# Properties

 Label 768.2.c.f.767.1 Level $768$ Weight $2$ Character 768.767 Analytic conductor $6.133$ 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] = [768,2,Mod(767,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("768.767");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$768 = 2^{8} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 768.c (of order $$2$$, degree $$1$$, 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: $$6.13251087523$$ 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 384) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 767.1 Root $$-1.41421i$$ of defining polynomial Character $$\chi$$ $$=$$ 768.767 Dual form 768.2.c.f.767.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.41421i) q^{3} -2.82843i q^{5} -2.82843i q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$$ $$q+(1.00000 - 1.41421i) q^{3} -2.82843i q^{5} -2.82843i q^{7} +(-1.00000 - 2.82843i) q^{9} +2.00000 q^{11} +4.00000 q^{13} +(-4.00000 - 2.82843i) q^{15} +5.65685i q^{17} +2.82843i q^{19} +(-4.00000 - 2.82843i) q^{21} -8.00000 q^{23} -3.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +2.82843i q^{29} -8.48528i q^{31} +(2.00000 - 2.82843i) q^{33} -8.00000 q^{35} +4.00000 q^{37} +(4.00000 - 5.65685i) q^{39} +2.82843i q^{43} +(-8.00000 + 2.82843i) q^{45} -1.00000 q^{49} +(8.00000 + 5.65685i) q^{51} +8.48528i q^{53} -5.65685i q^{55} +(4.00000 + 2.82843i) q^{57} +6.00000 q^{59} +4.00000 q^{61} +(-8.00000 + 2.82843i) q^{63} -11.3137i q^{65} -14.1421i q^{67} +(-8.00000 + 11.3137i) q^{69} -8.00000 q^{71} +10.0000 q^{73} +(-3.00000 + 4.24264i) q^{75} -5.65685i q^{77} +2.82843i q^{79} +(-7.00000 + 5.65685i) q^{81} +6.00000 q^{83} +16.0000 q^{85} +(4.00000 + 2.82843i) q^{87} +5.65685i q^{89} -11.3137i q^{91} +(-12.0000 - 8.48528i) q^{93} +8.00000 q^{95} -6.00000 q^{97} +(-2.00000 - 5.65685i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{3} - 2 q^{9}+O(q^{10})$$ 2 * q + 2 * q^3 - 2 * q^9 $$2 q + 2 q^{3} - 2 q^{9} + 4 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{21} - 16 q^{23} - 6 q^{25} - 10 q^{27} + 4 q^{33} - 16 q^{35} + 8 q^{37} + 8 q^{39} - 16 q^{45} - 2 q^{49} + 16 q^{51} + 8 q^{57} + 12 q^{59} + 8 q^{61} - 16 q^{63} - 16 q^{69} - 16 q^{71} + 20 q^{73} - 6 q^{75} - 14 q^{81} + 12 q^{83} + 32 q^{85} + 8 q^{87} - 24 q^{93} + 16 q^{95} - 12 q^{97} - 4 q^{99}+O(q^{100})$$ 2 * q + 2 * q^3 - 2 * q^9 + 4 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^21 - 16 * q^23 - 6 * q^25 - 10 * q^27 + 4 * q^33 - 16 * q^35 + 8 * q^37 + 8 * q^39 - 16 * q^45 - 2 * q^49 + 16 * q^51 + 8 * q^57 + 12 * q^59 + 8 * q^61 - 16 * q^63 - 16 * q^69 - 16 * q^71 + 20 * q^73 - 6 * q^75 - 14 * q^81 + 12 * q^83 + 32 * q^85 + 8 * q^87 - 24 * q^93 + 16 * q^95 - 12 * q^97 - 4 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$511$$ $$517$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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 1.41421i 0.577350 0.816497i
$$4$$ 0 0
$$5$$ 2.82843i 1.26491i −0.774597 0.632456i $$-0.782047\pi$$
0.774597 0.632456i $$-0.217953\pi$$
$$6$$ 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 2.82843i −0.333333 0.942809i
$$10$$ 0 0
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ −4.00000 2.82843i −1.03280 0.730297i
$$16$$ 0 0
$$17$$ 5.65685i 1.37199i 0.727607 + 0.685994i $$0.240633\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ 2.82843i 0.648886i 0.945905 + 0.324443i $$0.105177\pi$$
−0.945905 + 0.324443i $$0.894823\pi$$
$$20$$ 0 0
$$21$$ −4.00000 2.82843i −0.872872 0.617213i
$$22$$ 0 0
$$23$$ −8.00000 −1.66812 −0.834058 0.551677i $$-0.813988\pi$$
−0.834058 + 0.551677i $$0.813988\pi$$
$$24$$ 0 0
