# Properties

 Label 1152.2.k.b.289.1 Level $1152$ Weight $2$ Character 1152.289 Analytic conductor $9.199$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(289,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1152.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.k (of order $$4$$, 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: $$9.19876631285$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 16) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 289.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1152.289 Dual form 1152.2.k.b.865.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 1.00000i) q^{5} +2.00000i q^{7} +O(q^{10})$$ $$q+(-1.00000 + 1.00000i) q^{5} +2.00000i q^{7} +(1.00000 - 1.00000i) q^{11} +(1.00000 + 1.00000i) q^{13} +2.00000 q^{17} +(-3.00000 - 3.00000i) q^{19} +6.00000i q^{23} +3.00000i q^{25} +(3.00000 + 3.00000i) q^{29} -8.00000 q^{31} +(-2.00000 - 2.00000i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(-5.00000 + 5.00000i) q^{43} -8.00000 q^{47} +3.00000 q^{49} +(-5.00000 + 5.00000i) q^{53} +2.00000i q^{55} +(-3.00000 + 3.00000i) q^{59} +(9.00000 + 9.00000i) q^{61} -2.00000 q^{65} +(5.00000 + 5.00000i) q^{67} -10.0000i q^{71} +4.00000i q^{73} +(2.00000 + 2.00000i) q^{77} +(-1.00000 - 1.00000i) q^{83} +(-2.00000 + 2.00000i) q^{85} +4.00000i q^{89} +(-2.00000 + 2.00000i) q^{91} +6.00000 q^{95} -2.00000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{5}+O(q^{10})$$ 2 * q - 2 * q^5 $$2 q - 2 q^{5} + 2 q^{11} + 2 q^{13} + 4 q^{17} - 6 q^{19} + 6 q^{29} - 16 q^{31} - 4 q^{35} - 6 q^{37} - 10 q^{43} - 16 q^{47} + 6 q^{49} - 10 q^{53} - 6 q^{59} + 18 q^{61} - 4 q^{65} + 10 q^{67} + 4 q^{77} - 2 q^{83} - 4 q^{85} - 4 q^{91} + 12 q^{95} - 4 q^{97}+O(q^{100})$$ 2 * q - 2 * q^5 + 2 * q^11 + 2 * q^13 + 4 * q^17 - 6 * q^19 + 6 * q^29 - 16 * q^31 - 4 * q^35 - 6 * q^37 - 10 * q^43 - 16 * q^47 + 6 * q^49 - 10 * q^53 - 6 * q^59 + 18 * q^61 - 4 * q^65 + 10 * q^67 + 4 * q^77 - 2 * q^83 - 4 * q^85 - 4 * q^91 + 12 * q^95 - 4 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$641$$ $$901$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −1.00000 + 1.00000i −0.447214 + 0.447214i −0.894427 0.447214i $$-0.852416\pi$$
0.447214 + 0.894427i $$0.352416\pi$$
$$6$$ 0 0
$$7$$ 2.00000i 0.755929i 0.925820 + 0.377964i $$0.123376\pi$$
−0.925820 + 0.377964i $$0.876624\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.00000 1.00000i 0.301511 0.301511i −0.540094 0.841605i $$-0.681611\pi$$
0.841605 + 0.540094i $$0.181611\pi$$
$$12$$ 0 0
$$13$$ 1.00000 + 1.00000i 0.277350 + 0.277350i 0.832050 0.554700i $$-0.187167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ −3.00000 3.00000i −0.688247 0.688247i 0.273597 0.961844i $$-0.411786\pi$$
−0.961844 + 0.273597i $$0.911786\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 6.00000i 1.25109i 0.780189 + 0.625543i $$0.215123\pi$$
−0.780189 + 0.625543i $$0.784877\pi$$
$$24$$ 0 0
$$25$$ 3.00000i 0.600000i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 3.00000 + 3.00000i 0.557086 + 0.557086i 0.928477 0.371391i $$-0.121119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −2.00000 2.00000i −0.338062 0.338062i
$$36$$ 0 0
$$37$$ −3.00000 + 3.00000i −0.493197 + 0.493197i −0.909312 0.416115i $$-0.863391\pi$$
