# Properties

 Label 712.1.s.a.331.1 Level $712$ Weight $1$ Character 712.331 Analytic conductor $0.355$ Analytic rank $0$ Dimension $10$ Projective image $D_{11}$ CM discriminant -8 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$712 = 2^{3} \cdot 89$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 712.s (of order $$22$$, degree $$10$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.355334288995$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\Q(\zeta_{22})$$ Defining polynomial: $$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{11}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{11} - \cdots)$$

## Embedding invariants

 Embedding label 331.1 Root $$0.959493 + 0.281733i$$ of defining polynomial Character $$\chi$$ $$=$$ 712.331 Dual form 712.1.s.a.299.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.142315 - 0.989821i) q^{2} +(1.25667 + 0.368991i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.186393 - 1.29639i) q^{6} +(0.415415 + 0.909632i) q^{8} +(0.601808 + 0.386758i) q^{9} +O(q^{10})$$ $$q+(-0.142315 - 0.989821i) q^{2} +(1.25667 + 0.368991i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(0.186393 - 1.29639i) q^{6} +(0.415415 + 0.909632i) q^{8} +(0.601808 + 0.386758i) q^{9} +(0.345139 - 0.755750i) q^{11} -1.30972 q^{12} +(0.841254 - 0.540641i) q^{16} +(0.0405070 - 0.281733i) q^{17} +(0.297176 - 0.650724i) q^{18} +(0.698939 + 0.449181i) q^{19} +(-0.797176 - 0.234072i) q^{22} +(0.186393 + 1.29639i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(-0.244123 - 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{32} +(0.712591 - 0.822373i) q^{33} -0.284630 q^{34} +(-0.686393 - 0.201543i) q^{36} +(0.345139 - 0.755750i) q^{38} +(-1.91899 + 0.563465i) q^{41} +(-0.118239 + 0.258908i) q^{43} +(-0.118239 + 0.822373i) q^{44} +(1.25667 - 0.368991i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(0.841254 + 0.540641i) q^{50} +(0.154861 - 0.339098i) q^{51} +(-0.244123 + 0.281733i) q^{54} +(0.712591 + 0.822373i) q^{57} +(0.273100 - 0.0801894i) q^{59} +(-0.654861 + 0.755750i) q^{64} +(-0.915415 - 0.588302i) q^{66} +(-1.61435 - 0.474017i) q^{67} +(0.0405070 + 0.281733i) q^{68} +(-0.101808 + 0.708089i) q^{72} +(-1.10181 + 0.708089i) q^{73} +(-1.10181 + 0.708089i) q^{75} +(-0.797176 - 0.234072i) q^{76} +(-0.500000 - 1.09485i) q^{81} +(0.830830 + 1.81926i) q^{82} +(0.273100 - 1.89945i) q^{83} +(0.273100 + 0.0801894i) q^{86} +0.830830 q^{88} +(-0.654861 - 0.755750i) q^{89} +(-0.544078 - 1.19136i) q^{96} +(0.698939 + 1.53046i) q^{97} +(0.841254 + 0.540641i) q^{98} +(0.500000 - 0.321330i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q - q^{2} - 2q^{3} - q^{4} - 2q^{6} - q^{8} - 3q^{9} + O(q^{10})$$ $$10q - q^{2} - 2q^{3} - q^{4} - 2q^{6} - q^{8} - 3q^{9} + 9q^{11} - 2q^{12} - q^{16} + 9q^{17} - 3q^{18} - 2q^{19} - 2q^{22} - 2q^{24} - q^{25} + 7q^{27} - q^{32} - 4q^{33} - 2q^{34} - 3q^{36} + 9q^{38} - 2q^{41} - 2q^{43} - 2q^{44} - 2q^{48} - q^{49} - q^{50} - 4q^{51} + 7q^{54} - 4q^{57} - 2q^{59} - q^{64} - 4q^{66} - 2q^{67} + 9q^{68} + 8q^{72} - 2q^{73} - 2q^{75} - 2q^{76} - 5q^{81} - 2q^{82} - 2q^{83} - 2q^{86} - 2q^{88} - q^{89} - 2q^{96} - 2q^{97} - q^{98} + 5q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/712\mathbb{Z}\right)^\times$$.

