# Properties

 Label 1600.2.q.b.49.1 Level $1600$ Weight $2$ Character 1600.49 Analytic conductor $12.776$ 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] = [1600,2,Mod(49,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1600.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1600 = 2^{6} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1600.q (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: $$12.7760643234$$ 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 16) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 49.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1600.49 Dual form 1600.2.q.b.849.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.00000i) q^{3} +2.00000 q^{7} -1.00000i q^{9} +O(q^{10})$$ $$q+(1.00000 + 1.00000i) q^{3} +2.00000 q^{7} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{13} +2.00000i q^{17} +(3.00000 - 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +6.00000 q^{23} +(4.00000 - 4.00000i) q^{27} +(-3.00000 + 3.00000i) q^{29} +8.00000 q^{31} -2.00000i q^{33} +(3.00000 - 3.00000i) q^{37} -2.00000i q^{39} +(5.00000 - 5.00000i) q^{43} +8.00000i q^{47} -3.00000 q^{49} +(-2.00000 + 2.00000i) q^{51} +(5.00000 - 5.00000i) q^{53} +6.00000 q^{57} +(-3.00000 - 3.00000i) q^{59} +(-9.00000 + 9.00000i) q^{61} -2.00000i q^{63} +(-5.00000 - 5.00000i) q^{67} +(6.00000 + 6.00000i) q^{69} +10.0000i q^{71} +4.00000 q^{73} +(-2.00000 - 2.00000i) q^{77} +5.00000 q^{81} +(1.00000 + 1.00000i) q^{83} -6.00000 q^{87} -4.00000i q^{89} +(-2.00000 - 2.00000i) q^{91} +(8.00000 + 8.00000i) q^{93} +2.00000i q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{3} + 4 q^{7}+O(q^{10})$$ 2 * q + 2 * q^3 + 4 * q^7 $$2 q + 2 q^{3} + 4 q^{7} - 2 q^{11} - 2 q^{13} + 6 q^{19} + 4 q^{21} + 12 q^{23} + 8 q^{27} - 6 q^{29} + 16 q^{31} + 6 q^{37} + 10 q^{43} - 6 q^{49} - 4 q^{51} + 10 q^{53} + 12 q^{57} - 6 q^{59} - 18 q^{61} - 10 q^{67} + 12 q^{69} + 8 q^{73} - 4 q^{77} + 10 q^{81} + 2 q^{83} - 12 q^{87} - 4 q^{91} + 16 q^{93} - 2 q^{99}+O(q^{100})$$ 2 * q + 2 * q^3 + 4 * q^7 - 2 * q^11 - 2 * q^13 + 6 * q^19 + 4 * q^21 + 12 * q^23 + 8 * q^27 - 6 * q^29 + 16 * q^31 + 6 * q^37 + 10 * q^43 - 6 * q^49 - 4 * q^51 + 10 * q^53 + 12 * q^57 - 6 * q^59 - 18 * q^61 - 10 * q^67 + 12 * q^69 + 8 * q^73 - 4 * q^77 + 10 * q^81 + 2 * q^83 - 12 * q^87 - 4 * q^91 + 16 * q^93 - 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$$.

