$$663$$ 56.3405i 2.18808i
$$664$$ 0.270718 0.0105059
$$665$$ 0.329237 1.67076i 0.0127673 0.0647894i
$$666$$ 2.20617 0.0854873
$$667$$ 58.9465i 2.28242i
$$668$$ 9.84632i 0.380966i
$$669$$ 37.3449 1.44384
$$670$$ 2.26469 + 0.446274i 0.0874925 + 0.0172411i
$$671$$ 9.39401 0.362652
$$672$$ 2.10308i 0.0811282i
$$673$$ 12.2986i 0.474077i −0.971500 0.237039i $$-0.923823\pi$$
0.971500 0.237039i $$-0.0761768\pi$$
$$674$$ −26.3511 −1.01501
$$675$$ −8.51875 + 20.7755i −0.327887 + 0.799650i
$$676$$ 18.6541 0.717466
$$677$$ 35.9527i 1.38178i −0.722962 0.690888i $$-0.757220\pi$$
0.722962 0.690888i $$-0.242780\pi$$
$$678$$ 28.5081i 1.09485i
$$679$$ −6.47689 −0.248560
$$680$$ 7.95543 + 1.56768i 0.305077 + 0.0601178i
$$681$$ 37.5616 1.43937
$$682$$ 7.01832i 0.268745i
$$683$$ 9.00958i 0.344742i 0.985032 + 0.172371i $$0.0551428\pi$$
−0.985032 + 0.172371i $$0.944857\pi$$
$$684$$ −4.62620 −0.176887
$$685$$ 1.24448 6.31528i 0.0475490 0.241295i
$$686$$ 10.2201 0.390206
$$687$$ 37.5231i 1.43160i
$$688$$ 6.86464i 0.261712i
$$689$$ −13.3555 −0.508803
$$690$$ 9.56768 48.5527i 0.364235 1.84837i
$$691$$ −9.11078 −0.346590 −0.173295 0.984870i $$-0.555441\pi$$
−0.173295 + 0.984870i $$0.555441\pi$$
$$692$$ 2.98168i 0.113346i
$$693$$ 3.04623i 0.115717i
$$694$$ 2.77551 0.105357
$$695$$ 7.87090 + 1.55102i 0.298560 + 0.0588336i
$$696$$ −20.3126 −0.769946
$$697$$ 9.64015i 0.365147i
$$698$$ 11.5510i 0.437213i
$$699$$ −70.5606 −2.66885
$$700$$ −1.44461 + 3.52311i −0.0546011 + 0.133161i
$$701$$ −14.7476 −0.557009 −0.278505 0.960435i $$-0.589839\pi$$
−0.278505 + 0.960435i $$0.589839\pi$$
$$702$$ 25.2663i 0.953617i
$$703$$ 0.476886i 0.0179861i
$$704$$ 0.864641 0.0325874
$$705$$ −7.58767 1.49521i −0.285768 0.0563128i
$$706$$ −8.40171 −0.316202
$$707$$ 12.5015i 0.470166i
$$708$$ 12.4017i 0.466085i
$$709$$ 8.63389 0.324253 0.162126 0.986770i $$-0.448165\pi$$
0.162126 + 0.986770i $$0.448165\pi$$
$$710$$ −4.40171 + 22.3372i −0.165193 + 0.838299i
$$711$$ −58.1483 −2.18073
$$712$$ 0.387755i 0.0145317i
$$713$$ 65.0496i 2.43613i
$$714$$ −7.62620 −0.285403
$$715$$ 2.10308 10.6724i 0.0786509 0.399126i
$$716$$ 11.7938 0.440756
$$717$$ 31.2909i 1.16858i
$$718$$ 22.7895i 0.850495i
$$719$$ 38.2759 1.42745 0.713726 0.700425i $$-0.247006\pi$$
0.713726 + 0.700425i $$0.247006\pi$$
$$720$$ 10.1493 + 2.00000i 0.378243 + 0.0745356i
$$721$$ 7.34153 0.273413
$$722$$ 1.00000i 0.0372161i
$$723$$ 3.45856i 0.128625i
$$724$$ −14.5693 −0.541465
$$725$$ 34.0279 + 13.9527i 1.26376 + 0.518191i
$$726$$ −28.3126 −1.05078
$$727$$ 31.1893i 1.15675i −0.815772 0.578373i $$-0.803688\pi$$
