# Properties

 Label 1280.2.o.f.127.1 Level $1280$ Weight $2$ Character 1280.127 Analytic conductor $10.221$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(127,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1280.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.o (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$10.2208514587$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 160) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 127.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1280.127 Dual form 1280.2.o.f.383.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 1.00000i) q^{3} +(2.00000 - 1.00000i) q^{5} +(3.00000 - 3.00000i) q^{7} +1.00000i q^{9} +O(q^{10})$$ $$q+(-1.00000 + 1.00000i) q^{3} +(2.00000 - 1.00000i) q^{5} +(3.00000 - 3.00000i) q^{7} +1.00000i q^{9} -2.00000 q^{11} +(3.00000 + 3.00000i) q^{13} +(-1.00000 + 3.00000i) q^{15} +(1.00000 + 1.00000i) q^{17} +4.00000i q^{19} +6.00000i q^{21} +(1.00000 + 1.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} -10.0000i q^{31} +(2.00000 - 2.00000i) q^{33} +(3.00000 - 9.00000i) q^{35} +(-1.00000 + 1.00000i) q^{37} -6.00000 q^{39} +10.0000 q^{41} +(5.00000 - 5.00000i) q^{43} +(1.00000 + 2.00000i) q^{45} +(-3.00000 + 3.00000i) q^{47} -11.0000i q^{49} -2.00000 q^{51} +(5.00000 + 5.00000i) q^{53} +(-4.00000 + 2.00000i) q^{55} +(-4.00000 - 4.00000i) q^{57} +12.0000i q^{59} +2.00000i q^{61} +(3.00000 + 3.00000i) q^{63} +(9.00000 + 3.00000i) q^{65} +(-1.00000 - 1.00000i) q^{67} -2.00000 q^{69} +2.00000i q^{71} +(-1.00000 + 1.00000i) q^{73} +(1.00000 + 7.00000i) q^{75} +(-6.00000 + 6.00000i) q^{77} +8.00000 q^{79} +5.00000 q^{81} +(-5.00000 + 5.00000i) q^{83} +(3.00000 + 1.00000i) q^{85} -16.0000i q^{89} +18.0000 q^{91} +(10.0000 + 10.0000i) q^{93} +(4.00000 + 8.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} -2.00000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{3} + 4 q^{5} + 6 q^{7}+O(q^{10})$$ 2 * q - 2 * q^3 + 4 * q^5 + 6 * q^7 $$2 q - 2 q^{3} + 4 q^{5} + 6 q^{7} - 4 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 2 q^{23} + 6 q^{25} - 8 q^{27} + 4 q^{33} + 6 q^{35} - 2 q^{37} - 12 q^{39} + 20 q^{41} + 10 q^{43} + 2 q^{45} - 6 q^{47} - 4 q^{51} + 10 q^{53} - 8 q^{55} - 8 q^{57} + 6 q^{63} + 18 q^{65} - 2 q^{67} - 4 q^{69} - 2 q^{73} + 2 q^{75} - 12 q^{77} + 16 q^{79} + 10 q^{81} - 10 q^{83} + 6 q^{85} + 36 q^{91} + 20 q^{93} + 8 q^{95} - 6 q^{97}+O(q^{100})$$ 2 * q - 2 * q^3 + 4 * q^5 + 6 * q^7 - 4 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 2 * q^23 + 6 * q^25 - 8 * q^27 + 4 * q^33 + 6 * q^35 - 2 * q^37 - 12 * q^39 + 20 * q^41 + 10 * q^43 + 2 * q^45 - 6 * q^47 - 4 * q^51 + 10 * q^53 - 8 * q^55 - 8 * q^57 + 6 * q^63 + 18 * q^65 - 2 * q^67 - 4 * q^69 - 2 * q^73 + 2 * q^75 - 12 * q^77 + 16 * q^79 + 10 * q^81 - 10 * q^83 + 6 * q^85 + 36 * q^91 + 20 * q^93 + 8 * q^95 - 6 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$261$$ $$511$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$ $$-1$$

## 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 + 1.00000i −0.577350 + 0.577350i −0.934172 0.356822i $$-0.883860\pi$$
0.356822 + 0.934172i $$0.383860\pi$$
$$4$$ 0 0
$$5$$ 2.00000 1.00000i 0.894427 0.447214i
$$6$$ 0 0
$$7$$ 3.00000 3.00000i 1.13389 1.13389i 0.144370 0.989524i $$-0.453885\pi$$
0.989524 0.144370i $$-0.0461154\pi$$
$$8$$ 0 0
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i $$-0.0497784\pi$$
−0.155747 + 0.987797i $$0.549778\pi$$
$$14$$ 0 0
$$15$$ −1.00000 + 3.00000i −0.258199 + 0.774597i
$$16$$ 0 0
$$17$$ 1.00000 + 1.00000i 0.242536 + 0.242536i 0.817898 0.575363i $$-0.195139\pi$$
−0.575363 + 0.817898i $$0.695139\pi$$
$$18$$ 0 0
$$19$$ 4.00000i 0.917663i 0.888523 + 0.458831i $$0.151732\pi$$
−0.888523 + 0.458831i $$0.848268\pi$$
$$20$$ 0 0
$$21$$ 6.00000i 1.30931i
$$22$$ 0 0
$$23$$ 1.00000 + 1.00000i 0.208514 + 0.208514i 0.803636 0.595121i $$-0.202896\pi$$
−0.595121 + 0.803636i $$0.702896\pi$$
$$24$$ 0 0
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ 0 0
$$27$$ −4.00000 4.00000i −0.769800 0.769800i
