# Properties

 Label 2001.1.bf.c.68.1 Level $2001$ Weight $1$ Character 2001.68 Analytic conductor $0.999$ Analytic rank $0$ Dimension $24$ Projective image $D_{84}$ CM discriminant -23 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2001 = 3 \cdot 23 \cdot 29$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2001.bf (of order $$28$$, degree $$12$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.998629090279$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$2$$ over $$\Q(\zeta_{28})$$ Coefficient field: $$\Q(\zeta_{84})$$ Defining polynomial: $$x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{84}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{84} - \cdots)$$

## Embedding invariants

 Embedding label 68.1 Root $$0.997204 + 0.0747301i$$ of defining polynomial Character $$\chi$$ $$=$$ 2001.68 Dual form 2001.1.bf.c.206.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.940755 - 1.49720i) q^{2} +(0.365341 - 0.930874i) q^{3} +(-0.922715 + 1.91604i) q^{4} +(-1.73740 + 0.328735i) q^{6} +(1.97963 - 0.223051i) q^{8} +(-0.733052 - 0.680173i) q^{9} +O(q^{10})$$ $$q+(-0.940755 - 1.49720i) q^{2} +(0.365341 - 0.930874i) q^{3} +(-0.922715 + 1.91604i) q^{4} +(-1.73740 + 0.328735i) q^{6} +(1.97963 - 0.223051i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(1.44648 + 1.55894i) q^{12} +(-1.49419 + 1.19158i) q^{13} +(-0.870366 - 1.09140i) q^{16} +(-0.328735 + 1.73740i) q^{18} +(-0.974928 + 0.222521i) q^{23} +(0.515609 - 1.92428i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(3.18971 + 1.11613i) q^{26} +(-0.900969 + 0.433884i) q^{27} +(-0.997204 + 0.0747301i) q^{29} +(-1.63575 + 1.02781i) q^{31} +(-0.157284 + 0.449493i) q^{32} +(1.97963 - 0.776949i) q^{36} +(0.563320 + 1.82624i) q^{39} +(-1.13787 - 1.13787i) q^{41} +(1.25033 + 1.25033i) q^{46} +(-0.146066 + 1.29637i) q^{47} +(-1.33394 + 0.411466i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.197979 + 1.75711i) q^{50} +(-0.904396 - 3.96242i) q^{52} +(1.49720 + 0.940755i) q^{54} +(1.05001 + 1.42271i) q^{58} -1.80194i q^{59} +(3.07767 + 1.48213i) q^{62} +(-0.540010 + 0.123254i) q^{64} +(-0.149042 + 0.988831i) q^{69} +(-0.848162 - 1.06356i) q^{71} +(-1.60289 - 1.18298i) q^{72} +(1.66393 + 1.04551i) q^{73} +(-0.733052 + 0.680173i) q^{75} +(2.20431 - 2.56145i) q^{78} +(0.0747301 + 0.997204i) q^{81} +(-0.633168 + 2.77409i) q^{82} +(-0.294755 + 0.955573i) q^{87} +(0.473222 - 2.07332i) q^{92} +(0.359154 + 1.89817i) q^{93} +(2.07835 - 1.00088i) q^{94} +(0.360958 + 0.310630i) q^{96} +(-1.75711 - 0.197979i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} + O(q^{10})$$ $$24q - 2q^{2} + 2q^{3} + 14q^{4} - 2q^{6} + 6q^{8} + 2q^{9} - 6q^{12} - 6q^{16} + 4q^{18} - 6q^{24} - 4q^{25} + 2q^{26} - 4q^{27} - 2q^{31} + 4q^{32} + 6q^{36} + 2q^{41} + 2q^{46} - 2q^{47} - 4q^{48} - 4q^{49} - 2q^{50} - 10q^{52} + 12q^{54} + 4q^{58} + 4q^{62} - 28q^{64} + 14q^{72} - 2q^{73} + 2q^{75} + 10q^{78} + 2q^{81} - 4q^{82} + 4q^{92} - 2q^{93} - 8q^{94} - 24q^{96} - 2q^{98} + O(q^{100})$$

## Character values

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

 $$n$$ $$553$$ $$668$$ $$1132$$ $$\chi(n)$$ $$e\left(\frac{23}{28}\right)$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.940755 1.49720i −0.940755 1.49720i −0.866025 0.500000i $$-0.833333\pi$$
−0.0747301 0.997204i $$-0.523810\pi$$
$$3$$ 0.365341 0.930874i 0.365341 0.930874i
$$4$$ −0.922715 + 1.91604i −0.922715 + 1.91604i
$$5$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$6$$ −1.73740 + 0.328735i −1.73740 + 0.328735i
$$7$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$8$$ 1.97963 0.223051i 1.97963 0.223051i
$$9$$ −0.733052 0.680173i −0.733052 0.680173i
$$10$$ 0 0
$$11$$ 0 0 −0.993712 0.111964i $$-0.964286\pi$$
0.993712 + 0.111964i $$0.0357143\pi$$
$$12$$ 1.44648 + 1.55894i 1.44648 + 1.55894i
$$13$$ −1.49419 + 1.19158i −1.49419 + 1.19158i −0.563320 + 0.826239i $$0.690476\pi$$
−0.930874 + 0.365341i $$0.880952\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.870366 1.09140i −0.870366 1.09140i
