# Properties

 Label 21.38.g.a.17.1 Level $21$ Weight $38$ Character 21.17 Analytic conductor $182.099$ Analytic rank $0$ Dimension $2$ CM discriminant -3 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$21 = 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$38$$ Character orbit: $$[\chi]$$ $$=$$ 21.g (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$182.099480062$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

## Embedding invariants

 Embedding label 17.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 21.17 Dual form 21.38.g.a.5.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-5.81131e8 - 3.35516e8i) q^{3} +(-6.87195e10 + 1.19026e11i) q^{4} +(2.94136e15 - 3.14809e15i) q^{7} +(2.25142e17 + 3.89957e17i) q^{9} +O(q^{10})$$ $$q+(-5.81131e8 - 3.35516e8i) q^{3} +(-6.87195e10 + 1.19026e11i) q^{4} +(2.94136e15 - 3.14809e15i) q^{7} +(2.25142e17 + 3.89957e17i) q^{9} +(7.98700e19 - 4.61130e19i) q^{12} +3.52663e20i q^{13} +(-9.44473e21 - 1.63588e22i) q^{16} +(7.84496e23 - 4.52929e23i) q^{19} +(-2.76555e24 + 8.42580e23i) q^{21} +(3.63798e25 - 6.30116e25i) q^{25} -3.02155e26i q^{27} +(1.72575e26 + 5.66433e26i) q^{28} +(6.74022e27 + 3.89147e27i) q^{31} -6.18865e28 q^{36} +(-9.92707e27 - 1.71942e28i) q^{37} +(1.18324e29 - 2.04943e29i) q^{39} -3.12847e30 q^{43} +1.26754e31i q^{48} +(-1.25889e30 - 1.85194e31i) q^{49} +(-4.19760e31 - 2.42348e31i) q^{52} -6.07860e32 q^{57} +(-1.77999e33 + 1.02768e33i) q^{61} +(1.88985e33 + 4.38238e32i) q^{63} +2.59615e33 q^{64} +(-5.13785e33 + 8.89901e33i) q^{67} +(5.10751e34 + 2.94882e34i) q^{73} +(-4.22828e34 + 2.44120e34i) q^{75} +1.24500e35i q^{76} +(-1.11822e35 - 1.93681e35i) q^{79} +(-1.01378e35 + 1.75591e35i) q^{81} +(8.97587e34 - 3.87073e35i) q^{84} +(1.11022e36 + 1.03731e36i) q^{91} +(-2.61130e36 - 4.52290e36i) q^{93} -6.37793e36i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 1162261467q^{3} - 137438953472q^{4} + 5882725491086809q^{7} + 450283905890997363q^{9} + O(q^{10})$$ $$2q - 1162261467q^{3} - 137438953472q^{4} + 5882725491086809q^{7} + 450283905890997363q^{9} +$$$$15\!\cdots\!24$$$$q^{12} -$$$$18\!\cdots\!84$$$$q^{16} +$$$$15\!\cdots\!11$$$$q^{19} -$$$$55\!\cdots\!86$$$$q^{21} +$$$$72\!\cdots\!25$$$$q^{25} +$$$$34\!\cdots\!32$$$$q^{28} +$$$$13\!\cdots\!55$$$$q^{31} -$$$$12\!\cdots\!72$$$$q^{36} -$$$$19\!\cdots\!09$$$$q^{37} +$$$$23\!\cdots\!63$$$$q^{39} -$$$$62\!\cdots\!30$$$$q^{43} -$$$$25\!\cdots\!33$$$$q^{49} -$$$$83\!\cdots\!24$$$$q^{52} -$$$$12\!\cdots\!58$$$$q^{57} -$$$$35\!\cdots\!48$$$$q^{61} +$$$$37\!\cdots\!95$$$$q^{63} +$$$$51\!\cdots\!96$$$$q^{64} -$$$$10\!\cdots\!39$$$$q^{67} +$$$$10\!\cdots\!77$$$$q^{73} -$$$$84\!\cdots\!75$$$$q^{75} -$$$$22\!\cdots\!67$$$$q^{79} -$$$$20\!\cdots\!69$$$$q^{81} +$$$$17\!\cdots\!24$$$$q^{84} +$$$$22\!\cdots\!69$$$$q^{91} -$$$$52\!\cdots\!95$$$$q^{93} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$$.

