# Properties

 Label 3150.2.m.g.1457.1 Level 3150 Weight 2 Character 3150.1457 Analytic conductor 25.153 Analytic rank 0 Dimension 8 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.m (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.1528766367$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{24})$$ Coefficient ring: $$\Z[a_1, \ldots, a_{17}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 1457.1 Root $$-0.258819 - 0.965926i$$ Character $$\chi$$ = 3150.1457 Dual form 3150.2.m.g.2843.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$$ $$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.41421i q^{11} +(-2.02494 + 2.02494i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(4.37101 - 4.37101i) q^{17} -4.87832i q^{19} +(-2.41421 - 2.41421i) q^{22} +(3.74238 + 3.74238i) q^{23} -2.86370i q^{26} +(0.707107 - 0.707107i) q^{28} +5.21682 q^{29} -4.93942 q^{31} +(0.707107 - 0.707107i) q^{32} +6.18154i q^{34} +(6.87832 + 6.87832i) q^{37} +(3.44949 + 3.44949i) q^{38} -8.77729i q^{41} +(0.174857 - 0.174857i) q^{43} +3.41421 q^{44} -5.29253 q^{46} +(-3.42883 + 3.42883i) q^{47} +1.00000i q^{49} +(2.02494 + 2.02494i) q^{52} +(6.43916 + 6.43916i) q^{53} +1.00000i q^{56} +(-3.68885 + 3.68885i) q^{58} +2.22803 q^{59} -15.2526 q^{61} +(3.49269 - 3.49269i) q^{62} +1.00000i q^{64} +(-3.81382 - 3.81382i) q^{67} +(-4.37101 - 4.37101i) q^{68} +10.9282i q^{71} +(2.51059 - 2.51059i) q^{73} -9.72741 q^{74} -4.87832 q^{76} +(-2.41421 + 2.41421i) q^{77} -9.98414i q^{79} +(6.20648 + 6.20648i) q^{82} +(2.35640 + 2.35640i) q^{83} +0.247285i q^{86} +(-2.41421 + 2.41421i) q^{88} +4.07055 q^{89} -2.86370 q^{91} +(3.74238 - 3.74238i) q^{92} -4.84909i q^{94} +(5.64564 + 5.64564i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + O(q^{10})$$ $$8q - 8q^{13} - 8q^{14} - 8q^{16} - 8q^{22} + 16q^{23} + 16q^{37} + 8q^{38} + 8q^{43} + 16q^{44} + 8q^{46} - 8q^{47} + 8q^{52} + 32q^{53} + 8q^{58} - 8q^{59} - 32q^{61} + 32q^{62} - 16q^{67} - 16q^{74} - 8q^{77} + 8q^{82} - 8q^{83} - 8q^{88} + 16q^{89} + 8q^{91} + 16q^{92} - 16q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$2801$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 0.707107i −0.500000 + 0.500000i
$$3$$ 0 0
$$4$$ 1.00000i 0.500000i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0.707107 + 0.707107i 0.267261 + 0.267261i
$$8$$ 0.707107 + 0.707107i 0.250000 + 0.250000i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.41421i 1.02942i 0.857363 + 0.514712i $$0.172101\pi$$
−0.857363 + 0.514712i $$0.827899\pi$$
$$12$$ 0 0
$$13$$ −2.02494 + 2.02494i −0.561618 + 0.561618i −0.929767 0.368149i $$-0.879992\pi$$
0.368149 + 0.929767i $$0.379992\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 4.37101 4.37101i 1.06013 1.06013i 0.0620526 0.998073i $$-0.480235\pi$$
0.998073 0.0620526i $$-0.0197646\pi$$
$$18$$ 0 0
$$19$$ 4.87832i 1.11916i −0.828776 0.559581i $$-0.810962\pi$$
0.828776 0.559581i $$-0.189038\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −2.41421 2.41421i −0.514712 0.514712i
$$23$$ 3.74238 + 3.74238i 0.780341 + 0.780341i 0.979888 0.199547i $$-0.0639472\pi$$
−0.199547 + 0.979888i $$0.563947\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 2.86370i 0.561618i
$$27$$ 0 0
$$28$$ 0.707107 0.707107i 0.133631 0.133631i
$$29$$ 5.21682 0.968739 0.484369 0.874864i $$-0.339049\pi$$
0.484369 + 0.874864i $$0.339049\pi$$
$$30$$ 0 0
$$31$$ −4.93942 −0.887145 −0.443573 0.896238i $$-0.646289\pi$$
−0.443573 + 0.896238i $$0.646289\pi$$
$$32$$ 0.707107 0.707107i 0.125000 0.125000i
$$33$$ 0 0
$$34$$ 6.18154i 1.06013i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 6.87832 + 6.87832i 1.13079 + 1.13079i 0.990046 + 0.140742i $$0.0449487\pi$$
0.140742 + 0.990046i $$0.455051\pi$$
$$38$$ 3.44949 + 3.44949i 0.559581 + 0.559581i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 8.77729i 1.37078i −0.728175 0.685392i $$-0.759631\pi$$
0.728175 0.685392i $$-0.240369\pi$$
$$42$$ 0 0
$$43$$ 0.174857 0.174857i 0.0266654 0.0266654i −0.693648 0.720314i $$-0.743998\pi$$
0.720314 + 0.693648i $$0.243998\pi$$
$$44$$ 3.41421 0.514712
$$45$$ 0 0
$$46$$ −5.29253 −0.780341
$$47$$ −3.42883 + 3.42883i −0.500146 + 0.500146i −0.911483 0.411338i $$-0.865062\pi$$
0.411338 + 0.911483i $$0.365062\pi$$
$$48$$ 0 0
$$49$$ 1.00000i 0.142857i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 2.02494 + 2.02494i 0.280809 + 0.280809i