$$25$$ −3.00000 −0.600000
$$26$$ 0 0
$$27$$ −5.00000 1.41421i −0.962250 0.272166i
$$28$$ 0 0
$$29$$ 2.82843i 0.525226i 0.964901 + 0.262613i $$0.0845842\pi$$
−0.964901 + 0.262613i $$0.915416\pi$$
$$30$$ 0 0
$$31$$ 8.48528i 1.52400i −0.647576 0.762001i $$-0.724217\pi$$
0.647576 0.762001i $$-0.275783\pi$$
$$32$$ 0 0
$$33$$ 2.00000 2.82843i 0.348155 0.492366i
$$34$$ 0 0
$$35$$ −8.00000 −1.35225
$$36$$ 0 0
$$37$$ 4.00000 0.657596 0.328798 0.944400i $$-0.393356\pi$$
0.328798 + 0.944400i $$0.393356\pi$$
$$38$$ 0 0
$$39$$ 4.00000 5.65685i 0.640513 0.905822i
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 2.82843i 0.431331i 0.976467 + 0.215666i $$0.0691921\pi$$
−0.976467 + 0.215666i $$0.930808\pi$$
$$44$$ 0 0
$$45$$ −8.00000 + 2.82843i −1.19257 + 0.421637i
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 8.00000 + 5.65685i 1.12022 + 0.792118i
$$52$$ 0 0
$$53$$ 8.48528i 1.16554i 0.812636 + 0.582772i $$0.198032\pi$$
−0.812636 + 0.582772i $$0.801968\pi$$
$$54$$ 0 0
$$55$$ 5.65685i 0.762770i
$$56$$ 0 0
$$57$$ 4.00000 + 2.82843i 0.529813 + 0.374634i
$$58$$ 0 0
$$59$$ 6.00000 0.781133 0.390567 0.920575i $$-0.372279\pi$$
0.390567 + 0.920575i $$0.372279\pi$$
$$60$$ 0 0
$$61$$ 4.00000 0.512148 0.256074 0.966657i $$-0.417571\pi$$
0.256074 + 0.966657i $$0.417571\pi$$
$$62$$ 0 0
$$63$$ −8.00000 + 2.82843i −1.00791 + 0.356348i
$$64$$ 0 0
$$65$$ 11.3137i 1.40329i
$$66$$ 0 0
$$67$$ 14.1421i 1.72774i −0.503718 0.863868i $$-0.668035\pi$$
0.503718 0.863868i $$-0.331965\pi$$
$$68$$ 0 0
$$69$$ −8.00000 + 11.3137i −0.963087 + 1.36201i
$$70$$ 0 0
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ 0 0
$$73$$ 10.0000 1.17041 0.585206 0.810885i $$-0.301014\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ 0 0
$$75$$ −3.00000 + 4.24264i −0.346410 + 0.489898i
$$76$$ 0 0
$$77$$ 5.65685i 0.644658i
$$78$$ 0 0
$$79$$ 2.82843i 0.318223i 0.987261 + 0.159111i $$0.0508629\pi$$
−0.987261 + 0.159111i $$0.949137\pi$$
$$80$$ 0 0
$$81$$ −7.00000 + 5.65685i −0.777778 + 0.628539i
$$82$$ 0 0
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 16.0000 1.73544
$$86$$ 0 0
$$87$$ 4.00000 + 2.82843i 0.428845 + 0.303239i
$$88$$ 0 0
$$89$$ 5.65685i 0.599625i 0.953998 + 0.299813i $$0.0969242\pi$$
−0.953998 + 0.299813i $$0.903076\pi$$
$$90$$ 0 0
$$91$$ 11.3137i 1.18600i
$$92$$ 0 0
$$93$$ −12.0000 8.48528i −1.24434 0.879883i
$$94$$ 0 0
$$95$$ 8.00000 0.820783
$$96$$ 0 0
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 0 0
$$99$$ −2.00000 5.65685i −0.201008 0.568535i
$$100$$ 0 0
$$101$$ 2.82843i 0.281439i −0.990050 0.140720i $$-0.955058\pi$$
0.990050 0.140720i $$-0.0449416\pi$$
$$102$$ 0 0
$$103$$ 8.48528i 0.836080i 0.908429 + 0.418040i $$0.137283\pi$$
−0.908429 + 0.418040i $$0.862717\pi$$
$$104$$ 0 0
$$105$$ −8.00000 + 11.3137i −0.780720 + 1.10410i
$$106$$ 0 0
$$107$$ 6.00000 0.580042 0.290021 0.957020i $$-0.406338\pi$$
0.290021 + 0.957020i $$0.406338\pi$$
$$108$$ 0 0
$$109$$ 4.00000 0.383131 0.191565 0.981480i $$-0.438644\pi$$
0.191565 + 0.981480i $$0.438644\pi$$
$$110$$ 0 0
$$111$$ 4.00000 5.65685i 0.379663 0.536925i
$$112$$ 0 0
$$113$$ 11.3137i 1.06430i −0.846649 0.532152i $$-0.821383\pi$$
0.846649 0.532152i $$-0.178617\pi$$
$$114$$ 0 0
$$115$$ 22.6274i 2.11002i
$$116$$ 0 0
$$117$$ −4.00000 11.3137i −0.369800 1.04595i
$$118$$ 0 0
$$119$$ 16.0000 1.46672
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 5.65685i 0.505964i
$$126$$ 0 0
$$127$$ 14.1421i 1.25491i 0.778652 + 0.627456i $$0.215904\pi$$
−0.778652 + 0.627456i $$0.784096\pi$$
$$128$$ 0 0
$$129$$ 4.00000 + 2.82843i 0.352180 + 0.249029i
$$130$$ 0 0
$$131$$ −14.0000 −1.22319 −0.611593 0.791173i $$-0.709471\pi$$
−0.611593 + 0.791173i $$0.709471\pi$$
