# Properties

 Label 672.2.bi.b.17.2 Level $672$ Weight $2$ Character 672.17 Analytic conductor $5.366$ Analytic rank $0$ Dimension $4$ CM discriminant -24 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(17,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("672.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 672.bi (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$5.36594701583$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 168) Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

## Embedding invariants

 Embedding label 17.2 Root $$0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 672.17 Dual form 672.2.bi.b.593.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.50000 + 0.866025i) q^{3} +(3.62132 - 2.09077i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(1.50000 + 0.866025i) q^{3} +(3.62132 - 2.09077i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(1.50000 + 2.59808i) q^{9} +(0.0857864 - 0.148586i) q^{11} +7.24264 q^{15} +(-0.621320 - 4.54026i) q^{21} +(6.24264 - 10.8126i) q^{25} +5.19615i q^{27} -10.4142 q^{29} +(5.37868 + 3.10538i) q^{31} +(0.257359 - 0.148586i) q^{33} +(-10.2426 - 4.18154i) q^{35} +(10.8640 + 6.27231i) q^{45} +(-1.74264 + 6.77962i) q^{49} +(-5.03553 + 8.72180i) q^{53} -0.717439i q^{55} +(3.98528 + 2.30090i) q^{59} +(3.00000 - 7.34847i) q^{63} +(8.48528 + 4.89898i) q^{73} +(18.7279 - 10.8126i) q^{75} +(-0.449747 + 0.0615465i) q^{77} +(3.86396 + 6.69258i) q^{79} +(-4.50000 + 7.79423i) q^{81} +3.76127i q^{83} +(-15.6213 - 9.01897i) q^{87} +(5.37868 + 9.31615i) q^{93} -11.5300i q^{97} +0.514719 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 6 q^{3} + 6 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10})$$ 4 * q + 6 * q^3 + 6 * q^5 + 2 * q^7 + 6 * q^9 $$4 q + 6 q^{3} + 6 q^{5} + 2 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{15} + 6 q^{21} + 8 q^{25} - 36 q^{29} + 30 q^{31} + 18 q^{33} - 24 q^{35} + 18 q^{45} + 10 q^{49} - 6 q^{53} - 18 q^{59} + 12 q^{63} + 24 q^{75} + 18 q^{77} - 10 q^{79} - 18 q^{81} - 54 q^{87} + 30 q^{93} + 36 q^{99}+O(q^{100})$$ 4 * q + 6 * q^3 + 6 * q^5 + 2 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^15 + 6 * q^21 + 8 * q^25 - 36 * q^29 + 30 * q^31 + 18 * q^33 - 24 * q^35 + 18 * q^45 + 10 * q^49 - 6 * q^53 - 18 * q^59 + 12 * q^63 + 24 * q^75 + 18 * q^77 - 10 * q^79 - 18 * q^81 - 54 * q^87 + 30 * q^93 + 36 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$421$$ $$449$$ $$577$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.50000 + 0.866025i 0.866025 + 0.500000i
$$4$$ 0 0
$$5$$ 3.62132 2.09077i 1.61950 0.935021i 0.632456 0.774597i $$-0.282047\pi$$
0.987048 0.160424i $$-0.0512862\pi$$
$$6$$ 0 0
$$7$$ −1.62132 2.09077i −0.612801 0.790237i
$$8$$ 0 0
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ 0.0857864 0.148586i 0.0258656 0.0448005i −0.852803 0.522233i $$-0.825099\pi$$
0.878668 + 0.477432i $$0.158432\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 7.24264 1.87004
$$16$$ 0 0
$$17$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$18$$ 0 0
$$19$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$20$$ 0 0
$$21$$ −0.621320 4.54026i −0.135583 0.990766i
$$22$$ 0 0
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ 0 0
$$25$$ 6.24264 10.8126i 1.24853 2.16251i
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 0 0
$$29$$ −10.4142 −1.93387 −0.966935 0.255021i $$-0.917918\pi$$
−0.966935 + 0.255021i $$0.917918\pi$$
$$30$$ 0 0
$$31$$ 5.37868 + 3.10538i 0.966039 + 0.557743i 0.898027 0.439941i $$-0.145001\pi$$
