# Properties

 Label 380.2.k.b.343.1 Level $380$ Weight $2$ Character 380.343 Analytic conductor $3.034$ 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] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.k (of order $$4$$, 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: $$3.03431527681$$ 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: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 343.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 380.343 Dual form 380.2.k.b.267.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} +2.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +2.00000 q^{6} +(2.00000 + 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000i q^{9} +O(q^{10})$$ $$q+(1.00000 + 1.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} +2.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +2.00000 q^{6} +(2.00000 + 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000i q^{9} +(-3.00000 - 1.00000i) q^{10} +(2.00000 + 2.00000i) q^{12} +4.00000i q^{14} +(-1.00000 + 3.00000i) q^{15} -4.00000 q^{16} +(5.00000 - 5.00000i) q^{17} +(-1.00000 + 1.00000i) q^{18} +1.00000 q^{19} +(-2.00000 - 4.00000i) q^{20} +4.00000 q^{21} +(-4.00000 + 4.00000i) q^{23} +4.00000i q^{24} +(3.00000 - 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} +(-4.00000 + 4.00000i) q^{28} -6.00000i q^{29} +(-4.00000 + 2.00000i) q^{30} +(-4.00000 - 4.00000i) q^{32} +10.0000 q^{34} +(-6.00000 - 2.00000i) q^{35} -2.00000 q^{36} +(1.00000 + 1.00000i) q^{38} +(2.00000 - 6.00000i) q^{40} +2.00000 q^{41} +(4.00000 + 4.00000i) q^{42} +(6.00000 - 6.00000i) q^{43} +(-1.00000 - 2.00000i) q^{45} -8.00000 q^{46} +(2.00000 + 2.00000i) q^{47} +(-4.00000 + 4.00000i) q^{48} +1.00000i q^{49} +(7.00000 - 1.00000i) q^{50} -10.0000i q^{51} +(-10.0000 - 10.0000i) q^{53} +8.00000i q^{54} -8.00000 q^{56} +(1.00000 - 1.00000i) q^{57} +(6.00000 - 6.00000i) q^{58} -10.0000 q^{59} +(-6.00000 - 2.00000i) q^{60} +2.00000 q^{61} +(-2.00000 + 2.00000i) q^{63} -8.00000i q^{64} +(-3.00000 - 3.00000i) q^{67} +(10.0000 + 10.0000i) q^{68} +8.00000i q^{69} +(-4.00000 - 8.00000i) q^{70} +(-2.00000 - 2.00000i) q^{72} +(5.00000 + 5.00000i) q^{73} +(-1.00000 - 7.00000i) q^{75} +2.00000i q^{76} +10.0000 q^{79} +(8.00000 - 4.00000i) q^{80} +5.00000 q^{81} +(2.00000 + 2.00000i) q^{82} +(-4.00000 + 4.00000i) q^{83} +8.00000i q^{84} +(-5.00000 + 15.0000i) q^{85} +12.0000 q^{86} +(-6.00000 - 6.00000i) q^{87} -6.00000i q^{89} +(1.00000 - 3.00000i) q^{90} +(-8.00000 - 8.00000i) q^{92} +4.00000i q^{94} +(-2.00000 + 1.00000i) q^{95} -8.00000 q^{96} +(-10.0000 + 10.0000i) q^{97} +(-1.00000 + 1.00000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 2 q^{3} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10})$$ 2 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 $$2 q + 2 q^{2} + 2 q^{3} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{10} + 4 q^{12} - 2 q^{15} - 8 q^{16} + 10 q^{17} - 2 q^{18} + 2 q^{19} - 4 q^{20} + 8 q^{21} - 8 q^{23} + 6 q^{25} + 8 q^{27} - 8 q^{28} - 8 q^{30} - 8 q^{32} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 2 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 12 q^{43} - 2 q^{45} - 16 q^{46} + 4 q^{47} - 8 q^{48} + 14 q^{50} - 20 q^{53} - 16 q^{56} + 2 q^{57} + 12 q^{58} - 20 q^{59} - 12 q^{60} + 4 q^{61} - 4 q^{63} - 6 q^{67} + 20 q^{68} - 8 q^{70} - 4 q^{72} + 10 q^{73} - 2 q^{75} + 20 q^{79} + 16 q^{80} + 10 q^{81} + 4 q^{82} - 8 q^{83} - 10 q^{85} + 24 q^{86} - 12 q^{87} + 2 q^{90} - 16 q^{92} - 4 q^{95} - 16 q^{96} - 20 q^{97} - 2 q^{98}+O(q^{100})$$ 2 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 6 * q^10 + 4 * q^12 - 2 * q^15 - 8 * q^16 + 10 * q^17 - 2 * q^18 + 2 * q^19 - 4 * q^20 + 8 * q^21 - 8 * q^23 + 6 * q^25 + 8 * q^27 - 8 * q^28 - 8 * q^30 - 8 * q^32 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 2 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 12 * q^43 - 2 * q^45 - 16 * q^46 + 4 * q^47 - 8 * q^48 + 14 * q^50 - 20 * q^53 - 16 * q^56 + 2 * q^57 + 12 * q^58 - 20 * q^59 - 12 * q^60 + 4 * q^61 - 4 * q^63 - 6 * q^67 + 20 * q^68 - 8 * q^70 - 4 * q^72 + 10 * q^73 - 2 * q^75 + 20 * q^79 + 16 * q^80 + 10 * q^81 + 4 * q^82 - 8 * q^83 - 10 * q^85 + 24 * q^86 - 12 * q^87 + 2 * q^90 - 16 * q^92 - 4 * q^95 - 16 * q^96 - 20 * q^97 - 2 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$77$$ $$191$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 + 1.00000i 0.707107 + 0.707107i
$$3$$ 1.00000 1.00000i 0.577350 0.577350i −0.356822 0.934172i $$-0.616140\pi$$
0.934172 + 0.356822i $$0.116140\pi$$
$$4$$ 2.00000i 1.00000i
$$5$$ −2.00000 + 1.00000i −0.894427 + 0.447214i
$$6$$ 2.00000 0.816497
$$7$$ 2.00000 + 2.00000i 0.755929 + 0.755929i 0.975579 0.219650i $$-0.0704915\pi$$
−0.219650 + 0.975579i $$0.570491\pi$$
$$8$$ −2.00000 + 2.00000i −0.707107 + 0.707107i
$$9$$ 1.00000i 0.333333i
$$10$$ −3.00000 1.00000i −0.948683 0.316228i