$$132$$ 0 0
$$133$$ 8.00000 0.693688
$$134$$ 0 0
$$135$$ −4.00000 + 14.1421i −0.344265 + 1.21716i
$$136$$ 0 0
$$137$$ 11.3137i 0.966595i −0.875456 0.483298i $$-0.839439\pi$$
0.875456 0.483298i $$-0.160561\pi$$
$$138$$ 0 0
$$139$$ 8.48528i 0.719712i 0.933008 + 0.359856i $$0.117174\pi$$
−0.933008 + 0.359856i $$0.882826\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 8.00000 0.668994
$$144$$ 0 0
$$145$$ 8.00000 0.664364
$$146$$ 0 0
$$147$$ −1.00000 + 1.41421i −0.0824786 + 0.116642i
$$148$$ 0 0
$$149$$ 2.82843i 0.231714i −0.993266 0.115857i $$-0.963039\pi$$
0.993266 0.115857i $$-0.0369614\pi$$
$$150$$ 0 0
$$151$$ 8.48528i 0.690522i 0.938507 + 0.345261i $$0.112210\pi$$
−0.938507 + 0.345261i $$0.887790\pi$$
$$152$$ 0 0
$$153$$ 16.0000 5.65685i 1.29352 0.457330i
$$154$$ 0 0
$$155$$ −24.0000 −1.92773
$$156$$ 0 0
$$157$$ 20.0000 1.59617 0.798087 0.602542i $$-0.205846\pi$$
0.798087 + 0.602542i $$0.205846\pi$$
$$158$$ 0 0
$$159$$ 12.0000 + 8.48528i 0.951662 + 0.672927i
$$160$$ 0 0
$$161$$ 22.6274i 1.78329i
$$162$$ 0 0
$$163$$ 8.48528i 0.664619i −0.943170 0.332309i $$-0.892172\pi$$
0.943170 0.332309i $$-0.107828\pi$$
$$164$$ 0 0
$$165$$ −8.00000 5.65685i −0.622799 0.440386i
$$166$$ 0 0
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 8.00000 2.82843i 0.611775 0.216295i
$$172$$ 0 0
$$173$$ 2.82843i 0.215041i 0.994203 + 0.107521i $$0.0342912\pi$$
−0.994203 + 0.107521i $$0.965709\pi$$
$$174$$ 0 0
$$175$$ 8.48528i 0.641427i
$$176$$ 0 0
$$177$$ 6.00000 8.48528i 0.450988 0.637793i
$$178$$ 0 0
$$179$$ 18.0000 1.34538 0.672692 0.739923i $$-0.265138\pi$$
0.672692 + 0.739923i $$0.265138\pi$$
$$180$$ 0 0
$$181$$ −12.0000 −0.891953 −0.445976 0.895045i $$-0.647144\pi$$
−0.445976 + 0.895045i $$0.647144\pi$$
$$182$$ 0 0
$$183$$ 4.00000 5.65685i 0.295689 0.418167i
$$184$$ 0 0
$$185$$ 11.3137i 0.831800i
$$186$$ 0 0
$$187$$ 11.3137i 0.827340i
$$188$$ 0 0
$$189$$ −4.00000 + 14.1421i −0.290957 + 1.02869i
$$190$$ 0 0
$$191$$ −16.0000 −1.15772 −0.578860 0.815427i $$-0.696502\pi$$
−0.578860 + 0.815427i $$0.696502\pi$$
$$192$$ 0 0
$$193$$ −2.00000 −0.143963 −0.0719816 0.997406i $$-0.522932\pi$$
−0.0719816 + 0.997406i $$0.522932\pi$$
$$194$$ 0 0
$$195$$ −16.0000 11.3137i −1.14578 0.810191i
$$196$$ 0 0
$$197$$ 14.1421i 1.00759i −0.863825 0.503793i $$-0.831938\pi$$
0.863825 0.503793i $$-0.168062\pi$$
$$198$$ 0 0
$$199$$ 8.48528i 0.601506i 0.953702 + 0.300753i $$0.0972379\pi$$
−0.953702 + 0.300753i $$0.902762\pi$$
$$200$$ 0 0
$$201$$ −20.0000 14.1421i −1.41069 0.997509i
$$202$$ 0 0
$$203$$ 8.00000 0.561490
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 8.00000 + 22.6274i 0.556038 + 1.57271i
$$208$$ 0 0
$$209$$ 5.65685i 0.391293i
$$210$$ 0 0
$$211$$ 2.82843i 0.194717i −0.995249 0.0973585i $$-0.968961\pi$$
0.995249 0.0973585i $$-0.0310393\pi$$
$$212$$ 0 0
$$213$$ −8.00000 + 11.3137i −0.548151 + 0.775203i
$$214$$ 0 0
$$215$$ 8.00000 0.545595
$$216$$ 0 0
$$217$$ −24.0000 −1.62923
$$218$$ 0 0
$$219$$ 10.0000 14.1421i 0.675737 0.955637i
$$220$$ 0 0
$$221$$ 22.6274i 1.52208i
$$222$$ 0 0
$$223$$ 2.82843i 0.189405i 0.995506 + 0.0947027i $$0.0301901\pi$$
−0.995506 + 0.0947027i $$0.969810\pi$$
$$224$$ 0 0
$$225$$ 3.00000 + 8.48528i 0.200000 + 0.565685i
$$226$$ 0 0
$$227$$ 22.0000 1.46019 0.730096 0.683345i $$-0.239475\pi$$
0.730096 + 0.683345i $$0.239475\pi$$
$$228$$ 0 0
$$229$$ 4.00000 0.264327 0.132164 0.991228i $$-0.457808\pi$$
0.132164 + 0.991228i $$0.457808\pi$$
$$230$$ 0 0
$$231$$ −8.00000 5.65685i −0.526361 0.372194i
$$232$$ 0 0
$$233$$ 28.2843i 1.85296i 0.376339 + 0.926482i $$0.377183\pi$$
−0.376339 + 0.926482i $$0.622817\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 4.00000 + 2.82843i 0.259828 + 0.183726i
