# Properties

 Label 912.2.k.a.607.1 Level $912$ Weight $2$ Character 912.607 Analytic conductor $7.282$ 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] = [912,2,Mod(607,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("912.607");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.k (of order $$2$$, degree $$1$$, 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: $$7.28235666434$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-2})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 2$$ x^2 + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 607.1 Root $$-1.41421i$$ of defining polynomial Character $$\chi$$ $$=$$ 912.607 Dual form 912.2.k.a.607.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} -2.00000 q^{5} -2.82843i q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} -2.00000 q^{5} -2.82843i q^{7} +1.00000 q^{9} +1.41421i q^{11} +2.82843i q^{13} +2.00000 q^{15} -2.00000 q^{17} +(-1.00000 - 4.24264i) q^{19} +2.82843i q^{21} +1.41421i q^{23} -1.00000 q^{25} -1.00000 q^{27} +7.07107i q^{29} +6.00000 q^{31} -1.41421i q^{33} +5.65685i q^{35} +11.3137i q^{37} -2.82843i q^{39} +4.24264i q^{41} -2.00000 q^{45} +7.07107i q^{47} -1.00000 q^{49} +2.00000 q^{51} +9.89949i q^{53} -2.82843i q^{55} +(1.00000 + 4.24264i) q^{57} -8.00000 q^{59} -8.00000 q^{61} -2.82843i q^{63} -5.65685i q^{65} -2.00000 q^{67} -1.41421i q^{69} -8.00000 q^{71} +1.00000 q^{75} +4.00000 q^{77} -8.00000 q^{79} +1.00000 q^{81} +12.7279i q^{83} +4.00000 q^{85} -7.07107i q^{87} -9.89949i q^{89} +8.00000 q^{91} -6.00000 q^{93} +(2.00000 + 8.48528i) q^{95} -2.82843i q^{97} +1.41421i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{3} - 4 q^{5} + 2 q^{9}+O(q^{10})$$ 2 * q - 2 * q^3 - 4 * q^5 + 2 * q^9 $$2 q - 2 q^{3} - 4 q^{5} + 2 q^{9} + 4 q^{15} - 4 q^{17} - 2 q^{19} - 2 q^{25} - 2 q^{27} + 12 q^{31} - 4 q^{45} - 2 q^{49} + 4 q^{51} + 2 q^{57} - 16 q^{59} - 16 q^{61} - 4 q^{67} - 16 q^{71} + 2 q^{75} + 8 q^{77} - 16 q^{79} + 2 q^{81} + 8 q^{85} + 16 q^{91} - 12 q^{93} + 4 q^{95}+O(q^{100})$$ 2 * q - 2 * q^3 - 4 * q^5 + 2 * q^9 + 4 * q^15 - 4 * q^17 - 2 * q^19 - 2 * q^25 - 2 * q^27 + 12 * q^31 - 4 * q^45 - 2 * q^49 + 4 * q^51 + 2 * q^57 - 16 * q^59 - 16 * q^61 - 4 * q^67 - 16 * q^71 + 2 * q^75 + 8 * q^77 - 16 * q^79 + 2 * q^81 + 8 * q^85 + 16 * q^91 - 12 * q^93 + 4 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$229$$ $$305$$ $$799$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.00000 −0.577350
$$4$$ 0 0
$$5$$ −2.00000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0 0
$$7$$ 2.82843i 1.06904i −0.845154 0.534522i $$-0.820491\pi$$
0.845154 0.534522i $$-0.179509\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 1.41421i 0.426401i 0.977008 + 0.213201i $$0.0683888\pi$$
−0.977008 + 0.213201i $$0.931611\pi$$
$$12$$ 0 0
$$13$$ 2.82843i 0.784465i 0.919866 + 0.392232i $$0.128297\pi$$
−0.919866 + 0.392232i $$0.871703\pi$$
$$14$$ 0 0
$$15$$ 2.00000 0.516398
$$16$$ 0 0
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ −1.00000 4.24264i −0.229416 0.973329i
$$20$$ 0 0
$$21$$ 2.82843i 0.617213i
$$22$$ 0 0
$$23$$ 1.41421i 0.294884i 0.989071 + 0.147442i $$0.0471040\pi$$
−0.989071 + 0.147442i $$0.952896\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 7.07107i 1.31306i 0.754298 + 0.656532i $$0.227977\pi$$