$$53$$ 6.43916 + 6.43916i 0.884486 + 0.884486i 0.993987 0.109500i $$-0.0349251\pi$$
−0.109500 + 0.993987i $$0.534925\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.00000i 0.133631i
$$57$$ 0 0
$$58$$ −3.68885 + 3.68885i −0.484369 + 0.484369i
$$59$$ 2.22803 0.290065 0.145032 0.989427i $$-0.453671\pi$$
0.145032 + 0.989427i $$0.453671\pi$$
$$60$$ 0 0
$$61$$ −15.2526 −1.95290 −0.976448 0.215752i $$-0.930780\pi$$
−0.976448 + 0.215752i $$0.930780\pi$$
$$62$$ 3.49269 3.49269i 0.443573 0.443573i
$$63$$ 0 0
$$64$$ 1.00000i 0.125000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −3.81382 3.81382i −0.465932 0.465932i 0.434662 0.900594i $$-0.356868\pi$$
−0.900594 + 0.434662i $$0.856868\pi$$
$$68$$ −4.37101 4.37101i −0.530063 0.530063i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 10.9282i 1.29694i 0.761241 + 0.648470i $$0.224591\pi$$
−0.761241 + 0.648470i $$0.775409\pi$$
$$72$$ 0 0
$$73$$ 2.51059 2.51059i 0.293842 0.293842i −0.544754 0.838596i $$-0.683377\pi$$
0.838596 + 0.544754i $$0.183377\pi$$
$$74$$ −9.72741 −1.13079
$$75$$ 0 0
$$76$$ −4.87832 −0.559581
$$77$$ −2.41421 + 2.41421i −0.275125 + 0.275125i
$$78$$ 0 0
$$79$$ 9.98414i 1.12330i −0.827374 0.561652i $$-0.810166\pi$$
0.827374 0.561652i $$-0.189834\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 6.20648 + 6.20648i 0.685392 + 0.685392i
$$83$$ 2.35640 + 2.35640i 0.258648 + 0.258648i 0.824504 0.565856i $$-0.191454\pi$$
−0.565856 + 0.824504i $$0.691454\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0.247285i 0.0266654i
$$87$$ 0 0
$$88$$ −2.41421 + 2.41421i −0.257356 + 0.257356i
$$89$$ 4.07055 0.431478 0.215739 0.976451i $$-0.430784\pi$$
0.215739 + 0.976451i $$0.430784\pi$$
$$90$$ 0 0
$$91$$ −2.86370 −0.300198
$$92$$ 3.74238 3.74238i 0.390170 0.390170i
$$93$$ 0 0
$$94$$ 4.84909i 0.500146i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 5.64564 + 5.64564i 0.573228 + 0.573228i 0.933029 0.359801i $$-0.117155\pi$$
−0.359801 + 0.933029i $$0.617155\pi$$
$$98$$ −0.707107 0.707107i −0.0714286 0.0714286i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 4.91484i 0.489044i 0.969644 + 0.244522i $$0.0786311\pi$$
−0.969644 + 0.244522i $$0.921369\pi$$
$$102$$ 0 0
$$103$$ −8.07019 + 8.07019i −0.795179 + 0.795179i −0.982331 0.187152i $$-0.940074\pi$$
0.187152 + 0.982331i $$0.440074\pi$$
$$104$$ −2.86370 −0.280809
$$105$$ 0 0
$$106$$ −9.10634 −0.884486
$$107$$ 5.77729 5.77729i 0.558512 0.558512i −0.370372 0.928884i $$-0.620770\pi$$
0.928884 + 0.370372i $$0.120770\pi$$
$$108$$ 0 0
$$109$$ 6.07712i 0.582083i 0.956710 + 0.291041i $$0.0940017\pi$$
−0.956710 + 0.291041i $$0.905998\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −0.707107 0.707107i −0.0668153 0.0668153i
$$113$$ 6.76733 + 6.76733i 0.636617 + 0.636617i 0.949719 0.313103i $$-0.101368\pi$$
−0.313103 + 0.949719i $$0.601368\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 5.21682i 0.484369i
$$117$$ 0 0
$$118$$ −1.57545 + 1.57545i −0.145032 + 0.145032i
$$119$$ 6.18154 0.566661
$$120$$ 0 0
$$121$$ −0.656854 −0.0597140
$$122$$ 10.7852 10.7852i 0.976448 0.976448i
$$123$$ 0 0
$$124$$ 4.93942i 0.443573i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 11.0345 + 11.0345i 0.979158 + 0.979158i 0.999787 0.0206295i $$-0.00656703\pi$$
−0.0206295 + 0.999787i $$0.506567\pi$$
$$128$$ −0.707107 0.707107i −0.0625000 0.0625000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2.41370i 0.210886i 0.994425 + 0.105443i $$0.0336260\pi$$
−0.994425 + 0.105443i $$0.966374\pi$$
$$132$$ 0 0
$$133$$ 3.44949 3.44949i 0.299109 0.299109i
$$134$$ 5.39355 0.465932
$$135$$ 0 0
$$136$$ 6.18154 0.530063
$$137$$ 9.39836 9.39836i 0.802956 0.802956i −0.180601 0.983557i $$-0.557804\pi$$
0.983557 + 0.180601i $$0.0578042\pi$$
$$138$$ 0 0
$$139$$ 11.2621i 0.955236i 0.878568 + 0.477618i $$0.158500\pi$$
−0.878568 + 0.477618i $$0.841500\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −7.72741 7.72741i −0.648470 0.648470i
$$143$$ −6.91359 6.91359i −0.578144 0.578144i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 3.55051i 0.293842i
$$147$$ 0 0
$$148$$ 6.87832 6.87832i 0.565394 0.565394i
$$149$$ 3.18759 0.261138 0.130569 0.991439i $$-0.458320\pi$$
0.130569 + 0.991439i $$0.458320\pi$$
$$150$$ 0 0
$$151$$ 1.80725 0.147072 0.0735359 0.997293i $$-0.476572\pi$$
