# Properties

 Label 912.2.bb.a.31.1 Level $912$ Weight $2$ Character 912.31 Analytic conductor $7.282$ Analytic rank $1$ 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(31,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.bb (of order $$6$$, degree $$2$$, 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: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 31.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 912.31 Dual form 912.2.bb.a.559.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{3} +1.73205i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{3} +1.73205i q^{7} +(-0.500000 + 0.866025i) q^{9} +3.46410i q^{11} +(-4.50000 - 2.59808i) q^{13} +(-3.00000 - 5.19615i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(1.50000 - 0.866025i) q^{21} +(-3.00000 - 1.73205i) q^{23} +(2.50000 - 4.33013i) q^{25} +1.00000 q^{27} +(-3.00000 - 1.73205i) q^{29} +1.00000 q^{31} +(3.00000 - 1.73205i) q^{33} +8.66025i q^{37} +5.19615i q^{39} +(-6.00000 + 3.46410i) q^{41} +(-4.50000 + 2.59808i) q^{43} +(-9.00000 - 5.19615i) q^{47} +4.00000 q^{49} +(-3.00000 + 5.19615i) q^{51} +(-9.00000 - 5.19615i) q^{53} +(3.50000 + 2.59808i) q^{57} +(6.00000 + 10.3923i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-1.50000 - 0.866025i) q^{63} +(-6.50000 + 11.2583i) q^{67} +3.46410i q^{69} +(2.50000 + 4.33013i) q^{73} -5.00000 q^{75} -6.00000 q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -17.3205i q^{83} +3.46410i q^{87} +(4.50000 - 7.79423i) q^{91} +(-0.500000 - 0.866025i) q^{93} +(12.0000 - 6.92820i) q^{97} +(-3.00000 - 1.73205i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{3} - q^{9}+O(q^{10})$$ 2 * q - q^3 - q^9 $$2 q - q^{3} - q^{9} - 9 q^{13} - 6 q^{17} - 8 q^{19} + 3 q^{21} - 6 q^{23} + 5 q^{25} + 2 q^{27} - 6 q^{29} + 2 q^{31} + 6 q^{33} - 12 q^{41} - 9 q^{43} - 18 q^{47} + 8 q^{49} - 6 q^{51} - 18 q^{53} + 7 q^{57} + 12 q^{59} + 5 q^{61} - 3 q^{63} - 13 q^{67} + 5 q^{73} - 10 q^{75} - 12 q^{77} + q^{79} - q^{81} + 9 q^{91} - q^{93} + 24 q^{97} - 6 q^{99}+O(q^{100})$$ 2 * q - q^3 - q^9 - 9 * q^13 - 6 * q^17 - 8 * q^19 + 3 * q^21 - 6 * q^23 + 5 * q^25 + 2 * q^27 - 6 * q^29 + 2 * q^31 + 6 * q^33 - 12 * q^41 - 9 * q^43 - 18 * q^47 + 8 * q^49 - 6 * q^51 - 18 * q^53 + 7 * q^57 + 12 * q^59 + 5 * q^61 - 3 * q^63 - 13 * q^67 + 5 * q^73 - 10 * q^75 - 12 * q^77 + q^79 - q^81 + 9 * q^91 - q^93 + 24 * q^97 - 6 * q^99

## Character values

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

 $$n$$ $$97$$ $$229$$ $$305$$ $$799$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ 0 0
$$5$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 0 0
$$7$$ 1.73205i 0.654654i 0.944911 + 0.327327i $$0.106148\pi$$
−0.944911 + 0.327327i $$0.893852\pi$$
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 3.46410i 1.04447i 0.852803 + 0.522233i $$0.174901\pi$$
−0.852803 + 0.522233i $$0.825099\pi$$
$$12$$ 0 0
$$13$$ −4.50000 2.59808i −1.24808 0.720577i −0.277350 0.960769i $$-0.589456\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i $$-0.907299\pi$$
0.230285 0.973123i $$-0.426034\pi$$
$$18$$ 0 0
$$19$$ −4.00000 + 1.73205i −0.917663 + 0.397360i
$$20$$ 0 0
$$21$$ 1.50000 0.866025i 0.327327 0.188982i
$$22$$ 0 0
$$23$$ −3.00000 1.73205i −0.625543 0.361158i 0.153481 0.988152i $$-0.450952\pi$$
−0.779024 + 0.626994i $$0.784285\pi$$
$$24$$ 0 0
$$25$$ 2.50000 4.33013i 0.500000 0.866025i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −3.00000 1.73205i −0.557086 0.321634i 0.194889 0.980825i $$-0.437565\pi$$
−0.751975 + 0.659192i $$0.770899\pi$$
$$30$$ 0 0
$$31$$ 1.00000 0.179605 0.0898027 0.995960i $$-0.471376\pi$$
0.0898027 + 0.995960i $$0.471376\pi$$
$$32$$ 0 0
$$33$$ 3.00000 1.73205i 0.522233 0.301511i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 8.66025i 1.42374i 0.702313 + 0.711868i $$0.252151\pi$$
