# Properties

 Label 21.33.h.a.11.1 Level $21$ Weight $33$ Character 21.11 Analytic conductor $136.220$ Analytic rank $0$ Dimension $2$ CM discriminant -3 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$21 = 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$33$$ Character orbit: $$[\chi]$$ $$=$$ 21.h (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$136.219975799$$ 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 11.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 21.11 Dual form 21.33.h.a.2.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.15234e7 + 3.72796e7i) q^{3} +(-2.14748e9 + 3.71955e9i) q^{4} +(3.25760e13 + 6.57520e12i) q^{7} +(-9.26510e14 - 1.60476e15i) q^{9} +O(q^{10})$$ $$q+(-2.15234e7 + 3.72796e7i) q^{3} +(-2.14748e9 + 3.71955e9i) q^{4} +(3.25760e13 + 6.57520e12i) q^{7} +(-9.26510e14 - 1.60476e15i) q^{9} +(-9.24421e16 - 1.60114e17i) q^{12} +1.22181e17 q^{13} +(-9.22337e18 - 1.59753e19i) q^{16} +(3.91058e18 + 6.77332e18i) q^{19} +(-9.46265e20 + 1.07290e21i) q^{21} +(-1.16415e22 + 2.01637e22i) q^{25} +7.97664e22 q^{27} +(-9.44132e22 + 1.07048e23i) q^{28} +(7.06862e23 - 1.22432e24i) q^{31} +7.95866e24 q^{36} +(1.07781e25 + 1.86682e25i) q^{37} +(-2.62975e24 + 4.55487e24i) q^{39} +2.72890e26 q^{43} +7.94072e26 q^{48} +(1.01796e27 + 4.28387e26i) q^{49} +(-2.62383e26 + 4.54460e26i) q^{52} -3.36675e26 q^{57} +(1.97705e28 + 3.42436e28i) q^{61} +(-1.96303e28 - 5.83687e28i) q^{63} +7.92282e28 q^{64} +(-2.65665e27 + 4.60145e27i) q^{67} +(-3.83758e29 + 6.64688e29i) q^{73} +(-5.01130e29 - 8.67982e29i) q^{75} -3.35916e28 q^{76} +(-1.01348e30 - 1.75540e30i) q^{79} +(-1.71684e30 + 2.97366e30i) q^{81} +(-1.95861e30 - 5.82371e30i) q^{84} +(3.98018e30 + 8.03367e29i) q^{91} +(3.04281e31 + 5.27030e31i) q^{93} +1.21183e32 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 43046721q^{3} - 4294967296q^{4} + 65151959156159q^{7} - 1853020188851841q^{9} + O(q^{10})$$ $$2q - 43046721q^{3} - 4294967296q^{4} + 65151959156159q^{7} - 1853020188851841q^{9} - 184884258895036416q^{12} + 244362804407950078q^{13} - 18446744073709551616q^{16} + 7821153231347348161q^{19} -$$$$18\!\cdots\!06$$$$q^{21} -$$$$23\!\cdots\!25$$$$q^{25} +$$$$15\!\cdots\!22$$$$q^{27} -$$$$18\!\cdots\!56$$$$q^{28} +$$$$14\!\cdots\!13$$$$q^{31} +$$$$15\!\cdots\!72$$$$q^{36} +$$$$21\!\cdots\!61$$$$q^{37} -$$$$52\!\cdots\!19$$$$q^{39} +$$$$54\!\cdots\!54$$$$q^{43} +$$$$15\!\cdots\!72$$$$q^{48} +$$$$20\!\cdots\!79$$$$q^{49} -$$$$52\!\cdots\!44$$$$q^{52} -$$$$67\!\cdots\!62$$$$q^{57} +$$$$39\!\cdots\!26$$$$q^{61} -$$$$39\!\cdots\!93$$$$q^{63} +$$$$15\!\cdots\!72$$$$q^{64} -$$$$53\!\cdots\!59$$$$q^{67} -$$$$76\!\cdots\!79$$$$q^{73} -$$$$10\!\cdots\!25$$$$q^{75} -$$$$67\!\cdots\!12$$$$q^{76} -$$$$20\!\cdots\!39$$$$q^{79} -$$$$34\!\cdots\!81$$$$q^{81} -$$$$39\!\cdots\!68$$$$q^{84} +$$$$79\!\cdots\!01$$$$q^{91} +$$$$60\!\cdots\!73$$$$q^{93} +$$$$24\!\cdots\!28$$$$q^{97} + O(q^{100})$$

## Character values

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

 $$n$$ $$8$$ $$10$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$3$$ −2.15234e7 + 3.72796e7i −0.500000 + 0.866025i
$$4$$ −2.14748e9 + 3.71955e9i −0.500000 + 0.866025i
$$5$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$6$$ 0 0
$$7$$ 3.25760e13 + 6.57520e12i 0.980232 + 0.197852i
$$8$$ 0 0
$$9$$ −9.26510e14 1.60476e15i −0.500000 0.866025i
$$10$$ 0 0
$$11$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ −9.24421e16 1.60114e17i −0.500000 0.866025i
$$13$$ 1.22181e17 0.183616 0.0918082 0.995777i $$-0.470735\pi$$
0.0918082 + 0.995777i $$0.470735\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −9.22337e18 1.59753e19i −0.500000 0.866025i