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 10.0000i 1.79605i −0.439941 0.898027i $$-0.645001\pi$$
0.439941 0.898027i $$-0.354999\pi$$
$$32$$ 0 0
$$33$$ 2.00000 2.00000i 0.348155 0.348155i
$$34$$ 0 0
$$35$$ 3.00000 9.00000i 0.507093 1.52128i
$$36$$ 0 0
$$37$$ −1.00000 + 1.00000i −0.164399 + 0.164399i −0.784512 0.620113i $$-0.787087\pi$$
0.620113 + 0.784512i $$0.287087\pi$$
$$38$$ 0 0
$$39$$ −6.00000 −0.960769
$$40$$ 0 0
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ 5.00000 5.00000i 0.762493 0.762493i −0.214280 0.976772i $$-0.568740\pi$$
0.976772 + 0.214280i $$0.0687403\pi$$
$$44$$ 0 0
$$45$$ 1.00000 + 2.00000i 0.149071 + 0.298142i
$$46$$ 0 0
$$47$$ −3.00000 + 3.00000i −0.437595 + 0.437595i −0.891202 0.453607i $$-0.850137\pi$$
0.453607 + 0.891202i $$0.350137\pi$$
$$48$$ 0 0
$$49$$ 11.0000i 1.57143i
$$50$$ 0 0
$$51$$ −2.00000 −0.280056
$$52$$ 0 0
$$53$$ 5.00000 + 5.00000i 0.686803 + 0.686803i 0.961524 0.274721i $$-0.0885855\pi$$
−0.274721 + 0.961524i $$0.588586\pi$$
$$54$$ 0 0
$$55$$ −4.00000 + 2.00000i −0.539360 + 0.269680i
$$56$$ 0 0
$$57$$ −4.00000 4.00000i −0.529813 0.529813i
$$58$$ 0 0
$$59$$ 12.0000i 1.56227i 0.624364 + 0.781133i $$0.285358\pi$$
−0.624364 + 0.781133i $$0.714642\pi$$
$$60$$ 0 0
$$61$$ 2.00000i 0.256074i 0.991769 + 0.128037i $$0.0408676\pi$$
−0.991769 + 0.128037i $$0.959132\pi$$
$$62$$ 0 0
$$63$$ 3.00000 + 3.00000i 0.377964 + 0.377964i
$$64$$ 0 0
$$65$$ 9.00000 + 3.00000i 1.11631 + 0.372104i
$$66$$ 0 0
$$67$$ −1.00000 1.00000i −0.122169 0.122169i 0.643379 0.765548i $$-0.277532\pi$$
−0.765548 + 0.643379i $$0.777532\pi$$
$$68$$ 0 0
$$69$$ −2.00000 −0.240772
$$70$$ 0 0
$$71$$ 2.00000i 0.237356i 0.992933 + 0.118678i $$0.0378657\pi$$
−0.992933 + 0.118678i $$0.962134\pi$$
$$72$$ 0 0
$$73$$ −1.00000 + 1.00000i −0.117041 + 0.117041i −0.763202 0.646160i $$-0.776374\pi$$
0.646160 + 0.763202i $$0.276374\pi$$
$$74$$ 0 0
$$75$$ 1.00000 + 7.00000i 0.115470 + 0.808290i
$$76$$ 0 0
$$77$$ −6.00000 + 6.00000i −0.683763 + 0.683763i
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0 0
$$81$$ 5.00000 0.555556
$$82$$ 0 0
$$83$$ −5.00000 + 5.00000i −0.548821 + 0.548821i −0.926100 0.377279i $$-0.876860\pi$$
0.377279 + 0.926100i $$0.376860\pi$$
$$84$$ 0 0
$$85$$ 3.00000 + 1.00000i 0.325396 + 0.108465i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 16.0000i 1.69600i −0.529999 0.847998i $$-0.677808\pi$$
0.529999 0.847998i $$-0.322192\pi$$
$$90$$ 0 0
$$91$$ 18.0000 1.88691
$$92$$ 0 0
$$93$$ 10.0000 + 10.0000i 1.03695 + 1.03695i
$$94$$ 0 0
$$95$$ 4.00000 + 8.00000i 0.410391 + 0.820783i
$$96$$ 0 0
$$97$$ −3.00000 3.00000i −0.304604 0.304604i 0.538208 0.842812i $$-0.319101\pi$$
−0.842812 + 0.538208i $$0.819101\pi$$
$$98$$ 0 0
$$99$$ 2.00000i 0.201008i
$$100$$ 0 0
$$101$$ 6.00000i 0.597022i −0.954406 0.298511i $$-0.903510\pi$$
0.954406 0.298511i $$-0.0964900\pi$$
$$102$$ 0 0
$$103$$ 9.00000 + 9.00000i 0.886796 + 0.886796i 0.994214 0.107418i $$-0.0342582\pi$$
−0.107418 + 0.994214i $$0.534258\pi$$
$$104$$ 0 0
$$105$$ 6.00000 + 12.0000i 0.585540 + 1.17108i
$$106$$ 0 0
$$107$$ −3.00000 3.00000i −0.290021 0.290021i 0.547068 0.837088i $$-0.315744\pi$$
−0.837088 + 0.547068i $$0.815744\pi$$
$$108$$ 0 0
$$109$$ 4.00000 0.383131 0.191565 0.981480i $$-0.438644\pi$$
0.191565 + 0.981480i $$0.438644\pi$$
$$110$$ 0 0
$$111$$ 2.00000i 0.189832i
$$112$$ 0 0
$$113$$ −3.00000 + 3.00000i −0.282216 + 0.282216i −0.833992 0.551776i $$-0.813950\pi$$
0.551776 + 0.833992i $$0.313950\pi$$
$$114$$ 0 0
$$115$$ 3.00000 + 1.00000i 0.279751 + 0.0932505i
$$116$$ 0 0
$$117$$ −3.00000 + 3.00000i −0.277350 + 0.277350i
$$118$$ 0 0
$$119$$ 6.00000 0.550019
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ −10.0000 + 10.0000i −0.901670 + 0.901670i
$$124$$ 0 0
$$125$$ 2.00000 11.0000i 0.178885 0.983870i
$$126$$ 0 0
$$127$$ −7.00000 + 7.00000i −0.621150 + 0.621150i −0.945825 0.324676i $$-0.894745\pi$$
0.324676 + 0.945825i $$0.394745\pi$$
$$128$$ 0 0
$$129$$ 10.0000i 0.880451i
$$130$$ 0 0
$$131$$ 10.0000 0.873704 0.436852 0.899533i $$-0.356093\pi$$