0.0735359 + 0.997293i $$0.476572\pi$$
$$152$$ 3.44949 3.44949i 0.279791 0.279791i
$$153$$ 0 0
$$154$$ 3.41421i 0.275125i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 12.8577 + 12.8577i 1.02615 + 1.02615i 0.999649 + 0.0265035i $$0.00843732\pi$$
0.0265035 + 0.999649i $$0.491563\pi$$
$$158$$ 7.05986 + 7.05986i 0.561652 + 0.561652i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 5.29253i 0.417110i
$$162$$ 0 0
$$163$$ 10.0884 10.0884i 0.790188 0.790188i −0.191336 0.981525i $$-0.561282\pi$$
0.981525 + 0.191336i $$0.0612821\pi$$
$$164$$ −8.77729 −0.685392
$$165$$ 0 0
$$166$$ −3.33245 −0.258648
$$167$$ 3.31319 3.31319i 0.256383 0.256383i −0.567199 0.823581i $$-0.691973\pi$$
0.823581 + 0.567199i $$0.191973\pi$$
$$168$$ 0 0
$$169$$ 4.79920i 0.369169i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −0.174857 0.174857i −0.0133327 0.0133327i
$$173$$ 8.88437 + 8.88437i 0.675466 + 0.675466i 0.958971 0.283505i $$-0.0914972\pi$$
−0.283505 + 0.958971i $$0.591497\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 3.41421i 0.257356i
$$177$$ 0 0
$$178$$ −2.87832 + 2.87832i −0.215739 + 0.215739i
$$179$$ 24.6556 1.84285 0.921423 0.388560i $$-0.127027\pi$$
0.921423 + 0.388560i $$0.127027\pi$$
$$180$$ 0 0
$$181$$ −13.2432 −0.984356 −0.492178 0.870495i $$-0.663799\pi$$
−0.492178 + 0.870495i $$0.663799\pi$$
$$182$$ 2.02494 2.02494i 0.150099 0.150099i
$$183$$ 0 0
$$184$$ 5.29253i 0.390170i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 14.9236 + 14.9236i 1.09132 + 1.09132i
$$188$$ 3.42883 + 3.42883i 0.250073 + 0.250073i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 19.7228i 1.42709i 0.700610 + 0.713545i $$0.252911\pi$$
−0.700610 + 0.713545i $$0.747089\pi$$
$$192$$ 0 0
$$193$$ −7.01461 + 7.01461i −0.504923 + 0.504923i −0.912964 0.408041i $$-0.866212\pi$$
0.408041 + 0.912964i $$0.366212\pi$$
$$194$$ −7.98414 −0.573228
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −17.5394 + 17.5394i −1.24963 + 1.24963i −0.293752 + 0.955882i $$0.594904\pi$$
−0.955882 + 0.293752i $$0.905096\pi$$
$$198$$ 0 0
$$199$$ 15.9683i 1.13196i −0.824418 0.565981i $$-0.808498\pi$$
0.824418 0.565981i $$-0.191502\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −3.47531 3.47531i −0.244522 0.244522i
$$203$$ 3.68885 + 3.68885i 0.258906 + 0.258906i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 11.4130i 0.795179i
$$207$$ 0 0
$$208$$ 2.02494 2.02494i 0.140405 0.140405i
$$209$$ 16.6556 1.15209
$$210$$ 0 0
$$211$$ −26.2686 −1.80841 −0.904203 0.427102i $$-0.859535\pi$$
−0.904203 + 0.427102i $$0.859535\pi$$
$$212$$ 6.43916 6.43916i 0.442243 0.442243i
$$213$$ 0 0
$$214$$ 8.17033i 0.558512i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −3.49269 3.49269i −0.237100 0.237100i
$$218$$ −4.29717 4.29717i −0.291041 0.291041i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 17.7021i 1.19077i
$$222$$ 0 0
$$223$$ −12.6061 + 12.6061i −0.844166 + 0.844166i −0.989398 0.145232i $$-0.953607\pi$$
0.145232 + 0.989398i $$0.453607\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −9.57045 −0.636617
$$227$$ 3.02786 3.02786i 0.200966 0.200966i −0.599448 0.800414i $$-0.704613\pi$$
0.800414 + 0.599448i $$0.204613\pi$$
$$228$$ 0 0
$$229$$ 3.50543i 0.231645i −0.993270 0.115823i $$-0.963050\pi$$
0.993270 0.115823i $$-0.0369504\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 3.68885 + 3.68885i 0.242185 + 0.242185i
$$233$$ −8.98074 8.98074i −0.588348 0.588348i 0.348836 0.937184i $$-0.386577\pi$$
−0.937184 + 0.348836i $$0.886577\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 2.22803i 0.145032i
$$237$$ 0 0
$$238$$ −4.37101 + 4.37101i −0.283330 + 0.283330i
$$239$$ −16.4853 −1.06634 −0.533172 0.846007i $$-0.679000\pi$$
−0.533172 + 0.846007i $$0.679000\pi$$
$$240$$ 0 0
$$241$$ 27.8179 1.79191 0.895954 0.444147i $$-0.146493\pi$$
0.895954 + 0.444147i $$0.146493\pi$$
$$242$$ 0.464466 0.464466i 0.0298570 0.0298570i
$$243$$ 0 0
$$244$$ 15.2526i 0.976448i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 9.87832 + 9.87832i 0.628542 + 0.628542i
$$248$$ −3.49269 3.49269i −0.221786 0.221786i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 8.43969i 0.532708i 0.963875 + 0.266354i $$0.0858191\pi$$
−0.963875 + 0.266354i $$0.914181\pi$$
$$252$$ 0 0
$$253$$ −12.7773 + 12.7773i −0.803302 + 0.803302i
$$254$$ −15.6052 −0.979158