−0.702313 + 0.711868i $$0.747849\pi$$
$$38$$ 0 0
$$39$$ 5.19615i 0.832050i
$$40$$ 0 0
$$41$$ −6.00000 + 3.46410i −0.937043 + 0.541002i −0.889032 0.457845i $$-0.848621\pi$$
−0.0480106 + 0.998847i $$0.515288\pi$$
$$42$$ 0 0
$$43$$ −4.50000 + 2.59808i −0.686244 + 0.396203i −0.802203 0.597051i $$-0.796339\pi$$
0.115960 + 0.993254i $$0.463006\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −9.00000 5.19615i −1.31278 0.757937i −0.330228 0.943901i $$-0.607126\pi$$
−0.982556 + 0.185964i $$0.940459\pi$$
$$48$$ 0 0
$$49$$ 4.00000 0.571429
$$50$$ 0 0
$$51$$ −3.00000 + 5.19615i −0.420084 + 0.727607i
$$52$$ 0 0
$$53$$ −9.00000 5.19615i −1.23625 0.713746i −0.267920 0.963441i $$-0.586336\pi$$
−0.968325 + 0.249695i $$0.919670\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.50000 + 2.59808i 0.463586 + 0.344124i
$$58$$ 0 0
$$59$$ 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i $$0.118692\pi$$
−0.150148 + 0.988663i $$0.547975\pi$$
$$60$$ 0 0
$$61$$ 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i $$-0.729619\pi$$
0.980507 + 0.196485i $$0.0629528\pi$$
$$62$$ 0 0
$$63$$ −1.50000 0.866025i −0.188982 0.109109i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.50000 + 11.2583i −0.794101 + 1.37542i 0.129307 + 0.991605i $$0.458725\pi$$
−0.923408 + 0.383819i $$0.874609\pi$$
$$68$$ 0 0
$$69$$ 3.46410i 0.417029i
$$70$$ 0 0
$$71$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$72$$ 0 0
$$73$$ 2.50000 + 4.33013i 0.292603 + 0.506803i 0.974424 0.224716i $$-0.0721453\pi$$
−0.681822 + 0.731519i $$0.738812\pi$$
$$74$$ 0 0
$$75$$ −5.00000 −0.577350
$$76$$ 0 0
$$77$$ −6.00000 −0.683763
$$78$$ 0 0
$$79$$ 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i $$-0.148751\pi$$
−0.836527 + 0.547926i $$0.815418\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 17.3205i 1.90117i −0.310460 0.950586i $$-0.600483\pi$$
0.310460 0.950586i $$-0.399517\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 3.46410i 0.371391i
$$88$$ 0 0
$$89$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ 0 0
$$91$$ 4.50000 7.79423i 0.471728 0.817057i
$$92$$ 0 0
$$93$$ −0.500000 0.866025i −0.0518476 0.0898027i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 12.0000 6.92820i 1.21842 0.703452i 0.253837 0.967247i $$-0.418307\pi$$
0.964579 + 0.263795i $$0.0849741\pi$$
$$98$$ 0 0
$$99$$ −3.00000 1.73205i −0.301511 0.174078i
$$100$$ 0 0
$$101$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$102$$ 0 0
$$103$$ −1.00000 −0.0985329 −0.0492665 0.998786i $$-0.515688\pi$$
−0.0492665 + 0.998786i $$0.515688\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −12.0000 + 6.92820i −1.14939 + 0.663602i −0.948739 0.316061i $$-0.897640\pi$$
−0.200653 + 0.979662i $$0.564306\pi$$
$$110$$ 0 0
$$111$$ 7.50000 4.33013i 0.711868 0.410997i
$$112$$ 0 0
$$113$$ 6.92820i 0.651751i 0.945413 + 0.325875i $$0.105659\pi$$
−0.945413 + 0.325875i $$0.894341\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 4.50000 2.59808i 0.416025 0.240192i
$$118$$ 0 0
$$119$$ 9.00000 5.19615i 0.825029 0.476331i
$$120$$ 0 0
$$121$$ −1.00000 −0.0909091
$$122$$ 0 0
$$123$$ 6.00000 + 3.46410i 0.541002 + 0.312348i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −8.00000 + 13.8564i −0.709885 + 1.22956i 0.255014 + 0.966937i $$0.417920\pi$$
−0.964899 + 0.262620i $$0.915413\pi$$
$$128$$ 0 0
$$129$$ 4.50000 + 2.59808i 0.396203 + 0.228748i
$$130$$ 0 0
$$131$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$132$$ 0 0
$$133$$ −3.00000 6.92820i −0.260133 0.600751i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i $$-0.662010\pi$$
0.999893 0.0146279i $$-0.00465636\pi$$
$$138$$ 0 0
$$139$$ 7.50000 + 4.33013i 0.636142 + 0.367277i 0.783127 0.621862i $$-0.213624\pi$$
−0.146985 + 0.989139i $$0.546957\pi$$
$$140$$ 0 0