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 14.0000 0.901819 0.450910 0.892570i $$-0.351100\pi$$
0.450910 + 0.892570i $$0.351100\pi$$
$$242$$ 0 0
$$243$$ 1.00000 + 15.5563i 0.0641500 + 0.997940i
$$244$$ 0 0
$$245$$ 2.82843i 0.180702i
$$246$$ 0 0
$$247$$ 11.3137i 0.719874i
$$248$$ 0 0
$$249$$ 6.00000 8.48528i 0.380235 0.537733i
$$250$$ 0 0
$$251$$ 2.00000 0.126239 0.0631194 0.998006i $$-0.479895\pi$$
0.0631194 + 0.998006i $$0.479895\pi$$
$$252$$ 0 0
$$253$$ −16.0000 −1.00591
$$254$$ 0 0
$$255$$ 16.0000 22.6274i 1.00196 1.41698i
$$256$$ 0 0
$$257$$ 11.3137i 0.705730i 0.935674 + 0.352865i $$0.114792\pi$$
−0.935674 + 0.352865i $$0.885208\pi$$
$$258$$ 0 0
$$259$$ 11.3137i 0.703000i
$$260$$ 0 0
$$261$$ 8.00000 2.82843i 0.495188 0.175075i
$$262$$ 0 0
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ 24.0000 1.47431
$$266$$ 0 0
$$267$$ 8.00000 + 5.65685i 0.489592 + 0.346194i
$$268$$ 0 0
$$269$$ 14.1421i 0.862261i 0.902290 + 0.431131i $$0.141885\pi$$
−0.902290 + 0.431131i $$0.858115\pi$$
$$270$$ 0 0
$$271$$ 19.7990i 1.20270i −0.798985 0.601351i $$-0.794629\pi$$
0.798985 0.601351i $$-0.205371\pi$$
$$272$$ 0 0
$$273$$ −16.0000 11.3137i −0.968364 0.684737i
$$274$$ 0 0
$$275$$ −6.00000 −0.361814
$$276$$ 0 0
$$277$$ −12.0000 −0.721010 −0.360505 0.932757i $$-0.617396\pi$$
−0.360505 + 0.932757i $$0.617396\pi$$
$$278$$ 0 0
$$279$$ −24.0000 + 8.48528i −1.43684 + 0.508001i
$$280$$ 0 0
$$281$$ 5.65685i 0.337460i −0.985662 0.168730i $$-0.946033\pi$$
0.985662 0.168730i $$-0.0539665\pi$$
$$282$$ 0 0
$$283$$ 25.4558i 1.51319i −0.653882 0.756596i $$-0.726861\pi$$
0.653882 0.756596i $$-0.273139\pi$$
$$284$$ 0 0
$$285$$ 8.00000 11.3137i 0.473879 0.670166i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −15.0000 −0.882353
$$290$$ 0 0
$$291$$ −6.00000 + 8.48528i −0.351726 + 0.497416i
$$292$$ 0 0
$$293$$ 31.1127i 1.81762i 0.417207 + 0.908812i $$0.363009\pi$$
−0.417207 + 0.908812i $$0.636991\pi$$
$$294$$ 0 0
$$295$$ 16.9706i 0.988064i
$$296$$ 0 0
$$297$$ −10.0000 2.82843i −0.580259 0.164122i
$$298$$ 0 0
$$299$$ −32.0000 −1.85061
$$300$$ 0 0
$$301$$ 8.00000 0.461112
$$302$$ 0 0
$$303$$ −4.00000 2.82843i −0.229794 0.162489i
$$304$$ 0 0
$$305$$ 11.3137i 0.647821i
$$306$$ 0 0
$$307$$ 8.48528i 0.484281i 0.970241 + 0.242140i $$0.0778494\pi$$
−0.970241 + 0.242140i $$0.922151\pi$$
$$308$$ 0 0
$$309$$ 12.0000 + 8.48528i 0.682656 + 0.482711i
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 0 0
$$313$$ 2.00000 0.113047 0.0565233 0.998401i $$-0.481998\pi$$
0.0565233 + 0.998401i $$0.481998\pi$$
$$314$$ 0 0
$$315$$ 8.00000 + 22.6274i 0.450749 + 1.27491i
$$316$$ 0 0
$$317$$ 31.1127i 1.74746i −0.486408 0.873732i $$-0.661693\pi$$
0.486408 0.873732i $$-0.338307\pi$$
$$318$$ 0 0
$$319$$ 5.65685i 0.316723i
$$320$$ 0 0
$$321$$ 6.00000 8.48528i 0.334887 0.473602i
$$322$$ 0 0
$$323$$ −16.0000 −0.890264
$$324$$ 0 0
$$325$$ −12.0000 −0.665640
$$326$$ 0 0
$$327$$ 4.00000 5.65685i 0.221201 0.312825i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.82843i 0.155464i −0.996974 0.0777322i $$-0.975232\pi$$
0.996974 0.0777322i $$-0.0247679\pi$$
$$332$$ 0 0
$$333$$ −4.00000 11.3137i −0.219199 0.619987i
$$334$$ 0 0
$$335$$ −40.0000 −2.18543
$$336$$ 0 0
$$337$$ 6.00000 0.326841 0.163420 0.986557i $$-0.447747\pi$$
0.163420 + 0.986557i $$0.447747\pi$$
$$338$$ 0 0
$$339$$ −16.0000 11.3137i −0.869001 0.614476i
$$340$$ 0 0
$$341$$ 16.9706i 0.919007i
$$342$$ 0 0
$$343$$ 16.9706i 0.916324i
$$344$$ 0 0
$$345$$ 32.0000 + 22.6274i 1.72282 + 1.21822i
$$346$$ 0 0
$$347$$ 2.00000 0.107366 0.0536828 0.998558i $$-0.482904\pi$$
0.0536828 + 0.998558i $$0.482904\pi$$
$$348$$ 0 0