−0.754298 + 0.656532i $$0.772023\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 0 0
$$33$$ 1.41421i 0.246183i
$$34$$ 0 0
$$35$$ 5.65685i 0.956183i
$$36$$ 0 0
$$37$$ 11.3137i 1.85996i 0.367607 + 0.929981i $$0.380177\pi$$
−0.367607 + 0.929981i $$0.619823\pi$$
$$38$$ 0 0
$$39$$ 2.82843i 0.452911i
$$40$$ 0 0
$$41$$ 4.24264i 0.662589i 0.943527 + 0.331295i $$0.107485\pi$$
−0.943527 + 0.331295i $$0.892515\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ −2.00000 −0.298142
$$46$$ 0 0
$$47$$ 7.07107i 1.03142i 0.856763 + 0.515711i $$0.172472\pi$$
−0.856763 + 0.515711i $$0.827528\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 2.00000 0.280056
$$52$$ 0 0
$$53$$ 9.89949i 1.35980i 0.733305 + 0.679900i $$0.237977\pi$$
−0.733305 + 0.679900i $$0.762023\pi$$
$$54$$ 0 0
$$55$$ 2.82843i 0.381385i
$$56$$ 0 0
$$57$$ 1.00000 + 4.24264i 0.132453 + 0.561951i
$$58$$ 0 0
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 0 0
$$63$$ 2.82843i 0.356348i
$$64$$ 0 0
$$65$$ 5.65685i 0.701646i
$$66$$ 0 0
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 0 0
$$69$$ 1.41421i 0.170251i
$$70$$ 0 0
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 0 0
$$75$$ 1.00000 0.115470
$$76$$ 0 0
$$77$$ 4.00000 0.455842
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 12.7279i 1.39707i 0.715575 + 0.698535i $$0.246165\pi$$
−0.715575 + 0.698535i $$0.753835\pi$$
$$84$$ 0 0
$$85$$ 4.00000 0.433861
$$86$$ 0 0
$$87$$ 7.07107i 0.758098i
$$88$$ 0 0
$$89$$ 9.89949i 1.04934i −0.851304 0.524672i $$-0.824188\pi$$
0.851304 0.524672i $$-0.175812\pi$$
$$90$$ 0 0
$$91$$ 8.00000 0.838628
$$92$$ 0 0
$$93$$ −6.00000 −0.622171
$$94$$ 0 0
$$95$$ 2.00000 + 8.48528i 0.205196 + 0.870572i
$$96$$ 0 0
$$97$$ 2.82843i 0.287183i −0.989637 0.143592i $$-0.954135\pi$$
0.989637 0.143592i $$-0.0458652\pi$$
$$98$$ 0 0
$$99$$ 1.41421i 0.142134i
$$100$$ 0 0
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 0 0
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ 0 0
$$105$$ 5.65685i 0.552052i
$$106$$ 0 0
$$107$$ 20.0000 1.93347 0.966736 0.255774i $$-0.0823304\pi$$
0.966736 + 0.255774i $$0.0823304\pi$$
$$108$$ 0 0
$$109$$ 8.48528i 0.812743i −0.913708 0.406371i $$-0.866794\pi$$
0.913708 0.406371i $$-0.133206\pi$$
$$110$$ 0 0
$$111$$ 11.3137i 1.07385i
$$112$$ 0 0
$$113$$ 1.41421i 0.133038i 0.997785 + 0.0665190i $$0.0211893\pi$$
−0.997785 + 0.0665190i $$0.978811\pi$$
$$114$$ 0 0
$$115$$ 2.82843i 0.263752i
$$116$$ 0 0
$$117$$ 2.82843i 0.261488i
$$118$$ 0 0
$$119$$ 5.65685i 0.518563i
$$120$$ 0 0
$$121$$ 9.00000 0.818182
$$122$$ 0 0
$$123$$ 4.24264i 0.382546i
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 14.0000 1.24230 0.621150 0.783692i $$-0.286666\pi$$
0.621150 + 0.783692i $$0.286666\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 4.24264i 0.370681i −0.982674 0.185341i $$-0.940661\pi$$
0.982674 0.185341i $$-0.0593388\pi$$
$$132$$ 0 0
$$133$$ −12.0000 + 2.82843i −1.04053 + 0.245256i
$$134$$ 0 0
$$135$$ 2.00000 0.172133
$$136$$ 0 0
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ 0 0
$$139$$ 2.82843i 0.239904i 0.992780 + 0.119952i $$0.0382741\pi$$
−0.992780 + 0.119952i $$0.961726\pi$$
$$140$$ 0 0
$$141$$ 7.07107i 0.595491i
$$142$$ 0 0