$$141$$ 10.3923i 0.875190i
$$142$$ 0 0
$$143$$ 9.00000 15.5885i 0.752618 1.30357i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −2.00000 3.46410i −0.164957 0.285714i
$$148$$ 0 0
$$149$$ −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i $$-0.902763\pi$$
0.216394 0.976306i $$-0.430570\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 0 0
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 8.50000 + 14.7224i 0.678374 + 1.17498i 0.975470 + 0.220131i $$0.0706483\pi$$
−0.297097 + 0.954847i $$0.596018\pi$$
$$158$$ 0 0
$$159$$ 10.3923i 0.824163i
$$160$$ 0 0
$$161$$ 3.00000 5.19615i 0.236433 0.409514i
$$162$$ 0 0
$$163$$ 22.5167i 1.76364i −0.471585 0.881820i $$-0.656318\pi$$
0.471585 0.881820i $$-0.343682\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i $$-0.679641\pi$$
0.999169 + 0.0407502i $$0.0129748\pi$$
$$168$$ 0 0
$$169$$ 7.00000 + 12.1244i 0.538462 + 0.932643i
$$170$$ 0 0
$$171$$ 0.500000 4.33013i 0.0382360 0.331133i
$$172$$ 0 0
$$173$$ −21.0000 + 12.1244i −1.59660 + 0.921798i −0.604465 + 0.796632i $$0.706613\pi$$
−0.992136 + 0.125166i $$0.960054\pi$$
$$174$$ 0 0
$$175$$ 7.50000 + 4.33013i 0.566947 + 0.327327i
$$176$$ 0 0
$$177$$ 6.00000 10.3923i 0.450988 0.781133i
$$178$$ 0 0
$$179$$ 6.00000 0.448461 0.224231 0.974536i $$-0.428013\pi$$
0.224231 + 0.974536i $$0.428013\pi$$
$$180$$ 0 0
$$181$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$182$$ 0 0
$$183$$ −5.00000 −0.369611
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 18.0000 10.3923i 1.31629 0.759961i
$$188$$ 0 0
$$189$$ 1.73205i 0.125988i
$$190$$ 0 0
$$191$$ 6.92820i 0.501307i 0.968077 + 0.250654i $$0.0806455\pi$$
−0.968077 + 0.250654i $$0.919354\pi$$
$$192$$ 0 0
$$193$$ 13.5000 7.79423i 0.971751 0.561041i 0.0719816 0.997406i $$-0.477068\pi$$
0.899770 + 0.436365i $$0.143734\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ −10.5000 6.06218i −0.744325 0.429736i 0.0793146 0.996850i $$-0.474727\pi$$
−0.823640 + 0.567113i $$0.808060\pi$$
$$200$$ 0 0
$$201$$ 13.0000 0.916949
$$202$$ 0 0
$$203$$ 3.00000 5.19615i 0.210559 0.364698i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 3.00000 1.73205i 0.208514 0.120386i
$$208$$ 0 0
$$209$$ −6.00000 13.8564i −0.415029 0.958468i
$$210$$ 0 0
$$211$$ 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i $$-0.111609\pi$$
−0.767049 + 0.641588i $$0.778276\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 1.73205i 0.117579i
$$218$$ 0 0
$$219$$ 2.50000 4.33013i 0.168934 0.292603i
$$220$$ 0 0
$$221$$ 31.1769i 2.09719i
$$222$$ 0 0
$$223$$ −5.50000 9.52628i −0.368307 0.637927i 0.620994 0.783815i $$-0.286729\pi$$
−0.989301 + 0.145889i $$0.953396\pi$$
$$224$$ 0 0
$$225$$ 2.50000 + 4.33013i 0.166667 + 0.288675i
$$226$$ 0 0
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 0 0
$$229$$ 23.0000 1.51988 0.759941 0.649992i $$-0.225228\pi$$
0.759941 + 0.649992i $$0.225228\pi$$
$$230$$ 0 0
$$231$$ 3.00000 + 5.19615i 0.197386 + 0.341882i
$$232$$ 0 0
$$233$$ 12.0000 + 20.7846i 0.786146 + 1.36165i 0.928312 + 0.371802i $$0.121260\pi$$
−0.142166 + 0.989843i $$0.545407\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0.500000 0.866025i 0.0324785 0.0562544i
$$238$$ 0 0
$$239$$ 6.92820i 0.448148i −0.974572 0.224074i $$-0.928064\pi$$
0.974572 0.224074i $$-0.0719358\pi$$
$$240$$ 0 0
$$241$$ 7.50000 + 4.33013i 0.483117 + 0.278928i 0.721715 0.692191i $$-0.243354\pi$$
−0.238597 + 0.971119i $$0.576688\pi$$
$$242$$ 0 0
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 22.5000 + 2.59808i 1.43164 + 0.165312i
$$248$$ 0 0
$$249$$ −15.0000 + 8.66025i −0.950586 + 0.548821i
$$250$$ 0 0
$$251$$ −15.0000 8.66025i −0.946792 0.546630i −0.0547088 0.998502i $$-0.517423\pi$$
−0.892083 + 0.451872i $$0.850756\pi$$
$$252$$ 0 0