 $$n$$ $$357$$ $$535$$ $$537$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{11}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.142315 0.989821i −0.142315 0.989821i
$$3$$ 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i $$-0.181818\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$4$$ −0.959493 + 0.281733i −0.959493 + 0.281733i
$$5$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$6$$ 0.186393 1.29639i 0.186393 1.29639i
$$7$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$8$$ 0.415415 + 0.909632i 0.415415 + 0.909632i
$$9$$ 0.601808 + 0.386758i 0.601808 + 0.386758i
$$10$$ 0 0
$$11$$ 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i $$-0.727273\pi$$
1.00000 $$0$$
$$12$$ −1.30972 −1.30972
$$13$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0.841254 0.540641i 0.841254 0.540641i
$$17$$ 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i $$-0.909091\pi$$
1.00000 $$0$$
$$18$$ 0.297176 0.650724i 0.297176 0.650724i
$$19$$ 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i $$-0.181818\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −0.797176 0.234072i −0.797176 0.234072i
$$23$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$24$$ 0.186393 + 1.29639i 0.186393 + 1.29639i
$$25$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$26$$ 0 0
$$27$$ −0.244123 0.281733i −0.244123 0.281733i
$$28$$ 0 0
$$29$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$32$$ −0.654861 0.755750i −0.654861 0.755750i
$$33$$ 0.712591 0.822373i 0.712591 0.822373i
$$34$$ −0.284630 −0.284630
$$35$$ 0 0
$$36$$ −0.686393 0.201543i −0.686393 0.201543i
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0.345139 0.755750i 0.345139 0.755750i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.91899 + 0.563465i −1.91899 + 0.563465i −0.959493 + 0.281733i $$0.909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$42$$ 0 0
$$43$$ −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i $$-0.909091\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$44$$ −0.118239 + 0.822373i −0.118239 + 0.822373i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$48$$ 1.25667 0.368991i 1.25667 0.368991i
$$49$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$50$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$51$$ 0.154861 0.339098i 0.154861 0.339098i
$$52$$ 0 0
$$53$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$54$$ −0.244123 + 0.281733i −0.244123 + 0.281733i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0.712591 + 0.822373i 0.712591 + 0.822373i
$$58$$ 0 0
$$59$$ 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i $$-0.545455\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$65$$ 0 0
$$66$$ −0.915415 0.588302i −0.915415 0.588302i
$$67$$ −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i $$-0.727273\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$68$$ 0.0405070 + 0.281733i 0.0405070 + 0.281733i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$72$$ −0.101808 + 0.708089i −0.101808 + 0.708089i
$$73$$ −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i $$-0.909091\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$74$$ 0 0
$$75$$ −1.10181 + 0.708089i −1.10181 + 0.708089i
$$76$$ −0.797176 0.234072i −0.797176 0.234072i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$80$$ 0 0
$$81$$ −0.500000 1.09485i −0.500000 1.09485i
$$82$$ 0.830830 + 1.81926i 0.830830 + 1.81926i
$$83$$ 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i $$-0.545455\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0.273100 + 0.0801894i 0.273100 + 0.0801894i
$$87$$ 0 0
$$88$$ 0.830830 0.830830
$$89$$ −0.654861 0.755750i −0.654861 0.755750i
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −0.544078 1.19136i −0.544078 1.19136i
$$97$$ 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i $$0.181818\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$98$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$99$$ 0.500000 0.321330i 0.500000 0.321330i
$$100$$ 0.415415 0.909632i 0.415415 0.909632i
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ −0.357685 0.105026i −0.357685 0.105026i
$$103$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0.830830 1.81926i 0.830830 1.81926i 0.415415 0.909632i $$-0.363636\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$108$$ 0.313607 + 0.201543i 0.313607 + 0.201543i