0.0680129 + 0.997684i $$0.478334\pi$$
$$32$$ 0 0
$$33$$ 0.257359 0.148586i 0.0448005 0.0258656i
$$34$$ 0 0
$$35$$ −10.2426 4.18154i −1.73132 0.706809i
$$36$$ 0 0
$$37$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ 10.8640 + 6.27231i 1.61950 + 0.935021i
$$46$$ 0 0
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 0 0
$$49$$ −1.74264 + 6.77962i −0.248949 + 0.968517i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −5.03553 + 8.72180i −0.691684 + 1.19803i 0.279602 + 0.960116i $$0.409797\pi$$
−0.971286 + 0.237915i $$0.923536\pi$$
$$54$$ 0 0
$$55$$ 0.717439i 0.0967394i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 3.98528 + 2.30090i 0.518839 + 0.299552i 0.736460 0.676481i $$-0.236496\pi$$
−0.217620 + 0.976034i $$0.569829\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$62$$ 0 0
$$63$$ 3.00000 7.34847i 0.377964 0.925820i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 8.48528 + 4.89898i 0.993127 + 0.573382i 0.906208 0.422833i $$-0.138964\pi$$
0.0869195 + 0.996215i $$0.472298\pi$$
$$74$$ 0 0
$$75$$ 18.7279 10.8126i 2.16251 1.24853i
$$76$$ 0 0
$$77$$ −0.449747 + 0.0615465i −0.0512535 + 0.00701388i
$$78$$ 0 0
$$79$$ 3.86396 + 6.69258i 0.434730 + 0.752974i 0.997274 0.0737937i $$-0.0235106\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 3.76127i 0.412854i 0.978462 + 0.206427i $$0.0661835\pi$$
−0.978462 + 0.206427i $$0.933816\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −15.6213 9.01897i −1.67478 0.966935i
$$88$$ 0 0
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 5.37868 + 9.31615i 0.557743 + 0.966039i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 11.5300i 1.17070i −0.810782 0.585348i $$-0.800958\pi$$
0.810782 0.585348i $$-0.199042\pi$$
$$98$$ 0 0
$$99$$ 0.514719 0.0517312
$$100$$ 0 0
$$101$$ −3.00000 1.73205i −0.298511 0.172345i 0.343263 0.939239i $$-0.388468\pi$$
−0.641774 + 0.766894i $$0.721801\pi$$
$$102$$ 0 0
$$103$$ −12.7279 + 7.34847i −1.25412 + 0.724066i −0.971925 0.235291i $$-0.924396\pi$$
−0.282194 + 0.959357i $$0.591062\pi$$
$$104$$ 0 0
$$105$$ −11.7426 15.1427i −1.14596 1.47778i
$$106$$ 0 0
$$107$$ −10.3284 17.8894i −0.998487 1.72943i −0.546869 0.837218i $$-0.684180\pi$$
−0.451618 0.892211i $$-0.649153\pi$$
$$108$$ 0 0
$$109$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.48528 + 9.50079i 0.498662 + 0.863708i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 31.3000i 2.79956i
$$126$$ 0 0
$$127$$ −6.75736 −0.599619 −0.299809 0.953999i $$-0.596923\pi$$
−0.299809 + 0.953999i $$0.596923\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −18.4706 + 10.6640i −1.61378 + 0.931717i −0.625297 + 0.780387i $$0.715022\pi$$
−0.988483 + 0.151330i $$0.951644\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 10.8640 + 18.8169i 0.935021 + 1.61950i
$$136$$ 0 0
$$137$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −37.7132 + 21.7737i −3.13191 + 1.80821i
$$146$$ 0 0
$$147$$ −8.48528 + 8.66025i −0.699854 + 0.714286i
$$148$$ 0 0
$$149$$ 1.41421 + 2.44949i 0.115857 + 0.200670i 0.918122 0.396298i $$-0.129705\pi$$
−0.802265 + 0.596968i $$0.796372\pi$$
$$150$$ 0 0
$$151$$ 11.1066 19.2372i 0.903842 1.56550i 0.0813788 0.996683i $$-0.474068\pi$$
0.822464 0.568818i $$-0.192599\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 25.9706 2.08601
$$156$$ 0 0
$$157$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$158$$ 0 0
$$159$$ −15.1066 + 8.72180i −1.19803 + 0.691684i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$164$$ 0 0
$$165$$ 0.621320 1.07616i 0.0483697 0.0837788i