0.416115 + 0.909312i $$0.363391\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ −5.00000 + 5.00000i −0.762493 + 0.762493i −0.976772 0.214280i $$-0.931260\pi$$
0.214280 + 0.976772i $$0.431260\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ 0 0
$$49$$ 3.00000 0.428571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −5.00000 + 5.00000i −0.686803 + 0.686803i −0.961524 0.274721i $$-0.911414\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 0 0
$$55$$ 2.00000i 0.269680i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −3.00000 + 3.00000i −0.390567 + 0.390567i −0.874889 0.484323i $$-0.839066\pi$$
0.484323 + 0.874889i $$0.339066\pi$$
$$60$$ 0 0
$$61$$ 9.00000 + 9.00000i 1.15233 + 1.15233i 0.986084 + 0.166248i $$0.0531652\pi$$
0.166248 + 0.986084i $$0.446835\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −2.00000 −0.248069
$$66$$ 0 0
$$67$$ 5.00000 + 5.00000i 0.610847 + 0.610847i 0.943167 0.332320i $$-0.107831\pi$$
−0.332320 + 0.943167i $$0.607831\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 10.0000i 1.18678i −0.804914 0.593391i $$-0.797789\pi$$
0.804914 0.593391i $$-0.202211\pi$$
$$72$$ 0 0
$$73$$ 4.00000i 0.468165i 0.972217 + 0.234082i $$0.0752085\pi$$
−0.972217 + 0.234082i $$0.924791\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 2.00000 + 2.00000i 0.227921 + 0.227921i
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1.00000 1.00000i −0.109764 0.109764i 0.650092 0.759856i $$-0.274731\pi$$
−0.759856 + 0.650092i $$0.774731\pi$$
$$84$$ 0 0
$$85$$ −2.00000 + 2.00000i −0.216930 + 0.216930i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 4.00000i 0.423999i 0.977270 + 0.212000i $$0.0679975\pi$$
−0.977270 + 0.212000i $$0.932002\pi$$
$$90$$ 0 0
$$91$$ −2.00000 + 2.00000i −0.209657 + 0.209657i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 6.00000 0.615587
$$96$$ 0 0
$$97$$ −2.00000 −0.203069 −0.101535 0.994832i $$-0.532375\pi$$
−0.101535 + 0.994832i $$0.532375\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 11.0000 11.0000i 1.09454 1.09454i 0.0995037 0.995037i $$-0.468274\pi$$
0.995037 0.0995037i $$-0.0317255\pi$$
$$102$$ 0 0
$$103$$ 6.00000i 0.591198i −0.955312 0.295599i $$-0.904481\pi$$
0.955312 0.295599i $$-0.0955191\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −7.00000 + 7.00000i −0.676716 + 0.676716i −0.959256 0.282540i $$-0.908823\pi$$
0.282540 + 0.959256i $$0.408823\pi$$
$$108$$ 0 0
$$109$$ −3.00000 3.00000i −0.287348 0.287348i 0.548683 0.836031i $$-0.315129\pi$$
−0.836031 + 0.548683i $$0.815129\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ −6.00000 6.00000i −0.559503 0.559503i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 4.00000i 0.366679i
$$120$$ 0 0
$$121$$ 9.00000i 0.818182i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −8.00000 8.00000i −0.715542 0.715542i
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 11.0000 + 11.0000i 0.961074 + 0.961074i 0.999270 0.0381958i $$-0.0121611\pi$$
−0.0381958 + 0.999270i $$0.512161\pi$$
$$132$$ 0 0
$$133$$ 6.00000 6.00000i 0.520266 0.520266i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 8.00000i 0.683486i 0.939793 + 0.341743i $$0.111017\pi$$
−0.939793 + 0.341743i $$0.888983\pi$$
$$138$$ 0 0
$$139$$ 3.00000 3.00000i 0.254457 0.254457i −0.568338 0.822795i $$-0.692414\pi$$
0.822795 + 0.568338i $$0.192414\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.00000 0.167248