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 2.00000 + 2.00000i 0.577350 + 0.577350i
$$13$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$14$$ 4.00000i 1.06904i
$$15$$ −1.00000 + 3.00000i −0.258199 + 0.774597i
$$16$$ −4.00000 −1.00000
$$17$$ 5.00000 5.00000i 1.21268 1.21268i 0.242536 0.970143i $$-0.422021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ −1.00000 + 1.00000i −0.235702 + 0.235702i
$$19$$ 1.00000 0.229416
$$20$$ −2.00000 4.00000i −0.447214 0.894427i
$$21$$ 4.00000 0.872872
$$22$$ 0 0
$$23$$ −4.00000 + 4.00000i −0.834058 + 0.834058i −0.988069 0.154011i $$-0.950781\pi$$
0.154011 + 0.988069i $$0.450781\pi$$
$$24$$ 4.00000i 0.816497i
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ 0 0
$$27$$ 4.00000 + 4.00000i 0.769800 + 0.769800i
$$28$$ −4.00000 + 4.00000i −0.755929 + 0.755929i
$$29$$ 6.00000i 1.11417i −0.830455 0.557086i $$-0.811919\pi$$
0.830455 0.557086i $$-0.188081\pi$$
$$30$$ −4.00000 + 2.00000i −0.730297 + 0.365148i
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ −4.00000 4.00000i −0.707107 0.707107i
$$33$$ 0 0
$$34$$ 10.0000 1.71499
$$35$$ −6.00000 2.00000i −1.01419 0.338062i
$$36$$ −2.00000 −0.333333
$$37$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$38$$ 1.00000 + 1.00000i 0.162221 + 0.162221i
$$39$$ 0 0
$$40$$ 2.00000 6.00000i 0.316228 0.948683i
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 4.00000 + 4.00000i 0.617213 + 0.617213i
$$43$$ 6.00000 6.00000i 0.914991 0.914991i −0.0816682 0.996660i $$-0.526025\pi$$
0.996660 + 0.0816682i $$0.0260248\pi$$
$$44$$ 0 0
$$45$$ −1.00000 2.00000i −0.149071 0.298142i
$$46$$ −8.00000 −1.17954
$$47$$ 2.00000 + 2.00000i 0.291730 + 0.291730i 0.837763 0.546033i $$-0.183863\pi$$
−0.546033 + 0.837763i $$0.683863\pi$$
$$48$$ −4.00000 + 4.00000i −0.577350 + 0.577350i
$$49$$ 1.00000i 0.142857i
$$50$$ 7.00000 1.00000i 0.989949 0.141421i
$$51$$ 10.0000i 1.40028i
$$52$$ 0 0
$$53$$ −10.0000 10.0000i −1.37361 1.37361i −0.855034 0.518571i $$-0.826464\pi$$
−0.518571 0.855034i $$-0.673536\pi$$
$$54$$ 8.00000i 1.08866i
$$55$$ 0 0
$$56$$ −8.00000 −1.06904
$$57$$ 1.00000 1.00000i 0.132453 0.132453i
$$58$$ 6.00000 6.00000i 0.787839 0.787839i
$$59$$ −10.0000 −1.30189 −0.650945 0.759125i $$-0.725627\pi$$
−0.650945 + 0.759125i $$0.725627\pi$$
$$60$$ −6.00000 2.00000i −0.774597 0.258199i
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 0 0
$$63$$ −2.00000 + 2.00000i −0.251976 + 0.251976i
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −3.00000 3.00000i −0.366508 0.366508i 0.499694 0.866202i $$-0.333446\pi$$
−0.866202 + 0.499694i $$0.833446\pi$$
$$68$$ 10.0000 + 10.0000i 1.21268 + 1.21268i
$$69$$ 8.00000i 0.963087i
$$70$$ −4.00000 8.00000i −0.478091 0.956183i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ −2.00000 2.00000i −0.235702 0.235702i
$$73$$ 5.00000 + 5.00000i 0.585206 + 0.585206i 0.936329 0.351123i $$-0.114200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ 0 0
$$75$$ −1.00000 7.00000i −0.115470 0.808290i
$$76$$ 2.00000i 0.229416i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 10.0000 1.12509 0.562544 0.826767i $$-0.309823\pi$$
0.562544 + 0.826767i $$0.309823\pi$$
$$80$$ 8.00000 4.00000i 0.894427 0.447214i
$$81$$ 5.00000 0.555556
$$82$$ 2.00000 + 2.00000i 0.220863 + 0.220863i
$$83$$ −4.00000 + 4.00000i −0.439057 + 0.439057i −0.891695 0.452638i $$-0.850483\pi$$
0.452638 + 0.891695i $$0.350483\pi$$
$$84$$ 8.00000i 0.872872i
$$85$$ −5.00000 + 15.0000i −0.542326 + 1.62698i
$$86$$ 12.0000 1.29399
$$87$$ −6.00000 6.00000i −0.643268 0.643268i
$$88$$ 0 0
$$89$$ 6.00000i 0.635999i −0.948091 0.317999i $$-0.896989\pi$$
0.948091 0.317999i $$-0.103011\pi$$
$$90$$ 1.00000 3.00000i 0.105409 0.316228i
$$91$$ 0 0
$$92$$ −8.00000 8.00000i −0.834058 0.834058i
$$93$$ 0 0
$$94$$ 4.00000i 0.412568i
$$95$$ −2.00000 + 1.00000i −0.205196 + 0.102598i
$$96$$ −8.00000 −0.816497
$$97$$ −10.0000 + 10.0000i −1.01535 + 1.01535i −0.0154658 + 0.999880i $$0.504923\pi$$
−0.999880 + 0.0154658i $$0.995077\pi$$
$$98$$ −1.00000 + 1.00000i −0.101015 + 0.101015i
$$99$$ 0 0
$$100$$ 8.00000 + 6.00000i 0.800000 + 0.600000i
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 10.0000 10.0000i 0.990148 0.990148i
$$103$$ −9.00000 + 9.00000i −0.886796 + 0.886796i −0.994214 0.107418i $$-0.965742\pi$$
0.107418 + 0.994214i $$0.465742\pi$$
$$104$$ 0 0
$$105$$ −8.00000 + 4.00000i −0.780720 + 0.390360i
$$106$$ 20.0000i 1.94257i
$$107$$ 7.00000 + 7.00000i 0.676716 + 0.676716i 0.959256 0.282540i $$-0.0911770\pi$$
−0.282540 + 0.959256i $$0.591177\pi$$
$$108$$ −8.00000 + 8.00000i −0.769800 + 0.769800i
$$109$$ 6.00000i 0.574696i −0.957826 0.287348i $$-0.907226\pi$$
0.957826 0.287348i $$-0.0927736\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −8.00000 8.00000i −0.755929 0.755929i
$$113$$ −10.0000 10.0000i −0.940721 0.940721i 0.0576178 0.998339i $$-0.481650\pi$$
−0.998339 + 0.0576178i $$0.981650\pi$$