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −15.0000 + 8.66025i −1.14043 + 0.658427i −0.946537 0.322596i $$-0.895445\pi$$
−0.193892 + 0.981023i $$0.562111\pi$$
$$174$$ 0 0
$$175$$ −32.7279 + 4.47871i −2.47400 + 0.338559i
$$176$$ 0 0
$$177$$ 3.98528 + 6.90271i 0.299552 + 0.518839i
$$178$$ 0 0
$$179$$ −5.65685 + 9.79796i −0.422813 + 0.732334i −0.996213 0.0869415i $$-0.972291\pi$$
0.573400 + 0.819275i $$0.305624\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 10.8640 8.42463i 0.790237 0.612801i
$$190$$ 0 0
$$191$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ 0 0
$$193$$ 10.7426 18.6068i 0.773272 1.33935i −0.162488 0.986710i $$-0.551952\pi$$
0.935760 0.352636i $$-0.114715\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 14.1421 1.00759 0.503793 0.863825i $$-0.331938\pi$$
0.503793 + 0.863825i $$0.331938\pi$$
$$198$$ 0 0
$$199$$ 21.2132 + 12.2474i 1.50376 + 0.868199i 0.999990 + 0.00436292i $$0.00138876\pi$$
0.503774 + 0.863836i $$0.331945\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 16.8848 + 21.7737i 1.18508 + 1.52822i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −2.22792 16.2804i −0.151241 1.10519i
$$218$$ 0 0
$$219$$ 8.48528 + 14.6969i 0.573382 + 0.993127i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 29.8651i 1.99992i −0.00910984 0.999959i $$-0.502900\pi$$
0.00910984 0.999959i $$-0.497100\pi$$
$$224$$ 0 0
$$225$$ 37.4558 2.49706
$$226$$ 0 0
$$227$$ −25.7132 14.8455i −1.70665 0.985332i −0.938647 0.344881i $$-0.887919\pi$$
−0.767999 0.640451i $$-0.778747\pi$$
$$228$$ 0 0
$$229$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$230$$ 0 0
$$231$$ −0.727922 0.297173i −0.0478938 0.0195525i
$$232$$ 0 0
$$233$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 13.3852i 0.869459i
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −20.2279 11.6786i −1.30300 0.752285i −0.322078 0.946713i $$-0.604381\pi$$
−0.980917 + 0.194429i $$0.937715\pi$$
$$242$$ 0 0
$$243$$ −13.5000 + 7.79423i −0.866025 + 0.500000i
$$244$$ 0 0
$$245$$ 7.86396 + 28.1946i 0.502410 + 1.80129i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −3.25736 + 5.64191i −0.206427 + 0.357542i
$$250$$ 0 0
$$251$$ 20.4874i 1.29316i −0.762848 0.646578i $$-0.776200\pi$$
0.762848 0.646578i $$-0.223800\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −15.6213 27.0569i −0.966935 1.67478i
$$262$$ 0 0
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ 0 0
$$265$$ 42.1126i 2.58696i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −18.8345 10.8741i −1.14836 0.663007i −0.199874 0.979822i $$-0.564053\pi$$
−0.948487 + 0.316815i $$0.897387\pi$$
$$270$$ 0 0
$$271$$ 5.89340 3.40256i 0.357998 0.206691i −0.310204 0.950670i $$-0.600397\pi$$
0.668202 + 0.743980i $$0.267064\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.07107 1.85514i −0.0645878 0.111869i
$$276$$ 0 0
$$277$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$278$$ 0 0
$$279$$ 18.6323i 1.11549i
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8.50000 + 14.7224i 0.500000 + 0.866025i
$$290$$ 0 0
$$291$$ 9.98528 17.2950i 0.585348 1.01385i
$$292$$ 0 0
$$293$$ 3.34101i 0.195184i 0.995227 + 0.0975919i $$0.0311140\pi$$
−0.995227 + 0.0975919i $$0.968886\pi$$
$$294$$ 0 0
$$295$$ 19.2426 1.12035
$$296$$ 0 0
$$297$$ 0.772078 + 0.445759i 0.0448005 + 0.0258656i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −3.00000 5.19615i −0.172345 0.298511i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ −25.4558 −1.44813
$$310$$ 0 0
$$311$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$312$$ 0 0