$$253$$ 6.00000 10.3923i 0.377217 0.653359i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −3.00000 1.73205i −0.187135 0.108042i 0.403506 0.914977i $$-0.367792\pi$$
−0.590641 + 0.806935i $$0.701125\pi$$
$$258$$ 0 0
$$259$$ −15.0000 −0.932055
$$260$$ 0 0
$$261$$ 3.00000 1.73205i 0.185695 0.107211i
$$262$$ 0 0
$$263$$ −18.0000 + 10.3923i −1.10993 + 0.640817i −0.938811 0.344434i $$-0.888071\pi$$
−0.171117 + 0.985251i $$0.554738\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 6.00000 3.46410i 0.365826 0.211210i −0.305807 0.952093i $$-0.598926\pi$$
0.671634 + 0.740883i $$0.265593\pi$$
$$270$$ 0 0
$$271$$ 3.00000 1.73205i 0.182237 0.105215i −0.406106 0.913826i $$-0.633114\pi$$
0.588343 + 0.808611i $$0.299780\pi$$
$$272$$ 0 0
$$273$$ −9.00000 −0.544705
$$274$$ 0 0
$$275$$ 15.0000 + 8.66025i 0.904534 + 0.522233i
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 0 0
$$279$$ −0.500000 + 0.866025i −0.0299342 + 0.0518476i
$$280$$ 0 0
$$281$$ −6.00000 3.46410i −0.357930 0.206651i 0.310242 0.950657i $$-0.399590\pi$$
−0.668172 + 0.744007i $$0.732923\pi$$
$$282$$ 0 0
$$283$$ 3.00000 1.73205i 0.178331 0.102960i −0.408177 0.912903i $$-0.633835\pi$$
0.586509 + 0.809943i $$0.300502\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −6.00000 10.3923i −0.354169 0.613438i
$$288$$ 0 0
$$289$$ −9.50000 + 16.4545i −0.558824 + 0.967911i
$$290$$ 0 0
$$291$$ −12.0000 6.92820i −0.703452 0.406138i
$$292$$ 0 0
$$293$$ 24.2487i 1.41662i −0.705899 0.708312i $$-0.749457\pi$$
0.705899 0.708312i $$-0.250543\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 3.46410i 0.201008i
$$298$$ 0 0
$$299$$ 9.00000 + 15.5885i 0.520483 + 0.901504i
$$300$$ 0 0
$$301$$ −4.50000 7.79423i −0.259376 0.449252i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 2.00000 + 3.46410i 0.114146 + 0.197707i 0.917438 0.397879i $$-0.130253\pi$$
−0.803292 + 0.595585i $$0.796920\pi$$
$$308$$ 0 0
$$309$$ 0.500000 + 0.866025i 0.0284440 + 0.0492665i
$$310$$ 0 0
$$311$$ 20.7846i 1.17859i −0.807919 0.589294i $$-0.799406\pi$$
0.807919 0.589294i $$-0.200594\pi$$
$$312$$ 0 0
$$313$$ −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i $$-0.924536\pi$$
0.689412 + 0.724370i $$0.257869\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 24.0000 + 13.8564i 1.34797 + 0.778253i 0.987962 0.154694i $$-0.0494393\pi$$
0.360012 + 0.932948i $$0.382773\pi$$
$$318$$ 0 0
$$319$$ 6.00000 10.3923i 0.335936 0.581857i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 21.0000 + 15.5885i 1.16847 + 0.867365i
$$324$$ 0 0
$$325$$ −22.5000 + 12.9904i −1.24808 + 0.720577i
$$326$$ 0 0
$$327$$ 12.0000 + 6.92820i 0.663602 + 0.383131i
$$328$$ 0 0
$$329$$ 9.00000 15.5885i 0.496186 0.859419i
$$330$$ 0 0
$$331$$ −25.0000 −1.37412 −0.687062 0.726599i $$-0.741100\pi$$
−0.687062 + 0.726599i $$0.741100\pi$$
$$332$$ 0 0
$$333$$ −7.50000 4.33013i −0.410997 0.237289i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −7.50000 + 4.33013i −0.408551 + 0.235877i −0.690167 0.723650i $$-0.742463\pi$$
0.281616 + 0.959527i $$0.409130\pi$$
$$338$$ 0 0
$$339$$ 6.00000 3.46410i 0.325875 0.188144i
$$340$$ 0 0
$$341$$ 3.46410i 0.187592i
$$342$$ 0 0
$$343$$ 19.0526i 1.02874i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −12.0000 + 6.92820i −0.644194 + 0.371925i −0.786228 0.617936i $$-0.787969\pi$$
0.142034 + 0.989862i $$0.454636\pi$$
$$348$$ 0 0
$$349$$ −19.0000 −1.01705 −0.508523 0.861048i $$-0.669808\pi$$
−0.508523 + 0.861048i $$0.669808\pi$$
$$350$$ 0 0
$$351$$ −4.50000 2.59808i −0.240192 0.138675i
$$352$$ 0 0
$$353$$ 24.0000 1.27739 0.638696 0.769460i $$-0.279474\pi$$
0.638696 + 0.769460i $$0.279474\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −9.00000 5.19615i −0.476331 0.275010i
$$358$$ 0 0
$$359$$ −18.0000 + 10.3923i −0.950004 + 0.548485i −0.893082 0.449894i $$-0.851462\pi$$
−0.0569216 + 0.998379i $$0.518129\pi$$
