# Properties

 Label 3332.1.ce.b.1195.1 Level $3332$ Weight $1$ Character 3332.1195 Analytic conductor $1.663$ Analytic rank $0$ Dimension $16$ Projective image $D_{16}$ CM discriminant -4 Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3332,1,Mod(31,3332)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([24, 8, 27]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3332.31");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3332.ce (of order $$48$$, degree $$16$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$1.66288462209$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\Q(\zeta_{48})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{16} - x^{8} + 1$$ x^16 - x^8 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{16}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{16} - \cdots)$$

## Embedding invariants

 Embedding label 1195.1 Root $$-0.991445 - 0.130526i$$ of defining polynomial Character $$\chi$$ $$=$$ 3332.1195 Dual form 3332.1.ce.b.619.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.991445 + 0.130526i) q^{2} +(0.965926 + 0.258819i) q^{4} +(0.732626 - 0.835400i) q^{5} +(0.923880 + 0.382683i) q^{8} +(0.608761 + 0.793353i) q^{9} +O(q^{10})$$ $$q+(0.991445 + 0.130526i) q^{2} +(0.965926 + 0.258819i) q^{4} +(0.732626 - 0.835400i) q^{5} +(0.923880 + 0.382683i) q^{8} +(0.608761 + 0.793353i) q^{9} +(0.835400 - 0.732626i) q^{10} +(-1.00000 + 1.00000i) q^{13} +(0.866025 + 0.500000i) q^{16} +(0.608761 - 0.793353i) q^{17} +(0.500000 + 0.866025i) q^{18} +(0.923880 - 0.617317i) q^{20} +(-0.0306258 - 0.232626i) q^{25} +(-1.12197 + 0.860919i) q^{26} +(-1.63099 - 0.324423i) q^{29} +(0.793353 + 0.608761i) q^{32} +(0.707107 - 0.707107i) q^{34} +(0.382683 + 0.923880i) q^{36} +(-1.10876 + 0.0726721i) q^{37} +(0.996552 - 0.491445i) q^{40} +(-0.382683 + 0.0761205i) q^{41} +(1.10876 + 0.0726721i) q^{45} -0.234633i q^{50} +(-1.22474 + 0.707107i) q^{52} +(1.12484 - 1.46593i) q^{53} +(-1.57469 - 0.534534i) q^{58} +(-1.85747 - 0.630526i) q^{61} +(0.707107 + 0.707107i) q^{64} +(0.102774 + 1.56803i) q^{65} +(0.793353 - 0.608761i) q^{68} +(0.258819 + 0.965926i) q^{72} +(-0.534534 - 1.57469i) q^{73} +(-1.10876 - 0.0726721i) q^{74} +(1.05217 - 0.357164i) q^{80} +(-0.258819 + 0.965926i) q^{81} +(-0.389345 + 0.0255190i) q^{82} +(-0.216773 - 1.08979i) q^{85} +(1.93185 - 0.517638i) q^{89} +(1.08979 + 0.216773i) q^{90} +(-0.324423 + 1.63099i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q+O(q^{10})$$ 16 * q $$16 q - 16 q^{13} + 8 q^{18} - 8 q^{37} + 8 q^{45} - 8 q^{74}+O(q^{100})$$ 16 * q - 16 * q^13 + 8 * q^18 - 8 * q^37 + 8 * q^45 - 8 * q^74

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$885$$ $$1667$$ $$\chi(n)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.991445 + 0.130526i 0.991445 + 0.130526i
$$3$$ 0 0 −0.896873 0.442289i $$-0.854167\pi$$
0.896873 + 0.442289i $$0.145833\pi$$
$$4$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$5$$ 0.732626 0.835400i 0.732626 0.835400i −0.258819 0.965926i $$-0.583333\pi$$
0.991445 + 0.130526i $$0.0416667\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$9$$ 0.608761 + 0.793353i 0.608761 + 0.793353i
$$10$$ 0.835400 0.732626i 0.835400 0.732626i
$$11$$ 0 0 0.0654031 0.997859i $$-0.479167\pi$$
−0.0654031 + 0.997859i $$0.520833\pi$$
$$12$$ 0 0
$$13$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$17$$ 0.608761 0.793353i 0.608761 0.793353i
$$18$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$19$$ 0 0 0.130526 0.991445i $$-0.458333\pi$$
−0.130526 + 0.991445i $$0.541667\pi$$