$$17$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$18$$ 0 0
$$19$$ 3.91058e18 + 6.77332e18i 0.0135576 + 0.0234825i 0.872725 0.488213i $$-0.162351\pi$$
−0.859167 + 0.511695i $$0.829018\pi$$
$$20$$ 0 0
$$21$$ −9.46265e20 + 1.07290e21i −0.661461 + 0.749980i
$$22$$ 0 0
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ 0 0
$$25$$ −1.16415e22 + 2.01637e22i −0.500000 + 0.866025i
$$26$$ 0 0
$$27$$ 7.97664e22 1.00000
$$28$$ −9.44132e22 + 1.07048e23i −0.661461 + 0.749980i
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 7.06862e23 1.22432e24i 0.971734 1.68309i 0.281417 0.959585i $$-0.409195\pi$$
0.690317 0.723507i $$-0.257471\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 7.95866e24 1.00000
$$37$$ 1.07781e25 + 1.86682e25i 0.873603 + 1.51313i 0.858243 + 0.513244i $$0.171556\pi$$
0.0153605 + 0.999882i $$0.495110\pi$$
$$38$$ 0 0
$$39$$ −2.62975e24 + 4.55487e24i −0.0918082 + 0.159016i
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 2.72890e26 1.99752 0.998762 0.0497364i $$-0.0158381\pi$$
0.998762 + 0.0497364i $$0.0158381\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$48$$ 7.94072e26 1.00000
$$49$$ 1.01796e27 + 4.28387e26i 0.921709 + 0.387881i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −2.62383e26 + 4.54460e26i −0.0918082 + 0.159016i
$$53$$ 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
$$57$$ −3.36675e26 −0.0271152
$$58$$ 0 0
$$59$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$60$$ 0 0
$$61$$ 1.97705e28 + 3.42436e28i 0.537949 + 0.931755i 0.999014 + 0.0443885i $$0.0141340\pi$$
−0.461066 + 0.887366i $$0.652533\pi$$
$$62$$ 0 0
$$63$$ −1.96303e28 5.83687e28i −0.318771 0.947832i
$$64$$ 7.92282e28 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.65665e27 + 4.60145e27i −0.0161115 + 0.0279060i −0.873969 0.485982i $$-0.838462\pi$$
0.857857 + 0.513888i $$0.171795\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ −3.83758e29 + 6.64688e29i −0.590054 + 1.02200i 0.404171 + 0.914684i $$0.367560\pi$$
−0.994225 + 0.107320i $$0.965773\pi$$
$$74$$ 0 0
$$75$$ −5.01130e29 8.67982e29i −0.500000 0.866025i
$$76$$ −3.35916e28 −0.0271152
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1.01348e30 1.75540e30i −0.440334 0.762681i 0.557380 0.830257i $$-0.311807\pi$$
−0.997714 + 0.0675768i $$0.978473\pi$$
$$80$$ 0 0
$$81$$ −1.71684e30 + 2.97366e30i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ −1.95861e30 5.82371e30i −0.318771 0.947832i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$90$$ 0 0
$$91$$ 3.98018e30 + 8.03367e29i 0.179987 + 0.0363289i
$$92$$ 0 0
$$93$$ 3.04281e31 + 5.27030e31i 0.971734 + 1.68309i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1.21183e32 1.97285 0.986426 0.164204i $$-0.0525057\pi$$
0.986426 + 0.164204i $$0.0525057\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −5.00000e31 8.66025e31i −0.500000 0.866025i
$$101$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$102$$ 0 0
$$103$$ −4.30303e31 7.45307e31i −0.268151 0.464450i 0.700234 0.713914i $$-0.253079\pi$$
−0.968384 + 0.249463i $$0.919746\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$108$$ −1.71297e32 + 2.96695e32i −0.500000 + 0.866025i
$$109$$ −2.22684e32 + 3.85700e32i −0.560874 + 0.971462i 0.436546 + 0.899682i $$0.356202\pi$$
−0.997420 + 0.0717807i $$0.977132\pi$$
$$110$$ 0 0
$$111$$ −9.27923e32 −1.74721
$$112$$ −1.95419e32 5.81058e32i −0.318771 0.947832i
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.13202e32 1.96072e32i −0.0918082 0.159016i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.05569e33 1.82851e33i −0.500000 0.866025i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 3.03595e33 + 5.25842e33i 0.971734 + 1.68309i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 7.15599e33 1.56247 0.781233 0.624240i $$-0.214591\pi$$