$$360$$ 0 0
$$361$$ 13.0000 13.8564i 0.684211 0.729285i
$$362$$ 0 0
$$363$$ 0.500000 + 0.866025i 0.0262432 + 0.0454545i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.50000 + 0.866025i 0.0782994 + 0.0452062i 0.538639 0.842537i $$-0.318939\pi$$
−0.460339 + 0.887743i $$0.652272\pi$$
$$368$$ 0 0
$$369$$ 6.92820i 0.360668i
$$370$$ 0 0
$$371$$ 9.00000 15.5885i 0.467257 0.809312i
$$372$$ 0 0
$$373$$ 13.8564i 0.717458i −0.933442 0.358729i $$-0.883210\pi$$
0.933442 0.358729i $$-0.116790\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 9.00000 + 15.5885i 0.463524 + 0.802846i
$$378$$ 0 0
$$379$$ −25.0000 −1.28416 −0.642082 0.766636i $$-0.721929\pi$$
−0.642082 + 0.766636i $$0.721929\pi$$
$$380$$ 0 0
$$381$$ 16.0000 0.819705
$$382$$ 0 0
$$383$$ −9.00000 15.5885i −0.459879 0.796533i 0.539076 0.842257i $$-0.318774\pi$$
−0.998954 + 0.0457244i $$0.985440\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 5.19615i 0.264135i
$$388$$ 0 0
$$389$$ −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i $$-0.881939\pi$$
0.779895 + 0.625910i $$0.215272\pi$$
$$390$$ 0 0
$$391$$ 20.7846i 1.05112i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 3.50000 + 6.06218i 0.175660 + 0.304252i 0.940389 0.340099i $$-0.110461\pi$$
−0.764730 + 0.644351i $$0.777127\pi$$
$$398$$ 0 0
$$399$$ −4.50000 + 6.06218i −0.225282 + 0.303488i
$$400$$ 0 0
$$401$$ 24.0000 13.8564i 1.19850 0.691956i 0.238282 0.971196i $$-0.423416\pi$$
0.960221 + 0.279240i $$0.0900826\pi$$
$$402$$ 0 0
$$403$$ −4.50000 2.59808i −0.224161 0.129419i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −30.0000 −1.48704
$$408$$ 0 0
$$409$$ −18.0000 10.3923i −0.890043 0.513866i −0.0160862 0.999871i $$-0.505121\pi$$
−0.873956 + 0.486004i $$0.838454\pi$$
$$410$$ 0 0
$$411$$ −12.0000 −0.591916
$$412$$ 0 0
$$413$$ −18.0000 + 10.3923i −0.885722 + 0.511372i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 8.66025i 0.424094i
$$418$$ 0 0
$$419$$ 31.1769i 1.52309i 0.648111 + 0.761546i $$0.275559\pi$$
−0.648111 + 0.761546i $$0.724441\pi$$
$$420$$ 0 0
$$421$$ 18.0000 10.3923i 0.877266 0.506490i 0.00751023 0.999972i $$-0.497609\pi$$
0.869756 + 0.493482i $$0.164276\pi$$
$$422$$ 0 0
$$423$$ 9.00000 5.19615i 0.437595 0.252646i
$$424$$ 0 0
$$425$$ −30.0000 −1.45521
$$426$$ 0 0
$$427$$ 7.50000 + 4.33013i 0.362950 + 0.209550i
$$428$$ 0 0
$$429$$ −18.0000 −0.869048
$$430$$ 0 0
$$431$$ −15.0000 + 25.9808i −0.722525 + 1.25145i 0.237460 + 0.971397i $$0.423685\pi$$
−0.959985 + 0.280052i $$0.909648\pi$$
$$432$$ 0 0
$$433$$ −22.5000 12.9904i −1.08128 0.624278i −0.150039 0.988680i $$-0.547940\pi$$
−0.931242 + 0.364402i $$0.881273\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 15.0000 + 1.73205i 0.717547 + 0.0828552i
$$438$$ 0 0
$$439$$ 9.50000 + 16.4545i 0.453410 + 0.785330i 0.998595 0.0529862i $$-0.0168739\pi$$
−0.545185 + 0.838316i $$0.683541\pi$$
$$440$$ 0 0
$$441$$ −2.00000 + 3.46410i −0.0952381 + 0.164957i
$$442$$ 0 0
$$443$$ 21.0000 + 12.1244i 0.997740 + 0.576046i 0.907579 0.419882i $$-0.137928\pi$$
0.0901612 + 0.995927i $$0.471262\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −9.00000 + 15.5885i −0.425685 + 0.737309i
$$448$$ 0 0
$$449$$ 10.3923i 0.490443i 0.969467 + 0.245222i $$0.0788607\pi$$
−0.969467 + 0.245222i $$0.921139\pi$$
$$450$$ 0 0
$$451$$ −12.0000 20.7846i −0.565058 0.978709i
$$452$$ 0 0
$$453$$ −4.00000 6.92820i −0.187936 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.00000 −0.233890 −0.116945 0.993138i $$-0.537310\pi$$
−0.116945 + 0.993138i $$0.537310\pi$$
$$458$$ 0 0
$$459$$ −3.00000 5.19615i −0.140028 0.242536i
$$460$$ 0 0
$$461$$ −6.00000 10.3923i −0.279448 0.484018i 0.691800 0.722089i $$-0.256818\pi$$
−0.971248 + 0.238071i $$0.923485\pi$$
$$462$$ 0 0
$$463$$ 5.19615i 0.241486i 0.992684 + 0.120743i $$0.0385276\pi$$