$$20$$ 0.923880 0.617317i 0.923880 0.617317i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 −0.442289 0.896873i $$-0.645833\pi$$
0.442289 + 0.896873i $$0.354167\pi$$
$$24$$ 0 0
$$25$$ −0.0306258 0.232626i −0.0306258 0.232626i
$$26$$ −1.12197 + 0.860919i −1.12197 + 0.860919i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −1.63099 0.324423i −1.63099 0.324423i −0.707107 0.707107i $$-0.750000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.442289 0.896873i $$-0.354167\pi$$
−0.442289 + 0.896873i $$0.645833\pi$$
$$32$$ 0.793353 + 0.608761i 0.793353 + 0.608761i
$$33$$ 0 0
$$34$$ 0.707107 0.707107i 0.707107 0.707107i
$$35$$ 0 0
$$36$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$37$$ −1.10876 + 0.0726721i −1.10876 + 0.0726721i −0.608761 0.793353i $$-0.708333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0.996552 0.491445i 0.996552 0.491445i
$$41$$ −0.382683 + 0.0761205i −0.382683 + 0.0761205i −0.382683 0.923880i $$-0.625000\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$44$$ 0 0
$$45$$ 1.10876 + 0.0726721i 1.10876 + 0.0726721i
$$46$$ 0 0
$$47$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0.234633i 0.234633i
$$51$$ 0 0
$$52$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$53$$ 1.12484 1.46593i 1.12484 1.46593i 0.258819 0.965926i $$-0.416667\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −1.57469 0.534534i −1.57469 0.534534i
$$59$$ 0 0 0.991445 0.130526i $$-0.0416667\pi$$
−0.991445 + 0.130526i $$0.958333\pi$$
$$60$$ 0 0
$$61$$ −1.85747 0.630526i −1.85747 0.630526i −0.991445 0.130526i $$-0.958333\pi$$
−0.866025 0.500000i $$-0.833333\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$65$$ 0.102774 + 1.56803i 0.102774 + 1.56803i
$$66$$ 0 0
$$67$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$68$$ 0.793353 0.608761i 0.793353 0.608761i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.555570 0.831470i $$-0.687500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$72$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$73$$ −0.534534 1.57469i −0.534534 1.57469i −0.793353 0.608761i $$-0.791667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$74$$ −1.10876 0.0726721i −1.10876 0.0726721i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.896873 0.442289i $$-0.145833\pi$$
−0.896873 + 0.442289i $$0.854167\pi$$
$$80$$ 1.05217 0.357164i 1.05217 0.357164i
$$81$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$82$$ −0.389345 + 0.0255190i −0.389345 + 0.0255190i
$$83$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$84$$ 0 0
$$85$$ −0.216773 1.08979i −0.216773 1.08979i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1.93185 0.517638i 1.93185 0.517638i 0.965926 0.258819i $$-0.0833333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$90$$ 1.08979 + 0.216773i 1.08979 + 0.216773i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −0.324423 + 1.63099i −0.324423 + 1.63099i 0.382683 + 0.923880i $$0.375000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0.0306258 0.232626i 0.0306258 0.232626i
$$101$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$102$$ 0 0
$$103$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$104$$ −1.30656 + 0.541196i −1.30656 + 0.541196i
$$105$$ 0 0
$$106$$ 1.30656 1.30656i 1.30656 1.30656i
$$107$$ 0 0 −0.751840 0.659346i $$-0.770833\pi$$
0.751840 + 0.659346i $$0.229167\pi$$
$$108$$ 0 0
$$109$$ 1.47479 1.29335i 1.47479 1.29335i 0.608761 0.793353i $$-0.291667\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −0.324423 0.216773i −0.324423 0.216773i 0.382683 0.923880i $$-0.375000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −1.49144 0.735499i −1.49144 0.735499i