$$143$$ −4.00000 −0.334497
$$144$$ 0 0
$$145$$ 14.1421i 1.17444i
$$146$$ 0 0
$$147$$ 1.00000 0.0824786
$$148$$ 0 0
$$149$$ −14.0000 −1.14692 −0.573462 0.819232i $$-0.694400\pi$$
−0.573462 + 0.819232i $$0.694400\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ −12.0000 −0.963863
$$156$$ 0 0
$$157$$ 8.00000 0.638470 0.319235 0.947676i $$-0.396574\pi$$
0.319235 + 0.947676i $$0.396574\pi$$
$$158$$ 0 0
$$159$$ 9.89949i 0.785081i
$$160$$ 0 0
$$161$$ 4.00000 0.315244
$$162$$ 0 0
$$163$$ 8.48528i 0.664619i −0.943170 0.332309i $$-0.892172\pi$$
0.943170 0.332309i $$-0.107828\pi$$
$$164$$ 0 0
$$165$$ 2.82843i 0.220193i
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 5.00000 0.384615
$$170$$ 0 0
$$171$$ −1.00000 4.24264i −0.0764719 0.324443i
$$172$$ 0 0
$$173$$ 7.07107i 0.537603i −0.963196 0.268802i $$-0.913372\pi$$
0.963196 0.268802i $$-0.0866276\pi$$
$$174$$ 0 0
$$175$$ 2.82843i 0.213809i
$$176$$ 0 0
$$177$$ 8.00000 0.601317
$$178$$ 0 0
$$179$$ −20.0000 −1.49487 −0.747435 0.664335i $$-0.768715\pi$$
−0.747435 + 0.664335i $$0.768715\pi$$
$$180$$ 0 0
$$181$$ 8.48528i 0.630706i 0.948974 + 0.315353i $$0.102123\pi$$
−0.948974 + 0.315353i $$0.897877\pi$$
$$182$$ 0 0
$$183$$ 8.00000 0.591377
$$184$$ 0 0
$$185$$ 22.6274i 1.66360i
$$186$$ 0 0
$$187$$ 2.82843i 0.206835i
$$188$$ 0 0
$$189$$ 2.82843i 0.205738i
$$190$$ 0 0
$$191$$ 12.7279i 0.920960i 0.887670 + 0.460480i $$0.152323\pi$$
−0.887670 + 0.460480i $$0.847677\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 5.65685i 0.405096i
$$196$$ 0 0
$$197$$ −14.0000 −0.997459 −0.498729 0.866758i $$-0.666200\pi$$
−0.498729 + 0.866758i $$0.666200\pi$$
$$198$$ 0 0
$$199$$ 11.3137i 0.802008i −0.916076 0.401004i $$-0.868661\pi$$
0.916076 0.401004i $$-0.131339\pi$$
$$200$$ 0 0
$$201$$ 2.00000 0.141069
$$202$$ 0 0
$$203$$ 20.0000 1.40372
$$204$$ 0 0
$$205$$ 8.48528i 0.592638i
$$206$$ 0 0
$$207$$ 1.41421i 0.0982946i
$$208$$ 0 0
$$209$$ 6.00000 1.41421i 0.415029 0.0978232i
$$210$$ 0 0
$$211$$ −10.0000 −0.688428 −0.344214 0.938891i $$-0.611855\pi$$
−0.344214 + 0.938891i $$0.611855\pi$$
$$212$$ 0 0
$$213$$ 8.00000 0.548151
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 16.9706i 1.15204i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 5.65685i 0.380521i
$$222$$ 0 0
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 0 0
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 0 0
$$229$$ 22.0000 1.45380 0.726900 0.686743i $$-0.240960\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ 0 0
$$231$$ −4.00000 −0.263181
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 14.1421i 0.922531i
$$236$$ 0 0
$$237$$ 8.00000 0.519656
$$238$$ 0 0
$$239$$ 26.8701i 1.73808i 0.494742 + 0.869040i $$0.335262\pi$$
−0.494742 + 0.869040i $$0.664738\pi$$
$$240$$ 0 0
$$241$$ 2.82843i 0.182195i −0.995842 0.0910975i $$-0.970963\pi$$
0.995842 0.0910975i $$-0.0290375\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 0 0
$$245$$ 2.00000 0.127775
$$246$$ 0 0
$$247$$ 12.0000 2.82843i 0.763542 0.179969i
$$248$$ 0 0
$$249$$ 12.7279i 0.806599i
$$250$$ 0 0
$$251$$ 24.0416i 1.51749i −0.651385 0.758747i $$-0.725812\pi$$
0.651385 0.758747i $$-0.274188\pi$$
$$252$$ 0 0
$$253$$ −2.00000 −0.125739
$$254$$ 0 0
$$255$$ −4.00000 −0.250490
$$256$$ 0 0