 $$n$$ $$577$$ $$901$$ $$1151$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$ $$1$$

## 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 0
$$3$$ 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i $$-0.116140\pi$$
−0.356822 + 0.934172i $$0.616140\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.00000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ 0 0
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ −1.00000 1.00000i −0.301511 0.301511i 0.540094 0.841605i $$-0.318389\pi$$
−0.841605 + 0.540094i $$0.818389\pi$$
$$12$$ 0 0
$$13$$ −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i $$-0.312833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.00000i 0.485071i 0.970143 + 0.242536i $$0.0779791\pi$$
−0.970143 + 0.242536i $$0.922021\pi$$
$$18$$ 0 0
$$19$$ 3.00000 3.00000i 0.688247 0.688247i −0.273597 0.961844i $$-0.588214\pi$$
0.961844 + 0.273597i $$0.0882135\pi$$
$$20$$ 0 0
$$21$$ 2.00000 + 2.00000i 0.436436 + 0.436436i
$$22$$ 0 0
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 4.00000 4.00000i 0.769800 0.769800i
$$28$$ 0 0
$$29$$ −3.00000 + 3.00000i −0.557086 + 0.557086i −0.928477 0.371391i $$-0.878881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 0 0
$$33$$ 2.00000i 0.348155i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i $$-0.636609\pi$$
0.909312 + 0.416115i $$0.136609\pi$$
$$38$$ 0 0
$$39$$ 2.00000i 0.320256i
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 5.00000 5.00000i 0.762493 0.762493i −0.214280 0.976772i $$-0.568740\pi$$
0.976772 + 0.214280i $$0.0687403\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ −2.00000 + 2.00000i −0.280056 + 0.280056i
$$52$$ 0 0
$$53$$ 5.00000 5.00000i 0.686803 0.686803i −0.274721 0.961524i $$-0.588586\pi$$
0.961524 + 0.274721i $$0.0885855\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 6.00000 0.794719
$$58$$ 0 0
$$59$$ −3.00000 3.00000i −0.390567 0.390567i 0.484323 0.874889i $$-0.339066\pi$$
−0.874889 + 0.484323i $$0.839066\pi$$
$$60$$ 0 0
$$61$$ −9.00000 + 9.00000i −1.15233 + 1.15233i −0.166248 + 0.986084i $$0.553165\pi$$
−0.986084 + 0.166248i $$0.946835\pi$$
$$62$$ 0 0
$$63$$ 2.00000i 0.251976i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −5.00000 5.00000i −0.610847 0.610847i 0.332320 0.943167i $$-0.392169\pi$$
−0.943167 + 0.332320i $$0.892169\pi$$
$$68$$ 0 0
$$69$$ 6.00000 + 6.00000i 0.722315 + 0.722315i
$$70$$ 0 0
$$71$$ 10.0000i 1.18678i 0.804914 + 0.593391i $$0.202211\pi$$
−0.804914 + 0.593391i $$0.797789\pi$$
$$72$$ 0 0
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 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
$$81$$ 5.00000 0.555556
$$82$$ 0 0
$$83$$ 1.00000 + 1.00000i 0.109764 + 0.109764i 0.759856 0.650092i $$-0.225269\pi$$
−0.650092 + 0.759856i $$0.725269\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −6.00000 −0.643268
$$88$$ 0 0
$$89$$ 4.00000i 0.423999i −0.977270 0.212000i $$-0.932002\pi$$
0.977270 0.212000i $$-0.0679975\pi$$
$$90$$ 0 0
$$91$$ −2.00000 2.00000i −0.209657 0.209657i
$$92$$ 0 0
$$93$$ 8.00000 + 8.00000i 0.829561 + 0.829561i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 2.00000i 0.203069i 0.994832 + 0.101535i $$0.0323753\pi$$
−0.994832 + 0.101535i $$0.967625\pi$$
$$98$$ 0 0
$$99$$ −1.00000 + 1.00000i −0.100504 + 0.100504i
$$100$$ 0 0
$$101$$ 11.0000 + 11.0000i 1.09454 + 1.09454i 0.995037 + 0.0995037i $$0.0317255\pi$$