$$313$$ 21.2574 12.2729i 1.20154 0.693708i 0.240640 0.970614i $$-0.422643\pi$$
0.960897 + 0.276907i $$0.0893093\pi$$
$$314$$ 0 0
$$315$$ −4.50000 32.8835i −0.253546 1.85277i
$$316$$ 0 0
$$317$$ 15.2782 + 26.4626i 0.858108 + 1.48629i 0.873732 + 0.486408i $$0.161693\pi$$
−0.0156238 + 0.999878i $$0.504973\pi$$
$$318$$ 0 0
$$319$$ −0.893398 + 1.54741i −0.0500207 + 0.0866384i
$$320$$ 0 0
$$321$$ 35.7787i 1.99697i
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 36.4558 1.98588 0.992938 0.118633i $$-0.0378512\pi$$
0.992938 + 0.118633i $$0.0378512\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0.922836 0.532799i 0.0499743 0.0288527i
$$342$$ 0 0
$$343$$ 17.0000 7.34847i 0.917914 0.396780i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 14.1421 24.4949i 0.759190 1.31495i −0.184075 0.982912i $$-0.558929\pi$$
0.943264 0.332043i $$-0.107738\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$360$$ 0 0
$$361$$ 9.50000 16.4545i 0.500000 0.866025i
$$362$$ 0 0
$$363$$ 19.0016i 0.997324i
$$364$$ 0 0
$$365$$ 40.9706 2.14450
$$366$$ 0 0
$$367$$ 26.3787 + 15.2297i 1.37696 + 0.794986i 0.991792 0.127862i $$-0.0408116\pi$$
0.385164 + 0.922848i $$0.374145\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 26.3995 3.61269i 1.37059 0.187561i
$$372$$ 0 0
$$373$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$374$$ 0 0
$$375$$ 27.1066 46.9500i 1.39978 2.42449i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ −10.1360 5.85204i −0.519285 0.299809i
$$382$$ 0 0
$$383$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$384$$ 0 0
$$385$$ −1.50000 + 1.16320i −0.0764471 + 0.0592821i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 15.5563 26.9444i 0.788738 1.36613i −0.138002 0.990432i $$-0.544068\pi$$
0.926740 0.375703i $$-0.122599\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −36.9411 −1.86343
$$394$$ 0 0
$$395$$ 27.9853 + 16.1573i 1.40809 + 0.812962i
$$396$$ 0 0
$$397$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 37.6339i 1.87004i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 9.47056 + 5.46783i 0.468289 + 0.270367i 0.715523 0.698589i $$-0.246188\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −1.65076 12.0628i −0.0812285 0.593572i
$$414$$ 0 0
$$415$$ 7.86396 + 13.6208i 0.386027 + 0.668618i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 10.3923i 0.507697i 0.967244 + 0.253849i $$0.0816965\pi$$
−0.967244 + 0.253849i $$0.918303\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$432$$ 0 0
$$433$$ 39.1918i 1.88344i −0.336399 0.941720i $$-0.609209\pi$$
0.336399 0.941720i $$-0.390791\pi$$
$$434$$ 0 0
$$435$$ −75.4264 −3.61642
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −36.1066 + 20.8462i −1.72327 + 0.994933i −0.811366 + 0.584539i $$0.801275\pi$$
−0.911908 + 0.410394i $$0.865391\pi$$
$$440$$ 0 0
$$441$$ −20.2279 + 5.64191i −0.963234 + 0.268662i
$$442$$ 0 0
$$443$$ 20.5711 + 35.6301i 0.977361 + 1.69284i 0.671913 + 0.740630i $$0.265473\pi$$
0.305448 + 0.952209i $$0.401194\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 4.89898i 0.231714i
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 33.3198 19.2372i 1.56550 0.903842i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 17.9853 + 31.1514i 0.841316 + 1.45720i 0.888783 + 0.458329i $$0.151552\pi$$
−0.0474665 + 0.998873i $$0.515115\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 38.1051i 1.77473i 0.461065 + 0.887366i $$0.347467\pi$$
−0.461065 + 0.887366i $$0.652533\pi$$
$$462$$ 0 0
$$463$$ 26.0000 1.20832 0.604161 0.796862i $$-0.293508\pi$$
0.604161 + 0.796862i $$0.293508\pi$$
