# Properties

 Label 2001.1.i.b.1172.1 Level 2001 Weight 1 Character 2001.1172 Analytic conductor 0.999 Analytic rank 0 Dimension 2 Projective image $$D_{4}$$ CM disc. -23 Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ = $$2001 = 3 \cdot 23 \cdot 29$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 2001.i (of order $$4$$ and degree $$2$$)

## Newform invariants

 Self dual: No Analytic conductor: $$0.998629090279$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Projective image $$D_{4}$$ Projective field Galois closure of 4.0.116116029.1

## Embedding invariants

 Embedding label 1172.1 Root $$1.00000i$$ Character $$\chi$$ = 2001.1172 Dual form 2001.1.i.b.1931.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q$$$$+(1.00000 - 1.00000i) q^{2}$$ $$+1.00000i q^{3}$$ $$-1.00000i q^{4}$$ $$+(1.00000 + 1.00000i) q^{6}$$ $$-1.00000 q^{9}$$ $$+O(q^{10})$$ $$q$$$$+(1.00000 - 1.00000i) q^{2}$$ $$+1.00000i q^{3}$$ $$-1.00000i q^{4}$$ $$+(1.00000 + 1.00000i) q^{6}$$ $$-1.00000 q^{9}$$ $$+1.00000 q^{12}$$ $$+2.00000i q^{13}$$ $$+1.00000 q^{16}$$ $$+(-1.00000 + 1.00000i) q^{18}$$ $$+1.00000i q^{23}$$ $$+1.00000 q^{25}$$ $$+(2.00000 + 2.00000i) q^{26}$$ $$-1.00000i q^{27}$$ $$-1.00000i q^{29}$$ $$+(-1.00000 - 1.00000i) q^{31}$$ $$+(1.00000 - 1.00000i) q^{32}$$ $$+1.00000i q^{36}$$ $$-2.00000 q^{39}$$ $$+(-1.00000 - 1.00000i) q^{41}$$ $$+(1.00000 + 1.00000i) q^{46}$$ $$+(1.00000 + 1.00000i) q^{47}$$ $$+1.00000i q^{48}$$ $$+1.00000 q^{49}$$ $$+(1.00000 - 1.00000i) q^{50}$$ $$+2.00000 q^{52}$$ $$+(-1.00000 - 1.00000i) q^{54}$$ $$+(-1.00000 - 1.00000i) q^{58}$$ $$-2.00000i q^{59}$$ $$-2.00000 q^{62}$$ $$-1.00000i q^{64}$$ $$-1.00000 q^{69}$$ $$+(-1.00000 + 1.00000i) q^{73}$$ $$+1.00000i q^{75}$$ $$+(-2.00000 + 2.00000i) q^{78}$$ $$+1.00000 q^{81}$$ $$-2.00000 q^{82}$$ $$+1.00000 q^{87}$$ $$+1.00000 q^{92}$$ $$+(1.00000 - 1.00000i) q^{93}$$ $$+2.00000 q^{94}$$ $$+(1.00000 + 1.00000i) q^{96}$$ $$+(1.00000 - 1.00000i) q^{98}$$ $$+O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q$$ $$\mathstrut +\mathstrut 2q^{2}$$ $$\mathstrut +\mathstrut 2q^{6}$$ $$\mathstrut -\mathstrut 2q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$2q$$ $$\mathstrut +\mathstrut 2q^{2}$$ $$\mathstrut +\mathstrut 2q^{6}$$ $$\mathstrut -\mathstrut 2q^{9}$$ $$\mathstrut +\mathstrut 2q^{12}$$ $$\mathstrut +\mathstrut 2q^{16}$$ $$\mathstrut -\mathstrut 2q^{18}$$ $$\mathstrut +\mathstrut 2q^{25}$$ $$\mathstrut +\mathstrut 4q^{26}$$ $$\mathstrut -\mathstrut 2q^{31}$$ $$\mathstrut +\mathstrut 2q^{32}$$ $$\mathstrut -\mathstrut 4q^{39}$$ $$\mathstrut -\mathstrut 2q^{41}$$ $$\mathstrut +\mathstrut 2q^{46}$$ $$\mathstrut +\mathstrut 2q^{47}$$ $$\mathstrut +\mathstrut 2q^{49}$$ $$\mathstrut +\mathstrut 2q^{50}$$ $$\mathstrut +\mathstrut 4q^{52}$$ $$\mathstrut -\mathstrut 2q^{54}$$ $$\mathstrut -\mathstrut 2q^{58}$$ $$\mathstrut -\mathstrut 4q^{62}$$ $$\mathstrut -\mathstrut 2q^{69}$$ $$\mathstrut -\mathstrut 2q^{73}$$ $$\mathstrut -\mathstrut 4q^{78}$$ $$\mathstrut +\mathstrut 2q^{81}$$ $$\mathstrut -\mathstrut 4q^{82}$$ $$\mathstrut +\mathstrut 2q^{87}$$ $$\mathstrut +\mathstrut 2q^{92}$$ $$\mathstrut +\mathstrut 2q^{93}$$ $$\mathstrut +\mathstrut 4q^{94}$$ $$\mathstrut +\mathstrut 2q^{96}$$ $$\mathstrut +\mathstrut 2q^{98}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Character Values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$$.