$$117$$ −1.40211 0.184592i −1.40211 0.184592i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.991445 0.130526i −0.991445 0.130526i
$$122$$ −1.75928 0.867580i −1.75928 0.867580i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0.707107 + 0.472474i 0.707107 + 0.472474i
$$126$$ 0 0
$$127$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$128$$ 0.608761 + 0.793353i 0.608761 + 0.793353i
$$129$$ 0 0
$$130$$ −0.102774 + 1.56803i −0.102774 + 1.56803i
$$131$$ 0 0 −0.751840 0.659346i $$-0.770833\pi$$
0.751840 + 0.659346i $$0.229167\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0.866025 0.500000i 0.866025 0.500000i
$$137$$ −0.923880 1.60021i −0.923880 1.60021i −0.793353 0.608761i $$-0.791667\pi$$
−0.130526 0.991445i $$-0.541667\pi$$
$$138$$ 0 0
$$139$$ 0 0 0.831470 0.555570i $$-0.187500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0.130526 + 0.991445i 0.130526 + 0.991445i
$$145$$ −1.46593 + 1.12484i −1.46593 + 1.12484i
$$146$$ −0.324423 1.63099i −0.324423 1.63099i
$$147$$ 0 0
$$148$$ −1.08979 0.216773i −1.08979 0.216773i
$$149$$ −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i $$-0.833333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$150$$ 0 0
$$151$$ 0 0 −0.793353 0.608761i $$-0.791667\pi$$
0.793353 + 0.608761i $$0.208333\pi$$
$$152$$ 0 0
$$153$$ 1.00000 1.00000
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −0.198092 + 0.739288i −0.198092 + 0.739288i 0.793353 + 0.608761i $$0.208333\pi$$
−0.991445 + 0.130526i $$0.958333\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 1.08979 0.216773i 1.08979 0.216773i
$$161$$ 0 0
$$162$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$163$$ 0 0 0.321439 0.946930i $$-0.395833\pi$$
−0.321439 + 0.946930i $$0.604167\pi$$
$$164$$ −0.389345 0.0255190i −0.389345 0.0255190i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.555570 0.831470i $$-0.687500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$168$$ 0 0
$$169$$ 1.00000i 1.00000i
$$170$$ −0.0726721 1.10876i −0.0726721 1.10876i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0.0255190 + 0.389345i 0.0255190 + 0.389345i 0.991445 + 0.130526i $$0.0416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 1.98289 0.261052i 1.98289 0.261052i
$$179$$ 0 0 0.991445 0.130526i $$-0.0416667\pi$$
−0.991445 + 0.130526i $$0.958333\pi$$
$$180$$ 1.05217 + 0.357164i 1.05217 + 0.357164i
$$181$$ −1.08979 + 1.63099i −1.08979 + 1.63099i −0.382683 + 0.923880i $$0.625000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −0.751597 + 0.979500i −0.751597 + 0.979500i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$192$$ 0 0
$$193$$ 1.10876 + 0.0726721i 1.10876 + 0.0726721i 0.608761 0.793353i $$-0.291667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$194$$ −0.534534 + 1.57469i −0.534534 + 1.57469i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −0.382683 + 0.0761205i −0.382683 + 0.0761205i −0.382683 0.923880i $$-0.625000\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 0.946930 0.321439i $$-0.104167\pi$$
−0.946930 + 0.321439i $$0.895833\pi$$
$$200$$ 0.0607275 0.226638i 0.0607275 0.226638i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −0.216773 + 0.375461i −0.216773 + 0.375461i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.36603 + 0.366025i −1.36603 + 0.366025i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 −0.195090 0.980785i $$-0.562500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$212$$ 1.46593 1.12484i 1.46593 1.12484i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 1.63099 1.08979i 1.63099 1.08979i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0.184592 + 1.40211i 0.184592 + 1.40211i