$$17$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$18$$ −0.328735 + 1.73740i −0.328735 + 1.73740i
$$19$$ 0 0 −0.330279 0.943883i $$-0.607143\pi$$
0.330279 + 0.943883i $$0.392857\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −0.974928 + 0.222521i −0.974928 + 0.222521i
$$24$$ 0.515609 1.92428i 0.515609 1.92428i
$$25$$ −0.900969 0.433884i −0.900969 0.433884i
$$26$$ 3.18971 + 1.11613i 3.18971 + 1.11613i
$$27$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$28$$ 0 0
$$29$$ −0.997204 + 0.0747301i −0.997204 + 0.0747301i
$$30$$ 0 0
$$31$$ −1.63575 + 1.02781i −1.63575 + 1.02781i −0.680173 + 0.733052i $$0.738095\pi$$
−0.955573 + 0.294755i $$0.904762\pi$$
$$32$$ −0.157284 + 0.449493i −0.157284 + 0.449493i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.97963 0.776949i 1.97963 0.776949i
$$37$$ 0 0 −0.111964 0.993712i $$-0.535714\pi$$
0.111964 + 0.993712i $$0.464286\pi$$
$$38$$ 0 0
$$39$$ 0.563320 + 1.82624i 0.563320 + 1.82624i
$$40$$ 0 0
$$41$$ −1.13787 1.13787i −1.13787 1.13787i −0.988831 0.149042i $$-0.952381\pi$$
−0.149042 0.988831i $$-0.547619\pi$$
$$42$$ 0 0
$$43$$ 0 0 0.532032 0.846724i $$-0.321429\pi$$
−0.532032 + 0.846724i $$0.678571\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 1.25033 + 1.25033i 1.25033 + 1.25033i
$$47$$ −0.146066 + 1.29637i −0.146066 + 1.29637i 0.680173 + 0.733052i $$0.261905\pi$$
−0.826239 + 0.563320i $$0.809524\pi$$
$$48$$ −1.33394 + 0.411466i −1.33394 + 0.411466i
$$49$$ 0.623490 0.781831i 0.623490 0.781831i
$$50$$ 0.197979 + 1.75711i 0.197979 + 1.75711i
$$51$$ 0 0
$$52$$ −0.904396 3.96242i −0.904396 3.96242i
$$53$$ 0 0 −0.974928 0.222521i $$-0.928571\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$54$$ 1.49720 + 0.940755i 1.49720 + 0.940755i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.05001 + 1.42271i 1.05001 + 1.42271i
$$59$$ 1.80194i 1.80194i −0.433884 0.900969i $$-0.642857\pi$$
0.433884 0.900969i $$-0.357143\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.943883 0.330279i $$-0.892857\pi$$
0.943883 + 0.330279i $$0.107143\pi$$
$$62$$ 3.07767 + 1.48213i 3.07767 + 1.48213i
$$63$$ 0 0
$$64$$ −0.540010 + 0.123254i −0.540010 + 0.123254i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 −0.781831 0.623490i $$-0.785714\pi$$
0.781831 + 0.623490i $$0.214286\pi$$
$$68$$ 0 0
$$69$$ −0.149042 + 0.988831i −0.149042 + 0.988831i
$$70$$ 0 0
$$71$$ −0.848162 1.06356i −0.848162 1.06356i −0.997204 0.0747301i $$-0.976190\pi$$
0.149042 0.988831i $$-0.452381\pi$$
$$72$$ −1.60289 1.18298i −1.60289 1.18298i
$$73$$ 1.66393 + 1.04551i 1.66393 + 1.04551i 0.930874 + 0.365341i $$0.119048\pi$$
0.733052 + 0.680173i $$0.238095\pi$$
$$74$$ 0 0
$$75$$ −0.733052 + 0.680173i −0.733052 + 0.680173i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 2.20431 2.56145i 2.20431 2.56145i
$$79$$ 0 0 0.993712 0.111964i $$-0.0357143\pi$$
−0.993712 + 0.111964i $$0.964286\pi$$
$$80$$ 0 0
$$81$$ 0.0747301 + 0.997204i 0.0747301 + 0.997204i
$$82$$ −0.633168 + 2.77409i −0.633168 + 2.77409i
$$83$$ 0 0 0.433884 0.900969i $$-0.357143\pi$$
−0.433884 + 0.900969i $$0.642857\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −0.294755 + 0.955573i −0.294755 + 0.955573i
$$88$$ 0 0
$$89$$ 0 0 −0.532032 0.846724i $$-0.678571\pi$$
0.532032 + 0.846724i $$0.321429\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0.473222 2.07332i 0.473222 2.07332i
$$93$$ 0.359154 + 1.89817i 0.359154 + 1.89817i
$$94$$ 2.07835 1.00088i 2.07835 1.00088i
$$95$$ 0 0
$$96$$ 0.360958 + 0.310630i 0.360958 + 0.310630i
$$97$$ 0 0 0.943883 0.330279i $$-0.107143\pi$$
−0.943883 + 0.330279i $$0.892857\pi$$
$$98$$ −1.75711 0.197979i −1.75711 0.197979i
$$99$$ 0 0
$$100$$ 1.66267 1.32594i 1.66267 1.32594i
$$101$$ 0.559311 + 0.351438i 0.559311 + 0.351438i 0.781831 0.623490i $$-0.214286\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$102$$ 0 0
$$103$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$104$$ −2.69217 + 2.69217i −2.69217 + 2.69217i