−0.992684 + 0.120743i $$0.961472\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ −19.5000 11.2583i −0.900426 0.519861i
$$470$$ 0 0
$$471$$ 8.50000 14.7224i 0.391659 0.678374i
$$472$$ 0 0
$$473$$ −9.00000 15.5885i −0.413820 0.716758i
$$474$$ 0 0
$$475$$ −2.50000 + 21.6506i −0.114708 + 0.993399i
$$476$$ 0 0
$$477$$ 9.00000 5.19615i 0.412082 0.237915i
$$478$$ 0 0
$$479$$ 12.0000 + 6.92820i 0.548294 + 0.316558i 0.748434 0.663210i $$-0.230806\pi$$
−0.200140 + 0.979767i $$0.564140\pi$$
$$480$$ 0 0
$$481$$ 22.5000 38.9711i 1.02591 1.77693i
$$482$$ 0 0
$$483$$ −6.00000 −0.273009
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −8.00000 −0.362515 −0.181257 0.983436i $$-0.558017\pi$$
−0.181257 + 0.983436i $$0.558017\pi$$
$$488$$ 0 0
$$489$$ −19.5000 + 11.2583i −0.881820 + 0.509119i
$$490$$ 0 0
$$491$$ −12.0000 + 6.92820i −0.541552 + 0.312665i −0.745708 0.666273i $$-0.767889\pi$$
0.204155 + 0.978938i $$0.434555\pi$$
$$492$$ 0 0
$$493$$ 20.7846i 0.936092i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −7.50000 + 4.33013i −0.335746 + 0.193843i −0.658389 0.752678i $$-0.728762\pi$$
0.322643 + 0.946521i $$0.395429\pi$$
$$500$$ 0 0
$$501$$ −12.0000 −0.536120
$$502$$ 0 0
$$503$$ −15.0000 8.66025i −0.668817 0.386142i 0.126811 0.991927i $$-0.459526\pi$$
−0.795628 + 0.605785i $$0.792859\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 7.00000 12.1244i 0.310881 0.538462i
$$508$$ 0 0
$$509$$ −21.0000 12.1244i −0.930809 0.537403i −0.0437414 0.999043i $$-0.513928\pi$$
−0.887067 + 0.461640i $$0.847261\pi$$
$$510$$ 0 0
$$511$$ −7.50000 + 4.33013i −0.331780 + 0.191554i
$$512$$ 0 0
$$513$$ −4.00000 + 1.73205i −0.176604 + 0.0764719i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 18.0000 31.1769i 0.791639 1.37116i
$$518$$ 0 0
$$519$$ 21.0000 + 12.1244i 0.921798 + 0.532200i
$$520$$ 0 0
$$521$$ 3.46410i 0.151765i 0.997117 + 0.0758825i $$0.0241774\pi$$
−0.997117 + 0.0758825i $$0.975823\pi$$
$$522$$ 0 0
$$523$$ 14.5000 25.1147i 0.634041 1.09819i −0.352677 0.935745i $$-0.614728\pi$$
0.986718 0.162446i $$-0.0519382\pi$$
$$524$$ 0 0
$$525$$ 8.66025i 0.377964i
$$526$$ 0 0
$$527$$ −3.00000 5.19615i −0.130682 0.226348i
$$528$$ 0 0
$$529$$ −5.50000 9.52628i −0.239130 0.414186i
$$530$$ 0 0
$$531$$ −12.0000 −0.520756
$$532$$ 0 0
$$533$$ 36.0000 1.55933
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −3.00000 5.19615i −0.129460 0.224231i
$$538$$ 0 0
$$539$$ 13.8564i 0.596838i
$$540$$ 0 0
$$541$$ −12.5000 + 21.6506i −0.537417 + 0.930834i 0.461625 + 0.887075i $$0.347267\pi$$
−0.999042 + 0.0437584i $$0.986067\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 6.50000 11.2583i 0.277920 0.481371i −0.692948 0.720988i $$-0.743688\pi$$
0.970868 + 0.239616i $$0.0770217\pi$$
$$548$$ 0 0
$$549$$ 2.50000 + 4.33013i 0.106697 + 0.184805i
$$550$$ 0 0
$$551$$ 15.0000 + 1.73205i 0.639021 + 0.0737878i
$$552$$ 0 0
$$553$$ −1.50000 + 0.866025i −0.0637865 + 0.0368271i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 12.0000 20.7846i 0.508456 0.880672i −0.491496 0.870880i $$-0.663550\pi$$
0.999952 0.00979220i $$-0.00311700\pi$$
$$558$$ 0 0
$$559$$ 27.0000 1.14198
$$560$$ 0 0
$$561$$ −18.0000 10.3923i −0.759961 0.438763i
$$562$$ 0 0
$$563$$ −24.0000 −1.01148 −0.505740 0.862686i $$-0.668780\pi$$
−0.505740 + 0.862686i $$0.668780\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1.50000 0.866025i 0.0629941 0.0363696i
$$568$$ 0 0
$$569$$ 34.6410i 1.45223i 0.687575 + 0.726113i $$0.258675\pi$$
−0.687575 + 0.726113i $$0.741325\pi$$
$$570$$ 0 0
$$571$$ 32.9090i 1.37720i −0.725143 0.688599i $$-0.758226\pi$$
0.725143 0.688599i $$-0.241774\pi$$
$$572$$ 0 0
$$573$$ 6.00000 3.46410i 0.250654 0.144715i
$$574$$ 0 0
$$575$$ −15.0000 + 8.66025i −0.625543 + 0.361158i
$$576$$ 0 0
$$577$$ −38.0000 −1.58196 −0.790980 0.611842i $$-0.790429\pi$$