0.0995037 + 0.995037i $$0.468274\pi$$
$$102$$ 0 0
$$103$$ 6.00000 0.591198 0.295599 0.955312i $$-0.404481\pi$$
0.295599 + 0.955312i $$0.404481\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 7.00000 7.00000i 0.676716 0.676716i −0.282540 0.959256i $$-0.591177\pi$$
0.959256 + 0.282540i $$0.0911770\pi$$
$$108$$ 0 0
$$109$$ −3.00000 + 3.00000i −0.287348 + 0.287348i −0.836031 0.548683i $$-0.815129\pi$$
0.548683 + 0.836031i $$0.315129\pi$$
$$110$$ 0 0
$$111$$ 6.00000 0.569495
$$112$$ 0 0
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.00000 + 1.00000i −0.0924500 + 0.0924500i
$$118$$ 0 0
$$119$$ 4.00000i 0.366679i
$$120$$ 0 0
$$121$$ 9.00000i 0.818182i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 8.00000i 0.709885i 0.934888 + 0.354943i $$0.115500\pi$$
−0.934888 + 0.354943i $$0.884500\pi$$
$$128$$ 0 0
$$129$$ 10.0000 0.880451
$$130$$ 0 0
$$131$$ −11.0000 + 11.0000i −0.961074 + 0.961074i −0.999270 0.0381958i $$-0.987839\pi$$
0.0381958 + 0.999270i $$0.487839\pi$$
$$132$$ 0 0
$$133$$ 6.00000 6.00000i 0.520266 0.520266i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 8.00000 0.683486 0.341743 0.939793i $$-0.388983\pi$$
0.341743 + 0.939793i $$0.388983\pi$$
$$138$$ 0 0
$$139$$ −3.00000 3.00000i −0.254457 0.254457i 0.568338 0.822795i $$-0.307586\pi$$
−0.822795 + 0.568338i $$0.807586\pi$$
$$140$$ 0 0
$$141$$ −8.00000 + 8.00000i −0.673722 + 0.673722i
$$142$$ 0 0
$$143$$ 2.00000i 0.167248i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −3.00000 3.00000i −0.247436 0.247436i
$$148$$ 0 0
$$149$$ −7.00000 7.00000i −0.573462 0.573462i 0.359632 0.933094i $$-0.382902\pi$$
−0.933094 + 0.359632i $$0.882902\pi$$
$$150$$ 0 0
$$151$$ 10.0000i 0.813788i 0.913475 + 0.406894i $$0.133388\pi$$
−0.913475 + 0.406894i $$0.866612\pi$$
$$152$$ 0 0
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 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
$$159$$ 10.0000 0.793052
$$160$$ 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
$$167$$ 2.00000 0.154765 0.0773823 0.997001i $$-0.475344\pi$$
0.0773823 + 0.997001i $$0.475344\pi$$
$$168$$ 0 0
$$169$$ 11.0000i 0.846154i
$$170$$ 0 0
$$171$$ −3.00000 3.00000i −0.229416 0.229416i
$$172$$ 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
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 6.00000i 0.450988i
$$178$$ 0 0
$$179$$ −17.0000 + 17.0000i −1.27064 + 1.27064i −0.324887 + 0.945753i $$0.605326\pi$$
−0.945753 + 0.324887i $$0.894674\pi$$
$$180$$ 0 0
$$181$$ −9.00000 9.00000i −0.668965 0.668965i 0.288512 0.957476i $$-0.406840\pi$$
−0.957476 + 0.288512i $$0.906840\pi$$
$$182$$ 0 0
$$183$$ −18.0000 −1.33060
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 2.00000 2.00000i 0.146254 0.146254i
$$188$$ 0 0
$$189$$ 8.00000 8.00000i 0.581914 0.581914i
$$190$$ 0 0
$$191$$ 8.00000 0.578860 0.289430 0.957199i $$-0.406534\pi$$
0.289430 + 0.957199i $$0.406534\pi$$
$$192$$ 0 0
$$193$$ 14.0000i 1.00774i 0.863779 + 0.503871i $$0.168091\pi$$
−0.863779 + 0.503871i $$0.831909\pi$$
$$194$$ 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 $$0.165278\pi$$
−0.868199 + 0.496217i $$0.834722\pi$$
$$200$$ 0 0
$$201$$ 10.0000i 0.705346i
$$202$$ 0 0
$$203$$ −6.00000 + 6.00000i −0.421117 + 0.421117i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 6.00000i 0.417029i
$$208$$ 0 0
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ 9.00000 9.00000i 0.619586 0.619586i −0.325840 0.945425i $$-0.605647\pi$$