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −14.7275 + 14.7275i −0.918678 + 0.918678i −0.996933 0.0782557i $$-0.975065\pi$$
0.0782557 + 0.996933i $$0.475065\pi$$
$$258$$ 0 0
$$259$$ 9.72741i 0.604432i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −1.70674 1.70674i −0.105443 0.105443i
$$263$$ −3.42919 3.42919i −0.211453 0.211453i 0.593432 0.804884i $$-0.297773\pi$$
−0.804884 + 0.593432i $$0.797773\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 4.87832i 0.299109i
$$267$$ 0 0
$$268$$ −3.81382 + 3.81382i −0.232966 + 0.232966i
$$269$$ 5.33510 0.325287 0.162643 0.986685i $$-0.447998\pi$$
0.162643 + 0.986685i $$0.447998\pi$$
$$270$$ 0 0
$$271$$ 17.0479 1.03559 0.517794 0.855506i $$-0.326754\pi$$
0.517794 + 0.855506i $$0.326754\pi$$
$$272$$ −4.37101 + 4.37101i −0.265031 + 0.265031i
$$273$$ 0 0
$$274$$ 13.2913i 0.802956i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 6.36360 + 6.36360i 0.382351 + 0.382351i 0.871949 0.489597i $$-0.162856\pi$$
−0.489597 + 0.871949i $$0.662856\pi$$
$$278$$ −7.96348 7.96348i −0.477618 0.477618i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 6.14214i 0.366409i −0.983075 0.183205i $$-0.941353\pi$$
0.983075 0.183205i $$-0.0586471\pi$$
$$282$$ 0 0
$$283$$ −14.4600 + 14.4600i −0.859556 + 0.859556i −0.991286 0.131730i $$-0.957947\pi$$
0.131730 + 0.991286i $$0.457947\pi$$
$$284$$ 10.9282 0.648470
$$285$$ 0 0
$$286$$ 9.77729 0.578144
$$287$$ 6.20648 6.20648i 0.366357 0.366357i
$$288$$ 0 0
$$289$$ 21.2114i 1.24773i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −2.51059 2.51059i −0.146921 0.146921i
$$293$$ 3.55708 + 3.55708i 0.207807 + 0.207807i 0.803335 0.595528i $$-0.203057\pi$$
−0.595528 + 0.803335i $$0.703057\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 9.72741i 0.565394i
$$297$$ 0 0
$$298$$ −2.25397 + 2.25397i −0.130569 + 0.130569i
$$299$$ −15.1562 −0.876508
$$300$$ 0 0
$$301$$ 0.247285 0.0142533
$$302$$ −1.27792 + 1.27792i −0.0735359 + 0.0735359i
$$303$$ 0 0
$$304$$ 4.87832i 0.279791i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −4.32729 4.32729i −0.246971 0.246971i 0.572755 0.819727i $$-0.305875\pi$$
−0.819727 + 0.572755i $$0.805875\pi$$
$$308$$ 2.41421 + 2.41421i 0.137563 + 0.137563i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 3.69537i 0.209545i −0.994496 0.104773i $$-0.966589\pi$$
0.994496 0.104773i $$-0.0334114\pi$$
$$312$$ 0 0
$$313$$ 13.3390 13.3390i 0.753966 0.753966i −0.221251 0.975217i $$-0.571014\pi$$
0.975217 + 0.221251i $$0.0710140\pi$$
$$314$$ −18.1835 −1.02615
$$315$$ 0 0
$$316$$ −9.98414 −0.561652
$$317$$ 13.5601 13.5601i 0.761612 0.761612i −0.215002 0.976614i $$-0.568976\pi$$
0.976614 + 0.215002i $$0.0689757\pi$$
$$318$$ 0 0
$$319$$ 17.8113i 0.997243i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −3.74238 3.74238i −0.208555 0.208555i
$$323$$ −21.3232 21.3232i −1.18645 1.18645i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 14.2672i 0.790188i
$$327$$ 0 0
$$328$$ 6.20648 6.20648i 0.342696 0.342696i
$$329$$ −4.84909 −0.267339
$$330$$ 0 0
$$331$$ 12.1849 0.669745 0.334872 0.942263i $$-0.391307\pi$$
0.334872 + 0.942263i $$0.391307\pi$$
$$332$$ 2.35640 2.35640i 0.129324 0.129324i
$$333$$ 0 0
$$334$$ 4.68556i 0.256383i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −14.8403 14.8403i −0.808401 0.808401i 0.175991 0.984392i $$-0.443687\pi$$
−0.984392 + 0.175991i $$0.943687\pi$$
$$338$$ −3.39355 3.39355i −0.184585 0.184585i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 16.8642i 0.913249i
$$342$$ 0 0
$$343$$ −0.707107 + 0.707107i −0.0381802 + 0.0381802i
$$344$$ 0.247285 0.0133327
$$345$$ 0 0
$$346$$ −12.5644 −0.675466
$$347$$ −13.5731 + 13.5731i −0.728642 + 0.728642i −0.970349 0.241707i $$-0.922293\pi$$
0.241707 + 0.970349i $$0.422293\pi$$
$$348$$ 0 0
$$349$$ 23.9467i 1.28184i −0.767608 0.640920i $$-0.778553\pi$$
0.767608 0.640920i $$-0.221447\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 2.41421 + 2.41421i 0.128678 + 0.128678i
$$353$$ 17.0693 + 17.0693i 0.908508 + 0.908508i 0.996152 0.0876442i $$-0.0279339\pi$$
−0.0876442 + 0.996152i $$0.527934\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 4.07055i 0.215739i
$$357$$ 0 0
$$358$$ −17.4341 + 17.4341i −0.921423 + 0.921423i
$$359$$ −11.9223 −0.629236 −0.314618 0.949218i $$-0.601876\pi$$
−0.314618 + 0.949218i $$0.601876\pi$$
$$360$$ 0 0