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.781831 0.623490i $$-0.785714\pi$$
0.781831 + 0.623490i $$0.214286\pi$$
$$108$$ 2.12664i 2.12664i
$$109$$ 0 0 −0.433884 0.900969i $$-0.642857\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 −0.943883 0.330279i $$-0.892857\pi$$
0.943883 + 0.330279i $$0.107143\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0.776949 1.97963i 0.776949 1.97963i
$$117$$ 1.90580 + 0.142820i 1.90580 + 0.142820i
$$118$$ −2.69787 + 1.69518i −2.69787 + 1.69518i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.974928 + 0.222521i 0.974928 + 0.222521i
$$122$$ 0 0
$$123$$ −1.47493 + 0.643504i −1.47493 + 0.643504i
$$124$$ −0.459990 4.08252i −0.459990 4.08252i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0.205245 1.82160i 0.205245 1.82160i −0.294755 0.955573i $$-0.595238\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$128$$ 1.02929 + 1.02929i 1.02929 + 1.02929i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0.497204 0.791295i 0.497204 0.791295i −0.500000 0.866025i $$-0.666667\pi$$
0.997204 + 0.0747301i $$0.0238095\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 −0.111964 0.993712i $$-0.535714\pi$$
0.111964 + 0.993712i $$0.464286\pi$$
$$138$$ 1.62069 0.707101i 1.62069 0.707101i
$$139$$ −0.302705 1.32624i −0.302705 1.32624i −0.866025 0.500000i $$-0.833333\pi$$
0.563320 0.826239i $$-0.309524\pi$$
$$140$$ 0 0
$$141$$ 1.15339 + 0.609587i 1.15339 + 0.609587i
$$142$$ −0.794455 + 2.27042i −0.794455 + 2.27042i
$$143$$ 0 0
$$144$$ −0.104320 + 1.39205i −0.104320 + 1.39205i
$$145$$ 0 0
$$146$$ 3.47481i 3.47481i
$$147$$ −0.500000 0.866025i −0.500000 0.866025i
$$148$$ 0 0
$$149$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$150$$ 1.70798 + 0.457652i 1.70798 + 0.457652i
$$151$$ 0.974928 0.222521i 0.974928 0.222521i 0.294755 0.955573i $$-0.404762\pi$$
0.680173 + 0.733052i $$0.261905\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −4.01892 0.605755i −4.01892 0.605755i
$$157$$ 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
$$162$$ 1.42271 1.05001i 1.42271 1.05001i
$$163$$ −1.29637 0.146066i −1.29637 0.146066i −0.563320 0.826239i $$-0.690476\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$164$$ 3.23014 1.13027i 3.23014 1.13027i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i $$-0.571429\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$168$$ 0 0
$$169$$ 0.590232 2.58597i 0.590232 2.58597i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1.24698 −1.24698 −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$174$$ 1.70798 0.457652i 1.70798 0.457652i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −1.67738 0.658322i −1.67738 0.658322i
$$178$$ 0 0
$$179$$ 0.162592 0.712362i 0.162592 0.712362i −0.826239 0.563320i $$-0.809524\pi$$
0.988831 0.149042i $$-0.0476190\pi$$
$$180$$ 0 0
$$181$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −1.88037 + 0.657969i −1.88037 + 0.657969i
$$185$$ 0 0
$$186$$ 2.50408 2.32344i 2.50408 2.32344i
$$187$$ 0 0
$$188$$ −2.34912 1.47605i −2.34912 1.47605i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$192$$ −0.0825542 + 0.547711i −0.0825542 + 0.547711i
$$193$$ 0.122805 + 0.350958i 0.122805 + 0.350958i 0.988831 0.149042i $$-0.0476190\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0.922715 + 1.91604i 0.922715 + 1.91604i
$$197$$ 1.68862 0.385418i 1.68862 0.385418i 0.733052 0.680173i $$-0.238095\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$198$$ 0 0
$$199$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$200$$ −1.88037 0.657969i −1.88037 0.657969i
$$201$$ 0 0
$$202$$ 1.16802i 1.16802i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$208$$ 2.60099 + 0.593659i 2.60099 + 0.593659i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0.158342 + 1.40532i 0.158342 + 1.40532i 0.781831 + 0.623490i $$0.214286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$212$$ 0 0