0.781233 + 0.624240i $$0.214591\pi$$
$$128$$ 0 0
$$129$$ −5.87351e33 + 1.01732e34i −0.998762 + 1.72991i
$$130$$ 0 0
$$131$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$132$$ 0 0
$$133$$ 8.28550e31 + 2.46360e32i 0.00864355 + 0.0257007i
$$134$$ 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
$$139$$ −3.79001e34 −1.95166 −0.975829 0.218537i $$-0.929872\pi$$
−0.975829 + 0.218537i $$0.929872\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −1.70911e34 + 2.96026e34i −0.500000 + 0.866025i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −3.78800e34 + 2.87288e34i −0.796770 + 0.604283i
$$148$$ −9.25831e34 −1.74721
$$149$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$150$$ 0 0
$$151$$ −3.62428e34 + 6.27745e34i −0.496125 + 0.859314i −0.999990 0.00446863i $$-0.998578\pi$$
0.503865 + 0.863782i $$0.331911\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −1.12947e34 1.95630e34i −0.0918082 0.159016i
$$157$$ −1.35303e35 + 2.34352e35i −0.992917 + 1.71978i −0.393565 + 0.919297i $$0.628758\pi$$
−0.599352 + 0.800485i $$0.704575\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 1.77804e35 + 3.07966e35i 0.716046 + 1.24023i 0.962555 + 0.271088i $$0.0873833\pi$$
−0.246509 + 0.969141i $$0.579283\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −4.27851e35 −0.966285
$$170$$ 0 0
$$171$$ 7.24638e33 1.25511e34i 0.0135576 0.0234825i
$$172$$ −5.86027e35 + 1.01503e36i −0.998762 + 1.72991i
$$173$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$174$$ 0 0
$$175$$ −5.11815e35 + 5.80308e35i −0.661461 + 0.749980i
$$176$$ 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
$$181$$ −1.42721e36 −1.07555 −0.537777 0.843087i $$-0.680736\pi$$
−0.537777 + 0.843087i $$0.680736\pi$$
$$182$$ 0 0
$$183$$ −1.70211e36 −1.07590
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 2.59847e36 + 5.24480e35i 0.980232 + 0.197852i
$$190$$ 0 0
$$191$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ −1.70526e36 + 2.95359e36i −0.500000 + 0.866025i
$$193$$ 1.13971e36 1.97404e36i 0.307524 0.532647i −0.670296 0.742094i $$-0.733833\pi$$
0.977820 + 0.209447i $$0.0671663\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −3.77946e36 + 2.86640e36i −0.796770 + 0.604283i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 4.22546e36 7.31872e36i 0.698594 1.21000i −0.270360 0.962759i $$-0.587143\pi$$
0.968954 0.247241i $$-0.0795241\pi$$
$$200$$ 0 0
$$201$$ −1.14360e35 1.98077e35i −0.0161115 0.0279060i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.12692e36 1.95189e36i −0.0918082 0.159016i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 3.03417e37 1.96571 0.982856 0.184373i $$-0.0590256\pi$$
0.982856 + 0.184373i $$0.0590256\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 3.10769e37 3.52357e37i 1.28553 1.45756i
$$218$$ 0 0
$$219$$ −1.65195e37 2.86126e37i −0.590054 1.02200i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 2.75399e37 0.736349 0.368175 0.929757i $$-0.379983\pi$$
0.368175 + 0.929757i $$0.379983\pi$$
$$224$$ 0 0
$$225$$ 4.31440e37 1.00000
$$226$$ 0 0
$$227$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$228$$ 7.23004e35 1.25228e36i 0.0135576 0.0234825i
$$229$$ −2.14905e37 3.72226e37i −0.375732 0.650787i 0.614704 0.788758i $$-0.289275\pi$$
−0.990436 + 0.137971i $$0.955942\pi$$
$$230$$ 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
$$237$$ 8.72540e37 0.880668
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 9.57310e37 1.65811e38i 0.739231 1.28039i −0.213611 0.976919i $$-0.568523\pi$$
0.952842 0.303467i $$-0.0981441\pi$$
$$242$$ 0 0