$$114$$ 2.00000 0.187317
$$115$$ 4.00000 12.0000i 0.373002 1.11901i
$$116$$ 12.0000 1.11417
$$117$$ 0 0
$$118$$ −10.0000 10.0000i −0.920575 0.920575i
$$119$$ 20.0000 1.83340
$$120$$ −4.00000 8.00000i −0.365148 0.730297i
$$121$$ 11.0000 1.00000
$$122$$ 2.00000 + 2.00000i 0.181071 + 0.181071i
$$123$$ 2.00000 2.00000i 0.180334 0.180334i
$$124$$ 0 0
$$125$$ −2.00000 + 11.0000i −0.178885 + 0.983870i
$$126$$ −4.00000 −0.356348
$$127$$ 7.00000 + 7.00000i 0.621150 + 0.621150i 0.945825 0.324676i $$-0.105255\pi$$
−0.324676 + 0.945825i $$0.605255\pi$$
$$128$$ 8.00000 8.00000i 0.707107 0.707107i
$$129$$ 12.0000i 1.05654i
$$130$$ 0 0
$$131$$ 20.0000i 1.74741i −0.486458 0.873704i $$-0.661711\pi$$
0.486458 0.873704i $$-0.338289\pi$$
$$132$$ 0 0
$$133$$ 2.00000 + 2.00000i 0.173422 + 0.173422i
$$134$$ 6.00000i 0.518321i
$$135$$ −12.0000 4.00000i −1.03280 0.344265i
$$136$$ 20.0000i 1.71499i
$$137$$ 5.00000 5.00000i 0.427179 0.427179i −0.460487 0.887666i $$-0.652325\pi$$
0.887666 + 0.460487i $$0.152325\pi$$
$$138$$ −8.00000 + 8.00000i −0.681005 + 0.681005i
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 4.00000 12.0000i 0.338062 1.01419i
$$141$$ 4.00000 0.336861
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 4.00000i 0.333333i
$$145$$ 6.00000 + 12.0000i 0.498273 + 0.996546i
$$146$$ 10.0000i 0.827606i
$$147$$ 1.00000 + 1.00000i 0.0824786 + 0.0824786i
$$148$$ 0 0
$$149$$ 4.00000i 0.327693i 0.986486 + 0.163846i $$0.0523901\pi$$
−0.986486 + 0.163846i $$0.947610\pi$$
$$150$$ 6.00000 8.00000i 0.489898 0.653197i
$$151$$ 10.0000i 0.813788i 0.913475 + 0.406894i $$0.133388\pi$$
−0.913475 + 0.406894i $$0.866612\pi$$
$$152$$ −2.00000 + 2.00000i −0.162221 + 0.162221i
$$153$$ 5.00000 + 5.00000i 0.404226 + 0.404226i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −15.0000 + 15.0000i −1.19713 + 1.19713i −0.222108 + 0.975022i $$0.571294\pi$$
−0.975022 + 0.222108i $$0.928706\pi$$
$$158$$ 10.0000 + 10.0000i 0.795557 + 0.795557i
$$159$$ −20.0000 −1.58610
$$160$$ 12.0000 + 4.00000i 0.948683 + 0.316228i
$$161$$ −16.0000 −1.26098
$$162$$ 5.00000 + 5.00000i 0.392837 + 0.392837i
$$163$$ −14.0000 + 14.0000i −1.09656 + 1.09656i −0.101755 + 0.994809i $$0.532446\pi$$
−0.994809 + 0.101755i $$0.967554\pi$$
$$164$$ 4.00000i 0.312348i
$$165$$ 0 0
$$166$$ −8.00000 −0.620920
$$167$$ 7.00000 + 7.00000i 0.541676 + 0.541676i 0.924020 0.382344i $$-0.124883\pi$$
−0.382344 + 0.924020i $$0.624883\pi$$
$$168$$ −8.00000 + 8.00000i −0.617213 + 0.617213i
$$169$$ 13.0000i 1.00000i
$$170$$ −20.0000 + 10.0000i −1.53393 + 0.766965i
$$171$$ 1.00000i 0.0764719i
$$172$$ 12.0000 + 12.0000i 0.914991 + 0.914991i
$$173$$ −10.0000 10.0000i −0.760286 0.760286i 0.216088 0.976374i $$-0.430670\pi$$
−0.976374 + 0.216088i $$0.930670\pi$$
$$174$$ 12.0000i 0.909718i
$$175$$ 14.0000 2.00000i 1.05830 0.151186i
$$176$$ 0 0
$$177$$ −10.0000 + 10.0000i −0.751646 + 0.751646i
$$178$$ 6.00000 6.00000i 0.449719 0.449719i
$$179$$ −10.0000 −0.747435 −0.373718 0.927543i $$-0.621917\pi$$
−0.373718 + 0.927543i $$0.621917\pi$$
$$180$$ 4.00000 2.00000i 0.298142 0.149071i
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 2.00000 2.00000i 0.147844 0.147844i
$$184$$ 16.0000i 1.17954i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −4.00000 + 4.00000i −0.291730 + 0.291730i
$$189$$ 16.0000i 1.16383i
$$190$$ −3.00000 1.00000i −0.217643 0.0725476i
$$191$$ 20.0000i 1.44715i 0.690246 + 0.723575i $$0.257502\pi$$
−0.690246 + 0.723575i $$0.742498\pi$$
$$192$$ −8.00000 8.00000i −0.577350 0.577350i
$$193$$ −10.0000 10.0000i −0.719816 0.719816i 0.248752 0.968567i $$-0.419980\pi$$
−0.968567 + 0.248752i $$0.919980\pi$$
$$194$$ −20.0000 −1.43592
$$195$$ 0 0
$$196$$ −2.00000 −0.142857
$$197$$ −15.0000 + 15.0000i −1.06871 + 1.06871i −0.0712470 + 0.997459i $$0.522698\pi$$
−0.997459 + 0.0712470i $$0.977302\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 2.00000 + 14.0000i 0.141421 + 0.989949i
$$201$$ −6.00000 −0.423207
$$202$$ 12.0000 + 12.0000i 0.844317 + 0.844317i
$$203$$ 12.0000 12.0000i 0.842235 0.842235i
$$204$$ 20.0000 1.40028
$$205$$ −4.00000 + 2.00000i −0.279372 + 0.139686i
$$206$$ −18.0000 −1.25412
$$207$$ −4.00000 4.00000i −0.278019 0.278019i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ −12.0000 4.00000i −0.828079 0.276026i
$$211$$ 10.0000i 0.688428i 0.938891 + 0.344214i $$0.111855\pi$$
−0.938891 + 0.344214i $$0.888145\pi$$
$$212$$ 20.0000 20.0000i 1.37361 1.37361i
$$213$$ 0 0
$$214$$ 14.0000i 0.957020i
$$215$$ −6.00000 + 18.0000i −0.409197 + 1.22759i
$$216$$ −16.0000 −1.08866
$$217$$ 0 0
$$218$$ 6.00000 6.00000i 0.406371 0.406371i
$$219$$ 10.0000 0.675737
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −9.00000 + 9.00000i −0.602685 + 0.602685i −0.941024 0.338340i $$-0.890135\pi$$
0.338340 + 0.941024i $$0.390135\pi$$
$$224$$ 16.0000i 1.06904i
$$225$$ 4.00000 + 3.00000i 0.266667 + 0.200000i
$$226$$ 20.0000i 1.33038i