0.815772 0.578373i $$-0.196312\pi$$
$$728$$ 4.28467i 0.158800i
$$729$$ 44.0375 1.63102
$$730$$ −35.9833 7.09079i −1.33180 0.262442i
$$731$$ −24.8925 −0.920684
$$732$$ 30.0033i 1.10895i
$$733$$ 13.9634i 0.515748i 0.966179 + 0.257874i $$0.0830220\pi$$
−0.966179 + 0.257874i $$0.916978\pi$$
$$734$$ −4.06455 −0.150025
$$735$$ −7.66473 + 38.8959i −0.282718 + 1.43470i
$$736$$ −8.01395 −0.295398
$$737$$ 0.892548i 0.0328774i
$$738$$ 12.2986i 0.452719i
$$739$$ −9.02165 −0.331867 −0.165933 0.986137i $$-0.553064\pi$$
−0.165933 + 0.986137i $$0.553064\pi$$
$$740$$ −0.206167 + 1.04623i −0.00757886 + 0.0384601i
$$741$$ 15.5371 0.570768
$$742$$ 1.80779i 0.0663659i
$$743$$ 15.0342i 0.551550i 0.961222 + 0.275775i $$0.0889345\pi$$
−0.961222 + 0.275775i $$0.911066\pi$$
$$744$$ −22.4157 −0.821798
$$745$$ −36.9450 7.28030i −1.35356 0.266730i
$$746$$ −18.4017 −0.673734
$$747$$ 1.25240i 0.0458228i
$$748$$ 3.13536i 0.114640i
$$749$$ 3.26302 0.119228
$$750$$ −25.7632 17.0156i −0.940740 0.621322i
$$751$$ 29.6681 1.08260 0.541301 0.840829i $$-0.317932\pi$$
0.541301 + 0.840829i $$0.317932\pi$$
$$752$$ 1.25240i 0.0456702i
$$753$$ 29.2557i 1.06614i
$$754$$ 41.3834 1.50709
$$755$$ 37.2557 + 7.34153i 1.35587 + 0.267186i
$$756$$ −3.42003 −0.124385
$$757$$ 10.5819i 0.384604i 0.981336 + 0.192302i $$0.0615953\pi$$
−0.981336 + 0.192302i $$0.938405\pi$$
$$758$$ 1.23844i 0.0449823i
$$759$$ −19.1354 −0.694570
$$760$$ 0.432320 2.19388i 0.0156819 0.0795803i
$$761$$ −0.979789 −0.0355173 −0.0177587 0.999842i $$-0.505653\pi$$
−0.0177587 + 0.999842i $$0.505653\pi$$
$$762$$ 46.8959i 1.69886i
$$763$$ 10.2201i 0.369993i
$$764$$ −13.2384 −0.478950
$$765$$ 7.25240 36.8034i 0.262211 1.33063i
$$766$$ 16.8646 0.609344
$$767$$ 25.2663i 0.912315i
$$768$$ 2.76156i 0.0996491i
$$769$$ −43.1772 −1.55701 −0.778505 0.627638i $$-0.784022\pi$$
−0.778505 + 0.627638i $$0.784022\pi$$
$$770$$ 1.44461 + 0.284672i 0.0520601 + 0.0102589i
$$771$$ −0.424399 −0.0152844
$$772$$ 2.54144i 0.0914683i
$$773$$ 37.5250i 1.34968i −0.737964 0.674840i $$-0.764213\pi$$
0.737964 0.674840i $$-0.235787\pi$$
$$774$$ −31.7572 −1.14149
$$775$$ 37.5510 + 15.3973i 1.34887 + 0.553089i
$$776$$ −8.50479 −0.305304
$$777$$ 1.00293i 0.0359799i
$$778$$ 8.59392i 0.308107i
$$779$$ 2.65847 0.0952497
$$780$$ −34.0864 6.71699i −1.22049 0.240507i
$$781$$ 8.80342 0.315011
$$782$$ 29.0602i 1.03919i
$$783$$ 33.0323i 1.18048i
$$784$$ 6.42003 0.229287
$$785$$ 6.41566 32.5573i 0.228985 1.16202i
$$786$$ 1.49521 0.0533323
$$787$$ 22.5833i 0.805008i 0.915418 + 0.402504i $$0.131860\pi$$
−0.915418 + 0.402504i $$0.868140\pi$$
$$788$$ 19.9109i