$$213$$ −1.29991 + 0.400969i −1.29991 + 0.400969i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ −1.68681 + 1.05989i −1.68681 + 1.05989i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 1.58114 1.16694i 1.58114 1.16694i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i $$0.428571\pi$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0.365341 + 0.930874i 0.365341 + 0.930874i
$$226$$ 0 0
$$227$$ 0 0 −0.974928 0.222521i $$-0.928571\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$228$$ 0 0
$$229$$ 0 0 0.330279 0.943883i $$-0.392857\pi$$
−0.330279 + 0.943883i $$0.607143\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −1.95743 + 0.370366i −1.95743 + 0.370366i
$$233$$ 1.97766i 1.97766i 0.149042 + 0.988831i $$0.452381\pi$$
−0.149042 + 0.988831i $$0.547619\pi$$
$$234$$ −1.57906 2.98773i −1.57906 2.98773i
$$235$$ 0 0
$$236$$ 3.45258 + 1.66267i 3.45258 + 1.66267i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −0.129334 0.268565i −0.129334 0.268565i 0.826239 0.563320i $$-0.190476\pi$$
−0.955573 + 0.294755i $$0.904762\pi$$
$$240$$ 0 0
$$241$$ 0 0 −0.781831 0.623490i $$-0.785714\pi$$
0.781831 + 0.623490i $$0.214286\pi$$
$$242$$ −0.584010 1.66900i −0.584010 1.66900i
$$243$$ 0.955573 + 0.294755i 0.955573 + 0.294755i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 2.35100 + 1.60289i 2.35100 + 1.60289i
$$247$$ 0 0
$$248$$ −3.00892 + 2.39954i −3.00892 + 2.39954i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 0.943883 0.330279i $$-0.107143\pi$$
−0.943883 + 0.330279i $$0.892857\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −2.92039 + 1.40639i −2.92039 + 1.40639i
$$255$$ 0 0
$$256$$ 0.449493 1.96936i 0.449493 1.96936i
$$257$$ −0.865341 + 1.79690i −0.865341 + 1.79690i −0.365341 + 0.930874i $$0.619048\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0.781831 + 0.623490i 0.781831 + 0.623490i
$$262$$ −1.65248 −1.65248
$$263$$ 0 0 −0.532032 0.846724i $$-0.678571\pi$$
0.532032 + 0.846724i $$0.321429\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.82160 + 0.205245i −1.82160 + 0.205245i −0.955573 0.294755i $$-0.904762\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$270$$ 0 0
$$271$$ −1.00435 + 0.351438i −1.00435 + 0.351438i −0.781831 0.623490i $$-0.785714\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ −1.75711 1.19798i −1.75711 1.19798i
$$277$$ −0.914101 1.14625i −0.914101 1.14625i −0.988831 0.149042i $$-0.952381\pi$$
0.0747301 0.997204i $$-0.476190\pi$$
$$278$$ −1.70088 + 1.70088i −1.70088 + 1.70088i
$$279$$ 1.89817 + 0.359154i 1.89817 + 0.359154i
$$280$$ 0 0
$$281$$ 0 0 −0.781831 0.623490i $$-0.785714\pi$$
0.781831 + 0.623490i $$0.214286\pi$$
$$282$$ −0.172387 2.30034i −0.172387 2.30034i
$$283$$ 0 0 −0.433884 0.900969i $$-0.642857\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$284$$ 2.82043 0.643745i 2.82043 0.643745i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0.421030 0.222521i 0.421030 0.222521i
$$289$$ 1.00000i 1.00000i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −3.53857 + 2.22343i −3.53857 + 2.22343i
$$293$$ 0 0 0.330279 0.943883i $$-0.392857\pi$$
−0.330279 + 0.943883i $$0.607143\pi$$
$$294$$ −0.826239 + 1.56332i −0.826239 + 1.56332i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1.19158 1.49419i 1.19158 1.49419i
$$300$$ −0.626838 2.03216i −0.626838 2.03216i
$$301$$ 0 0
$$302$$ −1.25033 1.25033i −1.25033 1.25033i
$$303$$ 0.531484 0.392253i 0.531484 0.392253i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.33485 + 1.33485i 1.33485 + 1.33485i 0.900969 + 0.433884i $$0.142857\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0.00837297 + 0.0743122i 0.00837297 + 0.0743122i 0.997204 0.0747301i $$-0.0238095\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$312$$ 1.52251 + 3.48963i 1.52251 + 3.48963i
$$313$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1.43388 + 0.900969i −1.43388 + 0.900969i −0.433884 + 0.900969i $$0.642857\pi$$
−1.00000 $$1.00000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.97963 0.776949i −1.97963 0.776949i