$$257$$ 9.89949i 0.617514i −0.951141 0.308757i $$-0.900087\pi$$
0.951141 0.308757i $$-0.0999129\pi$$
$$258$$ 0 0
$$259$$ 32.0000 1.98838
$$260$$ 0 0
$$261$$ 7.07107i 0.437688i
$$262$$ 0 0
$$263$$ 24.0416i 1.48247i 0.671245 + 0.741235i $$0.265760\pi$$
−0.671245 + 0.741235i $$0.734240\pi$$
$$264$$ 0 0
$$265$$ 19.7990i 1.21624i
$$266$$ 0 0
$$267$$ 9.89949i 0.605839i
$$268$$ 0 0
$$269$$ 24.0416i 1.46584i −0.680313 0.732922i $$-0.738156\pi$$
0.680313 0.732922i $$-0.261844\pi$$
$$270$$ 0 0
$$271$$ 11.3137i 0.687259i −0.939105 0.343629i $$-0.888344\pi$$
0.939105 0.343629i $$-0.111656\pi$$
$$272$$ 0 0
$$273$$ −8.00000 −0.484182
$$274$$ 0 0
$$275$$ 1.41421i 0.0852803i
$$276$$ 0 0
$$277$$ −22.0000 −1.32185 −0.660926 0.750451i $$-0.729836\pi$$
−0.660926 + 0.750451i $$0.729836\pi$$
$$278$$ 0 0
$$279$$ 6.00000 0.359211
$$280$$ 0 0
$$281$$ 1.41421i 0.0843649i −0.999110 0.0421825i $$-0.986569\pi$$
0.999110 0.0421825i $$-0.0134311\pi$$
$$282$$ 0 0
$$283$$ 28.2843i 1.68133i 0.541559 + 0.840663i $$0.317834\pi$$
−0.541559 + 0.840663i $$0.682166\pi$$
$$284$$ 0 0
$$285$$ −2.00000 8.48528i −0.118470 0.502625i
$$286$$ 0 0
$$287$$ 12.0000 0.708338
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 2.82843i 0.165805i
$$292$$ 0 0
$$293$$ 29.6985i 1.73500i 0.497434 + 0.867502i $$0.334276\pi$$
−0.497434 + 0.867502i $$0.665724\pi$$
$$294$$ 0 0
$$295$$ 16.0000 0.931556
$$296$$ 0 0
$$297$$ 1.41421i 0.0820610i
$$298$$ 0 0
$$299$$ −4.00000 −0.231326
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −6.00000 −0.344691
$$304$$ 0 0
$$305$$ 16.0000 0.916157
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ 8.00000 0.455104
$$310$$ 0 0
$$311$$ 9.89949i 0.561349i 0.959803 + 0.280674i $$0.0905581\pi$$
−0.959803 + 0.280674i $$0.909442\pi$$
$$312$$ 0 0
$$313$$ 20.0000 1.13047 0.565233 0.824931i $$-0.308786\pi$$
0.565233 + 0.824931i $$0.308786\pi$$
$$314$$ 0 0
$$315$$ 5.65685i 0.318728i
$$316$$ 0 0
$$317$$ 7.07107i 0.397151i 0.980086 + 0.198575i $$0.0636315\pi$$
−0.980086 + 0.198575i $$0.936369\pi$$
$$318$$ 0 0
$$319$$ −10.0000 −0.559893
$$320$$ 0 0
$$321$$ −20.0000 −1.11629
$$322$$ 0 0
$$323$$ 2.00000 + 8.48528i 0.111283 + 0.472134i
$$324$$ 0 0
$$325$$ 2.82843i 0.156893i
$$326$$ 0 0
$$327$$ 8.48528i 0.469237i
$$328$$ 0 0
$$329$$ 20.0000 1.10264
$$330$$ 0 0
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ 0 0
$$333$$ 11.3137i 0.619987i
$$334$$ 0 0
$$335$$ 4.00000 0.218543
$$336$$ 0 0
$$337$$ 25.4558i 1.38667i 0.720616 + 0.693334i $$0.243859\pi$$
−0.720616 + 0.693334i $$0.756141\pi$$
$$338$$ 0 0
$$339$$ 1.41421i 0.0768095i
$$340$$ 0 0
$$341$$ 8.48528i 0.459504i
$$342$$ 0 0
$$343$$ 16.9706i 0.916324i
$$344$$ 0 0
$$345$$ 2.82843i 0.152277i
$$346$$ 0 0
$$347$$ 32.5269i 1.74614i −0.487598 0.873068i $$-0.662127\pi$$
0.487598 0.873068i $$-0.337873\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 0 0
$$351$$ 2.82843i 0.150970i
$$352$$ 0 0
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 0 0
$$355$$ 16.0000 0.849192
$$356$$ 0 0
$$357$$ 5.65685i 0.299392i
$$358$$ 0 0
$$359$$ 18.3848i 0.970311i −0.874428 0.485156i $$-0.838763\pi$$
0.874428 0.485156i $$-0.161237\pi$$
$$360$$ 0 0
$$361$$ −17.0000 + 8.48528i −0.894737 + 0.446594i
$$362$$ 0 0
$$363$$ −9.00000 −0.472377