 $$n$$ $$8$$ $$10$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$3$$ −5.81131e8 3.35516e8i −0.866025 0.500000i
$$4$$ −6.87195e10 + 1.19026e11i −0.500000 + 0.866025i
$$5$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 0 0
$$7$$ 2.94136e15 3.14809e15i 0.682708 0.730692i
$$8$$ 0 0
$$9$$ 2.25142e17 + 3.89957e17i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ 7.98700e19 4.61130e19i 0.866025 0.500000i
$$13$$ 3.52663e20i 0.869777i 0.900484 + 0.434889i $$0.143212\pi$$
−0.900484 + 0.434889i $$0.856788\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −9.44473e21 1.63588e22i −0.500000 0.866025i
$$17$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$18$$ 0 0
$$19$$ 7.84496e23 4.52929e23i 1.72842 0.997904i 0.831851 0.555000i $$-0.187282\pi$$
0.896569 0.442904i $$-0.146052\pi$$
$$20$$ 0 0
$$21$$ −2.76555e24 + 8.42580e23i −0.956588 + 0.291444i
$$22$$ 0 0
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ 0 0
$$25$$ 3.63798e25 6.30116e25i 0.500000 0.866025i
$$26$$ 0 0
$$27$$ 3.02155e26i 1.00000i
$$28$$ 1.72575e26 + 5.66433e26i 0.291444 + 0.956588i
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 6.74022e27 + 3.89147e27i 1.73174 + 0.999820i 0.875348 + 0.483493i $$0.160632\pi$$
0.856392 + 0.516327i $$0.172701\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −6.18865e28 −1.00000
$$37$$ −9.92707e27 1.71942e28i −0.0966250 0.167359i 0.813661 0.581340i $$-0.197471\pi$$
−0.910286 + 0.413981i $$0.864138\pi$$
$$38$$ 0 0
$$39$$ 1.18324e29 2.04943e29i 0.434889 0.753249i
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −3.12847e30 −1.88871 −0.944355 0.328927i $$-0.893313\pi$$
−0.944355 + 0.328927i $$0.893313\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 1.26754e31i 1.00000i
$$49$$ −1.25889e30 1.85194e31i −0.0678202 0.997698i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −4.19760e31 2.42348e31i −0.753249 0.434889i
$$53$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −6.07860e32 −1.99581
$$58$$ 0 0
$$59$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$60$$ 0 0
$$61$$ −1.77999e33 + 1.02768e33i −1.66654 + 0.962178i −0.697060 + 0.717012i $$0.745509\pi$$
−0.969481 + 0.245166i $$0.921158\pi$$
$$62$$ 0 0
$$63$$ 1.88985e33 + 4.38238e32i 0.974151 + 0.225897i
$$64$$ 2.59615e33 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −5.13785e33 + 8.89901e33i −0.848003 + 1.46878i 0.0349851 + 0.999388i $$0.488862\pi$$
−0.882988 + 0.469396i $$0.844472\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 5.10751e34 + 2.94882e34i 1.72479 + 0.995807i 0.908132 + 0.418684i $$0.137509\pi$$
0.816657 + 0.577123i $$0.195825\pi$$
$$74$$ 0 0
$$75$$ −4.22828e34 + 2.44120e34i −0.866025 + 0.500000i
$$76$$ 1.24500e35i 1.99581i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1.11822e35 1.93681e35i −0.875842 1.51700i −0.855863 0.517202i $$-0.826974\pi$$
−0.0199782 0.999800i $$-0.506360\pi$$
$$80$$ 0 0
$$81$$ −1.01378e35 + 1.75591e35i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 8.97587e34 3.87073e35i 0.225897 0.974151i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ 0 0
$$91$$ 1.11022e36 + 1.03731e36i 0.635539 + 0.593804i
$$92$$ 0 0
$$93$$ −2.61130e36 4.52290e36i −0.999820 1.73174i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 6.37793e36i 1.12048i −0.828332 0.560238i $$-0.810710\pi$$
0.828332 0.560238i $$-0.189290\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 5.00000e36 + 8.66025e36i 0.500000 + 0.866025i
$$101$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$102$$ 0 0
$$103$$ 2.68000e37 1.54730e37i 1.55112 0.895540i 0.553070 0.833135i $$-0.313456\pi$$
0.998051 0.0624056i $$-0.0198772\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$108$$ 3.59642e37 + 2.07639e37i 0.866025 + 0.500000i