$$144$$ 0 0
$$145$$ −6.00000 −0.498273
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 7.00000 7.00000i 0.573462 0.573462i −0.359632 0.933094i $$-0.617098\pi$$
0.933094 + 0.359632i $$0.117098\pi$$
$$150$$ 0 0
$$151$$ 10.0000i 0.813788i 0.913475 + 0.406894i $$0.133388\pi$$
−0.913475 + 0.406894i $$0.866612\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 8.00000 8.00000i 0.642575 0.642575i
$$156$$ 0 0
$$157$$ −15.0000 15.0000i −1.19713 1.19713i −0.975022 0.222108i $$-0.928706\pi$$
−0.222108 0.975022i $$-0.571294\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −12.0000 −0.945732
$$162$$ 0 0
$$163$$ 1.00000 + 1.00000i 0.0783260 + 0.0783260i 0.745184 0.666858i $$-0.232361\pi$$
−0.666858 + 0.745184i $$0.732361\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.00000i 0.154765i −0.997001 0.0773823i $$-0.975344\pi$$
0.997001 0.0773823i $$-0.0246562\pi$$
$$168$$ 0 0
$$169$$ 11.0000i 0.846154i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1.00000 1.00000i −0.0760286 0.0760286i 0.668070 0.744099i $$-0.267121\pi$$
−0.744099 + 0.668070i $$0.767121\pi$$
$$174$$ 0 0
$$175$$ −6.00000 −0.453557
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −17.0000 17.0000i −1.27064 1.27064i −0.945753 0.324887i $$-0.894674\pi$$
−0.324887 0.945753i $$-0.605326\pi$$
$$180$$ 0 0
$$181$$ 9.00000 9.00000i 0.668965 0.668965i −0.288512 0.957476i $$-0.593160\pi$$
0.957476 + 0.288512i $$0.0931604\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 6.00000i 0.441129i
$$186$$ 0 0
$$187$$ 2.00000 2.00000i 0.146254 0.146254i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 8.00000 0.578860 0.289430 0.957199i $$-0.406534\pi$$
0.289430 + 0.957199i $$0.406534\pi$$
$$192$$ 0 0
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −17.0000 + 17.0000i −1.21120 + 1.21120i −0.240567 + 0.970632i $$0.577334\pi$$
−0.970632 + 0.240567i $$0.922666\pi$$
$$198$$ 0 0
$$199$$ 14.0000i 0.992434i −0.868199 0.496217i $$-0.834722\pi$$
0.868199 0.496217i $$-0.165278\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −6.00000 + 6.00000i −0.421117 + 0.421117i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ 9.00000 + 9.00000i 0.619586 + 0.619586i 0.945425 0.325840i $$-0.105647\pi$$
−0.325840 + 0.945425i $$0.605647\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 10.0000i 0.681994i
$$216$$ 0 0
$$217$$ 16.0000i 1.08615i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 2.00000 + 2.00000i 0.134535 + 0.134535i
$$222$$ 0 0
$$223$$ 24.0000 1.60716 0.803579 0.595198i $$-0.202926\pi$$
0.803579 + 0.595198i $$0.202926\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 15.0000 + 15.0000i 0.995585 + 0.995585i 0.999990 0.00440533i $$-0.00140226\pi$$
−0.00440533 + 0.999990i $$0.501402\pi$$
$$228$$ 0 0
$$229$$ −7.00000 + 7.00000i −0.462573 + 0.462573i −0.899498 0.436925i $$-0.856068\pi$$
0.436925 + 0.899498i $$0.356068\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 4.00000i 0.262049i −0.991379 0.131024i $$-0.958173\pi$$
0.991379 0.131024i $$-0.0418266\pi$$
$$234$$ 0 0
$$235$$ 8.00000 8.00000i 0.521862 0.521862i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −3.00000 + 3.00000i −0.191663 + 0.191663i
$$246$$ 0 0
$$247$$ 6.00000i 0.381771i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 21.0000 21.0000i 1.32551 1.32551i 0.416265 0.909243i $$-0.363339\pi$$