$$325$$ 1.86323 0.425270i 1.86323 0.425270i
$$326$$ 1.00088 + 2.07835i 1.00088 + 2.07835i
$$327$$ 0 0
$$328$$ −2.50638 1.99877i −2.50638 1.99877i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −0.565533 + 0.565533i −0.565533 + 0.565533i −0.930874 0.365341i $$-0.880952\pi$$
0.365341 + 0.930874i $$0.380952\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −0.666318 0.418676i −0.666318 0.418676i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 −0.993712 0.111964i $$-0.964286\pi$$
0.993712 + 0.111964i $$0.0357143\pi$$
$$338$$ −4.42699 + 1.54907i −4.42699 + 1.54907i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 1.17310 + 1.86698i 1.17310 + 1.86698i
$$347$$ −1.56366 −1.56366 −0.781831 0.623490i $$-0.785714\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$348$$ −1.55894 1.44648i −1.55894 1.44648i
$$349$$ 0.149460 0.149460 0.0747301 0.997204i $$-0.476190\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$350$$ 0 0
$$351$$ 0.829215 1.72188i 0.829215 1.72188i
$$352$$ 0 0
$$353$$ −0.414278 + 1.81507i −0.414278 + 1.81507i 0.149042 + 0.988831i $$0.452381\pi$$
−0.563320 + 0.826239i $$0.690476\pi$$
$$354$$ 0.592359 + 3.13069i 0.592359 + 3.13069i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −1.21951 + 0.426725i −1.21951 + 0.426725i
$$359$$ 0 0 −0.993712 0.111964i $$-0.964286\pi$$
0.993712 + 0.111964i $$0.0357143\pi$$
$$360$$ 0 0
$$361$$ −0.781831 + 0.623490i −0.781831 + 0.623490i
$$362$$ 0 0
$$363$$ 0.563320 0.826239i 0.563320 0.826239i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 −0.330279 0.943883i $$-0.607143\pi$$
0.330279 + 0.943883i $$0.392857\pi$$
$$368$$ 1.09140 + 0.870366i 1.09140 + 0.870366i
$$369$$ 0.0601697 + 1.60807i 0.0601697 + 1.60807i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −3.96836 1.06332i −3.96836 1.06332i
$$373$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 2.59892i 2.59892i
$$377$$ 1.40097 1.29991i 1.40097 1.29991i
$$378$$ 0 0
$$379$$ 0 0 0.846724 0.532032i $$-0.178571\pi$$
−0.846724 + 0.532032i $$0.821429\pi$$
$$380$$ 0 0
$$381$$ −1.62069 0.856562i −1.62069 0.856562i
$$382$$ 0 0
$$383$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$384$$ 1.33418 0.582097i 1.33418 0.582097i
$$385$$ 0 0
$$386$$ 0.409925 0.514030i 0.409925 0.514030i
$$387$$ 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
$$392$$ 1.05989 1.68681i 1.05989 1.68681i
$$393$$ −0.554947 0.751927i −0.554947 0.751927i
$$394$$ −2.16563 2.16563i −2.16563 2.16563i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0.185853 0.233052i 0.185853 0.233052i −0.680173 0.733052i $$-0.738095\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0.310630 + 1.36096i 0.310630 + 1.36096i
$$401$$ 0 0 −0.974928 0.222521i $$-0.928571\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$402$$ 0 0
$$403$$ 1.21941 3.48486i 1.21941 3.48486i
$$404$$ −1.18945 + 0.747382i −1.18945 + 0.747382i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 1.51889 + 0.531484i 1.51889 + 0.531484i 0.955573 0.294755i $$-0.0952381\pi$$
0.563320 + 0.826239i $$0.309524\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −0.0661163 1.76699i −0.0661163 1.76699i
$$415$$ 0 0
$$416$$ −0.300593 0.859046i −0.300593 0.859046i
$$417$$ −1.34515 0.202749i −1.34515 0.202749i
$$418$$ 0 0
$$419$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$420$$ 0 0
$$421$$ 0 0 −0.846724 0.532032i $$-0.821429\pi$$
0.846724 + 0.532032i $$0.178571\pi$$
$$422$$ 1.95509 1.55913i 1.95509 1.55913i
$$423$$ 0.988831 0.850958i 0.988831 0.850958i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 1.82323 + 1.56902i 1.82323 + 1.56902i
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.433884 0.900969i $$-0.357143\pi$$
−0.433884 + 0.900969i $$0.642857\pi$$
$$432$$ 1.25771 + 0.605684i 1.25771 + 0.605684i
$$433$$ 0 0 −0.532032 0.846724i $$-0.678571\pi$$
0.532032 + 0.846724i $$0.321429\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −3.23461 1.26949i −3.23461 1.26949i
$$439$$ −0.129334 + 0.268565i −0.129334 + 0.268565i −0.955573 0.294755i $$-0.904762\pi$$