$$243$$ −7.39044e37 1.28006e38i −0.500000 0.866025i
$$244$$ −1.69828e38 −1.07590
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 4.77800e35 + 8.27573e35i 0.00248940 + 0.00431177i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 2.59261e38 + 5.23298e37i 0.980232 + 0.197852i
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −1.70141e38 + 2.94693e38i −0.500000 + 0.866025i
$$257$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$258$$ 0 0
$$259$$ 2.28360e38 + 6.79003e38i 0.556959 + 1.65606i
$$260$$ 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
$$268$$ −1.14102e37 1.97631e37i −0.0161115 0.0279060i
$$269$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ 0 0
$$271$$ −3.66940e38 6.35560e38i −0.433598 0.751013i 0.563582 0.826060i $$-0.309423\pi$$
−0.997180 + 0.0750466i $$0.976089\pi$$
$$272$$ 0 0
$$273$$ −1.15616e38 + 1.31088e38i −0.121455 + 0.137709i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −9.66328e38 + 1.67373e39i −0.804356 + 1.39319i 0.112369 + 0.993667i $$0.464156\pi$$
−0.916725 + 0.399519i $$0.869177\pi$$
$$278$$ 0 0
$$279$$ −2.61966e39 −1.94347
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ −1.54316e39 + 2.67283e39i −0.911650 + 1.57902i −0.0999165 + 0.994996i $$0.531858\pi$$
−0.811733 + 0.584028i $$0.801476\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1.18396e39 2.05067e39i −0.500000 0.866025i
$$290$$ 0 0
$$291$$ −2.60827e39 + 4.51766e39i −0.986426 + 1.70854i
$$292$$ −1.64823e39 2.85481e39i −0.590054 1.02200i
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 4.30467e39 1.00000
$$301$$ 8.88966e39 + 1.79431e39i 1.95804 + 0.395214i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 7.21374e37 1.24946e38i 0.0135576 0.0234825i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −1.43223e38 −0.0230038 −0.0115019 0.999934i $$-0.503661\pi$$
−0.0115019 + 0.999934i $$0.503661\pi$$
$$308$$ 0 0
$$309$$ 3.70463e39 0.536301
$$310$$ 0 0
$$311$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0 0
$$313$$ −3.33486e37 5.77614e37i −0.00392978 0.00680657i 0.864054 0.503399i $$-0.167918\pi$$
−0.867984 + 0.496593i $$0.834584\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 8.70573e39 0.880668
$$317$$ 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
$$324$$ −7.37378e39 1.27718e40i −0.500000 0.866025i
$$325$$ −1.42238e39 + 2.46363e39i −0.0918082 + 0.159016i
$$326$$ 0 0
$$327$$ −9.58582e39 1.66031e40i −0.560874 0.971462i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −1.32351e40 2.29238e40i −0.637498 1.10418i −0.985980 0.166863i $$-0.946636\pi$$
0.348482 0.937315i $$-0.386697\pi$$
$$332$$ 0 0
$$333$$ 1.99720e40 3.45926e40i 0.873603 1.51313i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 2.58677e40 + 5.22118e39i 0.980232 + 0.197852i
$$337$$ −1.85065e40 −0.668723 −0.334361 0.942445i $$-0.608521\pi$$
−0.334361 + 0.942445i $$0.608521\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 3.03444e40 + 2.06484e40i 0.826746 + 0.562576i
$$344$$ 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
$$349$$ 9.32145e40 1.92432 0.962159 0.272490i $$-0.0878472\pi$$
0.962159 + 0.272490i $$0.0878472\pi$$
$$350$$ 0 0
$$351$$ 9.74598e39 0.183616
$$352$$ 0 0
$$353$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ 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
$$361$$ 4.15686e40 7.19990e40i 0.499632 0.865389i
$$362$$ 0 0
$$363$$ 9.08879e40 1.00000
$$364$$ −1.15355e40 + 1.30793e40i −0.121455 + 0.137709i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −7.21361e40 + 1.24943e41i −0.666033 + 1.15360i 0.312971 + 0.949763i $$0.398676\pi$$
−0.979004 + 0.203840i $$0.934658\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −2.61375e41 −1.94347