0.909243 0.416265i $$-0.136661\pi$$
$$252$$ 0 0
$$253$$ 6.00000 + 6.00000i 0.377217 + 0.377217i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 22.0000 1.37232 0.686161 0.727450i $$-0.259294\pi$$
0.686161 + 0.727450i $$0.259294\pi$$
$$258$$ 0 0
$$259$$ −6.00000 6.00000i −0.372822 0.372822i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6.00000i 0.369976i 0.982741 + 0.184988i $$0.0592246\pi$$
−0.982741 + 0.184988i $$0.940775\pi$$
$$264$$ 0 0
$$265$$ 10.0000i 0.614295i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 3.00000 + 3.00000i 0.182913 + 0.182913i 0.792624 0.609711i $$-0.208714\pi$$
−0.609711 + 0.792624i $$0.708714\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 3.00000 + 3.00000i 0.180907 + 0.180907i
$$276$$ 0 0
$$277$$ −3.00000 + 3.00000i −0.180253 + 0.180253i −0.791466 0.611213i $$-0.790682\pi$$
0.611213 + 0.791466i $$0.290682\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 20.0000i 1.19310i −0.802576 0.596550i $$-0.796538\pi$$
0.802576 0.596550i $$-0.203462\pi$$
$$282$$ 0 0
$$283$$ 15.0000 15.0000i 0.891657 0.891657i −0.103022 0.994679i $$-0.532851\pi$$
0.994679 + 0.103022i $$0.0328511\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 15.0000 15.0000i 0.876309 0.876309i −0.116841 0.993151i $$-0.537277\pi$$
0.993151 + 0.116841i $$0.0372769\pi$$
$$294$$ 0 0
$$295$$ 6.00000i 0.349334i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −6.00000 + 6.00000i −0.346989 + 0.346989i
$$300$$ 0 0
$$301$$ −10.0000 10.0000i −0.576390 0.576390i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −18.0000 −1.03068
$$306$$ 0 0
$$307$$ 5.00000 + 5.00000i 0.285365 + 0.285365i 0.835244 0.549879i $$-0.185326\pi$$
−0.549879 + 0.835244i $$0.685326\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 30.0000i 1.70114i 0.525859 + 0.850572i $$0.323744\pi$$
−0.525859 + 0.850572i $$0.676256\pi$$
$$312$$ 0 0
$$313$$ 16.0000i 0.904373i −0.891923 0.452187i $$-0.850644\pi$$
0.891923 0.452187i $$-0.149356\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −5.00000 5.00000i −0.280828 0.280828i 0.552611 0.833439i $$-0.313631\pi$$
−0.833439 + 0.552611i $$0.813631\pi$$
$$318$$ 0 0
$$319$$ 6.00000 0.335936
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −6.00000 6.00000i −0.333849 0.333849i
$$324$$ 0 0
$$325$$ −3.00000 + 3.00000i −0.166410 + 0.166410i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 16.0000i 0.882109i
$$330$$ 0 0
$$331$$ −1.00000 + 1.00000i −0.0549650 + 0.0549650i −0.734055 0.679090i $$-0.762375\pi$$
0.679090 + 0.734055i $$0.262375\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −10.0000 −0.546358
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −8.00000 + 8.00000i −0.433224 + 0.433224i
$$342$$ 0 0
$$343$$ 20.0000i 1.07990i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 13.0000 13.0000i 0.697877 0.697877i −0.266076 0.963952i $$-0.585727\pi$$
0.963952 + 0.266076i $$0.0857271\pi$$
$$348$$ 0 0
$$349$$ −3.00000 3.00000i −0.160586 0.160586i 0.622240 0.782826i $$-0.286223\pi$$
−0.782826 + 0.622240i $$0.786223\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 10.0000 + 10.0000i 0.530745 + 0.530745i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 26.0000i 1.37223i −0.727494 0.686114i $$-0.759315\pi$$