$$109$$ −2.93868e37 + 5.08993e37i −0.596707 + 1.03353i 0.396596 + 0.917993i $$0.370191\pi$$
−0.993304 + 0.115534i $$0.963142\pi$$
$$110$$ 0 0
$$111$$ 1.33228e37i 0.193250i
$$112$$ −7.92793e37 1.83841e37i −0.974151 0.225897i
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.37524e38 + 7.93993e37i −0.753249 + 0.434889i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.70020e38 2.94483e38i −0.500000 0.866025i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −9.26368e38 + 5.34839e38i −1.73174 + 0.999820i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 9.33146e38 1.12094 0.560468 0.828176i $$-0.310621\pi$$
0.560468 + 0.828176i $$0.310621\pi$$
$$128$$ 0 0
$$129$$ 1.81805e39 + 1.04965e39i 1.63567 + 0.944355i
$$130$$ 0 0
$$131$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$132$$ 0 0
$$133$$ 8.81624e38 3.80190e39i 0.450846 1.94422i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ 1.37950e39i 0.311851i −0.987769 0.155925i $$-0.950164\pi$$
0.987769 0.155925i $$-0.0498360\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 4.25281e39 7.36609e39i 0.500000 0.866025i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −5.48197e39 + 1.11846e40i −0.440115 + 0.897942i
$$148$$ 2.72873e39 0.193250
$$149$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$150$$ 0 0
$$151$$ 4.75071e39 8.22847e39i 0.232105 0.402018i −0.726322 0.687354i $$-0.758772\pi$$
0.958427 + 0.285336i $$0.0921053\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 1.62623e40 + 2.81672e40i 0.434889 + 0.753249i
$$157$$ −7.27708e40 4.20142e40i −1.72907 0.998281i −0.893844 0.448378i $$-0.852002\pi$$
−0.835229 0.549902i $$-0.814665\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 5.89716e40 + 1.02142e41i 0.700120 + 1.21264i 0.968424 + 0.249309i $$0.0802036\pi$$
−0.268304 + 0.963334i $$0.586463\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 4.00295e40 0.243487
$$170$$ 0 0
$$171$$ 3.53246e41 + 2.03947e41i 1.72842 + 0.997904i
$$172$$ 2.14987e41 3.72368e41i 0.944355 1.63567i
$$173$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$174$$ 0 0
$$175$$ −9.13605e40 2.99867e41i −0.291444 0.956588i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$180$$ 0 0
$$181$$ 1.11293e42i 1.90289i −0.307823 0.951444i $$-0.599601\pi$$
0.307823 0.951444i $$-0.400399\pi$$
$$182$$ 0 0
$$183$$ 1.37921e42 1.92436
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −9.51212e41 8.88747e41i −0.730692 0.682708i
$$190$$ 0 0
$$191$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ −1.50870e42 8.71049e41i −0.866025 0.500000i
$$193$$ 1.03691e42 1.79597e42i 0.540666 0.936461i −0.458200 0.888849i $$-0.651506\pi$$
0.998866 0.0476117i $$-0.0151610\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 2.29079e42 + 1.12280e42i 0.897942 + 0.440115i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 5.77964e42 + 3.33688e42i 1.71048 + 0.987549i 0.933899 + 0.357538i $$0.116384\pi$$
0.776586 + 0.630011i $$0.216950\pi$$
$$200$$ 0 0
$$201$$ 5.97152e42 3.44766e42i 1.46878 0.848003i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 5.76913e42 3.33081e42i 0.753249 0.434889i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 7.97186e42 0.798609 0.399304 0.916818i $$-0.369252\pi$$
0.399304 + 0.916818i $$0.369252\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 3.20761e43 9.77263e42i 1.91283 0.582782i
$$218$$ 0 0
$$219$$ −1.97875e43 3.42730e43i −0.995807 1.72479i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 3.05912e43i 1.10143i −0.834693 0.550715i $$-0.814355\pi$$
0.834693 0.550715i $$-0.185645\pi$$
$$224$$ 0 0
$$225$$ 3.27625e43 1.00000
$$226$$ 0 0
$$227$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$228$$ 4.17718e43 7.23509e43i 0.997904 1.72842i