0.436852 + 0.899533i $$0.356093\pi$$
$$132$$ 0 0
$$133$$ 12.0000 + 12.0000i 1.04053 + 1.04053i
$$134$$ 0 0
$$135$$ −12.0000 4.00000i −1.03280 0.344265i
$$136$$ 0 0
$$137$$ 11.0000 + 11.0000i 0.939793 + 0.939793i 0.998288 0.0584943i $$-0.0186300\pi$$
−0.0584943 + 0.998288i $$0.518630\pi$$
$$138$$ 0 0
$$139$$ 12.0000i 1.01783i −0.860818 0.508913i $$-0.830047\pi$$
0.860818 0.508913i $$-0.169953\pi$$
$$140$$ 0 0
$$141$$ 6.00000i 0.505291i
$$142$$ 0 0
$$143$$ −6.00000 6.00000i −0.501745 0.501745i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 11.0000 + 11.0000i 0.907265 + 0.907265i
$$148$$ 0 0
$$149$$ −4.00000 −0.327693 −0.163846 0.986486i $$-0.552390\pi$$
−0.163846 + 0.986486i $$0.552390\pi$$
$$150$$ 0 0
$$151$$ 6.00000i 0.488273i −0.969741 0.244137i $$-0.921495\pi$$
0.969741 0.244137i $$-0.0785045\pi$$
$$152$$ 0 0
$$153$$ −1.00000 + 1.00000i −0.0808452 + 0.0808452i
$$154$$ 0 0
$$155$$ −10.0000 20.0000i −0.803219 1.60644i
$$156$$ 0 0
$$157$$ 1.00000 1.00000i 0.0798087 0.0798087i −0.666076 0.745884i $$-0.732027\pi$$
0.745884 + 0.666076i $$0.232027\pi$$
$$158$$ 0 0
$$159$$ −10.0000 −0.793052
$$160$$ 0 0
$$161$$ 6.00000 0.472866
$$162$$ 0 0
$$163$$ −1.00000 + 1.00000i −0.0783260 + 0.0783260i −0.745184 0.666858i $$-0.767639\pi$$
0.666858 + 0.745184i $$0.267639\pi$$
$$164$$ 0 0
$$165$$ 2.00000 6.00000i 0.155700 0.467099i
$$166$$ 0 0
$$167$$ −1.00000 + 1.00000i −0.0773823 + 0.0773823i −0.744739 0.667356i $$-0.767426\pi$$
0.667356 + 0.744739i $$0.267426\pi$$
$$168$$ 0 0
$$169$$ 5.00000i 0.384615i
$$170$$ 0 0
$$171$$ −4.00000 −0.305888
$$172$$ 0 0
$$173$$ −5.00000 5.00000i −0.380143 0.380143i 0.491011 0.871154i $$-0.336628\pi$$
−0.871154 + 0.491011i $$0.836628\pi$$
$$174$$ 0 0
$$175$$ −3.00000 21.0000i −0.226779 1.58745i
$$176$$ 0 0
$$177$$ −12.0000 12.0000i −0.901975 0.901975i
$$178$$ 0 0
$$179$$ 12.0000i 0.896922i −0.893802 0.448461i $$-0.851972\pi$$
0.893802 0.448461i $$-0.148028\pi$$
$$180$$ 0 0
$$181$$ 22.0000i 1.63525i −0.575753 0.817624i $$-0.695291\pi$$
0.575753 0.817624i $$-0.304709\pi$$
$$182$$ 0 0
$$183$$ −2.00000 2.00000i −0.147844 0.147844i
$$184$$ 0 0
$$185$$ −1.00000 + 3.00000i −0.0735215 + 0.220564i
$$186$$ 0 0
$$187$$ −2.00000 2.00000i −0.146254 0.146254i
$$188$$ 0 0
$$189$$ −24.0000 −1.74574
$$190$$ 0 0
$$191$$ 14.0000i 1.01300i 0.862239 + 0.506502i $$0.169062\pi$$
−0.862239 + 0.506502i $$0.830938\pi$$
$$192$$ 0 0
$$193$$ −15.0000 + 15.0000i −1.07972 + 1.07972i −0.0831899 + 0.996534i $$0.526511\pi$$
−0.996534 + 0.0831899i $$0.973489\pi$$
$$194$$ 0 0
$$195$$ −12.0000 + 6.00000i −0.859338 + 0.429669i
$$196$$ 0 0
$$197$$ −13.0000 + 13.0000i −0.926212 + 0.926212i −0.997459 0.0712470i $$-0.977302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ 0 0
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ 0 0
$$201$$ 2.00000 0.141069
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 20.0000 10.0000i 1.39686 0.698430i
$$206$$ 0 0
$$207$$ −1.00000 + 1.00000i −0.0695048 + 0.0695048i
$$208$$ 0 0
$$209$$ 8.00000i 0.553372i
$$210$$ 0 0
$$211$$ −14.0000 −0.963800 −0.481900 0.876226i $$-0.660053\pi$$
−0.481900 + 0.876226i $$0.660053\pi$$
$$212$$ 0 0
$$213$$ −2.00000 2.00000i −0.137038 0.137038i
$$214$$ 0 0
$$215$$ 5.00000 15.0000i 0.340997 1.02299i
$$216$$ 0 0
$$217$$ −30.0000 30.0000i −2.03653 2.03653i
$$218$$ 0 0
$$219$$ 2.00000i 0.135147i
$$220$$ 0 0
$$221$$ 6.00000i 0.403604i
$$222$$ 0 0
$$223$$ −1.00000 1.00000i −0.0669650 0.0669650i 0.672831 0.739796i $$-0.265078\pi$$
−0.739796 + 0.672831i $$0.765078\pi$$
$$224$$ 0 0
$$225$$ 4.00000 + 3.00000i 0.266667 + 0.200000i
$$226$$ 0 0
$$227$$ −5.00000 5.00000i −0.331862 0.331862i 0.521431 0.853293i $$-0.325398\pi$$
−0.853293 + 0.521431i $$0.825398\pi$$
$$228$$ 0 0
$$229$$ −8.00000 −0.528655 −0.264327 0.964433i $$-0.585150\pi$$
−0.264327 + 0.964433i $$0.585150\pi$$
$$230$$ 0 0
$$231$$ 12.0000i 0.789542i
$$232$$ 0 0
$$233$$ −21.0000 + 21.0000i −1.37576 + 1.37576i −0.524097 + 0.851658i $$0.675597\pi$$
−0.851658 + 0.524097i $$0.824403\pi$$
$$234$$ 0 0
$$235$$ −3.00000 + 9.00000i −0.195698 + 0.587095i