0.727494 0.686114i $$-0.240685\pi$$
$$360$$ 0 0
$$361$$ 1.00000i 0.0526316i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −4.00000 4.00000i −0.209370 0.209370i
$$366$$ 0 0
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −10.0000 10.0000i −0.519174 0.519174i
$$372$$ 0 0
$$373$$ 5.00000 5.00000i 0.258890 0.258890i −0.565712 0.824603i $$-0.691399\pi$$
0.824603 + 0.565712i $$0.191399\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 6.00000i 0.309016i
$$378$$ 0 0
$$379$$ 3.00000 3.00000i 0.154100 0.154100i −0.625847 0.779946i $$-0.715246\pi$$
0.779946 + 0.625847i $$0.215246\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 16.0000 0.817562 0.408781 0.912633i $$-0.365954\pi$$
0.408781 + 0.912633i $$0.365954\pi$$
$$384$$ 0 0
$$385$$ −4.00000 −0.203859
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −13.0000 + 13.0000i −0.659126 + 0.659126i −0.955173 0.296047i $$-0.904331\pi$$
0.296047 + 0.955173i $$0.404331\pi$$
$$390$$ 0 0
$$391$$ 12.0000i 0.606866i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 5.00000 + 5.00000i 0.250943 + 0.250943i 0.821357 0.570414i $$-0.193217\pi$$
−0.570414 + 0.821357i $$0.693217\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ −8.00000 8.00000i −0.398508 0.398508i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 6.00000i 0.297409i
$$408$$ 0 0
$$409$$ 16.0000i 0.791149i 0.918434 + 0.395575i $$0.129455\pi$$
−0.918434 + 0.395575i $$0.870545\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −6.00000 6.00000i −0.295241 0.295241i
$$414$$ 0 0
$$415$$ 2.00000 0.0981761
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 3.00000 + 3.00000i 0.146560 + 0.146560i 0.776579 0.630020i $$-0.216953\pi$$
−0.630020 + 0.776579i $$0.716953\pi$$
$$420$$ 0 0
$$421$$ 9.00000 9.00000i 0.438633 0.438633i −0.452919 0.891552i $$-0.649617\pi$$
0.891552 + 0.452919i $$0.149617\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 6.00000i 0.291043i
$$426$$ 0 0
$$427$$ −18.0000 + 18.0000i −0.871081 + 0.871081i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −32.0000 −1.54139 −0.770693 0.637207i $$-0.780090\pi$$
−0.770693 + 0.637207i $$0.780090\pi$$
$$432$$ 0 0
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 18.0000 18.0000i 0.861057 0.861057i
$$438$$ 0 0
$$439$$ 14.0000i 0.668184i −0.942541 0.334092i $$-0.891570\pi$$
0.942541 0.334092i $$-0.108430\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −15.0000 + 15.0000i −0.712672 + 0.712672i −0.967093 0.254422i $$-0.918115\pi$$
0.254422 + 0.967093i $$0.418115\pi$$
$$444$$ 0 0
$$445$$ −4.00000 4.00000i −0.189618 0.189618i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 4.00000i 0.187523i
$$456$$ 0 0
$$457$$ 32.0000i 1.49690i 0.663193 + 0.748448i $$0.269201\pi$$
−0.663193 + 0.748448i $$0.730799\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 11.0000 + 11.0000i 0.512321 + 0.512321i 0.915237 0.402916i $$-0.132003\pi$$
−0.402916 + 0.915237i $$0.632003\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −5.00000 5.00000i −0.231372 0.231372i 0.581893 0.813265i $$-0.302312\pi$$
−0.813265 + 0.581893i $$0.802312\pi$$
$$468$$ 0 0
$$469$$ −10.0000 + 10.0000i −0.461757 + 0.461757i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 10.0000i 0.459800i
$$474$$ 0 0
$$475$$ 9.00000 9.00000i 0.412948 0.412948i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 40.0000 1.82765 0.913823 0.406112i $$-0.133116\pi$$