$$222$$ 0 0
$$223$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$224$$ 0 0
$$225$$ 0.165911 0.165911i 0.165911 0.165911i
$$226$$ −0.293353 0.257264i −0.293353 0.257264i
$$227$$ 0 0 0.0654031 0.997859i $$-0.479167\pi$$
−0.0654031 + 0.997859i $$0.520833\pi$$
$$228$$ 0 0
$$229$$ 1.12484 + 1.46593i 1.12484 + 1.46593i 0.866025 + 0.500000i $$0.166667\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −1.38268 0.923880i −1.38268 0.923880i
$$233$$ 1.29335 1.47479i 1.29335 1.47479i 0.500000 0.866025i $$-0.333333\pi$$
0.793353 0.608761i $$-0.208333\pi$$
$$234$$ −1.36603 0.366025i −1.36603 0.366025i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 1.49144 + 0.735499i 1.49144 + 0.735499i 0.991445 0.130526i $$-0.0416667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$242$$ −0.965926 0.258819i −0.965926 0.258819i
$$243$$ 0 0
$$244$$ −1.63099 1.08979i −1.63099 1.08979i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0.639387 + 0.560728i 0.639387 + 0.560728i
$$251$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$257$$ −0.241181 + 1.83195i −0.241181 + 1.83195i 0.258819 + 0.965926i $$0.416667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −0.306563 + 1.54120i −0.306563 + 1.54120i
$$261$$ −0.735499 1.49144i −0.735499 1.49144i
$$262$$ 0 0
$$263$$ 0 0 −0.130526 0.991445i $$-0.541667\pi$$
0.130526 + 0.991445i $$0.458333\pi$$
$$264$$ 0 0
$$265$$ −0.400544 2.01367i −0.400544 2.01367i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −0.735499 + 1.49144i −0.735499 + 1.49144i 0.130526 + 0.991445i $$0.458333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$272$$ 0.923880 0.382683i 0.923880 0.382683i
$$273$$ 0 0
$$274$$ −0.707107 1.70711i −0.707107 1.70711i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −1.85747 + 0.630526i −1.85747 + 0.630526i −0.866025 + 0.500000i $$0.833333\pi$$
−0.991445 + 0.130526i $$0.958333\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −0.707107 + 1.70711i −0.707107 + 1.70711i 1.00000i $$0.5\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.997859 0.0654031i $$-0.979167\pi$$
0.997859 + 0.0654031i $$0.0208333\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000i 1.00000i
$$289$$ −0.258819 0.965926i −0.258819 0.965926i
$$290$$ −1.60021 + 0.923880i −1.60021 + 0.923880i
$$291$$ 0 0
$$292$$ −0.108761 1.65938i −0.108761 1.65938i
$$293$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −1.05217 0.357164i −1.05217 0.357164i
$$297$$ 0 0
$$298$$ −1.40211 + 0.184592i −1.40211 + 0.184592i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −1.88757 + 1.08979i −1.88757 + 1.08979i
$$306$$ 0.991445 + 0.130526i 0.991445 + 0.130526i
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.321439 0.946930i $$-0.604167\pi$$
0.321439 + 0.946930i $$0.395833\pi$$
$$312$$ 0 0
$$313$$ 0.630526 1.85747i 0.630526 1.85747i 0.130526 0.991445i $$-0.458333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$314$$ −0.292893 + 0.707107i −0.292893 + 0.707107i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.49144 0.735499i 1.49144 0.735499i 0.500000 0.866025i $$-0.333333\pi$$
0.991445 + 0.130526i $$0.0416667\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 1.10876 0.0726721i 1.10876 0.0726721i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$325$$ 0.263252 + 0.202000i 0.263252 + 0.202000i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ −0.382683 0.0761205i −0.382683 0.0761205i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 0.793353 0.608761i $$-0.208333\pi$$