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 16.9706i 0.885856i 0.896557 + 0.442928i $$0.146060\pi$$
−0.896557 + 0.442928i $$0.853940\pi$$
$$368$$ 0 0
$$369$$ 4.24264i 0.220863i
$$370$$ 0 0
$$371$$ 28.0000 1.45369
$$372$$ 0 0
$$373$$ 22.6274i 1.17160i 0.810454 + 0.585802i $$0.199220\pi$$
−0.810454 + 0.585802i $$0.800780\pi$$
$$374$$ 0 0
$$375$$ −12.0000 −0.619677
$$376$$ 0 0
$$377$$ −20.0000 −1.03005
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ 0 0
$$381$$ −14.0000 −0.717242
$$382$$ 0 0
$$383$$ −32.0000 −1.63512 −0.817562 0.575841i $$-0.804675\pi$$
−0.817562 + 0.575841i $$0.804675\pi$$
$$384$$ 0 0
$$385$$ −8.00000 −0.407718
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −22.0000 −1.11544 −0.557722 0.830028i $$-0.688325\pi$$
−0.557722 + 0.830028i $$0.688325\pi$$
$$390$$ 0 0
$$391$$ 2.82843i 0.143040i
$$392$$ 0 0
$$393$$ 4.24264i 0.214013i
$$394$$ 0 0
$$395$$ 16.0000 0.805047
$$396$$ 0 0
$$397$$ 10.0000 0.501886 0.250943 0.968002i $$-0.419259\pi$$
0.250943 + 0.968002i $$0.419259\pi$$
$$398$$ 0 0
$$399$$ 12.0000 2.82843i 0.600751 0.141598i
$$400$$ 0 0
$$401$$ 26.8701i 1.34183i 0.741536 + 0.670913i $$0.234098\pi$$
−0.741536 + 0.670913i $$0.765902\pi$$
$$402$$ 0 0
$$403$$ 16.9706i 0.845364i
$$404$$ 0 0
$$405$$ −2.00000 −0.0993808
$$406$$ 0 0
$$407$$ −16.0000 −0.793091
$$408$$ 0 0
$$409$$ 25.4558i 1.25871i −0.777118 0.629355i $$-0.783319\pi$$
0.777118 0.629355i $$-0.216681\pi$$
$$410$$ 0 0
$$411$$ 6.00000 0.295958
$$412$$ 0 0
$$413$$ 22.6274i 1.11342i
$$414$$ 0 0
$$415$$ 25.4558i 1.24958i
$$416$$ 0 0
$$417$$ 2.82843i 0.138509i
$$418$$ 0 0
$$419$$ 18.3848i 0.898155i −0.893493 0.449078i $$-0.851753\pi$$
0.893493 0.449078i $$-0.148247\pi$$
$$420$$ 0 0
$$421$$ 14.1421i 0.689246i 0.938741 + 0.344623i $$0.111993\pi$$
−0.938741 + 0.344623i $$0.888007\pi$$
$$422$$ 0 0
$$423$$ 7.07107i 0.343807i
$$424$$ 0 0
$$425$$ 2.00000 0.0970143
$$426$$ 0 0
$$427$$ 22.6274i 1.09502i
$$428$$ 0 0
$$429$$ 4.00000 0.193122
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 0 0
$$433$$ 33.9411i 1.63111i 0.578682 + 0.815553i $$0.303567\pi$$
−0.578682 + 0.815553i $$0.696433\pi$$
$$434$$ 0 0
$$435$$ 14.1421i 0.678064i
$$436$$ 0 0
$$437$$ 6.00000 1.41421i 0.287019 0.0676510i
$$438$$ 0 0
$$439$$ 32.0000 1.52728 0.763638 0.645644i $$-0.223411\pi$$
0.763638 + 0.645644i $$0.223411\pi$$
$$440$$ 0 0
$$441$$ −1.00000 −0.0476190
$$442$$ 0 0
$$443$$ 26.8701i 1.27663i −0.769773 0.638317i $$-0.779631\pi$$
0.769773 0.638317i $$-0.220369\pi$$
$$444$$ 0 0
$$445$$ 19.7990i 0.938562i
$$446$$ 0 0
$$447$$ 14.0000 0.662177
$$448$$ 0 0
$$449$$ 15.5563i 0.734150i 0.930191 + 0.367075i $$0.119641\pi$$
−0.930191 + 0.367075i $$0.880359\pi$$
$$450$$ 0 0
$$451$$ −6.00000 −0.282529
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −16.0000 −0.750092
$$456$$ 0 0
$$457$$ 8.00000 0.374224 0.187112 0.982339i $$-0.440087\pi$$
0.187112 + 0.982339i $$0.440087\pi$$
$$458$$ 0 0
$$459$$ 2.00000 0.0933520
$$460$$ 0 0
$$461$$ −14.0000 −0.652045 −0.326023 0.945362i $$-0.605709\pi$$
−0.326023 + 0.945362i $$0.605709\pi$$
$$462$$ 0 0
$$463$$ 16.9706i 0.788689i 0.918963 + 0.394344i $$0.129028\pi$$
−0.918963 + 0.394344i $$0.870972\pi$$
$$464$$ 0 0
$$465$$ 12.0000 0.556487
$$466$$ 0 0
$$467$$ 24.0416i 1.11251i −0.831010 0.556257i $$-0.812237\pi$$