$$349$$ −28.0000 −1.49881 −0.749403 0.662114i $$-0.769659\pi$$
−0.749403 + 0.662114i $$0.769659\pi$$
$$350$$ 0 0
$$351$$ −20.0000 5.65685i −1.06752 0.301941i
$$352$$ 0 0
$$353$$ 22.6274i 1.20434i −0.798369 0.602168i $$-0.794304\pi$$
0.798369 0.602168i $$-0.205696\pi$$
$$354$$ 0 0
$$355$$ 22.6274i 1.20094i
$$356$$ 0 0
$$357$$ 16.0000 22.6274i 0.846810 1.19757i
$$358$$ 0 0
$$359$$ −8.00000 −0.422224 −0.211112 0.977462i $$-0.567708\pi$$
−0.211112 + 0.977462i $$0.567708\pi$$
$$360$$ 0 0
$$361$$ 11.0000 0.578947
$$362$$ 0 0
$$363$$ −7.00000 + 9.89949i −0.367405 + 0.519589i
$$364$$ 0 0
$$365$$ 28.2843i 1.48047i
$$366$$ 0 0
$$367$$ 8.48528i 0.442928i −0.975169 0.221464i $$-0.928916\pi$$
0.975169 0.221464i $$-0.0710835\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 24.0000 1.24602
$$372$$ 0 0
$$373$$ 36.0000 1.86401 0.932005 0.362446i $$-0.118058\pi$$
0.932005 + 0.362446i $$0.118058\pi$$
$$374$$ 0 0
$$375$$ −8.00000 5.65685i −0.413118 0.292119i
$$376$$ 0 0
$$377$$ 11.3137i 0.582686i
$$378$$ 0 0
$$379$$ 25.4558i 1.30758i 0.756677 + 0.653789i $$0.226822\pi$$
−0.756677 + 0.653789i $$0.773178\pi$$
$$380$$ 0 0
$$381$$ 20.0000 + 14.1421i 1.02463 + 0.724524i
$$382$$ 0 0
$$383$$ 16.0000 0.817562 0.408781 0.912633i $$-0.365954\pi$$
0.408781 + 0.912633i $$0.365954\pi$$
$$384$$ 0 0
$$385$$ −16.0000 −0.815436
$$386$$ 0 0
$$387$$ 8.00000 2.82843i 0.406663 0.143777i
$$388$$ 0 0
$$389$$ 8.48528i 0.430221i 0.976590 + 0.215110i $$0.0690111\pi$$
−0.976590 + 0.215110i $$0.930989\pi$$
$$390$$ 0 0
$$391$$ 45.2548i 2.28864i
$$392$$ 0 0
$$393$$ −14.0000 + 19.7990i −0.706207 + 0.998727i
$$394$$ 0 0
$$395$$ 8.00000 0.402524
$$396$$ 0 0
$$397$$ −28.0000 −1.40528 −0.702640 0.711546i $$-0.747995\pi$$
−0.702640 + 0.711546i $$0.747995\pi$$
$$398$$ 0 0
$$399$$ 8.00000 11.3137i 0.400501 0.566394i
$$400$$ 0 0
$$401$$ 5.65685i 0.282490i −0.989975 0.141245i $$-0.954889\pi$$
0.989975 0.141245i $$-0.0451105\pi$$
$$402$$ 0 0
$$403$$ 33.9411i 1.69073i
$$404$$ 0 0
$$405$$ 16.0000 + 19.7990i 0.795046 + 0.983820i
$$406$$ 0 0
$$407$$ 8.00000 0.396545
$$408$$ 0 0
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 0 0
$$411$$ −16.0000 11.3137i −0.789222 0.558064i
$$412$$ 0 0
$$413$$ 16.9706i 0.835067i
$$414$$ 0 0
$$415$$ 16.9706i 0.833052i
$$416$$ 0 0
$$417$$ 12.0000 + 8.48528i 0.587643 + 0.415526i
$$418$$ 0 0
$$419$$ 6.00000 0.293119 0.146560 0.989202i $$-0.453180\pi$$
0.146560 + 0.989202i $$0.453180\pi$$
$$420$$ 0 0
$$421$$ −28.0000 −1.36464 −0.682318 0.731055i $$-0.739028\pi$$
−0.682318 + 0.731055i $$0.739028\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 16.9706i 0.823193i
$$426$$ 0 0
$$427$$ 11.3137i 0.547509i
$$428$$ 0 0
$$429$$ 8.00000 11.3137i 0.386244 0.546231i
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ −22.0000 −1.05725 −0.528626 0.848855i $$-0.677293\pi$$
−0.528626 + 0.848855i $$0.677293\pi$$
$$434$$ 0 0
$$435$$ 8.00000 11.3137i 0.383571 0.542451i
$$436$$ 0 0
$$437$$ 22.6274i 1.08242i
$$438$$ 0 0
$$439$$ 8.48528i 0.404980i 0.979284 + 0.202490i $$0.0649034\pi$$
−0.979284 + 0.202490i $$0.935097\pi$$
$$440$$ 0 0
$$441$$ 1.00000 + 2.82843i 0.0476190 + 0.134687i
$$442$$ 0 0
$$443$$ 18.0000 0.855206 0.427603 0.903967i $$-0.359358\pi$$
0.427603 + 0.903967i $$0.359358\pi$$
$$444$$ 0 0
$$445$$ 16.0000 0.758473
$$446$$ 0 0
$$447$$ −4.00000 2.82843i −0.189194 0.133780i
$$448$$ 0 0
$$449$$ 16.9706i 0.800890i −0.916321 0.400445i $$-0.868855\pi$$
0.916321 0.400445i $$-0.131145\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 12.0000 + 8.48528i 0.563809 + 0.398673i
$$454$$ 0 0
$$455$$ −32.0000 −1.50018
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 0 0
$$459$$ 8.00000 28.2843i 0.373408 1.32020i