$$361$$ −4.79796 −0.252524
$$362$$ 9.36433 9.36433i 0.492178 0.492178i
$$363$$ 0 0
$$364$$ 2.86370i 0.150099i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 17.6572 + 17.6572i 0.921699 + 0.921699i 0.997150 0.0754503i $$-0.0240394\pi$$
−0.0754503 + 0.997150i $$0.524039\pi$$
$$368$$ −3.74238 3.74238i −0.195085 0.195085i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 9.10634i 0.472778i
$$372$$ 0 0
$$373$$ 16.7980 16.7980i 0.869765 0.869765i −0.122681 0.992446i $$-0.539149\pi$$
0.992446 + 0.122681i $$0.0391491\pi$$
$$374$$ −21.1051 −1.09132
$$375$$ 0 0
$$376$$ −4.84909 −0.250073
$$377$$ −10.5638 + 10.5638i −0.544061 + 0.544061i
$$378$$ 0 0
$$379$$ 14.7821i 0.759306i 0.925129 + 0.379653i $$0.123957\pi$$
−0.925129 + 0.379653i $$0.876043\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −13.9461 13.9461i −0.713545 0.713545i
$$383$$ −19.2573 19.2573i −0.984000 0.984000i 0.0158744 0.999874i $$-0.494947\pi$$
−0.999874 + 0.0158744i $$0.994947\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 9.92016i 0.504923i
$$387$$ 0 0
$$388$$ 5.64564 5.64564i 0.286614 0.286614i
$$389$$ 7.50397 0.380466 0.190233 0.981739i $$-0.439076\pi$$
0.190233 + 0.981739i $$0.439076\pi$$
$$390$$ 0 0
$$391$$ 32.7160 1.65452
$$392$$ −0.707107 + 0.707107i −0.0357143 + 0.0357143i
$$393$$ 0 0
$$394$$ 24.8045i 1.24963i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 7.67324 + 7.67324i 0.385109 + 0.385109i 0.872939 0.487830i $$-0.162211\pi$$
−0.487830 + 0.872939i $$0.662211\pi$$
$$398$$ 11.2913 + 11.2913i 0.565981 + 0.565981i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1.80828i 0.0903011i 0.998980 + 0.0451506i $$0.0143768\pi$$
−0.998980 + 0.0451506i $$0.985623\pi$$
$$402$$ 0 0
$$403$$ 10.0020 10.0020i 0.498237 0.498237i
$$404$$ 4.91484 0.244522
$$405$$ 0 0
$$406$$ −5.21682 −0.258906
$$407$$ −23.4840 + 23.4840i −1.16406 + 1.16406i
$$408$$ 0 0
$$409$$ 35.3440i 1.74765i −0.486243 0.873824i $$-0.661633\pi$$
0.486243 0.873824i $$-0.338367\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 8.07019 + 8.07019i 0.397590 + 0.397590i
$$413$$ 1.57545 + 1.57545i 0.0775230 + 0.0775230i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 2.86370i 0.140405i
$$417$$ 0 0
$$418$$ −11.7773 + 11.7773i −0.576046 + 0.576046i
$$419$$ 27.4979 1.34336 0.671681 0.740841i $$-0.265573\pi$$
0.671681 + 0.740841i $$0.265573\pi$$
$$420$$ 0 0
$$421$$ −5.86194 −0.285694 −0.142847 0.989745i $$-0.545626\pi$$
−0.142847 + 0.989745i $$0.545626\pi$$
$$422$$ 18.5747 18.5747i 0.904203 0.904203i
$$423$$ 0 0
$$424$$ 9.10634i 0.442243i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −10.7852 10.7852i −0.521934 0.521934i
$$428$$ −5.77729 5.77729i −0.279256 0.279256i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 21.4794i 1.03463i 0.855796 + 0.517313i $$0.173068\pi$$
−0.855796 + 0.517313i $$0.826932\pi$$
$$432$$ 0 0
$$433$$ −16.0406 + 16.0406i −0.770862 + 0.770862i −0.978257 0.207395i $$-0.933501\pi$$
0.207395 + 0.978257i $$0.433501\pi$$
$$434$$ 4.93942 0.237100
$$435$$ 0 0
$$436$$ 6.07712 0.291041
$$437$$ 18.2565 18.2565i 0.873328 0.873328i
$$438$$ 0 0
$$439$$ 11.8583i 0.565967i −0.959125 0.282984i $$-0.908676\pi$$
0.959125 0.282984i $$-0.0913242\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −12.5173 12.5173i −0.595386 0.595386i
$$443$$ 19.9223 + 19.9223i 0.946538 + 0.946538i 0.998642 0.0521039i $$-0.0165927\pi$$
−0.0521039 + 0.998642i $$0.516593\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 17.8277i 0.844166i
$$447$$ 0 0
$$448$$ −0.707107 + 0.707107i −0.0334077 + 0.0334077i
$$449$$ 23.6138 1.11440 0.557201 0.830377i $$-0.311875\pi$$
0.557201 + 0.830377i $$0.311875\pi$$
$$450$$ 0 0
$$451$$ 29.9676 1.41112
$$452$$ 6.76733 6.76733i 0.318308 0.318308i
$$453$$ 0 0
$$454$$ 4.28205i 0.200966i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −19.4150 19.4150i −0.908196 0.908196i 0.0879308 0.996127i $$-0.471975\pi$$
−0.996127 + 0.0879308i $$0.971975\pi$$
$$458$$ 2.47871 + 2.47871i 0.115823 + 0.115823i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 29.8406i 1.38981i 0.719100 + 0.694906i $$0.244554\pi$$
−0.719100 + 0.694906i $$0.755446\pi$$
$$462$$ 0 0
$$463$$ 9.13505 9.13505i 0.424542 0.424542i −0.462222 0.886764i $$-0.652948\pi$$
0.886764 + 0.462222i $$0.152948\pi$$
$$464$$ −5.21682 −0.242185
$$465$$ 0 0
$$466$$ 12.7007 0.588348