 $$n$$ $$553$$ $$668$$ $$1132$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$3$$ 1.00000i 1.00000i
$$4$$ 1.00000i 1.00000i
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$12$$ 1.00000 1.00000
$$13$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$18$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$19$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.00000i 1.00000i
$$24$$ 0 0
$$25$$ 1.00000 1.00000
$$26$$ 2.00000 + 2.00000i 2.00000 + 2.00000i
$$27$$ 1.00000i 1.00000i
$$28$$ 0 0
$$29$$ 1.00000i 1.00000i
$$30$$ 0 0
$$31$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$32$$ 1.00000 1.00000i 1.00000 1.00000i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000i 1.00000i
$$37$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$38$$ 0 0
$$39$$ −2.00000 −2.00000
$$40$$ 0 0
$$41$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$47$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$48$$ 1.00000i 1.00000i
$$49$$ 1.00000 1.00000
$$50$$ 1.00000 1.00000i 1.00000 1.00000i
$$51$$ 0 0
$$52$$ 2.00000 2.00000
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ −1.00000 1.00000i −1.00000 1.00000i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −1.00000 1.00000i −1.00000 1.00000i
$$59$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$62$$ −2.00000 −2.00000
$$63$$ 0 0
$$64$$ 1.00000i 1.00000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ −1.00000 −1.00000
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 1.00000i 1.00000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ −2.00000 + 2.00000i −2.00000 + 2.00000i
$$79$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$80$$ 0 0
$$81$$ 1.00000 1.00000
$$82$$ −2.00000 −2.00000
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 1.00000 1.00000
$$88$$ 0 0
$$89$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 1.00000 1.00000
$$93$$ 1.00000 1.00000i 1.00000 1.00000i
$$94$$ 2.00000 2.00000
$$95$$ 0 0
$$96$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$97$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$98$$ 1.00000 1.00000i 1.00000 1.00000i
$$99$$ 0 0
$$100$$ 1.00000i 1.00000i
$$101$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ −1.00000 −1.00000
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −1.00000 −1.00000
$$117$$ 2.00000i 2.00000i
$$118$$ −2.00000 2.00000i −2.00000 2.00000i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000i 1.00000i
$$122$$ 0 0
$$123$$ 1.00000 1.00000i 1.00000 1.00000i
$$124$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$138$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −1.00000 −1.00000
$$145$$ 0 0
$$146$$ 2.00000i 2.00000i
$$147$$ 1.00000i 1.00000i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$151$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 2.00000i 2.00000i
$$157$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000 1.00000i 1.00000 1.00000i
$$163$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$164$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −3.00000 −3.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$174$$ 1.00000 1.00000i 1.00000 1.00000i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 2.00000 2.00000
$$178$$ 0 0
$$179$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 2.00000i 2.00000i
$$187$$ 0 0
$$188$$ 1.00000 1.00000i 1.00000 1.00000i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$192$$ 1.00000 1.00000
$$193$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 1.00000i 1.00000i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 2.00000i 2.00000i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 1.00000i 1.00000i
$$208$$ 2.00000i 2.00000i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −1.00000 1.00000i −1.00000 1.00000i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −1.00000
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ −2.00000 2.00000i −2.00000 2.00000i
$$235$$ 0 0
$$236$$ −2.00000 −2.00000
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ −1.00000 1.00000i −1.00000 1.00000i
$$243$$ 1.00000i 1.00000i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 2.00000i 2.00000i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −2.00000 −2.00000
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 1.00000i 1.00000i
$$262$$ −2.00000 −2.00000
$$263$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 1.00000i 1.00000i
$$277$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$278$$ 0 0
$$279$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 2.00000i 2.00000i
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$289$$ 1.00000i 1.00000i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$293$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$294$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −2.00000 −2.00000
$$300$$ 1.00000 1.00000
$$301$$ 0 0
$$302$$ −2.00000 2.00000i −2.00000 2.00000i
$$303$$ −1.00000 1.00000i −1.00000 1.00000i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000i 1.00000i
$$325$$ 2.00000i 2.00000i
$$326$$ 2.00000i 2.00000i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −2.00000 + 2.00000i −2.00000 + 2.00000i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$338$$ −3.00000 + 3.00000i −3.00000 + 3.00000i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 2.00000 2.00000i 2.00000 2.00000i
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 1.00000i 1.00000i
$$349$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$350$$ 0 0
$$351$$ 2.00000 2.00000
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 2.00000 2.00000i 2.00000 2.00000i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 2.00000 2.00000i 2.00000 2.00000i
$$359$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$360$$ 0 0
$$361$$ 1.00000i 1.00000i
$$362$$ 0 0
$$363$$ 1.00000 1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$368$$ 1.00000i 1.00000i
$$369$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −1.00000 1.00000i −1.00000 1.00000i
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 2.00000 2.00000
$$378$$ 0 0