$$373$$ 1.58690e39 + 2.74860e39i 0.0113034 + 0.0195781i 0.871622 0.490179i $$-0.163069\pi$$
−0.860318 + 0.509757i $$0.829735\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −2.75275e41 −1.51894 −0.759468 0.650545i $$-0.774541\pi$$
−0.759468 + 0.650545i $$0.774541\pi$$
$$380$$ 0 0
$$381$$ −1.54021e41 + 2.66772e41i −0.781233 + 1.35313i
$$382$$ 0 0
$$383$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −2.52835e41 4.37923e41i −0.998762 1.72991i
$$388$$ −2.60239e41 + 4.50747e41i −0.986426 + 1.70854i
$$389$$ 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
$$397$$ 3.69470e41 + 6.39941e41i 0.970356 + 1.68071i 0.694479 + 0.719513i $$0.255635\pi$$
0.275877 + 0.961193i $$0.411032\pi$$
$$398$$ 0 0
$$399$$ −1.09675e40 2.21370e39i −0.0265792 0.00536480i
$$400$$ 4.29497e41 1.00000
$$401$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$402$$ 0 0
$$403$$ 8.63654e40 1.49589e41i 0.178426 0.309043i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −4.62140e41 + 8.00450e41i −0.753703 + 1.30545i 0.192313 + 0.981334i $$0.438401\pi$$
−0.946016 + 0.324119i $$0.894932\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 3.69627e41 0.536301
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 8.15738e41 1.41290e42i 0.975829 1.69018i
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −1.85857e42 −1.90839 −0.954194 0.299190i $$-0.903284\pi$$
−0.954194 + 0.299190i $$0.903284\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 4.18886e41 + 1.24551e42i 0.342965 + 1.01977i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$432$$ −7.35716e41 1.27430e42i −0.500000 0.866025i
$$433$$ 2.59382e42 1.69877 0.849383 0.527777i $$-0.176974\pi$$
0.849383 + 0.527777i $$0.176974\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −9.56421e41 1.65657e42i −0.560874 0.971462i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 2.75863e41 + 4.77809e41i 0.144965 + 0.251086i 0.929360 0.369175i $$-0.120360\pi$$
−0.784395 + 0.620261i $$0.787027\pi$$
$$440$$ 0 0
$$441$$ −2.55692e41 2.03049e42i −0.124939 0.992164i
$$442$$ 0 0
$$443$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$444$$ 1.99270e42 3.45146e42i 0.873603 1.51313i
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 2.58094e42 + 5.20941e41i 0.980232 + 0.197852i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −1.56014e42 2.70223e42i −0.496125 0.859314i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 3.52910e42 + 6.11258e42i 0.975000 + 1.68875i 0.679937 + 0.733271i $$0.262007\pi$$
0.295063 + 0.955478i $$0.404659\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 6.17477e42 1.38460 0.692301 0.721609i $$-0.256597\pi$$
0.692301 + 0.721609i $$0.256597\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$468$$ 9.72400e41 0.183616
$$469$$ −1.16798e41 + 1.32429e41i −0.0213143 + 0.0241667i
$$470$$ 0 0
$$471$$ −5.82435e42 1.00881e43i −0.992917 1.71978i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −1.82100e41 −0.0271152
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ 0 0
$$481$$ 1.31688e42 + 2.28091e42i 0.160408 + 0.277835i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 9.06830e42 1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −9.14159e42 + 1.58337e43i −0.913185 + 1.58168i −0.103647 + 0.994614i $$0.533051\pi$$
−0.809538 + 0.587068i $$0.800282\pi$$
$$488$$ 0 0
$$489$$ −1.53078e43 −1.43209
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −2.60786e43 −1.94347
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.19381e43 + 2.06774e43i 0.807841 + 1.39922i 0.914356 + 0.404910i $$0.132697\pi$$
−0.106515 + 0.994311i $$0.533969\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 9.20879e42 1.59501e43i 0.483143 0.836827i