0.913823 + 0.406112i $$0.133116\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 2.00000 2.00000i 0.0908153 0.0908153i
$$486$$ 0 0
$$487$$ 2.00000i 0.0906287i 0.998973 + 0.0453143i $$0.0144289\pi$$
−0.998973 + 0.0453143i $$0.985571\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −19.0000 + 19.0000i −0.857458 + 0.857458i −0.991038 0.133580i $$-0.957353\pi$$
0.133580 + 0.991038i $$0.457353\pi$$
$$492$$ 0 0
$$493$$ 6.00000 + 6.00000i 0.270226 + 0.270226i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 20.0000 0.897123
$$498$$ 0 0
$$499$$ −23.0000 23.0000i −1.02962 1.02962i −0.999548 0.0300737i $$-0.990426\pi$$
−0.0300737 0.999548i $$-0.509574\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 6.00000i 0.267527i 0.991013 + 0.133763i $$0.0427062\pi$$
−0.991013 + 0.133763i $$0.957294\pi$$
$$504$$ 0 0
$$505$$ 22.0000i 0.978987i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 23.0000 + 23.0000i 1.01946 + 1.01946i 0.999807 + 0.0196502i $$0.00625524\pi$$
0.0196502 + 0.999807i $$0.493745\pi$$
$$510$$ 0 0
$$511$$ −8.00000 −0.353899
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 6.00000 + 6.00000i 0.264392 + 0.264392i
$$516$$ 0 0
$$517$$ −8.00000 + 8.00000i −0.351840 + 0.351840i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 40.0000i 1.75243i 0.481919 + 0.876216i $$0.339940\pi$$
−0.481919 + 0.876216i $$0.660060\pi$$
$$522$$ 0 0
$$523$$ −25.0000 + 25.0000i −1.09317 + 1.09317i −0.0979859 + 0.995188i $$0.531240\pi$$
−0.995188 + 0.0979859i $$0.968760\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −16.0000 −0.696971
$$528$$ 0 0
$$529$$ −13.0000 −0.565217
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 14.0000i 0.605273i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3.00000 3.00000i 0.129219 0.129219i
$$540$$ 0 0
$$541$$ 9.00000 + 9.00000i 0.386940 + 0.386940i 0.873595 0.486654i $$-0.161783\pi$$
−0.486654 + 0.873595i $$0.661783\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 6.00000 0.257012
$$546$$ 0 0
$$547$$ 5.00000 + 5.00000i 0.213785 + 0.213785i 0.805873 0.592088i $$-0.201696\pi$$
−0.592088 + 0.805873i $$0.701696\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 18.0000i 0.766826i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −25.0000 25.0000i −1.05928 1.05928i −0.998128 0.0611558i $$-0.980521\pi$$
−0.0611558 0.998128i $$-0.519479\pi$$
$$558$$ 0 0
$$559$$ −10.0000 −0.422955
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 19.0000 + 19.0000i 0.800755 + 0.800755i 0.983213 0.182459i $$-0.0584057\pi$$
−0.182459 + 0.983213i $$0.558406\pi$$
$$564$$ 0 0
$$565$$ −6.00000 + 6.00000i −0.252422 + 0.252422i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 24.0000i 1.00613i 0.864248 + 0.503066i $$0.167795\pi$$
−0.864248 + 0.503066i $$0.832205\pi$$
$$570$$ 0 0
$$571$$ −1.00000 + 1.00000i −0.0418487 + 0.0418487i −0.727721 0.685873i $$-0.759421\pi$$
0.685873 + 0.727721i $$0.259421\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −18.0000 −0.750652
$$576$$ 0 0
$$577$$ 18.0000 0.749350 0.374675 0.927156i $$-0.377754\pi$$
0.374675 + 0.927156i $$0.377754\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 2.00000 2.00000i 0.0829740 0.0829740i
$$582$$ 0 0