$$460$$ 0 0
$$461$$ 25.4558i 1.18560i 0.805351 + 0.592798i $$0.201977\pi$$
−0.805351 + 0.592798i $$0.798023\pi$$
$$462$$ 0 0
$$463$$ 8.48528i 0.394344i −0.980369 0.197172i $$-0.936824\pi$$
0.980369 0.197172i $$-0.0631758\pi$$
$$464$$ 0 0
$$465$$ −24.0000 + 33.9411i −1.11297 + 1.57398i
$$466$$ 0 0
$$467$$ −42.0000 −1.94353 −0.971764 0.235954i $$-0.924178\pi$$
−0.971764 + 0.235954i $$0.924178\pi$$
$$468$$ 0 0
$$469$$ −40.0000 −1.84703
$$470$$ 0 0
$$471$$ 20.0000 28.2843i 0.921551 1.30327i
$$472$$ 0 0
$$473$$ 5.65685i 0.260102i
$$474$$ 0 0
$$475$$ 8.48528i 0.389331i
$$476$$ 0 0
$$477$$ 24.0000 8.48528i 1.09888 0.388514i
$$478$$ 0 0
$$479$$ −32.0000 −1.46212 −0.731059 0.682315i $$-0.760973\pi$$
−0.731059 + 0.682315i $$0.760973\pi$$
$$480$$ 0 0
$$481$$ 16.0000 0.729537
$$482$$ 0 0
$$483$$ 32.0000 + 22.6274i 1.45605 + 1.02958i
$$484$$ 0 0
$$485$$ 16.9706i 0.770594i
$$486$$ 0 0
$$487$$ 42.4264i 1.92252i 0.275636 + 0.961262i $$0.411111\pi$$
−0.275636 + 0.961262i $$0.588889\pi$$
$$488$$ 0 0
$$489$$ −12.0000 8.48528i −0.542659 0.383718i
$$490$$ 0 0
$$491$$ 22.0000 0.992846 0.496423 0.868081i $$-0.334646\pi$$
0.496423 + 0.868081i $$0.334646\pi$$
$$492$$ 0 0
$$493$$ −16.0000 −0.720604
$$494$$ 0 0
$$495$$ −16.0000 + 5.65685i −0.719147 + 0.254257i
$$496$$ 0 0
$$497$$ 22.6274i 1.01498i
$$498$$ 0 0
$$499$$ 19.7990i 0.886325i 0.896441 + 0.443162i $$0.146143\pi$$
−0.896441 + 0.443162i $$0.853857\pi$$
$$500$$ 0 0
$$501$$ 8.00000 11.3137i 0.357414 0.505459i
$$502$$ 0 0
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ −8.00000 −0.355995
$$506$$ 0 0
$$507$$ 3.00000 4.24264i 0.133235 0.188422i
$$508$$ 0 0
$$509$$ 25.4558i 1.12831i 0.825669 + 0.564155i $$0.190798\pi$$
−0.825669 + 0.564155i $$0.809202\pi$$
$$510$$ 0 0
$$511$$ 28.2843i 1.25122i
$$512$$ 0 0
$$513$$ 4.00000 14.1421i 0.176604 0.624391i
$$514$$ 0 0
$$515$$ 24.0000 1.05757
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 4.00000 + 2.82843i 0.175581 + 0.124154i
$$520$$ 0 0
$$521$$ 33.9411i 1.48699i −0.668743 0.743494i $$-0.733167\pi$$
0.668743 0.743494i $$-0.266833\pi$$
$$522$$ 0 0
$$523$$ 14.1421i 0.618392i 0.950998 + 0.309196i $$0.100060\pi$$
−0.950998 + 0.309196i $$0.899940\pi$$
$$524$$ 0 0
$$525$$ 12.0000 + 8.48528i 0.523723 + 0.370328i
$$526$$ 0 0
$$527$$ 48.0000 2.09091
$$528$$ 0 0
$$529$$ 41.0000 1.78261
$$530$$ 0 0
$$531$$ −6.00000 16.9706i −0.260378 0.736460i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 16.9706i 0.733701i
$$536$$ 0 0
$$537$$ 18.0000 25.4558i 0.776757 1.09850i
$$538$$ 0 0
$$539$$ −2.00000 −0.0861461
$$540$$ 0 0
$$541$$ −28.0000 −1.20381 −0.601907 0.798566i $$-0.705592\pi$$
−0.601907 + 0.798566i $$0.705592\pi$$
$$542$$ 0 0
$$543$$ −12.0000 + 16.9706i −0.514969 + 0.728277i
$$544$$ 0 0
$$545$$ 11.3137i 0.484626i
$$546$$ 0 0
$$547$$ 25.4558i 1.08841i 0.838951 + 0.544207i $$0.183169\pi$$
−0.838951 + 0.544207i $$0.816831\pi$$
$$548$$ 0 0
$$549$$ −4.00000 11.3137i −0.170716 0.482857i
$$550$$ 0 0
$$551$$ −8.00000 −0.340811
$$552$$ 0 0
$$553$$ 8.00000 0.340195
$$554$$ 0 0
$$555$$ −16.0000 11.3137i −0.679162 0.480240i
$$556$$ 0 0
$$557$$ 36.7696i 1.55798i 0.627039 + 0.778988i $$0.284267\pi$$
−0.627039 + 0.778988i $$0.715733\pi$$
$$558$$ 0 0
$$559$$ 11.3137i 0.478519i
$$560$$ 0 0
$$561$$ 16.0000 + 11.3137i 0.675521 + 0.477665i
$$562$$ 0 0
$$563$$ −42.0000 −1.77009 −0.885044 0.465506i $$-0.845872\pi$$
−0.885044 + 0.465506i $$0.845872\pi$$
$$564$$ 0 0
$$565$$ −32.0000 −1.34625
$$566$$ 0 0
$$567$$ 16.0000 + 19.7990i 0.671937 + 0.831479i
$$568$$ 0 0
$$569$$ 11.3137i 0.474295i 0.971474 + 0.237148i $$0.0762125\pi$$
−0.971474 + 0.237148i $$0.923787\pi$$
$$570$$ 0 0
$$571$$ 42.4264i 1.77549i 0.460336 + 0.887745i $$0.347729\pi$$