$$109$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i $$0.363636\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$114$$ 0.712591 0.822373i 0.712591 0.822373i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −0.118239 0.258908i −0.118239 0.258908i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.202824 + 0.234072i 0.202824 + 0.234072i
$$122$$ 0 0
$$123$$ −2.61944 −2.61944
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$128$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$129$$ −0.244123 + 0.281733i −0.244123 + 0.281733i
$$130$$ 0 0
$$131$$ 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i $$-0.363636\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$132$$ −0.452036 + 0.989821i −0.452036 + 0.989821i
$$133$$ 0 0
$$134$$ −0.239446 + 1.66538i −0.239446 + 1.66538i
$$135$$ 0 0
$$136$$ 0.273100 0.0801894i 0.273100 0.0801894i
$$137$$ 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i $$-0.545455\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$138$$ 0 0
$$139$$ 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i $$-0.181818\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0.715370 0.715370
$$145$$ 0 0
$$146$$ 0.857685 + 0.989821i 0.857685 + 0.989821i
$$147$$ −1.10181 + 0.708089i −1.10181 + 0.708089i
$$148$$ 0 0
$$149$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$150$$ 0.857685 + 0.989821i 0.857685 + 0.989821i
$$151$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$152$$ −0.118239 + 0.822373i −0.118239 + 0.822373i
$$153$$ 0.133340 0.153882i 0.133340 0.153882i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.01255 + 0.650724i −1.01255 + 0.650724i
$$163$$ 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i $$0.181818\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$164$$ 1.68251 1.08128i 1.68251 1.08128i
$$165$$ 0 0
$$166$$ −1.91899 −1.91899
$$167$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$168$$ 0 0
$$169$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$170$$ 0 0
$$171$$ 0.246902 + 0.540641i 0.246902 + 0.540641i
$$172$$ 0.0405070 0.281733i 0.0405070 0.281733i
$$173$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.118239 0.822373i −0.118239 0.822373i
$$177$$ 0.372786 0.372786
$$178$$ −0.654861 + 0.755750i −0.654861 + 0.755750i
$$179$$ 1.68251 1.68251 0.841254 0.540641i $$-0.181818\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$180$$ 0 0
$$181$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −0.198939 0.127850i −0.198939 0.127850i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$192$$ −1.10181 + 0.708089i −1.10181 + 0.708089i
$$193$$ −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i $$-0.727273\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$194$$ 1.41542 0.909632i 1.41542 0.909632i
$$195$$ 0 0
$$196$$ 0.415415 0.909632i 0.415415 0.909632i
$$197$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$198$$ −0.389217 0.449181i −0.389217 0.449181i
$$199$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$200$$ −0.959493 0.281733i −0.959493 0.281733i
$$201$$ −1.85380 1.19136i −1.85380 1.19136i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −0.0530529 + 0.368991i −0.0530529 + 0.368991i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0.580699 0.373193i 0.580699 0.373193i
$$210$$ 0 0
$$211$$ 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i $$-0.727273\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −1.91899 0.563465i −1.91899 0.563465i
$$215$$ 0 0
$$216$$ 0.154861 0.339098i 0.154861 0.339098i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −1.64589 + 0.483276i −1.64589 + 0.483276i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$224$$ 0 0
$$225$$ −0.686393 + 0.201543i −0.686393 + 0.201543i
$$226$$ 1.84125 0.540641i 1.84125 0.540641i
$$227$$ 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i $$-0.545455\pi$$
1.00000 $$0$$
$$228$$ −0.915415 0.588302i −0.915415 0.588302i
$$229$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −1.91899 −1.91899 −0.959493 0.281733i $$-0.909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −0.239446 + 0.153882i −0.239446 + 0.153882i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$240$$ 0 0
$$241$$ 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i $$-0.545455\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$242$$ 0.202824 0.234072i 0.202824 0.234072i