$$508$$ −1.53674e43 + 2.66171e43i −0.781233 + 1.35313i
$$509$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$510$$ 0 0
$$511$$ −1.68717e43 + 1.91296e43i −0.780595 + 0.885057i
$$512$$ 0 0
$$513$$ 3.11933e41 + 5.40283e41i 0.0135576 + 0.0234825i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ −2.52265e43 4.36936e43i −0.998762 1.72991i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0 0
$$523$$ 2.89818e43 + 5.01980e43i 0.924909 + 1.60199i 0.791707 + 0.610901i $$0.209193\pi$$
0.133202 + 0.991089i $$0.457474\pi$$
$$524$$ 0 0
$$525$$ −1.06176e43 3.15704e43i −0.318771 0.947832i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −1.88045e43 + 3.25703e43i −0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −1.09428e42 2.20871e41i −0.0265792 0.00536480i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 4.84312e43 + 8.38854e43i 0.899434 + 1.55787i 0.828219 + 0.560405i $$0.189354\pi$$
0.0712152 + 0.997461i $$0.477312\pi$$
$$542$$ 0 0
$$543$$ 3.07184e43 5.32059e43i 0.537777 0.931456i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 2.05403e43 0.319750 0.159875 0.987137i $$-0.448891\pi$$
0.159875 + 0.987137i $$0.448891\pi$$
$$548$$ 0 0
$$549$$ 3.66352e43 6.34540e43i 0.537949 0.931755i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −2.14730e43 6.38477e43i −0.280731 0.834725i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 8.13899e43 1.40971e44i 0.975829 1.69018i
$$557$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$558$$ 0 0
$$559$$ 3.33421e43 0.366778
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −7.54802e43 + 8.55812e43i −0.661461 + 0.749980i
$$568$$ 0 0
$$569$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$570$$ 0 0
$$571$$ 1.05755e44 1.83173e44i 0.828176 1.43444i −0.0712925 0.997455i $$-0.522712\pi$$
0.899468 0.436987i $$-0.143954\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −7.34057e43 1.27142e44i −0.500000 0.866025i
$$577$$ −8.34478e43 + 1.44536e44i −0.552843 + 0.957552i 0.445225 + 0.895419i $$0.353124\pi$$
−0.998068 + 0.0621333i $$0.980210\pi$$
$$578$$ 0 0
$$579$$ 4.90609e43 + 8.49760e43i 0.307524 + 0.532647i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ −2.55115e43 2.02591e44i −0.124939 0.992164i
$$589$$ 1.10569e43 0.0526976
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.98821e44 3.44368e44i 0.873603 1.51313i
$$593$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 1.81892e44 + 3.15047e44i 0.698594 + 1.21000i
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ 0 0
$$601$$ 2.46883e44 0.852118 0.426059 0.904695i $$-0.359902\pi$$
0.426059 + 0.904695i $$0.359902\pi$$
$$602$$ 0 0
$$603$$ 9.84564e42 0.0322231
$$604$$ −1.55662e44 2.69614e44i −0.496125 0.859314i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 3.29972e44 + 5.71528e44i 0.971533 + 1.68274i 0.690932 + 0.722920i $$0.257201\pi$$
0.280601 + 0.959824i $$0.409466\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −3.87605e44 + 6.71351e44i −0.975038 + 1.68881i −0.295227 + 0.955427i $$0.595395\pi$$
−0.679811 + 0.733388i $$0.737938\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ −3.59678e44 + 6.22980e44i −0.774218 + 1.34098i 0.161016 + 0.986952i $$0.448523\pi$$
−0.935233 + 0.354032i $$0.884810\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 9.70208e43 0.183616
$$625$$ −2.71051e44 4.69473e44i −0.500000 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −5.81122e44 1.00653e45i −0.992917 1.71978i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1.15848e45 −1.83408 −0.917039 0.398798i $$-0.869428\pi$$
−0.917039 + 0.398798i $$0.869428\pi$$
$$632$$ 0 0
$$633$$ −6.53054e44 + 1.13112e45i −0.982856 + 1.70236i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.24376e44 + 5.23409e43i 0.169241 + 0.0712214i