−0.793353 + 0.608761i $$0.791667\pi$$
$$332$$ 0 0
$$333$$ −0.732626 0.835400i −0.732626 0.835400i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0.324423 0.216773i 0.324423 0.216773i −0.382683 0.923880i $$-0.625000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$338$$ 0.130526 0.991445i 0.130526 0.991445i
$$339$$ 0 0
$$340$$ 0.0726721 1.10876i 0.0726721 1.10876i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −0.0255190 + 0.389345i −0.0255190 + 0.389345i
$$347$$ 0 0 0.751840 0.659346i $$-0.229167\pi$$
−0.751840 + 0.659346i $$0.770833\pi$$
$$348$$ 0 0
$$349$$ −1.84776 0.765367i −1.84776 0.765367i −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 0.382683i $$-0.875000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −1.78480 0.478235i −1.78480 0.478235i −0.793353 0.608761i $$-0.791667\pi$$
−0.991445 + 0.130526i $$0.958333\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 2.00000 2.00000
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 −0.991445 0.130526i $$-0.958333\pi$$
0.991445 + 0.130526i $$0.0416667\pi$$
$$360$$ 0.996552 + 0.491445i 0.996552 + 0.491445i
$$361$$ −0.965926 0.258819i −0.965926 0.258819i
$$362$$ −1.29335 + 1.47479i −1.29335 + 1.47479i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1.70711 0.707107i −1.70711 0.707107i
$$366$$ 0 0
$$367$$ 0 0 0.751840 0.659346i $$-0.229167\pi$$
−0.751840 + 0.659346i $$0.770833\pi$$
$$368$$ 0 0
$$369$$ −0.293353 0.257264i −0.293353 0.257264i
$$370$$ −0.873017 + 0.873017i −0.873017 + 0.873017i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −0.662827 0.382683i −0.662827 0.382683i 0.130526 0.991445i $$-0.458333\pi$$
−0.793353 + 0.608761i $$0.791667\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 1.95541 1.30656i 1.95541 1.30656i
$$378$$ 0 0
$$379$$ 0 0 0.195090 0.980785i $$-0.437500\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.793353 0.608761i $$-0.208333\pi$$
−0.793353 + 0.608761i $$0.791667\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 1.08979 + 0.216773i 1.08979 + 0.216773i
$$387$$ 0 0
$$388$$ −0.735499 + 1.49144i −0.735499 + 1.49144i
$$389$$ 1.12197 + 0.860919i 1.12197 + 0.860919i 0.991445 0.130526i $$-0.0416667\pi$$
0.130526 + 0.991445i $$0.458333\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −0.389345 + 0.0255190i −0.389345 + 0.0255190i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0.349942 0.172572i 0.349942 0.172572i −0.258819 0.965926i $$-0.583333\pi$$
0.608761 + 0.793353i $$0.291667\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0.0897902 0.216773i 0.0897902 0.216773i
$$401$$ −0.357164 + 1.05217i −0.357164 + 1.05217i 0.608761 + 0.793353i $$0.291667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0.617317 + 0.923880i 0.617317 + 0.923880i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0.662827 0.382683i 0.662827 0.382683i −0.130526 0.991445i $$-0.541667\pi$$
0.793353 + 0.608761i $$0.208333\pi$$
$$410$$ −0.263926 + 0.343955i −0.263926 + 0.343955i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −1.40211 + 0.184592i −1.40211 + 0.184592i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 0.555570 0.831470i $$-0.312500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$420$$ 0 0
$$421$$ 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i $$-0.125000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 1.60021 0.923880i 1.60021 0.923880i
$$425$$ −0.203198 0.117317i −0.203198 0.117317i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.997859 0.0654031i $$-0.979167\pi$$
0.997859 + 0.0654031i $$0.0208333\pi$$