$$236$$ 0 0
$$237$$ −8.00000 + 8.00000i −0.519656 + 0.519656i
$$238$$ 0 0
$$239$$ 16.0000 1.03495 0.517477 0.855697i $$-0.326871\pi$$
0.517477 + 0.855697i $$0.326871\pi$$
$$240$$ 0 0
$$241$$ −2.00000 −0.128831 −0.0644157 0.997923i $$-0.520518\pi$$
−0.0644157 + 0.997923i $$0.520518\pi$$
$$242$$ 0 0
$$243$$ 7.00000 7.00000i 0.449050 0.449050i
$$244$$ 0 0
$$245$$ −11.0000 22.0000i −0.702764 1.40553i
$$246$$ 0 0
$$247$$ −12.0000 + 12.0000i −0.763542 + 0.763542i
$$248$$ 0 0
$$249$$ 10.0000i 0.633724i
$$250$$ 0 0
$$251$$ 6.00000 0.378717 0.189358 0.981908i $$-0.439359\pi$$
0.189358 + 0.981908i $$0.439359\pi$$
$$252$$ 0 0
$$253$$ −2.00000 2.00000i −0.125739 0.125739i
$$254$$ 0 0
$$255$$ −4.00000 + 2.00000i −0.250490 + 0.125245i
$$256$$ 0 0
$$257$$ 5.00000 + 5.00000i 0.311891 + 0.311891i 0.845642 0.533751i $$-0.179218\pi$$
−0.533751 + 0.845642i $$0.679218\pi$$
$$258$$ 0 0
$$259$$ 6.00000i 0.372822i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −11.0000 11.0000i −0.678289 0.678289i 0.281324 0.959613i $$-0.409226\pi$$
−0.959613 + 0.281324i $$0.909226\pi$$
$$264$$ 0 0
$$265$$ 15.0000 + 5.00000i 0.921443 + 0.307148i
$$266$$ 0 0
$$267$$ 16.0000 + 16.0000i 0.979184 + 0.979184i
$$268$$ 0 0
$$269$$ −20.0000 −1.21942 −0.609711 0.792624i $$-0.708714\pi$$
−0.609711 + 0.792624i $$0.708714\pi$$
$$270$$ 0 0
$$271$$ 14.0000i 0.850439i 0.905090 + 0.425220i $$0.139803\pi$$
−0.905090 + 0.425220i $$0.860197\pi$$
$$272$$ 0 0
$$273$$ −18.0000 + 18.0000i −1.08941 + 1.08941i
$$274$$ 0 0
$$275$$ −6.00000 + 8.00000i −0.361814 + 0.482418i
$$276$$ 0 0
$$277$$ 11.0000 11.0000i 0.660926 0.660926i −0.294672 0.955598i $$-0.595211\pi$$
0.955598 + 0.294672i $$0.0952105\pi$$
$$278$$ 0 0
$$279$$ 10.0000 0.598684
$$280$$ 0 0
$$281$$ −6.00000 −0.357930 −0.178965 0.983855i $$-0.557275\pi$$
−0.178965 + 0.983855i $$0.557275\pi$$
$$282$$ 0 0
$$283$$ −7.00000 + 7.00000i −0.416107 + 0.416107i −0.883859 0.467753i $$-0.845064\pi$$
0.467753 + 0.883859i $$0.345064\pi$$
$$284$$ 0 0
$$285$$ −12.0000 4.00000i −0.710819 0.236940i
$$286$$ 0 0
$$287$$ 30.0000 30.0000i 1.77084 1.77084i
$$288$$ 0 0
$$289$$ 15.0000i 0.882353i
$$290$$ 0 0
$$291$$ 6.00000 0.351726
$$292$$ 0 0
$$293$$ −11.0000 11.0000i −0.642627 0.642627i 0.308574 0.951200i $$-0.400148\pi$$
−0.951200 + 0.308574i $$0.900148\pi$$
$$294$$ 0 0
$$295$$ 12.0000 + 24.0000i 0.698667 + 1.39733i
$$296$$ 0 0
$$297$$ 8.00000 + 8.00000i 0.464207 + 0.464207i
$$298$$ 0 0
$$299$$ 6.00000i 0.346989i
$$300$$ 0 0
$$301$$ 30.0000i 1.72917i
$$302$$ 0 0
$$303$$ 6.00000 + 6.00000i 0.344691 + 0.344691i
$$304$$ 0 0
$$305$$ 2.00000 + 4.00000i 0.114520 + 0.229039i
$$306$$ 0 0
$$307$$ −17.0000 17.0000i −0.970241 0.970241i 0.0293286 0.999570i $$-0.490663\pi$$
−0.999570 + 0.0293286i $$0.990663\pi$$
$$308$$ 0 0
$$309$$ −18.0000 −1.02398
$$310$$ 0 0
$$311$$ 18.0000i 1.02069i 0.859971 + 0.510343i $$0.170482\pi$$
−0.859971 + 0.510343i $$0.829518\pi$$
$$312$$ 0 0
$$313$$ −9.00000 + 9.00000i −0.508710 + 0.508710i −0.914130 0.405420i $$-0.867125\pi$$
0.405420 + 0.914130i $$0.367125\pi$$
$$314$$ 0 0
$$315$$ 9.00000 + 3.00000i 0.507093 + 0.169031i
$$316$$ 0 0
$$317$$ 13.0000 13.0000i 0.730153 0.730153i −0.240497 0.970650i $$-0.577310\pi$$
0.970650 + 0.240497i $$0.0773105\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 6.00000 0.334887
$$322$$ 0 0
$$323$$ −4.00000 + 4.00000i −0.222566 + 0.222566i
$$324$$ 0 0
$$325$$ 21.0000 3.00000i 1.16487 0.166410i
$$326$$ 0 0
$$327$$ −4.00000 + 4.00000i −0.221201 + 0.221201i
$$328$$ 0 0
$$329$$ 18.0000i 0.992372i
$$330$$ 0 0
$$331$$ −26.0000 −1.42909 −0.714545 0.699590i $$-0.753366\pi$$
−0.714545 + 0.699590i $$0.753366\pi$$
$$332$$ 0 0
$$333$$ −1.00000 1.00000i −0.0547997 0.0547997i
$$334$$ 0 0
$$335$$ −3.00000 1.00000i −0.163908 0.0546358i
$$336$$ 0 0
$$337$$ −15.0000 15.0000i −0.817102 0.817102i 0.168585 0.985687i $$-0.446080\pi$$
−0.985687 + 0.168585i $$0.946080\pi$$
$$338$$ 0 0
$$339$$ 6.00000i 0.325875i
$$340$$ 0 0
$$341$$ 20.0000i 1.08306i
$$342$$ 0 0
$$343$$ −12.0000 12.0000i −0.647939 0.647939i
$$344$$ 0 0