−0.460336 + 0.887745i $$0.652271\pi$$
$$572$$ 0 0
$$573$$ −16.0000 + 22.6274i −0.668410 + 0.945274i
$$574$$ 0 0
$$575$$ 24.0000 1.00087
$$576$$ 0 0
$$577$$ 22.0000 0.915872 0.457936 0.888985i $$-0.348589\pi$$
0.457936 + 0.888985i $$0.348589\pi$$
$$578$$ 0 0
$$579$$ −2.00000 + 2.82843i −0.0831172 + 0.117545i
$$580$$ 0 0
$$581$$ 16.9706i 0.704058i
$$582$$ 0 0
$$583$$ 16.9706i 0.702849i
$$584$$ 0 0
$$585$$ −32.0000 + 11.3137i −1.32304 + 0.467764i
$$586$$ 0 0
$$587$$ −26.0000 −1.07313 −0.536567 0.843857i $$-0.680279\pi$$
−0.536567 + 0.843857i $$0.680279\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ 0 0
$$591$$ −20.0000 14.1421i −0.822690 0.581730i
$$592$$ 0 0
$$593$$ 22.6274i 0.929197i 0.885522 + 0.464598i $$0.153801\pi$$
−0.885522 + 0.464598i $$0.846199\pi$$
$$594$$ 0 0
$$595$$ 45.2548i 1.85527i
$$596$$ 0 0
$$597$$ 12.0000 + 8.48528i 0.491127 + 0.347279i
$$598$$ 0 0
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ −38.0000 −1.55005 −0.775026 0.631929i $$-0.782263\pi$$
−0.775026 + 0.631929i $$0.782263\pi$$
$$602$$ 0 0
$$603$$ −40.0000 + 14.1421i −1.62893 + 0.575912i
$$604$$ 0 0
$$605$$ 19.7990i 0.804943i
$$606$$ 0 0
$$607$$ 36.7696i 1.49243i 0.665705 + 0.746215i $$0.268131\pi$$
−0.665705 + 0.746215i $$0.731869\pi$$
$$608$$ 0 0
$$609$$ 8.00000 11.3137i 0.324176 0.458455i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −12.0000 −0.484675 −0.242338 0.970192i $$-0.577914\pi$$
−0.242338 + 0.970192i $$0.577914\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 5.65685i 0.227736i −0.993496 0.113868i $$-0.963676\pi$$
0.993496 0.113868i $$-0.0363242\pi$$
$$618$$ 0 0
$$619$$ 25.4558i 1.02316i −0.859237 0.511578i $$-0.829061\pi$$
0.859237 0.511578i $$-0.170939\pi$$
$$620$$ 0 0
$$621$$ 40.0000 + 11.3137i 1.60514 + 0.454003i
$$622$$ 0 0
$$623$$ 16.0000 0.641026
$$624$$ 0 0
$$625$$ −31.0000 −1.24000
$$626$$ 0 0
$$627$$ 8.00000 + 5.65685i 0.319489 + 0.225913i
$$628$$ 0 0
$$629$$ 22.6274i 0.902214i
$$630$$ 0 0
$$631$$ 25.4558i 1.01338i −0.862128 0.506691i $$-0.830869\pi$$
0.862128 0.506691i $$-0.169131\pi$$
$$632$$ 0 0
$$633$$ −4.00000 2.82843i −0.158986 0.112420i
$$634$$ 0 0
$$635$$ 40.0000 1.58735
$$636$$ 0 0
$$637$$ −4.00000 −0.158486
$$638$$ 0 0
$$639$$ 8.00000 + 22.6274i 0.316475 + 0.895127i
$$640$$ 0 0
$$641$$ 39.5980i 1.56403i 0.623262 + 0.782013i $$0.285807\pi$$
−0.623262 + 0.782013i $$0.714193\pi$$
$$642$$ 0 0
$$643$$ 25.4558i 1.00388i 0.864902 + 0.501940i $$0.167380\pi$$
−0.864902 + 0.501940i $$0.832620\pi$$
$$644$$ 0 0
$$645$$ 8.00000 11.3137i 0.315000 0.445477i
$$646$$ 0 0
$$647$$ 8.00000 0.314512 0.157256 0.987558i $$-0.449735\pi$$
0.157256 + 0.987558i $$0.449735\pi$$
$$648$$ 0 0
$$649$$ 12.0000 0.471041
$$650$$ 0 0
$$651$$ −24.0000 + 33.9411i −0.940634 + 1.33026i
$$652$$ 0 0
$$653$$ 42.4264i 1.66027i −0.557560 0.830137i $$-0.688262\pi$$
0.557560 0.830137i $$-0.311738\pi$$
$$654$$ 0 0
$$655$$ 39.5980i 1.54722i
$$656$$ 0 0
$$657$$ −10.0000 28.2843i −0.390137 1.10347i
$$658$$ 0 0
$$659$$ −14.0000 −0.545363 −0.272681 0.962104i $$-0.587910\pi$$
−0.272681 + 0.962104i $$0.587910\pi$$
$$660$$ 0 0
$$661$$ 4.00000 0.155582 0.0777910 0.996970i $$-0.475213\pi$$
0.0777910 + 0.996970i $$0.475213\pi$$
$$662$$ 0 0
$$663$$ 32.0000 + 22.6274i 1.24278 + 0.878776i
$$664$$ 0 0
$$665$$ 22.6274i 0.877454i
$$666$$ 0 0
$$667$$ 22.6274i 0.876137i
$$668$$ 0 0
$$669$$ 4.00000 + 2.82843i 0.154649 + 0.109353i
$$670$$ 0 0
$$671$$ 8.00000 0.308837
$$672$$ 0 0
$$673$$ −38.0000 −1.46479 −0.732396 0.680879i $$-0.761598\pi$$
−0.732396 + 0.680879i $$0.761598\pi$$
$$674$$ 0 0
$$675$$ 15.0000 + 4.24264i 0.577350 + 0.163299i
$$676$$ 0 0
$$677$$ 25.4558i 0.978348i −0.872186 0.489174i $$-0.837298\pi$$