−0.790980 + 0.611842i $$0.790429\pi$$
$$578$$ 0 0
$$579$$ −13.5000 7.79423i −0.561041 0.323917i
$$580$$ 0 0
$$581$$ 30.0000 1.24461
$$582$$ 0 0
$$583$$ 18.0000 31.1769i 0.745484 1.29122i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −36.0000 + 20.7846i −1.48588 + 0.857873i −0.999871 0.0160815i $$-0.994881\pi$$
−0.486008 + 0.873954i $$0.661548\pi$$
$$588$$ 0 0
$$589$$ −4.00000 + 1.73205i −0.164817 + 0.0713679i
$$590$$ 0 0
$$591$$ 6.00000 + 10.3923i 0.246807 + 0.427482i
$$592$$ 0 0
$$593$$ 12.0000 20.7846i 0.492781 0.853522i −0.507184 0.861838i $$-0.669314\pi$$
0.999965 + 0.00831589i $$0.00264706\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 12.1244i 0.496217i
$$598$$ 0 0
$$599$$ −21.0000 + 36.3731i −0.858037 + 1.48616i 0.0157622 + 0.999876i $$0.494983\pi$$
−0.873799 + 0.486287i $$0.838351\pi$$
$$600$$ 0 0
$$601$$ 46.7654i 1.90760i 0.300443 + 0.953800i $$0.402865\pi$$
−0.300443 + 0.953800i $$0.597135\pi$$
$$602$$ 0 0
$$603$$ −6.50000 11.2583i −0.264700 0.458475i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −47.0000 −1.90767 −0.953836 0.300329i $$-0.902903\pi$$
−0.953836 + 0.300329i $$0.902903\pi$$
$$608$$ 0 0
$$609$$ −6.00000 −0.243132
$$610$$ 0 0
$$611$$ 27.0000 + 46.7654i 1.09230 + 1.89192i
$$612$$ 0 0
$$613$$ 19.0000 + 32.9090i 0.767403 + 1.32918i 0.938967 + 0.344008i $$0.111785\pi$$
−0.171564 + 0.985173i $$0.554882\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −21.0000 + 36.3731i −0.845428 + 1.46432i 0.0398207 + 0.999207i $$0.487321\pi$$
−0.885249 + 0.465118i $$0.846012\pi$$
$$618$$ 0 0
$$619$$ 39.8372i 1.60119i 0.599205 + 0.800595i $$0.295483\pi$$
−0.599205 + 0.800595i $$0.704517\pi$$
$$620$$ 0 0
$$621$$ −3.00000 1.73205i −0.120386 0.0695048i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −12.5000 21.6506i −0.500000 0.866025i
$$626$$ 0 0
$$627$$ −9.00000 + 12.1244i −0.359425 + 0.484200i
$$628$$ 0 0
$$629$$ 45.0000 25.9808i 1.79427 1.03592i
$$630$$ 0 0
$$631$$ −19.5000 11.2583i −0.776283 0.448187i 0.0588285 0.998268i $$-0.481263\pi$$
−0.835111 + 0.550081i $$0.814597\pi$$
$$632$$ 0 0
$$633$$ 2.50000 4.33013i 0.0993661 0.172107i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −18.0000 10.3923i −0.713186 0.411758i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 3.00000 1.73205i 0.118493 0.0684119i −0.439582 0.898202i $$-0.644873\pi$$
0.558075 + 0.829790i $$0.311540\pi$$
$$642$$ 0 0
$$643$$ −10.5000 + 6.06218i −0.414080 + 0.239069i −0.692541 0.721378i $$-0.743509\pi$$
0.278462 + 0.960447i $$0.410176\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 24.2487i 0.953315i −0.879089 0.476658i $$-0.841848\pi$$
0.879089 0.476658i $$-0.158152\pi$$
$$648$$ 0 0
$$649$$ −36.0000 + 20.7846i −1.41312 + 0.815867i
$$650$$ 0 0
$$651$$ 1.50000 0.866025i 0.0587896 0.0339422i
$$652$$ 0 0
$$653$$ 48.0000 1.87839 0.939193 0.343391i $$-0.111576\pi$$
0.939193 + 0.343391i $$0.111576\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −5.00000 −0.195069
$$658$$ 0 0
$$659$$ −9.00000 + 15.5885i −0.350590 + 0.607240i −0.986353 0.164644i $$-0.947352\pi$$
0.635763 + 0.771885i $$0.280686\pi$$
$$660$$ 0 0
$$661$$ −6.00000 3.46410i −0.233373 0.134738i 0.378754 0.925497i $$-0.376353\pi$$
−0.612127 + 0.790759i $$0.709686\pi$$
$$662$$ 0 0
$$663$$ 27.0000 15.5885i 1.04859 0.605406i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 6.00000 + 10.3923i 0.232321 + 0.402392i
$$668$$ 0 0
$$669$$ −5.50000 + 9.52628i −0.212642 + 0.368307i
$$670$$ 0 0
$$671$$ 15.0000 + 8.66025i 0.579069 + 0.334325i
$$672$$ 0 0
$$673$$ 8.66025i 0.333828i −0.985971 0.166914i $$-0.946620\pi$$
0.985971 0.166914i $$-0.0533803\pi$$
$$674$$ 0 0
$$675$$ 2.50000 4.33013i 0.0962250 0.166667i
$$676$$ 0 0
$$677$$ 17.3205i 0.665681i 0.942983 + 0.332841i $$0.108007\pi$$
−0.942983 + 0.332841i $$0.891993\pi$$