$$345$$ −4.00000 + 2.00000i −0.215353 + 0.107676i
$$346$$ 0 0
$$347$$ 9.00000 + 9.00000i 0.483145 + 0.483145i 0.906135 0.422989i $$-0.139019\pi$$
−0.422989 + 0.906135i $$0.639019\pi$$
$$348$$ 0 0
$$349$$ 8.00000 0.428230 0.214115 0.976808i $$-0.431313\pi$$
0.214115 + 0.976808i $$0.431313\pi$$
$$350$$ 0 0
$$351$$ 24.0000i 1.28103i
$$352$$ 0 0
$$353$$ −15.0000 + 15.0000i −0.798369 + 0.798369i −0.982838 0.184469i $$-0.940943\pi$$
0.184469 + 0.982838i $$0.440943\pi$$
$$354$$ 0 0
$$355$$ 2.00000 + 4.00000i 0.106149 + 0.212298i
$$356$$ 0 0
$$357$$ −6.00000 + 6.00000i −0.317554 + 0.317554i
$$358$$ 0 0
$$359$$ −32.0000 −1.68890 −0.844448 0.535638i $$-0.820071\pi$$
−0.844448 + 0.535638i $$0.820071\pi$$
$$360$$ 0 0
$$361$$ 3.00000 0.157895
$$362$$ 0 0
$$363$$ 7.00000 7.00000i 0.367405 0.367405i
$$364$$ 0 0
$$365$$ −1.00000 + 3.00000i −0.0523424 + 0.157027i
$$366$$ 0 0
$$367$$ −15.0000 + 15.0000i −0.782994 + 0.782994i −0.980335 0.197341i $$-0.936769\pi$$
0.197341 + 0.980335i $$0.436769\pi$$
$$368$$ 0 0
$$369$$ 10.0000i 0.520579i
$$370$$ 0 0
$$371$$ 30.0000 1.55752
$$372$$ 0 0
$$373$$ 9.00000 + 9.00000i 0.466002 + 0.466002i 0.900617 0.434614i $$-0.143115\pi$$
−0.434614 + 0.900617i $$0.643115\pi$$
$$374$$ 0 0
$$375$$ 9.00000 + 13.0000i 0.464758 + 0.671317i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 20.0000i 1.02733i −0.857991 0.513665i $$-0.828287\pi$$
0.857991 0.513665i $$-0.171713\pi$$
$$380$$ 0 0
$$381$$ 14.0000i 0.717242i
$$382$$ 0 0
$$383$$ −1.00000 1.00000i −0.0510976 0.0510976i 0.681096 0.732194i $$-0.261504\pi$$
−0.732194 + 0.681096i $$0.761504\pi$$
$$384$$ 0 0
$$385$$ −6.00000 + 18.0000i −0.305788 + 0.917365i
$$386$$ 0 0
$$387$$ 5.00000 + 5.00000i 0.254164 + 0.254164i
$$388$$ 0 0
$$389$$ −4.00000 −0.202808 −0.101404 0.994845i $$-0.532333\pi$$
−0.101404 + 0.994845i $$0.532333\pi$$
$$390$$ 0 0
$$391$$ 2.00000i 0.101144i
$$392$$ 0 0
$$393$$ −10.0000 + 10.0000i −0.504433 + 0.504433i
$$394$$ 0 0
$$395$$ 16.0000 8.00000i 0.805047 0.402524i
$$396$$ 0 0
$$397$$ −15.0000 + 15.0000i −0.752828 + 0.752828i −0.975006 0.222178i $$-0.928683\pi$$
0.222178 + 0.975006i $$0.428683\pi$$
$$398$$ 0 0
$$399$$ −24.0000 −1.20150
$$400$$ 0 0
$$401$$ −22.0000 −1.09863 −0.549314 0.835616i $$-0.685111\pi$$
−0.549314 + 0.835616i $$0.685111\pi$$
$$402$$ 0 0
$$403$$ 30.0000 30.0000i 1.49441 1.49441i
$$404$$ 0 0
$$405$$ 10.0000 5.00000i 0.496904 0.248452i
$$406$$ 0 0
$$407$$ 2.00000 2.00000i 0.0991363 0.0991363i
$$408$$ 0 0
$$409$$ 20.0000i 0.988936i −0.869196 0.494468i $$-0.835363\pi$$
0.869196 0.494468i $$-0.164637\pi$$
$$410$$ 0 0
$$411$$ −22.0000 −1.08518
$$412$$ 0 0
$$413$$ 36.0000 + 36.0000i 1.77144 + 1.77144i
$$414$$ 0 0
$$415$$ −5.00000 + 15.0000i −0.245440 + 0.736321i
$$416$$ 0 0
$$417$$ 12.0000 + 12.0000i 0.587643 + 0.587643i
$$418$$ 0 0
$$419$$ 28.0000i 1.36789i 0.729534 + 0.683945i $$0.239737\pi$$
−0.729534 + 0.683945i $$0.760263\pi$$
$$420$$ 0 0
$$421$$ 34.0000i 1.65706i −0.559946 0.828529i $$-0.689178\pi$$
0.559946 0.828529i $$-0.310822\pi$$
$$422$$ 0 0
$$423$$ −3.00000 3.00000i −0.145865 0.145865i
$$424$$ 0 0
$$425$$ 7.00000 1.00000i 0.339550 0.0485071i
$$426$$ 0 0
$$427$$ 6.00000 + 6.00000i 0.290360 + 0.290360i
$$428$$ 0 0
$$429$$ 12.0000 0.579365
$$430$$ 0 0
$$431$$ 30.0000i 1.44505i 0.691345 + 0.722525i $$0.257018\pi$$
−0.691345 + 0.722525i $$0.742982\pi$$
$$432$$ 0 0
$$433$$ 21.0000 21.0000i 1.00920 1.00920i 0.00923827 0.999957i $$-0.497059\pi$$
0.999957 0.00923827i $$-0.00294067\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −4.00000 + 4.00000i −0.191346 + 0.191346i
$$438$$ 0 0
$$439$$ −16.0000 −0.763638 −0.381819 0.924237i $$-0.624702\pi$$
−0.381819 + 0.924237i $$0.624702\pi$$
$$440$$ 0 0
$$441$$ 11.0000 0.523810
$$442$$ 0 0
$$443$$ 25.0000 25.0000i 1.18779 1.18779i 0.210108 0.977678i $$-0.432619\pi$$
0.977678 0.210108i $$-0.0673814\pi$$
$$444$$ 0 0
$$445$$ −16.0000 32.0000i −0.758473 1.51695i
$$446$$ 0 0
$$447$$ 4.00000 4.00000i 0.189194 0.189194i
$$448$$ 0 0
$$449$$ 12.0000i 0.566315i −0.959073 0.283158i $$-0.908618\pi$$
0.959073 0.283158i $$-0.0913819\pi$$