$$229$$ 5.53910e43 3.19800e43i 1.22035 0.704567i 0.255354 0.966848i $$-0.417808\pi$$
0.964992 + 0.262281i $$0.0844747\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 1.50072e44i 1.75168i
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −5.91597e42 3.41559e42i −0.0506653 0.0292516i 0.474453 0.880281i $$-0.342646\pi$$
−0.525119 + 0.851029i $$0.675979\pi$$
$$242$$ 0 0
$$243$$ 1.17828e44 6.80277e43i 0.866025 0.500000i
$$244$$ 2.82486e44i 1.92436i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.59731e44 + 2.76663e44i 0.867954 + 1.50334i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ −1.82031e44 + 1.94825e44i −0.682708 + 0.730692i
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −1.78406e44 + 3.09008e44i −0.500000 + 0.866025i
$$257$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$258$$ 0 0
$$259$$ −8.33281e43 1.93230e43i −0.188255 0.0436545i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −7.06140e44 1.22307e45i −0.848003 1.46878i
$$269$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$270$$ 0 0
$$271$$ −1.76690e45 + 1.02012e45i −1.72695 + 0.997055i −0.825127 + 0.564947i $$0.808897\pi$$
−0.901822 + 0.432108i $$0.857770\pi$$
$$272$$ 0 0
$$273$$ −2.97147e44 9.75308e44i −0.253491 0.832019i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 5.15841e44 8.93463e44i 0.336233 0.582372i −0.647488 0.762076i $$-0.724180\pi$$
0.983721 + 0.179703i $$0.0575138\pi$$
$$278$$ 0 0
$$279$$ 3.50453e45i 1.99964i
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 3.91834e44 + 2.26226e44i 0.171812 + 0.0991957i 0.583440 0.812156i $$-0.301706\pi$$
−0.411628 + 0.911352i $$0.635040\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 1.68105e45 + 2.91166e45i 0.500000 + 0.866025i
$$290$$ 0 0
$$291$$ −2.13990e45 + 3.70641e45i −0.560238 + 0.970361i
$$292$$ −7.01970e45 + 4.05283e45i −1.72479 + 0.995807i
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 6.71032e45i 1.00000i
$$301$$ −9.20196e45 + 9.84872e45i −1.28944 + 1.38006i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −1.48187e46 8.55559e45i −1.72842 0.997904i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.98787e46i 1.93343i 0.255859 + 0.966714i $$0.417642\pi$$
−0.255859 + 0.966714i $$0.582358\pi$$
$$308$$ 0 0
$$309$$ −2.07657e46 −1.79108
$$310$$ 0 0
$$311$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$312$$ 0 0
$$313$$ 1.87985e46 1.08533e46i 1.27807 0.737892i 0.301574 0.953443i $$-0.402488\pi$$
0.976493 + 0.215551i $$0.0691547\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 3.07374e46 1.75168
$$317$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.39333e46 2.41331e46i −0.500000 0.866025i
$$325$$ 2.22219e46 + 1.28298e46i 0.753249 + 0.434889i
$$326$$ 0 0
$$327$$ 3.41551e46 1.97194e46i 1.03353 0.596707i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −3.51969e46 6.09628e46i −0.850524 1.47315i −0.880737 0.473607i $$-0.842952\pi$$
0.0302129 0.999543i $$-0.490381\pi$$
$$332$$ 0 0
$$333$$ 4.47000e45 7.74227e45i 0.0966250 0.167359i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 3.99035e46 + 3.72831e46i 0.730692 + 0.682708i
$$337$$ 1.08707e47 1.88410 0.942048 0.335479i $$-0.108898\pi$$
0.942048 + 0.335479i $$0.108898\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −6.20036e46 5.05091e46i −0.775311 0.631580i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$348$$ 0 0
$$349$$ 1.62094e46i 0.147061i 0.997293 + 0.0735305i $$0.0234266\pi$$
−0.997293 + 0.0735305i $$0.976573\pi$$
$$350$$ 0 0
$$351$$ 1.06559e47 0.869777
$$352$$ 0 0
$$353$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$360$$ 0 0
$$361$$ 3.07286e47 5.32234e47i 1.49162 2.58357i
$$362$$ 0 0
$$363$$ 2.28177e47i 1.00000i