0.826239 + 0.563320i $$0.190476\pi$$
$$440$$ 0 0
$$441$$ −0.988831 + 0.149042i −0.988831 + 0.149042i
$$442$$ 0 0
$$443$$ 0.369485 0.0416310i 0.369485 0.0416310i 0.0747301 0.997204i $$-0.476190\pi$$
0.294755 + 0.955573i $$0.404762\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 2.19108 + 0.246876i 2.19108 + 0.246876i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −0.900969 0.566116i −0.900969 0.566116i 1.00000i $$-0.5\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$450$$ 1.05001 1.42271i 1.05001 1.42271i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0.149042 0.988831i 0.149042 0.988831i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 −0.433884 0.900969i $$-0.642857\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −0.754903 0.264152i −0.754903 0.264152i −0.0747301 0.997204i $$-0.523810\pi$$
−0.680173 + 0.733052i $$0.738095\pi$$
$$462$$ 0 0
$$463$$ 0.445042i 0.445042i −0.974928 0.222521i $$-0.928571\pi$$
0.974928 0.222521i $$-0.0714286\pi$$
$$464$$ 0.949493 + 1.02331i 0.949493 + 1.02331i
$$465$$ 0 0
$$466$$ 2.96096 1.86050i 2.96096 1.86050i
$$467$$ 0 0 0.330279 0.943883i $$-0.392857\pi$$
−0.330279 + 0.943883i $$0.607143\pi$$
$$468$$ −2.03216 + 3.51980i −2.03216 + 3.51980i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −0.401924 3.56718i −0.401924 3.56718i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −0.280425 + 0.446293i −0.280425 + 0.446293i
$$479$$ 0 0 0.532032 0.846724i $$-0.321429\pi$$
−0.532032 + 0.846724i $$0.678571\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −1.32594 + 1.66267i −1.32594 + 1.66267i
$$485$$ 0 0
$$486$$ −0.457652 1.70798i −0.457652 1.70798i
$$487$$ −0.414278 1.81507i −0.414278 1.81507i −0.563320 0.826239i $$-0.690476\pi$$
0.149042 0.988831i $$-0.452381\pi$$
$$488$$ 0 0
$$489$$ −0.609587 + 1.15339i −0.609587 + 1.15339i
$$490$$ 0 0
$$491$$ −1.00560 + 0.631863i −1.00560 + 0.631863i −0.930874 0.365341i $$-0.880952\pi$$
−0.0747301 + 0.997204i $$0.523810\pi$$
$$492$$ 0.127959 3.41979i 0.127959 3.41979i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 2.54545 + 0.890691i 2.54545 + 0.890691i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0.145713 0.0332580i 0.145713 0.0332580i −0.149042 0.988831i $$-0.547619\pi$$
0.294755 + 0.955573i $$0.404762\pi$$
$$500$$ 0 0
$$501$$ −0.0332580 0.443797i −0.0332580 0.443797i
$$502$$ 0 0
$$503$$ 0 0 −0.330279 0.943883i $$-0.607143\pi$$
0.330279 + 0.943883i $$0.392857\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −2.19158 1.49419i −2.19158 1.49419i
$$508$$ 3.30087 + 2.07407i 3.30087 + 2.07407i
$$509$$ −0.880843 + 0.702449i −0.880843 + 0.702449i −0.955573 0.294755i $$-0.904762\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.99744 + 0.698934i −1.99744 + 0.698934i
$$513$$ 0 0
$$514$$ 3.50440 0.394851i 3.50440 0.394851i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −0.455573 + 1.16078i −0.455573 + 1.16078i
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0.197979 1.75711i 0.197979 1.75711i
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 1.05737 + 1.68280i 1.05737 + 1.68280i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0.900969 0.433884i 0.900969 0.433884i
$$530$$ 0 0
$$531$$ −1.22563 + 1.32091i −1.22563 + 1.32091i
$$532$$ 0 0
$$533$$ 3.05607 + 0.344336i 3.05607 + 0.344336i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −0.603718 0.411608i −0.603718 0.411608i
$$538$$ 2.02097 + 2.53422i 2.02097 + 2.53422i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0.500684 + 1.43087i 0.500684 + 1.43087i 0.866025 + 0.500000i $$0.166667\pi$$
−0.365341 + 0.930874i $$0.619048\pi$$
$$542$$ 1.47102 + 1.17310i 1.47102 + 1.17310i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.78181 0.858075i −1.78181 0.858075i −0.955573 0.294755i $$-0.904762\pi$$
−0.826239 0.563320i $$-0.809524\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −0.0744892 + 1.99077i −0.0744892 + 1.99077i
$$553$$ 0 0