$$638$$ 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
$$643$$ −4.74213e44 −0.555390 −0.277695 0.960669i $$-0.589571\pi$$
−0.277695 + 0.960669i $$0.589571\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 6.44692e44 + 1.91692e45i 0.619522 + 1.84208i
$$652$$ −1.52733e45 −1.43209
$$653$$ 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
$$657$$ 1.42222e45 1.18011
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 1.20637e45 2.08949e45i 0.908357 1.57332i 0.0920114 0.995758i $$-0.470670\pi$$
0.816346 0.577563i $$-0.195996\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −5.92750e44 + 1.02667e45i −0.368175 + 0.637697i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 3.41061e45 1.92571 0.962854 0.270022i $$-0.0870310\pi$$
0.962854 + 0.270022i $$0.0870310\pi$$
$$674$$ 0 0
$$675$$ −9.28604e44 + 1.60839e45i −0.500000 + 0.866025i
$$676$$ 9.18803e44 1.59141e45i 0.483143 0.836827i
$$677$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$678$$ 0 0
$$679$$ 3.94766e45 + 7.96804e44i 1.93385 + 0.390333i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$684$$ 3.11230e43 + 5.39065e43i 0.0135576 + 0.0234825i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.85019e45 0.751464
$$688$$ −2.51697e45 4.35951e45i −0.998762 1.72991i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −2.06721e45 3.58052e45i −0.765132 1.32525i −0.940177 0.340688i $$-0.889340\pi$$
0.175044 0.984561i $$-0.443993\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ −1.05937e45 3.14992e45i −0.318771 0.947832i
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ −8.42971e43 + 1.46007e44i −0.0236880 + 0.0410287i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −1.98784e45 3.44305e45i −0.487576 0.844507i 0.512322 0.858794i $$-0.328786\pi$$
−0.999898 + 0.0142869i $$0.995452\pi$$
$$710$$ 0 0
$$711$$ −1.87800e45 + 3.25279e45i −0.440334 + 0.762681i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$720$$ 0 0
$$721$$ −9.11700e44 2.71084e45i −0.170957 0.508323i
$$722$$ 0 0
$$723$$ 4.12091e45 + 7.13762e45i 0.739231 + 1.28039i
$$724$$ 3.06492e45 5.30860e45i 0.537777 0.931456i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 4.21369e45 0.692010 0.346005 0.938233i $$-0.387538\pi$$
0.346005 + 0.938233i $$0.387538\pi$$
$$728$$ 0 0
$$729$$ 6.36269e45 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 3.65526e45 6.33110e45i 0.537949 0.931755i
$$733$$ 3.71231e45 + 6.42992e45i 0.534541 + 0.925852i 0.999185 + 0.0403548i $$0.0128488\pi$$
−0.464644 + 0.885497i $$0.653818\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −4.83528e45 + 8.37495e45i −0.611098 + 1.05845i 0.379958 + 0.925004i $$0.375938\pi$$
−0.991056 + 0.133448i $$0.957395\pi$$
$$740$$ 0 0
$$741$$ −4.11354e43 −0.00497880
$$742$$ 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
$$751$$ 3.41961e45 + 5.92294e45i 0.333994 + 0.578494i 0.983291 0.182041i $$-0.0582703\pi$$
−0.649297 + 0.760535i $$0.724937\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −7.53100e45 + 8.53883e45i −0.661461 + 0.749980i
$$757$$ −2.32391e46 −1.99842 −0.999208 0.0397813i $$-0.987334\pi$$
−0.999208 + 0.0397813i $$0.987334\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$762$$ 0 0
$$763$$ −9.79021e45 + 1.11004e46i −0.741992 + 0.841289i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −7.32402e45 1.26856e46i −0.500000 0.866025i
$$769$$ −2.97413e46 −1.98856 −0.994281 0.106798i $$-0.965940\pi$$
−0.994281 + 0.106798i $$0.965940\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 4.89503e45 + 8.47845e45i 0.307524 + 0.532647i
$$773$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$