$$364$$ −1.99760e47 + 6.08609e46i −0.832019 + 0.253491i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −9.83590e46 5.67876e46i −0.351959 0.203204i 0.313589 0.949559i $$-0.398469\pi$$
−0.665548 + 0.746355i $$0.731802\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 7.17788e47 1.99964
$$373$$ 5.04704e46 + 8.74173e46i 0.133790 + 0.231731i 0.925135 0.379639i $$-0.123952\pi$$
−0.791345 + 0.611370i $$0.790619\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 6.68943e47 1.31997 0.659985 0.751279i $$-0.270563\pi$$
0.659985 + 0.751279i $$0.270563\pi$$
$$380$$ 0 0
$$381$$ −5.42280e47 3.13086e47i −0.970759 0.560468i
$$382$$ 0 0
$$383$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −7.04350e47 1.21997e48i −0.944355 1.63567i
$$388$$ 7.59137e47 + 4.38288e47i 0.970361 + 0.560238i
$$389$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −8.15997e47 + 4.71116e47i −0.682440 + 0.394007i −0.800774 0.598967i $$-0.795578\pi$$
0.118334 + 0.992974i $$0.462245\pi$$
$$398$$ 0 0
$$399$$ −1.78794e48 + 1.91360e48i −1.36255 + 1.45832i
$$400$$ −1.37439e48 −1.00000
$$401$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$402$$ 0 0
$$403$$ −1.37238e48 + 2.37703e48i −0.869621 + 1.50623i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −3.55113e48 2.05025e48i −1.71193 0.988382i −0.931959 0.362564i $$-0.881901\pi$$
−0.779969 0.625818i $$-0.784765\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 4.25318e48i 1.79108i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −4.62843e47 + 8.01668e47i −0.155925 + 0.270071i
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 6.10362e48 1.72333 0.861666 0.507477i $$-0.169422\pi$$
0.861666 + 0.507477i $$0.169422\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −2.00037e48 + 8.62636e48i −0.434705 + 1.87461i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$432$$ −4.94288e48 + 2.85377e48i −0.866025 + 0.500000i
$$433$$ 8.86530e48i 1.48822i −0.668057 0.744110i $$-0.732874\pi$$
0.668057 0.744110i $$-0.267126\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −4.03888e48 6.99555e48i −0.596707 1.03353i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −4.83459e48 + 2.79125e48i −0.629167 + 0.363250i −0.780429 0.625244i $$-0.784999\pi$$
0.151263 + 0.988494i $$0.451666\pi$$
$$440$$ 0 0
$$441$$ 6.93834e48 4.66040e48i 0.830121 0.557583i
$$442$$ 0 0
$$443$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$444$$ −1.58575e48 9.15534e47i −0.167359 0.0966250i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 7.63621e48 8.17292e48i 0.682708 0.730692i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −5.52156e48 + 3.18788e48i −0.402018 + 0.232105i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.65146e48 9.78862e48i −0.349713 0.605720i 0.636486 0.771288i $$-0.280387\pi$$
−0.986198 + 0.165569i $$0.947054\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 3.71811e49 1.80748 0.903741 0.428079i $$-0.140810\pi$$
0.903741 + 0.428079i $$0.140810\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$468$$ 2.18251e49i 0.869777i
$$469$$ 1.29027e49 + 4.23496e49i 0.494290 + 1.62238i
$$470$$ 0 0
$$471$$ 2.81929e49 + 4.88315e49i 0.998281 + 1.72907i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 6.59099e49i 1.99581i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$480$$ 0 0
$$481$$ 6.06376e48 3.50091e48i 0.145565 0.0840422i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 4.67347e49 1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 1.49323e49 2.58636e49i 0.284998 0.493631i −0.687611 0.726080i $$-0.741340\pi$$
0.972609 + 0.232449i $$0.0746737\pi$$
$$488$$ 0 0
$$489$$ 7.91437e49i 1.40024i