0.945425 + 0.325840i $$0.105647\pi$$
$$212$$ 0 0
$$213$$ −10.0000 + 10.0000i −0.685189 + 0.685189i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 16.0000 1.08615
$$218$$ 0 0
$$219$$ 4.00000 + 4.00000i 0.270295 + 0.270295i
$$220$$ 0 0
$$221$$ 2.00000 2.00000i 0.134535 0.134535i
$$222$$ 0 0
$$223$$ 24.0000i 1.60716i −0.595198 0.803579i $$-0.702926\pi$$
0.595198 0.803579i $$-0.297074\pi$$
$$224$$ 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 0.436925 0.899498i $$-0.356068\pi$$
−0.899498 + 0.436925i $$0.856068\pi$$
$$230$$ 0 0
$$231$$ 4.00000i 0.263181i
$$232$$ 0 0
$$233$$ 4.00000 0.262049 0.131024 0.991379i $$-0.458173\pi$$
0.131024 + 0.991379i $$0.458173\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 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
$$243$$ −7.00000 7.00000i −0.449050 0.449050i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −6.00000 −0.381771
$$248$$ 0 0
$$249$$ 2.00000i 0.126745i
$$250$$ 0 0
$$251$$ −21.0000 21.0000i −1.32551 1.32551i −0.909243 0.416265i $$-0.863339\pi$$
−0.416265 0.909243i $$-0.636661\pi$$
$$252$$ 0 0
$$253$$ −6.00000 6.00000i −0.377217 0.377217i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 22.0000i 1.37232i 0.727450 + 0.686161i $$0.240706\pi$$
−0.727450 + 0.686161i $$0.759294\pi$$
$$258$$ 0 0
$$259$$ 6.00000 6.00000i 0.372822 0.372822i
$$260$$ 0 0
$$261$$ 3.00000 + 3.00000i 0.185695 + 0.185695i
$$262$$ 0 0
$$263$$ 6.00000 0.369976 0.184988 0.982741i $$-0.440775\pi$$
0.184988 + 0.982741i $$0.440775\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 4.00000 4.00000i 0.244796 0.244796i
$$268$$ 0 0
$$269$$ −3.00000 + 3.00000i −0.182913 + 0.182913i −0.792624 0.609711i $$-0.791286\pi$$
0.609711 + 0.792624i $$0.291286\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 0 0
$$273$$ 4.00000i 0.242091i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 3.00000 3.00000i 0.180253 0.180253i −0.611213 0.791466i $$-0.709318\pi$$
0.791466 + 0.611213i $$0.209318\pi$$
$$278$$ 0 0
$$279$$ 8.00000i 0.478947i
$$280$$ 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 −0.994679 0.103022i $$-0.967149\pi$$
0.103022 + 0.994679i $$0.467149\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 13.0000 0.764706
$$290$$ 0 0
$$291$$ −2.00000 + 2.00000i −0.117242 + 0.117242i
$$292$$ 0 0
$$293$$ −15.0000 + 15.0000i −0.876309 + 0.876309i −0.993151 0.116841i $$-0.962723\pi$$
0.116841 + 0.993151i $$0.462723\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −8.00000 −0.464207
$$298$$ 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
$$303$$ 22.0000i 1.26387i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −5.00000 5.00000i −0.285365 0.285365i 0.549879 0.835244i $$-0.314674\pi$$
−0.835244 + 0.549879i $$0.814674\pi$$
$$308$$ 0 0
$$309$$ 6.00000 + 6.00000i 0.341328 + 0.341328i
$$310$$ 0 0
$$311$$ 30.0000i 1.70114i −0.525859 0.850572i $$-0.676256\pi$$
0.525859 0.850572i $$-0.323744\pi$$
$$312$$ 0 0
$$313$$ −16.0000 −0.904373 −0.452187 0.891923i $$-0.649356\pi$$
−0.452187 + 0.891923i $$0.649356\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 5.00000 + 5.00000i 0.280828 + 0.280828i 0.833439 0.552611i $$-0.186369\pi$$
−0.552611 + 0.833439i $$0.686369\pi$$
$$318$$ 0 0
$$319$$ 6.00000 0.335936
$$320$$ 0 0
$$321$$ 14.0000 0.781404
$$322$$ 0 0