$$583$$ 10.0000i 0.414158i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −7.00000 + 7.00000i −0.288921 + 0.288921i −0.836653 0.547733i $$-0.815491\pi$$
0.547733 + 0.836653i $$0.315491\pi$$
$$588$$ 0 0
$$589$$ 24.0000 + 24.0000i 0.988903 + 0.988903i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −34.0000 −1.39621 −0.698106 0.715994i $$-0.745974\pi$$
−0.698106 + 0.715994i $$0.745974\pi$$
$$594$$ 0 0
$$595$$ −4.00000 4.00000i −0.163984 0.163984i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 14.0000i 0.572024i 0.958226 + 0.286012i $$0.0923298\pi$$
−0.958226 + 0.286012i $$0.907670\pi$$
$$600$$ 0 0
$$601$$ 20.0000i 0.815817i −0.913023 0.407909i $$-0.866258\pi$$
0.913023 0.407909i $$-0.133742\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −9.00000 9.00000i −0.365902 0.365902i
$$606$$ 0 0
$$607$$ −32.0000 −1.29884 −0.649420 0.760430i $$-0.724988\pi$$
−0.649420 + 0.760430i $$0.724988\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −8.00000 8.00000i −0.323645 0.323645i
$$612$$ 0 0
$$613$$ 25.0000 25.0000i 1.00974 1.00974i 0.00978840 0.999952i $$-0.496884\pi$$
0.999952 0.00978840i $$-0.00311579\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 12.0000i 0.483102i −0.970388 0.241551i $$-0.922344\pi$$
0.970388 0.241551i $$-0.0776561\pi$$
$$618$$ 0 0
$$619$$ −17.0000 + 17.0000i −0.683288 + 0.683288i −0.960740 0.277452i $$-0.910510\pi$$
0.277452 + 0.960740i $$0.410510\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −8.00000 −0.320513
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −6.00000 + 6.00000i −0.239236 + 0.239236i
$$630$$ 0 0
$$631$$ 10.0000i 0.398094i 0.979990 + 0.199047i $$0.0637846\pi$$
−0.979990 + 0.199047i $$0.936215\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −8.00000 + 8.00000i −0.317470 + 0.317470i
$$636$$ 0 0
$$637$$ 3.00000 + 3.00000i 0.118864 + 0.118864i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 18.0000 0.710957 0.355479 0.934684i $$-0.384318\pi$$
0.355479 + 0.934684i $$0.384318\pi$$
$$642$$ 0 0
$$643$$ 21.0000 + 21.0000i 0.828159 + 0.828159i 0.987262 0.159103i $$-0.0508601\pi$$
−0.159103 + 0.987262i $$0.550860\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 42.0000i 1.65119i −0.564263 0.825595i $$-0.690840\pi$$
0.564263 0.825595i $$-0.309160\pi$$
$$648$$ 0 0
$$649$$ 6.00000i 0.235521i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 19.0000 + 19.0000i 0.743527 + 0.743527i 0.973255 0.229728i $$-0.0737835\pi$$
−0.229728 + 0.973255i $$0.573784\pi$$
$$654$$ 0 0
$$655$$ −22.0000 −0.859611
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −17.0000 17.0000i −0.662226 0.662226i 0.293678 0.955904i $$-0.405121\pi$$
−0.955904 + 0.293678i $$0.905121\pi$$
$$660$$ 0 0
$$661$$ 9.00000 9.00000i 0.350059 0.350059i −0.510072 0.860132i $$-0.670381\pi$$
0.860132 + 0.510072i $$0.170381\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 12.0000i 0.465340i
$$666$$ 0 0
$$667$$ −18.0000 + 18.0000i −0.696963 + 0.696963i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 18.0000 0.694882
$$672$$ 0 0
$$673$$ 14.0000 0.539660 0.269830 0.962908i $$-0.413032\pi$$
0.269830 + 0.962908i $$0.413032\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 3.00000 3.00000i 0.115299 0.115299i −0.647103 0.762402i $$-0.724020\pi$$
0.762402 + 0.647103i $$0.224020\pi$$
$$678$$ 0 0