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 1.47015e50i 1.99964i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 6.04884e49 + 1.04769e50i 0.735889 + 1.27460i 0.954332 + 0.298747i $$0.0965688\pi$$
−0.218443 + 0.975850i $$0.570098\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −2.32624e49 1.34306e49i −0.210866 0.121744i
$$508$$ −6.41253e49 + 1.11068e50i −0.560468 + 0.970759i
$$509$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$510$$ 0 0
$$511$$ 2.43062e50 7.40536e49i 1.90515 0.580443i
$$512$$ 0 0
$$513$$ −1.36855e50 2.37039e50i −0.997904 1.72842i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ −2.49871e50 + 1.44263e50i −1.63567 + 0.944355i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$522$$ 0 0
$$523$$ −2.30288e50 + 1.32957e50i −1.17487 + 0.678311i −0.954822 0.297178i $$-0.903954\pi$$
−0.220047 + 0.975489i $$0.570621\pi$$
$$524$$ 0 0
$$525$$ −4.75178e49 + 2.04915e50i −0.225897 + 0.974151i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −1.21032e50 + 2.09633e50i −0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 3.91938e50 + 3.66200e50i 1.45832 + 1.36255i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 8.30237e49 + 1.43801e50i 0.226492 + 0.392295i 0.956766 0.290859i $$-0.0939410\pi$$
−0.730274 + 0.683154i $$0.760608\pi$$
$$542$$ 0 0
$$543$$ −3.73405e50 + 6.46756e50i −0.951444 + 1.64795i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.27774e50 −0.506686 −0.253343 0.967377i $$-0.581530\pi$$
−0.253343 + 0.967377i $$0.581530\pi$$
$$548$$ 0 0
$$549$$ −8.01502e50 4.62747e50i −1.66654 0.962178i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −9.38635e50 2.17661e50i −1.70640 0.395699i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 1.64195e50 + 9.47983e49i 0.270071 + 0.155925i
$$557$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$558$$ 0 0
$$559$$ 1.10330e51i 1.64276i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 2.54590e50 + 8.35625e50i 0.291444 + 0.956588i
$$568$$ 0 0
$$569$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$570$$ 0 0
$$571$$ 8.27588e50 1.43343e51i 0.831853 1.44081i −0.0647150 0.997904i $$-0.520614\pi$$
0.896568 0.442907i $$-0.146053\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 5.84502e50 + 1.01239e51i 0.500000 + 0.866025i
$$577$$ 7.23872e50 + 4.17928e50i 0.599666 + 0.346217i 0.768910 0.639357i $$-0.220799\pi$$
−0.169244 + 0.985574i $$0.554133\pi$$
$$578$$ 0 0
$$579$$ −1.20516e51 + 6.95797e50i −0.936461 + 0.540666i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ −9.54531e50 1.42109e51i −0.557583 0.830121i
$$589$$ 7.05023e51 3.99090
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.87517e50 + 3.24789e50i −0.0966250 + 0.167359i
$$593$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −2.23915e51 3.87833e51i −0.987549 1.71048i
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ 0 0
$$601$$ 4.95401e51i 1.93099i 0.260428 + 0.965493i $$0.416136\pi$$
−0.260428 + 0.965493i $$0.583864\pi$$
$$602$$ 0 0
$$603$$ −4.62698e51 −1.69601
$$604$$ 6.52932e50 + 1.13091e51i 0.232105 + 0.402018i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 3.70756e51 2.14056e51i 1.20253 0.694283i 0.241416 0.970422i $$-0.422388\pi$$
0.961118 + 0.276138i $$0.0890548\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 3.49869e51 6.05991e51i 0.945991 1.63850i 0.192237 0.981349i $$-0.438426\pi$$
0.753754 0.657156i $$-0.228241\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 1.44378e51 + 8.33567e50i 0.326005 + 0.188219i 0.654066 0.756437i $$-0.273062\pi$$
−0.328061 + 0.944657i $$0.606395\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ −4.47016e51 −0.869777
$$625$$ −2.64698e51 4.58470e51i −0.500000 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 1.00015e52 5.77439e51i 1.72907 0.998281i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 1.23496e52 1.95483 0.977417 0.211318i $$-0.0677756\pi$$