$$243$$ −0.171292 1.19136i −0.171292 1.19136i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0.372786 + 2.59278i 0.372786 + 2.59278i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 1.04408 2.28621i 1.04408 2.28621i
$$250$$ 0 0
$$251$$ −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i $$0.727273\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.415415 0.909632i 0.415415 0.909632i
$$257$$ 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i $$-0.545455\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$258$$ 0.313607 + 0.201543i 0.313607 + 0.201543i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −0.544078 1.19136i −0.544078 1.19136i
$$263$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$264$$ 1.04408 + 0.306569i 1.04408 + 0.306569i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −0.544078 1.19136i −0.544078 1.19136i
$$268$$ 1.68251 1.68251
$$269$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$272$$ −0.118239 0.258908i −0.118239 0.258908i
$$273$$ 0 0
$$274$$ −0.118239 0.258908i −0.118239 0.258908i
$$275$$ 0.345139 + 0.755750i 0.345139 + 0.755750i
$$276$$ 0 0
$$277$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$278$$ 0.345139 0.755750i 0.345139 0.755750i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i $$-0.545455\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$282$$ 0 0
$$283$$ −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i $$0.727273\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −0.101808 0.708089i −0.101808 0.708089i
$$289$$ 0.881761 + 0.258908i 0.881761 + 0.258908i
$$290$$ 0 0
$$291$$ 0.313607 + 2.18119i 0.313607 + 2.18119i
$$292$$ 0.857685 0.989821i 0.857685 0.989821i
$$293$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$294$$ 0.857685 + 0.989821i 0.857685 + 0.989821i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −0.297176 + 0.0872586i −0.297176 + 0.0872586i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0.857685 0.989821i 0.857685 0.989821i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0.830830 0.830830
$$305$$ 0 0
$$306$$ −0.171292 0.110083i −0.171292 0.110083i
$$307$$ 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i $$-0.363636\pi$$
0.841254 0.540641i $$-0.181818\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$312$$ 0 0
$$313$$ 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i $$-0.545455\pi$$
0.841254 0.540641i $$-0.181818\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 1.71537 1.97964i 1.71537 1.97964i
$$322$$ 0 0
$$323$$ 0.154861 0.178719i 0.154861 0.178719i
$$324$$ 0.788201 + 0.909632i 0.788201 + 0.909632i
$$325$$ 0 0
$$326$$ 1.25667 0.368991i 1.25667 0.368991i
$$327$$ 0 0
$$328$$ −1.30972 1.51150i −1.30972 1.51150i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i $$-0.909091\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$332$$ 0.273100 + 1.89945i 0.273100 + 1.89945i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i $$-0.181818\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$338$$ 0.415415 0.909632i 0.415415 0.909632i
$$339$$ −0.357685 + 2.48775i −0.357685 + 2.48775i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0.500000 0.321330i 0.500000 0.321330i
$$343$$ 0 0
$$344$$ −0.284630 −0.284630
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i $$-0.909091\pi$$
−0.654861 0.755750i $$-0.727273\pi$$
$$348$$ 0 0
$$349$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −0.797176 + 0.234072i −0.797176 + 0.234072i
$$353$$ −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i $$-0.727273\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$354$$ −0.0530529 0.368991i −0.0530529 0.368991i
$$355$$ 0 0
$$356$$ 0.841254 + 0.540641i 0.841254 + 0.540641i
$$357$$ 0 0
$$358$$ −0.239446 1.66538i −0.239446 1.66538i
$$359$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$360$$ 0 0
$$361$$ −0.128663 0.281733i −0.128663 0.281733i
$$362$$ 0 0
$$363$$ 0.168513 + 0.368991i 0.168513 + 0.368991i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$368$$ 0 0
$$369$$ −1.37279 0.403086i −1.37279 0.403086i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$374$$ −0.0982369 + 0.215109i −0.0982369 + 0.215109i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 $$0$$
0.415415 + 0.909632i $$0.363636\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$384$$ 0.857685 + 0.989821i 0.857685 + 0.989821i