$$679$$ 4.00000i 0.153506i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 5.00000 5.00000i 0.191320 0.191320i −0.604946 0.796266i $$-0.706805\pi$$
0.796266 + 0.604946i $$0.206805\pi$$
$$684$$ 0 0
$$685$$ −8.00000 8.00000i −0.305664 0.305664i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −10.0000 −0.380970
$$690$$ 0 0
$$691$$ 9.00000 + 9.00000i 0.342376 + 0.342376i 0.857260 0.514884i $$-0.172165\pi$$
−0.514884 + 0.857260i $$0.672165\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6.00000i 0.227593i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 31.0000 + 31.0000i 1.17085 + 1.17085i 0.982006 + 0.188847i $$0.0604752\pi$$
0.188847 + 0.982006i $$0.439525\pi$$
$$702$$ 0 0
$$703$$ 18.0000 0.678883
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 22.0000 + 22.0000i 0.827395 + 0.827395i
$$708$$ 0 0
$$709$$ −27.0000 + 27.0000i −1.01401 + 1.01401i −0.0141058 + 0.999901i $$0.504490\pi$$
−0.999901 + 0.0141058i $$0.995510\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 48.0000i 1.79761i
$$714$$ 0 0
$$715$$ −2.00000 + 2.00000i −0.0747958 + 0.0747958i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 12.0000 0.446903
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −9.00000 + 9.00000i −0.334252 + 0.334252i
$$726$$ 0 0
$$727$$ 2.00000i 0.0741759i 0.999312 + 0.0370879i $$0.0118082\pi$$
−0.999312 + 0.0370879i $$0.988192\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −10.0000 + 10.0000i −0.369863 + 0.369863i
$$732$$ 0 0
$$733$$ 21.0000 + 21.0000i 0.775653 + 0.775653i 0.979088 0.203436i $$-0.0652108\pi$$
−0.203436 + 0.979088i $$0.565211\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 10.0000 0.368355
$$738$$ 0 0
$$739$$ −23.0000 23.0000i −0.846069 0.846069i 0.143571 0.989640i $$-0.454141\pi$$
−0.989640 + 0.143571i $$0.954141\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 46.0000i 1.68758i 0.536676 + 0.843788i $$0.319680\pi$$
−0.536676 + 0.843788i $$0.680320\pi$$
$$744$$ 0 0
$$745$$ 14.0000i 0.512920i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −14.0000 14.0000i −0.511549 0.511549i
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −10.0000 10.0000i −0.363937 0.363937i
$$756$$ 0 0
$$757$$ −23.0000 + 23.0000i −0.835949 + 0.835949i −0.988323 0.152374i $$-0.951308\pi$$
0.152374 + 0.988323i $$0.451308\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 6.00000 6.00000i 0.217215 0.217215i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −6.00000 −0.216647
$$768$$ 0 0
$$769$$ −50.0000 −1.80305 −0.901523 0.432731i $$-0.857550\pi$$
−0.901523 + 0.432731i $$0.857550\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −5.00000 + 5.00000i −0.179838 + 0.179838i −0.791285 0.611448i $$-0.790588\pi$$
0.611448 + 0.791285i $$0.290588\pi$$
$$774$$ 0 0
$$775$$ 24.0000i 0.862105i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −10.0000 10.0000i −0.357828 0.357828i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 30.0000 1.07075
$$786$$ 0 0
$$787$$ −15.0000 15.0000i −0.534692 0.534692i 0.387273 0.921965i $$-0.373417\pi$$
−0.921965 + 0.387273i $$0.873417\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 12.0000i 0.426671i
$$792$$ 0 0
$$793$$ 18.0000i 0.639199i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −25.0000 25.0000i −0.885545 0.885545i 0.108546 0.994091i $$-0.465381\pi$$
−0.994091 + 0.108546i $$0.965381\pi$$
$$798$$ 0 0