$$227$$ −13.0000 13.0000i −0.862840 0.862840i 0.128827 0.991667i $$-0.458879\pi$$
−0.991667 + 0.128827i $$0.958879\pi$$
$$228$$ 2.00000 + 2.00000i 0.132453 + 0.132453i
$$229$$ 6.00000i 0.396491i −0.980152 0.198246i $$-0.936476\pi$$
0.980152 0.198246i $$-0.0635244\pi$$
$$230$$ 16.0000 8.00000i 1.05501 0.527504i
$$231$$ 0 0
$$232$$ 12.0000 + 12.0000i 0.787839 + 0.787839i
$$233$$ 5.00000 + 5.00000i 0.327561 + 0.327561i 0.851658 0.524097i $$-0.175597\pi$$
−0.524097 + 0.851658i $$0.675597\pi$$
$$234$$ 0 0
$$235$$ −6.00000 2.00000i −0.391397 0.130466i
$$236$$ 20.0000i 1.30189i
$$237$$ 10.0000 10.0000i 0.649570 0.649570i
$$238$$ 20.0000 + 20.0000i 1.29641 + 1.29641i
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 4.00000 12.0000i 0.258199 0.774597i
$$241$$ 2.00000 0.128831 0.0644157 0.997923i $$-0.479482\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$242$$ 11.0000 + 11.0000i 0.707107 + 0.707107i
$$243$$ −7.00000 + 7.00000i −0.449050 + 0.449050i
$$244$$ 4.00000i 0.256074i
$$245$$ −1.00000 2.00000i −0.0638877 0.127775i
$$246$$ 4.00000 0.255031
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 8.00000i 0.506979i
$$250$$ −13.0000 + 9.00000i −0.822192 + 0.569210i
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ −4.00000 4.00000i −0.251976 0.251976i
$$253$$ 0 0
$$254$$ 14.0000i 0.878438i
$$255$$ 10.0000 + 20.0000i 0.626224 + 1.25245i
$$256$$ 16.0000 1.00000
$$257$$ −20.0000 + 20.0000i −1.24757 + 1.24757i −0.290774 + 0.956792i $$0.593913\pi$$
−0.956792 + 0.290774i $$0.906087\pi$$
$$258$$ 12.0000 12.0000i 0.747087 0.747087i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ 20.0000 20.0000i 1.23560 1.23560i
$$263$$ 16.0000 16.0000i 0.986602 0.986602i −0.0133092 0.999911i $$-0.504237\pi$$
0.999911 + 0.0133092i $$0.00423656\pi$$
$$264$$ 0 0
$$265$$ 30.0000 + 10.0000i 1.84289 + 0.614295i
$$266$$ 4.00000i 0.245256i
$$267$$ −6.00000 6.00000i −0.367194 0.367194i
$$268$$ 6.00000 6.00000i 0.366508 0.366508i
$$269$$ 26.0000i 1.58525i −0.609711 0.792624i $$-0.708714\pi$$
0.609711 0.792624i $$-0.291286\pi$$
$$270$$ −8.00000 16.0000i −0.486864 0.973729i
$$271$$ 20.0000i 1.21491i −0.794353 0.607457i $$-0.792190\pi$$
0.794353 0.607457i $$-0.207810\pi$$
$$272$$ −20.0000 + 20.0000i −1.21268 + 1.21268i
$$273$$ 0 0
$$274$$ 10.0000 0.604122
$$275$$ 0 0
$$276$$ −16.0000 −0.963087
$$277$$ 5.00000 5.00000i 0.300421 0.300421i −0.540758 0.841178i $$-0.681862\pi$$
0.841178 + 0.540758i $$0.181862\pi$$
$$278$$ 20.0000 + 20.0000i 1.19952 + 1.19952i
$$279$$ 0 0
$$280$$ 16.0000 8.00000i 0.956183 0.478091i
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 4.00000 + 4.00000i 0.238197 + 0.238197i
$$283$$ −4.00000 + 4.00000i −0.237775 + 0.237775i −0.815928 0.578153i $$-0.803774\pi$$
0.578153 + 0.815928i $$0.303774\pi$$
$$284$$ 0 0
$$285$$ −1.00000 + 3.00000i −0.0592349 + 0.177705i
$$286$$ 0 0
$$287$$ 4.00000 + 4.00000i 0.236113 + 0.236113i
$$288$$ 4.00000 4.00000i 0.235702 0.235702i
$$289$$ 33.0000i 1.94118i
$$290$$ −6.00000 + 18.0000i −0.352332 + 1.05700i
$$291$$ 20.0000i 1.17242i
$$292$$ −10.0000 + 10.0000i −0.585206 + 0.585206i
$$293$$ 10.0000 + 10.0000i 0.584206 + 0.584206i 0.936056 0.351850i $$-0.114447\pi$$
−0.351850 + 0.936056i $$0.614447\pi$$
$$294$$ 2.00000i 0.116642i
$$295$$ 20.0000 10.0000i 1.16445 0.582223i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −4.00000 + 4.00000i −0.231714 + 0.231714i
$$299$$ 0 0
$$300$$ 14.0000 2.00000i 0.808290 0.115470i
$$301$$ 24.0000 1.38334
$$302$$ −10.0000 + 10.0000i −0.575435 + 0.575435i
$$303$$ 12.0000 12.0000i 0.689382 0.689382i
$$304$$ −4.00000 −0.229416
$$305$$ −4.00000 + 2.00000i −0.229039 + 0.114520i
$$306$$ 10.0000i 0.571662i
$$307$$ −13.0000 13.0000i −0.741949 0.741949i 0.231004 0.972953i $$-0.425799\pi$$
−0.972953 + 0.231004i $$0.925799\pi$$
$$308$$ 0 0
$$309$$ 18.0000i 1.02398i
$$310$$ 0 0
$$311$$ 20.0000i 1.13410i 0.823685 + 0.567048i $$0.191915\pi$$
−0.823685 + 0.567048i $$0.808085\pi$$
$$312$$ 0 0
$$313$$ 5.00000 + 5.00000i 0.282617 + 0.282617i 0.834152 0.551535i $$-0.185958\pi$$
−0.551535 + 0.834152i $$0.685958\pi$$
$$314$$ −30.0000 −1.69300
$$315$$ 2.00000 6.00000i 0.112687 0.338062i
$$316$$ 20.0000i 1.12509i
$$317$$ 20.0000 20.0000i 1.12331 1.12331i 0.132072 0.991240i $$-0.457837\pi$$
0.991240 0.132072i $$-0.0421629\pi$$
$$318$$ −20.0000 20.0000i −1.12154 1.12154i
$$319$$ 0 0
$$320$$ 8.00000 + 16.0000i 0.447214 + 0.894427i
$$321$$ 14.0000 0.781404
$$322$$ −16.0000 16.0000i −0.891645 0.891645i
$$323$$ 5.00000 5.00000i 0.278207 0.278207i
$$324$$ 10.0000i 0.555556i
$$325$$ 0 0
$$326$$ −28.0000 −1.55078
$$327$$ −6.00000 6.00000i −0.331801 0.331801i
$$328$$ −4.00000 + 4.00000i −0.220863 + 0.220863i
$$329$$ 8.00000i 0.441054i
$$330$$ 0 0
$$331$$ 10.0000i 0.549650i −0.961494 0.274825i $$-0.911380\pi$$
0.961494 0.274825i $$-0.0886199\pi$$
$$332$$ −8.00000 8.00000i −0.439057 0.439057i
$$333$$ 0 0
$$334$$ 14.0000i 0.766046i