$$385$$ 0 0
$$386$$ −1.61435 + 0.474017i −1.61435 + 0.474017i
$$387$$ −0.171292 + 0.110083i −0.171292 + 0.110083i
$$388$$ −1.10181 1.27155i −1.10181 1.27155i
$$389$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −0.959493 0.281733i −0.959493 0.281733i
$$393$$ 1.71537 1.71537
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −0.389217 + 0.449181i −0.389217 + 0.449181i
$$397$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −0.142315 + 0.989821i −0.142315 + 0.989821i
$$401$$ −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i $$0.363636\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$402$$ −0.915415 + 2.00448i −0.915415 + 2.00448i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0.372786 0.372786
$$409$$ −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i $$-0.727273\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$410$$ 0 0
$$411$$ 0.372786 0.372786
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0.712591 + 0.822373i 0.712591 + 0.822373i
$$418$$ −0.452036 0.521678i −0.452036 0.521678i
$$419$$ −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i $$0.363636\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$420$$ 0 0
$$421$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$422$$ −0.239446 0.153882i −0.239446 0.153882i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0.186393 + 0.215109i 0.186393 + 0.215109i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.284630 + 1.97964i −0.284630 + 1.97964i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$432$$ −0.357685 0.105026i −0.357685 0.105026i
$$433$$ −1.30972 −1.30972 −0.654861 0.755750i $$-0.727273\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0.712591 + 1.56036i 0.712591 + 1.56036i
$$439$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$440$$ 0 0
$$441$$ −0.686393 + 0.201543i −0.686393 + 0.201543i
$$442$$ 0 0
$$443$$ 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i $$0.363636\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i $$-0.181818\pi$$
1.00000 $$0$$
$$450$$ 0.297176 + 0.650724i 0.297176 + 0.650724i
$$451$$ −0.236479 + 1.64475i −0.236479 + 1.64475i
$$452$$ −0.797176 1.74557i −0.797176 1.74557i
$$453$$ 0 0
$$454$$ −1.10181 0.708089i −1.10181 0.708089i
$$455$$ 0 0
$$456$$ −0.452036 + 0.989821i −0.452036 + 0.989821i
$$457$$ 1.68251 1.68251 0.841254 0.540641i $$-0.181818\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$458$$ 0 0
$$459$$ −0.0892619 + 0.0573652i −0.0892619 + 0.0573652i
$$460$$ 0 0
$$461$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$462$$ 0 0
$$463$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0.273100 + 1.89945i 0.273100 + 1.89945i
$$467$$ 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i $$-0.363636\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0.186393 + 0.215109i 0.186393 + 0.215109i
$$473$$ 0.154861 + 0.178719i 0.154861 + 0.178719i
$$474$$ 0 0
$$475$$ −0.797176 + 0.234072i −0.797176 + 0.234072i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −1.91899 −1.91899
$$483$$ 0 0
$$484$$ −0.260554 0.167448i −0.260554 0.167448i
$$485$$ 0 0
$$486$$ −1.15486 + 0.339098i −1.15486 + 0.339098i
$$487$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$488$$ 0 0
$$489$$ −0.244123 + 1.69791i −0.244123 + 1.69791i
$$490$$ 0 0
$$491$$ 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i $$-0.727273\pi$$
1.00000 $$0$$
$$492$$ 2.51334 0.737982i 2.51334 0.737982i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −2.41153 0.708089i −2.41153 0.708089i
$$499$$ 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i $$-0.363636\pi$$
0.841254 0.540641i $$-0.181818\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 1.25667 + 1.45027i 1.25667 + 1.45027i
$$503$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.857685 + 0.989821i 0.857685 + 0.989821i
$$508$$ 0 0
$$509$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.959493 0.281733i −0.959493 0.281733i
$$513$$ −0.0440780 0.306569i −0.0440780 0.306569i
$$514$$ −0.544078 0.627899i −0.544078 0.627899i
$$515$$ 0 0
$$516$$ 0.154861 0.339098i 0.154861 0.339098i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i $$-0.363636\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$522$$ 0 0