0.872186 0.489174i $$-0.162702\pi$$
$$678$$ 0 0
$$679$$ 16.9706i 0.651270i
$$680$$ 0 0
$$681$$ 22.0000 31.1127i 0.843042 1.19224i
$$682$$ 0 0
$$683$$ 18.0000 0.688751 0.344375 0.938832i $$-0.388091\pi$$
0.344375 + 0.938832i $$0.388091\pi$$
$$684$$ 0 0
$$685$$ −32.0000 −1.22266
$$686$$ 0 0
$$687$$ 4.00000 5.65685i 0.152610 0.215822i
$$688$$ 0 0
$$689$$ 33.9411i 1.29305i
$$690$$ 0 0
$$691$$ 31.1127i 1.18358i −0.806091 0.591791i $$-0.798421\pi$$
0.806091 0.591791i $$-0.201579\pi$$
$$692$$ 0 0
$$693$$ −16.0000 + 5.65685i −0.607790 + 0.214886i
$$694$$ 0 0
$$695$$ 24.0000 0.910372
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 40.0000 + 28.2843i 1.51294 + 1.06981i
$$700$$ 0 0
$$701$$ 31.1127i 1.17511i −0.809184 0.587555i $$-0.800091\pi$$
0.809184 0.587555i $$-0.199909\pi$$
$$702$$ 0 0
$$703$$ 11.3137i 0.426705i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −8.00000 −0.300871
$$708$$ 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 2.82843i 0.300023 0.106074i
$$712$$ 0 0
$$713$$ 67.8823i 2.54221i
$$714$$ 0 0
$$715$$ 22.6274i 0.846217i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 16.0000 0.596699 0.298350 0.954457i $$-0.403564\pi$$
0.298350 + 0.954457i $$0.403564\pi$$
$$720$$ 0 0
$$721$$ 24.0000 0.893807
$$722$$ 0 0
$$723$$ 14.0000 19.7990i 0.520666 0.736332i
$$724$$ 0 0
$$725$$ 8.48528i 0.315135i
$$726$$ 0 0
$$727$$ 31.1127i 1.15391i 0.816777 + 0.576953i $$0.195758\pi$$
−0.816777 + 0.576953i $$0.804242\pi$$
$$728$$ 0 0
$$729$$ 23.0000 + 14.1421i 0.851852 + 0.523783i
$$730$$ 0 0
$$731$$ −16.0000 −0.591781
$$732$$ 0 0
$$733$$ 36.0000 1.32969 0.664845 0.746981i $$-0.268498\pi$$
0.664845 + 0.746981i $$0.268498\pi$$
$$734$$ 0 0
$$735$$ 4.00000 + 2.82843i 0.147542 + 0.104328i
$$736$$ 0 0
$$737$$ 28.2843i 1.04186i
$$738$$ 0 0
$$739$$ 42.4264i 1.56068i 0.625355 + 0.780340i $$0.284954\pi$$
−0.625355 + 0.780340i $$0.715046\pi$$
$$740$$ 0 0
$$741$$ 16.0000 + 11.3137i 0.587775 + 0.415619i
$$742$$ 0 0
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ −8.00000 −0.293097
$$746$$ 0 0
$$747$$ −6.00000 16.9706i −0.219529 0.620920i
$$748$$ 0 0
$$749$$ 16.9706i 0.620091i
$$750$$ 0 0
$$751$$ 2.82843i 0.103211i 0.998668 + 0.0516054i $$0.0164338\pi$$
−0.998668 + 0.0516054i $$0.983566\pi$$
$$752$$ 0 0
$$753$$ 2.00000 2.82843i 0.0728841 0.103074i
$$754$$ 0 0
$$755$$ 24.0000 0.873449
$$756$$ 0 0
$$757$$ −12.0000 −0.436147 −0.218074 0.975932i $$-0.569977\pi$$
−0.218074 + 0.975932i $$0.569977\pi$$
$$758$$ 0 0
$$759$$ −16.0000 + 22.6274i −0.580763 + 0.821323i
$$760$$ 0 0
$$761$$ 22.6274i 0.820243i 0.912031 + 0.410122i $$0.134514\pi$$
−0.912031 + 0.410122i $$0.865486\pi$$
$$762$$ 0 0
$$763$$ 11.3137i 0.409584i
$$764$$ 0 0
$$765$$ −16.0000 45.2548i −0.578481 1.63619i
$$766$$ 0 0
$$767$$ 24.0000 0.866590
$$768$$ 0 0
$$769$$ −2.00000 −0.0721218 −0.0360609 0.999350i $$-0.511481\pi$$
−0.0360609 + 0.999350i $$0.511481\pi$$
$$770$$ 0 0
$$771$$ 16.0000 + 11.3137i 0.576226 + 0.407453i
$$772$$ 0 0
$$773$$ 2.82843i 0.101731i −0.998706 0.0508657i $$-0.983802\pi$$
0.998706 0.0508657i $$-0.0161981\pi$$
$$774$$ 0 0
$$775$$ 25.4558i 0.914401i
$$776$$ 0 0
$$777$$ −16.0000 11.3137i −0.573997 0.405877i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −16.0000 −0.572525
$$782$$ 0 0
$$783$$ 4.00000 14.1421i 0.142948 0.505399i
$$784$$ 0 0
$$785$$ 56.5685i 2.01902i
$$786$$ 0 0
$$787$$ 31.1127i 1.10905i −0.832168 0.554524i $$-0.812900\pi$$
0.832168 0.554524i $$-0.187100\pi$$
$$788$$ 0 0
$$789$$ 24.0000 33.9411i 0.854423 1.20834i
$$790$$ 0 0
$$791$$ −32.0000 −1.13779
$$792$$ 0 0
$$793$$ 16.0000 0.568177
$$794$$ 0 0
$$795$$ 24.0000 33.9411i 0.851192 1.20377i
$$796$$ 0