$$335$$ 9.00000 + 3.00000i 0.491723 + 0.163908i
$$336$$ −16.0000 −0.872872
$$337$$ 10.0000 10.0000i 0.544735 0.544735i −0.380178 0.924913i $$-0.624137\pi$$
0.924913 + 0.380178i $$0.124137\pi$$
$$338$$ 13.0000 13.0000i 0.707107 0.707107i
$$339$$ −20.0000 −1.08625
$$340$$ −30.0000 10.0000i −1.62698 0.542326i
$$341$$ 0 0
$$342$$ −1.00000 + 1.00000i −0.0540738 + 0.0540738i
$$343$$ 12.0000 12.0000i 0.647939 0.647939i
$$344$$ 24.0000i 1.29399i
$$345$$ −8.00000 16.0000i −0.430706 0.861411i
$$346$$ 20.0000i 1.07521i
$$347$$ −8.00000 8.00000i −0.429463 0.429463i 0.458983 0.888445i $$-0.348214\pi$$
−0.888445 + 0.458983i $$0.848214\pi$$
$$348$$ 12.0000 12.0000i 0.643268 0.643268i
$$349$$ 16.0000i 0.856460i −0.903670 0.428230i $$-0.859137\pi$$
0.903670 0.428230i $$-0.140863\pi$$
$$350$$ 16.0000 + 12.0000i 0.855236 + 0.641427i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 15.0000 + 15.0000i 0.798369 + 0.798369i 0.982838 0.184469i $$-0.0590565\pi$$
−0.184469 + 0.982838i $$0.559057\pi$$
$$354$$ −20.0000 −1.06299
$$355$$ 0 0
$$356$$ 12.0000 0.635999
$$357$$ 20.0000 20.0000i 1.05851 1.05851i
$$358$$ −10.0000 10.0000i −0.528516 0.528516i
$$359$$ −20.0000 −1.05556 −0.527780 0.849381i $$-0.676975\pi$$
−0.527780 + 0.849381i $$0.676975\pi$$
$$360$$ 6.00000 + 2.00000i 0.316228 + 0.105409i
$$361$$ 1.00000 0.0526316
$$362$$ 2.00000 + 2.00000i 0.105118 + 0.105118i
$$363$$ 11.0000 11.0000i 0.577350 0.577350i
$$364$$ 0 0
$$365$$ −15.0000 5.00000i −0.785136 0.261712i
$$366$$ 4.00000 0.209083
$$367$$ −18.0000 18.0000i −0.939592 0.939592i 0.0586842 0.998277i $$-0.481309\pi$$
−0.998277 + 0.0586842i $$0.981309\pi$$
$$368$$ 16.0000 16.0000i 0.834058 0.834058i
$$369$$ 2.00000i 0.104116i
$$370$$ 0 0
$$371$$ 40.0000i 2.07670i
$$372$$ 0 0
$$373$$ −10.0000 10.0000i −0.517780 0.517780i 0.399119 0.916899i $$-0.369316\pi$$
−0.916899 + 0.399119i $$0.869316\pi$$
$$374$$ 0 0
$$375$$ 9.00000 + 13.0000i 0.464758 + 0.671317i
$$376$$ −8.00000 −0.412568
$$377$$ 0 0
$$378$$ −16.0000 + 16.0000i −0.822951 + 0.822951i
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ −2.00000 4.00000i −0.102598 0.205196i
$$381$$ 14.0000 0.717242
$$382$$ −20.0000 + 20.0000i −1.02329 + 1.02329i
$$383$$ 21.0000 21.0000i 1.07305 1.07305i 0.0759373 0.997113i $$-0.475805\pi$$
0.997113 0.0759373i $$-0.0241949\pi$$
$$384$$ 16.0000i 0.816497i
$$385$$ 0 0
$$386$$ 20.0000i 1.01797i
$$387$$ 6.00000 + 6.00000i 0.304997 + 0.304997i
$$388$$ −20.0000 20.0000i −1.01535 1.01535i
$$389$$ 6.00000i 0.304212i −0.988364 0.152106i $$-0.951394\pi$$
0.988364 0.152106i $$-0.0486055\pi$$
$$390$$ 0 0
$$391$$ 40.0000i 2.02289i
$$392$$ −2.00000 2.00000i −0.101015 0.101015i
$$393$$ −20.0000 20.0000i −1.00887 1.00887i
$$394$$ −30.0000 −1.51138
$$395$$ −20.0000 + 10.0000i −1.00631 + 0.503155i
$$396$$ 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
$$399$$ 4.00000 0.200250
$$400$$ −12.0000 + 16.0000i −0.600000 + 0.800000i
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ −6.00000 6.00000i −0.299253 0.299253i
$$403$$ 0 0
$$404$$ 24.0000i 1.19404i
$$405$$ −10.0000 + 5.00000i −0.496904 + 0.248452i
$$406$$ 24.0000 1.19110
$$407$$ 0 0
$$408$$ 20.0000 + 20.0000i 0.990148 + 0.990148i
$$409$$ 34.0000i 1.68119i 0.541663 + 0.840596i $$0.317795\pi$$
−0.541663 + 0.840596i $$0.682205\pi$$
$$410$$ −6.00000 2.00000i −0.296319 0.0987730i
$$411$$ 10.0000i 0.493264i
$$412$$ −18.0000 18.0000i −0.886796 0.886796i
$$413$$ −20.0000 20.0000i −0.984136 0.984136i
$$414$$ 8.00000i 0.393179i
$$415$$ 4.00000 12.0000i 0.196352 0.589057i
$$416$$ 0 0
$$417$$ 20.0000 20.0000i 0.979404 0.979404i
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ −8.00000 16.0000i −0.390360 0.780720i
$$421$$ 2.00000 0.0974740 0.0487370 0.998812i $$-0.484480\pi$$
0.0487370 + 0.998812i $$0.484480\pi$$
$$422$$ −10.0000 + 10.0000i −0.486792 + 0.486792i
$$423$$ −2.00000 + 2.00000i −0.0972433 + 0.0972433i
$$424$$ 40.0000 1.94257
$$425$$ −5.00000 35.0000i −0.242536 1.69775i
$$426$$ 0 0
$$427$$ 4.00000 + 4.00000i 0.193574 + 0.193574i
$$428$$ −14.0000 + 14.0000i −0.676716 + 0.676716i
$$429$$ 0 0
$$430$$ −24.0000 + 12.0000i −1.15738 + 0.578691i
$$431$$ 10.0000i 0.481683i −0.970564 0.240842i $$-0.922577\pi$$
0.970564 0.240842i $$-0.0774234\pi$$
$$432$$ −16.0000 16.0000i −0.769800 0.769800i
$$433$$ 10.0000 + 10.0000i 0.480569 + 0.480569i 0.905313 0.424744i $$-0.139636\pi$$
−0.424744 + 0.905313i $$0.639636\pi$$
$$434$$ 0 0
$$435$$ 18.0000 + 6.00000i 0.863034 + 0.287678i
$$436$$ 12.0000 0.574696
$$437$$ −4.00000 + 4.00000i −0.191346 + 0.191346i
$$438$$ 10.0000 + 10.0000i 0.477818 + 0.477818i
$$439$$ −10.0000 −0.477274 −0.238637 0.971109i $$-0.576701\pi$$
−0.238637 + 0.971109i $$0.576701\pi$$
$$440$$ 0 0
$$441$$ −1.00000 −0.0476190
$$442$$ 0 0
$$443$$ −24.0000 + 24.0000i −1.14027 + 1.14027i −0.151875 + 0.988400i $$0.548531\pi$$
−0.988400 + 0.151875i $$0.951469\pi$$
$$444$$ 0 0
$$445$$ 6.00000 + 12.0000i 0.284427 + 0.568855i