$$464$$ 0 0
$$465$$ 38.9558 + 22.4912i 1.80653 + 1.04300i
$$466$$ 0 0
$$467$$ 15.0000 8.66025i 0.694117 0.400749i −0.111035 0.993816i $$-0.535417\pi$$
0.805153 + 0.593068i $$0.202083\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −30.2132 −1.38337
$$478$$ 0 0
$$479$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −24.1066 41.7539i −1.09462 1.89595i
$$486$$ 0 0
$$487$$ −18.5919 + 32.2021i −0.842479 + 1.45922i 0.0453143 + 0.998973i $$0.485571\pi$$
−0.887793 + 0.460243i $$0.847762\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −21.6863 −0.978689 −0.489344 0.872091i $$-0.662764\pi$$
−0.489344 + 0.872091i $$0.662764\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 1.86396 1.07616i 0.0837788 0.0483697i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ −14.4853 −0.644587
$$506$$ 0 0
$$507$$ −19.5000 11.2583i −0.866025 0.500000i
$$508$$ 0 0
$$509$$ −17.3787 + 10.0336i −0.770296 + 0.444731i −0.832980 0.553303i $$-0.813367\pi$$
0.0626839 + 0.998033i $$0.480034\pi$$
$$510$$ 0 0
$$511$$ −3.51472 25.6836i −0.155482 1.13618i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −30.7279 + 53.2223i −1.35403 + 2.34526i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −30.0000 −1.31685
$$520$$ 0 0
$$521$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$522$$ 0 0
$$523$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$524$$ 0 0
$$525$$ −52.9706 21.6251i −2.31182 0.943799i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −11.5000 + 19.9186i −0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ 13.8054i 0.599104i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −74.8051 43.1887i −3.23411 1.86721i
$$536$$ 0 0
$$537$$ −16.9706 + 9.79796i −0.732334 + 0.422813i
$$538$$ 0 0
$$539$$ 0.857864 + 0.840532i 0.0369508 + 0.0362043i
$$540$$ 0 0
$$541$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 7.72792 18.9295i 0.328625 0.804963i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 15.9645 27.6513i 0.676436 1.17162i −0.299611 0.954062i $$-0.596857\pi$$
0.976047 0.217560i $$-0.0698099\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −4.71320 2.72117i −0.198638 0.114684i 0.397382 0.917653i $$-0.369919\pi$$
−0.596020 + 0.802970i $$0.703252\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 23.5919 3.22848i 0.990766 0.135583i
$$568$$ 0 0
$$569$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$570$$ 0 0
$$571$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −41.2279 23.8030i −1.71634 0.990930i −0.925361 0.379088i $$-0.876238\pi$$
−0.790980 0.611842i $$-0.790429\pi$$
$$578$$ 0 0
$$579$$ 32.2279 18.6068i 1.33935 0.773272i
$$580$$ 0 0
$$581$$ 7.86396 6.09823i 0.326252 0.252997i
$$582$$ 0 0
$$583$$ 0.863961 + 1.49642i 0.0357816 + 0.0619756i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 30.5316i 1.26017i −0.776525 0.630087i $$-0.783019\pi$$
0.776525 0.630087i $$-0.216981\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 21.2132 + 12.2474i 0.872595 + 0.503793i
$$592$$ 0 0
$$593$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 21.2132 + 36.7423i 0.868199 + 1.50376i
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ 0 0
$$601$$ 22.7628i 0.928516i 0.885700 + 0.464258i $$0.153679\pi$$
−0.885700 + 0.464258i $$0.846321\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 39.7279 + 22.9369i 1.61517 + 0.932519i
$$606$$ 0 0
$$607$$ 35.5919 20.5490i 1.44463 0.834058i 0.446476 0.894795i $$-0.352679\pi$$
0.998154 + 0.0607380i $$0.0193454\pi$$
$$608$$ 0 0