$$432$$ 0 0
$$433$$ 0.292893 0.707107i 0.292893 0.707107i −0.707107 0.707107i $$-0.750000\pi$$
1.00000 $$0$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.75928 0.867580i 1.75928 0.867580i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 0.997859 0.0654031i $$-0.0208333\pi$$
−0.997859 + 0.0654031i $$0.979167\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 1.41421i 1.41421i
$$443$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$444$$ 0 0
$$445$$ 0.982890 1.99310i 0.982890 1.99310i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.324423 + 1.63099i 0.324423 + 1.63099i 0.707107 + 0.707107i $$0.250000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$450$$ 0.186147 0.142836i 0.186147 0.142836i
$$451$$ 0 0
$$452$$ −0.257264 0.293353i −0.257264 0.293353i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.184592 1.40211i 0.184592 1.40211i −0.608761 0.793353i $$-0.708333\pi$$
0.793353 0.608761i $$-0.208333\pi$$
$$458$$ 0.923880 + 1.60021i 0.923880 + 1.60021i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$462$$ 0 0
$$463$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$464$$ −1.25026 1.09645i −1.25026 1.09645i
$$465$$ 0 0
$$466$$ 1.47479 1.29335i 1.47479 1.29335i
$$467$$ 0 0 −0.608761 0.793353i $$-0.708333\pi$$
0.608761 + 0.793353i $$0.291667\pi$$
$$468$$ −1.30656 0.541196i −1.30656 0.541196i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 1.84776 1.84776
$$478$$ 0 0
$$479$$ 0 0 −0.896873 0.442289i $$-0.854167\pi$$
0.896873 + 0.442289i $$0.145833\pi$$
$$480$$ 0 0
$$481$$ 1.03609 1.18143i 1.03609 1.18143i
$$482$$ 1.38268 + 0.923880i 1.38268 + 0.923880i
$$483$$ 0 0
$$484$$ −0.923880 0.382683i −0.923880 0.382683i
$$485$$ 1.12484 + 1.46593i 1.12484 + 1.46593i
$$486$$ 0 0
$$487$$ 0 0 0.0654031 0.997859i $$-0.479167\pi$$
−0.0654031 + 0.997859i $$0.520833\pi$$
$$488$$ −1.47479 1.29335i −1.47479 1.29335i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$492$$ 0 0
$$493$$ −1.25026 + 1.09645i −1.25026 + 1.09645i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 −0.442289 0.896873i $$-0.645833\pi$$
0.442289 + 0.896873i $$0.354167\pi$$
$$500$$ 0.560728 + 0.639387i 0.560728 + 0.639387i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 −0.195090 0.980785i $$-0.562500\pi$$
0.195090 + 0.980785i $$0.437500\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i $$-0.458333\pi$$
0.793353 0.608761i $$-0.208333\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$513$$ 0 0
$$514$$ −0.478235 + 1.78480i −0.478235 + 1.78480i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −0.505107 + 1.48800i −0.505107 + 1.48800i
$$521$$ 0.389345 + 0.0255190i 0.389345 + 0.0255190i 0.258819 0.965926i $$-0.416667\pi$$
0.130526 + 0.991445i $$0.458333\pi$$
$$522$$ −0.534534 1.57469i −0.534534 1.57469i
$$523$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −0.608761 + 0.793353i −0.608761 + 0.793353i
$$530$$ −0.134280 2.04872i −0.134280 2.04872i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0.306563 0.458804i 0.306563 0.458804i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −0.923880 + 1.38268i −0.923880 + 1.38268i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0.0255190 + 0.389345i 0.0255190 + 0.389345i 0.991445 + 0.130526i $$0.0416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0.965926 0.258819i 0.965926 0.258819i
$$545$$ 2.17958i 2.17958i
$$546$$ 0 0
$$547$$ 0 0 −0.555570 0.831470i $$-0.687500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$548$$ −0.478235 1.78480i −0.478235 1.78480i