$$446$$ −18.0000 −0.852325
$$447$$ 4.00000 + 4.00000i 0.189194 + 0.189194i
$$448$$ 16.0000 16.0000i 0.755929 0.755929i
$$449$$ 14.0000i 0.660701i 0.943858 + 0.330350i $$0.107167\pi$$
−0.943858 + 0.330350i $$0.892833\pi$$
$$450$$ 1.00000 + 7.00000i 0.0471405 + 0.329983i
$$451$$ 0 0
$$452$$ 20.0000 20.0000i 0.940721 0.940721i
$$453$$ 10.0000 + 10.0000i 0.469841 + 0.469841i
$$454$$ 26.0000i 1.22024i
$$455$$ 0 0
$$456$$ 4.00000i 0.187317i
$$457$$ 15.0000 15.0000i 0.701670 0.701670i −0.263099 0.964769i $$-0.584744\pi$$
0.964769 + 0.263099i $$0.0847444\pi$$
$$458$$ 6.00000 6.00000i 0.280362 0.280362i
$$459$$ 40.0000 1.86704
$$460$$ 24.0000 + 8.00000i 1.11901 + 0.373002i
$$461$$ 2.00000 0.0931493 0.0465746 0.998915i $$-0.485169\pi$$
0.0465746 + 0.998915i $$0.485169\pi$$
$$462$$ 0 0
$$463$$ −4.00000 + 4.00000i −0.185896 + 0.185896i −0.793919 0.608023i $$-0.791963\pi$$
0.608023 + 0.793919i $$0.291963\pi$$
$$464$$ 24.0000i 1.11417i
$$465$$ 0 0
$$466$$ 10.0000i 0.463241i
$$467$$ 12.0000 + 12.0000i 0.555294 + 0.555294i 0.927964 0.372670i $$-0.121558\pi$$
−0.372670 + 0.927964i $$0.621558\pi$$
$$468$$ 0 0
$$469$$ 12.0000i 0.554109i
$$470$$ −4.00000 8.00000i −0.184506 0.369012i
$$471$$ 30.0000i 1.38233i
$$472$$ 20.0000 20.0000i 0.920575 0.920575i
$$473$$ 0 0
$$474$$ 20.0000 0.918630
$$475$$ 3.00000 4.00000i 0.137649 0.183533i
$$476$$ 40.0000i 1.83340i
$$477$$ 10.0000 10.0000i 0.457869 0.457869i
$$478$$ −20.0000 20.0000i −0.914779 0.914779i
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 16.0000 8.00000i 0.730297 0.365148i
$$481$$ 0 0
$$482$$ 2.00000 + 2.00000i 0.0910975 + 0.0910975i
$$483$$ −16.0000 + 16.0000i −0.728025 + 0.728025i
$$484$$ 22.0000i 1.00000i
$$485$$ 10.0000 30.0000i 0.454077 1.36223i
$$486$$ −14.0000 −0.635053
$$487$$ −3.00000 3.00000i −0.135943 0.135943i 0.635861 0.771804i $$-0.280645\pi$$
−0.771804 + 0.635861i $$0.780645\pi$$
$$488$$ −4.00000 + 4.00000i −0.181071 + 0.181071i
$$489$$ 28.0000i 1.26620i
$$490$$ 1.00000 3.00000i 0.0451754 0.135526i
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 4.00000 + 4.00000i 0.180334 + 0.180334i
$$493$$ −30.0000 30.0000i −1.35113 1.35113i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −8.00000 + 8.00000i −0.358489 + 0.358489i
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ −22.0000 4.00000i −0.983870 0.178885i
$$501$$ 14.0000 0.625474
$$502$$ 0 0
$$503$$ −24.0000 + 24.0000i −1.07011 + 1.07011i −0.0727574 + 0.997350i $$0.523180\pi$$
−0.997350 + 0.0727574i $$0.976820\pi$$
$$504$$ 8.00000i 0.356348i
$$505$$ −24.0000 + 12.0000i −1.06799 + 0.533993i
$$506$$ 0 0
$$507$$ −13.0000 13.0000i −0.577350 0.577350i
$$508$$ −14.0000 + 14.0000i −0.621150 + 0.621150i
$$509$$ 6.00000i 0.265945i −0.991120 0.132973i $$-0.957548\pi$$
0.991120 0.132973i $$-0.0424523\pi$$
$$510$$ −10.0000 + 30.0000i −0.442807 + 1.32842i
$$511$$ 20.0000i 0.884748i
$$512$$ 16.0000 + 16.0000i 0.707107 + 0.707107i
$$513$$ 4.00000 + 4.00000i 0.176604 + 0.176604i
$$514$$ −40.0000 −1.76432
$$515$$ 9.00000 27.0000i 0.396587 1.18976i
$$516$$ 24.0000 1.05654
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −20.0000 −0.877903
$$520$$ 0 0
$$521$$ 22.0000 0.963837 0.481919 0.876216i $$-0.339940\pi$$
0.481919 + 0.876216i $$0.339940\pi$$
$$522$$ 6.00000 + 6.00000i 0.262613 + 0.262613i
$$523$$ 21.0000 21.0000i 0.918266 0.918266i −0.0786374 0.996903i $$-0.525057\pi$$
0.996903 + 0.0786374i $$0.0250569\pi$$
$$524$$ 40.0000 1.74741
$$525$$ 12.0000 16.0000i 0.523723 0.698297i
$$526$$ 32.0000 1.39527
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 9.00000i 0.391304i
$$530$$ 20.0000 + 40.0000i 0.868744 + 1.73749i
$$531$$ 10.0000i 0.433963i
$$532$$ −4.00000 + 4.00000i −0.173422 + 0.173422i
$$533$$ 0 0
$$534$$ 12.0000i 0.519291i
$$535$$ −21.0000 7.00000i −0.907909 0.302636i
$$536$$ 12.0000 0.518321
$$537$$ −10.0000 + 10.0000i −0.431532 + 0.431532i
$$538$$ 26.0000 26.0000i 1.12094 1.12094i
$$539$$ 0 0
$$540$$ 8.00000 24.0000i 0.344265 1.03280i
$$541$$ −8.00000 −0.343947 −0.171973 0.985102i $$-0.555014\pi$$
−0.171973 + 0.985102i $$0.555014\pi$$
$$542$$ 20.0000 20.0000i 0.859074 0.859074i
$$543$$ 2.00000 2.00000i 0.0858282 0.0858282i
$$544$$ −40.0000 −1.71499
$$545$$ 6.00000 + 12.0000i 0.257012 + 0.514024i
$$546$$ 0 0
$$547$$ −23.0000 23.0000i −0.983409 0.983409i 0.0164556 0.999865i $$-0.494762\pi$$
−0.999865 + 0.0164556i $$0.994762\pi$$
$$548$$ 10.0000 + 10.0000i 0.427179 + 0.427179i
$$549$$ 2.00000i 0.0853579i
$$550$$ 0 0
$$551$$ 6.00000i 0.255609i
$$552$$ −16.0000 16.0000i −0.681005 0.681005i
$$553$$ 20.0000 + 20.0000i 0.850487 + 0.850487i
$$554$$ 10.0000 0.424859
$$555$$ 0 0
$$556$$ 40.0000i 1.69638i
$$557$$ −5.00000 + 5.00000i −0.211857 + 0.211857i −0.805056 0.593199i $$-0.797865\pi$$
0.593199 + 0.805056i $$0.297865\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 24.0000 + 8.00000i 1.01419 + 0.338062i
$$561$$ 0 0