$$467$$ −2.03591 + 2.03591i −0.0942106 + 0.0942106i −0.752641 0.658431i $$-0.771221\pi$$
0.658431 + 0.752641i $$0.271221\pi$$
$$468$$ 0 0
$$469$$ 5.39355i 0.249051i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.57545 + 1.57545i 0.0725162 + 0.0725162i
$$473$$ 0.596999 + 0.596999i 0.0274500 + 0.0274500i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 6.18154i 0.283330i
$$477$$ 0 0
$$478$$ 11.6569 11.6569i 0.533172 0.533172i
$$479$$ −38.9202 −1.77831 −0.889154 0.457608i $$-0.848706\pi$$
−0.889154 + 0.457608i $$0.848706\pi$$
$$480$$ 0 0
$$481$$ −27.8564 −1.27014
$$482$$ −19.6702 + 19.6702i −0.895954 + 0.895954i
$$483$$ 0 0
$$484$$ 0.656854i 0.0298570i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −23.6040 23.6040i −1.06960 1.06960i −0.997390 0.0722080i $$-0.976995\pi$$
−0.0722080 0.997390i $$-0.523005\pi$$
$$488$$ −10.7852 10.7852i −0.488224 0.488224i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 26.4735i 1.19473i 0.801969 + 0.597366i $$0.203786\pi$$
−0.801969 + 0.597366i $$0.796214\pi$$
$$492$$ 0 0
$$493$$ 22.8028 22.8028i 1.02698 1.02698i
$$494$$ −13.9700 −0.628542
$$495$$ 0 0
$$496$$ 4.93942 0.221786
$$497$$ −7.72741 + 7.72741i −0.346622 + 0.346622i
$$498$$ 0 0
$$499$$ 40.3855i 1.80790i 0.427634 + 0.903952i $$0.359347\pi$$
−0.427634 + 0.903952i $$0.640653\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −5.96776 5.96776i −0.266354 0.266354i
$$503$$ −18.8113 18.8113i −0.838756 0.838756i 0.149940 0.988695i $$-0.452092\pi$$
−0.988695 + 0.149940i $$0.952092\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 18.0698i 0.803302i
$$507$$ 0 0
$$508$$ 11.0345 11.0345i 0.489579 0.489579i
$$509$$ −28.6793 −1.27119 −0.635594 0.772024i $$-0.719245\pi$$
−0.635594 + 0.772024i $$0.719245\pi$$
$$510$$ 0 0
$$511$$ 3.55051 0.157065
$$512$$ −0.707107 + 0.707107i −0.0312500 + 0.0312500i
$$513$$ 0 0
$$514$$ 20.8279i 0.918678i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −11.7067 11.7067i −0.514862 0.514862i
$$518$$ −6.87832 6.87832i −0.302216 0.302216i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 16.4916i 0.722509i −0.932467 0.361254i $$-0.882349\pi$$
0.932467 0.361254i $$-0.117651\pi$$
$$522$$ 0 0
$$523$$ −22.8596 + 22.8596i −0.999579 + 0.999579i −1.00000 0.000420508i $$-0.999866\pi$$
0.000420508 1.00000i $$0.499866\pi$$
$$524$$ 2.41370 0.105443
$$525$$ 0 0
$$526$$ 4.84961 0.211453
$$527$$ −21.5902 + 21.5902i −0.940485 + 0.940485i
$$528$$ 0 0
$$529$$ 5.01086i 0.217863i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −3.44949 3.44949i −0.149554 0.149554i
$$533$$ 17.7735 + 17.7735i 0.769857 + 0.769857i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 5.39355i 0.232966i
$$537$$ 0 0
$$538$$ −3.77249 + 3.77249i −0.162643 + 0.162643i
$$539$$ −3.41421 −0.147061
$$540$$ 0 0
$$541$$ 30.4412 1.30877 0.654385 0.756161i $$-0.272927\pi$$
0.654385 + 0.756161i $$0.272927\pi$$
$$542$$ −12.0547 + 12.0547i −0.517794 + 0.517794i
$$543$$ 0 0
$$544$$ 6.18154i 0.265031i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −22.9103 22.9103i −0.979574 0.979574i 0.0202215 0.999796i $$-0.493563\pi$$
−0.999796 + 0.0202215i $$0.993563\pi$$
$$548$$ −9.39836 9.39836i −0.401478 0.401478i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 25.4493i 1.08418i
$$552$$ 0 0
$$553$$ 7.05986 7.05986i 0.300216 0.300216i
$$554$$ −8.99948 −0.382351
$$555$$ 0 0
$$556$$ 11.2621 0.477618
$$557$$ −4.43612 + 4.43612i −0.187965 + 0.187965i −0.794816 0.606851i $$-0.792432\pi$$
0.606851 + 0.794816i $$0.292432\pi$$
$$558$$ 0 0
$$559$$ 0.708151i 0.0299516i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 4.34315 + 4.34315i 0.183205 + 0.183205i
$$563$$ −8.80589 8.80589i −0.371124 0.371124i 0.496763 0.867886i $$-0.334522\pi$$
−0.867886 + 0.496763i $$0.834522\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 20.4495i 0.859556i
$$567$$ 0 0
$$568$$ −7.72741 + 7.72741i −0.324235 + 0.324235i
$$569$$ −17.6654 −0.740573 −0.370286 0.928918i $$-0.620740\pi$$
−0.370286 + 0.928918i $$0.620740\pi$$
$$570$$ 0 0
$$571$$ 30.9852 1.29669 0.648345 0.761347i $$-0.275462\pi$$
0.648345 + 0.761347i $$0.275462\pi$$
$$572$$ −6.91359 + 6.91359i −0.289072 + 0.289072i
$$573$$ 0 0
$$574$$ 8.77729i 0.366357i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 16.4860 + 16.4860i 0.686322 + 0.686322i 0.961417 0.275095i $$-0.0887094\pi$$
−0.275095 + 0.961417i $$0.588709\pi$$