$$323$$ 6.00000 + 6.00000i 0.333849 + 0.333849i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −6.00000 −0.331801
$$328$$ 0 0
$$329$$ 16.0000i 0.882109i
$$330$$ 0 0
$$331$$ −1.00000 1.00000i −0.0549650 0.0549650i 0.679090 0.734055i $$-0.262375\pi$$
−0.734055 + 0.679090i $$0.762375\pi$$
$$332$$ 0 0
$$333$$ −3.00000 3.00000i −0.164399 0.164399i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 18.0000i 0.980522i −0.871576 0.490261i $$-0.836901\pi$$
0.871576 0.490261i $$-0.163099\pi$$
$$338$$ 0 0
$$339$$ 6.00000 6.00000i 0.325875 0.325875i
$$340$$ 0 0
$$341$$ −8.00000 8.00000i −0.433224 0.433224i
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −13.0000 + 13.0000i −0.697877 + 0.697877i −0.963952 0.266076i $$-0.914273\pi$$
0.266076 + 0.963952i $$0.414273\pi$$
$$348$$ 0 0
$$349$$ −3.00000 + 3.00000i −0.160586 + 0.160586i −0.782826 0.622240i $$-0.786223\pi$$
0.622240 + 0.782826i $$0.286223\pi$$
$$350$$ 0 0
$$351$$ −8.00000 −0.427008
$$352$$ 0 0
$$353$$ 6.00000i 0.319348i −0.987170 0.159674i $$-0.948956\pi$$
0.987170 0.159674i $$-0.0510443\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −4.00000 + 4.00000i −0.211702 + 0.211702i
$$358$$ 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
$$363$$ 9.00000 9.00000i 0.472377 0.472377i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 8.00000i 0.417597i 0.977959 + 0.208798i $$0.0669552\pi$$
−0.977959 + 0.208798i $$0.933045\pi$$
$$368$$ 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
$$377$$ 6.00000 0.309016
$$378$$ 0 0
$$379$$ −3.00000 3.00000i −0.154100 0.154100i 0.625847 0.779946i $$-0.284754\pi$$
−0.779946 + 0.625847i $$0.784754\pi$$
$$380$$ 0 0
$$381$$ −8.00000 + 8.00000i −0.409852 + 0.409852i
$$382$$ 0 0
$$383$$ 16.0000i 0.817562i 0.912633 + 0.408781i $$0.134046\pi$$
−0.912633 + 0.408781i $$0.865954\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −5.00000 5.00000i −0.254164 0.254164i
$$388$$ 0 0
$$389$$ 13.0000 + 13.0000i 0.659126 + 0.659126i 0.955173 0.296047i $$-0.0956686\pi$$
−0.296047 + 0.955173i $$0.595669\pi$$
$$390$$ 0 0
$$391$$ 12.0000i 0.606866i
$$392$$ 0 0
$$393$$ −22.0000 −1.10975
$$394$$ 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
$$399$$ 12.0000 0.600751
$$400$$ 0 0
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ 0 0
$$403$$ −8.00000 8.00000i −0.398508 0.398508i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −6.00000 −0.297409
$$408$$ 0 0
$$409$$ 16.0000i 0.791149i 0.918434 + 0.395575i $$0.129455\pi$$
−0.918434 + 0.395575i $$0.870545\pi$$
$$410$$ 0 0
$$411$$ 8.00000 + 8.00000i 0.394611 + 0.394611i
$$412$$ 0 0
$$413$$ −6.00000 6.00000i −0.295241 0.295241i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 6.00000i 0.293821i
$$418$$ 0 0
$$419$$ 3.00000 3.00000i 0.146560 0.146560i −0.630020 0.776579i $$-0.716953\pi$$
0.776579 + 0.630020i $$0.216953\pi$$
$$420$$ 0 0
$$421$$ −9.00000 9.00000i −0.438633 0.438633i 0.452919 0.891552i $$-0.350383\pi$$
−0.891552 + 0.452919i $$0.850383\pi$$
$$422$$ 0 0
$$423$$ 8.00000 0.388973
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −18.0000 + 18.0000i −0.871081 + 0.871081i
$$428$$ 0 0
$$429$$ −2.00000 + 2.00000i −0.0965609 + 0.0965609i
$$430$$ 0 0
$$431$$ −32.0000 −1.54139 −0.770693 0.637207i $$-0.780090\pi$$
−0.770693 + 0.637207i $$0.780090\pi$$
$$432$$ 0 0
$$433$$ 14.0000i 0.672797i 0.941720 + 0.336399i $$0.109209\pi$$
−0.941720 + 0.336399i $$0.890791\pi$$