$$562$$ −18.0000 18.0000i −0.759284 0.759284i
$$563$$ 1.00000 1.00000i 0.0421450 0.0421450i −0.685720 0.727865i $$-0.740513\pi$$
0.727865 + 0.685720i $$0.240513\pi$$
$$564$$ 8.00000i 0.336861i
$$565$$ 30.0000 + 10.0000i 1.26211 + 0.420703i
$$566$$ −8.00000 −0.336265
$$567$$ 10.0000 + 10.0000i 0.419961 + 0.419961i
$$568$$ 0 0
$$569$$ 34.0000i 1.42535i 0.701492 + 0.712677i $$0.252517\pi$$
−0.701492 + 0.712677i $$0.747483\pi$$
$$570$$ −4.00000 + 2.00000i −0.167542 + 0.0837708i
$$571$$ 20.0000i 0.836974i −0.908223 0.418487i $$-0.862561\pi$$
0.908223 0.418487i $$-0.137439\pi$$
$$572$$ 0 0
$$573$$ 20.0000 + 20.0000i 0.835512 + 0.835512i
$$574$$ 8.00000i 0.333914i
$$575$$ 4.00000 + 28.0000i 0.166812 + 1.16768i
$$576$$ 8.00000 0.333333
$$577$$ −15.0000 + 15.0000i −0.624458 + 0.624458i −0.946668 0.322210i $$-0.895574\pi$$
0.322210 + 0.946668i $$0.395574\pi$$
$$578$$ 33.0000 33.0000i 1.37262 1.37262i
$$579$$ −20.0000 −0.831172
$$580$$ −24.0000 + 12.0000i −0.996546 + 0.498273i
$$581$$ −16.0000 −0.663792
$$582$$ −20.0000 + 20.0000i −0.829027 + 0.829027i
$$583$$ 0 0
$$584$$ −20.0000 −0.827606
$$585$$ 0 0
$$586$$ 20.0000i 0.826192i
$$587$$ 32.0000 + 32.0000i 1.32078 + 1.32078i 0.913144 + 0.407638i $$0.133647\pi$$
0.407638 + 0.913144i $$0.366353\pi$$
$$588$$ −2.00000 + 2.00000i −0.0824786 + 0.0824786i
$$589$$ 0 0
$$590$$ 30.0000 + 10.0000i 1.23508 + 0.411693i
$$591$$ 30.0000i 1.23404i
$$592$$ 0 0
$$593$$ 5.00000 + 5.00000i 0.205325 + 0.205325i 0.802277 0.596952i $$-0.203622\pi$$
−0.596952 + 0.802277i $$0.703622\pi$$
$$594$$ 0 0
$$595$$ −40.0000 + 20.0000i −1.63984 + 0.819920i
$$596$$ −8.00000 −0.327693
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −10.0000 −0.408589 −0.204294 0.978909i $$-0.565490\pi$$
−0.204294 + 0.978909i $$0.565490\pi$$
$$600$$ 16.0000 + 12.0000i 0.653197 + 0.489898i
$$601$$ 2.00000 0.0815817 0.0407909 0.999168i $$-0.487012\pi$$
0.0407909 + 0.999168i $$0.487012\pi$$
$$602$$ 24.0000 + 24.0000i 0.978167 + 0.978167i
$$603$$ 3.00000 3.00000i 0.122169 0.122169i
$$604$$ −20.0000 −0.813788
$$605$$ −22.0000 + 11.0000i −0.894427 + 0.447214i
$$606$$ 24.0000 0.974933
$$607$$ 17.0000 + 17.0000i 0.690009 + 0.690009i 0.962234 0.272225i $$-0.0877595\pi$$
−0.272225 + 0.962234i $$0.587759\pi$$
$$608$$ −4.00000 4.00000i −0.162221 0.162221i
$$609$$ 24.0000i 0.972529i
$$610$$ −6.00000 2.00000i −0.242933 0.0809776i
$$611$$ 0 0
$$612$$ −10.0000 + 10.0000i −0.404226 + 0.404226i
$$613$$ 25.0000 + 25.0000i 1.00974 + 1.00974i 0.999952 + 0.00978840i $$0.00311579\pi$$
0.00978840 + 0.999952i $$0.496884\pi$$
$$614$$ 26.0000i 1.04927i
$$615$$ −2.00000 + 6.00000i −0.0806478 + 0.241943i
$$616$$ 0 0
$$617$$ 15.0000 15.0000i 0.603877 0.603877i −0.337462 0.941339i $$-0.609568\pi$$
0.941339 + 0.337462i $$0.109568\pi$$
$$618$$ −18.0000 + 18.0000i −0.724066 + 0.724066i
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 0 0
$$621$$ −32.0000 −1.28412
$$622$$ −20.0000 + 20.0000i −0.801927 + 0.801927i
$$623$$ 12.0000 12.0000i 0.480770 0.480770i
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 10.0000i 0.399680i
$$627$$ 0 0
$$628$$ −30.0000 30.0000i −1.19713 1.19713i
$$629$$ 0 0
$$630$$ 8.00000 4.00000i 0.318728 0.159364i
$$631$$ 40.0000i 1.59237i −0.605050 0.796187i $$-0.706847\pi$$
0.605050 0.796187i $$-0.293153\pi$$
$$632$$ −20.0000 + 20.0000i −0.795557 + 0.795557i
$$633$$ 10.0000 + 10.0000i 0.397464 + 0.397464i
$$634$$ 40.0000 1.58860
$$635$$ −21.0000 7.00000i −0.833360 0.277787i
$$636$$ 40.0000i 1.58610i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −8.00000 + 24.0000i −0.316228 + 0.948683i
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 14.0000 + 14.0000i 0.552536 + 0.552536i
$$643$$ −4.00000 + 4.00000i −0.157745 + 0.157745i −0.781567 0.623822i $$-0.785579\pi$$
0.623822 + 0.781567i $$0.285579\pi$$
$$644$$ 32.0000i 1.26098i
$$645$$ 12.0000 + 24.0000i 0.472500 + 0.944999i
$$646$$ 10.0000 0.393445
$$647$$ 12.0000 + 12.0000i 0.471769 + 0.471769i 0.902487 0.430718i $$-0.141740\pi$$
−0.430718 + 0.902487i $$0.641740\pi$$
$$648$$ −10.0000 + 10.0000i −0.392837 + 0.392837i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −28.0000 28.0000i −1.09656 1.09656i
$$653$$ −25.0000 25.0000i −0.978326 0.978326i 0.0214444 0.999770i $$-0.493173\pi$$
−0.999770 + 0.0214444i $$0.993173\pi$$
$$654$$ 12.0000i 0.469237i
$$655$$ 20.0000 + 40.0000i 0.781465 + 1.56293i
$$656$$ −8.00000 −0.312348
$$657$$ −5.00000 + 5.00000i −0.195069 + 0.195069i
$$658$$ −8.00000 + 8.00000i −0.311872 + 0.311872i
$$659$$ 30.0000 1.16863 0.584317 0.811525i $$-0.301362\pi$$
0.584317 + 0.811525i $$0.301362\pi$$
$$660$$ 0 0
$$661$$ 2.00000 0.0777910 0.0388955 0.999243i $$-0.487616\pi$$
0.0388955 + 0.999243i $$0.487616\pi$$
$$662$$ 10.0000 10.0000i 0.388661 0.388661i
$$663$$ 0 0
$$664$$ 16.0000i 0.620920i
$$665$$ −6.00000 2.00000i −0.232670 0.0775567i
$$666$$ 0 0
$$667$$ 24.0000 + 24.0000i 0.929284 + 0.929284i