0.831010 0.556257i $$-0.187763\pi$$
$$468$$ 0 0
$$469$$ 5.65685i 0.261209i
$$470$$ 0 0
$$471$$ −8.00000 −0.368621
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 1.00000 + 4.24264i 0.0458831 + 0.194666i
$$476$$ 0 0
$$477$$ 9.89949i 0.453267i
$$478$$ 0 0
$$479$$ 7.07107i 0.323085i −0.986866 0.161543i $$-0.948353\pi$$
0.986866 0.161543i $$-0.0516469\pi$$
$$480$$ 0 0
$$481$$ −32.0000 −1.45907
$$482$$ 0 0
$$483$$ −4.00000 −0.182006
$$484$$ 0 0
$$485$$ 5.65685i 0.256865i
$$486$$ 0 0
$$487$$ 10.0000 0.453143 0.226572 0.973995i $$-0.427248\pi$$
0.226572 + 0.973995i $$0.427248\pi$$
$$488$$ 0 0
$$489$$ 8.48528i 0.383718i
$$490$$ 0 0
$$491$$ 24.0416i 1.08498i −0.840061 0.542492i $$-0.817481\pi$$
0.840061 0.542492i $$-0.182519\pi$$
$$492$$ 0 0
$$493$$ 14.1421i 0.636930i
$$494$$ 0 0
$$495$$ 2.82843i 0.127128i
$$496$$ 0 0
$$497$$ 22.6274i 1.01498i
$$498$$ 0 0
$$499$$ 25.4558i 1.13956i 0.821797 + 0.569780i $$0.192972\pi$$
−0.821797 + 0.569780i $$0.807028\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 12.7279i 0.567510i −0.958897 0.283755i $$-0.908420\pi$$
0.958897 0.283755i $$-0.0915802\pi$$
$$504$$ 0 0
$$505$$ −12.0000 −0.533993
$$506$$ 0 0
$$507$$ −5.00000 −0.222058
$$508$$ 0 0
$$509$$ 24.0416i 1.06563i −0.846233 0.532813i $$-0.821135\pi$$
0.846233 0.532813i $$-0.178865\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 1.00000 + 4.24264i 0.0441511 + 0.187317i
$$514$$ 0 0
$$515$$ 16.0000 0.705044
$$516$$ 0 0
$$517$$ −10.0000 −0.439799
$$518$$ 0 0
$$519$$ 7.07107i 0.310385i
$$520$$ 0 0
$$521$$ 1.41421i 0.0619578i 0.999520 + 0.0309789i $$0.00986247\pi$$
−0.999520 + 0.0309789i $$0.990138\pi$$
$$522$$ 0 0
$$523$$ 34.0000 1.48672 0.743358 0.668894i $$-0.233232\pi$$
0.743358 + 0.668894i $$0.233232\pi$$
$$524$$ 0 0
$$525$$ 2.82843i 0.123443i
$$526$$ 0 0
$$527$$ −12.0000 −0.522728
$$528$$ 0 0
$$529$$ 21.0000 0.913043
$$530$$ 0 0
$$531$$ −8.00000 −0.347170
$$532$$ 0 0
$$533$$ −12.0000 −0.519778
$$534$$ 0 0
$$535$$ −40.0000 −1.72935
$$536$$ 0 0
$$537$$ 20.0000 0.863064
$$538$$ 0 0
$$539$$ 1.41421i 0.0609145i
$$540$$ 0 0
$$541$$ 12.0000 0.515920 0.257960 0.966156i $$-0.416950\pi$$
0.257960 + 0.966156i $$0.416950\pi$$
$$542$$ 0 0
$$543$$ 8.48528i 0.364138i
$$544$$ 0 0
$$545$$ 16.9706i 0.726939i
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 0 0
$$549$$ −8.00000 −0.341432
$$550$$ 0 0
$$551$$ 30.0000 7.07107i 1.27804 0.301238i
$$552$$ 0 0
$$553$$ 22.6274i 0.962216i
$$554$$ 0 0
$$555$$ 22.6274i 0.960480i
$$556$$ 0 0
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 2.82843i 0.119416i
$$562$$ 0 0
$$563$$ 36.0000 1.51722 0.758610 0.651546i $$-0.225879\pi$$
0.758610 + 0.651546i $$0.225879\pi$$
$$564$$ 0 0
$$565$$ 2.82843i 0.118993i
$$566$$ 0 0
$$567$$ 2.82843i 0.118783i
$$568$$ 0 0
$$569$$ 32.5269i 1.36360i −0.731539 0.681800i $$-0.761198\pi$$
0.731539 0.681800i $$-0.238802\pi$$
$$570$$ 0 0
$$571$$ 45.2548i 1.89386i 0.321446 + 0.946928i $$0.395831\pi$$
−0.321446 + 0.946928i $$0.604169\pi$$
$$572$$ 0 0
$$573$$ 12.7279i 0.531717i
$$574$$ 0 0
$$575$$ 1.41421i 0.0589768i
$$576$$ 0 0
$$577$$ 20.0000 0.832611 0.416305 0.909225i $$-0.363325\pi$$
0.416305 + 0.909225i $$0.363325\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 36.0000 1.49353
$$582$$ 0 0
$$583$$ −14.0000 −0.579821