$$549$$ −0.630526 1.85747i −0.630526 1.85747i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −1.92388 + 0.382683i −1.92388 + 0.382683i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0.198092 0.739288i 0.198092 0.739288i −0.793353 0.608761i $$-0.791667\pi$$
0.991445 0.130526i $$-0.0416667\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −0.923880 + 1.60021i −0.923880 + 1.60021i
$$563$$ 0 0 −0.793353 0.608761i $$-0.791667\pi$$
0.793353 + 0.608761i $$0.208333\pi$$
$$564$$ 0 0
$$565$$ −0.418773 + 0.112210i −0.418773 + 0.112210i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0.607206 0.465926i 0.607206 0.465926i −0.258819 0.965926i $$-0.583333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$570$$ 0 0
$$571$$ 0 0 −0.659346 0.751840i $$-0.729167\pi$$
0.659346 + 0.751840i $$0.270833\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.130526 + 0.991445i −0.130526 + 0.991445i
$$577$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$578$$ −0.130526 0.991445i −0.130526 0.991445i
$$579$$ 0 0
$$580$$ −1.70711 + 0.707107i −1.70711 + 0.707107i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0.108761 1.65938i 0.108761 1.65938i
$$585$$ −1.18143 + 1.03609i −1.18143 + 1.03609i
$$586$$ −0.465926 0.607206i −0.465926 0.607206i
$$587$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −0.996552 0.491445i −0.996552 0.491445i
$$593$$ 0 0 0.130526 0.991445i $$-0.458333\pi$$
−0.130526 + 0.991445i $$0.541667\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −1.41421 −1.41421
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$600$$ 0 0
$$601$$ 1.63099 + 1.08979i 1.63099 + 1.08979i 0.923880 + 0.382683i $$0.125000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −0.835400 + 0.732626i −0.835400 + 0.732626i
$$606$$ 0 0
$$607$$ 0 0 −0.751840 0.659346i $$-0.770833\pi$$
0.751840 + 0.659346i $$0.229167\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −2.01367 + 0.834089i −2.01367 + 0.834089i
$$611$$ 0 0
$$612$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$613$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −0.382683 + 1.92388i −0.382683 + 1.92388i 1.00000i $$0.5\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.659346 0.751840i $$-0.729167\pi$$
0.659346 + 0.751840i $$0.270833\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.13939 0.305298i 1.13939 0.305298i
$$626$$ 0.867580 1.75928i 0.867580 1.75928i
$$627$$ 0 0
$$628$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$629$$ −0.617317 + 0.923880i −0.617317 + 0.923880i
$$630$$ 0 0
$$631$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 1.57469 0.534534i 1.57469 0.534534i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 1.10876 + 0.0726721i 1.10876 + 0.0726721i
$$641$$ 0.630526 + 1.85747i 0.630526 + 1.85747i 0.500000 + 0.866025i $$0.333333\pi$$
0.130526 + 0.991445i $$0.458333\pi$$
$$642$$ 0 0
$$643$$ 0 0 −0.555570 0.831470i $$-0.687500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$648$$ −0.608761 + 0.793353i −0.608761 + 0.793353i
$$649$$ 0 0
$$650$$ 0.234633 + 0.234633i 0.234633 + 0.234633i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.05217 + 0.357164i 1.05217 + 0.357164i 0.793353 0.608761i $$-0.208333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −0.369474 0.125419i −0.369474 0.125419i
$$657$$ 0.923880 1.38268i 0.923880 1.38268i
$$658$$ 0 0
$$659$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$660$$ 0 0
$$661$$ 0.860919 1.12197i 0.860919 1.12197i −0.130526 0.991445i $$-0.541667\pi$$
0.991445 0.130526i $$-0.0416667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −0.617317 0.923880i −0.617317 0.923880i