$$434$$ 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 $$0.108430\pi$$
−0.942541 + 0.334092i $$0.891570\pi$$
$$440$$ 0 0
$$441$$ 3.00000i 0.142857i
$$442$$ 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
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 14.0000i 0.662177i
$$448$$ 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
$$453$$ −10.0000 + 10.0000i −0.469841 + 0.469841i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −32.0000 −1.49690 −0.748448 0.663193i $$-0.769201\pi$$
−0.748448 + 0.663193i $$0.769201\pi$$
$$458$$ 0 0
$$459$$ 8.00000 + 8.00000i 0.373408 + 0.373408i
$$460$$ 0 0
$$461$$ 11.0000 11.0000i 0.512321 0.512321i −0.402916 0.915237i $$-0.632003\pi$$
0.915237 + 0.402916i $$0.132003\pi$$
$$462$$ 0 0
$$463$$ 16.0000i 0.743583i 0.928316 + 0.371792i $$0.121256\pi$$
−0.928316 + 0.371792i $$0.878744\pi$$
$$464$$ 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
$$471$$ 30.0000i 1.38233i
$$472$$ 0 0
$$473$$ −10.0000 −0.459800
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −5.00000 5.00000i −0.228934 0.228934i
$$478$$ 0 0
$$479$$ −40.0000 −1.82765 −0.913823 0.406112i $$-0.866884\pi$$
−0.913823 + 0.406112i $$0.866884\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 0 0
$$483$$ 12.0000 + 12.0000i 0.546019 + 0.546019i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 2.00000 0.0906287 0.0453143 0.998973i $$-0.485571\pi$$
0.0453143 + 0.998973i $$0.485571\pi$$
$$488$$ 0 0
$$489$$ 2.00000i 0.0904431i
$$490$$ 0 0
$$491$$ 19.0000 + 19.0000i 0.857458 + 0.857458i 0.991038 0.133580i $$-0.0426473\pi$$
−0.133580 + 0.991038i $$0.542647\pi$$
$$492$$ 0 0
$$493$$ −6.00000 6.00000i −0.270226 0.270226i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 20.0000i 0.897123i
$$498$$ 0 0
$$499$$ 23.0000 23.0000i 1.02962 1.02962i 0.0300737 0.999548i $$-0.490426\pi$$
0.999548 0.0300737i $$-0.00957421\pi$$
$$500$$ 0 0
$$501$$ 2.00000 + 2.00000i 0.0893534 + 0.0893534i
$$502$$ 0 0
$$503$$ 6.00000 0.267527 0.133763 0.991013i $$-0.457294\pi$$
0.133763 + 0.991013i $$0.457294\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 11.0000 11.0000i 0.488527 0.488527i
$$508$$ 0 0
$$509$$ −23.0000 + 23.0000i −1.01946 + 1.01946i −0.0196502 + 0.999807i $$0.506255\pi$$
−0.999807 + 0.0196502i $$0.993745\pi$$
$$510$$ 0 0
$$511$$ 8.00000 0.353899
$$512$$ 0 0
$$513$$ 24.0000i 1.05963i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 8.00000 8.00000i 0.351840 0.351840i
$$518$$ 0 0
$$519$$ 2.00000i 0.0877903i
$$520$$ 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 $$-0.468760\pi$$
0.995188 0.0979859i $$-0.0312400\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 16.0000i 0.696971i
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ −3.00000 + 3.00000i −0.130189 + 0.130189i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −34.0000 −1.46721
$$538$$ 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 $$-0.838217\pi$$
0.486654 + 0.873595i $$0.338217\pi$$
$$542$$ 0 0
$$543$$ 18.0000i 0.772454i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −5.00000 5.00000i −0.213785 0.213785i 0.592088 0.805873i $$-0.298304\pi$$
−0.805873 + 0.592088i $$0.798304\pi$$
$$548$$ 0 0
$$549$$ 9.00000 + 9.00000i 0.384111 + 0.384111i
$$550$$ 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 $$0.0194786\pi$$
0.0611558 + 0.998128i $$0.480521\pi$$
$$558$$ 0 0
$$559$$ −10.0000 −0.422955