$$450$$ 0 0
$$451$$ −20.0000 −0.941763
$$452$$ 0 0
$$453$$ 6.00000 + 6.00000i 0.281905 + 0.281905i
$$454$$ 0 0
$$455$$ 36.0000 18.0000i 1.68771 0.843853i
$$456$$ 0 0
$$457$$ −9.00000 9.00000i −0.421002 0.421002i 0.464546 0.885549i $$-0.346217\pi$$
−0.885549 + 0.464546i $$0.846217\pi$$
$$458$$ 0 0
$$459$$ 8.00000i 0.373408i
$$460$$ 0 0
$$461$$ 2.00000i 0.0931493i −0.998915 0.0465746i $$-0.985169\pi$$
0.998915 0.0465746i $$-0.0148305\pi$$
$$462$$ 0 0
$$463$$ 11.0000 + 11.0000i 0.511213 + 0.511213i 0.914898 0.403685i $$-0.132271\pi$$
−0.403685 + 0.914898i $$0.632271\pi$$
$$464$$ 0 0
$$465$$ 30.0000 + 10.0000i 1.39122 + 0.463739i
$$466$$ 0 0
$$467$$ −13.0000 13.0000i −0.601568 0.601568i 0.339160 0.940729i $$-0.389857\pi$$
−0.940729 + 0.339160i $$0.889857\pi$$
$$468$$ 0 0
$$469$$ −6.00000 −0.277054
$$470$$ 0 0
$$471$$ 2.00000i 0.0921551i
$$472$$ 0 0
$$473$$ −10.0000 + 10.0000i −0.459800 + 0.459800i
$$474$$ 0 0
$$475$$ 16.0000 + 12.0000i 0.734130 + 0.550598i
$$476$$ 0 0
$$477$$ −5.00000 + 5.00000i −0.228934 + 0.228934i
$$478$$ 0 0
$$479$$ −40.0000 −1.82765 −0.913823 0.406112i $$-0.866884\pi$$
−0.913823 + 0.406112i $$0.866884\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 0 0
$$483$$ −6.00000 + 6.00000i −0.273009 + 0.273009i
$$484$$ 0 0
$$485$$ −9.00000 3.00000i −0.408669 0.136223i
$$486$$ 0 0
$$487$$ 19.0000 19.0000i 0.860972 0.860972i −0.130479 0.991451i $$-0.541651\pi$$
0.991451 + 0.130479i $$0.0416515\pi$$
$$488$$ 0 0
$$489$$ 2.00000i 0.0904431i
$$490$$ 0 0
$$491$$ −10.0000 −0.451294 −0.225647 0.974209i $$-0.572450\pi$$
−0.225647 + 0.974209i $$0.572450\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −2.00000 4.00000i −0.0898933 0.179787i
$$496$$ 0 0
$$497$$ 6.00000 + 6.00000i 0.269137 + 0.269137i
$$498$$ 0 0
$$499$$ 28.0000i 1.25345i 0.779240 + 0.626726i $$0.215605\pi$$
−0.779240 + 0.626726i $$0.784395\pi$$
$$500$$ 0 0
$$501$$ 2.00000i 0.0893534i
$$502$$ 0 0
$$503$$ 17.0000 + 17.0000i 0.757993 + 0.757993i 0.975957 0.217964i $$-0.0699416\pi$$
−0.217964 + 0.975957i $$0.569942\pi$$
$$504$$ 0 0
$$505$$ −6.00000 12.0000i −0.266996 0.533993i
$$506$$ 0 0
$$507$$ −5.00000 5.00000i −0.222058 0.222058i
$$508$$ 0 0
$$509$$ −24.0000 −1.06378 −0.531891 0.846813i $$-0.678518\pi$$
−0.531891 + 0.846813i $$0.678518\pi$$
$$510$$ 0 0
$$511$$ 6.00000i 0.265424i
$$512$$ 0 0
$$513$$ 16.0000 16.0000i 0.706417 0.706417i
$$514$$ 0 0
$$515$$ 27.0000 + 9.00000i 1.18976 + 0.396587i
$$516$$ 0 0
$$517$$ 6.00000 6.00000i 0.263880 0.263880i
$$518$$ 0 0
$$519$$ 10.0000 0.438951
$$520$$ 0 0
$$521$$ 14.0000 0.613351 0.306676 0.951814i $$-0.400783\pi$$
0.306676 + 0.951814i $$0.400783\pi$$
$$522$$ 0 0
$$523$$ −15.0000 + 15.0000i −0.655904 + 0.655904i −0.954408 0.298504i $$-0.903512\pi$$
0.298504 + 0.954408i $$0.403512\pi$$
$$524$$ 0 0
$$525$$ 24.0000 + 18.0000i 1.04745 + 0.785584i
$$526$$ 0 0
$$527$$ 10.0000 10.0000i 0.435607 0.435607i
$$528$$ 0 0
$$529$$ 21.0000i 0.913043i
$$530$$ 0 0
$$531$$ −12.0000 −0.520756
$$532$$ 0 0
$$533$$ 30.0000 + 30.0000i 1.29944 + 1.29944i
$$534$$ 0 0
$$535$$ −9.00000 3.00000i −0.389104 0.129701i
$$536$$ 0 0
$$537$$ 12.0000 + 12.0000i 0.517838 + 0.517838i
$$538$$ 0 0
$$539$$ 22.0000i 0.947607i
$$540$$ 0 0
$$541$$ 30.0000i 1.28980i 0.764267 + 0.644900i $$0.223101\pi$$
−0.764267 + 0.644900i $$0.776899\pi$$
$$542$$ 0 0
$$543$$ 22.0000 + 22.0000i 0.944110 + 0.944110i
$$544$$ 0 0
$$545$$ 8.00000 4.00000i 0.342682 0.171341i
$$546$$ 0 0
$$547$$ 11.0000 + 11.0000i 0.470326 + 0.470326i 0.902020 0.431694i $$-0.142084\pi$$
−0.431694 + 0.902020i $$0.642084\pi$$
$$548$$ 0 0
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 24.0000 24.0000i 1.02058 1.02058i
$$554$$ 0 0
$$555$$ −2.00000 4.00000i −0.0848953 0.169791i
$$556$$ 0 0
$$557$$ −27.0000 + 27.0000i −1.14403 + 1.14403i −0.156320 + 0.987706i $$0.549963\pi$$
−0.987706 + 0.156320i $$0.950037\pi$$
$$558$$ 0 0
$$559$$ 30.0000 1.26886
$$560$$ 0 0
$$561$$ 4.00000 0.168880
$$562$$ 0 0
$$563$$ −33.0000 + 33.0000i −1.39078 + 1.39078i −0.567213 + 0.823571i $$0.691978\pi$$