$$609$$ 6.47056 + 47.2832i 0.262200 + 1.91601i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −34.2279 59.2845i −1.36912 2.37138i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −20.7574 −0.826337 −0.413169 0.910654i $$-0.635578\pi$$
−0.413169 + 0.910654i $$0.635578\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −24.4706 + 14.1281i −0.971085 + 0.560656i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$648$$ 0 0
$$649$$ 0.683766 0.394773i 0.0268402 0.0154962i
$$650$$ 0 0
$$651$$ 10.7574 26.3500i 0.421614 1.03274i
$$652$$ 0 0
$$653$$ −4.52082 7.83028i −0.176913 0.306423i 0.763909 0.645325i $$-0.223278\pi$$
−0.940822 + 0.338902i $$0.889945\pi$$
$$654$$ 0 0
$$655$$ −44.5919 + 77.2354i −1.74235 + 3.01784i
$$656$$ 0 0
$$657$$ 29.3939i 1.14676i
$$658$$ 0 0
$$659$$ 45.2548 1.76288 0.881439 0.472298i $$-0.156575\pi$$
0.881439 + 0.472298i $$0.156575\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 25.8640 44.7977i 0.999959 1.73198i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −50.9411 −1.96364 −0.981818 0.189824i $$-0.939208\pi$$
−0.981818 + 0.189824i $$0.939208\pi$$
$$674$$ 0 0
$$675$$ 56.1838 + 32.4377i 2.16251 + 1.24853i
$$676$$ 0 0
$$677$$ 24.6213 14.2151i 0.946274 0.546332i 0.0543526 0.998522i $$-0.482690\pi$$
0.891922 + 0.452190i $$0.149357\pi$$
$$678$$ 0 0
$$679$$ −24.1066 + 18.6938i −0.925126 + 0.717404i
$$680$$ 0 0
$$681$$ −25.7132 44.5366i −0.985332 1.70665i
$$682$$ 0 0
$$683$$ 21.0858 36.5217i 0.806825 1.39746i −0.108227 0.994126i $$-0.534517\pi$$
0.915052 0.403336i $$-0.132149\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$692$$ 0 0
$$693$$ −0.834524 1.07616i −0.0317009 0.0408799i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 51.3848 1.94078 0.970388 0.241551i $$-0.0776561\pi$$
0.970388 + 0.241551i $$0.0776561\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1.24264 + 9.08052i 0.0467343 + 0.341508i
$$708$$ 0 0
$$709$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$710$$ 0 0
$$711$$ −11.5919 + 20.0777i −0.434730 + 0.752974i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$720$$ 0 0
$$721$$ 36.0000 + 14.6969i 1.34071 + 0.547343i
$$722$$ 0 0
$$723$$ −20.2279 35.0358i −0.752285 1.30300i
$$724$$ 0 0
$$725$$ −65.0122 + 112.604i −2.41449 + 4.18202i
$$726$$ 0 0
$$727$$ 28.6764i 1.06355i 0.846886 + 0.531775i $$0.178475\pi$$
−0.846886 + 0.531775i $$0.821525\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$734$$ 0 0
$$735$$ −12.6213 + 49.1023i −0.465544 + 1.81117i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 10.2426 + 5.91359i 0.375261 + 0.216657i
$$746$$ 0 0
$$747$$ −9.77208 + 5.64191i −0.357542 + 0.206427i
$$748$$ 0 0
$$749$$ −20.6569 + 50.5988i −0.754785 + 1.84884i
$$750$$ 0 0
$$751$$ −25.8345 44.7467i −0.942715 1.63283i −0.760263 0.649616i $$-0.774930\pi$$
−0.182453 0.983215i $$-0.558404\pi$$
$$752$$ 0 0
$$753$$ 17.7426 30.7312i 0.646578 1.11991i
$$754$$ 0 0
$$755$$ 92.8854i 3.38045i
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 47.0116i 1.69528i 0.530572 + 0.847640i $$0.321977\pi$$
−0.530572 + 0.847640i $$0.678023\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −45.0000 25.9808i −1.61854 0.934463i −0.987299 0.158874i $$-0.949213\pi$$
−0.631239 0.775589i $$-0.717453\pi$$
$$774$$ 0 0
$$775$$ 67.1543 38.7716i 2.41225 1.39272i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 54.1138i 1.93387i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ −36.4706 + 63.1689i −1.29348 + 2.24037i
$$796$$ 0 0
$$797$$ 55.2006i 1.95530i −0.210230 0.977652i $$-0.567421\pi$$
0.210230 0.977652i $$-0.432579\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0