$$668$$ −14.0000 + 14.0000i −0.541676 + 0.541676i
$$669$$ 18.0000i 0.695920i
$$670$$ 6.00000 + 12.0000i 0.231800 + 0.463600i
$$671$$ 0 0
$$672$$ −16.0000 16.0000i −0.617213 0.617213i
$$673$$ −20.0000 20.0000i −0.770943 0.770943i 0.207328 0.978271i $$-0.433523\pi$$
−0.978271 + 0.207328i $$0.933523\pi$$
$$674$$ 20.0000 0.770371
$$675$$ 28.0000 4.00000i 1.07772 0.153960i
$$676$$ 26.0000 1.00000
$$677$$ −10.0000 + 10.0000i −0.384331 + 0.384331i −0.872660 0.488329i $$-0.837607\pi$$
0.488329 + 0.872660i $$0.337607\pi$$
$$678$$ −20.0000 20.0000i −0.768095 0.768095i
$$679$$ −40.0000 −1.53506
$$680$$ −20.0000 40.0000i −0.766965 1.53393i
$$681$$ −26.0000 −0.996322
$$682$$ 0 0
$$683$$ 11.0000 11.0000i 0.420903 0.420903i −0.464611 0.885515i $$-0.653806\pi$$
0.885515 + 0.464611i $$0.153806\pi$$
$$684$$ −2.00000 −0.0764719
$$685$$ −5.00000 + 15.0000i −0.191040 + 0.573121i
$$686$$ 24.0000 0.916324
$$687$$ −6.00000 6.00000i −0.228914 0.228914i
$$688$$ −24.0000 + 24.0000i −0.914991 + 0.914991i
$$689$$ 0 0
$$690$$ 8.00000 24.0000i 0.304555 0.913664i
$$691$$ 20.0000i 0.760836i 0.924815 + 0.380418i $$0.124220\pi$$
−0.924815 + 0.380418i $$0.875780\pi$$
$$692$$ 20.0000 20.0000i 0.760286 0.760286i
$$693$$ 0 0
$$694$$ 16.0000i 0.607352i
$$695$$ −40.0000 + 20.0000i −1.51729 + 0.758643i
$$696$$ 24.0000 0.909718
$$697$$ 10.0000 10.0000i 0.378777 0.378777i
$$698$$ 16.0000 16.0000i 0.605609 0.605609i
$$699$$ 10.0000 0.378235
$$700$$ 4.00000 + 28.0000i 0.151186 + 1.05830i
$$701$$ 2.00000 0.0755390 0.0377695 0.999286i $$-0.487975\pi$$
0.0377695 + 0.999286i $$0.487975\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ −8.00000 + 4.00000i −0.301297 + 0.150649i
$$706$$ 30.0000i 1.12906i
$$707$$ 24.0000 + 24.0000i 0.902613 + 0.902613i
$$708$$ −20.0000 20.0000i −0.751646 0.751646i
$$709$$ 16.0000i 0.600893i −0.953799 0.300446i $$-0.902864\pi$$
0.953799 0.300446i $$-0.0971356\pi$$
$$710$$ 0 0
$$711$$ 10.0000i 0.375029i
$$712$$ 12.0000 + 12.0000i 0.449719 + 0.449719i
$$713$$ 0 0
$$714$$ 40.0000 1.49696
$$715$$ 0 0
$$716$$ 20.0000i 0.747435i
$$717$$ −20.0000 + 20.0000i −0.746914 + 0.746914i
$$718$$ −20.0000 20.0000i −0.746393 0.746393i
$$719$$ 40.0000 1.49175 0.745874 0.666087i $$-0.232032\pi$$
0.745874 + 0.666087i $$0.232032\pi$$
$$720$$ 4.00000 + 8.00000i 0.149071 + 0.298142i
$$721$$ −36.0000 −1.34071
$$722$$ 1.00000 + 1.00000i 0.0372161 + 0.0372161i
$$723$$ 2.00000 2.00000i 0.0743808 0.0743808i
$$724$$ 4.00000i 0.148659i
$$725$$ −24.0000 18.0000i −0.891338 0.668503i
$$726$$ 22.0000 0.816497
$$727$$ −18.0000 18.0000i −0.667583 0.667583i 0.289573 0.957156i $$-0.406487\pi$$
−0.957156 + 0.289573i $$0.906487\pi$$
$$728$$ 0 0
$$729$$ 29.0000i 1.07407i
$$730$$ −10.0000 20.0000i −0.370117 0.740233i
$$731$$ 60.0000i 2.21918i
$$732$$ 4.00000 + 4.00000i 0.147844 + 0.147844i
$$733$$ 35.0000 + 35.0000i 1.29275 + 1.29275i 0.933076 + 0.359678i $$0.117113\pi$$
0.359678 + 0.933076i $$0.382887\pi$$
$$734$$ 36.0000i 1.32878i
$$735$$ −3.00000 1.00000i −0.110657 0.0368856i
$$736$$ 32.0000 1.17954
$$737$$ 0 0
$$738$$ −2.00000 + 2.00000i −0.0736210 + 0.0736210i
$$739$$ −20.0000 −0.735712 −0.367856 0.929883i $$-0.619908\pi$$
−0.367856 + 0.929883i $$0.619908\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 40.0000 40.0000i 1.46845 1.46845i
$$743$$ 31.0000 31.0000i 1.13728 1.13728i 0.148344 0.988936i $$-0.452606\pi$$
0.988936 0.148344i $$-0.0473942\pi$$
$$744$$ 0 0
$$745$$ −4.00000 8.00000i −0.146549 0.293097i
$$746$$ 20.0000i 0.732252i
$$747$$ −4.00000 4.00000i −0.146352 0.146352i
$$748$$ 0 0
$$749$$ 28.0000i 1.02310i
$$750$$ −4.00000 + 22.0000i −0.146059 + 0.803326i
$$751$$ 30.0000i 1.09472i −0.836899 0.547358i $$-0.815634\pi$$
0.836899 0.547358i $$-0.184366\pi$$
$$752$$ −8.00000 8.00000i −0.291730 0.291730i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −10.0000 20.0000i −0.363937 0.727875i
$$756$$ −32.0000 −1.16383
$$757$$ −25.0000 + 25.0000i −0.908640 + 0.908640i −0.996163 0.0875221i $$-0.972105\pi$$
0.0875221 + 0.996163i $$0.472105\pi$$
$$758$$ 20.0000 + 20.0000i 0.726433 + 0.726433i
$$759$$ 0 0
$$760$$ 2.00000 6.00000i 0.0725476 0.217643i
$$761$$ −48.0000 −1.74000 −0.869999 0.493053i $$-0.835881\pi$$
−0.869999 + 0.493053i $$0.835881\pi$$
$$762$$ 14.0000 + 14.0000i 0.507166 + 0.507166i
$$763$$ 12.0000 12.0000i 0.434429 0.434429i
$$764$$ −40.0000 −1.44715
$$765$$ −15.0000 5.00000i −0.542326 0.180775i
$$766$$ 42.0000 1.51752
$$767$$ 0 0
$$768$$ 16.0000 16.0000i 0.577350 0.577350i
$$769$$ 34.0000i 1.22607i 0.790055 + 0.613036i $$0.210052\pi$$
−0.790055 + 0.613036i $$0.789948\pi$$
$$770$$ 0 0
$$771$$ 40.0000i 1.44056i
$$772$$ 20.0000 20.0000i 0.719816 0.719816i
$$773$$ 20.0000 + 20.0000i 0.719350 + 0.719350i 0.968472 0.249122i $$-0.0801420\pi$$
−0.249122 + 0.968472i $$0.580142\pi$$
$$774$$ 12.0000i 0.431331i
$$775$$ 0 0
$$776$$ 40.0000i 1.43592i
$$777$$ 0 0
$$778$$ 6.00000 6.00000i 0.215110 0.215110i
$$779$$ 2.00000