$$678$$ 0 0
$$679$$ 12.0000 + 20.7846i 0.460518 + 0.797640i
$$680$$ 0 0
$$681$$ −6.00000 10.3923i −0.229920 0.398234i
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −11.5000 19.9186i −0.438752 0.759941i
$$688$$ 0 0
$$689$$ 27.0000 + 46.7654i 1.02862 + 1.78162i
$$690$$ 0 0
$$691$$ 3.46410i 0.131781i −0.997827 0.0658903i $$-0.979011\pi$$
0.997827 0.0658903i $$-0.0209887\pi$$
$$692$$ 0 0
$$693$$ 3.00000 5.19615i 0.113961 0.197386i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 36.0000 + 20.7846i 1.36360 + 0.787273i
$$698$$ 0 0
$$699$$ 12.0000 20.7846i 0.453882 0.786146i
$$700$$ 0 0
$$701$$ 12.0000 + 20.7846i 0.453234 + 0.785024i 0.998585 0.0531839i $$-0.0169370\pi$$
−0.545351 + 0.838208i $$0.683604\pi$$
$$702$$ 0 0
$$703$$ −15.0000 34.6410i −0.565736 1.30651i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 17.5000 30.3109i 0.657226 1.13835i −0.324104 0.946021i $$-0.605063\pi$$
0.981331 0.192328i $$-0.0616038\pi$$
$$710$$ 0 0
$$711$$ −1.00000 −0.0375029
$$712$$ 0 0
$$713$$ −3.00000 1.73205i −0.112351 0.0648658i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −6.00000 + 3.46410i −0.224074 + 0.129369i
$$718$$ 0 0
$$719$$ 39.0000 22.5167i 1.45445 0.839730i 0.455725 0.890121i $$-0.349380\pi$$
0.998730 + 0.0503909i $$0.0160467\pi$$
$$720$$ 0 0
$$721$$ 1.73205i 0.0645049i
$$722$$ 0 0
$$723$$ 8.66025i 0.322078i
$$724$$ 0 0
$$725$$ −15.0000 + 8.66025i −0.557086 + 0.321634i
$$726$$ 0 0
$$727$$ 16.5000 9.52628i 0.611951 0.353310i −0.161778 0.986827i $$-0.551723\pi$$
0.773729 + 0.633517i $$0.218389\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 27.0000 + 15.5885i 0.998631 + 0.576560i
$$732$$ 0 0
$$733$$ 22.0000 0.812589 0.406294 0.913742i $$-0.366821\pi$$
0.406294 + 0.913742i $$0.366821\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −39.0000 22.5167i −1.43658 0.829412i
$$738$$ 0 0
$$739$$ 28.5000 16.4545i 1.04839 0.605288i 0.126191 0.992006i $$-0.459725\pi$$
0.922198 + 0.386718i $$0.126391\pi$$
$$740$$ 0 0
$$741$$ −9.00000 20.7846i −0.330623 0.763542i
$$742$$ 0 0
$$743$$ −21.0000 36.3731i −0.770415 1.33440i −0.937336 0.348428i $$-0.886716\pi$$
0.166920 0.985970i $$-0.446618\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 15.0000 + 8.66025i 0.548821 + 0.316862i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 6.50000 11.2583i 0.237188 0.410822i −0.722718 0.691143i $$-0.757107\pi$$
0.959906 + 0.280321i $$0.0904408\pi$$
$$752$$ 0 0
$$753$$ 17.3205i 0.631194i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −17.5000 30.3109i −0.636048 1.10167i −0.986292 0.165009i $$-0.947235\pi$$
0.350244 0.936659i $$-0.386099\pi$$
$$758$$ 0 0
$$759$$ −12.0000 −0.435572
$$760$$ 0 0
$$761$$ 12.0000 0.435000 0.217500 0.976060i $$-0.430210\pi$$
0.217500 + 0.976060i $$0.430210\pi$$
$$762$$ 0 0
$$763$$ −12.0000 20.7846i −0.434429 0.752453i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 62.3538i 2.25147i
$$768$$ 0 0
$$769$$ −0.500000 + 0.866025i −0.0180305 + 0.0312297i −0.874900 0.484304i $$-0.839073\pi$$
0.856869 + 0.515534i $$0.172406\pi$$
$$770$$ 0 0
$$771$$ 3.46410i 0.124757i
$$772$$ 0 0
$$773$$ −3.00000 1.73205i −0.107903 0.0622975i 0.445078 0.895492i $$-0.353176\pi$$
−0.552980 + 0.833194i $$0.686509\pi$$
$$774$$ 0 0
$$775$$ 2.50000 4.33013i 0.0898027 0.155543i
$$776$$ 0 0
$$777$$ 7.50000 + 12.9904i 0.269061 + 0.466027i
$$778$$ 0 0
$$779$$ 18.0000 24.2487i 0.644917 0.868800i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −3.00000 1.73205i −0.107211 0.0618984i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 31.0000 1.10503 0.552515 0.833503i $$-0.313668\pi$$
0.552515 + 0.833503i $$0.313668\pi$$
$$788$$ 0 0
$$789$$ 18.0000 + 10.3923i 0.640817 + 0.369976i
$$790$$ 0 0
$$791$$ −12.0000 −0.426671
$$792$$ 0 0
$$793$$ −22.5000 + 12.9904i −0.798998 + 0.461302i