$$584$$ 0 0
$$585$$ 5.65685i 0.233882i
$$586$$ 0 0
$$587$$ 35.3553i 1.45927i −0.683836 0.729636i $$-0.739690\pi$$
0.683836 0.729636i $$-0.260310\pi$$
$$588$$ 0 0
$$589$$ −6.00000 25.4558i −0.247226 1.04889i
$$590$$ 0 0
$$591$$ 14.0000 0.575883
$$592$$ 0 0
$$593$$ −42.0000 −1.72473 −0.862367 0.506284i $$-0.831019\pi$$
−0.862367 + 0.506284i $$0.831019\pi$$
$$594$$ 0 0
$$595$$ 11.3137i 0.463817i
$$596$$ 0 0
$$597$$ 11.3137i 0.463039i
$$598$$ 0 0
$$599$$ 44.0000 1.79779 0.898896 0.438163i $$-0.144371\pi$$
0.898896 + 0.438163i $$0.144371\pi$$
$$600$$ 0 0
$$601$$ 28.2843i 1.15374i 0.816836 + 0.576870i $$0.195726\pi$$
−0.816836 + 0.576870i $$0.804274\pi$$
$$602$$ 0 0
$$603$$ −2.00000 −0.0814463
$$604$$ 0 0
$$605$$ −18.0000 −0.731804
$$606$$ 0 0
$$607$$ −34.0000 −1.38002 −0.690009 0.723801i $$-0.742393\pi$$
−0.690009 + 0.723801i $$0.742393\pi$$
$$608$$ 0 0
$$609$$ −20.0000 −0.810441
$$610$$ 0 0
$$611$$ −20.0000 −0.809113
$$612$$ 0 0
$$613$$ 16.0000 0.646234 0.323117 0.946359i $$-0.395269\pi$$
0.323117 + 0.946359i $$0.395269\pi$$
$$614$$ 0 0
$$615$$ 8.48528i 0.342160i
$$616$$ 0 0
$$617$$ −34.0000 −1.36879 −0.684394 0.729112i $$-0.739933\pi$$
−0.684394 + 0.729112i $$0.739933\pi$$
$$618$$ 0 0
$$619$$ 25.4558i 1.02316i 0.859237 + 0.511578i $$0.170939\pi$$
−0.859237 + 0.511578i $$0.829061\pi$$
$$620$$ 0 0
$$621$$ 1.41421i 0.0567504i
$$622$$ 0 0
$$623$$ −28.0000 −1.12180
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ −6.00000 + 1.41421i −0.239617 + 0.0564782i
$$628$$ 0 0
$$629$$ 22.6274i 0.902214i
$$630$$ 0 0
$$631$$ 14.1421i 0.562990i −0.959563 0.281495i $$-0.909170\pi$$
0.959563 0.281495i $$-0.0908302\pi$$
$$632$$ 0 0
$$633$$ 10.0000 0.397464
$$634$$ 0 0
$$635$$ −28.0000 −1.11115
$$636$$ 0 0
$$637$$ 2.82843i 0.112066i
$$638$$ 0 0
$$639$$ −8.00000 −0.316475
$$640$$ 0 0
$$641$$ 41.0122i 1.61988i 0.586510 + 0.809942i $$0.300502\pi$$
−0.586510 + 0.809942i $$0.699498\pi$$
$$642$$ 0 0
$$643$$ 39.5980i 1.56159i 0.624786 + 0.780796i $$0.285186\pi$$
−0.624786 + 0.780796i $$0.714814\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 7.07107i 0.277992i −0.990293 0.138996i $$-0.955612\pi$$
0.990293 0.138996i $$-0.0443876\pi$$
$$648$$ 0 0
$$649$$ 11.3137i 0.444102i
$$650$$ 0 0
$$651$$ 16.9706i 0.665129i
$$652$$ 0 0
$$653$$ −6.00000 −0.234798 −0.117399 0.993085i $$-0.537456\pi$$
−0.117399 + 0.993085i $$0.537456\pi$$
$$654$$ 0 0
$$655$$ 8.48528i 0.331547i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 8.00000 0.311636 0.155818 0.987786i $$-0.450199\pi$$
0.155818 + 0.987786i $$0.450199\pi$$
$$660$$ 0 0
$$661$$ 39.5980i 1.54018i −0.637934 0.770091i $$-0.720211\pi$$
0.637934 0.770091i $$-0.279789\pi$$
$$662$$ 0 0
$$663$$ 5.65685i 0.219694i
$$664$$ 0 0
$$665$$ 24.0000 5.65685i 0.930680 0.219363i
$$666$$ 0 0
$$667$$ −10.0000 −0.387202
$$668$$ 0 0
$$669$$ 16.0000 0.618596
$$670$$ 0 0
$$671$$ 11.3137i 0.436761i
$$672$$ 0 0
$$673$$ 28.2843i 1.09028i 0.838346 + 0.545139i $$0.183523\pi$$
−0.838346 + 0.545139i $$0.816477\pi$$
$$674$$ 0 0
$$675$$ 1.00000 0.0384900
$$676$$ 0 0
$$677$$ 9.89949i 0.380468i 0.981739 + 0.190234i $$0.0609248\pi$$
−0.981739 + 0.190234i $$0.939075\pi$$
$$678$$ 0 0
$$679$$ −8.00000 −0.307012
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ −32.0000 −1.22445 −0.612223 0.790685i $$-0.709725\pi$$