$$523$$ −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i $$0.363636\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$524$$ −1.10181 + 0.708089i −1.10181 + 0.708089i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0.154861 1.07708i 0.154861 1.07708i
$$529$$ 0.415415 + 0.909632i 0.415415 + 0.909632i
$$530$$ 0 0
$$531$$ 0.195368 + 0.0573652i 0.195368 + 0.0573652i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −1.10181 + 0.708089i −1.10181 + 0.708089i
$$535$$ 0 0
$$536$$ −0.239446 1.66538i −0.239446 1.66538i
$$537$$ 2.11435 + 0.620830i 2.11435 + 0.620830i
$$538$$ 0 0
$$539$$ 0.345139 + 0.755750i 0.345139 + 0.755750i
$$540$$ 0 0
$$541$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −0.239446 + 0.153882i −0.239446 + 0.153882i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i $$-0.545455\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$548$$ −0.239446 + 0.153882i −0.239446 + 0.153882i
$$549$$ 0 0
$$550$$ 0.698939 0.449181i 0.698939 0.449181i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.797176 0.234072i −0.797176 0.234072i
$$557$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −0.202824 0.234072i −0.202824 0.234072i
$$562$$ −0.544078 0.627899i −0.544078 0.627899i
$$563$$ 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 $$0$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 1.25667 + 1.45027i 1.25667 + 1.45027i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i $$0.545455\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$570$$ 0 0
$$571$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.686393 + 0.201543i −0.686393 + 0.201543i
$$577$$ 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i $$-0.727273\pi$$
1.00000 $$0$$
$$578$$ 0.130785 0.909632i 0.130785 0.909632i
$$579$$ 0.313607 2.18119i 0.313607 2.18119i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 2.11435 0.620830i 2.11435 0.620830i
$$583$$ 0 0
$$584$$ −1.10181 0.708089i −1.10181 0.708089i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i $$-0.545455\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$588$$ 0.857685 0.989821i 0.857685 0.989821i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i $$-0.909091\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$594$$ 0.128663 + 0.281733i 0.128663 + 0.281733i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$600$$ −1.10181 0.708089i −1.10181 0.708089i
$$601$$ 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i $$-0.181818\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$602$$ 0 0
$$603$$ −0.788201 0.909632i −0.788201 0.909632i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$608$$ −0.118239 0.822373i −0.118239 0.822373i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −0.0845850 + 0.185215i −0.0845850 + 0.185215i
$$613$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$614$$ −1.61435 1.03748i −1.61435 1.03748i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i $$-0.727273\pi$$
0.841254 0.540641i $$-0.181818\pi$$
$$618$$ 0 0
$$619$$ 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i $$-0.363636\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.142315 0.989821i −0.142315 0.989821i
$$626$$ −1.61435 0.474017i −1.61435 0.474017i
$$627$$ 0.867451 0.254707i 0.867451 0.254707i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$632$$ 0 0
$$633$$ 0.313607 0.201543i 0.313607 0.201543i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i $$0.363636\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$642$$ −2.20362 1.41618i −2.20362 1.41618i
$$643$$ −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i $$-0.909091\pi$$
−0.142315 0.989821i $$-0.545455\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −0.198939 0.127850i −0.198939 0.127850i
$$647$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$648$$ 0.788201 0.909632i 0.788201 0.909632i
$$649$$ 0.0336545 0.234072i 0.0336545 0.234072i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −0.544078 1.19136i −0.544078 1.19136i
$$653$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −1.30972 + 1.51150i −1.30972 + 1.51150i
$$657$$ −0.936936 −0.936936
$$658$$ 0 0
$$659$$ 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i $$-0.181818\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$660$$ 0 0
$$661$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$662$$ 0.698939 + 0.449181i 0.698939 + 0.449181i
$$663$$ 0 0