−0.823571 + 0.567213i $$0.808022\pi$$
$$564$$ 0 0
$$565$$ −3.00000 + 9.00000i −0.126211 + 0.378633i
$$566$$ 0 0
$$567$$ 15.0000 15.0000i 0.629941 0.629941i
$$568$$ 0 0
$$569$$ 12.0000i 0.503066i −0.967849 0.251533i $$-0.919065\pi$$
0.967849 0.251533i $$-0.0809347\pi$$
$$570$$ 0 0
$$571$$ −34.0000 −1.42286 −0.711428 0.702759i $$-0.751951\pi$$
−0.711428 + 0.702759i $$0.751951\pi$$
$$572$$ 0 0
$$573$$ −14.0000 14.0000i −0.584858 0.584858i
$$574$$ 0 0
$$575$$ 7.00000 1.00000i 0.291920 0.0417029i
$$576$$ 0 0
$$577$$ −19.0000 19.0000i −0.790980 0.790980i 0.190673 0.981654i $$-0.438933\pi$$
−0.981654 + 0.190673i $$0.938933\pi$$
$$578$$ 0 0
$$579$$ 30.0000i 1.24676i
$$580$$ 0 0
$$581$$ 30.0000i 1.24461i
$$582$$ 0 0
$$583$$ −10.0000 10.0000i −0.414158 0.414158i
$$584$$ 0 0
$$585$$ −3.00000 + 9.00000i −0.124035 + 0.372104i
$$586$$ 0 0
$$587$$ −23.0000 23.0000i −0.949312 0.949312i 0.0494643 0.998776i $$-0.484249\pi$$
−0.998776 + 0.0494643i $$0.984249\pi$$
$$588$$ 0 0
$$589$$ 40.0000 1.64817
$$590$$ 0 0
$$591$$ 26.0000i 1.06950i
$$592$$ 0 0
$$593$$ −7.00000 + 7.00000i −0.287456 + 0.287456i −0.836073 0.548618i $$-0.815154\pi$$
0.548618 + 0.836073i $$0.315154\pi$$
$$594$$ 0 0
$$595$$ 12.0000 6.00000i 0.491952 0.245976i
$$596$$ 0 0
$$597$$ −16.0000 + 16.0000i −0.654836 + 0.654836i
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 0 0
$$603$$ 1.00000 1.00000i 0.0407231 0.0407231i
$$604$$ 0 0
$$605$$ −14.0000 + 7.00000i −0.569181 + 0.284590i
$$606$$ 0 0
$$607$$ 5.00000 5.00000i 0.202944 0.202944i −0.598316 0.801260i $$-0.704163\pi$$
0.801260 + 0.598316i $$0.204163\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −18.0000 −0.728202
$$612$$ 0 0
$$613$$ −15.0000 15.0000i −0.605844 0.605844i 0.336013 0.941857i $$-0.390921\pi$$
−0.941857 + 0.336013i $$0.890921\pi$$
$$614$$ 0 0
$$615$$ −10.0000 + 30.0000i −0.403239 + 1.20972i
$$616$$ 0 0
$$617$$ −13.0000 13.0000i −0.523360 0.523360i 0.395224 0.918585i $$-0.370667\pi$$
−0.918585 + 0.395224i $$0.870667\pi$$
$$618$$ 0 0
$$619$$ 12.0000i 0.482321i 0.970485 + 0.241160i $$0.0775280\pi$$
−0.970485 + 0.241160i $$0.922472\pi$$
$$620$$ 0 0
$$621$$ 8.00000i 0.321029i
$$622$$ 0 0
$$623$$ −48.0000 48.0000i −1.92308 1.92308i
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 0 0
$$627$$ 8.00000 + 8.00000i 0.319489 + 0.319489i
$$628$$ 0 0
$$629$$ −2.00000 −0.0797452
$$630$$ 0 0
$$631$$ 14.0000i 0.557331i −0.960388 0.278666i $$-0.910108\pi$$
0.960388 0.278666i $$-0.0898921\pi$$
$$632$$ 0 0
$$633$$ 14.0000 14.0000i 0.556450 0.556450i
$$634$$ 0 0
$$635$$ −7.00000 + 21.0000i −0.277787 + 0.833360i
$$636$$ 0 0
$$637$$ 33.0000 33.0000i 1.30751 1.30751i
$$638$$ 0 0
$$639$$ −2.00000 −0.0791188
$$640$$ 0 0
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 0 0
$$643$$ 27.0000 27.0000i 1.06478 1.06478i 0.0670247 0.997751i $$-0.478649\pi$$
0.997751 0.0670247i $$-0.0213506\pi$$
$$644$$ 0 0
$$645$$ 10.0000 + 20.0000i 0.393750 + 0.787499i
$$646$$ 0 0
$$647$$ −29.0000 + 29.0000i −1.14011 + 1.14011i −0.151678 + 0.988430i $$0.548468\pi$$
−0.988430 + 0.151678i $$0.951532\pi$$
$$648$$ 0 0
$$649$$ 24.0000i 0.942082i
$$650$$ 0 0
$$651$$ 60.0000 2.35159
$$652$$ 0 0
$$653$$ −1.00000 1.00000i −0.0391330 0.0391330i 0.687270 0.726403i $$-0.258809\pi$$
−0.726403 + 0.687270i $$0.758809\pi$$
$$654$$ 0 0
$$655$$ 20.0000 10.0000i 0.781465 0.390732i
$$656$$ 0 0
$$657$$ −1.00000 1.00000i −0.0390137 0.0390137i
$$658$$ 0 0
$$659$$ 36.0000i 1.40236i −0.712984 0.701180i $$-0.752657\pi$$
0.712984 0.701180i $$-0.247343\pi$$
$$660$$ 0 0
$$661$$ 30.0000i 1.16686i 0.812162 + 0.583432i $$0.198291\pi$$
−0.812162 + 0.583432i $$0.801709\pi$$
$$662$$ 0 0
$$663$$ −6.00000 6.00000i −0.233021 0.233021i
$$664$$ 0 0
$$665$$ 36.0000 + 12.0000i 1.39602 + 0.465340i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 2.00000 0.0773245
$$670$$ 0 0
$$671$$ 4.00000i 0.154418i
$$672$$ 0 0
$$673$$ −3.00000 + 3.00000i −0.115642 + 0.115642i −0.762560 0.646918i $$-0.776058\pi$$
0.646918 + 0.762560i $$0.276058\pi$$
$$674$$ 0 0
$$675$$ −28.0000 + 4.00000i −1.07772 + 0.153960i