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0.382683 0.0761205i 0.382683 0.0761205i 1.00000i $$-0.5\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$674$$ 0.349942 0.172572i 0.349942 0.172572i
$$675$$ 0 0
$$676$$ 0.258819 0.965926i 0.258819 0.965926i
$$677$$ 1.65938 0.108761i 1.65938 0.108761i 0.793353 0.608761i $$-0.208333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0.216773 1.08979i 0.216773 1.08979i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.442289 0.896873i $$-0.354167\pi$$
−0.442289 + 0.896873i $$0.645833\pi$$
$$684$$ 0 0
$$685$$ −2.01367 0.400544i −2.01367 0.400544i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0.341081 + 2.59077i 0.341081 + 2.59077i
$$690$$ 0 0
$$691$$ 0 0 −0.442289 0.896873i $$-0.645833\pi$$
0.442289 + 0.896873i $$0.354167\pi$$
$$692$$ −0.0761205 + 0.382683i −0.0761205 + 0.382683i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −0.172572 + 0.349942i −0.172572 + 0.349942i
$$698$$ −1.73205 1.00000i −1.73205 1.00000i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −1.70711 0.707107i −1.70711 0.707107i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −1.09645 + 1.25026i −1.09645 + 1.25026i −0.130526 + 0.991445i $$0.541667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 1.98289 + 0.261052i 1.98289 + 0.261052i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.659346 0.751840i $$-0.270833\pi$$
−0.659346 + 0.751840i $$0.729167\pi$$
$$720$$ 0.923880 + 0.617317i 0.923880 + 0.617317i
$$721$$ 0 0
$$722$$ −0.923880 0.382683i −0.923880 0.382683i
$$723$$ 0 0
$$724$$ −1.47479 + 1.29335i −1.47479 + 1.29335i
$$725$$ −0.0255190 + 0.389345i −0.0255190 + 0.389345i
$$726$$ 0 0
$$727$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$728$$ 0 0
$$729$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$730$$ −1.60021 0.923880i −1.60021 0.923880i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −0.261052 + 1.98289i −0.261052 + 1.98289i −0.130526 + 0.991445i $$0.541667\pi$$
−0.130526 + 0.991445i $$0.541667\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ −0.257264 0.293353i −0.257264 0.293353i
$$739$$ 0 0 −0.130526 0.991445i $$-0.541667\pi$$
0.130526 + 0.991445i $$0.458333\pi$$
$$740$$ −0.979500 + 0.751597i −0.979500 + 0.751597i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.980785 0.195090i $$-0.937500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$744$$ 0 0
$$745$$ −0.695008 + 1.40934i −0.695008 + 1.40934i
$$746$$ −0.607206 0.465926i −0.607206 0.465926i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.997859 0.0654031i $$-0.0208333\pi$$
−0.997859 + 0.0654031i $$0.979167\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 2.10922 1.04015i 2.10922 1.04015i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i $$0.166667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0.732626 0.835400i 0.732626 0.835400i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 1.05217 + 0.357164i 1.05217 + 0.357164i
$$773$$ 1.83195 0.241181i 1.83195 0.241181i 0.866025 0.500000i $$-0.166667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −0.923880 + 1.38268i −0.923880 + 1.38268i
$$777$$ 0 0
$$778$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0.472474 + 0.707107i 0.472474 + 0.707107i
$$786$$ 0 0
$$787$$ 0 0 −0.321439 0.946930i $$-0.604167\pi$$
0.321439 + 0.946930i $$0.395833\pi$$
$$788$$ −0.389345 0.0255190i −0.389345 0.0255190i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 2.48800 1.22694i 2.48800 1.22694i
$$794$$ 0.369474 0.125419i 0.369474 0.125419i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0.541196 + 1.30656i 0.541196