$$379$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$380$$ 0 0
$$381$$ 1.00000 1.00000i 1.00000 1.00000i
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.00000 −2.00000
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 1.00000 1.00000i 1.00000 1.00000i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 2.00000 2.00000i 2.00000 2.00000i
$$404$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −1.00000 1.00000i −1.00000 1.00000i
$$415$$ 0 0
$$416$$ 2.00000 + 2.00000i 2.00000 + 2.00000i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$422$$ 2.00000i 2.00000i
$$423$$ −1.00000 1.00000i −1.00000 1.00000i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 1.00000i 1.00000i
$$433$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −2.00000 −2.00000
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ −1.00000 −1.00000
$$442$$ 0 0
$$443$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −2.00000 + 2.00000i −2.00000 + 2.00000i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$450$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 2.00000 2.00000
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 1.00000i 1.00000i
$$465$$ 0 0
$$466$$ 2.00000 + 2.00000i 2.00000 + 2.00000i
$$467$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$468$$ −2.00000 −2.00000
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −1.00000 −1.00000
$$485$$ 0 0
$$486$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$490$$ 0 0
$$491$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$492$$ −1.00000 1.00000i −1.00000 1.00000i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −1.00000 1.00000i −1.00000 1.00000i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 0 0
$$501$$ 2.00000i 2.00000i
$$502$$ 0 0
$$503$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 3.00000i 3.00000i
$$508$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 1.00000i 1.00000 1.00000i
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 2.00000i 2.00000i
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −1.00000 −1.00000
$$530$$ 0 0
$$531$$ 2.00000i 2.00000i
$$532$$ 0 0
$$533$$ 2.00000 2.00000i 2.00000 2.00000i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 2.00000i 2.00000i
$$538$$ 2.00000 2.00000
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$542$$ 2.00000i 2.00000i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 2.00000 2.00000i 2.00000 2.00000i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 2.00000 2.00000
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$564$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.00000i 1.00000i
$$576$$ 1.00000i 1.00000i
$$577$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$578$$ −1.00000 1.00000i −1.00000 1.00000i
$$579$$ 1.00000 1.00000i 1.00000 1.00000i
$$580$$ 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 $$\pi$$
$$588$$ 1.00000 1.00000
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ −2.00000 + 2.00000i −2.00000 + 2.00000i
$$599$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$600$$ 0 0
$$601$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −2.00000 −2.00000
$$605$$ 0 0
$$606$$ −2.00000 −2.00000
$$607$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −2.00000 + 2.00000i −2.00000 + 2.00000i
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ −2.00000 −2.00000
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$618$$ 0 0
$$619$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$620$$ 0 0
$$621$$ 1.00000 1.00000
$$622$$ 2.00000i 2.00000i
$$623$$ 0 0
$$624$$ −2.00000 −2.00000
$$625$$ 1.00000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ −1.00000 1.00000i −1.00000 1.00000i
$$634$$ 2.00000 2.00000
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 2.00000i 2.00000i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 2.00000 + 2.00000i 2.00000 + 2.00000i
$$651$$ 0 0
$$652$$ −1.00000 1.00000i −1.00000 1.00000i
$$653$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −1.00000 1.00000i −1.00000 1.00000i
$$657$$ 1.00000 1.00000i 1.00000 1.00000i
$$658$$ 0 0
$$659$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 2.00000i 2.00000i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.00000 1.00000
$$668$$ 2.00000i 2.00000i
$$669$$ 2.00000i 2.00000i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 1.00000i 1.00000i
$$676$$ 3.00000i 3.00000i
$$677$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 2.00000i 2.00000i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 2.00000 2.00000i 2.00000 2.00000i
$$699$$ −2.00000 −2.00000
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 2.00000 2.00000i 2.00000 2.00000i
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 2.00000i 2.00000i
$$709$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.00000 1.00000i 1.00000 1.00000i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 2.00000i 2.00000i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 1.00000i 1.00000i
$$726$$ 1.00000 1.00000i 1.00000 1.00000i
$$727$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$737$$ 0 0
$$738$$ 2.00000 2.00000
$$739$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$752$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$753$$ 0 0
$$754$$ 2.00000 2.00000i 2.00000 2.00000i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 2.00000i 2.00000i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 4.00000 4.00000
$$768$$ 1.00000i 1.00000i
$$769$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$773$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$774$$ 0 0
$$775$$ −1.00000 1.00000i −1.00000 1.00000i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −1.00000 −1.00000
$$784$$ 1.00000 1.00000
$$785$$ 0 0
$$786$$ 2.00000i 2.00000i
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.00000 1.00000i 1.00000 1.00000i
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 4.00000i 4.00000i
$$807$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$808$$ 0 0
$$809$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 2.00000 2.00000
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$