−0.612223 + 0.790685i $$0.709725\pi$$
$$684$$ 0 0
$$685$$ 12.0000 0.458496
$$686$$ 0 0
$$687$$ −22.0000 −0.839352
$$688$$ 0 0
$$689$$ −28.0000 −1.06672
$$690$$ 0 0
$$691$$ 16.9706i 0.645591i −0.946469 0.322795i $$-0.895377\pi$$
0.946469 0.322795i $$-0.104623\pi$$
$$692$$ 0 0
$$693$$ 4.00000 0.151947
$$694$$ 0 0
$$695$$ 5.65685i 0.214577i
$$696$$ 0 0
$$697$$ 8.48528i 0.321403i
$$698$$ 0 0
$$699$$ 6.00000 0.226941
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ 48.0000 11.3137i 1.81035 0.426705i
$$704$$ 0 0
$$705$$ 14.1421i 0.532624i
$$706$$ 0 0
$$707$$ 16.9706i 0.638244i
$$708$$ 0 0
$$709$$ 4.00000 0.150223 0.0751116 0.997175i $$-0.476069\pi$$
0.0751116 + 0.997175i $$0.476069\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ 8.48528i 0.317776i
$$714$$ 0 0
$$715$$ 8.00000 0.299183
$$716$$ 0 0
$$717$$ 26.8701i 1.00348i
$$718$$ 0 0
$$719$$ 32.5269i 1.21305i 0.795065 + 0.606525i $$0.207437\pi$$
−0.795065 + 0.606525i $$0.792563\pi$$
$$720$$ 0 0
$$721$$ 22.6274i 0.842689i
$$722$$ 0 0
$$723$$ 2.82843i 0.105190i
$$724$$ 0 0
$$725$$ 7.07107i 0.262613i
$$726$$ 0 0
$$727$$ 28.2843i 1.04901i 0.851409 + 0.524503i $$0.175749\pi$$
−0.851409 + 0.524503i $$0.824251\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −52.0000 −1.92066 −0.960332 0.278859i $$-0.910044\pi$$
−0.960332 + 0.278859i $$0.910044\pi$$
$$734$$ 0 0
$$735$$ −2.00000 −0.0737711
$$736$$ 0 0
$$737$$ 2.82843i 0.104186i
$$738$$ 0 0
$$739$$ 36.7696i 1.35259i −0.736631 0.676295i $$-0.763585\pi$$
0.736631 0.676295i $$-0.236415\pi$$
$$740$$ 0 0
$$741$$ −12.0000 + 2.82843i −0.440831 + 0.103905i
$$742$$ 0 0
$$743$$ 36.0000 1.32071 0.660356 0.750953i $$-0.270405\pi$$
0.660356 + 0.750953i $$0.270405\pi$$
$$744$$ 0 0
$$745$$ 28.0000 1.02584
$$746$$ 0 0
$$747$$ 12.7279i 0.465690i
$$748$$ 0 0
$$749$$ 56.5685i 2.06697i
$$750$$ 0 0
$$751$$ 40.0000 1.45962 0.729810 0.683650i $$-0.239608\pi$$
0.729810 + 0.683650i $$0.239608\pi$$
$$752$$ 0 0
$$753$$ 24.0416i 0.876126i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 22.0000 0.799604 0.399802 0.916602i $$-0.369079\pi$$
0.399802 + 0.916602i $$0.369079\pi$$
$$758$$ 0 0
$$759$$ 2.00000 0.0725954
$$760$$ 0 0
$$761$$ 18.0000 0.652499 0.326250 0.945284i $$-0.394215\pi$$
0.326250 + 0.945284i $$0.394215\pi$$
$$762$$ 0 0
$$763$$ −24.0000 −0.868858
$$764$$ 0 0
$$765$$ 4.00000 0.144620
$$766$$ 0 0
$$767$$ 22.6274i 0.817029i
$$768$$ 0 0
$$769$$ 20.0000 0.721218 0.360609 0.932717i $$-0.382569\pi$$
0.360609 + 0.932717i $$0.382569\pi$$
$$770$$ 0 0
$$771$$ 9.89949i 0.356522i
$$772$$ 0 0
$$773$$ 21.2132i 0.762986i −0.924372 0.381493i $$-0.875410\pi$$
0.924372 0.381493i $$-0.124590\pi$$
$$774$$ 0 0
$$775$$ −6.00000 −0.215526
$$776$$ 0 0
$$777$$ −32.0000 −1.14799
$$778$$ 0 0
$$779$$ 18.0000 4.24264i 0.644917 0.152008i
$$780$$ 0 0
$$781$$ 11.3137i 0.404836i
$$782$$ 0 0
$$783$$ 7.07107i 0.252699i
$$784$$ 0 0
$$785$$ −16.0000 −0.571064
$$786$$ 0 0
$$787$$ −42.0000 −1.49714 −0.748569 0.663057i $$-0.769259\pi$$
−0.748569 + 0.663057i $$0.769259\pi$$
$$788$$ 0 0
$$789$$ 24.0416i 0.855905i
$$790$$ 0 0
$$791$$ 4.00000 0.142224
$$792$$ 0 0
$$793$$ 22.6274i 0.803523i
$$794$$ 0 0
$$795$$ 19.7990i 0.702198i
$$796$$ 0 0
$$797$$ 7.07107i 0.250470i 0.992127 + 0.125235i