0.977417 + 0.211318i $$0.0677756\pi$$
$$632$$ 0 0
$$633$$ −4.63269e51 2.67469e51i −0.691615 0.399304i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.53110e51 4.43963e50i 0.867775 0.0589885i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ 0 0
$$643$$ 7.15200e51i 0.798959i 0.916742 + 0.399479i $$0.130809\pi$$
−0.916742 + 0.399479i $$0.869191\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −2.19193e52 5.08288e51i −1.94795 0.451712i
$$652$$ −1.62100e52 −1.40024
$$653$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 2.65561e52i 1.99161i
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 2.37929e52 + 1.37369e52i 1.59485 + 0.920789i 0.992457 + 0.122592i $$0.0391207\pi$$
0.602397 + 0.798197i $$0.294213\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −1.02638e52 + 1.77775e52i −0.550715 + 0.953866i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −3.71216e52 −1.78381 −0.891903 0.452227i $$-0.850630\pi$$
−0.891903 + 0.452227i $$0.850630\pi$$
$$674$$ 0 0
$$675$$ −1.90393e52 1.09923e52i −0.866025 0.500000i
$$676$$ −2.75081e51 + 4.76454e51i −0.121744 + 0.210866i
$$677$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$678$$ 0 0
$$679$$ −2.00783e52 1.87598e52i −0.818722 0.764958i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$684$$ −4.85498e52 + 2.80302e52i −1.72842 + 0.997904i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −4.29192e52 −1.40913
$$688$$ 2.95476e52 + 5.11779e52i 0.944355 + 1.63567i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 5.37229e52 3.10169e52i 1.58422 0.914650i 0.589987 0.807413i $$-0.299133\pi$$
0.994233 0.107237i $$-0.0342005\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 4.19701e52 + 9.73247e51i 0.974151 + 0.225897i
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ −1.55755e52 8.99252e51i −0.334017 0.192845i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 2.68621e51 + 4.65264e51i 0.0492248 + 0.0852598i 0.889588 0.456764i $$-0.150992\pi$$
−0.840363 + 0.542024i $$0.817658\pi$$
$$710$$ 0 0
$$711$$ 5.03516e52 8.72115e52i 0.875842 1.51700i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$720$$ 0 0
$$721$$ 3.01181e52 1.29880e53i 0.404599 1.74478i
$$722$$ 0 0
$$723$$ 2.29197e51 + 3.96981e51i 0.0292516 + 0.0506653i
$$724$$ 1.32467e53 + 7.64798e52i 1.64795 + 0.951444i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 3.95008e52i 0.455218i 0.973753 + 0.227609i $$0.0730909\pi$$
−0.973753 + 0.227609i $$0.926909\pi$$
$$728$$ 0 0
$$729$$ −9.12976e52 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −9.47786e52 + 1.64161e53i −0.962178 + 1.66654i
$$733$$ −1.47204e52 + 8.49885e51i −0.145713 + 0.0841272i −0.571084 0.820892i $$-0.693477\pi$$
0.425371 + 0.905019i $$0.360144\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 5.28868e52 9.16026e52i 0.450220 0.779805i −0.548179 0.836361i $$-0.684679\pi$$
0.998399 + 0.0565563i $$0.0180121\pi$$
$$740$$ 0 0
$$741$$ 2.14370e53i 1.73591i
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −2.30559e52 3.99340e52i −0.145695 0.252350i 0.783937 0.620840i $$-0.213208\pi$$
−0.929632 + 0.368490i $$0.879875\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 1.71150e53 5.21444e52i 0.956588 0.291444i
$$757$$ 2.19345e53 1.19634 0.598169 0.801370i $$-0.295895\pi$$
0.598169 + 0.801370i $$0.295895\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$762$$ 0 0
$$763$$ 7.37989e52 + 2.42226e53i 0.347813 + 1.14161i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 2.07354e53 1.19716e53i 0.866025 0.500000i
$$769$$ 3.55605e53i 1.44988i −0.688814 0.724938i $$-0.741868\pi$$
0.688814 0.724938i $$-0.258132\pi$$
$$770$$ 0 0
$$771$$ 0 0