$$560$$ 0 0
$$561$$ 4.00000 0.168880
$$562$$ 0 0
$$563$$ −19.0000 19.0000i −0.800755 0.800755i 0.182459 0.983213i $$-0.441594\pi$$
−0.983213 + 0.182459i $$0.941594\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 10.0000 0.419961
$$568$$ 0 0
$$569$$ 24.0000i 1.00613i −0.864248 0.503066i $$-0.832205\pi$$
0.864248 0.503066i $$-0.167795\pi$$
$$570$$ 0 0
$$571$$ −1.00000 1.00000i −0.0418487 0.0418487i 0.685873 0.727721i $$-0.259421\pi$$
−0.727721 + 0.685873i $$0.759421\pi$$
$$572$$ 0 0
$$573$$ 8.00000 + 8.00000i 0.334205 + 0.334205i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 18.0000i 0.749350i −0.927156 0.374675i $$-0.877754\pi$$
0.927156 0.374675i $$-0.122246\pi$$
$$578$$ 0 0
$$579$$ −14.0000 + 14.0000i −0.581820 + 0.581820i
$$580$$ 0 0
$$581$$ 2.00000 + 2.00000i 0.0829740 + 0.0829740i
$$582$$ 0 0
$$583$$ −10.0000 −0.414158
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7.00000 7.00000i 0.288921 0.288921i −0.547733 0.836653i $$-0.684509\pi$$
0.836653 + 0.547733i $$0.184509\pi$$
$$588$$ 0 0
$$589$$ 24.0000 24.0000i 0.988903 0.988903i
$$590$$ 0 0
$$591$$ −34.0000 −1.39857
$$592$$ 0 0
$$593$$ 34.0000i 1.39621i 0.715994 + 0.698106i $$0.245974\pi$$
−0.715994 + 0.698106i $$0.754026\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −14.0000 + 14.0000i −0.572982 + 0.572982i
$$598$$ 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 $$0.133742\pi$$
−0.913023 + 0.407909i $$0.866258\pi$$
$$602$$ 0 0
$$603$$ −5.00000 + 5.00000i −0.203616 + 0.203616i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 32.0000i 1.29884i −0.760430 0.649420i $$-0.775012\pi$$
0.760430 0.649420i $$-0.224988\pi$$
$$608$$ 0 0
$$609$$ −12.0000 −0.486265
$$610$$ 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
$$617$$ −12.0000 −0.483102 −0.241551 0.970388i $$-0.577656\pi$$
−0.241551 + 0.970388i $$0.577656\pi$$
$$618$$ 0 0
$$619$$ 17.0000 + 17.0000i 0.683288 + 0.683288i 0.960740 0.277452i $$-0.0894899\pi$$
−0.277452 + 0.960740i $$0.589490\pi$$
$$620$$ 0 0
$$621$$ 24.0000 24.0000i 0.963087 0.963087i
$$622$$ 0 0
$$623$$ 8.00000i 0.320513i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −6.00000 6.00000i −0.239617 0.239617i
$$628$$ 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
$$633$$ 18.0000 0.715436
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 3.00000 + 3.00000i 0.118864 + 0.118864i
$$638$$ 0 0
$$639$$ 10.0000 0.395594
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 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
$$647$$ 42.0000 1.65119 0.825595 0.564263i $$-0.190840\pi$$
0.825595 + 0.564263i $$0.190840\pi$$
$$648$$ 0 0
$$649$$ 6.00000i 0.235521i
$$650$$ 0 0
$$651$$ 16.0000 + 16.0000i 0.627089 + 0.627089i
$$652$$ 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
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 4.00000i 0.156055i
$$658$$ 0 0
$$659$$ −17.0000 + 17.0000i −0.662226 + 0.662226i −0.955904 0.293678i $$-0.905121\pi$$
0.293678 + 0.955904i $$0.405121\pi$$
$$660$$ 0 0
$$661$$ −9.00000 9.00000i −0.350059 0.350059i 0.510072 0.860132i $$-0.329619\pi$$
−0.860132 + 0.510072i $$0.829619\pi$$
$$662$$ 0 0
$$663$$ 4.00000 0.155347
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −18.0000 + 18.0000i −0.696963 + 0.696963i
$$668$$ 0 0
$$669$$ 24.0000 24.0000i 0.927894 0.927894i
$$670$$ 0 0
$$671$$ 18.0000 0.694882
$$672$$ 0 0