$$664$$ 1.84125 0.540641i 1.84125 0.540641i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.68251 + 1.08128i 1.68251 + 1.08128i 0.841254 + 0.540641i $$0.181818\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$674$$ 0.345139 0.755750i 0.345139 0.755750i
$$675$$ 0.372786 0.372786
$$676$$ −0.959493 0.281733i −0.959493 0.281733i
$$677$$ 0 0 0.654861 0.755750i $$-0.272727\pi$$
−0.654861 + 0.755750i $$0.727273\pi$$
$$678$$ 2.51334 2.51334
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.44306 0.927399i 1.44306 0.927399i
$$682$$ 0 0
$$683$$ −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i $$-0.909091\pi$$
0.415415 0.909632i $$-0.363636\pi$$
$$684$$ −0.389217 0.449181i −0.389217 0.449181i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0.0405070 + 0.281733i 0.0405070 + 0.281733i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i $$0.363636\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −0.797176 + 1.74557i −0.797176 + 1.74557i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0.0810141 + 0.563465i 0.0810141 + 0.563465i
$$698$$ 0 0
$$699$$ −2.41153 0.708089i −2.41153 0.708089i
$$700$$ 0 0
$$701$$ 0 0 0.415415 0.909632i $$-0.363636\pi$$
−0.415415 + 0.909632i $$0.636364\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0.345139 + 0.755750i 0.345139 + 0.755750i
$$705$$ 0 0
$$706$$ −0.239446 + 1.66538i −0.239446 + 1.66538i
$$707$$ 0 0
$$708$$ −0.357685 + 0.105026i −0.357685 + 0.105026i
$$709$$ 0 0 −0.959493 0.281733i $$-0.909091\pi$$
0.959493 + 0.281733i $$0.0909091\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0.415415 0.909632i 0.415415 0.909632i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −1.61435 + 0.474017i −1.61435 + 0.474017i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.415415 0.909632i $$-0.636364\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −0.260554 + 0.167448i −0.260554 + 0.167448i
$$723$$ 1.04408 2.28621i 1.04408 2.28621i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0.341254 0.219310i 0.341254 0.219310i
$$727$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$728$$ 0 0
$$729$$ 0.0530529 0.368991i 0.0530529 0.368991i
$$730$$ 0 0
$$731$$ 0.0681534 + 0.0437995i 0.0681534 + 0.0437995i
$$732$$ 0 0
$$733$$ 0 0 −0.142315 0.989821i $$-0.545455\pi$$
0.142315 + 0.989821i $$0.454545\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −0.915415 + 1.05645i −0.915415 + 1.05645i
$$738$$ −0.203616 + 1.41618i −0.203616 + 1.41618i
$$739$$ −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i $$-0.909091\pi$$
−0.142315 0.989821i $$-0.545455\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.841254 0.540641i $$-0.181818\pi$$
−0.841254 + 0.540641i $$0.818182\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0.898983 1.03748i 0.898983 1.03748i
$$748$$ 0.226900 + 0.0666238i 0.226900 + 0.0666238i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 −0.841254 0.540641i $$-0.818182\pi$$
0.841254 + 0.540641i $$0.181818\pi$$
$$752$$ 0 0
$$753$$ −2.41153 + 0.708089i −2.41153 + 0.708089i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 0.142315 0.989821i $$-0.454545\pi$$
−0.142315 + 0.989821i $$0.545455\pi$$
$$758$$ 0.698939 1.53046i 0.698939 1.53046i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i $$-0.909091\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.857685 0.989821i 0.857685 0.989821i
$$769$$ 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i $$0.181818\pi$$
0.415415 + 0.909632i $$0.363636\pi$$
$$770$$ 0 0
$$771$$ 1.04408 0.306569i 1.04408 0.306569i
$$772$$ 0.698939 + 1.53046i 0.698939 + 1.53046i
$$773$$ 0 0 −0.654861 0.755750i $$-0.727273\pi$$
0.654861 + 0.755750i $$0.272727\pi$$
$$774$$ 0.133340 + 0.153882i 0.133340 + 0.153882i
$$775$$ 0 0
$$776$$ −1.10181 + 1.27155i −1.10181 + 1.27155i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1.59435 0.468144i −1.59435 0.468144i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −0.142315 + 0.989821i −0.142315 + 0.989821i
$$785$$ 0 0
$$786$$ −0.244123 1.69791i −0.244123 1.69791i
$$787$$ −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i $$0.727273\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0.500000 + 0.321330i 0.500000 + 0.321330i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 0.959493 0.281733i $$-0.0909091\pi$$
−0.959493 + 0.281733i $$0.909091\pi$$
$$798$$ 0 0
$$799$$ 0 0