$$578$$ 14.9988 + 14.9988i 0.623866 + 0.623866i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 3.33245i 0.138253i
$$582$$ 0 0
$$583$$ −21.9847 + 21.9847i −0.910512 + 0.910512i
$$584$$ 3.55051 0.146921
$$585$$ 0 0
$$586$$ −5.03047 −0.207807
$$587$$ −29.4681 + 29.4681i −1.21628 + 1.21628i −0.247351 + 0.968926i $$0.579560\pi$$
−0.968926 + 0.247351i $$0.920440\pi$$
$$588$$ 0 0
$$589$$ 24.0960i 0.992859i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −6.87832 6.87832i −0.282697 0.282697i
$$593$$ −22.7874 22.7874i −0.935767 0.935767i 0.0622906 0.998058i $$-0.480159\pi$$
−0.998058 + 0.0622906i $$0.980159\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 3.18759i 0.130569i
$$597$$ 0 0
$$598$$ 10.7171 10.7171i 0.438254 0.438254i
$$599$$ 34.9314 1.42726 0.713629 0.700524i $$-0.247050\pi$$
0.713629 + 0.700524i $$0.247050\pi$$
$$600$$ 0 0
$$601$$ −39.8254 −1.62451 −0.812256 0.583301i $$-0.801761\pi$$
−0.812256 + 0.583301i $$0.801761\pi$$
$$602$$ −0.174857 + 0.174857i −0.00712663 + 0.00712663i
$$603$$ 0 0
$$604$$ 1.80725i 0.0735359i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 22.7675 + 22.7675i 0.924104 + 0.924104i 0.997316 0.0732124i $$-0.0233251\pi$$
−0.0732124 + 0.997316i $$0.523325\pi$$
$$608$$ −3.44949 3.44949i −0.139895 0.139895i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 13.8864i 0.561782i
$$612$$ 0 0
$$613$$ 3.99446 3.99446i 0.161335 0.161335i −0.621823 0.783158i $$-0.713608\pi$$
0.783158 + 0.621823i $$0.213608\pi$$
$$614$$ 6.11971 0.246971
$$615$$ 0 0
$$616$$ −3.41421 −0.137563
$$617$$ 1.46002 1.46002i 0.0587783 0.0587783i −0.677107 0.735885i $$-0.736766\pi$$
0.735885 + 0.677107i $$0.236766\pi$$
$$618$$ 0 0
$$619$$ 47.4138i 1.90572i −0.303407 0.952861i $$-0.598124\pi$$
0.303407 0.952861i $$-0.401876\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 2.61302 + 2.61302i 0.104773 + 0.104773i
$$623$$ 2.87832 + 2.87832i 0.115317 + 0.115317i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 18.8642i 0.753966i
$$627$$ 0 0
$$628$$ 12.8577 12.8577i 0.513076 0.513076i
$$629$$ 60.1304 2.39755
$$630$$ 0 0
$$631$$ 4.98665 0.198515 0.0992577 0.995062i $$-0.468353\pi$$
0.0992577 + 0.995062i $$0.468353\pi$$
$$632$$ 7.05986 7.05986i 0.280826 0.280826i
$$633$$ 0 0
$$634$$ 19.1769i 0.761612i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −2.02494 2.02494i −0.0802312 0.0802312i
$$638$$ −12.5945 12.5945i −0.498621 0.498621i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 37.4961i 1.48101i −0.672052 0.740504i $$-0.734587\pi$$
0.672052 0.740504i $$-0.265413\pi$$
$$642$$ 0 0
$$643$$ 4.58970 4.58970i 0.181000 0.181000i −0.610791 0.791792i $$-0.709149\pi$$
0.791792 + 0.610791i $$0.209149\pi$$
$$644$$ 5.29253 0.208555
$$645$$ 0 0
$$646$$ 30.1555 1.18645
$$647$$ 27.4412 27.4412i 1.07883 1.07883i 0.0822112 0.996615i $$-0.473802\pi$$
0.996615 0.0822112i $$-0.0261982\pi$$
$$648$$ 0 0
$$649$$ 7.60697i 0.298600i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −10.0884 10.0884i −0.395094 0.395094i
$$653$$ 13.3212 + 13.3212i 0.521300 + 0.521300i 0.917964 0.396664i $$-0.129832\pi$$
−0.396664 + 0.917964i $$0.629832\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 8.77729i 0.342696i
$$657$$ 0 0
$$658$$ 3.42883 3.42883i 0.133670 0.133670i
$$659$$ 13.9355 0.542851 0.271425 0.962459i $$-0.412505\pi$$
0.271425 + 0.962459i $$0.412505\pi$$
$$660$$ 0 0
$$661$$ 38.5879 1.50089 0.750447 0.660930i $$-0.229838\pi$$
0.750447 + 0.660930i $$0.229838\pi$$
$$662$$ −8.61605 + 8.61605i −0.334872 + 0.334872i
$$663$$ 0 0
$$664$$ 3.33245i 0.129324i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 19.5233 + 19.5233i 0.755946 + 0.755946i
$$668$$ −3.31319 3.31319i −0.128191 0.128191i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 52.0757i 2.01036i
$$672$$ 0 0
$$673$$ 28.1223 28.1223i 1.08403 1.08403i 0.0879048 0.996129i $$-0.471983\pi$$
0.996129 0.0879048i $$-0.0280171\pi$$
$$674$$ 20.9873 0.808401
$$675$$ 0 0
$$676$$ 4.79920 0.184585
$$677$$ −22.7408 + 22.7408i −0.873999 + 0.873999i −0.992905 0.118907i $$-0.962061\pi$$
0.118907 + 0.992905i $$0.462061\pi$$
$$678$$ 0 0
$$679$$ 7.98414i 0.306403i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 11.9248 + 11.9248i 0.456624 + 0.456624i
$$683$$ −11.9549 11.9549i −0.457442 0.457442i 0.440373 0.897815i $$-0.354846\pi$$