$$673$$ 14.0000i 0.539660i 0.962908 + 0.269830i $$0.0869676\pi$$
−0.962908 + 0.269830i $$0.913032\pi$$
$$674$$ 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
$$681$$ 30.0000i 1.14960i
$$682$$ 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
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 14.0000i 0.534133i
$$688$$ 0 0
$$689$$ −10.0000 −0.380970
$$690$$ 0 0
$$691$$ 9.00000 9.00000i 0.342376 0.342376i −0.514884 0.857260i $$-0.672165\pi$$
0.857260 + 0.514884i $$0.172165\pi$$
$$692$$ 0 0
$$693$$ −2.00000 + 2.00000i −0.0759737 + 0.0759737i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 4.00000 + 4.00000i 0.151294 + 0.151294i
$$700$$ 0 0
$$701$$ 31.0000 31.0000i 1.17085 1.17085i 0.188847 0.982006i $$-0.439525\pi$$
0.982006 0.188847i $$-0.0604752\pi$$
$$702$$ 0 0
$$703$$ 18.0000i 0.678883i
$$704$$ 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 −0.999901 0.0141058i $$-0.995510\pi$$
−0.0141058 0.999901i $$-0.504490\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 48.0000 1.79761
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 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
$$723$$ −18.0000 18.0000i −0.669427 0.669427i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 2.00000 0.0741759 0.0370879 0.999312i $$-0.488192\pi$$
0.0370879 + 0.999312i $$0.488192\pi$$
$$728$$ 0 0
$$729$$ 29.0000i 1.07407i
$$730$$ 0 0
$$731$$ 10.0000 + 10.0000i 0.369863 + 0.369863i
$$732$$ 0 0
$$733$$ −21.0000 21.0000i −0.775653 0.775653i 0.203436 0.979088i $$-0.434789\pi$$
−0.979088 + 0.203436i $$0.934789\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 10.0000i 0.368355i
$$738$$ 0 0
$$739$$ 23.0000 23.0000i 0.846069 0.846069i −0.143571 0.989640i $$-0.545859\pi$$
0.989640 + 0.143571i $$0.0458586\pi$$
$$740$$ 0 0
$$741$$ −6.00000 6.00000i −0.220416 0.220416i
$$742$$ 0 0
$$743$$ 46.0000 1.68758 0.843788 0.536676i $$-0.180320\pi$$
0.843788 + 0.536676i $$0.180320\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 1.00000 1.00000i 0.0365881 0.0365881i
$$748$$ 0 0
$$749$$ 14.0000 14.0000i 0.511549 0.511549i
$$750$$ 0 0
$$751$$ −32.0000 −1.16770 −0.583848 0.811863i $$-0.698454\pi$$
−0.583848 + 0.811863i $$0.698454\pi$$
$$752$$ 0 0
$$753$$ 42.0000i 1.53057i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 23.0000 23.0000i 0.835949 0.835949i −0.152374 0.988323i $$-0.548692\pi$$
0.988323 + 0.152374i $$0.0486917\pi$$
$$758$$ 0 0
$$759$$ 12.0000i 0.435572i
$$760$$ 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
$$767$$ 6.00000i 0.216647i
$$768$$ 0 0
$$769$$ 50.0000 1.80305 0.901523 0.432731i $$-0.142450\pi$$
0.901523 + 0.432731i $$0.142450\pi$$
$$770$$ 0 0
$$771$$ −22.0000 + 22.0000i −0.792311 + 0.792311i
$$772$$ 0 0
$$773$$ 5.00000 5.00000i 0.179838 0.179838i −0.611448 0.791285i $$-0.709412\pi$$
0.791285 + 0.611448i $$0.209412\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 12.0000 0.430498
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 10.0000 10.0000i 0.357828 0.357828i
$$782$$ 0 0
$$783$$ 24.0000i 0.857690i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 15.0000 + 15.0000i 0.534692 + 0.534692i 0.921965 0.387273i $$-0.126583\pi$$
−0.387273 + 0.921965i $$0.626583\pi$$
$$788$$ 0 0
$$789$$ 6.00000 + 6.00000i 0.213606 + 0.213606i
$$790$$ 0 0
$$791$$ 12.0000i 0.426671i
$$792$$ 0 0
$$793$$ 18.0000 0.639199
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0