$$676$$ 0 0
$$677$$ 3.00000 3.00000i 0.115299 0.115299i −0.647103 0.762402i $$-0.724020\pi$$
0.762402 + 0.647103i $$0.224020\pi$$
$$678$$ 0 0
$$679$$ −18.0000 −0.690777
$$680$$ 0 0
$$681$$ 10.0000 0.383201
$$682$$ 0 0
$$683$$ −11.0000 + 11.0000i −0.420903 + 0.420903i −0.885515 0.464611i $$-0.846194\pi$$
0.464611 + 0.885515i $$0.346194\pi$$
$$684$$ 0 0
$$685$$ 33.0000 + 11.0000i 1.26087 + 0.420288i
$$686$$ 0 0
$$687$$ 8.00000 8.00000i 0.305219 0.305219i
$$688$$ 0 0
$$689$$ 30.0000i 1.14291i
$$690$$ 0 0
$$691$$ −14.0000 −0.532585 −0.266293 0.963892i $$-0.585799\pi$$
−0.266293 + 0.963892i $$0.585799\pi$$
$$692$$ 0 0
$$693$$ −6.00000 6.00000i −0.227921 0.227921i
$$694$$ 0 0
$$695$$ −12.0000 24.0000i −0.455186 0.910372i
$$696$$ 0 0
$$697$$ 10.0000 + 10.0000i 0.378777 + 0.378777i
$$698$$ 0 0
$$699$$ 42.0000i 1.58859i
$$700$$ 0 0
$$701$$ 34.0000i 1.28416i 0.766637 + 0.642081i $$0.221929\pi$$
−0.766637 + 0.642081i $$0.778071\pi$$
$$702$$ 0 0
$$703$$ −4.00000 4.00000i −0.150863 0.150863i
$$704$$ 0 0
$$705$$ −6.00000 12.0000i −0.225973 0.451946i
$$706$$ 0 0
$$707$$ −18.0000 18.0000i −0.676960 0.676960i
$$708$$ 0 0
$$709$$ 48.0000 1.80268 0.901339 0.433114i $$-0.142585\pi$$
0.901339 + 0.433114i $$0.142585\pi$$
$$710$$ 0 0
$$711$$ 8.00000i 0.300023i
$$712$$ 0 0
$$713$$ 10.0000 10.0000i 0.374503 0.374503i
$$714$$ 0 0
$$715$$ −18.0000 6.00000i −0.673162 0.224387i
$$716$$ 0 0
$$717$$ −16.0000 + 16.0000i −0.597531 + 0.597531i
$$718$$ 0 0
$$719$$ 16.0000 0.596699 0.298350 0.954457i $$-0.403564\pi$$
0.298350 + 0.954457i $$0.403564\pi$$
$$720$$ 0 0
$$721$$ 54.0000 2.01107
$$722$$ 0 0
$$723$$ 2.00000 2.00000i 0.0743808 0.0743808i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 3.00000 3.00000i 0.111264 0.111264i −0.649283 0.760547i $$-0.724931\pi$$
0.760547 + 0.649283i $$0.224931\pi$$
$$728$$ 0 0
$$729$$ 29.0000i 1.07407i
$$730$$ 0 0
$$731$$ 10.0000 0.369863
$$732$$ 0 0
$$733$$ 27.0000 + 27.0000i 0.997268 + 0.997268i 0.999996 0.00272852i $$-0.000868517\pi$$
−0.00272852 + 0.999996i $$0.500869\pi$$
$$734$$ 0 0
$$735$$ 33.0000 + 11.0000i 1.21722 + 0.405741i
$$736$$ 0 0
$$737$$ 2.00000 + 2.00000i 0.0736709 + 0.0736709i
$$738$$ 0 0
$$739$$ 28.0000i 1.03000i −0.857191 0.514998i $$-0.827793\pi$$
0.857191 0.514998i $$-0.172207\pi$$
$$740$$ 0 0
$$741$$ 24.0000i 0.881662i
$$742$$ 0 0
$$743$$ 21.0000 + 21.0000i 0.770415 + 0.770415i 0.978179 0.207764i $$-0.0666185\pi$$
−0.207764 + 0.978179i $$0.566619\pi$$
$$744$$ 0 0
$$745$$ −8.00000 + 4.00000i −0.293097 + 0.146549i
$$746$$ 0 0
$$747$$ −5.00000 5.00000i −0.182940 0.182940i
$$748$$ 0 0
$$749$$ −18.0000 −0.657706
$$750$$ 0 0
$$751$$ 2.00000i 0.0729810i −0.999334 0.0364905i $$-0.988382\pi$$
0.999334 0.0364905i $$-0.0116179\pi$$
$$752$$ 0 0
$$753$$ −6.00000 + 6.00000i −0.218652 + 0.218652i
$$754$$ 0 0
$$755$$ −6.00000 12.0000i −0.218362 0.436725i
$$756$$ 0 0
$$757$$ 19.0000 19.0000i 0.690567 0.690567i −0.271790 0.962357i $$-0.587616\pi$$
0.962357 + 0.271790i $$0.0876156\pi$$
$$758$$ 0 0
$$759$$ 4.00000 0.145191
$$760$$ 0 0
$$761$$ −18.0000 −0.652499 −0.326250 0.945284i $$-0.605785\pi$$
−0.326250 + 0.945284i $$0.605785\pi$$
$$762$$ 0 0
$$763$$ 12.0000 12.0000i 0.434429 0.434429i
$$764$$ 0 0
$$765$$ −1.00000 + 3.00000i −0.0361551 + 0.108465i
$$766$$ 0 0
$$767$$ −36.0000 + 36.0000i −1.29988 + 1.29988i
$$768$$ 0 0
$$769$$ 8.00000i 0.288487i −0.989542 0.144244i $$-0.953925\pi$$
0.989542 0.144244i $$-0.0460749\pi$$
$$770$$ 0 0
$$771$$ −10.0000 −0.360141
$$772$$ 0 0
$$773$$ 17.0000 + 17.0000i 0.611448 + 0.611448i 0.943323 0.331876i $$-0.107681\pi$$
−0.331876 + 0.943323i $$0.607681\pi$$
$$774$$ 0 0
$$775$$ −40.0000 30.0000i −1.43684 1.07763i
$$776$$ 0 0
$$777$$ −6.00000 6.00000i −0.215249 0.215249i
$$778$$ 0 0
$$779$$ 40.0000i 1.43315i
$$780$$ 0 0
$$781$$ 4.00000i 0.143131i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 1.00000 3.00000i 0.0356915 0.107075i
$$786$$ 0 0
$$787$$ 31.0000 + 31.0000i 1.10503 + 1.10503i 0.993794 + 0.111237i $$0.0354812\pi$$
0.111237 + 0.993794i $$0.464519\pi$$
$$788$$ 0 0
$$789$$ 22.0000 0.783221