−0.897815 + 0.440373i $$0.854846\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1.00000i 0.0381802i
$$687$$ 0 0
$$688$$ −0.174857 + 0.174857i −0.00666635 + 0.00666635i
$$689$$ −26.0779 −0.993488
$$690$$ 0 0
$$691$$ 6.79167 0.258367 0.129184 0.991621i $$-0.458764\pi$$
0.129184 + 0.991621i $$0.458764\pi$$
$$692$$ 8.88437 8.88437i 0.337733 0.337733i
$$693$$ 0 0
$$694$$ 19.1953i 0.728642i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −38.3656 38.3656i −1.45320 1.45320i
$$698$$ 16.9329 + 16.9329i 0.640920 + 0.640920i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 40.7354i 1.53855i −0.638915 0.769277i $$-0.720617\pi$$
0.638915 0.769277i $$-0.279383\pi$$
$$702$$ 0 0
$$703$$ 33.5546 33.5546i 1.26554 1.26554i
$$704$$ −3.41421 −0.128678
$$705$$ 0 0
$$706$$ −24.1396 −0.908508
$$707$$ −3.47531 + 3.47531i −0.130703 + 0.130703i
$$708$$ 0 0
$$709$$ 30.8035i 1.15685i −0.815735 0.578425i $$-0.803667\pi$$
0.815735 0.578425i $$-0.196333\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 2.87832 + 2.87832i 0.107869 + 0.107869i
$$713$$ −18.4852 18.4852i −0.692276 0.692276i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 24.6556i 0.921423i
$$717$$ 0 0
$$718$$ 8.43035 8.43035i 0.314618 0.314618i
$$719$$ 13.0945 0.488341 0.244170 0.969732i $$-0.421484\pi$$
0.244170 + 0.969732i $$0.421484\pi$$
$$720$$ 0 0
$$721$$ −11.4130 −0.425041
$$722$$ 3.39267 3.39267i 0.126262 0.126262i
$$723$$ 0 0
$$724$$ 13.2432i 0.492178i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −34.4418 34.4418i −1.27738 1.27738i −0.942131 0.335246i $$-0.891181\pi$$
−0.335246 0.942131i $$-0.608819\pi$$
$$728$$ −2.02494 2.02494i −0.0750494 0.0750494i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 1.52860i 0.0565374i
$$732$$ 0 0
$$733$$ 20.9524 20.9524i 0.773895 0.773895i −0.204890 0.978785i $$-0.565684\pi$$
0.978785 + 0.204890i $$0.0656836\pi$$
$$734$$ −24.9711 −0.921699
$$735$$ 0 0
$$736$$ 5.29253 0.195085
$$737$$ 13.0212 13.0212i 0.479641 0.479641i
$$738$$ 0 0
$$739$$ 51.0850i 1.87919i −0.342288 0.939595i $$-0.611202\pi$$
0.342288 0.939595i $$-0.388798\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −6.43916 6.43916i −0.236389 0.236389i
$$743$$ 23.2763 + 23.2763i 0.853925 + 0.853925i 0.990614 0.136689i $$-0.0436461\pi$$
−0.136689 + 0.990614i $$0.543646\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 23.7559i 0.869765i
$$747$$ 0 0
$$748$$ 14.9236 14.9236i 0.545659 0.545659i
$$749$$ 8.17033 0.298537
$$750$$ 0 0
$$751$$ 16.7035 0.609520 0.304760 0.952429i $$-0.401424\pi$$
0.304760 + 0.952429i $$0.401424\pi$$
$$752$$ 3.42883 3.42883i 0.125036 0.125036i
$$753$$ 0 0
$$754$$ 14.9394i 0.544061i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −6.56461 6.56461i −0.238595 0.238595i 0.577673 0.816268i $$-0.303961\pi$$
−0.816268 + 0.577673i $$0.803961\pi$$
$$758$$ −10.4525 10.4525i −0.379653 0.379653i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 46.4642i 1.68433i −0.539223 0.842163i $$-0.681282\pi$$
0.539223 0.842163i $$-0.318718\pi$$
$$762$$ 0 0
$$763$$ −4.29717 + 4.29717i −0.155568 + 0.155568i
$$764$$ 19.7228 0.713545
$$765$$ 0 0
$$766$$ 27.2339 0.984000
$$767$$ −4.51163 + 4.51163i −0.162906 + 0.162906i
$$768$$ 0 0
$$769$$ 39.1177i 1.41062i 0.708898 + 0.705311i $$0.249193\pi$$
−0.708898 + 0.705311i $$0.750807\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 7.01461 + 7.01461i 0.252461 + 0.252461i
$$773$$ −4.88918 4.88918i −0.175851 0.175851i 0.613693 0.789545i $$-0.289683\pi$$
−0.789545 + 0.613693i $$0.789683\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 7.98414i 0.286614i
$$777$$ 0 0
$$778$$ −5.30611 + 5.30611i −0.190233 + 0.190233i
$$779$$ −42.8184 −1.53413
$$780$$ 0 0
$$781$$ −37.3112 −1.33510
$$782$$ −23.1337 + 23.1337i −0.827259 + 0.827259i
$$783$$ 0 0
$$784$$ 1.00000i 0.0357143i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −10.6549 10.6549i −0.379805 0.379805i 0.491226 0.871032i $$-0.336549\pi$$
−0.871032 + 0.491226i $$0.836549\pi$$
$$788$$ 17.5394 + 17.5394i 0.624817 + 0.624817i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 9.57045i 0.340286i
$$792$$ 0 0
$$793$$ 30.8857 30.8857i 1.09678 1.09678i
$$794$$ −10.8516 −0.385109
$$795$$ 0 0
$$796$$ −15.9683 −0.565981
$$797$$ 8.27135 8.27135i 0.292986 0.292986i −0.545273 0.838259i $$-0.683574\pi$$
0.838259 + 0.545273i $$0.183574\pi$$
$$798$$ 0 0
$$799$$