$$554$$ −0.856219 + 2.44693i −0.856219 + 2.44693i
$$555$$ 0 0
$$556$$ 2.82043 + 0.643745i 2.82043 + 0.643745i
$$557$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$558$$ −1.24799 3.17983i −1.24799 3.17983i
$$559$$ 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 $$0.250000\pi$$
$$564$$ −2.23224 + 1.64747i −2.23224 + 1.64747i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ −1.91628 1.91628i −1.91628 1.91628i
$$569$$ 0 0 0.111964 0.993712i $$-0.464286\pi$$
−0.111964 + 0.993712i $$0.535714\pi$$
$$570$$ 0 0
$$571$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0.974928 + 0.222521i 0.974928 + 0.222521i
$$576$$ 0.479690 + 0.276949i 0.479690 + 0.276949i
$$577$$ −0.264152 + 0.754903i −0.264152 + 0.754903i 0.733052 + 0.680173i $$0.238095\pi$$
−0.997204 + 0.0747301i $$0.976190\pi$$
$$578$$ −1.49720 + 0.940755i −1.49720 + 0.940755i
$$579$$ 0.371563 + 0.0139029i 0.371563 + 0.0139029i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 3.52717 + 1.69859i 3.52717 + 1.69859i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −0.807782 1.67738i −0.807782 1.67738i −0.733052 0.680173i $$-0.761905\pi$$
−0.0747301 0.997204i $$-0.523810\pi$$
$$588$$ 2.12069 0.158924i 2.12069 0.158924i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0.258149 1.71271i 0.258149 1.71271i
$$592$$ 0 0
$$593$$ 0.974928 + 1.22252i 0.974928 + 1.22252i 0.974928 + 0.222521i $$0.0714286\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ −3.35810 0.378367i −3.35810 0.378367i
$$599$$ 1.00435 0.351438i 1.00435 0.351438i 0.222521 0.974928i $$-0.428571\pi$$
0.781831 + 0.623490i $$0.214286\pi$$
$$600$$ −1.29946 + 1.51000i −1.29946 + 1.51000i
$$601$$ −0.514383 + 0.0579571i −0.514383 + 0.0579571i −0.365341 0.930874i $$-0.619048\pi$$
−0.149042 + 0.988831i $$0.547619\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −0.473222 + 2.07332i −0.473222 + 2.07332i
$$605$$ 0 0
$$606$$ −1.08728 0.426725i −1.08728 0.426725i
$$607$$ −1.05737 1.68280i −1.05737 1.68280i −0.623490 0.781831i $$-0.714286\pi$$
−0.433884 0.900969i $$-0.642857\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.32648 2.11108i −1.32648 2.11108i
$$612$$ 0 0
$$613$$ 0 0 0.433884 0.900969i $$-0.357143\pi$$
−0.433884 + 0.900969i $$0.642857\pi$$
$$614$$ 0.742776 3.25432i 0.742776 3.25432i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 0.993712 0.111964i $$-0.0357143\pi$$
−0.993712 + 0.111964i $$0.964286\pi$$
$$618$$ 0 0
$$619$$ 0 0 0.943883 0.330279i $$-0.107143\pi$$
−0.943883 + 0.330279i $$0.892857\pi$$
$$620$$ 0 0
$$621$$ 0.781831 0.623490i 0.781831 0.623490i
$$622$$ 0.103384 0.0824456i 0.103384 0.0824456i
$$623$$ 0 0
$$624$$ 1.50287 2.20431i 1.50287 2.20431i
$$625$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.433884 0.900969i $$-0.642857\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$632$$ 0 0
$$633$$ 1.36603 + 0.366025i 1.36603 + 0.366025i
$$634$$ 2.69787 + 1.29922i 2.69787 + 1.29922i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.91115i 1.91115i
$$638$$ 0 0
$$639$$ −0.101659 + 1.35654i −0.101659 + 1.35654i
$$640$$ 0 0
$$641$$ 0 0 0.330279 0.943883i $$-0.392857\pi$$
−0.330279 + 0.943883i $$0.607143\pi$$
$$642$$ 0 0
$$643$$ 0 0 −0.974928 0.222521i $$-0.928571\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0.702449 0.880843i 0.702449 0.880843i −0.294755 0.955573i $$-0.595238\pi$$
0.997204 + 0.0747301i $$0.0238095\pi$$
$$648$$ 0.370366 + 1.95743i 0.370366 + 1.95743i
$$649$$ 0 0
$$650$$ −2.38956 2.38956i −2.38956 2.38956i
$$651$$ 0 0
$$652$$ 1.47605 2.34912i 1.47605 2.34912i
$$653$$ 0.275400 0.438297i 0.275400 0.438297i −0.680173 0.733052i $$-0.738095\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −0.251514 + 2.23224i −0.251514 + 2.23224i
$$657$$ −0.508614 1.89817i −0.508614 1.89817i
$$658$$ 0 0
$$659$$ 0 0 −0.111964 0.993712i $$-0.535714\pi$$
0.111964 + 0.993712i $$0.464286\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$662$$ 1.37875 + 0.314690i 1.37875 + 0.314690i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0.955573 0.294755i 0.955573 0.294755i
$$668$$ 0.946444i 0.946444i
$$669$$ 0.623490 + 1.07992i 0.623490 + 1.07992i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.81507 0.414278i 1.81507 0.414278i 0.826239 0.563320i $$-0.190476\pi$$
0.988831 + 0.149042i $$0.0476190\pi$$
$$674$$ 0 0
$$675$$ 1.00000 1.00000
$$676$$ 4.41021 + 3.51702i 4.41021 + 3.51702i
$$677$$ 0 0 −0.330279 0.943883i $$-0.607143\pi$$
0.330279 + 0.943883i $$0.392857\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −1.55929 + 1.24349i −1.55929 + 1.24349i −0.733052 + 0.680173i $$0.761905\pi$$
−0.826239 + 0.563320i $$0.809524\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.433884 + 1.90097i −0.433884 + 1.90097i 1.00000i $$0.5\pi$$
−0.433884 + 0.900969i $$0.642857\pi$$
$$692$$ 1.15061 2.38926i 1.15061 2.38926i
$$693$$ 0 0
$$694$$ 1.47102 + 2.34112i 1.47102 + 2.34112i
$$695$$ 0 0
$$696$$ −0.370366 + 1.95743i −0.370366 + 1.95743i
$$697$$ 0 0
$$698$$ −0.140605 0.223772i −0.140605 0.223772i
$$699$$ 1.84095 + 0.722521i 1.84095 + 0.722521i
$$700$$ 0 0
$$701$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$702$$ −3.35810 + 0.378367i −3.35810 + 0.378367i
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 3.10726 1.08728i 3.10726 1.08728i
$$707$$ 0 0
$$708$$ 2.80911 2.60647i 2.80911 2.60647i
$$709$$ 0 0 0.781831 0.623490i $$-0.214286\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.36603 1.36603i 1.36603 1.36603i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 1.21489 + 0.968839i 1.21489 + 0.968839i
$$717$$ −0.297251 + 0.0222759i −0.297251 + 0.0222759i
$$718$$ 0 0
$$719$$ 1.90097 0.433884i 1.90097 0.433884i 0.900969 0.433884i $$-0.142857\pi$$
1.00000 $$0$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.66900 + 0.584010i 1.66900 + 0.584010i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0.930874 + 0.365341i 0.930874 + 0.365341i
$$726$$ −1.76699 0.0661163i −1.76699 0.0661163i
$$727$$ 0 0 0.846724 0.532032i $$-0.178571\pi$$
−0.846724 + 0.532032i $$0.821429\pi$$
$$728$$ 0 0
$$729$$ 0.623490 0.781831i 0.623490 0.781831i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 −0.111964 0.993712i $$-0.535714\pi$$
0.111964 + 0.993712i $$0.464286\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0.0533193 0.473222i 0.0533193 0.473222i
$$737$$ 0 0
$$738$$ 2.35100 1.60289i 2.35100 1.60289i
$$739$$ 0.856144 1.36254i 0.856144 1.36254i −0.0747301 0.997204i $$-0.523810\pi$$
0.930874 0.365341i $$-0.119048\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.111964 0.993712i $$-0.464286\pi$$
−0.111964 + 0.993712i $$0.535714\pi$$
$$744$$ 1.13438 + 3.67758i 1.13438 + 3.67758i
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.330279 0.943883i $$-0.392857\pi$$
−0.330279 + 0.943883i $$0.607143\pi$$
$$752$$ 1.54200 0.968901i 1.54200 0.968901i
$$753$$ 0 0
$$754$$ −3.26420 0.874639i −3.26420 0.874639i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 −0.943883 0.330279i $$-0.892857\pi$$
0.943883 + 0.330279i $$0.107143\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.636119 1.32091i −0.636119 1.32091i −0.930874 0.365341i $$-0.880952\pi$$
0.294755 0.955573i $$-0.404762\pi$$
$$762$$ 0.242229 + 3.23232i 0.242229 + 3.23232i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 2.14715 + 2.69244i 2.14715 + 2.69244i
$$768$$ −1.66900 1.13791i −1.66900 1.13791i
$$769$$ 0 0 −0.846724 0.532032i $$-0.821429\pi$$
0.846724 + 0.532032i $$0.178571\pi$$
$$770$$ 0 0
$$771$$ 1.35654 + 1.46200i 1.35654 + 1.46200i
$$772$$ −0.785762 0.0885341i −0.785762 0.0885341i
$$773$$ 0 0 0.943883 0.330279i $$-0.107143\pi$$
−0.943883 + 0.330279i $$0.892857\pi$$
$$774$$ 0 0
$$775$$ 1.91970 0.216299i 1.91970 0.216299i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0.866025 0.500000i 0.866025 0.500000i
$$784$$ −1.39596 −1.39596
$$785$$ 0 0
$$786$$ −0.603718 + 1.53825i −0.603718 + 1.53825i
$$787$$ 0 0 0.433884 0.900969i $$-0.357143\pi$$
−0.433884 + 0.900969i $$0.642857\pi$$
$$788$$ −0.819644 + 3.59110i −0.819644 + 3.59110i